diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0ae3cfc15648ab20ff04ac8d6d407d8fe2956e9e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE.srt
@@ -0,0 +1,1507 @@
+1
+00:00:21,290 --> 00:00:25,850
+بسم الله الرحمن الرحيم نستكمل الموضوع الذي بدأناه 
+
+2
+00:00:25,850 --> 00:00:31,590
+الصبح وهو موضوع ال external direct product بعد ما
+
+3
+00:00:31,590 --> 00:00:35,770
+أخذنا أمثلة من خلالها نُعين ال order لل element
+
+4
+00:00:35,770 --> 00:00:42,070
+وكذلك عدد ما هو ال elements ب order معين وعدد ال
+
+5
+00:00:42,070 --> 00:00:46,830
+cyclic groups ب order معين ننتقل الآن إلى هذه
+
+6
+00:00:46,830 --> 00:00:51,500
+النظرية النظرية تقول يفترض أن جي و اتش هما finite
+
+7
+00:00:51,500 --> 00:00:55,140
+cyclic groups  يبقى كل واحدة فيها عدد محدود من
+
+8
+00:00:55,140 --> 00:01:00,060
+العناصر والاثنتان are cyclic groups  يقول في هذه
+
+9
+00:01:00,060 --> 00:01:05,080
+الحلقين أن ال جي external product مع اتش is cyclic
+
+10
+00:01:05,080 --> 00:01:08,760
+in fact تقول إذا ال order جي و ال order اتش are
+
+11
+00:01:08,760 --> 00:01:13,240
+relatively prime يبقى من الآن فصاعدًا لو ال two
+
+12
+00:01:13,240 --> 00:01:17,080
+groups جي و اتش الاثنتان ال order  الذي هما are
+
+13
+00:01:17,080 --> 00:01:19,840
+relatively prime  الذي يبقى ال external product
+
+14
+00:01:19,840 --> 00:01:25,960
+معناه is a cyclic group مباشرة والعكس لو كانت
+
+15
+00:01:25,960 --> 00:01:28,860
+cyclic groups  يبقى ال two orders are relatively
+
+16
+00:01:28,860 --> 00:01:35,620
+prime هذا ما نريد أن نثبته الآن يبقى لذلك نثبته
+
+17
+00:01:35,620 --> 00:01:41,040
+افترض أن ال H لها order معين و ال G كذلك لها order
+
+18
+00:01:41,040 --> 00:01:47,800
+معين ونشوف كيف بدنا نعمله يبقى let ال order لل G
+
+19
+00:01:47,800 --> 00:01:55,680
+يُساوي ال M و ال order لل H يُساوي ال N
+
+20
+00:01:55,680 --> 00:02:00,200
+then
+
+21
+00:02:00,200 --> 00:02:11,180
+لو أردنا أن نجيب ال order لل G with H يبقى then الأردر 
+
+22
+00:02:11,180 --> 00:02:16,380
+للـ G External Direct Product مع H هكذا يُساوي
+
+23
+00:02:16,380 --> 00:02:20,040
+هذا يا شباب مكتوب معكم من المرة التي فاتت الأردر
+
+24
+00:02:20,040 --> 00:02:26,400
+للأولى في الأردر للثانية يبقى هذا الكلام يُساوي ال M
+
+25
+00:02:26,400 --> 00:02:33,020
+في N هذه المعلومة وضعتها قبل البدء والآن أريد أن أبدأ
+
+26
+00:02:33,020 --> 00:02:38,360
+لماذا وضعتها؟ لأن كل عمل بالحب له زمانه الآن نريد
+
+27
+00:02:38,360 --> 00:02:48,400
+أن نقول Assume that الـG external product مع الـH is
+
+28
+00:02:48,400 --> 00:02:54,540
+cyclic ماذا أريد أن أثبت؟ أن ال order التي جي و ال
+
+29
+00:02:54,540 --> 00:02:58,560
+order التي اتش اثنان are relatively prime يعني
+
+30
+00:02:58,560 --> 00:03:01,520
+أريد أن أثبت أن ال Euclidean common divisor ما بين
+
+31
+00:03:01,520 --> 00:03:05,920
+الاثنين سيكون كم؟ سيكون واحد، صحيح؟ طيب افترضنا هذه
+
+32
+00:03:05,920 --> 00:03:10,040
+Cyclic مدام الـ Cyclic يبقى لها generator صح ولا
+
+33
+00:03:10,040 --> 00:03:14,600
+لا؟ يبقى Cyclic assume
+
+34
+00:03:15,770 --> 00:03:25,370
+افترض كذلك أن الـ G والـ H is a generator is a
+
+35
+00:03:25,370 --> 00:03:33,870
+generator for ما هو external product للـ H مع G
+
+36
+00:03:34,700 --> 00:03:38,460
+ما دام هذا generator يبقى ال order الذي يُساوي
+
+37
+00:03:38,460 --> 00:03:43,860
+من أين ال order لل G modulo لل G external direct
+
+38
+00:03:43,860 --> 00:03:50,920
+product مع H هذا معناه أن ال order لل G وال H يُساوي
+
+39
+00:03:50,920 --> 00:03:56,600
+يُساوي ال order لل G external direct product مع من؟
+
+40
+00:03:56,600 --> 00:04:05,990
+مع ال H هذا يُساوي طيب ال order لل G والـ H أريد
+
+41
+00:04:05,990 --> 00:04:11,410
+أن يُساوي ال least common multiple لل order تبع ال G
+
+42
+00:04:11,410 --> 00:04:18,870
+وال order تبع ال H يبقى
+
+43
+00:04:18,870 --> 00:04:23,050
+ال order لل G و ال order تبع ال H بالشكل الذي عندنا
+
+44
+00:04:23,050 --> 00:04:28,730
+هذا الذي هو أريد أن يُساوي ال order لهذه كم اللي م في
+
+45
+00:04:28,730 --> 00:04:34,700
+ني يبقى أنا أقول ال order لل element هذا يُساوي ال
+
+46
+00:04:34,700 --> 00:04:38,300
+order لل element هذه يبقى بناء عليه ال order لل
+
+47
+00:04:38,300 --> 00:04:42,520
+element g و h يُساوي ال least common multiple ما
+
+48
+00:04:42,520 --> 00:04:46,360
+بين ال two orders طبقا للنظرية السابقة التي
+
+49
+00:04:46,360 --> 00:04:51,340
+برهنناها طيب هذا ال order هو عبارة عن من؟ عن m في
+
+50
+00:04:51,340 --> 00:04:57,020
+n خلي هذه المعلومة في ذهنك وسنعود إليها بعد قليل
+
+51
+00:04:57,020 --> 00:05:05,640
+طيب الآن ال order للـ G ال order للـ G يقسم ال
+
+52
+00:05:05,640 --> 00:05:11,840
+order للـ G الكبيرة صح ولا لا يبقى divide ال order
+
+53
+00:05:11,840 --> 00:05:19,250
+للـ G الذي يُساوي كم M يعني ال order الذي
+
+54
+00:05:19,250 --> 00:05:25,670
+جاء يُساوي يقسم من ال M وفي نفس الوقت ال order ل ال H
+
+55
+00:05:25,670 --> 00:05:33,390
+يُساوي يقسم ال order ل من ل ال H الذي هو
+
+56
+00:05:33,390 --> 00:05:38,870
+يُساوي ال N إذا
+
+57
+00:05:38,870 --> 00:05:44,710
+ما هي علاقة least common multiple لل two orders مع
+
+58
+00:05:44,710 --> 00:05:45,970
+M و N
+
+59
+00:05:48,440 --> 00:05:52,340
+ال least common multiple لل order مع ال least common multiple لل M
+
+60
+00:05:52,340 --> 00:05:55,360
+و N من هو الأصغر ومن هو الأكبر؟ لل least common multiple
+
+61
+00:05:55,360 --> 00:06:01,800
+لمن؟ لل H و G 100% أصغر من من؟ من ال least
+
+62
+00:06:01,800 --> 00:06:06,840
+common multiple لل M و N تمام؟ يبقى هذا يطيح
+
+63
+00:06:06,840 --> 00:06:12,840
+لكم؟ أن ال least common multiple لل order تبع ال
+
+64
+00:06:12,840 --> 00:06:24,040
+G وال order تبع ال H هذا كله ما له أقل من أو يُساوي
+
+65
+00:06:24,040 --> 00:06:32,930
+ال least common multiple لل M و N تمام؟ طيب ال least
+
+66
+00:06:32,930 --> 00:06:40,450
+common multiple لهذا الذي هو كم M في N يبقى بناء
+
+67
+00:06:40,450 --> 00:06:47,950
+عليه So ال M في N أقل من أو يُساوي ال least common
+
+68
+00:06:47,950 --> 00:06:56,450
+multiple لمن؟ لل M و N اعتبر هذه المعادلة رقم Star
+
+69
+00:06:58,800 --> 00:07:06,940
+السؤال هو نحن لم نجيب ال M و ال N أقل من ال
+
+70
+00:07:06,940 --> 00:07:12,720
+least common multiple لمن؟ لل M و N طيب in general
+
+71
+00:07:12,720 --> 00:07:24,720
+but و لكن we know that أن ال least common multiple
+
+72
+00:07:24,720 --> 00:07:26,840
+لل M و N
+
+73
+00:07:30,950 --> 00:07:35,450
+100% صحيح ولا لأ؟ دائمًا وأبدًا ال least common ..
+
+74
+00:07:35,450 --> 00:07:39,430
+أقصى حاجة حصل ضربهم ودائمًا وأبدًا يكون أقل من
+
+75
+00:07:39,430 --> 00:07:44,870
+هكذا يعني المضاعف المشترك أحيانًا يكون كبيرًا في أقل
+
+76
+00:07:44,870 --> 00:07:51,630
+ما يمكن يبقى هذا أقل من من؟ من M في N وهذه
+
+77
+00:07:51,630 --> 00:07:56,550
+العلاقة الثانية هي رقم Star إذا من الاثنين مع بعض
+
+78
+00:07:56,550 --> 00:08:02,130
+أقول إن الاثنان هذان ما لهما ريكم يبقى هنا سوي ال
+
+79
+00:08:02,130 --> 00:08:09,150
+least common multiple لل M و N يُساوي ال M في N
+
+80
+00:08:11,690 --> 00:08:17,290
+طيب نرجع بالذاكرة اصبر علينا قليلًا نرجع بالذاكرة
+
+81
+00:08:17,290 --> 00:08:22,650
+للخلف إلى ال first chapter إذا تذكرتم هنا قلنا ل
+
+82
+00:08:22,650 --> 00:08:26,290
+grace is common divisor between عددين في least
+
+83
+00:08:26,290 --> 00:08:29,990
+common multiple العدين يُعطينا من؟ نفس العددين
+
+84
+00:08:29,990 --> 00:08:40,950
+يبقى هنا آتي أقول له but و لكن that لا نعرف أن
+
+85
+00:08:40,950 --> 00:08:47,530
+ال greatest common divisor لل M وال N مضروب في
+
+86
+00:08:47,530 --> 00:08:55,510
+least common multiple لل M و N يُساوي M في N هذا
+
+87
+00:08:55,510 --> 00:09:01,790
+يُعطينا الآن ال least common multiple هو M في N
+
+88
+00:09:01,790 --> 00:09:07,570
+يبقى هذا يُعطيك أن ال greatest common divisor
+
+89
+00:09:07,570 --> 00:09:13,070
+لل M و N في ال least common multiple الذي هو M في
+
+90
+00:09:13,070 --> 00:09:20,040
+N يُساوي ال M في N يبقى هذا يُعطينا common divisor
+
+91
+00:09:20,040 --> 00:09:25,980
+لل M و N يبقى كمية طيب ال M أليس هو ال order تبع ال G و
+
+92
+00:09:25,980 --> 00:09:32,260
+ال N هو ال order تبع ال H يبقى هذا معناه أن ال M
+
+93
+00:09:32,260 --> 00:09:44,640
+و ال N are relatively prime هذا يُعطينا هذا أريد
+
+94
+00:09:44,640 --> 00:09:51,120
+أن يُعطينا أن ال order ل capital G لل group كلها و
+
+95
+00:09:51,120 --> 00:09:57,700
+ال order ل ال H are relatively prime
+
+96
+00:10:03,000 --> 00:10:07,320
+نحن انتهينا من الاتجاه الأول في النظرية، وهو أنه لو
+
+97
+00:10:07,320 --> 00:10:14,100
+كان الـ G external direct product مع H is cyclic يبقى
+
+98
+00:10:14,100 --> 00:10:17,080
+الأوردر لـ G و الأوردر لـ H are relatively
+
+99
+00:10:17,080 --> 00:10:22,010
+prime، لأننا بدأنا نمشي العملية العكسية أثبت وافترض
+
+100
+00:10:22,010 --> 00:10:27,250
+أن الاثنين هذان are relatively prime  ذاتس يعني إيش
+
+101
+00:10:27,250 --> 00:10:32,030
+ذاتس؟ لجريس ال common divisor لل M و N يُساوي
+
+102
+00:10:32,030 --> 00:10:37,350
+هكذا إيش؟ يُساوي واحد صحيح؟ طيب في حاجة موجودة في
+
+103
+00:10:37,350 --> 00:10:42,690
+النظرية وحتى الآن لم نستخدمها إشيًا .. التي كل واحدة
+
+104
+00:10:42,690 --> 00:10:47,350
+من ال two groups الاثنان هذان cyclic مدام كل واحدة
+
+105
+00:10:47,350 --> 00:10:56,270
+cyclic إذا كل واحدة فيها generator يبقى since ال g
+
+106
+00:10:56,270 --> 00:10:59,350
+since
+
+107
+00:10:59,350 --> 00:11:07,070
+ال g is cyclic we have since ال .. خلي ال g باثنين
+
+108
+00:11:07,070 --> 00:11:15,950
+مرة واحدة since ال g و ال h و ال h are cyclic
+
+109
+00:11:15,950 --> 00:11:24,510
+we have أن الـ G هذه فيها generator وليكن small
+
+110
+00:11:24,510 --> 00:11:33,050
+g و ال H فيها generator وليكن main
+
+111
+00:11:33,050 --> 00:11:38,110
+وليكن H طيب
+
+112
+00:11:38,110 --> 00:11:46,110
+إذا كم ال order ل G small M و ال order ل H M
+
+113
+00:11:46,110 --> 00:11:52,630
+يكون يساوي يبقى هذا يُعطينا أن ال order للـ G يُساوي
+
+114
+00:11:52,630 --> 00:11:58,430
+يُساوي ال M و ال order ل H يُساوي ال main يُساوي
+
+115
+00:11:58,430 --> 00:12:05,390
+يُساوي ال N طيب كويس يبقى أنا أريد أن آتي إلى ال order تبع
+
+116
+00:12:05,390 --> 00:12:11,630
+ال G و ال H مرة واحدة يبقى هذا الكلام يُساوي
+
+117
+00:12:11,630 --> 00:12:16,950
+least common multiple لل order تبع ال G و ال
+
+118
+00:12:16,950 --> 00:12:23,120
+order تبع ال H يبقى هذا الكلام يُساوي ال least
+
+119
+00:12:23,120 --> 00:12:30,180
+common multiple ال least common multiple لمن؟ لل
+
+120
+00:12:30,180 --> 00:12:39,940
+M و لل N أنا أدعي أن M في N طيب لماذا؟ لأن ال common
+
+121
+00:12:39,940 --> 00:12:47,400
+divisor يُساوي 1 يبقى هذا لماذا؟ لأن أن ال common
+
+122
+00:12:47,400 --> 00:12:54,480
+divisor لـ M و لـ N يبدو يُساوي واحد صحيح؟ طيب هذا
+
+123
+00:12:54,480 --> 00:13:00,120
+الـ M في الـ N هو عبارة عن ال order لمن؟ ال order
+
+124
+00:13:00,120 --> 00:13:03,970
+لل group الذي هو نسميه هذا هو عبارة عن ال order
+
+125
+00:13:03,970 --> 00:13:09,850
+للجروب يبقى هذا الكلام يُساوي ال order للـ G
+
+126
+00:13:09,850 --> 00:13:15,530
+external direct product لمن؟ للـ H يبقى الـ gate
+
+127
+00:13:15,530 --> 00:13:20,630
+element موجود في الـ external direct product الـ
+
+128
+00:13:20,630 --> 00:13:26,150
+order له يساوي الـ order لمن؟ للـ group يبقى الـ
+
+129
+00:13:26,150 --> 00:13:31,250
+group هذا ما يصير؟ Cyclic وهذا generator يبقى هنا
+
+130
+00:13:31,250 --> 00:13:43,780
+ساالـ G والـ H is a generator for اللي هو الـ G
+
+131
+00:13:43,780 --> 00:13:50,320
+external direct product مع مين؟ مع الـ H هذا بده يعطيلك
+
+132
+00:13:50,320 --> 00:13:57,620
+انه G external direct product مع H is cyclic وهو
+
+133
+00:13:57,620 --> 00:14:05,720
+المطلوب إذا قلت لك أثبت
+
+134
+00:14:05,720 --> 00:14:11,100
+الـexternal هذا direct product is cyclic تمام؟
+
+135
+00:14:11,100 --> 00:14:15,520
+بعدين بقوله إذا والله التنتين كل واحدة فيهم cyclic
+
+136
+00:14:15,520 --> 00:14:18,940
+والـ order تبع كل واحدة فيهم مع الثاني اثنين
+
+137
+00:14:18,940 --> 00:14:22,570
+relatively prime or than automatic على طول الخطأ
+
+138
+00:14:22,570 --> 00:14:27,210
+هذه النظرية الـ external direct product is cyclic
+
+139
+00:14:27,210 --> 00:14:31,670
+group يبقى الشرط الـ external direct product أن
+
+140
+00:14:31,670 --> 00:14:36,270
+يكون cyclic group أمرين الأمر الأول كل واحدة فيهم
+
+141
+00:14:36,270 --> 00:14:41,190
+تبقى cyclic الأمر الثاني الـ order للـ group الأولى
+
+142
+00:14:41,190 --> 00:14:43,850
+والـ order للـ group الثانية يكونوا اثنين مع بعضهم
+
+143
+00:15:00,200 --> 00:15:05,820
+النظرية هذه أثبتناها لمين؟ لـ two group طب لو صاروا
+
+144
+00:15:05,820 --> 00:15:11,810
+ثلاثة ثلاثة groups والله أربعة والله خمسة والله in
+
+145
+00:15:11,810 --> 00:15:16,550
+من الـ groups فالنظرية صحيحة وهذا الموضوع ل
+
+146
+00:15:16,550 --> 00:15:27,390
+corollary رقم واحد يبقى corollary رقم واحد بتقول أن
+
+147
+00:15:27,390 --> 00:15:34,230
+external direct product أن external direct
+
+148
+00:15:35,820 --> 00:15:44,680
+a product external direct product g one external
+
+149
+00:15:44,680 --> 00:15:50,520
+direct product مع g two external direct product مع
+
+150
+00:15:50,520 --> 00:16:03,000
+مين؟ مع g n of a finite of a finite number
+
+151
+00:16:04,660 --> 00:16:20,060
+finite number of finite cyclic groups is
+
+152
+00:16:20,060 --> 00:16:33,660
+cyclic if and only if الـ order للـ G I و الـ
+
+153
+00:16:33,660 --> 00:16:46,100
+order للـ G J are relatively prime are
+
+154
+00:16:46,100 --> 00:16:54,380
+relatively prime when الـ I لا تساوي مين؟ لا 
+
+155
+00:16:54,380 --> 00:17:02,540
+تساوي الـ G كمان corollary ثانية بتقول
+
+156
+00:17:02,540 --> 00:17:10,240
+let اللي هو الـ M عملناها تحليل صارت N واحد في N
+
+157
+00:17:10,240 --> 00:17:18,760
+اثنين في N K then الـ
+
+158
+00:17:18,760 --> 00:17:31,150
+ZM الـ ZM isomorphic لمن؟ لـ z n one external product
+
+159
+00:17:31,150 --> 00:17:43,350
+مع z n two external product مع من؟ مع z n k if and
+
+160
+00:17:43,350 --> 00:17:53,930
+only if if and only if الـ n i و الـ n j are
+
+161
+00:17:53,930 --> 00:18:06,240
+relatively prime are relatively prime when
+
+162
+00:18:06,240 --> 00:18:11,100
+I لا تساوي الـ J
+
+163
+00:18:38,860 --> 00:18:44,120
+الـ corollary الأولى هي تعميم للنظرية الـ corollary الثانية
+
+164
+00:18:44,120 --> 00:18:48,760
+كأنه تطبيق مباشر على النظرية تعال نشوف
+
+165
+00:18:48,760 --> 00:18:53,640
+التعميم في الأول ومن ثم بنروح للـ corollary الثانية
+
+166
+00:18:53,640 --> 00:18:59,380
+اللي هي رقم اثنين يبقى هذه الـ corollary الرقم اثنين
+
+167
+00:19:00,650 --> 00:19:03,590
+تعال اكرر لي رقم واحد بيقول أن external direct
+
+168
+00:19:03,590 --> 00:19:08,770
+product لمجموعة من الـ group of a finite number
+
+169
+00:19:08,770 --> 00:19:13,330
+يبقى عدد محدود من الـ groups وكل group has finite
+
+170
+00:19:13,330 --> 00:19:18,490
+order كل واحدة اللي عدد تبعها محدود يبقى هذا الـ
+
+171
+00:19:18,490 --> 00:19:21,710
+external direct product بيكون cyclic if and only
+
+172
+00:19:21,710 --> 00:19:26,230
+if الـ order لـ جي اي و الـ order لـ جي جي are
+
+173
+00:19:26,230 --> 00:19:31,510
+relatively prime و أن الـ I لا تساوي الـ جيه يعني ما بديش
+
+174
+00:19:31,510 --> 00:19:36,650
+أقول لـ group نفسه هي المقصود I لا تساوي الـ جيه يعني
+
+175
+00:19:36,650 --> 00:19:40,570
+هاد الـ group تختلف تماما مع من؟ مع هاد الـ group طب احنا
+
+176
+00:19:40,570 --> 00:19:47,290
+عندنا كم group أي واحدة مع الثانية بيكون relatively
+
+177
+00:19:47,290 --> 00:19:50,270
+prime يعني الأولى مع الثانية الأولى مع الثالثة
+
+178
+00:19:50,270 --> 00:19:54,350
+الأولى مع العاشرة الثانية مع الثالثة الثانية مع ...
+
+179
+00:19:54,350 --> 00:19:58,950
+كله are relatively prime تمام الـ order تبع كل
+
+180
+00:19:58,950 --> 00:20:01,550
+واحدة منهم مع الـ order مع الثانية بيكون are
+
+181
+00:20:01,550 --> 00:20:05,420
+relatively prime وهو تعميم للنظرية النظرية كانت
+
+182
+00:20:05,420 --> 00:20:08,620
+على two groups اللي هي G و H عممناها
+
+183
+00:20:08,620 --> 00:20:11,800
+خليناها ثلاثة خليناها أربعة خليناها خمسة مش
+
+184
+00:20:11,800 --> 00:20:16,900
+مشكلة قد ما يكون العدد يبقى هذه النظرية صحيحة عليهم
+
+185
+00:20:16,900 --> 00:20:21,700
+وهي هذه النتيجة رقم واحد أما النتيجة رقم اثنين
+
+186
+00:20:21,700 --> 00:20:27,780
+بيقول لو عندك رقم M حللته إلى حاصل ضرب أعداد زي
+
+187
+00:20:27,780 --> 00:20:33,700
+إيش مثلا زي ثلاثين ثلاثين بقدر أقول اثنين في ثلاثة
+
+188
+00:20:33,700 --> 00:20:38,780
+في خمسة يبقى هذه حللناها لحاصل ضرب ثلاثة أعداد
+
+189
+00:20:38,780 --> 00:20:43,480
+والثلاثة أعداد ما لهم؟ Primes اثنين والثلاثة
+
+190
+00:20:43,480 --> 00:20:48,500
+والخمسة are primes إيش بقول هنا؟ لو حللت الـ M لحاصل
+
+191
+00:20:48,500 --> 00:20:58,140
+ضرب أعداد يبقى ZM isomorphic لـ ZN1, ZN2, ZN3, ZNK,
+
+192
+00:20:58,400 --> 00:21:04,080
+if and only if كل عدد من هذه الأعداد are relatively
+
+193
+00:21:04,080 --> 00:21:10,580
+prime مع بعضهم البعض يعني ليس بالضرورة أن يكونوا
+
+194
+00:21:10,580 --> 00:21:15,240
+primes وإنما يكونوا relatively primes يعني ممكن آخذ
+
+195
+00:21:15,240 --> 00:21:21,360
+اللي هو العدد اثنين مع العدد سبعة ممكن آخذ ستة و
+
+196
+00:21:21,360 --> 00:21:24,800
+خمسة ستة وخمسة اثنين relatively primes رغم أنه
+
+197
+00:21:24,800 --> 00:21:29,980
+خمسة primes ستة لا تمام يبقى ليس بالضرورة أن تكون
+
+198
+00:21:29,980 --> 00:21:35,420
+هذه الأعداد primes مثل ما حللنا إيش الثلاثين يبقى
+
+199
+00:21:35,420 --> 00:21:40,310
+ممكن يكون أربعة وعشرين أربعة وعشرين هو ثلاثة في
+
+200
+00:21:40,310 --> 00:21:45,110
+ثمانية يعني اثنين في ثلاثة في أربعة مظبوط يبقى الأربعة
+
+201
+00:21:45,110 --> 00:21:47,730
+و عشرين اثنين في ثلاثة في ستة في أربعة وأربعة و
+
+202
+00:21:47,730 --> 00:21:53,010
+عشرين الآن يبقى هذول اثنين في ثلاثة في ستة اثنين و
+
+203
+00:21:53,010 --> 00:21:57,810
+ثلاثة هذول الـ primes بس إيش بيصير اثنين مع الأربعة
+
+204
+00:21:57,810 --> 00:22:01,880
+are not relatively prime يبقى بيصير كل ابن هذا صحيح
+
+205
+00:22:01,880 --> 00:22:06,600
+ولا مش صحيح؟ مش صحيح لازم تأخذ أي رقمين منهم
+
+206
+00:22:06,600 --> 00:22:10,640
+ويكونوا مع بعض اثنين مع بعضهم relatively primes
+
+207
+00:22:10,640 --> 00:22:16,220
+وليس بالضرورة أن يكونوا primes يبقى مرة ثانية
+
+208
+00:22:16,220 --> 00:22:22,740
+بقول حللت الـ M إلى حاصل ضرب أعداد ما دام حللت يجوز أن
+
+209
+00:22:22,740 --> 00:22:30,040
+الأصلية isomorphic لمين؟ للـ external direct product
+
+210
+00:22:30,040 --> 00:22:35,340
+اللي هم كلهم هذول if and only if أي اثنين منهم
+
+211
+00:22:35,340 --> 00:22:39,640
+بدهم يكونوا relatively prime مع بعضهم البعض الآن
+
+212
+00:22:39,640 --> 00:22:46,020
+نعطيك تمثيل عددي شغل عددي كيف هذا الكلام example
+
+213
+00:22:53,570 --> 00:22:58,310
+هذا هو التوضيح اللي قال لو جئت لـ z دي اثنين
+
+214
+00:22:58,310 --> 00:23:04,670
+external like product مع z دي اثنين external like
+
+215
+00:23:04,670 --> 00:23:11,390
+product مع z ثلاثة external like product مع مين؟
+
+216
+00:23:11,390 --> 00:23:14,590
+مع z خمسة بالشكل اللي عندنا
+
+217
+00:23:17,820 --> 00:23:21,800
+بدي أكون من هذه مجموعة milligroups بيكونوا
+
+218
+00:23:21,800 --> 00:23:27,260
+isomorphic لها باجي بقول والله كويس شرايك التنتين
+
+219
+00:23:27,260 --> 00:23:31,200
+هذول are relatively prime اثنين والثلاثة ولا لا
+
+220
+00:23:31,200 --> 00:23:38,460
+إذا هذه isomorphic لمين؟ زد ستة زد ستة لأن أنا قلت لك
+
+221
+00:23:38,460 --> 00:23:44,580
+M وهذا M فين؟ بس أصغر شوية واحدة واحدة يبقى هذه
+
+222
+00:23:44,580 --> 00:23:53,600
+isomorphic لمين؟ لزد اثنين كما هي لزد اثنين
+
+223
+00:23:53,600 --> 00:24:00,340
+اكستيرنا الـ product لزد ستة اكستيرنا الـ product
+
+224
+00:24:00,340 --> 00:24:11,060
+لمن؟ لزد خمسة ليش؟ since اثنين and ثلاثة are
+
+225
+00:24:11,430 --> 00:24:21,670
+relatively prime طيب ... الآن هذه بدي أجيب كمان
+
+226
+00:24:21,670 --> 00:24:28,630
+group أخرى isomorphic لها وهذه كمان isomorphic لزد
+
+227
+00:24:28,630 --> 00:24:32,750
+اثنين external by product هذول اثنين are
+
+228
+00:24:32,750 --> 00:24:39,110
+relatively prime يبقى زد مين؟ زد ثلاثين حاصلة ضرب
+
+229
+00:24:39,110 --> 00:24:49,230
+يبقى هذه لزد ثلاثين يبقى ليش؟ since الستة and
+
+230
+00:24:49,230 --> 00:24:53,650
+الخمسة are relatively
+
+231
+00:24:57,660 --> 00:25:04,940
+السؤال هو هل هذا isomorphic لزد ستين؟ لا ليش؟ لأن
+
+232
+00:25:04,940 --> 00:25:12,080
+هذا ليس عشان isomorphic لزد ستين وستين وهي هذا ليس
+
+233
+00:25:12,080 --> 00:25:24,880
+عشان isomorphic لزد ستين لأن السبب أن الاثنين and
+
+234
+00:25:25,300 --> 00:25:30,240
+الثلاثين ليسوا
+
+235
+00:25:30,240 --> 00:25:41,180
+مرتفعين بشكل عام طيب
+
+236
+00:25:41,180 --> 00:25:47,640
+إيش رأيك؟ بدي أخلق كمان groups أخرى isomorphic
+
+237
+00:25:47,640 --> 00:25:57,570
+لهذه الـ group also لو جئت أخذت اللي هو Z اثنين
+
+238
+00:25:57,570 --> 00:26:03,490
+external by-product لزد اثنين external by-product
+
+239
+00:26:03,490 --> 00:26:10,010
+لزد ثلاثة external by-product لزد خمسة is
+
+240
+00:26:10,010 --> 00:26:15,910
+isomorphic قلنا قبل قليل زد اثنين external by
+
+241
+00:26:15,910 --> 00:26:21,850
+-product is ستة external by-product لمن؟ لزد خمسة
+
+242
+00:26:23,460 --> 00:26:27,620
+هذا اللي قلناها قبل قليل من هذه بدي أخلق groups
+
+243
+00:26:27,620 --> 00:26:32,320
+أخرى تبقى isomorphic لنفس الـ group كيف كانت التالية
+
+244
+00:26:32,320 --> 00:26:39,840
+أطلع لي هنا بقدر أكتب هذه Z2 زي ما هي هذه Z6 نقول
+
+245
+00:26:39,840 --> 00:26:45,980
+Z2 external dichromate مع Z3 ولا Z3 external مع Z2
+
+246
+00:26:45,980 --> 00:26:50,160
+نفس الشيء لأنه حصل ضربهم يساوي 6 و 2 are relatively
+
+247
+00:26:50,160 --> 00:26:54,690
+prime بنفس النظرية اللي هي قبل قليل يبقى بناءً عليه
+
+248
+00:26:54,690 --> 00:27:00,210
+هذه بقدر أقول بدل ما هي z6 بدي أقول عليها z3
+
+249
+00:27:00,210 --> 00:27:05,690
+external by-product مع z2 external by-product مع
+
+250
+00:27:05,690 --> 00:27:16,790
+z5 طيب هذه isomorphic لمن؟ طلع لي لهذه relatively 
+
+251
+00:27:16,790 --> 00:27:24,330
+يبقى هذول الـ Z6 External Direct Product مع
+
+252
+00:27:24,330 --> 00:27:30,610
+Z2 External Direct Product مع Z5 يبقى هذه جروب 
+
+253
+00:27:30,610 --> 00:27:37,130
+جديدة بدي أطلع كمان جروب ثاني يبقى هذه isomorphic
+
+254
+00:27:37,130 --> 00:27:45,770
+كمان لمين؟ لـ Z6 External Direct Product مع Z5 يبقى
+
+255
+00:27:45,770 --> 00:27:54,900
+مع Z10 ليش؟ لأنه الستة والخمسة are... لأنه الاتنين
+
+256
+00:27:54,900 --> 00:28:00,140
+والخمسة are relatively prime يبقى هذا sense اتنين
+
+257
+00:28:00,140 --> 00:28:10,160
+and خمسة are relatively prime والخطوة الأولى اللي
+
+258
+00:28:10,160 --> 00:28:13,380
+عندنا زد ستة لإنه اتنين و تلاتة relatively prime
+
+259
+00:28:13,380 --> 00:28:20,600
+هذا كتبناه قبل قليل طب السؤال هو هل هذه isomorphic
+
+260
+00:28:20,600 --> 00:28:28,340
+لزد ستين ما فيها ستين عنصر طبعا لأ السبب because
+
+261
+00:28:29,790 --> 00:28:40,350
+إن الستة و العشرة ليسوا مرتبطين بشكل 
+
+262
+00:28:40,350 --> 00:28:40,370
+عام
+
+263
+00:28:47,410 --> 00:28:53,090
+بقول isomorphic وين هي؟ لأ لأ كله isomorphic يا
+
+264
+00:28:53,090 --> 00:28:57,310
+شباب ما عنديش ما قلت يساوي يبقى لو قلت يساوي معناته
+
+265
+00:28:57,310 --> 00:29:03,170
+كل عنصر يساوي نظيره لكن هذه group تختلف عن هذه
+
+266
+00:29:03,170 --> 00:29:08,050
+يعني مثلا عنصر اللي هنا لو بده ياخد الواحد و من هنا
+
+267
+00:29:08,050 --> 00:29:12,010
+بده ياخد اتنين و من هنا بده ياخد ال zero و من هنا
+
+268
+00:29:12,010 --> 00:29:16,350
+بده ياخد الأربعة مثلا بيختلف عن هذا اللي هنا وهكذا
+
+269
+00:29:16,350 --> 00:29:20,810
+إذا أي زمار فيك يعني لجروب الأولى و لجروب الثانية
+
+270
+00:29:20,810 --> 00:29:27,730
+لها نفس الخواص الرياضية يبقى هاي كل اللي بنقوله
+
+271
+00:29:27,730 --> 00:29:33,530
+بناسبة يعني هذا مثال عملي على الشغلانة طيب ننتقل
+
+272
+00:29:33,530 --> 00:29:39,110
+الآن لنقطة برضه لها علاقة بهذا الموضوع
+
+273
+00:29:58,550 --> 00:30:02,970
+في هنا تعريف أخذناه سابقا في chapter of subgroup
+
+274
+00:30:02,970 --> 00:30:11,090
+نذكره لأنه بدنا نبني الشغل عليه definition تعريف
+
+275
+00:30:11,090 --> 00:30:17,810
+يقول if ال K is a divisor of N if ال K is a
+
+276
+00:30:17,810 --> 00:30:30,020
+divisor of N لو كان ال K قاسم لل N و define بدنا
+
+277
+00:30:30,020 --> 00:30:40,800
+نروح نعرف ال U K of N هو كل العناصر X اللي موجودة
+
+278
+00:30:40,800 --> 00:30:48,740
+في U M X اللي موجودة في U N such that X modulo K
+
+279
+00:30:48,740 --> 00:30:57,410
+بده يساوي مين بده يساوي الواحد وهذا شباب sub group من
+
+280
+00:30:57,410 --> 00:30:58,850
+ال UN
+
+281
+00:31:20,410 --> 00:31:23,750
+طلع لي في الكلام اللي احنا كتبينه من أول و جديد
+
+282
+00:31:23,750 --> 00:31:29,610
+بدنا نعطي تعريف و هذا التعريف مر علينا قبل هيك
+
+283
+00:31:29,610 --> 00:31:35,150
+يبقى احنا بس بنذكر بالذكر بقول لو كان عندي K هو
+
+284
+00:31:35,150 --> 00:31:40,010
+divisor لل N يبقى الشرط أساسي ان ال K لازم يقسم ال N
+
+285
+00:31:42,860 --> 00:31:49,420
+بنعرف ستة جديدة سميتها U K of N U N نعرفها كل
+
+286
+00:31:49,420 --> 00:31:53,220
+الأعداد اللي هي relatively prime مع M بس U K دخلت
+
+287
+00:31:53,220 --> 00:31:59,960
+على الخط بيقول لمين كل ال X's اللي موجودة في UN يبقى
+
+288
+00:31:59,960 --> 00:32:04,720
+عناصر من UN بحيث ال X modulo K بيساوي جداش واحد
+
+289
+00:32:04,720 --> 00:32:09,800
+يعني كل الأعداد اللي الفرق بينها وبين الواحد يساوي
+
+290
+00:32:09,800 --> 00:32:15,880
+مضاعفات ال K كل الأعداد اللي موجودة في UN اللي
+
+291
+00:32:15,880 --> 00:32:19,740
+الفرق بينها وبين الواحد هي مضاعفات ال K يعني Zero
+
+292
+00:32:20,270 --> 00:32:26,410
+طبعا يعني لو طرحت هذا العدد من الواحد بدي يطلع لي
+
+293
+00:32:26,410 --> 00:32:32,030
+مضاعفات ال K يطلع لي K يطلع لي 2K مضاعفات يعني كأنه
+
+294
+00:32:32,030 --> 00:32:35,130
+المضاعفات ال K زائد واحد صحيح يبقى الفرق بينهم
+
+295
+00:32:35,130 --> 00:32:43,210
+بيساوي Zero نعطي مثال let ال
+
+296
+00:32:43,210 --> 00:32:50,020
+G بدها تساوي U أربعين U أربعين مين عناصرها شباب طيب
+
+297
+00:32:50,020 --> 00:32:57,220
+find بدنا تمانية بدنا عدد يقسم الأربعين وليكن
+
+298
+00:32:57,220 --> 00:33:05,100
+ثمانية مثلا find U ثمانية of أربعين هي اللي بدنا
+
+299
+00:33:05,100 --> 00:33:06,440
+solution
+
+300
+00:33:12,160 --> 00:33:16,040
+الأول اللي بدنا نعرفه هو عناصر الـU40 ومنهم بدنا
+
+301
+00:33:16,040 --> 00:33:22,480
+نبدأ نجّه يبقى بداجة أقول له الـU40 عناصرها اللي
+
+302
+00:33:22,480 --> 00:33:31,680
+هي واحد اتنين تلاتة أربعة خمسة ستة سبعة ثمانية
+
+303
+00:33:31,680 --> 00:33:44,690
+تسعة 11 .. 13 .. 14 .. 15 .. 16 .. 17 .. 19 .. 21
+
+304
+00:33:44,690 --> 00:33:47,710
+..
+
+305
+00:33:47,710 --> 00:33:59,490
+23 .. 24 .. 25 .. 26 .. 27 ..وكمان تسعة و عشرين
+
+306
+00:33:59,490 --> 00:34:07,490
+ثلاثين واحد و ثلاثين اثنين و ثلاثين تلاتة و
+
+307
+00:34:07,490 --> 00:34:12,670
+ثلاثين أربعة و ثلاثين خمسة و ثلاثين ستة و ثلاثين
+
+308
+00:34:12,670 --> 00:34:18,910
+سبعة و ثلاثين تسعة و ثلاثين يبقى هذه عناصر من
+
+309
+00:34:18,910 --> 00:34:21,050
+عناصر ال U أربعين
+
+310
+00:34:27,390 --> 00:34:33,650
+احنا بنشرح للكل مش لوحد، كنا بنشرح للكل، الضعيف
+
+311
+00:34:33,650 --> 00:34:37,190
+والوسط والقوي كله موجود، بدك تحكي كلام يتناسب مع
+
+312
+00:34:37,190 --> 00:34:41,010
+الجميع ماشي يعني أنا كان بيبقى مكان يقول لك ده هي
+
+313
+00:34:41,010 --> 00:34:44,270
+دغري خد اللي هي الرقمين تلاتة و أقول لك ده هم لكنها
+
+314
+00:34:44,270 --> 00:34:49,790
+بنشرح بنفهم كل خطوة بنعملها كيف جت هي طيب قال لي
+
+315
+00:34:49,790 --> 00:34:54,410
+احسب لي قداش ال U ثمانية و أربعين فباجي بقوله U
+
+316
+00:34:54,410 --> 00:35:05,110
+ثمانية و أربعين بده يساوي U يساوي هل الواحد منهم لو
+
+317
+00:35:05,110 --> 00:35:11,130
+قلت لي لأ هقولها غلط لأن قبل قليل جالك هذه ال
+
+318
+00:35:11,130 --> 00:35:16,510
+group تحتوي على ال identity اثنين واحد ناقص واحد
+
+319
+00:35:16,510 --> 00:35:22,090
+يساوي جداش ال zero له مضاعفات الأربعين أو مضاعفات
+
+320
+00:35:22,090 --> 00:35:26,310
+ال K مضاعفات الثمانية اللي عندنا يبقى الواحد منهم
+
+321
+00:35:27,330 --> 00:35:33,470
+يلا تسعة لو شيلت من أواها بيصير ثمانية تمام يبقى
+
+322
+00:35:33,470 --> 00:35:39,190
+هذه التسعة أحد عشر ثلاث عشر سبعة عشر شيلت من أواها بيضل
+
+323
+00:35:39,190 --> 00:35:44,600
+كذا ستة عشر هي مضاعفات الثمانية يبقى ايه سبعة عشر
+
+324
+00:35:44,600 --> 00:35:52,080
+تسعة عشر لأ واحد و عشرين تلاتة و عشرين سبعة و عشرين
+
+325
+00:35:52,080 --> 00:36:00,260
+تسعة و عشرين واحد و ثلاثين تلاتة و ثلاثين اه تلاتة
+
+326
+00:36:00,260 --> 00:36:06,160
+و ثلاثين منها تلاتة و ثلاثين لأن لو أقل منها واحد
+
+327
+00:36:06,160 --> 00:36:10,780
+فتبقى اثنين و ثلاثين تسمع ثمانية ستة و ثلاثين لأ
+
+328
+00:36:10,780 --> 00:36:16,160
+ثمانية و ثلاثين لأ يبقى ما عنديش إلا الأربعة عناصر
+
+329
+00:36:16,160 --> 00:36:19,820
+اللي قدامي يعني يبقى إذن ال U ثمانية و أربعين هي
+
+330
+00:36:19,820 --> 00:36:23,860
+واحد و تسعة و سبعة عشر و تلاتة و ثلاثين و كل منها
+
+331
+00:36:23,860 --> 00:36:29,490
+يحقق من المعادلة أو حسبناهم بناء على التعريف اللي
+
+332
+00:36:29,490 --> 00:36:37,550
+اعطيناه ل UKM هذا كلام مهم لأن بدنا نبني عليه شغل
+
+333
+00:36:37,550 --> 00:36:42,230
+ثاني بعد قليل الآن بدنا نيجي لنظرية أخرى في هذا
+
+334
+00:36:42,230 --> 00:36:47,350
+الشابتر النظرية بتقول ما يأتي IRM
+
+335
+00:36:52,330 --> 00:37:06,230
+theorem suppose that suppose that أن ال S and T ال
+
+336
+00:37:06,230 --> 00:37:18,490
+S and T are relatively prime are relatively prime
+
+337
+00:37:20,290 --> 00:37:31,510
+are relatively prime then then
+
+338
+00:37:31,510 --> 00:37:40,830
+ال U S T ال U S T isomorphic
+
+339
+00:37:40,830 --> 00:37:50,770
+لل U S external product مع مين مع U T moreover
+
+340
+00:37:50,770 --> 00:37:54,230
+وأكثر
+
+341
+00:37:54,230 --> 00:37:59,050
+من ذلك ال
+
+342
+00:37:59,050 --> 00:38:12,930
+subgroup U S of ST isomorphic ل U T and ال U T لمن
+
+343
+00:38:12,930 --> 00:38:22,170
+لل ST isomorphic لمن ل US الشكل اللي عندنا أنا
+
+344
+00:38:22,170 --> 00:38:32,050
+isomorphic ل US وفي نتيجة عليها ك رولري بتقول
+
+345
+00:38:32,050 --> 00:38:44,170
+ما يأتي let ال M بدها تساوي N واحد N اثنين ولغاية NK
+
+346
+00:38:44,170 --> 00:38:55,190
+أن واحد أن اثنين لغاية NK where حيث لجلس ال common
+
+347
+00:38:55,190 --> 00:39:08,010
+divisor لل N I و N J بدها تساوي واحد for I لا تساوي
+
+348
+00:39:08,010 --> 00:39:09,810
+J then
+
+349
+00:39:11,580 --> 00:39:19,920
+الـ UM ايزو مورفك لمن؟ لل U N 1 اكستاناضايك برودك
+
+350
+00:39:19,920 --> 00:39:28,200
+مع U N 2 اكستاناضايك برودك مع مين؟ مع U N K بالشكل
+
+351
+00:39:28,200 --> 00:39:28,860
+اللي عندنا هنا
+
+352
+00:39:42,060 --> 00:39:48,760
+مرة ثانية بقول بقول لو عندك رقمين S وT are
+
+353
+00:39:48,760 --> 00:39:57,880
+relatively prime then ال U S T يبقى ال group اللي
+
+354
+00:39:57,880 --> 00:40:03,080
+عندنا ال U S T isomorphic لل externa تاكرودك تبقى
+
+355
+00:40:03,080 --> 00:40:09,120
+حاصل الضرب زي ايش مثلا لو قلت لك U خمسة عشر بقدر
+
+356
+00:40:09,120 --> 00:40:15,260
+أكتبها U تلاتة في خمسة مظبوط إذا هذه ال U خمسة عشر
+
+357
+00:40:15,260 --> 00:40:19,820
+ايزو مورفك ل U تلاتة اكسترنه ضايقة ضعفك مع مين مع
+
+358
+00:40:19,820 --> 00:40:24,740
+U خمسة هتقول لي تلاتة و خمسة relatively prime بقول لك
+
+359
+00:40:24,740 --> 00:40:33,900
+ماشي ايش رأيك U ثلاثين تساوي U خمسة في ستة صح خمسة
+
+360
+00:40:33,900 --> 00:40:39,070
+في ستة أو عشرة في تلاتة هذه وهذه أو اثنين في
+
+361
+00:40:39,070 --> 00:40:43,410
+خمسة عشر كلها أرقام are relatively prime إذا ال U
+
+362
+00:40:43,410 --> 00:40:47,930
+ثلاثين isomorphic الى U عشرة في تلاتة أو
+
+363
+00:40:47,930 --> 00:40:53,830
+isomorphic ل U خمسة في ستة أو isomorphic للاتنين
+
+364
+00:40:53,830 --> 00:40:58,390
+في U اثنين external like product مع U خمسة عشر و
+
+365
+00:40:58,390 --> 00:41:03,670
+هكذا ما دام الرقمين أو التلاتة اللي عندك تلاتة من
+
+366
+00:41:03,670 --> 00:41:08,790
+أين جبتها دي؟ جبتها من الكرولري الكرولري بتقول إذا
+
+367
+00:41:08,790 --> 00:41:11,490
+ما عندك ليس بضرر رقمين ممكن الأرقام اللي عندك
+
+368
+00:41:11,490 --> 00:41:16,090
+تحللها إلى حاصل ضرب تلاتة أرقام أو أربعة أرقام أو
+
+369
+00:41:16,090 --> 00:41:21,690
+خمسة أو عشرة أو كم من الأرقام حلل قد ما بدك يبقى لو
+
+370
+00:41:21,690 --> 00:41:27,990
+عندي الـ M هذا حللناه إلى حاصل ضرب N من الأرقام N1
+
+371
+00:41:27,990 --> 00:41:32,450
+N2 لغاية NK بحيث الـ greatest common divisor بين
+
+372
+00:41:32,450 --> 00:41:37,250
+أي اثنين بدي يكون relatively prime بدي يكون واحد
+
+373
+00:41:37,250 --> 00:41:41,690
+صحيح يعني الاثنين هذول are relatively prime يبقى
+
+374
+00:41:41,690 --> 00:41:46,830
+ال U M isomorphic ل U of الرقم الأول كستانادايكو
+
+375
+00:41:46,830 --> 00:41:51,030
+برودك U مع الرقم الثاني كستانادايكو برودك مع الرقم 
+
+376
+00:41:51,030 --> 00:41:55,250
+كي وهكذا المرة القادمة إن شاء الله بناخد أمثلة
+
+377
+00:41:55,250 --> 00:41:59,890
+توضحية على كيفية استخدام الكلام اللي عندنا هذا 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bb8b7560dc99eae89925cd2595a93c7ddf35d0c9
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/3SF3yRg1VtE_raw.srt
@@ -0,0 +1,1508 @@
+1
+00:00:21,290 --> 00:00:25,850
+بسم الله الرحمن الرحيم نستكمل الموضوع اللى بدأناه
+
+2
+00:00:25,850 --> 00:00:31,590
+الصبح وهو موضوع ال external direct product بعد ما
+
+3
+00:00:31,590 --> 00:00:35,770
+أخدنا أمثلة من خلالها بنعين ال order لل element
+
+4
+00:00:35,770 --> 00:00:42,070
+وكذلك عدد اللى هو ال elements ب order معين وعدد ال
+
+5
+00:00:42,070 --> 00:00:46,830
+cyclic groups ب order معين ننتقل الآن الى هذه
+
+6
+00:00:46,830 --> 00:00:51,500
+النظريةالنظرية بتقول يفترض ان جي و اتش بيه finite
+
+7
+00:00:51,500 --> 00:00:55,140
+cyclic groups يبقى كل واحدة فيها عدد محدود من
+
+8
+00:00:55,140 --> 00:01:00,060
+العناصر والتنتين are cyclic groups بيقول في هذه
+
+9
+00:01:00,060 --> 00:01:05,080
+الحلقين ال جي eccentric product مع اتش is cyclic
+
+10
+00:01:05,080 --> 00:01:08,760
+in fact تقول يف ال order جي و ال order اتش are
+
+11
+00:01:08,760 --> 00:01:13,240
+relatively prime يبقى من الآن فصاعدا لو ال two
+
+12
+00:01:13,240 --> 00:01:17,080
+groups جي و اتشتنين ال order اللي هم are
+
+13
+00:01:17,080 --> 00:01:19,840
+relatively prime اللي يبقى ال external product
+
+14
+00:01:19,840 --> 00:01:25,960
+معناه is a cyclic group مباشرة و العكس لو كانت
+
+15
+00:01:25,960 --> 00:01:28,860
+cyclic groups يبقى ال two orders are relatively
+
+16
+00:01:28,860 --> 00:01:35,620
+prime هذا اللي عايزين نثبته الآن يبقى لذلك نثبته
+
+17
+00:01:35,620 --> 00:01:41,040
+افترض ان ال H لها order معين و ال G كذلك لها order
+
+18
+00:01:41,040 --> 00:01:47,800
+معين و نشوف كيف بدنا نعمليبقى let ال order لل G
+
+19
+00:01:47,800 --> 00:01:55,680
+بده يساوي ال M and ال order لل H بده يساوي ال N
+
+20
+00:01:55,680 --> 00:02:00,200
+then
+
+21
+00:02:00,200 --> 00:02:11,180
+لو بده اجيب ال order لل G with H يبقى thenالأردر
+
+22
+00:02:11,180 --> 00:02:16,380
+للـ G External Hierarchical Product مع H كده يسوى
+
+23
+00:02:16,380 --> 00:02:20,040
+هذا يا شباب مكتوب معاكم من المرة اللي فاتت الأردر
+
+24
+00:02:20,040 --> 00:02:26,400
+للأولى في الأردر لثانية يبقى هذا الكلام يسوى ال M
+
+25
+00:02:26,400 --> 00:02:33,020
+في Nهذه المعلومة حطيتها قبل المبدأ و الأن بدي أبدأ
+
+26
+00:02:33,020 --> 00:02:38,360
+لإيش حطيتها؟ لأن كل شغل بالحب هو لازمانه الأن بدنا
+
+27
+00:02:38,360 --> 00:02:48,400
+نقول Assume that الـG external product مع الـH is
+
+28
+00:02:48,400 --> 00:02:54,540
+cyclicماذا أريد أن أثبت؟ أن الـ order اللي جي و ال
+
+29
+00:02:54,540 --> 00:02:58,560
+order اللي اتش اتنين are relatively prime يعني
+
+30
+00:02:58,560 --> 00:03:01,520
+أريد أن أثبت أن ال Euclides common divisor ما بين
+
+31
+00:03:01,520 --> 00:03:05,920
+الاتنين سيكون كم؟ سيكون واحد، صحيح طب افترضنا هذه
+
+32
+00:03:05,920 --> 00:03:10,040
+Cyclic مدام الـ Cyclic يبقى لها generator صح ولا
+
+33
+00:03:10,040 --> 00:03:14,600
+لا؟ يبقى Cyclic assume
+
+34
+00:03:15,770 --> 00:03:25,370
+أفترض كذلك إن الـ G والـ H is a generator is a
+
+35
+00:03:25,370 --> 00:03:33,870
+generator for اللي هو external product للـ H مع G
+
+36
+00:03:34,700 --> 00:03:38,460
+ما دام هذا generator يبقى ال order اللي بده يساوي
+
+37
+00:03:38,460 --> 00:03:43,860
+منين ال order لل G موديل لل G external direct
+
+38
+00:03:43,860 --> 00:03:50,920
+product مع H هذا معناه ان ال order لل G والH بده
+
+39
+00:03:50,920 --> 00:03:56,600
+يساوي ال order لل G external direct product مع من؟
+
+40
+00:03:56,600 --> 00:04:05,990
+مع ال H هذا بده يعطيني طيب ال order لل Gوالـ H بدي
+
+41
+00:04:05,990 --> 00:04:11,410
+يساوي ال least common multiple لل order تبع ال G
+
+42
+00:04:11,410 --> 00:04:18,870
+وال order تبع ال H يبقى
+
+43
+00:04:18,870 --> 00:04:23,050
+ال order لل G وال order تبع ال H بالشكل اللي عندنا
+
+44
+00:04:23,050 --> 00:04:28,730
+هذا اللي هو بدي يساوي ال order لهذه قداش اللي م في
+
+45
+00:04:28,730 --> 00:04:34,700
+نيبقى أنا بقول ال order لل element هذا بيساوي ال
+
+46
+00:04:34,700 --> 00:04:38,300
+order لل element هذه بيبقى بناء عليه ال order لل
+
+47
+00:04:38,300 --> 00:04:42,520
+element g و h بيساوي ال least common multiple ما
+
+48
+00:04:42,520 --> 00:04:46,360
+بين ال two orders طبقا للنظرية السابقة اللي
+
+49
+00:04:46,360 --> 00:04:51,340
+برهنناها طيب هذا ال order هو عبارة عن مين؟ عن m في
+
+50
+00:04:51,340 --> 00:04:57,020
+n خلي هذه المعلومة في دماغك و هنرجعلها بعد قليل
+
+51
+00:04:57,020 --> 00:05:05,640
+طيب الآنالـ order للـ G ال order للـ G يقسم ال
+
+52
+00:05:05,640 --> 00:05:11,840
+order للـ G كبتار صح ولا لا يبقى divide ال order
+
+53
+00:05:11,840 --> 00:05:19,250
+للـ G اللي هو بدي ساوي قداشM يعني ال order اللي
+
+54
+00:05:19,250 --> 00:05:25,670
+جيه بده يقسم من ال M وفي نفس الوقت ال order ل ال H
+
+55
+00:05:25,670 --> 00:05:33,390
+بده يقسم من بده يقسم ال order ل من ل ال H اللي هو
+
+56
+00:05:33,390 --> 00:05:38,870
+بده يساوي ال N إذا
+
+57
+00:05:38,870 --> 00:05:44,710
+ما هو علاقة least common multiple لل two orders مع
+
+58
+00:05:44,710 --> 00:05:45,970
+M و N
+
+59
+00:05:48,440 --> 00:05:52,340
+الليز كومل ملتبل لل اوضة مع الليز كومل ملتبل لل M
+
+60
+00:05:52,340 --> 00:05:55,360
+و N مين اللي اصغر و مين اللي اكبر؟ لليز كومل ملتبل
+
+61
+00:05:55,360 --> 00:06:01,800
+لمن؟ لل H و G مية لمية اصغر من من؟من ال least
+
+62
+00:06:01,800 --> 00:06:06,840
+common multiple لل M و N تمام؟ يبقى هذا يطيء
+
+63
+00:06:06,840 --> 00:06:12,840
+لكمين؟ ان ال least common multiple لل order تبع ال
+
+64
+00:06:12,840 --> 00:06:24,040
+G وال order تبع ال H هذا كله ماله أقل من أو يساوي
+
+65
+00:06:24,040 --> 00:06:32,930
+ال least common multiple لل M و Nتمام طيب ال least
+
+66
+00:06:32,930 --> 00:06:40,450
+common multiple لهذا اللي هو قداش M في N يبقى بناء
+
+67
+00:06:40,450 --> 00:06:47,950
+عليه So ال M في N أقل من أو يسوى ال least common
+
+68
+00:06:47,950 --> 00:06:56,450
+multiple لمن؟ لل M و N اعتبر هذه المعادلة رقم Star
+
+69
+00:06:58,800 --> 00:07:06,940
+السؤال هو احنا لان جيبنا ال M و ال N اقل من ال
+
+70
+00:07:06,940 --> 00:07:12,720
+least common multiple لمن؟ لل M و N طب in general
+
+71
+00:07:12,720 --> 00:07:24,720
+but و لكن we know that ان ال least common multiple
+
+72
+00:07:24,720 --> 00:07:26,840
+لل M و N
+
+73
+00:07:30,950 --> 00:07:35,450
+100% صحيح ولا لأ؟ دائما و أبدا ال least common ..
+
+74
+00:07:35,450 --> 00:07:39,430
+أقصى حاجة حصل ضربهم و دائما و أبدا بيكون أقل من
+
+75
+00:07:39,430 --> 00:07:44,870
+هيك يعني المضاعف المشترك أحيان بيكون كبيره في أقل
+
+76
+00:07:44,870 --> 00:07:51,630
+ما يمكن يبقى هذا أقل من مين؟ من M في N و هذه
+
+77
+00:07:51,630 --> 00:07:56,550
+العلاقة التانية هي رقم Star إذا من الإتنين مع بعض
+
+78
+00:07:56,550 --> 00:08:02,130
+بقول إن إتنين هدول ما لهماريكم يبقى هنا سوا ال
+
+79
+00:08:02,130 --> 00:08:09,150
+least common multiple لل M و N بده يساوي ال M في N
+
+80
+00:08:11,690 --> 00:08:17,290
+طيب نرجع بالذاكرة اصبر علينا شوية نرجع بالذاكرة
+
+81
+00:08:17,290 --> 00:08:22,650
+للوراء خلف الاول chapter اذا بتذكروا هنا قلنا ل
+
+82
+00:08:22,650 --> 00:08:26,290
+grace is common divided between عددين في least
+
+83
+00:08:26,290 --> 00:08:29,990
+common multiple العدين بيعطينا مين؟ نفس العددين
+
+84
+00:08:29,990 --> 00:08:40,950
+يبقى هنا باجي بقوله بط ولكن و لاthat لابنعرف ان
+
+85
+00:08:40,950 --> 00:08:47,530
+الـ greatest common divisor لل M والN مضروب في
+
+86
+00:08:47,530 --> 00:08:55,510
+least common multiple لل M وN بده يساوي M في N هذا
+
+87
+00:08:55,510 --> 00:09:01,790
+بده يعطيناالان ال least common multiple هو M في N
+
+88
+00:09:01,790 --> 00:09:07,570
+يبقى هذا بدي اعطيك انه ال greatest common divisor
+
+89
+00:09:07,570 --> 00:09:13,070
+لل M و N في ال least common multiple اللي هو M في
+
+90
+00:09:13,070 --> 00:09:20,040
+N بده يسوى ال M في Nيبقى هذا يعطينا common divisor
+
+91
+00:09:20,040 --> 00:09:25,980
+لل M و N يبقى كمية طب ال M مش ال order تبع ال G و
+
+92
+00:09:25,980 --> 00:09:32,260
+ال N هو ال order تبع ال H يبقى هذا معناه ان ال M
+
+93
+00:09:32,260 --> 00:09:44,640
+and ال N are relatively prime هذا يعطيناهذا بدي
+
+94
+00:09:44,640 --> 00:09:51,120
+يعطينا ان ال order ل capital G لل group كلها and
+
+95
+00:09:51,120 --> 00:09:57,700
+ال order ل ال H are relatively right
+
+96
+00:10:03,000 --> 00:10:07,320
+أحنا خلصنا الاتجاه الأول في النظرية، وهو أنه لو
+
+97
+00:10:07,320 --> 00:10:14,100
+كان الـ G إكسيندرايكالبرودك مع H is cyclic يبقى
+
+98
+00:10:14,100 --> 00:10:17,080
+الأوردر لـ G و الأوردر لـ H are relatively
+
+99
+00:10:17,080 --> 00:10:22,010
+primary، لأننا بدأ نمشي العملية العكسيةأثبت و افرض
+
+100
+00:10:22,010 --> 00:10:27,250
+ان اتنين هدول are relatively prime ذاتس يعني ايش
+
+101
+00:10:27,250 --> 00:10:32,030
+ذاتس؟ لجريس ال common divisor لل M و N بده يساوي
+
+102
+00:10:32,030 --> 00:10:37,350
+كده ايش؟ بده يساوي واحد صحيح طيب في حاجة موجودة في
+
+103
+00:10:37,350 --> 00:10:42,690
+النصر وحتى الآن لم نستخدمها اشيو .. اللي كل واحدة
+
+104
+00:10:42,690 --> 00:10:47,350
+من ال two groups اتنين هدول cycling مدام كل واحدة
+
+105
+00:10:47,350 --> 00:10:56,270
+cycling اذا كل واحدة فيهاgenerator يبقى since ال g
+
+106
+00:10:56,270 --> 00:10:59,350
+since
+
+107
+00:10:59,350 --> 00:11:07,070
+ال g is cyclic we have since ال .. خلي ال g باتنين
+
+108
+00:11:07,070 --> 00:11:15,950
+مرة واحدة since ال g and ال h and ال h are cyclic
+
+109
+00:11:15,950 --> 00:11:24,510
+we haveإن الـ G هذه في الها generator وليكن small
+
+110
+00:11:24,510 --> 00:11:33,050
+g and ال H الهاهاها اللي هو generator وليكن main
+
+111
+00:11:33,050 --> 00:11:38,110
+وليكن H طيب
+
+112
+00:11:38,110 --> 00:11:46,110
+إذا قداش ال order ل G small M و ال order ل H M
+
+113
+00:11:46,110 --> 00:11:52,630
+يكويس يبقى هذا بده يعطيناإن ال order للـ G بده
+
+114
+00:11:52,630 --> 00:11:58,430
+يساوي ال M and ال order ل H بده يساوي ال main بده
+
+115
+00:11:58,430 --> 00:12:05,390
+يساوي ال N طيب كويس يبقى أنا بده أجي لل order تبع
+
+116
+00:12:05,390 --> 00:12:11,630
+ال G و ال H مرة واحدة يبقى هذا الكلام بده يساوي
+
+117
+00:12:11,630 --> 00:12:16,950
+least common multiple لل order بتبع ال G و ال
+
+118
+00:12:16,950 --> 00:12:23,120
+order بتبع ال Hيبقى هذا الكلام بدي يسوى ال least
+
+119
+00:12:23,120 --> 00:12:30,180
+common multiple ال least common multiple لمين؟ لل
+
+120
+00:12:30,180 --> 00:12:39,940
+M و لل N أنا أدعي ان M في N طيب ليش؟ لأن ال common
+
+121
+00:12:39,940 --> 00:12:47,400
+divisor يسوى 1 يبقى هذا ليش؟ لأنإن الـ common
+
+122
+00:12:47,400 --> 00:12:54,480
+divisor لـ M و لـ N يبدو يساوي واحد صحيح طب هذا
+
+123
+00:12:54,480 --> 00:13:00,120
+الـ M في الـ N هو عبارة عن ال order لمن؟ ال order
+
+124
+00:13:00,120 --> 00:13:03,970
+لل group اللي هو نسميه هايوهو عبارة عن الـ order
+
+125
+00:13:03,970 --> 00:13:09,850
+للجروب يبقى هذا الكلام يساوي ال order للـ G
+
+126
+00:13:09,850 --> 00:13:15,530
+external direct product لمن؟ لل H يبقى ال gate
+
+127
+00:13:15,530 --> 00:13:20,630
+element موجود في ال external direct product ال
+
+128
+00:13:20,630 --> 00:13:26,150
+order له يساوي ال order لمن؟ لل group يبقى ال
+
+129
+00:13:26,150 --> 00:13:31,250
+group هذا ما يصير؟ Cyclic وهذا generator يبقى هنا
+
+130
+00:13:31,250 --> 00:13:43,780
+ساالـ G والـ H is a generator for اللي هو الـ G
+
+131
+00:13:43,780 --> 00:13:50,320
+external direct product مع مين مع H هذا بده يعطيلك
+
+132
+00:13:50,320 --> 00:13:57,620
+انه G external direct product مع H is cyclic وهو
+
+133
+00:13:57,620 --> 00:14:05,720
+المطلوبإذا قلت لك إثبت
+
+134
+00:14:05,720 --> 00:14:11,100
+الـexternal هذا direct product is cyclic تمام؟
+
+135
+00:14:11,100 --> 00:14:15,520
+بعدين بقوله إذا والله التنتين كل واحدة فيهم cyclic
+
+136
+00:14:15,520 --> 00:14:18,940
+وال order تبع كل واحدة فيهم مع التاني اتنين
+
+137
+00:14:18,940 --> 00:14:22,570
+relatively primeor than automatic على طول الخطب
+
+138
+00:14:22,570 --> 00:14:27,210
+هذه النظرية ال external direct product is cyclic
+
+139
+00:14:27,210 --> 00:14:31,670
+group يبقى الشرط ال external direct product أن
+
+140
+00:14:31,670 --> 00:14:36,270
+يكون cyclic group أمرين الأمر الأول كل واحدة فيهم
+
+141
+00:14:36,270 --> 00:14:41,190
+تبقى cyclic الأمر الثاني ال order لل group الأولى
+
+142
+00:14:41,190 --> 00:14:43,850
+و ال order لل group التاني يكونوا اتنين معاهم
+
+143
+00:15:00,200 --> 00:15:05,820
+النظرية هذه أثبتناها لمين لتو group طب لو صاروا
+
+144
+00:15:05,820 --> 00:15:11,810
+تلاتةتلاتة groups والله أربعة والله خمسة والله in
+
+145
+00:15:11,810 --> 00:15:16,550
+من ال groups فالنظرية صحيحة وهذا الموضوع ل
+
+146
+00:15:16,550 --> 00:15:27,390
+crawlery رقم واحد يبقى crawlery رقم واحد بتقول ان
+
+147
+00:15:27,390 --> 00:15:34,230
+external direct product ان external direct
+
+148
+00:15:35,820 --> 00:15:44,680
+a product external direct product g one external
+
+149
+00:15:44,680 --> 00:15:50,520
+direct product مع g two external direct product مع
+
+150
+00:15:50,520 --> 00:16:03,000
+مين مع g n of a finite of a finite number
+
+151
+00:16:04,660 --> 00:16:20,060
+finite number of finite cyclic groups is
+
+152
+00:16:20,060 --> 00:16:33,660
+cyclic if and only ifالـ order للـ G I and ال
+
+153
+00:16:33,660 --> 00:16:46,100
+order للـ G J are relatively a prime are
+
+154
+00:16:46,100 --> 00:16:54,380
+relatively a prime when ال I لا تساوي مين؟ لا
+
+155
+00:16:54,380 --> 00:17:02,540
+تساوي ال Gكمان كرولري تانية بتقول
+
+156
+00:17:02,540 --> 00:17:10,240
+let اللي هو ال M عملناها تحليل صارت N واحد في N
+
+157
+00:17:10,240 --> 00:17:18,760
+اتنين في N K then ال
+
+158
+00:17:18,760 --> 00:17:31,150
+ZM ال ZM isomorphicلمن؟ ل z n one external product
+
+159
+00:17:31,150 --> 00:17:43,350
+مع z n two external product مع من؟ مع z n k if and
+
+160
+00:17:43,350 --> 00:17:53,930
+only if if and only if ال n i and ال n j are
+
+161
+00:17:53,930 --> 00:18:06,240
+relatively primeare relatively prime when
+
+162
+00:18:06,240 --> 00:18:11,100
+I لا تساوي الجهة
+
+163
+00:18:38,860 --> 00:18:44,120
+الكرولري الأولى هي تعميم للنظرية الكرولري الثانية
+
+164
+00:18:44,120 --> 00:18:48,760
+كأنه تطبيق مباشر عالمين على النظرية تعالى نشوف
+
+165
+00:18:48,760 --> 00:18:53,640
+التعميم في الأول ومن ثم بنروح للكرولري التانية
+
+166
+00:18:53,640 --> 00:18:59,380
+اللى هي رقم اتنين يبقى هذه الكرولري الرقم اتنين
+
+167
+00:19:00,650 --> 00:19:03,590
+تعالى اكررلى رقم واحد بيقول ان external direct
+
+168
+00:19:03,590 --> 00:19:08,770
+product لمجموعة من ال group of a finite number
+
+169
+00:19:08,770 --> 00:19:13,330
+يبقى عدد محدود من ال groups وكل group has finite
+
+170
+00:19:13,330 --> 00:19:18,490
+order كل واحدة اللى عدد تبعها محدود يبقى هذا ال
+
+171
+00:19:18,490 --> 00:19:21,710
+external direct product بيكون cyclic if and only
+
+172
+00:19:21,710 --> 00:19:26,230
+if ال order لجي اي and ال order لجي جي are
+
+173
+00:19:26,230 --> 00:19:31,510
+relatively primeوان ال I لا تساوي ال جيه يعني بديش
+
+174
+00:19:31,510 --> 00:19:36,650
+اقول لجروبه نفسه هى المقصود I لا تساوي الجيه يعني
+
+175
+00:19:36,650 --> 00:19:40,570
+هاد الجروب تختلف تماما مع من مع هاد الجروب طب احنا
+
+176
+00:19:40,570 --> 00:19:47,290
+عندنا كام جروبأي واحدة مع التانية بيكون relatively
+
+177
+00:19:47,290 --> 00:19:50,270
+prime يعني الأولى مع التانية الأولى مع التالتة
+
+178
+00:19:50,270 --> 00:19:54,350
+الأولى مع العاشرة التانية مع التالتة التانية مع ..
+
+179
+00:19:54,350 --> 00:19:58,950
+كله are relatively prime تمام ال order تبع كل
+
+180
+00:19:58,950 --> 00:20:01,550
+واحدة منهم مع ال order مع التانية بيكون are
+
+181
+00:20:01,550 --> 00:20:05,420
+relatively primeوهو تعميم للنظرية النظرية كانت
+
+182
+00:20:05,420 --> 00:20:08,620
+عالميا على two groups اللي هي GUH عمّمناها
+
+183
+00:20:08,620 --> 00:20:11,800
+خلّيناهم تلاتة خلّيناهم أربعة خلّيناهم خمسة مش
+
+184
+00:20:11,800 --> 00:20:16,900
+مشكلة قد ما يكون العدد يبقى هذه النظرية صحيح عليهم
+
+185
+00:20:16,900 --> 00:20:21,700
+وهي هذه النتيجة رقم واحد الا للنتيجة رقم اتنين
+
+186
+00:20:21,700 --> 00:20:27,780
+بيقول لو عندك رقم M حللته إلى حاصل ضرب أعداد زي
+
+187
+00:20:27,780 --> 00:20:33,700
+ايش مثلا زي تلاتينتلاتين بقدر اقول اتنين في تلاتة
+
+188
+00:20:33,700 --> 00:20:38,780
+في خمسة يبقى هاي حلته لحاصل ضرب ثلاثة اعداد
+
+189
+00:20:38,780 --> 00:20:43,480
+والثلاثة اعداد ما لهم؟ Primes اتنين والتلاتة
+
+190
+00:20:43,480 --> 00:20:48,500
+والخمسة are primes ايش بقول هنا؟لو حللت ال M لحاصل
+
+191
+00:20:48,500 --> 00:20:58,140
+ضرب أعداد يبقى ZM isomorphic ل ZN1, ZN2, ZN3, ZNK,
+
+192
+00:20:58,400 --> 00:21:04,080
+F and only F كل عدد من هذه الأعداد are relatively
+
+193
+00:21:04,080 --> 00:21:10,580
+prime مع بعضهم البعض يعني ليس بالضرورة أن يكونوا
+
+194
+00:21:10,580 --> 00:21:15,240
+primes وإنما يكونوا relatively primesيعني ممكن اخد
+
+195
+00:21:15,240 --> 00:21:21,360
+اللي هو العدد اتنين مع العدد سبعة ممكن اخد ستة و
+
+196
+00:21:21,360 --> 00:21:24,800
+خمسة ستة و خمسة اتنين relatively primes رغم انه
+
+197
+00:21:24,800 --> 00:21:29,980
+خمسة primes ستة لأ تمام يبقى ليس بالضرورة ان تكون
+
+198
+00:21:29,980 --> 00:21:35,420
+هذه الاعداد primes مثل ما حللنا اش التلاتين يبقى
+
+199
+00:21:35,420 --> 00:21:40,310
+ممكن يكون اربعة و عشرينأربعة و عشرين هو تلاتة في
+
+200
+00:21:40,310 --> 00:21:45,110
+تمان يعني اتنين في تلاتة في اربع مظبوط يبقى الاربع
+
+201
+00:21:45,110 --> 00:21:47,730
+و عشرين اتنين في تلاتة في ستة في اربع و اربع و
+
+202
+00:21:47,730 --> 00:21:53,010
+عشرين الان يبقى هذول اتنين في تلاتة في ستة اتنين و
+
+203
+00:21:53,010 --> 00:21:57,810
+تلاتة هذول الـprimes بس إيش بيصير اتنين مع الأربع
+
+204
+00:21:57,810 --> 00:22:01,880
+are not relatively primeيبقى بصير كل ابن هذا صحيح
+
+205
+00:22:01,880 --> 00:22:06,600
+ولا مش صحيح؟ مش صحيح لازم تاخد أي رقمين منهم
+
+206
+00:22:06,600 --> 00:22:10,640
+ودمكونوا مع بعض اتنين معاهم relatively a primes
+
+207
+00:22:10,640 --> 00:22:16,220
+وليس بالضرورة ان يكونوا a primes يبقى مرة تانية
+
+208
+00:22:16,220 --> 00:22:22,740
+بقول حللت ال M الى حاصل ضرب اعدادمدام حللت يجزد ام
+
+209
+00:22:22,740 --> 00:22:30,040
+الأصلية isomorphic لمام لل external direct product
+
+210
+00:22:30,040 --> 00:22:35,340
+اللي هم كلهم هدول if and only if أي اتنين منهم
+
+211
+00:22:35,340 --> 00:22:39,640
+بدهم يكونوا relatively prime مع بعضهم البعض الان
+
+212
+00:22:39,640 --> 00:22:46,020
+نعطيك تمثيل عددي شغل عددي كيف هذا الكلام example
+
+213
+00:22:53,570 --> 00:22:58,310
+هذا هو التوضيح اللي قال لو جيت ل z دي اتنين
+
+214
+00:22:58,310 --> 00:23:04,670
+external like product مع z دي اتنين external like
+
+215
+00:23:04,670 --> 00:23:11,390
+product مع z تلاتة external like product مع مين؟
+
+216
+00:23:11,390 --> 00:23:14,590
+مع z خمسة بالشكل اللي عندنا
+
+217
+00:23:17,820 --> 00:23:21,800
+بدي أكوّن من هذه مجموعة milligroups بيكونوا
+
+218
+00:23:21,800 --> 00:23:27,260
+isomorphic لها باجي بقول والله كويس شرايك التنتين
+
+219
+00:23:27,260 --> 00:23:31,200
+هذول are relatively prime اتنين والتلاتة ولا لأ
+
+220
+00:23:31,200 --> 00:23:38,460
+اذا هذه isomorphic لمين زد ستة زد ستة لأن انا قولك
+
+221
+00:23:38,460 --> 00:23:44,580
+M و هذا M فين بس أصغر شوية واحدة واحدةيبقى هذه
+
+222
+00:23:44,580 --> 00:23:53,600
+isomorphic لمين؟ لزد اتنين كما هي لزد اتنين
+
+223
+00:23:53,600 --> 00:24:00,340
+اكستيرنا ال product لزد ستة اكستيرنا ال product
+
+224
+00:24:00,340 --> 00:24:11,060
+لمن؟ لزد خمسة ليش؟ since اتنين and التلاتة are
+
+225
+00:24:11,430 --> 00:24:21,670
+relatively prime طيب ..الان هذى بدي اجيب كمان
+
+226
+00:24:21,670 --> 00:24:28,630
+group اخرى isomorphic لهاوهذه كمان isomorphic لزد
+
+227
+00:24:28,630 --> 00:24:32,750
+اتنين external by product هدول اتنين are
+
+228
+00:24:32,750 --> 00:24:39,110
+relatively prime يبقى زد مين؟ زد تلاتين حاصلة ضرب
+
+229
+00:24:39,110 --> 00:24:49,230
+يبقى هذه لزد تلاتين يبقى ليش؟ since الستة and
+
+230
+00:24:49,230 --> 00:24:53,650
+الخمسة are relatively
+
+231
+00:24:57,660 --> 00:25:04,940
+السؤال هو هل هذا ايزو مورفك لزد ستين لأ ليش لأن
+
+232
+00:25:04,940 --> 00:25:12,080
+هذا ليس عشان ايزو مورفك لزد ستين وستين وهي هذا ليس
+
+233
+00:25:12,080 --> 00:25:24,880
+عشان ايزو مورفك لزد ستين لأن السبب ان الاتنين and
+
+234
+00:25:25,300 --> 00:25:30,240
+الثلاثين ليسوا
+
+235
+00:25:30,240 --> 00:25:41,180
+مرتفعين بشكل عام طيب
+
+236
+00:25:41,180 --> 00:25:47,640
+ايش رايك؟ بدي اخلق كمان groups اخرى ايزو مورفة
+
+237
+00:25:47,640 --> 00:25:57,570
+لهذه ال group also لو جيت اخدتاللي هو Z اتنين
+
+238
+00:25:57,570 --> 00:26:03,490
+external by-product لزد اتنين external by-product
+
+239
+00:26:03,490 --> 00:26:10,010
+لزد تلاتة external by-product لزد خمسة is
+
+240
+00:26:10,010 --> 00:26:15,910
+isomorphic قلنا قبل قليل زد اتنين external by
+
+241
+00:26:15,910 --> 00:26:21,850
+-product is ستة external by-product لمن لزد خمسة
+
+242
+00:26:23,460 --> 00:26:27,620
+هذا اللي قلناها قبل قليل من هذه بدي أخلق groups
+
+243
+00:26:27,620 --> 00:26:32,320
+أخرى تبقى isomorphic لنفس ال group كيف كانت تالية
+
+244
+00:26:32,320 --> 00:26:39,840
+أطلع لي هنا بقدر أكتب هذه Z2 زي ما هي هذه Z6 انقول
+
+245
+00:26:39,840 --> 00:26:45,980
+Z2 external dichromate مع Z3 ولا Z3 external مع Z2
+
+246
+00:26:45,980 --> 00:26:50,160
+نفس الشيء لأنه حصل ضربهم يسوء 6 و 2 are relatively
+
+247
+00:26:50,160 --> 00:26:54,690
+prime بنفس النظرية اللي هي قبل قليليبقى بناءً عليه
+
+248
+00:26:54,690 --> 00:27:00,210
+هذه بقدر أقول بدل ما هي z6 بدي أقول عليها z3
+
+249
+00:27:00,210 --> 00:27:05,690
+external by-product مع z2 external by-product مع
+
+250
+00:27:05,690 --> 00:27:16,790
+z5 طيب هذه isomorphic لمن؟ طلعلي لهذه relatively
+
+251
+00:27:16,790 --> 00:27:24,330
+primeيبقى هذول الـ Z6 External Direct Product مع
+
+252
+00:27:24,330 --> 00:27:30,610
+Z2 External Direct Product مع Z5 يبقى هذه جروب
+
+253
+00:27:30,610 --> 00:27:37,130
+جديدة بدي أطلع كمان جروب تاني يبقى هذه isomorphic
+
+254
+00:27:37,130 --> 00:27:45,770
+كمان لمين؟ لـ Z6 External Direct Product 2 5 يبقى
+
+255
+00:27:45,770 --> 00:27:54,900
+مع Z10ليش؟ لأنه الستة والخمسة are .. لأنه الاتنين
+
+256
+00:27:54,900 --> 00:28:00,140
+والخمسة are relatively prime يبقى هذا sense اتنين
+
+257
+00:28:00,140 --> 00:28:10,160
+and خمسة are relatively primeوالخطوة الأولى اللى
+
+258
+00:28:10,160 --> 00:28:13,380
+عندنا زد ستة لإنه اتنين و تلاتة relatively prime
+
+259
+00:28:13,380 --> 00:28:20,600
+هذا كتبناه قبل قليل طب السؤال هو هل هذه isomorphic
+
+260
+00:28:20,600 --> 00:28:28,340
+لزد ستين ما يفيها ستين عنصر طبعا لأ السبب because
+
+261
+00:28:29,790 --> 00:28:40,350
+إن الستة و العشرة ليسوا مرتبطين بشكل
+
+262
+00:28:40,350 --> 00:28:40,370
+عام
+
+263
+00:28:47,410 --> 00:28:53,090
+بقول isomorphic وين هي؟ لأ لأ كله isomorphic يا
+
+264
+00:28:53,090 --> 00:28:57,310
+شباب ماعنديش ماقلتش يساوي يبقى لو قلت يساوي معناته
+
+265
+00:28:57,310 --> 00:29:03,170
+كل عنصر يساوي نظيره لكن هذه group تختلف عن هذه
+
+266
+00:29:03,170 --> 00:29:08,050
+يعني مثلا عنصر اللي هنا لو بده أخد الواحد و من هنا
+
+267
+00:29:08,050 --> 00:29:12,010
+بده أخد اتنين و من هنا بده أخد ال zero و من هنا
+
+268
+00:29:12,010 --> 00:29:16,350
+بده أخد الأربعة مثلابيختلف عن هذا اللي هنا وهكذا
+
+269
+00:29:16,350 --> 00:29:20,810
+إذا أي زمار فيك يعني لجروب الأولى و لجروب التانية
+
+270
+00:29:20,810 --> 00:29:27,730
+لها نفس الخواص الرياضية يبقى هاي كل اللي بنقوله
+
+271
+00:29:27,730 --> 00:29:33,530
+بناسمة يعني هذا مثال عملي على الشغلانة طيب ننتقل
+
+272
+00:29:33,530 --> 00:29:39,110
+الآن لنقطة برضه لها علاقة بهذا الموضوع
+
+273
+00:29:58,550 --> 00:30:02,970
+في هنا تعريف أخدناه سابقا في chapter of subgroup
+
+274
+00:30:02,970 --> 00:30:11,090
+نذكره لأنه بدنا نبني الشغل عليه definition تعريف
+
+275
+00:30:11,090 --> 00:30:17,810
+يقول if ال K is a divisor of N if ال K is a
+
+276
+00:30:17,810 --> 00:30:30,020
+divisor of N لو كان ال K قاسم لل N وdefine بدنا
+
+277
+00:30:30,020 --> 00:30:40,800
+نروح انعرف ال U K of N هو كل العناصر X اللي موجودة
+
+278
+00:30:40,800 --> 00:30:48,740
+في U M X اللي موجودة في U N such that X modulo K
+
+279
+00:30:48,740 --> 00:30:57,410
+بده ساوي مين بده ساوي الواحدوهذا شباب sub group من
+
+280
+00:30:57,410 --> 00:30:58,850
+ال UN
+
+281
+00:31:20,410 --> 00:31:23,750
+طلعلي في الكلام اللى احنا كتبينه من أول و جديد
+
+282
+00:31:23,750 --> 00:31:29,610
+بدنا نعطي تعريف و هذا التعريف مر علينا قبل هيك
+
+283
+00:31:29,610 --> 00:31:35,150
+يبقى احنا بس بنذكر بالذكر بقول لو كان عندي K هو
+
+284
+00:31:35,150 --> 00:31:40,010
+divisor لل N يبقى الشرط أساسي ان ال K لازم يقسمين
+
+285
+00:31:42,860 --> 00:31:49,420
+بنعرف ستة جديدة سميتها U K of N U N نعرفينها كل
+
+286
+00:31:49,420 --> 00:31:53,220
+الإعداد اللي هي relatively prime مع M بس U K دخلت
+
+287
+00:31:53,220 --> 00:31:59,960
+على خط بيقول لمينكل ال X's اللي موجودة في UN يبقى
+
+288
+00:31:59,960 --> 00:32:04,720
+عناصر من UN بحيث ال X modulo K بيسوي جداش واحد
+
+289
+00:32:04,720 --> 00:32:09,800
+يعني كل الأعداد اللي الفرق بينها وبين الواحد يسوي
+
+290
+00:32:09,800 --> 00:32:15,880
+مضاعفات ال K كل الأعداد اللي موجودة في UN اللي
+
+291
+00:32:15,880 --> 00:32:19,740
+الفرق بينها وبين الواحد هي مضاعفات ال K يعني Zero
+
+292
+00:32:20,270 --> 00:32:26,410
+طبعا يعني لو طرحت هذا العدد من الواحد بدي يطلعلي
+
+293
+00:32:26,410 --> 00:32:32,030
+مضاعفات ال K يطلعلي K يطلعلي 2K مضاعفات يعني كأنه
+
+294
+00:32:32,030 --> 00:32:35,130
+المضاعفات ال K زائد واحد صحيح يبقى الفرق بينهم
+
+295
+00:32:35,130 --> 00:32:43,210
+بيساوي Zero نعطي مثال let ال
+
+296
+00:32:43,210 --> 00:32:50,020
+G بدها تساوي U أربعينU اربعين مين عناصرها شباب طيب
+
+297
+00:32:50,020 --> 00:32:57,220
+find بدنا تمانية بدنا عدد يقسم الاربعين وليكن
+
+298
+00:32:57,220 --> 00:33:05,100
+تمانية مثلا find U تمانية of اربعين هي اللي بدنا
+
+299
+00:33:05,100 --> 00:33:06,440
+solution
+
+300
+00:33:12,160 --> 00:33:16,040
+الأول اللي بدنا نعرفه هو عناصر الـU40 ومنهم بدنا
+
+301
+00:33:16,040 --> 00:33:22,480
+نبدأ نجّه يبقى بداجة أقول له الـU40 عناصرها اللي
+
+302
+00:33:22,480 --> 00:33:31,680
+هي واحد اتنين تلاتة أربع خمسة ستة انسة سبعة تمانية
+
+303
+00:33:31,680 --> 00:33:44,690
+تسعة11 .. 13 .. 14 .. 15 .. 16 .. 17 .. 19 .. 21
+
+304
+00:33:44,690 --> 00:33:47,710
+..
+
+305
+00:33:47,710 --> 00:33:59,490
+23 .. 24 .. 25 .. 26 .. 27 ..وكمان تسعة و عشرين
+
+306
+00:33:59,490 --> 00:34:07,490
+تلاتين انسى واحد و تلاتين اتنين و تلاتين تلاتة و
+
+307
+00:34:07,490 --> 00:34:12,670
+تلاتين اربعة و تلاتين خمسة و تلاتين ستة و تلاتين
+
+308
+00:34:12,670 --> 00:34:18,910
+سبعة و تلاتين تسعة و تلاتين يبقى هذه عناصر من
+
+309
+00:34:18,910 --> 00:34:21,050
+عناصر ال U اربعين
+
+310
+00:34:27,390 --> 00:34:33,650
+أحنا بنشرح للكل مش لوحد، كنا بنشرح للكل، الضعيف
+
+311
+00:34:33,650 --> 00:34:37,190
+والوسط والقوي كله موجود، بدك تحكي كلام يتناسب مع
+
+312
+00:34:37,190 --> 00:34:41,010
+الجميعماشي يعني انا كان بيبقى مكان يقولك ده هي
+
+313
+00:34:41,010 --> 00:34:44,270
+دغري خد اللي هي الرقمين تلاتة و اقولك ده هم لكنها
+
+314
+00:34:44,270 --> 00:34:49,790
+بناشك بننفم كل خطوة بنعملها كيف جت هالي طيب قاللي
+
+315
+00:34:49,790 --> 00:34:54,410
+احسبلي قداش ال U تمانية و أربعين فباجي بقوله U
+
+316
+00:34:54,410 --> 00:35:05,110
+تمانية و أربعين بده تساوي U ساوي هل الواحد منهملو
+
+317
+00:35:05,110 --> 00:35:11,130
+قلت لي لأ هقولها غلط لأن قبل قليل جالك هذه ال
+
+318
+00:35:11,130 --> 00:35:16,510
+group تحتوي على ال identity اتنين واحد ناقص واحد
+
+319
+00:35:16,510 --> 00:35:22,090
+يسوى جداش ال zero له مضاعفات الأربعين أو مضاعفات
+
+320
+00:35:22,090 --> 00:35:26,310
+ال K مضاعفات التمانية اللي عندنا يبقى الواحد منهم
+
+321
+00:35:27,330 --> 00:35:33,470
+يالا تسعة لو شيلت من أواها بصير تمانية تمام يبقى
+
+322
+00:35:33,470 --> 00:35:39,190
+هذه التسعة أحداشر تلتاشر سبعتاشر شيلت من أواها بضل
+
+323
+00:35:39,190 --> 00:35:44,600
+كده ستاشر هي مضاعفات التمانيةيبقى ايه سبعتاشر
+
+324
+00:35:44,600 --> 00:35:52,080
+تسعتاشر لأ واحد و عشرين تلاتة و عشرين سبعة و عشرين
+
+325
+00:35:52,080 --> 00:36:00,260
+تسعة و عشرين واحد و تلاتين تلاتة و تلاتين اه تلاتة
+
+326
+00:36:00,260 --> 00:36:06,160
+و تلاتين منهمتلاتة و تلاتين لإن لو أقل منها واحد
+
+327
+00:36:06,160 --> 00:36:10,780
+فتبقى اتنين و تلاتين تسمع تمانية ستة و تلاتين لأ
+
+328
+00:36:10,780 --> 00:36:16,160
+تمانية و تلاتين لأ يبقى ماعنديش إلا الأربعة عناصر
+
+329
+00:36:16,160 --> 00:36:19,820
+اللي قدامي يعني يبقى إذن ال U تمانية و أربعين هي
+
+330
+00:36:19,820 --> 00:36:23,860
+واحد و تسعة و سبتاشر و تلاتة و تلاتين و كل منها
+
+331
+00:36:23,860 --> 00:36:29,490
+يحقق منالمعادلة او حسبناهم بناء على التعريف اللى
+
+332
+00:36:29,490 --> 00:36:37,550
+اعطناه ل UKM هذا كلام مهم لان بدنا نبني عليه شغل
+
+333
+00:36:37,550 --> 00:36:42,230
+تاني بعد قليل الان بدنا نيجي لنظرية اخرى في هذا
+
+334
+00:36:42,230 --> 00:36:47,350
+الشبتر النظرية بتقول ما يأتي IRM
+
+335
+00:36:52,330 --> 00:37:06,230
+theorem suppose that suppose that ان ال S and T ال
+
+336
+00:37:06,230 --> 00:37:18,490
+S and T are relatively prime are relatively prime
+
+337
+00:37:20,290 --> 00:37:31,510
+are relatively prime then then
+
+338
+00:37:31,510 --> 00:37:40,830
+ال U S T ال U S T isomorphic
+
+339
+00:37:40,830 --> 00:37:50,770
+لل U S external product مع مين مع U Tmoreover
+
+340
+00:37:50,770 --> 00:37:54,230
+وأكثر
+
+341
+00:37:54,230 --> 00:37:59,050
+من ذلك ال
+
+342
+00:37:59,050 --> 00:38:12,930
+subgroup U S of ST isomorphic ل U T and ال U Tلمن
+
+343
+00:38:12,930 --> 00:38:22,170
+لل ST isomorphic لمن ل US الشكل اللي عندنا انا
+
+344
+00:38:22,170 --> 00:38:32,050
+isomorphic ل US وفي نتيجة عليها ك رولري بتقول
+
+345
+00:38:32,050 --> 00:38:44,170
+ما يأتي let ال M بدأ تساوي N واحد N اتنينولغاية NK
+
+346
+00:38:44,170 --> 00:38:55,190
+ان واحد ان اتنين لغاية NK where حيث لجلس ال common
+
+347
+00:38:55,190 --> 00:39:08,010
+divisor لل N I و N J بدها تساوي واحد for I لاتساوي
+
+348
+00:39:08,010 --> 00:39:09,810
+جي then
+
+349
+00:39:11,580 --> 00:39:19,920
+الـ UM ايزو مورفك لمن؟ لل U N 1 اكستاناضايك برودك
+
+350
+00:39:19,920 --> 00:39:28,200
+مع U N 2 اكستاناضايك برودك مع مين؟ مع U N K بالشكل
+
+351
+00:39:28,200 --> 00:39:28,860
+اللي عندنا هنا
+
+352
+00:39:42,060 --> 00:39:48,760
+مرة تانية بقول بقول لو عندك رقمين S وT are
+
+353
+00:39:48,760 --> 00:39:57,880
+relatively prime then ال U S T يبقى ال group اللي
+
+354
+00:39:57,880 --> 00:40:03,080
+عندنا ال U S T isomorphic لل externa تاكرودك تبقى
+
+355
+00:40:03,080 --> 00:40:09,120
+حاصل الضرب زي ايش مثلا لو قلتلك U خمستاشربقدر
+
+356
+00:40:09,120 --> 00:40:15,260
+اكتبها U تلاتة في خمسة مظبوط اذا هذه ال U خمساش
+
+357
+00:40:15,260 --> 00:40:19,820
+ايزو مورفك ل U تلاته اكسترنه ضايقة ضعفك مع مين مع
+
+358
+00:40:19,820 --> 00:40:24,740
+U خمسه هتقولي تلاته و خمسه relatively prime بقولك
+
+359
+00:40:24,740 --> 00:40:33,900
+ماشي اش رايك U تلاتين تساوي U خمسه في ستة صح خمسه
+
+360
+00:40:33,900 --> 00:40:39,070
+في ستة او عشرة في تلاتههذه وهذه او اتنين في
+
+361
+00:40:39,070 --> 00:40:43,410
+خمستاشر كلها أرقام are relatively prime اذا ال U
+
+362
+00:40:43,410 --> 00:40:47,930
+تلاتين isomorphic الى U عشرة في تلاتة او
+
+363
+00:40:47,930 --> 00:40:53,830
+isomorphic ل U خمسة في ستة او isomorphic للاتنين
+
+364
+00:40:53,830 --> 00:40:58,390
+في U اتنين external like product مع U خمستاشر و
+
+365
+00:40:58,390 --> 00:41:03,670
+هكذامدام الرقامين او التلاتة اللى عندك تلاتة من
+
+366
+00:41:03,670 --> 00:41:08,790
+اين جبتها دى؟ جبتها من الكرولري الكرولري بتقول اذا
+
+367
+00:41:08,790 --> 00:41:11,490
+ما عندك ليس بضرر رقامين ممكن الرقام اللى عندك
+
+368
+00:41:11,490 --> 00:41:16,090
+تحلله الى حصل ضرب ثلاثة رقام او اربعة ارقام او
+
+369
+00:41:16,090 --> 00:41:21,690
+خمسة او عشرة او كم من الأرقام حلل قد ما بدكيبقى لو
+
+370
+00:41:21,690 --> 00:41:27,990
+عندي الـ M هذا حللناه إلى حاصل ضرب N من الأرقام N1
+
+371
+00:41:27,990 --> 00:41:32,450
+N2 لغاية NK بحيث الـ greatest common divisor بين
+
+372
+00:41:32,450 --> 00:41:37,250
+أي اتنين بدي يكون relatively prime بدي يكون واحد
+
+373
+00:41:37,250 --> 00:41:41,690
+صحيح يعني الاتنين هذول are relatively prime يبقى
+
+374
+00:41:41,690 --> 00:41:46,830
+ال U M isomorphic ل U of الرقم الأول كستانادايكو
+
+375
+00:41:46,830 --> 00:41:51,030
+برودك U مع الرقم التاني كستانادايكو برودكمع الرقم
+
+376
+00:41:51,030 --> 00:41:55,250
+كي و هكذا المرة الجاية ان شاء الله بناخد أمثلة
+
+377
+00:41:55,250 --> 00:41:59,890
+توضحية على كيفية استخدام الكلام اللي عندنا هذا
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d92aebbfa461121ef7666a43233b439ea97fe030
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA.srt
@@ -0,0 +1,1495 @@
+1
+00:00:22,040 --> 00:00:27,360
+بسم الله الرحمن الرحيم طبعا نقول لكم قبل أن نبدأ
+
+2
+00:00:27,360 --> 00:00:34,520
+في موضوعنا الحمد لله على سلامتكم بسبب الحالة 
+
+3
+00:00:34,520 --> 00:00:40,750
+الجوية السيئة التي مر بها قطاع غزة قبل اللي هو خمسة
+
+4
+00:00:40,750 --> 00:00:45,650
+أيام واستمرت لمدة أربعة أيام وكانت سببا في غرق 
+
+5
+00:00:45,650 --> 00:00:52,570
+كثير من البيوت وإصابة بعض الناس بإصابات مؤلمة
+
+6
+00:00:52,570 --> 00:01:00,250
+فالحمد لله على سلامتكم جميعا ونعود الآن لإكمال ما
+
+7
+00:01:00,250 --> 00:01:06,180
+كنا ندرسه قبل أسبوع بعد هذا الغياب الطويل
+
+8
+00:01:06,180 --> 00:01:11,560
+موضوعنا كان chapter 9 موضوع ال normal subgroups و
+
+9
+00:01:11,560 --> 00:01:16,980
+ال factor groups آخر حاجة  اتكلمنا عنها المرة الماضية كان
+
+10
+00:01:17,450 --> 00:01:21,470
+إن لو كانت الـ group الـ G modulo Z of the G الـ
+
+11
+00:01:21,470 --> 00:01:26,470
+Cyclic يبقى then G is abelian وقد برهنا هذه النظرية
+
+12
+00:01:26,470 --> 00:01:32,190
+في المرة السابقة، نستنتج منها ما يأتي: إن لو أخدت 
+
+13
+00:01:32,190 --> 00:01:38,250
+subgroup من ال center تبع ال group فإن ال G على H
+
+14
+00:01:38,250 --> 00:01:42,520
+لو كانت Cyclic يبقى G is abelian والبرهان نفس
+
+15
+00:01:42,520 --> 00:01:47,900
+البرهان تبع النظرية حرفيا بس بصير إنك أنت مقيد في H
+
+16
+00:01:47,900 --> 00:01:52,700
+اللي هي ال subset أو subgroup من ال center تبع ال
+
+17
+00:01:52,700 --> 00:01:56,640
+group الآن ال remark بيقول ال contrapositive of
+
+18
+00:01:56,640 --> 00:02:01,860
+the above theorem is يعني بمعنى آخر ال negation
+
+19
+00:02:01,860 --> 00:02:06,260
+لنص النظرية، احنا بنعرف إن ال proposition لو كانت 
+
+20
+00:02:06,260 --> 00:02:10,200
+من اليمين لشمال، ال negation ببدأ من وين؟ من الشمال
+
+21
+00:02:10,200 --> 00:02:15,560
+لليمين يبقى ال contrapositive لو كانت الـ G هذه
+
+22
+00:02:15,560 --> 00:02:20,760
+non-abelian إذا ال group هذه ما لهاش non-cyclic
+
+23
+00:02:20,760 --> 00:02:24,920
+وهذه أبسط الأشياء اللي تعلمناها في مبادئ الرياضيات
+
+24
+00:02:24,920 --> 00:02:30,180
+نكمل على نفس الموضوع for any group G modulo Z of the G
+
+25
+00:02:30,440 --> 00:02:34,840
+هذا يكون isomorphic للـ Inner Automorphism لـ  
+
+26
+00:02:34,840 --> 00:02:43,380
+G لذلك نذهب و نعرف Function، Define
+
+27
+00:02:43,380 --> 00:02:49,000
+A Mapping، Define
+
+28
+00:02:49,000 --> 00:02:55,320
+A Mapping T مثلا من الـ G و أديله الـ Center تبع
+
+29
+00:02:55,320 --> 00:02:59,600
+الـ G إلى الـ Inner Automorphism لـ G
+
+30
+00:03:02,800 --> 00:03:08,360
+طبعا كل element هنا هو عبارة عن left coset G في
+
+31
+00:03:08,360 --> 00:03:12,960
+ال center بتاع الجي، كل ال elements اللي هنا عبارة
+
+32
+00:03:12,960 --> 00:03:17,640
+عن isomorphism من ال group إلى نفس ال group يبقى
+
+33
+00:03:17,640 --> 00:03:26,480
+بدي أسميه ΦG حيث ال ΦG بنذكر بها as a
+
+34
+00:03:26,480 --> 00:03:32,300
+function of x بده يساوي الـ G x G inverse لكل ال X
+
+35
+00:03:32,300 --> 00:03:38,880
+اللي موجودة في G يبقى أخدنا element من هنا اللي هو
+
+36
+00:03:38,880 --> 00:03:43,240
+left coset وليكن G في ال center بتاع الجي، خلينا T
+
+37
+00:03:43,240 --> 00:03:48,240
+تأثر عليها، افترضنا إن الصورة بتاعتها كانت هي Φ
+
+38
+00:03:48,240 --> 00:03:52,740
+of G، بدنا نثبت إن هذا isomorphism بس قبل ال
+
+39
+00:03:52,740 --> 00:03:57,380
+isomorphism بدنا نؤكد على إن T هذه is well defined
+
+40
+00:03:57,380 --> 00:04:01,700
+يعني تعريفنا هذا تعريف استعريف سليم مائة بالمائة
+
+41
+00:04:01,700 --> 00:04:05,700
+يبقى T is well defined
+
+42
+00:04:07,890 --> 00:04:13,330
+هي معرفة تعريفا سليما، يبقى عشان كده بدأ أخد عنصرين
+
+43
+00:04:13,330 --> 00:04:22,930
+متساويين، نفترض إن الـG في الـZ of the G بده يساوي الـH
+
+44
+00:04:22,930 --> 00:04:32,210
+في الـZ of the G مثلا، و الـG و الـH هدول موجودين في
+
+45
+00:04:32,210 --> 00:04:39,650
+الـG يبقى أخدت عنصرين متساويين من هذين العنصرين بدي
+
+46
+00:04:39,650 --> 00:04:45,970
+أستنتج ما يأتي: لو ضربت الطرفين في G inverse يبقى
+
+47
+00:04:45,970 --> 00:04:53,330
+بدي يصير عندك ال Z of the G بده يساوي ال G inverse H في
+
+48
+00:04:53,330 --> 00:04:59,750
+Z of the G، طبعا ال Z of the G is a subgroup للاتنين هدول
+
+49
+00:04:59,750 --> 00:05:09,160
+متساويين، نستنتج من ذلك إن الـG inverse H موجودة في
+
+50
+00:05:09,160 --> 00:05:17,540
+الـZ of the G، معناه هذا الكلام إن الـG inverse HX بدي
+
+51
+00:05:17,540 --> 00:05:23,800
+يساوي الـX في الـG inverse H لكل الـX اللي موجود في
+
+52
+00:05:23,800 --> 00:05:27,800
+G بلا استثناء، ما دام element موجود في ال center
+
+53
+00:05:27,800 --> 00:05:31,600
+تبع الـ group، إذا الـ commutes مع جميع عناصر الـ
+
+54
+00:05:31,600 --> 00:05:36,460
+group بلا استثناء، يبقى بناء عليه اللي هو main
+
+55
+00:05:36,460 --> 00:05:42,980
+اللي هو الـ G inverse H X بدي أساوي X، G inverse H
+
+56
+00:05:42,980 --> 00:05:49,960
+من هذا الكلام بدي أحاول أوصل إلى إن ΦG هي ΦH
+
+57
+00:05:49,960 --> 00:05:56,080
+بالضبط تماما، وبالتالي بوصل للأصل بتاعها، يبقى هذا
+
+58
+00:05:56,080 --> 00:06:02,840
+يعطينا ما يأتي: بدي أحاول أخل ال H في ناحية ومين؟ و
+
+59
+00:06:02,840 --> 00:06:09,060
+ال G في ناحية، إذا هذه المعادلة لو ضربت في G من جهة
+
+60
+00:06:09,060 --> 00:06:14,840
+الشمال وضربت في H inverse من جهة اليمين يبقى هذا
+
+61
+00:06:14,840 --> 00:06:22,440
+الشيء حتعطينا إن الـ H X H inverse بده يساوي الـ G
+
+62
+00:06:22,440 --> 00:06:28,320
+X G inverse، طلع ليه كويس، هضرب من جهة اليمين في H
+
+63
+00:06:28,320 --> 00:06:33,480
+inverse بتروح هذه وبتيجي هنا H inverse، هاي الـ H
+
+64
+00:06:33,480 --> 00:06:38,780
+inverse تمام؟ الآن بده أضرب من جهة الشمال في G
+
+65
+00:06:39,040 --> 00:06:45,740
+بتروح حياتي بيظل H X H inverse هتدي لك هنا G X G
+
+66
+00:06:45,740 --> 00:06:51,340
+inverse بالشكل اللي عندنا هذا، يعني إيه؟ يعني إن
+
+67
+00:06:51,340 --> 00:06:59,820
+ΦH هي نفسها ΦG يعني تأثير ΦH على أي 
+
+68
+00:06:59,820 --> 00:07:05,240
+element من ال group بيكون تأثير ΦG على نفس ال
+
+69
+00:07:05,240 --> 00:07:12,140
+element هذا، معناه ΦH هي عبارة عن T of H في ال
+
+70
+00:07:12,140 --> 00:07:18,880
+center بتاع ال group G بيكون تأثير T على G مضروبة
+
+71
+00:07:18,880 --> 00:07:25,680
+في ال center بتاع G بالشكل هذا، لذلك T is one to one
+
+72
+00:07:25,870 --> 00:07:33,050
+T is well-defined، بنيجي الآن لـ T is one to one
+
+73
+00:07:33,050 --> 00:07:37,090
+يبقى بدي أعمل العملية العكسية، بدي أخد صورتين
+
+74
+00:07:37,090 --> 00:07:45,370
+متساويتين، Assume T للـ G في ال center بتاع الـ G
+
+75
+00:07:45,370 --> 00:07:52,670
+بده يساوي T في ال H في ال center بتاع الـ G
+
+76
+00:07:52,670 --> 00:07:58,300
+بالشكل اللي عندنا هنا، يبقى هذا يعطينا إيه؟ يبقى
+
+77
+00:07:58,300 --> 00:08:06,100
+يعطينا إن الـ ΦG يساوي الـ ΦH، يبقى لو خلنا كل
+
+78
+00:08:06,100 --> 00:08:13,540
+واحدة تأثر على X يساوي تأثير الـ H على X، هذا الكلام
+
+79
+00:08:13,540 --> 00:08:21,540
+صحيح لكل الـ X اللي موجود في G يبقى بناء عليها جيكس
+
+80
+00:08:21,540 --> 00:08:30,340
+جي انفرس هكس هانفرس لكل ال X اللي موجود في جي بلا
+
+81
+00:08:30,340 --> 00:08:37,160
+استثناء، طيب كويس هذا الكلام بده يعطينا ما يأتي بدي
+
+82
+00:08:37,160 --> 00:08:43,080
+أستنتج الشغلة من هذا الكلام، لو ضربت الطرفين في الـ
+
+83
+00:08:43,080 --> 00:08:49,540
+H من جهتي اليمين يبقى بيصير عندك جي
+
+84
+00:08:49,540 --> 00:08:57,950
+اكس جي انفرس H بده يساوي الـ HX يبقى ضربت من جهة
+
+85
+00:08:57,950 --> 00:09:03,990
+اليمين في مين؟ في H بتجينا هنا H ومن هنا بتروح
+
+86
+00:09:03,990 --> 00:09:09,730
+الـH، هي أجت وهنا راحت، الآن بدي أضرب من جهة الشمال
+
+87
+00:09:09,730 --> 00:09:14,430
+في G inverse، يبقى لو ضربت من جهة الشمال في G
+
+88
+00:09:14,430 --> 00:09:21,750
+inverse بيصير X في G inverse H بدي يساوي G inverse H
+
+89
+00:09:21,750 --> 00:09:29,410
+في X هذا الكلام صحيح لكل الـ X اللي موجودة في G، شو
+
+90
+00:09:29,410 --> 00:09:34,110
+تفسيرك لهذا الكلام إن عندي هذا ال element هو نفس
+
+91
+00:09:34,110 --> 00:09:37,710
+ال element يبقى معناه هذا ال element موجود وين؟
+
+92
+00:09:37,710 --> 00:09:42,860
+في ال center بتاع ال group يبقى هذا الوضع يعطيني إن
+
+93
+00:09:42,860 --> 00:09:48,700
+الـ G inverse H موجودة في الـ Center بتاع الـ Group
+
+94
+00:09:48,700 --> 00:09:54,400
+يعني بمعنى آخر هذا معناه إن الـ G inverse H في الـ
+
+95
+00:09:54,400 --> 00:09:57,960
+Center بتاع الـ Group يساوي الـ Center بتاع الـ
+
+96
+00:09:57,960 --> 00:10:04,390
+Group لو ضربنا الطرفين في G بيصير عندك H في الـ
+
+97
+00:10:04,390 --> 00:10:09,430
+Center بتاع الـ G بيساوي G في الـ Center بتاع الـ G
+
+98
+00:10:09,430 --> 00:10:15,970
+بالشكل هذا وبالتالي أخدنا صورتين متساويتين أثبتنا
+
+99
+00:10:15,970 --> 00:10:21,350
+إن أصلهم متساوي يبقى بناء عليه G أو T is one to
+
+100
+00:10:21,350 --> 00:10:28,780
+one، بنيجي نثبت هنا T is onto يبقى بدي أروح أخد
+
+101
+00:10:28,780 --> 00:10:34,000
+element اللي هو ΦG موجود في ال inner
+
+102
+00:10:34,000 --> 00:10:43,360
+automorphism إلى جي then ال Φ of جي هذا ال Φ of G
+
+103
+00:10:43,360 --> 00:10:51,800
+هو عبارة بالضبط عن صورة T للـ G لـ Z of the G بالشكل 
+
+104
+00:10:51,800 --> 00:10:58,060
+اللي عندنا، أنا T G Z of the G يبقى بناء عليه Φ is onto
+
+105
+00:10:58,060 --> 00:11:06,350
+T is onto، ضايل علينا T is an isomorphism يبقى بروح
+
+106
+00:11:06,350 --> 00:11:13,930
+أخد T لجي في ال center بتاع الجي مضروب في ال H في
+
+107
+00:11:13,930 --> 00:11:19,690
+ال center بتاع الجي بالشكل اللي عندنا، هذا الكلام
+
+108
+00:11:19,690 --> 00:11:25,150
+يساوي T of هذه left coset وهذه left coset تانية
+
+109
+00:11:25,150 --> 00:11:33,550
+حسب ما أخدنا التعريف، يبقى هذا بيصير GH ل Z of the G
+
+110
+00:11:33,550 --> 00:11:41,470
+left coset جديدة حسب تعريف الـ T، هذه بيصير Φ GH
+
+111
+00:11:42,370 --> 00:11:49,850
+الشكل اللي عندنا هنا، طيب الآن لو جيت خط في جي إتش
+
+112
+00:11:49,850 --> 00:11:56,530
+تأثيرها على element X يبقى هذا الكلام بدي يساوي GH
+
+113
+00:11:56,530 --> 00:12:03,830
+X GH inverse لأنه ماخد وين ال ΦG هادي؟ وين؟ في ال
+
+114
+00:12:03,830 --> 00:12:12,860
+inner automorphism طيب هذه لو رجعت لتعريف ΦG X H
+
+115
+00:12:12,860 --> 00:12:18,600
+انفرس جي انفرس، هذا بندخل انفرس على جوا وبالتالي
+
+116
+00:12:18,600 --> 00:12:22,660
+بنجلب إيه؟ ووضعهم، لأن ماعنديش جي إز قابيل يعني
+
+117
+00:12:22,660 --> 00:12:31,630
+ماقلناش قابيل طيب كويس هذه هتعني ΦG لل HX H
+
+118
+00:12:31,630 --> 00:12:36,830
+inverse يعني بدي افترض إن هذا كله element واحد
+
+119
+00:12:36,830 --> 00:12:41,810
+وبالتالي بدي يصير جي لل element هذا لل G inverse
+
+120
+00:12:41,810 --> 00:12:48,280
+تعريف ΦG هذا اللي جوا تعريف main اللي هو في اتش
+
+121
+00:12:48,280 --> 00:12:56,520
+يبقى هذا ΦG لمين؟ لفي اتش كل هذا as a function
+
+122
+00:12:56,520 --> 00:13:04,710
+of x، طب ال ΦG هذه مش هي عبارة عن اللي تساوي T في
+
+123
+00:13:04,710 --> 00:13:11,610
+G في الـ Center بتاع الـ G والتانية ΦH هي عبارة
+
+124
+00:13:11,610 --> 00:13:17,510
+عن T للـ H في الـ Center بتاع مين؟ بتاع الـ G
+
+125
+00:13:17,510 --> 00:13:22,370
+وبالتالي صارت isomorphism وبالتالي برهنا من؟
+
+126
+00:13:22,370 --> 00:13:25,630
+برهننا هذه النظرية
+
+127
+00:13:33,190 --> 00:13:37,610
+في نظرية هذا اسمها نظرية كايلي برضه لل abelian
+
+128
+00:13:37,610 --> 00:13:44,190
+groups يبقى هنا theorem لكايلي
+
+129
+00:13:44,190 --> 00:13:51,950
+theorem كايلي
+
+130
+00:13:51,950 --> 00:13:58,810
+theorem for abelian groups
+
+131
+00:14:01,880 --> 00:14:09,780
+بتقول ما يتلت الـ G بيه
+
+132
+00:14:09,780 --> 00:14:21,560
+finite بيه finite abelian group finite abelian
+
+133
+00:14:21,560 --> 00:14:36,120
+groupو .. دع ال P بيه قطعة بيه قطعة بيه
+
+134
+00:14:36,120 --> 00:14:36,140
+قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه
+
+135
+00:14:36,140 --> 00:14:40,580
+قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه
+
+136
+00:14:40,580 --> 00:14:42,020
+قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه
+
+137
+00:14:42,020 --> 00:14:42,060
+قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه قطعة بيه
+
+138
+00:14:42,060 --> 00:14:47,180
+قطعة بيه قطعة بيه
+
+139
+00:14:47,180 --> 00:14:50,880
+قطعة بيه قطعة بي
+
+140
+00:15:09,720 --> 00:15:26,080
+الجي لبروفة بتقدر ترجعله Page صفحات الـ 187 و188
+
+141
+00:15:53,820 --> 00:16:01,320
+فينا تعريف جديد وهذا التعريف مهم شوية لما بعده
+
+142
+00:16:01,320 --> 00:16:12,480
+definition suppose that افترض
+
+143
+00:16:12,480 --> 00:16:25,270
+ان ال h and ال k are subgroups of G are subgroups
+
+144
+00:16:25,270 --> 00:16:39,130
+of G define the set define the set HK
+
+145
+00:16:39,130 --> 00:16:47,150
+حاصل الضرب HK by HK
+
+146
+00:16:48,210 --> 00:16:56,390
+هو الـ set of all elements H في K such that الـ H
+
+147
+00:16:56,390 --> 00:17:07,610
+موجودة في H و K موجودة في K التعريف
+
+148
+00:17:07,610 --> 00:17:11,350
+اللي بعده بيعتمد عليه definition
+
+149
+00:17:14,660 --> 00:17:23,020
+we say that ان
+
+150
+00:17:23,020 --> 00:17:31,900
+الـ G ليه بدها تساوي ال H مضروبة في K الشكل اللي
+
+151
+00:17:31,900 --> 00:17:39,120
+عندنا هذا is the internal direct product is the
+
+152
+00:17:39,120 --> 00:17:50,430
+internal direct product of
+
+153
+00:17:50,430 --> 00:18:03,650
+the subgroups
+
+154
+00:18:03,650 --> 00:18:14,590
+ال H and الـ K F إذا تحقق ثلاثة شروط الشرط الأول ال
+
+155
+00:18:14,590 --> 00:18:23,850
+H and ال K are normal subgroups are normal
+
+156
+00:18:23,850 --> 00:18:34,950
+subgroups normal subgroups of G الشرط
+
+157
+00:18:34,950 --> 00:18:35,650
+الثاني
+
+158
+00:18:38,640 --> 00:18:48,280
+ان الـ G بدها تساوي H في K الشرط الثالث والاخير ان
+
+159
+00:18:48,280 --> 00:18:55,880
+الـ H intersection K بده يساوي ال identity element
+
+160
+00:18:55,880 --> 00:19:03,820
+examples let
+
+161
+00:19:05,880 --> 00:19:15,240
+الـ G بدها تساوي الـ S3 and الـ H هي الـ subgroup
+
+162
+00:19:15,240 --> 00:19:25,460
+generated by واحد اتنين تلاتة and K هي ال subgroup
+
+163
+00:19:25,460 --> 00:19:34,640
+generated by واحد اتنين السؤال
+
+164
+00:19:34,640 --> 00:19:47,640
+هو is الـ S3 بدها تساوي H مضروبة في K أم لا هذا
+
+165
+00:19:47,640 --> 00:19:48,260
+السؤال
+
+166
+00:20:18,320 --> 00:20:21,800
+طبعا اترضنا على تعريف الـ External direct product
+
+167
+00:20:21,800 --> 00:20:25,240
+سابقا في ال section اللي قبله وفي ال chapter اللي
+
+168
+00:20:25,240 --> 00:20:30,000
+قبله واخدنا عليه أمثلة واسئلة ونظريات لما نجي
+
+169
+00:20:30,000 --> 00:20:33,620
+لحاجة اسمها ال internal direct product اللي هو حاصل
+
+170
+00:20:33,620 --> 00:20:38,950
+الضرب الداخلي ده كان حاصل الضرب الخارجي بقول افترض
+
+171
+00:20:38,950 --> 00:20:45,450
+ان الـH وK subgroups من G عرفنا ستة HK حاصلة ضرب
+
+172
+00:20:45,450 --> 00:20:51,710
+بأنها كل العناصر اللي على الشكل H في K بحيث H
+
+173
+00:20:51,710 --> 00:20:59,780
+موجودة في H وK موجودة في K بنفس التارتيتتعريف آخر
+
+174
+00:20:59,780 --> 00:21:03,880
+بيناعرف حاجة اسمه ال internal direct product حصل
+
+175
+00:21:03,880 --> 00:21:08,220
+الضرب الداخلي فبجي بقول جي هي ال internal direct
+
+176
+00:21:08,220 --> 00:21:13,640
+product لل H وK وسنعطيها الرمز H علامة الضرب
+
+177
+00:21:13,640 --> 00:21:19,000
+العادية في K طبعا ال external بقول زائد ودائرة هذه
+
+178
+00:21:19,000 --> 00:21:24,040
+تدل على ال external وكل عنصر على الشكل two
+
+179
+00:21:24,040 --> 00:21:28,260
+components three components in components بس هذا
+
+180
+00:21:28,260 --> 00:21:33,780
+لا بيختلف هذا هنا جيه كل عنصر هنا على الشكل main
+
+181
+00:21:33,780 --> 00:21:38,870
+على الشكل يعني اتنين مضروبات في بعض ضرب مباشرة يبقى
+
+182
+00:21:38,870 --> 00:21:43,350
+هذا بسميه الـ Internal Direct Product لـ Subgroups H و K
+
+183
+00:21:43,350 --> 00:21:49,110
+إذا تحققت عندي ثلاثة شروط الشرط الأول لازم يكون كل
+
+184
+00:21:49,110 --> 00:21:53,650
+من H و K Normal Subgroups الشرط الثاني عملية
+
+185
+00:21:53,650 --> 00:21:57,970
+الضرب بدها تجيب ليه كل عناصر الجروب بيه لا إستثناء
+
+186
+00:21:57,970 --> 00:22:03,090
+لا زيادة ولا نقصان هاي الشرط الثاني الشرط الثالث
+
+187
+00:22:03,090 --> 00:22:06,370
+ال intersection بين الـH و الـK بده يكون باسمين
+
+188
+00:22:08,220 --> 00:22:13,220
+identity موجود في اي subgroup من ال group الأصلي
+
+189
+00:22:22,370 --> 00:22:28,010
+ستة عناصر يعطيني ال subgroup و كمان subgroup تمام
+
+190
+00:22:28,010 --> 00:22:33,950
+و بيقوللي هل ال S3 هي ال internal direct product تبع ال H
+
+191
+00:22:33,950 --> 00:22:37,710
+و K ولا لأ بنقوله والله ما احنا عارفين تعالى نشوف
+
+192
+00:22:37,790 --> 00:22:43,350
+يبقى هنا باجي بقوله solution مشان نعرف بأنه نعرف
+
+193
+00:22:43,350 --> 00:22:49,670
+مين هي H في الأول طبعا ال identity element وهذا
+
+194
+00:22:49,670 --> 00:22:54,930
+اللي هو واحد اتنين تلاتة ولو ضربنا في نفسه تربيع
+
+195
+00:22:54,930 --> 00:23:03,240
+بيعطينا واحد تلاتة اتنين و انتهينا منها and ال K هي
+
+196
+00:23:03,240 --> 00:23:08,300
+عبارة عن ال identity element والواحد دي اتنين ولو
+
+197
+00:23:08,300 --> 00:23:13,000
+جيبناه تربيع بيعطينا ال identity element يبقى
+
+198
+00:23:13,000 --> 00:23:18,180
+هذا هذا اللي موجود عندنا مشان أدربك على هذا الشغل
+
+199
+00:23:18,180 --> 00:23:23,640
+بديش أبدأ بأول شرط بدي أبدأ بالشرط الثاني وبعد هيك
+
+200
+00:23:23,640 --> 00:23:31,910
+بروح لمين لباقي الشروط إذا لو جيت لل H في K يبقى
+
+201
+00:23:31,910 --> 00:23:35,750
+بدي أبدأ أضرب العناصر اللي عندنا في هذه العناصر
+
+202
+00:23:35,750 --> 00:23:39,710
+يبقى ب ذات ساوية ال identity في ال identity
+
+203
+00:23:39,710 --> 00:23:44,570
+بتعطيني ال identity element ال identity في واحد
+
+204
+00:23:44,570 --> 00:23:49,230
+اتنين بتعطيني واحد اتنين بعدين بدي أضرب هذا في
+
+205
+00:23:49,230 --> 00:23:56,390
+العنصرين 123 في ال identity تعطيني 123 و هذه
+
+206
+00:23:56,390 --> 00:24:01,170
+بتعطيني .. بدي أضرب اتنين هذول في بعض أشوف شو
+
+207
+00:24:01,170 --> 00:24:07,390
+بيعطيني الواحد صورته اتنين و اتنين صورته قداشر
+
+208
+00:24:07,390 --> 00:24:14,830
+واحد يبقى الواحد احنا بدنا نبدأ من هنا هذا واحد
+
+209
+00:24:15,250 --> 00:24:21,610
+تمام؟ يبقى الواحد صورته اتنين تمام؟ اه اتنين صورته
+
+210
+00:24:21,610 --> 00:24:27,890
+تلاته تمام؟ طب الآن التلاته صورتها تلاته هنا
+
+211
+00:24:27,890 --> 00:24:33,170
+التلاته صورتها قداش صورتها واحد و هكذا مرة تانية
+
+212
+00:24:33,170 --> 00:24:38,050
+بقول الواحد صورته اتنين اتنين صورته تلاته هيحطينا
+
+213
+00:24:38,050 --> 00:24:42,190
+التلاته التلاته صورتها تلاته التلاته صورتها واحد
+
+214
+00:24:42,190 --> 00:24:49,880
+هيخلصنا من هنا تمام؟ العنصر اللي بعده اللي هو واحد
+
+215
+00:24:49,880 --> 00:24:54,900
+ثلاثة اتنين ضربنا في ال identity بنفسه العنصر اللي
+
+216
+00:24:54,900 --> 00:25:00,620
+بعده بالداجي هذا الواحد الواحد صورته اتنين و اتنين
+
+217
+00:25:00,620 --> 00:25:06,000
+صورته واحد يبقى جفل هذا راح مع السلامة يبقى بدنا
+
+218
+00:25:06,000 --> 00:25:10,120
+نيجي للعنصر اللي بعده اللي هو اتنين اتنين صورته
+
+219
+00:25:10,120 --> 00:25:16,040
+واحد الواحد صورته تلاتة التلاتة صورتها تلاتة
+
+220
+00:25:16,040 --> 00:25:22,400
+التلاتة صورتها اتنين يبقى جفلة خلصنا اكم عنصر هدول
+
+221
+00:25:22,400 --> 00:25:29,440
+ستة هم عناصر S3 بالضبط يبقى هذا هم S3 بالضبط يبقى
+
+222
+00:25:29,440 --> 00:25:34,940
+ال condition هذا معله صحيح نجي لل H intersection K
+
+223
+00:25:34,940 --> 00:25:39,180
+هذا هو ال condition الأول أو ال condition بده
+
+224
+00:25:39,180 --> 00:25:43,420
+أسميه الأول ال condition الثاني ال H intersection
+
+225
+00:25:43,420 --> 00:25:48,620
+K واضح اللي هو مافيش غير ال identity element
+
+226
+00:25:48,620 --> 00:25:53,360
+ما بين الأتنين هيه وهيه ومافيش غيره الآن بدأجي هل
+
+227
+00:25:53,360 --> 00:26:00,100
+ال H normal ام لا؟ تعالى نشوف ال H فيها كم عنصر؟
+
+228
+00:26:00,100 --> 00:26:05,280
+تلاتة و ال S3 فيها قداشر؟ يبقى ال index سبعة
+
+229
+00:26:05,280 --> 00:26:11,680
+قداشر؟ اتنين او اي subgroup او اي group ال index
+
+230
+00:26:11,680 --> 00:26:15,260
+لها اي subgroup ال index لها يسوى اتنين عبارة عن
+
+231
+00:26:15,260 --> 00:26:21,200
+normal واخدناه كمثال الان بدي اجيب .. بدي اقول بدي
+
+232
+00:26:21,200 --> 00:26:25,720
+اجيب ال index ال condition الثالث الان ال index
+
+233
+00:26:25,720 --> 00:26:34,200
+تبع اللي هو ال H في S3 ال H في S3
+
+234
+00:26:34,200 --> 00:26:42,320
+اللي هو يساوي ال order بتبع ال S3 مقسوما على ال
+
+235
+00:26:42,320 --> 00:26:48,900
+order بتبع ال H هذا ستة و هذا تلاتة يساوي اتنين هذا
+
+236
+00:26:48,900 --> 00:26:57,240
+سيعطينا ان الـ H is a normal subgroup من SC3 نعود
+
+237
+00:26:57,240 --> 00:27:04,760
+الان لـ K هل هي normal subgroup ولا لا الله أعلم
+
+238
+00:27:05,130 --> 00:27:10,690
+تعالى نشوف هل هذا الكلام لو جيت أخد element من S
+
+239
+00:27:10,690 --> 00:27:19,110
+من من H3 وبدى أشوف احنا بدنا نشوفها normal ولا لأ
+
+240
+00:27:19,110 --> 00:27:25,750
+بدى أروح أخد element من S3 وضربه في هذا ال element
+
+241
+00:27:25,750 --> 00:27:29,750
+ومعكسه أشوف موجود في K ولا لأ إذا كان موجود كان
+
+242
+00:27:29,750 --> 00:27:35,660
+بها مش موجود يبقى هذه ماهياش normal الان عندك واحد
+
+243
+00:27:35,660 --> 00:27:42,900
+و تلاتة موجود في ال S3 واحد و اتنين موجود وين؟
+
+244
+00:27:42,900 --> 00:27:48,660
+موجود في ال H بدي اشوف ال normality بدي اخد واحد
+
+245
+00:27:48,660 --> 00:27:54,860
+تلاتة في واحد اتنين واحد تلاتة inverse مش هيك شرط
+
+246
+00:27:54,860 --> 00:27:55,780
+ال normality؟
+
+247
+00:27:58,540 --> 00:28:02,400
+احنا في الـK هذي بدل الـH فيك خلصنا من الـH هذي في
+
+248
+00:28:02,400 --> 00:28:07,000
+الـK صحيح مضبوط يبقى بدنا ناخد الأول في التاني في
+
+249
+00:28:07,000 --> 00:28:13,500
+معكوس الأول هذا الكلام بدي يساوي واحد تلاتة واحد
+
+250
+00:28:13,500 --> 00:28:18,400
+اتنين اظن واحد تلاتة زي ما هو لإن ال transposition
+
+251
+00:28:18,400 --> 00:28:22,260
+ال inverse له هو نفسه أو ال cycle طولها اثنين ال
+
+252
+00:28:22,260 --> 00:28:26,680
+transposition له هو نفسه بدي اضرب دغري مش كل اثنين
+
+253
+00:28:26,680 --> 00:28:30,340
+بدي اضرب الثلاثة مرة واحدة يبقى بدي أبدأ من
+
+254
+00:28:30,340 --> 00:28:35,960
+بالواحد الواحد صورته ثلاثة والثلاثة صورتها ثلاثة
+
+255
+00:28:35,960 --> 00:28:40,240
+والثلاثة صورتها واحد يبقى مع السلامة ال identity
+
+256
+00:28:40,830 --> 00:28:46,950
+هو الاثنين الاثنين صورته اثنين اثنين صورته واحد
+
+257
+00:28:46,950 --> 00:28:52,830
+الواحد صورته ثلاثة نجي للثلاثة صورتها واحد الواحد
+
+258
+00:28:52,830 --> 00:28:58,550
+صورته اثنين اثنين صورته اثنين هيوا جفلة يبقى هذا
+
+259
+00:28:58,550 --> 00:29:05,360
+بده يسوي قداش اثنين ثلاثة هل هذا موجود في K طبعاً
+
+260
+00:29:05,360 --> 00:29:10,300
+مش موجود في K يبقى لا يمكن تبقى هذه normal في
+
+261
+00:29:10,300 --> 00:29:17,260
+subgroup من G يبقى هنا so ال K هذه is not normal
+
+262
+00:29:17,260 --> 00:29:26,280
+subgroup من S3 هذا معناه أن ال G أو ال S3 لا يمكن
+
+263
+00:29:26,280 --> 00:29:32,940
+أن تساوي الـH اللي هو مضروبة في K يعني في هذه
+
+264
+00:29:32,940 --> 00:29:38,600
+الحالة الـG is not the internal product تبع الـH
+
+265
+00:29:38,600 --> 00:29:49,460
+والـK خذ لك مثال آخر example 2 خذ للـG تساوي Z12
+
+266
+00:29:51,300 --> 00:29:58,080
+واخذ الـ H هي الـ subgroup generated by ثلاثة و K
+
+267
+00:29:58,080 --> 00:30:03,760
+هي ال subgroup generated by أربعة بالشكل اللي
+
+268
+00:30:03,760 --> 00:30:15,240
+عندنا هذا تمام والسؤال هو Is الـ Z8 Z12 تساوي الـ
+
+269
+00:30:15,240 --> 00:30:21,360
+Internal Direct Product ما بين الـ H والـ K أم الـ
+
+270
+00:30:21,360 --> 00:30:23,280
+Solution
+
+271
+00:30:27,020 --> 00:30:33,700
+بسأل السؤال التالي هل عندك H اللي هي تساوي العناصر
+
+272
+00:30:33,700 --> 00:30:44,660
+تبعها 0,3,6,9 والـ K عناصرها 0,4,8 السؤال هو هل
+
+273
+00:30:44,660 --> 00:30:49,120
+الـ H و K normal subgroup من Z12
+
+274
+00:31:04,170 --> 00:31:09,730
+أول مثال أخذنا أن any subgroup of an abelian group
+
+275
+00:31:09,730 --> 00:31:10,770
+is normal
+
+276
+00:31:24,780 --> 00:31:33,720
+subgroups subgroups of z12 ايه السبب؟ because أن
+
+277
+00:31:33,720 --> 00:31:37,620
+z12 is abelian
+
+278
+00:31:39,890 --> 00:31:44,630
+طيب إذا ال condition الأول هذا معناه تحقق بدنا نيجي
+
+279
+00:31:44,630 --> 00:31:50,970
+لل condition الثاني بدنا نيجي نضرب ال H في K يبقى
+
+280
+00:31:50,970 --> 00:31:59,270
+هذا ال H في K بده يساوي المقصود ب H في K هو H زائد
+
+281
+00:31:59,270 --> 00:32:05,080
+K لأن العملية فيما بينهم عملية جمع يبقى لما
+
+282
+00:32:05,080 --> 00:32:12,580
+نقول هذا H في K بالضبط هي H زائد K بالشكل اللي
+
+283
+00:32:12,580 --> 00:32:17,220
+عندنا هنا يبقى بدي أبدأ أجمع Zero مع Zero ب Zero
+
+284
+00:32:17,220 --> 00:32:22,120
+Zero مع أربعة بأربعة Zero مع ثمانية بثمانية خلصت
+
+285
+00:32:22,120 --> 00:32:26,800
+العنصر هذا مع جميع العناصر بدي أجي للثلاثة ثلاثة مع
+
+286
+00:32:26,800 --> 00:32:33,420
+Zero بثلاثة ثلاثة ثلاثة وأربعة سبعة ثلاثة وثمانية أحد عشر
+
+287
+00:32:33,420 --> 00:32:38,960
+خلصنا منها بدنا نيجي للستة ستة وZero عبارة عن Zero
+
+288
+00:32:38,960 --> 00:32:44,720
+ستة وأربعة أربعة عشر ستة وثمانية ثمانية عشر في Z12
+
+289
+00:32:44,720 --> 00:32:50,750
+ب اثنين خلصنا من الستة بدنا نروح للتسعة تسعة
+
+290
+00:32:50,750 --> 00:32:56,470
+زائد Zero ب Zero تسعة وأربعة ثلاثة عشر تعني واحد تسعة و
+
+291
+00:32:56,470 --> 00:33:02,890
+ثمانية سبعة عشر تعني ستة ب هذا .. تعني خمسة وليس
+
+292
+00:33:02,890 --> 00:33:08,630
+ستة تعني خمسة ب هذا الشكل الطلق هدول كلهم بتلاقيهم
+
+293
+00:33:08,630 --> 00:33:16,190
+هم عناصر من؟ Z12 تمام هل عندك ال Zero موجود
+
+294
+00:33:16,190 --> 00:33:24,970
+واحد اثنين ثلاثة أربعة خمسة ستة سبعة ثمانية تسعة
+
+295
+00:33:24,970 --> 00:33:30,550
+عشرة أحد عشر كلهم موجودة هل العناصر كلها يبقى تحقق
+
+296
+00:33:30,550 --> 00:33:34,420
+من عند ال condition الثاني بتروح لل condition
+
+297
+00:33:34,420 --> 00:33:39,940
+الثالث يبقى ال condition الثالث H intersection K
+
+298
+00:33:39,940 --> 00:33:45,220
+واضح ما عنديش إلا ال Zero يبقى بأجي بقول له so
+
+299
+00:33:45,220 --> 00:33:54,080
+Z12 بدها تساوي ال H زائد Zero زائد ال K بدل
+
+300
+00:33:54,080 --> 00:33:58,540
+ما هي H في K لأن ال operation اللي عندنا عبارة عن
+
+301
+00:33:58,540 --> 00:34:02,740
+عملية جمع عبارة عن عملية الجمع
+
+302
+00:34:09,180 --> 00:34:14,040
+طب يا شو رأيك ال internal direct product دي لو جيه
+
+303
+00:34:14,040 --> 00:34:18,720
+ساوت ال internal direct product فهي isomorphic لل
+
+304
+00:34:18,720 --> 00:34:21,520
+external direct product
+
+305
+00:34:24,820 --> 00:34:30,600
+هذا الكلام لو خليناه لمجموعة من الجروس مش اثنتين
+
+306
+00:34:30,600 --> 00:34:35,140
+ممكن يكونوا اثنتين، ثلاثة، أربعة، خمسة جد ما يكون
+
+307
+00:34:35,140 --> 00:34:38,360
+يبقى بدنا نعطي ال definition ومن بعدين نكتب
+
+308
+00:34:38,360 --> 00:34:44,120
+النظرية ال definition بيقول ما يأتي ال let each
+
+309
+00:34:44,120 --> 00:34:51,540
+واحد H2 ولغاية HN يعني يا شباب بدنا نعمم حاصل
+
+310
+00:34:51,540 --> 00:34:57,360
+الضرب H في K بدل ما هو اثنتين بدنا نخليه ل N من ال
+
+311
+00:34:57,360 --> 00:35:04,940
+subgroups ب finite collection
+
+312
+00:35:04,940 --> 00:35:11,880
+finite collection of normal
+
+313
+00:35:16,320 --> 00:35:29,340
+subgroups of G we say that we say that بروح نقول
+
+314
+00:35:29,340 --> 00:35:40,320
+ال G هي ال internal byproduct H1 في H2 في في HN
+
+315
+00:35:41,690 --> 00:35:51,590
+اللي هو الـ Internal Direct Product تبع الـ H's
+
+316
+00:35:51,590 --> 00:36:02,870
+هدول and the Internal Direct Product of H1 وH2
+
+317
+00:36:02,870 --> 00:36:06,190
+ولغاية HNF
+
+318
+00:36:10,090 --> 00:36:17,230
+إذا تحققت الشروط التالية نمرا واحد الـ G يساوي H1
+
+319
+00:36:17,230 --> 00:36:28,650
+في H2 في HN بالشكل اللي عندنا هذا واللي هي تساوي
+
+320
+00:36:28,650 --> 00:36:37,770
+the set of all elements h1, h2, h3, hn such that
+
+321
+00:36:37,770 --> 00:36:45,410
+hi موجودة في الـ hi بالشكل اللي عندنا هذا ال
+
+322
+00:36:45,410 --> 00:36:54,070
+condition الثاني condition الثاني أن ال h1, h2 و
+
+323
+00:36:54,070 --> 00:37:03,170
+لغاية ال hiIntersection hi plus one بده يساوي Zero
+
+324
+00:37:03,170 --> 00:37:12,790
+بده يساوي ال identity element for i تساوي واحد
+
+325
+00:37:12,790 --> 00:37:21,190
+واثنين ولغاية ال n ناقص واحد نجي لل theorem
+
+326
+00:37:32,660 --> 00:37:45,840
+from if a group g if a group g is the internal
+
+327
+00:37:45,840 --> 00:37:54,300
+direct product of
+
+328
+00:37:54,300 --> 00:37:59,400
+a finite number
+
+329
+00:38:01,140 --> 00:38:09,180
+of a finite number of subgroups
+
+330
+00:38:09,180 --> 00:38:20,680
+subgroups اللي هو H واحد وH اثنين ولغاية HN then
+
+331
+00:38:20,680 --> 00:38:33,310
+G اللي بيساوي H واحد في H اثنين في HN ايزو مورفك لل H
+
+332
+00:38:33,310 --> 00:38:39,390
+واحد Extended product مع H اثنين Extended product
+
+333
+00:38:39,390 --> 00:38:41,970
+مع HN
+
+334
+00:39:08,260 --> 00:39:11,440
+يبقى هنا بقول جي عبارة عن ال internal direct
+
+335
+00:39:11,440 --> 00:39:16,040
+product لمين اللي finite number subgroups H1 وH2
+
+336
+00:39:16,040 --> 00:39:22,450
+لغاية HN then ال جي تعني أن ال internal direct
+
+337
+00:39:22,450 --> 00:39:27,390
+product ايزو مورفك لمين لل external direct product
+
+338
+00:39:27,390 --> 00:39:35,790
+بمعنى آخر لو حبيت تبرهن بدك تعملي function ال
+
+339
+00:39:35,790 --> 00:39:43,930
+function هذه بدك تقولي مثلا في of او بدك تعرف في
+
+340
+00:39:46,160 --> 00:39:55,820
+بتعرف فاي define فاي من الـ H واحد external direct
+
+341
+00:39:55,820 --> 00:39:59,660
+product لـ H اثنين .. internal direct product
+
+342
+00:39:59,660 --> 00:40:06,220
+internal direct product للـ H N إلى الـ H واحد
+
+343
+00:40:06,220 --> 00:40:10,560
+external direct product مع H اثنين external direct
+
+344
+00:40:10,560 --> 00:40:19,460
+product مع H N بفاي اوف بتأخذ element
+
+345
+00:40:19,460 --> 00:40:27,980
+هنا يبقى ال element هذا هو H1 مضروب في H2 مضروب في
+
+346
+00:40:27,980 --> 00:40:36,760
+H3 ولغاية HN بنوديه على الجروب الثاني اللي هو H1
+
+347
+00:40:36,760 --> 00:40:45,180
+فاصلة H2 فاصلة فاصلة HN بالشكل اللي عندنا هذا يبقى
+
+348
+00:40:45,180 --> 00:40:56,840
+H N تمام هذه مكونة من N من المركبات هذه ل N من
+
+349
+00:40:56,840 --> 00:41:00,980
+ال elements المضروبة في بعضها يبقى هنا هذول
+
+350
+00:41:00,980 --> 00:41:05,320
+المضروبات في بعض يبقى كل هذا يعتبر element واحد
+
+351
+00:41:05,320 --> 00:41:11,220
+فصلنا إلى N من المركبات يبقى وتثبت لهذه one to
+
+352
+00:41:11,220 --> 00:41:15,040
+one وانت وتخدم خاصية ال isomorphism مثبوطة عندك
+
+353
+00:41:15,040 --> 00:41:18,860
+في الكتاب تريد تطلع عليها من الكتاب وهذا يعطيك ال
+
+354
+00:41:18,860 --> 00:41:22,520
+function هذا إذا ما عرفتش تسويها عرفت اعمالها
+
+355
+00:41:22,520 --> 00:41:28,580
+بيكون كفى الله المؤمنين القتال في عندك نظرية بتقول
+
+356
+00:41:28,580 --> 00:41:34,800
+ماشي سيارة بتقول
+
+357
+00:41:34,800 --> 00:41:38,140
+every group every
+
+358
+00:41:39,600 --> 00:41:49,740
+مجموعة من رتبة P تربيع P أكبر من رتبة P أكبر من
+
+359
+00:41:49,740 --> 00:41:54,040
+رتبة P أكبر من رتبة P أكبر من رتبة P أكبر من
+
+360
+00:41:54,040 --> 00:41:55,380
+رتبة P أكبر من رتبة P أكبر من رتبة P أكبر من
+
+361
+00:41:55,380 --> 00:41:55,620
+رتبة P أكبر من رتبة P أكبر من رتبة P أكبر من
+
+362
+00:41:55,620 --> 00:41:55,740
+رتبة P أكبر من رتبة P أكبر من رتبة P أكبر من
+
+363
+00:41:55,740 --> 00:42:01,520
+رتبة P أكبر من رتبة P أكبر من رتبة P أكبر من
+
+364
+00:42:01,520 --> 00:42:13,410
+رتبة P أكبر من رتبة Z بي تربيع أو ل Z بي external
+
+365
+00:42:13,410 --> 00:42:25,590
+product مع مين مع Z بي وفي كورلري عليها كورلري
+
+366
+00:42:25,590 --> 00:42:39,010
+بيقول لو كانت ال G is a group of order P تربيع
+
+367
+00:42:39,010 --> 00:42:42,050
+where
+
+368
+00:42:42,050 --> 00:42:52,810
+ال P is a prime ال P is a prime then ال G is
+
+369
+00:42:52,810 --> 00:42:58,290
+abelian ال G is abelian
+
+370
+00:43:02,970 --> 00:43:08,190
+على أي حال أنتم لاحظين أن احنا ما برهناش أكثر من
+
+371
+00:43:08,190 --> 00:43:13,110
+نظرية نظرية اللي سوء لحوالي الجوية والارضية خلص
+
+372
+00:43:13,110 --> 00:43:17,250
+الجزء النظري يوم الأربعاء إن شاء الله بنعمل مناقشة
+
+373
+00:43:17,250 --> 00:43:21,930
+لهذا الشابتر حتى الأسبوع اللي بعده ندخل في الشابتر
+
+374
+00:43:21,930 --> 00:43:23,250
+الأخير 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7910945189865b40c5115e0eb69988b53ee25eff
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ADO1lqCgDBA_postprocess.srt
@@ -0,0 +1,1496 @@
+1
+00:00:22,040 --> 00:00:27,360
+بسم الله الرحمن الرحيم طبعا نقول لكم قبل أن نبدأ
+
+2
+00:00:27,360 --> 00:00:34,520
+في موضوعنا الحمد لله على سلامتكم بسبب الحالة
+
+3
+00:00:34,520 --> 00:00:40,750
+الجوية السيئة التي مر بها قطاع غزةقبل اللي هو خمسة
+
+4
+00:00:40,750 --> 00:00:45,650
+أيام واستمرت لمدة أربعة أيام وكانت سببا في غرق
+
+5
+00:00:45,650 --> 00:00:52,570
+كثير من البيوت وإصابة بعض الناس بإصابات موتة فاوتة
+
+6
+00:00:52,570 --> 00:01:00,250
+فالحمد لله على سلامتكم جميعا ونعود الآن لإكمال ما
+
+7
+00:01:00,250 --> 00:01:06,180
+كناانا ندرسه قبل واسبوع بعد هذا الغياب الطويل
+
+8
+00:01:06,180 --> 00:01:11,560
+موضوعنا كان chapter 9 موضوع ال normal subgroups و
+
+9
+00:01:11,560 --> 00:01:16,980
+ال factory groups اخر حاجة اعتنف المرة الماضية كان
+
+10
+00:01:17,450 --> 00:01:21,470
+إن لو كانت الـ group الـ G modulo Z of G الـ
+
+11
+00:01:21,470 --> 00:01:26,470
+Cyclic يبقى then G is abelian وقد برهن هذه النظرية
+
+12
+00:01:26,470 --> 00:01:32,190
+في المرة السابقة بنسنتج منها ما يأتي إن لو أخدت
+
+13
+00:01:32,190 --> 00:01:38,250
+sub group من ال center تبع ال group فإن ال G على H
+
+14
+00:01:38,250 --> 00:01:42,520
+لو كانت Cyclic يبقىجي إزابيلين والبرهان نفس
+
+15
+00:01:42,520 --> 00:01:47,900
+البرهان تبع النظرية حرفيا بس بصير ان انت مقيد في H
+
+16
+00:01:47,900 --> 00:01:52,700
+اللي هي ال subset او subgroup من ال center تبع ال
+
+17
+00:01:52,700 --> 00:01:56,640
+group الان ال remark بيقول ال contrapositive of
+
+18
+00:01:56,640 --> 00:02:01,860
+the above theorem is يعني بمعنى اخر ال negation
+
+19
+00:02:01,860 --> 00:02:06,260
+لنص النظرية احنا بنعرف ان ال proposition لو كانت
+
+20
+00:02:06,260 --> 00:02:10,200
+من اليمين لشمالي ال negation ببدأ من وينمن الشمال
+
+21
+00:02:10,200 --> 00:02:15,560
+لليامين يبقى الكون robotisitive لو كانت الـ G هذه
+
+22
+00:02:15,560 --> 00:02:20,760
+non-abelian إذا ال group هذه ما لها non-cyclic
+
+23
+00:02:20,760 --> 00:02:24,920
+وهذه أبسط الأشياء اللي تعلمناها في مبادئ الرياضيين
+
+24
+00:02:24,920 --> 00:02:30,180
+نكمل على نفس الموضوع for any group G modulo z of G
+
+25
+00:02:30,440 --> 00:02:34,840
+هذا يكون إيزو مورفك للـ Inner Atomorphism لـ Main
+
+26
+00:02:34,840 --> 00:02:43,380
+لـ G لذلك نذهب و نعرف Function Define
+
+27
+00:02:43,380 --> 00:02:49,000
+A Mapping Define
+
+28
+00:02:49,000 --> 00:02:55,320
+A Mapping T مثلا من الـ G و ادّيله الـ Center تبع
+
+29
+00:02:55,320 --> 00:02:59,600
+الـ G إلى الـ Inner Atomorphism لـ G
+
+30
+00:03:02,800 --> 00:03:08,360
+طبعا كل element هنا هو عبارة عن left coset جي في
+
+31
+00:03:08,360 --> 00:03:12,960
+ال center بتابع الجي كل ال elements اللي هنا عبارة
+
+32
+00:03:12,960 --> 00:03:17,640
+عن isomorphism من ال group إلى نفس ال group يبقى
+
+33
+00:03:17,640 --> 00:03:26,480
+بدي أسميه في جي حيث الفايجي بنذكر بها as a
+
+34
+00:03:26,480 --> 00:03:32,300
+function of x بده ساوي الـ G x G inverse لكل ال X
+
+35
+00:03:32,300 --> 00:03:38,880
+اللي موجودة في جييبقى أخدنا element من هنا اللي هو
+
+36
+00:03:38,880 --> 00:03:43,240
+left coset وليكن جي في ال center تبع الجي خلينا T
+
+37
+00:03:43,240 --> 00:03:48,240
+تأثر عليها افترضنا انه الصورة تبعتها كانت هي Phi
+
+38
+00:03:48,240 --> 00:03:52,740
+of G بدنا نثبت ان هذا isomorphism بس قبل ال
+
+39
+00:03:52,740 --> 00:03:57,380
+isomorphism بدنا نؤكد على ان T هذه is well defined
+
+40
+00:03:57,380 --> 00:04:01,700
+يعني تعريفنا هذا تعليم استعريف سليم مائة بالمائة
+
+41
+00:04:01,700 --> 00:04:05,700
+يبقى T is well defined
+
+42
+00:04:07,890 --> 00:04:13,330
+هي معرفة تعريفا سليما يبقى مشان هيك بدأ أخد عنصرين
+
+43
+00:04:13,330 --> 00:04:22,930
+متساوين أسيوم أن الـG في الـZ of G بده يساوي الـH
+
+44
+00:04:22,930 --> 00:04:32,210
+في الـZ of G مثلا و الـG و الـH هدولة موجودة في
+
+45
+00:04:32,210 --> 00:04:39,650
+الـGيبقى أخدت عنصرين متساويين من هذين العنصرين بدي
+
+46
+00:04:39,650 --> 00:04:45,970
+أستنتج ما يأتي لو ضربت الطرفين في G inverse يبقى
+
+47
+00:04:45,970 --> 00:04:53,330
+بدي يصير عندك ال Z of G بدي سوى ال G inverse H في
+
+48
+00:04:53,330 --> 00:04:59,750
+Z of G طبعا ال Z of G is a subgroup لاتنين هدول
+
+49
+00:04:59,750 --> 00:05:09,160
+متساويينبنستنتج من ذلك إن الـG inverse H موجودة في
+
+50
+00:05:09,160 --> 00:05:17,540
+الـZ of G معناه هذا الكلام إن الـG inverse HX بدي
+
+51
+00:05:17,540 --> 00:05:23,800
+ساوي الـX في الـG inverse H لكل الـX اللي موجود في
+
+52
+00:05:23,800 --> 00:05:27,800
+G بلا استثناءما دام element موجود في الـ center
+
+53
+00:05:27,800 --> 00:05:31,600
+تبع الـ group، اذا الـ commutes مع جميع عناصر الـ
+
+54
+00:05:31,600 --> 00:05:36,460
+group بلا استثناء، يبقى بناء عليه اللي هو main
+
+55
+00:05:36,460 --> 00:05:42,980
+اللي هو الـ G inverse H X بدي أسوأ X، G inverse H
+
+56
+00:05:42,980 --> 00:05:49,960
+من هذا الكلام بدي أحاول أوصل إلى أن فاي G هي فاي H
+
+57
+00:05:49,960 --> 00:05:56,080
+بالضبط تماما، وبالتالي بوصل للأصل بتبعهايبقى هذا
+
+58
+00:05:56,080 --> 00:06:02,840
+يعطينا ما يأتي بدا أحاول أخل ال H في ناحية ومين و
+
+59
+00:06:02,840 --> 00:06:09,060
+ال G في ناحية إذا هذه المعادلة لو ضربت في G من جهة
+
+60
+00:06:09,060 --> 00:06:14,840
+الشمال وضربت في H inverse من جهة اليمينيبقى هذا
+
+61
+00:06:14,840 --> 00:06:22,440
+الشي حتعطينا ان الـ H X H inverse بده يساوي الـ G
+
+62
+00:06:22,440 --> 00:06:28,320
+X G inverse طلع ليه كويس هضرب من جهة اليمين في H
+
+63
+00:06:28,320 --> 00:06:33,480
+inverse بتروح هذه وابتجيني هنا H inverse هاي الـ H
+
+64
+00:06:33,480 --> 00:06:38,780
+inverse تمام؟ الآن بده اضرب من جهة الشمال في G
+
+65
+00:06:39,040 --> 00:06:45,740
+بتروح حياتي بيظل H X H inverse هتيدي لك هنا G X G
+
+66
+00:06:45,740 --> 00:06:51,340
+inverse بالشكل اللي عندنا هذا يعني ايه؟ يعني ان
+
+67
+00:06:51,340 --> 00:06:59,820
+فاي H هي نفسها فاي Gيعني تأثير فاي H على أي
+
+68
+00:06:59,820 --> 00:07:05,240
+element من ال group بيكون تأثير فاي G على نفس ال
+
+69
+00:07:05,240 --> 00:07:12,140
+element هذا معناه فاي H هي عبارة عن T of H في ال
+
+70
+00:07:12,140 --> 00:07:18,880
+center تبع ال group G بيكون تأثير T على G مضروبة
+
+71
+00:07:18,880 --> 00:07:25,680
+في ال center تبع G بالشكل هذا لذلك T is one to one
+
+72
+00:07:25,870 --> 00:07:33,050
+T is well-defined بنا نيجي الآن لـ T is one to one
+
+73
+00:07:33,050 --> 00:07:37,090
+يبقى بدي أعمل العملية العكسية بدي أخد صورتين
+
+74
+00:07:37,090 --> 00:07:45,370
+متساويتين Assume T للـ G في ال center بتابع الـ G
+
+75
+00:07:45,370 --> 00:07:52,670
+بدي ساوي T في main في ال H في ال center تابع الـ G
+
+76
+00:07:52,670 --> 00:07:58,300
+بالشكل اللي عندنا هنايبقى هذا يعطينا ايه؟ يبقى
+
+77
+00:07:58,300 --> 00:08:06,100
+يعطينا ان الـ Phi G يسوى الـ Phi H يبقى لو خلنا كل
+
+78
+00:08:06,100 --> 00:08:13,540
+واحدة تأثر على X يسوى تأثير الـ H على X هذا الكلام
+
+79
+00:08:13,540 --> 00:08:21,540
+صحيح لكل الـ X اللي موجود في Gيبقى بناء عليها جيكس
+
+80
+00:08:21,540 --> 00:08:30,340
+جي انفرس هكس هانفرس لكل ال X اللي موجود في جي بلا
+
+81
+00:08:30,340 --> 00:08:37,160
+استثناء طيب كويس هذا الكلام بده يعطينا ما يأتيبدي
+
+82
+00:08:37,160 --> 00:08:43,080
+أسنت الشغلة من هذا الكلام لو ضربت الطرفين في الـ
+
+83
+00:08:43,080 --> 00:08:49,540
+Main في الـ H من جهتي اليمين يبقاش بصير عندك جي
+
+84
+00:08:49,540 --> 00:08:57,950
+اكس جي انفرس H بده يساوي الـ HXيبقى ضربت من جهة
+
+85
+00:08:57,950 --> 00:09:03,990
+اليمين في من؟ في H بتجينا هنا H و من هنا بتروح
+
+86
+00:09:03,990 --> 00:09:09,730
+الـH هي أجت و هنا راحت الآن بدي أضرب من جهة الشمال
+
+87
+00:09:09,730 --> 00:09:14,430
+في G inverse يبقى لو ضربت من جهة الشمال في G
+
+88
+00:09:14,430 --> 00:09:21,750
+inverse بصير X في G inverse H بدي ساوي G inverse H
+
+89
+00:09:21,750 --> 00:09:29,410
+في Xهذا الكلام صحيح لكل الـ X اللي موجودة في G شو
+
+90
+00:09:29,410 --> 00:09:34,110
+تفسيرك لهذا الكلام ان عندي هذا ال element هو نفس
+
+91
+00:09:34,110 --> 00:09:37,710
+ال element يبقى معناته هذا ال element موجود وين؟
+
+92
+00:09:37,710 --> 00:09:42,860
+في ال center تبع ال groupيبقى هذا الوضع يعطيني ان
+
+93
+00:09:42,860 --> 00:09:48,700
+الـ G inverse H موجودة في الـ Center تبع الـ Group
+
+94
+00:09:48,700 --> 00:09:54,400
+يعني بمعنى اخر هذا معناه ان الـ G inverse H في الـ
+
+95
+00:09:54,400 --> 00:09:57,960
+Center تبع الـ Group يساوي الـ Center تبع الـ
+
+96
+00:09:57,960 --> 00:10:04,390
+Groupلو ضربنا الطرفين في G بيصير عندك H في الـ
+
+97
+00:10:04,390 --> 00:10:09,430
+Center تبع الـ G بيساوي G في الـ Center تبع الـ G
+
+98
+00:10:09,430 --> 00:10:15,970
+بالشكل هذا وبالتالي أخدنا صورتين متساويتين أثبتنا
+
+99
+00:10:15,970 --> 00:10:21,350
+إن أصلهم متساوي يبقى بناءً عليه G أو T is one to
+
+100
+00:10:21,350 --> 00:10:28,780
+one بيجي نثبت هنا T is untoيبقى بدي أروح أخد
+
+101
+00:10:28,780 --> 00:10:34,000
+element ههه اللي هو في جي موجود في ال inner
+
+102
+00:10:34,000 --> 00:10:43,360
+atomorphism إلى جي then الفي of جي هذاالـ Phi of G
+
+103
+00:10:43,360 --> 00:10:51,800
+هو عبارة بالضبط عن صورة T للـ G لـ Z of G بالشكل
+
+104
+00:10:51,800 --> 00:10:58,060
+اللي عندنا أنا TGZ of G يبقى بناء عليه Phi is unto
+
+105
+00:10:58,060 --> 00:11:06,350
+T is unto ضايل علينا T is an isomorphismيبقى بروح
+
+106
+00:11:06,350 --> 00:11:13,930
+اخد T لجي في ال center تبع الجي مضروب في ال H في
+
+107
+00:11:13,930 --> 00:11:19,690
+ال center تبع الجي بالشكل اللي عندناهذا الكلام
+
+108
+00:11:19,690 --> 00:11:25,150
+يساوي T of هذه left coset و هذه left coset تانية
+
+109
+00:11:25,150 --> 00:11:33,550
+حسب ما أخدنا التعريف يبقى هذا بيصير GH ل Z of G
+
+110
+00:11:33,550 --> 00:11:41,470
+left coset جديدة حسب تعريف الـ T هذه بيصير Phi GH
+
+111
+00:11:42,370 --> 00:11:49,850
+الشكل اللي عندنا هنا طيب الان لو جيت خط في جي إتش
+
+112
+00:11:49,850 --> 00:11:56,530
+تأثيرها على element X يبقى هذا الكلام بدي يساوي GH
+
+113
+00:11:56,530 --> 00:12:03,830
+X GH inverse لأنه ماخد وين ال في جي هادي وين في ال
+
+114
+00:12:03,830 --> 00:12:12,860
+inner atomorphismطيب هذه لو رجعت لتعريفة جي هكس ه
+
+115
+00:12:12,860 --> 00:12:18,600
+انفرس جي انفرس هذا بندخل انفرس على جوا وبالتالي
+
+116
+00:12:18,600 --> 00:12:22,660
+بنجلب إيه ووضعهم لإن ماعنديش جي إز قابيل يعني
+
+117
+00:12:22,660 --> 00:12:31,630
+ماقولناش قابيلطيب كويس هذه هتعني فاي جي لل HX H
+
+118
+00:12:31,630 --> 00:12:36,830
+inverse يعني بدي افترض ان هذا كله element واحد
+
+119
+00:12:36,830 --> 00:12:41,810
+وبالتالي بدي يصير جي لل element هذا لل G inverse
+
+120
+00:12:41,810 --> 00:12:48,280
+تعريف فاي جيهذا اللي جوا تعريف main اللي هو في اتش
+
+121
+00:12:48,280 --> 00:12:56,520
+يبقى هذا في جي لمين لفي اتش كل هذا as a function
+
+122
+00:12:56,520 --> 00:13:04,710
+of x طب ال في جي هذه مش هي عبارة عن اللي تساويT في
+
+123
+00:13:04,710 --> 00:13:11,610
+G في الـ Center تبع الـ G والتانية Phi H هي عبارة
+
+124
+00:13:11,610 --> 00:13:17,510
+عن T للـ H في الـ Center بتبع من؟ بتبع الـ G
+
+125
+00:13:17,510 --> 00:13:22,370
+وبالتالي صارت isomorphism وبالتالي برهننا من؟
+
+126
+00:13:22,370 --> 00:13:25,630
+برهننا هذه النظرية
+
+127
+00:13:33,190 --> 00:13:37,610
+في نظرية هذا اسمها نظرية كيلي برضه لل abelian
+
+128
+00:13:37,610 --> 00:13:44,190
+groups يبقى هنا theorem لكلس
+
+129
+00:13:44,190 --> 00:13:51,950
+theorem كلس
+
+130
+00:13:51,950 --> 00:13:58,810
+theorem for abelian groups
+
+131
+00:14:01,880 --> 00:14:09,780
+بتقول ما يتلت الـ G بيه
+
+132
+00:14:09,780 --> 00:14:21,560
+finite بيه finite abelian group finite abelian
+
+133
+00:14:21,560 --> 00:14:36,120
+groupو .. دع ال P بيه قطع بيه قطع بيه
+
+134
+00:14:36,120 --> 00:14:36,140
+قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه
+
+135
+00:14:36,140 --> 00:14:40,580
+قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه
+
+136
+00:14:40,580 --> 00:14:42,020
+قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه
+
+137
+00:14:42,020 --> 00:14:42,060
+قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه قطع بيه
+
+138
+00:14:42,060 --> 00:14:47,180
+قطع بيه قطع بيه
+
+139
+00:14:47,180 --> 00:14:50,880
+قطع بيه قطع بي
+
+140
+00:15:09,720 --> 00:15:26,080
+الجي لبروفة بتقدر ترجعلهPage صفحات الـ 187 و188
+
+141
+00:15:53,820 --> 00:16:01,320
+فينا تعريف جديد وهذا التعريف مهم شوية لما بعده
+
+142
+00:16:01,320 --> 00:16:12,480
+definition suppose that افترض
+
+143
+00:16:12,480 --> 00:16:25,270
+ان ال h and ال kare subgroups of G are subgroups
+
+144
+00:16:25,270 --> 00:16:39,130
+of G define the set define the set HK
+
+145
+00:16:39,130 --> 00:16:47,150
+حاصل الدرب HK by HK
+
+146
+00:16:48,210 --> 00:16:56,390
+هو الـ set of all elements H في K such that الـ H
+
+147
+00:16:56,390 --> 00:17:07,610
+موجودة في H و K موجودة في K التعريف
+
+148
+00:17:07,610 --> 00:17:11,350
+اللي بعده بيعتمد عليه definition
+
+149
+00:17:14,660 --> 00:17:23,020
+we say that ان
+
+150
+00:17:23,020 --> 00:17:31,900
+الـ G ليه بدها تساوي ال H مضروبة في K الشكل اللي
+
+151
+00:17:31,900 --> 00:17:39,120
+عندنا هذا is the internal direct product is the
+
+152
+00:17:39,120 --> 00:17:50,430
+internal directproduct of
+
+153
+00:17:50,430 --> 00:18:03,650
+the subgroups
+
+154
+00:18:03,650 --> 00:18:14,590
+ال H andالـ K F إذا تحقق ثلاثة شروط الشرط الأول ال
+
+155
+00:18:14,590 --> 00:18:23,850
+H and ال K are normal subgroups are normal
+
+156
+00:18:23,850 --> 00:18:34,950
+subgroups normal subgroups of G الشرط
+
+157
+00:18:34,950 --> 00:18:35,650
+الثاني
+
+158
+00:18:38,640 --> 00:18:48,280
+ان الـ G بدأ تساوي H في K الشرط التالت والاخير ان
+
+159
+00:18:48,280 --> 00:18:55,880
+الـ H intersection K بده يساوي ال identity element
+
+160
+00:18:55,880 --> 00:19:03,820
+examples let
+
+161
+00:19:05,880 --> 00:19:15,240
+الـ G بدأت تساوي الـ S3 and الـ H هي الـ subgroup
+
+162
+00:19:15,240 --> 00:19:25,460
+generated by واحد اتنين تلاتة and K هي ال subgroup
+
+163
+00:19:25,460 --> 00:19:34,640
+generated by واحد اتنين السؤال
+
+164
+00:19:34,640 --> 00:19:47,640
+هوis الـ S3 بدها تساوي H مضروبة في K أم لا هذا
+
+165
+00:19:47,640 --> 00:19:48,260
+السؤال
+
+166
+00:20:18,320 --> 00:20:21,800
+طبعا اترضنا على تعريف الـ External like product
+
+167
+00:20:21,800 --> 00:20:25,240
+سابقا في ال section اللي قبله وفي ال chapter اللي
+
+168
+00:20:25,240 --> 00:20:30,000
+قبله واخدنا عليه أمثلة واسئلة ونظريات لما نجي
+
+169
+00:20:30,000 --> 00:20:33,620
+لحاجة اسمها ال internal like product اللي هو حاصل
+
+170
+00:20:33,620 --> 00:20:38,950
+الضرب الداخلي ده كان حاصل الضرب الخارجيبقول افترض
+
+171
+00:20:38,950 --> 00:20:45,450
+ان الـH وK subgroups من G عرفنا ستة HK حاصلة ضرب
+
+172
+00:20:45,450 --> 00:20:51,710
+بأنها كل العناصر اللي على الشكل H في K بحيث H
+
+173
+00:20:51,710 --> 00:20:59,780
+موجودة في H وK موجودة في K بنفس التارتيتتعريف آخر
+
+174
+00:20:59,780 --> 00:21:03,880
+بيناعرف حاجة اسمه ال internal die product حصل
+
+175
+00:21:03,880 --> 00:21:08,220
+الضرب الداخلي فبجي بقول جي هي ال internal die
+
+176
+00:21:08,220 --> 00:21:13,640
+product لل H وK وسنعطيها الرمز H علامة الضرب
+
+177
+00:21:13,640 --> 00:21:19,000
+العادية في K طبعا ال external بقول زائد ودائرة هذه
+
+178
+00:21:19,000 --> 00:21:24,040
+تدول على ال externalوكل عنصر على الشكل two
+
+179
+00:21:24,040 --> 00:21:28,260
+components three components in components بس هذا
+
+180
+00:21:28,260 --> 00:21:33,780
+لا بيختلف هذا هنا جيه كل عنصر هنا على الشكل main
+
+181
+00:21:33,780 --> 00:21:38,870
+على الشكل يعني اتنين مضربات في بعض ضربمباشرة يبقى
+
+182
+00:21:38,870 --> 00:21:43,350
+هذا بسميه الـ Internal Product لـ Subgroups H و K
+
+183
+00:21:43,350 --> 00:21:49,110
+إذا تحققت عندي ثلاثة شروط الشرط الأول لازم يكون كل
+
+184
+00:21:49,110 --> 00:21:53,650
+ما هو H و K Normal Subgroups الشرط التاني عملية
+
+185
+00:21:53,650 --> 00:21:57,970
+الضرب بدها تجيب ليه كل عناصر الجروب بيه لا إستثناء
+
+186
+00:21:57,970 --> 00:22:03,090
+لا زيادة ولا نقصان هاي الشرط التاني الشرط التالت
+
+187
+00:22:03,090 --> 00:22:06,370
+ال intersection بين الـH و الـK بده يكون باسمين
+
+188
+00:22:08,220 --> 00:22:13,220
+identity موجود في اي subgroup من ال group الأصلي
+
+189
+00:22:22,370 --> 00:22:28,010
+ستة عناصر يعطيني ال subgroup و كمان subgroup تمام
+
+190
+00:22:28,010 --> 00:22:33,950
+و بيقوللي هل ال S3 هي ال internal product تبع ال H
+
+191
+00:22:33,950 --> 00:22:37,710
+و K ولا لأ بنقوله والله ما احنا عارفين تعالى نشوف
+
+192
+00:22:37,790 --> 00:22:43,350
+يبقى هنا باجي بقوله solution مشان نعرف بأنه نعرف
+
+193
+00:22:43,350 --> 00:22:49,670
+مين هي H في الأول طبعا ال identity element وهذا
+
+194
+00:22:49,670 --> 00:22:54,930
+اللي هو واحد اتنين تلاتة ولو ضربنا في نفسه تربيع
+
+195
+00:22:54,930 --> 00:23:03,240
+بيعطينا واحد تلاتة اتنينوانتهينا منها and ال K هي
+
+196
+00:23:03,240 --> 00:23:08,300
+عبارة عن ال identity element والواحد دي اتنين ولو
+
+197
+00:23:08,300 --> 00:23:13,000
+جيبناه تربيع بيعطينا main ال identity element يبقى
+
+198
+00:23:13,000 --> 00:23:18,180
+هذا هذا اللي موجود عندنا مشان أدربك على هذا الشغل
+
+199
+00:23:18,180 --> 00:23:23,640
+بديش أبدأ بأول شرط بدي أبدأ بالشرط الثاني وبعد هيك
+
+200
+00:23:23,640 --> 00:23:31,910
+بروح لمين لباقي الشروطإذا لو جيت لل H في K يبقى
+
+201
+00:23:31,910 --> 00:23:35,750
+بدي أبدأ أضرب العناصر اللي عندنا في هذه العناصر
+
+202
+00:23:35,750 --> 00:23:39,710
+يبقى ب ذات ساوية ال identity في ال identity
+
+203
+00:23:39,710 --> 00:23:44,570
+بتعطيني ال identity element ال identity في واحد
+
+204
+00:23:44,570 --> 00:23:49,230
+اتنين بتعطيني واحد اتنينبعدين بدي أضرب هذا في
+
+205
+00:23:49,230 --> 00:23:56,390
+العنصرين 123 في ال identity تعطيني 123 و هذه
+
+206
+00:23:56,390 --> 00:24:01,170
+بتعطيني .. بدي أضرب اتنين هذول في بعض أشوف شو
+
+207
+00:24:01,170 --> 00:24:07,390
+بيعطيني الواحد صورته اتنين و اتنين صورته قداشر
+
+208
+00:24:07,390 --> 00:24:14,830
+واحد يبقى الواحد احنا بدنا نبدأ من هنا هذا واحد
+
+209
+00:24:15,250 --> 00:24:21,610
+تمام؟ يبقى الواحد صورته اتنين تمام؟ اه اتنين صورته
+
+210
+00:24:21,610 --> 00:24:27,890
+تلاته تمام؟ طب الآن التلاته صورتها تلاته هنا
+
+211
+00:24:27,890 --> 00:24:33,170
+التلاته صورتها قداش صورتها واحد و هكذا مرة تانية
+
+212
+00:24:33,170 --> 00:24:38,050
+بقول الواحد صورته اتنين اتنين صورته تلاته هيحطينا
+
+213
+00:24:38,050 --> 00:24:42,190
+التلاته التلاته صورتها تلاته التلاته صورتها واحد
+
+214
+00:24:42,190 --> 00:24:49,880
+هيخلصنا من هنا تمام؟العنصر اللي بعده اللي هو واحد
+
+215
+00:24:49,880 --> 00:24:54,900
+ثلاثة اتنين ضربنا في ال identity بنفسه العنصر اللي
+
+216
+00:24:54,900 --> 00:25:00,620
+بعده بالداجي هذا الواحد الواحد صورته اتنين و اتنين
+
+217
+00:25:00,620 --> 00:25:06,000
+صورته واحد يبقى جفل هذا راح مع السلامة يبقى بدنا
+
+218
+00:25:06,000 --> 00:25:10,120
+نيجي للعنصر اللي بعده اللي هو اتنين اتنين صورته
+
+219
+00:25:10,120 --> 00:25:16,040
+واحد الواحد صورته تلاتةالتلاتة صورتها تلاتة
+
+220
+00:25:16,040 --> 00:25:22,400
+التلاتة صورتها اتنين يبقى جفلة خلصنا اكم عنصر هدول
+
+221
+00:25:22,400 --> 00:25:29,440
+ستة هم عناصر S3 بالضبط يبقى هذا هم S3 بالضبطيبقى
+
+222
+00:25:29,440 --> 00:25:34,940
+ال condition هذا معله صحيح نجي لل H intersection K
+
+223
+00:25:34,940 --> 00:25:39,180
+هذا هو ال condition الأول أو ال condition بده
+
+224
+00:25:39,180 --> 00:25:43,420
+أسميه الأول ال condition التاني ال H intersection
+
+225
+00:25:43,420 --> 00:25:48,620
+K واضح اللي هو مافيش غير main ال identity element
+
+226
+00:25:48,620 --> 00:25:53,360
+ما بين الأتنين هيه وهيه ومافيش غيره الآن بدأجي هل
+
+227
+00:25:53,360 --> 00:26:00,100
+ال H normal ام لا؟تعالى نشوف ال H فيها كم عنصر؟
+
+228
+00:26:00,100 --> 00:26:05,280
+تلاتة و ال S3 فيها قداشر؟ يبقى ال index سبعة
+
+229
+00:26:05,280 --> 00:26:11,680
+قداشر؟ اتنين او اي subgroup او اي group ال index
+
+230
+00:26:11,680 --> 00:26:15,260
+لها اي subgroup ال index لها يسوى اتنين عبارة عن
+
+231
+00:26:15,260 --> 00:26:21,200
+normal واخدناه كمثالالان بدي اجيب .. بدي اقول بدي
+
+232
+00:26:21,200 --> 00:26:25,720
+اجيب ال index ال condition التالت الان ال index
+
+233
+00:26:25,720 --> 00:26:34,200
+تبع اللي هو main اللي هو ال H في S3 ال H في S3
+
+234
+00:26:34,200 --> 00:26:42,320
+اللي هو يساوي ال order بتبع ال S3 مقسوما على ال
+
+235
+00:26:42,320 --> 00:26:48,900
+order بتبع ال H هذا ستة و هذا تلاتة يساوي اتنينهذا
+
+236
+00:26:48,900 --> 00:26:57,240
+سيعطينا ان الـ H is a normal subgroup من SC3 نعود
+
+237
+00:26:57,240 --> 00:27:04,760
+الان لـ K هل هي normal subgroup ولا لا الله أعلم
+
+238
+00:27:05,130 --> 00:27:10,690
+تعالى نشوف هل هذا الكلام لو جيت أخد element من S
+
+239
+00:27:10,690 --> 00:27:19,110
+من من H3 وبدى أشوف احنا بدنا نشوفها normal ولا لأ
+
+240
+00:27:19,110 --> 00:27:25,750
+بدى أروح أخد element من S3 وضربه في هذا ال element
+
+241
+00:27:25,750 --> 00:27:29,750
+ومعكسه أشوف موجود في K ولا لأ إذا كان موجود كان
+
+242
+00:27:29,750 --> 00:27:35,660
+بها مش موجود يبقى هذه ماهياش normalالان عندك واحد
+
+243
+00:27:35,660 --> 00:27:42,900
+و تلاتة موجود في ال S3 واحد و اتنين موجود وين؟
+
+244
+00:27:42,900 --> 00:27:48,660
+موجود في ال H بدي اشوف ال normality بدي اخد واحد
+
+245
+00:27:48,660 --> 00:27:54,860
+تلاتة في واحد اتنين واحد تلاتة inverse مش هيك شرط
+
+246
+00:27:54,860 --> 00:27:55,780
+ال normality؟
+
+247
+00:27:58,540 --> 00:28:02,400
+أحنا في الـK هذي بدل الـH فيك خلصنا من الـH هذي في
+
+248
+00:28:02,400 --> 00:28:07,000
+الـK صحيح مضبوط يبقى بدنا ناخد الأول في التاني في
+
+249
+00:28:07,000 --> 00:28:13,500
+معكوس الأول هذا الكلام بدي يساوي واحد تلاتة واحد
+
+250
+00:28:13,500 --> 00:28:18,400
+اتنين اظن واحد تلاتة زي ما هو لإن ال transposition
+
+251
+00:28:18,400 --> 00:28:22,260
+ال inverse له هو نفسه او ال cycle طولها اتنين ال
+
+252
+00:28:22,260 --> 00:28:26,680
+transposition له هو نفسهبدي اضرب دغري مش كل اتنين
+
+253
+00:28:26,680 --> 00:28:30,340
+بدي اضرب التلاتة مرة واحدة يبقى بدي ابدأ من
+
+254
+00:28:30,340 --> 00:28:35,960
+بالواحد الواحد صورته تلاتة و التلاتة صورتها تلاتة
+
+255
+00:28:35,960 --> 00:28:40,240
+و التلاتة صورتها واحد يبقى مع السلامة ال identity
+
+256
+00:28:40,830 --> 00:28:46,950
+هو الاتنين الاتنين صورته اتنين اتنين صورته واحد
+
+257
+00:28:46,950 --> 00:28:52,830
+الواحد صورته تلاتة نجي التلاتة صورتها واحد الواحد
+
+258
+00:28:52,830 --> 00:28:58,550
+صورته اتنين اتنين صورته اتنين هيوا جفلة يبقى هذا
+
+259
+00:28:58,550 --> 00:29:05,360
+بده يسوي قداش اتنين تلاتة هل هذا موجود في كطبعاً
+
+260
+00:29:05,360 --> 00:29:10,300
+مش موجود في K يبقى لا يمكن تبقى هذه normal في
+
+261
+00:29:10,300 --> 00:29:17,260
+subgroup من G يبقى هنا so ال K هذه is not normal
+
+262
+00:29:17,260 --> 00:29:26,280
+subgroup من S3 هذا معناه ان ال G او ال S3لا يمكن
+
+263
+00:29:26,280 --> 00:29:32,940
+أن تساوي الـH اللي هو مضروبة في K يعني في هذه
+
+264
+00:29:32,940 --> 00:29:38,600
+الحالة الـG is not the internal product تبع الـH
+
+265
+00:29:38,600 --> 00:29:49,460
+والـK خد لك مثال آخر example 2 خد للـG تساوي زد 12
+
+266
+00:29:51,300 --> 00:29:58,080
+وخد الـ H هي الـ subgroup generated by تلاتة و K
+
+267
+00:29:58,080 --> 00:30:03,760
+هي ال subgroup generated by أربعة بالشكل اللي
+
+268
+00:30:03,760 --> 00:30:15,240
+عندنا هذا تمام والسؤال هوIs الـ Z8 Z12 تساوي الـ
+
+269
+00:30:15,240 --> 00:30:21,360
+Internal Direct Product ما بين الـ H والـ K أم الـ
+
+270
+00:30:21,360 --> 00:30:23,280
+Solution
+
+271
+00:30:27,020 --> 00:30:33,700
+بسأل السؤال التالي هى عندك H اللى هى تساوي العناصر
+
+272
+00:30:33,700 --> 00:30:44,660
+تبعتها 0,3,6,9 والـ K عناصرها 0,4,8 السؤال هو هل
+
+273
+00:30:44,660 --> 00:30:49,120
+الـ H و K normal subgroup من Z إتناش
+
+274
+00:31:04,170 --> 00:31:09,730
+أول مثال أخدنا ان any subgroup of an abelian group
+
+275
+00:31:09,730 --> 00:31:10,770
+is normal
+
+276
+00:31:24,780 --> 00:31:33,720
+subgroups subgroups of z12 ايه السبب؟ because ان
+
+277
+00:31:33,720 --> 00:31:37,620
+z12 is abelian
+
+278
+00:31:39,890 --> 00:31:44,630
+طيب إذا ال condition الأول هذا معله تحقق بدنا نيجي
+
+279
+00:31:44,630 --> 00:31:50,970
+لل condition الثاني بدنا نيجي نضرب ال H في K يبقى
+
+280
+00:31:50,970 --> 00:31:59,270
+هذا ال H في K بده ساوي المقصود ب H في K هو H زائد
+
+281
+00:31:59,270 --> 00:32:05,080
+Kلأن العملية فيما بينهم عملية H جامعة يبقى لما
+
+282
+00:32:05,080 --> 00:32:12,580
+نقول هذا H في K بالضبط هي H زائد K الشكل اللي
+
+283
+00:32:12,580 --> 00:32:17,220
+عندنا هنا يبقى بدي أبدأ أجمع Zero مع Zero ب Zero
+
+284
+00:32:17,220 --> 00:32:22,120
+Zero مع أربعة ب أربعة Zero مع تمانية ب تمانية خلصت
+
+285
+00:32:22,120 --> 00:32:26,800
+العنصر هذا مع جميع العناصر بدي أجي لتلاتةتلاتة مع
+
+286
+00:32:26,800 --> 00:32:33,420
+زيرو بتلاتة تلاتة وأربعة سبعة تلاتة وتمانية احداش
+
+287
+00:32:33,420 --> 00:32:38,960
+خلصنا منها بدنا نيجي للستة ستة وزيرو عبارة عن زيرو
+
+288
+00:32:38,960 --> 00:32:44,720
+ستة وأربعة عشرة ستة وتمانية اربعتاش في زد اتناش
+
+289
+00:32:44,720 --> 00:32:50,750
+باتنينخلصنا من التسعة الستة بدنا نروح للتسعة تسعة
+
+290
+00:32:50,750 --> 00:32:56,470
+زائد zero ب zero تسعة واربع تلتاش تعني واحد تسعة و
+
+291
+00:32:56,470 --> 00:33:02,890
+تمانية سبعتاش تعني ستة ب هذا .. تعني خمسة و ليس
+
+292
+00:33:02,890 --> 00:33:08,630
+زتة تعني خمسة ب هذا الشكل الطلق هدول كلهم بتلاقيهم
+
+293
+00:33:08,630 --> 00:33:16,190
+هم عناصر من؟ ضد اتناشتمام هى عندك ال zero موجود
+
+294
+00:33:16,190 --> 00:33:24,970
+واحد اتنين تلاتة اربع خمسة ستة سبعة تمانية تسعة
+
+295
+00:33:24,970 --> 00:33:30,550
+عشرة احداش كلهم موجودة هى العناصر كلها يبقى اتحقق
+
+296
+00:33:30,550 --> 00:33:34,420
+من عند ال condition التانىبتروح لل condition
+
+297
+00:33:34,420 --> 00:33:39,940
+التالت يبقى ال condition التالت H intersection K
+
+298
+00:33:39,940 --> 00:33:45,220
+واضح ماعنديش إلا main ال zero يبقى باجي بقول له so
+
+299
+00:33:45,220 --> 00:33:54,080
+زد اتناش بدها تساوي ال H زائد main زائد ال K بدل
+
+300
+00:33:54,080 --> 00:33:58,540
+ما هي H في K لإن ال operation اللي عندنا عبارة عن
+
+301
+00:33:58,540 --> 00:34:02,740
+عملية main عبارة عن عملية الجامعة
+
+302
+00:34:09,180 --> 00:34:14,040
+طب يا شو رأيك ال internal direct product دي لو جيه
+
+303
+00:34:14,040 --> 00:34:18,720
+ساوة ال internal direct product فهي isomorphic لل
+
+304
+00:34:18,720 --> 00:34:21,520
+external direct product
+
+305
+00:34:24,820 --> 00:34:30,600
+هذا الكلام لو خلّينها لمجموعة من الجروس مش تنتين
+
+306
+00:34:30,600 --> 00:34:35,140
+ممكن يكونوا تنتين، تلاتة، أربعة، خمسة جد ما يكون
+
+307
+00:34:35,140 --> 00:34:38,360
+يبقى بدنا نعطي ال definition و من بعدين نكتب
+
+308
+00:34:38,360 --> 00:34:44,120
+النظرية ال definition بيقول ما ياتي ال let each
+
+309
+00:34:44,120 --> 00:34:51,540
+واحدوH2 و لغاية HN يعني يا شباب بدنا نعمم حاصل
+
+310
+00:34:51,540 --> 00:34:57,360
+الضرب H في K بدل ما هو تنتين بدنا نخليه ل N من ال
+
+311
+00:34:57,360 --> 00:35:04,940
+subgroups ب finite collection
+
+312
+00:35:04,940 --> 00:35:11,880
+finite collection of normal
+
+313
+00:35:16,320 --> 00:35:29,340
+subgroups of G we say that we say that بروح نقول
+
+314
+00:35:29,340 --> 00:35:40,320
+ال G هي ال internal byproduct H1 في H2 في في HN
+
+315
+00:35:41,690 --> 00:35:51,590
+اللي هو الـ Internal Direct Product تبع الـ H's
+
+316
+00:35:51,590 --> 00:36:02,870
+هدول and the Internal Direct Product of H1 وH2
+
+317
+00:36:02,870 --> 00:36:06,190
+ولغاية HNF
+
+318
+00:36:10,090 --> 00:36:17,230
+إذا تحققت الشروط التالية نمرا واحد الـ G يساوي H1
+
+319
+00:36:17,230 --> 00:36:28,650
+في H2 في HN بالشكل اللي عندنا هذاواللي هي تساوي
+
+320
+00:36:28,650 --> 00:36:37,770
+the set of all elements h1, h2, h3, hn such that
+
+321
+00:36:37,770 --> 00:36:45,410
+hi موجودة في الـ hi بالشكل اللي عندنا هذا ال
+
+322
+00:36:45,410 --> 00:36:54,070
+condition الثاني condition الثاني ان ال h1, h2 و
+
+323
+00:36:54,070 --> 00:37:03,170
+لغاية ال hiIntersection hi plus one بده يساوي ماين
+
+324
+00:37:03,170 --> 00:37:12,790
+بده يساوي ال identity element for i تساوي واحد
+
+325
+00:37:12,790 --> 00:37:21,190
+واتنين و لغاية ال n ناقص واحد نجي لل theorem
+
+326
+00:37:32,660 --> 00:37:45,840
+from if a group g if a group g is the internal
+
+327
+00:37:45,840 --> 00:37:54,300
+direct product of
+
+328
+00:37:54,300 --> 00:37:59,400
+a finite number
+
+329
+00:38:01,140 --> 00:38:09,180
+of a finite number of subgroups
+
+330
+00:38:09,180 --> 00:38:20,680
+subgroups اللي هو H واحد وH اتنين و لغاية HN then
+
+331
+00:38:20,680 --> 00:38:33,310
+G اللي بيساوي H واحد فH اتنينفي HN ايزو مارفك لل H
+
+332
+00:38:33,310 --> 00:38:39,390
+واحد Extended product مع H اتنين Extended product
+
+333
+00:38:39,390 --> 00:38:41,970
+مع HN
+
+334
+00:39:08,260 --> 00:39:11,440
+يبقى هنا بقول جي عبارة عن ال internal direct
+
+335
+00:39:11,440 --> 00:39:16,040
+product لمين اللي finite number subgroups H1 وH2
+
+336
+00:39:16,040 --> 00:39:22,450
+لغاية HNthen ال جي تعني ان ال internal direct
+
+337
+00:39:22,450 --> 00:39:27,390
+product ايزو مورفك لمين لل external direct product
+
+338
+00:39:27,390 --> 00:39:35,790
+بمعنى اخر لو حبيت تبرهن بدك تعملي function ال
+
+339
+00:39:35,790 --> 00:39:43,930
+function هذه بدك تقولي مثلا في of او بدك تعرف في
+
+340
+00:39:46,160 --> 00:39:55,820
+بتعرف فاى define فاى من الـ H واحد external direct
+
+341
+00:39:55,820 --> 00:39:59,660
+product لـ H اتنين .. انترنال direct product
+
+342
+00:39:59,660 --> 00:40:06,220
+انترنال direct product للـ H N إلى الـ H واحد
+
+343
+00:40:06,220 --> 00:40:10,560
+external direct product مع H اتنين external direct
+
+344
+00:40:10,560 --> 00:40:19,460
+product مع H N باىفاي اوف بتاكتيشي تاخد element
+
+345
+00:40:19,460 --> 00:40:27,980
+هنا يبقى ال element هذا هو H1 مضروب في H2 مضروب في
+
+346
+00:40:27,980 --> 00:40:36,760
+H3 و لغاية HN بنوديه على الجروب التاني اللي هو H1
+
+347
+00:40:36,760 --> 00:40:45,180
+فاصلة H2 فاصلة فاصلة HN بالشكل اللي عندنا هذايبقى
+
+348
+00:40:45,180 --> 00:40:56,840
+H N تمام هذه مكوّنة من N من المُركّبات هذه لأ N من
+
+349
+00:40:56,840 --> 00:41:00,980
+ال elements المضروبة في بعضها يبقى هنا هذول
+
+350
+00:41:00,980 --> 00:41:05,320
+المضروبات في بعض يبقى كل هذا يعتبر element واحد
+
+351
+00:41:05,320 --> 00:41:11,220
+فصلنا إلى N من المُركّباتيبقى و تثبت لهذه one to
+
+352
+00:41:11,220 --> 00:41:15,040
+one و أنت وتخدم خاصية ال isomorphism مثبوطة عندك
+
+353
+00:41:15,040 --> 00:41:18,860
+في الكتاب يريد تطلع عليها من الكتاب وهذا يعطيك ال
+
+354
+00:41:18,860 --> 00:41:22,520
+function هذا إذا ما عرفتش تسويها عرفت اعمالها
+
+355
+00:41:22,520 --> 00:41:28,580
+بيكون كفى الله المؤمنين القتال في عندك نظرية بتقول
+
+356
+00:41:28,580 --> 00:41:34,800
+ماتي سيارة بتقول
+
+357
+00:41:34,800 --> 00:41:38,140
+every group every
+
+358
+00:41:39,600 --> 00:41:49,740
+مجموعة من حرارة P تربيع P أكتر من حرارة P أكتر من
+
+359
+00:41:49,740 --> 00:41:54,040
+حرارة P أكتر من حرارة P أكتر من حرارة P أكتر من
+
+360
+00:41:54,040 --> 00:41:55,380
+حرارة P أكتر من حرارة P أكتر من حرارة P أكتر من
+
+361
+00:41:55,380 --> 00:41:55,620
+حرارة P أكتر من حرارة P أكتر من حرارة P أكتر من
+
+362
+00:41:55,620 --> 00:41:55,740
+حرارة P أكتر من حرارة P أكتر من حرارة P أكتر من
+
+363
+00:41:55,740 --> 00:42:01,520
+حرارة P أكتر من حرارة P أكتر من حرارة P أكتر من
+
+364
+00:42:01,520 --> 00:42:13,410
+حرارة P أكتر من حرارزد بي تربية أو لزد بي external
+
+365
+00:42:13,410 --> 00:42:25,590
+product مع مين مع زد بي وفي كرولري عليها كرولري
+
+366
+00:42:25,590 --> 00:42:39,010
+بيقول لو كانت ال G is a groupof order P تربيع
+
+367
+00:42:39,010 --> 00:42:42,050
+where
+
+368
+00:42:42,050 --> 00:42:52,810
+ال P is a prime ال P is a prime then ال G is
+
+369
+00:42:52,810 --> 00:42:58,290
+abelian ال G is abelian
+
+370
+00:43:02,970 --> 00:43:08,190
+على اي حال انتوا لاحظين ان احنا مابرهناش اكتر من
+
+371
+00:43:08,190 --> 00:43:13,110
+نظرية نظر اللي سوء لحوالي الجوية والارضية خلص
+
+372
+00:43:13,110 --> 00:43:17,250
+الجزء النظري يوم الأربعاء ان شاء الله بنعمل مناقشة
+
+373
+00:43:17,250 --> 00:43:21,930
+لهذا الشبتر حتى الأسبوع اللي بعده ندخل في الشبتر
+
+374
+00:43:21,930 --> 00:43:23,250
+الأخير
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7acb90a79a596cc68fd40e594960cb17f5d86ac5
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY.srt
@@ -0,0 +1,1791 @@
+1
+00:00:21,990 --> 00:00:24,230
+السلام عليكم ورحمة الله وبركاته بسم الله الرحمن الرحيم
+
+2
+00:00:24,230 --> 00:00:27,590
+اليوم إن شاء الله هنكمل الجزء الثالث من مناقشة
+
+3
+00:00:27,590 --> 00:00:31,630
+اللي هو الشابتر الرابع chapter ال cyclic groups
+
+4
+00:00:31,630 --> 00:00:36,310
+المرة الماضية أنهينا سؤال عشرين وتوقفنا عن سؤال
+
+5
+00:00:36,310 --> 00:00:41,970
+واحد وعشرين سؤال واحد وعشرين سؤال تطبيقي مش صعب 
+
+6
+00:00:41,970 --> 00:00:47,250
+كتير لو جينا نقرأه let g be a group and let a be an
+
+7
+00:00:47,250 --> 00:00:51,390
+element of g لو ال a أس 12 بيساوي ال identity what
+
+8
+00:00:51,390 --> 00:00:55,410
+can you say about the order of a نفس الفكرة في فرع
+
+9
+00:00:55,410 --> 00:00:58,710
+ب لو ال a أس 5 بيساوي ال identity what can we say
+
+10
+00:00:58,710 --> 00:01:04,750
+about the order of a طبعًا الجواب على السؤالين هو
+
+11
+00:01:04,750 --> 00:01:10,330
+جواب واحد أن order ال a في الأول هيقسم ال 12 في 
+
+12
+00:01:10,330 --> 00:01:13,050
+الفرع a وفي ب هيقسم مين
+
+13
+00:01:16,270 --> 00:01:22,710
+في الفرع c suppose that ال order ل g يساوي 24 g
+
+14
+00:01:22,710 --> 00:01:27,830
+is cyclic وال a أس 8 لا يساوي ال identity و
+
+15
+00:01:27,830 --> 00:01:31,730
+ال a أس 12 لا يساوي ال identity show that أن
+
+16
+00:01:31,730 --> 00:01:38,530
+order ال a أو ال generated by a هو ال g فرع c
+
+17
+00:01:38,530 --> 00:01:45,060
+order ال g يساوي 24 ال a أس 8 لا يساوي ال
+
+18
+00:01:45,060 --> 00:01:51,800
+identity وال a أس 12 لا يساوي ال identity طبعًا
+
+19
+00:01:51,800 --> 00:01:59,840
+في معلومة أخرى أن ال g is cyclic مدام 
+
+20
+00:01:59,840 --> 00:02:06,220
+ال g is cyclic و
+
+21
+00:02:06,220 --> 00:02:12,060
+ال a ينتمي لل g هذا معناه أن order ال a هيقسم
+
+22
+00:02:12,060 --> 00:02:19,240
+order ال g هذه إحدى الكورلرز على النظرية الأولى
+
+23
+00:02:19,240 --> 00:02:23,300
+أنه أي عنصر في ال cyclic group ال order له بيقسم
+
+24
+00:02:23,300 --> 00:02:26,740
+order ال group في حالة ال finite case هذا معناه
+
+25
+00:02:26,740 --> 00:02:35,840
+order ال a بيقسم ال 24 وبالتالي order ال a يا 1 يا
+
+26
+00:02:35,840 --> 00:02:47,310
+2 يا 3 يا 4 يا 6 يا 8 يا 12 يا 24 نقدر نرفض
+
+27
+00:02:47,310 --> 00:02:51,610
+بعضهم since
+
+28
+00:02:51,610 --> 00:02:59,330
+أن ال a أس 8 لا يساوي ال identity هذا معناه order
+
+29
+00:02:59,330 --> 00:03:04,550
+ال a لا يساوي 1 لا يساوي 2 لا يساوي 4
+
+30
+00:03:04,550 --> 00:03:11,310
+ولا يساوي 8 نشطب ال 1 نشطب ال 2 نشطب
+
+31
+00:03:11,310 --> 00:03:21,130
+ال 4 نشطب ال 8 نفس الفكرة also ال a أس 12 لا
+
+32
+00:03:21,130 --> 00:03:27,550
+يساوي ال identity معناه order ال a لا يساوي 3
+
+33
+00:03:27,550 --> 00:03:34,870
+ولا يساوي 6 ولا يساوي 12 نشطب ال 3 نشطب
+
+34
+00:03:34,870 --> 00:03:38,290
+ال 6 نشطب ال 12 ايش حيضل عندك؟ 24
+
+35
+00:03:38,290 --> 00:03:42,690
+وبالتالي order ال a بدها تساوي 24 اللي هو
+
+36
+00:03:42,690 --> 00:03:52,600
+order ال g يكبر جيه الانصار
+
+37
+00:03:52,600 --> 00:03:57,140
+اللي اسمه a موجود في الجروب g اللي هي cyclic و
+
+38
+00:03:57,140 --> 00:04:02,610
+هي finite هي group ال order لها 24 يكبر order ل a
+
+39
+00:04:02,610 --> 00:04:06,530
+بيخسم ال 24 يكبر يا 1 يا 2 يا 3 يا 4
+
+40
+00:04:06,530 --> 00:04:09,890
+يا 6 يا 8 يا 12 يا 24 هيجيت ال a
+
+41
+00:04:09,890 --> 00:04:12,450
+وال 8 وال a وال 12 لا يساوي ال identity
+
+42
+00:04:12,450 --> 00:04:15,990
+بستثني ال 1 وال 2 وال 4 وال 8 في
+
+43
+00:04:15,990 --> 00:04:19,790
+الأول بعدين بستثني ال 3 وال 6 وال 12 من
+
+44
+00:04:19,790 --> 00:04:27,610
+حيضلان دي خلص السؤال السؤال
+
+45
+00:04:27,610 --> 00:04:33,840
+ال 22 Any group of order 3 must be cyclic هذا
+
+46
+00:04:33,840 --> 00:04:36,680
+هيناخد له تعميمات في chapter 7 لما ناخد ال grand
+
+47
+00:04:36,680 --> 00:04:41,300
+theorem أن أي group of prime order لازم تكون
+
+48
+00:04:41,300 --> 00:04:48,020
+cyclic لو كان ال g ال order إيه لها 3 ف g is
+
+49
+00:04:48,020 --> 00:04:50,700
+cyclic
+
+50
+00:05:00,270 --> 00:05:09,970
+let g فيها تلت عناصر أكيد واحد منهم مين اخذ
+
+51
+00:05:09,970 --> 00:05:19,870
+ال a اخذ ال b with a لا يساوي ال a a لا يساوي ال b
+
+52
+00:05:19,870 --> 00:05:24,710
+a لا يساوي ال b عشان أقول أنه تلت عناصر أشمللهم
+
+53
+00:05:24,710 --> 00:05:27,090
+distinct مختلفات
+
+54
+00:05:29,800 --> 00:05:36,980
+هذا معناه أن a و b وين هيكون في ال g كم حالة
+
+55
+00:05:36,980 --> 00:05:46,820
+عندك تلاتة cases هذا معناه case واحد أن ال a و b
+
+56
+00:05:46,820 --> 00:05:53,260
+بدا يساوي e لو ال a و b بدا يساوي e يبقى b بدا
+
+57
+00:05:53,260 --> 00:05:58,060
+يساوي ال identity وهذا مستحيل الحالة الثانية
+
+58
+00:06:00,790 --> 00:06:05,990
+إن ال a بيبقى يساوي ال b في هذه الحالة سيصبح ال a
+
+59
+00:06:05,990 --> 00:06:12,270
+بيبقى يساوي ال identity وهذا مستحيل case
+
+60
+00:06:12,270 --> 00:06:19,110
+ثلاثة إن ال a بيبقى يساوي ال identity وبالتالي ال
+
+61
+00:06:19,110 --> 00:06:26,070
+b بيبقى يساوي ال a inverse طبعًا صارت ال g عبارة عن
+
+62
+00:06:26,070 --> 00:06:28,930
+ال identity و a و a inverse
+
+63
+00:06:33,620 --> 00:06:42,040
+cyclics جيناتك ضايق من انتوا يك ب g is cycling
+
+64
+00:06:42,040 --> 00:06:46,000
+وخلص
+
+65
+00:06:46,000 --> 00:07:00,360
+واضح
+
+66
+00:07:00,360 --> 00:07:07,880
+السؤال هذا واضح السؤال هذا طيب سؤال تلاتة وعشرين
+
+67
+00:07:07,880 --> 00:07:12,220
+تكلمنا عنه في سياق الشرح اللي إبن كنت أشرحه في
+
+68
+00:07:12,220 --> 00:07:17,020
+ال chapter بقول لك ال z  ليه عبارة عن ال integers
+
+69
+00:07:17,020 --> 00:07:23,620
+مع الجمع هل كل subgroup من ال z cyclic؟ هل كل
+
+70
+00:07:23,620 --> 00:07:29,260
+subgroup من ال z cyclic؟ لو أخدت h subgroup من ال
+
+71
+00:07:29,260 --> 00:07:32,680
+z ال integers مع الجمع أكيد ال h cyclic
+
+72
+00:07:36,910 --> 00:07:43,350
+ليش؟ since z itself is cyclic مدام ال z is a
+
+73
+00:07:43,350 --> 00:07:47,710
+cyclic group فكل sub group منه ايش هيكون؟ cyclic
+
+74
+00:07:47,710 --> 00:07:53,330
+طبعًا ال h هتكون generated by some element مثلًا m و
+
+75
+00:07:53,330 --> 00:07:59,030
+ال m ينتمي ل z هذا مش معناه هذا معناه هي عبارة
+
+76
+00:07:59,030 --> 00:08:03,930
+عن ال 0 موجب سالب m موجب سالب 2 m موجب
+
+77
+00:08:03,930 --> 00:08:13,230
+سالب 3 m إلخ هذا
+
+78
+00:08:13,230 --> 00:08:16,790
+السؤال
+
+79
+00:08:16,790 --> 00:08:23,010
+23 السؤال 24 find
+
+80
+00:08:23,010 --> 00:08:26,470
+for any element a in any group g prove that أن
+
+81
+00:08:26,470 --> 00:08:30,150
+generated by a is a subgroup من ال centralizer a
+
+82
+00:08:34,580 --> 00:08:43,360
+هذه trivial since a في a بيبقى يساوي a في a يكبر
+
+83
+00:08:43,360 --> 00:08:49,720
+ال a أشملله commute مع نفسه مدام commute مع نفسه
+
+84
+00:08:49,720 --> 00:08:54,440
+يكبر a موجود في ال centralizer لل a يكبر generated
+
+85
+00:08:54,440 --> 00:09:03,060
+by a sub group من ال centralizer وخلص اثبات خلص
+
+86
+00:09:04,830 --> 00:09:09,990
+خلصوها ال 24 بسرعة أربع
+
+87
+00:09:09,990 --> 00:09:15,370
+أسئلة اللي حليناها واضحة، في أي مشكلة فيها؟ في أي
+
+88
+00:09:15,370 --> 00:09:19,110
+مشكلة في الأسئلة اللي حليناها؟ أي نقطة غير مفهومة؟
+
+89
+00:09:24,500 --> 00:09:28,860
+هو يبدأ بالجنرالتر ال a بالساقية هذي السبب بقى
+
+90
+00:09:28,860 --> 00:09:32,520
+تبدأ في answer انت بتاخد a أس 2 بعدين تدبط ان a
+
+91
+00:09:32,520 --> 00:09:38,800
+أس 2 commute مع ال a عارف تلات تسطر ليش تجي ع راسك
+
+92
+00:09:38,800 --> 00:09:42,140
+بعدين كده بدأت ك a أس 2 بساقية مش ال a commute مع
+
+93
+00:09:42,140 --> 00:09:46,480
+نفسه فموجود في ال centralizer تبع نفسه وبعدين
+
+94
+00:09:46,480 --> 00:09:48,960
+موجود في ال centralizer تبع نفسه ال centralizer
+
+95
+00:09:48,960 --> 00:09:53,170
+subgroup فال generated by a هيكون subset من ال
+
+96
+00:09:53,170 --> 00:09:57,490
+centralizer لأنه مدام ال a موجودة يعني فكل powers
+
+97
+00:09:57,490 --> 00:09:58,710
+ال a موجودة يعني
+
+98
+00:10:03,030 --> 00:10:06,690
+سؤال 25 أنا ما طلبتوش لكن هو محلول في الخلف وسهل
+
+99
+00:10:06,690 --> 00:10:12,130
+انت بتشتغل في ال Dn ال Dn عبارة عن جزئين جزء مكونا
+
+100
+00:10:12,130 --> 00:10:16,490
+من n من العناصر بتكون لل cyclic subgroup generated
+
+101
+00:10:16,490 --> 00:10:23,990
+by r 360 على n والجزء الثاني عبارة عن مجموعة من
+
+102
+00:10:23,990 --> 00:10:27,350
+ال reflections اللي ال order لكل واحد اش فيه يساوي
+
+103
+00:10:28,270 --> 00:10:32,210
+2 عندك صحب الجروب ال order اللي هان فلو كان دي
+
+104
+00:10:32,210 --> 00:10:35,350
+يقسم ال n هتلاقي عدد من العناصر ال order اللي هم
+
+105
+00:10:35,350 --> 00:10:40,130
+دي يساوي 2 في ال d بالنسبة لسؤال ستة وعشرين
+
+106
+00:10:40,130 --> 00:10:45,290
+generator ال z قلناهم موجب سالب 1 generator أي
+
+107
+00:10:45,290 --> 00:10:52,390
+group infinite و cyclic هيكون ال a و a inverse
+
+108
+00:10:52,390 --> 00:10:57,850
+يعني في ال z السؤال ستة وعشرين ال z ال generator
+
+109
+00:10:57,850 --> 00:11:02,810
+إليها موجب سالب 1 طب لو كان عندك generated by a
+
+110
+00:11:02,810 --> 00:11:07,710
+و order ال a بدها تساوي ما لا نهاية مين ال generator
+
+111
+00:11:07,710 --> 00:11:15,410
+هان؟ a و a inverse لأنه أصلاً كل .. هنكتشف لاحقًا أن
+
+112
+00:11:15,410 --> 00:11:21,650
+كل cyclic group و infinite هتكون copy من ال z
+
+113
+00:11:22,690 --> 00:11:27,450
+السابع والعشرين ال c star the group of non-zero
+
+114
+00:11:27,450 --> 00:11:31,210
+complex number under multiplication has a cyclic
+
+115
+00:11:31,210 --> 00:11:39,090
+subgroup of order c star عبارة عن اللي هي كل ما
+
+116
+00:11:39,090 --> 00:11:47,330
+عدا ال zero اللي هي ممكن نكتبها زي هيك black c كل
+
+117
+00:11:47,330 --> 00:11:52,780
+ما عدا ال zero مع عملية الضرب هذا ما نثبت أنه موجود
+
+118
+00:11:52,780 --> 00:11:58,300
+فيها cyclic group أو
+
+119
+00:11:58,300 --> 00:12:04,480
+cyclic subgroup في order n لت أن ينتمي لإنه يشغل
+
+120
+00:12:04,480 --> 00:12:09,180
+number بخط
+
+121
+00:12:09,180 --> 00:12:11,080
+complex analysis
+
+122
+00:12:14,570 --> 00:12:19,310
+طيب هيجيت أي polynomial ال coefficient اللي لها من
+
+123
+00:12:19,310 --> 00:12:25,270
+ال c حلولها وين موجودة؟ أي polynomial ال
+
+124
+00:12:25,270 --> 00:12:28,650
+coefficient اللي هي المعاملات تبعتها من ال complex
+
+125
+00:12:28,650 --> 00:12:32,290
+number ال coefficient تبعتها وين؟ أو ال solution 
+
+126
+00:12:32,290 --> 00:12:37,250
+تبعتها وين؟ برضه في الـ complex طبعا هذا سببه أن الـ
+
+127
+00:12:37,250 --> 00:12:41,910
+.. الـ .. الـ .. الـ C مع الضرب و الجمع تملي حاجة
+
+128
+00:12:41,910 --> 00:12:44,810
+احنا بنسميها algebraically closed field of
+
+129
+00:12:44,810 --> 00:12:48,610
+characteristics zero طبعا هو أكمل تقريبا اللي هو
+
+130
+00:12:48,610 --> 00:12:51,370
+أكمل الـ .. الـ .. الـ هيئة الجبرية لأن كل الـ
+
+131
+00:12:51,370 --> 00:12:57,050
+polynomials بتكون محلولة داخله هجيت السؤال أنا بدي
+
+132
+00:12:57,050 --> 00:13:01,730
+أجيب subgroup الـ order L, H, N و تكون cyclic في الـ
+
+133
+00:13:01,730 --> 00:13:07,500
+C فبدي أنصر يولدها the answer يولد هذه الـ subgroup
+
+134
+00:13:07,500 --> 00:13:14,040
+طبعا consider the
+
+135
+00:13:14,040 --> 00:13:23,380
+equation x to n بساوي واحد هذه
+
+136
+00:13:23,380 --> 00:13:29,840
+المعادلة we know that
+
+137
+00:13:29,840 --> 00:13:33,380
+this equation
+
+138
+00:13:35,180 --> 00:13:43,600
+أو the solution أو the roots of this أو of this
+
+139
+00:13:43,600 --> 00:13:50,060
+polynomial أو equation are
+
+140
+00:13:50,060 --> 00:14:01,200
+all lies in C ولا
+
+141
+00:14:01,200 --> 00:14:04,240
+واحد منهم يساوي Zero none
+
+142
+00:14:06,700 --> 00:14:16,400
+of them is zero ولا واحد منهم
+
+143
+00:14:16,400 --> 00:14:28,660
+ساوي صفر let a,n بكل الـ X في الـ C اللي X أس N بده
+
+144
+00:14:28,660 --> 00:14:29,280
+يساوي واحد
+
+145
+00:14:36,570 --> 00:14:41,190
+بتعلم معايا احنا هن في الـ C و لو واحد منهم صفر
+
+146
+00:14:41,190 --> 00:14:49,150
+فأول هنتقل للـ C star using the
+
+147
+00:14:49,150 --> 00:14:53,610
+concepts of
+
+148
+00:14:53,610 --> 00:14:59,830
+complex analysis we
+
+149
+00:14:59,830 --> 00:15:02,870
+can write
+
+150
+00:15:04,970 --> 00:15:12,650
+الآن عبارة عن الواحد و و تغبيه لأن و أس n ماينس
+
+151
+00:15:12,650 --> 00:15:17,110
+واحد where
+
+152
+00:15:17,110 --> 00:15:20,210
+و
+
+153
+00:15:20,210 --> 00:15:23,710
+is a primitive root
+
+154
+00:15:34,970 --> 00:15:45,650
+of unity primitive and root of unity طبعا
+
+155
+00:15:45,650 --> 00:15:48,650
+لو رجعت للـ complex analysis احنا بتعرف أن هذه
+
+156
+00:15:48,650 --> 00:15:53,210
+المعادلة كيف بنحلها هنا x اثنان بدي يساوي واحد أو
+
+157
+00:15:53,210 --> 00:15:55,250
+أنا بدي أحل المعادلة اللي عبارة عن z اثنان بدي
+
+158
+00:15:55,250 --> 00:15:59,670
+يساوي واحد بروح بجيب الواحد على شكل اللي هو الـ الـ
+
+159
+00:15:59,670 --> 00:16:04,330
+polar form و بتطلع الـ theta تبعته صفر فبجمع صفر
+
+160
+00:16:04,330 --> 00:16:12,130
+زاد اثنين k πاي على n ف الـ w عبارة عن اللي هو
+
+161
+00:16:12,130 --> 00:16:22,010
+cosine اثنين πاي على n زائد i sin 2pi على n هذا من
+
+162
+00:16:22,010 --> 00:16:27,970
+الـ complex analysis هيتلاحظ أن باقي العناصر عبارة
+
+163
+00:16:27,970 --> 00:16:31,890
+عن مين هنا
+
+164
+00:16:31,890 --> 00:16:41,370
+unity النتيجة أن a n generated by w
+
+165
+00:16:46,100 --> 00:16:53,520
+and since w أُس n بدأت تساوي واحد طبعا لما أبدأ
+
+166
+00:16:53,520 --> 00:16:59,920
+أجي أكمل أجيب w أُس n هترجع لمين للواحد w أُس n
+
+167
+00:16:59,920 --> 00:17:04,240
+زائد الواحد هتروح لمين للـ w بعدين الـ powers تبعين
+
+168
+00:17:04,240 --> 00:17:14,260
+الـ w بصير اشمالهم يتكرر النتيجة أن subgroup من
+
+169
+00:17:14,260 --> 00:17:18,080
+الـ black sea تبعا black sea لما أشهد منصة صفر ده
+
+170
+00:17:18,080 --> 00:17:27,840
+C star و الـ order لأن بدي يساوي n and n is
+
+171
+00:17:27,840 --> 00:17:34,860
+cyclic مشكلة هنا أن اللي بدأ يجيح حل السؤال يكون
+
+172
+00:17:34,860 --> 00:17:40,320
+عنده خلفية عن الـ complex analysisلأ لأ مش .. هذه
+
+173
+00:17:40,320 --> 00:17:44,400
+القاعدة أنت خدتها في الثانوية المعادلة اللي هي كيف
+
+174
+00:17:44,400 --> 00:17:47,760
+.. كيف .. كيف كنت تجيب جذور الـ .. الـ .. الـ
+
+175
+00:17:47,760 --> 00:17:54,440
+الواحد الصحيح الـ .. الواحد الصحيح هو بده إجاوب أو
+
+176
+00:17:54,440 --> 00:17:59,580
+صرف إجاوب الـ order لها فاشتغلت علي هذه المعادلة أنا
+
+177
+00:17:59,580 --> 00:18:04,440
+مش هقدر أخد أنصر عشوائي و أضل أرفع فيه الأساس و
+
+178
+00:18:04,440 --> 00:18:08,740
+بعدين أجيبه بواحد إلا لما أكون عارف واحد معين بعرف
+
+179
+00:18:08,740 --> 00:18:18,920
+أنه لما بعرفه هو لأنه بيعطيني واحد عشو
+
+180
+00:18:18,920 --> 00:18:28,090
+فيه بعد 27؟ أو 26؟ 27؟ عندي سؤال تسعة و عشرين list
+
+181
+00:18:28,090 --> 00:18:33,550
+all the elements of O أخضر ثمانية إن زد ثمانتلاف
+
+182
+00:18:33,550 --> 00:18:37,130
+محلول .. محلول السؤال هذا ورا تحلي السؤال اللي
+
+183
+00:18:37,130 --> 00:18:42,700
+بعده أو حتى لو مش ثمانية و ثمانية تريليون نفس الفكرة
+
+184
+00:18:42,700 --> 00:18:47,080
+list all elements of order ثمانية عشان تشتغل على
+
+185
+00:18:47,080 --> 00:18:50,700
+order ثمانية بدك تجيب واحد الـ order له ثمانية و
+
+186
+00:18:50,700 --> 00:18:52,600
+تكمل بعد هيك عشان تشتغل عشان تشتغل عشان تشتغل عشان
+
+187
+00:18:52,600 --> 00:18:53,280
+تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل
+
+188
+00:18:53,280 --> 00:18:54,720
+عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان
+
+189
+00:18:54,720 --> 00:18:54,980
+تشتغل عشان تشتغل عشان تشتغل عشان تشتغل عشان تشتغل
+
+190
+00:18:54,980 --> 00:19:01,340
+عشان تشتغل عشان تشتغل عشان تشتغل
+
+191
+00:19:03,140 --> 00:19:07,240
+بتجيب واحد منهم اللي هو عبارة عن واحد قص ثمانية
+
+192
+00:19:07,240 --> 00:19:11,040
+مليون ع ثمانية يعني واحد قص مليون عن المليون بترفع
+
+193
+00:19:11,040 --> 00:19:13,880
+على القصص اللي بتكون relative to prime ع ثمانية
+
+194
+00:19:13,880 --> 00:19:18,300
+واحد و ثلاثة و خمسة و سبعة فهي الأرقام اللي أو
+
+195
+00:19:18,300 --> 00:19:21,440
+العناصر اللي في زيد ثمانية مليون اللي الـ order
+
+196
+00:19:21,440 --> 00:19:24,180
+اللي ثمانية هتكون المليون و الثلاثة مليون و الخمسة
+
+197
+00:19:24,180 --> 00:19:29,770
+مليون و السبعة مليون نفس الفكرة لو كان الـ .. الـ
+
+198
+00:19:29,770 --> 00:19:33,230
+يعني copy من الـ z ثمانية مليون generated by a و الـ
+
+199
+00:19:33,230 --> 00:19:38,250
+order لـ a ثمانية مليون هل السؤال ثلاثين؟ ساعات
+
+200
+00:19:38,250 --> 00:19:42,290
+عشرين بتقول ساعات عشرين أحله بحله مع أنه سهل يعني
+
+201
+00:19:42,290 --> 00:19:45,610
+بدك
+
+202
+00:19:45,610 --> 00:19:49,830
+الـ .. الـ .. الـ order للـ a بيبقى تساوي ثمانية و a
+
+203
+00:19:49,830 --> 00:19:57,430
+ينتمي لـ z ثمانية مليون أول شيء ده number
+
+204
+00:20:00,790 --> 00:20:11,490
+of elements in زد ثمانية مليون with order ثمانية
+
+205
+00:20:11,490 --> 00:20:16,530
+is five ثمانية له بيساوي أربعة because أو since
+
+206
+00:20:16,530 --> 00:20:26,110
+the group is cyclic to find one of them
+
+207
+00:20:32,650 --> 00:20:42,450
+we have that واحد اص ثمانية مليون على ثمانية اللي
+
+208
+00:20:42,450 --> 00:20:53,590
+واحد اص مليون اللي عبارة عن مليون has order ثمانية
+
+209
+00:20:53,590 --> 00:20:57,130
+sure
+
+210
+00:20:59,400 --> 00:21:05,520
+هو بده الارض بده العناصر بلاش أخدها إيه وهنا بقولك
+
+211
+00:21:05,520 --> 00:21:11,040
+find الارض على بيبن ساوة ثمانية و الـ b ينتمي بزية
+
+212
+00:21:11,040 --> 00:21:15,460
+ثمانية مليون اوجد العناصر b اللي الارض أغلى
+
+213
+00:21:15,460 --> 00:21:18,720
+ثمانية بزية ثمانية مليون باقي العناصر هالجيتها
+
+214
+00:21:18,720 --> 00:21:26,560
+شهدكون these
+
+215
+00:21:26,560 --> 00:21:27,060
+elements
+
+216
+00:21:33,300 --> 00:21:46,100
+R مليون أس واحد مليون أس ثلاثة مليون أس خمسة و
+
+217
+00:21:46,100 --> 00:21:52,960
+مليون و السبعة اللي هما يبقى عن المليون و الثلاثة
+
+218
+00:21:52,960 --> 00:21:58,720
+مليون و الخمسة مليون و السبعة مليون
+
+219
+00:22:02,150 --> 00:22:05,190
+طب أنت تكمل السؤال بنفس الطريقة بس بدل الواحد مش
+
+220
+00:22:05,190 --> 00:22:10,650
+هتاخد A فهيصير A أُس مليون A أُس ثلاثة مليون A أُس
+
+221
+00:22:10,650 --> 00:22:16,290
+خمسة مليون أو A أُس سبعة مليون سؤال
+
+222
+00:22:16,290 --> 00:22:20,810
+ثلاثين order
+
+223
+00:22:20,810 --> 00:22:32,300
+الـ A قد تنين N زي الواحد و A B A inverse بيساوي P
+
+224
+00:22:32,300 --> 00:22:38,240
+inverse show that P
+
+225
+00:22:38,240 --> 00:22:45,800
+تربيع بيساوي الـ identity السؤال
+
+226
+00:22:45,800 --> 00:22:48,160
+الثلاثين سؤال حلو بيشغل
+
+227
+00:23:26,320 --> 00:23:32,360
+عشان أقول أن الـ P تربيع بدي يساوي الـ identity لازم
+
+228
+00:23:32,360 --> 00:23:40,180
+أطلع الـ P من العلاقة اللي قدامك يعني P A في B في A
+
+229
+00:23:40,180 --> 00:23:43,920
+inverse بدي يساوي P inverse تعالى نخربش على جدب
+
+230
+00:23:43,920 --> 00:23:47,960
+عشان نعرف كيف نبدأ نحل السؤال عشان يكون الـ P تربيع
+
+231
+00:23:47,960 --> 00:23:52,650
+بدي يساوي الـ identity فP بدي يساوي إيش؟ بإنفارس
+
+232
+00:23:52,650 --> 00:23:56,990
+بإنفارس
+
+233
+00:23:56,990 --> 00:24:00,470
+بإنفارس
+
+234
+00:24:00,470 --> 00:24:05,810
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+235
+00:24:05,810 --> 00:24:09,110
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+236
+00:24:09,110 --> 00:24:09,130
+بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس بإنفارس
+
+237
+00:24:09,130 --> 00:24:16,330
+بإنفارس بإنفارس بإنفارس
+
+238
+00:24:16,330 --> 00:24:19,570
+بإنفارس
+
+239
+00:24:19,570 --> 00:24:27,570
+بـCommute تبقى ده ليه طيب في شفى معضلة لحد تلات ما
+
+240
+00:24:27,570 --> 00:24:32,030
+استعملتوش اللي هو إيش order الـ A بدي يساوي odd لما
+
+241
+00:24:32,030 --> 00:24:35,710
+يكون order الـ A بدي يساوي odd ف generated by الـ A
+
+242
+00:24:35,710 --> 00:24:40,070
+الـ order اللي هي إيش ثاني إيه أن زاد الـ واحد
+
+243
+00:24:40,070 --> 00:24:45,310
+فمعناته generated by الـ A هي نفسها generated by الـ
+
+244
+00:24:45,310 --> 00:24:45,890
+A تربيع
+
+245
+00:24:48,590 --> 00:24:52,770
+طيب لما يكون الـ A P بدي يساوي P A معناته الـ A أنصر
+
+246
+00:24:52,770 --> 00:24:59,670
+وين؟ في الـ centralizer الـ P الـ A أنصر في الـ
+
+247
+00:24:59,670 --> 00:25:03,390
+centralizer الـ P ف generated by الـ A subset من
+
+248
+00:25:03,390 --> 00:25:07,790
+centralizer الـ P طب generated by الـ A هنافسة
+
+249
+00:25:07,790 --> 00:25:14,120
+generated by الـ A تربيع فA تربيع أنصر في الـ
+
+250
+00:25:14,120 --> 00:25:19,100
+centralizer الـ P فأنا لو أثبتت أن A تربيع P بيكون 
+
+251
+00:25:19,100 --> 00:25:22,440
+حصلت
+
+252
+00:25:22,440 --> 00:25:28,940
+المطلوب بس بي .. A تربيع P بيكون حصلت المطلوب بس
+
+253
+00:25:28,940 --> 00:25:32,900
+بي .. A تربيع P بيكون حصلت المطلوب بس بي .. A
+
+254
+00:25:32,900 --> 00:25:33,200
+تربيع P بيكون حصلت المطلوب بيكون حصلت المطلوب
+
+255
+00:25:33,200 --> 00:25:36,880
+بيكون حصلت المطلوب بيكون حصلت المطلوب بيكون حصلت
+
+256
+00:25:36,880 --> 00:25:39,440
+المطلوب بيكون حصلت المطلوب بيكون حصلت المطلوب
+
+257
+00:25:39,440 --> 00:25:47,400
+بيكون حصلعبارة عن A P A inverse لكل inverse اللي
+
+258
+00:25:47,400 --> 00:25:58,980
+يشبه تساوي A P inverse A inverse طيب
+
+259
+00:25:58,980 --> 00:26:07,540
+هذه عبارة عن A A P A inverse في A inverse اللي
+
+260
+00:26:07,540 --> 00:26:13,950
+عبارة عن A P inverse A inverseوبالتالي هذه هي
+
+261
+00:26:13,950 --> 00:26:20,990
+نفسها طبعا أنا بدأت من تحت عشان أفهم نقطة البداية
+
+262
+00:26:20,990 --> 00:26:27,070
+تبعتي مين هي لازم أبدأ بهذه و بهذه هعيد تشكيل الحل
+
+263
+00:26:27,070 --> 00:26:35,850
+و أصل للمطلوب since
+
+264
+00:26:35,850 --> 00:26:39,030
+a
+
+265
+00:26:39,030 --> 00:26:47,890
+p a inverseبدي أسوي P inverse خذ inverse للطرفين A
+
+266
+00:26:47,890 --> 00:26:54,750
+P A inverse بدي تسوي P inverse ولكل inverse هذه
+
+267
+00:26:54,750 --> 00:27:02,170
+هتصير A P inverse A inverse بدي تسوي P
+
+268
+00:27:10,610 --> 00:27:14,950
+طيب خلّيه على جانب اتذكر ايش الكون اللي بنجيبه
+
+269
+00:27:14,950 --> 00:27:21,770
+احنا بنثبت ان a تربيع b a inverse ايش ده تساوي بي
+
+270
+00:27:21,770 --> 00:27:27,730
+بقى دي اي سالب اتنين هقعد
+
+271
+00:27:27,730 --> 00:27:34,330
+امسك ال a تربيع بي a inverse كيف ده تيجيه also a b
+
+272
+00:27:34,330 --> 00:27:38,690
+inverse a inverse ده تساوي مين بي انفرس
+
+273
+00:27:43,670 --> 00:27:51,510
+أنا أنا أخدت A P Inverse A Inverse ماشي
+
+274
+00:27:51,510 --> 00:27:59,530
+هجيت أضرب A A A B A Inverse A Inverse هد يبقى عنين
+
+275
+00:27:59,530 --> 00:28:10,650
+A P Inverse A Inverse الي مين الي B هي فوق هي
+
+276
+00:28:10,650 --> 00:28:17,330
+فوق Pهذه عبارة عن a تربيع بي a سالب اتنين ايش
+
+277
+00:28:17,330 --> 00:28:27,310
+بيساوي بي يعني a تربيع بي بتساوي بي a تربيع ايش
+
+278
+00:28:27,310 --> 00:28:34,030
+يعني a تربيع بي بتساوي بي a تربيع يعني a تربيع
+
+279
+00:28:34,030 --> 00:28:40,430
+ينتمي ل centralizer ال بي وبالتالي generated by ال
+
+280
+00:28:40,430 --> 00:28:52,240
+a تربيعsome group من الـcentralizer الـB Now order
+
+281
+00:28:52,240 --> 00:29:01,040
+الـA بيساوى 2N زي الواحد odd ايش يعني؟
+
+282
+00:29:01,040 --> 00:29:09,030
+ايش يعني؟ يعني generated by الـA تربيعبدي أساوي
+
+283
+00:29:09,030 --> 00:29:14,650
+generated by الـ A أُس common divisor للتانين
+
+284
+00:29:14,650 --> 00:29:22,610
+والتانين N زاد الواحد اللي هو A أُس واحد يعني
+
+285
+00:29:22,610 --> 00:29:28,700
+generated by الـ Aأحنا خدنا قاعدة انه ال generated
+
+286
+00:29:28,700 --> 00:29:32,800
+by a to m هو نفس ال generated by a أصل grease
+
+287
+00:29:32,800 --> 00:29:38,360
+common divisor لm و order ال a حط ال m اتنين و
+
+288
+00:29:38,360 --> 00:29:42,160
+order ال a اتنين n زادي ال واحد هدولة relatively
+
+289
+00:29:42,160 --> 00:29:45,840
+prime فال grease common divisor له مقداش واحد
+
+290
+00:29:45,840 --> 00:29:50,020
+فgenerated by ال a تربيع هي نفس ال generated by ال
+
+291
+00:29:50,020 --> 00:30:00,670
+a طيب اش يعنييعني generated by ال A صارت sub group
+
+292
+00:30:00,670 --> 00:30:08,170
+من مين؟ من ال centralizer ال B إيش يعني؟ يعني AB
+
+293
+00:30:08,170 --> 00:30:22,110
+بدت ساوي PA AB بدت ساوي PA يعني ABA inverse إيش
+
+294
+00:30:22,110 --> 00:30:29,740
+بدت ساوي؟B بس ABA inverse إيش بتساوي أصلا؟ B
+
+295
+00:30:29,740 --> 00:30:34,040
+inverse يعني B inverse بتساوي B و الخلاصة اللي
+
+296
+00:30:34,040 --> 00:30:40,800
+احنا مطلوب نجيبها أنه B تغبيا بتساوي ال identity
+
+297
+00:30:40,800 --> 00:30:44,840
+واضح؟
+
+298
+00:30:44,840 --> 00:30:47,820
+واضح السؤال يا شباب؟
+
+299
+00:31:04,450 --> 00:31:09,130
+بس وقت فيه .. فيه أفكار يعني طلعت كيف فكرنا في حل
+
+300
+00:31:09,130 --> 00:31:13,710
+و بدأنا من وين؟ من اللي مطلوب نثبته، اشتغلنا
+
+301
+00:31:13,710 --> 00:31:17,550
+ووصلنا لمين؟ للشغل اللي المطلوب احنا نشتغل عليها
+
+302
+00:31:17,550 --> 00:31:25,530
+عشان نصلّى المطلوب بصراحة
+
+303
+00:31:25,530 --> 00:31:25,810
+كتب
+
+304
+00:31:45,950 --> 00:31:50,790
+سنة واحدة و تلاتين على السريع بقولك
+
+305
+00:31:50,790 --> 00:31:58,490
+لو كانت ال order لل J مثلا بيساوي M finite بقولك
+
+306
+00:31:58,490 --> 00:32:04,130
+أثبت أنه يوجد يوجد
+
+307
+00:32:04,130 --> 00:32:08,090
+N such that أن A أُس N بدت ساوي ال identity لكل A
+
+308
+00:32:08,090 --> 00:32:14,280
+في ال J طبعا انا بقولكالـ N هي عبارة عن ال least
+
+309
+00:32:14,280 --> 00:32:19,920
+common multiple ل order A حيث A في الـ G مش شغل
+
+310
+00:32:19,920 --> 00:32:26,100
+على هذه القاعدة خد ال N المطلوبة هي least common
+
+311
+00:32:26,100 --> 00:32:31,320
+multiple ل order العناصر الموجودة فين في الـ G
+
+312
+00:32:31,320 --> 00:32:39,380
+سؤال 32 تبع ال lattice 32 33 34 35 تكلمنا عنهم فضل
+
+313
+00:32:41,970 --> 00:32:46,870
+31 يقولك اثبت انه يوجد عدد بترفع كل عناصر الجي الو
+
+314
+00:32:46,870 --> 00:32:51,170
+بيعطيك ال identity انا بقولك العدد هذا هو ال least
+
+315
+00:32:51,170 --> 00:32:58,450
+common multiple لكل ال orders وبالتالي اي عنصر ال
+
+316
+00:32:58,450 --> 00:33:03,120
+n هذا multiple لل order تبعهفلما ترفع ال a to n
+
+317
+00:33:03,120 --> 00:33:08,840
+هسير ال a او order ال a في رقم ال a مع order ال a
+
+318
+00:33:08,840 --> 00:33:11,180
+بيعطيك ال اد ان انت بتخلص الموضوع طبعا انت عشان
+
+319
+00:33:11,180 --> 00:33:14,600
+تشغل في finite case فالعناصر تبعتي ال a finite
+
+320
+00:33:14,600 --> 00:33:21,060
+يعني عددها محدود وال order الها برضه محدود وبتالي
+
+321
+00:33:21,060 --> 00:33:23,980
+انت بتشغل ال least common multiple العدد محدود من
+
+322
+00:33:23,980 --> 00:33:28,600
+العناصر وكل رقم داخل في الحسبة ايضا محدود فالنتيجة
+
+323
+00:33:28,600 --> 00:33:33,570
+ان رقم اللي هيطلع معاك هو رقمأو عدد طبيعي مش هيكون
+
+324
+00:33:33,570 --> 00:33:37,650
+infinity هان واضح؟
+
+325
+00:33:37,650 --> 00:33:41,950
+طب مش نستفيد منه order ال J بسوا M نستفيد منه هان؟
+
+326
+00:33:41,950 --> 00:33:45,710
+لأ يعني المعضلة أن أنت بتشتغل في finite case فكل
+
+327
+00:33:45,710 --> 00:33:59,970
+ال order تبعت ال J الكبير تبعهم M بفطوش ال M طيب
+
+328
+00:33:59,970 --> 00:34:01,670
+سؤال 36 في شغل برضه
+
+329
+00:34:07,140 --> 00:34:18,500
+ثم اثبت ان الـ j عبارة عن union of a proper صحيح
+
+330
+00:34:18,500 --> 00:34:23,500
+بيجيبوا اركزوا على كلمة proper if and only if j is
+
+331
+00:34:23,500 --> 00:34:35,800
+not cyclic اثبت
+
+332
+00:34:35,800 --> 00:34:42,770
+ان الـ jعبارة عن اتحاد proper subgroup if and only
+
+333
+00:34:42,770 --> 00:34:47,650
+if J is not cyclic طب أنا ده الإثبات اتجاهين
+
+334
+00:34:47,650 --> 00:35:01,490
+assume that we can write J عبارة عن union H حيث و H
+
+335
+00:35:01,490 --> 00:35:09,120
+proper subgroup من الـ Jأن احنا بنقدر نكتب ال j
+
+336
+00:35:09,120 --> 00:35:14,960
+على شكل اتحاد ل subgroups عشان انا اميزها خليها
+
+337
+00:35:14,960 --> 00:35:19,400
+أصغر من ال j ل
+
+338
+00:35:19,400 --> 00:35:27,140
+subgroups proper من ال j ايش بدي اثبت انا ان ال j
+
+339
+00:35:27,140 --> 00:35:30,900
+not cyclic كيف بدي استعمل او اي طريقة بدي استعملها
+
+340
+00:35:30,900 --> 00:35:34,800
+ايش افضل طريقة بدي استعملها
+
+341
+00:35:40,760 --> 00:35:46,760
+شباب كيف بنثبت ان الجروب ليس Cyclic نثبت
+
+342
+00:35:46,760 --> 00:35:54,100
+ان ولا عنصر ال order له بيساوي order للجروب طب
+
+343
+00:35:54,100 --> 00:35:58,780
+انت لا تنساش ان ال j finite ال order لل j بيساوي n
+
+344
+00:35:58,780 --> 00:36:07,780
+finite طب هذه العملية سهلة ولا صعبة؟انت بتاخد عنصر
+
+345
+00:36:07,780 --> 00:36:11,840
+عشوائي بتثبت ان ال order إله لا يساوي n مين
+
+346
+00:36:11,840 --> 00:36:14,860
+الأسهل؟
+
+347
+00:36:14,860 --> 00:36:20,540
+مين الأسهل؟ أستعمل الأسطوب المباشر ولا الغير
+
+348
+00:36:20,540 --> 00:36:26,100
+مباشر؟ أستعمل ال direct ولا ال indirect؟ الأسهل
+
+349
+00:36:26,100 --> 00:36:31,020
+هان أستعمل ال indirect assume that
+
+350
+00:36:31,020 --> 00:36:33,940
+J is cyclic
+
+351
+00:36:37,530 --> 00:36:44,250
+هذا معناته ان الـ J is generated by some A هذا
+
+352
+00:36:44,250 --> 00:36:50,090
+معناته الـ A ينتمي للـ J اللي هي ال union لـ H
+
+353
+00:36:50,090 --> 00:36:56,230
+subgroup من الـ J لـ H لأن الـ G عبارة عن اتحاد
+
+354
+00:36:56,230 --> 00:37:00,210
+بربر subgroups والـ A في الـ J يقبل A موجود في
+
+355
+00:37:00,210 --> 00:37:09,130
+الاتحاد هذا معناته الـ A ينتمي ل some H for someH
+
+356
+00:37:09,130 --> 00:37:14,190
+proper subgroup من الجيه ال A عنصر في proper
+
+357
+00:37:14,190 --> 00:37:20,410
+subgroup من جيه من الجيه هذا معناته انه generated
+
+358
+00:37:20,410 --> 00:37:27,790
+by ال A صارت subgroup من مين من ال H مين generated
+
+359
+00:37:27,790 --> 00:37:30,390
+by ال A يا شباب جيه
+
+360
+00:37:36,010 --> 00:37:44,290
+J subgroup من الـH و الـH أصلا subgroup من مين من
+
+361
+00:37:44,290 --> 00:37:52,190
+الـJ صارت الـJ subgroup من بوبر subgroup منها يعني
+
+362
+00:37:52,190 --> 00:37:59,350
+المبنى اللي انت فيه صار جزء من الغرفة تخيل كيف
+
+363
+00:37:59,350 --> 00:38:04,960
+المبنى طيبة صار جزء من الغرفة اللي انت فيها هناطب
+
+364
+00:38:04,960 --> 00:38:10,700
+و الناس اللي برا الغرفة وين موجودين؟ صارت تناقض
+
+365
+00:38:10,700 --> 00:38:16,000
+لإنه حاسيب معاك ال J بوبر sub group من نفسها و هذا
+
+366
+00:38:16,000 --> 00:38:25,400
+مستحيل تناقض contradiction so J is not cyclic
+
+367
+00:38:25,400 --> 00:38:29,660
+و
+
+368
+00:38:29,660 --> 00:38:33,160
+أصلا ال H بوبر صحيح
+
+369
+00:38:39,820 --> 00:38:46,980
+طيب الجزء التاني لسه شوف
+
+370
+00:38:46,980 --> 00:38:53,600
+قارط سؤال كويس احنا بنثبت ان ال J اتحاد مجموعات
+
+371
+00:38:53,600 --> 00:39:00,240
+جزئية proper منها if and only if هي مش cyclic فلو
+
+372
+00:39:00,240 --> 00:39:04,000
+كانت اتحاد ل proper subgroup اثبتت انها مش cyclic
+
+373
+00:39:04,000 --> 00:39:09,370
+لان لو كانت cyclic هسي في مشكلةيقبل جيه not cyclic
+
+374
+00:39:09,370 --> 00:39:16,590
+حاجة تنتج الاتجاه العكسي نقول assume that
+
+375
+00:39:16,590 --> 00:39:26,530
+جيه is not cyclic اش يعني يعني 
+
+376
+00:39:26,530 --> 00:39:34,670
+لكل  a في الـ J generated by الـ a لا يساوي الـ J 
+
+377
+00:39:34,670 --> 00:39:41,380
+يعني generated by الـ A  proper subset من
+
+378
+00:39:41,380 --> 00:39:47,720
+مين؟ من الـ J هذا
+
+379
+00:39:47,720 --> 00:39:55,560
+معناته اتحاد الـ A في الـ J مش 
+
+380
+00:39:55,560 --> 00:40:02,060
+كلهم subset من الـ J فالاتحاد تبعه مش هيكون
+
+381
+00:40:05,460 --> 00:40:10,220
+كل واحد من هدول subset من الـ j فاتحادهم هيظل
+
+382
+00:40:10,220 --> 00:40:16,020
+subset من الـ j طبعا
+
+383
+00:40:16,020 --> 00:40:21,200
+أنا بتكلم عليهم كـ اتحاد كـ set مش كـ subgroup لإن لو
+
+384
+00:40:21,200 --> 00:40:23,780
+عندك two subgroup الاتحاد تبعه مش ضروري يكون
+
+385
+00:40:23,780 --> 00:40:34,740
+subgroup اعطيها واحد now if a في الـ J فـ a ينتمي لـ
+
+386
+00:40:34,740 --> 00:40:41,980
+generated by الـ a فـ a ينتمي للـ union يعني
+
+387
+00:40:41,980 --> 00:40:49,440
+الـ J صارت subset من الـ union و
+
+388
+00:40:49,440 --> 00:40:56,560
+اعطيها اتنين واحد و اتنين هتصير الـ J هي الاتحاد
+
+389
+00:40:59,600 --> 00:41:04,300
+صارت الـ J عبارة عن اتحاد subgroup منها وكل واحدة
+
+390
+00:41:04,300 --> 00:41:13,300
+منهم هدول أشملهم with generated
+
+391
+00:41:13,300 --> 00:41:21,140
+by الـ a is a proper subgroup of
+
+392
+00:41:21,140 --> 00:41:26,700
+J لكل a في الـ J صارت عبارة عن اتحاد proper
+
+393
+00:41:26,700 --> 00:41:27,420
+subgroup
+
+394
+00:41:31,040 --> 00:41:36,440
+واضحة؟ لأن إثبات السؤال لها .. لأ لها .. هذا الـ F
+
+395
+00:41:36,440 --> 00:41:40,000
+and only F لها .. لها .. لها .. لها الـ F و لها الـ
+
+396
+00:41:40,000 --> 00:41:40,480
+only F
+
+397
+00:42:24,110 --> 00:42:28,890
+37 show that the group of positive rational number
+
+398
+00:42:28,890 --> 00:42:37,850
+under multiplication is not cyclic يعني Q+ مع
+
+399
+00:42:37,850 --> 00:42:45,270
+ضرب not cyclic Q
+
+400
+00:42:45,270 --> 00:42:54,070
++ يعني الأعداد النسبية الموجبة هأقول assume الـ
+
+401
+00:42:54,070 --> 00:43:00,750
+Q generated by some a على b with
+
+402
+00:43:00,750 --> 00:43:06,510
+the greatest common divisor لـ a و b بدي يساوي واحد
+
+403
+00:43:06,510 --> 00:43:14,710
+حيث الـ a و الـ b موجودين في الـ initial number طب
+
+404
+00:43:14,710 --> 00:43:19,250
+علشان ماخدتهمش في الـ Z لإن أنا بتعامل مع مين؟ مع
+
+405
+00:43:19,250 --> 00:43:29,550
+positive هي التنين بتساوي a على b قص
+
+406
+00:43:29,550 --> 00:43:39,730
+أن طبعا .. طبعا clearly أن لا يساوي zero لأن
+
+407
+00:43:39,730 --> 00:43:45,710
+التنين لا تساوي a على b قص صفر ليها واحد also
+
+408
+00:43:47,400 --> 00:43:56,140
+if n بدأت تساوي واحد فالتنين بدأت تساوي a على b هذا
+
+409
+00:43:56,140 --> 00:44:06,220
+معناته إن الـ Q* generated by تنين أو
+
+410
+00:44:06,220 --> 00:44:11,000
+Q+ generated by تنين هذا معناته إن التلاتة بدأت
+
+411
+00:44:11,000 --> 00:44:17,610
+تساوي تنين أس m for some m في الـ Z وهذا مستحيل
+
+412
+00:44:17,610 --> 00:44:20,930
+التلاتة
+
+413
+00:44:20,930 --> 00:44:27,910
+تلاتة تساوي power للتنين طيب if n بدأت تساوي سالب واحد
+
+414
+00:44:27,910 --> 00:44:35,730
+يعني الـ a على b بدأت تساوي نص وبالتالي التلاتة بدأت
+
+415
+00:44:35,730 --> 00:44:41,330
+تساوي نص أس m والم من الـ Z يعني التلاتة تبدأ تساوي
+
+416
+00:44:41,330 --> 00:44:47,950
+تنين أس m والم من الـ Z وهذا تناقض يكبي يا صفر
+
+417
+00:44:47,950 --> 00:44:53,270
+ولا واحد ولا سالب واحد يكبي يا أكبر من واحد يا
+
+418
+00:44:53,270 --> 00:45:00,430
+أصغر من سالب واحد if n أكبر من الواحد يكبي اتنين
+
+419
+00:45:00,430 --> 00:45:06,590
+بدأت تساوي a على b أس n بدأت تساوي a أس n على b أس n
+
+420
+00:45:06,590 --> 00:45:13,530
+وبالتالي a أس n بدأت تساوي اتنين b أس n
+
+421
+00:45:17,400 --> 00:45:22,520
+هذا معناته تنين تقسم الـ a أس n وبالتالي تنين تقسم
+
+422
+00:45:22,520 --> 00:45:31,640
+الـ a يكبر a بدأت تساوي تنين k و الـ k من الـ n يكبر
+
+423
+00:45:31,640 --> 00:45:37,280
+اتنين p أس n بدأت تساوي تنين k أس n بدأت تساوي تنين
+
+424
+00:45:37,280 --> 00:45:42,060
+أس n k أس n يكبر p أس n بدأت تساوي تنين n minus
+
+425
+00:45:42,060 --> 00:45:48,600
+واحدك اص ان تنساش ان الان اكبر من الواحد يكبر الان
+
+426
+00:45:48,600 --> 00:45:53,160
+ماينوس الواحد على الاقل واحد يكبر هنا فيه اتنين
+
+427
+00:45:53,160 --> 00:45:57,580
+موجود وبالتالي اتنين تقسم الـ b أس n يكبر اتنين
+
+428
+00:45:57,580 --> 00:46:05,020
+تقسم الـ b اعطي هذه star وهذه double star هيعطيك
+
+429
+00:46:05,020 --> 00:46:10,480
+إن الـ gcd لـ a و b أكبر أو يساوي اتنين
+
+430
+00:46:10,480 --> 00:46:17,140
+وده مستحيل ليش؟ لإن أنا جالي اللي gcd تبعهم
+
+431
+00:46:17,140 --> 00:46:22,640
+زورجات دي إيش؟ واحد طبعا لا صفر ولا واحد ولا أكبر
+
+432
+00:46:22,640 --> 00:46:29,560
+من الواحد ولا سالب واحد إيش بيضال عندي؟ if n أقل
+
+433
+00:46:29,560 --> 00:46:39,860
+من سالب واحد نفس الفكرة هسي معاك a على b أس n بدأت
+
+434
+00:46:39,860 --> 00:46:48,200
+تساوي إيش؟ تنين يعني طبعا الـ N أقل من سلب واحد فسلب
+
+435
+00:46:48,200 --> 00:46:57,420
+الـ N أكبر من الـ واحد معناته A على B طبعا
+
+436
+00:46:57,420 --> 00:47:04,480
+مش هجلبها لغاية هتصير B على A السالب N بدأت تساوي 2
+
+437
+00:47:04,480 --> 00:47:11,440
+وبالتالي B السالب N بدأت تساوي 2 A السالب N
+
+438
+00:47:19,340 --> 00:47:24,340
+يكبر تنين تقسم الـ B والسالب N يكبر تنين تقسم الـ B
+
+439
+00:47:24,340 --> 00:47:30,220
+Similarly تنين
+
+440
+00:47:30,220 --> 00:47:35,260
+هتقسم الـ B والسالب N يكبر تنين هتقسم الـ A وهذا ما
+
+441
+00:47:35,260 --> 00:47:39,140
+هيعطيك تناقض يكبر لا صفر ولا واحد ولا أكبر من
+
+442
+00:47:39,140 --> 00:47:42,880
+الواحد ولا سالب واحد ولا أصغر من سالب واحد مين
+
+443
+00:47:42,880 --> 00:47:47,420
+ضايل؟ So Q
+
+444
+00:47:48,780 --> 00:47:53,720
++ is not cyclic
+
+445
+00:47:53,720 --> 00:47:57,440
+يعطيكم العافية بنجا فان السؤال هذا وحضرة القادمة
+
+446
+00:47:57,440 --> 00:48:02,140
+إن شاء الله هنكمل من سؤال تمانية وتلاتين بس هنحاول
+
+447
+00:48:02,140 --> 00:48:08,080
+إنّه ننهي المناقشة يعني لن مش هحل كل الأسئلة اللي
+
+448
+00:48:08,080 --> 00:48:10,900
+ضايلة مطلوبة هعطيك فقط هنتائج إليها 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f6597b9e9f3d9810554a8587d5c7eca09809ffb7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/C2WK84f79TY_raw.json
@@ -0,0 +1 @@
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{"start": 54.61, "end": 55.13, "word": " في", "probability": 0.86181640625}, {"start": 55.13, "end": 55.41, "word": " فرع", "probability": 0.7630208333333334}, {"start": 55.41, "end": 55.65, "word": " بي", "probability": 0.721435546875}, {"start": 55.65, "end": 55.83, "word": " لو", "probability": 0.798828125}, {"start": 55.83, "end": 56.01, "word": " ال", "probability": 0.93994140625}, {"start": 56.01, "end": 56.23, "word": " a", "probability": 0.93212890625}, {"start": 56.23, "end": 56.65, "word": " تقام", "probability": 0.740234375}, {"start": 56.65, "end": 57.05, "word": " بيساوي", "probability": 0.962890625}, {"start": 57.05, "end": 57.15, "word": " ال", "probability": 0.98681640625}, {"start": 57.15, "end": 57.57, "word": " identity", "probability": 0.93505859375}, {"start": 57.57, "end": 57.85, "word": " what", "probability": 0.9248046875}, {"start": 57.85, "end": 58.19, "word": " can", "probability": 0.95751953125}, {"start": 58.19, "end": 58.41, "word": " we", "probability": 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"word": " واحد", "probability": 0.9853515625}, {"start": 65.61, "end": 65.85, "word": " ان", "probability": 0.46923828125}, {"start": 65.85, "end": 66.37, "word": " order", "probability": 0.7890625}, {"start": 66.37, "end": 66.67, "word": " ال", "probability": 0.6103515625}, {"start": 66.67, "end": 67.07, "word": " a", "probability": 0.8876953125}, {"start": 67.07, "end": 68.41, "word": " في", "probability": 0.75}, {"start": 68.41, "end": 68.79, "word": " الأول", "probability": 0.8857421875}, {"start": 68.79, "end": 69.23, "word": " هيقسم", "probability": 0.7198079427083334}, {"start": 69.23, "end": 69.39, "word": " ال", "probability": 0.5341796875}, {"start": 69.39, "end": 69.95, "word": " 12", "probability": 0.85595703125}, {"start": 69.95, "end": 70.33, "word": " في", "probability": 0.8232421875}, {"start": 70.33, "end": 70.63, "word": " الفرع", "probability": 0.8819986979166666}, {"start": 70.63, "end": 70.93, "word": " a", "probability": 0.80419921875}, {"start": 70.93, "end": 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0.9305419921875}, {"start": 87.01, "end": 87.13, "word": " ال", "probability": 0.95947265625}, {"start": 87.13, "end": 87.57, "word": " identity", "probability": 0.9033203125}, {"start": 87.57, "end": 87.83, "word": " و", "probability": 0.5400390625}, {"start": 87.83, "end": 87.93, "word": " ال", "probability": 0.7890625}, {"start": 87.93, "end": 88.07, "word": " a", "probability": 0.93212890625}, {"start": 88.07, "end": 88.27, "word": " أُس", "probability": 0.9806315104166666}, {"start": 88.27, "end": 88.71, "word": " اتناش", "probability": 0.71148681640625}, {"start": 88.71, "end": 88.91, "word": " لا", "probability": 0.884765625}, {"start": 88.91, "end": 89.51, "word": " يساوي", "probability": 0.9752197265625}, {"start": 89.51, "end": 89.69, "word": " ال", "probability": 0.97998046875}, {"start": 89.69, "end": 90.19, "word": " identity", "probability": 0.94091796875}, {"start": 90.19, "end": 90.87, "word": " show", "probability": 0.8193359375}, {"start": 90.87, "end": 91.39, "word": " that", "probability": 0.9462890625}, {"start": 91.39, "end": 91.73, "word": " ان", "probability": 0.3642578125}, {"start": 91.73, "end": 92.17, "word": " order", "probability": 0.462890625}, {"start": 92.17, "end": 92.45, "word": " ال", "probability": 0.65185546875}, {"start": 92.45, "end": 92.75, "word": " a", "probability": 0.88037109375}, {"start": 92.75, "end": 93.49, "word": " او", "probability": 0.6123046875}, {"start": 93.49, "end": 93.89, "word": " ال", "probability": 0.75244140625}, {"start": 93.89, "end": 94.39, "word": " generated", "probability": 0.440673828125}, {"start": 94.39, "end": 94.67, "word": " by", "probability": 0.97705078125}, {"start": 94.67, "end": 94.87, "word": " a", "probability": 0.93701171875}, {"start": 94.87, "end": 95.23, "word": " هو", "probability": 0.95068359375}, {"start": 95.23, "end": 96.63, "word": " الجيب", "probability": 0.7113444010416666}, {"start": 96.63, "end": 97.31, "word": " فرع", "probability": 0.8141276041666666}, {"start": 97.31, "end": 98.53, "word": " c", "probability": 0.79345703125}, {"start": 98.53, "end": 99.59, "word": " order", "probability": 0.9267578125}, {"start": 99.59, "end": 100.03, "word": " الجيب", "probability": 0.8597005208333334}, {"start": 100.03, "end": 100.49, "word": " يساوي", "probability": 0.9295654296875}, {"start": 100.49, "end": 101.05, "word": " 24", "probability": 0.87158203125}, {"start": 101.05, "end": 102.43, "word": " ال", "probability": 0.343994140625}, {"start": 102.43, "end": 102.65, "word": " a", "probability": 0.97509765625}, {"start": 102.65, "end": 102.85, "word": " أُس", "probability": 0.9396158854166666}, {"start": 102.85, "end": 103.33, "word": " تمانية", "probability": 0.9723307291666666}], "temperature": 1.0}, {"id": 4, "seek": 13274, "start": 104.1, "end": 132.74, "text": "لأ يساوي ال identity و ال a أُس 12 لأ يساوي ال identity طبعا في معلومة أخرى ان ال j is cyclic مدام ال j is cyclic و ال a ينتمي لل j هذا معناته ان order ال a هيقسم order من", "tokens": [1211, 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complex", "probability": 0.88525390625}, {"start": 687.95, "end": 688.41, "word": " number", "probability": 0.8251953125}, {"start": 688.41, "end": 688.87, "word": " under", "probability": 0.837890625}, {"start": 688.87, "end": 690.11, "word": " multiplication", "probability": 0.80224609375}, {"start": 690.11, "end": 690.57, "word": " has", "probability": 0.88623046875}, {"start": 690.57, "end": 690.83, "word": " a", "probability": 0.98193359375}, {"start": 690.83, "end": 691.21, "word": " cyclic", "probability": 0.918212890625}, {"start": 691.21, "end": 691.63, "word": " subgroup", "probability": 0.801513671875}, {"start": 691.63, "end": 691.81, "word": " of", "probability": 0.96142578125}, {"start": 691.81, "end": 692.11, "word": " order", "probability": 0.95556640625}, {"start": 692.11, "end": 692.77, "word": " c", "probability": 0.16845703125}, {"start": 692.77, "end": 694.99, "word": " star", "probability": 0.375244140625}, {"start": 694.99, "end": 696.33, "word": " عبارة", 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26, "seek": 73108, "start": 711.38, "end": 731.08, "text": "هذا ما نثبت أنه موجود فيها Cyclic group أو Cyclic subgroup في أوردر n لت ان ينتمي لإنه يشغل number بخط Complex analysis", "tokens": [3224, 15730, 19446, 8717, 12984, 3555, 2655, 14739, 3224, 3714, 29245, 23328, 8978, 11296, 10295, 66, 1050, 1594, 34051, 10295, 66, 1050, 1422, 17377, 8978, 5551, 13063, 3215, 2288, 297, 5296, 2655, 16472, 7251, 29399, 2304, 1829, 5296, 28814, 1863, 3224, 7251, 8592, 17082, 1211, 1230, 4724, 9778, 9566, 41184, 5215], "avg_logprob": -0.4332932634995534, "compression_ratio": 1.198581560283688, "no_speech_prob": 0.0, "words": [{"start": 711.38, "end": 711.74, "word": "هذا", "probability": 0.7353515625}, {"start": 711.74, "end": 711.84, "word": " ما", "probability": 0.09747314453125}, {"start": 711.84, "end": 712.2, "word": " نثبت", "probability": 0.9263916015625}, {"start": 712.2, "end": 712.4, "word": " أنه", "probability": 0.7091064453125}, {"start": 712.4, "end": 712.78, "word": " موجود", 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the concepts of complex analysis we can write", "tokens": [3555, 2655, 3615, 19528, 20449, 995, 25528, 1975, 5016, 8315, 8032, 1863, 6156, 7578, 2423, 383, 4032, 45164, 36764, 24401, 9154, 16095, 20328, 5172, 2288, 6156, 10721, 12610, 8032, 29399, 4587, 1211, 24976, 383, 3543, 1228, 264, 10392, 295, 3997, 5215, 321, 393, 2464], "avg_logprob": -0.2996527724795871, "compression_ratio": 1.1798561151079137, "no_speech_prob": 0.0, "words": [{"start": 876.57, "end": 876.85, "word": "بتعلم", "probability": 0.750244140625}, {"start": 876.85, "end": 877.33, "word": " معايا", "probability": 0.9339192708333334}, {"start": 877.33, "end": 878.69, "word": " احنا", "probability": 0.8326822916666666}, {"start": 878.69, "end": 878.85, "word": " هن", "probability": 0.595458984375}, {"start": 878.85, "end": 878.97, "word": " فى", "probability": 0.57147216796875}, {"start": 878.97, "end": 879.11, "word": " ال", "probability": 0.919921875}, {"start": 879.11, "end": 879.35, "word": " C", "probability": 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1117.59, "text": "عندي سؤال تسعة و عشرين list all the elements of O أخضر تمانية ان زد تمانتلاف محلول .. محلول السؤال هذا ورا تحلي السؤال اللي بعده", "tokens": [3615, 1863, 16254, 8608, 33604, 6027, 6055, 3794, 27884, 4032, 6225, 46309, 9957, 1329, 439, 264, 4959, 295, 422, 5551, 9778, 11242, 2288, 46811, 7649, 10632, 16472, 30767, 3215, 46811, 7649, 2655, 15040, 5172, 3714, 5016, 1211, 12610, 4386, 3714, 5016, 1211, 12610, 21136, 33604, 6027, 23758, 4032, 23557, 6055, 5016, 20292, 21136, 33604, 6027, 13672, 1829, 39182, 3224], "avg_logprob": -0.2135416644314925, "compression_ratio": 1.4246575342465753, "no_speech_prob": 0.0, "words": [{"start": 1104.45, "end": 1104.91, "word": "عندي", "probability": 0.8714192708333334}, {"start": 1104.91, "end": 1105.35, "word": " سؤال", "probability": 0.9951171875}, {"start": 1105.35, "end": 1105.83, "word": " تسعة", "probability": 0.8951822916666666}, {"start": 1105.83, "end": 1105.97, "word": " و", "probability": 0.96923828125}, {"start": 1105.97, 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0.564453125}, {"start": 2018.05, "end": 2018.55, "word": " نستفيد", "probability": 0.83087158203125}, {"start": 2018.55, "end": 2018.85, "word": " منه", "probability": 0.825927734375}, {"start": 2018.85, "end": 2019.17, "word": " order", "probability": 0.857421875}, {"start": 2019.17, "end": 2019.45, "word": " ال", "probability": 0.44140625}, {"start": 2019.45, "end": 2019.47, "word": " J", "probability": 0.2108154296875}, {"start": 2019.47, "end": 2019.79, "word": " بسوا", "probability": 0.5995279947916666}, {"start": 2019.79, "end": 2020.01, "word": " M", "probability": 0.29443359375}, {"start": 2020.01, "end": 2020.49, "word": " نستفيد", "probability": 0.8917236328125}, {"start": 2020.49, "end": 2020.75, "word": " منه", "probability": 0.858642578125}, {"start": 2020.75, "end": 2021.95, "word": " هان؟", "probability": 0.6766764322916666}, {"start": 2021.95, "end": 2022.21, "word": " لأ", "probability": 0.951416015625}, {"start": 2022.21, "end": 2022.53, "word": " يعني", "probability": 0.6763916015625}, {"start": 2022.53, "end": 2023.01, "word": " المعضلة", "probability": 0.766845703125}, {"start": 2023.01, "end": 2023.17, "word": " أن", "probability": 0.626953125}, {"start": 2023.17, "end": 2023.47, "word": " أنت", "probability": 0.68701171875}, {"start": 2023.47, "end": 2023.87, "word": " بتشتغل", "probability": 0.917578125}, {"start": 2023.87, "end": 2024.03, "word": " في", "probability": 0.7763671875}, {"start": 2024.03, "end": 2024.39, "word": " finite", "probability": 0.42041015625}, {"start": 2024.39, "end": 2024.87, "word": " case", "probability": 0.9619140625}, {"start": 2024.87, "end": 2025.71, "word": " فكل", "probability": 0.970703125}, {"start": 2025.71, "end": 2025.85, "word": " ال", "probability": 0.8076171875}, {"start": 2025.85, "end": 2026.23, "word": " order", "probability": 0.96875}, {"start": 2026.23, "end": 2026.69, "word": " تبعت", "probability": 0.6927083333333334}, {"start": 2026.69, "end": 2026.85, "word": " ال", "probability": 0.8505859375}, {"start": 2026.85, "end": 2027.11, "word": " J", "probability": 0.9560546875}, {"start": 2027.11, "end": 2027.97, "word": " الكبير", "probability": 0.84716796875}, {"start": 2027.97, "end": 2028.35, "word": " تبعهم", "probability": 0.83941650390625}, {"start": 2028.35, "end": 2028.61, "word": " M", "probability": 0.99169921875}, {"start": 2028.61, "end": 2031.05, "word": " بفطوش", "probability": 0.701318359375}, {"start": 2031.05, "end": 2031.19, "word": " ال", "probability": 0.9697265625}, {"start": 2031.19, "end": 2033.47, "word": " M", "probability": 0.9912109375}, {"start": 2033.47, "end": 2039.97, "word": " طيب", "probability": 0.9005533854166666}, {"start": 2039.97, "end": 2040.21, "word": " سؤال", "probability": 0.8343098958333334}, {"start": 2040.21, "end": 2040.65, "word": " 36", "probability": 0.56982421875}, {"start": 2040.65, "end": 2040.97, "word": " في", "probability": 0.955078125}, {"start": 2040.97, "end": 2041.31, "word": " شغل", "probability": 0.9231770833333334}, {"start": 2041.31, "end": 2041.67, "word": " برضه", "probability": 0.9931640625}], "temperature": 1.0}, {"id": 73, "seek": 207623, "start": 2047.14, "end": 2076.24, "text": "ثم اثبت ان الـ j عبارة عن union of a proper صحيح بيجيبوا اركزوا على كلمة proper if and only if j is not cyclic اثبت ان الـ j", "tokens": [12984, 2304, 1975, 12984, 3555, 2655, 16472, 2423, 39184, 361, 6225, 3555, 9640, 3660, 18871, 11671, 295, 257, 2296, 20328, 5016, 1829, 5016, 4724, 1829, 7435, 1829, 3555, 14407, 1975, 31747, 11622, 14407, 15844, 9122, 19528, 3660, 2296, 498, 293, 787, 498, 361, 307, 406, 38154, 1050, 1975, 12984, 3555, 2655, 16472, 2423, 39184, 361], "avg_logprob": -0.36523436329194475, "compression_ratio": 1.3257575757575757, "no_speech_prob": 0.0, "words": [{"start": 2047.14, "end": 2047.42, "word": "ثم", "probability": 0.52142333984375}, {"start": 2047.42, "end": 2047.92, "word": " اثبت", "probability": 0.8662109375}, {"start": 2047.92, "end": 2048.06, "word": " ان", "probability": 0.84619140625}, {"start": 2048.06, "end": 2048.24, "word": " الـ", "probability": 0.606201171875}, {"start": 2048.24, "end": 2048.38, "word": " j", "probability": 0.35791015625}, {"start": 2048.38, "end": 2050.96, "word": " عبارة", "probability": 0.81634521484375}, {"start": 2050.96, "end": 2051.78, "word": " عن", "probability": 0.99658203125}, {"start": 2051.78, "end": 2053.2, "word": " union", "probability": 0.84716796875}, {"start": 2053.2, "end": 2054.26, "word": " of", "probability": 0.8564453125}, {"start": 2054.26, "end": 2054.42, "word": " a", "probability": 0.765625}, {"start": 2054.42, "end": 2054.74, "word": " proper", "probability": 0.1810302734375}, {"start": 2054.74, "end": 2058.5, "word": " صحيح", "probability": 0.56817626953125}, {"start": 2058.5, "end": 2058.78, "word": " بيجيبوا", "probability": 0.6500244140625}, {"start": 2058.78, "end": 2059.2, "word": " اركزوا", "probability": 0.720916748046875}, {"start": 2059.2, "end": 2059.28, "word": " على", "probability": 0.609375}, {"start": 2059.28, "end": 2059.56, "word": " كلمة", "probability": 0.9650065104166666}, {"start": 2059.56, "end": 2059.9, "word": " proper", "probability": 0.9130859375}, {"start": 2059.9, "end": 2061.32, "word": " if", "probability": 0.83056640625}, {"start": 2061.32, "end": 2061.64, "word": " and", "probability": 0.94091796875}, {"start": 2061.64, "end": 2061.94, "word": " only", "probability": 0.89990234375}, {"start": 2061.94, "end": 2062.32, "word": " if", "probability": 0.96875}, {"start": 2062.32, "end": 2062.86, "word": " j", "probability": 0.423583984375}, {"start": 2062.86, "end": 2063.5, "word": " is", "probability": 0.9423828125}, {"start": 2063.5, "end": 2065.28, "word": " not", "probability": 0.951171875}, {"start": 2065.28, "end": 2066.58, "word": " cyclic", "probability": 0.6458740234375}, {"start": 2066.58, "end": 2075.8, "word": " اثبت", "probability": 0.93310546875}, {"start": 2075.8, "end": 2075.92, "word": " ان", 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{"start": 2077.71, "end": 2077.89, "word": " عن", "probability": 0.9755859375}, {"start": 2077.89, "end": 2078.85, "word": " اتحاد", "probability": 0.9591064453125}, {"start": 2078.85, "end": 2081.13, "word": " proper", "probability": 0.400390625}, {"start": 2081.13, "end": 2081.89, "word": " subgroup", "probability": 0.811279296875}, {"start": 2081.89, "end": 2082.17, "word": " if", "probability": 0.818359375}, {"start": 2082.17, "end": 2082.45, "word": " and", "probability": 0.8984375}, {"start": 2082.45, "end": 2082.77, "word": " only", "probability": 0.89892578125}, {"start": 2082.77, "end": 2083.11, "word": " if", "probability": 0.97314453125}, {"start": 2083.11, "end": 2083.41, "word": " J", "probability": 0.323486328125}, {"start": 2083.41, "end": 2083.67, "word": " is", "probability": 0.91162109375}, {"start": 2083.67, "end": 2083.91, "word": " not", "probability": 0.9404296875}, {"start": 2083.91, "end": 2084.47, "word": " cyclic", "probability": 0.904052734375}, {"start": 2084.47, "end": 2084.81, "word": " طب", "probability": 0.9140625}, {"start": 2084.81, "end": 2084.93, "word": " أنا", "probability": 0.55029296875}, {"start": 2084.93, "end": 2085.09, "word": " ده", "probability": 0.657470703125}, {"start": 2085.09, "end": 2085.89, "word": " الإثبات", "probability": 0.79302978515625}, {"start": 2085.89, "end": 2087.65, "word": " اتجاهين", "probability": 0.95595703125}, {"start": 2087.65, "end": 2088.79, "word": " assume", "probability": 0.58349609375}, {"start": 2088.79, "end": 2091.17, "word": " that", "probability": 0.9130859375}, {"start": 2091.17, "end": 2092.77, "word": " we", "probability": 0.8955078125}, {"start": 2092.77, "end": 2093.25, "word": " can", "probability": 0.97119140625}, {"start": 2093.25, "end": 2094.95, "word": " write", "probability": 0.95556640625}, {"start": 2094.95, "end": 2096.29, "word": " J", "probability": 0.861328125}, {"start": 2096.29, "end": 2097.15, "word": " بارة", "probability": 0.796875}, {"start": 2097.15, "end": 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subgroups عشان انا اميزها خليها اصغر من ال j ل subgroups proper من ال j ايش بدي اثبت انا ان ال j not cyclic كيف بدي استعمل او اي طريقة بدي استعملها ايش افضل طريقة بدي استعملها", "tokens": [7649, 1975, 5016, 8315, 44945, 28543, 2288, 8717, 4117, 2655, 3555, 2423, 361, 15844, 13412, 28820, 1975, 2655, 5016, 18513, 5296, 1422, 17377, 82, 6225, 8592, 7649, 1975, 8315, 1975, 2304, 1829, 11622, 11296, 16490, 20292, 11296, 1975, 9381, 17082, 2288, 9154, 2423, 361, 5296, 1422, 17377, 82, 2296, 9154, 2423, 361, 1975, 1829, 8592, 4724, 16254, 1975, 12984, 3555, 2655, 1975, 8315, 16472, 2423, 361, 406, 38154, 1050, 9122, 33911, 4724, 16254, 44713, 25957, 1211, 1975, 2407, 1975, 1829, 23032, 16572, 28671, 4724, 16254, 44713, 25957, 1211, 11296, 1975, 1829, 8592, 1975, 5172, 11242, 1211, 23032, 16572, 28671, 4724, 16254, 44713, 25957, 1211, 11296], "avg_logprob": -0.164504718246325, "compression_ratio": 1.8556149732620322, "no_speech_prob": 0.0, "words": [{"start": 2107.52, "end": 2107.74, "word": 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0.9287109375}, {"start": 2122.48, "end": 2123.96, "word": " ايش", "probability": 0.8076171875}, {"start": 2123.96, "end": 2124.12, "word": " بدي", "probability": 0.6375732421875}, {"start": 2124.12, "end": 2124.48, "word": " اثبت", "probability": 0.9639892578125}, {"start": 2124.48, "end": 2124.78, "word": " انا", "probability": 0.85546875}, {"start": 2124.78, "end": 2126.64, "word": " ان", "probability": 0.8837890625}, {"start": 2126.64, "end": 2126.82, "word": " ال", "probability": 0.88720703125}, {"start": 2126.82, "end": 2127.14, "word": " j", "probability": 0.9169921875}, {"start": 2127.14, "end": 2127.96, "word": " not", "probability": 0.59228515625}, {"start": 2127.96, "end": 2128.42, "word": " cyclic", "probability": 0.8583984375}, {"start": 2128.42, "end": 2128.66, "word": " كيف", "probability": 0.899169921875}, {"start": 2128.66, "end": 2128.78, "word": " بدي", "probability": 0.792236328125}, {"start": 2128.78, "end": 2129.32, "word": " استعمل", "probability": 0.80908203125}, {"start": 2129.32, "end": 2129.78, "word": " او", "probability": 0.85107421875}, {"start": 2129.78, "end": 2129.92, "word": " اي", "probability": 0.93212890625}, {"start": 2129.92, "end": 2130.2, "word": " طريقة", "probability": 0.99169921875}, {"start": 2130.2, "end": 2130.34, "word": " بدي", "probability": 0.958740234375}, {"start": 2130.34, "end": 2130.9, "word": " استعملها", "probability": 0.93994140625}, {"start": 2130.9, "end": 2133.46, "word": " ايش", "probability": 0.8968098958333334}, {"start": 2133.46, "end": 2133.76, "word": " افضل", "probability": 0.92138671875}, {"start": 2133.76, "end": 2134.1, "word": " طريقة", "probability": 0.9952799479166666}, {"start": 2134.1, "end": 2134.24, "word": " بدي", "probability": 0.79150390625}, {"start": 2134.24, "end": 2134.8, "word": " استعملها", "probability": 0.973388671875}], "temperature": 1.0}, {"id": 76, "seek": 216464, "start": 2140.76, "end": 2164.64, "text": "شباب كيف بنثبت ان الجروب ليس Cyclic نثبت ان ولا عنصر ال order له بيساوي order للجروب طب انت لا تنساش ان ال j finite ال order لل j بيساوي n finite طب هذه العملية سهلة ولا صعبة؟", "tokens": [8592, 3555, 16758, 9122, 33911, 44945, 12984, 3555, 2655, 16472, 25724, 32887, 3555, 32239, 3794, 10295, 66, 1050, 8717, 12984, 3555, 2655, 16472, 49429, 18871, 9381, 2288, 2423, 1668, 46740, 4724, 1829, 3794, 995, 45865, 1668, 24976, 7435, 32887, 3555, 23032, 3555, 16472, 2655, 20193, 6055, 1863, 3794, 33599, 16472, 2423, 361, 19362, 2423, 1668, 24976, 361, 4724, 1829, 3794, 995, 45865, 297, 19362, 23032, 3555, 29538, 18863, 42213, 10632, 8608, 3224, 37977, 49429, 20328, 3615, 49401, 22807], "avg_logprob": -0.3370253074018261, "compression_ratio": 1.6890243902439024, "no_speech_prob": 0.0, "words": [{"start": 2140.76, "end": 2141.04, "word": "شباب", "probability": 0.6173502604166666}, {"start": 2141.04, "end": 2141.26, "word": " كيف", "probability": 0.82470703125}, {"start": 2141.26, "end": 2141.72, "word": " بنثبت", "probability": 0.8978271484375}, {"start": 2141.72, "end": 2141.82, "word": " ان", "probability": 0.48193359375}, {"start": 2141.82, "end": 2142.26, "word": " الجروب", "probability": 0.7162272135416666}, {"start": 2142.26, "end": 2142.42, "word": " ليس", "probability": 0.666259765625}, {"start": 2142.42, "end": 2142.98, "word": " Cyclic", "probability": 0.70166015625}, {"start": 2142.98, "end": 2146.76, "word": " نثبت", "probability": 0.795257568359375}, {"start": 2146.76, "end": 2146.92, "word": " ان", "probability": 0.74072265625}, {"start": 2146.92, "end": 2147.34, "word": " ولا", "probability": 0.646484375}, {"start": 2147.34, "end": 2148.16, "word": " عنصر", "probability": 0.9485677083333334}, {"start": 2148.16, "end": 2148.36, "word": " ال", "probability": 0.6552734375}, {"start": 2148.36, "end": 2148.76, "word": " order", "probability": 0.85107421875}, {"start": 2148.76, "end": 2149.16, "word": " له", "probability": 0.38525390625}, {"start": 2149.16, "end": 2149.66, "word": " بيساوي", "probability": 0.76435546875}, {"start": 2149.66, "end": 2150.04, "word": " order", "probability": 0.89990234375}, {"start": 2150.04, "end": 2150.7, "word": " للجروب", "probability": 0.764892578125}, {"start": 2150.7, "end": 2154.1, "word": " طب", "probability": 0.660400390625}, {"start": 2154.1, "end": 2154.28, "word": " انت", "probability": 0.610107421875}, {"start": 2154.28, "end": 2154.44, "word": " لا", "probability": 0.39404296875}, {"start": 2154.44, "end": 2154.58, "word": " تنساش", "probability": 0.76043701171875}, {"start": 2154.58, "end": 2154.72, "word": " ان", "probability": 0.84375}, {"start": 2154.72, "end": 2154.86, "word": " ال", "probability": 0.6279296875}, {"start": 2154.86, "end": 2154.98, "word": " j", "probability": 0.436279296875}, {"start": 2154.98, "end": 2155.4, "word": " finite", "probability": 0.80126953125}, {"start": 2155.4, "end": 2155.92, "word": " ال", "probability": 0.47314453125}, {"start": 2155.92, "end": 2156.2, "word": " order", "probability": 0.90234375}, {"start": 2156.2, "end": 2156.44, "word": " لل", "probability": 0.5751953125}, {"start": 2156.44, "end": 2156.74, "word": " j", "probability": 0.57080078125}, {"start": 2156.74, "end": 2158.54, "word": " بيساوي", "probability": 0.8880859375}, {"start": 2158.54, "end": 2158.78, "word": " n", "probability": 0.329345703125}, {"start": 2158.78, "end": 2159.4, "word": " finite", "probability": 0.966796875}, {"start": 2159.4, "end": 2162.24, "word": " طب", "probability": 0.82275390625}, {"start": 2162.24, "end": 2162.44, "word": " هذه", "probability": 0.319091796875}, {"start": 2162.44, "end": 2163.02, "word": " العملية", "probability": 0.9192708333333334}, {"start": 2163.02, "end": 2163.74, "word": " سهلة", "probability": 0.9420572916666666}, {"start": 2163.74, "end": 2163.96, "word": " ولا", "probability": 0.845703125}, {"start": 2163.96, "end": 2164.64, "word": " صعبة؟", "probability": 0.9166259765625}], "temperature": 1.0}, {"id": 77, "seek": 219394, "start": 2166.56, "end": 2193.94, "text": "انت بتاخد عنصر عشوائي بتثبت ان ال order إله لا يساوي n مين الأسهل؟ مين الأسهل؟ أستعمل الأسطوب المباشر ولا الغير مباشر؟ أستعمل ال direct ولا ال indirect؟ الأسهل هان أستعمل ال indirect assume that J is cyclic", "tokens": [7649, 2655, 39894, 47283, 3215, 18871, 9381, 2288, 6225, 8592, 2407, 16373, 1829, 39894, 12984, 3555, 2655, 16472, 2423, 1668, 11933, 43761, 20193, 7251, 3794, 995, 45865, 297, 3714, 9957, 16247, 3794, 3224, 1211, 22807, 3714, 9957, 16247, 3794, 3224, 1211, 22807, 5551, 14851, 25957, 1211, 16247, 3794, 9566, 37746, 9673, 3555, 33599, 2288, 49429, 6024, 118, 13546, 3714, 3555, 33599, 2288, 22807, 5551, 14851, 25957, 1211, 2423, 2047, 49429, 2423, 19523, 22807, 16247, 3794, 3224, 1211, 8032, 7649, 5551, 14851, 25957, 1211, 2423, 19523, 6552, 300, 508, 307, 38154, 1050], "avg_logprob": -0.2992527050816495, "compression_ratio": 1.8121546961325967, "no_speech_prob": 0.0, "words": [{"start": 2166.56, "end": 2166.84, "word": "انت", "probability": 0.30426025390625}, {"start": 2166.84, 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{"start": 2183.92, "end": 2184.2, "word": " ولا", "probability": 0.94921875}, {"start": 2184.2, "end": 2184.34, "word": " ال", "probability": 0.90380859375}, {"start": 2184.34, "end": 2185.08, "word": " indirect؟", "probability": 0.826904296875}, {"start": 2185.08, "end": 2186.1, "word": " الأسهل", "probability": 0.9150390625}, {"start": 2186.1, "end": 2186.26, "word": " هان", "probability": 0.5439453125}, {"start": 2186.26, "end": 2186.66, "word": " أستعمل", "probability": 0.87017822265625}, {"start": 2186.66, "end": 2186.76, "word": " ال", "probability": 0.67724609375}, {"start": 2186.76, "end": 2187.04, "word": " indirect", "probability": 0.99560546875}, {"start": 2187.04, "end": 2187.56, "word": " assume", "probability": 0.52734375}, {"start": 2187.56, "end": 2191.02, "word": " that", "probability": 0.91015625}, {"start": 2191.02, "end": 2192.38, "word": " J", "probability": 0.5126953125}, {"start": 2192.38, "end": 2193.14, "word": " is", "probability": 0.927734375}, {"start": 2193.14, "end": 2193.94, "word": " cyclic", "probability": 0.885498046875}], "temperature": 1.0}, {"id": 78, "seek": 222653, "start": 2197.53, "end": 2226.53, "text": "هذا معناته ان الـ J is generated by some A هذا معناته الـ A ينتمي للـ J اللي هي ال union لـ H subgroup من الـ J لـ H لأن الـ G عبارة عن اتحاد بربر subgroups والـ A في الـ J يقبل A موجود في الاتحاد هذا معناته الـ A ينتمي ل some H for some", "tokens": [3224, 15730, 20449, 8315, 47395, 16472, 2423, 39184, 508, 307, 10833, 538, 512, 316, 23758, 20449, 8315, 47395, 2423, 39184, 316, 7251, 29399, 2304, 1829, 24976, 39184, 508, 13672, 1829, 39896, 2423, 11671, 5296, 39184, 389, 1422, 17377, 9154, 2423, 39184, 508, 5296, 39184, 389, 5296, 33456, 2423, 39184, 460, 6225, 3555, 9640, 3660, 18871, 1975, 2655, 5016, 18513, 4724, 25513, 2288, 1422, 17377, 82, 16070, 39184, 316, 8978, 2423, 39184, 508, 7251, 4587, 36150, 316, 3714, 29245, 23328, 8978, 2423, 9307, 5016, 18513, 23758, 20449, 8315, 47395, 2423, 39184, 316, 7251, 29399, 2304, 1829, 5296, 512, 389, 337, 512], "avg_logprob": -0.22787746816578477, "compression_ratio": 1.8983957219251337, "no_speech_prob": 0.0, "words": [{"start": 2197.53, "end": 2197.79, "word": "هذا", "probability": 0.936767578125}, {"start": 2197.79, "end": 2198.29, "word": " معناته", "probability": 0.9444986979166666}, {"start": 2198.29, "end": 2199.49, "word": " ان", "probability": 0.5185546875}, {"start": 2199.49, "end": 2199.73, "word": " الـ", "probability": 0.5992431640625}, {"start": 2199.73, "end": 2199.77, "word": " J", "probability": 0.367919921875}, {"start": 2199.77, "end": 2199.89, "word": " is", "probability": 0.210205078125}, {"start": 2199.89, "end": 2200.35, "word": " generated", "probability": 0.8515625}, {"start": 2200.35, "end": 2200.61, "word": " by", "probability": 0.921875}, {"start": 2200.61, "end": 2201.05, "word": " some", "probability": 0.84765625}, {"start": 2201.05, "end": 2202.43, "word": " A", "probability": 0.595703125}, {"start": 2202.43, "end": 2204.25, "word": " هذا", "probability": 0.755859375}, {"start": 2204.25, "end": 2204.81, "word": " معناته", "probability": 0.98583984375}, {"start": 2204.81, "end": 2205.87, "word": " الـ", "probability": 0.644287109375}, {"start": 2205.87, "end": 2206.03, "word": " A", "probability": 0.84619140625}, {"start": 2206.03, "end": 2206.65, "word": " ينتمي", "probability": 0.984130859375}, {"start": 2206.65, "end": 2206.91, "word": " للـ", "probability": 0.619140625}, {"start": 2206.91, "end": 2207.11, "word": " J", "probability": 0.7880859375}, {"start": 2207.11, "end": 2207.93, "word": " اللي", "probability": 0.696533203125}, {"start": 2207.93, "end": 2208.05, "word": " هي", "probability": 0.5751953125}, {"start": 2208.05, "end": 2208.17, "word": " ال", "probability": 0.79541015625}, {"start": 2208.17, "end": 2208.41, "word": " union", "probability": 0.76123046875}, {"start": 2208.41, "end": 2209.67, "word": " لـ", "probability": 0.7744140625}, {"start": 2209.67, "end": 2210.09, "word": " H", "probability": 0.89111328125}, {"start": 2210.09, "end": 2211.37, "word": " subgroup", "probability": 0.6444091796875}, {"start": 2211.37, "end": 2211.55, "word": " من", "probability": 0.9892578125}, {"start": 2211.55, "end": 2211.75, "word": " الـ", "probability": 0.78369140625}, {"start": 2211.75, "end": 2212.01, "word": " J", "probability": 0.82568359375}, {"start": 2212.01, "end": 2213.31, "word": " لـ", "probability": 0.95068359375}, {"start": 2213.31, "end": 2213.61, "word": " H", "probability": 0.7763671875}, {"start": 2213.61, "end": 2215.05, "word": " لأن", "probability": 0.339111328125}, {"start": 2215.05, "end": 2215.17, "word": " الـ", "probability": 0.777099609375}, {"start": 2215.17, "end": 2215.25, "word": " G", "probability": 0.59912109375}, {"start": 2215.25, "end": 2215.65, "word": " عبارة", "probability": 0.955810546875}, {"start": 2215.65, "end": 2215.81, "word": " عن", "probability": 0.99560546875}, {"start": 2215.81, "end": 2216.23, "word": " اتحاد", "probability": 0.892822265625}, {"start": 2216.23, "end": 2216.59, "word": " بربر", "probability": 0.7646484375}, {"start": 2216.59, "end": 2217.55, "word": " subgroups", "probability": 0.861328125}, {"start": 2217.55, "end": 2217.99, "word": " والـ", "probability": 0.6937255859375}, {"start": 2217.99, "end": 2218.11, "word": " A", "probability": 0.95263671875}, {"start": 2218.11, "end": 2218.23, "word": " في", "probability": 0.9521484375}, {"start": 2218.23, "end": 2218.37, "word": " الـ", "probability": 0.79931640625}, {"start": 2218.37, "end": 2218.57, "word": " J", "probability": 0.900390625}, {"start": 2218.57, "end": 2218.95, "word": " يقبل", "probability": 0.7998046875}, {"start": 2218.95, "end": 2219.33, "word": " A", "probability": 0.90771484375}, {"start": 2219.33, "end": 2220.11, "word": " موجود", "probability": 0.9602864583333334}, {"start": 2220.11, "end": 2220.21, "word": " في", "probability": 0.95751953125}, {"start": 2220.21, "end": 2220.83, "word": " الاتحاد", "probability": 0.9635009765625}, {"start": 2220.83, "end": 2221.57, "word": " هذا", "probability": 0.93212890625}, {"start": 2221.57, "end": 2222.11, "word": " معناته", "probability": 0.9847005208333334}, {"start": 2222.11, "end": 2222.49, "word": " الـ", "probability": 0.8671875}, {"start": 2222.49, "end": 2222.81, "word": " A", "probability": 0.97119140625}, {"start": 2222.81, "end": 2224.03, "word": " ينتمي", "probability": 0.9915771484375}, {"start": 2224.03, "end": 2224.15, "word": " ل", "probability": 0.92138671875}, {"start": 2224.15, "end": 2224.49, "word": " some", "probability": 0.375244140625}, {"start": 2224.49, "end": 2225.01, "word": " H", "probability": 0.97412109375}, {"start": 2225.01, "end": 2225.79, "word": " for", "probability": 0.921875}, {"start": 2225.79, "end": 2226.53, "word": " some", "probability": 0.921875}], "temperature": 1.0}, {"id": 79, "seek": 225039, "start": 2228.25, "end": 2250.39, "text": "H proper subgroup من الجيه ال A عنصر في proper subgroup من جيه من الجيه هذا معناته انه generated by ال A صارت subgroup من مين من ال H مين generated by ال A يا شباب جيه", "tokens": [39, 2296, 1422, 17377, 9154, 25724, 1829, 3224, 2423, 316, 18871, 9381, 2288, 8978, 2296, 1422, 17377, 9154, 10874, 1829, 3224, 9154, 25724, 1829, 3224, 23758, 20449, 8315, 47395, 16472, 3224, 10833, 538, 2423, 316, 20328, 9640, 2655, 1422, 17377, 9154, 3714, 9957, 9154, 2423, 389, 3714, 9957, 10833, 538, 2423, 316, 35186, 13412, 3555, 16758, 10874, 1829, 3224], "avg_logprob": -0.34374999354283015, "compression_ratio": 1.7407407407407407, "no_speech_prob": 0.0, "words": [{"start": 2228.25, "end": 2229.13, "word": "H", "probability": 0.427978515625}, {"start": 2229.13, "end": 2230.01, "word": " proper", "probability": 0.28564453125}, {"start": 2230.01, "end": 2230.61, "word": " subgroup", "probability": 0.795166015625}, {"start": 2230.61, "end": 2230.81, "word": " من", "probability": 0.98681640625}, {"start": 2230.81, "end": 2231.27, "word": " الجيه", "probability": 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"probability": 0.91796875}, {"start": 2246.31, "end": 2247.35, "word": " مين", "probability": 0.617431640625}, {"start": 2247.35, "end": 2247.79, "word": " generated", "probability": 0.62353515625}, {"start": 2247.79, "end": 2248.03, "word": " by", "probability": 0.96337890625}, {"start": 2248.03, "end": 2248.17, "word": " ال", "probability": 0.41748046875}, {"start": 2248.17, "end": 2248.21, "word": " A", "probability": 0.91796875}, {"start": 2248.21, "end": 2248.39, "word": " يا", "probability": 0.72998046875}, {"start": 2248.39, "end": 2248.67, "word": " شباب", "probability": 0.9900716145833334}, {"start": 2248.67, "end": 2250.39, "word": " جيه", "probability": 0.7344563802083334}], "temperature": 1.0}, {"id": 80, "seek": 228385, "start": 2256.01, "end": 2283.85, "text": "J subgroup من الـH و الـH أصلا subgroup من مين من الـJ صارت الـJ subgroup من بوبر subgroup منها يعني المبنى اللي انت فيه صار جزء من الغرفة تخيل كيف المبنى طيبة صار جزء من الغرفة اللي انت فيها هنا", "tokens": [41, 1422, 17377, 9154, 2423, 39184, 39, 4032, 2423, 39184, 39, 5551, 9381, 15040, 1422, 17377, 9154, 3714, 9957, 9154, 2423, 39184, 41, 20328, 9640, 2655, 2423, 39184, 41, 1422, 17377, 9154, 4724, 37746, 2288, 1422, 17377, 9154, 11296, 37495, 22653, 9673, 3555, 1863, 7578, 13672, 1829, 16472, 2655, 8978, 3224, 20328, 9640, 10874, 11622, 38207, 9154, 6024, 118, 28480, 3660, 6055, 9778, 26895, 9122, 33911, 9673, 3555, 1863, 7578, 23032, 1829, 49401, 20328, 9640, 10874, 11622, 38207, 9154, 6024, 118, 28480, 3660, 13672, 1829, 16472, 2655, 8978, 11296, 34105], "avg_logprob": -0.26270604395604397, "compression_ratio": 2.038961038961039, "no_speech_prob": 0.0, "words": [{"start": 2256.0099999999998, "end": 2256.93, "word": "J", "probability": 0.1834716796875}, {"start": 2256.93, "end": 2257.85, "word": " subgroup", "probability": 0.46502685546875}, {"start": 2257.85, "end": 2258.03, "word": " من", "probability": 0.9716796875}, {"start": 2258.03, "end": 2258.43, "word": " الـH", "probability": 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"probability": 0.970703125}, {"start": 2267.61, "end": 2268.07, "word": " بوبر", "probability": 0.4839680989583333}, {"start": 2268.07, "end": 2268.65, "word": " subgroup", "probability": 0.6688232421875}, {"start": 2268.65, "end": 2269.15, "word": " منها", "probability": 0.98828125}, {"start": 2269.15, "end": 2272.19, "word": " يعني", "probability": 0.89697265625}, {"start": 2272.19, "end": 2272.69, "word": " المبنى", "probability": 0.9769287109375}, {"start": 2272.69, "end": 2272.83, "word": " اللي", "probability": 0.775146484375}, {"start": 2272.83, "end": 2273.09, "word": " انت", "probability": 0.760009765625}, {"start": 2273.09, "end": 2273.97, "word": " فيه", "probability": 0.986328125}, {"start": 2273.97, "end": 2274.43, "word": " صار", "probability": 0.96728515625}, {"start": 2274.43, "end": 2274.77, "word": " جزء", "probability": 0.9959309895833334}, {"start": 2274.77, "end": 2274.97, "word": " من", "probability": 0.99462890625}, {"start": 2274.97, "end": 2277.17, "word": " الغرفة", "probability": 0.968505859375}, {"start": 2277.17, "end": 2278.89, "word": " تخيل", "probability": 0.6909993489583334}, {"start": 2278.89, "end": 2279.35, "word": " كيف", "probability": 0.8212890625}, {"start": 2279.35, "end": 2280.23, "word": " المبنى", "probability": 0.9029541015625}, {"start": 2280.23, "end": 2281.61, "word": " طيبة", "probability": 0.8336588541666666}, {"start": 2281.61, "end": 2282.29, "word": " صار", "probability": 0.947998046875}, {"start": 2282.29, "end": 2282.53, "word": " جزء", "probability": 0.9943033854166666}, {"start": 2282.53, "end": 2282.67, "word": " من", "probability": 0.9892578125}, {"start": 2282.67, "end": 2283.09, "word": " الغرفة", "probability": 0.96337890625}, {"start": 2283.09, "end": 2283.21, "word": " اللي", "probability": 0.96240234375}, {"start": 2283.21, "end": 2283.37, "word": " انت", "probability": 0.89892578125}, {"start": 2283.37, "end": 2283.63, "word": " فيها", "probability": 0.94189453125}, {"start": 2283.63, "end": 2283.85, "word": " هنا", "probability": 0.67138671875}], "temperature": 1.0}, {"id": 81, "seek": 231316, "start": 2284.74, "end": 2313.16, "text": "طب و الناس اللي برا الغرفة وين موجودين؟ صارت تناقض لإنه حاسيب معاك ال J بوبر sub group من نفسها و هذا مستحيل تناقض contradiction so J is not cyclic و أصلا ال H بوبر صحيح", "tokens": [9566, 3555, 4032, 2423, 8315, 3794, 13672, 1829, 4724, 23557, 6024, 118, 28480, 3660, 4032, 9957, 3714, 29245, 23328, 9957, 22807, 20328, 9640, 2655, 6055, 8315, 4587, 11242, 5296, 28814, 1863, 3224, 11331, 32277, 1829, 3555, 20449, 995, 4117, 2423, 508, 4724, 37746, 2288, 1422, 1594, 9154, 8717, 36178, 11296, 4032, 23758, 3714, 14851, 5016, 26895, 6055, 8315, 4587, 11242, 34937, 370, 508, 307, 406, 38154, 1050, 4032, 5551, 9381, 15040, 2423, 389, 4724, 37746, 2288, 20328, 5016, 1829, 5016], "avg_logprob": -0.2654321105391891, "compression_ratio": 1.4074074074074074, "no_speech_prob": 0.0, "words": [{"start": 2284.74, "end": 2284.96, "word": "طب", "probability": 0.6221923828125}, {"start": 2284.96, "end": 2285.08, "word": " و", "probability": 0.4189453125}, {"start": 2285.08, "end": 2285.28, "word": " الناس", "probability": 0.9723307291666666}, {"start": 2285.28, "end": 2285.46, "word": " اللي", "probability": 0.79931640625}, {"start": 2285.46, "end": 2285.72, "word": " برا", "probability": 0.90673828125}, {"start": 2285.72, "end": 2286.52, "word": " الغرفة", "probability": 0.975830078125}, {"start": 2286.52, "end": 2286.74, "word": " وين", "probability": 0.6103515625}, {"start": 2286.74, "end": 2288.82, "word": " موجودين؟", "probability": 0.9091796875}, {"start": 2288.82, "end": 2290.16, "word": " صارت", "probability": 0.61962890625}, {"start": 2290.16, "end": 2290.7, "word": " تناقض", "probability": 0.9530029296875}, {"start": 2290.7, "end": 2291.54, "word": " لإنه", "probability": 0.65167236328125}, {"start": 2291.54, "end": 2291.88, "word": " حاسيب", "probability": 0.7879638671875}, {"start": 2291.88, "end": 2292.14, "word": " معاك", "probability": 0.9739583333333334}, {"start": 2292.14, "end": 2292.32, "word": " ال", "probability": 0.916015625}, {"start": 2292.32, "end": 2292.54, "word": " J", "probability": 0.353271484375}, {"start": 2292.54, "end": 2293.58, "word": " بوبر", "probability": 0.5370686848958334}, {"start": 2293.58, "end": 2294.32, "word": " sub", "probability": 0.66748046875}, {"start": 2294.32, "end": 2294.62, "word": " group", "probability": 0.53271484375}, {"start": 2294.62, "end": 2294.8, "word": " من", "probability": 0.568359375}, {"start": 2294.8, "end": 2295.36, "word": " نفسها", "probability": 0.9796549479166666}, {"start": 2295.36, "end": 2295.86, "word": " و", "probability": 0.72216796875}, {"start": 2295.86, "end": 2296.0, "word": " هذا", "probability": 0.471923828125}, {"start": 2296.0, "end": 2296.64, "word": " مستحيل", "probability": 0.98388671875}, {"start": 2296.64, "end": 2298.34, "word": " تناقض", "probability": 0.9683837890625}, {"start": 2298.34, "end": 2298.86, "word": " contradiction", "probability": 0.73291015625}, {"start": 2298.86, "end": 2300.32, "word": " so", "probability": 0.4755859375}, {"start": 2300.32, "end": 2301.26, "word": " J", "probability": 0.73291015625}, {"start": 2301.26, "end": 2301.66, "word": " is", "probability": 0.9521484375}, {"start": 2301.66, "end": 2302.02, "word": " not", "probability": 0.94970703125}, {"start": 2302.02, "end": 2305.4, "word": " cyclic", "probability": 0.83642578125}, {"start": 2305.4, "end": 2309.66, "word": " و", "probability": 0.51123046875}, {"start": 2309.66, "end": 2309.98, "word": " أصلا", "probability": 0.6961263020833334}, {"start": 2309.98, "end": 2310.12, "word": " ال", "probability": 0.9541015625}, {"start": 2310.12, "end": 2310.26, "word": " H", "probability": 0.927734375}, {"start": 2310.26, "end": 2310.76, "word": " بوبر", "probability": 0.9361979166666666}, {"start": 2310.76, "end": 2313.16, "word": " صحيح", "probability": 0.85943603515625}], "temperature": 1.0}, {"id": 82, "seek": 234726, "start": 2319.82, "end": 2347.26, "text": "طيب الجزء التاني لسه شوف قارط سؤال كويس احنا بنثبت ان ال J اتحاد مجموعات جزئية proper منها if and only if هي مش cyclic فلو كانت اتحاد ل proper subgroup اثبتت انها مش cyclic لان لو كانت cyclic هسي في مشكلة", "tokens": [9566, 1829, 3555, 25724, 11622, 38207, 16712, 7649, 1829, 5296, 3794, 3224, 13412, 38688, 12174, 9640, 9566, 8608, 33604, 6027, 9122, 45865, 3794, 1975, 5016, 8315, 44945, 12984, 3555, 2655, 16472, 2423, 508, 1975, 2655, 5016, 18513, 3714, 7435, 2304, 45367, 9307, 10874, 11622, 19986, 10632, 2296, 9154, 11296, 498, 293, 787, 498, 39896, 37893, 38154, 1050, 6156, 1211, 2407, 25961, 2655, 1975, 2655, 5016, 18513, 5296, 2296, 1422, 17377, 1975, 12984, 3555, 2655, 2655, 16472, 11296, 37893, 38154, 1050, 5296, 7649, 45164, 25961, 2655, 38154, 1050, 8032, 3794, 1829, 8978, 37893, 28820, 3660], "avg_logprob": -0.2361842155456543, "compression_ratio": 1.5771144278606966, "no_speech_prob": 0.0, "words": [{"start": 2319.82, "end": 2320.2, "word": "طيب", "probability": 0.796630859375}, {"start": 2320.2, "end": 2320.54, "word": " الجزء", "probability": 0.8528645833333334}, {"start": 2320.54, "end": 2320.86, "word": " التاني", "probability": 0.86279296875}, {"start": 2320.86, "end": 2321.14, "word": " لسه", "probability": 0.9371744791666666}, {"start": 2321.14, "end": 2326.98, "word": " شوف", "probability": 0.517547607421875}, {"start": 2326.98, "end": 2327.88, "word": " قارط", "probability": 0.5794270833333334}, {"start": 2327.88, "end": 2328.08, "word": " سؤال", "probability": 0.9158528645833334}, {"start": 2328.08, "end": 2328.5, "word": " كويس", "probability": 0.8846028645833334}, {"start": 2328.5, "end": 2330.54, "word": " احنا", "probability": 0.8863932291666666}, {"start": 2330.54, "end": 2330.98, "word": " بنثبت", "probability": 0.968994140625}, {"start": 2330.98, "end": 2331.14, "word": " ان", "probability": 0.7568359375}, {"start": 2331.14, "end": 2331.3, "word": " ال", "probability": 0.67431640625}, {"start": 2331.3, "end": 2331.5, "word": " J", "probability": 0.356201171875}, {"start": 2331.5, "end": 2332.62, "word": " اتحاد", "probability": 0.9189453125}, {"start": 2332.62, "end": 2333.6, "word": " مجموعات", "probability": 0.96904296875}, {"start": 2333.6, "end": 2334.4, "word": " جزئية", "probability": 0.94775390625}, {"start": 2334.4, "end": 2334.72, "word": " proper", "probability": 0.8681640625}, {"start": 2334.72, "end": 2335.28, "word": " منها", "probability": 0.99072265625}, {"start": 2335.28, "end": 2337.0, "word": " if", "probability": 0.90869140625}, {"start": 2337.0, "end": 2337.24, "word": " and", "probability": 0.9521484375}, {"start": 2337.24, "end": 2337.54, "word": " only", "probability": 0.90869140625}, {"start": 2337.54, "end": 2337.92, "word": " if", "probability": 0.9775390625}, {"start": 2337.92, "end": 2338.16, "word": " هي", "probability": 0.8671875}, {"start": 2338.16, "end": 2338.54, "word": " مش", "probability": 0.994140625}, {"start": 2338.54, "end": 2339.48, "word": " cyclic", "probability": 0.780517578125}, {"start": 2339.48, "end": 2340.24, "word": " فلو", "probability": 0.6072184244791666}, {"start": 2340.24, "end": 2340.62, "word": " كانت", "probability": 0.988037109375}, {"start": 2340.62, "end": 2341.18, "word": " اتحاد", "probability": 0.9718017578125}, {"start": 2341.18, "end": 2341.64, "word": " ل", "probability": 0.309326171875}, {"start": 2341.64, "end": 2341.9, "word": " proper", "probability": 0.4384765625}, {"start": 2341.9, "end": 2342.54, "word": " subgroup", "probability": 0.647705078125}, {"start": 2342.54, "end": 2343.26, "word": " اثبتت", "probability": 0.77373046875}, {"start": 2343.26, "end": 2343.38, "word": " انها", "probability": 0.70166015625}, {"start": 2343.38, "end": 2343.5, "word": " مش", "probability": 0.99267578125}, {"start": 2343.5, "end": 2344.0, "word": " cyclic", "probability": 0.884033203125}, {"start": 2344.0, "end": 2345.5, "word": " لان", "probability": 0.6962890625}, {"start": 2345.5, "end": 2345.68, "word": " لو", "probability": 0.95263671875}, {"start": 2345.68, "end": 2346.02, "word": " كانت", "probability": 0.989501953125}, {"start": 2346.02, "end": 2346.28, "word": " cyclic", "probability": 0.854248046875}, {"start": 2346.28, "end": 2346.58, "word": " هسي", "probability": 0.6805013020833334}, {"start": 2346.58, "end": 2346.72, "word": " في", "probability": 0.63720703125}, {"start": 2346.72, "end": 2347.26, "word": " مشكلة", "probability": 0.8955078125}], "temperature": 1.0}, {"id": 83, "seek": 237496, "start": 2348.15, "end": 2374.97, "text": "يقبل جيه not cyclic حاجة تنتج الاتجاه العكسي نقول assume that جيه is not cyclic اش يعني يعني لكل a في الجيه generated by ال a لا يساوي الجيه اش يعني", "tokens": [1829, 4587, 36150, 10874, 1829, 3224, 406, 38154, 1050, 11331, 26108, 3660, 6055, 29399, 7435, 2423, 9307, 7435, 40294, 18863, 4117, 3794, 1829, 8717, 39648, 6552, 300, 10874, 1829, 3224, 307, 406, 38154, 1050, 1975, 8592, 37495, 22653, 37495, 22653, 5296, 28820, 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0.6339111328125}, {"start": 2351.87, "end": 2352.47, "word": " assume", "probability": 0.783203125}, {"start": 2352.47, "end": 2356.59, "word": " that", "probability": 0.85986328125}, {"start": 2356.59, "end": 2358.53, "word": " جيه", "probability": 0.8357747395833334}, {"start": 2358.53, "end": 2359.31, "word": " is", "probability": 0.85888671875}, {"start": 2359.31, "end": 2359.75, "word": " not", "probability": 0.9638671875}, {"start": 2359.75, "end": 2362.31, "word": " cyclic", "probability": 0.857421875}, {"start": 2362.31, "end": 2362.85, "word": " اش", "probability": 0.62255859375}, {"start": 2362.85, "end": 2363.25, "word": " يعني", "probability": 0.90869140625}, {"start": 2363.25, "end": 2366.53, "word": " يعني", "probability": 0.6939697265625}, {"start": 2366.53, "end": 2367.25, "word": " لكل", "probability": 0.951904296875}, {"start": 2367.25, "end": 2367.57, "word": " a", "probability": 0.5087890625}, {"start": 2367.57, "end": 2367.73, "word": " في", "probability": 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لو", "probability": 0.34228515625}, {"start": 2421.2, "end": 2421.52, "word": " عندك", "probability": 0.961669921875}, {"start": 2421.52, "end": 2421.62, "word": " two", "probability": 0.8701171875}, {"start": 2421.62, "end": 2422.06, "word": " subgroup", "probability": 0.96875}, {"start": 2422.06, "end": 2422.46, "word": " الاتحاد", "probability": 0.917724609375}, {"start": 2422.46, "end": 2422.86, "word": " تبعه", "probability": 0.753173828125}, {"start": 2422.86, "end": 2423.04, "word": " مش", "probability": 0.9755859375}, {"start": 2423.04, "end": 2423.36, "word": " ضرر", "probability": 0.6424153645833334}, {"start": 2423.36, "end": 2423.78, "word": " يكون", "probability": 0.989013671875}, {"start": 2423.78, "end": 2425.06, "word": " subgroup", "probability": 0.96875}, {"start": 2425.06, "end": 2426.28, "word": " اعطيها", "probability": 0.918359375}, {"start": 2426.28, "end": 2426.74, "word": " واحد", "probability": 0.97705078125}, {"start": 2426.74, "end": 2429.38, "word": " now", 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{"start": 2491.52, "end": 2491.74, "word": " لأن", "probability": 0.5908203125}, {"start": 2491.74, "end": 2492.08, "word": " اثبات", "probability": 0.8115234375}, {"start": 2492.08, "end": 2492.36, "word": " السؤال", "probability": 0.984375}, {"start": 2492.36, "end": 2492.68, "word": " لها", "probability": 0.40655517578125}, {"start": 2492.68, "end": 2492.86, "word": " ..", "probability": 0.14453125}, {"start": 2492.86, "end": 2493.86, "word": " لأ", "probability": 0.68212890625}, {"start": 2493.86, "end": 2494.2, "word": " لها", "probability": 0.9228515625}, {"start": 2494.2, "end": 2494.56, "word": " ..", "probability": 0.43603515625}, {"start": 2494.56, "end": 2496.16, "word": " هذا", "probability": 0.494384765625}, {"start": 2496.16, "end": 2496.28, "word": " ال", "probability": 0.475830078125}, {"start": 2496.28, "end": 2496.44, "word": " F", "probability": 0.7177734375}, {"start": 2496.44, "end": 2496.62, "word": " and", "probability": 0.312744140625}, {"start": 2496.62, "end": 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"probability": 0.5928955078125}, {"start": 2499.86, "end": 2500.0, "word": " ال", "probability": 0.6064453125}, {"start": 2500.0, "end": 2500.18, "word": " only", "probability": 0.888671875}, {"start": 2500.18, "end": 2500.48, "word": " F", "probability": 0.99072265625}], "temperature": 1.0}, {"id": 89, "seek": 256935, "start": 2544.11, "end": 2569.35, "text": "37 show that the group of positive rational number under multiplication is not cyclic يعني Q زائد مع ضرب not cyclic Q زائد يعني الأعداد النسبية الموجبة", "tokens": [12851, 855, 300, 264, 1594, 295, 3353, 15090, 1230, 833, 27290, 307, 406, 38154, 1050, 37495, 22653, 1249, 30767, 16373, 3215, 20449, 48812, 25513, 406, 38154, 1050, 1249, 30767, 16373, 3215, 37495, 22653, 16247, 22488, 18513, 28239, 35457, 10632, 9673, 29245, 49401], "avg_logprob": -0.23510174973066464, "compression_ratio": 1.2866666666666666, "no_speech_prob": 0.0, "words": [{"start": 2544.1099999999997, "end": 2545.39, "word": "37", "probability": 0.190185546875}, {"start": 2545.39, "end": 2546.67, "word": " show", "probability": 0.135986328125}, {"start": 2546.67, "end": 2546.89, "word": " that", "probability": 0.923828125}, {"start": 2546.89, "end": 2547.05, "word": " the", "probability": 0.740234375}, {"start": 2547.05, "end": 2547.33, "word": " group", "probability": 0.9658203125}, {"start": 2547.33, "end": 2547.51, "word": " of", "probability": 0.95166015625}, {"start": 2547.51, "end": 2547.93, "word": " positive", "probability": 0.8955078125}, {"start": 2547.93, "end": 2548.35, "word": " rational", "probability": 0.9326171875}, {"start": 2548.35, "end": 2548.89, "word": " number", "probability": 0.7578125}, {"start": 2548.89, "end": 2549.63, "word": " under", "probability": 0.814453125}, {"start": 2549.63, "end": 2550.17, "word": " multiplication", "probability": 0.802734375}, {"start": 2550.17, "end": 2550.53, "word": " is", "probability": 0.943359375}, {"start": 2550.53, "end": 2550.85, "word": " not", "probability": 0.89599609375}, {"start": 2550.85, "end": 2551.57, "word": " cyclic", "probability": 0.890625}, {"start": 2551.57, "end": 2552.51, "word": " يعني", "probability": 0.93212890625}, {"start": 2552.51, "end": 2553.93, "word": " Q", "probability": 0.344482421875}, {"start": 2553.93, "end": 2554.71, "word": " زائد", "probability": 0.6976725260416666}, {"start": 2554.71, "end": 2557.85, "word": " مع", "probability": 0.96728515625}, {"start": 2557.85, "end": 2558.49, "word": " ضرب", "probability": 0.875732421875}, {"start": 2558.49, "end": 2560.05, "word": " not", "probability": 0.52783203125}, {"start": 2560.05, "end": 2561.11, "word": " cyclic", "probability": 0.885498046875}, {"start": 2561.11, "end": 2565.27, "word": " Q", "probability": 0.76318359375}, {"start": 2565.27, "end": 2565.59, "word": " زائد", "probability": 0.9073893229166666}, {"start": 2565.59, "end": 2565.81, "word": " يعني", "probability": 0.96435546875}, {"start": 2565.81, "end": 2566.81, "word": " الأعداد", "probability": 0.87744140625}, {"start": 2566.81, "end": 2568.83, "word": " النسبية", "probability": 0.90087890625}, {"start": 2568.83, "end": 2569.35, "word": " الموجبة", "probability": 0.8995768229166666}], "temperature": 1.0}, {"id": 90, "seek": 259948, "start": 2570.63, "end": 2599.49, "text": "هأقول assume الـ Q generated by some a على b with the greatest common divisor ل a و b بدي يسوي واحد حيث ال a و ال b موجودين في ال initial number طب علشان ماخدتهمش في ال z لإن أنا بتعامل مع مين؟ مع positive", "tokens": [3224, 10721, 39648, 6552, 2423, 39184, 1249, 10833, 538, 512, 257, 15844, 272, 365, 264, 6636, 2689, 25974, 284, 5296, 257, 4032, 272, 4724, 16254, 7251, 3794, 45865, 36764, 24401, 11331, 1829, 12984, 2423, 257, 4032, 2423, 272, 3714, 29245, 23328, 9957, 8978, 2423, 5883, 1230, 23032, 3555, 11203, 8592, 7649, 3714, 47283, 3215, 2655, 16095, 8592, 8978, 2423, 710, 5296, 28814, 1863, 41850, 39894, 3615, 10943, 1211, 20449, 3714, 9957, 22807, 20449, 3353], "avg_logprob": -0.34041667143503823, 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قص أن طبعا .. طبعا clearly أن لا يساوي zero لأن التنين لا يساوي a على b قص صفر ليها واحد also", "tokens": [3224, 1829, 16712, 1863, 9957, 4724, 28259, 6055, 3794, 995, 45865, 257, 15844, 272, 12174, 9381, 14739, 23032, 3555, 3615, 995, 4386, 23032, 3555, 3615, 995, 4448, 14739, 20193, 7251, 3794, 995, 45865, 4018, 5296, 33456, 16712, 1863, 9957, 20193, 7251, 3794, 995, 45865, 257, 15844, 272, 12174, 9381, 20328, 5172, 2288, 32239, 11296, 36764, 24401, 611], "avg_logprob": -0.31681033712008905, "compression_ratio": 1.5078125, "no_speech_prob": 0.0, "words": [{"start": 2600.79, "end": 2601.07, "word": "هي", "probability": 0.581787109375}, {"start": 2601.07, "end": 2601.83, "word": " التنين", "probability": 0.7604166666666666}, {"start": 2601.83, "end": 2602.97, "word": " بدا", "probability": 0.1983642578125}, {"start": 2602.97, "end": 2603.43, "word": " تساوي", "probability": 0.94482421875}, {"start": 2603.43, "end": 2603.69, "word": " a", "probability": 0.49853515625}, {"start": 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92, "seek": 265316, "start": 2627.4, "end": 2653.16, "text": "if n بدت ساوي واحد فالتنين بدت ساوي a على b هذا معناته ان ال q star generated by تنين او q زاد generated by تنين هذا معناته ان التلاتة بدت ساوي تنين أسام for some", "tokens": [351, 297, 47525, 2655, 8608, 995, 45865, 36764, 24401, 6156, 6027, 2655, 1863, 9957, 47525, 2655, 8608, 995, 45865, 257, 15844, 272, 23758, 20449, 8315, 47395, 16472, 2423, 9505, 3543, 10833, 538, 6055, 1863, 9957, 1975, 2407, 9505, 30767, 18513, 10833, 538, 6055, 1863, 9957, 23758, 20449, 8315, 47395, 16472, 16712, 1211, 9307, 3660, 47525, 2655, 8608, 995, 45865, 6055, 1863, 9957, 5551, 3794, 10943, 337, 512], "avg_logprob": -0.2750459484317723, "compression_ratio": 1.7659574468085106, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2627.4, "end": 2627.74, "word": "if", "probability": 0.131103515625}, {"start": 2627.74, "end": 2628.14, "word": " n", "probability": 0.60693359375}, {"start": 2628.14, "end": 2628.54, "word": " بدت", 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"temperature": 1.0}, {"id": 99, "seek": 286742, "start": 2839.34, "end": 2867.42, "text": "يكبر تنين تقسم ال B والسالب N يكبر تنين تقسم ال B Similarly تنين هتقسم ال E والسالب N يكبر تنين هتقسم ال A وهذا ما هيعطيك تناقض يكبر لا صفر ولا واحد ولا أكبر من الواحد ولا سالب واحد ولا أصغر من سالب واحد مين ضال؟ So Q", "tokens": [1829, 4117, 3555, 2288, 6055, 1863, 9957, 6055, 4587, 38251, 2423, 363, 16070, 3794, 6027, 3555, 426, 7251, 4117, 26890, 6055, 1863, 9957, 6055, 4587, 38251, 2423, 363, 13157, 6055, 1863, 9957, 8032, 2655, 4587, 38251, 2423, 462, 16070, 3794, 6027, 3555, 426, 7251, 4117, 26890, 6055, 1863, 9957, 8032, 2655, 4587, 38251, 2423, 316, 37037, 15730, 19446, 39896, 3615, 9566, 1829, 4117, 6055, 8315, 4587, 11242, 7251, 4117, 26890, 20193, 20328, 5172, 2288, 49429, 36764, 24401, 49429, 5551, 4117, 26890, 9154, 2423, 14407, 24401, 49429, 8608, 6027, 3555, 36764, 24401, 49429, 5551, 9381, 17082, 2288, 9154, 8608, 6027, 3555, 36764, 24401, 3714, 9957, 48812, 6027, 22807, 407, 1249], "avg_logprob": -0.19559658400037072, "compression_ratio": 2.2303030303030305, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2839.34, "end": 2839.74, "word": "يكبر", "probability": 0.61602783203125}, {"start": 2839.74, "end": 2840.06, "word": " تنين", "probability": 0.76513671875}, {"start": 2840.06, "end": 2840.7, "word": " تقسم", "probability": 0.9661458333333334}, {"start": 2840.7, "end": 2841.88, "word": " ال", "probability": 0.7451171875}, {"start": 2841.88, "end": 2842.0, "word": " B", "probability": 0.293212890625}, {"start": 2842.0, "end": 2842.54, "word": " والسالب", "probability": 0.6669769287109375}, {"start": 2842.54, "end": 2842.78, "word": " N", "probability": 0.5869140625}, {"start": 2842.78, "end": 2843.22, "word": " يكبر", "probability": 0.75927734375}, {"start": 2843.22, "end": 2843.54, "word": " تنين", "probability": 0.9729817708333334}, {"start": 2843.54, "end": 2843.96, "word": " تقسم", "probability": 0.9886067708333334}, {"start": 2843.96, "end": 2844.12, "word": " ال", "probability": 0.95556640625}, {"start": 2844.12, "end": 2844.34, "word": " B", "probability": 0.966796875}, {"start": 2844.34, "end": 2845.62, "word": " Similarly", "probability": 0.1690673828125}, {"start": 2845.62, "end": 2850.22, "word": " تنين", "probability": 0.9306640625}, {"start": 2850.22, "end": 2850.8, "word": " هتقسم", "probability": 0.939453125}, {"start": 2850.8, "end": 2851.0, "word": " ال", "probability": 0.962890625}, {"start": 2851.0, "end": 2851.12, "word": " E", "probability": 0.84228515625}, {"start": 2851.12, "end": 2851.6, "word": " والسالب", "probability": 0.965576171875}, {"start": 2851.6, "end": 2851.86, "word": " N", "probability": 0.97705078125}, {"start": 2851.86, "end": 2852.2, "word": " يكبر", "probability": 0.9217122395833334}, {"start": 2852.2, "end": 2852.46, "word": " تنين", "probability": 0.98876953125}, {"start": 2852.46, "end": 2853.0, "word": " هتقسم", "probability": 0.9796142578125}, {"start": 2853.0, "end": 2853.22, "word": " ال", "probability": 0.982421875}, {"start": 2853.22, "end": 2853.5, "word": " A", "probability": 0.943359375}, {"start": 2853.5, "end": 2855.06, "word": " وهذا", "probability": 0.798095703125}, {"start": 2855.06, "end": 2855.26, "word": " ما", "probability": 0.412841796875}, {"start": 2855.26, "end": 2855.88, "word": " هيعطيك", "probability": 0.8075439453125}, {"start": 2855.88, "end": 2856.82, "word": " تناقض", "probability": 0.84625244140625}, {"start": 2856.82, "end": 2857.52, "word": " يكبر", "probability": 0.8515625}, {"start": 2857.52, "end": 2857.66, "word": " لا", "probability": 0.919921875}, {"start": 2857.66, "end": 2858.04, "word": " صفر", "probability": 0.9671223958333334}, {"start": 2858.04, "end": 2858.2, "word": " ولا", "probability": 0.85986328125}, {"start": 2858.2, "end": 2858.56, "word": " واحد", "probability": 0.978759765625}, {"start": 2858.56, "end": 2858.72, "word": " ولا", "probability": 0.939453125}, {"start": 2858.72, "end": 2859.0, "word": " أكبر", "probability": 0.9051106770833334}, {"start": 2859.0, "end": 2859.14, "word": " من", "probability": 0.9853515625}, {"start": 2859.14, "end": 2859.62, "word": " الواحد", "probability": 0.8455403645833334}, {"start": 2859.62, "end": 2860.1, "word": " ولا", "probability": 0.95068359375}, {"start": 2860.1, "end": 2860.52, "word": " سالب", "probability": 0.9632161458333334}, {"start": 2860.52, "end": 2860.8, "word": " واحد", "probability": 0.98828125}, {"start": 2860.8, "end": 2860.98, "word": " ولا", "probability": 0.97265625}, {"start": 2860.98, "end": 2861.38, "word": " أصغر", "probability": 0.9700927734375}, {"start": 2861.38, "end": 2861.54, "word": " من", "probability": 0.99658203125}, {"start": 2861.54, "end": 2861.84, "word": " سالب", "probability": 0.9563802083333334}, {"start": 2861.84, "end": 2862.28, "word": " واحد", "probability": 0.993896484375}, {"start": 2862.28, "end": 2862.88, "word": " مين", "probability": 0.8330078125}, {"start": 2862.88, "end": 2864.8, "word": " ضال؟", "probability": 0.60693359375}, {"start": 2864.8, "end": 2865.16, "word": " So", "probability": 0.342041015625}, {"start": 2865.16, "end": 2867.42, "word": " Q", "probability": 0.7314453125}], "temperature": 1.0}, {"id": 100, "seek": 289090, "start": 2868.78, "end": 2890.9, "text": "زائد is not cyclic يعطيكوا العافية بنجا فان السؤال هذا وحضرة القادمة ان شاء الله هنكمل من سؤال تمانية وتلاتين بس هنحاول انه ننهي المناقشة يعني لن مش هحل كل الأسئلة اللي ضايلة مطلوبة هعطيك فقط هنتائج إليها", "tokens": [11622, 16373, 3215, 307, 406, 38154, 1050, 7251, 3615, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 44945, 7435, 995, 6156, 7649, 21136, 33604, 6027, 23758, 4032, 5016, 11242, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984, 8032, 1863, 24793, 1211, 9154, 8608, 33604, 6027, 6055, 2304, 7649, 10632, 34683, 1211, 9307, 9957, 4724, 3794, 8032, 1863, 5016, 995, 12610, 16472, 3224, 8717, 1863, 3224, 1829, 9673, 8315, 4587, 8592, 3660, 37495, 22653, 5296, 1863, 37893, 8032, 5016, 1211, 28242, 16247, 3794, 19986, 37977, 13672, 1829, 48812, 995, 26895, 3660, 3714, 9566, 1211, 37746, 3660, 8032, 3615, 9566, 1829, 4117, 6156, 47432, 8032, 29399, 16373, 7435, 11933, 20292, 11296], "avg_logprob": -0.21932339941689727, "compression_ratio": 1.6744186046511629, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2868.78, "end": 2869.5, "word": "زائد", "probability": 0.6494954427083334}, {"start": 2869.5, "end": 2870.18, "word": " is", "probability": 0.7216796875}, {"start": 2870.18, "end": 2870.6, "word": " not", "probability": 0.9609375}, {"start": 2870.6, "end": 2873.72, "word": " cyclic", "probability": 0.788330078125}, {"start": 2873.72, "end": 2874.64, "word": " يعطيكوا", "probability": 0.6891276041666666}, {"start": 2874.64, "end": 2874.98, "word": " العافية", "probability": 0.8253580729166666}, {"start": 2874.98, "end": 2875.22, "word": " بنجا", "probability": 0.6275227864583334}, {"start": 2875.22, "end": 2875.4, "word": " فان", "probability": 0.515625}, {"start": 2875.4, "end": 2875.7, "word": " السؤال", "probability": 0.8430989583333334}, {"start": 2875.7, "end": 2876.0, "word": " هذا", "probability": 0.77685546875}, {"start": 2876.0, "end": 2876.8, "word": " وحضرة", "probability": 0.5269775390625}, {"start": 2876.8, "end": 2877.44, "word": " القادمة", "probability": 0.9879557291666666}, {"start": 2877.44, "end": 2877.64, "word": " ان", "probability": 0.859375}, {"start": 2877.64, "end": 2877.88, "word": " شاء", "probability": 0.98876953125}, {"start": 2877.88, "end": 2878.16, "word": " الله", "probability": 0.94873046875}, {"start": 2878.16, "end": 2879.42, "word": " هنكمل", "probability": 0.957275390625}, {"start": 2879.42, "end": 2879.58, "word": " من", "probability": 0.91357421875}, {"start": 2879.58, "end": 2879.84, "word": " سؤال", "probability": 0.93310546875}, {"start": 2879.84, "end": 2880.16, "word": " تمانية", "probability": 0.8350830078125}, {"start": 2880.16, "end": 2880.68, "word": " وتلاتين", "probability": 0.8697509765625}, {"start": 2880.68, "end": 2881.44, "word": " بس", "probability": 0.979248046875}, {"start": 2881.44, "end": 2882.14, "word": " هنحاول", "probability": 0.97001953125}, {"start": 2882.14, "end": 2882.78, "word": " انه", "probability": 0.635009765625}, {"start": 2882.78, "end": 2883.58, "word": " ننهي", "probability": 0.9891357421875}, {"start": 2883.58, "end": 2884.68, "word": " المناقشة", "probability": 0.96923828125}, {"start": 2884.68, "end": 2884.84, "word": " يعني", "probability": 0.916748046875}, {"start": 2884.84, "end": 2885.16, "word": " لن", "probability": 0.681884765625}, {"start": 2885.16, "end": 2885.96, "word": " مش", "probability": 0.70751953125}, {"start": 2885.96, "end": 2886.22, "word": " هحل", "probability": 0.9674479166666666}, {"start": 2886.22, "end": 2886.48, "word": " كل", "probability": 0.97412109375}, {"start": 2886.48, "end": 2887.06, "word": " الأسئلة", "probability": 0.9847412109375}, {"start": 2887.06, "end": 2888.08, "word": " اللي", "probability": 0.927734375}, {"start": 2888.08, "end": 2888.48, "word": " ضايلة", "probability": 0.8370361328125}, {"start": 2888.48, "end": 2889.06, "word": " مطلوبة", "probability": 0.94921875}, {"start": 2889.06, "end": 2889.44, "word": " هعطيك", "probability": 0.97685546875}, {"start": 2889.44, "end": 2889.84, "word": " فقط", "probability": 0.98486328125}, {"start": 2889.84, "end": 2890.54, "word": " هنتائج", "probability": 0.5621337890625}, {"start": 2890.54, "end": 2890.9, "word": " إليها", "probability": 0.599853515625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2891.488, "duration_after_vad": 2578.4731249999872}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4f1f66ae361c3b22aa2d2e896ea89a218686bcaf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/FMJWMW6O3rs.srt
@@ -0,0 +1,1635 @@
+1
+00:00:21,350 --> 00:00:24,670
+السلام عليكم ورحمة الله وبركاته طبعا هنكمل إن 
+
+2
+00:00:24,670 --> 00:00:28,250
+شاء الله زي ما اتفقنا في المحاضرة السابقة الصبح هنكمل
+
+3
+00:00:28,250 --> 00:00:33,030
+مناقشة الوحدة الرابعة أعتقد وصلنا لسؤال ثلاثة عشر سؤال
+
+4
+00:00:33,030 --> 00:00:38,610
+أربعة عشر خلصناه سؤال ثلاثة عشر أربعة عشر خمسة عشر خليني بس 
+
+5
+00:00:38,610 --> 00:00:40,750
+أشوف المجموعة تبعت الأسئلة اللي حطناها
+
+6
+00:00:45,690 --> 00:00:51,590
+سؤال 12 أو 13 إن زد 24 find a generator of
+
+7
+00:00:51,590 --> 00:00:58,070
+generated by 21 and generated by 10 خلينا نجيب
+
+8
+00:00:58,070 --> 00:01:02,770
+generated by 21 generated by 21 يا شباب هي عبارة
+
+9
+00:01:02,770 --> 00:01:08,650
+عن generated by مين ال
+
+10
+00:01:08,650 --> 00:01:14,790
+21 والـ 24 إيش الجريتست كومون ديفايزر لهم
+
+11
+00:01:14,790 --> 00:01:20,690
+ثلاثة هذا عبارة عن generated by واحد  واحد و
+
+12
+00:01:20,690 --> 00:01:23,890
+عشرين اللي يجب أن يساوي generated by واحد جريتست كومون ديفايزر
+
+13
+00:01:23,890 --> 00:01:28,910
+الـ common divisor لواحد وعشرين وأربعة وعشرين اللي
+
+14
+00:01:28,910 --> 00:01:33,030
+generated by واحد ثلاثة كان generated by ثلاثة
+
+15
+00:01:33,030 --> 00:01:42,440
+مين يا generated by ثلاثة identity 3 6 9 12 15 18
+
+16
+00:01:42,440 --> 00:01:48,800
+21 وبس نفس القصة generated by 10 هنكتشف أنها
+
+17
+00:01:48,800 --> 00:01:57,560
+generated by 2 اللي هي عبارة عن identity 2 4 6 8 و
+
+18
+00:01:57,560 --> 00:02:03,860
+22 لو بتجيب التقاطع generated by 21 تقاطع
+
+19
+00:02:03,860 --> 00:02:11,420
+generated by 10 هنلاقي الـ identity ستة واثنا عشر و
+
+20
+00:02:11,420 --> 00:02:17,180
+ثمانية عشر هذا generated by مين يا شباب؟
+
+21
+00:02:17,180 --> 00:02:26,240
+ستة بتقدر تعمم تكمل
+
+22
+00:02:26,240 --> 00:02:31,220
+السؤال بتقدر تعمم generated by a to m تقاطع
+
+23
+00:02:31,220 --> 00:02:34,580
+generated by a to n عبارة عن إيش؟
+
+24
+00:02:42,150 --> 00:02:47,150
+generated by a to m and generated by a to n تقاطع
+
+25
+00:02:47,150 --> 00:02:51,650
+generated by مين لاحظ إن احنا هنا وصلنا لـ generated
+
+26
+00:02:51,650 --> 00:02:56,990
+by ثلاثة و generated by اثنين يعني واحد وثلاثة وواحد
+
+27
+00:02:56,990 --> 00:03:01,210
+واثنين لو قلنا a والثلاثة و a والاثنين يعني a
+
+28
+00:03:01,210 --> 00:03:04,810
+والستة اللي هو الـ least common multiple يعني هذا
+
+29
+00:03:04,810 --> 00:03:08,890
+عبارة عن generated by a الـ least common multiple
+
+30
+00:03:08,890 --> 00:03:15,980
+لأ مهم هذا حاصل fact generated by a to m تقاطع
+
+31
+00:03:15,980 --> 00:03:20,680
+generated by a to n هي generated by a الـ least
+
+32
+00:03:20,680 --> 00:03:25,540
+common multiple لـ m الـ least common multiple ل
+
+33
+00:03:25,540 --> 00:03:26,080
+m الـ least common multiple لـ M الـ least
+
+34
+00:03:26,080 --> 00:03:28,680
+common multiple لـ M الـ least common multiple ل
+
+35
+00:03:28,680 --> 00:03:32,620
+M الـ least common multiple لـ M الـ least
+
+36
+00:03:32,620 --> 00:03:32,720
+common multiple لـ M الـ least common multiple ل
+
+37
+00:03:32,720 --> 00:03:33,380
+common multiple لـ M الـ least common multiple ل
+
+38
+00:03:33,380 --> 00:03:33,520
+common multiple لـ M الـ least common multiple ل
+
+39
+00:03:33,520 --> 00:03:36,860
+M الـ least common multiple لـ M الـ least
+
+40
+00:03:36,860 --> 00:03:37,280
+common multiple 
+
+41
+00:03:40,270 --> 00:03:47,850
+الـ 0 تنتشر في Z أربعة وعشرين نفس
+
+42
+00:03:47,850 --> 00:03:52,870
+الشيء بعده أربعة عشر suppose that a cyclic group
+
+43
+00:03:52,870 --> 00:03:56,990
+J has exactly three subgroups J identity and a
+
+44
+00:03:56,990 --> 00:04:03,810
+subgroup of order سبعة what is order J J cyclic
+
+45
+00:04:03,810 --> 00:04:08,690
+generated by الـ A اللي هو only
+
+46
+00:04:11,530 --> 00:04:25,630
+subgroups of j are الـ identity و الـ h حيث order الـ
+
+47
+00:04:25,630 --> 00:04:33,250
+h بيساوي سبعة and j itself المطلوب
+
+48
+00:04:33,250 --> 00:04:33,990
+order الـ j
+
+49
+00:04:47,620 --> 00:04:53,640
+فكروا إن نلخص معلوماتنا قلنا لو أنا بشتغل في cyclic
+
+50
+00:04:53,640 --> 00:04:59,760
+group الـ subgroups كلهم cyclic الـ subgroups الـ
+
+51
+00:04:59,760 --> 00:05:04,160
+order اللي يقسم الـ order للـ group وكل قاسم لـ order
+
+52
+00:05:04,160 --> 00:05:10,280
+الـ group اللي قاسم لـ order له هذا القاسم let
+
+53
+00:05:10,280 --> 00:05:17,430
+order الجي بده يساوي n نجمع المعلومات السبعة تقسم
+
+54
+00:05:17,430 --> 00:05:22,730
+الـ n ليش H subgroup من الـ j و order الـ H ودي
+
+55
+00:05:22,730 --> 00:05:34,610
+ساوي سبعة ثانية الـ n لا يساوي سبعة ليش لإن H
+
+56
+00:05:34,610 --> 00:05:40,050
+proper subgroup من الـ j ليش proper لإن جالي فيه
+
+57
+00:05:40,050 --> 00:05:46,930
+الـ H وفيه الـ j والتنتين مختلفة إذا أريد الـ N
+
+58
+00:05:46,930 --> 00:05:56,430
+الـ 7 تقسم الـ N والـ N لا تساوي 7 الـ
+
+59
+00:05:56,430 --> 00:06:03,930
+N مثلا تساوي 7K الـ
+
+60
+00:06:03,930 --> 00:06:14,630
+N ماذا تساوي؟ 7K حيث K أكبر من 1 ليش K أكبر من
+
+61
+00:06:14,630 --> 00:06:23,150
+الواحد؟ لأن الـ n لا يساوي سبعة But J is cyclic إيش
+
+62
+00:06:23,150 --> 00:06:33,130
+يعني؟ يعني يوجد subgroup T من الـ J and order T
+
+63
+00:06:38,280 --> 00:06:42,520
+قدامي ثلاثة خيارات يا إما T بده تساوي الـ identity
+
+64
+00:06:42,520 --> 00:06:50,980
+وبالتالي K بده يساوي واحد وهذا تناقض أو
+
+65
+00:06:50,980 --> 00:06:57,580
+T بده تساوي H وبالتالي
+
+66
+00:06:57,580 --> 00:07:03,120
+K بده يساوي سبعة وأنا الـ N بده يساوي تسعة وأربعين
+
+67
+00:07:03,120 --> 00:07:07,080
+وهذا مافيش فيه مشكلة أو
+
+68
+00:07:08,540 --> 00:07:19,940
+كيس واحد هذا كيس اثنين وهذا كيس ثلاثة الـ T بتتساوي
+
+69
+00:07:19,940 --> 00:07:25,600
+الـ G نفسها هذا
+
+70
+00:07:25,600 --> 00:07:37,640
+ماعنته إن الـ K بتتساوي N إيش يعني؟ يعني سبعة K مش
+
+71
+00:07:37,640 --> 00:07:42,220
+الـ n بده تساوي 7k وبالتالي واحد بده يساوي سبعة وده
+
+72
+00:07:42,220 --> 00:07:45,520
+عبارة عن إيش؟ من الحالة الوحيدة اللي مافيش فيها
+
+73
+00:07:45,520 --> 00:07:49,240
+تناقض الـ n
+
+74
+00:07:49,240 --> 00:07:57,580
+بده تساوي تسعة وأربعين وهذا هو الحل الصحيح
+
+75
+00:07:57,580 --> 00:08:03,820
+طيب نرجع للمعطيات تبعت السؤال بيقول لي يوجد الـ
+
+76
+00:08:03,820 --> 00:08:10,400
+cyclic group لها فقط ثلاثة subgroup الـ identity و
+
+77
+00:08:10,400 --> 00:08:13,700
+subgroup H الـ order اللي لها سبعة و الـ J نفسها
+
+78
+00:08:13,700 --> 00:08:17,860
+بهيك بيقول لإنه الـ J الـ order اللي لها أكبر من
+
+79
+00:08:17,860 --> 00:08:23,560
+السبعة والسبعة بتقسم الـ order للـ J لإن هو J
+
+80
+00:08:23,560 --> 00:08:28,120
+Cyclic بس الـ n بدأت تساوي 7K والـ K أكبر من
+
+81
+00:08:28,120 --> 00:08:33,800
+الواحد حاجة الـ J Cyclic فأكيد لازم تلاقي subgroup
+
+82
+00:08:33,800 --> 00:08:39,250
+الـ order اللي لها K طيب هذه الـ subgroup يا بده
+
+83
+00:08:39,250 --> 00:08:44,050
+تساوي الـ identity إن مافيش غير ثلاثة دول وهذا
+
+84
+00:08:44,050 --> 00:08:50,690
+تناقض هيخلي الـ K بيساوي واحد أو الـ H بده تساوي أو
+
+85
+00:08:50,690 --> 00:08:54,850
+الـ T بده تساوي الـ H وأنا مافيش مشاكل بيعطيني الـ
+
+86
+00:08:54,850 --> 00:08:58,950
+Ant سواء باين أو الـ H هي نفس الـ J وأنا بيعطيني
+
+87
+00:08:58,950 --> 00:09:03,170
+تناقض يعني بالحالة الوحيدة اللي زبطت معايا هي مين
+
+88
+00:09:03,170 --> 00:09:08,990
+الحالة الثانية والـ n بتطلع قد إيش؟ تسعة وأربعين واضحة
+
+89
+00:09:08,990 --> 00:09:19,870
+هذه؟ واضحة يا شباب؟ طيب إيش
+
+90
+00:09:19,870 --> 00:09:26,930
+يا شمش ده؟ إيش .. وإن بتكتب؟ هنا؟ احنا بنشد ..
+
+91
+00:09:44,880 --> 00:09:48,500
+حسب النظريات اللي عندي لكل قاسم فيه subgroup الـ order
+
+92
+00:09:48,500 --> 00:09:53,820
+لهذه الـ subgroup بيساوي القاسم الـ
+
+93
+00:09:53,820 --> 00:09:59,640
+K رقم طب والسبعة؟ الـ K قاسم ثاني غير السبعة
+
+94
+00:10:03,160 --> 00:10:07,260
+طيب خمسة عشر let j be an abelian group at rest
+
+95
+00:10:07,260 --> 00:10:13,280
+what can you say if سبعة is replaced by بيه الـ
+
+96
+00:10:13,280 --> 00:10:20,120
+order لـ j هي سوى بيه تربيع لو بنستبدل السبعة بيه
+
+97
+00:10:20,120 --> 00:10:25,220
+هيكون الـ order عبارة عن بيه تربيع سؤال خمسة عشر
+
+98
+00:10:30,230 --> 00:10:41,970
+suppose that a cyclic group J أو JAB يعني group و
+
+99
+00:10:41,970 --> 00:10:50,570
+الـ H عبارة عن كل الـ J في الـ J حيث الـ order لـ J
+
+100
+00:10:50,570 --> 00:10:58,850
+يقسم 12 prove that H is a subgroup of J مطلوب إن
+
+101
+00:10:58,850 --> 00:11:08,770
+يثبت هل ممكن
+
+102
+00:11:08,770 --> 00:11:27,590
+نغير 12 بأي رقم هل ممكن نغير 12 بأي رقم هل ممكن
+
+103
+00:11:27,590 --> 00:11:33,090
+نغير 12 بأي رقم المجموعة بتمثل subgroup كل العناصر
+
+104
+00:11:33,090 --> 00:11:40,650
+اللي في j اللي الـ order اللي هي بيقسم 12 طيب تبدأ
+
+105
+00:11:40,650 --> 00:11:48,910
+تثبت إن هي subgroup موضوع تقليدي first H لا يساوي 5
+
+106
+00:11:48,910 --> 00:11:55,430
+since الـ identity في الـ H since الـ order للـ
+
+107
+00:11:55,430 --> 00:11:57,310
+identity بيساوي 1 يقسم 12
+
+108
+00:12:00,090 --> 00:12:10,230
+طيب ف a و b ينتمي للـ H يعني الـ order لـ a والـ
+
+109
+00:12:10,230 --> 00:12:16,870
+order لـ b كلاهما بيقسم مين الـ 12 إيش بدي أشوف أنا
+
+110
+00:12:16,870 --> 00:12:23,770
+هذا معناه إن a و 12 بيساوي الـ identity بيساوي b و
+
+111
+00:12:23,770 --> 00:12:29,810
+12 بغض النظر لو أقدر اثنين، ثلاثة، ستة، أربعة،
+
+112
+00:12:29,810 --> 00:12:33,650
+اثنا عشر، لأ بهمني إن الـ a أس اثنا عشر والـ b أس اثنا عشر
+
+113
+00:12:33,650 --> 00:12:41,070
+بيعطيني مين؟ الـ identity for a P inverse اللي هي
+
+114
+00:12:41,070 --> 00:12:49,990
+one step الـ a P inverse أس اثنا عشر عبارة عن a أس
+
+115
+00:12:49,990 --> 00:12:59,640
+اثنا عشر P inverse أس اثنا عشر هذا السبب على سبب إيش؟
+
+116
+00:12:59,640 --> 00:13:06,020
+ليش قدرت أعمل هذه الحركة؟ عشان الـ B يعني طيب الـ A
+
+117
+00:13:06,020 --> 00:13:13,180
+وصلة واثنا عشر identity الـ B وصلة واثنا عشر هذا
+
+118
+00:13:13,180 --> 00:13:17,440
+هيساوي الـ identity في B وصلة واثنا عشر inverse يعني
+
+119
+00:13:17,440 --> 00:13:24,830
+identity inverse هيساوي identity الـ A P inverse الـ
+
+120
+00:13:24,830 --> 00:13:31,150
+order اللي بيقسم الـ 12 a,b,in,out ينتمي لمين؟ للـ
+
+121
+00:13:31,150 --> 00:13:38,490
+H فبالتالي الـ H sub group من مين؟ من الـ G هل
+
+122
+00:13:38,490 --> 00:13:45,070
+الرقم 12 special؟ لو بدلت 12 بأي رقم ثاني؟ مش
+
+123
+00:13:45,070 --> 00:13:50,630
+ضروري مضاعفة لو حطيت 7 بدل 12، في مشكلة؟ لو حطيت
+
+124
+00:13:50,630 --> 00:13:59,680
+1000؟ مافيش مشكلة، 12 is not special يعني ممكن تبدل
+
+125
+00:13:59,680 --> 00:14:05,000
+الـ 12 بأي رقم مين الحاجة الضرورية هنا الـ abelian
+
+126
+00:14:05,000 --> 00:14:13,000
+مش الـ 12 لو مش abelian ماقدرتش أنا أعمل الفكرة هذه
+
+127
+00:14:13,000 --> 00:14:19,180
+طيب
+
+128
+00:14:20,740 --> 00:14:25,380
+ليش 12 مش special؟ شيل 12 وحط أي رقم بدك إياها،
+
+129
+00:14:25,380 --> 00:14:28,960
+بيفرق معاك؟ طيب، هيك بـ 12 مش special
+
+130
+00:14:50,820 --> 00:14:56,200
+أه اللي خلانى أقدر أشتغل هنا بالأسلوب أو وأطلع
+
+131
+00:14:56,200 --> 00:15:05,020
+النتيجة اللي موجودة قدامك هو أنه لجروب آبيليان يعني
+
+132
+00:15:05,020 --> 00:15:10,720
+17 complete the statement order الـ A بتساوي order 
+
+133
+00:15:10,720 --> 00:15:16,280
+الـ A تربيع if and only if order الـ A is is ايش
+
+134
+00:15:20,770 --> 00:15:24,890
+17 complete the following statement order A بتساوي
+
+135
+00:15:24,890 --> 00:15:38,950
+order A تربيع if and only if order A is يبسط
+
+136
+00:15:38,950 --> 00:15:47,750
+الـ order لإيه؟ طلع معايا نشوف بعض الحالات ونجمعهم
+
+137
+00:15:47,750 --> 00:15:51,940
+عشان نحط كيس واحدة order الـ A بتساوي order الـ A تربيع
+
+138
+00:15:51,940 --> 00:15:58,780
+مين ممكن تلاقي تحت هذا الإطار ممكن نضمه أولا
+
+139
+00:15:58,780 --> 00:16:04,260
+الـ identity order الـ E بتساوي order الـ E تربيع بتساوي
+
+140
+00:16:04,260 --> 00:16:09,620
+واحدة اثنين لو
+
+141
+00:16:09,620 --> 00:16:16,460
+order الـ A infinite برضه
+
+142
+00:16:16,460 --> 00:16:17,580
+order الـ E تربيع infinite
+
+143
+00:16:22,670 --> 00:16:28,250
+بس ايش بيظل عندي حالة؟ حالة الـ finite في الـ finite
+
+144
+00:16:28,250 --> 00:16:34,930
+كم كيس عندي؟ فردي وزوجي لو كان order الـ a زوجي هل
+
+145
+00:16:34,930 --> 00:16:41,270
+هذا الكلام يكون صحيح؟ لو order الـ a بتساوي 2q فـ order
+
+146
+00:16:41,270 --> 00:16:48,190
+الـ a تقريبا بتساوي q ايه كده؟ بدي انفذ زوجي طب
+
+147
+00:16:48,190 --> 00:16:53,670
+نشوف الفردي لو order الـ A بتساوي 2Q زي 1 برضه order
+
+148
+00:16:53,670 --> 00:17:01,370
+الـ A تربيع 2Q زي 1 ايه بقى الـ identity زبطت طب
+
+149
+00:17:01,370 --> 00:17:06,550
+هتنساش إن الـ identity ممكن تدخل وين في حالة الـ
+
+150
+00:17:06,550 --> 00:17:12,930
+order الفردي الـ identity الـ order الهيش واحد وال
+
+151
+00:17:12,930 --> 00:17:17,160
+infinite يجب الفردي بظبط والـ infinite بظبط مين
+
+152
+00:17:17,160 --> 00:17:23,760
+اللي بظبط ايش يجب ايش نقول if order a is not even
+
+153
+00:17:23,760 --> 00:17:30,840
+if and سبعة عشر بدك تكملها if and only if order a
+
+154
+00:17:30,840 --> 00:17:34,700
+is not even
+
+155
+00:17:34,700 --> 00:17:39,780
+ركز معايا مافيش infinite even مافيش infinite even
+
+156
+00:17:39,780 --> 00:17:44,910
+و odd الـ Infinite مش فيه even أو odd الـ Infinite
+
+157
+00:17:44,910 --> 00:17:49,570
+Infinite واضح؟
+
+158
+00:17:49,570 --> 00:17:52,850
+يعني هي لو حالة واحدة كانت قولت if and only if
+
+159
+00:17:52,850 --> 00:17:56,890
+order الـ A infinite مثلا لو نفينا هذه وهذه بس أنا
+
+160
+00:17:56,890 --> 00:18:01,230
+نفينا واحدة وأثبتنا اثنتين فبدل ما أقول if and only
+
+161
+00:18:01,230 --> 00:18:05,150
+if order الـ A is infinite أو order الـ A is odd
+
+162
+00:18:05,150 --> 00:18:09,190
+بقول لأ not even بغيّر حالي طب كيف الوضع اللي قلت
+
+163
+00:18:09,190 --> 00:18:15,350
+من الـ Q يعني؟ order a بيبقى اثنين اثنين اثنين اثنين
+
+164
+00:18:15,350 --> 00:18:18,650
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+165
+00:18:18,650 --> 00:18:20,710
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+166
+00:18:20,710 --> 00:18:20,750
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+167
+00:18:20,750 --> 00:18:22,010
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+168
+00:18:22,010 --> 00:18:24,130
+اثنين اثنين اثنين اثنين اثنين اثنين اثنين اثنين
+
+169
+00:18:24,130 --> 00:18:30,430
+اثنين اثنين ا
+
+170
+00:18:39,470 --> 00:18:45,210
+بتساوي order of a تربيع هجيت قدامي order of a تلت
+
+171
+00:18:45,210 --> 00:18:53,290
+حالات even, odd, infinite هجيت هذه بتظبط وهذه
+
+172
+00:18:53,290 --> 00:19:00,950
+بتظبط وهذه لأ فأوحان في هذه if and only if order
+
+173
+00:19:00,950 --> 00:19:08,530
+of a is not even طيب
+
+174
+00:19:11,590 --> 00:19:17,390
+مش فاهم مش فاهم الـ even والـ odd ده مش يعني even
+
+175
+00:19:17,390 --> 00:19:24,990
+طيب فلو كان order الـ A بتساوي اثنين Q يعني A أس
+
+176
+00:19:24,990 --> 00:19:28,610
+اثنين Q بتساوي الـ identity يعني A تربيع أس Q بتساوي
+
+177
+00:19:28,610 --> 00:19:34,250
+الـ identity فـ order الـ A تربيع على الأكثر Q أقل
+
+178
+00:19:34,250 --> 00:19:38,450
+من order الـ A ايه؟ فلو كان order الـ A even هذه
+
+179
+00:19:38,450 --> 00:19:47,360
+ما بتنفعش هذه غير مفيدة، واضحة؟ حجزت، لو كان order
+
+180
+00:19:47,360 --> 00:19:51,120
+الـ A بتساوي ماله نهاية فأكيد order الـ A تربيع
+
+181
+00:19:51,120 --> 00:19:58,680
+ماله نهاية يقبل even، ما بتنفعش الـ infinite بتنفع،
+
+182
+00:19:58,680 --> 00:20:04,160
+بيضال مين؟ الـ odd حجزت order الـ A بتساوي un و un
+
+183
+00:20:04,160 --> 00:20:10,990
+odd فـ order الـ A بتساوي order الـ A أس K حيث إن
+
+184
+00:20:10,990 --> 00:20:16,770
+اجيز common divisor لـ K و M يساوي 1 صح ولا لأ؟ طب
+
+185
+00:20:16,770 --> 00:20:24,070
+حط بدل K 2 هل هذا الكلام صحيح؟ خلط يجب أن أقدر لـ A
+
+186
+00:20:24,070 --> 00:20:30,890
+تربيع لكي اجيز common divisor لـ 2 و 1 يساوي 2 و M
+
+187
+00:20:30,890 --> 00:20:34,590
+يساوي 1 بس بسرعة
+
+188
+00:20:38,830 --> 00:20:44,910
+لو في عندك J Cyclic يوجد
+
+189
+00:20:44,910 --> 00:20:51,370
+A في الـ J الـ order لـ A يساوي ماله نهاية كم عنصر
+
+190
+00:20:51,370 --> 00:20:56,630
+الـ order له finite في الـ J طالع معايا الـ A الـ
+
+191
+00:20:56,630 --> 00:21:00,570
+order له infinite فـ A و A تربيع و A تكعيب و A أس
+
+192
+00:21:00,570 --> 00:21:05,250
+خمسة و A أس أي حاجة هيكون الـ order له infinite بعد
+
+193
+00:21:05,250 --> 00:21:19,540
+مين الـ identity the only element of finite order is
+
+194
+00:21:19,540 --> 00:21:26,120
+E هذا فقط في الـ cyclic لو أنت بتشتغل في group مش
+
+195
+00:21:26,120 --> 00:21:30,700
+cyclic ممكن تلاقي عناصر الـ order اللي هم finite
+
+196
+00:21:30,700 --> 00:21:36,580
+حتى لو كانت الـ group infinite حتى لو كانت الـ group
+
+197
+00:21:36,580 --> 00:21:41,020
+infinite إذا أسمي كل جريس كمان بقايا سلطانة، فالأمر
+
+198
+00:21:41,020 --> 00:21:44,440
+ما فيه سواء حد؟
+
+199
+00:21:57,580 --> 00:22:01,480
+عشان يكون الـ order لـ A أس K بتساوي order لـ A يعني
+
+200
+00:22:01,480 --> 00:22:05,980
+بتساوي N فالـ N بتساوي N على الـ divisor لـ K و N
+
+201
+00:22:05,980 --> 00:22:08,680
+يعني الـ order لـ A أس K بتساوي order لـ A
+
+202
+00:22:22,780 --> 00:22:27,960
+سؤال تسعة عشر سهل بتشوف الـ generators للعناصر في U
+
+203
+00:22:27,960 --> 00:22:34,240
+ثلاثين أو بتمسك العناصر بتشوف ايش بولته سؤال عشرين
+
+204
+00:22:34,240 --> 00:22:37,500
+suppose that J is a pelian group of order خمسة وثلاثين و
+
+205
+00:22:37,500 --> 00:22:39,840
+ثلاثين and every element of J satisfies the
+
+206
+00:22:39,840 --> 00:22:43,500
+equation X وخمسة وثلاثين دي بتساوي identity proof
+
+207
+00:22:43,500 --> 00:22:49,340
+that J is cyclic order
+
+208
+00:22:49,340 --> 00:22:59,540
+للـ J دي بتساوي خمسة وثلاثين J is Abelian لكل
+
+209
+00:22:59,540 --> 00:23:15,800
+X في J X و 35 بتساوي الـ identity يثبت أن J صحيح هل
+
+210
+00:23:15,800 --> 00:23:18,500
+35 special تعال نشوف
+
+211
+00:23:24,150 --> 00:23:27,670
+جي آبيليان وكل عنصر فيها بيحقق العلاقة إن x أس
+
+212
+00:23:27,670 --> 00:23:38,010
+خمسة وثلاثين بتساوي الـ identity هل الـ جي Cyclic
+
+213
+00:23:38,010 --> 00:23:43,550
+عشان أثبت إن الجي Cyclic لازم يلاقي عنصر يعني
+
+214
+00:23:43,550 --> 00:23:52,770
+المطلوب prove that يوجد g في الـ جي أو a في الـ جي أو
+
+215
+00:23:52,770 --> 00:24:07,990
+أخضر أنت ابني سنة وخمسة وثلاثين هاطوني
+
+216
+00:24:07,990 --> 00:24:15,910
+حلولكم لم أحضر السؤال أو اعتبوني ما شوفتش السؤال
+
+217
+00:24:15,910 --> 00:24:18,890
+قبل هيك فكوا معايا
+
+218
+00:24:21,730 --> 00:24:29,470
+I'm here ولا أنا ايش
+
+219
+00:24:29,470 --> 00:24:36,390
+نعمل ايش الموضوع اللي عندك يا شباب جي آبيليان زائد
+
+220
+00:24:36,390 --> 00:24:46,490
+الأخضر خمسة وثلاثين طيب زائد إن كل
+
+221
+00:24:46,490 --> 00:24:52,250
+العناصر بتحقق إن x أس خمسة وثلاثين بتساوي الـ
+
+222
+00:24:52,250 --> 00:24:57,210
+identity أنا بدي أثبت إنه يوجد عنصر الـ order له
+
+223
+00:24:57,210 --> 00:25:08,070
+خمسة وثلاثين كيف؟
+
+224
+00:25:08,070 --> 00:25:12,570
+فكروا
+
+225
+00:25:15,710 --> 00:25:22,530
+أسس الطريقة لإثبات جمل بهذا الشكل هي تنقض هفترض إن
+
+226
+00:25:22,530 --> 00:25:32,730
+لا يوجد عنصر الـ order له 35 تنساش إن الـ .. لو
+
+227
+00:25:32,730 --> 00:25:37,730
+بدي أخد أي عنصر هنا ويكون عندك x و 35 بتساوي الـ
+
+228
+00:25:37,730 --> 00:25:43,490
+identity و X في الـ J معناته order كل العناصر
+
+229
+00:25:43,490 --> 00:25:48,270
+الموجودين في الـ J قواسم للخمسة والثلاثين قلنا مافيش
+
+230
+00:25:48,270 --> 00:25:52,070
+عنصر الـ order له خمسة وثلاثين فكل عنصر أنا باخد
+
+231
+00:25:52,070 --> 00:25:58,810
+غير الـ identity الـ order له أما خمسة
+
+232
+00:25:58,810 --> 00:26:07,610
+أو سبعة هجي تواجد العناصر حسب الـ order خمسة بيجي
+
+233
+00:26:07,610 --> 00:26:08,890
+في أي شكل
+
+234
+00:26:11,690 --> 00:26:15,170
+عناصر الـ order لهم خمسة، لو كان عند الـ X الـ order
+
+235
+00:26:15,170 --> 00:26:22,430
+لهم خمسة أكمل عنصر زي بلاج الـ order لهم خمسة X X
+
+236
+00:26:22,430 --> 00:26:29,570
+تربيع X تكعيب X أربعة هدولة كلهم الـ order اللي هم
+
+237
+00:26:29,570 --> 00:26:33,850
+خمسة لو أنا لو أخدت X في هذه لجروب الـ order اللي هو
+
+238
+00:26:33,850 --> 00:26:37,770
+خمسة وأخدت الـ generated by X اللي هو الـ identity
+
+239
+00:26:37,770 --> 00:26:41,550
+هو X و X تربيع و X تكعيب و X أربعة مع هذا الـ
+
+240
+00:26:41,550 --> 00:26:45,270
+identity الأربع عناصر هدولة اللي هم فيها الخمسة الـ
+
+241
+00:26:45,270 --> 00:26:49,150
+order اللي هم خمسة يجب تواجد الـ order الخمسة هيكون
+
+242
+00:26:49,150 --> 00:26:53,810
+في ايش؟ في أربع شيل الـ identity من الخمسة
+
+243
+00:26:53,810 --> 00:27:04,360
+وثلاثين كده هيظل أربعة وثلاثين، شيل كل الأربعات،
+
+244
+00:27:04,360 --> 00:27:11,660
+يجب مش كل العناصر الـ order لهم خمسة، بنفس الطريقة
+
+245
+00:27:11,660 --> 00:27:18,020
+الـ order سبعة بيجي في ستة X تربيع لإن X هو الستة
+
+246
+00:27:18,020 --> 00:27:22,940
+شيل الستات من الأربعة والثلاثين بيظل أربعة يكبر مش
+
+247
+00:27:22,940 --> 00:27:26,620
+كل العناصر الـ order اللي لهم سبعة مش كل العناصر الـ
+
+248
+00:27:26,620 --> 00:27:31,680
+order اللي لهم خمسة فش الـ order خمسة وثلاثين يكبر
+
+249
+00:27:31,680 --> 00:27:34,620
+في عنصر الـ order اللي له خمسة وفي عنصر الـ order
+
+250
+00:27:34,620 --> 00:27:40,920
+اللي له سبعة خدها ده A خدها ده B الـ order لـ A و B 
+
+251
+00:27:40,920 --> 00:27:45,260
+هيكون كده؟ خمسة و ثلاثين و هو هيكون الـ generator
+
+252
+00:27:46,570 --> 00:27:52,910
+فجهز حالك للسؤال ده في شغل Assume
+
+253
+00:27:52,910 --> 00:28:06,930
+that there is no element in J with order خمسة و 
+
+254
+00:28:06,930 --> 00:28:13,430
+ثلاثين فش أنصر في الـ J الـ order الو خمسة و ثلاثين
+
+255
+00:28:13,430 --> 00:28:15,110
+since
+
+256
+00:28:16,700 --> 00:28:24,260
+X<sup>35</sup> يساوي الـ identity لكل X في J معناته order X
+
+257
+00:28:24,260 --> 00:28:32,920
+هيقسم 35 لكل X في J order
+
+258
+00:28:32,920 --> 00:28:42,500
+X يساوي 35 لكل X في J if X لا يساوي الـ identity
+
+259
+00:28:45,790 --> 00:28:52,070
+Order of X بيدى يساوي خمسة Or order of X بيدى يساوي
+
+260
+00:28:52,070 --> 00:28:59,910
+سبعة طبعا أكيد order of X لا يساوي خمسة و ثلاثين
+
+261
+00:28:59,910 --> 00:29:04,950
+يكبر جميع العناصر مع عدل identity يعني الـ order له
+
+262
+00:29:04,950 --> 00:29:12,110
+خمسة أو سبعة إجازة اللي هنعمله كانت تالي We will
+
+263
+00:29:12,110 --> 00:29:13,650
+show that
+
+264
+00:29:19,910 --> 00:29:23,490
+احنا هننفيها عشان نشرح الخمسة و السابعة لحالنا و
+
+265
+00:29:23,490 --> 00:29:28,930
+نصلّى تناقض لهذه الجملة اللي نفنها We will show
+
+266
+00:29:28,930 --> 00:29:35,690
+that there
+
+267
+00:29:35,690 --> 00:29:46,310
+is elements in D with order
+
+268
+00:29:47,650 --> 00:29:58,350
+خمسة and elements with order سبعة هاتبت إنه يوجد
+
+269
+00:29:58,350 --> 00:30:02,550
+عناصر الـ order له خمسة و يوجد عناصر الـ order له
+
+270
+00:30:02,550 --> 00:30:07,930
+ايش سبعة برضه هشغل هالجتنا في داخلي هنفي إنه ..
+
+271
+00:30:07,930 --> 00:30:11,610
+يعني هقول إنه مافيش order سبعة يعني كل الـ order
+
+272
+00:30:11,610 --> 00:30:14,610
+خمسة to show that
+
+273
+00:30:17,330 --> 00:30:25,890
+we will first assume that
+
+274
+00:30:25,890 --> 00:30:43,830
+there is no elements in J with order 7 assume that
+
+275
+00:30:43,830 --> 00:30:46,050
+all
+
+276
+00:30:48,400 --> 00:31:00,780
+x لا يساوي الـ identity in j has order خمسة Note
+
+277
+00:31:00,780 --> 00:31:05,080
+that if
+
+278
+00:31:05,080 --> 00:31:10,500
+order الـ x بيدى يساوي خمسة then order الـ x تربيع بيدى
+
+279
+00:31:10,500 --> 00:31:13,800
+يساوي order الـ x تكعيب بيدى يساوي order الـ x أربعة
+
+280
+00:31:13,800 --> 00:31:22,530
+بيدى يساوي خمسة طبعا هذه بدأ إثبات prove it إثباتها
+
+281
+00:31:22,530 --> 00:31:30,370
+سهل الـ order لـ exos k بيدى ساوي الـ o اللي هو n اللي
+
+282
+00:31:30,370 --> 00:31:34,430
+هي خمسة على order لجيسكم و الـ divisor لـ الخمسة و
+
+283
+00:31:34,430 --> 00:31:41,170
+الـ k في نهاية تصل لكلام هذا هذا معناته the order
+
+284
+00:31:41,170 --> 00:31:46,350
+خمسة is found in
+
+285
+00:31:47,360 --> 00:32:02,040
+J in six contains four elements هذا
+
+286
+00:32:02,040 --> 00:32:10,580
+معناته J هتساوي الـ identity اتحاد X1 X1 تربيع X2
+
+287
+00:32:10,580 --> 00:32:29,670
+X1 تكعيب X1 أقص 4 اتحاد X2 X2 تربيع X2 تكعيب لأن X2
+
+288
+00:32:29,670 --> 00:32:43,030
+أقص 4 اتحاد وصولا لـ XI أو XT XT تربيع XT تكعيب
+
+289
+00:32:59,740 --> 00:33:04,000
+X لا يساوي X تربيع X لا يساوي X تكعيب
+
+290
+00:33:06,760 --> 00:33:12,100
+X تربيع لا يساوي X تكعيب X تربيع لا يساوي X أربعة
+
+291
+00:33:12,100 --> 00:33:17,800
+X تكعيب لا يساوي X أربعة عشان ماحدش يقولي هدول
+
+292
+00:33:17,800 --> 00:33:22,000
+ممكن يكونوا مكررين ولا واحد من ربعي هذا بيساوي
+
+293
+00:33:22,000 --> 00:33:26,880
+التاني لا هذا بيساوي هدول ولا هذا بيساوي هدول ولا
+
+294
+00:33:26,880 --> 00:33:33,940
+هذا بيساوي هذا هذا معناته order الـ J بيساوي أربعة
+
+295
+00:33:33,940 --> 00:33:44,120
+T زاد واحد واحد زيادة أربعة زيادة أربعة بعد الواحد
+
+296
+00:33:44,120 --> 00:33:48,860
+بصيح تجمع أربعات يعني الخمسة و ثلاثين بيدى يساوي
+
+297
+00:33:48,860 --> 00:33:56,360
+ايش أربعة T زيادة الواحد 2T بيدى يساوي سبعة عشر
+
+298
+00:33:56,360 --> 00:34:02,580
+و هذا تناقض هذا
+
+299
+00:34:02,580 --> 00:34:07,620
+تناقض so not
+
+300
+00:34:08,250 --> 00:34:19,910
+all elements in j has order واحد أو خمسة ايش يعني؟
+
+301
+00:34:19,910 --> 00:34:24,130
+مش الكل واحد مش الكل خمسة، مافيش خمسة و ثلاثين،
+
+302
+00:34:24,130 --> 00:34:33,710
+ايش هيضل؟ ايش بقى؟ at least there is a ينتمي للـ j
+
+303
+00:34:33,710 --> 00:34:42,620
+and order الـ a بيدى يساوي سبعة أعطيها نجمة Similarly
+
+304
+00:34:42,620 --> 00:34:49,820
+بنفس الطريقة there
+
+305
+00:34:49,820 --> 00:34:58,440
+is P إذا فيها نكسة لا اطلع فيها اجيت على الواجب
+
+306
+00:34:58,440 --> 00:35:06,300
+فادي there is P ينتمي نرجع with order الـ P بيدى
+
+307
+00:35:06,300 --> 00:35:11,830
+ساوي خمسة طبعا نفس الطريقة بفترض إنه فيش order خمسة
+
+308
+00:35:11,830 --> 00:35:16,310
+فكله يا سبعات يا واحد الـ order تبع السبعات بيجي
+
+309
+00:35:16,310 --> 00:35:22,050
+فياش؟ هشيل الـ واحد الـ order تبع السبعات بيجي فياش؟
+
+310
+00:35:22,050 --> 00:35:26,190
+في شكل مجموعات كل مجموعة فيها ست عناصر بيكون عندك
+
+311
+00:35:26,190 --> 00:35:29,750
+خمسة و ثلاثين بيكون ستة T زاد الواحد ستة T بيكون
+
+312
+00:35:29,750 --> 00:35:36,190
+أربعة و ثلاثين أنا هى السبعة و ايه الخمسة؟ ستة T
+
+313
+00:35:36,190 --> 00:35:38,310
+بيدى ساوي أربع تلات تلات تلات تلات تلات تلات تلات
+
+314
+00:35:38,310 --> 00:35:38,770
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+315
+00:35:38,770 --> 00:35:39,390
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+316
+00:35:39,390 --> 00:35:47,630
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+317
+00:35:47,630 --> 00:35:53,070
+تلات تلات تلات تلات تلات تلات تلات تلات تلات تلات
+
+318
+00:35:53,070 --> 00:35:54,910
+تلات تلات تلات تلات
+
+319
+00:36:05,570 --> 00:36:10,470
+لأ واحدة تلاتة أربعة التيش ده تكون، عداد، العداد
+
+320
+00:36:10,470 --> 00:36:18,750
+ينتمي لأن مش للـ Z كمان طيب claim order
+
+321
+00:36:18,750 --> 00:36:22,990
+الـ A B بيدى ساوي خمسة و ثلاثين طبعا اتباع الـ claim
+
+322
+00:36:22,990 --> 00:36:25,710
+بصير تناقض مع مين؟ مع الـ assumption
+
+323
+00:36:31,200 --> 00:36:35,160
+Since الـ order لـ الـ A بيدى تساوي خمسة أو الـ A بيدى
+
+324
+00:36:35,160 --> 00:36:41,620
+تساوي سبعة الـ order لـ الـ B بيدى تساوي خمسة لو قلنا الـ
+
+325
+00:36:41,620 --> 00:36:46,160
+A بيقص خمسة و ثلاثين عبارة عن A أقص خمسة و ثلاثين
+
+326
+00:36:46,160 --> 00:36:52,000
+في B أقص خمسة و ثلاثين identity في identity ايش
+
+327
+00:36:52,000 --> 00:36:57,640
+بيدى تساوي identity هذا معناته order لـ الـ A بي
+
+328
+00:37:01,460 --> 00:37:10,920
+أشماله يقسم الخمسة و ثلاثين خلصناش case واحد order
+
+329
+00:37:10,920 --> 00:37:17,190
+الـ AB بيدى يساوي واحد يكبى a,b بيدى يساوي الـ identity a
+
+330
+00:37:17,190 --> 00:37:23,290
+بيدى يساوي b inverse يكبى o الخمسة بيدى تساوي او
+
+331
+00:37:23,290 --> 00:37:27,450
+السبعة بيدى تساوي order الـ a اللي هو order الـ b
+
+332
+00:37:27,450 --> 00:37:30,430
+inverse اللي هو order الـ b بيدى يساوي خمسة وهذا
+
+333
+00:37:30,430 --> 00:37:39,330
+تناقض case اتنين الـ
+
+334
+00:37:39,330 --> 00:37:47,120
+order للـ a,b بيدى ساوي خمسة الـ
+
+335
+00:37:47,120 --> 00:37:51,200
+order للـ a,b بيدى ساوي خمسة ده ايش معناته هذا معناته
+
+336
+00:37:51,200 --> 00:37:59,180
+a,b أس خمسة بيدى ساوي الـ identity a,b أس خمسة بيدى
+
+337
+00:37:59,180 --> 00:38:06,560
+ساوي الـ identity ايش يعني يعني a أس خمسة,b أس خمسة
+
+338
+00:38:06,560 --> 00:38:10,640
+بيدى ساوي الـ identity يعني a أس خمسة بيدى ساوي الـ
+
+339
+00:38:10,640 --> 00:38:17,320
+identity هذا معناته السبعة بيديساوي order الـ a أقل
+
+340
+00:38:17,320 --> 00:38:26,680
+أو يساوي الخمسة و هذا تناقض case ثلاثة order الـ a
+
+341
+00:38:26,680 --> 00:38:31,780
+,b بيديساوي سبعة order
+
+342
+00:38:31,780 --> 00:38:36,300
+الـ a,b بيديساوي سبعة يعني a,b والسبعة بيديساوي الـ
+
+343
+00:38:36,300 --> 00:38:36,720
+identity
+
+344
+00:38:42,000 --> 00:38:46,340
+ماذا يعني؟ يعني a والسبعة بيه السبعة بيدى يسووا الـ
+
+345
+00:38:46,340 --> 00:38:50,980
+identity يعني الـ identity في بيه الخمسة في بيه
+
+346
+00:38:50,980 --> 00:38:55,020
+تربيع بيدى يسووا الـ identity بيه تربيع بيدى يسووا الـ
+
+347
+00:38:55,020 --> 00:39:00,980
+identity هذا معناته خمسة تسوي order الـ بيه فقال لو
+
+348
+00:39:00,980 --> 00:39:08,240
+يسووا اتنين تنقض مين ضال؟ الواحد لأ الخمسة لأ
+
+349
+00:39:08,240 --> 00:39:17,150
+السبعة لأ هذا معناته order الـ a,b يسوى 35 هدف نقض
+
+350
+00:39:17,150 --> 00:39:23,810
+مين contradiction contradiction
+
+351
+00:39:23,810 --> 00:39:29,850
+مع مين مع الفرض اللي أنا فرضه ان الـ a,b أو فيش
+
+352
+00:39:29,850 --> 00:39:38,230
+عنصر اللي orderedه 35 with the assumption that
+
+353
+00:39:38,230 --> 00:39:44,700
+there is no X ينتمي من الـ J و أغضر الـ X بالساعة 35
+
+354
+00:39:44,700 --> 00:39:48,040
+الفرض
+
+355
+00:39:48,040 --> 00:39:56,220
+اللي أنا فرضه خاطئ، ايش الصواب؟ عكسه طب ايش عكسه؟
+
+356
+00:39:56,220 --> 00:40:02,860
+أنا قولت فش الأغضر 35؟ يوجد X ينتمي للـ J Order X
+
+357
+00:40:02,860 --> 00:40:08,540
+يتساوي خمسة و ثلاثين Order X يتساوي order جي جي
+
+358
+00:40:08,540 --> 00:40:20,060
+جنيريتد by الـ X جي الصارت
+
+359
+00:40:20,060 --> 00:40:24,340
+طبعا
+
+360
+00:40:24,340 --> 00:40:27,540
+هل الخمسة و ثلاثين special
+
+361
+00:40:32,600 --> 00:40:38,240
+لو جربت التلاتة و ثلاثين مش هينفع لأ، من التلاتة و
+
+362
+00:40:38,240 --> 00:40:41,700
+ثلاثين عندك التلاتة و الـ 11 التلاتة بتكون موجودة
+
+363
+00:40:41,700 --> 00:40:49,460
+في ايش؟ في أزواج طيب،
+
+364
+00:40:49,460 --> 00:40:54,320
+معناته ممكن يكون عندك حالة يكون الأرض إلها تلاتة؟
+
+365
+00:40:54,320 --> 00:41:06,180
+ايه الشعير؟ هل 35 special ولا لا؟
+
+366
+00:41:06,180 --> 00:41:09,980
+تلاتة
+
+367
+00:41:09,980 --> 00:41:14,660
+و ثلاثين هل
+
+368
+00:41:14,660 --> 00:41:23,300
+ايه special؟
+
+369
+00:41:23,300 --> 00:41:29,040
+اه
+
+370
+00:41:29,040 --> 00:41:41,320
+شبابو نعمل تلاتة آلاف تسيتيش حاجة طيب و
+
+371
+00:41:41,320 --> 00:41:47,520
+دم هناخد نظرية تجاوب على السؤال هدا هنشتغل على الـ
+
+372
+00:41:47,520 --> 00:41:51,760
+ground theorem هنشتغل على الـ factor جوهر بالنسبالي
+
+373
+00:41:51,760 --> 00:41:56,100
+التلاتة و ثلاثين أنا
+
+374
+00:41:56,100 --> 00:42:01,560
+بقدر اجزم دائما إنه يوجد عنصر الأرض غيله تلاتة إن
+
+375
+00:42:01,560 --> 00:42:04,920
+اشتغلت على إحدى عشات، الإحدى عشات بتتواجد فيها في 
+
+376
+00:42:04,920 --> 00:42:09,020
+شكل عشرات فدائما بيظل عنصر الأرض غيله تلاتة طب هل
+
+377
+00:42:09,020 --> 00:42:12,200
+كل العناصر لو اشتغلت على التلاتات، التلاتات 
+
+378
+00:42:12,200 --> 00:42:19,800
+يتواجدوا في أزواج فبيظل ال identity لكن هل ده يعني
+
+379
+00:42:19,800 --> 00:42:25,100
+ممكن انا لاي .. بالطريقة اللي اشتغلت فيها أصل لقنع
+
+380
+00:42:25,100 --> 00:42:31,980
+أنه بقدر يكون كل group الأردن والعصر فيه تلتات هل
+
+381
+00:42:31,980 --> 00:42:35,280
+ممكن أن احصل على group فيها تلت و تلتين عنصر و
+
+382
+00:42:35,280 --> 00:42:38,920
+الأردن غيره تلتات؟
+
+383
+00:42:38,920 --> 00:42:43,960
+ايش رايكو؟ انا
+
+384
+00:42:43,960 --> 00:42:47,260
+مش حاجة تجربك على السؤال هذا لما اتأكد منه بس انا 
+
+385
+00:42:47,260 --> 00:42:54,310
+على اعتقادي ان الخمسة و تلتين قد تكون special يعني
+
+386
+00:42:54,310 --> 00:43:02,050
+ممكن يكون عند جروب ال order إلها P في Q ومش Cyclic
+
+387
+00:43:02,050 --> 00:43:14,890
+تلاتة
+
+388
+00:43:14,890 --> 00:43:20,980
+تلاتين عند تلاتة بيزيد شطب انا يا جد هبطمن ان ال 4
+
+389
+00:43:20,980 --> 00:43:23,720
+جديد و 3 جديد معايا يردوا يطلحوا مش 7 انا انا
+
+390
+00:43:23,720 --> 00:43:29,000
+معايا بحنا يا جد قولنا لو كل 1 و 5 ال 1 و 5
+
+391
+00:43:29,000 --> 00:43:33,460
+هيكونوا على الاكتر جداش تنين و تلاتين زي 1 تلات و
+
+392
+00:43:33,460 --> 00:43:40,260
+تلاتين هيضال عنصرين هدول العنصرين يا 7 يا 35 انا
+
+393
+00:43:40,260 --> 00:43:45,520
+نافل 35 فإيش بيضال عندي سبعة فهي كده انا اجزمت انه
+
+394
+00:43:45,520 --> 00:43:48,950
+في عنصر قدرله سبعة عشان ايه كده ان انا فيت ال 35 في
+
+395
+00:43:48,950 --> 00:43:53,570
+الأول عشان نشر على السبعة لحالي عشان ماقلتش كل
+
+396
+00:43:53,570 --> 00:43:58,030
+شوية جولة أبقى لو ال 35 خلصت لو مش 35 ف7 لأ لما
+
+397
+00:43:58,030 --> 00:44:03,910
+فيت ال 35 ضايحت حالي لما جيت جولة لكل سبعة واحد ال
+
+398
+00:44:03,910 --> 00:44:07,890
+maximum تبقى مجدهاش 31 بيبقى الأربعة أكيد منهم
+
+399
+00:44:07,890 --> 00:44:12,570
+الخمسة فدائما في سبعة دائما في خمسة هات واحد سبعة
+
+400
+00:44:12,570 --> 00:44:16,650
+و واحد خمسة بيطلع ال .. طبعا فادات نهانة كتير مين
+
+401
+00:44:17,540 --> 00:44:21,340
+موضوع ال abelian لو مش abelian بقدرش أشغل الشغل
+
+402
+00:44:21,340 --> 00:44:25,200
+اللي موجود هنا في ال cases اللي موجودين في الحالة
+
+403
+00:44:25,200 --> 00:44:30,160
+اللي موجودة ضمن الكلام واضح؟
+
+404
+00:44:30,160 --> 00:44:36,080
+أي سؤال؟ صحيح
+
+405
+00:44:36,080 --> 00:44:41,580
+قفتلك إياها؟ طب عشان حكينا دلوقتي لأن وكسوس خمسة
+
+406
+00:44:41,580 --> 00:44:46,710
+موجهة identityو X6 برجع ال X و X1 مش الأقدر ال X
+
+407
+00:44:46,710 --> 00:44:55,990
+كمسة ف X5 يبقوا عليا أي سؤال يا شباب؟ أي سؤال؟
+
+408
+00:44:55,990 --> 00:44:58,750
+واضح؟ يا عزيزي يا عزيزي يا شباب من كام اليوم
+
+409
+00:44:58,750 --> 00:44:59,990
+اتنين؟ 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4cf9e59dd648a4d7671bc29780c99e027f3ff084
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/G00BJLS6eH8_postprocess.srt
@@ -0,0 +1,1960 @@
+1
+00:00:21,400 --> 00:00:25,980
+الان بنرجع لشبتر ال permutation groups اللى خدتهم
+
+2
+00:00:25,980 --> 00:00:31,800
+مع الأستاذ محمود السرساوي ونقش لكوا أول عشرة مسائل
+
+3
+00:00:31,800 --> 00:00:37,780
+بنحاول نناقش بقية المسائل ان شاء الله وتبرك وتعالى
+
+4
+00:00:38,220 --> 00:00:42,540
+اللي انا بنيجي لسؤال 11، السؤال 11 بيقولي خدلي a
+
+5
+00:00:42,540 --> 00:00:47,060
+positive integer و
+
+6
+00:00:47,060 --> 00:00:53,580
+if ال a is odd و في عندى cycle طولها n طبعا
+
+7
+00:00:56,780 --> 00:01:01,840
+السؤال بيقول مرة تانية السؤال 11 بيقول ال n
+
+8
+00:01:01,840 --> 00:01:09,380
+positive integer و ال a is odd والا ال alpha is
+
+9
+00:01:09,380 --> 00:01:17,260
+odd و طولها n cycle ف ال n cycle هد بتبقى odd والا
+
+10
+00:01:17,260 --> 00:01:21,820
+even قالي بالك معاك الآن
+
+11
+00:01:22,280 --> 00:01:30,160
+أنا عندي ال n مااخد ليه اللي هو positive integer
+
+12
+00:01:30,160 --> 00:01:40,410
+لو كان ال n is oddو أنا عندي ال cycle ال cycle هذه
+
+13
+00:01:40,410 --> 00:01:49,190
+طولها n يعني بمعنى a1 a2 و لغاية an بهذا الشكل هل
+
+14
+00:01:49,190 --> 00:01:55,070
+ال permutation هذه بتبقى even والله قد علما ان ان
+
+15
+00:01:55,070 --> 00:02:01,620
+هذه عبارة عن aعن odd هذا هو السؤال طب لو كانت in
+
+16
+00:02:01,620 --> 00:02:06,580
+even برضه إيش اللي بد يكون يبقى ال on سواء كانت
+
+17
+00:02:06,580 --> 00:02:12,580
+odd و الله even بدنا نعرف هذه إيش بدتكون إذا بدي
+
+18
+00:02:12,580 --> 00:02:18,380
+أخد الحالة الأولى لو كانت ال on ال in is is odd
+
+19
+00:02:18,380 --> 00:02:24,200
+يبقى هدول عددهم odd أكم Transposition بقدر أسوي
+
+20
+00:02:24,200 --> 00:02:30,460
+منهملما يكون عددهم in a chemical composition او
+
+21
+00:02:30,460 --> 00:02:36,900
+two cycles بقدر اعمل منهم قداش عددهم يعني
+
+22
+00:02:36,900 --> 00:02:41,540
+اكتر من عددهم مقدار واحد والله اقل من عددهم مقدار
+
+23
+00:02:41,540 --> 00:02:46,120
+واحد اقل من عددهم مقدار واحد طب لو كان in فردي
+
+24
+00:02:46,120 --> 00:02:52,720
+يبقى الاقل منه بواحد ايش بيكون زوجي يبقى هنا if ال
+
+25
+00:02:52,720 --> 00:03:01,250
+in is odd او evenيبقى هذه بتبقى is even أو odd
+
+26
+00:03:01,250 --> 00:03:02,870
+permutation
+
+27
+00:03:05,030 --> 00:03:10,890
+يعني يعني عكس العدد اللي عندنا هذا لو كان العدد زي
+
+28
+00:03:10,890 --> 00:03:14,310
+مثال و ذلك لو قلت انا اشير انزل سايكل فيها واحد
+
+29
+00:03:14,310 --> 00:03:19,390
+اتنين تلاتة هيبقى هذه الطول فردي مظبوط اكمل
+
+30
+00:03:19,390 --> 00:03:23,170
+ترانسبوزش ان بقدر اعمل واحد تلاتة واحد اتنين يبقى
+
+31
+00:03:23,170 --> 00:03:28,620
+اتنين فقط يبقى هذه بيصير even permutationيبقى إذا
+
+32
+00:03:28,620 --> 00:03:33,520
+ال cycle عدد العناصر فيها odd أو الطول تبعها عبارة
+
+33
+00:03:33,520 --> 00:03:37,520
+عن odd يبقى عدد ال transposition is even أو ال
+
+34
+00:03:37,520 --> 00:03:42,160
+permutation هذه بقول عنها even وإن كان العدد هذا
+
+35
+00:03:42,160 --> 00:03:45,840
+even يبقى ال permutation بقول عنهاأو odd و هكذا
+
+36
+00:03:45,840 --> 00:03:51,100
+يبقى هذا المقصود بسؤال 11 اذا كان السؤال 12 يقول
+
+37
+00:03:51,100 --> 00:03:56,040
+لو كان ال alpha even شوف لل alpha inverse او اثبت
+
+38
+00:03:56,040 --> 00:03:59,820
+ان ال alpha inverse even و لو كانت ال alpha odd
+
+39
+00:03:59,820 --> 00:04:07,260
+اثبت ان ال alpha inverse is even يبقى هنا سؤال 12
+
+40
+00:04:07,260 --> 00:04:15,830
+يقول if ال alpha is even او oddthen ال alpha
+
+41
+00:04:15,830 --> 00:04:22,930
+inverse is even او اقل هذا اللي عايزين ان تبدأ
+
+42
+00:04:22,930 --> 00:04:29,450
+يبقى هنا solution حليت
+
+43
+00:04:29,450 --> 00:04:32,690
+السؤال هذا انت يا أبو الأعداد هذي طب هذي أعداد
+
+44
+00:04:32,690 --> 00:04:38,190
+even و odd يعني حليت السؤال هذا مش مستاهل كلام
+
+45
+00:04:38,190 --> 00:04:43,660
+ذاري يعنيانت عندك الان لو افترضت انه alpha even
+
+46
+00:04:43,660 --> 00:04:51,600
+يبقى if ال alpha is even معناته ان ال alpha هذه
+
+47
+00:04:51,600 --> 00:04:56,980
+بقدر اكتبها alpha one alpha اتنين لغاية alpha
+
+48
+00:04:56,980 --> 00:05:04,180
+اتنين and هدول مالهم two cycles او transpositions
+
+49
+00:05:04,180 --> 00:05:08,720
+مظبوطيبقى هذه ال alpha واحد وال alpha اتنين و
+
+50
+00:05:08,720 --> 00:05:12,240
+لغاية ال alpha اتنين ان كل واحدة فيهم الطول تبقى
+
+51
+00:05:12,240 --> 00:05:17,620
+اتنينيبقى كتبت على شكل في ال cycles أوى
+
+52
+00:05:17,620 --> 00:05:22,240
+transpositions طب ليش كتبت اتنين in لأنه قال لي
+
+53
+00:05:22,240 --> 00:05:28,080
+alpha is even يعني عدد هدول كلهم اتنين in اللي انا
+
+54
+00:05:28,080 --> 00:05:32,480
+بده اجيب المعكوس تبعها يبقى باجي بقوله ال alpha
+
+55
+00:05:32,480 --> 00:05:37,780
+inverse بدها تساوي alpha واحد alpha اتنين alpha
+
+56
+00:05:37,780 --> 00:05:40,640
+اتنين in و كله inverse
+
+57
+00:05:45,080 --> 00:05:50,420
+الأن ال inverse لهذه بعيد كتابتهم من الخلف إلى
+
+58
+00:05:50,420 --> 00:05:56,580
+الأمام على الشكل التالي Alpha 2 N inverse اللي
+
+59
+00:05:56,580 --> 00:06:01,400
+جابله Alpha 2 N ناقص واحد inverse بضل ماشي لغاية
+
+60
+00:06:01,400 --> 00:06:07,770
+Alpha 2 inverse Alpha 1 inverseالسؤال هو اخدته في
+
+61
+00:06:07,770 --> 00:06:12,850
+الجزء النظري انه ال transposition المعكوس تبع هو
+
+62
+00:06:12,850 --> 00:06:18,250
+نفسه ولا بيختلف نفسه اذا بقدر اشيل كل واحد و احط
+
+63
+00:06:18,250 --> 00:06:23,670
+main و احط اللي هو نفسه اذا هذا الكلام بده يساوي
+
+64
+00:06:23,670 --> 00:06:30,550
+Alpha 2N Alpha 2N minus ال one لغاية Alpha 2 Alpha
+
+65
+00:06:30,550 --> 00:06:38,790
+واحد قداش عددهم هدول؟عددهم اتنين ان يعني even يبقى
+
+66
+00:06:38,790 --> 00:06:45,310
+هذا even تمام اذا لو كانت ال alpha even ال alpha
+
+67
+00:06:45,310 --> 00:06:50,510
+inverse even لو كانت ال alpha odd يبقى ال alpha
+
+68
+00:06:50,510 --> 00:06:57,190
+inverse كذلك odd similarly بنفس الطريقة similarly
+
+69
+00:06:57,190 --> 00:07:07,710
+if ال alpha is oddthen alpha inverse is odd
+
+70
+00:07:07,710 --> 00:07:14,490
+وانتهينا من هذه الشغلة هذه صعبة يعني برضه صعبة
+
+71
+00:07:14,490 --> 00:07:19,670
+تجيب ال inverse تبعها وترده لأصله طيب هذا سؤال
+
+72
+00:07:19,670 --> 00:07:26,310
+اتناش نيجي لسؤال سبعتاش ماتيني alpha و beta سؤال
+
+73
+00:07:26,310 --> 00:07:33,600
+سبعتاشمعطيلي Alpha و Beta Alpha تساوي اللي هي ال
+
+74
+00:07:33,600 --> 00:07:38,660
+permutation من واحد لغاية ستة اتنين تلاتة اربعة
+
+75
+00:07:38,660 --> 00:07:43,720
+خمسة ستة والصفر تانية اتنين واحد تلاتة خمسة اتنين
+
+76
+00:07:43,720 --> 00:07:53,110
+واحد تلاتة خمسة اربعة و هنا ستة و Beta تساويبارضه
+
+77
+00:07:53,110 --> 00:07:58,670
+من واحد لستة اتنين تلاتة اربعة خمسة ستة والصفر
+
+78
+00:07:58,670 --> 00:08:03,210
+التاني ستة واحد اتنين اربعة ستة واحد اتنين اربعة
+
+79
+00:08:03,210 --> 00:08:08,670
+تلاتة خمسة بالشكل اللي عندنا هنا طلب مني تلات
+
+80
+00:08:08,670 --> 00:08:13,170
+شغلات alpha inverse و beta alpha و alpha beta طلب
+
+81
+00:08:13,170 --> 00:08:21,510
+find alpha inverse و alpha beta و beta alpha
+
+82
+00:08:30,000 --> 00:08:34,020
+الخيار يا بنجيب ال alpha مباشرة من هذا الوضع يا
+
+83
+00:08:34,020 --> 00:08:38,400
+بنحولها لل cycles و بعدين بنجيب ال inverse على زي
+
+84
+00:08:38,400 --> 00:08:42,000
+ما بدك ع الشكتين ماشي طيب احنا الان لو بدنا نجيب
+
+85
+00:08:42,000 --> 00:08:48,400
+معكوس هذين مباشرة كيف بنجيب معكوس هذين؟ حد بيعرف؟
+
+86
+00:08:48,400 --> 00:08:50,320
+نفس نفسه
+
+87
+00:08:54,870 --> 00:08:59,970
+كيف بنجيب معكس الفيريماتيش اللى بتبقى مكتوبة صفين؟
+
+88
+00:08:59,970 --> 00:09:03,190
+يعني
+
+89
+00:09:03,190 --> 00:09:06,870
+إيش قالكوا لأستاذ محمود إيش بنعمل مشان يجيب المعكس
+
+90
+00:09:06,870 --> 00:09:13,650
+تبعها؟ إيش بنعمل؟ cycle كيش يا راجل؟ أنا ماعطيك
+
+91
+00:09:13,650 --> 00:09:16,750
+فيريماتيش اللي لأ .. ماحولتهاش لcycles، بدأتش
+
+92
+00:09:16,750 --> 00:09:21,290
+يبهيكد مباشرة بدون cycles كل واحد لواحد يعني واحد
+
+93
+00:09:21,290 --> 00:09:28,900
+لواحديعني ايش نسوي بالظبط فاهمني على اي حال كلمتين
+
+94
+00:09:28,900 --> 00:09:33,020
+اصغار مفيش غيرهم ببدل الصف الأول مكان التاني
+
+95
+00:09:33,020 --> 00:09:36,900
+والتاني مكان الأول وبعيد ترتيب ال permutation بس
+
+96
+00:09:36,900 --> 00:09:43,140
+جلها الكوالا ماجلهاش الكهاجر ماحسبش الكوالا معكوس
+
+97
+00:09:43,140 --> 00:09:48,340
+ل permutation كيف؟ بتاعة ال cycles
+
+98
+00:09:52,010 --> 00:09:55,090
+استفيد كمان هذه المعلومة مدى ما قالكوا الطريقة هذه
+
+99
+00:09:55,090 --> 00:09:59,730
+خدها الطريقة هذه يبقى بدى اخد ال alpha inverse
+
+100
+00:09:59,730 --> 00:10:04,810
+يبقى يساوي الصفر تاني اثنين واحد تلاتة خمسة اربعة
+
+101
+00:10:04,810 --> 00:10:09,550
+ستة واحد اتنين تلاتة اربعة خمسة ستة يبقى هذا
+
+102
+00:10:09,550 --> 00:10:15,490
+المعكوس بس بدى اعيد الترتيب بحيث فعلا الصف الأول
+
+103
+00:10:15,490 --> 00:10:22,550
+يكون هو الأرقام اللي اهالمرتبة ترتيب حسب وضعها
+
+104
+00:10:22,550 --> 00:10:27,690
+يفجأي واحد اتنين تلاتة اربعة خمسة ستة وهيجفلنا
+
+105
+00:10:27,690 --> 00:10:32,510
+الواحد ايش صورته؟ اتنين يفجأي اتنين اتنين ايش
+
+106
+00:10:32,510 --> 00:10:39,050
+صورتها؟ واحد الان التلاتة صورتها تلاتةالخمسة
+
+107
+00:10:39,050 --> 00:10:44,050
+صورتها اش لأ قبلها الأربعة صورتها اش صورتها خمسة
+
+108
+00:10:44,050 --> 00:10:49,530
+والخمسة صورتها اربعة والستة صورتها ستة اذا هذا
+
+109
+00:10:49,530 --> 00:10:54,150
+المعكوس تبع ال ال permutation طب ده تاكد حل الصح و
+
+110
+00:10:54,150 --> 00:10:58,150
+الله غلط ما عليك اللي تمسك هذه و تضربها في هذه
+
+111
+00:10:58,150 --> 00:11:05,620
+لازم يطلع مينidentity permutation 123456 123456
+
+112
+00:11:05,620 --> 00:11:11,820
+تمام؟ يبقى ده تشكلك اعمليه وشوف هذه صح ولا غلط بدك
+
+113
+00:11:11,820 --> 00:11:15,220
+عن طريق ال cycles ماعناش مشكلة زي ما علمك عن طريق
+
+114
+00:11:15,220 --> 00:11:23,300
+ال cycles اللي علموهلك كلام صحيح مئة بالمئة على
+
+115
+00:11:23,300 --> 00:11:28,420
+أي حال هذا المطلوب اللي مطلوب التاني قاللي بده
+
+116
+00:11:28,420 --> 00:11:34,050
+الفا بيتاالان بدنا نجيبله alpha beta ماعليك إلا
+
+117
+00:11:34,050 --> 00:11:39,350
+تعمل ال permutations مباشرة أوي تحولهم إلى ال
+
+118
+00:11:39,350 --> 00:11:43,650
+cycle و تجيب إيه عشان ال composition تبعهم حسبلكوا
+
+119
+00:11:43,650 --> 00:11:47,250
+ال composition مباشرة زي هيك و لا زي .. يعني
+
+120
+00:11:47,250 --> 00:11:52,950
+حسبلكوا هذه طيب ماشي يا سيديهي هذه الأولى هي ال
+
+121
+00:11:52,950 --> 00:11:58,350
+alpha واحد اتنين تلاتة اربعة خمسة ستة اتنين واحد
+
+122
+00:11:58,350 --> 00:12:05,290
+تلاتة خمسة اربعة ستة والتاني واحد اتنين تلاتة
+
+123
+00:12:05,290 --> 00:12:12,630
+اربعة خمسة ستة الصف التاني ستة واحد اتنين اربعة
+
+124
+00:12:12,630 --> 00:12:20,820
+تلاتة خمسة ويساوي بذكر تذكير يبقىبعدين ابدأ هاي
+
+125
+00:12:20,820 --> 00:12:26,840
+واحد اتنين تلاتة اربعة خمسة ستة وهيجفلنا الان ببدأ
+
+126
+00:12:26,840 --> 00:12:32,580
+بالواحد ببدأ من اليمين للشمال الواحد صورته اه ستة
+
+127
+00:12:32,580 --> 00:12:37,740
+باجي طالع هنا على الستة صورتها صورتها اه يبقى
+
+128
+00:12:37,740 --> 00:12:42,740
+الواحد صورته ستة بعدين بدي اجي للاتنين اتنين
+
+129
+00:12:42,740 --> 00:12:47,860
+صورتها واحد والواحد صورتها اهأتنين يبقى اتنين ده
+
+130
+00:12:47,860 --> 00:12:52,220
+يجي اللي بعده التلاتة صورته اتنين و اتنين صورته
+
+131
+00:12:52,220 --> 00:12:56,560
+واحد بالشكل اللي عندنا اللي بعده وصلنا للاربعة
+
+132
+00:12:56,560 --> 00:13:01,580
+الاربعة صورتها اربعة و الاربعة صورتها خمسة الخمسة
+
+133
+00:13:01,580 --> 00:13:06,460
+صورتها تلاتة و التلاتة صورتها تلاتة الستة صورتها
+
+134
+00:13:06,460 --> 00:13:11,910
+خمسة و الخمسة صورتها اربعة زي ما انت شايفيبقى هذا
+
+135
+00:13:11,910 --> 00:13:14,230
+ال composition انت تلاحظ انه لما تجيب ال
+
+136
+00:13:14,230 --> 00:13:19,770
+composition ولا رقم يتكرر مرتين الرقم لا يظهر الا
+
+137
+00:13:19,770 --> 00:13:22,530
+المرة الواحدة لأن ال permutation هي عبارة عن
+
+138
+00:13:22,530 --> 00:13:26,670
+function وهذه ال function one to one and unto
+
+139
+00:13:26,670 --> 00:13:31,350
+بتغطي لجميع العناصر ومافيش عنصر يشتركوا في نفس
+
+140
+00:13:31,350 --> 00:13:36,330
+الصورة على الإطلاقيبقى هذا بالنسبة لل alpha beta
+
+141
+00:13:36,330 --> 00:13:40,530
+من ال beta alpha زيها ماعنديش مشكلة فيها طيب هذا
+
+142
+00:13:40,530 --> 00:13:46,530
+كان سؤال سبعتاش بدنا نروح لتسعتاش قل اتش subgroup
+
+143
+00:13:46,530 --> 00:13:57,390
+من ال sn سؤال تسعتاش قل اتش subgroup من ال sn هذا
+
+144
+00:13:57,390 --> 00:14:11,740
+بده يعطيلك اللي هو anyElement of H is even or half
+
+145
+00:14:11,740 --> 00:14:16,920
+elements of
+
+146
+00:14:16,920 --> 00:14:21,740
+S and R are even
+
+147
+00:14:31,780 --> 00:14:39,360
+قبل ما نبدأ الشغل الـ Sn فيها permutations إيش
+
+148
+00:14:39,360 --> 00:14:45,360
+even وإيش odd؟ روحنا أثبتنا له من خلال جزء النظري
+
+149
+00:14:45,360 --> 00:14:49,600
+أن الـ set of all even permutations ودّيناها الرمز
+
+150
+00:14:49,600 --> 00:14:55,940
+An is a subgroup من مين؟ من ال Snوفي المقابل قلنا
+
+151
+00:14:55,940 --> 00:14:59,080
+له the set of all odd permutation is not a
+
+152
+00:14:59,080 --> 00:15:03,560
+subgroup ليش؟ مافيش فيها ال identity ال identity
+
+153
+00:15:03,560 --> 00:15:08,780
+even permutation تمام اتنين لو ضربتوا odd
+
+154
+00:15:08,780 --> 00:15:12,740
+permutation يعطيني even يعني ال operation عليها is
+
+155
+00:15:12,740 --> 00:15:18,260
+not a binary operation او is not closed under the
+
+156
+00:15:18,260 --> 00:15:21,580
+composition of functions او of permutations
+
+157
+00:15:21,930 --> 00:15:25,570
+وبالتالي مجموعة الـ odd permutation لا يمكن تكون
+
+158
+00:15:25,570 --> 00:15:28,030
+في يوم من الأيام اللي هي ال subgroup هذا السؤال
+
+159
+00:15:28,030 --> 00:15:34,710
+الموجود عندك في التمرينالان بيقولش انها خدنا h
+
+160
+00:15:34,710 --> 00:15:40,310
+subgroup من sn يبدأك تروح تثبتلي انه كل element من
+
+161
+00:15:40,310 --> 00:15:44,190
+h بيكون even permutation وهو واضح على الطبيعي لإن
+
+162
+00:15:44,190 --> 00:15:47,330
+ال odd permutations عمرهم مش بيعملولي ال subgroup
+
+163
+00:15:47,330 --> 00:15:57,330
+بدكش بلاش اثبتلي ان ال elements of h نص عناصر sn
+
+164
+00:15:57,330 --> 00:16:03,740
+بدهم يكونوا evenيعني لو كانت ال sn فيها عشرين عنصر
+
+165
+00:16:03,740 --> 00:16:08,680
+فعشرة even وعشرة odd هاي اللي بقوله يثبته بقوله
+
+166
+00:16:08,680 --> 00:16:13,140
+بسيطة جدا يبقى بقوليش اثبت لإثنين بقولي بكفيني منك
+
+167
+00:16:13,140 --> 00:16:17,960
+واحد اللي تقدر تثبته فيهم لإنه or or تعني هذا او
+
+168
+00:16:17,960 --> 00:16:22,470
+هذاطيب ماشي تمام انا بدي احاول اتنطلع ان نص
+
+169
+00:16:22,470 --> 00:16:28,210
+العناصر تبع ال SN بيكونوا even وبالتالي عدد ال odd
+
+170
+00:16:28,210 --> 00:16:32,250
+permutation جد عدد ال even permutation واعتقد ان
+
+171
+00:16:32,250 --> 00:16:35,490
+الأستاذ محمود جالكوا في الجزء النظري ان ال order
+
+172
+00:16:35,490 --> 00:16:40,870
+لل alternating group AN هو عبارة عن N factorial
+
+173
+00:16:40,870 --> 00:16:45,890
+على اتنين مظبوط طيب مدام جالكوا احنا بدأنا بتهدى
+
+174
+00:16:45,890 --> 00:16:52,720
+عمليا ال Aمش هنتبت عمليا بضروح افترض اني عندي odd
+
+175
+00:16:52,720 --> 00:17:03,260
+permutation beta يبقى assume that ان ال beta is an
+
+176
+00:17:03,260 --> 00:17:10,040
+odd permutation كويس
+
+177
+00:17:12,170 --> 00:17:18,110
+طيب انا عندي odd وعندي even بدي اعرف function من
+
+178
+00:17:18,110 --> 00:17:23,090
+ال even permutations لل odd permutations واذا طلعت
+
+179
+00:17:23,090 --> 00:17:26,870
+هذه ال function one to one and unto يبقى عدد ال
+
+180
+00:17:26,870 --> 00:17:32,270
+odd بصير جد عدد من ال even يبقى عدد ال even بيكون
+
+181
+00:17:32,270 --> 00:17:37,770
+نص عدد اللي هو ال S انه بيكون خلصنا مظبوط يبقى
+
+182
+00:17:37,770 --> 00:17:39,630
+بداجي اقوله define
+
+183
+00:17:44,730 --> 00:17:50,370
+من الـ Alternating group of degree n إلى الـ set
+
+184
+00:17:50,370 --> 00:17:58,970
+of all odd permutations للـ S ناقص الـ An هذه ال
+
+185
+00:17:58,970 --> 00:18:03,730
+group هذه ال set كلها
+
+186
+00:18:03,730 --> 00:18:11,520
+طيب مين هي هذا يا شباب؟الـ Sn لما شيل منها الـ
+
+187
+00:18:11,520 --> 00:18:16,320
+even مين بيظل الـ odd يبقى هدول الـ set of all odd
+
+188
+00:18:16,320 --> 00:18:21,260
+permutations و هدى ال set of all even permutations
+
+189
+00:18:21,260 --> 00:18:33,920
+باي فاي of alpha بده يسوى alpha beta مثلا بتتأكد
+
+190
+00:18:33,920 --> 00:18:38,450
+تعريفي صح ولا غلطأنا معرف Function Phi من ال set
+
+191
+00:18:38,450 --> 00:18:41,490
+of all even permutation لل set of all odd
+
+192
+00:18:41,490 --> 00:18:46,090
+permutation باي Phi of Alpha يبقى Alpha ياش even
+
+193
+00:18:46,090 --> 00:18:52,390
+موجودة في ال a in بدت روح لمين لل odd الآن هذه
+
+194
+00:18:52,390 --> 00:18:57,850
+even وهذه ايش فرضها انا odd طب odd في even ايش
+
+195
+00:18:57,850 --> 00:19:05,090
+بيعطيني odd في evenأد يبقى اد يبقى مية المية هذه
+
+196
+00:19:05,090 --> 00:19:09,170
+موجودة هنا يبقى تعريف يسليم مائة بالمائة هذه ال
+
+197
+00:19:09,170 --> 00:19:11,790
+function لو جلسنا نثبت انها one to one and انتوا
+
+198
+00:19:11,790 --> 00:19:16,030
+بيقول خلصنا بصير عدد ال odd permutation جد عدد ال
+
+199
+00:19:16,030 --> 00:19:21,110
+even permutation يبقى مص عناصر s ان بصيروا even
+
+200
+00:19:21,110 --> 00:19:24,210
+permutation بصيروا even permutation او odd
+
+201
+00:19:24,210 --> 00:19:29,520
+permutationزي ما بدك وهذا يتفق مع عدد ال a n يسوى
+
+202
+00:19:29,520 --> 00:19:33,440
+n factorial على اتنين اللي اقالكمين الأستاذ محمود
+
+203
+00:19:33,440 --> 00:19:39,480
+يبقى الآن انا بتدعي ان فاي is one to one مشان هيك
+
+204
+00:19:39,480 --> 00:19:47,180
+بدأت أخد صورتين متساويتين assume that ان في of
+
+205
+00:19:47,180 --> 00:19:53,130
+alpha one يسوى في of alpha twoإذا قلت أثبت أن ألف
+
+206
+00:19:53,130 --> 00:19:58,430
+وان يتساوي ألف اتو بتم المطلوب يبقى بناء عليه هذا
+
+207
+00:19:58,430 --> 00:20:05,910
+معناته أن ألف وان بيتا يساوي ألف اتو بيتا بال
+
+208
+00:20:05,910 --> 00:20:10,170
+right cancellation law يبقى هذا ما يريد أن يعطيك
+
+209
+00:20:10,170 --> 00:20:17,270
+أن ألف وان يتساوي ألف اتو لذلك فاي هو واحد اتو
+
+210
+00:20:17,270 --> 00:20:26,390
+واحدبدى اثبت الان الـ fi is unto يفجر بروح اخد let
+
+211
+00:20:26,390 --> 00:20:33,030
+هه بديش اقول بي تبدى سميها مثلا جامع موجودة في
+
+212
+00:20:33,030 --> 00:20:39,330
+الاس ان نقص الام يعني اخدت element موجود في ال
+
+213
+00:20:39,330 --> 00:20:44,110
+code domain تبع ال function و بدي اثبت انه له أصل
+
+214
+00:20:44,110 --> 00:20:46,890
+في ال domain اللى عندنا then
+
+215
+00:20:50,300 --> 00:20:56,780
+الـ gamma is odd مظبوط ولا لأ؟ ليش؟ لإنها موجودة
+
+216
+00:20:56,780 --> 00:21:02,120
+في ال set of all odd permutation implies that ممكن
+
+217
+00:21:02,120 --> 00:21:10,190
+أكتب الجامعة هذه على الشكل alpha betaيعني حاصل ضرب
+
+218
+00:21:10,190 --> 00:21:15,470
+even في قد اللي هو مين قد صح ولا لأ يبقى هالكلام
+
+219
+00:21:15,470 --> 00:21:20,310
+هذا ممكن ولا غير ممكن الإجابة ممكن لإن هذه قد وهذه
+
+220
+00:21:20,310 --> 00:21:26,830
+قد فعلا طب حسب ال definition هذه بتعطينا مينفاي of
+
+221
+00:21:26,830 --> 00:21:31,610
+alpha يبقى جامل حتى في ال code main لقيت اللي أصل
+
+222
+00:21:31,610 --> 00:21:35,990
+في ال domain اللي هو alpha يبقى بناء عليه فاي is
+
+223
+00:21:35,990 --> 00:21:44,150
+unto يبقى بناء عليه اللي هو الفاي is one to one
+
+224
+00:21:44,150 --> 00:21:50,430
+and untoمدام one to one and one to hada بده يعطينا
+
+225
+00:21:50,430 --> 00:21:57,530
+ان ال order لل AN بده ساوي ال order لل SN ناقص ال
+
+226
+00:21:57,530 --> 00:22:09,610
+AM هذا بده يعطينا اللي هو half of the elements of
+
+227
+00:22:09,610 --> 00:22:18,670
+SN is evenيبقى نصهم بيكون even مثل ما طلب في
+
+228
+00:22:18,670 --> 00:22:31,410
+السؤال وهو المطلوب طيب
+
+229
+00:22:31,410 --> 00:22:39,930
+هذا كان سؤال تسعتاشالان بعد تسعة اتاش انا سؤال
+
+230
+00:22:39,930 --> 00:22:45,530
+اتنين وعشرين مائتين alpha و beta موجودة في sn و
+
+231
+00:22:45,530 --> 00:22:49,490
+اثبت ان ال alpha inverse beta inverse alpha beta
+
+232
+00:22:49,490 --> 00:22:55,890
+even permutation على طول الخط الان سؤال اتنين
+
+233
+00:22:55,890 --> 00:23:03,130
+وعشرين بقولي alpha و beta موجودة في ال sn اثبت انه
+
+234
+00:23:03,830 --> 00:23:11,190
+Alpha inverse Beta inverse Alpha Beta is even
+
+235
+00:23:11,190 --> 00:23:12,350
+دائما وأبدا
+
+236
+00:23:26,840 --> 00:23:29,940
+محطليش ميودة على alpha و beta اللهم إلا
+
+237
+00:23:29,940 --> 00:23:34,240
+permutation موجودة في ال sn هل even و odd خد زي ما
+
+238
+00:23:34,240 --> 00:23:39,820
+بدك اذا انا عندي ثلاث احتمالات العربي عليها
+
+239
+00:23:39,820 --> 00:23:44,060
+الاحتمال الأول ان alpha و beta التنتين even
+
+240
+00:23:44,060 --> 00:23:48,800
+الاحتمال الثاني ان alpha و beta التنتين odd
+
+241
+00:23:48,800 --> 00:23:54,450
+الاحتمال الثالث واحدة odd واحدة even مش هيكعلى كده
+
+242
+00:23:54,450 --> 00:23:58,290
+الاحتمالات الثلاثة بدي اثبت له انه حصل ضربة ده او
+
+243
+00:23:58,290 --> 00:24:02,810
+حصل composition ما بين الأربع permutation even
+
+244
+00:24:02,810 --> 00:24:09,990
+تمام يبقى الآن بداية اخدله المقطة الأولى if alpha
+
+245
+00:24:09,990 --> 00:24:19,150
+and beta are even then ال alpha inverse beta
+
+246
+00:24:19,150 --> 00:24:26,090
+inverse alpha betaتوا قبل قليل أثبتنا أنه لو كانت
+
+247
+00:24:26,090 --> 00:24:29,990
+ال alpha even يبقى معكوسة even لو كانت ال alpha
+
+248
+00:24:29,990 --> 00:24:36,030
+odd يبقى معكوسة odd كذلك إذا هذه الأولى even
+
+249
+00:24:36,030 --> 00:24:43,350
+والتانية even والتالتة even والرابعة even يبقى
+
+250
+00:24:43,350 --> 00:24:50,310
+ناتج جداش يبقى إن كانوا التنتين even في المجموع او
+
+251
+00:24:50,310 --> 00:24:55,900
+ال composition ما بينهم evenالحالة الثانية لو كانت
+
+252
+00:24:55,900 --> 00:25:05,880
+ال alpha and ال beta are both odd تمام then ايش
+
+253
+00:25:05,880 --> 00:25:11,000
+اللي بدي يحصل ال alpha inverse beta inverse alpha
+
+254
+00:25:11,000 --> 00:25:16,640
+beta بتبقى على الشكل التالي الحين التنتين odd يبقى
+
+255
+00:25:16,640 --> 00:25:24,380
+المعكوس تبعهم odd تمام يبقى oddوالتانية odd
+
+256
+00:25:24,380 --> 00:25:32,200
+والتالتة odd والرابعة odd لكن odd زائد odd إيش
+
+257
+00:25:32,200 --> 00:25:38,500
+بتعطينا؟ even و odd زائد odd التانية بتعطينا؟ و
+
+258
+00:25:38,500 --> 00:25:42,440
+even زائد even إيش بتعطينا؟ even يبقى على كل
+
+259
+00:25:42,440 --> 00:25:46,360
+الأمرين سواء التنتين odd أو التنتين even الناتج
+
+260
+00:25:46,360 --> 00:25:54,050
+even وصلنا للحالة الثالثة والأخيرةلو كانت ال alpha
+
+261
+00:25:54,050 --> 00:26:03,330
+is odd and beta is even then بدنا ناخد alpha
+
+262
+00:26:03,330 --> 00:26:09,370
+inverse beta inverse alpha beta الان alpha odd
+
+263
+00:26:09,370 --> 00:26:18,080
+يبقى معكوسة كذلك oddالان beta even يبقى مع كوسة
+
+264
+00:26:18,080 --> 00:26:25,140
+even alpha قلنا عليها odd و beta even هذا الكلام
+
+265
+00:26:25,140 --> 00:26:31,420
+بده يساوي اطلعلي لهذه اض زائد اد شو بتعطينا even
+
+266
+00:26:31,420 --> 00:26:40,520
+يبقى evenهو عندك زائد even زائد even يبقى كل وش
+
+267
+00:26:40,520 --> 00:26:45,880
+بيعطيلك even على كل الاحتمالات الممكنة فإن ال
+
+268
+00:26:45,880 --> 00:26:50,260
+composition بين الأربعة permutations دائما و أبدا
+
+269
+00:26:50,260 --> 00:26:57,680
+even هي permutationيبقى هنا س ال alpha inverse
+
+270
+00:26:57,680 --> 00:27:04,400
+beta inverse alpha beta is even لكل ال alpha و
+
+271
+00:27:04,400 --> 00:27:10,300
+beta اللي موجودة في مين موجودة في sn بلا استثناء
+
+272
+00:27:34,070 --> 00:27:39,810
+طيب هذا كان سؤال اتنين وعشرين الان بدنا نروح لسؤال
+
+273
+00:27:39,810 --> 00:27:44,810
+ستة وعشرين بيقول لي اثبت ان ال cycle واحد اتنين
+
+274
+00:27:44,810 --> 00:27:51,290
+تلاتة اربعة is not the product of three cycle يبقى
+
+275
+00:27:51,290 --> 00:28:00,270
+هنا ستة وعشرين show that ان واحد اتنين تلاتة اربعة
+
+276
+00:28:00,270 --> 00:28:10,170
+is notis a product of three cycles هذا الكلام مش
+
+277
+00:28:10,170 --> 00:28:17,990
+ممكن يحصل أبدا طيب تعالى نشوف صحة هذا الكلام الان
+
+278
+00:28:17,990 --> 00:28:24,030
+ال permutation هادي even والله odd يا شباب odd
+
+279
+00:28:24,030 --> 00:28:30,530
+اتكلمتش عن ال order لها ال order لها يسبب أربعة
+
+280
+00:28:30,530 --> 00:28:36,710
+صحيحوهو طول ال cycle مظبوط انا اتكلمت اكمتوا cycle
+
+281
+00:28:36,710 --> 00:28:43,310
+بتقدر تكون منها تلاتة اذا هذه odd فباجي بقوله هنا
+
+282
+00:28:43,310 --> 00:28:50,950
+solution يبقى the cycle او the permutation
+
+283
+00:28:50,950 --> 00:28:54,470
+permutation
+
+284
+00:28:54,470 --> 00:29:02,430
+اللي هو واحد اتنين تلاتة او اربعة is oddأد ليش؟
+
+285
+00:29:02,430 --> 00:29:10,470
+لأنه تلاتة transpositions هي تلاتة اللي هو واحد
+
+286
+00:29:10,470 --> 00:29:15,570
+اربعة واحد تلاتة واحد اتنين تمام يبقى هذه اد بدي
+
+287
+00:29:15,570 --> 00:29:23,310
+افترض جدلا ان جدرت اكتب هذه على شكل cycle واحدة
+
+288
+00:29:23,310 --> 00:29:27,730
+طولها يساوي تلاتة يبقى لما اكتب ال cycle طولها
+
+289
+00:29:27,730 --> 00:29:32,150
+تلاتة even والله اديعني بنفعل permutation تكون
+
+290
+00:29:32,150 --> 00:29:37,530
+even و odd معناته فيه شغل غلط يبقى اللي فرضته أنا
+
+291
+00:29:37,530 --> 00:29:42,110
+هذا غلط و عكسه هو الصح إذا لا يمكن كتابة ال
+
+292
+00:29:42,110 --> 00:29:46,630
+permutation اللي عندي على شكل three cycle وماقلش
+
+293
+00:29:46,630 --> 00:29:51,030
+three cycle قال لي product وين قال لي product of
+
+294
+00:29:51,030 --> 00:29:57,000
+three cycle بدي أفترضي الآنان بقدر اكتبها على شكل
+
+295
+00:29:57,000 --> 00:30:02,160
+product of three cycles وشوف هذا فرضي بوصلني الى
+
+296
+00:30:02,160 --> 00:30:06,980
+نتيجة صحيحة ولا الى نتيجة خاطئة اذا وصلني الى
+
+297
+00:30:06,980 --> 00:30:12,260
+نتيجة صحيحة معناته شغل صح وصلني الى نتيجة خاطئة
+
+298
+00:30:12,260 --> 00:30:17,060
+معناته فرض اللي انا فرضته خطأ وعكسه ايه هو الصح
+
+299
+00:30:17,060 --> 00:30:19,920
+اذا هروح اقول assume
+
+300
+00:30:22,800 --> 00:30:32,800
+إن الواحد اتنين تلاتة أربعة is a product of three
+
+301
+00:30:32,800 --> 00:30:41,400
+cycles that is I N الواحد اتنين تلاتة أربعة بدي
+
+302
+00:30:41,400 --> 00:30:51,420
+أكتب على شكل ABC في DEF بالشكل اللي عندناهي
+
+303
+00:30:51,420 --> 00:30:59,900
+product of three cycles then الان
+
+304
+00:30:59,900 --> 00:31:09,060
+ال a,b,c في d,e,f يساوي بدي اكتبها على شكل
+
+305
+00:31:09,060 --> 00:31:17,800
+transposition يبقى هذا بدي يعطينا a,c و هنا a,b و
+
+306
+00:31:17,800 --> 00:31:26,210
+التانية d,fوالتالتة دي ايه؟ كده عددهم؟ اربعة يعني
+
+307
+00:31:26,210 --> 00:31:32,930
+even صح ولا لا؟ يعني معناته هذه even permutation
+
+308
+00:31:32,930 --> 00:31:41,070
+ايش
+
+309
+00:31:41,070 --> 00:31:45,090
+رأيك؟ وصلنا للتناقض ولا لا؟ مش واحد اتنين تلاتة
+
+310
+00:31:45,090 --> 00:31:51,130
+اربعة قدلما كتبت على شكل three ال cycle صارت ايش؟
+
+311
+00:31:51,130 --> 00:31:56,810
+صارت even يبقى هذه even تسمح له أنه وصلنا إلى
+
+312
+00:31:56,810 --> 00:32:02,510
+contradiction يبقى هذا تناقض معناته فرض اللي انا
+
+313
+00:32:02,510 --> 00:32:10,250
+فرضته هذا صح ولا غلط؟ غلط يبقى هنا so الواحد اتنين
+
+314
+00:32:10,250 --> 00:32:24,680
+تلاتة اربع كانت ب writtenas a product of three
+
+315
+00:32:24,680 --> 00:32:31,250
+cyclesطيب يجي واحد تاني يقولي انت خدتين تانى طب
+
+316
+00:32:31,250 --> 00:32:34,690
+انا ممكن احط كمان واحدة تالتة اقوله حط مش تالتة حط
+
+317
+00:32:34,690 --> 00:32:37,990
+رابعة او خمسة او سادة او زى ما بدك الحين اللى ما
+
+318
+00:32:37,990 --> 00:32:41,230
+تحطلي كمان واحدة three cycle هدول عددهم اربعة
+
+319
+00:32:41,230 --> 00:32:46,530
+الواحدة بتجيبلي قداش two transposition بتصير قداش؟
+
+320
+00:32:46,530 --> 00:32:50,910
+ستة يعني even لو اخدتين تانى مش واحدة بتجيبلك
+
+321
+00:32:50,910 --> 00:32:55,650
+اربعة او اربعة تمانية evenوهكذا يعني أيش ما تحط في
+
+322
+00:32:55,650 --> 00:33:00,070
+three cycles بتطلع even يبقى هذا الكلام غير ممكن
+
+323
+00:33:00,070 --> 00:33:05,570
+على الإطلاق وبالتالي هذه مالها دائما و أبدا لا
+
+324
+00:33:05,570 --> 00:33:13,670
+يمكن كتابت على شكل product of three cycles طيب هذا
+
+325
+00:33:13,670 --> 00:33:19,870
+كان سؤال ستة و عشرين سبعة و عشرين جالي beta موجودة
+
+326
+00:33:19,870 --> 00:33:28,970
+في S7جالي سبعة و عشرين Beta موجودة في أس سبعة
+
+327
+00:33:28,970 --> 00:33:37,730
+وزيادة على ذلك جالي ال Beta أس أربعة ال Beta أس
+
+328
+00:33:37,730 --> 00:33:41,990
+أربعة ليه اتنين واحد اربعة تلاتة اتنين واحد اربعة
+
+329
+00:33:41,990 --> 00:33:50,630
+تلاتة خمسة ستة سبعة خمسة ستة سبعة جالي find Beta
+
+330
+00:33:53,520 --> 00:33:58,940
+بيتا بده اعرف البيتا هذه ايه شكلها يعني ما هي شكل
+
+331
+00:33:58,940 --> 00:34:06,020
+العناصر او قداش ما هي العناصر الموجودة في اللي هو
+
+332
+00:34:06,020 --> 00:34:09,720
+بيتا علم ان بيتا أقصى أربعة بالشكل اللي عندنا هذا
+
+333
+00:34:09,720 --> 00:34:16,480
+حد فيك وحل السؤال هذا احليت يعني ايوة احكي الفكرة
+
+334
+00:34:16,480 --> 00:34:20,940
+شوف مربع البيت أربعة وربيحها ال CBS تانية وعند ال
+
+335
+00:34:20,940 --> 00:34:28,640
+order البيت سبعةأشعرفك أن ال order لل بيسم يعني كل
+
+336
+00:34:28,640 --> 00:34:36,700
+element موجود في ال سبعة ال order له سبعة هي
+
+337
+00:34:36,700 --> 00:34:42,300
+موجودة في السبعة أنا موافق أنها موجودة في السبعة
+
+338
+00:34:42,300 --> 00:34:45,020
+لكن هل ال order له يسوى سبعة
+
+339
+00:34:50,030 --> 00:34:53,610
+أنا منافق إنها سبعة بس كيف جيبتها بك تثبتها مش
+
+340
+00:34:53,610 --> 00:34:58,210
+عشوائية و اخ بتطلع غير انه طلعت سبعة ها هي سبعة صح
+
+341
+00:34:58,210 --> 00:35:03,410
+بس كيف نثبتها بتثبت ان ال order ل beta يساوي سبعة
+
+342
+00:35:03,410 --> 00:35:09,470
+حتى يطلع كلامك صحيح الحين هذي beta أُس أربعة ال
+
+343
+00:35:09,470 --> 00:35:13,730
+order لها كمان يساوي سبعة ليش ان هاي هال cycle
+
+344
+00:35:13,730 --> 00:35:19,260
+كلها سبعة و كلهم are disjoint elements مظبوطيعني
+
+345
+00:35:19,260 --> 00:35:23,860
+هذه permutation او cycle موجودة في السبعة صحيح وال
+
+346
+00:35:23,860 --> 00:35:27,960
+order الها يساوي طولها يساوي السبعة صحيح هذا ال
+
+347
+00:35:27,960 --> 00:35:32,520
+order ل beta اربعة يساوي سبعة انا بد ال order ل
+
+348
+00:35:32,520 --> 00:35:37,340
+beta وبالتالي اذا جبت ال order ل beta صارت قصتنا
+
+349
+00:35:37,340 --> 00:35:44,670
+بسيطة تمام طيب نرجع هنانرجع هنا مرة تانية من خلال
+
+350
+00:35:44,670 --> 00:35:49,370
+الكلام اللي احنا كتبينه خليني اسألكوا سؤال لستاذ
+
+351
+00:35:49,370 --> 00:35:55,050
+محمود حسبلكوا جداش ال order .. اي جداش ال order لل
+
+352
+00:35:55,050 --> 00:36:01,110
+elements لل S7 جداش
+
+353
+00:36:01,110 --> 00:36:05,170
+ال orders الممكنة لعناصر S7
+
+354
+00:36:07,770 --> 00:36:11,930
+جديش؟ مش عدد العناصر بتكلمش عن عدد العناصر،
+
+355
+00:36:11,930 --> 00:36:14,530
+العناصر كله عارف أنه السبعة فقه سبعة factorial
+
+356
+00:36:14,530 --> 00:36:22,130
+بقول ال order لعناصر ل group السبعة، جيش ال orders
+
+357
+00:36:22,130 --> 00:36:30,150
+الممكنة؟ من واحد لسبعة بس، مزيدش أكتر من هيك؟ طب
+
+358
+00:36:30,150 --> 00:36:34,750
+احنا مشان نجيب ال order ل cycles كيف بجيب ال order
+
+359
+00:36:34,750 --> 00:36:40,290
+لcycles مضربات في بعض؟two cycles مثلا هذه طولها
+
+360
+00:36:40,290 --> 00:36:44,610
+تلاتة وهذه طولها خمسة وموافق التنتين دوس جوينت
+
+361
+00:36:44,610 --> 00:36:48,150
+تلاتة وخمسة يعني التنتين دوس جوينت ال least common
+
+362
+00:36:48,150 --> 00:36:53,810
+multiple ممتاز جدا يبقى لو عندي cycle واحدة فال
+
+363
+00:36:53,810 --> 00:36:58,770
+order لها يساوي طولها إذا عندي تنتين والتنتين are
+
+364
+00:36:58,770 --> 00:37:02,630
+disjoint بجيب ال least common multiple للإتنين
+
+365
+00:37:02,630 --> 00:37:06,590
+بيكون هو ال order لل permutationلو كانوا التلاتة
+
+366
+00:37:06,590 --> 00:37:10,410
+والتلاتة are disjoint بجيب ال is common multiple
+
+367
+00:37:10,410 --> 00:37:15,290
+للتلاتة وبالتالي هذا هو ال order لهم تمام يبقى
+
+368
+00:37:15,290 --> 00:37:20,630
+الآن ما هي ال orders الممكنة لعناصر السبعة هذا
+
+369
+00:37:20,630 --> 00:37:25,030
+ضروري لازم لفي العلم لازم اعرفهم وهو مثال محلول
+
+370
+00:37:25,030 --> 00:37:29,770
+عندك في الكتاب يعني الأستاذ محمود لازم يكون شرحه
+
+371
+00:37:29,770 --> 00:37:37,080
+مائة بالمائةأه مين مذكر ال orders يعني مغششك في
+
+372
+00:37:37,080 --> 00:37:42,160
+صفحة قداش كمان يا سيدي هذا في الكتاب موجود عندك
+
+373
+00:37:42,160 --> 00:37:49,080
+تفصيليا المثال يا سيدي المثال في الكتاب اللي هو
+
+374
+00:37:49,080 --> 00:37:58,080
+صفحة 102 و 103 example 4 صفحة 102 و 103 أكيد
+
+375
+00:37:58,080 --> 00:38:00,500
+شرحلكوا تفصيليا
+
+376
+00:38:02,040 --> 00:38:07,740
+أي نعم اتنين ناقش لكل مسائل من واحد الى عشر اطلعلي
+
+377
+00:38:07,740 --> 00:38:12,180
+في سؤال سبعة في الأسئلة بتلاقي نفس السؤال السؤال
+
+378
+00:38:12,180 --> 00:38:15,520
+السابعة بيقولي what are the possible orders of the
+
+379
+00:38:15,520 --> 00:38:22,420
+elements of A6 وA6 و what about A7 يعني معناته إذا
+
+380
+00:38:22,420 --> 00:38:26,340
+ما انشرحش في النظري انحل في المحاضرة بس انت مش
+
+381
+00:38:26,340 --> 00:38:29,850
+قاري هذه القصة تانية بتقول اعداد ما هذه اعدادطب
+
+382
+00:38:29,850 --> 00:38:34,810
+تروح تراجع في الكتاب و ال orders واحد اتنين تلتة
+
+383
+00:38:34,810 --> 00:38:42,250
+اربعة خمسة ستة سبعة عشر اتناش هدول بس يبقى الان
+
+384
+00:38:42,250 --> 00:38:47,390
+solution the
+
+385
+00:38:47,390 --> 00:38:52,650
+possible orders
+
+386
+00:38:52,650 --> 00:39:04,140
+the possible orders ofthe elements of
+
+387
+00:39:04,140 --> 00:39:11,540
+السبعة are الواحد والاتنين والتلاتة والاربعة
+
+388
+00:39:11,540 --> 00:39:18,460
+والخمسة والستة والسبعة والعشرة والاثمان عشر خلّي
+
+389
+00:39:18,460 --> 00:39:24,000
+هؤلاء العشقاء نعود لهم بعد قليل الان نعود لمين؟
+
+390
+00:39:24,000 --> 00:39:30,080
+لصاحبتنا هذا البيت أربعةالان ال order ل beta 4
+
+391
+00:39:30,080 --> 00:39:38,020
+يساوي طولها كم طولها سبعة يبقى سبعة هذا معناته ان
+
+392
+00:39:38,020 --> 00:39:43,140
+beta أس أربعة أس سبعة ستعطي ال identity
+
+393
+00:39:43,140 --> 00:39:51,110
+permutationهذا معناته ان بيتا اص تمانية وعشرين بده
+
+394
+00:39:51,110 --> 00:39:57,590
+يساوي ال identity السؤال هو ما علاقة ال order تبع
+
+395
+00:39:57,590 --> 00:40:04,790
+بيتا بالتمانية وعشرين يجي اسمه ممتاز جدا الان هذا
+
+396
+00:40:04,790 --> 00:40:11,450
+بده يعطينا ان ال order لبيتا divide التمانية
+
+397
+00:40:11,450 --> 00:40:19,360
+وعشرينطيب كل ال possible orders هاي هم قدامي يبقى
+
+398
+00:40:19,360 --> 00:40:25,720
+بده أروح أدور مين منهم بيقسم ال 28 يبقى باجي بقول
+
+399
+00:40:25,720 --> 00:40:31,540
+saw the possible orders
+
+400
+00:40:31,540 --> 00:40:42,300
+of beta R الواحد بيقسم ال 28والاتنين يقسم الـ 28
+
+401
+00:40:42,300 --> 00:40:50,880
+والاربعة يقسم الـ 28 والسبعة يقسم الـ 28 في غيرهم
+
+402
+00:40:50,880 --> 00:40:56,240
+تقول الـ 14 بقولك الـ 14 مش منهم مافيش عندي
+
+403
+00:40:56,240 --> 00:41:01,140
+permutation في السبعة ال order الى يسوى 14يبقى انا
+
+404
+00:41:01,140 --> 00:41:06,780
+بدي اخد من هدول الارقام اللي بتقسم للتمانية وعشرين
+
+405
+00:41:06,780 --> 00:41:12,040
+طلعت هذه الان اذا استبعدت الواحد واتنين والاربعة
+
+406
+00:41:12,040 --> 00:41:17,120
+بيصير ال order ل beta هو سبعة مظبوط هيك دي اخ
+
+407
+00:41:17,120 --> 00:41:23,780
+العران شو اسمك انت؟ على ايش؟ على ابعودة على ابعودة
+
+408
+00:41:23,780 --> 00:41:29,380
+خلانا نعود الى السؤال من جديديعني احنا بدنا نوصل
+
+409
+00:41:29,380 --> 00:41:32,840
+لكلام اللى قاله ان ال order يساوي سبعة واني بصمته
+
+410
+00:41:32,840 --> 00:41:36,580
+بس سألنا كيف قال خبطها من عندى مافيش حاجة يسمع
+
+411
+00:41:36,580 --> 00:41:41,880
+خبطها ماتش تشتغل رياضى سليم تمام الان بداجي اقوله
+
+412
+00:41:41,880 --> 00:41:48,780
+if ال order ل beta كان يساوي واحد هل هذا ممكن ولا
+
+413
+00:41:48,780 --> 00:41:54,700
+غير ممكنغير ممكن ان بيتا لا يمكن يسوى ال identity
+
+414
+00:41:54,700 --> 00:42:00,980
+بدليل ان بيتا أص أربعة تسوى هذه لو كانت بيتا تسوى
+
+415
+00:42:00,980 --> 00:42:04,280
+ال identity ليه كان بيتا أص أربعة يسوى ال identity
+
+416
+00:42:04,280 --> 00:42:11,480
+يبقى ال order لبيتا يسوى واحد impossible غير ممكن
+
+417
+00:42:11,480 --> 00:42:19,500
+السبب becauseان بيتا لا يساوي ال identity
+
+418
+00:42:19,500 --> 00:42:24,460
+permutation لأن لو كانت ال beta بال identity يبقى
+
+419
+00:42:24,460 --> 00:42:28,640
+beta و أربعة بال identity يبقى هذا مستبعد تماما
+
+420
+00:42:28,640 --> 00:42:41,880
+طيب نيجي ناخد الاحتمال الثاني بعدك
+
+421
+00:42:41,880 --> 00:42:48,750
+باجي بقوله لو كانال order ل beta بده يساوي أربعة
+
+422
+00:42:48,750 --> 00:42:57,190
+اسمع يا راجل then تمام ال beta أُص أربعة بده يساوي
+
+423
+00:42:57,190 --> 00:43:01,870
+ال identity هذا كلام حقيقي لأ لأن beta أُص أربعة
+
+424
+00:43:01,870 --> 00:43:14,310
+هيها يبقى هنا this is impossible ليش becauseإن الـ
+
+425
+00:43:14,310 --> 00:43:20,890
+beta أُس أربعة ليست ال identity وإنما تساوي وراحت
+
+426
+00:43:20,890 --> 00:43:26,790
+اتنين واحد اربعة تلاتة اتنين واحد اربعة تلاتة خمسة
+
+427
+00:43:26,790 --> 00:43:32,550
+ستة سبعة هذا اللي مستعجل عليه الاحتمال الثالث اللي
+
+428
+00:43:32,550 --> 00:43:40,430
+هو Fبتا تربيع بده يساوي اتنين ثم بتا تربيع بده
+
+429
+00:43:40,430 --> 00:43:43,690
+يساوي اتنين ثم بتا تربيع بده يساوي اتنين ثم بتا
+
+430
+00:43:43,690 --> 00:43:51,930
+تربيع بده يساوي اتنين ثم بتا تربيع بده يساوي اتنين
+
+431
+00:43:52,550 --> 00:43:58,650
+يبقى سؤال order ل beta كده؟ سبعة يبقى سؤال order ل
+
+432
+00:43:58,650 --> 00:44:03,850
+beta بده يسوى السبعة يعني معناته beta و السبعة بده
+
+433
+00:44:03,850 --> 00:44:10,310
+يسوى من ال identity element طب انا بدي beta بقدر
+
+434
+00:44:10,310 --> 00:44:17,790
+اجيب او اخلك من هنا beta؟ كيف؟واضرب في Beta يبقى
+
+435
+00:44:17,790 --> 00:44:24,470
+لو ضربت في Beta بصير Beta أس تمانية بده يساوي Beta
+
+436
+00:44:24,470 --> 00:44:32,150
+يبقى صارت Beta بدها تساوي Beta أس أربعة في Beta أس
+
+437
+00:44:32,150 --> 00:44:38,160
+أربعة ليه Beta أس تمانية؟مظبوط هذا معناه ان بيتا
+
+438
+00:44:38,160 --> 00:44:43,000
+تساوي بيتا وصة أربعة هي جاهزة عندنا اتنين واحد
+
+439
+00:44:43,000 --> 00:44:49,940
+اربعة تلاتة خمسة ستة سبعة خمسة ستة سبعة اتنين واحد
+
+440
+00:44:49,940 --> 00:44:59,690
+اربعة تلاتة خمسة ستة سبعةيبقى صورة beta تساوي يبقى
+
+441
+00:44:59,690 --> 00:45:03,890
+صورة
+
+442
+00:45:03,890 --> 00:45:14,650
+تساوي
+
+443
+00:45:14,650 --> 00:45:15,290
+يبقى صورة تساوي يبقى صورة تساوي يبقى صورة تساوي
+
+444
+00:45:15,290 --> 00:45:20,350
+يبقتمام الان وصلتي التلاتة التلاتة موجودة هنا
+
+445
+00:45:20,350 --> 00:45:26,070
+موجودة صورتها مين؟ و الخمسة مين صورتها؟ هاي الستة
+
+446
+00:45:26,070 --> 00:45:31,130
+الستة صورتها سبعة و السبعة صورتها اتنين صورته واحد
+
+447
+00:45:31,130 --> 00:45:36,270
+و الواحد صورته الأربع صورته تلاتة و التلاتة صورته
+
+448
+00:45:36,270 --> 00:45:41,830
+الخمسة صورته ستة و الستة صورتها سبعة السبعة صورتها
+
+449
+00:45:41,830 --> 00:45:46,770
+اتنين و اتنين صورتها واحد جفلتطب السؤال هو خلصنا و
+
+450
+00:45:46,770 --> 00:45:51,070
+لا ضايق الأرقام واحد اتنين تلتة اربعة خمسة ستة
+
+451
+00:45:51,070 --> 00:45:55,390
+سبعة تمام خلصنا يبقى ايه ال cycle يبقى هذه ال beta
+
+452
+00:45:55,390 --> 00:46:01,110
+اللي عندنا تمام يبقى هذا الشغل الرياضي بيخرج شمال
+
+453
+00:46:01,110 --> 00:46:06,950
+ولا واحد بيقدر يقولكإنه في شغلة ضعيفة أو شغلة غلطة
+
+454
+00:46:06,950 --> 00:46:11,670
+بس تقولي إنها سبعة مباشرة هحطلك علامة تفهم لو كان
+
+455
+00:46:11,670 --> 00:46:16,210
+السؤال يجيلك ويقولك why يعني كيف نزلت من السماء ال
+
+456
+00:46:16,210 --> 00:46:20,550
+order يساوي سبعة لأ هو لو قلتلي ال order ل beta
+
+457
+00:46:20,550 --> 00:46:23,470
+أقصى أربعة يساوي سبعة ده ال order ل beta يساوي
+
+458
+00:46:23,470 --> 00:46:24,670
+سبعة هو كلام غلط
+
+459
+00:46:28,000 --> 00:46:34,400
+طيب، هذا كان سؤال سبعة وعشرين، الآن وصلنا لسؤال
+
+460
+00:46:34,400 --> 00:46:39,100
+تسعة وعشرين وما أدرك ما تسعة وعشرين، ها يا أخويا
+
+461
+00:46:39,100 --> 00:46:44,480
+عدوا، وشوفوا كيف حلتوا هذا، هاي السؤال تسعة وعشرين
+
+462
+00:46:46,720 --> 00:46:51,700
+تسعة و عشرين بيقول اجالي find the element sigma
+
+463
+00:46:51,700 --> 00:46:58,660
+اللي موجودة في S تسعة بدنا sigma اللي موجودة في S
+
+464
+00:46:58,660 --> 00:47:09,260
+تسعة such that اللي هو sigma تقريب بده يساوي واحد
+
+465
+00:47:09,260 --> 00:47:16,230
+خمسة سبعة واحد خمسة سبعةاتنين تمانية تلاتة اتنين
+
+466
+00:47:16,230 --> 00:47:23,770
+تمانية تلاتة و هنا اربعة ستة تسعة اربعة ستة تسعة
+
+467
+00:47:27,170 --> 00:47:32,670
+أه في عندنا sigma موجودة في اس تسعة بحيث sigma
+
+468
+00:47:32,670 --> 00:47:39,390
+تقريب يسوى هذا الرقم قلي هاتلي تلت سيجمات بحيث
+
+469
+00:47:39,390 --> 00:47:45,890
+يعطونا الرقم هذا والسيجمات هدول موجودة وانفي S9
+
+470
+00:47:45,890 --> 00:47:55,210
+يعني بدي تلاتة permutations من S9 لو لو كعبت
+
+471
+00:47:55,210 --> 00:48:00,250
+الواحدة فيهم تعطيني حاصل ضرب ل three cycles اللي
+
+472
+00:48:00,250 --> 00:48:05,910
+عندنا هذون خلص
+
+473
+00:48:05,910 --> 00:48:12,410
+الوقت طيب بدي أعطيك واحدة لبعد الظهر تجيبلي كمان
+
+474
+00:48:12,410 --> 00:48:16,980
+غيرها تمامو الواحدة بدي أخذها من الأرقام اللي
+
+475
+00:48:16,980 --> 00:48:24,180
+قدامك يبقى اخذ هي sigma one sigma one شوف كيف بدي
+
+476
+00:48:24,180 --> 00:48:29,400
+أخذها طلع معايا هي جوس بدي أبدأ بالواحد هنا
+
+477
+00:48:29,400 --> 00:48:36,680
+والواحد هنا يعني أول رقم يبقى هي واحد اتنين اربع
+
+478
+00:48:36,680 --> 00:48:45,290
+بدي أبدأ بالتانيخمسة تمانية ستة التالت سبعة تلاتة
+
+479
+00:48:45,290 --> 00:48:54,490
+تسعة تمام تقولك كمان واحدة طيب سيجما اتنين من هذه
+
+480
+00:48:54,490 --> 00:48:59,830
+بدي اجيبهابدي أخلي الواحد ثابت زي ما هو بدي أقول
+
+481
+00:48:59,830 --> 00:49:05,090
+اربعة اتنين بدلت اتنين مع بعض الخمسة ثابت زي ما هو
+
+482
+00:49:05,090 --> 00:49:10,810
+ستة تمانية بدل الستة تمانية السابعة ثابت تسعة
+
+483
+00:49:10,810 --> 00:49:18,410
+تلاتة تاخد لك كمان واحدة سجمة تلاتة بجيبلك ستة مش
+
+484
+00:49:18,410 --> 00:49:23,830
+تلاتة بجيبلك جد ببدأك مرتينتمام يبقى sigma تلاتة
+
+485
+00:49:23,830 --> 00:49:28,710
+انا بدأت هنا بالواحد بدأ ابدأ بالاتنين يبقى لو قلت
+
+486
+00:49:28,710 --> 00:49:35,530
+اتنين اه اه واحد اربع بدأ ابدأ باللي في المص يبقى
+
+487
+00:49:35,530 --> 00:49:41,110
+تمانية خمسة ستة يبقى بدأ اخد اللي في المص يبقى
+
+488
+00:49:41,110 --> 00:49:47,050
+تلاتة سبعة تسعةالحين انت من هنا لبعد الظهر مسكلي
+
+489
+00:49:47,050 --> 00:49:52,450
+أي واحدة فيهم وضربها في نفسها تلت مرات إذا ما
+
+490
+00:49:52,450 --> 00:49:55,330
+طالعشي الجواب هذا بتيجي قرجعني
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6733efea98516ff3fa9ddd250914774c1d801e61
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_postprocess.srt
@@ -0,0 +1,2076 @@
+1
+00:00:22,310 --> 00:00:28,070
+في محاضرة الصبح قبل ساعتين بدأنا في موضوع ال
+
+2
+00:00:28,070 --> 00:00:31,530
+groups اللي هو اول موضوع في ال alphabet algebra
+
+3
+00:00:31,530 --> 00:00:37,070
+المقرر علينا مشان نعرف ال group لازم نعرف حاجة
+
+4
+00:00:37,070 --> 00:00:41,750
+اسمها binary operation و بعد ذلك بندخل الى موضوع
+
+5
+00:00:41,750 --> 00:00:47,070
+ال groupعرفنا ال binary operation على set هي عبارة
+
+6
+00:00:47,070 --> 00:00:52,710
+عن function من ال 6 cross ال 6 إلى set أخرى بحيث
+
+7
+00:00:52,710 --> 00:00:55,990
+ال order paired اللي في ال 6 cross ال 6 بيكون
+
+8
+00:00:55,990 --> 00:01:01,450
+موجود وين في ال set itself وعطينا على ذلك مثالين
+
+9
+00:01:01,450 --> 00:01:07,000
+وهذا هو المثال رقم 3يبقى انا عرفت ال function star
+
+10
+00:01:07,000 --> 00:01:12,480
+من z cross z إلى z by a star b يسوى a b نقص واحد
+
+11
+00:01:12,480 --> 00:01:16,880
+يعني ال star صارت عبارة عن عمليتين في انا واحد
+
+12
+00:01:16,880 --> 00:01:20,160
+عملية الضرب ما بين ال a و ال b و عملية الطرح من
+
+13
+00:01:20,160 --> 00:01:26,640
+واحد لكن على set of integers السؤال هو لما اضرب ال
+
+14
+00:01:26,640 --> 00:01:31,100
+a في b حصل ضرب two integers بيعطيني integer ولا
+
+15
+00:01:31,100 --> 00:01:35,970
+بيعطيني شغل تانيتطرح منه واحد بيظل انتجر ولا بيبقى
+
+16
+00:01:35,970 --> 00:01:40,730
+يصير انتجر؟ معناته هذه binary operation يبقى هذه
+
+17
+00:01:40,730 --> 00:01:50,350
+ال .. then .. then star is a binary operation
+
+18
+00:01:50,350 --> 00:01:59,030
+السبب because ان العدد اللي عندنا a b minus ال one
+
+19
+00:01:59,030 --> 00:02:03,140
+موجود في zما دام موجود في Z يبقى هذه ال operation
+
+20
+00:02:03,140 --> 00:02:09,440
+is a binary operation طيب نتجل الأمثلة شوية مثال
+
+21
+00:02:09,440 --> 00:02:25,060
+رقم أربعة بيقول let ال X ب any non empty set any
+
+22
+00:02:25,060 --> 00:02:28,240
+non empty set define
+
+23
+00:02:31,160 --> 00:02:36,600
+capital P of X to
+
+24
+00:02:36,600 --> 00:02:43,020
+be the
+
+25
+00:02:43,020 --> 00:02:56,140
+power set فئة القوة of set X اللي عندنا يعني اللي
+
+26
+00:02:56,140 --> 00:03:07,960
+هي the set of allthe set of all subsets of x
+
+27
+00:03:07,960 --> 00:03:11,260
+define
+
+28
+00:03:11,260 --> 00:03:14,820
+star
+
+29
+00:03:14,820 --> 00:03:19,120
+by
+
+30
+00:03:19,120 --> 00:03:22,900
+a
+
+31
+00:03:22,900 --> 00:03:33,460
+star b بده يساوي a union bلكل ال a و ال b اللي
+
+32
+00:03:33,460 --> 00:03:44,040
+موجودة في ال power set of x ال power set of x then
+
+33
+00:03:44,040 --> 00:03:47,220
+star
+
+34
+00:03:47,220 --> 00:03:57,140
+then star هذه is a binary operation
+
+35
+00:03:58,950 --> 00:04:07,810
+بينيري اوبريشن on ال power set لل X because
+
+36
+00:04:41,540 --> 00:04:46,380
+طبعا ال power set اللي هي فئة القوة أو فئة القوة
+
+37
+00:04:46,380 --> 00:04:51,520
+درسناها في مبدأ الرياضيات والان بنعيد دراستها مرة
+
+38
+00:04:51,520 --> 00:04:57,380
+ثانيةفلو أخدت الـ x أي non-empty set ركز على non
+
+39
+00:04:57,380 --> 00:05:03,260
+-empty يعني ليست في فيها عناصر بدي أعرف ال power
+
+40
+00:05:03,260 --> 00:05:07,940
+set of x هي ال power set of x أو the set of all
+
+41
+00:05:07,940 --> 00:05:12,520
+subset of x يبقى بداجي على ال set x أشوف عناصرها
+
+42
+00:05:12,520 --> 00:05:18,540
+أجيب كل ال subsets الممكنة بما فيهم في و ال x
+
+43
+00:05:18,540 --> 00:05:23,000
+itselfهذه بسميها الـtrivial subset وهذه أكبر
+
+44
+00:05:23,000 --> 00:05:26,840
+subset من ال 6 because أخدنا في مادة الرجالات أن
+
+45
+00:05:26,840 --> 00:05:32,180
+ال 6 is a subset of itself يبقى كل ال subsets اللي
+
+46
+00:05:32,180 --> 00:05:37,240
+عنده بيكونوله ميهم بيكونوله ال power set لل 6x بدا
+
+47
+00:05:37,240 --> 00:05:41,480
+أعرف اللي هو ال relation اللي .. ال operation اللي
+
+48
+00:05:41,480 --> 00:05:47,450
+عندنا a star b بده يساوي a union bلكل ال a و ال b
+
+49
+00:05:47,450 --> 00:05:51,570
+اللي موجودة في ال power set السؤال هو هل star هذه
+
+50
+00:05:51,570 --> 00:05:56,980
+binary operation ولا لا؟بقول والله إذا نتيجة أستر
+
+51
+00:05:56,980 --> 00:06:01,640
+بيجبتلي عنصر دائما و أبدا و هذا العنصر موجود في ال
+
+52
+00:06:01,640 --> 00:06:06,280
+power set إذا هذه binary operation يعني نتيجة
+
+53
+00:06:06,280 --> 00:06:12,220
+للعملية ما بين الاتنين لعملية ال union ههه بدها
+
+54
+00:06:12,220 --> 00:06:15,900
+تجيبلي عنصر موجود في ال power set إذا هذه binary
+
+55
+00:06:15,900 --> 00:06:20,580
+operation لو جبت عنصر طالع برا يبقى ليست binary
+
+56
+00:06:20,580 --> 00:06:25,300
+operationيبقى ال operation a star b a union b لكل
+
+57
+00:06:25,300 --> 00:06:29,280
+ال a و ال b اللي موجودة في ال P of x then star is
+
+58
+00:06:29,280 --> 00:06:32,900
+a binary operation على power set because نجي نشوف
+
+59
+00:06:32,900 --> 00:06:39,120
+ما هو السبب الآن ال operation a star b بدي يسوي a
+
+60
+00:06:39,120 --> 00:06:44,800
+union b السؤال هو a union b هل هذه ال subset من X
+
+61
+00:06:44,800 --> 00:06:52,390
+يا شباب؟لو أخدت any two subsets من الـ6X وجبت لهم
+
+62
+00:06:52,390 --> 00:06:56,870
+الـunion يكون موجود في الـX itself ولا بتطلع برا؟
+
+63
+00:06:56,870 --> 00:07:00,710
+لاتطلعش برا يبقى هذا موجود دائما و أبدا في X طب
+
+64
+00:07:00,710 --> 00:07:07,700
+والـX هذه أليس subset من ال power set of X؟يبقى
+
+65
+00:07:07,700 --> 00:07:15,340
+star ال element هذا موجود في ال power set ال x هذه
+
+66
+00:07:15,340 --> 00:07:21,700
+as a أعلى مش subset ال x هذه belongs موجودة في ال
+
+67
+00:07:21,700 --> 00:07:25,700
+power set لكن ال a union b ال subset من ال x والx
+
+68
+00:07:25,700 --> 00:07:31,500
+belong في ال power set of x معناه هذا كلام ال star
+
+69
+00:07:31,500 --> 00:07:35,320
+is a binary operation طب السؤال هوهل ال
+
+70
+00:07:35,320 --> 00:07:41,520
+intersection ما بين ال two sets a و b is a subset؟
+
+71
+00:07:41,520 --> 00:07:48,080
+يعني هل هو موجود في ال power set؟ليش؟ على أسوأ
+
+72
+00:07:48,080 --> 00:07:53,100
+الاحتمالات بدي يطلع في فحو ولا لأ في subset من ال
+
+73
+00:07:53,100 --> 00:07:58,760
+X ولا لأ يبقى في موجودة في ال power set وبناء عليه
+
+74
+00:07:58,760 --> 00:08:02,620
+سعر ال intersection كمان also is a binary
+
+75
+00:08:02,620 --> 00:08:07,320
+operation يبقى باجي بقول ان similarly كمان شغلة
+
+76
+00:08:07,320 --> 00:08:13,550
+تانيةsimilarly ال
+
+77
+00:08:13,550 --> 00:08:21,930
+.. ال .. ال star او a star b ال a star b بدي يسوي
+
+78
+00:08:21,930 --> 00:08:32,130
+a intersection b ها دي is a binary is a binary
+
+79
+00:08:32,130 --> 00:08:33,930
+operation
+
+80
+00:08:40,500 --> 00:08:44,000
+بارضه بنفس الطريقة ليش ان ال intersection ما بين
+
+81
+00:08:44,000 --> 00:08:48,520
+ال A والB موجود في ال set X
+
+82
+00:08:54,460 --> 00:09:01,960
+بسبب أن a intersection b هو subset من set x وهذا
+
+83
+00:09:01,960 --> 00:09:14,020
+سيعطينا أن a intersection b هو subset من set x طيب
+
+84
+00:09:14,020 --> 00:09:21,390
+ناخد كمان مثال بيختلف عن شكل هذه الأمثلة كلياlet
+
+85
+00:09:21,390 --> 00:09:29,970
+خمسة let الجي capital g بدي ساوي كل ال real
+
+86
+00:09:29,970 --> 00:09:34,010
+numbers x اللي موجودة في ال set of real numbers
+
+87
+00:09:34,010 --> 00:09:42,690
+بحيث ان ال x أكبر من أو تساوي واحد define عرفلي a
+
+88
+00:09:42,690 --> 00:09:45,750
+star by
+
+89
+00:09:48,020 --> 00:10:01,220
+x star y يساوي x y ناقص x ناقص y زائدي اتنين then
+
+90
+00:10:01,220 --> 00:10:13,680
+star اللي عندنا هذا is a binary operation is
+
+91
+00:10:13,680 --> 00:10:16,880
+a binary operation because
+
+92
+00:10:26,450 --> 00:10:34,230
+السبب؟ خلّي بالك هناالان انا اخد ست جديدة على غير
+
+93
+00:10:34,230 --> 00:10:40,710
+الأمثلة السابقة سميتها G مين هي G؟ اخدت عناصر من
+
+94
+00:10:40,710 --> 00:10:44,830
+set of real numbers اللي مين هم العناصر كلهم اللي
+
+95
+00:10:44,830 --> 00:10:50,470
+بيكونوا دائما وأبدا أكبر من الواحد الصحية كسور مش
+
+96
+00:10:50,470 --> 00:10:54,870
+كسور اللي وهم اعداد موجبة دائما وأبدا وكلها أكبر
+
+97
+00:10:54,870 --> 00:11:00,950
+من الواحد الصحيحعرفت star على ال G cross ال G إلى
+
+98
+00:11:00,950 --> 00:11:06,630
+G على الشكل التالي X star Y بده يساوي XY ناقص X
+
+99
+00:11:06,630 --> 00:11:12,830
+ناقص Y زائد اتنين يبقى عملية ضرب و طرح و جمع في آن
+
+100
+00:11:12,830 --> 00:11:18,270
+واحد من هذه ال star عرفتها بهذه الطريقة أنا أدعي
+
+101
+00:11:28,250 --> 00:11:35,690
+السبب اذا طلع هذا ال elementموجود في جي بقى كلامي
+
+102
+00:11:35,690 --> 00:11:41,310
+صح ماطلع موجود في جي بقى كلامي ماله مش صحيح بمعنى
+
+103
+00:11:41,310 --> 00:11:46,750
+أخر لو طلع هذا المقدار كله أكبر من الواحد الصحيح
+
+104
+00:11:46,750 --> 00:11:51,610
+معناته موجود في جي ماطلع يبقى كلامي ماله ليس صحيحا
+
+105
+00:11:51,610 --> 00:11:56,370
+ممتاز جدا يبقى باجي بقوله بدي أبيله ليش هذه binary
+
+106
+00:11:56,370 --> 00:12:06,430
+operation because ifx و y موجودة في g then ال x
+
+107
+00:12:06,430 --> 00:12:11,650
+هذا تبقى أكبر من الواحد و في نفس الوقت ال y أكبر
+
+108
+00:12:11,650 --> 00:12:17,890
+من الواحدعسب الـ definition تبع الـ G ماخد two
+
+109
+00:12:17,890 --> 00:12:22,290
+elements موجودات في G يبقى الـ two elements كل
+
+110
+00:12:22,290 --> 00:12:27,970
+واحد يوم أكبر من مين؟ من الواحد طيب هذا معناته ان
+
+111
+00:12:27,970 --> 00:12:33,330
+ال X greater than one and ال Y ناقص واحد أكبر من
+
+112
+00:12:33,330 --> 00:12:38,430
+مين؟ من ال zero إذا هذا ال term موجب و الله سالم
+
+113
+00:12:40,620 --> 00:12:45,140
+أكبر من Zero موجب ولا عمره حتى بيصير Zero يعني لا
+
+114
+00:12:45,140 --> 00:12:50,420
+Zero ولا سالب هذا موجب طب لو مسكت هذا الرقم الموجب
+
+115
+00:12:50,420 --> 00:12:54,360
+وضربته في ال inequality هذه بتتغير ولا بيظلها زي
+
+116
+00:12:54,360 --> 00:13:00,060
+ما هي يعني الأكبر من هذه بتتغير ولا بتغير إلى أقل
+
+117
+00:13:00,060 --> 00:13:04,340
+منه ولا بتظل أكبر منه يبقى بدي أمسك ال term هذا و
+
+118
+00:13:04,340 --> 00:13:09,020
+أضربه في ال inequality هذهيبقى بدي اشوف هذا ايش
+
+119
+00:13:09,020 --> 00:13:14,000
+بيعطينا يبقى مشان اوضح لك الصورة بدي اقول لك multi
+
+120
+00:13:14,000 --> 00:13:23,560
+apply the inequality المتباينة
+
+121
+00:13:23,560 --> 00:13:31,690
+x greater than one by y minus one we getبنحصل على
+
+122
+00:13:31,690 --> 00:13:39,390
+يبقى هذا ال X في Y minus ال one أكبر من ال Y minus
+
+123
+00:13:39,390 --> 00:13:44,310
+ال one مظبوط؟
+
+124
+00:13:44,310 --> 00:13:51,010
+طيب، إيش رأيك؟ بدي أفك الطرف الشمال يبقى XY ناقص X
+
+125
+00:13:51,010 --> 00:13:57,410
+إيش رأيك؟ هجيب ال Y على الشجة التانية ناقص Y أكبر
+
+126
+00:13:57,410 --> 00:13:59,870
+من اللي هو سالب واحد
+
+127
+00:14:03,300 --> 00:14:11,750
+طيب ايش رايك لو اضفت للطرفين اتنين؟مرة واحدة بضيف
+
+128
+00:14:11,750 --> 00:14:15,310
+رقم هنا زي ما اضيف رقم هنا عادي جدا واتنين
+
+129
+00:14:15,310 --> 00:14:17,590
+positive positive ولا negative في حالة الجامعة
+
+130
+00:14:17,590 --> 00:14:22,010
+ماتفرجش عندي المشكلة في حالة الضرب او القسمة يبقى
+
+131
+00:14:22,010 --> 00:14:29,670
+هنا لو اضفت اتنين بيصير x في y ناقص x ناقص y زائدي
+
+132
+00:14:29,670 --> 00:14:36,330
+اتنين اكبر من قداش اضفت اتنين للطرفين طب الطرف هذا
+
+133
+00:14:36,330 --> 00:14:42,130
+مش هو هذايبقى star العدد اللي عندي هذا أكبر من
+
+134
+00:14:42,130 --> 00:14:49,670
+واحد يبقى موجود في جي يبقى هذا بده يعطيلك ان ال X
+
+135
+00:14:49,670 --> 00:14:57,330
+Y ناقص X ناقص Y زي دي اتنين belongs to G لذلك star
+
+136
+00:14:57,330 --> 00:15:02,190
+is a binary operation لأن تحت العملية اللي عندنا
+
+137
+00:15:02,190 --> 00:15:06,210
+هذه ال star طلع الناتج موجود في G إذا هذه مالها
+
+138
+00:15:06,210 --> 00:15:12,400
+binary operationطيب احنا مهدنا لل group بموضوع ال
+
+139
+00:15:12,400 --> 00:15:17,380
+binary operation الان بدنا ندخل في صميم الموضوع و
+
+140
+00:15:17,380 --> 00:15:23,580
+هو تعريف ال groupالجروب يا شباب هي ال set بدي أضع
+
+141
+00:15:23,580 --> 00:15:30,580
+عليها binary operation بحيث تحققلي ثلاثة شروط ان
+
+142
+00:15:30,580 --> 00:15:35,400
+تحققتي ثلاثة شروط بسمي ال set مع ال binary
+
+143
+00:15:35,400 --> 00:15:41,540
+operation is a group ايش الشروط التلاتة؟ اول شيء
+
+144
+00:15:41,540 --> 00:15:47,270
+ال binary operation هذه بتبقى associativeادماجية
+
+145
+00:15:47,270 --> 00:15:54,150
+تمام او تجميعية زي ما بتسموها انتوا اتنين في عنصر
+
+146
+00:15:54,150 --> 00:15:59,270
+بده اسميه عنصر الوحدة ال identity element انتوا
+
+147
+00:15:59,270 --> 00:16:04,260
+بالعربي بجهة السماوية الثانوية العنصر المحايديبقى
+
+148
+00:16:04,260 --> 00:16:08,720
+المحايد أو الوحدة هو ال identity element الشرط
+
+149
+00:16:08,720 --> 00:16:14,260
+التالت كل عنصر في ال group تحت هذه العملية بدي
+
+150
+00:16:14,260 --> 00:16:20,400
+يكون له معكوس بحيث لو ضربت عنصر في معكوسه بدي يطين
+
+151
+00:16:20,400 --> 00:16:25,080
+من عنصر المحايد ال identity element لو تحققت
+
+152
+00:16:25,080 --> 00:16:30,020
+الشروط هذه التلاتة بقول يبقى الجيل اللي عندي is a
+
+153
+00:16:30,020 --> 00:16:34,390
+groupالكلام اللى سمعته بناروح نكتبه لإنه كل ال
+
+154
+00:16:34,390 --> 00:16:39,490
+section مبني على مين على الكلمتين اللى سمعتهم يبقى
+
+155
+00:16:39,490 --> 00:16:50,510
+بداجي الى definition يبقى definition let ال g be a
+
+156
+00:16:50,510 --> 00:16:56,830
+non empty non empty set
+
+157
+00:16:58,880 --> 00:17:09,840
+and let a star be a
+
+158
+00:17:09,840 --> 00:17:17,640
+binary operation
+
+159
+00:17:17,640 --> 00:17:24,840
+on اللي هو g على set g then
+
+160
+00:17:27,230 --> 00:17:33,170
+ال جي والستار مع بعض هدول يعني الست جي والستار
+
+161
+00:17:33,170 --> 00:17:43,230
+عملية عليها هدى is called a group بنسميها مجموعة
+
+162
+00:17:43,230 --> 00:17:50,750
+if the following properties
+
+163
+00:17:55,710 --> 00:18:00,170
+if the following reporters are satisfied are
+
+164
+00:18:00,170 --> 00:18:08,230
+satisfied ايش
+
+165
+00:18:08,230 --> 00:18:18,110
+الخواص هذه اللي هو الخاصية الأولى the star is
+
+166
+00:18:18,110 --> 00:18:24,030
+associative associative
+
+167
+00:18:24,800 --> 00:18:29,100
+that is a
+
+168
+00:18:29,100 --> 00:18:42,300
+star b a star c بدو يساوي a star b star c لكل
+
+169
+00:18:42,300 --> 00:18:49,140
+ال a و ال b و ال c اللي موجودة في ال group g ال
+
+170
+00:18:49,140 --> 00:18:50,760
+condition الثاني
+
+171
+00:18:52,870 --> 00:19:09,190
+condition الثاني there is an element such
+
+172
+00:19:09,190 --> 00:19:12,550
+that
+
+173
+00:19:12,550 --> 00:19:23,830
+بحيث انA Star A يساوي E Star A يساوي الـ A السلف
+
+174
+00:19:23,830 --> 00:19:33,730
+لكل الـ A الموجودة في G بلا استثناء يبقى الـ E is
+
+175
+00:19:33,730 --> 00:19:42,330
+called the identity element
+
+176
+00:19:42,330 --> 00:19:45,530
+of
+
+177
+00:19:46,970 --> 00:20:11,510
+G condition
+
+178
+00:20:11,510 --> 00:20:13,330
+الثالث والأخير
+
+179
+00:20:20,360 --> 00:20:34,280
+for each a الموجود في g there exist b in g such
+
+180
+00:20:34,280 --> 00:20:45,800
+thatبحيث ان such that ال a star b بده يساوي b star
+
+181
+00:20:45,800 --> 00:20:53,500
+a بده يساوي ال identity e بيه
+
+182
+00:20:53,500 --> 00:20:58,880
+is called يبقى
+
+183
+00:20:58,880 --> 00:21:09,490
+بيه في هذه الحالة بنسميه is theinverse element of
+
+184
+00:21:09,490 --> 00:21:21,950
+a معكوس العنصر a and denoted by ال b بده يساوي ال
+
+185
+00:21:21,950 --> 00:21:26,870
+a inverse command
+
+186
+00:21:26,870 --> 00:21:30,970
+definition the group
+
+187
+00:21:33,590 --> 00:21:39,610
+الـ G is called abelian
+
+188
+00:21:39,610 --> 00:21:45,090
+if
+
+189
+00:21:45,090 --> 00:21:54,250
+ال X Y متساوي Y X لكل ال X و Y الموجودة في ال
+
+190
+00:21:54,250 --> 00:21:55,450
+group G
+
+191
+00:22:25,540 --> 00:22:31,040
+يبقى احنا ابتداء من هذا التعريف بكون بدأنا ندخل في
+
+192
+00:22:31,040 --> 00:22:35,680
+علم ال groups او علم المجموعات اللي هو موضوع
+
+193
+00:22:35,680 --> 00:22:40,220
+دراستنا لهذا الفصل اللي هو ال abstract algebra
+
+194
+00:22:40,220 --> 00:22:44,460
+يبقى اول موضوع في موضوع الجبر اللي هو الموضوع
+
+195
+00:22:44,460 --> 00:22:50,330
+المجموعات الان نعرف المجموعة و بعدين ناخدأمثلة
+
+196
+00:22:50,330 --> 00:22:54,310
+متعددة على المجموعة بدل المثال عشر او احد مثال
+
+197
+00:22:54,310 --> 00:23:00,010
+وبعد ذلك ناخد بعض خواص المجموعات البسيطة يبقى
+
+198
+00:23:00,010 --> 00:23:04,470
+التعليف بيقول ما يتفترض ان G هو عبارة عن non-empty
+
+199
+00:23:04,470 --> 00:23:10,230
+set يبقى ليست الفئة الخاوية وانما على الأقل فيها
+
+200
+00:23:10,230 --> 00:23:15,000
+ولو عنصر واحدand let the star be a binary
+
+201
+00:23:15,000 --> 00:23:20,760
+operation على g الست
+
+202
+00:23:20,760 --> 00:23:26,400
+جي معالي الstar مع بعض هدول بيكونولي a group إذا
+
+203
+00:23:26,400 --> 00:23:32,990
+تحققت عندي ثلاثة خواص أو ثلاثة شروطالشروط أو
+
+204
+00:23:32,990 --> 00:23:37,790
+الخواصة دي لـ star اللي عندي is associative يبقى
+
+205
+00:23:37,790 --> 00:23:43,430
+هي عملية إدماجية بمعنى ان a star b star c يساوي
+
+206
+00:23:43,430 --> 00:23:48,250
+يعني بتخلي a تأثر على b في الأول حسب تعريف ال star
+
+207
+00:23:48,360 --> 00:23:52,300
+والعنصر اللى ينتج يخلّيه أثر على مين؟ على C
+
+208
+00:23:52,300 --> 00:23:57,580
+النتيجة تماما كما لو B أثرت على C طالع عنصر جديد
+
+209
+00:23:57,580 --> 00:24:01,820
+هذا العنصر بدأ أثر عليه بإيه لازم يكون اتنين are
+
+210
+00:24:01,820 --> 00:24:06,140
+equal ان حدث ذلك يبقى بقوله خاصية ال associativity
+
+211
+00:24:06,140 --> 00:24:11,160
+الصحيحة لجميع العناصر يعني لما بدأ أخد A وB وC مش
+
+212
+00:24:11,160 --> 00:24:15,060
+بدأ اختارهم عناصر محددة فلان وفلان بدأ أخد أي
+
+213
+00:24:15,060 --> 00:24:20,770
+عناصر بغض النظر شو شكلهمالنقطة الثانية بيقول لي
+
+214
+00:24:20,770 --> 00:24:26,570
+there is an element E بحيث اذا لجيت عنصر اعطيته
+
+215
+00:24:26,570 --> 00:24:32,090
+الرمز E بس هذا إله خواص طبعا العنصر هذا موجود في
+
+216
+00:24:32,090 --> 00:24:38,570
+جي itself بحيث ان لو أثرت بال A على ال E بال star
+
+217
+00:24:38,570 --> 00:24:44,330
+هذه تماما كما لو أثرت بال E على A والنتج طالع ال A
+
+218
+00:24:44,330 --> 00:24:49,240
+itselfيبقى هذا اللي كنا بنسميه عنصر المحيد لا
+
+219
+00:24:49,240 --> 00:24:54,200
+يتأثر أي element في المجموعة بهذا ال element تحت
+
+220
+00:24:54,200 --> 00:24:58,300
+العملية star أثر عليه star بهذا العنصر ويبقى ال
+
+221
+00:24:58,300 --> 00:25:02,780
+element كما هو يبقى إن حدث ذلك هذا بسميه عنصر
+
+222
+00:25:02,780 --> 00:25:07,040
+المحيد او في لغة ال groups احنا هنسميه identity
+
+223
+00:25:07,040 --> 00:25:12,390
+element اللي هو عنصر الوحدة لهذه المجموعةبنضل عند
+
+224
+00:25:12,390 --> 00:25:18,210
+ال condition التالت والاخير قال لي 4H اللي موجود
+
+225
+00:25:18,210 --> 00:25:24,290
+في G لأي عنصر A موجود في G هلاقي عنصر تاني اسمه B
+
+226
+00:25:24,290 --> 00:25:29,830
+موجود في G بحيث لو ضربته من اليمين او من الشمال A
+
+227
+00:25:29,830 --> 00:25:34,590
+Star B بلاقي النتيجة هو B Star A يسوى ال identity
+
+228
+00:25:34,590 --> 00:25:39,450
+element itself يبقى هذا بده يعطيني عنصر الوحدة
+
+229
+00:25:39,450 --> 00:25:47,580
+نفسهإن حدث ذلك يبقى هذا العنصر معكوس العنصر A يبقى
+
+230
+00:25:47,580 --> 00:25:51,980
+في هذه الحالة ال B is called the inverse element
+
+231
+00:25:51,980 --> 00:25:52,520
+of A
+
+232
+00:25:58,500 --> 00:26:01,920
+هذا الـ A كلها اللي فوق واسة اللي بسميه the
+
+233
+00:26:01,920 --> 00:26:07,460
+inverse element of A معكوس العنصر A يبقى B اللي
+
+234
+00:26:07,460 --> 00:26:12,460
+لجيته هذا بدي أسميه معكوس العنصر اللي هو A طب
+
+235
+00:26:12,460 --> 00:26:19,980
+السؤال هو هل كل عنصر في G لازم يجيه معكوس يعني مش
+
+236
+00:26:19,980 --> 00:26:26,940
+بالضرورة بعضهم ما و بعضهم لأ طب إيش جاي ال A لأfor
+
+237
+00:26:26,940 --> 00:26:32,260
+each لكل عنصر يبقى كل عنصر في جي بدأت تجيله معكوس
+
+238
+00:26:32,260 --> 00:26:38,020
+مش بعضهم له و بعضهم مالواشي كل عنصر في جي له معكوس
+
+239
+00:26:38,020 --> 00:26:45,080
+يعني لو أتصورت أن جي هذه خمس عناصر يبقى فيهم اللي
+
+240
+00:26:45,080 --> 00:26:49,020
+هو أربعة واحد معكوس للتاني و ال identity element
+
+241
+00:26:49,020 --> 00:26:55,290
+معكوس لنفسهلو كانوا ستة يبقى تلاتة معكوسات التلاتة
+
+242
+00:26:55,290 --> 00:27:01,430
+التانيات و هكذا يبقى كل عنصر في ال group جي حلقيله
+
+243
+00:27:01,430 --> 00:27:05,990
+معكوس موجود في جي بعد لو ضربت العنصر في معكوسه من
+
+244
+00:27:05,990 --> 00:27:10,290
+الشمال والله لمين بدي يطلع عنصر الوحدة طب عنصر
+
+245
+00:27:10,290 --> 00:27:15,960
+الوحدة هذا هو الصفر ولا واحد صحيحيقول حسب ال
+
+246
+00:27:15,960 --> 00:27:20,600
+operation المعرفة على ال group يبقى حسب ال group
+
+247
+00:27:20,600 --> 00:27:23,820
+وحسب ال operation اللي عليها ملاجئ ال identity
+
+248
+00:27:23,820 --> 00:27:27,570
+اللي يمكن ال identity is zeroيمكن ال identity يطلع
+
+249
+00:27:27,570 --> 00:27:33,750
+واحد يمكن ال identity يطلع عشرة مثلا هادئ جدا يبقى
+
+250
+00:27:33,750 --> 00:27:37,930
+حسب ال operation اللى موجودة عندك وقد نستغرب هذا
+
+251
+00:27:37,930 --> 00:27:41,950
+لان نستغرب ولا حاجة وحنوريك بعض الأمثلة نحسب فيها
+
+252
+00:27:41,950 --> 00:27:47,550
+ال identity element ومايطلعش لا zero ولا واحديبقى
+
+253
+00:27:47,550 --> 00:27:52,430
+هذا يعني ان الشخص ما يكون شكله يكون بهمنيش يبقى ال
+
+254
+00:27:52,430 --> 00:27:55,570
+identity يعتمد على ال group ويعتمد على ال
+
+255
+00:27:55,570 --> 00:28:00,790
+operation على ال group اتفضل معناته
+
+256
+00:28:00,790 --> 00:28:07,410
+مش معكوس يبقى ليست group يبقى اذا اختل اي شرط من
+
+257
+00:28:07,410 --> 00:28:11,550
+الشروط التلاتة بالبطرة ستصبح groupيبقى مشان تكون
+
+258
+00:28:11,550 --> 00:28:16,810
+ال group بدي any non zero set والتلت شروط يتحققوا
+
+259
+00:28:16,810 --> 00:28:21,190
+هدول بدي ال operation هذه تبقى binary operation
+
+260
+00:28:21,190 --> 00:28:25,830
+نمرا واحد لو ماكنتش binary operation الصبح أخدنا
+
+261
+00:28:25,830 --> 00:28:29,030
+مثل ماهياش binary operation يبقى ده مينفعش يتكون
+
+262
+00:28:29,030 --> 00:28:35,060
+ال groupلازم نبقى بيناري اوبريشن أولا ثم تتحقق
+
+263
+00:28:35,060 --> 00:28:40,240
+الشروط التلتة تطلع الشجرة التعريف جينامتستاتار بي
+
+264
+00:28:40,240 --> 00:28:44,880
+بيناري اوبريشن يبقى هذه بسميها group لو تحققت
+
+265
+00:28:44,880 --> 00:28:48,340
+الشروط التلتة يبقى انا في الحقيقة عندي تلت شروط
+
+266
+00:28:48,340 --> 00:28:54,260
+ولا اربعةأربعة بدك هدى binary operation لستار
+
+267
+00:28:54,260 --> 00:28:59,780
+بتبقى associative أو اختصارا بروح بقول هم التلاتة
+
+268
+00:28:59,780 --> 00:29:04,000
+لستار هدى بدي associative binary operation يبقى
+
+269
+00:29:04,000 --> 00:29:08,020
+جمعت الشرطين مين بشرط واحد اتنين وجود ال identity
+
+270
+00:29:08,020 --> 00:29:13,200
+element تلاتة وجود معكوس العنصر لأى عنصر موجود وين
+
+271
+00:29:13,200 --> 00:29:18,130
+موجود في ال group Gإن حدث ذلك بقول يبقى الـ 6G
+
+272
+00:29:18,130 --> 00:29:22,350
+اللي عندنا هذه مالها is A group وحتى أرسخ هذا
+
+273
+00:29:22,350 --> 00:29:27,330
+المفهوم من دماغك و أسحب المفهوم اللي في دماغك إن
+
+274
+00:29:27,330 --> 00:29:31,690
+ال operation هذه هي عملية ضرب لحالها أو عملية قسمة
+
+275
+00:29:31,690 --> 00:29:36,290
+لحالها أو عملية طرح لحالهاهتشوف أمثلة مختلفة و
+
+276
+00:29:36,290 --> 00:29:42,070
+عديدة حتى مصبح احنا مقيدين بشكل ال six اللي عندنا
+
+277
+00:29:42,070 --> 00:29:46,650
+و ماناش دعوة في ال six الأخرى اتنين مقيدين بال
+
+278
+00:29:46,650 --> 00:29:49,070
+binary operation اللي عندنا و غيرها من ال
+
+279
+00:29:49,070 --> 00:29:53,550
+operations ماليش علاقة فيهم تمام؟ وهذا يختلف من
+
+280
+00:29:53,550 --> 00:29:58,890
+group إلى الأخرى نعطي أول مثال على ذلك قبله نعطي
+
+281
+00:29:58,890 --> 00:30:04,910
+أول مثال كلمة AbelianAbelian بالعربي يعني ابدالي
+
+282
+00:30:04,910 --> 00:30:10,190
+ابدالي زي ما يقول commutative ابدالي فبجي بقول
+
+283
+00:30:10,190 --> 00:30:15,430
+group G is called abelian اذا كان ال X في Y بده
+
+284
+00:30:15,430 --> 00:30:19,730
+ساوي Y في X لكل ال X و Y اللي موجودة بلا استثناء
+
+285
+00:30:19,730 --> 00:30:25,210
+يعني لو جيت شباب اللي في القاعة خمسين طالب تمام لو
+
+286
+00:30:25,210 --> 00:30:29,150
+بدل كل واحد مقعد و مكان التاني ماصارش تغيير عندى
+
+287
+00:30:29,150 --> 00:30:34,520
+ولا حاجةكويس يبقى ما عدش فيه طول ولا قصر مع تبديل
+
+288
+00:30:34,520 --> 00:30:38,920
+مقعده ولا نقص من مقامه لا يبقى طالب زي ما هو مسجل
+
+289
+00:30:38,920 --> 00:30:43,480
+المادة وقاعد عندنا إذا لما بدل واحد مكان التاني
+
+290
+00:30:43,480 --> 00:30:49,480
+لجيته يساوي نفس التبديل الأصلي إن حدث ذلك يبقى هذا
+
+291
+00:30:49,480 --> 00:30:53,960
+بقول عنك commutative group أو abelian group لكن
+
+292
+00:30:53,960 --> 00:30:59,810
+بقولش commutative commutative بقول عن درجاتالتسمية
+
+293
+00:30:59,810 --> 00:31:04,550
+أو التعريف في حالة ال rings اللي هو تبعت الفصل
+
+294
+00:31:04,550 --> 00:31:08,450
+الثاني ان شاء الله ان شاء الله اللي باخد جبر حديثة
+
+295
+00:31:08,450 --> 00:31:12,790
+نمسكو ال commutative ring لكن في ال group هسميها
+
+296
+00:31:12,790 --> 00:31:17,640
+abelian group نسبة للعالمهي ابيل اللى اكتشف هالشغل
+
+297
+00:31:17,640 --> 00:31:23,340
+هذى وسميت باسمه ابيليان جروب اذا من حد ما تسمع
+
+298
+00:31:23,340 --> 00:31:28,120
+كلمة ابيليان جروب بدك تفهم ان العناصر بقدر ابدلهم
+
+299
+00:31:28,120 --> 00:31:33,000
+مكان بعض بدون اي مشاكل تمام؟ فهذا معنى ابيليان
+
+300
+00:31:33,000 --> 00:31:40,150
+جروبنأخد أبسط الأمثلة و نتدرج إلى الأثقال فالأثقال
+
+301
+00:31:40,150 --> 00:31:45,310
+فالأثقال حتى نصل إلى أمثلة مختلفة يبقى examples
+
+302
+00:31:45,310 --> 00:31:48,990
+أمثلة
+
+303
+00:31:48,990 --> 00:31:58,170
+أول مثال على ذلك الآن ال Z وال Q and set of real
+
+304
+00:31:58,170 --> 00:32:09,760
+numbers هذول underusual addition تحت عملية الجمع
+
+305
+00:32:09,760 --> 00:32:17,740
+العادي under usual addition اللي هو ال plus are
+
+306
+00:32:17,740 --> 00:32:26,160
+abelian groups are
+
+307
+00:32:26,160 --> 00:32:28,580
+abelian groups because
+
+308
+00:32:36,540 --> 00:32:42,300
+السبب يبقى انا ادعى انه زد تحت عملية الجامعة
+
+309
+00:32:42,300 --> 00:32:46,020
+العادى اقول لك usual addition الجامعة العادى تبع
+
+310
+00:32:46,020 --> 00:32:51,060
+ال real numberالـ Q تحت الجامعه العادى الـ R تحت
+
+311
+00:32:51,060 --> 00:32:54,020
+الجامعه العادى يعني عملش معرف على الـ set of
+
+312
+00:32:54,020 --> 00:32:56,680
+integers ومعرف على ال set of rational numbers
+
+313
+00:32:56,680 --> 00:32:59,440
+ومعرف على ال set of .. يعني هدول يعتبروا إيه؟
+
+314
+00:32:59,440 --> 00:33:05,620
+ثلاثة أمثلة يعني هدول three groups تحت العملية الـ
+
+315
+00:33:05,620 --> 00:33:09,780
+plus هذا و ال groups هدول are abelian احنا بنعرف
+
+316
+00:33:09,780 --> 00:33:14,270
+لما أقول A زائد B يعني اتنين زائد تلاتةسوى تلاتة
+
+317
+00:33:14,270 --> 00:33:18,890
+زي اتنين جامعه عادي صح ولا لا هذا على زد لو جيت
+
+318
+00:33:18,890 --> 00:33:24,610
+على ال IQ اتنين عدديا نسبيا مجموعهم عدد نسبي كذلك
+
+319
+00:33:24,610 --> 00:33:29,610
+لو جيت مجموع عددين حقيقيا بيعطينا ايه؟ عدد حقيقي
+
+320
+00:33:29,610 --> 00:33:35,860
+بجهة دي binary operationيبقى هنا بقوله because a
+
+321
+00:33:35,860 --> 00:33:43,060
+plus is a by أو associative بالمرة كمان is
+
+322
+00:33:43,060 --> 00:33:46,080
+associative
+
+323
+00:33:46,080 --> 00:33:53,300
+binary operation
+
+324
+00:33:53,300 --> 00:33:56,320
+on
+
+325
+00:33:56,320 --> 00:34:07,850
+z والي qand كذلك من ال set of real numbers طب كويس
+
+326
+00:34:07,850 --> 00:34:11,170
+أظن
+
+327
+00:34:11,170 --> 00:34:14,730
+أخدنا هذه الكثير حكاية ال associativity للأعداد
+
+328
+00:34:14,730 --> 00:34:18,730
+الحقيقية ما هي النسبية والصحيها جزء من الأعداد
+
+329
+00:34:18,730 --> 00:34:22,510
+الحقيقية يبقى الأعداد الحقيقية لما أقول اتنين زي
+
+330
+00:34:22,510 --> 00:34:26,650
+التلاتة زي الخمسة هو تلاتة زي الخمسة والإنتاج يضيف
+
+331
+00:34:26,650 --> 00:34:30,410
+له اتنين عادى جدا مافيش فيها مشكلةيبقى هذه بالنسبة
+
+332
+00:34:30,410 --> 00:34:35,590
+لل associative طب مين ال identity element في حالة
+
+333
+00:34:35,590 --> 00:34:43,310
+الجامعة ال zero يبقى هنا is هذه النقطة الأولى
+
+334
+00:34:43,310 --> 00:34:49,810
+النقطة الثانية النقطة الثانية ال zero is the
+
+335
+00:34:49,810 --> 00:34:56,310
+identity element because
+
+336
+00:35:00,180 --> 00:35:07,120
+الـ zero زائد ال بي مثلا يساوي بي زائد ال zero بده
+
+337
+00:35:07,120 --> 00:35:15,720
+يساوي ال بي itself الكلام هذا for all بي اللي
+
+338
+00:35:15,720 --> 00:35:24,240
+موجودة في z أوي q and ال a طيب النقطة التالتة
+
+339
+00:35:27,080 --> 00:35:33,000
+لو أخدت element a موجود في أي منهما من المعكوس
+
+340
+00:35:33,000 --> 00:35:38,940
+تبعه يعني مين العدد اللي بدي أضيفه إليه يطلع من؟
+
+341
+00:35:38,940 --> 00:35:50,730
+يطلع zero سالم العدد يبقى هنا the inverse ofأي
+
+342
+00:35:50,730 --> 00:36:00,010
+اللي موجود في الـ Z أو الـ Q and ال R is سالب A
+
+343
+00:36:00,010 --> 00:36:10,770
+since لأن ال A زائد ناقص A يسوى ناقص A زائد A يسوى
+
+344
+00:36:10,770 --> 00:36:17,490
+Zero لهمين ال identity element طيب
+
+345
+00:36:17,490 --> 00:36:26,910
+نمر اتنينروح ناخد مثال اخر لو أخدت الآن z و تحت
+
+346
+00:36:26,910 --> 00:36:35,250
+عملية الضرب العادي z is
+
+347
+00:36:35,250 --> 00:36:46,010
+not a group يبقى هذه ماهياش group under usual
+
+348
+00:36:46,010 --> 00:36:47,810
+multiplication
+
+349
+00:36:50,890 --> 00:37:00,830
+تحت عملية الضرب العادية ليش؟ because because
+
+350
+00:37:00,830 --> 00:37:14,270
+if ال a موجود في z and ال a لا يسوى واحد وبحيث ال
+
+351
+00:37:14,270 --> 00:37:20,450
+a لا يسوى واحدالان تحت عملية الضرب من ال identity
+
+352
+00:37:20,450 --> 00:37:25,650
+element الواحد ممتاز جدا يبقى هذا واحد لان اي عدد
+
+353
+00:37:25,650 --> 00:37:29,910
+اضربه في واحد بيطلع نفسي لوحده السؤال هو هل بقدر
+
+354
+00:37:29,910 --> 00:37:34,370
+الاقي element اضربه في اي عدد يطلع واحد
+
+355
+00:37:37,270 --> 00:37:43,510
+أنا بدي في Z أنا بحكي على Z فقط أنا مقيد بال 6
+
+356
+00:37:43,510 --> 00:37:47,590
+بتبعتي ال 6 الأخرى ماليش علاقة فيها و مقيد بال
+
+357
+00:37:47,590 --> 00:37:52,950
+operation اللي عندي بقدر ألاقي في الشمكانية يبقى F
+
+358
+00:37:52,950 --> 00:37:59,150
+ال A موجودة under ال A لا تساوي واحد then there is
+
+359
+00:37:59,150 --> 00:38:12,610
+أو there exists no element Bن اللي هو z such that
+
+360
+00:38:12,610 --> 00:38:21,170
+بحيث ان ال a في b بده يساوي الواحد الصحيح يعني for
+
+361
+00:38:21,170 --> 00:38:25,830
+example if
+
+362
+00:38:25,830 --> 00:38:33,190
+ال a تساوي تلتة بقدر الاقي عدد بي اضروف تلتة يطلع
+
+363
+00:38:33,190 --> 00:38:39,390
+واحد بس بحيث العدد فيه zفالـ a تسوى تلاتة then
+
+364
+00:38:39,390 --> 00:38:45,910
+there is no integer
+
+365
+00:38:45,910 --> 00:38:55,950
+بي such that بحيث ان تلاتة بيبدوا يساوي واحد
+
+366
+00:38:55,950 --> 00:39:03,250
+مالاجيش هذا العدد بتاتا يبقى هذه زد تحت عملية ضرب
+
+367
+00:39:03,250 --> 00:39:11,270
+مالهاطيب خليني أسأل كمان سؤال لو قلتلك ال set of
+
+368
+00:39:11,270 --> 00:39:16,770
+real numbers كويس؟ بس أصبر شوية ال set of real
+
+369
+00:39:16,770 --> 00:39:26,430
+numbers تحت عملية الضرب هل هي group؟ ليش؟بالنسبة
+
+370
+00:39:26,430 --> 00:39:29,750
+للصفر بلا جيش و لا inverse ليش ان ال identity قلت
+
+371
+00:39:29,750 --> 00:39:34,890
+هو مين بلا جيش ولا عدد اضربه في الصفر يطلع واحد
+
+372
+00:39:34,890 --> 00:39:40,730
+صحيح يدي ليست جروب و هكذا اذا احنا ال set مقيدين
+
+373
+00:39:40,730 --> 00:39:45,410
+بال set بشكل الاعداد اللى موجودة فيها مقيد بال
+
+374
+00:39:45,410 --> 00:39:48,750
+identity اللى عندى فيها مقيد بال binary
+
+375
+00:39:48,750 --> 00:39:52,150
+operational اللى موجودة عندى حققت الشروط بقول جروب
+
+376
+00:39:52,150 --> 00:39:58,830
+ما حققت بقوله ماهياش جروبطيب لو جيت قولش لك تلاتة
+
+377
+00:39:58,830 --> 00:40:06,490
+let الاي تساوي الجدر التربيعي للسالب واحد define
+
+378
+00:40:06,490 --> 00:40:10,090
+define
+
+379
+00:40:10,090 --> 00:40:17,610
+usual multiplication multiplication
+
+380
+00:40:17,610 --> 00:40:19,550
+on
+
+381
+00:40:38,180 --> 00:40:46,550
+عرفت حصل الضرب على set of complex numbersواحد ناقص
+
+382
+00:40:46,550 --> 00:40:51,330
+واحد اي ناقص اي ناقص اي حيث اي هو الجدر التربية
+
+383
+00:40:51,330 --> 00:40:56,550
+للسالب واحد يبقى دول complex ولا لا وعليهم عملية
+
+384
+00:40:56,550 --> 00:41:01,430
+ضرب العادية تبع ال complex number السؤال هو هل هذه
+
+385
+00:41:01,430 --> 00:41:05,470
+group ولا لا في الأول بدي أشوف هل ال
+
+386
+00:41:05,470 --> 00:41:12,990
+multiplication هذهلو ضرب اي عددين في بعض من دول
+
+387
+00:41:12,990 --> 00:41:18,430
+بيبقى complex و لا بيبطل يصير complexany real
+
+388
+00:41:18,430 --> 00:41:22,270
+number is complex هذا complex وهذا complex وهذا
+
+389
+00:41:22,270 --> 00:41:25,670
+complex وهذا complex وهذا complex يبقى العملية هذه
+
+390
+00:41:25,670 --> 00:41:30,790
+طيب لو ضربت ال I في ناقص I أليست مثل ناقص I في I
+
+391
+00:41:30,790 --> 00:41:34,950
+لأن العملية إبدالية هذا ناقص واحد في I زي I في
+
+392
+00:41:34,950 --> 00:41:40,230
+ناقص واحد سياد يبقى هذه اللي هي عبارة عن
+
+393
+00:41:40,230 --> 00:41:45,610
+associative binary operation يبقى let then
+
+394
+00:41:52,020 --> 00:41:58,380
+النقطة الان هي نقطة
+
+395
+00:41:58,380 --> 00:42:03,500
+عملية عملية عملية عملية عملية عملية
+
+396
+00:42:03,500 --> 00:42:06,700
+عملية عملية
+
+397
+00:42:10,880 --> 00:42:17,480
+طب كويس، مين ال identity element؟ واحد، يبقى واحد
+
+398
+00:42:17,480 --> 00:42:22,740
+is the identity element
+
+399
+00:42:24,480 --> 00:42:28,440
+يبقى الواحد هو عنصر الواحد اللي دي لو ضربته في أي
+
+400
+00:42:28,440 --> 00:42:32,580
+واحد من هدول بيطلع نفس الواحد هدول طيب السؤال مين
+
+401
+00:42:32,580 --> 00:42:38,060
+معكوس السلب واحد السلب واحد itself يبقى السلب واحد
+
+402
+00:42:38,060 --> 00:42:44,740
+is the inverse of itself يبقى هو معكوس لنفسي هنا
+
+403
+00:42:44,740 --> 00:42:55,030
+سلب واحد is the inverse of itselfطيب مين معكوس
+
+404
+00:42:55,030 --> 00:42:58,590
+الواحد؟ الواحد نفسه، ضربه نفسه بيطلع واحد، ماعنديش
+
+405
+00:42:58,590 --> 00:43:01,650
+أمر يبقى هذا ال identity دائما و أبدا شباب ال
+
+406
+00:43:01,650 --> 00:43:06,150
+identity هو معكوسه لنفسه، يتدورش عليه أي group
+
+407
+00:43:06,150 --> 00:43:08,810
+تطلع في الدنيا عندك ال identity ان هو معكوسه
+
+408
+00:43:08,810 --> 00:43:13,490
+لنفسها طيب الان مين معكوس ال I؟ ال سالب I طب و
+
+409
+00:43:13,490 --> 00:43:20,880
+السالب I؟لو ضربت اي في اي باي ترميلي بسالب واحد و
+
+410
+00:43:20,880 --> 00:43:27,520
+عندك سالب بصير موجة بواحد يبقى هنا باجي بقول له ال
+
+411
+00:43:27,520 --> 00:43:34,580
+اي is the inverse of سالب اي
+
+412
+00:43:39,980 --> 00:43:46,020
+من هذول التلاتة مع اللي فوق يبقى صلة هذه ال group
+
+413
+00:43:46,020 --> 00:43:52,260
+تحت عملية ضرب is a group يبقى هذا بدي يعطيلك انه g
+
+414
+00:43:52,260 --> 00:43:59,920
+تحت عملية الضرب اللي عندنا هذه is a group يبقى هذه
+
+415
+00:43:59,920 --> 00:44:02,160
+عبارة عن مجموعة
+
+416
+00:44:17,760 --> 00:44:23,720
+مثال رقم أربعة مثال
+
+417
+00:44:23,720 --> 00:44:31,880
+رقم أربعة هذا سؤال تلاتة من الكتاب بيقول لي show
+
+418
+00:44:31,880 --> 00:44:41,860
+that the set اللي هي مين؟ واحد واثنين وتلاتة
+
+419
+00:44:41,860 --> 00:44:45,680
+واربعة under
+
+420
+00:44:50,830 --> 00:45:01,410
+multiplication module خمسة module خمسة is an
+
+421
+00:45:01,410 --> 00:45:14,950
+abelian group is an abelian group but ولكن اللي هو
+
+422
+00:45:14,950 --> 00:45:26,710
+واحدو اتنين و تلاتة under multiplication
+
+423
+00:45:26,710 --> 00:45:30,410
+modulo
+
+424
+00:45:30,410 --> 00:45:34,850
+أربعة
+
+425
+00:45:34,850 --> 00:45:39,970
+is not a group
+
+426
+00:46:15,380 --> 00:46:20,710
+سؤال مرة تانية السؤال يعتبر سؤالينعندما أعطيني
+
+427
+00:46:20,710 --> 00:46:25,010
+أربعة أعداد واحد اتنين تلاتة عرفنا عليهم عملية ضرب
+
+428
+00:46:25,010 --> 00:46:30,430
+module خمسة عملية ضرب بالمقياس خمسة قال لي أثبت إن
+
+429
+00:46:30,430 --> 00:46:34,050
+هذه عبارة عن abelian group abelian سهلة تلاتة في
+
+430
+00:46:34,050 --> 00:46:36,550
+اتنين هي اتنين في تلاتة تلاتة في اربع هي اربع في
+
+431
+00:46:36,550 --> 00:46:40,050
+تلاتة اتنين في اربع هي اربع في اتنين والباقي في
+
+432
+00:46:40,050 --> 00:46:43,070
+واحد ما هي بطلع نفسها تمام؟ إذا أنا حكيت ال
+
+433
+00:46:43,070 --> 00:46:46,630
+abelian هذه تحصيل حصل يبقى أنا بالزمن ال
+
+434
+00:46:46,630 --> 00:46:51,690
+associative و بالزمن من؟ال binary operation في
+
+435
+00:46:51,690 --> 00:46:55,830
+الأول و لزمنا ال identity و المعكوس بقوله بسيطة
+
+436
+00:46:55,830 --> 00:47:00,370
+جدا الان بدي أشوف هل هي associ .. هي قبل ال
+
+437
+00:47:00,370 --> 00:47:04,190
+associative هل هي binary operation ولا لا بقوله
+
+438
+00:47:04,190 --> 00:47:10,110
+الله كويس يعني لو تعرفت أي عنصرين في بعضهم بدي
+
+439
+00:47:10,110 --> 00:47:14,170
+يكون ناتج داخل الستة دي ان حدث ذلك بقوله هذه
+
+440
+00:47:14,170 --> 00:47:18,880
+binary operation الان تعال خدلي اتنين في واحدبتنين
+
+441
+00:47:18,880 --> 00:47:21,840
+موجودة تلاتة في واحد تلاتة موجودة اربعة في واحد
+
+442
+00:47:21,840 --> 00:47:26,960
+باربعة موجودة نمسك اتنين اتنين في تلاتة ستة modulo
+
+443
+00:47:26,960 --> 00:47:31,740
+خمسة بيظل قداش واحد موجود اتنين في اربعة تمانية
+
+444
+00:47:31,740 --> 00:47:36,080
+modulo خمسة تلاتة موجود خلصنا اتنين ضربنا في تلاتة
+
+445
+00:47:36,080 --> 00:47:39,940
+و اربعة لان تلاتة في اربعة باطمعشر modulo خمسة
+
+446
+00:47:39,940 --> 00:47:45,980
+باتنين موجود يبقى داشت صارت binary operation يبقى
+
+447
+00:47:45,980 --> 00:47:55,650
+باجي بقوله اول شيءالـ multiplication modulo
+
+448
+00:47:55,650 --> 00:48:12,890
+خمسة is a binary operation on the set اللي واحد
+
+449
+00:48:12,890 --> 00:48:17,950
+واثنين وتلاتة واربع because السبب
+
+450
+00:48:20,570 --> 00:48:29,870
+الـ A, B modulo خمسة موجود في الست واحد واتنين
+
+451
+00:48:29,870 --> 00:48:35,430
+وتلاتة واربعة لكل ال A و ال B شو رايك أسميها
+
+452
+00:48:35,430 --> 00:48:41,430
+للسهولة أسميها S و هذا يبدأ أسميها S يبغى لكل ال A
+
+453
+00:48:41,430 --> 00:48:47,850
+و ال B اللي موجودة وين في Sيبقى حاصل ضرب اي اتنين
+
+454
+00:48:47,850 --> 00:48:52,430
+كله موجود وين موجود لذلك بايناري وبرجانت اتنين هذا
+
+455
+00:48:52,430 --> 00:48:55,870
+ضرب عادي بس باخد الموديولو في الآخر يبقى
+
+456
+00:48:55,870 --> 00:49:03,570
+associative ولا لا يبقى هنا كمان لاحظ انه note انه
+
+457
+00:49:03,570 --> 00:49:09,510
+multiplication modulo
+
+458
+00:49:09,510 --> 00:49:12,310
+خمسة
+
+459
+00:49:15,220 --> 00:49:21,640
+is associative بدّك
+
+460
+00:49:21,640 --> 00:49:25,640
+تشكل بساطرة هذا مافي مشكلة احنا ال I هو ال
+
+461
+00:49:25,640 --> 00:49:29,040
+identity الواحد يبقى هذا سهل لكن ضالي عند مين
+
+462
+00:49:29,040 --> 00:49:31,700
+الاتنين والتلاتة والاربعة يبقى بقدر أخدهم مع بعض
+
+463
+00:49:31,700 --> 00:49:37,040
+او يبقى خلصت ال group كله مظبوط يعني for example
+
+464
+00:49:40,060 --> 00:49:49,900
+لو أخدت اتنين أستار تلاتة أستار أربع طيب، هذا
+
+465
+00:49:49,900 --> 00:49:56,040
+اتنين في تلاتة بستة موديولو خمسة صح ولا لأ؟ يبقى
+
+466
+00:49:56,040 --> 00:50:02,220
+ستة موديولو خمسة فيها قداشر؟ واحد يبقى بظل واحد
+
+467
+00:50:02,220 --> 00:50:11,280
+أستار أربعأربعة مد يولو خمسة يبقى هذا بده يساوي
+
+468
+00:50:11,280 --> 00:50:18,860
+أربعة and لو أخدت اتنين star تلاتة star أربعة
+
+469
+00:50:18,860 --> 00:50:27,510
+ويساوي تلاتة في أربعةب12 modulo 5 ب2 يبقى يساوي 2
+
+470
+00:50:27,510 --> 00:50:35,110
+star 2 يعني 2 في 2 ب4 modulo 5 اللي هي ب4 يبقى هذا
+
+471
+00:50:35,110 --> 00:50:41,450
+بده يعطينا 4 يبقى star هذه هي نفس هذه بالظبط يبقى
+
+472
+00:50:41,450 --> 00:50:44,750
+العملية أساسية وضل بس دور مين الواحد واحد اللي
+
+473
+00:50:44,750 --> 00:50:47,490
+هيقدمه لأخر بالنسبة لعملية الدور لأن هو ال
+
+474
+00:50:47,490 --> 00:50:53,510
+identity elementيبقى على طول الخطب نقول واحد is
+
+475
+00:50:53,510 --> 00:51:01,430
+the identity element لأن
+
+476
+00:51:01,430 --> 00:51:05,250
+الواحد في أي رقم من الباقي module وخمسة هيعطيني
+
+477
+00:51:05,250 --> 00:51:12,230
+نفس الرقم مش هيغير حاجة طيب مين معكوس اي واحد فيهم
+
+478
+00:51:12,230 --> 00:51:14,270
+يالا شوف
+
+479
+00:51:17,900 --> 00:51:24,760
+من معكوس أي رقم من هذه الأرقام اتنين
+
+480
+00:51:24,760 --> 00:51:30,440
+والتلاتة معكوسات لبعض لأن اتنين في تلاتة موديول
+
+481
+00:51:30,440 --> 00:51:34,040
+وخمسة بطلع جداش واحد اللي هو ال identity element
+
+482
+00:51:34,040 --> 00:51:42,230
+طب والاربعة في اربعةيبقى اربعة معكوس لنفسه و اتنين
+
+483
+00:51:42,230 --> 00:51:46,430
+معكوس للتلاتة و ال identity هو معكوس لنفسه إذا صار
+
+484
+00:51:46,430 --> 00:51:56,550
+كل عنصر له معكوس يبقى هنا باجي بقول every element
+
+485
+00:51:56,550 --> 00:52:05,310
+in S has an inverse
+
+486
+00:52:07,290 --> 00:52:22,690
+since الواحد is the inverse of واحد بعدها
+
+487
+00:52:22,690 --> 00:52:35,280
+اتنين is the inverse of تلاتة sinceلأن اتنين في
+
+488
+00:52:35,280 --> 00:52:43,720
+تلاتة modulo خمسة بده يساوي واحد and الأربعة is
+
+489
+00:52:43,720 --> 00:52:58,530
+the inverse of itself since اللي همينأربعة مضروبة
+
+490
+00:52:58,530 --> 00:53:06,150
+في أربعة Modulo خمسة يساوي واحد يبقى كل عنصر له
+
+491
+00:53:06,150 --> 00:53:14,310
+معكوس يبقى بناء عليه أصبحت هذه group يبقى هنا ال S
+
+492
+00:53:14,310 --> 00:53:23,330
+تساوي واحد واتنين وتلاتة واربعة is a group under
+
+493
+00:53:29,300 --> 00:53:33,920
+multiplication multiplication modulo
+
+494
+00:53:35,390 --> 00:53:41,550
+خمسة طب أنا لسه خلصت الشطر الأول من السؤال جالي
+
+495
+00:53:41,550 --> 00:53:47,530
+لكن المجموعة هذه module أربعة is not a group بقوله
+
+496
+00:53:47,530 --> 00:53:52,670
+كويس ايش عرفك بدي و لو شرط واحد يختل من الشروط
+
+497
+00:53:52,670 --> 00:53:59,510
+اللي عندي بتبطل الصير a group صح ولا لا طيب حد
+
+498
+00:53:59,510 --> 00:54:01,530
+بقدر يجيبلي هذا الشرط
+
+499
+00:54:06,800 --> 00:54:11,660
+ممتاز جدا تعالى نشوف تلاتة هذه بيقول مالهاش معكوس
+
+500
+00:54:11,660 --> 00:54:17,320
+ليش؟ لأني قلت تلاتة في تلاتة تسعة تسعة شيل منهم
+
+501
+00:54:17,320 --> 00:54:24,200
+أربعتين بيظل واحد إذا التلاتة معكوس لنفسي صح يبقى
+
+502
+00:54:24,200 --> 00:54:31,020
+معكوسالان اتنين في تلاتة ايه بستة شيل منهم اربعة
+
+503
+00:54:31,020 --> 00:54:35,500
+بطلع اتنين يبجى ده مش اتنين معكسه مش التلاتة لكن
+
+504
+00:54:35,500 --> 00:54:41,720
+اتنين في اتنين اربعة تعني زيرو يبجى اتنين او هذه
+
+505
+00:54:41,720 --> 00:54:45,680
+ماهياش closed under يعني هذه ال operation ماهياش
+
+506
+00:54:45,680 --> 00:54:50,780
+binary operationلأن ال element موجود في نفس ال set
+
+507
+00:54:50,780 --> 00:54:57,180
+يبقى هذه بقول له that set اللي هو واحد و اتنين و
+
+508
+00:54:57,180 --> 00:55:11,200
+تلاتة under multi application modulo أربعة is not
+
+509
+00:55:11,200 --> 00:55:15,920
+a group since
+
+510
+00:55:18,430 --> 00:55:25,610
+الاتنين مستار اتنين يساوي أربعة modulo أربعة ليه
+
+511
+00:55:25,610 --> 00:55:30,730
+تساوي زيرو وهذا does not belong للست واحد واتنين
+
+512
+00:55:30,730 --> 00:55:34,930
+وتلاتة يبقى الشرط الأول تبقى binary operation لأنه
+
+513
+00:55:34,930 --> 00:55:38,110
+تحت عملية ضرب modulo أربعة التي بيكون موجود في
+
+514
+00:55:38,110 --> 00:55:43,260
+الست هذه هذا مش موجوديبقى يبعتلك الله لازلنا في
+
+515
+00:55:43,260 --> 00:55:48,000
+الأمثلة السهلة حتى هذه اللحظة لسه عندنا أمثلة
+
+516
+00:55:48,000 --> 00:55:53,000
+كثيرة بدنا على قلبي كمان محاضرتين مشان نخلص
+
+517
+00:55:53,000 --> 00:55:57,500
+الأمثلة على موضوع ال group لإن هذا الأساس اللى
+
+518
+00:55:57,500 --> 00:56:02,420
+بدنا نبني عليه كل دراستنا في موضوع ال groups بعد
+
+519
+00:56:02,420 --> 00:56:04,080
+ذلك يعطيكوا العجب
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6733efea98516ff3fa9ddd250914774c1d801e61
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/GcfT10Kln48_raw.srt
@@ -0,0 +1,2076 @@
+1
+00:00:22,310 --> 00:00:28,070
+في محاضرة الصبح قبل ساعتين بدأنا في موضوع ال
+
+2
+00:00:28,070 --> 00:00:31,530
+groups اللي هو اول موضوع في ال alphabet algebra
+
+3
+00:00:31,530 --> 00:00:37,070
+المقرر علينا مشان نعرف ال group لازم نعرف حاجة
+
+4
+00:00:37,070 --> 00:00:41,750
+اسمها binary operation و بعد ذلك بندخل الى موضوع
+
+5
+00:00:41,750 --> 00:00:47,070
+ال groupعرفنا ال binary operation على set هي عبارة
+
+6
+00:00:47,070 --> 00:00:52,710
+عن function من ال 6 cross ال 6 إلى set أخرى بحيث
+
+7
+00:00:52,710 --> 00:00:55,990
+ال order paired اللي في ال 6 cross ال 6 بيكون
+
+8
+00:00:55,990 --> 00:01:01,450
+موجود وين في ال set itself وعطينا على ذلك مثالين
+
+9
+00:01:01,450 --> 00:01:07,000
+وهذا هو المثال رقم 3يبقى انا عرفت ال function star
+
+10
+00:01:07,000 --> 00:01:12,480
+من z cross z إلى z by a star b يسوى a b نقص واحد
+
+11
+00:01:12,480 --> 00:01:16,880
+يعني ال star صارت عبارة عن عمليتين في انا واحد
+
+12
+00:01:16,880 --> 00:01:20,160
+عملية الضرب ما بين ال a و ال b و عملية الطرح من
+
+13
+00:01:20,160 --> 00:01:26,640
+واحد لكن على set of integers السؤال هو لما اضرب ال
+
+14
+00:01:26,640 --> 00:01:31,100
+a في b حصل ضرب two integers بيعطيني integer ولا
+
+15
+00:01:31,100 --> 00:01:35,970
+بيعطيني شغل تانيتطرح منه واحد بيظل انتجر ولا بيبقى
+
+16
+00:01:35,970 --> 00:01:40,730
+يصير انتجر؟ معناته هذه binary operation يبقى هذه
+
+17
+00:01:40,730 --> 00:01:50,350
+ال .. then .. then star is a binary operation
+
+18
+00:01:50,350 --> 00:01:59,030
+السبب because ان العدد اللي عندنا a b minus ال one
+
+19
+00:01:59,030 --> 00:02:03,140
+موجود في zما دام موجود في Z يبقى هذه ال operation
+
+20
+00:02:03,140 --> 00:02:09,440
+is a binary operation طيب نتجل الأمثلة شوية مثال
+
+21
+00:02:09,440 --> 00:02:25,060
+رقم أربعة بيقول let ال X ب any non empty set any
+
+22
+00:02:25,060 --> 00:02:28,240
+non empty set define
+
+23
+00:02:31,160 --> 00:02:36,600
+capital P of X to
+
+24
+00:02:36,600 --> 00:02:43,020
+be the
+
+25
+00:02:43,020 --> 00:02:56,140
+power set فئة القوة of set X اللي عندنا يعني اللي
+
+26
+00:02:56,140 --> 00:03:07,960
+هي the set of allthe set of all subsets of x
+
+27
+00:03:07,960 --> 00:03:11,260
+define
+
+28
+00:03:11,260 --> 00:03:14,820
+star
+
+29
+00:03:14,820 --> 00:03:19,120
+by
+
+30
+00:03:19,120 --> 00:03:22,900
+a
+
+31
+00:03:22,900 --> 00:03:33,460
+star b بده يساوي a union bلكل ال a و ال b اللي
+
+32
+00:03:33,460 --> 00:03:44,040
+موجودة في ال power set of x ال power set of x then
+
+33
+00:03:44,040 --> 00:03:47,220
+star
+
+34
+00:03:47,220 --> 00:03:57,140
+then star هذه is a binary operation
+
+35
+00:03:58,950 --> 00:04:07,810
+بينيري اوبريشن on ال power set لل X because
+
+36
+00:04:41,540 --> 00:04:46,380
+طبعا ال power set اللي هي فئة القوة أو فئة القوة
+
+37
+00:04:46,380 --> 00:04:51,520
+درسناها في مبدأ الرياضيات والان بنعيد دراستها مرة
+
+38
+00:04:51,520 --> 00:04:57,380
+ثانيةفلو أخدت الـ x أي non-empty set ركز على non
+
+39
+00:04:57,380 --> 00:05:03,260
+-empty يعني ليست في فيها عناصر بدي أعرف ال power
+
+40
+00:05:03,260 --> 00:05:07,940
+set of x هي ال power set of x أو the set of all
+
+41
+00:05:07,940 --> 00:05:12,520
+subset of x يبقى بداجي على ال set x أشوف عناصرها
+
+42
+00:05:12,520 --> 00:05:18,540
+أجيب كل ال subsets الممكنة بما فيهم في و ال x
+
+43
+00:05:18,540 --> 00:05:23,000
+itselfهذه بسميها الـtrivial subset وهذه أكبر
+
+44
+00:05:23,000 --> 00:05:26,840
+subset من ال 6 because أخدنا في مادة الرجالات أن
+
+45
+00:05:26,840 --> 00:05:32,180
+ال 6 is a subset of itself يبقى كل ال subsets اللي
+
+46
+00:05:32,180 --> 00:05:37,240
+عنده بيكونوله ميهم بيكونوله ال power set لل 6x بدا
+
+47
+00:05:37,240 --> 00:05:41,480
+أعرف اللي هو ال relation اللي .. ال operation اللي
+
+48
+00:05:41,480 --> 00:05:47,450
+عندنا a star b بده يساوي a union bلكل ال a و ال b
+
+49
+00:05:47,450 --> 00:05:51,570
+اللي موجودة في ال power set السؤال هو هل star هذه
+
+50
+00:05:51,570 --> 00:05:56,980
+binary operation ولا لا؟بقول والله إذا نتيجة أستر
+
+51
+00:05:56,980 --> 00:06:01,640
+بيجبتلي عنصر دائما و أبدا و هذا العنصر موجود في ال
+
+52
+00:06:01,640 --> 00:06:06,280
+power set إذا هذه binary operation يعني نتيجة
+
+53
+00:06:06,280 --> 00:06:12,220
+للعملية ما بين الاتنين لعملية ال union ههه بدها
+
+54
+00:06:12,220 --> 00:06:15,900
+تجيبلي عنصر موجود في ال power set إذا هذه binary
+
+55
+00:06:15,900 --> 00:06:20,580
+operation لو جبت عنصر طالع برا يبقى ليست binary
+
+56
+00:06:20,580 --> 00:06:25,300
+operationيبقى ال operation a star b a union b لكل
+
+57
+00:06:25,300 --> 00:06:29,280
+ال a و ال b اللي موجودة في ال P of x then star is
+
+58
+00:06:29,280 --> 00:06:32,900
+a binary operation على power set because نجي نشوف
+
+59
+00:06:32,900 --> 00:06:39,120
+ما هو السبب الآن ال operation a star b بدي يسوي a
+
+60
+00:06:39,120 --> 00:06:44,800
+union b السؤال هو a union b هل هذه ال subset من X
+
+61
+00:06:44,800 --> 00:06:52,390
+يا شباب؟لو أخدت any two subsets من الـ6X وجبت لهم
+
+62
+00:06:52,390 --> 00:06:56,870
+الـunion يكون موجود في الـX itself ولا بتطلع برا؟
+
+63
+00:06:56,870 --> 00:07:00,710
+لاتطلعش برا يبقى هذا موجود دائما و أبدا في X طب
+
+64
+00:07:00,710 --> 00:07:07,700
+والـX هذه أليس subset من ال power set of X؟يبقى
+
+65
+00:07:07,700 --> 00:07:15,340
+star ال element هذا موجود في ال power set ال x هذه
+
+66
+00:07:15,340 --> 00:07:21,700
+as a أعلى مش subset ال x هذه belongs موجودة في ال
+
+67
+00:07:21,700 --> 00:07:25,700
+power set لكن ال a union b ال subset من ال x والx
+
+68
+00:07:25,700 --> 00:07:31,500
+belong في ال power set of x معناه هذا كلام ال star
+
+69
+00:07:31,500 --> 00:07:35,320
+is a binary operation طب السؤال هوهل ال
+
+70
+00:07:35,320 --> 00:07:41,520
+intersection ما بين ال two sets a و b is a subset؟
+
+71
+00:07:41,520 --> 00:07:48,080
+يعني هل هو موجود في ال power set؟ليش؟ على أسوأ
+
+72
+00:07:48,080 --> 00:07:53,100
+الاحتمالات بدي يطلع في فحو ولا لأ في subset من ال
+
+73
+00:07:53,100 --> 00:07:58,760
+X ولا لأ يبقى في موجودة في ال power set وبناء عليه
+
+74
+00:07:58,760 --> 00:08:02,620
+سعر ال intersection كمان also is a binary
+
+75
+00:08:02,620 --> 00:08:07,320
+operation يبقى باجي بقول ان similarly كمان شغلة
+
+76
+00:08:07,320 --> 00:08:13,550
+تانيةsimilarly ال
+
+77
+00:08:13,550 --> 00:08:21,930
+.. ال .. ال star او a star b ال a star b بدي يسوي
+
+78
+00:08:21,930 --> 00:08:32,130
+a intersection b ها دي is a binary is a binary
+
+79
+00:08:32,130 --> 00:08:33,930
+operation
+
+80
+00:08:40,500 --> 00:08:44,000
+بارضه بنفس الطريقة ليش ان ال intersection ما بين
+
+81
+00:08:44,000 --> 00:08:48,520
+ال A والB موجود في ال set X
+
+82
+00:08:54,460 --> 00:09:01,960
+بسبب أن a intersection b هو subset من set x وهذا
+
+83
+00:09:01,960 --> 00:09:14,020
+سيعطينا أن a intersection b هو subset من set x طيب
+
+84
+00:09:14,020 --> 00:09:21,390
+ناخد كمان مثال بيختلف عن شكل هذه الأمثلة كلياlet
+
+85
+00:09:21,390 --> 00:09:29,970
+خمسة let الجي capital g بدي ساوي كل ال real
+
+86
+00:09:29,970 --> 00:09:34,010
+numbers x اللي موجودة في ال set of real numbers
+
+87
+00:09:34,010 --> 00:09:42,690
+بحيث ان ال x أكبر من أو تساوي واحد define عرفلي a
+
+88
+00:09:42,690 --> 00:09:45,750
+star by
+
+89
+00:09:48,020 --> 00:10:01,220
+x star y يساوي x y ناقص x ناقص y زائدي اتنين then
+
+90
+00:10:01,220 --> 00:10:13,680
+star اللي عندنا هذا is a binary operation is
+
+91
+00:10:13,680 --> 00:10:16,880
+a binary operation because
+
+92
+00:10:26,450 --> 00:10:34,230
+السبب؟ خلّي بالك هناالان انا اخد ست جديدة على غير
+
+93
+00:10:34,230 --> 00:10:40,710
+الأمثلة السابقة سميتها G مين هي G؟ اخدت عناصر من
+
+94
+00:10:40,710 --> 00:10:44,830
+set of real numbers اللي مين هم العناصر كلهم اللي
+
+95
+00:10:44,830 --> 00:10:50,470
+بيكونوا دائما وأبدا أكبر من الواحد الصحية كسور مش
+
+96
+00:10:50,470 --> 00:10:54,870
+كسور اللي وهم اعداد موجبة دائما وأبدا وكلها أكبر
+
+97
+00:10:54,870 --> 00:11:00,950
+من الواحد الصحيحعرفت star على ال G cross ال G إلى
+
+98
+00:11:00,950 --> 00:11:06,630
+G على الشكل التالي X star Y بده يساوي XY ناقص X
+
+99
+00:11:06,630 --> 00:11:12,830
+ناقص Y زائد اتنين يبقى عملية ضرب و طرح و جمع في آن
+
+100
+00:11:12,830 --> 00:11:18,270
+واحد من هذه ال star عرفتها بهذه الطريقة أنا أدعي
+
+101
+00:11:28,250 --> 00:11:35,690
+السبب اذا طلع هذا ال elementموجود في جي بقى كلامي
+
+102
+00:11:35,690 --> 00:11:41,310
+صح ماطلع موجود في جي بقى كلامي ماله مش صحيح بمعنى
+
+103
+00:11:41,310 --> 00:11:46,750
+أخر لو طلع هذا المقدار كله أكبر من الواحد الصحيح
+
+104
+00:11:46,750 --> 00:11:51,610
+معناته موجود في جي ماطلع يبقى كلامي ماله ليس صحيحا
+
+105
+00:11:51,610 --> 00:11:56,370
+ممتاز جدا يبقى باجي بقوله بدي أبيله ليش هذه binary
+
+106
+00:11:56,370 --> 00:12:06,430
+operation because ifx و y موجودة في g then ال x
+
+107
+00:12:06,430 --> 00:12:11,650
+هذا تبقى أكبر من الواحد و في نفس الوقت ال y أكبر
+
+108
+00:12:11,650 --> 00:12:17,890
+من الواحدعسب الـ definition تبع الـ G ماخد two
+
+109
+00:12:17,890 --> 00:12:22,290
+elements موجودات في G يبقى الـ two elements كل
+
+110
+00:12:22,290 --> 00:12:27,970
+واحد يوم أكبر من مين؟ من الواحد طيب هذا معناته ان
+
+111
+00:12:27,970 --> 00:12:33,330
+ال X greater than one and ال Y ناقص واحد أكبر من
+
+112
+00:12:33,330 --> 00:12:38,430
+مين؟ من ال zero إذا هذا ال term موجب و الله سالم
+
+113
+00:12:40,620 --> 00:12:45,140
+أكبر من Zero موجب ولا عمره حتى بيصير Zero يعني لا
+
+114
+00:12:45,140 --> 00:12:50,420
+Zero ولا سالب هذا موجب طب لو مسكت هذا الرقم الموجب
+
+115
+00:12:50,420 --> 00:12:54,360
+وضربته في ال inequality هذه بتتغير ولا بيظلها زي
+
+116
+00:12:54,360 --> 00:13:00,060
+ما هي يعني الأكبر من هذه بتتغير ولا بتغير إلى أقل
+
+117
+00:13:00,060 --> 00:13:04,340
+منه ولا بتظل أكبر منه يبقى بدي أمسك ال term هذا و
+
+118
+00:13:04,340 --> 00:13:09,020
+أضربه في ال inequality هذهيبقى بدي اشوف هذا ايش
+
+119
+00:13:09,020 --> 00:13:14,000
+بيعطينا يبقى مشان اوضح لك الصورة بدي اقول لك multi
+
+120
+00:13:14,000 --> 00:13:23,560
+apply the inequality المتباينة
+
+121
+00:13:23,560 --> 00:13:31,690
+x greater than one by y minus one we getبنحصل على
+
+122
+00:13:31,690 --> 00:13:39,390
+يبقى هذا ال X في Y minus ال one أكبر من ال Y minus
+
+123
+00:13:39,390 --> 00:13:44,310
+ال one مظبوط؟
+
+124
+00:13:44,310 --> 00:13:51,010
+طيب، إيش رأيك؟ بدي أفك الطرف الشمال يبقى XY ناقص X
+
+125
+00:13:51,010 --> 00:13:57,410
+إيش رأيك؟ هجيب ال Y على الشجة التانية ناقص Y أكبر
+
+126
+00:13:57,410 --> 00:13:59,870
+من اللي هو سالب واحد
+
+127
+00:14:03,300 --> 00:14:11,750
+طيب ايش رايك لو اضفت للطرفين اتنين؟مرة واحدة بضيف
+
+128
+00:14:11,750 --> 00:14:15,310
+رقم هنا زي ما اضيف رقم هنا عادي جدا واتنين
+
+129
+00:14:15,310 --> 00:14:17,590
+positive positive ولا negative في حالة الجامعة
+
+130
+00:14:17,590 --> 00:14:22,010
+ماتفرجش عندي المشكلة في حالة الضرب او القسمة يبقى
+
+131
+00:14:22,010 --> 00:14:29,670
+هنا لو اضفت اتنين بيصير x في y ناقص x ناقص y زائدي
+
+132
+00:14:29,670 --> 00:14:36,330
+اتنين اكبر من قداش اضفت اتنين للطرفين طب الطرف هذا
+
+133
+00:14:36,330 --> 00:14:42,130
+مش هو هذايبقى star العدد اللي عندي هذا أكبر من
+
+134
+00:14:42,130 --> 00:14:49,670
+واحد يبقى موجود في جي يبقى هذا بده يعطيلك ان ال X
+
+135
+00:14:49,670 --> 00:14:57,330
+Y ناقص X ناقص Y زي دي اتنين belongs to G لذلك star
+
+136
+00:14:57,330 --> 00:15:02,190
+is a binary operation لأن تحت العملية اللي عندنا
+
+137
+00:15:02,190 --> 00:15:06,210
+هذه ال star طلع الناتج موجود في G إذا هذه مالها
+
+138
+00:15:06,210 --> 00:15:12,400
+binary operationطيب احنا مهدنا لل group بموضوع ال
+
+139
+00:15:12,400 --> 00:15:17,380
+binary operation الان بدنا ندخل في صميم الموضوع و
+
+140
+00:15:17,380 --> 00:15:23,580
+هو تعريف ال groupالجروب يا شباب هي ال set بدي أضع
+
+141
+00:15:23,580 --> 00:15:30,580
+عليها binary operation بحيث تحققلي ثلاثة شروط ان
+
+142
+00:15:30,580 --> 00:15:35,400
+تحققتي ثلاثة شروط بسمي ال set مع ال binary
+
+143
+00:15:35,400 --> 00:15:41,540
+operation is a group ايش الشروط التلاتة؟ اول شيء
+
+144
+00:15:41,540 --> 00:15:47,270
+ال binary operation هذه بتبقى associativeادماجية
+
+145
+00:15:47,270 --> 00:15:54,150
+تمام او تجميعية زي ما بتسموها انتوا اتنين في عنصر
+
+146
+00:15:54,150 --> 00:15:59,270
+بده اسميه عنصر الوحدة ال identity element انتوا
+
+147
+00:15:59,270 --> 00:16:04,260
+بالعربي بجهة السماوية الثانوية العنصر المحايديبقى
+
+148
+00:16:04,260 --> 00:16:08,720
+المحايد أو الوحدة هو ال identity element الشرط
+
+149
+00:16:08,720 --> 00:16:14,260
+التالت كل عنصر في ال group تحت هذه العملية بدي
+
+150
+00:16:14,260 --> 00:16:20,400
+يكون له معكوس بحيث لو ضربت عنصر في معكوسه بدي يطين
+
+151
+00:16:20,400 --> 00:16:25,080
+من عنصر المحايد ال identity element لو تحققت
+
+152
+00:16:25,080 --> 00:16:30,020
+الشروط هذه التلاتة بقول يبقى الجيل اللي عندي is a
+
+153
+00:16:30,020 --> 00:16:34,390
+groupالكلام اللى سمعته بناروح نكتبه لإنه كل ال
+
+154
+00:16:34,390 --> 00:16:39,490
+section مبني على مين على الكلمتين اللى سمعتهم يبقى
+
+155
+00:16:39,490 --> 00:16:50,510
+بداجي الى definition يبقى definition let ال g be a
+
+156
+00:16:50,510 --> 00:16:56,830
+non empty non empty set
+
+157
+00:16:58,880 --> 00:17:09,840
+and let a star be a
+
+158
+00:17:09,840 --> 00:17:17,640
+binary operation
+
+159
+00:17:17,640 --> 00:17:24,840
+on اللي هو g على set g then
+
+160
+00:17:27,230 --> 00:17:33,170
+ال جي والستار مع بعض هدول يعني الست جي والستار
+
+161
+00:17:33,170 --> 00:17:43,230
+عملية عليها هدى is called a group بنسميها مجموعة
+
+162
+00:17:43,230 --> 00:17:50,750
+if the following properties
+
+163
+00:17:55,710 --> 00:18:00,170
+if the following reporters are satisfied are
+
+164
+00:18:00,170 --> 00:18:08,230
+satisfied ايش
+
+165
+00:18:08,230 --> 00:18:18,110
+الخواص هذه اللي هو الخاصية الأولى the star is
+
+166
+00:18:18,110 --> 00:18:24,030
+associative associative
+
+167
+00:18:24,800 --> 00:18:29,100
+that is a
+
+168
+00:18:29,100 --> 00:18:42,300
+star b a star c بدو يساوي a star b star c لكل
+
+169
+00:18:42,300 --> 00:18:49,140
+ال a و ال b و ال c اللي موجودة في ال group g ال
+
+170
+00:18:49,140 --> 00:18:50,760
+condition الثاني
+
+171
+00:18:52,870 --> 00:19:09,190
+condition الثاني there is an element such
+
+172
+00:19:09,190 --> 00:19:12,550
+that
+
+173
+00:19:12,550 --> 00:19:23,830
+بحيث انA Star A يساوي E Star A يساوي الـ A السلف
+
+174
+00:19:23,830 --> 00:19:33,730
+لكل الـ A الموجودة في G بلا استثناء يبقى الـ E is
+
+175
+00:19:33,730 --> 00:19:42,330
+called the identity element
+
+176
+00:19:42,330 --> 00:19:45,530
+of
+
+177
+00:19:46,970 --> 00:20:11,510
+G condition
+
+178
+00:20:11,510 --> 00:20:13,330
+الثالث والأخير
+
+179
+00:20:20,360 --> 00:20:34,280
+for each a الموجود في g there exist b in g such
+
+180
+00:20:34,280 --> 00:20:45,800
+thatبحيث ان such that ال a star b بده يساوي b star
+
+181
+00:20:45,800 --> 00:20:53,500
+a بده يساوي ال identity e بيه
+
+182
+00:20:53,500 --> 00:20:58,880
+is called يبقى
+
+183
+00:20:58,880 --> 00:21:09,490
+بيه في هذه الحالة بنسميه is theinverse element of
+
+184
+00:21:09,490 --> 00:21:21,950
+a معكوس العنصر a and denoted by ال b بده يساوي ال
+
+185
+00:21:21,950 --> 00:21:26,870
+a inverse command
+
+186
+00:21:26,870 --> 00:21:30,970
+definition the group
+
+187
+00:21:33,590 --> 00:21:39,610
+الـ G is called abelian
+
+188
+00:21:39,610 --> 00:21:45,090
+if
+
+189
+00:21:45,090 --> 00:21:54,250
+ال X Y متساوي Y X لكل ال X و Y الموجودة في ال
+
+190
+00:21:54,250 --> 00:21:55,450
+group G
+
+191
+00:22:25,540 --> 00:22:31,040
+يبقى احنا ابتداء من هذا التعريف بكون بدأنا ندخل في
+
+192
+00:22:31,040 --> 00:22:35,680
+علم ال groups او علم المجموعات اللي هو موضوع
+
+193
+00:22:35,680 --> 00:22:40,220
+دراستنا لهذا الفصل اللي هو ال abstract algebra
+
+194
+00:22:40,220 --> 00:22:44,460
+يبقى اول موضوع في موضوع الجبر اللي هو الموضوع
+
+195
+00:22:44,460 --> 00:22:50,330
+المجموعات الان نعرف المجموعة و بعدين ناخدأمثلة
+
+196
+00:22:50,330 --> 00:22:54,310
+متعددة على المجموعة بدل المثال عشر او احد مثال
+
+197
+00:22:54,310 --> 00:23:00,010
+وبعد ذلك ناخد بعض خواص المجموعات البسيطة يبقى
+
+198
+00:23:00,010 --> 00:23:04,470
+التعليف بيقول ما يتفترض ان G هو عبارة عن non-empty
+
+199
+00:23:04,470 --> 00:23:10,230
+set يبقى ليست الفئة الخاوية وانما على الأقل فيها
+
+200
+00:23:10,230 --> 00:23:15,000
+ولو عنصر واحدand let the star be a binary
+
+201
+00:23:15,000 --> 00:23:20,760
+operation على g الست
+
+202
+00:23:20,760 --> 00:23:26,400
+جي معالي الstar مع بعض هدول بيكونولي a group إذا
+
+203
+00:23:26,400 --> 00:23:32,990
+تحققت عندي ثلاثة خواص أو ثلاثة شروطالشروط أو
+
+204
+00:23:32,990 --> 00:23:37,790
+الخواصة دي لـ star اللي عندي is associative يبقى
+
+205
+00:23:37,790 --> 00:23:43,430
+هي عملية إدماجية بمعنى ان a star b star c يساوي
+
+206
+00:23:43,430 --> 00:23:48,250
+يعني بتخلي a تأثر على b في الأول حسب تعريف ال star
+
+207
+00:23:48,360 --> 00:23:52,300
+والعنصر اللى ينتج يخلّيه أثر على مين؟ على C
+
+208
+00:23:52,300 --> 00:23:57,580
+النتيجة تماما كما لو B أثرت على C طالع عنصر جديد
+
+209
+00:23:57,580 --> 00:24:01,820
+هذا العنصر بدأ أثر عليه بإيه لازم يكون اتنين are
+
+210
+00:24:01,820 --> 00:24:06,140
+equal ان حدث ذلك يبقى بقوله خاصية ال associativity
+
+211
+00:24:06,140 --> 00:24:11,160
+الصحيحة لجميع العناصر يعني لما بدأ أخد A وB وC مش
+
+212
+00:24:11,160 --> 00:24:15,060
+بدأ اختارهم عناصر محددة فلان وفلان بدأ أخد أي
+
+213
+00:24:15,060 --> 00:24:20,770
+عناصر بغض النظر شو شكلهمالنقطة الثانية بيقول لي
+
+214
+00:24:20,770 --> 00:24:26,570
+there is an element E بحيث اذا لجيت عنصر اعطيته
+
+215
+00:24:26,570 --> 00:24:32,090
+الرمز E بس هذا إله خواص طبعا العنصر هذا موجود في
+
+216
+00:24:32,090 --> 00:24:38,570
+جي itself بحيث ان لو أثرت بال A على ال E بال star
+
+217
+00:24:38,570 --> 00:24:44,330
+هذه تماما كما لو أثرت بال E على A والنتج طالع ال A
+
+218
+00:24:44,330 --> 00:24:49,240
+itselfيبقى هذا اللي كنا بنسميه عنصر المحيد لا
+
+219
+00:24:49,240 --> 00:24:54,200
+يتأثر أي element في المجموعة بهذا ال element تحت
+
+220
+00:24:54,200 --> 00:24:58,300
+العملية star أثر عليه star بهذا العنصر ويبقى ال
+
+221
+00:24:58,300 --> 00:25:02,780
+element كما هو يبقى إن حدث ذلك هذا بسميه عنصر
+
+222
+00:25:02,780 --> 00:25:07,040
+المحيد او في لغة ال groups احنا هنسميه identity
+
+223
+00:25:07,040 --> 00:25:12,390
+element اللي هو عنصر الوحدة لهذه المجموعةبنضل عند
+
+224
+00:25:12,390 --> 00:25:18,210
+ال condition التالت والاخير قال لي 4H اللي موجود
+
+225
+00:25:18,210 --> 00:25:24,290
+في G لأي عنصر A موجود في G هلاقي عنصر تاني اسمه B
+
+226
+00:25:24,290 --> 00:25:29,830
+موجود في G بحيث لو ضربته من اليمين او من الشمال A
+
+227
+00:25:29,830 --> 00:25:34,590
+Star B بلاقي النتيجة هو B Star A يسوى ال identity
+
+228
+00:25:34,590 --> 00:25:39,450
+element itself يبقى هذا بده يعطيني عنصر الوحدة
+
+229
+00:25:39,450 --> 00:25:47,580
+نفسهإن حدث ذلك يبقى هذا العنصر معكوس العنصر A يبقى
+
+230
+00:25:47,580 --> 00:25:51,980
+في هذه الحالة ال B is called the inverse element
+
+231
+00:25:51,980 --> 00:25:52,520
+of A
+
+232
+00:25:58,500 --> 00:26:01,920
+هذا الـ A كلها اللي فوق واسة اللي بسميه the
+
+233
+00:26:01,920 --> 00:26:07,460
+inverse element of A معكوس العنصر A يبقى B اللي
+
+234
+00:26:07,460 --> 00:26:12,460
+لجيته هذا بدي أسميه معكوس العنصر اللي هو A طب
+
+235
+00:26:12,460 --> 00:26:19,980
+السؤال هو هل كل عنصر في G لازم يجيه معكوس يعني مش
+
+236
+00:26:19,980 --> 00:26:26,940
+بالضرورة بعضهم ما و بعضهم لأ طب إيش جاي ال A لأfor
+
+237
+00:26:26,940 --> 00:26:32,260
+each لكل عنصر يبقى كل عنصر في جي بدأت تجيله معكوس
+
+238
+00:26:32,260 --> 00:26:38,020
+مش بعضهم له و بعضهم مالواشي كل عنصر في جي له معكوس
+
+239
+00:26:38,020 --> 00:26:45,080
+يعني لو أتصورت أن جي هذه خمس عناصر يبقى فيهم اللي
+
+240
+00:26:45,080 --> 00:26:49,020
+هو أربعة واحد معكوس للتاني و ال identity element
+
+241
+00:26:49,020 --> 00:26:55,290
+معكوس لنفسهلو كانوا ستة يبقى تلاتة معكوسات التلاتة
+
+242
+00:26:55,290 --> 00:27:01,430
+التانيات و هكذا يبقى كل عنصر في ال group جي حلقيله
+
+243
+00:27:01,430 --> 00:27:05,990
+معكوس موجود في جي بعد لو ضربت العنصر في معكوسه من
+
+244
+00:27:05,990 --> 00:27:10,290
+الشمال والله لمين بدي يطلع عنصر الوحدة طب عنصر
+
+245
+00:27:10,290 --> 00:27:15,960
+الوحدة هذا هو الصفر ولا واحد صحيحيقول حسب ال
+
+246
+00:27:15,960 --> 00:27:20,600
+operation المعرفة على ال group يبقى حسب ال group
+
+247
+00:27:20,600 --> 00:27:23,820
+وحسب ال operation اللي عليها ملاجئ ال identity
+
+248
+00:27:23,820 --> 00:27:27,570
+اللي يمكن ال identity is zeroيمكن ال identity يطلع
+
+249
+00:27:27,570 --> 00:27:33,750
+واحد يمكن ال identity يطلع عشرة مثلا هادئ جدا يبقى
+
+250
+00:27:33,750 --> 00:27:37,930
+حسب ال operation اللى موجودة عندك وقد نستغرب هذا
+
+251
+00:27:37,930 --> 00:27:41,950
+لان نستغرب ولا حاجة وحنوريك بعض الأمثلة نحسب فيها
+
+252
+00:27:41,950 --> 00:27:47,550
+ال identity element ومايطلعش لا zero ولا واحديبقى
+
+253
+00:27:47,550 --> 00:27:52,430
+هذا يعني ان الشخص ما يكون شكله يكون بهمنيش يبقى ال
+
+254
+00:27:52,430 --> 00:27:55,570
+identity يعتمد على ال group ويعتمد على ال
+
+255
+00:27:55,570 --> 00:28:00,790
+operation على ال group اتفضل معناته
+
+256
+00:28:00,790 --> 00:28:07,410
+مش معكوس يبقى ليست group يبقى اذا اختل اي شرط من
+
+257
+00:28:07,410 --> 00:28:11,550
+الشروط التلاتة بالبطرة ستصبح groupيبقى مشان تكون
+
+258
+00:28:11,550 --> 00:28:16,810
+ال group بدي any non zero set والتلت شروط يتحققوا
+
+259
+00:28:16,810 --> 00:28:21,190
+هدول بدي ال operation هذه تبقى binary operation
+
+260
+00:28:21,190 --> 00:28:25,830
+نمرا واحد لو ماكنتش binary operation الصبح أخدنا
+
+261
+00:28:25,830 --> 00:28:29,030
+مثل ماهياش binary operation يبقى ده مينفعش يتكون
+
+262
+00:28:29,030 --> 00:28:35,060
+ال groupلازم نبقى بيناري اوبريشن أولا ثم تتحقق
+
+263
+00:28:35,060 --> 00:28:40,240
+الشروط التلتة تطلع الشجرة التعريف جينامتستاتار بي
+
+264
+00:28:40,240 --> 00:28:44,880
+بيناري اوبريشن يبقى هذه بسميها group لو تحققت
+
+265
+00:28:44,880 --> 00:28:48,340
+الشروط التلتة يبقى انا في الحقيقة عندي تلت شروط
+
+266
+00:28:48,340 --> 00:28:54,260
+ولا اربعةأربعة بدك هدى binary operation لستار
+
+267
+00:28:54,260 --> 00:28:59,780
+بتبقى associative أو اختصارا بروح بقول هم التلاتة
+
+268
+00:28:59,780 --> 00:29:04,000
+لستار هدى بدي associative binary operation يبقى
+
+269
+00:29:04,000 --> 00:29:08,020
+جمعت الشرطين مين بشرط واحد اتنين وجود ال identity
+
+270
+00:29:08,020 --> 00:29:13,200
+element تلاتة وجود معكوس العنصر لأى عنصر موجود وين
+
+271
+00:29:13,200 --> 00:29:18,130
+موجود في ال group Gإن حدث ذلك بقول يبقى الـ 6G
+
+272
+00:29:18,130 --> 00:29:22,350
+اللي عندنا هذه مالها is A group وحتى أرسخ هذا
+
+273
+00:29:22,350 --> 00:29:27,330
+المفهوم من دماغك و أسحب المفهوم اللي في دماغك إن
+
+274
+00:29:27,330 --> 00:29:31,690
+ال operation هذه هي عملية ضرب لحالها أو عملية قسمة
+
+275
+00:29:31,690 --> 00:29:36,290
+لحالها أو عملية طرح لحالهاهتشوف أمثلة مختلفة و
+
+276
+00:29:36,290 --> 00:29:42,070
+عديدة حتى مصبح احنا مقيدين بشكل ال six اللي عندنا
+
+277
+00:29:42,070 --> 00:29:46,650
+و ماناش دعوة في ال six الأخرى اتنين مقيدين بال
+
+278
+00:29:46,650 --> 00:29:49,070
+binary operation اللي عندنا و غيرها من ال
+
+279
+00:29:49,070 --> 00:29:53,550
+operations ماليش علاقة فيهم تمام؟ وهذا يختلف من
+
+280
+00:29:53,550 --> 00:29:58,890
+group إلى الأخرى نعطي أول مثال على ذلك قبله نعطي
+
+281
+00:29:58,890 --> 00:30:04,910
+أول مثال كلمة AbelianAbelian بالعربي يعني ابدالي
+
+282
+00:30:04,910 --> 00:30:10,190
+ابدالي زي ما يقول commutative ابدالي فبجي بقول
+
+283
+00:30:10,190 --> 00:30:15,430
+group G is called abelian اذا كان ال X في Y بده
+
+284
+00:30:15,430 --> 00:30:19,730
+ساوي Y في X لكل ال X و Y اللي موجودة بلا استثناء
+
+285
+00:30:19,730 --> 00:30:25,210
+يعني لو جيت شباب اللي في القاعة خمسين طالب تمام لو
+
+286
+00:30:25,210 --> 00:30:29,150
+بدل كل واحد مقعد و مكان التاني ماصارش تغيير عندى
+
+287
+00:30:29,150 --> 00:30:34,520
+ولا حاجةكويس يبقى ما عدش فيه طول ولا قصر مع تبديل
+
+288
+00:30:34,520 --> 00:30:38,920
+مقعده ولا نقص من مقامه لا يبقى طالب زي ما هو مسجل
+
+289
+00:30:38,920 --> 00:30:43,480
+المادة وقاعد عندنا إذا لما بدل واحد مكان التاني
+
+290
+00:30:43,480 --> 00:30:49,480
+لجيته يساوي نفس التبديل الأصلي إن حدث ذلك يبقى هذا
+
+291
+00:30:49,480 --> 00:30:53,960
+بقول عنك commutative group أو abelian group لكن
+
+292
+00:30:53,960 --> 00:30:59,810
+بقولش commutative commutative بقول عن درجاتالتسمية
+
+293
+00:30:59,810 --> 00:31:04,550
+أو التعريف في حالة ال rings اللي هو تبعت الفصل
+
+294
+00:31:04,550 --> 00:31:08,450
+الثاني ان شاء الله ان شاء الله اللي باخد جبر حديثة
+
+295
+00:31:08,450 --> 00:31:12,790
+نمسكو ال commutative ring لكن في ال group هسميها
+
+296
+00:31:12,790 --> 00:31:17,640
+abelian group نسبة للعالمهي ابيل اللى اكتشف هالشغل
+
+297
+00:31:17,640 --> 00:31:23,340
+هذى وسميت باسمه ابيليان جروب اذا من حد ما تسمع
+
+298
+00:31:23,340 --> 00:31:28,120
+كلمة ابيليان جروب بدك تفهم ان العناصر بقدر ابدلهم
+
+299
+00:31:28,120 --> 00:31:33,000
+مكان بعض بدون اي مشاكل تمام؟ فهذا معنى ابيليان
+
+300
+00:31:33,000 --> 00:31:40,150
+جروبنأخد أبسط الأمثلة و نتدرج إلى الأثقال فالأثقال
+
+301
+00:31:40,150 --> 00:31:45,310
+فالأثقال حتى نصل إلى أمثلة مختلفة يبقى examples
+
+302
+00:31:45,310 --> 00:31:48,990
+أمثلة
+
+303
+00:31:48,990 --> 00:31:58,170
+أول مثال على ذلك الآن ال Z وال Q and set of real
+
+304
+00:31:58,170 --> 00:32:09,760
+numbers هذول underusual addition تحت عملية الجمع
+
+305
+00:32:09,760 --> 00:32:17,740
+العادي under usual addition اللي هو ال plus are
+
+306
+00:32:17,740 --> 00:32:26,160
+abelian groups are
+
+307
+00:32:26,160 --> 00:32:28,580
+abelian groups because
+
+308
+00:32:36,540 --> 00:32:42,300
+السبب يبقى انا ادعى انه زد تحت عملية الجامعة
+
+309
+00:32:42,300 --> 00:32:46,020
+العادى اقول لك usual addition الجامعة العادى تبع
+
+310
+00:32:46,020 --> 00:32:51,060
+ال real numberالـ Q تحت الجامعه العادى الـ R تحت
+
+311
+00:32:51,060 --> 00:32:54,020
+الجامعه العادى يعني عملش معرف على الـ set of
+
+312
+00:32:54,020 --> 00:32:56,680
+integers ومعرف على ال set of rational numbers
+
+313
+00:32:56,680 --> 00:32:59,440
+ومعرف على ال set of .. يعني هدول يعتبروا إيه؟
+
+314
+00:32:59,440 --> 00:33:05,620
+ثلاثة أمثلة يعني هدول three groups تحت العملية الـ
+
+315
+00:33:05,620 --> 00:33:09,780
+plus هذا و ال groups هدول are abelian احنا بنعرف
+
+316
+00:33:09,780 --> 00:33:14,270
+لما أقول A زائد B يعني اتنين زائد تلاتةسوى تلاتة
+
+317
+00:33:14,270 --> 00:33:18,890
+زي اتنين جامعه عادي صح ولا لا هذا على زد لو جيت
+
+318
+00:33:18,890 --> 00:33:24,610
+على ال IQ اتنين عدديا نسبيا مجموعهم عدد نسبي كذلك
+
+319
+00:33:24,610 --> 00:33:29,610
+لو جيت مجموع عددين حقيقيا بيعطينا ايه؟ عدد حقيقي
+
+320
+00:33:29,610 --> 00:33:35,860
+بجهة دي binary operationيبقى هنا بقوله because a
+
+321
+00:33:35,860 --> 00:33:43,060
+plus is a by أو associative بالمرة كمان is
+
+322
+00:33:43,060 --> 00:33:46,080
+associative
+
+323
+00:33:46,080 --> 00:33:53,300
+binary operation
+
+324
+00:33:53,300 --> 00:33:56,320
+on
+
+325
+00:33:56,320 --> 00:34:07,850
+z والي qand كذلك من ال set of real numbers طب كويس
+
+326
+00:34:07,850 --> 00:34:11,170
+أظن
+
+327
+00:34:11,170 --> 00:34:14,730
+أخدنا هذه الكثير حكاية ال associativity للأعداد
+
+328
+00:34:14,730 --> 00:34:18,730
+الحقيقية ما هي النسبية والصحيها جزء من الأعداد
+
+329
+00:34:18,730 --> 00:34:22,510
+الحقيقية يبقى الأعداد الحقيقية لما أقول اتنين زي
+
+330
+00:34:22,510 --> 00:34:26,650
+التلاتة زي الخمسة هو تلاتة زي الخمسة والإنتاج يضيف
+
+331
+00:34:26,650 --> 00:34:30,410
+له اتنين عادى جدا مافيش فيها مشكلةيبقى هذه بالنسبة
+
+332
+00:34:30,410 --> 00:34:35,590
+لل associative طب مين ال identity element في حالة
+
+333
+00:34:35,590 --> 00:34:43,310
+الجامعة ال zero يبقى هنا is هذه النقطة الأولى
+
+334
+00:34:43,310 --> 00:34:49,810
+النقطة الثانية النقطة الثانية ال zero is the
+
+335
+00:34:49,810 --> 00:34:56,310
+identity element because
+
+336
+00:35:00,180 --> 00:35:07,120
+الـ zero زائد ال بي مثلا يساوي بي زائد ال zero بده
+
+337
+00:35:07,120 --> 00:35:15,720
+يساوي ال بي itself الكلام هذا for all بي اللي
+
+338
+00:35:15,720 --> 00:35:24,240
+موجودة في z أوي q and ال a طيب النقطة التالتة
+
+339
+00:35:27,080 --> 00:35:33,000
+لو أخدت element a موجود في أي منهما من المعكوس
+
+340
+00:35:33,000 --> 00:35:38,940
+تبعه يعني مين العدد اللي بدي أضيفه إليه يطلع من؟
+
+341
+00:35:38,940 --> 00:35:50,730
+يطلع zero سالم العدد يبقى هنا the inverse ofأي
+
+342
+00:35:50,730 --> 00:36:00,010
+اللي موجود في الـ Z أو الـ Q and ال R is سالب A
+
+343
+00:36:00,010 --> 00:36:10,770
+since لأن ال A زائد ناقص A يسوى ناقص A زائد A يسوى
+
+344
+00:36:10,770 --> 00:36:17,490
+Zero لهمين ال identity element طيب
+
+345
+00:36:17,490 --> 00:36:26,910
+نمر اتنينروح ناخد مثال اخر لو أخدت الآن z و تحت
+
+346
+00:36:26,910 --> 00:36:35,250
+عملية الضرب العادي z is
+
+347
+00:36:35,250 --> 00:36:46,010
+not a group يبقى هذه ماهياش group under usual
+
+348
+00:36:46,010 --> 00:36:47,810
+multiplication
+
+349
+00:36:50,890 --> 00:37:00,830
+تحت عملية الضرب العادية ليش؟ because because
+
+350
+00:37:00,830 --> 00:37:14,270
+if ال a موجود في z and ال a لا يسوى واحد وبحيث ال
+
+351
+00:37:14,270 --> 00:37:20,450
+a لا يسوى واحدالان تحت عملية الضرب من ال identity
+
+352
+00:37:20,450 --> 00:37:25,650
+element الواحد ممتاز جدا يبقى هذا واحد لان اي عدد
+
+353
+00:37:25,650 --> 00:37:29,910
+اضربه في واحد بيطلع نفسي لوحده السؤال هو هل بقدر
+
+354
+00:37:29,910 --> 00:37:34,370
+الاقي element اضربه في اي عدد يطلع واحد
+
+355
+00:37:37,270 --> 00:37:43,510
+أنا بدي في Z أنا بحكي على Z فقط أنا مقيد بال 6
+
+356
+00:37:43,510 --> 00:37:47,590
+بتبعتي ال 6 الأخرى ماليش علاقة فيها و مقيد بال
+
+357
+00:37:47,590 --> 00:37:52,950
+operation اللي عندي بقدر ألاقي في الشمكانية يبقى F
+
+358
+00:37:52,950 --> 00:37:59,150
+ال A موجودة under ال A لا تساوي واحد then there is
+
+359
+00:37:59,150 --> 00:38:12,610
+أو there exists no element Bن اللي هو z such that
+
+360
+00:38:12,610 --> 00:38:21,170
+بحيث ان ال a في b بده يساوي الواحد الصحيح يعني for
+
+361
+00:38:21,170 --> 00:38:25,830
+example if
+
+362
+00:38:25,830 --> 00:38:33,190
+ال a تساوي تلتة بقدر الاقي عدد بي اضروف تلتة يطلع
+
+363
+00:38:33,190 --> 00:38:39,390
+واحد بس بحيث العدد فيه zفالـ a تسوى تلاتة then
+
+364
+00:38:39,390 --> 00:38:45,910
+there is no integer
+
+365
+00:38:45,910 --> 00:38:55,950
+بي such that بحيث ان تلاتة بيبدوا يساوي واحد
+
+366
+00:38:55,950 --> 00:39:03,250
+مالاجيش هذا العدد بتاتا يبقى هذه زد تحت عملية ضرب
+
+367
+00:39:03,250 --> 00:39:11,270
+مالهاطيب خليني أسأل كمان سؤال لو قلتلك ال set of
+
+368
+00:39:11,270 --> 00:39:16,770
+real numbers كويس؟ بس أصبر شوية ال set of real
+
+369
+00:39:16,770 --> 00:39:26,430
+numbers تحت عملية الضرب هل هي group؟ ليش؟بالنسبة
+
+370
+00:39:26,430 --> 00:39:29,750
+للصفر بلا جيش و لا inverse ليش ان ال identity قلت
+
+371
+00:39:29,750 --> 00:39:34,890
+هو مين بلا جيش ولا عدد اضربه في الصفر يطلع واحد
+
+372
+00:39:34,890 --> 00:39:40,730
+صحيح يدي ليست جروب و هكذا اذا احنا ال set مقيدين
+
+373
+00:39:40,730 --> 00:39:45,410
+بال set بشكل الاعداد اللى موجودة فيها مقيد بال
+
+374
+00:39:45,410 --> 00:39:48,750
+identity اللى عندى فيها مقيد بال binary
+
+375
+00:39:48,750 --> 00:39:52,150
+operational اللى موجودة عندى حققت الشروط بقول جروب
+
+376
+00:39:52,150 --> 00:39:58,830
+ما حققت بقوله ماهياش جروبطيب لو جيت قولش لك تلاتة
+
+377
+00:39:58,830 --> 00:40:06,490
+let الاي تساوي الجدر التربيعي للسالب واحد define
+
+378
+00:40:06,490 --> 00:40:10,090
+define
+
+379
+00:40:10,090 --> 00:40:17,610
+usual multiplication multiplication
+
+380
+00:40:17,610 --> 00:40:19,550
+on
+
+381
+00:40:38,180 --> 00:40:46,550
+عرفت حصل الضرب على set of complex numbersواحد ناقص
+
+382
+00:40:46,550 --> 00:40:51,330
+واحد اي ناقص اي ناقص اي حيث اي هو الجدر التربية
+
+383
+00:40:51,330 --> 00:40:56,550
+للسالب واحد يبقى دول complex ولا لا وعليهم عملية
+
+384
+00:40:56,550 --> 00:41:01,430
+ضرب العادية تبع ال complex number السؤال هو هل هذه
+
+385
+00:41:01,430 --> 00:41:05,470
+group ولا لا في الأول بدي أشوف هل ال
+
+386
+00:41:05,470 --> 00:41:12,990
+multiplication هذهلو ضرب اي عددين في بعض من دول
+
+387
+00:41:12,990 --> 00:41:18,430
+بيبقى complex و لا بيبطل يصير complexany real
+
+388
+00:41:18,430 --> 00:41:22,270
+number is complex هذا complex وهذا complex وهذا
+
+389
+00:41:22,270 --> 00:41:25,670
+complex وهذا complex وهذا complex يبقى العملية هذه
+
+390
+00:41:25,670 --> 00:41:30,790
+طيب لو ضربت ال I في ناقص I أليست مثل ناقص I في I
+
+391
+00:41:30,790 --> 00:41:34,950
+لأن العملية إبدالية هذا ناقص واحد في I زي I في
+
+392
+00:41:34,950 --> 00:41:40,230
+ناقص واحد سياد يبقى هذه اللي هي عبارة عن
+
+393
+00:41:40,230 --> 00:41:45,610
+associative binary operation يبقى let then
+
+394
+00:41:52,020 --> 00:41:58,380
+النقطة الان هي نقطة
+
+395
+00:41:58,380 --> 00:42:03,500
+عملية عملية عملية عملية عملية عملية
+
+396
+00:42:03,500 --> 00:42:06,700
+عملية عملية
+
+397
+00:42:10,880 --> 00:42:17,480
+طب كويس، مين ال identity element؟ واحد، يبقى واحد
+
+398
+00:42:17,480 --> 00:42:22,740
+is the identity element
+
+399
+00:42:24,480 --> 00:42:28,440
+يبقى الواحد هو عنصر الواحد اللي دي لو ضربته في أي
+
+400
+00:42:28,440 --> 00:42:32,580
+واحد من هدول بيطلع نفس الواحد هدول طيب السؤال مين
+
+401
+00:42:32,580 --> 00:42:38,060
+معكوس السلب واحد السلب واحد itself يبقى السلب واحد
+
+402
+00:42:38,060 --> 00:42:44,740
+is the inverse of itself يبقى هو معكوس لنفسي هنا
+
+403
+00:42:44,740 --> 00:42:55,030
+سلب واحد is the inverse of itselfطيب مين معكوس
+
+404
+00:42:55,030 --> 00:42:58,590
+الواحد؟ الواحد نفسه، ضربه نفسه بيطلع واحد، ماعنديش
+
+405
+00:42:58,590 --> 00:43:01,650
+أمر يبقى هذا ال identity دائما و أبدا شباب ال
+
+406
+00:43:01,650 --> 00:43:06,150
+identity هو معكوسه لنفسه، يتدورش عليه أي group
+
+407
+00:43:06,150 --> 00:43:08,810
+تطلع في الدنيا عندك ال identity ان هو معكوسه
+
+408
+00:43:08,810 --> 00:43:13,490
+لنفسها طيب الان مين معكوس ال I؟ ال سالب I طب و
+
+409
+00:43:13,490 --> 00:43:20,880
+السالب I؟لو ضربت اي في اي باي ترميلي بسالب واحد و
+
+410
+00:43:20,880 --> 00:43:27,520
+عندك سالب بصير موجة بواحد يبقى هنا باجي بقول له ال
+
+411
+00:43:27,520 --> 00:43:34,580
+اي is the inverse of سالب اي
+
+412
+00:43:39,980 --> 00:43:46,020
+من هذول التلاتة مع اللي فوق يبقى صلة هذه ال group
+
+413
+00:43:46,020 --> 00:43:52,260
+تحت عملية ضرب is a group يبقى هذا بدي يعطيلك انه g
+
+414
+00:43:52,260 --> 00:43:59,920
+تحت عملية الضرب اللي عندنا هذه is a group يبقى هذه
+
+415
+00:43:59,920 --> 00:44:02,160
+عبارة عن مجموعة
+
+416
+00:44:17,760 --> 00:44:23,720
+مثال رقم أربعة مثال
+
+417
+00:44:23,720 --> 00:44:31,880
+رقم أربعة هذا سؤال تلاتة من الكتاب بيقول لي show
+
+418
+00:44:31,880 --> 00:44:41,860
+that the set اللي هي مين؟ واحد واثنين وتلاتة
+
+419
+00:44:41,860 --> 00:44:45,680
+واربعة under
+
+420
+00:44:50,830 --> 00:45:01,410
+multiplication module خمسة module خمسة is an
+
+421
+00:45:01,410 --> 00:45:14,950
+abelian group is an abelian group but ولكن اللي هو
+
+422
+00:45:14,950 --> 00:45:26,710
+واحدو اتنين و تلاتة under multiplication
+
+423
+00:45:26,710 --> 00:45:30,410
+modulo
+
+424
+00:45:30,410 --> 00:45:34,850
+أربعة
+
+425
+00:45:34,850 --> 00:45:39,970
+is not a group
+
+426
+00:46:15,380 --> 00:46:20,710
+سؤال مرة تانية السؤال يعتبر سؤالينعندما أعطيني
+
+427
+00:46:20,710 --> 00:46:25,010
+أربعة أعداد واحد اتنين تلاتة عرفنا عليهم عملية ضرب
+
+428
+00:46:25,010 --> 00:46:30,430
+module خمسة عملية ضرب بالمقياس خمسة قال لي أثبت إن
+
+429
+00:46:30,430 --> 00:46:34,050
+هذه عبارة عن abelian group abelian سهلة تلاتة في
+
+430
+00:46:34,050 --> 00:46:36,550
+اتنين هي اتنين في تلاتة تلاتة في اربع هي اربع في
+
+431
+00:46:36,550 --> 00:46:40,050
+تلاتة اتنين في اربع هي اربع في اتنين والباقي في
+
+432
+00:46:40,050 --> 00:46:43,070
+واحد ما هي بطلع نفسها تمام؟ إذا أنا حكيت ال
+
+433
+00:46:43,070 --> 00:46:46,630
+abelian هذه تحصيل حصل يبقى أنا بالزمن ال
+
+434
+00:46:46,630 --> 00:46:51,690
+associative و بالزمن من؟ال binary operation في
+
+435
+00:46:51,690 --> 00:46:55,830
+الأول و لزمنا ال identity و المعكوس بقوله بسيطة
+
+436
+00:46:55,830 --> 00:47:00,370
+جدا الان بدي أشوف هل هي associ .. هي قبل ال
+
+437
+00:47:00,370 --> 00:47:04,190
+associative هل هي binary operation ولا لا بقوله
+
+438
+00:47:04,190 --> 00:47:10,110
+الله كويس يعني لو تعرفت أي عنصرين في بعضهم بدي
+
+439
+00:47:10,110 --> 00:47:14,170
+يكون ناتج داخل الستة دي ان حدث ذلك بقوله هذه
+
+440
+00:47:14,170 --> 00:47:18,880
+binary operation الان تعال خدلي اتنين في واحدبتنين
+
+441
+00:47:18,880 --> 00:47:21,840
+موجودة تلاتة في واحد تلاتة موجودة اربعة في واحد
+
+442
+00:47:21,840 --> 00:47:26,960
+باربعة موجودة نمسك اتنين اتنين في تلاتة ستة modulo
+
+443
+00:47:26,960 --> 00:47:31,740
+خمسة بيظل قداش واحد موجود اتنين في اربعة تمانية
+
+444
+00:47:31,740 --> 00:47:36,080
+modulo خمسة تلاتة موجود خلصنا اتنين ضربنا في تلاتة
+
+445
+00:47:36,080 --> 00:47:39,940
+و اربعة لان تلاتة في اربعة باطمعشر modulo خمسة
+
+446
+00:47:39,940 --> 00:47:45,980
+باتنين موجود يبقى داشت صارت binary operation يبقى
+
+447
+00:47:45,980 --> 00:47:55,650
+باجي بقوله اول شيءالـ multiplication modulo
+
+448
+00:47:55,650 --> 00:48:12,890
+خمسة is a binary operation on the set اللي واحد
+
+449
+00:48:12,890 --> 00:48:17,950
+واثنين وتلاتة واربع because السبب
+
+450
+00:48:20,570 --> 00:48:29,870
+الـ A, B modulo خمسة موجود في الست واحد واتنين
+
+451
+00:48:29,870 --> 00:48:35,430
+وتلاتة واربعة لكل ال A و ال B شو رايك أسميها
+
+452
+00:48:35,430 --> 00:48:41,430
+للسهولة أسميها S و هذا يبدأ أسميها S يبغى لكل ال A
+
+453
+00:48:41,430 --> 00:48:47,850
+و ال B اللي موجودة وين في Sيبقى حاصل ضرب اي اتنين
+
+454
+00:48:47,850 --> 00:48:52,430
+كله موجود وين موجود لذلك بايناري وبرجانت اتنين هذا
+
+455
+00:48:52,430 --> 00:48:55,870
+ضرب عادي بس باخد الموديولو في الآخر يبقى
+
+456
+00:48:55,870 --> 00:49:03,570
+associative ولا لا يبقى هنا كمان لاحظ انه note انه
+
+457
+00:49:03,570 --> 00:49:09,510
+multiplication modulo
+
+458
+00:49:09,510 --> 00:49:12,310
+خمسة
+
+459
+00:49:15,220 --> 00:49:21,640
+is associative بدّك
+
+460
+00:49:21,640 --> 00:49:25,640
+تشكل بساطرة هذا مافي مشكلة احنا ال I هو ال
+
+461
+00:49:25,640 --> 00:49:29,040
+identity الواحد يبقى هذا سهل لكن ضالي عند مين
+
+462
+00:49:29,040 --> 00:49:31,700
+الاتنين والتلاتة والاربعة يبقى بقدر أخدهم مع بعض
+
+463
+00:49:31,700 --> 00:49:37,040
+او يبقى خلصت ال group كله مظبوط يعني for example
+
+464
+00:49:40,060 --> 00:49:49,900
+لو أخدت اتنين أستار تلاتة أستار أربع طيب، هذا
+
+465
+00:49:49,900 --> 00:49:56,040
+اتنين في تلاتة بستة موديولو خمسة صح ولا لأ؟ يبقى
+
+466
+00:49:56,040 --> 00:50:02,220
+ستة موديولو خمسة فيها قداشر؟ واحد يبقى بظل واحد
+
+467
+00:50:02,220 --> 00:50:11,280
+أستار أربعأربعة مد يولو خمسة يبقى هذا بده يساوي
+
+468
+00:50:11,280 --> 00:50:18,860
+أربعة and لو أخدت اتنين star تلاتة star أربعة
+
+469
+00:50:18,860 --> 00:50:27,510
+ويساوي تلاتة في أربعةب12 modulo 5 ب2 يبقى يساوي 2
+
+470
+00:50:27,510 --> 00:50:35,110
+star 2 يعني 2 في 2 ب4 modulo 5 اللي هي ب4 يبقى هذا
+
+471
+00:50:35,110 --> 00:50:41,450
+بده يعطينا 4 يبقى star هذه هي نفس هذه بالظبط يبقى
+
+472
+00:50:41,450 --> 00:50:44,750
+العملية أساسية وضل بس دور مين الواحد واحد اللي
+
+473
+00:50:44,750 --> 00:50:47,490
+هيقدمه لأخر بالنسبة لعملية الدور لأن هو ال
+
+474
+00:50:47,490 --> 00:50:53,510
+identity elementيبقى على طول الخطب نقول واحد is
+
+475
+00:50:53,510 --> 00:51:01,430
+the identity element لأن
+
+476
+00:51:01,430 --> 00:51:05,250
+الواحد في أي رقم من الباقي module وخمسة هيعطيني
+
+477
+00:51:05,250 --> 00:51:12,230
+نفس الرقم مش هيغير حاجة طيب مين معكوس اي واحد فيهم
+
+478
+00:51:12,230 --> 00:51:14,270
+يالا شوف
+
+479
+00:51:17,900 --> 00:51:24,760
+من معكوس أي رقم من هذه الأرقام اتنين
+
+480
+00:51:24,760 --> 00:51:30,440
+والتلاتة معكوسات لبعض لأن اتنين في تلاتة موديول
+
+481
+00:51:30,440 --> 00:51:34,040
+وخمسة بطلع جداش واحد اللي هو ال identity element
+
+482
+00:51:34,040 --> 00:51:42,230
+طب والاربعة في اربعةيبقى اربعة معكوس لنفسه و اتنين
+
+483
+00:51:42,230 --> 00:51:46,430
+معكوس للتلاتة و ال identity هو معكوس لنفسه إذا صار
+
+484
+00:51:46,430 --> 00:51:56,550
+كل عنصر له معكوس يبقى هنا باجي بقول every element
+
+485
+00:51:56,550 --> 00:52:05,310
+in S has an inverse
+
+486
+00:52:07,290 --> 00:52:22,690
+since الواحد is the inverse of واحد بعدها
+
+487
+00:52:22,690 --> 00:52:35,280
+اتنين is the inverse of تلاتة sinceلأن اتنين في
+
+488
+00:52:35,280 --> 00:52:43,720
+تلاتة modulo خمسة بده يساوي واحد and الأربعة is
+
+489
+00:52:43,720 --> 00:52:58,530
+the inverse of itself since اللي همينأربعة مضروبة
+
+490
+00:52:58,530 --> 00:53:06,150
+في أربعة Modulo خمسة يساوي واحد يبقى كل عنصر له
+
+491
+00:53:06,150 --> 00:53:14,310
+معكوس يبقى بناء عليه أصبحت هذه group يبقى هنا ال S
+
+492
+00:53:14,310 --> 00:53:23,330
+تساوي واحد واتنين وتلاتة واربعة is a group under
+
+493
+00:53:29,300 --> 00:53:33,920
+multiplication multiplication modulo
+
+494
+00:53:35,390 --> 00:53:41,550
+خمسة طب أنا لسه خلصت الشطر الأول من السؤال جالي
+
+495
+00:53:41,550 --> 00:53:47,530
+لكن المجموعة هذه module أربعة is not a group بقوله
+
+496
+00:53:47,530 --> 00:53:52,670
+كويس ايش عرفك بدي و لو شرط واحد يختل من الشروط
+
+497
+00:53:52,670 --> 00:53:59,510
+اللي عندي بتبطل الصير a group صح ولا لا طيب حد
+
+498
+00:53:59,510 --> 00:54:01,530
+بقدر يجيبلي هذا الشرط
+
+499
+00:54:06,800 --> 00:54:11,660
+ممتاز جدا تعالى نشوف تلاتة هذه بيقول مالهاش معكوس
+
+500
+00:54:11,660 --> 00:54:17,320
+ليش؟ لأني قلت تلاتة في تلاتة تسعة تسعة شيل منهم
+
+501
+00:54:17,320 --> 00:54:24,200
+أربعتين بيظل واحد إذا التلاتة معكوس لنفسي صح يبقى
+
+502
+00:54:24,200 --> 00:54:31,020
+معكوسالان اتنين في تلاتة ايه بستة شيل منهم اربعة
+
+503
+00:54:31,020 --> 00:54:35,500
+بطلع اتنين يبجى ده مش اتنين معكسه مش التلاتة لكن
+
+504
+00:54:35,500 --> 00:54:41,720
+اتنين في اتنين اربعة تعني زيرو يبجى اتنين او هذه
+
+505
+00:54:41,720 --> 00:54:45,680
+ماهياش closed under يعني هذه ال operation ماهياش
+
+506
+00:54:45,680 --> 00:54:50,780
+binary operationلأن ال element موجود في نفس ال set
+
+507
+00:54:50,780 --> 00:54:57,180
+يبقى هذه بقول له that set اللي هو واحد و اتنين و
+
+508
+00:54:57,180 --> 00:55:11,200
+تلاتة under multi application modulo أربعة is not
+
+509
+00:55:11,200 --> 00:55:15,920
+a group since
+
+510
+00:55:18,430 --> 00:55:25,610
+الاتنين مستار اتنين يساوي أربعة modulo أربعة ليه
+
+511
+00:55:25,610 --> 00:55:30,730
+تساوي زيرو وهذا does not belong للست واحد واتنين
+
+512
+00:55:30,730 --> 00:55:34,930
+وتلاتة يبقى الشرط الأول تبقى binary operation لأنه
+
+513
+00:55:34,930 --> 00:55:38,110
+تحت عملية ضرب modulo أربعة التي بيكون موجود في
+
+514
+00:55:38,110 --> 00:55:43,260
+الست هذه هذا مش موجوديبقى يبعتلك الله لازلنا في
+
+515
+00:55:43,260 --> 00:55:48,000
+الأمثلة السهلة حتى هذه اللحظة لسه عندنا أمثلة
+
+516
+00:55:48,000 --> 00:55:53,000
+كثيرة بدنا على قلبي كمان محاضرتين مشان نخلص
+
+517
+00:55:53,000 --> 00:55:57,500
+الأمثلة على موضوع ال group لإن هذا الأساس اللى
+
+518
+00:55:57,500 --> 00:56:02,420
+بدنا نبني عليه كل دراستنا في موضوع ال groups بعد
+
+519
+00:56:02,420 --> 00:56:04,080
+ذلك يعطيكوا العجب
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..09c0efcdcb5fe9379f6b226d3aebc00666900fbb
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_postprocess.srt
@@ -0,0 +1,1620 @@
+1
+00:00:21,500 --> 00:00:25,180
+الرحيم استكملنا محاضرة الصبح اتكلمنا في البداية عن
+
+2
+00:00:25,180 --> 00:00:32,480
+بعض الأسئلة ودخلنا في شكل قصير وسريع عن الواحدة
+
+3
+00:00:32,480 --> 00:00:35,240
+الخامسة ال permutation ال group ان عيدا اللي ماكنش
+
+4
+00:00:35,240 --> 00:00:39,820
+موجود الفكرة ان انا بدي اروح اصنع group فيه
+
+5
+00:00:39,820 --> 00:00:44,440
+functions مع عملية ال composition فعلشان انا اقدر
+
+6
+00:00:44,440 --> 00:00:49,540
+اتعامل مع الكلام هذا لازم اتعامل ك function بهذا
+
+7
+00:00:49,540 --> 00:00:55,310
+الشكلمن مجموعة لنفسها و عشان عملية ال composition
+
+8
+00:00:55,310 --> 00:00:59,410
+بعد كده لو بدأ أخد J تانية مثلا لو بدأ أقول F من X
+
+9
+00:00:59,410 --> 00:01:03,670
+ل Y لازم J تكون من Y لحاجة تانية و علشان أنا بدأ
+
+10
+00:01:03,670 --> 00:01:07,830
+أشغل بحيث أن أحقق عملية ال .. ال .. اللي هو ال
+
+11
+00:01:07,830 --> 00:01:10,230
+pile يتكون موجودة و تكون العملية مغلقة على
+
+12
+00:01:10,230 --> 00:01:15,120
+المجموعة لازم أثبت شغلي على مجموعة واحدةاللي بتكون
+
+13
+00:01:15,120 --> 00:01:21,160
+من المجموعة لمين لنفسها طبعا ال identity موجود ال
+
+14
+00:01:21,160 --> 00:01:24,680
+associative موجود ال closed موجود بيبقى شغلة ال
+
+15
+00:01:24,680 --> 00:01:29,020
+inverse عشان أقدر أعرف F inverse لازم F يكون إيش
+
+16
+00:01:29,020 --> 00:01:32,720
+one to one وعشان يكون ال inverse معرف ك function
+
+17
+00:01:32,720 --> 00:01:35,920
+من ال X نفسه لازم يكون ال onto موجود فانا بدي
+
+18
+00:01:35,920 --> 00:01:44,480
+أتكلم عن J بتحتوى من كل ال projections F من X لXو
+
+19
+00:01:44,480 --> 00:01:50,720
+f is bijection و
+
+20
+00:01:50,720 --> 00:01:57,780
+اقول ان ال j مع ال composition تمثل ال group هجيت
+
+21
+00:01:57,780 --> 00:02:03,220
+في هذا ال chapter هروح اقول ان ال x finite فقط
+
+22
+00:02:03,220 --> 00:02:07,420
+عشان
+
+23
+00:02:07,420 --> 00:02:12,670
+احنا نتعامل مع مساقلة undergraduatesفاحنا نتعامل
+
+24
+00:02:12,670 --> 00:02:16,070
+مع الـ finite set و ال functions عليها تكون
+
+25
+00:02:16,070 --> 00:02:24,830
+بيجيكشن ال function اللي بتكون بهذا الشكل بنسميها
+
+26
+00:02:24,830 --> 00:02:29,770
+permutation يعني لما تكون ال function one to one
+
+27
+00:02:29,770 --> 00:02:34,570
+على مجموعة بنقول طبعا لو بيشتغل من مجموعة لنفسها
+
+28
+00:02:34,570 --> 00:02:39,450
+او لجزء اكبر منها بنسميها permutation فحروح اقول
+
+29
+00:02:39,450 --> 00:02:47,760
+ان اي functionمن X ل X في مساقنا ال X finite و
+
+30
+00:02:47,760 --> 00:02:51,740
+تكون one to one هذه هنسميها أيش permutation طبعا
+
+31
+00:02:51,740 --> 00:02:55,100
+في ميزة ان لو كانت ال function one to one على
+
+32
+00:02:55,100 --> 00:02:59,260
+finite set فال on two موجود ال one to one على
+
+33
+00:02:59,260 --> 00:03:04,060
+finite set يؤدي إلى ال on two فتخيل مجموعة محدودة
+
+34
+00:03:04,060 --> 00:03:10,240
+زي هيك مثلا A B C D انا بدي أصنع function من ال X
+
+35
+00:03:10,240 --> 00:03:17,760
+لنفسهاالـ A هتروح لمين؟ لـ F الـ A الـ B لـ F الـ
+
+36
+00:03:17,760 --> 00:03:25,860
+B الـ C لـ F الـ D ايه الـ C؟ الـ D لـ F الـ D هجت
+
+37
+00:03:25,860 --> 00:03:29,700
+F الـ A و F الـ B و F الـ C و F الـ D هم نفسهم الـ
+
+38
+00:03:29,700 --> 00:03:32,960
+A و الـ B و الـ C و الـ D فالـ F الـ A كم احتمال
+
+39
+00:03:32,960 --> 00:03:43,470
+له؟ لأ أربع يا A يا B يا C يا Dطيب لو ايه اخد F في
+
+40
+00:03:43,470 --> 00:03:47,530
+ايه اخد واحد من هدول يكبر هذا اربع احتمالات F في
+
+41
+00:03:47,530 --> 00:03:51,770
+ال B كم احتمال هيكون له تلاتة لإن واحد واحد فضله
+
+42
+00:03:51,770 --> 00:03:57,590
+تلاتة F في ال C اتنين و F في ال D يكبر كم function
+
+43
+00:03:57,590 --> 00:04:02,370
+بقدر اصنع هنا اربع في تلاتة في اتنين في واحد اربع
+
+44
+00:04:02,370 --> 00:04:07,150
+factorialأنا بقدر أصنع اربعة factorial من
+
+45
+00:04:07,150 --> 00:04:10,970
+الاقترانات على مجموعة فيها اربع عناصر وتكون هذه
+
+46
+00:04:10,970 --> 00:04:13,330
+الاقترانات one to one او one to one او one to one
+
+47
+00:04:13,330 --> 00:04:14,290
+او one to one او one to one او one to one او one
+
+48
+00:04:14,290 --> 00:04:15,250
+to one او one to one او one to one او one to one
+
+49
+00:04:15,250 --> 00:04:15,270
+to one او one to one او one to one او one to one
+
+50
+00:04:15,270 --> 00:04:15,670
+او one to one او one to one او one to one او one
+
+51
+00:04:15,670 --> 00:04:15,890
+او one to one او one to one او one to one او one
+
+52
+00:04:15,890 --> 00:04:29,730
+to one او one to one او one
+
+53
+00:04:29,730 --> 00:04:35,250
+to oneما هي مش هتفرق معايا كتير هذا ايه او اي واحد
+
+54
+00:04:35,250 --> 00:04:38,690
+او اي تنين او اي ان كانت قيمته هتظل نفس النتاج
+
+55
+00:04:38,690 --> 00:04:44,990
+متحققة نخلي العناصر هذه بهذا الشكل واحد و اتنين و
+
+56
+00:04:44,990 --> 00:04:51,030
+تلاتة يعني انا باشتغل المجموعة اللي فيها الأقام
+
+57
+00:04:51,030 --> 00:04:55,850
+واحد لانه واخدت جميع الاقترانات اللي بتكون one to
+
+58
+00:04:55,850 --> 00:05:02,600
+one نقنتوا علي هذه المجموعة هحطها فيمجموعة اسمها
+
+59
+00:05:02,600 --> 00:05:12,840
+sn اللي هي the set of all one to one functions on
+
+60
+00:05:12,840 --> 00:05:19,480
+واحد اتنين لعند n هذه الـ sn هنسميها symmetry
+
+61
+00:05:19,480 --> 00:05:25,340
+group او
+
+62
+00:05:25,340 --> 00:05:31,500
+symmetry n group هنظبط تسميها كما شويةهذه هي مجلة
+
+63
+00:05:31,500 --> 00:05:37,220
+شغلنا اليوم سواء كانت على مجموع 1,2,3 ل N أو كانت
+
+64
+00:05:37,220 --> 00:05:41,340
+ال A1,A2 and An مش عارف مين بالظبط هذه اللي انا
+
+65
+00:05:41,340 --> 00:05:45,860
+هسميهم permutation طبعا احنا درسنا شغلة زيها قبل
+
+66
+00:05:45,860 --> 00:05:55,200
+هيك درسنا ل group D3 اش كان فيها؟ R0
+
+67
+00:05:58,110 --> 00:06:03,930
+R120 R240 F1
+
+68
+00:06:03,930 --> 00:06:12,370
+F2 F3 D3 عبارة عن ايش؟ تعامل مع المثلث اذا قلنا 1
+
+69
+00:06:12,370 --> 00:06:24,160
+2 3 ايش ال R0؟بتظل مكاني طيب تعالي أفهمش يعني اظل
+
+70
+00:06:24,160 --> 00:06:28,660
+مكاني الواحد ظل مكانه في الواحد يعني أف الواحد
+
+71
+00:06:28,660 --> 00:06:34,860
+ممكن اعتبره واحد اتنين ظل وين؟ يعني أف التنين و
+
+72
+00:06:34,860 --> 00:06:40,140
+التلاتة ظل وين؟ مكانه يعني أف التلاتة بيساو تلاتة
+
+73
+00:06:40,140 --> 00:06:45,320
+يعني أنا بتكلم عن مين؟ يعني انا بتكلم عن لو خدت
+
+74
+00:06:45,320 --> 00:06:50,030
+مثلا المجموعة Jو اتكلمت عن ال identity function و
+
+75
+00:06:50,030 --> 00:06:59,210
+أخطّلها رمز إبسلون زي هيك طيب لو قلنا ال R Zero
+
+76
+00:06:59,210 --> 00:07:06,170
+هذا هي ال R مية و عشرين أبدا يش دوران بمقدار مية و
+
+77
+00:07:06,170 --> 00:07:11,890
+عشرين درجة في أي اتجاه عكس عقارب الساعة يعني هيك
+
+78
+00:07:11,890 --> 00:07:18,990
+يعني حاسيب معايا واحد اتنينتلاتة وكأنه F الواحد
+
+79
+00:07:18,990 --> 00:07:26,010
+صار تلاتة و F التنين صار واحد و F التلاتة صار
+
+80
+00:07:26,010 --> 00:07:30,010
+اتنين طبعا انا هذا الاقتران واحد اتنين تلاتة
+
+81
+00:07:30,010 --> 00:07:34,730
+الواحد ايش صار تلاتة التلاتة ايش صار
+
+82
+00:07:37,450 --> 00:07:40,430
+ممكن اكتبه بدل من اقول F الواحد يساوي F التانين F
+
+83
+00:07:40,430 --> 00:07:45,210
+التلاتة اكتب الواحد والتانين والتلاتة تغير ترتيبهم
+
+84
+00:07:45,210 --> 00:07:51,630
+لتلاتة واحد اتنين فهذا ال identity عبارة عن ايش
+
+85
+00:07:51,630 --> 00:07:56,370
+الواحد مكانه التانين مكانه التلاتة مكانه يعني هذا
+
+86
+00:07:56,370 --> 00:08:02,970
+هو واحد اتنين تلاتة واحد اتنين تلاتة لكن ال R
+
+87
+00:08:02,970 --> 00:08:08,830
+ميعني عشرينصارت الواحد اتنين تلاتة صارت ايش تلاتة
+
+88
+00:08:08,830 --> 00:08:16,310
+واحد اتنين مش صارت ترتيبة زي هيك طيب هذه بالنسبالي
+
+89
+00:08:16,310 --> 00:08:24,590
+ال R0 ال R 240 كمان لفة واحد اتنين تلاتة يعني F
+
+90
+00:08:24,590 --> 00:08:29,150
+الواحد صارت اتنين F التنين صارت تلاتة F التلاتة
+
+91
+00:08:29,150 --> 00:08:36,050
+صارت ايش واحد يعنيواحد اتنين تلاتة صارت اتنين
+
+92
+00:08:36,050 --> 00:08:42,610
+تلاتة واحد طيب
+
+93
+00:08:42,610 --> 00:08:47,930
+شوية بس مين رجع مكانه؟ محدش هدول رجع مكانه يعني
+
+94
+00:08:47,930 --> 00:08:53,590
+اللي لف التالتة ماهترج على identity اه بس انا خلصت
+
+95
+00:08:53,590 --> 00:08:59,040
+دورانات هفوت على مين هالجير؟ ع reflectionsهي انا
+
+96
+00:08:59,040 --> 00:09:02,900
+لما بدى اجي اعمل هي واحد اتنين تلاتة بدي اعمل
+
+97
+00:09:02,900 --> 00:09:07,560
+reflection بالنسبة للواحد و اجلب هتصير واحد تلاتة
+
+98
+00:09:07,560 --> 00:09:12,880
+اتنين يعني اف الواحد زي ما هي اف التانين تلاتة اف
+
+99
+00:09:12,880 --> 00:09:17,660
+التلاتة اتنين يعني واحد اتنين تلاتة واحد تلاتة
+
+100
+00:09:17,660 --> 00:09:24,150
+اتنين حاجة اقول واحد تلاتة اتنينوهذه بالنسبة لي
+
+101
+00:09:24,150 --> 00:09:27,270
+محايدة، ضالت مكانها الواحد ضال مكانه، مايكبهاش
+
+102
+00:09:27,270 --> 00:09:32,350
+التبديلة صارت تلاتة و اتنين تلاتة و اتنين يعني
+
+103
+00:09:32,350 --> 00:09:36,850
+وكانها تلاتة و اتنين طبعا اللي بعدها هتكون واحد و
+
+104
+00:09:36,850 --> 00:09:42,070
+تلاتة و واحد و اتنين فعليا،
+
+105
+00:09:42,070 --> 00:09:47,190
+طبعا هذه تنساش عبارة عن مين؟S3 ان صارت مجموعة
+
+106
+00:09:47,190 --> 00:09:52,890
+التباديل للمجموعة اللي فيها مين 1 2 3 ال D3 و ال
+
+107
+00:09:52,890 --> 00:10:00,390
+S3 هما واحد هما نفس ال group لكن هذا منطلع إلها من
+
+108
+00:10:00,390 --> 00:10:07,970
+الزاوية وهذا منطلع من زاوية طيب هل ممكن أنعمم هل
+
+109
+00:10:07,970 --> 00:10:18,030
+ال D4 هتصير S4 تعالى نشوف ال D4اكم هنصه فيها ال S4
+
+110
+00:10:18,030 --> 00:10:21,210
+ال
+
+111
+00:10:21,210 --> 00:10:26,710
+D4 مش هي ال S4 لأ هتكون جزء من ال S4 هناخد في مثال
+
+112
+00:10:26,710 --> 00:10:31,110
+كمان شوية كيف هذا الكلام يكون واقعى هنكتب التعريف
+
+113
+00:10:31,110 --> 00:10:37,350
+ناخد أنثلاف بعدك إذا ضال وقت هنصل لمثال ال D4 ان
+
+114
+00:10:37,350 --> 00:10:43,630
+شاء الله كيف؟
+
+115
+00:10:52,890 --> 00:10:59,990
+definition C4 مش الاسفار دي واحد
+
+116
+00:10:59,990 --> 00:11:06,490
+a permutation of
+
+117
+00:11:06,490 --> 00:11:12,730
+a set A زي ما قلنا is a function
+
+118
+00:11:16,040 --> 00:11:33,840
+from A to A that is both one to one and unto كلمة
+
+119
+00:11:33,840 --> 00:11:41,760
+واحدة يعنيش projection تانين الـPermutation group
+
+120
+00:11:44,770 --> 00:11:48,590
+هنا اتكلمنا عن البرموتاشن نفسها البرموتاشن ال
+
+121
+00:11:48,590 --> 00:11:53,810
+group عبارة عن مجموعة بتحتوي برموتاشن مع عملية مين
+
+122
+00:11:53,810 --> 00:11:59,030
+ال composition لان انا بتكلم عن functions و انا
+
+123
+00:11:59,030 --> 00:12:02,370
+اصلا صنعت الموضوع هذا عشان اتناول عملية ال
+
+124
+00:12:02,370 --> 00:12:06,250
+composition و اخليها ضمن ال group ال permutation
+
+125
+00:12:06,250 --> 00:12:13,880
+groupعبارة عن جروب طبعا تحت عملية ال composition
+
+126
+00:12:13,880 --> 00:12:17,700
+العناصر اللي فيها عبارة عن permutation على مجموعة
+
+127
+00:12:17,700 --> 00:12:27,320
+ما permutation group of asset
+
+128
+00:12:27,320 --> 00:12:33,740
+permutation group of asset a is
+
+129
+00:12:40,670 --> 00:12:49,470
+asset of permutations on
+
+130
+00:12:49,470 --> 00:13:02,790
+a that form a group under
+
+131
+00:13:02,790 --> 00:13:06,510
+function
+
+132
+00:13:06,510 --> 00:13:09,010
+composition
+
+133
+00:13:17,160 --> 00:13:22,380
+عبارة عن مجموعة
+
+134
+00:13:22,380 --> 00:13:29,020
+بتعمل جروب مع عملية تركيب الدولة في هذا ال chapter
+
+135
+00:13:29,020 --> 00:13:43,560
+we study here the case where a is finiteيعني في
+
+136
+00:13:43,560 --> 00:13:48,660
+مصراخنا شباب هندرس الحالة اللي بيكون فيها المجموعة
+
+137
+00:13:48,660 --> 00:13:53,200
+مثال ناخد
+
+138
+00:13:53,200 --> 00:13:58,160
+مثال على permutation و بعد هيك ناخد مثال على
+
+139
+00:13:58,160 --> 00:14:03,880
+permutation الجرم كيف؟
+
+140
+00:14:05,440 --> 00:14:10,260
+لأ في هذا المثال تحديدًا هنشتغل يعني ال A عبارة عن
+
+141
+00:14:10,260 --> 00:14:14,680
+واحد اتنين تلاتة لعند N طبعًا انا شراحت في البداية
+
+142
+00:14:14,680 --> 00:14:17,860
+ليش اخترت واحد اتنين تلاتة لعند N لو كان بدل واحد
+
+143
+00:14:17,860 --> 00:14:21,580
+اتنين تلاتة A واحد اتنين لعند AN نفس الخصائص
+
+144
+00:14:21,580 --> 00:14:25,990
+الموجودةممكن تكون موجودة على المجموعة من واحد
+
+145
+00:14:25,990 --> 00:14:31,790
+لاتنين لتلاتة لعندان هي هي انا مش هاهتم كتير عنصر
+
+146
+00:14:31,790 --> 00:14:36,570
+ايش قيمته بدي انا هان خصائص اللي هي التبديل على
+
+147
+00:14:36,570 --> 00:14:41,710
+هذه العناصر فبختار مجموعة سهلة عشان اقدر اتعامل
+
+148
+00:14:41,710 --> 00:14:49,930
+اتكون الكتوبة اسهل طيب ناخد ال اتش اولدت ال ايه
+
+149
+00:14:49,930 --> 00:14:57,160
+عبارة عن الواحد واتنين وتلاتة واربعةlet alpha من a
+
+150
+00:14:57,160 --> 00:15:05,800
+ل a be given as alpha الواحد بدي ساوي تلاتة الف
+
+151
+00:15:05,800 --> 00:15:09,600
+اتنين بدي ساوي واحد الف التلاتة بدي تساوي أربعة
+
+152
+00:15:09,600 --> 00:15:12,640
+والف
+
+153
+00:15:12,640 --> 00:15:17,140
+الأربعة بدي تساوي اتنين
+
+154
+00:15:21,680 --> 00:15:31,740
+بيتا من a ل a be given as بيتا التنين او بيتا
+
+155
+00:15:31,740 --> 00:15:38,260
+الواحد بدت ساوي واحد بيتا التنين بدت ساوي تلاتة
+
+156
+00:15:38,260 --> 00:15:44,060
+بيتا التلاتة بدت ساوي أربعة و بيتا الأربعة بدت
+
+157
+00:15:44,060 --> 00:15:48,100
+ساوي اتنين هيتوا functions clearly
+
+158
+00:15:52,440 --> 00:16:05,880
+الفا and بيتا are permutation on a ليش ال one to
+
+159
+00:16:05,880 --> 00:16:09,700
+one و ال on two واضح من التعريف التعريف موجود عندك
+
+160
+00:16:09,700 --> 00:16:13,760
+بطريقة السرد ولا عنصر بروح ل .. ولا .. مافيش
+
+161
+00:16:13,760 --> 00:16:18,660
+عنصرين بروحوا لنفس القيمة طبعا و لعملية on two
+
+162
+00:16:24,210 --> 00:16:30,290
+طيب ال alpha و ال beta ممكن اكتبهم كتالة we can
+
+163
+00:16:30,290 --> 00:16:40,430
+write ال alpha عبارة عن واحد اتنين تلاتة اربعة ال
+
+164
+00:16:40,430 --> 00:16:46,250
+واحد لمين بيروح لمين بيروح الواحد التانية لمين
+
+165
+00:16:46,250 --> 00:17:01,430
+بيروح التلاتة والاربعةطيب ال beta 1,2,3,4 ال 1,2,3
+
+166
+00:17:01,430 --> 00:17:12,710
+,4,2 هدا هي ال alpha و هدا هي ال beta طيب for
+
+167
+00:17:12,710 --> 00:17:18,390
+alpha beta طبعا انا هجيت هتعامل alpha permutation
+
+168
+00:17:18,390 --> 00:17:22,460
+و beta permutationالعملية اللي بينهم عملية ايش
+
+169
+00:17:22,460 --> 00:17:27,900
+composition المفروض ان يكون Alpha Beta عبارة عن
+
+170
+00:17:27,900 --> 00:17:37,640
+اقتران من A ل A with Alpha Beta ل X عبارة عن Alpha
+
+171
+00:17:37,640 --> 00:17:41,060
+Beta
+
+172
+00:17:41,060 --> 00:17:50,960
+ل X لأن العملية Alpha Beta فعليا هو AlphaComposite
+
+173
+00:17:50,960 --> 00:17:55,980
+Beta طب ليش؟ هذا كانت الزمرة الدليل قال لأ يا عمي
+
+174
+00:17:55,980 --> 00:18:00,380
+هو تعريف العملية أنا مانتش أحط هنا نقطة ال Alpha
+
+175
+00:18:00,380 --> 00:18:03,740
+في Beta عبارة عن أنصف ال group و أنصف ال group
+
+176
+00:18:03,740 --> 00:18:06,540
+العملية اللي بينهم عملية composition بين function
+
+177
+00:18:06,540 --> 00:18:12,880
+و function طيب طب تعالى نشوف Alpha Beta للواحد
+
+178
+00:18:12,880 --> 00:18:19,140
+عبارة عن Alpha Beta الواحد Beta الواحد يا ديش يا
+
+179
+00:18:19,140 --> 00:18:25,470
+شباببيتا الواحد واحد طب الف الواحد جديش تلاتة طب
+
+180
+00:18:25,470 --> 00:18:32,610
+الف بيتا and التنين عبارة عن الف بيتا التنين بيتا
+
+181
+00:18:32,610 --> 00:18:39,210
+التنين جديش تلاتة طب و الف الأربع التلاتة أربع طب
+
+182
+00:18:39,210 --> 00:18:45,850
+الف بيتا and التلاتة عبارة عن الف بيتا التلاتة
+
+183
+00:18:45,850 --> 00:18:52,280
+بيتا التلاتة جديشبيتا التلاتة كده؟ أربعة ألفة
+
+184
+00:18:52,280 --> 00:18:56,160
+الاربعة ألفة
+
+185
+00:18:56,160 --> 00:19:02,640
+بيتا للاربعة عبارة عن ألفة بيتا يعني ألفة التنين
+
+186
+00:19:02,640 --> 00:19:12,060
+ألفة التنين كده؟ واحد طيب هذا معناته أن ألفة بيتا
+
+187
+00:19:12,060 --> 00:19:17,620
+بقدر أكتب زيك واحد اتنين تلاتة أربعة الواحد لمين
+
+188
+00:19:17,620 --> 00:19:26,830
+راح؟الواحد لمين للتلاتة والتنين والتلاتة والاربع
+
+189
+00:19:26,830 --> 00:19:41,870
+للواحد طيب تعالى نشوف beta alpha for beta alpha هو
+
+190
+00:19:41,870 --> 00:19:47,930
+مش قاعدة انهم يتساوي هي مش قاعدة انهم يتساوي تعالى
+
+191
+00:19:47,930 --> 00:19:56,830
+نشوفبيتا ألفة للواحد عبارة
+
+192
+00:19:56,830 --> 00:20:02,330
+عن بيتا ألف الواحد ألف الواحد كده؟ ألف الواحد
+
+193
+00:20:02,330 --> 00:20:09,710
+تلاتة بيتا التلاتة أربع طيب بيتا ألفة للتانين يعني
+
+194
+00:20:09,710 --> 00:20:17,250
+بيتا ألف التانين ألف التانين كده؟ واحد بيتا للواحد
+
+195
+00:20:21,150 --> 00:20:28,410
+بيتا ألفة للتلاتة بيتا ألفة التلاتة بيتا ألفة
+
+196
+00:20:28,410 --> 00:20:35,770
+التلاتة جديش؟ طيب بيتا ألفة للأربعة بيتا ألفة
+
+197
+00:20:35,770 --> 00:20:42,550
+للأربعة ألفة للأربعة جديش؟ اتنين و بيتا التالين
+
+198
+00:20:42,550 --> 00:20:50,610
+بيتا ألفةعبارة عن واحد اتنين تلاتة اربعة الواحد
+
+199
+00:20:50,610 --> 00:20:58,350
+للاربعة تلين الواحد و اتنين و تلاتة ايش بتلاحظ؟ in
+
+200
+00:20:58,350 --> 00:21:05,290
+general Alpha
+
+201
+00:21:05,290 --> 00:21:11,810
+Beta ليسوا Beta Alpha ليش قولت in general؟ قد يكون
+
+202
+00:21:11,810 --> 00:21:12,710
+هناك حالات
+
+203
+00:21:16,150 --> 00:21:20,970
+أو هناك حالات لـ .. لـ .. لت .. ان كل عملية تبدلية
+
+204
+00:21:20,970 --> 00:21:24,650
+هذا
+
+205
+00:21:24,650 --> 00:21:29,690
+مش صورة، هذا مثال مثال لنفهم العملية كده بالتم، بس
+
+206
+00:21:39,190 --> 00:21:43,670
+هل كل مرة يا شباب بدي أقدر أعرفلك Alpha Beta and
+
+207
+00:21:43,670 --> 00:21:46,570
+الواحد يعني Alpha Beta الواحد يعني Alpha مثلا
+
+208
+00:21:46,570 --> 00:21:53,870
+الواحد يعني مستوى تلاتة لأ how to
+
+209
+00:21:53,870 --> 00:22:00,950
+do this using
+
+210
+00:22:00,950 --> 00:22:11,090
+the notation واحد اتنين تلاتةالف الواحد الف التاني
+
+211
+00:22:11,090 --> 00:22:18,170
+الاند الف انا كيف نستعمل ال notation هذا في الحساب
+
+212
+00:22:18,170 --> 00:22:27,490
+نحسب الف بيتا الف بيتا عبارة عن مين هاي الالفة كده
+
+213
+00:22:27,490 --> 00:22:34,530
+الالفة هنا تلاتة واحد اربعة اتنين وبيتا واحد اتنين
+
+214
+00:22:34,530 --> 00:22:39,310
+تلاتة اربعةكداش؟ واحد .. تلاتة .. اربعة .. اتنين
+
+215
+00:22:39,310 --> 00:22:42,990
+كيف بدي اتم الامر هذا؟ هي واحد .. هي اتنين .. هي
+
+216
+00:22:42,990 --> 00:22:48,470
+تلاتة .. هي اربعة؟ بنبدأ من وين؟ الواحد مين اقرب
+
+217
+00:22:48,470 --> 00:22:51,990
+للواحد
+
+218
+00:22:51,990 --> 00:22:57,990
+هنا؟ الالف ولا البيتا؟ البيتا ببدأ البيتا وان
+
+219
+00:22:57,990 --> 00:23:02,670
+بتاخد الواحد؟ للواحد بنجي هنا الالف وان بتاخد
+
+220
+00:23:02,670 --> 00:23:04,850
+الواحد؟ يجب الواحد يروح للتلاتة
+
+221
+00:23:07,750 --> 00:23:11,730
+الواحد باجي من هنا بروح للواحد باجي هنا الواحد لمن
+
+222
+00:23:11,730 --> 00:23:18,510
+بيروح؟ لل تلاتة طيب التنين التلاتة لمن؟ اتنين
+
+223
+00:23:18,510 --> 00:23:23,270
+تلاتة تلاتة اربعة يكبر اتنين للاربعة تلاتة للاربعة
+
+224
+00:23:23,270 --> 00:23:27,490
+اربعة للتنين يكبر تلاتة للتنين اربعة للتنين واتنين
+
+225
+00:23:27,490 --> 00:23:33,190
+للواحد يكبر اربعة لمن؟ للواحد ماشي بس بدون الكتابة
+
+226
+00:23:33,190 --> 00:23:35,930
+هذه كلها بدون الكتابة هذه كلها
+
+227
+00:23:40,500 --> 00:23:45,000
+نبدأ بالواحد الواحد لمين بروح انا؟ بمسك الواحد انا
+
+228
+00:23:45,000 --> 00:23:49,400
+و بطلع فيه فوق لمين هيروح؟ يجب احد لمين؟ انا بتبدأ
+
+229
+00:23:49,400 --> 00:23:54,880
+من ال beta اه من ال beta التاني لمين؟ التلاتة
+
+230
+00:23:54,880 --> 00:23:59,980
+لمين؟ يجب اتنين للاربعة تلاتة اربعة اربعة اتنين
+
+231
+00:23:59,980 --> 00:24:04,300
+يجب تلاتة للتانين اربعة اتنين اتنين واحد يجب اربعة
+
+232
+00:24:04,300 --> 00:24:12,180
+للواحد طيب نفس الطريقة beta alphaواحد اتنين تلاتة
+
+233
+00:24:12,180 --> 00:24:19,240
+اربعة واحد تلاتة اربعة اتنين فيه
+
+234
+00:24:19,240 --> 00:24:26,980
+واحد اتنين تلاتة اربعة تلاتة واحد اربعة اتنين طيب
+
+235
+00:24:26,980 --> 00:24:30,680
+واحد
+
+236
+00:24:30,680 --> 00:24:36,740
+اتنين تلاتة اربعة الواحد لمن بيروح تلاتة لمن هيروح
+
+237
+00:24:36,740 --> 00:24:41,630
+يقبل واحد تلاتة تلاتة اربعة يقبل واحد للاربعةطيب
+
+238
+00:24:41,630 --> 00:24:46,250
+اتنين واحد واحد واحد يكبر اتنين للواحد تلاتة
+
+239
+00:24:46,250 --> 00:24:50,690
+للاربعة واربعة للتانين يكبر تلاتة لمن للتانين
+
+240
+00:24:50,690 --> 00:24:56,490
+اربعة للتانين واتنين للتلاتة يكبر اربعة لمن بيروح
+
+241
+00:24:56,490 --> 00:25:08,910
+بيروح للتلاتة واضح
+
+242
+00:25:18,740 --> 00:25:25,980
+symmetric group etc طبعا المثال هذا شباب اتعاملنا
+
+243
+00:25:25,980 --> 00:25:30,460
+معاه مع ال permutation على شكل عناصر permutation و
+
+244
+00:25:30,460 --> 00:25:32,340
+permutation تانية كيف بنضرب كيف
+
+245
+00:25:32,340 --> 00:25:43,100
+ببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببببب
+
+246
+00:25:43,500 --> 00:25:47,360
+يعني ناخد مجموعة تكون جروب و فيها permutation
+
+247
+00:25:47,360 --> 00:25:57,040
+الثلاثة is the set of all طب أنا ماجول all يعني كل
+
+248
+00:25:57,040 --> 00:26:00,160
+ال permutation الممكنة لكن أنا ماجول a set of
+
+249
+00:26:00,160 --> 00:26:03,400
+permutations on يعني مجموعة permutation على
+
+250
+00:26:03,400 --> 00:26:08,840
+المجموعة قد يكونوا كلهم و قد يكون جزء الثلاثة is
+
+251
+00:26:08,840 --> 00:26:11,440
+the set of all permutations
+
+252
+00:26:16,490 --> 00:26:29,850
+on the set واحد اتنين تلاتة which
+
+253
+00:26:29,850 --> 00:26:34,010
+called هذه
+
+254
+00:26:34,010 --> 00:26:44,110
+الأستلاتة بسميها the symmetric الجروب
+
+255
+00:26:45,820 --> 00:26:52,420
+of order تلاتة طب انا بقول هنا of order تلاتة مش
+
+256
+00:26:52,420 --> 00:26:56,280
+القصد انه عدد العناصر تلاتة لأ ال order تلاتة يعني
+
+257
+00:26:56,280 --> 00:27:01,780
+order المجموعة اللي انا اشتغلت عليها مش order ال
+
+258
+00:27:01,780 --> 00:27:08,700
+permutation اللي بيطلع معايا هبدأ بال E عبارة عن
+
+259
+00:27:08,700 --> 00:27:12,600
+واحد اتنين تلاتة واحد اتنين تلاتة اللي هو
+
+260
+00:27:16,300 --> 00:27:19,800
+الـ E نفسه الواحد بيروح للواحد التاني بيروح للتاني
+
+261
+00:27:19,800 --> 00:27:26,400
+التلاتة بتروح لمين و أخد ال alpha واحد اتنين تلاتة
+
+262
+00:27:26,400 --> 00:27:32,360
+و الواحد هيروح للتانين والتانين هيروح للتلاتة
+
+263
+00:27:32,360 --> 00:27:39,620
+والتلاتة هيروح للواحد هذا عبارة عن ايش عن دوران R
+
+264
+00:27:39,620 --> 00:27:46,410
+مياشي و أخد ال betaإبعاداً 1 2 3 أدخل الواحد يذهب
+
+265
+00:27:46,410 --> 00:27:52,070
+لنفسه والتاني يذهب للثالث والثالث للاثنين يعني هذه
+
+266
+00:27:52,070 --> 00:27:56,610
+عبارة عن ال identity ودوران و reflection وانتوا
+
+267
+00:27:56,610 --> 00:28:01,990
+عارفين ان ال DN بتكونه بدوران و reflection و بيصير
+
+268
+00:28:01,990 --> 00:28:06,630
+تعمل دوران تتكرر مع بعضه وكل تكرار متكررات الدوران
+
+269
+00:28:06,630 --> 00:28:11,450
+مع reflection الأولاني يعطيك reflection جديد تعالى
+
+270
+00:28:11,450 --> 00:28:12,450
+نشوف Alpha تربيع
+
+271
+00:28:18,920 --> 00:28:26,320
+Alpha تغبية عبارة عن الـ Alpha في Alpha عشان
+
+272
+00:28:26,320 --> 00:28:29,020
+شرحتنا الكلام في الأول فاحنا فاهمين أنه هذا
+
+273
+00:28:29,020 --> 00:28:32,760
+reflection لكن مفترض أنه أنا أشر عليه و أتفاجأ أنه
+
+274
+00:28:32,760 --> 00:28:38,880
+هذا reflection بس احنا ضيعنا المفاجأة يعني واحد
+
+275
+00:28:38,880 --> 00:28:45,540
+اتنين تلاتة واحد اتنين تلاتة هذا اتنين تلاتة واحد
+
+276
+00:28:45,540 --> 00:28:52,360
+اتنين تلاتة واحدهذا عبارة عن ايش؟ واحد اتنين تلاتة
+
+277
+00:28:52,360 --> 00:28:56,880
+الواحد للتانين والتانين للتلاتة التانين للتلاتة
+
+278
+00:28:56,880 --> 00:29:01,700
+والتلاتة للواحد التلاتة للواحد والواحد للتانين
+
+279
+00:29:01,700 --> 00:29:08,700
+هيبقى بنكتبه بهذا الشكل طيب ال alpha تكايب عبارة
+
+280
+00:29:08,700 --> 00:29:16,400
+عن alpha تغبيه في alpha يعني واحد اتنين تلاتة
+
+281
+00:29:16,400 --> 00:29:25,510
+تلاتة واحد اتنين1 2 3 2 3 1 1 للتانين و تنين
+
+282
+00:29:25,510 --> 00:29:29,050
+للواحد يعني واحد للواحد تنين للتلتة و تلتة للتانين
+
+283
+00:29:29,050 --> 00:29:33,570
+يجب اتنين للتانين تلتة للتلتة اللي هو مين الايتين
+
+284
+00:29:33,570 --> 00:29:41,350
+التانين طيب Beta تربيع يعني
+
+285
+00:29:41,350 --> 00:29:53,170
+1 2 3 و 1 3 2 1 2 3 1 3 2هيعطيك 123 123 اللى هو ال
+
+286
+00:29:53,170 --> 00:30:02,170
+identity سهل هذى لو جينا حسبنا alpha beta يعني 123
+
+287
+00:30:02,170 --> 00:30:06,790
+132
+
+288
+00:30:06,790 --> 00:30:15,430
+او احنا كنا ال alpha في الاول 231 و ال beta 123
+
+289
+00:30:15,430 --> 00:30:22,230
+132يعمل العملية هذه ايش
+
+290
+00:30:22,230 --> 00:30:29,950
+هيعضيك؟ المطلوب يعطينا مركز صحيح واحد لواحد واحد
+
+291
+00:30:29,950 --> 00:30:33,930
+لاتنين يكبر واحد لاتنين تنين لتلاتة و تلاتة لتنين
+
+292
+00:30:33,930 --> 00:30:37,730
+لواحد يكبر تنين لمين؟ لواحد تلاتة لتنين و تلاتة
+
+293
+00:30:37,730 --> 00:30:41,250
+لتلاتة يكبر تلاتة لمين؟ لتلاتة
+
+294
+00:30:50,810 --> 00:30:55,490
+طب على المفروض يا شباب S3 هيكون كام عنصر ستة تعالى
+
+295
+00:30:55,490 --> 00:31:00,870
+نشوف كام عنصر و حصلنا عليه ستة هي الأول هي التاني
+
+296
+00:31:00,870 --> 00:31:08,650
+هي التالت هي الرابع وهي الخامس لإن هي خمس عناصر
+
+297
+00:31:08,650 --> 00:31:12,810
+مختلفة ايه يا ابو عزوز بيتا ألف كيف تجدها ألف بيتا
+
+298
+00:31:12,810 --> 00:31:18,130
+ألف زي ما عملت عمال يضغبها نفس الفكرة تعاشوا ببيتا
+
+299
+00:31:18,130 --> 00:31:18,550
+ألفة
+
+300
+00:31:24,260 --> 00:31:30,780
+واحد اتنين تلاتة واحد اتنين تلاتة ال alpha عبارة
+
+301
+00:31:30,780 --> 00:31:36,260
+عن تلاتة او تنين تلاتة واحد و انا واحد تلاتة اتنين
+
+302
+00:31:36,260 --> 00:31:44,500
+اعمل عملية واحد اتنين تلاتة واحد للتانين تانين
+
+303
+00:31:44,500 --> 00:31:48,380
+للتلاتة واحد للتلاتة تانين للتلاتة و تلاتة للتانين
+
+304
+00:31:48,380 --> 00:31:52,400
+نجمة تانين للتانين تلاتة للواحد هذا أنصار جديد ولا
+
+305
+00:31:52,400 --> 00:31:59,390
+لأ؟بدا نضمن انه مافيش تكرار يعني المفروض احنا
+
+306
+00:31:59,390 --> 00:32:02,870
+هالجيت Alpha Beta المفروض انا احسب Alpha تغبيه
+
+307
+00:32:02,870 --> 00:32:06,350
+Beta Alpha
+
+308
+00:32:06,350 --> 00:32:12,250
+تغبيه Beta عبارة عن ايش ال Alpha تغبيه؟ واحد اتنين
+
+309
+00:32:12,250 --> 00:32:19,630
+تلاتة ايه؟ تلاتة واحد اتنين واحد اتنين تلاتة وال
+
+310
+00:32:19,630 --> 00:32:22,310
+Beta عبارة عن واحد تلاتة اتنين تحسب
+
+311
+00:32:25,380 --> 00:32:30,200
+واحد ل واحد و واحد ل تلاتة تنين ل تلاتة اتنين و
+
+312
+00:32:30,200 --> 00:32:34,700
+تلاتة ل اتنين اللي هو ال main بيتا الفا ايش يعني
+
+313
+00:32:34,700 --> 00:32:43,080
+يعني الف تربية بيتا سوا بيتا الفا يعني انص و واحد
+
+314
+00:32:43,080 --> 00:32:54,200
+يعني كم انص عندي هنا انا
+
+315
+00:32:54,200 --> 00:32:54,280
+انا انا انا انا انا انا انا انا انا انا انا انا
+
+316
+00:32:54,280 --> 00:32:55,370
+انا انا انا انا انا انا انا انا انا افيه ال
+
+317
+00:32:55,370 --> 00:33:00,890
+identity وفيه ال alpha وفيه ال alpha تغبيه وفيه ال
+
+318
+00:33:00,890 --> 00:33:07,190
+beta وفيه ال alpha beta وفيه ال alpha تغبيه beta
+
+319
+00:33:07,190 --> 00:33:21,150
+ال S3 فيها كمنصر ست عناصر زي ما انت شايف طيب
+
+320
+00:33:24,580 --> 00:33:27,820
+أيش أهمية القاعدة اللي انا حطيتها غير دي أنه Alpha
+
+321
+00:33:27,820 --> 00:33:33,420
+تربيع Beta بيسوا Beta Alpha؟
+
+322
+00:33:33,420 --> 00:33:38,260
+ايش أهميتها؟
+
+323
+00:33:38,260 --> 00:33:41,440
+هي
+
+324
+00:33:41,440 --> 00:33:46,400
+الأهمية أنا ماكتبتها عبثا يعني أهميتها أنه أنا لما
+
+325
+00:33:46,400 --> 00:33:51,600
+بدي أجي أضغط Powers تانيينهيجيب كل ال powers ال
+
+326
+00:33:51,600 --> 00:33:55,780
+alpha كبير و اتنين و ال beta كبير و واحد يعني
+
+327
+00:33:55,780 --> 00:34:00,760
+alpha تقريب يعني على ال identity و beta تقريب على
+
+328
+00:34:00,760 --> 00:34:07,280
+ال identity تخيل مثلا انا بدي اضرب alpha beta مثلا
+
+329
+00:34:07,280 --> 00:34:13,220
+alpha beta بدي اضربه في alpha تقريب من beta هذا
+
+330
+00:34:13,220 --> 00:34:19,180
+ايش بدي اساوي هذا عبارة عنفى betaف Beta Alpha يعني
+
+331
+00:34:19,180 --> 00:34:24,480
+Alpha Beta تربية طبعا هذه عملية composition وهي
+
+332
+00:34:24,480 --> 00:34:28,720
+associative Beta تربية يبقى بعناش يعني Alpha
+
+333
+00:34:28,720 --> 00:34:34,480
+Identity Alpha Alpha تربية يعني انا لو بدي اعمل
+
+334
+00:34:34,480 --> 00:34:39,100
+هنا multiplication table بقدر من خلال العلاقة هذه
+
+335
+00:34:39,100 --> 00:34:47,320
+انا احصل بهذا الشكل هي ال identity هي ال Alphaهي
+
+336
+00:34:47,320 --> 00:34:52,960
+ال alpha تربيع هى ال beta هى ال beta تربيع او ال
+
+337
+00:34:52,960 --> 00:34:57,280
+alpha beta تربيع او ال alpha beta قصدي و alpha
+
+338
+00:34:57,280 --> 00:35:03,620
+تربيع beta وهنا ال identity وهنا ال alpha وهنا ال
+
+339
+00:35:03,620 --> 00:35:08,580
+alpha تربيع وحط هنا ال alpha beta او ال beta في
+
+340
+00:35:08,580 --> 00:35:15,180
+الأول و ال alpha beta و ال alpha تربيع beta وكمل
+
+341
+00:35:15,180 --> 00:35:15,620
+الجدول
+
+342
+00:35:18,300 --> 00:35:23,640
+تعالى نشوف مش هيطلع معايا طب ال identity نفس
+
+343
+00:35:23,640 --> 00:35:35,560
+العناصر عملت
+
+344
+00:35:35,560 --> 00:35:41,960
+ضغم اللي هو صف بعدين عمود هجت ألفة في ألفة ألفة في
+
+345
+00:35:41,960 --> 00:35:49,810
+ألفة ألف تربيع ألفة في ألف تربيعidentity Alpha في
+
+346
+00:35:49,810 --> 00:35:56,410
+Beta Alpha Beta Alpha في Alpha Beta Alpha تربيع
+
+347
+00:35:56,410 --> 00:36:02,450
+Beta Alpha في Alpha تربيع Beta Alpha تكييب Beta
+
+348
+00:36:02,450 --> 00:36:09,300
+Identity في Beta Beta Alpha تربيع في Alphaidentity
+
+349
+00:36:09,300 --> 00:36:13,180
+ألفة تربية في ألفة تربية ألفة أقصر أربعة أربعة
+
+350
+00:36:13,180 --> 00:36:14,180
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+351
+00:36:14,180 --> 00:36:14,440
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+352
+00:36:14,440 --> 00:36:16,300
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+353
+00:36:16,300 --> 00:36:20,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+354
+00:36:20,360 --> 00:36:22,680
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+355
+00:36:22,680 --> 00:36:24,120
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+356
+00:36:24,120 --> 00:36:28,080
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+357
+00:36:28,080 --> 00:36:37,820
+أرب
+
+358
+00:36:38,830 --> 00:36:51,650
+بيتا ألفة بقالها معايا حاجة بيتا عبارة
+
+359
+00:36:51,650 --> 00:36:56,530
+عن بيتا ألفة ألفة عبارة عن بيتا ألفة عبارة عن أيش
+
+360
+00:36:56,530 --> 00:37:04,050
+ألفة تربية بيتا عبارة عن ألف تربية في ألف تربية
+
+361
+00:37:04,050 --> 00:37:06,950
+بيتا يعني ألف بيتا
+
+362
+00:37:10,200 --> 00:37:14,920
+Beta في Beta Identity
+
+363
+00:37:14,920 --> 00:37:22,000
+Beta في Alpha Beta عبارة عن ايش؟ عبارة عن Alpha
+
+364
+00:37:22,000 --> 00:37:25,460
+تربية Beta في Beta يعني Alpha تربية في ال identity
+
+365
+00:37:25,460 --> 00:37:33,360
+يعني Alpha تربية مين ضال هان؟ ضال ال Alpha طيب
+
+366
+00:37:33,360 --> 00:37:38,880
+Alpha Beta في Alpha وين؟
+
+367
+00:37:48,030 --> 00:37:54,210
+مش فاهمش .. اه .. صحيح
+
+368
+00:37:54,210 --> 00:38:01,690
+.. صحيح .. صحيح .. احنا .. لأ انت خربطني يا شيخ ..
+
+369
+00:38:01,690 --> 00:38:04,250
+صحيح .. بيتا ألفة تربيع .. يعني بيتا ألفة في ألفة
+
+370
+00:38:04,250 --> 00:38:08,250
+.. هذه ألفة .. ألفة تربيع بيتا .. لأ بيصيح ألف
+
+371
+00:38:08,250 --> 00:38:12,560
+تكييب في بيتها .. كل المسلمينهجيت الـ Alpha Beta
+
+372
+00:38:12,560 --> 00:38:17,160
+هادي عبارة عن Alpha تربيع في Beta يعني Alpha أُص
+
+373
+00:38:17,160 --> 00:38:21,680
+أربع في Beta يعني Alpha Beta مين؟
+
+374
+00:38:21,680 --> 00:38:27,440
+في واحدة عملناها اللي بيتا Alpha Beta عبارة عن
+
+375
+00:38:27,440 --> 00:38:34,380
+Alpha تربيع Beta في Beta بتساوي Alpha تربيع مين
+
+376
+00:38:34,380 --> 00:38:39,920
+جاي يعني انها هجيت Alpha Beta في Alpha عبارة عن
+
+377
+00:38:39,920 --> 00:38:47,660
+بدّل هاديBeta Alpha Alpha في Alpha تربيع Beta اللي
+
+378
+00:38:47,660 --> 00:38:58,560
+هي Beta طبعا Alpha Beta في Alpha تربيع عبارة
+
+379
+00:38:58,560 --> 00:39:05,000
+عن أيش Alpha Beta Alpha في Alpha اللي عبارة عن
+
+380
+00:39:05,000 --> 00:39:09,180
+Alpha Alpha تربيع Beta في Alpha عبارة عن Beta
+
+381
+00:39:09,180 --> 00:39:14,170
+Alpha Beta Alpha عبارة عن أيشAlpha تربيع Beta
+
+382
+00:39:14,170 --> 00:39:18,550
+Alpha
+
+383
+00:39:18,550 --> 00:39:23,250
+في Beta في Beta Alpha Alpha Beta في Alpha Beta
+
+384
+00:39:23,250 --> 00:39:26,630
+Alpha
+
+385
+00:39:26,630 --> 00:39:34,170
+Beta Alpha تربيع Alpha Beta Alpha Alpha
+
+386
+00:39:34,170 --> 00:39:36,730
+Beta Alpha Alpha Beta Alpha Alpha Alpha Alpha
+
+387
+00:39:36,730 --> 00:39:38,250
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+388
+00:39:38,250 --> 00:39:40,910
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+389
+00:39:40,910 --> 00:39:41,130
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+390
+00:39:41,130 --> 00:39:41,410
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+391
+00:39:41,410 --> 00:39:41,430
+Alpha Alpha Alpha Alpha Alpha Alpha Alpha Alpha
+
+392
+00:39:41,430 --> 00:39:46,460
+Alpha Alpha Alphaتنتين هدول بيتا
+
+393
+00:39:46,460 --> 00:39:51,880
+ألف عبارة عن ألف تربيه بيتا بيتا
+
+394
+00:39:51,880 --> 00:39:56,040
+ألف عبارة عن ألف تربيه بيتا ألف ألف مع ألف تربيه
+
+395
+00:39:56,040 --> 00:40:00,380
+identity و بيتا ألف بيظل طبعا الجواب أنها ألف
+
+396
+00:40:00,380 --> 00:40:07,940
+تربيه بيتا ألف بيتا في ألف بيتا عبارة عن ألف ألف
+
+397
+00:40:07,940 --> 00:40:10,100
+تربيه بيتا بيتا بي سوى ال identity
+
+398
+00:40:12,800 --> 00:40:16,640
+و أنا هيظل alpha تربيع طبعا تقدر تكمل الجدول هجت
+
+399
+00:40:16,640 --> 00:40:22,300
+لحالك أنا هيكون identity و أنا alpha أنا alpha
+
+400
+00:40:22,300 --> 00:40:32,160
+تربيع و أنا beta و أنا alpha beta طبعا
+
+401
+00:40:32,160 --> 00:40:35,300
+we
+
+402
+00:40:35,300 --> 00:40:41,020
+will show later that
+
+403
+00:40:43,140 --> 00:40:56,800
+S3 and D3 is the same thing
+
+404
+00:40:56,800 --> 00:41:00,200
+ماشي
+
+405
+00:41:00,200 --> 00:41:05,960
+نفس الحاجة يعطيكوا العفو يا شباب
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d47a052673ce940ce5baa0be72de4beef0db3f32
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/MDWmOYiQ1Mk_raw.json
@@ -0,0 +1 @@
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"text": "definition C4 مش الاسفار دي واحد a permutation of a set A زي ما قلنا is a function", "tokens": [1479, 5194, 849, 383, 19, 37893, 2423, 32277, 5172, 9640, 11778, 1829, 36764, 24401, 257, 4784, 11380, 295, 257, 992, 316, 30767, 1829, 19446, 12174, 1211, 8315, 307, 257, 2445], "avg_logprob": -0.34576613095498854, "compression_ratio": 1.0194174757281553, "no_speech_prob": 0.0, "words": [{"start": 652.8900000000001, "end": 654.0500000000001, "word": "definition", "probability": 0.7007242838541666}, {"start": 654.0500000000001, "end": 655.21, "word": " C4", "probability": 0.7174072265625}, {"start": 655.21, "end": 655.35, "word": " مش", "probability": 0.478515625}, {"start": 655.35, "end": 655.87, "word": " الاسفار", "probability": 0.703887939453125}, {"start": 655.87, "end": 656.19, "word": " دي", "probability": 0.818115234375}, {"start": 656.19, "end": 659.99, "word": " واحد", "probability": 0.795166015625}, {"start": 659.99, "end": 660.49, "word": " a", "probability": 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is both one to one and unto كلمة واحدة يعنيش projection تانين الـPermutation group", "tokens": [20579, 316, 281, 316, 300, 307, 1293, 472, 281, 472, 293, 16521, 9122, 19528, 3660, 36764, 24401, 3660, 37495, 22653, 8592, 22743, 6055, 7649, 9957, 2423, 39184, 47, 966, 11380, 1594], "avg_logprob": -0.4047851599752903, "compression_ratio": 1.0707964601769913, "no_speech_prob": 0.0, "words": [{"start": 676.04, "end": 676.6, "word": "from", "probability": 0.5126953125}, {"start": 676.6, "end": 678.22, "word": " A", "probability": 0.56103515625}, {"start": 678.22, "end": 679.7, "word": " to", "probability": 0.94677734375}, {"start": 679.7, "end": 680.12, "word": " A", "probability": 0.95947265625}, {"start": 680.12, "end": 681.36, "word": " that", "probability": 0.603515625}, {"start": 681.36, "end": 684.08, "word": " is", "probability": 0.94384765625}, {"start": 684.08, "end": 685.28, "word": " both", "probability": 0.75732421875}, {"start": 685.28, "end": 688.28, "word": " one", 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"probability": 0.70928955078125}, {"start": 723.75, "end": 724.09, "word": " ضمن", "probability": 0.98388671875}, {"start": 724.09, "end": 724.85, "word": " ال", "probability": 0.828125}, {"start": 724.85, "end": 725.13, "word": " group", "probability": 0.9833984375}, {"start": 725.13, "end": 725.69, "word": " ال", "probability": 0.9814453125}, {"start": 725.69, "end": 726.25, "word": " permutation", "probability": 0.77490234375}, {"start": 726.25, "end": 726.81, "word": " group", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 27, "seek": 75374, "start": 728.9, "end": 753.74, "text": "عبارة عن جروب طبعا تحت عملية ال composition العناصر اللي فيها عبارة عن permutation على مجموعة ما permutation group of asset permutation group of asset a is", "tokens": [3615, 3555, 9640, 3660, 18871, 10874, 32887, 3555, 23032, 3555, 3615, 995, 6055, 33753, 6225, 42213, 10632, 2423, 12686, 18863, 1863, 33546, 2288, 13672, 1829, 8978, 11296, 6225, 3555, 9640, 3660, 18871, 4784, 11380, 15844, 3714, 7435, 2304, 2407, 27884, 19446, 4784, 11380, 1594, 295, 11999, 4784, 11380, 1594, 295, 11999, 257, 307], "avg_logprob": -0.20037616347825085, "compression_ratio": 1.5547445255474452, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 728.9, "end": 729.48, "word": "عبارة", "probability": 0.78387451171875}, {"start": 729.48, "end": 730.28, "word": " عن", "probability": 0.9951171875}, {"start": 730.28, "end": 731.02, "word": " جروب", "probability": 0.7294108072916666}, {"start": 731.02, "end": 732.1, "word": " طبعا", "probability": 0.832763671875}, {"start": 732.1, "end": 732.78, "word": " تحت", "probability": 0.98486328125}, {"start": 732.78, "end": 733.24, "word": " عملية", "probability": 0.98583984375}, {"start": 733.24, "end": 733.42, "word": " ال", "probability": 0.90234375}, {"start": 733.42, "end": 733.88, "word": " composition", "probability": 0.6357421875}, {"start": 733.88, "end": 735.18, "word": " العناصر", "probability": 0.9283447265625}, {"start": 735.18, "end": 735.34, "word": " اللي", "probability": 0.84521484375}, {"start": 735.34, "end": 735.76, "word": " فيها", "probability": 0.964599609375}, {"start": 735.76, "end": 736.2, "word": " عبارة", "probability": 0.9859619140625}, {"start": 736.2, "end": 736.36, "word": " عن", "probability": 0.98486328125}, {"start": 736.36, "end": 736.9, "word": " permutation", "probability": 0.911865234375}, {"start": 736.9, "end": 737.18, "word": " على", "probability": 0.7333984375}, {"start": 737.18, "end": 737.7, "word": " مجموعة", "probability": 0.890771484375}, {"start": 737.7, "end": 737.9, "word": " ما", "probability": 0.77099609375}, {"start": 737.9, "end": 739.06, "word": " permutation", "probability": 0.60382080078125}, {"start": 739.06, "end": 739.62, "word": " group", "probability": 0.30419921875}, {"start": 739.62, "end": 740.84, "word": " of", "probability": 0.90478515625}, {"start": 740.84, "end": 747.32, "word": " asset", "probability": 0.744140625}, {"start": 747.32, "end": 749.1, "word": " permutation", "probability": 0.9248046875}, {"start": 749.1, "end": 749.48, "word": " group", "probability": 0.97900390625}, {"start": 749.48, "end": 749.68, "word": " of", "probability": 0.97802734375}, {"start": 749.68, "end": 750.34, "word": " asset", "probability": 0.90576171875}, {"start": 750.34, "end": 753.34, "word": " a", "probability": 0.5732421875}, {"start": 753.34, "end": 753.74, "word": " is", "probability": 0.890625}], "temperature": 1.0}, {"id": 28, "seek": 78901, "start": 760.67, "end": 789.01, "text": "asset of permutations on a that form a group under function composition", "tokens": [640, 302, 295, 4784, 325, 763, 322, 257, 300, 1254, 257, 1594, 833, 2445, 12686], "avg_logprob": -0.26489258743822575, "compression_ratio": 1.109375, "no_speech_prob": 0.0, "words": [{"start": 760.6700000000001, "end": 762.07, "word": "asset", "probability": 0.488128662109375}, {"start": 762.07, "end": 763.47, "word": " of", "probability": 0.939453125}, {"start": 763.47, "end": 765.15, "word": " permutations", "probability": 0.9384765625}, {"start": 765.15, "end": 769.47, "word": " on", "probability": 0.90185546875}, {"start": 769.47, "end": 769.99, "word": " a", "probability": 0.493896484375}, {"start": 769.99, "end": 772.83, "word": " that", "probability": 0.85546875}, {"start": 772.83, "end": 775.45, "word": " form", "probability": 0.93896484375}, {"start": 775.45, "end": 778.05, "word": " a", "probability": 0.97265625}, {"start": 778.05, "end": 778.61, "word": " group", "probability": 0.98095703125}, {"start": 778.61, "end": 782.79, "word": " under", "probability": 0.8994140625}, {"start": 782.79, "end": 786.51, "word": " function", "probability": 0.9599609375}, {"start": 786.51, "end": 789.01, "word": " composition", "probability": 0.919921875}], "temperature": 1.0}, {"id": 29, "seek": 82148, "start": 797.16, "end": 821.48, "text": "عبارة عن مجموعة بتعمل جروب مع عملية تركيب الدولة في هذا ال chapter we study here the case where a is finite", "tokens": [3615, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 39894, 25957, 1211, 10874, 32887, 3555, 20449, 6225, 42213, 10632, 6055, 31747, 1829, 3555, 32748, 12610, 3660, 8978, 23758, 2423, 7187, 321, 2979, 510, 264, 1389, 689, 257, 307, 19362], "avg_logprob": -0.14662728077027856, "compression_ratio": 1.2222222222222223, "no_speech_prob": 0.0, "words": [{"start": 797.16, "end": 797.7, "word": "عبارة", "probability": 0.97998046875}, {"start": 797.7, "end": 798.28, "word": " عن", "probability": 0.99658203125}, {"start": 798.28, "end": 802.38, "word": " مجموعة", "probability": 0.94619140625}, {"start": 802.38, "end": 803.54, "word": " بتعمل", "probability": 0.9734700520833334}, {"start": 803.54, "end": 804.16, "word": " جروب", "probability": 0.7696940104166666}, {"start": 804.16, "end": 804.84, "word": " مع", "probability": 0.9951171875}, {"start": 804.84, "end": 805.5, "word": " عملية", "probability": 0.9899088541666666}, {"start": 805.5, "end": 806.5, "word": " تركيب", "probability": 0.97607421875}, {"start": 806.5, "end": 808.06, "word": " الدولة", "probability": 0.6460774739583334}, {"start": 808.06, "end": 808.32, "word": " في", "probability": 0.82177734375}, {"start": 808.32, "end": 808.58, "word": " هذا", "probability": 0.96044921875}, {"start": 808.58, "end": 808.7, "word": " ال", "probability": 0.634765625}, {"start": 808.7, "end": 809.02, "word": " chapter", "probability": 0.85693359375}, {"start": 809.02, "end": 810.72, "word": " we", "probability": 0.599609375}, {"start": 810.72, "end": 813.2, "word": " study", "probability": 0.98095703125}, {"start": 813.2, "end": 814.5, "word": " here", "probability": 0.7216796875}, {"start": 814.5, "end": 816.08, "word": " the", "probability": 0.86669921875}, {"start": 816.08, "end": 816.8, "word": " case", "probability": 0.9521484375}, {"start": 816.8, "end": 818.24, "word": " where", "probability": 0.953125}, {"start": 818.24, "end": 820.44, "word": " a", "probability": 0.7265625}, {"start": 820.44, "end": 821.04, "word": " is", "probability": 0.9091796875}, {"start": 821.04, "end": 821.48, "word": " finite", "probability": 0.98876953125}], "temperature": 1.0}, {"id": 30, "seek": 84388, "start": 823.16, "end": 843.88, "text": "يعني في مصراخنا شباب هندرس الحالة اللي بيكون فيها المجموعة مثال ناخد مثال على permutation و بعد هيك ناخد مثال على permutation الجرم كيف؟", "tokens": [40228, 22653, 8978, 3714, 9381, 23557, 9778, 8315, 13412, 3555, 16758, 8032, 1863, 3215, 2288, 3794, 21542, 6027, 3660, 13672, 1829, 4724, 1829, 30544, 8978, 11296, 9673, 7435, 2304, 2407, 27884, 50113, 6027, 8717, 47283, 3215, 50113, 6027, 15844, 4784, 11380, 4032, 39182, 39896, 4117, 8717, 47283, 3215, 50113, 6027, 15844, 4784, 11380, 25724, 2288, 2304, 9122, 33911, 22807], "avg_logprob": -0.1623697931567828, "compression_ratio": 1.5763888888888888, "no_speech_prob": 0.0, "words": [{"start": 823.16, "end": 823.42, "word": "يعني", "probability": 0.71728515625}, {"start": 823.42, "end": 823.56, "word": " في", "probability": 0.900390625}, {"start": 823.56, "end": 824.08, "word": " مصراخنا", "probability": 0.77529296875}, {"start": 824.08, "end": 824.52, "word": " شباب", "probability": 0.87548828125}, {"start": 824.52, "end": 826.06, "word": " هندرس", "probability": 0.8248046875}, {"start": 826.06, "end": 827.02, "word": " الحالة", "probability": 0.9850260416666666}, {"start": 827.02, "end": 827.12, "word": " اللي", "probability": 0.81298828125}, {"start": 827.12, "end": 827.44, "word": " بيكون", "probability": 0.94384765625}, {"start": 827.44, "end": 827.72, "word": " فيها", "probability": 0.98388671875}, {"start": 827.72, "end": 828.66, "word": " المجموعة", "probability": 0.93857421875}, {"start": 828.66, "end": 829.86, "word": " مثال", "probability": 0.87255859375}, {"start": 829.86, "end": 833.2, "word": " ناخد", "probability": 0.9375}, {"start": 833.2, "end": 833.46, "word": " مثال", "probability": 0.96533203125}, {"start": 833.46, "end": 833.6, "word": " على", "probability": 0.853515625}, {"start": 833.6, "end": 834.2, "word": " permutation", "probability": 0.9345703125}, {"start": 834.2, "end": 835.6, "word": " و", "probability": 0.607421875}, {"start": 835.6, "end": 835.88, "word": " بعد", "probability": 0.9248046875}, {"start": 835.88, "end": 836.38, "word": " هيك", "probability": 0.95458984375}, {"start": 836.38, "end": 837.56, "word": " ناخد", "probability": 0.9915364583333334}, {"start": 837.56, "end": 837.86, "word": " مثال", "probability": 0.9404296875}, {"start": 837.86, "end": 838.16, "word": " على", "probability": 0.876953125}, {"start": 838.16, "end": 839.38, "word": " permutation", "probability": 0.982421875}, {"start": 839.38, "end": 840.56, "word": " الجرم", "probability": 0.4683430989583333}, {"start": 840.56, "end": 843.88, "word": " كيف؟", "probability": 0.8678385416666666}], "temperature": 1.0}, {"id": 31, "seek": 86238, "start": 845.44, "end": 862.38, "text": "لأ في هذا المثال تحديدًا هنشتغل يعني ال A عبارة عن واحد اتنين تلاتة لعند N طبعًا انا شراحت في البداية ليش اخترت واحد اتنين تلاتة لعند N لو كان بدل واحد اتنين تلاتة A واحد اتنين لعند AN نفس الخصائص الموجودة", "tokens": [1211, 10721, 8978, 23758, 9673, 12984, 6027, 6055, 5016, 16254, 3215, 14111, 995, 8032, 1863, 8592, 2655, 17082, 1211, 37495, 22653, 2423, 316, 6225, 3555, 9640, 3660, 18871, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 5296, 3615, 41260, 426, 23032, 3555, 3615, 14111, 995, 1975, 8315, 13412, 23557, 33753, 8978, 29739, 28259, 10632, 32239, 8592, 1975, 46456, 43500, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 5296, 3615, 41260, 426, 45164, 25961, 47525, 1211, 36764, 24401, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 316, 36764, 24401, 1975, 2655, 1863, 9957, 5296, 3615, 41260, 5252, 8717, 36178, 33962, 9381, 16373, 9381, 9673, 29245, 23328, 3660], "avg_logprob": -0.17511260804829296, "compression_ratio": 2.0625, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 845.44, "end": 845.7, "word": 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"probability": 0.9324951171875}, {"start": 850.96, "end": 851.66, "word": " تلاتة", "probability": 0.933349609375}, {"start": 851.66, "end": 852.26, "word": " لعند", "probability": 0.7960611979166666}, {"start": 852.26, "end": 852.44, "word": " N", "probability": 0.5244140625}, {"start": 852.44, "end": 853.54, "word": " طبعًا", "probability": 0.88212890625}, {"start": 853.54, "end": 853.78, "word": " انا", "probability": 0.75244140625}, {"start": 853.78, "end": 854.16, "word": " شراحت", "probability": 0.8269856770833334}, {"start": 854.16, "end": 854.26, "word": " في", "probability": 0.88671875}, {"start": 854.26, "end": 854.68, "word": " البداية", "probability": 0.98046875}, {"start": 854.68, "end": 854.9, "word": " ليش", "probability": 0.940673828125}, {"start": 854.9, "end": 855.22, "word": " اخترت", "probability": 0.8429361979166666}, {"start": 855.22, "end": 855.42, "word": " واحد", "probability": 0.92138671875}, {"start": 855.42, "end": 855.64, "word": " اتنين", "probability": 0.978759765625}, {"start": 855.64, "end": 855.98, "word": " تلاتة", "probability": 0.99169921875}, {"start": 855.98, "end": 856.22, "word": " لعند", "probability": 0.9661458333333334}, {"start": 856.22, "end": 856.42, "word": " N", "probability": 0.83837890625}, {"start": 856.42, "end": 857.02, "word": " لو", "probability": 0.92333984375}, {"start": 857.02, "end": 857.26, "word": " كان", "probability": 0.98681640625}, {"start": 857.26, "end": 857.54, "word": " بدل", "probability": 0.96435546875}, {"start": 857.54, "end": 857.86, "word": " واحد", "probability": 0.969482421875}, {"start": 857.86, "end": 858.12, "word": " اتنين", "probability": 0.984619140625}, {"start": 858.12, "end": 858.46, "word": " تلاتة", "probability": 0.9940185546875}, {"start": 858.46, "end": 858.58, "word": " A", "probability": 0.46337890625}, {"start": 858.58, "end": 858.9, "word": " واحد", "probability": 0.85546875}, {"start": 858.9, "end": 859.32, "word": " اتنين", "probability": 0.8040771484375}, {"start": 859.32, "end": 859.64, "word": " لعند", "probability": 0.9376627604166666}, {"start": 859.64, "end": 860.04, "word": " AN", "probability": 0.482177734375}, {"start": 860.04, "end": 860.86, "word": " نفس", "probability": 0.97998046875}, {"start": 860.86, "end": 861.58, "word": " الخصائص", "probability": 0.9896240234375}, {"start": 861.58, "end": 862.38, "word": " الموجودة", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 32, "seek": 89273, "start": 863.63, "end": 892.73, "text": "ممكن تكون موجودة على المجموعة من واحد لاتنين لتلاتة لعندان هي هي انا مش هاهتم كتير عنصر ايش قيمته بدي انا هان خصائص اللي هي التبديل على هذه العناصر فبختار مجموعة سهلة عشان اقدر اتعامل اتكون الكتوبة اسهل طيب ناخد ال اتش اولدت ال ايه عبارة عن الواحد واتنين وتلاتة واربعة", "tokens": [2304, 43020, 6055, 30544, 3714, 29245, 23328, 3660, 15844, 9673, 7435, 2304, 2407, 27884, 9154, 36764, 24401, 5296, 9307, 1863, 9957, 5296, 2655, 1211, 9307, 3660, 5296, 3615, 41260, 7649, 39896, 39896, 1975, 8315, 37893, 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864.39, "end": 864.79, "word": " موجودة", "probability": 0.9793701171875}, {"start": 864.79, "end": 864.97, "word": " على", "probability": 0.8955078125}, {"start": 864.97, "end": 865.57, "word": " المجموعة", "probability": 0.863818359375}, {"start": 865.57, "end": 865.71, "word": " من", "probability": 0.9208984375}, {"start": 865.71, "end": 865.99, "word": " واحد", "probability": 0.5994873046875}, {"start": 865.99, "end": 866.33, "word": " لاتنين", "probability": 0.7786865234375}, {"start": 866.33, "end": 867.49, "word": " لتلاتة", "probability": 0.8384765625}, {"start": 867.49, "end": 867.97, "word": " لعندان", "probability": 0.704833984375}, {"start": 867.97, "end": 868.53, "word": " هي", "probability": 0.20263671875}, {"start": 868.53, "end": 868.87, "word": " هي", "probability": 0.76416015625}, {"start": 868.87, "end": 869.49, "word": " انا", "probability": 0.659423828125}, {"start": 869.49, "end": 869.67, "word": " مش", "probability": 0.98876953125}, {"start": 869.67, "end": 870.79, "word": " هاهتم", "probability": 0.7491861979166666}, {"start": 870.79, "end": 871.31, "word": " كتير", "probability": 0.970703125}, {"start": 871.31, "end": 871.79, "word": " عنصر", "probability": 0.7157389322916666}, {"start": 871.79, "end": 871.93, "word": " ايش", "probability": 0.7338053385416666}, {"start": 871.93, "end": 872.39, "word": " قيمته", "probability": 0.9913736979166666}, {"start": 872.39, "end": 873.25, "word": " بدي", "probability": 0.61199951171875}, {"start": 873.25, "end": 873.45, "word": " انا", "probability": 0.760498046875}, {"start": 873.45, "end": 873.67, "word": " هان", "probability": 0.838623046875}, {"start": 873.67, "end": 874.41, "word": " خصائص", "probability": 0.9542236328125}, {"start": 874.41, "end": 874.91, "word": " اللي", "probability": 0.797119140625}, {"start": 874.91, "end": 875.27, "word": " هي", "probability": 0.81005859375}, {"start": 875.27, "end": 876.03, "word": " التبديل", "probability": 0.8583984375}, {"start": 876.03, "end": 876.57, "word": " على", "probability": 0.79833984375}, {"start": 876.57, "end": 876.83, "word": " هذه", "probability": 0.88623046875}, {"start": 876.83, "end": 877.37, "word": " العناصر", "probability": 0.899658203125}, {"start": 877.37, "end": 878.15, "word": " فبختار", "probability": 0.883056640625}, {"start": 878.15, "end": 878.61, "word": " مجموعة", "probability": 0.9451171875}, {"start": 878.61, "end": 879.37, "word": " سهلة", "probability": 0.9803059895833334}, {"start": 879.37, "end": 879.63, "word": " عشان", "probability": 0.9879557291666666}, {"start": 879.63, "end": 880.05, "word": " اقدر", "probability": 0.8447265625}, {"start": 880.05, "end": 881.71, "word": " اتعامل", "probability": 0.909375}, {"start": 881.71, "end": 882.95, "word": " اتكون", "probability": 0.8024088541666666}, {"start": 882.95, "end": 883.57, "word": " الكتوبة", "probability": 0.8944091796875}, {"start": 883.57, "end": 884.71, "word": " اسهل", "probability": 0.85302734375}, {"start": 884.71, "end": 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"word": " واربعة", "probability": 0.872802734375}], "temperature": 1.0}, {"id": 33, "seek": 91714, "start": 894.0, "end": 917.14, "text": "let alpha من a ل a be given as alpha الواحد بدي ساوي تلاتة الف اتنين بدي ساوي واحد الف التلاتة بدي تساوي أربعة والف الأربعة بدي تساوي اتنين", "tokens": [2631, 8961, 9154, 257, 5296, 257, 312, 2212, 382, 8961, 2423, 14407, 24401, 4724, 16254, 8608, 995, 45865, 6055, 1211, 9307, 3660, 27188, 1975, 2655, 1863, 9957, 4724, 16254, 8608, 995, 45865, 36764, 24401, 27188, 16712, 1211, 9307, 3660, 4724, 16254, 6055, 3794, 995, 45865, 5551, 25513, 27884, 4032, 6027, 5172, 16247, 25513, 27884, 4724, 16254, 6055, 3794, 995, 45865, 1975, 2655, 1863, 9957], "avg_logprob": -0.29134615384615387, "compression_ratio": 1.8373983739837398, "no_speech_prob": 0.0, "words": [{"start": 894.0, "end": 894.48, "word": "let", "probability": 0.34814453125}, {"start": 894.48, "end": 895.86, "word": " alpha", "probability": 0.41748046875}, {"start": 895.86, "end": 896.88, "word": " من", "probability": 0.92578125}, {"start": 896.88, "end": 897.16, "word": " a", "probability": 0.603515625}, {"start": 897.16, "end": 897.32, "word": " ل", "probability": 0.81884765625}, {"start": 897.32, "end": 897.68, "word": " a", "probability": 0.90625}, {"start": 897.68, "end": 898.98, "word": " be", "probability": 0.480224609375}, {"start": 898.98, "end": 900.28, "word": " given", "probability": 0.7919921875}, {"start": 900.28, "end": 902.2, "word": " as", "probability": 0.94921875}, {"start": 902.2, "end": 903.3, "word": " alpha", "probability": 0.5029296875}, {"start": 903.3, "end": 903.88, "word": " الواحد", "probability": 0.9435221354166666}, {"start": 903.88, "end": 904.16, "word": " بدي", "probability": 0.5263671875}, {"start": 904.16, "end": 904.44, "word": " ساوي", "probability": 0.4712727864583333}, {"start": 904.44, "end": 905.06, "word": " تلاتة", "probability": 0.915283203125}, {"start": 905.06, "end": 905.8, "word": " الف", "probability": 0.245849609375}, {"start": 905.8, "end": 906.16, "word": " اتنين", "probability": 0.8743896484375}, {"start": 906.16, "end": 906.36, "word": " بدي", "probability": 0.94970703125}, {"start": 906.36, "end": 906.68, "word": " ساوي", "probability": 0.9191080729166666}, {"start": 906.68, "end": 907.2, "word": " واحد", "probability": 0.978759765625}, {"start": 907.2, "end": 907.92, "word": " الف", "probability": 0.740234375}, {"start": 907.92, "end": 908.46, "word": " التلاتة", "probability": 0.8695068359375}, {"start": 908.46, "end": 908.62, "word": " بدي", "probability": 0.758544921875}, {"start": 908.62, "end": 908.96, "word": " تساوي", "probability": 0.8653564453125}, {"start": 908.96, "end": 909.6, "word": " أربعة", "probability": 0.7224934895833334}, {"start": 909.6, "end": 912.64, "word": " والف", "probability": 0.5511881510416666}, {"start": 912.64, "end": 913.9, "word": " الأربعة", "probability": 0.8684895833333334}, {"start": 913.9, "end": 914.1, "word": " بدي", "probability": 0.834716796875}, {"start": 914.1, "end": 914.44, "word": " تساوي", "probability": 0.9693603515625}, {"start": 914.44, "end": 917.14, "word": " اتنين", "probability": 0.961181640625}], "temperature": 1.0}, {"id": 34, "seek": 94810, "start": 921.68, "end": 948.1, "text": "بيتا من a ل a be given as بيتا التنين او بيتا الواحد بدت ساوي واحد بيتا التنين بدت ساوي تلاتة بيتا التلاتة بدت ساوي أربعة و بيتا الأربعة بدت ساوي اتنين هيتوا functions clearly", "tokens": [3555, 36081, 995, 9154, 257, 5296, 257, 312, 2212, 382, 4724, 36081, 995, 16712, 1863, 9957, 1975, 2407, 4724, 36081, 995, 2423, 14407, 24401, 47525, 2655, 8608, 995, 45865, 36764, 24401, 4724, 36081, 995, 16712, 1863, 9957, 47525, 2655, 8608, 995, 45865, 6055, 1211, 9307, 3660, 4724, 36081, 995, 16712, 1211, 9307, 3660, 47525, 2655, 8608, 995, 45865, 5551, 25513, 27884, 4032, 4724, 36081, 995, 16247, 25513, 27884, 47525, 2655, 8608, 995, 45865, 1975, 2655, 1863, 9957, 8032, 36081, 14407, 6828, 4448], "avg_logprob": -0.24868223466068864, "compression_ratio": 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"probability": 0.919189453125}, {"start": 939.86, "end": 940.26, "word": " ساوي", "probability": 0.96240234375}, {"start": 940.26, "end": 941.54, "word": " أربعة", "probability": 0.7669270833333334}, {"start": 941.54, "end": 942.54, "word": " و", "probability": 0.53173828125}, {"start": 942.54, "end": 942.88, "word": " بيتا", "probability": 0.8204752604166666}, {"start": 942.88, "end": 943.54, "word": " الأربعة", "probability": 0.94921875}, {"start": 943.54, "end": 944.06, "word": " بدت", "probability": 0.9443359375}, {"start": 944.06, "end": 944.32, "word": " ساوي", "probability": 0.9055989583333334}, {"start": 944.32, "end": 945.08, "word": " اتنين", "probability": 0.9549560546875}, {"start": 945.08, "end": 946.22, "word": " هيتوا", "probability": 0.4385579427083333}, {"start": 946.22, "end": 946.8, "word": " functions", "probability": 0.79931640625}, {"start": 946.8, "end": 948.1, "word": " clearly", "probability": 0.57861328125}], "temperature": 1.0}, {"id": 35, "seek": 97866, "start": 952.44, "end": 978.66, "text": "الفا and بيتا are permutation on a ليش ال one to one و ال on two واضح من التعريف التعريف موجود عندك بطريقة السرد ولا عنصر بروح ل .. ولا .. مافيش عنصرين بروحوا لنفس القيمة طبعا و لعملية on two", "tokens": [6027, 5172, 995, 293, 4724, 36081, 995, 366, 4784, 11380, 322, 257, 32239, 8592, 2423, 472, 281, 472, 4032, 2423, 322, 732, 4032, 46958, 5016, 9154, 16712, 3615, 16572, 5172, 16712, 3615, 16572, 5172, 3714, 29245, 23328, 43242, 4117, 4724, 9566, 16572, 28671, 21136, 2288, 3215, 49429, 18871, 9381, 2288, 4724, 32887, 5016, 5296, 4386, 49429, 4386, 19446, 41185, 8592, 18871, 9381, 2288, 9957, 4724, 32887, 5016, 14407, 5296, 1863, 36178, 25062, 32640, 3660, 23032, 3555, 3615, 995, 4032, 5296, 25957, 1211, 10632, 322, 732], "avg_logprob": -0.24909156872782595, "compression_ratio": 1.6216216216216217, "no_speech_prob": 0.0, "words": [{"start": 952.4399999999999, "end": 953.3, "word": "الفا", "probability": 0.5397135416666666}, {"start": 953.3, "end": 954.16, "word": " and", "probability": 0.386962890625}, {"start": 954.16, "end": 955.08, "word": " بيتا", "probability": 0.8522135416666666}, {"start": 955.08, "end": 956.66, "word": " are", "probability": 0.6904296875}, {"start": 956.66, "end": 959.6, "word": " permutation", "probability": 0.90478515625}, {"start": 959.6, "end": 962.52, "word": " on", "probability": 0.794921875}, {"start": 962.52, "end": 962.86, "word": " a", "probability": 0.4951171875}, {"start": 962.86, "end": 964.9, "word": " ليش", "probability": 0.6259765625}, {"start": 964.9, "end": 965.52, "word": " ال", "probability": 0.7255859375}, {"start": 965.52, "end": 965.7, "word": " one", "probability": 0.80712890625}, {"start": 965.7, "end": 965.88, "word": " to", "probability": 0.88720703125}, {"start": 965.88, "end": 966.16, "word": " one", "probability": 0.9619140625}, {"start": 966.16, "end": 966.7, "word": " و", "probability": 0.60791015625}, {"start": 966.7, "end": 966.78, "word": " ال", "probability": 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"probability": 0.8271484375}, {"start": 1640.26, "end": 1640.84, "word": " بتروح", "probability": 0.87109375}, {"start": 1640.84, "end": 1641.58, "word": " لمين", "probability": 0.649169921875}, {"start": 1641.58, "end": 1642.64, "word": " و", "probability": 0.5439453125}, {"start": 1642.64, "end": 1642.96, "word": " أخد", "probability": 0.68603515625}, {"start": 1642.96, "end": 1643.1, "word": " ال", "probability": 0.890625}, {"start": 1643.1, "end": 1643.54, "word": " alpha", "probability": 0.25634765625}, {"start": 1643.54, "end": 1645.3, "word": " واحد", "probability": 0.65283203125}, {"start": 1645.3, "end": 1645.7, "word": " اتنين", "probability": 0.958740234375}, {"start": 1645.7, "end": 1646.4, "word": " تلاتة", "probability": 0.974609375}, {"start": 1646.4, "end": 1647.32, "word": " و", "probability": 0.36865234375}, {"start": 1647.32, "end": 1648.02, "word": " الواحد", "probability": 0.9568684895833334}, {"start": 1648.02, "end": 1648.46, "word": " هيروح", "probability": 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{"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.58984375}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.57373046875}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.50390625}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.47607421875}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.400634765625}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.4951171875}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.399169921875}, {"start": 2381.43, "end": 2381.43, "word": " Alpha", "probability": 0.451904296875}], "temperature": 1.0}, {"id": 83, "seek": 241010, "start": 2382.28, "end": 2410.1, "text": "تنتين هدول بيتا ألف عبارة عن ألف تربيه بيتا بيتا ألف عبارة عن ألف تربيه بيتا ألف ألف مع ألف تربيه identity و بيتا ألف بيظل طبعا الجواب أنها ألف تربيه بيتا ألف بيتا في ألف بيتا عبارة عن ألف ألف تربيه بيتا بيتا بي سوى ال identity", "tokens": 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"end": 2383.16, "word": " هدول", "probability": 0.7703450520833334}, {"start": 2383.16, "end": 2386.46, "word": " بيتا", "probability": 0.4799601236979167}, {"start": 2386.46, "end": 2386.72, "word": " ألف", "probability": 0.707275390625}, {"start": 2386.72, "end": 2387.06, "word": " عبارة", "probability": 0.80975341796875}, {"start": 2387.06, "end": 2387.22, "word": " عن", "probability": 0.98486328125}, {"start": 2387.22, "end": 2387.44, "word": " ألف", "probability": 0.850830078125}, {"start": 2387.44, "end": 2387.84, "word": " تربيه", "probability": 0.731689453125}, {"start": 2387.84, "end": 2388.8, "word": " بيتا", "probability": 0.8240559895833334}, {"start": 2388.8, "end": 2391.88, "word": " بيتا", "probability": 0.7467447916666666}, {"start": 2391.88, "end": 2392.18, "word": " ألف", "probability": 0.966552734375}, {"start": 2392.18, "end": 2392.88, "word": " عبارة", "probability": 0.84552001953125}, {"start": 2392.88, "end": 2393.04, "word": " عن", "probability": 0.98291015625}, {"start": 2393.04, "end": 2393.2, "word": " ألف", "probability": 0.96728515625}, {"start": 2393.2, "end": 2393.62, "word": " تربيه", "probability": 0.9810791015625}, {"start": 2393.62, "end": 2394.1, "word": " بيتا", "probability": 0.9625651041666666}, {"start": 2394.1, "end": 2394.9, "word": " ألف", "probability": 0.805908203125}, {"start": 2394.9, "end": 2395.4, "word": " ألف", "probability": 0.64697265625}, {"start": 2395.4, "end": 2395.58, "word": " مع", "probability": 0.96044921875}, {"start": 2395.58, "end": 2395.68, "word": " ألف", "probability": 0.972412109375}, {"start": 2395.68, "end": 2396.04, "word": " تربيه", "probability": 0.9814453125}, {"start": 2396.04, "end": 2396.4, "word": " identity", "probability": 0.50634765625}, {"start": 2396.4, "end": 2396.6, "word": " و", "probability": 0.53466796875}, {"start": 2396.6, "end": 2396.84, "word": " بيتا", "probability": 0.81640625}, {"start": 2396.84, "end": 2397.0, "word": " ألف", "probability": 0.978759765625}, {"start": 2397.0, "end": 2397.42, "word": " بيظل", "probability": 0.60400390625}, {"start": 2397.42, "end": 2399.78, "word": " طبعا", "probability": 0.775360107421875}, {"start": 2399.78, "end": 2400.0, "word": " الجواب", "probability": 0.637451171875}, {"start": 2400.0, "end": 2400.2, "word": " أنها", "probability": 0.646728515625}, {"start": 2400.2, "end": 2400.38, "word": " ألف", "probability": 0.923583984375}, {"start": 2400.38, "end": 2400.76, "word": " تربيه", "probability": 0.97509765625}, {"start": 2400.76, "end": 2401.12, "word": " بيتا", "probability": 0.9202473958333334}, {"start": 2401.12, "end": 2402.86, "word": " ألف", "probability": 0.826171875}, {"start": 2402.86, "end": 2403.18, "word": " بيتا", "probability": 0.9444986979166666}, {"start": 2403.18, "end": 2403.28, "word": " في", "probability": 0.92041015625}, {"start": 2403.28, "end": 2403.48, "word": " ألف", "probability": 0.976806640625}, {"start": 2403.48, "end": 2405.08, "word": " بيتا", "probability": 0.9659830729166666}, {"start": 2405.08, "end": 2406.66, "word": " عبارة", "probability": 0.9920654296875}, {"start": 2406.66, "end": 2406.88, "word": " عن", "probability": 0.98583984375}, {"start": 2406.88, "end": 2407.24, "word": " ألف", "probability": 0.975341796875}, {"start": 2407.24, "end": 2407.94, "word": " ألف", "probability": 0.93408203125}, {"start": 2407.94, "end": 2408.54, "word": " تربيه", "probability": 0.976318359375}, {"start": 2408.54, "end": 2408.94, "word": " بيتا", "probability": 0.8606770833333334}, {"start": 2408.94, "end": 2409.24, "word": " بيتا", "probability": 0.888671875}, {"start": 2409.24, "end": 2409.4, "word": " بي", "probability": 0.78515625}, {"start": 2409.4, "end": 2409.64, "word": " سوى", "probability": 0.5563151041666666}, {"start": 2409.64, "end": 2409.72, "word": " ال", "probability": 0.970703125}, {"start": 2409.72, "end": 2410.1, "word": " identity", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 84, "seek": 244102, "start": 2412.8, "end": 2441.02, "text": "و أنا هيظل alpha تربيع طبعا تقدر تكمل الجدول هجت لحالك أنا هيكون identity و أنا alpha أنا alpha تربيع و أنا beta و أنا alpha beta طبعا we will show later that", "tokens": [2407, 41850, 8032, 1829, 19913, 1211, 8961, 6055, 2288, 21292, 3615, 23032, 3555, 3615, 995, 6055, 28543, 2288, 6055, 24793, 1211, 25724, 3215, 12610, 8032, 7435, 2655, 5296, 5016, 6027, 4117, 41850, 8032, 1829, 30544, 6575, 4032, 41850, 8961, 41850, 8961, 6055, 2288, 21292, 3615, 4032, 41850, 9861, 4032, 41850, 8961, 9861, 23032, 3555, 3615, 995, 321, 486, 855, 1780, 300], "avg_logprob": -0.250882048760691, "compression_ratio": 1.5902777777777777, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2412.8, "end": 2413.0, "word": "و", "probability": 0.88427734375}, {"start": 2413.0, "end": 2413.12, "word": " أنا", "probability": 0.5146484375}, {"start": 2413.12, "end": 2413.5, "word": " هيظل", "probability": 0.7366943359375}, {"start": 2413.5, "end": 2413.8, "word": " alpha", "probability": 0.33154296875}, {"start": 2413.8, "end": 2414.48, "word": " تربيع", "probability": 0.850830078125}, {"start": 2414.48, "end": 2415.38, "word": " طبعا", "probability": 0.9195556640625}, {"start": 2415.38, "end": 2415.7, "word": " تقدر", "probability": 0.82421875}, {"start": 2415.7, "end": 2416.04, "word": " تكمل", "probability": 0.9684244791666666}, {"start": 2416.04, "end": 2416.36, "word": " الجدول", "probability": 0.8575846354166666}, {"start": 2416.36, "end": 2416.64, "word": " هجت", "probability": 0.5540364583333334}, {"start": 2416.64, "end": 2417.18, "word": " لحالك", "probability": 0.9647216796875}, {"start": 2417.18, "end": 2418.32, "word": " أنا", "probability": 0.310546875}, {"start": 2418.32, "end": 2418.66, "word": " هيكون", "probability": 0.7521158854166666}, {"start": 2418.66, "end": 2419.34, "word": " identity", "probability": 0.87353515625}, {"start": 2419.34, "end": 2420.26, "word": " و", "probability": 0.65869140625}, {"start": 2420.26, "end": 2420.4, "word": " أنا", "probability": 0.8193359375}, {"start": 2420.4, "end": 2420.84, "word": " alpha", "probability": 0.7509765625}, {"start": 2420.84, "end": 2422.02, "word": " أنا", "probability": 0.271484375}, {"start": 2422.02, "end": 2422.3, "word": " alpha", "probability": 0.7529296875}, {"start": 2422.3, "end": 2423.1, "word": " تربيع", "probability": 0.9521484375}, {"start": 2423.1, "end": 2424.22, "word": " و", "probability": 0.8369140625}, {"start": 2424.22, "end": 2424.5, "word": " أنا", "probability": 0.90673828125}, {"start": 2424.5, "end": 2425.16, "word": " beta", "probability": 0.2401123046875}, {"start": 2425.16, "end": 2426.56, "word": " و", "probability": 0.95947265625}, {"start": 2426.56, "end": 2426.7, "word": " أنا", "probability": 0.92529296875}, {"start": 2426.7, "end": 2426.96, "word": " alpha", "probability": 0.82177734375}, {"start": 2426.96, "end": 2427.4, "word": " beta", "probability": 0.93310546875}, {"start": 2427.4, "end": 2432.16, "word": " طبعا", "probability": 0.9796142578125}, {"start": 2432.16, "end": 2435.3, "word": " we", "probability": 0.8076171875}, {"start": 2435.3, "end": 2437.02, "word": " will", "probability": 0.91064453125}, {"start": 2437.02, "end": 2438.48, "word": " show", "probability": 0.96728515625}, {"start": 2438.48, "end": 2439.92, "word": " later", "probability": 0.91064453125}, {"start": 2439.92, "end": 2441.02, "word": " that", "probability": 0.958984375}], "temperature": 1.0}, {"id": 85, "seek": 246596, "start": 2443.14, "end": 2465.96, "text": "S3 and D3 is the same thing ماشي نفس الحاجة يعطيكوا العفو يا شباب", "tokens": [50, 18, 293, 413, 18, 307, 264, 912, 551, 3714, 33599, 1829, 8717, 36178, 21542, 26108, 3660, 37495, 9566, 1829, 4117, 14407, 18863, 5172, 2407, 35186, 13412, 3555, 16758], "avg_logprob": -0.24895834624767305, "compression_ratio": 1.0, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2443.14, "end": 2444.0, "word": "S3", "probability": 0.471435546875}, {"start": 2444.0, "end": 2445.46, "word": " and", "probability": 0.810546875}, {"start": 2445.46, "end": 2446.54, "word": " D3", "probability": 0.859130859375}, {"start": 2446.54, "end": 2447.4, "word": " is", "probability": 0.95849609375}, {"start": 2447.4, "end": 2447.94, "word": " the", "probability": 0.93896484375}, {"start": 2447.94, "end": 2449.08, "word": " same", "probability": 0.921875}, {"start": 2449.08, "end": 2456.8, "word": " thing", "probability": 0.9716796875}, {"start": 2456.8, "end": 2460.2, "word": " ماشي", "probability": 0.6833902994791666}, {"start": 2460.2, "end": 2461.66, "word": " نفس", "probability": 0.923828125}, {"start": 2461.66, "end": 2462.68, "word": " الحاجة", "probability": 0.9899088541666666}, {"start": 2462.68, "end": 2465.5, "word": " يعطيكوا", "probability": 0.793505859375}, {"start": 2465.5, "end": 2465.7, "word": " العفو", "probability": 0.787109375}, {"start": 2465.7, "end": 2465.82, "word": " يا", "probability": 0.60009765625}, {"start": 2465.82, "end": 2465.96, "word": " شباب", "probability": 0.9484049479166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2467.5845, "duration_after_vad": 2291.888749999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e931acf91d9bcb83167975cbd21351f15236d4bd
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/PXZxPZyPNPE.srt
@@ -0,0 +1,1786 @@
+1
+00:00:22,310 --> 00:00:26,410
+بسم الله الرحمن الرحيم بدأنا المرة الماضية في
+
+2
+00:00:26,410 --> 00:00:31,130
+موضوع الـ groups اللي هي المجموعات وعرفنا أن الـ set
+
+3
+00:00:31,130 --> 00:00:34,990
+وعليها binary operation بقول عنها group إذا 
+
+4
+00:00:34,990 --> 00:00:39,190
+حققت لي ثلاث خواص، الخاصية الأولى خاصية الـ
+
+5
+00:00:39,190 --> 00:00:43,650
+associativity، الخاصية الثانية خاصية الـ identity
+
+6
+00:00:43,650 --> 00:00:47,350
+element، الخاصية الثالثة هي خاصية الـ inverse
+
+7
+00:00:47,350 --> 00:00:53,380
+element لأي element موجود في group G،  واخدنا على ذلك 
+
+8
+00:00:53,380 --> 00:00:59,440
+قبل المثال أربعة، وهذا هو المثال رقم خمسة، يبقى الـ
+
+9
+00:00:59,440 --> 00:01:04,380
+ZN هي عبارة عن المجموعة عناصرها Zero، واحد، اتنين،
+
+10
+00:01:04,380 --> 00:01:10,720
+ثلاثة لغاية N ناقص واحد، العملية المعرفة عليها اللي 
+
+11
+00:01:10,720 --> 00:01:17,560
+هي الـ addition modulo N، يبقى العملية اللي على ZN
+
+12
+00:01:17,560 --> 00:01:25,440
+هي عملية الجمع العادية بس إيش كل ما يصير N بنهملهم.
+
+13
+00:01:25,440 --> 00:01:30,460
+يعني المقياس تبعه هو N، هذه عبارة عن إيش؟ عبارة عن
+
+14
+00:01:30,460 --> 00:01:35,440
+group under addition، ليش؟ الـ a اللي من Zero لغاية N 
+
+15
+00:01:35,440 --> 00:01:40,180
+ناقص واحد، كلها أعداد عادية بس modulo N، ما زاد على
+
+16
+00:01:40,180 --> 00:01:45,140
+الـ N ناقص واحد اللي هو N، ببدأ من Zero، إذا زاد واحد
+
+17
+00:01:45,140 --> 00:01:48,820
+يصبح واحد، وإذا زاد اثنين يصبح اثنين، وكذلك، يبقى أنا
+
+18
+00:01:48,820 --> 00:01:51,940
+عند الأعداد هذه، هذه الأعداد لو جمعتها، واحد زاد
+
+19
+00:01:51,940 --> 00:01:55,840
+اثنين، اثنين زاد واحد، أي رقم إن أجمعه بدل ما عندناش
+
+20
+00:01:55,840 --> 00:02:01,280
+مشكلة في هذه الحالة، اثنين لو جمعت أي عددين يعني 
+
+21
+00:02:01,280 --> 00:02:06,160
+هذه الـ group abelian، لو جمعت أي عددين هيعطيك عدد
+
+22
+00:02:06,160 --> 00:02:14,750
+موجود في هذه المجموعة، طيب النقطة الثانية لو عملت
+
+23
+00:02:14,750 --> 00:02:19,270
+associative بين أي ثلاثة أعداد منهم، فهيطلع نفس
+
+24
+00:02:19,270 --> 00:02:23,770
+العدد، مشكلتنا مش هذا، مشكلتنا من هو الـ identity
+
+25
+00:02:23,770 --> 00:02:28,530
+element تحت عملية الجمع؟ من؟
+
+26
+00:02:31,650 --> 00:02:36,090
+بدي معكوس أي عنصر موجود فيها.
+
+27
+00:02:39,720 --> 00:02:45,260
+هذه بعض الكتب يا شباب بتعبر عنها ZN هكذا، وبتحط
+
+28
+00:02:45,260 --> 00:02:50,680
+لعملية الجمع في دائرة، من حد ما تشوف عملية الجمع في 
+
+29
+00:02:50,680 --> 00:02:55,280
+دائرة معناته هذه عملية الجمع modulo N، مشان
+
+30
+00:02:55,280 --> 00:02:59,700
+يفرقوها ويميزوا بينها وبين عملية الجمع العادية.
+
+31
+00:02:59,700 --> 00:03:06,440
+يبقى هنا Zero is the identity 
+
+32
+00:03:11,970 --> 00:03:24,010
+the inverse of k الموجود في ZN، يعني مين العدد
+
+33
+00:03:24,010 --> 00:03:29,690
+اللي بدي أضيفه لهذا العدد يطلع Zero أو يطلع N
+
+34
+00:03:29,690 --> 00:03:37,160
+اللي همين N minus الـ k، يبقى the inverse of k  اللي هو 
+
+35
+00:03:37,160 --> 00:03:42,080
+N minus الـ k، لأن احنا عندنا عملية جمع modulo N، لو
+
+36
+00:03:42,080 --> 00:03:46,260
+جمعته الاثنين هدول بيطلع N، اللي همين N بيصير الـ Zero
+
+37
+00:03:46,260 --> 00:03:51,360
+اللي هو N، الـ identity element، طيب هذه group بسيطة و
+
+38
+00:03:51,360 --> 00:03:55,660
+زي ما تشوف هي abelian لأن اثنين زائد خمسة هي خمسة
+
+39
+00:03:55,660 --> 00:04:02,180
+زائد اثنين وهكذا، طيب نروح لمثال أثقل شوية وأثقل
+
+40
+00:04:02,180 --> 00:04:14,520
+شويات، مش شوية، بيقول let الـ UN be the set of all 
+
+41
+00:04:14,520 --> 00:04:23,500
+positive integers
+
+42
+00:04:23,500 --> 00:04:25,220
+less than
+
+43
+00:04:27,620 --> 00:04:40,840
+less than الـ N، less than الـ N and relatively prime
+
+44
+00:04:40,840 --> 00:04:49,100
+relatively prime to N، then
+
+45
+00:04:49,100 --> 00:05:02,620
+الـ UN هذه الـ UN and the set UN is an
+
+46
+00:05:02,620 --> 00:05:11,000
+abelian group under
+
+47
+00:05:11,000 --> 00:05:12,780
+multiplication modulo N.
+
+48
+00:05:46,170 --> 00:05:55,400
+بسبب، نرجع للست UN، هذه مين هي الـ UN؟ بقول الـ UN هي
+
+49
+00:05:55,400 --> 00:05:59,700
+set of all positive integers، مجموعة الأعداد
+
+50
+00:05:59,700 --> 00:06:05,620
+الصحيحة الموجبة واللي عليها شرط ثاني، less than N.
+
+51
+00:06:05,620 --> 00:06:12,160
+يبقى أقل من العدد N وفي نفس الوقت relatively prime
+
+52
+00:06:12,160 --> 00:06:18,500
+مع N، طب وقف شوية خلينا نعرف مين هذه الأرقام، لو جيت 
+
+53
+00:06:18,500 --> 00:06:25,220
+قلت لك بدي الـ U خمسة، بس الواحد والثلاثة، طب والأربعة
+
+54
+00:06:25,220 --> 00:06:33,220
+والاثنين، يبقى الأعداد كلهم واحد، اثنين، ثلاثة، أربعة،
+
+55
+00:06:33,220 --> 00:06:38,180
+كلهم are relatively prime to خمسة، يبقى هذه mainly
+
+56
+00:06:38,180 --> 00:06:42,960
+وخمسة، لكن لو قلت U ستة، U ستة اللي هي واحد 
+
+57
+00:06:42,960 --> 00:06:47,580
+وخمسة، في غيرهم بس هدول هم اللي relatively prime لـ
+
+58
+00:06:47,580 --> 00:06:53,270
+U ستة، لو قلت لك U عشرة، لك تقول الواحد والثلاثة 
+
+59
+00:06:53,270 --> 00:06:58,870
+والسبعة والتسعة، مش غيرهم، يبقى هي الـ U خمسة، الأعداد
+
+60
+00:06:58,870 --> 00:07:03,130
+اللي أقل من الرقم المعطى اللي بيكون relatively
+
+61
+00:07:03,130 --> 00:07:09,990
+prime لهذا الرقم، مثلا لو جت ليه خمسة عشر، يبقى الواحد 
+
+62
+00:07:09,990 --> 00:07:15,010
+والاثنين والأربعة والسبعة
+
+63
+00:07:16,510 --> 00:07:22,530
+والثمانية، تسعة لأ، العشرة لأ، أحد عشر، اثنا عشر لأ، ثلاثة عشر
+
+64
+00:07:22,530 --> 00:07:25,870
+لأ، أربعة عشر لأ، يبقى لغاية ثمانية، لغاية ثلاثة عشر، وها
+
+65
+00:07:25,870 --> 00:07:30,730
+كده، يبقى بجيب الأرقام اللي أقل من الرقم المعطى 
+
+66
+00:07:30,730 --> 00:07:34,390
+واللي بيكون relatively prime لهذا الرقم، وكلهم
+
+67
+00:07:34,390 --> 00:07:39,210
+أرقام صحيحة موجبة، هاي المقصود بالـ UN، يبقى هذه
+
+68
+00:07:39,210 --> 00:07:44,400
+الست UN، مين الـ operation اللي عليها؟ gallery in 
+
+69
+00:07:44,400 --> 00:07:49,040
+the UN is an abelian group under multiplication
+
+70
+00:07:49,040 --> 00:07:56,160
+modulo N، يبقى العملية عملية ضرب modulo N، يعني
+
+71
+00:07:56,160 --> 00:08:01,280
+المقياس تبعها هو مين؟ هو N، أول شيء بدنا نثبت إنه
+
+72
+00:08:01,280 --> 00:08:07,920
+هذه group، طيب الـ group هذه بدي لسه ما قلتش إنه هذه
+
+73
+00:08:07,920 --> 00:08:14,220
+binary operation under multiplication modulo N، هل هذه 
+
+74
+00:08:14,220 --> 00:08:19,440
+binary operation على الـ UN أم لا؟ لم نقول ذلك، لكن
+
+75
+00:08:19,440 --> 00:08:26,280
+أنا بدي آخذ عددين واضربهم في بعض وأشوف هل الاثنين
+
+76
+00:08:26,280 --> 00:08:31,940
+هدول modulo N بيكونوا... إن كان طلع الـ remainder
+
+77
+00:08:31,940 --> 00:08:36,860
+تبعهم موجود في الـ UN بيكون تم المطلوب، إن ما طلعش
+
+78
+00:08:36,860 --> 00:08:41,880
+بيصير كلامنا مش صحيح، وفيش داعي أروح لبقية الشروط.
+
+79
+00:08:41,880 --> 00:08:46,360
+تمام، إذا خلّيني أشوف الـ condition الأول، النقطة 
+
+80
+00:08:46,360 --> 00:08:51,480
+الأولى، بدي أثبت إنه هذه binary operation، لذلك بدي 
+
+81
+00:08:51,480 --> 00:08:58,700
+أقوله افترض إن الـ A والـ B موجودة في الـ UN، إيش بدي
+
+82
+00:08:58,700 --> 00:09:03,620
+أثبت إنها binary operation؟ بدي أثبت إن الـ A B
+
+83
+00:09:03,620 --> 00:09:08,520
+modulo N موجود وين؟ موجود في الـ UN، هذا اللي عايز
+
+84
+00:09:08,520 --> 00:09:11,720
+أثبته، فبكويس بقوله then
+
+85
+00:09:14,480 --> 00:09:19,740
+مرت علينا الـ division algorithm احنا صح؟ division
+
+86
+00:09:19,740 --> 00:09:25,080
+algorithm ومر علينا الـ greatest common divisor، يبقى
+
+87
+00:09:25,080 --> 00:09:29,140
+أنا بروح بختار المناسب اللي بيخدمني في هذه الحالة.
+
+88
+00:09:29,410 --> 00:09:34,290
+لو جينا نقول لك الـ greatest common divisor لـ الـ A
+
+89
+00:09:34,290 --> 00:09:40,090
+والـ N قداش بتقول إيه؟ واحد، ليش؟ لأن الـ elements
+
+90
+00:09:40,090 --> 00:09:45,870
+اللي موجودة are relatively prime to N، يبقى and وفي
+
+91
+00:09:45,870 --> 00:09:49,910
+نفس الوقت الـ greatest common divisor لـ الـ B و
+
+92
+00:09:49,910 --> 00:09:55,830
+الـ N بتساوي قداش؟ إذاً كل واحدة منهم بقدر أكتبها على
+
+93
+00:09:55,830 --> 00:10:03,030
+صيغة linear combination، يبقى باجي بقول AS1 زائد
+
+94
+00:10:03,030 --> 00:10:15,640
+NT1 بدها تساوي واحد، الـ B S2 زائد الـ N T2 بدها تساوي
+
+95
+00:10:15,640 --> 00:10:26,580
+واحد، وهذا for some اللي هو S1 و S2 و T1 و T2، كلها
+
+96
+00:10:26,580 --> 00:10:29,880
+اللي موجودة وين؟ في الـ set of integers.
+
+97
+00:10:32,880 --> 00:10:38,280
+طب أنا بدي أحصل الضرب A في B modulo N يكون موجودة
+
+98
+00:10:38,280 --> 00:10:42,900
+في الـ UN، مشان هيك خليني أروح أضربهم في بعض وأشوف
+
+99
+00:10:42,900 --> 00:10:47,860
+كده يكون الناتج اللي عندنا، إذا لو جيت أضربهم في
+
+100
+00:10:47,860 --> 00:10:54,400
+بعض، فباجي بقول A S1 زائد N T1
+
+101
+00:10:57,930 --> 00:11:05,290
+B S2 زائد الـ N T2 بدها تساوي واحد في واحد اللي هو واحد، طبعاً
+
+102
+00:11:05,290 --> 00:11:08,370
+يبقى ضرب في الطرف الشمال في الشمال واليمين في 
+
+103
+00:11:08,370 --> 00:11:14,110
+اليمين، تعال في كحاصل ضرب القوسين هدول، يبقى هذا A
+
+104
+00:11:14,110 --> 00:11:20,570
+B S1 S2 زائد الـ element هذا ضربته هنا، إذا
+
+105
+00:11:20,570 --> 00:11:27,650
+بدي أضربه في الثاني هذا، يبقى زائد N A S1 T2
+
+106
+00:11:27,650 --> 00:11:36,460
+زائد بدي أضرب هذا هنا، يبقى زائد N في N في T1 في
+
+107
+00:11:36,460 --> 00:11:45,780
+B في الـ S2، زائد في الثاني يبقى N تربيع T1 T2، كله
+
+108
+00:11:45,780 --> 00:11:52,040
+بدها تساوي واحد، صحيح، أظن هذا فيه N خليها لحالها
+
+109
+00:11:52,390 --> 00:11:58,730
+يبقى هذا الـ A B في الـ S1 S2 زائد شو رأيك هدول
+
+110
+00:11:58,730 --> 00:12:04,490
+بدي آخذ منهم إن عامل مشترك، إيه شو بيظل عندك؟ A S
+
+111
+00:12:04,490 --> 00:12:13,930
+1 T2 زائد T1 B S2 زائد N T1 T2
+
+112
+00:12:13,930 --> 00:12:20,810
+كله بدها تساوي واحد، إيش تفسيرك لهذه العبارة؟ طلع أنا 
+
+113
+00:12:20,810 --> 00:12:25,270
+عندي هنا رقم وهنا N، يبقى الـ A,B والـ N are
+
+114
+00:12:25,270 --> 00:12:28,990
+relatively prime ولا لا؟ أو greatest common divisor
+
+115
+00:12:28,990 --> 00:12:34,390
+لهم بدها تساوي واحد، يبقى هذا معناته إن الـ greatest
+
+116
+00:12:34,390 --> 00:12:40,290
+common divisor للـ A والـ B والـ N بدها تساوي الواحد.
+
+117
+00:12:40,290 --> 00:12:50,050
+هذا بدي يعطيك إن الـ A,B and الـ N are relatively
+
+118
+00:12:50,050 --> 00:12:57,000
+prime، هذا شو معناه يا شباب؟ هذا معناه إن الـ A والـ B
+
+119
+00:12:57,000 --> 00:13:04,440
+موجودين في الـ UN، يعني عملية ضرب modulo N is a
+
+120
+00:13:04,440 --> 00:13:10,080
+binary operation، يبقى هذا معناته إن الـ multi
+
+121
+00:13:10,080 --> 00:13:18,900
+plication modulo N is
+
+122
+00:13:18,900 --> 00:13:21,100
+a binary
+
+123
+00:13:26,380 --> 00:13:31,700
+operation، بدنا نيجي للنقطة الثانية، النقطة الثانية
+
+124
+00:13:31,700 --> 00:13:38,200
+بدي أخليها عليك تمرن دق فيها في البيت، check that
+
+125
+00:13:38,200 --> 00:13:47,540
+this operation is associative. 
+
+126
+00:13:50,690 --> 00:13:57,810
+on الـ UN يعني وكذبت لي أنه إيه في B في C بده 
+
+127
+00:13:57,810 --> 00:14:04,130
+يساوي إيه لحالها مضروبة في B وC النقطة التالتة مين
+
+128
+00:14:04,130 --> 00:14:10,930
+الـ identity element لهذه الـ group واحد يبقى واحد
+
+129
+00:14:10,930 --> 00:14:17,010
+is the identity element
+
+130
+00:14:19,980 --> 00:14:26,980
+شو السبب إن لو ضاربته في a modulo n بطلع الـ a
+
+131
+00:14:26,980 --> 00:14:38,860
+itself يبقى هذا because واحد في a modulo n بده
+
+132
+00:14:38,860 --> 00:14:46,240
+يساوي الـ a modulo n اللي بده يساوي الـ a itself لكل
+
+133
+00:14:46,240 --> 00:14:48,680
+الـ a الموجودة في الـ UN
+
+134
+00:14:51,590 --> 00:15:00,510
+طب النقطة الرابعة بدّه الـ inverse the inverse of إيه
+
+135
+00:15:00,510 --> 00:15:07,130
+اللي موجود في الـ U N is N
+
+136
+00:15:07,130 --> 00:15:13,070
+مين قال هذا الكلام يعني لما أقول N زائد واحد على N
+
+137
+00:15:13,070 --> 00:15:19,130
+كله مجسوم على N مش هيك على إيه طب هل هذا أنتج 
+
+138
+00:15:22,690 --> 00:15:27,290
+طب كيف بدّه يصير عادي؟ برّة الـ z ده ده يعني مو صبطتش
+
+139
+00:15:27,290 --> 00:15:31,750
+معاناة أو برّة الـ UN صحيح؟ يبقى هذا الكلام ليس
+
+140
+00:15:31,750 --> 00:15:37,230
+صحيحًا يبقى لو جيه تقولك the inverse of L is X
+
+141
+00:15:37,230 --> 00:15:43,070
+where X
+
+142
+00:15:43,070 --> 00:15:56,700
+is the solution of the equation هو حل المعادلة ax
+
+143
+00:15:56,700 --> 00:16:04,260
+modulo n بدّه يساوي مين؟ بدّه يساوي واحد لأن هذا 
+
+144
+00:16:04,260 --> 00:16:10,160
+الواحد هو الـ identity element يبقى حل المعادلة هذه
+
+145
+00:16:10,160 --> 00:16:15,620
+طبعًا هذا بيعتمد على الـ a من هي وعلى الـ n من هي إذا
+
+146
+00:16:15,620 --> 00:16:20,390
+عرفت الـ n وعرفت الـ a بقدر أجيب له الـ x بسهولة وهذه
+
+147
+00:16:20,390 --> 00:16:24,210
+القصة بصير سهلة يبقى هذه صارت appealing group
+
+148
+00:16:24,210 --> 00:16:29,490
+لأنها حققت لمن؟ حققت للـ أربعة شروط يبقى لو أعطيتك
+
+149
+00:16:29,490 --> 00:16:34,970
+مثال for example تفضل
+
+150
+00:16:34,970 --> 00:16:35,330
+قول
+
+151
+00:16:39,840 --> 00:16:44,360
+إحنا اللي بنقولك الحل تبع هذه المعادلة بيكون هو
+
+152
+00:16:44,360 --> 00:16:50,200
+المعكوس تبع الـA وهذا يختلف من عنصر إلى آخر قد
+
+153
+00:16:50,200 --> 00:16:57,260
+يكون الـA معكوس لنفسه وقد يكون معكوس آخر كما سأريك
+
+154
+00:16:57,260 --> 00:17:02,200
+الآن إن كانت هذه الـ group لازم غصب عن و عن ما اسمك
+
+155
+00:17:02,200 --> 00:17:09,400
+أنت ماهر ماهر إيه خريس غصب إن هو عنده مهر يخلص لازم
+
+156
+00:17:09,400 --> 00:17:12,940
+يجي معكوس لهذا الـ المطور اللي بس بطل يصير group
+
+157
+00:17:12,940 --> 00:17:17,840
+تمام؟ يبقى الـ group لازم كل عنصر في الـ group اللي
+
+158
+00:17:17,840 --> 00:17:22,800
+جيه له معكوس طيب يبقى هو حالة نعطي مثال توضح لو
+
+159
+00:17:22,800 --> 00:17:27,920
+أخذت you اللي بدك إياها مش ممكن تدحك أنت you إيش
+
+160
+00:17:27,920 --> 00:17:35,280
+بدك إياها؟ you خمسة دي كم رشد؟ you عشر مثلا، you
+
+161
+00:17:35,280 --> 00:17:44,420
+عشرة عشريش عناصرها الواحد والاتنين التلاتة
+
+162
+00:17:44,420 --> 00:17:54,460
+أربعة خمسة ستة سبعة ثمانية تسعة يبقى ما عنديش إلا 
+
+163
+00:17:54,460 --> 00:18:01,250
+هذه العناصر تمام الواحد هو الـ identity element يبقى
+
+164
+00:18:01,250 --> 00:18:07,290
+إحنا كله modulo عشرة بدي أشوف التلاتة مين معكوسها
+
+165
+00:18:07,290 --> 00:18:12,750
+ماهو العدد اللي بدي أضربه في التلاتة modulo عشرة
+
+166
+00:18:12,750 --> 00:18:18,310
+يعطينا الواحد الصحيح مين؟ السبعة سبعة في تلاتة
+
+167
+00:18:18,310 --> 00:18:22,670
+واحد وعشرين شيل منهم عشرتين يبقى الـ identity
+
+168
+00:18:22,670 --> 00:18:27,090
+element يبقى التلاتة هو معكوس السبعة والسبعة هي
+
+169
+00:18:27,090 --> 00:18:34,070
+معكوس من الأدلي والتلاتة يبقى التلاتة is the
+
+170
+00:18:34,070 --> 00:18:44,560
+inverse element of سبعة طب التسعة مين معكوسها؟ نفسها
+
+171
+00:18:44,560 --> 00:18:49,620
+لإن التسعة في تسعة وثمان عشرات بظلمين الـ identity
+
+172
+00:18:49,620 --> 00:19:02,500
+element and تسعة is the inverse of itself يبقى
+
+173
+00:19:02,500 --> 00:19:05,180
+التسعة هو معكوس لنفسه
+
+174
+00:19:10,080 --> 00:19:23,920
+يبقى خريص لقيناله معكوس ولا لا طبعًا
+
+175
+00:19:23,920 --> 00:19:29,500
+هذه الـ group شباب عليها سنة كتيرة وعليها شغل كتير
+
+176
+00:19:29,500 --> 00:19:35,320
+يبقى هذه الـ group very important طيب ننتقل الآن
+
+177
+00:19:35,320 --> 00:19:45,710
+إلى المثال اللي بعده يبقى مثال سبعة مثال سبعة بيقول
+
+178
+00:19:45,710 --> 00:19:55,490
+the set لو أخدت الـ z وعليها عملية الطرح of
+
+179
+00:19:55,490 --> 00:20:06,590
+integers of integers under subtraction
+
+180
+00:20:10,490 --> 00:20:14,950
+هل يا ترى هذه group ولا ما هيّاش group؟ اه ده السؤال
+
+181
+00:20:14,950 --> 00:20:23,050
+أنا أدعي is not a group because
+
+182
+00:20:27,790 --> 00:20:31,090
+طبعًا لو طرحت أي عنصر من بعض سواء طالع إنّها تجميل
+
+183
+00:20:31,090 --> 00:20:35,370
+وجود والله سالم فيها وموجود في z إذا عملية الطرح
+
+184
+00:20:35,370 --> 00:20:39,250
+على z is a binary operation ما فيش فيها مشكلة لكن
+
+185
+00:20:39,250 --> 00:20:44,890
+هل هذه associative أم لا الله أعلم يبقى هنا
+
+186
+00:20:44,890 --> 00:20:52,350
+because if التلاتة مثلًا والخمسة والسبعة موجودة في
+
+187
+00:20:52,350 --> 00:21:04,340
+z then أنا بدي تلاتة ناقص وعندك خمسة ناقص سبعة بدي
+
+188
+00:21:04,340 --> 00:21:08,340
+أستخدم خاصية الـ associativity أشوف أصحيها عليها
+
+189
+00:21:08,340 --> 00:21:13,420
+ولا لأ يبقى هذا تلاتة ناقص خمسة ناقص سبعة مقداش يا
+
+190
+00:21:13,420 --> 00:21:19,180
+شباب ناقص اثنين يعني تلاتة زيدي اثنين يساوي مقداش
+
+191
+00:21:19,180 --> 00:21:27,320
+خمسة بطولكن تلاتة ناقص خمسة ناقص سبعة ويساوي
+
+192
+00:21:27,320 --> 00:21:34,420
+تلاتة ناقص خمسة سالب اثنين سالب اثنين سالب سبعة
+
+193
+00:21:35,270 --> 00:21:39,810
+سالب تسعة يبقى هذا الكلام معناه إن العملية
+
+194
+00:21:39,810 --> 00:21:46,390
+associative ولا not associative يبقى هذا معناه إنّ
+
+195
+00:21:46,390 --> 00:21:57,210
+subtraction عملية الطرح is not associative من هنا
+
+196
+00:21:57,210 --> 00:22:04,380
+زعمنا قبل قليل إنّها ليست group إذا عملية الأعداد أو
+
+197
+00:22:04,380 --> 00:22:11,260
+مجموعة الأعداد الصحيحة تحت عملية الطرح ما هيّاش group
+
+198
+00:22:11,260 --> 00:22:21,340
+المثال رقم ثمانية بيقول إذا set R star مين هي هذه
+
+199
+00:22:21,340 --> 00:22:30,220
+الـ star اللي هي عبارة عن الـ set R بدي أشيل منها الـ
+
+200
+00:22:30,220 --> 00:22:44,300
+zero six star of non zero real numbers non
+
+201
+00:22:44,300 --> 00:22:56,160
+zero real numbers is a group under the ordinary
+
+202
+00:23:00,560 --> 00:23:01,520
+السبق
+
+203
+00:23:39,270 --> 00:23:45,230
+مرة ثانية الـ set of real numbers اللي هي اللي بدي
+
+204
+00:23:45,230 --> 00:23:49,750
+أشيل منها الـ zero وبدي أسميها R star يبقى مجموعة
+
+205
+00:23:49,750 --> 00:23:55,450
+الأعداد الحقيقية استثنت منها الـ zero عرفت عليها
+
+206
+00:23:55,450 --> 00:24:02,970
+عملية الضرب العادية طبعًا الأعداد الـ real numbers
+
+207
+00:24:03,810 --> 00:24:07,670
+أضرب أي two real numbers في بعض بيطلع إيه اش ولا
+
+208
+00:24:07,670 --> 00:24:12,910
+بيطلع يعني natural اطلع real تمام يبقى هذا معناه
+
+209
+00:24:12,910 --> 00:24:16,370
+إن الـ multiplication is a binary operation اثنين
+
+210
+00:24:16,370 --> 00:24:22,470
+عملية الضرب العادية is associative عالمين على الـ
+
+211
+00:24:22,470 --> 00:24:25,970
+set of real numbers يبقى ده اللي عندي بدّه الـ
+
+212
+00:24:25,970 --> 00:24:31,290
+identity element وبدّه الـ inverse element يبقى 
+
+213
+00:24:31,290 --> 00:24:39,780
+because we know that إحنا بنعرف إن الـ multi
+
+214
+00:24:39,780 --> 00:24:50,540
+plication is a binary binary
+
+215
+00:24:50,540 --> 00:25:00,180
+associative binary associative operation
+
+216
+00:25:09,630 --> 00:25:17,030
+بالنسبة للدرب الوحيد هو
+
+217
+00:25:17,030 --> 00:25:30,340
+الـ identity element of R star طب لو أخدت عنصر A
+
+218
+00:25:30,340 --> 00:25:36,380
+معكوسه في R والله K موجود في R مين معكوسه بيكون؟
+
+219
+00:25:36,380 --> 00:25:40,640
+ممتاز جدًا يبقى مقلوبه هو بيكون معكوسه لأن لو ضربت 
+
+220
+00:25:40,640 --> 00:25:45,060
+اثنين في بعض بيطلع من؟ الـ identity element يبقى
+
+221
+00:25:45,060 --> 00:25:57,010
+باجي بقوله the inverse element of A اللي موجود في R
+
+222
+00:25:57,010 --> 00:26:06,330
+star is واحد على إيه since إيه في واحد على إيه بدّه
+
+223
+00:26:06,330 --> 00:26:14,010
+يساوي واحد طب السؤال هو ليش استبعد الـ zero؟ أيوة
+
+224
+00:26:14,010 --> 00:26:18,610
+يبقى الـ zero ما لهوش معكس لو ضربته في أي رقم لا يمكن
+
+225
+00:26:18,610 --> 00:26:24,410
+يطلع من؟ لا يمكن يطلع الواحد الصحيح على الإطلاق
+
+226
+00:26:26,780 --> 00:26:39,060
+مثال تسعة بيقول الدراسات جي ال to over R الـ general
+
+227
+00:26:39,060 --> 00:26:43,720
+linear group of two by two matrices over R اللي هي
+
+228
+00:26:43,720 --> 00:26:52,760
+كل المصوفات A, B, C, D بحيث أن الـ A والـ B والـ C والـ D 
+
+229
+00:26:52,760 --> 00:27:00,120
+موجودة في set of real numbers وفي نفس الوقت الـ A D
+
+230
+00:27:00,120 --> 00:27:03,820
+ناقص B C لا يساوي Zero
+
+231
+00:27:07,870 --> 00:27:13,870
+under matrix multiplication
+
+232
+00:27:13,870 --> 00:27:24,050
+is
+
+233
+00:27:24,050 --> 00:27:26,110
+a group
+
+234
+00:27:41,310 --> 00:27:45,450
+طبعًا إحنا درسنا في الجبر الخطي المصوفة لنظامها
+
+235
+00:27:45,450 --> 00:27:49,590
+اثنين في اثنين يبقى فيها صفين وعمودين يبقى هذه
+
+236
+00:27:49,590 --> 00:27:54,490
+المصفوفة بقول إن نظامها اثنين في اثنين أو الـ size
+
+237
+00:27:54,490 --> 00:27:59,350
+تبعها اثنين في اثنين مش اثنين في اثنين يساوي أربعة
+
+238
+00:27:59,770 --> 00:28:02,750
+الاثنين الأولى تدل على رقم الصفوف والاثنين الثانية
+
+239
+00:28:02,750 --> 00:28:07,670
+تدل على رقم الأعمدة يبقى هذه بدي أسميها الـ general
+
+240
+00:28:07,670 --> 00:28:13,130
+linear group of two by two matrices over R هكذا
+
+241
+00:28:13,130 --> 00:28:19,790
+تقرأ general linear group of two by two matrices
+
+242
+00:28:19,790 --> 00:28:25,210
+over R مين هي هذه أنا ما همّنيش التسمية بهمني التركيب
+
+243
+00:28:25,210 --> 00:28:29,930
+الداخلي مين هي هذه يبقى هي كل المصوفات اللي نظامها
+
+244
+00:28:29,930 --> 00:28:34,550
+اثنين في اثنين والـ elements اللي داخل المصفوفة
+
+245
+00:28:34,550 --> 00:28:39,150
+كلهم عناصر موجودة فيها سواء كان zero ولا واحد ولا
+
+246
+00:28:39,150 --> 00:28:43,830
+نص ولا ثلث ولا أي رقم سالب موجب كثير ما عندناش
+
+247
+00:28:43,830 --> 00:28:49,660
+مشكلة and وفي نفس الوقت الـ A D ناقص B C ليسوا Zero
+
+248
+00:28:49,660 --> 00:28:56,420
+يطلع لي A D ناقص B C شو يعني هنا يعني المحدد تبع
+
+249
+00:28:56,420 --> 00:29:01,520
+المصفوفة المحدد تبع المصفوفة ليسوا Zero يبقى إحنا كل
+
+250
+00:29:01,520 --> 00:29:09,580
+المصفوفات اللي عناصرها بيكونوا أعداد حقيقية 
+
+251
+00:29:09,580 --> 00:29:14,760
+ومحدداتها لا تساوي صفراً عرفت عليها عملية ضرب
+
+252
+00:29:14,760 --> 00:29:19,780
+العادية تبع المصفوفات under matrix multiplication
+
+253
+00:29:19,780 --> 00:29:25,840
+عملية ضرب المصفوفات بدعي أنا هذا أن هذا is a group
+
+254
+00:29:25,840 --> 00:29:30,220
+نرجع للجبر الخطي أظن حاصل ضرب ثلاث مصفوفات
+
+255
+00:29:30,220 --> 00:29:34,820
+associative ولا لا اثنين لما نضرب مصفوفتين نظامهم
+
+256
+00:29:34,820 --> 00:29:38,390
+اثنين في اثنين تطلع مصفوفة النظام أربعة في أربعة و
+
+257
+00:29:38,390 --> 00:29:42,650
+الله اثنين في اثنين يبقى اثنين في اثنين كذلك إذا
+
+258
+00:29:42,650 --> 00:29:48,610
+عملية ضرب المصفوفات is a binary operation يبقى
+
+259
+00:29:48,610 --> 00:29:55,150
+بقوله النقطة الأولى we know that من الجبر الخطي
+
+260
+00:29:55,150 --> 00:30:04,170
+we know from linear algebra that
+
+261
+00:30:08,510 --> 00:30:16,590
+matrix multiplication is
+
+262
+00:30:16,590 --> 00:30:25,210
+an associative binary
+
+263
+00:30:25,210 --> 00:30:28,390
+operation
+
+264
+00:30:28,390 --> 00:30:33,050
+on
+
+265
+00:30:45,410 --> 00:30:53,190
+النقطة الثانية the identity element
+
+266
+00:30:55,420 --> 00:31:00,180
+In the general linear group of two by two matrices
+
+267
+00:31:00,180 --> 00:31:06,100
+over R, which is 1,000,000,000,000,000,000,000,000
+
+268
+00:31:06,100 --> 00:31:14,820
+,000,000,000,000,000
+
+269
+00:31:14,820 --> 00:31:16,120
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+270
+00:31:16,120 --> 00:31:17,440
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+271
+00:31:17,440 --> 00:31:18,320
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+272
+00:31:18,320 --> 00:31:20,040
+,000,000,000,000,000,000,000,000,000,000,000,000
+
+273
+00:31:42,710 --> 00:31:48,570
+بنبدل عناصر القطر الرئيسي ونغير إشارات عناصر
+
+274
+00:31:48,570 --> 00:31:58,290
+القطر الثانوي يبقى دي واحد على أ دي ناقص بي سي في
+
+275
+00:31:58,290 --> 00:32:04,650
+المصفوفة هذه أ دي بيصير هنا وال أ مكانها بنبدل ال أ
+
+276
+00:32:04,650 --> 00:32:11,070
+وال د مكان بعض ونغير إشارات عناصر القطر الثانويين
+
+277
+00:32:13,760 --> 00:32:19,640
+يبقى من هنا صارت هذه group السؤال هو is it abelian
+
+278
+00:32:19,640 --> 00:32:26,900
+group أيوة يبقى هنا ال general linear group of two
+
+279
+00:32:26,900 --> 00:32:39,500
+by two matrices is not abelian because السبب أن ال
+
+280
+00:32:39,500 --> 00:32:48,980
+a b لا يساوي BA وال A وال B موجودات في ال general
+
+281
+00:32:48,980 --> 00:32:53,380
+linear group of two by two matrices over R دير
+
+282
+00:32:53,380 --> 00:32:59,720
+بالك ما كتبتش for all A وB لأنه يمكن يوصف بيحصل
+
+283
+00:32:59,720 --> 00:33:03,380
+أحيان يطلع ال A في B ويساوي ال B في ال A لكن مش
+
+284
+00:33:03,380 --> 00:33:07,340
+دائماً يعني لو جيت حالة حالتين ثلاثة بيشدوا عن
+
+285
+00:33:07,340 --> 00:33:12,170
+القاعدة لكن ال general الكلام هذا ما لهمش صحيح يبقى
+
+286
+00:33:12,170 --> 00:33:17,530
+هذا مثال عملي فعلاً ومتعرف عليه واشتغلناه في ال
+
+287
+00:33:17,530 --> 00:33:22,090
+linear algebra أن هذه ال group عبارة عن non
+
+288
+00:33:22,090 --> 00:33:26,850
+abelian group تمام و ال identity element عرفنا
+
+289
+00:33:26,850 --> 00:33:37,290
+ممكن نيجي ناخد منها حالة خاصة يا جماعة إيه
+
+290
+00:33:37,290 --> 00:33:38,730
+بيه لا يساوي بيه
+
+291
+00:33:41,490 --> 00:33:49,370
+هي واحد على أ دي ناقص بي سي
+
+292
+00:33:49,370 --> 00:33:53,030
+دي ناقص بي سي اللي هو المحدد طبعاً
+
+293
+00:34:01,350 --> 00:34:06,390
+أنا كان بإمكاني أقول لك هذه matrix is an
+
+294
+00:34:06,390 --> 00:34:11,050
+associative binary operation ال binary operation
+
+295
+00:34:11,050 --> 00:34:15,270
+كان بإمكاني أعملها لك كالتالي أنا عندي شرط إن
+
+296
+00:34:15,270 --> 00:34:20,970
+المحدد لا يساوي صفر صح ولا لا إذا لو أخدت مصفوفتين
+
+297
+00:34:20,970 --> 00:34:26,980
+محددهم لا يساوي صفر لو ضربتهم في بعض وأخدت المحدد
+
+298
+00:34:26,980 --> 00:34:29,740
+تبعهم و دي يطلع معناه لا يساوي ذلك لأن ال
+
+299
+00:34:29,740 --> 00:34:33,220
+determinant لل A في ال B يساوي ال determinant لل A
+
+300
+00:34:33,220 --> 00:34:37,740
+في ال determinant يعني كان بإمكاني ها دي ها ها
+
+301
+00:34:37,740 --> 00:34:41,450
+اللي ال binary operation أقول كان أنا عندي ال
+
+302
+00:34:41,450 --> 00:34:48,010
+determinant لـA لا يساوي 0 و ال determinant لـB لا
+
+303
+00:34:48,010 --> 00:34:52,750
+يساوي 0 صح ولا لأ حسب ال condition اللي هما طينيها
+
+304
+00:34:52,750 --> 00:34:59,350
+الآن لو أخدت ال determinant للـA في الـB حسب
+
+305
+00:34:59,350 --> 00:35:02,570
+معلوماتنا من ال linear algebra اللي احنا قلنا
+
+306
+00:35:02,570 --> 00:35:07,170
+عليها ال linear algebra يبقى هذا بده يساوي
+
+307
+00:35:07,170 --> 00:35:14,630
+determinantللـ A determinant للـ B تمام؟ يبقى هذا
+
+308
+00:35:14,630 --> 00:35:20,110
+كله ما له لا يساوي Zero معناته حصل الضرب هذا موجود
+
+309
+00:35:20,110 --> 00:35:23,530
+وين؟ موجود في الـ U من هنا هذه صارت binary
+
+310
+00:35:23,530 --> 00:35:26,990
+operation و لا associative يا أخدناها في الثانوية
+
+311
+00:35:26,990 --> 00:35:33,650
+وكذلك أخدناها وين؟ في الجبر الخطي طيب ممكن نيجي
+
+312
+00:35:33,650 --> 00:35:39,030
+نروح ناخد حالة خاصة من ال general linear group هذه
+
+313
+00:35:39,030 --> 00:35:44,270
+بدل المحدد لا يساوي 0 بدي أقول محدد يساوي 1 صحيح
+
+314
+00:35:44,270 --> 00:35:48,370
+وهذه بسميها ال special linear group of two by two
+
+315
+00:35:48,370 --> 00:35:53,430
+matrices over R وهذه كمان بتلعب دور كبير في عين
+
+316
+00:35:53,430 --> 00:35:57,850
+الجبر عندنا في المسائل المختلفة
+
+317
+00:36:10,900 --> 00:36:19,600
+نمرة عشرة the set هي ال special linear a group
+
+318
+00:36:19,600 --> 00:36:26,860
+of two by two matrices over R اللي هي كل المصفوفات
+
+319
+00:36:26,860 --> 00:36:33,580
+اللي على الشكل اللي عندنا a,b,c,d بحيث أن ال a و
+
+320
+00:36:33,580 --> 00:36:43,020
+ال b و ال c و ال d هذه موجودة موجودة في ال Q أو ال
+
+321
+00:36:43,020 --> 00:37:01,080
+R أو ال C or ZP or ZP and وفي نفس الوقت and
+
+322
+00:37:03,500 --> 00:37:17,060
+الـ a d ناقص بي سي يساوي واحد هذه
+
+323
+00:37:17,060 --> 00:37:32,400
+is called the special linear a group of degree
+
+324
+00:37:34,480 --> 00:37:42,220
+of degree two over a يبقى دي بدل مكانة general هنا
+
+325
+00:37:42,220 --> 00:37:47,720
+قلنا special حالة خاصة منها المحدد يساوي واحد و
+
+326
+00:37:47,720 --> 00:37:57,140
+برضه هذه ما لها is هذه a group under matrix
+
+327
+00:37:57,140 --> 00:37:59,100
+multiplication
+
+328
+00:38:11,310 --> 00:38:17,870
+طيب تعالى نتفهم شوية ال general أنا أخدتها بس على
+
+329
+00:38:17,870 --> 00:38:23,330
+set of real numbers هنا إيش كاتب؟ كاتب ال elements
+
+330
+00:38:23,330 --> 00:38:28,470
+هدول ممكن يكونوا rational number و ممكن يكونوا
+
+331
+00:38:28,470 --> 00:38:32,470
+real number و ممكن يكونوا complex number و ممكن
+
+332
+00:38:32,470 --> 00:38:39,290
+يكونوا ZP حيث ال P is prime يبقى ال P هذا شباب هذا
+
+333
+00:38:39,290 --> 00:38:46,600
+prime يعني ممكن أخد العناصر من زد اثنين و من زد
+
+334
+00:38:46,600 --> 00:38:51,020
+ثلاثة و من زد خمسة و من زد سبعة و من زد أحد عشر و من
+
+335
+00:38:51,020 --> 00:38:58,440
+زد ثلاثة عشر لكن باخدهامش من مين باخدهامش من z6 باخدهامش
+
+336
+00:38:58,440 --> 00:39:03,800
+من z8 باخدهامش من z9 يبقى شرطنا أن zp prime يعني
+
+337
+00:39:03,800 --> 00:39:09,340
+بمعنى آخر أن هذه المصفوفات المجموعة المصفوفات
+
+338
+00:39:09,340 --> 00:39:14,260
+العناصر ممكن يكونوا من ال Q بس والمحدد لا يساوي
+
+339
+00:39:14,260 --> 00:39:18,740
+zero ممكن يكونوا من ال real numbers والمحدد لا
+
+340
+00:39:18,740 --> 00:39:21,360
+يساوي zero ممكن يكونوا من ال complex numbers
+
+341
+00:39:21,670 --> 00:39:26,050
+والمحدد لا يساوي Zero ممكن يكونوا من ال ZP والمحدد
+
+342
+00:39:26,050 --> 00:39:30,510
+ما له لا يساوي Zero الآن لو قلت هدول من ال real
+
+343
+00:39:30,510 --> 00:39:34,670
+number بيصير هذه حالة خاصة من مين؟ من السؤال اللي
+
+344
+00:39:34,670 --> 00:39:39,030
+جبله ال identity element هو واحد Zero Zero واحد
+
+345
+00:39:39,030 --> 00:39:44,570
+معكوس المصفوفة هو نفس المعكوس اللي عندنا هذا بس هذا
+
+346
+00:39:44,570 --> 00:39:49,450
+إيش بيصير؟ بروح بواحد لأن المحدد يساوي واحد يبقى
+
+347
+00:39:49,450 --> 00:40:01,580
+باجي بقوله هنا الواحد هو المصفوفة اللي هو ال matrix
+
+348
+00:40:01,580 --> 00:40:05,060
+اللي
+
+349
+00:40:05,060 --> 00:40:14,360
+هي واحد زيرو زيرو واحد is the identity element
+
+350
+00:40:16,350 --> 00:40:21,410
+In the special linear group of two by two matrices
+
+351
+00:40:21,410 --> 00:40:31,730
+over R The inverse of الـ A والـ B والـ C والـ D
+
+352
+00:40:31,730 --> 00:40:36,070
+اللي موجودة في ال general linear group of two by
+
+353
+00:40:36,070 --> 00:40:41,490
+two ال special linear group of two by two matrices
+
+354
+00:40:59,540 --> 00:41:07,060
+ما ينطبق على R ينطبق على ال special linear of two
+
+355
+00:41:07,060 --> 00:41:14,180
+by two matrices over q و over c و over zp يبقى
+
+356
+00:41:14,180 --> 00:41:25,700
+this is a true for ال general for ال special الـ
+
+357
+00:41:25,700 --> 00:41:32,940
+Special Linear Group of 2x2 matrices over Q والـ
+
+358
+00:41:32,940 --> 00:41:39,580
+Special Linear Group of 2x2 matrices over C والـ
+
+359
+00:41:39,580 --> 00:41:46,480
+Special Linear Group of 2x2 matrices over ZT
+
+360
+00:41:48,480 --> 00:41:53,700
+أظن هدول كلهم طبيعي بسهولة الحسابات لكن تعالى نحسب
+
+361
+00:41:53,700 --> 00:42:01,380
+لك شغلة زي هذه نعطيك مصفوفة موجودة في zp ونشوف إيش
+
+362
+00:42:01,380 --> 00:42:10,100
+اللي حصل for example consider
+
+363
+00:42:13,480 --> 00:42:26,520
+زد بي هي زد فايف يبقى
+
+364
+00:42:26,520 --> 00:42:33,500
+then اللي هو غرض واحد zero zero واحد is the
+
+365
+00:42:33,500 --> 00:42:40,020
+identity element
+
+366
+00:42:42,350 --> 00:42:46,330
+طب بنفع يا شباب أقول في زد خمسة في عندنا واحد خمسة
+
+367
+00:42:46,330 --> 00:42:54,070
+ثلاثة أربعة واحد خمسة ثلاثة أربعة بنفع؟ لا الخمسة
+
+368
+00:42:54,070 --> 00:43:00,710
+مش موجودة هذا زد خمسة معاك من zero واحد اثنين
+
+369
+00:43:00,710 --> 00:43:06,090
+ثلاثة لغاية أربعة أقل من أنه بتبدأ من وين؟ بتبدأ
+
+370
+00:43:06,090 --> 00:43:13,020
+من ال zero يبقى الأرقام اللي بدك تاخدها تبقى zero
+
+371
+00:43:13,020 --> 00:43:17,820
+واحد اثنين ثلاثة أربعة فقط لغير ما تزيد عليهم هاي
+
+372
+00:43:17,820 --> 00:43:23,220
+واحدة الثانية بد المحدد تبعه يكون كده مشان يكون
+
+373
+00:43:23,220 --> 00:43:27,000
+يكون كلامها صحيح طيب يبقى هذا هو ال identity
+
+374
+00:43:27,000 --> 00:43:30,460
+element لمين لل group هذي
+
+375
+00:43:34,350 --> 00:43:49,710
+the inverse of a b c d is نفس القصة d a ناقص b و
+
+376
+00:43:49,710 --> 00:44:00,380
+هنا ناقص c نعطي مثال عددي غالي يعني ناخد مصفوفة
+
+377
+00:44:00,380 --> 00:44:05,360
+عناصرها من زد خمسة ونشوف كيف بدنا نجبلها من
+
+378
+00:44:05,360 --> 00:44:07,260
+المعكوس
+
+379
+00:44:26,010 --> 00:44:34,470
+تساوي مثلا تلاتة أربعة أربعة أربعة بالشكل اللي
+
+380
+00:44:34,470 --> 00:44:38,230
+عندنا بدأ
+
+381
+00:44:38,230 --> 00:44:46,270
+أشوف هل المصفوفة هذه موجودة في ال special linear
+
+382
+00:44:46,270 --> 00:44:51,030
+group هذه ولا لأ بمعنى آخر العناصر تبقى تلاتة و
+
+383
+00:44:51,030 --> 00:44:54,970
+أربعة و أربعة و أربعة موجودة في Z خمسة كلام مظبوط
+
+384
+00:44:54,970 --> 00:45:01,770
+اثنين هل المحدد بدي يساوي واحد أم لا ماجي بقوله هذا
+
+385
+00:45:01,770 --> 00:45:11,410
+بدي determinant  للـ A يبقى تلاتة في أربعة ناقص اللي
+
+386
+00:45:11,410 --> 00:45:16,830
+هو أربعة في أربعة كل هذا موديولو
+
+387
+00:45:19,400 --> 00:45:24,280
+يبقى هذا الكلام يبدو يساوي تلاتة في أربعة اثنا عشر
+
+388
+00:45:24,280 --> 00:45:33,440
+ناقص ستة عشر موديولو خمسة ويساوي ناقص أربعة موديولو
+
+389
+00:45:33,440 --> 00:45:40,100
+خمسة طيب الناقص أربعة هذه لو ضفت لها المقياس اللي
+
+390
+00:45:40,100 --> 00:45:46,890
+هو خمسة بيطلع كده واحد يبقى هذه بيطلع واحد module
+
+391
+00:45:46,890 --> 00:45:51,870
+وخمسة يعني بواحد يبقى بناء عليها شباب ال
+
+392
+00:45:51,870 --> 00:45:56,350
+determinant للـ A ساوى واحد معناته المصفوفة
+
+393
+00:45:56,350 --> 00:46:03,790
+هذه موجودة يبقى هذا معناه أن المصفوفة تلاتة أربعة
+
+394
+00:46:03,790 --> 00:46:09,490
+أربعة أربعة belongs للـ special linear group of two
+
+395
+00:46:09,490 --> 00:46:17,130
+by two matrices over z five طيب بدنا نجيب المعكوس
+
+396
+00:46:17,130 --> 00:46:29,770
+تبعها باجي بقول الآن the inverse matrix of اللي هي
+
+397
+00:46:29,770 --> 00:46:37,010
+تلاتة أربعة أربعة أربعة is المحدد بواحد صحيح يبقى
+
+398
+00:46:37,010 --> 00:46:42,110
+بنقسم عليه يبقى باجي بقوله بيصير هنا أربعة و هنا
+
+399
+00:46:42,110 --> 00:46:48,210
+تلاتة بدلنا عناصر القطر الرئيسي مكان بعض عناصر قطر
+
+400
+00:46:48,210 --> 00:46:56,850
+الفرعي بيكون بالمن؟ بالصالب بالشكل هذا طيب
+
+401
+00:46:56,850 --> 00:47:02,290
+لو جينا لبعضكم وقلنا له طب أربعة في تلاتة باثنا عشر
+
+402
+00:47:02,630 --> 00:47:09,590
+ناقص 16 يظهر ناقص 4 يعني واحد طيب أنا بدي أجيبها
+
+403
+00:47:09,590 --> 00:47:15,470
+لك بطريقة أخرى لو جيت قلت لك بالشكل اللي عندنا هنا
+
+404
+00:47:15,470 --> 00:47:20,550
+لأن هتيجي تقول الـ ZP فش فيها سالب أربعة وسالب
+
+405
+00:47:20,550 --> 00:47:25,790
+أربعة زد P تبدأ من وندي Zero واحد اثنين لغاية P
+
+406
+00:47:25,790 --> 00:47:29,950
+ناقص واحد ما نشوفش عندي سالب طب والسالب هذا كيف
+
+407
+00:47:29,950 --> 00:47:35,510
+جبته بقول لك بسيطة جدا الآن هذا السالب بدي أحوله إلى
+
+408
+00:47:35,510 --> 00:47:40,730
+موجب الموجب بخليها زي ما هي السالب أنا زد خمسة
+
+409
+00:47:40,730 --> 00:47:46,570
+يبقى المقياس عندي قداش خمسة إذا بدي أروح أضيف خمسة
+
+410
+00:47:46,570 --> 00:47:51,810
+للسالب أربعة بيطلع قداش واحد يبقى هذا عندنا واحد و
+
+411
+00:47:51,810 --> 00:47:57,590
+هذه واحد وهذه تلاتة تمام؟
+
+412
+00:47:59,780 --> 00:48:06,160
+أنا أدعي أن هذه المصفوفة هي معكوس من؟ معكوس
+
+413
+00:48:06,160 --> 00:48:11,920
+المصفوفة الأصلية، مشان يبقى كلام صحيح لو ضربتها من
+
+414
+00:48:11,920 --> 00:48:16,400
+اليمين أو من الشمال بدي يطلع من؟ مصفوفة الوحدة
+
+415
+00:48:16,400 --> 00:48:20,540
+يبقى دير بالك، أي مصفوفة أخرى تأخذها بعد ذلك
+
+416
+00:48:20,540 --> 00:48:23,520
+موجودة في ال especially بقيت عاملها بنفس الطريقة
+
+417
+00:48:23,830 --> 00:48:26,990
+يعني أنا مش جايبها للناس اللي هو إنما مش هنعلمك
+
+418
+00:48:26,990 --> 00:48:33,550
+كيفية الحسابات في ZP بدك تجيب عناصر المصفوفة لعناصر
+
+419
+00:48:33,550 --> 00:48:38,830
+اليوم اللي ميكونوا من ZP اثنين النتيجة اللي اتضارب
+
+420
+00:48:38,830 --> 00:48:45,210
+نتيجة اللي أخد المحدد بدك تتقيد بخاصة ZP وشروط ال
+
+421
+00:48:45,210 --> 00:48:48,590
+special linear group أن المحدد تبعها بده يساوي 
+422
+00:48:48,590 --> 00:48:56,450
+بده يساوي واحد الآن لو ضربت
+
+423
+00:48:56,450 --> 00:48:59,950
+اثنين في بعض إذا ما طلعش مصفوفة الوحدة بيصير كلامي
+
+424
+00:48:59,950 --> 00:49:07,160
+غلط اثنين أنا لما أدعي أن هذه المعكوس المصفوفة هذه
+
+425
+00:49:07,160 --> 00:49:12,240
+لازم العناصر اللي يطلعوا دول يكون موجودات في Z فيه
+
+426
+00:49:12,240 --> 00:49:15,760
+يبقى الواحد والتلاتة والأربعة والواحد كلهم
+
+427
+00:49:15,760 --> 00:49:21,520
+موجودة في Z خمسة مظبوط يبقى كله من Z خمسة الآن أنا
+
+428
+00:49:21,520 --> 00:49:26,560
+لازم أقول it was كذا because ليش هذه هي المعكوس
+
+429
+00:49:26,560 --> 00:49:32,280
+أنا الآن حسبت عمليا بس بدي أثبتها رياضيا لو قلت
+
+430
+00:49:32,280 --> 00:49:35,560
+تلاتة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+431
+00:49:35,560 --> 00:49:37,500
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+432
+00:49:37,500 --> 00:49:38,180
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+433
+00:49:38,180 --> 00:49:41,000
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+434
+00:49:41,000 --> 00:49:43,560
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+435
+00:49:43,560 --> 00:49:44,860
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+436
+00:49:44,860 --> 00:49:45,360
+أربعة أربعة أربعة أربعة أربعة أربعة أربعة أربعة
+
+437
+00:49:45,360 --> 00:49:51,580
+أربعة أربعة أربعة أربعة أربعة أربعة 
+
+438
+00:49:53,510 --> 00:49:57,510
+طيب الصفر الثاني في العمود الثاني تلاتة وأربعة في
+
+439
+00:49:57,510 --> 00:50:03,870
+تلاتة باثنا عشر اثنا عشر وتلاتة خمسة عشر أربعة في أربع
+
+440
+00:50:03,870 --> 00:50:11,870
+ستة عشر وأربعة وعشرين الآن أربعة في واحد بأربعة وأربعة في
+
+441
+00:50:11,870 --> 00:50:18,250
+تلاتة باثنا عشر اللي هي ستة عشر لكن أنا بدي هذا كله
+
+442
+00:50:18,250 --> 00:50:24,590
+موديول خمسة موديول الخمسة هنا واحد زيرو وهنا زيرو
+
+443
+00:50:24,590 --> 00:50:30,610
+واحد هو الـ identity matrix يبقى فعلا هذه هي هذه
+
+444
+00:50:30,610 --> 00:50:35,490
+اللي هي المصفوفة ومعكوس هذه المصفوفة هي المصفوفة اللي
+
+445
+00:50:35,490 --> 00:50:39,310
+عندنا يبقى عند الحسابات في زد خمسة في زد سبعة في
+
+446
+00:50:39,310 --> 00:50:45,240
+زد أحد عشان بدك تحسب بنفس الطريقة اللي عندنا ازلنا
+
+447
+00:50:45,240 --> 00:50:50,920
+في المحاضرة القادمة مع مزيد من الأمثلة على Legros 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e749a61c5e9ec72646b12f19e3a13be4ae55a864
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_postprocess.srt
@@ -0,0 +1,1848 @@
+1
+00:00:21,090 --> 00:00:25,950
+أحنا واصل ما بدأنا فيه المرة الماضية و هو حل اللي
+
+2
+00:00:25,950 --> 00:00:30,570
+هو المسائل على شبتر تمانية الاكستاناداركت برودرك
+
+3
+00:00:30,570 --> 00:00:35,110
+وصلنا لسؤال واحد واربعين بقول express automorphism
+
+4
+00:00:35,110 --> 00:00:40,070
+ل U خمسة وعشرين in the form ZM اكستاناداركت برودرك
+
+5
+00:00:40,070 --> 00:00:41,390
+مع ZN
+
+6
+00:00:43,960 --> 00:00:48,680
+بمعنى اخر بدي اجيب جروب لجروب هذه تبقى isomorphic
+
+7
+00:00:48,680 --> 00:00:54,060
+لمام لل U خمسة وعشرين طب احنا عندنا ال U خمسة
+
+8
+00:00:54,060 --> 00:00:59,680
+وعشرين solution عندنا
+
+9
+00:00:59,680 --> 00:01:07,500
+ال U خمسة وعشرين اللي هو U خمسة لكل تربيع الشكل
+
+10
+00:01:07,500 --> 00:01:16,670
+اللي عندنا هذه isomorphicأو ال atomorphism ل U
+
+11
+00:01:16,670 --> 00:01:23,730
+خمسة وعشرين هذه تساوي U خمسة تربيع مباشرة طبعا
+
+12
+00:01:23,730 --> 00:01:32,770
+اخدت عندك ان ال U مرفوعة ل prime P ومرفوعة ل أس N
+
+13
+00:01:32,770 --> 00:01:39,550
+U P أس N ناقص P أس N minus ال one كتبناها معاكم
+
+14
+00:01:39,550 --> 00:01:45,390
+المرة الماضيةفي آخر محاضرة تجدها موجودة معاك نحاول
+
+15
+00:01:45,390 --> 00:01:50,950
+نطبق هذا الكلام عالميا على أرض الواقع يبقى بناء
+
+16
+00:01:50,950 --> 00:01:55,330
+عليه يو خمسة وعشرين كتبناها بالشكل هذه بقدر اقول
+
+17
+00:01:55,330 --> 00:01:58,070
+هذه isomorphic لمين
+
+18
+00:02:02,510 --> 00:02:09,870
+Isomorphic لزد P اللي هي خمسة تربيع ناقص خمسة أس
+
+19
+00:02:09,870 --> 00:02:14,390
+اتنين ناقص واحد بالشكل اللي عندنا هنايبقى هذا
+
+20
+00:02:14,390 --> 00:02:19,790
+الكلام هذه تساوي من خمسة ترابيع ليه خمسة وعشرين
+
+21
+00:02:19,790 --> 00:02:27,090
+وهذه خمسة وسواحد يبقى زد عشرين شكل اللي عندنا هنا
+
+22
+00:02:27,090 --> 00:02:31,710
+هذا U خمسة وعشرين انا مابدي U خمسة وعشرين بدي
+
+23
+00:02:31,710 --> 00:02:38,540
+اتومورفزم ل U خمسة وعشرينإذا بناء عليه atomorphism
+
+24
+00:02:38,540 --> 00:02:47,580
+ل U خمسة وعشرين اللي هي isomorphic لمهم اللي هو
+
+25
+00:02:47,580 --> 00:02:54,750
+atomorphism ل Z عشرين الشكل اللي عندنا هناأخذنا
+
+26
+00:02:54,750 --> 00:03:03,470
+كمان نظرية سابقة اتومورفزم ل ZN ايزو مورفك ل UN
+
+27
+00:03:03,470 --> 00:03:10,830
+شبطر اللي قبله اخر نظرية يبقى هذا ايزو مورفك ل U20
+
+28
+00:03:11,920 --> 00:03:19,120
+U20 هذه اللي بقدر اكتبها اللي هي تساوي U أربعة في
+
+29
+00:03:19,120 --> 00:03:25,440
+خمسة والاربعة خمسة are relatively prime يبقى هذه
+
+30
+00:03:25,440 --> 00:03:34,070
+isomorphic لمينلأ اللي هو isomorphic او هدى تساوي
+
+31
+00:03:34,070 --> 00:03:39,990
+او isomorphic دُغري لمهم ل U أربعة external
+
+32
+00:03:39,990 --> 00:03:49,530
+product مع U خمسة مرة تانية ل U أربعة هدى U تنين
+
+33
+00:03:49,530 --> 00:03:58,130
+تربيعهذه اخدناها ايزو مورفك لمين لزد دي اتنين وهذه
+
+34
+00:03:58,130 --> 00:04:03,170
+بتطبق عليها القاعدة اللي طبقناها فوق تماما يبقى
+
+35
+00:04:03,170 --> 00:04:10,730
+بالداجي اقول هذا زد خمسة أس واحد ناقص خمسة أس واحد
+
+36
+00:04:10,730 --> 00:04:17,180
+ناقص واحدهذا الكلام يساوي زد اتنين external by
+
+37
+00:04:17,180 --> 00:04:22,880
+product هذه خمسة وهذه خمسة وزيرو خمسة وزيرو أبواحد
+
+38
+00:04:22,880 --> 00:04:29,420
+خمسة ناقص واحد اللي هي أربعة زد اربعة زد اربعة اه
+
+39
+00:04:29,420 --> 00:04:35,300
+زد اربعة يبقى هذه زد اربعة معناه هذا الكلام ان ال
+
+40
+00:04:35,300 --> 00:04:41,050
+atomorphism ليه خمسة وعشرين isomorphic لمهملزد
+
+41
+00:04:41,050 --> 00:04:45,490
+اتنين external product زد اربعة وبالتالي عندي
+
+42
+00:04:45,490 --> 00:04:50,030
+تمانية atomorphism من ال U خمسة وعشرين الى ال U
+
+43
+00:04:50,030 --> 00:04:54,910
+خمسة وعشرين اتسل بغض النظر عن شكلهم قال لي اكتبلي
+
+44
+00:04:54,910 --> 00:05:01,170
+ال atomorphism ل U خمسة وعشرين على شكل ZM في ZN
+
+45
+00:05:01,170 --> 00:05:05,310
+يبقى هي كتبتله بالشكل هذا باستخدام القواعد اللي
+
+46
+00:05:05,310 --> 00:05:08,130
+أخدناها المرة الماضية
+
+47
+00:05:10,010 --> 00:05:20,890
+بعدها بيقول ليه في 46 يبقى 46 بيقول ما يأتي بيقول
+
+48
+00:05:20,890 --> 00:05:28,510
+هاتلي isomorphism بدنا isomorphism من وين لوين في
+
+49
+00:05:28,510 --> 00:05:34,770
+من اللي هو ال group Z12 إلى مين
+
+50
+00:05:37,910 --> 00:05:46,330
+السؤال ستة اربع يقول ز أربع في ز تلاتة يبقى ز أربع
+
+51
+00:05:46,330 --> 00:05:52,270
+كستينو دايكا product مع ز تلاتة مع ز تلاتة بقول
+
+52
+00:05:52,270 --> 00:05:56,740
+عرف ليه اللي هو isomorphismمن ال group هذه لل
+
+53
+00:05:56,740 --> 00:06:01,240
+group هذه انا بعطيك ال function وانت عليك تثبت
+
+54
+00:06:01,240 --> 00:06:05,620
+انها one to one and انت وتخدم خاصيات ال
+
+55
+00:06:05,620 --> 00:06:08,680
+isomorphism ال function اللي بتقول عليها شبه
+
+56
+00:06:08,680 --> 00:06:14,630
+بالشكل التالي phi of x يبقى x وين موجودة هذه؟في
+
+57
+00:06:14,630 --> 00:06:19,810
+Z12 بدي أجسمها إلى مركبتين واحدة موجودة في Z4
+
+58
+00:06:19,810 --> 00:06:25,390
+واحدة موجودة في Z3 يبقى بقدر أقول له هذه على الشكل
+
+59
+00:06:25,390 --> 00:06:33,210
+التالي طبعا العدد اللي هنا في Z12 اللي هو مين اللي
+
+60
+00:06:33,210 --> 00:06:38,470
+هو العدد قد يكون من عند ال zero لغاية من ال 11
+
+61
+00:06:38,470 --> 00:06:44,350
+وهكذاإذا بدى أخلي مركبة موجودة في Z4 و مركبة
+
+62
+00:06:44,350 --> 00:06:51,030
+موجودة في Z3 إذا بقدر أقول هذا X modulo 4 و
+
+63
+00:06:51,030 --> 00:06:57,070
+المركبة التانية X modulo 3 يعني العدد اللى باخده
+
+64
+00:06:57,070 --> 00:07:04,230
+من Z12 أكبر من 4 ولا أكبر من 3 افترض كان 2يبقى
+
+65
+00:07:04,230 --> 00:07:07,830
+باجي بقول فاي اف اتنين يسوى اتنين موديوله أربعة
+
+66
+00:07:07,830 --> 00:07:11,130
+اللي هو باتنين و اتنين موديوله تلاتة اللي هو
+
+67
+00:07:11,130 --> 00:07:16,510
+باتنين لكن لو قلتله خمسة فاي خمسة بدي يكون هنا
+
+68
+00:07:16,510 --> 00:07:20,370
+واحد و هنا كداش و هنا اتنين و هكذا يبقى هاي
+
+69
+00:07:20,370 --> 00:07:23,490
+المقصودة هاي ال function قدامك بس تبتليها one to
+
+70
+00:07:23,490 --> 00:07:30,670
+one and on to وتخدم خاصية ال isomorphismهذا قال له
+
+71
+00:07:30,670 --> 00:07:35,210
+ستة واربعين تمانية واربعين بيقولوا show that five
+
+72
+00:07:35,210 --> 00:07:42,310
+is an isomorphism
+
+73
+00:07:42,310 --> 00:07:48,650
+من زد تلاتة cross زد خمسة لزد خمستاشر يبقى تمانية
+
+74
+00:07:48,650 --> 00:07:59,630
+واربعين ان في من من زد تلاتة external productمع
+
+75
+00:07:59,630 --> 00:08:07,090
+مين؟ مع z خمسة لمن؟ ل z خمستاشر بالشكل اللي عندنا
+
+76
+00:08:07,090 --> 00:08:14,410
+هذا z خمستاشر و بحيث انه ال five of اتنين و تلاتة
+
+77
+00:08:14,410 --> 00:08:20,370
+بده يسوى اتنين بقول find an element a و b في هذا
+
+78
+00:08:20,370 --> 00:08:26,050
+بحيث ال maps to one يبقى انا بدي اوجداللي هو
+
+79
+00:08:26,050 --> 00:08:31,950
+element a و b صورته main صورته الواحد او five of a
+
+80
+00:08:31,950 --> 00:08:36,570
+و b اللي بتعطينا main بتعطينا الواحد
+
+81
+00:08:41,470 --> 00:08:46,970
+سؤال مرة تانية في انا isomorphism ال isomorphism
+
+82
+00:08:46,970 --> 00:08:55,090
+من ال group z3 external to z5 إلى z15 وفي انا معطع
+
+83
+00:08:55,090 --> 00:08:58,810
+ان فيلم اتأثر على الاتنين والتلاتة النتيجة تساوي
+
+84
+00:08:58,810 --> 00:09:05,390
+اتنين جليهات للعنصر a وb لصورته من؟ لصورته الواحد
+
+85
+00:09:05,390 --> 00:09:09,190
+الصحيح حد فيكو حل هذا السؤال
+
+86
+00:09:12,670 --> 00:09:19,130
+أه يعني مدن امتحانات مش داعي للحل كويس طيب على أي
+
+87
+00:09:19,130 --> 00:09:24,310
+حال أنا مرة حلتلكوا سؤال شبيه بهذا في اللي قبل لما
+
+88
+00:09:24,310 --> 00:09:28,110
+أخدنا ال isomorphism حلتكوا سؤال شبيه به بس هذا
+
+89
+00:09:28,110 --> 00:09:33,060
+الفرق بينه وبين هذا هذا مكون من مين منorder pair
+
+90
+00:09:33,060 --> 00:09:36,880
+order pair والله مش order pair بتفرجش عنها شوف يا
+
+91
+00:09:36,880 --> 00:09:41,180
+سيدي انا بدي العنصر a و b اللي صورته تحت أثير الفا
+
+92
+00:09:41,180 --> 00:09:47,540
+يساوي واحد هناك كان بدي شكل ال isomorphism عبارة
+
+93
+00:09:47,540 --> 00:09:51,440
+عن إيش كان في السؤال اللي جابله لكن هذا لأ بدي ال
+
+94
+00:09:51,440 --> 00:09:57,040
+order a و b اللي صورته تساوي مين تساوي واحد صحيح
+
+95
+00:09:57,460 --> 00:10:02,300
+بقول كويس بحاول استخدام المعلومة هذه بقدر الإمكان
+
+96
+00:10:02,300 --> 00:10:08,820
+ولذلك بحاول أجيب المعطى هذا اللي هو واحد في الصورة
+
+97
+00:10:08,820 --> 00:10:12,920
+اللي قدامي هنا يعني بدي أجيب علقة تربط بين الواحد
+
+98
+00:10:12,920 --> 00:10:18,140
+واتنين اللي عندنا حتى نقدر نحسب كم هذا ال element
+
+99
+00:10:18,140 --> 00:10:24,930
+الان لو جيت واحد الواحد هذا موجود في أي groupفنيات
+
+100
+00:10:24,930 --> 00:10:31,430
+زد خمستاشر هل هذا الواحد يكافئ رقم تاني اللي هو
+
+101
+00:10:31,430 --> 00:10:37,490
+مين ستاشر ممتاز يعني الواحد هذا بالضبط هو عبارة عن
+
+102
+00:10:37,490 --> 00:10:45,610
+ستاشر modulo خمستاشر تمام الستاشر مش هي عبارة عن
+
+103
+00:10:45,610 --> 00:10:53,640
+تمانية في اتنين modulo خمستاشرتمام طب اتنين مديله
+
+104
+00:10:53,640 --> 00:10:58,380
+خمستاشر ما هو اتنين صح ولا لأ يبقى اتنين اللي عندي
+
+105
+00:10:58,380 --> 00:11:02,580
+هذه بقدر اشيلها و اكتر بدلها في او في اتنين و
+
+106
+00:11:02,580 --> 00:11:08,740
+تلاتة يبقى هذا الكلام بدي يساوي تمانية في في او في
+
+107
+00:11:08,740 --> 00:11:16,810
+اتنين و تلاتة كأن المثل ايشكأنه تمانية انا هدم
+
+108
+00:11:16,810 --> 00:11:21,250
+طلعها من جوا الجوس وطلعها مين؟ برا وزي ما كنا نقول
+
+109
+00:11:21,250 --> 00:11:27,190
+Alpha of خمسة يسوى خمسة في Alpha of واحد تمام هنا
+
+110
+00:11:27,190 --> 00:11:31,850
+نفس الفكرة بالضبط تماما كأنه تمانية كانت جوا وانا
+
+111
+00:11:31,850 --> 00:11:36,310
+طلعتها برا اذا بدأ دخلها جوا يبقى لو دخلتها جوا
+
+112
+00:11:36,310 --> 00:11:41,710
+هضربها وين في كل عنصر من هذه العناصر بس اتنين هذه
+
+113
+00:11:41,710 --> 00:11:47,790
+موجودة وينفي زد تلاتة والتلاتة هذه موجودة في زد
+
+114
+00:11:47,790 --> 00:11:51,730
+خمسة إذا عند الضرب بدك اتراعي من؟ بدك اتراعي
+
+115
+00:11:51,730 --> 00:11:57,430
+النتيجة إذا هذا الكلام بده يساوي بيده يساوي five
+
+116
+00:11:57,430 --> 00:12:04,190
+تمانية في اتنين modulo الأولى اللي هي تلاتة
+
+117
+00:12:04,190 --> 00:12:11,000
+والمركبة التانية تمانية في تلاتة modulo خمسةهذا
+
+118
+00:12:11,000 --> 00:12:16,680
+الكلام بده يسوى five تمانية في اتنين بستعش مضيله
+
+119
+00:12:16,680 --> 00:12:22,800
+تلاتة بيبقى واحد يبقى واحد و تلاتة في تمانية اربعة
+
+120
+00:12:22,800 --> 00:12:28,320
+وعشرين مضيله خمسة اللي هو اربع يبقى الواحد اللي
+
+121
+00:12:28,320 --> 00:12:33,520
+عندي هو صورة ال order per man واحد واربعة هذا
+
+122
+00:12:33,520 --> 00:12:40,200
+معناه ان ال a و ال b بده يسوى جداش واحد واربع
+
+123
+00:12:45,820 --> 00:12:52,020
+طيب هذا كان سؤال اللي هو تمانية واربعين بدنا نروح
+
+124
+00:12:52,020 --> 00:12:57,840
+لسؤال تمانية وخمسينتمانية و خمسين بيقول لي without
+
+125
+00:12:57,840 --> 00:13:02,100
+doing any calculations in atomorphism Z عشرين
+
+126
+00:13:02,100 --> 00:13:07,940
+determine how many elements of atomorphism Z عشرين
+
+127
+00:13:07,940 --> 00:13:16,560
+ال order لهم يساوي أربعة بدي سؤال تمانية و خمسين
+
+128
+00:13:16,560 --> 00:13:31,780
+the number of elements ofOrder four in atomorphism
+
+129
+00:13:31,780 --> 00:13:33,640
+لزاد عشرين
+
+130
+00:13:40,950 --> 00:13:46,130
+بقول اجيبلي اكام انصر في الاتومورفزم لزد عشرين ال
+
+131
+00:13:46,130 --> 00:13:51,070
+order اللي لهم يساوي اربعة بدونها بدون ما اروح
+
+132
+00:13:51,070 --> 00:13:56,330
+تبحث في شكل الاتومورفزم هدول بدك تعرفلي كده بدون
+
+133
+00:13:56,330 --> 00:14:01,850
+ما تعرفلي شكل ولا function بقوله كويسيبقى solution
+
+134
+00:14:01,850 --> 00:14:07,150
+يبقى معنى هذا الكلام انا بدي استخدم اي شغلة لها
+
+135
+00:14:07,150 --> 00:14:11,470
+علاقة بال atomorphism ل Z عشرين احنا عندنا ال
+
+136
+00:14:11,470 --> 00:14:16,790
+atomorphism ل Z عشرين ايزو مورفك لمين يا شباب ل ال
+
+137
+00:14:16,790 --> 00:14:23,750
+U عشرين ممتاز و ال U عشرين هذه اللي هي U اللي هي
+
+138
+00:14:23,750 --> 00:14:31,010
+عبارة عن U اربعة في خمسةوالاربعة في الخمسة are
+
+139
+00:14:31,010 --> 00:14:35,870
+relatively primeمدام relatively prime يبقى هذه
+
+140
+00:14:35,870 --> 00:14:47,070
+isomorphic لمام ل U4 external product مع U5 ال U4
+
+141
+00:14:47,070 --> 00:14:54,570
+هذه اللي هي isomorphic لمام ل Z2 external product
+
+142
+00:14:54,570 --> 00:14:56,230
+مع U5
+
+143
+00:15:00,200 --> 00:15:05,120
+عشان أضيع وقت فيها يبقى isomorphic لزد اربعة اذا
+
+144
+00:15:05,120 --> 00:15:11,720
+عندي تمانية اتومورفزم لمان لزد عشرين بدى ادور من
+
+145
+00:15:11,720 --> 00:15:17,440
+التمانية هدول يبقى ما ينطبق على الاتومورفزم لزد
+
+146
+00:15:17,440 --> 00:15:23,540
+عشرين ينطبق على الاتومورفزم لمانلزد اتنين اكس تانو
+
+147
+00:15:23,540 --> 00:15:28,120
+ضايق product مع مين مع زد اربعة معناه هذا الكلام
+
+148
+00:15:28,120 --> 00:15:34,060
+مادام هذه ايزو مورفك لهذه اذا لو لجيت جديش عدد
+
+149
+00:15:34,060 --> 00:15:38,300
+العناصر في ال group هذه لل order إلهم يساوي أربعة
+
+150
+00:15:38,300 --> 00:15:42,340
+بكون جبت عدد ال atom morphisms اللي ال order إلهم
+
+151
+00:15:42,340 --> 00:15:48,060
+يساوي مين أربعة يعني هذه صعب العمل فيها لكن هذه
+
+152
+00:15:48,060 --> 00:15:54,020
+سهل العمل فيهاومن هنا التحويلات هذه بتنقلنا من
+
+153
+00:15:54,020 --> 00:15:59,480
+جروب صعب التعامل معاها إلى جروب سهل التعامل معاها
+
+154
+00:16:01,670 --> 00:16:05,970
+أنا بدي أبحث من العناصر اللي في Z2 Extended
+
+155
+00:16:05,970 --> 00:16:11,390
+Product كده عددهم ال order لهم بده يساوي من؟ بده
+
+156
+00:16:11,390 --> 00:16:16,970
+يساوي الأربعة يبقى بداتي أقول له assume افترض انه
+
+157
+00:16:16,970 --> 00:16:23,250
+عندي element a و b موجود في Z2 Extended Product مع
+
+158
+00:16:23,250 --> 00:16:31,480
+Z4 such that بحيث انالأردر لـ A و لـ B اللي هو
+
+159
+00:16:31,480 --> 00:16:36,660
+لساوي ال least common multiple للأردر بتابع ال A
+
+160
+00:16:36,660 --> 00:16:41,340
+والأردر بتابع ال B هذا الكلام دي ساوي كده؟ دي ساوي
+
+161
+00:16:41,340 --> 00:16:45,220
+أربعة الأردر
+
+162
+00:16:45,220 --> 00:16:56,900
+المحتملة ال orders of A are مين يا شباب؟ كده؟ واحد
+
+163
+00:16:56,900 --> 00:17:02,030
+و كده؟واحد واثنين هذه الـ elements بتاع الـ z
+
+164
+00:17:02,030 --> 00:17:05,630
+اتنين Zero و واحد Zero هو ال identity ال order له
+
+165
+00:17:05,630 --> 00:17:09,230
+بواحد و الواحد له ال order اتنين اللي لو جمعت واحد
+
+166
+00:17:09,230 --> 00:17:11,830
+زي واحد يسوى اتنين فزي اتنين ب Zero اللي هو ال
+
+167
+00:17:11,830 --> 00:17:16,090
+identity يبقى ال orders المحتملة اللي هي واحد و
+
+168
+00:17:16,090 --> 00:17:28,660
+اتنين and ال orders of B areممكن واحد واتنين واربع
+
+169
+00:17:28,660 --> 00:17:32,760
+تمام تلاتة مافيش حاجة لإن التلاتة لا تقسم الأربع
+
+170
+00:17:32,760 --> 00:17:36,740
+يبقى اما ال order اي واحد او اتنين او اربع طيب
+
+171
+00:17:36,740 --> 00:17:40,140
+هدول الرقامين لو بدى اجيب ال least common multiple
+
+172
+00:17:40,140 --> 00:17:45,620
+مع هدول بشكلولي مشكلة؟لأ واحد اتنين هي واحد و
+
+173
+00:17:45,620 --> 00:17:49,900
+اتنين اذا هدال بدون تفكير بدي اخد الانصارين زي ما
+
+174
+00:17:49,900 --> 00:17:55,280
+هم لكن بدي ادور هنا الارقام اللي بتعملي ال least
+
+175
+00:17:55,280 --> 00:17:58,920
+common multiple مع مين مع هدول بيعطيني اربعة
+
+176
+00:17:58,920 --> 00:18:03,180
+السؤال هو لو كان خدت العناصر ال order اللي لهم
+
+177
+00:18:03,180 --> 00:18:08,020
+واحد و اتنين بيجيبولي عناصر يبقى مفيش insert يبقى
+
+178
+00:18:08,020 --> 00:18:12,980
+مفيش اخد الا اللي ال order له يسوى manأربعة فقط و
+
+179
+00:18:12,980 --> 00:18:16,760
+هدول بدي أخدهم هم اتنين زي ما هم كويس هدول شوف
+
+180
+00:18:16,760 --> 00:18:20,860
+هدول بيعطوني تبدل تان او بيعطوني اتنين على طول
+
+181
+00:18:20,860 --> 00:18:27,940
+الخط و هدول تعالى نشوف ايش بدي نعمل فيهم الآن z
+
+182
+00:18:27,940 --> 00:18:34,100
+four هذا كم أنصر ال order اللي بيساوي أربعة في z
+
+183
+00:18:34,100 --> 00:18:43,270
+four و مين كمانوالتلاتة فيش غيرهم فيش غيرهم يبقى
+
+184
+00:18:43,270 --> 00:18:51,870
+ال Z for has واحد and تلاتة of order أربع يعني كام
+
+185
+00:18:51,870 --> 00:18:58,170
+خيار عندى؟ اتنين يبقى ال A لها خيارات two choices
+
+186
+00:18:58,170 --> 00:19:06,930
+for A for B هذا بدي يعطينا two choices for Bطيب كم
+
+187
+00:19:06,930 --> 00:19:10,530
+بقى كم خيار لإيه؟ خد زي ما بدك لإن order واحد
+
+188
+00:19:10,530 --> 00:19:14,990
+واتنين بيفرجوش معايا مع الأربع يبقى هنا كمان two
+
+189
+00:19:14,990 --> 00:19:24,550
+choices for b إذن عدد العدد تبعهم يساوي يبقى هنا
+
+190
+00:19:24,550 --> 00:19:35,450
+the number of elements of order for
+
+191
+00:19:37,350 --> 00:19:44,950
+is اتنين في اتنين ويساوي اربعة elements يبقى
+
+192
+00:19:44,950 --> 00:19:49,650
+ماعنديش الا اربعة عناصر ال order لهم يساوي four
+
+193
+00:19:49,650 --> 00:19:54,110
+وبالتالي ال atom morphism لزد عشرين يوجد فيه جداش
+
+194
+00:19:54,110 --> 00:19:59,690
+يبقى اربعة عناصر ال order لها بده يساوي مان بده
+
+195
+00:19:59,690 --> 00:20:05,310
+يساوي عشرين تمام يبقى هذا اللي عندنا
+
+196
+00:20:12,060 --> 00:20:17,500
+لاحظ ان هذه الأسئلة كلها تطبيق مباشر على ما درسناه
+
+197
+00:20:17,500 --> 00:20:23,240
+في الجزء النظري في آخر محاضرة في هذا section الآن
+
+198
+00:20:23,240 --> 00:20:30,840
+ننتقل إلى الشبتر اللذي يليه وهو شبتر تسعة تسعة
+
+199
+00:20:30,840 --> 00:20:37,300
+normal subgroups
+
+200
+00:20:37,300 --> 00:20:40,680
+and factor
+
+201
+00:20:44,630 --> 00:20:49,990
+and factor groups
+
+202
+00:20:49,990 --> 00:20:56,610
+definition
+
+203
+00:20:56,610 --> 00:21:01,010
+a
+
+204
+00:21:01,010 --> 00:21:05,670
+subgroup H
+
+205
+00:21:05,670 --> 00:21:13,250
+of a group G is called
+
+206
+00:21:16,320 --> 00:21:29,000
+is called a normal is called a normal subgroup of
+
+207
+00:21:29,000 --> 00:21:40,680
+g subgroup of g f ال a h بده يساوي ال h a لكل
+
+208
+00:21:40,680 --> 00:21:50,920
+ال a اللي موجودة في g b لا استخدامwe denote this
+
+209
+00:21:50,920 --> 00:22:02,720
+by ال H is a normal subgroup of G note
+
+210
+00:22:02,720 --> 00:22:05,880
+ال
+
+211
+00:22:05,880 --> 00:22:11,680
+A H دي ساوي ال H A does not
+
+212
+00:22:15,740 --> 00:22:21,240
+imply that ان
+
+213
+00:22:21,240 --> 00:22:36,120
+ال a h بدر يساوي ال h a but means that ان ال a h
+
+214
+00:22:36,120 --> 00:22:41,700
+one بدر يساوي ال h two a
+
+215
+00:22:44,410 --> 00:22:50,070
+أول نظرية theorem a
+
+216
+00:22:50,070 --> 00:22:54,430
+subgroup a
+
+217
+00:22:54,430 --> 00:23:07,070
+subgroup H a subgroup H of G is normal is normal
+
+218
+00:23:07,070 --> 00:23:18,730
+in G if and only ifالـ X H X inverse subset من H
+
+219
+00:23:18,730 --> 00:23:24,870
+لكل ال X اللي موجودة في ال group G
+
+220
+00:24:16,580 --> 00:24:22,060
+نرجع مرة تانيةيبقى انا عندى جروب جديدة هسميها
+
+221
+00:24:22,060 --> 00:24:27,040
+normal subgroup اللى بتحققلى الشرط معين ال factor
+
+222
+00:24:27,040 --> 00:24:32,640
+group بدى انشئ جروب جديدة بواسطة ال subgroup اللى
+
+223
+00:24:32,640 --> 00:24:36,340
+عرفته دى فخلينا في الأول مع ال normal subgroup
+
+224
+00:24:36,340 --> 00:24:41,720
+وهتلعب دور كبير في علم الجبر وخاصة في موضوع الجروب
+
+225
+00:24:41,720 --> 00:24:46,880
+ال subgroup H من الجروب G بسميها normal subgroup
+
+226
+00:24:46,880 --> 00:24:53,390
+من Gإذا كان الـ A H هو الـ H A for all A belongs
+
+227
+00:24:53,390 --> 00:24:57,970
+to G يعني إذا كان ال right coset هي ال left coset
+
+228
+00:24:57,970 --> 00:25:04,280
+لجميع عناصر G يبقى بقول هذابقول عليها ال normal
+
+229
+00:25:04,280 --> 00:25:10,660
+subgroup من G طبعا احنا سابقا بقين اقول ال A H ليس
+
+230
+00:25:10,660 --> 00:25:15,300
+بالضرورة ان تكون subgroup لكن ان كانت normal يبقى
+
+231
+00:25:15,300 --> 00:25:21,240
+automatic هذا subgroup انت معمل يبقى ال H اللي هي
+
+232
+00:25:21,240 --> 00:25:26,010
+subgroup من G بقول عليها normal subgroupإذا كان
+
+233
+00:25:26,010 --> 00:25:30,510
+الـ left coset يساوي الـ right coset واختصارا بدل
+
+234
+00:25:30,510 --> 00:25:34,910
+ما أقول الـ H is a normal subgroup من G بدي أعبر
+
+235
+00:25:34,910 --> 00:25:41,230
+بالرمز المثلث قاعدته جهة G والرأس تبعه جهة من؟ جهة
+
+236
+00:25:41,230 --> 00:25:44,950
+H قعدي لبالك مش حيال الله تخلي القاعدة تحت و الرأس
+
+237
+00:25:44,950 --> 00:25:50,570
+فوقالرأس دائما جهة ال subgroup والقاعدة جهة من جهة
+
+238
+00:25:50,570 --> 00:25:54,950
+ال group طب في شغل ممكن يفهمها الواحد غلط من خلال
+
+239
+00:25:54,950 --> 00:25:58,610
+ال condition اللي حاطه هذا ايش الحاجة الغلط لو جيت
+
+240
+00:25:58,610 --> 00:26:04,790
+قولتك a h يساوي h a هذا كلام خطأ انا لما اقول a h
+
+241
+00:26:04,790 --> 00:26:08,370
+بيساوي شي يعني ال left coset بيساوي ال right coset
+
+242
+00:26:08,370 --> 00:26:14,570
+اذا بدى اتكلم بلغة ال elements بيقول a h one يساوي
+
+243
+00:26:16,110 --> 00:26:20,010
+هو الـ H2 رقم تاني و element تاني ليس نفس ال
+
+244
+00:26:20,010 --> 00:26:24,930
+element قد يكون نفس ال element لكن in general لأ
+
+245
+00:26:24,930 --> 00:26:31,370
+مش صحيح يبقى لما أقول هذه H بيسوي HA يعني AH1
+
+246
+00:26:31,370 --> 00:26:37,290
+بيسوي H2A رقم تاني أو element تاني غير ال element
+
+247
+00:26:37,290 --> 00:26:42,350
+اللي عندنا يبقى بقولش AH بيسوي HA و لما بقول AH1
+
+248
+00:26:42,350 --> 00:26:45,090
+يسوى 100 H2A
+
+249
+00:26:46,550 --> 00:26:51,370
+التعريف هذا اللي عندنا بدي أحاول أصيغه صياغة أخرى،
+
+250
+00:26:51,370 --> 00:26:55,910
+تمام؟ ليهاشي الصياغة الأخرى؟ بل بدل الصياغة تلاتة
+
+251
+00:26:56,420 --> 00:27:01,320
+أيش الصيغة الأخرى؟ أنا بإمكاني هنا لو ضربت في ال A
+
+252
+00:27:01,320 --> 00:27:05,300
+inverse من جهة اليمين أو A inverse من جهة الشمال
+
+253
+00:27:05,300 --> 00:27:10,540
+فبصير عندي A H A inverse يساوي من؟ يساوي ال H شرط
+
+254
+00:27:10,540 --> 00:27:15,920
+ال normality أو لو ضربت من جهة الشمال بصير ال H
+
+255
+00:27:15,920 --> 00:27:23,260
+يساوي A inverse H A شرطاني لل normality ممكن أقول
+
+256
+00:27:23,260 --> 00:27:31,150
+AH small A inverse موجودة في H كابتل لأن هذا
+
+257
+00:27:31,150 --> 00:27:36,170
+بيستوى H يبقى ال A H small A inverse ك element
+
+258
+00:27:36,170 --> 00:27:42,450
+موجود في H برضه شرط اللي اللي هو صيغة أخرى
+
+259
+00:27:42,450 --> 00:27:46,550
+للnormalty نظريها ده إيش بتقولي بقول افترض ال H
+
+260
+00:27:46,550 --> 00:27:50,070
+normal subgroup أو ال H هي normal subgroup من G if
+
+261
+00:27:50,070 --> 00:27:55,300
+and only ifالـ X H X inverse subset من مين؟ من H
+
+262
+00:27:55,300 --> 00:28:00,140
+ما هو إن كان التساوي حاصل إذن automatic هدي مين؟
+
+263
+00:28:00,140 --> 00:28:04,420
+هذه subset من هذه طبعا التساوي حصل من هنا قلتلك لو
+
+264
+00:28:04,420 --> 00:28:08,480
+ضربت في ال A inverse من اليمين أو لشمال بيطلع
+
+265
+00:28:08,480 --> 00:28:12,800
+التساوي أنا بدأ أختصر و لا أقول التساوي بدأ أقول
+
+266
+00:28:12,800 --> 00:28:17,220
+ال subset رغم أن التساوي كمان صحيح طيب مشان هيك
+
+267
+00:28:17,220 --> 00:28:23,480
+بنروح نثبت صحة هذا الكلاميبقى بداجي أقوله أسيوم
+
+268
+00:28:23,480 --> 00:28:30,780
+اللي هو ال H is a normal subgroup من G then
+
+269
+00:28:34,230 --> 00:28:39,130
+يبقى انا فرضت ان الـ H هذه normal subgroup من G
+
+270
+00:28:39,130 --> 00:28:45,790
+يبقى بناء عليه بدي أصير عندي A H يساوي H A حسب مام
+
+271
+00:28:45,790 --> 00:28:52,070
+حسب ال definition او مشان خلي نفس الرموز يبقى بده
+
+272
+00:28:52,070 --> 00:28:58,950
+اقول X H بدي يساوي الـ H X لكل ال X اللي موجودة في
+
+273
+00:28:58,950 --> 00:29:01,090
+G بلا استثناء
+
+274
+00:29:03,680 --> 00:29:10,640
+طيب تمام انا بدي اخلق في المثلة X H X inverse يبقى
+
+275
+00:29:10,640 --> 00:29:15,440
+بناء عليه لو ضربت الطرفين من جهتي اليمين في X
+
+276
+00:29:15,440 --> 00:29:21,840
+inverse ايش اللي بدي يصير؟ بدي يصير عندي ال X H X
+
+277
+00:29:21,840 --> 00:29:26,950
+inverse بدي ساوي ماين؟بدى يساوي ال H هذا معناه
+
+278
+00:29:26,950 --> 00:29:34,030
+مدام تساوي يبقى ال X H X inverse subset من مين من
+
+279
+00:29:34,030 --> 00:29:39,110
+ال H و ال H subset من ال X H X inverse ما علينا
+
+280
+00:29:39,110 --> 00:29:43,770
+يبقى هاي جيبتله مين الشرط الأول بدي أجيبله الشرط
+
+281
+00:29:43,770 --> 00:29:45,630
+الثاني conversely
+
+282
+00:29:49,190 --> 00:29:57,170
+assume افترض ان الـ X H X inverse subset من مين؟
+
+283
+00:29:57,170 --> 00:30:03,330
+subset من H بدي احاول اثبت ان الـ H هذه معلها is a
+
+284
+00:30:03,330 --> 00:30:09,690
+normal subgroup من جي طيب بجي بقوله then
+
+285
+00:30:12,460 --> 00:30:19,120
+أو قبل then هذه الصحيحة احنا فرضينها لكل ال X اللي
+
+286
+00:30:19,120 --> 00:30:24,920
+موجود أويا في ال group G بدي أسأل السؤال التالي ال
+
+287
+00:30:24,920 --> 00:30:28,680
+X inverse موجودة في G ولا لا؟ لإن ال G جروبه
+
+288
+00:30:28,680 --> 00:30:35,210
+المعكس موجود يبقى بجي بقوله thenالـ X inverse
+
+289
+00:30:35,210 --> 00:30:41,390
+موجودة في G implies بدي اطبق عليها الشرط هذا يبقى
+
+290
+00:30:41,390 --> 00:30:47,370
+لو جيت طبقت عليها الشرط هذا بصير X inverse H X
+
+291
+00:30:47,370 --> 00:30:52,850
+inverse inverse اللي هو subset من من؟ subset من H
+
+292
+00:30:55,030 --> 00:31:02,150
+او بمعنى اخر بقدر اقول هنا main ان ال X inverse H
+
+293
+00:31:02,150 --> 00:31:11,830
+X subset من main subset من main من H طيب
+
+294
+00:31:11,830 --> 00:31:19,130
+كويسيبقى هذه الخطوة الأولى لو جبت او قدرت اثبت ان
+
+295
+00:31:19,130 --> 00:31:26,430
+ال H هي ال subset من من ال X inverse HX بتم
+
+296
+00:31:26,430 --> 00:31:31,550
+المطلوب يبقى بدي اعتبر هذه الخطوة رقم واحد بدي اجي
+
+297
+00:31:31,550 --> 00:31:38,030
+للخطوة رقم اتنين الخطوة رقم واحدلو ضربتها في X من
+
+298
+00:31:38,030 --> 00:31:45,830
+جهة الشمال يبقى ايش بيصير ال X X inverse في من؟ في
+
+299
+00:31:45,830 --> 00:31:54,050
+ال H وهنا X بدي تبقى subset من ال X H ضربت من جهة
+
+300
+00:31:54,050 --> 00:31:58,610
+الشمال في X يبقى هذا ايش بدي يعطيلك؟ هذا بدي
+
+301
+00:31:58,610 --> 00:32:06,330
+يعطيلك ان ال H X subset من ال X Hبنفس الطريقة اضرب
+
+302
+00:32:06,330 --> 00:32:12,090
+من جهة اليمين في الـ X inverse يبقى لو ضربنا في ال
+
+303
+00:32:12,090 --> 00:32:19,250
+X inverse بصير ال H هي subset من X H X inverse و
+
+304
+00:32:19,250 --> 00:32:22,550
+هذه العلاقة رقم اتنين اتطلع ليه في الواحد و اتنين
+
+305
+00:32:22,550 --> 00:32:33,120
+يبقى باجي بقوله هنا from واحد and اتنين we haveإن
+
+306
+00:32:33,120 --> 00:32:40,620
+ال X H X inverse بده يساوي مين؟ بده يساوي ال H طب
+
+307
+00:32:40,620 --> 00:32:47,100
+أضرب للطرفين في X من جهتي اليامين يبقى X H بده
+
+308
+00:32:47,100 --> 00:32:52,780
+يساوي H X هالتعريف مين؟ ال normal هذا بده يعطيلك
+
+309
+00:32:52,780 --> 00:32:57,660
+إن ال H is a normal subgroup من مين؟ من G و أنت
+
+310
+00:32:57,660 --> 00:33:00,120
+هنا من المسألة
+
+311
+00:33:04,330 --> 00:33:12,130
+الان خدلي هالملاحظة اللي قلتلك قبل قليل وهي صورة
+
+312
+00:33:12,130 --> 00:33:17,030
+من صورة ال normality بيقولي the above theorem the
+
+313
+00:33:17,030 --> 00:33:26,450
+above theorem the above theorem can be written as
+
+314
+00:33:26,450 --> 00:33:36,160
+can bewritten as ممكن نكتبها على الشكل ا التالي ان
+
+315
+00:33:36,160 --> 00:33:46,820
+ال a او ال h is a normal subgroup من g if and only
+
+316
+00:33:46,820 --> 00:33:56,180
+if ال x h x inversebelongs لمن؟ belongs ل ال H لكل
+
+317
+00:33:56,180 --> 00:34:01,340
+ال X اللي موجود وين في جيب لا استثناء
+
+318
+00:34:18,040 --> 00:34:25,960
+مرة تانية الملاحظة هذه بتقول ان التعريف ال
+
+319
+00:34:25,960 --> 00:34:32,640
+normality استنتج من النظريةالنظرية الآن أنا بدي
+
+320
+00:34:32,640 --> 00:34:37,240
+أصيغها هذه مرة تانية فبجي بقول ال H normal
+
+321
+00:34:37,240 --> 00:34:42,220
+subgroup من G إذا كان X H يا small يعني element من
+
+322
+00:34:42,220 --> 00:34:47,460
+H في X inverse بقول belong to H لأنه صار عنصر
+
+323
+00:34:47,460 --> 00:34:51,640
+العنصر بقولش substitute انما بقول main belong to H
+
+324
+00:34:51,640 --> 00:34:55,760
+يعني حصل ضرب ال X اللي هو من G في ال element اللي
+
+325
+00:34:55,760 --> 00:34:58,580
+هو من H في معكوس ال element تبع ال G التلاتة
+
+326
+00:34:58,580 --> 00:35:02,970
+بديكون oneموجود في H وهي الموضوع تبعها هذي normal
+
+327
+00:35:02,970 --> 00:35:07,290
+إذا كان ال X H X inverse belongs to the main للـH
+
+328
+00:35:07,290 --> 00:35:12,130
+يبقى لو قلي من الآن فصادم اثبت ان ال H is a normal
+
+329
+00:35:12,130 --> 00:35:18,130
+subgroup من G يكفيني main هذا الشرطأو هذا الشرط أو
+
+330
+00:35:18,130 --> 00:35:22,190
+هذا الشرط يبقى اللي تقدر عليه من التلت اشتغله
+
+331
+00:35:22,190 --> 00:35:26,970
+وتوكل على الله طيب بدنا نبدأ ناخد بعض الأمثلة
+
+332
+00:35:26,970 --> 00:35:32,330
+ونبدأ بأبسط أنواع الأمثلة السؤال هو لو عندي group
+
+333
+00:35:32,330 --> 00:35:37,470
+abelian والجروب هذه أخدت منها ال subgroup السؤال
+
+334
+00:35:37,470 --> 00:35:45,270
+هو هل ال subgroup هذه بتبقى normalيعني هل يتحقق ال
+
+335
+00:35:45,270 --> 00:35:50,160
+condition اللي عندي هذاليش؟ لأن أبيليان انا بقول
+
+336
+00:35:50,160 --> 00:35:55,420
+بقدر ابدل هدول ايه مكان بعض لو بدلتهم بصير H XX
+
+337
+00:35:55,420 --> 00:36:00,320
+inverse لو H في E لهو بـH يبقى H موجودة وان موجودة
+
+338
+00:36:00,320 --> 00:36:03,720
+في H وبالتالي الشرط متحقق إذا ال group هذي ايه؟
+
+339
+00:36:03,720 --> 00:36:08,580
+normal group يبقى أول قاعدة باخدها انه لو كانت ال
+
+340
+00:36:08,580 --> 00:36:13,940
+group أبيليان يبقى any sub group is normal يبقى
+
+341
+00:36:13,940 --> 00:36:29,400
+أول مثال بيقول anysubgroup of an abelian group is
+
+342
+00:36:29,400 --> 00:36:36,380
+normal مثال
+
+343
+00:36:36,380 --> 00:36:42,000
+اتنين طبعا
+
+344
+00:36:42,000 --> 00:36:47,080
+ال condition هيه عندك اقولك هذهلو تحقق ال
+
+345
+00:36:47,080 --> 00:36:51,820
+condition هنا موجود الان ابيليان بقدر ابدله
+
+346
+00:36:51,820 --> 00:36:58,420
+وبالتالي بيبقى عندى H موجود فيه H طيب النقطة
+
+347
+00:36:58,420 --> 00:37:02,600
+الثانية ال center تبع ال group هل هو ال sub group
+
+348
+00:37:02,600 --> 00:37:03,460
+من ال group G
+
+349
+00:37:06,550 --> 00:37:14,770
+الـ Center تبع بجروب الـ Z of G أنا أدعي أن الـ A
+
+350
+00:37:14,770 --> 00:37:18,510
+normal sub group منين؟ من G
+
+351
+00:37:21,130 --> 00:37:24,530
+ماجي بقوله كويس اذا اتحقق اي condition من ال
+
+352
+00:37:24,530 --> 00:37:28,850
+conditions اللي عندي هدول بكون خلصنا امن الموضوع
+
+353
+00:37:28,850 --> 00:37:34,670
+تمام كيف الان خلاني نحقق اي condition هادي هادي
+
+354
+00:37:34,670 --> 00:37:40,550
+هادي السيانة بتفرجش عننا الان لو روحت اخد اي عنصر
+
+355
+00:37:40,550 --> 00:37:44,550
+عندي في ال group G و بدي اضربه في ال center طبع ال
+
+356
+00:37:44,550 --> 00:37:47,350
+H هنا solution
+
+357
+00:37:50,630 --> 00:38:00,150
+الان Z of G هو مجلد من G بدي اعمل left coset عندى
+
+358
+00:38:00,150 --> 00:38:08,330
+يبقى بادي بقوله لات ال X موجود في G then ال X في
+
+359
+00:38:08,330 --> 00:38:16,500
+ال center بتابع ال G بده يساويأظن الـ X هذي تتعامل
+
+360
+00:38:16,500 --> 00:38:23,060
+مع جميع عناصر Z أو عناصر Z of G تتعامل مع جميع
+
+361
+00:38:23,060 --> 00:38:28,820
+عناصر G إذا هذي تتعامل مع الـ Z كلها اللي عندنا
+
+362
+00:38:28,820 --> 00:38:37,780
+يبقى هذا بده يعطيني Z of G Z of G في X الشكل اللي
+
+363
+00:38:37,780 --> 00:38:42,440
+عندنا هنا كان بإمكاني أبدأ غير هيكأروح أقول له
+
+364
+00:38:42,440 --> 00:38:49,540
+تعالى نشوف X Z of G X inverse شو بده تعطيني و أجيب
+
+365
+00:38:49,540 --> 00:38:54,260
+من و أجيب ال X أبدلها بالشكل هذا بتيجي ال X يعني
+
+366
+00:38:54,260 --> 00:38:59,060
+كان بإمكاني بدل ما أقول هيك أقول تعالى نشوف ال
+
+367
+00:38:59,060 --> 00:39:04,100
+group يعني و أروح أحط هنا من X inverse أشوف وين
+
+368
+00:39:04,100 --> 00:39:09,030
+بده توصلني يعنيبقول لك كويس هذا الكلام ال X كميوت
+
+369
+00:39:09,030 --> 00:39:14,850
+مع جميع العناصر اللي موجودة في Z إذا هذه بقدر أقول
+
+370
+00:39:14,850 --> 00:39:21,320
+Z of G وهنا X وهذه ال X انفرس اللي عندناهذه
+
+371
+00:39:21,320 --> 00:39:26,380
+بتعطينا مين ال identity element ال identity
+
+372
+00:39:26,380 --> 00:39:31,580
+element في أي subgroup والله بتعطيني نفس ال
+
+373
+00:39:31,580 --> 00:39:38,320
+subgroup تمام يبقى أسار X Z of G X inverse بدي
+
+374
+00:39:38,320 --> 00:39:44,480
+أسوأ من Z of G أضرب من جهة اليمين في X هذا بدي
+
+375
+00:39:44,480 --> 00:39:52,350
+يعطيكإن ال X في Z of G في ال X inverse بده تجيلك
+
+376
+00:39:52,350 --> 00:39:59,750
+كمان X بده يساوي Z of G في من في ال X هذا بده
+
+377
+00:39:59,750 --> 00:40:06,210
+يعطيلك إن ال X في Z of Gطلعلي هذا الشي بيعطينا ال
+
+378
+00:40:06,210 --> 00:40:10,250
+identity في أي element من نفس ال element و الطرف
+
+379
+00:40:10,250 --> 00:40:17,650
+اليمين Z of G أو ال X في .. هذا بيعطيك Z of G في
+
+380
+00:40:17,650 --> 00:40:23,550
+من؟ في ال X هذا بدي أعطيلك ان Z of G is a normal
+
+381
+00:40:23,550 --> 00:40:27,590
+subgroup من G يعني .. يعني قلت الفكرة البسيطة
+
+382
+00:40:27,590 --> 00:40:31,710
+الأولى اللي قلناها أوي الثانية كله بيأدي إلى نفس
+
+383
+00:40:31,710 --> 00:40:37,100
+الموضوعوالله بيكفل اللي قلناها بس احنا مسحناها
+
+384
+00:40:37,100 --> 00:40:43,080
+القطب اللي كنا .. هذه الان X Z X inverse بده سوى
+
+385
+00:40:43,080 --> 00:40:47,080
+مين؟ بده سوى ..
+
+386
+00:40:47,080 --> 00:40:51,160
+خليكم معايا احنا هذي ال sub group أخدنا X في G
+
+387
+00:40:51,160 --> 00:40:55,440
+وقلنا تعالي شوف المقدر هذا إيش بيعطينا يعني أنا
+
+388
+00:40:55,440 --> 00:41:00,220
+جيت اشوف هذا شو بدي يعطينا امشي طلع مين طلع هو Z
+
+389
+00:41:00,220 --> 00:41:06,350
+of G اللي هي النظرية subsetالنظرية صبست وماقلناش
+
+390
+00:41:06,350 --> 00:41:12,730
+تساوي لإن احنا الصبس جيبنا من اليساوي لو قدرت تثبت
+
+391
+00:41:12,730 --> 00:41:17,230
+هذا الكلام إن هذا بيساوي هذا بيكون قد الواجب بس
+
+392
+00:41:17,230 --> 00:41:21,710
+أنا بدي أحاول أحطلك التعريف كلام صح مظبوط ماحدش
+
+393
+00:41:21,710 --> 00:41:24,790
+بيقدر يقول غلط فيه هذا بس أنا حبيت أجيب التعريف
+
+394
+00:41:24,790 --> 00:41:28,910
+الأساسي لكن لو قلت لحد هنا يبقى normal خلاصنا ولا
+
+395
+00:41:28,910 --> 00:41:34,440
+واحد اللي اعترض عليكيبقى هذا بالنسبة للمثال رقم
+
+396
+00:41:34,440 --> 00:41:40,000
+اتنين طب نجيب لك مثال رقم تلاتة انا بدي اجيبلك من
+
+397
+00:41:40,000 --> 00:41:44,800
+الشغلات اللي مرت عليك بدنا مش نبعد لسه سمعت بال
+
+398
+00:41:44,800 --> 00:41:49,000
+special linear group of two by two matrices over R
+
+399
+00:41:49,000 --> 00:41:56,770
+انا ادعي ان هذه كمان normalالان ال special linear
+
+400
+00:41:56,770 --> 00:42:02,150
+group of two by two matrices over R هذي normal من
+
+401
+00:42:02,150 --> 00:42:06,070
+ال general linear group of two by two matrices
+
+402
+00:42:06,070 --> 00:42:11,990
+over R ليش هذي؟ بدي اثبت شرطين الشرط الأول انها
+
+403
+00:42:11,990 --> 00:42:17,230
+subgroup اتنين بدي اثبت خاصية ال normality يبقى
+
+404
+00:42:17,230 --> 00:42:19,450
+الان solution
+
+405
+00:42:22,250 --> 00:42:26,870
+بتروح تقول ايه ال special linear group of two by
+
+406
+00:42:26,870 --> 00:42:31,330
+two matrices over R sub group من ال general linear
+
+407
+00:42:31,330 --> 00:42:38,350
+group of two by two matrices over R وهذه مثال
+
+408
+00:42:38,350 --> 00:42:47,010
+سابق هذه أثبتناها قبل ذلكطب كويس الان بروح اخد
+
+409
+00:42:47,010 --> 00:42:51,990
+element من G و بدي اخد element من ال special و
+
+410
+00:42:51,990 --> 00:42:55,690
+اشوف حصل ضرب ال element من G في ال element من ال
+
+411
+00:42:55,690 --> 00:43:00,390
+special في معكوس ال element تبعي انطلع والله ال
+
+412
+00:43:00,390 --> 00:43:03,330
+determinant ايه اللي بدي يساوي واحد بيكون حصل
+
+413
+00:43:03,330 --> 00:43:06,260
+الضرب هذا موجود وانفي ال special وبالتالي ال
+
+414
+00:43:06,260 --> 00:43:11,840
+special هه normal subgroup من main من G يبقى
+
+415
+00:43:11,840 --> 00:43:14,480
+بالداخل اكتب لك الحل على الشجرة التانية
+
+416
+00:43:28,720 --> 00:43:34,740
+أفترض أن ال A موجودة في ال general linear group of
+
+417
+00:43:34,740 --> 00:43:41,000
+2 by 2 matrices over R ويكون موجودة في ال special
+
+418
+00:43:41,000 --> 00:43:48,000
+linear group of 2 by 2 matrices over Rأريد أن أخذ
+
+419
+00:43:48,000 --> 00:43:54,640
+الـ A بـ A إنفرس إذا كنت أثبت إن هذه موجودة في الـ
+
+420
+00:43:54,640 --> 00:43:58,860
+Special يبقى هو الشرط اللي قلنا عليه الشرط التالت
+
+421
+00:43:58,860 --> 00:44:03,200
+هو المساحنة أه هذه موجودة تمام يبقى بدي أحاول
+
+422
+00:44:03,200 --> 00:44:09,300
+أثبتها فبدي أخدي determinant لمين لهذه المصوفة
+
+423
+00:44:09,300 --> 00:44:15,530
+يبقى حسب الجبرة الخاطية هذه determinant للـ Aفى
+
+424
+00:44:15,530 --> 00:44:19,970
+الـ determinant للـ B فى الـ determinant للـ A
+
+425
+00:44:19,970 --> 00:44:23,650
+inverse صاروا هدور الـ real numbers الـ real
+
+426
+00:44:23,650 --> 00:44:28,350
+numbers are commutes يبقى هذا الـ determinant للـ
+
+427
+00:44:28,350 --> 00:44:33,070
+A فى الـ determinant للـ A inverse فى الـ
+
+428
+00:44:33,070 --> 00:44:37,870
+determinant للـ B يبقى .. بدى أرجعه إلى أصله يبقى
+
+429
+00:44:37,870 --> 00:44:42,170
+الـ determinant للـ A فى الـ A inverse فى الـ
+
+430
+00:44:42,170 --> 00:44:47,280
+determinant للـ Bالمصوفة فيما عكوزها بالـ
+
+431
+00:44:47,280 --> 00:44:52,240
+determinant لمصوفة الوحدة في الـ determinant للـ P
+
+432
+00:44:52,240 --> 00:44:58,920
+محدد مصوفة الوحدة جداش؟ واحد صحيح محدد المصوفة بـ
+
+433
+00:44:58,920 --> 00:45:03,320
+B برضه بواحد لأنها موجودة وين؟بالـ Special يبقى
+
+434
+00:45:03,320 --> 00:45:09,800
+الـ
+
+435
+00:45:09,800 --> 00:45:14,980
+ABA inverse موجودة في الـ Special Linear Group of
+
+436
+00:45:14,980 --> 00:45:20,280
+2x2 matrices over R بناء عليه الـ Special Linear
+
+437
+00:45:20,280 --> 00:45:25,400
+Group of 2x2 matrices over R is a normal subgroup
+
+438
+00:45:25,400 --> 00:45:30,620
+من الـ General Linear Group of 2x2 matrices over R
+
+439
+00:45:31,450 --> 00:45:38,970
+يبقى هذا مثال آخر على ال .. على اللي عندنا خد مثال
+
+440
+00:45:38,970 --> 00:45:43,390
+أربعة مثال
+
+441
+00:45:43,390 --> 00:45:49,030
+أربعة the alternating
+
+442
+00:45:49,030 --> 00:45:53,490
+group
+
+443
+00:45:53,490 --> 00:45:59,850
+the alternating group اربعة
+
+444
+00:46:04,190 --> 00:46:10,170
+التاني جروب AN is
+
+445
+00:46:10,170 --> 00:46:19,130
+a normal subgroup من من ال SN ليش
+
+446
+00:46:19,130 --> 00:46:22,450
+هذي normal باجي بقوله because
+
+447
+00:46:26,200 --> 00:46:31,900
+بدي اخد element في sn و element في an طبعا انا
+
+448
+00:46:31,900 --> 00:46:36,460
+اخدناها سابقا انها ال subgroup مظبوط ال a for
+
+449
+00:46:36,460 --> 00:46:42,680
+because ال an هدى ال subgroup من ال sn and
+
+450
+00:46:45,520 --> 00:46:55,140
+Alpha موجودة في الـS in and Beta موجودة في الـA in
+
+451
+00:46:55,140 --> 00:47:05,920
+thenأخذ العنصر SN والعنصر AN ومعكس العنصر SM لو
+
+452
+00:47:05,920 --> 00:47:11,420
+طلع هذا الكلام even يبقى هذا حصلت ضربوين في SN
+
+453
+00:47:11,420 --> 00:47:19,110
+يكون خلصنا يبقى هذا الكلام هادئةقد تكون even وقد
+
+454
+00:47:19,110 --> 00:47:24,150
+تكون odd لنا في ال sense إن كان even يبقى معكوسة
+
+455
+00:47:24,150 --> 00:47:28,370
+even هذه even ماعنديش مشكلة إن كان هذه odd هذه
+
+456
+00:47:28,370 --> 00:47:32,370
+even هذه odd يبقى المجموع اللي هو even وبالتالي
+
+457
+00:47:32,370 --> 00:47:36,770
+هذه موجودة على طول الخططبعا أثبتناها قبل إيه
+
+458
+00:47:36,770 --> 00:47:44,930
+أخدناها سؤال وحلناه يبقى then هذه موجودة في الان
+
+459
+00:47:44,930 --> 00:47:54,870
+because السبب أن even زائد even زائد even بده
+
+460
+00:47:54,870 --> 00:48:05,410
+يساوي even and odd زائد evenزائد اد بده يعطينا
+
+461
+00:48:05,410 --> 00:48:10,870
+even مشان هيك هذه normal طبعا بنكمل في المحاضرة
+
+462
+00:48:10,870 --> 00:48:12,950
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..e22c3a4d9af0e5e68b507c3cc3c08b22f09d7aa9
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/Qh2nKxpZzJc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4139, "start": 21.09, "end": 41.39, "text": "أحنا واصل ما بدأنا فيه المرة الماضية و هو حل اللي هو المسائل على شبتر تمانية الاكستاناداركت برودرك وصلنا لسؤال واحد واربعين بقول express automorphism ل U خمسة وعشرين in the form ZM اكستاناداركت برودرك مع ZN", "tokens": [10721, 5016, 8315, 4032, 33546, 1211, 19446, 47525, 10721, 8315, 8978, 3224, 9673, 25720, 9673, 46958, 10632, 4032, 31439, 11331, 1211, 13672, 1829, 31439, 9673, 3794, 16373, 1211, 15844, 13412, 3555, 2655, 2288, 46811, 7649, 10632, 42963, 4117, 14851, 7649, 18513, 9640, 4117, 2655, 4724, 32887, 3215, 31747, 4032, 36520, 8315, 5296, 3794, 33604, 6027, 36764, 24401, 4032, 9640, 3555, 3615, 9957, 4724, 39648, 5109, 3553, 18191, 1434, 5296, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 294, 264, 1254, 1176, 44, 1975, 4117, 14851, 7649, 18513, 9640, 4117, 2655, 4724, 32887, 3215, 31747, 20449, 1176, 45], "avg_logprob": -0.2571022865748165, "compression_ratio": 1.6490384615384615, 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{"start": 26.07, "end": 26.67, "word": " المسائل", "probability": 0.8974609375}, {"start": 26.67, "end": 26.91, "word": " على", "probability": 0.861328125}, {"start": 26.91, "end": 27.61, "word": " شبتر", "probability": 0.70135498046875}, {"start": 27.61, "end": 28.37, "word": " تمانية", "probability": 0.92333984375}, {"start": 28.37, "end": 30.11, "word": " الاكستاناداركت", "probability": 0.6162185668945312}, {"start": 30.11, "end": 30.57, "word": " برودرك", "probability": 0.64520263671875}, {"start": 30.57, "end": 31.05, "word": " وصلنا", "probability": 0.88134765625}, {"start": 31.05, "end": 31.63, "word": " لسؤال", "probability": 0.9647216796875}, {"start": 31.63, "end": 31.97, "word": " واحد", "probability": 0.847900390625}, {"start": 31.97, "end": 32.51, "word": " واربعين", "probability": 0.89404296875}, {"start": 32.51, "end": 33.53, "word": " بقول", "probability": 0.8603515625}, {"start": 33.53, "end": 34.01, "word": " express", "probability": 0.9248046875}, {"start": 34.01, 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"probability": 0.91552734375}], "temperature": 1.0}, {"id": 2, "seek": 7216, "start": 43.96, "end": 72.16, "text": "بمعنى اخر بدي اجيب جروب لجروب هذه تبقى isomorphic لمام لل U خمسة وعشرين طب احنا عندنا ال U خمسة وعشرين solution عندنا ال U خمسة وعشرين اللي هو U خمسة لكل تربيع الشكل اللي عندنا هذه isomorphic", "tokens": [3555, 2304, 3615, 1863, 7578, 1975, 34740, 4724, 16254, 1975, 7435, 1829, 3555, 10874, 32887, 3555, 5296, 7435, 32887, 3555, 29538, 6055, 3555, 4587, 7578, 307, 32702, 299, 32767, 10943, 24976, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 23032, 3555, 1975, 5016, 8315, 43242, 8315, 2423, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 3827, 43242, 8315, 2423, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 13672, 1829, 31439, 624, 16490, 2304, 3794, 3660, 5296, 28820, 6055, 2288, 21292, 3615, 25124, 28820, 13672, 1829, 43242, 8315, 29538, 307, 32702, 299], "avg_logprob": -0.23421052788433275, "compression_ratio": 1.896969696969697, 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80.69, "end": 81.69, "word": " مباشرة", "probability": 0.9901123046875}, {"start": 81.69, "end": 83.73, "word": " طبعا", "probability": 0.8551025390625}, {"start": 83.73, "end": 84.57, "word": " اخدت", "probability": 0.809326171875}, {"start": 84.57, "end": 85.11, "word": " عندك", "probability": 0.9716796875}, {"start": 85.11, "end": 85.43, "word": " ان", "probability": 0.79443359375}, {"start": 85.43, "end": 86.21, "word": " ال", "probability": 0.912109375}, {"start": 86.21, "end": 86.63, "word": " U", "probability": 0.9619140625}, {"start": 86.63, "end": 89.27, "word": " مرفوعة", "probability": 0.79449462890625}, {"start": 89.27, "end": 89.89, "word": " ل", "probability": 0.9287109375}, {"start": 89.89, "end": 90.47, "word": " prime", "probability": 0.529296875}, {"start": 90.47, "end": 91.05, "word": " P", "probability": 0.94189453125}, {"start": 91.05, "end": 91.85, "word": " ومرفوعة", "probability": 0.81982421875}, {"start": 91.85, "end": 92.03, "word": " ل", "probability": 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الكلام", "probability": 0.935546875}, {"start": 106.63, "end": 107.17, "word": " عالميا", "probability": 0.8092447916666666}, {"start": 107.17, "end": 107.93, "word": " على", "probability": 0.830078125}, {"start": 107.93, "end": 108.71, "word": " أرض", "probability": 0.940185546875}, {"start": 108.71, "end": 109.69, "word": " الواقع", "probability": 0.9859619140625}, {"start": 109.69, "end": 110.59, "word": " يبقى", "probability": 0.900390625}, {"start": 110.59, "end": 110.95, "word": " بناء", "probability": 0.92919921875}, {"start": 110.95, "end": 111.37, "word": " عليه", "probability": 0.8349609375}, {"start": 111.37, "end": 111.59, "word": " يو", "probability": 0.4898681640625}, {"start": 111.59, "end": 112.03, "word": " خمسة", "probability": 0.8387451171875}, {"start": 112.03, "end": 112.43, "word": " وعشرين", "probability": 0.9013671875}, {"start": 112.43, "end": 113.05, "word": " كتبناها", "probability": 0.98349609375}, {"start": 113.05, "end": 113.57, "word": " بالشكل", "probability": 0.8447265625}, {"start": 113.57, "end": 114.01, "word": " هذه", "probability": 0.552734375}, {"start": 114.01, "end": 114.99, "word": " بقدر", "probability": 0.92919921875}, {"start": 114.99, "end": 115.33, "word": " اقول", "probability": 0.794921875}, {"start": 115.33, "end": 115.93, "word": " هذه", "probability": 0.8125}, {"start": 115.93, "end": 117.61, "word": " isomorphic", "probability": 0.7747395833333334}, {"start": 117.61, "end": 118.07, "word": " لمين", "probability": 0.4945068359375}], "temperature": 1.0}, {"id": 5, "seek": 13275, "start": 122.51, "end": 132.75, "text": "Isomorphic لزد P اللي هي خمسة تربيع ناقص خمسة أس اتنين ناقص واحد بالشكل اللي عندنا هنا", "tokens": [40, 539, 76, 18191, 299, 5296, 11622, 3215, 430, 13672, 1829, 39896, 16490, 2304, 3794, 3660, 6055, 2288, 21292, 3615, 8717, 995, 4587, 9381, 16490, 2304, 3794, 3660, 5551, 3794, 1975, 2655, 1863, 9957, 8717, 995, 4587, 9381, 36764, 24401, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.27040815353393555, "compression_ratio": 1.2831858407079646, "no_speech_prob": 0.0, "words": [{"start": 122.50999999999999, "end": 123.63, "word": "Isomorphic", "probability": 0.65703125}, {"start": 123.63, "end": 124.75, "word": " لزد", "probability": 0.5157063802083334}, {"start": 124.75, "end": 125.31, "word": " P", "probability": 0.66796875}, {"start": 125.31, "end": 125.65, "word": " اللي", "probability": 0.43975830078125}, {"start": 125.65, "end": 125.91, "word": " هي", "probability": 0.88037109375}, {"start": 125.91, "end": 126.65, "word": " خمسة", "probability": 0.8946533203125}, {"start": 126.65, "end": 127.45, "word": " تربيع", "probability": 0.90380859375}, {"start": 127.45, "end": 128.57, "word": " ناقص", "probability": 0.972412109375}, {"start": 128.57, "end": 129.55, "word": " خمسة", "probability": 0.9129638671875}, {"start": 129.55, "end": 129.87, "word": " أس", "probability": 0.4219970703125}, {"start": 129.87, "end": 130.49, "word": " اتنين", "probability": 0.8253173828125}, {"start": 130.49, "end": 131.23, "word": " ناقص", "probability": 0.9677734375}, {"start": 131.23, "end": 131.59, "word": " واحد", "probability": 0.990234375}, {"start": 131.59, "end": 132.05, "word": " بالشكل", "probability": 0.9599609375}, {"start": 132.05, "end": 132.19, "word": " اللي", "probability": 0.979248046875}, {"start": 132.19, "end": 132.59, "word": " عندنا", "probability": 0.776123046875}, {"start": 132.59, "end": 132.75, "word": " هنا", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 6, "seek": 15457, "start": 133.61, "end": 154.57, "text": "يبقى هذا الكلام هذه تساوي من خمسة ترابيع ليه خمسة وعشرين وهذه خمسة وسواحد يبقى زد عشرين شكل اللي عندنا هنا هذا U خمسة وعشرين انا مابدي U خمسة وعشرين بدي اتومورفزم ل U خمسة وعشرين", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 29538, 6055, 3794, 995, 45865, 9154, 16490, 2304, 3794, 3660, 6055, 2288, 16758, 40228, 32239, 3224, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 37037, 24192, 16490, 2304, 3794, 3660, 46952, 14407, 24401, 7251, 3555, 4587, 7578, 30767, 3215, 6225, 46309, 9957, 13412, 28820, 13672, 1829, 43242, 8315, 34105, 23758, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 1975, 8315, 3714, 16758, 16254, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 4724, 16254, 1975, 2655, 20498, 13063, 5172, 11622, 2304, 5296, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957], "avg_logprob": -0.2363861344828464, "compression_ratio": 2.1059602649006623, "no_speech_prob": 0.0, "words": [{"start": 133.61, "end": 134.11, "word": "يبقى", "probability": 0.76019287109375}, {"start": 134.11, "end": 134.39, "word": " هذا", "probability": 0.79833984375}, {"start": 134.39, "end": 135.05, "word": " الكلام", "probability": 0.8689778645833334}, {"start": 135.05, "end": 135.47, "word": " هذه", "probability": 0.1519775390625}, {"start": 135.47, "end": 136.23, "word": " تساوي", "probability": 0.8990478515625}, {"start": 136.23, "end": 136.63, "word": " من", "probability": 0.91943359375}, {"start": 136.63, "end": 137.97, "word": " خمسة", "probability": 0.9412841796875}, {"start": 137.97, "end": 138.41, "word": " ترابيع", "probability": 0.619140625}, {"start": 138.41, "end": 138.63, "word": " ليه", "probability": 0.51495361328125}, {"start": 138.63, "end": 139.11, "word": " خمسة", "probability": 0.94189453125}, {"start": 139.11, "end": 139.79, "word": " وعشرين", "probability": 0.907470703125}, {"start": 139.79, "end": 140.67, "word": " وهذه", "probability": 0.73779296875}, {"start": 140.67, "end": 141.27, "word": " خمسة", "probability": 0.9825439453125}, {"start": 141.27, "end": 142.07, "word": " وسواحد", "probability": 0.6146647135416666}, {"start": 142.07, "end": 143.31, "word": " يبقى", "probability": 0.9442138671875}, {"start": 143.31, "end": 144.03, "word": " زد", "probability": 0.5069580078125}, {"start": 144.03, "end": 145.35, "word": " عشرين", "probability": 0.9724934895833334}, {"start": 145.35, "end": 146.23, "word": " شكل", "probability": 0.62841796875}, {"start": 146.23, "end": 146.37, "word": " اللي", "probability": 0.960693359375}, {"start": 146.37, "end": 146.77, "word": " عندنا", "probability": 0.671142578125}, {"start": 146.77, "end": 147.09, "word": " هنا", "probability": 0.697265625}, {"start": 147.09, "end": 147.85, "word": " هذا", "probability": 0.7373046875}, {"start": 147.85, "end": 147.97, "word": " U", "probability": 0.73681640625}, {"start": 147.97, "end": 148.45, "word": " خمسة", "probability": 0.97216796875}, {"start": 148.45, "end": 148.83, "word": " وعشرين", "probability": 0.9757080078125}, {"start": 148.83, "end": 149.17, "word": " انا", "probability": 0.7091064453125}, {"start": 149.17, "end": 149.59, "word": " مابدي", "probability": 0.7664388020833334}, {"start": 149.59, "end": 149.81, "word": " U", "probability": 0.93310546875}, {"start": 149.81, "end": 150.27, "word": " خمسة", "probability": 0.991455078125}, {"start": 150.27, "end": 150.91, "word": " وعشرين", "probability": 0.9764404296875}, {"start": 150.91, "end": 151.71, "word": " بدي", "probability": 0.854736328125}, {"start": 151.71, "end": 153.07, "word": " اتومورفزم", "probability": 0.6970563616071429}, {"start": 153.07, "end": 153.25, "word": " ل", "probability": 0.8994140625}, {"start": 153.25, "end": 153.49, "word": " U", "probability": 0.87939453125}, {"start": 153.49, "end": 153.97, "word": " خمسة", "probability": 0.9888916015625}, {"start": 153.97, "end": 154.57, "word": " وعشرين", "probability": 0.984375}], "temperature": 1.0}, {"id": 7, "seek": 17312, "start": 154.88, "end": 173.12, "text": "إذا بناء عليه atomorphism ل U خمسة وعشرين اللي هي isomorphic لمهم اللي هو atomorphism ل Z عشرين الشكل اللي عندنا هنا", "tokens": [28814, 15730, 44945, 16606, 47356, 12018, 18191, 1434, 5296, 624, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 13672, 1829, 39896, 307, 32702, 299, 32767, 16095, 13672, 1829, 31439, 12018, 18191, 1434, 5296, 1176, 6225, 46309, 9957, 25124, 28820, 13672, 1829, 43242, 8315, 34105], "avg_logprob": -0.35052083598242867, "compression_ratio": 1.4508196721311475, "no_speech_prob": 0.0, "words": [{"start": 154.88, "end": 155.3, "word": "إذا", "probability": 0.53863525390625}, {"start": 155.3, "end": 155.84, "word": " بناء", "probability": 0.870361328125}, {"start": 155.84, "end": 156.46, "word": " عليه", "probability": 0.90673828125}, {"start": 156.46, "end": 158.54, "word": " atomorphism", "probability": 0.6211751302083334}, {"start": 158.54, "end": 159.26, "word": " ل", "probability": 0.625}, {"start": 159.26, "end": 159.6, "word": " U", "probability": 0.41064453125}, {"start": 159.6, "end": 160.72, "word": " خمسة", "probability": 0.91357421875}, {"start": 160.72, "end": 162.0, "word": " وعشرين", "probability": 0.91162109375}, {"start": 162.0, "end": 162.76, "word": " اللي", "probability": 0.52056884765625}, {"start": 162.76, "end": 162.96, "word": " هي", "probability": 0.75732421875}, {"start": 162.96, "end": 164.48, "word": " isomorphic", "probability": 0.76953125}, {"start": 164.48, "end": 165.06, "word": " لمهم", "probability": 0.4635009765625}, {"start": 165.06, "end": 167.38, "word": " اللي", "probability": 0.815185546875}, {"start": 167.38, "end": 167.58, "word": " هو", "probability": 0.931640625}, {"start": 167.58, "end": 169.46, "word": " atomorphism", "probability": 0.69287109375}, {"start": 169.46, "end": 170.12, "word": " ل", "probability": 0.9453125}, {"start": 170.12, "end": 170.56, "word": " Z", "probability": 0.67578125}, {"start": 170.56, "end": 171.82, "word": " عشرين", "probability": 0.9524739583333334}, {"start": 171.82, "end": 172.46, "word": " الشكل", "probability": 0.7744140625}, {"start": 172.46, "end": 172.64, "word": " اللي", "probability": 0.981201171875}, {"start": 172.64, "end": 172.92, "word": " عندنا", "probability": 0.777587890625}, {"start": 172.92, "end": 173.12, "word": " هنا", "probability": 0.46240234375}], "temperature": 1.0}, {"id": 8, "seek": 19083, "start": 173.89, "end": 190.83, "text": "أخذنا كمان نظرية سابقة اتومورفزم ل ZN ايزو مورفك ل UN شبطر اللي قبله اخر نظرية يبقى هذا ايزو مورفك ل U20", "tokens": [10721, 9778, 8848, 8315, 9122, 2304, 7649, 8717, 19913, 2288, 10632, 8608, 16758, 28671, 1975, 2655, 20498, 13063, 5172, 11622, 2304, 5296, 1176, 45, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 8229, 13412, 3555, 9566, 2288, 13672, 1829, 12174, 36150, 3224, 1975, 34740, 8717, 19913, 2288, 10632, 7251, 3555, 4587, 7578, 23758, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 5296, 624, 2009], "avg_logprob": -0.31344696202061395, "compression_ratio": 1.4634146341463414, "no_speech_prob": 0.0, "words": [{"start": 173.89, "end": 174.75, "word": "أخذنا", "probability": 0.68707275390625}, {"start": 174.75, "end": 175.25, "word": " كمان", "probability": 0.7110188802083334}, {"start": 175.25, "end": 176.09, "word": " نظرية", "probability": 0.9757080078125}, {"start": 176.09, "end": 176.89, "word": " سابقة", "probability": 0.9627278645833334}, {"start": 176.89, "end": 178.89, "word": " اتومورفزم", "probability": 0.5095999581473214}, {"start": 178.89, "end": 179.49, "word": " ل", "probability": 0.78564453125}, {"start": 179.49, "end": 180.93, "word": " ZN", "probability": 0.3651123046875}, {"start": 180.93, "end": 181.69, "word": " ايزو", "probability": 0.68408203125}, {"start": 181.69, "end": 182.25, "word": " مورفك", "probability": 0.9014892578125}, {"start": 182.25, "end": 182.57, "word": " ل", "probability": 0.9501953125}, {"start": 182.57, "end": 183.47, "word": " UN", "probability": 0.6767578125}, {"start": 183.47, "end": 184.23, "word": " شبطر", "probability": 0.6033935546875}, {"start": 184.23, "end": 184.41, "word": " اللي", "probability": 0.856201171875}, {"start": 184.41, "end": 184.81, "word": " قبله", "probability": 0.733154296875}, {"start": 184.81, "end": 185.27, "word": " اخر", "probability": 0.766357421875}, {"start": 185.27, "end": 186.03, "word": " نظرية", "probability": 0.991455078125}, {"start": 186.03, "end": 187.03, "word": " يبقى", "probability": 0.9427490234375}, {"start": 187.03, "end": 187.45, "word": " هذا", "probability": 0.80322265625}, {"start": 187.45, "end": 188.31, "word": " ايزو", "probability": 0.96875}, {"start": 188.31, "end": 189.07, "word": " مورفك", "probability": 0.9781494140625}, {"start": 189.07, "end": 189.47, "word": " ل", "probability": 0.91748046875}, {"start": 189.47, "end": 190.83, "word": " U20", "probability": 0.809814453125}], "temperature": 1.0}, {"id": 9, "seek": 20762, "start": 191.92, "end": 207.62, "text": "U20 هذه اللي بقدر اكتبها اللي هي تساوي U أربعة في خمسة والاربعة خمسة are relatively prime يبقى هذه isomorphic لمين", "tokens": [52, 2009, 29538, 13672, 1829, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 13672, 1829, 39896, 6055, 3794, 995, 45865, 624, 5551, 25513, 27884, 8978, 16490, 2304, 3794, 3660, 16070, 9640, 3555, 27884, 16490, 2304, 3794, 3660, 366, 7226, 5835, 7251, 3555, 4587, 7578, 29538, 307, 32702, 299, 32767, 9957], "avg_logprob": -0.31035539566301834, "compression_ratio": 1.2661870503597121, "no_speech_prob": 0.0, "words": [{"start": 191.92, "end": 193.0, "word": "U20", "probability": 0.3555908203125}, {"start": 193.0, "end": 193.58, "word": " هذه", "probability": 0.38525390625}, {"start": 193.58, "end": 193.9, "word": " اللي", "probability": 0.648193359375}, {"start": 193.9, "end": 194.5, "word": " بقدر", "probability": 0.9513346354166666}, {"start": 194.5, "end": 195.54, "word": " اكتبها", "probability": 0.9265625}, {"start": 195.54, "end": 196.24, "word": " اللي", "probability": 0.5787353515625}, {"start": 196.24, "end": 196.48, "word": " هي", "probability": 0.379638671875}, {"start": 196.48, "end": 197.24, "word": " تساوي", "probability": 0.9356689453125}, {"start": 197.24, "end": 197.8, "word": " U", "probability": 0.83837890625}, {"start": 197.8, "end": 198.84, "word": " أربعة", "probability": 0.6131591796875}, {"start": 198.84, "end": 199.12, "word": " في", "probability": 0.85595703125}, {"start": 199.12, "end": 199.94, "word": " خمسة", "probability": 0.973388671875}, {"start": 199.94, "end": 201.22, "word": " والاربعة", "probability": 0.779541015625}, {"start": 201.22, "end": 201.9, "word": " خمسة", "probability": 0.941162109375}, {"start": 201.9, "end": 202.22, "word": " are", "probability": 0.5498046875}, {"start": 202.22, "end": 203.12, "word": " relatively", "probability": 0.78466796875}, {"start": 203.12, "end": 203.86, "word": " prime", "probability": 0.9033203125}, {"start": 203.86, "end": 205.0, "word": " يبقى", "probability": 0.9716796875}, {"start": 205.0, "end": 205.44, "word": " هذه", "probability": 0.828125}, {"start": 205.44, "end": 207.02, "word": " isomorphic", "probability": 0.6394856770833334}, {"start": 207.02, "end": 207.62, "word": " لمين", "probability": 0.4718017578125}], "temperature": 1.0}, {"id": 10, "seek": 23051, "start": 207.93, "end": 230.51, "text": "لأ اللي هو isomorphic او هدى تساوي او isomorphic دُغري لمهم ل U أربعة external product مع U خمسة مرة تانية ل U أربعة هدى U تنين تربيع", "tokens": [1211, 10721, 13672, 1829, 31439, 307, 32702, 299, 1975, 2407, 8032, 3215, 7578, 6055, 3794, 995, 45865, 1975, 2407, 307, 32702, 299, 11778, 10859, 17082, 16572, 32767, 16095, 5296, 624, 5551, 25513, 27884, 8320, 1674, 20449, 624, 16490, 2304, 3794, 3660, 3714, 25720, 6055, 7649, 10632, 5296, 624, 5551, 25513, 27884, 8032, 3215, 7578, 624, 6055, 1863, 9957, 6055, 25513, 40228], "avg_logprob": -0.32560484640059933, "compression_ratio": 1.36986301369863, "no_speech_prob": 0.0, "words": [{"start": 207.93, "end": 208.63, "word": "لأ", "probability": 0.592529296875}, {"start": 208.63, "end": 209.07, "word": " اللي", "probability": 0.45916748046875}, {"start": 209.07, "end": 209.51, "word": " هو", "probability": 0.9423828125}, {"start": 209.51, "end": 211.67, "word": " isomorphic", "probability": 0.7633463541666666}, {"start": 211.67, "end": 212.89, "word": " او", "probability": 0.705078125}, {"start": 212.89, "end": 213.27, "word": " هدى", 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" وخاصة", "probability": 0.8116455078125}, {"start": 1480.24, "end": 1480.38, "word": " في", "probability": 0.81787109375}, {"start": 1480.38, "end": 1481.04, "word": " موضوع", "probability": 0.9805908203125}, {"start": 1481.04, "end": 1481.72, "word": " الجروب", "probability": 0.7369791666666666}, {"start": 1481.72, "end": 1482.56, "word": " ال", "probability": 0.642578125}, {"start": 1482.56, "end": 1483.08, "word": " subgroup", "probability": 0.9482421875}, {"start": 1483.08, "end": 1483.44, "word": " H", "probability": 0.630859375}, {"start": 1483.44, "end": 1483.72, "word": " من", "probability": 0.9453125}, {"start": 1483.72, "end": 1484.22, "word": " الجروب", "probability": 0.8108723958333334}, {"start": 1484.22, "end": 1484.42, "word": " G", "probability": 0.7294921875}, {"start": 1484.42, "end": 1485.34, "word": " بسميها", "probability": 0.95263671875}, {"start": 1485.34, "end": 1486.04, "word": " normal", "probability": 0.84423828125}, {"start": 1486.04, "end": 1486.88, 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G بدي أعبر بالرمز المثلث قاعدته جهة G والرأس تبعه جهة من؟ جهة H قعدي لبالك مش حيال الله تخلي القاعدة تحت و الرأس فوق", "tokens": [28814, 15730, 25961, 2423, 39184, 1411, 3792, 302, 7251, 3794, 995, 45865, 2423, 39184, 558, 3792, 302, 4032, 47283, 2655, 9381, 9640, 995, 47525, 1211, 19446, 5551, 39648, 2423, 39184, 389, 307, 257, 2710, 1422, 17377, 9154, 460, 4724, 16254, 5551, 3615, 3555, 2288, 20666, 2288, 2304, 11622, 9673, 12984, 1211, 12984, 12174, 995, 22488, 47395, 10874, 3224, 3660, 460, 16070, 2288, 10721, 3794, 6055, 3555, 3615, 3224, 10874, 3224, 3660, 9154, 22807, 10874, 3224, 3660, 389, 12174, 22488, 1829, 5296, 3555, 6027, 4117, 37893, 11331, 1829, 6027, 21984, 6055, 9778, 20292, 25062, 995, 22488, 3660, 6055, 33753, 4032, 34892, 10721, 3794, 6156, 30543], "avg_logprob": -0.25252977325802756, "compression_ratio": 1.6113744075829384, "no_speech_prob": 0.0, "words": [{"start": 1525.09, "end": 1525.67, "word": "إذا", "probability": 0.75390625}, {"start": 1525.67, "end": 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coset اذا بدى اتكلم بلغة ال elements بيقول a h one يساوي", "tokens": [6027, 2288, 10721, 3794, 11778, 16373, 15042, 10874, 3224, 3660, 2423, 1422, 17377, 16070, 4587, 995, 22488, 3660, 10874, 3224, 3660, 9154, 10874, 3224, 3660, 2423, 1594, 23032, 3555, 8978, 13412, 17082, 1211, 3714, 43020, 7251, 5172, 16095, 11296, 2423, 14407, 24401, 32771, 1211, 9566, 9154, 16490, 1211, 6027, 2423, 4188, 13672, 1829, 11331, 41193, 3224, 23758, 1975, 1829, 8592, 21542, 26108, 3660, 6024, 118, 1211, 9566, 45164, 10874, 36081, 12174, 12610, 2655, 4117, 257, 276, 7251, 3794, 995, 45865, 276, 257, 23758, 28242, 10943, 16490, 9566, 10721, 1975, 8315, 5296, 15042, 1975, 39648, 257, 276, 4724, 1829, 3794, 995, 45865, 44049, 37495, 22653, 2423, 1411, 3792, 302, 4724, 1829, 3794, 995, 45865, 2423, 558, 3792, 302, 1975, 15730, 47525, 7578, 1975, 2655, 4117, 19528, 4724, 1211, 17082, 3660, 2423, 4959, 4724, 1829, 39648, 257, 276, 472, 7251, 3794, 995, 45865], "avg_logprob": -0.2528609186410904, 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{"start": 1777.65, "end": 1778.41, "word": " ما", "probability": 0.884765625}, {"start": 1778.41, "end": 1779.11, "word": " علينا", "probability": 0.896240234375}, {"start": 1779.11, "end": 1779.79, "word": " يبقى", "probability": 0.972900390625}, {"start": 1779.79, "end": 1779.99, "word": " هاي", "probability": 0.51171875}, {"start": 1779.99, "end": 1780.39, "word": " جيبتله", "probability": 0.74853515625}, {"start": 1780.39, "end": 1780.73, "word": " مين", "probability": 0.822265625}, {"start": 1780.73, "end": 1781.71, "word": " الشرط", "probability": 0.9402669270833334}, {"start": 1781.71, "end": 1782.25, "word": " الأول", "probability": 0.890380859375}, {"start": 1782.25, "end": 1782.91, "word": " بدي", "probability": 0.580322265625}, {"start": 1782.91, "end": 1783.27, "word": " أجيبله", "probability": 0.8021484375}, {"start": 1783.27, "end": 1783.77, "word": " الشرط", "probability": 0.9773763020833334}, {"start": 1783.77, "end": 1784.37, "word": " الثاني", "probability": 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"probability": 0.402587890625}, {"start": 1827.88, "end": 1828.08, "word": " G", "probability": 0.806640625}, {"start": 1828.08, "end": 1828.68, "word": " جروبه", "probability": 0.64813232421875}, {"start": 1828.68, "end": 1829.2, "word": " المعكس", "probability": 0.977294921875}, {"start": 1829.2, "end": 1829.78, "word": " موجود", "probability": 0.9866536458333334}, {"start": 1829.78, "end": 1830.72, "word": " يبقى", "probability": 0.947265625}, {"start": 1830.72, "end": 1831.12, "word": " بجي", "probability": 0.7743326822916666}, {"start": 1831.12, "end": 1831.72, "word": " بقوله", "probability": 0.9384765625}, {"start": 1831.72, "end": 1832.16, "word": " then", "probability": 0.88525390625}], "temperature": 1.0}, {"id": 75, "seek": 185285, "start": 1833.59, "end": 1852.85, "text": "الـ X inverse موجودة في G implies بدي اطبق عليها الشرط هذا يبقى لو جيت طبقت عليها الشرط هذا بصير X inverse H X inverse inverse اللي هو subset من من؟ subset من H", "tokens": [6027, 39184, 1783, 17340, 3714, 29245, 23328, 3660, 8978, 460, 18779, 4724, 16254, 1975, 9566, 3555, 4587, 25894, 11296, 25124, 2288, 9566, 23758, 7251, 3555, 4587, 7578, 45164, 10874, 36081, 23032, 3555, 38149, 25894, 11296, 25124, 2288, 9566, 23758, 4724, 9381, 13546, 1783, 17340, 389, 1783, 17340, 17340, 13672, 1829, 31439, 25993, 9154, 9154, 22807, 25993, 9154, 389], "avg_logprob": -0.23450741676960962, "compression_ratio": 1.570469798657718, "no_speech_prob": 0.0, "words": [{"start": 1833.59, "end": 1834.07, "word": "الـ", "probability": 0.56640625}, {"start": 1834.07, "end": 1834.41, "word": " X", "probability": 0.55419921875}, {"start": 1834.41, "end": 1835.21, "word": " inverse", "probability": 0.7705078125}, {"start": 1835.21, "end": 1836.15, "word": " موجودة", "probability": 0.953369140625}, {"start": 1836.15, "end": 1836.41, "word": " في", "probability": 0.9169921875}, {"start": 1836.41, "end": 1836.75, "word": " G", "probability": 0.5673828125}, {"start": 1836.75, "end": 1838.15, "word": " implies", "probability": 0.82275390625}, {"start": 1838.15, "end": 1838.93, "word": " بدي", "probability": 0.378662109375}, {"start": 1838.93, "end": 1839.39, "word": " اطبق", "probability": 0.85546875}, {"start": 1839.39, "end": 1839.75, "word": " عليها", "probability": 0.986083984375}, {"start": 1839.75, "end": 1840.29, "word": " الشرط", "probability": 0.9606119791666666}, {"start": 1840.29, "end": 1840.69, "word": " هذا", "probability": 0.86328125}, {"start": 1840.69, "end": 1841.39, "word": " يبقى", "probability": 0.8272705078125}, {"start": 1841.39, "end": 1841.57, "word": " لو", "probability": 0.81298828125}, {"start": 1841.57, "end": 1841.85, "word": " جيت", "probability": 0.68115234375}, {"start": 1841.85, "end": 1842.33, "word": " طبقت", "probability": 0.9285481770833334}, {"start": 1842.33, "end": 1842.79, "word": " عليها", "probability": 0.986328125}, {"start": 1842.79, "end": 1843.35, "word": " الشرط", "probability": 0.9755859375}, {"start": 1843.35, "end": 1843.79, "word": " هذا", "probability": 0.9287109375}, {"start": 1843.79, "end": 1844.95, "word": " بصير", "probability": 0.9324544270833334}, {"start": 1844.95, "end": 1845.45, "word": " X", "probability": 0.92578125}, {"start": 1845.45, "end": 1846.23, "word": " inverse", "probability": 0.904296875}, {"start": 1846.23, "end": 1846.75, "word": " H", "probability": 0.79296875}, {"start": 1846.75, "end": 1847.37, "word": " X", "probability": 0.55224609375}, {"start": 1847.37, "end": 1848.31, "word": " inverse", "probability": 0.91064453125}, {"start": 1848.31, "end": 1849.33, "word": " inverse", "probability": 0.2509765625}, {"start": 1849.33, "end": 1849.95, "word": " اللي", "probability": 0.892822265625}, {"start": 1849.95, "end": 1850.13, "word": " هو", "probability": 0.9794921875}, {"start": 1850.13, "end": 1850.57, "word": " subset", "probability": 0.822265625}, {"start": 1850.57, "end": 1850.95, "word": " من", "probability": 0.99658203125}, {"start": 1850.95, "end": 1851.47, "word": " من؟", "probability": 0.41864013671875}, {"start": 1851.47, "end": 1852.13, "word": " subset", "probability": 0.84033203125}, {"start": 1852.13, "end": 1852.53, "word": " من", "probability": 0.98876953125}, {"start": 1852.53, "end": 1852.85, "word": " H", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 76, "seek": 187239, "start": 1855.03, "end": 1872.39, "text": "او بمعنى اخر بقدر اقول هنا main ان ال X inverse H X subset من main subset من main من H طيب كويس", "tokens": [995, 2407, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 4724, 28543, 2288, 1975, 39648, 34105, 2135, 16472, 2423, 1783, 17340, 389, 1783, 25993, 9154, 2135, 25993, 9154, 2135, 9154, 389, 23032, 1829, 3555, 9122, 45865, 3794], "avg_logprob": -0.24429898970835917, "compression_ratio": 1.2201834862385321, "no_speech_prob": 0.0, "words": [{"start": 1855.03, "end": 1855.37, "word": "او", "probability": 0.60546875}, {"start": 1855.37, "end": 1855.95, "word": " بمعنى", "probability": 0.98125}, {"start": 1855.95, "end": 1856.59, "word": " اخر", "probability": 0.859619140625}, {"start": 1856.59, "end": 1857.69, "word": " بقدر", "probability": 0.9269205729166666}, {"start": 1857.69, "end": 1858.11, "word": " اقول", "probability": 0.965576171875}, {"start": 1858.11, "end": 1858.53, "word": " هنا", "probability": 0.9404296875}, {"start": 1858.53, "end": 1858.87, "word": " main", "probability": 0.294189453125}, {"start": 1858.87, "end": 1859.57, "word": " ان", "probability": 0.8564453125}, {"start": 1859.57, "end": 1859.85, "word": " ال", "probability": 0.85693359375}, {"start": 1859.85, "end": 1860.35, "word": " X", "probability": 0.6767578125}, {"start": 1860.35, "end": 1861.43, "word": " inverse", "probability": 0.732421875}, {"start": 1861.43, "end": 1862.15, "word": " H", "probability": 0.81298828125}, {"start": 1862.15, "end": 1863.21, "word": " X", "probability": 0.71044921875}, {"start": 1863.21, "end": 1864.19, "word": " subset", "probability": 0.73583984375}, {"start": 1864.19, "end": 1864.55, "word": " من", "probability": 0.99072265625}, {"start": 1864.55, "end": 1864.89, "word": " main", "probability": 0.280029296875}, {"start": 1864.89, "end": 1865.73, "word": " subset", "probability": 0.63232421875}, {"start": 1865.73, "end": 1866.21, "word": " من", "probability": 0.98974609375}, {"start": 1866.21, "end": 1866.57, "word": " main", "probability": 0.6162109375}, {"start": 1866.57, "end": 1867.25, "word": " من", "probability": 0.984375}, {"start": 1867.25, "end": 1867.73, "word": " H", "probability": 0.853515625}, {"start": 1867.73, "end": 1871.83, "word": " طيب", "probability": 0.8269856770833334}, {"start": 1871.83, "end": 1872.39, "word": " كويس", "probability": 0.9754231770833334}], "temperature": 1.0}, {"id": 77, "seek": 189507, "start": 1873.33, "end": 1895.07, "text": "يبقى هذه الخطوة الأولى لو جبت او قدرت اثبت ان ال H هي ال subset من من ال X inverse HX بتم المطلوب يبقى بدي اعتبر هذه الخطوة رقم واحد بدي اجي للخطوة رقم اتنين الخطوة رقم واحد", "tokens": [1829, 3555, 4587, 7578, 29538, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 45164, 10874, 3555, 2655, 1975, 2407, 12174, 3215, 43500, 1975, 12984, 3555, 2655, 16472, 2423, 389, 39896, 2423, 25993, 9154, 9154, 2423, 1783, 17340, 389, 55, 4724, 39237, 9673, 9566, 1211, 37746, 7251, 3555, 4587, 7578, 4724, 16254, 1975, 34268, 26890, 29538, 33962, 9566, 2407, 3660, 12602, 4587, 2304, 36764, 24401, 4724, 16254, 1975, 7435, 1829, 24976, 9778, 9566, 2407, 3660, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 33962, 9566, 2407, 3660, 12602, 4587, 2304, 36764, 24401], "avg_logprob": -0.1789930534031656, "compression_ratio": 1.813664596273292, "no_speech_prob": 0.0, "words": [{"start": 1873.33, "end": 1873.81, "word": "يبقى", "probability": 0.8365478515625}, {"start": 1873.81, "end": 1874.25, "word": " هذه", "probability": 0.8193359375}, {"start": 1874.25, "end": 1875.15, "word": " الخطوة", "probability": 0.938720703125}, {"start": 1875.15, "end": 1875.65, "word": " الأولى", "probability": 0.97607421875}, {"start": 1875.65, "end": 1876.49, "word": " لو", "probability": 0.5537109375}, {"start": 1876.49, "end": 1877.25, "word": " جبت", "probability": 0.9410807291666666}, {"start": 1877.25, "end": 1877.97, "word": " او", "probability": 0.6396484375}, {"start": 1877.97, "end": 1878.41, "word": " قدرت", "probability": 0.94189453125}, {"start": 1878.41, "end": 1878.91, "word": " اثبت", "probability": 0.927978515625}, {"start": 1878.91, "end": 1879.13, "word": " ان", "probability": 0.9208984375}, {"start": 1879.13, "end": 1879.33, "word": " ال", "probability": 0.92919921875}, {"start": 1879.33, "end": 1879.63, "word": " H", "probability": 0.492431640625}, {"start": 1879.63, "end": 1880.11, "word": " هي", "probability": 0.8837890625}, {"start": 1880.11, "end": 1880.45, "word": " ال", "probability": 0.415771484375}, {"start": 1880.45, "end": 1881.05, "word": " subset", "probability": 0.88916015625}, {"start": 1881.05, "end": 1881.93, "word": " من", "probability": 0.98046875}, {"start": 1881.93, "end": 1882.17, "word": " من", "probability": 0.30712890625}, {"start": 1882.17, "end": 1882.65, "word": " ال", "probability": 0.4482421875}, {"start": 1882.65, "end": 1883.01, "word": " X", "probability": 0.84912109375}, {"start": 1883.01, "end": 1883.85, "word": " inverse", "probability": 0.78515625}, {"start": 1883.85, "end": 1885.57, "word": " HX", "probability": 0.618896484375}, {"start": 1885.57, "end": 1886.43, "word": " بتم", "probability": 0.5469970703125}, {"start": 1886.43, "end": 1887.11, "word": " المطلوب", "probability": 0.97314453125}, {"start": 1887.11, "end": 1887.83, "word": " يبقى", "probability": 0.9317626953125}, {"start": 1887.83, "end": 1888.09, "word": " بدي", "probability": 0.69140625}, {"start": 1888.09, "end": 1888.57, "word": " اعتبر", "probability": 0.9539388020833334}, {"start": 1888.57, "end": 1888.91, "word": " هذه", "probability": 0.83447265625}, {"start": 1888.91, "end": 1889.55, "word": " الخطوة", "probability": 0.9639892578125}, {"start": 1889.55, "end": 1890.09, "word": " رقم", "probability": 0.9894205729166666}, {"start": 1890.09, "end": 1890.63, "word": " واحد", "probability": 0.926513671875}, {"start": 1890.63, "end": 1891.39, "word": " بدي", "probability": 0.74267578125}, {"start": 1891.39, "end": 1891.55, "word": " اجي", "probability": 0.81787109375}, {"start": 1891.55, "end": 1892.21, "word": " للخطوة", "probability": 0.81513671875}, {"start": 1892.21, "end": 1892.75, "word": " رقم", "probability": 0.9807942708333334}, {"start": 1892.75, "end": 1893.29, "word": " اتنين", "probability": 0.9615478515625}, {"start": 1893.29, "end": 1894.31, "word": " الخطوة", "probability": 0.973876953125}, {"start": 1894.31, "end": 1894.73, "word": " رقم", "probability": 0.9947916666666666}, {"start": 1894.73, "end": 1895.07, "word": " واحد", "probability": 0.984375}], "temperature": 1.0}, {"id": 78, "seek": 192387, "start": 1895.73, "end": 1923.87, "text": "لو ضربتها في X من جهة الشمال يبقى ايش بيصير ال X X inverse في من؟ في ال H وهنا X بدي تبقى subset من ال X H ضربت من جهة الشمال في X يبقى هذا ايش بدي يعطيلك؟ هذا بدي يعطيلك ان ال H X subset من ال X H", "tokens": [1211, 2407, 48812, 25513, 2655, 11296, 8978, 1783, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 7251, 3555, 4587, 7578, 1975, 1829, 8592, 4724, 1829, 9381, 13546, 2423, 1783, 1783, 17340, 8978, 9154, 22807, 8978, 2423, 389, 37037, 8315, 1783, 4724, 16254, 6055, 3555, 4587, 7578, 25993, 9154, 2423, 1783, 389, 48812, 25513, 2655, 9154, 10874, 3224, 3660, 25124, 2304, 6027, 8978, 1783, 7251, 3555, 4587, 7578, 23758, 1975, 1829, 8592, 4724, 16254, 37495, 9566, 1829, 23275, 22807, 23758, 4724, 16254, 37495, 9566, 1829, 23275, 16472, 2423, 389, 1783, 25993, 9154, 2423, 1783, 389], "avg_logprob": -0.17470079343369666, "compression_ratio": 1.8855421686746987, "no_speech_prob": 0.0, "words": [{"start": 1895.73, "end": 1896.23, "word": "لو", "probability": 0.732666015625}, {"start": 1896.23, "end": 1896.95, "word": " ضربتها", "probability": 0.916748046875}, {"start": 1896.95, "end": 1897.27, "word": " في", "probability": 0.90576171875}, {"start": 1897.27, "end": 1897.69, "word": " X", "probability": 0.482666015625}, {"start": 1897.69, "end": 1898.03, "word": " من", "probability": 0.94580078125}, {"start": 1898.03, "end": 1898.77, "word": " جهة", "probability": 0.96337890625}, {"start": 1898.77, "end": 1899.81, "word": " الشمال", "probability": 0.9803059895833334}, {"start": 1899.81, "end": 1900.71, "word": " يبقى", "probability": 0.87451171875}, {"start": 1900.71, "end": 1900.85, "word": " ايش", "probability": 0.7056477864583334}, {"start": 1900.85, "end": 1901.45, "word": " بيصير", "probability": 0.8992919921875}, {"start": 1901.45, "end": 1902.23, "word": " ال", "probability": 0.744140625}, {"start": 1902.23, "end": 1902.71, "word": " X", "probability": 0.806640625}, {"start": 1902.71, "end": 1903.33, "word": " X", "probability": 0.6513671875}, {"start": 1903.33, "end": 1904.23, "word": " inverse", "probability": 0.79052734375}, {"start": 1904.23, "end": 1904.89, "word": " في", "probability": 0.80712890625}, {"start": 1904.89, "end": 1905.37, "word": " من؟", "probability": 0.4462890625}, {"start": 1905.37, "end": 1905.83, "word": " في", "probability": 0.9140625}, {"start": 1905.83, "end": 1906.13, "word": " ال", "probability": 0.66796875}, {"start": 1906.13, "end": 1906.55, "word": " H", "probability": 0.70849609375}, {"start": 1906.55, "end": 1907.73, "word": " وهنا", "probability": 0.7357177734375}, {"start": 1907.73, "end": 1908.21, "word": " X", "probability": 0.89306640625}, {"start": 1908.21, "end": 1909.11, "word": " بدي", "probability": 0.5098876953125}, {"start": 1909.11, "end": 1909.87, "word": " تبقى", "probability": 0.97265625}, {"start": 1909.87, "end": 1910.41, "word": " subset", "probability": 0.96630859375}, {"start": 1910.41, "end": 1911.21, "word": " من", "probability": 0.99462890625}, {"start": 1911.21, "end": 1911.55, "word": " ال", "probability": 0.89111328125}, {"start": 1911.55, "end": 1911.91, "word": " X", "probability": 0.93994140625}, {"start": 1911.91, "end": 1912.47, "word": " H", "probability": 0.6484375}, {"start": 1912.47, "end": 1913.53, "word": " ضربت", "probability": 0.9864908854166666}, {"start": 1913.53, "end": 1913.67, "word": " من", "probability": 0.9501953125}, {"start": 1913.67, "end": 1914.05, "word": " جهة", "probability": 0.982421875}, {"start": 1914.05, "end": 1914.67, "word": " الشمال", "probability": 0.9918619791666666}, {"start": 1914.67, "end": 1915.13, "word": " في", "probability": 0.9638671875}, {"start": 1915.13, "end": 1915.53, "word": " X", "probability": 0.958984375}, {"start": 1915.53, "end": 1916.35, "word": " يبقى", "probability": 0.96630859375}, {"start": 1916.35, "end": 1916.61, "word": " هذا", "probability": 0.7724609375}, {"start": 1916.61, "end": 1916.77, "word": " ايش", "probability": 0.8772786458333334}, {"start": 1916.77, "end": 1917.05, "word": " بدي", "probability": 0.774658203125}, {"start": 1917.05, "end": 1918.05, "word": " يعطيلك؟", "probability": 0.76142578125}, {"start": 1918.05, "end": 1918.29, "word": " هذا", "probability": 0.875}, {"start": 1918.29, "end": 1918.61, "word": " بدي", "probability": 0.947509765625}, {"start": 1918.61, "end": 1919.27, "word": " يعطيلك", "probability": 0.9580078125}, {"start": 1919.27, "end": 1919.67, "word": " ان", "probability": 0.91259765625}, {"start": 1919.67, "end": 1919.97, "word": " ال", "probability": 0.89697265625}, {"start": 1919.97, "end": 1920.43, "word": " H", "probability": 0.67724609375}, {"start": 1920.43, "end": 1921.05, "word": " X", "probability": 0.8427734375}, {"start": 1921.05, "end": 1922.07, "word": " subset", "probability": 0.9287109375}, {"start": 1922.07, "end": 1922.71, "word": " من", "probability": 0.9970703125}, {"start": 1922.71, "end": 1922.93, "word": " ال", "probability": 0.85498046875}, {"start": 1922.93, "end": 1923.39, "word": " X", "probability": 0.97900390625}, {"start": 1923.39, "end": 1923.87, "word": " H", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 79, "seek": 195117, "start": 1924.59, "end": 1951.17, "text": "بنفس الطريقة اضرب من جهة اليمين في الـ X inverse يبقى لو ضربنا في ال X inverse بصير ال H هي subset من X H X inverse و هذه العلاقة رقم اتنين اتطلع ليه في الواحد و اتنين يبقى باجي بقوله هنا from واحد and اتنين we have", "tokens": [3555, 1863, 36178, 41950, 16572, 28671, 1975, 11242, 25513, 9154, 10874, 3224, 3660, 2423, 32640, 9957, 8978, 2423, 39184, 1783, 17340, 7251, 3555, 4587, 7578, 45164, 48812, 25513, 8315, 8978, 2423, 1783, 17340, 4724, 9381, 13546, 2423, 389, 39896, 25993, 9154, 1783, 389, 1783, 17340, 4032, 29538, 18863, 15040, 28671, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 1975, 2655, 9566, 1211, 3615, 32239, 3224, 8978, 2423, 14407, 24401, 4032, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 34105, 490, 36764, 24401, 293, 1975, 2655, 1863, 9957, 321, 362], "avg_logprob": -0.22499999529437015, "compression_ratio": 1.7106598984771573, 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" have", "probability": 0.966796875}], "temperature": 1.0}, {"id": 80, "seek": 198012, "start": 1952.74, "end": 1980.12, "text": "إن ال X H X inverse بده يساوي مين؟ بده يساوي ال H طب أضرب للطرفين في X من جهتي اليامين يبقى X H بده يساوي H X هالتعريف مين؟ ال normal هذا بده يعطيلك إن ال H is a normal subgroup من مين؟ من G و أنت هنا من المسألة", "tokens": [28814, 1863, 2423, 1783, 389, 1783, 17340, 47525, 3224, 7251, 3794, 995, 45865, 3714, 9957, 22807, 47525, 3224, 7251, 3794, 995, 45865, 2423, 389, 23032, 3555, 5551, 11242, 25513, 24976, 9566, 28480, 9957, 8978, 1783, 9154, 10874, 3224, 31371, 45595, 10943, 9957, 7251, 3555, 4587, 7578, 1783, 389, 47525, 3224, 7251, 3794, 995, 45865, 389, 1783, 8032, 6027, 2655, 3615, 16572, 5172, 3714, 9957, 22807, 2423, 2710, 23758, 47525, 3224, 37495, 9566, 1829, 23275, 36145, 2423, 389, 307, 257, 2710, 1422, 17377, 9154, 3714, 9957, 22807, 9154, 460, 4032, 14739, 2655, 34105, 9154, 9673, 3794, 10721, 37977], "avg_logprob": -0.22640306365733243, 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أنت", "probability": 0.73291015625}, {"start": 1977.66, "end": 1978.06, "word": " هنا", "probability": 0.98486328125}, {"start": 1978.06, "end": 1978.62, "word": " من", "probability": 0.923828125}, {"start": 1978.62, "end": 1980.12, "word": " المسألة", "probability": 0.81298828125}], "temperature": 1.0}, {"id": 81, "seek": 200845, "start": 1984.33, "end": 2008.45, "text": "الان خدلي هالملاحظة اللي قلتلك قبل قليل وهي صورة من صورة ال normality بيقولي the above theorem the above theorem the above theorem can be written as can be", "tokens": [6027, 7649, 16490, 3215, 20292, 8032, 6027, 2304, 15040, 5016, 19913, 3660, 13672, 1829, 12174, 1211, 2655, 23275, 12174, 36150, 12174, 20292, 1211, 37037, 1829, 20328, 13063, 3660, 9154, 20328, 13063, 3660, 2423, 2026, 1860, 4724, 1829, 39648, 1829, 264, 3673, 20904, 264, 3673, 20904, 264, 3673, 20904, 393, 312, 3720, 382, 393, 312], "avg_logprob": -0.28465908765792847, "compression_ratio": 1.5714285714285714, "no_speech_prob": 0.0, "words": 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2513.65, "end": 2539.45, "text": "الان ال special linear group of two by two matrices over R هذي normal من ال general linear group of two by two matrices over R ليش هذي؟ بدي اثبت شرطين الشرط الأول انها subgroup اتنين بدي اثبت خاصية ال normality يبقى الان solution", "tokens": [6027, 7649, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 8032, 8848, 1829, 2710, 9154, 2423, 2674, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 32239, 8592, 8032, 8848, 1829, 22807, 4724, 16254, 1975, 12984, 3555, 2655, 13412, 2288, 9566, 9957, 25124, 2288, 9566, 16247, 12610, 16472, 11296, 1422, 17377, 1975, 2655, 1863, 9957, 4724, 16254, 1975, 12984, 3555, 2655, 16490, 33546, 10632, 2423, 2026, 1860, 7251, 3555, 4587, 7578, 2423, 7649, 3827], "avg_logprob": -0.21033654381067324, "compression_ratio": 1.6593406593406594, "no_speech_prob": 0.0, "words": [{"start": 2513.65, "end": 2514.41, "word": "الان", "probability": 0.679931640625}, {"start": 2514.41, "end": 2514.97, "word": " ال", 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"end": 2552.05, "word": " of", "probability": 0.95458984375}, {"start": 2552.05, "end": 2552.27, "word": " two", "probability": 0.93798828125}, {"start": 2552.27, "end": 2552.49, "word": " by", "probability": 0.97607421875}, {"start": 2552.49, "end": 2552.71, "word": " two", "probability": 0.939453125}, {"start": 2552.71, "end": 2553.19, "word": " matrices", "probability": 0.97705078125}, {"start": 2553.19, "end": 2553.77, "word": " over", "probability": 0.89306640625}, {"start": 2553.77, "end": 2554.25, "word": " R", "probability": 0.984375}, {"start": 2554.25, "end": 2555.25, "word": " وهذه", "probability": 0.5350341796875}, {"start": 2555.25, "end": 2558.35, "word": " مثال", "probability": 0.6309814453125}, {"start": 2558.35, "end": 2558.95, "word": " سابق", "probability": 0.8751627604166666}, {"start": 2558.95, "end": 2559.89, "word": " هذه", "probability": 0.389404296875}, {"start": 2559.89, "end": 2560.91, "word": " أثبتناها", "probability": 0.9654947916666666}, {"start": 2560.91, "end": 2561.49, "word": " قبل", "probability": 0.9921875}, {"start": 2561.49, "end": 2562.31, "word": " ذلك", "probability": 0.99462890625}], "temperature": 1.0}, {"id": 106, "seek": 258461, "start": 2563.77, "end": 2584.61, "text": "طب كويس الان بروح اخد element من G و بدي اخد element من ال special و اشوف حصل ضرب ال element من G في ال element من ال special في معكوس ال element تبعي انطلع والله ال determinant ايه اللي بدي يساوي واحد بيكون حصل الضرب هذا موجود وان", "tokens": [9566, 3555, 9122, 45865, 3794, 2423, 7649, 4724, 32887, 5016, 1975, 9778, 3215, 4478, 9154, 460, 4032, 4724, 16254, 1975, 9778, 3215, 4478, 9154, 2423, 2121, 4032, 1975, 8592, 38688, 11331, 36520, 48812, 25513, 2423, 4478, 9154, 460, 8978, 2423, 4478, 9154, 2423, 2121, 8978, 20449, 4117, 41779, 2423, 4478, 6055, 3555, 3615, 1829, 16472, 9566, 1211, 3615, 16070, 43761, 2423, 41296, 1975, 1829, 3224, 13672, 1829, 4724, 16254, 7251, 3794, 995, 45865, 36764, 24401, 4724, 1829, 30544, 11331, 36520, 6024, 114, 25513, 23758, 3714, 29245, 23328, 4032, 7649], "avg_logprob": -0.26666666203074985, "compression_ratio": 1.8333333333333333, "no_speech_prob": 0.0, "words": [{"start": 2563.77, "end": 2564.01, "word": "طب", "probability": 0.5556640625}, {"start": 2564.01, "end": 2564.69, "word": " كويس", "probability": 0.9775390625}, {"start": 2564.69, "end": 2565.57, "word": " الان", "probability": 0.656982421875}, {"start": 2565.57, "end": 2566.61, "word": " بروح", "probability": 0.6133626302083334}, {"start": 2566.61, "end": 2567.01, "word": " اخد", "probability": 0.7615559895833334}, {"start": 2567.01, "end": 2567.45, "word": " element", "probability": 0.9306640625}, {"start": 2567.45, "end": 2567.93, "word": " من", "probability": 0.984375}, {"start": 2567.93, "end": 2568.21, "word": " G", "probability": 0.321044921875}, {"start": 2568.21, "end": 2568.95, "word": " و", "probability": 0.7978515625}, {"start": 2568.95, "end": 2569.23, "word": " بدي", "probability": 0.525634765625}, {"start": 2569.23, "end": 2569.75, "word": " اخد", "probability": 0.9231770833333334}, {"start": 2569.75, "end": 2570.19, "word": " element", "probability": 0.9521484375}, {"start": 2570.19, "end": 2570.57, "word": " من", "probability": 0.98681640625}, {"start": 2570.57, "end": 2570.71, "word": " ال", "probability": 0.943359375}, {"start": 2570.71, "end": 2571.19, "word": " special", "probability": 0.89599609375}, {"start": 2571.19, "end": 2571.99, "word": " و", "probability": 0.94970703125}, {"start": 2571.99, "end": 2572.47, "word": " اشوف", "probability": 0.802734375}, {"start": 2572.47, "end": 2573.03, "word": " حصل", "probability": 0.94287109375}, {"start": 2573.03, "end": 2573.37, "word": " ضرب", "probability": 0.975830078125}, {"start": 2573.37, "end": 2573.57, "word": " ال", "probability": 0.8896484375}, {"start": 2573.57, "end": 2574.03, "word": " element", "probability": 0.97412109375}, {"start": 2574.03, "end": 2574.35, "word": " من", "probability": 0.986328125}, {"start": 2574.35, "end": 2574.65, "word": " G", "probability": 0.94384765625}, {"start": 2574.65, "end": 2574.83, "word": " في", "probability": 0.81201171875}, {"start": 2574.83, "end": 2574.95, "word": " ال", "probability": 0.7099609375}, {"start": 2574.95, "end": 2575.31, "word": " element", "probability": 0.9658203125}, {"start": 2575.31, "end": 2575.53, "word": " من", "probability": 0.9794921875}, {"start": 2575.53, "end": 2575.69, "word": " ال", "probability": 0.96337890625}, {"start": 2575.69, "end": 2576.03, "word": " special", "probability": 0.96728515625}, {"start": 2576.03, "end": 2576.31, "word": " في", "probability": 0.83837890625}, {"start": 2576.31, "end": 2576.93, "word": " معكوس", "probability": 0.8361002604166666}, {"start": 2576.93, "end": 2577.15, "word": " ال", "probability": 0.93212890625}, {"start": 2577.15, "end": 2577.63, "word": " element", "probability": 0.98583984375}, {"start": 2577.63, "end": 2578.41, "word": " تبعي", "probability": 0.5728759765625}, {"start": 2578.41, "end": 2578.95, "word": " انطلع", "probability": 0.6964111328125}, {"start": 2578.95, "end": 2579.57, "word": " والله", "probability": 0.868896484375}, {"start": 2579.57, "end": 2580.39, "word": " ال", "probability": 0.9599609375}, {"start": 2580.39, "end": 2581.25, "word": " determinant", "probability": 0.96533203125}, {"start": 2581.25, "end": 2581.61, "word": " ايه", "probability": 0.773681640625}, {"start": 2581.61, "end": 2581.67, "word": " اللي", "probability": 0.763427734375}, {"start": 2581.67, "end": 2581.91, "word": " بدي", "probability": 0.5682373046875}, {"start": 2581.91, "end": 2582.31, "word": " يساوي", "probability": 0.7830810546875}, {"start": 2582.31, "end": 2582.61, "word": " واحد", "probability": 0.721923828125}, {"start": 2582.61, "end": 2582.95, "word": " بيكون", "probability": 0.90625}, {"start": 2582.95, "end": 2583.33, "word": " حصل", "probability": 0.98828125}, {"start": 2583.33, "end": 2583.67, "word": " الضرب", "probability": 0.8610026041666666}, {"start": 2583.67, "end": 2583.89, "word": " هذا", "probability": 0.69921875}, {"start": 2583.89, "end": 2584.27, "word": " موجود", "probability": 0.98681640625}, {"start": 2584.27, "end": 2584.61, "word": " وان", "probability": 0.63720703125}], "temperature": 1.0}, {"id": 107, "seek": 259448, "start": 2584.86, "end": 2594.48, "text": "في ال special وبالتالي ال special هه normal subgroup من main من G يبقى بالداخل اكتب لك الحل على الشجرة التانية", "tokens": [41185, 2423, 2121, 46599, 6027, 2655, 6027, 1829, 2423, 2121, 8032, 3224, 2710, 1422, 17377, 9154, 2135, 9154, 460, 7251, 3555, 4587, 7578, 20666, 3215, 47283, 1211, 1975, 4117, 2655, 3555, 5296, 4117, 21542, 1211, 15844, 25124, 7435, 25720, 16712, 7649, 10632], "avg_logprob": -0.37536336654840513, "compression_ratio": 1.3253968253968254, "no_speech_prob": 0.0, "words": [{"start": 2584.86, "end": 2585.02, "word": "في", "probability": 0.12200927734375}, {"start": 2585.02, "end": 2585.16, "word": " ال", "probability": 0.94482421875}, {"start": 2585.16, "end": 2585.52, "word": " special", "probability": 0.73193359375}, {"start": 2585.52, "end": 2586.12, "word": " وبالتالي", "probability": 0.90205078125}, {"start": 2586.12, "end": 2586.26, "word": " ال", "probability": 0.9697265625}, {"start": 2586.26, "end": 2587.02, "word": " special", "probability": 0.974609375}, {"start": 2587.02, "end": 2587.72, "word": " هه", "probability": 0.33648681640625}, {"start": 2587.72, "end": 2588.2, "word": " normal", "probability": 0.69384765625}, {"start": 2588.2, "end": 2588.82, "word": " subgroup", "probability": 0.69287109375}, {"start": 2588.82, "end": 2589.0, "word": " من", "probability": 0.9931640625}, {"start": 2589.0, "end": 2589.32, "word": " main", "probability": 0.572265625}, {"start": 2589.32, "end": 2589.94, "word": " من", "probability": 0.330322265625}, {"start": 2589.94, "end": 2590.76, "word": " G", "probability": 0.5029296875}, {"start": 2590.76, "end": 2591.84, "word": " يبقى", "probability": 0.8563232421875}, {"start": 2591.84, "end": 2592.3, "word": " بالداخل", "probability": 0.54779052734375}, {"start": 2592.3, "end": 2592.7, "word": " اكتب", "probability": 0.915771484375}, {"start": 2592.7, "end": 2592.88, "word": " لك", "probability": 0.768798828125}, {"start": 2592.88, "end": 2593.24, "word": " الحل", "probability": 0.959716796875}, {"start": 2593.24, "end": 2593.44, "word": " على", "probability": 0.79931640625}, {"start": 2593.44, "end": 2593.96, "word": " الشجرة", "probability": 0.7171223958333334}, {"start": 2593.96, "end": 2594.48, "word": " التانية", "probability": 0.9090169270833334}], "temperature": 1.0}, {"id": 108, "seek": 262466, "start": 2608.72, "end": 2624.66, "text": "أفترض أن ال A موجودة في ال general linear group of 2 by 2 matrices over R ويكون موجودة في ال special linear group of 2 by 2 matrices over R", "tokens": [10721, 5172, 2655, 43042, 14739, 2423, 316, 3714, 29245, 23328, 3660, 8978, 2423, 2674, 8213, 1594, 295, 568, 538, 568, 32284, 670, 497, 4032, 1829, 30544, 3714, 29245, 23328, 3660, 8978, 2423, 2121, 8213, 1594, 295, 568, 538, 568, 32284, 670, 497], "avg_logprob": -0.337572667487832, "compression_ratio": 1.4913793103448276, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2608.72, "end": 2609.6, "word": "أفترض", "probability": 0.71832275390625}, {"start": 2609.6, "end": 2610.48, "word": " أن", "probability": 0.533203125}, {"start": 2610.48, "end": 2610.72, "word": " ال", "probability": 0.54931640625}, {"start": 2610.72, "end": 2611.1, "word": " A", "probability": 0.1572265625}, {"start": 2611.1, "end": 2612.28, "word": " موجودة", "probability": 0.954345703125}, {"start": 2612.28, "end": 2612.42, "word": " في", "probability": 0.91845703125}, {"start": 2612.42, "end": 2612.6, "word": " ال", "probability": 0.84619140625}, {"start": 2612.6, "end": 2613.04, "word": " general", "probability": 0.345458984375}, {"start": 2613.04, "end": 2613.44, "word": " linear", "probability": 0.52490234375}, {"start": 2613.44, "end": 2614.1, "word": " group", "probability": 0.97802734375}, {"start": 2614.1, "end": 2614.74, "word": " of", "probability": 0.72900390625}, {"start": 2614.74, "end": 2615.02, "word": " 2", "probability": 0.63818359375}, {"start": 2615.02, "end": 2615.3, "word": " by", "probability": 0.41552734375}, {"start": 2615.3, "end": 2615.54, "word": " 2", "probability": 0.9638671875}, {"start": 2615.54, "end": 2616.3, "word": " matrices", "probability": 0.96142578125}, {"start": 2616.3, "end": 2616.92, "word": " over", "probability": 0.7314453125}, {"start": 2616.92, "end": 2617.44, "word": " R", "probability": 0.9833984375}, {"start": 2617.44, "end": 2618.72, "word": " ويكون", "probability": 0.4910074869791667}, {"start": 2618.72, "end": 2620.16, "word": " موجودة", "probability": 0.82415771484375}, {"start": 2620.16, "end": 2620.34, "word": " في", "probability": 0.9482421875}, {"start": 2620.34, "end": 2620.48, "word": " ال", "probability": 0.95751953125}, {"start": 2620.48, "end": 2621.0, "word": " special", "probability": 0.9189453125}, {"start": 2621.0, "end": 2621.44, "word": " linear", "probability": 0.86376953125}, {"start": 2621.44, "end": 2622.02, "word": " group", "probability": 0.9697265625}, {"start": 2622.02, "end": 2622.3, "word": " of", "probability": 0.9287109375}, {"start": 2622.3, "end": 2622.52, "word": " 2", "probability": 0.96728515625}, {"start": 2622.52, "end": 2622.76, "word": " by", "probability": 0.97509765625}, {"start": 2622.76, "end": 2623.0, "word": " 2", "probability": 0.98193359375}, {"start": 2623.0, "end": 2623.62, "word": " matrices", "probability": 0.98486328125}, {"start": 2623.62, "end": 2624.18, "word": " over", "probability": 0.88330078125}, {"start": 2624.18, "end": 2624.66, "word": " R", "probability": 0.984375}], "temperature": 1.0}, {"id": 109, "seek": 265480, "start": 2627.08, "end": 2654.8, "text": "أريد أن أخذ الـ A بـ A إنفرس إذا كنت أثبت إن هذه موجودة في الـ Special يبقى هو الشرط اللي قلنا عليه الشرط التالت هو المساحنة أه هذه موجودة تمام يبقى بدي أحاول أثبتها فبدي أخدي determinant لمين لهذه المصوفة يبقى حسب الجبرة الخاطية هذه determinant للـ A", "tokens": [10721, 16572, 3215, 14739, 5551, 9778, 8848, 2423, 39184, 316, 4724, 39184, 316, 11933, 1863, 5172, 2288, 3794, 11933, 15730, 9122, 29399, 5551, 12984, 3555, 2655, 36145, 29538, 3714, 29245, 23328, 3660, 8978, 2423, 39184, 11863, 7251, 3555, 4587, 7578, 31439, 25124, 2288, 9566, 13672, 1829, 12174, 1211, 8315, 47356, 25124, 2288, 9566, 16712, 6027, 2655, 31439, 9673, 3794, 39319, 1863, 3660, 5551, 3224, 29538, 3714, 29245, 23328, 3660, 46811, 10943, 7251, 3555, 4587, 7578, 4724, 16254, 5551, 5016, 995, 12610, 5551, 12984, 3555, 2655, 11296, 6156, 3555, 16254, 5551, 9778, 16254, 41296, 32767, 9957, 46740, 24192, 9673, 9381, 38688, 3660, 7251, 3555, 4587, 7578, 11331, 35457, 25724, 3555, 25720, 33962, 41193, 10632, 29538, 41296, 24976, 39184, 316], "avg_logprob": -0.3198529406755912, "compression_ratio": 1.8111587982832618, "no_speech_prob": 0.0, "words": [{"start": 2627.08, "end": 2627.48, "word": "أريد", "probability": 0.4032796223958333}, {"start": 2627.48, "end": 2627.74, "word": " أن", "probability": 0.67333984375}, {"start": 2627.74, "end": 2628.0, "word": " أخذ", "probability": 0.7112630208333334}, {"start": 2628.0, "end": 2628.54, "word": " الـ", "probability": 0.700439453125}, {"start": 2628.54, "end": 2628.92, "word": " A", "probability": 0.471435546875}, {"start": 2628.92, "end": 2630.36, "word": " بـ", "probability": 0.735107421875}, {"start": 2630.36, "end": 2630.66, "word": " A", "probability": 0.77978515625}, {"start": 2630.66, "end": 2631.42, "word": " إنفرس", "probability": 0.67362060546875}, {"start": 2631.42, "end": 2632.44, "word": " إذا", "probability": 0.797119140625}, {"start": 2632.44, "end": 2632.68, "word": " كنت", "probability": 0.77294921875}, {"start": 2632.68, "end": 2633.18, "word": " أثبت", "probability": 0.95654296875}, {"start": 2633.18, "end": 2633.34, "word": " إن", "probability": 0.421630859375}, {"start": 2633.34, "end": 2633.7, "word": " هذه", "probability": 0.537109375}, {"start": 2633.7, "end": 2634.34, "word": " موجودة", "probability": 0.9224853515625}, {"start": 2634.34, "end": 2634.5, "word": " في", "probability": 0.9189453125}, {"start": 2634.5, "end": 2634.64, "word": " الـ", "probability": 0.830078125}, {"start": 2634.64, "end": 2635.38, "word": " Special", "probability": 0.5185546875}, {"start": 2635.38, "end": 2636.26, "word": " يبقى", "probability": 0.87158203125}, {"start": 2636.26, "end": 2636.48, "word": " هو", "probability": 0.80029296875}, {"start": 2636.48, "end": 2636.96, "word": " الشرط", "probability": 0.97021484375}, {"start": 2636.96, "end": 2637.14, "word": " اللي", "probability": 0.849365234375}, {"start": 2637.14, "end": 2637.64, "word": " قلنا", "probability": 0.76171875}, {"start": 2637.64, "end": 2637.92, "word": " عليه", "probability": 0.947265625}, {"start": 2637.92, "end": 2638.38, "word": " الشرط", "probability": 0.95361328125}, {"start": 2638.38, "end": 2638.86, "word": " التالت", "probability": 0.8699544270833334}, {"start": 2638.86, "end": 2639.02, "word": " هو", "probability": 0.07208251953125}, {"start": 2639.02, "end": 2639.8, "word": " المساحنة", "probability": 0.669091796875}, {"start": 2639.8, "end": 2640.48, "word": " أه", "probability": 0.471832275390625}, {"start": 2640.48, "end": 2640.76, "word": " هذه", "probability": 0.295166015625}, {"start": 2640.76, "end": 2641.26, "word": " موجودة", "probability": 0.9332275390625}, {"start": 2641.26, "end": 2641.66, "word": " تمام", "probability": 0.853515625}, {"start": 2641.66, "end": 2642.44, "word": " يبقى", "probability": 0.85223388671875}, {"start": 2642.44, "end": 2642.68, "word": " بدي", "probability": 0.4813232421875}, {"start": 2642.68, "end": 2643.2, "word": " أحاول", "probability": 0.9788818359375}, {"start": 2643.2, "end": 2643.74, "word": " أثبتها", "probability": 0.95263671875}, {"start": 2643.74, "end": 2644.16, "word": " فبدي", "probability": 0.7180989583333334}, {"start": 2644.16, "end": 2644.7, "word": " أخدي", "probability": 0.7958984375}, {"start": 2644.7, "end": 2645.66, "word": " determinant", "probability": 0.58544921875}, {"start": 2645.66, "end": 2647.4, "word": " لمين", "probability": 0.658935546875}, {"start": 2647.4, "end": 2648.36, "word": " لهذه", "probability": 0.8935546875}, {"start": 2648.36, "end": 2649.3, "word": " المصوفة", "probability": 0.9090576171875}, {"start": 2649.3, "end": 2650.32, "word": " يبقى", "probability": 0.98095703125}, {"start": 2650.32, "end": 2650.84, "word": " حسب", "probability": 0.98828125}, {"start": 2650.84, "end": 2651.46, "word": " الجبرة", "probability": 0.6411946614583334}, {"start": 2651.46, "end": 2652.3, "word": " الخاطية", "probability": 0.706787109375}, {"start": 2652.3, "end": 2652.74, "word": " هذه", "probability": 0.7421875}, {"start": 2652.74, "end": 2653.46, "word": " determinant", "probability": 0.7998046875}, {"start": 2653.46, "end": 2654.54, "word": " للـ", "probability": 0.8486328125}, {"start": 2654.54, "end": 2654.8, "word": " A", "probability": 0.7392578125}], "temperature": 1.0}, {"id": 110, "seek": 268397, "start": 2655.25, "end": 2683.97, "text": "فى الـ determinant للـ B فى الـ determinant للـ A inverse صاروا هدور الـ real numbers الـ real numbers are commutes يبقى هذا الـ determinant للـ A فى الـ determinant للـ A inverse فى الـ determinant للـ B يبقى .. بدى أرجعه إلى أصله يبقى الـ determinant للـ A فى الـ A inverse فى الـ determinant للـ B", "tokens": [5172, 7578, 2423, 39184, 41296, 24976, 39184, 363, 6156, 7578, 2423, 39184, 41296, 24976, 39184, 316, 17340, 20328, 9640, 14407, 8032, 3215, 2407, 2288, 2423, 39184, 957, 3547, 2423, 39184, 957, 3547, 366, 800, 1819, 7251, 3555, 4587, 7578, 23758, 2423, 39184, 41296, 24976, 39184, 316, 6156, 7578, 2423, 39184, 41296, 24976, 39184, 316, 17340, 6156, 7578, 2423, 39184, 41296, 24976, 39184, 363, 7251, 3555, 4587, 7578, 4386, 47525, 7578, 5551, 47341, 3615, 3224, 30731, 5551, 36520, 3224, 7251, 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"probability": 0.963623046875}, {"start": 2677.87, "end": 2678.03, "word": " الـ", "probability": 0.776611328125}, {"start": 2678.03, "end": 2678.61, "word": " determinant", "probability": 0.9384765625}, {"start": 2678.61, "end": 2679.59, "word": " للـ", "probability": 0.952880859375}, {"start": 2679.59, "end": 2679.89, "word": " A", "probability": 0.966796875}, {"start": 2679.89, "end": 2680.21, "word": " فى", "probability": 0.938232421875}, {"start": 2680.21, "end": 2680.45, "word": " الـ", "probability": 0.98486328125}, {"start": 2680.45, "end": 2680.75, "word": " A", "probability": 0.986328125}, {"start": 2680.75, "end": 2681.39, "word": " inverse", "probability": 0.86865234375}, {"start": 2681.39, "end": 2682.03, "word": " فى", "probability": 0.9912109375}, {"start": 2682.03, "end": 2682.17, "word": " الـ", "probability": 0.962890625}, {"start": 2682.17, "end": 2682.65, "word": " determinant", "probability": 0.94970703125}, {"start": 2682.65, "end": 2683.59, "word": " للـ", 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"start": 2786.2, "end": 2802.68, "text": "بدي اخد element في sn و element في an طبعا انا اخدناها سابقا انها ال subgroup مظبوط ال a for because ال an هدى ال subgroup من ال sn and", "tokens": [3555, 16254, 1975, 9778, 3215, 4478, 8978, 2406, 4032, 4478, 8978, 364, 23032, 3555, 3615, 995, 1975, 8315, 1975, 9778, 3215, 8315, 11296, 8608, 16758, 4587, 995, 16472, 11296, 2423, 1422, 17377, 3714, 19913, 3555, 2407, 9566, 2423, 257, 337, 570, 2423, 364, 8032, 3215, 7578, 2423, 1422, 17377, 9154, 2423, 2406, 293], "avg_logprob": -0.28284142580297256, "compression_ratio": 1.4881889763779528, "no_speech_prob": 0.0, "words": [{"start": 2786.2, "end": 2786.54, "word": "بدي", "probability": 0.20880126953125}, {"start": 2786.54, "end": 2786.86, "word": " اخد", "probability": 0.7584635416666666}, {"start": 2786.86, "end": 2787.58, "word": " element", "probability": 0.90625}, {"start": 2787.58, "end": 2788.2, "word": " في", "probability": 0.93017578125}, {"start": 2788.2, "end": 2789.18, "word": " sn", 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بنكمل", "probability": 0.7936197916666666}, {"start": 2890.03, "end": 2890.15, "word": " في", "probability": 0.8525390625}, {"start": 2890.15, "end": 2890.87, "word": " المحاضرة", "probability": 0.986572265625}, {"start": 2890.87, "end": 2892.19, "word": " القادمة", "probability": 0.99365234375}, {"start": 2892.19, "end": 2892.49, "word": " ان", "probability": 0.75439453125}, {"start": 2892.49, "end": 2892.81, "word": " شاء", "probability": 0.971435546875}, {"start": 2892.81, "end": 2892.95, "word": " الله", "probability": 0.94384765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2893.9495, "duration_after_vad": 2698.4137499999906}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7ff3999ea3a6a412d56810def276f0446218be11
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RNahrP2LIYY_raw.srt
@@ -0,0 +1,1824 @@
+1
+00:00:21,580 --> 00:00:26,400
+بسم الله الرحمن الرحيم في نهاية المحاضرة الماضية
+
+2
+00:00:26,400 --> 00:00:31,940
+أخدنا نظرية النظرية بتقول لو عندي رقمين S و T are
+
+3
+00:00:31,940 --> 00:00:37,970
+relatively prime يبقى ال U S T isomorphicللـ US
+
+4
+00:00:37,970 --> 00:00:43,470
+External Product مع من مع الـ UT يعني بقدر أكتب
+
+5
+00:00:43,470 --> 00:00:48,230
+الـ UN على صيغة External Product لمن؟ لـ two
+
+6
+00:00:48,230 --> 00:00:52,070
+groups لـ three groups لـ four groups وما إلى ذلك
+
+7
+00:00:52,070 --> 00:00:57,840
+بشرط يكون ال S و ال T are relatively a primeواخدنا
+
+8
+00:00:57,840 --> 00:01:06,060
+كمان نقطة ان U S T على S isomorphic ل U T وكذلك U
+
+9
+00:01:06,060 --> 00:01:12,820
+T ل U S T isomorphic ل U S وزيادة على ذلك رولر
+
+10
+00:01:12,820 --> 00:01:18,300
+عليها بنقول لو عندنا الرقم M واستطعنا ال M نكتبه
+
+11
+00:01:18,300 --> 00:01:23,100
+على الشكل التالي يبقى M بده يسوى N واحد
+
+12
+00:01:26,550 --> 00:01:32,090
+بحيث اي اتنين من هذه الأرقام are relatively prime
+
+13
+00:01:32,090 --> 00:01:37,790
+يعني ni مع ng اتنين are relatively prime لكل i لا
+
+14
+00:01:37,790 --> 00:01:43,440
+تساوي الجييبقى في هذه الحالة بقدر اقول ان ال UM
+
+15
+00:01:43,440 --> 00:01:54,000
+ايزو مورف كلمة ل ال UN 1 UN 2 UN 3 UN UN لغاية ال
+
+16
+00:01:54,000 --> 00:02:02,330
+UUNالان ان والله ان كهذه عملها ل ان كهذه يبقى هذه
+
+17
+00:02:02,330 --> 00:02:07,890
+بالصغيرة ان كهذه بالشكل اللي عندنا هذا طبعا الان
+
+18
+00:02:07,890 --> 00:02:13,210
+بدي الان اشتغل عمليابيقول لي هاي عندك اليوم 105
+
+19
+00:02:13,210 --> 00:02:17,990
+بتقدر تكتبها لي على الشكل اللي عندك كده؟ بمعنى هل
+
+20
+00:02:17,990 --> 00:02:23,410
+بتقدر تكتب ال 105 على شكل isomorphic ل two groups؟
+
+21
+00:02:23,410 --> 00:02:29,370
+الإجابة نعم نعم كيفي؟ بتدور على رقمين ال relative
+
+22
+00:02:29,370 --> 00:02:34,330
+to prime وحاصل ضربه ما يساومين 105 بتقدر تعطوني
+
+23
+00:02:34,330 --> 00:02:43,090
+رقمين؟وحد وعشرين وخمسة كويس يبقى هذا اللي هو عبارة
+
+24
+00:02:43,090 --> 00:02:54,010
+عن U اللي هو واحد وعشرين مضروبة في خمسة
+
+25
+00:02:54,010 --> 00:02:59,620
+يبقى هذه isomorphic ل U واحد وعشرينExternal
+
+26
+00:02:59,620 --> 00:03:11,640
+Product مع U5 كمان ال U 105 عبارة عن U الخمس عشر
+
+27
+00:03:11,640 --> 00:03:19,260
+في سبعة7 في 15% أو 5 يبقى هذا الكلام isomorphic
+
+28
+00:03:19,260 --> 00:03:27,060
+لمن؟ ل U 15 Extended like product مع مين؟ مع U 7
+
+29
+00:03:27,060 --> 00:03:34,950
+أجواح التالت منكم سمعت بيقولالـ U 105 هي عبارة عن
+
+30
+00:03:34,950 --> 00:03:41,990
+U خمسة و تلاتين في تلاتة بقوله كلامك صح يبقى هذه
+
+31
+00:03:41,990 --> 00:03:47,510
+isomorphic لـ U خمسة و تلاتين external product مع
+
+32
+00:03:47,510 --> 00:03:54,550
+U تلاتة هجوا على التالت قال الـ U 105 هذه الـ U
+
+33
+00:03:54,550 --> 00:04:03,020
+105 بدها تساوي الـ U تلاتة في خمسة في سبعةتلاتة و
+
+34
+00:04:03,020 --> 00:04:06,760
+كلهم تلاتة are relatively prime يبقى هذي
+
+35
+00:04:06,760 --> 00:04:12,360
+isomorphic لمين؟ ليه تلاتة external direct product
+
+36
+00:04:12,360 --> 00:04:17,500
+ليه خمسة external direct product لمين؟ ليه سبعة
+
+37
+00:04:17,500 --> 00:04:21,140
+يعني ليس بالضرورة أن يكون two groups و هنا ممكن
+
+38
+00:04:21,140 --> 00:04:27,850
+يكون تلاتة ممكن أربعةممكن يكون K من الأرقام اللي
+
+39
+00:04:27,850 --> 00:04:31,770
+كلها relative لأن اذا أخذت اي اتنين مع بعض بيكونوا
+
+40
+00:04:31,770 --> 00:04:35,890
+relatively main و relatively prime هذا بالنسبة
+
+41
+00:04:35,890 --> 00:04:40,950
+لمن؟ للنقطة الأولى و النقطة التالتة لو جهت للنقطة
+
+42
+00:04:40,950 --> 00:04:48,430
+الثانية و بدي أحسب لأي رقم منهم بدي أحسب U مثلا
+
+43
+00:04:48,430 --> 00:04:55,200
+خمس تاشر لمين لمية وخمسة يساويبتعرف مين عناصرها
+
+44
+00:04:55,200 --> 00:05:00,540
+المرة اللى فاتت اعطيناكوا تعريف لها وقلنا كل
+
+45
+00:05:00,540 --> 00:05:05,640
+العناصر X بحيث ان ال X modulo K بدي اعطيني الواحد
+
+46
+00:05:05,640 --> 00:05:10,220
+الصحيح تعريف كتبناه معاكوا المرة اللى فاتت اذا بدي
+
+47
+00:05:10,220 --> 00:05:17,680
+ادور على عناصر ال 105 واروح اجيب عناصر ال U15 على
+
+48
+00:05:17,680 --> 00:05:23,610
+105 اظن لو بدي اقعد اكتب عناصر ال 105 كلهمهتاخدنا
+
+49
+00:05:23,610 --> 00:05:27,350
+خمس دقايق و احنا قاعدين نستنتج مين اللي رتب ال
+
+50
+00:05:27,350 --> 00:05:33,530
+prime مع مية و خمسة لذلك بقول لأ بدي احسب مباشرة
+
+51
+00:05:33,530 --> 00:05:39,750
+فيو خمستاشر مية و خمسة الواحد منهم لإن الواحد ناقص
+
+52
+00:05:39,750 --> 00:05:45,190
+واحد يساوي زيرو مضاعفات الخمستاشر طيب الست عشر
+
+53
+00:05:45,190 --> 00:05:50,660
+منهميعني انت الخامس و الستاشر ده مانحط رقم قدامه و
+
+54
+00:05:50,660 --> 00:05:54,460
+لما تحط رقم قدامه تتأكد ان الرقم هذا relatively
+
+55
+00:05:54,460 --> 00:05:58,160
+prime على المية و خمسة ولا لا تمام؟ حتى يكون من
+
+56
+00:05:58,160 --> 00:06:02,200
+عناصر المية و خمسة الستاشر من عناصر المية و خمسة
+
+57
+00:06:02,200 --> 00:06:05,340
+لأنهم بيقسمش غير على اتنين و اربعة و تمانية وهذه
+
+58
+00:06:05,340 --> 00:06:10,480
+كلها relatively prime على المية و خمسة يبقى ستاشر
+
+59
+00:06:10,480 --> 00:06:16,330
+شريك واحد و تلاتين منهم؟وأحد وثلاثين وخمس عشر في
+
+60
+00:06:16,330 --> 00:06:20,630
+اتنين وثلاثين وواحد واحد وثلاثين والواحد وثلاثين
+
+61
+00:06:20,630 --> 00:06:24,210
+is a prime وبالتالي relative to the prime مع أي
+
+62
+00:06:24,210 --> 00:06:30,630
+منها طيب ستة واربعين ستة واربعين relative to the
+
+63
+00:06:30,630 --> 00:06:35,590
+prime مع المية وخمسة له اتنين في تلاتة وعشرين
+
+64
+00:06:35,590 --> 00:06:38,590
+اتنين relative to the prime والتلاتة وعشرين يبقى
+
+65
+00:06:38,590 --> 00:06:43,900
+فعلا الستة واربعين منهم طيب الواحد والستينانا بضيف
+
+66
+00:06:43,900 --> 00:06:48,380
+كله خمسة عشان تمام الواحد و ستين منهم لان واحد و
+
+67
+00:06:48,380 --> 00:06:54,060
+ستين is a prime كذلك طيب الأن لو جيت على الستة و
+
+68
+00:06:54,060 --> 00:07:00,300
+سبعين ستة و سبعين اه هذا لما نشيل من خمس عشر مضل
+
+69
+00:07:00,300 --> 00:07:03,580
+جداش مضل واحد كلام صحيح لكن هل الستة و سبعين
+
+70
+00:07:03,580 --> 00:07:08,000
+relative ل prime مع المية و خمسةعلى خمسة بتجيش
+
+71
+00:07:08,000 --> 00:07:13,920
+وعلى سبعة بتجيش وعلى تلاتة برضه بتجيش ويبقى الستة
+
+72
+00:07:13,920 --> 00:07:20,600
+وسبعين كذلك منهم طيب الواحد وتسعين خمسة وسبعين
+
+73
+00:07:20,600 --> 00:07:25,280
+وخمستاشر تسعين كمان واحد واحد وتسعين معاهم حط يعني
+
+74
+00:07:25,280 --> 00:07:33,410
+طب سبعة في تلاتاشر بقداش؟و 91 طب السبعة بتكسب على
+
+75
+00:07:33,410 --> 00:07:38,070
+سبعة و ال 105 بتكسب على سبعة يبقى ال 91 مش منهم
+
+76
+00:07:38,070 --> 00:07:43,910
+بدي كمان خمساش بكون فى التواصل 105,106 برا الرقم
+
+77
+00:07:43,910 --> 00:07:50,630
+انتهينا منهيبقى لا يوجد الا هذه الأرقام تمام شوفت
+
+78
+00:07:50,630 --> 00:07:55,630
+كيف بنحسبها اختارلي اي رقم من عندك من الأرقام اللي
+
+79
+00:07:55,630 --> 00:08:01,470
+هي اللي بتقسم 105 حتى نحسبها طيب هدها اللي هو 15
+
+80
+00:08:01,470 --> 00:08:11,800
+أليس isomorphic ليه 7لأن سبعة في خمستاشر بمية
+
+81
+00:08:11,800 --> 00:08:16,340
+وخمسة و احنا قلنا هنا ال U S على ST isomorphic
+
+82
+00:08:16,340 --> 00:08:21,360
+لمين؟ ل U T يبقى احنا هنا قلنا U خمستاشر و هذا
+
+83
+00:08:21,360 --> 00:08:25,000
+عبارة عن خمستاشر في سبعة يبقى isomorphic ل U سبعة
+
+84
+00:08:25,000 --> 00:08:30,170
+U سبعة كم عنصر فيه؟ست عناصر هدول ستة واحد اتنين
+
+85
+00:08:30,170 --> 00:08:34,490
+تلاتة اربع خمسة ستة كلها مناصعية مية لمية تمام
+
+86
+00:08:34,490 --> 00:08:39,450
+اختار لي كمار رقم اخر نحسبه لك بنفس الطريقة اللي
+
+87
+00:08:39,450 --> 00:08:48,470
+بدك هيها يومين نحسب تحسب كمان واحد بكفي يوم قداشر
+
+88
+00:08:48,470 --> 00:08:54,730
+خمسة و تلاتين خمسة و تلاتين انت جيبت اسهل حاجةطب
+
+89
+00:08:54,730 --> 00:08:57,270
+من انا ماعرف يعطيني الشمال اللى فيه يالله يا أبو
+
+90
+00:08:57,270 --> 00:09:02,170
+واحد اول واحد منهم ست و تلاتين الواحد اه معروف
+
+91
+00:09:02,170 --> 00:09:06,310
+اجنب عليه ست و تلاتين ست و تلاتين منهم ماختلف منهم
+
+92
+00:09:06,310 --> 00:09:11,550
+بص بص بص ست و تلاتين منهم ست و تلاتين اللى تبلى
+
+93
+00:09:11,550 --> 00:09:15,850
+prime مع مية و خمسة مش بيكسب مع تلاتة ست و تلاتين
+
+94
+00:09:15,850 --> 00:09:20,170
+ايه ده مش منهم حطه ع شجة يالله سبعين واحد و سبعين
+
+95
+00:09:20,170 --> 00:09:30,240
+واحد و سبعين منهمأكيد؟ اسمها يا راجل يعني
+
+96
+00:09:30,240 --> 00:09:37,060
+مش منهم طب انا بدأ أحط منهم هذا هو طب خلصنا ولا
+
+97
+00:09:37,060 --> 00:09:43,860
+فيه كمان؟ كده ايش بصير؟
+
+98
+00:09:43,860 --> 00:09:48,760
+بره يبقى ماعنديش إلا رقمين، تمام؟هذا اللي هو مين
+
+99
+00:09:48,760 --> 00:09:56,340
+اللي هو يو خمسة و تلاتين وهذا isomorphic لمن؟ ليهو
+
+100
+00:09:56,340 --> 00:10:02,120
+تلاتةلما قلنا هنا isomorphic لـ U تلاتة و هكذا
+
+101
+00:10:02,120 --> 00:10:07,060
+تمام؟ الخطر ان نجيب رقم كبير لان هذا سهل يعني جيب
+
+102
+00:10:07,060 --> 00:10:13,540
+عندي اعداد كتيرة زي ايش مثلا زي U مية و خمسة أبصار
+
+103
+00:10:13,540 --> 00:10:18,640
+قديش يلا اختارلك سبعة خمستاشر خمستاشر خدناه يبقى
+
+104
+00:10:18,640 --> 00:10:22,640
+بدك واحد و عشرين خمسة اه واحد و عشرين
+
+105
+00:10:44,500 --> 00:10:48,020
+مين الرقم اللي لو ضربت في خمسة و تلاتين بيعطيك مية
+
+106
+00:10:48,020 --> 00:10:52,880
+و خمسة اللي هو تلاتةمصبوط وبالتالي هذا isomorphic
+
+107
+00:10:52,880 --> 00:10:58,740
+ل U تلاتة و هكذا طيب لو قلنا رقم تاني U قداش قلتوا
+
+108
+00:10:58,740 --> 00:11:06,060
+واحد و عشرين واحد و عشرين يفجل واحد منهم بعدك
+
+109
+00:11:06,060 --> 00:11:11,880
+اتنين و عشرين منهم اكيد ولا لا مش اتنين و عشرين
+
+110
+00:11:11,880 --> 00:11:13,780
+اللي هو اتنين في احد و عشرين اللي في ال prime هو
+
+111
+00:11:13,780 --> 00:11:18,900
+عمية و خمسة اللي هو اتنين و عشرين طب تلاتة و
+
+112
+00:11:18,900 --> 00:11:27,800
+اربعين منهم21 في 2 ب 42 اضغط اضغط اضغط اضغط اضغط
+
+113
+00:11:27,800 --> 00:11:27,960
+اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط
+
+114
+00:11:27,960 --> 00:11:33,820
+اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط
+
+115
+00:11:33,820 --> 00:11:34,800
+اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط
+
+116
+00:11:34,800 --> 00:11:36,780
+اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط
+
+117
+00:11:36,780 --> 00:11:46,880
+اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغط اضغ
+
+118
+00:11:47,650 --> 00:11:53,250
+يبقى هذه اللي هي من الأربعة وستين طب لو ضربته في
+
+119
+00:11:53,250 --> 00:11:59,390
+أربعة بصير أربعة و تمانين و واحد خمسة و تمانين ليس
+
+120
+00:11:59,390 --> 00:12:01,850
+relatively prime مع مين معي مية و خمسة لإن هو
+
+121
+00:12:01,850 --> 00:12:06,910
+بيكسب على خمسة يبقى حطه على شجرة الآن بعد الأربعة
+
+122
+00:12:06,910 --> 00:12:13,350
+و تمانين لو ضربت في خمسة بصير المية و خمسةيبقى
+
+123
+00:12:13,350 --> 00:12:18,170
+انتهينا منه مظبوط يبقى لا يوجد عندي الا هذه
+
+124
+00:12:18,170 --> 00:12:25,630
+الأرقام وهذا isomorphic ليه خمسة تمام لإنه خمسة في
+
+125
+00:12:25,630 --> 00:12:31,050
+واحد وعشرين هو اللي بمية .. مية وخمسة تطلع يه خمسة
+
+126
+00:12:31,050 --> 00:12:35,070
+فيها واحد واتنين وتلاتة واربعة أربعة أرقام وماعناش
+
+127
+00:12:35,070 --> 00:12:41,100
+هنا إلا مين إلا أربعة أرقام ووضع الشغل هذا كدهيبقى
+
+128
+00:12:41,100 --> 00:12:46,320
+الـU اللى عندى جدر تجيبها isomorphic لمين لـgroups
+
+129
+00:12:46,320 --> 00:12:51,460
+او الـexternal product لماين لـgroups مختلفة ولسه
+
+130
+00:12:51,460 --> 00:12:57,100
+فى كلام فى هذا الموضوع الكلام ماشي بدي أنتقل من
+
+131
+00:12:57,100 --> 00:13:03,120
+الـU groups أحولها إلى isomorphic لـcyclic اللى هو
+
+132
+00:13:03,120 --> 00:13:09,240
+لـgroups اللى هى Z2 وZ3 وZ4 وZ5 وZ10 وZ30 وما إلى
+
+133
+00:13:09,240 --> 00:13:14,770
+ذلكفي عندنا .. اللي هو .. اللي هو قاعدة القاعدة
+
+134
+00:13:14,770 --> 00:13:19,430
+هذه طبعا برهنت في إحدى المراجع التي اعتمد عليها
+
+135
+00:13:19,430 --> 00:13:28,230
+هذا الكتاب ولذلك بدنا ناخدها كحقائق we have the
+
+136
+00:13:28,230 --> 00:13:36,170
+following notes أو the following facts دي عندي
+
+137
+00:13:36,170 --> 00:13:45,210
+حقائق مهمة جداالحقيقة الأولى ان ال U2 isomorphic
+
+138
+00:13:45,210 --> 00:13:51,430
+فقط لست لفش فيها الواحد إلا الواحد الصحيح and ال
+
+139
+00:13:51,430 --> 00:14:04,550
+U4 isomorphic لمام ل U isomorphic ل U2 تربيعأو
+
+140
+00:14:04,550 --> 00:14:13,770
+تساوية U2 ترابيع واللي هي isomorphic ل Z2 النقطة
+
+141
+00:14:13,770 --> 00:14:25,110
+الثانية ال U2 أُس N isomorphic ل Z2 External
+
+142
+00:14:25,110 --> 00:14:36,130
+Direct Product مع Zزد اتنين اوس ان ناقص اتنين اوس
+
+143
+00:14:36,130 --> 00:14:43,630
+ان fourن أكبر من أو تساوي تلاتة النقطة الثالثة
+
+144
+00:14:43,630 --> 00:14:51,230
+والاخيرة ال U P to the power in isomorphic لمين ل
+
+145
+00:14:51,230 --> 00:15:08,110
+Z P N ناقص P أس N ناقص واحد for P and D primeالـ P
+
+146
+00:15:08,110 --> 00:15:13,090
+and odd a prime so
+
+147
+00:15:13,090 --> 00:15:25,230
+we can write we can write ال U-groups ال U-groups
+
+148
+00:15:25,230 --> 00:15:31,490
+as an external direct product as an external
+
+149
+00:15:31,490 --> 00:15:36,970
+direct product
+
+150
+00:15:39,750 --> 00:15:52,890
+external product of cyclic groups نعطي
+
+151
+00:15:52,890 --> 00:15:59,750
+مثال example write
+
+152
+00:16:03,490 --> 00:16:13,370
+يو سبعمية وعشرين يو سبعمية وعشرين as
+
+153
+00:16:13,370 --> 00:16:21,070
+an external direct product as an external direct
+
+154
+00:16:21,070 --> 00:16:28,950
+product external
+
+155
+00:16:28,950 --> 00:16:31,610
+direct product of
+
+156
+00:16:34,130 --> 00:16:50,950
+cyclic growth نرجع
+
+157
+00:16:50,950 --> 00:16:56,230
+لهذه الحقائق مرة أخرى ونشوف كيف بدنا نشتغل عليها
+
+158
+00:16:56,230 --> 00:17:02,010
+أو ماذا نستفيد من هذه الحقائق الثلاثالنقطة الأولى
+
+159
+00:17:02,010 --> 00:17:08,350
+جال ال U2 isomorphic للعدد اللي هو واحد as a set
+
+160
+00:17:08,350 --> 00:17:12,510
+طبعا U2 مافيش فيها إلا man للعنصر اللي هو الواحد
+
+161
+00:17:12,510 --> 00:17:18,370
+يبقى هذا وضع طبيعي لل trivial case الحالة البديهية
+
+162
+00:17:18,370 --> 00:17:26,850
+U4 ل U2 تربية isomorphic ل Z2 لأن U4 فيها كام عنصر
+
+163
+00:17:28,400 --> 00:17:31,100
+تلاتة يو أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة
+
+164
+00:17:31,100 --> 00:17:31,580
+يو أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة يو
+
+165
+00:17:31,580 --> 00:17:33,480
+أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة يو أربعة
+
+166
+00:17:33,480 --> 00:17:36,180
+تلاتة يو أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة
+
+167
+00:17:36,180 --> 00:17:44,480
+يو أربعة تلاتة يو أربعة تلاتة يو أربعة
+
+168
+00:17:44,480 --> 00:17:45,540
+تلاتة يو أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة
+
+169
+00:17:45,540 --> 00:17:45,540
+يو أربعة تلاتة يو أربعة تلاتة يو أربعة تلاتة يو
+
+170
+00:17:45,540 --> 00:17:53,960
+أربعة تلاتة يو أربعة تلاتة
+
+171
+00:17:53,960 --> 00:18:00,350
+يو أربأتنين ناقص اتنين من الآن فصاعدا نشتغل بشكل
+
+172
+00:18:00,350 --> 00:18:06,610
+هذا يعني ال N ناقص اتنين هو أس لمين للإتنين الآن
+
+173
+00:18:06,610 --> 00:18:15,470
+ال UPN isomorphic لزد P أس N مطروحا منه P أس N
+
+174
+00:18:15,470 --> 00:18:21,030
+ناقص واحد وإنما يكون P prime و P أكبر من مين من
+
+175
+00:18:21,030 --> 00:18:24,620
+الإتنين يعني أنت تلاتة فصاعدايبقى هذا الكلام
+
+176
+00:18:24,620 --> 00:18:29,060
+قدامنا موجود بالشكل هنا هذا ايش فايديته؟ فايديته
+
+177
+00:18:29,060 --> 00:18:34,420
+ان ال group UN مهما كان شكلها ممكن اخليها
+
+178
+00:18:34,420 --> 00:18:40,300
+isomorphic لمين ل cyclic groups شو ال cyclic
+
+179
+00:18:40,300 --> 00:18:44,560
+groups اللي كلها بدي اكتبها بدلالة z والاعداد اللي
+
+180
+00:18:44,560 --> 00:18:50,160
+موجودة في z2 في z3 في z4 سهل حسابتهم لكن لو جتلى
+
+181
+00:18:50,160 --> 00:18:55,300
+720 بدي اكتب أرقامهامن هنا للدهر دوب نخلص و احنا
+
+182
+00:18:55,300 --> 00:18:59,320
+بدنا نجيب الألقام اللي relative ل prime مع مين مع
+
+183
+00:18:59,320 --> 00:19:04,000
+ال 720 قصتنا طويلة و حزينة لكن لما انا اكتبها بهذا
+
+184
+00:19:04,000 --> 00:19:08,480
+الشكل بداية ال Z بصير سهل التعامل معاها يبقى فائدة
+
+185
+00:19:08,480 --> 00:19:14,800
+هذه الحقيقة تسهيل التعامل مع مين مع ال U-groups
+
+186
+00:19:15,040 --> 00:19:20,560
+نعطيك مثال توضيحي على ذلك اللي اكتب ل U720 as a
+
+187
+00:19:20,560 --> 00:19:25,600
+product of cyclic aggregate بقى دي بقوله الحل
+
+188
+00:19:25,600 --> 00:19:31,060
+كتالة solution يبقى
+
+189
+00:19:31,060 --> 00:19:34,620
+انا بده اروح ل U720
+
+190
+00:19:35,530 --> 00:19:42,230
+هذه اللي بقدر اكتبها Uly بدي احطها على حاصل ضرب
+
+191
+00:19:42,230 --> 00:19:52,190
+اعداد لو قلتلك هذه عبارة عن 16×9×5 5×16 بـ 80 80×9
+
+192
+00:19:52,190 --> 00:19:58,260
+8×9 بـ 72 يعني 720يبقى هذا الكلام صحيح بالمائة
+
+193
+00:19:58,260 --> 00:20:05,660
+بالمائة هذه الان ايزو مورفك لمين ليه ستاشر
+
+194
+00:20:05,660 --> 00:20:11,260
+اكستيرنال دايكا product معاه تسعة اكستيرنال دايكا
+
+195
+00:20:11,260 --> 00:20:19,020
+product معاه خمسةطيب هذه مين هي ؟ أليست U2 أُص
+
+196
+00:20:19,020 --> 00:20:25,200
+أربع Extended product تلاتة ترابيع Extended
+
+197
+00:20:25,200 --> 00:20:33,380
+product ل U خمسة ست عشر اللي هي اتنين أُص أربع و
+
+198
+00:20:33,380 --> 00:20:36,880
+تلاتة ترابيع اللي هي تسعة و الخمسة زمان طيب السؤال
+
+199
+00:20:36,880 --> 00:20:41,880
+هو ليش كتبته زي هيك؟سوف أحاول أن أقوم بالتحويل إلى
+
+200
+00:20:41,880 --> 00:20:49,060
+الـ Cyclic Group. لكن عندما أحاول تحويلها بدلالة
+
+201
+00:20:49,060 --> 00:20:53,260
+الزد اللي لدي حسب القواعد اللي لدي بقدر أتأكد أن
+
+202
+00:20:53,260 --> 00:20:56,760
+كلامي مائة في المائة كله external product لل
+
+203
+00:20:56,760 --> 00:20:57,700
+Cyclic Group
+
+204
+00:21:02,550 --> 00:21:08,190
+ماشي ما احنا قلنا مشان هيك بدنا نبسط هالشغل هذه
+
+205
+00:21:08,190 --> 00:21:14,710
+بدنا نبسط هالشغل هذه و .. و نروح نكتبها بهذا الشكل
+
+206
+00:21:14,710 --> 00:21:22,410
+طيب يبقى لان كتبت الـ U 720 على الشكل اللي عندي
+
+207
+00:21:22,410 --> 00:21:29,400
+وهذه كتبتها بالشكل هذاالان هذه U2 أقصى 4 هنا U2
+
+208
+00:21:29,400 --> 00:21:35,560
+أقصى N و N أكبر من أو يسوى 3 ايزو مورفك لهذه إذا
+
+209
+00:21:35,560 --> 00:21:41,320
+بدي أقول له هذه ايزو مورفك لزد اتنين external
+
+210
+00:21:41,320 --> 00:21:47,700
+direct product مع زد بيقول لي مين اتنين هي زي ما
+
+211
+00:21:47,700 --> 00:21:53,650
+هيو ال n اللي هي اربعة ناقص اتنين يبقى طبقت هذه
+
+212
+00:21:53,650 --> 00:21:58,210
+على main على الأولى اللي هي اتنين اقص اربعة و
+
+213
+00:21:58,210 --> 00:22:04,370
+وصلنا هذه زى ال n التلاتة هذا prime مظبوط اذا
+
+214
+00:22:04,370 --> 00:22:09,490
+بيدروح لمين للحالة التالتة يبقى isomorphic لمين
+
+215
+00:22:09,490 --> 00:22:18,300
+لزىP التي هي ثلاثة و N اتنين ناقص ثلاثة أس اتنين
+
+216
+00:22:18,300 --> 00:22:23,920
+ناقص واحد ثم خلصنا هذه الامر وهناك استيقظنا ضايق
+
+217
+00:22:23,920 --> 00:22:30,900
+كتابة مع U خمسة اللي هي عبارة عن Z كده
+
+218
+00:22:30,900 --> 00:22:39,380
+اش قلنا ZP يعني Z خمسة أس واحد ناقص خمسة أس واحد
+
+219
+00:22:39,380 --> 00:22:46,500
+ناقص واحديبقى اوطة ويد مباشرة هذا P بثلاثة و P
+
+220
+00:22:46,500 --> 00:22:52,960
+بخمسة و N بواحد خمسة و S واحد ناقص واحد شوف هذه
+
+221
+00:22:52,960 --> 00:22:59,920
+ايش صارت صرت هذه Z دي اتنين external product مع Z
+
+222
+00:22:59,920 --> 00:23:06,470
+أبصر جداشأربعة ناقص اتنين باتنين اتنين تربيع باربع
+
+223
+00:23:06,470 --> 00:23:13,110
+يبقى هذه isomorphic لزاد اربع نجي لهذه تلاتة تربيع
+
+224
+00:23:13,110 --> 00:23:19,270
+تسعة و هنا تلاتة أس واحد تلاتة تسعة ناقص تلاتة
+
+225
+00:23:19,270 --> 00:23:26,640
+بستة يبقى isomorphic لزاد ستةوهذه الآن خمسة أس
+
+226
+00:23:26,640 --> 00:23:32,880
+زيرو بواحد وهنا خمسة أس واحد بخمسة ناقص واحد يبقى
+
+227
+00:23:32,880 --> 00:23:39,580
+زد أربع يبقى لان كتابة زد سبعمائة وعشرين على صيغة
+
+228
+00:23:39,580 --> 00:23:42,840
+زد اتنين external product لزد أربع external
+
+229
+00:23:42,840 --> 00:23:48,220
+product لزد ستة external product لزد أربع والاربع
+
+230
+00:23:48,220 --> 00:23:53,580
+cyclic groupsيبقى بناء عليه ال group اللي عندنا يو
+
+231
+00:23:53,580 --> 00:23:58,840
+سبعمية وعشرين جبت group بتعمل معاها isomorphism
+
+232
+00:23:58,840 --> 00:24:03,460
+وبالتالي خواص ال يو سبعمية وعشرين هي نفس الخواص
+
+233
+00:24:03,460 --> 00:24:06,940
+اللي عندنا يبقى بناء عليه لو جالي هاتلي element ال
+
+234
+00:24:06,940 --> 00:24:12,020
+order الو كذا في سبعمية وعشرينبروح على هذه هذه سهل
+
+235
+00:24:12,020 --> 00:24:16,840
+التعامل معاها بس ليه 720 صعب التعامل معاها إذا
+
+236
+00:24:16,840 --> 00:24:22,600
+بجيب هذه المكافئة لها ومن خلالها بقدر أجيب من اللي
+
+237
+00:24:22,600 --> 00:24:28,160
+هو ال element اللي ال order عنده يعطيني إياه في
+
+238
+00:24:28,160 --> 00:24:28,960
+السؤال
+
+239
+00:24:31,410 --> 00:24:38,470
+يبقى هذا الشكل وضع لتبسيط الحسابات العملية في ال
+
+240
+00:24:38,470 --> 00:24:42,270
+groups المختلفة
+
+241
+00:24:42,270 --> 00:24:49,730
+نعطيك
+
+242
+00:24:49,730 --> 00:24:55,230
+مثال على هذا الكلاموبالتالي المثال انت تعودت على
+
+243
+00:24:55,230 --> 00:25:00,750
+external product مكوّن من رقمين احنا هنعطيك سنة من
+
+244
+00:25:00,750 --> 00:25:06,910
+تلاتة من اربعة اكثر من ذلك يبقى باجي بقول example
+
+245
+00:25:06,910 --> 00:25:11,430
+how
+
+246
+00:25:11,430 --> 00:25:16,950
+many elements
+
+247
+00:25:16,950 --> 00:25:20,290
+of
+
+248
+00:25:20,290 --> 00:25:21,930
+order
+
+249
+00:25:51,070 --> 00:25:57,340
+سؤال مرة تانيةالسؤال بيقول ايه؟ بيقول اكم عنصر ال
+
+250
+00:25:57,340 --> 00:26:03,080
+order الو اتناش في ال U سبعمية و عشرين طبعا بدنا
+
+251
+00:26:03,080 --> 00:26:07,160
+نقعد نحسب كل element لحاله تطلع روحنا مش هنقدر
+
+252
+00:26:07,160 --> 00:26:10,800
+نحسبهم لكن هذه سبعمية و عشرين اللي جاتها
+
+253
+00:26:10,800 --> 00:26:15,580
+isomorphic لمين للي عندنا هذه بيبقى الحسابات هنا
+
+254
+00:26:15,580 --> 00:26:22,700
+أسهل كتير جدا من الحسابات هناك ايوةطب بتخلص بالله
+
+255
+00:26:22,700 --> 00:26:26,580
+في الساعتين اللي بتقدر تجيبهم؟ طب وكمان ساعتين من
+
+256
+00:26:26,580 --> 00:26:31,460
+9D واحسبلي كل ال elements اللي relatively prime مع
+
+257
+00:26:31,460 --> 00:26:38,780
+720 وادور عليهم من ال order اللي يساوي 12 انت حورر
+
+258
+00:26:38,780 --> 00:26:43,120
+جيب اللي بدك إياه أنا مش زعلان بس هتاخد وقت رهيب
+
+259
+00:26:43,120 --> 00:26:48,550
+جدا ساعتينك مش هيكفو لحساب اللي هو السؤال هذاالان
+
+260
+00:26:48,550 --> 00:26:57,170
+solution from the above example
+
+261
+00:26:58,670 --> 00:27:07,090
+من المثال اللي فوق الـ U720 أيزو مورفك ل Z2
+
+262
+00:27:07,090 --> 00:27:13,590
+Extended like product مع Z4 Extended like product
+
+263
+00:27:13,590 --> 00:27:19,470
+مع Z6 Extended like product مع Z4
+
+264
+00:27:22,860 --> 00:27:31,920
+أى element هنا ال order إليه يساوي اتناش يبقى بناء
+
+265
+00:27:31,920 --> 00:27:41,380
+عليه يبدو لو حسب فيه التانية يبقى so the number of
+
+266
+00:27:41,380 --> 00:27:52,660
+elements of order اتناش in u سبعمية او عشرين
+
+267
+00:27:54,980 --> 00:28:07,680
+equal of the number of elements of
+
+268
+00:28:07,680 --> 00:28:09,280
+order
+
+269
+00:28:26,260 --> 00:28:32,140
+طب احنا اخدنا اول نظرية في هذا section وكان مشان
+
+270
+00:28:32,140 --> 00:28:38,950
+اجيب ال order لل elementالمُركّب مثلا من مُركّبة
+
+271
+00:28:38,950 --> 00:28:43,370
+هنا بجيب ال list common multiple لمن ل ال two
+
+272
+00:28:43,370 --> 00:28:47,330
+orders اللي عنده وبالتالي بكون جابت ال order لل
+
+273
+00:28:47,330 --> 00:28:50,690
+element اللي موجود في ال external direct product
+
+274
+00:28:50,690 --> 00:28:57,210
+لذلك بروح أخد element هناو افترض ان هذا ال element
+
+275
+00:28:57,210 --> 00:29:03,010
+ال order له يساوي 12 و ابحث عن ال orders المختلفة
+
+276
+00:29:03,010 --> 00:29:09,530
+في هذه الحالة يبقى بداجي اقول له let ال a و ال b و
+
+277
+00:29:09,530 --> 00:29:18,610
+ال cوالدى موجودة في z2 similar product مع z4
+
+278
+00:29:18,610 --> 00:29:26,570
+similar product مع z6 similar product مع z4 such
+
+279
+00:29:26,570 --> 00:29:37,490
+that بحيث ان ال order لل a والb والc والd كله
+
+280
+00:29:37,490 --> 00:29:43,740
+بده يساوي كده؟ بده يساوي ماشيطيب الآن لما نقادي
+
+281
+00:29:43,740 --> 00:29:49,060
+لزد اتنين زد اتنين كم عنصر فيها اتنين يعني ال
+
+282
+00:29:49,060 --> 00:29:53,520
+order واحد وال order للعنصر التاني اتنين صح ولا لا
+
+283
+00:29:53,520 --> 00:29:57,980
+يبقى اي element في زد اتنين ال order له يا اما
+
+284
+00:29:57,980 --> 00:30:02,280
+واحد اللي هو ال identity يا اما اتنين طيب تاخدلي
+
+285
+00:30:02,280 --> 00:30:09,080
+زد اربع ال order اللي فيها واحد و كدهش و اتنين
+
+286
+00:30:09,740 --> 00:30:14,620
+تلاتة بتجسم الأربعة بتتكلم
+
+287
+00:30:14,620 --> 00:30:17,820
+على order بتتكلمش على العناصر اللي موجودة فيها
+
+288
+00:30:17,820 --> 00:30:20,900
+واحد واثنين واربعة واحد واثنين واربعة وفيش غيرهم
+
+289
+00:30:20,900 --> 00:30:25,140
+مظبوط لإن ال order لل element بيجسم لل order لل
+
+290
+00:30:25,140 --> 00:30:28,280
+group زد اربعة في اربعة عناصر اذا قوسم واحد اتنين
+
+291
+00:30:28,280 --> 00:30:33,550
+اربعة فقط لغير فيش حاجة اسمها تلاتةالعناصر اللي
+
+292
+00:30:33,550 --> 00:30:41,750
+موجودة في الـ Z6 واحد اتنين تلاتة ستة في شغلهم الـ
+
+293
+00:30:41,750 --> 00:30:46,770
+Z4 قبل قليل يبقى بدي أضع هذه المعلومة دي وبناء
+
+294
+00:30:46,770 --> 00:30:53,970
+عليه بدي أبدأ أحدد كم عنصر عندي يبقى هنا any
+
+295
+00:30:53,970 --> 00:30:55,850
+element
+
+296
+00:30:57,770 --> 00:31:09,390
+ن زدتر از اردت واحد واثنينAny element in Z4 has
+
+297
+00:31:09,390 --> 00:31:19,910
+order 1,2,4 أي element في Z6 has order 1,2,3,6 أي
+
+298
+00:31:19,910 --> 00:31:27,930
+element في Z4 في Z4 has element 1,2,4
+
+299
+00:31:30,490 --> 00:31:34,090
+طيب انا لما بدي اجيب ال order ل ال element بدي
+
+300
+00:31:34,090 --> 00:31:38,870
+اجيب ال least common multiples لمين للاربع orders
+
+301
+00:31:38,870 --> 00:31:43,390
+مش هيك بقول كويسة طلعلي ال order الأول واحد و
+
+302
+00:31:43,390 --> 00:31:48,290
+اتنين موجود مع هدول ولا لأ موجود مع هذه موجود مع
+
+303
+00:31:48,290 --> 00:31:53,850
+هذهيعني وجود إيش بس بيخر بشكل بيخليها كبيرة يبقى
+
+304
+00:31:53,850 --> 00:31:58,330
+في الحقيقة أنا بدي أبحث بس عن A وB وC تمام؟ لكن
+
+305
+00:31:58,330 --> 00:32:01,970
+هداك بدي أخليه في حسابي مش باهيم له يبقى الذي
+
+306
+00:32:01,970 --> 00:32:06,390
+يتحكم في ال order اللي هو ال 12 اللي هو التلاتة
+
+307
+00:32:06,390 --> 00:32:12,520
+الأخيرات هدولوالهدا 1 و 2 مش مشكلة يبقى عندي
+
+308
+00:32:12,520 --> 00:32:18,140
+عنصرين بدخلهم في الحساب بعد ذلك يبقى بدالي لل 2 و
+
+309
+00:32:18,140 --> 00:32:23,420
+4 اللي عندي يبقى هنا ال element ايه ال order ايه 1
+
+310
+00:32:23,420 --> 00:32:31,450
+و 2الـ element بي 1,2,4 ال element c 1,2,3,6 ال
+
+311
+00:32:31,450 --> 00:32:38,570
+element 4 1,2,4 طب الآن انا بدي ادور ال main ال
+
+312
+00:32:38,570 --> 00:32:42,910
+least common multiple اللي هم بده يعطيني قداش 12
+
+313
+00:32:42,910 --> 00:32:49,670
+وبحيث ها طلعلي هناالان الواحد و الاتنين مكررة
+
+314
+00:32:49,670 --> 00:32:54,210
+مالواحد و اتنين يبقى لا قيمة لها مظبوط يبقى هنا
+
+315
+00:32:54,210 --> 00:32:58,690
+ضال عند مينالاربعة يبقى لو كان ال order اللى بيه
+
+316
+00:32:58,690 --> 00:33:04,170
+بده يساوي الاربعة و ال order اللى يسيه كان تلاتة
+
+317
+00:33:04,170 --> 00:33:08,830
+او ستة طب ليش تلاتة او ستة؟ لأن تلاتة او اربعة
+
+318
+00:33:08,830 --> 00:33:12,730
+ليسكم ال multiple اللي قلهم كداش اتناش والستة
+
+319
+00:33:12,730 --> 00:33:15,290
+والاربعة ليسكم ال multiple اللي قلهم كمان مين
+
+320
+00:33:15,290 --> 00:33:21,820
+اتناش يبقى هذا اللى يساه يتحكمفى من؟ فى ال order
+
+321
+00:33:21,820 --> 00:33:25,900
+طب و اللى تحت هذا لتحت ما هو داخل فى الحساب لإن
+
+322
+00:33:25,900 --> 00:33:30,920
+واحد اتنين هي موجودة والاربعة موجودة هنا يبقى ال D
+
+323
+00:33:30,920 --> 00:33:36,140
+مش هتأثر عندي مش هتجيبلي معلومات جديدة يبقى باضيفة
+
+324
+00:33:36,140 --> 00:33:41,240
+تحصيل حاصل هي الحالة الأولى يبقى الحالة الأولى
+
+325
+00:33:41,240 --> 00:33:44,040
+اللى ال order ال list common multiple اللى بده
+
+326
+00:33:44,040 --> 00:33:48,460
+يطلع اتناش خد الحالة التانيةممكن يكون ال order
+
+327
+00:33:48,460 --> 00:33:54,180
+اللي دي هو أربعة و ال C له تلاتة و ستة مش هيك وارد
+
+328
+00:33:54,180 --> 00:33:59,180
+تمام و الباقي اللي هو اللي بيتحصيل حاصل بسيط تمام
+
+329
+00:33:59,180 --> 00:34:03,200
+يبقى بدنا نيجي نشتغل الشغل اللي عندنا هادي
+
+330
+00:34:13,770 --> 00:34:18,010
+الان قلنا بالنسبة للأولى اللي اسمها multiple تحصيل
+
+331
+00:34:18,010 --> 00:34:24,210
+حصل يبقى دي مش هتدخل في الحساب عندنا يبقى we have
+
+332
+00:34:24,210 --> 00:34:30,050
+two cases
+
+333
+00:34:30,050 --> 00:34:35,910
+هي عندي حالتين الحالة الأولى ان ال order لل B بده
+
+334
+00:34:35,910 --> 00:34:41,150
+يسوى الأربعة و ال order ل C يا إما تلاتة يا إما
+
+335
+00:34:41,150 --> 00:34:45,350
+ستةيبقى تلاتة واربعة الـ least common multiple
+
+336
+00:34:45,350 --> 00:34:48,730
+يبقى 12 الستة والاربعة ال least common multiple
+
+337
+00:34:48,730 --> 00:34:53,290
+يبقى 12 يبقى هدول يجيبولي ال element ال order يسوى
+
+338
+00:34:53,290 --> 00:35:00,190
+كم؟ ال 12 طب أكم انصر في زيد أربعة ال order يسوى
+
+339
+00:35:00,190 --> 00:35:08,630
+أربعة؟ بسأتنين هو الواحد والتلاتة الواحد والتلاتة
+
+340
+00:35:08,630 --> 00:35:14,850
+في زد أربعة ال order يساوي مين؟ الاربعة يمجى بيه
+
+341
+00:35:14,850 --> 00:35:20,890
+هنا يا بدها تساوي واحد يا بدها تساوي تلاتة طيب سي
+
+342
+00:35:20,890 --> 00:35:27,370
+هنا بدها تساوي ال order له تلاتة او ال order له
+
+343
+00:35:27,370 --> 00:35:34,150
+ستة اظن الواحد ال order له ستة طب و اتنين طب و
+
+344
+00:35:34,150 --> 00:35:41,700
+الأربعةالأردر ماذا؟ ثلاثة ثلاثة؟ طب و الست؟ واحد
+
+345
+00:35:41,700 --> 00:35:45,780
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+346
+00:35:45,780 --> 00:35:48,240
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+347
+00:35:48,240 --> 00:35:48,920
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+348
+00:35:48,920 --> 00:35:49,520
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+349
+00:35:49,520 --> 00:35:50,300
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+350
+00:35:50,300 --> 00:35:50,340
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+351
+00:35:50,340 --> 00:35:53,380
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+352
+00:35:53,380 --> 00:35:58,440
+واحد، واحد، واحد، واحد، واحد، واحد، واحد، واحد،
+
+353
+00:35:58,440 --> 00:36:03,500
+واحد،
+
+354
+00:36:03,500 --> 00:36:04,480
+وا
+
+355
+00:36:11,410 --> 00:36:17,450
+الرقم يا باخد C بواحد يا باخد الست يعني اتنين هذا
+
+356
+00:36:17,450 --> 00:36:21,650
+ال component يا بتكون واحد يا بتكون ست صفر ماشي
+
+357
+00:36:21,650 --> 00:36:25,790
+الحاجة بتزعلان ليه هذا
+
+358
+00:36:25,790 --> 00:36:31,450
+احنا بنحكي الآن في order كبير مش لحاله تمامأحنا
+
+359
+00:36:31,450 --> 00:36:36,310
+بنحكي الآن ال order لل element بده يساوي ستة مين
+
+360
+00:36:36,310 --> 00:36:40,550
+ال elements اللي ال order اللي هم يساوي .. ده مش
+
+361
+00:36:40,550 --> 00:36:46,770
+ستة .. ده خمسة .. ده خمسة الواحد و الخمسة ال order
+
+362
+00:36:46,770 --> 00:36:52,470
+اللي هم ستة صحيح؟ اتنين و الأربعة هم ال order اللي
+
+363
+00:36:52,470 --> 00:37:01,030
+هم تلاتة طيب هذا ال B و ال C طب و ال D؟لا خدها أي
+
+364
+00:37:01,030 --> 00:37:11,890
+شيء اي نعم and ادي arbitrary يعني خدها زي ما بدك
+
+365
+00:37:12,760 --> 00:37:17,280
+كويس؟ طيب لما اخدها زي المبدأ بقول اخد الأربعة لما
+
+366
+00:37:17,280 --> 00:37:21,700
+انا اخد يعني الأربعة مش هيتغير ليش؟ لأن ال order
+
+367
+00:37:21,700 --> 00:37:24,960
+سبعة هي واحد، هي اتنين، هي أربعة هي وماخدناهم
+
+368
+00:37:24,960 --> 00:37:31,340
+معاهدي يعني مش هيجيبولي إيش؟ ليش دي؟ يبقى الآن the
+
+369
+00:37:31,340 --> 00:37:40,380
+number of elements of order
+
+370
+00:37:45,070 --> 00:37:52,890
+الحين ال A كم عنصر فيها؟ اتنين ال B كم عنصر؟ اتنين
+
+371
+00:37:52,890 --> 00:37:59,590
+ال C كم عنصر؟ اربعة ال D خد زي ما بدك اجدش اربعة
+
+372
+00:37:59,590 --> 00:38:04,370
+يبقى أربعة في أربعة في ستاشر في أربعة باربعة وستين
+
+373
+00:38:04,370 --> 00:38:11,490
+يبقى اربعة وستين elementهذول ال order يساوي 12 لو
+
+374
+00:38:11,490 --> 00:38:12,090
+كان
+
+375
+00:38:19,370 --> 00:38:23,850
+هدول ال orders لكن انا كام عنصر هدول عندى اربعة نص
+
+376
+00:38:23,850 --> 00:38:27,330
+خد اللى بدك اياه ال orders واحد واتنين واربعة زى
+
+377
+00:38:27,330 --> 00:38:30,630
+الواحد واتنين واربعة اذا هدول قلت مصفع شجعون
+
+378
+00:38:30,630 --> 00:38:36,590
+اشتغلت في هدول تمام هدول الان هذا بضيف تحصيل حاصل
+
+379
+00:38:36,590 --> 00:38:40,590
+يعني ايش ما كان يكون كان ال zero كان الواحد كان
+
+380
+00:38:40,590 --> 00:38:44,350
+الاتنين كان التلاتة لن يغير في النتيجة شيئا وكوان
+
+381
+00:38:44,350 --> 00:38:48,990
+انت بتكتب element مكون من اربع مركباتيعني عندك
+
+382
+00:38:48,990 --> 00:38:54,110
+بدائل اتنين لل A وبدائل اتنين لل B لأن ال order
+
+383
+00:38:54,110 --> 00:38:59,190
+يسوى اربعة وعندك اربع بدائل لل C واربع بدائل لل D
+
+384
+00:38:59,190 --> 00:39:03,210
+صحيح ولا لا؟ يبقى على بعضهم كله مصيره جداش اربعة
+
+385
+00:39:03,210 --> 00:39:09,590
+وستين عنصر هذا هي الحالة الأولى الحالة التانيةال
+
+386
+00:39:09,590 --> 00:39:16,150
+order اللى دى ممكن يكون اربعة and ال order لسه يا
+
+387
+00:39:16,150 --> 00:39:26,910
+اما تلاتة يا اما ستة يبقى
+
+388
+00:39:26,910 --> 00:39:31,650
+في هذه الحالة لما ال order اللى دى بدى يساوي اربعة
+
+389
+00:39:31,650 --> 00:39:38,600
+اكم element بيعطينا اتنين مظبوطيبقى هنا في عندي
+
+390
+00:39:38,600 --> 00:39:46,080
+اتنين elements طيب لما يكون هنا في عندي جداش؟
+
+391
+00:39:46,080 --> 00:39:52,440
+جداش؟ اربع elements طيب
+
+392
+00:39:52,440 --> 00:39:59,200
+نيجي لل a جداش؟ اربع elements اتنين elements نيجي
+
+393
+00:39:59,200 --> 00:40:03,240
+لل b جداش عندي؟ اتنين elements
+
+394
+00:40:05,800 --> 00:40:12,760
+يبقى صغر الآن اتنين اخدناها
+
+395
+00:40:12,760 --> 00:40:16,240
+اربعة مع الخطوة اللي قبلها اه اخدناها اربعة مع
+
+396
+00:40:16,240 --> 00:40:19,580
+الخطوة اللي قبلها لاش نكررها لان التكرار هذا بجيب
+
+397
+00:40:19,580 --> 00:40:24,300
+شغلات اكتر من اللازم يبقى so we have العنصر
+
+398
+00:40:24,300 --> 00:40:28,400
+الأولاني اتنين والتاني اربعة واللي بعده اتنين
+
+399
+00:40:28,400 --> 00:40:33,370
+واللي بعده اتنينيبقى تمانية في أربعة بجداش بتنين و
+
+400
+00:40:33,370 --> 00:40:41,650
+تلاتين element of order اللي هو أتناشر طب إذا على
+
+401
+00:40:41,650 --> 00:40:43,210
+بعضهم جداش
+
+402
+00:40:45,410 --> 00:40:52,270
+يو سبعمية وعشرين has اللي هو قداش في الأول اربعة
+
+403
+00:40:52,270 --> 00:41:00,330
+وستين زائد اتنين وتلاتين ويساوي ستة وتسعين element
+
+404
+00:41:00,330 --> 00:41:08,010
+of order اللي هو اتناشر
+
+405
+00:41:17,690 --> 00:41:22,970
+يبقى بناء عليها من الآن فصاعدا لو قاللي شوف لقداش
+
+406
+00:41:22,970 --> 00:41:29,050
+عدد العناصر اللي ال order لهم يساوية رقم معين في
+
+407
+00:41:29,050 --> 00:41:34,770
+UN ال UN ال N مينما كانت تكون بدي احولها الى مين؟
+
+408
+00:41:34,770 --> 00:41:41,160
+بدي احولها الى ال cyclic groupsمدالة z2 و z3 و z4
+
+409
+00:41:41,160 --> 00:41:45,840
+و z5 و z6 و بيبقوا أحسب من مين من هذه ال z اللي هو
+
+410
+00:41:45,840 --> 00:41:51,000
+هذه العناصر على هيك بيكون انتهى ال section طيب في
+
+411
+00:41:51,000 --> 00:41:57,800
+عندك سؤال زي سؤال تلاتة بيقول ما يأتي سؤال
+
+412
+00:41:57,800 --> 00:42:06,820
+تلاتةبقول الـ G group with identity والـ H بيه
+
+413
+00:42:06,820 --> 00:42:12,440
+group with identity prove that الـ G isomorphic
+
+414
+00:42:12,440 --> 00:42:20,340
+الـ G isomorphic لمين؟ لل external direct product
+
+415
+00:42:20,730 --> 00:42:26,850
+للـ G external like product مع ال identity element
+
+416
+00:42:26,850 --> 00:42:38,850
+تبع ال H and ال H is isomorphic لمن؟
+
+417
+00:42:38,850 --> 00:42:45,570
+لل identity تبع ال G external like product مع من؟
+
+418
+00:42:45,570 --> 00:42:48,350
+مع ال H
+
+419
+00:42:56,050 --> 00:43:04,540
+خلّي بالك أني أنا عندي الـ G و ال H are groupsمش
+
+420
+00:43:04,540 --> 00:43:07,580
+هتقول الـH subgroup من G اللي مالعاش علاقة هذي
+
+421
+00:43:07,580 --> 00:43:12,880
+group و هذي group تاني بقول اثبت ان الـG هي
+
+422
+00:43:12,880 --> 00:43:17,580
+isomorphic لمين لـG وال external direct product
+
+423
+00:43:17,580 --> 00:43:23,680
+يبقى هنا بتروح اعرفله Phi من الـG الى الـG
+
+424
+00:43:23,680 --> 00:43:31,520
+external direct product مع E H Piفاي اف جي ممكن
+
+425
+00:43:31,520 --> 00:43:37,900
+اخد صورته هنا ممكن اخدها جي والاي تبع ال H
+
+426
+00:43:44,530 --> 00:43:52,370
+لو جيت أخدت بدل في أخدت مثلا اللي هو ال F من ال H
+
+427
+00:43:52,370 --> 00:44:01,290
+إلى ال identity element تبع ال G across ال H by ال
+
+428
+00:44:01,290 --> 00:44:09,030
+F of H بده يساوي ال external direct product لل
+
+429
+00:44:09,030 --> 00:44:16,920
+E تبع ال Gللـ A تابع الـ G و H بالشكل اللي عندنا
+
+430
+00:44:16,920 --> 00:44:25,020
+هنا او بلاش هون هذا ايه جوز وهذا ايه جي و H جوز
+
+431
+00:44:25,020 --> 00:44:29,540
+مباشرة يبقى بدنا نثبت من هذا طبعا إذا أثبتنا الأول
+
+432
+00:44:29,540 --> 00:44:36,510
+بصير التاني حرفيا زيهطيب لو جيت له الأولى يبقى بدي
+
+433
+00:44:36,510 --> 00:44:41,830
+اثبت له ان الـ Phi is one to one يبقى بدي اقول له
+
+434
+00:44:41,830 --> 00:44:50,310
+assume افترض ان Phi of G1 بدي ساوي Phi of G2 هذا
+
+435
+00:44:50,310 --> 00:44:56,050
+معناته ان الـ G1 و ال identity تبع ال H بدي ساوي
+
+436
+00:44:56,050 --> 00:45:03,780
+G2 و ال identity تبع ال Hطبعا two order pair are
+
+437
+00:45:03,780 --> 00:45:07,220
+equal يبقى المراكبة الأولى سواء المراكبة الأولى أو
+
+438
+00:45:07,220 --> 00:45:12,540
+المراكبة الثانية سواء مين المراكبة الثانية يبقى G1
+
+439
+00:45:12,540 --> 00:45:19,400
+سواء G2 وهذا الـEH هو نفسه الـEH أظن و هو المطلوب
+
+440
+00:45:19,400 --> 00:45:26,030
+الآن مداجي أثبت له أن فاي is ontoيبقى بالدرجة
+
+441
+00:45:26,030 --> 00:45:32,190
+اقوله افترض ان ال X موجود في ال G external product
+
+442
+00:45:32,190 --> 00:45:40,210
+مع ال identity تبع ال H ثم شكل ال X هذا بده يساوي
+
+443
+00:45:40,210 --> 00:45:47,120
+element من G و ال identity element تبع ال Hطيب هذا
+
+444
+00:45:47,120 --> 00:45:53,980
+حسب التعريف هو مين؟ Phi of G لذلك Phi is أنتوا بقى
+
+445
+00:45:53,980 --> 00:45:59,380
+لدينا Phi is an isomorphism يبقى Phi is an
+
+446
+00:45:59,380 --> 00:46:09,480
+isomorphism يبقى بدي أقعد أخد ال Phi of G و G2
+
+447
+00:46:09,480 --> 00:46:15,750
+الشكل اللي عندنا هنا يبقى هذا الكلام بده يساوياللي
+
+448
+00:46:15,750 --> 00:46:24,070
+هو مين اللي هو five of g one g two بده يساوي اللي
+
+449
+00:46:24,070 --> 00:46:33,170
+هو g one g two وال إيه hهذا الكلام بده يساوي بده
+
+450
+00:46:33,170 --> 00:46:39,370
+احاول اكتب هذا على صيغة حاصل ضرب قوسين اذا لو جيت
+
+451
+00:46:39,370 --> 00:46:49,530
+قلت جي واحد مع ال E H وهنا جي اتنين مع ال E H لو
+
+452
+00:46:49,530 --> 00:46:53,370
+ضربت ضرب component wise يبقى بيصير جي ون جي تون
+
+453
+00:46:53,370 --> 00:46:59,060
+وال E H في ال E H هي بال E H itselfيبقى هذا الكلام
+
+454
+00:46:59,060 --> 00:47:07,300
+بده يساوي هذا Phi of G1 و هذا Phi of G2 يبقى هنا
+
+455
+00:47:07,300 --> 00:47:17,080
+Phi is an isomorphism وهكذا بالنسبة لمن؟ بالنسبة
+
+456
+00:47:17,080 --> 00:47:17,900
+للثاني
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a97dc8f216435e032622cea628e3baa021350e31
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s.srt
@@ -0,0 +1,1743 @@
+1
+00:00:21,850 --> 00:00:25,810
+بسم الله الرحمن الرحيم نواصل ما بدأنا فيه في
+
+2
+00:00:25,810 --> 00:00:30,430
+المحاضرة الماضية بدأنا بالnormal subgroups أعطينا
+
+3
+00:00:30,430 --> 00:00:34,310
+تعريف للnormal subgroups وعرفنا أن التعريف له 
+
+4
+00:00:34,310 --> 00:00:39,230
+أوجه مختلفة بدل وجه ثلاثة ثم انتقلنا بعد ذلك إلى
+
+5
+00:00:39,230 --> 00:00:44,970
+الfactor groups وعناصر الfactor groups كلها هي
+
+6
+00:00:44,970 --> 00:00:49,930
+left cosets واخذنا على ذلك مثالا واحدا وهذا هو
+
+7
+00:00:49,930 --> 00:00:55,520
+المثال رقم 2 بقول يفترض أن جي هي عبارة عن Z18
+
+8
+00:00:55,520 --> 00:00:59,600
+واخدنا الsubgroup منها هي الsubgroup generated
+
+9
+00:00:59,600 --> 00:01:06,820
+by 6 العناصر تبعها 0 6 12 الآن السؤال هو هل الـ H
+
+10
+00:01:06,820 --> 00:01:15,780
+normal subgroup من Z18 أم لا؟ بدنا الإجابة Normal
+
+11
+00:01:15,780 --> 00:01:19,220
+ليش؟ لأن جي
+
+12
+00:01:22,380 --> 00:01:27,080
+أول مثال أخدته معاك لو كانت الـ group abelian يبقى
+
+13
+00:01:27,080 --> 00:01:31,660
+any subgroup is normal تمام يبقى في هذه الحالة
+
+14
+00:01:31,660 --> 00:01:37,800
+بقوله then الـ H is a normal subgroup من Z18
+
+15
+00:01:37,800 --> 00:01:48,050
+because اللي هو Z18 is abelian كويس إذا بدي أروح
+
+16
+00:01:48,050 --> 00:01:52,990
+أكون الfactor group أو بدي أعرف الfactor group
+
+17
+00:01:52,990 --> 00:02:00,710
+فيها كم element هذي تمام يبقى الـ order الـ order لـ
+
+18
+00:02:00,710 --> 00:02:09,490
+Z18 الموديولو 6 بده يساوي كله لفتكوه 6 يبقى الـ
+
+19
+00:02:09,490 --> 00:02:16,510
+order لـ Z18 مقسوما على الـ order للـ H واللي هو
+
+20
+00:02:16,510 --> 00:02:25,600
+عبارة عن 18 على 3 يبقى 6 elements يبقى الـ group هذه
+
+21
+00:02:25,600 --> 00:02:31,460
+فيها ستة عناصر بدي أعرف من هذه العناصر يبقى بروح
+
+22
+00:02:31,460 --> 00:02:41,160
+بقول له the elements of Z التمنتاشر modulo 6 are
+
+23
+00:02:43,100 --> 00:02:49,600
+الأولان هو H itself أو الـ subgroup generated by 6
+
+24
+00:02:49,600 --> 00:02:55,000
+الثاني هو 1 زائد الـ subgroup generated by 6
+
+25
+00:02:55,000 --> 00:03:00,580
+الثالث 2 زائد الـ subgroup generated by 6
+
+26
+00:03:00,580 --> 00:03:06,280
+الرابع هو 3 زائد الـ subgroup generated by 6
+
+27
+00:03:14,080 --> 00:03:20,300
+السادس والأخير له 5 زي الـ subgroup generated by
+
+28
+00:03:20,300 --> 00:03:26,920
+6 أي أي أي left coset 6 بعد ذلك لو جيت لي قلت لي 6
+
+29
+00:03:26,920 --> 00:03:31,040
+زي الـ subgroup generated by 6 بقول لك هي مين هي
+
+30
+00:03:31,040 --> 00:03:36,640
+الأصلية الـ subgroup الأصلية لو جيت لي قلت لي 7 زي
+
+31
+00:03:36,640 --> 00:03:40,000
+الـ subgroup generated by 6 بقول لك هي الـ 1 وهكذا
+
+32
+00:03:40,610 --> 00:03:45,190
+الآن داخل هذه الـ group لو بدي أجمع أو بدي أعرف الـ
+
+33
+00:03:45,190 --> 00:03:50,610
+order كيف بدي أحسبه يبقى لحد هنا احنا انتهينا من
+
+34
+00:03:50,610 --> 00:03:57,450
+عناصر هذه الـ group لو بدي أجي آخذ مثلا 3 زائد
+
+35
+00:03:57,450 --> 00:04:03,350
+الـ subgroup generated by 6 بدي أجمع مع مين؟ مع
+
+36
+00:04:03,350 --> 00:04:08,560
+الـ 5 زائد الـ subgroup generated by 6 يعني كأن
+
+37
+00:04:08,560 --> 00:04:14,100
+.. كأن بدي أضرب two left cosets في بعضهم لكن لما
+
+38
+00:04:14,100 --> 00:04:19,000
+كانت العملية عملية جمعية يبقى ضرب بس يتحول إلى
+
+39
+00:04:19,000 --> 00:04:22,720
+جمعية المرة اللي فاتت قلنا الـ operation اللي على
+
+40
+00:04:22,720 --> 00:04:28,010
+الـ left cosets هذه إن الـ A H مضروب في B H بيكون A
+
+41
+00:04:28,010 --> 00:04:35,270
+B F H يبقى معنى هذا الكلام هذا بيكون 3 زائد
+
+42
+00:04:35,270 --> 00:04:40,770
+5 زائد الـ subgroup generated by 6 3 زائد
+
+43
+00:04:40,770 --> 00:04:46,450
+5 قداش؟ 8 8 بشيل منهم الـ 6 بظل قداش؟
+
+44
+00:04:46,450 --> 00:04:51,490
+2 يبقى هذا 2 زائد الـ subgroup generated
+
+45
+00:04:51,490 --> 00:04:58,110
+by 6 هيها يبقى any two left cosets لو جمعتهم
+
+46
+00:04:58,110 --> 00:05:03,790
+هيعطيني واحدة من الست لإتنين هذول لو بدي أجيب مثلا
+
+47
+00:05:03,790 --> 00:05:08,550
+الـ order لأي واحدة منهم يبقى بدي أروح أشوف قداش
+
+48
+00:05:08,550 --> 00:05:13,550
+الرقم اللي بدي أحط أس لهذا الـ element بحيث يعطيني
+
+49
+00:05:13,550 --> 00:05:17,590
+main الـ identity يعني يعطيني الـ subgroup generated
+
+50
+00:05:17,590 --> 00:05:23,420
+by الـ 6 بالضبط تماما مثلًا لو جيت قلت بدي أعرف
+
+51
+00:05:23,420 --> 00:05:27,920
+قداش الـ order للي 2 زائد الـ subgroup generated
+
+52
+00:05:27,920 --> 00:05:34,380
+by 6 بدي بقوله كويس الآن مش هنحيب الـ order لهذا
+
+53
+00:05:34,380 --> 00:05:39,160
+بدي أروح أرفع للأس 1 والأس 2 والأس 3
+
+54
+00:05:39,160 --> 00:05:45,560
+لغاية ما أوصل لمين؟ للـ identity element فمثلًا لو بد
+
+55
+00:05:45,560 --> 00:05:50,380
+الـ 2 زائد الـ subgroup generated by 6 لكل
+
+56
+00:05:50,380 --> 00:05:56,100
+تربيع ثاني اللي هو حاصل ضرب الـ 2 يعني حاصل
+
+57
+00:05:56,100 --> 00:06:00,640
+جمع الـ 2 يعني 2 مضروبة في هذا الـ element
+
+58
+00:06:00,640 --> 00:06:05,910
+لأن الـ operation عملية جمعية يبقى هذا عبارة عن مين؟
+
+59
+00:06:05,910 --> 00:06:11,150
+عبارة عن 4 زي الـ subgroup generated by 6 لا
+
+60
+00:06:11,150 --> 00:06:15,770
+يساوي الـ identity element يبقى بناء عليه بدي آخذ
+
+61
+00:06:15,770 --> 00:06:21,410
+2 زي الـ subgroup generated by 6 الكل تكعيب
+
+62
+00:06:21,410 --> 00:06:26,350
+يبقى هذا بدي يساوي 6 زي الـ subgroup generated
+
+63
+00:06:26,350 --> 00:06:32,940
+by 6 قداش يعطيني هذا؟ 6 itself يبقى الـ order لهذا
+
+64
+00:06:32,940 --> 00:06:37,720
+الـ element يساوي 3 يبقى هذا الكلام يعطيني أن
+
+65
+00:06:37,720 --> 00:06:42,840
+الـ order لـ 2 زائد subgroup generated by 6 is
+
+66
+00:06:42,840 --> 00:06:47,600
+equal to 3 وهكذا يبقى كيف بدنا نضرب؟ كيف بدنا
+
+67
+00:06:47,600 --> 00:06:53,780
+نجمع؟ كيف بدنا نسوي؟ هي مثال قدامك طيب نيجي نأخذ
+
+68
+00:06:53,780 --> 00:06:56,160
+مثال example three
+
+69
+00:07:02,940 --> 00:07:13,320
+بقول لك إن الـ G تساوي D4 والـ subgroup اللي هي K
+
+70
+00:07:13,320 --> 00:07:20,740
+هي الـ subgroup generated by R180 طبعا هذه لا
+
+71
+00:07:20,740 --> 00:07:27,220
+يوجد فيها إلا عنصرين اللي هو الـ R0 والـ R180
+
+72
+00:07:27,220 --> 00:07:34,160
+أظن كمان هي هذا الـ center تبع الـ D4 ولا لأ؟ خلينا
+
+73
+00:07:34,160 --> 00:07:38,620
+نجرب هكذا إنه لو كانت الـ Z لـ D N يا فيها الـ
+
+74
+00:07:38,620 --> 00:07:43,800
+Identity فقط يا إما فيها الـ Identity والـ 180
+
+75
+00:07:43,800 --> 00:07:49,980
+حسب الـ D هذه هل هي حسب الـ N؟ هل هي odd ولا
+
+76
+00:07:49,980 --> 00:07:57,460
+even؟ يبقى بالشكل اللي عندنا هذا بدنا find the
+
+77
+00:07:57,460 --> 00:08:04,590
+elements of طبعا في هذا الكلام بده يعطينا مدام هذي
+
+78
+00:08:04,590 --> 00:08:11,650
+هيك بالشكل اللي عندنا هنا Z of D4 السؤال هو هل هذه
+
+79
+00:08:11,650 --> 00:08:17,130
+normal subgroup من D4؟ ليش؟ لأن عناصرها دائما
+
+80
+00:08:17,130 --> 00:08:23,210
+تتعامل مع جميع عناصر الجروب وقد أخذناهم مثلا سابقا
+
+81
+00:08:23,210 --> 00:08:31,840
+يبقى بجي بقوله then الـ K is normal subgroup في D4
+
+82
+00:08:31,840 --> 00:08:43,840
+يبقى find the elements بدنا عناصر of D4 modulo K
+
+83
+00:08:43,840 --> 00:08:47,720
+يبقى عناصر الfactor group اللي عندنا هذه
+
+84
+00:08:54,650 --> 00:08:58,190
+يبقى بدأ أروح أدور على عناصر الfactor group اللي
+
+85
+00:08:58,190 --> 00:09:02,750
+عندنا هنا أول شيء بدأ أعرف قداش فيها عناصر قبل
+
+86
+00:09:02,750 --> 00:09:08,850
+ما أروح أدور طيب العناصر تبعها كل الـ left cosets أو
+
+87
+00:09:08,850 --> 00:09:15,050
+كل distinct left cosets يبقى الـ order لـ D4 modulo
+
+88
+00:09:15,050 --> 00:09:22,990
+K بده يساوي الـ order لـ D4 مقسوما على الـ order لـ K
+
+89
+00:09:22,990 --> 00:09:28,790
+هذه 8 وهذه 2 يبقى عدد العناصر فيها يساوي
+
+90
+00:09:28,790 --> 00:09:34,690
+قدر 4 عناصر بدي أروح أدور على هذه العناصر
+
+91
+00:09:34,690 --> 00:09:40,790
+يبقى بدي أبدأ بالـ left coset الأولى طبعا R0 وR180
+
+92
+00:09:40,790 --> 00:09:46,330
+لو ضربتها في K بتظلها كما هي يبقى بقولها صفعة شجة و
+
+93
+00:09:46,330 --> 00:09:52,840
+بروح آخذ R90 في main في الـ K يبقى بدأ أضربها في
+
+94
+00:09:52,840 --> 00:09:59,920
+العناصر اللي جوا بصير R90 وهذه R90 في R180 اللي
+
+95
+00:09:59,920 --> 00:10:11,200
+يبقى داشرة R270 هي بالضبط تماما كمان R270 في K يبقى
+
+96
+00:10:11,200 --> 00:10:14,840
+هدول مش تنتهي الـ left coset سواء إنما في الحقيقة
+
+97
+00:10:14,840 --> 00:10:22,280
+left coset واحدة بالمّثل بدي أروح أجيب له مين؟ الـ H
+
+98
+00:10:22,280 --> 00:10:29,200
+في K هذا الكلام بده يساوي اللي هو لما أضرب الـ H في
+
+99
+00:10:29,200 --> 00:10:37,040
+R0 بتعطينا H أو هنا بتعطينا H في R180 بالشكل
+
+100
+00:10:37,040 --> 00:10:42,850
+اللي عندنا هذا هذا الكلام بده يساوي الـ H هنا عندك
+
+101
+00:10:42,850 --> 00:10:46,990
+في الـ جدول في صفحة 1 و80 الـ H في الـ R180
+
+102
+00:10:46,990 --> 00:10:54,250
+اللي هي main of V وتساوي كذلك الـ V في K
+
+103
+00:10:54,250 --> 00:10:59,950
+لإن لو ضربت الـ V في K بصير هنا V وهنا V بR180 اللي
+
+104
+00:10:59,950 --> 00:11:04,210
+هي عبارة عن main ع الـ H يبقى صاروا
+
+105
+00:11:04,210 --> 00:11:11,700
+إثنتين وليست واحدة بالمّثل لو روحت جبت له الـ D في
+
+106
+00:11:11,700 --> 00:11:18,900
+main في الـ K يبقى هذه بدها تعطيك D وهنا D في R
+
+107
+00:11:18,900 --> 00:11:25,660
+180 هذه بدها تعطيك D وD' واللي هي
+
+108
+00:11:25,660 --> 00:11:31,800
+بدها تساوي D' كذلك K يبقى أصبح عندي the
+
+109
+00:11:31,800 --> 00:11:33,740
+elements
+
+110
+00:11:36,580 --> 00:11:43,360
+The elements of D4
+
+111
+00:11:43,360 --> 00:11:50,720
+modulo K R الـ element الأول اللي هو الـ K itself
+
+112
+00:11:50,720 --> 00:11:57,140
+والـ element الثاني اللي هو الـ R90 في الـ K اللي
+
+113
+00:11:57,140 --> 00:12:02,720
+بده يساوي R270 في K والـ element الثالث
+
+114
+00:12:02,720 --> 00:12:08,300
+اللي هو الـ HK والـ element الرابع والأخير اللي هو
+
+115
+00:12:08,300 --> 00:12:14,220
+DK يبقى هي الأربعة عناصر اللي موجودة عندنا والتي
+
+116
+00:12:14,220 --> 00:12:19,460
+تمثل عناصر الـ factor group اللي عندنا بالضبط تماما
+
+117
+00:12:19,460 --> 00:12:26,620
+طيب اللي خاطر أعطيك exercise هكذا exercise لو قلت لك
+
+118
+00:12:26,620 --> 00:12:35,490
+little g تساوي D4 itself وخذ لي الـ H هي الـ
+
+119
+00:12:35,490 --> 00:12:47,270
+subgroup generated by R90 السؤال هو is الـ
+
+120
+00:12:47,270 --> 00:12:59,970
+D4 is D4 modulo H exist هل هذه موجودة؟ if so
+
+121
+00:13:01,510 --> 00:13:05,110
+if so find it
+
+122
+00:13:07,500 --> 00:13:12,220
+إذا كان الأمر كذلك بدنا إياها طبعا الـ subgroup
+
+123
+00:13:12,220 --> 00:13:16,500
+generated by R90 فيها قداش كام عنصر؟ 4
+
+124
+00:13:16,500 --> 00:13:21,420
+عناصر وD4 فيها قداش 8 عناصر يبقى الـ index لها
+
+125
+00:13:21,420 --> 00:13:25,800
+قداش؟ مرة اللي فاتت أخذنا لو الـ group الـ index لها 
+
+126
+00:13:25,800 --> 00:13:29,180
+أو الـ subgroup الـ index لها يساوى اثنين إيش بتكون
+
+127
+00:13:29,180 --> 00:13:33,360
+هذه؟ إيش بتكون؟ normal subgroup مدام normal
+
+128
+00:13:33,360 --> 00:13:38,010
+subgroup يبقى الـ factor group exist ما دام exist
+
+129
+00:13:38,010 --> 00:13:41,670
+هذا جواب السؤال أول يوم نهلك شفوي بدنا نعرف من
+
+130
+00:13:41,670 --> 00:13:47,470
+هالعنصرين فقط اللي موجودين في الـ main في الـ factor a
+
+131
+00:13:47,470 --> 00:13:52,190
+group هذا بالنسبة اللي عندنا نيجي ناخد مثال آخر
+
+132
+00:14:11,040 --> 00:14:17,680
+مثال رقم أربعة بيقول
+
+133
+00:14:17,680 --> 00:14:28,420
+little g بدها تساوي A4 و الـ H is a subgroup من
+
+134
+00:14:28,420 --> 00:14:38,780
+مين؟ من G حيث الـ H هذه فيها العناصر التالية
+
+135
+00:14:39,460 --> 00:14:47,660
+identity element واحد اثنين ثلاثة أربعة العنصر
+
+136
+00:14:47,660 --> 00:14:52,880
+اللي بعده واحد ثلاثة اثنين أربعة واحد ثلاثة اثنين 
+
+137
+00:14:52,880 --> 00:15:00,240
+أربعة العنصر اللي بعده واحد أربعة اثنين ثلاثة واحد
+
+138
+00:15:00,240 --> 00:15:06,540
+أربعة اثنين ثلاثة بالشكل اللي عندنا هذا number a
+
+139
+00:15:06,540 --> 00:15:16,060
+show that بيّن لي أن الـ H is a normal subgroup من من
+
+140
+00:15:16,060 --> 00:15:27,760
+الـ G نمرة B show that بيّن لي أن الـ A for modulo H
+
+141
+00:15:27,760 --> 00:15:31,640
+is cyclic
+
+142
+00:16:01,560 --> 00:16:09,740
+الآن مواطين الـ G هي الـ A4 من الـ A4 هذي ممتاز جدا
+
+143
+00:16:09,740 --> 00:16:14,760
+يبقى هذي the sixth of all even permutations of S4
+
+144
+00:16:14,760 --> 00:16:21,810
+عدد أنصارها كدهش؟ 12 عنصر تمام يبقى عدد الـ A4 12
+
+145
+00:16:21,810 --> 00:16:26,530
+عنصر أخذنا الـ subgroup منها الـ subgroup اللي هي H
+
+146
+00:16:26,530 --> 00:16:31,710
+زي ما أنت شايف بنقل عليه بسأل السؤال هل الـ H هذي
+
+147
+00:16:31,710 --> 00:16:37,510
+normal subgroup من G أم لا؟ إن كانت عامة إذا كانت
+
+148
+00:16:37,510 --> 00:16:45,410
+عامة إذا كانت عامة إذا كانت عامة
+
+149
+00:16:45,410 --> 00:16:47,170
+إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا 
+
+150
+00:16:47,170 --> 00:16:47,450
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+151
+00:16:47,450 --> 00:16:47,470
+عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+152
+00:16:47,470 --> 00:16:47,730
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+153
+00:16:47,730 --> 00:16:48,330
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+154
+00:16:48,330 --> 00:17:00,070
+عامة إذا كانت عامة إذا كانت عامة إذا 
+
+155
+00:17:00,070 --> 00:17:08,110
+كانت عامة قداش الـ order لأي element موجود في H أو
+
+156
+00:17:08,110 --> 00:17:14,690
+أو أربعة أو ثلاثة يعني اثنين أو أربعة أو ثلاثة
+
+157
+00:17:14,690 --> 00:17:20,970
+عناصر ليليتش هيهم قدامك قداش الـ اثنين أو أربعة بس
+
+158
+00:17:20,970 --> 00:17:26,850
+اثنين ما فيش غير واحد ما فيش واحد يعني يبقى الـ order
+
+159
+00:17:26,850 --> 00:17:33,370
+إلا واحد أو اثنين الـ least common multiple لمين؟ للـ
+
+160
+00:17:33,370 --> 00:17:38,230
+cycles اللي عندنا يبقى الـ order يا إما واحد يا إما
+
+161
+00:17:38,230 --> 00:17:44,550
+اثنين لا يزيد عن ذلك طبعا هذه ممكن تعمل فيها
+
+162
+00:17:44,550 --> 00:17:47,250
+composition وهذه ممكن تعمل فيها composition إن
+
+163
+00:17:47,250 --> 00:17:51,650
+كانت تقدر طبعا هذه ما فيش إمكانية هذه ما فيش إمكانية
+
+164
+00:17:51,650 --> 00:17:56,190
+هذه كمان ما فيش إمكانية يبقى هؤلاء الـ order is giant
+
+165
+00:17:56,190 --> 00:17:59,390
+cycle يبقى الـ اسكومة المطلوبة اللي طول كل واحدة
+
+166
+00:17:59,390 --> 00:18:02,030
+منهم الـ اسكومة اللي طول الاثنين والاثنين اللي هو B2
+
+167
+00:18:02,630 --> 00:18:10,430
+يبقى هدول كمان هدول كل العناصر اللي في A4 واللي الـ
+
+168
+00:18:10,430 --> 00:18:16,410
+order اللي لهم يساوي اثنين صح؟ يعني أنت لو رحت
+
+169
+00:18:16,410 --> 00:18:21,470
+للتفصيلات تبعت A4 في صفحة 107 من الكتاب 107 من
+
+170
+00:18:21,470 --> 00:18:28,330
+الكتاب حط لك كل عناصر الـ A4 لـ 12 صفهم لك صف هدول فقط
+
+171
+00:18:28,630 --> 00:18:33,710
+هم اللي الـ order لهم يساوي واحد أو اثنين غير هيك
+
+172
+00:18:33,710 --> 00:18:37,430
+ما جابش هايب الأوضة ومعظمها كلهم جابوا ماء قدامهم
+
+173
+00:18:37,430 --> 00:18:47,850
+يبقى أول شغلة observe that observe that لاحظ أن الـ
+
+174
+00:18:47,850 --> 00:18:53,610
+elements of
+
+175
+00:18:53,610 --> 00:18:58,290
+H are all
+
+176
+00:19:01,630 --> 00:19:14,830
+الأشياء من A4 التي لديها order 2 أو 1
+
+177
+00:19:18,250 --> 00:19:23,730
+يبقى عناصر H هما كل عناصر A4 اللي الـ order لهم
+
+178
+00:19:23,730 --> 00:19:28,050
+يساوي إما اثنين أو واحد طبعا الـ order اللي هذه
+
+179
+00:19:28,050 --> 00:19:30,430
+اثنين الـ order اللي هذه اثنين الـ order اللي هذه
+
+180
+00:19:30,430 --> 00:19:35,990
+اثنين الـ order اللي هذه واحد تمام يبقى هدول كلهم
+
+181
+00:19:35,990 --> 00:19:39,270
+عناصر A4 بلا استثناء
+
+182
+00:19:42,420 --> 00:19:50,300
+هذه المعلومة لازم تكون عامة لازم تكون عامة
+
+183
+00:19:55,440 --> 00:19:58,680
+و أثبت أن حاصل الـ element تبع الـ G في الـ element
+
+184
+00:19:58,680 --> 00:20:02,120
+تبع الـ H في معكوس الـ element تبع الـ G بدي يكون
+
+185
+00:20:02,120 --> 00:20:08,260
+موجود وين؟ في H ممتاز إذا يبقى أنا بروح أقول له خد لي
+
+186
+00:20:08,260 --> 00:20:15,080
+Alpha موجودة في الـ A4 و الـ Alpha does not belong
+
+187
+00:20:15,080 --> 00:20:21,940
+to H بدي أخذها من وين؟ من خارج الـ H و الـ Beta
+
+188
+00:20:21,940 --> 00:20:29,210
+موجودة وين؟ في H يبقى أنا أخذت Alpha موجودة في A4 و
+
+189
+00:20:29,210 --> 00:20:34,710
+خارج H وأخذت الـ Beta موجودة في H موجودة في اين؟
+
+190
+00:20:34,710 --> 00:20:43,380
+موجودة في H موجودة في H ولا لا؟ بمعنى آخر الله إن
+
+191
+00:20:43,380 --> 00:20:47,120
+كان الـ Alpha Beta Alpha يتشيل كل تربيع يعطاني الـ
+
+192
+00:20:47,120 --> 00:20:52,640
+identity إذا الـ order يساوي اثنين إذا هتكون واحد من
+
+193
+00:20:52,640 --> 00:20:58,440
+هدول يبقى بتكون one بتكون فائدة يبقى هنا الـ order
+
+194
+00:20:58,440 --> 00:21:04,110
+لا بيقدرش ثانية لأنها موجودة في H لأنه في H كل واحد
+
+195
+00:21:04,110 --> 00:21:09,110
+الـ order له يساوي اثنين يبقى بداجي آخذ له الآن
+
+196
+00:21:09,110 --> 00:21:15,430
+Alpha Beta Alpha Inverse لكل تربيع هي Alpha Beta
+
+197
+00:21:15,430 --> 00:21:21,440
+Alpha Inverse Alpha Beta Alpha Inverse هذا التربيع
+
+198
+00:21:21,440 --> 00:21:26,520
+تبعها الآن من خاصية الـ associativity هذه Alpha
+
+199
+00:21:26,520 --> 00:21:33,520
+Beta في Alpha Inverse Alpha في Beta Alpha Inverse
+
+200
+00:21:33,520 --> 00:21:38,060
+خاصية الـ associativity دمجت اثنين هدول مالهم مع
+
+201
+00:21:38,060 --> 00:21:41,640
+بعض طب هذا العنصر في المعكس هو مش بيعطينا الـ
+
+202
+00:21:41,640 --> 00:21:47,180
+identity يبقى بروح مع السلامة يبقى بصير Alpha Beta
+
+203
+00:21:47,180 --> 00:21:53,500
+تربيع Alpha Inverse بيتا تربيع أبجداش لأنها موجودة
+
+204
+00:21:53,500 --> 00:22:00,540
+وين؟ في H يبقى هذا الكلام بده يساوي Alpha الـ
+
+205
+00:22:00,540 --> 00:22:07,780
+identity في الـ Alpha Inverse السبب because إن الـ
+
+206
+00:22:07,780 --> 00:22:14,060
+order لـ Beta بده يساوي قداش؟ بده يساوي اثنين هذا
+
+207
+00:22:14,060 --> 00:22:18,020
+البرنامج سيعطينا الـ Alpha Alpha Inverse اللي هو
+
+208
+00:22:18,020 --> 00:22:21,000
+الـ Main الـ Identity احنا حطيناها بواحد ولا
+
+209
+00:22:21,000 --> 00:22:25,880
+نغيرها يبقى عدلها بواحد يبقى هذا البرنامج سيعطينا
+
+210
+00:22:25,880 --> 00:22:30,710
+الـ Main اللي هو بواحد صحيح يبقى بناء عليه هذا
+
+211
+00:22:30,710 --> 00:22:36,170
+سيعطينا أن الـ order لـ Alpha Beta Alpha Inverse هو
+
+212
+00:22:36,170 --> 00:22:43,370
+اثنين هذا معناه أن الـ Alpha Beta Alpha Inverse
+
+213
+00:22:43,370 --> 00:22:46,910
+موجودة في normal subgroup
+
+214
+00:22:59,830 --> 00:23:06,380
+هذا الحل اللي حليناه هو المطلوب الأول نمرا a المطلوب
+
+215
+00:23:06,380 --> 00:23:12,220
+الثاني نمرا b بيقول لي في نمرا b اثبت لي أن الـ
+
+216
+00:23:12,220 --> 00:23:17,120
+factor group اللي عندنا هذه is a cyclic group
+
+217
+00:23:17,120 --> 00:23:25,220
+بيقول لك خيص تعال نشوف قداش الـ order للـ A for modulo
+
+218
+00:23:25,220 --> 00:23:32,140
+H اللي بقول عليها يبقى هذا بده يساوي الـ order للـ A4
+
+219
+00:23:32,140 --> 00:23:37,480
+على الـ order للـ H هذه عبارة عن اثنا عشر على أربعة
+
+220
+00:23:37,480 --> 00:23:42,380
+يساوي كدهش؟ ثلاثة
+
+221
+00:23:42,380 --> 00:23:52,590
+is prime نرجع لمين؟ نرجع لأخذنا نظرية مشهورة قلنا في
+
+222
+00:23:52,590 --> 00:23:57,050
+الجبر نظرية الـ grunge و الـ crawlers اللي عليها الـ
+
+223
+00:23:57,050 --> 00:24:01,870
+crawlers رقمتهم كان بيقول لي إذا كان الـ order للـ
+
+224
+00:24:01,870 --> 00:24:06,550
+group أو للـ sub group الـ prime number يبقى هي...
+
+225
+00:24:06,550 --> 00:24:16,750
+هي cyclic group يبقى by her previous corollary
+
+226
+00:24:19,010 --> 00:24:26,770
+اللي هي اثنين على نظرية Lagrange we have إن الـ A4
+
+227
+00:24:26,770 --> 00:24:35,790
+modulo H is cyclic طيب
+
+228
+00:24:35,790 --> 00:24:45,560
+حابب أتعرف على شكل العناصر check that تأكد لي أن الـ
+
+229
+00:24:45,560 --> 00:24:53,820
+A4 modulo H عناصرها اللي هم على الشكل التالي الـ H
+
+230
+00:24:53,820 --> 00:25:03,560
+واحد اثنين ثلاثة في H واحد ثلاثة اثنين في H كيف
+
+231
+00:25:03,560 --> 00:25:12,180
+بدي أعرفها؟ يبقى بدي أمسك العناصر من خارج H لأن أي
+
+232
+00:25:12,180 --> 00:25:15,660
+عنصر ما نشتغله في H بده تطلع نفس الـ H إذا كتروح
+
+233
+00:25:15,660 --> 00:25:22,100
+أجيب للعناصر اللي ضايلة في A4 صفحة 107 وتضربهم وين
+
+234
+00:25:22,100 --> 00:25:26,800
+تضرب من في العناصر اللي عندك دائما وابدا حيطلع
+
+235
+00:25:26,800 --> 00:25:33,870
+واحد من الثلاثة دول إذا لازم أجيبها لك كأي حاجة
+
+236
+00:25:33,870 --> 00:25:42,110
+بتلزم كجدول بيجيبوها لك أنا بديك تبقى فاهم وليس
+
+237
+00:25:42,110 --> 00:25:47,870
+حافظ تمام يبقى الـ A for module H اللي عناصرها H
+
+238
+00:25:47,870 --> 00:25:53,690
+واحد اثنين ثلاثة H واحد ثلاثة اثنين H طب السؤال هو
+
+239
+00:25:53,690 --> 00:25:57,230
+قداش الـ order لهذه الـ element
+
+240
+00:26:05,570 --> 00:26:17,390
+أربعة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة
+
+241
+00:26:17,390 --> 00:26:21,630
+ستة
+
+242
+00:26:23,010 --> 00:26:27,830
+يا واحد يا ثلاثة وغير هيك ما فيش فيش بالمرة واحد هي
+
+243
+00:26:27,830 --> 00:26:31,830
+يبقى غصب عني وعنك الـ order إلى يساوي ثلاثة الحين
+
+244
+00:26:31,830 --> 00:26:35,750
+هذه لم تجد طولها ثلاثة المهوض لما تقول تربيع تبدأ
+
+245
+00:26:35,750 --> 00:26:39,610
+تربيع هذه وهذه ثابتة تقول تكعيد الكعب هذه وهذه
+
+246
+00:26:39,610 --> 00:26:43,870
+ثابتة هذه طولها يساوي ثلاثة يعني الـ order إلى يساوي
+
+247
+00:26:43,870 --> 00:26:48,070
+ثلاثة يبقى الـ order لكل واحد من هذول ثلاثة يبقى كل
+
+248
+00:26:48,070 --> 00:26:53,990
+واحد عبارة عن generator لمن؟ للـ group اللي عندنا
+
+249
+00:26:53,990 --> 00:27:03,170
+يعني يبقى باجي بقول clearly كمان إنه الواحد اثنين
+
+250
+00:27:03,170 --> 00:27:14,650
+ثلاثة each and clearly إنه each of هـ of الواحد 
+
+251
+00:27:14,650 --> 00:27:24,930
+اتنين تلاتة في H وواحد تلاتة اتنين في H is a
+
+252
+00:27:24,930 --> 00:27:36,580
+generator for الـ a4 modulo H والسبب because إن الـ
+
+253
+00:27:36,580 --> 00:27:44,760
+order للواحد اتنين ثلاثة في H بده يساوي الـ order
+
+254
+00:27:44,760 --> 00:27:51,780
+للواحد تلاتة اتنين في H بده يساوي كده تلاتة يبقى
+
+255
+00:27:51,780 --> 00:27:55,580
+كل واحد فيهم عبارة عن generator
+
+256
+00:27:59,280 --> 00:28:04,300
+طب خلّيني أسأل كل واحد معكوس لنفسه والله واحد
+
+257
+00:28:04,300 --> 00:28:10,640
+فيهم معكوس الثاني بمعنى هل الواحد اتنين تلاتة و
+
+258
+00:28:10,640 --> 00:28:15,620
+الواحد تلاتة اتنين معكوس لنفسه كل واحد والله
+
+259
+00:28:15,620 --> 00:28:19,820
+اتنين معكوسة لبعض تعالوا اضربهم في بعض الواحد
+
+260
+00:28:19,820 --> 00:28:24,800
+بيروح لوين؟ والتلاتة بيروح لمين؟ صف على شجر الـ
+
+261
+00:28:24,800 --> 00:28:28,850
+identity الواحد راح على الواحد بنمسك التلاتة بتروح
+
+262
+00:28:28,850 --> 00:28:34,190
+لمين؟ لاتنين والاتنين بتروح صف على شجر الـ identity
+
+263
+00:28:34,190 --> 00:28:37,950
+الاتنين بيروح للواحد والواحد بيروح لاتنين يبقى الـ
+
+264
+00:28:37,950 --> 00:28:43,630
+identity يبقى كل واحد فيهم معكوس للآخر وليس معكوس
+
+265
+00:28:43,630 --> 00:28:51,040
+لنفسه إذا الـ element هذا في حد ذاته هو معكوس لمن؟
+
+266
+00:28:51,040 --> 00:28:57,480
+لهذا الـ element وفي نفس الوقت الـ element هذا كله
+
+267
+00:28:57,480 --> 00:29:03,160
+هو معكوس لهذا الـ element في الـ factor group لأن لو
+
+268
+00:29:03,160 --> 00:29:12,730
+ضربتهم في بعضهم سأحصل على الـ identity not that ان
+
+269
+00:29:12,730 --> 00:29:22,690
+الواحد اتنين تلاتة each is the inverse of الواحد
+
+270
+00:29:22,690 --> 00:29:24,870
+تلاتة اتنين each because
+
+271
+00:29:28,030 --> 00:29:33,110
+لو ضربت في بعض بدي أطين مين الـ identity element في
+
+272
+00:29:33,110 --> 00:29:39,630
+H في 1 3 2 H حسب التعريف على الـ factor group الـ
+
+273
+00:29:39,630 --> 00:29:44,090
+operation قولنا بنضرب الـ two elements في بعض يبقى
+
+274
+00:29:44,090 --> 00:29:54,540
+123 132 في H ويساوي نمسك الأول مرة تانية الواحد
+
+275
+00:29:54,540 --> 00:30:00,420
+صورته تلاتة والتلاتة صورتها واحد يبقى ما عنديش إلا
+
+276
+00:30:00,420 --> 00:30:05,780
+الواحد نمسك اللي بعده اتنين اتنين صورته واحد
+
+277
+00:30:05,780 --> 00:30:11,540
+والواحد صورته اتنين يبقى جافلة نمسك التلاتة تلاتة
+
+278
+00:30:11,540 --> 00:30:16,930
+صورتها اتنين واتنين صورتها تلاتة يبقى جافلة وهذا
+
+279
+00:30:16,930 --> 00:30:22,850
+الـ main الـ H اللي بتعطيك الـ H itself لأن هذا
+
+280
+00:30:22,850 --> 00:30:28,890
+كله بالـ identity element يبقى بناء عليه فعلا هذا
+
+281
+00:30:28,890 --> 00:30:33,470
+الـ element هو معكوس لمين؟ معكوس للـ element اللي
+
+282
+00:30:33,470 --> 00:30:34,550
+عندنا هذا
+
+283
+00:30:52,470 --> 00:31:00,730
+يبقى هذا كان مثال أربعة مثال
+
+284
+00:31:00,730 --> 00:31:01,470
+خمسة
+
+285
+00:31:06,680 --> 00:31:14,420
+بقول لي U 32 بتساوي U 32 اللي عناصرها
+
+286
+00:31:14,420 --> 00:31:22,540
+طبعا اللي هي واحد وتلاتة وخمسة وسبعة وتمانية
+
+287
+00:31:22,540 --> 00:31:39,910
+تسعة عشر احداش تلتاش اربعتاش خمستاش 15 16 17 19 20
+
+288
+00:31:39,910 --> 00:32:00,830
+21 20 23 بعد 23 24 25 27 28 29 31 ما فيش غيرها طيب
+
+289
+00:32:00,830 --> 00:32:06,930
+هذا بده يعطيني إن الـ order لليو اتنين وتلاتين بده
+
+290
+00:32:06,930 --> 00:32:12,030
+يساوي واحد اتنين تلاتة أربعة خمسة ستة سبعة تمانية
+
+291
+00:32:12,030 --> 00:32:15,550
+تسعة عشر احداشر اتناشر تلاتاشر اربعاشر خمساشر
+
+292
+00:32:15,550 --> 00:32:20,730
+ستاشر عنصر في الـ group اللي عندنا هنا بدنا نروح
+
+293
+00:32:20,730 --> 00:32:26,980
+ناخد sub group منها let الـ H هي الـ subgroup
+
+294
+00:32:26,980 --> 00:32:32,420
+generated by خمستاشر واللي ما فيش فيها إلا العنصرين
+
+295
+00:32:32,420 --> 00:32:41,000
+واحد وخمستاشر السؤال هو هل الـ H هذي abelian؟ الـ
+
+296
+00:32:41,000 --> 00:32:46,150
+H just a normal subgroup من الـ U تلاتة؟ نعم لأن
+
+297
+00:32:46,150 --> 00:32:52,690
+هذيك الـ U اتنين وتلاتين is abelian يبقى then الـ
+
+298
+00:32:52,690 --> 00:32:59,110
+H is a normal subgroup من الـ U اتنين وتلاتين
+
+299
+00:32:59,110 --> 00:33:07,010
+because السبب because إن U اتنين وتلاتين is a
+
+300
+00:33:07,010 --> 00:33:11,990
+abelian معناته بقدر أكون الـ factor group يعني الـ
+
+301
+00:33:11,990 --> 00:33:18,650
+factor group exist يبقى هذا بده يعطيك إن الـ U 32
+
+302
+00:33:18,650 --> 00:33:29,290
+modulo H modulo H exist موجودة السؤال هو طب بنقدر
+
+303
+00:33:29,290 --> 00:33:34,730
+نجيب عناصرها قبل السؤال يبقى الـ order ليه 32
+
+304
+00:33:34,730 --> 00:33:42,390
+modulo H بده يساوي اللي هو 16 على قداش على 2 و
+
+305
+00:33:42,390 --> 00:33:48,630
+يساوي 8 يبقى هذا الـ group هذه فيها ثمانية عناصر
+
+306
+00:33:48,630 --> 00:33:52,230
+اسمع السؤال الـ question is
+
+307
+00:33:58,580 --> 00:34:09,400
+السؤال هو هل is الـ G modulo H isomorphic لـ Z
+
+308
+00:34:09,400 --> 00:34:12,160
+تمانية ولا Z
+
+309
+00:34:35,940 --> 00:34:43,120
+طيب نرجع لسوالنا مرة تانية بقول لي احنا جه أخدنا الـ
+
+310
+00:34:43,120 --> 00:34:47,540
+U32 أخدنا الـ subgroup generated by خمستاشر اللي
+
+311
+00:34:47,540 --> 00:34:53,220
+فيهاش اللي غير عنصرين واحد وخمستاشر وخمستاشر تربيع
+
+312
+00:34:53,220 --> 00:35:02,080
+متين وخمسة وعشرين اللي هي عبارة عن واحد في U32 لأن
+
+313
+00:35:02,080 --> 00:35:09,100
+الـ 224 هي مضاعفات 32 يبقى ما فيش فيها إلا عنصرين
+
+314
+00:35:09,100 --> 00:35:13,780
+any subgroup من الـ abelian group is normal يبقى الـ
+
+315
+00:35:13,780 --> 00:35:18,000
+subgroup اللي أخدناها normal subgroup من الـ U32
+
+316
+00:35:18,000 --> 00:35:23,420
+يبقى الـ factor group exist وفيها ثمانية عناصر
+
+317
+00:35:23,730 --> 00:35:30,010
+السؤال هو هل الـ G-modulation isomorphic لـ Z8 ولا لـ
+
+318
+00:35:30,010 --> 00:35:35,050
+Z4 external product مع Z2 ولا لـ Z2 external
+
+319
+00:35:35,050 --> 00:35:40,730
+product مع Z2 external product مع Z2 كذلك أم لا؟
+
+320
+00:35:40,730 --> 00:35:46,920
+هذه تمان عناصر هذه تمان عناصرهذه تمام عناصر تمام
+
+321
+00:35:46,920 --> 00:35:52,680
+التمام بدنا نيجي نشوف مين نستبعد ومين نخليه قداش
+
+322
+00:35:52,680 --> 00:35:57,560
+أكبر order لأي element موجود هنا تمانية تمانية
+
+323
+00:35:57,560 --> 00:36:03,960
+قداش أكبر order لأي element هنا كداش أربعة ما يزيدش
+
+324
+00:36:03,960 --> 00:36:06,740
+عن أربعة اللي هو least common multiple للأربعة
+
+325
+00:36:06,740 --> 00:36:10,620
+واتنين أو للأربعة والواحد سيام قداش الـ maximum
+
+326
+00:36:10,620 --> 00:36:14,510
+order لأي element هنا اتنين يبقى أكبر واحد هناك
+
+327
+00:36:14,510 --> 00:36:19,050
+تمانية أكبر واحد اتنين وأكبر واحد هنا أربعة طب
+
+328
+00:36:19,050 --> 00:36:24,590
+السؤال هو الـ G modulo H فيها ثمانية عناصر لو روحت
+
+329
+00:36:24,590 --> 00:36:29,770
+عناصرها كلهم lift كو ستة لو روحت للأور السبع lift
+
+330
+00:36:29,770 --> 00:36:34,730
+كو ستة ولجيته يساوي تمانية معناته هذا generator
+
+331
+00:36:34,730 --> 00:36:39,470
+وبالتالي isomorphic لـ Z تمانية لكن إذا ما لجيتهش
+
+332
+00:36:39,470 --> 00:36:44,600
+فيها ولا generator إذا لا يمكن أن تكون isomorphic
+
+333
+00:36:44,600 --> 00:36:49,580
+لمعنى لـ Z تمانية بيظل احتمال هنا يا إما لـ Z
+
+334
+00:36:49,580 --> 00:36:52,440
+أربعة cross product مع Z اتنين أو Z اتنين
+
+335
+00:36:52,440 --> 00:36:55,700
+cross product مع Z اتنين cross product مع
+
+336
+00:36:55,700 --> 00:37:01,600
+Z اتنين الثانية لذلك هذه العناصر قدامك كلها
+
+337
+00:37:01,600 --> 00:37:07,260
+نستطيع أن نحصل على left coset أول واحدة تبقى الأول
+
+338
+00:37:07,260 --> 00:37:11,800
+واحد بتضرب التلاتة في K في H مش هذي left coset
+
+339
+00:37:11,800 --> 00:37:18,600
+كذلك يعني أحد عناصر من الـ group الآن بداجي أقوله
+
+340
+00:37:18,600 --> 00:37:26,880
+تلاتة H هذي موجودة في الـ U تنين وتلاتين modulo
+
+341
+00:37:26,880 --> 00:37:35,790
+اللي هو من H لو جيت تلاتة H هل هذه تساوي H تسلف؟
+
+342
+00:37:35,790 --> 00:37:40,950
+يعني لو ضربت هنا في من في تلاتة بصير تلاتة وتلاتة
+
+343
+00:37:40,950 --> 00:37:45,470
+في خمستاشر بخمسة وأربعين شيء اللي بيبقى تلتاش هل
+
+344
+00:37:45,470 --> 00:37:52,790
+هي H؟ لأ اتنين لو جيت قلت لك تلاتة H لكل تربيع
+
+345
+00:37:55,240 --> 00:37:59,440
+آه يعني لو طلع الـ identity اتنين هذي بتجسم
+
+346
+00:37:59,440 --> 00:38:03,620
+التمانية يعني ممكن مش في مشكلة هذا الكلام بده
+
+347
+00:38:03,620 --> 00:38:12,460
+يساوي تسعة H هل تسعة H تساوي H اضربها تسعة وهذي
+
+348
+00:38:12,460 --> 00:38:17,400
+تسعة في خمستاشر إذا لا يمكن أن تساوي مين H أخد تلاتة
+
+349
+00:38:17,400 --> 00:38:24,320
+H تكيب لأ لأن التلاتة لا تقسم مين التمانية يبقى
+
+350
+00:38:24,320 --> 00:38:27,420
+فيش element الـ order إله يساوي التلاتة يبقى ما
+
+351
+00:38:27,420 --> 00:38:36,620
+تغلبش حالك روح على مين؟ على تلاتة H أُس أربعة يبقى
+
+352
+00:38:36,620 --> 00:38:41,060
+هذه عبارة عن قداش تسعة في تسعة بواحد وتمانين H
+
+353
+00:38:41,060 --> 00:38:45,400
+هذا الكلام يساوي تنين وتلاتين وتنين وتلاتين
+
+354
+00:38:45,400 --> 00:38:49,840
+أربعة وستون من واحد وتمانين ستاشر وواحد و
+
+355
+00:38:49,840 --> 00:38:57,580
+سبعتاشر يبقى هذه سبعتاشر H هل السبعتاشر H بيساوي
+
+356
+00:38:57,580 --> 00:39:03,980
+H؟ لأ يبقى سعر الـ order لهذا الـ element لا يمكن أن
+
+357
+00:39:03,980 --> 00:39:08,800
+يكون أربعة أروح أدور على خمسة وستة وسبعة يبقى
+
+358
+00:39:08,800 --> 00:39:13,020
+automatic الـ order إله يساوي قداش تمانية لأن الـ order
+
+359
+00:39:13,020 --> 00:39:16,100
+للـ element اللي بيجسم للـ order اللي جمده ما تحصل
+
+360
+00:39:16,100 --> 00:39:21,540
+على طول الخطة بنستنتجها يبقى هذا بده يعطينا إن الـ
+
+361
+00:39:21,540 --> 00:39:27,480
+order لتلاتة H بده يساوي قداش تمانية because
+
+362
+00:39:30,700 --> 00:39:36,000
+the order of
+
+363
+00:39:36,000 --> 00:39:46,880
+the element divide the order of the group
+
+364
+00:39:51,730 --> 00:39:55,870
+لأن الـ order للـ element بيجسم الـ order للـ group
+
+365
+00:39:55,870 --> 00:40:02,370
+يبقى لا يمكن أن أنا أجد الـ order خمسة ولا ستة ولا
+
+366
+00:40:02,370 --> 00:40:07,230
+سبعة إذا الـ order يساوي كمان تمانية معناته هذا الـ
+
+367
+00:40:07,230 --> 00:40:17,290
+element ماله generator يبقى هنا الـ ثلاثة H is a
+
+368
+00:40:17,290 --> 00:40:19,150
+generator
+
+369
+00:40:20,550 --> 00:40:29,770
+Four اللي هو من الـ U اتنين وتلاتين modulo H مدام
+
+370
+00:40:29,770 --> 00:40:36,150
+generator يبقى هذه مالها Cyclic يبقى هذا يعطينا إن
+
+371
+00:40:36,150 --> 00:40:45,570
+U اتنين وتلاتين U اتنين وتلاتين modulo 11 is
+
+372
+00:40:45,570 --> 00:40:51,500
+cyclic Madame Cyclic يبقى هل يمكن أن تكون
+
+373
+00:40:51,500 --> 00:40:56,460
+isomorphic لهذه لأن هذا أكبر order لها يساوي اتنين
+
+374
+00:40:56,460 --> 00:41:02,160
+isomorphic لهذه لأ لأن أكبر order عنها مين يساوي
+
+375
+00:41:02,160 --> 00:41:08,980
+أربعة يبقى هنا الـ U تنين وتلاتي موديل أحداشر 
+
+376
+00:41:08,980 --> 00:41:12,780
+isomorphic لـ Z8 because
+
+377
+00:41:16,450 --> 00:41:31,430
+Z4 external like product مع Z2 has
+
+378
+00:41:31,430 --> 00:41:34,490
+no element
+
+379
+00:41:36,400 --> 00:41:43,400
+of order  مافيش ولا عنصر يبقى هذي صارت
+
+380
+00:41:43,400 --> 00:41:51,220
+isomorphic لـ مين؟ لـ .. لـ group اللي عندنا هذي الآن
+
+381
+00:41:51,220 --> 00:41:56,900
+بدنا نيجي لنظرية طبعا أخدت أمثلة لا بأس بها كثيرة
+
+382
+00:41:56,900 --> 00:42:01,700
+على الـ normal و على الـ factor group بنيجي لأول
+
+383
+00:42:01,700 --> 00:42:08,430
+نظرية في هذا الموضوع بتقول الـ Center تبع الـ
+
+384
+00:42:08,430 --> 00:42:16,690
+Group G of
+
+385
+00:42:16,690 --> 00:42:22,430
+a
+
+386
+00:42:22,430 --> 00:42:30,570
+group G if الـ G modulo Center بتبع الـ G is
+
+387
+00:42:30,570 --> 00:42:36,820
+cyclic then الـ G is abelian
+
+388
+00:43:06,770 --> 00:43:07,570
+خلّي بركة
+
+389
+00:43:10,260 --> 00:43:14,500
+عندنا Z of G الـ Center تبع لـ Group G وبنعرف الـ
+
+390
+00:43:14,500 --> 00:43:18,780
+Center اللي بيجمع كل العناصر الكميوس مع جميع عناصر
+
+391
+00:43:18,780 --> 00:43:23,120
+G بالاستثناء يبقى لو كانت الـ G modulo Z Cyclic
+
+392
+00:43:23,120 --> 00:43:29,000
+يبقى بنثبت له إنه G الأصلية is Abelian يبقى
+
+393
+00:43:29,000 --> 00:43:35,800
+المعطيات اللي عندي أ assume that إن الـ G modulo Z
+
+394
+00:43:35,800 --> 00:43:43,120
+of G is Cyclic ما دام Cyclic يبقى إيه ايش؟لها
+
+395
+00:43:43,120 --> 00:43:54,560
+generator ما دام Cyclic يبقى الـG في الـZ of G بـA
+
+396
+00:43:54,560 --> 00:43:56,160
+generator
+
+397
+00:43:57,710 --> 00:44:03,690
+يفترض ان هذا generator اله يعني أي element فيها
+
+398
+00:44:03,690 --> 00:44:11,230
+يكون هذا ال element مرفوع لمين؟ لأس محددة يبقى then
+
+399
+00:44:11,230 --> 00:44:18,190
+الـ g modulo center بتبع الـ g هي sub group أو ال
+
+400
+00:44:18,190 --> 00:44:23,850
+group generated by g في الـ z of g بالشكل اللي
+
+401
+00:44:23,850 --> 00:44:30,950
+عندنا الآن بدي أقول له let الـ a و الـ b موجودة في g
+
+402
+00:44:30,950 --> 00:44:37,430
+إذا قدرت أثبت له إن الـ a في b هي الـ b في a بتما
+
+403
+00:44:37,430 --> 00:44:44,990
+المطلوب تمام؟ إذا حاجة أقوله الآن الـ a موجودة في
+
+404
+00:44:44,990 --> 00:44:50,630
+الـ a في الـ center بتبع الـ g صح ولا لا؟ الـ element
+
+405
+00:44:50,630 --> 00:44:57,550
+A موجود في أي lift-go set طب هذا الـ element موجود
+
+406
+00:44:57,550 --> 00:45:04,750
+في الـ group هذه ولا لا؟ إيه في الـ center؟ موجود
+
+407
+00:45:04,750 --> 00:45:08,690
+هنا ولا لا؟ صح؟ مالكه بلعته
+
+408
+00:45:16,880 --> 00:45:28,400
+يبقى هنا هذا الكلام يبقى ميم يبقى ميم
+
+409
+00:45:28,400 --> 00:45:29,320
+ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم
+
+410
+00:45:29,320 --> 00:45:29,380
+يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى
+
+411
+00:45:29,380 --> 00:45:35,820
+ميم يبقى واللي هو بده يساوي GI في الـ center اللي
+
+412
+00:45:35,820 --> 00:45:45,210
+تبع الـ G for some I  بالمثل الـ B موجود في الـ B في
+
+413
+00:45:45,210 --> 00:45:50,450
+الـ Center بتابع الـ G و اللي هو بده يساوي G في
+
+414
+00:45:50,450 --> 00:45:57,570
+الـ Center بتابع الـ G مرفوع لأُس J وهذا GG للـ
+
+415
+00:45:57,570 --> 00:46:05,970
+Center بتابع الـ Group G for some J الآن خدلي AB
+
+416
+00:46:08,110 --> 00:46:15,830
+يبقى الـ a,b بده يساوي الـ a,b هذه a موجودة هنا يبقى
+
+417
+00:46:15,830 --> 00:46:21,990
+موجودة هنا مدام موجودة هنا يبقى بقدر أقول إن الـ a
+
+418
+00:46:21,990 --> 00:46:31,550
+تساوي g,i,x for some x وهذا بده يعطيني إن b تساوي
+
+419
+00:46:31,550 --> 00:46:42,650
+g,j,y for some y وارسم Y يبقى الـ A بي بده يساوي ال
+
+420
+00:46:42,650 --> 00:46:49,630
+A اللي عندي اللي هي main اللي هي GIX والـ B اللي هي
+
+421
+00:46:49,630 --> 00:46:52,070
+GJY
+
+422
+00:46:54,390 --> 00:46:59,310
+الإكس والواي والإكس والواي والإكس والواي يا سيدي
+
+423
+00:46:59,310 --> 00:47:03,910
+اللي هم في الـ center إذا بقدر أبدل زي ما بدي تمام
+
+424
+00:47:03,910 --> 00:47:12,040
+يبقى هذا بتقدر تقولي GI جي جي في الـ X Y بدلت
+
+425
+00:47:12,040 --> 00:47:17,700
+التنتين هذول مع بعض لإن X موجودة في الـ center طيب
+
+426
+00:47:17,700 --> 00:47:26,200
+هذه بقدر أبدل كمان بقدر أقول جي جي في جي I وهذه Y
+
+427
+00:47:26,200 --> 00:47:26,860
+في X
+
+428
+00:47:30,120 --> 00:47:34,100
+الآن بدي أبدل هدول مع بعض لإن الـ X و الـ Y في ال
+
+429
+00:47:34,100 --> 00:47:37,980
+center يبدلوا مع بعض دوري يبقى هذا الكلام يبدو
+
+430
+00:47:37,980 --> 00:47:51,200
+يساوي GJ و هنا Y و هنا GIX هذا B وهذا A يبقى G
+
+431
+00:47:51,200 --> 00:47:54,180
+Abelian يبقى هنا Das
+
+432
+00:48:02,290 --> 00:48:10,990
+يبقى من الانفة ساعدا اه
+
+433
+00:48:10,990 --> 00:48:15,070
+طبعا
+
+434
+00:48:15,070 --> 00:48:23,230
+هاي موجودة هنا يبقى تساوي GI في element من ال
+
+435
+00:48:23,230 --> 00:48:28,890
+center الـ X موجودة في الـ center والـ Y موجودة في ال
+
+436
+00:48:28,890 --> 00:48:30,590
+center كذلك 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e3a7ad6c5bafc45d86fc391e62cc3dfdd65aecdb
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/RPZqJGhUV7s_raw.srt
@@ -0,0 +1,1756 @@
+1
+00:00:21,850 --> 00:00:25,810
+بسم الله الرحمن الرحيم نواصل ما بدأنا فيه في
+
+2
+00:00:25,810 --> 00:00:30,430
+المحاضرة الماضية بدأنا بال normal subgroups أعطينا
+
+3
+00:00:30,430 --> 00:00:34,310
+تعريف لل normal subgroups وعرفنا أن التعريف له
+
+4
+00:00:34,310 --> 00:00:39,230
+أوجه مختلفة بدل وجه تلاتة ثم انتقلنا بعد ذلك إلى
+
+5
+00:00:39,230 --> 00:00:44,970
+ال factor groups وعناصر ال factor groups كلها هي
+
+6
+00:00:44,970 --> 00:00:49,930
+left cosets واخذنا على ذلك مثالا واحدا وهذا هو
+
+7
+00:00:49,930 --> 00:00:55,520
+المثال رقم 2بقول يفترض ان جي هي عبارة عن Z 18
+
+8
+00:00:55,520 --> 00:00:59,600
+واخدنا ال subgroup منها هي ال subgroup generated
+
+9
+00:00:59,600 --> 00:01:06,820
+by 6 العناصر تبعها 0 6 12 الآن السؤال هو هل ال H
+
+10
+00:01:06,820 --> 00:01:15,780
+normal subgroup من Z 18 ام لا؟ بدنا الإجابة Normal
+
+11
+00:01:15,780 --> 00:01:19,220
+ليش؟ لأن جي
+
+12
+00:01:22,380 --> 00:01:27,080
+أول مثال أخدته معاك لو كانت ال group abelian يبقى
+
+13
+00:01:27,080 --> 00:01:31,660
+any subgroup is normal تمام يبقى في هذه الحالة
+
+14
+00:01:31,660 --> 00:01:37,800
+بقوله then ال H is a normal subgroup من Z18
+
+15
+00:01:37,800 --> 00:01:48,050
+because اللي هو Z18 is abelianكويس اذا بدي اروح
+
+16
+00:01:48,050 --> 00:01:52,990
+اكون ال factor group او بدي اعرف ال factor group
+
+17
+00:01:52,990 --> 00:02:00,710
+فيها كم element هذي تمام يبقى ال orderالـ order لـ
+
+18
+00:02:00,710 --> 00:02:09,490
+z 18 الموديولو 11 بده يساوي كله لفتكوه 6 يبقى ال
+
+19
+00:02:09,490 --> 00:02:16,510
+order ل z 18 مقسوما على ال order لل h و اللي هو
+
+20
+00:02:16,510 --> 00:02:25,600
+عبارة عن 18 ع 3 يبقى 6 elementsيبقى ال group هذه
+
+21
+00:02:25,600 --> 00:02:31,460
+فيها ستة عناصر بدي أعرف من هذه العناصر يبقى بروح
+
+22
+00:02:31,460 --> 00:02:41,160
+بقول له the elements of z التمنتاشر module 11 are
+
+23
+00:02:43,100 --> 00:02:49,600
+الأولان هو H itself أو الـ subgroup generated by 6
+
+24
+00:02:49,600 --> 00:02:55,000
+التاني هو واحد زائد ال subgroup generated by 6
+
+25
+00:02:55,000 --> 00:03:00,580
+التالت اتنين زائد ال subgroup generated by 6
+
+26
+00:03:00,580 --> 00:03:06,280
+الرابع هو تلاتة زائد ال subgroup generated by 6
+
+27
+00:03:14,080 --> 00:03:20,300
+السادس والاخير له خمسة زي ال subgroup generated by
+
+28
+00:03:20,300 --> 00:03:26,920
+ستةأي اي اي lift cos 6 بعد ذلك لو جيتلي قولتلي 6
+
+29
+00:03:26,920 --> 00:03:31,040
+زي ال subgroup generated by 6 بقولك هي مين هي
+
+30
+00:03:31,040 --> 00:03:36,640
+الأصلية ال subgroup الأصلية لو جيتلي قولتلي 7 زي
+
+31
+00:03:36,640 --> 00:03:40,000
+ال subgroup generated by 6 بقولك هي الواحد و هكذا
+
+32
+00:03:40,610 --> 00:03:45,190
+الان داخل هذه ال group لو بدى اجمع او بدى اعرف ال
+
+33
+00:03:45,190 --> 00:03:50,610
+order كيف بدى احاسبه يبقى لحد هنا احنا انتهينا من
+
+34
+00:03:50,610 --> 00:03:57,450
+عناصر هذه ال group لو بدى اجي اخد مثلا تلاتة زائد
+
+35
+00:03:57,450 --> 00:04:03,350
+ال sub group generated by ستة بدى اجمع مع مين مع
+
+36
+00:04:03,350 --> 00:04:08,560
+الخمسة زائد ال sub group generated by ستةيعني كأن
+
+37
+00:04:08,560 --> 00:04:14,100
+.. كأن بدي أضرب two left cosets في بعضهم لكن لما
+
+38
+00:04:14,100 --> 00:04:19,000
+كانت العملية عملية جامعة يبقى ضرب بس يتحول إلى
+
+39
+00:04:19,000 --> 00:04:22,720
+جامعة المرة اللي فاتت قلنا ال operation اللي على
+
+40
+00:04:22,720 --> 00:04:28,010
+ال left cosets هذهإن الـ A H مضروب في B H بيكون A
+
+41
+00:04:28,010 --> 00:04:35,270
+B F H يبقى معنى هذا الكلام هذا بيكون تلاتة زائد
+
+42
+00:04:35,270 --> 00:04:40,770
+خمسة زائد ال sub group generated by ستة تلاتة زائد
+
+43
+00:04:40,770 --> 00:04:46,450
+خمسة قداش تمانية تمانية بشيل منهم الستة بظل قداش
+
+44
+00:04:46,450 --> 00:04:51,490
+اتنين يبقى هذا اتنين زائد ال sub group generated
+
+45
+00:04:51,490 --> 00:04:58,110
+by ستة هيهايبقى any two left cosets لو جمعتهم
+
+46
+00:04:58,110 --> 00:05:03,790
+هيعطيني واحدة من الست لإتنين هذول لو بدي أجيب مثلا
+
+47
+00:05:03,790 --> 00:05:08,550
+ال order لأي واحدة منهم يبقى بدي أروح أشوف قدش
+
+48
+00:05:08,550 --> 00:05:13,550
+الرقم اللي بدي أحط اس لهذا ال element بحيث يعطيني
+
+49
+00:05:13,550 --> 00:05:17,590
+main ال identity يعني يعطيني ال subgroup generated
+
+50
+00:05:17,590 --> 00:05:23,420
+by الست بالضبط تمامافمثلًا لو جيت قولت بدي أعرف
+
+51
+00:05:23,420 --> 00:05:27,920
+قداش ال order للي اتنين زيدي ال subgroup generated
+
+52
+00:05:27,920 --> 00:05:34,380
+by ستة بدي بقوله كويس الان مش هنجيب ال order لهذا
+
+53
+00:05:34,380 --> 00:05:39,160
+بدي أروح أرفع لل أس واحد والأس اتنين والأس تلاتة
+
+54
+00:05:39,160 --> 00:05:45,560
+لغاية موصل لمين لل identity element فمثلًالو بد
+
+55
+00:05:45,560 --> 00:05:50,380
+الاتنين زاد ال sub group generated by ستة لكل
+
+56
+00:05:50,380 --> 00:05:56,100
+تربيع تاني اللي هو حاصل ضرب الاتنين يعني حاصل
+
+57
+00:05:56,100 --> 00:06:00,640
+جامعة الاتنين يعني اتنين مضروبة في هذا ال element
+
+58
+00:06:00,640 --> 00:06:05,910
+لأن ال operation عملية جامعةيبقى هذا عبارة عن مين
+
+59
+00:06:05,910 --> 00:06:11,150
+عبارة عن أربعة زي ال sub group generated by ستة لا
+
+60
+00:06:11,150 --> 00:06:15,770
+يساوي ال identity element يبقى بناء عليه بدي أخد
+
+61
+00:06:15,770 --> 00:06:21,410
+اتنين زي ال sub group generated by ستة الكل تكعيب
+
+62
+00:06:21,410 --> 00:06:26,350
+يبقى هذا بدي يساوي ستة زي ال sub group generated
+
+63
+00:06:26,350 --> 00:06:32,940
+by ستة جدش يعطيني هذا؟6 itself يبقى ال order لهذا
+
+64
+00:06:32,940 --> 00:06:37,720
+ال element يساوي تلاتة يبقى هذا الكلام يعطيني ان
+
+65
+00:06:37,720 --> 00:06:42,840
+ال order لإتنين زائد subgroup generated by ستة is
+
+66
+00:06:42,840 --> 00:06:47,600
+equal to three و هكذا يبقى كيف بدنا نضرب كيف بدنا
+
+67
+00:06:47,600 --> 00:06:53,780
+نجمع كيف بدنا نسوي هي مثال قدامك طيب نيجي ناخد
+
+68
+00:06:53,780 --> 00:06:56,160
+مثال example three
+
+69
+00:07:02,940 --> 00:07:13,320
+بقول الات ال G تساوي D4 and ال sub group اللي هي K
+
+70
+00:07:13,320 --> 00:07:20,740
+هي ال sub group generated by R 180 طبعا هذه لا
+
+71
+00:07:20,740 --> 00:07:27,220
+يوجد فيها إلا عنصرين اللي هو ال R نود وال R 180
+
+72
+00:07:27,220 --> 00:07:34,160
+اظن كمان هي هذا ال centerتبع الـ D4 ولا لأ؟ خلّينا
+
+73
+00:07:34,160 --> 00:07:38,620
+نجرب هكذا إنه لو كانت الـ Z لـ D N يا فيها الـ
+
+74
+00:07:38,620 --> 00:07:43,800
+Identity فقط يا إما فيها الـ Identity و الـ 180
+
+75
+00:07:43,800 --> 00:07:49,980
+حسب الـ D هذه هل هي حسب الـ N؟ هل هي odd و لا
+
+76
+00:07:49,980 --> 00:07:57,460
+even؟ يبقى بالشكل اللي عندنا هذا بدنا find the
+
+77
+00:07:57,460 --> 00:08:04,590
+elements ofطبعا في هذا الكلام بده يعطينا مدام هذي
+
+78
+00:08:04,590 --> 00:08:11,650
+هيك بالشكل اللي عندنا هنا Z of D4 السؤال هو هل هذه
+
+79
+00:08:11,650 --> 00:08:17,130
+normal subgroup من D4؟ ليش؟ لأن عناصرها دائما
+
+80
+00:08:17,130 --> 00:08:23,210
+تتعامل مع جميع عناصر الجروم وقد أخذناهم مثلا سابقا
+
+81
+00:08:23,210 --> 00:08:31,840
+يبقى بجي بقوله thenالـ K is normal subgroup في D4
+
+82
+00:08:31,840 --> 00:08:43,840
+يبقى find the elements بدنا عناصر of D4 modulo K
+
+83
+00:08:43,840 --> 00:08:47,720
+يبقى عناصر ال factor group اللي عندنا هذه
+
+84
+00:08:54,650 --> 00:08:58,190
+يبقى بدأ اروح ادور على عناصر ال factor group اللى
+
+85
+00:08:58,190 --> 00:09:02,750
+عندنا هنا الاول شىء بدأ اعرف قداش فيها عناصر قبل
+
+86
+00:09:02,750 --> 00:09:08,850
+ما اروح ادورطب العناصر تبعتها كل ال lift cosets أو
+
+87
+00:09:08,850 --> 00:09:15,050
+كل distance lift cosets يبقى ال order ل D4 modulo
+
+88
+00:09:15,050 --> 00:09:22,990
+K بده سوى ال order ل D4 maximum على ال order ل K
+
+89
+00:09:22,990 --> 00:09:28,790
+هذه تمانيةوهذه اتنين يبقى عدد العناصر فيها يساوي
+
+90
+00:09:28,790 --> 00:09:34,690
+قدرت اربعة عناصر بدي اروح ادور على هذه العناصر
+
+91
+00:09:34,690 --> 00:09:40,790
+يبقى بدي ابدأ بال liftco6 الأولى طبعا ارنود وR180
+
+92
+00:09:40,790 --> 00:09:46,330
+لو ضربتها في K بتظلها كما هي يبقى بقولها صفع شجة و
+
+93
+00:09:46,330 --> 00:09:52,840
+بروح اخد R90 في main في ال Kيبقى بدأ ضربها في
+
+94
+00:09:52,840 --> 00:09:59,920
+العناصر اللي جوا بصير R90 و هذه R90 في R180 اللي
+
+95
+00:09:59,920 --> 00:10:11,200
+يبقى داشر R270 هي بالضبط تماما كمان R278 في K يبقى
+
+96
+00:10:11,200 --> 00:10:14,840
+هدول مش تنتهي ال left coset سواء إنما في الحقيقة
+
+97
+00:10:14,840 --> 00:10:22,280
+left coset واحدةبالمثل بدي اروح اجيب له مين ال H
+
+98
+00:10:22,280 --> 00:10:29,200
+في K هذا الكلام بده يساوي اللي هو لما اضرب ال H في
+
+99
+00:10:29,200 --> 00:10:37,040
+R node بتعطينا H او هنا بتعطينا H في R 180 بالشكل
+
+100
+00:10:37,040 --> 00:10:42,850
+اللي عندنا هذاهذا الكلام بده يساوي ال H هنا عندك
+
+101
+00:10:42,850 --> 00:10:46,990
+في ال جدول في صفحة واحد و تمانين ال H في ال R مية
+
+102
+00:10:46,990 --> 00:10:54,250
+و تمانين اللي هي main of V وتساوي كذلك ال V في K
+
+103
+00:10:54,250 --> 00:10:59,950
+لإن لو ضربت ال V في K بصير هنا V و هنا V بR مية و
+
+104
+00:10:59,950 --> 00:11:04,210
+تمانين اللي هي عبارة عن main ع ال H يبقى صاروا
+
+105
+00:11:04,210 --> 00:11:11,700
+تنتين و ليست واحدةبالمثل لو روحت جبت له ال D في
+
+106
+00:11:11,700 --> 00:11:18,900
+main في ال K يبقى هذه بدها تعطيك D و هنا D في R
+
+107
+00:11:18,900 --> 00:11:25,660
+مية و تمانين هذه بدها تعطيك D و D Prime و اللي هي
+
+108
+00:11:25,660 --> 00:11:31,800
+بدها تساوي D Prime كذلك K يبقى أصبح عندي the
+
+109
+00:11:31,800 --> 00:11:33,740
+elements
+
+110
+00:11:36,580 --> 00:11:43,360
+The elements of D4
+
+111
+00:11:43,360 --> 00:11:50,720
+modulo K R ال element الأول اللي هو ال K itself
+
+112
+00:11:50,720 --> 00:11:57,140
+وال element التاني اللي هو ال R تسعين في ال K اللي
+
+113
+00:11:57,140 --> 00:12:02,720
+بده يساوي R متين وسبعين في K وال element التالت
+
+114
+00:12:02,720 --> 00:12:08,300
+اللي هو ال HKو ال element الرابع والاخير اللي هو
+
+115
+00:12:08,300 --> 00:12:14,220
+dk يبقى هي الأربعة عناصر اللي موجودة عندنا والتي
+
+116
+00:12:14,220 --> 00:12:19,460
+تمثل عناصر ال factor group اللي عندنا بالضبط تماما
+
+117
+00:12:19,460 --> 00:12:26,620
+طيب اللي خاطر أعطيك exercise هك exercise لو قلت لك
+
+118
+00:12:26,620 --> 00:12:35,490
+little g تساوي d for itself andخد لي ال H هي ال
+
+119
+00:12:35,490 --> 00:12:47,270
+sub group generated by R تسعين السؤال هو is ال
+
+120
+00:12:47,270 --> 00:12:59,970
+D for is D for modulo H exist هل هذه موجودة if so
+
+121
+00:13:01,510 --> 00:13:05,110
+if so find it
+
+122
+00:13:07,500 --> 00:13:12,220
+إذا كان الأمر كذلك بدنا إياها طبعا ال subgroup
+
+123
+00:13:12,220 --> 00:13:16,500
+generated by R تسعين فيها جداش كام عنصر؟ أربع
+
+124
+00:13:16,500 --> 00:13:21,420
+عناصر و D4 فيها جداش تمان عناصر يبقى ال index لها
+
+125
+00:13:21,420 --> 00:13:25,800
+جداش مرة اللي فاتت أخدنا لو ال group ال index لها
+
+126
+00:13:25,800 --> 00:13:29,180
+أو ال subgroup ال index لها يساوى اتنين إيش بتكون
+
+127
+00:13:29,180 --> 00:13:33,360
+هذه؟ إيش بتكون؟ normal subgroup مدام normal
+
+128
+00:13:33,360 --> 00:13:38,010
+subgroup يبقى ال factor group existما دام exist
+
+129
+00:13:38,010 --> 00:13:41,670
+هذا جواب السؤال اول يوم نهلك شفوي بدنا نعرف من
+
+130
+00:13:41,670 --> 00:13:47,470
+هالعنصرين فقط اللي موجودين في main في ال factor a
+
+131
+00:13:47,470 --> 00:13:52,190
+group هذا بالنسبة اللي عندنا نيجي ناخد مثال اخر
+
+132
+00:14:11,040 --> 00:14:17,680
+مثال رقم أربعة بيقول
+
+133
+00:14:17,680 --> 00:14:28,420
+little g بدها تساوي A4 and ال H is a subgroup من
+
+134
+00:14:28,420 --> 00:14:38,780
+مين؟ من G where حيث ال H هذه فيها العناصر التالية
+
+135
+00:14:39,460 --> 00:14:47,660
+identity element واحد اتنين تلاتة اربعة العنصر
+
+136
+00:14:47,660 --> 00:14:52,880
+اللي بعده واحد تلاتة اتنين اربعة واحد تلاتة اتنين
+
+137
+00:14:52,880 --> 00:15:00,240
+اربعة العنصر اللي بعده واحد اربعة اتنين تلاتة واحد
+
+138
+00:15:00,240 --> 00:15:06,540
+اربعة اتنين تلاتة بالشكل اللي عندنا هذا number a
+
+139
+00:15:06,540 --> 00:15:16,060
+show thatبيّلي ان ال H is a normal subgroup من من
+
+140
+00:15:16,060 --> 00:15:27,760
+ال G نمرة B show that بيّلي ان ال A for modulo H
+
+141
+00:15:27,760 --> 00:15:31,640
+is cyclic
+
+142
+00:16:01,560 --> 00:16:09,740
+الان مواطين الجيه هي ال a4 من ال a4 هذي ممتاز جدا
+
+143
+00:16:09,740 --> 00:16:14,760
+يبقى هذي the sixth of all even permutations of s4
+
+144
+00:16:14,760 --> 00:16:21,810
+عدد أنصارها كدهش؟12 عنصر تمام يبقى عدد ال A4 12
+
+145
+00:16:21,810 --> 00:16:26,530
+عنصر أخدنا ال subgroup منها ال subgroup اللي هي H
+
+146
+00:16:26,530 --> 00:16:31,710
+زي ما انت شايف بنقل عليه بسأل السؤال هل ال H هذي
+
+147
+00:16:31,710 --> 00:16:37,510
+normal subgroup من G ام لاإن كانت عامة إذا كانت
+
+148
+00:16:37,510 --> 00:16:45,410
+عامة إذا كانت عامة إذا كانت عامة
+
+149
+00:16:45,410 --> 00:16:47,170
+إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+150
+00:16:47,170 --> 00:16:47,450
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+151
+00:16:47,450 --> 00:16:47,470
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+152
+00:16:47,470 --> 00:16:47,730
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+153
+00:16:47,730 --> 00:16:47,730
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+154
+00:16:47,730 --> 00:16:47,730
+عامة إذا كانت عامة إذا كانت عامة إذا كانت عامة إذا
+
+155
+00:16:47,730 --> 00:16:48,330
+كانت عامة إذا كانت عامة إذا كانت عامة إذا كانت
+
+156
+00:16:48,330 --> 00:17:00,070
+عامة إذا كانت عامة إذا كانت عامة إذا
+
+157
+00:17:00,070 --> 00:17:08,110
+كانت عامةقداش ال order لأي element موجود في H او
+
+158
+00:17:08,110 --> 00:17:14,690
+او اربعة او تلاتة يعني اتنين او اربعة او تلاتة
+
+159
+00:17:14,690 --> 00:17:20,970
+عناصر ليليتش هيهم قدامك قداش ال اتنين او اربعة بس
+
+160
+00:17:20,970 --> 00:17:26,850
+اتنين مافيش غير واحد مافيش واحد يعنييبقى ال order
+
+161
+00:17:26,850 --> 00:17:33,370
+إلا واحد أو اتنين ال least common multiple لمين لل
+
+162
+00:17:33,370 --> 00:17:38,230
+cycles اللي عندنا يبقى ال order يا إما واحد يا إما
+
+163
+00:17:38,230 --> 00:17:44,550
+اتنين لا يزيد عن ذلك طبعاهذه ممكن تعمل فيها
+
+164
+00:17:44,550 --> 00:17:47,250
+composition وهذه ممكن تعمل فيها composition ان
+
+165
+00:17:47,250 --> 00:17:51,650
+كانت تقدر طبعا هذه مفيش إمكانية هذه مفيش إمكانية
+
+166
+00:17:51,650 --> 00:17:56,190
+هذه كمان مفيش إمكانية يبقى هؤلاء الارديس جاينت
+
+167
+00:17:56,190 --> 00:17:59,390
+سايكل يبقى ال اسكومة الملطبة اللي طول كل واحدة
+
+168
+00:17:59,390 --> 00:18:02,030
+منهم الاسكومة اللي طول الاتنين والاتنين اللي هو B2
+
+169
+00:18:02,630 --> 00:18:10,430
+يبقى هدول كمان هدول كل العناصر اللي في A4 واللي ال
+
+170
+00:18:10,430 --> 00:18:16,410
+order اللي لهم يساوي اتنين صح يعني انت لو روحت
+
+171
+00:18:16,410 --> 00:18:21,470
+للتفصيلات تبعت A4 في صفحة 107 من الكتاب 107 من
+
+172
+00:18:21,470 --> 00:18:28,330
+الكتاب حطلك كل عناصر ال A4 ل 12 صفهملك صف هدول فقط
+
+173
+00:18:28,630 --> 00:18:33,710
+هم اللي ال order لهم يساوي واحد او اتنين غير هيك
+
+174
+00:18:33,710 --> 00:18:37,430
+ما جابش هايب الأوضة ومعظمها كلهم جابوا مياه قدامهم
+
+175
+00:18:37,430 --> 00:18:47,850
+يبقى أول شغلة observe that observe that لاحظ ان ال
+
+176
+00:18:47,850 --> 00:18:53,610
+elements of
+
+177
+00:18:53,610 --> 00:18:58,290
+h are all
+
+178
+00:19:01,630 --> 00:19:14,830
+الأشياء من A4 التي لديها أردم 2 او 1
+
+179
+00:19:18,250 --> 00:19:23,730
+يبقى عناصر اتش هما كل عناصر a4 اللي ال order لهم
+
+180
+00:19:23,730 --> 00:19:28,050
+يساوي اما اتنين او احد طبعا ال order اللي هذه
+
+181
+00:19:28,050 --> 00:19:30,430
+اتنين ال order اللي هذه اتنين ال order اللي هذه
+
+182
+00:19:30,430 --> 00:19:35,990
+اتنين ال order اللي هذه واحد تمام يبقى هدول كلهم
+
+183
+00:19:35,990 --> 00:19:39,270
+عناصر a4 بلاستيثناء
+
+184
+00:19:42,420 --> 00:19:50,300
+هذا المعلومة لازمان تكون عامة لازمان تكون عامة
+
+185
+00:19:55,440 --> 00:19:58,680
+و اثبت ان حاصر ال element تبع ال G في ال element
+
+186
+00:19:58,680 --> 00:20:02,120
+تبع ال H في معكوس ال element تبع ال G بدي يكون
+
+187
+00:20:02,120 --> 00:20:08,260
+موجود وين في H ممتاز اذا يبقى انا بروح اقوله خدلي
+
+188
+00:20:08,260 --> 00:20:15,080
+Alpha موجودة في ال A4 و ال Alpha does not belong
+
+189
+00:20:15,080 --> 00:20:21,940
+to H بدي اخدها من وين من خارج ال H and ال Beta
+
+190
+00:20:21,940 --> 00:20:29,210
+موجودة وين في Hيبقى انا اخدت alpha موجودة في a4 و
+
+191
+00:20:29,210 --> 00:20:34,710
+خارج h واخدت ال b موجودة في h موجودة في اين؟
+
+192
+00:20:34,710 --> 00:20:43,380
+موجودة في h موجودة في h ولا لا؟ بمعنى اخروالله إن
+
+193
+00:20:43,380 --> 00:20:47,120
+كان ال alpha beta alpha يتشيل كل تربيع يعطاني ال
+
+194
+00:20:47,120 --> 00:20:52,640
+identity إذا ال order يسوى اتنين إذا هتكون واحد من
+
+195
+00:20:52,640 --> 00:20:58,440
+هدول يبقى بتكون one بتكون فائدة يبقى هنا ال order
+
+196
+00:20:58,440 --> 00:21:04,110
+لا بيقدرشتانية لانها موجودة في H لانه في H كل واحد
+
+197
+00:21:04,110 --> 00:21:09,110
+ال order له يساوي اتنين يبقى بداجي اخدله الان
+
+198
+00:21:09,110 --> 00:21:15,430
+Alpha Beta Alpha Inverse لكل تربية هي Alpha Beta
+
+199
+00:21:15,430 --> 00:21:21,440
+Alpha Inverse Alpha Beta Alpha Inverseهذا التربية
+
+200
+00:21:21,440 --> 00:21:26,520
+تبعها الآن من خاصية ال associativity هذه Alpha
+
+201
+00:21:26,520 --> 00:21:33,520
+Beta في Alpha Inverse Alpha في Beta Alpha Inverse
+
+202
+00:21:33,520 --> 00:21:38,060
+خاصية ال associativity دمجت اتنين هدول مالهم مع
+
+203
+00:21:38,060 --> 00:21:41,640
+بعض طب هذا العنصر في المعكس هو مش بيعطينا ال
+
+204
+00:21:41,640 --> 00:21:47,180
+identity يبقى بروح مع السلامة يبقى بصير Alpha Beta
+
+205
+00:21:47,180 --> 00:21:53,500
+تربيع Alpha Inverseبيتا تربية أبجداش لأنها موجودة
+
+206
+00:21:53,500 --> 00:22:00,540
+وين في H يبقى هذا الكلام بده يساوي alpha ال
+
+207
+00:22:00,540 --> 00:22:07,780
+identity في ال alpha inverse السبب because ان ال
+
+208
+00:22:07,780 --> 00:22:14,060
+order ل beta بده يساوي جداش بده يساوي اتنينهذا
+
+209
+00:22:14,060 --> 00:22:18,020
+البرنامج سيعطينا الـ Alpha Alpha Inverse اللي هو
+
+210
+00:22:18,020 --> 00:22:21,000
+الـ Main الـ Identity احنا حطيناها بواحد ولا
+
+211
+00:22:21,000 --> 00:22:25,880
+نغيرها يبقى عدلها بواحد يبقى هذا البرنامج سيعطينا
+
+212
+00:22:25,880 --> 00:22:30,710
+الـ Main اللي هو بواحد صحيح يبقى بناء عليههذا
+
+213
+00:22:30,710 --> 00:22:36,170
+سيعطينا ان ال order ل alpha beta alpha inverse هو
+
+214
+00:22:36,170 --> 00:22:43,370
+اتنين هذا معناه ان ال alpha beta alpha inverse
+
+215
+00:22:43,370 --> 00:22:46,910
+موجودة في normal subgroup
+
+216
+00:22:59,830 --> 00:23:06,380
+هذا الحل اللي حلناه هو المطموب الأول نمرا aالمطموب
+
+217
+00:23:06,380 --> 00:23:12,220
+التاني نمرا بي بيقول لي في نمرا بي اثبتلي ان ال
+
+218
+00:23:12,220 --> 00:23:17,120
+factor group اللي عندنا هذه is a cyclic group
+
+219
+00:23:17,120 --> 00:23:25,220
+بقولك خيص تعالى نشوف قداش ال order لل a for modulo
+
+220
+00:23:25,220 --> 00:23:32,140
+h اللي بقول عليهايبقى هذا بده يساوي ال order لل a4
+
+221
+00:23:32,140 --> 00:23:37,480
+على ال order لل h هذه عبارة عن اتناشر على اربع
+
+222
+00:23:37,480 --> 00:23:42,380
+يساوي كدهش والتلاتة
+
+223
+00:23:42,380 --> 00:23:52,590
+is prime نرجع لمين نرجع لخدنا نظرية مشهورة قلنا في
+
+224
+00:23:52,590 --> 00:23:57,050
+الجبر نظرية الـ grunge و ال crawlers اللي عليها ال
+
+225
+00:23:57,050 --> 00:24:01,870
+crawlers رقمتهم كان بيقولي إذا كان ال order لل
+
+226
+00:24:01,870 --> 00:24:06,550
+group أو لل sub group ال prime number يبقى هي ..
+
+227
+00:24:06,550 --> 00:24:16,750
+هي cyclic group يبقى by her previous crawlery
+
+228
+00:24:19,010 --> 00:24:26,770
+اللي هي اتنين على نظرية Lagrange we have ان ال a4
+
+229
+00:24:26,770 --> 00:24:35,790
+modulo h is cyclic طيب
+
+230
+00:24:35,790 --> 00:24:45,560
+حابب اتعرف على شكل العناصر check thatتأكدلي ان ال
+
+231
+00:24:45,560 --> 00:24:53,820
+a4 modulo h عناصرها اللي هم على الشكل التالي ال h
+
+232
+00:24:53,820 --> 00:25:03,560
+واحد اتنين تلاتة في h واحد تلاتة اتنين في h كيف
+
+233
+00:25:03,560 --> 00:25:12,180
+بدي اعرفها؟يبقى بدي أمسك العناصر من خارج H لإن أي
+
+234
+00:25:12,180 --> 00:25:15,660
+عنصر ما نشتغله في H بده تطلع نفس ال H إذا كتروح
+
+235
+00:25:15,660 --> 00:25:22,100
+اجيب للعناصر اللي ضايلة في A4 صفحة 107 وتضربهم وين
+
+236
+00:25:22,100 --> 00:25:26,800
+تضرب من في العناصر اللي عندك دائما وابنا حيطلع
+
+237
+00:25:26,800 --> 00:25:33,870
+واحد من التلاتة دول إذا لازم أجيبها لكأى حاجة
+
+238
+00:25:33,870 --> 00:25:42,110
+بتلزم كجدول بيجيبوها لك انا بديك تبقى فاهم وليس
+
+239
+00:25:42,110 --> 00:25:47,870
+حافظ تمام يبقى ال a for module h اللي عناصره h
+
+240
+00:25:47,870 --> 00:25:53,690
+واحد اتنين تلاتة h واحد تلاتة اتنين h طب السؤال هو
+
+241
+00:25:53,690 --> 00:25:57,230
+كداش ال order لهذه ال element
+
+242
+00:26:05,570 --> 00:26:17,390
+أربعة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة ستة
+
+243
+00:26:17,390 --> 00:26:21,630
+ستة
+
+244
+00:26:23,010 --> 00:26:27,830
+يا واحد يا تلاتة وغير هيك مافيش فيش بالمرة واحد هي
+
+245
+00:26:27,830 --> 00:26:31,830
+يبقى غصب عني وعنك ال order إلى يسوى تلاتة الحين
+
+246
+00:26:31,830 --> 00:26:35,750
+هذه لم تجد طولها تلاتة المهوض لما تقولي تربية تبدأ
+
+247
+00:26:35,750 --> 00:26:39,610
+تربع هذه وهذه ثابتة تقولي تكعيد الكعب هذه وهذه
+
+248
+00:26:39,610 --> 00:26:43,870
+ثابتة هذه طولها يسوى تلاتة يعني ال order إلى يسوى
+
+249
+00:26:43,870 --> 00:26:48,070
+تلاتة يبقى ال order لكل واحد من هذول تلاتة يبقى كل
+
+250
+00:26:48,070 --> 00:26:53,990
+واحدعبارة عن generator لمن؟ لل group اللي عندنا
+
+251
+00:26:53,990 --> 00:27:03,170
+يعني يبقى باجي بقول clearly كمان انه الواحد اتنين
+
+252
+00:27:03,170 --> 00:27:14,650
+تلاتة each and clearly انه each ofه of الواحد
+
+253
+00:27:14,650 --> 00:27:24,930
+اتنين تلاتة في h and واحد تلاتة اتنين في h is a
+
+254
+00:27:24,930 --> 00:27:36,580
+generator for ال a4 modulo h والسبب becauseإن ال
+
+255
+00:27:36,580 --> 00:27:44,760
+order للواحد اتنين ثلاثة في H بده يساوي ال order
+
+256
+00:27:44,760 --> 00:27:51,780
+للواحد تلاتة اتنين في H بده يساوي كده تلاتة يبقى
+
+257
+00:27:51,780 --> 00:27:55,580
+كل واحد فيهم عبارة عن generator
+
+258
+00:27:59,280 --> 00:28:04,300
+طب خلّيني أسأل كل واحد معكوس لنفسه و الله واحد
+
+259
+00:28:04,300 --> 00:28:10,640
+فيهم معكوس التاني بمعنى هل الواحد اتنين تلاتة و
+
+260
+00:28:10,640 --> 00:28:15,620
+الواحد تلاتة اتنين معكوس لنفسه كل واحد و الله
+
+261
+00:28:15,620 --> 00:28:19,820
+اتنين معكوسة لبعض تعالوا اضربهم في بعض الواحد
+
+262
+00:28:19,820 --> 00:28:24,800
+بيروح لوين و التلاتة بيروح لمين صف على شجر ال
+
+263
+00:28:24,800 --> 00:28:28,850
+identity الواحد را على الواحدبنمسك التلاتة بتروح
+
+264
+00:28:28,850 --> 00:28:34,190
+لمين؟ لاتنين و الاتنين بتروح صف على شج ال identity
+
+265
+00:28:34,190 --> 00:28:37,950
+الاتنين بيروح للواحد و الواحد بيروح لاتنين يبقى ال
+
+266
+00:28:37,950 --> 00:28:43,630
+identity يبقى كل واحد فيهم معكوس للآخر و ليس معكوس
+
+267
+00:28:43,630 --> 00:28:51,040
+لنفسهإذا الـ element هذا في حد ذاته هو معكوس لمن؟
+
+268
+00:28:51,040 --> 00:28:57,480
+لهذا ال element وفي نفس الوقت ال element هذا كله
+
+269
+00:28:57,480 --> 00:29:03,160
+هو معكوس لهذا ال element في ال factor group لأن لو
+
+270
+00:29:03,160 --> 00:29:12,730
+ضربتهم في بعضهم سأحصل على ال identitynot that ان
+
+271
+00:29:12,730 --> 00:29:22,690
+الواحد اتنين تلاتة each is the inverse of الواحد
+
+272
+00:29:22,690 --> 00:29:24,870
+تلاتة اتنين each because
+
+273
+00:29:28,030 --> 00:29:33,110
+لو ضربت في بعض بدي أطين مين ال identity element في
+
+274
+00:29:33,110 --> 00:29:39,630
+H في 1 3 2 H حسب التعريف على ال factor group ال
+
+275
+00:29:39,630 --> 00:29:44,090
+operation قولنا بنضرب ال two elements في بعض يبقى
+
+276
+00:29:44,090 --> 00:29:54,540
+123 132 في H ويساوينمسك الأول مرة تانية الواحد
+
+277
+00:29:54,540 --> 00:30:00,420
+صورته تلاتة والتلاتة صورتها واحد يبقى ماعنديش إلا
+
+278
+00:30:00,420 --> 00:30:05,780
+الواحد نمسك اللي بعده اتنين اتنين صورته واحد
+
+279
+00:30:05,780 --> 00:30:11,540
+والواحد صورته اتنين يبقى جافلة نمسك التلاتة تلاتة
+
+280
+00:30:11,540 --> 00:30:16,930
+صورتها اتنين واتنين صورتها تلاتة يبقى جافلةوهذا
+
+281
+00:30:16,930 --> 00:30:22,850
+الـ main الـ H اللي بتعطيك الـ H itself لأن هذا
+
+282
+00:30:22,850 --> 00:30:28,890
+كله بال identity element يبقى بناء عليه فعلا هذا
+
+283
+00:30:28,890 --> 00:30:33,470
+ال element هو معكوس لمين؟ معكوس لل element اللي
+
+284
+00:30:33,470 --> 00:30:34,550
+عندنا هذا
+
+285
+00:30:52,470 --> 00:31:00,730
+يبقى هذا كان مثال أربعة مثال
+
+286
+00:31:00,730 --> 00:31:01,470
+خمسة
+
+287
+00:31:06,680 --> 00:31:14,420
+بقول لطل جي تده تساوي يوتنين و تلاتين اللي عناصرها
+
+288
+00:31:14,420 --> 00:31:22,540
+طبعا اللي هي واحد و تلاتة و خمسة و سبعة و تمانية
+
+289
+00:31:22,540 --> 00:31:39,910
+تسعة عشرة احداش تلتاش اربعتاش خمستاش15 16 17 19 20
+
+290
+00:31:39,910 --> 00:32:00,830
+21 20 23 بعد 23 24 25 27 28 29 31 مافيش غيرهاطيب
+
+291
+00:32:00,830 --> 00:32:06,930
+هذا بده يعطيني ان ال order لليو اتنين و تلاتين بده
+
+292
+00:32:06,930 --> 00:32:12,030
+يساوي واحد اتنين تلاتة اربعة خمسة ستة سبعة تمانية
+
+293
+00:32:12,030 --> 00:32:15,550
+تسعة عشر احداشر اتناشر تلاتاشر اربعاشر خمساشر
+
+294
+00:32:15,550 --> 00:32:20,730
+ستاشر عنصر في ال group اللي عندنا هنا بدنا نروح
+
+295
+00:32:20,730 --> 00:32:26,980
+ناخد sub group منها letالـ H هي الـ subgroup
+
+296
+00:32:26,980 --> 00:32:32,420
+generated by خمستاشر واللي مافيش فيها إلا العنصرين
+
+297
+00:32:32,420 --> 00:32:41,000
+واحد وخمستاشر السؤال هو هل الـ H هذي abelian؟ الـ
+
+298
+00:32:41,000 --> 00:32:46,150
+H just a normal subgroup من الـ U تلاتة؟نعم لأن
+
+299
+00:32:46,150 --> 00:32:52,690
+هذيك ال U اتنين و تلاتين is a billion يبقى then ال
+
+300
+00:32:52,690 --> 00:32:59,110
+H is a normal subgroup من ال U اتنين و تلاتين
+
+301
+00:32:59,110 --> 00:33:07,010
+because السبب because ان U اتنين و تلاتين is a
+
+302
+00:33:07,010 --> 00:33:11,990
+billionمعناته بقدر اكوّن ال factor group يعني ال
+
+303
+00:33:11,990 --> 00:33:18,650
+factor group exist يبقى هذا بده يعطيك ان ال U 32
+
+304
+00:33:18,650 --> 00:33:29,290
+modulo H modulo H exist موجودة السؤال هوطب بنقدر
+
+305
+00:33:29,290 --> 00:33:34,730
+نجيب عناصرها قبل السؤال يبقى ال order ليه 32
+
+306
+00:33:34,730 --> 00:33:42,390
+modulo h بده يساوي اللي هو 16 على قداش على 2 و
+
+307
+00:33:42,390 --> 00:33:48,630
+يساوي 8 يبقى هذا ال group هذه فيها ثمانية عناصر
+
+308
+00:33:48,630 --> 00:33:52,230
+اسمع السؤال ال question is
+
+309
+00:33:58,580 --> 00:34:09,400
+السؤال هو هل is الجي موديلو H ايزو مارفك لزد
+
+310
+00:34:09,400 --> 00:34:12,160
+تمانية ولا زد
+
+311
+00:34:35,940 --> 00:34:43,120
+طيب نرجع لسوالنا مرة تانيةبقول لي احنا جه أخدنا ال
+
+312
+00:34:43,120 --> 00:34:47,540
+U32 أخدنا ال subgroup generated by خمساش اللي
+
+313
+00:34:47,540 --> 00:34:53,220
+فيهاش اللي غير عنصرين واحد وخمساش وخمستاشر تربيع
+
+314
+00:34:53,220 --> 00:35:02,080
+متين وخمسة وعشرين اللي هي عبارة عن واحد في U32لأن
+
+315
+00:35:02,080 --> 00:35:09,100
+الـ 224 هي مضاعفات 32 يبقى مافيش فيها إلا عنصرين
+
+316
+00:35:09,100 --> 00:35:13,780
+any subgroup من الabelian group is normal يبقى ال
+
+317
+00:35:13,780 --> 00:35:18,000
+subgroup اللي أخدناها normal subgroup من ال U32
+
+318
+00:35:18,000 --> 00:35:23,420
+يبقى ال factor group exist وفيها ثمانية عناصر
+
+319
+00:35:23,730 --> 00:35:30,010
+السؤال هو هل ال G-modulation isomorphic ل Z8 ولا ل
+
+320
+00:35:30,010 --> 00:35:35,050
+Z4 external product مع Z2 ولا ل Z2 external
+
+321
+00:35:35,050 --> 00:35:40,730
+product مع Z2 external product مع Z2 كذلك أم لا؟
+
+322
+00:35:40,730 --> 00:35:46,920
+هذه تمان عناصر هذه تمان عناصرهذه تمام عناصر تمام
+
+323
+00:35:46,920 --> 00:35:52,680
+التمام بدنا نيجي نشوف مين نستبعد ومين نخليه قداش
+
+324
+00:35:52,680 --> 00:35:57,560
+أكبر order لأي element موجود هنا تمانية تمانية
+
+325
+00:35:57,560 --> 00:36:03,960
+قداش أكبر order لأي element هنا كداش أربعة مزيدش
+
+326
+00:36:03,960 --> 00:36:06,740
+عن أربعة اللي هو least common multiple للأربعة
+
+327
+00:36:06,740 --> 00:36:10,620
+واتنين أو للأربعة والواحد سيام قداش ال maximum
+
+328
+00:36:10,620 --> 00:36:14,510
+order لأي element هنا اتنينيبقى اكبر واحد هناك
+
+329
+00:36:14,510 --> 00:36:19,050
+تمانية اكبر واحد اتنين واكبر واحد هنا اربع طب
+
+330
+00:36:19,050 --> 00:36:24,590
+السؤال هو الجي موديل H فيها ثمانية عناصر لو روحت
+
+331
+00:36:24,590 --> 00:36:29,770
+عناصرها كلهم lift كو ستة لو روحت للأور السبع lift
+
+332
+00:36:29,770 --> 00:36:34,730
+كو ستة و لجيته يساوي تمانية معناته هذا generator
+
+333
+00:36:34,730 --> 00:36:39,470
+وبالتالي isomorphic لزيد تمانية لكن اذا ما لجيتش
+
+334
+00:36:39,470 --> 00:36:44,600
+فيهاولا generator إذا لا يمكن أن تكون isomorphic
+
+335
+00:36:44,600 --> 00:36:49,580
+لميعنى لزيت تمانية بيظل احتمال هنا يا اما لزيت
+
+336
+00:36:49,580 --> 00:36:52,440
+اربعة كسن داية product مع زيت اتنين او زيت اتنين
+
+337
+00:36:52,440 --> 00:36:55,700
+كسن داية product مع زيت اتنين كسن داية product مع
+
+338
+00:36:55,700 --> 00:37:01,600
+زيت اتنين الثانية لذلك هذه العناصر قداميكلها
+
+339
+00:37:01,600 --> 00:37:07,260
+نستطيع ان نحصل على left coset اول واحدة تبقى الاول
+
+340
+00:37:07,260 --> 00:37:11,800
+واحد بتضرب التلاتة في K في H مش هذي left coset
+
+341
+00:37:11,800 --> 00:37:18,600
+كذلك يعني احد عناصر من ال group الان بداجي اقوله
+
+342
+00:37:18,600 --> 00:37:26,880
+تلاتة H هذي موجودة في ال U تنين وتلاتين modulo
+
+343
+00:37:26,880 --> 00:37:35,790
+اللي هو من Hلو جيت تلاتة H هل هذه تساوي H تسلف؟
+
+344
+00:37:35,790 --> 00:37:40,950
+يعني لو ضربت هنا في من في تلاتة بصير تلاتة و تلاتة
+
+345
+00:37:40,950 --> 00:37:45,470
+في خمستاشر بخمسة واربعين شيء اللي بيبقى تلتاش هل
+
+346
+00:37:45,470 --> 00:37:52,790
+هي H؟ لأ اتنين لو جيت قلتلك تلاتة H لكل تربيع
+
+347
+00:37:55,240 --> 00:37:59,440
+أه يعني لو طلع ال identity اتنين هذي بتجسم
+
+348
+00:37:59,440 --> 00:38:03,620
+التمانية يعني ممكن مش في مشكلة هذا الكلام بده
+
+349
+00:38:03,620 --> 00:38:12,460
+يساوي تسعة H هل تسعة H تساوي H اضربها تسعة و هذي
+
+350
+00:38:12,460 --> 00:38:17,400
+تسعة في خمساش إذا لا يمكن أن تساوي مين H أخد تلاتة
+
+351
+00:38:17,400 --> 00:38:24,320
+H تكيبلأ لإن التلاتة لا تقسم مين التمانية يبقى
+
+352
+00:38:24,320 --> 00:38:27,420
+fish element ال order إله يسوي التلاتة يبقى ما
+
+353
+00:38:27,420 --> 00:38:36,620
+تغلبش حالك روح على مينعلى تلاتة H أُس أربعة يبقى
+
+354
+00:38:36,620 --> 00:38:41,060
+هذه عبارة عن قداش تسعة في تسعة بواحد و تمانين H
+
+355
+00:38:41,060 --> 00:38:45,400
+هذا الكلام يساوي تنين و تلاتين و تنين و تلاتين
+
+356
+00:38:45,400 --> 00:38:49,840
+أربعة و ستين من واحد و تمانين ستاشر و واحد و
+
+357
+00:38:49,840 --> 00:38:57,580
+سبعتاشر يبقى هذه سبعتاشر H هل السبعتاشر H بيساوي
+
+358
+00:38:57,580 --> 00:39:03,980
+H؟ لأيبقى سعر ال order لهذا ال element لا يمكن أن
+
+359
+00:39:03,980 --> 00:39:08,800
+يكون أربعة أروح أدور على خمسة وستة وسبعة يبقى
+
+360
+00:39:08,800 --> 00:39:13,020
+automatic ال order له سوى قداش تمانية لأن ال order
+
+361
+00:39:13,020 --> 00:39:16,100
+لل element اللي بيجسم لل order اللي جمده ماتحصل
+
+362
+00:39:16,100 --> 00:39:21,540
+على طول الخطة بنستنتجها يبقى هذا بده يعطينا أن ال
+
+363
+00:39:21,540 --> 00:39:27,480
+order لتلاتة H بده سوى قداش تمانية because
+
+364
+00:39:30,700 --> 00:39:36,000
+the order of
+
+365
+00:39:36,000 --> 00:39:46,880
+the element divide the order of the group
+
+366
+00:39:51,730 --> 00:39:55,870
+لأن ال order لل element بيجسم ال order لل group
+
+367
+00:39:55,870 --> 00:40:02,370
+يبقى لا يمكن ان انا اجد ال order خمسة ولا ستة ولا
+
+368
+00:40:02,370 --> 00:40:07,230
+سبعة اذا ال order يسوى كمان تمانية معناته هذا ال
+
+369
+00:40:07,230 --> 00:40:17,290
+element ماله generator يبقى هنا ال ثلاثة h is a
+
+370
+00:40:17,290 --> 00:40:19,150
+generator
+
+371
+00:40:20,550 --> 00:40:29,770
+Four اللي هو من ال U اتنين و تلاتين modulo H مدام
+
+372
+00:40:29,770 --> 00:40:36,150
+generator يبقى هذه مالها Cyclic يبقى هذا يعطينا ان
+
+373
+00:40:36,150 --> 00:40:45,570
+U اتنين و تلاتين U اتنين و تلاتين modulo 11 is
+
+374
+00:40:45,570 --> 00:40:51,500
+cyclicMadame Cyclic يبقى هل يمكن أن تكون
+
+375
+00:40:51,500 --> 00:40:56,460
+isomorphic لهذه لأن هذا أكبر order لها يساوي اتنين
+
+376
+00:40:56,460 --> 00:41:02,160
+isomorphic لهذه لأ لأن أكبر order عنها مين يساوي
+
+377
+00:41:02,160 --> 00:41:08,980
+أربعة يبقى هنا ال U تنين و تلاتي موديل أحداشر
+
+378
+00:41:08,980 --> 00:41:12,780
+isomorphic لزيد تمانية because
+
+379
+00:41:16,450 --> 00:41:31,430
+زد اربعة external like product مع زد اتنين has
+
+380
+00:41:31,430 --> 00:41:34,490
+no element
+
+381
+00:41:36,400 --> 00:41:43,400
+of order همان مافيش ولا عنصر يبقى هذي صارت
+
+382
+00:41:43,400 --> 00:41:51,220
+isomorphic لمين ل .. ل group اللي عندنا هذي الآن
+
+383
+00:41:51,220 --> 00:41:56,900
+بدنا نيجي لنظرية طبعا أخدت أمثلة لا بأس بها كثيرة
+
+384
+00:41:56,900 --> 00:42:01,700
+على ال normal و على ال factor group بنيجي لأول
+
+385
+00:42:01,700 --> 00:42:08,430
+نظرية في هذا الموضوع بتقولتالـ Center تبع الـ
+
+386
+00:42:08,430 --> 00:42:16,690
+Group G of
+
+387
+00:42:16,690 --> 00:42:22,430
+a
+
+388
+00:42:22,430 --> 00:42:30,570
+group G if الـ G Modulus Center بتبع الـ G is
+
+389
+00:42:30,570 --> 00:42:36,820
+cyclicthen الجي is abelian
+
+390
+00:43:06,770 --> 00:43:07,570
+خلّي بركة
+
+391
+00:43:10,260 --> 00:43:14,500
+عندنا Z of G الـ Center تبع لـ Group G وبنعرف الـ
+
+392
+00:43:14,500 --> 00:43:18,780
+Center اللي بيجمع كل العناصر الكميوس مع جميع عناصر
+
+393
+00:43:18,780 --> 00:43:23,120
+G بالاستثناء يبقى لو كانت الـ G modulo Z Cyclic
+
+394
+00:43:23,120 --> 00:43:29,000
+يبقى بنثبت له إنه G الأصلية is Abelian يبقى
+
+395
+00:43:29,000 --> 00:43:35,800
+المعطيات اللي عندي أ assume that إن الـ G modulo Z
+
+396
+00:43:35,800 --> 00:43:43,120
+of G is Cyclicما دام Cyclic يبقى ايه ايش؟يلها
+
+397
+00:43:43,120 --> 00:43:54,560
+generator ما دام Cyclic يبقى الـG في الـZ of G بـA
+
+398
+00:43:54,560 --> 00:43:56,160
+generator
+
+399
+00:43:57,710 --> 00:44:03,690
+يفترض ان هذا generator اله يعني اي element فيها
+
+400
+00:44:03,690 --> 00:44:11,230
+يكون هذا ال element مرفوع لمين لأس محددة يبقى then
+
+401
+00:44:11,230 --> 00:44:18,190
+ال g modulus center بتبع ال g هي sub group او ال
+
+402
+00:44:18,190 --> 00:44:23,850
+group generated by g في ال z of g بالشكل اللي
+
+403
+00:44:23,850 --> 00:44:30,950
+عندناالان بدي اقول له let ال a و ال b موجودة في g
+
+404
+00:44:30,950 --> 00:44:37,430
+اذا قدرت اثبت له ان ال a في b هي ال b في a بتما
+
+405
+00:44:37,430 --> 00:44:44,990
+المطلوب تمام؟ اذا حاجة اقوله الان ال a موجودة في
+
+406
+00:44:44,990 --> 00:44:50,630
+ال a في ال center بتبع ال g صح ولا لا؟الـ element
+
+407
+00:44:50,630 --> 00:44:57,550
+A موجود في أي lift-go set طب هذا ال element موجود
+
+408
+00:44:57,550 --> 00:45:04,750
+في ال group هذه ولا لا؟ ايه في ال center؟ موجود
+
+409
+00:45:04,750 --> 00:45:08,690
+هنا ولا لا؟ صح؟ مالكه بلعته
+
+410
+00:45:16,880 --> 00:45:28,400
+يبقى هنا هذا الكلام يبقى ميم يبقى ميم
+
+411
+00:45:28,400 --> 00:45:28,400
+يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى
+
+412
+00:45:28,400 --> 00:45:29,320
+ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم
+
+413
+00:45:29,320 --> 00:45:29,380
+يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى ميم يبقى
+
+414
+00:45:29,380 --> 00:45:35,820
+ميم يبقىواللي هو بده يساوي GI في ال center اللي
+
+415
+00:45:35,820 --> 00:45:45,210
+تبع ال G for some Iبالمثل الـ B موجود في الـ B في
+
+416
+00:45:45,210 --> 00:45:50,450
+الـ Center بتابع الـ G و اللي هو بده يساوي G في
+
+417
+00:45:50,450 --> 00:45:57,570
+الـ Center بتابع الـ G مرفوع لأخر J وهذا GG للـ
+
+418
+00:45:57,570 --> 00:46:05,970
+Center بتابع الـ Group G for some J الآن خدلي AB
+
+419
+00:46:08,110 --> 00:46:15,830
+يبقى ال a,b بده يساوي ال a,b هذه a موجودة هنا يبقى
+
+420
+00:46:15,830 --> 00:46:21,990
+موجودة هنا مدام موجودة هنا يبقى بقدر اقول ان ال a
+
+421
+00:46:21,990 --> 00:46:31,550
+تساوي g,i,x for some x وهذا بده يعطيني ان b تساوي
+
+422
+00:46:31,550 --> 00:46:42,650
+g,j,y for some yوارسم Y يبقى ال A بي بده يساوي ال
+
+423
+00:46:42,650 --> 00:46:49,630
+A اللي عندي اللي هي main اللي هي GIX وال B اللي هي
+
+424
+00:46:49,630 --> 00:46:52,070
+GJY
+
+425
+00:46:54,390 --> 00:46:59,310
+الإكس والواي والإكس والواي والإكس والواي يا سيدي
+
+426
+00:46:59,310 --> 00:47:03,910
+اللي هم في ال center إذا بقدر أبدل زي ما بدي تمام
+
+427
+00:47:03,910 --> 00:47:12,040
+يبقى هذا بتقدر تقولي GIجي جي في ال X Y بدلت
+
+428
+00:47:12,040 --> 00:47:17,700
+التنتين هذول مع بعض لإن X موجودة في ال center طيب
+
+429
+00:47:17,700 --> 00:47:26,200
+هذه بقدر أبدل كمان بقدر أقول جي جي في جي I وهذه Y
+
+430
+00:47:26,200 --> 00:47:26,860
+في X
+
+431
+00:47:30,120 --> 00:47:34,100
+الان بدي أبدل هدول مع بعض لإن ال X و ال Y في ال
+
+432
+00:47:34,100 --> 00:47:37,980
+center يبدلوا مع بعض دوري يبقى هذا الكلام يبدو
+
+433
+00:47:37,980 --> 00:47:51,200
+يساوي GJ و هنا Y و هنا GIX هذا B وهذا A يبقى G
+
+434
+00:47:51,200 --> 00:47:54,180
+Abelian يبقى هنا Das
+
+435
+00:48:02,290 --> 00:48:10,990
+يبقى من الانفة ساعدا اه
+
+436
+00:48:10,990 --> 00:48:15,070
+طبعا
+
+437
+00:48:15,070 --> 00:48:23,230
+هاي موجودة هنايبقى تساوي GI في element من ال
+
+438
+00:48:23,230 --> 00:48:28,890
+center ال X موجودة في ال center وال Y موجودة في ال
+
+439
+00:48:28,890 --> 00:48:30,590
+center كذلك
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a9acc4650f5c74c5624b171fe75a169d2b2feed0
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_postprocess.srt
@@ -0,0 +1,1656 @@
+1
+00:00:21,090 --> 00:00:23,650
+السلام عليكم و رحمة الله و بركاته باسم الله أحمد
+
+2
+00:00:23,650 --> 00:00:28,010
+أحيم طبعا بنراحل فيكم مرة تانية مستكملة لمحاضراتنا
+
+3
+00:00:28,010 --> 00:00:32,350
+و كل عامة بخير مناسبة العيد ان شاء الله خلافه
+
+4
+00:00:32,350 --> 00:00:37,970
+هتذكر ان شاء الله بس بسرعة الأخر محاضرة قبل العيد
+
+5
+00:00:37,970 --> 00:00:41,230
+كان كنا بنتكلم عن نظرية اسمها ال fundamental
+
+6
+00:00:41,230 --> 00:00:48,200
+theorem of cyclic groups طبعا كان فيها تلتالجزء
+
+7
+00:00:48,200 --> 00:00:54,620
+الاول ان اي subgroup من cyclic group بتكون cyclic
+
+8
+00:00:54,620 --> 00:00:59,860
+اي subgroup من cyclic group بتكون cyclic الجزء
+
+9
+00:00:59,860 --> 00:01:06,900
+التانى اي subgroup هيكون ال order لها بيقسم ال
+
+10
+00:01:06,900 --> 00:01:10,600
+order لل group في حالة طبعا ال cyclic group الشغل
+
+11
+00:01:10,600 --> 00:01:15,910
+التالتة لو كان عندي قاسم لل orderلأ الجروب او الـ
+
+12
+00:01:15,910 --> 00:01:20,250
+cyclic group انا بقدر عليها جيونيكسة بالجروب داخل
+
+13
+00:01:20,250 --> 00:01:24,470
+الـ cyclic group و بيكون لها نفس ال order هناخد
+
+14
+00:01:24,470 --> 00:01:34,630
+مثال سريع في هذه الجزئية هنقول التالي example let
+
+15
+00:01:34,630 --> 00:01:45,610
+j generated by a with order ال aبساوة تلاتين
+
+16
+00:01:45,610 --> 00:01:55,770
+المطلوب list all subgroups
+
+17
+00:01:55,770 --> 00:02:00,750
+of G عندي
+
+18
+00:02:00,750 --> 00:02:04,630
+group Cyclic الـ all ضاقينها تلاتين المطلوب مني
+
+19
+00:02:04,630 --> 00:02:11,770
+أجيب كل group Cyclic من الـ G تعالوا نشوف قليل
+
+20
+00:02:11,770 --> 00:02:13,070
+الحل قبل أن نبدأ الحل
+
+21
+00:02:15,780 --> 00:02:23,260
+cyclic group و بدوّع على ال subgroups اللي موجودين
+
+22
+00:02:23,260 --> 00:02:27,480
+ضمن ال group إيش هيكونوا ال subgroups subgroups
+
+23
+00:02:27,480 --> 00:02:28,380
+subgroups subgroups subgroups subgroups subgroups
+
+24
+00:02:28,380 --> 00:02:28,800
+subgroups subgroups subgroups subgroups subgroups
+
+25
+00:02:28,800 --> 00:02:28,880
+subgroups subgroups subgroups subgroups subgroups
+
+26
+00:02:28,880 --> 00:02:29,220
+subgroups subgroups subgroups subgroups subgroups
+
+27
+00:02:29,220 --> 00:02:35,780
+subgroups subgroups subgroups subgroups
+
+28
+00:02:35,780 --> 00:02:41,420
+subgroups subgroups subgroups subgroups subgroups
+
+29
+00:02:41,420 --> 00:02:41,760
+subgroups subgroups subgroups subgroups subgroups
+
+30
+00:02:41,760 --> 00:02:45,720
+subgroups subgroups subgroupssubgroup يجب أن نبدأ
+
+31
+00:02:45,720 --> 00:02:53,140
+من أين؟ من قواصم ال order لمن؟ لل جي since order
+
+32
+00:02:53,140 --> 00:02:58,160
+ال جي بدى يساوي order ال ايه؟ بدى يساوي تلاتين and
+
+33
+00:02:58,160 --> 00:03:08,180
+جي is cyclic هذا مش معناته هذا معناته for any دي
+
+34
+00:03:08,180 --> 00:03:11,040
+يقسم التلاتين there exist
+
+35
+00:03:15,010 --> 00:03:29,290
+A unique subgroup H of J with order HD الـ
+
+36
+00:03:29,290 --> 00:03:35,510
+subgroups المطلوب ان نجيبهم هم عبارة عن مجموعاتأو
+
+37
+00:03:35,510 --> 00:03:40,070
+subgroups من الـ J ال order له عبارة عن قواصم من؟
+
+38
+00:03:40,070 --> 00:03:43,750
+التلاتين في البداية هجيب قواصم التلاتين و لكل
+
+39
+00:03:43,750 --> 00:03:51,670
+قواصم هجيب ال subgroup المناسبة the divisors of
+
+40
+00:03:51,670 --> 00:04:03,040
+تلاتين are من؟ واحد اتنين تلاتة اربعة؟ لأخمسة ..
+
+41
+00:04:03,040 --> 00:04:13,480
+ستة .. عشرة .. خمستاشر .. تلاتين طيب هدول القواسم
+
+42
+00:04:13,480 --> 00:04:18,460
+تبعون التلاتين الجزء التالت من النظرية بيعطينا شغل
+
+43
+00:04:18,460 --> 00:04:25,600
+تانية ان ال subgroup هذي generated by مين؟
+
+44
+00:04:29,140 --> 00:04:34,400
+تذكروني for any divisor k of n generated by a أُس
+
+45
+00:04:34,400 --> 00:04:44,380
+n على k now for h واحد إيش يعني h واحد يعني ال sub
+
+46
+00:04:44,380 --> 00:04:48,860
+group من ال j اللي ال order إيها إيش واحد هذه
+
+47
+00:04:48,860 --> 00:04:54,830
+بتكون generated by مين؟by a أُس تلاتين على واحد
+
+48
+00:04:54,830 --> 00:04:59,310
+يعني generated by a أُس تلاتين a أُس تلاتين كده
+
+49
+00:04:59,310 --> 00:05:05,970
+الشباب a أُس تلاتين ال identity لأن الأرض على ال a
+
+50
+00:05:05,970 --> 00:05:09,690
+بيسوا تلاتين يكبر هذا generated by ال identity
+
+51
+00:05:09,690 --> 00:05:15,750
+ومافيش فيها غير مين مافيش فيها غير مين غير ال
+
+52
+00:05:15,750 --> 00:05:17,970
+identity طيب H2
+
+53
+00:05:20,000 --> 00:05:23,120
+H2 يعني الـ subgroup للـ order اللي هتنين
+
+54
+00:05:23,120 --> 00:05:29,340
+generated by مين؟ by A أُس ثلاثين على اتنين يعني A
+
+55
+00:05:29,340 --> 00:05:35,140
+أُس خمستاشر اللي عبارة عن ال identity والـ A أُس
+
+56
+00:05:35,140 --> 00:05:43,580
+خمستاشر H3 عبارة عن generated by A أُس ثلاثين على
+
+57
+00:05:43,580 --> 00:05:49,370
+تلاتة يعني by A أُس عشرةيعني ال identity a أُس
+
+58
+00:05:49,370 --> 00:05:58,030
+عشرة a أُس أشرين حمسة حمسة حمسة حمسة حمسة حمسة
+
+59
+00:05:58,030 --> 00:06:03,830
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+60
+00:06:03,830 --> 00:06:07,990
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+61
+00:06:07,990 --> 00:06:10,390
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+62
+00:06:10,390 --> 00:06:10,650
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+63
+00:06:10,650 --> 00:06:16,430
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حA أُس 12 A أُس
+
+64
+00:06:16,430 --> 00:06:22,470
+18 A أُس 24 و بجف لإن A أُس 30 حتي سلمين لل
+
+65
+00:06:22,470 --> 00:06:27,330
+identity أتش 6 عبارة
+
+66
+00:06:27,330 --> 00:06:33,990
+عن generated by A أُس 30 على 6 يعني A أُس 5
+
+67
+00:06:35,060 --> 00:06:41,960
+Identity اوس خمسة اوس عشرة اوس خمستاش اوس عشرين
+
+68
+00:06:41,960 --> 00:06:47,640
+اوس خمسة عشرين ابن جاف لحظة شباب اتش ستة تحتوي
+
+69
+00:06:47,640 --> 00:06:56,820
+داخلها مين اتش تلاتة و اتش اتنين ليش؟ لأن الخمسة
+
+70
+00:06:56,820 --> 00:07:02,620
+او الستة او التلاتة بتقسم الستة والتنين بتقسم
+
+71
+00:07:02,620 --> 00:07:10,840
+الستةطيب اتش مين بعد الستة؟ عشرة فهذا هيساوى ال
+
+72
+00:07:10,840 --> 00:07:16,980
+identity a والثلاثة a والستة a والتسعة لعند a
+
+73
+00:07:16,980 --> 00:07:25,580
+والسبعة وعشرين و اتش خمستائش هصير a a التربية a
+
+74
+00:07:25,580 --> 00:07:34,820
+والاربعة لعند a والتمانية وعشرينواخر واحدة H30 الى
+
+75
+00:07:34,820 --> 00:07:41,580
+الـ generated by الـ A الى الـ G نفسها طبعا يكسر
+
+76
+00:07:41,580 --> 00:07:45,660
+عندي listing لكل ال cyclic subgroup او لكل ال
+
+77
+00:07:45,660 --> 00:07:51,900
+subgroup من ال group J اللي ال order لها بساوي 30
+
+78
+00:07:51,900 --> 00:07:59,620
+اي سؤال يا شباب؟ اي
+
+79
+00:07:59,620 --> 00:08:00,240
+سؤال؟
+
+80
+00:08:03,650 --> 00:08:12,610
+طيب لو خلنا هذا نفس المثال لكن على group معروف ال
+
+81
+00:08:12,610 --> 00:08:19,010
+generator إلها بشكل واضح يعني مش a كرقم لو قولنا
+
+82
+00:08:19,010 --> 00:08:27,510
+مثلا find all subgroups
+
+83
+00:08:27,510 --> 00:08:37,120
+of Z 13 إيش هنعمل؟هنعمل نفس الفكرة اللي اشتغلناها
+
+84
+00:08:37,120 --> 00:08:51,440
+مع فرق واحد ان الـ A أشماله الـ
+
+85
+00:08:51,440 --> 00:08:56,100
+A معروف هو الواحد solution
+
+86
+00:08:56,100 --> 00:09:02,400
+الـ Z 30 عبارة عن generated Pi الواحد و ال order
+
+87
+00:09:02,400 --> 00:09:09,680
+للواحد 100تلاتين using the
+
+88
+00:09:09,680 --> 00:09:18,720
+same method in the last example
+
+89
+00:09:18,720 --> 00:09:26,520
+we get the following cyclic
+
+90
+00:09:26,520 --> 00:09:28,980
+subgroups
+
+91
+00:09:32,670 --> 00:09:41,790
+generated by الواحد الـ H1 الواحد ولا مين الواحد
+
+92
+00:09:41,790 --> 00:09:46,550
+ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا
+
+93
+00:09:46,550 --> 00:09:46,730
+مين الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+94
+00:09:46,730 --> 00:09:46,870
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+95
+00:09:46,870 --> 00:09:47,230
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+96
+00:09:47,230 --> 00:09:47,790
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+97
+00:09:47,790 --> 00:09:49,670
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+98
+00:09:49,670 --> 00:09:49,970
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+99
+00:09:49,970 --> 00:09:50,910
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+100
+00:09:50,910 --> 00:09:52,310
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+101
+00:09:52,310 --> 00:09:53,610
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+102
+00:09:53,610 --> 00:09:55,950
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+103
+00:09:55,950 --> 00:09:58,750
+الواحد
+
+104
+00:10:04,130 --> 00:10:13,790
+H5 الـ 0 الـ 6 الـ 12 الـ 18 الـ 24 وصولا لـ H30
+
+105
+00:10:13,790 --> 00:10:19,970
+اللي عبارة عن الـ Z30 نفسه واضح يا عادي؟ واضح يا
+
+106
+00:10:19,970 --> 00:10:22,870
+شباب؟ في كرولر عن مظهرية اللي فاتت
+
+107
+00:10:28,780 --> 00:10:32,780
+هي نفس الجزئية التالتة من النظرية لكن على group
+
+108
+00:10:32,780 --> 00:10:44,280
+معروفة وهي z,n for every k
+
+109
+00:10:44,280 --> 00:10:50,760
+يقسم ال n there exists a unique subgroup
+
+110
+00:10:57,500 --> 00:11:14,340
+of ZN with order K namely generated
+
+111
+00:11:14,340 --> 00:11:20,260
+by مين؟ طبق الـ band التالت من النظرية السابقة لكن
+
+112
+00:11:20,260 --> 00:11:26,080
+على ZN هكون واحد أسفل N على K اللي هو أبعد عن مين؟
+
+113
+00:11:27,110 --> 00:11:34,170
+ان على ك مش
+
+114
+00:11:34,170 --> 00:11:40,970
+بس هيك these are
+
+115
+00:11:40,970 --> 00:11:47,630
+the only subgroups
+
+116
+00:11:47,630 --> 00:11:55,110
+of z طبعا مافيش غيرها مافيش غيرهم هدولة لكل قاسم
+
+117
+00:11:55,110 --> 00:12:01,530
+للانملاقي subgroup ال order لها هذا القاسم وهي
+
+118
+00:12:01,530 --> 00:12:07,090
+generated by من؟ by n على القاسم طبعا هذا طبقنا
+
+119
+00:12:07,090 --> 00:12:17,970
+عليه المثال الموجود جانب دي مثال سريع for زد مثلا
+
+120
+00:12:17,970 --> 00:12:23,910
+عشرين عند من؟ generated by الواحدgenerated by
+
+121
+00:12:23,910 --> 00:12:29,270
+التنين generated by الأربعة generated by الخمسة
+
+122
+00:12:29,270 --> 00:12:36,490
+and generated by العشرة and generated by الأشعين
+
+123
+00:12:36,490 --> 00:12:50,990
+دول هم ال only cyclic subgroups ل ال z أشعين أيه
+
+124
+00:12:50,990 --> 00:13:02,430
+السؤال يا شبابأي سؤال سؤال عالسريع find the number
+
+125
+00:13:02,430 --> 00:13:15,750
+of subgroups of j generated by a if order a بسوى
+
+126
+00:13:15,750 --> 00:13:16,810
+خمسة وعشرين
+
+127
+00:13:22,100 --> 00:13:28,380
+أوجد عدد الـ subgroups اللي موجودين في الجروب جيه
+
+128
+00:13:28,380 --> 00:13:33,620
+اللي ال order لل generator إلها عبارة عن 25 نجيب
+
+129
+00:13:33,620 --> 00:13:39,400
+عدد قواسم الخمسة وعشرين ويكون هو عدد ال subgroups
+
+130
+00:13:39,400 --> 00:13:44,040
+the divisors of
+
+131
+00:13:44,040 --> 00:13:51,560
+خمسة وعشرين are واحد خمسة وخمسة وعشرين يجب كموحدة
+
+132
+00:13:52,410 --> 00:14:02,190
+there are only three subgroups
+
+133
+00:14:02,190 --> 00:14:09,910
+of G فقط تلاتة cyclic subgroups أو subgroups
+
+134
+00:14:09,910 --> 00:14:16,630
+موجودين هنا أنهينا السؤال المتعلق بعدد ال cyclic
+
+135
+00:14:16,630 --> 00:14:22,350
+subgroup بيجي سؤال تانيسؤال الأول هو قداش عدد ال
+
+136
+00:14:22,350 --> 00:14:27,970
+generator في ال cyclic group؟سؤال التاني لو كان
+
+137
+00:14:27,970 --> 00:14:35,190
+عندي قاسم لل order لل group cyclic نقول لو كان
+
+138
+00:14:35,190 --> 00:14:38,610
+عندي قاسم فانا بلاقي sub group ال order لهذا
+
+139
+00:14:38,610 --> 00:14:41,950
+القاسم لما اقول sub group من cyclic و ال order
+
+140
+00:14:41,950 --> 00:14:45,090
+لهذا القاسم معناته انها generator وهذا ال
+
+141
+00:14:45,090 --> 00:14:49,170
+generator ال order له بيساوي القاسم يعني لكل قاسم
+
+142
+00:14:49,170 --> 00:14:56,310
+ل order ال finite group cyclic بلاقي عنصر جواالـ
+
+143
+00:14:56,310 --> 00:15:00,210
+لـ group ال order إيه له هذا القاسم طب السؤال كم
+
+144
+00:15:00,210 --> 00:15:06,410
+عنصر من هذا النوع بلاجي بلاجي واحد أه طب جديش
+
+145
+00:15:06,410 --> 00:15:12,430
+بالظبط عشان نقدر نعرف هذا الجواب هنعرف function
+
+146
+00:15:12,430 --> 00:15:17,670
+اسمه الearlier phi function هتدرس بالتفصيل في مساق
+
+147
+00:15:17,670 --> 00:15:20,950
+نظرية الأعداد definition
+
+148
+00:15:23,750 --> 00:15:35,810
+Euler Phi Function متعرفة
+
+149
+00:15:35,810 --> 00:15:45,290
+بالشكل التالي فايل واحد بيساوي واحد اتنين if n
+
+150
+00:15:45,290 --> 00:15:52,530
+أكبر من واحد then فايل n يساوي ال number
+
+151
+00:15:56,000 --> 00:16:03,600
+of integers less than
+
+152
+00:16:03,600 --> 00:16:11,360
+أن عدد العدد الصحيح اللي أقل من الان and
+
+153
+00:16:11,360 --> 00:16:14,400
+relatively
+
+154
+00:16:14,400 --> 00:16:17,600
+prime
+
+155
+00:16:17,600 --> 00:16:21,300
+with
+
+156
+00:16:24,550 --> 00:16:27,690
+طبعا أنا بتكلم مش عن integers بس انا ممكن اضيف
+
+157
+00:16:27,690 --> 00:16:32,750
+كلمة the number of positive integers
+
+158
+00:16:32,750 --> 00:16:38,010
+عشان ماحدش يروح يحسبلي الاعداد السالبة في ملاحظة
+
+159
+00:16:38,010 --> 00:16:45,870
+غير ان note that file and عبارة عن ال order لل
+
+160
+00:16:45,870 --> 00:16:47,830
+group UN
+
+161
+00:16:49,930 --> 00:16:54,650
+فايل ان عبارة عن order لجروب UN وهذا من المنطقى
+
+162
+00:16:54,650 --> 00:17:01,930
+لأن جروب UN تأخذ الأعداد المحصورة بين الواحد و
+
+163
+00:17:01,930 --> 00:17:12,590
+الان والتي تكون relatively prime with الان الان
+
+164
+00:17:12,590 --> 00:17:16,810
+أكبر من واحد ده لكن أنا ما أعد الان بعد الأعداد
+
+165
+00:17:16,810 --> 00:17:20,860
+الأقل منها فلازم يكونوا positive عشان اناأشغل صح
+
+166
+00:17:20,860 --> 00:17:34,600
+طيب كمثال سريع لو
+
+167
+00:17:34,600 --> 00:17:39,080
+قولنا في التنين كده؟
+
+168
+00:17:39,080 --> 00:17:44,520
+واحد كم عدد جاب للتنين لغاية الابراهيم مع التنين؟
+
+169
+00:17:44,520 --> 00:17:45,440
+في العشرة
+
+170
+00:17:49,180 --> 00:17:57,880
+1 و 3 و 7 و 9 جديش؟ اربعة فاي ل prime كم عدد جابل
+
+171
+00:17:57,880 --> 00:18:04,780
+اي عدد اولي relatively prime مع بي minus one بي is
+
+172
+00:18:04,780 --> 00:18:16,320
+prime طيب في اتنين اص كيه؟ جديش؟
+
+173
+00:18:17,630 --> 00:18:20,690
+العداد الـ relatively prime مع ال power للتنين هي
+
+174
+00:18:20,690 --> 00:18:25,390
+العداد الفردية فقط اللي عبارة عن إيش؟ تنين قصه K
+
+175
+00:18:25,390 --> 00:18:33,390
+minus one لو قلنا file P to K عبارة
+
+176
+00:18:33,390 --> 00:18:37,030
+عن إيش؟
+
+177
+00:18:37,030 --> 00:18:42,590
+P to
+
+178
+00:18:42,590 --> 00:18:47,350
+K minus one
+
+179
+00:18:48,650 --> 00:18:53,070
+هذا بصورة عميم لهذه العلاقة عشان نعممها على الأكتر
+
+180
+00:18:53,070 --> 00:19:02,490
+if n إبتدت عن P1 to K1 P2 to K2 and PR to KR هيكون
+
+181
+00:19:02,490 --> 00:19:18,850
+then في ال N إبتدت عن P1 to K1-P1 to K1-1 فيP2-P2
+
+182
+00:19:18,850 --> 00:19:26,810
+-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2
+
+183
+00:19:26,810 --> 00:19:28,430
+-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2
+
+184
+00:19:28,430 --> 00:19:33,490
+-P2-P2-P2
+
+185
+00:19:33,910 --> 00:19:40,010
+و التفاصيل التفاصيل لكن بستعمل فيها concepts مش
+
+186
+00:19:40,010 --> 00:19:43,210
+موجودة عندي في هذا المساق اشتغل على ال
+
+187
+00:19:43,210 --> 00:19:47,710
+multiplicative functions و بعض الأمور من هذا النوع
+
+188
+00:19:47,710 --> 00:19:54,370
+طيب
+
+189
+00:19:54,370 --> 00:19:58,010
+ايش دخل ال function هذه في موضوعنا هتيجي النظرية
+
+190
+00:19:58,010 --> 00:20:01,230
+اربع اربع و توضح
+
+191
+00:20:05,040 --> 00:20:09,440
+بنخلصه ان شاء الله بضايق نظرية واحدة بيساوي رقم
+
+192
+00:20:09,440 --> 00:20:17,120
+معين let J بيساوي generated by ال A و أخضر ال A
+
+193
+00:20:17,120 --> 00:20:18,100
+بيساوي N
+
+194
+00:20:21,780 --> 00:20:25,380
+دى يقسم الان طبعا دى يقسم الان احنا هيك بنقول ان
+
+195
+00:20:25,380 --> 00:20:29,600
+يوجد only one sub group of order دى namely
+
+196
+00:20:29,600 --> 00:20:34,500
+generated by a to n على d هيت السؤال جداش عدد ال
+
+197
+00:20:34,500 --> 00:20:40,600
+generator then the
+
+198
+00:20:40,600 --> 00:20:48,320
+elements او the number of
+
+199
+00:20:48,320 --> 00:20:49,080
+elements
+
+200
+00:20:51,850 --> 00:21:05,150
+in J with order D is فاية D عدد العناصر في J اللي
+
+201
+00:21:05,150 --> 00:21:12,610
+ال order لهم بيساوي D بيساوياش فاية D نيجي نتبت
+
+202
+00:21:12,610 --> 00:21:16,270
+نيجي
+
+203
+00:21:16,270 --> 00:21:17,690
+نتبت العلاقة
+
+204
+00:21:20,740 --> 00:21:28,020
+اربع تلاتة part c ايش ال part c في النظرية هذه
+
+205
+00:21:28,020 --> 00:21:35,760
+بيقول؟ there exist a unique .. طبعا there exist
+
+206
+00:21:35,760 --> 00:21:42,040
+unique subgroup of
+
+207
+00:21:42,040 --> 00:21:48,440
+j with order d
+
+208
+00:21:48,440 --> 00:21:50,100
+namely
+
+209
+00:21:53,030 --> 00:22:01,270
+generated by a to n على d طيب
+
+210
+00:22:01,270 --> 00:22:06,550
+هل جيت؟ مده مافيش غير هذه ال subgroup ال order
+
+211
+00:22:06,550 --> 00:22:10,570
+اللي هي دي فالعناصر لل order اللي هي دي ممكن تكون
+
+212
+00:22:10,570 --> 00:22:11,350
+موجودة برا
+
+213
+00:22:15,080 --> 00:22:19,640
+الـ uniqueness لهذه ال subgroup بخليني أقول إنه
+
+214
+00:22:19,640 --> 00:22:24,920
+جميع العناصر اللي ال order إلها دي و اللي موجودة
+
+215
+00:22:24,920 --> 00:22:35,780
+دي هو هذه ال subgroup هذا معناته all elements in J
+
+216
+00:22:35,780 --> 00:22:48,500
+with order D are in thissubgroup طيب
+
+217
+00:22:48,500 --> 00:22:52,840
+كل
+
+218
+00:22:52,840 --> 00:22:57,080
+العناصر لل order اللي دي موجودين هنا يعني بلو أنا
+
+219
+00:22:57,080 --> 00:23:01,960
+عرفت أكمع عنصر ال order اللي دي في هذه ال subgroup
+
+220
+00:23:01,960 --> 00:23:08,420
+بكون خلصت now each
+
+221
+00:23:08,420 --> 00:23:12,900
+one of these elements
+
+222
+00:23:16,390 --> 00:23:23,370
+is a generator of
+
+223
+00:23:23,370 --> 00:23:30,930
+this subgroup
+
+224
+00:23:30,930 --> 00:23:38,070
+ليش؟ العنصر هذا ال order له دي وموجود في group ال
+
+225
+00:23:38,070 --> 00:23:44,130
+order له دي ايه بيكون لها؟ بيكون لها مولّب، بيكون
+
+226
+00:23:44,130 --> 00:23:49,090
+generatorNow if
+
+227
+00:23:49,090 --> 00:23:56,370
+generated by A to N على D ممكن اكتبها generated by
+
+228
+00:23:56,370 --> 00:24:05,470
+P with order ال P بدي سو D then the other
+
+229
+00:24:05,470 --> 00:24:10,130
+generators
+
+230
+00:24:10,130 --> 00:24:13,110
+are of the form
+
+231
+00:24:16,330 --> 00:24:29,370
+B to K والجريس common divisor لD وK وD سوى 1 رجع
+
+232
+00:24:29,370 --> 00:24:34,030
+ليش لنظرية اللي أخدناها في أول الشبتر ان ال
+
+233
+00:24:34,030 --> 00:24:39,090
+generator او ال .. ال .. حيكون عبارة عن عناصرالـ
+
+234
+00:24:39,090 --> 00:24:42,790
+order او ال .. ال .. ال .. ال .. ال power تبعها
+
+235
+00:24:42,790 --> 00:24:47,230
+لجيسكم ال divisor إله relative لبرايم مع order ل
+
+236
+00:24:47,230 --> 00:24:53,030
+group نفسها أكم كيب اللاجي أكم
+
+237
+00:24:53,030 --> 00:24:59,410
+كيب اللاجي relative لبرايم مع دي يا شباب and we
+
+238
+00:24:59,410 --> 00:25:12,810
+can find .. find ال Dof this such K بقدر ألاقي
+
+239
+00:25:12,810 --> 00:25:22,790
+فاية D من هذه الأرقام K so the number of elements
+
+240
+00:25:22,790 --> 00:25:35,510
+in J with order D is فاية D وهو المطلوب
+
+241
+00:25:42,170 --> 00:25:45,330
+اللي صار كانت تانية يا شباب انا بدور على عناصر لل
+
+242
+00:25:45,330 --> 00:25:49,450
+order الهدى نقلت المسألة من اني ابحث في ال ج كلها
+
+243
+00:25:49,450 --> 00:25:54,170
+لاني ابحث وين في ال sub group لل order الهدى ميزة
+
+244
+00:25:54,170 --> 00:25:58,610
+العناصر هنا لل order الهدى انها generator انا عشان
+
+245
+00:25:58,610 --> 00:26:02,430
+اعدى كام generator باخد واحد من هذه ال generators
+
+246
+00:26:02,430 --> 00:26:06,890
+فليكن بيه و باقى ال generators عبارة عن P to K و
+
+247
+00:26:06,890 --> 00:26:11,250
+ال K relative لبرايم مع مينمع ال D أكم عمصر بقدر
+
+248
+00:26:11,250 --> 00:26:15,110
+أجري راتب لبرايم مع ال D و أجال من ال D محصوب من
+
+249
+00:26:15,110 --> 00:26:19,390
+ال D والواحد و عبارة عن فاية D و بتالي وجد فاية D
+
+250
+00:26:19,390 --> 00:26:25,270
+subgroup
+
+251
+00:26:25,270 --> 00:26:30,010
+وحيدة في ال G لكن أكم element بولدها وحيد
+
+252
+00:26:36,100 --> 00:26:42,140
+يعني مثلا ال z يوجد في ال z 30 only subgroup of
+
+253
+00:26:42,140 --> 00:26:47,240
+order 15 هي generated by a 2 طبعا ال a 2 في ال z
+
+254
+00:26:47,240 --> 00:26:52,120
+30 يعني هي by 2 بس أكم generator ل ال generated by
+
+255
+00:26:52,120 --> 00:26:58,260
+2 في ال z 30 بولد
+
+256
+00:26:58,260 --> 00:27:03,520
+ال generated by 2 ماتقوليش في عيه 2 لأ في عيه 30
+
+257
+00:27:03,520 --> 00:27:13,280
+على 2 في عيه 15لو اعتقد بيطلع تمانية طيب ناخد مثال
+
+258
+00:27:13,280 --> 00:27:27,140
+رقمى من في ال chapter then
+
+259
+00:27:27,140 --> 00:27:33,260
+find the
+
+260
+00:27:33,260 --> 00:27:39,200
+numberof elements in
+
+261
+00:27:39,200 --> 00:27:49,720
+z اربعين with order عشرين
+
+262
+00:27:49,720 --> 00:28:02,020
+اكم عنصر في z اربعين ال order لهم عشرين فعل
+
+263
+00:28:02,020 --> 00:28:09,740
+عشرين هذه النظرية اللي قدامكسلوشين هناك
+
+264
+00:28:09,740 --> 00:28:20,800
+فايل عشرين فايل
+
+265
+00:28:20,800 --> 00:28:31,900
+عشرين كده فايل عشرين تمانية تقدر
+
+266
+00:28:31,900 --> 00:28:32,320
+تجيبهم
+
+267
+00:28:35,510 --> 00:28:43,310
+تقدر تجيبهم؟ هذه العناصر الأخضر إلها تمانية تعالوا
+
+268
+00:28:43,310 --> 00:28:55,170
+نفكر We to find them We
+
+269
+00:28:55,170 --> 00:29:02,810
+find one Let
+
+270
+00:29:06,040 --> 00:29:13,900
+مثلا a ينتمي لزد اربعين و order ال a بيساوي ايش؟
+
+271
+00:29:13,900 --> 00:29:22,420
+عشرين ال a ايش هيساوي؟ مين هو العنصر اللي في زد
+
+272
+00:29:22,420 --> 00:29:25,020
+عشرين؟ او اتل واحد من العناصر اللي في زد اربعين
+
+273
+00:29:25,020 --> 00:29:29,540
+اللي ال order العشرين؟
+
+274
+00:29:29,540 --> 00:29:33,980
+ال a او
+
+275
+00:29:33,980 --> 00:29:39,490
+findممكن ناخد الاي عبارة عن واحد اصر اربعين على
+
+276
+00:29:39,490 --> 00:29:45,350
+عشرين اللي هو عبارة عن جد ياشر واحد اصر عشرين و
+
+277
+00:29:45,350 --> 00:29:50,790
+واحد اصر اتنين اللي هو اتنين في زد اربعين ايه
+
+278
+00:29:50,790 --> 00:29:53,850
+بالعنصر اللي ال order ايه له عشرين او واحد العناصر
+
+279
+00:29:53,850 --> 00:29:59,210
+اللي ال order ايه له عشرين في زد اربعين هو مين ال
+
+280
+00:29:59,210 --> 00:30:02,570
+other elements are
+
+281
+00:30:06,130 --> 00:30:12,190
+تانية نقص كتانية
+
+282
+00:30:12,190 --> 00:30:17,070
+نقص تسعة
+
+283
+00:30:17,070 --> 00:30:21,430
+أو سبعة في الأول تانية نقص تسعة تانية نقص احداش
+
+284
+00:30:21,430 --> 00:30:35,650
+تانية نقص تلاتاش تانية نقص17 2 19 2 6 14 18 22 26
+
+285
+00:30:35,650 --> 00:30:48,250
+34 38 هذه هي العناصر اللي ال order لها يساوي 20 في
+
+286
+00:30:48,250 --> 00:30:54,450
+z أربع تمام
+
+287
+00:30:58,650 --> 00:31:05,490
+ما هو هذا زد ان الاص بيصير تنين اص واحد يعني انا
+
+288
+00:31:05,490 --> 00:31:07,790
+واحد في اتنين اتنين تنين اص ثلاثة انا تلاتة في
+
+289
+00:31:07,790 --> 00:31:20,350
+اتنين ستة تنين اص واحد هذي لأ هذي سهل هنفوت
+
+290
+00:31:20,350 --> 00:31:26,250
+هناخد جزء discussion مناقشة طبعا محاضرة الجزء اللي
+
+291
+00:31:26,250 --> 00:31:29,550
+ضال من محاضرة اليوم زادالمحاضرة اللى هناخدها
+
+292
+00:31:29,550 --> 00:31:34,270
+الساعة 12 زاد محاضرة الأتنين هنناقش فيهم مجموعة من
+
+293
+00:31:34,270 --> 00:31:39,770
+أسئلة chapter 4 ما بعرف هل هنخلص أو لأ إذا ما
+
+294
+00:31:39,770 --> 00:31:43,870
+خلصنا ممكن ناخد محاضرة الأربع أو محاضرة تعويضية
+
+295
+00:31:43,870 --> 00:31:55,450
+للمناقشة أنا همسح الجزء هذا طبعا
+
+296
+00:31:57,470 --> 00:31:59,950
+زي ما انت شاير هذا ال chapter الأسئلة عددها كبير
+
+297
+00:31:59,950 --> 00:32:05,030
+يعني ما يقارب حوالي من خمسة ربيع لخمسين سؤال فانا
+
+298
+00:32:05,030 --> 00:32:07,990
+مش هعمل زي ال chapter الفاتوح اللي الجميع هي بعض
+
+299
+00:32:07,990 --> 00:32:13,730
+الأسئلة هعطيك مساعدة إليك فيها و أنت تكمل يعني
+
+300
+00:32:13,730 --> 00:32:17,810
+خصوصا الأسئلة من واحد لخمس عشر إما أسئلة حسابية أو
+
+301
+00:32:17,810 --> 00:32:23,730
+أسئلة سهل إن الطالب يقدر يعرفها لوحده
+
+302
+00:32:43,420 --> 00:32:49,200
+السؤال الأول find all generator of z6, z8, z20
+
+303
+00:32:49,200 --> 00:32:56,660
+طبعا ال generator غيرنا عبارة عن مين؟ لو طلعنا على
+
+304
+00:32:56,660 --> 00:33:02,540
+نظرية أو corollary لنظرية الأولى كان بيقولك ال
+
+305
+00:33:02,540 --> 00:33:06,660
+generator ل zn هي عبارة عن مين؟ عن الأرقام اللي
+
+306
+00:33:06,660 --> 00:33:10,160
+relative ل برايم مع ال n اللي هي فعليا عبارة عناش؟
+
+307
+00:33:10,160 --> 00:33:15,950
+عناصر ال UNفلو داشت على ز داش ز تلاتين او ز عشرين
+
+308
+00:33:15,950 --> 00:33:21,470
+منهم ما هيكونوا واحد و تلاتة و سبعة و تسعة احداش
+
+309
+00:33:21,470 --> 00:33:26,250
+تلاتاش سبعتاش تسعة عشر اعتقد حلنا السؤال على ز
+
+310
+00:33:26,250 --> 00:33:36,580
+تلاتين اتناء الحل لو دينا سؤال اتنينSuppose that
+
+311
+00:33:36,580 --> 00:33:39,960
+A, B or generated by A, generated by B, generated
+
+312
+00:33:39,960 --> 00:33:45,040
+by C are cyclic group of order 6,8,20 Find all
+
+313
+00:33:45,040 --> 00:33:49,300
+generators generated by A, generated by B,
+
+314
+00:33:49,540 --> 00:33:53,780
+generated by C حلنا سؤال على هذا النمط، لو اشتغلنا
+
+315
+00:33:53,780 --> 00:33:58,680
+مثلا على generated by C و ال order لـ C بدي يسوى
+
+316
+00:33:58,680 --> 00:34:03,420
+20 فgenerated by C هو نفسه generated by C تكيب
+
+317
+00:34:04,170 --> 00:34:08,850
+Generated by C أُس سبعة Generated by C أُس تسعة
+
+318
+00:34:08,850 --> 00:34:08,930
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+319
+00:34:08,930 --> 00:34:10,850
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+320
+00:34:10,850 --> 00:34:12,410
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+321
+00:34:12,410 --> 00:34:12,690
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+322
+00:34:12,690 --> 00:34:12,710
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+323
+00:34:12,710 --> 00:34:15,370
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+324
+00:34:15,370 --> 00:34:21,850
+Generated by C أُس تسعة Generated
+
+325
+00:34:21,850 --> 00:34:29,600
+by C أُس تسعة Generated bylist all elements of the
+
+326
+00:34:29,600 --> 00:34:35,580
+subgroups generated by 20 generated by 10 in z 30
+
+327
+00:34:35,580 --> 00:34:42,040
+let a,b طبعا سؤال تلاتة هو نفسه واحد واتنين لكن
+
+328
+00:34:42,040 --> 00:34:50,240
+على مين على ال order 30 تقل
+
+329
+00:34:50,240 --> 00:34:51,960
+السؤال الرابع when
+
+330
+00:34:56,310 --> 00:35:07,450
+C plus 1 هي نفس الـ C سؤال
+
+331
+00:35:07,450 --> 00:35:19,490
+أربعة زي سؤال تلاتة سؤال خمسة في شغل نشغل في U20يو
+
+332
+00:35:19,490 --> 00:35:24,790
+عشرين جديش يا شباب؟ واحد، تلاتة، سبعة، تسعة، داشر،
+
+333
+00:35:24,790 --> 00:35:30,650
+تلتاشر، سبعتاشر، تسعة، اتاشر List the elements of
+
+334
+00:35:30,650 --> 00:35:34,430
+generated by تلاتة وسبعة ناخد generated by سبعة
+
+335
+00:35:34,430 --> 00:35:43,250
+مثلا اللي عبارة عن الواحد السبعة سبعة تغبيع جديش؟
+
+336
+00:35:43,250 --> 00:35:50,760
+تسعة واربعين مدة عشرين جديش؟ تسعةسبعة تكيب يعني
+
+337
+00:35:50,760 --> 00:36:02,320
+سبعة في تسعة تلاتة قصتين تلاتة سبعة أربعة يعني
+
+338
+00:36:02,320 --> 00:36:07,200
+سبعة في تلاتة يعني واحد و عشرين و واحد طبعا
+
+339
+00:36:07,200 --> 00:36:14,020
+generated by تلاتة عبارة عن من؟ واحد تلاتة تلاتة
+
+340
+00:36:14,020 --> 00:36:17,980
+تربية تسعة بعدين سبعة و عشرين سبعة بعدين حتيجة
+
+341
+00:36:21,630 --> 00:36:26,370
+طيب سؤال السادس what do exercises تلاتة و أربعة و
+
+342
+00:36:26,370 --> 00:36:29,510
+خمسة have in common try to make a generalization
+
+343
+00:36:29,510 --> 00:36:36,730
+that includes these three cases انت لما تحل سؤال
+
+344
+00:36:36,730 --> 00:36:43,070
+تلاتة و أربعة و خمسة ايش بتستنتجه؟
+
+345
+00:36:43,070 --> 00:36:49,430
+ايش السنتجات اللي ممكن تستنتجها؟ لو طلعنا على خمسة
+
+346
+00:36:50,250 --> 00:36:54,730
+هنستنتج ان ال generated by ال element و ال
+
+347
+00:36:54,730 --> 00:37:00,530
+generated by ال inverse تبعوا نفس الشيء طيب لو
+
+348
+00:37:00,530 --> 00:37:03,410
+جينا السؤال 4 list the elements of the subgroups 3
+
+349
+00:37:03,410 --> 00:37:08,490
+and 15 in Z18 التلاتة و الخمس عشر في Z18 شمالهم
+
+350
+00:37:08,490 --> 00:37:12,310
+برضه inverse لو جينا السؤال تلاتة
+
+351
+00:37:16,050 --> 00:37:19,390
+عشرة و عشرين في زي التلاتين اشمالهم برضه inverse
+
+352
+00:37:19,390 --> 00:37:24,630
+يجب الاستنتاج تبع سؤال تلاتة او اربع او خمسة اللي
+
+353
+00:37:24,630 --> 00:37:30,010
+انا بدي احطه في سؤال ستة انه generated by ال a
+
+354
+00:37:30,010 --> 00:37:38,670
+generated by ال a inverse وهذا اثبتناه في شبتر
+
+355
+00:37:38,670 --> 00:37:39,450
+تلاتة
+
+356
+00:37:42,190 --> 00:37:47,870
+طيب سبعة find an example of a non-cyclic group all
+
+357
+00:37:47,870 --> 00:37:53,810
+of whose proper subgroup are cyclic اعطيني group
+
+358
+00:37:53,810 --> 00:38:01,210
+not cyclic لأن كل ال subgroup اسمينها cyclic مارت
+
+359
+00:38:01,210 --> 00:38:07,730
+علينا في ال chapter اللي فات خدناها D6
+
+360
+00:38:07,730 --> 00:38:11,490
+وD4 اي واحدة من ال D
+
+361
+00:38:14,340 --> 00:38:23,440
+بتكون صحيحة دي اربعة او دي ستة او دي تمانية بكون
+
+362
+00:38:23,440 --> 00:38:33,260
+صح ال U تمانية سائق لك ال U تمانية صح
+
+363
+00:38:33,260 --> 00:38:39,200
+صح ال U تمانية تمانية
+
+364
+00:38:41,150 --> 00:38:44,110
+let a be an element of a group and let order a
+
+365
+00:38:44,110 --> 00:38:47,990
+بسوا 15 compute the orders of the following طبعا
+
+366
+00:38:47,990 --> 00:38:57,390
+هذا سهل مثلا ال order ل a أس 9 عبارة عن عبارة عن
+
+367
+00:38:57,390 --> 00:39:04,510
+إيش ال order ل a أس k عبارة عن إيش في نظرية في أول
+
+368
+00:39:04,510 --> 00:39:10,650
+واحدة خدناها and علىالـ order ل a of k عبارة عن n
+
+369
+00:39:10,650 --> 00:39:14,690
+على الجيز common divisor ل n mark a يعني عبارة عن
+
+370
+00:39:14,690 --> 00:39:20,170
+خمستاش على جيز common divisor لخمستاش تسعة فتطلع
+
+371
+00:39:20,170 --> 00:39:27,450
+خمسة طبعا نفس القصة في b و نفس القصة في c
+
+372
+00:39:33,530 --> 00:39:41,330
+سؤال تسعة how many subgroups of Z20 توحى لنا توحى
+
+373
+00:39:41,330 --> 00:39:47,070
+لنا شباب في Z20 كام subgroup اللي أجى؟ عوام ال 20
+
+374
+00:39:47,070 --> 00:39:51,850
+عوام ال 20 و لا عوام ال 20؟ لأ عوام ال 20
+
+375
+00:39:51,850 --> 00:39:56,530
+generator لكن subgroup احنا قلنا فيه عددين عدد ال
+
+376
+00:39:56,530 --> 00:40:01,370
+subgroups اللي هو عدد القواسملكن عدد ال generator
+
+377
+00:40:01,370 --> 00:40:08,170
+اللي هو ال file عدد القواسم من ال 20 جديش 6 1 2 4
+
+378
+00:40:08,170 --> 00:40:14,250
+5 10 و 20 طبعا سهل انك تتعامل مع هذا السؤال سؤال
+
+379
+00:40:14,250 --> 00:40:20,770
+10 انزد 24 list all generator سؤال 10 زي سؤال 9
+
+380
+00:40:20,770 --> 00:40:27,470
+سؤال 11 generated by ال A inverse ممكن تساوي
+
+381
+00:40:27,470 --> 00:40:28,410
+generated by D
+
+382
+00:40:33,860 --> 00:40:42,580
+أه كيف نثبتها دى فى
+
+383
+00:40:42,580 --> 00:40:46,980
+طريقة تانية اما طريقة الـ C3 answer hand موجودة
+
+384
+00:40:46,980 --> 00:40:53,420
+هنا و العكس او طريقة مباشرة generated by ال A
+
+385
+00:40:53,420 --> 00:41:00,740
+عبارة عن ايش عبارة عن ال A to K I to K من وين
+
+386
+00:41:06,270 --> 00:41:14,650
+هو نفسه عبارة عن a أس سالب k حيث سالب k في زي اين
+
+387
+00:41:14,650 --> 00:41:23,710
+طب a أس سالب k عبارة عن ايش a inverse أس k حيث k
+
+388
+00:41:23,710 --> 00:41:30,670
+في زي اللي هو عبارة عن generated by a inverseطبعا
+
+389
+00:41:30,670 --> 00:41:37,550
+السبب ان هذه الجملة K في Z و A to K تكافئ A و سالب
+
+390
+00:41:37,550 --> 00:41:42,310
+K و سالب K في Z هجيتها دي خلتها زي ما هي سالب K في
+
+391
+00:41:42,310 --> 00:41:49,110
+Z تكافئ ان K و A موجودة في Z بصر Generated by A هي
+
+392
+00:41:49,110 --> 00:41:52,370
+نفسه Generated by A inverse إذا كان حاسس انك مش
+
+393
+00:41:52,370 --> 00:41:58,750
+فاهم هذا الطريقة بإمكانك تاخد answer هناعنصر P
+
+394
+00:41:58,750 --> 00:42:02,110
+ينتبه الـ generated by الـ A فعبارة عن ال A to T
+
+395
+00:42:02,110 --> 00:42:06,970
+فهو نفس ال A inverse السلب T فصار العنصر موجود في
+
+396
+00:42:06,970 --> 00:42:18,610
+generated by ال A inverse والعكس صحيح السؤال
+
+397
+00:42:18,610 --> 00:42:21,930
+12 in Z find all generators of the subgroup
+
+398
+00:42:21,930 --> 00:42:25,270
+generated by تلاتة طبعا
+
+399
+00:42:28,140 --> 00:42:31,620
+فى z generated by التلاتة عبارة عن إيش يا شباب
+
+400
+00:42:31,620 --> 00:42:35,000
+generated
+
+401
+00:42:35,000 --> 00:42:40,540
+by التلاتة فى z صفر موجب سالب تلاتة موجب سالب ستة
+
+402
+00:42:40,540 --> 00:42:49,360
+موجب سالب ست تسعة إلى آخرين بدنا ال generator لهذه
+
+403
+00:42:49,360 --> 00:42:54,980
+ال subgroup ال
+
+404
+00:42:54,980 --> 00:42:56,420
+generators عبارة عن
+
+405
+00:43:00,720 --> 00:43:08,300
+التلاتة ومين كمان؟ والسالب تلاتة حالي بيقدر يقول
+
+406
+00:43:08,300 --> 00:43:13,980
+لي ليش ماخدتش غيره؟ أنا لو أخدت الستة، الستة مش
+
+407
+00:43:13,980 --> 00:43:19,880
+هتولد التلاتة، أنا بشغل في infinite الجهود، لو
+
+408
+00:43:19,880 --> 00:43:23,660
+أخدت التسعة، التسعة مش هتولد الستة، يعني مافيش
+
+409
+00:43:23,660 --> 00:43:28,510
+جدام غير مين؟موجب سالب تلاتة طب هنتعميمها في ال
+
+410
+00:43:28,510 --> 00:43:36,410
+infinite order ال generator by a تكييب هي نفس ال a
+
+411
+00:43:36,410 --> 00:43:46,090
+تكييب وال a والسالب تلاتة هننهي عن السؤال تلتاشر
+
+412
+00:43:46,090 --> 00:43:50,610
+ان شاء الله بنكمل في محاضرة اليوم الساعة اتناشر
+
+413
+00:43:50,610 --> 00:43:53,550
+بقى في الأسئلة يعطيكوا العافية كل عام تبقى مرة
+
+414
+00:43:53,550 --> 00:43:53,910
+تانية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5da0eaf8e67ff8f37969a5713350f6c0c6e11961
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TTuKgG0leug_raw.srt
@@ -0,0 +1,1688 @@
+1
+00:00:21,090 --> 00:00:23,650
+السلام عليكم و رحمة الله و بركاته باسم الله أحمد
+
+2
+00:00:23,650 --> 00:00:28,010
+أحيم طبعا بنراحل فيكم مرة تانية مستكملة لمحاضراتنا
+
+3
+00:00:28,010 --> 00:00:32,350
+و كل عامة بخير مناسبة العيد ان شاء الله خلافه
+
+4
+00:00:32,350 --> 00:00:37,970
+هتذكر ان شاء الله بس بسرعة الأخر محاضرة قبل العيد
+
+5
+00:00:37,970 --> 00:00:41,230
+كان كنا بنتكلم عن نظرية اسمها ال fundamental
+
+6
+00:00:41,230 --> 00:00:48,200
+theorem of cyclic groups طبعا كان فيها تلتالجزء
+
+7
+00:00:48,200 --> 00:00:54,620
+الاول ان اي subgroup من cyclic group بتكون cyclic
+
+8
+00:00:54,620 --> 00:00:59,860
+اي subgroup من cyclic group بتكون cyclic الجزء
+
+9
+00:00:59,860 --> 00:01:06,900
+التانى اي subgroup هيكون ال order لها بيقسم ال
+
+10
+00:01:06,900 --> 00:01:10,600
+order لل group في حالة طبعا ال cyclic group الشغل
+
+11
+00:01:10,600 --> 00:01:15,910
+التالتة لو كان عندي قاسم لل orderلأ الجروب او الـ
+
+12
+00:01:15,910 --> 00:01:20,250
+cyclic group انا بقدر عليها جيونيكسة بالجروب داخل
+
+13
+00:01:20,250 --> 00:01:24,470
+الـ cyclic group و بيكون لها نفس ال order هناخد
+
+14
+00:01:24,470 --> 00:01:34,630
+مثال سريع في هذه الجزئية هنقول التالي example let
+
+15
+00:01:34,630 --> 00:01:45,610
+j generated by a with order ال aبساوة تلاتين
+
+16
+00:01:45,610 --> 00:01:55,770
+المطلوب list all subgroups
+
+17
+00:01:55,770 --> 00:02:00,750
+of G عندي
+
+18
+00:02:00,750 --> 00:02:04,630
+group Cyclic الـ all ضاقينها تلاتين المطلوب مني
+
+19
+00:02:04,630 --> 00:02:11,770
+أجيب كل group Cyclic من الـ G تعالوا نشوف قليل
+
+20
+00:02:11,770 --> 00:02:13,070
+الحل قبل أن نبدأ الحل
+
+21
+00:02:15,780 --> 00:02:23,260
+cyclic group و بدوّع على ال subgroups اللي موجودين
+
+22
+00:02:23,260 --> 00:02:27,480
+ضمن ال group إيش هيكونوا ال subgroups subgroups
+
+23
+00:02:27,480 --> 00:02:28,380
+subgroups subgroups subgroups subgroups subgroups
+
+24
+00:02:28,380 --> 00:02:28,800
+subgroups subgroups subgroups subgroups subgroups
+
+25
+00:02:28,800 --> 00:02:28,880
+subgroups subgroups subgroups subgroups subgroups
+
+26
+00:02:28,880 --> 00:02:28,880
+subgroups subgroups subgroups subgroups subgroups
+
+27
+00:02:28,880 --> 00:02:28,880
+subgroups subgroups subgroups subgroups subgroups
+
+28
+00:02:28,880 --> 00:02:29,220
+subgroups subgroups subgroups subgroups subgroups
+
+29
+00:02:29,220 --> 00:02:35,780
+subgroups subgroups subgroups subgroups
+
+30
+00:02:35,780 --> 00:02:41,420
+subgroups subgroups subgroups subgroups subgroups
+
+31
+00:02:41,420 --> 00:02:41,760
+subgroups subgroups subgroups subgroups subgroups
+
+32
+00:02:41,760 --> 00:02:41,760
+subgroups subgroups subgroups subgroups subgroups
+
+33
+00:02:41,760 --> 00:02:41,760
+subgroups subgroups subgroups subgroups subgroups
+
+34
+00:02:41,760 --> 00:02:41,760
+subgroups subgroups subgroups subgroups subgroups
+
+35
+00:02:41,760 --> 00:02:45,720
+subgroups subgroups subgroupssubgroup يجب أن نبدأ
+
+36
+00:02:45,720 --> 00:02:53,140
+من أين؟ من قواصم ال order لمن؟ لل جي since order
+
+37
+00:02:53,140 --> 00:02:58,160
+ال جي بدى يساوي order ال ايه؟ بدى يساوي تلاتين and
+
+38
+00:02:58,160 --> 00:03:08,180
+جي is cyclic هذا مش معناته هذا معناته for any دي
+
+39
+00:03:08,180 --> 00:03:11,040
+يقسم التلاتين there exist
+
+40
+00:03:15,010 --> 00:03:29,290
+A unique subgroup H of J with order HD الـ
+
+41
+00:03:29,290 --> 00:03:35,510
+subgroups المطلوب ان نجيبهم هم عبارة عن مجموعاتأو
+
+42
+00:03:35,510 --> 00:03:40,070
+subgroups من الـ J ال order له عبارة عن قواصم من؟
+
+43
+00:03:40,070 --> 00:03:43,750
+التلاتين في البداية هجيب قواصم التلاتين و لكل
+
+44
+00:03:43,750 --> 00:03:51,670
+قواصم هجيب ال subgroup المناسبة the divisors of
+
+45
+00:03:51,670 --> 00:04:03,040
+تلاتين are من؟ واحد اتنين تلاتة اربعة؟ لأخمسة ..
+
+46
+00:04:03,040 --> 00:04:13,480
+ستة .. عشرة .. خمستاشر .. تلاتين طيب هدول القواسم
+
+47
+00:04:13,480 --> 00:04:18,460
+تبعون التلاتين الجزء التالت من النظرية بيعطينا شغل
+
+48
+00:04:18,460 --> 00:04:25,600
+تانية ان ال subgroup هذي generated by مين؟
+
+49
+00:04:29,140 --> 00:04:34,400
+تذكروني for any divisor k of n generated by a أُس
+
+50
+00:04:34,400 --> 00:04:44,380
+n على k now for h واحد إيش يعني h واحد يعني ال sub
+
+51
+00:04:44,380 --> 00:04:48,860
+group من ال j اللي ال order إيها إيش واحد هذه
+
+52
+00:04:48,860 --> 00:04:54,830
+بتكون generated by مين؟by a أُس تلاتين على واحد
+
+53
+00:04:54,830 --> 00:04:59,310
+يعني generated by a أُس تلاتين a أُس تلاتين كده
+
+54
+00:04:59,310 --> 00:05:05,970
+الشباب a أُس تلاتين ال identity لأن الأرض على ال a
+
+55
+00:05:05,970 --> 00:05:09,690
+بيسوا تلاتين يكبر هذا generated by ال identity
+
+56
+00:05:09,690 --> 00:05:15,750
+ومافيش فيها غير مين مافيش فيها غير مين غير ال
+
+57
+00:05:15,750 --> 00:05:17,970
+identity طيب H2
+
+58
+00:05:20,000 --> 00:05:23,120
+H2 يعني الـ subgroup للـ order اللي هتنين
+
+59
+00:05:23,120 --> 00:05:29,340
+generated by مين؟ by A أُس ثلاثين على اتنين يعني A
+
+60
+00:05:29,340 --> 00:05:35,140
+أُس خمستاشر اللي عبارة عن ال identity والـ A أُس
+
+61
+00:05:35,140 --> 00:05:43,580
+خمستاشر H3 عبارة عن generated by A أُس ثلاثين على
+
+62
+00:05:43,580 --> 00:05:49,370
+تلاتة يعني by A أُس عشرةيعني ال identity a أُس
+
+63
+00:05:49,370 --> 00:05:58,030
+عشرة a أُس أشرين حمسة حمسة حمسة حمسة حمسة حمسة
+
+64
+00:05:58,030 --> 00:06:03,830
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+65
+00:06:03,830 --> 00:06:07,990
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+66
+00:06:07,990 --> 00:06:10,390
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+67
+00:06:10,390 --> 00:06:10,650
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة حمسة
+
+68
+00:06:10,650 --> 00:06:16,430
+حمسة حمسة حمسة حمسة حمسة حمسة حمسة حA أُس 12 A أُس
+
+69
+00:06:16,430 --> 00:06:22,470
+18 A أُس 24 و بجف لإن A أُس 30 حتي سلمين لل
+
+70
+00:06:22,470 --> 00:06:27,330
+identity أتش 6 عبارة
+
+71
+00:06:27,330 --> 00:06:33,990
+عن generated by A أُس 30 على 6 يعني A أُس 5
+
+72
+00:06:35,060 --> 00:06:41,960
+Identity اوس خمسة اوس عشرة اوس خمستاش اوس عشرين
+
+73
+00:06:41,960 --> 00:06:47,640
+اوس خمسة عشرين ابن جاف لحظة شباب اتش ستة تحتوي
+
+74
+00:06:47,640 --> 00:06:56,820
+داخلها مين اتش تلاتة و اتش اتنين ليش؟ لأن الخمسة
+
+75
+00:06:56,820 --> 00:07:02,620
+او الستة او التلاتة بتقسم الستة والتنين بتقسم
+
+76
+00:07:02,620 --> 00:07:10,840
+الستةطيب اتش مين بعد الستة؟ عشرة فهذا هيساوى ال
+
+77
+00:07:10,840 --> 00:07:16,980
+identity a والثلاثة a والستة a والتسعة لعند a
+
+78
+00:07:16,980 --> 00:07:25,580
+والسبعة وعشرين و اتش خمستائش هصير a a التربية a
+
+79
+00:07:25,580 --> 00:07:34,820
+والاربعة لعند a والتمانية وعشرينواخر واحدة H30 الى
+
+80
+00:07:34,820 --> 00:07:41,580
+الـ generated by الـ A الى الـ G نفسها طبعا يكسر
+
+81
+00:07:41,580 --> 00:07:45,660
+عندي listing لكل ال cyclic subgroup او لكل ال
+
+82
+00:07:45,660 --> 00:07:51,900
+subgroup من ال group J اللي ال order لها بساوي 30
+
+83
+00:07:51,900 --> 00:07:59,620
+اي سؤال يا شباب؟ اي
+
+84
+00:07:59,620 --> 00:08:00,240
+سؤال؟
+
+85
+00:08:03,650 --> 00:08:12,610
+طيب لو خلنا هذا نفس المثال لكن على group معروف ال
+
+86
+00:08:12,610 --> 00:08:19,010
+generator إلها بشكل واضح يعني مش a كرقم لو قولنا
+
+87
+00:08:19,010 --> 00:08:27,510
+مثلا find all subgroups
+
+88
+00:08:27,510 --> 00:08:37,120
+of Z 13 إيش هنعمل؟هنعمل نفس الفكرة اللي اشتغلناها
+
+89
+00:08:37,120 --> 00:08:51,440
+مع فرق واحد ان الـ A أشماله الـ
+
+90
+00:08:51,440 --> 00:08:56,100
+A معروف هو الواحد solution
+
+91
+00:08:56,100 --> 00:09:02,400
+الـ Z 30 عبارة عن generated Pi الواحد و ال order
+
+92
+00:09:02,400 --> 00:09:09,680
+للواحد 100تلاتين using the
+
+93
+00:09:09,680 --> 00:09:18,720
+same method in the last example
+
+94
+00:09:18,720 --> 00:09:26,520
+we get the following cyclic
+
+95
+00:09:26,520 --> 00:09:28,980
+subgroups
+
+96
+00:09:32,670 --> 00:09:41,790
+generated by الواحد الـ H1 الواحد ولا مين الواحد
+
+97
+00:09:41,790 --> 00:09:46,550
+ولا مين الواحد ولا مين الواحد ولا مين الواحد ولا
+
+98
+00:09:46,550 --> 00:09:46,730
+مين الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+99
+00:09:46,730 --> 00:09:46,870
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+100
+00:09:46,870 --> 00:09:47,230
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+101
+00:09:47,230 --> 00:09:47,790
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+102
+00:09:47,790 --> 00:09:49,670
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+103
+00:09:49,670 --> 00:09:49,970
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+104
+00:09:49,970 --> 00:09:50,910
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+105
+00:09:50,910 --> 00:09:52,310
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+106
+00:09:52,310 --> 00:09:53,610
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+107
+00:09:53,610 --> 00:09:55,950
+الواحد ولا مين الواحد ولا مين الواحد ولا مين
+
+108
+00:09:55,950 --> 00:09:58,750
+الواحد
+
+109
+00:10:04,130 --> 00:10:13,790
+H5 الـ 0 الـ 6 الـ 12 الـ 18 الـ 24 وصولا لـ H30
+
+110
+00:10:13,790 --> 00:10:19,970
+اللي عبارة عن الـ Z30 نفسه واضح يا عادي؟ واضح يا
+
+111
+00:10:19,970 --> 00:10:22,870
+شباب؟ في كرولر عن مظهرية اللي فاتت
+
+112
+00:10:28,780 --> 00:10:32,780
+هي نفس الجزئية التالتة من النظرية لكن على group
+
+113
+00:10:32,780 --> 00:10:44,280
+معروفة وهي z,n for every k
+
+114
+00:10:44,280 --> 00:10:50,760
+يقسم ال n there exists a unique subgroup
+
+115
+00:10:57,500 --> 00:11:14,340
+of ZN with order K namely generated
+
+116
+00:11:14,340 --> 00:11:20,260
+by مين؟ طبق الـ band التالت من النظرية السابقة لكن
+
+117
+00:11:20,260 --> 00:11:26,080
+على ZN هكون واحد أسفل N على K اللي هو أبعد عن مين؟
+
+118
+00:11:27,110 --> 00:11:34,170
+ان على ك مش
+
+119
+00:11:34,170 --> 00:11:40,970
+بس هيك these are
+
+120
+00:11:40,970 --> 00:11:47,630
+the only subgroups
+
+121
+00:11:47,630 --> 00:11:55,110
+of z طبعا مافيش غيرها مافيش غيرهم هدولة لكل قاسم
+
+122
+00:11:55,110 --> 00:12:01,530
+للانملاقي subgroup ال order لها هذا القاسم وهي
+
+123
+00:12:01,530 --> 00:12:07,090
+generated by من؟ by n على القاسم طبعا هذا طبقنا
+
+124
+00:12:07,090 --> 00:12:17,970
+عليه المثال الموجود جانب دي مثال سريع for زد مثلا
+
+125
+00:12:17,970 --> 00:12:23,910
+عشرين عند من؟ generated by الواحدgenerated by
+
+126
+00:12:23,910 --> 00:12:29,270
+التنين generated by الأربعة generated by الخمسة
+
+127
+00:12:29,270 --> 00:12:36,490
+and generated by العشرة and generated by الأشعين
+
+128
+00:12:36,490 --> 00:12:50,990
+دول هم ال only cyclic subgroups ل ال z أشعين أيه
+
+129
+00:12:50,990 --> 00:13:02,430
+السؤال يا شبابأي سؤال سؤال عالسريع find the number
+
+130
+00:13:02,430 --> 00:13:15,750
+of subgroups of j generated by a if order a بسوى
+
+131
+00:13:15,750 --> 00:13:16,810
+خمسة وعشرين
+
+132
+00:13:22,100 --> 00:13:28,380
+أوجد عدد الـ subgroups اللي موجودين في الجروب جيه
+
+133
+00:13:28,380 --> 00:13:33,620
+اللي ال order لل generator إلها عبارة عن 25 نجيب
+
+134
+00:13:33,620 --> 00:13:39,400
+عدد قواسم الخمسة وعشرين ويكون هو عدد ال subgroups
+
+135
+00:13:39,400 --> 00:13:44,040
+the divisors of
+
+136
+00:13:44,040 --> 00:13:51,560
+خمسة وعشرين are واحد خمسة وخمسة وعشرين يجب كموحدة
+
+137
+00:13:52,410 --> 00:14:02,190
+there are only three subgroups
+
+138
+00:14:02,190 --> 00:14:09,910
+of G فقط تلاتة cyclic subgroups أو subgroups
+
+139
+00:14:09,910 --> 00:14:16,630
+موجودين هنا أنهينا السؤال المتعلق بعدد ال cyclic
+
+140
+00:14:16,630 --> 00:14:22,350
+subgroup بيجي سؤال تانيسؤال الأول هو قداش عدد ال
+
+141
+00:14:22,350 --> 00:14:27,970
+generator في ال cyclic group؟سؤال التاني لو كان
+
+142
+00:14:27,970 --> 00:14:35,190
+عندي قاسم لل order لل group cyclic نقول لو كان
+
+143
+00:14:35,190 --> 00:14:38,610
+عندي قاسم فانا بلاقي sub group ال order لهذا
+
+144
+00:14:38,610 --> 00:14:41,950
+القاسم لما اقول sub group من cyclic و ال order
+
+145
+00:14:41,950 --> 00:14:45,090
+لهذا القاسم معناته انها generator وهذا ال
+
+146
+00:14:45,090 --> 00:14:49,170
+generator ال order له بيساوي القاسم يعني لكل قاسم
+
+147
+00:14:49,170 --> 00:14:56,310
+ل order ال finite group cyclic بلاقي عنصر جواالـ
+
+148
+00:14:56,310 --> 00:15:00,210
+لـ group ال order إيه له هذا القاسم طب السؤال كم
+
+149
+00:15:00,210 --> 00:15:06,410
+عنصر من هذا النوع بلاجي بلاجي واحد أه طب جديش
+
+150
+00:15:06,410 --> 00:15:12,430
+بالظبط عشان نقدر نعرف هذا الجواب هنعرف function
+
+151
+00:15:12,430 --> 00:15:17,670
+اسمه الearlier phi function هتدرس بالتفصيل في مساق
+
+152
+00:15:17,670 --> 00:15:20,950
+نظرية الأعداد definition
+
+153
+00:15:23,750 --> 00:15:35,810
+Euler Phi Function متعرفة
+
+154
+00:15:35,810 --> 00:15:45,290
+بالشكل التالي فايل واحد بيساوي واحد اتنين if n
+
+155
+00:15:45,290 --> 00:15:52,530
+أكبر من واحد then فايل n يساوي ال number
+
+156
+00:15:56,000 --> 00:16:03,600
+of integers less than
+
+157
+00:16:03,600 --> 00:16:11,360
+أن عدد العدد الصحيح اللي أقل من الان and
+
+158
+00:16:11,360 --> 00:16:14,400
+relatively
+
+159
+00:16:14,400 --> 00:16:17,600
+prime
+
+160
+00:16:17,600 --> 00:16:21,300
+with
+
+161
+00:16:24,550 --> 00:16:27,690
+طبعا أنا بتكلم مش عن integers بس انا ممكن اضيف
+
+162
+00:16:27,690 --> 00:16:32,750
+كلمة the number of positive integers
+
+163
+00:16:32,750 --> 00:16:38,010
+عشان ماحدش يروح يحسبلي الاعداد السالبة في ملاحظة
+
+164
+00:16:38,010 --> 00:16:45,870
+غير ان note that file and عبارة عن ال order لل
+
+165
+00:16:45,870 --> 00:16:47,830
+group UN
+
+166
+00:16:49,930 --> 00:16:54,650
+فايل ان عبارة عن order لجروب UN وهذا من المنطقى
+
+167
+00:16:54,650 --> 00:17:01,930
+لأن جروب UN تأخذ الأعداد المحصورة بين الواحد و
+
+168
+00:17:01,930 --> 00:17:12,590
+الان والتي تكون relatively prime with الان الان
+
+169
+00:17:12,590 --> 00:17:16,810
+أكبر من واحد ده لكن أنا ما أعد الان بعد الأعداد
+
+170
+00:17:16,810 --> 00:17:20,860
+الأقل منها فلازم يكونوا positive عشان اناأشغل صح
+
+171
+00:17:20,860 --> 00:17:34,600
+طيب كمثال سريع لو
+
+172
+00:17:34,600 --> 00:17:39,080
+قولنا في التنين كده؟
+
+173
+00:17:39,080 --> 00:17:44,520
+واحد كم عدد جاب للتنين لغاية الابراهيم مع التنين؟
+
+174
+00:17:44,520 --> 00:17:45,440
+في العشرة
+
+175
+00:17:49,180 --> 00:17:57,880
+1 و 3 و 7 و 9 جديش؟ اربعة فاي ل prime كم عدد جابل
+
+176
+00:17:57,880 --> 00:18:04,780
+اي عدد اولي relatively prime مع بي minus one بي is
+
+177
+00:18:04,780 --> 00:18:16,320
+prime طيب في اتنين اص كيه؟ جديش؟
+
+178
+00:18:17,630 --> 00:18:20,690
+العداد الـ relatively prime مع ال power للتنين هي
+
+179
+00:18:20,690 --> 00:18:25,390
+العداد الفردية فقط اللي عبارة عن إيش؟ تنين قصه K
+
+180
+00:18:25,390 --> 00:18:33,390
+minus one لو قلنا file P to K عبارة
+
+181
+00:18:33,390 --> 00:18:37,030
+عن إيش؟
+
+182
+00:18:37,030 --> 00:18:42,590
+P to
+
+183
+00:18:42,590 --> 00:18:47,350
+K minus one
+
+184
+00:18:48,650 --> 00:18:53,070
+هذا بصورة عميم لهذه العلاقة عشان نعممها على الأكتر
+
+185
+00:18:53,070 --> 00:19:02,490
+if n إبتدت عن P1 to K1 P2 to K2 and PR to KR هيكون
+
+186
+00:19:02,490 --> 00:19:18,850
+then في ال N إبتدت عن P1 to K1-P1 to K1-1 فيP2-P2
+
+187
+00:19:18,850 --> 00:19:26,810
+-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2
+
+188
+00:19:26,810 --> 00:19:28,430
+-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2
+
+189
+00:19:28,430 --> 00:19:28,430
+-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2-P2
+
+190
+00:19:28,430 --> 00:19:33,490
+-P2-P2-P2
+
+191
+00:19:33,910 --> 00:19:40,010
+و التفاصيل التفاصيل لكن بستعمل فيها concepts مش
+
+192
+00:19:40,010 --> 00:19:43,210
+موجودة عندي في هذا المساق اشتغل على ال
+
+193
+00:19:43,210 --> 00:19:47,710
+multiplicative functions و بعض الأمور من هذا النوع
+
+194
+00:19:47,710 --> 00:19:54,370
+طيب
+
+195
+00:19:54,370 --> 00:19:58,010
+ايش دخل ال function هذه في موضوعنا هتيجي النظرية
+
+196
+00:19:58,010 --> 00:20:01,230
+اربع اربع و توضح
+
+197
+00:20:05,040 --> 00:20:09,440
+بنخلصه ان شاء الله بضايق نظرية واحدة بيساوي رقم
+
+198
+00:20:09,440 --> 00:20:17,120
+معين let J بيساوي generated by ال A و أخضر ال A
+
+199
+00:20:17,120 --> 00:20:18,100
+بيساوي N
+
+200
+00:20:21,780 --> 00:20:25,380
+دى يقسم الان طبعا دى يقسم الان احنا هيك بنقول ان
+
+201
+00:20:25,380 --> 00:20:29,600
+يوجد only one sub group of order دى namely
+
+202
+00:20:29,600 --> 00:20:34,500
+generated by a to n على d هيت السؤال جداش عدد ال
+
+203
+00:20:34,500 --> 00:20:40,600
+generator then the
+
+204
+00:20:40,600 --> 00:20:48,320
+elements او the number of
+
+205
+00:20:48,320 --> 00:20:49,080
+elements
+
+206
+00:20:51,850 --> 00:21:05,150
+in J with order D is فاية D عدد العناصر في J اللي
+
+207
+00:21:05,150 --> 00:21:12,610
+ال order لهم بيساوي D بيساوياش فاية D نيجي نتبت
+
+208
+00:21:12,610 --> 00:21:16,270
+نيجي
+
+209
+00:21:16,270 --> 00:21:17,690
+نتبت العلاقة
+
+210
+00:21:20,740 --> 00:21:28,020
+اربع تلاتة part c ايش ال part c في النظرية هذه
+
+211
+00:21:28,020 --> 00:21:35,760
+بيقول؟ there exist a unique .. طبعا there exist
+
+212
+00:21:35,760 --> 00:21:42,040
+unique subgroup of
+
+213
+00:21:42,040 --> 00:21:48,440
+j with order d
+
+214
+00:21:48,440 --> 00:21:50,100
+namely
+
+215
+00:21:53,030 --> 00:22:01,270
+generated by a to n على d طيب
+
+216
+00:22:01,270 --> 00:22:06,550
+هل جيت؟ مده مافيش غير هذه ال subgroup ال order
+
+217
+00:22:06,550 --> 00:22:10,570
+اللي هي دي فالعناصر لل order اللي هي دي ممكن تكون
+
+218
+00:22:10,570 --> 00:22:11,350
+موجودة برا
+
+219
+00:22:15,080 --> 00:22:19,640
+الـ uniqueness لهذه ال subgroup بخليني أقول إنه
+
+220
+00:22:19,640 --> 00:22:24,920
+جميع العناصر اللي ال order إلها دي و اللي موجودة
+
+221
+00:22:24,920 --> 00:22:35,780
+دي هو هذه ال subgroup هذا معناته all elements in J
+
+222
+00:22:35,780 --> 00:22:48,500
+with order D are in thissubgroup طيب
+
+223
+00:22:48,500 --> 00:22:52,840
+كل
+
+224
+00:22:52,840 --> 00:22:57,080
+العناصر لل order اللي دي موجودين هنا يعني بلو أنا
+
+225
+00:22:57,080 --> 00:23:01,960
+عرفت أكمع عنصر ال order اللي دي في هذه ال subgroup
+
+226
+00:23:01,960 --> 00:23:08,420
+بكون خلصت now each
+
+227
+00:23:08,420 --> 00:23:12,900
+one of these elements
+
+228
+00:23:16,390 --> 00:23:23,370
+is a generator of
+
+229
+00:23:23,370 --> 00:23:30,930
+this subgroup
+
+230
+00:23:30,930 --> 00:23:38,070
+ليش؟ العنصر هذا ال order له دي وموجود في group ال
+
+231
+00:23:38,070 --> 00:23:44,130
+order له دي ايه بيكون لها؟ بيكون لها مولّب، بيكون
+
+232
+00:23:44,130 --> 00:23:49,090
+generatorNow if
+
+233
+00:23:49,090 --> 00:23:56,370
+generated by A to N على D ممكن اكتبها generated by
+
+234
+00:23:56,370 --> 00:24:05,470
+P with order ال P بدي سو D then the other
+
+235
+00:24:05,470 --> 00:24:10,130
+generators
+
+236
+00:24:10,130 --> 00:24:13,110
+are of the form
+
+237
+00:24:16,330 --> 00:24:29,370
+B to K والجريس common divisor لD وK وD سوى 1 رجع
+
+238
+00:24:29,370 --> 00:24:34,030
+ليش لنظرية اللي أخدناها في أول الشبتر ان ال
+
+239
+00:24:34,030 --> 00:24:39,090
+generator او ال .. ال .. حيكون عبارة عن عناصرالـ
+
+240
+00:24:39,090 --> 00:24:42,790
+order او ال .. ال .. ال .. ال .. ال power تبعها
+
+241
+00:24:42,790 --> 00:24:47,230
+لجيسكم ال divisor إله relative لبرايم مع order ل
+
+242
+00:24:47,230 --> 00:24:53,030
+group نفسها أكم كيب اللاجي أكم
+
+243
+00:24:53,030 --> 00:24:59,410
+كيب اللاجي relative لبرايم مع دي يا شباب and we
+
+244
+00:24:59,410 --> 00:25:12,810
+can find .. find ال Dof this such K بقدر ألاقي
+
+245
+00:25:12,810 --> 00:25:22,790
+فاية D من هذه الأرقام K so the number of elements
+
+246
+00:25:22,790 --> 00:25:35,510
+in J with order D is فاية D وهو المطلوب
+
+247
+00:25:42,170 --> 00:25:45,330
+اللي صار كانت تانية يا شباب انا بدور على عناصر لل
+
+248
+00:25:45,330 --> 00:25:49,450
+order الهدى نقلت المسألة من اني ابحث في ال ج كلها
+
+249
+00:25:49,450 --> 00:25:54,170
+لاني ابحث وين في ال sub group لل order الهدى ميزة
+
+250
+00:25:54,170 --> 00:25:58,610
+العناصر هنا لل order الهدى انها generator انا عشان
+
+251
+00:25:58,610 --> 00:26:02,430
+اعدى كام generator باخد واحد من هذه ال generators
+
+252
+00:26:02,430 --> 00:26:06,890
+فليكن بيه و باقى ال generators عبارة عن P to K و
+
+253
+00:26:06,890 --> 00:26:11,250
+ال K relative لبرايم مع مينمع ال D أكم عمصر بقدر
+
+254
+00:26:11,250 --> 00:26:15,110
+أجري راتب لبرايم مع ال D و أجال من ال D محصوب من
+
+255
+00:26:15,110 --> 00:26:19,390
+ال D والواحد و عبارة عن فاية D و بتالي وجد فاية D
+
+256
+00:26:19,390 --> 00:26:25,270
+subgroup
+
+257
+00:26:25,270 --> 00:26:30,010
+وحيدة في ال G لكن أكم element بولدها وحيد
+
+258
+00:26:36,100 --> 00:26:42,140
+يعني مثلا ال z يوجد في ال z 30 only subgroup of
+
+259
+00:26:42,140 --> 00:26:47,240
+order 15 هي generated by a 2 طبعا ال a 2 في ال z
+
+260
+00:26:47,240 --> 00:26:52,120
+30 يعني هي by 2 بس أكم generator ل ال generated by
+
+261
+00:26:52,120 --> 00:26:58,260
+2 في ال z 30 بولد
+
+262
+00:26:58,260 --> 00:27:03,520
+ال generated by 2 ماتقوليش في عيه 2 لأ في عيه 30
+
+263
+00:27:03,520 --> 00:27:13,280
+على 2 في عيه 15لو اعتقد بيطلع تمانية طيب ناخد مثال
+
+264
+00:27:13,280 --> 00:27:27,140
+رقمى من في ال chapter then
+
+265
+00:27:27,140 --> 00:27:33,260
+find the
+
+266
+00:27:33,260 --> 00:27:39,200
+numberof elements in
+
+267
+00:27:39,200 --> 00:27:49,720
+z اربعين with order عشرين
+
+268
+00:27:49,720 --> 00:28:02,020
+اكم عنصر في z اربعين ال order لهم عشرين فعل
+
+269
+00:28:02,020 --> 00:28:09,740
+عشرين هذه النظرية اللي قدامكسلوشين هناك
+
+270
+00:28:09,740 --> 00:28:20,800
+فايل عشرين فايل
+
+271
+00:28:20,800 --> 00:28:31,900
+عشرين كده فايل عشرين تمانية تقدر
+
+272
+00:28:31,900 --> 00:28:32,320
+تجيبهم
+
+273
+00:28:35,510 --> 00:28:43,310
+تقدر تجيبهم؟ هذه العناصر الأخضر إلها تمانية تعالوا
+
+274
+00:28:43,310 --> 00:28:55,170
+نفكر We to find them We
+
+275
+00:28:55,170 --> 00:29:02,810
+find one Let
+
+276
+00:29:06,040 --> 00:29:13,900
+مثلا a ينتمي لزد اربعين و order ال a بيساوي ايش؟
+
+277
+00:29:13,900 --> 00:29:22,420
+عشرين ال a ايش هيساوي؟ مين هو العنصر اللي في زد
+
+278
+00:29:22,420 --> 00:29:25,020
+عشرين؟ او اتل واحد من العناصر اللي في زد اربعين
+
+279
+00:29:25,020 --> 00:29:29,540
+اللي ال order العشرين؟
+
+280
+00:29:29,540 --> 00:29:33,980
+ال a او
+
+281
+00:29:33,980 --> 00:29:39,490
+findممكن ناخد الاي عبارة عن واحد اصر اربعين على
+
+282
+00:29:39,490 --> 00:29:45,350
+عشرين اللي هو عبارة عن جد ياشر واحد اصر عشرين و
+
+283
+00:29:45,350 --> 00:29:50,790
+واحد اصر اتنين اللي هو اتنين في زد اربعين ايه
+
+284
+00:29:50,790 --> 00:29:53,850
+بالعنصر اللي ال order ايه له عشرين او واحد العناصر
+
+285
+00:29:53,850 --> 00:29:59,210
+اللي ال order ايه له عشرين في زد اربعين هو مين ال
+
+286
+00:29:59,210 --> 00:30:02,570
+other elements are
+
+287
+00:30:06,130 --> 00:30:12,190
+تانية نقص كتانية
+
+288
+00:30:12,190 --> 00:30:17,070
+نقص تسعة
+
+289
+00:30:17,070 --> 00:30:21,430
+أو سبعة في الأول تانية نقص تسعة تانية نقص احداش
+
+290
+00:30:21,430 --> 00:30:35,650
+تانية نقص تلاتاش تانية نقص17 2 19 2 6 14 18 22 26
+
+291
+00:30:35,650 --> 00:30:48,250
+34 38 هذه هي العناصر اللي ال order لها يساوي 20 في
+
+292
+00:30:48,250 --> 00:30:54,450
+z أربع تمام
+
+293
+00:30:58,650 --> 00:31:05,490
+ما هو هذا زد ان الاص بيصير تنين اص واحد يعني انا
+
+294
+00:31:05,490 --> 00:31:07,790
+واحد في اتنين اتنين تنين اص ثلاثة انا تلاتة في
+
+295
+00:31:07,790 --> 00:31:20,350
+اتنين ستة تنين اص واحد هذي لأ هذي سهل هنفوت
+
+296
+00:31:20,350 --> 00:31:26,250
+هناخد جزء discussion مناقشة طبعا محاضرة الجزء اللي
+
+297
+00:31:26,250 --> 00:31:29,550
+ضال من محاضرة اليوم زادالمحاضرة اللى هناخدها
+
+298
+00:31:29,550 --> 00:31:34,270
+الساعة 12 زاد محاضرة الأتنين هنناقش فيهم مجموعة من
+
+299
+00:31:34,270 --> 00:31:39,770
+أسئلة chapter 4 ما بعرف هل هنخلص أو لأ إذا ما
+
+300
+00:31:39,770 --> 00:31:43,870
+خلصنا ممكن ناخد محاضرة الأربع أو محاضرة تعويضية
+
+301
+00:31:43,870 --> 00:31:55,450
+للمناقشة أنا همسح الجزء هذا طبعا
+
+302
+00:31:57,470 --> 00:31:59,950
+زي ما انت شاير هذا ال chapter الأسئلة عددها كبير
+
+303
+00:31:59,950 --> 00:32:05,030
+يعني ما يقارب حوالي من خمسة ربيع لخمسين سؤال فانا
+
+304
+00:32:05,030 --> 00:32:07,990
+مش هعمل زي ال chapter الفاتوح اللي الجميع هي بعض
+
+305
+00:32:07,990 --> 00:32:13,730
+الأسئلة هعطيك مساعدة إليك فيها و أنت تكمل يعني
+
+306
+00:32:13,730 --> 00:32:17,810
+خصوصا الأسئلة من واحد لخمس عشر إما أسئلة حسابية أو
+
+307
+00:32:17,810 --> 00:32:23,730
+أسئلة سهل إن الطالب يقدر يعرفها لوحده
+
+308
+00:32:43,420 --> 00:32:49,200
+السؤال الأول find all generator of z6, z8, z20
+
+309
+00:32:49,200 --> 00:32:56,660
+طبعا ال generator غيرنا عبارة عن مين؟ لو طلعنا على
+
+310
+00:32:56,660 --> 00:33:02,540
+نظرية أو corollary لنظرية الأولى كان بيقولك ال
+
+311
+00:33:02,540 --> 00:33:06,660
+generator ل zn هي عبارة عن مين؟ عن الأرقام اللي
+
+312
+00:33:06,660 --> 00:33:10,160
+relative ل برايم مع ال n اللي هي فعليا عبارة عناش؟
+
+313
+00:33:10,160 --> 00:33:15,950
+عناصر ال UNفلو داشت على ز داش ز تلاتين او ز عشرين
+
+314
+00:33:15,950 --> 00:33:21,470
+منهم ما هيكونوا واحد و تلاتة و سبعة و تسعة احداش
+
+315
+00:33:21,470 --> 00:33:26,250
+تلاتاش سبعتاش تسعة عشر اعتقد حلنا السؤال على ز
+
+316
+00:33:26,250 --> 00:33:36,580
+تلاتين اتناء الحل لو دينا سؤال اتنينSuppose that
+
+317
+00:33:36,580 --> 00:33:39,960
+A, B or generated by A, generated by B, generated
+
+318
+00:33:39,960 --> 00:33:45,040
+by C are cyclic group of order 6,8,20 Find all
+
+319
+00:33:45,040 --> 00:33:49,300
+generators generated by A, generated by B,
+
+320
+00:33:49,540 --> 00:33:53,780
+generated by C حلنا سؤال على هذا النمط، لو اشتغلنا
+
+321
+00:33:53,780 --> 00:33:58,680
+مثلا على generated by C و ال order لـ C بدي يسوى
+
+322
+00:33:58,680 --> 00:34:03,420
+20 فgenerated by C هو نفسه generated by C تكيب
+
+323
+00:34:04,170 --> 00:34:08,850
+Generated by C أُس سبعة Generated by C أُس تسعة
+
+324
+00:34:08,850 --> 00:34:08,930
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+325
+00:34:08,930 --> 00:34:10,850
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+326
+00:34:10,850 --> 00:34:12,410
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+327
+00:34:12,410 --> 00:34:12,410
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+328
+00:34:12,410 --> 00:34:12,690
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+329
+00:34:12,690 --> 00:34:12,710
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+330
+00:34:12,710 --> 00:34:12,710
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+331
+00:34:12,710 --> 00:34:15,370
+Generated by C أُس تسعة Generated by C أُس تسعة
+
+332
+00:34:15,370 --> 00:34:21,850
+Generated by C أُس تسعة Generated
+
+333
+00:34:21,850 --> 00:34:29,600
+by C أُس تسعة Generated bylist all elements of the
+
+334
+00:34:29,600 --> 00:34:35,580
+subgroups generated by 20 generated by 10 in z 30
+
+335
+00:34:35,580 --> 00:34:42,040
+let a,b طبعا سؤال تلاتة هو نفسه واحد واتنين لكن
+
+336
+00:34:42,040 --> 00:34:50,240
+على مين على ال order 30 تقل
+
+337
+00:34:50,240 --> 00:34:51,960
+السؤال الرابع when
+
+338
+00:34:56,310 --> 00:35:07,450
+C plus 1 هي نفس الـ C سؤال
+
+339
+00:35:07,450 --> 00:35:19,490
+أربعة زي سؤال تلاتة سؤال خمسة في شغل نشغل في U20يو
+
+340
+00:35:19,490 --> 00:35:24,790
+عشرين جديش يا شباب؟ واحد، تلاتة، سبعة، تسعة، داشر،
+
+341
+00:35:24,790 --> 00:35:30,650
+تلتاشر، سبعتاشر، تسعة، اتاشر List the elements of
+
+342
+00:35:30,650 --> 00:35:34,430
+generated by تلاتة وسبعة ناخد generated by سبعة
+
+343
+00:35:34,430 --> 00:35:43,250
+مثلا اللي عبارة عن الواحد السبعة سبعة تغبيع جديش؟
+
+344
+00:35:43,250 --> 00:35:50,760
+تسعة واربعين مدة عشرين جديش؟ تسعةسبعة تكيب يعني
+
+345
+00:35:50,760 --> 00:36:02,320
+سبعة في تسعة تلاتة قصتين تلاتة سبعة أربعة يعني
+
+346
+00:36:02,320 --> 00:36:07,200
+سبعة في تلاتة يعني واحد و عشرين و واحد طبعا
+
+347
+00:36:07,200 --> 00:36:14,020
+generated by تلاتة عبارة عن من؟ واحد تلاتة تلاتة
+
+348
+00:36:14,020 --> 00:36:17,980
+تربية تسعة بعدين سبعة و عشرين سبعة بعدين حتيجة
+
+349
+00:36:21,630 --> 00:36:26,370
+طيب سؤال السادس what do exercises تلاتة و أربعة و
+
+350
+00:36:26,370 --> 00:36:29,510
+خمسة have in common try to make a generalization
+
+351
+00:36:29,510 --> 00:36:36,730
+that includes these three cases انت لما تحل سؤال
+
+352
+00:36:36,730 --> 00:36:43,070
+تلاتة و أربعة و خمسة ايش بتستنتجه؟
+
+353
+00:36:43,070 --> 00:36:49,430
+ايش السنتجات اللي ممكن تستنتجها؟ لو طلعنا على خمسة
+
+354
+00:36:50,250 --> 00:36:54,730
+هنستنتج ان ال generated by ال element و ال
+
+355
+00:36:54,730 --> 00:37:00,530
+generated by ال inverse تبعوا نفس الشيء طيب لو
+
+356
+00:37:00,530 --> 00:37:03,410
+جينا السؤال 4 list the elements of the subgroups 3
+
+357
+00:37:03,410 --> 00:37:08,490
+and 15 in Z18 التلاتة و الخمس عشر في Z18 شمالهم
+
+358
+00:37:08,490 --> 00:37:12,310
+برضه inverse لو جينا السؤال تلاتة
+
+359
+00:37:16,050 --> 00:37:19,390
+عشرة و عشرين في زي التلاتين اشمالهم برضه inverse
+
+360
+00:37:19,390 --> 00:37:24,630
+يجب الاستنتاج تبع سؤال تلاتة او اربع او خمسة اللي
+
+361
+00:37:24,630 --> 00:37:30,010
+انا بدي احطه في سؤال ستة انه generated by ال a
+
+362
+00:37:30,010 --> 00:37:38,670
+generated by ال a inverse وهذا اثبتناه في شبتر
+
+363
+00:37:38,670 --> 00:37:39,450
+تلاتة
+
+364
+00:37:42,190 --> 00:37:47,870
+طيب سبعة find an example of a non-cyclic group all
+
+365
+00:37:47,870 --> 00:37:53,810
+of whose proper subgroup are cyclic اعطيني group
+
+366
+00:37:53,810 --> 00:38:01,210
+not cyclic لأن كل ال subgroup اسمينها cyclic مارت
+
+367
+00:38:01,210 --> 00:38:07,730
+علينا في ال chapter اللي فات خدناها D6
+
+368
+00:38:07,730 --> 00:38:11,490
+وD4 اي واحدة من ال D
+
+369
+00:38:14,340 --> 00:38:23,440
+بتكون صحيحة دي اربعة او دي ستة او دي تمانية بكون
+
+370
+00:38:23,440 --> 00:38:33,260
+صح ال U تمانية سائق لك ال U تمانية صح
+
+371
+00:38:33,260 --> 00:38:39,200
+صح ال U تمانية تمانية
+
+372
+00:38:41,150 --> 00:38:44,110
+let a be an element of a group and let order a
+
+373
+00:38:44,110 --> 00:38:47,990
+بسوا 15 compute the orders of the following طبعا
+
+374
+00:38:47,990 --> 00:38:57,390
+هذا سهل مثلا ال order ل a أس 9 عبارة عن عبارة عن
+
+375
+00:38:57,390 --> 00:39:04,510
+إيش ال order ل a أس k عبارة عن إيش في نظرية في أول
+
+376
+00:39:04,510 --> 00:39:10,650
+واحدة خدناها and علىالـ order ل a of k عبارة عن n
+
+377
+00:39:10,650 --> 00:39:14,690
+على الجيز common divisor ل n mark a يعني عبارة عن
+
+378
+00:39:14,690 --> 00:39:20,170
+خمستاش على جيز common divisor لخمستاش تسعة فتطلع
+
+379
+00:39:20,170 --> 00:39:27,450
+خمسة طبعا نفس القصة في b و نفس القصة في c
+
+380
+00:39:33,530 --> 00:39:41,330
+سؤال تسعة how many subgroups of Z20 توحى لنا توحى
+
+381
+00:39:41,330 --> 00:39:47,070
+لنا شباب في Z20 كام subgroup اللي أجى؟ عوام ال 20
+
+382
+00:39:47,070 --> 00:39:51,850
+عوام ال 20 و لا عوام ال 20؟ لأ عوام ال 20
+
+383
+00:39:51,850 --> 00:39:56,530
+generator لكن subgroup احنا قلنا فيه عددين عدد ال
+
+384
+00:39:56,530 --> 00:40:01,370
+subgroups اللي هو عدد القواسملكن عدد ال generator
+
+385
+00:40:01,370 --> 00:40:08,170
+اللي هو ال file عدد القواسم من ال 20 جديش 6 1 2 4
+
+386
+00:40:08,170 --> 00:40:14,250
+5 10 و 20 طبعا سهل انك تتعامل مع هذا السؤال سؤال
+
+387
+00:40:14,250 --> 00:40:20,770
+10 انزد 24 list all generator سؤال 10 زي سؤال 9
+
+388
+00:40:20,770 --> 00:40:27,470
+سؤال 11 generated by ال A inverse ممكن تساوي
+
+389
+00:40:27,470 --> 00:40:28,410
+generated by D
+
+390
+00:40:33,860 --> 00:40:42,580
+أه كيف نثبتها دى فى
+
+391
+00:40:42,580 --> 00:40:46,980
+طريقة تانية اما طريقة الـ C3 answer hand موجودة
+
+392
+00:40:46,980 --> 00:40:53,420
+هنا و العكس او طريقة مباشرة generated by ال A
+
+393
+00:40:53,420 --> 00:41:00,740
+عبارة عن ايش عبارة عن ال A to K I to K من وين
+
+394
+00:41:06,270 --> 00:41:14,650
+هو نفسه عبارة عن a أس سالب k حيث سالب k في زي اين
+
+395
+00:41:14,650 --> 00:41:23,710
+طب a أس سالب k عبارة عن ايش a inverse أس k حيث k
+
+396
+00:41:23,710 --> 00:41:30,670
+في زي اللي هو عبارة عن generated by a inverseطبعا
+
+397
+00:41:30,670 --> 00:41:37,550
+السبب ان هذه الجملة K في Z و A to K تكافئ A و سالب
+
+398
+00:41:37,550 --> 00:41:42,310
+K و سالب K في Z هجيتها دي خلتها زي ما هي سالب K في
+
+399
+00:41:42,310 --> 00:41:49,110
+Z تكافئ ان K و A موجودة في Z بصر Generated by A هي
+
+400
+00:41:49,110 --> 00:41:52,370
+نفسه Generated by A inverse إذا كان حاسس انك مش
+
+401
+00:41:52,370 --> 00:41:58,750
+فاهم هذا الطريقة بإمكانك تاخد answer هناعنصر P
+
+402
+00:41:58,750 --> 00:42:02,110
+ينتبه الـ generated by الـ A فعبارة عن ال A to T
+
+403
+00:42:02,110 --> 00:42:06,970
+فهو نفس ال A inverse السلب T فصار العنصر موجود في
+
+404
+00:42:06,970 --> 00:42:18,610
+generated by ال A inverse والعكس صحيح السؤال
+
+405
+00:42:18,610 --> 00:42:21,930
+12 in Z find all generators of the subgroup
+
+406
+00:42:21,930 --> 00:42:25,270
+generated by تلاتة طبعا
+
+407
+00:42:28,140 --> 00:42:31,620
+فى z generated by التلاتة عبارة عن إيش يا شباب
+
+408
+00:42:31,620 --> 00:42:35,000
+generated
+
+409
+00:42:35,000 --> 00:42:40,540
+by التلاتة فى z صفر موجب سالب تلاتة موجب سالب ستة
+
+410
+00:42:40,540 --> 00:42:49,360
+موجب سالب ست تسعة إلى آخرين بدنا ال generator لهذه
+
+411
+00:42:49,360 --> 00:42:54,980
+ال subgroup ال
+
+412
+00:42:54,980 --> 00:42:56,420
+generators عبارة عن
+
+413
+00:43:00,720 --> 00:43:08,300
+التلاتة ومين كمان؟ والسالب تلاتة حالي بيقدر يقول
+
+414
+00:43:08,300 --> 00:43:13,980
+لي ليش ماخدتش غيره؟ أنا لو أخدت الستة، الستة مش
+
+415
+00:43:13,980 --> 00:43:19,880
+هتولد التلاتة، أنا بشغل في infinite الجهود، لو
+
+416
+00:43:19,880 --> 00:43:23,660
+أخدت التسعة، التسعة مش هتولد الستة، يعني مافيش
+
+417
+00:43:23,660 --> 00:43:28,510
+جدام غير مين؟موجب سالب تلاتة طب هنتعميمها في ال
+
+418
+00:43:28,510 --> 00:43:36,410
+infinite order ال generator by a تكييب هي نفس ال a
+
+419
+00:43:36,410 --> 00:43:46,090
+تكييب وال a والسالب تلاتة هننهي عن السؤال تلتاشر
+
+420
+00:43:46,090 --> 00:43:50,610
+ان شاء الله بنكمل في محاضرة اليوم الساعة اتناشر
+
+421
+00:43:50,610 --> 00:43:53,550
+بقى في الأسئلة يعطيكوا العافية كل عام تبقى مرة
+
+422
+00:43:53,550 --> 00:43:53,910
+تانية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TxbkO72dNBs_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TxbkO72dNBs_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..944cfb404576ff516c8bc387c94551697ae2cf2e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/TxbkO72dNBs_raw.srt
@@ -0,0 +1,1700 @@
+1
+00:00:22,350 --> 00:00:26,430
+بنكمل برهانة اللمة اللى ابتدأنا فيه المحاضرة
+
+2
+00:00:26,430 --> 00:00:30,950
+الماضية طبعا اللمة هذه عبارة عن ثمانى نقاط برهانة
+
+3
+00:00:30,950 --> 00:00:36,090
+منها اللى هو خمس نقاط بنجي الأن لنقطة السادسة
+
+4
+00:00:36,090 --> 00:00:43,270
+النقطة رقم ستة بيقوللي ان ال order لل A H يساوي ال
+
+5
+00:00:43,270 --> 00:00:50,110
+order لل B Hالمقصود من ذلك انه لو عملت اي left
+
+6
+00:00:50,110 --> 00:00:54,430
+coset او right coset لsub group من ال group
+
+7
+00:00:54,430 --> 00:00:59,690
+الأساسية بدي يطلع في كل left coset نفس العدد من
+
+8
+00:00:59,690 --> 00:01:03,810
+العناصر او لو كانت right cosets بضبط بدي يطلع في
+
+9
+00:01:03,810 --> 00:01:09,290
+كل تنتين او كلهم هيطلع في كل واحدة فيهم نفس العدد
+
+10
+00:01:09,290 --> 00:01:14,770
+من العناصريبقى order للـ A H يسوى order للـ B H
+
+11
+00:01:14,770 --> 00:01:20,510
+لكل الـ A والـ B الموجودة في group G يبقى هذا صحيح
+
+12
+00:01:20,510 --> 00:01:27,460
+لكل الـ A والـ B الموجودة في group Gمشان نثبت ان
+
+13
+00:01:27,460 --> 00:01:30,700
+ال order ل group يسوي ال order ل group قولنا يكفي
+
+14
+00:01:30,700 --> 00:01:33,940
+نثبت انه في function ما بين الاتنين و ال function
+
+15
+00:01:33,940 --> 00:01:38,000
+تبقى one to one and unto هذا بيعطيني ان عدد
+
+16
+00:01:38,000 --> 00:01:44,140
+العناصر في الأولى يسوي عدد العناصر في الثانية لذلك
+
+17
+00:01:44,140 --> 00:01:47,940
+بدي اجي ابرهن هذه النقطة بقوله define
+
+18
+00:01:51,950 --> 00:02:01,920
+فاي من ال A H الى ال B H بايالـ FI لما تأثر على
+
+19
+00:02:01,920 --> 00:02:07,520
+ايه بدي أخد element من H وليكن AH بوديها لل BH
+
+20
+00:02:07,520 --> 00:02:15,440
+يبقى بده يساوي BH الكلام هذا صحيح لكل ال H اللي
+
+21
+00:02:15,440 --> 00:02:20,920
+موجودة وين موجودة في H بدي نثبت هذه one to one and
+
+22
+00:02:20,920 --> 00:02:30,880
+untoيبقى باجي بقوله في هذه الحالة Phi is one to
+
+23
+00:02:30,880 --> 00:02:39,040
+one Assume بروح ناخد صورتين متساويتين أن Phi of A
+
+24
+00:02:39,040 --> 00:02:48,390
+H1 يسوى Phi of A H2بدي احاول اثبت ان الـ AH1 يساوي
+
+25
+00:02:48,390 --> 00:02:53,570
+الـ PH1 يساوي الـ PH2 ان تم ذلك يبقى بيصير PH1 to
+
+26
+00:02:53,570 --> 00:03:00,070
+PH1 بناء على التعريف يبقى هذا بيساوي BH1 وهذا
+
+27
+00:03:00,070 --> 00:03:08,310
+بيساوي BH2 بالـ left cancellation law هذه بتعطينا
+
+28
+00:03:15,660 --> 00:03:22,020
+لو ضربت الطرفين من جهتي اليسار في a بيصير a h1
+
+29
+00:03:22,020 --> 00:03:27,420
+يساوي a h2 وبالتالي فاي is one to one
+
+30
+00:03:33,850 --> 00:03:41,170
+بتروح و أخد element من ال code main و أثبت إنه أصل
+
+31
+00:03:41,170 --> 00:03:45,590
+وين في ال domain يبقى بدي أجي على ال BH بدي أخد
+
+32
+00:03:45,590 --> 00:03:50,430
+element منها و أثبت إن هذا ال element له أصل في
+
+33
+00:03:50,430 --> 00:03:57,330
+main في ال AH يبقى باجي بقول افترض إن X موجود وين
+
+34
+00:03:57,330 --> 00:04:03,350
+موجود في ال BH تمام؟
+
+35
+00:04:03,690 --> 00:04:13,470
+يبقى then ال X هذا بده يساوي BH for some H اللي
+
+36
+00:04:13,470 --> 00:04:22,190
+belongs to man to H طيب هذا أليس هو BH طبقا اللي
+
+37
+00:04:22,190 --> 00:04:28,900
+التعريف هو Phi of Hمعنى هذا الكلام ان فاي is on
+
+38
+00:04:28,900 --> 00:04:32,520
+two خلاص
+
+39
+00:04:32,520 --> 00:04:40,800
+ننتهي هنا منها يبقى هنا Sir فاي is one to one and
+
+40
+00:04:40,800 --> 00:04:50,090
+on twoوهذا يتطلب ان ال order لله هو order لل بيه
+
+41
+00:04:50,090 --> 00:04:55,610
+يبقى من الآن فصاعدا لما ناخد subgroup من ال group
+
+42
+00:04:55,610 --> 00:05:00,970
+جي و اضرب اي element من جي في هذا اله من جهة
+
+43
+00:05:00,970 --> 00:05:05,690
+الشمال او جهة اليمينان شاء الله يطلع عنده مائة
+
+44
+00:05:05,690 --> 00:05:11,030
+كاسات يبقى المية كل واحدة فيها نفس العدد من
+
+45
+00:05:11,030 --> 00:05:15,210
+العناصر فيها عشرين يبقى التانية فيها عشرين التالتة
+
+46
+00:05:15,210 --> 00:05:20,010
+عشرين إلى أخره وهكذا هذا بالنسبة للنقطة رقم ستة
+
+47
+00:05:20,010 --> 00:05:26,770
+بنجلة النقطة رقم سبعةيبقى النقطة رقم سبعة بتقول إن
+
+48
+00:05:26,770 --> 00:05:35,690
+الـ A H بده يساوي الـ H A if and only if الـ H بده
+
+49
+00:05:35,690 --> 00:05:44,610
+يساوي A H A inverse بدنا نبرهن صحة هذا الكلام ل
+
+50
+00:05:44,610 --> 00:05:51,030
+proveخلّي ابقى لك هنا الان الوضع سيكون في اتجاهين
+
+51
+00:05:51,030 --> 00:05:56,350
+لكن ممكن نجيب الاتجاهين مع بعض مرتين واحدة الان
+
+52
+00:05:56,350 --> 00:06:01,990
+اذا كنت قاعد اقول له ايه اتش سيكون اتش ايه اف و
+
+53
+00:06:01,990 --> 00:06:09,900
+فقط افلو ضربت الطرفين من جهتي اليمين في الـ A
+
+54
+00:06:09,900 --> 00:06:17,600
+inverse يبقى هذا الكلام بيصير A H A inverse بالشكل
+
+55
+00:06:17,600 --> 00:06:24,720
+اللي عندنا هذا يساوي H A في ال A inverse بالشكل
+
+56
+00:06:24,720 --> 00:06:29,470
+اللي عندنا هذايبقى هذا الكلام if and only if من
+
+57
+00:06:29,470 --> 00:06:33,990
+خاصية ال associativity ممكن اعمل دمج ما بين
+
+58
+00:06:33,990 --> 00:06:41,860
+الاتنين هدول فبصير عندي a h a inverse بده يساويهذا
+
+59
+00:06:41,860 --> 00:06:47,440
+الـ H وخاصية ال associativity يبقى ال A في ال A
+
+60
+00:06:47,440 --> 00:06:52,760
+inverse بالشكل اللي عندنا هنا طب الكلام هذا صحيح
+
+61
+00:06:52,760 --> 00:07:01,200
+if and only if ال A H A inverse A H A inverse بده
+
+62
+00:07:01,200 --> 00:07:02,680
+يساوي تمام
+
+63
+00:07:09,090 --> 00:07:13,510
+يبقى h في الـ identity element تبع الـ group اللي
+
+64
+00:07:13,510 --> 00:07:23,450
+هو g هذا f and only f a h a inverse بده يساوي من
+
+65
+00:07:23,450 --> 00:07:27,110
+itself لأن ال identity element او ضربه في اي
+
+66
+00:07:27,110 --> 00:07:31,930
+element بطلع نفس ال element اللي هو هو المطلوب
+
+67
+00:07:32,700 --> 00:07:38,240
+النقطة الأخيرة اللي هي النقطة الثامنة بتقول ..
+
+68
+00:07:38,240 --> 00:07:46,480
+بتقول ان ال A H is a subgroup من G if and only if
+
+69
+00:07:46,480 --> 00:07:51,980
+ال A belongs to main if and only if ال A belongs
+
+70
+00:07:51,980 --> 00:07:55,360
+لمين ل ال H طيب تمام
+
+71
+00:07:59,780 --> 00:08:03,740
+المرة السابقة قلنا ان الـ left cosets قد تكون
+
+72
+00:08:03,740 --> 00:08:08,100
+subgroup و قد لا تكون subgroup تمام؟ لكن in
+
+73
+00:08:08,100 --> 00:08:12,760
+general ماهياش subgroup هنا بحطلي ال chart ايش
+
+74
+00:08:12,760 --> 00:08:17,340
+اللي يخلي ال left coset subgroupهو ان ضربها في
+
+75
+00:08:17,340 --> 00:08:24,600
+عنصر من عناصر من من عناصر H itself يبقى ال A H
+
+76
+00:08:24,600 --> 00:08:29,140
+عبارة عن subgroup من G إذا كان ال A اللي ضربته هذي
+
+77
+00:08:29,140 --> 00:08:35,760
+من H نفسها وليس وليس من خارجها يبقى الآن بدأجي
+
+78
+00:08:35,760 --> 00:08:44,660
+أقوله assume that افترض ان ال A H is a subgroup من
+
+79
+00:08:44,660 --> 00:08:50,820
+Gبنحاول نثبت ان الـA موجود في الـH وهذا هو الاتجاه
+
+80
+00:08:50,820 --> 00:08:58,440
+الأول طيب تمام السؤال هو هل يا شباب هذه تحتوي على
+
+81
+00:08:58,440 --> 00:09:04,340
+ال identity element؟ ليش؟ لأنها subgroup يبقى باجي
+
+82
+00:09:04,340 --> 00:09:12,640
+بقوله الـE موجودة في الـH since الـH is a subgroup
+
+83
+00:09:12,640 --> 00:09:22,170
+من G تمام؟طيب and ال E موجودة في ال H ولا لا؟ لأن
+
+84
+00:09:22,170 --> 00:09:27,890
+ال H كذلك هي subgroup يبقى ال E موجودة هنا و ال E
+
+85
+00:09:27,890 --> 00:09:35,600
+موجودة هنا طب ال H أليست هي E في H؟يعني صارت هذه
+
+86
+00:09:35,600 --> 00:09:41,480
+left corset وهذه left corset لجهة element موجودة
+
+87
+00:09:41,480 --> 00:09:46,540
+في الإتنين يبقى ال intersection تبعهم لا يمكن أن
+
+88
+00:09:46,540 --> 00:09:58,430
+يساوي في يبقى سا اللي هو E belongs to AH andالـEH
+
+89
+00:09:58,430 --> 00:10:05,450
+هذا معناته ان الـEH لا
+
+90
+00:10:05,450 --> 00:10:13,580
+يمكن ان يساوي فيما دام لا يمكن أن يساوي في معناته
+
+91
+00:10:13,580 --> 00:10:17,680
+اتنين هدول are equal من النقطة ما بعرف كده رقمها
+
+92
+00:10:17,680 --> 00:10:22,200
+خمسة او تلاتة عندنا من اللي ملم المرة الماضية يبقى
+
+93
+00:10:22,200 --> 00:10:29,120
+هذا معناه ان ال a h بده يساوي ال e h يعني ال a h
+
+94
+00:10:29,120 --> 00:10:37,380
+بده يساوي ال h itselfطيب إذا هدول بتساو أليسة ال A
+
+95
+00:10:37,380 --> 00:10:41,900
+موجودة في H النقطة برهنها برضه المرة الماضية ما
+
+96
+00:10:41,900 --> 00:10:47,500
+بعرف اتنين او تلاتة بالكتير مادام ال A H يساوي H
+
+97
+00:10:47,500 --> 00:10:52,780
+هذا معناه ان ال A belongs to H اللي هو الاتجاه
+
+98
+00:10:52,780 --> 00:10:58,060
+الأول بدنا نيجي الاتجاه الثاني فباجي بقوله
+
+99
+00:10:58,060 --> 00:11:00,080
+conversely
+
+100
+00:11:01,310 --> 00:11:09,050
+بالعكس يبقى assume افترض ان ال a belongs to h بدا
+
+101
+00:11:09,050 --> 00:11:14,570
+احاول اثبت ان ال a h is a subgroup مدام ال a
+
+102
+00:11:14,570 --> 00:11:23,350
+belongs to h then ال a h بده يساوي ال h مظبوط؟
+
+103
+00:11:25,320 --> 00:11:30,400
+صح برهنة مدام ال a belongs to h لأن f and only f
+
+104
+00:11:30,400 --> 00:11:34,280
+يعني كانت النقطة عندها بتقول ان ال a h بدي سوى h
+
+105
+00:11:34,280 --> 00:11:38,420
+if and only if ال a belongs to h طب احنا فرضين ال
+
+106
+00:11:38,420 --> 00:11:43,060
+a belongs to h بجه اتنين هدول بيسووا بعض تماما طب
+
+107
+00:11:43,060 --> 00:11:49,000
+هدى subgroup ولا لأ اذا هدى من subgroupهذا بدي
+
+108
+00:11:49,000 --> 00:11:57,220
+يعطينا ان ال a h is a subgroup من g because ال h
+
+109
+00:11:57,220 --> 00:12:05,920
+is a subgroup من gعلى هيك بيكون برهنة النقاط
+
+110
+00:12:05,920 --> 00:12:12,120
+الثماني لهذه اللملة وهي علاقة ال co sets مع بعضها
+
+111
+00:12:12,120 --> 00:12:18,280
+أو مع بعضهم البعض طيب في عندي ملاحظة هنا منحب نشير
+
+112
+00:12:18,280 --> 00:12:26,460
+اليها ال remark بتقول ما يأتيإذا الـ H هي الـ
+
+113
+00:12:26,460 --> 00:12:31,460
+special linear group of two by two matrices over R
+
+114
+00:12:31,460 --> 00:12:35,720
+وهذه الـ subgroup من الـ general linear group of
+
+115
+00:12:35,720 --> 00:12:43,560
+two by two matrices over R فهذه الـ subgroup من
+
+116
+00:12:43,560 --> 00:12:50,910
+الـ general linear group of two by two matricesA
+
+117
+00:12:50,910 --> 00:12:59,170
+and G the coset
+
+118
+00:12:59,170 --> 00:13:13,930
+الهو ال A H is the set of all two
+
+119
+00:13:13,930 --> 00:13:16,590
+by two matrices
+
+120
+00:13:23,780 --> 00:13:30,740
+with the same
+
+121
+00:13:30,740 --> 00:13:35,500
+determinant
+
+122
+00:13:35,500 --> 00:13:42,860
+as a for
+
+123
+00:13:42,860 --> 00:13:48,360
+example كمثال
+
+124
+00:13:48,360 --> 00:13:49,300
+على ذلك
+
+125
+00:13:52,640 --> 00:14:01,220
+المصفوفة اللي تلاتة zero واحد اتنين لو ضربتها فيه
+
+126
+00:14:01,220 --> 00:14:16,280
+H is the set of all two by two matrices with
+
+127
+00:14:16,280 --> 00:14:18,060
+determinant
+
+128
+00:14:25,120 --> 00:14:30,420
+ستة طيب بدنا نسأل السؤال التالي ليش هذا الكلام
+
+129
+00:14:30,420 --> 00:14:38,260
+صحيح طلعلي فيها كويس طلعلي فيها كويس حتى نحاول ان
+
+130
+00:14:38,260 --> 00:14:44,740
+نصل الى الإجابة لهذا السؤال الذي زعمناه ان ال
+
+131
+00:14:44,740 --> 00:14:50,980
+order لها يساوي ستة قلي بلا كده ال remark بتقول ما
+
+132
+00:14:50,980 --> 00:14:55,170
+يأتيلو كانت الـ subgroup هي الـ special linear
+
+133
+00:14:55,170 --> 00:14:59,270
+group ملي جروب اللي هو ال general linear group of
+
+134
+00:14:59,270 --> 00:15:04,470
+two by two matrices over R طبعا هذه كل المصوفات
+
+135
+00:15:04,470 --> 00:15:09,410
+اللي determinant لها لا يساوي zero هذه كل المصوفات
+
+136
+00:15:09,410 --> 00:15:13,670
+اللي determinant لها لا يساوي مين واحد صحيحبقول
+
+137
+00:15:13,670 --> 00:15:19,330
+لأي matrix A في ال group اللي عندنا هذه the coset
+
+138
+00:15:19,330 --> 00:15:26,270
+of H أنا أخدت A من وين؟ من ال general ضربت في من؟
+
+139
+00:15:26,270 --> 00:15:29,730
+في H لل special linear group of two by two
+
+140
+00:15:29,730 --> 00:15:35,770
+matrices overallبقول الـAH هذه كل مصحوفة فيها
+
+141
+00:15:35,770 --> 00:15:41,030
+المحدد تبعها يسوى المحدد تبع المصحوفة ايه بالضبط
+
+142
+00:15:41,030 --> 00:15:48,750
+تماما، ليش؟ لإن هذه المصحوفة كل matrix فيها المحدد
+
+143
+00:15:48,750 --> 00:15:52,830
+دي لها بجداش يبقى لما تجيب ال determinant لأي
+
+144
+00:15:52,830 --> 00:15:57,640
+ألمصير ال determinant لإيه في ال determinantلأ
+
+145
+00:15:57,640 --> 00:16:01,560
+بيهيب واحد يبقى بيظلمين ال determinant ليه بيبقى
+
+146
+00:16:01,560 --> 00:16:05,660
+كل عنصر فيها بدي يكون ال determinant له ك
+
+147
+00:16:05,660 --> 00:16:11,580
+determinant لمين لإيه مثال على ذلكالمصحوفة اللي
+
+148
+00:16:11,580 --> 00:16:15,840
+عندها دي element هذا موجود في ال general linear
+
+149
+00:16:15,840 --> 00:16:22,400
+group لإن المحدد تبعه بقداش بستة يعني لا يساوي
+
+150
+00:16:22,400 --> 00:16:26,520
+زينو معناته موجود في ال general يبقى the set of
+
+151
+00:16:26,520 --> 00:16:30,160
+all two by two matrices اللي هذا مضروبة فيه with
+
+152
+00:16:30,160 --> 00:16:34,380
+determinant ستة السبب لإنه بدي يكون ال determinant
+
+153
+00:16:34,830 --> 00:16:39,990
+لأ ال element هذا مضروب في أي element تاني وليكن
+
+154
+00:16:39,990 --> 00:16:43,770
+بيسوء ال determinant لهذه في ال determinant اللي
+
+155
+00:16:43,770 --> 00:16:46,450
+بيبقى ال determinant اللي بيبقى بواحد صحيح بيبقى
+
+156
+00:16:46,450 --> 00:16:50,550
+ال determinant لهذه بستة في واحد اللي بستة هذه
+
+157
+00:16:50,550 --> 00:16:57,330
+مجرد ملاحظةطيب نجي الآن لنظرية very important في
+
+158
+00:16:57,330 --> 00:17:04,130
+الجبر وهذه أساسية ولا كتاب جبر بيخلوا منها هذه
+
+159
+00:17:04,130 --> 00:17:07,910
+النظرية اسمها لظرية Lagrange Lagrange هو اللي
+
+160
+00:17:07,910 --> 00:17:13,010
+اكتشفها بالبلد هيك ال order لو كانت ال G finite
+
+161
+00:17:13,010 --> 00:17:19,400
+فال order لل sub group بيقسم ال order لل groupوهذه
+
+162
+00:17:19,400 --> 00:17:23,560
+شرطها لكم من أول ما بدأت تقولوا دير بالك قدام
+
+163
+00:17:23,560 --> 00:17:26,960
+هناخد ان ال order لل element بده يقسم ال order لل
+
+164
+00:17:26,960 --> 00:17:30,960
+group و ال order لل sub group بده يقسم ال order لل
+
+165
+00:17:30,960 --> 00:17:36,980
+group كذلك فبدنا نيجي ل Lagrange theorem يبقى هنا
+
+166
+00:17:36,980 --> 00:17:42,060
+Lagrange theorem
+
+167
+00:17:44,840 --> 00:17:52,660
+النظرية هذه بتقول ما ياتي if ال H is
+
+168
+00:17:52,660 --> 00:18:07,120
+a subgroup of a finite group G then
+
+169
+00:18:07,120 --> 00:18:13,560
+ال order ل H divides
+
+170
+00:18:15,730 --> 00:18:25,210
+الـ order لـ G وزيادة على ذلك moreover و أكثر من
+
+171
+00:18:25,210 --> 00:18:35,810
+ذلك the number of this connect the number of
+
+172
+00:18:35,810 --> 00:18:43,010
+this connect the number of this connect left أو
+
+173
+00:18:43,010 --> 00:18:50,370
+right leftاو رايت هدى والله هدى الاتنين are the
+
+174
+00:18:50,370 --> 00:19:03,570
+same left او right cassettes of H in G is ال order
+
+175
+00:19:03,570 --> 00:19:11,110
+ل G على ال order ال main لل H بنبرهن
+
+176
+00:19:11,110 --> 00:19:13,510
+صحة هذا الكلام ال approve
+
+177
+00:19:29,970 --> 00:19:35,150
+خلّي بالا كدا الان H sub group من مين؟ من finite
+
+178
+00:19:35,150 --> 00:19:44,050
+group Gو ال H هي ال sub group من ل group G بدي
+
+179
+00:19:44,050 --> 00:19:49,370
+اثبت ان ال order ل G بيقسم ال order ال order ل H
+
+180
+00:19:49,370 --> 00:19:55,210
+بيقسم ال order ل G يعني عدد العناصر في H يقسم عدد
+
+181
+00:19:55,210 --> 00:20:01,370
+العناصر في من في Gوزيادة على ذلك عدد ال left او
+
+182
+00:20:01,370 --> 00:20:07,310
+right destined cosets في H and G بيسوي ال order لل
+
+183
+00:20:07,310 --> 00:20:13,330
+H على ال order لمين لل G هذا اللي عايزين نتبته في
+
+184
+00:20:13,330 --> 00:20:14,650
+العدد
+
+185
+00:20:19,350 --> 00:20:24,070
+الـ order اللى جى على ال order لل H بيعطينى عدد ال
+
+186
+00:20:24,070 --> 00:20:27,210
+left cosets وهنا كاتبين ال order اللى جى على ال
+
+187
+00:20:27,210 --> 00:20:31,810
+order اللى H تمام طب خلّينى نثبت النقطة الأولى
+
+188
+00:20:31,810 --> 00:20:37,710
+بيقولى هنا عدد ال left .. destined left cosets او
+
+189
+00:20:37,710 --> 00:20:41,970
+right cosets اذا انا بدى اروح اجيب كل ال left
+
+190
+00:20:41,970 --> 00:20:47,250
+cosets اللى موجودات على اللى هو ال sub group من ال
+
+191
+00:20:47,250 --> 00:20:50,460
+group اللى عندنالما أخدنا الأمثلة المرة اللى فاتت
+
+192
+00:20:50,460 --> 00:20:56,520
+لجينا انه أحيانا ال lift corsets بتساوي مظبوط يبقى
+
+193
+00:20:56,520 --> 00:21:00,220
+انا بدي أجيب كل ال lift corsets اللى بيكون ولا
+
+194
+00:21:00,220 --> 00:21:05,300
+واحدة فيهم بتساوي ات تانية يبقى بدي أجي أقوله let
+
+195
+00:21:05,300 --> 00:21:15,620
+a1h a2h ونظل ماشيين the arh ب the
+
+196
+00:21:18,560 --> 00:21:24,940
+Left Destinate Cosets
+
+197
+00:21:24,940 --> 00:21:28,780
+of
+
+198
+00:21:28,780 --> 00:21:38,760
+H and G بدأ افترض ان هذا عبارة عن ايش؟ عبارة عن كل
+
+199
+00:21:38,760 --> 00:21:42,720
+Destinate Left Cosets اللي ولا واحدة بتساوي
+
+200
+00:21:42,720 --> 00:21:53,010
+التانيةطيب، الآن بداجي أقول let ال A belongs to G
+
+201
+00:21:53,010 --> 00:22:06,300
+then ال A H is a left cassetteصحيح ولا لأ يعني
+
+202
+00:22:06,300 --> 00:22:11,740
+معناته ان ال a h هساوي واحدة من هدول هتكون واحدة
+
+203
+00:22:11,740 --> 00:22:23,580
+منهم صح يبقى الآن ساعة ال a h هذه بدها ساوي a i h
+
+204
+00:22:23,580 --> 00:22:27,420
+تمام
+
+205
+00:22:27,420 --> 00:22:39,760
+طيب كويس butwe know that احنا بنعرف ان ال a موجودة
+
+206
+00:22:39,760 --> 00:22:45,800
+في ال a h فموجودة في ال a h مظبوط
+
+207
+00:22:47,230 --> 00:22:51,190
+بارهنها المرة اللى فاتت مدام موجودة هنا وهذه
+
+208
+00:22:51,190 --> 00:22:55,490
+بتساوي هذه يبقى ال element وين موجود؟ في ال A I H
+
+209
+00:22:55,490 --> 00:23:05,750
+يبقى هذا بده يعطينا ان ال A belongs to A I H طب
+
+210
+00:23:05,750 --> 00:23:09,830
+انا لما أخدت ال A في G أخدت عنصر عشوائي ولا عنصر
+
+211
+00:23:09,830 --> 00:23:16,430
+محددعشوائي مدام عشوائي ينطبق على أي عنصر موجود في
+
+212
+00:23:16,430 --> 00:23:23,210
+ال group G بفهم من هذا الكلام انه كل عنصر موجود في
+
+213
+00:23:23,210 --> 00:23:28,910
+جي حالة جي في واحدة من ال lift cassettes صح ولا لأ
+
+214
+00:23:28,910 --> 00:23:35,440
+سكت الشعبمرة تانية انا اخدت a عشوائيا من g تمام
+
+215
+00:23:35,440 --> 00:23:40,820
+لجيت ال a هذا موجود في واحدة من هدول ايه موجود في
+
+216
+00:23:40,820 --> 00:23:48,340
+ال aiH مظبوط ممتاز جدا يبقى هذا يعني انه كل عنصر
+
+217
+00:23:48,340 --> 00:23:52,740
+بتاخده من G لازم تلاقيه في main في واحدة من ال
+
+218
+00:23:52,740 --> 00:23:58,120
+left distant cosets مظبوط يبقى this means that
+
+219
+00:23:58,120 --> 00:24:06,280
+this means that any element
+
+220
+00:24:09,860 --> 00:24:17,240
+in G belongs to
+
+221
+00:24:17,240 --> 00:24:24,440
+one coset of
+
+222
+00:24:24,440 --> 00:24:32,280
+A1H A2H و لغاية ARH
+
+223
+00:24:35,230 --> 00:24:42,990
+أذا كل عنصر باخده من جيه لما أخده من جيه بلاقيه في
+
+224
+00:24:42,990 --> 00:24:48,390
+واحدة من هدول طب السؤال هو هل هدول بيسووا بعضهم
+
+225
+00:24:48,390 --> 00:24:54,110
+يبقى ال intersection five ممتاز جدا و لو واحدة جال
+
+226
+00:24:54,110 --> 00:24:57,230
+بيسوى تاني نجال عليهم this and that يبقى ال
+
+227
+00:24:57,230 --> 00:25:01,990
+intersection تبعهم يسوى five إذا لا يمكن لعنصر
+
+228
+00:25:01,990 --> 00:25:09,190
+يكون confidentين منهمصح ولا لا يبقى هنا بقول هنا
+
+229
+00:25:09,190 --> 00:25:22,110
+but ولكن اللي هو ال aih لا يساوي ال ajh for اللي
+
+230
+00:25:22,110 --> 00:25:29,290
+هو ال I لا يساوي ال jلما هؤلاء ما يتساووش يبقى
+
+231
+00:25:29,290 --> 00:25:33,530
+هؤلاء ما يتساووش بعض إذا الـI والـJ لا يتساووش بعض
+
+232
+00:25:33,530 --> 00:25:40,090
+إذا كل element موجود بالضبط في واحدة من من هؤلاء
+
+233
+00:25:40,090 --> 00:25:45,350
+طيب إذا الـG مش هي عبارة عن ال union تبع هؤلاء
+
+234
+00:25:45,350 --> 00:25:47,170
+كلهم ولا لأ؟
+
+235
+00:25:56,620 --> 00:26:08,300
+لجروب G هي عبارة عن A1H اتحاد A2H اتحاد اتحاد ARH
+
+236
+00:26:08,300 --> 00:26:18,180
+كويس يعني هذا يعني ان ال order ل G ال order ل G
+
+237
+00:26:18,180 --> 00:26:26,120
+بدي سوى ال order ل A1H زائد ال order ل A2H
+
+238
+00:26:28,500 --> 00:26:39,220
+زائد زائد زائد ال order لل ARH طيب
+
+239
+00:26:39,220 --> 00:26:45,760
+سؤال انا H فيها عشرة elements مثلاو جيت ضربت ال H
+
+240
+00:26:45,760 --> 00:26:51,380
+في أي عنصر من عناصر G بيطلع عندى عشرة elements ولا
+
+241
+00:26:51,380 --> 00:26:55,920
+أكتر ولا أقل عشرة بالضبط لما يكون عندى ال sub
+
+242
+00:26:55,920 --> 00:27:00,120
+group و اضربها في أي element من ال group بيضلوا
+
+243
+00:27:00,120 --> 00:27:04,460
+العشرة العددهم عشرة صحيح بيختلفوا لكن بيضلوا عشرة
+
+244
+00:27:04,460 --> 00:27:09,780
+من ناحية العدد معناته ال order لل a1h يساوي ال
+
+245
+00:27:09,780 --> 00:27:15,730
+order للhو ال order ل A to H هو ال order ل H و ال
+
+246
+00:27:15,730 --> 00:27:22,130
+order ل A RH هو ال order ل H يعني هذا الكلام يعني
+
+247
+00:27:22,130 --> 00:27:28,770
+ان ال order ل G بده يساوي ال order ل H زائد ال
+
+248
+00:27:28,770 --> 00:27:36,690
+order ل H زائد زائد ال order ل H اكم مرة هدول؟ R
+
+249
+00:27:37,380 --> 00:27:46,440
+لأن عددهم R يبقى هذا الكلام معناته R times يبقى R
+
+250
+00:27:46,440 --> 00:27:52,500
+من المرات يبقى أصبح الأن ال order اللي جيه بده
+
+251
+00:27:52,500 --> 00:27:58,900
+يساوي ال R في ال order ال H لأن عددهم Rطب ايش
+
+252
+00:27:58,900 --> 00:28:06,300
+تفسيرك لهذه ان ال order لل H بيقسم ال order ل G
+
+253
+00:28:06,300 --> 00:28:15,420
+هذا معناه ان ال order ل H divides ال order ل G
+
+254
+00:28:15,420 --> 00:28:23,410
+وبالتالي انت هنامن نظرية Lagrange راح قلي واكثر من
+
+255
+00:28:23,410 --> 00:28:27,050
+ذلك the number of distinct left cosets او right
+
+256
+00:28:27,050 --> 00:28:31,570
+cosets of H and G يساوي ال order لل G على ال order
+
+257
+00:28:31,570 --> 00:28:41,810
+لمين لل H باجي بقوله هنا اكم
+
+258
+00:28:41,810 --> 00:28:52,620
+واحدة left cosets عندنا هناare يبقى هنا the number
+
+259
+00:28:52,620 --> 00:29:05,780
+of left أو حتى right cassettes of each the number
+
+260
+00:29:05,780 --> 00:29:07,460
+of destined
+
+261
+00:29:11,540 --> 00:29:19,860
+Left or Right Cosets of H in G is R طب ال R قد
+
+262
+00:29:19,860 --> 00:29:28,080
+يساوي هنا مش هو ال order ل G على ال order لل H
+
+263
+00:29:28,080 --> 00:29:38,160
+يبقى ال order ل G على ال order لل H طب كويس شوفوا
+
+264
+00:29:38,160 --> 00:29:46,030
+شوفوابعد هذا البرهان عندي تعريف متعلق بالنتيجة
+
+265
+00:29:46,030 --> 00:29:50,550
+اللى توصلنا إليها من نظرية لاجرانج التعريف هذا
+
+266
+00:29:50,550 --> 00:30:00,170
+بيقول ما يأتي the number of left the number of
+
+267
+00:30:00,170 --> 00:30:12,050
+distinct left أو rightهذا او هذا left dissonant
+
+268
+00:30:12,050 --> 00:30:21,410
+right او left cosets of HNG
+
+269
+00:30:21,410 --> 00:30:32,370
+of HNG is called هذا بنسميه ال index is called the
+
+270
+00:30:32,370 --> 00:30:38,490
+index of
+
+271
+00:30:41,030 --> 00:30:47,870
+a subgroup a subgroup
+
+272
+00:30:47,870 --> 00:30:54,070
+H in G and
+
+273
+00:30:54,070 --> 00:31:05,130
+denoted by وبنعطيله الرمز التالي الـ G مقطعتين فوق
+
+274
+00:31:05,130 --> 00:31:09,090
+بعض وH بالشكل اللي عندنا هذا
+
+275
+00:31:14,520 --> 00:31:18,480
+طيب هذا بيقولي عدد الـdestinate left او right
+
+276
+00:31:18,480 --> 00:31:23,880
+cosets of H and G بسميه ال index تبع ال subgroup H
+
+277
+00:31:23,880 --> 00:31:30,220
+في من في ال group G طب قداش عددهم هدول؟ R يبقى
+
+278
+00:31:30,220 --> 00:31:35,400
+احنا عندنا ملاحظة بسيطة جدا من ال grand theorem
+
+279
+00:31:35,400 --> 00:31:42,190
+قلنا ال order ل G بدي سوى ال R في ال order ل Hصح
+
+280
+00:31:42,190 --> 00:31:48,330
+ولا لا؟ إذا بقدر أكتب نظرية Lagrange بطريقة أخرى
+
+281
+00:31:48,330 --> 00:31:53,110
+إن ال order ل G بده يساوي ال R هو عدد ال left
+
+282
+00:31:53,110 --> 00:31:59,050
+coset اللي أعطيته الرمز ال index تبع ال H in G في
+
+283
+00:31:59,050 --> 00:32:06,870
+ال order ل Hيبقى بصيغة نتيجة نظرية لاجرانج بالصيغة
+
+284
+00:32:06,870 --> 00:32:11,050
+اللى عندنا اللى توصلنا لها هذه ان ال order ل G بده
+
+285
+00:32:11,050 --> 00:32:15,590
+يسوي R في ال order ل H يا بقول ال order ل G بده
+
+286
+00:32:15,590 --> 00:32:19,890
+يسوي ال index تبع ال subgroup H في ال group G
+
+287
+00:32:19,890 --> 00:32:26,210
+مضروب في ال order تبع من تبع ال H الشكل اللى عندنا
+
+288
+00:32:26,210 --> 00:32:34,150
+هذا تمام بدنا نبدأ نعطي أمثلة على ذلكأول مثال
+
+289
+00:32:34,150 --> 00:32:46,610
+example بقول let ال G تساوي S4 and
+
+290
+00:32:48,180 --> 00:32:54,280
+الـ H هي الـ sub group generated by ال permutation
+
+291
+00:32:54,280 --> 00:33:00,660
+واحد اتنين تلاتة اربعة اتنين تلاتة اربعة واحد
+
+292
+00:33:00,660 --> 00:33:03,720
+بالشكل اللي عندنا هنا find
+
+293
+00:33:26,290 --> 00:33:27,690
+S4S4S4S4S4S4S4S4S4S4
+
+294
+00:33:38,910 --> 00:33:44,450
+سؤال مرة تانية السؤال بيقول احنا عندنا GS4 اللى
+
+295
+00:33:44,450 --> 00:33:50,650
+فيها اربعة وعشرين عنصر اخدنا منها subgroup H مين
+
+296
+00:33:50,650 --> 00:33:54,650
+هي ال subgroup هذا ال subgroup اللى تتولد بال
+
+297
+00:33:54,650 --> 00:34:00,390
+permutation اللى عندنا جداش ال index تبع ال H in
+
+298
+00:34:00,390 --> 00:34:01,430
+S4
+
+299
+00:34:05,930 --> 00:34:09,950
+الاندكس يساوي ال order لل group على ال order لل
+
+300
+00:34:09,950 --> 00:34:13,690
+subgroup ال order تبع ال group يعرفينه 24 لكن ال
+
+301
+00:34:13,690 --> 00:34:18,460
+order تبع ال subgroup مش عارفهمش عارفه لكن لازم
+
+302
+00:34:18,460 --> 00:34:23,280
+تعرفه إذا بدي أبدأ أضرب هذه في نفسي مرة ما طلعش ال
+
+303
+00:34:23,280 --> 00:34:27,780
+identity كمان مرة ما طلعش لغاية ما يطلع من ال
+
+304
+00:34:27,780 --> 00:34:32,020
+identity وبالتالي بيكون الأس اللي عندي هو من ال
+
+305
+00:34:32,020 --> 00:34:37,430
+order تبع ال group هذه وجهة نظر قديمةهو ايش وجهة
+
+306
+00:34:37,430 --> 00:34:43,230
+النظر الجديدة ان انت هذى اجيب لل order تبعها بكل
+
+307
+00:34:43,230 --> 00:34:50,570
+بساطة بكل بساطة كده بقوله انا هذا let alpha تساوي
+
+308
+00:34:50,570 --> 00:34:55,390
+ال permutation واحد اتنين تلاتة اربعة اتنين تلاتة
+
+309
+00:34:55,390 --> 00:35:04,550
+اربعة واحد thenالألف تساوي بقدر اكتبها على ال
+
+310
+00:35:04,550 --> 00:35:09,210
+cycle form اما ال cycle واحدة او product of two
+
+311
+00:35:09,210 --> 00:35:14,270
+cycles حسب اللي موجود عندى تمام اذا باجي بقوله بدي
+
+312
+00:35:14,270 --> 00:35:17,390
+اكتب على شكل cycle الواحد مين صوبته يا شباب
+
+313
+00:35:17,390 --> 00:35:25,230
+والاتنين والتلاتة والاربعة قفلت اذا بقدر اجيب ال
+
+314
+00:35:25,230 --> 00:35:31,250
+order لالف ولا ليبقى هذا بيعطينا ان ال order ل
+
+315
+00:35:31,250 --> 00:35:35,990
+alpha بده يساوي طول ال cycle اللي عندنا هو قداش
+
+316
+00:35:35,990 --> 00:35:41,530
+أربعة يبقى ال order ل alpha بده يساوي أربعة طيب
+
+317
+00:35:41,530 --> 00:35:46,040
+لما يكون عندنا ال cycle ك groomشو العلاقة بين
+
+318
+00:35:46,040 --> 00:35:50,740
+order لل group و order لل generator؟ اتنين نفس
+
+319
+00:35:50,740 --> 00:35:56,040
+الشيء يعني معنى هذا الكلام ان ال order لل H ساوى
+
+320
+00:35:56,040 --> 00:36:01,220
+ال order ل alpha وهذا بدي يعطيني من؟ بدي يعطيني
+
+321
+00:36:01,220 --> 00:36:07,280
+اللي هو النتيجة اللي هو أربعةهذا سيعطيني ان ال
+
+322
+00:36:07,280 --> 00:36:16,060
+order ل H هو order ل alpha اربعة ليش؟ لان H هى
+
+323
+00:36:16,060 --> 00:36:20,720
+الـcyclic subgroup generated by ال permutation
+
+324
+00:36:20,720 --> 00:36:24,100
+alpha اللى عندنا يبقى اثار ال order ل alpha هو
+
+325
+00:36:24,100 --> 00:36:29,790
+order ل Hما دام هيكي بقى صارت قصتنا بسيطة قال لي
+
+326
+00:36:29,790 --> 00:36:36,210
+هاتلي ال index بقوله الآن ال index ل ال subgroup H
+
+327
+00:36:36,210 --> 00:36:43,450
+في ال group S4 يساوي ال order لل S4 على ال order
+
+328
+00:36:43,450 --> 00:36:49,530
+لل H ال order لل S4 اللي هو أربعة factorial وهذه
+
+329
+00:36:49,530 --> 00:36:58,980
+أربعةيبقى هذه بنقول أربعة في تلاتة factorial على
+
+330
+00:36:58,980 --> 00:37:04,460
+أربعة يبقى تلاتة factorial تلاتة factorial يسوى
+
+331
+00:37:04,460 --> 00:37:09,860
+كده؟ يسوى ستةإذاً ال index تبع ال subgroup اللي
+
+332
+00:37:09,860 --> 00:37:15,920
+عندنا هذه في ال group G الأصلية هو عبارة عن ستة،
+
+333
+00:37:15,920 --> 00:37:21,520
+إيش يعني ستة؟ يعني أنا ضمنت عدد ال left destined
+
+334
+00:37:21,520 --> 00:37:28,080
+cosets لل S4 لما نضربهم في ال .. لما ينضربوا في ال
+
+335
+00:37:28,080 --> 00:37:31,140
+permutation اللي في ال .. في ال H اللي عند ال
+
+336
+00:37:31,140 --> 00:37:36,870
+subgroup بطلع عندى بس ستة left destined cosetsيعني
+
+337
+00:37:36,870 --> 00:37:42,830
+معناه كل أربعة هيتساووا عشان يطلع عندى ستة صح ولا
+
+338
+00:37:42,830 --> 00:37:47,950
+لا يعني كل أربعة left cosets هيطلعوا نفس الشيء
+
+339
+00:37:47,950 --> 00:37:52,530
+وبالتالي ضمنت عدد ال left cosets يساوي ستة كان
+
+340
+00:37:52,530 --> 00:37:56,810
+بيمكني أصيغ نفس السؤال و بدل ما اقول هاتل ال index
+
+341
+00:37:56,810 --> 00:38:02,950
+اقول find the number of left cosets of H in S4
+
+342
+00:38:02,950 --> 00:38:07,970
+واسكتمش هو نفس السؤال نفس السؤال حرفية لكن قعدت
+
+343
+00:38:07,970 --> 00:38:20,270
+صيغته بطريقة اخرى نعطي مثال اخر كمان example ال
+
+344
+00:38:20,270 --> 00:38:26,370
+example يا شباب هذا سؤال 14 من الكتاب بقول suppose
+
+345
+00:38:26,370 --> 00:38:27,030
+that
+
+346
+00:38:30,100 --> 00:38:40,900
+suppose that افترض ان الـ K is a proper subgroup
+
+347
+00:38:40,900 --> 00:38:44,540
+of
+
+348
+00:38:44,540 --> 00:38:48,720
+H and
+
+349
+00:38:48,720 --> 00:38:56,380
+الـ H is a proper subgroup
+
+350
+00:38:59,010 --> 00:39:04,150
+of G if
+
+351
+00:39:04,150 --> 00:39:18,050
+ال order لل K هو اتنين واربعين and ال order لل G
+
+352
+00:39:18,050 --> 00:39:23,150
+هو اربع مية وعشرين what
+
+353
+00:39:24,410 --> 00:39:35,730
+are the possible orders of
+
+354
+00:39:35,730 --> 00:39:37,190
+H
+
+355
+00:40:06,270 --> 00:40:10,790
+مرة تانية انا عندي K proper subgroup من H ايش يعني
+
+356
+00:40:10,790 --> 00:40:15,890
+proper subgroup؟ لأ تساوي H subset منها لكن لا
+
+357
+00:40:15,890 --> 00:40:21,350
+تساويها وعندي في نفس الوقت ال H proper subgroup من
+
+358
+00:40:21,350 --> 00:40:26,850
+G يعني K subgroup من H و ال H subgroup من G وكل
+
+359
+00:40:26,850 --> 00:40:31,110
+واحدة فيهم عبارة عن ال proper يعني لا تساوي الجروب
+
+360
+00:40:31,110 --> 00:40:35,940
+التانيقال لو كان ال order ل K الأولى هو اتنين
+
+361
+00:40:35,940 --> 00:40:40,500
+واربعين وال order ل الأخرى أربع مائة وعشرين ما هي
+
+362
+00:40:40,500 --> 00:40:47,100
+الاحتمالات الممكنة لل order تبع ال H فنقوله ماشي
+
+363
+00:40:47,100 --> 00:40:49,160
+يبقى هنا solution
+
+364
+00:40:54,430 --> 00:41:02,450
+الآن نحن لدينا K subgroup يبقى K subgroup من H هذا
+
+365
+00:41:02,450 --> 00:41:12,730
+معناته ان ال order لل K بيقسم ال order لل H مظبوط؟
+
+366
+00:41:12,730 --> 00:41:19,150
+طب ال order لل H كده انا مش عارف يبقى هنا كده
+
+367
+00:41:21,550 --> 00:41:27,510
+K subgroup من H هي K proper subgroup من H K
+
+368
+00:41:27,510 --> 00:41:31,830
+subgroup من H يبقى ال order ل K بده يقسم ال order
+
+369
+00:41:31,830 --> 00:41:38,370
+ل H يبقى بداجي اقوله هنا assume افترض ان ال order
+
+370
+00:41:38,370 --> 00:41:47,080
+ل H بده يساوي ال M مثلا يبقى بناء عليهالـ order لـ
+
+371
+00:41:47,080 --> 00:41:55,440
+K ميعطيني ياله جداش 42 تقسم من ال M يعني معناته
+
+372
+00:41:55,440 --> 00:42:06,600
+هذا ال M تساوي مضعفات 42 يساوي هذا S مثلا في فيل
+
+373
+00:42:06,600 --> 00:42:13,080
+42 و هنا for some
+
+374
+00:42:25,520 --> 00:42:31,280
+يبقى كتابة الـ M مجهولة على شكل رقم مضروب جداش
+
+375
+00:42:31,280 --> 00:42:40,090
+اتنين او اربعينالان انا عندي كذلك ال order ل ال H
+
+376
+00:42:40,090 --> 00:42:46,930
+او ال H هذه ال sub group من G sub group من G هذا
+
+377
+00:42:46,930 --> 00:42:53,390
+معناته ان ال order ل ال H divide ال order ل G طبقا
+
+378
+00:42:53,390 --> 00:43:00,760
+لنظرية Lagrange مدام هيك هذا معناهإن ال order للـ
+
+379
+00:43:00,760 --> 00:43:09,980
+G هنا بدي ساوي ال R في ال order لـ H مثلايبقى هذا
+
+380
+00:43:09,980 --> 00:43:15,340
+معناه ان ال order اللي جيه ليه أربعمية وعشرين
+
+381
+00:43:15,340 --> 00:43:22,540
+تساوي R في مين في ال M لأن انا فرض ال order ال H
+
+382
+00:43:22,540 --> 00:43:27,440
+يساوي مدى كده؟ يساوي M اطلعلي في المعادلة اللي
+
+383
+00:43:27,440 --> 00:43:33,640
+عندنا هذه واطلعلي في المعادلة اللي عندنا هذه اذا
+
+384
+00:43:33,640 --> 00:43:40,320
+انا بقدر اخلق من المعادلتين معادلةما هي هذه
+
+385
+00:43:40,320 --> 00:43:48,720
+المعادلة؟ اللي هي أربعمية وعشرين بده يساوي RS في
+
+386
+00:43:48,720 --> 00:43:54,940
+من؟ في اتنين واربعين يعني شيلت ال M اللي عندنا هذه
+
+387
+00:43:54,940 --> 00:44:00,240
+ويرحلت شيلت ال M اللي عندنا هذه وكتبت بدلها S في
+
+388
+00:44:00,240 --> 00:44:07,430
+اتنين واربعينتمام طيب في قسم ما بين الطرفين اه
+
+389
+00:44:07,430 --> 00:44:12,430
+يبقى لو جسمت كله على اتنين واربعين هذا بدي يعطيني
+
+390
+00:44:12,430 --> 00:44:20,590
+R S تساوي عشرة مدام عشرة احتمال ال R بواحد وال S
+
+391
+00:44:20,590 --> 00:44:31,920
+بعشرةاحتمال ان S بواحد وR بعشرة احتمال R بخمسة وS
+
+392
+00:44:31,920 --> 00:44:36,280
+باتنين احتمال R باتنين وS بخمسة هي الاحتمالات
+
+393
+00:44:36,280 --> 00:44:48,040
+الأربعة في غيرهم؟ لأ يبقى هنا so we have four
+
+394
+00:44:48,040 --> 00:44:50,280
+possibilities four
+
+395
+00:44:57,390 --> 00:45:05,110
+أربعة احتمالات الاحتمال الأول ان الار تساوي واحد
+
+396
+00:45:05,110 --> 00:45:12,510
+والاس تساوي عشرةهل هذا الكلام ممكن؟ والله مش ممكن
+
+397
+00:45:12,510 --> 00:45:20,310
+الحين لو ال S وتعشرة يبقى ال M كده؟ 420 ممكن هذا
+
+398
+00:45:20,310 --> 00:45:27,730
+الكلام؟ يتناقض مع كلمة proper تمام يبقى هذا this
+
+399
+00:45:27,730 --> 00:45:31,310
+is impossible
+
+400
+00:45:33,850 --> 00:45:43,190
+هذا غير ممكن السبب because ان ال H is proper
+
+401
+00:45:43,190 --> 00:45:49,210
+subgroup من G لان على الجهة ده مش ممكن ممكن العكس
+
+402
+00:45:49,210 --> 00:45:57,130
+نقطة ثانية ان ال R تساوي عشرة و ال S تساوي واحد
+
+403
+00:45:58,440 --> 00:46:04,560
+تمام؟ طب بدنا نأتي إلى ال S تساوي واحد لو ال S سوى
+
+404
+00:46:04,560 --> 00:46:12,060
+واحد يبقى ال M قداش؟ يعني قد مين؟ قد K ال H صارت
+
+405
+00:46:12,060 --> 00:46:16,760
+قد K مظبوط و هذا كلام غلط لأن احنا نقولين K proper
+
+406
+00:46:16,760 --> 00:46:24,020
+يبقى برضه هذا this is impossible because capital K
+
+407
+00:46:24,020 --> 00:46:25,680
+is proper
+
+408
+00:46:28,120 --> 00:46:33,920
+يبقى هذا لا يمكن يحصل بالمرة طب نجي النقطة التالتة
+
+409
+00:46:33,920 --> 00:46:40,460
+النقطة التالتة ممكن ال R يساوي اتنين وال S يساوي
+
+410
+00:46:40,460 --> 00:46:48,020
+خمسةطيب لو حطيت ال S هنا بخمسة بصير هدول كده؟ 210
+
+411
+00:46:48,020 --> 00:46:55,520
+ممكن؟ اه ممكن مافيش مشكلة يبقى هنا ال R سواء S
+
+412
+00:46:55,520 --> 00:47:03,540
+then ال M بدها تساوي ال S لخمسة في اتنين واربعين
+
+413
+00:47:03,540 --> 00:47:08,540
+واللي هو بده يساوي متين وعشر خمسة في اتنين بعشر
+
+414
+00:47:08,540 --> 00:47:13,880
+وخمسة في اربع باشرين واحد واحدهو عشرين تمام هذا لو
+
+415
+00:47:13,880 --> 00:47:21,260
+كانت ال S بخمسة وال R باتنين الاحتمال الرابع ان ال
+
+416
+00:47:21,260 --> 00:47:30,930
+R تساوي خمسة وال S يساوي اتنينال M يساوي ال M
+
+417
+00:47:30,930 --> 00:47:37,050
+يساوي S في اتنين واربعين ال S عندي باتنين في اتنين
+
+418
+00:47:37,050 --> 00:47:42,830
+واربعين ويساوي قداش اربعة و تمانين ممكن ولا مش
+
+419
+00:47:42,830 --> 00:47:49,570
+ممكن برضه ممكن يبقى باجي هنا بقوله the possible
+
+420
+00:47:49,570 --> 00:47:52,290
+orders
+
+421
+00:47:54,230 --> 00:48:06,190
+of H are أربعة وتمانين or متين وعشرة يبقى كله
+
+422
+00:48:06,190 --> 00:48:11,170
+اعتمدنا فيه على مين على Lagrange theorem الان
+
+423
+00:48:11,170 --> 00:48:16,170
+وصلنا لنتائج على نظرية Lagrange حصلنا حوالي أربع
+
+424
+00:48:16,170 --> 00:48:21,830
+نتائج و بكلهم بيفيدونا كتير في حل المسائل المرة
+
+425
+00:48:21,830 --> 00:48:23,330
+القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..899313e343fadb9d4ca9742013892edf310e055f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UV0i1PfJFLc_raw.srt
@@ -0,0 +1,1760 @@
+1
+00:00:22,610 --> 00:00:27,190
+المرة اللى فاتت بدأنا في خواص ال isomorphism
+
+2
+00:00:27,190 --> 00:00:31,930
+وقسمنا هذه الخواص الى جزءين الجزء الاول اخدناه
+
+3
+00:00:31,930 --> 00:00:35,870
+المرة الماضية واليوم هناخد الجزء الثاني الجزء
+
+4
+00:00:35,870 --> 00:00:40,030
+الاول من خواص ال isomorphism كان يتحدث عن تأثير ال
+
+5
+00:00:40,030 --> 00:00:45,650
+isomorphism على عناصر ال group واخدنا على ذلك سبع
+
+6
+00:00:45,650 --> 00:00:50,920
+نقاطاليوم أربع نقاط تتحدث عن تأثير الـ isomorphism
+
+7
+00:00:50,920 --> 00:00:57,980
+على الشكل العام لمن؟ لـ group دون الخوض في العناصر
+
+8
+00:00:57,980 --> 00:01:01,220
+لأن المرة اللى فاتت كنا في العناصر مرة هدى في
+
+9
+00:01:01,220 --> 00:01:06,540
+الشكل العام لـ groupيبقى تتكون أو النظرية هذه
+
+10
+00:01:06,540 --> 00:01:12,500
+تتحدث عن ال isomorphism acting on groups التي تؤثر
+
+11
+00:01:12,500 --> 00:01:17,000
+على ال groups قال افترض ان في هذه عبارة عن
+
+12
+00:01:17,000 --> 00:01:22,920
+isomorphism من ال group G onto ال group G bar then
+
+13
+00:01:23,830 --> 00:01:27,870
+الـ Phi inverse عبارة عن isomorphism يبقى Phi اللي
+
+14
+00:01:27,870 --> 00:01:32,990
+عندناها دي كانت isomorphism إذا معكوسة هو عبارة عن
+
+15
+00:01:32,990 --> 00:01:39,670
+isomorphism من G bar onto G يعني كأنها عملية عكسية
+
+16
+00:01:39,670 --> 00:01:45,470
+تماما لمين لPhi الأصليةالنقطة الثانية لو كان الـG
+
+17
+00:01:45,470 --> 00:01:50,810
+abelian فإن الـG bar abelian والعكس صحيح لو كان
+
+18
+00:01:50,810 --> 00:01:53,890
+الـG bar abelian يبقى الـG abelian يبقى الـG is
+
+19
+00:01:53,890 --> 00:01:57,990
+abelian if and only if الـG bar is abelian بالمثل
+
+20
+00:01:57,990 --> 00:02:02,390
+الـG is cyclic if and only if الـG bar is cyclic
+
+21
+00:02:02,920 --> 00:02:07,860
+العمر الرابع والاخير لو كان K subgroup من G فإن
+
+22
+00:02:07,860 --> 00:02:14,760
+صورة اللي هو ال K هذه Phi of capital K هي عبارة عن
+
+23
+00:02:14,760 --> 00:02:20,260
+subgroup كذلك من من من G bar يبقى لو كان K
+
+24
+00:02:20,260 --> 00:02:25,040
+subgroup من G فإن صورة هذه ال K اللي هي Phi of K
+
+25
+00:02:25,040 --> 00:02:31,030
+بيبقى subgroup من من من G barالان بدنا نحاول نبرهن
+
+26
+00:02:31,030 --> 00:02:35,330
+النقاط الأربع اللي عندنا و بدنا نأتي إلى النقطة
+
+27
+00:02:35,330 --> 00:02:41,710
+الأولى النقطة الأولى بدنا نعتمد في برهانها على ما
+
+28
+00:02:41,710 --> 00:02:47,600
+نعرف من مبادئ الرياضيةأخدنا في مبادئ الرياضيات إن
+
+29
+00:02:47,600 --> 00:02:52,780
+لو عندي function و ال function هذه كانت one to one
+
+30
+00:02:52,780 --> 00:02:59,340
+and unto فإن المعكوس تبعها exist و في نفس الوقت
+
+31
+00:02:59,340 --> 00:03:04,120
+one to one and unto تذكروا هذه خدناها و راجعناهافي
+
+32
+00:03:04,120 --> 00:03:08,760
+أول chapter إذا هذا العمود الأساسي أو النقطة
+
+33
+00:03:08,760 --> 00:03:12,420
+الأساسية في إثبات أن الـPhi inverse عبارة عن
+
+34
+00:03:12,420 --> 00:03:16,700
+isomorphism إذا مدام Phi one to one and unto إذا
+
+35
+00:03:16,700 --> 00:03:20,140
+Phi inverse exist وكذلك one to one and unto إذا ما
+
+36
+00:03:20,140 --> 00:03:25,140
+بضلش علينا إلا خاصية ال isomorphism ل Phi of A
+
+37
+00:03:25,140 --> 00:03:28,080
+بيبدوا يسوي Phi of B في Phi of B بدنا نطبقها
+
+38
+00:03:28,080 --> 00:03:33,970
+عالميا على Phi inverseيبقى باجي بقوله هنا since
+
+39
+00:03:33,970 --> 00:03:37,010
+بمعنى
+
+40
+00:03:37,010 --> 00:03:46,710
+فاي is one to one and onto function then since we
+
+41
+00:03:46,710 --> 00:03:56,790
+have ان الفاي inverse is one to one and onto
+
+42
+00:03:56,790 --> 00:03:58,530
+function
+
+43
+00:04:00,990 --> 00:04:05,070
+يبقى هذه معلومة من مبادئ رياضية من المستوى الثاني
+
+44
+00:04:05,070 --> 00:04:13,550
+يبقاش ضايل عندنا it remains يبقى that it remains
+
+45
+00:04:13,550 --> 00:04:23,420
+to show thatإن فاي انفرس of a,b سيكون فاي انفرس of
+
+46
+00:04:23,420 --> 00:04:30,580
+a في في انفرس of b هذا الكلام صحيح لكل ال a و ال b
+
+47
+00:04:30,580 --> 00:04:37,450
+اللي موجودة في جيلذلك بدي اروح اقولكوا consider فى
+
+48
+00:04:37,450 --> 00:04:43,210
+انتظار هذا الكلام consider فاي انفرست لما اتأثر
+
+49
+00:04:43,210 --> 00:04:50,490
+على فاي a b نشوف ايش بتعطينا الان
+
+50
+00:04:50,490 --> 00:04:53,890
+الفاي function و الفاي انفرست اللى هو كمان
+
+51
+00:04:53,890 --> 00:04:59,620
+functionبدي ارجع تعريف ال composition of functions
+
+52
+00:04:59,620 --> 00:05:07,740
+إلى أصله يبقى هذه بتعطينا في انفرس لفي of a و b
+
+53
+00:05:07,740 --> 00:05:15,020
+تمام يبقى بناء عليه الدالة ومعكسة ال composition
+
+54
+00:05:15,020 --> 00:05:20,660
+تبعهم بيعطينا mainالـ Identity Function الـ
+
+55
+00:05:20,660 --> 00:05:25,020
+Identity Function لما تأثر على الـ Element بتعطينا
+
+56
+00:05:25,020 --> 00:05:30,540
+نفس الـ Element اللي هو A B تعالى نشوف تأثير الـ
+
+57
+00:05:30,540 --> 00:05:37,340
+Phi Inverse على مين؟ على الـ Phi of A في من؟ في
+
+58
+00:05:37,340 --> 00:05:39,420
+الـ Phi of B
+
+59
+00:05:42,860 --> 00:05:49,440
+تأثير الفاي انفرس على الفاي of a في الفاي of b أو
+
+60
+00:05:49,440 --> 00:05:57,540
+تأثير الفاي على مين؟ على الفاي انفرس الأولين يا
+
+61
+00:05:57,540 --> 00:06:04,490
+شباب تأثير الفايعلى الفاي انفرس عشان اه فايفاي
+
+62
+00:06:04,490 --> 00:06:08,970
+انفرس عشان اه فايفاي انفرس عشان اه فايفاي
+
+63
+00:06:08,970 --> 00:06:17,990
+انفرس عشان اه فايفاي انفرس عشان اه فايفاي
+
+64
+00:06:17,990 --> 00:06:25,020
+انفرس عشان اه فايفاي انفرس عشان اهيبقى بناء عليه
+
+65
+00:06:25,020 --> 00:06:30,520
+هذا الكلام يساوي انا عندي في is an isomorphism
+
+66
+00:06:30,520 --> 00:06:34,660
+معناته في لما تأثر على حصر ضرب two elements يساوي
+
+67
+00:06:34,660 --> 00:06:38,700
+تأثير الفي على الأولى مضروب في تأثير الفي على
+
+68
+00:06:38,700 --> 00:06:46,560
+الثانية يبقى هذا بده يعطينا في لفي inverse of a في
+
+69
+00:06:46,560 --> 00:06:55,560
+في لمين لفي inverse of bالكلام هذا ليش؟ نظرا لإن
+
+70
+00:06:55,560 --> 00:07:02,160
+الـ Phi is an isomorphism نظرا لإن Phi is
+
+71
+00:07:02,160 --> 00:07:05,640
+isomorphism قدرت أكتبها بالشكل اللي عندنا هذا
+
+72
+00:07:05,640 --> 00:07:10,420
+فبهذا التعريف ال composition of function يبقى بيظل
+
+73
+00:07:10,420 --> 00:07:19,740
+Phi Phi inverse of A وهنا منوهنا كذلك في لفي انفرس
+
+74
+00:07:19,740 --> 00:07:26,100
+of بي بالشكل اللي عندنا هذا الكلام يساوي طبعا في
+
+75
+00:07:26,100 --> 00:07:30,260
+في انفرس هتطلع ال identity function يبقى هنا مش
+
+76
+00:07:30,260 --> 00:07:34,200
+هيضل عندي إلا ال element a و هنا في في انفرس
+
+77
+00:07:34,200 --> 00:07:37,900
+هيعطينا ال identity function تأثيره على بي مش
+
+78
+00:07:37,900 --> 00:07:44,290
+هيعطينا إلا من إلا بيأطلع للنقطة الأولى هذه star
+
+79
+00:07:44,290 --> 00:07:50,870
+والنقطة هذه اللي بدي أسميها double star هذه بتساوي
+
+80
+00:07:50,870 --> 00:07:55,490
+AB وهذه بتساوي AB يبقى الطرف الشمال بتساوي من؟
+
+81
+00:07:55,490 --> 00:07:59,570
+الطرف الشمال اللي عندنا هذا يبقى باجي بقوله هنا
+
+82
+00:07:59,570 --> 00:08:09,460
+from star and double star we haveهنحصل على ما يأتي
+
+83
+00:08:09,460 --> 00:08:20,100
+انه فاي لفاي inverse of a b بدر ساوي فا بدر ساوي
+
+84
+00:08:20,100 --> 00:08:27,500
+مين بدر ساوي فاي لفاي inverse of a في فاي inverse
+
+85
+00:08:27,500 --> 00:08:35,070
+of b بالشكل اللي عندهاطب الآن أنا طلعت قيمتين
+
+86
+00:08:35,070 --> 00:08:40,710
+متساويتين السؤال هو فاي هدي one to one ولا لأ؟
+
+87
+00:08:40,710 --> 00:08:45,770
+مظبوط لأنها isomorphism يبقى فاي one to one وعندي
+
+88
+00:08:45,770 --> 00:08:52,230
+صورتين متساويتين يبقى الأصل ماله متساوي يبقى هذا
+
+89
+00:08:52,230 --> 00:08:58,700
+بده يعطيني مين؟بدي يعطيني انه في انفرس of a,b اللي
+
+90
+00:08:58,700 --> 00:09:03,560
+هو أصل الطرف الشمال بدي اسوي أصل الطرف اليمين اللي
+
+91
+00:09:03,560 --> 00:09:10,780
+هو في انفرس of a في في انفرس ماله of b هذا الكلام
+
+92
+00:09:10,780 --> 00:09:17,580
+ليش؟ because في is one to oneقضينا أثبتنا هنا
+
+93
+00:09:17,580 --> 00:09:24,060
+أثبتنا أن ال inverse هذا أصبح عبارة عن isomorphism
+
+94
+00:09:24,060 --> 00:09:31,060
+يبقى بروح بقوله thus وهكذا في inverse is an
+
+95
+00:09:31,060 --> 00:09:37,960
+isomorphism وبالتالي أثبتنا النقطة الأولىالنقطة
+
+96
+00:09:37,960 --> 00:09:44,980
+الثانية بيقول جي أبيليان إذا كانت الـG بار أبيليان
+
+97
+00:09:44,980 --> 00:09:51,340
+والعكس بالعكس إذا أنا بداجي أقوله إن الـG is
+
+98
+00:09:51,340 --> 00:09:58,630
+abelianF and all F وقتها يجب أن تكون G Ab يعني إذا
+
+99
+00:09:58,630 --> 00:10:03,330
+كان ال A بي بدل سوى بي A لكل ال A و ال B اللي
+
+100
+00:10:03,330 --> 00:10:09,490
+موجودة في G صحيح ولا لأ يبقى F and all F ال A بي
+
+101
+00:10:09,490 --> 00:10:17,580
+بدل سوى بي A لكل ال A و ال B اللي موجودة في Gطيب
+
+102
+00:10:17,580 --> 00:10:22,960
+الان في ايزو مورفزم مدام ايزو مورفزم يبقى صورة
+
+103
+00:10:22,960 --> 00:10:28,360
+العنصر الأول بده تساوي صورة العنصر الثاني يبقى اذا
+
+104
+00:10:28,360 --> 00:10:38,540
+كان في of a,b بده تساوي في of b,aالكلام هذا صحيح
+
+105
+00:10:38,540 --> 00:10:44,160
+إذا كان الان في ايزو مورفزم يبقى بقدر ادخل على اي
+
+106
+00:10:44,160 --> 00:10:52,620
+واحدة فيهم يبقى if and only if في of a في في of b
+
+107
+00:10:52,620 --> 00:11:01,200
+يسوى في of b في main في في of aهذا الكلام لماذا؟
+
+108
+00:11:01,200 --> 00:11:09,620
+لأن فاية عشوائية عشوائية عشوائية عشوائية
+
+109
+00:11:09,620 --> 00:11:11,920
+عشوائية عشوائية عشوائية عشوائية عشوائية عشوائية
+
+110
+00:11:11,920 --> 00:11:20,680
+عشوائية عشوائية عشوائية عشوائية
+
+111
+00:11:20,680 --> 00:11:24,020
+عشوائية
+
+112
+00:11:24,020 --> 00:11:27,860
+عشوائية عشوائية عشوائية عشوائية
+
+113
+00:11:35,170 --> 00:11:42,350
+النقطة الثالثة بيقول لي g is cyclic if and only if
+
+114
+00:11:42,350 --> 00:11:50,170
+g bar is cyclic يبقى بدي أبداله ب g is cyclic if
+
+115
+00:11:50,170 --> 00:11:58,840
+and only if ال g is cyclic لأ كيف؟أثبتناها لل
+
+116
+00:11:58,840 --> 00:12:04,940
+elements تمام؟ لكن احنا بنثبتها in general يبقى
+
+117
+00:12:04,940 --> 00:12:08,820
+انا بقول ان ال G ال cyclic عارف انا عارف تأثيرها
+
+118
+00:12:08,820 --> 00:12:12,500
+اللي بقولنا G تساوي ال sub group generated by A if
+
+119
+00:12:12,500 --> 00:12:15,420
+and only if ال G بار ال sub group generated by Phi
+
+120
+00:12:15,420 --> 00:12:19,820
+of A يعني أثبتناها على العناصر الآن بنثبت in
+
+121
+00:12:19,820 --> 00:12:23,820
+general G ال cyclic if and only if ال G هذه اللي
+
+122
+00:12:23,820 --> 00:12:28,980
+جيتلها ولو generator واحد مظبوط؟يبقى if and only
+
+123
+00:12:28,980 --> 00:12:37,040
+if الـ G هي ال group generated by A يبقى G الصحيح
+
+124
+00:12:37,040 --> 00:12:43,780
+لك إذا كان G قدرت أولدها بعنصر واحد طب لو حدث ذلك
+
+125
+00:12:43,780 --> 00:12:48,640
+شو العلاقة بين ال order تبع ال G و ال order تبع ال
+
+126
+00:12:48,640 --> 00:12:57,020
+A؟إتنين متساويت يبقى هذا الكلام صحيح if and only
+
+127
+00:12:57,020 --> 00:13:04,200
+if ال order لل A سوى ال order ل G طيب هذا الكلام
+
+128
+00:13:04,200 --> 00:13:11,160
+صحيح if and only if نرجع للمحاضرة اللي فاتت ال
+
+129
+00:13:11,160 --> 00:13:16,620
+order ل A شو بيساوي النقطة خمسة عندك في المحاضرة
+
+130
+00:13:16,620 --> 00:13:23,080
+الماضيةالـ order لـ A بدي سوى ال order لـ Phi of A
+
+131
+00:13:23,080 --> 00:13:29,700
+والنقطة رقم سبعة ال order ل G بدي سوى ال order ل G
+
+132
+00:13:29,700 --> 00:13:35,720
+bar ليش؟ لأنه Phi isomorphism يبقى F and only F ال
+
+133
+00:13:35,720 --> 00:13:43,160
+order تبع ال A سوى ال order ل Phi of A تمام؟
+
+134
+00:13:44,730 --> 00:13:49,870
+صوى ال order للـ Fi of A يبقى هذا الكلام صحيح إذا
+
+135
+00:13:49,870 --> 00:13:56,590
+كان ال order ل A قلنا هو عبارة عن مين ال order ل G
+
+136
+00:13:56,590 --> 00:14:04,230
+و ال order ل G هذا هو ال order تبع ال G bar يبقى
+
+137
+00:14:04,230 --> 00:14:09,930
+بده يساوي ال order تبع ال G bar و هذا بده يساوي
+
+138
+00:14:09,930 --> 00:14:18,170
+مدام هذا هو ال order تبع ال G barولا تقول اتلاخبط
+
+139
+00:14:18,170 --> 00:14:24,110
+فى خطوة واحدة يبقى هذا الكلام صحيح إذا كان هدول
+
+140
+00:14:24,110 --> 00:14:28,750
+اتنين بيصووا بعض هدى خلته زى ما هو و ال order ل G
+
+141
+00:14:28,750 --> 00:14:33,350
+بدأجله شوية أخدت ال order ل A بده يساوي ال order
+
+142
+00:14:33,350 --> 00:14:39,290
+لل Phi of A و هذا الكلام بده يساوي ال order ل G
+
+143
+00:14:39,690 --> 00:14:44,170
+يبقى شيلت ال order ل a و حطيت بدا ال order ل phi
+
+144
+00:14:44,170 --> 00:14:49,910
+of a و هنا ال order ل g الان هذا f and only f
+
+145
+00:14:49,910 --> 00:14:58,750
+طلعلي لهذا ال order لل phi of a ال order لل phi of
+
+146
+00:14:58,750 --> 00:15:05,730
+a ماله؟الـ order ل G هو ال order ل G bar هذا
+
+147
+00:15:05,730 --> 00:15:11,810
+الكلام بده يساوي ال order ل G bar هذا الكلام جبته
+
+148
+00:15:11,810 --> 00:15:17,010
+من وين؟ from سبعة من النقطة السابعة في النظرية
+
+149
+00:15:17,010 --> 00:15:21,310
+السابقة وهذا جبته من وين؟ من النقطة الخامسة في
+
+150
+00:15:21,310 --> 00:15:28,050
+النظرية الماضيةيبقى إن حدث ذلك إن ال order لـPhi
+
+151
+00:15:28,050 --> 00:15:34,510
+of A سوى ال order لـG bar السؤال هو Phi of A هذا
+
+152
+00:15:34,510 --> 00:15:38,590
+موجود في G ولا في G bar؟ طيب ال order له سوى ال
+
+153
+00:15:38,590 --> 00:15:43,610
+order لـG bar إذا هذا إيش بيكون؟ generator يبقى
+
+154
+00:15:43,610 --> 00:15:50,720
+هذا الكلام if and only ifإن الـ G bar بده تساوي لـ
+
+155
+00:15:50,720 --> 00:15:57,140
+group generated by Phi of A طب إن حدث ذلك يبقى G
+
+156
+00:15:57,140 --> 00:16:03,340
+bar مالها مال G bar في هذه الحالة if and only if
+
+157
+00:16:03,340 --> 00:16:12,270
+الـ G bar is cyclic وهو المطلوبيبقى اعتمادنا في
+
+158
+00:16:12,270 --> 00:16:18,590
+برهان هذه النظرية على نقطتين من النظرية السابقة
+
+159
+00:16:18,590 --> 00:16:22,450
+وهي ال order لإيه بده يسوى ال order لـPhi of V
+
+160
+00:16:22,450 --> 00:16:26,190
+النقطة الأولى النقطة الثانية ال order لـG هو ال
+
+161
+00:16:26,190 --> 00:16:31,050
+order لـG bar كل هذا تحت تأثير أن ال Phi اللي
+
+162
+00:16:31,050 --> 00:16:37,490
+عندها عبارة عن isomorphismبذلك نصل الى النقطة
+
+163
+00:16:37,490 --> 00:16:41,090
+الرابعة حد يلو سؤال هنا قبل ان ننتقل الى النقطة
+
+164
+00:16:41,090 --> 00:16:49,240
+الرابعة اللى بحب يسألى سؤال هنا فيش بلاشنجي للنقطة
+
+165
+00:16:49,240 --> 00:16:54,360
+الرابعة بيقول لو كان capital K هو subgroup من J
+
+166
+00:16:54,360 --> 00:17:00,220
+فإن في of capital K كل العناصر في of small k بحيث
+
+167
+00:17:00,220 --> 00:17:06,000
+ك موجود في ك كابتل عبارة عن subgroup من جي بار إذا
+
+168
+00:17:06,000 --> 00:17:10,220
+بنحاول نثبت إن الست اللي عندنا هذه ال subgroup من
+
+169
+00:17:10,220 --> 00:17:17,090
+جي بارلما كنا بنثبت ال subgroup كان عندي اكثر من
+
+170
+00:17:17,090 --> 00:17:22,810
+طريقة لإثبات ال subgroup أبسطهم و أسرعهم اني أثبت
+
+171
+00:17:22,810 --> 00:17:27,810
+نقطتين ان ال 6 اللي عندها دي is none امتى الخطوة
+
+172
+00:17:27,810 --> 00:17:31,960
+الأولىخطوة ثانية لو أخدت منها عنصرين ضربت الأول في
+
+173
+00:17:31,960 --> 00:17:35,960
+المعكوس التاني اللي جيتهم فيها إذا بصير هذه عبارة
+
+174
+00:17:35,960 --> 00:17:43,980
+عن عبارة عن subgroup طب الآن انا أدعي ان five of K
+
+175
+00:17:43,980 --> 00:17:55,120
+is non empty طيب
+
+176
+00:17:55,120 --> 00:18:02,730
+ليش؟الان السؤال هو K هذه ال sub group من G بنفع
+
+177
+00:18:02,730 --> 00:18:08,250
+يكون sub group وما فيها identity element؟ بنفع؟ لأ
+
+178
+00:18:08,250 --> 00:18:12,910
+يبقى sub group ال identity element تبع ال K هو ال
+
+179
+00:18:12,910 --> 00:18:20,780
+identity element تبع من؟طبع الجي الأصلية تمام إذا
+
+180
+00:18:20,780 --> 00:18:28,340
+هذه non-empty since ليش؟ لأن الـPhi of ال identity
+
+181
+00:18:28,340 --> 00:18:36,780
+تبع الـG موجود في الـPhi of كابتل Kليش؟ لأن الـ
+
+182
+00:18:36,780 --> 00:18:42,880
+identity تبع الـ G موجود في كابتال K هذه يعني هنا
+
+183
+00:18:42,880 --> 00:18:48,980
+that is أي أن هذه Phi of E جي من المرة الماضية
+
+184
+00:18:48,980 --> 00:18:55,680
+النقطة الأولى الـ E تبع الـ G bar موجودة في Phi of
+
+185
+00:18:55,680 --> 00:19:03,000
+كابتال K هذه ههه بالضبط هي هذهخدنا المرة اللي فتت
+
+186
+00:19:03,000 --> 00:19:05,980
+أول نقطة في برهانة النظرية الماضية كان
+
+187
+00:19:10,840 --> 00:19:17,020
+يبقى Phi of K is non-empty لان نحاول نجد عمصرين في
+
+188
+00:19:17,020 --> 00:19:22,680
+Phi of K ونثبت ان الأول في معكوس التاني موجود فيها
+
+189
+00:19:22,680 --> 00:19:28,660
+ان حدث ذلك يبقى بقول Phi of K is a subgroup لذلك
+
+190
+00:19:28,660 --> 00:19:34,500
+لو جيت قلت افترض ان X وY موجودات في K
+
+191
+00:19:38,240 --> 00:19:45,760
+اخدت عنصرين موجودات في كابتل كيه then الـ phi of x
+
+192
+00:19:45,760 --> 00:19:53,600
+والـ phi of y موجودات هدول وين؟ في مين؟في جي بار
+
+193
+00:19:53,600 --> 00:19:58,660
+صحيح لكن انا بدي احصرهم اكتر ال X و ال Y موجودات
+
+194
+00:19:58,660 --> 00:20:07,100
+في K يبقى Phi of X موجود في Phi of K و Phi of Y
+
+195
+00:20:07,100 --> 00:20:14,120
+موجودة في Phi of K يبقى هذا الكلام موجود في Phi of
+
+196
+00:20:14,120 --> 00:20:20,870
+K بالشكل اللي عندنايبقى استطعت ان اجد عنصر ينعش
+
+197
+00:20:20,870 --> 00:20:27,210
+واقيا انوان في في of k اذا بدي اخد الأول في معكوس
+
+198
+00:20:27,210 --> 00:20:36,160
+الثاني يبقى بدي اخد في of x في في of y inverseإذا
+
+199
+00:20:36,160 --> 00:20:42,520
+قدرت أثبت إن هذا موجود في Phi of K قصرت Phi of K
+
+200
+00:20:42,520 --> 00:20:47,360
+subgroup وانتهينا من القصة هذه خالص.الأن هذا
+
+201
+00:20:47,360 --> 00:20:53,860
+الكلام من الخواص اللي درسناها قبل ذلك Phi of X في
+
+202
+00:20:53,860 --> 00:20:59,870
+Phi of Y inverse.الرقم اللى بيكون عندنا هنا او
+
+203
+00:20:59,870 --> 00:21:04,190
+ينما كان يكون بنزل عالمين على العنصر سواء كان هذا
+
+204
+00:21:04,190 --> 00:21:09,650
+رقم موجب او سالب او صفر المرة اللى فاتت اخدنا
+
+205
+00:21:09,650 --> 00:21:14,310
+النقطة الثانية اللى five of a to the power n بيبقى
+
+206
+00:21:14,310 --> 00:21:19,090
+سوى five of a كله to the power n وهذا اللى حاصل
+
+207
+00:21:19,090 --> 00:21:24,500
+عندنا هناطيب الآن في ايزو مورفزم مادام ايزو مورفزم
+
+208
+00:21:24,500 --> 00:21:33,040
+بقدر عليهم هم بفي واحدة يبقى هذا في of x y inverse
+
+209
+00:21:33,040 --> 00:21:44,660
+ليش؟ since ال في is an isomorphismهذا الكلام يساوي
+
+210
+00:21:44,660 --> 00:21:53,300
+في of x y inverse هل يا ترى هذا موجود في في of
+
+211
+00:21:53,300 --> 00:21:54,400
+كابتل ك؟
+
+212
+00:21:57,290 --> 00:22:03,990
+مش K subgroup واخدت عنصرين فيها يبقى الأول فيه
+
+213
+00:22:03,990 --> 00:22:07,650
+معاكس الثاني موجودة فيها لإن ال K زي ال subgroup
+
+214
+00:22:07,650 --> 00:22:15,270
+يبقى موجود sense اللي هو من X Y inverse موجودة في
+
+215
+00:22:15,270 --> 00:22:21,160
+capital K وK عبارة عن subgroup من Gطيب بناء علي
+
+216
+00:22:21,160 --> 00:22:27,220
+اذا اثبت كل الخواص اللازمة لاثبات ان فاي of K is a
+
+217
+00:22:27,220 --> 00:22:33,920
+subgroup مدام اثبتها بروح بقول له غص و هكذا فاي of
+
+218
+00:22:33,920 --> 00:22:42,720
+كبتل K is a subgroup من جي بار وهو المضمون حدا
+
+219
+00:22:42,720 --> 00:22:45,780
+فيكم بيحب يسأل اي سؤال قبل ما فوت على النقطة اللي
+
+220
+00:22:45,780 --> 00:22:48,760
+بعدها اي تساؤل
+
+221
+00:22:53,040 --> 00:22:59,140
+إيش بتقول؟ وين؟
+
+222
+00:22:59,140 --> 00:23:03,320
+تعال هنا على اللوحة شوف تعال بس شوف شرايك إيش
+
+223
+00:23:03,320 --> 00:23:12,760
+بتقول تعال، أيوة، أه ماله؟ لأ من ال A و ال B وين
+
+224
+00:23:12,760 --> 00:23:17,970
+موجودة؟الـ A والـ B موجودات في جي وبالتالي Phi
+
+225
+00:23:17,970 --> 00:23:21,050
+inverse of A وPhi inverse of B هدول موجودات في جي
+
+226
+00:23:21,050 --> 00:23:26,530
+بار لكن الأصل أنا ماخد A وB هدول من وين؟ من جي
+
+227
+00:23:26,530 --> 00:23:31,610
+وليس من جي بار در بالك اه الكلام هذا سليم فيش فيه
+
+228
+00:23:31,610 --> 00:23:37,470
+لا غبارة عليها حد بدي أسأل تاني؟ طيب ننتقل الآن
+
+229
+00:23:37,470 --> 00:23:40,230
+إلى النقطة التي تليها
+
+230
+00:23:59,000 --> 00:24:09,480
+نقضى تعريف جديد يبقى definition and isomorphism
+
+231
+00:24:09,480 --> 00:24:14,980
+and isomorphism
+
+232
+00:24:14,980 --> 00:24:30,500
+from a groupجي onto onto
+
+233
+00:24:30,500 --> 00:24:46,240
+itself onto itself اله نفسها is called is
+
+234
+00:24:46,240 --> 00:24:48,900
+called and
+
+235
+00:24:54,010 --> 00:24:57,410
+Atomorphism Atomorphism of G
+
+236
+00:25:40,700 --> 00:25:45,060
+أحنا لان موضوعنا موضوع الـ isomorphism الان بدينا
+
+237
+00:25:45,060 --> 00:25:51,600
+نخصص شوية ايش نخصص ال isomorphism هو function من
+
+238
+00:25:51,600 --> 00:25:55,840
+جروب إلى جروب تانية بحيث ال function هادي one to
+
+239
+00:25:55,840 --> 00:26:00,840
+one and and هو تحقق الخاصية phi of a b بده سوى phi
+
+240
+00:26:00,840 --> 00:26:08,660
+of a في phi of b تمام؟ الانالان ايش بنقول؟ بنقول
+
+241
+00:26:08,660 --> 00:26:13,280
+لو كانت ال function هذه من الجروب لنفس الجروب مش
+
+242
+00:26:13,280 --> 00:26:18,300
+لجروب تانية ان حدث ذلك باجي بقول ان كانت ال
+
+243
+00:26:18,300 --> 00:26:22,420
+function هذه من الجروب لنفس الجروب مش لجروب تانية
+
+244
+00:26:22,420 --> 00:26:27,610
+يبقى بدي اسميه ايش؟ atomorphismفال definition
+
+245
+00:26:27,610 --> 00:26:32,810
+بيقوللي ال isomorphism من ال group G onto itself
+
+246
+00:26:32,810 --> 00:26:38,730
+يبقى من G إلى G نفسها دي is a is called an
+
+247
+00:26:38,730 --> 00:26:42,770
+atomorphism ايش رأيك؟ احنا خدنا مثال على ال
+
+248
+00:26:42,770 --> 00:26:47,960
+atomorphism و احنا مش دارينأخدنا المثال أعتقد رقم
+
+249
+00:26:47,960 --> 00:26:51,160
+خمسة أو رقم أربع معاك في الأمثلة تبع الـ
+
+250
+00:26:51,160 --> 00:26:59,440
+isomorphism يبقى أول example الخدنا define اللي هو
+
+251
+00:26:59,440 --> 00:27:03,500
+five من ال special linear group of two by two
+
+252
+00:27:03,500 --> 00:27:09,380
+matrices over R لل special linear group of two by
+
+253
+00:27:09,380 --> 00:27:19,920
+two matrices over RDefine Phi by عرفنا اللي هو Phi
+
+254
+00:27:19,920 --> 00:27:30,340
+M of A بدي ساوي الـ M A M inverse والـ M هذه
+
+255
+00:27:30,340 --> 00:27:34,820
+مصفوفة نظامها 2 في 2 قد تكون في ال special و قد لا
+
+256
+00:27:34,820 --> 00:27:40,360
+تكون لكن نظامها 2 في 2يبقى هاي ال function اللي
+
+257
+00:27:40,360 --> 00:27:46,240
+عندنا نظرا اثبتناها احنا isomorphism وهيها من ال
+
+258
+00:27:46,240 --> 00:27:51,460
+group الى نفس ال group يبقى في is an atomorphism
+
+259
+00:27:51,460 --> 00:28:02,680
+يبقى هنا بدي بقوله since في م is an isomorphism
+
+260
+00:28:02,680 --> 00:28:09,610
+وهذا previousexample مش هنقعد هنا أعيد فيه تاني
+
+261
+00:28:09,610 --> 00:28:18,570
+and الـ phi m من ال special linear group لل
+
+262
+00:28:18,570 --> 00:28:28,810
+special linear group هيها نفسها يبقى we have أنه
+
+263
+00:28:28,810 --> 00:28:33,070
+phi is an atomorphism
+
+264
+00:28:35,930 --> 00:28:40,410
+هذا مثال كنا عاملينه و احنا مش عارفينه او ندريش
+
+265
+00:28:40,410 --> 00:28:45,050
+انه atomorphism اثبتنا انه isomorphism و سكتنا لكن
+
+266
+00:28:45,050 --> 00:28:48,810
+لما كان من ال group إلى نفس ال group اذا صار هذا
+
+267
+00:28:48,810 --> 00:28:57,450
+معله صار atomorphism نعطي مثال اخر تبقى هذا اعتبره
+
+268
+00:28:57,450 --> 00:29:05,890
+المثال الأول نجي للمثال الرقم اتنين بيقول الاتالـ
+
+269
+00:29:05,890 --> 00:29:13,150
+R تربيع هي عبارة عن كل ال order pairs A و B بحيث
+
+270
+00:29:13,150 --> 00:29:17,990
+ان ال A و ال B موجودة في ال set of real numbers
+
+271
+00:29:17,990 --> 00:29:27,650
+then ال R square و عليها عملية الجمع is a group
+
+272
+00:29:27,650 --> 00:29:34,730
+هذا لما اتروح في الدار شيكلي عليها و اتأكدانه هذه
+
+273
+00:29:34,730 --> 00:29:41,790
+عبارة عن group define a
+
+274
+00:29:41,790 --> 00:29:52,150
+function phi من ال R square لل R square by phi of
+
+275
+00:29:52,150 --> 00:29:58,810
+A و B بده يساوي ال B و ال A
+
+276
+00:30:03,430 --> 00:30:08,090
+show that أن
+
+277
+00:30:08,090 --> 00:30:17,370
+فاي is an atomorphism بيجيلي أن فاي عبارة عن
+
+278
+00:30:17,370 --> 00:30:18,950
+atomorphism
+
+279
+00:30:28,120 --> 00:30:32,080
+يبقى احنا الـ function اللى عندنا قال يعرف الـ
+
+280
+00:30:32,080 --> 00:30:36,340
+function define a function في من R تربيع الى R
+
+281
+00:30:36,340 --> 00:30:41,980
+تربيع بحيث في of A وB بتقلب وضع اللى هو ال A و ال
+
+282
+00:30:41,980 --> 00:30:49,910
+B إلى B و Aو كأننا نقلب عناصر المستوى XY عبر الخط
+
+283
+00:30:49,910 --> 00:30:52,970
+Y تساوي X اللي على الشجة هذه بنقولها هنا و اللي
+
+284
+00:30:52,970 --> 00:30:58,170
+هنا بنقولها على الشجة التانية جال يبين لي ان ال
+
+285
+00:30:58,170 --> 00:31:03,310
+Phi هذه عبارة عن اتومورفزم و واضح ان Phi هيها من
+
+286
+00:31:03,310 --> 00:31:06,710
+وين لوين من R تربيع إلى R تربيع يعني من اللي جروم
+
+287
+00:31:06,710 --> 00:31:10,800
+إلى نفسهايبقى مش ضايق لعيننا نثبت إلا في عبارة عن
+
+288
+00:31:10,800 --> 00:31:14,380
+isomorphism إن أثبتناها isomorphism بتصير
+
+289
+00:31:14,380 --> 00:31:19,460
+atomorphism بمعنى أخر بدي أثبت إن في one to one
+
+290
+00:31:19,460 --> 00:31:24,220
+and one to one تخدم خاصية ال isomorphism إذا بدي
+
+291
+00:31:24,220 --> 00:31:31,600
+أبدأ أول شغلة بفي is one to oneيبقى بدى احاول اثبت
+
+292
+00:31:31,600 --> 00:31:38,600
+ان فاي is one to one لذلك بروح اخد صورتين
+
+293
+00:31:38,600 --> 00:31:44,480
+متساويتين و اثبت ان اصلهم متساوي فبروح بقوله
+
+294
+00:31:44,480 --> 00:31:54,680
+assume افترض that ان فاي of a و b بدى يساوي فاي of
+
+295
+00:31:54,680 --> 00:32:01,240
+c و dيبقى مطلوب اثبت ان ال A و ال B بيبقى ساوية
+
+296
+00:32:01,240 --> 00:32:10,240
+مين؟ بيبقى ساوية C و D مطلوب نثبت ان ال A و ال B
+
+297
+00:32:10,240 --> 00:32:16,180
+بيبقى ساوية CD ثم ال
+
+298
+00:32:16,180 --> 00:32:24,090
+Phi of A و B هي عبارة عن مين؟ B و Aالـ5 of C وD هي
+
+299
+00:32:24,090 --> 00:32:32,370
+عبارة عن مين؟ عبارة عن D وC بناء عليه إذا عندي two
+
+300
+00:32:32,370 --> 00:32:36,010
+ordered pairs are equal يبقى المركبة الأولى تساوي
+
+301
+00:32:36,010 --> 00:32:40,150
+المركبة الأولى والمركبة الثانية تساوي المركبة
+
+302
+00:32:40,150 --> 00:32:45,490
+الثانية من ال linear algebra يبقى هذا يطينا مين؟
+
+303
+00:32:45,670 --> 00:32:52,350
+بدوا يعطينا ان ال b تساوي ال d وفي نفس الوقت ال a
+
+304
+00:32:52,350 --> 00:32:58,370
+بدوا يساوي من ال c هذا بدوا يعطينا انا بدأ حاول
+
+305
+00:32:58,370 --> 00:33:03,790
+اثبت ان ال a و ال b بدوا يساوي .. بدأ .. بدأ حاول
+
+306
+00:33:03,790 --> 00:33:07,830
+اثبت ان و أنا خدنا .. بدأ حاول اثبت ان ال a و ال b
+
+307
+00:33:07,830 --> 00:33:13,810
+بدوا يساوي من ال c و ال d إذا لو أخدت ال a و ال b
+
+308
+00:33:15,180 --> 00:33:20,240
+الـ A عبارة عن مين؟ C يبقى بقدر أشيلها و أكتب
+
+309
+00:33:20,240 --> 00:33:26,560
+بدالها C والـ B عبارة عن مين؟ عبارة عن D و هو
+
+310
+00:33:26,560 --> 00:33:30,520
+المطلوب إذا الـ A و الـ B ال order pair ساوى ال
+
+311
+00:33:30,520 --> 00:33:33,520
+order pair التاني الـ C و D معناه هذا الكلام أنه
+
+312
+00:33:33,520 --> 00:33:39,640
+Phi is one to one بالدرجة الأقل ال Phi is onto
+
+313
+00:33:42,100 --> 00:33:49,840
+يبقى بدي اروح اخد اي element A وB موجود في ال R²
+
+314
+00:33:49,840 --> 00:33:56,300
+بدي اثبت انه اي element في المستوى XY له اصل كذلك
+
+315
+00:33:56,300 --> 00:34:07,120
+في المستوى XY يبقى then ال A و ال B لو جلبته ايش
+
+316
+00:34:07,120 --> 00:34:13,230
+بده يصير؟B و A بيظل في R تربيع ولا بيطلع برا؟ بيظل
+
+317
+00:34:13,230 --> 00:34:18,610
+في R تربيع يبقى هنا then بدل ما اقول A و B بدي
+
+318
+00:34:18,610 --> 00:34:28,110
+اقول B و A كذلك موجود في ال R تربيع يبقى and ال A
+
+319
+00:34:28,110 --> 00:34:41,230
+و ال B ده بقدر اقول عليه Phi of B و Aفى الـ
+
+320
+00:34:41,230 --> 00:34:46,390
+element اللى أخدته في R تربية لقيت له أصل موجود
+
+321
+00:34:46,390 --> 00:34:51,990
+كذلك في R تربية اللى هو بي و إيه يبقى فاي is on to
+
+322
+00:34:51,990 --> 00:34:56,590
+يبقى أي element أخدته في ال group لقيتله أصل في
+
+323
+00:34:56,590 --> 00:35:02,500
+نفس ال group يبقى بناء عليه فاي is on toضايل علينا
+
+324
+00:35:02,500 --> 00:35:09,820
+خاصية الـ isomorphism فاي is an isomorphism بدا
+
+325
+00:35:09,820 --> 00:35:17,180
+أقول له فاي of بدي أخد a و b ال operation عملية
+
+326
+00:35:17,180 --> 00:35:24,320
+الجامع ل c و d أخد تأثير في على main على two
+
+327
+00:35:24,320 --> 00:35:29,290
+elements وال two elements موجودات في ال R²يبقى هذا
+
+328
+00:35:29,290 --> 00:35:40,470
+الكلام بده يساوي في او يبقى a زائد c و b زائد d
+
+329
+00:35:40,470 --> 00:35:47,190
+كله ك element واحد بناء على التعريف هذا الكلام بده
+
+330
+00:35:47,190 --> 00:35:56,060
+يساوي المركبة a ثانيةبزائد دي والمركبة الأولى a
+
+331
+00:35:56,060 --> 00:36:03,540
+زائد c بالشكل اللي عندناها يبقى صورة العنصر هذا
+
+332
+00:36:03,540 --> 00:36:09,600
+بجلب وضع المركبتين هاي جلبناهم السؤال هو هل يمكن
+
+333
+00:36:09,600 --> 00:36:17,380
+كتابة الجثة على شكل مجموع قوسين الإجابة نعم كيف
+
+334
+00:36:17,380 --> 00:36:25,640
+كانت تاليهذا الكلام بقدر اقول b و a زائد d و c
+
+335
+00:36:25,640 --> 00:36:33,840
+طبعا ال b و ال a طبقا لل definition مش هي عبارة عن
+
+336
+00:36:33,840 --> 00:36:41,580
+five of a و b و التانية d و c هي عبارة عن five of
+
+337
+00:36:41,580 --> 00:36:49,470
+c و dطب ايش اللي عملنا؟ طلع هنا أخدت مجموع اللي هو
+
+338
+00:36:49,470 --> 00:36:54,910
+two ordered pair لجيت تأثير الفي عليهم يسوى تأثير
+
+339
+00:36:54,910 --> 00:37:00,370
+الفي على ال element الأول زي تأثير الفي على ال
+
+340
+00:37:00,370 --> 00:37:06,870
+element الثاني هنا ظلت النقطة الأخيرة يبقى since
+
+341
+00:37:07,360 --> 00:37:16,480
+فاي من R تربية الى R تربية is an isomorphism يبقى
+
+342
+00:37:16,480 --> 00:37:28,040
+الفاي is an atomorphism وهو المطلوبيبقى من الأنفا
+
+343
+00:37:28,040 --> 00:37:34,660
+صاعدا مشان أثبت أنه في اتو مورفزم بدي أتأكد أنه
+
+344
+00:37:34,660 --> 00:37:39,120
+لازم تبقى من ال group لنفس ال group و بعد هيك ايزو
+
+345
+00:37:39,120 --> 00:37:44,780
+مورفزم فباقى عندنا في هذه المحاضرة تعريف له علاقة
+
+346
+00:37:44,780 --> 00:37:53,360
+بهذه النقطة تعريف بقول ما يأتي definition little
+
+347
+00:37:53,360 --> 00:38:02,420
+gb grouplet الـ G بي A group and
+
+348
+00:38:02,420 --> 00:38:13,380
+let ال A موجود في هذه ال group define a function
+
+349
+00:38:13,380 --> 00:38:22,820
+فاي A من ال group G إلى ال group G by
+
+350
+00:38:25,000 --> 00:38:36,580
+فاي a of x يساوي a x a inverse لكل
+
+351
+00:38:36,580 --> 00:38:46,740
+ال x اللي موجود في g بالاستثناء يبقى then فاي a is
+
+352
+00:38:46,740 --> 00:38:52,120
+called is called an
+
+353
+00:38:54,790 --> 00:39:01,530
+و الله is called the inner the
+
+354
+00:39:01,530 --> 00:39:05,550
+inner atomorphism
+
+355
+00:39:05,550 --> 00:39:20,910
+atomorphism of g induced by a ناخد
+
+356
+00:39:20,910 --> 00:39:21,670
+مثال
+
+357
+00:39:25,360 --> 00:39:35,000
+example let الـ G تساوي D4 D4 عناصرها عارفينهم ر
+
+358
+00:39:35,000 --> 00:39:43,740
+نود و R تسعين و R مية و تمانين و R ميتين و سبعين و
+
+359
+00:39:43,740 --> 00:39:51,400
+H و V و D و D prime عارفينها من قبل with
+
+360
+00:39:53,530 --> 00:40:06,890
+R 360 هي الـ R نوت R 360 هي الـ R نوت وكذلك الـ H
+
+361
+00:40:06,890 --> 00:40:14,450
+تربيع تساوي الـ V تربيع تساوي الـ D تربيع تساوي
+
+362
+00:40:14,450 --> 00:40:18,630
+الـ D تربيع تساوي الـ D تربيع تساوي من الـ
+
+363
+00:40:18,630 --> 00:40:19,830
+Identity
+
+364
+00:40:26,700 --> 00:40:44,820
+define a function في تسعين من D4 إلى D4 by في
+
+365
+00:40:44,820 --> 00:40:48,800
+تسعين of X ساوي
+
+366
+00:40:50,750 --> 00:41:08,450
+ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين ر تسعين
+
+367
+00:41:08,450 --> 00:41:12,330
+ر تسعين
+
+368
+00:41:24,400 --> 00:41:37,300
+الفاي R تسعين is an inner atomorphism
+
+369
+00:41:51,150 --> 00:41:56,130
+العربى بنرجع لتعريف ال inner atom morphism جالي جي
+
+370
+00:41:56,130 --> 00:42:00,870
+جروب وخد فيها element عرف function سماها في a من g
+
+371
+00:42:00,870 --> 00:42:07,050
+إلى g باي في a of x يسوي a x a inverse الشبيه
+
+372
+00:42:07,050 --> 00:42:12,610
+بمين؟ الشبيه بالتو مثلا احنا اللي في m of a يسوي m
+
+373
+00:42:12,610 --> 00:42:16,830
+a m inverseبس هنا أخدها على مين؟ على element وليس
+
+374
+00:42:16,830 --> 00:42:20,810
+على مصفوفة مين ما تكون ال group سواء مصفوفات ولا
+
+375
+00:42:20,810 --> 00:42:27,030
+غير مصفوفات يبقى في a x يسوو ال a x انفرست لكل ال
+
+376
+00:42:27,030 --> 00:42:31,850
+x اللي موجودة في g يبقى في of a بنسميها inner
+
+377
+00:42:31,850 --> 00:42:37,350
+atomorphism يعني أكنه atomorphism داخلي على مين؟
+
+378
+00:42:37,350 --> 00:42:42,310
+على ال groupالان انا اعطي مثال توضيحي اخدنا D4 و
+
+379
+00:42:42,310 --> 00:42:47,310
+كتبنا خواص ال D4 كما كانت مكتوبة معانا من قبل قال
+
+380
+00:42:47,310 --> 00:42:52,030
+يعرف ال function Phi R تسعين طبعا هم نقدر نجيب Phi
+
+381
+00:42:52,030 --> 00:42:56,390
+R مية و تمانين و Phi R متين و سبعين و Phi R H و
+
+382
+00:42:56,390 --> 00:43:02,650
+Phi R V و Phi R D و Phi D Prime كلهم نقدر نجيبهم
+
+383
+00:43:02,940 --> 00:43:07,580
+يعني بنقدر نجيب تمانية atomorphism ممكن يكون بعضهم
+
+384
+00:43:07,580 --> 00:43:11,480
+يساوي بعضه وبالتالي ماتطلعوش تمانية يطلعوا أقل بس
+
+385
+00:43:11,480 --> 00:43:16,020
+احنا بدنا ناخد فاي ار تسعين وما نعمله عليها بنقدر
+
+386
+00:43:16,020 --> 00:43:22,020
+نعمله لكل العناصر بالاستثناء يبقى هنا show that ان
+
+387
+00:43:22,020 --> 00:43:28,800
+هذه atomorphism باجي بقوله solutionبدنا نروح نجيب
+
+388
+00:43:28,800 --> 00:43:37,480
+اول شي FI R تسعين of ال R noteبدي امسك جميع عناصر
+
+389
+00:43:37,480 --> 00:43:44,100
+ال D4 ليش؟ لإن فاي هذه ارند من D4 إلى D4 وانا جاي
+
+390
+00:43:44,100 --> 00:43:50,720
+لمعرفها ان فاي R90X تساوي R90X لكل ال X اللي
+
+391
+00:43:50,720 --> 00:43:56,700
+موجودة في D4 يعني هذا الكلام صحيح لكل ال X اللي
+
+392
+00:43:56,700 --> 00:44:04,190
+موجودة في D4إذا ميدالي ل R تسعين R نود هي عبارة عن
+
+393
+00:44:04,190 --> 00:44:13,090
+R تسعين R نود R تسعين inverse ال R نود مش هدا ال
+
+394
+00:44:13,090 --> 00:44:18,630
+identity طب وال R تسعين فيه R تسعين inverse يبقى
+
+395
+00:44:18,630 --> 00:44:26,660
+ده هيطلع ال R نود itselfلن يتغير فيها شيء لو بدى
+
+396
+00:44:26,660 --> 00:44:36,320
+اجيب الان في ار تسعين يبقى
+
+397
+00:44:36,320 --> 00:44:46,980
+بده ساول ار تسعين ار تسعين ار تسعين انفرسالـ
+
+398
+00:44:46,980 --> 00:44:51,440
+element هذا في ال inverse شو بيعطينا ال identity
+
+399
+00:44:51,440 --> 00:44:59,720
+في R تسعين بيعطينا R تسعين itself ماتغيرتش طيب لو
+
+400
+00:44:59,720 --> 00:45:08,100
+بده أروح أجيب الفاي R تسعين R مية و تمانين يبقى
+
+401
+00:45:08,100 --> 00:45:16,000
+بيصير عندنا R تسعين R مية و تمانين R تسعين inverse
+
+402
+00:45:16,760 --> 00:45:23,180
+هل ليست هذه R 180 كمان؟
+
+403
+00:45:23,180 --> 00:45:28,130
+R كميوت مع نفسها، كل ال rotation كميوت مع نفسهاطيب
+
+404
+00:45:28,130 --> 00:45:35,910
+لو روحنا جيبنا R تسعين او Phi R تسعين of R ميتين
+
+405
+00:45:35,910 --> 00:45:44,750
+وسبعين يبقى R تسعين R ميتين وسبعين R تسعين inverse
+
+406
+00:45:44,750 --> 00:45:50,590
+يبقى كمان R ميتين وسبعين لأنه بدلناهم مع بعض
+
+407
+00:45:50,590 --> 00:45:55,150
+بجيبنا ال identity ايه المشكلة فيما بعد؟يبقى بدنا
+
+408
+00:45:55,150 --> 00:46:04,930
+نيجي لل R تسعين of H يبقى R تسعين H R تسعين
+
+409
+00:46:04,930 --> 00:46:11,950
+inverse طب استنا في الهم الشيء R تلت مية و ستين
+
+410
+00:46:11,950 --> 00:46:19,210
+بده يساوي ال R note مظبوط؟طب لو ضربنا الطرفين في
+
+411
+00:46:19,210 --> 00:46:24,750
+ال R inverse مش معنى هذا الكلام ان ال R ميتين و
+
+412
+00:46:24,750 --> 00:46:33,150
+سبعين بدي ساوي ال R تسعين inverse ولا لا؟ مظبوط
+
+413
+00:46:33,150 --> 00:46:43,100
+اذا هذه بقدر اكتبها R تسعين H R ميتين و سبعينبعد ر
+
+414
+00:46:43,100 --> 00:46:52,480
+تسعين اتش ر تسعين
+
+415
+00:46:52,480 --> 00:46:58,980
+اتش قداش تساوي يبقى لو رجعت لهذا الجدول عندك ر
+
+416
+00:46:58,980 --> 00:47:08,940
+تسعين اتش بتعطيك D primeفى R270 ومن نفس الجدول D'
+
+417
+00:47:09,260 --> 00:47:24,160
+فى R270 بتديلك V طيب لو روح جبت فاي R90 V
+
+418
+00:47:24,160 --> 00:47:28,260
+بدي ساوي R90
+
+419
+00:47:29,780 --> 00:47:38,080
+في V في R تسعين inverse ويساوي R تسعين V R تسعين V
+
+420
+00:47:38,080 --> 00:47:48,640
+اللي هي ب D وهذه ب R متين وسبعين متين وسبعين وهذه
+
+421
+00:47:48,640 --> 00:47:57,370
+عبارة عن مين عبارة عن H الآنيبقى هاد H بالمثل لو
+
+422
+00:47:57,370 --> 00:48:08,430
+جيبنا فاي R تسعين اللي هو D بدي ساوي R تسعين D R
+
+423
+00:48:08,430 --> 00:48:17,170
+تسعين inverse R تسعين V R تسعين D اللي هي عبارة عن
+
+424
+00:48:17,170 --> 00:48:25,370
+Hفى R ميتين وسبعين والـ H فى R ميتين وسبعين اللى
+
+425
+00:48:25,370 --> 00:48:32,970
+عبارة عن مين عن D Prime الان بقيت عندنا الأخيرة
+
+426
+00:48:32,970 --> 00:48:41,410
+Phi R تسعين فى D Prime اختصارا من الآخر هتعطى لك D
+
+427
+00:48:43,390 --> 00:48:47,670
+يبقى بناء عليه هذا ال inner-automorphism جاب لي
+
+428
+00:48:47,670 --> 00:48:55,510
+مين؟ جاب ليه كل عناصر D4 بلا استثناء تماما يبقى
+
+429
+00:48:55,510 --> 00:49:03,770
+أصبح هنا الساعة اللي هو 5R90
+
+430
+00:49:03,770 --> 00:49:12,280
+لما انأثرت على D4 كلها اعطتني D4 كلهاانت ممكن تروح
+
+431
+00:49:12,280 --> 00:49:17,500
+تاخد في ر مية و تمانين و ممكن تاخد في ر ميتين و
+
+432
+00:49:17,500 --> 00:49:23,840
+سبعين و ممكن تاخد في ر اتش او تاخد في اتش و في دي
+
+433
+00:49:23,840 --> 00:49:28,340
+و في دي و في دي prime و اطلع كل واحدة على حده ليس
+
+434
+00:49:28,340 --> 00:49:33,840
+بالضرورة ان هجيبلك دي prime لكن لو اتخيلت معكوس ال
+
+435
+00:49:33,840 --> 00:49:40,340
+R تسعين هجيبلك نفس ال D prime لكن الباقي لاطيب على
+
+436
+00:49:40,340 --> 00:49:43,880
+اي حال حتى لان ما انتهناش من هذا ال section يوم
+
+437
+00:49:43,880 --> 00:49:49,400
+السبت عندك ساعتين فياريت يعني يوم السبت اتحضري اول
+
+438
+00:49:49,400 --> 00:49:54,620
+عشرة اسئلة من التمرين لان الساعة ان شاء الله بنكمل
+
+439
+00:49:54,620 --> 00:49:58,120
+فيها ال section و الساعة التانية بناخد فيها مناقشة
+
+440
+00:49:58,120 --> 00:49:58,860
+ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UVkw5CqJOVY_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UVkw5CqJOVY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7528d5525bf4cd9124f2d15289b75bca02a2487e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/UVkw5CqJOVY_postprocess.srt
@@ -0,0 +1,1844 @@
+1
+00:00:20,650 --> 00:00:24,730
+الله رحمه ورحمه أنهينا في المحاضرة الماضية شبتر
+
+2
+00:00:24,730 --> 00:00:28,550
+تمانية كجزء نظري والان هذه المحاضرة ان شاء الله
+
+3
+00:00:28,550 --> 00:00:35,150
+سنناقش بعض الأسئلة بقدر ما نستطيع خلال هذه الساعة
+
+4
+00:00:35,150 --> 00:00:43,140
+ان شاء الله تعالىنبدأ بالاسئلة على chapter 8 والتي
+
+5
+00:00:43,140 --> 00:00:47,920
+تتعلق بال product external direct هو نبدأ بالسؤال
+
+6
+00:00:47,920 --> 00:00:52,620
+السادس مثلا بيقول prove by comparing orders of the
+
+7
+00:00:52,620 --> 00:00:57,200
+element يبقى اللي بدك تستخدم طريقة المقارنة بين
+
+8
+00:00:57,200 --> 00:01:08,610
+العناصر لإثبات أنه لإثبات أن Z8external direct
+
+9
+00:01:08,610 --> 00:01:17,670
+product مع z2 is not isomorphic
+
+10
+00:01:17,670 --> 00:01:18,970
+الى z4
+
+11
+00:01:23,930 --> 00:01:28,970
+يبقى دلني على طريقة يقولي استخدملي ال orders لل
+
+12
+00:01:28,970 --> 00:01:33,270
+element في كلا ال two groups للحكم على أن ال group
+
+13
+00:01:33,270 --> 00:01:37,930
+الأولى ليست isomorphic لل group التانية فمثلا لو
+
+14
+00:01:37,930 --> 00:01:41,810
+جيت لل group الأولى هل فيها element of order
+
+15
+00:01:41,810 --> 00:01:49,270
+تمانية بالمرة Z تمانية X تانية ضايقة product مع Z
+
+16
+00:01:49,270 --> 00:01:49,730
+اتنين
+
+17
+00:01:53,360 --> 00:01:59,800
+بس فيها .. فيها اتنين والتمانية ولا جزاك؟ تمانية
+
+18
+00:01:59,800 --> 00:02:05,740
+واتنين الواحد
+
+19
+00:02:05,740 --> 00:02:09,080
+والواحد
+
+20
+00:02:09,080 --> 00:02:14,500
+كويس، في غيره؟الواحد والصفر يبقى عندي بدل ال
+
+21
+00:02:14,500 --> 00:02:18,020
+element اتنين ال orders اللي هم يسووا تمانية
+
+22
+00:02:18,020 --> 00:02:22,560
+الواحد في ال Z تمانية ال order اللي هو تمانية ال
+
+23
+00:02:22,560 --> 00:02:25,280
+zero ال order اللي هو واحد ال least common
+
+24
+00:02:25,280 --> 00:02:28,660
+multiple بين التمانية والواحد اللي هو تمانية مظبوط
+
+25
+00:02:28,660 --> 00:02:35,800
+يبقى هنا عندي ال element واحد و zero موجود في Z
+
+26
+00:02:35,800 --> 00:02:42,970
+تمانية external direct product with orderاللي هو
+
+27
+00:02:42,970 --> 00:02:48,030
+تمانية ال order لهذا ال element تمانية الآن بنجي ل
+
+28
+00:02:48,030 --> 00:02:52,590
+Z أربعة كسنة product مع Z أربعة هل بتلاقي في
+
+29
+00:02:52,590 --> 00:02:56,430
+element ال order اللي بيساوي تمانية رغم أنه ستة
+
+30
+00:02:56,430 --> 00:03:02,410
+عشر عنصر ها في element Z أربعة ال order لهم يا اما
+
+31
+00:03:02,410 --> 00:03:06,790
+واحد يا اما اتنين يا اربعة والتاني واحد واتنين
+
+32
+00:03:06,790 --> 00:03:10,410
+واربعة هل في least common multiple فيهم اكتر من
+
+33
+00:03:10,410 --> 00:03:15,710
+اربعةالذي يسكب الملتقب لهذه ال order فيه أكتر من
+
+34
+00:03:15,710 --> 00:03:24,090
+أربعة ماعنديهش يبقى باجي بقوله بطولكن ال Z أربعة
+
+35
+00:03:24,090 --> 00:03:34,830
+external product مع Z أربعة has no element of
+
+36
+00:03:34,830 --> 00:03:38,990
+order تمانية because
+
+37
+00:03:41,450 --> 00:03:54,550
+The maximum order in Z4 is 4
+
+38
+00:03:57,180 --> 00:04:00,700
+لأن ال order لل element بيقسم ال order لل group
+
+39
+00:04:00,700 --> 00:04:04,580
+إذا z أربعة لا يوجد فيها إلا ال elements ال order
+
+40
+00:04:04,580 --> 00:04:09,580
+الواحد اللي هو ال identity والتنين اللي هو العدد
+
+41
+00:04:09,580 --> 00:04:13,740
+اتنين وكذلك الأربعة اللي هو العدد واحد وتلاتة
+
+42
+00:04:13,740 --> 00:04:19,380
+تمام؟ يبقى من هنا أقصى order عندي في z أربعة كسيرة
+
+43
+00:04:19,380 --> 00:04:23,760
+ضيقة كبيرة زي z أربعة هو أربعة وهذه تمانية يبقى
+
+44
+00:04:23,760 --> 00:04:29,010
+اتنين هذول ما لهم ارنبisomorphic يبقى التزام في
+
+45
+00:04:29,010 --> 00:04:33,810
+الكلام اللي قاليا وصلت للنتيجة بدنا نروح لسؤال
+
+46
+00:04:33,810 --> 00:04:42,490
+أربعتاش سؤال أربعتاش بيقول ما ياتي suppose ال G1
+
+47
+00:04:42,490 --> 00:04:53,490
+isomorphic إلى G2 و group تانية H1 isomorphic لمن؟
+
+48
+00:04:53,490 --> 00:05:03,330
+لH2هو H1 ايزو مارفك لـ H2 prove that اثبت انه الـ
+
+49
+00:05:03,330 --> 00:05:10,530
+G1 externodic product مع H1 ايزو مارفك لـ G2
+
+50
+00:05:10,530 --> 00:05:19,550
+externodic product مع H2 هذا اللي احنا بدنا نروح
+
+51
+00:05:19,550 --> 00:05:26,330
+نثبتهإذا دائما و أبدا بنحاول نستفيد من المعطيات
+
+52
+00:05:26,330 --> 00:05:31,190
+اللي عندنا في إثبات المطلوب هدول two groups are
+
+53
+00:05:31,190 --> 00:05:35,790
+isomorphic هدول two groups are isomorphic أخدت ال
+
+54
+00:05:35,790 --> 00:05:38,830
+external product ما بين ال group الأولى و ال group
+
+55
+00:05:38,830 --> 00:05:42,280
+الأولى من المجموعة التانيةوالجروب التانية مع
+
+56
+00:05:42,280 --> 00:05:46,480
+الجروب التانية بدي أثبت انه اللي هو ال external
+
+57
+00:05:46,480 --> 00:05:50,460
+product هذا ماله isomorphic لل external product
+
+58
+00:05:50,460 --> 00:05:55,480
+اللي عندنا هذا يبقى الحلقة التالية solution
+
+59
+00:06:00,220 --> 00:06:09,660
+أفترض أن الـ Alpha من الـ G1 إلى الـ G2 و الـ Beta
+
+60
+00:06:09,660 --> 00:06:18,860
+من الـ H1 إلى الـ H2 هم إيزو مورفيزم
+
+61
+00:06:20,010 --> 00:06:24,330
+يبقى بدي افترض ان هدول الاتنين ايزو مورفزم الان
+
+62
+00:06:24,330 --> 00:06:29,750
+هذا مشان اثبت ان اتنين ايزو مورفزم بدي اعرف
+
+63
+00:06:29,750 --> 00:06:33,530
+function من الجروب الاولى الى الجروب التانى و اثبت
+
+64
+00:06:33,530 --> 00:06:37,390
+انها one to one and one to one وتخدم خاصية الايزو
+
+65
+00:06:37,390 --> 00:06:40,710
+مورفزم اذا بدي اقوله define
+
+66
+00:06:43,180 --> 00:06:52,220
+A function في من الـ G1 وH1 كإكستير نضايق product
+
+67
+00:06:52,220 --> 00:06:55,760
+من
+
+68
+00:06:55,760 --> 00:07:05,860
+الـ G1 وH1 لمين؟ لـ G2 كإكستير نضايق product مع H2
+
+69
+00:07:05,860 --> 00:07:16,200
+باي في ofبدي اخد element من G1 واليكن G وH فعلي ما
+
+70
+00:07:16,200 --> 00:07:24,520
+تأثر على G وH بدي اوديها وين؟ في ال group G2 وH2
+
+71
+00:07:24,520 --> 00:07:31,280
+طيب G2 هذه مش هي G2 هذه صح؟ اذا ال element اللي
+
+72
+00:07:31,280 --> 00:07:37,350
+هنا هو صورة ل element من هناالفانكشن من هنا لهنا
+
+73
+00:07:37,350 --> 00:07:44,510
+شو سميتها Alpha يبقى هذه بقدر اخدها Alpha of G
+
+74
+00:07:44,510 --> 00:07:52,690
+يبقى هذه بقدر اقول Alpha of G ليش؟ لأن Alpha of GG
+
+75
+00:07:52,690 --> 00:07:59,210
+موجودة في G1 واحنا عندنا هنا G موجودة في G1 يبقى
+
+76
+00:07:59,210 --> 00:08:04,350
+هنا صورتها في G2 صورتها في G2 اللي Alpha of G
+
+77
+00:08:05,900 --> 00:08:12,960
+بتداجر لل H ال H موجودة في ال H1 تمام انا عندي
+
+78
+00:08:12,960 --> 00:08:18,140
+Beta من H1 الى H2 يبقى H اللي موجودة في H1 ثورة
+
+79
+00:08:18,140 --> 00:08:25,520
+تبقى Beta of H يبقى هذا Beta of H بالشكل اللي
+
+80
+00:08:25,520 --> 00:08:32,520
+عندنايبقى هكذا اعرفت الدالة تعريفا سليما الان هذه
+
+81
+00:08:32,520 --> 00:08:37,400
+الدالة بدى احاول اثبت انها one to one and unto
+
+82
+00:08:37,400 --> 00:08:42,120
+وتخدم خاصية ال isomorphism ان تم لذلك يبقى بيكونوا
+
+83
+00:08:42,120 --> 00:08:45,660
+اتنين هذول are isomorphic وبكون انت هنا من هالشغل
+
+84
+00:08:45,660 --> 00:08:51,020
+هادى يبقى بدى اجي للخطوة الاولى بدى اثبتله ان فاي
+
+85
+00:08:51,020 --> 00:08:58,240
+is one to oneمشان هيك بدي أخد صورتين متساويتين
+
+86
+00:08:58,240 --> 00:09:08,360
+Assume Phi of G وH بدي ساوي Phi of X وY مثلا إذا
+
+87
+00:09:08,360 --> 00:09:14,420
+قدرت أثبت إن ال order pair G وH هو ال order pair X
+
+88
+00:09:14,420 --> 00:09:16,540
+وY بكون انتهينا من الشغل يعني
+
+89
+00:09:19,880 --> 00:09:25,740
+بتداجي لصورة ال element الأول حسب التعريف يبقى
+
+90
+00:09:25,740 --> 00:09:35,420
+Alpha of G و Beta of H يبقى هذه تبقى Alpha of G و
+
+91
+00:09:35,420 --> 00:09:41,760
+Beta of H بالشكل اللي عندنا هناالـ Phi of X بنفس
+
+92
+00:09:41,760 --> 00:09:51,500
+الطريقة يبقى هادي Alpha of X الصورة والتانية Beta
+
+93
+00:09:51,500 --> 00:09:53,920
+of Y الشكل اللي عندها
+
+94
+00:09:57,060 --> 00:10:01,740
+بناء على هذا الكلام صار عندى two ordered pair are
+
+95
+00:10:01,740 --> 00:10:05,240
+equal يبقى المركبة الأولى هتساوي المركبة الأولى
+
+96
+00:10:05,240 --> 00:10:10,020
+والمركبة الثانية هتساوي المركبة الثانية يبقى بناء
+
+97
+00:10:10,020 --> 00:10:17,900
+عليه Alpha of G بديه يساوي Alpha of X and Beta of
+
+98
+00:10:17,900 --> 00:10:24,180
+H بديه يساوي Beta of Y شوف هذا شو بديه يعطيناالآن
+
+99
+00:10:24,180 --> 00:10:29,940
+الـ Alpha هذي isomorphism يبقى one to one and unto
+
+100
+00:10:29,940 --> 00:10:34,960
+إذا مدام one to one يبقى الـ G بده يساوي اللي هو
+
+101
+00:10:34,960 --> 00:10:42,960
+main ال X يبقى هنا الـ G بده يساوي ال X and ال H
+
+102
+00:10:42,960 --> 00:10:51,920
+بده يساوي ال Y السبب بسبب أن Alpha و Beta هم one
+
+103
+00:10:51,920 --> 00:10:57,500
+to oneما دام صورتين متساويتين إذا الأصل متساوي لإن
+
+104
+00:10:57,500 --> 00:11:02,000
+ال alpha one to one و كذلك ال beta is one to one
+
+105
+00:11:02,000 --> 00:11:08,360
+يبقى بناء عليه هذا بدي يعطينا لو أخدت ال G و ال H
+
+106
+00:11:08,360 --> 00:11:15,900
+as an ordered ال G عبارة عن مين؟ X و ال H عبارة عن
+
+107
+00:11:15,900 --> 00:11:20,420
+مين؟ Y عبارة عن Y بالشكل اللي عندنا هذا يبقى أخد
+
+108
+00:11:20,420 --> 00:11:26,890
+صورتين متساويتينو اثبت ان اصل هماله متساوي لذلك
+
+109
+00:11:26,890 --> 00:11:28,630
+فاي is one to one
+
+110
+00:11:34,980 --> 00:11:43,220
+يبقى انا بأخد element في الـ G2 و X2 و H2 يبقى
+
+111
+00:11:43,220 --> 00:11:50,340
+بالدرجة يقول لو أخدت الـ X موجود مثلا في الـ G2
+
+112
+00:11:50,340 --> 00:12:00,280
+external product مع H2 بشكل لعين هذا يبقى then بدي
+
+113
+00:12:00,280 --> 00:12:06,570
+أدور على شكل هذا ال elementيبقى شكل ال element x
+
+114
+00:12:06,570 --> 00:12:12,370
+هذا بده يسوي element من g2 و element من one من h2
+
+115
+00:12:12,370 --> 00:12:20,370
+يبقى هذا الكلام بده يسوي element وليكن g2 وh2 من
+
+116
+00:12:20,370 --> 00:12:30,200
+h2طيب هذا الكلام يساوي ال G2 موجودة في G2 تمام و
+
+117
+00:12:30,200 --> 00:12:38,180
+Alpha is on 2 يبقى هذا ال element له أصل في G1
+
+118
+00:12:38,180 --> 00:12:43,260
+صحيح ولا لأ يبقى هذا الكلام بقدر أشيل ال G2 و
+
+119
+00:12:43,260 --> 00:12:51,940
+أكتبها Alpha of G1 مثلاو بقدر اكتب هذا beta of
+
+120
+00:12:51,940 --> 00:12:57,180
+each one شو السبب في ذلك لأن alpha and beta are
+
+121
+00:12:57,180 --> 00:13:10,440
+onto يبقى هنا since ال alpha and beta are ontoهذا
+
+122
+00:13:10,440 --> 00:13:15,400
+الكلام لو رجعته إلى أصله بلاقي هو التعريف اللي أنا
+
+123
+00:13:15,400 --> 00:13:21,100
+قايله هنا يبقى الأصل اللي بتابعه هو عبارة عن Phi
+
+124
+00:13:21,100 --> 00:13:28,960
+of G1 وH1يبقى ال element اللي أخدته في G2 وH2 اللي
+
+125
+00:13:28,960 --> 00:13:36,600
+جاتله أصل في G1 وH1 اللي هو G1 وH1 صغير يبقى Phi
+
+126
+00:13:36,600 --> 00:13:41,600
+is in two ضايل عليه نثبت أن Phi is an isomorphism
+
+127
+00:13:41,600 --> 00:13:50,020
+يبقى باجي بقول Phi is an isomorphismيبقى بدي انا
+
+128
+00:13:50,020 --> 00:13:55,920
+اخد اللي هو الـPhi of حصل ضرب two elements ال
+
+129
+00:13:55,920 --> 00:14:01,100
+element الأول اللي هو بدك تاخده من هنا من مكان
+
+130
+00:14:01,100 --> 00:14:08,120
+يكون يبقى لو جيت قلت G وH مضرب في element تاني
+
+131
+00:14:08,120 --> 00:14:14,720
+وليكن مثلا G prime وH prime بالشكل اللي عندنا هذا
+
+132
+00:14:15,810 --> 00:14:21,390
+يبقى هذا الكلام بده يساوي في of هذا الضرب عليه
+
+133
+00:14:21,390 --> 00:14:25,770
+بنضرب component wise حسب ما أعرفنا عملية الضرب على
+
+134
+00:14:25,770 --> 00:14:32,350
+ال external product يبقى ج ج prime و H H prime
+
+135
+00:14:32,350 --> 00:14:39,440
+بالشكل اللي عندنا هذا هذا الكلام بده يساويفاي لما
+
+136
+00:14:39,440 --> 00:14:43,900
+تأثر على هذا ال element يبقى Alpha للأول و Beta
+
+137
+00:14:43,900 --> 00:14:52,700
+للتاني يبقى هذا Alpha of G G prime و Beta of H H
+
+138
+00:14:52,700 --> 00:14:58,950
+primeالألف والبيتا كل واحدة فيهم isomorphism مدام
+
+139
+00:14:58,950 --> 00:15:04,790
+كل واحدة فيهم isomorphism إذا هذه Alpha of G وهذه
+
+140
+00:15:04,790 --> 00:15:14,430
+Alpha of G' وهذه Beta of H وهذه Beta of H' بالشكل
+
+141
+00:15:14,430 --> 00:15:19,000
+اللي عندنا هنايبقى أثار على شكل order pair السؤال
+
+142
+00:15:19,000 --> 00:15:25,600
+هو هل ال order pair هذا بقدر أكتبه على شكل حاصل
+
+143
+00:15:25,600 --> 00:15:31,240
+ضرب two ordered pairs؟ الإجابة نعم، كيف؟ كالتالي،
+
+144
+00:15:31,240 --> 00:15:36,140
+شوفوا يا سيدتي، هاي باجي بقوله هنا Alpha of G بدي
+
+145
+00:15:36,140 --> 00:15:43,870
+أخدها مع Beta of H عسب الترتيبوهنا Alpha of G
+
+146
+00:15:43,870 --> 00:15:50,450
+prime بدي اخدها مع Beta of H prime يبقى هاي كتبتهم
+
+147
+00:15:50,450 --> 00:15:55,830
+على شكل حاصل ضرب قوسية يبقى هذا الكلام بده يساوي
+
+148
+00:15:55,830 --> 00:16:04,650
+الان لو جيت للقوس الأوليبقى هذا Phi of GH يبقى هذا
+
+149
+00:16:04,650 --> 00:16:16,880
+Phi of GH التاني عبارة عن Phi of G' وH'أطلع بدأت
+
+150
+00:16:16,880 --> 00:16:22,020
+بحاصل ضرب القوسين وصلت لفايلة الأول مضروبة في مين
+
+151
+00:16:22,020 --> 00:16:26,700
+في فايلة التانية يبقى بناء عليه فاي is an
+
+152
+00:16:26,700 --> 00:16:29,640
+isomorphism يبقى
+
+153
+00:16:34,510 --> 00:16:42,450
+Isomorphism that is أي أن الـ G1 external product
+
+154
+00:16:42,450 --> 00:16:51,850
+مع H1 isomorphic ل G2 external product مع G2 وهو
+
+155
+00:16:51,850 --> 00:16:57,590
+المطلوب الشغل مش صعب سهل بس طويل شوية يعني بده
+
+156
+00:16:57,590 --> 00:17:07,460
+تمشي بدقة كبيرةطيب كان هذا هو السؤال رقم 14 خدلي
+
+157
+00:17:07,460 --> 00:17:15,260
+16 بيقول في ال group Z 40 Z 30 هاتلي two subgroups
+
+158
+00:17:15,260 --> 00:17:20,980
+of order 12 and
+
+159
+00:17:20,980 --> 00:17:24,360
+هذا
+
+160
+00:17:24,360 --> 00:17:33,400
+سؤال كده ايش قلناه؟16 16 يبقى in z 40 external
+
+161
+00:17:33,400 --> 00:17:42,880
+product مع z 30 find two subgroups
+
+162
+00:17:42,880 --> 00:17:47,780
+of order 12
+
+163
+00:17:57,100 --> 00:18:02,960
+طيب جالي في ال group هذي Z 30 Z 40 Extended like a
+
+164
+00:18:02,960 --> 00:18:07,480
+project مع Z 30 هاتلي two sub groups of order 12
+
+165
+00:18:07,480 --> 00:18:11,720
+لا جالي Cyclic ولا غير Cyclic لكن اللي أسهل ليه أن
+
+166
+00:18:11,720 --> 00:18:17,660
+أجيب Cyclic إن جدرتها طيب بقوله كويسة طب كيف بدي
+
+167
+00:18:17,660 --> 00:18:21,440
+أجيب Cyclic ال order اللي هي سوية 12 بقوله كويسة
+
+168
+00:18:21,440 --> 00:18:27,530
+إذا بتقدريجب ان اجرب الـ order لـ element فيها
+
+169
+00:18:27,530 --> 00:18:30,910
+أربعة و التاني تلاتة يبقى الـ least common
+
+170
+00:18:30,910 --> 00:18:35,270
+multiple المجداش اتناش وكفى الله المنقتل هذا ال
+
+171
+00:18:35,270 --> 00:18:40,390
+element وولد ال subgroup من المطلوب اذا انا بدى
+
+172
+00:18:40,390 --> 00:18:46,710
+ادور على عناصر من زد اربعين ال order اللي يكون
+
+173
+00:18:46,710 --> 00:18:53,750
+جداش أربعة صح؟طيب مين العناصر اللي في Z أربعين
+
+174
+00:18:53,750 --> 00:18:59,530
+اللي ال order لهم يساوي أربعة حد بيقدر يجيبلي و لو
+
+175
+00:18:59,530 --> 00:19:07,200
+عنصر واحد عشرة ممتاز جدا يبقى عاشرةموجودة في Z
+
+176
+00:19:07,200 --> 00:19:14,560
+أربعين و ال order للعشرة بده يساوي أربعة ممتاز جدا
+
+177
+00:19:14,560 --> 00:19:21,220
+اذا انا بده اروح على Z تلاتين كمان برضه عشرة طيب
+
+178
+00:19:21,220 --> 00:19:27,980
+العشرة موجودة في Z تلاتين and ال order للعشرة بده
+
+179
+00:19:27,980 --> 00:19:34,370
+يساوي كدهش بده يساوي تلاتة اذاالـ Element اللي هو
+
+180
+00:19:34,370 --> 00:19:40,370
+عشرة و عشرة موجود في Z أربعين External Direct
+
+181
+00:19:40,370 --> 00:19:50,070
+Product مع Z تلاتينالـ order للعشرة وعشرة هو عبارة
+
+182
+00:19:50,070 --> 00:19:55,130
+عن ال least common multiple للاربعة والتلاتة اللي
+
+183
+00:19:55,130 --> 00:20:00,470
+هو يساوي قداش اتناش اذا هذا ال element بيعطيني ال
+
+184
+00:20:00,470 --> 00:20:02,910
+cyclic subgroup of order اتناش
+
+185
+00:20:05,800 --> 00:20:14,800
+يبقى الساعة العاشرة وعشرة العشرة وعشرة هو عبارة عن
+
+186
+00:20:14,800 --> 00:20:26,480
+Cyclic Subgroup Cyclic Subgroup of order أتناشر
+
+187
+00:20:26,480 --> 00:20:34,000
+بدي أدور على غيره بدي أدور كمان على عنصر تاني
+
+188
+00:20:38,630 --> 00:20:47,730
+كيف؟ اتنين وستة .. لا بدك .. ستة واربعة ماشي ..
+
+189
+00:20:47,730 --> 00:20:51,470
+ستة واربعة ماشي .. واحد واطناش ماشي .. بس يلا
+
+190
+00:20:51,470 --> 00:20:55,250
+نلاقي .. يبقى الان بدي أروح أدور على مين على
+
+191
+00:20:55,250 --> 00:21:04,750
+orders أخرطيب ال order تبع العشرة هو أربعة نقدر
+
+192
+00:21:04,750 --> 00:21:10,550
+نجيب من z تلاتين واحد ال order إله ستة أربعة و ستة
+
+193
+00:21:10,550 --> 00:21:13,250
+ال order اللي مصير اتناش least common multiple
+
+194
+00:21:13,250 --> 00:21:21,010
+مظبوط يبقى هنا مرة تانية also أيضا العشرة أو ال
+
+195
+00:21:21,010 --> 00:21:28,440
+order للعشرة بده يساوي أربعة في z أربعينالآن
+
+196
+00:21:28,440 --> 00:21:37,500
+الخامسة الخامسة ال order إيه يساوي قداش؟ ستة مظبوط
+
+197
+00:21:37,670 --> 00:21:45,150
+الـ order له يساوي ستة N زي التلاتين يبقى اذا ال
+
+198
+00:21:45,150 --> 00:21:51,910
+order للعشرة وخمسة بده يساوي ال least common
+
+199
+00:21:51,910 --> 00:21:58,630
+multiple اللي هو من الأربعة والستة اللي هو كده
+
+200
+00:21:58,630 --> 00:22:04,970
+اتناش يبقى اذا ال sub group generated by عشرة
+
+201
+00:22:04,970 --> 00:22:19,620
+وخمسةis a cyclic group of order أتماشيبقى بناء
+
+202
+00:22:19,620 --> 00:22:24,000
+عليه هاي طلعنا له تنتين subgroups ورغم انه
+
+203
+00:22:24,000 --> 00:22:28,120
+مااشترطش وقال هاتلي subgroups وخلصنا يبقى انا
+
+204
+00:22:28,120 --> 00:22:33,620
+جبتله subgroups وجبتهمله تنتين زيادة على مقال انه
+
+205
+00:22:33,620 --> 00:22:39,160
+تنتين cyclic subgroups ال order لهم يساوي 12
+
+206
+00:22:39,160 --> 00:22:45,120
+اعتمدت في ذلك على من على ال order لل elements و هم
+
+207
+00:22:45,120 --> 00:22:48,540
+اللي ريحون في من في الحل
+
+208
+00:22:51,060 --> 00:23:04,520
+طيب كان هذا سؤال ستة عشر خدلي سؤال ستة وعشرين سؤال
+
+209
+00:23:04,520 --> 00:23:12,180
+ستة وعشرين ستة وعشرين بيقولي هتلي ال subgroup من z
+
+210
+00:23:12,180 --> 00:23:16,400
+أربعة بدي مثلا subgroup
+
+211
+00:23:18,720 --> 00:23:28,460
+of subgroup من مين من z4 external direct product
+
+212
+00:23:28,460 --> 00:23:35,640
+z4 external direct product مع z دي اتنين that is
+
+213
+00:23:35,640 --> 00:23:46,880
+not of the form not in the formاللي هو H external
+
+214
+00:23:46,880 --> 00:23:59,480
+product ل K where حياته where ال H subgroup من
+
+215
+00:23:59,480 --> 00:24:10,530
+Z4 and ال K subgroup من main subgroupمن z2 و ال k
+
+216
+00:24:10,530 --> 00:24:17,230
+sub group من من z2
+
+217
+00:24:17,230 --> 00:24:27,190
+شوفوا يا سيدي نرجع مرة تانية انا عندى الآن ال z4
+
+218
+00:24:27,190 --> 00:24:33,250
+external direct product مع z2 هدى groupالان بدي
+
+219
+00:24:33,250 --> 00:24:39,410
+subgroup من هذه ال group بحيث ما تكونش على الشكل H
+
+220
+00:24:39,410 --> 00:24:45,890
+اللي هو external product مع K حيث H subgroup من Z
+
+221
+00:24:45,890 --> 00:24:51,590
+أربعة وال K subgroup من من من Z يعني بدي جيبلي ال
+
+222
+00:24:51,590 --> 00:24:56,910
+subgroup تانية غير ال external product تبع هدول
+
+223
+00:24:58,090 --> 00:25:03,850
+تعالى نشوف كيف بدنا نحل السؤال السؤال يحتاج الى
+
+224
+00:25:03,850 --> 00:25:09,720
+تفكير ومن التفكير بنقدر نوصل للمطلبزد اربعة
+
+225
+00:25:09,720 --> 00:25:14,100
+external product لزد اتنين not in the form ليست في
+
+226
+00:25:14,100 --> 00:25:17,840
+هذا الشكل احنا ده جيبنا ال subgroup و جيبنا ال
+
+227
+00:25:17,840 --> 00:25:20,820
+subgroup بنجيبلهم ال external product منطلع
+
+228
+00:25:20,820 --> 00:25:25,200
+subgroup جديدة بقول ال subgroup الجديدة بديش إياها
+
+229
+00:25:25,200 --> 00:25:28,830
+ولا واحدة منها دول اللي انت بتقول عليهمقلت له
+
+230
+00:25:28,830 --> 00:25:32,410
+تعالى نشوف مين هم ال subgroups و بعدين بصير خير
+
+231
+00:25:32,410 --> 00:25:38,710
+تمام الان لو جيت على z4 بدي ادور مين هم ال
+
+232
+00:25:38,710 --> 00:25:44,990
+subgroups تبعات z4 فبقى اجيب يقوله the only
+
+233
+00:25:44,990 --> 00:25:56,370
+subgroups of z4 areاللي ال order إلها واحد واللي
+
+234
+00:25:56,370 --> 00:25:59,590
+ال order إلها اتنين واللي ال order إلها أربعة
+
+235
+00:25:59,590 --> 00:26:06,190
+مظبوط يبقى اللي ال order إلها واحد هي ال identity
+
+236
+00:26:06,190 --> 00:26:12,170
+واللي ال order إلها اتنين هي ال sub group
+
+237
+00:26:12,170 --> 00:26:18,630
+generated by اتنينأيش ضال عندي؟ واحد و تلاتة واحد
+
+238
+00:26:18,630 --> 00:26:23,230
+و تلاتة بوالدولي نفس ال subgroup z أربعة يبقى هدول
+
+239
+00:26:23,230 --> 00:26:28,650
+تلاتة لكن في الحقيقة هي واحدة بس يبقى التالتة اللي
+
+240
+00:26:28,650 --> 00:26:37,930
+هي main z أربعة itself تمام؟ طيب الآن also the
+
+241
+00:26:37,930 --> 00:26:51,930
+only subgroupsonly subgroups of z2 are طبعا ال
+
+242
+00:26:51,930 --> 00:26:56,950
+identity ومين كمان والإتنين اللي هي ال subgroup
+
+243
+00:26:56,950 --> 00:27:04,350
+generated by one اللي هي z2 itself z2 itself طيب
+
+244
+00:27:04,350 --> 00:27:09,850
+لو بدى أكوّنه ال external product هذا يبقى بدى
+
+245
+00:27:09,850 --> 00:27:18,330
+أقوله الأولىمع الأولى اللى هى zero طبعا هذه فىش
+
+246
+00:27:18,330 --> 00:27:23,570
+فىها إلا مين عنصر واحد صحيح ال cyclic وفىش فىها
+
+247
+00:27:23,570 --> 00:27:28,730
+أقل عنصر واحد بدي أمسك التانية التانية اللى هى ال
+
+248
+00:27:28,730 --> 00:27:35,230
+zero نفسها مع ال subject ال zero نفسها مع z2
+
+249
+00:27:35,230 --> 00:27:41,450
+standardized product مع z2التالتة خلصنا منها اللي
+
+250
+00:27:41,450 --> 00:27:46,710
+هي ال subgroup generated by اتنين external like
+
+251
+00:27:46,710 --> 00:27:55,350
+product مع من؟ مع ال zero ال subgroup generated by
+
+252
+00:27:55,350 --> 00:28:01,390
+اتنين external like product مع من؟ مع زد اتنينالان
+
+253
+00:28:01,390 --> 00:28:07,950
+الـ z4 external product مع الـ zero أخر حاجة الـ
+
+254
+00:28:07,950 --> 00:28:16,830
+z4 external product مع الـ z2 هؤلاء كل الـ
+
+255
+00:28:16,830 --> 00:28:20,990
+subgroups اللي على الشكل اللي قدامي هذا جالي هذا
+
+256
+00:28:20,990 --> 00:28:25,480
+اللي بديش منهم ولا واحدةولا واحدة من هدول قال لي
+
+257
+00:28:25,480 --> 00:28:29,080
+بيدي ال subgroup من هذا ماهياش على الشكل اللي
+
+258
+00:28:29,080 --> 00:28:34,180
+عندنا هنا بقوله تعالي ندور الآن لو جالسله قوله
+
+259
+00:28:34,180 --> 00:28:39,780
+consider خدلي أول شيء ال subgroup لازم يكون فيها
+
+260
+00:28:39,780 --> 00:28:46,750
+ال identity elementidentity element تمام طيب لو
+
+261
+00:28:46,750 --> 00:28:58,130
+جيت أخد عندي هنا مثلا ال zero و ال one ال zero
+
+262
+00:28:58,130 --> 00:29:04,650
+أخدته من z و لا أخدت خليك معايا بدي أخدي اتنين و
+
+263
+00:29:04,650 --> 00:29:11,500
+ال zeroأتنين وزيرو موجود في زد اربعة external
+
+264
+00:29:11,500 --> 00:29:16,300
+product لزيد دي اتنين وزيد اربعة لزيد تلاتة
+
+265
+00:29:16,300 --> 00:29:25,590
+اتاكدلي بالله سؤال جديد شو قلناهستة وعشرين ..ستة
+
+266
+00:29:25,590 --> 00:29:32,910
+وعشرين ..ستة وعشرين ..ستة وعشرين ..ستة وعشرين
+
+267
+00:29:32,910 --> 00:29:40,130
+..ستة وعشرين ..ستة وعشرين ..ستة وعشرين ..ستة
+
+268
+00:29:40,130 --> 00:29:40,870
+وعشرين ..ستة وعشرين ..ستة وعشرين ..ستة وعشرين
+
+269
+00:29:40,870 --> 00:29:41,150
+وعشرين ..ستة وعشرين ..ستة وعشرين ..ستة وعشرين
+
+270
+00:29:41,150 --> 00:29:42,010
+..ستة وعشرين ..ستة وعشرين ..ستة وعشرين ..ستة
+
+271
+00:29:42,010 --> 00:29:47,740
+وعشرين ..ستة وعشرين ..ستة وعشرين ..طيب يبقى الأن
+
+272
+00:29:47,740 --> 00:29:54,880
+بدي أخد ال element zero و zero بدي أخد element
+
+273
+00:29:54,880 --> 00:30:01,140
+تاني اتنين و zero موجود في واحدة من هدول اتنين
+
+274
+00:30:01,140 --> 00:30:05,380
+موجود فيها ده استنى شوية لأ لأ بدي أجيب هو قاللي
+
+275
+00:30:05,380 --> 00:30:08,840
+النقط ماهياش في الشكل اللي عندنا هل هادي ال
+
+276
+00:30:08,840 --> 00:30:13,480
+subgroup هادي ال subgroup صحيح بس استنى نشوفها هى
+
+277
+00:30:13,480 --> 00:30:14,440
+هادي ولا لأ
+
+278
+00:30:17,170 --> 00:30:23,010
+لأ لأ لأ استنى شوف بدنا نغيرها لو جيت قول واحد
+
+279
+00:30:23,010 --> 00:30:30,790
+وزيرو وزيرو وواحد وواحد وواحد الشكل اللي عندنا
+
+280
+00:30:30,790 --> 00:30:38,370
+نيجي نشوف هل هذه تسوي اي واحدة من هدول ولا لأ لأ
+
+281
+00:30:38,370 --> 00:30:42,970
+لو جيت لهذه خلصنا منها Zero واتنين يعني Zero Zero
+
+282
+00:30:42,970 --> 00:30:49,360
+Zero واحدهذه مافيش إلا عنصرين فيها طيب هذه برضه
+
+283
+00:30:49,360 --> 00:30:57,140
+كذلك مافيش فيها إلا زت اتنين برضه عنصرين طيب هذه
+
+284
+00:30:57,140 --> 00:31:02,130
+اللي هي زت اتنين مع زت اتنينالكتير اللي بيكبره في
+
+285
+00:31:02,130 --> 00:31:07,050
+ال Z أربع اللي هو بال identity Zero وبعدين اتنين
+
+286
+00:31:07,050 --> 00:31:12,130
+بس عنصرين مع عنصرين أربع عناصر اللي هم مين اللي هم
+
+287
+00:31:12,130 --> 00:31:21,090
+Zero و Zero Zero و واحد وبعدها بيجيني اتنين اتنين
+
+288
+00:31:21,090 --> 00:31:27,180
+مش من هدول يبقى ليست هذهوالـ Z أربعة فيها أربعة
+
+289
+00:31:27,180 --> 00:31:31,720
+عناصر طبعا مش هادى والـ Z أربعة مع Z two طبعا
+
+290
+00:31:31,720 --> 00:31:36,140
+ماهياش هادى يبجى هذه ليست ولا واحدة من هدول اللي
+
+291
+00:31:36,140 --> 00:31:41,120
+عندنا يبجى هذه هي ال sub group المطلوبة وهي ليست
+
+292
+00:31:41,120 --> 00:31:43,660
+اي واحدة من الست الأولين ايوة
+
+293
+00:31:49,130 --> 00:31:54,590
+لو بدك subgroup من هدفك بنفس الطريقة هذي بقصة
+
+294
+00:31:54,590 --> 00:31:59,850
+بتطول، ليش؟ انه عندك عناصر كتير، أربعين في تلاتين،
+
+295
+00:31:59,850 --> 00:32:04,850
+ألف و متين عنصر، مش سهلة، بس دول تمان عناصر مش
+
+296
+00:32:04,850 --> 00:32:08,890
+كتير، تمانية زي ألف و متين، في السوق اللي هو محل
+
+297
+00:32:08,890 --> 00:32:12,690
+لهم من الإعراب، ايه نعم، هذا بزهج، بصدق
+
+298
+00:32:17,470 --> 00:32:27,870
+أنا ممتاز طب شوف الهدف
+
+299
+00:32:27,870 --> 00:32:32,630
+من ذلك الهدف من ذلك أن انت ما تكونش عليه الشكل هذا
+
+300
+00:32:32,630 --> 00:32:37,490
+هي الأشكال كلها كتبناها بدك تجيب أي subgroup تكون
+
+301
+00:32:37,490 --> 00:32:42,490
+تستبعد منها هذه الأشكال طبعا ال subgroup يال order
+
+302
+00:32:42,490 --> 00:32:47,530
+إلا واحديا اتنين، يا اربعة، يا تمانية، لأنه زد
+
+303
+00:32:47,530 --> 00:32:51,950
+اربعة كسنوات بتمان عناصر، مظبوط؟ يبقى بدك تجيبلك
+
+304
+00:32:51,950 --> 00:32:57,210
+واحدة من هدول، اي نعم، لو بدك تسامد الآن اللي هو
+
+305
+00:32:57,210 --> 00:33:02,370
+ال order اللي هيو سوى تمانية، ليش؟ لأن هي هيه،
+
+306
+00:33:02,370 --> 00:33:06,630
+يبقى صف على شجرة، بدك تجي واحد او اتنين او اربع،
+
+307
+00:33:06,630 --> 00:33:11,430
+ال order اللي هي واحد هيهايبقى صف على شجة يبقى بضل
+
+308
+00:33:11,430 --> 00:33:14,710
+اتنين والاربعة اتنين هاي هاي بضلش الا الاربعة
+
+309
+00:33:14,710 --> 00:33:20,150
+عناصر يبقى إجباري اينا ايوة هذه مش مغنقة
+
+310
+00:33:23,720 --> 00:33:27,000
+لو عملت العنصر التاني مع العنصر الأخير فتبقى لك
+
+311
+00:33:27,000 --> 00:33:34,560
+اتنين واحد العنصر الثاني مع الأخير يبقى هذا طبعا
+
+312
+00:33:34,560 --> 00:33:39,960
+الأملاني اللي اتجمع يبقى بصير اتنين واحد استنى
+
+313
+00:33:39,960 --> 00:33:45,400
+شوية هذا طب لو قلت هذه اتنين .. لأ لو قلت هذه
+
+314
+00:33:45,400 --> 00:33:51,400
+اتنين واحد التانية طب
+
+315
+00:33:51,400 --> 00:33:58,760
+استنى نشوفهذه الآن واحد و اتنين بيصير تلاتة موجودة
+
+316
+00:33:58,760 --> 00:34:04,200
+تلاتة و واحد مش مشكلة كمان مرة اه هذه بيصير انيا
+
+317
+00:34:04,200 --> 00:34:13,600
+اتنين و قلت هذه اه ايش هذه؟أتنين و صفر فعلا شوف طب
+
+318
+00:34:13,600 --> 00:34:19,180
+اتنين تربية بصير اربعة و زيرو موجودة اتنين و اتنين
+
+319
+00:34:19,180 --> 00:34:25,340
+اللي هو بصير زيرو واحد زيرو واحد موجود صحيح وهذا
+
+320
+00:34:25,340 --> 00:34:29,260
+لو بدنا نربعها بصير اربعة و اتنين زيرو زيرو مظبوط
+
+321
+00:34:29,260 --> 00:34:36,500
+صحيح ايش ثلاثة و واحدلأ لأ ماشي هيك ماشي مقبول
+
+322
+00:34:36,500 --> 00:34:41,880
+فصحيح وين
+
+323
+00:34:41,880 --> 00:34:47,260
+صفر و واحد؟ ضرب اتنين و واحد هنا جامعة جامعة مش
+
+324
+00:34:47,260 --> 00:34:51,380
+ضاربة اه اه الصفر هي موجود اه ال operation عليها
+
+325
+00:34:51,380 --> 00:34:59,970
+عملية جامعة وهي كده طيب هذا سؤال ستة و عشرينخدي
+
+326
+00:34:59,970 --> 00:35:05,470
+سؤال 28 بيقولي هاتلي كل ال subgroups اللي ال order
+
+327
+00:35:05,470 --> 00:35:12,450
+إلها 4 في z 4 external direct product مع z 4 يبقى
+
+328
+00:35:12,450 --> 00:35:23,690
+سؤال 28 28 بيقولي find all subgroups بدنا ال all
+
+329
+00:35:23,690 --> 00:35:25,970
+subgroups
+
+330
+00:35:28,190 --> 00:35:38,450
+of order أربعة in z أربعة external product مع z
+
+331
+00:35:38,450 --> 00:35:39,030
+أربعة
+
+332
+00:35:41,620 --> 00:35:45,240
+سؤال مرة تانية زد اربعة كتير نضالك ال product مع
+
+333
+00:35:45,240 --> 00:35:50,940
+زد اربعة فيها ست عشر عنصر، مظبوط؟ الان بدي كل ال
+
+334
+00:35:50,940 --> 00:35:54,520
+sub groups اللي ال order اللي لهم يساوي اربعة
+
+335
+00:35:54,520 --> 00:36:01,040
+تعالى نفكر احنا و اياكم تفكير بهذا الشكل الان لو
+
+336
+00:36:01,040 --> 00:36:08,500
+جيت للعنصر اللي هو واحد و zero كداش ال order له؟
+
+337
+00:36:12,150 --> 00:36:17,190
+أربعة يبقى هذا بيولدلي ال sub group ال order إلها
+
+338
+00:36:17,190 --> 00:36:24,710
+يسوى أربعة طيب لو جيت ل zero و واحد أربعة يبقى
+
+339
+00:36:24,710 --> 00:36:32,030
+بالشكل اللي عندنا هنا طيب لو جيت لمين ل ال واحد و
+
+340
+00:36:32,030 --> 00:36:39,710
+واحدأربعة subgroup generated by واحد وواحد أربعة
+
+341
+00:36:39,710 --> 00:36:44,290
+طب لو قلتلك subgroup generated by واحد واتنين
+
+342
+00:36:44,290 --> 00:36:47,950
+أربعة
+
+343
+00:36:47,950 --> 00:36:54,390
+طب لو قلتلك subgroup generated by اتنين وواحد
+
+344
+00:36:54,390 --> 00:36:55,370
+أربعة
+
+345
+00:36:58,860 --> 00:37:06,840
+طب لو قلت لك subgroup generated by واحد و تلاتة
+
+346
+00:37:06,840 --> 00:37:15,150
+طيب لو قلت لك subgroup generated by تلاتة و واحدو
+
+347
+00:37:15,150 --> 00:37:18,010
+نفس ال group زد اربع زد اربع هي نفسه اللي بسهل
+
+348
+00:37:18,010 --> 00:37:23,530
+العملية اي نعم جداش صاروا هدول اتنين اربع خمسة و
+
+349
+00:37:23,530 --> 00:37:28,910
+اتنين سبعة طيب خدلك هال group هذي مش زيهم cyclic
+
+350
+00:37:28,910 --> 00:37:35,170
+عادي زي ما جيبنا هذي لو جيت قولتلك zero و zero و
+
+351
+00:37:35,170 --> 00:37:41,510
+zero و اتنين و اتنين و zero و اتنين و اتنينتعالى
+
+352
+00:37:41,510 --> 00:37:45,370
+فى الأول نشوفها subgroup ولا لأ طبع ال order اللى
+
+353
+00:37:45,370 --> 00:37:51,150
+هيه يسوى أربعة تمام لو جاتى لهذه اتنين و اتنين
+
+354
+00:37:51,150 --> 00:37:58,190
+جمعنا بصير كده اتنين و اتنين نربعهايعني لو بتضرب
+
+355
+00:37:58,190 --> 00:38:04,450
+العنصر في نفسه يبقى بيطلع 00 هي موجود طبعا طب لو
+
+356
+00:38:04,450 --> 00:38:10,590
+هذا مع هذا بصير ال zero و اربعة يعني اتنين و zero
+
+357
+00:38:10,590 --> 00:38:17,320
+اتنين و zero هي موجودتمام؟ لو جيت قولتلي zero و
+
+358
+00:38:17,320 --> 00:38:21,400
+اتنين او اتنين او زيرو في هذا هتلاقي موجود تمام؟
+
+359
+00:38:21,400 --> 00:38:24,640
+طب لو هده ضربت بنفسه اربعة و اربعة هي zero و zero
+
+360
+00:38:24,640 --> 00:38:29,360
+يبقى هو ال sub group على طول الخط لكن هدى مش زيهم
+
+361
+00:38:29,360 --> 00:38:34,860
+ماهياش cyclic تعالى امسك اي element اخر اللى يمكن
+
+362
+00:38:34,860 --> 00:38:39,370
+تلاقي يجيبك ايه اش اربع عناظر فمثلاهاتلي اي
+
+363
+00:38:39,370 --> 00:38:43,330
+element غير اللي قدامك في ال group هذه نشوف و كم
+
+364
+00:38:43,330 --> 00:38:50,030
+عنصر بده يجيب يلا اختاروا اي رقم غير الارقام اي
+
+365
+00:38:50,030 --> 00:38:56,070
+عنصر غير العناصر هذه تلاتة و تلاتة موجودة تلاتة و
+
+366
+00:38:56,070 --> 00:39:03,230
+تلاتة تربيعيعني ستة و ستة جامعة يعني ستة و ستة
+
+367
+00:39:03,230 --> 00:39:09,010
+يعني اتنين و اتنين تلاتة و تلاتة كعيب يعني تسعة
+
+368
+00:39:10,910 --> 00:39:17,470
+تسعة و تسعة اللي هي واحد و واحد و واحد و واحد طيب
+
+369
+00:39:17,470 --> 00:39:25,890
+لو جيت قول تلاتة و تلاتة يبقى اللي هي تلاتة
+
+370
+00:39:25,890 --> 00:39:28,310
+و أربعة اللي هي الصفر و الصفر مظبوط اللي هو ال
+
+371
+00:39:28,310 --> 00:39:33,010
+identity كمان هذه منهم ولا لا اه هذه طلعت كمان
+
+372
+00:39:33,010 --> 00:39:39,700
+منهم و قال لي كل ال sub group اللي ال order إلهاطب
+
+373
+00:39:39,700 --> 00:39:46,380
+اتنين و اتنين ما هو
+
+374
+00:39:46,380 --> 00:39:49,860
+السهل انك تحط العناصر قدامك و تبدأ تدور فيهم فيش
+
+375
+00:39:49,860 --> 00:39:51,200
+شغلة محددة
+
+376
+00:40:00,460 --> 00:40:03,360
+هذه الخطوة مختلفة عن هذه الخطوة و هي سهلة للغاية
+
+377
+00:40:03,360 --> 00:40:07,620
+لكن هذه الخطوة بتجيبها من أين؟ انا بحط قدامي عناصر
+
+378
+00:40:07,620 --> 00:40:09,980
+ال group اللي كلها زي اربعة كسنوات او اربعة كسنوات
+
+379
+00:40:09,980 --> 00:40:10,200
+او اربعة كسنوات او اربعة كسنوات او اربعة كسنوات او
+
+380
+00:40:10,200 --> 00:40:12,500
+اربعة كسنوات او اربعة كسنوات او اربعة كسنوات او
+
+381
+00:40:12,500 --> 00:40:12,720
+اربعة كسنوات او اربعة كسنوات او اربعة كسنوات او
+
+382
+00:40:12,720 --> 00:40:13,140
+اربعة كسنوات او اربعة كسنوات او اربعة كسنوات او
+
+383
+00:40:13,140 --> 00:40:17,680
+اربعة كسنوات او اربعة
+
+384
+00:40:17,680 --> 00:40:23,570
+كسنوات او اربعة كالحين دلت مننا ناله تلاتة و تلاتة
+
+385
+00:40:23,570 --> 00:40:29,030
+الان كمان هذه تلاتة و تلاتة نسيناها يبقى ال sub
+
+386
+00:40:29,030 --> 00:40:33,650
+group generated by تلاتة و تلاتة طيب لإنه فيه
+
+387
+00:40:33,650 --> 00:40:37,850
+قبلها واحد و واحد لكن اتنين و اتنين لا اتنين ال
+
+388
+00:40:37,850 --> 00:40:40,770
+order إليها يسوى اتنين يبقى كل ال sub groups
+
+389
+00:40:40,770 --> 00:40:47,050
+الممكنة اللي عندنا طيب لو جاء zero و تلاتة
+
+390
+00:40:54,230 --> 00:40:59,930
+أه اربعة اربعة ليش ما تكونش منهم ال zero و التلاتة
+
+391
+00:40:59,930 --> 00:41:05,650
+و التلاتة و zero كمان اه حط عليهم ال zero و
+
+392
+00:41:05,650 --> 00:41:13,310
+التلاتة and التلاتة و zero طب ليش اختارت التلاتة
+
+393
+00:41:13,310 --> 00:41:17,310
+ليش ما اختارت اتنين لإن التلاتة و الواحد هدول
+
+394
+00:41:17,310 --> 00:41:24,600
+relatively prime مع mainمع اللي هو أربعة يبقى هدول
+
+395
+00:41:24,600 --> 00:41:29,020
+كلهم اش ما تاخد zero واحد واحد و zero أخدناه مش
+
+396
+00:41:29,020 --> 00:41:32,440
+هيك هاي أول مبادئنا فيهم يبقى مافيش مشكلة هيك
+
+397
+00:41:32,440 --> 00:41:36,700
+بيكون خلصنا كل اللي هو ال subgroups اللي ال order
+
+398
+00:41:36,700 --> 00:41:40,480
+اللي يساوي أربعة في ال group اللي عندنا
+
+399
+00:41:51,560 --> 00:41:57,420
+طيب هذا سؤال تمانية و عشرين سؤال اتنين و تلاتين
+
+400
+00:41:57,420 --> 00:42:04,380
+find a subgroup من z12, z4, z15 ال order لها يساوي
+
+401
+00:42:04,380 --> 00:42:17,760
+تسعة يبقى سؤال اتنين و تلاتين بدنا subgroup of z12
+
+402
+00:42:19,790 --> 00:42:25,210
+External Direct Product مع زد أربعة External
+
+403
+00:42:25,210 --> 00:42:31,710
+Direct Product مع زد خمستاش
+
+404
+00:42:31,710 --> 00:42:38,590
+that has order
+
+405
+00:42:38,590 --> 00:42:48,190
+تسعة خلّي
+
+406
+00:42:48,190 --> 00:42:52,930
+بالك هنا كويسخلّيني أسألكم سؤال تاني، هل في
+
+407
+00:42:52,930 --> 00:42:58,470
+element هنا ال order إيه اللي بيساوي تسعة؟ ولا بدي
+
+408
+00:42:58,470 --> 00:43:02,850
+أشوف، أنا بحكي عليه هادي بس، لأن تسعة دقيقة مش
+
+409
+00:43:02,850 --> 00:43:07,200
+اتناشولا element هنا ال order يسوى تسعة ولا
+
+410
+00:43:07,200 --> 00:43:11,520
+element هنا ال order يسوى تسعة يبقى ماعنديش ولا
+
+411
+00:43:11,520 --> 00:43:15,920
+element ال order يسوى تسعة في أي من ال group
+
+412
+00:43:15,920 --> 00:43:20,920
+المنفردات التلاتة اللي عندنا هذه طيب انا مش هنجيب
+
+413
+00:43:20,920 --> 00:43:25,300
+ال order تسعة مش هنجيب ال order تسعة تبع هذه ال
+
+414
+00:43:25,300 --> 00:43:33,410
+sub group بدي يكون عندي هدول تلاتةثلاثة او تلاتة
+
+415
+00:43:33,410 --> 00:43:35,850
+او تلاتة او تلاتة او تلاتة او تلاتة او تلاتة او
+
+416
+00:43:35,850 --> 00:43:39,370
+تلاتة او تلاتة او تلاتة او تلاتة او تلاتة او تلاتة
+
+417
+00:43:39,370 --> 00:43:42,410
+او تلاتة او تلاتة او تلاتة او تلاتة او تلاتة او
+
+418
+00:43:42,410 --> 00:43:43,570
+تلاتة او تلاتة او تلاتة او تلاتة او تلاتة او تلاتة
+
+419
+00:43:43,570 --> 00:43:44,930
+او تلاتة او تلاتة او تلاتة او تلاتة او تلاتة او
+
+420
+00:43:44,930 --> 00:43:53,390
+تلاتة او تلاتة او تلاتة او
+
+421
+00:43:53,390 --> 00:43:56,850
+تلاتة
+
+422
+00:43:57,140 --> 00:44:01,440
+لو أخدت اجروب ال order إلها تلاتة و واحدة ال order
+
+423
+00:44:01,440 --> 00:44:05,140
+إلها واحد و واحدة ال order إلها تلاتة بيصير عندي
+
+424
+00:44:05,140 --> 00:44:12,590
+قداشر ال order لل external product تسعةالـ order
+
+425
+00:44:12,590 --> 00:44:17,110
+للـ group كلها بصير تسعة مش باخدش elements باخد
+
+426
+00:44:17,110 --> 00:44:21,150
+group كاملة ال order لها تلاتة أو sub group تمام
+
+427
+00:44:21,150 --> 00:44:27,370
+يعني بناء عليه لا يمكن ألاقي sub group من ال
+
+428
+00:44:27,370 --> 00:44:32,150
+groups هدول ال order لها يسوى تسعة مش إمكانية لكن
+
+429
+00:44:32,150 --> 00:44:36,750
+بنعمل عملية تحايل بالداجة الأولى بدي أخد منها ال
+
+430
+00:44:36,750 --> 00:44:41,020
+sub group ال order لها يسوى تلاتةومن التانية ال
+
+431
+00:44:41,020 --> 00:44:45,020
+subgroup ال order إلها يساوي تلاتة أو تلاتة في شيء
+
+432
+00:44:45,020 --> 00:44:48,760
+ممكن نقول واحد مثلا و التالتة بتاخد subgroup ال
+
+433
+00:44:48,760 --> 00:44:51,760
+order إلها يساوي تلاتة يبقى دول لو ضربتها مكون
+
+434
+00:44:51,760 --> 00:44:57,300
+جديش تسعة تقدر تجيب أه بقدر ليش لإن زد اتناش وزد
+
+435
+00:44:57,300 --> 00:45:01,820
+اربع وزد خمساش كلهم cyclic groupوفي نظرية كانت في
+
+436
+00:45:01,820 --> 00:45:06,840
+chapter أربعة بتقولي أي subgroup من cyclic group
+
+437
+00:45:06,840 --> 00:45:11,380
+بتكون cyclic تمام باجي بقوله كويسة الان لو جيت
+
+438
+00:45:11,380 --> 00:45:26,980
+أخطط ال HBA subgroup of Z12 with order مثلا with
+
+439
+00:45:26,980 --> 00:45:39,970
+order تلاتة andk is a subgroup من z4 with order
+
+440
+00:45:39,970 --> 00:45:49,510
+one and ال
+
+441
+00:45:49,510 --> 00:45:59,370
+subgroup من z15 with order oneتلاتة طبعا كله ممكن
+
+442
+00:45:59,370 --> 00:46:04,030
+لإن التلاتة بتجسم الخمستاش والواحد بيجسم الأربعة
+
+443
+00:46:04,030 --> 00:46:11,990
+والتلاتة بتجسم الأتناش يعني for example for
+
+444
+00:46:11,990 --> 00:46:17,190
+example ال
+
+445
+00:46:17,190 --> 00:46:21,450
+group generated by أربعة ال order اللي قدش ساوي
+
+446
+00:46:21,450 --> 00:46:21,810
+هنا
+
+447
+00:46:24,580 --> 00:46:30,860
+ثلاثة تمام هاي ليش اربعة ال zero اربعة تمانية يبقى
+
+448
+00:46:30,860 --> 00:46:37,000
+ال order لها تساوي تلاتة و ال zero ال order له
+
+449
+00:46:37,000 --> 00:46:43,230
+يساوي كدهش واحد من التانية هذهوالثالثة بداخل من
+
+450
+00:46:43,230 --> 00:46:48,510
+خمستاشر بداخل ال group generated by خمسة ال order
+
+451
+00:46:48,510 --> 00:46:54,250
+كمان يساوي كم؟ يساوي تلاتة يبقى ال order يساوي
+
+452
+00:46:54,250 --> 00:46:58,670
+تلاتة بالشكل اللي عندنا هنا يبقى ال least يبقى ال
+
+453
+00:46:58,670 --> 00:47:04,610
+order لل external direct product ال order لل
+
+454
+00:47:04,610 --> 00:47:13,540
+external direct productمع من؟ مع الـ zero مع من؟
+
+455
+00:47:13,540 --> 00:47:18,280
+مع الـ subgroup generated by خمسة ال order لها
+
+456
+00:47:18,280 --> 00:47:23,140
+يساوي ال order لل subgroup generated by أربعة لمن
+
+457
+00:47:23,140 --> 00:47:28,100
+ال order ل ال zero في ال order لل subgroup
+
+458
+00:47:28,100 --> 00:47:34,100
+generated by خمسة و يساوي تلاتة في واحد في تلاتة و
+
+459
+00:47:34,100 --> 00:47:38,660
+يساوي تسعةيبقى هي جبتله subgroup من ال group
+
+460
+00:47:38,660 --> 00:47:44,260
+الأصلية ال order إلها يساوي تسعة كان هذا سؤال
+
+461
+00:47:44,260 --> 00:47:46,360
+اتنين و تلاتين
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8d277c855d5d387b6bf6a7e52d3dcc423ba5d025
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/V133cZxPx_0_postprocess.srt
@@ -0,0 +1,1980 @@
+1
+00:00:21,190 --> 00:00:26,610
+بسم الله الرحمن الرحيم المرة الماضية بدأنا في خواص
+
+2
+00:00:26,610 --> 00:00:31,330
+ال group الخواص الأولى لل group واخدنا أول خاصية
+
+3
+00:00:31,330 --> 00:00:35,930
+الخاصية الأولى بتقول لو كان عندى identity element
+
+4
+00:00:35,930 --> 00:00:39,980
+في ال group يبقى هذا ال identity element يكونو
+
+5
+00:00:39,980 --> 00:00:43,540
+أثبتنا ان الاتنين مرتبطين و اثبتنا ان الاتنين
+
+6
+00:00:43,540 --> 00:00:45,200
+مرتبطين و اثبتنا ان الاتنين مرتبطين و اثبتنا ان
+
+7
+00:00:45,200 --> 00:00:47,820
+الاتنين مرتبطين و اثبتنا ان الاتنين مرتبطين و
+
+8
+00:00:47,820 --> 00:00:48,960
+اثبتنا ان الاتنين مرتبطين و أثبتنا ان الاتنين
+
+9
+00:00:48,960 --> 00:00:50,300
+مرتبطين و أثبتنا ان الاتنين مرتبطين و أثبتنا ان
+
+10
+00:00:50,300 --> 00:00:52,420
+الاتنين مرتبطين و أثبتنا ان الاتنين مرتبطين و
+
+11
+00:00:52,420 --> 00:00:56,700
+أثبتنا ان الاتنين مرتبطين و أثبتنا ان الاتنين
+
+12
+00:00:56,700 --> 00:01:01,140
+مرتبطين و أثبتنا ان الاتنين مرتبطين و أثبتنا ان
+
+13
+00:01:01,140 --> 00:01:06,290
+الاتنين مرتبطينبلغة أخرى لما نقول بي ايه بده يساوي
+
+14
+00:01:06,290 --> 00:01:12,450
+ca then بيه يساوي c يعني كأنه شاطبنا a مع a وده
+
+15
+00:01:12,450 --> 00:01:18,250
+اسمه قانون الشاطب الأيمن التاني هذا a بيه بده
+
+16
+00:01:18,250 --> 00:01:23,630
+يساوي ac يبقى طالع انه بيه بتساوي c يبقى كأنه
+
+17
+00:01:23,630 --> 00:01:29,510
+شاطبنا من جهة الشماليبقى قانون الشاطب الأيسر قانون
+
+18
+00:01:29,510 --> 00:01:32,810
+الشاطب الأيمن قانون الشاطب الأيسر هذه تسميات
+
+19
+00:01:32,810 --> 00:01:37,310
+بتهمنيش كتير بهمني ان انا نصل الى اثبات هذه
+
+20
+00:01:37,310 --> 00:01:43,170
+العلاقة يبقى بدنا نروح نثبتها فباجي بقوله ل proof
+
+21
+00:01:46,430 --> 00:01:51,850
+الان بي في اه موجود
+
+22
+00:01:51,850 --> 00:01:56,150
+في ال group جي والبي موجود في ال group جي مشان
+
+23
+00:01:56,150 --> 00:02:02,210
+تكون group لازم يكون فيها لكل عنصر معكوس لهذا
+
+24
+00:02:02,210 --> 00:02:07,650
+العنصر اذا بدي افترض انه معكوس لعنصر ا مثلا وليه
+
+25
+00:02:07,650 --> 00:02:12,230
+اكون a prime او اي رمز اخر ونشوف هذا هيوصلنا لوين
+
+26
+00:02:12,230 --> 00:02:14,790
+يبقى حاجة اقوله assume
+
+27
+00:02:34,810 --> 00:02:43,090
+الحين احنا عندنا BA بده يساوي CAبدأ أضرب من جهة
+
+28
+00:02:43,090 --> 00:02:51,850
+اليمين في الـ A' يبقى بي ايه في الـ A' يبقى C A في
+
+29
+00:02:51,850 --> 00:02:59,230
+الـ A' هذا الكلام سيعطينا بدأ أستخدم خاصية ال
+
+30
+00:02:59,230 --> 00:03:03,880
+associativityيبقى من خاصية ال associativity بصير
+
+31
+00:03:03,880 --> 00:03:10,660
+ان بي في a a prime يساوي
+
+32
+00:03:10,660 --> 00:03:17,700
+c في a a prime هذا بدي يعطينا اي عنصر في معكسه شو
+
+33
+00:03:17,700 --> 00:03:22,860
+بيعطيناه عنصر الوحدة ال identity element يبقى بناء
+
+34
+00:03:22,860 --> 00:03:34,390
+عليه هذا هيعطينا ان ال bالـ B في الـ E بدر يساوي
+
+35
+00:03:34,390 --> 00:03:38,890
+مين؟ بدر يساوي الـ C في الـ E طب ال identity
+
+36
+00:03:38,890 --> 00:03:42,870
+element لما أضربه في أي عنصر إيش بيعطينا؟ نفس
+
+37
+00:03:42,870 --> 00:03:49,950
+العنصر يبقى هذا بدر يعطينا B تساوي C هذا هو
+
+38
+00:03:49,950 --> 00:04:01,090
+المطلوب الأول المطلوب الثاني andو كذلك ال a b بده
+
+39
+00:04:01,090 --> 00:04:08,390
+يسوي a c implies ان ال a prime في ال a b بده يسوي
+
+40
+00:04:08,390 --> 00:04:15,350
+ال a prime في ال a c من خاصية ال associativity هذا
+
+41
+00:04:15,350 --> 00:04:18,110
+يعني ان ال a prime a
+
+42
+00:04:26,160 --> 00:04:31,040
+العنصر في معكسه بيعطينا ال identity element دير
+
+43
+00:04:31,040 --> 00:04:34,320
+بالك بس مش عنصر تضرب من اليمين و التاني من الشمال
+
+44
+00:04:34,320 --> 00:04:37,720
+ضربت من الشمال يبقى التاني من الشمال ضربت من
+
+45
+00:04:37,720 --> 00:04:40,960
+اليمين يبقى التاني من اليمين ليش؟ لأنه ماقليش ال
+
+46
+00:04:40,960 --> 00:04:44,780
+group abelianلو قالي لجروب أبيلي ان ضربت واحدة من
+
+47
+00:04:44,780 --> 00:04:47,560
+اليمين و واحدة من الشمال، انت فريقش عننا بس إن كان
+
+48
+00:04:47,560 --> 00:04:49,880
+الضرب من اليمين، الثاني من اليمين، الضرب من
+
+49
+00:04:49,880 --> 00:04:53,280
+الشمال، الطرف التاني من الشمال زي ما أنت شايفلازم
+
+50
+00:04:53,280 --> 00:04:58,420
+نرى الترتيب عند عملية الشغل في ال groups يبقى هذا
+
+51
+00:04:58,420 --> 00:05:03,720
+معناه ان ال identity element في B يسوى ال identity
+
+52
+00:05:03,720 --> 00:05:11,320
+element في C يبقى هذا معناه ان B بيبدأ تسوى C إذا
+
+53
+00:05:11,320 --> 00:05:15,520
+من الآن فصادم قانون الشطب الأيمن وقانون الشطب
+
+54
+00:05:15,520 --> 00:05:23,320
+الأيسر على ال group exist موجود ومتعرف عليهالنقطة
+
+55
+00:05:23,320 --> 00:05:27,880
+الثالثة أو الخاصية التالتة من خواص ال group بيقول
+
+56
+00:05:27,880 --> 00:05:38,920
+for each element for each element لأي عنصر for
+
+57
+00:05:38,920 --> 00:05:47,040
+each element a in a group g
+
+58
+00:05:49,680 --> 00:05:55,360
+لأي عنصر في ال group G there is a unique element
+
+59
+00:05:55,360 --> 00:06:10,620
+there is a unique element there is
+
+60
+00:06:10,620 --> 00:06:17,880
+a unique element B in G such that
+
+61
+00:06:21,290 --> 00:06:29,150
+بعد ذلك اي بي ساوي بي في اي ساوي ال identity
+
+62
+00:06:29,150 --> 00:06:40,070
+element مرة
+
+63
+00:06:40,070 --> 00:06:44,940
+تانيةالمرة اللى فاتت اول خاصية اثبتنا ان عنصر
+
+64
+00:06:44,940 --> 00:06:49,080
+الوحدة يكون وحيدا مافيش غير عنصر واحدة واحدة في ال
+
+65
+00:06:49,080 --> 00:06:53,500
+group كلها من اولها الى اخرها الان بيقول لو اخدت
+
+66
+00:06:53,500 --> 00:07:00,060
+اي عنصر ايه موجود في جيل لازم نلاقي عنصر وحيد لاحظ
+
+67
+00:07:00,060 --> 00:07:05,080
+الكلمة هذه a unique element يبقى عنصرا وحيدا مافيش
+
+68
+00:07:05,080 --> 00:07:10,910
+غيرهوين في جي بي موجود في جي بحيث ان ال a في b
+
+69
+00:07:10,910 --> 00:07:14,710
+بيساوي ال a في b بيساوي ال identity شو معنى هذا
+
+70
+00:07:14,710 --> 00:07:20,990
+الكلام معنى ان المعكوس لكل عنصر يكونه وحيدا مافيش
+
+71
+00:07:20,990 --> 00:07:26,540
+غيرهيعني كل عنصر في موجود في ال group له معكوس لا
+
+72
+00:07:26,540 --> 00:07:31,740
+يشاركه أحد في هذا المعكوس إذا بدنا نروح نثبت هذا
+
+73
+00:07:31,740 --> 00:07:35,840
+الكلام بنفس الفكرة اللي أثبتنا فيها ال identity
+
+74
+00:07:35,840 --> 00:07:39,360
+element يبقى العنصر إيه اللي موجود في ال group بدي
+
+75
+00:07:39,360 --> 00:07:43,960
+أفترض أنه إيه معكوسين و أحاول أثبت أن هذين
+
+76
+00:07:43,960 --> 00:07:49,260
+المعكوسين متساويان يبقى باجي بقوله ال proof
+
+77
+00:07:53,660 --> 00:08:07,940
+Assume افترض ان B وC هم اكتر
+
+78
+00:08:07,940 --> 00:08:18,200
+من الاسم
+
+79
+00:08:18,200 --> 00:08:20,080
+الموجود في G
+
+80
+00:08:26,860 --> 00:08:35,980
+الـ A B بيساوي B A الـ A B بيساوي B A بيساوي ال
+
+81
+00:08:35,980 --> 00:08:44,760
+identity E and الـ A C بيساوي C في A بيساوي ال
+
+82
+00:08:44,760 --> 00:08:50,540
+identity E هذا حسب تعريف من؟ حسب تعريف المعكوس
+
+83
+00:08:50,540 --> 00:08:57,810
+الآن هذا ال elementبدو يساوي ال identity و هذا ال
+
+84
+00:08:57,810 --> 00:09:01,850
+element بدو يساوي ال identity معناته ال two
+
+85
+00:09:01,850 --> 00:09:08,270
+elements are equal يبقى هذا بدو يعطينا ايه انه a
+
+86
+00:09:08,270 --> 00:09:14,230
+في b بدو يساوي ال ac لإنه كل واحد مالهم بدو يساوي
+
+87
+00:09:14,230 --> 00:09:19,310
+ال identity بالخاصية اللي فوق الأولانية رقم اتنين
+
+88
+00:09:19,310 --> 00:09:23,030
+يبقى by property
+
+89
+00:09:29,720 --> 00:09:37,400
+بتساوي الـ C لو أخدنا الجزء الثاني similarly بنفس
+
+90
+00:09:37,400 --> 00:09:38,420
+الطريقة
+
+91
+00:09:40,770 --> 00:09:49,050
+اللي هو BA بده يساوي CA implies ان ال B تساوي C
+
+92
+00:09:49,050 --> 00:09:53,330
+يبقى بناء عليه لو وجد معكوسين ان شاء الله يكونوا
+
+93
+00:09:53,330 --> 00:09:57,970
+عشرة لعنصر ما العشرة هدول لازم يكونوا are equal
+
+94
+00:09:57,970 --> 00:10:02,850
+يعني معنى هذا الكلام ان معكوس العنصر يكونوا ايه؟
+
+95
+00:10:02,850 --> 00:10:05,490
+يكونوا وحيدا مفيش غيره
+
+96
+00:10:13,790 --> 00:10:20,370
+الخاصية الرابعة الرابعة الرابعة الرابعة الرابعة
+
+97
+00:10:20,370 --> 00:10:20,490
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+98
+00:10:20,490 --> 00:10:21,050
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+99
+00:10:21,050 --> 00:10:21,450
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+100
+00:10:21,450 --> 00:10:22,370
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+101
+00:10:22,370 --> 00:10:26,570
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+102
+00:10:26,570 --> 00:10:29,330
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+103
+00:10:29,330 --> 00:10:29,610
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+104
+00:10:29,610 --> 00:10:31,270
+الرابعة الرابعة الرابعة الرابعة الرابعة الرابعة
+
+105
+00:10:31,270 --> 00:10:40,590
+الرابعة الرابعة
+
+106
+00:10:40,590 --> 00:10:46,180
+الروالعكس من جيه
+
+107
+00:10:46,180 --> 00:10:57,840
+هو denoted by جيه انفسيعني يا شباب من الأن فاصاعدا
+
+108
+00:10:57,840 --> 00:11:03,700
+بدنا نبطل نقول let A' B is inverse of A على طول
+
+109
+00:11:03,700 --> 00:11:08,640
+الخط معكوس ال A هقوله A inverse معكوس ال G هو G
+
+110
+00:11:08,640 --> 00:11:20,880
+inverse و هكذا نقطة ثانية if ال N is A positive
+
+111
+00:11:22,440 --> 00:11:32,780
+integer عدد صحيح موجة باللي ال N then ال G to the
+
+112
+00:11:32,780 --> 00:11:40,440
+power N معناته ايه؟ معناته G مضروبة في G مضروبة في
+
+113
+00:11:40,440 --> 00:11:47,800
+G هذا الكلام in times يعني in من المراتيا شباب هنا
+
+114
+00:11:47,800 --> 00:11:50,760
+الدرب هذه النقاط اللي شايفينها مش عملية الدرب
+
+115
+00:11:50,760 --> 00:11:55,860
+العادية يعني g star g g star g star g star g إلى
+
+116
+00:11:55,860 --> 00:11:59,920
+آخرية ال star mean ما كانت تكون بس احنا اختصارا
+
+117
+00:11:59,920 --> 00:12:07,490
+بنكتبها بالشكل هذاالنقطة الثالثة
+
+118
+00:12:07,490 --> 00:12:13,930
+الجي مرفوع للأس زيرو بده يساوي اي element في ال
+
+119
+00:12:13,930 --> 00:12:18,890
+group جي ارفع له الصفر بيعطينا ال identity element
+
+120
+00:12:18,890 --> 00:12:26,550
+يبقى هذا ال E نمره أربع الجي to the power n بقدر
+
+121
+00:12:26,550 --> 00:12:35,520
+اقول جي انفرس أس سالب nلما أقول GN بقدر أكتبها على
+
+122
+00:12:35,520 --> 00:12:36,620
+الشكل التالي
+
+123
+00:12:47,300 --> 00:12:56,760
+بقول ال GM في ال GN بده سوى GM زائد ال N يبقى تجمع
+
+124
+00:12:56,760 --> 00:13:06,260
+الأسس عادي جدا خمسة نمرا ستة نمرا ستة GM كله أس N
+
+125
+00:13:06,260 --> 00:13:14,390
+زي هذه بالضبط تمامايبقى هذه أسس مُركّبة وليست مثل
+
+126
+00:13:14,390 --> 00:13:19,430
+هذه هنا الأساسات هم ال element مرفوعة لنفس الأسس M
+
+127
+00:13:19,430 --> 00:13:24,950
+و N يبقى عند ال operation هذه تجمع الأسس لكن هذه
+
+128
+00:13:24,950 --> 00:13:32,650
+كانها GM Star GM Star GM Star GM يعني إيش يعني N
+
+129
+00:13:32,650 --> 00:13:42,050
+من المراتإذا هذه بالضبط تماما هي GMN أو بقدر أقول
+
+130
+00:13:42,050 --> 00:13:50,250
+GNM ليش؟لأن الان و الام انتجار عملية ضرب العادية
+
+131
+00:13:50,250 --> 00:13:54,910
+للأعداد عملية إبدالية خمسة في ستة هي ستة في خمسة
+
+132
+00:13:54,910 --> 00:14:01,710
+إذا هذه بقدر أروح أكتبها كذلك على الشكل التالي GNM
+
+133
+00:14:01,710 --> 00:14:07,170
+بهمنيش من الأسل ولا على كل الأمرين كله بعطيني نفس
+
+134
+00:14:07,170 --> 00:14:14,580
+النتيجة النقطة السابعةالنقطة السابعة لو قلت a b
+
+135
+00:14:14,580 --> 00:14:23,820
+كله to the power n هل يسوى a n b n يعني
+
+136
+00:14:23,820 --> 00:14:29,680
+لو قلتك اتنين هل ال a b تربيع يسوى a تربيع b تربيع
+
+137
+00:14:29,680 --> 00:14:36,300
+في حالة واحدة لو كانت ال g أبيليا غير هيك بعتلك
+
+138
+00:14:36,300 --> 00:14:41,400
+اللهيبقى هذا الكلام لا يمكن أن يساوي هذا على
+
+139
+00:14:41,400 --> 00:14:49,880
+الاطلاق بروح بستثني و بقول but if g is abelian
+
+140
+00:14:49,880 --> 00:14:58,160
+then اللي هو ال a b to the power n بده يساوي a n b
+
+141
+00:14:58,160 --> 00:15:04,290
+nغير هيك لأ لإنه بقدر أبدل أي عنصر مكان التاني
+
+142
+00:15:04,290 --> 00:15:07,430
+بدون أي مشكلة إن كان تميل لكن if it's not
+
+143
+00:15:07,430 --> 00:15:12,830
+appealing بيصير كلامي هذا كله ليس صحيحا طيب النقطة
+
+144
+00:15:12,830 --> 00:15:23,270
+الثامنة بيقول if ال g و ال plus is a group is a
+
+145
+00:15:23,270 --> 00:15:28,190
+group then
+
+146
+00:15:30,130 --> 00:15:47,370
+الـ inverse of g is minus g that is a n الـ g
+
+147
+00:15:47,370 --> 00:15:53,710
+inverse هي عبارة عن سلب g and
+
+148
+00:15:55,880 --> 00:16:04,480
+الـ G Inverse كل تكييب بده يساوي سالب تلاتة G
+
+149
+00:16:28,420 --> 00:16:34,920
+بترجع مرة تانية لهذه النقاط الأساسية الثمانية لأن
+
+150
+00:16:34,920 --> 00:16:40,000
+هذه الأساسية عندنا بتظل معانا طيلة شغلنا في علم
+
+151
+00:16:40,000 --> 00:16:45,400
+الجبار من الآن فسعدم أن نتفق على هذه النقاط مرة
+
+152
+00:16:45,400 --> 00:16:50,680
+أخرى يبقى النقطة الأخرى احنا بنشغل داخل ال group
+
+153
+00:16:50,680 --> 00:16:55,240
+وليس داخل ال set of real number احنا بنشغل داخل ال
+
+154
+00:16:55,240 --> 00:16:59,380
+group من ما كانت ال group تكون هذهبقول لو كانت جي
+
+155
+00:16:59,380 --> 00:17:04,760
+جروب واخدت عنصر جي موجود في جي يبقى معكوس الجي من
+
+156
+00:17:04,760 --> 00:17:11,040
+الأن فساعدا هنرمزله بالرمز G inverse وليس G أسالب
+
+157
+00:17:11,040 --> 00:17:16,140
+واحد يعني هذه ليست واحد على جي تمام ايوة مشان
+
+158
+00:17:16,140 --> 00:17:22,000
+متوهش بين غسيل اكتب ل G inverse لا تساوي واحد على
+
+159
+00:17:22,000 --> 00:17:26,600
+جييمكن في بعض التعريفات هيها صحيح الـ G inverse
+
+160
+00:17:26,600 --> 00:17:31,920
+واحد على G بس in general الكلام هذا ليس صحيحاً طيب
+
+161
+00:17:31,920 --> 00:17:35,900
+النقطة التانية لو كانت ال N positive integer عدد
+
+162
+00:17:35,900 --> 00:17:41,900
+صحيح موجب يبقى المقصود ب G N هي G star G star G
+
+163
+00:17:41,900 --> 00:17:46,740
+star G N من المرات يعني بدي أطبق ال binary
+
+164
+00:17:46,740 --> 00:17:51,510
+operation على ال element هذا N من المراتالنقطة
+
+165
+00:17:51,510 --> 00:17:56,070
+التالتة الـ A element في ال group G لو حطيت له
+
+166
+00:17:56,070 --> 00:17:59,570
+الأس Zero بدي يعطيني دائما و أبدا ال identity
+
+167
+00:17:59,570 --> 00:18:06,590
+elementلما أقول GN يمكن صياغتها بصياغة أخرى و
+
+168
+00:18:06,590 --> 00:18:11,990
+هتشوفوا و احنا بنبرهن هنضطر نصيغ ال GN بالصياغة
+
+169
+00:18:11,990 --> 00:18:19,070
+هذه يبقى هي G inverse و سالب N هذه و هذه الاتنين
+
+170
+00:18:19,070 --> 00:18:27,180
+are the sameالنقطة الخامسة GM مضروبة في GN يبقى
+
+171
+00:18:27,180 --> 00:18:31,960
+بنجمع الأسس جامعة هذه ليست ضربة وإنما ما المقصود
+
+172
+00:18:31,960 --> 00:18:40,770
+بيها Star GM Star GN يبقى GM زائد Mلو كان الأُس
+
+173
+00:18:40,770 --> 00:18:46,010
+أُسًا مُركّبًا يبقى بنضرب هذه الأُس في بعض يبقى G
+
+174
+00:18:46,010 --> 00:18:52,030
+M N يساوي G أُس M N بدّل ال N و ال M لأن هم هدول
+
+175
+00:18:52,030 --> 00:18:57,470
+integers و اتنين are positive يبقى G N M أو G N
+
+176
+00:18:57,470 --> 00:19:03,240
+أُس M كله are the sameلأ لو جيت لحاصل ضرب a b to
+
+177
+00:19:03,240 --> 00:19:10,360
+the power n لا يساوي a n في b n ولكن هذا يساوي a b
+
+178
+00:19:10,360 --> 00:19:18,160
+a b a b a b a b n من المرات ولا يساوي a n b n لكن
+
+179
+00:19:18,160 --> 00:19:23,100
+إن كانت ال g abelian بقدر أبدل ال a مكان ال b
+
+180
+00:19:23,100 --> 00:19:28,220
+وبالتالي يطلع عند ال a b to the power n يساوي a n
+
+181
+00:19:28,220 --> 00:19:35,950
+b nيبقى دي ربالق اه لو قلتلك a زائد b لكل تربية مش
+
+182
+00:19:35,950 --> 00:19:39,610
+هتقول اه تربية زائد اتنين a b زائد b تربية هذا
+
+183
+00:19:39,610 --> 00:19:44,490
+الكلام غلط a تربية او زائد b تربية صح بس مش اتنين
+
+184
+00:19:44,490 --> 00:19:50,830
+a b يبقى زائد a b زائد b a يعني بهذا الشكل هذا لما
+
+185
+00:19:50,830 --> 00:19:56,770
+اقولك a زائد b لكل تربية لو حبيت اشوفهم هذول في ال
+
+186
+00:19:56,770 --> 00:20:02,110
+group شو شكلهميبقى باجي بقولك هذا a تربية مظبوط و
+
+187
+00:20:02,110 --> 00:20:09,990
+هذا زائد a b و هذا زائد b a و هذا زائد b تربية هيك
+
+188
+00:20:09,990 --> 00:20:14,690
+صح لكن تقوللي a تربية زائد اتنين a b زائد b تربية
+
+189
+00:20:14,690 --> 00:20:19,010
+هذا كلام غلط إلا إذا كانت أبيلا غير هيك يبعتلك
+
+190
+00:20:19,010 --> 00:20:24,580
+الله يبقى دير بالك من الشغل هذهطيب النقطة الثامنة
+
+191
+00:20:24,580 --> 00:20:30,020
+والاخيرة لو كانت العملية ال binary operation معرفة
+
+192
+00:20:30,020 --> 00:20:36,120
+على ال group G هي عملية الجامع يبقى ال G inverse
+
+193
+00:20:36,120 --> 00:20:42,380
+في هذه الحالة هيكون هو سالب G يبقى معكوس ال G هو
+
+194
+00:20:42,380 --> 00:20:47,600
+سالب G that is ال G inverse هي سالب Gوفي هذه
+
+195
+00:20:47,600 --> 00:20:55,100
+الحالة اقول جي انفرس اوس تكييب يعني ايش؟ يعني سالب
+
+196
+00:20:55,100 --> 00:21:01,480
+جي الكل تكييب وهذه تعتبر سالب تلاتة جي لان عند
+
+197
+00:21:01,480 --> 00:21:06,080
+الجامعة بدي اقول سالب جي سالب جي سالب جي بيبقى
+
+198
+00:21:06,080 --> 00:21:13,530
+سالب تلاتة جيوكأنه بيضرب الأسس في بعضها وبنزله تحت
+
+199
+00:21:13,530 --> 00:21:18,110
+بالشكل اللي عنده هذا بيطلع الكلام مائة بالمائة طيب
+
+200
+00:21:18,110 --> 00:21:22,650
+ورسو لو بده أقول جي تكيبه العملية عملية الجامعة
+
+201
+00:21:22,650 --> 00:21:28,750
+يبقى بده أقول جي زائد جي زائد جي وليس تضرب يبقى
+
+202
+00:21:28,750 --> 00:21:33,670
+هذه كلها تساوي من تساوي تلاتة جي يبقى إذا العملية
+
+203
+00:21:33,670 --> 00:21:39,080
+على ال group G هي عملية الجامعة العاديةيبقى جي
+
+204
+00:21:39,080 --> 00:21:44,420
+تكيب هي عبارة عن تلاتة جي جي أس عشرة تعني عشرة جي
+
+205
+00:21:44,420 --> 00:21:50,620
+جي أس ناقص تمانية تعني ناقص تمانية جي and so on و
+
+206
+00:21:50,620 --> 00:21:59,680
+هكذا طيب في الأن بدنا نيجي للنقطة الخامسة if ال a
+
+207
+00:21:59,680 --> 00:22:07,020
+نقطة الخامسة if ال a and ال b belong
+
+208
+00:22:14,690 --> 00:22:24,890
+بالنسبة للمجموع جي ثم اي بي الكل انفرس بدي يسوي بي
+
+209
+00:22:24,890 --> 00:22:37,030
+انفرس اي انفرس خلي
+
+210
+00:22:37,030 --> 00:22:43,070
+بالك هنالأ لو في عنصرين في قلوبه وضربتهم في بعضه
+
+211
+00:22:43,070 --> 00:22:48,230
+بدي أجيب المعكوس تبعهم يبقى المعكوس بقول A B كل
+
+212
+00:22:48,230 --> 00:22:54,110
+inverse عمليا بقدر أقول هذا B inverse A inverse
+
+213
+00:22:54,110 --> 00:22:58,950
+يعني كتبت ال inverse لكل واحد فيهم و جلبت الوضع
+
+214
+00:22:58,950 --> 00:23:04,990
+هروح نبره صحة هذا الكلام احنا قبل قليل أثبتنا ان
+
+215
+00:23:04,990 --> 00:23:09,140
+ال inverse elementوحيد و الله اكتر من واحد الا
+
+216
+00:23:09,140 --> 00:23:14,040
+انصار واحد هو واحد يبقى ال a بي مالوش الا معكوس
+
+217
+00:23:14,040 --> 00:23:20,180
+واحد هدف يقول انه يله جداش اتنين مدام اتنين لازم
+
+218
+00:23:20,180 --> 00:23:25,000
+اتنين يتساوى طبقا للخاصية اللي قبل قليل يبقى انا
+
+219
+00:23:25,000 --> 00:23:30,200
+لو جدرت اثبت ان ال b inverse a inverse هو معكوس ال
+
+220
+00:23:30,200 --> 00:23:32,940
+a بيبتمن المطلوب مظبوط
+
+221
+00:23:37,330 --> 00:23:46,230
+بما ان ال a و ال b موجود في ال g, we have ان حاصل
+
+222
+00:23:46,230 --> 00:23:51,570
+الضرب a,b موجود في gلماذا؟ لمشان ال binary
+
+223
+00:23:51,570 --> 00:23:56,210
+operation a to elements a star b لازم يكون موجود
+
+224
+00:23:56,210 --> 00:24:03,250
+في جي مادام موجود في جي هذا معناته there exists
+
+225
+00:24:03,250 --> 00:24:15,690
+inverse for the element a,b لازم نجيله معكوس that
+
+226
+00:24:15,690 --> 00:24:23,790
+isA B الكل inverse مش شاكب انها رمز المعكوس تبع ال
+
+227
+00:24:23,790 --> 00:24:29,730
+A B A B inverse طيب انا بده اشوف اللي كاتبهلي هذا
+
+228
+00:24:29,730 --> 00:24:34,670
+اذا ضربت في A B من اليمين و من الشمال و طلع ال
+
+229
+00:24:34,670 --> 00:24:39,250
+identity ال ماتيبقى هذا كمان inverse صح ولا لا
+
+230
+00:24:39,250 --> 00:24:48,090
+الان لو جيت و قولتلك consider خدليالـ A B في الـ B
+
+231
+00:24:48,090 --> 00:24:53,590
+inverse A inverse هشوف كده بده يعطيني هذا الان بده
+
+232
+00:24:53,590 --> 00:24:58,450
+أستخدم خاصية ال associativity يبقى هذا بده يعطيني
+
+233
+00:24:58,450 --> 00:25:05,910
+A في B في ال B inverse في ال A inverse ال B في ال
+
+234
+00:25:05,910 --> 00:25:12,210
+B inverse بيعطيني ال identity يبقى ال A في ال E في
+
+235
+00:25:12,210 --> 00:25:17,700
+ال A inverseالـ E أضرب في أي عنصر بيطلع؟ نفس
+
+236
+00:25:17,700 --> 00:25:23,320
+العنصر يبقى هذا A A inverse يبقى بده يساوي ال
+
+237
+00:25:23,320 --> 00:25:28,960
+identity E مانفعش من الشمال و بس و من اليمين لازم
+
+238
+00:25:28,960 --> 00:25:35,410
+يكون من وين؟ من الطرفينيبقى باجي بقوله and ال b
+
+239
+00:25:35,410 --> 00:25:42,670
+inverse a inverse في ال a b بده يساوي b inverse في
+
+240
+00:25:42,670 --> 00:25:50,410
+ال a inverse a في ال a inverse a في من؟ في ال b
+
+241
+00:25:50,410 --> 00:25:56,190
+طيب هذا العنصر و معكوسه بيعطيني من؟ ال identity
+
+242
+00:25:56,190 --> 00:26:02,420
+elementيبقى هذا بدي يعطينا P inverse AB اللي هو
+
+243
+00:26:02,420 --> 00:26:07,200
+بدي يعطينا P inverse P بدي يعطينا من ال identity
+
+244
+00:26:07,200 --> 00:26:12,400
+element بناء عليه هذا ال element P inverse A
+
+245
+00:26:12,400 --> 00:26:18,840
+inverse حقق ليه خاصية معكوس العنصر AB يبقى من
+
+246
+00:26:18,840 --> 00:26:25,940
+الاتنين هدول مع بعضبقدر اقول هذا بده يعطيني ان b
+
+247
+00:26:25,940 --> 00:26:37,140
+inverse a inverse is the inverse element of a,b
+
+248
+00:26:37,140 --> 00:26:41,800
+يبجى هذا العنصر هو معكوس ال a,b لكن احنا عندنا
+
+249
+00:26:41,800 --> 00:26:46,900
+معكوس ال a,b مين هو اللي فاج يبجى دول اتنين معاهم
+
+250
+00:26:47,490 --> 00:26:55,110
+لازم يتساوى فبجي بقوله since بما أن the inverse
+
+251
+00:26:55,110 --> 00:27:05,950
+element of a group G is unique
+
+252
+00:27:13,670 --> 00:27:20,850
+إن ال A بي الكل inverse يساوي B inverse A inverse
+
+253
+00:27:20,850 --> 00:27:24,010
+اللي
+
+254
+00:27:24,010 --> 00:27:28,830
+خاضر أسالكوا هذا السؤال و أشوف إيش رأيكوا فيه طيب
+
+255
+00:27:28,830 --> 00:27:36,510
+يا شباب انا لو بدي A B C كل inverse ايش بده يساوي
+
+256
+00:27:40,480 --> 00:27:44,280
+C inverse B inverse A inverse يعني يبقى شكل من
+
+257
+00:27:44,280 --> 00:27:51,260
+الآخر للأول يبقى هذا الكلام بدي يعطيني C inverse و
+
+258
+00:27:51,260 --> 00:27:56,600
+هنا B inverse و هنا A inverse تلاتة أربعة عشان
+
+259
+00:27:56,600 --> 00:28:01,440
+الله يكونوا مية بدك تبدأ من الآخر و ترجع رجوع يبقى
+
+260
+00:28:01,440 --> 00:28:09,060
+هذا هو المعكوس لمن؟ للعنفر اللي عندناالان في سؤال
+
+261
+00:28:09,060 --> 00:28:15,840
+في الكتاب سؤال تمانتاش برضه بدي اعتبره خاصية مهمة
+
+262
+00:28:15,840 --> 00:28:22,540
+جدا بتلزمنا أثناء الشغل سؤال تمانتاش بيقول لي if G
+
+263
+00:28:22,540 --> 00:28:31,610
+is a group لو كانت ال G group thenالـ A Inverse
+
+264
+00:28:31,610 --> 00:28:39,910
+Inverse بده يساوي A itself هذا الكلام صحيح لكل ال
+
+265
+00:28:39,910 --> 00:28:42,390
+A الموجود في ال group G
+
+266
+00:29:05,530 --> 00:29:11,690
+خلّيني أقول له في ال group G معكوس المعكوس بيعطينا
+
+267
+00:29:11,690 --> 00:29:17,730
+الأصل A inverse انفرس بيعطينا A قبل ما توجد A
+
+268
+00:29:17,730 --> 00:29:23,630
+المعكوس تبعه يبقى من الأن فصاعدا معكوس معكوس ال
+
+269
+00:29:23,630 --> 00:29:28,130
+element بيرجعني لل element itself بدنا نروح نثبت
+
+270
+00:29:28,130 --> 00:29:32,090
+صحة هذا الكلام يبقى باجي بقوله ل ال professor
+
+271
+00:29:38,960 --> 00:29:49,840
+لت ال a موجود في ال group g then a inverse موجود
+
+272
+00:29:49,840 --> 00:29:57,830
+في gمعكوسه موجود في جيه كمان معكوس هذا لازم يكون
+
+273
+00:29:57,830 --> 00:30:06,150
+موجود في جيه صحيح يبقى then and a inverse inverse
+
+274
+00:30:06,150 --> 00:30:12,530
+موجود في جيه ليش لأنه إذا وجد عنصر في ال group
+
+275
+00:30:12,530 --> 00:30:17,610
+لازم يكون معكوسه موجود شو معكوسه اللي هو a inverse
+
+276
+00:30:17,610 --> 00:30:25,060
+inverse طيب مدام هيكلو جيت أخدت ال a inverse
+
+277
+00:30:25,060 --> 00:30:33,820
+inverse inverse مش هذا العنصر و هذا معكوسه حاصل
+
+278
+00:30:33,820 --> 00:30:40,860
+ضربه ما شو بده يطيني ال identity element طيب إيش
+
+279
+00:30:40,860 --> 00:30:47,440
+رأيك لو روحت ضربت من جهة الشمال بالعنصر a اتصلت من
+
+280
+00:30:47,440 --> 00:30:54,760
+جهة الشمال هاهدر بالكيبقى هذا الـ A مضروب في الـ A
+
+281
+00:30:54,760 --> 00:31:02,060
+inverse في الـ A inverse inverse يبقى هذا الـ A
+
+282
+00:31:02,060 --> 00:31:03,360
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+283
+00:31:03,360 --> 00:31:04,500
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+284
+00:31:04,500 --> 00:31:06,880
+مضروب في الـ A inverse inverse يبقى هذا الـ A
+
+285
+00:31:06,880 --> 00:31:11,880
+مضروب في الـ A inverse inverse يبقى
+
+286
+00:31:11,880 --> 00:31:15,540
+هذا الـ A مضروب في الـ A inverse inverse يبقى هذا
+
+287
+00:31:26,790 --> 00:31:33,030
+العنصر في المعكوس يعطينا ال identity element يبقى
+
+288
+00:31:33,030 --> 00:31:38,970
+هذا يعطينا ان ال E في A inverse inverse
+
+289
+00:31:41,540 --> 00:31:45,380
+الـ identity element لما نقضبه في أي عنصر بيطلع
+
+290
+00:31:45,380 --> 00:31:51,460
+نفس العنصر يبقى بناء عليه a inverse inverse بده
+
+291
+00:31:51,460 --> 00:31:57,240
+يساوي ال a itself عزيزي و هو المطلوب؟ طيب و هو
+
+292
+00:31:57,240 --> 00:32:02,360
+المطلوب و كنتها هذا ال section و إليكم ال
+
+293
+00:32:02,360 --> 00:32:10,730
+exercises بدنا ياكم تمرني أديكم بسؤال خمسة و ستةو
+
+294
+00:32:10,730 --> 00:32:21,230
+تمانية و عشرة و اتناش و سبعتاش و تسعتاش و اربعة و
+
+295
+00:32:21,230 --> 00:32:30,690
+عشرين و خمسة و عشرين و ستة و عشرين و تلاتة و
+
+296
+00:32:30,690 --> 00:32:39,050
+تلاتين و تلاتة و تلاتين و خمسة و تلاتين و تسعة و
+
+297
+00:32:39,050 --> 00:32:39,730
+تلاتين
+
+298
+00:32:44,920 --> 00:32:49,500
+هذا لا يعني ان بقى الناس مشطوبة لا مش مشطوبة اذا
+
+299
+00:32:49,500 --> 00:32:54,500
+بتحل هدوله كمان جدهم بيكونوا كويس مش غلط لكن انا
+
+300
+00:32:54,500 --> 00:32:59,720
+بهمني هدول انتقنهم انتقان بحيث يغطوا فكرة كثيرة
+
+301
+00:32:59,720 --> 00:33:05,780
+موجودة في التمرين ولذلك هدول من اهم المسائل اللي
+
+302
+00:33:05,780 --> 00:33:10,440
+موجودة في التمرين لعل يكون فيها فكرة جديدة نحاول
+
+303
+00:33:10,440 --> 00:33:15,190
+نستفيد هذه الفكرةطبعا عندكم محاضرة اليوم الاطناشر
+
+304
+00:33:15,190 --> 00:33:20,270
+الواحدة مش حاجة حل الأسئلة لأ حابد محاضرة جديدة
+
+305
+00:33:20,270 --> 00:33:24,710
+لكن الأسئلة ليوم ايش؟ ليوم الإثنين مش هتروح تحل
+
+306
+00:33:24,710 --> 00:33:29,690
+عليك مش هنحل و أنت تنسخ ولا عمرك بتستفيد حاجة بدك
+
+307
+00:33:29,690 --> 00:33:34,510
+تفكر من هنا لبعد بكرة في حل هذه المسألة و تحول تحل
+
+308
+00:33:34,510 --> 00:33:38,430
+بقدر الإمكان و اللي يصعب عليك بعد بكرة ان شاء الله
+
+309
+00:33:38,430 --> 00:33:43,610
+بنحله مهما كان شكل هذا السؤالواضح كلام ايه؟ يعني
+
+310
+00:33:43,610 --> 00:33:47,970
+بديك بعض المكره تيجي جاهز نفسك للنقاش، هيكون في
+
+311
+00:33:47,970 --> 00:33:51,950
+نقاش كتير حسب اللي يمكن اللي يسألكوا كلكوا أو تلت
+
+312
+00:33:51,950 --> 00:33:56,330
+رباعكوا أو نصكوا حسب ما الوقت اللي ايه المتاحيعني
+
+313
+00:33:56,330 --> 00:34:00,050
+كل وحدة انت تتوجهلك السؤال ايش رأيك في السؤال لوين
+
+314
+00:34:00,050 --> 00:34:04,970
+وصلت فيه ايش حلت ايش كده الى اخرين هيك بيصير مخك
+
+315
+00:34:04,970 --> 00:34:10,210
+يفهم اللي هو جبر و بتستطيع انه تمشي معانا ماحلتش
+
+316
+00:34:10,210 --> 00:34:14,250
+والله عمرك ماحتمشي هتضلك جاعد عندنا هنا على طول
+
+317
+00:34:14,250 --> 00:34:21,770
+هاي نعم يبقى الآنحاول بقدر الإمكان تحل هذه المسائل
+
+318
+00:34:21,770 --> 00:34:26,830
+أنا متأكد أنه مش هتعرف تحلهم كلهم لكن على الأقل
+
+319
+00:34:26,830 --> 00:34:32,350
+بتحل شيء كثير منهم ولذلك المناقشة حتى اللي
+
+320
+00:34:32,350 --> 00:34:38,670
+ماعرفناش نحله الروح نحله في محاضرة المناقشةطيب
+
+321
+00:34:38,670 --> 00:34:43,230
+عليكي بكون انتهينا من هذا ال chapter بدنا نروح لل
+
+322
+00:34:43,230 --> 00:34:48,010
+chapter اللي بعده اللي هو chapter تلاتة chapter
+
+323
+00:34:48,010 --> 00:34:54,690
+تلاتة يا شباب اللي هو بتحدث عن ال subgroups يعني
+
+324
+00:34:54,690 --> 00:34:59,110
+احنا كنا بنشتغل في ال groups الآن بدنا نبدأ ناخد
+
+325
+00:34:59,110 --> 00:35:12,310
+مجموعات جزئية منها يبقى chapter تلاتةفاينايت جروبز
+
+326
+00:35:12,310 --> 00:35:20,390
+فاينايت جروبز فاينايت
+
+327
+00:35:20,390 --> 00:35:21,110
+جروبز فاينايت جروبز فاينايت جروبز فاينايت جروبز
+
+328
+00:35:21,110 --> 00:35:22,930
+فاينايت جروبز فاينايت جروبز فاينايت جروبز فاينايت
+
+329
+00:35:22,930 --> 00:35:24,850
+جروبز فاينايت جروبز فاينايت جروبز فاينايت جروبز
+
+330
+00:35:24,850 --> 00:35:26,470
+فاينايت جروبز فاينايت جروبز فاينايت جروبز فاينايت
+
+331
+00:35:26,470 --> 00:35:34,790
+جروبز فاينايت جروبجديدة قبل أن نبدأ في الـ
+
+332
+00:35:34,790 --> 00:35:40,570
+subgroups حاجة اسمة ال order لل group وال order لل
+
+333
+00:35:40,570 --> 00:35:46,090
+element اللي موجود في ال group أول شي بالبلد هيك
+
+334
+00:35:46,090 --> 00:35:50,900
+قبل ما نكتبلو أردت ال order لجروب فأذهب بعد
+
+335
+00:35:50,900 --> 00:35:56,000
+عناصرها جداش ال order لجروب هو عدد العناصر في
+
+336
+00:35:56,000 --> 00:35:59,620
+الجروب جروب فيها أربع عناصر يبقى ال order لها
+
+337
+00:35:59,620 --> 00:36:04,480
+يساوي أربعة جروب فيها عشر عناصر يبقى ال order لها
+
+338
+00:36:04,480 --> 00:36:11,770
+يساوي عشرة و هكذالكن ال order لل element اللي
+
+339
+00:36:11,770 --> 00:36:18,150
+موجود في ال group هو أصغر عدد صحيح موجب بحطه ك أسل
+
+340
+00:36:18,150 --> 00:36:21,170
+هذا ال element بيعطينا ال identity
+
+341
+00:36:26,400 --> 00:36:29,720
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+342
+00:36:29,720 --> 00:36:32,280
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+343
+00:36:32,280 --> 00:36:34,300
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+344
+00:36:34,300 --> 00:36:38,640
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+345
+00:36:38,640 --> 00:36:43,420
+أصغر عدد صحيح موجب أصغر عدد صحيح موجب أصغر عدد
+
+346
+00:36:43,420 --> 00:36:45,120
+صحيح موجب أصغر عدد صحيح موجب أصغر عدد صحيح موجب
+
+347
+00:36:45,120 --> 00:36:49,640
+أصغر عدد
+
+348
+00:36:49,640 --> 00:37:01,290
+صحيح موجبG as the number
+
+349
+00:37:01,290 --> 00:37:08,950
+of elements
+
+350
+00:37:08,950 --> 00:37:18,050
+in G which is denoted by
+
+351
+00:37:22,800 --> 00:37:29,120
+by جيه ما بين خطين و تقرأ ال order لجيه مش
+
+352
+00:37:29,120 --> 00:37:34,400
+absolute value لجيه يبقى هذا هو ال order لجيه
+
+353
+00:37:34,400 --> 00:37:39,440
+command definition تاني ال order لل element the
+
+354
+00:37:39,440 --> 00:37:53,720
+order of an element of an elementاللي موجود في G
+
+355
+00:37:53,720 --> 00:38:04,040
+is the smallest positive
+
+356
+00:38:04,040 --> 00:38:07,580
+integer
+
+357
+00:38:37,950 --> 00:38:46,780
+بنروح نكتب ال order لا جي بده يساوي ال inفي عندنا
+
+358
+00:38:46,780 --> 00:38:59,960
+بعض ال notes البسيطة أول واحدة if the operation on
+
+359
+00:38:59,960 --> 00:39:11,100
+g is addition is addition عملية الجامعة then
+
+360
+00:39:30,230 --> 00:39:38,950
+النقطة الثانية is the order of
+
+361
+00:39:38,950 --> 00:39:41,250
+identity
+
+362
+00:39:42,600 --> 00:40:00,500
+Element E is واحدة صحية مقطة تالتة if there is if
+
+363
+00:40:00,500 --> 00:40:10,380
+there is no positive integer in
+
+364
+00:40:11,810 --> 00:40:17,310
+such that الـ
+
+365
+00:40:17,310 --> 00:40:25,310
+G to the power N بده سوى ال identity then ال order
+
+366
+00:40:25,310 --> 00:40:29,270
+لجي is infinite
+
+367
+00:41:00,880 --> 00:41:05,620
+نرجع لهذه التعريفين والملاحظات اللي على التعريفين
+
+368
+00:41:05,620 --> 00:41:10,920
+مرة ثانية بقول the order of a group G is the
+
+369
+00:41:10,920 --> 00:41:16,980
+number of elements in G عدد العناصر في G واللي
+
+370
+00:41:16,980 --> 00:41:22,280
+بتدرمزله بالرمز G ما بين خطين ليست absolute value
+
+371
+00:41:22,280 --> 00:41:28,140
+ل G وإنما ال order ل Gيبقى ال order لcapital G هو
+
+372
+00:41:28,140 --> 00:41:33,360
+عدد العناصر في ال group السؤال هو هل ممكن عدد
+
+373
+00:41:33,360 --> 00:41:37,960
+العناصر يكون محدود يعني رقم و ممكن يكون كذلك
+
+374
+00:41:37,960 --> 00:41:43,760
+infinity ممكن اتنين وردات يعني ال group قد تنتهي
+
+375
+00:41:43,760 --> 00:41:48,700
+وبالتالي عدد العناصر يكون finiteوقد لا تنتهي
+
+376
+00:41:48,700 --> 00:41:54,340
+وبالتالي هذا العناصر in finite زي ال R star اللي
+
+377
+00:41:54,340 --> 00:41:57,760
+هي set of real numbers لما أشيل منها zero تحت
+
+378
+00:41:57,760 --> 00:42:01,680
+عملية الضرب أكم أنصر فيها دي group طبعا أكم أنصر
+
+379
+00:42:01,680 --> 00:42:06,200
+فيها مالا نهاية من العناصر إذا من ال order لل
+
+380
+00:42:06,200 --> 00:42:11,430
+group G في هذه الحالة بيكون in finite لكنلو روحت ل
+
+381
+00:42:11,430 --> 00:42:17,110
+ZN و لا UN و لا كل الأمثلة اللي أخدناهم هذه بيصير
+
+382
+00:42:17,110 --> 00:42:21,630
+مالة finite أربع عناصر ستة عناصر عشرين عنصر حسب
+
+383
+00:42:21,630 --> 00:42:27,110
+قيمة N طيب تعريف التانيبقول ال order of an element
+
+384
+00:42:27,110 --> 00:42:31,850
+g اللي موجود في g is the smallest positive integer
+
+385
+00:42:31,850 --> 00:42:37,870
+in such that ال g n بده يساوي ايه وحدله نفس الرمز
+
+386
+00:42:37,870 --> 00:42:41,750
+ال order لل element g بده يساوي مين؟ بده يساوي ال
+
+387
+00:42:41,750 --> 00:42:46,770
+n استنى شويةطيب انا افترض بقدر اللائك باش كباش
+
+388
+00:42:46,770 --> 00:42:52,290
+تعنصر من ال group مين ما كان يسميته ايه؟ رفعتله أس
+
+389
+00:42:52,290 --> 00:42:57,850
+عشرين لجيته ال identity element إذا ال order لإيه
+
+390
+00:42:57,850 --> 00:43:05,060
+يساوي عشرين؟قد يكون وقد لا يكون كيف قد يكون؟ احنا
+
+391
+00:43:05,060 --> 00:43:08,600
+قلين the smallest positive integer يمكن في رقم تحت
+
+392
+00:43:08,600 --> 00:43:13,320
+العشرين زي عشرة يكون A أُس عشرة يسوى ال identity
+
+393
+00:43:13,320 --> 00:43:17,600
+فإن كان A أُس عشرة يسوى ال identity إذا A أُس
+
+394
+00:43:17,600 --> 00:43:20,720
+عشرين يسوى ال identity A أُس تلاتين يسوى ال
+
+395
+00:43:20,720 --> 00:43:26,800
+identity A أُس خمسين يبقى أصغر رقم إن بحطه كأس
+
+396
+00:43:26,800 --> 00:43:30,990
+لهذا ال element بده يعطيه ال identityان حدث ذلك
+
+397
+00:43:30,990 --> 00:43:35,150
+يبقى هذا الاص هو ال order تبع من؟ تبع هذا ال
+
+398
+00:43:35,150 --> 00:43:39,190
+element يبقى لو قال show that the element of this
+
+399
+00:43:39,190 --> 00:43:45,410
+element is كزواطن رقم تمام احط اص لهذا الرقم يطلع
+
+400
+00:43:45,410 --> 00:43:50,040
+ال identity ماقدرش اقولهذا هو ال order يا ال order
+
+401
+00:43:50,040 --> 00:43:55,380
+يا أقل منه إذا بدأ أستبعد اللي أقل منه يبقى إجباري
+
+402
+00:43:55,380 --> 00:43:59,080
+بيصير هذا ياش هذا هو ال order و هنشوف هذا الكلام
+
+403
+00:43:59,080 --> 00:44:05,000
+من خلال المسائل يبقى بديك تعرف أن ال order لهذا ال
+
+404
+00:44:05,000 --> 00:44:11,040
+element أقل عدد صحيح موجب بحط أس لهذا ال element
+
+405
+00:44:11,040 --> 00:44:15,490
+بتنميةالـ Identity اللى جيت غيره ماليش علاقة فيهم
+
+406
+00:44:15,490 --> 00:44:21,630
+و قدام شوية هنقول لك ان ال order هذا بيقسم اي رقم
+
+407
+00:44:21,630 --> 00:44:25,490
+تاني يحطه كاسئوله و يعطينا ال identity ما علينا
+
+408
+00:44:25,490 --> 00:44:29,870
+لسه بعيد عننا شوية يبقى باجي بقول ال order لل
+
+409
+00:44:29,870 --> 00:44:36,290
+element U هو اصغر smallest و positive integer in
+
+410
+00:44:36,290 --> 00:44:40,290
+such that g to the power n بده يساوي ال ايه و حدله
+
+411
+00:44:40,290 --> 00:44:46,630
+الرمزجي بين خطين وقول الرمز هذا يقرأ ال order لجي
+
+412
+00:44:46,630 --> 00:44:50,690
+وليس ال absolute value لجي absolute للكل كلاص مش
+
+413
+00:44:50,690 --> 00:44:54,930
+للجبر يبقى هنا بنقول اه بنقول ال order لجي يساوي
+
+414
+00:44:54,930 --> 00:45:00,230
+مين؟ يساوي ال n طيب ممكن ل group زي ما شوفنا في
+
+415
+00:45:00,230 --> 00:45:05,160
+الأمثل على group تبقى العملية عملية جامعةطب لو
+
+416
+00:45:05,160 --> 00:45:10,780
+كانت عملية جمع إيش بصير شكل هذا ال element يبقى لو
+
+417
+00:45:10,780 --> 00:45:14,520
+كانت ال operation على G هو الجمع إذا ال element
+
+418
+00:45:14,520 --> 00:45:19,320
+هذا بيصير in G يساوي ال identity element تحت عملية
+
+419
+00:45:19,320 --> 00:45:23,140
+الجمع اللي هو main اللي هو ال zero يبقى ال G to
+
+420
+00:45:23,140 --> 00:45:26,840
+the power in يساوي ال identity بترجم إلى in G
+
+421
+00:45:26,840 --> 00:45:31,480
+يساوي main ال zero بشرط تبقى العملية المعرفة على
+
+422
+00:45:31,480 --> 00:45:36,980
+ال groupهي عملية الجامعة العادية طيب بداج ال
+
+423
+00:45:36,980 --> 00:45:41,900
+identity element ايه بدى اعرف قداش ال order اصغر
+
+424
+00:45:41,900 --> 00:45:46,220
+رقم بحطه لل ايه بطلع ال ايه مين واحد يساوي ايه
+
+425
+00:45:46,220 --> 00:45:50,880
+واحد يساوي مين واحد اذا ال order لأي identity
+
+426
+00:45:50,880 --> 00:45:53,600
+element مهما كان شكل ال group
+
+427
+00:46:11,020 --> 00:46:19,800
+لو لم أجد عدد صحيح فأضعه كأسلجي يعطينا ال identity
+
+428
+00:46:19,800 --> 00:46:25,040
+elementيقول جي أس مية ما طلعش ال identity element
+
+429
+00:46:25,040 --> 00:46:29,100
+يقول جي أس مليون ما طلعش ال identity كل ما يجي
+
+430
+00:46:29,100 --> 00:46:32,740
+ذالي رقم ما يطلعش ال identity element يبقى في هذه
+
+431
+00:46:32,740 --> 00:46:37,820
+الحالة ال order لجي قدش بيكون على نهاية يبقى باجي
+
+432
+00:46:37,820 --> 00:46:42,880
+بقول ال element هذا is of infinite orderيبقى ال
+
+433
+00:46:42,880 --> 00:46:48,820
+order لهذا ال element بيكون infinite وقد تستغربوا
+
+434
+00:46:48,820 --> 00:46:53,000
+انه ممكن يكون و احنا بنشتغل هيك في ال groups
+
+435
+00:46:53,000 --> 00:46:57,720
+element اخده في ال group ال order له finite اتنين
+
+436
+00:46:57,720 --> 00:47:01,520
+تلاتة عشرة جد ما يكونوا element تاني ال order له
+
+437
+00:47:01,520 --> 00:47:07,120
+finite اضرب اتنين في بعض يطلع ال order infinite
+
+438
+00:47:09,630 --> 00:47:13,130
+طبعا انت مش تغربين لكن هنعطيكوا مثال ان شاء الله
+
+439
+00:47:13,130 --> 00:47:16,830
+نوضح فيه هذا الكلام يعني ان كان ال order لل
+
+440
+00:47:16,830 --> 00:47:21,470
+element finite و ال order التاني finite لو ضربت
+
+441
+00:47:21,470 --> 00:47:25,030
+اتنين في بعض بال operation start طلع element جديد
+
+442
+00:47:25,030 --> 00:47:29,910
+ال element جديد ليس بضرورة ان يكون finite و ربما
+
+443
+00:47:29,910 --> 00:47:36,270
+infinite و خاصة في موضوع المصفوفات طيب نبدأ ناخد
+
+444
+00:47:36,270 --> 00:47:42,220
+بعض الأمثلة على هذه التعريفمشان يثبت هذه المعلومات
+
+445
+00:47:42,220 --> 00:47:50,340
+ولو على الأقل مثالا واحدا يبقى examples أول مثال
+
+446
+00:47:50,340 --> 00:47:59,440
+بيقول ال let ال G يساوي U خمستاشر يبقى بدنا عناصر
+
+447
+00:47:59,440 --> 00:48:05,120
+ال U خمستاشر شبه مين ال واحد والاتنين تلاتة منهم
+
+448
+00:48:05,960 --> 00:48:16,160
+الاربعة الخمسة الستة السبعة التمانية التسعة العشرة
+
+449
+00:48:16,160 --> 00:48:25,120
+الاحداشر اتناش تلاتاش وكمان اربعتاش يبقى هاي
+
+450
+00:48:25,120 --> 00:48:32,240
+كتبتله ال U خمستاش طيب بناء عليه ال order ل U
+
+451
+00:48:32,240 --> 00:48:38,520
+خمستاش انا بقول خمستاش ولا لألأ، وش جاب الخمسة؟ عد
+
+452
+00:48:38,520 --> 00:48:41,640
+العناصر واحد، اتنين، تلاتة، اربعة، خمسة، ستة،
+
+453
+00:48:41,640 --> 00:48:46,220
+سبعة، تمانية يبقى ال order اللي أجيبه يسوى تمانية
+
+454
+00:48:46,220 --> 00:48:53,560
+طيب، لو بد أجيب ال order للواحد كدهش؟
+
+455
+00:48:53,560 --> 00:48:57,500
+واحد، لأن هذا هو ال identity element يبقى ال order
+
+456
+00:48:57,500 --> 00:49:03,630
+للواحد يسوى واحد طب، بد ال order لليتنين؟شوف عاد
+
+457
+00:49:03,630 --> 00:49:07,570
+نضرب اتنين في نفسه كام مرة حتى يطلع عندى ال
+
+458
+00:49:07,570 --> 00:49:11,230
+identity element طبعا هنا عملية ضرب العادية اتنين
+
+459
+00:49:11,230 --> 00:49:19,370
+في اتنين في اتنين اساس ميارات في اتنين تمانية في
+
+460
+00:49:19,370 --> 00:49:24,070
+اتنين ستة عشر شيله هنا و خمسة عشر بضل اللي يقولوا
+
+461
+00:49:24,070 --> 00:49:29,400
+حد يبقى ال order اللي جديشأربعة يبقى ال order للي
+
+462
+00:49:29,400 --> 00:49:36,220
+اتنين يساوي اربعة because شو السبب انه اتنين اص
+
+463
+00:49:36,220 --> 00:49:42,660
+واحد يساوي اتنين اتنين تربية يساوي اتنين
+
+464
+00:49:42,660 --> 00:49:49,020
+تكيب يساوي تمانية اتنين اص اربعة يساوي ستاشر
+
+465
+00:49:49,020 --> 00:49:55,150
+modulo خمستاشر يبقى هذا الكلام يساوي واحدهذا بدي
+
+466
+00:49:55,150 --> 00:50:00,770
+اعطيك ان ال order للي اتنين هو اربعة طب ال order
+
+467
+00:50:00,770 --> 00:50:08,110
+لاربعة similarly ال order لاربعة بده يساوي اتنين
+
+468
+00:50:08,110 --> 00:50:13,750
+ليش لإنه اربعة في اربعة ستاشر موديله خمس تاشر اين
+
+469
+00:50:13,750 --> 00:50:17,870
+عم يبقى باتنين طيب لو روحتي و قولتلك ال order لي
+
+470
+00:50:17,870 --> 00:50:27,030
+سبعة بدنا نعرف في هذا كدهيبقى بالضبط سبعة اوس واحد
+
+471
+00:50:27,030 --> 00:50:30,290
+يساوي
+
+472
+00:50:30,290 --> 00:50:36,770
+سبعة هو سبعة تربيع يساوي تسعة واربعين موديولو
+
+473
+00:50:36,770 --> 00:50:43,200
+خمستاش خمستاش في تلاتة وخمسة واربعين يطلع أربعةطيب
+
+474
+00:50:43,200 --> 00:50:50,160
+لو جيت قولتلك سبعة تكيب يبقى يساوي سبعة مضروبة في
+
+475
+00:50:50,160 --> 00:50:55,770
+أربعة modulo خمستاشر أربعة في سبعةتمنية وعشرين
+
+476
+00:50:55,770 --> 00:50:57,190
+تمنية وعشرين تمنية وعشرين تمنية وعشرين تمنية
+
+477
+00:50:57,190 --> 00:51:01,690
+وعشرين تمنية وعشرين تمنية وعشرين تمنية تمنية تمنية
+
+478
+00:51:01,690 --> 00:51:06,870
+تمنية تمنية
+
+479
+00:51:06,870 --> 00:51:10,250
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+480
+00:51:10,250 --> 00:51:10,430
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+481
+00:51:10,430 --> 00:51:11,310
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+482
+00:51:11,310 --> 00:51:11,770
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+483
+00:51:11,770 --> 00:51:14,370
+تمنية تمنية تمنية تمنية تمنية تمنية تمنية تمنية
+
+484
+00:51:14,370 --> 00:51:21,670
+تمنية تمنية تمنية تيبقى بناء عليه ان ال order ل
+
+485
+00:51:21,670 --> 00:51:28,430
+سبعة بده يساوي قداش بده يساوي أربعة و هكذا طيب
+
+486
+00:51:28,430 --> 00:51:35,250
+التمانية تمانية في تمانية أربعة و ستين شيل الستين
+
+487
+00:51:35,250 --> 00:51:39,810
+لأنه مضاعف لخمساش تظل أربعة في تمانية باتنين و
+
+488
+00:51:39,810 --> 00:51:45,130
+تلاتين شيل تلاتين بظل اتنين في تمانية بستعش يبقى
+
+489
+00:51:45,130 --> 00:51:51,460
+ال order ل تمانية بقداش أربعةيبقى similarly كمان
+
+490
+00:51:51,460 --> 00:52:00,140
+ال order ل 8 بده يسوى كذلك 4 و هكذا طب خلينا نسأل
+
+491
+00:52:00,140 --> 00:52:06,740
+ال order ل 11 11
+
+492
+00:52:06,740 --> 00:52:14,040
+و 11 121 121 مش بتكسبها 15 لأنها بتكسبها 30 و 30
+
+493
+00:52:14,040 --> 00:52:20,250
+يبقىيبقى واحد يبقى ال order للإحداش هو اتنين و ال
+
+494
+00:52:20,250 --> 00:52:27,710
+order للإحداش بده يساوي اتنين فقط و هكذا يلا بنكمل
+
+495
+00:52:27,710 --> 00:52:29,070
+ان شاء الله بعد الظهر
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d554d7fe31c5f8f3c3bbb5297ab590012593423f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY.srt
@@ -0,0 +1,1707 @@
+1
+00:00:21,290 --> 00:00:25,550
+بسم الله الرحمن الرحيم نكمل chapter عشرة اللي كنا 
+
+2
+00:00:25,550 --> 00:00:30,790
+بنتحدث فيه المرة اللي فاتت وآخر مرة أعطينا نظرية
+
+3
+00:00:30,790 --> 00:00:34,710
+أو أول نظرية في الـ isomorphism vs isomorphism
+
+4
+00:00:34,710 --> 00:00:38,270
+theorem ثم أخدنا بعد ذلك كرولري عليها والآن
+
+5
+00:00:38,270 --> 00:00:42,690
+بنواصل في نفس الـ chapter في هنا مثال بيقول هاتلي 
+
+6
+00:00:42,690 --> 00:00:49,520
+كل الـ homomorphism من Z12 إلى Z13 يبقى بدي أقول 
+
+7
+00:00:49,520 --> 00:00:59,220
+الحلقة التالية solution assume افترض أن الـ Phi من
+
+8
+00:00:59,220 --> 00:01:09,720
+Z12 إلى Z13 هو homomorphism افترض أن هذا هو 
+
+9
+00:01:09,720 --> 00:01:15,260
+homomorphism وبدي أعرف ما هو شكل هذه الـ
+
+10
+00:01:15,260 --> 00:01:20,620
+homomorphism الآن شكل الـ homomorphism هو الـ Phi
+
+11
+00:01:20,620 --> 00:01:26,820
+يؤثر على element من مين؟ من Z12 الـ element هذا قد
+
+12
+00:01:26,820 --> 00:01:32,060
+يكون 0، قد يكون 1، 2، 3، لغاية 12، لغاية 12،
+
+13
+00:01:32,060 --> 00:01:37,160
+لو افترضنا خمسة ده أقول five of خمسة الخمسة بقدر
+
+14
+00:01:37,160 --> 00:01:40,280
+أكتبها 1 زائد 1 زائد 1 زائد 1 زائد
+
+15
+00:01:40,280 --> 00:01:42,800
+1 زائد 1 زائد 1 زائد 1 زائد 1 زائد
+
+16
+00:01:42,800 --> 00:01:43,280
+1 زائد 1 زائد 1 زائد 1 زائد 1 زائد
+
+17
+00:01:43,280 --> 00:01:43,400
+1 زائد 1 زائد 1 زائد 1 زائد 1 زائد
+
+18
+00:01:43,400 --> 00:01:47,960
+1 هي عملية الجمع إذا بقدر أقول مدام homomorphism
+
+19
+00:01:47,960 --> 00:01:50,960
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد 
+
+20
+00:01:50,960 --> 00:01:55,880
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+21
+00:01:55,880 --> 00:01:57,780
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+22
+00:01:57,780 --> 00:02:01,180
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+23
+00:02:01,180 --> 00:02:02,820
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+24
+00:02:02,820 --> 00:02:03,020
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+25
+00:02:03,020 --> 00:02:03,760
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+26
+00:02:03,760 --> 00:02:05,080
+Phi of 1 زائد Phi of 1 زائد Phi of 1 زائد
+
+27
+00:02:05,080 --> 00:02:10,530
+Phi of 1 زائد Phi of 1 إذا شكل الـ homomorphism اللي
+
+28
+00:02:10,530 --> 00:02:14,930
+عندنا لو عرفت ما هو شكل الـ five of one بكون عرفت
+
+29
+00:02:14,930 --> 00:02:23,210
+شكل مين؟ اللي هو شكل الـ homomorphism طيب we shall
+
+30
+00:02:24,890 --> 00:02:33,810
+Find نحاول أن نجد Form of Phi of 1 بدي أعرف إيه 
+
+31
+00:02:33,810 --> 00:02:40,390
+شكل Phi of 1 اللي عندنا هنا طيب كويس الآن Phi of 1
+
+32
+00:02:40,390 --> 00:02:46,730
+موجودة في Z12 ولا في Z13؟ في Z13 ممتاز جدا
+
+33
+00:02:46,730 --> 00:02:52,230
+يبقى الـ order لـ Phi of 1 بده يقسم الـ order
+
+34
+00:02:52,230 --> 00:02:56,650
+للواحد مش هيك؟ أخدنا الـ order للـ Phi of g بيقسم
+
+35
+00:02:56,650 --> 00:03:03,370
+الـ order للـ g لذلك بروح بقوله الـ order للـ Phi of
+
+36
+00:03:03,370 --> 00:03:10,990
+one divides الـ order للـ one الـ order للـ one قداش؟
+
+37
+00:03:15,020 --> 00:03:21,100
+معنى هذا الكلام أن الـ order لـ Phi of one بده
+
+38
+00:03:21,100 --> 00:03:26,880
+يساوي مدام يقسم 12 يبقى قد يكون 1 وقد يكون
+
+39
+00:03:26,880 --> 00:03:33,880
+2 وقد يكون 3، 4 طبعا و4 كذلك فتقسم
+
+40
+00:03:33,880 --> 00:03:41,060
+12، 5، 6، 12 يبقى كل هدول قواسمين الـ 12
+
+41
+00:03:41,060 --> 00:03:45,100
+جبتها من العلاقة الـ order لـ Phi of one divides
+
+42
+00:03:45,100 --> 00:03:53,660
+الـ order للـ one but ولكن الـ Phi of one هذا موجود
+
+43
+00:03:53,660 --> 00:04:00,840
+أين؟ في Z13 معناه هذا الكلام أن الـ order لـ Phi
+
+44
+00:04:00,840 --> 00:04:04,260
+of one divide Z13
+
+45
+00:04:06,850 --> 00:04:11,550
+يبقى معنى هذا الكلام أن الـ order للـ Phi of one
+
+46
+00:04:11,550 --> 00:04:16,830
+كذلك بدنا نشوف قواصم الـ 13 اللي هي 1 و2
+
+47
+00:04:16,830 --> 00:04:23,790
+و3 طبعا 4 لأ ولكن تجينا 5 و6 وعشرة
+
+48
+00:04:23,790 --> 00:04:31,370
+و15 و13 كل هدول قواسمين قواسم اللي هو
+
+49
+00:04:31,370 --> 00:04:37,930
+الـ 13 من الاتنين هدول مع بعض بقدر أستنتج أن الـ
+
+50
+00:04:37,930 --> 00:04:46,260
+order للـ Phi of 1 اللي هو بده يساوي 1 و2
+
+51
+00:04:46,260 --> 00:04:53,600
+و3 طبعا 4 و5 لأ أو 6 بهذا الشكل في غير 
+
+52
+00:04:53,600 --> 00:04:59,720
+هيك؟ ما فيش يبقى هذه القواسم المشتركة ما بين الـ two
+
+53
+00:04:59,720 --> 00:05:05,160
+orders يبقى كل احتمالات الممكنة للـ order للـ Phi of 1
+
+54
+00:05:05,160 --> 00:05:12,390
+أن يكون 1 و2 و3 وكذلك مين؟ وكذلك 6
+
+55
+00:05:12,390 --> 00:05:18,010
+هي العناصر أو هي الأعداد أو الأرقام المشتركة ما
+
+56
+00:05:18,010 --> 00:05:22,450
+بين النقطة الأولى والنقطة الثانية طيب Phi of one
+
+57
+00:05:22,450 --> 00:05:27,210
+احنا بنقول هذه قبل قليل موجودة وين؟ في Z13
+
+58
+00:05:27,210 --> 00:05:32,150
+إذا بروح في Z13 سهل جدا أدور على العناصر
+
+59
+00:05:32,150 --> 00:05:34,570
+اللي الـ order إلها بده يساوي مين؟
+
+60
+00:05:39,930 --> 00:05:45,210
+معنى هذا الكلام أن الـ Phi of one قد يكون الـ one
+
+61
+00:05:45,210 --> 00:05:51,810
+مظبوط لأن الـ one الـ order عليه عفوا ستكون الـ zero
+
+62
+00:05:51,810 --> 00:05:57,600
+وليس الـ one قد يكون الـ zero تمام يبقى Phi of one
+
+63
+00:05:57,600 --> 00:06:02,280
+قد يكون zero ليش؟ لأن الـ order للـ zero سيكون كم؟
+
+64
+00:06:02,280 --> 00:06:07,000
+1 طب مين الـ element اللي الـ order له يساوي
+
+65
+00:06:07,000 --> 00:06:13,020
+2؟ هل يوجد غير الـ 7 هذا؟ لأ يبقى zero أو
+
+66
+00:06:13,020 --> 00:06:18,900
+7 نجي للثلاثة مين العناصر اللي الـ order لها
+
+67
+00:06:18,900 --> 00:06:24,460
+يساوي 3 في Z13؟ مين؟ 4 طب و 9؟
+
+68
+00:06:25,460 --> 00:06:31,520
+وكمان 3 لأن الـ order للـ 9 هو 3 والـ order
+
+69
+00:06:31,520 --> 00:06:36,040
+للـ 3 كذلك هو 3 ضايل عليه باسمين الـ order
+
+70
+00:06:36,040 --> 00:06:43,180
+اللي هو 6 مين العنصر الـ order يساوي 6؟ 5 ماشي
+
+71
+00:06:43,180 --> 00:06:50,340
+موافقين؟ طيب في غيره هذا بالمرة؟ طيب 6 في 5
+
+72
+00:06:50,340 --> 00:06:51,440
+وعشرين بقداش؟
+
+73
+00:06:54,600 --> 00:06:58,200
+ما هي أو 5 مضاعفات الـ 13 ولا لا؟ يبقى الـ 5
+
+74
+00:06:58,200 --> 00:07:05,280
+و7 منهم يبقى الـ 5 و7 في غيرهم؟ امسك كل
+
+75
+00:07:05,280 --> 00:07:09,940
+عناصر الـ Z13 ما تجد إلا عناصر هذه الـ order
+
+76
+00:07:09,940 --> 00:07:14,940
+اللي هي 1، الـ order 2 هدول 2، 3 هذا
+
+77
+00:07:14,940 --> 00:07:20,350
+اللي هو الـ 6 يبقى هي العناصر كم واحدة دول؟ 4
+
+78
+00:07:20,350 --> 00:07:26,370
+و6 يعني معناته كم homomorphism يكون عندنا؟ 6 
+
+79
+00:07:26,370 --> 00:07:38,710
+homomorphism يبقى هنا إذا نحن لدينا 6 homomorphism من
+
+80
+00:07:38,710 --> 00:07:45,850
+Z12 إلى Z13 يبقى بدي اسميه Phi 1 of x بدي أساوي قداش؟
+
+81
+00:07:45,850 --> 00:07:53,930
+zero الثاني بده يسمى Phi 2 of x يساوي 7 x
+
+82
+00:07:53,930 --> 00:08:01,970
+الثالث اللي هو Phi 3 of x بده يساوي 4 x
+
+83
+00:08:01,970 --> 00:08:09,740
+الرابع x وده 7 x الآن الـ Phi 4 of x
+
+84
+00:08:09,740 --> 00:08:17,560
+بده يساوي كده؟ بده يساوي 9 x Phi 5 of x بده
+
+85
+00:08:17,560 --> 00:08:25,640
+يساوي 5 x والآن Phi of .. والله Phi 6 of x بده
+
+86
+00:08:25,640 --> 00:08:30,660
+يساوي 3 x يبقى هذه الـ 6 homomorphisms
+
+87
+00:08:31,360 --> 00:08:36,440
+اللي عندنا اللي استطعنا نستنتجهم من خلال معرفتنا
+
+88
+00:08:36,440 --> 00:08:41,200
+لشكل الـ Phi 1 يبقى هدول جبناهم من وين؟ جبناهم
+
+89
+00:08:41,200 --> 00:08:45,240
+الكلام اللي جالينه احنا إنه Phi of x تساوي الـ x في
+
+90
+00:08:45,240 --> 00:08:51,080
+Phi of 1 يبقى شيلت قيمة كل Phi of 1 وحطيت قيمتها
+
+91
+00:08:51,080 --> 00:08:56,380
+هنا وبالتالي حصلت على مين؟ على الـ 6 homomorphisms
+
+92
+00:08:56,380 --> 00:09:04,110
+اللي عندنا تبعات هذه الـ group نبدأ نيجي لآخر نظرية
+
+93
+00:09:04,110 --> 00:09:12,410
+في هذا الـ section بتقول ما يأتي theorem every
+
+94
+00:09:12,410 --> 00:09:22,810
+normal subgroup of
+
+95
+00:09:22,810 --> 00:09:23,570
+a group
+
+96
+00:09:30,050 --> 00:09:41,470
+G any group G is the kernel is the kernel of a
+
+97
+00:09:41,470 --> 00:09:50,650
+homomorphism of a homomorphism of g in particular
+
+98
+00:09:50,650 --> 00:09:58,110
+in
+
+99
+00:09:58,110 --> 00:10:06,000
+particular a normal subgroup بقى a normal subgroup
+
+100
+00:10:06,000 --> 00:10:09,020
+بدي
+
+101
+00:10:09,020 --> 00:10:14,580
+أعطيها الرمز n a normal subgroup is the kernel is
+
+102
+00:10:14,580 --> 00:10:25,520
+the kernel of the mapping kernel of the mapping
+
+103
+00:10:26,970 --> 00:10:36,010
+اللي هو Phi من G إلى G modular N given by ..
+
+104
+00:10:36,010 --> 00:10:46,010
+given by Phi of G بدي أساوي G في الـ N
+
+105
+00:10:59,320 --> 00:11:04,200
+نجي لنفس النظرية مرة ثانية يبقى النظرية مرة ثانية
+
+106
+00:11:04,200 --> 00:11:10,080
+بتقول every normal subgroup of a group G is the
+
+107
+00:11:10,080 --> 00:11:15,260
+kernel of a homomorphism of G يعني لو عندي normal
+
+108
+00:11:15,260 --> 00:11:19,940
+subgroup من a group G والـ G عليها homomorphism
+
+109
+00:11:19,940 --> 00:11:24,400
+لازم يكون الـ normal subgroup اللي عندنا هي kernel
+
+110
+00:11:24,400 --> 00:11:30,150
+لواحد من الـ homomorphism قلنا نعطيك توضيح
+
+111
+00:11:30,150 --> 00:11:35,050
+in particular كمثال على ذلك لو كانت الـ N هي normal
+
+112
+00:11:35,050 --> 00:11:40,670
+subgroup يبقى الـ N هي الـ kernel للـ function Phi من
+
+113
+00:11:40,670 --> 00:11:45,830
+G إلى G modulo N والتي تُعطى بالشكل التالي Phi of
+
+114
+00:11:45,830 --> 00:11:50,270
+G يساوي left coset من الـ factor group اللي عندنا
+
+115
+00:11:50,270 --> 00:12:00,200
+اللي هو من GN بدنا نحاول نثبت بعد ما نفرض أن الـ N
+
+116
+00:12:00,200 --> 00:12:05,220
+is a normal subgroup من G بدنا نحاول نحسب الـ
+
+117
+00:12:05,220 --> 00:12:11,660
+kernel لهذه الـ Phi ونثبت إنه مين؟ اللي هو الـ
+
+118
+00:12:11,660 --> 00:12:16,400
+subgroup اللي عندنا بالضبط تماما هذه يبقى بأجي
+
+119
+00:12:16,400 --> 00:12:21,320
+بقوله أول شيء بدي أبرهن أن هذا homomorphism وبعد
+
+120
+00:12:21,320 --> 00:12:25,640
+هيك بدي أروح أجيب الـ kernel له يبقى بأجي
+
+121
+00:12:25,640 --> 00:12:30,240
+بقوله Phi is homomorphism هذا اللي بدي أروح إيه
+
+122
+00:12:30,240 --> 00:12:37,840
+أثبته لذلك لو روحت أخدت Phi of G1 G2 يبقى حسب
+
+123
+00:12:37,840 --> 00:12:48,240
+التعريف اللي عندنا بيصير G1 G2 في N طيب ليش؟ لأنها
+
+124
+00:12:48,240 --> 00:12:51,180
+normal لو ما كانتش normal اللي بصي كلامك مش صحيح
+
+125
+00:12:51,180 --> 00:13:00,160
+يبقى هذا الكلام بده يساوي G1 N في G2 N السبب في 
+
+126
+00:13:00,160 --> 00:13:07,880
+ذلك since  الـ N is a normal subgroup من G هذه هي الـ
+
+127
+00:13:07,880 --> 00:13:14,860
+Main لـ Phi of G1 وهذه Phi of G2 لذلك Phi
+
+128
+00:13:14,860 --> 00:13:22,340
+Homomorphism نحسب الـ Kernel لهذا الـ Phi يبقى هو
+
+129
+00:13:22,340 --> 00:13:30,090
+كل الـ X الموجودة في الـ Group G بحيث أن اللي هو
+
+130
+00:13:30,090 --> 00:13:36,390
+Phi of X بده يساوي ال identity element تبع ال G
+
+131
+00:13:36,390 --> 00:13:43,090
+modulo N يبقى هذا الكلام كل ال X اللي موجودة في ال
+
+132
+00:13:43,090 --> 00:13:48,170
+group G such that ال Phi of X اللي هي مين عندنا ال
+
+133
+00:13:48,170 --> 00:13:54,090
+X N بده يساوي ال identity element تبع ال factor
+
+134
+00:13:54,090 --> 00:14:00,910
+group هذي اللي هو مين من الـ identity هنا؟ N كويس
+
+135
+00:14:00,910 --> 00:14:06,230
+يبقى مادام N هذا شو معناه اللي بقول X N يساوي ال N
+
+136
+00:14:06,230 --> 00:14:11,550
+هذا الكلام صحيح إذا ال X موجودة في ال N يبقى هذا
+
+137
+00:14:11,550 --> 00:14:19,210
+اللي هو كل ال X اللي موجودة في G such that ال X 
+
+138
+00:14:19,210 --> 00:14:25,430
+موجودة في ال N يبقى هذا بدي يسوي ال in itself يبقى
+
+139
+00:14:25,430 --> 00:14:28,750
+معنى هذا الكلام الكيرني لهذا ال function هو عبارة
+
+140
+00:14:28,750 --> 00:14:33,530
+عن مين؟ عن ال normal subgroup اللي عمناه الآن في
+
+141
+00:14:33,530 --> 00:14:39,650
+two definitions آخر two definitions بيقول الأول ما
+
+142
+00:14:39,650 --> 00:14:47,530
+يأتي definition let ال h be a subgroup من ال group
+
+143
+00:14:47,530 --> 00:14:53,860
+G يبقى هذا الـ sub-group من مين؟ من جيه الـ
+
+144
+00:14:53,860 --> 00:14:55,940
+Normalizer of
+
+145
+00:15:13,820 --> 00:15:17,340
+الشكل التالي هو
+
+146
+00:15:34,250 --> 00:15:44,750
+وبدنا نعرف التعريف الثاني and the centralizer يا
+
+147
+00:15:44,750 --> 00:15:55,570
+رحمكم الله and the centralizer of H in G is defined
+
+148
+00:15:55,570 --> 00:16:03,940
+by بنروح نعرفه على الشكل التالي الـ Centralizer للـ
+
+149
+00:16:03,940 --> 00:16:11,700
+H وكل الـ X اللي موجودة في G such that بحيث أن الـ
+
+150
+00:16:11,700 --> 00:16:19,560
+X H X inverse بده يساوي H itself لكل الـ H اللي
+
+151
+00:16:19,560 --> 00:16:26,680
+موجودة في ال subgroup H example
+
+152
+00:16:34,430 --> 00:16:42,450
+لت الـ H be a sub group من G define a mapping
+
+153
+00:16:42,450 --> 00:16:50,810
+define a mapping define
+
+154
+00:16:50,810 --> 00:16:58,490
+a mapping ابسعي من ال normalizer بتبع ال H إلى ال
+
+155
+00:16:58,490 --> 00:17:06,790
+inner automorphism الـ Inner Automorphism لمن؟ للـ
+
+156
+00:17:06,790 --> 00:17:20,490
+H باي إبساي of X بده يساوي فاي X where حيث الفاي X
+
+157
+00:17:20,490 --> 00:17:33,600
+من الـ H إلى H is defined by as defined by five X
+
+158
+00:17:33,600 --> 00:17:45,700
+of H بده يساوي ال X H X inverse لكل ال H اللي
+
+159
+00:17:45,700 --> 00:17:53,880
+موجودة في capital H السؤال هو show that بيلي انه
+
+160
+00:17:54,950 --> 00:18:03,050
+النقطة الأولى إبساي is a homomorphism النقطة
+
+161
+00:18:03,050 --> 00:18:07,190
+الثانية بدنا
+
+162
+00:18:07,190 --> 00:18:17,090
+نثبت إن كيرنل للإبساي بد سواء ال centralizer of
+
+163
+00:18:17,090 --> 00:18:18,850
+H in G
+
+164
+00:19:09,240 --> 00:19:13,520
+نعود للتعريف اللى بين أيدنا هذا مرة تانية احنا
+
+165
+00:19:13,520 --> 00:19:18,240
+خدنا الـcentralizer لل element لكن ما خدناهوش لل
+
+166
+00:19:18,240 --> 00:19:22,220
+subgroup خدنا ال normalizer لل element لكن لل
+
+167
+00:19:22,220 --> 00:19:29,640
+subgroup ومن هنا بدنا نجي نعطي تعريف لل centralizer
+
+168
+00:19:29,640 --> 00:19:34,680
+لل subgroup H وال normalizer كذلك لل subgroup H
+
+169
+00:19:34,680 --> 00:19:39,680
+التعريف بقول ما ياتي the normalizer of subgroup H
+
+170
+00:19:39,680 --> 00:19:45,220
+اللي أخدناها منجي هو عبارة عن the set of all
+
+171
+00:19:45,220 --> 00:19:49,940
+elements x اللي belongs to G such that ال X H X
+
+172
+00:19:49,940 --> 00:19:55,460
+inverse بده يسوى من ال H يعني كل العناصر اللي
+
+173
+00:19:55,460 --> 00:20:01,460
+موجودة في G والتي تحقق هذه المعادلة بتكون هي عناصر
+
+174
+00:20:01,460 --> 00:20:06,820
+ال normalizer شو هذه العناصر هذه لو ضربتها في H من
+
+175
+00:20:06,820 --> 00:20:11,040
+جهة الشمال لو ضربت معكوسها في H من جهة الجميل تبقى
+
+176
+00:20:11,040 --> 00:20:17,940
+ال H كما هي إن حدث ذلك يبقى كل هذه العناصر بتعطين
+
+177
+00:20:17,940 --> 00:20:24,040
+إيمان الـ Normalizer طب السؤال هو هل ال identity
+
+178
+00:20:24,040 --> 00:20:28,180
+element موجود في ال normalizer؟ نعم ليش؟ ال
+
+179
+00:20:28,180 --> 00:20:32,980
+identity المعكوس تبع هو نفسه اضربه في ال subgroup
+
+180
+00:20:32,980 --> 00:20:36,840
+يمين و الله شمال تبقى ال subgroup كما هي لإن ال
+
+181
+00:20:36,840 --> 00:20:41,850
+identity موجود وراموجود في الـ H itself وبالتالي
+
+182
+00:20:41,850 --> 00:20:46,330
+أبسط حاجة عند ال identity element موجود في ال
+
+183
+00:20:46,330 --> 00:20:51,330
+normalizer أو أحد عناصر منه ال normalizer تعني دي
+
+184
+00:20:51,330 --> 00:20:55,330
+لل centralizer تبع ال subgroup H في G بنعرفه
+
+185
+00:20:55,330 --> 00:21:01,660
+كالتالي بارضه كل العناصر اللي موجودة في X بس عنا X
+
+186
+00:21:01,660 --> 00:21:07,960
+H X inverse بدي سوى mean H لكل ال H اللي موجودة في
+
+187
+00:21:07,960 --> 00:21:14,340
+H او ممكن اصيغ هذا مرة تانية و اقول لو ضربت في X
+
+188
+00:21:14,340 --> 00:21:21,600
+من جهة اليمين H بصير ال XH بدي يسوى مين؟ HX يعني كل
+
+189
+00:21:21,600 --> 00:21:29,300
+العناصر اللى موجودة في في G و اللى بتبقى commutes
+
+190
+00:21:29,300 --> 00:21:35,040
+مع جميع عناصر H بلا استثناء فلما أقول XH بقدر أقول
+
+191
+00:21:35,040 --> 00:21:42,500
+يسوى HX يبقى كل ال X's اللى موجودة في G و commutes مع
+
+192
+00:21:42,500 --> 00:21:47,720
+جميع عناصر H بلا استثناء اذا هذا يختلف عن هذا ولو
+
+193
+00:21:47,720 --> 00:21:53,840
+انه في ظاهره كأنه هو لكن لو بدأجي اطبق هذا عمليا
+
+194
+00:21:53,840 --> 00:22:01,540
+بقول X H X inverse بقولش H بقول H one يعني element
+
+195
+00:22:01,540 --> 00:22:06,360
+تاني ليس بالضرورة يكون نفس ال element بس هنا نفس
+
+196
+00:22:06,360 --> 00:22:10,470
+ال element بالضبط تمام الآن الـ Centralizer جاء من
+
+197
+00:22:10,470 --> 00:22:14,850
+كلمة Center المركز و احنا عرفنا الـ Center كل
+
+198
+00:22:14,850 --> 00:22:18,910
+العناصر الـ commutes مع مين مع جميع العناصر إذا
+
+199
+00:22:18,910 --> 00:22:23,410
+هنا جبنا الـ Center للجروب و جبنا الـ
+
+200
+00:22:23,410 --> 00:22:26,850
+Centralizer ل element في الجروب بس هنا الـ
+
+201
+00:22:26,850 --> 00:22:31,250
+Centralizer لل subgroup كله يبقى كل ال X اللي
+
+202
+00:22:31,250 --> 00:22:36,070
+موجود في G و الذي يحقق المعادل X H X inverse بدي
+
+203
+00:22:36,070 --> 00:22:41,700
+سوى من؟ بدي سوى H مثال يرتبط بالاتنين هذول بيقول خد
+
+204
+00:22:41,700 --> 00:22:47,100
+الاتش subgroup وعرفلي ده لإبساى من ال normalizer
+
+205
+00:22:47,100 --> 00:22:52,980
+لل inner automorphism لجي باي إبساى of X يبقى هذا
+
+206
+00:22:52,980 --> 00:22:57,420
+normalizer عناصر اللي فيه يقول بدي أقول إبساى of X
+
+207
+00:22:57,420 --> 00:23:02,520
+بدي اوديها وين؟ على ال inner ال inner هذا كل
+
+208
+00:23:02,520 --> 00:23:06,240
+العناصر اللي فيها عبارة عن functions و ال
+
+209
+00:23:06,240 --> 00:23:11,400
+functions هذه بتحقق العلاقة اللي عندنا هذه يبقى ال
+
+210
+00:23:11,400 --> 00:23:14,780
+inner عبارة عن في اكس من ال group او من ال sub
+
+211
+00:23:14,780 --> 00:23:19,540
+group الى نفسها بحيث ان ال a في اكس of h بده سوى
+
+212
+00:23:19,540 --> 00:23:22,960
+ال x اتش انفرطة خدناها قبل هيك يعني مش جديدة علينا
+
+213
+00:23:22,960 --> 00:23:29,710
+لكل ال h اللي موجود في g إذا إبساى of X بدي ساوي في
+
+214
+00:23:29,710 --> 00:23:35,770
+X قال يبينلي إن إبساى is a homomorphism يبقى بدروح
+
+215
+00:23:35,770 --> 00:23:43,560
+أثبتله من الخطوة الأولى يبقى ل proof و بدي اخد
+
+216
+00:23:43,560 --> 00:23:50,740
+النقطة الأولى بدي اخد a psi of حاصل ضرب to elements
+
+217
+00:23:50,740 --> 00:23:56,400
+حسب ال operation اللي موجود عالميا على g يبقى هذا
+
+218
+00:23:56,400 --> 00:24:04,020
+الكلام بده يساوي phi x y حسب التعريف تمام؟ طيب
+
+219
+00:24:04,020 --> 00:24:08,860
+سيبلي هذه على الشكة و بدنا نرجع لها بعد قليل لو
+
+220
+00:24:08,860 --> 00:24:16,860
+جيت قولتلك في x y as a function of h ايش بدي
+
+221
+00:24:16,860 --> 00:24:24,020
+اعطيني؟ حسب التاريف x y h x y inverse يعني هذا
+
+222
+00:24:24,020 --> 00:24:31,360
+الكلام يعني x y h y inverse x inverse بالشكل اللي
+
+223
+00:24:31,360 --> 00:24:37,530
+عندنا هذا الآن هذا بده اعتبره كله element واحد يبقى
+
+224
+00:24:37,530 --> 00:24:41,130
+لو اعتبرته كله element واحد بيصير هذا
+
+225
+00:24:48,320 --> 00:24:56,820
+اللي هو H Y inverse هذا الكلام بدي يساوي في X of
+
+226
+00:24:56,820 --> 00:25:03,280
+هذا كله اللي هو عبارة عن اين في Y as a function of
+
+227
+00:25:03,280 --> 00:25:10,910
+X يعني هذا بالضبط هو في X composition في Y كله as a
+
+228
+00:25:10,910 --> 00:25:16,810
+function of x لذلك كان عندنا مين؟ كان عندنا f psi
+
+229
+00:25:16,810 --> 00:25:26,610
+of x y بيسوي في x y يسوي يبقى في x y هو في x في
+
+230
+00:25:26,610 --> 00:25:33,470
+مين؟ في في y طب فاي إكس حسب ال definition لإب ساي
+
+231
+00:25:33,470 --> 00:25:38,930
+of إكس و الفاي of واي يبقى هي إب ساي of واي لذلك
+
+232
+00:25:38,930 --> 00:25:46,230
+الإب ساي is a homomorphism يبقى سائل إب ساي is a
+
+233
+00:25:46,230 --> 00:25:51,330
+homomorphism أنت هنا من النقطة الأولى النقطة
+
+234
+00:25:51,330 --> 00:25:56,050
+الثانية قال يحسب لل kernel تبع هذا الإبصاى يبقى
+
+235
+00:25:56,050 --> 00:26:01,070
+باجي بقوله ال kernel بتبع الإبصاى هو
+
+236
+00:26:06,680 --> 00:26:14,900
+يبقى كل الـ X الموجودة في Normalizer للـ H بحيث أن
+
+237
+00:26:14,900 --> 00:26:21,540
+صورتها Epsi of X بده يساوي الـ Identity Element
+
+238
+00:26:21,540 --> 00:26:27,200
+تبع الـ Inner طب شكل ال function في ال inner هيك أو
+
+239
+00:26:27,200 --> 00:26:32,220
+بمعنى أخر هيك يبقى ياش بد يكون ال identity تبع ال
+
+240
+00:26:32,220 --> 00:26:38,080
+inner هو مين ال inner نفسه مين ال inner نفسه هذا؟
+
+241
+00:26:38,990 --> 00:26:47,930
+هو ليس هو فاي اي ليش انه فاي اي of X فاي اي of X
+
+242
+00:26:47,930 --> 00:26:54,590
+بديساوي E H X inverse اللي هيعطيك ال H itself يبقى
+
+243
+00:26:54,590 --> 00:26:59,550
+هذا وعملتها لكوا قبل هيك أكتر من مرة عدة مرات يبقى
+
+244
+00:26:59,550 --> 00:27:05,190
+Psi of X بديساوي مين؟ فاي اي طب هذا الكلام بديساوي
+
+245
+00:27:05,190 --> 00:27:10,580
+مين؟ بتساوي كل العناصر اللي موجودة في الـ
+
+246
+00:27:10,580 --> 00:27:16,960
+Normalizer للـ H بحيث ان ال Epsilon of X هي مين
+
+247
+00:27:16,960 --> 00:27:26,630
+فاي X بتساوي فاي E أو بمعنى آخر هذه كل العناصر X
+
+248
+00:27:26,630 --> 00:27:33,910
+اللي موجودة في ال Normalizer للـH بحيث أن فاي X of
+
+249
+00:27:33,910 --> 00:27:40,830
+H بدها تساوي فاي E of H لكل الـH اللي موجود في
+
+250
+00:27:40,830 --> 00:27:46,670
+الـH بلا استثناء ليش عملت هك؟ لأن فاي X أصلا من
+
+251
+00:27:46,670 --> 00:27:52,320
+من؟ من الـH إلى الـH أو من الـH إلى الـH itself هذا
+
+252
+00:27:52,320 --> 00:27:56,940
+الكلام بده يساوي كل العناصر اللي موجودة في الـ
+
+253
+00:27:56,940 --> 00:28:04,160
+Normalizer للـ H بحيث أن الـ X H X Inverse بده 
+
+254
+00:28:04,160 --> 00:28:10,160
+يساوي الـ E H E Inverse لكل الـ H اللي Belongs to
+
+255
+00:28:10,160 --> 00:28:16,260
+The H أو بمعنى آخر كل الـ X اللي موجودة في الـ
+
+256
+00:28:16,260 --> 00:28:22,480
+Normalizer اللي موجودة في الـ Normalizer للـ H بحيث
+
+257
+00:28:22,480 --> 00:28:29,360
+أن الـ X H X inverse يساوي هذي كلها بقداش؟ بـ H
+
+258
+00:28:29,360 --> 00:28:35,330
+لكل الـ H اللي موجود وان في H، السؤال هو طلع لي في
+
+259
+00:28:35,330 --> 00:28:40,450
+تعريف الـcentralizer كل العناصر اللي موجودة في جيب
+
+260
+00:28:40,450 --> 00:28:46,890
+بحيث تحقق هذه العلاقة إذا هذا يعتبر الـmain يعتبر 
+
+261
+00:28:46,890 --> 00:28:51,830
+الـcentralizer لمن؟ لـH يبقى هذا يعتبر
+
+262
+00:28:51,830 --> 00:28:59,930
+الـcentralizer لمن؟ لـH وهو المقلوب طبعاً بالنخاطر
+
+263
+00:28:59,930 --> 00:29:05,520
+حلينا احنا هيك انتهينا بنحلها كمان أكمل سؤال من
+
+264
+00:29:05,520 --> 00:29:08,260
+مسائل التمرين
+
+265
+00:29:52,800 --> 00:30:00,460
+خذ يا للسؤال التالي اللي هو السؤال أربعة عشر من
+
+266
+00:30:00,460 --> 00:30:12,960
+التمرين بقول X plane X plane Y اللي هو في من زد
+
+267
+00:30:12,960 --> 00:30:26,550
+إثنا عشر إلى زد عشرة defined by defined by phi of x
+
+268
+00:30:26,550 --> 00:30:36,310
+يساوي ثلاثة x phi of x يساوي ثلاثة x is not a
+
+269
+00:30:36,310 --> 00:30:42,610
+homomorphism اثبت لي ليش هذه ما هي homomorphism
+
+270
+00:30:44,250 --> 00:30:48,310
+احنا أخذنا نظريات الهمومورفزم الأساسيات اللي هما
+
+271
+00:30:48,310 --> 00:30:52,670
+اثنتين واحدة فيها ست نقاط وواحدة فيها تسعة نقاط
+
+272
+00:30:52,670 --> 00:30:59,090
+يعني خمسة عشر نقطة وأثبتناهم عملياً لو جينا تناقض
+
+273
+00:30:59,090 --> 00:31:04,510
+بين هذا التعريف وأي نقطة من هذه التناقض بيبطل
+
+274
+00:31:04,510 --> 00:31:10,100
+يصير homomorphism، مظبوط؟ هو يدعى لماذا هذا اللي
+
+275
+00:31:10,100 --> 00:31:14,560
+عرفناه بشكل أنه هو homomorphism نقوله بسيطة تعال
+
+276
+00:31:14,560 --> 00:31:21,680
+نشوف إيش ممكن يتناقض معنا طبعاً احنا أخذنا اللي هو 
+
+277
+00:31:21,680 --> 00:31:22,600
+solution
+
+278
+00:31:24,720 --> 00:31:31,180
+أخذنا اللي هو main sentence فى of الـG to the
+
+279
+00:31:31,180 --> 00:31:39,320
+power N بده يساوي فى of G كله to the power N هذا
+
+280
+00:31:39,320 --> 00:31:49,580
+الكلام لكل الـN اللي موجودة في Z مش هذه الخاصية رقم
+
+281
+00:31:49,580 --> 00:31:56,220
+اثنين في أول نظرية تمام يبقى هذه الخاصية نشوف هل
+
+282
+00:31:56,220 --> 00:32:01,440
+هذه الخاصية تنطبق على الدعاء انه homomorphism ولا
+
+283
+00:32:01,440 --> 00:32:09,180
+لا ماشي نقوله ماشي خد لي مثلاً five of أربعة تكعيب
+
+284
+00:32:09,180 --> 00:32:16,000
+الأربعة موجودة في Z12 وحط لها أس in طبعاً ال
+
+285
+00:32:16,000 --> 00:32:20,560
+operation اللي على زد 12 هي عملية من جامعة يبقى الأس
+
+286
+00:32:20,560 --> 00:32:27,880
+هذا بتحول إلى يمين five of ثلاثة في أربعة مش أربعة
+
+287
+00:32:27,880 --> 00:32:31,400
+أس ثلاثة وإنما ثلاثة ضرب أربعة ثلاثة في أربعة
+
+288
+00:32:31,400 --> 00:32:39,200
+بقداش اثنا عشر تاني قداش zero طب أول خاصية من خواص ال
+
+289
+00:32:39,200 --> 00:32:44,300
+homomorphism أن ال identity هو صورة ال identity صح
+
+290
+00:32:44,300 --> 00:32:47,820
+ولا لأ يبقى ال five of zero يساوي قداش هدي مباشرة
+
+291
+00:32:47,820 --> 00:32:54,440
+قداش zero ال zero تبع مين زد عشرة وهذا هو ال zero
+
+292
+00:32:54,440 --> 00:33:00,320
+تبع مين تبع زد اثنا عشر هذا الفرق بينهم طيب تعال
+
+293
+00:33:00,320 --> 00:33:12,860
+خذ لي five of أربعة الكل تكعيب يساوي ثلاثة في فاي of
+
+294
+00:33:12,860 --> 00:33:21,680
+أربعة هذا الكلام يساوي ثلاثة فيه نجي لفاي of أربعة
+
+295
+00:33:21,680 --> 00:33:29,660
+اللي ثلاثة في أربعة يبقى هذا ثلاثة في أربعة اللي هو
+
+296
+00:33:29,660 --> 00:33:34,960
+بده يساوي ثلاثة في ثلاثة في أربعة في قداش اثنا عشر
+
+297
+00:33:34,960 --> 00:33:38,720
+هذه في الأول ولا في الثانية في الثانية مادام في
+
+298
+00:33:38,720 --> 00:33:43,580
+الثانية يبقى هذا باثنين يعني هذا اثنا عشر موديله
+
+299
+00:33:43,580 --> 00:33:49,440
+عشرة يبقى هذا اثنين ثلاثة في اثنين في قداش بستة
+
+300
+00:33:49,440 --> 00:33:54,080
+الستة موجودة في زد عشرة ميلي اثنين هدول إيش بقدر
+
+301
+00:33:54,080 --> 00:34:01,190
+أستنتج إن الـ Phi of أربعة تكعيب لا تساوي Phi of
+
+302
+00:34:01,190 --> 00:34:08,390
+أربعة لكل تكعيب هذا يعني إن Phi of X بدها تساوي
+
+303
+00:34:08,390 --> 00:34:17,630
+ثلاثة X is not a homomorphism طبعاً يبقى هذا كان
+
+304
+00:34:17,630 --> 00:34:27,570
+سؤال أربعة عشر من الكتاب خد لي سؤال ثاني سؤال خمسة
+
+305
+00:34:27,570 --> 00:34:34,950
+وثلاثين سؤال خمسة وثلاثين بيقول prove that the
+
+306
+00:34:34,950 --> 00:34:39,690
+mapping النقطة الأولى prove that
+
+307
+00:34:55,650 --> 00:35:04,990
+Proof Proof that the mapping Phi من Z external
+
+308
+00:35:04,990 --> 00:35:16,770
+product لـZ إلى Z given by والمعطاة بالتعريف التالي
+
+309
+00:35:16,770 --> 00:35:25,330
+Phi of A وB بدها تساوي الـ A ناقص الـ B as a
+
+310
+00:35:25,330 --> 00:35:32,810
+homomorphism النقطة الثانية النقطة
+
+311
+00:35:32,810 --> 00:35:40,970
+الثانية Find ال kernel لـ Phi النقطة الثالثة
+
+312
+00:35:40,970 --> 00:35:42,770
+Describe
+
+313
+00:35:45,300 --> 00:35:53,960
+describe the set اللي هو في
+
+314
+00:35:53,960 --> 00:35:56,820
+inverse من ثلاثة
+
+315
+00:36:38,410 --> 00:36:43,810
+السؤال مرة ثانية في عندنا function من z أكثرين أو
+
+316
+00:36:43,810 --> 00:36:48,150
+like product مع z إلى z موضع بالشكل التالي في of a
+
+317
+00:36:48,150 --> 00:36:53,730
+و b بده يساوي ال a ناقص ال b وهدي homomorphism بدنا
+
+318
+00:36:53,730 --> 00:36:57,550
+نثبتها بعد أن نثبت تهمورفازيا بنا نجيب لها ال
+
+319
+00:36:57,550 --> 00:37:02,370
+kernel بعد ال kernel بنا نوصف مين هي الست اللي
+
+320
+00:37:02,370 --> 00:37:07,330
+عندنا هذه خلينا مع النقطة الأولى بجباجي للنقطة
+
+321
+00:37:07,330 --> 00:37:13,150
+الأولى مشان اثبتها انها homomorphism بدروح أخد fi
+
+322
+00:37:13,150 --> 00:37:19,290
+of بداخل عنصر أول يبقى بقوله ال a وال b ال
+
+323
+00:37:19,290 --> 00:37:24,310
+operation اللي على زدها دي كلها هي عملية من الجامع
+
+324
+00:37:24,310 --> 00:37:31,170
+ولا الضرب الجامع يبقى بدروح اقوله زائد c و d
+
+325
+00:37:31,170 --> 00:37:36,880
+بالشكل اللي عندنا يبقى هي أخذ تأثير الفاي على two
+
+326
+00:37:36,880 --> 00:37:42,980
+elements هذا الكلام بده يساوي في of هذا بده يجمع
+
+327
+00:37:42,980 --> 00:37:53,700
+component wise يبقى a زائد c و b زائد d حسب تعريف
+
+328
+00:37:53,700 --> 00:38:01,650
+الفاي اللي عندنا هذا يبقى الأول ناقص الثاني يعني
+
+329
+00:38:01,650 --> 00:38:09,750
+مين؟ يعني ال A زائد ال C نقص ال B نقص ال D اللي
+
+330
+00:38:09,750 --> 00:38:15,910
+بقدر أكتبها على الشكل التالي ال A نقص ال B في قوس
+
+331
+00:38:15,910 --> 00:38:23,130
+وال C نقص ال D في قوس آخر السؤال هو هذا هو التعريف
+
+332
+00:38:23,130 --> 00:38:31,810
+اللي فوق يبقى هذا الكلام Phi of A وB زائد الثاني
+
+333
+00:38:31,810 --> 00:38:38,930
+Phi of C وD لذلك Phi is A homomorphism بدنا نروح
+
+334
+00:38:38,930 --> 00:38:45,430
+نجيب له main الكيرنل للفاي يبقى الكيرنل للفاي كل
+
+335
+00:38:45,430 --> 00:38:52,910
+العناصر a و b اللي موجودة في z external by product
+
+336
+00:38:52,910 --> 00:39:01,890
+مع z such that الفاي of a و b بده يساوي ال identity
+
+337
+00:39:01,890 --> 00:39:06,950
+element تبع man تبع ال z من ال identity element
+
+338
+00:39:06,950 --> 00:39:14,180
+تبع ال z اللي هو ال zero طيب هذا الكلام كل العناصر
+
+339
+00:39:14,180 --> 00:39:21,380
+a و b اللي موجودة في z external like product مع z
+
+340
+00:39:21,380 --> 00:39:28,600
+such that ال a ناقص ال b بده يساوي ال zero يبقى كل
+
+341
+00:39:28,600 --> 00:39:34,560
+العناصر a وb اللي موجودة في z external like
+
+342
+00:39:34,560 --> 00:39:41,870
+product مع z such that ال a تساوي ال b يعني
+
+343
+00:39:41,870 --> 00:39:46,250
+المركبة الأولى تساوي مين؟ المركبة الثانية يبقى
+
+344
+00:39:46,250 --> 00:39:52,950
+هذا الكلام يبقى the set of all a و a such that ال a
+
+345
+00:39:52,950 --> 00:39:59,710
+عنصر من مين؟ من ال z المركبتين زي بعض يبقى the
+
+346
+00:39:59,710 --> 00:40:04,510
+set of all are pair a و a b و b c و c زي ما بدك
+
+347
+00:40:04,510 --> 00:40:07,410
+يعني بيطلعوا هدول عناصر منهم
+
+348
+00:40:11,840 --> 00:40:19,580
+وناقص اثنين وناقص واحد وناقص واحد وزيرو وزيرو وكذلك
+
+349
+00:40:19,580 --> 00:40:25,640
+واحد وواحد اثنين واثنين وهكذا إلى ما شاء الله نعم
+
+350
+00:40:25,640 --> 00:40:30,640
+هذه كلها عناصر من عناصر الكيرن يعني كم عنصر فيه
+
+351
+00:40:31,430 --> 00:40:35,790
+ما له نهاية من ال elements يبقى ال order لل kernel
+
+352
+00:40:35,790 --> 00:40:41,730
+في هذه الحالة infinite وليس finite حسب نهاية ال
+
+353
+00:40:41,730 --> 00:40:48,490
+kernel مطلوب الثاني بدنا نروح للمطلوب الثالث إيش
+
+354
+00:40:48,490 --> 00:40:54,910
+بيقول هنا هات الست اللي عندنا هذه باجي بيقوله ال
+
+355
+00:40:54,910 --> 00:41:01,420
+phi inverse of ثلاثة ال fire inverse of ثلاثة
+
+356
+00:41:01,420 --> 00:41:05,900
+موجودة وهنا يا شباب في زد والله في زد external
+
+357
+00:41:05,900 --> 00:41:09,400
+like a product مع زد في ال external لأن هذا
+
+358
+00:41:09,400 --> 00:41:16,380
+بترجعها من زد إلى يبجي كل العناصر the set of all
+
+359
+00:41:16,380 --> 00:41:21,960
+elements a و b اللي موجودة في زد external like a
+
+360
+00:41:21,960 --> 00:41:30,840
+product مع زد such that بحيث أن ال fi of a و b
+
+361
+00:41:30,840 --> 00:41:40,480
+بدها تساوي ثلاثة مظبوط يبقى كل العناصر اللي صورتها
+
+362
+00:41:40,480 --> 00:41:46,980
+بدها تساوي ثلاثة يعني مين يعني كل العناصر a و b
+
+363
+00:41:46,980 --> 00:41:53,920
+اللي موجودة في z external like product إلى z such
+
+364
+00:41:53,920 --> 00:41:59,520
+that fi of a و b اللي هو مين ال a ناقص ال b بده
+
+365
+00:41:59,520 --> 00:42:08,660
+يساوي مين يبقى هذا الكلام كل العناصر a وb اللي
+
+366
+00:42:08,660 --> 00:42:15,580
+موجودة في z external by product مع z such that ال a
+
+367
+00:42:15,580 --> 00:42:22,760
+بدها تساوي ال b زائد الثلاثة يعني بالبلد يطلع من
+
+368
+00:42:22,760 --> 00:42:29,360
+هدول يبقى هدول the set of all المركبة الأولى بدها
+
+369
+00:42:29,360 --> 00:42:35,160
+تبقى b زائد ثلاثة والمركبة الثانية اللي هي مين
+
+370
+00:42:35,160 --> 00:42:42,400
+اللي هي b itself وال b هذه موجودة وان موجود في
+
+371
+00:42:42,400 --> 00:42:49,430
+زد يعني خد لي أي رقم موجود في زد وحط هو المركبة
+
+372
+00:42:49,430 --> 00:42:54,330
+الثانية وحط للمركبة الأولى نفس هذه المركبة وأضيف
+
+373
+00:42:54,330 --> 00:42:58,650
+عليها ماذا؟ أضيف عليها .. كم عنصر هدول بيطلعون؟
+
+374
+00:42:58,650 --> 00:43:03,490
+برضه ما له نهاية يبني ما له نهاية من العناصر كلهم
+
+375
+00:43:03,490 --> 00:43:08,810
+يروح لماذا؟ للعنصر الثلاثة أو لصورتهم بتكون ثلاثة 
+
+376
+00:43:09,160 --> 00:43:14,200
+خدلي سؤال قريب يعني أو حوالين هذا السؤال كمان
+
+377
+00:43:14,200 --> 00:43:20,620
+السؤال اللي بعضه على طوله سؤال 36 بيقول لي suppose
+
+378
+00:43:20,620 --> 00:43:31,010
+that suppose that افترض أنه الـ five من Z external
+
+379
+00:43:31,010 --> 00:43:38,050
+by-product إلى Z لمين لا group G وعليها عملية
+
+380
+00:43:38,050 --> 00:43:53,290
+الجامعة is a homomorphism such that بحيث أن الـ
+
+381
+00:43:53,290 --> 00:43:56,230
+Phi of ثلاثة واثنين
+
+382
+00:44:17,490 --> 00:44:25,890
+سؤال مرة ثانية جال افترض في عندنا function في من زد
+
+383
+00:44:25,890 --> 00:44:30,970
+external like product مع زد إلى group مين ما كانت
+
+384
+00:44:30,970 --> 00:44:35,090
+الـ group ما حددش شكلها لكن الـ operation اللي عليها
+
+385
+00:44:35,090 --> 00:44:41,070
+اللي هي عملية الجمع تمام افترض أن هذا هو
+
+386
+00:44:41,070 --> 00:44:46,650
+homomorphism وعندي أن Phi of ثلاثة واثنين بده يساوي
+
+387
+00:44:46,650 --> 00:44:52,430
+الـ a طبعا الـ a وين موجودة لأن في g وعندي Phi of
+
+388
+00:44:52,430 --> 00:44:56,330
+اثنين واحد اللي موجودة اللي بده تساوي بيه موجودة
+
+389
+00:44:56,330 --> 00:45:01,330
+في g كذلك قالي هت لل Phi of أربعة وأربعة طبعا
+
+390
+00:45:01,330 --> 00:45:05,290
+الـ Phi of أربعة وأربعة حاجيهم دلالة مين؟ A و B لأن
+
+391
+00:45:05,290 --> 00:45:10,390
+A و B أنا مش عارفهم يعني عناصر، مين هم؟ الله أعلم
+
+392
+00:45:10,390 --> 00:45:13,930
+بحالهما، يبقى باجي بقول solution
+
+393
+00:45:19,590 --> 00:45:24,750
+بدي أحاول أستفيد من المعطيات اللي عندنا Phi of
+
+394
+00:45:24,750 --> 00:45:29,590
+ثلاثة واثنين و Phi of اثنين وواحد وأربطهم بمين
+
+395
+00:45:29,590 --> 00:45:37,770
+بـ Phi of أربعة وأربعة الآن لو جيت ليه الـ Phi of
+
+396
+00:45:37,770 --> 00:45:46,570
+ثلاثة واثنين ناقص Phi of اثنين وواحد أشوف قداش
+
+397
+00:45:46,570 --> 00:45:48,390
+هذا الكلام بده يساوي
+
+398
+00:45:52,580 --> 00:45:57,700
+هذا الـ element موجود في جي وهذا الـ element موجود
+
+399
+00:45:57,700 --> 00:46:02,720
+في جي إذا المجموع تبعهم أو الفرق بينهم هذا معكوس
+
+400
+00:46:02,720 --> 00:46:06,980
+سالب الـ Phi of اثنين وواحد هو معكوس الـ Phi of
+
+401
+00:46:06,980 --> 00:46:10,140
+اثنين وواحد لأن الـ operation اللي عليها عملية جي
+
+402
+00:46:10,140 --> 00:46:14,820
+وبالتالي ما حدش إلا اعتراض عنها السؤال هو مش Phi
+
+403
+00:46:14,820 --> 00:46:22,510
+homomorphism يبقى هذا معناه Phi of الثلاثه واثنين
+
+404
+00:46:22,510 --> 00:46:29,070
+بدي أطرح منها اثنين وواحد يساوي Phi of اللي هو
+
+405
+00:46:29,070 --> 00:46:36,210
+مين ثلاثة ناقص اثنين واثنين ناقص واحد يبقى هذا
+
+406
+00:46:36,210 --> 00:46:45,190
+الكلام بدي يساوي Phi of واحد واحد إذا الفرق ما بين
+
+407
+00:46:45,190 --> 00:46:50,570
+الصورتين هدول Phi of العنصر واحد وواحد الآن
+
+408
+00:46:50,570 --> 00:46:56,470
+الواحد وواحد له علاقة بالـ Phi أربعة وأربعة بقدر
+
+409
+00:46:56,470 --> 00:46:59,690
+أجيب العلاقة اللي بتربط منهم تتقبل يا قليل إذا
+
+410
+00:46:59,690 --> 00:47:04,750
+كنتم ذاكرين قولنا Phi of x يساوي الـ x في Phi of one
+
+411
+00:47:04,960 --> 00:47:10,380
+يبقى نفس المفهوم اللي عندنا، الآن بروح أخدله Phi
+
+412
+00:47:10,380 --> 00:47:16,620
+of أربعة وأربعة، أليست أربعة في الـ Phi of one
+
+413
+00:47:16,620 --> 00:47:24,470
+one؟ طيب احنا طلعنا هنا الـ Phi of one و one اللي
+
+414
+00:47:24,470 --> 00:47:32,050
+هو الفرق ما بين الاثنين هدول يبقى هذه العلاقة رقم
+
+415
+00:47:32,050 --> 00:47:37,170
+واحد بدي أجيب العلاقة اللي فوق لما أقول Phi of
+
+416
+00:47:37,170 --> 00:47:43,230
+ثلاثة واثنين ناقص Phi of اثنين وواحد أليس الـ A
+
+417
+00:47:43,230 --> 00:47:49,350
+ناقص الـ B؟ مش الأولى A والثانية B يبقى هذه العلاقة
+
+418
+00:47:49,350 --> 00:47:54,410
+اللي عندنا اللي هي الرقم اثنين طب الفرق ما بين
+
+419
+00:47:54,410 --> 00:48:01,110
+هدول طالع مين يبقى من الاثنين هدول مع بعض بس تنتج
+
+420
+00:48:01,110 --> 00:48:08,450
+ما يأتي هذه عبارة عن الـ Phi of أربعة وأربعة بدها
+
+421
+00:48:08,450 --> 00:48:15,550
+تساوي أربعة في Phi of one one وتساوي أربعة في
+
+422
+00:48:16,570 --> 00:48:22,830
+Phi of أربعة واحد واحد الفرق في ما بينهم لمين a
+
+423
+00:48:22,830 --> 00:48:31,030
+ناقص الـ b يبقى النتيجة تساوي أربعة a ناقص أربعة b
+
+424
+00:48:31,030 --> 00:48:37,730
+إذا بنينا عليه صورة الـ Phi أربعة وأربعة هي أربعة
+
+425
+00:48:37,730 --> 00:48:44,630
+مضروبة في الـ a ناقص الـ b لحد هنا انتهى الـ section
+
+426
+00:48:45,380 --> 00:48:50,120
+والله يعطيكم العافية ونسامح أو يسامح بعضنا
+
+427
+00:48:50,120 --> 00:48:54,920
+بعضا إن كان صار فيه خطأ أو تقصير أو ما إلى ذلك 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..730473a006fbf95c96fb7d6bd3a93180afd68331
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/VxBMD5useYY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4751, "start": 21.29, "end": 47.51, "text": "بسم الله الرحمن الرحيم نكمل chapter عشرة اللي كنا بنتحدث فيه المرة اللي فاتت و آخر مرة أعطينا نظرية أو أول نظرية في ال isomorphism vs isomorphism theorem ثم أخدنا بعد ذلك كرولري عليها و الآن بنواصل في نفس ال chapter في هنا مثال بيقول هاتلي كل ال homomorphism من z12 إلى z13", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8717, 24793, 1211, 7187, 6225, 8592, 25720, 13672, 1829, 9122, 8315, 4724, 29399, 24401, 12984, 8978, 3224, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 4032, 19753, 34740, 3714, 25720, 5551, 3615, 9566, 1829, 8315, 8717, 19913, 2288, 10632, 34051, 5551, 12610, 8717, 19913, 2288, 10632, 8978, 2423, 307, 32702, 1434, 12041, 307, 32702, 1434, 20904, 38637, 2304, 5551, 9778, 3215, 8315, 39182, 29910, 23275, 9122, 2288, 12610, 16572, 25894, 11296, 4032, 6024, 48506, 44945, 2407, 33546, 1211, 8978, 8717, 36178, 2423, 7187, 8978, 34105, 50113, 6027, 4724, 1829, 39648, 8032, 9307, 20292, 28242, 2423, 3655, 32702, 1434, 9154, 710, 4762, 30731, 710, 7668], "avg_logprob": -0.1980088474476232, "compression_ratio": 1.7309236947791165, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 21.29, "end": 21.65, "word": "بسم", "probability": 0.84326171875}, {"start": 21.65, "end": 21.81, "word": " الله", "probability": 0.97265625}, {"start": 21.81, "end": 22.25, "word": " الرحمن", "probability": 0.9401041666666666}, {"start": 22.25, "end": 22.73, "word": " الرحيم", "probability": 0.9925130208333334}, {"start": 22.73, "end": 23.89, "word": " نكمل", "probability": 0.8904622395833334}, {"start": 23.89, "end": 24.25, "word": " chapter", "probability": 0.44775390625}, {"start": 24.25, "end": 24.93, "word": " عشرة", "probability": 0.7802734375}, {"start": 24.93, "end": 25.35, "word": " اللي", "probability": 0.83447265625}, {"start": 25.35, "end": 25.55, "word": " كنا", "probability": 0.967529296875}, {"start": 25.55, "end": 26.05, "word": " بنتحدث", "probability": 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"word": " ال", "probability": 0.9140625}, {"start": 43.53, "end": 44.51, "word": " homomorphism", "probability": 0.9567057291666666}, {"start": 44.51, "end": 44.77, "word": " من", "probability": 0.98779296875}, {"start": 44.77, "end": 45.63, "word": " z12", "probability": 0.487548828125}, {"start": 45.63, "end": 46.07, "word": " إلى", "probability": 0.765625}, {"start": 46.07, "end": 47.51, "word": " z13", "probability": 0.7470703125}], "temperature": 1.0}, {"id": 2, "seek": 7623, "start": 48.14, "end": 76.24, "text": "يبقى بدي اقول الحلقة التالية solution assume افترض ان الـ Phi من Z12 الى Z13 هو homomorphism افترض ان هذا هو homomorphism و بدي اعرف ما هو شكل هذه ال homomorphism", "tokens": [1829, 3555, 4587, 7578, 4724, 16254, 1975, 39648, 21542, 1211, 28671, 16712, 6027, 10632, 3827, 6552, 1975, 5172, 2655, 43042, 16472, 2423, 39184, 41435, 9154, 1176, 4762, 2423, 7578, 1176, 7668, 31439, 3655, 32702, 1434, 1975, 5172, 2655, 43042, 16472, 23758, 31439, 3655, 32702, 1434, 4032, 4724, 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{"start": 58.16, "end": 58.58, "word": " Phi", "probability": 0.1358642578125}, {"start": 58.58, "end": 59.22, "word": " من", "probability": 0.97607421875}, {"start": 59.22, "end": 60.72, "word": " Z12", "probability": 0.49365234375}, {"start": 60.72, "end": 61.86, "word": " الى", "probability": 0.81396484375}, {"start": 61.86, "end": 63.68, "word": " Z13", "probability": 0.880126953125}, {"start": 63.68, "end": 65.18, "word": " هو", "probability": 0.68115234375}, {"start": 65.18, "end": 67.62, "word": " homomorphism", "probability": 0.748046875}, {"start": 67.62, "end": 69.0, "word": " افترض", "probability": 0.958740234375}, {"start": 69.0, "end": 69.24, "word": " ان", "probability": 0.9375}, {"start": 69.24, "end": 69.6, "word": " هذا", "probability": 0.8388671875}, {"start": 69.6, "end": 69.72, "word": " هو", "probability": 0.5673828125}, {"start": 69.72, "end": 70.54, "word": " homomorphism", "probability": 0.908203125}, {"start": 70.54, "end": 71.22, "word": " و", "probability": 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واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد زائد واحد", "tokens": [6027, 7649, 13412, 28820, 2423, 39184, 3655, 32702, 1434, 31439, 2423, 39184, 1025, 7251, 33604, 49115, 15844, 4478, 9154, 3714, 9957, 22807, 9154, 1176, 4762, 2423, 4478, 23758, 12174, 3215, 7251, 30544, 1958, 12399, 12174, 3215, 7251, 30544, 502, 12399, 568, 12399, 805, 12399, 5296, 17082, 995, 10632, 9122, 3215, 3224, 8592, 12399, 5296, 17082, 995, 10632, 9122, 3215, 3224, 8592, 12399, 45164, 1975, 5172, 2655, 43042, 8315, 16490, 2304, 3794, 3660, 11778, 3224, 1975, 39648, 1732, 295, 16490, 2304, 3794, 3660, 33962, 2304, 3794, 3660, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 3215, 36764, 24401, 30767, 16373, 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"end": 709.57, "word": " اللي", "probability": 0.93505859375}, {"start": 709.57, "end": 710.27, "word": " عندنا", "probability": 0.830078125}, {"start": 710.27, "end": 710.55, "word": " اللي", "probability": 0.910400390625}, {"start": 710.55, "end": 710.73, "word": " هو", "probability": 0.650390625}, {"start": 710.73, "end": 711.05, "word": " من", "probability": 0.499267578125}, {"start": 711.05, "end": 712.07, "word": " GN", "probability": 0.6943359375}], "temperature": 1.0}, {"id": 29, "seek": 72936, "start": 713.1, "end": 729.36, "text": "بدنا نحاول نثبت بعد ما نفرض ان ال N is a normal subgroup من G بدنا نحاول نحسب ال kernel لهذه ال Phi و نثبت انه مين", "tokens": [44510, 8315, 8717, 5016, 995, 12610, 8717, 12984, 3555, 2655, 39182, 19446, 8717, 5172, 43042, 16472, 2423, 426, 307, 257, 2710, 1422, 17377, 9154, 460, 47525, 8315, 8717, 5016, 995, 12610, 8717, 5016, 35457, 2423, 28256, 46740, 24192, 2423, 41435, 4032, 8717, 12984, 3555, 2655, 16472, 3224, 3714, 9957], "avg_logprob": 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"word": " normal", "probability": 0.80810546875}, {"start": 721.8, "end": 722.66, "word": " subgroup", "probability": 0.704833984375}, {"start": 722.66, "end": 722.98, "word": " من", "probability": 0.98046875}, {"start": 722.98, "end": 723.18, "word": " G", "probability": 0.8740234375}, {"start": 723.18, "end": 724.08, "word": " بدنا", "probability": 0.6724853515625}, {"start": 724.08, "end": 724.46, "word": " نحاول", "probability": 0.9866943359375}, {"start": 724.46, "end": 725.02, "word": " نحسب", "probability": 0.9908854166666666}, {"start": 725.02, "end": 725.22, "word": " ال", "probability": 0.82958984375}, {"start": 725.22, "end": 725.94, "word": " kernel", "probability": 0.5595703125}, {"start": 725.94, "end": 726.98, "word": " لهذه", "probability": 0.9638671875}, {"start": 726.98, "end": 727.32, "word": " ال", "probability": 0.8642578125}, {"start": 727.32, "end": 727.72, "word": " Phi", "probability": 0.1798095703125}, {"start": 727.72, "end": 728.22, "word": " و", 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تماما", "probability": 0.97802734375}, {"start": 734.66, "end": 735.02, "word": " هذه", "probability": 0.51171875}, {"start": 735.02, "end": 736.12, "word": " يبقى", "probability": 0.927978515625}, {"start": 736.12, "end": 736.4, "word": " باجي", "probability": 0.8330078125}, {"start": 736.4, "end": 737.08, "word": " بقوله", "probability": 0.9212239583333334}, {"start": 737.08, "end": 738.04, "word": " أول", "probability": 0.762939453125}, {"start": 738.04, "end": 738.42, "word": " شيء", "probability": 0.4814453125}, {"start": 738.42, "end": 738.6, "word": " بدي", "probability": 0.57470703125}, {"start": 738.6, "end": 739.04, "word": " أبيله", "probability": 0.65185546875}, {"start": 739.04, "end": 739.3, "word": " أن", "probability": 0.467041015625}, {"start": 739.3, "end": 739.72, "word": " هذا", "probability": 0.69140625}, {"start": 739.72, "end": 740.88, "word": " homomorphism", "probability": 0.8064778645833334}, {"start": 740.88, "end": 741.06, "word": " و", "probability": 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أخد", "probability": 0.8824869791666666}, {"start": 753.26, "end": 753.94, "word": " Phi", "probability": 0.35498046875}, {"start": 753.94, "end": 754.42, "word": " of", "probability": 0.8447265625}, {"start": 754.42, "end": 755.14, "word": " G1", "probability": 0.869384765625}, {"start": 755.14, "end": 756.14, "word": " G2", "probability": 0.76123046875}], "temperature": 1.0}, {"id": 31, "seek": 78614, "start": 756.96, "end": 786.14, "text": "يبقى حسب التعريف اللي عندنا بيصير G1 G2 في N طيب ليش؟ لأنها normal لو ماكنتش normal اللي بصي كلامك مش صحيح يبقى هذا الكلام بده يساوي G1 N في G2 N السبب في ذلك since ال N is a normal subgroup من G", "tokens": [1829, 3555, 4587, 7578, 11331, 35457, 16712, 3615, 16572, 5172, 13672, 1829, 43242, 8315, 4724, 1829, 9381, 13546, 460, 16, 460, 17, 8978, 426, 23032, 1829, 3555, 32239, 8592, 22807, 5296, 33456, 11296, 2710, 45164, 19446, 19452, 2655, 8592, 2710, 13672, 1829, 4724, 9381, 1829, 28242, 10943, 4117, 37893, 20328, 5016, 1829, 5016, 7251, 3555, 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Proof that the mapping Phi من Z external product لZ إلى Z given by", "tokens": [12681, 2670, 1705, 2670, 300, 264, 18350, 41435, 9154, 1176, 8320, 1674, 5296, 57, 30731, 1176, 2212, 538], "avg_logprob": -0.509868395955939, "compression_ratio": 0.9629629629629629, "no_speech_prob": 0.0, "words": [{"start": 2095.6499999999996, "end": 2097.0499999999997, "word": "Proof", "probability": 0.418701171875}, {"start": 2097.0499999999997, "end": 2098.45, "word": " Proof", "probability": 0.647705078125}, {"start": 2098.45, "end": 2098.65, "word": " that", "probability": 0.466552734375}, {"start": 2098.65, "end": 2098.87, "word": " the", "probability": 0.84033203125}, {"start": 2098.87, "end": 2099.49, "word": " mapping", "probability": 0.921875}, {"start": 2099.49, "end": 2100.89, "word": " Phi", "probability": 0.190185546875}, {"start": 2100.89, "end": 2102.55, "word": " من", "probability": 0.9189453125}, {"start": 2102.55, "end": 2103.83, "word": " Z", "probability": 0.517578125}, {"start": 2103.83, "end": 2104.99, "word": " external", "probability": 0.67041015625}, {"start": 2104.99, "end": 2105.97, "word": " product", "probability": 0.59033203125}, {"start": 2105.97, "end": 2107.65, "word": " لZ", "probability": 0.5986328125}, {"start": 2107.65, "end": 2108.81, "word": " إلى", "probability": 0.685546875}, {"start": 2108.81, "end": 2109.93, "word": " Z", "probability": 0.97119140625}, {"start": 2109.93, "end": 2111.23, "word": " given", "probability": 0.6669921875}, {"start": 2111.23, "end": 2112.19, "word": " by", "probability": 0.958984375}], "temperature": 1.0}, {"id": 85, "seek": 214277, "start": 2113.29, "end": 2142.77, "text": "والمعطاه بالتعريف التالي Phi of A وB بديساوي الـ A ناقص الـ B as a homomorphism النقطة الثانية النقطة الثانية Find ال kernel لـ Phi النقطة التالتة Describe", "tokens": [2407, 45340, 3615, 9566, 40294, 20666, 2655, 3615, 16572, 5172, 16712, 6027, 1829, 41435, 295, 316, 4032, 33, 4724, 16254, 3794, 995, 45865, 2423, 39184, 316, 8717, 995, 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"probability": 0.42977294921875}, {"start": 2120.71, "end": 2120.95, "word": " الـ", "probability": 0.5263671875}, {"start": 2120.95, "end": 2121.19, "word": " A", "probability": 0.525390625}, {"start": 2121.19, "end": 2122.07, "word": " ناقص", "probability": 0.8983154296875}, {"start": 2122.07, "end": 2122.37, "word": " الـ", "probability": 0.813232421875}, {"start": 2122.37, "end": 2122.79, "word": " B", "probability": 0.818359375}, {"start": 2122.79, "end": 2124.01, "word": " as", "probability": 0.388427734375}, {"start": 2124.01, "end": 2125.33, "word": " a", "probability": 0.900390625}, {"start": 2125.33, "end": 2127.11, "word": " homomorphism", "probability": 0.9363606770833334}, {"start": 2127.11, "end": 2128.57, "word": " النقطة", "probability": 0.9666341145833334}, {"start": 2128.57, "end": 2129.43, "word": " الثانية", "probability": 0.972412109375}, {"start": 2129.43, "end": 2132.81, "word": " النقطة", "probability": 0.8986002604166666}, {"start": 2132.81, "end": 2133.23, "word": " الثانية", "probability": 0.984619140625}, {"start": 2133.23, "end": 2133.95, "word": " Find", "probability": 0.3994140625}, {"start": 2133.95, "end": 2136.45, "word": " ال", "probability": 0.69775390625}, {"start": 2136.45, "end": 2136.97, "word": " kernel", "probability": 0.361572265625}, {"start": 2136.97, "end": 2137.43, "word": " لـ", "probability": 0.600830078125}, {"start": 2137.43, "end": 2137.87, "word": " Phi", "probability": 0.81787109375}, {"start": 2137.87, "end": 2139.69, "word": " النقطة", "probability": 0.986328125}, {"start": 2139.69, "end": 2140.97, "word": " التالتة", "probability": 0.94384765625}, {"start": 2140.97, "end": 2142.77, "word": " Describe", "probability": 0.868896484375}], "temperature": 1.0}, {"id": 86, "seek": 215682, "start": 2145.3, "end": 2156.82, "text": "describe the set اللي هو في انفرس من تلاتة", "tokens": [14792, 8056, 264, 992, 13672, 1829, 31439, 8978, 16472, 5172, 2288, 3794, 9154, 6055, 1211, 9307, 3660], "avg_logprob": 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product مع z الى z موطع بالشكل التاليفي of a و b بده يسوى ال a ناقص ال b وهدي homomorphism بدنا نثبتها", "tokens": [6027, 3794, 33604, 6027, 3714, 25720, 6055, 7649, 10632, 8978, 43242, 8315, 2445, 9154, 710, 1975, 4117, 2655, 2288, 9957, 1975, 2407, 411, 1674, 20449, 710, 2423, 7578, 710, 3714, 2407, 9566, 3615, 20666, 8592, 28820, 16712, 6027, 33911, 1829, 295, 257, 4032, 272, 47525, 3224, 7251, 3794, 2407, 7578, 2423, 257, 8717, 995, 4587, 9381, 2423, 272, 37037, 16254, 3655, 32702, 1434, 47525, 8315, 8717, 12984, 3555, 2655, 11296], "avg_logprob": -0.3910651299315439, "compression_ratio": 1.4011627906976745, "no_speech_prob": 0.0, "words": [{"start": 2198.41, "end": 2198.85, "word": "السؤال", "probability": 0.78131103515625}, {"start": 2198.85, "end": 2199.15, "word": " مرة", "probability": 0.91748046875}, {"start": 2199.15, "end": 2199.85, "word": " تانية", "probability": 0.8395182291666666}, {"start": 2199.85, "end": 2200.67, "word": " في", "probability": 0.31640625}, {"start": 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2205.63, "end": 2206.43, "word": " موطع", "probability": 0.62628173828125}, {"start": 2206.43, "end": 2206.95, "word": " بالشكل", "probability": 0.8819986979166666}, {"start": 2206.95, "end": 2207.69, "word": " التاليفي", "probability": 0.717437744140625}, {"start": 2207.69, "end": 2207.91, "word": " of", "probability": 0.7705078125}, {"start": 2207.91, "end": 2208.15, "word": " a", "probability": 0.87451171875}, {"start": 2208.15, "end": 2208.29, "word": " و", "probability": 0.8076171875}, {"start": 2208.29, "end": 2208.51, "word": " b", "probability": 0.438232421875}, {"start": 2208.51, "end": 2208.89, "word": " بده", "probability": 0.3538818359375}, {"start": 2208.89, "end": 2209.27, "word": " يسوى", "probability": 0.76336669921875}, {"start": 2209.27, "end": 2209.39, "word": " ال", "probability": 0.66259765625}, {"start": 2209.39, "end": 2209.59, "word": " a", "probability": 0.8408203125}, {"start": 2209.59, "end": 2210.17, "word": " ناقص", "probability": 0.898193359375}, {"start": 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" kernel", "probability": 0.4169921875}, {"start": 2218.05, "end": 2218.79, "word": " بعد", "probability": 0.445068359375}, {"start": 2218.79, "end": 2219.01, "word": " ال", "probability": 0.72900390625}, {"start": 2219.01, "end": 2219.35, "word": " kernel", "probability": 0.833984375}, {"start": 2219.35, "end": 2219.69, "word": " بنا", "probability": 0.6253662109375}, {"start": 2219.69, "end": 2220.43, "word": " نوصف", "probability": 0.9825439453125}, {"start": 2220.43, "end": 2221.01, "word": " مين", "probability": 0.9091796875}, {"start": 2221.01, "end": 2221.31, "word": " هي", "probability": 0.6806640625}, {"start": 2221.31, "end": 2221.85, "word": " ال", "probability": 0.64697265625}, {"start": 2221.85, "end": 2222.13, "word": " 6", "probability": 0.35205078125}, {"start": 2222.13, "end": 2222.37, "word": " اللي", "probability": 0.8447265625}, {"start": 2222.37, "end": 2222.97, "word": " عندنا", "probability": 0.98779296875}, {"start": 2222.97, "end": 2223.51, "word": " هذه", 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"probability": 0.8439127604166666}, {"start": 2924.03, "end": 2924.29, "word": " ال", "probability": 0.73388671875}, {"start": 2924.29, "end": 2924.63, "word": " section", "probability": 0.85400390625}], "temperature": 1.0}, {"id": 119, "seek": 293492, "start": 2925.38, "end": 2934.92, "text": "والله يعطيكوا العافية ونسامحوا أو يسامحوا بعضنا بعضا إن كان صار فيه خطأ أو تقسير أو ما إلى ذلك", "tokens": [2407, 6027, 43761, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 1863, 3794, 10943, 5016, 14407, 34051, 7251, 3794, 10943, 5016, 14407, 45030, 11242, 8315, 45030, 11242, 995, 36145, 25961, 20328, 9640, 8978, 3224, 16490, 9566, 10721, 34051, 6055, 4587, 3794, 13546, 34051, 19446, 30731, 29910, 23275], "avg_logprob": -0.15943878037588938, "compression_ratio": 1.5044247787610618, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2925.38, "end": 2925.72, "word": "والله", "probability": 0.8502604166666666}, {"start": 2925.72, "end": 2926.12, "word": " يعطيكوا", "probability": 0.68154296875}, {"start": 2926.12, "end": 2927.0, "word": " العافية", "probability": 0.9620768229166666}, {"start": 2927.0, "end": 2928.8, "word": " ونسامحوا", "probability": 0.8146565755208334}, {"start": 2928.8, "end": 2928.98, "word": " أو", "probability": 0.720703125}, {"start": 2928.98, "end": 2929.64, "word": " يسامحوا", "probability": 0.9890625}, {"start": 2929.64, "end": 2930.12, "word": " بعضنا", "probability": 0.98974609375}, {"start": 2930.12, "end": 2930.86, "word": " بعضا", "probability": 0.9739583333333334}, {"start": 2930.86, "end": 2931.48, "word": " إن", "probability": 0.6123046875}, {"start": 2931.48, "end": 2931.82, "word": " كان", "probability": 0.9853515625}, {"start": 2931.82, "end": 2932.1, "word": " صار", "probability": 0.799072265625}, {"start": 2932.1, "end": 2932.38, "word": " فيه", "probability": 0.818603515625}, {"start": 2932.38, "end": 2932.8, "word": " خطأ", "probability": 0.9944661458333334}, {"start": 2932.8, "end": 2933.12, "word": " أو", "probability": 0.8388671875}, {"start": 2933.12, "end": 2933.74, "word": " تقسير", "probability": 0.8714599609375}, {"start": 2933.74, "end": 2933.96, "word": " أو", "probability": 0.775390625}, {"start": 2933.96, "end": 2934.16, "word": " ما", "probability": 0.96240234375}, {"start": 2934.16, "end": 2934.42, "word": " إلى", "probability": 0.962890625}, {"start": 2934.42, "end": 2934.92, "word": " ذلك", "probability": 0.99462890625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2935.79175, "duration_after_vad": 2727.9106249999923}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6b7ad1a81a5848ec8a1e4a321f2282736c048604
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_postprocess.srt
@@ -0,0 +1,1688 @@
+1
+00:00:21,260 --> 00:00:26,820
+بسم الله الرحمن الرحيم نعود ثانية إلى إكمال ما
+
+2
+00:00:26,820 --> 00:00:34,400
+بدأنا به حيث تركتكم بعد أنهينا chapter ال
+
+3
+00:00:34,400 --> 00:00:39,120
+subgroups والأستاذ محمود شرح لكم chapterين اللي هو
+
+4
+00:00:39,120 --> 00:00:43,660
+ال cyclic groups و كذلك ال permutations groups إذا
+
+5
+00:00:43,660 --> 00:00:48,250
+نصل الآن إلى ال isomorphismبالبلد هيك ال
+
+6
+00:00:48,250 --> 00:00:52,770
+isomorphism عبارة عن function بس مش ما بين two
+
+7
+00:00:52,770 --> 00:00:57,810
+sets ما بين two groups بده تحقق ليه ثلاثة شروط
+
+8
+00:00:57,810 --> 00:01:03,710
+يبقى function وزيادة على ذلك بده تحقق ثلاث شروط
+
+9
+00:01:03,710 --> 00:01:07,210
+الشرط الأول هذه ال function بده تبقى one to one
+
+10
+00:01:07,210 --> 00:01:12,510
+الشرط الثاني بده تبقى on two الشرط الثالث بده تحقق
+
+11
+00:01:12,510 --> 00:01:18,350
+الخاصية اللي عندنا هذههذه التعريف يقول ان ايزو
+
+12
+00:01:18,350 --> 00:01:25,110
+مورفزم ايزو مورفزم بالعربي هيك التشاكل النماطي او
+
+13
+00:01:25,110 --> 00:01:29,690
+التشابه النماطي ولان هنقول لك ايش معناها من
+
+14
+00:01:29,690 --> 00:01:34,230
+الناحية الرياضية بس اصبر علينا شويةيبقى انا ايزو
+
+15
+00:01:34,230 --> 00:01:39,930
+مورفزم في حديله رمز في من الجروب جي لجروب جي بار
+
+16
+00:01:39,930 --> 00:01:46,130
+is one to one function يبقى function وكذلك one to
+
+17
+00:01:46,130 --> 00:01:52,110
+one from جي on to جي بار مش to جي بار يا شباب on
+
+18
+00:01:52,110 --> 00:02:00,700
+to on to جي بارsuch that بحيث أن الـPhi of A بيبقى
+
+19
+00:02:00,700 --> 00:02:05,360
+يسوى Phi of A في Phi of B يعني تأثير الـPhi على
+
+20
+00:02:05,360 --> 00:02:09,820
+حاصل الضرب الـtwo elements A وB بيبقى يسوى تأثير
+
+21
+00:02:09,820 --> 00:02:15,160
+الـPhi علي A مضروبا في تأثير الـPhi علي B دي ربالك
+
+22
+00:02:15,160 --> 00:02:21,100
+بديفهم كل شيء في مكانه كيف كل شيء في مكانه الآن
+
+23
+00:02:21,100 --> 00:02:26,040
+الـA و الـB وين موجودات؟في جي جي عليها operation
+
+24
+00:02:26,040 --> 00:02:30,380
+غير ال operation اللي على جي بار وبالتالي لما اقول
+
+25
+00:02:30,380 --> 00:02:36,060
+a بي اللي بينهم operation تبعت من تبعت الجي لكن
+
+26
+00:02:36,060 --> 00:02:39,760
+لما اقول في of ا في في of بي ال operation اللي
+
+27
+00:02:39,760 --> 00:02:45,450
+بينهم ايه ال operation تبعت من تبعت جي بارلما اقول
+
+28
+00:02:45,450 --> 00:02:51,450
+two elements في جي بار هدول a وb two elements في g
+
+29
+00:02:51,450 --> 00:02:59,990
+لما اقول a في b ال operation بينهم
+
+30
+00:02:59,990 --> 00:03:07,230
+تبعت جي بارطيب الان لو كان five من جي إلى جي بار
+
+31
+00:03:07,230 --> 00:03:12,010
+هو عبارة عن isomorphism بقدر اقول عن جي و جي بار
+
+32
+00:03:12,010 --> 00:03:17,810
+are isomorphic يبقى ال two groups دول في تشابه
+
+33
+00:03:17,810 --> 00:03:25,810
+رياضي، تشابه نماطي، تشاكل نماطي فيما بينهمو باكتب
+
+34
+00:03:25,810 --> 00:03:32,410
+الـ isomorphism مش باكتبه يساوي باكتبه جي و خطين
+
+35
+00:03:32,410 --> 00:03:38,090
+متعرجين بالشكل هادى جي بار و تقرا جي ايزو مورفكت
+
+36
+00:03:38,090 --> 00:03:44,030
+جي بارطب بالمعنى الرياضي ايش يعني معنى isomorphism
+
+37
+00:03:44,030 --> 00:03:49,690
+او G isomorphic ل G bar لاحظ من خلال التعريف لما
+
+38
+00:03:49,690 --> 00:03:53,750
+يقول ال group هذي و ال group هذي في function بينهم
+
+39
+00:03:53,750 --> 00:03:59,510
+one to one and unto السؤال الأول هل سيختلف عدد
+
+40
+00:03:59,510 --> 00:04:03,150
+العناصر في ال group الأولى عن عدد عناصر ال group
+
+41
+00:04:03,150 --> 00:04:10,130
+التانية؟ في اختلاف؟ لأ لإن واحد لواحداتنين ال
+
+42
+00:04:10,130 --> 00:04:15,110
+domain بيغطي جميع عناصر جي مدام انت بيغطي جميع
+
+43
+00:04:15,110 --> 00:04:20,210
+عناصر جي بار و لا واحد زي التاني يبقى بناء عندي
+
+44
+00:04:20,210 --> 00:04:26,050
+عدد عناصر جي يساوي عدد عناصر جي بارعدد ال subgroup
+
+45
+00:04:26,050 --> 00:04:31,910
+في G يسوى عدد ال subgroup في G bar عدد العناصر
+
+46
+00:04:31,910 --> 00:04:37,050
+التي لها نفس ال order في G يسوى عدد العناصر التي
+
+47
+00:04:37,050 --> 00:04:42,690
+لها نفس ال order من G barبمعنى لو عندي 6 عناصر ال
+
+48
+00:04:42,690 --> 00:04:49,410
+order يسوى 4 في G لازم اجد 6 عناصر ال order يسوى 4
+
+49
+00:04:49,410 --> 00:04:54,770
+في G bar لو عندي 10 عناصر في G ال order يسوى 2
+
+50
+00:04:54,770 --> 00:05:03,380
+لازم اجد 10 عناصر في G bar ال order يسوى 2لو كانت
+
+51
+00:05:03,380 --> 00:05:07,680
+ال group Cyclic هذه التانية Cyclic لو كانت Abelian
+
+52
+00:05:07,680 --> 00:05:11,900
+التانية Abelian يعني بمعنى هيكب البلدي ال two
+
+53
+00:05:11,900 --> 00:05:16,460
+groups اللي اتنية اللي لهم نفس الخواصة الرياضية
+
+54
+00:05:16,460 --> 00:05:21,950
+يعني كل ما تعرفه اللي عن ال groupينطبق على الأولى
+
+55
+00:05:21,950 --> 00:05:25,830
+الريكولوجيا ينطبق على مين؟ على الثانية هذي non
+
+56
+00:05:25,830 --> 00:05:29,650
+-abelian إذا التانية non-abelian متنفعش واحدة
+
+57
+00:05:29,650 --> 00:05:33,450
+cyclic والتانية لأ واحدة abelian والتانية لأ واحدة
+
+58
+00:05:33,450 --> 00:05:38,090
+finite والتانية infinite برضه لأ لو فيها عدد عناصر
+
+59
+00:05:38,090 --> 00:05:41,970
+يساوي infinite بجهد فيها عدد عناصر يساوي infinite
+
+60
+00:05:41,970 --> 00:05:46,530
+وهكذايبقى بناء عليه لما أقول في isomorphism ما بين
+
+61
+00:05:46,530 --> 00:05:50,470
+two groups يبقى ال two groups اللي لهم جميع
+
+62
+00:05:50,470 --> 00:05:55,190
+الخواصة الرياضية بالضبط تماما الخواصة اللي في
+
+63
+00:05:55,190 --> 00:05:59,230
+الجروب الأولى تنطبق تماما على الجروب التاني وإن
+
+64
+00:05:59,230 --> 00:06:04,650
+كانت العناصر مختلفة ما بين الاتنين وكانت ال binary
+
+65
+00:06:04,650 --> 00:06:07,810
+operation على الأولى تختلف عن ال binary operation
+
+66
+00:06:07,810 --> 00:06:12,650
+عن مينع الجروب التاني وهكذا يبقى هذا اللي بدي ايه
+
+67
+00:06:12,650 --> 00:06:16,890
+المعنى اللي بدي اترسخه في دماغك عن معنى ال
+
+68
+00:06:16,890 --> 00:06:22,690
+isomorphism اظن واضح كلامي نبدأ ناخد مجموعة من
+
+69
+00:06:22,690 --> 00:06:29,670
+الأمثلة على ال isomorphism اول مثال بيقول define a
+
+70
+00:06:29,670 --> 00:06:40,890
+function define a functionفاي من ال R تحت عملية
+
+71
+00:06:40,890 --> 00:06:53,750
+الجامعة ل R plus تحت عملية الضرب باي فاي
+
+72
+00:06:53,750 --> 00:07:00,310
+of X بده يساوي اتنين to the power X لكل ال X اللي
+
+73
+00:07:00,310 --> 00:07:18,440
+موجودة في Rهنا show that phi is an isomorphism مرة
+
+74
+00:07:18,440 --> 00:07:24,940
+تانيةأحنا قلنا في التعريف أربع شروط للايزمورفزية
+
+75
+00:07:24,940 --> 00:07:28,960
+function هذي ال function one to one هذي ال
+
+76
+00:07:28,960 --> 00:07:32,000
+function one to .. ال function اللي عندنا تحقق
+
+77
+00:07:32,000 --> 00:07:37,540
+الخاصية هذه طبعا؟ طيب قال لي define a function
+
+78
+00:07:37,540 --> 00:07:41,900
+يبقى ريحني من مين؟ من الشرط اللي هو قال لي خدها ال
+
+79
+00:07:41,900 --> 00:07:47,980
+function هذهمعرفة من R تحت عملية الجامعة الى R
+
+80
+00:07:47,980 --> 00:07:53,100
+Plus تحت عملية الضرب يبقى هذه جميع الأعداد
+
+81
+00:07:53,100 --> 00:07:58,500
+الحقيقية بلا استثناء تحت عملية الجامعة هذه عملية
+
+82
+00:07:58,500 --> 00:08:04,520
+مجموعة الأعداد الحقيقية الموجبة فقط تحت عملية
+
+83
+00:08:04,520 --> 00:08:10,100
+الضرب قال يعرف ال function Phi of X بدل سوى 2X لكل
+
+84
+00:08:10,100 --> 00:08:16,160
+X الموجودة في Rالان بدى اسأل السؤال التالي هل ال
+
+85
+00:08:16,160 --> 00:08:21,920
+function هدى فعلا هدى معرفة من R عليها عملية الجمع
+
+86
+00:08:21,920 --> 00:08:27,680
+الى R plus تحت عملية الضرب ام لا باجي بقول ال X
+
+87
+00:08:27,680 --> 00:08:33,230
+هدى موجود وين هناإذا قد يكون موجب و قد يكون سلب و
+
+88
+00:08:33,230 --> 00:08:39,370
+قد يكون صفر تمام ما هي صوت صوت اتنين to the power
+
+89
+00:08:39,370 --> 00:08:44,150
+X هل اتنين to the power X موجودة في R plus يعني
+
+90
+00:08:44,150 --> 00:08:48,550
+اتنين to the power X لابتاخد Zero ولا بتاخد قيمة
+
+91
+00:08:48,550 --> 00:08:55,030
+سالبةطبعًا الـ exponential function دائمًا وأبدًا
+
+92
+00:08:55,030 --> 00:09:01,410
+أقل من زيرو عمرهاش بتكون أقل من زيرو سواء كان U of
+
+93
+00:09:01,410 --> 00:09:06,290
+X والله A to the power X لو رجعت لرسمتها دائمًا
+
+94
+00:09:06,290 --> 00:09:10,950
+أعلى محور X يبقى أقل من زيرو إذا كلامنا هذا
+
+95
+00:09:10,950 --> 00:09:15,790
+تعريفنا سليم مائة بالمائة يبقى إيش ضايل علينا؟ one
+
+96
+00:09:15,790 --> 00:09:20,260
+to one and one to one نرجع لمبادئ الرياضيةلما
+
+97
+00:09:20,260 --> 00:09:24,980
+بنقول one to one بالبلد العناصر المختلفة لها صور
+
+98
+00:09:24,980 --> 00:09:29,940
+مختلفة يعني لو أخدت x1 لا يساوي x2 بدي أثبت أن ال
+
+99
+00:09:29,940 --> 00:09:34,720
+f of x1 لا يساوي ال f of x2 أو ال contrapositive
+
+100
+00:09:34,720 --> 00:09:40,040
+إيها لو كان ال f of x1 بدي يساوي f of x2 بدي أثبت
+
+101
+00:09:40,040 --> 00:09:45,620
+أن ال x1 يساوي x2 إن حدث ذلك يبقى ال function one
+
+102
+00:09:45,620 --> 00:09:51,490
+to oneيبقى بدى اثبتله الخطوة الأولى في is one to
+
+103
+00:09:51,490 --> 00:09:58,890
+one مشان هيك بداجي اقوله assume اللي هو main في of
+
+104
+00:09:58,890 --> 00:10:05,680
+x يساوي في of yإذا قررت أثبت له إن الـ X بدها
+
+105
+00:10:05,680 --> 00:10:10,740
+تساوي Y بيتم المطلوب طيب فاي أوف X هي كده يا شباب؟
+
+106
+00:10:10,740 --> 00:10:19,390
+اتنين أص X فاي أوف Y اتنين أص Yلما يكون الطرفين
+
+107
+00:10:19,390 --> 00:10:25,070
+متساوين و تتساوى الأساسات يبقى الأساس متساوية واحد
+
+108
+00:10:25,070 --> 00:10:30,490
+تاني ماعجبوش كلامي قال خد لن للطرفين بنقوله ماشي
+
+109
+00:10:30,490 --> 00:10:37,570
+لو أخدنا لن للطرفين بيصير X في لن اتنين يساوي Y في
+
+110
+00:10:37,570 --> 00:10:42,540
+لن اتنينلو قسمنا الطرفين على الان اتنين هذا
+
+111
+00:10:42,540 --> 00:10:48,720
+بيعطينا مين انه ال X يساوي ال Y مدام ال X يساوي ال
+
+112
+00:10:48,720 --> 00:10:54,240
+Y يبقى Phi is one to one الان بدنا نيجي نثبت ان
+
+113
+00:10:54,240 --> 00:11:02,810
+Phi is ontoمش هنثبت انه في is onto بضروحه اخد عنصر
+
+114
+00:11:02,810 --> 00:11:09,970
+في R plus و اثبت انه له اصل في R ان حدث ذلك بصير
+
+115
+00:11:09,970 --> 00:11:16,190
+الفي is onto يبقى بداجي اقوله لاتفترض ان ال Y
+
+116
+00:11:16,190 --> 00:11:23,610
+موجودة في ال R plusيبقى الـY هذي أكبر من الـ0 ولا
+
+117
+00:11:23,610 --> 00:11:31,690
+أقل من الـ0؟ يبقى هذا يعطيك أن الـY أكبر من الـ0
+
+118
+00:11:31,690 --> 00:11:38,890
+يعني الـY هذي موجبة مدام موجبة يبقى الـlog Y
+
+119
+00:11:38,890 --> 00:11:45,980
+للأساس اتنين exist ولا does not exist؟exist لأن
+
+120
+00:11:45,980 --> 00:11:50,920
+اللغة الرتم مش معرفة إلا لقيمة موجبة لكن لو قلت له
+
+121
+00:11:50,920 --> 00:11:56,700
+Y هذه موجودة في R بصير كلامي هذا ماله مش صحيح لأنه
+
+122
+00:11:56,700 --> 00:12:00,460
+قد تكون exist و قد لا تكون exist لكن كونها موجبة
+
+123
+00:12:00,460 --> 00:12:07,980
+يبقى هذا exist مدام exist يبقى بدي أروح أسمي تسمية
+
+124
+00:12:07,980 --> 00:12:15,300
+لغة Y للأساس اتنين بدي أسمي X مثلالو رجعنا ل
+
+125
+00:12:15,300 --> 00:12:20,720
+calculus P بدي اكتب ال log بدلالة ال len يبقى هذا
+
+126
+00:12:20,720 --> 00:12:29,140
+len y على len 2 بده يساوي ال x لو ضربنا ضرب تبادل
+
+127
+00:12:29,140 --> 00:12:38,330
+يبقى len y يساوي ال x في len 2لو استخدمت خواص ال
+
+128
+00:12:38,330 --> 00:12:46,830
+len يبقى len y بده يساوي len اتنين اص اكس مظبوط
+
+129
+00:12:46,830 --> 00:12:54,010
+ايك؟ يبقى بناء عليه لو رفعت اتنين كأس للعدد ايه؟
+
+130
+00:12:54,010 --> 00:13:00,450
+بيصير y يساوي قداش اتنين اص اكس اتنين اص اكس مين
+
+131
+00:13:00,450 --> 00:13:07,680
+هي هذه حسب التعريف مش عبارة عن five of xاذا اي
+
+132
+00:13:07,680 --> 00:13:15,560
+element y موجود في الار بلس لاجتله اصل x موجود في
+
+133
+00:13:15,560 --> 00:13:20,180
+الار معناه هذا الكلام ان الار موجود في الار طيب
+
+134
+00:13:20,180 --> 00:13:23,740
+خلصنا ال condition التاني بدنا نروح لل condition
+
+135
+00:13:23,740 --> 00:13:30,140
+التاني يبقى باجي بقوله لو كان ال x و y موجودة في
+
+136
+00:13:30,140 --> 00:13:38,720
+الار then بدي اخد في of خلي بالك هنابدي اخد x في y
+
+137
+00:13:38,720 --> 00:13:45,420
+والله x زائد yيبقى ال operation هنا ال operation
+
+138
+00:13:45,420 --> 00:13:49,040
+اللي موجودة في ال group الأولى ال operation اللي
+
+139
+00:13:49,040 --> 00:13:57,560
+عنده زائد يبقى بقوله في x زائد y وليست x في y لأن
+
+140
+00:13:57,560 --> 00:14:01,320
+ال operation ما بين ال a و ال b هي ال operation
+
+141
+00:14:01,320 --> 00:14:04,740
+اللي موجودة في جيه الأولى ال operation اللي موجودة
+
+142
+00:14:04,740 --> 00:14:11,460
+عنده هي الجامعةيبقى حسب التعريف هذا بدل ساوي اتنين
+
+143
+00:14:11,460 --> 00:14:21,020
+اص X زائد Y او اتنين اص X في اتنين اص Yهذا الكلام
+
+144
+00:14:21,020 --> 00:14:26,120
+يساوي رياضيا كلام سليم 100% يبقى هنا اللي بينهم
+
+145
+00:14:26,120 --> 00:14:29,760
+صلة عملية ضرب وليست عملية جمع
+
+146
+00:14:38,750 --> 00:14:43,910
+يبقى تحقق ال condition main التاني يبقى بناء عليه
+
+147
+00:14:43,910 --> 00:14:54,690
+فاي is an isomorphism فاي is an isomorphism حد
+
+148
+00:14:54,690 --> 00:15:03,350
+يلقي تساول هنا علي صوتك بس اه
+
+149
+00:15:04,080 --> 00:15:09,060
+لما قلنا لغة why الأساس اتنين exist ليش؟ لأن Y
+
+150
+00:15:09,060 --> 00:15:16,420
+قيمة موجبة لو كانت صفر أو سالبة فاللغة غير معرفة
+
+151
+00:15:16,420 --> 00:15:22,220
+تمام؟ يبقى انا عندي رقم موجب اخد اللغة للأساس
+
+152
+00:15:22,220 --> 00:15:28,230
+اتنين ليش اتنين؟ انا متعمد اخد اتنينلأن لو كانت
+
+153
+00:15:28,230 --> 00:15:33,650
+المسألة five of x سوى تلاتة of x سوف أقول له while
+
+154
+00:15:33,650 --> 00:15:37,270
+أساس تلاتة لو كانت أربعة سوف أقول له أساس أربعة و
+
+155
+00:15:37,270 --> 00:15:44,070
+هكذا لكي نوصل للإتنين of x خلاص واضحة ليش أخدنا
+
+156
+00:15:44,070 --> 00:15:50,430
+هذه يبقى exist لإن هذه greater than zeroو روحت
+
+157
+00:15:50,430 --> 00:15:55,770
+قولت هذه كل عبض ايش ما تطلع سميتها X تمام عملت
+
+158
+00:15:55,770 --> 00:15:59,490
+الشغل الرياضي تبع ال calculus لغاية ما وصلت لمين
+
+159
+00:15:59,490 --> 00:16:05,730
+وصلت لل Y يساوي 2 و 6 اللي هي Phi of X نجي ناخد
+
+160
+00:16:05,730 --> 00:16:10,430
+كمان مثال ثاني مثال اتنين
+
+161
+00:16:13,030 --> 00:16:20,950
+بقول let g be a cyclic group let g be a cyclic
+
+162
+00:16:20,950 --> 00:16:39,430
+group of order n of order n let g bar سوى z n of
+
+163
+00:16:42,960 --> 00:16:52,120
+إثبت لي إن الـ G isomorphic لمن؟ لـ ZN G
+
+164
+00:16:52,120 --> 00:17:06,000
+isomorphic ل ZN نرجع
+
+165
+00:17:06,000 --> 00:17:10,920
+لسؤالنا مرة ثانيةبقول ياخد الـG الـcyclic group
+
+166
+00:17:10,920 --> 00:17:16,800
+الـorder Lها يساوي M مادام الـcyclic على الأقل
+
+167
+00:17:16,800 --> 00:17:23,380
+فيها كام generator؟ اتنين generator ومعكسه تمام؟
+
+168
+00:17:23,380 --> 00:17:28,720
+مابناش المعكس احنا مكفين واحد بدي افترض انه فيها
+
+169
+00:17:28,720 --> 00:17:36,820
+generator وليكن A يبقى باجي بقوله since الـG is
+
+170
+00:17:36,820 --> 00:17:45,160
+cyclicيبقى نحن لدينا ان الـ G هذه بدها تساوي ال
+
+171
+00:17:45,160 --> 00:17:51,560
+identity و ال A و ال A ترابيع و نظل ماشيين لغاية
+
+172
+00:17:51,560 --> 00:17:58,490
+ال A M minus ال oneمظبوط كما فهمت من الشبطر قبل
+
+173
+00:17:58,490 --> 00:18:04,850
+السابق الـcyclic subgroups يبقى هذه كإنها group
+
+174
+00:18:04,850 --> 00:18:09,770
+generated by a مكتوبة بالشكل اللي عندنا هنا هاي
+
+175
+00:18:09,770 --> 00:18:14,690
+الـcyclic group وال order اللي هيسوي إن ال element
+
+176
+00:18:14,690 --> 00:18:20,550
+الأخر يصير am ناقص واحد لإن an بدو يسوى ال
+
+177
+00:18:20,550 --> 00:18:28,430
+identity elementقال لي خد الجيبار تساوي ZN خليني
+
+178
+00:18:28,430 --> 00:18:32,890
+أسألكوا السؤال التالي ZN ال operation اللي عليها
+
+179
+00:18:32,890 --> 00:18:37,750
+الجامع ولا ضرب حسب ما خدناه في تعريف ال groups
+
+180
+00:18:37,750 --> 00:18:42,170
+جامع ممتاز يدني بقى حطلي المعلومة هذه في إيدك في
+
+181
+00:18:42,170 --> 00:18:49,150
+دماغك لإن جامع موديولو N كل N بتبدأ الدورة من جديد
+
+182
+00:18:49,760 --> 00:18:54,400
+طب كويس قال لي اثبت لي ان اتنين هذول ايزو مورفكت
+
+183
+00:18:54,400 --> 00:18:59,380
+اذا انا بده اروح اعرف function من الجروب الاولى
+
+184
+00:18:59,380 --> 00:19:03,740
+الى الجروب التانى ونشوف هذه ال function هل هي one
+
+185
+00:19:03,740 --> 00:19:07,560
+to one و one to two بتخدم الخاصية اللى عندنا هذه
+
+186
+00:19:07,560 --> 00:19:10,460
+ولا لأ اذا بده اروح اقوله define
+
+187
+00:19:13,750 --> 00:19:24,190
+فانكشن فاي من جي الى زد ن باى عشان تبقى فانكشن
+
+188
+00:19:24,190 --> 00:19:29,090
+تتأثر على العنصر اللى في جي من جي أيه يبقى ايه
+
+189
+00:19:29,090 --> 00:19:36,530
+الشكل العنصر اللى هنا ايه ال power معينة يبقى a to
+
+190
+00:19:36,530 --> 00:19:43,510
+the power k مثلاطبعا k محصورة ما بين ال zero و ما
+
+191
+00:19:43,510 --> 00:19:48,370
+بين ال main ال n minus ال one ما بين ال zero و ما
+
+192
+00:19:48,370 --> 00:19:52,890
+بين ال n minus ال one بدها تساوي مين؟ بدها تساوي
+
+193
+00:19:52,890 --> 00:20:01,030
+عنصر في z n بقدر اقول k itself و ال k هذا اكبر من
+
+194
+00:20:01,030 --> 00:20:06,030
+او يساوي zero اقل من n بصير الكلام هكذا صح ولا
+
+195
+00:20:06,030 --> 00:20:15,340
+غلط؟صح 100% لأن ك محصورة بين ال zero و ال N يبقى
+
+196
+00:20:15,340 --> 00:20:22,330
+واحد من هذول AKK اللي عندنا هذه هي element من ZN
+
+197
+00:20:22,330 --> 00:20:30,610
+لأن عناصر الـ ZN 0,1,2,3 لغاية N minus الـ 1 مظبوط
+
+198
+00:20:30,610 --> 00:20:35,390
+يبقى هذا التعريف سليم مائة مائة ك function الآن
+
+199
+00:20:35,390 --> 00:20:41,840
+بدي أثبت أن هذه one to oneيبقى بدى اثبتله ان فاي
+
+200
+00:20:41,840 --> 00:20:47,960
+is one to one مشان هيك بدى اخد صورتين متساوي او
+
+201
+00:20:47,960 --> 00:20:55,860
+صورتين متساوياتين يبقى باجي بقوله assume فاي of AK
+
+202
+00:20:55,860 --> 00:21:09,220
+تساوي فاي of AJ مثلاعشان اثبت ان الـ A K بده يساوي
+
+203
+00:21:09,220 --> 00:21:14,940
+الـ A J كويس يبقى حسب ال definition Phi of AK اللي
+
+204
+00:21:14,940 --> 00:21:22,300
+هي بقداش K Phi of AJ اللي هي بقداش BGأو ان شئتم
+
+205
+00:21:22,300 --> 00:21:30,020
+فقولوا k minus الجيه بده يسوي قداش zero او ان شئتم
+
+206
+00:21:30,020 --> 00:21:36,380
+فقولوا a to the k minus الجيه بده يسوي a to the
+
+207
+00:21:36,380 --> 00:21:46,460
+zero او بمعنى اخرالـ A K في الـ A مينوس الـ J بده
+
+208
+00:21:46,460 --> 00:21:51,420
+يسوى ال identity لأن ال element مرفوع للـ O Zero
+
+209
+00:21:51,420 --> 00:21:55,960
+دائما و أبدا بده يسوى ال identity تبع ال group طب
+
+210
+00:21:55,960 --> 00:22:02,000
+لو ضربت الطرفين في A J بصير عندى هنا جداش بضل في
+
+211
+00:22:02,000 --> 00:22:08,100
+الطرف الشمالأيه كي بده يساوي اي جي اظن و هو
+
+212
+00:22:08,100 --> 00:22:12,820
+المطلوب يبقى اخذ صورتين متساويتين اثبت ان الاصل
+
+213
+00:22:12,820 --> 00:22:19,520
+متساوي يبقى فاي is one to one يبقى بداجي اثبت ان
+
+214
+00:22:19,520 --> 00:22:21,080
+فاي is onto
+
+215
+00:22:25,800 --> 00:22:33,620
+مشان هيك بيروح أخد element وين في ZN يبقى هنا let
+
+216
+00:22:33,620 --> 00:22:41,960
+K موجود في ZN then ال
+
+217
+00:22:41,960 --> 00:22:52,470
+K هذا أكبر من أو يسوى zero أقل من ال Nهذا يعني أن
+
+218
+00:22:52,470 --> 00:23:01,170
+الـ A to the power of K موجود في G؟ سكت الناس طلع
+
+219
+00:23:01,170 --> 00:23:06,410
+لتعريف الـ D هذا يعني أن A to the power of K موجود
+
+220
+00:23:06,410 --> 00:23:11,690
+في G ولا لا؟ يعني الـ Phi هتأثر عليه، صحيح ولا لا؟
+
+221
+00:23:11,690 --> 00:23:20,730
+يبقى هذا معناته أن K بدأ تساوي Phi of A Kيبقى ال
+
+222
+00:23:20,730 --> 00:23:27,190
+element K اللي أخدته في Z ان لقيتله أصل A K موجود
+
+223
+00:23:27,190 --> 00:23:34,270
+في جيه معناه هذا الكلام أن فاي is on to الآن دلت
+
+224
+00:23:34,270 --> 00:23:42,790
+خاصية الأخيرة finally بدي five of بدي أخد two
+
+225
+00:23:42,790 --> 00:23:52,780
+elements A K في A G مثلايبقى هذا element من جي و
+
+226
+00:23:52,780 --> 00:23:58,240
+هذا element ثاني من جي تمام؟ يبقى هذا الكلام بدر
+
+227
+00:23:58,240 --> 00:24:10,770
+يساوي نظرا لإنه هذا بدر يساوي في اك زائد جيصار هذا
+
+228
+00:24:10,770 --> 00:24:17,450
+كله element واحد حسب التعريف يبقى هذا الكلام تبع
+
+229
+00:24:17,450 --> 00:24:26,610
+ال fi بده يساوي k زائد j هذا الكلام بده يساوي ال k
+
+230
+00:24:26,610 --> 00:24:38,340
+هي fi of kوهذه Z Phi of AJ حسب التعريف طبعا ال
+
+231
+00:24:38,340 --> 00:24:42,880
+operation بينهم هي عملية جامعة لأن Z in ال
+
+232
+00:24:42,880 --> 00:24:48,140
+operation اللي عليها جامعة يبقى تحققت الخاصية مع
+
+233
+00:24:48,140 --> 00:24:55,440
+أن هذا الكلام Phi is an isomorphism يبقى دص وهكذا
+
+234
+00:24:55,440 --> 00:25:00,380
+Phi is an isomorphism
+
+235
+00:25:25,380 --> 00:25:37,020
+خدلي ال exercise هذا يك علك تمرن إيدك فيه if g is
+
+236
+00:25:37,020 --> 00:25:46,220
+infinite .. infinite cyclic
+
+237
+00:25:46,220 --> 00:25:56,510
+group .. cyclic group thenالـ G isomorphic
+
+238
+00:25:56,510 --> 00:26:03,010
+إلى Z سأعطيك
+
+239
+00:26:03,010 --> 00:26:06,990
+الـ function و أنت تثبت one to one و تحقق الخاصية
+
+240
+00:26:06,990 --> 00:26:17,530
+يبقى بدك تاخد لي Phi من Zالى G جلبت الوضع اني فوق
+
+241
+00:26:17,530 --> 00:26:22,750
+اخدتها من جيه لزد ان هنا بدي اخليها من Z الى G
+
+242
+00:26:22,750 --> 00:26:30,350
+define by
+
+243
+00:26:30,350 --> 00:26:38,890
+Phi of K بدي سوى A to the power K
+
+244
+00:26:41,890 --> 00:26:46,750
+اثبتلي ان هذه one to one و one to خاصية ال
+
+245
+00:26:46,750 --> 00:26:58,190
+isomorphism ناخد المثال رقم تلاتة ايش
+
+246
+00:26:58,190 --> 00:27:05,090
+رايك فيه ستة؟ مين عناصرها؟
+
+247
+00:27:05,090 --> 00:27:12,900
+واحد اتنين تلاتة اربعة خمسة في غيرهم؟السؤال هو هل
+
+248
+00:27:12,900 --> 00:27:21,780
+هذه group Cyclic؟ كيف
+
+249
+00:27:21,780 --> 00:27:27,360
+لا؟ خمسة و زير و واحد، خمسة و واحد و خمسة، خمسة
+
+250
+00:27:27,360 --> 00:27:33,420
+تربيعخمسة وعشرين شيل منهم أربعة ستات بيظل ال
+
+251
+00:27:33,420 --> 00:27:37,940
+identity يبقى الخمسة generator مظبوط يبقى هذه is
+
+252
+00:27:37,940 --> 00:27:44,380
+cyclic group شوف ليه بالله هذه isomorphic لزد ولا
+
+253
+00:27:44,380 --> 00:27:52,800
+لأ الأولى كام عنصر فيها والتانية والأولى is cyclic
+
+254
+00:27:52,800 --> 00:27:58,850
+والتانيةZn Cyclic اصلا انهم عليها عملية الجمع اذا
+
+255
+00:27:58,850 --> 00:28:01,990
+زد اتنين Cyclic زد تلاتة Cyclic زد اربعة Cyclic
+
+256
+00:28:01,990 --> 00:28:06,730
+طيب واني ال Cyclic group is Abelian يبقى هذي
+
+257
+00:28:06,730 --> 00:28:12,590
+Abelian هذي Abelian ال order للخمسة يساوي اتنين
+
+258
+00:28:12,590 --> 00:28:17,350
+وال order للواحد كذلك يساوي اتنين لأن هذا مافيش
+
+259
+00:28:17,350 --> 00:28:27,990
+فيها الا العنصر 01مظبوط هيك؟ طيب شوف ليه كمان and
+
+260
+00:28:27,990 --> 00:28:35,930
+لو أخدتيه عشرة شوف هالي اللي هي عبارة عن واحد،
+
+261
+00:28:35,930 --> 00:28:46,590
+تلاتة، سبعة، تسعة شوف هالي isomorphic لزد أربعة أم
+
+262
+00:28:46,590 --> 00:28:47,310
+لا؟
+
+263
+00:28:50,240 --> 00:28:58,120
+الـ U10 ايزو مورفك لـ Z4 ولا لأ ها هذي Cyclic ولا
+
+264
+00:28:58,120 --> 00:29:02,620
+لأ طيب تعالى نشوف هذي Cyclic ولا لأ نشوف فيها
+
+265
+00:29:02,620 --> 00:29:07,970
+Generator ولا لأتلاتة وزيرة بواحد تلاتة و أس واحد
+
+266
+00:29:07,970 --> 00:29:13,910
+بتلاتة تلاتة ربيع تسعة تلاتة تكيب بسبعة و عشرين
+
+267
+00:29:13,910 --> 00:29:18,950
+بشيل عشرتين بظال سبعة تلاتة و أس اربعة بواحد واحد
+
+268
+00:29:18,950 --> 00:29:23,250
+و تمانين تمان عشرات بواحد يبقى الـcyclic والتلاتة
+
+269
+00:29:23,250 --> 00:29:28,550
+generatorأحدكم يقدر يجيب الجنريتر التاني هو السبعة
+
+270
+00:29:28,550 --> 00:29:32,730
+لكن تسعة ما هوش generator لأن تسعة فتسعة بواحد و
+
+271
+00:29:32,730 --> 00:29:37,230
+تمانين تسعة تربيع بال identity لكن تلاتة و أربعة
+
+272
+00:29:37,230 --> 00:29:40,970
+هو اللي بال identity يبقى هذي ال cycle يبقى هذي
+
+273
+00:29:40,970 --> 00:29:49,370
+isomorphic كمان لزد أربعة طيب السؤال هو but هل
+
+274
+00:29:49,370 --> 00:29:57,440
+اليوم ماشي اللي هو ماميم واحدو خمسة و سبعة و
+
+275
+00:29:57,440 --> 00:30:08,200
+أحداشر هل هذه isomorphic ل Z أربعة؟
+
+276
+00:30:08,200 --> 00:30:15,780
+هل هذه Cyclic ولا لا؟ هل هذه Cyclic؟
+
+277
+00:30:17,220 --> 00:30:22,900
+خمسة وعشرين كده؟ خمسة في خمسة في خمسة وعشرين شيلهم
+
+278
+00:30:22,900 --> 00:30:25,780
+اتناش يصير ال identity يبقى خمسة تربيع بال
+
+279
+00:30:25,780 --> 00:30:30,400
+identity سبعة تربيع بال identity تسعة واربعين
+
+280
+00:30:30,400 --> 00:30:33,980
+تمانية واربعين ومضال واحد احداشر في احداشر مية
+
+281
+00:30:33,980 --> 00:30:37,060
+واحد وعشرين ع اتناش مضال واحد يبقى مش فيها ولا
+
+282
+00:30:37,060 --> 00:30:44,770
+generatorيبقى هذه is not isomorphic because السبب
+
+283
+00:30:44,770 --> 00:30:59,850
+ان Z4 is cyclic but و لكن U12 is not cyclic
+
+284
+00:30:59,850 --> 00:31:04,850
+طيب U18
+
+285
+00:31:07,130 --> 00:31:12,030
+Isomorphic لـ Z6 نقول
+
+286
+00:31:12,030 --> 00:31:18,800
+لك مين اليو 18يكون تمنتاش اللي هي تساوي العناصر
+
+287
+00:31:18,800 --> 00:31:26,300
+واحد، اتنين، تلاتة، اربعة، خمسة، ستة، سبعة،
+
+288
+00:31:26,300 --> 00:31:32,420
+تمانية، تسعة، عشرة، احداشر، اتناشر، تلاتاشر،
+
+289
+00:31:32,420 --> 00:31:39,200
+اربعتاشر، خمستاشر، ستاشر، سبعتاشركم منصر هذول؟ ستة
+
+290
+00:31:39,200 --> 00:31:48,900
+هل هذه isomorphic لزد ستة ولا لا؟
+
+291
+00:31:48,900 --> 00:31:53,960
+طيب
+
+292
+00:31:53,960 --> 00:31:59,960
+يالا افحص براحتك في الدار isomorphic لزد ستة ليش؟
+
+293
+00:31:59,960 --> 00:32:05,230
+ان هذه Cyclic وهذه كمان Cyclicيبقى قدلي بدناش
+
+294
+00:32:05,230 --> 00:32:08,810
+اتنين generator بيكفي واحد جيبلي واحد منهم
+
+295
+00:32:08,810 --> 00:32:17,570
+generator بتجيب يولد كل العناصر أيه؟ مثال
+
+296
+00:32:17,570 --> 00:32:23,850
+اتنين هذا؟ any operation قلت cyclic ايش ما كانت
+
+297
+00:32:23,850 --> 00:32:29,530
+تكون لم أحدد قلت تجرب وcyclic تمام؟ وبالتالي اي
+
+298
+00:32:29,530 --> 00:32:30,570
+عملية؟
+
+299
+00:32:33,770 --> 00:32:39,290
+علي صوتك شوية لا
+
+300
+00:32:39,290 --> 00:32:45,850
+انت انت لما زد خمسة فيها كام عنصر؟ خمس عناصر زد
+
+301
+00:32:45,850 --> 00:32:51,110
+ستة فيها ست عناصر و هكذا كيف واحدة فيها ست عناصر و
+
+302
+00:32:51,110 --> 00:32:55,730
+واحدة خمس عناصر فيها ايزو مورف فيهم؟أبسط الأشياء
+
+303
+00:32:55,730 --> 00:32:59,470
+قلتلك أول ما بديت عدد العناصر في الجروب الأولى جد
+
+304
+00:32:59,470 --> 00:33:02,890
+عدد العناصر في الجروب التانى اختلفوا العناصر مافيش
+
+305
+00:33:02,890 --> 00:33:07,790
+isomorphism وانت مغمق بدون نقاش تمام؟ إذا عدد
+
+306
+00:33:07,790 --> 00:33:10,730
+العناصر في الجروب الأولى يختلف عن عدد العناصر في
+
+307
+00:33:10,730 --> 00:33:13,950
+الجروب التانى there is no isomorphism between two
+
+308
+00:33:13,950 --> 00:33:20,030
+groups مافيش بالمرة حد بدي أسأل تاني طيب نجيبلك
+
+309
+00:33:20,030 --> 00:33:27,770
+مثال من نوعين جديدمثال أربعة مثال
+
+310
+00:33:27,770 --> 00:33:33,670
+أربعة بيقول let ال G هي ال special linear group of
+
+311
+00:33:33,670 --> 00:33:39,490
+two by two matrices over R وهي كل المصوات اللي على
+
+312
+00:33:39,490 --> 00:33:49,710
+الشكل A,B,C,D بحيث ان ال A,D ناقص ال B,C بدوا ساوي
+
+313
+00:33:49,710 --> 00:34:02,810
+الواحد الصحيحlet الـ M be any two by two matrix
+
+314
+00:34:02,810 --> 00:34:06,050
+matrix
+
+315
+00:34:06,050 --> 00:34:17,030
+with a determinant لـ M لا يساوي Zero define
+
+316
+00:34:20,640 --> 00:34:31,460
+A mapping Define A mapping Phi M
+
+317
+00:34:31,460 --> 00:34:49,180
+من G إلى G by Phi M of A يساوي M A M inverse لكل
+
+318
+00:34:49,970 --> 00:35:00,990
+الـ A اللي موجودة في G show that الـ
+
+319
+00:35:00,990 --> 00:35:05,890
+Phi M is an isomorphism
+
+320
+00:35:43,290 --> 00:35:48,490
+نرجع مرة تانية أخد لجروب جيله ال special linear
+
+321
+00:35:48,490 --> 00:35:52,890
+group of two by two matrices over R و هي كل
+
+322
+00:35:52,890 --> 00:35:56,670
+المصفوفات لنظامها اتنين في اتنين بعيادة المحدد
+
+323
+00:35:56,670 --> 00:36:01,590
+تبعها بده يساوي واحد صحيح قال افترض انه عندي
+
+324
+00:36:01,590 --> 00:36:05,490
+مصفوفة من نظامها اتنين في اتنين ومحددها لا يساوي
+
+325
+00:36:05,490 --> 00:36:10,520
+zero لم أقل واحد صحيحالـ M ليس بالضرورة محددها
+
+326
+00:36:10,520 --> 00:36:15,880
+يسوى واحد صحيح قلت M محدد تبعي ليه يسوى Zero عرفت
+
+327
+00:36:15,880 --> 00:36:21,620
+Function Phi M من G إلى G by Phi M of A يسوى M A M
+
+328
+00:36:21,620 --> 00:36:26,180
+inverse لكل الـ A اللي موجودة في G بيقول أن Phi M
+
+329
+00:36:26,180 --> 00:36:31,220
+is an isomorphism النقطة الأولى بتتأكد هل ال
+
+330
+00:36:31,220 --> 00:36:36,220
+function اللي عرفتها تعريفي صحيح ولا لأ بمعنى آخر
+
+331
+00:36:36,220 --> 00:36:44,240
+واللهإذا طلع محدد المصوفة هذه بواحد صحيح معناته
+
+332
+00:36:44,240 --> 00:36:49,580
+المصوفة هذه موجودة في G فعلا يبقى تعريفي هذا من G
+
+333
+00:36:49,580 --> 00:36:55,120
+ل G بصير كلام سليم ليش؟ لإن ايه اللي عندي هذه أنا
+
+334
+00:36:55,120 --> 00:36:59,960
+ماخدها من G يعني المحدد تبعها بجداش بواحد صحيح نحن
+
+335
+00:36:59,960 --> 00:37:05,150
+متأكدين منه لكن ال M بعرفش أنا تمام؟إذا بدي أثبت
+
+336
+00:37:05,150 --> 00:37:09,510
+أول شيء أن الـ Phi is well defined يعني معرفة
+
+337
+00:37:09,510 --> 00:37:16,530
+تعريفا صحيحا فبناجي بقوله هنا ال Phi is well
+
+338
+00:37:16,530 --> 00:37:23,130
+defined well defined يعني معرفة تعريفا صحيحا
+
+339
+00:37:25,810 --> 00:37:30,210
+بمعنى آخر بدي أثبت أن هذا element موجود في الـ G
+
+340
+00:37:30,210 --> 00:37:39,290
+لذلك بدي أخد ال determinant للـ M A M inverse بدي
+
+341
+00:37:39,290 --> 00:37:44,450
+أرجع لمين؟ لل linear algebra يبقى هذا معناته ال
+
+342
+00:37:44,450 --> 00:37:50,810
+determinant لل M في ال determinant لل A في ال
+
+343
+00:37:50,810 --> 00:37:57,450
+determinant لل M inverseالأن الـ determinant يعني
+
+344
+00:37:57,450 --> 00:38:02,010
+قيمة حقيقية يعني التلث قيم حقيقية مضروبة في بعضها
+
+345
+00:38:02,010 --> 00:38:07,250
+والقيم الحقيقية commutative يبقى هذا الكلام بده
+
+346
+00:38:07,250 --> 00:38:14,820
+يساوي ال determinant لل Mفي ال determinant لل M
+
+347
+00:38:14,820 --> 00:38:20,660
+inverse في ال determinant لل A او بقدر اقول ال
+
+348
+00:38:20,660 --> 00:38:25,720
+determinant لل M في ال M inverse في ال determinant
+
+349
+00:38:25,720 --> 00:38:33,080
+لل A هذا الكلام يساويالمصوفة في معكوسة المعكوسة
+
+350
+00:38:33,080 --> 00:38:39,400
+موجودة هنا ولا لا؟ موجودة لأن أنا جايل أن المحدد
+
+351
+00:38:39,400 --> 00:38:45,160
+لا يساوي zero إذا المصوفة في معكوسة بتعطيني مصوفة
+
+352
+00:38:45,660 --> 00:38:52,240
+الوحدة يبقى هذا ال determinant لمصوفة الوحدة في ال
+
+353
+00:38:52,240 --> 00:38:57,500
+determinant لل a الآن ال determinant لمصوفة الوحدة
+
+354
+00:38:57,500 --> 00:39:04,780
+بقداش بواحد ال determinant ل a, a موجودة في g, g
+
+355
+00:39:04,780 --> 00:39:10,430
+هي المحدد تبعها بقداش بواحديبقى في واحد الجواب
+
+356
+00:39:10,430 --> 00:39:20,150
+يساوي قداش واحد يبقى هنا الساعة ال m a m inverse
+
+357
+00:39:20,150 --> 00:39:25,190
+belongs to g يبقى تعريفي هذا معله تعريفا صحيحا
+
+358
+00:39:25,190 --> 00:39:32,190
+الان بدى اثبت ان فاي is one to one حاجة اقوله as
+
+359
+00:39:32,190 --> 00:39:42,600
+you فايم طبعاهنا ا assume ان فايم of a فايم of a
+
+360
+00:39:42,600 --> 00:39:50,900
+بدر سوى فايم of b طبعا
+
+361
+00:39:50,900 --> 00:39:57,100
+a و b مصهوفات في gيبقى هدول بيبقى يسووا بعض ثم
+
+362
+00:39:57,100 --> 00:40:08,960
+فايم اف ايه م ا م انفرست مبم انفرست طيب بال right
+
+363
+00:40:08,960 --> 00:40:13,200
+cancellation لو وال left cancellation لو هذا
+
+364
+00:40:13,200 --> 00:40:20,490
+بيعطينا ان ا تسوى بيه لذلك فايم is one to oneيبقى
+
+365
+00:40:20,490 --> 00:40:28,550
+بداجي اخد الان يبقى
+
+366
+00:40:28,550 --> 00:40:35,670
+بداجي اخد الان يبقى بداجي
+
+367
+00:40:35,670 --> 00:40:38,630
+اخد الان يبقى بداجي اخد الان يبقى بداجي اخد الان
+
+368
+00:40:38,630 --> 00:40:38,690
+يبقى بداجي اخد الان يبقى بداجي اخد الان يبقى بداجي
+
+369
+00:40:38,690 --> 00:40:38,870
+اخد الان يبقى بداجي اخد الان يبقى بداجي اخد الان
+
+370
+00:40:38,870 --> 00:40:42,130
+يبقى بداجي اخد الان يبقى بداجي اخد الان يبقى بداجي
+
+371
+00:40:42,130 --> 00:40:49,210
+اخد الان يبقى
+
+372
+00:40:49,210 --> 00:40:49,810
+بداجي ا
+
+373
+00:40:54,890 --> 00:41:02,870
+الـ B هذه بقدر اكتبها على الشكل التالي M M Inverse
+
+374
+00:41:02,870 --> 00:41:14,550
+B M M Inverse بنفع ولا مانفعش هذه مين ال identity
+
+375
+00:41:14,550 --> 00:41:20,680
+وهذه مينخلص يبقى بالضالة المصوفة هذه بيه كما هي
+
+376
+00:41:20,680 --> 00:41:27,760
+هذه بقدر اكتبها على الشكل التالي M في M inverse
+
+377
+00:41:27,760 --> 00:41:35,620
+بيه M و هنا M inverse من خاصية ال associativity
+
+378
+00:41:35,620 --> 00:41:41,480
+يبقى فاصلتي التلاتة هدول لحالي ايش رأيك هدول بدي
+
+379
+00:41:41,480 --> 00:41:51,860
+اسمهم تسمية جديدة Mام انفرس هذه كل التلاتة حصل ضرب
+
+380
+00:41:51,860 --> 00:41:58,320
+سميته ايه يبقى بناء عليه هذا الكلام بدر ساوي من
+
+381
+00:41:58,320 --> 00:42:06,700
+بدر ساوي في ام او ايه يبقى المصوفة بيه اللي خدتها
+
+382
+00:42:06,700 --> 00:42:12,780
+لاجيتلها اصل ايه يبقى بناء عليه الـfi m is onto
+
+383
+00:42:13,410 --> 00:42:17,490
+يبقى المصحوفة B اللي أخدتها عشوائيا في ال special
+
+384
+00:42:17,490 --> 00:42:22,130
+linear group of two by two matrices over R لجت لها
+
+385
+00:42:22,130 --> 00:42:29,570
+أصل اللي هو A موجودة من مين هي A والـ A اللي هي M
+
+386
+00:42:29,570 --> 00:42:38,050
+inverse ب M طب خليني أسأل السؤال التالي هل عملية
+
+387
+00:42:38,050 --> 00:42:40,430
+الضرب هذه ممكن اتم
+
+388
+00:42:44,800 --> 00:42:49,700
+بالتم ولا بالتم مش؟ بالتم لأن كله نظام اتنين في
+
+389
+00:42:49,700 --> 00:42:56,080
+اتنين انا فرض ان من البداية ال M اتنين باتنين
+
+390
+00:42:56,080 --> 00:43:00,380
+matrix و determinant لا يساوي ديري اذا كل واحدة
+
+391
+00:43:00,380 --> 00:43:04,370
+فيهم نظام اتنين في اتنينولو اختلف النظام يمكن ما
+
+392
+00:43:04,370 --> 00:43:07,870
+نقدرش نضرب يمكن نقدر ويمكن ما نقدرش لكن هاد
+
+393
+00:43:07,870 --> 00:43:12,970
+اتنينات كله اذا عملية الضرب possible وبالتالي no
+
+394
+00:43:12,970 --> 00:43:17,110
+problem يمكن بكلامنا وشغلنا مية مية بقيت عندنا
+
+395
+00:43:17,110 --> 00:43:23,850
+النقطة الأخيرة finally النقطة الأخيرة بدي اخد five
+
+396
+00:43:23,850 --> 00:43:26,970
+m of a b
+
+397
+00:43:29,580 --> 00:43:35,740
+عاملية ضرب المصفقة يبقى هذا يا شباب بدأ تساوي M A
+
+398
+00:43:35,740 --> 00:43:42,780
+B M inverse هذه
+
+399
+00:43:42,780 --> 00:43:50,080
+K بدأ تيجي في of A في في of Vمش جاية هذه ولا لا
+
+400
+00:43:50,080 --> 00:43:57,460
+لكن لو دخلت مصوفة الوحدة في الموضوع مافيش مشكلة ان
+
+401
+00:43:57,460 --> 00:44:00,860
+مصوفة الوحدة ضربها في المصوفة بتعطينا نفس المصوفة
+
+402
+00:44:00,860 --> 00:44:11,180
+لكن هذا بقدر اكتبه M A و بدي ادخل M inverse M وهذه
+
+403
+00:44:11,180 --> 00:44:18,290
+ال B وهذه ال B اللي عندنا وهذه ال M inverseهذه
+
+404
+00:44:18,290 --> 00:44:29,890
+عبارة عن مصوف الواحدة يبقى مصففتين مصففين
+
+405
+00:44:29,890 --> 00:44:30,810
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+406
+00:44:30,810 --> 00:44:31,390
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+407
+00:44:31,390 --> 00:44:32,510
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+408
+00:44:32,510 --> 00:44:36,350
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+409
+00:44:36,350 --> 00:44:36,470
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+410
+00:44:36,470 --> 00:44:43,510
+مصففين مصففين مصففين مصففينيبقى تحققت الخاصية يبقى
+
+411
+00:44:43,510 --> 00:44:57,970
+بقدر أقوله thus و هكذا فاي ام is an isomorphism طب
+
+412
+00:44:57,970 --> 00:45:09,130
+example خمسة في شيء؟ لأ بس مش هنشتغل سؤال هل ال S
+
+413
+00:45:10,480 --> 00:45:18,680
+تلاتة هكم عنصر فيها؟ ستة، مظبوط؟ three factorial
+
+414
+00:45:18,680 --> 00:45:23,440
+تلاتة في اتنين في واحد يبقى ست عناصر هل هذه
+
+415
+00:45:23,440 --> 00:45:30,120
+isomorphic ل Z6؟
+
+416
+00:45:31,610 --> 00:45:38,490
+أيوة ممتازة زد ستة كوميوتاتيف ابدأ ليه لك ال S3 is
+
+417
+00:45:38,490 --> 00:45:44,830
+not هادي cyclic هادي not cyclic وهكذا يبقى هادي is
+
+418
+00:45:44,830 --> 00:45:52,020
+not isomorphic to z6 becauseجيب ليه ولو سبب واحد
+
+419
+00:45:52,020 --> 00:45:56,100
+بديش اسباب كتيرة رغم ان هذه فيها ست عناصر وهذه
+
+420
+00:45:56,100 --> 00:46:06,480
+فيها ست عناصر يبقى because ال S3 is not cyclic but
+
+421
+00:46:06,480 --> 00:46:15,340
+ولكن Z6 اللي هو subgroup of Y1 is cyclic
+
+422
+00:46:19,060 --> 00:46:21,000
+بنكمل ان شاء الله بعد الظهر
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7ad1dc4d861de33ab601c5e7eb2ae9ef13a08dbe
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.json
@@ -0,0 +1 @@
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"end": 206.01, "word": " الـ", "probability": 0.3109130859375}, {"start": 206.01, "end": 206.71, "word": " isomorphism", "probability": 0.8082682291666666}, {"start": 206.71, "end": 206.95, "word": " مش", "probability": 0.34326171875}, {"start": 206.95, "end": 207.63, "word": " باكتبه", "probability": 0.8426920572916666}, {"start": 207.63, "end": 208.43, "word": " يساوي", "probability": 0.9678955078125}, {"start": 208.43, "end": 209.89, "word": " باكتبه", "probability": 0.8951822916666666}, {"start": 209.89, "end": 210.33, "word": " جي", "probability": 0.62646484375}, {"start": 210.33, "end": 210.69, "word": " و", "probability": 0.70458984375}, {"start": 210.69, "end": 212.41, "word": " خطين", "probability": 0.7327473958333334}, {"start": 212.41, "end": 213.35, "word": " متعرجين", "probability": 0.931396484375}, {"start": 213.35, "end": 213.85, "word": " بالشكل", "probability": 0.84619140625}, {"start": 213.85, "end": 214.19, "word": " هادى", "probability": 0.556396484375}, {"start": 214.19, "end": 214.43, "word": " جي", "probability": 0.725341796875}, {"start": 214.43, "end": 214.63, "word": " بار", "probability": 0.981689453125}, {"start": 214.63, "end": 214.77, "word": " و", "probability": 0.513671875}, {"start": 214.77, "end": 215.37, "word": " تقرا", "probability": 0.8631184895833334}, {"start": 215.37, "end": 216.51, "word": " جي", "probability": 0.84130859375}, {"start": 216.51, "end": 217.25, "word": " ايزو", "probability": 0.72088623046875}, {"start": 217.25, "end": 218.09, "word": " مورفكت", "probability": 0.9220703125}, {"start": 218.09, "end": 218.53, "word": " جي", "probability": 0.980712890625}, {"start": 218.53, "end": 218.99, "word": " بار", "probability": 0.980224609375}], "temperature": 1.0}, {"id": 10, "seek": 24853, "start": 219.71, "end": 248.53, "text": "طب بالمعنى الرياضي ايش يعني معنى isomorphism او G isomorphic ل G bar لاحظ من خلال التعريف لما يقول ال group هذي و ال group هذي في function بينهم one to one and unto السؤال الأول هل سيختلف عدد العناصر في ال group الأولى عن عدد عناصر ال group التانية؟ في اختلاف؟ لأ لإن واحد لواحد", "tokens": [9566, 3555, 20666, 2304, 3615, 1863, 7578, 2423, 16572, 46958, 1829, 1975, 1829, 8592, 37495, 22653, 20449, 1863, 7578, 307, 32702, 1434, 1975, 2407, 460, 307, 32702, 299, 5296, 460, 2159, 20193, 5016, 19913, 9154, 16490, 1211, 6027, 16712, 3615, 16572, 5172, 5296, 15042, 7251, 39648, 2423, 1594, 8032, 8848, 1829, 4032, 2423, 1594, 8032, 8848, 1829, 8978, 2445, 49374, 16095, 472, 281, 472, 293, 16521, 2423, 3794, 33604, 6027, 16247, 12610, 8032, 1211, 8608, 1829, 46456, 46538, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 8978, 2423, 1594, 16247, 12610, 7578, 18871, 6225, 3215, 3215, 6225, 1863, 33546, 2288, 2423, 1594, 16712, 7649, 10632, 22807, 8978, 1975, 46456, 15040, 5172, 22807, 5296, 10721, 5296, 28814, 1863, 36764, 24401, 5296, 14407, 24401], "avg_logprob": -0.1685450784251338, "compression_ratio": 1.8, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 219.71, "end": 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"word": " bar", "probability": 0.7197265625}, {"start": 226.89, "end": 228.13, "word": " لاحظ", "probability": 0.8008626302083334}, {"start": 228.13, "end": 228.31, "word": " من", "probability": 0.98828125}, {"start": 228.31, "end": 228.77, "word": " خلال", "probability": 0.9947916666666666}, {"start": 228.77, "end": 229.33, "word": " التعريف", "probability": 0.98974609375}, {"start": 229.33, "end": 229.69, "word": " لما", "probability": 0.90283203125}, {"start": 229.69, "end": 229.99, "word": " يقول", "probability": 0.75244140625}, {"start": 229.99, "end": 230.19, "word": " ال", "probability": 0.5849609375}, {"start": 230.19, "end": 230.47, "word": " group", "probability": 0.95556640625}, {"start": 230.47, "end": 230.91, "word": " هذي", "probability": 0.61474609375}, {"start": 230.91, "end": 231.03, "word": " و", "probability": 0.89599609375}, {"start": 231.03, "end": 231.17, "word": " ال", "probability": 0.751953125}, {"start": 231.17, "end": 231.49, "word": " group", "probability": 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238.15, "end": 238.93, "word": " سيختلف", "probability": 0.9913330078125}, {"start": 238.93, "end": 239.51, "word": " عدد", "probability": 0.9860026041666666}, {"start": 239.51, "end": 240.47, "word": " العناصر", "probability": 0.92431640625}, {"start": 240.47, "end": 240.63, "word": " في", "probability": 0.94482421875}, {"start": 240.63, "end": 240.77, "word": " ال", "probability": 0.90625}, {"start": 240.77, "end": 241.03, "word": " group", "probability": 0.98193359375}, {"start": 241.03, "end": 241.69, "word": " الأولى", "probability": 0.9305013020833334}, {"start": 241.69, "end": 241.87, "word": " عن", "probability": 0.978515625}, {"start": 241.87, "end": 242.23, "word": " عدد", "probability": 0.9962565104166666}, {"start": 242.23, "end": 242.83, "word": " عناصر", "probability": 0.80377197265625}, {"start": 242.83, "end": 242.97, "word": " ال", "probability": 0.6494140625}, {"start": 242.97, "end": 243.15, "word": " group", "probability": 0.982421875}, {"start": 243.15, "end": 243.87, "word": " التانية؟", "probability": 0.789794921875}, {"start": 243.87, "end": 244.85, "word": " في", "probability": 0.642578125}, {"start": 244.85, "end": 246.01, "word": " اختلاف؟", "probability": 0.91181640625}, {"start": 246.01, "end": 246.55, "word": " لأ", "probability": 0.9541015625}, {"start": 246.55, "end": 246.97, "word": " لإن", "probability": 0.7687174479166666}, {"start": 246.97, "end": 247.63, "word": " واحد", "probability": 0.800537109375}, {"start": 247.63, "end": 248.53, "word": " لواحد", "probability": 0.8797200520833334}], "temperature": 1.0}, {"id": 11, "seek": 26402, "start": 248.85, "end": 264.03, "text": "اتنين ال domain بيغطي جميع عناصر جي مدام انت بيغطي جميع عناصر جي بار و لا واحد زي التاني يبقى بناء عندي عدد عناصر جي يساوي عدد عناصر جي بار", "tokens": [9307, 1863, 9957, 2423, 9274, 4724, 1829, 17082, 9566, 1829, 10874, 2304, 40228, 18871, 33546, 2288, 10874, 1829, 3714, 3215, 10943, 16472, 2655, 4724, 1829, 17082, 9566, 1829, 10874, 2304, 40228, 18871, 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"end": 253.41, "word": " مدام", "probability": 0.4896647135416667}, {"start": 253.41, "end": 253.81, "word": " انت", "probability": 0.7373046875}, {"start": 253.81, "end": 254.61, "word": " بيغطي", "probability": 0.848779296875}, {"start": 254.61, "end": 255.11, "word": " جميع", "probability": 0.7848307291666666}, {"start": 255.11, "end": 255.65, "word": " عناصر", "probability": 0.9820963541666666}, {"start": 255.65, "end": 256.85, "word": " جي", "probability": 0.82177734375}, {"start": 256.85, "end": 257.07, "word": " بار", "probability": 0.775634765625}, {"start": 257.07, "end": 257.19, "word": " و", "probability": 0.11749267578125}, {"start": 257.19, "end": 257.39, "word": " لا", "probability": 0.81640625}, {"start": 257.39, "end": 257.75, "word": " واحد", "probability": 0.970458984375}, {"start": 257.75, "end": 258.05, "word": " زي", "probability": 0.934814453125}, {"start": 258.05, "end": 258.79, "word": " التاني", "probability": 0.814453125}, {"start": 258.79, "end": 259.53, "word": " يبقى", "probability": 0.8992919921875}, {"start": 259.53, "end": 259.83, "word": " بناء", "probability": 0.769775390625}, {"start": 259.83, "end": 260.21, "word": " عندي", "probability": 0.54229736328125}, {"start": 260.21, "end": 260.73, "word": " عدد", "probability": 0.97314453125}, {"start": 260.73, "end": 261.49, "word": " عناصر", "probability": 0.98779296875}, {"start": 261.49, "end": 261.77, "word": " جي", "probability": 0.970458984375}, {"start": 261.77, "end": 262.27, "word": " يساوي", "probability": 0.8665771484375}, {"start": 262.27, "end": 262.69, "word": " عدد", "probability": 0.9869791666666666}, {"start": 262.69, "end": 263.37, "word": " عناصر", "probability": 0.9886067708333334}, {"start": 263.37, "end": 263.69, "word": " جي", "probability": 0.9892578125}, {"start": 263.69, "end": 264.03, "word": " بار", "probability": 0.988525390625}], "temperature": 1.0}, {"id": 12, "seek": 27923, "start": 264.51, "end": 279.23, "text": "عدد ال subgroup في G يسوى عدد ال subgroup في G bar عدد العناصر التي لها نفس ال order في G يسوى عدد العناصر التي لها نفس ال order من G bar", "tokens": [3615, 3215, 3215, 2423, 1422, 17377, 8978, 460, 7251, 3794, 2407, 7578, 6225, 3215, 3215, 2423, 1422, 17377, 8978, 460, 2159, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 38392, 5296, 11296, 8717, 36178, 2423, 1668, 8978, 460, 7251, 3794, 2407, 7578, 6225, 3215, 3215, 18863, 1863, 33546, 2288, 38392, 5296, 11296, 8717, 36178, 2423, 1668, 9154, 460, 2159], "avg_logprob": -0.1472457556401269, "compression_ratio": 2.0294117647058822, "no_speech_prob": 0.0, "words": [{"start": 264.51, "end": 265.15, "word": "عدد", "probability": 0.7906087239583334}, {"start": 265.15, "end": 265.33, "word": " ال", "probability": 0.74462890625}, {"start": 265.33, "end": 266.05, "word": " subgroup", "probability": 0.43597412109375}, {"start": 266.05, "end": 266.39, "word": " في", "probability": 0.8017578125}, {"start": 266.39, "end": 266.65, "word": " G", "probability": 0.50244140625}, {"start": 266.65, "end": 267.15, "word": " يسوى", "probability": 0.61993408203125}, {"start": 267.15, "end": 267.57, "word": " عدد", "probability": 0.98779296875}, {"start": 267.57, "end": 267.71, "word": " ال", "probability": 0.75732421875}, {"start": 267.71, "end": 268.29, "word": " subgroup", "probability": 0.84228515625}, {"start": 268.29, "end": 268.53, "word": " في", "probability": 0.9580078125}, {"start": 268.53, "end": 268.91, "word": " G", "probability": 0.90283203125}, {"start": 268.91, "end": 269.29, "word": " bar", "probability": 0.681640625}, {"start": 269.29, "end": 270.53, "word": " عدد", "probability": 0.9375}, {"start": 270.53, "end": 271.91, "word": " العناصر", "probability": 0.92138671875}, {"start": 271.91, "end": 272.63, "word": " التي", "probability": 0.89404296875}, {"start": 272.63, "end": 273.09, "word": " لها", "probability": 0.9716796875}, {"start": 273.09, "end": 273.51, "word": " نفس", "probability": 0.994384765625}, {"start": 273.51, "end": 273.71, "word": 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بينهم صلة عملية ضرب وليست عملية جمع", "tokens": [3224, 15730, 2423, 28820, 10943, 7251, 3794, 995, 45865, 12602, 1829, 46958, 25528, 28242, 10943, 8608, 20292, 2304, 2319, 4, 7251, 3555, 4587, 7578, 34105, 13672, 1829, 49374, 16095, 20328, 37977, 6225, 42213, 10632, 48812, 25513, 4032, 20292, 14851, 6225, 42213, 10632, 10874, 2304, 3615], "avg_logprob": -0.16151494468035904, "compression_ratio": 1.4311926605504588, "no_speech_prob": 0.0, "words": [{"start": 859.8, "end": 860.34, "word": "هذا", "probability": 0.92333984375}, {"start": 860.34, "end": 861.02, "word": " الكلام", "probability": 0.9573567708333334}, {"start": 861.02, "end": 861.68, "word": " يساوي", "probability": 0.94677734375}, {"start": 861.68, "end": 862.56, "word": " رياضيا", "probability": 0.9403076171875}, {"start": 862.56, "end": 863.12, "word": " كلام", "probability": 0.85986328125}, {"start": 863.12, "end": 863.62, "word": " سليم", "probability": 0.9085286458333334}, {"start": 863.62, "end": 863.86, "word": " 100", 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1.0}, {"id": 80, "seek": 187305, "start": 1867.13, "end": 1873.05, "text": "Isomorphic لـ Z6 نقول لك مين اليو 18", "tokens": [40, 539, 76, 18191, 299, 5296, 39184, 1176, 21, 8717, 39648, 5296, 4117, 3714, 9957, 45595, 2407, 2443], "avg_logprob": -0.4782072619387978, "compression_ratio": 0.8947368421052632, "no_speech_prob": 0.0, "words": [{"start": 1867.1299999999999, "end": 1867.77, "word": "Isomorphic", "probability": 0.691162109375}, {"start": 1867.77, "end": 1868.09, "word": " لـ", "probability": 0.6376953125}, {"start": 1868.09, "end": 1868.89, "word": " Z6", "probability": 0.816650390625}, {"start": 1868.89, "end": 1872.03, "word": " نقول", "probability": 0.642822265625}, {"start": 1872.03, "end": 1872.25, "word": " لك", "probability": 0.57330322265625}, {"start": 1872.25, "end": 1872.45, "word": " مين", "probability": 0.88525390625}, {"start": 1872.45, "end": 1872.77, "word": " اليو", "probability": 0.5665283203125}, {"start": 1872.77, "end": 1873.05, "word": " 18", 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"avg_logprob": -0.2111191900317059, "compression_ratio": 2.037593984962406, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1953.77, "end": 1954.61, "word": "علي", "probability": 0.29644775390625}, {"start": 1954.61, "end": 1954.99, "word": " صوتك", "probability": 0.8343098958333334}, {"start": 1954.99, "end": 1955.57, "word": " شوية", "probability": 0.8199869791666666}, {"start": 1955.57, "end": 1959.29, "word": " لا", "probability": 0.12255859375}, {"start": 1959.29, "end": 1961.19, "word": " انت", "probability": 0.772216796875}, {"start": 1961.19, "end": 1961.83, "word": " انت", "probability": 0.665283203125}, {"start": 1961.83, "end": 1962.17, "word": " لما", "probability": 0.88818359375}, {"start": 1962.17, "end": 1962.49, "word": " زد", "probability": 0.85205078125}, {"start": 1962.49, "end": 1962.99, "word": " خمسة", "probability": 0.9443359375}, {"start": 1962.99, "end": 1963.25, "word": " فيها", "probability": 0.96630859375}, {"start": 1963.25, "end": 1963.51, "word": " كام", "probability": 0.851806640625}, {"start": 1963.51, "end": 1964.55, "word": " عنصر؟", "probability": 0.8316650390625}, {"start": 1964.55, "end": 1964.83, "word": " خمس", "probability": 0.90185546875}, {"start": 1964.83, "end": 1965.43, "word": " عناصر", "probability": 0.9876302083333334}, {"start": 1965.43, "end": 1965.85, "word": " زد", "probability": 0.853759765625}, {"start": 1965.85, "end": 1966.29, "word": " ستة", "probability": 0.9723307291666666}, {"start": 1966.29, "end": 1966.53, "word": " فيها", "probability": 0.982666015625}, {"start": 1966.53, "end": 1966.81, "word": " ست", "probability": 0.978515625}, {"start": 1966.81, "end": 1967.33, "word": " عناصر", "probability": 0.98974609375}, {"start": 1967.33, "end": 1967.45, "word": " و", "probability": 0.6904296875}, {"start": 1967.45, "end": 1967.91, "word": " هكذا", "probability": 0.784912109375}, {"start": 1967.91, "end": 1968.67, "word": " كيف", "probability": 0.913330078125}, {"start": 1968.67, "end": 1969.17, "word": " واحدة", "probability": 0.9358723958333334}, {"start": 1969.17, "end": 1969.63, "word": " فيها", "probability": 0.989013671875}, {"start": 1969.63, "end": 1970.53, "word": " ست", "probability": 0.86376953125}, {"start": 1970.53, "end": 1971.01, "word": " عناصر", "probability": 0.9939778645833334}, {"start": 1971.01, "end": 1971.11, "word": " و", "probability": 0.88427734375}, {"start": 1971.11, "end": 1971.39, "word": " واحدة", "probability": 0.9298502604166666}, {"start": 1971.39, "end": 1971.75, "word": " خمس", "probability": 0.9837239583333334}, {"start": 1971.75, "end": 1972.17, "word": " عناصر", "probability": 0.98291015625}, {"start": 1972.17, "end": 1972.39, "word": " فيها", "probability": 0.7861328125}, {"start": 1972.39, "end": 1972.69, "word": " ايزو", "probability": 0.73382568359375}, {"start": 1972.69, "end": 1973.03, "word": " مورف", "probability": 0.5374348958333334}, {"start": 1973.03, "end": 1973.43, "word": " فيهم؟", "probability": 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1976.89, "end": 1977.33, "word": " بديت", "probability": 0.73486328125}, {"start": 1977.33, "end": 1977.71, "word": " عدد", "probability": 0.9612630208333334}, {"start": 1977.71, "end": 1978.37, "word": " العناصر", "probability": 0.9425048828125}, {"start": 1978.37, "end": 1978.49, "word": " في", "probability": 0.92626953125}, {"start": 1978.49, "end": 1978.87, "word": " الجروب", "probability": 0.8523763020833334}, {"start": 1978.87, "end": 1979.23, "word": " الأولى", "probability": 0.953125}, {"start": 1979.23, "end": 1979.47, "word": " جد", "probability": 0.807373046875}, {"start": 1979.47, "end": 1979.81, "word": " عدد", "probability": 0.9933268229166666}, {"start": 1979.81, "end": 1980.31, "word": " العناصر", "probability": 0.98974609375}, {"start": 1980.31, "end": 1980.41, "word": " في", "probability": 0.962890625}, {"start": 1980.41, "end": 1980.67, "word": " الجروب", "probability": 0.9339192708333334}, {"start": 1980.67, "end": 1980.97, "word": " التانى", "probability": 0.84228515625}, {"start": 1980.97, "end": 1981.97, "word": " اختلفوا", "probability": 0.75030517578125}, {"start": 1981.97, "end": 1982.49, "word": " العناصر", "probability": 0.9776611328125}, {"start": 1982.49, "end": 1982.89, "word": " مافيش", "probability": 0.91552734375}, {"start": 1982.89, "end": 1983.71, "word": " isomorphism", "probability": 0.9228515625}, {"start": 1983.71, "end": 1984.31, "word": " وانت", "probability": 0.8009440104166666}, {"start": 1984.31, "end": 1984.95, "word": " مغمق", "probability": 0.85321044921875}, {"start": 1984.95, "end": 1985.35, "word": " بدون", "probability": 0.965087890625}, {"start": 1985.35, "end": 1985.99, "word": " نقاش", "probability": 0.9913736979166666}, {"start": 1985.99, "end": 1987.39, "word": " تمام؟", "probability": 0.59228515625}, {"start": 1987.39, "end": 1987.51, "word": " إذا", "probability": 0.7939453125}, {"start": 1987.51, "end": 1987.79, "word": " عدد", "probability": 0.8751627604166666}, {"start": 1987.79, "end": 1988.27, "word": " العناصر", "probability": 0.9947509765625}, {"start": 1988.27, "end": 1988.37, "word": " في", "probability": 0.9794921875}, {"start": 1988.37, "end": 1988.77, "word": " الجروب", "probability": 0.9630533854166666}, {"start": 1988.77, "end": 1989.13, "word": " الأولى", "probability": 0.9659830729166666}, {"start": 1989.13, "end": 1989.61, "word": " يختلف", "probability": 0.99169921875}, {"start": 1989.61, "end": 1989.77, "word": " عن", "probability": 0.97607421875}, {"start": 1989.77, "end": 1990.09, "word": " عدد", "probability": 0.99560546875}, {"start": 1990.09, "end": 1990.63, "word": " العناصر", "probability": 0.9949951171875}, {"start": 1990.63, "end": 1990.73, "word": " في", "probability": 0.97705078125}, {"start": 1990.73, "end": 1990.99, "word": " الجروب", "probability": 0.9622395833333334}, {"start": 1990.99, "end": 1991.33, "word": " التانى", "probability": 0.8074544270833334}, {"start": 1991.33, "end": 1991.55, "word": " there", "probability": 0.428466796875}, {"start": 1991.55, "end": 1991.77, "word": " is", "probability": 0.9521484375}, {"start": 1991.77, "end": 1992.29, "word": " no", "probability": 0.947265625}, {"start": 1992.29, "end": 1993.31, "word": " isomorphism", "probability": 0.9576822916666666}, {"start": 1993.31, "end": 1993.67, "word": " between", "probability": 0.95556640625}, {"start": 1993.67, "end": 1993.95, "word": " two", "probability": 0.935546875}, {"start": 1993.95, "end": 1994.33, "word": " groups", "probability": 0.96435546875}, {"start": 1994.33, "end": 1995.15, "word": " مافيش", "probability": 0.9187825520833334}, {"start": 1995.15, "end": 1995.79, "word": " بالمرة", "probability": 0.9485677083333334}, {"start": 1995.79, "end": 1996.83, "word": " حد", "probability": 0.882080078125}, {"start": 1996.83, "end": 1997.07, "word": " بدي", "probability": 0.842529296875}, {"start": 1997.07, "end": 1997.33, "word": " أسأل", "probability": 0.865478515625}, {"start": 1997.33, "end": 1998.13, "word": " تاني", "probability": 0.8751627604166666}, {"start": 1998.13, "end": 1999.17, "word": " طيب", "probability": 0.8167317708333334}, {"start": 1999.17, "end": 2000.03, "word": " نجيبلك", "probability": 0.839208984375}, {"start": 2000.03, "end": 2000.77, "word": " مثال", "probability": 0.9599609375}, {"start": 2000.77, "end": 2001.01, "word": " من", "probability": 0.99609375}, {"start": 2001.01, "end": 2001.71, "word": " نوعين", "probability": 0.8505859375}, {"start": 2001.71, "end": 2002.53, "word": " جديد", "probability": 0.98828125}], "temperature": 1.0}, {"id": 86, "seek": 203117, "start": 2003.23, "end": 2031.17, "text": "مثال أربعة مثال أربعة بيقول let ال G هي ال special linear group of two by two matrices over R وهي كل المصوات اللي على الشكل A,B,C,D بحيث ان ال A,D ناقص ال B,C بدوا ساوي الواحد الصحيح", "tokens": [2304, 12984, 6027, 5551, 25513, 27884, 50113, 6027, 5551, 25513, 27884, 4724, 1829, 39648, 718, 2423, 460, 39896, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 37037, 1829, 28242, 9673, 9381, 2407, 9307, 13672, 1829, 15844, 25124, 28820, 316, 11, 33, 11, 34, 11, 35, 4724, 5016, 1829, 12984, 16472, 2423, 316, 11, 35, 8717, 995, 4587, 9381, 2423, 363, 11, 34, 47525, 14407, 8608, 995, 45865, 2423, 14407, 24401, 31767, 5016, 1829, 5016], "avg_logprob": -0.2305689173249098, "compression_ratio": 1.446236559139785, "no_speech_prob": 0.0, "words": [{"start": 2003.23, "end": 2003.85, "word": "مثال", "probability": 0.8815104166666666}, {"start": 2003.85, "end": 2004.51, "word": " أربعة", "probability": 0.6861165364583334}, {"start": 2004.51, "end": 2007.77, "word": " مثال", "probability": 0.812744140625}, {"start": 2007.77, "end": 2008.41, "word": " أربعة", "probability": 0.9220377604166666}, {"start": 2008.41, "end": 2008.85, "word": " بيقول", "probability": 0.8299153645833334}, {"start": 2008.85, "end": 2009.51, "word": " let", "probability": 0.27197265625}, {"start": 2009.51, "end": 2010.85, "word": " ال", "probability": 0.54345703125}, {"start": 2010.85, "end": 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"word": " R", "probability": 0.97998046875}, {"start": 2016.89, "end": 2017.99, "word": " وهي", "probability": 0.7255859375}, {"start": 2017.99, "end": 2018.45, "word": " كل", "probability": 0.955078125}, {"start": 2018.45, "end": 2019.25, "word": " المصوات", "probability": 0.906005859375}, {"start": 2019.25, "end": 2019.39, "word": " اللي", "probability": 0.793701171875}, {"start": 2019.39, "end": 2019.49, "word": " على", "probability": 0.66748046875}, {"start": 2019.49, "end": 2019.89, "word": " الشكل", "probability": 0.9072265625}, {"start": 2019.89, "end": 2020.33, "word": " A", "probability": 0.591796875}, {"start": 2020.33, "end": 2020.69, "word": ",B", "probability": 0.589111328125}, {"start": 2020.69, "end": 2021.45, "word": ",C", "probability": 0.987060546875}, {"start": 2021.45, "end": 2022.17, "word": ",D", "probability": 0.977783203125}, {"start": 2022.17, "end": 2023.75, "word": " بحيث", "probability": 0.9814453125}, {"start": 2023.75, "end": 2024.17, "word": " ان", "probability": 0.43896484375}, {"start": 2024.17, "end": 2025.27, "word": " ال", "probability": 0.86376953125}, {"start": 2025.27, "end": 2025.85, "word": " A", "probability": 0.87255859375}, {"start": 2025.85, "end": 2026.53, "word": ",D", "probability": 0.738037109375}, {"start": 2026.53, "end": 2027.53, "word": " ناقص", "probability": 0.946533203125}, {"start": 2027.53, "end": 2027.79, "word": " ال", "probability": 0.9736328125}, {"start": 2027.79, "end": 2028.13, "word": " B", "probability": 0.89599609375}, {"start": 2028.13, "end": 2028.59, "word": ",C", "probability": 0.985107421875}, {"start": 2028.59, "end": 2029.25, "word": " بدوا", "probability": 0.346435546875}, {"start": 2029.25, "end": 2029.71, "word": " ساوي", "probability": 0.8536783854166666}, {"start": 2029.71, "end": 2030.51, "word": " الواحد", "probability": 0.9417317708333334}, {"start": 2030.51, "end": 2031.17, "word": " الصحيح", "probability": 0.8740234375}], "temperature": 1.0}, {"id": 87, "seek": 205703, "start": 2031.97, "end": 2057.03, "text": "let الـ M be any two by two matrix matrix with a determinant لـ M لا يساوي Zero define", "tokens": [2631, 2423, 39184, 376, 312, 604, 732, 538, 732, 8141, 8141, 365, 257, 41296, 5296, 39184, 376, 20193, 7251, 3794, 995, 45865, 17182, 6964], "avg_logprob": -0.44281250953674317, "compression_ratio": 1.101123595505618, "no_speech_prob": 0.0, "words": [{"start": 2031.97, "end": 2032.89, "word": "let", "probability": 0.224365234375}, {"start": 2032.89, "end": 2034.29, "word": " الـ", "probability": 0.4954833984375}, {"start": 2034.29, "end": 2034.71, "word": " M", "probability": 0.56640625}, {"start": 2034.71, "end": 2036.45, "word": " be", "probability": 0.471435546875}, {"start": 2036.45, "end": 2038.17, "word": " any", "probability": 0.90087890625}, {"start": 2038.17, "end": 2039.33, "word": " two", "probability": 0.470947265625}, {"start": 2039.33, "end": 2039.81, "word": " by", "probability": 0.80908203125}, {"start": 2039.81, "end": 2040.57, "word": " two", "probability": 0.9501953125}, {"start": 2040.57, "end": 2042.81, "word": " matrix", "probability": 0.89599609375}, {"start": 2042.81, "end": 2046.05, "word": " matrix", "probability": 0.2978515625}, {"start": 2046.05, "end": 2047.43, "word": " with", "probability": 0.93701171875}, {"start": 2047.43, "end": 2049.39, "word": " a", "probability": 0.62548828125}, {"start": 2049.39, "end": 2050.45, "word": " determinant", "probability": 0.92041015625}, {"start": 2050.45, "end": 2051.77, "word": " لـ", "probability": 0.5789794921875}, {"start": 2051.77, "end": 2052.09, "word": " M", "probability": 0.91015625}, {"start": 2052.09, "end": 2052.93, "word": " لا", "probability": 0.68896484375}, {"start": 2052.93, "end": 2053.61, "word": " يساوي", "probability": 0.83978271484375}, {"start": 2053.61, "end": 2054.07, "word": " Zero", "probability": 0.368896484375}, {"start": 2054.07, "end": 2057.03, "word": " define", "probability": 0.89404296875}], "temperature": 1.0}, {"id": 88, "seek": 208917, "start": 2060.64, "end": 2089.18, "text": "A mapping Define A mapping Phi M من G إلى G by Phi M of A يساوي M A M inverse لكل", "tokens": [32, 18350, 9548, 533, 316, 18350, 41435, 376, 9154, 460, 30731, 460, 538, 41435, 376, 295, 316, 7251, 3794, 995, 45865, 376, 316, 376, 17340, 5296, 28820], "avg_logprob": -0.37695312393563135, "compression_ratio": 1.1058823529411765, "no_speech_prob": 0.0, "words": [{"start": 2060.64, "end": 2061.04, "word": "A", "probability": 0.2183837890625}, {"start": 2061.04, "end": 2061.94, "word": " mapping", "probability": 0.857421875}, {"start": 2061.94, "end": 2064.94, "word": " Define", "probability": 0.5928955078125}, {"start": 2064.94, "end": 2065.28, "word": " A", "probability": 0.6318359375}, {"start": 2065.28, "end": 2065.9, "word": " mapping", "probability": 0.962890625}, {"start": 2065.9, "end": 2066.8, "word": " Phi", "probability": 0.1900634765625}, {"start": 2066.8, "end": 2071.46, "word": " M", "probability": 0.861328125}, {"start": 2071.46, "end": 2072.62, "word": " من", "probability": 0.9658203125}, {"start": 2072.62, "end": 2073.74, "word": " G", "probability": 0.861328125}, {"start": 2073.74, "end": 2074.88, "word": " إلى", "probability": 0.7138671875}, {"start": 2074.88, "end": 2075.52, "word": " G", "probability": 0.77587890625}, {"start": 2075.52, "end": 2076.16, "word": " by", "probability": 0.449951171875}, {"start": 2076.16, "end": 2078.62, "word": " Phi", "probability": 0.8447265625}, {"start": 2078.62, "end": 2080.06, "word": " M", "probability": 0.955078125}, {"start": 2080.06, "end": 2081.1, "word": " of", "probability": 0.91650390625}, {"start": 2081.1, "end": 2081.8, "word": " A", "probability": 0.96630859375}, {"start": 2081.8, "end": 2083.08, "word": " يساوي", "probability": 0.7437744140625}, {"start": 2083.08, "end": 2083.84, "word": " M", "probability": 0.42529296875}, {"start": 2083.84, "end": 2084.82, "word": " A", "probability": 0.619140625}, {"start": 2084.82, "end": 2085.52, "word": " M", "probability": 0.9599609375}, {"start": 2085.52, "end": 2086.44, "word": " inverse", "probability": 0.84375}, {"start": 2086.44, "end": 2089.18, "word": " لكل", "probability": 0.927001953125}], "temperature": 1.0}, {"id": 89, "seek": 210589, "start": 2089.97, "end": 2105.89, "text": "الـ A اللي موجودة في G show that الـ Phi M is an isomorphism", "tokens": [6027, 39184, 316, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 460, 855, 300, 2423, 39184, 41435, 376, 307, 364, 307, 32702, 1434], "avg_logprob": -0.3459578908008078, "compression_ratio": 1.0129870129870129, "no_speech_prob": 0.0, "words": [{"start": 2089.97, "end": 2090.57, "word": "الـ", "probability": 0.701416015625}, {"start": 2090.57, "end": 2091.01, "word": " A", "probability": 0.47216796875}, {"start": 2091.01, "end": 2091.91, "word": " اللي", "probability": 0.496826171875}, {"start": 2091.91, "end": 2092.91, "word": " موجودة", "probability": 0.965576171875}, {"start": 2092.91, "end": 2093.17, "word": " في", "probability": 0.96630859375}, {"start": 2093.17, "end": 2093.99, "word": " G", "probability": 0.434326171875}, {"start": 2093.99, "end": 2096.15, "word": " show", "probability": 0.1739501953125}, {"start": 2096.15, "end": 2096.79, "word": " that", "probability": 0.9384765625}, {"start": 2096.79, "end": 2100.99, "word": " الـ", "probability": 0.7529296875}, {"start": 2100.99, "end": 2101.35, "word": " Phi", "probability": 0.441162109375}, {"start": 2101.35, "end": 2101.95, "word": " M", "probability": 0.8251953125}, {"start": 2101.95, "end": 2102.97, "word": " is", "probability": 0.9169921875}, {"start": 2102.97, "end": 2104.13, "word": " an", "probability": 0.58544921875}, {"start": 2104.13, "end": 2105.89, "word": " isomorphism", "probability": 0.9484049479166666}], "temperature": 1.0}, {"id": 90, "seek": 216733, "start": 2143.29, "end": 2167.33, "text": "نرجع مرة تانية أخد لجروب جيله ال special linear group of two by two matrices over R و هي كل المصفوفات لنظامها اتنين في اتنين بعيادة المحدد تبعها بده يساوي واحد صحيح قال افترض انه عندي مصفوفة من نظامها اتنين في اتنين ومحددها لا يساوي zero لم أقل واحد صحيح", "tokens": [1863, 47341, 3615, 3714, 25720, 6055, 7649, 10632, 5551, 9778, 3215, 5296, 7435, 32887, 3555, 10874, 26895, 3224, 2423, 2121, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 4032, 39896, 28242, 9673, 9381, 5172, 38688, 9307, 5296, 1863, 19913, 10943, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 4724, 3615, 1829, 18513, 3660, 9673, 24401, 3215, 6055, 3555, 3615, 11296, 47525, 3224, 7251, 3794, 995, 45865, 36764, 24401, 20328, 5016, 1829, 5016, 50239, 1975, 5172, 2655, 43042, 16472, 3224, 18871, 16254, 3714, 9381, 5172, 38688, 3660, 9154, 8717, 19913, 10943, 11296, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 4032, 2304, 24401, 3215, 11296, 20193, 7251, 3794, 995, 45865, 4018, 32767, 5551, 4587, 1211, 36764, 24401, 20328, 5016, 1829, 5016], "avg_logprob": -0.26725000381469727, "compression_ratio": 1.6967213114754098, 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"probability": 0.92431640625}, {"start": 2259.55, "end": 2260.57, "word": " لمين؟", "probability": 0.60443115234375}, {"start": 2260.57, "end": 2261.05, "word": " لل", "probability": 0.78466796875}, {"start": 2261.05, "end": 2261.43, "word": " linear", "probability": 0.465087890625}, {"start": 2261.43, "end": 2262.19, "word": " algebra", "probability": 0.78271484375}, {"start": 2262.19, "end": 2263.27, "word": " يبقى", "probability": 0.9404296875}, {"start": 2263.27, "end": 2263.63, "word": " هذا", "probability": 0.92626953125}, {"start": 2263.63, "end": 2264.27, "word": " معناته", "probability": 0.9724934895833334}, {"start": 2264.27, "end": 2264.45, "word": " ال", "probability": 0.4609375}, {"start": 2264.45, "end": 2265.07, "word": " determinant", "probability": 0.978515625}, {"start": 2265.07, "end": 2265.97, "word": " لل", "probability": 0.8916015625}, {"start": 2265.97, "end": 2267.03, "word": " M", "probability": 0.74853515625}, {"start": 2267.03, "end": 2267.45, "word": " في", "probability": 0.7060546875}, {"start": 2267.45, "end": 2267.63, "word": " ال", "probability": 0.88134765625}, {"start": 2267.63, "end": 2268.55, "word": " determinant", "probability": 0.9921875}, {"start": 2268.55, "end": 2269.37, "word": " لل", "probability": 0.9453125}, {"start": 2269.37, "end": 2270.01, "word": " A", "probability": 0.96630859375}, {"start": 2270.01, "end": 2270.61, "word": " في", "probability": 0.9052734375}, {"start": 2270.61, "end": 2270.81, "word": " ال", "probability": 0.95263671875}, {"start": 2270.81, "end": 2271.67, "word": " determinant", "probability": 0.9892578125}, {"start": 2271.67, "end": 2272.31, "word": " لل", "probability": 0.9482421875}, {"start": 2272.31, "end": 2273.15, "word": " M", "probability": 0.99560546875}, {"start": 2273.15, "end": 2273.75, "word": " inverse", "probability": 0.8291015625}], "temperature": 1.0}, {"id": 95, "seek": 229096, "start": 2275.93, "end": 2290.97, "text": "الأن الـ determinant يعني قيمة حقيقية يعني التلث قيم حقيقية مضروبة في بعضها والقيم الحقيقية commutative يبقى هذا الكلام بده يساوي ال determinant لل M", "tokens": [6027, 33456, 2423, 39184, 41296, 37495, 22653, 12174, 32640, 3660, 11331, 38436, 4587, 10632, 37495, 22653, 16712, 1211, 12984, 12174, 32640, 11331, 38436, 4587, 10632, 3714, 11242, 32887, 49401, 8978, 45030, 11242, 11296, 16070, 4587, 32640, 21542, 38436, 4587, 10632, 800, 325, 1166, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 2423, 41296, 24976, 376], "avg_logprob": -0.19443044450975233, "compression_ratio": 1.5686274509803921, "no_speech_prob": 0.0, "words": [{"start": 2275.93, "end": 2276.39, "word": "الأن", "probability": 0.636474609375}, {"start": 2276.39, "end": 2276.61, "word": " الـ", "probability": 0.565185546875}, {"start": 2276.61, "end": 2276.97, "word": " determinant", "probability": 0.37353515625}, {"start": 2276.97, "end": 2277.45, "word": " يعني", "probability": 0.7822265625}, {"start": 2277.45, "end": 2277.95, "word": " قيمة", "probability": 0.978515625}, {"start": 2277.95, "end": 2278.77, "word": " حقيقية", "probability": 0.9951171875}, {"start": 2278.77, "end": 2279.27, "word": " يعني", "probability": 0.76953125}, {"start": 2279.27, "end": 2279.91, "word": " التلث", "probability": 0.6839192708333334}, {"start": 2279.91, "end": 2280.29, "word": " قيم", "probability": 0.965576171875}, {"start": 2280.29, "end": 2281.05, "word": " حقيقية", "probability": 0.9913330078125}, {"start": 2281.05, "end": 2281.51, "word": " مضروبة", "probability": 0.953125}, {"start": 2281.51, "end": 2281.65, "word": " في", "probability": 0.94189453125}, {"start": 2281.65, "end": 2282.01, "word": " بعضها", "probability": 0.9827473958333334}, {"start": 2282.01, "end": 2282.41, "word": " والقيم", "probability": 0.7657063802083334}, {"start": 2282.41, "end": 2283.45, "word": " الحقيقية", "probability": 0.9857177734375}, {"start": 2283.45, "end": 2284.69, "word": " commutative", "probability": 0.6955159505208334}, {"start": 2284.69, "end": 2285.89, "word": " يبقى", "probability": 0.957275390625}, {"start": 2285.89, "end": 2286.19, "word": " هذا", "probability": 0.97314453125}, {"start": 2286.19, "end": 2286.79, "word": " الكلام", "probability": 0.9606119791666666}, {"start": 2286.79, "end": 2287.25, "word": " بده", "probability": 0.829833984375}, {"start": 2287.25, "end": 2287.99, "word": " يساوي", "probability": 0.84356689453125}, {"start": 2287.99, "end": 2288.75, "word": " ال", "probability": 0.85888671875}, {"start": 2288.75, "end": 2289.59, "word": " determinant", "probability": 0.912109375}, {"start": 2289.59, "end": 2290.39, "word": " لل", "probability": 0.6328125}, {"start": 2290.39, "end": 2290.97, "word": " M", "probability": 0.4853515625}], "temperature": 1.0}, {"id": 96, "seek": 230914, "start": 2291.76, "end": 2309.14, "text": "في ال determinant لل M inverse في ال determinant لل A او بقدر اقول ال determinant لل M في ال M inverse في ال determinant لل A هذا الكلام يساوي", "tokens": [41185, 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2296.08, "end": 2297.0, "word": " determinant", "probability": 0.98388671875}, {"start": 2297.0, "end": 2297.6, "word": " لل", "probability": 0.93212890625}, {"start": 2297.6, "end": 2298.02, "word": " A", "probability": 0.85498046875}, {"start": 2298.02, "end": 2299.24, "word": " او", "probability": 0.802490234375}, {"start": 2299.24, "end": 2300.1, "word": " بقدر", "probability": 0.9676106770833334}, {"start": 2300.1, "end": 2300.42, "word": " اقول", "probability": 0.92626953125}, {"start": 2300.42, "end": 2300.66, "word": " ال", "probability": 0.322509765625}, {"start": 2300.66, "end": 2301.54, "word": " determinant", "probability": 0.984375}, {"start": 2301.54, "end": 2302.2, "word": " لل", "probability": 0.8662109375}, {"start": 2302.2, "end": 2302.7, "word": " M", "probability": 0.98095703125}, {"start": 2302.7, "end": 2303.02, "word": " في", "probability": 0.7412109375}, {"start": 2303.02, "end": 2303.36, "word": " ال", "probability": 0.79296875}, {"start": 2303.36, "end": 2303.84, "word": " M", "probability": 0.99365234375}, {"start": 2303.84, "end": 2304.68, "word": " inverse", "probability": 0.873046875}, {"start": 2304.68, "end": 2304.92, "word": " في", "probability": 0.89501953125}, {"start": 2304.92, "end": 2305.08, "word": " ال", "probability": 0.94384765625}, {"start": 2305.08, "end": 2305.72, "word": " determinant", "probability": 0.97802734375}, {"start": 2305.72, "end": 2306.62, "word": " لل", "probability": 0.94384765625}, {"start": 2306.62, "end": 2307.0, "word": " A", "probability": 0.9736328125}, {"start": 2307.0, "end": 2307.8, "word": " هذا", "probability": 0.76953125}, {"start": 2307.8, "end": 2308.4, "word": " الكلام", "probability": 0.96728515625}, {"start": 2308.4, "end": 2309.14, "word": " يساوي", "probability": 0.912353515625}], "temperature": 1.0}, {"id": 97, "seek": 232516, "start": 2310.34, "end": 2325.16, "text": "المصوفة في معكوسة المعكوسة موجودة هنا ولا لا؟ موجودة لأن أنا جايل أن المحدد لا يساوي zero إذا المصوفة في معكوسة بتعطيني مصوفة", "tokens": [45340, 9381, 38688, 3660, 8978, 20449, 4117, 41779, 3660, 9673, 3615, 4117, 41779, 3660, 3714, 29245, 23328, 3660, 34105, 49429, 20193, 22807, 3714, 29245, 23328, 3660, 5296, 33456, 41850, 10874, 995, 26895, 14739, 9673, 24401, 3215, 20193, 7251, 3794, 995, 45865, 4018, 11933, 15730, 9673, 9381, 38688, 3660, 8978, 20449, 4117, 41779, 3660, 39894, 3615, 9566, 9957, 1829, 3714, 9381, 38688, 3660], "avg_logprob": -0.29067458992912654, "compression_ratio": 1.7230769230769232, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2310.34, "end": 2311.16, "word": "المصوفة", "probability": 0.889404296875}, {"start": 2311.16, "end": 2311.32, "word": " في", "probability": 0.93359375}, {"start": 2311.32, "end": 2312.18, "word": " معكوسة", "probability": 0.8892822265625}, {"start": 2312.18, "end": 2313.08, "word": " المعكوسة", "probability": 0.7435302734375}, {"start": 2313.08, "end": 2313.52, "word": " موجودة", "probability": 0.7491302490234375}, {"start": 2313.52, "end": 2313.7, "word": " هنا", "probability": 0.4150390625}, {"start": 2313.7, "end": 2313.9, "word": " ولا", "probability": 0.498291015625}, {"start": 2313.9, "end": 2314.62, "word": " لا؟", "probability": 0.65869140625}, {"start": 2314.62, "end": 2316.76, "word": " موجودة", "probability": 0.873779296875}, {"start": 2316.76, "end": 2317.0, "word": " لأن", "probability": 0.659423828125}, {"start": 2317.0, "end": 2317.42, "word": " أنا", "probability": 0.260986328125}, {"start": 2317.42, "end": 2318.02, "word": " جايل", "probability": 0.699462890625}, {"start": 2318.02, "end": 2318.3, "word": " أن", "probability": 0.439453125}, {"start": 2318.3, "end": 2319.4, "word": " المحدد", "probability": 0.9889322916666666}, {"start": 2319.4, "end": 2319.96, "word": " لا", "probability": 0.79052734375}, {"start": 2319.96, "end": 2320.74, "word": " يساوي", "probability": 0.8878173828125}, {"start": 2320.74, "end": 2321.2, "word": " zero", "probability": 0.247314453125}, {"start": 2321.2, "end": 2322.12, "word": " إذا", "probability": 0.633056640625}, {"start": 2322.12, "end": 2322.92, "word": " المصوفة", "probability": 0.97900390625}, {"start": 2322.92, "end": 2323.04, "word": " في", "probability": 0.96923828125}, {"start": 2323.04, "end": 2323.64, "word": " معكوسة", "probability": 0.9642333984375}, {"start": 2323.64, "end": 2324.24, "word": " بتعطيني", "probability": 0.81044921875}, {"start": 2324.24, "end": 2325.16, "word": " مصوفة", "probability": 0.9483642578125}], "temperature": 1.0}, {"id": 98, "seek": 234794, "start": 2325.66, "end": 2347.94, "text": "الوحدة يبقى هذا ال determinant لمصوفة الوحدة في ال determinant لل a الآن ال determinant لمصوفة الوحدة بقداش بواحد ال determinant ل a, a موجودة في g, g هي المحدد تبعها بقداش بواحد", "tokens": [6027, 2407, 24401, 3660, 7251, 3555, 4587, 7578, 23758, 2423, 41296, 32767, 9381, 38688, 3660, 2423, 2407, 24401, 3660, 8978, 2423, 41296, 24976, 257, 6024, 48506, 2423, 41296, 32767, 9381, 38688, 3660, 2423, 2407, 24401, 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0.9248046875}, {"start": 2340.56, "end": 2341.28, "word": " determinant", "probability": 0.98486328125}, {"start": 2341.28, "end": 2341.8, "word": " ل", "probability": 0.892578125}, {"start": 2341.8, "end": 2342.28, "word": " a,", "probability": 0.8056640625}, {"start": 2342.52, "end": 2342.8, "word": " a", "probability": 0.87841796875}, {"start": 2342.8, "end": 2343.54, "word": " موجودة", "probability": 0.975341796875}, {"start": 2343.54, "end": 2343.78, "word": " في", "probability": 0.97314453125}, {"start": 2343.78, "end": 2344.18, "word": " g,", "probability": 0.63818359375}, {"start": 2344.4, "end": 2344.78, "word": " g", "probability": 0.8994140625}, {"start": 2344.78, "end": 2345.48, "word": " هي", "probability": 0.92626953125}, {"start": 2345.48, "end": 2346.34, "word": " المحدد", "probability": 0.9680989583333334}, {"start": 2346.34, "end": 2346.78, "word": " تبعها", "probability": 0.9100341796875}, {"start": 2346.78, "end": 2347.3, "word": " بقداش", "probability": 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0.476806640625}], "temperature": 1.0}, {"id": 107, "seek": 258216, "start": 2564.8, "end": 2582.16, "text": "بالتم ولا بالتم مش؟ بالتم لأن كله نظام اتنين في اتنين انا فرض ان من البداية ال M اتنين باتنين matrix و determinant لا يساوي ديري اذا كل واحدة فيهم نظام اتنين في اتنين", "tokens": [3555, 6027, 39237, 49429, 20666, 39237, 37893, 22807, 20666, 39237, 5296, 33456, 28242, 3224, 8717, 19913, 10943, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957, 1975, 8315, 6156, 43042, 16472, 9154, 29739, 28259, 10632, 2423, 376, 1975, 2655, 1863, 9957, 4724, 9307, 1863, 9957, 8141, 4032, 41296, 20193, 7251, 3794, 995, 45865, 11778, 13546, 1829, 1975, 15730, 28242, 36764, 24401, 3660, 8978, 16095, 8717, 19913, 10943, 1975, 2655, 1863, 9957, 8978, 1975, 2655, 1863, 9957], "avg_logprob": -0.2295048770966468, "compression_ratio": 1.7898089171974523, "no_speech_prob": 0.0, "words": [{"start": 2564.8, "end": 2565.36, "word": "بالتم", "probability": 0.59521484375}, {"start": 2565.36, "end": 2565.56, 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" ال", "probability": 0.8828125}, {"start": 2651.6, "end": 2652.0, "word": " B", "probability": 0.625}, {"start": 2652.0, "end": 2653.16, "word": " وهذه", "probability": 0.82373046875}, {"start": 2653.16, "end": 2653.36, "word": " ال", "probability": 0.9248046875}, {"start": 2653.36, "end": 2653.56, "word": " B", "probability": 0.6787109375}, {"start": 2653.56, "end": 2653.76, "word": " اللي", "probability": 0.910888671875}, {"start": 2653.76, "end": 2654.22, "word": " عندنا", "probability": 0.923583984375}, {"start": 2654.22, "end": 2654.7, "word": " وهذه", "probability": 0.77880859375}, {"start": 2654.7, "end": 2654.92, "word": " ال", "probability": 0.7255859375}, {"start": 2654.92, "end": 2655.18, "word": " M", "probability": 0.994140625}, {"start": 2655.18, "end": 2655.7, "word": " inverse", "probability": 0.794921875}], "temperature": 1.0}, {"id": 111, "seek": 268057, "start": 2657.81, "end": 2680.57, "text": "هذه عبارة عن مصوف الواحدة يبقى مصففتين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين مصففين", "tokens": [3224, 24192, 6225, 3555, 9640, 3660, 18871, 3714, 9381, 38688, 2423, 14407, 24401, 3660, 7251, 3555, 4587, 7578, 3714, 9381, 5172, 5172, 2655, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 5172, 5172, 9957, 3714, 9381, 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0.98564453125}, {"start": 2672.45, "end": 2672.45, "word": " مصففين", "probability": 0.9875}, {"start": 2672.45, "end": 2672.51, "word": " مصففين", "probability": 0.9888671875}, {"start": 2672.51, "end": 2672.61, "word": " مصففين", "probability": 0.990234375}, {"start": 2672.61, "end": 2674.01, "word": " مصففين", "probability": 0.9912109375}, {"start": 2674.01, "end": 2675.21, "word": " مصففين", "probability": 0.9921875}, {"start": 2675.21, "end": 2676.35, "word": " مصففين", "probability": 0.99296875}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.9935546875}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.99404296875}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.99453125}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.994921875}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.99501953125}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.99541015625}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.995703125}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.995703125}, {"start": 2676.35, "end": 2676.35, "word": " مصففين", "probability": 0.9958984375}, {"start": 2676.35, "end": 2676.47, "word": " مصففين", "probability": 0.99599609375}, {"start": 2676.47, "end": 2677.53, "word": " مصففين", "probability": 0.99599609375}, {"start": 2677.53, "end": 2678.67, "word": " مصففين", "probability": 0.99599609375}, {"start": 2678.67, "end": 2679.83, "word": " مصففين", "probability": 0.99580078125}, {"start": 2679.83, "end": 2680.57, "word": " مصففين", "probability": 0.994921875}], "temperature": 1.0}, {"id": 112, "seek": 270913, "start": 2680.83, "end": 2709.13, "text": "يبقى تحققت الخاصية يبقى بقدر أقوله thus و هكذا فاي ام is an isomorphism طب example خمسة في شيء؟ لأ بس مش هنشتغل سؤال هل ال S", "tokens": [1829, 3555, 4587, 7578, 6055, 5016, 4587, 4587, 2655, 33962, 33546, 10632, 7251, 3555, 4587, 7578, 4724, 28543, 2288, 5551, 39648, 3224, 8807, 4032, 8032, 4117, 15730, 6156, 47302, 1975, 2304, 307, 364, 307, 32702, 1434, 23032, 3555, 1365, 16490, 2304, 3794, 3660, 8978, 44049, 38207, 22807, 5296, 10721, 4724, 3794, 37893, 8032, 1863, 8592, 2655, 17082, 1211, 8608, 33604, 6027, 8032, 1211, 2423, 318], "avg_logprob": -0.29261363726673706, "compression_ratio": 1.2745098039215685, "no_speech_prob": 0.0, "words": [{"start": 2680.83, "end": 2681.41, "word": "يبقى", "probability": 0.84051513671875}, {"start": 2681.41, "end": 2682.23, "word": " تحققت", "probability": 0.790576171875}, {"start": 2682.23, "end": 2683.11, "word": " الخاصية", "probability": 0.9864908854166666}, {"start": 2683.11, "end": 2683.51, "word": " يبقى", "probability": 0.8624267578125}, {"start": 2683.51, "end": 2684.01, "word": " بقدر", "probability": 0.9072265625}, {"start": 2684.01, "end": 2684.57, "word": " أقوله", "probability": 0.6990559895833334}, {"start": 2684.57, "end": 2685.11, "word": " thus", "probability": 0.2008056640625}, {"start": 2685.11, "end": 2685.75, "word": " و", "probability": 0.53662109375}, {"start": 2685.75, "end": 2686.61, "word": " هكذا", "probability": 0.786376953125}, {"start": 2686.61, "end": 2687.69, "word": " فاي", "probability": 0.31976318359375}, {"start": 2687.69, "end": 2688.29, "word": " ام", "probability": 0.763916015625}, {"start": 2688.29, "end": 2689.21, "word": " is", "probability": 0.45556640625}, {"start": 2689.21, "end": 2690.55, "word": " an", "probability": 0.6845703125}, {"start": 2690.55, "end": 2693.29, "word": " isomorphism", "probability": 0.9554036458333334}, {"start": 2693.29, "end": 2697.97, "word": " طب", "probability": 0.672119140625}, {"start": 2697.97, "end": 2698.47, "word": " example", "probability": 0.86767578125}, {"start": 2698.47, "end": 2699.51, "word": " خمسة", "probability": 0.8380126953125}, {"start": 2699.51, "end": 2701.73, "word": " في", "probability": 0.1768798828125}, {"start": 2701.73, "end": 2703.61, "word": " شيء؟", "probability": 0.5862630208333334}, {"start": 2703.61, "end": 2704.03, "word": " لأ", "probability": 0.702880859375}, {"start": 2704.03, "end": 2704.23, "word": " بس", "probability": 0.954345703125}, {"start": 2704.23, "end": 2704.41, "word": " مش", "probability": 0.990234375}, {"start": 2704.41, "end": 2705.13, "word": " هنشتغل", "probability": 0.9833984375}, {"start": 2705.13, "end": 2706.77, "word": " سؤال", "probability": 0.9601236979166666}, {"start": 2706.77, "end": 2708.27, "word": " هل", "probability": 0.968994140625}, {"start": 2708.27, "end": 2708.61, "word": " ال", "probability": 0.97314453125}, {"start": 2708.61, "end": 2709.13, "word": " S", "probability": 0.53955078125}], "temperature": 1.0}, {"id": 113, "seek": 273012, "start": 2710.48, "end": 2730.12, "text": "تلاتة هكم عنصر فيها؟ ستة، مظبوط؟ three factorial تلاتة في اتنين في واحد يبقى ست عناصر هل هذه isomorphic ل Z6؟", "tokens": [2655, 1211, 9307, 3660, 8032, 24793, 18871, 9381, 2288, 8978, 11296, 22807, 8608, 2655, 3660, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 1045, 36916, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 8978, 36764, 24401, 7251, 3555, 4587, 7578, 8608, 2655, 18871, 33546, 2288, 8032, 1211, 29538, 307, 32702, 299, 5296, 1176, 21, 22807], "avg_logprob": -0.27469307450311525, "compression_ratio": 1.2285714285714286, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2710.48, "end": 2711.56, "word": "تلاتة", "probability": 0.777557373046875}, {"start": 2711.56, "end": 2712.42, "word": " هكم", "probability": 0.2474365234375}, {"start": 2712.42, "end": 2712.9, "word": " عنصر", "probability": 0.9599609375}, {"start": 2712.9, "end": 2714.88, "word": " فيها؟", "probability": 0.7970377604166666}, {"start": 2714.88, "end": 2716.42, "word": " ستة،", "probability": 0.67803955078125}, {"start": 2716.42, "end": 2717.58, "word": " مظبوط؟", "probability": 0.8374837239583334}, {"start": 2717.58, "end": 2717.82, "word": " three", "probability": 0.55322265625}, {"start": 2717.82, "end": 2718.68, "word": " factorial", "probability": 0.8896484375}, {"start": 2718.68, "end": 2719.6, "word": " تلاتة", "probability": 0.879150390625}, {"start": 2719.6, "end": 2719.72, "word": " في", "probability": 0.74609375}, {"start": 2719.72, "end": 2720.04, "word": " اتنين", "probability": 0.9532470703125}, {"start": 2720.04, "end": 2720.16, "word": " في", "probability": 0.88720703125}, {"start": 2720.16, "end": 2720.44, "word": " واحد", "probability": 0.9912109375}, {"start": 2720.44, "end": 2720.66, "word": " يبقى", "probability": 0.8707275390625}, {"start": 2720.66, "end": 2721.04, "word": " ست", "probability": 0.95068359375}, {"start": 2721.04, "end": 2721.66, "word": " عناصر", "probability": 0.9578450520833334}, {"start": 2721.66, "end": 2722.78, "word": " هل", "probability": 0.751708984375}, {"start": 2722.78, "end": 2723.44, "word": " هذه", "probability": 0.546875}, {"start": 2723.44, "end": 2725.5, "word": " isomorphic", "probability": 0.86962890625}, {"start": 2725.5, "end": 2725.94, "word": " ل", "probability": 0.92236328125}, {"start": 2725.94, "end": 2730.12, "word": " Z6؟", "probability": 0.62744140625}], "temperature": 1.0}, {"id": 114, "seek": 274857, "start": 2731.61, "end": 2748.57, "text": "أيوة ممتازة زد ستة كوميوتاتيف ابدأ ليه لك ال S3 is not هادي cyclic هادي not cyclic وهكذا يبقى هادي is not isomorphic to z6 because", "tokens": [10721, 1829, 2407, 3660, 3714, 2304, 2655, 31377, 3660, 30767, 3215, 8608, 2655, 3660, 9122, 20498, 1829, 35473, 9307, 1829, 5172, 1975, 44510, 10721, 32239, 3224, 5296, 4117, 2423, 318, 18, 307, 406, 8032, 995, 16254, 38154, 1050, 8032, 995, 16254, 406, 38154, 1050, 37037, 4117, 15730, 7251, 3555, 4587, 7578, 8032, 995, 16254, 307, 406, 307, 32702, 299, 281, 710, 21, 570], "avg_logprob": -0.415283203125, "compression_ratio": 1.3169014084507042, "no_speech_prob": 0.0, "words": [{"start": 2731.61, "end": 2732.31, "word": "أيوة", "probability": 0.5482025146484375}, {"start": 2732.31, "end": 2733.03, "word": " ممتازة", "probability": 0.9619140625}, {"start": 2733.03, "end": 2734.01, "word": " زد", "probability": 0.29473876953125}, {"start": 2734.01, "end": 2734.79, "word": " ستة", "probability": 0.8837890625}, {"start": 2734.79, "end": 2736.09, "word": " كوميوتاتيف", "probability": 0.6462751116071429}, {"start": 2736.09, "end": 2736.73, "word": " ابدأ", "probability": 0.6158040364583334}, {"start": 2736.73, "end": 2736.95, "word": " ليه", "probability": 0.66552734375}, {"start": 2736.95, "end": 2737.21, "word": " لك", "probability": 0.5787353515625}, {"start": 2737.21, "end": 2737.37, "word": " ال", "probability": 0.904296875}, {"start": 2737.37, "end": 2738.15, "word": " S3", "probability": 0.58056640625}, {"start": 2738.15, "end": 2738.49, "word": " is", "probability": 0.63134765625}, {"start": 2738.49, "end": 2738.93, "word": " not", "probability": 0.92431640625}, {"start": 2738.93, "end": 2739.91, "word": " هادي", "probability": 0.5076497395833334}, {"start": 2739.91, "end": 2740.83, "word": " cyclic", "probability": 0.519561767578125}, {"start": 2740.83, "end": 2741.31, "word": " هادي", "probability": 0.81884765625}, {"start": 2741.31, "end": 2741.67, "word": " not", "probability": 0.81591796875}, {"start": 2741.67, "end": 2742.47, "word": " cyclic", "probability": 0.88037109375}, {"start": 2742.47, "end": 2743.17, "word": " وهكذا", "probability": 0.783935546875}, {"start": 2743.17, "end": 2743.95, "word": " يبقى", "probability": 0.9427490234375}, {"start": 2743.95, "end": 2744.27, "word": " هادي", "probability": 0.8196614583333334}, {"start": 2744.27, "end": 2744.83, "word": " is", "probability": 0.93994140625}, {"start": 2744.83, "end": 2745.51, "word": " not", "probability": 0.9619140625}, {"start": 2745.51, "end": 2746.79, "word": " isomorphic", "probability": 0.8922526041666666}, {"start": 2746.79, "end": 2746.95, "word": " to", "probability": 0.82763671875}, {"start": 2746.95, "end": 2747.63, "word": " z6", "probability": 0.68115234375}, {"start": 2747.63, "end": 2748.57, "word": " because", "probability": 0.83740234375}], "temperature": 1.0}, {"id": 115, "seek": 277534, "start": 2750.3, "end": 2775.34, "text": "جيب ليه ولو سبب واحد بديش اسباب كتيرة رغم ان هذه فيها ست عناصر وهذه فيها ست عناصر يبقى because ال S3 is not cyclic but ولكن Z6 اللي هو subgroup of Y1 is cyclic", "tokens": [7435, 1829, 3555, 32239, 3224, 35525, 2407, 8608, 3555, 3555, 36764, 24401, 4724, 16254, 8592, 24525, 3555, 16758, 9122, 2655, 48923, 12602, 17082, 2304, 16472, 29538, 8978, 11296, 8608, 2655, 18871, 33546, 2288, 37037, 24192, 8978, 11296, 8608, 2655, 18871, 33546, 2288, 7251, 3555, 4587, 7578, 570, 2423, 318, 18, 307, 406, 38154, 1050, 457, 35525, 19452, 1176, 21, 13672, 1829, 31439, 1422, 17377, 295, 398, 16, 307, 38154, 1050], "avg_logprob": -0.25770245723321406, "compression_ratio": 1.4226190476190477, "no_speech_prob": 0.0, "words": [{"start": 2750.3, "end": 2750.72, "word": "جيب", "probability": 0.6728108723958334}, {"start": 2750.72, "end": 2751.0, "word": " ليه", "probability": 0.3948974609375}, {"start": 2751.0, "end": 2751.34, "word": " ولو", "probability": 0.64892578125}, {"start": 2751.34, "end": 2751.76, "word": " سبب", "probability": 0.97509765625}, {"start": 2751.76, "end": 2752.02, "word": " واحد", "probability": 0.990966796875}, {"start": 2752.02, "end": 2752.44, "word": " بديش", "probability": 0.68408203125}, {"start": 2752.44, "end": 2752.84, "word": " اسباب", "probability": 0.8779296875}, {"start": 2752.84, "end": 2753.36, "word": " كتيرة", "probability": 0.82763671875}, {"start": 2753.36, "end": 2754.04, "word": " رغم", "probability": 0.8889973958333334}, {"start": 2754.04, "end": 2754.18, "word": " ان", "probability": 0.67919921875}, {"start": 2754.18, "end": 2754.44, "word": " هذه", "probability": 0.337646484375}, {"start": 2754.44, "end": 2754.76, "word": " فيها", "probability": 0.893310546875}, {"start": 2754.76, "end": 2755.12, "word": " ست", "probability": 0.788330078125}, {"start": 2755.12, "end": 2755.76, "word": " عناصر", "probability": 0.9720052083333334}, {"start": 2755.76, "end": 2756.1, "word": " وهذه", "probability": 0.779296875}, {"start": 2756.1, "end": 2756.48, "word": " فيها", "probability": 0.955078125}, {"start": 2756.48, "end": 2756.84, "word": " ست", "probability": 0.972900390625}, {"start": 2756.84, "end": 2757.44, "word": " عناصر", "probability": 0.9895833333333334}, {"start": 2757.44, "end": 2758.46, "word": " يبقى", "probability": 0.9503173828125}, {"start": 2758.46, "end": 2759.2, "word": " because", "probability": 0.607421875}, {"start": 2759.2, "end": 2759.94, "word": " ال", "probability": 0.89599609375}, {"start": 2759.94, "end": 2761.14, "word": " S3", "probability": 0.7919921875}, {"start": 2761.14, "end": 2762.12, "word": " is", "probability": 0.89404296875}, {"start": 2762.12, "end": 2763.3, "word": " not", "probability": 0.9375}, {"start": 2763.3, "end": 2765.14, "word": " cyclic", "probability": 0.8720703125}, {"start": 2765.14, "end": 2766.48, "word": " but", "probability": 0.7412109375}, {"start": 2766.48, "end": 2768.26, "word": " ولكن", "probability": 0.6754150390625}, {"start": 2768.26, "end": 2769.8, "word": " Z6", "probability": 0.853271484375}, {"start": 2769.8, "end": 2770.66, "word": " اللي", "probability": 0.748779296875}, {"start": 2770.66, "end": 2770.96, "word": " هو", "probability": 0.9921875}, {"start": 2770.96, "end": 2771.72, "word": " subgroup", "probability": 0.764892578125}, {"start": 2771.72, "end": 2771.88, "word": " of", "probability": 0.23583984375}, {"start": 2771.88, "end": 2773.06, "word": " Y1", "probability": 0.895751953125}, {"start": 2773.06, "end": 2773.88, "word": " is", "probability": 0.8564453125}, {"start": 2773.88, "end": 2775.34, "word": " cyclic", "probability": 0.911865234375}], "temperature": 1.0}, {"id": 116, "seek": 278100, "start": 2779.06, "end": 2781.0, "text": "بنكمل ان شاء الله بعد الظهر", "tokens": [3555, 1863, 24793, 1211, 16472, 13412, 16606, 21984, 39182, 6024, 116, 3224, 2288], "avg_logprob": -0.16852679210049765, "compression_ratio": 0.9245283018867925, "no_speech_prob": 0.0, "words": [{"start": 2779.06, "end": 2779.64, "word": "بنكمل", "probability": 0.8221435546875}, {"start": 2779.64, "end": 2779.74, "word": " ان", "probability": 0.51171875}, {"start": 2779.74, "end": 2780.02, "word": " شاء", "probability": 0.99365234375}, {"start": 2780.02, "end": 2780.2, "word": " الله", "probability": 0.9697265625}, {"start": 2780.2, "end": 2780.5, "word": " بعد", "probability": 0.92626953125}, {"start": 2780.5, "end": 2781.0, "word": " الظهر", "probability": 0.906982421875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2782.30775, "duration_after_vad": 2613.769999999992}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..89c97ee8be8b9427f45b4c425783b7325fd18b0f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W89d5Az0ySQ_raw.srt
@@ -0,0 +1,1696 @@
+1
+00:00:21,260 --> 00:00:26,820
+بسم الله الرحمن الرحيم نعود ثانية إلى إكمال ما
+
+2
+00:00:26,820 --> 00:00:34,400
+بدأنا به حيث تركتكم بعد أنهينا chapter ال
+
+3
+00:00:34,400 --> 00:00:39,120
+subgroups والأستاذ محمود شرح لكم chapterين اللي هو
+
+4
+00:00:39,120 --> 00:00:43,660
+ال cyclic groups و كذلك ال permutations groups إذا
+
+5
+00:00:43,660 --> 00:00:48,250
+نصل الآن إلى ال isomorphismبالبلد هيك ال
+
+6
+00:00:48,250 --> 00:00:52,770
+isomorphism عبارة عن function بس مش ما بين two
+
+7
+00:00:52,770 --> 00:00:57,810
+sets ما بين two groups بده تحقق ليه ثلاثة شروط
+
+8
+00:00:57,810 --> 00:01:03,710
+يبقى function وزيادة على ذلك بده تحقق ثلاث شروط
+
+9
+00:01:03,710 --> 00:01:07,210
+الشرط الأول هذه ال function بده تبقى one to one
+
+10
+00:01:07,210 --> 00:01:12,510
+الشرط الثاني بده تبقى on two الشرط الثالث بده تحقق
+
+11
+00:01:12,510 --> 00:01:18,350
+الخاصية اللي عندنا هذههذه التعريف يقول ان ايزو
+
+12
+00:01:18,350 --> 00:01:25,110
+مورفزم ايزو مورفزم بالعربي هيك التشاكل النماطي او
+
+13
+00:01:25,110 --> 00:01:29,690
+التشابه النماطي ولان هنقول لك ايش معناها من
+
+14
+00:01:29,690 --> 00:01:34,230
+الناحية الرياضية بس اصبر علينا شويةيبقى انا ايزو
+
+15
+00:01:34,230 --> 00:01:39,930
+مورفزم في حديله رمز في من الجروب جي لجروب جي بار
+
+16
+00:01:39,930 --> 00:01:46,130
+is one to one function يبقى function وكذلك one to
+
+17
+00:01:46,130 --> 00:01:52,110
+one from جي on to جي بار مش to جي بار يا شباب on
+
+18
+00:01:52,110 --> 00:02:00,700
+to on to جي بارsuch that بحيث أن الـPhi of A بيبقى
+
+19
+00:02:00,700 --> 00:02:05,360
+يسوى Phi of A في Phi of B يعني تأثير الـPhi على
+
+20
+00:02:05,360 --> 00:02:09,820
+حاصل الضرب الـtwo elements A وB بيبقى يسوى تأثير
+
+21
+00:02:09,820 --> 00:02:15,160
+الـPhi علي A مضروبا في تأثير الـPhi علي B دي ربالك
+
+22
+00:02:15,160 --> 00:02:21,100
+بديفهم كل شيء في مكانه كيف كل شيء في مكانه الآن
+
+23
+00:02:21,100 --> 00:02:26,040
+الـA و الـB وين موجودات؟في جي جي عليها operation
+
+24
+00:02:26,040 --> 00:02:30,380
+غير ال operation اللي على جي بار وبالتالي لما اقول
+
+25
+00:02:30,380 --> 00:02:36,060
+a بي اللي بينهم operation تبعت من تبعت الجي لكن
+
+26
+00:02:36,060 --> 00:02:39,760
+لما اقول في of ا في في of بي ال operation اللي
+
+27
+00:02:39,760 --> 00:02:45,450
+بينهم ايه ال operation تبعت من تبعت جي بارلما اقول
+
+28
+00:02:45,450 --> 00:02:51,450
+two elements في جي بار هدول a وb two elements في g
+
+29
+00:02:51,450 --> 00:02:59,990
+لما اقول a في b ال operation بينهم
+
+30
+00:02:59,990 --> 00:03:07,230
+تبعت جي بارطيب الان لو كان five من جي إلى جي بار
+
+31
+00:03:07,230 --> 00:03:12,010
+هو عبارة عن isomorphism بقدر اقول عن جي و جي بار
+
+32
+00:03:12,010 --> 00:03:17,810
+are isomorphic يبقى ال two groups دول في تشابه
+
+33
+00:03:17,810 --> 00:03:25,810
+رياضي، تشابه نماطي، تشاكل نماطي فيما بينهمو باكتب
+
+34
+00:03:25,810 --> 00:03:32,410
+الـ isomorphism مش باكتبه يساوي باكتبه جي و خطين
+
+35
+00:03:32,410 --> 00:03:38,090
+متعرجين بالشكل هادى جي بار و تقرا جي ايزو مورفكت
+
+36
+00:03:38,090 --> 00:03:44,030
+جي بارطب بالمعنى الرياضي ايش يعني معنى isomorphism
+
+37
+00:03:44,030 --> 00:03:49,690
+او G isomorphic ل G bar لاحظ من خلال التعريف لما
+
+38
+00:03:49,690 --> 00:03:53,750
+يقول ال group هذي و ال group هذي في function بينهم
+
+39
+00:03:53,750 --> 00:03:59,510
+one to one and unto السؤال الأول هل سيختلف عدد
+
+40
+00:03:59,510 --> 00:04:03,150
+العناصر في ال group الأولى عن عدد عناصر ال group
+
+41
+00:04:03,150 --> 00:04:10,130
+التانية؟ في اختلاف؟ لأ لإن واحد لواحداتنين ال
+
+42
+00:04:10,130 --> 00:04:15,110
+domain بيغطي جميع عناصر جي مدام انت بيغطي جميع
+
+43
+00:04:15,110 --> 00:04:20,210
+عناصر جي بار و لا واحد زي التاني يبقى بناء عندي
+
+44
+00:04:20,210 --> 00:04:26,050
+عدد عناصر جي يساوي عدد عناصر جي بارعدد ال subgroup
+
+45
+00:04:26,050 --> 00:04:31,910
+في G يسوى عدد ال subgroup في G bar عدد العناصر
+
+46
+00:04:31,910 --> 00:04:37,050
+التي لها نفس ال order في G يسوى عدد العناصر التي
+
+47
+00:04:37,050 --> 00:04:42,690
+لها نفس ال order من G barبمعنى لو عندي 6 عناصر ال
+
+48
+00:04:42,690 --> 00:04:49,410
+order يسوى 4 في G لازم اجد 6 عناصر ال order يسوى 4
+
+49
+00:04:49,410 --> 00:04:54,770
+في G bar لو عندي 10 عناصر في G ال order يسوى 2
+
+50
+00:04:54,770 --> 00:05:03,380
+لازم اجد 10 عناصر في G bar ال order يسوى 2لو كانت
+
+51
+00:05:03,380 --> 00:05:07,680
+ال group Cyclic هذه التانية Cyclic لو كانت Abelian
+
+52
+00:05:07,680 --> 00:05:11,900
+التانية Abelian يعني بمعنى هيكب البلدي ال two
+
+53
+00:05:11,900 --> 00:05:16,460
+groups اللي اتنية اللي لهم نفس الخواصة الرياضية
+
+54
+00:05:16,460 --> 00:05:21,950
+يعني كل ما تعرفه اللي عن ال groupينطبق على الأولى
+
+55
+00:05:21,950 --> 00:05:25,830
+الريكولوجيا ينطبق على مين؟ على الثانية هذي non
+
+56
+00:05:25,830 --> 00:05:29,650
+-abelian إذا التانية non-abelian متنفعش واحدة
+
+57
+00:05:29,650 --> 00:05:33,450
+cyclic والتانية لأ واحدة abelian والتانية لأ واحدة
+
+58
+00:05:33,450 --> 00:05:38,090
+finite والتانية infinite برضه لأ لو فيها عدد عناصر
+
+59
+00:05:38,090 --> 00:05:41,970
+يساوي infinite بجهد فيها عدد عناصر يساوي infinite
+
+60
+00:05:41,970 --> 00:05:46,530
+وهكذايبقى بناء عليه لما أقول في isomorphism ما بين
+
+61
+00:05:46,530 --> 00:05:50,470
+two groups يبقى ال two groups اللي لهم جميع
+
+62
+00:05:50,470 --> 00:05:55,190
+الخواصة الرياضية بالضبط تماما الخواصة اللي في
+
+63
+00:05:55,190 --> 00:05:59,230
+الجروب الأولى تنطبق تماما على الجروب التاني وإن
+
+64
+00:05:59,230 --> 00:06:04,650
+كانت العناصر مختلفة ما بين الاتنين وكانت ال binary
+
+65
+00:06:04,650 --> 00:06:07,810
+operation على الأولى تختلف عن ال binary operation
+
+66
+00:06:07,810 --> 00:06:12,650
+عن مينع الجروب التاني وهكذا يبقى هذا اللي بدي ايه
+
+67
+00:06:12,650 --> 00:06:16,890
+المعنى اللي بدي اترسخه في دماغك عن معنى ال
+
+68
+00:06:16,890 --> 00:06:22,690
+isomorphism اظن واضح كلامي نبدأ ناخد مجموعة من
+
+69
+00:06:22,690 --> 00:06:29,670
+الأمثلة على ال isomorphism اول مثال بيقول define a
+
+70
+00:06:29,670 --> 00:06:40,890
+function define a functionفاي من ال R تحت عملية
+
+71
+00:06:40,890 --> 00:06:53,750
+الجامعة ل R plus تحت عملية الضرب باي فاي
+
+72
+00:06:53,750 --> 00:07:00,310
+of X بده يساوي اتنين to the power X لكل ال X اللي
+
+73
+00:07:00,310 --> 00:07:18,440
+موجودة في Rهنا show that phi is an isomorphism مرة
+
+74
+00:07:18,440 --> 00:07:24,940
+تانيةأحنا قلنا في التعريف أربع شروط للايزمورفزية
+
+75
+00:07:24,940 --> 00:07:28,960
+function هذي ال function one to one هذي ال
+
+76
+00:07:28,960 --> 00:07:32,000
+function one to .. ال function اللي عندنا تحقق
+
+77
+00:07:32,000 --> 00:07:37,540
+الخاصية هذه طبعا؟ طيب قال لي define a function
+
+78
+00:07:37,540 --> 00:07:41,900
+يبقى ريحني من مين؟ من الشرط اللي هو قال لي خدها ال
+
+79
+00:07:41,900 --> 00:07:47,980
+function هذهمعرفة من R تحت عملية الجامعة الى R
+
+80
+00:07:47,980 --> 00:07:53,100
+Plus تحت عملية الضرب يبقى هذه جميع الأعداد
+
+81
+00:07:53,100 --> 00:07:58,500
+الحقيقية بلا استثناء تحت عملية الجامعة هذه عملية
+
+82
+00:07:58,500 --> 00:08:04,520
+مجموعة الأعداد الحقيقية الموجبة فقط تحت عملية
+
+83
+00:08:04,520 --> 00:08:10,100
+الضرب قال يعرف ال function Phi of X بدل سوى 2X لكل
+
+84
+00:08:10,100 --> 00:08:16,160
+X الموجودة في Rالان بدى اسأل السؤال التالي هل ال
+
+85
+00:08:16,160 --> 00:08:21,920
+function هدى فعلا هدى معرفة من R عليها عملية الجمع
+
+86
+00:08:21,920 --> 00:08:27,680
+الى R plus تحت عملية الضرب ام لا باجي بقول ال X
+
+87
+00:08:27,680 --> 00:08:33,230
+هدى موجود وين هناإذا قد يكون موجب و قد يكون سلب و
+
+88
+00:08:33,230 --> 00:08:39,370
+قد يكون صفر تمام ما هي صوت صوت اتنين to the power
+
+89
+00:08:39,370 --> 00:08:44,150
+X هل اتنين to the power X موجودة في R plus يعني
+
+90
+00:08:44,150 --> 00:08:48,550
+اتنين to the power X لابتاخد Zero ولا بتاخد قيمة
+
+91
+00:08:48,550 --> 00:08:55,030
+سالبةطبعًا الـ exponential function دائمًا وأبدًا
+
+92
+00:08:55,030 --> 00:09:01,410
+أقل من زيرو عمرهاش بتكون أقل من زيرو سواء كان U of
+
+93
+00:09:01,410 --> 00:09:06,290
+X والله A to the power X لو رجعت لرسمتها دائمًا
+
+94
+00:09:06,290 --> 00:09:10,950
+أعلى محور X يبقى أقل من زيرو إذا كلامنا هذا
+
+95
+00:09:10,950 --> 00:09:15,790
+تعريفنا سليم مائة بالمائة يبقى إيش ضايل علينا؟ one
+
+96
+00:09:15,790 --> 00:09:20,260
+to one and one to one نرجع لمبادئ الرياضيةلما
+
+97
+00:09:20,260 --> 00:09:24,980
+بنقول one to one بالبلد العناصر المختلفة لها صور
+
+98
+00:09:24,980 --> 00:09:29,940
+مختلفة يعني لو أخدت x1 لا يساوي x2 بدي أثبت أن ال
+
+99
+00:09:29,940 --> 00:09:34,720
+f of x1 لا يساوي ال f of x2 أو ال contrapositive
+
+100
+00:09:34,720 --> 00:09:40,040
+إيها لو كان ال f of x1 بدي يساوي f of x2 بدي أثبت
+
+101
+00:09:40,040 --> 00:09:45,620
+أن ال x1 يساوي x2 إن حدث ذلك يبقى ال function one
+
+102
+00:09:45,620 --> 00:09:51,490
+to oneيبقى بدى اثبتله الخطوة الأولى في is one to
+
+103
+00:09:51,490 --> 00:09:58,890
+one مشان هيك بداجي اقوله assume اللي هو main في of
+
+104
+00:09:58,890 --> 00:10:05,680
+x يساوي في of yإذا قررت أثبت له إن الـ X بدها
+
+105
+00:10:05,680 --> 00:10:10,740
+تساوي Y بيتم المطلوب طيب فاي أوف X هي كده يا شباب؟
+
+106
+00:10:10,740 --> 00:10:19,390
+اتنين أص X فاي أوف Y اتنين أص Yلما يكون الطرفين
+
+107
+00:10:19,390 --> 00:10:25,070
+متساوين و تتساوى الأساسات يبقى الأساس متساوية واحد
+
+108
+00:10:25,070 --> 00:10:30,490
+تاني ماعجبوش كلامي قال خد لن للطرفين بنقوله ماشي
+
+109
+00:10:30,490 --> 00:10:37,570
+لو أخدنا لن للطرفين بيصير X في لن اتنين يساوي Y في
+
+110
+00:10:37,570 --> 00:10:42,540
+لن اتنينلو قسمنا الطرفين على الان اتنين هذا
+
+111
+00:10:42,540 --> 00:10:48,720
+بيعطينا مين انه ال X يساوي ال Y مدام ال X يساوي ال
+
+112
+00:10:48,720 --> 00:10:54,240
+Y يبقى Phi is one to one الان بدنا نيجي نثبت ان
+
+113
+00:10:54,240 --> 00:11:02,810
+Phi is ontoمش هنثبت انه في is onto بضروحه اخد عنصر
+
+114
+00:11:02,810 --> 00:11:09,970
+في R plus و اثبت انه له اصل في R ان حدث ذلك بصير
+
+115
+00:11:09,970 --> 00:11:16,190
+الفي is onto يبقى بداجي اقوله لاتفترض ان ال Y
+
+116
+00:11:16,190 --> 00:11:23,610
+موجودة في ال R plusيبقى الـY هذي أكبر من الـ0 ولا
+
+117
+00:11:23,610 --> 00:11:31,690
+أقل من الـ0؟ يبقى هذا يعطيك أن الـY أكبر من الـ0
+
+118
+00:11:31,690 --> 00:11:38,890
+يعني الـY هذي موجبة مدام موجبة يبقى الـlog Y
+
+119
+00:11:38,890 --> 00:11:45,980
+للأساس اتنين exist ولا does not exist؟exist لأن
+
+120
+00:11:45,980 --> 00:11:50,920
+اللغة الرتم مش معرفة إلا لقيمة موجبة لكن لو قلت له
+
+121
+00:11:50,920 --> 00:11:56,700
+Y هذه موجودة في R بصير كلامي هذا ماله مش صحيح لأنه
+
+122
+00:11:56,700 --> 00:12:00,460
+قد تكون exist و قد لا تكون exist لكن كونها موجبة
+
+123
+00:12:00,460 --> 00:12:07,980
+يبقى هذا exist مدام exist يبقى بدي أروح أسمي تسمية
+
+124
+00:12:07,980 --> 00:12:15,300
+لغة Y للأساس اتنين بدي أسمي X مثلالو رجعنا ل
+
+125
+00:12:15,300 --> 00:12:20,720
+calculus P بدي اكتب ال log بدلالة ال len يبقى هذا
+
+126
+00:12:20,720 --> 00:12:29,140
+len y على len 2 بده يساوي ال x لو ضربنا ضرب تبادل
+
+127
+00:12:29,140 --> 00:12:38,330
+يبقى len y يساوي ال x في len 2لو استخدمت خواص ال
+
+128
+00:12:38,330 --> 00:12:46,830
+len يبقى len y بده يساوي len اتنين اص اكس مظبوط
+
+129
+00:12:46,830 --> 00:12:54,010
+ايك؟ يبقى بناء عليه لو رفعت اتنين كأس للعدد ايه؟
+
+130
+00:12:54,010 --> 00:13:00,450
+بيصير y يساوي قداش اتنين اص اكس اتنين اص اكس مين
+
+131
+00:13:00,450 --> 00:13:07,680
+هي هذه حسب التعريف مش عبارة عن five of xاذا اي
+
+132
+00:13:07,680 --> 00:13:15,560
+element y موجود في الار بلس لاجتله اصل x موجود في
+
+133
+00:13:15,560 --> 00:13:20,180
+الار معناه هذا الكلام ان الار موجود في الار طيب
+
+134
+00:13:20,180 --> 00:13:23,740
+خلصنا ال condition التاني بدنا نروح لل condition
+
+135
+00:13:23,740 --> 00:13:30,140
+التاني يبقى باجي بقوله لو كان ال x و y موجودة في
+
+136
+00:13:30,140 --> 00:13:38,720
+الار then بدي اخد في of خلي بالك هنابدي اخد x في y
+
+137
+00:13:38,720 --> 00:13:45,420
+والله x زائد yيبقى ال operation هنا ال operation
+
+138
+00:13:45,420 --> 00:13:49,040
+اللي موجودة في ال group الأولى ال operation اللي
+
+139
+00:13:49,040 --> 00:13:57,560
+عنده زائد يبقى بقوله في x زائد y وليست x في y لأن
+
+140
+00:13:57,560 --> 00:14:01,320
+ال operation ما بين ال a و ال b هي ال operation
+
+141
+00:14:01,320 --> 00:14:04,740
+اللي موجودة في جيه الأولى ال operation اللي موجودة
+
+142
+00:14:04,740 --> 00:14:11,460
+عنده هي الجامعةيبقى حسب التعريف هذا بدل ساوي اتنين
+
+143
+00:14:11,460 --> 00:14:21,020
+اص X زائد Y او اتنين اص X في اتنين اص Yهذا الكلام
+
+144
+00:14:21,020 --> 00:14:26,120
+يساوي رياضيا كلام سليم 100% يبقى هنا اللي بينهم
+
+145
+00:14:26,120 --> 00:14:29,760
+صلة عملية ضرب وليست عملية جمع
+
+146
+00:14:38,750 --> 00:14:43,910
+يبقى تحقق ال condition main التاني يبقى بناء عليه
+
+147
+00:14:43,910 --> 00:14:54,690
+فاي is an isomorphism فاي is an isomorphism حد
+
+148
+00:14:54,690 --> 00:15:03,350
+يلقي تساول هنا علي صوتك بس اه
+
+149
+00:15:04,080 --> 00:15:09,060
+لما قلنا لغة why الأساس اتنين exist ليش؟ لأن Y
+
+150
+00:15:09,060 --> 00:15:16,420
+قيمة موجبة لو كانت صفر أو سالبة فاللغة غير معرفة
+
+151
+00:15:16,420 --> 00:15:22,220
+تمام؟ يبقى انا عندي رقم موجب اخد اللغة للأساس
+
+152
+00:15:22,220 --> 00:15:28,230
+اتنين ليش اتنين؟ انا متعمد اخد اتنينلأن لو كانت
+
+153
+00:15:28,230 --> 00:15:33,650
+المسألة five of x سوى تلاتة of x سوف أقول له while
+
+154
+00:15:33,650 --> 00:15:37,270
+أساس تلاتة لو كانت أربعة سوف أقول له أساس أربعة و
+
+155
+00:15:37,270 --> 00:15:44,070
+هكذا لكي نوصل للإتنين of x خلاص واضحة ليش أخدنا
+
+156
+00:15:44,070 --> 00:15:50,430
+هذه يبقى exist لإن هذه greater than zeroو روحت
+
+157
+00:15:50,430 --> 00:15:55,770
+قولت هذه كل عبض ايش ما تطلع سميتها X تمام عملت
+
+158
+00:15:55,770 --> 00:15:59,490
+الشغل الرياضي تبع ال calculus لغاية ما وصلت لمين
+
+159
+00:15:59,490 --> 00:16:05,730
+وصلت لل Y يساوي 2 و 6 اللي هي Phi of X نجي ناخد
+
+160
+00:16:05,730 --> 00:16:10,430
+كمان مثال ثاني مثال اتنين
+
+161
+00:16:13,030 --> 00:16:20,950
+بقول let g be a cyclic group let g be a cyclic
+
+162
+00:16:20,950 --> 00:16:39,430
+group of order n of order n let g bar سوى z n of
+
+163
+00:16:42,960 --> 00:16:52,120
+إثبت لي إن الـ G isomorphic لمن؟ لـ ZN G
+
+164
+00:16:52,120 --> 00:17:06,000
+isomorphic ل ZN نرجع
+
+165
+00:17:06,000 --> 00:17:10,920
+لسؤالنا مرة ثانيةبقول ياخد الـG الـcyclic group
+
+166
+00:17:10,920 --> 00:17:16,800
+الـorder Lها يساوي M مادام الـcyclic على الأقل
+
+167
+00:17:16,800 --> 00:17:23,380
+فيها كام generator؟ اتنين generator ومعكسه تمام؟
+
+168
+00:17:23,380 --> 00:17:28,720
+مابناش المعكس احنا مكفين واحد بدي افترض انه فيها
+
+169
+00:17:28,720 --> 00:17:36,820
+generator وليكن A يبقى باجي بقوله since الـG is
+
+170
+00:17:36,820 --> 00:17:45,160
+cyclicيبقى نحن لدينا ان الـ G هذه بدها تساوي ال
+
+171
+00:17:45,160 --> 00:17:51,560
+identity و ال A و ال A ترابيع و نظل ماشيين لغاية
+
+172
+00:17:51,560 --> 00:17:58,490
+ال A M minus ال oneمظبوط كما فهمت من الشبطر قبل
+
+173
+00:17:58,490 --> 00:18:04,850
+السابق الـcyclic subgroups يبقى هذه كإنها group
+
+174
+00:18:04,850 --> 00:18:09,770
+generated by a مكتوبة بالشكل اللي عندنا هنا هاي
+
+175
+00:18:09,770 --> 00:18:14,690
+الـcyclic group وال order اللي هيسوي إن ال element
+
+176
+00:18:14,690 --> 00:18:20,550
+الأخر يصير am ناقص واحد لإن an بدو يسوى ال
+
+177
+00:18:20,550 --> 00:18:28,430
+identity elementقال لي خد الجيبار تساوي ZN خليني
+
+178
+00:18:28,430 --> 00:18:32,890
+أسألكوا السؤال التالي ZN ال operation اللي عليها
+
+179
+00:18:32,890 --> 00:18:37,750
+الجامع ولا ضرب حسب ما خدناه في تعريف ال groups
+
+180
+00:18:37,750 --> 00:18:42,170
+جامع ممتاز يدني بقى حطلي المعلومة هذه في إيدك في
+
+181
+00:18:42,170 --> 00:18:49,150
+دماغك لإن جامع موديولو N كل N بتبدأ الدورة من جديد
+
+182
+00:18:49,760 --> 00:18:54,400
+طب كويس قال لي اثبت لي ان اتنين هذول ايزو مورفكت
+
+183
+00:18:54,400 --> 00:18:59,380
+اذا انا بده اروح اعرف function من الجروب الاولى
+
+184
+00:18:59,380 --> 00:19:03,740
+الى الجروب التانى ونشوف هذه ال function هل هي one
+
+185
+00:19:03,740 --> 00:19:07,560
+to one و one to two بتخدم الخاصية اللى عندنا هذه
+
+186
+00:19:07,560 --> 00:19:10,460
+ولا لأ اذا بده اروح اقوله define
+
+187
+00:19:13,750 --> 00:19:24,190
+فانكشن فاي من جي الى زد ن باى عشان تبقى فانكشن
+
+188
+00:19:24,190 --> 00:19:29,090
+تتأثر على العنصر اللى في جي من جي أيه يبقى ايه
+
+189
+00:19:29,090 --> 00:19:36,530
+الشكل العنصر اللى هنا ايه ال power معينة يبقى a to
+
+190
+00:19:36,530 --> 00:19:43,510
+the power k مثلاطبعا k محصورة ما بين ال zero و ما
+
+191
+00:19:43,510 --> 00:19:48,370
+بين ال main ال n minus ال one ما بين ال zero و ما
+
+192
+00:19:48,370 --> 00:19:52,890
+بين ال n minus ال one بدها تساوي مين؟ بدها تساوي
+
+193
+00:19:52,890 --> 00:20:01,030
+عنصر في z n بقدر اقول k itself و ال k هذا اكبر من
+
+194
+00:20:01,030 --> 00:20:06,030
+او يساوي zero اقل من n بصير الكلام هكذا صح ولا
+
+195
+00:20:06,030 --> 00:20:15,340
+غلط؟صح 100% لأن ك محصورة بين ال zero و ال N يبقى
+
+196
+00:20:15,340 --> 00:20:22,330
+واحد من هذول AKK اللي عندنا هذه هي element من ZN
+
+197
+00:20:22,330 --> 00:20:30,610
+لأن عناصر الـ ZN 0,1,2,3 لغاية N minus الـ 1 مظبوط
+
+198
+00:20:30,610 --> 00:20:35,390
+يبقى هذا التعريف سليم مائة مائة ك function الآن
+
+199
+00:20:35,390 --> 00:20:41,840
+بدي أثبت أن هذه one to oneيبقى بدى اثبتله ان فاي
+
+200
+00:20:41,840 --> 00:20:47,960
+is one to one مشان هيك بدى اخد صورتين متساوي او
+
+201
+00:20:47,960 --> 00:20:55,860
+صورتين متساوياتين يبقى باجي بقوله assume فاي of AK
+
+202
+00:20:55,860 --> 00:21:09,220
+تساوي فاي of AJ مثلاعشان اثبت ان الـ A K بده يساوي
+
+203
+00:21:09,220 --> 00:21:14,940
+الـ A J كويس يبقى حسب ال definition Phi of AK اللي
+
+204
+00:21:14,940 --> 00:21:22,300
+هي بقداش K Phi of AJ اللي هي بقداش BGأو ان شئتم
+
+205
+00:21:22,300 --> 00:21:30,020
+فقولوا k minus الجيه بده يسوي قداش zero او ان شئتم
+
+206
+00:21:30,020 --> 00:21:36,380
+فقولوا a to the k minus الجيه بده يسوي a to the
+
+207
+00:21:36,380 --> 00:21:46,460
+zero او بمعنى اخرالـ A K في الـ A مينوس الـ J بده
+
+208
+00:21:46,460 --> 00:21:51,420
+يسوى ال identity لأن ال element مرفوع للـ O Zero
+
+209
+00:21:51,420 --> 00:21:55,960
+دائما و أبدا بده يسوى ال identity تبع ال group طب
+
+210
+00:21:55,960 --> 00:22:02,000
+لو ضربت الطرفين في A J بصير عندى هنا جداش بضل في
+
+211
+00:22:02,000 --> 00:22:08,100
+الطرف الشمالأيه كي بده يساوي اي جي اظن و هو
+
+212
+00:22:08,100 --> 00:22:12,820
+المطلوب يبقى اخذ صورتين متساويتين اثبت ان الاصل
+
+213
+00:22:12,820 --> 00:22:19,520
+متساوي يبقى فاي is one to one يبقى بداجي اثبت ان
+
+214
+00:22:19,520 --> 00:22:21,080
+فاي is onto
+
+215
+00:22:25,800 --> 00:22:33,620
+مشان هيك بيروح أخد element وين في ZN يبقى هنا let
+
+216
+00:22:33,620 --> 00:22:41,960
+K موجود في ZN then ال
+
+217
+00:22:41,960 --> 00:22:52,470
+K هذا أكبر من أو يسوى zero أقل من ال Nهذا يعني أن
+
+218
+00:22:52,470 --> 00:23:01,170
+الـ A to the power of K موجود في G؟ سكت الناس طلع
+
+219
+00:23:01,170 --> 00:23:06,410
+لتعريف الـ D هذا يعني أن A to the power of K موجود
+
+220
+00:23:06,410 --> 00:23:11,690
+في G ولا لا؟ يعني الـ Phi هتأثر عليه، صحيح ولا لا؟
+
+221
+00:23:11,690 --> 00:23:20,730
+يبقى هذا معناته أن K بدأ تساوي Phi of A Kيبقى ال
+
+222
+00:23:20,730 --> 00:23:27,190
+element K اللي أخدته في Z ان لقيتله أصل A K موجود
+
+223
+00:23:27,190 --> 00:23:34,270
+في جيه معناه هذا الكلام أن فاي is on to الآن دلت
+
+224
+00:23:34,270 --> 00:23:42,790
+خاصية الأخيرة finally بدي five of بدي أخد two
+
+225
+00:23:42,790 --> 00:23:52,780
+elements A K في A G مثلايبقى هذا element من جي و
+
+226
+00:23:52,780 --> 00:23:58,240
+هذا element ثاني من جي تمام؟ يبقى هذا الكلام بدر
+
+227
+00:23:58,240 --> 00:24:10,770
+يساوي نظرا لإنه هذا بدر يساوي في اك زائد جيصار هذا
+
+228
+00:24:10,770 --> 00:24:17,450
+كله element واحد حسب التعريف يبقى هذا الكلام تبع
+
+229
+00:24:17,450 --> 00:24:26,610
+ال fi بده يساوي k زائد j هذا الكلام بده يساوي ال k
+
+230
+00:24:26,610 --> 00:24:38,340
+هي fi of kوهذه Z Phi of AJ حسب التعريف طبعا ال
+
+231
+00:24:38,340 --> 00:24:42,880
+operation بينهم هي عملية جامعة لأن Z in ال
+
+232
+00:24:42,880 --> 00:24:48,140
+operation اللي عليها جامعة يبقى تحققت الخاصية مع
+
+233
+00:24:48,140 --> 00:24:55,440
+أن هذا الكلام Phi is an isomorphism يبقى دص وهكذا
+
+234
+00:24:55,440 --> 00:25:00,380
+Phi is an isomorphism
+
+235
+00:25:25,380 --> 00:25:37,020
+خدلي ال exercise هذا يك علك تمرن إيدك فيه if g is
+
+236
+00:25:37,020 --> 00:25:46,220
+infinite .. infinite cyclic
+
+237
+00:25:46,220 --> 00:25:56,510
+group .. cyclic group thenالـ G isomorphic
+
+238
+00:25:56,510 --> 00:26:03,010
+إلى Z سأعطيك
+
+239
+00:26:03,010 --> 00:26:06,990
+الـ function و أنت تثبت one to one و تحقق الخاصية
+
+240
+00:26:06,990 --> 00:26:17,530
+يبقى بدك تاخد لي Phi من Zالى G جلبت الوضع اني فوق
+
+241
+00:26:17,530 --> 00:26:22,750
+اخدتها من جيه لزد ان هنا بدي اخليها من Z الى G
+
+242
+00:26:22,750 --> 00:26:30,350
+define by
+
+243
+00:26:30,350 --> 00:26:38,890
+Phi of K بدي سوى A to the power K
+
+244
+00:26:41,890 --> 00:26:46,750
+اثبتلي ان هذه one to one و one to خاصية ال
+
+245
+00:26:46,750 --> 00:26:58,190
+isomorphism ناخد المثال رقم تلاتة ايش
+
+246
+00:26:58,190 --> 00:27:05,090
+رايك فيه ستة؟ مين عناصرها؟
+
+247
+00:27:05,090 --> 00:27:12,900
+واحد اتنين تلاتة اربعة خمسة في غيرهم؟السؤال هو هل
+
+248
+00:27:12,900 --> 00:27:21,780
+هذه group Cyclic؟ كيف
+
+249
+00:27:21,780 --> 00:27:27,360
+لا؟ خمسة و زير و واحد، خمسة و واحد و خمسة، خمسة
+
+250
+00:27:27,360 --> 00:27:33,420
+تربيعخمسة وعشرين شيل منهم أربعة ستات بيظل ال
+
+251
+00:27:33,420 --> 00:27:37,940
+identity يبقى الخمسة generator مظبوط يبقى هذه is
+
+252
+00:27:37,940 --> 00:27:44,380
+cyclic group شوف ليه بالله هذه isomorphic لزد ولا
+
+253
+00:27:44,380 --> 00:27:52,800
+لأ الأولى كام عنصر فيها والتانية والأولى is cyclic
+
+254
+00:27:52,800 --> 00:27:58,850
+والتانيةZn Cyclic اصلا انهم عليها عملية الجمع اذا
+
+255
+00:27:58,850 --> 00:28:01,990
+زد اتنين Cyclic زد تلاتة Cyclic زد اربعة Cyclic
+
+256
+00:28:01,990 --> 00:28:06,730
+طيب واني ال Cyclic group is Abelian يبقى هذي
+
+257
+00:28:06,730 --> 00:28:12,590
+Abelian هذي Abelian ال order للخمسة يساوي اتنين
+
+258
+00:28:12,590 --> 00:28:17,350
+وال order للواحد كذلك يساوي اتنين لأن هذا مافيش
+
+259
+00:28:17,350 --> 00:28:27,990
+فيها الا العنصر 01مظبوط هيك؟ طيب شوف ليه كمان and
+
+260
+00:28:27,990 --> 00:28:35,930
+لو أخدتيه عشرة شوف هالي اللي هي عبارة عن واحد،
+
+261
+00:28:35,930 --> 00:28:46,590
+تلاتة، سبعة، تسعة شوف هالي isomorphic لزد أربعة أم
+
+262
+00:28:46,590 --> 00:28:47,310
+لا؟
+
+263
+00:28:50,240 --> 00:28:58,120
+الـ U10 ايزو مورفك لـ Z4 ولا لأ ها هذي Cyclic ولا
+
+264
+00:28:58,120 --> 00:29:02,620
+لأ طيب تعالى نشوف هذي Cyclic ولا لأ نشوف فيها
+
+265
+00:29:02,620 --> 00:29:07,970
+Generator ولا لأتلاتة وزيرة بواحد تلاتة و أس واحد
+
+266
+00:29:07,970 --> 00:29:13,910
+بتلاتة تلاتة ربيع تسعة تلاتة تكيب بسبعة و عشرين
+
+267
+00:29:13,910 --> 00:29:18,950
+بشيل عشرتين بظال سبعة تلاتة و أس اربعة بواحد واحد
+
+268
+00:29:18,950 --> 00:29:23,250
+و تمانين تمان عشرات بواحد يبقى الـcyclic والتلاتة
+
+269
+00:29:23,250 --> 00:29:28,550
+generatorأحدكم يقدر يجيب الجنريتر التاني هو السبعة
+
+270
+00:29:28,550 --> 00:29:32,730
+لكن تسعة ما هوش generator لأن تسعة فتسعة بواحد و
+
+271
+00:29:32,730 --> 00:29:37,230
+تمانين تسعة تربيع بال identity لكن تلاتة و أربعة
+
+272
+00:29:37,230 --> 00:29:40,970
+هو اللي بال identity يبقى هذي ال cycle يبقى هذي
+
+273
+00:29:40,970 --> 00:29:49,370
+isomorphic كمان لزد أربعة طيب السؤال هو but هل
+
+274
+00:29:49,370 --> 00:29:57,440
+اليوم ماشي اللي هو ماميم واحدو خمسة و سبعة و
+
+275
+00:29:57,440 --> 00:30:08,200
+أحداشر هل هذه isomorphic ل Z أربعة؟
+
+276
+00:30:08,200 --> 00:30:15,780
+هل هذه Cyclic ولا لا؟ هل هذه Cyclic؟
+
+277
+00:30:17,220 --> 00:30:22,900
+خمسة وعشرين كده؟ خمسة في خمسة في خمسة وعشرين شيلهم
+
+278
+00:30:22,900 --> 00:30:25,780
+اتناش يصير ال identity يبقى خمسة تربيع بال
+
+279
+00:30:25,780 --> 00:30:30,400
+identity سبعة تربيع بال identity تسعة واربعين
+
+280
+00:30:30,400 --> 00:30:33,980
+تمانية واربعين ومضال واحد احداشر في احداشر مية
+
+281
+00:30:33,980 --> 00:30:37,060
+واحد وعشرين ع اتناش مضال واحد يبقى مش فيها ولا
+
+282
+00:30:37,060 --> 00:30:44,770
+generatorيبقى هذه is not isomorphic because السبب
+
+283
+00:30:44,770 --> 00:30:59,850
+ان Z4 is cyclic but و لكن U12 is not cyclic
+
+284
+00:30:59,850 --> 00:31:04,850
+طيب U18
+
+285
+00:31:07,130 --> 00:31:12,030
+Isomorphic لـ Z6 نقول
+
+286
+00:31:12,030 --> 00:31:18,800
+لك مين اليو 18يكون تمنتاش اللي هي تساوي العناصر
+
+287
+00:31:18,800 --> 00:31:26,300
+واحد، اتنين، تلاتة، اربعة، خمسة، ستة، سبعة،
+
+288
+00:31:26,300 --> 00:31:32,420
+تمانية، تسعة، عشرة، احداشر، اتناشر، تلاتاشر،
+
+289
+00:31:32,420 --> 00:31:39,200
+اربعتاشر، خمستاشر، ستاشر، سبعتاشركم منصر هذول؟ ستة
+
+290
+00:31:39,200 --> 00:31:48,900
+هل هذه isomorphic لزد ستة ولا لا؟
+
+291
+00:31:48,900 --> 00:31:53,960
+طيب
+
+292
+00:31:53,960 --> 00:31:59,960
+يالا افحص براحتك في الدار isomorphic لزد ستة ليش؟
+
+293
+00:31:59,960 --> 00:32:05,230
+ان هذه Cyclic وهذه كمان Cyclicيبقى قدلي بدناش
+
+294
+00:32:05,230 --> 00:32:08,810
+اتنين generator بيكفي واحد جيبلي واحد منهم
+
+295
+00:32:08,810 --> 00:32:17,570
+generator بتجيب يولد كل العناصر أيه؟ مثال
+
+296
+00:32:17,570 --> 00:32:23,850
+اتنين هذا؟ any operation قلت cyclic ايش ما كانت
+
+297
+00:32:23,850 --> 00:32:29,530
+تكون لم أحدد قلت تجرب وcyclic تمام؟ وبالتالي اي
+
+298
+00:32:29,530 --> 00:32:30,570
+عملية؟
+
+299
+00:32:33,770 --> 00:32:39,290
+علي صوتك شوية لا
+
+300
+00:32:39,290 --> 00:32:45,850
+انت انت لما زد خمسة فيها كام عنصر؟ خمس عناصر زد
+
+301
+00:32:45,850 --> 00:32:51,110
+ستة فيها ست عناصر و هكذا كيف واحدة فيها ست عناصر و
+
+302
+00:32:51,110 --> 00:32:55,730
+واحدة خمس عناصر فيها ايزو مورف فيهم؟أبسط الأشياء
+
+303
+00:32:55,730 --> 00:32:59,470
+قلتلك أول ما بديت عدد العناصر في الجروب الأولى جد
+
+304
+00:32:59,470 --> 00:33:02,890
+عدد العناصر في الجروب التانى اختلفوا العناصر مافيش
+
+305
+00:33:02,890 --> 00:33:07,790
+isomorphism وانت مغمق بدون نقاش تمام؟ إذا عدد
+
+306
+00:33:07,790 --> 00:33:10,730
+العناصر في الجروب الأولى يختلف عن عدد العناصر في
+
+307
+00:33:10,730 --> 00:33:13,950
+الجروب التانى there is no isomorphism between two
+
+308
+00:33:13,950 --> 00:33:20,030
+groups مافيش بالمرة حد بدي أسأل تاني طيب نجيبلك
+
+309
+00:33:20,030 --> 00:33:27,770
+مثال من نوعين جديدمثال أربعة مثال
+
+310
+00:33:27,770 --> 00:33:33,670
+أربعة بيقول let ال G هي ال special linear group of
+
+311
+00:33:33,670 --> 00:33:39,490
+two by two matrices over R وهي كل المصوات اللي على
+
+312
+00:33:39,490 --> 00:33:49,710
+الشكل A,B,C,D بحيث ان ال A,D ناقص ال B,C بدوا ساوي
+
+313
+00:33:49,710 --> 00:34:02,810
+الواحد الصحيحlet الـ M be any two by two matrix
+
+314
+00:34:02,810 --> 00:34:06,050
+matrix
+
+315
+00:34:06,050 --> 00:34:17,030
+with a determinant لـ M لا يساوي Zero define
+
+316
+00:34:20,640 --> 00:34:31,460
+A mapping Define A mapping Phi M
+
+317
+00:34:31,460 --> 00:34:49,180
+من G إلى G by Phi M of A يساوي M A M inverse لكل
+
+318
+00:34:49,970 --> 00:35:00,990
+الـ A اللي موجودة في G show that الـ
+
+319
+00:35:00,990 --> 00:35:05,890
+Phi M is an isomorphism
+
+320
+00:35:43,290 --> 00:35:48,490
+نرجع مرة تانية أخد لجروب جيله ال special linear
+
+321
+00:35:48,490 --> 00:35:52,890
+group of two by two matrices over R و هي كل
+
+322
+00:35:52,890 --> 00:35:56,670
+المصفوفات لنظامها اتنين في اتنين بعيادة المحدد
+
+323
+00:35:56,670 --> 00:36:01,590
+تبعها بده يساوي واحد صحيح قال افترض انه عندي
+
+324
+00:36:01,590 --> 00:36:05,490
+مصفوفة من نظامها اتنين في اتنين ومحددها لا يساوي
+
+325
+00:36:05,490 --> 00:36:10,520
+zero لم أقل واحد صحيحالـ M ليس بالضرورة محددها
+
+326
+00:36:10,520 --> 00:36:15,880
+يسوى واحد صحيح قلت M محدد تبعي ليه يسوى Zero عرفت
+
+327
+00:36:15,880 --> 00:36:21,620
+Function Phi M من G إلى G by Phi M of A يسوى M A M
+
+328
+00:36:21,620 --> 00:36:26,180
+inverse لكل الـ A اللي موجودة في G بيقول أن Phi M
+
+329
+00:36:26,180 --> 00:36:31,220
+is an isomorphism النقطة الأولى بتتأكد هل ال
+
+330
+00:36:31,220 --> 00:36:36,220
+function اللي عرفتها تعريفي صحيح ولا لأ بمعنى آخر
+
+331
+00:36:36,220 --> 00:36:44,240
+واللهإذا طلع محدد المصوفة هذه بواحد صحيح معناته
+
+332
+00:36:44,240 --> 00:36:49,580
+المصوفة هذه موجودة في G فعلا يبقى تعريفي هذا من G
+
+333
+00:36:49,580 --> 00:36:55,120
+ل G بصير كلام سليم ليش؟ لإن ايه اللي عندي هذه أنا
+
+334
+00:36:55,120 --> 00:36:59,960
+ماخدها من G يعني المحدد تبعها بجداش بواحد صحيح نحن
+
+335
+00:36:59,960 --> 00:37:05,150
+متأكدين منه لكن ال M بعرفش أنا تمام؟إذا بدي أثبت
+
+336
+00:37:05,150 --> 00:37:09,510
+أول شيء أن الـ Phi is well defined يعني معرفة
+
+337
+00:37:09,510 --> 00:37:16,530
+تعريفا صحيحا فبناجي بقوله هنا ال Phi is well
+
+338
+00:37:16,530 --> 00:37:23,130
+defined well defined يعني معرفة تعريفا صحيحا
+
+339
+00:37:25,810 --> 00:37:30,210
+بمعنى آخر بدي أثبت أن هذا element موجود في الـ G
+
+340
+00:37:30,210 --> 00:37:39,290
+لذلك بدي أخد ال determinant للـ M A M inverse بدي
+
+341
+00:37:39,290 --> 00:37:44,450
+أرجع لمين؟ لل linear algebra يبقى هذا معناته ال
+
+342
+00:37:44,450 --> 00:37:50,810
+determinant لل M في ال determinant لل A في ال
+
+343
+00:37:50,810 --> 00:37:57,450
+determinant لل M inverseالأن الـ determinant يعني
+
+344
+00:37:57,450 --> 00:38:02,010
+قيمة حقيقية يعني التلث قيم حقيقية مضروبة في بعضها
+
+345
+00:38:02,010 --> 00:38:07,250
+والقيم الحقيقية commutative يبقى هذا الكلام بده
+
+346
+00:38:07,250 --> 00:38:14,820
+يساوي ال determinant لل Mفي ال determinant لل M
+
+347
+00:38:14,820 --> 00:38:20,660
+inverse في ال determinant لل A او بقدر اقول ال
+
+348
+00:38:20,660 --> 00:38:25,720
+determinant لل M في ال M inverse في ال determinant
+
+349
+00:38:25,720 --> 00:38:33,080
+لل A هذا الكلام يساويالمصوفة في معكوسة المعكوسة
+
+350
+00:38:33,080 --> 00:38:39,400
+موجودة هنا ولا لا؟ موجودة لأن أنا جايل أن المحدد
+
+351
+00:38:39,400 --> 00:38:45,160
+لا يساوي zero إذا المصوفة في معكوسة بتعطيني مصوفة
+
+352
+00:38:45,660 --> 00:38:52,240
+الوحدة يبقى هذا ال determinant لمصوفة الوحدة في ال
+
+353
+00:38:52,240 --> 00:38:57,500
+determinant لل a الآن ال determinant لمصوفة الوحدة
+
+354
+00:38:57,500 --> 00:39:04,780
+بقداش بواحد ال determinant ل a, a موجودة في g, g
+
+355
+00:39:04,780 --> 00:39:10,430
+هي المحدد تبعها بقداش بواحديبقى في واحد الجواب
+
+356
+00:39:10,430 --> 00:39:20,150
+يساوي قداش واحد يبقى هنا الساعة ال m a m inverse
+
+357
+00:39:20,150 --> 00:39:25,190
+belongs to g يبقى تعريفي هذا معله تعريفا صحيحا
+
+358
+00:39:25,190 --> 00:39:32,190
+الان بدى اثبت ان فاي is one to one حاجة اقوله as
+
+359
+00:39:32,190 --> 00:39:42,600
+you فايم طبعاهنا ا assume ان فايم of a فايم of a
+
+360
+00:39:42,600 --> 00:39:50,900
+بدر سوى فايم of b طبعا
+
+361
+00:39:50,900 --> 00:39:57,100
+a و b مصهوفات في gيبقى هدول بيبقى يسووا بعض ثم
+
+362
+00:39:57,100 --> 00:40:08,960
+فايم اف ايه م ا م انفرست مبم انفرست طيب بال right
+
+363
+00:40:08,960 --> 00:40:13,200
+cancellation لو وال left cancellation لو هذا
+
+364
+00:40:13,200 --> 00:40:20,490
+بيعطينا ان ا تسوى بيه لذلك فايم is one to oneيبقى
+
+365
+00:40:20,490 --> 00:40:28,550
+بداجي اخد الان يبقى
+
+366
+00:40:28,550 --> 00:40:35,670
+بداجي اخد الان يبقى بداجي
+
+367
+00:40:35,670 --> 00:40:38,630
+اخد الان يبقى بداجي اخد الان يبقى بداجي اخد الان
+
+368
+00:40:38,630 --> 00:40:38,690
+يبقى بداجي اخد الان يبقى بداجي اخد الان يبقى بداجي
+
+369
+00:40:38,690 --> 00:40:38,870
+اخد الان يبقى بداجي اخد الان يبقى بداجي اخد الان
+
+370
+00:40:38,870 --> 00:40:38,870
+يبقى بداجي اخد الان يبقى بداجي اخد الان يبقى بداجي
+
+371
+00:40:38,870 --> 00:40:38,870
+اخد الان يبقى بداجي اخد الان يبقى بداجي اخد الان
+
+372
+00:40:38,870 --> 00:40:42,130
+يبقى بداجي اخد الان يبقى بداجي اخد الان يبقى بداجي
+
+373
+00:40:42,130 --> 00:40:49,210
+اخد الان يبقى
+
+374
+00:40:49,210 --> 00:40:49,810
+بداجي ا
+
+375
+00:40:54,890 --> 00:41:02,870
+الـ B هذه بقدر اكتبها على الشكل التالي M M Inverse
+
+376
+00:41:02,870 --> 00:41:14,550
+B M M Inverse بنفع ولا مانفعش هذه مين ال identity
+
+377
+00:41:14,550 --> 00:41:20,680
+وهذه مينخلص يبقى بالضالة المصوفة هذه بيه كما هي
+
+378
+00:41:20,680 --> 00:41:27,760
+هذه بقدر اكتبها على الشكل التالي M في M inverse
+
+379
+00:41:27,760 --> 00:41:35,620
+بيه M و هنا M inverse من خاصية ال associativity
+
+380
+00:41:35,620 --> 00:41:41,480
+يبقى فاصلتي التلاتة هدول لحالي ايش رأيك هدول بدي
+
+381
+00:41:41,480 --> 00:41:51,860
+اسمهم تسمية جديدة Mام انفرس هذه كل التلاتة حصل ضرب
+
+382
+00:41:51,860 --> 00:41:58,320
+سميته ايه يبقى بناء عليه هذا الكلام بدر ساوي من
+
+383
+00:41:58,320 --> 00:42:06,700
+بدر ساوي في ام او ايه يبقى المصوفة بيه اللي خدتها
+
+384
+00:42:06,700 --> 00:42:12,780
+لاجيتلها اصل ايه يبقى بناء عليه الـfi m is onto
+
+385
+00:42:13,410 --> 00:42:17,490
+يبقى المصحوفة B اللي أخدتها عشوائيا في ال special
+
+386
+00:42:17,490 --> 00:42:22,130
+linear group of two by two matrices over R لجت لها
+
+387
+00:42:22,130 --> 00:42:29,570
+أصل اللي هو A موجودة من مين هي A والـ A اللي هي M
+
+388
+00:42:29,570 --> 00:42:38,050
+inverse ب M طب خليني أسأل السؤال التالي هل عملية
+
+389
+00:42:38,050 --> 00:42:40,430
+الضرب هذه ممكن اتم
+
+390
+00:42:44,800 --> 00:42:49,700
+بالتم ولا بالتم مش؟ بالتم لأن كله نظام اتنين في
+
+391
+00:42:49,700 --> 00:42:56,080
+اتنين انا فرض ان من البداية ال M اتنين باتنين
+
+392
+00:42:56,080 --> 00:43:00,380
+matrix و determinant لا يساوي ديري اذا كل واحدة
+
+393
+00:43:00,380 --> 00:43:04,370
+فيهم نظام اتنين في اتنينولو اختلف النظام يمكن ما
+
+394
+00:43:04,370 --> 00:43:07,870
+نقدرش نضرب يمكن نقدر ويمكن ما نقدرش لكن هاد
+
+395
+00:43:07,870 --> 00:43:12,970
+اتنينات كله اذا عملية الضرب possible وبالتالي no
+
+396
+00:43:12,970 --> 00:43:17,110
+problem يمكن بكلامنا وشغلنا مية مية بقيت عندنا
+
+397
+00:43:17,110 --> 00:43:23,850
+النقطة الأخيرة finally النقطة الأخيرة بدي اخد five
+
+398
+00:43:23,850 --> 00:43:26,970
+m of a b
+
+399
+00:43:29,580 --> 00:43:35,740
+عاملية ضرب المصفقة يبقى هذا يا شباب بدأ تساوي M A
+
+400
+00:43:35,740 --> 00:43:42,780
+B M inverse هذه
+
+401
+00:43:42,780 --> 00:43:50,080
+K بدأ تيجي في of A في في of Vمش جاية هذه ولا لا
+
+402
+00:43:50,080 --> 00:43:57,460
+لكن لو دخلت مصوفة الوحدة في الموضوع مافيش مشكلة ان
+
+403
+00:43:57,460 --> 00:44:00,860
+مصوفة الوحدة ضربها في المصوفة بتعطينا نفس المصوفة
+
+404
+00:44:00,860 --> 00:44:11,180
+لكن هذا بقدر اكتبه M A و بدي ادخل M inverse M وهذه
+
+405
+00:44:11,180 --> 00:44:18,290
+ال B وهذه ال B اللي عندنا وهذه ال M inverseهذه
+
+406
+00:44:18,290 --> 00:44:29,890
+عبارة عن مصوف الواحدة يبقى مصففتين مصففين
+
+407
+00:44:29,890 --> 00:44:30,810
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+408
+00:44:30,810 --> 00:44:31,390
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+409
+00:44:31,390 --> 00:44:32,510
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+410
+00:44:32,510 --> 00:44:36,350
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+411
+00:44:36,350 --> 00:44:36,470
+مصففين مصففين مصففين مصففين مصففين مصففين مصففين
+
+412
+00:44:36,470 --> 00:44:43,510
+مصففين مصففين مصففين مصففينيبقى تحققت الخاصية يبقى
+
+413
+00:44:43,510 --> 00:44:57,970
+بقدر أقوله thus و هكذا فاي ام is an isomorphism طب
+
+414
+00:44:57,970 --> 00:45:09,130
+example خمسة في شيء؟ لأ بس مش هنشتغل سؤال هل ال S
+
+415
+00:45:10,480 --> 00:45:18,680
+تلاتة هكم عنصر فيها؟ ستة، مظبوط؟ three factorial
+
+416
+00:45:18,680 --> 00:45:23,440
+تلاتة في اتنين في واحد يبقى ست عناصر هل هذه
+
+417
+00:45:23,440 --> 00:45:30,120
+isomorphic ل Z6؟
+
+418
+00:45:31,610 --> 00:45:38,490
+أيوة ممتازة زد ستة كوميوتاتيف ابدأ ليه لك ال S3 is
+
+419
+00:45:38,490 --> 00:45:44,830
+not هادي cyclic هادي not cyclic وهكذا يبقى هادي is
+
+420
+00:45:44,830 --> 00:45:52,020
+not isomorphic to z6 becauseجيب ليه ولو سبب واحد
+
+421
+00:45:52,020 --> 00:45:56,100
+بديش اسباب كتيرة رغم ان هذه فيها ست عناصر وهذه
+
+422
+00:45:56,100 --> 00:46:06,480
+فيها ست عناصر يبقى because ال S3 is not cyclic but
+
+423
+00:46:06,480 --> 00:46:15,340
+ولكن Z6 اللي هو subgroup of Y1 is cyclic
+
+424
+00:46:19,060 --> 00:46:21,000
+بنكمل ان شاء الله بعد الظهر
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f79016766d7eb115f92f454f79b777e930aa61f7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_postprocess.srt
@@ -0,0 +1,1544 @@
+1
+00:00:22,140 --> 00:00:26,780
+بسم الله الرحمن الرحيم المرة اللي فاتت أعطينا
+
+2
+00:00:26,780 --> 00:00:31,760
+ساعتين فيه اللي هو ال chapter 7 اللي بتحدث عن
+
+3
+00:00:31,760 --> 00:00:38,300
+Cossets and Lagrange theoremو أعرفنا ال coset و
+
+4
+00:00:38,300 --> 00:00:42,520
+حسبنا ال cosets لمجموعة من ال subgroups يعني
+
+5
+00:00:42,520 --> 00:00:47,080
+أعطينا بدل المثال ثلاثة ثم انتقلنا بعد ذلك إلى
+
+6
+00:00:47,080 --> 00:00:51,500
+Lagrange theorem وهذه النظرية في الجبر مشهورة في
+
+7
+00:00:51,500 --> 00:00:56,980
+كل كتب الجبر نظرية
+
+8
+00:00:56,980 --> 00:01:00,320
+Lagrange ما بعرف إيش كان نص اللي قاعد بيقرا هذا
+
+9
+00:01:00,320 --> 00:01:04,450
+إيش كان نص Lagrange theorem يعنيطبعا جى finite
+
+10
+00:01:04,450 --> 00:01:10,310
+group هذه البداية وبعدها بصرشو اه
+
+11
+00:01:10,310 --> 00:01:13,570
+اشتر
+
+12
+00:01:13,570 --> 00:01:23,130
+نصرية لجراجأيش كان نصنا طريقة Lagrange؟ هاي
+
+13
+00:01:23,130 --> 00:01:27,570
+بدر أضائلكوا يعني الطريقة Lagrange theorem بيقول
+
+14
+00:01:27,570 --> 00:01:31,870
+لو أخدت أي subgroup من ال group اللي عندك فإن ال
+
+15
+00:01:31,870 --> 00:01:36,170
+order لل subgroup يقسم ال order لل group وهذا ما
+
+16
+00:01:36,170 --> 00:01:40,560
+برناه في المرة الماضيةيعني لو أنا عندي group G
+
+17
+00:01:40,560 --> 00:01:45,360
+واخدت any subgroup ان شاء الله ل trivial subgroup
+
+18
+00:01:45,360 --> 00:01:50,060
+كويس؟ يبقى ال order لهذه ال subgroup بيقسم ال
+
+19
+00:01:50,060 --> 00:01:54,760
+order للي group تمام؟ هذا كان نص نظرية Lagrange
+
+20
+00:01:54,760 --> 00:02:00,360
+أعطينا عليها بدل المثال اتنين الآن بدنا نيجي لأول
+
+21
+00:02:00,360 --> 00:02:04,380
+crawlerي عندنا مجموعة من ال crawlers على نظرية
+
+22
+00:02:04,380 --> 00:02:08,890
+Lagrange يعني مجموعة من النتائج النتيجة الأولىبقول
+
+23
+00:02:08,890 --> 00:02:12,950
+في الـ finite group the order of each element of
+
+24
+00:02:12,950 --> 00:02:16,170
+the group divides the order of the group that is
+
+25
+00:02:16,170 --> 00:02:21,030
+لو كان عندي element x موجود في ال group g يبقى ال
+
+26
+00:02:21,030 --> 00:02:26,050
+order ل x بدي يقسمين بدي يقسم ال order ل g يعني
+
+27
+00:02:26,050 --> 00:02:30,270
+الأجران قال لي ال order تبع ال sub group بيقسمين
+
+28
+00:02:30,270 --> 00:02:34,370
+ال order لل group النتيجة هذه تقول لي لأالـ order
+
+29
+00:02:34,370 --> 00:02:37,790
+للـ element كذلك لأي element في ال group بدي أقسم
+
+30
+00:02:37,790 --> 00:02:43,070
+إياه بدي أقسم ال order لل group بدنا نبره صحة هذا
+
+31
+00:02:43,070 --> 00:02:48,130
+الكلام مشان نبره صحة هذا الكلام بدي أقول له افترض
+
+32
+00:02:48,130 --> 00:02:54,530
+ان X هذا موجود في ال group بدي أثبت أن ال order
+
+33
+00:02:54,530 --> 00:02:58,710
+لهذا ال element بدي أقسم إياه ال order لل group
+
+34
+00:02:58,710 --> 00:03:06,550
+بقول له ماشي thenالـ H هذه اللي بدي أخدها subgroup
+
+35
+00:03:06,550 --> 00:03:14,810
+اللي عبارة عن ال subgroup generated by X تمام هذه
+
+36
+00:03:14,810 --> 00:03:24,610
+الآن subgroup الـ H هذه is a subgroup of G طيب
+
+37
+00:03:24,610 --> 00:03:29,290
+تمام بال Lagrange theorem ال order لـ H بدي يقسم
+
+38
+00:03:29,290 --> 00:03:36,020
+من ال order ل Gيبقى بروح بقوله هنا by Lagrange
+
+39
+00:03:36,020 --> 00:03:39,400
+theorem
+
+40
+00:03:39,400 --> 00:03:51,300
+ال order لل H divides ال order ل G طيب لما تبقى
+
+41
+00:03:51,300 --> 00:03:55,160
+هذه ال cyclic شو علاقة ما بين ال order ل H و ال
+
+42
+00:03:55,160 --> 00:04:03,270
+order ل X متساوية بقوله هنا بطء ولكنالأردر لل H
+
+43
+00:04:03,270 --> 00:04:10,070
+بده يساوي الأردر لل X يبقى هذا بده يعطيني بدل ما
+
+44
+00:04:10,070 --> 00:04:13,810
+يقول ال order تبع ال H بده يقسم ال G بده يشيل ال
+
+45
+00:04:13,810 --> 00:04:17,970
+order تبع ال H و يكتب بداله man ال order ل X
+
+46
+00:04:17,970 --> 00:04:24,500
+dividesالأردر لجي وكان الله بالسر علينا إذا من
+
+47
+00:04:24,500 --> 00:04:28,980
+الآن أساعد ان بديك تعرف ان لو عندي group خدت منها
+
+48
+00:04:28,980 --> 00:04:32,540
+subgroup يبقى ال order لهذا ال subgroup يقسم ل
+
+49
+00:04:32,540 --> 00:04:37,180
+group وفي المقابل لو كان عندي أي element x موجود
+
+50
+00:04:37,180 --> 00:04:41,920
+في ال group جي يبقى ال order ل x كمان يقسم ال
+
+51
+00:04:41,920 --> 00:04:46,200
+order ل جي نجي ل ال crawler التانية
+
+52
+00:04:50,810 --> 00:04:57,570
+corollar اتنين بتقول a group of a prime order a
+
+53
+00:04:57,570 --> 00:05:08,570
+group of a prime order is
+
+54
+00:05:08,570 --> 00:05:10,230
+cyclic
+
+55
+00:05:13,050 --> 00:05:19,910
+يعني اي group ال order لها بتكون ال prime اتنين،
+
+56
+00:05:19,910 --> 00:05:24,450
+تلاتة، خمسة، سبعة، احداشر، تلتاشر دائما تبقى
+
+57
+00:05:24,450 --> 00:05:29,710
+Cyclic وإذا Cyclic يبقى abelian لأنه أخدته قبل ذلك
+
+58
+00:05:29,710 --> 00:05:35,950
+في chapter 4 ان any cyclic group isأبيلن لكن العكس
+
+59
+00:05:35,950 --> 00:05:40,310
+ما هواش صحيح طيب a group of a prime order is
+
+60
+00:05:40,310 --> 00:05:44,850
+cyclic بدنا نروح نثبت هذا الكلام بدي أجي أقوله
+
+61
+00:05:44,850 --> 00:06:02,150
+assume that افترض ان ال g is a group with order P
+
+62
+00:06:02,150 --> 00:06:10,640
+that isthat is ال
+
+63
+00:06:10,640 --> 00:06:19,540
+order اللى جى بدى يساوي ال P and ال P is prime
+
+64
+00:06:19,540 --> 00:06:25,600
+يبقى ال order اللى جى هو عبارة عن عدد اول اتنين
+
+65
+00:06:25,600 --> 00:06:30,520
+تلاتة خمسة سبعة احداشر تلاتاشر سبعتاشر تسعتاشر زى
+
+66
+00:06:30,520 --> 00:06:37,650
+ما بدكيبقى جي جروب with order P و ال P هذا عبارة
+
+67
+00:06:37,650 --> 00:06:42,990
+عن a prime number كويس؟ بدي أثبت أن هذا ال group
+
+68
+00:06:42,990 --> 00:06:48,470
+دائما و أبدا تبقى Cycling، كويس؟ يبقى بدأجي أقوله
+
+69
+00:06:48,470 --> 00:06:56,210
+خدلي عنصر A موجود في G طب العنصر A هذا بولدلي ال
+
+70
+00:06:56,210 --> 00:06:57,650
+sub group ولا لأ؟
+
+71
+00:07:00,140 --> 00:07:03,500
+أى element في الجروب بيولد ليه subgroup صحيح ولا
+
+72
+00:07:03,500 --> 00:07:07,240
+لأ يمكن يكون فيش فيها إلا ال identity يمكن عنصرين
+
+73
+00:07:07,240 --> 00:07:12,260
+يمكن تلاتة يمكن أربعة إلى آخرين تمام يبقى little a
+
+74
+00:07:12,260 --> 00:07:23,880
+belongs to g then هذه هي is a is a cyclic subgroup
+
+75
+00:07:26,920 --> 00:07:35,500
+cyclic subgroup of G يبقى
+
+76
+00:07:35,500 --> 00:07:43,660
+ال order لها يقسم من ال order ل G يبقى then ال
+
+77
+00:07:43,660 --> 00:07:48,520
+order لل subgroup generated by A divides
+
+78
+00:07:51,870 --> 00:07:59,770
+divide ال order لجى اللى بده يساوي ال P إيش قواسم
+
+79
+00:07:59,770 --> 00:08:08,310
+ال P واحد و ال P itself يبقى هنالو قلنا little a
+
+80
+00:08:08,310 --> 00:08:14,750
+belongs to g و قللي ال a لا يسوى ال identity كمان
+
+81
+00:08:14,750 --> 00:08:20,410
+اضيف عليها ان ال a لا يسوى ال identity حتى لا نقع
+
+82
+00:08:20,410 --> 00:08:26,920
+في اي مشكلة بعد ذلك تمامطيب يبقى ال order اللى جيه
+
+83
+00:08:26,920 --> 00:08:33,460
+بده يساوي ال P معناه هذا الكلام ان ال order ل ال
+
+84
+00:08:33,460 --> 00:08:39,920
+sub group generated by A بده يساوي واحد or P يبقى
+
+85
+00:08:39,920 --> 00:08:46,060
+هاي القواسم اللى بتقسم ال P الآن هل يمكن لهذا ال
+
+86
+00:08:46,060 --> 00:08:51,020
+order انه يساوي واحد لأ لأنه اشتراط مع ان ال E لا
+
+87
+00:08:51,020 --> 00:08:58,970
+يساوي ال identityبقول له ولكن ال order لل subgroup
+
+88
+00:08:58,970 --> 00:09:05,210
+generated by a لا يمكن أن يساوي الواحد السبب لإن
+
+89
+00:09:05,210 --> 00:09:11,470
+ال a does not equal to a يبقى هذا شو بدي يعطينا
+
+90
+00:09:11,470 --> 00:09:15,530
+هذا بدي يعطينا ان ال order لل subgroup generated
+
+91
+00:09:15,530 --> 00:09:21,050
+by a بدي ساوي 100بدي يساوي ال P طب هذا ايش بدي
+
+92
+00:09:21,050 --> 00:09:25,750
+يعطينا صار ال order لهذه ال sub group بدي يساوي ال
+
+93
+00:09:25,750 --> 00:09:29,850
+P يبقى ال sub group هذه عبارة عن مين عبارة عن G
+
+94
+00:09:29,850 --> 00:09:36,510
+itself تمام يبقى هذا بدي يعطينا ان ال sub group
+
+95
+00:09:36,510 --> 00:09:41,610
+generated by A هي عبارة عن مين ال G itself لإن ال
+
+96
+00:09:41,610 --> 00:09:45,550
+order ل G بدي يساوي ال P و ال order لل sub group
+
+97
+00:09:45,550 --> 00:09:50,080
+هذا بدي يساوي ال Pيبقى الاتنين are equal يبقى هذا
+
+98
+00:09:50,080 --> 00:09:59,080
+معناه إيش؟ معناه إن الـG لجروب الـG is cyclic لو
+
+99
+00:09:59,080 --> 00:10:02,780
+كان السؤال اثبتها إنها abelian، بدي أثبتها إنها
+
+100
+00:10:02,780 --> 00:10:08,180
+الـcyclic ومن ثم بقول لما دام cyclic، يبقى abelian
+
+101
+00:10:08,180 --> 00:10:12,780
+هذه الكرولري رقم اتنين، بدنا نروح للكرولري رقم
+
+102
+00:10:12,780 --> 00:10:16,420
+تلاتة يبقى الكرولري
+
+103
+00:10:18,200 --> 00:10:24,040
+رقم تلاتة او النتيجة رقم تلاتة بتقول little g be a
+
+104
+00:10:24,040 --> 00:10:34,440
+finite group little g be a finite group يبقى
+
+105
+00:10:34,440 --> 00:10:42,020
+group محدودة العدد من العناصر little g be a finite
+
+106
+00:10:42,020 --> 00:10:45,220
+group and let and
+
+107
+00:10:51,350 --> 00:10:57,830
+يبقى الـ A أُصل order للـ G يبقى الـ A أُصل order
+
+108
+00:10:57,830 --> 00:11:01,430
+للـ G يبقى الـ A أُصل order للـ G
+
+109
+00:11:09,240 --> 00:11:13,740
+يعني لو أخدت أي element من ال group و حطيت له أس
+
+110
+00:11:13,740 --> 00:11:18,920
+ال order تبع ال group دائما و أبدا بده يسوى ال
+
+111
+00:11:18,920 --> 00:11:28,960
+identity طيب
+
+112
+00:11:28,960 --> 00:11:34,990
+كويس نشوف نؤكد على صحة ما تكونبنقول ايش احنا عندنا
+
+113
+00:11:34,990 --> 00:11:39,410
+g finite group و ال a belongs to g قال لي اثبت ان
+
+114
+00:11:39,410 --> 00:11:43,890
+ال a مرفوعة للأردر السابع ال g بتساومين ال
+
+115
+00:11:43,890 --> 00:11:47,430
+identity element ال ا لو جيت على ال a corollary
+
+116
+00:11:47,430 --> 00:11:53,770
+one يبقى ال order لل a بتقسمين ال order ل g يبقى
+
+117
+00:11:53,770 --> 00:11:59,970
+by a corollary one
+
+118
+00:12:01,250 --> 00:12:10,590
+الـ order للـ A divides ال order لل G هذا معناته
+
+119
+00:12:10,590 --> 00:12:16,390
+ان ال order لل G بده ساوي ال order لل A في رقم و
+
+120
+00:12:16,390 --> 00:12:25,970
+ليكن K for some positive integer
+
+121
+00:12:25,970 --> 00:12:27,990
+K
+
+122
+00:12:29,620 --> 00:12:35,640
+for some positive integer لكيه الان انا بدى اثبت
+
+123
+00:12:35,640 --> 00:12:43,060
+ان ال a مرفوعة لل أس اللى هو ال order لل g بدى
+
+124
+00:12:43,060 --> 00:12:48,220
+يساوي ال identity بناء عليها بقدر اقول هذا ايه ال
+
+125
+00:12:48,220 --> 00:12:54,260
+order لل g اللى هو عبارة عن ال order لل a مضروب في
+
+126
+00:12:54,260 --> 00:13:01,570
+مينمضروب في K هذا معناه ان ال A مرفوعة لل order
+
+127
+00:13:01,570 --> 00:13:08,350
+تبع ال A كل هذا أس K طب ال A لما يكون مرفوع لل
+
+128
+00:13:08,350 --> 00:13:13,070
+order تبعه كده بيعطينا ال identity يبقى هذا
+
+129
+00:13:13,070 --> 00:13:17,310
+بيعطينا ال identity أس K ال identity أس K بيعطينا
+
+130
+00:13:17,310 --> 00:13:23,230
+من ال identity يبقى بناء علي أسار ال A أس ال order
+
+131
+00:13:23,230 --> 00:13:27,970
+لل Gدائما و أبدا بدي أعطينا ماذا؟ بدي أعطينا ال
+
+132
+00:13:27,970 --> 00:13:33,850
+identity element تمام بدي أخاطر قبل مفروض نعطي بعض
+
+133
+00:13:33,850 --> 00:13:39,310
+الأمثلة على هذه ال crawlers بدنا نيجي لأول مثال
+
+134
+00:13:39,310 --> 00:13:42,090
+examples او example one
+
+135
+00:13:45,840 --> 00:13:52,120
+example one بيقول show that
+
+136
+00:13:52,120 --> 00:14:00,260
+بيّلي ان every group
+
+137
+00:14:00,260 --> 00:14:09,300
+of order less than or equal to 5
+
+138
+00:14:16,890 --> 00:14:32,590
+less than or equal to five is abelian يعني
+
+139
+00:14:32,590 --> 00:14:35,550
+بنثبت أن أي group
+
+140
+00:14:38,460 --> 00:14:43,920
+الـ order تبعها بده يساوي خمسة دائما و أبدا أو أقل
+
+141
+00:14:43,920 --> 00:14:47,440
+من خمسة is abelian يعني لو عندي group فيها عنصر
+
+142
+00:14:47,440 --> 00:14:51,540
+واحد أو group فيها عنصرين أو group فيها تلتة عناصر
+
+143
+00:14:51,540 --> 00:14:55,880
+أو أربعة عناصر أو خمسة عناصر كل هذه الأنموعة من ال
+
+144
+00:14:55,880 --> 00:15:01,600
+group تبقى دائما و أبدا abelian طيب الآن solution
+
+145
+00:15:06,050 --> 00:15:11,890
+أخذ الان لو ال order اللى جى هو عبارة عن واحد يعني
+
+146
+00:15:11,890 --> 00:15:15,930
+ايش فيها فقط ال identity element و ال identity
+
+147
+00:15:15,930 --> 00:15:21,310
+الموجودة مع نفسه صحيح ولا لأ يبقى أبيل يعني يبقى
+
+148
+00:15:21,310 --> 00:15:27,180
+هنا بدأ أخد النقطة الأولى Fلو كان ال order لل G
+
+149
+00:15:27,180 --> 00:15:33,360
+بده يسوي واحد صحيح then ال G بده يسوي ال identity
+
+150
+00:15:33,360 --> 00:15:42,340
+فقط لا غير و هذا بده يعطينا ان ال G is abelian طيب
+
+151
+00:15:42,340 --> 00:15:51,100
+لو كان ال order لل G بده يسوي اتنين و تلاتة or
+
+152
+00:15:51,100 --> 00:15:59,130
+خمسةيبقى كل هما دول مالهم primes then ال order لل
+
+153
+00:15:59,130 --> 00:16:05,970
+G is prime في الحالات التلاتة ايش بيقول ال crawler
+
+154
+00:16:05,970 --> 00:16:10,790
+اتنين ال group of prime order is cyclic يبقى هذا
+
+155
+00:16:10,790 --> 00:16:17,250
+بده يعطينا ان ال G is cyclic طب و اذا ال G is
+
+156
+00:16:17,250 --> 00:16:18,910
+cyclic ابيه يعني
+
+157
+00:16:23,770 --> 00:16:29,690
+يبقى الان اثبتنا ان في حالة الواحد واتنين والتلاتة
+
+158
+00:16:29,690 --> 00:16:34,710
+والخمسة ابيليان ضالت ايه؟ ضالت الأربعة يبقى بداجي
+
+159
+00:16:34,710 --> 00:16:41,010
+اقوله هنا F ال order لل G بده يساوي أربعة
+
+160
+00:16:44,930 --> 00:16:51,590
+لو افترضت ان ال order للجي يكون 4 لو اخذت اي non
+
+161
+00:16:51,590 --> 00:16:56,470
+identity element في ال group جي كده احتمال ال
+
+162
+00:16:56,470 --> 00:17:02,890
+order يكون له واحد استبعدناه انا قلت non identity
+
+163
+00:17:02,890 --> 00:17:07,750
+ليه بيبقى فيش الا اتنين او اربعة طب لو كان ال
+
+164
+00:17:07,750 --> 00:17:14,810
+order لل element يسوى 4بكون generator لـ G لأن ال
+
+165
+00:17:14,810 --> 00:17:17,990
+order يبقى الـ G الـ cyclic وبالتالي أبدا طلت
+
+166
+00:17:17,990 --> 00:17:24,390
+المشكلة وين عند اتنين فبداش أقوله هنا if يبقى if
+
+167
+00:17:24,390 --> 00:17:33,590
+ال order لـ G بده يسوى أربعة then any non identity
+
+168
+00:17:33,590 --> 00:17:39,490
+element has
+
+169
+00:17:40,760 --> 00:17:44,540
+order اتنين
+
+170
+00:17:44,540 --> 00:17:50,560
+واربع if
+
+171
+00:17:50,560 --> 00:18:01,960
+order لأ بدوا يساوي اربع then order لأ بدوا يساوي
+
+172
+00:18:01,960 --> 00:18:09,370
+order لجيمعنى هذا الكلام ان الـ G هذه بدها تساوي ل
+
+173
+00:18:09,370 --> 00:18:16,010
+group generated by A هذا يعني ان الـ G هو Cyclic
+
+174
+00:18:16,010 --> 00:18:25,910
+وهذا يعني ان الـ G هو Abelian بلت مشكلتنا وين؟
+
+175
+00:18:25,910 --> 00:18:40,540
+ايوة يبقى Fالـ A موجود في G with ال order للـ A
+
+176
+00:18:40,540 --> 00:18:48,760
+بده يساوي اتنين then ال A تربيه بده يساوي ال
+
+177
+00:18:48,760 --> 00:18:55,660
+identity مظبوط يعني ال A صار بده يساوي ال A
+
+178
+00:18:55,660 --> 00:18:56,060
+inverse
+
+179
+00:19:01,020 --> 00:19:07,280
+يبقى انا باخد two elements من G و اثبت ان ال X في
+
+180
+00:19:07,280 --> 00:19:12,460
+Y بيساوي ال Y X باستخدام المعلومة اللي عندنا هذا
+
+181
+00:19:12,460 --> 00:19:19,100
+يبقى بروح اقوله افترض ان ال X و ال Y عناصر موجودة
+
+182
+00:19:19,100 --> 00:19:19,580
+عندنا
+
+183
+00:19:37,640 --> 00:19:47,160
+داجة اقول له let ال X و ال Y موجودة في G then ال X
+
+184
+00:19:47,160 --> 00:19:56,920
+Y موجودة في G if ال order لل X Y يساوي اتنين then
+
+185
+00:19:56,920 --> 00:20:05,460
+ال X Y لكل تربيع يساوي من؟ يساوي ال identityطب ال
+
+186
+00:20:05,460 --> 00:20:11,760
+X Y تربيع هذا بقدر اقول X تربيع Y تربيع لا تبقى
+
+187
+00:20:11,760 --> 00:20:16,980
+بيلا ما هي اشابه لاني بقدرش مظبوط لكن كل اللي بقدر
+
+188
+00:20:16,980 --> 00:20:23,960
+اقوله then اللي هو من ال X Y في ال X Y يسوى ال
+
+189
+00:20:23,960 --> 00:20:31,570
+identity تمامطب لو ضربت الطرفين في y inverse من
+
+190
+00:20:31,570 --> 00:20:39,630
+جهة اليمين يبقى بيصير عندي x y x بده يساوي e في y
+
+191
+00:20:39,630 --> 00:20:45,010
+inverse اللي هو بمين؟ ب y inverse طب اضرب كمان في
+
+192
+00:20:45,010 --> 00:20:51,350
+x inverse من جهة اليمين هذا يعني ان ال x في y بده
+
+193
+00:20:51,350 --> 00:20:57,090
+يساوي ال y inverse في ال x inverseالان احنا قلنا
+
+194
+00:20:57,090 --> 00:21:02,790
+هنا ايش ان ال element اللي ال order له يساوي اتنين
+
+195
+00:21:02,790 --> 00:21:09,650
+ال element يساوي معكوسه تمام طيب بناء عليه هذا بده
+
+196
+00:21:09,650 --> 00:21:16,030
+يعطينا ان ال x في ال y بده يساوي من ال y في ال x
+
+197
+00:21:17,170 --> 00:21:23,450
+يعني شيلت كل X وحطيت بدلها X وشيلت كل Y وحطيت
+
+198
+00:21:23,450 --> 00:21:31,830
+بدلها Y هذا يعني ان ال G is abelianيبقى معنى هذا
+
+199
+00:21:31,830 --> 00:21:35,950
+الكلام أن الـ G abelian سواء كان ال order إلها
+
+200
+00:21:35,950 --> 00:21:39,470
+واحد و لا اتنين و لا تلاتة و لا أربع و لا خمسة من
+
+201
+00:21:39,470 --> 00:21:44,470
+الآن فصاعدا بدك تاخدها قاعدة أي group ال order
+
+202
+00:21:44,470 --> 00:21:48,750
+اللي هيسوي خمسة أو أقل من خمسة يبقى هذه ال group
+
+203
+00:21:48,750 --> 00:21:54,330
+عبارة عن abelian group خد كمان مثال، المثال هذا هو
+
+204
+00:21:54,330 --> 00:22:02,450
+أحد أسئلة الكتاب يبقى example twoexample 2 هو
+
+205
+00:22:02,450 --> 00:22:10,690
+عبارة عن سؤال 26 من الكتاب بيقول let g
+
+206
+00:22:10,690 --> 00:22:25,890
+be a group of order 25 prove that
+
+207
+00:22:25,890 --> 00:22:34,580
+اثبت انهالـ G is cyclic
+
+208
+00:22:34,580 --> 00:22:40,580
+or الـ
+
+209
+00:22:40,580 --> 00:22:48,600
+G فُس خمسة بده يساوي ال identity for all G اللي
+
+210
+00:22:48,600 --> 00:22:49,720
+belongs to G
+
+211
+00:23:04,000 --> 00:23:09,320
+خلّيني أبقى معناه هنا السؤال مرة تانية انا عندي
+
+212
+00:23:09,320 --> 00:23:14,300
+group فيها خمسة وعشرين عنصر ال order لها يسوى خمسة
+
+213
+00:23:14,300 --> 00:23:20,800
+وعشرين قال لي بتثبت ان جي هذي Cyclic يا اما الجي
+
+214
+00:23:20,800 --> 00:23:24,940
+أسخمسة بده يسوى ال identity لكل الجي اللي belongs
+
+215
+00:23:24,940 --> 00:23:30,640
+to جي اذا انا بدي استبعد واحد و اثبت مين لانه قال
+
+216
+00:23:30,640 --> 00:23:35,230
+لي or هذا او هذايبقى انا لو روحته قولتله هنا
+
+217
+00:23:35,230 --> 00:23:46,330
+assume افترض ان ال G is non-cyclic ماهياش
+
+218
+00:23:46,330 --> 00:23:54,310
+cyclic and ال order لل G بده يساوي خمسة وعشرين
+
+219
+00:23:54,310 --> 00:24:01,760
+يبقاش بتثبت يا شبابالجيوس خمسة يسوى من ال identity
+
+220
+00:24:01,760 --> 00:24:06,500
+element الان ال جي موجود في جي يبقى ال order له
+
+221
+00:24:06,500 --> 00:24:14,680
+يقسم من الخمسة وعشرين يبقى هنا since لما ان ال جي
+
+222
+00:24:14,680 --> 00:24:19,660
+belongs to جي ال order لل جي divide
+
+223
+00:24:21,710 --> 00:24:26,870
+اللي هو الخمسة وعشرين معنى هذا الكلام ان ال order
+
+224
+00:24:26,870 --> 00:24:35,230
+للجي يا اما واحد يا اما خمسة or خمسة وعشرينبنستبعد
+
+225
+00:24:35,230 --> 00:24:40,550
+لخمسة وعشرين لأن لو كان ال order خمسة وعشرين لصارة
+
+226
+00:24:40,550 --> 00:24:45,630
+ال G Cyclic قال لا هي ما هي ال Cyclic إذا لا يمكن
+
+227
+00:24:45,630 --> 00:24:52,330
+لل order تبع ال element هذا أنه يسوى من ال order ل
+
+228
+00:24:52,330 --> 00:24:56,110
+G small هذا شباب مش جي كتر الجي كتر هي خمسة وعشرين
+
+229
+00:24:56,110 --> 00:25:00,050
+ال order لل element يا بده يسوى واحد يا إما خمسة
+
+230
+00:25:00,050 --> 00:25:06,310
+يا إما خمسة وعشرينالان انا باجي بقوله ال order لل
+
+231
+00:25:06,310 --> 00:25:13,770
+G بدي سوى خمسة و عشرين impossible هذا الكلام غير
+
+232
+00:25:13,770 --> 00:25:26,190
+ممكن because السبب ان ال G is not cyclicيبقى الـ G
+
+233
+00:25:26,190 --> 00:25:30,690
+ما هياش Cycle طيب استبعدنا منين؟ الخمسة و عشرين
+
+234
+00:25:30,690 --> 00:25:36,250
+ضايلة عندنا الـ G ال order له يبدو يساوي واحد يبدو
+
+235
+00:25:36,250 --> 00:25:45,550
+يساوي خمسة الان لو كان ال order F ال order ل ال G
+
+236
+00:25:45,550 --> 00:25:51,260
+يبدو يساوي واحد thenلما يكون الارض اللي جي بده
+
+237
+00:25:51,260 --> 00:25:54,680
+يساوي واحد يبقى مين هي جي هذه ال identity element
+
+238
+00:25:54,680 --> 00:26:01,260
+يبقى then الجي بدها تساوي ال identity element يبقى
+
+239
+00:26:01,260 --> 00:26:07,660
+الجي أس خمسة بده يساوي ال identity element أس خمسة
+
+240
+00:26:07,660 --> 00:26:12,600
+يبقى جي أس خمسة ال identity أس خمسة من بال
+
+241
+00:26:12,600 --> 00:26:19,940
+identity وهو المطلوب الحالة التانية لو كانالـ
+
+242
+00:26:19,940 --> 00:26:26,180
+order للـ G بده يساوي خمسة then الـ G أُس خمسة بده
+
+243
+00:26:26,180 --> 00:26:32,180
+يساوي ال identity و هو المفتوح يبقى بناء عليه مدام
+
+244
+00:26:32,180 --> 00:26:37,200
+الـ G non-cyclic الـ G أُس خمسة بده يساوي ال
+
+245
+00:26:37,200 --> 00:26:41,140
+identity element دائما و أبدا
+
+246
+00:27:02,160 --> 00:27:09,020
+طب ننتقل الى تعريف جئى او لكرولري رقم اربعة كرولري
+
+247
+00:27:09,020 --> 00:27:18,180
+رقم اربعة بسموها
+
+248
+00:27:18,180 --> 00:27:23,420
+Fermat Fermat's
+
+249
+00:27:23,420 --> 00:27:26,260
+little theorem
+
+250
+00:27:31,620 --> 00:27:39,240
+نصها كتالة بيقول for every integer a for every
+
+251
+00:27:39,240 --> 00:27:56,220
+integer a and every prime p and every prime p ال a
+
+252
+00:27:56,220 --> 00:28:05,260
+to the power p modulo pبدو يساوي ال a modulo p
+
+253
+00:28:05,260 --> 00:28:08,480
+بدنا
+
+254
+00:28:08,480 --> 00:28:11,720
+نبرهم صحيتها ل proof
+
+255
+00:28:16,540 --> 00:28:21,300
+هذه سميت باسم FairMaths لانه الاكتشاف هذه الشغلة
+
+256
+00:28:21,300 --> 00:28:26,420
+وسميت little لان انا بظغر الرقم الكبير انا عند رقم
+
+257
+00:28:26,420 --> 00:28:32,620
+كبير ضخم بظغره على طول الخط يعني بجيب رقم مكافئ له
+
+258
+00:28:32,620 --> 00:28:38,980
+في حالة اذا كان المقياس هو P فبقول أي integer A و
+
+259
+00:28:38,980 --> 00:28:43,630
+every prime Pالـ A to the power of P موديولو P
+
+260
+00:28:43,630 --> 00:28:49,090
+اللاحظ ال موديولو P هو الأس اللي عندى هذا و هذا
+
+261
+00:28:49,090 --> 00:28:54,040
+لازم يكون ال prime number شرط أساسي مش أي رقمإن
+
+262
+00:28:54,040 --> 00:28:59,300
+حدث ذلك يبقى بقوله هذا a modulo p يعني هذا ال p
+
+263
+00:28:59,300 --> 00:29:03,800
+بكون اتخلصت منها وبالتالي الرقم الضخم هذا صغرته
+
+264
+00:29:03,800 --> 00:29:08,260
+إلى رقم a modulo p ال a هذه يمكن تكون أكبر من ال p
+
+265
+00:29:08,260 --> 00:29:12,980
+ويمكن تكون أصغر من ال p محط الشرط عندى كل اللي
+
+266
+00:29:12,980 --> 00:29:17,480
+حطوا انه انتجار و ال p is a prime نروح نسبة صحة
+
+267
+00:29:17,480 --> 00:29:22,090
+هذا الكلام بأنا بدي أخد حالتينالحالة الأولى لو كان
+
+268
+00:29:22,090 --> 00:29:27,790
+ال A أقل من P و الحالة الثانية لو كان ال A أكبر من
+
+269
+00:29:27,790 --> 00:29:34,610
+P بدي أدرس ايه الحالة تانية طب لو يساو لو ال A ساو
+
+270
+00:29:34,610 --> 00:29:38,790
+ال P يبقى من 100 لما يبقى Zero بدي أساوي Zero على
+
+271
+00:29:38,790 --> 00:29:43,710
+طول الخطط طيب يبقى بدي أجي يبقى ماعنديش مشكلة في
+
+272
+00:29:43,710 --> 00:29:47,930
+حالة ال Zero ليش بصيحة خلاص Zero بساوي Zero طيب
+
+273
+00:29:47,930 --> 00:29:59,460
+بدي أخد Fالـ P less than 0 لأ
+
+274
+00:29:59,460 --> 00:30:08,740
+لو كان less than A لو كان F ال A less than P لو
+
+275
+00:30:08,740 --> 00:30:19,080
+كان ال A أقل من P then ال P ال .. ال A هذابتكون
+
+276
+00:30:19,080 --> 00:30:25,500
+موجود في مجموعته الأعداد واحد و اتنين و تلاتة و
+
+277
+00:30:25,500 --> 00:30:33,740
+لغاية P minus ال one أكيد مية المية مدام A integer
+
+278
+00:30:33,740 --> 00:30:38,820
+أصغر من P يبقى A موجود في المجموعة هذه طب مين هي
+
+279
+00:30:38,820 --> 00:30:46,580
+المجموعة هذه مش UP يبقى هذه اللي هي تساوي UP
+
+280
+00:30:49,020 --> 00:30:59,020
+يبقى معنى هذا الكلام ان ال a موجود في ال U P طيب
+
+281
+00:30:59,020 --> 00:31:08,500
+يبقى قداش ال order ل U P نقص واحد، كويس هذا بيقين
+
+282
+00:31:08,500 --> 00:31:20,930
+اللي عند ال order ل U P بيسوي P ناقص واحدطبعا طيب
+
+283
+00:31:20,930 --> 00:31:26,950
+الآن ان يأتي crawler فيهم هذه اللي قالتلي اه
+
+284
+00:31:26,950 --> 00:31:31,070
+مشحناها اللي هو a او زي اظن ال crawler رقم تلاتة
+
+285
+00:31:31,070 --> 00:31:36,270
+ال a او ال order لل a بدو يشتوي ال ID تلاتة طيب
+
+286
+00:31:36,270 --> 00:31:43,790
+هنا from crawler ثلاثة
+
+287
+00:31:43,790 --> 00:31:52,450
+اي element بد أخد امرفوع لل order تبع ال U P بدي
+
+288
+00:31:52,450 --> 00:32:00,810
+يسوى ال identity اللي هو واحد هذا الكلام
+
+289
+00:32:00,810 --> 00:32:06,510
+ايش معناه؟ معناه ال A أس ال P ناقص واحد بدي يسوى
+
+290
+00:32:06,510 --> 00:32:15,030
+واحد طيب لو ضربت الطرفين في A ايش بيصير عندي؟ A أس
+
+291
+00:32:15,030 --> 00:32:21,900
+P بدي يسوى ال Aيبقى معناه هذا كلمة ان a is p
+
+292
+00:32:21,900 --> 00:32:28,960
+modulo p بدي سوى a modulo p مادة ما الرقمين هذا
+
+293
+00:32:28,960 --> 00:32:33,320
+اللي بيسووا بعض اذا بدي يكون هذا modulo p بدي سوى
+
+294
+00:32:33,320 --> 00:32:38,060
+هذا modulo p تماما وهو المطلوب هذا لو كانت ايش ال
+
+295
+00:32:38,060 --> 00:32:44,840
+a اقل من p طب لو كانت ال a اكبر من p يبقى f ال a
+
+296
+00:32:44,840 --> 00:32:46,940
+greater than p
+
+297
+00:32:51,570 --> 00:32:57,570
+يعني ال A هذي P زائد شوية اتنين P زائد شوية تلتة P
+
+298
+00:32:57,570 --> 00:33:01,970
+عشرين P زائد زائد شوية تمام يبقى بال division
+
+299
+00:33:01,970 --> 00:33:09,730
+algorithm بقول له then ال A هذا بده يساوي ال M P
+
+300
+00:33:09,730 --> 00:33:15,870
+زائد ال R يعني مضاعفة ال P زائد ال R و ال R هذي
+
+301
+00:33:15,870 --> 00:33:25,010
+اكبر من أو تساوي Zero اقل من مينأقل من P طيب لو
+
+302
+00:33:25,010 --> 00:33:31,190
+جيت مدام عرفت زيك اللي هو خدت الآن ال A modulo P
+
+303
+00:33:31,190 --> 00:33:39,730
+كده ايش بده تساوي؟ R انا عند ال A بده تساوي MP زي
+
+304
+00:33:39,730 --> 00:33:43,630
+ده انا خدت ال A modulo P بقى مضاعفات ال P بطيروا
+
+305
+00:33:43,630 --> 00:33:49,810
+ايش بظهر عندي؟ بظهر عندي Rيبقى هذا بيبقى عندى مين؟
+
+306
+00:33:49,810 --> 00:33:56,570
+بيبقى عندى R فقط لا غير طيب الان ال R محصورة من
+
+307
+00:33:56,570 --> 00:34:01,590
+اين الى اين؟ من Zero الى P وانا جايل ان ال A
+
+308
+00:34:01,590 --> 00:34:08,210
+modulo P بده ساوى ال R ال R يعني موجودة وين؟ في ال
+
+309
+00:34:08,210 --> 00:34:17,490
+U P صح ولا لا؟موجودة في ال U P ليش؟ لأنها محصورة
+
+310
+00:34:17,490 --> 00:34:25,050
+من صفر إلى P طبعا طيب مدام محصورة هذه تساوي هذه
+
+311
+00:34:25,050 --> 00:34:31,030
+وهذه موجودة هنا اذا automatic على طول الخطأيش قلنا
+
+312
+00:34:31,030 --> 00:34:35,970
+هنا لو كان في البرهان الأول بقول لما تبقى ال a
+
+313
+00:34:35,970 --> 00:34:41,750
+موجودة في ال U P استنتجنا ان هذا الكلام ماله صحيح
+
+314
+00:34:41,750 --> 00:34:52,610
+تمام يبقى باجي بقول from the above from من البرهان
+
+315
+00:34:52,610 --> 00:35:00,500
+أعلاهيبقى ال a modulo p modulo p بدى يسوى a أس p
+
+316
+00:35:00,500 --> 00:35:07,300
+modulo p وانتهينا منها يبقى على كل الأمر يعنى سواء
+
+317
+00:35:07,300 --> 00:35:12,360
+كان ال a أكبر من p ولا أصغر من p فإن ال a to the
+
+318
+00:35:12,360 --> 00:35:18,220
+power p modulo p بدى يسوى منها ال a modulo p حد
+
+319
+00:35:18,220 --> 00:35:24,110
+يلقى أي استفسار هناطب نحاول نعطي اكثر من مثال على
+
+320
+00:35:24,110 --> 00:35:30,770
+هذه النقطة المثال الأول يبقى
+
+321
+00:35:30,770 --> 00:35:41,150
+examples find
+
+322
+00:35:41,150 --> 00:35:54,640
+the exact value متجددش القيمة الحقيقيةof خمستاشر
+
+323
+00:35:54,640 --> 00:36:04,480
+أس احداش موديولو أحداش of وهذا يجب أن أعتبرها ايه
+
+324
+00:36:04,480 --> 00:36:11,760
+ويجب أن نأتي إلى الـ B يجب أن يكون سبعة أس تلتاش
+
+325
+00:36:11,760 --> 00:36:15,880
+موديولو أحداش
+
+326
+00:36:29,550 --> 00:36:35,690
+خلّي أبقى لك هنا بقول هات للقيمة الحقيقية للخمستاش
+
+327
+00:36:35,690 --> 00:36:41,550
+أس احداش موديولو أحداش وكذلك سبعة أس تلتاش موديولو
+
+328
+00:36:41,550 --> 00:36:47,610
+أحداش الحل كالتالي بيروح أخد إيه؟ نمر إيه؟ نمر
+
+329
+00:36:47,610 --> 00:36:54,530
+إيه؟ بدي أخدله الخمستاشر أس إحداش موديولو أحداش
+
+330
+00:36:54,530 --> 00:37:01,420
+النتج خمستاشروديولو أحداشر صحيك يا شباب
+
+331
+00:37:05,780 --> 00:37:11,120
+لو كان هذا P و هذا P يتماين نفس بعض يبقى هذا يقول
+
+332
+00:37:11,120 --> 00:37:17,060
+الى E modulo P يبقى انا عندي خمستاش و احداش modulo
+
+333
+00:37:17,060 --> 00:37:20,380
+احداش يبقى انا عندي خمستاش modulo احداش يبقى انا
+
+334
+00:37:20,380 --> 00:37:20,420
+عندي خمستاش modulo احداش يبقى انا عندي خمستاش
+
+335
+00:37:20,420 --> 00:37:23,320
+modulo احداش هي خمستاش modulo احداش خمستاش modulo
+
+336
+00:37:23,320 --> 00:37:28,240
+احداش اكبر من الاحداش اذا بدى اشيل منها الاحداش او
+
+337
+00:37:28,240 --> 00:37:32,840
+مضاعفات الاحداش كدهش بطلع يبقى النتيجة تساوي اربع
+
+338
+00:37:33,130 --> 00:37:39,010
+يبقى هذا سؤال direct مباشر لكن قد يكون السؤال غير
+
+339
+00:37:39,010 --> 00:37:46,030
+مباشر غير مباشر كيف؟ زي ما قال لي سبعة أس تلتاشر
+
+340
+00:37:46,030 --> 00:37:56,510
+موديولو أحداش بده يساوي يعني
+
+341
+00:37:56,510 --> 00:37:59,850
+مانفعش أقول الجواب اللي هو سبعة موديولو أحداش؟
+
+342
+00:37:59,850 --> 00:38:02,290
+خلط؟
+
+343
+00:38:03,320 --> 00:38:09,060
+غلطة و نصف بدي يكون الرقم هذا الأس هو المقياس اللي
+
+344
+00:38:09,060 --> 00:38:15,220
+عندي طيب يعني ايش؟ يعني سبعة أس تلتاش بدي اكتبها
+
+345
+00:38:15,220 --> 00:38:21,920
+بدلالة سبعة أس أحداش يبقى هذه بدها تساوي سبعة أسي
+
+346
+00:38:21,920 --> 00:38:30,490
+أحداش كدهش بيظل سبعة ترابيع كل موديولو أحداشهذه هي
+
+347
+00:38:30,490 --> 00:38:37,810
+عبارة عن سبعة أوسى احداش موديولو احداش مضروبة في
+
+348
+00:38:37,810 --> 00:38:46,530
+من في سبعة ترابية موديولو احداشيبقى حولتها إلى حصل
+
+349
+00:38:46,530 --> 00:38:50,850
+ضرب الرقمين اللي عندنا الان من firmat theorem هذه
+
+350
+00:38:50,850 --> 00:38:55,210
+شكلة شكل firmat theorem يبقى هذا سبعة موديولو
+
+351
+00:38:55,210 --> 00:39:01,570
+احداش يبقى هنا سبعة موديولو احداش من firmat
+
+352
+00:39:01,570 --> 00:39:07,610
+theorem وهذه سبعة تربية يعني تسعة واربعين موديولو
+
+353
+00:39:07,610 --> 00:39:14,600
+من احداش يبقى هذا الكلام يسامالان هذه السابعة
+
+354
+00:39:14,600 --> 00:39:20,400
+موديولو احداش لان تسعة واربعين موديولو احداش فيها
+
+355
+00:39:20,400 --> 00:39:27,020
+قداش لان احداش في اربعة من تسعة واربعين بظال خمسة
+
+356
+00:39:27,020 --> 00:39:34,180
+يبقى مضروبة في من مضروبة في خمسة موديولو احداش
+
+357
+00:39:37,280 --> 00:39:44,860
+خمسة و تلاتين عبارة
+
+358
+00:39:44,860 --> 00:39:51,290
+عن أحد عشر في تلاتة تلاتة و تلاتين زائدأتنين يبقى
+
+359
+00:39:51,290 --> 00:39:56,130
+الناتج كله يساوي اتنين يبقى هالرقم الضخم اللى
+
+360
+00:39:56,130 --> 00:40:00,650
+عندنا هذا اللى هو سبعة أس طلع تاشر يعني بدي أضرب
+
+361
+00:40:00,650 --> 00:40:04,990
+سبعة في نفسها طلع تاشر مرة و أجيبلها الموديل
+
+362
+00:40:04,990 --> 00:40:09,150
+أحداشر اختصرناها و قولنا ناتج يساوي قداشر يساوي
+
+363
+00:40:09,150 --> 00:40:11,490
+اتنين على طول الخط
+
+364
+00:40:16,940 --> 00:40:24,100
+تحسب شو ماعليكش قيود مدام انت ماشي سليم يبقى احسب
+
+365
+00:40:24,100 --> 00:40:29,680
+اللي بدك يام متى لازم القمع عارف قصده لو حطينا
+
+366
+00:40:29,680 --> 00:40:35,960
+element وحطينا له قص كبير وبتصغر هذا القص قصده اه
+
+367
+00:40:35,960 --> 00:40:43,830
+طيب في عندنا خد بالك شغلة بدي اشير اليهانظرية
+
+368
+00:40:43,830 --> 00:40:50,950
+Lagrange بتقول ال order لل subgroup بيقسم من؟
+
+369
+00:40:50,950 --> 00:40:57,230
+بيقسم ل group السؤال هو هل في هذه الحلقة كل خاسم
+
+370
+00:40:57,230 --> 00:41:03,490
+لل group بديه جابله subgroup؟ بالتأكيد؟ يعني عكس
+
+371
+00:41:03,490 --> 00:41:08,550
+النظرية الصحية؟ في شفتر أربعة هيك؟ طيب
+
+372
+00:41:13,820 --> 00:41:20,700
+هذا كلامك مش صحيح بدليل مثال خمسة على ال section
+
+373
+00:41:20,700 --> 00:41:25,480
+الان وصلنا له لأن عكس نظرية Lagrange غير صحيح
+
+374
+00:41:25,480 --> 00:41:30,100
+وعندك مثال اتطلع عليه في الكتاب اللي هو مثال خمسة
+
+375
+00:41:30,100 --> 00:41:37,280
+بالكتابيعني .. يعني .. يعني لو عندي قواسم لل order
+
+376
+00:41:37,280 --> 00:41:41,780
+تبع ال .. تبع ال group ليس بالضرورة انه الاجي ال
+
+377
+00:41:41,780 --> 00:41:47,220
+sub group ال order اللي هيسوي هذا القواسم قد .. يا
+
+378
+00:41:47,220 --> 00:41:53,010
+شيخ انت اسمعلي شوية بقى ..أحنا بيقول ما ياتي انا
+
+379
+00:41:53,010 --> 00:41:56,750
+وك تفهم ان عكس نظرية لاجراني ليس صحيح حالة ما هو
+
+380
+00:41:56,750 --> 00:42:01,310
+عكس نظرية لاجراني لو جيبت قواسم ال order ليلي جروب
+
+381
+00:42:01,310 --> 00:42:07,090
+ليس بالضرورة كل قاسم يجيبله sub group قد يكون و قد
+
+382
+00:42:07,090 --> 00:42:11,110
+لا يكون ممكن بعض القواسم يجيلهم sub group يحمل نفس
+
+383
+00:42:11,110 --> 00:42:15,200
+ال orderلكن بعض الأخر ممكن مالاجيش له أعطى مثال
+
+384
+00:42:15,200 --> 00:42:20,940
+عندك اللى هو على ال A4 تمام؟ يبقى ماعلك إلا أن
+
+385
+00:42:20,940 --> 00:42:26,320
+تطلع على هذا المثال و لنا إلى ذلك عودة ان شاء الله
+
+386
+00:42:26,320 --> 00:42:28,500
+على نفس الموضوع في المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..7c906248afdfb2e4531d2d361783184991faed72
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/W9PL51hnoPc_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 3414, "start": 22.14, "end": 34.14, "text": "بسم الله الرحمن الرحيم المرة اللي فاتت أعطينا ساعتين فيه اللي هو ال chapter 7 اللي بتحدث عن Cossets and Lagrange theorem", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 5551, 3615, 9566, 1829, 8315, 8608, 995, 34268, 9957, 8978, 3224, 13672, 1829, 31439, 2423, 7187, 1614, 13672, 1829, 39894, 24401, 12984, 18871, 383, 772, 1385, 293, 24886, 14521, 20904], "avg_logprob": -0.18567153748045576, "compression_ratio": 1.3478260869565217, "no_speech_prob": 0.0, "words": [{"start": 22.14, "end": 22.5, "word": "بسم", "probability": 0.8134765625}, {"start": 22.5, "end": 22.74, "word": " الله", "probability": 0.9716796875}, {"start": 22.74, "end": 23.16, "word": " الرحمن", "probability": 0.9461263020833334}, {"start": 23.16, "end": 23.92, "word": " الرحيم", "probability": 0.9939778645833334}, {"start": 23.92, "end": 25.02, "word": " المرة", "probability": 0.84521484375}, {"start": 25.02, "end": 25.14, "word": " اللي", "probability": 0.67041015625}, {"start": 25.14, "end": 25.76, "word": " فاتت", "probability": 0.9845377604166666}, {"start": 25.76, "end": 26.78, "word": " أعطينا", "probability": 0.86962890625}, {"start": 26.78, "end": 27.98, "word": " ساعتين", "probability": 0.9610595703125}, {"start": 27.98, "end": 28.68, "word": " فيه", "probability": 0.91650390625}, {"start": 28.68, "end": 28.98, "word": " اللي", "probability": 0.857177734375}, {"start": 28.98, "end": 29.1, "word": " هو", "probability": 0.99072265625}, {"start": 29.1, "end": 29.24, "word": " ال", "probability": 0.6240234375}, {"start": 29.24, "end": 29.62, "word": " chapter", "probability": 0.93359375}, {"start": 29.62, "end": 30.52, "word": " 7", "probability": 0.470458984375}, {"start": 30.52, "end": 30.82, "word": " اللي", "probability": 0.972412109375}, {"start": 30.82, "end": 31.46, "word": " بتحدث", "probability": 0.9078776041666666}, {"start": 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"word": " is", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 14, "seek": 36379, "start": 334.49, "end": 363.79, "text": "أبيلن لكن العكس ما هواش صحيح طيب a group of a prime order is cyclic بدنا نروح نثبت هذا الكلام بدي أجي أقوله assume that افترض ان ال g is a group with order P that is", "tokens": [10721, 21292, 1211, 1863, 44381, 18863, 4117, 3794, 19446, 31439, 33599, 20328, 5016, 1829, 5016, 23032, 1829, 3555, 257, 1594, 295, 257, 5835, 1668, 307, 38154, 1050, 47525, 8315, 8717, 32887, 5016, 8717, 12984, 3555, 2655, 23758, 2423, 28820, 10943, 4724, 16254, 5551, 7435, 1829, 5551, 39648, 3224, 6552, 300, 1975, 5172, 2655, 43042, 16472, 2423, 290, 307, 257, 1594, 365, 1668, 430, 300, 307], "avg_logprob": -0.22005208626841055, "compression_ratio": 1.3647058823529412, "no_speech_prob": 0.0, "words": [{"start": 334.49, "end": 335.07, "word": "أبيلن", "probability": 0.477294921875}, {"start": 335.07, "end": 335.27, "word": " لكن", "probability": 0.6513671875}, {"start": 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cyclic", "probability": 0.828857421875}, {"start": 340.97, "end": 341.35, "word": " بدنا", "probability": 0.75341796875}, {"start": 341.35, "end": 341.59, "word": " نروح", "probability": 0.9654947916666666}, {"start": 341.59, "end": 342.23, "word": " نثبت", "probability": 0.980712890625}, {"start": 342.23, "end": 342.61, "word": " هذا", "probability": 0.96875}, {"start": 342.61, "end": 343.17, "word": " الكلام", "probability": 0.9208984375}, {"start": 343.17, "end": 344.03, "word": " بدي", "probability": 0.6446533203125}, {"start": 344.03, "end": 344.29, "word": " أجي", "probability": 0.7003580729166666}, {"start": 344.29, "end": 344.85, "word": " أقوله", "probability": 0.8829752604166666}, {"start": 344.85, "end": 345.63, "word": " assume", "probability": 0.8486328125}, {"start": 345.63, "end": 348.49, "word": " that", "probability": 0.85986328125}, {"start": 348.49, "end": 349.51, "word": " افترض", "probability": 0.92822265625}, {"start": 349.51, "end": 350.13, "word": " ان", 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اول اتنين تلاتة خمسة سبعة احداشر تلاتاشر سبعتاشر تسعتاشر زى ما بدك", "tokens": [6780, 307, 2423, 1668, 13672, 7578, 10874, 7578, 47525, 7578, 7251, 3794, 995, 45865, 2423, 430, 293, 2423, 430, 307, 5835, 7251, 3555, 4587, 7578, 2423, 1668, 13672, 7578, 10874, 7578, 31439, 6225, 3555, 9640, 3660, 18871, 6225, 3215, 3215, 1975, 12610, 1975, 2655, 1863, 9957, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 3555, 27884, 1975, 24401, 33599, 2288, 6055, 1211, 9307, 33599, 2288, 8608, 3555, 34268, 33599, 2288, 6055, 3794, 34268, 33599, 2288, 30767, 7578, 19446, 47525, 4117], "avg_logprob": -0.21894055259663883, "compression_ratio": 1.6838709677419355, "no_speech_prob": 0.0, "words": [{"start": 366.12, "end": 366.64, "word": "that", "probability": 0.123046875}, {"start": 366.64, "end": 367.3, "word": " is", "probability": 0.95068359375}, {"start": 367.3, "end": 370.64, "word": " ال", "probability": 0.6142578125}, {"start": 370.64, "end": 371.3, "word": " order", "probability": 0.50634765625}, {"start": 371.3, "end": 372.1, "word": " اللى", "probability": 0.429443359375}, {"start": 372.1, "end": 372.54, "word": " جى", "probability": 0.8916015625}, {"start": 372.54, "end": 373.12, "word": " بدى", "probability": 0.52093505859375}, {"start": 373.12, "end": 373.54, "word": " يساوي", "probability": 0.827392578125}, {"start": 373.54, "end": 373.84, "word": " ال", "probability": 0.935546875}, {"start": 373.84, "end": 374.22, "word": " P", "probability": 0.83056640625}, {"start": 374.22, "end": 375.74, "word": " and", "probability": 0.79638671875}, {"start": 375.74, "end": 377.04, "word": " ال", "probability": 0.87841796875}, {"start": 377.04, "end": 377.54, "word": " P", "probability": 0.98974609375}, {"start": 377.54, "end": 378.72, "word": " is", "probability": 0.93896484375}, {"start": 378.72, "end": 379.54, "word": " prime", "probability": 0.82470703125}, {"start": 379.54, "end": 382.24, "word": " يبقى", "probability": 0.7674560546875}, {"start": 382.24, "end": 382.36, "word": " ال", "probability": 0.97998046875}, {"start": 382.36, "end": 382.68, "word": " order", "probability": 0.98046875}, {"start": 382.68, "end": 382.9, "word": " اللى", "probability": 0.988525390625}, {"start": 382.9, "end": 383.14, "word": " جى", "probability": 0.955810546875}, {"start": 383.14, "end": 383.34, "word": " هو", "probability": 0.77685546875}, {"start": 383.34, "end": 383.78, "word": " عبارة", "probability": 0.984375}, {"start": 383.78, "end": 384.04, "word": " عن", "probability": 0.98681640625}, {"start": 384.04, "end": 384.54, "word": " عدد", "probability": 0.96826171875}, {"start": 384.54, "end": 385.06, "word": " اول", "probability": 0.713134765625}, {"start": 385.06, "end": 385.6, "word": " اتنين", "probability": 0.968505859375}, {"start": 385.6, "end": 386.34, "word": " تلاتة", "probability": 0.9029541015625}, {"start": 386.34, "end": 387.08, "word": " خمسة", "probability": 0.9775390625}, {"start": 387.08, "end": 387.58, "word": " سبعة", "probability": 0.9500325520833334}, {"start": 387.58, "end": 388.08, "word": " احداشر", "probability": 0.81884765625}, {"start": 388.08, "end": 388.94, "word": " تلاتاشر", "probability": 0.92216796875}, {"start": 388.94, "end": 389.86, "word": " سبعتاشر", "probability": 0.878515625}, {"start": 389.86, "end": 390.32, "word": " تسعتاشر", "probability": 0.89599609375}, {"start": 390.32, "end": 390.52, "word": " زى", "probability": 0.887939453125}, {"start": 390.52, "end": 390.62, "word": " ما", "probability": 0.75830078125}, {"start": 390.62, "end": 391.04, "word": " بدك", "probability": 0.917724609375}], "temperature": 1.0}, {"id": 16, "seek": 41765, "start": 393.03, "end": 417.65, "text": "يبقى جي جروب with order P و ال P هذا عبارة عن a prime number كويس؟ بدي أثبت أن هذا ال group دائما و أبدا تبقى Cycling، كويس؟ يبقى بدأجي أقوله خدلي عنصر A موجود في G طب العنصر A هذا بولدلي ال sub group ولا لأ؟", "tokens": [1829, 3555, 4587, 7578, 10874, 1829, 10874, 32887, 3555, 365, 1668, 430, 4032, 2423, 430, 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order تبعها بده يساوي خمسة دائما و أبدا أو أقل من خمسة is abelian يعني لو عندي group فيها عنصر واحد أو group فيها عنصرين أو group فيها تلتة عناصر أو أربعة عناصر أو خمسة عناصر كل هذه الأنموعة من ال group تبقى دائما و أبدا abelian طيب الآن solution", "tokens": [6027, 39184, 1668, 6055, 3555, 3615, 11296, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 34051, 5551, 4587, 1211, 9154, 16490, 2304, 3794, 3660, 307, 410, 338, 952, 37495, 22653, 45164, 18871, 16254, 1594, 8978, 11296, 18871, 9381, 2288, 36764, 24401, 34051, 1594, 8978, 11296, 18871, 9381, 2288, 9957, 34051, 1594, 8978, 11296, 6055, 1211, 2655, 3660, 18871, 33546, 2288, 34051, 5551, 25513, 27884, 18871, 33546, 2288, 34051, 16490, 2304, 3794, 3660, 18871, 33546, 2288, 28242, 29538, 16247, 1863, 2304, 2407, 27884, 9154, 2423, 1594, 6055, 3555, 4587, 7578, 11778, 16373, 15042, 4032, 5551, 3555, 28259, 410, 338, 952, 23032, 1829, 3555, 6024, 48506, 3827], "avg_logprob": 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"word": " خمسة", "probability": 0.9744873046875}, {"start": 893.68, "end": 894.14, "word": " عناصر", "probability": 0.9905598958333334}, {"start": 894.14, "end": 894.62, "word": " كل", "probability": 0.71142578125}, {"start": 894.62, "end": 895.1, "word": " هذه", "probability": 0.94482421875}, {"start": 895.1, "end": 895.62, "word": " الأنموعة", "probability": 0.734228515625}, {"start": 895.62, "end": 895.76, "word": " من", "probability": 0.95458984375}, {"start": 895.76, "end": 895.88, "word": " ال", "probability": 0.666015625}, {"start": 895.88, "end": 896.12, "word": " group", "probability": 0.94140625}, {"start": 896.12, "end": 896.5, "word": " تبقى", "probability": 0.81024169921875}, {"start": 896.5, "end": 896.84, "word": " دائما", "probability": 0.96142578125}, {"start": 896.84, "end": 896.96, "word": " و", "probability": 0.8076171875}, {"start": 896.96, "end": 897.42, "word": " أبدا", "probability": 0.8968098958333334}, {"start": 897.42, "end": 899.0, "word": " abelian", 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1269.19, "end": 1269.65, "word": " بده", "probability": 0.635009765625}, {"start": 1269.65, "end": 1270.41, "word": " يعطينا", "probability": 0.9449462890625}, {"start": 1270.41, "end": 1270.87, "word": " ان", "probability": 0.9296875}, {"start": 1270.87, "end": 1271.15, "word": " ال", "probability": 0.8994140625}, {"start": 1271.15, "end": 1271.63, "word": " x", "probability": 0.5634765625}, {"start": 1271.63, "end": 1271.97, "word": " في", "probability": 0.97216796875}, {"start": 1271.97, "end": 1272.21, "word": " ال", "probability": 0.95947265625}, {"start": 1272.21, "end": 1272.65, "word": " y", "probability": 0.9404296875}, {"start": 1272.65, "end": 1273.57, "word": " بده", "probability": 0.818359375}, {"start": 1273.57, "end": 1274.05, "word": " يساوي", "probability": 0.97314453125}, {"start": 1274.05, "end": 1274.39, "word": " من", "probability": 0.98095703125}, {"start": 1274.39, "end": 1274.71, "word": " ال", "probability": 0.91455078125}, {"start": 1274.71, "end": 1275.37, "word": " y", "probability": 0.94775390625}, {"start": 1275.37, "end": 1275.59, "word": " في", "probability": 0.9287109375}, {"start": 1275.59, "end": 1275.73, "word": " ال", "probability": 0.96728515625}, {"start": 1275.73, "end": 1276.03, "word": " x", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 50, "seek": 128917, "start": 1277.17, "end": 1289.17, "text": "يعني شيلت كل X وحطيت بدلها X وشيلت كل Y وحطيت بدلها Y هذا يعني ان ال G is abelian", "tokens": [40228, 22653, 13412, 26895, 2655, 28242, 1783, 4032, 5016, 9566, 36081, 47525, 1211, 11296, 1783, 4032, 8592, 26895, 2655, 28242, 398, 4032, 5016, 9566, 36081, 47525, 1211, 11296, 398, 23758, 37495, 22653, 16472, 2423, 460, 307, 410, 338, 952], "avg_logprob": -0.30078124478459356, "compression_ratio": 1.4021739130434783, "no_speech_prob": 0.0, "words": [{"start": 1277.17, "end": 1277.61, "word": "يعني", "probability": 0.51776123046875}, {"start": 1277.61, "end": 1278.29, "word": " شيلت", "probability": 0.772216796875}, {"start": 1278.29, "end": 1278.63, "word": " كل", "probability": 0.94482421875}, {"start": 1278.63, "end": 1280.45, "word": " X", "probability": 0.5908203125}, {"start": 1280.45, "end": 1281.19, "word": " وحطيت", "probability": 0.78289794921875}, {"start": 1281.19, "end": 1281.57, "word": " بدلها", "probability": 0.5265299479166666}, {"start": 1281.57, "end": 1281.71, "word": " X", "probability": 0.93603515625}, {"start": 1281.71, "end": 1282.19, "word": " وشيلت", "probability": 0.8870849609375}, {"start": 1282.19, "end": 1282.39, "word": " كل", "probability": 0.9560546875}, {"start": 1282.39, "end": 1282.57, "word": " Y", "probability": 0.95654296875}, {"start": 1282.57, "end": 1283.45, "word": " وحطيت", "probability": 0.8814697265625}, {"start": 1283.45, "end": 1283.97, "word": " بدلها", "probability": 0.9593098958333334}, {"start": 1283.97, "end": 1284.33, "word": " Y", "probability": 0.9892578125}, {"start": 1284.33, "end": 1285.25, "word": " هذا", "probability": 0.6357421875}, {"start": 1285.25, "end": 1285.91, "word": " يعني", "probability": 0.962158203125}, {"start": 1285.91, "end": 1286.25, "word": " ان", "probability": 0.54345703125}, {"start": 1286.25, "end": 1286.53, "word": " ال", "probability": 0.75830078125}, {"start": 1286.53, "end": 1286.91, "word": " G", "probability": 0.6572265625}, {"start": 1286.91, "end": 1287.95, "word": " is", "probability": 0.3623046875}, {"start": 1287.95, "end": 1289.17, "word": " abelian", "probability": 0.8097330729166666}], "temperature": 1.0}, {"id": 51, "seek": 132007, "start": 1290.83, "end": 1320.07, "text": "يبقى معنى هذا الكلام أن الـ G abelian سواء كان ال order إلها واحد و لا اتنين و لا تلاتة و لا أربع و لا خمسة من الآن فصاعدا بدك تاخدها قاعدة أي group ال order اللي هيسوي خمسة أو أقل من خمسة يبقى هذه ال group عبارة عن abelian group خد كمان مثال، المثال هذا هو أحد أسئلة الكتاب يبقى example two", "tokens": [1829, 3555, 4587, 7578, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 14739, 2423, 39184, 460, 410, 338, 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1318.41, "word": " example", "probability": 0.81005859375}, {"start": 1318.41, "end": 1320.07, "word": " two", "probability": 0.4501953125}], "temperature": 1.0}, {"id": 52, "seek": 134805, "start": 1320.91, "end": 1348.05, "text": "example 2 هو عبارة عن سؤال 26 من الكتاب بيقول let g be a group of order 25 prove that اثبت انه", "tokens": [3121, 335, 781, 568, 31439, 6225, 3555, 9640, 3660, 18871, 8608, 33604, 6027, 7551, 9154, 33251, 2655, 16758, 4724, 1829, 39648, 718, 290, 312, 257, 1594, 295, 1668, 3552, 7081, 300, 1975, 12984, 3555, 2655, 16472, 3224], "avg_logprob": -0.27302631265238714, "compression_ratio": 1.0854700854700854, "no_speech_prob": 0.0, "words": [{"start": 1320.91, "end": 1321.71, "word": "example", "probability": 0.6866455078125}, {"start": 1321.71, "end": 1322.09, "word": " 2", "probability": 0.373779296875}, {"start": 1322.09, "end": 1322.45, "word": " هو", "probability": 0.304443359375}, {"start": 1322.45, "end": 1322.99, "word": " عبارة", "probability": 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1335.97, "end": 1337.85, "word": " order", "probability": 0.90771484375}, {"start": 1337.85, "end": 1340.11, "word": " 25", "probability": 0.59033203125}, {"start": 1340.11, "end": 1342.27, "word": " prove", "probability": 0.677734375}, {"start": 1342.27, "end": 1345.89, "word": " that", "probability": 0.92041015625}, {"start": 1345.89, "end": 1347.43, "word": " اثبت", "probability": 0.901123046875}, {"start": 1347.43, "end": 1348.05, "word": " انه", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 53, "seek": 136972, "start": 1348.48, "end": 1369.72, "text": "الـ G is cyclic or الـ G فُس خمسة بده يساوي ال identity for all G اللي belongs to G", "tokens": [6027, 39184, 460, 307, 38154, 1050, 420, 2423, 39184, 460, 6156, 10859, 3794, 16490, 2304, 3794, 3660, 47525, 3224, 7251, 3794, 995, 45865, 2423, 6575, 337, 439, 460, 13672, 1829, 12953, 281, 460], "avg_logprob": -0.3226103046361138, "compression_ratio": 1.0784313725490196, "no_speech_prob": 0.0, "words": [{"start": 1348.48, 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belongs to جي ال order لل جي divide", "tokens": [6027, 7435, 1829, 41779, 16490, 2304, 3794, 3660, 7251, 3794, 2407, 7578, 9154, 2423, 6575, 4478, 2423, 7649, 2423, 10874, 1829, 3714, 29245, 23328, 8978, 10874, 1829, 7251, 3555, 4587, 7578, 2423, 1668, 46740, 7251, 4587, 38251, 9154, 33962, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 7251, 3555, 4587, 7578, 34105, 1670, 5296, 15042, 16472, 2423, 10874, 1829, 12953, 281, 10874, 1829, 2423, 1668, 24976, 10874, 1829, 9845], "avg_logprob": -0.36277172530906787, "compression_ratio": 1.6025641025641026, "no_speech_prob": 0.0, "words": [{"start": 1438.24, "end": 1439.16, "word": "الجيوس", "probability": 0.41619873046875}, {"start": 1439.16, "end": 1439.62, "word": " خمسة", "probability": 0.8197021484375}, {"start": 1439.62, "end": 1440.1, "word": " يسوى", "probability": 0.635986328125}, {"start": 1440.1, "end": 1440.4, "word": " من", "probability": 0.30810546875}, {"start": 1440.4, "end": 1441.04, "word": " ال", "probability": 0.81298828125}, {"start": 1441.04, "end": 1441.76, "word": " identity", "probability": 0.52294921875}, {"start": 1441.76, "end": 1442.4, "word": " element", "probability": 0.81494140625}, {"start": 1442.4, "end": 1443.46, "word": " الان", "probability": 0.4091796875}, {"start": 1443.46, "end": 1443.72, "word": " ال", "probability": 0.4990234375}, {"start": 1443.72, "end": 1443.92, "word": " جي", "probability": 0.66162109375}, {"start": 1443.92, "end": 1444.46, "word": " موجود", "probability": 0.9451497395833334}, {"start": 1444.46, "end": 1444.64, "word": " في", "probability": 0.93896484375}, {"start": 1444.64, "end": 1444.96, "word": " جي", "probability": 0.725830078125}, {"start": 1444.96, "end": 1445.3, "word": " يبقى", "probability": 0.8541259765625}, {"start": 1445.3, "end": 1445.44, "word": " ال", "probability": 0.71435546875}, {"start": 1445.44, "end": 1446.0, "word": " order", "probability": 0.96240234375}, {"start": 1446.0, "end": 1446.5, "word": " له", "probability": 0.47265625}, {"start": 1446.5, "end": 1447.12, "word": " يقسم", "probability": 0.637939453125}, {"start": 1447.12, "end": 1447.56, "word": " من", "probability": 0.85107421875}, {"start": 1447.56, "end": 1448.8, "word": " الخمسة", "probability": 0.9393310546875}, {"start": 1448.8, "end": 1449.58, "word": " وعشرين", "probability": 0.8216552734375}, {"start": 1449.58, "end": 1450.74, "word": " يبقى", "probability": 0.9327392578125}, {"start": 1450.74, "end": 1451.08, "word": " هنا", "probability": 0.978515625}, {"start": 1451.08, "end": 1452.04, "word": " since", "probability": 0.440673828125}, {"start": 1452.04, "end": 1453.04, "word": " لما", "probability": 0.793212890625}, {"start": 1453.04, "end": 1453.46, "word": " ان", "probability": 0.6005859375}, {"start": 1453.46, "end": 1454.34, "word": " ال", "probability": 0.6533203125}, {"start": 1454.34, "end": 1454.68, "word": " جي", "probability": 0.8671875}, {"start": 1454.68, "end": 1455.28, "word": " belongs", "probability": 0.47119140625}, {"start": 1455.28, "end": 1455.64, "word": " to", "probability": 0.9765625}, {"start": 1455.64, "end": 1456.1, "word": " جي", "probability": 0.8994140625}, {"start": 1456.1, "end": 1456.7, "word": " ال", "probability": 0.90234375}, {"start": 1456.7, "end": 1457.38, "word": " order", "probability": 0.9755859375}, {"start": 1457.38, "end": 1457.9, "word": " لل", "probability": 0.67626953125}, {"start": 1457.9, "end": 1458.46, "word": " جي", "probability": 0.795166015625}, {"start": 1458.46, "end": 1459.66, "word": " divide", "probability": 0.358154296875}], "temperature": 1.0}, {"id": 57, "seek": 147257, "start": 1461.71, "end": 1472.57, "text": "اللي هو الخمسة وعشرين معنى هذا الكلام ان ال order للجي يا اما واحد يا اما خمسة or خمسة وعشرين", "tokens": [6027, 20292, 31439, 33962, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 20449, 1863, 7578, 23758, 2423, 28820, 10943, 16472, 2423, 1668, 24976, 7435, 1829, 35186, 1975, 15042, 36764, 24401, 35186, 1975, 15042, 16490, 2304, 3794, 3660, 420, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957], "avg_logprob": -0.23335597437361014, "compression_ratio": 1.5533980582524272, "no_speech_prob": 0.0, "words": [{"start": 1461.71, "end": 1462.01, "word": "اللي", "probability": 0.322265625}, {"start": 1462.01, "end": 1462.23, "word": " هو", "probability": 0.97900390625}, {"start": 1462.23, "end": 1462.75, "word": " الخمسة", "probability": 0.9337158203125}, {"start": 1462.75, "end": 1463.45, "word": " وعشرين", "probability": 0.9129638671875}, {"start": 1463.45, "end": 1464.61, "word": " معنى", "probability": 0.6788736979166666}, {"start": 1464.61, "end": 1464.87, "word": " هذا", "probability": 0.94873046875}, {"start": 1464.87, "end": 1465.59, "word": " الكلام", "probability": 0.9625651041666666}, {"start": 1465.59, "end": 1466.09, "word": " ان", "probability": 0.5546875}, {"start": 1466.09, "end": 1466.37, "word": " ال", "probability": 0.69873046875}, {"start": 1466.37, "end": 1466.87, "word": " order", "probability": 0.79443359375}, {"start": 1466.87, "end": 1467.67, "word": " للجي", "probability": 0.6494140625}, {"start": 1467.67, "end": 1467.85, "word": " يا", "probability": 0.296875}, {"start": 1467.85, "end": 1468.13, "word": " اما", "probability": 0.766357421875}, {"start": 1468.13, "end": 1468.63, "word": " واحد", "probability": 0.969482421875}, {"start": 1468.63, "end": 1469.37, "word": " يا", "probability": 0.42138671875}, {"start": 1469.37, "end": 1469.79, "word": " اما", "probability": 0.963134765625}, {"start": 1469.79, "end": 1470.81, "word": " خمسة", "probability": 0.9732666015625}, {"start": 1470.81, "end": 1471.37, "word": " or", "probability": 0.701171875}, {"start": 1471.37, "end": 1472.07, "word": " خمسة", "probability": 0.96337890625}, {"start": 1472.07, "end": 1472.57, "word": " وعشرين", "probability": 0.9508056640625}], "temperature": 1.0}, {"id": 58, "seek": 150263, "start": 1474.51, "end": 1502.63, "text": "بنستبعد لخمسة وعشرين لأن لو كان ال order خمسة وعشرين لصارة ال G Cyclic قال لا هي ما هي ال Cyclic إذا لا يمكن لل order تبع ال element هذا أنه يسوى من ال order ل G small هذا شباب مش جي كتر الجي كتر هي خمسة وعشرين ال order لل element يا بده يسوى واحد يا إما خمسة يا إما خمسة وعشرين", "tokens": [3555, 1863, 14851, 3555, 22488, 5296, 9778, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 5296, 33456, 45164, 25961, 2423, 1668, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 5296, 9381, 9640, 3660, 2423, 460, 10295, 66, 1050, 50239, 20193, 39896, 19446, 39896, 2423, 10295, 66, 1050, 11933, 15730, 20193, 7251, 43020, 24976, 1668, 6055, 3555, 3615, 2423, 4478, 23758, 14739, 3224, 7251, 3794, 2407, 7578, 9154, 2423, 1668, 5296, 460, 1359, 23758, 13412, 3555, 16758, 37893, 10874, 1829, 9122, 2655, 2288, 25724, 1829, 9122, 2655, 2288, 39896, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957, 2423, 1668, 24976, 4478, 35186, 47525, 3224, 7251, 3794, 2407, 7578, 36764, 24401, 35186, 11933, 15042, 16490, 2304, 3794, 3660, 35186, 11933, 15042, 16490, 2304, 3794, 3660, 4032, 3615, 46309, 9957], "avg_logprob": 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0.978271484375}, {"start": 1495.59, "end": 1496.11, "word": " وعشرين", "probability": 0.972900390625}, {"start": 1496.11, "end": 1496.63, "word": " ال", "probability": 0.86181640625}, {"start": 1496.63, "end": 1497.01, "word": " order", "probability": 0.9765625}, {"start": 1497.01, "end": 1497.25, "word": " لل", "probability": 0.73779296875}, {"start": 1497.25, "end": 1497.65, "word": " element", "probability": 0.958984375}, {"start": 1497.65, "end": 1497.93, "word": " يا", "probability": 0.5400390625}, {"start": 1497.93, "end": 1498.21, "word": " بده", "probability": 0.939453125}, {"start": 1498.21, "end": 1498.59, "word": " يسوى", "probability": 0.931640625}, {"start": 1498.59, "end": 1499.05, "word": " واحد", "probability": 0.942626953125}, {"start": 1499.05, "end": 1499.29, "word": " يا", "probability": 0.732421875}, {"start": 1499.29, "end": 1499.51, "word": " إما", "probability": 0.837158203125}, {"start": 1499.51, "end": 1500.05, "word": " خمسة", "probability": 0.9869384765625}, {"start": 1500.05, "end": 1500.17, "word": " يا", "probability": 0.78955078125}, {"start": 1500.17, "end": 1500.43, "word": " إما", "probability": 0.972412109375}, {"start": 1500.43, "end": 1501.97, "word": " خمسة", "probability": 0.9892578125}, {"start": 1501.97, "end": 1502.63, "word": " وعشرين", "probability": 0.9671630859375}], "temperature": 1.0}, {"id": 59, "seek": 152375, "start": 1502.99, "end": 1523.75, "text": "الان انا باجي بقوله ال order لل G بدي سوى خمسة و عشرين impossible هذا الكلام غير ممكن because السبب ان ال G is not cyclic", "tokens": [6027, 7649, 1975, 8315, 4724, 26108, 1829, 4724, 39648, 3224, 2423, 1668, 24976, 460, 4724, 16254, 8608, 2407, 7578, 16490, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 6243, 23758, 2423, 28820, 10943, 32771, 13546, 3714, 43020, 570, 21136, 3555, 3555, 16472, 2423, 460, 307, 406, 38154, 1050], "avg_logprob": -0.17578125093132257, "compression_ratio": 1.2465753424657535, "no_speech_prob": 0.0, "words": [{"start": 1502.99, "end": 1503.55, 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not", "probability": 0.962890625}, {"start": 1522.37, "end": 1523.75, "word": " cyclic", "probability": 0.85888671875}], "temperature": 1.0}, {"id": 60, "seek": 154815, "start": 1525.33, "end": 1548.15, "text": "يبقى الـ G ما هياش Cycle طيب استبعدنا منين؟ الخمسة و عشرين ضايلة عندنا الـ G ال order له يبدو يساوي واحد يبدو يساوي خمسة الان لو كان ال order F ال order ل ال G يبدو يساوي واحد then", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 460, 19446, 39896, 33599, 10295, 2160, 23032, 1829, 3555, 44713, 3555, 22488, 8315, 9154, 9957, 22807, 33962, 2304, 3794, 3660, 4032, 6225, 46309, 9957, 48812, 995, 26895, 3660, 43242, 8315, 2423, 39184, 460, 2423, 1668, 46740, 7251, 44510, 2407, 7251, 3794, 995, 45865, 36764, 24401, 7251, 44510, 2407, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 2423, 7649, 45164, 25961, 2423, 1668, 479, 2423, 1668, 5296, 2423, 460, 7251, 44510, 2407, 7251, 3794, 995, 45865, 36764, 24401, 550], "avg_logprob": -0.2829044075573192, "compression_ratio": 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خمسة then الـ G أُس خمسة بده يساوي ال identity و هو المفتوح يبقى بناء عليه مدام الـ G non-cyclic الـ G أُس خمسة بده يساوي ال identity element دائما و أبدا", "tokens": [6027, 39184, 1668, 24976, 39184, 460, 47525, 3224, 7251, 3794, 995, 45865, 16490, 2304, 3794, 3660, 550, 2423, 39184, 460, 5551, 10859, 3794, 16490, 2304, 3794, 3660, 47525, 3224, 7251, 3794, 995, 45865, 2423, 6575, 4032, 31439, 9673, 5172, 2655, 2407, 5016, 7251, 3555, 4587, 7578, 44945, 16606, 47356, 3714, 3215, 10943, 2423, 39184, 460, 2107, 12, 1344, 66, 1050, 2423, 39184, 460, 5551, 10859, 3794, 16490, 2304, 3794, 3660, 47525, 3224, 7251, 3794, 995, 45865, 2423, 6575, 4478, 11778, 16373, 15042, 4032, 5551, 3555, 28259], "avg_logprob": -0.2266522964526867, "compression_ratio": 1.73125, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1579.5, "end": 1579.94, "word": "الـ", "probability": 0.42083740234375}, {"start": 1579.94, "end": 1580.44, "word": " order", "probability": 0.71142578125}, {"start": 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diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..44623264756e75dcb15980ce5aee4659110ee3df
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.json
@@ -0,0 +1 @@
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694.16, "end": 694.76, "word": " بدها", "probability": 0.8857421875}, {"start": 694.76, "end": 695.58, "word": " تساوي", "probability": 0.9638671875}, {"start": 695.58, "end": 696.6, "word": " الصف", "probability": 0.96142578125}, {"start": 696.6, "end": 697.14, "word": " الأول", "probability": 0.980712890625}, {"start": 697.14, "end": 697.32, "word": " في", "probability": 0.97412109375}, {"start": 697.32, "end": 697.9, "word": " العمود", "probability": 0.9191080729166666}, {"start": 697.9, "end": 698.66, "word": " الأول", "probability": 0.982177734375}, {"start": 698.66, "end": 699.16, "word": " اللي", "probability": 0.900390625}, {"start": 699.16, "end": 699.5, "word": " هو", "probability": 0.9677734375}, {"start": 699.5, "end": 700.4, "word": " AB", "probability": 0.396240234375}, {"start": 700.4, "end": 701.82, "word": " الصف", "probability": 0.960205078125}, {"start": 701.82, "end": 702.48, "word": " الأول", "probability": 0.98046875}, {"start": 702.48, "end": 702.68, "word": " في", "probability": 0.9912109375}, {"start": 702.68, "end": 703.28, "word": " العمود", "probability": 0.9676106770833334}, {"start": 703.28, "end": 703.98, "word": " الثاني", "probability": 0.9775390625}, {"start": 703.98, "end": 704.4, "word": " يبقى", "probability": 0.9547119140625}, {"start": 704.4, "end": 705.48, "word": " بAC", "probability": 0.61083984375}, {"start": 705.48, "end": 706.92, "word": " الصف", "probability": 0.9736328125}, {"start": 706.92, "end": 707.56, "word": " الثاني", "probability": 0.9764404296875}, {"start": 707.56, "end": 707.76, "word": " في", "probability": 0.99609375}, {"start": 707.76, "end": 708.38, "word": " العمود", "probability": 0.9876302083333334}, {"start": 708.38, "end": 709.02, "word": " الأول", "probability": 0.9853515625}, {"start": 709.02, "end": 709.58, "word": " يبقى", "probability": 0.9903564453125}, {"start": 709.58, "end": 710.6, "word": " بAD", "probability": 0.93701171875}, {"start": 710.6, "end": 711.9, "word": " الصف", "probability": 0.98046875}, {"start": 711.9, "end": 712.5, "word": " الثاني", "probability": 0.9853515625}, {"start": 712.5, "end": 712.7, "word": " في", "probability": 0.99658203125}, {"start": 712.7, "end": 713.26, "word": " العمود", "probability": 0.9886067708333334}, {"start": 713.26, "end": 713.94, "word": " الثاني", "probability": 0.985107421875}, {"start": 713.94, "end": 715.52, "word": " بAF", "probability": 0.869873046875}], "temperature": 1.0}, {"id": 29, "seek": 73359, "start": 716.63, "end": 733.59, "text": "اللي بقدر اكتبها a في b,c,d,f الان بداتي اخدله اللي هو b,c,d,f في ال a,0,0,a", "tokens": [6027, 20292, 4724, 28543, 2288, 1975, 4117, 2655, 3555, 11296, 257, 8978, 272, 11, 66, 11, 67, 11, 69, 2423, 7649, 47525, 9307, 1829, 1975, 9778, 3215, 43761, 13672, 1829, 31439, 272, 11, 66, 11, 67, 11, 69, 8978, 2423, 257, 11, 15, 11, 15, 11, 64], "avg_logprob": -0.23876953652749458, "compression_ratio": 1.2608695652173914, "no_speech_prob": 0.0, "words": [{"start": 716.63, "end": 717.07, "word": "اللي", "probability": 0.80810546875}, {"start": 717.07, "end": 717.57, "word": " بقدر", "probability": 0.9742838541666666}, {"start": 717.57, "end": 718.65, "word": " اكتبها", "probability": 0.930078125}, {"start": 718.65, "end": 719.29, "word": " a", "probability": 0.463623046875}, {"start": 719.29, "end": 720.65, "word": " في", "probability": 0.41943359375}, {"start": 720.65, "end": 721.19, "word": " b", "probability": 0.60205078125}, {"start": 721.19, "end": 722.07, "word": ",c", "probability": 0.5655517578125}, {"start": 722.07, "end": 723.01, "word": ",d", "probability": 0.988037109375}, {"start": 723.01, "end": 723.69, "word": ",f", "probability": 0.982177734375}, {"start": 723.69, "end": 725.55, "word": " الان", "probability": 0.6375732421875}, {"start": 725.55, "end": 726.45, "word": " بداتي", "probability": 0.52978515625}, {"start": 726.45, "end": 727.29, "word": " اخدله", "probability": 0.8316650390625}, {"start": 727.29, "end": 727.67, "word": " اللي", 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الأول في العمود الأول BA الصف الأول في العمود الثاني CA الصف الثاني في العمود الأول DA الصف الثاني في العمود الثاني يبقى FA", "tokens": [1829, 3555, 4587, 7578, 23758, 20449, 8315, 3224, 20328, 5172, 16247, 12610, 8978, 18863, 2304, 23328, 16247, 12610, 21050, 31767, 5172, 16247, 12610, 8978, 18863, 2304, 23328, 6024, 104, 7649, 1829, 22852, 31767, 5172, 6024, 104, 7649, 1829, 8978, 18863, 2304, 23328, 16247, 12610, 9578, 31767, 5172, 6024, 104, 7649, 1829, 8978, 18863, 2304, 23328, 6024, 104, 7649, 1829, 7251, 3555, 4587, 7578, 19894], "avg_logprob": -0.06526442307692308, "compression_ratio": 2.5463917525773194, "no_speech_prob": 0.0, "words": [{"start": 734.38, "end": 735.1, "word": "يبقى", "probability": 0.928955078125}, {"start": 735.1, "end": 735.52, "word": " هذا", "probability": 0.94921875}, {"start": 735.52, "end": 736.42, "word": " معناه", "probability": 0.97509765625}, {"start": 736.42, "end": 737.14, "word": " صف", "probability": 0.9716796875}, {"start": 737.14, "end": 737.74, "word": " الأول", "probability": 0.95361328125}, {"start": 737.74, "end": 737.94, "word": " في", "probability": 0.9541015625}, {"start": 737.94, "end": 738.44, "word": " العمود", "probability": 0.94873046875}, {"start": 738.44, "end": 739.2, "word": " الأول", "probability": 0.984130859375}, {"start": 739.2, "end": 740.36, "word": " BA", "probability": 0.2705078125}, {"start": 740.36, "end": 741.76, "word": " الصف", "probability": 0.77001953125}, {"start": 741.76, "end": 742.38, "word": " الأول", "probability": 0.98486328125}, {"start": 742.38, "end": 742.58, "word": " في", "probability": 0.99169921875}, {"start": 742.58, "end": 743.18, "word": " العمود", "probability": 0.984375}, {"start": 743.18, "end": 743.88, "word": " الثاني", "probability": 0.972900390625}, {"start": 743.88, "end": 744.9, "word": " CA", "probability": 0.93017578125}, {"start": 744.9, "end": 745.94, "word": " الصف", "probability": 0.818359375}, {"start": 745.94, "end": 746.5, "word": " الثاني", "probability": 0.9776611328125}, {"start": 746.5, "end": 746.66, "word": " في", "probability": 0.99609375}, {"start": 746.66, "end": 747.22, "word": " العمود", "probability": 0.9900716145833334}, {"start": 747.22, "end": 747.96, "word": " الأول", "probability": 0.988525390625}, {"start": 747.96, "end": 748.84, "word": " DA", "probability": 0.83349609375}, {"start": 748.84, "end": 749.96, "word": " الصف", "probability": 0.98388671875}, {"start": 749.96, "end": 750.5, "word": " الثاني", "probability": 0.9852294921875}, {"start": 750.5, "end": 750.64, "word": " في", "probability": 0.9970703125}, {"start": 750.64, "end": 751.2, "word": " العمود", "probability": 0.9889322916666666}, {"start": 751.2, "end": 751.88, "word": " الثاني", "probability": 0.9842529296875}, {"start": 751.88, "end": 752.52, "word": " يبقى", "probability": 0.9521484375}, {"start": 752.52, "end": 753.34, "word": " FA", "probability": 0.9453125}], "temperature": 1.0}, {"id": 31, "seek": 77000, "start": 754.16, "end": 770.0, "text": "لو أخدت ال a من كل element موجود داخل المصوفة بيظهر لنا مين بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 2423, 257, 9154, 28242, 4478, 3714, 29245, 23328, 11778, 47283, 1211, 9673, 9381, 38688, 3660, 4724, 1829, 19913, 3224, 2288, 5296, 8315, 3714, 9957, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829, 4724, 1829], "avg_logprob": -0.19972153229288536, "compression_ratio": 2.84375, "no_speech_prob": 0.0, "words": [{"start": 754.16, "end": 754.58, "word": "لو", "probability": 0.896240234375}, {"start": 754.58, 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710, 295, 290, 307, 294, 264, 1254, 15844, 25124, 28820, 13672, 1829, 31439, 257, 4018, 4018, 257], "avg_logprob": -0.32606909149571467, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 791.32, "end": 792.42, "word": "in", "probability": 0.08612060546875}, {"start": 792.42, "end": 793.86, "word": " z", "probability": 0.479248046875}, {"start": 793.86, "end": 794.46, "word": " of", "probability": 0.90283203125}, {"start": 794.46, "end": 794.98, "word": " g", "probability": 0.8349609375}, {"start": 794.98, "end": 795.92, "word": " is", "probability": 0.919921875}, {"start": 795.92, "end": 796.98, "word": " in", "probability": 0.9658203125}, {"start": 796.98, "end": 797.9, "word": " the", "probability": 0.8525390625}, {"start": 797.9, "end": 798.9, "word": " form", "probability": 0.95361328125}, {"start": 798.9, "end": 799.92, "word": " على", "probability": 0.62060546875}, {"start": 799.92, "end": 800.8, "word": " الشكل", "probability": 0.978759765625}, {"start": 800.8, "end": 801.5, "word": " اللي", "probability": 0.824951171875}, {"start": 801.5, "end": 801.6, "word": " هو", "probability": 0.84033203125}, {"start": 801.6, "end": 802.02, "word": " a", "probability": 0.845703125}, {"start": 802.02, "end": 802.86, "word": " zero", "probability": 0.425048828125}, {"start": 802.86, "end": 803.96, "word": " zero", "probability": 0.84619140625}, {"start": 803.96, "end": 804.62, "word": " a", "probability": 0.85888671875}], "temperature": 1.0}, {"id": 34, "seek": 82709, "start": 805.09, "end": 827.09, "text": "والـ A does not equal to zero يبقى من الأن فصاعدا لما بد ال center لل general linear group of two by two matrices over R بيكون عندي واحد زيرو زيرو واحد اتنين زيرو زيرو واحد مص زيرو زيرو واحد واحد على مية زيرو زيرو واحد على مية و هكذا", "tokens": [2407, 6027, 39184, 316, 775, 406, 2681, 281, 4018, 7251, 3555, 4587, 7578, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995, 5296, 15042, 47525, 2423, 3056, 24976, 2674, 8213, 1594, 295, 732, 538, 732, 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824.21, "end": 825.15, "word": " زيرو", "probability": 0.8907877604166666}, {"start": 825.15, "end": 825.51, "word": " زيرو", "probability": 0.9892578125}, {"start": 825.51, "end": 825.85, "word": " واحد", "probability": 0.98388671875}, {"start": 825.85, "end": 826.03, "word": " على", "probability": 0.85693359375}, {"start": 826.03, "end": 826.37, "word": " مية", "probability": 0.96240234375}, {"start": 826.37, "end": 826.51, "word": " و", "probability": 0.6572265625}, {"start": 826.51, "end": 827.09, "word": " هكذا", "probability": 0.83154296875}], "temperature": 1.0}, {"id": 35, "seek": 85433, "start": 827.31, "end": 854.33, "text": "يبقى كل العناصر القطرة الرئيسى بيكون عناصرهم متساوية وهذه بقينا نسميها في ال linear algebra بقيناها نسميها المصوفة شو اسمها؟ مصوفة الواحدة قطرية لما العناصر القطرة الرئيسى يكونوا متساوية بقيناش نسميها مثلثية", "tokens": [1829, 3555, 4587, 7578, 28242, 18863, 1863, 33546, 2288, 25062, 9566, 25720, 34892, 19986, 1829, 3794, 7578, 4724, 1829, 30544, 18871, 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"probability": 0.8014322916666666}, {"start": 830.05, "end": 831.29, "word": " الرئيسى", "probability": 0.888427734375}, {"start": 831.29, "end": 831.99, "word": " بيكون", "probability": 0.8367513020833334}, {"start": 831.99, "end": 832.69, "word": " عناصرهم", "probability": 0.7193603515625}, {"start": 832.69, "end": 833.31, "word": " متساوية", "probability": 0.8365234375}, {"start": 833.31, "end": 833.59, "word": " وهذه", "probability": 0.759521484375}, {"start": 833.59, "end": 833.95, "word": " بقينا", "probability": 0.673095703125}, {"start": 833.95, "end": 834.69, "word": " نسميها", "probability": 0.9814453125}, {"start": 834.69, "end": 835.31, "word": " في", "probability": 0.68798828125}, {"start": 835.31, "end": 836.39, "word": " ال", "probability": 0.943359375}, {"start": 836.39, "end": 836.79, "word": " linear", "probability": 0.450439453125}, {"start": 836.79, "end": 837.47, "word": " algebra", "probability": 0.9404296875}, {"start": 837.47, "end": 838.29, "word": " بقيناها", "probability": 0.81982421875}, {"start": 838.29, "end": 839.17, "word": " نسميها", "probability": 0.930419921875}, {"start": 839.17, "end": 839.83, "word": " المصوفة", "probability": 0.79482421875}, {"start": 839.83, "end": 839.99, "word": " شو", "probability": 0.8310546875}, {"start": 839.99, "end": 841.07, "word": " اسمها؟", "probability": 0.877685546875}, {"start": 841.07, "end": 841.95, "word": " مصوفة", "probability": 0.81064453125}, {"start": 841.95, "end": 842.57, "word": " الواحدة", "probability": 0.857177734375}, {"start": 842.57, "end": 845.83, "word": " قطرية", "probability": 0.76318359375}, {"start": 845.83, "end": 847.75, "word": " لما", "probability": 0.747314453125}, {"start": 847.75, "end": 848.35, "word": " العناصر", "probability": 0.96044921875}, {"start": 848.35, "end": 848.67, "word": " القطرة", "probability": 0.927734375}, {"start": 848.67, "end": 849.01, "word": " الرئيسى", "probability": 0.97041015625}, {"start": 849.01, "end": 849.41, "word": " يكونوا", "probability": 0.8186848958333334}, {"start": 849.41, "end": 850.69, "word": " متساوية", "probability": 0.98427734375}, {"start": 850.69, "end": 852.15, "word": " بقيناش", "probability": 0.73369140625}, {"start": 852.15, "end": 853.03, "word": " نسميها", "probability": 0.9931640625}, {"start": 853.03, "end": 854.33, "word": " مثلثية", "probability": 0.804150390625}], "temperature": 1.0}, {"id": 36, "seek": 87788, "start": 857.7, "end": 877.88, "text": "بنسميها scalar matrix او مقياسية لو كان القطرين غير متسوين بيقول دياجون الماتريك دياجون الماتريك هي فعلا دياجون الماتريك في المصحوف القطرية بس إذا تسابق عناصر القطر الرئيسي بنسميها scalar matrix", "tokens": [3555, 1863, 38251, 1829, 11296, 39684, 8141, 1975, 2407, 3714, 4587, 25528, 3794, 10632, 45164, 25961, 25062, 9566, 2288, 9957, 32771, 13546, 44650, 3794, 2407, 9957, 4724, 1829, 39648, 11778, 1829, 26108, 11536, 9673, 9307, 16572, 4117, 11778, 1829, 26108, 11536, 9673, 9307, 16572, 4117, 39896, 6156, 3615, 15040, 11778, 1829, 26108, 11536, 9673, 9307, 16572, 4117, 8978, 9673, 9381, 5016, 38688, 25062, 9566, 2288, 10632, 4724, 3794, 11933, 15730, 6055, 3794, 16758, 4587, 18871, 33546, 2288, 25062, 9566, 2288, 34892, 19986, 1829, 3794, 1829, 44945, 38251, 1829, 11296, 39684, 8141], "avg_logprob": -0.3145380431543226, "compression_ratio": 1.964705882352941, "no_speech_prob": 0.0, "words": [{"start": 857.7, "end": 858.56, "word": "بنسميها", "probability": 0.6635498046875}, {"start": 858.56, "end": 858.98, "word": " scalar", "probability": 0.84521484375}, {"start": 858.98, "end": 859.94, "word": " matrix", "probability": 0.95068359375}, {"start": 859.94, "end": 860.34, "word": " او", "probability": 0.4615478515625}, {"start": 860.34, "end": 864.52, "word": " مقياسية", "probability": 0.7810546875}, {"start": 864.52, "end": 865.26, "word": " لو", "probability": 0.210205078125}, {"start": 865.26, "end": 865.64, "word": " كان", "probability": 0.89111328125}, {"start": 865.64, "end": 866.28, "word": " القطرين", "probability": 0.7796630859375}, {"start": 866.28, "end": 866.68, "word": " غير", "probability": 0.984375}, {"start": 866.68, "end": 867.66, "word": " متسوين", "probability": 0.8583984375}, {"start": 867.66, "end": 868.02, "word": " بيقول", "probability": 0.74755859375}, {"start": 868.02, "end": 868.66, "word": " دياجون", "probability": 0.5740966796875}, {"start": 868.66, "end": 868.94, "word": " الماتريك", "probability": 0.6864013671875}, {"start": 868.94, "end": 869.1, "word": " دياجون", "probability": 0.76092529296875}, {"start": 869.1, "end": 869.1, "word": " الماتريك", "probability": 0.8896484375}, {"start": 869.1, "end": 869.1, "word": " هي", "probability": 0.419189453125}, {"start": 869.1, "end": 869.58, "word": " فعلا", "probability": 0.830078125}, {"start": 869.58, "end": 870.34, "word": " دياجون", "probability": 0.768310546875}, {"start": 870.34, "end": 870.78, "word": " الماتريك", "probability": 0.9432373046875}, {"start": 870.78, "end": 870.88, "word": " في", "probability": 0.66259765625}, {"start": 870.88, "end": 871.24, "word": " المصحوف", "probability": 0.5635986328125}, {"start": 871.24, "end": 871.9, "word": " القطرية", "probability": 0.861328125}, {"start": 871.9, "end": 872.48, "word": " بس", "probability": 0.8759765625}, {"start": 872.48, "end": 872.78, "word": " إذا", "probability": 0.7398681640625}, {"start": 872.78, "end": 873.6, "word": " تسابق", "probability": 0.725341796875}, {"start": 873.6, "end": 874.18, "word": " عناصر", "probability": 0.97607421875}, {"start": 874.18, "end": 874.7, "word": " القطر", "probability": 0.9637044270833334}, {"start": 874.7, "end": 875.26, "word": " الرئيسي", "probability": 0.9541015625}, {"start": 875.26, "end": 876.06, "word": " بنسميها", "probability": 0.900146484375}, {"start": 876.06, "end": 876.56, "word": " scalar", "probability": 0.95654296875}, {"start": 876.56, "end": 877.88, "word": " matrix", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 37, "seek": 90527, "start": 878.21, "end": 905.27, "text": "يبقى كل scalar matrix في ال general linear group of two by two matrices بيكونولي main بيكونولي ال center لل group اللي عندنا طيب نمرتنا example two بدنا z of D4 يساوي أكيد ال R node منهم هذا كل مجمع ليه لأنه ال identity", "tokens": [1829, 3555, 4587, 7578, 28242, 39684, 8141, 8978, 2423, 2674, 8213, 1594, 295, 732, 538, 732, 32284, 4724, 1829, 30544, 12610, 1829, 2135, 4724, 1829, 30544, 12610, 1829, 2423, 3056, 24976, 1594, 13672, 1829, 43242, 8315, 23032, 1829, 3555, 8717, 29973, 2655, 8315, 1365, 732, 47525, 8315, 710, 295, 413, 19, 7251, 3794, 995, 45865, 5551, 4117, 25708, 2423, 497, 9984, 9154, 16095, 23758, 28242, 3714, 7435, 2304, 3615, 32239, 3224, 5296, 33456, 3224, 2423, 6575], "avg_logprob": -0.3062094093917252, "compression_ratio": 1.4476190476190476, "no_speech_prob": 0.0, "words": [{"start": 878.21, "end": 878.73, "word": "يبقى", "probability": 0.78643798828125}, {"start": 878.73, "end": 879.23, "word": " كل", "probability": 0.93359375}, {"start": 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"seek": 95952, "start": 933.96, "end": 959.52, "text": "الـ R180 فقط لا غير يبقى هذه والـ R180 فقط لا غير يبقى هدول بس عناصر الـ Center تبعي الـ D4 غير هيك مافيش ولا elements طبعا لو رجعت للجدول اللي في الصفحة واحدة و تلاتين الكليتابل للـ D4", "tokens": [6027, 39184, 497, 37078, 6156, 47432, 20193, 32771, 13546, 7251, 3555, 4587, 7578, 29538, 16070, 39184, 497, 37078, 6156, 47432, 20193, 32771, 13546, 7251, 3555, 4587, 7578, 8032, 3215, 12610, 4724, 3794, 18871, 33546, 2288, 2423, 39184, 5169, 6055, 3555, 3615, 1829, 2423, 39184, 413, 19, 32771, 13546, 39896, 4117, 19446, 41185, 8592, 49429, 4959, 23032, 3555, 3615, 995, 45164, 12602, 7435, 34268, 24976, 7435, 3215, 12610, 13672, 1829, 8978, 31767, 5172, 5016, 3660, 36764, 24401, 3660, 4032, 6055, 1211, 9307, 9957, 33251, 20292, 2655, 16758, 1211, 24976, 39184, 413, 19], "avg_logprob": -0.22435461632583453, "compression_ratio": 1.6813186813186813, "no_speech_prob": 0.0, "words": [{"start": 933.96, "end": 934.42, "word": "الـ", 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"temperature": 1.0}, {"id": 58, "seek": 144832, "start": 1438.78, "end": 1448.32, "text": "ارنود ال identity element اتحرك مع اي element اخر في ال group ارنود هو دوران بصفر درجة", "tokens": [9640, 1863, 23328, 2423, 6575, 4478, 1975, 2655, 5016, 31747, 20449, 1975, 1829, 4478, 1975, 34740, 8978, 2423, 1594, 1975, 2288, 1863, 23328, 31439, 11778, 13063, 7649, 4724, 9381, 5172, 2288, 11778, 47341, 3660], "avg_logprob": -0.35781251192092894, "compression_ratio": 1.2285714285714286, "no_speech_prob": 0.0, "words": [{"start": 1438.78, "end": 1439.82, "word": "ارنود", "probability": 0.5999959309895834}, {"start": 1439.82, "end": 1439.96, "word": " ال", "probability": 0.40966796875}, {"start": 1439.96, "end": 1440.48, "word": " identity", "probability": 0.4267578125}, {"start": 1440.48, "end": 1441.34, "word": " element", "probability": 0.92138671875}, {"start": 1441.34, "end": 1442.2, "word": " اتحرك", "probability": 0.613372802734375}, {"start": 1442.2, "end": 1442.58, "word": " مع", 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"probability": 0.91748046875}, {"start": 1681.35, "end": 1681.87, "word": " عليه", "probability": 0.383544921875}, {"start": 1681.87, "end": 1682.41, "word": " أقول", "probability": 0.898193359375}, {"start": 1682.41, "end": 1683.07, "word": " هذه", "probability": 0.693359375}, {"start": 1683.07, "end": 1683.73, "word": " هي", "probability": 0.89501953125}, {"start": 1683.73, "end": 1684.45, "word": " ال", "probability": 0.92431640625}, {"start": 1684.45, "end": 1685.01, "word": " F", "probability": 0.7490234375}, {"start": 1685.01, "end": 1685.89, "word": " R", "probability": 0.58837890625}, {"start": 1685.89, "end": 1686.61, "word": " inverse", "probability": 0.916015625}, {"start": 1686.61, "end": 1689.47, "word": " طيب", "probability": 0.8160807291666666}, {"start": 1689.47, "end": 1690.05, "word": " استنى", "probability": 0.68017578125}, {"start": 1690.05, "end": 1690.51, "word": " شوية", "probability": 0.943359375}], "temperature": 1.0}, {"id": 69, "seek": 170998, "start": 1707.18, "end": 1709.98, "text": "مصبوط هكذا؟", "tokens": [2304, 9381, 3555, 2407, 9566, 8032, 4117, 15730, 22807], "avg_logprob": -0.5144531071186066, "compression_ratio": 0.65625, "no_speech_prob": 0.0, "words": [{"start": 1707.1799999999998, "end": 1708.58, "word": "مصبوط", "probability": 0.704248046875}, {"start": 1708.58, "end": 1709.98, "word": " هكذا؟", "probability": 0.68743896484375}], "temperature": 1.0}, {"id": 70, "seek": 172610, "start": 1718.16, "end": 1726.1, "text": "طيب هذا كلام صحيح if and only if ال R F بدها تساوي", "tokens": [9566, 1829, 3555, 23758, 28242, 10943, 20328, 5016, 1829, 5016, 498, 293, 787, 498, 2423, 497, 479, 47525, 11296, 6055, 3794, 995, 45865], "avg_logprob": -0.24446613217393556, "compression_ratio": 0.9375, "no_speech_prob": 0.0, "words": [{"start": 1718.16, "end": 1718.58, "word": "طيب", "probability": 0.6841227213541666}, {"start": 1718.58, "end": 1718.98, "word": " هذا", "probability": 0.83447265625}, {"start": 1718.98, "end": 1719.56, "word": 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يبقى هذه اف ار اف بدي ساوي ال .. اذا كانت الار اف بدي ساوي الاف ار طيب وين الاف ار؟ طيب خليها ماشية", "tokens": [2407, 9957, 2423, 9640, 1975, 5172, 39896, 11296, 22807, 9122, 3215, 3224, 1975, 8592, 23032, 6027, 3615, 4724, 1829, 3794, 995, 45865, 22807, 1975, 5172, 1975, 2288, 16472, 5172, 2288, 3794, 12399, 3714, 19913, 3555, 2407, 9566, 22807, 7251, 3555, 4587, 7578, 29538, 1975, 5172, 1975, 2288, 1975, 5172, 4724, 16254, 8608, 995, 45865, 2423, 4386, 1975, 15730, 25961, 2655, 2423, 9640, 1975, 5172, 4724, 16254, 8608, 995, 45865, 2423, 31845, 1975, 2288, 23032, 1829, 3555, 4032, 9957, 2423, 31845, 1975, 2288, 22807, 23032, 1829, 3555, 16490, 20292, 11296, 3714, 33599, 10632], "avg_logprob": -0.3293010778324578, "compression_ratio": 1.8972602739726028, "no_speech_prob": 0.0, "words": [{"start": 1727.59, "end": 1728.11, "word": "وين", "probability": 0.32366943359375}, {"start": 1728.11, "end": 1728.47, "word": " الار", "probability": 0.51251220703125}, {"start": 1728.47, "end": 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يبقى هذا الكلام صحيء إذا كان الـ RF بدي ساومين الـ FR inverse", "tokens": [3555, 1863, 7435, 3555, 8717, 39648, 23758, 2423, 28820, 10943, 2423, 39184, 26204, 4724, 16254, 8608, 995, 45865, 2423, 39184, 15288, 17340, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 34105, 7251, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 38207, 11933, 15730, 25961, 2423, 39184, 26204, 4724, 16254, 8608, 995, 20498, 9957, 2423, 39184, 15288, 17340], "avg_logprob": -0.3053495803121793, "compression_ratio": 1.6492537313432836, "no_speech_prob": 0.0, "words": [{"start": 1750.9, "end": 1751.46, "word": "بنجب", "probability": 0.445831298828125}, {"start": 1751.46, "end": 1751.78, "word": " نقول", "probability": 0.771484375}, {"start": 1751.78, "end": 1752.2, "word": " هذا", "probability": 0.69775390625}, {"start": 1752.2, "end": 1752.8, "word": " الكلام", "probability": 0.8995768229166666}, {"start": 1752.8, "end": 1753.12, "word": " الـ", "probability": 0.32647705078125}, {"start": 1753.12, 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"word": " لا", "probability": 0.92919921875}, {"start": 2341.94, "end": 2342.92, "word": " يسوى", "probability": 0.9390869140625}, {"start": 2342.92, "end": 2344.12, "word": " تمام؟", "probability": 0.6990559895833334}, {"start": 2344.12, "end": 2344.5, "word": " يبقى", "probability": 0.9737548828125}, {"start": 2344.5, "end": 2344.9, "word": " بناء", "probability": 0.9677734375}, {"start": 2344.9, "end": 2345.46, "word": " عليه", "probability": 0.9716796875}, {"start": 2345.46, "end": 2345.92, "word": " بقول", "probability": 0.955322265625}, {"start": 2345.92, "end": 2346.22, "word": " هذه", "probability": 0.55810546875}, {"start": 2346.22, "end": 2346.7, "word": " النقطة", "probability": 0.9723307291666666}, {"start": 2346.7, "end": 2347.3, "word": " الأولى", "probability": 0.9759114583333334}, {"start": 2347.3, "end": 2348.06, "word": " النقطة", "probability": 0.9775390625}, {"start": 2348.06, "end": 2348.48, "word": " التانية", "probability": 0.9677734375}, {"start": 2348.48, 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"probability": 0.8055013020833334}, {"start": 2372.62, "end": 2373.56, "word": " Group", "probability": 0.58935546875}, {"start": 2373.56, "end": 2375.2, "word": " طيب", "probability": 0.8623046875}, {"start": 2375.2, "end": 2376.12, "word": " ناخد", "probability": 0.9498697916666666}, {"start": 2376.12, "end": 2376.7, "word": " مثال", "probability": 0.985595703125}, {"start": 2376.7, "end": 2377.38, "word": " بسيط", "probability": 0.997314453125}, {"start": 2377.38, "end": 2378.08, "word": " example", "probability": 0.185546875}, {"start": 2378.08, "end": 2379.2, "word": " let", "probability": 0.62353515625}], "temperature": 1.0}, {"id": 98, "seek": 240642, "start": 2384.05, "end": 2406.43, "text": "الـ G تسوي الـ D4 الـ D4 ثم بدّي الـ Centralizer للـ R نوت مين بيطلع دي كلها طيب هل هو الـ Centralizer للـ R 180", "tokens": [6027, 39184, 460, 6055, 3794, 45865, 2423, 39184, 413, 19, 2423, 39184, 413, 19, 38637, 2304, 47525, 11703, 1829, 2423, 39184, 9701, 6545, 24976, 39184, 497, 8717, 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"probability": 0.9931640625}, {"start": 2403.07, "end": 2403.53, "word": " الـ", "probability": 0.6082763671875}, {"start": 2403.53, "end": 2404.81, "word": " Centralizer", "probability": 0.944091796875}, {"start": 2404.81, "end": 2405.35, "word": " للـ", "probability": 0.927978515625}, {"start": 2405.35, "end": 2405.73, "word": " R", "probability": 0.92041015625}, {"start": 2405.73, "end": 2406.43, "word": " 180", "probability": 0.443359375}], "temperature": 1.0}, {"id": 99, "seek": 243471, "start": 2408.15, "end": 2434.71, "text": "صحيح لغرمية ابنكم يسمع الكل يريد عن جديكوا بس و هذا بدي يسوي D4 كله يبقى هذا بدي يعطينا D4 كله طب لو بدي ال centralizer لل R90 هل هذا هو ال centralizer لل R270؟", "tokens": [9381, 5016, 1829, 5016, 5296, 17082, 2288, 2304, 10632, 48127, 1863, 24793, 7251, 38251, 3615, 2423, 28820, 7251, 16572, 3215, 18871, 10874, 16254, 4117, 14407, 4724, 3794, 4032, 23758, 4724, 16254, 7251, 3794, 45865, 413, 19, 28242, 3224, 7251, 3555, 4587, 7578, 23758, 4724, 16254, 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"probability": 0.406005859375}, {"start": 2926.47, "end": 2926.83, "word": " واحد", "probability": 0.992431640625}, {"start": 2926.83, "end": 2927.11, "word": " بس", "probability": 0.8662109375}, {"start": 2927.11, "end": 2927.39, "word": " يحكي،", "probability": 0.84130859375}, {"start": 2927.39, "end": 2927.69, "word": " واحد", "probability": 0.970947265625}, {"start": 2927.69, "end": 2928.05, "word": " يحكي", "probability": 0.97412109375}, {"start": 2928.05, "end": 2928.17, "word": " بقى،", "probability": 0.708740234375}, {"start": 2928.17, "end": 2928.91, "word": " ايه؟", "probability": 0.64068603515625}, {"start": 2928.91, "end": 2936.69, "word": " اه،", "probability": 0.5677897135416666}, {"start": 2936.69, "end": 2936.97, "word": " يعني", "probability": 0.981689453125}, {"start": 2936.97, "end": 2937.45, "word": " هيك،", "probability": 0.7639973958333334}, {"start": 2937.45, "end": 2938.17, "word": " برضه", "probability": 0.9601236979166666}, {"start": 2938.17, "end": 2938.67, "word": " مظبوط،", "probability": 0.7835286458333334}, {"start": 2938.67, "end": 2938.97, "word": " ممكن", "probability": 0.990234375}, {"start": 2938.97, "end": 2939.35, "word": " ناخد", "probability": 0.93359375}, {"start": 2939.35, "end": 2939.61, "word": " x", "probability": 0.47021484375}, {"start": 2939.61, "end": 2939.85, "word": ",y", "probability": 0.6278076171875}, {"start": 2939.85, "end": 2940.21, "word": " وممكن", "probability": 0.796875}, {"start": 2940.21, "end": 2940.47, "word": " ناخد", "probability": 0.99072265625}, {"start": 2940.47, "end": 2940.65, "word": " x", "probability": 0.92578125}, {"start": 2940.65, "end": 2940.85, "word": ",y", "probability": 0.920654296875}, {"start": 2940.85, "end": 2941.17, "word": " inverse", "probability": 0.69677734375}, {"start": 2941.17, "end": 2941.43, "word": " مرة", "probability": 0.9814453125}, {"start": 2941.43, "end": 2941.73, "word": " واحد،", "probability": 0.7554524739583334}, {"start": 2941.73, "end": 2942.43, "word": " عشقتين،", "probability": 0.79736328125}, {"start": 2942.43, "end": 2942.61, "word": " يا", "probability": 0.54541015625}, {"start": 2942.61, "end": 2942.87, "word": " ناس", "probability": 0.98193359375}, {"start": 2942.87, "end": 2943.75, "word": " بضرورة،", "probability": 0.6078694661458334}, {"start": 2943.75, "end": 2944.09, "word": " ممكن", "probability": 0.98681640625}, {"start": 2944.09, "end": 2944.65, "word": " استفيد", "probability": 0.8057861328125}, {"start": 2944.65, "end": 2944.81, "word": " من", "probability": 0.99462890625}, {"start": 2944.81, "end": 2945.43, "word": " هذه،", "probability": 0.827880859375}, {"start": 2945.43, "end": 2945.87, "word": " ان", "probability": 0.77001953125}, {"start": 2945.87, "end": 2946.77, "word": " الـA", "probability": 0.603759765625}], "temperature": 1.0}, {"id": 120, "seek": 296215, "start": 2957.33, "end": 2962.15, "text": "على أي حال بنكمل المرة القادمة ان شاء الله", "tokens": [3615, 23942, 36632, 11331, 6027, 4724, 1863, 24793, 1211, 9673, 25720, 25062, 18513, 46007, 16472, 13412, 16606, 21984], "avg_logprob": -0.35053453633659765, "compression_ratio": 1.1014492753623188, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 2957.3300000000004, "end": 2958.01, "word": "على", "probability": 0.391357421875}, {"start": 2958.01, "end": 2958.19, "word": " أي", "probability": 0.54052734375}, {"start": 2958.19, "end": 2959.43, "word": " حال", "probability": 0.99755859375}, {"start": 2959.43, "end": 2960.35, "word": " بنكمل", "probability": 0.7166748046875}, {"start": 2960.35, "end": 2960.69, "word": " المرة", "probability": 0.810302734375}, {"start": 2960.69, "end": 2961.29, "word": " القادمة", "probability": 0.9861653645833334}, {"start": 2961.29, "end": 2961.51, "word": " ان", "probability": 0.64013671875}, {"start": 2961.51, "end": 2961.83, "word": " شاء", "probability": 0.98046875}, {"start": 2961.83, "end": 2962.15, "word": " الله", "probability": 0.9384765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2963.14475, "duration_after_vad": 2779.2287499999916}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f8374a9a83535b4df5cc8f7c37ca5a245f8f27a7
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XA6IR2bmMHM_raw.srt
@@ -0,0 +1,1836 @@
+1
+00:00:21,330 --> 00:00:26,210
+بسم الله الرحمن الرحيم المرة الماضية اخر حاجة
+
+2
+00:00:26,210 --> 00:00:29,750
+اتكلمنا فيها اعطينا definition لل center لل group
+
+3
+00:00:30,390 --> 00:00:36,030
+بنعيد هذا ال definition ومن ثم ناخد نظرية عليه
+
+4
+00:00:36,030 --> 00:00:41,050
+فقلنا المرة اللي فاتت ان ال center تبع ال group G
+
+5
+00:00:41,050 --> 00:00:47,610
+هديله رمز Z of G وقلنا هو كل العلاصر ال A اللي
+
+6
+00:00:47,610 --> 00:00:55,510
+موجودة في G بحيث ان ال AX بده يساوي ال XA لكل ال X
+
+7
+00:00:55,510 --> 00:01:02,150
+اللي belongs to main to group Gإذا ما معنى الـ
+
+8
+00:01:02,150 --> 00:01:05,510
+Center تبع الـ Group؟ معنى الـ Center تبع الـ
+
+9
+00:01:05,510 --> 00:01:11,070
+Group هو كل ال elements اللي كميوتس عمّا بقية
+
+10
+00:01:11,070 --> 00:01:15,090
+عناصر الـ Group يعني لو أخدت element لجيته كميوتس
+
+11
+00:01:15,090 --> 00:01:18,030
+مع جميع عناصر الـ Group بقول هذا من الـ Center
+
+12
+00:01:18,030 --> 00:01:22,970
+اللي بعد اللي بعد لغاية ما طلع كل العناصر اللي
+
+13
+00:01:22,970 --> 00:01:28,500
+بتكون كميوتس مع جميع عناصر الـ Groupيبقى هذول
+
+14
+00:01:28,500 --> 00:01:32,560
+بيكونول مين؟ بيكونول ال center تبع ال group أبسط
+
+15
+00:01:32,560 --> 00:01:37,380
+الأشياء ال identity element موجود في مين؟ في ال
+
+16
+00:01:37,380 --> 00:01:40,260
+center تبع ال group لأن ال identity elements
+
+17
+00:01:40,260 --> 00:01:45,740
+commutes with all elements of G يبقى كل العناصر
+
+18
+00:01:45,740 --> 00:01:51,520
+اللي موجودة في G و اللي بتبقى commutes مع أي عنصر
+
+19
+00:01:51,520 --> 00:01:56,490
+موجود في G يبقى هذا بسميه ال center of Gالان في
+
+20
+00:01:56,490 --> 00:02:01,530
+نظرية بتقول الـ center هذا هو الـ subgroup فبدنا
+
+21
+00:02:01,530 --> 00:02:06,670
+نروح نبره انصحة هذا الكلام يبقى النظرية بتقول ما
+
+22
+00:02:06,670 --> 00:02:13,070
+يأتي theorem z
+
+23
+00:02:13,070 --> 00:02:18,430
+of g the
+
+24
+00:02:18,430 --> 00:02:23,570
+center of
+
+25
+00:02:23,570 --> 00:02:33,340
+a groupG is a
+
+26
+00:02:33,340 --> 00:02:39,720
+subgroup of
+
+27
+00:02:39,720 --> 00:02:41,020
+G
+
+28
+00:02:51,670 --> 00:02:56,290
+يبقى انا مشان اثبت انه ال 6 المعرفة بالشكل هنا
+
+29
+00:02:56,290 --> 00:03:02,490
+subgroup من لجروب الأساسية دي بدي اثبت النقطتين
+
+30
+00:03:02,490 --> 00:03:08,810
+اول شئ انه Z of G none empty الأمر الثاني بدي اثبت
+
+31
+00:03:08,810 --> 00:03:15,350
+انه انه اي عنصر لو أخدته او اي عنصرين لو أخدته من
+
+32
+00:03:15,350 --> 00:03:18,750
+ال center بدي يكون الأول في معكوس الثاني موجود
+
+33
+00:03:18,750 --> 00:03:25,220
+وين؟ موجود في ال centerيبقى أول شي أنا أدعي ان ال
+
+34
+00:03:25,220 --> 00:03:32,400
+z of g is non-empty وهذه هي النقطة الأولى في
+
+35
+00:03:32,400 --> 00:03:40,150
+البرهان non-empty ليش؟ becauseالـ E موجود في الـ Z
+
+36
+00:03:40,150 --> 00:03:47,610
+of G لأيش؟ لأن الـ E X بده يساوي X E لكل الـ X
+
+37
+00:03:47,610 --> 00:03:56,650
+اللي موجود لأن الـ E X بده يساوي الـ X في الـ E
+
+38
+00:03:56,650 --> 00:04:04,040
+لكل الـ X اللي موجودة في G بلا استثناءيبقى نظرا
+
+39
+00:04:04,040 --> 00:04:07,780
+لإنه يحقق الخاصية تبع الـ center تبع ال group إذا
+
+40
+00:04:07,780 --> 00:04:13,680
+على الأقل فيها element واحد اللي هو ال E الآن
+
+41
+00:04:13,680 --> 00:04:20,700
+بتروح اخد two elements النقطة الثانية let a و b
+
+42
+00:04:20,700 --> 00:04:27,960
+belongs to z of gلما أقول two elements هدول
+
+43
+00:04:27,960 --> 00:04:34,760
+موجودات في Z of G يبقى بد يكون عندنا ال A X بد
+
+44
+00:04:34,760 --> 00:04:44,800
+يساوي ال X A and ال B X بد يساوي X B لكل ال X اللي
+
+45
+00:04:44,800 --> 00:04:47,400
+موجود في G بي less تتنعى
+
+46
+00:04:50,150 --> 00:04:54,250
+يبقى هذا ال element موجود في ال center إذا بدي
+
+47
+00:04:54,250 --> 00:04:58,790
+أحقق للخاصية اللي فوق تبعت ال center بي موجود في
+
+48
+00:04:58,790 --> 00:05:03,590
+ال center إذا بدي أحقق لنفس الخاصية يبقى أنا أخدت
+
+49
+00:05:03,590 --> 00:05:08,050
+عنصرين موجودات في ال center تبع ال group بدي أثبت
+
+50
+00:05:08,050 --> 00:05:13,350
+إن الأول في معكوسي ثاني موجود في مين في ال center
+
+51
+00:05:13,350 --> 00:05:21,040
+بمعنى آخرأريد أن أثبت أن a b inverse x هو x a b
+
+52
+00:05:21,040 --> 00:05:27,360
+inverse لكل x موجودة في g بلا استثناء يبقى بداجي
+
+53
+00:05:27,360 --> 00:05:34,740
+أقول له consider خد أن a b inverse x
+
+54
+00:05:38,410 --> 00:05:46,950
+بتشوف هذا بدي أثبت و بدي أثبت و بدي أثبت
+
+55
+00:05:46,950 --> 00:05:48,290
+و بدي أثبت و بدي أثبت و بدي أثبت و بدي أثبت و بدي
+
+56
+00:05:48,290 --> 00:05:57,150
+أثبت و بدي أثبت و بدي أثبت
+
+57
+00:05:57,980 --> 00:06:03,900
+يبقى هذا الكلام بده يساوي بدي أحاول أربط ما بين ال
+
+58
+00:06:03,900 --> 00:06:08,780
+X و ال B اللي عندنا يبقى لو جيت قولت هذا A B
+
+59
+00:06:08,780 --> 00:06:16,420
+inverse ال X أخدتها X inverse inverse طبعا برهنها
+
+60
+00:06:16,420 --> 00:06:23,600
+سابقا يبقى هذا الكلام بده يساوي A فاهمين؟ فبصير X
+
+61
+00:06:23,600 --> 00:06:30,770
+inverse B لكل inverseهذه انفرس وهذه انفرس يبقى
+
+62
+00:06:30,770 --> 00:06:35,330
+رجعتهم للأصل اللي بتبعهم بالشكل اللي عندنا هذا طيب
+
+63
+00:06:35,330 --> 00:06:40,170
+الآن P موجودة في ال center ولا لأ يبقى commutes مع
+
+64
+00:06:40,170 --> 00:06:43,270
+ال X وال X انفرس لأنها موجودة في ال center يعني
+
+65
+00:06:43,270 --> 00:06:47,910
+commutes مع any element موجود في ال group G يبقى
+
+66
+00:06:47,910 --> 00:06:56,670
+هذا الكلام بده يساوي A و هنا B X انفرس الكل انفرس
+
+67
+00:07:00,860 --> 00:07:05,520
+ليش هذا الخطوة عملتها؟ لأن بي موجودة في الـ Center
+
+68
+00:07:05,520 --> 00:07:11,600
+يبقى هذه الـ Sense بي موجودة في الـ Center تبع الـ
+
+69
+00:07:11,600 --> 00:07:17,580
+G هذا الكلام بده يساوي لو جيتلي هذا الآن بده أطبق
+
+70
+00:07:17,580 --> 00:07:22,940
+عليها تعريف المعكوس لحظة حصل ضرب two elements يبقى
+
+71
+00:07:22,940 --> 00:07:26,020
+هذا بيصير A في X
+
+72
+00:07:28,710 --> 00:07:37,090
+إنفرس إنفرس وهنا اللي هو بي انفرس يبقى وزعة ال
+
+73
+00:07:37,090 --> 00:07:42,210
+inverse لكل واحدة من هدول يبقى هذه ابتنقلة يبقى
+
+74
+00:07:42,210 --> 00:07:49,770
+هذه إيش بصير ax في ال b inverseالان انا عندى من
+
+75
+00:07:49,770 --> 00:07:57,330
+المعطيات ان a x يساوي main x a يبقى هذا الكلام بدي
+
+76
+00:07:57,330 --> 00:08:06,810
+يعطينا x a في ال b inverse ليش هذا ال sense ال a
+
+77
+00:08:06,810 --> 00:08:13,150
+موجودة في ال center تبع ال gطيب هذا الكلام بده
+
+78
+00:08:13,150 --> 00:08:19,770
+يساوي من خاصية ال associativity XAB inverse بالشكل
+
+79
+00:08:19,770 --> 00:08:25,090
+اللي عندناطب ايش اللي عملته انا حتى اللحظة اخدت a
+
+80
+00:08:25,090 --> 00:08:31,250
+b inverse x لجيته يساوي x a b inverse هذا الكلام
+
+81
+00:08:31,250 --> 00:08:37,590
+صحيح لكل ال x اللي موجودة في g plus تتنى ايش
+
+82
+00:08:37,590 --> 00:08:42,370
+تفسيرك لهذا الكلام يبقى ال a b inverse موجود وين
+
+83
+00:08:42,370 --> 00:08:45,990
+في ال center تبع ال group وبالتالي ال center عبارة
+
+84
+00:08:45,990 --> 00:08:53,880
+عن sub groupيبقى هنا سوا ال a b inverse belongs لل
+
+85
+00:08:53,880 --> 00:09:03,920
+z of g and hence ومن ثم ال z of g is a subgroup من
+
+86
+00:09:03,920 --> 00:09:05,060
+g وهو المطلوب
+
+87
+00:09:08,760 --> 00:09:14,200
+يبقى من الآن فصاعدا ال center تبع ال group هو sub
+
+88
+00:09:14,200 --> 00:09:20,440
+group من من ال group الأساسية طيب يا شباب في عندنا
+
+89
+00:09:20,440 --> 00:09:28,000
+سؤال السؤال لو كانت جي أبيليان جي أبيليان يبقى ال
+
+90
+00:09:28,000 --> 00:09:34,040
+center تبع ال group بيكون كل group يبقى هذه اكتبها
+
+91
+00:09:34,040 --> 00:09:46,500
+ملاحظة not fالـ G is abelian then ال center تبع
+
+92
+00:09:46,500 --> 00:09:53,280
+الـ G بده يسوي الـ G itself كلها بلا استثناء نبدأ
+
+93
+00:09:53,280 --> 00:10:04,080
+ناخد أمثلة examples أول مثال بيقول let ال G هي ال
+
+94
+00:10:04,080 --> 00:10:09,550
+generalLinear group of two by two matrices over R
+
+95
+00:10:09,550 --> 00:10:21,390
+Then بدنا Z of G بد Z of G هو عبارة عن مين أنا
+
+96
+00:10:21,390 --> 00:10:31,090
+أدعي أن Z of G كل المصوفة على صيغة A 00A و بحيث ال
+
+97
+00:10:31,090 --> 00:10:41,300
+A موجود في Rوالـ A هذا لا يساوي Zero الكلام
+
+98
+00:10:41,300 --> 00:10:44,760
+هذا صحيح ولا ما هو مش صحيح الله وعلا أنا أدعي
+
+99
+00:10:44,760 --> 00:10:51,040
+ادعاء باجي بقول والله إذا لقيت هذا المصوفات كلهم
+
+100
+00:10:51,040 --> 00:10:56,540
+اللي موجودة في Z of G commutes with any element في
+
+101
+00:10:56,540 --> 00:11:00,180
+ال general linear غروب يصيب كلامنا صحيح من اليمين
+
+102
+00:11:00,180 --> 00:11:05,450
+ومن الشمال ماطلة يبقى كلامنا معله غير صحيحلذلك
+
+103
+00:11:05,450 --> 00:11:11,310
+بأجي بقولك هذا الكلام because بدي أجي ال element
+
+104
+00:11:11,310 --> 00:11:17,230
+اللي موجود في ال center a zero zero a بدي أضربه في
+
+105
+00:11:17,230 --> 00:11:21,230
+أي element موجود في ال general linear group بدي
+
+106
+00:11:21,230 --> 00:11:28,810
+أخد b, c, d, f مثلا بديش اكتب ال a بلاش تقولي ايه
+
+107
+00:11:28,810 --> 00:11:34,160
+هذا هو ال identity elementإذا هذه لو جيت ضربتها
+
+108
+00:11:34,160 --> 00:11:40,400
+بدها تساوي الصف الأول في العمود الأول اللي هو AB
+
+109
+00:11:40,400 --> 00:11:47,560
+الصف الأول في العمود الثاني يبقى بAC الصف الثاني
+
+110
+00:11:47,560 --> 00:11:53,260
+في العمود الأول يبقى بAD الصف الثاني في العمود
+
+111
+00:11:53,260 --> 00:12:06,450
+الثاني بAFاللي بقدر اكتبها a في b,c,d,f الان بداتي
+
+112
+00:12:06,450 --> 00:12:16,420
+اخدله اللي هو b,c,d,f في ال a,0,0,aيبقى هذا معناه
+
+113
+00:12:16,420 --> 00:12:23,180
+صف الأول في العمود الأول BA الصف الأول في العمود
+
+114
+00:12:23,180 --> 00:12:29,960
+الثاني CA الصف الثاني في العمود الأول DA الصف
+
+115
+00:12:29,960 --> 00:12:37,240
+الثاني في العمود الثاني يبقى FAلو أخدت ال a من كل
+
+116
+00:12:37,240 --> 00:12:42,340
+element موجود داخل المصوفة بيظهر لنا مين بي بي بي
+
+117
+00:12:42,340 --> 00:12:43,680
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+118
+00:12:43,680 --> 00:12:50,000
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+119
+00:12:50,780 --> 00:12:56,080
+ما دام اريكوا المعناته فعلا هذا يمثل main ال
+
+120
+00:12:56,080 --> 00:13:01,480
+center او المصفوفة اللي عندنا هذه هي element موجود
+
+121
+00:13:01,480 --> 00:13:07,380
+وان موجود في ال center هذا بدي اعطيلك ان any
+
+122
+00:13:07,380 --> 00:13:09,140
+element
+
+123
+00:13:11,320 --> 00:13:22,860
+in z of g is in the form على الشكل اللي هو a zero
+
+124
+00:13:22,860 --> 00:13:30,410
+zero aوالـ A does not equal to zero يبقى من الأن
+
+125
+00:13:30,410 --> 00:13:34,110
+فصاعدا لما بد ال center لل general linear group of
+
+126
+00:13:34,110 --> 00:13:38,670
+two by two matrices over R بيكون عندي واحد زيرو
+
+127
+00:13:38,670 --> 00:13:43,030
+زيرو واحد اتنين زيرو زيرو واحد مص زيرو زيرو واحد
+
+128
+00:13:43,030 --> 00:13:48,310
+واحد على مية زيرو زيرو واحد على مية و هكذايبقى كل
+
+129
+00:13:48,310 --> 00:13:53,590
+العناصر القطرة الرئيسى بيكون عناصرهم متساوية وهذه
+
+130
+00:13:53,590 --> 00:13:59,170
+بقينا نسميها في ال linear algebra بقيناها نسميها
+
+131
+00:13:59,170 --> 00:14:05,830
+المصوفة شو اسمها؟ مصوفة الواحدة قطرية
+
+132
+00:14:05,830 --> 00:14:12,150
+لما العناصر القطرة الرئيسى يكونوا متساوية بقيناش
+
+133
+00:14:12,150 --> 00:14:14,330
+نسميها مثلثية
+
+134
+00:14:17,700 --> 00:14:24,520
+بنسميها scalar matrix او مقياسية
+
+135
+00:14:24,520 --> 00:14:28,940
+لو كان القطرين غير متسوين بيقول دياجون الماتريك
+
+136
+00:14:28,940 --> 00:14:31,240
+دياجون الماتريك هي فعلا دياجون الماتريك في المصحوف
+
+137
+00:14:31,240 --> 00:14:36,060
+القطرية بس إذا تسابق عناصر القطر الرئيسي بنسميها
+
+138
+00:14:36,060 --> 00:14:41,070
+scalar matrixيبقى كل scalar matrix في ال general
+
+139
+00:14:41,070 --> 00:14:44,790
+linear group of two by two matrices بيكونولي main
+
+140
+00:14:44,790 --> 00:14:50,790
+بيكونولي ال center لل group اللي عندنا طيب نمرتنا
+
+141
+00:14:50,790 --> 00:15:01,990
+example two بدنا z of D4 يساوي أكيد ال R node منهم
+
+142
+00:15:01,990 --> 00:15:07,240
+هذا كل مجمع ليه لأنه ال identityحد بيقدر يجيبلي
+
+143
+00:15:07,240 --> 00:15:16,240
+كمان element اخر تسعين commutes مع الكل تسعين
+
+144
+00:15:16,240 --> 00:15:19,860
+commutes مع المية وتمانين ومع الميتين وسبعين مع ال
+
+145
+00:15:19,860 --> 00:15:25,580
+rotations نعم لكن مع ال reflections ليس صحيحا
+
+146
+00:15:25,580 --> 00:15:31,960
+واثبتلك ان ر تسعين في H ليسوا ال H في R تسعين
+
+147
+00:15:31,960 --> 00:15:39,720
+وحسبتهم لك انتالـ R180 فقط لا غير يبقى هذه والـ
+
+148
+00:15:39,720 --> 00:15:48,060
+R180 فقط لا غير يبقى هدول بس عناصر الـ Center تبعي
+
+149
+00:15:48,060 --> 00:15:52,600
+الـ D4 غير هيك مافيش ولا elements طبعا لو رجعت
+
+150
+00:15:52,600 --> 00:15:58,720
+للجدول اللي في الصفحة واحدة و تلاتين الكليتابل للـ
+
+151
+00:15:58,720 --> 00:16:05,880
+D4بتلاقي ان ال R180 هي ال commutes مع جميع عناصر
+
+152
+00:16:05,880 --> 00:16:10,280
+D4 بالاضافة الى ال identity element اللي هو main
+
+153
+00:16:10,670 --> 00:16:16,350
+اللي هو Arnold يبقى هذول ال two elements هم اللي
+
+154
+00:16:16,350 --> 00:16:21,890
+commutes مع جميع عناصر D4 فقط لا غير طيب إيش رأيك
+
+155
+00:16:21,890 --> 00:16:27,650
+بدي أعمملك هالشغل هذه بدل ما أاخد D4 بدي أاخد DN
+
+156
+00:16:27,650 --> 00:16:35,950
+يبقى الآن in general لو
+
+157
+00:16:35,950 --> 00:16:46,670
+أخدت ال Z of DMهذه أحد أمرين يا إما الارنود والار
+
+158
+00:16:46,670 --> 00:16:55,750
+مية و تمانين فقط يا إما الارنود السؤال هو متى يحدث
+
+159
+00:16:55,750 --> 00:17:01,950
+هذا و متى يحدث هذا الان في D4 الرقم هذا زوجي والله
+
+160
+00:17:01,950 --> 00:17:09,870
+فردي زوجييبقى هذا يحدث لو كان ال in فرديا يبقى هنا
+
+161
+00:17:09,870 --> 00:17:21,630
+هذا الكلام if in is even او هذا if ال in is odd
+
+162
+00:17:21,630 --> 00:17:29,050
+فقط لا غير طبعا يمكن يسأل واحد بعض منكم لماذا هذا
+
+163
+00:17:29,050 --> 00:17:29,750
+الكلام
+
+164
+00:17:40,760 --> 00:17:46,140
+الإجابة بدنا نعطي تفسير ليش هذا الكلام مافيش غرض
+
+165
+00:17:46,140 --> 00:17:54,220
+يبقى اكتب لي this is because يبقى this is because
+
+166
+00:17:54,220 --> 00:18:05,940
+هذا الكلام لإنه this is because every rotation in
+
+167
+00:18:05,940 --> 00:18:07,680
+DN
+
+168
+00:18:09,750 --> 00:18:19,790
+is a power is a power of
+
+169
+00:18:19,790 --> 00:18:28,450
+R تلت مية و ستين على N and
+
+170
+00:18:28,450 --> 00:18:37,790
+rotations and rotations commute
+
+171
+00:18:42,200 --> 00:18:49,400
+and the rotations commute with each other with
+
+172
+00:18:49,400 --> 00:18:59,060
+each other نجي
+
+173
+00:18:59,060 --> 00:19:03,760
+الان لو كان حاصل ضبر rotation في reflection بدا
+
+174
+00:19:03,760 --> 00:19:10,280
+اقولك بدا اعطي تسمية التالية little r b any
+
+175
+00:19:12,530 --> 00:19:31,450
+rotation in DN and let ال F be any reflection برضه
+
+176
+00:19:31,450 --> 00:19:36,290
+in DN in DN
+
+177
+00:19:49,990 --> 00:19:57,070
+مرة أخرى ندعي أن الـ Center تبع ال group D ان سواء
+
+178
+00:19:57,070 --> 00:20:04,330
+كانت D3، D4، D5، D6، جد ما يكون يكون طبعا ال N هذه
+
+179
+00:20:04,330 --> 00:20:10,410
+أكبر من أو تساوي تلاتة ال N اللي عندنا أكبر من أو
+
+180
+00:20:10,410 --> 00:20:15,330
+تساوي تلاتة يعني ممكن يكون مثلث منتظم مربع منتظم
+
+181
+00:20:15,330 --> 00:20:20,390
+مخلص منتظم مسدس منتظم إلى آخرهمإذا والله ال N
+
+182
+00:20:20,390 --> 00:20:28,030
+موجبة زي D4, D6, D8, D10 إلى آخره يبقى العناصر
+
+183
+00:20:28,030 --> 00:20:33,070
+اللي في ال center بس Arnold و R180 الأقل لو كانت
+
+184
+00:20:33,070 --> 00:20:36,670
+ال N فردي تلاتة خمسة سبعة تسعة إلى آخره يبقى لا
+
+185
+00:20:36,670 --> 00:20:40,990
+يوجد في ال center إلا عنصر الوحدة اللي همين Arnold
+
+186
+00:20:40,990 --> 00:20:46,720
+ليش هذا؟لأن أي روتاشن يتعامل مع أي روتاشن أخر مثلا
+
+187
+00:20:46,720 --> 00:20:52,220
+في D4 اذا قلت لك R90 يتعامل مع R180 ويتعامل مع
+
+188
+00:20:52,220 --> 00:20:57,520
+R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+189
+00:20:57,520 --> 00:21:01,300
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+190
+00:21:01,300 --> 00:21:02,380
+يتعامل مع R270 وR270 يتعامل مع R270 وR270 يتعامل
+
+191
+00:21:02,380 --> 00:21:03,200
+مع R270 وR270 يتعامل مع R270 وR270 يتعامل مع R270
+
+192
+00:21:03,200 --> 00:21:07,000
+وR270 يتعامل مع R270 وR270 يتعامل مع R270 وR270
+
+193
+00:21:07,000 --> 00:21:12,500
+يتعامل مع R270 وR270 يتعامل مع R270
+
+194
+00:21:12,500 --> 00:21:17,410
+وR2يبقى ده كميوس باجي بقوله بدي اجي اخد R هي any
+
+195
+00:21:17,410 --> 00:21:23,670
+rotation يعني جربلك الفكرة لو كان ال D4 عندنا يبقى
+
+196
+00:21:23,670 --> 00:21:27,610
+ال R هادي اما R تسعين او مية و تمانين او ميتين و
+
+197
+00:21:27,610 --> 00:21:34,730
+سبعين اي واحدة منهم تمام؟يبقى ال F في كذلك any
+
+198
+00:21:34,730 --> 00:21:39,670
+reflection أي انقلاب سواء كان H و لا V و لا D و لا
+
+199
+00:21:39,670 --> 00:21:45,430
+D' أي واحدة منهم مكتوب معاك ان reflection ضرب
+
+200
+00:21:45,430 --> 00:21:51,530
+rotation يساوي rotation ضرب reflection كله بيعطيني
+
+201
+00:21:51,530 --> 00:21:55,850
+reflection ماقولش يساوي يعني على كل الأمرين بطلعلي
+
+202
+00:21:55,850 --> 00:21:59,090
+reflectionلو ضربت rotation في reflection بده
+
+203
+00:21:59,090 --> 00:22:01,570
+يطلعلي reflection، لو ضربت reflection في rotation
+
+204
+00:22:01,570 --> 00:22:05,170
+بده يطلعلي reflection على كلا الأمرين و مكتوبة
+
+205
+00:22:05,170 --> 00:22:08,130
+معاك هذه كتبناها قبل ذلك
+
+206
+00:22:10,970 --> 00:22:16,690
+أي rotation في ديو 4 هو power of r 360 على n ايش
+
+207
+00:22:16,690 --> 00:22:24,630
+360 على n باجي بقول اه لو كانت n تساوي 4 مثلا يبقى
+
+208
+00:22:24,630 --> 00:22:29,230
+360 على 4 فيها جداش 90 اذا ال rotation الواحدة
+
+209
+00:22:29,230 --> 00:22:35,080
+بتسعين درجةهذا لما يكون مربع طب لو كان مثلث بدي
+
+210
+00:22:35,080 --> 00:22:39,660
+اقسم على تلاتة يبقى ال rotation مقداش مية و عشرين
+
+211
+00:22:39,660 --> 00:22:45,740
+درجة لو كان مخمس لو كان مسدس منتظر يبقى تلاتمية و
+
+212
+00:22:45,740 --> 00:22:49,460
+ستين على ست اللي فيه مقداش ستين يبقى بصير عندي R
+
+213
+00:22:49,460 --> 00:22:55,740
+نوت R ستين R مية و عشرين R مية و تمانين R متينو40
+
+214
+00:22:55,740 --> 00:23:02,820
+R300 R node وهكذا يبقى هكذا تكتب من العناصر وبعدين
+
+215
+00:23:02,820 --> 00:23:06,800
+بروح بدور من ال reflections إلى آخرين ما علينا
+
+216
+00:23:06,800 --> 00:23:13,880
+يبقى المقصود من R360 على N أطلع جداش مقدار الزاوية
+
+217
+00:23:13,880 --> 00:23:18,250
+اللي بأعملبها الدورالة المضلع المنتظم اللي عندي
+
+218
+00:23:18,250 --> 00:23:23,830
+مين مكان ايه يكون تمام اي rotation هديها الرمز R
+
+219
+00:23:23,830 --> 00:23:30,150
+اي reflection هديها ايه هديها الرمز R تمام طيب
+
+220
+00:23:30,150 --> 00:23:36,890
+الان rotation بدي اقول any rotation في reflection
+
+221
+00:23:36,890 --> 00:23:41,930
+بيعطينا reflection او اي reflection في rotation
+
+222
+00:23:41,930 --> 00:23:44,250
+بيعطينا reflection
+
+223
+00:23:58,780 --> 00:24:03,600
+ارنود ال identity element اتحرك مع اي element اخر
+
+224
+00:24:03,600 --> 00:24:10,860
+في ال group ارنود هو دوران بصفر درجةيبقى هذا هو ال
+
+225
+00:24:10,860 --> 00:24:15,860
+identity element كنت حاضر يوم شرحنا ال D4 هذه؟
+
+226
+00:24:15,860 --> 00:24:24,180
+بعوض الله طيب ولا قريتها كمان؟ ماشي طيب هذه دلوقتي
+
+227
+00:24:24,180 --> 00:24:28,440
+عمود فقري روح اقراها تاني غلبتك حاجة حتى و تعالي
+
+228
+00:24:28,440 --> 00:24:32,980
+نشرحلك ماعناش مشكلة المهم لأن هذه عمود فقري كل
+
+229
+00:24:32,980 --> 00:24:37,860
+شوية لجروب و هيطلعانة بدنا نشتغل عليها تمام؟ طيب
+
+230
+00:24:38,150 --> 00:24:43,490
+نرجع لموضوعنا احنا بندعي الان ان ال center لدى N
+
+231
+00:24:43,490 --> 00:24:47,690
+اذا كانت N عددا زوجين ماعنديش الا Arnold وR180
+
+232
+00:24:47,690 --> 00:24:53,970
+واذا كان فاردي ماعنديش الا من Arnold الان بنقول ال
+
+233
+00:24:53,970 --> 00:24:58,950
+rotation ب commutes مع اي rotation اخرى وضربتلك من
+
+234
+00:24:58,950 --> 00:25:04,490
+93 مع 180 مع 270 كلهم commutes هدول مع بعض مع ال
+
+235
+00:25:04,490 --> 00:25:09,480
+Arnold كمان اللي هو ال identityالان اي rotation
+
+236
+00:25:09,480 --> 00:25:15,000
+حديها الرمز R اي reflection حديها الرمز F الان
+
+237
+00:25:15,000 --> 00:25:22,600
+احنا سابقا برضه باجي بقول since اللي هو ال R في F
+
+238
+00:25:22,600 --> 00:25:25,800
+is a reflection
+
+239
+00:25:28,280 --> 00:25:32,260
+هذه reflection يعني حاصر ضرب ال rotation في ال
+
+240
+00:25:32,260 --> 00:25:36,860
+reflection بيعطيني reflection أو العكس لو كان F في
+
+241
+00:25:36,860 --> 00:25:41,700
+R كمان بيعطينا مين reflection و ما إلى ذلك يبقى
+
+242
+00:25:41,700 --> 00:25:46,300
+نظرا لإن ال R في F is a reflection معناته هذا
+
+243
+00:25:46,300 --> 00:25:55,630
+العنصر معكسه قداشي بيعطينا معكس العنصر هذاأرجع ال
+
+244
+00:25:55,630 --> 00:26:00,450
+D4 مش ال D4 قولنا H تربيعه يسوى ال identity يبقى
+
+245
+00:26:00,450 --> 00:26:05,530
+ال H inverse يبقى كده بال H itself يبقى هو معكوس
+
+246
+00:26:05,530 --> 00:26:12,210
+لنفسه يبقى في هذه لأ it's a reflection we have
+
+247
+00:26:12,210 --> 00:26:22,430
+يبقى بده يصير ال RF بده يسوى ال RF لكل inverseيبقى
+
+248
+00:26:22,430 --> 00:26:29,210
+باجي بقول يبقى صار الار اف بده يساوي الار اف في
+
+249
+00:26:29,210 --> 00:26:35,290
+الكل انفرست وبلغة ال F inverse هذا هو ال F inverse
+
+250
+00:26:35,290 --> 00:26:40,190
+في الار انفرست بلغة المعكوس بتنقل بيقول معكوس
+
+251
+00:26:40,190 --> 00:26:45,290
+الأول للآخر طب ال F reflection لما تبقى ال F
+
+252
+00:26:45,290 --> 00:26:51,340
+reflection يبقى F square قداش مديوطن يا شباباللي
+
+253
+00:26:51,340 --> 00:26:55,420
+هنضل هو ال identity يعني لو جيت قلت ال identity
+
+254
+00:26:55,420 --> 00:27:00,880
+يبقى ال F بالصير هي ال F inverse ولا لا يعني لو
+
+255
+00:27:00,880 --> 00:27:04,480
+ضربت الطرفين في ال F inverse من جهة اليمين او من
+
+256
+00:27:04,480 --> 00:27:09,220
+جهة الشماليبقى هنا بظل قداش بظل F والطرف اليامين
+
+257
+00:27:09,220 --> 00:27:13,620
+هي G F inverse مكتوب معاك هذا V تربية تسوى ال
+
+258
+00:27:13,620 --> 00:27:17,420
+identity في D4 يبقى V بتسوى V inverse H تربية تسوى
+
+259
+00:27:17,420 --> 00:27:20,200
+ال identity يبقى H تسوى H inverse D تربية تسوى ال
+
+260
+00:27:20,200 --> 00:27:23,340
+identity يبقى D بتسوى D ال inverse وD prime زيهم
+
+261
+00:27:23,340 --> 00:27:29,300
+يبقى كل هذا مكتوب معاك يوم أخدنا D4يبقى بناء عليه
+
+262
+00:27:29,300 --> 00:27:34,320
+لما كانت ال F هي reflection يبقى ال F و ال F
+
+263
+00:27:34,320 --> 00:27:41,300
+inverse الشي العلاقة بينهما اتنين are ال F و ال F
+
+264
+00:27:41,300 --> 00:27:42,540
+inverse ال reflection
+
+265
+00:27:47,690 --> 00:27:52,230
+ماذا يحصل علاقة بينهم؟ علاقة تساوي يعني بقدر أشيل
+
+266
+00:27:52,230 --> 00:27:55,590
+ال F و أحط مكانها F inverse و بقدر أشيل F inverse
+
+267
+00:27:55,590 --> 00:27:59,730
+و أحط مكانها ال F هيها قدامك هي على اللوح مكتوبة
+
+268
+00:27:59,730 --> 00:28:09,470
+يبقى بقدر بناء عليه أقول هذه هي ال F R inverse طيب
+
+269
+00:28:09,470 --> 00:28:10,510
+استنى شوية
+
+270
+00:28:27,180 --> 00:28:29,980
+مصبوط هكذا؟
+
+271
+00:28:38,160 --> 00:28:46,100
+طيب هذا كلام صحيح if and only if ال R F بدها تساوي
+
+272
+00:28:47,590 --> 00:28:53,690
+وين الار اف هيها؟ كده اش طالع بيساوي؟ اف ار انفرس،
+
+273
+00:28:53,690 --> 00:29:03,130
+مظبوط؟ يبقى هذه اف ار اف بدي ساوي ال .. اذا كانت
+
+274
+00:29:03,130 --> 00:29:09,630
+الار اف بدي ساوي الاف ار طيب وين الاف ار؟ طيب
+
+275
+00:29:09,630 --> 00:29:16,200
+خليها ماشيةبنجب نقول هذا الكلام الـ RF بدي ساوي
+
+276
+00:29:16,200 --> 00:29:20,220
+الـ
+
+277
+00:29:20,220 --> 00:29:27,760
+FR inverse بالشكل اللي عندنا هنا يبقى هذا الكلام
+
+278
+00:29:27,760 --> 00:29:33,570
+صحيء إذا كان الـ RF بدي ساومين الـ FR inverseطيب
+
+279
+00:29:33,570 --> 00:29:40,070
+الان انا بقدر اشيل ال F و احط مكانها من ال F
+
+280
+00:29:40,070 --> 00:29:46,290
+inverse و ارجعها كيف ده سيه لحظة شوية طيب عندك ال
+
+281
+00:29:46,290 --> 00:29:51,230
+RF يسوى ال FR inverse مظبوط ال R كما نسميه اذا كان
+
+282
+00:29:51,230 --> 00:29:58,350
+ال FR بديه يسوى اذا كان ال FR بديه يسوى RF استنى
+
+283
+00:29:58,350 --> 00:30:01,130
+شوية اذا كان ال F
+
+284
+00:30:04,870 --> 00:30:19,850
+فار فار فار فار فار فار فار فار فار فار فار
+
+285
+00:30:28,490 --> 00:30:34,610
+الـ R F Inverse لأيش؟ لأن الـ F هي تساوي مين؟
+
+286
+00:30:34,610 --> 00:30:40,450
+تساوي الـ F Inverse itself تمام؟ يبقى هذا بيساوي
+
+287
+00:30:40,450 --> 00:30:47,150
+الـ R Inverse F itself يبقى أصار F R Inverse
+
+288
+00:30:50,680 --> 00:30:57,700
+يبقى فان ال F R بدينا فيها بدي يساوي R F وهذا R F
+
+289
+00:30:57,700 --> 00:31:07,380
+اللي عندنا يساوي F R Inverse هذي بدي يساوي F R
+
+290
+00:31:07,380 --> 00:31:12,680
+Inverse هي الكلام صحيح يبقى أنا بديت هدول التنين
+
+291
+00:31:12,680 --> 00:31:18,160
+كموسي ده كان ال F R بدي يساوي من R Fهذا الكلام
+
+292
+00:31:18,160 --> 00:31:24,080
+يساوي هاي RF من فوق شيلتها و جيبت بدالها مين؟ F R
+
+293
+00:31:24,080 --> 00:31:30,340
+inverse يبقى اطلعلي لهذه و اطلعلي لهذه تمام؟ بال
+
+294
+00:31:30,340 --> 00:31:35,360
+lift cancellation law يبقى هذه ال F بتروح مع هذه
+
+295
+00:31:35,360 --> 00:31:43,480
+بظل F and only F ال R بدها تساوي R inverseإذا كان
+
+296
+00:31:43,480 --> 00:31:49,820
+الـR يسوى الـR inverse الـR يسوى
+
+297
+00:31:49,820 --> 00:31:57,820
+الـR inverse بس في حالة الـ180 يبقى هذا معناه أن R
+
+298
+00:31:57,820 --> 00:32:06,440
+تسوى R 180 درجة وهذا الكلام صحيح لو كانت الـN is
+
+299
+00:32:06,440 --> 00:32:19,190
+even فقط this is a trueفالن is even يبقى بناء عليه
+
+300
+00:32:19,190 --> 00:32:27,310
+z of d فالz of dn بدي يسوى رن ورمية و تمانين في
+
+301
+00:32:27,310 --> 00:32:34,730
+حالة الزوجي والارنود في حالة من في حالة الفرديطب
+
+302
+00:32:34,730 --> 00:32:39,990
+فينا تعريف جديد برضه جريب من ال center بس بيسميه
+
+303
+00:32:39,990 --> 00:32:46,610
+centralizer يبقى definition let
+
+304
+00:32:46,610 --> 00:32:55,270
+ال a be a fixed element
+
+305
+00:32:55,270 --> 00:32:58,350
+of
+
+306
+00:32:58,350 --> 00:33:01,330
+a group G
+
+307
+00:33:04,040 --> 00:33:18,140
+the centralizer of
+
+308
+00:33:18,140 --> 00:33:28,120
+ال element a اللي موجود في g هديله الرمز center of
+
+309
+00:33:28,120 --> 00:33:28,600
+a
+
+310
+00:33:31,400 --> 00:33:42,920
+is the set of all elements the set of all elements
+
+311
+00:33:42,920 --> 00:33:53,620
+in G that commute with
+
+312
+00:33:53,620 --> 00:33:57,700
+A with
+
+313
+00:33:57,700 --> 00:34:01,020
+A that is
+
+314
+00:34:03,590 --> 00:34:12,050
+Centralizer لإيه كل العناصر جي اللي موجودة في جي
+
+315
+00:34:12,050 --> 00:34:18,790
+بحيث ان جي في ايه ساوي ايه في جي
+
+316
+00:34:48,240 --> 00:34:52,400
+نعود للتعريف اللي قلناه و نعود له تاني و نشوف شو
+
+317
+00:34:52,400 --> 00:34:58,360
+بيقولالتعريف بيقول خدلي a fixed element من ال
+
+318
+00:34:58,360 --> 00:35:02,660
+group g بيبقى أخدت عنصر من g سميته a the
+
+319
+00:35:02,660 --> 00:35:08,840
+centralizer of a اللي موجود فيه g يبقى أنا بدى
+
+320
+00:35:08,840 --> 00:35:15,540
+أدور على العناصر اللي بتبقى commutes مع a فقط وبدى
+
+321
+00:35:15,540 --> 00:35:20,900
+أسميهم ال centralizer بهذا ال element aبتعطيه C of
+
+322
+00:35:20,900 --> 00:35:25,400
+A يبقى C of A the centralizer of the element A مين
+
+323
+00:35:25,400 --> 00:35:30,900
+هي؟ هي كل العناصر اللي موجودة في G that commutes
+
+324
+00:35:30,900 --> 00:35:37,060
+with A اللي بتعمل عملية تبديل فقط مع العنصر A مش
+
+325
+00:35:37,060 --> 00:35:40,700
+مع باقي عناصريبقى فيه فرق ما بين الـcenter
+
+326
+00:35:40,700 --> 00:35:44,940
+والـcentralizer الـelement اللي موجود في الـcenter
+
+327
+00:35:44,940 --> 00:35:50,460
+commutes مع جميع عناصر A مع جميع عناصر الجروب G
+
+328
+00:35:50,460 --> 00:35:54,960
+لكن الـcentralizer ليه؟ بس العناصر ي commutes مع
+
+329
+00:35:54,960 --> 00:36:01,260
+مين؟ مع A فقط لغيروالذالك قلنا الـ Centralizer لكل
+
+330
+00:36:01,260 --> 00:36:05,180
+العناصر اللي موجودة في جيه اللي بتبقى commutes مع
+
+331
+00:36:05,180 --> 00:36:11,260
+مين مع ايه فقط بناء على ذلك سنطرح بعض الأسئلة
+
+332
+00:36:11,260 --> 00:36:16,120
+السؤال الأول مين
+
+333
+00:36:16,120 --> 00:36:19,840
+اللي أكبر ال center ولا ال centralizer في ال group
+
+334
+00:36:19,840 --> 00:36:28,240
+العادىالـ Center أكبر يعني بلاقي في عناصر أكتر من
+
+335
+00:36:28,240 --> 00:36:31,020
+عناصر الـ Centralizer لإيه؟
+
+336
+00:36:34,970 --> 00:36:40,990
+طيب سؤال سؤال بدي أجيب نفس السؤال بصيغة أخرى لو
+
+337
+00:36:40,990 --> 00:36:46,550
+أخد element في ال center تبع ال group بلاجيه في ال
+
+338
+00:36:46,550 --> 00:36:50,410
+centralizer تبع ال ايه؟ بلاجية طب نعمل العملية
+
+339
+00:36:50,410 --> 00:36:54,430
+العكسية بدي أخد element في ال centralizer هل
+
+340
+00:36:54,430 --> 00:36:57,170
+بلاجيه موجود في ال center؟
+
+341
+00:37:00,330 --> 00:37:05,270
+يعني قد يكون و قد لا يكون موجود، مظبوط؟ إذا صار ال
+
+342
+00:37:05,270 --> 00:37:10,630
+center صغير لأنه بدكم يسمع جميع عناصر جهة بس هدا
+
+343
+00:37:10,630 --> 00:37:14,650
+كم يسمع عنصر واحد فقط يبقى ال center هيكون في
+
+344
+00:37:14,650 --> 00:37:18,710
+عناصر كتيرة بدليل أخدت أوسع عنصر من ال center
+
+345
+00:37:18,710 --> 00:37:21,970
+وجدته موجود في ال centralizerلكن اذا ذهبت لختم
+
+346
+00:37:21,970 --> 00:37:25,210
+الـcentralizer ليس بالضرورة ان يكون وين في
+
+347
+00:37:25,210 --> 00:37:29,850
+الـcenter يبقى اول ملاحظة ان الـcenter تبع لجروب
+
+348
+00:37:29,850 --> 00:37:36,030
+هو الـsubset من الـcentralizer تمام؟ يبقى باجي
+
+349
+00:37:36,030 --> 00:37:37,750
+بقوله هنا note
+
+350
+00:37:40,820 --> 00:37:48,020
+النقطة الأولى ال center تبع ال group G subset من
+
+351
+00:37:48,020 --> 00:37:51,200
+ال
+
+352
+00:37:51,200 --> 00:37:59,660
+centralizer ل A و ال A عنصر موجود في جي مش ال A و
+
+353
+00:37:59,660 --> 00:38:03,300
+لا ال B و ال C يعني هذا كلام صحيح لكل ال A اللي
+
+354
+00:38:03,300 --> 00:38:08,940
+موجود في جي بدل هيك بقول لكل ال A اللي موجودة في
+
+355
+00:38:08,940 --> 00:38:15,310
+جييعني لو روحت لأى عنصر غيرت لإيه بعنصر تانى و
+
+356
+00:38:15,310 --> 00:38:18,830
+جبتله ال centralizer بلاج ال center subset منه و
+
+357
+00:38:18,830 --> 00:38:22,210
+روحت جبت ال centralizer لعنصر تالت و جبت ال
+
+358
+00:38:22,210 --> 00:38:24,770
+central group بلاج ال central subset من ال
+
+359
+00:38:24,770 --> 00:38:29,070
+centralizer للعنصر التالت و هكذاهى اللى قصدناه من
+
+360
+00:38:29,070 --> 00:38:36,050
+هنا طيب كمان سؤال لو كانت ال جي أبيليان قداش ال
+
+361
+00:38:36,050 --> 00:38:42,450
+centralizer لل إيه؟ جي جي كلها طب و ال center؟ جي
+
+362
+00:38:42,450 --> 00:38:46,080
+كلهايبقى صرت سما بين الـ Central و الـ Centralizer
+
+363
+00:38:46,080 --> 00:38:50,740
+يبقى إذا كانت الـ G Abelian فإن الـ Center يسوى
+
+364
+00:38:50,740 --> 00:38:55,540
+الـ Centralizer و يسوى الجروب G كله لكن لو ماكنتش
+
+365
+00:38:55,540 --> 00:38:59,840
+Abelian بيظل الـ Center تبع الجروب هو الـ Subset
+
+366
+00:38:59,840 --> 00:39:06,220
+قد يسوى و قد لا يسوى تمام؟ يبقى بناء عليه بقول هذه
+
+367
+00:39:06,220 --> 00:39:14,040
+النقطة الأولى النقطة التانية F G is AbelianThen
+
+368
+00:39:14,040 --> 00:39:20,220
+الـ Center تبع لـ Group G هو بالضبط الـ
+
+369
+00:39:20,220 --> 00:39:26,060
+Centralizer لـ A لكل الـ A اللي موجودة في G وهذا
+
+370
+00:39:26,060 --> 00:39:31,500
+بده يساوي G itself هذا في حالة ما تكون A ما تكون
+
+371
+00:39:31,500 --> 00:39:39,200
+Abelian Group طيب ناخد مثال بسيط example let
+
+372
+00:39:44,050 --> 00:39:52,830
+الـ G تسوي الـ D4 الـ D4 ثم بدّي
+
+373
+00:39:52,830 --> 00:40:02,670
+الـ Centralizer للـ R نوت مين بيطلع دي كلها طيب هل
+
+374
+00:40:02,670 --> 00:40:10,150
+هو الـ Centralizer للـ R 180صحيح لغرمية ابنكم يسمع
+
+375
+00:40:10,150 --> 00:40:16,270
+الكل يريد عن جديكوا بس و هذا بدي يسوي D4 كله يبقى
+
+376
+00:40:16,270 --> 00:40:22,070
+هذا بدي يعطينا D4 كله طب لو بدي ال centralizer لل
+
+377
+00:40:22,070 --> 00:40:28,270
+R90 هل
+
+378
+00:40:28,270 --> 00:40:34,710
+هذا هو ال centralizer لل R270؟
+
+379
+00:40:38,690 --> 00:40:46,030
+انظروا معاكوسه طب بد العناصر تبعتهم مين هم ارنود و
+
+380
+00:40:46,030 --> 00:40:54,230
+R180 و ال R90 كمان لأن ال R90 يسمع نفسه صحيح ولا
+
+381
+00:40:54,230 --> 00:41:00,540
+لا؟ ضل عليك كمان واحد بسحد معاه الجدول يطلع لبسه
+
+382
+00:41:00,540 --> 00:41:04,000
+فتش الجدول و بتعرف الإجابة منه في صفحة واحد و
+
+383
+00:41:04,000 --> 00:41:09,500
+تلاتين يبقى لو رجعنا بنلاقي بس اللي هي ال R ميتين
+
+384
+00:41:09,500 --> 00:41:16,710
+و سبعين يبقى هذه ال R ميتين و سبعينهذا الكلام يعني
+
+385
+00:41:16,710 --> 00:41:20,230
+ايش مين بدي اعطيه لك؟ بدي اعطيه لك ال subgroup
+
+386
+00:41:20,230 --> 00:41:26,470
+generated by R 90 وفي نفس الوقت هي ال subgroup
+
+387
+00:41:26,470 --> 00:41:36,590
+generated by R 270 مظبوط؟ R 90 R 90 تربية 180 R 90
+
+388
+00:41:36,590 --> 00:41:42,400
+تكيب 270 R أسبوع أربعة بال identityيبقى لو بدى
+
+389
+00:41:42,400 --> 00:41:46,780
+اجيب كمان الـcentralizer لمين للـH يبقى
+
+390
+00:41:46,780 --> 00:41:55,200
+الـcentralizer للـH اللى عندنا هذه يبقى هذا بده
+
+391
+00:41:55,200 --> 00:42:00,140
+يعطيلك الـR non والـR100U80
+
+392
+00:42:00,140 --> 00:42:03,700
+والـH وحط عليها الـV كمان
+
+393
+00:42:06,390 --> 00:42:13,330
+أليس هذا هو الـcentralizer للـ V كذلك؟ لو الجدول
+
+394
+00:42:13,330 --> 00:42:17,970
+معاك كان عرفت لحالك جدول في صفحة واحد و تلاتيه
+
+395
+00:42:17,970 --> 00:42:22,390
+بالمثل لو روحنا جيبنا الـcentralizer ل D
+
+396
+00:42:22,390 --> 00:42:30,450
+الـcentralizer ل D هو عبارة عن الـR node والـR مية
+
+397
+00:42:30,450 --> 00:42:38,000
+و تمانين والـD itself والـD primeهذا سيكون الـ
+
+398
+00:42:38,000 --> 00:42:46,540
+Centralizer لـ D' من هذا الكلام بقدر استنتج ان H
+
+399
+00:42:46,540 --> 00:42:54,040
+في V سيكون V في H و بقدر استنتج من هذا اللي تحت ان
+
+400
+00:42:54,040 --> 00:43:02,460
+D D' سيكون D' D يبقى هذا استنتاج من خلال الكلام
+
+401
+00:43:02,460 --> 00:43:03,760
+اللي عندنا هنا
+
+402
+00:43:23,420 --> 00:43:30,680
+الآن اخر نظرية موجودة في هذا ال chapter وهي ان ال
+
+403
+00:43:30,680 --> 00:43:39,220
+centralizer عبارة عن subgroup يبقى theorem for
+
+404
+00:43:39,220 --> 00:43:51,840
+any element a اللي موجود في جيب ال centralizer ل a
+
+405
+00:43:53,260 --> 00:44:02,720
+is a subgroup من G من من من من من
+
+406
+00:44:02,720 --> 00:44:03,440
+من من من من من من من من من من من من من من من من من
+
+407
+00:44:03,440 --> 00:44:03,500
+من من من من من من من من من من من من من من من من من
+
+408
+00:44:03,500 --> 00:44:08,840
+من من من من من من من من من من من من
+
+409
+00:44:08,840 --> 00:44:08,920
+من من من من من من من من من من من من من من من من من
+
+410
+00:44:08,920 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+411
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+412
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+413
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+414
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+415
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+416
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+417
+00:44:10,740 --> 00:44:10,740
+من من من من من من من من من من من من من من من من من
+
+418
+00:44:10,740 --> 00:44:14,560
+من من من من من من من من من من من
+
+419
+00:44:14,560 --> 00:44:15,840
+من من من
+
+420
+00:44:36,070 --> 00:44:43,020
+النقطة الثانية بداية ياخد letعشان ناخد ال a و نقول
+
+421
+00:44:43,020 --> 00:44:51,400
+x y لت ال x y موجود في ال centralizer ل a then ال
+
+422
+00:44:51,400 --> 00:45:02,980
+x a بده ساوي ال a x and ال y a بده ساوي ال a y ايش
+
+423
+00:45:02,980 --> 00:45:09,100
+بدنا نثبت؟بنثبت ان الـxy inverse موجود في
+
+424
+00:45:09,100 --> 00:45:14,360
+الـcentralizer لإيه يعني بنثبت ان الـxy inverse a
+
+425
+00:45:14,360 --> 00:45:20,360
+بدو يساوي الaxy inverse يبقى فرضنا هدول الاتنين
+
+426
+00:45:20,360 --> 00:45:30,020
+بيساووا بعض يبقى now لو أجى أخدت الـya بدو يساوي
+
+427
+00:45:30,020 --> 00:45:37,890
+الayهذا بدى يعطينا شرايك بدى اضرب في ال y inverse
+
+428
+00:45:37,890 --> 00:45:44,690
+من جهة اليمين يبقى بيصير y a y inverse يساوي قداش
+
+429
+00:45:44,690 --> 00:45:50,210
+يساوي ال a بدى اضرب في y inverse من جهة الشمال
+
+430
+00:45:50,210 --> 00:45:56,310
+يبقى لو ضربت من جهة الشمال بيظل a y inverse تساوي
+
+431
+00:45:56,310 --> 00:46:03,130
+y inverse في aيبقى ايش معنى هذا الكلام ان ال y
+
+432
+00:46:03,130 --> 00:46:09,370
+inverse موجود في ال centralizer لإيه هذا معناه ان
+
+433
+00:46:09,370 --> 00:46:14,450
+ال y inverse موجود في ال centralizer لإيه يبقى
+
+434
+00:46:14,450 --> 00:46:20,870
+بناء عليهالـ element y موجود في الـ centralizer
+
+435
+00:46:20,870 --> 00:46:27,030
+لإيه إذا معكسه يكون كذلك موجود في الـ centralizer
+
+436
+00:46:27,030 --> 00:46:31,110
+لإيه هذا معناته أن y inverse موجود في الـ
+
+437
+00:46:31,110 --> 00:46:37,710
+centralizer لإيه واعتبر لهذه الهيمينةالنقطة الأولى
+
+438
+00:46:37,710 --> 00:46:45,670
+يبقى نكتب الكلمة اللى قولناها يبقى this means that
+
+439
+00:46:45,670 --> 00:46:52,710
+هذا يعني ان if ال y موجود في ال centralizer ل a
+
+440
+00:46:52,710 --> 00:47:03,380
+thenالـ Y موجود في الـ Centralizer لـ
+
+441
+00:47:03,380 --> 00:47:10,880
+A ثم الـ Y Inverse ثم أو الـ Y موجودة في الـ
+
+442
+00:47:10,880 --> 00:47:17,780
+Centralizer لـ A Inverse لا لا الـ Y Inverse
+
+443
+00:47:17,780 --> 00:47:24,550
+موجودة في الـ Centralizer لـ Aتمام الان لو جيت
+
+444
+00:47:24,550 --> 00:47:39,110
+قولتلك consider خدلي اللي هو ال X Y inverse A هذا
+
+445
+00:47:39,110 --> 00:47:45,310
+الكلام بده يساويإذا قدرت أثبت ان الـ x y inverse a
+
+446
+00:47:45,310 --> 00:47:52,290
+بيكون a x y inverse بيتم المطلوب يبقى هذا x y
+
+447
+00:47:52,290 --> 00:47:58,010
+inverse ال a بقدر أكتبها a inverse inverse يبقى
+
+448
+00:47:58,010 --> 00:48:07,470
+هذا الكلام بيكون x و هنا a inverse y الكل inverse
+
+449
+00:48:07,470 --> 00:48:09,510
+مظبوط
+
+450
+00:48:10,530 --> 00:48:16,310
+يعني جمعت هنا ال inverse inverse رجعتهم لأصلهم
+
+451
+00:48:16,310 --> 00:48:24,110
+واحدة بالشكل هنا الان انا عندي هنا a inverse
+
+452
+00:48:24,110 --> 00:48:30,990
+مكتوبا اه سنة سنة شوية ايش اللي سويتها a inverse y
+
+453
+00:48:30,990 --> 00:48:34,990
+طيب هنا قلت دي اسم الالكترون موجود في ال
+
+454
+00:48:34,990 --> 00:48:38,910
+centralizer then y inverse موجود
+
+455
+00:48:45,110 --> 00:48:56,690
+كيف؟ بدي واحد بس يحكي، واحد يحكي بقى، ايه؟ اه،
+
+456
+00:48:56,690 --> 00:49:00,850
+يعني هيك، برضه مظبوط، ممكن ناخد x,y وممكن ناخد x,y
+
+457
+00:49:00,850 --> 00:49:04,090
+inverse مرة واحد، عشقتين، يا ناس بضرورة، ممكن
+
+458
+00:49:04,090 --> 00:49:06,770
+استفيد من هذه، ان الـA
+
+459
+00:49:17,330 --> 00:49:22,150
+على أي حال بنكمل المرة القادمة ان شاء الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ddba1fda9762796ccbaf641cc5e193346dc7899
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA.srt
@@ -0,0 +1,1575 @@
+1
+00:00:21,210 --> 00:00:26,110
+بسم الله الرحمن الرحيم نكمل ما ابتدأنا في 
+
+2
+00:00:26,110 --> 00:00:30,870
+المحاضرة السابقة عرفنا الـ isomorphism أخذنا عليه 
+
+3
+00:00:30,870 --> 00:00:36,030
+خمسة أمثلة في الفترة الصباحية الآن بدنا نيجي لأول 
+
+4
+00:00:36,030 --> 00:00:42,150
+نظرية هذه النظرية نظرية كيلي تنص على ما يلي أن أي 
+
+5
+00:00:42,150 --> 00:00:47,310
+group تبقى isomorphic to a group of permutations
+
+6
+00:00:48,010 --> 00:00:53,130
+الجروب of permutations بدي أنشئها من خلال الجروب 
+
+7
+00:00:53,130 --> 00:00:58,570
+اللي عندي طبعا هذا بيختلف عن كل ما سبق أنه لم يبين 
+
+8
+00:00:58,570 --> 00:01:03,210
+ايش شكل الجروب ولا مبين شكل الـ group of permutation
+
+9
+00:01:03,210 --> 00:01:07,890
+مش مبين عندي ولا عاجز لذلك بدنا نبدأ البرهان 
+
+10
+00:01:07,890 --> 00:01:14,430
+كالتالي فبجي بقول let G be a group
+
+11
+00:01:17,890 --> 00:01:32,690
+for any g اللي موجودة فيه g define a function TG
+
+12
+00:01:32,690 --> 00:01:46,470
+من G إلى G by TG of X بده يساوي GX لكل الـ X اللي 
+
+13
+00:01:46,470 --> 00:01:55,050
+موجود في جي يبقى 
+
+14
+00:01:55,050 --> 00:02:01,030
+أنا الآن بدي أسعى إلى أن أكون من الـ group of 
+
+15
+00:02:01,030 --> 00:02:06,390
+permutation من الـ group اللي موجودة لذلك من الـ 
+
+16
+00:02:06,390 --> 00:02:13,420
+group اللي موجودة عند جي بدي أكونها بالتالي يجب أن 
+
+17
+00:02:13,420 --> 00:02:18,020
+يكون الـ group of all permutations التي تعتمد على 
+
+18
+00:02:18,020 --> 00:02:22,660
+الجروب اللي عندنا لذلك لو أخدت أي جي موجود في جي 
+
+19
+00:02:22,660 --> 00:02:28,960
+يجب أن أعرف الدالة كالتالي تأتي من جي إلى جي by
+
+20
+00:02:28,960 --> 00:02:34,140
+يجب أن أعرفها كالتالي TG of x يساوي g of x لكل 
+
+21
+00:02:34,140 --> 00:02:38,650
+الـ x الموجود في جي السؤال هو هل هذا التعريف صحيح 
+
+22
+00:02:38,650 --> 00:02:44,910
+ولا غير صحيح الإجابة التعريف صحيح لأن الـ TG من G 
+
+23
+00:02:44,910 --> 00:02:50,710
+إلى G الـ G والـ X موجودات في G إذا حصل ضربهمَا 
+
+24
+00:02:50,710 --> 00:02:55,550
+موجود في G لأنه G closed under multiplication أو 
+
+25
+00:02:55,550 --> 00:02:58,550
+الـ operation اللي على G هي عبارة عن binary
+
+26
+00:02:58,550 --> 00:03:03,500
+operation يبقى الـ G في X موجودة في الـ group اللي 
+
+27
+00:03:03,500 --> 00:03:09,380
+عندنا يبقى تعريفي هذا صحيح الآن أنا أدعي أن هذه الـ 
+
+28
+00:03:09,380 --> 00:03:15,900
+function is a permutation أنا أدعي أن TG هذه 
+
+29
+00:03:15,900 --> 00:03:19,980
+عبارة عن permutation طيب هي الـ permutation عبارة 
+
+30
+00:03:19,980 --> 00:03:23,780
+عن ايش؟ function والـ function بتكون one to one
+
+31
+00:03:23,780 --> 00:03:27,620
+and onto إذا طلعت هذه الـ function one to one and 
+
+32
+00:03:27,620 --> 00:03:32,500
+onto يبقى هي بال فهي تكون permutation مظبوط؟ يبقى 
+
+33
+00:03:32,500 --> 00:03:45,080
+هنا باجي بقول now الـ TG is a permutation طبعا؟
+
+34
+00:03:45,080 --> 00:03:55,740
+طيب ليش؟ because السبب النقطة الأولى الـ TG هادي is 
+
+35
+00:03:55,740 --> 00:04:02,960
+one to one الـ TG is one to one بدنا نثبت صحة هذا 
+
+36
+00:04:02,960 --> 00:04:11,500
+الكلام يبقى باجي بقوله let الـ TG of X يساوي TG of 
+
+37
+00:04:11,500 --> 00:04:20,520
+Y then حسب التعريف الـ TG of X بده يساوي الـ G في 
+
+38
+00:04:20,520 --> 00:04:29,350
+X الـ TG of Y بده يساوي GY بالـ left cancellation law 
+
+39
+00:04:29,350 --> 00:04:35,470
+بنقدر نشطب الـ G والـ G يطلع لنا قداش أن الـ X بده 
+
+40
+00:04:35,470 --> 00:04:40,130
+يساوي الـ Y أو كون الـ G في الـ G والـ G اجروا بيبقى 
+
+41
+00:04:40,130 --> 00:04:44,110
+G inverse موجود يبقى لو ضربت الطرفين في G inverse 
+
+42
+00:04:44,110 --> 00:04:48,830
+هيعطينا أن X يساوي Y معناه هذا الكلام أن TG is one 
+
+43
+00:04:48,830 --> 00:04:53,230
+to one لأنه خدت صورتين متساويتين أثبتت أن أصلهم 
+
+44
+00:04:53,570 --> 00:05:01,690
+متساوين الآن بدنا نثبت النقطة الثانية أنه تي جي is 
+
+45
+00:05:01,690 --> 00:05:11,290
+onto لذلك بدروح أخد element في جي وأثبت أنه له أصل 
+
+46
+00:05:11,290 --> 00:05:19,440
+في جي يبقى باجي بقوله let y موجودة في جي في جيله من 
+
+47
+00:05:19,440 --> 00:05:24,360
+الـ codomain تبع الـ TG يعني في الـ G التانية هذه 
+
+48
+00:05:24,360 --> 00:05:32,380
+ماهي هذه؟ هي هذه كويس موجود في الـ TG then الـ Y 
+
+49
+00:05:32,380 --> 00:05:40,650
+تساوي بدي أحاول أكتب الـ Y هذه كصورة لعنصر من G 
+
+50
+00:05:40,650 --> 00:05:48,590
+الأولى إذا لو جيت قلت لك الـ Y هذه قلت لك هي G G 
+
+51
+00:05:48,590 --> 00:05:56,910
+inverse Y بنفع؟ بنفع؟ لإيش؟ لأن الـ G G inverse هو 
+
+52
+00:05:56,910 --> 00:06:01,350
+الـ identity element والـ identity element تضربه في 
+
+53
+00:06:01,350 --> 00:06:06,210
+أي element بيعطيك نفس الـ element إذا بقدر أقول هذه 
+
+54
+00:06:06,210 --> 00:06:10,490
+G في G inverse Y
+
+55
+00:06:13,170 --> 00:06:17,550
+فباش رأيك هذا اللي بين قصيره؟ بدي أسميه أي عنصر 
+
+56
+00:06:17,550 --> 00:06:24,990
+آخر للسهولة إذا بقدر أقول هذه جي إكس مثلا إذا 
+
+57
+00:06:24,990 --> 00:06:31,030
+العنصر هذا شيلته وحاطه بدله مين؟ إكس طيب جي إكس 
+
+58
+00:06:31,030 --> 00:06:39,080
+هذه عبارة عن مين؟ عبارة عن TG of x يبقى الـ 
+
+59
+00:06:39,080 --> 00:06:44,740
+element y اللي موجود في الـ group g لجت له أصل x 
+
+60
+00:06:44,740 --> 00:06:51,000
+موجود في g التانية يبقى بناء عليه هي is onto يبقى 
+
+61
+00:06:51,000 --> 00:06:56,340
+صار في عندي function من g إلى g هذه one to one and 
+
+62
+00:06:56,340 --> 00:07:00,060
+onto واحنا لما عرفنا الـ permutation قلنا هي 
+
+63
+00:07:00,060 --> 00:07:05,630
+function عبارة عن one to one and onto يبقى بناء 
+
+64
+00:07:05,630 --> 00:07:12,050
+عليه الـ TG هذي عبارة عن ايش permutation يبقى الـ 
+
+65
+00:07:12,050 --> 00:07:18,090
+element G من الجروب جاب لي permutation اسمها مين 
+
+66
+00:07:18,090 --> 00:07:25,870
+اسمها TG الآن بدي آخذ هدول كل الـ permutations وبده 
+
+67
+00:07:25,870 --> 00:07:34,750
+أحطهم في set يبقى الآن consider جي
+
+68
+00:07:34,750 --> 00:07:44,650
+بار جي بار هذي بتعطيها الرمز SG مين الـ SG هذي كل TG 
+
+69
+00:07:44,650 --> 00:07:52,550
+بحيث الـ g موجودة في جي يعني 
+
+70
+00:07:53,310 --> 00:07:58,270
+لو جينا قولنا الـ G هذه فيها خمسين elements مثلا 
+
+71
+00:07:58,270 --> 00:08:02,910
+يبقى ابو دي اطلع هنا كم element عندي؟ خمسين 
+
+72
+00:08:02,910 --> 00:08:08,570
+elements لأنه TG1, TG2, TG3, TG4 لغاية ما أكمل 
+
+73
+00:08:08,570 --> 00:08:14,390
+الخمسين يبقى الـ SG هذي mean the set of all 
+
+74
+00:08:14,390 --> 00:08:20,210
+permutations اللي محطوطة على الـ group G هذه the 
+
+75
+00:08:20,210 --> 00:08:28,300
+set of all permutations
+
+76
+00:08:28,300 --> 00:08:32,060
+of 
+
+77
+00:08:32,060 --> 00:08:40,640
+G كل الـ permutations اللي على G الآن أنا هأدعي أن 
+
+78
+00:08:40,640 --> 00:08:47,450
+SG هذي is a group وبنفعش تدعي يا صاحبي بدك تبين أنه 
+
+79
+00:08:47,450 --> 00:08:52,810
+فعلا أن SG هذه ايه هي group لأنه إذا أثبتت أنها 
+
+80
+00:08:52,810 --> 00:08:58,150
+group وصلت للنص اللي أنا بقول عنه كل group 
+
+81
+00:08:58,150 --> 00:09:02,210
+isomorphic إلى permutation group أو الـ group of 
+
+82
+00:09:02,210 --> 00:09:08,190
+permutation تمام يبقى الخطوة التالية بعد ما خلقت 
+
+83
+00:09:08,590 --> 00:09:13,950
+permutations لكل عنصر موجود في دي خلقت له 
+
+84
+00:09:13,950 --> 00:09:18,230
+permutation أقبله الـ Permutations حطيتهم في set 
+
+85
+00:09:18,230 --> 00:09:24,930
+واحدة سميتها G bar أو سميتها SG من العناصر تبعتها 
+
+86
+00:09:24,930 --> 00:09:30,190
+كل الـ Permutations اللي خلقتهم على الـ group G
+
+87
+00:09:30,190 --> 00:09:37,510
+الآن أنا بأدعي أن SG هذه is a group يبقى بدي أشوف 
+
+88
+00:09:37,510 --> 00:09:44,450
+هل الـ SG بتحقق شروط الـ group ولا لا يبقى أول شيء الـ 
+
+89
+00:09:44,450 --> 00:09:47,370
+operation اللي عليها madam permutation هو الـ 
+
+90
+00:09:47,370 --> 00:09:52,690
+composition of functions الآن الـ composition of 
+
+91
+00:09:52,690 --> 00:09:57,430
+functions بدي أثبت إنها binary operation ايش يعني 
+
+92
+00:09:57,430 --> 00:10:01,430
+binary operation؟ يعني لو جبت composition بين two
+
+93
+00:10:01,430 --> 00:10:06,190
+permutations بدي يعطيني مين؟ permutation واحدة إن 
+
+94
+00:10:06,190 --> 00:10:10,590
+حدث ذلك يبقى فعلا تبقى الـ operation اللي عليها هي 
+
+95
+00:10:10,590 --> 00:10:22,300
+binary operation يبقى we claim that نقول يدعي أن
+
+96
+00:10:22,300 --> 00:10:32,520
+الـ SG is a group under the
+
+97
+00:10:32,520 --> 00:10:38,240
+composition of 
+
+98
+00:10:38,240 --> 00:10:39,100
+functions
+
+99
+00:10:41,910 --> 00:10:47,890
+أنا هأدعي أن اس جي هذي is a group تحت عملية تحصيل 
+
+100
+00:10:47,890 --> 00:10:53,770
+أو تركيب من الـ function بدي أروح أثبت هذا الكلام 
+
+101
+00:10:53,770 --> 00:11:02,990
+يبقى باجي بقوله for all G و H اللي موجودة في جي 
+
+102
+00:11:02,990 --> 00:11:04,190
+we have
+
+103
+00:11:20,200 --> 00:11:24,840
+البيانات مضروبات ضرب لكن في الحقيقة هي عبارة عن 
+
+104
+00:11:26,540 --> 00:11:34,960
+composition تحصيل يبقى بناء عليه هذا بيصير TG of 
+
+105
+00:11:34,960 --> 00:11:45,440
+TH of x composition يبقى بناء عليه هذا بيعطيني TG
+
+106
+00:11:45,440 --> 00:11:55,980
+of TH of x حسب التعريف بيعطيني الـ H of x تمام حسب 
+
+107
+00:11:55,980 --> 00:12:04,760
+التعريف كمان بده يعطيني G of H of x الـ G والـ H والـ 
+
+108
+00:12:04,760 --> 00:12:09,420
+X موجودات في G ولا لأ والـ G associative الـ 
+
+109
+00:12:09,420 --> 00:12:15,920
+operation اللي عليها يبقى هذا بده يعطيني GH في X
+
+110
+00:12:15,920 --> 00:12:26,650
+يبقى هذا بده يعطيني TH of x هذه موجودة في SD ولا لأ 
+
+111
+00:12:26,650 --> 00:12:34,570
+يبقى هذه موجودة في SD يبقى بناء عليه الـ 
+
+112
+00:12:34,570 --> 00:12:38,250
+composition of function is a binary operation على
+
+113
+00:12:38,250 --> 00:12:48,750
+SG على SD يبقى الـ composition of 
+
+114
+00:12:48,750 --> 00:12:57,500
+functions is a binary operation
+
+115
+00:12:57,500 --> 00:13:00,540
+on
+
+116
+00:13:00,540 --> 00:13:08,540
+SG طب ايش رأيك؟ الـ composition of function قبلك 
+
+117
+00:13:08,540 --> 00:13:12,300
+أخذناها كثير associative ولا لأ؟ associative
+
+118
+00:13:12,300 --> 00:13:20,460
+associative also وكذلك we know that
+
+119
+00:13:22,880 --> 00:13:29,140
+the composition of 
+
+120
+00:13:29,140 --> 00:13:38,660
+functions is associative يبقى 
+
+121
+00:13:38,660 --> 00:13:46,260
+مش ضايقني اللي عندي الـ identity element يبقى TE is
+
+122
+00:13:46,260 --> 00:13:52,380
+the identity element
+
+123
+00:13:54,350 --> 00:14:03,070
+في اس جي ليش؟ because بتاخد
+
+124
+00:14:03,070 --> 00:14:11,050
+تي في تي اتش as a function of x هأشوف كده الشي 
+
+125
+00:14:11,050 --> 00:14:19,050
+يعطيني يبقى هذا بده يعطيني تي في تي اتش of x يبقى 
+
+126
+00:14:19,050 --> 00:14:26,320
+تي في ال اتش اكس هذه حسب التعريف وحسب التعريف كذلك
+
+127
+00:14:26,320 --> 00:14:36,620
+E في HX اللي هو بده يساوي HX يبقى TH of X يبقى
+
+128
+00:14:36,620 --> 00:14:43,220
+بناء عليه TE في TH of X هتانمين TH of X هذا لو كان
+
+129
+00:14:43,220 --> 00:14:49,880
+الضرب من جهة الشمال لو كان من جهة اليمين and TH
+
+130
+00:14:59,520 --> 00:15:16,000
+يبقى هذا الكلام يبقى تي اتش تي
+
+131
+00:15:16,000 --> 00:15:20,190
+اتش تي اتش تي اتش تي اتش تي اتش تي اتش إذا لو ضربت
+
+132
+00:15:20,190 --> 00:15:26,970
+من اليمين وضربت من الشمال بيعطيني TE of x يبقى TE
+
+133
+00:15:26,970 --> 00:15:35,230
+هو الوضع الوحدة الوحدة الوحدة الوحدة
+
+134
+00:15:35,230 --> 00:15:41,630
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+135
+00:15:41,630 --> 00:15:46,210
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+136
+00:15:46,210 --> 00:15:46,570
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+137
+00:15:46,570 --> 00:15:46,590
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+138
+00:15:46,590 --> 00:15:47,270
+الو
+
+139
+00:15:52,000 --> 00:16:02,180
+تعالى نشوف الآن ال TG inverse TG as a function of X
+
+140
+00:16:02,180 --> 00:16:13,040
+يبقى هذا بده يعطينا TG inverse ل TG of X هذا الكلام
+
+141
+00:16:13,040 --> 00:16:21,780
+بده يعطينا TG inverse TG of x هيها بمين بجي اكس
+
+142
+00:16:21,780 --> 00:16:25,160
+يبقى
+
+143
+00:16:25,160 --> 00:16:31,420
+صار ال GX كله element في domain TG inverse يبقى
+
+144
+00:16:31,420 --> 00:16:39,230
+هذا الكلام بده يساوي جي انفرس ل جي اكس هذول الـ
+
+145
+00:16:39,230 --> 00:16:44,010
+three elements كلهم موجودات في ال group G خاصية ال
+
+146
+00:16:44,010 --> 00:16:48,730
+associativity عليها الصحيحة يبقى هذا الكلام بده
+
+147
+00:16:48,730 --> 00:16:56,610
+يعطينا G inverse G في ال X يبقى هذا بده يعطينا E X
+
+148
+00:16:56,610 --> 00:17:06,160
+ال E X هي عبارة عن TE of X إذا حصل ضرب الـElement
+
+149
+00:17:06,160 --> 00:17:13,200
+في معكوسه إعطاني الـIdentity Element بالمثل يبقى
+
+150
+00:17:13,200 --> 00:17:26,900
+and الـTG of X في الـTG and الـTG في الـTG inverse
+
+151
+00:17:26,900 --> 00:17:36,560
+as a function of X هذا الكلام بده يعطيني TG في TG
+
+152
+00:17:36,560 --> 00:17:46,020
+inverse of X هذا الكلام بيساوي اي TG اللي برا و
+
+153
+00:17:46,020 --> 00:17:51,580
+اللي جوا هادي اللي هي في G inverse X طبقا لل
+
+154
+00:17:51,580 --> 00:17:58,980
+definition اللي عنديهذا الكلام بده يساوي جي للجي
+
+155
+00:17:58,980 --> 00:18:05,560
+انفرست اكس هذا نظرة لخاصية ال associativity بده
+
+156
+00:18:05,560 --> 00:18:12,140
+يساوي جي جي انفرست اكس ال جي جي انفرست بتعطيني ال
+
+157
+00:18:12,140 --> 00:18:20,930
+identity element يبقى هذه بتعطيني AX ل TE of x إذا
+
+158
+00:18:20,930 --> 00:18:29,000
+أصبح TG inverse هو هو بالضبط TG لكل انفرس ليش ان
+
+159
+00:18:29,000 --> 00:18:33,000
+ضربته من اليمين و الشمال اعطاني نفس ال identity
+
+160
+00:18:33,000 --> 00:18:38,020
+element إذا binary operation associative ال
+
+161
+00:18:38,020 --> 00:18:41,600
+identity element ال inverse element لكل element
+
+162
+00:18:41,600 --> 00:18:46,360
+يبقى ال SG صارت مالها a group under the
+
+163
+00:18:46,360 --> 00:18:54,540
+composition of functions يبقى هنا so ال SG is a
+
+164
+00:18:54,540 --> 00:19:05,910
+group under the composition of
+
+165
+00:19:05,910 --> 00:19:16,570
+functions خلصنا يا شباب؟ لسه مخلصناش احنا جبنا
+
+166
+00:19:16,570 --> 00:19:21,430
+جروب جي وجبنا جروب ثاني اللي هو the set of all
+
+167
+00:19:21,430 --> 00:19:25,960
+permutations لجروبة المكونة من permutation الآن
+
+168
+00:19:25,960 --> 00:19:31,940
+بدي أثبت أنه اتنين هذول are isomorphic أي اللي
+
+169
+00:19:31,940 --> 00:19:42,600
+بديها يبقى الآن بقوله define a function Phi من G
+
+170
+00:19:42,600 --> 00:19:45,520
+إلى SG by
+
+171
+00:19:51,950 --> 00:20:01,320
+5 of G بدر يساوي TG ال element اللي في ال group
+
+172
+00:20:01,320 --> 00:20:07,680
+capital يبدأ يسميه G ال element اللي في S G ال S G
+
+173
+00:20:07,680 --> 00:20:15,820
+قلنا وين حطنا لها تعرف قلنا ال S G where are the
+
+174
+00:20:15,820 --> 00:20:19,940
+composition binary operations اه ال S G وين
+
+175
+00:20:19,940 --> 00:20:25,780
+كتبناها this is a group اه هي ال S G يبقى ال
+
+176
+00:20:25,780 --> 00:20:30,900
+element اللي في S G على شكل اللي هو الـ permutation
+
+177
+00:20:30,900 --> 00:20:37,820
+TG يبقى لكل element جي موجود في G عرفنا منهم اللي
+
+178
+00:20:37,820 --> 00:20:43,540
+هو الـ TG اللي موجودة في SG الآن أنا بدي ابين ان
+
+179
+00:20:43,540 --> 00:20:50,080
+هذه ال function is well defined يبقى الخطوة الأولى
+
+180
+00:20:50,080 --> 00:20:58,740
+Phi is well defined Well-defined يعني معرفة تعريفا
+
+181
+00:20:58,740 --> 00:21:05,960
+صحيحا كيف تعريفا صحيحا كالتالي بدأ أخد عنصرين
+
+182
+00:21:05,960 --> 00:21:12,860
+متساويين و أثبت أنه إلهم نفس الصورة على عكس مين ال
+
+183
+00:21:12,860 --> 00:21:17,000
+one to one ال one to one بتاخد صورتين و بتثبت أن
+
+184
+00:21:17,000 --> 00:21:26,920
+أصلهم متساوي يبقى هنا F ال G و H موجودات في ال G
+
+185
+00:21:29,890 --> 00:21:36,850
+إن الـ G بده يساوي الـ H then بده يتأثر الـ Phi
+
+186
+00:21:36,850 --> 00:21:45,730
+على الطرفين يبقى Phi of G بده يساوي Phi of H حسب
+
+187
+00:21:45,730 --> 00:21:51,590
+ال definition Phi of G بده يساوي TG
+
+188
+00:21:53,140 --> 00:22:00,700
+فاي اف اتش تساوي ت اتش إذا العنصرين المتساويين في
+
+189
+00:22:00,700 --> 00:22:06,140
+جيوز صورتهم متساوي تبقى ال function معرفة تعريفا
+
+190
+00:22:06,140 --> 00:22:12,540
+صحيا بعد ذلك أثبت أن هذا isomorphism يعني ال
+
+191
+00:22:12,540 --> 00:22:17,620
+function f صارت موجودة شو ضايل عندي one to one
+
+192
+00:22:18,000 --> 00:22:22,720
+و أنتوا و تخدم خاصية الهيزمورفزيوم لإيه Phi of a بي
+
+193
+00:22:22,720 --> 00:22:27,940
+بده يساوي Phi of a في Phi of b يبقى بالدرجة يقوله
+
+194
+00:22:27,940 --> 00:22:35,980
+Phi النقطة الثانية is one to one يبقى بالدرجة
+
+195
+00:22:35,980 --> 00:22:45,700
+يقوله assume افترض أن Phi of g بده يساوي Phi of h
+
+196
+00:22:46,380 --> 00:22:55,240
+بدي احاول اثبتله ان الـ G تساوي مين تساوي ال H ثم
+
+197
+00:22:55,240 --> 00:23:06,800
+الـ Phi of G اللي هي TG بيديها تساوي TH تمام إذا تي
+
+198
+00:23:06,800 --> 00:23:11,700
+جي لما تأثر على أي element بده يساوي تأثير تي اتش
+
+199
+00:23:11,700 --> 00:23:15,680
+على أي element سواء كان ال element هذا ال identity
+
+200
+00:23:15,680 --> 00:23:19,980
+element أو أي element موجود في ال group يعني لو
+
+201
+00:23:19,980 --> 00:23:26,200
+قلت لك تي جي of اي أو قلت لك تي جي of اكس هذه
+
+202
+00:23:26,200 --> 00:23:31,190
+والله هذه الاتنين هيأديني إلى نفس النتيجة هذا بده
+
+203
+00:23:31,190 --> 00:23:45,350
+يعطينا ان TG of X بده يساوي TH of X هذا
+
+204
+00:23:45,350 --> 00:23:51,770
+بده يعطينا ان G of X بده تساوي H
+
+205
+00:23:58,390 --> 00:24:04,470
+بال right cancellation law يبقى هذا معناه ان ال G
+
+206
+00:24:04,470 --> 00:24:12,850
+بده يساوي ال H إذا أخدنا صورتين متساويتين أثبتنا
+
+207
+00:24:12,850 --> 00:24:19,070
+أن الأصل متساوي يبقى Phi is one to one النقطة
+
+208
+00:24:19,070 --> 00:24:22,510
+الثالثة Phi is onto
+
+209
+00:24:28,880 --> 00:24:37,080
+أظن هذه لا تحتاج برهان لماذا؟ لأن كل element في S
+
+210
+00:24:37,080 --> 00:24:48,460
+G يعتمد على element من جي؟ من جي يبقى because any
+
+211
+00:24:48,460 --> 00:24:50,600
+element
+
+212
+00:24:53,320 --> 00:24:59,140
+any element TG اللي موجود في اس جي
+
+213
+00:24:59,140 --> 00:25:05,660
+corresponding to
+
+214
+00:25:05,660 --> 00:25:19,520
+جي اللي موجودة في جي يعني بمعنى آخر اللي هو ال ال
+
+215
+00:25:19,520 --> 00:25:28,860
+five is on ليش؟ لأن كل element من SG له أصل في جي
+
+216
+00:25:28,860 --> 00:25:34,720
+اللي هو جي يبقى إيش ضايل علينا؟ الخاصية الأخيرة
+
+217
+00:25:34,720 --> 00:25:41,600
+الخاصية الأخيرة كانت تالية يبقى بدي أجي أخد Phi
+
+218
+00:25:41,600 --> 00:25:53,740
+الخاصية الرابعة بدي أخد Phi of HG أو GH سياني يبقى
+
+219
+00:25:53,740 --> 00:26:02,520
+هذه حسب ال definition بدأت تساوي تي اتش جي تمام تي
+
+220
+00:26:02,520 --> 00:26:09,580
+اتش جي لو رجعتها لأصلها بصير تي اتش composition تي
+
+221
+00:26:09,580 --> 00:26:16,980
+جي تي اتش حسب التعريف اللي عرفناه هنا اللي هو تي
+
+222
+00:26:16,980 --> 00:26:18,480
+جي هي في
+
+223
+00:26:21,140 --> 00:26:30,370
+of H في التانية Phi of G هذا الكلام صحيح لكل الـ H
+
+224
+00:26:30,370 --> 00:26:37,930
+والـ G اللي موجودة في G يبقى بناء عليه أثبتنا الآن
+
+225
+00:26:37,930 --> 00:26:44,230
+إن Phi of HG بدأ يساوي Phi of H في Phi of G يبقى
+
+226
+00:26:44,230 --> 00:26:51,210
+بناء عليه هذا يعني إن خواص الأيزومورفزم تحصلت يبقى
+
+227
+00:26:51,210 --> 00:27:00,060
+بأني بقوله غاصوهكذا اللي هو من الـG isomorphic
+
+228
+00:27:00,060 --> 00:27:08,840
+لمن؟ للـSG اللي هي the set of all permutations أظن
+
+229
+00:27:08,840 --> 00:27:14,500
+دوّقتكوا شوية النظرية هيك لذلك بنروح أعيدها لكم
+
+230
+00:27:14,500 --> 00:27:21,160
+مرة ثانية حتى نثبت هذه المعلومات عندكم طبعا هي من
+
+231
+00:27:21,160 --> 00:27:27,120
+أطول النظريات برهانة اللي موجودة في الكتاب ليش
+
+232
+00:27:27,120 --> 00:27:31,960
+لأنها تحدث عن نقطة واحدة وليس عن مجموعة من النقاط
+
+233
+00:27:31,960 --> 00:27:38,700
+النظرية بتقول ما يأتي every group is isomorphic to
+
+234
+00:27:38,700 --> 00:27:42,480
+a group of permutation هو هذا اللي ما قلناه في الآخر
+
+235
+00:27:42,910 --> 00:27:46,810
+أنه ال group G isomorphic لل set of all
+
+236
+00:27:46,810 --> 00:27:52,590
+permutations اللي كونها على G اللي وعطناها الرمز
+
+237
+00:27:52,590 --> 00:28:00,370
+من SD لما أنا قاعد أقرا النص هذا بقول group G ماشي
+
+238
+00:28:00,370 --> 00:28:04,690
+لكن ال group permutation مش عارف الشكلها يبقى أنا
+
+239
+00:28:04,690 --> 00:28:08,890
+بدأ أخلق ال group هذه وبعد هيك نبدأ نتفاهم على
+
+240
+00:28:08,890 --> 00:28:11,410
+حكاية من ال isomorphism
+
+241
+00:28:14,910 --> 00:28:21,690
+أخذ أي عنصر جي موجود في جي من مكان يكون عرفت عليه
+
+242
+00:28:21,690 --> 00:28:26,830
+function TG من جي إلى جي by TG of X يساوي G of X
+
+243
+00:28:26,830 --> 00:28:31,470
+التعريف هذا صحيح لأن X و G موجودات في الجي و الجي
+
+244
+00:28:31,470 --> 00:28:35,070
+group closed under multiplication يبقى فعلا ال
+
+245
+00:28:35,070 --> 00:28:41,300
+element هذا موجود في جيبعدين بقول و الله لو كانت
+
+246
+00:28:41,300 --> 00:28:46,740
+ال function هذه one to one and onto يبقى بيصير
+
+247
+00:28:46,740 --> 00:28:51,260
+permutation لأن لما نعرفنا ال permutation على set
+
+248
+00:28:51,260 --> 00:28:55,340
+قلنا هي function من ال set إلى نفسها بعدين تبقى
+
+249
+00:28:55,340 --> 00:28:59,900
+one to one and onto هي function من ال set إلى
+
+250
+00:28:59,900 --> 00:29:03,740
+نفسها يبقى ضايل علي بس أثبت إنها one to one هذه ال 
+
+251
+00:29:03,740 --> 00:29:09,070
+وكذلك function on to يبقى روحت لل one to one قلت 
+
+252
+00:29:09,070 --> 00:29:15,330
+افترض صوتين متساويتين بدي اثبت ان ال X يساوي Y حسب
+
+253
+00:29:15,330 --> 00:29:18,830
+التعريف اللي احنا جايليه يبقى هذا G X بدي اساوي
+
+254
+00:29:18,830 --> 00:29:22,450
+بـ G Y بال left cancellation اللي هو يبقى ال X
+
+255
+00:29:22,450 --> 00:29:28,090
+يساوي Y يبقى ال T G one to one بدي اثبتها انها on
+
+256
+00:29:28,090 --> 00:29:34,450
+to فاخدت Y موجود في الـ G Y بدي أحاول أصيغه بصيغة
+
+257
+00:29:34,450 --> 00:29:41,650
+تعطيني TG of X كيف؟ قلت الـ Y يساوي ال identity في
+
+258
+00:29:41,650 --> 00:29:48,760
+Y ال identity بقدر أقول عليها GG inverse بعد ذلك
+
+259
+00:29:48,760 --> 00:29:56,460
+باخد اتنين هذول مع بعض جي انفرس واي وجي لحاله باجي
+
+260
+00:29:56,460 --> 00:30:02,930
+بقول هذول لو سميتم تاسم جديدة XZW اللي بدكيا يبقى
+
+261
+00:30:02,930 --> 00:30:09,050
+اقولنا X مثلا يبقى جي X باجي لجي X من التعريف
+
+262
+00:30:09,050 --> 00:30:15,930
+عبارة عن TG of X يبقى سارة TG of X يبقى ال element
+
+263
+00:30:15,930 --> 00:30:21,850
+Y اللي موجود في جي اللي عندنا هذه اللي جاتله أصل X
+
+264
+00:30:21,850 --> 00:30:27,070
+موجود في جي الأولى يبقى بناء عليه الدالة هذه is
+
+265
+00:30:27,070 --> 00:30:33,500
+onto بناء عليه هذه الـ function أصبحت تشكل ليه
+
+266
+00:30:33,500 --> 00:30:38,480
+permutation تمام؟ جيت على ال permutations هدول و
+
+267
+00:30:38,480 --> 00:30:43,900
+حطيتهم كلهم في مين؟ في ستة جديدة روحت سميتها SG
+
+268
+00:30:43,900 --> 00:30:50,400
+سميتها SG مشان العناصر تبعات G يكونوا من مين
+
+269
+00:30:50,400 --> 00:30:56,540
+ناخدهم من G itself من عناصرها كل ال permutations
+
+270
+00:30:56,540 --> 00:31:01,530
+اللي حصلنا عليها في القطغة الأولى يبقى لما يقولي
+
+271
+00:31:01,530 --> 00:31:05,130
+isomorphic to group of permutations يبقى الجروب
+
+272
+00:31:05,130 --> 00:31:10,990
+هذه خلقتها جديد وسميتها SG بس أنا مش عارفة اللي هي
+
+273
+00:31:10,990 --> 00:31:15,390
+group ولا .. هي صارت عندي set و ال set فيها مجموعة
+
+274
+00:31:15,390 --> 00:31:20,130
+من العناظة بدي أثبتله إنها group إذا أثبتله إنها
+
+275
+00:31:20,130 --> 00:31:24,570
+group بصير هي عندي group و جروب تانية بقدر اعمل ال
+
+276
+00:31:24,570 --> 00:31:29,630
+isomorphism ما بين الاتنين طب سؤال هامشي هيه جاب
+
+277
+00:31:29,630 --> 00:31:34,930
+المكمل بنفع اعمل isomorphism ما بين جروب و ما بين
+
+278
+00:31:34,930 --> 00:31:38,150
+set؟
+
+279
+00:31:38,150 --> 00:31:43,700
+بنفعلا يمكن ينفع لأن هذه عليها binary operation
+
+280
+00:31:43,700 --> 00:31:47,820
+وهذه ما عليها اش احنا بيقول isomorphism الأولى
+
+281
+00:31:47,820 --> 00:31:52,100
+والتانية كله لهم نفس القواصة الرياضية فكيف علي هذه
+
+282
+00:31:52,100 --> 00:31:56,380
+binary operation وهذه لأ إذا لا يمكن أن يكون هناك
+
+283
+00:31:56,380 --> 00:31:59,720
+isomorphism ما بين group ما بين set لازم يكون
+
+284
+00:31:59,720 --> 00:32:06,800
+التنتين are groups طيب نرجع الأن لل SG أنا أدعى إن
+
+285
+00:32:06,800 --> 00:32:11,400
+الـ S جي هذي اللي كونها مالها is a group تحت ال
+
+286
+00:32:11,400 --> 00:32:18,020
+composition of function لذلك أخد GH بدي أثبت إنها
+
+287
+00:32:18,020 --> 00:32:25,820
+closed under multiplication أو closed under أخد تي
+
+288
+00:32:25,820 --> 00:32:36,360
+جي composition th of x يساوي تي جي في th of x
+
+289
+00:32:36,360 --> 00:32:42,540
+استخدم تعريف th of x اللي هو hx وبعدين استخدم
+
+290
+00:32:42,540 --> 00:32:48,850
+تعريف أو تي جي فسرة جي اتش اكس او جي اتش كله في اكس
+
+291
+00:32:48,850 --> 00:32:53,030
+او تي جي اتش كله في اكس لان جي في اتش يعطينا
+
+292
+00:32:53,030 --> 00:32:57,830
+element من جي يبقى بناء عليه هذا موجود في S يبقى
+
+293
+00:32:57,830 --> 00:33:02,030
+ال S جي is a closed under multiplication أو ال
+
+294
+00:33:02,030 --> 00:33:05,770
+operation اللي عليها ال composition of function is
+
+295
+00:33:05,770 --> 00:33:13,220
+a binary operation الآن صار عندنا binary operation
+
+296
+00:33:13,220 --> 00:33:15,800
+كمان ال composition of a function ثم نعرف انها
+
+297
+00:33:15,800 --> 00:33:19,440
+associative يبقى ماضلش عندي الا main two
+
+298
+00:33:19,440 --> 00:33:26,480
+conditions ال identity element أنا ادعي ان TA هو ال
+
+299
+00:33:26,480 --> 00:33:31,400
+identity element وروح نثبتنا ان هو ال identity
+
+300
+00:33:31,400 --> 00:33:37,420
+element اتدعيت ان تجي انفرس بالضبط هو ت وال انفرس
+
+301
+00:33:37,420 --> 00:33:42,860
+بحطه على ال element من اين لك هذا روحت اثبتته وهيه
+
+302
+00:33:42,860 --> 00:33:48,620
+وهيه كله طلع ليه ال identity element يبقى فعلا كل
+
+303
+00:33:48,620 --> 00:33:54,460
+element في SG له معكوس يبقى بناء عليه ال SG the
+
+304
+00:33:54,460 --> 00:33:59,540
+group of permutation صارت group إذا مدام صارت
+
+305
+00:33:59,540 --> 00:34:05,980
+group وعند group بقدر اكون ايش isomorphism تعرف الـ
+
+306
+00:34:05,980 --> 00:34:11,860
+Function Phi من G إلى SG بـ Phi of G بيساوي من T of
+
+307
+00:34:11,860 --> 00:34:18,780
+G جي هذه موجودة في جي الـ TG موجودة في SG بدي أروح
+
+308
+00:34:18,780 --> 00:34:23,300
+أبين إنه فعلا هذه الـ Function معرفة من هنا إلى
+
+309
+00:34:23,300 --> 00:34:28,950
+هنا باخد عنصرين متساوين و بثبت ان عنصرته متساوية ان
+
+310
+00:34:28,950 --> 00:34:34,210
+حدث ذلك بقول هذه well-defined function يعني ال
+
+311
+00:34:34,210 --> 00:34:39,990
+function معرفة تعريفا صحيحا فجيه تقول خد لي G و H
+
+312
+00:34:39,990 --> 00:34:44,470
+موجودات بحيث الـ G يساوي الـ H أثر على الطرفين بـ
+
+313
+00:34:44,470 --> 00:34:49,800
+Phi Phi of G بده يساوي TG وهذه تساوي الـ TH يبقى صورة
+
+314
+00:34:49,800 --> 00:34:53,580
+العنصر الأول تساوي صورة العنصر التانية يبقى Phi
+
+315
+00:34:53,580 --> 00:34:58,160
+is well defined ال one to one خد لي صورتين
+
+316
+00:34:58,160 --> 00:35:03,240
+متساويتين وبدأ أثبت أن أصلهم متساوي يبقى TG بدأ
+
+317
+00:35:03,240 --> 00:35:07,260
+يساوي TH بدأ أخلي كل واحد يتأثر على X عشان أقدر
+
+318
+00:35:07,260 --> 00:35:13,100
+أطبق التعريف اللي عندنا هذا فصار عندنا TG of X بده
+
+319
+00:35:13,100 --> 00:35:21,120
+يساوي اللي هو TH of X تمام
+
+320
+00:35:21,120 --> 00:35:26,800
+يبقى GX يساوي HX بدنا ن cancel ال X من الطرفين
+
+321
+00:35:26,800 --> 00:35:30,660
+يبقى ال G يساوي ال H وبالتالي Phi is one to one
+
+322
+00:35:30,660 --> 00:35:36,120
+ال onto صحيحة لإن كل TG في SG بده يقابله main
+
+323
+00:35:36,470 --> 00:35:40,050
+الخطوة الأخيرة موجودة في جيو مين و جيونتو موجودة
+
+324
+00:35:40,050 --> 00:35:46,310
+في جيو
+
+325
+00:35:46,310 --> 00:35:56,560
+مين و جيونتو موجودة في جيونتو أي كتاب جبر تلاقيه في
+
+326
+00:35:56,560 --> 00:36:00,620
+المكتب على النت بس اكتب Cayley theorem بفتح لك
+
+327
+00:36:00,620 --> 00:36:05,740
+علامين على Cayley theorem نظرية اللي هو العالم كايلي
+
+328
+00:36:05,740 --> 00:36:11,260
+اللي اكتشفها اللي أنا أنا بدي اعطيك مثال تطبيقي
+
+329
+00:36:11,260 --> 00:36:15,680
+على الشغل هذي تمام؟ ايوة تعال هنا اللي هو تعال
+
+330
+00:36:20,700 --> 00:36:24,500
+أيوة جيد كويس
+
+331
+00:36:24,500 --> 00:36:30,230
+أثبتنا ان فاي is onto تبع التعريف هذاهي التعريف
+
+332
+00:36:30,230 --> 00:36:36,270
+هذه file is under كيف أثبتنا هذا؟ لأن أي element
+
+333
+00:36:36,270 --> 00:36:41,950
+في S جي هيه هذا بيعتمد على مين؟ على G جي من وين جي
+
+334
+00:36:41,950 --> 00:36:48,790
+بناها؟ من G كبتر يبقى كل permutation هنا تعتمد على
+
+335
+00:36:48,790 --> 00:36:53,070
+element من اللي هناك يعني لا يمكن أن يكون هنا
+
+336
+00:36:53,070 --> 00:36:57,610
+permutation ما لم يكن مناظر إلها element من G
+
+337
+00:36:57,610 --> 00:37:04,720
+فضعت؟ أه حد بدى يسأل تانى طب نعطى مثال عددي توضيحى
+
+338
+00:37:04,720 --> 00:37:13,680
+كيف نحسب هالشغل هذه example
+
+339
+00:37:48,300 --> 00:37:59,760
+find the group SG where ال
+
+340
+00:37:59,760 --> 00:38:04,540
+G بدأت ساوي ال U عشرة
+
+341
+00:38:17,140 --> 00:38:23,660
+أظهر لو وجدنا عناصر SG بيصير الجيل الأصلي اللي هي
+
+342
+00:38:23,660 --> 00:38:30,600
+U10 isomorphic لمين؟ للـ SG حسب نظرية كايلي الآن لو
+
+343
+00:38:30,600 --> 00:38:40,340
+جيت للـ U10 مين عناصرها؟ الواحد، اتنين، تلاتة،
+
+344
+00:38:40,340 --> 00:38:49,730
+أربعة، خمسة، ستة، سبعة، تسعة، في غيرهم؟ طيب يبقى
+
+345
+00:38:49,730 --> 00:38:59,910
+بناء عليه ال S G ال S G أو ال S U عشرة بدها تساوي
+
+346
+00:38:59,910 --> 00:39:09,110
+T واحد و T تلاتة و T سبعة و T تسعة بس مين T واحد و
+
+347
+00:39:09,110 --> 00:39:14,530
+T تلاتة و T سبعة مش عارفين بدنا نعرف تمام باجي
+
+348
+00:39:14,530 --> 00:39:15,950
+بقولهم where
+
+349
+00:39:18,450 --> 00:39:26,230
+حيث الـ T1 هذه هي ال identity permutation الصف
+
+350
+00:39:26,230 --> 00:39:31,070
+الأول بقولش واحد اتنين تلاتة اربعة العناصر هذه
+
+351
+00:39:31,070 --> 00:39:38,110
+تبعات الـ G لإن هذه ال permutation على ال group مش
+
+352
+00:39:38,110 --> 00:39:43,990
+على أعداد عادية يبقى الصف الأول واحد تلاتة سبعة
+
+353
+00:39:43,990 --> 00:39:52,810
+تسعة انتهينا بدي اجيب صورهم تمام؟ قبل شوية عرفنا ان
+
+354
+00:39:52,810 --> 00:40:00,870
+TG of X بده يساوي حصل ضرب G في X مظبوط؟ يبقى أنا
+
+355
+00:40:00,870 --> 00:40:08,730
+ايش؟ بدي T واحد of واحد بدي اعطيك الواحد T1 of
+
+356
+00:40:08,730 --> 00:40:15,130
+تلاتة سبعة تسعة كما هي ال identity كل شي بده ينزل
+
+357
+00:40:15,130 --> 00:40:21,010
+زي ما هو كيف؟
+
+358
+00:40:21,010 --> 00:40:29,650
+واحد في تلاتة واحد في سبعة واحد في تسعة بين ايش؟
+
+359
+00:40:29,650 --> 00:40:38,000
+طيب يبقى هذه ال identity هذه ال T1 بدي هنا T ثلاثة
+
+360
+00:40:38,000 --> 00:40:47,340
+بده يساوي الصف الأول واحد تلاتة سبعة تسعة طيب
+
+361
+00:40:47,340 --> 00:40:53,480
+بدي أجيب الصف الثاني بقول لي T G of X بده يساوي GX
+
+362
+00:40:53,480 --> 00:41:00,160
+يعني أنا بدي أحسبله T تلاتة of واحد يبقى تلاتة في
+
+363
+00:41:00,160 --> 00:41:07,720
+واحد يبقى تلاتة يبقى العنصر هنا تلاتة بدي T ثلاثة و
+
+364
+00:41:07,720 --> 00:41:12,740
+ثلاثة يبقى ثلاثة في ثلاثة اللي هو تسعة يبقى هنا
+
+365
+00:41:12,740 --> 00:41:19,640
+تسعة بدي T ثلاثة و سبعة اللي هو تلاتة في سبعة
+
+366
+00:41:19,640 --> 00:41:27,060
+بقدرش؟ واحد و عشري مضيله عشرة بواحد يبقى هذه تساوي
+
+367
+00:41:27,060 --> 00:41:33,500
+واحد إذا هنا واحد بجيلك هنا T ثلاثة و تسعة يبقى
+
+368
+00:41:33,500 --> 00:41:38,020
+ثلاثة في تسعة في قدر؟ سبعة و عشرين موديه العاشرة
+
+369
+00:41:38,020 --> 00:41:44,900
+بسبعة يبقى هنا السبعة لاحظ مجانيش ولا رقم الا اللي
+
+370
+00:41:44,900 --> 00:41:50,340
+موجودة في الصف الأول اتنين لم يتكرر اي رقم مرتين
+
+371
+00:41:50,340 --> 00:41:56,120
+على الإطلاق ليش انها one to one and onto طيب لو
+
+372
+00:41:56,120 --> 00:42:04,270
+بدنا الآن T سبعة يبقى واحد ثلاثة سبعة تسعة نحسبهم
+
+373
+00:42:04,270 --> 00:42:08,910
+بنفس الطريقة اللي هناك ت سبعة وواحد يبقى سبعة في
+
+374
+00:42:08,910 --> 00:42:15,170
+واحد بسبعة الان ت سبعة تلاتة يعني سبعة في تلاتة
+
+375
+00:42:15,170 --> 00:42:21,500
+بواحد وعشرين مضيوله عشرة أب واحد سبعة في سبعة بتسعة 
+
+376
+00:42:21,500 --> 00:42:27,340
+واربعين موديولو سبعة بتسعة، سبعة في تسعة بتلاتة وثلاثين
+
+377
+00:42:27,340 --> 00:42:32,760
+وستين موديولو عشرة بتلاتة اللي هي بجداش بتلاتة
+
+378
+00:42:32,760 --> 00:42:40,940
+ضلت عندنا مين؟ تتسعة واحد تلاتة سبعة تسعة تسعة في
+
+379
+00:42:40,940 --> 00:42:46,580
+واحد بتسعة، تسعة في تلاتة بسبعة وعشرين، سبعة في
+
+380
+00:42:46,580 --> 00:42:51,260
+تسعة على تسعة في سبعة بتلاتة وستين، تسعة في تسعة 
+
+381
+00:42:51,260 --> 00:43:00,650
+بواحد وثمانين، يبقى الآن عرفنا كيف بنكوّم الـT1 وT3
+
+382
+00:43:00,650 --> 00:43:08,110
+وT7، يبقى الـSG بكتب كل عنصر فيهم بدلالة عناصر G
+
+383
+00:43:08,110 --> 00:43:12,980
+مين ما تكون جيهش ما يكون شكل هيكون، يبقى بقول TG1
+
+384
+00:43:12,980 --> 00:43:18,740
+TG2 TG3 TG4 لغاية ما أخلصهم كلهم، كيف بحسب كل واحد
+
+385
+00:43:18,740 --> 00:43:23,520
+منهم؟ بالطريقة اللي عندنا هنا، بحط الصف الأول عناصر
+
+386
+00:43:23,520 --> 00:43:28,280
+G وبعدين بخلي الـT تأثر على العنصر الأول الثاني
+
+387
+00:43:28,280 --> 00:43:33,660
+الثالث الرابع وبكتب الصفوف، يبقى هذه العناصر يبقى 
+
+388
+00:43:33,660 --> 00:43:38,020
+في هذه الحالة باي كلي
+
+389
+00:43:39,710 --> 00:43:46,930
+أو Keyless theorem، الـU عشرة الـU عشرة
+
+390
+00:43:46,930 --> 00:43:57,550
+isomorphic للـS U عشرة، هاي المقصود يعني يبقى G
+
+391
+00:43:57,550 --> 00:44:03,330
+isomorphic للست of all permutations اللي كوّنها
+
+392
+00:44:03,330 --> 00:44:08,780
+على الـgroup عشرة، وكذا، يبقى فهمنا كيف تطبيق
+
+393
+00:44:08,780 --> 00:44:15,540
+النظرية، الآن بدنا نخش لنظرية مكونة من سبعة نقاط
+
+394
+00:44:15,540 --> 00:44:19,560
+للمرة القادمة، إن شاء الله، ما فيش إمكانية اليوم
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..440b6acbedd6470887e1641a2b049956fcfff9be
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/XiCuaL9yLrA_raw.srt
@@ -0,0 +1,1584 @@
+1
+00:00:21,210 --> 00:00:26,110
+بسم الله الرحمن الرحيم نكمل ما ابتدأناه في
+
+2
+00:00:26,110 --> 00:00:30,870
+المحاضرة السابقة عرفنا ال isomorphism أخدنا عليه
+
+3
+00:00:30,870 --> 00:00:36,030
+خمسة أمثلة في الفترة الصبحية الآن بدنا نيجي لأول
+
+4
+00:00:36,030 --> 00:00:42,150
+نظرية هذه النظرية نظرية كيلي تنص على ما يتيح أن أي
+
+5
+00:00:42,150 --> 00:00:47,310
+group تبقى isomorphic to a group of permutations
+
+6
+00:00:48,010 --> 00:00:53,130
+الجروب of permutations بدي أنشئها من خلال الجروب
+
+7
+00:00:53,130 --> 00:00:58,570
+اللي عندي طبعا هذا بيختلف عن كل ما سبق انه لم يبين
+
+8
+00:00:58,570 --> 00:01:03,210
+ايش شكل الجروب ولا مبين شكل الجروب of permutation
+
+9
+00:01:03,210 --> 00:01:07,890
+مش مبين عندي ولا عاجز لذلك بدنا نبدأ البرهان
+
+10
+00:01:07,890 --> 00:01:14,430
+كالتالي فبجي بقول let G بي أ grow
+
+11
+00:01:17,890 --> 00:01:32,690
+for any g اللي موجودة فيه g define a function TG
+
+12
+00:01:32,690 --> 00:01:46,470
+من G إلى G by TG of X بده ساوي GXلكل الـ X اللي
+
+13
+00:01:46,470 --> 00:01:55,050
+موجود في جي يبقى
+
+14
+00:01:55,050 --> 00:02:01,030
+أنا الأن بدي أسعى إلى أكون من ال group of
+
+15
+00:02:01,030 --> 00:02:06,390
+permutation من ال group اللي موجودة لذلك فرط ال
+
+16
+00:02:06,390 --> 00:02:13,420
+group اللي موجودة عند جي بدي أكونبالتالي يجب أن
+
+17
+00:02:13,420 --> 00:02:18,020
+يكون الجروب of all permutations التي تعتمد على
+
+18
+00:02:18,020 --> 00:02:22,660
+الجروب اللي عندنا لذلك لو أخدت أي جي موجود في جي
+
+19
+00:02:22,660 --> 00:02:28,960
+يجب أن أعرف الدالة كالتالي تجي من جي إلى جي باي
+
+20
+00:02:28,960 --> 00:02:34,140
+يجب أن أعرفها كالتالي تجي of x يساوي جي of x لكل
+
+21
+00:02:34,140 --> 00:02:38,650
+ال x الموجود في جيالسؤال هو هل هذا التعريف صحيح
+
+22
+00:02:38,650 --> 00:02:44,910
+ولا غير صحيح الإجابة التعريف صحيح لأن الـTG من G
+
+23
+00:02:44,910 --> 00:02:50,710
+إلى G الـG و الـX موجودات في G إذا حصل ضربهما
+
+24
+00:02:50,710 --> 00:02:55,550
+موجود في G لأنه G closed under multiplication أو
+
+25
+00:02:55,550 --> 00:02:58,550
+ال operation اللي على G هي عبارة عن binary
+
+26
+00:02:58,550 --> 00:03:03,500
+operation يبقى الـG في X موجودة في ال groupاللي
+
+27
+00:03:03,500 --> 00:03:09,380
+عندنا يبقى تعريفي هذا صحيح الان انا ادعي ان هذه ال
+
+28
+00:03:09,380 --> 00:03:15,900
+function is a permutation انا ادعي ان تيجي هذه
+
+29
+00:03:15,900 --> 00:03:19,980
+عبارة عن permutation طيب هي ال permutation عبارة
+
+30
+00:03:19,980 --> 00:03:23,780
+عن ايش؟ function و ال function بتكبر one to one
+
+31
+00:03:23,780 --> 00:03:27,620
+and on two اذا طلعت هذه ال function one to one and
+
+32
+00:03:27,620 --> 00:03:32,500
+on two يبقى بال فهي تكون permutation مظبوط؟يبقى
+
+33
+00:03:32,500 --> 00:03:45,080
+هنا باجي بقول now ال TG is a permutation طبعا؟
+
+34
+00:03:45,080 --> 00:03:55,740
+طيب ليش؟ because السبب النقطة الأولىالـ TG هادي is
+
+35
+00:03:55,740 --> 00:04:02,960
+one to one الـ TG is one to one بدنا نثبت صحة هذا
+
+36
+00:04:02,960 --> 00:04:11,500
+الكلام يبقى باجي بقوله let الـ TG of X يساوي TG of
+
+37
+00:04:11,500 --> 00:04:20,520
+Y then حسب التعريف الـ TG of X بده يساوي الـ G في
+
+38
+00:04:20,520 --> 00:04:29,350
+Xالـ TG of Y بده ساوي GYبالـ left cancellation law
+
+39
+00:04:29,350 --> 00:04:35,470
+بنقدر نشطب الجي والجي يطلع لنا قداش ان ال X بده
+
+40
+00:04:35,470 --> 00:04:40,130
+يساوي ال Y او كون الجي في الجي والجي اجروا بيبقى
+
+41
+00:04:40,130 --> 00:04:44,110
+جي انفرست موجود يبقى لو ضربت الطرفين في جي انفرست
+
+42
+00:04:44,110 --> 00:04:48,830
+هيعطينا ان X يساوي Y معناه هذا الكلام ان TG is one
+
+43
+00:04:48,830 --> 00:04:53,230
+to one لانه خدت صورتين متساويتين اثبتت ان اصلهم
+
+44
+00:04:53,570 --> 00:05:01,690
+متساوين الان بدنا نثبت النقطة الثانية انه تي جي is
+
+45
+00:05:01,690 --> 00:05:11,290
+onto لذلك بدروح اخد element في جي و اثبت انه اصل
+
+46
+00:05:11,290 --> 00:05:19,440
+في جي يبقى باجي بقوله let y موجودة في جيفي جيله من
+
+47
+00:05:19,440 --> 00:05:24,360
+الـcodomain تبع الـTG يعني في الـG التانية هذه
+
+48
+00:05:24,360 --> 00:05:32,380
+ماهي هذه هي هذه كويس موجود في الـTG then الـY
+
+49
+00:05:32,380 --> 00:05:40,650
+تساوي بدي أحاولأكتب الـ Y هذه كصورة لعنصر من G
+
+50
+00:05:40,650 --> 00:05:48,590
+الأولى إذا لو جيت قلت لك ال Y هذه قلت لك هي G G
+
+51
+00:05:48,590 --> 00:05:56,910
+inverse Y بنفع؟ بنفع؟ لإيش؟ لأن الـ G G inverse هو
+
+52
+00:05:56,910 --> 00:06:01,350
+ال identity element و ال identity element تضربه في
+
+53
+00:06:01,350 --> 00:06:06,210
+أي element بيعطيك نفس ال elementإذا بقدر أقول هذه
+
+54
+00:06:06,210 --> 00:06:10,490
+G في G inverse Y
+
+55
+00:06:13,170 --> 00:06:17,550
+فباش رأيك هذا اللي بين قصيره؟ بدي أسميه أي عنصر
+
+56
+00:06:17,550 --> 00:06:24,990
+آخر للسهولة إذا بقدر أقول هذه جي إكس مثلا إذا
+
+57
+00:06:24,990 --> 00:06:31,030
+العنصر هذا شيلته و حاطه بدله مين؟ إكس طيب جي إكس
+
+58
+00:06:31,030 --> 00:06:39,080
+هذه عبارة عن مين؟ عبارة عن تجي of إكسيبقى ال
+
+59
+00:06:39,080 --> 00:06:44,740
+element y اللي موجود في ال group g لجت له أصل x
+
+60
+00:06:44,740 --> 00:06:51,000
+موجود في g التانية يبقى بناء عليه في is onto يبقى
+
+61
+00:06:51,000 --> 00:06:56,340
+صار في عندي function من g إلى g هذه one to one and
+
+62
+00:06:56,340 --> 00:07:00,060
+onto واحنا لما عرفنا ال permutation قلنا هي
+
+63
+00:07:00,060 --> 00:07:05,630
+functionعبارة عن one to one and on to يبقى بناء
+
+64
+00:07:05,630 --> 00:07:12,050
+عليه ال TG هذي عبارة عن ايش permutation يبقى ال
+
+65
+00:07:12,050 --> 00:07:18,090
+element G من الجروب جاب لي permutation اسمها مين
+
+66
+00:07:18,090 --> 00:07:25,870
+اسمها TG الآن بده لم هدول كل ال permutation و بده
+
+67
+00:07:25,870 --> 00:07:34,750
+حطهم في set يبقى الآنconsider جي
+
+68
+00:07:34,750 --> 00:07:44,650
+بار جي بار هذي بتعطيها الرمز SG مين ال SG هذي كل ت
+
+69
+00:07:44,650 --> 00:07:52,550
+جي بحيث الجي موجودة في جي يعني
+
+70
+00:07:53,310 --> 00:07:58,270
+لو جينا قولنا الـ G هذه فيها خمسين elements مثلا
+
+71
+00:07:58,270 --> 00:08:02,910
+يبقى ابو دي اطلع هنا كم element عندى؟ خمسين
+
+72
+00:08:02,910 --> 00:08:08,570
+elements لإنه TG1, TG2, TG3, TG4 لغاية مكمله
+
+73
+00:08:08,570 --> 00:08:14,390
+الخمسين يبقى ال SG هذي mean the set of all
+
+74
+00:08:14,390 --> 00:08:20,210
+permutations اللي محطوطة على ال group G هذه the
+
+75
+00:08:20,210 --> 00:08:28,300
+setof all permutations
+
+76
+00:08:28,300 --> 00:08:32,060
+of
+
+77
+00:08:32,060 --> 00:08:40,640
+G كل ال permutations اللي على G الان انا هتدعي ان
+
+78
+00:08:40,640 --> 00:08:47,450
+SG هدى is a groupوبنفعش تدعى يا صاحبي بدك تبين انه
+
+79
+00:08:47,450 --> 00:08:52,810
+فعلا انه SG هذه ايه هي group لانه اذا اثبتت انها
+
+80
+00:08:52,810 --> 00:08:58,150
+group وصلت للنص اللى انا بقول عنه كل group
+
+81
+00:08:58,150 --> 00:09:02,210
+isomorphic الى permutation group او ال group of
+
+82
+00:09:02,210 --> 00:09:08,190
+permutation تمام يبقى الخطوة التالية بعد ما خلقت
+
+83
+00:09:08,590 --> 00:09:13,950
+permutations لكل عنصر موجود في دي خلقتله
+
+84
+00:09:13,950 --> 00:09:18,230
+permutation اقبلهالـ Perimotations حطيتهم في ست
+
+85
+00:09:18,230 --> 00:09:24,930
+واحدة سميتها G bar أو سميتها SG من العناصر تبعتها
+
+86
+00:09:24,930 --> 00:09:30,190
+كل الـ Perimotations اللي خلقتهم على ال group G
+
+87
+00:09:30,190 --> 00:09:37,510
+الآن أنا بتدعي ان SG هذه is a group يبقى بدى أشوف
+
+88
+00:09:37,510 --> 00:09:44,450
+هل ال SG بتحقق شروط ال group ولا لايبقى أول شيء ال
+
+89
+00:09:44,450 --> 00:09:47,370
+operation اللي عليها madam permutation هو ال
+
+90
+00:09:47,370 --> 00:09:52,690
+composition of functions الآن ال composition of
+
+91
+00:09:52,690 --> 00:09:57,430
+functions بدي أثبت إنها binary operation إيش يعني
+
+92
+00:09:57,430 --> 00:10:01,430
+binary operation؟ يعني لو جبت composition بين two
+
+93
+00:10:01,430 --> 00:10:06,190
+permutations بدي أعطيني مين؟ permutation واحدة إن
+
+94
+00:10:06,190 --> 00:10:10,590
+حدث ذلك يبقى فعلا تبقى ال operation اللي عليها هي
+
+95
+00:10:10,590 --> 00:10:22,300
+binaryoperation يبقى we a claim that اكليم يدعي ان
+
+96
+00:10:22,300 --> 00:10:32,520
+ال SG is a group under the
+
+97
+00:10:32,520 --> 00:10:38,240
+composition of
+
+98
+00:10:38,240 --> 00:10:39,100
+functions
+
+99
+00:10:41,910 --> 00:10:47,890
+انا هتدعي ان اس جي هدى is a group تحت عملية تحصيل
+
+100
+00:10:47,890 --> 00:10:53,770
+او تركيب من ال function بيدروح اثبت هذا الكلام
+
+101
+00:10:53,770 --> 00:11:02,990
+يبقى باجي بقوله for all جي و H اللى موجودة في جي
+
+102
+00:11:02,990 --> 00:11:04,190
+we have
+
+103
+00:11:20,200 --> 00:11:24,840
+البيانات مضربات ضرب لكن في الحقيقة هي عبارة عن
+
+104
+00:11:26,540 --> 00:11:34,960
+composition تحصيل يبقى بناء عليه هذا بيصير تجي of
+
+105
+00:11:34,960 --> 00:11:45,440
+th of x composition يبقى بناء عليه هذا بيعطيني تجي
+
+106
+00:11:45,440 --> 00:11:55,980
+of th of x حسب التعريف بيعطيني ال h of xتمام حسب
+
+107
+00:11:55,980 --> 00:12:04,760
+التعريف كمان بده يعطيني g of h of x ال g و ال h و
+
+108
+00:12:04,760 --> 00:12:09,420
+ال x موجودات في g ولا لأ و ال g associative ال
+
+109
+00:12:09,420 --> 00:12:15,920
+operation اللي عليها يبقى هذا بده يعطيني gh في x
+
+110
+00:12:15,920 --> 00:12:26,650
+يبقى هذا بده يعطيني th of xهذه موجودة في SD ولا لأ
+
+111
+00:12:26,650 --> 00:12:34,570
+يبقى هذه موجودة في SD يبقى بناء عليه ال
+
+112
+00:12:34,570 --> 00:12:38,250
+composition of function is a binary operation على
+
+113
+00:12:38,250 --> 00:12:48,750
+main على SD يبقى ال composition of
+
+114
+00:12:48,750 --> 00:12:57,500
+functions isa binary operation
+
+115
+00:12:57,500 --> 00:13:00,540
+on
+
+116
+00:13:00,540 --> 00:13:08,540
+SG طب إيش رأيك؟ ال composition of function قبلك
+
+117
+00:13:08,540 --> 00:13:12,300
+أخدناها كثير associative ولا لأ؟ associative
+
+118
+00:13:12,300 --> 00:13:20,460
+associative also وكذلك we know that
+
+119
+00:13:22,880 --> 00:13:29,140
+the composition of
+
+120
+00:13:29,140 --> 00:13:38,660
+functions is associative يبقى
+
+121
+00:13:38,660 --> 00:13:46,260
+مش ضايق اللي عندى ال identity element يبقى TE is
+
+122
+00:13:46,260 --> 00:13:52,380
+the identity element
+
+123
+00:13:54,350 --> 00:14:03,070
+ن اس جي ليش because بتاخد
+
+124
+00:14:03,070 --> 00:14:11,050
+تي في تي اتش as a function of x هشوف كده الشي
+
+125
+00:14:11,050 --> 00:14:19,050
+يعطيني يبقى هذا بده يعطيني تي في تي اتش of x يبقى
+
+126
+00:14:19,050 --> 00:14:26,320
+تي في ال اتش اكس هذه حسب التعريفوحسب التعريف كذلك
+
+127
+00:14:26,320 --> 00:14:36,620
+E في HX اللي هو بده يساوي HX يبقى TH of X يبقى
+
+128
+00:14:36,620 --> 00:14:43,220
+بناء عليه TE في TH of X هتانمين TH of X هذا لو كان
+
+129
+00:14:43,220 --> 00:14:49,880
+الضرب من جهة الشمال لو كان من جهة اليامين and TH
+
+130
+00:14:59,520 --> 00:15:16,000
+يبقى هذا الكلام يبقى تي اتش تي
+
+131
+00:15:16,000 --> 00:15:20,190
+اتش تي اتش تي اتش تي اتش تي اتش تي اتشإذا لو ضربت
+
+132
+00:15:20,190 --> 00:15:26,970
+من اليمين وضربت من الشمال بيعطيني ته of x يبقى ته
+
+133
+00:15:26,970 --> 00:15:35,230
+هو الوضع الوحدة الوحدة الوحدة الوحدة
+
+134
+00:15:35,230 --> 00:15:41,630
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+135
+00:15:41,630 --> 00:15:46,210
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+136
+00:15:46,210 --> 00:15:46,570
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+137
+00:15:46,570 --> 00:15:46,570
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+138
+00:15:46,570 --> 00:15:46,570
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+139
+00:15:46,570 --> 00:15:46,590
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+140
+00:15:46,590 --> 00:15:47,270
+الو
+
+141
+00:15:52,000 --> 00:16:02,180
+تعالى نشوف الان ال TG انفرس TG as a function of X
+
+142
+00:16:02,180 --> 00:16:13,040
+يبقى هذا بدى يعطينا TG انفرس ل TG of Xهذا الكلام
+
+143
+00:16:13,040 --> 00:16:21,780
+بدي اعطينا تجي انفرست تجي of x هيها بمين بجي اكس
+
+144
+00:16:21,780 --> 00:16:25,160
+يبقى
+
+145
+00:16:25,160 --> 00:16:31,420
+صار الجي اكس كله element في domain تجي انفرست يبقى
+
+146
+00:16:31,420 --> 00:16:39,230
+هذا الكلام بدي اساوي جي انفرست لجي اكسهدول الـ
+
+147
+00:16:39,230 --> 00:16:44,010
+three elements كلهم موجودات في ال group G خاصية ال
+
+148
+00:16:44,010 --> 00:16:48,730
+associativity عليها الصحيحة يبقى هذا الكلام بده
+
+149
+00:16:48,730 --> 00:16:56,610
+يعطينا G inverse G في ال X يبقى هذا بده يعطينا E X
+
+150
+00:16:56,610 --> 00:17:06,160
+ال E X هي عبارة عن T E of Xإذا حصل ضرب الـElement
+
+151
+00:17:06,160 --> 00:17:13,200
+في معكوسه إعطاني الـIdentity Element بالمثل يبقى
+
+152
+00:17:13,200 --> 00:17:26,900
+and الـTG of X في الـTG and الـTG في الـTG inverse
+
+153
+00:17:26,900 --> 00:17:36,560
+as a function of Xهذا الكلام بدي يعطيني TG في TG
+
+154
+00:17:36,560 --> 00:17:46,020
+inverse of X هذا الكلام بيساوي اي TG اللي برا و
+
+155
+00:17:46,020 --> 00:17:51,580
+اللي جوا هادي اللي هي في G inverse X طبقا لل
+
+156
+00:17:51,580 --> 00:17:58,980
+definition اللي عنديهذا الكلام بده يساوي جي للجي
+
+157
+00:17:58,980 --> 00:18:05,560
+انفرست اكس هذا نظرة لخاصية ال associativity بده
+
+158
+00:18:05,560 --> 00:18:12,140
+يساوي جي جي انفرست اكس الجي جي انفرست بتعطيني ال
+
+159
+00:18:12,140 --> 00:18:20,930
+identity element يبقى هذه بتعطيني ax لte of xإذا
+
+160
+00:18:20,930 --> 00:18:29,000
+أصبح تجي انفرس هو هو بالضبط تجي لكل انفرسليش ان
+
+161
+00:18:29,000 --> 00:18:33,000
+ضربته من اليمين و الشمال اعطاني نفس ال identity
+
+162
+00:18:33,000 --> 00:18:38,020
+element اذا binary operation associative ال
+
+163
+00:18:38,020 --> 00:18:41,600
+identity element ال inverse element لكل element
+
+164
+00:18:41,600 --> 00:18:46,360
+يبقى ال SG صارت مالها a group under the
+
+165
+00:18:46,360 --> 00:18:54,540
+composition of functions يبقى هنا so ال SG is a
+
+166
+00:18:54,540 --> 00:19:05,910
+groupunder the composition of
+
+167
+00:19:05,910 --> 00:19:16,570
+functions خلصنا يا شباب؟ لسه مخلصناش احنا جبنا
+
+168
+00:19:16,570 --> 00:19:21,430
+جروب جي وجبنا جروب تاني اللي هو the set of all
+
+169
+00:19:21,430 --> 00:19:25,960
+permutationsلجروبة المكوّنة من permutation الأن
+
+170
+00:19:25,960 --> 00:19:31,940
+بدي أثبت أنه اتنين هذول are isomorphic أي اللي
+
+171
+00:19:31,940 --> 00:19:42,600
+بديها يبقى الأن بقوله define a function Phi من G
+
+172
+00:19:42,600 --> 00:19:45,520
+إلى SG by
+
+173
+00:19:51,950 --> 00:20:01,320
+5 of G بدر ساوي TG ال elementاللي في ال group
+
+174
+00:20:01,320 --> 00:20:07,680
+capital يبدأ يسميه G ال element اللي في S G ال S G
+
+175
+00:20:07,680 --> 00:20:15,820
+قلنا وين حطنا لها تعرف قلنا ال S G where are the
+
+176
+00:20:15,820 --> 00:20:19,940
+composition binary operations اه ال S G وين
+
+177
+00:20:19,940 --> 00:20:25,780
+كتبناها this is a group اه هي ال S G يبقى ال
+
+178
+00:20:25,780 --> 00:20:30,900
+element اللي في S G على شكلاللي هو الـ permutation
+
+179
+00:20:30,900 --> 00:20:37,820
+TG يبقى لكل element جي موجود في G عرفنا منهم اللي
+
+180
+00:20:37,820 --> 00:20:43,540
+هو الـ TG اللي موجودة في SG الان انا بدى ابين ان
+
+181
+00:20:43,540 --> 00:20:50,080
+هذه ال function is well defined يبقى الخطوة الأولى
+
+182
+00:20:50,080 --> 00:20:58,740
+Phi is well definedWell-defined يعني معرفة تعريفا
+
+183
+00:20:58,740 --> 00:21:05,960
+صحيحاكيف تعريفا صحيحا كالتالي بدأ أخد عنصرين
+
+184
+00:21:05,960 --> 00:21:12,860
+متساوين و أثبت أنه إلهم نفس الصورة على عكس مين ال
+
+185
+00:21:12,860 --> 00:21:17,000
+one to one ال one to one بتاخد صورتين و بتثبت أن
+
+186
+00:21:17,000 --> 00:21:26,920
+أصلهم متساوي يبقى هنا F ال G و H موجودات في ال G
+
+187
+00:21:29,890 --> 00:21:36,850
+إن الـ G بده يساوي الـ H then بده يتأثر الـ Phi
+
+188
+00:21:36,850 --> 00:21:45,730
+على الطرفين يبقى Phi of G بده يساوي Phi of H حسب
+
+189
+00:21:45,730 --> 00:21:51,590
+ال definition Phi of G بده يساوي TG
+
+190
+00:21:53,140 --> 00:22:00,700
+فاي اف اتش تساوي ت اتش اذا العنصرين المتساويين في
+
+191
+00:22:00,700 --> 00:22:06,140
+جيوز صورتهم متساوي تبقى ال function معرفة تعريفا
+
+192
+00:22:06,140 --> 00:22:12,540
+صحيا بعد ذلك اثبت ان هذا isomorphism يعني ال
+
+193
+00:22:12,540 --> 00:22:17,620
+function f صارت موجودة شو ضايل عندى one to one
+
+194
+00:22:18,000 --> 00:22:22,720
+وانتوا وتخدم خاصية الهيزمورفزيوم لإيه فاي of a بي
+
+195
+00:22:22,720 --> 00:22:27,940
+بده يساوي فاي of a في فاي of b يبقى بالدرجة يقوله
+
+196
+00:22:27,940 --> 00:22:35,980
+فاي النقطة الثانية is one to one يبقى بالدرجة
+
+197
+00:22:35,980 --> 00:22:45,700
+يقوله assume افترض ان فاي of g بده يساوي فاي of h
+
+198
+00:22:46,380 --> 00:22:55,240
+بدي احاول اثبتله ان الـ G تساوي مين تساوي ال H ثم
+
+199
+00:22:55,240 --> 00:23:06,800
+الـ Phi of G اللي هي TG بيديها تساوي THتمام إذا تي
+
+200
+00:23:06,800 --> 00:23:11,700
+جي لما تأثر على أي element بده يسوى تأثير تي إتش
+
+201
+00:23:11,700 --> 00:23:15,680
+على أي element سواء كان ال element هذا ال identity
+
+202
+00:23:15,680 --> 00:23:19,980
+element أو أي element موجود في ال group يعني لو
+
+203
+00:23:19,980 --> 00:23:26,200
+قلت لك تي جي of اي أو قلت لك تي جي of اكسيان هذه
+
+204
+00:23:26,200 --> 00:23:31,190
+والله هذه الاتنين هيأديني إلى نفس النتيجةهذا بده
+
+205
+00:23:31,190 --> 00:23:45,350
+يعطينا ان TG of X بده يساوي TH of X هذا
+
+206
+00:23:45,350 --> 00:23:51,770
+بده يعطينا ان G of X بده تساوي H
+
+207
+00:23:58,390 --> 00:24:04,470
+بال right cancellation law يبقى هذا معناه ان ال G
+
+208
+00:24:04,470 --> 00:24:12,850
+بده يساوي ال H إذا أخدنا صورتين متساويتين أثبتنا
+
+209
+00:24:12,850 --> 00:24:19,070
+أن الأصل متساوي يبقى Phi is one to one النقطة
+
+210
+00:24:19,070 --> 00:24:22,510
+الثالثة Phi is onto
+
+211
+00:24:28,880 --> 00:24:37,080
+أظن هذه لا تحتاج برهان لماذا؟ لأن كل element في S
+
+212
+00:24:37,080 --> 00:24:48,460
+G يعتمد على element من جي؟ من جي يبقى because any
+
+213
+00:24:48,460 --> 00:24:50,600
+element
+
+214
+00:24:53,320 --> 00:24:59,140
+any element تي جي اللي موجود في اس جي
+
+215
+00:24:59,140 --> 00:25:05,660
+corresponding to
+
+216
+00:25:05,660 --> 00:25:19,520
+جي اللي موجودة في جي يعني بمعنى أخر اللي هو ال ال
+
+217
+00:25:19,520 --> 00:25:28,860
+five is onليش؟ لأن كل element من SG له أصل في جي
+
+218
+00:25:28,860 --> 00:25:34,720
+اللي هو جي يبقى إيش ضايل علينا؟ الخاصية الأخيرة
+
+219
+00:25:34,720 --> 00:25:41,600
+الخاصية الأخيرة كانت تالية يبقى بدي أجي أخد Phi
+
+220
+00:25:41,600 --> 00:25:53,740
+الخاصية الرابعة بدي أخد Phi of HG أو GH سيانيبقى
+
+221
+00:25:53,740 --> 00:26:02,520
+هذه حسب ال definition بدأت تساوي تي اتش جي تمام تي
+
+222
+00:26:02,520 --> 00:26:09,580
+اتش جي لو رجعتها الاصلة بصير تي اتش composition تي
+
+223
+00:26:09,580 --> 00:26:16,980
+جي تي اتش حسب التعريف اللي عرفناه هنا اللي هو تي
+
+224
+00:26:16,980 --> 00:26:18,480
+جي هي في
+
+225
+00:26:21,140 --> 00:26:30,370
+of H في التانية Phi of Gهذا الكلام صحيح لكل الـ H
+
+226
+00:26:30,370 --> 00:26:37,930
+والـ G اللي موجودة في G يبقى بناء عليه أثبتنا الآن
+
+227
+00:26:37,930 --> 00:26:44,230
+إن Phi of HG بدأ يساوي Phi of H في Phi of G يبقى
+
+228
+00:26:44,230 --> 00:26:51,210
+بناء عليه هذا يعني إن خواص الأيزومورفزم تحصلت يبقى
+
+229
+00:26:51,210 --> 00:27:00,060
+باني بقوله غاصوهكذا اللي هو من الـG isomorphic
+
+230
+00:27:00,060 --> 00:27:08,840
+لمن؟ للـSG اللي هي the set of all permutations أظن
+
+231
+00:27:08,840 --> 00:27:14,500
+دوّقتكوا شوية النظرية هيك لذلك بنروح أعيدها لكم
+
+232
+00:27:14,500 --> 00:27:21,160
+مرة تانية حتى نثبت هذه المعلومات عندكمطبعا هي من
+
+233
+00:27:21,160 --> 00:27:27,120
+أطول النظريات برهانة اللى موجودة فى الكتاب ليش
+
+234
+00:27:27,120 --> 00:27:31,960
+لأنها تحدث عن نقطة واحدة وليس عن مجموعة من النقاط
+
+235
+00:27:31,960 --> 00:27:38,700
+النظرية بتقول ما يأتي every group is isomorphic to
+
+236
+00:27:38,700 --> 00:27:42,480
+group if permutation هو هذا اللى ما قلناه فى الآخر
+
+237
+00:27:42,910 --> 00:27:46,810
+إنه ال group G isomorphic لل set of all
+
+238
+00:27:46,810 --> 00:27:52,590
+permutations اللي كوّنها على G اللي وعطناها الرمز
+
+239
+00:27:52,590 --> 00:28:00,370
+من SD لما أنا قاعد أقرا النص هذا بقول group G ماشي
+
+240
+00:28:00,370 --> 00:28:04,690
+لكن ال group permutation مش عارف الشكلها يبقى أنا
+
+241
+00:28:04,690 --> 00:28:08,890
+بدأ أخلق ال group هذي وبعد هيك نبدأ نتفاهم على
+
+242
+00:28:08,890 --> 00:28:11,410
+حكاية من ال isomorphism
+
+243
+00:28:14,910 --> 00:28:21,690
+أخذ أي عنصر جي موجود في جي من مكان يكون عرفت عليه
+
+244
+00:28:21,690 --> 00:28:26,830
+function TG من جي إلى جي by TG of X ساوية G of X
+
+245
+00:28:26,830 --> 00:28:31,470
+التعريف هذا صحيح لأن X و G موجودات في الجي والجي
+
+246
+00:28:31,470 --> 00:28:35,070
+group closed under multiplication يبقى فعلا ال
+
+247
+00:28:35,070 --> 00:28:41,300
+element هذا موجود في جيبعدين بقول و الله لو كانت
+
+248
+00:28:41,300 --> 00:28:46,740
+ال function هذه one to one and unto يبقى بيصير
+
+249
+00:28:46,740 --> 00:28:51,260
+permutation لأن لما نعرفنا ال permutation على set
+
+250
+00:28:51,260 --> 00:28:55,340
+قلنا هي function من ال set إلى نفسها بعدين تبقى
+
+251
+00:28:55,340 --> 00:28:59,900
+one to one and unto هي function من ال set إلى
+
+252
+00:28:59,900 --> 00:29:03,740
+نفسها يبقى ضال علي بس أثبت إنها one to one هذه ال
+
+253
+00:29:03,740 --> 00:29:09,070
+functionوكذلك on to يبقى روحت لل one to one قولت
+
+254
+00:29:09,070 --> 00:29:15,330
+افترض صوتين متساويتين بدي اثبت ان ال X يساوي Y حسب
+
+255
+00:29:15,330 --> 00:29:18,830
+التعريف اللي احنا جايليه يبقى هذا G X بدي اساوي
+
+256
+00:29:18,830 --> 00:29:22,450
+main G Y بال left cancellation اللي هو يبقى ال X
+
+257
+00:29:22,450 --> 00:29:28,090
+يساوي Y يبقى ال T G one to one بدي اثبتها انها on
+
+258
+00:29:28,090 --> 00:29:34,450
+to فاخدت Y موجود في Gالـ Y بدي أحاول أصيغه بصيغة
+
+259
+00:29:34,450 --> 00:29:41,650
+تعطيني TG of X كيف؟ قلت الـ Y يسوى ال identity في
+
+260
+00:29:41,650 --> 00:29:48,760
+Y ال identity بقدر أقول عليها GG inverseبعد ذلك
+
+261
+00:29:48,760 --> 00:29:56,460
+باخد اتنين هذول مع بعض جي انفرس واي وجي لحاله باجي
+
+262
+00:29:56,460 --> 00:30:02,930
+بقول هذول لو سميتم تاسم جديدة XZW اللي بدكيايبقى
+
+263
+00:30:02,930 --> 00:30:09,050
+اقولنا X مثلا يبقى جي X باجي لجي X من التعريف
+
+264
+00:30:09,050 --> 00:30:15,930
+عبارة عن TG of X يبقى سارة TG of X يبقى ال element
+
+265
+00:30:15,930 --> 00:30:21,850
+Y اللي موجود في جي اللي عندنا هذه اللي جاتله أصل X
+
+266
+00:30:21,850 --> 00:30:27,070
+موجود في جي الأولى يبقى بناء عليه الدالة هذه is
+
+267
+00:30:27,070 --> 00:30:33,500
+ontoبناء عليه هذه الـ function أصبحت تشكل ليه
+
+268
+00:30:33,500 --> 00:30:38,480
+permutationتمام؟ جيت على ال permutations هدول و
+
+269
+00:30:38,480 --> 00:30:43,900
+حطيتهم كلهم في مين؟ في ستة جديدة روحت سميتها SG
+
+270
+00:30:43,900 --> 00:30:50,400
+سميتها SG مشان العناصر تبعات G يكونوا من مين
+
+271
+00:30:50,400 --> 00:30:56,540
+ناخدهم من G itself من عناصرها كل ال permutations
+
+272
+00:30:56,540 --> 00:31:01,530
+اللي حصلنا عليها في القطغة الأولىيبقى لما يقولي
+
+273
+00:31:01,530 --> 00:31:05,130
+isomorphic to group of perimutations يبقى الجروب
+
+274
+00:31:05,130 --> 00:31:10,990
+هذه خلقتها جديد وسميتها SG بس أنا مش عارفة اللي هي
+
+275
+00:31:10,990 --> 00:31:15,390
+group ولا .. هي صارت عندي set و ال set فيها مجموعة
+
+276
+00:31:15,390 --> 00:31:20,130
+من العناظة بدي أثبتله إنها group إذا أثبتله إنها
+
+277
+00:31:20,130 --> 00:31:24,570
+group بصير هي عندي groupوجروب تانية بقدر اعمل ال
+
+278
+00:31:24,570 --> 00:31:29,630
+isomorphism ما بين الاتنين طب سؤال هامشي هيه جاب
+
+279
+00:31:29,630 --> 00:31:34,930
+المكمل بنفع اعمل isomorphism ما بين جروب و ما بين
+
+280
+00:31:34,930 --> 00:31:38,150
+set؟
+
+281
+00:31:38,150 --> 00:31:43,700
+بنفعلا يمكن ينفع لأن هذه عليها binary operation
+
+282
+00:31:43,700 --> 00:31:47,820
+وهذه ما عليها اش احنا بيقول isomorphism الأولى
+
+283
+00:31:47,820 --> 00:31:52,100
+والتانية كله لهم نفس القواصة الرياضية فكيف علي هذه
+
+284
+00:31:52,100 --> 00:31:56,380
+binary operation وهذه لأ إذا لا يمكن أن يكون هناك
+
+285
+00:31:56,380 --> 00:31:59,720
+isomorphism ما بين group ما بين set لازم يكون
+
+286
+00:31:59,720 --> 00:32:06,800
+التنتين are groups طيب نرجع الأن لل SG أنا أدعىإن
+
+287
+00:32:06,800 --> 00:32:11,400
+الـ Sجي هذي اللي كونها مالها is a group تحت ال
+
+288
+00:32:11,400 --> 00:32:18,020
+composition of function لذلك أخد GH بدي أثبت إنها
+
+289
+00:32:18,020 --> 00:32:25,820
+closed under multiplication أو closed underأخد تي
+
+290
+00:32:25,820 --> 00:32:36,360
+جي composition th of x يساوي تي جي في th of x
+
+291
+00:32:36,360 --> 00:32:42,540
+استخدم تعريف th of x اللي هو hx وبعدين استخدم
+
+292
+00:32:42,540 --> 00:32:48,850
+تعريفأو تي جي فسرة جي اتش اكس او جي اتش كله في اكس
+
+293
+00:32:48,850 --> 00:32:53,030
+او تي جي اتش كله في اكس لان جي في اتش يعطينا
+
+294
+00:32:53,030 --> 00:32:57,830
+element من جي يبقى بناء عليه هذا موجود في S يبقى
+
+295
+00:32:57,830 --> 00:33:02,030
+ال S جي is a closed under multiplication أو ال
+
+296
+00:33:02,030 --> 00:33:05,770
+operation اللي عليها ال composition of function is
+
+297
+00:33:05,770 --> 00:33:13,220
+a binary operationالان صار عندنا binary operation
+
+298
+00:33:13,220 --> 00:33:15,800
+كمان ال composition of a function ثم نعرف انها
+
+299
+00:33:15,800 --> 00:33:19,440
+associative يبقى ماضلش عندي الا main two
+
+300
+00:33:19,440 --> 00:33:26,480
+conditions ال identity elementانا ادعي ان TA هو ال
+
+301
+00:33:26,480 --> 00:33:31,400
+identity element وروح نثبتنا ان هو ال identity
+
+302
+00:33:31,400 --> 00:33:37,420
+element اتدعيت ان تجي انفرس بالضبط هو ت وال انفرس
+
+303
+00:33:37,420 --> 00:33:42,860
+بحطه على ال elementمن اين لك هذا روحت اثبتته وهيه
+
+304
+00:33:42,860 --> 00:33:48,620
+وهيه كله طلع ليه ال identity element يبقى فعلا كل
+
+305
+00:33:48,620 --> 00:33:54,460
+element في SG له معكوس يبقى بناء عليه ال SG the
+
+306
+00:33:54,460 --> 00:33:59,540
+group of permutation صارت group إذا مدام صارت
+
+307
+00:33:59,540 --> 00:34:05,980
+group وعند group بقدر اكون ايش isomorphismتعرف الـ
+
+308
+00:34:05,980 --> 00:34:11,860
+Function Phi من G إلى SG بـPhi of G بيسوء من T of
+
+309
+00:34:11,860 --> 00:34:18,780
+G جي هذه موجودة في جي الـTG موجودة في SG بدي أروح
+
+310
+00:34:18,780 --> 00:34:23,300
+أبين إنه فعلا هذه الـ Function معرفة من هنا إلى
+
+311
+00:34:23,300 --> 00:34:28,950
+هناباخد عنصرين متساوين و بثبت ان عنصرته متساوية ان
+
+312
+00:34:28,950 --> 00:34:34,210
+حدث ذلك بقول هذه well-defined function يعني ال
+
+313
+00:34:34,210 --> 00:34:39,990
+function معرفة تعريفا صحيحا فجيه تقول خد لي G و H
+
+314
+00:34:39,990 --> 00:34:44,470
+موجودات بحيث الـ G يستوى الـ H أثر على الطرفين بـ
+
+315
+00:34:44,470 --> 00:34:49,800
+Phi Phi of G بده سوى TGوهذه تساوي الـTH يبقى صورة
+
+316
+00:34:49,800 --> 00:34:53,580
+الأنصار الأول تساوي صورة الأنصار التانية يبقى Phi
+
+317
+00:34:53,580 --> 00:34:58,160
+is well defined ال one to one خد لي صورتين
+
+318
+00:34:58,160 --> 00:35:03,240
+متساويتين وبدأ أثبت أن أصلهم متساوي يبقى TG بدأ
+
+319
+00:35:03,240 --> 00:35:07,260
+يساوي TH بدأ أخلي كل واحد أتأثر على X عشان أقدر
+
+320
+00:35:07,260 --> 00:35:13,100
+أطبق التعريف اللي عندنا هذا فصار عندنا TG of X بده
+
+321
+00:35:13,100 --> 00:35:21,120
+يساوياللي هو TH of X تمام
+
+322
+00:35:21,120 --> 00:35:26,800
+يبقى GX يساوي HX بدنا ن cancel ال X من الطرفين
+
+323
+00:35:26,800 --> 00:35:30,660
+يبقى ال G يساوي ال H وبالتالي Phi is one to one
+
+324
+00:35:30,660 --> 00:35:36,120
+الانتوا صحيحة لإن كل TG في SG بده يقابله main
+
+325
+00:35:36,470 --> 00:35:40,050
+الخطوة الأخيرة موجودة في جيو مين و جيونتو موجودة
+
+326
+00:35:40,050 --> 00:35:46,310
+في جيو
+
+327
+00:35:46,310 --> 00:35:56,560
+مين و جيونتو موجودة في جيونتوأي كتاب جبر تلاقيه في
+
+328
+00:35:56,560 --> 00:36:00,620
+المكتب على النت بس اكتب Kiley theorem بفتح لك
+
+329
+00:36:00,620 --> 00:36:05,740
+علامين على Kiley theorem نظرية اللي هو العالم كيلي
+
+330
+00:36:05,740 --> 00:36:11,260
+اللي اكتشفها اللي انا انا بدي اعطيك مثال تطبيقي
+
+331
+00:36:11,260 --> 00:36:15,680
+على الشغل هذي تمام؟ ايوة تعال هنا اللي هو تعال
+
+332
+00:36:20,700 --> 00:36:24,500
+أيوة جيد كويس
+
+333
+00:36:24,500 --> 00:36:30,230
+أثبتنا ان فاي is onto تبع التعريف هذاهي التعريف
+
+334
+00:36:30,230 --> 00:36:36,270
+هذه file is under كيف أثبتنا هذا؟ لأن أي element
+
+335
+00:36:36,270 --> 00:36:41,950
+في Sجي هيه هذا بيعتمد على مين؟ على G جي من وين جي
+
+336
+00:36:41,950 --> 00:36:48,790
+بناها؟ من G كبتر يبقى كل permutation هنا تعتمد على
+
+337
+00:36:48,790 --> 00:36:53,070
+element من اللي هناك يعني لا يمكن أن يكون هنا
+
+338
+00:36:53,070 --> 00:36:57,610
+permutation ما لم يكن مناظر إلها element من G
+
+339
+00:36:57,610 --> 00:37:04,720
+فضعت؟أه حد بدى يسأل تانى طب نعطى مثال عددي توضيحى
+
+340
+00:37:04,720 --> 00:37:13,680
+كيف نحسب هالشغل هذه example
+
+341
+00:37:48,300 --> 00:37:59,760
+find الاجرب SG where ال
+
+342
+00:37:59,760 --> 00:38:04,540
+G بدأت ساوي ال U عشرة
+
+343
+00:38:17,140 --> 00:38:23,660
+أظهر لو وجدنا عناصر SG بيصير الجيل الأصلي اللي هي
+
+344
+00:38:23,660 --> 00:38:30,600
+U10 isomorphic لمين؟ للـ SG حسب نظرية كلب الأن لو
+
+345
+00:38:30,600 --> 00:38:40,340
+جيت للـU10 مين عناصرها؟ الواحد، اتنين، تلاتة،
+
+346
+00:38:40,340 --> 00:38:49,730
+أربعة، خمسة، ستة، سبعة، تسعة، في غيرهم؟طيب يبقى
+
+347
+00:38:49,730 --> 00:38:59,910
+بناء عليه ال S G ال S G أو ال S U عشرة بدها تساوي
+
+348
+00:38:59,910 --> 00:39:09,110
+T واحد و T تلاتة و T سبعة و T تسعة بس مين T واحد و
+
+349
+00:39:09,110 --> 00:39:14,530
+T تلاتة و T سبعة مش عارفين بدنا نعرف تمام باجي
+
+350
+00:39:14,530 --> 00:39:15,950
+بقولهم where
+
+351
+00:39:18,450 --> 00:39:26,230
+حيث الـ T1 هذه هي ال identity permutation الصف
+
+352
+00:39:26,230 --> 00:39:31,070
+الأول بقولش واحد اتنين تلاتة اربعة العناصر هذه
+
+353
+00:39:31,070 --> 00:39:38,110
+تبعات الـ G لإن هذه ال permutation على ال group مش
+
+354
+00:39:38,110 --> 00:39:43,990
+على أعداد عادية يبقى الصف الأول واحد تلاتة سبعة
+
+355
+00:39:43,990 --> 00:39:52,810
+تسعة انتهينابدي اجيب صورهم تمام؟ قبل شوية عرفنا ان
+
+356
+00:39:52,810 --> 00:40:00,870
+TG of X بده يساوي حصل ضرب G في X مظبوط؟ يبقى انا
+
+357
+00:40:00,870 --> 00:40:08,730
+ايش؟ بدي T واحد of واحد بدي اعطيك الواحدT1 of
+
+358
+00:40:08,730 --> 00:40:15,130
+تلاتة سبعة تسعة كما هي ال identity كل شي بده ينزل
+
+359
+00:40:15,130 --> 00:40:21,010
+زي ما هو كيف؟
+
+360
+00:40:21,010 --> 00:40:29,650
+واحد في تلاتة واحد في سبعة واحد في تسعة بين إيش؟
+
+361
+00:40:29,650 --> 00:40:38,000
+طيب يبقى هذه ال identity هذه ال T1بدي هنا T ثلاثة
+
+362
+00:40:38,000 --> 00:40:47,340
+بده يساوي الصف الأول واحد تلاتة سبعة تسعة طيب
+
+363
+00:40:47,340 --> 00:40:53,480
+بدي أجيب الصف الثاني بقول لي T G of X بده يساوي GX
+
+364
+00:40:53,480 --> 00:41:00,160
+يعني أنا بدي أحسبله T تلاتة of واحد يبقى تلاتة في
+
+365
+00:41:00,160 --> 00:41:07,720
+واحد يبقى تلاتة يبقى العنصر هنا تلاتةبدي T ثلاثة و
+
+366
+00:41:07,720 --> 00:41:12,740
+ثلاثة يبقى ثلاثة في ثلاثة اللي هو تسعة يبقى هنا
+
+367
+00:41:12,740 --> 00:41:19,640
+تسعة بدي T ثلاثة و سبعة اللي هو تلاتة في سبعة
+
+368
+00:41:19,640 --> 00:41:27,060
+بقدرش؟ واحد و عشري مضيله عشرة بواحد يبقى هذه تساوي
+
+369
+00:41:27,060 --> 00:41:33,500
+واحد إذا هنا واحدبجيلك هنا T ثلاثة و تسعة يبقى
+
+370
+00:41:33,500 --> 00:41:38,020
+ثلاثة في تسعة في قدر؟ سبعة و عشرين موديه العاشرة
+
+371
+00:41:38,020 --> 00:41:44,900
+بسبعة يبقى هنا السبعة لاحظ مجانيش ولا رقم الا اللي
+
+372
+00:41:44,900 --> 00:41:50,340
+موجودة في الصف الأول اتنين لم يتكرر اي رقم مرتين
+
+373
+00:41:50,340 --> 00:41:56,120
+على الإطلاق ليش انها one to one and unto طيب لو
+
+374
+00:41:56,120 --> 00:42:04,270
+بدنا الآن T سبعةيبقى واحد ثلاثة سبعة تسعة نحسبهم
+
+375
+00:42:04,270 --> 00:42:08,910
+بنفس الطريقة اللي هناك ت سبعة وواحد يبقى سبعة في
+
+376
+00:42:08,910 --> 00:42:15,170
+واحد بسبعة الان ت سبعة تلاتة يعني سبعة في تلاتة
+
+377
+00:42:15,170 --> 00:42:21,500
+بواحد وعشرين مضيوله عشرةأب واحد سبعة في سبعة بتسعة
+
+378
+00:42:21,500 --> 00:42:27,340
+واربعين موديولو سبعة ابتسعة سبعة في تسعة بتلاتة
+
+379
+00:42:27,340 --> 00:42:32,760
+وستين موديولو عشرة بتلاتة اللي هي بجداش بتلاتة
+
+380
+00:42:32,760 --> 00:42:40,940
+ضالت عندنا مين تتسعة واحد تلاتة سبعة تسعةتسعة في
+
+381
+00:42:40,940 --> 00:42:46,580
+واحد بتسعة، تسعة في تلاتة بسبعة وعشرين، سبعة في
+
+382
+00:42:46,580 --> 00:42:51,260
+تسعة على تسعة في سبعة بتلاتة وستين، تسعة في تسعة
+
+383
+00:42:51,260 --> 00:43:00,650
+بواحد وتمانينيبقى الأن عرفنا كيف بنكوّم الـT1 وT3
+
+384
+00:43:00,650 --> 00:43:08,110
+وT7 يبقى الـSG بكتب كل عنصر فيهم بدلالة عناصر G
+
+385
+00:43:08,110 --> 00:43:12,980
+مين ما تكون جيهش ما يكون شكل هيكونيبقى بقول TG1
+
+386
+00:43:12,980 --> 00:43:18,740
+TG2 TG3 TG4 لغاية ما أخلصهم كلهم كيف بحسب كل واحد
+
+387
+00:43:18,740 --> 00:43:23,520
+منهم؟ بالطريقة اللي عندنا هنا بحط الصف الأول عناصر
+
+388
+00:43:23,520 --> 00:43:28,280
+G و بعدين بخلي ال T تأثر على العنصر الأول التاني
+
+389
+00:43:28,280 --> 00:43:33,660
+التالت الرابع و بكتب الصفوف يبقى هذه العناصر يبقى
+
+390
+00:43:33,660 --> 00:43:38,020
+في هذه الحالة باي كلي
+
+391
+00:43:39,710 --> 00:43:46,930
+أو Keyless theorem الـ U عشرة الـ U عشرة
+
+392
+00:43:46,930 --> 00:43:57,550
+isomorphic للـ S U عشرة هاي المقصود يعني يبقى G
+
+393
+00:43:57,550 --> 00:44:03,330
+isomorphic للست of all permutations اللي كوّنها
+
+394
+00:44:03,330 --> 00:44:08,780
+على ال group عشرة و كذايبقى فهمنا كيف تطبيق
+
+395
+00:44:08,780 --> 00:44:15,540
+النظرية، الآن بدنا نخش لنظرية مكونة من سبعة نقاط
+
+396
+00:44:15,540 --> 00:44:19,560
+للمرة القادمة، ان شاء الله مافيش إمكانية اليوم
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..64673276abfc6e1dda3e8657aff54cf6fde2d292
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/ZdAO6udksT8_postprocess.srt
@@ -0,0 +1,1956 @@
+1
+00:00:20,690 --> 00:00:24,770
+بسم الله الرحمن الرحيم عودنا على بدأ في المحاضر في
+
+2
+00:00:24,770 --> 00:00:29,010
+الفترة الصباحية كتبنا نظرية نظرية عبارة عن ست نقاط
+
+3
+00:00:29,010 --> 00:00:33,450
+نقطتين كانوا مبرهنات سابقا في موضوع ال isomorphism
+
+4
+00:00:33,450 --> 00:00:38,870
+مبرهننا نقطتين وهذه هي النقطة الخامسة يبقى النقطة
+
+5
+00:00:38,870 --> 00:00:42,430
+الخامسة بتقول انه five of a بدو يساوي five of b if
+
+6
+00:00:42,430 --> 00:00:46,990
+and only if ال a في ال kernel بدو يساوي بي في ال
+
+7
+00:00:46,990 --> 00:00:52,660
+kernelيبقى بدنا نبرهن صحة هذه النقطة فباجي بقوله
+
+8
+00:00:52,660 --> 00:00:59,340
+ال proof لو كان ال phi of a بده يساوي ال phi of b
+
+9
+00:00:59,340 --> 00:01:06,210
+هذا الكلام صحيح if and only ifلو ضربنا في المعكوث
+
+10
+00:01:06,210 --> 00:01:11,990
+تبعها هذه من جهة الشمال بيكون مين؟ بيكون في of بي
+
+11
+00:01:11,990 --> 00:01:18,190
+لكل inverse في في of a بدي ساوي ال identity
+
+12
+00:01:18,190 --> 00:01:25,690
+element تبع من؟ تبع الـG bar لأن في of a وفي of b
+
+13
+00:01:25,690 --> 00:01:32,440
+موجودة تاتوين في الـG barالكلام هذا صحيح if and
+
+14
+00:01:32,440 --> 00:01:48,720
+only if الكلام
+
+15
+00:01:48,720 --> 00:01:53,570
+هذا صحيح if and only ifالـ Phi أول ما أخدناها هو
+
+16
+00:01:53,570 --> 00:02:03,110
+Homomorphism، إذا Phi of B inverse A بدل
+
+17
+00:02:03,110 --> 00:02:08,650
+سبب من الـ Identity Element تبع الـ G¯أيش تفسيرك
+
+18
+00:02:08,650 --> 00:02:13,810
+لهذه العبارة فاي لما أثرت على element أعطتني ال
+
+19
+00:02:13,810 --> 00:02:17,510
+identity element يبقى هذا ال element وين موجود؟ ال
+
+20
+00:02:17,510 --> 00:02:22,950
+kernel يبقى هذا .. والله هذا معناته if and only if
+
+21
+00:02:22,950 --> 00:02:28,770
+كله ماشيين ب if and only if ال B inverse A موجود
+
+22
+00:02:28,770 --> 00:02:35,190
+في ال kernel الفايمعنى هذا الكلام أن الـP inverse
+
+23
+00:02:35,190 --> 00:02:41,030
+A في الـkernel للـPhi بده يساوي الـkernel للـPhi
+
+24
+00:02:41,030 --> 00:02:46,350
+itself لو ضربنا الطرفين في الـP من جهتي الشمال
+
+25
+00:02:46,350 --> 00:02:50,650
+يبقى بصير if and only if الـA في الkernel للـPhi
+
+26
+00:02:50,650 --> 00:02:56,130
+بده يساوي P في الkernel للـPhi أظن و هو المطلوب
+
+27
+00:02:56,130 --> 00:03:05,820
+النقطة السادسةالنقطة السادسة بتقول ما يأتي لو كان
+
+28
+00:03:05,820 --> 00:03:12,220
+الـ Phi of G بده ساوي الـ G Prime ال Phi of G بده
+
+29
+00:03:12,220 --> 00:03:20,470
+ساوي ال G PrimeالـPhi Inverse of G' بدي يساوي الـG
+
+30
+00:03:20,470 --> 00:03:24,430
+في الـKernel للـPhi وراح المعرفة هذه كل الـX اللى
+
+31
+00:03:24,430 --> 00:03:27,750
+موجودة في G بيحيط الـPhi of X بدي يساوي مين؟ بدي
+
+32
+00:03:27,750 --> 00:03:33,490
+يساوي G' بدنا نروح نثبت صحة هذا الكلام النقطة هذه
+
+33
+00:03:33,490 --> 00:03:38,030
+تعالى نشوف ايش مفهومها قبل ما نبرهن بدنا نفهم ما
+
+34
+00:03:38,030 --> 00:03:42,770
+هو موضوع هذه النقطة شوف يا سيديأحنا عندنا فاي من
+
+35
+00:03:42,770 --> 00:03:48,150
+ال group G إلى ال group G bar تمام قال لي فاي of G
+
+36
+00:03:48,150 --> 00:03:52,200
+بده يسوي G prime يقولي G prime وين موجودةفي الـG
+
+37
+00:03:52,200 --> 00:03:56,840
+بار والـG هذه موجودة في الـG طيب كويس إذا هذه
+
+38
+00:03:56,840 --> 00:04:02,140
+معلومة الآن ايش بقولي بقي بدي يكون الـPhi inverse
+
+39
+00:04:02,140 --> 00:04:07,960
+للـG prime تسوي G مضربة في الكنز يعني لما ناخد Phi
+
+40
+00:04:07,960 --> 00:04:11,260
+inverse للطرفين مش هروح اقول Phi inverse of G
+
+41
+00:04:11,260 --> 00:04:16,930
+prime تسوي G ليش؟ ليش؟ لأ وكانت one to one صحيحهذا
+
+42
+00:04:16,930 --> 00:04:20,250
+ليس إيزو مورفزم، إن هؤلاء عبارة عن مجموعة من
+
+43
+00:04:20,250 --> 00:04:24,690
+النقاط صورتهم الـIdentity. إذن عندما أدخل للعكس،
+
+44
+00:04:24,690 --> 00:04:28,170
+فإن الـPhi Inverse لهذا العلم سيكون مجموعة من
+
+45
+00:04:28,170 --> 00:04:33,490
+النقاط وليس نقطة واحدة. وهذا ما سنثبته بعد قليل في
+
+46
+00:04:33,490 --> 00:04:38,420
+النظرية القادمة.يبقى في انفرس جي برايم يبقى مين
+
+47
+00:04:38,420 --> 00:04:41,680
+يسوى جي في الكرنة اللي في هذا اللي عايزين ان تبدو
+
+48
+00:04:41,680 --> 00:04:45,340
+هدول two sets are equal يبقى بدي اروح اخد element
+
+49
+00:04:45,340 --> 00:04:48,800
+هنا اثبت انه موجود هنا و اعمل الأعمال العكسية اخد
+
+50
+00:04:48,800 --> 00:04:52,840
+element هنا و اثبت انه موجود هنا يبقى مشان هيك
+
+51
+00:04:52,840 --> 00:04:59,900
+بداجي اقوله let ال X موجودة في في انفرس جي برايم
+
+52
+00:05:01,340 --> 00:05:09,260
+طبعا يبقى لو أثرت بمين بفاي على الطرفين بصير فاي
+
+53
+00:05:09,260 --> 00:05:17,880
+of X بدها تساوي G prime طيب هذا معناه انه فاي of X
+
+54
+00:05:17,880 --> 00:05:24,500
+يساوي اظن G prime مواطعه مقدرش بفاي of G يبقى هذا
+
+55
+00:05:24,500 --> 00:05:31,090
+فاي of G بالشكل اللي عندنا هنا طيب لو روحتمن هذا
+
+56
+00:05:31,090 --> 00:05:37,250
+الكلام ضربت الطرفين في معكوس هذا ال element يبقى
+
+57
+00:05:37,250 --> 00:05:45,810
+بده يصير main بده يصير phi of g الكل inverse في ال
+
+58
+00:05:45,810 --> 00:05:50,290
+phi of x بده يساوي الطرف اليمين اللي هو ال
+
+59
+00:05:50,290 --> 00:05:56,610
+identity element تبع main تبع ال g بعضبنفس المفهوم
+
+60
+00:05:56,610 --> 00:06:02,810
+هذا ايش معناه؟ معناه انه Phi of G inverse في Phi
+
+61
+00:06:02,810 --> 00:06:08,310
+of X بده ساوي ال identity element تبع ال G bar او
+
+62
+00:06:08,310 --> 00:06:15,250
+انشئتم فقولوا Phi of G inverse X بده ساوي ال
+
+63
+00:06:15,250 --> 00:06:20,470
+identity element تبع ال G barمعنى هذا الكلام أن
+
+64
+00:06:20,470 --> 00:06:24,690
+هذا الـElement بين القوسين وين موجود في الـKernel
+
+65
+00:06:24,690 --> 00:06:29,690
+لأنه صورته الـIdentity يبقى بده يصير G inverse X
+
+66
+00:06:29,690 --> 00:06:36,490
+موجود في الـKernel للـPhi طب لو ضربت الطرفين في G
+
+67
+00:06:36,490 --> 00:06:42,130
+من جهة الشمال يبقى بظل X موجود في الـG في
+
+68
+00:06:42,130 --> 00:06:48,480
+الـKernel للـPhiيبقى انا اخدت X موجود في الـPhi
+
+69
+00:06:48,480 --> 00:06:53,940
+inverse للـG' لقيته موجود وين؟ في G في الـkernel
+
+70
+00:06:53,940 --> 00:07:00,020
+معناته الست الأولانية subset من الست التانية يبقى
+
+71
+00:07:00,020 --> 00:07:08,060
+هنا سا Phi inverse of G' subset من مين؟ من الـG في
+
+72
+00:07:08,060 --> 00:07:13,580
+ال kernel للـPhiاعتبر هذه هي النقطة الأولى بالدرجة
+
+73
+00:07:13,580 --> 00:07:21,300
+للنقطة التانية on the other hand بالدرجة
+
+74
+00:07:21,300 --> 00:07:28,940
+ياخد X موجودة في الـG في الكيرن للـPhiخُد للـ X
+
+75
+00:07:28,940 --> 00:07:35,380
+موجودة في الـ G في الكيرنل للـ Phi إذا كنت أثبت إن
+
+76
+00:07:35,380 --> 00:07:39,700
+الـ X هذه موجودة هنا بيكون تم المطلوب يكون انتهينا
+
+77
+00:07:39,700 --> 00:07:45,600
+من المسألة اللي عندنا يبقى then الـ X هذه يا شباب
+
+78
+00:07:45,600 --> 00:07:51,200
+بقدر أقول هي الـ G مضروبة في element من مين؟ من
+
+79
+00:07:51,200 --> 00:07:59,080
+الكيرنل تبع الـ Phi وليكن اللي هو Kيبقى x بدأ
+
+80
+00:07:59,080 --> 00:08:09,660
+تساوي gk for some for some k اللي موجودة في الكيرن
+
+81
+00:08:09,660 --> 00:08:17,100
+لفاي طيب شو رأيك أثر على تنتين بفاي يبقى ايش بده
+
+82
+00:08:17,100 --> 00:08:25,960
+يصير بده يصير في of x بده يساوي في of g في kيعني
+
+83
+00:08:25,960 --> 00:08:32,540
+معنى هذا الكلام أنه Phi of X بدر يساوي Phi of G في
+
+84
+00:08:32,540 --> 00:08:42,240
+Phi of .. اللي هو small K هذا الكلام يساوي أو هذا
+
+85
+00:08:42,240 --> 00:08:49,680
+بدر يعطيناالطرف الشمال Phi of X الطرف اليمين Phi
+
+86
+00:08:49,680 --> 00:08:55,860
+of G كدهش مُعطَى من الرأس المسألة؟ G prime يبقى
+
+87
+00:08:55,860 --> 00:09:04,900
+هذا Phi of G بده يساوي G prime طيب Phi of K كدهش؟
+
+88
+00:09:04,900 --> 00:09:10,080
+طلع ليه هنا، احنا جيبناها من وين الـK هذا؟موجودة
+
+89
+00:09:10,080 --> 00:09:13,200
+في الـ Kernel for some K الموجودة في الـ Kernel
+
+90
+00:09:13,200 --> 00:09:18,880
+يبقى Phi of K بقداش بال Identity يبقى هذا بال
+
+91
+00:09:18,880 --> 00:09:27,880
+Identity تبع الـ G ليش؟ since اللي هو الـ K هذه
+
+92
+00:09:27,880 --> 00:09:33,300
+موجودة في ال Kernel للـ Phiالنظر اللي موجودة هنا
+
+93
+00:09:33,300 --> 00:09:39,400
+تعطينا الـ Identity Element يبقى هنا الساعة الـ
+
+94
+00:09:39,400 --> 00:09:45,860
+Phi of X بده يساوي من الـ G' ليش ان الـ G' موجودة
+
+95
+00:09:45,860 --> 00:09:50,380
+في G' و الـ Identity هي تبع الـ G' يبقى حاصل الدرب
+
+96
+00:09:50,380 --> 00:09:58,050
+يعطينا من G' يبقى معنى هذا الكلام ان الـ Xبتكون
+
+97
+00:09:58,050 --> 00:10:06,270
+موجودة في الـPhi inverse of G' لاحظ ما يأتي اش
+
+98
+00:10:06,270 --> 00:10:11,070
+كتبت أنا السطر الأخير انا وصلت لغاية هنا Phi of X
+
+99
+00:10:11,070 --> 00:10:15,470
+بده يساوي G' في ال identity يبقى Phi of X بده
+
+100
+00:10:15,470 --> 00:10:22,230
+يساوي G'أيش روحت كتبتي يبقى ال X ما كتبتش تساوي في
+
+101
+00:10:22,230 --> 00:10:27,490
+انفرس of G' كتبت ال X موجودة في ال في انفرس of G'
+
+102
+00:10:27,890 --> 00:10:33,270
+ليش ان ال في انفرس of G' عدت نقات مش نقطة واحدة لو
+
+103
+00:10:33,270 --> 00:10:39,650
+كانت نقطة واحدة لكتبت ايش لكتبت اليساوي تمام اذا X
+
+104
+00:10:41,450 --> 00:10:43,270
+ماشي و لو وانت وانت وانت وانت وانت وانت وانت وانت
+
+105
+00:10:43,270 --> 00:10:44,270
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+106
+00:10:44,270 --> 00:10:44,630
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+107
+00:10:44,630 --> 00:10:45,630
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+108
+00:10:45,630 --> 00:10:47,230
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+109
+00:10:47,230 --> 00:10:50,470
+وانت وانت وانت وانت وانت وانت وانت وانت وانت وانت
+
+110
+00:10:50,470 --> 00:10:54,770
+وانت وانت وانت وانت
+
+111
+00:11:02,630 --> 00:11:07,710
+اللي هو subset من مين من الـ Phi inverse of G
+
+112
+00:11:07,710 --> 00:11:12,990
+prime وهذه العلاقة رقم اتنين يبقى باجي بقول from
+
+113
+00:11:12,990 --> 00:11:23,810
+واحد and اتنين we have ان ال Phi inverse of G
+
+114
+00:11:23,810 --> 00:11:28,510
+prime بده يساوي G في الكيرن للـ Phi
+
+115
+00:11:34,710 --> 00:11:38,890
+نعطيك مثال توضيح على ذلك لإن هي خلصت النظرية
+
+116
+00:11:38,890 --> 00:11:44,870
+example بقول
+
+117
+00:11:44,870 --> 00:11:49,610
+suppose that
+
+118
+00:11:49,610 --> 00:12:01,130
+افترض ان الفاي من z تلاتين الى z تلاتينA
+
+119
+00:12:01,130 --> 00:12:07,730
+homomorphism suppose that فاي is a homomorphism
+
+120
+00:12:07,730 --> 00:12:12,510
+and الكيرنل
+
+121
+00:12:12,510 --> 00:12:22,390
+للفاي هي العناصر zero و عشرة و عشرينبيقول لـ F إذا
+
+122
+00:12:22,390 --> 00:12:30,290
+كان الـ Phi لـ 23 هي عبارة عن 9 السؤال هو
+
+123
+00:12:30,290 --> 00:12:33,990
+determine
+
+124
+00:12:33,990 --> 00:12:38,510
+all
+
+125
+00:12:41,760 --> 00:12:51,300
+Elements that map maps to تسعة كل ال elements اللي
+
+126
+00:12:51,300 --> 00:13:02,040
+هم maps to تسعة السؤال
+
+127
+00:13:02,040 --> 00:13:06,480
+مرة تانية فيها النفاي من Z تلاتين ل Z تلاتين
+
+128
+00:13:06,480 --> 00:13:10,870
+homomorphismوهذا حسبنا له كيرن اللي جينا كيرنه
+
+129
+00:13:10,870 --> 00:13:16,190
+zero وعشرة وعشرين هذه معلومة وزيادة على ذلك five
+
+130
+00:13:16,190 --> 00:13:20,590
+of تلاتة وعشرين يساوي تسعة قال لي هاتلي كل ال
+
+131
+00:13:20,590 --> 00:13:25,250
+elements اللي maps to تسعة يعني بدي كل العناصر
+
+132
+00:13:25,250 --> 00:13:29,810
+اللي في زد تلاتين واللي صارتهم بتكون مان تسعة يعني
+
+133
+00:13:29,810 --> 00:13:33,750
+مش ع جد تلاتة وعشرينبقى باقي ال elements اللي
+
+134
+00:13:33,750 --> 00:13:39,990
+وصرتهم بتكون تسعة تطلعلي في النقطة الأخيرة رقم ستة
+
+135
+00:13:39,990 --> 00:13:45,270
+وخليها في دماغك انا عندي في of G يسوى G prime كأنه
+
+136
+00:13:45,270 --> 00:13:50,030
+G هدى main تلاتة وعشرين وال G prime هي main التسعة
+
+137
+00:13:50,030 --> 00:13:55,510
+يبقى ال في inverse of G prime بده سوى ال G في ال
+
+138
+00:13:55,510 --> 00:14:00,750
+kernel للفييبقى بناء عليه انا عندي فاي of تلاتة
+
+139
+00:14:00,750 --> 00:14:07,250
+وعشرين يساوي تسعة شو رايك اخد معكوس الفاي للطرفين
+
+140
+00:14:07,250 --> 00:14:14,370
+يبقى ايش بصير عندي بصير الفاي inverse of تسعة بده
+
+141
+00:14:14,370 --> 00:14:18,930
+يساوي ال element اللي عندنا اللي هو تلاتة وعشرين
+
+142
+00:14:18,930 --> 00:14:27,530
+في ال kernel للفايتمام؟ لكن لما كانت العملية عملية
+
+143
+00:14:27,530 --> 00:14:31,890
+جامعة إذا ما بكتبش تلاتة وعشرين مضروبة في ال
+
+144
+00:14:31,890 --> 00:14:37,990
+kernel وإنما بكتب تلاتة وعشرين زائد ال kernel لمن؟
+
+145
+00:14:37,990 --> 00:14:44,890
+لل في يبقى هذا الكلام بدرساوي تلاتة وعشرين زائد ال
+
+146
+00:14:44,890 --> 00:14:53,110
+kernel لل في هي موجود فوق يبقى zero وعشرة وعشرينمش
+
+147
+00:14:53,110 --> 00:14:57,070
+تروح تقول هنا فاينفرس وتسعة الفاينفرس وتضرع
+
+148
+00:14:57,070 --> 00:14:57,650
+الفاينفرس وتضرع الفاينفرس تضرع الفاينفرس تضرع
+
+149
+00:14:57,650 --> 00:14:57,950
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+150
+00:14:57,950 --> 00:14:58,630
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+151
+00:14:58,630 --> 00:14:59,010
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+152
+00:14:59,010 --> 00:15:01,730
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+153
+00:15:01,730 --> 00:15:07,210
+الفاينفرس تضرع الفاينفرس تضرع الفاينفرس تضرع
+
+154
+00:15:07,210 --> 00:15:14,830
+الفاينفرس تضرع الفاينفرس
+
+155
+00:15:14,830 --> 00:15:18,880
+تفي المثل لأن ال operation عملية جمع هذا الكلام
+
+156
+00:15:18,880 --> 00:15:22,460
+بده يساوي بده يجمع كل عنصر مع اناظره يبقى هذا
+
+157
+00:15:22,460 --> 00:15:27,460
+تلاتة وعشرين تلاتة وعشرين وعشرة تلاتة وتلاتين في
+
+158
+00:15:27,460 --> 00:15:32,980
+زد تلاتين بطلع تلاتةتلاتة واربعين في زي التلاتين
+
+159
+00:15:32,980 --> 00:15:37,340
+بيطلع تلاتاش بيطلع تلاتاش إذا العناصر لو صرتهم
+
+160
+00:15:37,340 --> 00:15:42,140
+تسعة هي تلاتة وعشرين وهي معطاة وكذلك في of تلاتة
+
+161
+00:15:42,140 --> 00:15:46,160
+وفي of تلاتاش هي اللي بتساومهم هي اللي بتساوي تسعة
+
+162
+00:15:46,160 --> 00:15:52,240
+يبقى دير بالك من هذه النقطة ننتقل الآن إلى النظرية
+
+163
+00:15:52,240 --> 00:15:56,480
+التالية يبقى بالداجي ل theorem
+
+164
+00:15:59,090 --> 00:16:07,770
+هذه نظرية بتتحدث عن properties of
+
+165
+00:16:07,770 --> 00:16:15,270
+subgroups under
+
+166
+00:16:15,270 --> 00:16:18,470
+homomorphism
+
+167
+00:16:27,200 --> 00:16:36,600
+تنص على مياتي لت الفاي ب homomorphism
+
+168
+00:16:36,600 --> 00:16:47,240
+from a group g to a group g bar
+
+169
+00:17:02,150 --> 00:17:10,650
+النقطة الأولى فاي اف اتش كابتل اتش اللي هي كل
+
+170
+00:17:10,650 --> 00:17:19,080
+العناصر في اف اتش بحيث الاتش موجودة في الاتشis a
+
+171
+00:17:19,080 --> 00:17:24,240
+subgroup من الـ G bar يبقى هذه ال subgroup من ال G
+
+172
+00:17:24,240 --> 00:17:34,120
+bar النقطة الثانية لو كانت ال H Cyclic F ال H is
+
+173
+00:17:34,120 --> 00:17:43,340
+Cyclic لو كانت ال H Cyclic then Phi of H صورتها is
+
+174
+00:17:43,340 --> 00:17:56,420
+Cyclicالنقطة التالتة لو كانت ال h is abelian then
+
+175
+00:17:56,420 --> 00:18:04,740
+لو five of h is abelian five of h is abelian
+
+176
+00:18:04,740 --> 00:18:14,120
+النقطة الرابعةلو كانت الـ H is a normal subgroup
+
+177
+00:18:14,120 --> 00:18:25,200
+من G then Phi of H is a normal subgroup من Phi of
+
+178
+00:18:25,200 --> 00:18:28,620
+G النقطة
+
+179
+00:18:28,620 --> 00:18:42,540
+الخامسةإذا كانت أعضاء كيرنال فيا هي نة ثم فيا ثم
+
+180
+00:18:42,540 --> 00:18:56,080
+فيا هي نة إلى واحدة نة إلى واحدة مابينج من
+
+181
+00:18:58,300 --> 00:19:10,500
+from g to phi of g النقطة
+
+182
+00:19:10,500 --> 00:19:22,480
+السادسة بيقول if ال order لل H كان يسوى N then ال
+
+183
+00:19:22,480 --> 00:19:27,420
+order لل phi of H بده يقسم
+
+184
+00:19:29,960 --> 00:19:33,980
+الـ N النقطة
+
+185
+00:19:33,980 --> 00:19:46,000
+السابعة بيقول لي if ال K bar if ال K bar is a
+
+186
+00:19:46,000 --> 00:19:55,620
+subgroup من ال G bar thenالـ Phi inverse of الـ K
+
+187
+00:19:55,620 --> 00:20:05,940
+bar اللي هو كل ال K اللي موجودة في G such that Phi
+
+188
+00:20:05,940 --> 00:20:16,410
+of K Phi of K موجودة في ال K barما لها هذه is a
+
+189
+00:20:16,410 --> 00:20:28,390
+subgroup of G يبقى هذه is a subgroup of G النقطة
+
+190
+00:20:28,390 --> 00:20:35,370
+الثامنة بقول لو كان ال K bar is a normal subgroup
+
+191
+00:20:35,370 --> 00:20:43,010
+if ال K bar is a normal subgroup من ال G bar then
+
+192
+00:20:45,860 --> 00:20:54,920
+then الـ Phi inverse of K bar هذه
+
+193
+00:20:54,920 --> 00:21:04,360
+كل العناصر K اللي موجودة في G بحيث ان Phi of K
+
+194
+00:21:04,360 --> 00:21:07,620
+موجود في K bar
+
+195
+00:21:24,440 --> 00:21:31,720
+النقطة التاسعة والاخيرة بقول لو كانت الفاي is onto
+
+196
+00:21:31,720 --> 00:21:39,240
+f الفاي is ontoلو كانت الـphi صندوق الـ and
+
+197
+00:21:39,240 --> 00:21:42,260
+الكيرنل
+
+198
+00:21:42,260 --> 00:21:49,120
+للـphi بده يساوي الـ identity element تبع الـG
+
+199
+00:22:03,460 --> 00:22:14,140
+من اين الى اين من جيه لجيه بار من جيه
+
+200
+00:22:14,140 --> 00:22:16,980
+لجيه بار
+
+201
+00:22:41,150 --> 00:22:48,850
+Nigel will prove the
+
+202
+00:22:48,850 --> 00:23:02,990
+parts الواحد واتنين and تلاتة are identical
+
+203
+00:23:02,990 --> 00:23:05,510
+to
+
+204
+00:23:07,260 --> 00:23:17,740
+are identical to the probes of أربعة
+
+205
+00:23:17,740 --> 00:23:27,640
+واتنين and واحد of
+
+206
+00:23:27,640 --> 00:23:40,060
+theorem of theoremستة تلاتة بصفحات
+
+207
+00:23:40,060 --> 00:23:44,540
+مية وسبعة وعشرين respectively
+
+208
+00:24:12,850 --> 00:24:16,630
+نرجع تاني للنظرية اللى احنا كاتبينها حاول نقرأها
+
+209
+00:24:16,630 --> 00:24:21,250
+كمان مرة نتفهم كل ما فيها بعد هيك بنروح الى
+
+210
+00:24:21,250 --> 00:24:26,610
+البرهان المرة اللى فاتت النظرية اللى فاتت كانت
+
+211
+00:24:26,610 --> 00:24:29,610
+بيشتغل على ال elements homomorphism على ال
+
+212
+00:24:29,610 --> 00:24:34,010
+elements هنا ال subgroups under ال homomorphism
+
+213
+00:24:34,010 --> 00:24:36,970
+يجيب جال ال homomorphism يشتغل عالميا على ال
+
+214
+00:24:36,970 --> 00:24:41,500
+subgroups وليس على ال elementsمقول لو كانت فاي من
+
+215
+00:24:41,500 --> 00:24:46,180
+جي إلى جي بار هي hemomorphism وكانت ال H subgroup
+
+216
+00:24:46,180 --> 00:24:52,620
+من جي then فاي of H، H هذه sub set من مين او
+
+217
+00:24:52,620 --> 00:24:56,260
+subgroup من جي إذا صورتهاأذا كنت أريد أن تكون
+
+218
+00:24:56,260 --> 00:25:02,380
+موجودة في جي بار في جي بار في جي بار في جي بار في
+
+219
+00:25:02,380 --> 00:25:06,980
+جي بار في جي بار في جي بار في جي بار في جي بار في
+
+220
+00:25:06,980 --> 00:25:13,870
+جي بارمن الجيل المقابل يبقى ال subgroup صورتها
+
+221
+00:25:13,870 --> 00:25:18,130
+subgroup أخرى تحت تأثير ال homomorphism الناحية
+
+222
+00:25:18,130 --> 00:25:22,650
+التانية لو كانت هذه ال subgroup cyclic يبقى صورتها
+
+223
+00:25:22,650 --> 00:25:27,570
+كمان cyclic يعني ليست فقط subgroup و كذلك cycle
+
+224
+00:25:27,570 --> 00:25:32,530
+group طب لو كانت ال H abelian يبقى صورتها كذلك ما
+
+225
+00:25:32,530 --> 00:25:37,520
+لها abelian groupهذول واحد واتنين وتلاتة برهنهم
+
+226
+00:25:37,520 --> 00:25:43,680
+قبل هيك في النظرية اللي في صفحة 127 نظرية 6 3 لذلك
+
+227
+00:25:43,680 --> 00:25:48,000
+النقطة الأولى مكافئة هي نفس النقطة 4 في النظرية
+
+228
+00:25:48,000 --> 00:25:53,670
+النقطة 2 هي 2 النقطة 3 هي نقطة 1لو رجعنا لهذه
+
+229
+00:25:53,670 --> 00:25:57,530
+النظرية في صحفة 127 من الكتاب نجد التلاتة اللي
+
+230
+00:25:57,530 --> 00:26:01,410
+عندنا هذا نجي للربع الرابع بيقول لو كانت ال H
+
+231
+00:26:01,410 --> 00:26:06,990
+normal subgroup يجي صورتها normal في صورة ال G
+
+232
+00:26:06,990 --> 00:26:12,810
+كلها لأن ال Phi of G ليس بالضرورة ان تغطيلي كل
+
+233
+00:26:12,810 --> 00:26:17,730
+عناصر G برشوية منهم و ممكن تغطيهم كلهم سيان سواء
+
+234
+00:26:17,730 --> 00:26:21,840
+كان لكن احنا in general بيقول لأطيب يبقى لو كانت
+
+235
+00:26:21,840 --> 00:26:27,620
+هذه normal صورتها normal في صورة G طب لو كان ال
+
+236
+00:26:27,620 --> 00:26:33,200
+kernel في N من العناصر ال order له يساوي N يبقى ال
+
+237
+00:26:33,200 --> 00:26:35,300
+N هدول بدهم يروحوا لوين؟
+
+238
+00:26:37,710 --> 00:26:42,050
+لوين؟ للـ identity، ممتاز جدا يبقى أثار ال
+
+239
+00:26:42,050 --> 00:26:47,010
+homomorphism N to 1 التلاتة أو الأربعة أو العشرة
+
+240
+00:26:47,010 --> 00:26:50,490
+راحوا العنصر واحد يبقى بقول عشرة to one مش one to
+
+241
+00:26:50,490 --> 00:26:54,950
+one بقول الأربعة to one أو الخمسة to one أو الستة
+
+242
+00:26:54,950 --> 00:26:59,950
+جدما يكون ال order one to one mapping من ال G on
+
+243
+00:26:59,950 --> 00:27:04,840
+twoانتوا هادى، دي البالك مش هنقول انتوا انه وخلاص
+
+244
+00:27:04,840 --> 00:27:09,280
+وننسى لابد تغطي جميع أناصر five of G وهذا اللي
+
+245
+00:27:09,280 --> 00:27:12,540
+مطلوب مش روح نبره ان هدى وننسى هدى، لأ لأ لأ هدول
+
+246
+00:27:12,540 --> 00:27:18,020
+نقطتين وليست نقطة واحدة السادسة لو كان ال order ل
+
+247
+00:27:18,020 --> 00:27:23,620
+in بده يساوي ال H يبقى ال order للصورة بده يقسم ال
+
+248
+00:27:23,620 --> 00:27:28,640
+order تبع من؟ تبع ال H أظن حلينا مثال شبيه بو قبل
+
+249
+00:27:28,640 --> 00:27:36,540
+شويةالان لو كانت كيابار subgroup من جيبار يبقى
+
+250
+00:27:36,540 --> 00:27:40,780
+صورتها subgroup و لو كانت هذه ال subgroup normal
+
+251
+00:27:40,780 --> 00:27:46,400
+يبقى صورتها normal اتنين هذول بنقدر ندمجهم ب band
+
+252
+00:27:46,400 --> 00:27:47,060
+واحد
+
+253
+00:28:06,500 --> 00:28:12,150
+النقطة الأخيرة لو كانت Phi is ontoوالـ Kernel
+
+254
+00:28:12,150 --> 00:28:15,930
+مافيش فيه إلا الـ Identity Element يبقى الـ Phi
+
+255
+00:28:15,930 --> 00:28:20,970
+عبارة عن إيش؟ Isomorphism طب هيا أعطاني Phi أنتوا
+
+256
+00:28:20,970 --> 00:28:25,710
+و أعطاني هنا Phi همومورفزم بقى عليه باسمين يعني لو
+
+257
+00:28:25,710 --> 00:28:29,470
+أثبتت أن Phi one to one بيكون خلصنا من الموضوع
+
+258
+00:28:29,470 --> 00:28:33,910
+بيكون خلاص انتهينا منه يبقى بس مطلوب أثبت أن Phi
+
+259
+00:28:33,910 --> 00:28:38,240
+one to one طيب نيجي للبرهاميبقى أول ثلاث نقاط
+
+260
+00:28:38,240 --> 00:28:42,260
+تفاجئنا عليهم نجي للرابعة الربعة H Normal بدي أثبت
+
+261
+00:28:42,260 --> 00:28:46,760
+ان الـ Phi of H هذي ايه اللي همالها normal
+
+262
+00:28:46,760 --> 00:28:51,700
+subgroup من main من الـ Phi of G لذلك بدي أروح
+
+263
+00:28:51,700 --> 00:28:57,080
+أخدلي element في H و أخد element من G و أشوف لوين
+
+264
+00:28:57,080 --> 00:29:03,160
+بده اتوصل هالدنيا هذه يبقى باجي بقوله هنا لو أخدنا
+
+265
+00:29:03,160 --> 00:29:15,050
+الـ G موجود في Gواخدنا ال H موجود في H then ايه
+
+266
+00:29:15,050 --> 00:29:18,710
+شرايك في ال GHG inverse؟
+
+267
+00:29:22,660 --> 00:29:29,260
+بينتمي لمين؟ ايوة يبقى هذا belongs to H السبب
+
+268
+00:29:29,260 --> 00:29:35,860
+because ان ال H is a normal subgroup من G طب احنا
+
+269
+00:29:35,860 --> 00:29:40,260
+لما نتكلم على فيات يبقى نبدأ ناخد الفيات هنا يبقى
+
+270
+00:29:40,260 --> 00:29:47,560
+لو روحت اخدت ال phi of GHG inverse هيكون موجود في
+
+271
+00:29:47,560 --> 00:29:55,310
+ال phi of Hطب الـ Phi homomorphism يبقى بدي افك
+
+272
+00:29:55,310 --> 00:30:04,710
+هدول يبقاش بصير انها Phi of G Phi of H Phi of G
+
+273
+00:30:04,710 --> 00:30:14,450
+inverseهذا موجود في مين؟ في الـ Phi of H طيب، ألسا
+
+274
+00:30:14,450 --> 00:30:23,910
+هذا Phi of G Phi of H Phi of G لكل Inverse موجود
+
+275
+00:30:23,910 --> 00:30:30,950
+في Phi of H تعالى نشوف تعالى نشوف هذا وين موجود يا
+
+276
+00:30:30,950 --> 00:30:37,790
+شباب؟في الـ Phi of G يبقى هذا belongs to Phi of G
+
+277
+00:30:37,790 --> 00:30:46,670
+طيب هذا Phi of H belongs to Phi of H هذا بelongs
+
+278
+00:30:46,670 --> 00:30:54,540
+to Phi of G صح؟طيب ممتاز جدا يبقى الان انا هاي
+
+279
+00:30:54,540 --> 00:30:59,000
+اللي بدفتها ال normality يبقى اخدت element من هنا
+
+280
+00:30:59,000 --> 00:31:03,220
+و element من هنا ضربت ال element من هنا في ال
+
+281
+00:31:03,220 --> 00:31:07,180
+element من هنا في معكوس هذا ال element لجته موجود
+
+282
+00:31:07,180 --> 00:31:12,760
+في Phi H يبقى ايش تفتيرك لهذا الكلام ان Phi H is
+
+283
+00:31:12,760 --> 00:31:18,830
+normalيبقى هذا بده يعطينا الـPhi of H is a normal
+
+284
+00:31:18,830 --> 00:31:24,670
+subgroup من من الـPhi of G طبعا رب واحد فيكوا قاعد
+
+285
+00:31:24,670 --> 00:31:28,910
+بيفكر هك وقال لي طب استنى شوية انت جيبت نص البرهان
+
+286
+00:31:28,910 --> 00:31:32,890
+و اين النص التاني بقوله ايش النص التاني قال لي ال
+
+287
+00:31:32,890 --> 00:31:36,070
+Phi of H is a subgroup بقوله اه ما هيوا عندك رقم
+
+288
+00:31:36,070 --> 00:31:40,110
+واحدهذا مطلوب، هيبقى باعتباره مثبت، هيبقى مثبت
+
+289
+00:31:40,110 --> 00:31:45,790
+معاك وإن لم يكن مثبتًا، لأثبتناه أولًا، ثم أثبتنا
+
+290
+00:31:45,790 --> 00:31:50,430
+مين؟ الـNormality يبقى هي الكلام صحيح، هذا النقطة
+
+291
+00:31:50,430 --> 00:31:55,370
+أربعة بدنا نروح للنقطة رقم خمسة النقطة رقم خمسة
+
+292
+00:31:55,370 --> 00:31:58,770
+بتقول لي لو كان assume
+
+293
+00:32:23,000 --> 00:32:24,960
+إذا أردت أن أردت أن أردت أن أردت أن أردت أن أردت
+
+294
+00:32:24,960 --> 00:32:25,500
+أن أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+295
+00:32:25,500 --> 00:32:25,840
+أردت أن أردت أن أردت أن أردت أن أردت أن أردت أن
+
+296
+00:32:25,840 --> 00:32:30,720
+أردت أن أردت أن أرالـ Kernel لـ Phi يجب أن يساوي،
+
+297
+00:32:30,720 --> 00:32:34,320
+يجب أن أضع فيه N من العناصر، أظن أن الـ Identity
+
+298
+00:32:34,320 --> 00:32:41,520
+تبع الـ G منهم يبقى G منهم، ويجب أن أقول G1 وG2
+
+299
+00:32:41,520 --> 00:32:43,280
+ويبقى مازالة مازالة مازالة مازالة مازالة مازالة
+
+300
+00:32:43,280 --> 00:32:43,920
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+301
+00:32:43,920 --> 00:32:48,960
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+302
+00:32:48,960 --> 00:32:49,280
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+303
+00:32:49,280 --> 00:32:49,320
+مازالة مازالة مازالة مازالة مازالة مازالة مازالة
+
+304
+00:32:49,320 --> 00:32:53,270
+مازالة مازالة مازالة مازاليبقى let الكلام then هذا
+
+305
+00:32:53,270 --> 00:32:59,450
+ايش معناه؟ معناه ان الـPhi of الـidentity element
+
+306
+00:32:59,450 --> 00:33:03,510
+تبع الـG بده يساوي الـidentity element تبع الـG
+
+307
+00:33:03,510 --> 00:33:09,430
+bar والـPhi of G1 بده يساوي الـidentity element
+
+308
+00:33:09,430 --> 00:33:15,110
+تبع الـG bar والـPhi of G2 بده يساوي الـidentity
+
+309
+00:33:15,110 --> 00:33:20,820
+element تبع الـG barوالـ Phi of G N minus الـ one
+
+310
+00:33:20,820 --> 00:33:26,600
+بده يساوي الـ identity تبع الـ G bar يبقى أنا صار
+
+311
+00:33:26,600 --> 00:33:30,980
+عندي N من العناصر لهم صورة واحدة يبقى الـ Phi is
+
+312
+00:33:30,980 --> 00:33:41,960
+into one يبقى هذا this means that ان الـ Phi is
+
+313
+00:33:41,960 --> 00:33:45,440
+into one
+
+314
+00:33:52,040 --> 00:34:02,440
+يبقى هايات مثلا من جي لجي من from جي to جي بار ولم
+
+315
+00:34:02,440 --> 00:34:09,970
+اقول unto جي باريبقى دلت قصة الـ onto هذه بدها
+
+316
+00:34:09,970 --> 00:34:15,270
+إثبات يبقى بدأ أروح أخد element في five of G و
+
+317
+00:34:15,270 --> 00:34:24,870
+أثبت أنه له أصل وين في G طيب كويس أه مش بدنا نثبت
+
+318
+00:34:24,870 --> 00:34:30,760
+أنها ontoلأ جي بار لأ في of جي هي من عناصر جي بار
+
+319
+00:34:30,760 --> 00:34:35,380
+جزء منها لكن هل تسويها او لا تسويها قد يكون و قد
+
+320
+00:34:35,380 --> 00:34:41,120
+لا يكون يعني يا شباب لو اتخيلنا ان هذه كلها هي جي
+
+321
+00:34:41,120 --> 00:34:49,500
+بار وانا عندي في من الجي من الجي الى الجي بار يمكن
+
+322
+00:34:49,500 --> 00:34:57,460
+هدولهذا كله يطلع هو في of جي لكن هذا هنا مافيش ولا
+
+323
+00:34:57,460 --> 00:35:04,100
+عنصر تمام يبقى جزء بقول لذلك انا مركز على في of جي
+
+324
+00:35:04,100 --> 00:35:10,160
+on to في of جي يعني كل element في هذه ال set بدي
+
+325
+00:35:10,160 --> 00:35:15,580
+اثبت انه له اصل وين في جي كويس لذلك مضاجي اقوله
+
+326
+00:35:15,580 --> 00:35:25,360
+خدلي yالان بدي اثبتله ان فاي is onto يبقى بداجة
+
+327
+00:35:25,360 --> 00:35:34,880
+اقوله let مثلا y belongs to فاي of g فاي of كابتل
+
+328
+00:35:34,880 --> 00:35:44,120
+جي تمام؟ then ال y هذه بدها تسوي فاي of g for some
+
+329
+00:35:44,120 --> 00:35:52,310
+g اللي موجودة في جيمصبوط هيك يبقى انا اخدت element
+
+330
+00:35:52,310 --> 00:35:56,610
+في الصورة و روحت اخدت element من هنا يبقى ال five
+
+331
+00:35:56,610 --> 00:36:02,890
+ده سواء five of g for some ايوة طيب انا بدي ايش ال
+
+332
+00:36:02,890 --> 00:36:07,490
+element اللي اخدته في ال five of g بدي اثبت انه له
+
+333
+00:36:07,490 --> 00:36:13,810
+اصل في g او له اصولممكن يكون أصول مش أصل ممكن يكون
+
+334
+00:36:13,810 --> 00:36:20,230
+كتار انتوا أثبتنا ان انتوا يبقى أصول وليس أصل تمام
+
+335
+00:36:20,230 --> 00:36:29,110
+يبقى الفي انفرس يبقى بناء على لو أخدت الفي انفرس
+
+336
+00:36:29,110 --> 00:36:35,230
+of Y يبقى الفي انفرس of Y عشان بده يساويG في الـ
+
+337
+00:36:35,230 --> 00:36:40,450
+Kernel ها دي ربالك يبقى هذا بده يساوي الـ Phi
+
+338
+00:36:40,450 --> 00:36:46,970
+inverse of Y بده يساوي الـ G في ال Kernel لمين؟ في
+
+339
+00:36:46,970 --> 00:36:52,490
+ال Kernel للـ Phi معناه هذا الكلام أنه طبعا Phi
+
+340
+00:36:52,490 --> 00:36:57,850
+inverse of Y مش عنصر واحد لو بدي أشتغل حرفي لو
+
+341
+00:36:57,850 --> 00:37:02,830
+بقول عنصر واحدلكن هذه عناصر وبالتالي كثير من
+
+342
+00:37:02,830 --> 00:37:08,390
+العناصر اللي هو الـ Y هذه قد يكون هو صورتها فبجي
+
+343
+00:37:08,390 --> 00:37:15,650
+بقوله يبقى ال order للـ Phi inverse of Y بده يساوي
+
+344
+00:37:15,650 --> 00:37:22,990
+ال order للـ G في ال kernel للـ Phi. مظبوط ولا لا؟
+
+345
+00:37:22,990 --> 00:37:29,150
+طب ايش العلاقة؟ الآن هذا ليس left cosetجي في
+
+346
+00:37:29,150 --> 00:37:33,350
+الكيرن الفاي مش left coset صح ولا لا؟ طب إذا ال
+
+347
+00:37:33,350 --> 00:37:37,990
+order إيه اللي هيسوي ال order ل ال subgroup نفسه
+
+348
+00:37:37,990 --> 00:37:43,090
+يبقى هذا الكلام بدي يسوي ال order للكيرن الفاي
+
+349
+00:37:43,090 --> 00:37:49,190
+اللي هو جداش ال N يعني معنى هذا الكلام إن ال Y
+
+350
+00:37:49,190 --> 00:37:55,770
+اللي عندي أخدت هذه لجتلها أصول عددهم N تمام يبقى
+
+351
+00:37:55,770 --> 00:38:04,900
+on twoيبقى this means that .. يبقى this means that
+
+352
+00:38:04,900 --> 00:38:08,240
+ان
+
+353
+00:38:08,240 --> 00:38:16,600
+الفاي maps in elements from
+
+354
+00:38:18,360 --> 00:38:26,080
+جي تو واي اللي موجود وين في جي بار او موجود في في
+
+355
+00:38:26,080 --> 00:38:37,560
+of جي بالتحديد موجود في في of جي so في is ontoطيب،
+
+356
+00:38:37,560 --> 00:38:43,320
+هذه النقطة أيه؟ النقطة الخامسة اللي خاطر مدام حلنا
+
+357
+00:38:43,320 --> 00:38:48,680
+زيها يبقى النقطة السادسة هذه أقولكوا exercise طبعا
+
+358
+00:38:48,680 --> 00:38:52,780
+مبرهنة في الكتاب، بس بعمل restriction على الـfi
+
+359
+00:38:52,780 --> 00:38:56,700
+يعني بيخليهاش على أطلقها، بس على عناصر إيش، يبقى
+
+360
+00:38:56,700 --> 00:39:02,300
+يا ريت من الكتاب تروح تجرها وترتب أمورهاالان كي
+
+361
+00:39:02,300 --> 00:39:07,660
+بار سابق روب من جي بار يبقى في انفرست اوف كي بده
+
+362
+00:39:07,660 --> 00:39:12,780
+اثبتها السابق روب من مين؟ من الجي طيب مشان اثبتها
+
+363
+00:39:12,780 --> 00:39:18,600
+السابق روب بده اثبته conditionsيبقى بدي أروح لمين؟
+
+364
+00:39:18,600 --> 00:39:24,620
+للنقطة السابعة مشان أروح للنقطة السابعة بدي أثبت
+
+365
+00:39:24,620 --> 00:39:31,160
+هذه Phi inverse subgroup من مين؟ من الـG هذا اللي
+
+366
+00:39:31,160 --> 00:39:35,460
+عايزيني أثبته مشان هيك بدي أثبتله أن هذه non-empty
+
+367
+00:39:35,460 --> 00:39:39,000
+و لو أخدت عنصرين منها بدي أثبت أن الأول في معكوسي
+
+368
+00:39:39,000 --> 00:39:43,020
+الثاني موجود فيها وبالتالي بيصير a subgroup
+
+369
+00:39:45,060 --> 00:39:52,840
+يبقى بضاجي أقول له assume أفترض أن الـK bar هي
+
+370
+00:39:52,840 --> 00:40:01,600
+عبارة عن subgroup من الـG bar يبقى
+
+371
+00:40:01,600 --> 00:40:10,020
+هذه subgroup من الـG bar then الـPhi inverse of K
+
+372
+00:40:10,020 --> 00:40:14,180
+bar is non-empty
+
+373
+00:40:20,320 --> 00:40:25,200
+الـ Phi of الـ Identity تبع الـ G بده يعطيني مين
+
+374
+00:40:25,200 --> 00:40:33,300
+الـ Identity تبع من؟ تبع الـ G bar يعني إيش؟ هذا
+
+375
+00:40:33,300 --> 00:40:43,430
+بده يعطيلكإن الـ Phi Inverse of الـ Identity تبع
+
+376
+00:40:43,430 --> 00:40:48,190
+الـ G Bar بدي سوى الـ Identity Element تبع الـ G
+
+377
+00:40:48,190 --> 00:40:55,030
+مظبوط؟ يبقى معنا هذا الكلام إن الـ Identity تبع
+
+378
+00:40:55,030 --> 00:41:02,830
+الـ G موجود في الـ Phi Inverse of الـ K Bar بعد
+
+379
+00:41:02,830 --> 00:41:10,120
+هيك بتروح أخد two elementsالـ X و الـ Y موجودة في
+
+380
+00:41:10,120 --> 00:41:18,780
+الـ Phi inverse of الـ K bar معنى هذا الكلام ان
+
+381
+00:41:18,780 --> 00:41:28,520
+الـ X بده يساوي Phi inverse of K1 مثلا و الـ Y بده
+
+382
+00:41:28,520 --> 00:41:32,800
+يساوي Phi inverse of K2
+
+383
+00:41:36,280 --> 00:41:42,310
+كويسيبقى بدي أروح أخد الـ X Y inverse أشوف هل
+
+384
+00:41:42,310 --> 00:41:45,930
+موجودة هنا ولا لأ إذا طلعت موجودة بيكون كفى الله
+
+385
+00:41:45,930 --> 00:41:53,370
+المؤمنين يبقى بدي أروح أخد له الـ X Y inverse يبقى
+
+386
+00:41:53,370 --> 00:41:59,190
+او الـ Phi خلّي
+
+387
+00:41:59,190 --> 00:42:03,610
+أشوف الـ X Y inverse يبقى الـ X اللي عبارة عن Phi
+
+388
+00:42:03,610 --> 00:42:12,100
+inverse of الكوانفي الـ Phi inverse of K2 لكل
+
+389
+00:42:12,100 --> 00:42:25,400
+inverse يبقى هذا الكلام بده يساوي هذا
+
+390
+00:42:25,400 --> 00:42:31,900
+الكلام بده يساوي Phi inverse of K1 في Phi inverse
+
+391
+00:42:31,900 --> 00:42:40,870
+of K2 inverseهذا الكلام بده يساوي في انفرس of K1
+
+392
+00:42:40,870 --> 00:42:49,640
+K2 انفرسهذا كله مين؟ اللي هو الـ X Y inverse هل
+
+393
+00:42:49,640 --> 00:43:00,080
+هذا الان موجود في الـ Phi inverse of K bar؟ ليش؟
+
+394
+00:43:00,080 --> 00:43:04,740
+لأن هدول حاصل ضربهم موجود في K bar لأن أول ما جينا
+
+395
+00:43:04,740 --> 00:43:09,220
+كنا K bar ما لها subgroup من G بقى closed under
+
+396
+00:43:09,220 --> 00:43:13,480
+multiplicationيبقى هذا موجود في الـPhi inverse of
+
+397
+00:43:13,480 --> 00:43:22,060
+K bar يبقى بناء عليه الـPhi inverse of K bar is a
+
+398
+00:43:22,060 --> 00:43:27,160
+subgroup من جيه؟ من جيه وانتهينا منها بدنا نروح
+
+399
+00:43:27,160 --> 00:43:36,840
+للنقطة اللي بعدها وهي خاصية ال normality ايوة عرف
+
+400
+00:43:36,840 --> 00:43:42,730
+لو ماكنتش homomorphismأمرها ما بيصير كلامها ده
+
+401
+00:43:42,730 --> 00:43:51,470
+صحيح وحسب
+
+402
+00:43:51,470 --> 00:43:55,670
+التعريف اللي عندك حسب التعريف يعني أعرفنا الـPhi
+
+403
+00:43:55,670 --> 00:44:00,210
+Inverse وين أعرفناه و الله مسحنا .. مسحنا .. لا
+
+404
+00:44:00,210 --> 00:44:04,230
+أيوة أيوة كل الـK اللي موجودة في جبهات الـPhi of K
+
+405
+00:44:04,230 --> 00:44:07,670
+موجودة وين؟ في الـK bar أيوة
+
+406
+00:44:14,620 --> 00:44:30,300
+تاني تاني سؤالك سطر التاني هنا لفوق اه اه
+
+407
+00:44:30,300 --> 00:44:37,200
+هذا يا ابني انا بقول يساوي ال identity تبع ال جي
+
+408
+00:44:37,200 --> 00:44:42,220
+بار اثر على الطرفين بالفاي انفرستلا مانعثرنا بفعل
+
+409
+00:44:42,220 --> 00:44:46,900
+مش هتاطنين ال identity يعنياللي هو .. هذا لو كنت
+
+410
+00:44:46,900 --> 00:44:51,000
+أريد مورفزم، عنصر واحد. أنا بهمني العنصر، بدي أجيب
+
+411
+00:44:51,000 --> 00:44:55,000
+عنصر، بديش أجيب كتير، بكفيني منك عنصر، هذا همش أن
+
+412
+00:44:55,000 --> 00:45:02,260
+أثبت أنها non-empty، تمام؟ طيب، أنا إلي وجهة نظر
+
+413
+00:45:02,260 --> 00:45:07,980
+أخرى، إلي وجهة نظر أخرى في هذا الكلام، يعني لو
+
+414
+00:45:07,980 --> 00:45:12,820
+بدنا نشك في هذا هل هو homomorphism ولا لا، بنقدر
+
+415
+00:45:12,820 --> 00:45:18,450
+نقول الخطوة هذه استني شوية،الحين لو جيت هنا فاي of
+
+416
+00:45:18,450 --> 00:45:26,950
+ال X Y inverse أليست هي فاي لفاي inverse of K1 K2
+
+417
+00:45:26,950 --> 00:45:35,530
+inverse صح ولا لا أثر هنا بفاي و أثر هنا بفاييبقى
+
+418
+00:45:35,530 --> 00:45:40,250
+النتيجة
+
+419
+00:45:40,250 --> 00:45:47,640
+K1 K2 Inverse اللي موجودة في الـK barصح ولا لا
+
+420
+00:45:47,640 --> 00:45:55,440
+يبقى صار عندك اللي هو ال X Y inverse موجودة ال X Y
+
+421
+00:45:55,440 --> 00:46:05,560
+inverse بدها تساوي اللي بدها تساوي او هذه مو ..
+
+422
+00:46:05,560 --> 00:46:11,190
+استنى شويةبدي ألغي هذه ألغيتها بمين أثرت عليها فهي
+
+423
+00:46:11,190 --> 00:46:16,070
+أصبح X Y inverse بدي أجيبها هنا يبقى بدها تساوي
+
+424
+00:46:16,070 --> 00:46:24,030
+الـ Phi of الـ K واحد K اتنين inverse اللي هي هذه
+
+425
+00:46:24,030 --> 00:46:32,490
+موجودة في المين في ال Phi of Phi of K وPhi of K
+
+426
+00:46:32,490 --> 00:46:43,590
+Phi of Kلأ احنا احنا خليك معايا احنا خليك .. هاي
+
+427
+00:46:43,590 --> 00:46:49,270
+اللي وصلنا X Y inverse بده يساوي في انفرست ل K1 K2
+
+428
+00:46:49,270 --> 00:46:53,830
+بده اثر هنا بفي و اثر هنا بفي هاي اثرنا بفي و
+
+429
+00:46:53,830 --> 00:46:59,390
+اثرنا هنا بفي هذه هتلغي التانية بصير اللي هو X Y
+
+430
+00:46:59,390 --> 00:47:06,100
+inverse بده يساوي في of K1 K2 inverse تمام؟يبقى
+
+431
+00:47:06,100 --> 00:47:20,100
+هذه موجودة في Phi of K و Phi of K لحظة
+
+432
+00:47:20,100 --> 00:47:25,880
+شوية عندك اعتراض على هذه العبارة؟الخطوة اللى بعدها
+
+433
+00:47:25,880 --> 00:47:31,680
+تمام انا جيت اثره بفاي على XY inverse طب هدى تساوي
+
+434
+00:47:31,680 --> 00:47:35,460
+هدى مشينا لغاية هنا لو قلنا مش عارفين هى
+
+435
+00:47:35,460 --> 00:47:40,240
+homomorphism ولا لأ يبقى كان صار كل الشغل هدى مش
+
+436
+00:47:40,240 --> 00:47:45,350
+صحيحإذا هي homomorphism غصب على ما يرضى وإلا كان
+
+437
+00:47:45,350 --> 00:47:48,530
+هذا الكلام .. لقد قلت ال inverse صح لكن مصير هذا
+
+438
+00:47:48,530 --> 00:47:52,910
+الكلام صحيح ليس صحيحا إلا إذا كانت homomorphism
+
+439
+00:47:52,910 --> 00:48:00,130
+تمام؟ على .. ايوة ال homomorphism مش ضروري يكون
+
+440
+00:48:00,130 --> 00:48:04,010
+مدبن صحيح لما تجيب في انفص بطل افتران أصلا مصير
+
+441
+00:48:04,010 --> 00:48:08,490
+الواحد اللي عند الصور مظبوطمش متبطل اختراع اصلا مش
+
+442
+00:48:08,490 --> 00:48:12,350
+متبطل homomorphism متبطل اختراع معرف اصلا تصير
+
+443
+00:48:12,350 --> 00:48:15,470
+الصورة العنصر اللي هو اكتر من الصورة فكيف انت
+
+444
+00:48:15,470 --> 00:48:18,130
+بتاخد اللي هو اكتر من الصورة العنصر اللي هو اكتر
+
+445
+00:48:18,130 --> 00:48:21,210
+من الصورة احنا بنحكي homomorphism وليس function
+
+446
+00:48:21,210 --> 00:48:27,050
+اذا قلنا function ماهو isomorphism function يعني
+
+447
+00:48:27,050 --> 00:48:30,230
+مية المية بس ال homomorphism قد يكون و قد لا يكون
+
+448
+00:48:31,440 --> 00:48:36,400
+أه قد يكون و قد لا يكون تمام طيب احنا هذه النقطة
+
+449
+00:48:36,400 --> 00:48:42,740
+رقم قداش هي سبعة النقطة هذه رقم سبعة رقم سبعة
+
+450
+00:48:42,740 --> 00:48:50,600
+ماشيين كله صح وهذه تمام واخدنا x y inverse و أثرنا
+
+451
+00:48:50,600 --> 00:48:55,180
+عليها بفاية و طلع ك واحد كتنين اللي موجودة في ك
+
+452
+00:48:55,180 --> 00:49:01,270
+مظبوط يبقى من هذا الكلامبنقدر نقول X Y inverse
+
+453
+00:49:01,270 --> 00:49:08,490
+موجودة في الـ Phi في ال Phi of K صحيح يبقى بنقول
+
+454
+00:49:08,490 --> 00:49:16,550
+هنا النقطة الأخيرة ان ال X Y inverse هذه موجودة في
+
+455
+00:49:16,550 --> 00:49:25,650
+ال Phi inverse في ال Phi inverse في ال Phi inverse
+
+456
+00:49:25,650 --> 00:49:31,360
+of K باراللي فوق بالظبط تماما خلاص يبقى ليش يعيدها
+
+457
+00:49:31,360 --> 00:49:36,220
+هذي كلها مالاش نزول هي ال X Y انفرست موجودة في
+
+458
+00:49:36,220 --> 00:49:40,840
+الفاي انفرست هذا كله زيادة صوتناهذه الخطوة زيادة
+
+459
+00:49:40,840 --> 00:49:45,660
+تمام يبقى موجودة في الـ Phi inverse of K bar يبقى
+
+460
+00:49:45,660 --> 00:49:50,920
+بناء اللي عليه Phi inverse of K bar is a subgroup
+
+461
+00:49:50,920 --> 00:49:59,100
+يبقى هنا Phi inverse of K bar is a subgroup من
+
+462
+00:49:59,100 --> 00:50:05,840
+مين؟ من ال G بدنا نيجي للنقطة الثامنة خلي بالك
+
+463
+00:50:05,840 --> 00:50:10,900
+معاياالنقطة الثامنة اللى جبناها هذه الـ subgroup
+
+464
+00:50:10,900 --> 00:50:16,160
+من G بنا نثبت انها normal بس بشرط ان ال K bar
+
+465
+00:50:16,160 --> 00:50:23,320
+normal من G يبقى باجي بقوله assume افترض ان ال K
+
+466
+00:50:23,320 --> 00:50:30,840
+bar is a normal subgroup من G barبالدالي اثبت ان
+
+467
+00:50:30,840 --> 00:50:38,520
+الفاي
+
+468
+00:50:38,520 --> 00:50:49,580
+انفرس of K bar is a normal subgroup من من من ال G
+
+469
+00:50:50,950 --> 00:51:00,270
+كويس لذلك بدروع اخد let الجي موجودة في جي and ال X
+
+470
+00:51:00,270 --> 00:51:11,210
+موجود في الفاي انفرس of الكبار then الجي موجودة في
+
+471
+00:51:11,210 --> 00:51:20,950
+الجيوالـ X هذه بدها تساوي في انفرس في انفرس of K
+
+472
+00:51:20,950 --> 00:51:29,760
+على سبيل المثاليبقى هذا معناه ان جي موجود في جي
+
+473
+00:51:29,760 --> 00:51:37,360
+and فاي of اكس فاي of اكس بده يساوي كم؟ بده يساوي
+
+474
+00:51:37,360 --> 00:51:44,700
+كم طب لو أخدت الجي اكس جي انفرس مشان اثبات ال
+
+475
+00:51:44,700 --> 00:51:51,000
+normalityواخد تأثير الـ Phi عليها يبقى هذا الكلام
+
+476
+00:51:51,000 --> 00:51:59,700
+بدل يساوي Phi of G Phi of X Phi of G inverse يبقى
+
+477
+00:51:59,700 --> 00:52:06,420
+هذا الكلام بدل يساوي Phi of G Phi of X اللي هي
+
+478
+00:52:06,420 --> 00:52:12,400
+main اللي هي اب K Phi of X اللي هي و ال K normal
+
+479
+00:52:12,400 --> 00:52:21,200
+اللي هو Kوالـ Phi هذه of G لكل inverse بالشكل اللي
+
+480
+00:52:21,200 --> 00:52:28,620
+عندنا هنا تمام؟ الحين هذه موجودة في Gوهذه موجودة
+
+481
+00:52:28,620 --> 00:52:36,240
+في الـPhi inverse of K وهذه موجودة في G أخدنا
+
+482
+00:52:36,240 --> 00:52:41,720
+تأثير الـPhi عليهم وطلع عندنا هذا الـElement وهذا
+
+483
+00:52:41,720 --> 00:52:49,100
+وهذا الـK bar أنا جال عليها normal يبقى لو أخدت
+
+484
+00:52:49,100 --> 00:52:56,580
+element من G bar هذا موجود في G barوهذا موجود في
+
+485
+00:52:56,580 --> 00:53:04,000
+جي بار وهذا موجود في الفاي انفرس هذا موجود في
+
+486
+00:53:04,000 --> 00:53:10,460
+الفاي انفرس of K إذا هذا كله موجود في الفاي انفرس
+
+487
+00:53:10,460 --> 00:53:17,680
+of K بار بالشكل اللي عندنا K بار يبقى بناء عليه
+
+488
+00:53:17,680 --> 00:53:21,500
+الفاي
+
+489
+00:53:21,890 --> 00:53:30,270
+إنفرست من K بار هو عضو عام من جيه
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..967f3317eaf9f4e51e8db0c959c38e1420cb9f5f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/cYW9I6E5mF4.srt
@@ -0,0 +1,1795 @@
+1
+00:00:21,180 --> 00:00:26,920
+بسم الله الرحمن الرحيم انتهينا من شبتر ستة اللي هو
+
+2
+00:00:26,920 --> 00:00:32,320
+الـ isomorphism والآن بندخل لشبتر سبعة شبتر سبعة
+
+3
+00:00:32,320 --> 00:00:36,640
+اللي هو Cosets and Lagrange theorem بتكلم عن
+
+4
+00:00:36,640 --> 00:00:41,980
+نقطتين والنقطتين مرتبطتين مع بعض ارتباطا وثيقا كما
+
+5
+00:00:41,980 --> 00:00:49,330
+سنرى Coset بالعربي يعني الفئة المرافقة لـ Lagrange 
+
+6
+00:00:49,330 --> 00:00:53,410
+theorem نظرية لاجرانج بالنسبة للعالم الرياضي لاجرانج
+
+7
+00:00:53,410 --> 00:00:59,970
+الذي اكتشف هذه النظرية اليوم خلينا مع الـ Cosets و
+
+8
+00:00:59,970 --> 00:01:04,030
+المرة القادمة إن شاء الله نتكلم عن لاجرانج theorem
+
+9
+00:01:04,650 --> 00:01:11,170
+بنقدر نعطي تعريف للـ Cosets ثم نبدأ بملاحظاتنا على
+
+10
+00:01:11,170 --> 00:01:15,750
+الـ Cosets in general يبقى التعريف يقول ياخد الـ H
+
+11
+00:01:15,750 --> 00:01:22,330
+subgroup من G وروحنا أخدنا أي element A في G بضربه 
+
+12
+00:01:22,330 --> 00:01:27,950
+أعرف الـ Coset اللي هي AH يعني الـ subgroup بدأ
+
+13
+00:01:27,950 --> 00:01:33,670
+ضربها من جهة الشمال في أي element من G وليكن A من
+
+14
+00:01:33,670 --> 00:01:38,530
+الـ set هذه A H يبقى the set of all elements A H
+
+15
+00:01:38,530 --> 00:01:43,570
+such that الـ H الصغيرة موجودة في H الكبيرة يعني
+
+16
+00:01:43,570 --> 00:01:51,350
+عناصر الـ A H هو الـ Element A مضروب في من في عنصر
+
+17
+00:01:51,350 --> 00:01:55,890
+من عناصر H من ما يكون شكله A يكون بالشكل اللي
+
+18
+00:01:55,890 --> 00:02:00,330
+عندنا هذا ضرب من جهة الشمال لذلك هذه بسميها left
+
+19
+00:02:00,330 --> 00:02:06,370
+coset of H in G وهذه الـ left coset تحتوي دائما وأبدا
+
+20
+00:02:06,370 --> 00:02:11,810
+عالميا على العنصر A حد يقدر يقول لي ليش هذه
+
+21
+00:02:11,810 --> 00:02:17,210
+بتحتوي على العنصر A لأن فيها الـ Identity الـ A في
+
+22
+00:02:17,210 --> 00:02:20,710
+الـ Identity بيعطينا الـ A itself يبقى الـ left
+
+23
+00:02:20,710 --> 00:02:26,310
+coset دائما وأبدا الـ element A موجود فيها بالمثل
+
+24
+00:02:26,310 --> 00:02:29,770
+مثل ما عرفنا الـ left coset بتروح أعرفها الـ right
+
+25
+00:02:29,770 --> 00:02:34,690
+coset فبقول الـ H الكبيرة A هي عبارة عن H A such
+
+26
+00:02:34,690 --> 00:02:38,410
+that الـ H تنتمي لـ H وهذه بسميها الـ right
+
+27
+00:02:38,410 --> 00:02:44,460
+coset of H in G وفي نفس الوقت containing Aلاحظ لما
+
+28
+00:02:44,460 --> 00:02:50,800
+أقول a h أو h a الـ operation اللي بين الـ a و الـ h
+
+29
+00:02:50,800 --> 00:02:54,500
+هي نفس الـ operation اللي موجودة على g و اللي
+
+30
+00:02:54,500 --> 00:03:02,390
+موجودة على h يعني إذا كان ضرب بدأ أقول ضرب إذا جمع
+
+31
+00:03:02,390 --> 00:03:07,490
+يبقى الـ binary operation ما بين الـ element a و الـ
+
+32
+00:03:07,490 --> 00:03:12,310
+element h حسب الـ operation اللي موجودة في g أو الـ
+
+33
+00:03:12,310 --> 00:03:16,610
+operation اللي موجودة في h طيب الـ a اللي خلى الـ
+
+34
+00:03:16,610 --> 00:03:20,510
+left coset سواء كان الـ right و الله left بسمي ايه
+
+35
+00:03:20,510 --> 00:03:25,670
+الـ element ايه بسميه the coset representative of a
+
+36
+00:03:25,670 --> 00:03:30,350
+H أو الـ H ايه سواء كان الـ left أو الـ right بتفرقش
+
+37
+00:03:30,350 --> 00:03:37,330
+أمامنا طب نروح نبدأ ذلك عمليا بمثال ونتوقف مع هذا
+
+38
+00:03:37,330 --> 00:03:44,080
+المثال نوعا ما وناقش بعض الشغلات ما أعطيني G هي S3
+
+39
+00:03:44,080 --> 00:03:50,180
+وهي كتبناها بالكامل ليها ستة عناصر واخد الـ H هي الـ
+
+40
+00:03:50,180 --> 00:03:55,700
+sub group الـ E والواحد و تلاتة قال هاتلي كل الـ left
+
+41
+00:03:55,700 --> 00:04:01,300
+cosets of H in S3 بقوله كويس إذا بدي أبدأ مدام
+
+42
+00:04:01,300 --> 00:04:05,620
+قاله هاتلي كل الـ left cosets إذا بدي أبدأ بمعنى
+
+43
+00:04:05,620 --> 00:04:10,320
+بالعنصر الأول بدي أضربه في H واشوف شو بيعطيني يبقى
+
+44
+00:04:10,320 --> 00:04:18,570
+بدأت أخد له E H يبقى هذا E في E واحد و تلاتة طبعا
+
+45
+00:04:18,570 --> 00:04:22,910
+الـ identity element لما أضربه فيه الـ element بيطلع
+
+46
+00:04:22,910 --> 00:04:27,530
+نفس الـ element أضربه في الثاني بدي يطلع نفس الثاني
+
+47
+00:04:27,530 --> 00:04:33,730
+الـ H مين هي يا شباب اللي هي H نفسها طيب اضرب الآن
+
+48
+00:04:33,730 --> 00:04:39,430
+واحد و تلاتة الـ permutation في الـ H يبقى هذا
+
+49
+00:04:39,430 --> 00:04:44,970
+الكلام بده يساوي لما أضربها بده يطلع واحد و تلاتة
+
+50
+00:04:44,970 --> 00:04:50,750
+و هنا من واحد و تلاتة في واحد و تلاتة بالشكل اللي
+
+51
+00:04:50,750 --> 00:04:56,580
+عندنا هذه هتعطينا مين؟ هتعطينا الـ permutation
+
+52
+00:04:56,580 --> 00:05:01,700
+واحد، تلاتة، طب هذه نفسها إيش بتعطينا؟ الـ
+
+53
+00:05:01,700 --> 00:05:06,560
+identity، تمام يبقى هذه عطتنا الـ identity، طلعت
+
+54
+00:05:06,560 --> 00:05:14,480
+مين؟ نفس الـ H يبقى هذه طلعت نفس الـ H نفسها يبقى
+
+55
+00:05:14,480 --> 00:05:20,680
+بناء عليه بقدر أستنتج من هذا الكلام أن الـ E في H
+
+56
+00:05:20,680 --> 00:05:27,920
+ساوي واحد تلاتة في H ساوي الـ H نفسها وهذا بدي
+
+57
+00:05:27,920 --> 00:05:34,740
+أحط علامة استفهام سارجع لها بعد قليل طيب الآن بده
+
+58
+00:05:34,740 --> 00:05:39,240
+أخد الـ elements الأخرى بدل ما أخذنا واحد و تلاتة
+
+59
+00:05:39,240 --> 00:05:45,320
+بده أخد واحد و اتنين في h أشوف إيش بده يعطينا يبقى
+
+60
+00:05:45,320 --> 00:05:51,420
+هذا بده يعطينا واحد و اتنين واحد و اتنين مضروبة في
+
+61
+00:05:51,420 --> 00:05:56,000
+من؟ في واحد و تلاتة يبقى واحد و اتنين في الـ
+
+62
+00:05:56,000 --> 00:05:59,340
+identity بواحد و اتنين واحد اتنين في واحد تلاتة
+
+63
+00:05:59,340 --> 00:06:03,840
+بواحد اتنين واحد تلاتة هذا الكلام بدي يعطينا الواحد
+
+64
+00:06:03,840 --> 00:06:09,200
+اتنين كما هي وهذه بدي أجيب الـ composition ما بين
+
+65
+00:06:09,200 --> 00:06:14,180
+الـ two transpositions الاتنين هدول يبقى باجي بقول
+
+66
+00:06:14,180 --> 00:06:20,170
+هاي الواحد الواحد صورته و التلاتة صورتها تلاتة يبقى
+
+67
+00:06:20,170 --> 00:06:26,050
+هي التلاتة التلاتة صورتها واحد والواحد صورته اتنين
+
+68
+00:06:26,050 --> 00:06:30,630
+يبقى هي الاتنين الآن اتنين صورته اتنين و اتنين
+
+69
+00:06:30,630 --> 00:06:35,890
+صورته هي موجود يبقى انقفلت بالشكل اللي عندنا هنا
+
+70
+00:06:35,890 --> 00:06:43,940
+تمام؟ لاحظ أن هذا بالضبط تماما هو واحد تلات اثنين
+
+71
+00:06:43,940 --> 00:06:52,540
+كما لو ضربت في main ضربت في H بناء على يسار واحد
+
+72
+00:06:52,540 --> 00:06:58,240
+اتنين اتش هو واحد تلات اتنين اتش يبقى هذا بدي
+
+73
+00:06:58,240 --> 00:07:03,780
+يعطيك أن واحد اتنين الـ permutation لما تضربها في
+
+74
+00:07:03,780 --> 00:07:09,800
+اتش كليا بدي يساوي واحد تلات اتنين كما لو ضربتها
+
+75
+00:07:09,800 --> 00:07:17,240
+في اتش وهذا كمان بدي يولد علامة استفهام أخرى نكمل
+
+76
+00:07:18,800 --> 00:07:24,440
+بدي آجي لليه اتنين و تلاتة بدي أضربها في مين في اتش
+
+77
+00:07:24,440 --> 00:07:32,100
+يبقى الناتج اتنين تلاتة و اتنين تلاتة واحد تلاتة و
+
+78
+00:07:32,100 --> 00:07:37,750
+يساوي اتنين تلاتة واحد يبقى اتنين تلاتة في اتش
+
+79
+00:07:37,750 --> 00:07:42,050
+بـ اتنين تلاتة لأن الـ identity بعدها اتنين تلاتة في
+
+80
+00:07:42,050 --> 00:07:47,030
+واحد تلاتة هي إذا أن النتج يساوي هي اتنين تلاتة
+
+81
+00:07:47,030 --> 00:07:51,130
+الأولانية الـ permutation الأولى وهذه بضرب أجيب الـ
+
+82
+00:07:51,130 --> 00:07:55,830
+composition في ما بينهما إذا ببدأ بالواحد الواحد
+
+83
+00:07:55,830 --> 00:08:02,130
+صورته و التلاتة صورتها اتنين يبقى هي واحد اتنين
+
+84
+00:08:02,640 --> 00:08:08,840
+تلاتة صورته اتنين و اتنين صورته تلاتة الآن بالداجي
+
+85
+00:08:08,840 --> 00:08:14,400
+التلاتة صورتها واحد و الواحد صورته هي موجود إذا
+
+86
+00:08:14,400 --> 00:08:20,370
+أنقفلت بالشكل اللي عندنا هذاهذا بالضبط تماما بده
+
+87
+00:08:20,370 --> 00:08:26,010
+يساوي اللي هو واحد اتنين تلاتة كما لو ضربتها في H
+
+88
+00:08:26,010 --> 00:08:32,730
+اعمل الـ H كانت كويس؟ يبقى هاي خلاصنا ضايل فيه شيء؟
+
+89
+00:08:33,500 --> 00:08:39,680
+كل element هيو مضروب عندي من جهة الشمال فيه H بناء
+
+90
+00:08:39,680 --> 00:08:53,770
+عليه صار the left cosets of H in S3R أول واحد H ههه
+
+91
+00:08:53,770 --> 00:08:59,450
+H أو الـ E في الـ H أو واحد تلاتة H الـ element
+
+92
+00:08:59,450 --> 00:09:06,990
+الثاني اللي هو من واحد اتنين في من في H و الـ
+
+93
+00:09:06,990 --> 00:09:15,330
+element الثالث اللي هو اتنين تلاتة كله في H أحنا
+
+94
+00:09:15,330 --> 00:09:21,690
+هكذا خلصنا المتوقع كان من البداية أنه لما أضرب الـ
+
+95
+00:09:21,690 --> 00:09:25,490
+elements الستة اللي عندنا تبعات الـ agromfets يطلع
+
+96
+00:09:25,490 --> 00:09:30,150
+عندي الست elements مظبوط طلعوا الست elements بس ما
+
+97
+00:09:30,150 --> 00:09:34,570
+همّاش disjoint هاي الملاحظة الأولى لأن هدول طلعوا
+
+98
+00:09:34,570 --> 00:09:39,600
+شيء بيساوي بعضه هاي طلعوا هاي تلاتة بيساوي بعض هدول
+
+99
+00:09:39,600 --> 00:09:43,700
+اتنين بيساووا بعض، هدول اتنين كمان بيساووا بعض،
+
+100
+00:09:43,700 --> 00:09:48,220
+تمام؟ إذا ليس بالضرورة لما أجيب الـ left coset الـ
+
+101
+00:09:48,220 --> 00:09:53,650
+elements يكونوا disjoint هذه الملاحظة الأولى
+
+102
+00:09:53,650 --> 00:09:58,170
+الملاحظة الثانية أطلع لي في الحالتين الاتنين هدول
+
+103
+00:09:58,170 --> 00:10:03,430
+هنا ضربت في ايه و هنا ضربت في واحد تلاتة يعني ضربت
+
+104
+00:10:03,430 --> 00:10:10,330
+في عناصر H إذا لو أخدت element من H و ضربته في H
+
+105
+00:10:10,330 --> 00:10:16,680
+بدي أطلع منهم each itself مش واحدة ثانية أطلع عندي
+
+106
+00:10:16,680 --> 00:10:22,080
+ايه اتش ثوات لمين اتش نفسها الواحد تلاتة فيه اتش
+
+107
+00:10:22,080 --> 00:10:27,100
+ثوات لمين الواحد تلاتة يعني اتش نفسها يبقى الـ
+
+108
+00:10:27,100 --> 00:10:31,880
+left coset لو ضربت اللي هو الـ subgroup في element
+
+109
+00:10:31,880 --> 00:10:35,820
+من نفس الـ subgroup دي يطلع مين الـ subgroup هاي
+
+110
+00:10:35,820 --> 00:10:42,520
+الملاحظة الثانية الملاحظة الثالثة إن الـ left cosets
+
+111
+00:10:42,520 --> 00:10:49,180
+ممكن يتساوى رغم أن العنصر اللي ضرب فيه مش نفسه طلع
+
+112
+00:10:49,180 --> 00:10:54,280
+لي هنا هي عندي واحد اتنين ضربتها في H سواتلي مام
+
+113
+00:10:54,280 --> 00:10:59,220
+واحد تلات اتنين في H هل الواحد اتنين هو الواحد
+
+114
+00:10:59,220 --> 00:11:05,600
+تلات اتنين؟ لأ مختلف إذا ليس بالضرورة لو قلت لك A H
+
+115
+00:11:05,600 --> 00:11:11,370
+يساوي BH إذا الـ A يساوي الـ B صح ولا غلط؟ غلط قد يحدث
+
+116
+00:11:11,370 --> 00:11:16,450
+أنه صح بس in general غلط يعني ممكن تحصل حالة علتين
+
+117
+00:11:16,450 --> 00:11:21,870
+ثلاثة تبقى صح لكن in general ليس صحيحا يبقى هذه
+
+118
+00:11:21,870 --> 00:11:25,750
+الملاحظة هذه أنه في حالة الـ left cosets ممكن
+
+119
+00:11:25,750 --> 00:11:30,470
+يتساوي الـ two left cosets لكن الـ a ليساوي الـ b وهي
+
+120
+00:11:30,470 --> 00:11:36,050
+الكلام واضح قدامنا وهكذا يبقى هذه ملاحظات أساسية
+
+121
+00:11:36,050 --> 00:11:40,890
+موجودة من خلال هذا المثال و بنقدر نسحبها على
+
+122
+00:11:40,890 --> 00:11:49,210
+cosets أخرى نعطي مثال آخر example
+
+123
+00:11:49,210 --> 00:11:59,280
+two example two بيقول الـ G تساوي D4 و D4 احنا
+
+124
+00:11:59,280 --> 00:12:05,540
+عارفين عناصرها اللي هي R نود و R تسعين و R مية و
+
+125
+00:12:05,540 --> 00:12:14,800
+ثمانين و R مية و سبعين و H و V و D و D Prime و بدي 
+
+126
+00:12:14,800 --> 00:12:21,740
+أخذ اللي هو K subgroup اللي هي subgroup generated 
+
+127
+00:12:21,740 --> 00:12:32,800
+by R180 اللي عناصرها Arnold وR180 فقط لا غير تمام؟
+
+128
+00:12:32,800 --> 00:12:41,600
+find the left cosets of 
+
+129
+00:12:54,930 --> 00:12:59,790
+الآن بدي أبدأ بالـ elements كلهم قال لي هات لي lift
+
+130
+00:12:59,790 --> 00:13:06,950
+cos 6 يبقى أنا بدي أجيب له Arnold في capital K  كابيتال K
+
+131
+00:13:06,950 --> 00:13:11,930
+الـ K موجودة عندي Arnold في Arnold مين بتعطينا Arnold
+
+132
+00:13:11,930 --> 00:13:16,410
+في 180 بتعطينا مين R 180 اللي هي
+
+133
+00:13:16,410 --> 00:13:25,190
+الـ K itself طيب خذ R 180 R 180 في
+
+134
+00:13:25,190 --> 00:13:31,550
+اللي هو K يبقى هذا الكلام بده يساوي R 180
+
+135
+00:13:31,550 --> 00:13:39,080
+والتانية بصير Arnold لأن الـ R 180 هو R 180 و R 360
+
+136
+00:13:39,080 --> 00:13:46,720
+هو الـ R node طلعت من هذا الـ K نفسه من الاثنين
+
+137
+00:13:46,720 --> 00:13:55,510
+هذول نستنتج الـ R node K بده يساوي R180K بده يساوي
+
+138
+00:13:55,510 --> 00:14:00,350
+K itself أظن هذا يتفق مع النتيجة اللي توصلنا لها
+
+139
+00:14:00,350 --> 00:14:04,890
+هنا أنه لو ضربت الـ subgroup في أي element من الـ
+
+140
+00:14:04,890 --> 00:14:09,310
+subgroup بتطلع نفس من نفس الـ subgroup وهذا اللي
+
+141
+00:14:09,310 --> 00:14:13,330
+حصل في الحالتين الاثنين هذول زي المثال اللي هناك
+
+142
+00:14:13,330 --> 00:14:20,020
+بالضبط تمام طيب الآن لو جئت أخذت الـ R 200 و
+
+143
+00:14:20,020 --> 00:14:25,940
+70 في K مثلا يبقى هذا الكلام بده يسوي بده أضربه
+
+144
+00:14:25,940 --> 00:14:31,840
+هنا يبقى بده يعطيني R 270 وعندك R 100 و
+
+145
+00:14:31,840 --> 00:14:37,540
+80 في R 270 اللي هي من R 90
+
+146
+00:14:39,600 --> 00:14:45,860
+270×180 خذ منها R 90 بيصير هذه R 360 الـ identity
+
+147
+00:14:45,860 --> 00:14:54,920
+بيظل R 90 السؤال هو هل هذا الكلام هو R 90
+
+148
+00:14:54,920 --> 00:15:02,760
+في K أم لا اضرب هاي R 90 وR 90 في R 180 بـ R 270
+
+149
+00:15:04,630 --> 00:15:10,250
+مظبوط ولا لا؟ يبقى من هذا الكلام بس تنتج أن الـ R
+
+150
+00:15:10,250 --> 00:15:19,810
+270 K هي عبارة عن الـ R 90 K بالشكل
+
+151
+00:15:19,810 --> 00:15:25,070
+اللي عندنا تمام يبقى هذول مش أربعة هذول بس اثنتين
+
+152
+00:15:25,070 --> 00:15:29,950
+left cosets لأن واحدة بتساوي الثانية طيب بدأت آخذ
+
+153
+00:15:29,950 --> 00:15:36,450
+الآن اللي هو الـ H في K أشوف إيش بدها تعطينا الـ H
+
+154
+00:15:36,450 --> 00:15:44,630
+في R node بالـ H وهذه H في R 180 هذه بدها
+
+155
+00:15:44,630 --> 00:15:47,730
+تساوي H وهذه نجي نشوف
+
+156
+00:15:51,960 --> 00:15:58,420
+HVR180 افتح الكتاب صفحة 1 و 31 واحد و
+
+157
+00:15:58,420 --> 00:16:03,500
+30 على الـ table الـ table بتاعة الـ product ما
+
+158
+00:16:03,500 --> 00:16:10,550
+بين اللي هو عناصر الـ D4 مع بعضها البعض يبقى احنا
+
+159
+00:16:10,550 --> 00:16:15,850
+بدنا H في R 180 يبقى عندنا H في R 180 و
+
+160
+00:16:15,850 --> 00:16:20,410
+تمانين وين راحت؟ H في R 180 اللي هي بـ V
+
+161
+00:16:20,410 --> 00:16:28,650
+يبقى هذا الكلام بده يساوي H و V طب خليني آخذ VK
+
+162
+00:16:28,650 --> 00:16:33,910
+وأشوف إيش بدها تساوي يبقى الـ VK الشكل اللي عندنا
+
+163
+00:16:33,910 --> 00:16:40,670
+هذا بدها تساوي الـ V والـ V في من في الـ R 180 و
+
+164
+00:16:40,670 --> 00:16:45,970
+تمانين هذا الكلام بده يعطينا V ونجي الـ V في الـ R
+
+165
+00:16:45,970 --> 00:16:55,370
+180 الـ V في الـ R 180 بتعطينا H يبقى ناتج هو H إيش
+
+166
+00:16:55,370 --> 00:17:01,130
+بتلاحظوا على الاثنين هذول اثنين متساويين يبقى هذا
+
+167
+00:17:01,130 --> 00:17:09,360
+بده يعطينا أن الـ HK بده يساوي الـ VK بنفس الطريقة
+
+168
+00:17:09,360 --> 00:17:19,080
+اعملها similarly بدي يكون الـ D K هتلاقي هو الـ D' K
+
+169
+00:17:19,080 --> 00:17:28,020
+كذلك تمام؟ بناء عليه بقدر أقول له the left corsets
+
+170
+00:17:28,020 --> 00:17:36,360
+of the left corsets of
+
+171
+00:17:38,820 --> 00:17:49,140
+the left cosets of اللي هو K and D for R الأولى
+
+172
+00:17:49,140 --> 00:17:56,760
+الـ K itself والثانية اللي هو الـ R 90 في K
+
+173
+00:17:56,760 --> 00:18:05,600
+والثالثة لـ HK والرابعة اللي هو DK يبقى هذا left
+
+174
+00:18:05,600 --> 00:18:10,680
+cursive فقط لا غير اطلع على الملاحظات اللي عندك
+
+175
+00:18:10,680 --> 00:18:17,920
+هنا تجدها منطبقة تماما هيتنتين متساويتين رغم أن الـ
+
+176
+00:18:17,920 --> 00:18:22,510
+element هذا مش هو الـ element الـ H بيختلف عن V هنا
+
+177
+00:18:22,510 --> 00:18:26,830
+برضه الـ D K بده يسوي D' رغم أن الـ D تختلف عادة
+
+178
+00:18:26,830 --> 00:18:33,030
+عن D' وهكذا يعني الـ two left cosets are equal رغم
+
+179
+00:18:33,030 --> 00:18:35,670
+أن الـ element اللي مضروب فيه H يختلف عن الـ
+
+180
+00:18:35,670 --> 00:18:39,710
+element الثاني اللي مضروب فيه H الحالة الثانية
+
+181
+00:18:39,710 --> 00:18:44,550
+لو أخذنا الـ K اللي عندنا وضربناها في عنصر من
+
+182
+00:18:44,550 --> 00:18:50,790
+عناصر K تبقى K كما هي وهذه الملاحظة اللي عندنا طيب
+
+183
+00:18:50,790 --> 00:18:55,470
+السؤال هو هل الـ right corset ممكن تساوي الـ left
+
+184
+00:18:55,470 --> 00:19:02,070
+corset؟ بتساوي يعني؟ تعال نجرب قد يحدث بس in 
+
+185
+00:19:02,070 --> 00:19:07,310
+general مش صحيح في هذول أول اثنتين صحيح بمظبوط
+
+186
+00:19:07,310 --> 00:19:10,850
+الكلام ليش؟ لأنه من نفس الـ group أو من نفس الـ
+
+187
+00:19:10,850 --> 00:19:14,450
+subgroup بس بدي أجيب element من برا وبين أنه هذا
+
+188
+00:19:14,450 --> 00:19:20,190
+الكلام مش صحيح فمثلا احنا أخذنا وين R 90 في K
+
+189
+00:19:20,190 --> 00:19:27,630
+هذه R 90 في K وأخذنا HK وغيره إلى آخرين طب
+
+190
+00:19:27,630 --> 00:19:33,030
+بدي أجرب K في H أشوف إيش بتعطيني هنا now
+
+191
+00:19:34,850 --> 00:19:41,830
+بدأ آخذ اللي هو K في H يبقى هذا الكلام بده يساوي
+
+192
+00:19:41,830 --> 00:19:54,310
+اللي هو الـ K في H بده يساوي H وهنا R 180
+
+193
+00:19:54,310 --> 00:20:00,800
+في من في H نجي نشوف إيش بده يساوي هذا الكلام بده
+
+194
+00:20:00,800 --> 00:20:07,520
+يساوي H والـ R 180 في H الـ R 180
+
+195
+00:20:07,520 --> 00:20:16,840
+في H في H بطلع كده؟ بطلع V بطلع V طيب طلعت هذه هي
+
+196
+00:20:16,840 --> 00:20:24,540
+بالضبط هذه V و H حد بقدر يقول لي ليش؟ أيوة 100 100
+
+197
+00:20:24,540 --> 00:20:29,960
+المي R 180 في الـ center وبالتالي هذا طلع
+
+198
+00:20:29,960 --> 00:20:34,840
+متساويين لكن لو برا الـ center بصير كلام هذا معلوم
+
+199
+00:20:34,840 --> 00:20:39,020
+ليس صحيحا يبقى in general هذا الكلام ليس صحيحا
+
+200
+00:20:39,020 --> 00:20:43,840
+الممكن آخذ من هنا هذا ما فيش فيها الـ center هذه S3
+
+201
+00:20:43,840 --> 00:20:47,380
+ما فيش فيها إلا الـ identity element تعال نأخذ من
+
+202
+00:20:47,380 --> 00:20:54,770
+هنا هي الصارة عندك هذا يعني أن الـ K في H بده يساوي
+
+203
+00:20:54,770 --> 00:20:56,230
+الـ H في K
+
+204
+00:20:59,010 --> 00:21:08,290
+ولكن لو جئت من المثال الأول أخذت واحد اثنين
+
+205
+00:21:08,290 --> 00:21:15,610
+هذا مضروب في H إن H قداش طلع واحد اثنين في H
+
+206
+00:21:15,610 --> 00:21:21,390
+طلع واحد ثلاثة اثنين H طلع واحد ثلاثة اثنين في
+
+207
+00:21:21,390 --> 00:21:28,700
+H and بدي آخذ H في main في واحد اثنين يبقى H في
+
+208
+00:21:28,700 --> 00:21:34,440
+الـ permutation واحد اثنين بدي يعطينا واحد اثنين
+
+209
+00:21:34,440 --> 00:21:40,760
+والآن اللي هو الـ H قلنا هناك بقداش بواحد ثلاثة
+
+210
+00:21:40,760 --> 00:21:48,220
+يبقى واحد ثلاثة في واحد اثنين لأن الضرب من وين؟ من
+
+211
+00:21:48,220 --> 00:21:54,510
+جهة اليمين يبقى هذا الكلام بده يعطينا واحد اثنين و
+
+212
+00:21:54,510 --> 00:21:59,630
+هذا بده يعطينا الواحد صورته اثنين واثنين صورته
+
+213
+00:21:59,630 --> 00:22:05,050
+اثنين الآن اثنين صورته الواحد والواحد صورته ثلاثة
+
+214
+00:22:05,050 --> 00:22:11,680
+الثلاثة صورتها ثلاثة والثلاثة واحد قفلت هديها اللي
+
+215
+00:22:11,680 --> 00:22:18,860
+هو واحد اثنين ثلاثة في H اطلع شوف لي واحد اثنين في
+
+216
+00:22:18,860 --> 00:22:25,200
+H هل هي H في واحد اثنين طب لا هذه واحد ثلاثة اثنين
+
+217
+00:22:25,200 --> 00:22:30,000
+هذه واحد اثنين ثلاثة يبقى بيساويش بعض يبقى بأجي
+
+218
+00:22:30,000 --> 00:22:37,600
+بقول له هنا 1 2 في H does not equal للـ H
+
+219
+00:22:37,600 --> 00:22:43,660
+في 1 2 يبقى in general الـ left cosets
+
+220
+00:22:43,660 --> 00:22:48,960
+والـ right cosets are not equal يعني قد يحدث تساوي
+
+221
+00:22:48,960 --> 00:22:54,540
+وقد لا يحدث سبب التساوي في النقطة الأولى اللي
+
+222
+00:22:54,540 --> 00:23:00,600
+أخذناها من D4 أن الـ R180 كانت في الـ center
+
+223
+00:23:00,600 --> 00:23:05,640
+وبالتالي حصل التساوي النقطة الثانية ليست في الـ
+
+224
+00:23:05,640 --> 00:23:11,600
+center وبالتالي لم يحدث تساوينعطي كمان مثال ثلاثة
+
+225
+00:23:11,600 --> 00:23:23,820
+example ثلاثة بيقول خد لي G هو هي Z 9 تمام and
+
+226
+00:23:23,820 --> 00:23:31,230
+الـ H هي الـ sub group generated by ثلاثة هات لي الـ left
+
+227
+00:23:31,230 --> 00:23:44,070
+cosets find the left cosets of H and the تسعة
+
+228
+00:23:47,960 --> 00:23:52,880
+خلي بالك كده بدنا نجيب الـ left cosets اللي عندنا
+
+229
+00:23:52,880 --> 00:24:00,180
+طبعا G معروفة Z 9 هي عبارة عن 0 و1 و
+
+230
+00:24:00,180 --> 00:24:05,900
+2 لغاية 8 تمام الآن الـ H الـ sub group
+
+231
+00:24:05,900 --> 00:24:11,560
+generated by 3 هي 0 و3 و6 و9 اللي
+
+232
+00:24:11,560 --> 00:24:16,480
+هي 0 وهكذا بدنا نروح نجيب الـ left cosets الـ
+
+233
+00:24:16,480 --> 00:24:21,300
+operation على Z 9 جامع ولا ضاربة جامع ممدر جدا
+
+234
+00:24:21,610 --> 00:24:29,110
+يبقى أنا بدي أبدأ بالعنصر الأول 0 زائد H يعني
+
+235
+00:24:29,110 --> 00:24:35,050
+اللي هو 0 زائد الـ sub group generated by 3
+
+236
+00:24:35,050 --> 00:24:41,230
+من عناصرها هيهم بدي أضيف 0 لكل عنصر من هذه
+
+237
+00:24:41,230 --> 00:24:47,820
+العناصر بتغير شيء يقول تطلع H itself يبقى هذا بده
+
+238
+00:24:47,820 --> 00:24:53,780
+يعطينا H itself ليش؟ لأن الـ 0 موجود في H طيب لو
+
+239
+00:24:53,780 --> 00:25:00,840
+رحت قلت لك أليس هذا هو 3 زائد H؟ نفسه ولا لا؟
+
+240
+00:25:00,840 --> 00:25:05,460
+لأن 3 تضيف فلك كل عنصر 3 زائد 0 بـ 3
+
+241
+00:25:05,460 --> 00:25:09,700
+3 زائد 3 بـ 6 3 زائد 9 بـ 0 يبقى
+
+242
+00:25:09,700 --> 00:25:16,200
+0, 6, 3، تمام؟ طيب، أليست هذه هي 6 زائد
+
+243
+00:25:16,200 --> 00:25:23,570
+H كذلك؟ يبقى هاي 3، هاي واحدة وهي اثنتين وهي
+
+244
+00:25:23,570 --> 00:25:28,950
+3 وهي الأصلية كلهم بيساوي بعض مرة واحدة طب لو
+
+245
+00:25:28,950 --> 00:25:36,000
+جئت 1 زائد H يبقى هذا الكلام بده يساوي 1 زائد
+
+246
+00:25:36,000 --> 00:25:40,840
+0 بـ 1، 1 زائد 3 بـ 4، 1 زائد 6
+
+247
+00:25:40,840 --> 00:25:47,960
+بـ 7 السؤال هو شوف ليه، احنا أخذنا هنا، هل شوف
+
+248
+00:25:47,960 --> 00:25:53,910
+ليه هل هو 4 زائد each ولا لأ، تعال نشوف 4
+
+249
+00:25:53,910 --> 00:25:58,770
+زائد 0 بـ 4 هيها 4 زائد 3 بـ 7 هيها
+
+250
+00:25:58,770 --> 00:26:04,450
+4 زائد 6 بـ 10 في زي التسعة بـ 1 هيها تمام 
+
+251
+00:26:04,450 --> 00:26:13,270
+طيب شوف ليه هل هذا بالضبط سبعة زائد H نفس الفكرة طب
+
+252
+00:26:13,270 --> 00:26:19,510
+لو روحت لان للي اتنين زائد H يبقى هذا الكلام بده
+
+253
+00:26:19,510 --> 00:26:24,110
+يسويه بده آجي هنا و أضيف لكل واحد اتنين يبقى هذه
+
+254
+00:26:24,110 --> 00:26:32,190
+بصير اتنين و هنا خمسة و هنا ثمانية طب شوف لبالله
+
+255
+00:26:32,190 --> 00:26:40,250
+هذه هل هي خمسة زائد H أم لا و شوف هل هي ثمانية زائد 
+
+256
+00:26:40,250 --> 00:26:47,730
+H أم لا هي نفسها يبقى ما عنديش إلا رغم هذه تسع
+
+257
+00:26:47,730 --> 00:26:52,310
+عناصر لكن رغم ذلك ما عنديش إلا ثلاثة left cosets
+
+258
+00:26:52,310 --> 00:27:02,300
+يبقى بجي بقوله so the left cosets are اللي هو مين
+
+259
+00:27:02,300 --> 00:27:08,760
+الـ H نفسه Zero زائد H الـ H نفسه و الـ واحد زائد H و
+
+260
+00:27:08,760 --> 00:27:16,780
+اتنين زائد H فقط لا غير لا يوجد غيرها طيب
+
+261
+00:27:16,780 --> 00:27:23,540
+الآن لاحظ هذه و هذه و هذه و هذه كلهم دول are
+
+262
+00:27:23,540 --> 00:27:27,360
+equal ليش؟ لأن الـ element اللي هنا ده أخذناه من
+
+263
+00:27:27,360 --> 00:27:32,440
+داخل الـ H لما انطلعنا برا الـ H لجيت واحد زائد تش
+
+264
+00:27:32,440 --> 00:27:36,600
+يساوي أربعة زائد تش رغم أن الواحد لا تساوي أربعة في
+
+265
+00:27:36,600 --> 00:27:41,640
+زي التسعة و لجينا هذا الكلام يساوي سبعة زائد تش رغم
+
+266
+00:27:41,640 --> 00:27:46,480
+أن السبعة لا تساوي أربعة لا تساوي واحد وهكذا بالنسبة
+
+267
+00:27:46,480 --> 00:27:51,070
+للآخر هذا يتفق مع الكلام اللي قلناه قبل قليل أن ال
+
+268
+00:27:51,070 --> 00:27:56,970
+A H لو كانت تساوي B H ليس بالضرورة أن A تساوي B
+
+269
+00:27:56,970 --> 00:28:02,430
+يعني قد يكون و قد لا يكون in general حد عنده أي
+
+270
+00:28:02,430 --> 00:28:03,810
+سؤال هنا شباب؟
+
+271
+00:28:19,180 --> 00:28:23,240
+حاجة بقول بدي أحب أسألها سؤال؟ طيب احنا من حاب
+
+272
+00:28:23,240 --> 00:28:28,600
+نسألها الحين السؤال اللي بدنا نعطيك لمّة ونروح
+
+273
+00:28:28,600 --> 00:28:35,240
+نبرهن عناصرها و حنسأل واحنا بنبرهن إن شاء الله يبقى
+
+274
+00:28:35,240 --> 00:28:40,860
+أول لمّة في هذا الـ section بتتكلم عن ما يأتي عن
+
+275
+00:28:40,860 --> 00:28:47,520
+خواص الـ cosets يبقى اللمّة اللي هي عبارة عن the
+
+276
+00:28:47,520 --> 00:28:52,940
+properties of cosets
+
+277
+00:28:54,980 --> 00:29:07,360
+ايش الخواص هذه بيقول let الـ h be a subgroup of g
+
+278
+00:29:07,360 --> 00:29:10,700
+let
+
+279
+00:29:10,700 --> 00:29:19,240
+الـ a will be موجودة في الـ group g then النقطة
+
+280
+00:29:19,240 --> 00:29:29,050
+الأولى الـ A موجود في الـ H بنفس الطريقة بقدر أقوله
+
+281
+00:29:29,050 --> 00:29:34,170
+الـ A موجودة في الـ H سواء كان هذه و الله هذه
+
+282
+00:29:34,170 --> 00:29:42,050
+سيامة النقطة الثانية الـ A H بده يساوي الـ H if
+
+283
+00:29:42,050 --> 00:29:50,600
+and only if الـ A موجود في الـ H النقطة الثالثة ال
+
+284
+00:29:50,600 --> 00:29:59,880
+A H بده يساوي B H if and only if الـ A موجودة في ال
+
+285
+00:29:59,880 --> 00:30:10,300
+B H النقطة الرابعة الـ A H بده يساوي الـ B H أو الـ A H
+
+286
+00:30:10,300 --> 00:30:20,400
+intersection BH بده يساوي الـ Φ النقطة الخامسة
+
+287
+00:30:20,400 --> 00:30:30,000
+بتقول الـ A H بده يساوي الـ B H if and only if A
+
+288
+00:30:30,000 --> 00:30:38,380
+inverse B belongs to H النقطة السادسة بتقول أن ال
+
+289
+00:30:38,380 --> 00:30:45,740
+order للـ A H بده يساوي الـ order للـ B H النقطة
+
+290
+00:30:45,740 --> 00:30:55,500
+السابعة بتقول أن الـ A H بده يساوي الـ H A if and
+
+291
+00:30:55,500 --> 00:31:02,360
+only if if and only if الـ H بده يساوي الـ A H A
+
+292
+00:31:02,360 --> 00:31:09,400
+inverse النقطة الثامنة و الأخيرة بيقول الـ A H is a
+
+293
+00:31:09,400 --> 00:31:17,050
+subgroup main G if and only ifF and only F ال A
+
+294
+00:31:17,050 --> 00:31:22,350
+موجودة في H Approved
+
+295
+00:31:39,310 --> 00:31:43,790
+خلّي بالك معانا كويس هنا الآن أنا عندي H subgroup
+
+296
+00:31:43,790 --> 00:31:49,370
+من G أخدت عنصرين موجودات فيه G النقطة الأولى بتقول
+
+297
+00:31:49,370 --> 00:31:53,190
+الـ A موجود في الـ H طبعا احنا قرناها في التعريف لكم
+
+298
+00:31:53,190 --> 00:31:59,470
+النتبه رياضيا الـ A H بده يساوي الـ H إذا كان الـ A
+
+299
+00:31:59,470 --> 00:32:03,530
+موجود في H يعني لو ضربت الـ subgroup في element
+
+300
+00:32:03,530 --> 00:32:07,550
+منها بيطلع نفس الـ H و شوفنا تو في الثلاثة أمثلة نفس
+
+301
+00:32:07,550 --> 00:32:12,790
+الكلام بس احنا بنثبت نظرية للجميع النقطة الثالثة A
+
+302
+00:32:12,790 --> 00:32:17,670
+H بدي تساوي BH إذا كان الـ A موجود و أن في الـ BH
+
+303
+00:32:17,670 --> 00:32:23,430
+الرابعة any two left cosets يا إما اتنين بتسووا
+
+304
+00:32:23,430 --> 00:32:27,490
+بالكامل يا إما الـ intersection تبعهم بدي تساوي Φ
+
+305
+00:32:27,490 --> 00:32:32,570
+طلع في نهاية كل مثال قولنا يبقى left cosets كذا
+
+306
+00:32:32,570 --> 00:32:37,710
+طلع فش ولا عنصر مشترك ما بين التلاتة في المثال الأول
+
+307
+00:32:48,150 --> 00:32:54,550
+تساوى لو حدث يبقى a inverse b موجود في h عدد
+
+308
+00:32:54,550 --> 00:32:59,050
+العناصر في كل left coset يساوي عدد العناصر في left
+
+309
+00:32:59,050 --> 00:33:04,280
+coset a الثانية بالضبط تماما هذا الـ A H بده يساوي
+
+310
+00:33:04,280 --> 00:33:08,280
+H A إذا كان الـ H بده يساوي يعني الـ right coset
+
+311
+00:33:08,280 --> 00:33:12,600
+تساوي الـ left coset إذا كان الـ H قدرت أكتبها على
+
+312
+00:33:12,600 --> 00:33:18,180
+صيغة A H A inverse الأمر الأخير أنه الـ A H
+
+313
+00:33:18,180 --> 00:33:23,180
+subgroup من G إذا كان الـ A موجود في H يعني الـ left
+
+314
+00:33:23,180 --> 00:33:28,040
+cosets اللي حسبناهم قبل قليل بعضهم subgroup و بعضهم
+
+315
+00:33:28,040 --> 00:33:32,550
+لا أو subgroup وقتاش لما كان الـ element اللي بنضرب
+
+316
+00:33:32,550 --> 00:33:35,970
+فيه جاي من نفس الـ subgroup لإنه بطلع لنفس ال
+
+317
+00:33:35,970 --> 00:33:40,830
+subgroup لكن لما نيجي من برا ما هو subgroup يطلع
+
+318
+00:33:40,830 --> 00:33:45,610
+مثلا للواحد اتنين في الـ H في أول مثالإذا أعطاني
+
+319
+00:33:45,610 --> 00:33:49,930
+two elements فش فيهم الـ identity element إذا هذه
+
+320
+00:33:49,930 --> 00:33:55,370
+ليست subgroup يبقى أنا بقول coset وليست subgroup
+
+321
+00:33:55,370 --> 00:33:59,630
+إذا الـ coset in general ليست بالضرورة تكون
+
+322
+00:33:59,630 --> 00:34:03,450
+subgroup تكون subgroup لو كان الـ element من نفس ال
+
+323
+00:34:03,450 --> 00:34:08,900
+subgroup itself نجي للنقطة الأولى بيقول يثبت أن ال
+
+324
+00:34:08,900 --> 00:34:13,780
+a موجودة في الـ a h باجي بقوله الـ a اللي عندنا هذه
+
+325
+00:34:13,780 --> 00:34:19,760
+مش بقدر اكتبها الـ a في الـ identity element صح ولا
+
+326
+00:34:19,760 --> 00:34:24,720
+لا طيب الـ identity element هذا المنظر فيه أليس
+
+327
+00:34:24,720 --> 00:34:32,180
+موجود في الـ a h لأن أي subgroup تحتوي على الـ
+
+328
+00:34:32,180 --> 00:34:36,640
+Identity Element. إذاً الـ E هذه موجود في H و A هي
+
+329
+00:34:36,640 --> 00:34:42,600
+A نفسها. بناءً عليه الـ A صارت موجودة في الـ H وهو
+
+330
+00:34:42,600 --> 00:34:48,700
+المطلوب يبقى الـ A belongs to H. و بالفعل احنا لما
+
+331
+00:34:48,700 --> 00:34:52,800
+أخدنا الـ subgroup تاو قبل شوية و ضربنا الـ element
+
+332
+00:34:52,800 --> 00:34:57,960
+في الـ identity طالع من نفس الـ element موجود فيها
+
+333
+00:34:57,960 --> 00:35:02,680
+طيب هذا النقطة الأولى بسيطة نيجي للنقطة الثانية
+
+334
+00:35:03,090 --> 00:35:06,970
+النقطة الثانية بيقول الـ A H بده يساوي الـ H if and
+
+335
+00:35:06,970 --> 00:35:12,210
+only if الـ A belongs to H بنقوله كويس يبقى البرهان
+
+336
+00:35:12,210 --> 00:35:16,890
+بده يصير في اتجاهين لإنه if and only if يبقى
+
+337
+00:35:16,890 --> 00:35:22,210
+الاتجاه الأول بداجي أقوله assume الـ A H بده يساوي
+
+338
+00:35:22,210 --> 00:35:28,820
+الـ H itself ايش بدي أثباته؟ الـ A موجود في الـ H
+
+339
+00:35:28,820 --> 00:35:37,900
+الـ A لو جت من النقطة الأولى from one الـ A موجود
+
+340
+00:35:37,900 --> 00:35:44,680
+في مين؟ في الـ H طيب و الـ H ايش تساوي؟ يبقى الـ A
+
+341
+00:35:44,680 --> 00:35:49,140
+موجودة في الـ H يبقى هذا بدي يعطيني أن الـ A
+
+342
+00:35:49,140 --> 00:35:59,040
+موجودة في الـ H ليش since H أو الـ H بدها تساوي H
+
+343
+00:35:59,040 --> 00:36:03,540
+بدها موجود هنا إذا موجود هنا هذا الاتجاه الأول نجي
+
+344
+00:36:03,540 --> 00:36:11,560
+لاتجاه الثاني conversely assume
+
+345
+00:36:11,560 --> 00:36:21,640
+افترض أن ال a موجود في ال H ماذا نريد أن نثبت؟ نريد
+
+346
+00:36:21,640 --> 00:36:27,920
+أن نثبت أن الـ H هي subgroup من الـ H تساوي H
+
+347
+00:36:27,920 --> 00:36:31,780
+itself طبعا في المبادئ الرياضية دخلنا لما بدأ أثبت
+
+348
+00:36:31,780 --> 00:36:35,520
+أن two sets are equal بأخد element هنا بأثبته في
+
+349
+00:36:35,520 --> 00:36:38,400
+التاني بيصير الأولى أعصاب ساتمة التانية هو العملية
+
+350
+00:36:38,400 --> 00:36:42,220
+العكسية بنفس الطريقة بدأ أثبت أنه التانية أعصاب
+
+351
+00:36:42,220 --> 00:36:47,660
+ساتمة الأولى بيحدث تساوي يبقى الخطوة الأولى بدأ
+
+352
+00:36:47,660 --> 00:36:54,300
+أحاول أثبت أنه الـ A H subset من من؟ subset من ال H
+
+353
+00:36:54,300 --> 00:37:05,710
+طيب الـ N from one الـ A موجودة في الـ A H مظبوط؟ و أنا
+
+354
+00:37:05,710 --> 00:37:10,790
+عند ايش؟ و أنا عند الـ A H أنا فرضها بتساوي 100 .. لا
+
+355
+00:37:10,790 --> 00:37:12,310
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+356
+00:37:12,310 --> 00:37:12,590
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+357
+00:37:12,590 --> 00:37:14,650
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+358
+00:37:14,650 --> 00:37:15,290
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+359
+00:37:15,290 --> 00:37:15,490
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+360
+00:37:15,490 --> 00:37:15,590
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+361
+00:37:15,590 --> 00:37:21,630
+لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا
+
+362
+00:37:21,630 --> 00:37:21,690
+.. لا .. لا .. لا .. لا .. لا .. لا .. لا .. لا ..
+
+363
+00:37:21,690 --> 00:37:31,710
+لا .. لا .. الآن الـ a كذلك from واحد موجودة في مين؟
+
+364
+00:37:31,710 --> 00:37:37,730
+في الـ a H و الـ a موجودة في H يبقى معنا هذا الكلام
+
+365
+00:37:37,730 --> 00:37:46,670
+أن الـ a H subset من مين؟ subset من الـ H يبقى أنا عندي A
+
+366
+00:37:46,670 --> 00:37:52,370
+موجودة في الـ H من الواحد و من الفرض تبعي A موجودة
+
+367
+00:37:52,370 --> 00:37:57,870
+في H إذا الـ A H subset من من؟ subset من الـ H هذا
+
+368
+00:37:57,870 --> 00:38:03,310
+الاتجاه السهل الاتجاه الصعب الثاني يبقى هنا on the
+
+369
+00:38:03,310 --> 00:38:08,830
+other hand on the other hand
+
+370
+00:38:13,180 --> 00:38:19,160
+الآن لما أقول يا شباب أن الـ a موجودة في H هذا معطى
+
+371
+00:38:19,160 --> 00:38:24,540
+طب H sub group ولا لا يبقى معكوس الـ element هذا
+
+372
+00:38:24,540 --> 00:38:30,060
+موجود صح ولا لا يبقى then
+
+373
+00:38:31,810 --> 00:38:38,330
+اللي هو الـ A inverse موجود في H طيب بدأ آجي أقوله
+
+374
+00:38:38,330 --> 00:38:44,710
+خدلي X موجود في H أنا بدي أثبت إن H subset من مين؟
+
+375
+00:38:44,710 --> 00:38:50,670
+من الـ H يبقى خت element موجود في وين؟ في الـ H 
+
+376
+00:38:50,670 --> 00:38:51,650
+then
+
+377
+00:38:54,840 --> 00:39:00,800
+then هلحين هذا موجود في H و هذا موجود في H إذا حصل
+
+378
+00:39:00,800 --> 00:39:08,760
+ضربهم موجود في H يبقى then A inverse X موجود وين؟
+
+379
+00:39:08,760 --> 00:39:18,000
+موجود في H هذا معناه إن ال A inverse X بده يساوي H
+
+380
+00:39:18,000 --> 00:39:29,930
+for some h اللي موجودة في H مادام هذا في H
+
+381
+00:39:29,930 --> 00:39:36,170
+إذا هيساوي الـ h طيب هذا معناه أنا بدي الـ x يبقى
+
+382
+00:39:36,170 --> 00:39:42,190
+هذا معناه أن الـ x تساوي لو ضربت الطرفين في العنصر
+
+383
+00:39:42,190 --> 00:39:48,630
+A يبقى بضل على شمال x وهنا بجينا mean a h هذه h
+
+384
+00:39:48,630 --> 00:39:55,960
+وين موجودة؟ موجودة في الـ H يبقى أنا فرضت x في H لجيت
+
+385
+00:39:55,960 --> 00:40:02,600
+الـ x موجود وان في الـ H يبقى هذا معناه أن الـ H هذه الـ
+
+386
+00:40:02,600 --> 00:40:09,540
+subset من الـ H اطلع لي سميلي هذه star وسميلي هذه 
+
+387
+00:40:09,540 --> 00:40:13,840
+double star من التنتين مع بعض from
+
+388
+00:40:28,680 --> 00:40:33,490
+الشكل اللي عندنا هنا طيب هذه هي النقطة الثانية دير
+
+389
+00:40:33,490 --> 00:40:37,970
+بالك هتلزمنا كتير خلال البراهين بده اروح للنقطة
+
+390
+00:40:37,970 --> 00:40:44,570
+الثالثة النقطة الثالثة بيقول الـ a H الـ a الـ a H
+
+391
+00:40:44,570 --> 00:40:50,510
+بده يساوي الـ b H f عنده اللي f الـ a موجودة في b
+
+392
+00:40:50,510 --> 00:40:57,670
+H يبقى بداجي اقوله assume افترض أن الـ a H بده
+
+393
+00:40:57,670 --> 00:41:03,560
+يساوي b H بدي احاول اثبت أن الـ a موجودة في الـ b
+
+394
+00:41:03,560 --> 00:41:10,520
+H الان يا شباب from واحد الـ a موجودة في الـ H
+
+395
+00:41:10,520 --> 00:41:17,260
+صح؟ و اللي عند الـ a H بدي يساوي الـ b H يبقى
+
+396
+00:41:17,260 --> 00:41:22,040
+هذا معناه أن الـ a موجودة في الـ b H و هو المطلوب
+
+397
+00:41:23,190 --> 00:41:29,710
+مظبوط؟ طيب الاتجاه الثاني يبقى هنا أخدنا الاتجابات
+
+398
+00:41:29,710 --> 00:41:36,130
+دي اجي اقوله هنا و الرقاهي رقم تلاتة conversely
+
+399
+00:41:39,490 --> 00:41:48,910
+conversely assume افترض أن الـ a موجودة في الـ b H
+
+400
+00:41:48,910 --> 00:41:55,430
+بده احاول اثبت أن الـ a H بده يساوي مين بيه الـ a H
+
+401
+00:41:55,430 --> 00:42:05,210
+موجودة في B capital H تمام طيب assume كذا then الـ a
+
+402
+00:42:05,210 --> 00:42:13,490
+هذه بدها تساوي b H for some h اللي belongs to H
+
+403
+00:42:13,490 --> 00:42:21,250
+للـ H طب لو ضربت الطرفين في H يبقى باجي بقوله هذا
+
+404
+00:42:21,250 --> 00:42:29,790
+معناه أن الـ a capital H بده يساوي b H capital H هذا
+
+405
+00:42:29,790 --> 00:42:37,130
+معناه أن الـ a H بده يساوي b H في H من خاصية الـ
+
+406
+00:42:37,130 --> 00:42:44,700
+associativity هذا معناه أن الـ a H بده يساوي b الـ
+
+407
+00:42:44,700 --> 00:42:49,700
+element h لما يكون في H و تضربه في H بتظهر زي مهي
+
+408
+00:42:49,700 --> 00:42:55,300
+H كابتن يبقى هدف بيه H عزيزي و هو المطلوب خلصنا
+
+409
+00:42:55,300 --> 00:43:00,820
+الاتجاهين طيب الان بدنا نجي لنقطة رابعا النقطة
+
+410
+00:43:00,820 --> 00:43:05,540
+الرابعة بيقول يا إما الـ two left cosets بدوا
+
+411
+00:43:05,540 --> 00:43:09,560
+يتساووا يا إما الـ intersection تبعهم بدوا يساوي
+
+412
+00:43:09,560 --> 00:43:15,480
+الـ phi إذا لو نفيت واحدة منهم بدي أثبت إيه تانية
+
+413
+00:43:15,480 --> 00:43:22,040
+يبقى بالداجة أقوله assume افترض أن الـ a H
+
+414
+00:43:22,040 --> 00:43:30,160
+intersection ب a H لا يساوي الـ phi لا يساوي الـ phi
+
+415
+00:43:30,160 --> 00:43:36,080
+معناته في عناصر مشتركة ما بين الاتنين يبقى هنا
+
+416
+00:43:36,080 --> 00:43:41,540
+بداية اقوله افترض أن الـ X موجود في الـ A H
+
+417
+00:43:41,540 --> 00:43:47,660
+intersection B H معناه هذا الكلام أن الـ X موجود في
+
+418
+00:43:47,660 --> 00:43:55,840
+الـ A H و الـ X موجود في الـ B H معنى هذا الكلام أن الـ
+
+419
+00:43:55,840 --> 00:44:07,320
+X بده يساوي A H1 مثلا and الـ X بده يساوي B H2 مش
+
+420
+00:44:07,320 --> 00:44:12,290
+هنا ميز فيه ما بينهم مش نفس الـ element طب كويس مدام
+
+421
+00:44:12,290 --> 00:44:17,710
+هذا بيساوي هذا إذا الاتنين are equal يبقى لإن
+
+422
+00:44:17,710 --> 00:44:26,170
+الطرف الشمال كله X يبقى A H1 بده يساوي الـ B H2 طيب
+
+423
+00:44:26,170 --> 00:44:33,570
+هذا لو جيت قلت A H 1 بضربته في H بديه يساوي الـ B H
+
+424
+00:44:33,570 --> 00:44:40,190
+2 كله في H من خاصية الـ associativity يبقى الـ A في
+
+425
+00:44:40,190 --> 00:44:48,330
+الـ H 1 H بديه يساوي B في الـ H 2 H يبقى هذا الكلام
+
+426
+00:44:48,330 --> 00:44:54,770
+بديه يعطينا أنه A H بديه يساوي من B H وهو المطلوب
+
+427
+00:44:55,410 --> 00:45:00,810
+يبقى هنا فيت واحدة و أثبت له main الثانية طيب بدنا
+
+428
+00:45:00,810 --> 00:45:06,610
+نيجي لرقم خمسة رقم خمسة بيقول إيه H بيبقى طيب
+
+429
+00:45:06,610 --> 00:45:13,630
+هنا الـ a H بده يساوي b H if and only if
+
+430
+00:45:16,890 --> 00:45:23,450
+ما هو رأيك لو ضربت الطرفين في a inverse يبقى عندي
+
+431
+00:45:23,450 --> 00:45:31,270
+a inverse في الـ a H بده يساوي الـ a inverse في الـ b H
+
+432
+00:45:32,250 --> 00:45:37,870
+من خاصية الـ associative طبعا هذا if and only if الـ
+
+433
+00:45:37,870 --> 00:45:47,310
+a inverse a في الـ H بده يساوي a inverse b في الـ H
+
+434
+00:45:47,310 --> 00:45:51,970
+الشكل اللي عندنا هنا طيب هذا بيعطينا مين؟ الـ
+
+435
+00:45:51,970 --> 00:45:56,630
+identity لما اضربه في H بدي يطلع مين؟ بدي يطلع الـ
+
+436
+00:45:56,630 --> 00:46:03,970
+H itself يبقى if and only if if and only if الـ H
+
+437
+00:46:03,970 --> 00:46:13,300
+هذه بدها تساوي A inverse B في الـ H فلسنا يبقى هنا
+
+438
+00:46:13,300 --> 00:46:20,880
+إيش بيقولي هذا يتساوى إذا كان لجيت الـ A inverse B
+
+439
+00:46:20,880 --> 00:46:27,240
+في H بده يساوي الـ H لو رجعت للخاصية رقم اتنين
+
+440
+00:46:27,240 --> 00:46:36,280
+يبقى if and only if قولي if and only if الـ A inverse B هذا موجود وين؟
+
+441
+00:46:36,300 --> 00:46:43,560
+موجود في الـ H وهذا من الـ property اتنين بالشكل
+
+442
+00:46:43,560 --> 00:46:53,810
+اللي عندنا هذا طيب ستة هه ستة بدك اتعرف function ما
+
+443
+00:46:53,810 --> 00:46:58,910
+بين الاتنين و الناس بينها one to one and onto يبقى
+
+444
+00:46:58,910 --> 00:47:09,010
+بداجي اقوله define a function phi من الـ a H الى الـ
+
+445
+00:47:09,010 --> 00:47:19,260
+b H by phi of a H بده يساوي b H واثبتلي انها
+
+446
+00:47:19,260 --> 00:47:23,560
+one to one and onto إذا اثبتناها one to one and
+
+447
+00:47:23,560 --> 00:47:29,640
+onto يحصلوا التساوي بصير الـ order للأولى بده يساوي
+
+448
+00:47:29,640 --> 00:47:35,800
+من الـ order للثانية بنكمل المرة الجاية إن شاء الله
+
+449
+00:47:35,800 --> 00:47:36,300
+وتعالى 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ.srt
new file mode 100644
index 0000000000000000000000000000000000000000..65eb4cb16519490b111cc66e878bf72ef61178ab
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ.srt
@@ -0,0 +1,1847 @@
+1
+00:00:21,410 --> 00:00:27,670
+نكمل نبدأ في محاضرة الصباح وصلنا إلى المثال
+
+2
+00:00:27,670 --> 00:00:33,930
+compute the automorphism من Z<sub>10</sub> إلى Z<sub>10</sub> مشان هيك روحت
+
+3
+00:00:33,930 --> 00:00:37,710
+افترض أن الـ α من Z<sub>10</sub> إلى Z<sub>10</sub> يبقى يعني
+
+4
+00:00:37,710 --> 00:00:43,290
+automorphism شو شكل الـ α الله أعلم تمام يبقى
+
+5
+00:00:43,290 --> 00:00:48,010
+احنا بنبحث قداش الـ α دي أو إيش قيمتها شو تساوي
+
+6
+00:00:48,010 --> 00:00:54,990
+ماهو نوع هذه الـ function فبجي بقول الآن لو كان الـ
+
+7
+00:00:54,990 --> 00:01:00,930
+k موجود في Z<sub>10</sub> then يعني الـ K يبدو يساوي Zero
+
+8
+00:01:00,930 --> 00:01:05,830
+يا واحد اثنين ثلاثة أربعة لغاية تسعة تمام؟ then لو
+
+9
+00:01:05,830 --> 00:01:13,010
+جيت أخدت α of K لأن α بدأت تؤثر على K اللي
+
+10
+00:01:13,010 --> 00:01:18,810
+موجودة في Z<sub>10</sub> يبقى هذا الكلام بده يساوي α
+
+11
+00:01:18,810 --> 00:01:25,790
+of واحد زائد واحد زائد واحد كم مرة هدول؟ كم واحد
+
+12
+00:01:25,790 --> 00:01:35,250
+هدول؟ K من المرات يبقى هدول K times يبقى K من
+
+13
+00:01:35,250 --> 00:01:39,490
+المرات الآن أنا جاي الـ α عبارة عن إيش
+
+14
+00:01:39,490 --> 00:01:45,210
+automorphism automorphism يعني isomorphism معناته
+
+15
+00:01:45,210 --> 00:01:51,910
+هذه هتساوي α of one زائد α of one زائد
+
+16
+00:01:51,910 --> 00:02:00,190
+زائد α of one كم مرة هدول كمان؟ K times يبقى هذا
+
+17
+00:02:00,190 --> 00:02:07,330
+الكلام بده يساوي K في α of one ضاعت مشكلتنا مع
+
+18
+00:02:07,330 --> 00:02:12,490
+α of one قائمة قداش α of one هذه بده تكون
+
+19
+00:02:12,490 --> 00:02:19,110
+الآن α of one موجودة وين؟ موجودة في Z<sub>10</sub> بده
+
+20
+00:02:19,110 --> 00:02:25,600
+أروح أدور على الـ order تبعها يبقى باجي بقوله و الـ
+
+21
+00:02:25,600 --> 00:02:34,680
+α of one موجودة في Z<sub>10</sub> طيب باجي بقول كمان
+
+22
+00:02:34,680 --> 00:02:42,820
+in Z<sub>10</sub> قداش الـ order للواحد؟ قداش الـ order
+
+23
+00:02:42,820 --> 00:02:48,760
+للواحد في Z<sub>10</sub> مين الـ operation اللي على Z<sub>10</sub>
+
+24
+00:02:49,640 --> 00:02:54,060
+الجمع الجامعة مظبوط الجامعة هي الـ operation
+
+25
+00:02:54,060 --> 00:02:58,460
+الموجودة على Z<sub>10</sub> إذا الواحد قداش الـ order له
+
+26
+00:02:58,460 --> 00:03:05,440
+الواحد لو أجمعه كام مرة بيعطيني الـ zero عشر مرات
+
+27
+00:03:05,440 --> 00:03:10,660
+يعني الـ order للواحد يساوي قداش؟ يساوي عشرة يبقى الـ
+
+28
+00:03:10,660 --> 00:03:17,060
+order للواحد يساوي عشرة هذا بده يعطينا أن الـ order
+
+29
+00:03:17,060 --> 00:03:24,120
+للـ α of واحد أخذنا في النظرية السابقة رقم خمسة
+
+30
+00:03:24,120 --> 00:03:28,900
+النظرية مش السابقة اللي قبلها اللي فيها السبع نقاط
+
+31
+00:03:28,900 --> 00:03:33,780
+النقطة رقم خمسة الـ order اللي إيه بيساوي مين الـ
+
+32
+00:03:33,780 --> 00:03:39,200
+order لـ φ of إذا كان φ isomorphism أنا أفرض أن
+
+33
+00:03:39,200 --> 00:03:44,860
+automorphism هو isomorphism من الـ group إلى نفسه هذا
+
+34
+00:03:44,860 --> 00:03:52,000
+بيعطينا أن هذا بيساوي عشرة because إن الـ order للـ
+
+35
+00:03:52,000 --> 00:03:57,940
+a بده يساوي الـ order لـ φ of A هذا previous
+
+36
+00:03:57,940 --> 00:03:58,780
+theorem
+
+37
+00:04:01,950 --> 00:04:07,450
+Theorem part 5 كان الجزء الخامس من النظرية اللي
+
+38
+00:04:07,450 --> 00:04:12,350
+فيها سبع نقاط يبقى الـ order لـ α of واحد بده
+
+39
+00:04:12,350 --> 00:04:17,410
+يساوي عشرة الآن أنا بقول الـ α واحد وين موجود
+
+40
+00:04:17,410 --> 00:04:24,090
+في Z<sub>10</sub> مين العناصر اللي في Z<sub>10</sub> اللي الـ order
+
+41
+00:04:24,090 --> 00:04:32,380
+اللي يساوي عشرة الواحد ومين كمان؟ كل رقم relatively
+
+42
+00:04:32,380 --> 00:04:36,740
+prime مع العشرة وأنت بتجري مين كمان؟ relatively
+
+43
+00:04:36,740 --> 00:04:44,040
+prime مع العشرة مين؟ مين؟ ثلاثة والسبعة والتسعة
+
+44
+00:04:44,040 --> 00:04:48,220
+يبقى هدول بس يبقى α of one هتساوي واحد من
+
+45
+00:04:48,220 --> 00:04:55,320
+الأربعة هدول فقط يبقى هذا بده يعطينا أن الـ α of
+
+46
+00:04:55,320 --> 00:05:03,720
+one equal one أو ثلاثة أو سبعة أو تسعة because
+
+47
+00:05:03,720 --> 00:05:13,220
+السبب each of واحد وثلاثة وسبعة وتسعة is of
+
+48
+00:05:13,220 --> 00:05:21,920
+order عشر كويس مادام α of one ساوت يا واحد يا
+
+49
+00:05:21,920 --> 00:05:27,660
+ثلاثة يا سبعة يا تسعة معناته كم Automorphism عندي
+
+50
+00:05:28,860 --> 00:05:36,460
+أربعة فقط لا غير ما فيش غيرهم يبقى بدي أروح أقول أن
+
+51
+00:05:36,460 --> 00:05:41,480
+الـ α هذه لو أثرت على الواحد بدي أخلي صورتها
+
+52
+00:05:41,480 --> 00:05:45,720
+واحد لأن الـ order اللي هذا بدي يساوي الـ order اللي
+
+53
+00:05:45,720 --> 00:05:51,720
+هذا أو الـ α لو أثرت على الـ واحد بدي تبقى صورتها
+
+54
+00:05:51,720 --> 00:05:58,040
+ثلاثة هتكون الـ order الاتنين كله كم؟ عشرة أو الـ
+
+55
+00:05:58,040 --> 00:06:03,280
+α of واحد ممكن يتساوي السبعة أو الـ α of
+
+56
+00:06:03,280 --> 00:06:09,340
+واحد ممكن الصورة كم؟ ممكن الصورة تسعة يبقى كم
+
+57
+00:06:09,340 --> 00:06:15,670
+Automorphism صار عندي أربعة الـ α لو أثرت على الـ
+
+58
+00:06:15,670 --> 00:06:18,770
+identity element تعطيني الـ identity element الـ
+
+59
+00:06:18,770 --> 00:06:22,290
+α لو أثرت على الـ identity element ممكن تكون
+
+60
+00:06:22,290 --> 00:06:25,950
+الصورة ثلاثة عفواً مش الـ identity لأن واحد مش الـ
+
+61
+00:06:25,950 --> 00:06:29,970
+identity في Z<sub>10</sub> الـ identity هو الـ zero الـ α
+
+62
+00:06:29,970 --> 00:06:33,750
+لما تؤثر على واحد ممكن تكون الصورة واحد الـ α
+
+63
+00:06:33,750 --> 00:06:36,350
+لما تؤثر على واحد ممكن تكون الصورة ثلاثة الـ α
+
+64
+00:06:36,350 --> 00:06:39,670
+لو أثرت على واحد ممكن تكون الصورة سبعة الـ α لو
+
+65
+00:06:39,670 --> 00:06:42,250
+أثرت على واحد ممكن تكون الصورة تسعة
+
+66
+00:06:59,950 --> 00:07:05,730
+مشان أميز في ما بينهم إيش رأيك؟ هذا بدي اسميه α
+
+67
+00:07:05,730 --> 00:07:12,530
+one وهذا بدي اسميه α<sub>3</sub> واللي بعده بدي اسميه
+
+68
+00:07:12,530 --> 00:07:19,270
+α<sub>7</sub> واللي بعده بدي اسميه α<sub>9</sub> عشان أميزهم
+
+69
+00:07:19,270 --> 00:07:28,250
+عن بعضهم هدول كلهم بدهم يشكلولي الـ Automorphism
+
+70
+00:07:28,250 --> 00:07:31,070
+لمن؟ لـ Z<sub>10</sub>
+
+71
+00:07:35,390 --> 00:07:40,590
+يبقى هدول بدهم يشكلولي الـ Automorphism لمن؟ لـ Z
+
+72
+00:07:40,590 --> 00:07:47,970
+<sub>10</sub> الآن أنا بدي أتأكد أن كل واحد من هدول هو
+
+73
+00:07:47,970 --> 00:07:53,890
+عبارة عن Automorphism تمام؟ مشان هيك بدي الـ α
+
+74
+00:07:53,890 --> 00:07:57,550
+كل واحدة فيهم الأولى أو الثانية أو الثالثة أو
+
+75
+00:07:57,550 --> 00:08:03,120
+الرابعة بديها تبقى one to one و بديها onto و بديها
+
+76
+00:08:03,120 --> 00:08:09,400
+تخدم خاصية الـ isomorphism تمام طيب أنا بدي أشيكلك
+
+77
+00:08:09,400 --> 00:08:13,560
+على واحدة أُثبتها أنها isomorphism وأنت بتسوي
+
+78
+00:08:13,560 --> 00:08:18,370
+الباقي بنفس الطريقة أول شيء هذه هي الـ identity ليش؟
+
+79
+00:08:18,370 --> 00:08:21,530
+أن الـ α of one بدي يساوي one هذه هي الـ
+
+80
+00:08:21,530 --> 00:08:25,730
+identity function هذه دائماً one to one and onto
+
+81
+00:08:25,730 --> 00:08:29,430
+و بتخدم خاصية الـ isomorphism وقد رأينا ذلك في
+
+82
+00:08:29,430 --> 00:08:33,330
+النظرية تبعت الصباح يبقى أسيبني منها هذه شغلها سهل
+
+83
+00:08:33,330 --> 00:08:38,530
+بتروح تأخذ مين؟ α<sub>3</sub> أو α<sub>7</sub> أو α<sub>9</sub> بعمل
+
+84
+00:08:38,530 --> 00:08:42,990
+واحدة منهم والاثنتين التانيات بدي يكون بنفس
+
+85
+00:08:42,990 --> 00:08:55,210
+الطريقة يبقى باجي بقول هنا now we shall show that
+
+86
+00:08:55,210 --> 00:09:12,030
+each of the above four elements is an
+
+87
+00:09:17,630 --> 00:09:26,790
+Automorphism يبقى بده أعمل check لمن؟ للـ α<sub>3</sub>
+
+88
+00:09:26,790 --> 00:09:34,470
+كويس طيب أنا في الأول لما أخذت α من Z<sub>10</sub> إلى Z<sub>10</sub>
+
+89
+00:09:34,470 --> 00:09:41,440
+أعطيتها تعريف ما تدهاش تعريف لكن بدي أروح أخذهلها الـ
+
+90
+00:09:41,440 --> 00:09:51,980
+α<sub>3</sub> of X بدي اسميها 3X مثلاً واحد
+
+91
+00:09:51,980 --> 00:09:56,340
+يقول استنى كله كيف؟ استنى قال لي تعريفه غلط بقول
+
+92
+00:09:56,340 --> 00:10:02,620
+كيف تعريفه غلط؟ بقول أنت بتضرب ضرب ثلاثة في X بقوله
+
+93
+00:10:02,620 --> 00:10:07,480
+لأ مش صحيح أنا قلت X زائد X زائد X لأن الـ
+
+94
+00:10:07,480 --> 00:10:12,320
+operation على Z<sub>10</sub> هي عملية الجمع بس X زائد X زائد
+
+95
+00:10:12,320 --> 00:10:17,000
+X يعني قداش؟ ثلاثة X إذا تعريفه سليم مية المية ولا
+
+96
+00:10:17,000 --> 00:10:25,460
+يوجد فيه أي خطأ طيب الآن لما أقول α<sub>3</sub> of
+
+97
+00:10:25,460 --> 00:10:30,580
+واحد بده يساوي قداش؟ بده يساوي ثلاثة يبقى هذا معناته
+
+98
+00:10:30,750 --> 00:10:39,710
+α<sub>3</sub> of واحد بده يساوي ثلاثة سؤال التلاتة
+
+99
+00:10:39,710 --> 00:10:46,320
+generator لـ Z<sub>10</sub> ولا لا؟ يبقى الـ α<sub>3</sub> one
+
+100
+00:10:46,320 --> 00:10:51,080
+to one and onto ليش؟ إنها generator اللي بتأثر
+
+101
+00:10:51,080 --> 00:10:54,040
+بتجيب element من Z<sub>10</sub> والثاني بتجيب element
+
+102
+00:10:54,040 --> 00:10:57,980
+ثاني والثالث لما تجيب لي كل Z<sub>10</sub> صحيح ولا لا؟
+
+103
+00:10:57,980 --> 00:11:06,680
+يبقى هنا باجي بقوله since الـ ثلاثة is a generator
+
+104
+00:11:06,680 --> 00:11:11,760
+of Z<sub>10</sub>
+
+105
+00:11:16,370 --> 00:11:22,110
+الـ α<sub>3</sub> على
+
+106
+00:11:22,110 --> 00:11:29,370
+طول الخط is one to one and onto function
+
+107
+00:11:39,060 --> 00:11:44,800
+one to one and onto كلمة function بدنا نثبتها أنها
+
+108
+00:11:44,800 --> 00:11:50,060
+well defined يبقى أثبتها أنها one to one and onto
+
+109
+00:11:50,060 --> 00:11:59,760
+and onto الآن الـ α<sub>3</sub> is well defined يبقى
+
+110
+00:11:59,760 --> 00:12:05,080
+بدنا نثبت أنها معرفة الأصل اللي عملها قبل هذه
+
+111
+00:12:05,080 --> 00:12:10,010
+الخطوة لكن ما فيش مشكلة طيب what do you find؟ بدأ
+
+112
+00:12:10,010 --> 00:12:16,090
+أخذ عنصرين متساويين وأثبت أن صورتهم متساوية يبقى
+
+113
+00:12:16,090 --> 00:12:23,090
+باجي أقوله لو كان الـ X مديله 10 بده يساوي الـ Y
+
+114
+00:12:23,090 --> 00:12:29,930
+مديله 10 هذا إيش بيعطينا؟ لو ضربت فيه ثلاثة بيصير
+
+115
+00:12:29,930 --> 00:12:38,490
+ثلاثة X modulo 10 يساوي ثلاثة Y modulo 10 صحيح
+
+116
+00:12:38,490 --> 00:12:45,070
+ولا لا؟ طب أنا معرفها هنا α of X يساوي ثلاثة X
+
+117
+00:12:45,070 --> 00:12:53,950
+معناته أن الـ α<sub>3</sub> of X بيساوي α<sub>3</sub> of
+
+118
+00:12:53,950 --> 00:13:01,760
+Y تمام؟ يبقى أخذت عنصرين متساويين أثبتت أن عنصرهم
+
+119
+00:13:01,760 --> 00:13:06,820
+متساويين يبقى في هذه الحالة هي is well defined
+
+120
+00:13:06,820 --> 00:13:11,440
+يبقى well defined one to one and onto إيش ضايل
+
+121
+00:13:11,440 --> 00:13:14,860
+عليك بس الخاصية الأخيرة اللي هي خاصية الـ
+
+122
+00:13:14,860 --> 00:13:21,680
+isomorphism لذلك باجي أقوله بدأ أخذ finally بدأ
+
+123
+00:13:21,680 --> 00:13:30,800
+أخذ α<sub>3</sub> of A زائد B مثلاً A زائد B نظراً لأن
+
+124
+00:13:30,800 --> 00:13:36,140
+العملية على Z<sub>N</sub> هي عملية الجمع يبقى A زائد B
+
+125
+00:13:36,140 --> 00:13:41,600
+حسب الـ definition تبعنا يبقى ثلاثة في A زائد B 
+
+126
+00:13:41,600 --> 00:13:49,020
+يبقى ثلاثة A زائد ثلاثة B هذه عبارة عن مين؟ عبارة
+
+127
+00:13:49,020 --> 00:13:56,640
+عن Alpha 3 of A والثانية Alpha 3 of B إذا ال
+
+128
+00:13:56,640 --> 00:14:02,320
+Alpha 3 خدمت خاصية الـ isomorphism بعد هيك الـ Alpha 
+
+129
+00:14:02,320 --> 00:14:07,800
+احنا عرفناها من الـ 6 إلى نفسها يبقى بناء عليه
+
+130
+00:14:07,800 --> 00:14:14,560
+Alpha 3 is an automorphism يبقى هذا بيعطينا أن
+
+131
+00:14:14,560 --> 00:14:20,940
+Alpha 3 is an automorphism 
+
+132
+00:14:22,720 --> 00:14:31,600
+يبقى بنفس الطريقة similarly اللي هو من Alpha 7 and
+
+133
+00:14:31,600 --> 00:14:37,900
+Alpha 9 are automorphisms
+
+134
+00:14:37,900 --> 00:14:41,940
+where
+
+135
+00:14:41,940 --> 00:14:51,080
+كذلك حيث أن الـ Alpha 1 is the identity
+
+136
+00:14:52,010 --> 00:14:52,570
+element 
+
+137
+00:14:55,760 --> 00:15:03,020
+identity element يبقى الآن أثبتنا أن الـ automorphism
+
+138
+00:15:03,020 --> 00:15:06,020
+لـ Z10 بالضبط
+
+139
+00:15:25,840 --> 00:15:31,840
+يبقى هذه حسبت له مين؟ الـ automorphism لمين؟ لـ Z10
+
+140
+00:15:31,840 --> 00:15:36,680
+طلعته ما فيها إلا أربعة عناصر وكل عنصر منها دول
+
+141
+00:15:36,680 --> 00:15:43,660
+عبارة عن automorphism طيب خلينا نعطي بعض التوضيحات
+
+142
+00:15:43,660 --> 00:15:50,220
+أكثر اللي خاطر أشوف لحد هنا انتهى الشغل لكن احنا
+
+143
+00:15:50,220 --> 00:15:54,180
+بدنا بعض التوضيحات، ايش بعض التوضيحات؟ هذه
+
+144
+00:15:54,180 --> 00:16:00,580
+isomorphic لمين؟ ولو ضربت ربعت هذه، ايش بدي يكون 
+
+145
+00:16:00,580 --> 00:16:04,200
+الناتج؟ لو عملت composition ما بين الأولى
+
+146
+00:16:04,200 --> 00:16:07,140
+والثانية، شو بيكون الناتج؟ composition بين
+
+147
+00:16:07,140 --> 00:16:11,600
+الثانية، هل بتبقى closed فعلا ولا لأ؟ بس مجرد
+
+148
+00:16:11,600 --> 00:16:17,110
+معلومات كيف بدنا نشتغل العناصر هدول مع بعض يبقى
+
+149
+00:16:17,110 --> 00:16:27,230
+ممكن أقوله زيادة على ذلك it should be noted that
+
+150
+00:16:27,230 --> 00:16:38,990
+من الملاحظة أنه لو بدي Alpha 3 تربيع of 1 هذا
+
+151
+00:16:38,990 --> 00:16:42,450
+المقصود ليس تربيع وضرب وفرقة المقصود هو
+
+152
+00:16:42,450 --> 00:16:48,310
+composition بين الاتنين يعني هذه معناها Alpha تكعيب
+
+153
+00:16:48,310 --> 00:16:55,610
+لـ Alpha 3 لـ Alpha 3 of 1 حسب تعريف الـ
+
+154
+00:16:55,610 --> 00:17:00,730
+composition of function Alpha 3 لـ Alpha 3
+
+155
+00:17:00,730 --> 00:17:07,490
+of 1 هذا الكلام بده يساوي Alpha 3 Alpha 3
+
+156
+00:17:07,490 --> 00:17:13,450
+of 1 حسب التعريف Alpha 3 of X يساوي 3 في
+
+157
+00:17:13,450 --> 00:17:18,490
+X يبقى هذا ايش بده تكون 3 في 1 اللي هي
+
+158
+00:17:18,490 --> 00:17:23,590
+بـ 3 Alpha 3 of X بتصير 3 في 3 اللي
+
+159
+00:17:23,590 --> 00:17:32,360
+هي بـ مين؟ بـ 9 هذه أليست Alpha 9 of 1 يبقى
+
+160
+00:17:32,360 --> 00:17:37,200
+اللي صار عندي Alpha 3 تربيع of 1 هي Alpha 9
+
+161
+00:17:37,200 --> 00:17:41,940
+of 1 يعني موجودة وين؟ موجودة داخل الـ automorphism
+
+162
+00:17:41,940 --> 00:17:47,080
+الـ Z10 طب لو كملتها تطلع واحدة من هدول والله
+
+163
+00:17:47,080 --> 00:17:53,320
+بتيجي برا تعال نشوف لو جيت أخذت له Alpha تكعيب
+
+164
+00:17:53,320 --> 00:18:00,420
+تكعيب of 1 يعني Alpha 3 لـ Alpha تر 3
+
+165
+00:18:00,420 --> 00:18:06,860
+تربيع of 1 ويساوي Alpha 3 لبرا اللي جوا هيها
+
+166
+00:18:06,860 --> 00:18:09,940
+حسبناها قداش طلعت عنها؟ 9
+
+167
+00:18:12,470 --> 00:18:17,970
+حسب التقريب في الجدول 3 في 9 27
+
+168
+00:18:17,970 --> 00:18:23,590
+27 في الـ Z10 يعني بـ 7 يعني بـ 7 هذه
+
+169
+00:18:23,590 --> 00:18:29,770
+الـ Alpha 7 of 1 إذا هذا الـ element لما انكعكت
+
+170
+00:18:30,250 --> 00:18:35,810
+جاب للعنصر هذه يعني لازم تكون closed وهكذا طب لو
+
+171
+00:18:35,810 --> 00:18:42,750
+جبت له هنا Alpha تكعيب أس 4 of 1 أليست Alpha
+
+172
+00:18:42,750 --> 00:18:51,070
+3 في Alpha 3 تكعيب of 1 تمام هذه تساوي
+
+173
+00:18:51,070 --> 00:18:58,230
+Alpha 3 of ألفا 3 تكعيب of 1 هاي امشي امشي
+
+174
+00:18:58,230 --> 00:19:04,550
+كده ايش كانت؟ 7 يبقى هذه الـ 7 حسب التعريف يبقى
+
+175
+00:19:04,550 --> 00:19:09,010
+تصير 3 في 7 21 شيل الـ 20 بتطلع
+
+176
+00:19:09,010 --> 00:19:15,830
+من اللي هو 1 اللي هو بدها تساوي Alpha 1 of 1
+
+177
+00:19:20,890 --> 00:19:28,350
+أو Alpha 1 of 1 Alpha 1 of 1 يبقى بناء على
+
+178
+00:19:28,350 --> 00:19:34,670
+اليسار المقابل اتنين الـ identity element إذا صار
+
+179
+00:19:34,670 --> 00:19:42,010
+عندنا هذا سيعطيك أن Alpha تكعيب الـ order يساوي كم؟
+
+180
+00:19:42,010 --> 00:19:50,000
+يساوي 4 طيب الـ order إلها يساوي 4 يبقى هذه
+
+181
+00:19:50,000 --> 00:19:57,730
+ايش بتنفع؟ Generator لمين؟ لـ Atomorphism لمين؟
+
+182
+00:19:57,730 --> 00:20:00,830
+لـ Atomorphism
+
+183
+00:20:00,830 --> 00:20:05,890
+لـ Z10 يبقى هذا .. ليش؟ لأنه ما فيها إلا الأربعة عناصر
+
+184
+00:20:05,890 --> 00:20:11,450
+وكل مربع تكعيب بيطلع واحد من العنصر يبقى باستفيد من
+
+185
+00:20:11,450 --> 00:20:16,730
+هذا الكلام أن الـ Atomorphism لـ Z10 Cyclic ولا لأ؟
+
+186
+00:20:16,730 --> 00:20:24,610
+Cyclic يبقى هذا بده يعطيلك أن الـ automorphism لـ Z10
+
+187
+00:20:24,610 --> 00:20:33,450
+فيها generator اسمه Alpha 3 يبقى هذا بده يعطيلك أن
+
+188
+00:20:33,450 --> 00:20:40,010
+الـ automorphism لـ Z10 is cyclic
+
+189
+00:20:46,280 --> 00:20:53,240
+خليني أفكر قليلا، لدي أربعة عناصر، من من
+
+190
+00:20:53,240 --> 00:20:57,520
+الـ groups اللي مرت علينا واللي ممكن يكون فيها صلة
+
+191
+00:20:57,520 --> 00:21:03,620
+قرابة بينها وبين الـ group هذين، خليني أشوف U
+
+192
+00:21:03,620 --> 00:21:09,420
+10، U10 من عناصرها؟ 1 و 3 و 7 و 9،
+
+193
+00:21:09,420 --> 00:21:16,530
+تمام تمام إذا لو جيت للـ group هذي وحسبت الـ key ل
+
+194
+00:21:16,530 --> 00:21:33,490
+table لكل منها يبقى
+
+195
+00:21:33,490 --> 00:21:39,070
+ملاحظة هذي remark from
+
+196
+00:21:42,080 --> 00:21:53,900
+Cayley table for U10 and automorphism
+
+197
+00:21:53,900 --> 00:22:03,600
+لـ Z10 we have أن الـ automorphism لـ Z10
+
+198
+00:22:03,600 --> 00:22:11,710
+isomorphic لـ U10 تعال نعمل Cayley table طلع لي
+
+199
+00:22:11,710 --> 00:22:18,630
+الـ Cayley table هذا بدي آخذ U10 عنصرها 1 و 3
+
+200
+00:22:18,630 --> 00:22:24,730
+و 7 و 9 وهاي قفلنا وهنا 1 3 7
+
+201
+00:22:24,730 --> 00:22:29,550
+9 بالشكل اللي عندنا هنا وهذه التفصيل تبعها
+
+202
+00:22:29,550 --> 00:22:38,480
+كالتالي هذا الرأس هذا الشكل تعال نحسبها 1 في
+
+203
+00:22:38,480 --> 00:22:44,620
+1 بـ 1 3 7 9 الآن 3 في 1
+
+204
+00:22:44,620 --> 00:22:48,600
+بـ 3 طبعا الـ operation اللي عليه 10 هي عملية
+
+205
+00:22:48,600 --> 00:22:53,660
+الضرب عارفينه مسبقا الآن 3 في 3 بـ 9
+
+206
+00:22:53,660 --> 00:23:01,140
+3 في 7 كده ايش؟ يعني 1 3 في 9 7
+
+207
+00:23:01,140 --> 00:23:06,180
+و 20 شيل 10 بيظل 7 الآن 7 في 1
+
+208
+00:23:06,180 --> 00:23:10,840
+بـ 7 7 في 3 بـ 21 7 في 7
+
+209
+00:23:10,840 --> 00:23:17,320
+بـ 49 7 في 9 بـ 63 الآن 9
+
+210
+00:23:17,320 --> 00:23:22,640
+في 1 بـ 9 9 في 3 بـ 27 9 في
+
+211
+00:23:22,640 --> 00:23:28,660
+7 بـ 63 9 في 9 بـ 81 هذه
+
+212
+00:23:28,660 --> 00:23:35,560
+Cayley table لمين؟ لـ U10 طب خد لي Cayley table لـ
+
+213
+00:23:35,560 --> 00:23:44,660
+Atomorphism لـ Z10 اللي هي Alpha 1 و Alpha
+
+214
+00:23:44,660 --> 00:23:53,440
+3 و Alpha 7 و Alpha 9 تمام؟ وهنا هذه
+
+215
+00:23:53,440 --> 00:24:03,040
+Alpha 1 وهنا ألفا 3 وهنا ألفا 7 وهنا ألفا
+
+216
+00:24:03,040 --> 00:24:12,060
+9 شكل أنها طيب ألفا 1 في ألفا 1 بألفا 1
+
+217
+00:24:12,060 --> 00:24:18,320
+ألفا 1 في ألفا 3 بألفا 3 ألفا 1 في ألفا
+
+218
+00:24:18,320 --> 00:24:25,150
+7 بألفا 7 ألفا 9 ألفا 3 في ألفا 1 بألفا
+
+219
+00:24:25,150 --> 00:24:31,890
+3 ألفا 3 في ألفا 3 بألفا 9 ألفا 3
+
+220
+00:24:31,890 --> 00:24:38,710
+في ألفا 7 بألفا 1 ألفا 3 في ألفا 9 بألفا
+
+221
+00:24:38,710 --> 00:24:47,020
+7 الآن ألفا 7 في ألفا 1 بتديلك ألفا 7 و
+
+222
+00:24:47,020 --> 00:24:57,260
+هذه Alpha 1 وهذه Alpha 9 وهذه Alpha 3 وهذه Alpha 9
+
+223
+00:24:57,260 --> 00:25:09,540
+وهذه Alpha 7 وهذه Alpha 7 وهذه Alpha 3 وهذه Alpha
+
+224
+00:25:09,540 --> 00:25:13,440
+1 طيب
+
+225
+00:25:13,440 --> 00:25:19,930
+يعني احنا لو عمليا اشتغلنا زي الشغل اللي عندنا هذا
+
+226
+00:25:19,930 --> 00:25:25,270
+ورحنا جبنا Alpha 3 في Alpha 7 لازم يطلع عندك Alpha 1
+
+227
+00:25:25,270 --> 00:25:34,360
+Alpha نعملها شفويا ألفا 3 في ألفا 7 ألفا 7 من
+
+228
+00:25:34,360 --> 00:25:38,920
+1 اللي هي بـ 7 ألفا 3 لا 7 اللي هي بـ 1
+
+229
+00:25:38,920 --> 00:25:43,120
+و 20 بيبقى الـ 1 يبقى هي ألفا 1 وهكذا بالنسبة
+
+230
+00:25:43,120 --> 00:25:47,340
+لمين؟ بالنسبة للباقي يعني لو بدي أضرب واحدة في
+
+231
+00:25:47,340 --> 00:25:51,740
+الثانية هي نفسها يطلع على هذا الجدول وهذا الجدول تجد
+
+232
+00:25:51,740 --> 00:25:56,320
+اتنين نفس الخواص هذه فيها أربعة عناصر وهذه فيها
+
+233
+00:25:56,320 --> 00:26:00,720
+أربعة عناصر هذه Cyclic وهذه Cyclic مادام Cyclic
+
+234
+00:26:00,720 --> 00:26:03,940
+إذا أبيلن الـ order of the element هنا هي الـ order
+
+235
+00:26:03,940 --> 00:26:08,960
+of the element هنا يبقى اتنين هذول are isomorphic
+
+236
+00:26:08,960 --> 00:26:15,340
+مش عقدة اتنين هذول حروح أعّمّم هذا الكلام وبدل
+
+237
+00:26:15,340 --> 00:26:21,680
+ما هي Z10 هأقول Zn وبدل ما هي U10 هأقول U
+
+238
+00:26:21,680 --> 00:26:30,430
+n ونبرهن صحّة هذا الكلام as a theorem كنظرية آخر
+
+239
+00:26:30,430 --> 00:26:37,890
+نظرية في هذا الشابتر هي automorphism لـ Zn is
+
+240
+00:26:37,890 --> 00:26:52,150
+isomorphic للغروبي Un يا
+
+241
+00:26:52,150 --> 00:26:53,790
+أبقى بدنا نيجي لـ theorem
+
+242
+00:27:02,010 --> 00:27:09,650
+for every positive integer n for every positive
+
+243
+00:27:09,650 --> 00:27:14,970
+integer n
+
+244
+00:27:14,970 --> 00:27:26,890
+الـ automorphism لـ Zn is isomorphic لمين؟ لـ Un
+
+245
+00:27:37,760 --> 00:27:48,780
+from the previous example من المثال السابق لاحظنا
+
+246
+00:27:48,780 --> 00:27:56,280
+ما يأتي any automorphism
+
+247
+00:27:56,280 --> 00:27:58,620
+Alpha
+
+248
+00:28:02,400 --> 00:28:10,380
+is determined by 
+
+249
+00:28:10,380 --> 00:28:24,760
+the value of Alpha of 1 اللي موجودة في الـ Un
+
+250
+00:28:24,760 --> 00:28:28,220
+بدنا 
+
+251
+00:28:28,220 --> 00:28:39,330
+نروح نقول define a mapping بنعرف function T من ال
+
+252
+00:28:39,330 --> 00:28:53,070
+automorphism ل ZN إلى ال UN by كتالي T of alpha بده
+
+253
+00:28:53,070 --> 00:28:55,390
+يساوي alpha of one
+
+254
+00:28:59,500 --> 00:29:05,940
+بنثبت أن الـ T هادى is one to one and onto وكذلك
+
+255
+00:29:05,940 --> 00:29:11,640
+تخدم خاصية ال isomorphism لأن احنا مش هنثبت ال
+
+256
+00:29:11,640 --> 00:29:14,680
+isomorphism بنثبت أن ال function لأنها one to one
+
+257
+00:29:14,680 --> 00:29:19,200
+and onto وتخدم الخاصية Phi of A بيبدي يساوي ال Phi
+
+258
+00:29:19,200 --> 00:29:26,020
+of A في ال Phi of B مرة ثانية من خلال شغلنا في هذا
+
+259
+00:29:26,020 --> 00:29:32,600
+المثال لاحظنا أن قيمة Alpha تعتمد على قيمة Alpha
+
+260
+00:29:32,600 --> 00:29:39,580
+of 1 Alpha of 1 هي بتحدد شكل الـ Automorphism فروح
+
+261
+00:29:39,580 --> 00:29:43,440
+نقول من المثال السابق any automorphism alpha is
+
+262
+00:29:43,440 --> 00:29:48,420
+determined by the value of alpha of one و alpha of 
+
+263
+00:29:48,420 --> 00:29:54,960
+one لقيناها موجودة في ال U N يعني alpha of z عاشرة
+
+264
+00:29:54,960 --> 00:30:00,390
+لقيناها موجودة في ال U عاشرة يبقى Alpha of 1 موجودة
+
+265
+00:30:00,390 --> 00:30:04,230
+في الـ UN لذلك نروح نعرف Function من الـ
+
+266
+00:30:04,230 --> 00:30:09,170
+Automorphism إلى ZN للـ UN بدي أخد ال element هنا
+
+267
+00:30:09,170 --> 00:30:12,730
+ال element هنا دي نالو الرمز اللي هو Alpha بدي
+
+268
+00:30:12,730 --> 00:30:17,670
+صورته في UN الصورة هي دائما و أبدا Alpha of 1 اللي
+
+269
+00:30:17,670 --> 00:30:24,030
+موجودة في TN الآن بدي أثبت أن T is one to one لكل
+
+270
+00:30:24,030 --> 00:30:28,370
+ال elements اللي موجودة في ال Automorphism لمين إلى
+
+271
+00:30:28,370 --> 00:30:37,350
+ZN يبقى بداجي أقوله ال N T is one to one مشان هيك
+
+272
+00:30:37,350 --> 00:30:45,630
+بداجي أقوله assume أن T of Alpha بده يساوي T of Beta
+
+273
+00:30:45,630 --> 00:30:53,990
+بده أحاول أثبت أن Alpha تساوي مين تساوي Beta هذا يعني
+
+274
+00:30:53,990 --> 00:31:04,070
+T of α لـ α of one هو beta of one هذا العلاقة رقم
+
+275
+00:31:04,070 --> 00:31:10,750
+واحد لكن لو رجعت ل ZN هي فيها بس ال one ولا فيها
+
+276
+00:31:10,750 --> 00:31:16,910
+أعداد كتيرة فيها أعداد كتيرة إذا أنا بدي أروح أثبت
+
+277
+00:31:16,910 --> 00:31:21,210
+أن ال alpha تساوي ال beta على كل الأعداد الكثيرة
+
+278
+00:31:21,210 --> 00:31:31,090
+وليست على ال one فقط فباجي بقوله لو كان ال K موجود
+
+279
+00:31:31,090 --> 00:31:41,220
+في Z then ال alpha of K مش تساوي alpha ل واحد زائد
+
+280
+00:31:41,220 --> 00:31:46,900
+واحد زائد واحد يعني هذه بدها تساوي k في alpha of
+
+281
+00:31:46,900 --> 00:31:57,180
+one مظبوط طيب بدي أخد ال beta of k برضه تساوي ال k
+
+282
+00:31:57,180 --> 00:32:04,920
+في beta of one مظبوط طيب ايش رأيك من هذه beta of
+
+283
+00:32:04,920 --> 00:32:10,210
+one هي عبارة عن مين؟ Alpha of one إذا بقدر أشيل هذه
+
+284
+00:32:10,210 --> 00:32:19,570
+و أكتب كيف Alpha of one هذه from one من ال one طب
+
+285
+00:32:19,570 --> 00:32:24,810
+اطلعلي في الطرف اليمين هذا و الطرف اليمين هذا ايش
+
+286
+00:32:24,810 --> 00:32:27,610
+بنستنتج من اتنين مع بعض
+
+287
+00:32:32,490 --> 00:32:39,490
+الشيء الوحيد اللي بدي أعطانيه هو alpha of K بيساوي
+
+288
+00:32:39,490 --> 00:32:46,070
+beta of K K هذا رقم عشوائي أخدته من كل زدن و أثبت
+
+289
+00:32:46,070 --> 00:32:52,010
+قبله أن Alpha of 1 يبقى يساوي Beta of 1 يبقى
+
+290
+00:32:52,010 --> 00:32:59,510
+يساوي الـ Alpha تساوي Beta لكل الـ K الموجود في الـ
+
+291
+00:32:59,510 --> 00:33:03,630
+ZN طيب
+
+292
+00:33:03,630 --> 00:33:13,770
+بنا نيجي ناخد TS Onto مين اللي بيحكي و ايش بيقول مش
+
+293
+00:33:13,770 --> 00:33:19,910
+سامع لأ
+
+294
+00:33:19,910 --> 00:33:25,870
+كي رقم وليس اتومورفيزم ال alpha كي هو الاتومورفيزم
+
+295
+00:33:25,870 --> 00:33:26,930
+ال alpha كي هو الاتومورفيزم ال alpha كي هو
+
+296
+00:33:26,930 --> 00:33:29,910
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+297
+00:33:29,910 --> 00:33:30,990
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+298
+00:33:30,990 --> 00:33:32,070
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+299
+00:33:32,070 --> 00:33:32,090
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+300
+00:33:32,090 --> 00:33:34,630
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+301
+00:33:34,630 --> 00:33:40,990
+كي هو الاتومورفيزم ال alpha كي هو الفي ال code
+
+302
+00:33:40,990 --> 00:33:47,430
+domain و أثبت أنه له أصل في ال domain يبقى بالداجة
+
+303
+00:33:47,430 --> 00:33:58,190
+أقول له let ال R موجود في وين؟ في ال UN يبقى
+
+304
+00:33:58,190 --> 00:34:02,830
+أخدت ال R موجود في ال UN يبقى ال R هذا relatively
+
+305
+00:34:02,830 --> 00:34:10,380
+prime بالنسبة لمين؟ ل ال UN ل ال N طيب، الآن بندروح
+
+306
+00:34:10,380 --> 00:34:15,160
+نعرف function من .. اه اه define
+
+307
+00:34:17,450 --> 00:34:26,530
+Alpha من ZN إلى ZN يعني بمعنى آخر بدي أخلق
+
+308
+00:34:26,530 --> 00:34:32,550
+Automorphism علاقة بالأرض اللي عندنا هذه فقلت افترض
+
+309
+00:34:32,550 --> 00:34:42,970
+أن Alpha من ZN إلى ZM is a function defined by
+
+310
+00:34:47,820 --> 00:34:56,500
+Alpha of S مثلا ال S موجودة وين؟ هنا يبقى هذا
+
+311
+00:34:56,500 --> 00:35:08,500
+الكلام بده يساوي SR modulo N مرة
+
+312
+00:35:08,500 --> 00:35:13,820
+ثانية أنا خدت R موجودة في ال UN في ال code domain
+
+313
+00:35:13,820 --> 00:35:18,460
+هذا ال element بدي أثبت أنه له أصل هنا ايش يعني له
+
+314
+00:35:18,460 --> 00:35:23,600
+أصل هنا يعني لازم ألاقي automorphism في ال
+
+315
+00:35:23,600 --> 00:35:29,100
+automorphism أجي بحيث ال R يكون صورة لمين صورة
+
+316
+00:35:29,100 --> 00:35:35,970
+لهذه ال function يبقى بتروح أخلق أتومورفزيوم هنا له
+
+317
+00:35:35,970 --> 00:35:41,550
+علاقة بالـ R هذه فاجينا نعرف فانكشن Alpha من Z إلى
+
+318
+00:35:41,550 --> 00:35:47,090
+N Z N نعرفها بالتالي Alpha لو أثرت على ال S بتساوي
+
+319
+00:35:47,090 --> 00:35:53,830
+ال SR modulo N تمام؟ بدنا نيجي نشوف هل هذه one to
+
+320
+00:35:53,830 --> 00:35:59,950
+one؟ and onto وهل هي isomorphism إن تم ذلك يبقى هذه
+
+321
+00:35:59,950 --> 00:36:06,830
+صارت automorphism الآن بدنا نروح نثبت أن ال alpha
+
+322
+00:36:06,830 --> 00:36:13,810
+هذه is one to one كويس
+
+323
+00:36:14,530 --> 00:36:21,130
+الآن مشان هيك بتروح أخد صورتين متساويتين يبقى
+
+324
+00:36:21,130 --> 00:36:28,890
+هقوله assume افترض أن alpha طبعا هذا يا شباب لكل
+
+325
+00:36:28,890 --> 00:36:35,230
+ال S اللي موجودة في ZN مشان نقولش ال S هذي من وين
+
+326
+00:36:35,230 --> 00:36:39,980
+جبناها هذه Alpha of S يساوي S R موضوعين لكل S
+
+327
+00:36:39,980 --> 00:36:45,440
+الموجودة في ZM الآن أنا أدعي أن Alpha is one to
+
+328
+00:36:45,440 --> 00:36:50,440
+one فبدي أثبت صحة هذا الكلام فقلنا افترض أن Alpha
+
+329
+00:36:50,440 --> 00:36:59,120
+of S1 يساوي Alpha of S2 بدي أحاول أثبت أن ال S1 بدي
+
+330
+00:36:59,120 --> 00:37:09,480
+يساوي S2 هذا معناه ايش alpha of S1 يعني S1R modulo
+
+331
+00:37:09,480 --> 00:37:18,040
+N بدي يساوي S2R modulo N ايش رأيك بدي أعملها
+
+332
+00:37:18,040 --> 00:37:24,150
+معادلة صفرية جابت داجي هذا على الشجة الثانية بإشارة
+
+333
+00:37:24,150 --> 00:37:32,990
+سالب يعني بقدر أقول S1 ناقص S2 أخدت R عامل مشترك
+
+334
+00:37:32,990 --> 00:37:38,930
+موديله N بده يساوي مين؟ بده يساوي Zero يعني كأني
+
+335
+00:37:38,930 --> 00:37:43,570
+نقلت هذه على الشجة الثانية و أخدت R من الطرفين عامل
+
+336
+00:37:43,570 --> 00:37:49,970
+مشترك الآن الـR أين موجود يا شباب؟ الها معكس ولا
+
+337
+00:37:49,970 --> 00:37:57,380
+لا؟ ممتاز جدا يبقى هنا باجي بقوله since R موجودة في
+
+338
+00:37:57,380 --> 00:38:06,080
+ال UN we have أن ال R inverse موجودة في ال UN ايش
+
+339
+00:38:06,080 --> 00:38:11,200
+رأيك المعادلة هذي بدي اضربها في R inverse هذي بدي
+
+340
+00:38:11,200 --> 00:38:19,900
+أسميها مثلا star يبقى بداجي أقوله multiply multi
+
+341
+00:38:22,080 --> 00:38:32,200
+ply star by R inverse we get لو ضربنا هنا في R
+
+342
+00:38:32,200 --> 00:38:40,920
+inverse بتروح معاها S واحد ناقص S اتنين موديولو N
+
+343
+00:38:40,920 --> 00:38:47,300
+بده يساوي Zero في R inverse اللي هو من من Zero طيب
+
+344
+00:38:47,300 --> 00:38:54,780
+هذه بقدر أفكها و أحولها إلى S1 modulo N بده يساوي
+
+345
+00:38:54,780 --> 00:39:04,720
+ال S2 modulo N يبقى هذا معناه أن ال S1 هي نفس ال
+
+346
+00:39:04,720 --> 00:39:13,440
+S2 طبعا يبقى هكذا أثبت أن ال alpha is one to one بدنا
+
+347
+00:39:13,440 --> 00:39:25,640
+نثبت أن ال alpha is onto الآن
+
+348
+00:39:25,640 --> 00:39:33,480
+ال alpha is onto هو ال
+
+349
+00:39:33,480 --> 00:39:41,790
+alpha من وين لوين من ZN إلى Z و أنا أخدت هنا S
+
+350
+00:39:41,790 --> 00:39:50,450
+موجودة في ZN يبقى باجي بقوله F ال S موجودة في ZN
+
+351
+00:39:50,450 --> 00:39:53,710
+then ال S تساوي
+
+352
+00:39:56,350 --> 00:40:08,010
+عشان رأيك بقدر أكتبها هذه S مثلا في ال R inverse R
+
+353
+00:40:08,010 --> 00:40:18,410
+منفع الله ما نفعش ايه أنا السما عندي لسه ما بجمعش كويس
+
+354
+00:40:18,410 --> 00:40:22,370
+حتى اللحظة علي صوتك عشرين ايه
+
+355
+00:40:29,070 --> 00:40:36,890
+ممتاز لكن احنا بنشغل داخل مين هذا الكلام ورا in z
+
+356
+00:40:36,890 --> 00:40:42,210
+in بس يعني احنا بنشغل داخل دي اللي عناصر برا ما ليش
+
+357
+00:40:42,210 --> 00:40:46,210
+علاقة فيها يعني علاقتي مع ال zero والواحد والاتنين
+
+358
+00:40:46,210 --> 00:40:57,910
+لغاية التسعة يبقى S1 تساوي S2 داخل Z10 يبقى
+
+359
+00:40:57,910 --> 00:41:08,730
+الـ S يساوي SR inverse R طيب هذه ال S أنا ماخدها في
+
+360
+00:41:08,730 --> 00:41:17,130
+ZN يعني ال S modulo N تساوي ال S R inverse R كذلك
+
+361
+00:41:17,130 --> 00:41:24,930
+modulo N يعني هذه modulo N وهنا لو حطيت modulo N
+
+362
+00:41:24,930 --> 00:41:31,090
+مش مشكلة طيب ايش رأيك في SR inverse بدي أشيلها و
+
+363
+00:41:31,090 --> 00:41:38,350
+أكتب بدالها element 10 لو جيت كتبت بدالها S1R
+
+364
+00:41:38,350 --> 00:41:46,050
+modulo N أيوه
+
+365
+00:41:46,050 --> 00:41:51,510
+احنا بأي وسيلة رياضية بتحاول تثبت أن ال function
+
+366
+00:41:51,510 --> 00:41:57,070
+اللي عندك is onto تمام؟ بدك تشتغل شغل صحيح ما حدش
+
+367
+00:41:57,070 --> 00:42:02,370
+يقدر يمسك عليك فيه غلطة أيوة علي
+
+368
+00:42:02,370 --> 00:42:09,490
+صوتك مش هنسمع تعال شوف هنا شوف ايش بتقول بالظبط
+
+369
+00:42:09,490 --> 00:42:17,710
+اسمع يا شباب ايش بيقول اه احنا بدنا نوصل للرفض
+
+370
+00:42:17,710 --> 00:42:23,730
+الآن اقعد هتقول لك ايش بيقول أنا قلت بس أنت ما أخدتش
+
+371
+00:42:23,730 --> 00:42:29,170
+بالك أنا الآن ايش بدي أثبت بدي أثبت أن T is onto
+
+372
+00:42:30,060 --> 00:42:37,120
+قلت لك خد R موجود في UN بدي أحاول أخلق automorphism
+
+373
+00:42:37,120 --> 00:42:44,560
+في الـ set اللي عندنا هذه بحيث يكون صورة لل R اللي
+
+374
+00:42:44,560 --> 00:42:48,900
+أنا أخدته هذا كل الفكرة في الموضوع تمام فروحت قلت
+
+375
+00:42:48,900 --> 00:42:53,420
+اعرف function بالشكل اللي عندنا هذا و بدور هل ال 
+
+376
+00:42:53,420 --> 00:42:58,220
+هل هذه atomorphism أم لا؟ حتى هذه اللحظة لم 
+
+377
+00:42:58,220 --> 00:43:03,660
+نثبت أن هذه atomorphism مظبوط، وإذا طلعت atomorphism
+
+378
+00:43:03,660 --> 00:43:07,740
+بدي بيجيلك أن صورتها الـ R اللي عندنا وبالتالي يكون
+
+379
+00:43:07,740 --> 00:43:13,280
+حلنا المشكلة واضحة تمامًا، واضحة يا شباب، هيك طيب يبقى
+
+380
+00:43:13,280 --> 00:43:17,680
+أنا أخذت S موجودة في Z أن الـ S بقدر أكتبها SR
+
+381
+00:43:17,680 --> 00:43:23,570
+inverse R modulo N عادي، جداماعناش مشكلة، طب الـ S في
+
+382
+00:43:23,570 --> 00:43:31,130
+الـ R inverse بدي أسميها S1R modulo N، أليست هذه هي
+
+383
+00:43:31,130 --> 00:43:37,910
+Alpha of S1، مش هي الـ alpha of S يساوي SR modulo N؟
+
+384
+00:43:37,910 --> 00:43:47,130
+طلعناها S1R، يبقى alpha of S1، يبقى صار الـ element S
+
+385
+00:43:47,130 --> 00:43:55,250
+اللي أخدته في Z in لجتله أصل اسمه إيش اسمه؟ S1 يبقى
+
+386
+00:43:55,250 --> 00:43:59,030
+الـ alpha  أنتوا ولا لا؟ يبقى الـ alpha انتوا يبقى
+
+387
+00:43:59,030 --> 00:44:02,750
+أثبت الآن أن الـ alpha اللي أخدتها دي one to one
+
+388
+00:44:02,750 --> 00:44:07,970
+and انتوا شو ضايل عندي؟ أثبت أنه بتخدم خاصية الـ
+
+389
+00:44:07,970 --> 00:44:14,790
+isomorphism، لذلك بتروح أخد alpha of مثلاً a زائد الـ
+
+390
+00:44:14,790 --> 00:44:24,050
+... أو S1 زائد S2، خليها نفس الرمز، خليها S1 و S2، S1
+
+391
+00:44:24,050 --> 00:44:31,430
+زائد S2 بده يساوي الـ
+
+392
+00:44:31,430 --> 00:44:38,860
+S1 والـ S2 أرقام، هذهمش هيك اه يعني بقدر أخدهم زي
+
+393
+00:44:38,860 --> 00:44:46,820
+ما بدي، أو خلينا بلاشي نغلط شوية، هذه قولنا is on to
+
+394
+00:44:46,820 --> 00:44:53,940
+خلصنا منها S1 و S2، مظبوط حسب الـ definition هذه
+
+395
+00:44:53,940 --> 00:45:05,740
+بدها تساوي S1 زي S2 في R modulo N، يعني هذه بقدر
+
+396
+00:45:05,740 --> 00:45:18,760
+أقول S1R زي S2R كله modulo N، أو إن شئتم فقولوا S1R
+
+397
+00:45:18,760 --> 00:45:30,060
+modulo N، S2R modulo N، هل أليست هذه اللي هو Alpha of S
+
+398
+00:45:30,060 --> 00:45:36,160
+واحد، وهذه Alpha of S اتنين؟ يبقى بناء عليها صارت
+
+399
+00:45:36,160 --> 00:45:42,600
+هذه إيش؟ صارت Atomorphism لأنها من الـ group إلى
+
+400
+00:45:42,600 --> 00:45:51,860
+نفسها، يبقى هنا Sir Alpha is an Atomorphism.
+
+401
+00:45:57,050 --> 00:46:03,470
+يبقى حتى لأن خلقنا atomorphism موجود عندنا الآن لو
+
+402
+00:46:03,470 --> 00:46:11,690
+جيت now لو أخدت alpha of S اللي هي مين قلنا عليها؟
+
+403
+00:46:11,690 --> 00:46:19,070
+اللي هي alpha of S اللي هي الـ S R modulo N، هذا بده
+
+404
+00:46:19,070 --> 00:46:26,340
+يعطيلك الـ alpha of S، مش S موجود في ZN، يعني هذا
+
+405
+00:46:26,340 --> 00:46:34,840
+الكلام بده يساوي S في alpha of one، مظبوط؟
+
+406
+00:46:36,980 --> 00:46:42,940
+S α of خمسة يعني خمسة ... أي واحد واحد واحد أثر
+
+407
+00:46:42,940 --> 00:46:47,760
+alpha تأثر عليهم كلهم، يبقى الرقم نفسه في alpha of
+
+408
+00:46:47,760 --> 00:46:55,140
+one بده يساوي مين؟ بده يساوي الـ S R modulo M بالـ
+
+409
+00:46:55,140 --> 00:47:01,160
+left cancellation law شط بالأيسر، يبقى alpha of one
+
+410
+00:47:01,160 --> 00:47:09,870
+بده يساوي الـ R modulo N، هذه موجودة في UN ولا لا؟
+
+411
+00:47:09,870 --> 00:47:15,450
+موجودة في UN اللي إحنا أخدناها من البداية وانراحت
+
+412
+00:47:15,450 --> 00:47:23,390
+تي وزنت، أخدنا R موجودة في UN، وإحنا أخدنا T وانراحت
+
+413
+00:47:23,390 --> 00:47:30,070
+T of Alpha يسوى من؟ Alpha of one، يبقى صار الـ R
+
+414
+00:47:30,070 --> 00:47:37,870
+modulo N، الـ R modulo N اللي هي تساوي Alpha of one
+
+415
+00:47:37,870 --> 00:47:44,230
+والـ Alpha of one هي T of Alpha، هذا بده يعطيلك أن
+
+416
+00:47:44,230 --> 00:47:49,950
+T is onto، يبقى
+
+417
+00:47:49,950 --> 00:47:55,950
+كلها اللف لفة مشان نوصل أن R هي عبارة عن T of
+
+418
+00:47:55,950 --> 00:48:02,030
+Alpha، وبالتالي T of Alpha is onto، خلصنا؟ ما خلصناش،
+
+419
+00:48:02,030 --> 00:48:08,090
+ضايل خاصية الـ isomorphism، إذا بدي أخد تأثير الـ T
+
+420
+00:48:08,090 --> 00:48:11,990
+على حاصل ضرب two permutations اللي هي أو two
+
+421
+00:48:11,990 --> 00:48:17,730
+automorphisms Alpha و Beta، يبقى بدي أخد finally
+
+422
+00:48:17,730 --> 00:48:21,010
+بدي
+
+423
+00:48:21,010 --> 00:48:27,610
+أخد T of Alpha Beta أو Beta Alpha، سيئة Beta Alpha
+
+424
+00:48:28,150 --> 00:48:31,850
+أعتقد الكتاب ماخد alpha beta، أنا بدي أخد beta
+
+425
+00:48:31,850 --> 00:48:35,990
+alpha، يعني على كل الأمرين الكلام صحيح لو أخدت
+
+426
+00:48:35,990 --> 00:48:40,470
+alpha beta ولا beta alpha، بتفرقش عنها، طيب هذا
+
+427
+00:48:40,470 --> 00:48:47,710
+الكلام بده يساوي الآن إيش بيقول لي T لما تأثر على الـ
+
+428
+00:48:47,710 --> 00:48:51,790
+... وين راحت؟ T of Alpha بديه يساوي Alpha of one
+
+429
+00:48:51,790 --> 00:49:01,650
+يبقى هذا بديه يساوي Beta Alpha كله of one، طيب
+
+430
+00:49:01,650 --> 00:49:08,990
+هذا الكلام بديه يساوي Beta في Alpha of one
+
+431
+00:49:12,500 --> 00:49:19,480
+طب alpha of one وين موجودة؟ وين موجودة؟ في UN
+
+432
+00:49:19,480 --> 00:49:26,020
+مظبوط ايه، alpha of one حطناها موجودة وين؟ في UN
+
+433
+00:49:26,020 --> 00:49:34,280
+وين كتبناها؟ alpha وين راحت؟ المهم كتبنا هاية Alpha
+
+434
+00:49:34,280 --> 00:49:38,540
+of one موجودة في UN، يبقى Alpha of one لو قلنا مثلاً
+
+435
+00:49:38,540 --> 00:49:44,140
+U عشرة، يبقى يا واحد يا ثلاثة يا سبعة يا تسعة وهكذا
+
+436
+00:49:44,140 --> 00:49:50,850
+قيص عليها الباقي، إذا هذه هاهاهتساوي واحد زائد واحد
+
+437
+00:49:50,850 --> 00:49:58,390
+زائد واحد، جدّيش Alpha of one times، مظبوط؟ يعني هذه
+
+438
+00:49:58,390 --> 00:50:05,550
+بدها تساوي Beta of واحد زائد واحد زائد واحد، كام
+
+439
+00:50:05,550 --> 00:50:14,430
+مرة، هذا كله Alpha of one times، يعني لو كان Alpha
+
+440
+00:50:14,430 --> 00:50:21,550
+of one يساوي ثلاثة، لو كان Alpha of one بده يساوي ثلاثة
+
+441
+00:50:21,550 --> 00:50:27,450
+يبقى يصير واحد زي واحد زي واحد فقط لا غير طبعًا، طب
+
+442
+00:50:27,450 --> 00:50:33,510
+لو كان سبعة بدي أكتبها سبعة من المرات، يعني قداش
+
+443
+00:50:33,510 --> 00:50:37,710
+بتكون النتيجة، بدي أكرهها يعني Alpha of one times
+
+444
+00:50:37,710 --> 00:50:42,250
+إن كانت سبعة بدي أكررها سبعة مرات، إن كانت ثلاثة
+
+445
+00:50:42,250 --> 00:50:45,330
+ثلاثة مرات، إن كانت تسعة تسعة مرات، إن كانت أحد عشر
+
+446
+00:50:45,330 --> 00:50:51,240
+أحد عشر مرة وهكذا، طيب كويس، هذا الكلام بده يشاوي
+
+447
+00:50:51,240 --> 00:51:00,460
+اللي هو beta of one زائد beta of one زائد زائد
+
+448
+00:51:00,460 --> 00:51:10,460
+beta of one، هذا alpha of one كمان times، إذا
+
+449
+00:51:10,460 --> 00:51:19,030
+هذا الكلام بده يشاوي، اكمر هدول alpha of one و هدولة
+
+450
+00:51:19,030 --> 00:51:25,270
+كم واحدة في beta one، يبقى هذا بده يساوي beta of
+
+451
+00:51:25,270 --> 00:51:33,230
+one في alpha of one، beta of one مكررة alpha one
+
+452
+00:51:33,230 --> 00:51:42,170
+من المرات، طيب الـ beta of one، الـ beta of one أليس
+
+453
+00:51:42,170 --> 00:51:51,360
+هي T of beta، يبقى هذه هي T of Beta، والثانية هي T
+
+454
+00:51:51,360 --> 00:51:57,500
+of Alpha، يبقى أثبتنا له أن T of Beta Alpha هي T
+
+455
+00:51:57,500 --> 00:52:02,860
+Beta Alpha، لو روحت للكتاب هيكون جلب الوضع أخد لك T
+
+456
+00:52:02,860 --> 00:52:08,130
+Alpha Beta وهنا تقول لك T Alpha T، فماعناش مشكلة بس
+
+457
+00:52:08,130 --> 00:52:10,830
+بدل ما أقول لك أن alpha of one times بقول لك beta
+
+458
+00:52:10,830 --> 00:52:15,870
+of one time، إذا لا مشكلة، أنا اتعمد أجيبك بشكل هذا
+
+459
+00:52:15,870 --> 00:52:20,250
+حتى تتعرف أنه ليس بالضرورة قرآن كريم، لكن إحنا
+
+460
+00:52:20,250 --> 00:52:30,070
+فهمنا هذا الكلام، يبقى ... يبقى بناء عليه so T is an
+
+461
+00:52:30,070 --> 00:52:37,470
+isomorphism، هذا بدي أعطيلك أن الـ atomorphism لـ ZN
+
+462
+00:52:37,470 --> 00:52:43,230
+ايزو مارفك لـ UN من الآن فصاعدًا
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8c9e9a9e4d9953737ae2b0dadda7b3f5c23dd3d5
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/djM5m13WWBQ_postprocess.srt
@@ -0,0 +1,1848 @@
+1
+00:00:21,410 --> 00:00:27,670
+نكمل نبدأ في محاضرة الصباح وصلنا الى المثال
+
+2
+00:00:27,670 --> 00:00:33,930
+compute ال atomorphism لمن الى z عشرةمشان هيك روحت
+
+3
+00:00:33,930 --> 00:00:37,710
+افترض ان ال alpha من z عشرة الى z عشرة يبقى اعنى
+
+4
+00:00:37,710 --> 00:00:43,290
+atomorphism شو شكل ال alpha الله اعلم تمام يبقى
+
+5
+00:00:43,290 --> 00:00:48,010
+احنا بنبحث قداش ال alpha دي او ايش قيمتها شو تساوي
+
+6
+00:00:48,010 --> 00:00:54,990
+ماهو نوع هذه ال function فبجي بقول الان لو كان ال
+
+7
+00:00:54,990 --> 00:01:00,930
+k موجود في z عشرة thenيعني الـ K يبدو يساوي Zero
+
+8
+00:01:00,930 --> 00:01:05,830
+يا واحد اتنين تلاتة اربعة لغاية تسعة تمام؟ then لو
+
+9
+00:01:05,830 --> 00:01:13,010
+جيت أخدت Alpha of K لأن Alpha بدت أثر على K اللي
+
+10
+00:01:13,010 --> 00:01:18,810
+موجودة في Z عشرة يبقى هذا الكلام بده يساوي Alpha
+
+11
+00:01:18,810 --> 00:01:25,790
+of واحد زائد واحد زائد واحد كم مرة هدول؟ كم واحد
+
+12
+00:01:25,790 --> 00:01:35,250
+هدول؟ K من المراتيبقى هدول K times يبقى K من
+
+13
+00:01:35,250 --> 00:01:39,490
+المرات الان انا جاي ال alpha عبارة عن ايش
+
+14
+00:01:39,490 --> 00:01:45,210
+atomorphism atomorphism يعني isomorphism معناته
+
+15
+00:01:45,210 --> 00:01:51,910
+هذه هتساوي alpha of one زائد alpha of one زائد
+
+16
+00:01:51,910 --> 00:02:00,190
+زائد alpha of one كم مرة هدول كمان؟كتايمز يبقى هذا
+
+17
+00:02:00,190 --> 00:02:07,330
+الكلام بده يساوي ك في alpha of one ضالت مشكلتنا مع
+
+18
+00:02:07,330 --> 00:02:12,490
+alpha of one قائمة قداش alpha of one هذي بده تكون
+
+19
+00:02:12,490 --> 00:02:19,110
+الان alpha of one موجودة وين موجودة في z عشرة بده
+
+20
+00:02:19,110 --> 00:02:25,600
+اروح ادور على ال order تبعهايبقى باجي بقوله و ال
+
+21
+00:02:25,600 --> 00:02:34,680
+alpha of one موجودة في z عشرة طيب باجي بقول كمان
+
+22
+00:02:34,680 --> 00:02:42,820
+in z عشرة قداش ال order للواحد قداش ال order
+
+23
+00:02:42,820 --> 00:02:48,760
+للواحد في z عشرة مين ال operation اللي على z عشرة
+
+24
+00:02:49,640 --> 00:02:54,060
+أزايد الجامعة مظبوط الجامعة هي ال operation
+
+25
+00:02:54,060 --> 00:02:58,460
+الموجودة على ز عشرة إذا الواحد قداش ال order له
+
+26
+00:02:58,460 --> 00:03:05,440
+الواحد لو أشبهك كام مرة بيعطيني ال zero عشر مرات
+
+27
+00:03:05,440 --> 00:03:10,660
+يعني ال order للواحد يسوى قداش يسوى عشرة يبقى ال
+
+28
+00:03:10,660 --> 00:03:17,060
+order للواحد يسوى عشرة هذا بده يعطينا أن ال order
+
+29
+00:03:17,060 --> 00:03:24,120
+لل alpha of واحدخدنا في النظرية السابقة رقم خمسة
+
+30
+00:03:24,120 --> 00:03:28,900
+النظرية مش السابقة اللي قبلها اللي فيها السبع نقاط
+
+31
+00:03:28,900 --> 00:03:33,780
+النقطة رقم خمسة ال order اللي ايه بيساوي مين ال
+
+32
+00:03:33,780 --> 00:03:39,200
+order ل phi of اذا كان phi ايزو مورفزم انا افرض ان
+
+33
+00:03:39,200 --> 00:03:44,860
+اتومورفزم هو ايزو مورفزم من ال group الى نفسه هذا
+
+34
+00:03:44,860 --> 00:03:52,000
+بيعطينا ان هذا بيساوي عشرة becauseإن الـ order للـ
+
+35
+00:03:52,000 --> 00:03:57,940
+A بدي سوى ال order لـ Phi of A هذا previous
+
+36
+00:03:57,940 --> 00:03:58,780
+theorem
+
+37
+00:04:01,950 --> 00:04:07,450
+Theorem part 5 كان الجزء الخامس من النظرية اللي
+
+38
+00:04:07,450 --> 00:04:12,350
+فيها سبع نقاط يبقى ال order ل alpha of واحد بده
+
+39
+00:04:12,350 --> 00:04:17,410
+يساوي عشرة الان انا بقول ال alpha واحد وين موجود
+
+40
+00:04:17,410 --> 00:04:24,090
+في z عشرة مين العناصر اللي في z عشرة اللي ال order
+
+41
+00:04:24,090 --> 00:04:32,380
+اللي يساوي عشرة الواحد ومين كمانكل رقم relative
+
+42
+00:04:32,380 --> 00:04:36,740
+prime مع العشرة وانت بتجري مين كمان؟ relative
+
+43
+00:04:36,740 --> 00:04:44,040
+prime مع العشرة مين؟ مين؟ تلاتة والسبعة والتسعة
+
+44
+00:04:44,040 --> 00:04:48,220
+يبقى هدول بس يبقى alpha of one هتسوى واحد من
+
+45
+00:04:48,220 --> 00:04:55,320
+الأربع هدول فقط يبقى هذا بده يعطينا ان ال alpha of
+
+46
+00:04:55,320 --> 00:05:03,720
+one equalone او تلاتة او سبعة او تسعة because
+
+47
+00:05:03,720 --> 00:05:13,220
+السبب each of واحد و تلاتة و سبعة و تسعة is of
+
+48
+00:05:13,220 --> 00:05:21,920
+order عشر كويس مادام alpha of one ساوت يا واحد يا
+
+49
+00:05:21,920 --> 00:05:27,660
+تلاتة يا سبعة يا تسعة معناته اكم اوتومورفزم عندى
+
+50
+00:05:28,860 --> 00:05:36,460
+اربع فقط لا غير مافيش غيرهم يبقى بدي أروح أقول أن
+
+51
+00:05:36,460 --> 00:05:41,480
+ال alpha هذه لو أثرت على الواحد بدي أخلي صورتها
+
+52
+00:05:41,480 --> 00:05:45,720
+واحدلأن ال order اللي هذا بدي يسوى ال order اللي
+
+53
+00:05:45,720 --> 00:05:51,720
+هذا أو ال alpha لو أثرت على ال واحد بديت تبقى صورة
+
+54
+00:05:51,720 --> 00:05:58,040
+تلاتة هتكون ال order الاتنين كله كم؟ عشرة أو ال
+
+55
+00:05:58,040 --> 00:06:03,280
+alpha of واحد ممكن يتساوي السبعة أو ال alpha of
+
+56
+00:06:03,280 --> 00:06:09,340
+واحد ممكن الصورة كم؟ ممكن الصورة تسعة يبقى اكم
+
+57
+00:06:09,340 --> 00:06:15,670
+اتومورفزم الصار عندىأربعة ال alpha لو أثرت على ال
+
+58
+00:06:15,670 --> 00:06:18,770
+identity element تعطين ال identity element ال
+
+59
+00:06:18,770 --> 00:06:22,290
+alpha لو أثرت على ال identity element ممكن تكون
+
+60
+00:06:22,290 --> 00:06:25,950
+الصورة تلاتة عفوا مش ال identity لأن واحد مش ال
+
+61
+00:06:25,950 --> 00:06:29,970
+identity في زد عشر ال identity هو ال zero ال alpha
+
+62
+00:06:29,970 --> 00:06:33,750
+لما تأثر على واحد ممكن تكون الصورة واحد ال alpha
+
+63
+00:06:33,750 --> 00:06:36,350
+لما تأثر على واحد ممكن تكون الصورة تلاتة ال alpha
+
+64
+00:06:36,350 --> 00:06:39,670
+لو أثرت على واحد ممكن تكون الصورة سبعة ال alpha لو
+
+65
+00:06:39,670 --> 00:06:42,250
+أثرت على واحد ممكن تكون الصورة تسعة
+
+66
+00:06:59,950 --> 00:07:05,730
+مشان اميز في مابينهم ايش رايك هذا بده يسميه alpha
+
+67
+00:07:05,730 --> 00:07:12,530
+oneوهذا بدي أسميه Alpha 3 واللي بعده بدي أسميه
+
+68
+00:07:12,530 --> 00:07:19,270
+Alpha 7 واللي بعده بدي أسميه Alpha 9 عشان أميزهم
+
+69
+00:07:19,270 --> 00:07:28,250
+عن بعضهم هدول كلهم بدهم يشكلولي ال Atomorphism
+
+70
+00:07:28,250 --> 00:07:31,070
+لمن؟ لزد عشرة
+
+71
+00:07:35,390 --> 00:07:40,590
+يبقى هدول بدهم يشكلولي الـautomorphism لمن؟ لزد
+
+72
+00:07:40,590 --> 00:07:47,970
+عشرة الان انا بدي اتأكد ان كل واحد من هدول هو
+
+73
+00:07:47,970 --> 00:07:53,890
+عبارة عن automorphism تمام؟ مشان هيك بد ال alpha
+
+74
+00:07:53,890 --> 00:07:57,550
+كل واحدة فيهم الاولة او التانية او التالتة او
+
+75
+00:07:57,550 --> 00:08:03,120
+الرابعةبديها تبقى one to one و بديها انتوا و بديها
+
+76
+00:08:03,120 --> 00:08:09,400
+تخدم خاصية ال isomorphism تمام طيب انا بدى شيكلك
+
+77
+00:08:09,400 --> 00:08:13,560
+على واحدة اثبتها انها isomorphism و انت بتسوي
+
+78
+00:08:13,560 --> 00:08:18,370
+الباقي بنفس الطريقة اول شئهذه هو ال identity ليش؟
+
+79
+00:08:18,370 --> 00:08:21,530
+ان ال alpha of one بدي يساوي one هذه هي ال
+
+80
+00:08:21,530 --> 00:08:25,730
+identity function هذه دائما one to one and on two
+
+81
+00:08:25,730 --> 00:08:29,430
+و بتخدم خاصية ال isomorphism و قد رأينا ذلك في
+
+82
+00:08:29,430 --> 00:08:33,330
+النظرية تبعت الصبح يبقى أسيبني منها هذه شغلها سهل
+
+83
+00:08:33,330 --> 00:08:38,530
+بتروح أخد مين alpha 3 أو alpha 7 أو alpha 9 بعمل
+
+84
+00:08:38,530 --> 00:08:42,990
+واحدة منهم و التنتين التانيات بدي يكون بنفس
+
+85
+00:08:42,990 --> 00:08:55,210
+الطريقةيبقى باجي بقول هنا now we shall show that
+
+86
+00:08:55,210 --> 00:09:12,030
+each of the above four elements is an
+
+87
+00:09:17,630 --> 00:09:26,790
+Atomorphism يبقى بده اعمل check لمن لل alpha تلاتة
+
+88
+00:09:26,790 --> 00:09:34,470
+كويس طيب انا في الاول لما اخدت alpha من z الى عشرة
+
+89
+00:09:34,470 --> 00:09:41,440
+اعطيتها تعريفماتدهاش تعريف لكن بدي أروح أخذهلها ال
+
+90
+00:09:41,440 --> 00:09:51,980
+alpha تلاتة of of X بدي أسميها تلاتة X مثلا واحد
+
+91
+00:09:51,980 --> 00:09:56,340
+يقول استنى كله كيف استنى قال لي تعريفه غلط بقول
+
+92
+00:09:56,340 --> 00:10:02,620
+كيف تعريفه غلط بقول انت بتضرب ضربتلاتة في X بقوله
+
+93
+00:10:02,620 --> 00:10:07,480
+لأ مش صحيح انا قلت X زائد X زائد X لأن ال
+
+94
+00:10:07,480 --> 00:10:12,320
+operation على Z هي عملية الجامعة بس X زائد X زائد
+
+95
+00:10:12,320 --> 00:10:17,000
+X يعني قداش تلاتة X إذا تعريفه سليم مية المية ولا
+
+96
+00:10:17,000 --> 00:10:25,460
+يوجد فيه أي خطأ طيب الآن لما أقول Alpha تلاتة of
+
+97
+00:10:25,460 --> 00:10:30,580
+واحد بده يسوى قداش بده يسوى تلاتة يبقى هذا معناته
+
+98
+00:10:30,750 --> 00:10:39,710
+ألف تلاتة of واحد بده يساوي تلاتة سؤال التلاتة
+
+99
+00:10:39,710 --> 00:10:46,320
+generator لازد عشرة ولا لا؟يبقى ال alpha تلاتة one
+
+100
+00:10:46,320 --> 00:10:51,080
+to one and unto ليش انها generator اللي بتأثر
+
+101
+00:10:51,080 --> 00:10:54,040
+بتجيب element من z عشرة و التاني بتجيب element
+
+102
+00:10:54,040 --> 00:10:57,980
+تاني و التالت لما تجيبلي كل z عشرة صحيح ولا لا
+
+103
+00:10:57,980 --> 00:11:06,680
+يبقى هنا باجي بقوله since ال تلاتة is a generator
+
+104
+00:11:06,680 --> 00:11:11,760
+of z عشرة
+
+105
+00:11:16,370 --> 00:11:22,110
+الألف تلاتة على
+
+106
+00:11:22,110 --> 00:11:29,370
+طول الخط is one to one and one to function
+
+107
+00:11:39,060 --> 00:11:44,800
+one to one and unto كلمة function بدنا نثبتها انها
+
+108
+00:11:44,800 --> 00:11:50,060
+well defined يبقى اثبتها انها one to one and unto
+
+109
+00:11:50,060 --> 00:11:59,760
+and unto الان ال alpha تلاتة is well defined يبقى
+
+110
+00:11:59,760 --> 00:12:05,080
+بدنا نثبت انها معرفة الاصل اللي عملها قبل هذه
+
+111
+00:12:05,080 --> 00:12:10,010
+الخطوة لكن مافيش مشكلةطيب what do you find؟ بدأ
+
+112
+00:12:10,010 --> 00:12:16,090
+أخد عنصرين متساوين و أثبت أن صورتهم متساوية يبقى
+
+113
+00:12:16,090 --> 00:12:23,090
+باجب أقوله لو كان ال X مديله عشرة بده يساوي ال Y
+
+114
+00:12:23,090 --> 00:12:29,930
+مديله عشرة هذا إيش بيعطينا؟لو ضربت فيه تلاتة بيصير
+
+115
+00:12:29,930 --> 00:12:38,490
+تلاتة X modulo عشرة يسوى تلاتة Y modulo عشرة صحيح
+
+116
+00:12:38,490 --> 00:12:45,070
+ولا لا؟ طب انا معرفها هنا Alpha of X يسوى تلاتة X
+
+117
+00:12:45,070 --> 00:12:53,950
+معناته ان ال Alpha تلاتة of X بيسوى Alpha تلاتة of
+
+118
+00:12:53,950 --> 00:13:01,760
+Y تمام؟يبقى أخدت عنصرين متساويين اثبتت ان عنصرهم
+
+119
+00:13:01,760 --> 00:13:06,820
+متساويين يبقى في هذه الحالة في is well defined
+
+120
+00:13:06,820 --> 00:13:11,440
+يبقى well defined one to one and انتوا ايش ضايل
+
+121
+00:13:11,440 --> 00:13:14,860
+عليك بس الخاصية الأخيرة اللي هي خاصية ال
+
+122
+00:13:14,860 --> 00:13:21,680
+isomorphism لذلك بدأجي أقوله بدأ أخد finally بدأ
+
+123
+00:13:21,680 --> 00:13:30,800
+أخد alpha تلاتة ofA زائد B مثلا A زائد B نظرا لأن
+
+124
+00:13:30,800 --> 00:13:36,140
+العملية على زد N هي عملية الجامعة يبقى A زائد B
+
+125
+00:13:36,140 --> 00:13:41,600
+حسب ال definition تبعنا يبقى تلاتة في A زائد B
+
+126
+00:13:41,600 --> 00:13:49,020
+يبقى تلاتة A زائد تلاتة B هذه عبارة عن مين عبارة
+
+127
+00:13:49,020 --> 00:13:56,640
+عن Alpha تلاتة of Aوالتانية alpha 3 of b إذا ال
+
+128
+00:13:56,640 --> 00:14:02,320
+alpha 3 خدمت خاصية ال isomorphism بعد هيك ال alpha
+
+129
+00:14:02,320 --> 00:14:07,800
+احنا عرفناها من ال 6 إلى نفسها يبقى بناء عن عليه
+
+130
+00:14:07,800 --> 00:14:14,560
+alpha 3 is an atomorphism يبقى هذا بيعطينا أن
+
+131
+00:14:14,560 --> 00:14:20,940
+alpha 3 is an atomorphism
+
+132
+00:14:22,720 --> 00:14:31,600
+يبقى بنفس الطريقة similarly اللي هو من alpha 7 and
+
+133
+00:14:31,600 --> 00:14:37,900
+alpha 9 are automorphisms
+
+134
+00:14:37,900 --> 00:14:41,940
+where
+
+135
+00:14:41,940 --> 00:14:51,080
+كذلك حيثهم اللي هو ال alpha 1 is the identity
+
+136
+00:14:52,010 --> 00:14:52,570
+Animal
+
+137
+00:14:55,760 --> 00:15:03,020
+identity element يبقى الأن اثبتنا ان الاتومورفيزم
+
+138
+00:15:03,020 --> 00:15:06,020
+لزد عشرة بالضبط
+
+139
+00:15:25,840 --> 00:15:31,840
+يبقى هذه حسبتله مين الاتومورفزم لمين لزد عشرة
+
+140
+00:15:31,840 --> 00:15:36,680
+طلعته مافيش فيها الا اربعة عناصر وكل عنصر منها دول
+
+141
+00:15:36,680 --> 00:15:43,660
+عبارة عن اتومورفزم طيب خلينا نعطي بعض التوضيحات
+
+142
+00:15:43,660 --> 00:15:50,220
+اكتر اللي خاطر اشوف لحد هنا انتهى الشغللكن احنا
+
+143
+00:15:50,220 --> 00:15:54,180
+بدنا بعض التوضيحات، ايش بعض التوضيحات؟ هذه
+
+144
+00:15:54,180 --> 00:16:00,580
+isomorphic لمين؟ و لو ضربت ربعت هذه، ايش بدي يكون
+
+145
+00:16:00,580 --> 00:16:04,200
+الناتج؟ لو عملت composition ما بين الأولى
+
+146
+00:16:04,200 --> 00:16:07,140
+والتانية، شو بيكون الناتج؟ composition بين
+
+147
+00:16:07,140 --> 00:16:11,600
+التانية، هل بتبقى closed فعلا ولا لأ؟ بس مجرد
+
+148
+00:16:11,600 --> 00:16:17,110
+معلومات كيف بدنا نشتغل العناصر هدول مع بعضيبقى
+
+149
+00:16:17,110 --> 00:16:27,230
+ممكن اقوله زيادة على ذلك it should be noted that
+
+150
+00:16:27,230 --> 00:16:38,990
+من الملاحظة انه لو بدي alpha تلاتة تربيع of oneهذا
+
+151
+00:16:38,990 --> 00:16:42,450
+المقصود ليس تربية وضرب وفرقة المقصود هو
+
+152
+00:16:42,450 --> 00:16:48,310
+composition بين الاتنين يعني هذه معناها alpha تكيب
+
+153
+00:16:48,310 --> 00:16:55,610
+ل alpha تلاتة ل alpha تلاتة of one حسب تعريف ال
+
+154
+00:16:55,610 --> 00:17:00,730
+composition of function alpha تلاتة ل alpha تلاتة
+
+155
+00:17:00,730 --> 00:17:07,490
+of oneهذا الكلام بده يساوي Alpha تلاتة Alpha تلاتة
+
+156
+00:17:07,490 --> 00:17:13,450
+of one حسب التعريف Alpha تلاتة of X يساوي تلاتة في
+
+157
+00:17:13,450 --> 00:17:18,490
+X يبقى هذا ايش بده تكون تلاتة في واحد اللي هي
+
+158
+00:17:18,490 --> 00:17:23,590
+بتلاتة Alpha تلاتة of X بتصيب تلاتة في تلاتة اللي
+
+159
+00:17:23,590 --> 00:17:32,360
+هي بمين بتسعة هذه أليست Alpha تسعة of oneيبقى
+
+160
+00:17:32,360 --> 00:17:37,200
+الصار عندى alpha تلاتة تربيع of one هي alpha تسعة
+
+161
+00:17:37,200 --> 00:17:41,940
+of one يعني موجودة وين موجودة داخل الاتو مورفيزم
+
+162
+00:17:41,940 --> 00:17:47,080
+ال Z عشرة طب لو كعبدها تطلع واحدة من هدول والله
+
+163
+00:17:47,080 --> 00:17:53,320
+بتيجي برا تعالى نشوفلو جيت أخدتله alpha تكييب
+
+164
+00:17:53,320 --> 00:18:00,420
+تكييب of one يعني alpha تلاتة ل alpha تر تلاتة
+
+165
+00:18:00,420 --> 00:18:06,860
+تربيع of one ويساوي alpha تلاتة لبرا اللي جوا هيها
+
+166
+00:18:06,860 --> 00:18:09,940
+حسبناها قداشر طالت عنها تسعة
+
+167
+00:18:12,470 --> 00:18:17,970
+حسب التقريب في الجهد التالتة في التسعة سبعة وعشرين
+
+168
+00:18:17,970 --> 00:18:23,590
+سبعة وعشرين في الزد عشرة يعني بسبعة يعني بسبعة هذه
+
+169
+00:18:23,590 --> 00:18:29,770
+ال alpha سبعة of one إذا هذا ال element لما انكعت
+
+170
+00:18:30,250 --> 00:18:35,810
+جاب للعنصر هذه يعني لازالة closed و هكذا طب لو
+
+171
+00:18:35,810 --> 00:18:42,750
+جبتله هنا Alpha تكيب أس أربعة of one أليست Alpha
+
+172
+00:18:42,750 --> 00:18:51,070
+تلاتة في Alpha تلاتة تكيب of one تمام هذه تساوي
+
+173
+00:18:51,070 --> 00:18:58,230
+Alpha تلاتة ofالفا تلاتة كيب of one هاي امشي امشي
+
+174
+00:18:58,230 --> 00:19:04,550
+كده ايش كانت سبعة يبقى هذه السبعة حسب التعريف يبقى
+
+175
+00:19:04,550 --> 00:19:09,010
+تصير تلاتة في سبعة واحدة وعشرين شيل العشرين بتطلع
+
+176
+00:19:09,010 --> 00:19:15,830
+من اللي هو واحد اللي هو بدها تساوي alpha of one
+
+177
+00:19:20,890 --> 00:19:28,350
+أو Alpha one of one Alpha one of one يبقى بناء على
+
+178
+00:19:28,350 --> 00:19:34,670
+اليسار المقابل اتانمين ال identity element اذا صار
+
+179
+00:19:34,670 --> 00:19:42,010
+عندنا هذا سيعطيك ان Alpha تكيب ال order يساوي كم؟
+
+180
+00:19:42,010 --> 00:19:50,000
+يساوي أربعطيب ال order إلها يسوى أربعة يبقى هذه
+
+181
+00:19:50,000 --> 00:19:57,730
+إيش بتنفعGenerator لمن؟ لـAtomorphism لمن؟
+
+182
+00:19:57,730 --> 00:20:00,830
+لـAtomorphism
+
+183
+00:20:00,830 --> 00:20:05,890
+لـZ10 يبقى هذا .. ليش؟ لأنه مافيهاش الأربع عناصر
+
+184
+00:20:05,890 --> 00:20:11,450
+وكل مربع كعب بيطلع واحد من العنصر يبقى باستفيد من
+
+185
+00:20:11,450 --> 00:20:16,730
+هذا الكلام أن الـAtomorphism لـZ10 Cyclic ولا لأ؟
+
+186
+00:20:16,730 --> 00:20:24,610
+Cyclicيبقى هذا بده يعطيلك ان الاتمورفزم ل z عشرة
+
+187
+00:20:24,610 --> 00:20:33,450
+فيها generator اسمه alpha 3 يبقى هذا بده يعطيلك ان
+
+188
+00:20:33,450 --> 00:20:40,010
+الاتمورفزم ل z عشرة is cyclic
+
+189
+00:20:46,280 --> 00:20:53,240
+خلّيني أفكر قليلا، لدي أربعة عناصر، من من
+
+190
+00:20:53,240 --> 00:20:57,520
+الـgroups اللي مرت علينا و اللي ممكن يكون فيها صلة
+
+191
+00:20:57,520 --> 00:21:03,620
+قرابة بينها وبين الـgroup هذين، خلّيني أشوف U
+
+192
+00:21:03,620 --> 00:21:09,420
+عشرة، U عشرة من عناصرها؟ واحد و تلاتة وسبعة وتسعة،
+
+193
+00:21:09,420 --> 00:21:16,530
+تمام تمامإذا لو جيت لل group هذي و حسبت ال key ل
+
+194
+00:21:16,530 --> 00:21:33,490
+table لكل منها يبقى
+
+195
+00:21:33,490 --> 00:21:39,070
+ملاحظة هذي remark from
+
+196
+00:21:42,080 --> 00:21:53,900
+كالي تابل for U عشرة and اتومورفزم
+
+197
+00:21:53,900 --> 00:22:03,600
+لزد عشرة we have ان الاتومورفزم لزد عشرة
+
+198
+00:22:03,600 --> 00:22:11,710
+isomorphic ل U عشرةتعالى نعمل كيلة تابل طلعلي
+
+199
+00:22:11,710 --> 00:22:18,630
+الكيلة تابل هذا بدي اخد U عشرة عنصرها واحد و تلاتة
+
+200
+00:22:18,630 --> 00:22:24,730
+و سبعة و تسعة و هاي قفلنا و هنا واحد تلاتة سبعة
+
+201
+00:22:24,730 --> 00:22:29,550
+تسعة بالشكل اللي عندنا هنا وهذه التفصيل تبعها
+
+202
+00:22:29,550 --> 00:22:38,480
+كالتالي هذا الرأسهذا الشكل تعالى نحسبها واحد في
+
+203
+00:22:38,480 --> 00:22:44,620
+واحد بواحد تلاتة سابعة تسعة الان تلاتة في واحد
+
+204
+00:22:44,620 --> 00:22:48,600
+بتلاتة طبعا ال operation اللى علياه عشرة هي عملية
+
+205
+00:22:48,600 --> 00:22:53,660
+الضرب عارفينه مسبقا الان تلاتة في تلاتة بتسعة
+
+206
+00:22:53,660 --> 00:23:01,140
+تلاتة في سابعة كدهش؟يعني واحد تلاتة في تسعة سبعة
+
+207
+00:23:01,140 --> 00:23:06,180
+وعشرين شيل عشرتين بيظل سبعة الان سبعة في واحد
+
+208
+00:23:06,180 --> 00:23:10,840
+بسبعة سبعة في تلاتة بواحد وعشرين سبعة في سبعة
+
+209
+00:23:10,840 --> 00:23:17,320
+بتسعة واربعين سبعة في تسعة بتلاتة وستين الان تسعة
+
+210
+00:23:17,320 --> 00:23:22,640
+في واحد بتسعة تسعة في تلاتة بسبعة وعشرين تسعة في
+
+211
+00:23:22,640 --> 00:23:28,660
+سبعة بتلاتة وستين تسعة في تسعة بواحدو تمانين هذه
+
+212
+00:23:28,660 --> 00:23:35,560
+كيلي تابل لمين لـ U عشرة طب خدلي كيلي تابل لـ
+
+213
+00:23:35,560 --> 00:23:44,660
+Atomorphism لـ Z عشرة اللي هي Alpha واحد و Alpha
+
+214
+00:23:44,660 --> 00:23:53,440
+تلاتة و Alpha سبعة و Alpha تسعة تمام؟ و هنا هذه
+
+215
+00:23:53,440 --> 00:24:03,040
+Alpha واحدوهنا ألف تلاتة وهنا ألف سبعة وهنا ألف
+
+216
+00:24:03,040 --> 00:24:12,060
+تسعة شكل أنها طيب ألف واحد في ألف واحد بألف واحد
+
+217
+00:24:12,060 --> 00:24:18,320
+ألف واحد في ألف تلاتة بألف تلاتة ألف واحد في ألف
+
+218
+00:24:18,320 --> 00:24:25,150
+سبعة بألف سبعة ألف تسعةألف تلاتة في ألف واحد بألف
+
+219
+00:24:25,150 --> 00:24:31,890
+تلاتة ألف تلاتة في ألف تلاتة بألف تسعة ألف تلاتة
+
+220
+00:24:31,890 --> 00:24:38,710
+في ألف سبعة بألف واحد ألف تلاتة في ألف تسعة بألف
+
+221
+00:24:38,710 --> 00:24:47,020
+سبعة الآن ألف سبعة في ألف واحد بتديلك ألف سبعةو
+
+222
+00:24:47,020 --> 00:24:57,260
+هذه Alpha 1 وهذه Alpha 9 وهذه Alpha 3 وهذه Alpha 9
+
+223
+00:24:57,260 --> 00:25:09,540
+وهذه Alpha 7 وهذه Alpha 7 وهذه Alpha 3 وهذه Alpha
+
+224
+00:25:09,540 --> 00:25:13,440
+1 طيب
+
+225
+00:25:13,440 --> 00:25:19,930
+يعني احنالو عمليا اشتغلنا زى الشغل اللى عندنا هذا
+
+226
+00:25:19,930 --> 00:25:25,270
+وروحنا جيبنا alpha 3 في alpha 7 لازم يطلع عندك 100
+
+227
+00:25:25,270 --> 00:25:34,360
+alpha نعملها شفويألف تلاتة في ألف سبعة ألف سبعة من
+
+228
+00:25:34,360 --> 00:25:38,920
+واحد اللي هي بسبعة ألف تلاتة لا سبعة اللي هي بواحد
+
+229
+00:25:38,920 --> 00:25:43,120
+وعشرين بيبقى الواحد يبقى هي ألف واحد وهكذا بالنسبة
+
+230
+00:25:43,120 --> 00:25:47,340
+لمن؟ بالنسبة للباقي يعني لو بدي أضرب واحدة في
+
+231
+00:25:47,340 --> 00:25:51,740
+التانية هي نفسيطلع على هذا الجدول و هذا الجدول تجد
+
+232
+00:25:51,740 --> 00:25:56,320
+اتنين نفسي الخواص هذه فيها اربعة عناصر وهذه فيها
+
+233
+00:25:56,320 --> 00:26:00,720
+اربعة عناصر هذه Cyclic وهذه Cyclic مادام Cyclic
+
+234
+00:26:00,720 --> 00:26:03,940
+إذا أبيلن ال order of the element هنا هي ال order
+
+235
+00:26:03,940 --> 00:26:08,960
+of the element هنا يبقى اتنين هذول are isomorphic
+
+236
+00:26:08,960 --> 00:26:15,340
+مش عقدة اتنتين هذول حروحان عمّم هذا الكلام و بدل
+
+237
+00:26:15,340 --> 00:26:21,680
+ما هي Z عشرة هقول Z in و بدل ما هي و عشرة هقول U
+
+238
+00:26:21,680 --> 00:26:30,430
+in و نبرهن صحيتان الكلام as a theorem كنظريةأخر
+
+239
+00:26:30,430 --> 00:26:37,890
+نظرية في هذا الشبتر هي atomorphism ل ZN is
+
+240
+00:26:37,890 --> 00:26:52,150
+isomorphic للغروبيوين يا
+
+241
+00:26:52,150 --> 00:26:53,790
+أبقى بيدنا نيجي لtheorem
+
+242
+00:27:02,010 --> 00:27:09,650
+for every positive integer in for every positive
+
+243
+00:27:09,650 --> 00:27:14,970
+integer in
+
+244
+00:27:14,970 --> 00:27:26,890
+الـ Atomorphism لزد ان is isomorphic لمن لل UN
+
+245
+00:27:37,760 --> 00:27:48,780
+from the previous example من المثال السابق لاحظنا
+
+246
+00:27:48,780 --> 00:27:56,280
+ما يأتي any atomorphism
+
+247
+00:27:56,280 --> 00:27:58,620
+alpha
+
+248
+00:28:02,400 --> 00:28:10,380
+is determined determined
+
+249
+00:28:10,380 --> 00:28:24,760
+by the value of alpha of one اللي موجودة في ال UN
+
+250
+00:28:24,760 --> 00:28:28,220
+بدنا
+
+251
+00:28:28,220 --> 00:28:39,330
+نروح نقوله defineA mapping بنعرف function T من ال
+
+252
+00:28:39,330 --> 00:28:53,070
+atomorphism ل ZN إلى ال UN by كتالي T of alpha بده
+
+253
+00:28:53,070 --> 00:28:55,390
+يساوي alpha of one
+
+254
+00:28:59,500 --> 00:29:05,940
+بنثبت ان الـ T هادى is one to one and unto وكذلك
+
+255
+00:29:05,940 --> 00:29:11,640
+تخدم خاصية ال isomorphism لإن احنا مش هنثبت ال
+
+256
+00:29:11,640 --> 00:29:14,680
+isomorphism نثبت ان ال function لإنها one to one
+
+257
+00:29:14,680 --> 00:29:19,200
+and unto وتخدم الخاصية Phi of A بيبدى يساوي ال Phi
+
+258
+00:29:19,200 --> 00:29:26,020
+of A في ال Phi of B مرة تانيةمن خلال شغلنا في هذا
+
+259
+00:29:26,020 --> 00:29:32,600
+المثال لاحظنا ان قيمة Alpha تعتمد على قيمة Alpha
+
+260
+00:29:32,600 --> 00:29:39,580
+of 1 Alpha of 1 هي بتحدد شكل الـ Atomorphismفروح
+
+261
+00:29:39,580 --> 00:29:43,440
+نقول من المثال السابق any automorphism alpha is
+
+262
+00:29:43,440 --> 00:29:48,420
+determined by the value of alpha of one و alpha of
+
+263
+00:29:48,420 --> 00:29:54,960
+one لقناها موجودة في ال U N يعني alpha of z عاشرة
+
+264
+00:29:54,960 --> 00:30:00,390
+لقناها موجودة في ال U عاشرةيبقى Alpha of 1 موجودة
+
+265
+00:30:00,390 --> 00:30:04,230
+في الـ UN لذلك نروح نعرف Function من الـ
+
+266
+00:30:04,230 --> 00:30:09,170
+Atomorphism إلى ZN للـ UN بدي أخد ال element هنا
+
+267
+00:30:09,170 --> 00:30:12,730
+ال element هنا دي نالو الرمز اللي هو Alpha بدي
+
+268
+00:30:12,730 --> 00:30:17,670
+صورته في UN الصورة هي دائما و أبدا Alpha of 1 اللي
+
+269
+00:30:17,670 --> 00:30:24,030
+موجودة في TN الآن بدي أثبت ان T is one to one لكل
+
+270
+00:30:24,030 --> 00:30:28,370
+ال elements اللي موجودة في ال Atomorphism لمينالى
+
+271
+00:30:28,370 --> 00:30:37,350
+ZN يبقى بداجي اقوله ال N T is one to one مشان هيك
+
+272
+00:30:37,350 --> 00:30:45,630
+بداجي اقوله assume ان T of Alpha بده سوى T of Beta
+
+273
+00:30:45,630 --> 00:30:53,990
+بده احاول اثبت ان Alpha تسوى مين تسوى Betaهذا يعني
+
+274
+00:30:53,990 --> 00:31:04,070
+T of α لـ α of one هو beta of one هذا العلاقة رقم
+
+275
+00:31:04,070 --> 00:31:10,750
+واحد لكن لو رجعت ل ZN هي فيها بس ال one ولا فيها
+
+276
+00:31:10,750 --> 00:31:16,910
+اعداد كتيرةفيها اعداد كتيرة اذا انا بده اروح اثبت
+
+277
+00:31:16,910 --> 00:31:21,210
+ان ال alpha تساوي ال beta على كل الاعداد الكثيرة
+
+278
+00:31:21,210 --> 00:31:31,090
+وليست على ال one فقط فباجي بقوله لو كان ال K موجود
+
+279
+00:31:31,090 --> 00:31:41,220
+في Z then ال alpha of Kمش تساوي alpha ل واحد زائد
+
+280
+00:31:41,220 --> 00:31:46,900
+واحد زائد واحد يعني هذه بده تساوي k في alpha of
+
+281
+00:31:46,900 --> 00:31:57,180
+one مظبوط طيب بده اخد ال beta of k برضه تساوي ال k
+
+282
+00:31:57,180 --> 00:32:04,920
+في beta of one مظبوط طيب ايش رأيك من هذه beta of
+
+283
+00:32:04,920 --> 00:32:10,210
+one هي عبارة عن مين؟Alpha of one إذا بقدر أشيل هذه
+
+284
+00:32:10,210 --> 00:32:19,570
+و أكتب كيف Alpha of one هذه from one من ال one طب
+
+285
+00:32:19,570 --> 00:32:24,810
+اطلعلي في الطرف اليمين هذا و الطرف اليمين هذا إيش
+
+286
+00:32:24,810 --> 00:32:27,610
+بنستنتج ملي اتنين مع بعض
+
+287
+00:32:32,490 --> 00:32:39,490
+الشيء الوحيد اللي بدي اعطانيه هو alpha of K بيساوي
+
+288
+00:32:39,490 --> 00:32:46,070
+beta of KK هذا رقم عشوائي أخدته من كل زدن و أثبت
+
+289
+00:32:46,070 --> 00:32:52,010
+قبله أن Alpha of 1 يبقى أسوأ من Beta of 1 يبقى
+
+290
+00:32:52,010 --> 00:32:59,510
+أسوأ الـ Alpha تساوي Beta لكل الـ K الموجود في الـ
+
+291
+00:32:59,510 --> 00:33:03,630
+ZN طيب
+
+292
+00:33:03,630 --> 00:33:13,770
+بنا نيجي ناخد TS Onto مين اللي بيحكي و ايش بيقولمش
+
+293
+00:33:13,770 --> 00:33:19,910
+سامع لأ
+
+294
+00:33:19,910 --> 00:33:25,870
+كي رقم وليس اتومورفيزم ال alpha كي هو الاتومورفيزم
+
+295
+00:33:25,870 --> 00:33:26,930
+ال alpha كي هو الاتومورفيزم ال alpha كي هو
+
+296
+00:33:26,930 --> 00:33:29,910
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+297
+00:33:29,910 --> 00:33:30,990
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+298
+00:33:30,990 --> 00:33:32,070
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+299
+00:33:32,070 --> 00:33:32,090
+كي هو الاتومورفيزم ال alpha كي هو الاتومورفيزم ال
+
+300
+00:33:32,090 --> 00:33:34,630
+الاتومورفيزم ال alpha كي هو الاتومورفيزم ال alpha
+
+301
+00:33:34,630 --> 00:33:40,990
+كي هو الاتومورفيزم ال alpha كي هو الفي ال code
+
+302
+00:33:40,990 --> 00:33:47,430
+domain و أثبت أنه له أصل في ال domain يبقى بالداجة
+
+303
+00:33:47,430 --> 00:33:58,190
+أقول له let ال R موجود في وين؟ في ال UN يبقى
+
+304
+00:33:58,190 --> 00:34:02,830
+أخدت ال R موجود في ال UN يبقى ال R هذا relatively
+
+305
+00:34:02,830 --> 00:34:10,380
+prime بالنسبة لمين؟ ل ال UN ل ال Nطيب، الآن بندروح
+
+306
+00:34:10,380 --> 00:34:15,160
+اعرف function من .. اه اه define
+
+307
+00:34:17,450 --> 00:34:26,530
+Alpha من ZN إلى ZN يعني بمعنى أخر بدي أخلق
+
+308
+00:34:26,530 --> 00:34:32,550
+Atomorphism علاقة بالأرض اللي عندنا هذه فقلت افترض
+
+309
+00:34:32,550 --> 00:34:42,970
+أن Alpha من ZN إلى ZM is a function defined by
+
+310
+00:34:47,820 --> 00:34:56,500
+Alpha of S مثلا ال S موجودة وين؟ هنا يبقى هذا
+
+311
+00:34:56,500 --> 00:35:08,500
+الكلام بده يساوي SR modulo N مرة
+
+312
+00:35:08,500 --> 00:35:13,820
+تانيةأنا خدت R موجودة في ال UN في ال code domain
+
+313
+00:35:13,820 --> 00:35:18,460
+هذا ال element بدي أثبت أنه له أصل هنا إيش يعني له
+
+314
+00:35:18,460 --> 00:35:23,600
+أصل هنا يعني لازم ألاقي atomorphism في ال
+
+315
+00:35:23,600 --> 00:35:29,100
+atomorphism لاجي بحيث ال R يكون صورة لمين صورة
+
+316
+00:35:29,100 --> 00:35:35,970
+لهذه ال function يبقى بتروح أخلقأتومورفزيوم هنا له
+
+317
+00:35:35,970 --> 00:35:41,550
+علاقة بالـ R هذه فاجينا نعرف فانكشن Alpha من Z إلى
+
+318
+00:35:41,550 --> 00:35:47,090
+N Z N نعرفها بالتالي Alpha لو أثرت على ال S بتساوي
+
+319
+00:35:47,090 --> 00:35:53,830
+ال SR modulo N تمام؟ بدنا نيجي نشوف هل هذه one to
+
+320
+00:35:53,830 --> 00:35:59,950
+one؟and unto وهل هي isomorphism ان تم ذلك يبقى هذه
+
+321
+00:35:59,950 --> 00:36:06,830
+صارت atomorphism الان بدنا نروح نثبت ان ال alpha
+
+322
+00:36:06,830 --> 00:36:13,810
+هذه is one to one كويس
+
+323
+00:36:14,530 --> 00:36:21,130
+الان مشان هيك بتروح اخد صورتين متساويتين يبقى
+
+324
+00:36:21,130 --> 00:36:28,890
+هقوله assume افترض انه alpha طبعا هذا يا شباب لكل
+
+325
+00:36:28,890 --> 00:36:35,230
+ال S اللي موجودة في ZN مشان نقولش ال S هذي من وين
+
+326
+00:36:35,230 --> 00:36:39,980
+جيبناهاهذه Alpha of S يساوي S R موضوعين لكل S
+
+327
+00:36:39,980 --> 00:36:45,440
+الموجودة في ZM الان انا ادعي ان Alpha is one to
+
+328
+00:36:45,440 --> 00:36:50,440
+one فبدي اثبت صحة هذا الكلام فقلنا افترض ان Alpha
+
+329
+00:36:50,440 --> 00:36:59,120
+of S1 يساوي Alpha of S2بدي احاول اثبت ان ال S1 بدى
+
+330
+00:36:59,120 --> 00:37:09,480
+يساوي S2 هذا معناه ايش alpha of S1 يعني S1R modulo
+
+331
+00:37:09,480 --> 00:37:18,040
+N بدى يساوي S2R modulo N ايش رأيك بدي اعملها
+
+332
+00:37:18,040 --> 00:37:24,150
+معادلة صفريةجابت داجي هذا ع الشجة التانية بإشارة
+
+333
+00:37:24,150 --> 00:37:32,990
+سالب يعني بقدر أقول S1 ناقص S2 أخدت R عامل مشترك
+
+334
+00:37:32,990 --> 00:37:38,930
+موديله N بده ساوي مين؟ بده ساوي Zero يعني كأني
+
+335
+00:37:38,930 --> 00:37:43,570
+نجلت هذه ع الشجة التانية و أخدت R من الطرفين عامل
+
+336
+00:37:43,570 --> 00:37:49,970
+مشترك الآن الـR أين موجود يا شباب؟ الها معكس ولا
+
+337
+00:37:49,970 --> 00:37:57,380
+لا؟ممتاز جدا يبقى هنا باجي بقوله since R موجودة في
+
+338
+00:37:57,380 --> 00:38:06,080
+ال UN we have ان ال R inverse موجودة في ال UN ايش
+
+339
+00:38:06,080 --> 00:38:11,200
+رايك المعادلة هذي بدي اضربها في R inverse هذي بدي
+
+340
+00:38:11,200 --> 00:38:19,900
+اسميها مثلا star يبقى بداجي اقوله multiply multi
+
+341
+00:38:22,080 --> 00:38:32,200
+ply star by R inverse we get لو ضربنا هنا في R
+
+342
+00:38:32,200 --> 00:38:40,920
+inverse بتروح معاها S واحد ناقص S اتنين موديولو N
+
+343
+00:38:40,920 --> 00:38:47,300
+بده يساوي Zero في R inverse اللي هو من من Zeroطيب
+
+344
+00:38:47,300 --> 00:38:54,780
+هذه بقدر افكها و احولها الى S1 modulo N بده يساوي
+
+345
+00:38:54,780 --> 00:39:04,720
+ال S2 modulo N يبقى هذا معناه ان ال S1 هي نفس ال
+
+346
+00:39:04,720 --> 00:39:13,440
+S2طبعا يبقى هك اثبت ان ال alpha is one to one بدنا
+
+347
+00:39:13,440 --> 00:39:25,640
+نثبت ان ال alpha is on الان
+
+348
+00:39:25,640 --> 00:39:33,480
+ال alpha is on هو ال
+
+349
+00:39:33,480 --> 00:39:41,790
+alpha من وين لوينمن ZN إلى Z وانا أخدت هنا S
+
+350
+00:39:41,790 --> 00:39:50,450
+موجودة في ZN يبقى باجي بقوله F ال S موجودة في ZN
+
+351
+00:39:50,450 --> 00:39:53,710
+then ال S تساوي
+
+352
+00:39:56,350 --> 00:40:08,010
+عشان رايك بقدر اكتبها هذه S مثلا في ال R inverse R
+
+353
+00:40:08,010 --> 00:40:18,410
+منفع الله مانفعش ايه انا السما عندي لسه بجمعش كويس
+
+354
+00:40:18,410 --> 00:40:22,370
+حتى اللحظة علي صوتك عشرين ايه
+
+355
+00:40:29,070 --> 00:40:36,890
+ممتاز لكن احنا بنشغل داخل مين هذا الكلام ورا in z
+
+356
+00:40:36,890 --> 00:40:42,210
+in بس يعني احنا بنشغل داخل دي اللي عناصر برا ماليش
+
+357
+00:40:42,210 --> 00:40:46,210
+علاقة فيها يعني علاقتي مع ال zero والواحد والاتنين
+
+358
+00:40:46,210 --> 00:40:57,910
+لغتي التسعةيبقى S1 تساوي S2 داخل Z10 يبقى
+
+359
+00:40:57,910 --> 00:41:08,730
+الـ S يساوي SR inverse Rطيب هذه ال S أنا ماخدها في
+
+360
+00:41:08,730 --> 00:41:17,130
+ZN يعني ال S modulo N تساوي ال S R inverse R كذلك
+
+361
+00:41:17,130 --> 00:41:24,930
+modulo N يعني هذه modulo N وهنا لو حطيت modulo N
+
+362
+00:41:24,930 --> 00:41:31,090
+مش مشكلةطيب إيش رأيك في SR inverse بدي أشيلها و
+
+363
+00:41:31,090 --> 00:41:38,350
+أكتب بدالها element 10 لو جيت كتبت بدالها S1R
+
+364
+00:41:38,350 --> 00:41:46,050
+modulo N ايوه
+
+365
+00:41:46,050 --> 00:41:51,510
+احنا بأي وسيلة رياضية بتحاول تثبت ان ال function
+
+366
+00:41:51,510 --> 00:41:57,070
+اللي عندك is on 2تمام؟ بدك تشتغل شغل صحيح ماحدش
+
+367
+00:41:57,070 --> 00:42:02,370
+يقدر يمسك عليك فيه غلطة ايوة اعلي
+
+368
+00:42:02,370 --> 00:42:09,490
+صوتك مش هنسمع تعالى شوف هنا شوف ايش بتقول بالظبط
+
+369
+00:42:09,490 --> 00:42:17,710
+اسمع يا شباب ايش بيقول اه احنا بدنا نوصل للرفض
+
+370
+00:42:17,710 --> 00:42:23,730
+الآن اقعد هتقولك ايش بيقولأنا قلت بس انت مااخدتش
+
+371
+00:42:23,730 --> 00:42:29,170
+بالك انا الأن ايش بدي أثبت بدي أثبت ان T is onto
+
+372
+00:42:30,060 --> 00:42:37,120
+قلت لك خد R موجود في UN بدي احاول اخلق atomorphism
+
+373
+00:42:37,120 --> 00:42:44,560
+في الـ set اللي عندنا هذه بحيث يكون صورة لل R اللي
+
+374
+00:42:44,560 --> 00:42:48,900
+انا اخدته هذا كل الفكرة في الموضوع تمام فروحت قلت
+
+375
+00:42:48,900 --> 00:42:53,420
+اعرف function بالشكل اللي عندنا هذا و بدور هل ال
+
+376
+00:42:53,420 --> 00:42:58,220
+function هذه atomorphism ولا لأ حتى هذه اللحظة لم
+
+377
+00:42:58,220 --> 00:43:03,660
+اثبت انها atomorphismمظبوط واذا طلعت atomorphism
+
+378
+00:43:03,660 --> 00:43:07,740
+بدي بيجيلك ان صورتها R اللى عندنا وبالتالي يكون
+
+379
+00:43:07,740 --> 00:43:13,280
+حلنا المشكلة واضحة تمام واضحة يا شباب هيك طيب يبقى
+
+380
+00:43:13,280 --> 00:43:17,680
+انا اخدت S موجودة في Z ان ال S بقدر اكتبها SR
+
+381
+00:43:17,680 --> 00:43:23,570
+inverse R modulo N عادي جداماعناش مشكلة طب ال S في
+
+382
+00:43:23,570 --> 00:43:31,130
+ال R inverse بدي أسميها S1R modulo N أليست هذه هي
+
+383
+00:43:31,130 --> 00:43:37,910
+Alpha of S1مش هي ال alpha of S يساوي SR modulo N
+
+384
+00:43:37,910 --> 00:43:47,130
+طلعناها S1R يبقى alpha of S1 يبقى صار ال element S
+
+385
+00:43:47,130 --> 00:43:55,250
+اللي أخدته في Z in لجتله أصل اسمه ايش اسمه S1 يبقى
+
+386
+00:43:55,250 --> 00:43:59,030
+ال alpha انتوا ولا لا يبقى ال alpha انتوا يبقى
+
+387
+00:43:59,030 --> 00:44:02,750
+أثبت الآن ان ال alpha اللي أخدتها دي one to one
+
+388
+00:44:02,750 --> 00:44:07,970
+and انتوا شو ضايل عندىأثبت أنه بتخدم خاصية ال
+
+389
+00:44:07,970 --> 00:44:14,790
+isomorphism لذلك بتروح أخد alpha of مثلا a زائد ال
+
+390
+00:44:14,790 --> 00:44:24,050
+.. او S1 زائد S2 خليها نفس الرمز خليها S1 و S2 S1
+
+391
+00:44:24,050 --> 00:44:31,430
+زائد S2 بده يساوي ال
+
+392
+00:44:31,430 --> 00:44:38,860
+S1 و ال S2 أرقام هذهمش هيك اه يعني بقدر اخدهم زي
+
+393
+00:44:38,860 --> 00:44:46,820
+ما بدي او خلينا بلاشي نغلط شوية هذه قولنا is on to
+
+394
+00:44:46,820 --> 00:44:53,940
+خلصنا منها S1 و S2 مظبوط حسب ال definition هذه
+
+395
+00:44:53,940 --> 00:45:05,740
+بدها تساوي S1 زي S2 في R modulo Nيعني هذه بقدر
+
+396
+00:45:05,740 --> 00:45:18,760
+اقول S1R زي S2R كله modulo N او ان شئتم فقولوا S1R
+
+397
+00:45:18,760 --> 00:45:30,060
+modulo N S2R modulo Nهلأيست هذه اللي هو Alpha of S
+
+398
+00:45:30,060 --> 00:45:36,160
+واحد وهذه Alpha of S اتنى؟ يبقى بناء عليها صارت
+
+399
+00:45:36,160 --> 00:45:42,600
+هذه ايش؟ صارت Atomorphism لأنها من ال group إلى
+
+400
+00:45:42,600 --> 00:45:51,860
+نفسها يبقى هنا Sir Alpha is an Atomorphism
+
+401
+00:45:57,050 --> 00:46:03,470
+يبقى حتى لأن خلقنا atomorphism موجود عندنا الان لو
+
+402
+00:46:03,470 --> 00:46:11,690
+جيت now لو أخدت alpha of S اللي هى مين قلنا عليها
+
+403
+00:46:11,690 --> 00:46:19,070
+اللي هى alpha of S اللي هى ال S R modulo N هذا بده
+
+404
+00:46:19,070 --> 00:46:26,340
+يعطيلكالـ alpha of S مش S موجود في ZN يعني هذا
+
+405
+00:46:26,340 --> 00:46:34,840
+الكلام بده يساوي S في alpha of one مظبوط؟
+
+406
+00:46:36,980 --> 00:46:42,940
+S α of خمسة يعني خمسة .. اي واحد واحد واحد أثر
+
+407
+00:46:42,940 --> 00:46:47,760
+alpha تأثر عليهم كلهم يبقى الرقم نفسه في alpha of
+
+408
+00:46:47,760 --> 00:46:55,140
+one بده يساوي مين؟ بده يساوي ال S R modulo M بال
+
+409
+00:46:55,140 --> 00:47:01,160
+left cancellation law شط بالأيسر يبقى alpha of one
+
+410
+00:47:01,160 --> 00:47:09,870
+بده يساوي ال R modulo Nهذه موجودة في UN ولا لا؟
+
+411
+00:47:09,870 --> 00:47:15,450
+موجودة في UN اللي احنا أخدناها من البداية وانراحت
+
+412
+00:47:15,450 --> 00:47:23,390
+تي وزنت أخدنا R موجودة في UN واحنا أخدنا T وانراحت
+
+413
+00:47:23,390 --> 00:47:30,070
+T of Alpha يسوى من؟ Alpha of one يبقى صار ال R
+
+414
+00:47:30,070 --> 00:47:37,870
+modulo N ال R modulo Nاللي هي تساوي Alpha of one
+
+415
+00:47:37,870 --> 00:47:44,230
+والـ Alpha of one هي T of Alpha هذا بده يعطيلك ان
+
+416
+00:47:44,230 --> 00:47:49,950
+T is onto يبقى
+
+417
+00:47:49,950 --> 00:47:55,950
+كلها اللف لفة مشان نوصل ان R هي عبارة عن T of
+
+418
+00:47:55,950 --> 00:48:02,030
+Alpha وبالتالي T of Alpha is onto خلصنا؟ما خلصناش،
+
+419
+00:48:02,030 --> 00:48:08,090
+ضالت خاصية الـ isomorphism إذا بدي أخد تأثير الـ T
+
+420
+00:48:08,090 --> 00:48:11,990
+على حاصل ضرب two permutations اللي هي او two
+
+421
+00:48:11,990 --> 00:48:17,730
+automorphisms Alpha و Beta يبقى بدي أخد finally
+
+422
+00:48:17,730 --> 00:48:21,010
+بدي
+
+423
+00:48:21,010 --> 00:48:27,610
+أخد T of Alpha Beta أو Beta Alpha سيئة Beta Alpha
+
+424
+00:48:28,150 --> 00:48:31,850
+اعتقد الكتاب ماخد alpha beta انا بدي اخد beta
+
+425
+00:48:31,850 --> 00:48:35,990
+alpha يعني على كل الأمرين الكلام صحيح لو اخدت
+
+426
+00:48:35,990 --> 00:48:40,470
+alpha beta ولا beta alpha بتفرقش عنها طيب هذا
+
+427
+00:48:40,470 --> 00:48:47,710
+الكلام بده يساويالان ايش بيقولي T لما تأثر على ال
+
+428
+00:48:47,710 --> 00:48:51,790
+.. وين راحت؟ T of Alpha بديه يساوي Alpha of one
+
+429
+00:48:51,790 --> 00:49:01,650
+يبقى هذا بديه يساوي Beta Alpha كله of one طيب
+
+430
+00:49:01,650 --> 00:49:08,990
+هذا الكلام بديه يساوي Beta في Alpha of one
+
+431
+00:49:12,500 --> 00:49:19,480
+طب alpha of one وين موجودة؟ وين موجودة؟ في UN
+
+432
+00:49:19,480 --> 00:49:26,020
+مظبوط ايه alpha of one حطناها موجودة وين؟ في UN
+
+433
+00:49:26,020 --> 00:49:34,280
+وين كتبناها؟ alpha وين راحت؟المهم كتبنا هاية Alpha
+
+434
+00:49:34,280 --> 00:49:38,540
+of one موجودة في UN يبقى Alpha of one لو قلنا مثلا
+
+435
+00:49:38,540 --> 00:49:44,140
+U عشرة يبقى يا واحد يا تلاتة يا سبعة يا تسعة وهكذا
+
+436
+00:49:44,140 --> 00:49:50,850
+قيص عليها الباقى إذا هذه هاهاهتساوي واحد زائد واحد
+
+437
+00:49:50,850 --> 00:49:58,390
+زائد واحد جديش Alpha of one times مظبوط يعني هذه
+
+438
+00:49:58,390 --> 00:50:05,550
+بدها تساوي Beta of واحد زائد واحد زائد واحد كام
+
+439
+00:50:05,550 --> 00:50:14,430
+مرة هذا كله Alpha of one times يعني لو كان Alpha
+
+440
+00:50:14,430 --> 00:50:21,550
+of one يساوي تلتةلو كانAlpha of one بده يسوى تلاتة
+
+441
+00:50:21,550 --> 00:50:27,450
+يبقى يصير واحد زي واحد زي واحد فقط لا غير طبعا طب
+
+442
+00:50:27,450 --> 00:50:33,510
+لو كان سبعة بدي اكتبها سبعة من المرات يعني قداش
+
+443
+00:50:33,510 --> 00:50:37,710
+بتكون النتيجة بدي اكرهها يعني Alpha of one times
+
+444
+00:50:37,710 --> 00:50:42,250
+ان كانت سبعة بدي اكررها سبعة مرات ان كانت تلاتة
+
+445
+00:50:42,250 --> 00:50:45,330
+تلات مرات ان كانت تسعة تسعة مرات ان كانت احداشر
+
+446
+00:50:45,330 --> 00:50:51,240
+احداشر مرة و هكذاطيب كويس هذا الكلام بده يشاوي
+
+447
+00:50:51,240 --> 00:51:00,460
+اللي هو beta of one زائد beta of one زائد زائد
+
+448
+00:51:00,460 --> 00:51:10,460
+beta of one هذا alpha of one كمان times اذا
+
+449
+00:51:10,460 --> 00:51:19,030
+هذا الكلام بده يشاوي اكمر هدولالفا of one و هدولة
+
+450
+00:51:19,030 --> 00:51:25,270
+كم واحدة في beta one يبقى هذا بده يساوي beta of
+
+451
+00:51:25,270 --> 00:51:33,230
+one في alpha of one beta of one امكررة alpha one
+
+452
+00:51:33,230 --> 00:51:42,170
+من المرات طيب ال beta of one ال beta of one أليس
+
+453
+00:51:42,170 --> 00:51:51,360
+تية T of betaيبقى هذه هي T of Beta والتانية هي T
+
+454
+00:51:51,360 --> 00:51:57,500
+of Alpha يبقى أثبتنا له أن T of Beta Alpha هي T
+
+455
+00:51:57,500 --> 00:52:02,860
+Beta Alpha لو روحت للكتاب هيكون جلب الوضع أخد لك T
+
+456
+00:52:02,860 --> 00:52:08,130
+Alpha Beta وهنا تقول لك T Alpha T فماعناش مشكلةبس
+
+457
+00:52:08,130 --> 00:52:10,830
+بدل ما اقول لك ان alpha of one times بقول لك beta
+
+458
+00:52:10,830 --> 00:52:15,870
+of one time اذا لا مشكلة انا اتعمد اجيبك بشكل هذا
+
+459
+00:52:15,870 --> 00:52:20,250
+حتى تتعرف انه ليس بالضرورة قرآن كريم لكن احنا
+
+460
+00:52:20,250 --> 00:52:30,070
+فهمنا هذا الكلام يبقى .. يبقى بناء عليه so T is an
+
+461
+00:52:30,070 --> 00:52:37,470
+isomorphism هذا بدي اعطيلك ان ال atomorphismلزد ان
+
+462
+00:52:37,470 --> 00:52:43,230
+ايزو مارفك ل يو ان من الآن فصاعدا
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..961c9bf40284b8a59cfbbd63b06cd1292d6324e1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/dzZQ4_29NT8_raw.srt
@@ -0,0 +1,1792 @@
+1
+00:00:21,380 --> 00:00:26,260
+بسم الله الرحمن الرحيم المرة الماضية بدأنا نناقش
+
+2
+00:00:26,260 --> 00:00:30,500
+الأسئلة المتعلقة بشبتر ستة وهو ال isomorphism
+
+3
+00:00:30,500 --> 00:00:36,220
+ووقفنا عند سؤال رقم تسعة عشر سؤال تسعة عشر مختصر
+
+4
+00:00:36,220 --> 00:00:41,400
+بيقول في عند two isomorphism واحد اسمه في والتاني
+
+5
+00:00:41,400 --> 00:00:47,620
+اسمه جامع من اللي هو ال cycle group generated by a
+
+6
+00:00:47,620 --> 00:00:54,090
+إلى أي group أخرىوعندى معلومة ان في او ا تساوي
+
+7
+00:00:54,090 --> 00:00:59,750
+جامعة او ا قاللي اثبت ان في تساوي ا تساوي جامعة
+
+8
+00:01:00,460 --> 00:01:05,340
+بنقوله بسيطة بنفكر فى الموضوع الآن فاى وجامع لما
+
+9
+00:01:05,340 --> 00:01:10,120
+يؤثروا على uniform subgroup generated by a معناته
+
+10
+00:01:10,120 --> 00:01:14,740
+a مرفوع لأس مظبوط لإن ده ال cycle group معناته ال
+
+11
+00:01:14,740 --> 00:01:19,200
+a و ال a و ال a تربيع و ال a تكعيب و هو إلى آخرى
+
+12
+00:01:19,200 --> 00:01:29,180
+يبقى مناء عليه عندنا احنا هنا ايه اللي هومثلا ال a
+
+13
+00:01:29,180 --> 00:01:33,720
+to the power of k موجودة في ال sub group generated
+
+14
+00:01:33,720 --> 00:01:40,520
+by a معناته كل من فاي وجامع ستؤثر على من؟ على هذا
+
+15
+00:01:40,520 --> 00:01:50,160
+العنصر هذا بده يعطينا انه فاي a of k أبصر قديش بده
+
+16
+00:01:50,160 --> 00:01:56,390
+يساوي الله أعلم تمامطب بدي بقول هذا الكلام بده
+
+17
+00:01:56,390 --> 00:02:06,600
+يساوي اللي هو Phi of A كله to the power Kof a كله
+
+18
+00:02:06,600 --> 00:02:11,000
+to the power of k وهذه نظرية السابقة أخدناها
+
+19
+00:02:11,000 --> 00:02:17,560
+وبرهناها لكن في معطيات عندى بتقولي في of a تسوى
+
+20
+00:02:17,560 --> 00:02:23,080
+جامعة of a إذا بقدر أشيل اللي هو في of a و أحط
+
+21
+00:02:23,080 --> 00:02:28,980
+بدلها جامعة of a يبقى هذا الكلام بدي يعطيني جامعة
+
+22
+00:02:28,980 --> 00:02:37,100
+of a كله to the power of kيبقى أصبح اندي في of ا ك
+
+23
+00:02:37,100 --> 00:02:45,340
+بده ساوي جامع of a كله to the power كل الكي هذه
+
+24
+00:02:45,340 --> 00:02:54,910
+ممكن تنزل هنا يبقى جامع كله لمن؟ لل a اص كييبقى
+
+25
+00:02:54,910 --> 00:02:59,930
+معنى هذا الكلام إنه تأثير في على أي element في ال
+
+26
+00:02:59,930 --> 00:03:06,050
+group هذي يسوى تأثير جامعة على أي element موجود في
+
+27
+00:03:06,050 --> 00:03:11,810
+ال subgroup generated by A لكن بقدرش أقول التسوي
+
+28
+00:03:11,810 --> 00:03:17,710
+حاصل نتيجة لهذا التسوي لأن A أنصر محدد هو اللي ولد
+
+29
+00:03:17,710 --> 00:03:21,300
+ال groupلكن عندما أقول a to the power of k أي
+
+30
+00:03:21,300 --> 00:03:26,120
+element أخدت من الجروب عشوائيا من مكان يكون إذا في
+
+31
+00:03:26,120 --> 00:03:30,440
+عند أي element موجود في الجروب ده تساوي جامع عند
+
+32
+00:03:30,440 --> 00:03:34,680
+نفس ال element موجود في الجروب هذا معناته أن في
+
+33
+00:03:34,680 --> 00:03:41,510
+تساوي جامع وهو المطلوبيعني كل الفكرة كانت تبدل
+
+34
+00:03:41,510 --> 00:03:47,010
+تأثير بفاي على أي element من g بتأثير جامعه على أي
+
+35
+00:03:47,010 --> 00:03:52,510
+element من g هذا كان سؤال تسعة عشر سؤال عشرين
+
+36
+00:03:52,510 --> 00:04:05,450
+بيقول لي سؤال عشرين بيقول لي فاي من z خمسين إلى z
+
+37
+00:04:05,450 --> 00:04:15,020
+خمسينعبارة عن اتومورفزم هذا اتومورفزم وفي نفس
+
+38
+00:04:15,020 --> 00:04:23,620
+الوقت عندنا في of 11 يسوى تلتاشر وقال لي determine
+
+39
+00:04:23,620 --> 00:04:30,960
+formula for في of x find في of x بدنا نعرف ايش
+
+40
+00:04:30,960 --> 00:04:33,740
+شكلها في هذه الحالة
+
+41
+00:04:37,840 --> 00:04:44,420
+أنا عندي في من z50 إلى z50 عبارة عن atomorphism
+
+42
+00:04:44,420 --> 00:04:49,460
+عندي ال atomorphism في تأثيره على ال element 11
+
+43
+00:04:49,460 --> 00:04:55,260
+اللي موجود في z50 بده يسوى 13 اللي موجودة في z50
+
+44
+00:04:55,260 --> 00:05:00,690
+كذلك قال لي هاتلي الصيغةلأ مين للـautomorphism في
+
+45
+00:05:00,690 --> 00:05:06,890
+of X بدي أعرف في of X in general قداش بيساوي حتى
+
+46
+00:05:06,890 --> 00:05:13,350
+يكون في of 11 بدي يساوي مين؟ بدي يساوي 13 طيب بدي
+
+47
+00:05:13,350 --> 00:05:18,730
+أحاول أستفيد من المعطى هذا في حل المسألة حتى أعرف
+
+48
+00:05:18,730 --> 00:05:24,210
+أقدر أجيب من في of 50 حد فكر في حل السؤال وجابه
+
+49
+00:05:24,210 --> 00:05:27,950
+يعني هك؟ ولا واحد؟
+
+50
+00:05:31,180 --> 00:05:37,900
+كيف؟ ماوصلناش لنا نتيجة الساوة
+
+51
+00:05:37,900 --> 00:05:45,680
+جداش؟ ليش يعني X زي 2؟لا بدك تشغل رياضة صح انت
+
+52
+00:05:45,680 --> 00:05:50,940
+بتشغل في Z50 و Z50 ال operation عليها اللي هي
+
+53
+00:05:50,940 --> 00:05:56,100
+الجامعة طبعا طيب خلي بالك هنا بنحاول نستفيد من
+
+54
+00:05:56,100 --> 00:05:59,300
+المعلومات اللي عندنا الحين يا جماعة بقى انا لما
+
+55
+00:05:59,300 --> 00:06:07,170
+اجي اقول ما يأتيإن الـ Phi of 11 بده يسوى تلتاشر
+
+56
+00:06:07,170 --> 00:06:12,050
+بقدر اكتب هذه المعادلة بالصيغة تانية هذه عبارة عن
+
+57
+00:06:12,050 --> 00:06:15,270
+ايش Phi of واحد زيادة واحد زيادة واحد زيادة واحد
+
+58
+00:06:15,270 --> 00:06:19,970
+احداشر مرة Phi atomorphism حتى تدخل على كل واحد
+
+59
+00:06:19,970 --> 00:06:23,230
+فيهم يبقى Phi of واحد Phi of واحد Phi .. كم مرة
+
+60
+00:06:23,230 --> 00:06:29,180
+يعني هذا كأن احداش مضروبة في Phi of واحديبقى هذا
+
+61
+00:06:29,180 --> 00:06:39,440
+معناته ان 11 في 5 of 1 يساوي 13 تمام؟ اذا انا هنا
+
+62
+00:06:39,440 --> 00:06:47,120
+5 of 11 يساوي 13 جدرت اكتبها بدلالة main 5 of 1 لو
+
+63
+00:06:47,120 --> 00:06:53,120
+عرفت قداش ال 5 of 1 بيتم المطلوب لو عرفت قداش
+
+64
+00:06:53,120 --> 00:06:58,480
+القيمة العددية ل 5 of 1 بتم المطلوب بمعنى اخرلو
+
+65
+00:06:58,480 --> 00:07:03,760
+قدرت تخلص من الاحداش هذي بيكون اه حصلنا على five
+
+66
+00:07:03,760 --> 00:07:07,140
+one هيجي واحد مثلا يقول انت بيكسب على five واحد
+
+67
+00:07:07,760 --> 00:07:10,400
+وأقول لك شو هذه تلتاشة على أحداشة هذا rational
+
+68
+00:07:10,400 --> 00:07:13,740
+number احنا بنشتغل في rational ماعناهش rational
+
+69
+00:07:13,740 --> 00:07:17,600
+مرة انا ماعنديش إلا زية خمسين يبقى هذا كلام فارغ
+
+70
+00:07:17,600 --> 00:07:24,140
+لكن بدي أخلق هنا رقم الرقم يجسم على الأحداشة
+
+71
+00:07:24,140 --> 00:07:28,100
+وعملتلكم مرة في ال subgroups إذا كنتم بضروري يبقى
+
+72
+00:07:28,100 --> 00:07:35,120
+بدي أفكر بنفس المفهوم بمعناه أخر أنا بدي أدور على
+
+73
+00:07:35,120 --> 00:07:42,830
+رقمأضربه في إحداش يطين الواحد الصحيح يبقى هنا
+
+74
+00:07:42,830 --> 00:07:48,270
+أفترض أن
+
+75
+00:07:48,270 --> 00:07:58,630
+هناك ن في حيث أن ال H في ال N يساوي الواحد الصحيح
+
+76
+00:08:01,880 --> 00:08:05,720
+افترض ان عندي N بحيث 11N موديولو خمسين افترض ان
+
+77
+00:08:05,720 --> 00:08:09,860
+عندي N بحيث 11N موديولو
+
+78
+00:08:09,860 --> 00:08:15,900
+خمسين افترض ان عندي N بحيث 11N موديولو خمسين افترض
+
+79
+00:08:15,900 --> 00:08:19,280
+ان عندي N بحيث 11N موديولو خمسين افترض ان عندي N
+
+80
+00:08:19,280 --> 00:08:29,140
+بحيث 11N موديولو خمسين افترض ان عندي N بحيث
+
+81
+00:08:29,790 --> 00:08:34,850
+إذا قدرت اتخلص من ال 11 اللي عنها دي بكون حصلت على
+
+82
+00:08:34,850 --> 00:08:41,150
+n وبالتالي بكون جبت الرقم اللي لو ضربته في 11 بطلع
+
+83
+00:08:41,150 --> 00:08:46,110
+واحد صحيح بضل عندي main phi of one وبالتالي جبت
+
+84
+00:08:47,570 --> 00:08:54,090
+بالتالي سهل إيجاد Phi of X لأن Phi of X هي X في
+
+85
+00:08:54,090 --> 00:08:59,710
+Phi of 1 يعني كل مشكلة زي ما كان في الجزء النظري
+
+86
+00:08:59,710 --> 00:09:04,450
+بكنا نروح نجيب Alpha و ندور عليها لف لف لما نطلع
+
+87
+00:09:04,450 --> 00:09:10,060
+نجيب قد إيش قيمتها وهذا المقصود عندنا هناطيب انا
+
+88
+00:09:10,060 --> 00:09:15,480
+بدى أجيب رقم بدل هذا الرقم يكون يجسم على ال 11
+
+89
+00:09:15,480 --> 00:09:23,220
+بحيث نجيب قيمة M الان انا ايش عندي عندي 11 N
+
+90
+00:09:23,220 --> 00:09:31,640
+modulo 50 بده يساوي ال 1 modulo 50 هل بنقدر نجيب
+
+91
+00:09:31,640 --> 00:09:37,740
+رقم يكافئ ال 1 اه بنقدر نحط خمسينات عليه زى ما بدك
+
+92
+00:09:38,090 --> 00:09:42,790
+زائد خمسين زائد مية زائد مية و خمسين زائد متين صح
+
+93
+00:09:42,790 --> 00:09:46,310
+ولا لا بس كله بيقسمش على الأحداث اللي كان فيها
+
+94
+00:09:46,310 --> 00:09:51,890
+عندي رقم لو حطيته سهل جدا بدل ما اضيف خمسين بدي
+
+95
+00:09:51,890 --> 00:09:57,900
+اضيف سالب خمسينتينبنفع ولا ماينفعش؟ بنفع يا بضيف
+
+96
+00:09:57,900 --> 00:10:02,180
+خمسين بالمود يا بضيف خمسين بالسالب يبقى هذا لو ضفت
+
+97
+00:10:02,180 --> 00:10:08,080
+عليه مية بيظل جداش سالب تسعة وتسعين إذا سالب تسعة
+
+98
+00:10:08,080 --> 00:10:11,120
+وتسعين بتكسب على أحداش وبالتالي اتخلص من الأحداش
+
+99
+00:10:11,120 --> 00:10:17,560
+وحصلت على مية حصلت على N يبقى الرقم المكافئ هذا
+
+100
+00:10:17,560 --> 00:10:22,140
+سالب تسعة وتسعين موديولو خمسين
+
+101
+00:10:24,730 --> 00:10:31,310
+تمام طيب الان هذا بيقسم على ال 11 لو قسمت كله على
+
+102
+00:10:31,310 --> 00:10:39,890
+ال 11 بيصير ال N modulo خمسين يساوي سالب تسعة
+
+103
+00:10:39,890 --> 00:10:46,530
+modulo خمسين طب انا ماعنديش سالب تسعة modulo خمسين
+
+104
+00:10:46,530 --> 00:10:52,020
+انا عندي ارقام مجمعةضيف عليها خمسين يبقى هذه العدد
+
+105
+00:10:52,020 --> 00:10:58,420
+المكافئ لها هو مين هو واحد واربعين موديولو خمسين
+
+106
+00:10:58,420 --> 00:11:04,500
+يبقى الآن هذا يا شباب لو كانت واحد واربعين
+
+107
+00:11:04,500 --> 00:11:09,180
+وضربناها في الاحداشر اللي عندنا بضيع وبحصل على مين
+
+108
+00:11:09,180 --> 00:11:14,660
+على five of واحد وبكون خلصنا القصة هذه تمام يبقى
+
+109
+00:11:14,660 --> 00:11:22,090
+الآنبجي بقوله احداشر five of one بده يساوي تلتاشر
+
+110
+00:11:22,090 --> 00:11:29,030
+implies انه واحد واربعين في احداشر في five of واحد
+
+111
+00:11:29,030 --> 00:11:34,750
+طبعا كله module وخمسين هذا بده يساوي اللي هو واحد
+
+112
+00:11:34,750 --> 00:11:41,850
+واربعين في تلتاشر module وخمسين طب لو ضربت واحد
+
+113
+00:11:41,850 --> 00:11:46,120
+واربعين في احداشر ايش بتعطيك هي واحد واربعينفي
+
+114
+00:11:46,120 --> 00:11:51,480
+احداشر بواحد واربعين وواحد واربعين اربعة خمسة وحدة
+
+115
+00:11:51,480 --> 00:11:56,120
+اربعمية وواحد وخمسين شيل من الخمسينات مضال قداشر
+
+116
+00:11:56,120 --> 00:12:00,160
+في five of واحد يبقى five of واحد يبقى صار في
+
+117
+00:12:00,160 --> 00:12:05,200
+الصرف الشمال اللي عندنا five of one اللي انا بدور
+
+118
+00:12:05,200 --> 00:12:09,720
+عليه الان بنفس الطريقة بنضرب اللي هو الواحد
+
+119
+00:12:09,720 --> 00:12:15,560
+واربعين في تلاتاشروشوف ايش بتعطينا يبقى لو جيت
+
+120
+00:12:15,560 --> 00:12:21,420
+واحد واربعين في تلتاش تلاتة و تلاتة في اربع باطناش
+
+121
+00:12:21,420 --> 00:12:26,700
+وهنا واحد واربعين هنا تلاتة تلاتة خمسمية و تلاتة و
+
+122
+00:12:26,700 --> 00:12:31,940
+تلاتين خمسمية و تلاتة و تلاتين شيل منها عشر
+
+123
+00:12:31,940 --> 00:12:38,670
+خمسينات بظل جدات بظل تلاتة و تلاتينفاي اف وان اللي
+
+124
+00:12:38,670 --> 00:12:43,430
+أنا بدور عليه هو الرقم تلاتة و تلاتين طيب قال لي
+
+125
+00:12:43,430 --> 00:12:49,930
+هاتلي formula لفاي اف اكس بقوله هنا فاي اف اكس اكس
+
+126
+00:12:49,930 --> 00:12:56,130
+هذا موجود وان في زد خمسين يعني رقم يبقى هذا الكلام
+
+127
+00:12:56,130 --> 00:13:03,900
+بده يساوي اكس في فاي اف وانيبقى هذا الكلام يساوي X
+
+128
+00:13:03,900 --> 00:13:09,900
+في جداش في تلاتة و تلاتين يبقى أصبحت Phi of X
+
+129
+00:13:09,900 --> 00:13:15,900
+يساوي تلاتة و تلاتين X بالشكل اللي عندنا هذا يبقى
+
+130
+00:13:15,900 --> 00:13:21,400
+هذا صيغة تبعت من؟ تبعت Phi اللي عندنا وليست كما
+
+131
+00:13:21,400 --> 00:13:25,340
+زعمت X زائد تلاتة و لا X زائد اتنين عمرها ما
+
+132
+00:13:25,340 --> 00:13:31,140
+هتجيبها ولا هتجيبهايبقى هذا سؤال 19 فكرته كويسة
+
+133
+00:13:31,140 --> 00:13:36,880
+ومتعلقة بالجزء النظري اللي شرحناه لكنا نحسب في
+
+134
+00:13:36,880 --> 00:13:45,270
+alpha of oneطيب هذا كان سؤال عشرين بعديها سؤال
+
+135
+00:13:45,270 --> 00:13:50,570
+اربع وعشرين approve or disapprove ان ال U عشرين
+
+136
+00:13:50,570 --> 00:13:56,990
+and ال U اربع وعشرين are isomorphic U عشرين و U
+
+137
+00:13:56,990 --> 00:14:04,850
+اربع وعشرين اه مش سامع تلاتة و تلاتين اكس اه مش
+
+138
+00:14:04,850 --> 00:14:11,490
+كتبين اكس اه تلاتة و تلاتين اكس كلام مظبوطيبقى هذا
+
+139
+00:14:11,490 --> 00:14:16,510
+الصيغة تبع ثمين تبعت الدالة السؤال اللي بعده بيقول
+
+140
+00:14:16,510 --> 00:14:21,170
+لي اللي هو السؤال قداش ستة وعشرين ولا كان قلنا ليه
+
+141
+00:14:21,170 --> 00:14:26,410
+سؤال اربعة وعشرين سؤال اربعة وعشرين سؤال اربعة
+
+142
+00:14:26,410 --> 00:14:33,930
+وعشرين بيقول ليه عشرين وليه اربعة وعشرين شوف ليه
+
+143
+00:14:33,930 --> 00:14:39,750
+هدول isomorphic ولا not isomorphic السؤال هوالـ U
+
+144
+00:14:39,750 --> 00:14:44,430
+عشرين هذه عبارة عن مين؟ عبارة عن واحد، اتنين،
+
+145
+00:14:44,430 --> 00:14:51,830
+تلاتة، اربع، خمسة، ستة، سبعة، تمانية، تسعة، عشرة،
+
+146
+00:14:51,830 --> 00:14:57,750
+احداش، تلاتاش، اربعتاش، خمستاش، ستاش، سبعتاش،
+
+147
+00:14:57,750 --> 00:15:04,070
+تسعتاش، تمام؟ وهذه اللي هي عبارة عن مين؟ اللي هي
+
+148
+00:15:04,070 --> 00:15:11,640
+عبارة عن الواحداتنين تلاتة اربعة خمسة ستة سابعة
+
+149
+00:15:11,640 --> 00:15:23,020
+تمانية تسعة عشرة احداش تلاتاش اربعتاش خمستاش ستاش
+
+150
+00:15:23,020 --> 00:15:31,900
+سبعتاش وهنا تمانتاش تسعتاش عشرين واحد وعشرين اتنين
+
+151
+00:15:31,900 --> 00:15:38,370
+وعشرين تلاتة وعشرينتلاتة و تلاتة و اتنين تمانية
+
+152
+00:15:38,370 --> 00:15:44,210
+تلاتة و تلاتة و اتنين تمان عناصر و تمان عناصر هل
+
+153
+00:15:44,210 --> 00:15:49,190
+اتنين هدول are isomorphic ولا لأ تعالى نشوف الان
+
+154
+00:15:49,190 --> 00:15:57,530
+لو جاتلي خمسة تربيع بواحد سبعة تربيعأحداش تربية
+
+155
+00:15:57,530 --> 00:16:03,310
+تلتاش تربية كل أي element من هدول تربية بيعطينا
+
+156
+00:16:03,310 --> 00:16:09,090
+main ال identity element يبقى هذه cyclic لأ not
+
+157
+00:16:09,090 --> 00:16:17,950
+cyclic هذا not cyclic because any
+
+158
+00:16:17,950 --> 00:16:25,170
+non identity element
+
+159
+00:16:27,880 --> 00:16:35,360
+has order اتنين كله حطول الأس اتنين بصيلة ال
+
+160
+00:16:35,360 --> 00:16:41,120
+identity نجي لهذه تلاتة و زيره بواحد تلاتة و أس
+
+161
+00:16:41,120 --> 00:16:48,400
+واحد بتلاتة تلاتة ربيع بتسعة تلاتة كيب سبعة و
+
+162
+00:16:48,400 --> 00:16:55,320
+عشرين تمام؟ يعني السبعة تلاتة أس أربع بواحد و
+
+163
+00:16:55,320 --> 00:17:01,290
+تمانينواحد و تمانين الهمان الواحد و هكذا يبقى
+
+164
+00:17:01,290 --> 00:17:06,170
+التلاتة مرتين تلاتة و Zero بواحد تلاتة اص واحد
+
+165
+00:17:06,170 --> 00:17:11,190
+بواحد تلاتة تربيه بتسعة تلاتة تكيب بسبعة و عشرين
+
+166
+00:17:11,190 --> 00:17:15,530
+تلاتة اص اربع بواحد و تمانين يبقى ال order لتلاتة
+
+167
+00:17:15,530 --> 00:17:22,070
+كدهاش اربعة مظبوط لكن هنا ال order لأي element
+
+168
+00:17:22,070 --> 00:17:28,040
+كدهاش اتنين يبقى اتنين are isomorphicطبعاً لأ يبقى
+
+169
+00:17:28,040 --> 00:17:34,380
+هدول هذه التلاتة
+
+170
+00:17:34,380 --> 00:17:43,820
+is an element of order أربعة هذه أي element of
+
+171
+00:17:43,820 --> 00:17:47,680
+order له ساوى اتنين يبقى اتنين are isomorphic لأ
+
+172
+00:17:47,680 --> 00:17:52,700
+يبقى هذا بدى يعطينا ان اليوم عشرينis not
+
+173
+00:17:52,700 --> 00:17:58,600
+isomorphic لـ U 24 يمكن نلاقيها الـ cyclic element
+
+174
+00:17:58,600 --> 00:18:04,380
+تانية الله أعلم أنا مش عارف قد يكون طيب هذا السؤال
+
+175
+00:18:04,380 --> 00:18:12,320
+اللي هو 24 بعد هيك عندنا سؤال 28 بيقول prove that
+
+176
+00:18:12,320 --> 00:18:21,700
+the group of equaterion سؤال 28 بيقول كيو اتثم
+
+177
+00:18:21,700 --> 00:18:29,680
+اثبت هذا الجروب انه ليس ايزو مورفك ل D4 يبقى هذا
+
+178
+00:18:29,680 --> 00:18:37,400
+الجروب ليس ايزو مورفك .. ليس ايزو مورفك لمن؟ لدى
+
+179
+00:18:37,400 --> 00:18:43,640
+دا هدر الجروب اللي هو D4 لماذا؟ الأعلى جروب
+
+180
+00:18:43,640 --> 00:18:47,780
+افيكواتريون ماشوفتهاش قبل هيك يبقى أول مرة
+
+181
+00:18:47,780 --> 00:18:55,540
+بينشوفهاإذاً لـ Group هدهها لـ Q8 اللي هي عناصرها
+
+182
+00:18:55,540 --> 00:19:04,640
+زائد أو ناقص I زائد أو ناقص J زائد أو ناقص K زائد
+
+183
+00:19:04,640 --> 00:19:12,650
+أو ناقص Lايش ال I و ال J و ال K و ال L هذا سؤال و
+
+184
+00:19:12,650 --> 00:19:18,550
+إيش علاقتهم أبعاد أول شيء الآن ال I هذه هي مصوفة
+
+185
+00:19:18,550 --> 00:19:23,810
+الوحدة من النظام هتنين في اتنين ناقص I هي مصوفة
+
+186
+00:19:23,810 --> 00:19:27,650
+الوحدة نظامها اتنين في اتنين بس مضروبة في مين سالب
+
+187
+00:19:27,650 --> 00:19:34,540
+واحد الآن ال Jمن خلاصة ان ال j في ال k بده يعطينا
+
+188
+00:19:34,540 --> 00:19:44,200
+ال L و يسوى ناقص k في j يعني لو جلبتهم بيعطيني نفس
+
+189
+00:19:44,200 --> 00:19:50,380
+النتيجة بس ب ا ب سالب واحد بنفس الطريقة لو جت
+
+190
+00:19:50,380 --> 00:19:57,300
+قلتلك ال k في ال L بده يسوى j و اللي هو بده يسوى
+
+191
+00:19:57,300 --> 00:20:08,100
+ناقص L في kو كذلك لو جينا ل L في J يبقى L في J بده
+
+192
+00:20:08,100 --> 00:20:16,960
+يساوي K و يساوي ناقص J في L مش عاجزكوا بس و عندك J
+
+193
+00:20:16,960 --> 00:20:22,860
+تربيع بده يساوي K تربيع بده يساوي L تربيع بده
+
+194
+00:20:22,860 --> 00:20:24,520
+يساوي ناقص I
+
+195
+00:20:27,300 --> 00:20:31,120
+يبقى هذه الخواصة الأساسية لهذه ال group اللي خاطر
+
+196
+00:20:31,120 --> 00:20:36,160
+اكتب لك مين ال I والJ والK كل واحدة مصفوفة نظامها
+
+197
+00:20:36,160 --> 00:20:47,400
+2 في 2 بحيث ال J هي المصفوفة اللي هي I 0 0 سالب I
+
+198
+00:20:48,010 --> 00:20:56,250
+الـ K هي المصفوفة اللي هي Zero واحد سلب واحد Zero
+
+199
+00:20:56,250 --> 00:21:03,470
+ال L هي المصفوفة Zero I I Zero بالشكل اللي عندي
+
+200
+00:21:04,720 --> 00:21:08,860
+الكتاب كتبها في عندك بالدلالة في الرموز A وB
+
+201
+00:21:08,860 --> 00:21:14,040
+ومخليها طلاس مش جايلك من ال A ومن ال B احنا
+
+202
+00:21:14,040 --> 00:21:19,300
+بنكتبها لك بصيغة اوضح هي ال Q وهي الخواص بتاعتها
+
+203
+00:21:19,300 --> 00:21:26,400
+الآن بيقوللي اثبت ان ال Q تمانية ل not isomorphic
+
+204
+00:21:26,400 --> 00:21:32,960
+لمين ل D4 ال Q تمانية كم element فيها هنا شباب كم
+
+205
+00:21:32,960 --> 00:21:38,240
+elementتمانية زايد او ناقص وD for فيها كمان قداش
+
+206
+00:21:38,240 --> 00:21:42,780
+تمانية ايه بقى دي هنا تمان عناصر و هنا تمان عناصر
+
+207
+00:21:42,780 --> 00:21:51,420
+امسكلي وين راحت ال J و ال K و ال L ال J هادي ال I
+
+208
+00:21:51,420 --> 00:21:54,760
+هادي يا شباب اللي هي الجدر التربيعي لسالب واحد ال
+
+209
+00:21:54,760 --> 00:22:00,780
+I يعني ال complex هي الجدر التربيعي لسالب واحدالان
+
+210
+00:22:00,780 --> 00:22:05,500
+لو جيت هنا خاصية بيقول جيت تربية يسوى كتربية يسوى
+
+211
+00:22:05,500 --> 00:22:11,540
+ال تربية يسوى قداش سالب I يبقى هذه ال order لها
+
+212
+00:22:11,540 --> 00:22:20,160
+قداش أربعة جيوس أربعة يعني سالب I في سالب I ب I
+
+213
+00:22:20,160 --> 00:22:23,820
+اللي هو ال identity يبقى هنا ال order لهذه أربعة
+
+214
+00:22:23,820 --> 00:22:27,300
+ال order لهذه أربعة ال order لهذه قداش أربعة
+
+215
+00:22:27,300 --> 00:22:32,650
+بالمثلالأردر لسالب جي والأردر لسالب كي والأردر
+
+216
+00:22:32,650 --> 00:22:37,950
+لسالب ال كمان أربعة يبقى أنا عندي كم element ال
+
+217
+00:22:37,950 --> 00:22:44,010
+order اللي يسوى أربعة ستة elements ال order اللي
+
+218
+00:22:44,010 --> 00:22:50,110
+يسوى أربعة تعالوا نروح على D4 هل D4 فيها ستة
+
+219
+00:22:50,110 --> 00:22:55,850
+elements ال order اللي يسوى أربعة ال H وال V وال D
+
+220
+00:22:55,850 --> 00:22:59,660
+وال D prime ال order اللي يسوى اتنينو ال R مية و
+
+221
+00:22:59,660 --> 00:23:04,600
+تمانين ال order يسوي اتنين هاي سعر خمسة و ال
+
+222
+00:23:04,600 --> 00:23:08,020
+identity element ال order ايه لو واحد حطه على شجة
+
+223
+00:23:08,020 --> 00:23:12,980
+بيضلش عندى الا مين الا اتنين اللي هو ال R تسعين و
+
+224
+00:23:12,980 --> 00:23:15,560
+ال R متين و السبعين يبقى اتنين هل هو ال R
+
+225
+00:23:15,560 --> 00:23:23,850
+isomorphic لأ يبقى هناالـ D أو الـ Q8 is not
+
+226
+00:23:23,850 --> 00:23:34,030
+isomorphic لـ D4 because اللي هو Q8 has six
+
+227
+00:23:34,030 --> 00:23:42,810
+elements أو ستة elements ستة elements اللي هم زد
+
+228
+00:23:42,810 --> 00:23:52,270
+أو نقص Jوزادة أو ناقص k وزادة أو ناقص l of order
+
+229
+00:23:52,270 --> 00:24:09,050
+أربع but of order أربع but ال D4 has two elements
+
+230
+00:24:10,170 --> 00:24:21,750
+اللي هما main are 90 and are 270 of order 4 مدام
+
+231
+00:24:21,750 --> 00:24:26,510
+العدد هنا يختلف عن العدد هنا إذا الإثنين لا يمكن
+
+232
+00:24:26,510 --> 00:24:29,670
+يكونوا معاهم isomorphic
+
+233
+00:24:44,510 --> 00:24:51,370
+هذا كان سؤال سؤال تمانية وعشرين لان عندنا سؤال
+
+234
+00:24:51,370 --> 00:24:56,510
+تلاتين سؤال تلاتين يعطينا ال R N هي ال components
+
+235
+00:24:56,510 --> 00:25:03,870
+من واحد لغاية M وقال لي بيانه ال mapping Phi Phi
+
+236
+00:25:03,870 --> 00:25:12,690
+من من ال R N إلى ال R N عبارة عن اتومورفزمتحت
+
+237
+00:25:12,690 --> 00:25:18,050
+عملية الجامعة و هذا ال .. ال .. ال atomorphism
+
+238
+00:25:18,050 --> 00:25:25,610
+بنسميه ال inversion atomorphism يبقى سؤال تلاتين
+
+239
+00:25:25,610 --> 00:25:29,190
+سؤال
+
+240
+00:25:29,190 --> 00:25:43,320
+تلاتين بيقول ليش؟ بيقوللي في من ال rn لل rndefine
+
+241
+00:25:43,320 --> 00:25:53,920
+by فاي لما تأثر على ال element a1 و a2 و لغاية an
+
+242
+00:25:53,920 --> 00:26:02,960
+بيعطيني سالب a1 سالب a2 سالب an بالشكل اللي عندنا
+
+243
+00:26:02,960 --> 00:26:08,120
+هذا بيقول شو ذات ال mapping هذه عبارة عن
+
+244
+00:26:08,120 --> 00:26:13,350
+atomorphismعلى ال group under the component wise
+
+245
+00:26:13,350 --> 00:26:19,110
+addition تحت الجامعه العادى بالنسبه لمن؟ لل space
+
+246
+00:26:19,110 --> 00:26:23,130
+RN يبقى
+
+247
+00:26:23,130 --> 00:26:28,870
+انا عندي function معرفه من RN الى RN بهذا الشكل
+
+248
+00:26:28,870 --> 00:26:33,470
+اللى بدى اطلب انه Phi one to one وانتوا وعباره عن
+
+249
+00:26:33,470 --> 00:26:38,680
+atomorphismيبقى الخطوة الأولى بدأت بيقوله أنه five
+
+250
+00:26:38,680 --> 00:26:46,160
+is one to one بدأ أروح أاخد assume اللي هو five of
+
+251
+00:26:46,160 --> 00:26:52,960
+a واحد و a اتنين و لغاية a n بدر يساوي five of b
+
+252
+00:26:52,960 --> 00:27:03,930
+واحد و b اتنين و لغاية b nصورة الأول ناقص A1 ناقص
+
+253
+00:27:03,930 --> 00:27:15,610
+A2 ناقص AN ناقص B1 ناقص B2 ناقص BN ناقصمن هذا
+
+254
+00:27:15,610 --> 00:27:21,130
+الكلام مش بستنتج، بستنتج ان ناقص A1 بدري يسوي ناقص
+
+255
+00:27:21,130 --> 00:27:28,650
+B1 يبقى ناقص A1 بدري يسوي ناقص B1 و ناقص A2 بدري
+
+256
+00:27:28,650 --> 00:27:35,250
+يسوي ناقص B2 و تظلك ماشي لغاية ناقص AN بدري يسوي
+
+257
+00:27:35,250 --> 00:27:43,040
+ناقص BMلو ضربنا هذا كله في إشارة ناقص بصير ال a1
+
+258
+00:27:43,040 --> 00:27:50,180
+بدر يساوي ال b1 وال a2 بدر يساوي ال b2 وال an بدر
+
+259
+00:27:50,180 --> 00:27:58,770
+يساوي ال bnبناء عليه لو أخدت ال order pair a1 و a2
+
+260
+00:27:58,770 --> 00:28:04,750
+و لغاية an هلاقيه يساويه هشيل ال a1 و أحط قيمتها
+
+261
+00:28:04,750 --> 00:28:11,330
+من ال b1 و أشيل ال a2 و أحط قيمتها اللي هي b2 و
+
+262
+00:28:11,330 --> 00:28:17,230
+أشيل ال an و أحط قيمتها bn إذا أخدت صورتين
+
+263
+00:28:17,230 --> 00:28:23,640
+متساويتينأثبت ان الاصل متساوي لذلك فاي is one to
+
+264
+00:28:23,640 --> 00:28:26,040
+one بدروح اخد element
+
+265
+00:28:34,730 --> 00:28:46,990
+let x1 و x2 و xn موجود في الارن بدي اثبت هذا انه
+
+266
+00:28:46,990 --> 00:28:58,910
+يلو اصل هذا الاصل موجود في ارن بقوله then ال
+
+267
+00:28:58,910 --> 00:29:09,270
+x1و X2 و XN بده يساوي شو رايك بنفع اقول هيك اللي
+
+268
+00:29:09,270 --> 00:29:18,570
+هو سالب X واحد و سالب X اتنين و لغاية سالب XN؟
+
+269
+00:29:18,570 --> 00:29:26,890
+بنفع؟ اه طيب مدام بنفع يبقى هيه كتبته بالشكل اللي
+
+270
+00:29:26,890 --> 00:29:33,860
+عندنايبقى هذا الكلام بده يساوي اللي هو سالب برا
+
+271
+00:29:33,860 --> 00:29:39,860
+هذه سالب X واحد لو سميتها Y واحد والتانية Y اتنين
+
+272
+00:29:39,860 --> 00:29:47,020
+والاخيرة YN يعني هذه كتبت Y واحد وهذه Y اتنين وهذه
+
+273
+00:29:47,020 --> 00:29:53,040
+YN بالشكل اللي عندنا هنا يبقى هذا الكلام بده يساوي
+
+274
+00:29:53,040 --> 00:29:55,800
+اللي هو مين سالب Y واحد
+
+275
+00:30:01,060 --> 00:30:09,680
+أليس هذا هو صورة five of y واحد و y اتنين و لغاية
+
+276
+00:30:09,680 --> 00:30:17,660
+ynإذا ال element اللي أخدته في RN لجيت له أصل في
+
+277
+00:30:17,660 --> 00:30:24,660
+ال main في ال RN كذلك و هو Y1 و Y2 و هو ينحل من
+
+278
+00:30:24,660 --> 00:30:31,440
+بينهم Y1 هي سلب X1 و Y2 هي سلب X2 و YN هو سلب XN و
+
+279
+00:30:31,440 --> 00:30:37,300
+هكذا لذلك صارت أن ال main Phi is on itالان بدي اجي
+
+280
+00:30:37,300 --> 00:30:44,940
+للنقطة الأخيرة five is an isomorphism بدي اروح اخد
+
+281
+00:30:44,940 --> 00:30:51,840
+five of مجموع two elements يبقى a واحد و a اتنين و
+
+282
+00:30:51,840 --> 00:31:02,600
+a n زائد b واحد و b اتنين و لغاية b n كتبتم ليه
+
+283
+00:31:02,600 --> 00:31:08,260
+شكل ان ال operation اللي على ال groupهي عملية جمعة
+
+284
+00:31:08,260 --> 00:31:22,380
+طيب
+
+285
+00:31:22,380 --> 00:31:27,360
+الان طب خل الجامعة اللي قاللي عليكم component wise
+
+286
+00:31:27,360 --> 00:31:36,430
+حاجة مع كل مركبة مع نظيرتها يبقى a1 زائد b1 a2زائد
+
+287
+00:31:36,430 --> 00:31:45,910
+B2 وظل مستمر لغاية AN زائد BN بهذا الشكل الآن أصبح
+
+288
+00:31:45,910 --> 00:31:51,550
+هذا كله element واحد يبقى الصورة تبعته سالب هذا ال
+
+289
+00:31:51,550 --> 00:31:58,670
+element يبقى هذا الكلام بالدرس ساوي سالب A1 زائد
+
+290
+00:31:58,670 --> 00:32:02,850
+B1 سالب A2 زائد B2
+
+291
+00:32:11,310 --> 00:32:17,390
+بقدر ادخل السلب على كل term من هذه الترمات يبقى
+
+292
+00:32:17,390 --> 00:32:25,530
+هذا الكلام بده يساوي سالب a1 سالب b1 و سالب a2
+
+293
+00:32:38,400 --> 00:32:44,420
+هذا قوس واحدمكوّن من N من المُركّبات بدي أحاول
+
+294
+00:32:44,420 --> 00:32:50,040
+أحطه على صيغة مجموعة قوسين إذا لو روحت كتبته على
+
+295
+00:32:50,040 --> 00:32:57,700
+صيغة مجموعة قوسين بده يساوي ا واحد أو سالب ا واحد
+
+296
+00:32:58,410 --> 00:33:07,810
+سالب A1 سالب A2 ونظل ماشيين لغاية سالب AN كله زائد
+
+297
+00:33:07,810 --> 00:33:16,170
+اللي هو سالب B1 وسالب B2 ونظل ماشيين لغاية سالب BM
+
+298
+00:33:16,170 --> 00:33:24,390
+هذا الكلام يساوي الأول هذا هو عبارة عن Phi of A1
+
+299
+00:33:24,390 --> 00:33:36,900
+وA2و لغاية AN زائد الاتاني هو Phi of B1 و B2 و
+
+300
+00:33:36,900 --> 00:33:42,760
+لغاية BN بالشكل اللي عندنا يبقى بناء ان عليه Phi
+
+301
+00:33:42,760 --> 00:33:49,660
+أصبح ماله Atomorphism لإن Phi من نفس ال group إلى
+
+302
+00:33:49,660 --> 00:33:56,890
+نفس ال groupيبقى باجي بقوله هنا thus وهكذا فاي is
+
+303
+00:33:56,890 --> 00:34:03,310
+an atomorphism وانت هنا من مين؟ من المثلة بيسأل
+
+304
+00:34:03,310 --> 00:34:13,110
+بيقولي ما هو المعنى الهندسي لهذا ال atomorphism لو
+
+305
+00:34:13,110 --> 00:34:17,680
+اتخيلت انا في ال space are in اللي جال عنه هناوفي
+
+306
+00:34:17,680 --> 00:34:24,140
+عندى نقطة هنا احداثيها اولا احداثيتها a1 و a2 و a3
+
+307
+00:34:24,140 --> 00:34:30,020
+و a4 و a5 لغاية an في المقابل صورتها نقطة ناقص a1
+
+308
+00:34:30,020 --> 00:34:33,260
+و ناقص a2 او لا يعني ايش بيعمل ال homomorphism هذا
+
+309
+00:34:33,260 --> 00:34:40,740
+او ليس homomorphism بيقلب النقطة عبر مين عبر نقطة
+
+310
+00:34:40,740 --> 00:34:52,360
+الاصل يبقى هنا هبروح بقوله لاmeaning of this
+
+311
+00:34:52,360 --> 00:34:56,360
+atomorphism
+
+312
+00:34:56,360 --> 00:35:12,200
+reflect معنى هذا is the reflection of the points
+
+313
+00:35:12,200 --> 00:35:14,400
+أثرا
+
+314
+00:35:17,910 --> 00:35:26,350
+the origin يبقى كأننا نقلب النقاط عبر نقطة الأصل
+
+315
+00:35:26,350 --> 00:35:29,670
+اللي كانت على اليمين بنخليها على الشمال و اللي
+
+316
+00:35:29,670 --> 00:35:34,040
+كانت على الشمال بنوديها على اليمين و هكذايعني
+
+317
+00:35:34,040 --> 00:35:40,780
+بنقلب وضع النقاط عبر نقطة الأصل، هذا كان هو سؤال
+
+318
+00:35:40,780 --> 00:35:47,000
+اللي هو تلاتين، عندك هنا سؤال خمسة و .. والله سؤال
+
+319
+00:35:47,000 --> 00:35:48,400
+تلاتة و تلاتين
+
+320
+00:36:05,810 --> 00:36:10,170
+يبقى السؤال تلاتة وتلاتين
+
+321
+00:36:25,230 --> 00:36:31,360
+سؤال مرة تانيةبقول في عندي two inner atomorphism
+
+322
+00:36:31,360 --> 00:36:37,800
+الفاي جي والفاي زيد جي بقول اثبت ان الاتنين هدول
+
+323
+00:36:37,800 --> 00:36:42,880
+are equal علما بان الـ z هذه موجودة في ال center
+
+324
+00:36:42,880 --> 00:36:46,640
+تبع الجي الـ z موجودة في ال center تبع الجي يعني
+
+325
+00:36:46,640 --> 00:36:54,580
+commutes مع كل عناصر جي بلا استثناءالأن الـ Inner
+
+326
+00:36:54,580 --> 00:37:01,620
+Atomorphism Phi G of X بنذكر بتعريفه كان G X G
+
+327
+00:37:01,620 --> 00:37:06,140
+Inverse يبقى هذا ال Inner Atomorphism طيب تمام
+
+328
+00:37:06,140 --> 00:37:11,000
+الان انا بدي اثبت ان اتنين هذول are equal بمعنى
+
+329
+00:37:11,000 --> 00:37:16,620
+اخر تأثير لاتنين على اي element موجود في G بده
+
+330
+00:37:16,620 --> 00:37:21,430
+يتساوى مظبوط ولا لا يبقى المقصود فيهميبقى باجي
+
+331
+00:37:21,430 --> 00:37:26,830
+بقوله هنا solution if
+
+332
+00:37:26,830 --> 00:37:33,490
+ال X موجود for all
+
+333
+00:37:33,490 --> 00:37:42,230
+لكل ال X اللي موجود في G لو جيت أخدت تأثير ال 5G
+
+334
+00:37:42,230 --> 00:37:48,250
+على X يبقى ال G X G inverse and
+
+335
+00:37:49,700 --> 00:38:00,500
+بتاخد تأثير الـ Phi ZG على X يبقى ZGX ZG inverse
+
+336
+00:38:00,500 --> 00:38:03,740
+تمام؟
+
+337
+00:38:03,740 --> 00:38:10,340
+يبقى هذا الكلام بده يساوي ZGX
+
+338
+00:38:10,340 --> 00:38:15,080
+G inverse Z inverse
+
+339
+00:38:17,430 --> 00:38:27,390
+هذا الكلام بده يساو G X G Inverse Z Inverse و هنا
+
+340
+00:38:27,390 --> 00:38:34,210
+Zليش؟ لأن الـ Z موجودة في الـ Center يبقى هذا
+
+341
+00:38:34,210 --> 00:38:40,830
+الكلام صحيح لأن الـ Z موجودة في الـ Center تبع الـ
+
+342
+00:38:40,830 --> 00:38:45,290
+Group G يعني الـ Z مرتبط مع أي Element موجود في
+
+343
+00:38:45,290 --> 00:38:50,110
+الـ G وهذا كله Element موجود في الـ G يبقى خلّينا
+
+344
+00:38:50,110 --> 00:38:54,110
+الـ Z تجوان على الناحية التانية الـ Element في
+
+345
+00:38:54,110 --> 00:39:01,940
+معكوسه من يعطينا؟الـ Identity الـ GXG inverse في
+
+346
+00:39:01,940 --> 00:39:07,820
+الـ Identity Element اللي هو الـ GXG inverse الـ
+
+347
+00:39:07,820 --> 00:39:15,600
+GX inverse G مين هو عبارة عبارة عن Phi G of X يبقى
+
+348
+00:39:15,600 --> 00:39:21,260
+بناء عليه أصبح Phi ZG على جميع أناصر G يسوي تأثير
+
+349
+00:39:21,260 --> 00:39:27,160
+Phi G على جميع أناصر G يبقى معنا هذا الكلامإنه في
+
+350
+00:39:27,160 --> 00:39:33,280
+زد جي بده يساوي بين في جي وانت هنا من مين من
+
+351
+00:39:33,280 --> 00:39:40,940
+المسألةهذا كان سؤال تلاتة و تلاتين بعد سؤال خمسة و
+
+352
+00:39:40,940 --> 00:39:47,920
+تلاتين جي و اتش induce the same inner atomorphism
+
+353
+00:39:47,920 --> 00:39:57,280
+of جي يبقى الاسئلة
+
+354
+00:39:57,280 --> 00:40:04,180
+علاقة مباشرة بهذا السؤالخمسة و تلاتين خمسة و
+
+355
+00:40:04,180 --> 00:40:13,500
+تلاتين بيقول ان ال G and ال H اتنين هدول induce
+
+356
+00:40:13,500 --> 00:40:25,000
+the same inner atomorphism the same inner
+
+357
+00:40:25,000 --> 00:40:34,140
+atomorphism of G نقول proveهذا سيعطيك ان الـ H
+
+358
+00:40:34,140 --> 00:40:41,260
+inverse G موجود في الـ Center تبع الـ G بنا نثبت
+
+359
+00:40:41,260 --> 00:40:48,060
+ان هذا موجود في الـ Center تبع من؟ تبع الـ G طيب
+
+360
+00:40:48,060 --> 00:40:54,640
+اتنين هذول بيعملولي نفس ال Inner Atomorphism بمعنى
+
+361
+00:40:54,640 --> 00:40:57,820
+اخر انه solution
+
+362
+00:41:00,540 --> 00:41:11,860
+إن الـ Phi G تأثيره على X بده يساوي Phi H تأثيره
+
+363
+00:41:11,860 --> 00:41:19,360
+على X هذا المقصود فيه لمن؟ هذا الكلام صحيح لكل X
+
+364
+00:41:19,360 --> 00:41:20,760
+الموجودة في G
+
+365
+00:41:24,660 --> 00:41:29,800
+تعريف ال inner atomorphism
+
+366
+00:41:29,800 --> 00:41:34,320
+بالشكل اللي عندنا يبقى اتنين هدول are equal مدام
+
+367
+00:41:34,320 --> 00:41:40,720
+are equal then الأولى اللي عبارة عن g x g inverse
+
+368
+00:41:40,720 --> 00:41:51,300
+والتانى عبارة عن مين عبارة عن h x h inverseقال لي
+
+369
+00:41:51,300 --> 00:41:56,940
+اثبتلي ان ال H inverse D موجودة في ال center يعني
+
+370
+00:41:56,940 --> 00:42:03,040
+ال H inverse G لما اثربها على اي انصار في G من
+
+371
+00:42:03,040 --> 00:42:07,950
+اليمين او من الشمال يكونوا اتنين عريقابنقوله بسيطة
+
+372
+00:42:07,950 --> 00:42:12,550
+جدا قال لي H inverse يبقى هذه ال H inverse مش هفرط
+
+373
+00:42:12,550 --> 00:42:17,170
+فيها لكن ال G inverse بده افرط فيها مش انا افرط
+
+374
+00:42:17,170 --> 00:42:23,710
+فيها لو روحت ضربت اتنين من طرف اليمين في مام في ال
+
+375
+00:42:23,710 --> 00:42:33,530
+G يبقاش بيضل عند هنا G X وبده يساوي H X و هنا H
+
+376
+00:42:33,530 --> 00:42:42,850
+inverse Gيبقى ضرب من جهة اليمين الطرفين فقط في G
+
+377
+00:42:42,850 --> 00:42:47,790
+يبقى جي انفرس جي لو بال identity يبقى بظل عندي G X
+
+378
+00:42:47,790 --> 00:42:54,850
+بده يساوي ال H X H inverse بده أضربها في G يبقى
+
+379
+00:42:54,850 --> 00:43:00,190
+هيدربناها في G كمان ال H هذه مش لازمالييبقى بيضروح
+
+380
+00:43:00,190 --> 00:43:06,210
+اضرب الطرفين في الـ H inverse إذا لو ضربت الطرفين
+
+381
+00:43:06,210 --> 00:43:13,630
+في الـ H inverse بيصير H inverse G X بده يساوي
+
+382
+00:43:13,630 --> 00:43:20,150
+ضربت الطرفين من جهتي الشمال يبقى بيصير H inverse
+
+383
+00:43:20,150 --> 00:43:27,810
+من جهتي الشمال بيصير هذه الـ X H inverse Gيبقى
+
+384
+00:43:27,810 --> 00:43:32,170
+ضربت هنا H انفرس اتجيني H انفرس H اللي هي بال
+
+385
+00:43:32,170 --> 00:43:38,250
+identity بظهر X H انفرس G اطلعلي لهذا ال element
+
+386
+00:43:38,250 --> 00:43:44,190
+واطلعلي لهذا ال element هو نفسه و ال X هذه ايش
+
+387
+00:43:44,190 --> 00:43:51,120
+قلنا عليهاأي x موجودة في جي يبقى هذا الكلام صحيح
+
+388
+00:43:51,120 --> 00:43:57,480
+لكل ال x اللي موجودة في جي ايش تفسيرك لهذا ان ال h
+
+389
+00:43:57,480 --> 00:44:02,660
+inverse g موجودة في ال center تبع الجي وهو المطلوب
+
+390
+00:44:02,660 --> 00:44:08,460
+هذا بده يعطيلك ان ال h inverse g موجودة في ال
+
+391
+00:44:08,460 --> 00:44:11,560
+center تبع الجي وهو المطلوب
+
+392
+00:44:36,580 --> 00:44:43,440
+هذا كان سؤال خمسة و تلاتين الان عنا تمانية و
+
+393
+00:44:43,440 --> 00:44:50,080
+تلاتين او عنا تسعة و تلاتين بفضل نحل تسعة و تلاتين
+
+394
+00:44:50,080 --> 00:44:54,440
+و نضل وقت نحل تمانية و تلاتين بس بعطيك ال function
+
+395
+00:44:54,440 --> 00:44:59,200
+تبع التمانية و تلاتين و انت بتكمل يبقى في تمانية و
+
+396
+00:44:59,200 --> 00:45:06,270
+تلاتين ال function عنا فيمن مين؟ من الست اللي
+
+397
+00:45:06,270 --> 00:45:13,630
+عناصرها اللي هو zero وزاد او ناقص اتنين وزاد او
+
+398
+00:45:13,630 --> 00:45:20,610
+ناقص اربع وزاد او ناقص ستة الى ما شاء الله هادي
+
+399
+00:45:20,610 --> 00:45:27,030
+بين هادي جي و هادي بدنا نسميها جي والتانية H اللي
+
+400
+00:45:27,030 --> 00:45:33,770
+عناصرهازيرو زائد او ناقص تلاتة زائد او ناقص ستة
+
+401
+00:45:33,770 --> 00:45:38,850
+زائد او ناقص تسعة إلى ما شاء الله يبقى هذه الـ
+
+402
+00:45:38,850 --> 00:45:44,270
+five بده اعرفها كالتالي five of اتنين ان يساوي
+
+403
+00:45:44,270 --> 00:45:50,710
+تلاتة ان يبقى هى ال element هنا موجود هنا حط ان
+
+404
+00:45:50,710 --> 00:45:55,190
+بزيرو بيعطيك زيرو حط ان بواحد بيعطيك اتنين حط ان
+
+405
+00:45:55,190 --> 00:46:00,740
+باثنين باربعة تلاتة ستة تمامحط ان بزيرو بصير تلات
+
+406
+00:46:00,740 --> 00:46:05,780
+.. زيرو حط ان بواحد بصير تلاتة حط ان باتنين بناقص
+
+407
+00:46:05,780 --> 00:46:09,320
+واحد بناقص كله تمام يبقى التعريف سليم مائة في
+
+408
+00:46:09,320 --> 00:46:16,620
+المائة باكتبت ان هذا عبارة عن ايزو مورفزم السؤال
+
+409
+00:46:16,620 --> 00:46:18,240
+تسعة وتلاتين
+
+410
+00:46:20,220 --> 00:46:26,280
+سؤال تسعة و تلاتين بيقول ليش بيقول ي support that
+
+411
+00:46:26,280 --> 00:46:35,100
+الفي is an atomorphism ل D4 يبقى في من D4 إلى D4
+
+412
+00:46:35,100 --> 00:46:43,500
+هذا atomorphism و such that الفي of R تسعين و الفي
+
+413
+00:46:43,500 --> 00:46:52,500
+of R تسعين بده يسوى R متين و سبعينمتين وسبعين هو
+
+414
+00:46:52,500 --> 00:46:59,760
+عندك الفاي of V فاي of V بده ساوي ال V قال لي find
+
+415
+00:46:59,760 --> 00:47:08,520
+بدنا نوجد فاي of D و فاي of H فاي of D و فاي of H
+
+416
+00:47:08,520 --> 00:47:11,540
+هذا اللي عايزين نوجده
+
+417
+00:47:21,410 --> 00:47:25,930
+بلزمنا طبعا ال table في صفة واحد و تلاتين تبع ال
+
+418
+00:47:25,930 --> 00:47:31,430
+day four الكل شوية ايه ابنه ارجعنا الان ميعطيني
+
+419
+00:47:31,430 --> 00:47:37,130
+هذا atomorphism وميعطيني قيمتين وطالب قيمتين
+
+420
+00:47:37,130 --> 00:47:42,390
+بنقوله بسيطة جدا يبقى هذا solution
+
+421
+00:47:49,780 --> 00:47:57,720
+السؤال هو هل بقدر اكتب D؟بدلالة ال R تسعين و ال V
+
+422
+00:47:57,720 --> 00:47:58,560
+ولا لا
+
+423
+00:48:28,720 --> 00:48:35,000
+طب هو قاللي هذا في ايزو مورفزم يعني ايزو مورفزم
+
+424
+00:48:35,000 --> 00:48:42,680
+اذا هذا الكلام بدل ساوي في of R تسعين في في of V
+
+425
+00:48:43,580 --> 00:48:48,800
+الـ Phi of R90 هي R270
+
+426
+00:48:48,800 --> 00:48:54,920
+والـ Phi of V بدها تساوي الـ V itself برجع على
+
+427
+00:48:54,920 --> 00:49:00,720
+الجدل برضه بده أشوف R270 في V إيش بتعطينا يبقى
+
+428
+00:49:00,720 --> 00:49:10,250
+R270 في V بتعطينا D primeيبقى ناتج دي prime يبقى
+
+429
+00:49:10,250 --> 00:49:15,930
+هاي حسبتله فاي اف دي يساوي قداش دي prime الان قال
+
+430
+00:49:15,930 --> 00:49:22,710
+هاتلي فاي اف اتش باجي بقوله فاي اف اتش يساوي فاي
+
+431
+00:49:22,710 --> 00:49:29,530
+اف هل بقدر اكتب ال H بدلالة ال R تسعين و ال V ولا
+
+432
+00:49:29,530 --> 00:49:37,650
+لأ تعالى نشوفR تسعين في إيش بتعطيني من ال H يبقى
+
+433
+00:49:37,650 --> 00:49:45,730
+هاي ال R تسعين ال H هي عبارة عن ال H هي عبارة عن R
+
+434
+00:49:45,730 --> 00:49:54,290
+تسعين في D يبقى R تسعين في D لأ احنا بدنا من؟ بدنا
+
+435
+00:49:54,290 --> 00:50:06,030
+R تسعين و V مظبوط؟يعني بديها R تسعين في D كيف؟ مش
+
+436
+00:50:06,030 --> 00:50:12,310
+سامع احنا وجدناها بنفع برضه بنفع من فور كويس يبقى
+
+437
+00:50:12,310 --> 00:50:18,030
+انا كل اللي عند ال H بقدر اشيله و اكتب له R تسعين
+
+438
+00:50:18,030 --> 00:50:26,910
+في D R تسعين في D يبقى هذه R تسعين في Dيبقى هدف
+
+439
+00:50:26,910 --> 00:50:34,590
+تعطينا فاي of R تسعين في فاي of D ويساوي فاي of R
+
+440
+00:50:34,590 --> 00:50:40,090
+تسعين اللي هي R ميتين وسبعين و فاي of D حسبناها
+
+441
+00:50:40,090 --> 00:50:46,210
+اللي هي D primeيبقى بدي اشوف ر متين و سبعين في دي
+
+442
+00:50:46,210 --> 00:50:53,630
+prime قدش بتعطينا يبقى ر متين و سبعين في دي prime
+
+443
+00:50:53,630 --> 00:50:58,030
+اللي هي الأخيرة بتعطينا H
+
+444
+00:51:01,120 --> 00:51:08,160
+يبقى هذي بتعطينا H يبقى صار في of H يساوي من H
+
+445
+00:51:08,160 --> 00:51:15,940
+itself يبقى في of H يساوي من H itself هذي هنا في
+
+446
+00:51:15,940 --> 00:51:21,520
+of D يساوي من D prime
+
+447
+00:51:24,210 --> 00:51:29,170
+طيب المرة القادمة ان شاء الله بدنا نرجع لأسئلة ال
+
+448
+00:51:29,170 --> 00:51:30,930
+permutations
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d4e3c096e64573137e07557baa79f1d60e22f99b
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eMvQIylQxkk.srt
@@ -0,0 +1,1547 @@
+1
+00:00:21,500 --> 00:00:24,340
+السلام عليكم ورحمة الله وبركاته اليوم إن شاء
+
+2
+00:00:24,340 --> 00:00:27,260
+الله هننهي المناقشة chapter الرابع هنبدأ زي ما 
+
+3
+00:00:27,260 --> 00:00:29,860
+اتوقفنا المرة الماضية السؤال سبعة و ثلاثين حليناه
+
+4
+00:00:29,860 --> 00:00:35,290
+هنبدأ من السؤال ثمانية و ثلاثين طبعًا سؤال 38 ما أعطيك
+
+5
+00:00:35,290 --> 00:00:40,210
+أربعة عناصر في مجموعة بقول لك أثبت إن هذه بتعمل group
+
+6
+00:00:40,210 --> 00:00:46,190
+مع عملية الضرب مد الـ 20 عشان أنا أقدر أتعامل مع
+
+7
+00:00:46,190 --> 00:00:49,330
+هذا الأسئلة .. نوع من الأسئلة لما يعطيني group فيه
+
+8
+00:00:49,330 --> 00:00:53,090
+عدد محدود جدًا من العناصر ثلاثة أربعة خمسة ويثبت
+
+9
+00:00:53,090 --> 00:00:57,030
+إنها أو يطلب مني أن أثبت إنها group أسهل طريقة هي
+
+10
+00:00:57,030 --> 00:01:02,940
+multiplication table جدول الضرب بروح بحط الثمانية
+
+11
+00:01:02,940 --> 00:01:09,060
+أو الأربعة في الأول الثمانية والاثنا عشر والستة عشر
+
+12
+00:01:09,060 --> 00:01:16,120
+واندي أربعة ثمانية اثنا عشر ستة عشر طبعًا مدام الضرب
+
+13
+00:01:16,120 --> 00:01:21,920
+تقليدي يعني أنا بتعامل مع عملية ضرب صحيح مدة
+
+14
+00:01:21,920 --> 00:01:25,520
+العشرين لكن في نهاية أساسها عبارة عن إيش؟ عن ضرب
+
+15
+00:01:25,520 --> 00:01:31,170
+أرقام فأكيد العملية هتكون إيش؟ تبديلية أربعة في أربعة
+
+16
+00:01:31,170 --> 00:01:34,730
+ستة عشر مد الـ 20 ستة عشر أربعة في ثمانية اثنا عشر
+
+17
+00:01:34,730 --> 00:01:37,970
+اثنين و ثلاثين مد الـ 20 اثنا عشر أربعة في اثنا عشر
+
+18
+00:01:37,970 --> 00:01:42,810
+ثمانية و أربعين أربعة في ستة عشر أربعة ثمانية في
+
+19
+00:01:42,810 --> 00:01:45,850
+أربعة اثنين و ثلاثين باتنا عشر ثمانية في ثمانية أربعة
+
+20
+00:01:45,850 --> 00:01:51,110
+و ستين بأربعة ثمانية في اثنا عشر ستة و تسعين يعني ستة
+
+21
+00:01:51,110 --> 00:01:57,240
+عشر و ثمانية في ستة عشر كده 128 يعني
+
+22
+00:01:57,240 --> 00:02:01,500
+ثمانية اثنا عشر في أربعة ثمانية و أربعين يعني ثمانية
+
+23
+00:02:01,500 --> 00:02:04,560
+اثنا عشر في ثمانية ستة و تسعين يعني ستة عشر اثنا عشر
+
+24
+00:02:04,560 --> 00:02:08,600
+اثنا عشر مية و أربعة و أربعين يعني أربعة اثنا عشر في ستة
+
+25
+00:02:08,600 --> 00:02:13,420
+عشر هيظل اثنا عشر طبعًا ستة عشر في أربعة هيكون عبارة
+
+26
+00:02:13,420 --> 00:02:17,540
+عن أربعة و ستين يظل أربعة ستة عشر في ثمانية هيظل
+
+27
+00:02:17,540 --> 00:02:22,470
+ثمانية و اثنا عشر ستة عشر من الواضح إنه أول حاجة
+
+28
+00:02:22,470 --> 00:02:27,070
+العملية عشانها أصلًا ضرب عادي ف associative موجود
+
+29
+00:02:27,070 --> 00:02:31,050
+الـ ال binary أو إن العملية مغلقة على المجموعة
+
+30
+00:02:31,050 --> 00:02:34,390
+موجودة ما طلعش عناصر من برة المجموعة ال abelian
+
+31
+00:02:34,390 --> 00:02:43,330
+موجود في identity؟ في identity؟ في محايد؟ في ..
+
+32
+00:02:43,330 --> 00:02:49,390
+مين؟ الـ 16 .. ليش؟ لأنه أنا بضرب الـ 16 في أي رقم
+
+33
+00:02:50,300 --> 00:02:55,120
+بيظل زي ما هو بيظل لدي ال inverse هل لكل رقم بلاقي
+
+34
+00:02:55,120 --> 00:02:59,260
+عنصر بضربه فيه بيعطيه ال identity بقدر أعرفه
+
+35
+00:02:59,260 --> 00:03:03,600
+لما أتأكد إنه في كل سطر فيه ستة عشر وفي كل عمود
+
+36
+00:03:03,600 --> 00:03:10,400
+فيه ستة عشر وبالتالي هذا عبارة عن group ومش group
+
+37
+00:03:10,400 --> 00:03:16,840
+مش group بس لأ abelian abelian ال group what is
+
+38
+00:03:16,840 --> 00:03:19,560
+the identity هو الستة عشر هل هي ال cyclic
+
+39
+00:03:23,610 --> 00:03:28,370
+هل هي Cyclic؟ عشان تكون Cyclic شباب بدي عنصر
+
+40
+00:03:28,370 --> 00:03:33,370
+يولدها يعني بدي عنصر ال order لـ 4 طبعًا ال order لـ
+
+41
+00:03:33,370 --> 00:03:42,090
+4 بنجيبه 4 في 4 16 بدي يساوي ال identity بقى ال
+
+42
+00:03:42,090 --> 00:03:48,270
+order لـ 4 بدي يساوي 2 ال order لـ 8 8 في 8 كده؟
+
+43
+00:03:48,990 --> 00:03:53,450
+أربعة و ستين أربعة ثمانية في ثمانية في ثمانية اثنا عشر
+
+44
+00:03:53,450 --> 00:03:58,410
+ثمانية في ثمانية في ثمانية في ثمانية ستة عشريك
+
+45
+00:03:58,410 --> 00:04:03,630
+بأوردر الثمانية بتساوي أربعة وبالتالي هذه الجروب
+
+46
+00:04:03,630 --> 00:04:10,310
+جي generated by main من الثمانية وبالتالي هي
+
+47
+00:04:10,310 --> 00:04:17,150
+Cyclic واضح السؤال ده واضح
+
+48
+00:04:17,150 --> 00:04:17,630
+السؤال
+
+49
+00:04:22,570 --> 00:04:26,490
+تسعة و ثلاثين give an example of a group that has
+
+50
+00:04:26,490 --> 00:04:30,770
+that has exactly six subgroups including the
+
+51
+00:04:30,770 --> 00:04:34,210
+trivial subgroup and the group itself generalized
+
+52
+00:04:34,210 --> 00:04:38,050
+exactly any subgroup for any positive integer and
+
+53
+00:04:38,050 --> 00:04:48,690
+إيش رأيكم؟ بدك group J فيها only six subgroups
+
+54
+00:05:06,200 --> 00:05:11,860
+عشان أعطيك ال group أنت تجيبها و تكون لها six
+
+55
+00:05:11,860 --> 00:05:17,100
+subgroup يعني القواسم عددهم ستة بالظبط إيش يعني
+
+56
+00:05:17,100 --> 00:05:22,260
+القواسم عددهم ستة صارت ثمانية و ثلاثين هذا صارت
+
+57
+00:05:22,260 --> 00:05:28,280
+تسعة و ثلاثين يعني بدك ال group ال order لها n
+
+58
+00:05:29,840 --> 00:05:33,820
+وعدد قواسم الـ n بدي يساوي ستة عشان تشتغل بناء على
+
+59
+00:05:33,820 --> 00:05:39,120
+إنه تكون هذه الساكنك أعطيني جواب عدد القواسم تبع
+
+60
+00:05:39,120 --> 00:05:45,840
+ال order لها بساوي ستة الـ 24 كم
+
+61
+00:05:45,840 --> 00:05:51,380
+قاسم؟ واحد، اثنين، ثلاثة، أربعة، ستة، ثمانية،
+
+62
+00:05:51,380 --> 00:05:55,060
+اثنا عشر، أربعة و عشرين، ثمانية طيب عشان أنا عارف ش
+
+63
+00:05:55,060 --> 00:06:06,740
+البداية we need a group أو a cyclic جي
+
+64
+00:06:06,740 --> 00:06:17,280
+with order الـ J بيساوي n و الـ n has only six
+
+65
+00:06:17,280 --> 00:06:27,460
+divisors أعطيني group ال order لها n و الـ n له ستة
+
+66
+00:06:27,460 --> 00:06:28,180
+من القواسم
+
+67
+00:06:32,310 --> 00:06:38,210
+اثنا عشر كم قاسم؟ واحد اثنين ثلاثة أربعة ستة اثنا عشر
+
+68
+00:06:38,210 --> 00:06:47,010
+Take جبدة تساوي إيش؟ زد اثنا عشر من الـ six subgroup
+
+69
+00:06:47,010 --> 00:06:51,610
+هدول generated by واحد generated by اثنين generated
+
+70
+00:06:51,610 --> 00:06:56,010
+by ثلاثة generated by أربعة generated by ستة
+
+71
+00:06:56,010 --> 00:07:00,410
+و generated by اثنا عشر عمّمها لإيه n؟
+
+72
+00:07:03,870 --> 00:07:13,010
+for n هنا في مشكلة شباب هنا
+
+73
+00:07:13,010 --> 00:07:17,990
+في مشكلة تبدأ
+
+74
+00:07:17,990 --> 00:07:28,730
+تشتغل على جروب عدد القواسم دي يكون إله n طيب كم
+
+75
+00:07:28,730 --> 00:07:29,450
+قاسم؟
+
+76
+00:07:32,370 --> 00:07:37,230
+خلصنا من الستة لنشتغل على عدد القواسم يكونوا even
+
+77
+00:07:37,230 --> 00:07:42,270
+لو ال uneven فإيش
+
+78
+00:07:42,270 --> 00:07:49,110
+بيعمل تعالى نرجع شوية نظرية الأعداد إيش عدد
+
+79
+00:07:49,110 --> 00:07:56,750
+القواسم بيساوي؟ إيش رمز سبعة في الأول؟ تاولان؟ طيب،
+
+80
+00:07:56,750 --> 00:08:04,050
+لو الـ n بدأت تساوي P1 P2 لعند PK K1 K2 لعند K إيش
+
+81
+00:08:04,050 --> 00:08:07,790
+تقوى الـ n بيساوي؟
+
+82
+00:08:07,790 --> 00:08:14,830
+إيش تقوى الـ n بيساوي؟ K1 زاد الواحد K2 زاد الواحد
+
+83
+00:08:14,830 --> 00:08:20,710
+لعند KR زاد الواحد عد
+
+84
+00:08:20,710 --> 00:08:30,810
+القواسم يا حبيبي على المهم هذا بدي يساوي N عدد
+
+85
+00:08:30,810 --> 00:08:41,830
+القواسم بدي يساوي الـ N المطلوبة اتبعوا فش غير واحد
+
+86
+00:08:41,830 --> 00:08:48,210
+زي هيك فأنت بتشرح على مين N بدي تساوي K واحد زي
+
+87
+00:08:48,210 --> 00:08:52,110
+واحد خطة K زي واحد يعني أنت بدأت تشتغل على n بدأت
+
+88
+00:08:52,110 --> 00:08:57,870
+تصير عندك P to K هتاخد الـ n بدي يساوي K زاد الواحد
+
+89
+00:08:57,870 --> 00:09:04,970
+اختار الـ P بـ Prime هتاخد مين n بدأت تساوي اثنين to
+
+90
+00:09:04,970 --> 00:09:08,530
+K جي
+
+91
+00:09:08,530 --> 00:09:11,910
+بدأت تساوي زد اثنين to K
+
+92
+00:09:20,720 --> 00:09:26,220
+طبعًا الـ K بدأت تساوي N minus واحد اثنين
+
+93
+00:09:26,220 --> 00:09:33,720
+to N minus واحد اثنين و N minus واحد has N divisors
+
+94
+00:09:33,720 --> 00:09:41,640
+من هما واحد، اثنين، اثنين تربيع، اثنين تكعيب يعني اثنين
+
+95
+00:09:41,640 --> 00:09:47,220
+N minus واحد هدول قواسم الـ اثنين أُس N minus واحد
+
+96
+00:09:52,160 --> 00:09:59,300
+The n subgroups are generated by 1, generated by
+
+97
+00:09:59,300 --> 00:10:04,900
+2, generated by 4, generated by 8 لأن generated by
+
+98
+00:10:04,900 --> 00:10:11,320
+2 أُس n minus 1 و أنت بتشتغل في مين؟ في Z 2 أُس n
+
+99
+00:10:11,320 --> 00:10:17,120
+minus كيف؟ اه و أنا هي اللي حليته قدامك
+
+100
+00:10:22,180 --> 00:10:26,000
+أنا مش راحتش حاجة علاقة في نظرية الأعداد أنا مطلوب
+
+101
+00:10:26,000 --> 00:10:31,840
+مني أدور على رقم الـ N من القواسم أي
+
+102
+00:10:31,840 --> 00:10:37,420
+P to N minus واحد الـ N من القواسم احصل حالك في
+
+103
+00:10:37,420 --> 00:10:44,460
+prime واحد تمشي و بتجيب المطلوب واضح؟
+
+104
+00:10:44,460 --> 00:10:47,880
+مش
+
+105
+00:10:47,880 --> 00:10:48,500
+واضح؟
+
+106
+00:10:51,100 --> 00:10:58,260
+لأ هذا غير هذا مثال
+
+107
+00:10:58,260 --> 00:11:02,300
+بخص الستة لوحدها لو بدك تجي على السبعة مش هتقدر
+
+108
+00:11:02,300 --> 00:11:06,460
+تيجي تأخذ مثلًا زد أربعة عاش لأ للستة هتقدر تأخذ زد
+
+109
+00:11:06,460 --> 00:11:13,420
+اثنين و نص خمس يعني زد اثنين و ثلاثين اه جرب اثنين
+
+110
+00:11:13,420 --> 00:11:25,030
+أربعة أربعة اثنين أربعة ثمانية 16 و 32 هيهم 6 لكن
+
+111
+00:11:25,030 --> 00:11:28,990
+مش هي الوحيدة يعني مش هي الوحيدة معناه لو أخدت زد
+
+112
+00:11:28,990 --> 00:11:32,770
+ثلاثة أُس N minus واحد بنفع زد سبعة أُس N minus
+
+113
+00:11:32,770 --> 00:11:40,070
+واحد بنفع في أكثر من واحدة طيب
+
+114
+00:11:40,070 --> 00:11:45,090
+سؤال 42 prove that an infinite group must have an
+
+115
+00:11:45,090 --> 00:11:51,210
+infinite number of subgroups جي generated by الـ a و
+
+116
+00:11:51,210 --> 00:11:56,870
+order الـ a بدي يساوي مانا نهاية بدك infinite sub
+
+117
+00:11:56,870 --> 00:12:01,810
+group كيف؟
+
+118
+00:12:01,810 --> 00:12:09,030
+let a عبارة عن generated by a to i حيث i is the
+
+119
+00:12:09,030 --> 00:12:13,770
+prime since
+
+120
+00:12:13,770 --> 00:12:27,110
+the number of the primes is infinite عدد
+
+121
+00:12:27,110 --> 00:12:34,310
+لا نهائي فش في even أو odd and generated by a to i
+
+122
+00:12:34,310 --> 00:12:41,510
+لا تساوي generated by a to j for i لا يساوي j هل الـ
+
+123
+00:12:41,510 --> 00:12:45,130
+generated by A أو السبعة بيساوي generated by A أو
+
+124
+00:12:45,130 --> 00:12:50,090
+السادس عشر؟ صعب و مستحيل تقدرش تجيب الـ A أو السبعة من
+
+125
+00:12:50,090 --> 00:12:52,830
+الـ A أو السادس عشر ولا الـ A أو السادس عشر من الـ A أو
+
+126
+00:12:52,830 --> 00:12:59,990
+السبعة هدول العداد تبعي لنهائي و أنا ما فيش تكرار
+
+127
+00:12:59,990 --> 00:13:06,030
+النتيجة A has infinite number
+
+128
+00:13:08,470 --> 00:13:17,190
+of elements يوجد في الـ A عدد لانهائي من العناصر كل
+
+129
+00:13:17,190 --> 00:13:22,390
+عنصر من هذه العناصر مش ممثلك where
+
+130
+00:13:22,390 --> 00:13:35,630
+each one is a cyclic subgroup of
+
+131
+00:13:35,630 --> 00:13:42,900
+G بالعدد أنا طبعا بقدر ألاجي غيرهم بقدر لكن بشغل
+
+132
+00:13:42,900 --> 00:13:51,050
+أنا على هذا الشكل أو على هذا النمط أثر ليعني
+
+133
+00:13:51,050 --> 00:13:54,770
+أعطيك أيام مثال رقمي لو أنت بتشغل في Z في عندك
+
+134
+00:13:54,770 --> 00:13:58,390
+generated by اثنين generated by ثلاثة generated by
+
+135
+00:13:58,390 --> 00:14:03,910
+خمسة generated by سبعة generated by أحد عشر إلى آخر
+
+136
+00:14:03,910 --> 00:14:07,690
+بتضلك إلى ما له نهاية ولا واحد زي الثاني هذا
+
+137
+00:14:07,690 --> 00:14:11,470
+مضاعفات الاثنين هذا مضاعفات الثلاثة هذا مضاعفات
+
+138
+00:14:11,470 --> 00:14:19,480
+الخمسة هذا مضاعفات السبعة ولا واحد زي فيه غيره بس 
+
+139
+00:14:19,480 --> 00:14:37,400
+أنا اشتغلت عليه برايم علشان ما ..
+
+140
+00:14:37,400 --> 00:14:44,340
+سؤال خمسة وأربعين بداك
+
+141
+00:14:44,340 --> 00:14:57,680
+العناصر في Z 40 اللي الـ order بدي يساوي عشرة بنجيب
+
+142
+00:14:57,680 --> 00:15:04,440
+واحد أول شيء بنجيب عددهم و بنجيب واحد و بنرفع هذا
+
+143
+00:15:04,440 --> 00:15:10,440
+لمين لـ relative prime مع العشرة the number of
+
+144
+00:15:10,440 --> 00:15:20,170
+elements in Z 40 with order عشرة is فايل عشرة
+
+145
+00:15:20,170 --> 00:15:25,770
+بدي يساوي أربعة ليش
+
+146
+00:15:25,770 --> 00:15:36,630
+أنت بتشغل في ZN و ZN شمالها Cyclic one of them is
+
+147
+00:15:36,630 --> 00:15:45,860
+مين A بدي يساوي أربعين على عشرة بدي يساوي الأربع الأربع
+
+148
+00:15:45,860 --> 00:15:53,580
+الـ order إيه له عشرة باقي العناصر الـ other
+
+149
+00:15:53,580 --> 00:15:58,780
+elements are
+
+150
+00:15:58,780 --> 00:16:03,980
+أربعة أوس واحد أربعة أوس ثلاثة أربعة أوس سبعة أربعة
+
+151
+00:16:03,980 --> 00:16:08,240
+أوس تسعة اللي هو ما عبارة عن الأربع والاثنا عشر
+
+152
+00:16:08,240 --> 00:16:13,940
+والثمانية والعشرين والستة والثلاثين هذا في سؤال في
+
+153
+00:16:13,940 --> 00:16:19,080
+التلخيص حلناه من هذا النمط لما تيجي تشترط على الـ
+
+154
+00:16:19,080 --> 00:16:24,260
+order بدي يساوي أربعين list all the elements of that
+
+155
+00:16:24,260 --> 00:16:29,700
+have order عشرة هنا تعميم يعني في تكملة السؤال
+
+156
+00:16:29,700 --> 00:16:37,880
+هتأخذ اللي هو X أوس أربعة الـ X generated و X أُس
+
+157
+00:16:37,880 --> 00:16:47,000
+12 و X أُس 28 و X أُس 36 تكملة للسؤال
+
+158
+00:17:06,320 --> 00:17:11,680
+ماشي سؤال 47 بدنا نجيب عدد الـ order للعناصر في D33
+
+159
+00:17:11,680 --> 00:17:19,800
+طبعا D33 عبارة عن 66 عنصر 33 منهم عبارة عن دورات
+
+160
+00:17:19,800 --> 00:17:26,480
+و 33 الثانيين عبارة عن reflection الدورات بيبدأ ب
+
+161
+00:17:26,480 --> 00:17:37,460
+R0 R 360 على 33 وصولنا لـ R N-1 يعني اثنين و ثلاثين
+
+162
+00:17:37,460 --> 00:17:43,240
+على ثلاثة و ثلاثين في ثلاثة مية و ستين وبعدين بيبدأ
+
+163
+00:17:43,240 --> 00:17:48,500
+بـ F واحد F في اثنين لأن F في ثلاثة و ثلاثين
+
+164
+00:17:48,500 --> 00:17:54,980
+الأولانية التواغنات والباقي عبارة عن reflections
+
+165
+00:17:54,980 --> 00:18:02,350
+الـ order لأي F I بدي يساوي اثنين لأن أنت لما تعمل
+
+166
+00:18:02,350 --> 00:18:09,130
+انعكاس وتعكس الانعكاس بيرجع مكانه الـ order لـ R
+
+167
+00:18:09,130 --> 00:18:15,310
+ماشي بدي يساوي طبعا
+
+168
+00:18:15,310 --> 00:18:22,130
+هدول عبارة عن R اي في ثلاثة مية أو ثلاثة مية و ستين
+
+169
+00:18:22,130 --> 00:18:29,030
+مثلا ك على ثلاثة و ثلاثين والك
+
+170
+00:18:32,470 --> 00:18:40,730
+محصور بين الـ 32 و الـ 0 بنجيب الـ orders اللي باقي
+
+171
+00:18:40,730 --> 00:18:45,250
+العناصر اللي هي عبارة عن الدورات كل عنصر بهذا
+
+172
+00:18:45,250 --> 00:18:49,430
+الشكل الـ order إله هيكون
+
+173
+00:18:55,620 --> 00:19:00,300
+انسى هدول شباب هذا أشبه بالـ Zero هذا بالواحد هذا
+
+174
+00:19:00,300 --> 00:19:05,380
+بالاثنين هذا بالاثنين والثلاثين يعني هم زي عناصر مين
+
+175
+00:19:05,380 --> 00:19:10,320
+الـ Z ثلاثة وثلاثين يعني هم كلهم أصلا هذا الـ
+
+176
+00:19:10,320 --> 00:19:16,340
+answer الـ R ثلاثة وستين K على ثلاثة و ثلاثين
+
+177
+00:19:16,340 --> 00:19:22,460
+عبارة عن الـ R ثلاثة وستين على ثلاثة و ثلاثين أُس K
+
+178
+00:19:25,710 --> 00:19:36,130
+طيب يعني لو أخذت أنا لـ مثلا A عبارة عن R 360 على
+
+179
+00:19:36,130 --> 00:19:43,110
+33 هيكون الـ order للـ A جديش اللي هو اللي بيولد
+
+180
+00:19:43,110 --> 00:19:50,950
+الجزئية هذه من الـ D 33 الـ order له 33 فأنت لما بدك
+
+181
+00:19:50,950 --> 00:19:52,570
+تيجي تتعامل مع الـ order
+
+182
+00:19:57,580 --> 00:20:02,520
+لـ R ثلاثة وستين كي على ثلاثة و ثلاثين اللي هو
+
+183
+00:20:02,520 --> 00:20:07,160
+عبارة عن الـ order لـ a to k إيش الـ order لـ a to k
+
+184
+00:20:07,160 --> 00:20:13,780
+عبارة عن ثلاثة و ثلاثين على الجريس common divisor
+
+185
+00:20:13,780 --> 00:20:19,940
+لكي ثلاثة و ثلاثين و
+
+186
+00:20:19,940 --> 00:20:26,360
+حسب إيش في عندك عناصر هان بيطلع الـ order يلو بهذا
+
+187
+00:20:26,360 --> 00:20:32,610
+الشكل عيد بسرعة دي ثلاثة و ثلاثين جزئين جزء سهل
+
+188
+00:20:32,610 --> 00:20:36,150
+اللي هو reflections كل عنصر الـ order له اثنين و
+
+189
+00:20:36,150 --> 00:20:43,990
+جزء بيشابه مين الـ ZN فالـ order له لو أنا أخذت اتبعت
+
+190
+00:20:43,990 --> 00:20:49,030
+الـ A هو الـ generator فكل عنصر مثلا عبارة عن الـ A
+
+191
+00:20:49,030 --> 00:20:53,330
+أُس K و الـ order لـ A أُس K عبارة عن الثلاثة و
+
+192
+00:20:53,330 --> 00:20:56,350
+ثلاثين اللي هو order الـ A على gcd common divisor
+
+193
+00:20:56,350 --> 00:21:04,230
+لـ K و ثلاثة و ثلاثين طيب
+
+194
+00:21:04,230 --> 00:21:17,230
+ثمانية
+
+195
+00:21:17,230 --> 00:21:21,170
+وأربعين if J is cyclic group and خمسة عشر divide by
+
+196
+00:21:21,170 --> 00:21:24,950
+order of J then the number of solution of J of
+
+197
+00:21:24,950 --> 00:21:32,630
+equation x to خمسة عشر سوى a J is cyclic خمسة عشر
+
+198
+00:21:32,630 --> 00:21:41,530
+تقسم order of J وأنا ب dash على X أُس خمسة عشر بدي
+
+199
+00:21:41,530 --> 00:21:42,330
+يساوي الـ identity
+
+200
+00:21:54,710 --> 00:21:57,970
+أوجد عدد العناصر اللي بيحلوا المعادلة هذه في الـ J
+
+201
+00:21:57,970 --> 00:22:07,670
+طبعا since الـ 15 تقسم الـ order للـ J و الـ J is
+
+202
+00:22:07,670 --> 00:22:15,850
+cyclic هذا معناه يوجد A ينتمي للـ J with A أُس 15
+
+203
+00:22:15,850 --> 00:22:21,750
+أو with order الـ A بدي يساوي 15 احنا قلنا نظرية أو
+
+204
+00:22:21,750 --> 00:22:25,990
+caller على نظرية لأي group لو في قاسم بيقسم الـ
+
+205
+00:22:25,990 --> 00:22:30,370
+order إليها ففي عنصر في الـ group هذه الـ order اللي
+
+206
+00:22:30,370 --> 00:22:37,590
+بيسوي هذا القاسم هذا معناه the set H أو بلاش H
+
+207
+00:22:37,590 --> 00:22:41,830
+عشان ما تفكر أشهر بالـ group the set T عبارة عن كل X
+
+208
+00:22:41,830 --> 00:22:47,270
+في J X أُس 15 بدي يساوي الـ identity is none أو is
+
+209
+00:22:47,270 --> 00:22:56,500
+not empty هذه المجموعة غير خالية لماذا؟
+
+210
+00:22:56,500 --> 00:23:07,600
+لأن هناك عناصر موجودة فيها نستطيع أن نكتب T عبارة
+
+211
+00:23:07,600 --> 00:23:14,860
+عن الـ identity اتحاد كل الـ X في J order الـ X يكون 3
+
+212
+00:23:16,060 --> 00:23:21,940
+اتحاد كل الـ X في J order الـ X بدي يساوي خمسة اتحاد
+
+213
+00:23:21,940 --> 00:23:28,120
+كل الـ X في J order الـ X بدي يساوي خمسة عشر عشان
+
+214
+00:23:28,120 --> 00:23:31,600
+يكون الـ X أُس خمسة عشر بدي يساوي الـ identity فـ order
+
+215
+00:23:31,600 --> 00:23:40,940
+الـ X يا واحد يا ثلاثة يا خمسة يا خمسة عشر هذه
+
+216
+00:23:40,940 --> 00:23:47,950
+المجموعة كمانصور كمانصور هان عنصر واحد طب هذا كم
+
+217
+00:23:47,950 --> 00:23:58,690
+عنصر فايل ثلاثة أكمن عنصر الـ order له خمسة فايل خمسة
+
+218
+00:23:58,690 --> 00:24:06,310
+أكمن عنصر الـ order له خمسة عشر فايل خمسة عشر إجبار عدد
+
+219
+00:24:06,310 --> 00:24:14,810
+عناصر الـ T بدي يساوي واحد زائد فايل ثلاثة فايل خمسة زائد
+
+220
+00:24:14,810 --> 00:24:19,910
+فايل خمسة عشر اللي هو واحد زائد اثنين زائد أربعة فايل
+
+221
+00:24:19,910 --> 00:24:27,670
+خمسة عشر جديش برضه أربعة جديش المجموعة دي عشرة كم
+
+222
+00:24:27,670 --> 00:24:36,240
+عنصر في الـ J بيحقق المعادلة دي عشرة عناصر عيد بسرعة
+
+223
+00:24:36,240 --> 00:24:40,820
+علشان يكون عندي الـ X أُس خمسة عشر بيساوي الـ identity
+
+224
+00:24:40,820 --> 00:24:45,380
+أولا أنا متأكد أن في عندي عنصر ليش؟ لأن الخمسة عشر
+
+225
+00:24:45,380 --> 00:24:49,360
+تقسم الـ J وبالتالي في عنصر order الخمسة عشر ممكن
+
+226
+00:24:49,360 --> 00:24:52,280
+أتأكد بطريقة ثانية E أُس خمسة عشر بيساوي E
+
+227
+00:24:57,840 --> 00:25:01,320
+العناصر اللي بيحققوا إن X أُس 15 يساوي الـ identity
+
+228
+00:25:01,320 --> 00:25:05,380
+عشان أنا بشتغل في الـ group يا الـ order واحد يا
+
+229
+00:25:05,380 --> 00:25:10,920
+ثلاثة يا خمسة يا خمسة عشر العناصر اللي الـ order لهم
+
+230
+00:25:10,920 --> 00:25:14,440
+واحد عددهم واحد العناصر اللي الـ order ثلاثة فايل
+
+231
+00:25:14,440 --> 00:25:17,840
+ثلاثة العناصر اللي الـ order خمسة فايل خمسة
+
+232
+00:25:17,840 --> 00:25:22,020
+والعناصر اللي الـ order خمسة عشر فايل خمسة عشر
+
+233
+00:25:22,020 --> 00:25:27,770
+المحصلة واحد زي اثنين زي أربعة زي أربعة دي عشر عناصر
+
+234
+00:25:27,770 --> 00:25:41,450
+عشان
+
+235
+00:25:41,450 --> 00:25:44,970
+تشتغل order بيساوي خمسة عشر يعني X أُس خمسة عشر احنا
+
+236
+00:25:44,970 --> 00:25:47,910
+قلنا يبنى ها بطريقة الـ order X أُس خمسة عشر سواء الـ
+
+237
+00:25:47,910 --> 00:25:53,010
+identity بقى الـ order خمسة عشر واحد و خمسين
+
+238
+00:25:54,660 --> 00:25:59,460
+عشان نرجع للسؤال رقم 51 no group can have exactly
+
+239
+00:25:59,460 --> 00:26:03,920
+two elements of order اثنين يعني لو في عنصرين الـ
+
+240
+00:26:03,920 --> 00:26:09,660
+order اللي لهم اثنين ففي ثالث لو في عنصرين الـ order
+
+241
+00:26:09,660 --> 00:26:21,340
+اللي لهم اثنين ففي ثالث let J be a group with
+
+242
+00:26:22,180 --> 00:26:27,120
+A و B ينتمي للـ J and order الـ B بدي يساوي order
+
+243
+00:26:27,120 --> 00:26:33,500
+الـ A بدي يساوي order الـ B بدي يساوي إيش اثنين هذا
+
+244
+00:26:33,500 --> 00:26:43,860
+معناه إنه A طبعا with عشان أتكلم عنهم A لا يساوي
+
+245
+00:26:43,860 --> 00:26:46,660
+B note that
+
+246
+00:26:49,910 --> 00:26:54,430
+order الـ A بدي يساوي 2 يعني A inverse بدي يساوي A
+
+247
+00:26:54,430 --> 00:27:00,510
+order الـ B بدي يساوي 2 يعني B inverse بدي يساوي B
+
+248
+00:27:00,510 --> 00:27:03,790
+عشان ما حدش يقول لي ماشي الـ A لا يساوي B لأ ممكن يساوي
+
+249
+00:27:03,790 --> 00:27:12,010
+الـ inverse ما بيساويش الـ inverse طيب
+
+250
+00:27:32,110 --> 00:27:39,730
+كيف نكمل الـ A
+
+251
+00:27:39,730 --> 00:27:56,570
+والـ P بيسووا ال inverse تبعتهم مش 
+
+252
+00:27:56,570 --> 00:27:56,890
+فاهم
+
+253
+00:28:03,880 --> 00:28:07,280
+طيب طب أنا فرضت أنه فيه اثنين مدتبت أنه فيه تالت لو
+
+254
+00:28:07,280 --> 00:28:12,860
+فرضت أنه أنه فش غير الاتنين هتروح تجيب التالت و
+
+255
+00:28:12,860 --> 00:28:17,500
+تعمل تناقض يعني في نهاية نفس السياق فقط بتضيف جملة 
+
+256
+00:28:17,500 --> 00:28:22,360
+و بتحط contradiction في الآخر فضل عاطف طب أنا عارف
+
+257
+00:28:22,360 --> 00:28:26,820
+حال السؤال طيب
+
+258
+00:28:26,820 --> 00:28:28,140
+ايش حالك؟
+
+259
+00:28:31,380 --> 00:28:34,040
+تأخذ عنصر تثبت أن ال order للـ اثنين غير الـ a و الـ b
+
+260
+00:28:34,040 --> 00:28:45,340
+زي مين a,b,a صحيح طيب now a
+
+261
+00:28:45,340 --> 00:28:51,920
+,b,a ينتمي لمين؟ ده الـ D تعالوا نشوف ال order لـ a,b
+
+262
+00:28:51,920 --> 00:29:01,230
+,a a,b,a تربيع عبارة عن a,b,a,a,b,a الو عبارة عن a
+
+263
+00:29:01,230 --> 00:29:08,070
+b a تربيع بي a يعني a بي identity بي ايه a بي
+
+264
+00:29:08,070 --> 00:29:12,690
+تربيع ايه a identity ايه ايه تربيع بيساوي identity
+
+265
+00:29:12,690 --> 00:29:24,790
+معناته order الـ a بي ايه مش بيساوي يا واحد يا اتنين
+
+266
+00:29:24,790 --> 00:29:33,280
+طبعا أنا غلطت يعني لأنه لو أنا بتعامل مع group
+
+267
+00:29:33,280 --> 00:29:38,860
+abelian فال a,b,a إيش هيساوي بيه؟ أنا ماجبتش إيش
+
+268
+00:29:38,860 --> 00:29:49,360
+جديد يقبل أنا بضيف جملة if j is non abelian let و
+
+269
+00:29:49,360 --> 00:29:58,780
+then a,b,a في الـ j طيب يقبل order لـ a,b,a يا واحد
+
+270
+00:29:58,780 --> 00:29:59,260
+يا اتنين
+
+271
+00:30:02,100 --> 00:30:08,020
+ف order a,b,a بدي يساوي واحد a,b,a بدي يساوي ال
+
+272
+00:30:08,020 --> 00:30:13,200
+identity يعني a,b بدي تساوي a inverse بدي تساوي a
+
+273
+00:30:13,200 --> 00:30:17,640
+يعني a,b بدي تساوي a يعني b بدي تساوي ال identity
+
+274
+00:30:17,640 --> 00:30:28,960
+تناقض المحصلة ان order b,a بدي يساوي ايش اتنين
+
+275
+00:30:32,420 --> 00:30:36,760
+عشان اثبت ان هو عنصر تالت ال order له اتنين لا بدي
+
+276
+00:30:36,760 --> 00:30:43,960
+يساوي ال a ولا بدي يساوي ال b if a,b,a بدي يساوي a,b
+
+277
+00:30:43,960 --> 00:30:47,460
+,a بدي يساوي ال identity,b بدي تساوي a inverse بدي
+
+278
+00:30:47,460 --> 00:30:56,360
+يساوي a,b بدي تساوي a تناقض if a,b,a بدي تساوي b
+
+279
+00:31:05,480 --> 00:31:10,640
+هذا معناته، مع أن النطق بيليان، مش ضروري أن ال A
+
+280
+00:31:10,640 --> 00:31:20,620
+بي تساوي بيه A، ليش بقاش راح لازم أعمل، أنا فرضت
+
+281
+00:31:20,620 --> 00:31:24,860
+أنه نمأ بيليان على مين؟ ع الجيه كلها لما أنا بدي
+
+282
+00:31:24,860 --> 00:31:28,780
+أجي أقول لها انا a b بتساوي بي a inverse بتساوي بي
+
+283
+00:31:28,780 --> 00:31:34,440
+ايه يعني a b بتساوي بي a هذا لا يناقض انها non
+
+284
+00:31:34,440 --> 00:31:40,740
+abelian هذا لا يناقض انها non abelian طيب بدأ أروح
+
+285
+00:31:40,740 --> 00:31:44,900
+معناته أغير الفرض تبعي علشان يعطيني تناقض مع هذه
+
+286
+00:31:44,900 --> 00:31:55,060
+الجملة بدل ما أقول جيه non abelian اش عمل AB لا
+
+287
+00:31:55,060 --> 00:32:01,320
+يساوي BA عشان هذه تصير تناقض مين؟ هذه وبالتالي
+
+288
+00:32:01,320 --> 00:32:13,040
+صارت تناقض so ABA is another element with
+
+289
+00:32:13,040 --> 00:32:26,570
+order 2 in J so we have At least كم واحد؟ الـ three
+
+290
+00:32:26,570 --> 00:32:35,850
+elements in J with order تنين
+
+291
+00:32:35,850 --> 00:32:42,530
+خلصنا؟ لأ أنا الحالة اللي ال A,B لا يساوي بيه A
+
+292
+00:32:42,530 --> 00:32:47,790
+أنهيتها طب الحالة التانية لما ال A,B يساوي بيه
+
+293
+00:32:47,790 --> 00:32:52,170
+اتفضل اللي بيساوي بي إيه ليه التناقض دس فاطل التناقض
+
+294
+00:32:52,170 --> 00:33:01,090
+اللي بيساوي بي إيه ليه التناقض دس فاطل
+
+295
+00:33:01,090 --> 00:33:04,270
+التناقض اللي بيساوي بي إيه ليه التناقض اللي بيساو
+
+296
+00:33:04,270 --> 00:33:05,030
+بي إيه ليه التناقض اللي بيساو بي إيه ليه التناقض
+
+297
+00:33:05,030 --> 00:33:05,350
+اللي بيساو بي إيه ليه التناقض اللي بيساو بي إيه
+
+298
+00:33:05,350 --> 00:33:08,970
+ليه التناقض اللي بيساو بي إيه ليه التناقض اللي
+
+299
+00:33:08,970 --> 00:33:13,610
+بيساو بي إيه ليه التناقض اللي بيساو بي إيه ليه
+
+300
+00:33:13,610 --> 00:33:18,710
+التناقض اللي بيساو بي إيه ليه التناقض اللي بيساو ب
+
+301
+00:33:19,890 --> 00:33:25,590
+غير الـ a,b,a طيب
+
+302
+00:33:25,590 --> 00:33:36,950
+if a,b بدي تساوي b,a then a,b ينتمي للـ j ال a,b
+
+303
+00:33:36,950 --> 00:33:43,670
+تربيع يعني a,b a,b يعني a تربيع b تربيع identity
+
+304
+00:33:43,670 --> 00:33:51,380
+في identity واحد عشان abelian طيب هذا معناته ان
+
+305
+00:33:51,380 --> 00:33:57,720
+order ال a,b بدي تساوي واحد او اتنين if order ال a
+
+306
+00:33:57,720 --> 00:33:59,620
+,b بدي تساوي واحد if order ال a,b بدي تساوي واحد if
+
+307
+00:33:59,620 --> 00:34:00,040
+order ال a,b بدي تساوي واحد if order ال a,b بدت
+
+308
+00:34:00,040 --> 00:34:00,400
+تساوي واحد if order ال a,b بدي تساوي واحد if order
+
+309
+00:34:00,400 --> 00:34:00,880
+ال a,b بدي تساوي واحد if order ال a,b بدي تساوي واحد
+
+310
+00:34:00,880 --> 00:34:01,900
+if order ال a,b بدي تساوي واحد if order ال a,b بدي
+
+311
+00:34:01,900 --> 00:34:05,340
+تساوي واحد if order ال a,b بدي تساوي واحد if order
+
+312
+00:34:05,340 --> 00:34:06,400
+ال a,b بدي تساوي واحد if order ال a,b بدي تساوي واحد
+
+313
+00:34:06,400 --> 00:34:09,800
+if order ال a,b بدي تساوي واحد if order ال a,b بدي
+
+314
+00:34:09,800 --> 00:34:16,720
+تساوي واحد if order ال a,b بدي تساوي واحد if order
+
+315
+00:34:16,720 --> 00:34:20,120
+ال a,b بدي يساوي ايه بدي بدي بدي بدي بدي بدي بدي بدي
+
+316
+00:34:20,120 --> 00:34:24,120
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+317
+00:34:24,120 --> 00:34:26,340
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+318
+00:34:26,340 --> 00:34:26,740
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+319
+00:34:26,740 --> 00:34:29,140
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+320
+00:34:29,140 --> 00:34:29,180
+بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي بدي
+
+321
+00:34:29,180 --> 00:34:43,000
+بدي بدي
+
+322
+00:34:43,000 --> 00:34:50,630
+بدي يجيب في حالة ما يكونوا مش متبادلين بلاقي تلت
+
+323
+00:34:50,630 --> 00:34:55,310
+عناصر في حالة ما يكونوا متبادلين برضه بلاقي تلت
+
+324
+00:34:55,310 --> 00:35:00,550
+عناصر يجب مستحيل ألاقي عنصرين بس دائما أي عنصرين
+
+325
+00:35:00,550 --> 00:35:06,490
+بيعطوني مين؟ التالت هل في رابع خامس سادس ما يخصنيش 
+
+326
+00:35:06,490 --> 00:35:11,470
+بس أنا على الأقل عند مين؟ تلتة هل ممكن ألاقي عنصر
+
+327
+00:35:11,470 --> 00:35:12,770
+واحد ال order الاتنين
+
+328
+00:35:15,280 --> 00:35:20,740
+بقدر؟ اه بقدر وين؟ مستحيل لإن معكوسه اتنين طبعا هو
+
+329
+00:35:20,740 --> 00:35:26,400
+بيساوي معكوسه في الزد اتنين في الزد اتنين اللي
+
+330
+00:35:26,400 --> 00:35:30,520
+فيها الصفر و الواحد يوجد عنصر واحد فقط ال order له
+
+331
+00:35:30,520 --> 00:35:36,060
+اتنين وهو الواحد
+
+332
+00:35:36,060 --> 00:35:41,840
+مستبعد
+
+333
+00:35:41,840 --> 00:35:44,700
+يا أمان طيب
+
+334
+00:35:46,110 --> 00:35:51,350
+تنين و خمسين Given the fact that U تسعة و أربعين
+
+335
+00:35:51,350 --> 00:35:54,090
+is cyclic and has تنين و أربعين elements that use
+
+336
+00:35:54,090 --> 00:35:57,110
+the number of generator جديش عدد ال generator اللي
+
+337
+00:35:57,110 --> 00:36:03,250
+تبعون ال U تسعة و أربعين جديش ال U تسعة و أربعين
+
+338
+00:36:03,250 --> 00:36:05,770
+هي ال cyclic group و ال order لها تنين و أربعين
+
+339
+00:36:05,770 --> 00:36:13,140
+أكم generator لها فايه تنين و أربعين لما يكون عندك
+
+340
+00:36:13,140 --> 00:36:16,860
+Cyclic جروب ال order يلها N جديش عدد ال generator
+
+341
+00:36:16,860 --> 00:36:28,880
+فايل ان طبق مباشرة مانت
+
+342
+00:36:28,880 --> 00:36:37,190
+السؤال 52 الجواب تبع في 42 سؤال 53 الـ A و الـ B
+
+343
+00:36:37,190 --> 00:36:39,850
+elements in the group ال order لـ A بدي يساوي عشرة ال
+
+344
+00:36:39,850 --> 00:36:43,010
+order لـ B بدي يساوي واحد و عشرين show that انه
+
+345
+00:36:43,010 --> 00:36:45,590
+generated by الـ A تقاطع generated by الـ B بدي يساوي
+
+346
+00:36:45,590 --> 00:36:52,290
+ال identity طيب يعني let X ينتمي ل generated by ال
+
+347
+00:36:52,290 --> 00:36:57,770
+A تقاطع generated by الـ B هذا
+
+348
+00:36:57,770 --> 00:37:03,380
+معناته ال X ينتمي ل generated by الـ A يكبر order ال
+
+349
+00:37:03,380 --> 00:37:09,820
+X بيقسم order الـ A بدي يساوي عداش؟ عشرة ال X ينتمي ل
+
+350
+00:37:09,820 --> 00:37:14,540
+generated by الـ B يكبر order الـ X يقسم ال order ل
+
+351
+00:37:14,540 --> 00:37:19,220
+الـ B بدي يساوي واحد و عشرين بنتو order الـ X بدي
+
+352
+00:37:19,220 --> 00:37:22,320
+يقسم ل greatest common divisor ل العشرة والواحد و
+
+353
+00:37:22,320 --> 00:37:27,060
+عشرين بدي يساوي واحد order الـ X بدي يساوي واحد وال X
+
+354
+00:37:27,060 --> 00:37:30,770
+بدي يساوي ال identity اللي صار كالتالي أنا بدي أثبت
+
+355
+00:37:30,770 --> 00:37:34,570
+ان التقاطع لا يوجد فيه غير المحايد أخدت عنصر ان
+
+356
+00:37:34,570 --> 00:37:38,930
+التقاطع ال order له بيقسم العشرة لإنه موجود في
+
+357
+00:37:38,930 --> 00:37:42,410
+group ال order له عشرة و ال order له بيقسم ال واحد
+
+358
+00:37:42,410 --> 00:37:45,690
+و عشرين لإنه موجود في group ال order له واحد و
+
+359
+00:37:45,690 --> 00:37:49,750
+عشرين بيقسم العشرة و ال واحد و عشرين هيقسم ال greatest
+
+360
+00:37:49,750 --> 00:37:52,210
+common divisor لعشرة و ال واحد و عشرين و بيساوي
+
+361
+00:37:52,210 --> 00:37:58,500
+واحد مين عنصر ال order له واحد؟ Generated by الـ A
+
+362
+00:37:58,500 --> 00:38:03,860
+تقاطع Generated by الـ B بيساوي ال Identity سؤال
+
+363
+00:38:03,860 --> 00:38:13,920
+54 تعميم ل 53 بس
+
+364
+00:38:13,920 --> 00:38:19,480
+بدل العشر والخمستعش M و N و ال M و N relative ال
+
+365
+00:38:19,480 --> 00:38:19,740
+prime
+
+366
+00:38:30,570 --> 00:38:39,010
+سؤال خمسة و خمسين what are possibilities of order
+
+367
+00:38:39,010 --> 00:38:44,030
+type؟
+
+368
+00:38:44,030 --> 00:38:49,510
+ال order لل a بيكون عشرة
+
+369
+00:38:49,860 --> 00:38:54,260
+فلو كان ال X ينتمي ل generated by ال A تقاطع
+
+370
+00:38:54,260 --> 00:38:58,000
+generated by ال B ف order ال X بيقسم ل greatest
+
+371
+00:38:58,000 --> 00:39:03,980
+common divisor لل 24 و 10 جديش؟ ف order ال X بيقسم
+
+372
+00:39:03,980 --> 00:39:09,060
+ل 2 يجب العناصر اللي موجودة في التقاطع هذا ال
+
+373
+00:39:09,060 --> 00:39:18,530
+order إلا يا 1 يا 2 كم واحد؟ طبعا أنت بتتكلم عن
+
+374
+00:39:18,530 --> 00:39:22,130
+Cyclic group أنت عندك Cyclic sub group ع Cyclic
+
+375
+00:39:22,130 --> 00:39:26,210
+sub group التقاطع تبعهم Cyclic sub group هيكون ال 
+
+376
+00:39:26,210 --> 00:39:31,970
+order له كم
+
+377
+00:39:31,970 --> 00:39:39,290
+أنصر ال identity هو أنصر ال order له جدّيش اثنين
+
+378
+00:39:39,290 --> 00:39:44,270
+يجب ال order له جدّيش اثنين أنه هيساوي ال identity
+
+379
+00:39:47,930 --> 00:39:54,770
+و X و order X سيكون اثنين ايه بقى ال order ل هذا
+
+380
+00:39:54,770 --> 00:40:02,670
+ال generator سيكون اثنين ستة
+
+381
+00:40:02,670 --> 00:40:09,410
+و خمسين ال
+
+382
+00:40:09,410 --> 00:40:10,890
+E و تلانوس N is not
+
+383
+00:40:14,600 --> 00:40:18,520
+خلاص، ضال عندي أول سؤال ستة و خمسين، ثمانية و
+
+384
+00:40:18,520 --> 00:40:20,900
+خمسين، تسعة و خمسين، أربعة، هذا سؤال مهم يا شباب
+
+385
+00:40:20,900 --> 00:40:24,820
+عشان الخامس أسئلة اللي ضايلة بنحلها في بداية
+
+386
+00:40:24,820 --> 00:40:28,900
+المحاضرة القادمة و بعد هيك بنكمل أو بنفوض إن شاء
+
+387
+00:40:28,900 --> 00:40:30,520
+الله في الشبطة الخامس، أعطيكم العافية 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eNtIlTkhU3g_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/eNtIlTkhU3g_raw.srt
new file mode 100644
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@@ -0,0 +1,1852 @@
+1
+00:00:21,160 --> 00:00:25,200
+بسم الله الرحمن الرحيم اليوم ان شاء الله بنكمل ما
+
+2
+00:00:25,200 --> 00:00:30,420
+ابتدأناه في المحاضرة الماضية و هو اننا لازمنا في
+
+3
+00:00:30,420 --> 00:00:35,180
+chapter المقدمة اللازمة لل abstract algebra لهذا
+
+4
+00:00:35,180 --> 00:00:41,350
+الفصلفي المرة الماضية اتعرضنا لتقسيمات ال sets ال
+
+5
+00:00:41,350 --> 00:00:46,410
+natural numbers ال set of integers ال rational
+
+6
+00:00:46,410 --> 00:00:49,870
+numbers ال real numbers ال complex numbers ثم
+
+7
+00:00:49,870 --> 00:00:55,970
+اتعرضنا للقسمة و خوارزمية القسمة و ال primes اللي
+
+8
+00:00:55,970 --> 00:01:02,310
+هي من الأعداد الأولية و كذلك لمضاعفات الأشياءاليوم
+
+9
+00:01:02,310 --> 00:01:05,890
+ان شاء الله بدنا نبدأ في او طبعه هو ال regression
+
+10
+00:01:05,890 --> 00:01:10,510
+common divisor وكتابة اللي هو regression common
+
+11
+00:01:10,510 --> 00:01:15,490
+divisor على شكل linear combination من الرقمين
+
+12
+00:01:15,490 --> 00:01:18,930
+تبعات regression common divisor ل two elements a و
+
+13
+00:01:18,930 --> 00:01:24,230
+b بقولنا بإمكانكم كتابته على شكل a s زائد t في b
+
+14
+00:01:24,230 --> 00:01:30,230
+حيث ال s و t رقمين موجودين في set of integersبدنا
+
+15
+00:01:30,230 --> 00:01:39,270
+نيجي لان للمة اللي بتقول ما يأتي لما بيقول
+
+16
+00:01:39,270 --> 00:01:49,070
+if P is a prime if P is a prime لو كان P عدد أولي
+
+17
+00:01:49,070 --> 00:02:00,310
+and ال P divide حصل الضرب A في B thenال P بتقسم ال
+
+18
+00:02:00,310 --> 00:02:15,850
+A او ال P بتقسم ال B لما
+
+19
+00:02:15,850 --> 00:02:20,880
+بالعربي يا شباب يعني فرضية مساعدةزي و لا تشبيه
+
+20
+00:02:20,880 --> 00:02:25,180
+بقينا نقول في الهندسة زمان تمرين مشهور يبقى هذه ما
+
+21
+00:02:25,180 --> 00:02:31,240
+نسميها فرضية مساعدة الترجمة العربية لكلمة لمّة بس
+
+22
+00:02:31,240 --> 00:02:36,100
+احنا أنا في العربي في لمّة و ليس لمّة سمعتوا فيها
+
+23
+00:02:36,100 --> 00:02:41,400
+لمّة في اللغة العربية موجودة في آية من القرآن
+
+24
+00:02:41,400 --> 00:02:44,540
+الكريم حد بعرفلي هذه الآية
+
+25
+00:02:48,770 --> 00:02:54,810
+لأ مش ولما أنا بقول لك لما فقط بدون واحد في صورة
+
+26
+00:02:54,810 --> 00:03:02,150
+ايش في صورة ايش الحجرات لأ يا راجل تاجي الله
+
+27
+00:03:02,150 --> 00:03:10,830
+وتأكلون التراث أكل اللما في الفجر ممتاز جدا طيب
+
+28
+00:03:10,830 --> 00:03:16,460
+ايش معنى لما هنا في اللغة العربيةو تأكلون التراث
+
+29
+00:03:16,460 --> 00:03:18,020
+أكل اللمّا
+
+30
+00:03:28,940 --> 00:03:33,400
+يعني بهذا المعنى قريبا هو تأكلون التراث أكلا لما
+
+31
+00:03:33,400 --> 00:03:38,440
+التراث المقصود به هو الميراث فبعض الوراثة بروح
+
+32
+00:03:38,440 --> 00:03:42,860
+بستاسر بروح اه بروح على الطاب و بسجل الميراث كله
+
+33
+00:03:42,860 --> 00:03:45,880
+باسمه و بحرم مين بحرم الباقي
+
+34
+00:04:00,840 --> 00:04:05,380
+يبقى لما يقول ف ال P is a prime لو كان ال P عددا
+
+35
+00:04:05,380 --> 00:04:11,850
+اولياوالـ P بيقسم حصلت ضرب A في B يبقى P في هذه
+
+36
+00:04:11,850 --> 00:04:17,650
+الحالة إما أن يقسم ال A وإما أن يقسم ال B واحدة
+
+37
+00:04:17,650 --> 00:04:22,170
+منهم مش التنتين في آن واحد نروح نثبت صحة هذا
+
+38
+00:04:22,170 --> 00:04:30,410
+الكلام يبقى بالداجي أقوله assume افترض ان ال P is
+
+39
+00:04:30,410 --> 00:04:40,910
+primeand ال P divide ال A بي هذا المعطيات ايش
+
+40
+00:04:40,910 --> 00:04:46,710
+بيقولي يبقى بيقول ال P يبدأ تقسم ال A يبدأ تقسم ال
+
+41
+00:04:46,710 --> 00:04:52,270
+B يبقى انا بدأ افترض انها مثلا لا تقسم ال A واروح
+
+42
+00:04:52,270 --> 00:05:00,380
+اثبت انها تقسم ال B يبقى هنا بدأجي اقول letالـP
+
+43
+00:05:00,380 --> 00:05:07,500
+بتقسم الـA لا تقسم الـA مثلا يبقى شو بدنا نعمل one
+
+44
+00:05:07,500 --> 00:05:14,700
+to show بدنا نروح نبين ان الـP بتقسم الـB هذا اللي
+
+45
+00:05:14,700 --> 00:05:22,480
+عايزين نثبته الآن بجي بقوله since بما ان الـP لا
+
+46
+00:05:22,480 --> 00:05:24,080
+تقسم الـA
+
+47
+00:05:26,430 --> 00:05:32,090
+إذا شو العلاقة بين ال P و ال A اتنين ال Primes
+
+48
+00:05:32,090 --> 00:05:37,590
+والله Relatively Primes Relatively Primes تمام
+
+49
+00:05:37,590 --> 00:05:49,830
+تمام يبقى since then ال A and ال P are Relatively
+
+50
+00:05:49,830 --> 00:05:52,490
+Primes
+
+51
+00:05:54,370 --> 00:05:57,890
+طيب كويس يبقى كده ال agressives common divisors ما
+
+52
+00:05:57,890 --> 00:06:04,070
+بين الاتنين واحد صحيح يبقى relatively a prime هذا
+
+53
+00:06:04,070 --> 00:06:09,470
+بده يعطينا لل agressives common divisors لمن لل a
+
+54
+00:06:09,470 --> 00:06:16,050
+و ال p بده يساوي كده؟ واحد صحيحأخر حاجة في محاضرة
+
+55
+00:06:16,050 --> 00:06:19,970
+المرة الماضية قلنا لـgressus common divisor بقدر
+
+56
+00:06:19,970 --> 00:06:24,430
+اكتبه على صيغة linear combination من ال a و ال p
+
+57
+00:06:24,430 --> 00:06:34,870
+مظبوط يبقى هدف يتطلب ان هناك s و t موجودة في z
+
+58
+00:06:34,870 --> 00:06:45,620
+integers such that بحيث انالـ A S زائد ال P T كله
+
+59
+00:06:45,620 --> 00:06:49,800
+بده يساوي مين؟ بده يساوي واحد، صحيح طب احنا ايش
+
+60
+00:06:49,800 --> 00:06:57,020
+بدنا نثبت؟ احنا بدنا نثبت ان P تقسم ال B، تمام؟
+
+61
+00:06:57,020 --> 00:07:02,440
+اذا هذه المعادلة بقدر اخلق فيها ال B في شجة صحيح
+
+62
+00:07:02,440 --> 00:07:05,980
+ولا لأ؟ كيف أسوي في المعادلة ده مش خلّي اخلي هنا
+
+63
+00:07:05,980 --> 00:07:12,140
+P، شو بنعمل؟عندى معادلة بدى اخلها بدل واحد بيهيش
+
+64
+00:07:12,140 --> 00:07:18,680
+اعمل نضرب الطرفين في بي يبقى لو ضربنا في بي هذه
+
+65
+00:07:18,680 --> 00:07:27,300
+المعادلة بتصير abs زائد bt في ال b بده يسوى ال b
+
+66
+00:07:28,940 --> 00:07:32,180
+يبقى الـlinear combination تبع الأجرسيس كومون
+
+67
+00:07:32,180 --> 00:07:36,260
+ديفاز واضدربتها في P ليش؟ مشان أخلق في الطرف
+
+68
+00:07:36,260 --> 00:07:42,320
+اليمين P الآن، شو اللي مطلوب؟ بدي أثبت أن P بتقسم
+
+69
+00:07:42,320 --> 00:07:48,100
+بي لو ال P قسمت الطرف الشمال، إذن automatic هتقسم
+
+70
+00:07:48,100 --> 00:07:51,760
+الطرف اليمين صحيح ولا لأ؟ لأن الطرفين هدول are
+
+71
+00:07:51,760 --> 00:07:57,540
+equal، اتنين متساوية الآن السؤال هوهل P بتقسم هذا
+
+72
+00:07:57,540 --> 00:08:03,660
+ال term الصغير هذا؟ اه مُعطى معانا ان P بتقسم ال A
+
+73
+00:08:03,660 --> 00:08:07,760
+في B يبقى بتقسم ال A في ال B في ال S يبقى باجي
+
+74
+00:08:07,760 --> 00:08:16,040
+بقوله since بما ان ال P بتقسم ال A في ال B we have
+
+75
+00:08:16,040 --> 00:08:24,830
+ان ال P بتقسم ال A بي في ال S اللي عندنا هذاطيب
+
+76
+00:08:24,830 --> 00:08:29,870
+الان P بتقسم هذا كمان ولا لأ؟ لأنه هي يبقى بتقسم
+
+77
+00:08:29,870 --> 00:08:39,490
+ال term هذا يبقى باجي بقوله and ال P بتقسم ال PTP
+
+78
+00:08:40,520 --> 00:08:47,000
+هذا معناه ايش ان ال P بتقسم مجموع لاتنين يبقى
+
+79
+00:08:47,000 --> 00:08:57,360
+بتقسم ال A B S زائد ال P T B مدام بتقسم لاتنين
+
+80
+00:08:57,360 --> 00:09:02,840
+هدول معناته بتقسمين بتقسم ال P اللي بيسويهم هذا
+
+81
+00:09:02,840 --> 00:09:08,320
+بده يعطينا ان P بتقسم ال P وهو المطلوب
+
+82
+00:09:11,000 --> 00:09:15,400
+مرة تانية بقول طبعا هدا هو الشغل اللي بنبره هنا
+
+83
+00:09:15,400 --> 00:09:20,660
+وشغل بسيط لسه ماخش هناش في التقيل بيقول ايه لو كان
+
+84
+00:09:20,660 --> 00:09:25,900
+P prime و ال P بتقسم ال A في B يبقى ال P يا بدها
+
+85
+00:09:25,900 --> 00:09:30,580
+تقسم الرقم الأول يا بدها تقسم الرقم الثاني و طبعا
+
+86
+00:09:30,580 --> 00:09:36,290
+اتنين two integers مش real numberيبقى اما P بتقسم
+
+87
+00:09:36,290 --> 00:09:41,330
+ال A يبقى P بتقسم ال B يبقى فرضنا P prime وP تقسم
+
+88
+00:09:41,330 --> 00:09:46,910
+ال A في B بدي افترض ان P لا تقسم ال A و احاول اثبت
+
+89
+00:09:46,910 --> 00:09:52,090
+ان P بتقسم ال B او العكسيان هذين او هذين او هذين
+
+90
+00:09:52,090 --> 00:09:53,250
+او هذين او هذين او هذين او هذين او هذين او هذين او
+
+91
+00:09:53,250 --> 00:10:00,240
+هذين او هذين او هذين او هذين او هذين او هذينمدام
+
+92
+00:10:00,240 --> 00:10:05,020
+relatively prime يبقى ال graces common divisor بده
+
+93
+00:10:05,020 --> 00:10:09,600
+يساوي قداش واحد اخر حاجة كتبناها المرة الماضية انه
+
+94
+00:10:09,600 --> 00:10:13,300
+ل graces common divisor بقدر اكتب على صيغة linear
+
+95
+00:10:13,300 --> 00:10:17,760
+combination من الرقمين اللي عندنا يبقى there
+
+96
+00:10:17,760 --> 00:10:23,320
+exists S وT في Z بحيث ان ال AS زائد BT بده يساوي
+
+97
+00:10:23,320 --> 00:10:27,980
+قداش واحد صحيحالمعادلة هذه كلها بدى ضربها فى الرقم
+
+98
+00:10:27,980 --> 00:10:32,760
+بى اللى انا بدى اثبت انه P بتقسمه يبقى لو ضربناه
+
+99
+00:10:32,760 --> 00:10:37,680
+فى بيصير عندى A B S زايد B T B بدى يساوي من بى
+
+100
+00:10:37,680 --> 00:10:43,950
+الان ال P بتقسم ال A فى B هذا معطىإذا ال P بتقسم
+
+101
+00:10:43,950 --> 00:10:50,930
+الرقم هذا كله اتنين ال P بتقسم ال P تي بي معناته
+
+102
+00:10:50,930 --> 00:10:55,670
+ال P بتقسم مجموعة الإتنين مدام تقسم مجموعة الإتنين
+
+103
+00:10:55,670 --> 00:11:02,810
+إذا بتقسم بي وهو المطلوب طب السؤال هو لو P ماكنش
+
+104
+00:11:02,810 --> 00:11:10,480
+prime هل اللمة هذه بتظل صحيحة أم لا هذا تساؤلفي
+
+105
+00:11:10,480 --> 00:11:14,760
+الشمكانية في الشمكانية يبقى ضروري لازم يكون P
+
+106
+00:11:14,760 --> 00:11:21,000
+Prime طبعا هعطيك مثال على كل منها الان لو جينا
+
+107
+00:11:21,000 --> 00:11:26,420
+قولنا خدلي الملاحظة هذه اللي احنا سألناكوا ياها
+
+108
+00:11:26,420 --> 00:11:31,620
+فبعدين بقول note if
+
+109
+00:11:31,620 --> 00:11:47,010
+ال P is not a primeلو ماكنش prime ليه above لما
+
+110
+00:11:47,010 --> 00:12:00,030
+false يبقى هذه ماهياش صحيحة for example for
+
+111
+00:12:00,030 --> 00:12:01,830
+example
+
+112
+00:12:04,510 --> 00:12:12,290
+الست بتقسم الأربعة ضرب تلاتة مظبوط أربعة في تلاتة
+
+113
+00:12:12,290 --> 00:12:21,650
+باطماشي ستة بتقسم اتناشي but الست لا تقسم الأربعةو
+
+114
+00:12:21,650 --> 00:12:31,470
+كذلك ال 6 لا تقسم ال 3 لماذا؟ لأن ال 6 ليس أمامي
+
+115
+00:12:31,470 --> 00:12:43,590
+يبقى هنا لأن ال 6 ليس أمامي يبقى
+
+116
+00:12:43,590 --> 00:12:50,890
+ضروري جدا لكي تقسم واحد منهم لازم تكون P عند أمامي
+
+117
+00:12:51,390 --> 00:12:55,850
+مثلا but الخمسة
+
+118
+00:12:55,850 --> 00:13:03,110
+device اتنين في عشرة مظبوط هكذا؟ اتنين في عشرة انا
+
+119
+00:13:03,110 --> 00:13:10,970
+ماقدرش عشرين الخمسة بتقسم العشرين هنا but
+
+120
+00:13:10,970 --> 00:13:17,750
+ولكن الخمسة لا تقسم اتنينبتقسمش اتنين لكن الخمسة
+
+121
+00:13:17,750 --> 00:13:24,250
+بتقسم من؟ بتقسم العشرة يبقى part and الخمسة divide
+
+122
+00:13:24,250 --> 00:13:29,830
+العشرة ليش؟ لأن الخمسة is prime يبقى بقدر اقوله
+
+123
+00:13:29,830 --> 00:13:38,890
+هنا because ان الخمسة هذه is primeيبقى لو كانت الـ
+
+124
+00:13:38,890 --> 00:13:44,250
+prime بتقسم أحدهما لو ماكنتش الـ prime يبقى بصير
+
+125
+00:13:44,250 --> 00:13:48,510
+اللمة اللي عندي ماهياش صحيحة لا يمكن أن تقسم أيا
+
+126
+00:13:48,510 --> 00:13:55,350
+منهما ابنجي لنظرية النظرية هذه هي ال fundamental
+
+127
+00:13:55,350 --> 00:13:59,570
+theorem of arithmetic fundamental
+
+128
+00:14:07,260 --> 00:14:12,800
+fundamental theorem of
+
+129
+00:14:12,800 --> 00:14:27,020
+arithmetic بتقول
+
+130
+00:14:27,020 --> 00:14:38,650
+معناتي every integer every integer a greaterthan
+
+131
+00:14:38,650 --> 00:14:51,790
+one أكبر من الواحد is a prime or a
+
+132
+00:14:51,790 --> 00:14:56,370
+product of
+
+133
+00:14:56,370 --> 00:15:00,830
+primes that is
+
+134
+00:15:05,140 --> 00:15:16,880
+I am any integer a greater than one can be
+
+135
+00:15:16,880 --> 00:15:23,900
+factored ممكن
+
+136
+00:15:23,900 --> 00:15:31,880
+تابته على شكل عوامل uniquely as
+
+137
+00:15:31,880 --> 00:15:32,700
+a product
+
+138
+00:15:40,530 --> 00:15:46,590
+as a product of primes
+
+139
+00:15:46,590 --> 00:15:52,450
+as product
+
+140
+00:15:52,450 --> 00:16:01,890
+of a prime in the form الشكل
+
+141
+00:16:01,890 --> 00:16:11,070
+التالي ال A سواء P1 أص Alpha 1 في P2بص alpha two
+
+142
+00:16:11,070 --> 00:16:23,050
+ونظل ماشيين لغاية P in بص alpha in where حيثهم ال
+
+143
+00:16:23,050 --> 00:16:34,590
+P واحد أقل من P اتنين أقل أقل من P in and the
+
+144
+00:16:34,590 --> 00:16:37,410
+exponents
+
+145
+00:16:41,710 --> 00:16:49,950
+الألفة واحد والألفة اتنين و لغاية الألفة in R
+
+146
+00:17:40,000 --> 00:17:47,700
+بالبلد هيك قبل ما نقرأ الناس اي عدد صحيح عندك هنا
+
+147
+00:17:47,700 --> 00:17:52,360
+بقول every integer greater than one يبقى اي عدد
+
+148
+00:17:52,360 --> 00:17:58,300
+صحيح اكبر من الواحدة الصحية بقدر اكتبه على صيغة
+
+149
+00:17:58,300 --> 00:18:05,600
+حاصل ضرب اعداد اوليةيبقى يابا كتب على شكل prime
+
+150
+00:18:05,600 --> 00:18:11,500
+واحد يا إما حاصل ضرب primes الـprimes هدول قد يكون
+
+151
+00:18:11,500 --> 00:18:15,600
+الأس تبع واحد وقد يكون الأس اتنين تلاتة اربع عشرة
+
+152
+00:18:15,600 --> 00:18:20,420
+جد ما يكون تختلف من الرقم الاخريبقى بيقول أي عدد
+
+153
+00:18:20,420 --> 00:18:24,260
+صحية اكبر من الواحد يعني موجب و اكبر من الواحد
+
+154
+00:18:24,260 --> 00:18:28,960
+الصحية يا بيكون prime يا اما products of a prime
+
+155
+00:18:28,960 --> 00:18:35,280
+يبقى يا حاصل ضرب اعداد اولية السطر هذا بدنا نعيد
+
+156
+00:18:35,280 --> 00:18:40,410
+صياغته من جديديبقى لما نقل صيغة 8 يقول that is أي
+
+157
+00:18:40,410 --> 00:18:45,230
+أن اي integer a مثلا greater than one can be
+
+158
+00:18:45,230 --> 00:18:50,810
+factored عوامل يعني بقدر اكتب على شكل عوامل
+
+159
+00:18:50,810 --> 00:18:57,570
+uniquely بطريقة وحيدة فقط لا غير as a product of a
+
+160
+00:18:57,570 --> 00:19:02,990
+prime كحاصل ضرب a prime in the form a يسوى P1 α1
+
+161
+00:19:02,990 --> 00:19:09,920
+P2 α2 مضرب في PN αNالـ P1 والـ P2 والـ PN كلهم الـ
+
+162
+00:19:09,920 --> 00:19:14,800
+Primes وبدي أدرج من الأصغر للأكبر يعني مين أصغر
+
+163
+00:19:14,800 --> 00:19:19,910
+الـ Prime عندى؟ اتنين اللي بعده .. اللي بعدهاللي
+
+164
+00:19:19,910 --> 00:19:24,670
+بعده وهكذا بده يظل ماشي هذا ال prime حُطها للأسس
+
+165
+00:19:24,670 --> 00:19:30,310
+اللي بدكيها حسب طبيعة الرقم اللي موجود عندك بيقول
+
+166
+00:19:30,310 --> 00:19:34,730
+حيث ال P1 أقل من P2 أقل من PN والأسس هذه ال
+
+167
+00:19:34,730 --> 00:19:39,750
+exponents الأسس Alpha 1 و Alpha 2 كلهم بالموجة
+
+168
+00:19:39,750 --> 00:19:45,780
+نبدأ ناخد مثلا أمثلة السابعةيبقى هذا prime لحاله
+
+169
+00:19:45,780 --> 00:19:52,300
+محل لو خلص فيش غيره طيب لو جيت قولت عشرين عشرين
+
+170
+00:19:52,300 --> 00:19:56,660
+اللي هي أربعة في خمسة تمام أربعة اللي هي اتنين
+
+171
+00:19:56,660 --> 00:20:02,760
+ترابيع في خمسة اللي هي اتنين prime والخمسة أس واحد
+
+172
+00:20:02,760 --> 00:20:07,680
+واتنين أس اتنين يبقى Alpha واحد باتنين وAlpha
+
+173
+00:20:07,680 --> 00:20:12,640
+اتنين بقداش بواحد يعني هنا لو جيت قولت for example
+
+174
+00:20:13,750 --> 00:20:20,090
+for example لو
+
+175
+00:20:20,090 --> 00:20:25,810
+جيت قلت عشرين عشرين تساوي أربعة في خمسة يساوي
+
+176
+00:20:25,810 --> 00:20:30,830
+اتنين تربيع في خمسة اطلع الاتنين ال prime والخمسة
+
+177
+00:20:30,830 --> 00:20:35,310
+ال prime الاتنين الأصغر والخمسة أكبر منه طبقا ل ال
+
+178
+00:20:35,310 --> 00:20:40,730
+conditional والأسس اللي عندنا هذه موجبة طيب لو جيت
+
+179
+00:20:40,730 --> 00:20:43,550
+قلت على سبيل المثال ستين
+
+180
+00:20:49,240 --> 00:20:59,130
+أربعة في خمستاش بستين يعني أربعة في خمستاشطب
+
+181
+00:20:59,130 --> 00:21:04,110
+الأربعة هذه عبارة عن اتنين تربية و الخمستاشر تلاتة
+
+182
+00:21:04,110 --> 00:21:10,570
+في خمسة يبقى تلاتة كذلك في خمسة يبقى اتنين تربية
+
+183
+00:21:10,570 --> 00:21:15,050
+تلاتة في خمسة اتنين ا prime و التلاتة prime و
+
+184
+00:21:15,050 --> 00:21:19,510
+الخمسة prime و الأسس اتنين واحد واحد عادي جدا لو
+
+185
+00:21:19,510 --> 00:21:24,370
+جيتي قولتلك مش ستين كبرها كتير مثلا تلاتمية و ستين
+
+186
+00:21:26,060 --> 00:21:31,920
+تلاتمية و ستين اللي هي عبارة عن تمانية في خمسة و
+
+187
+00:21:31,920 --> 00:21:37,210
+اربعينمظبوط ولا لا؟ يبقى خمسة واربعين وخمسة
+
+188
+00:21:37,210 --> 00:21:42,570
+واربعين تسعين في أربع مظبوط إذا خمسة واربعين في
+
+189
+00:21:42,570 --> 00:21:49,210
+تمانية التمانية هذه عبارة عن اتنين تكعيب الخمسة
+
+190
+00:21:49,210 --> 00:21:54,170
+واربعين اللي عبارة عن تسعة في خمسة هذه اللي بقدر
+
+191
+00:21:54,170 --> 00:22:01,030
+اكتبها اتنين تكعيب في تلاتة تربية في خمسةلاحظ
+
+192
+00:22:01,030 --> 00:22:08,010
+الـPrice مرتبة 2 3 5 والأسس 3 2 1 عادي جدا ماعناش
+
+193
+00:22:08,010 --> 00:22:12,810
+مشكلة يبقى كل الـAlpha اللي عند هدول الـPrimes كل
+
+194
+00:22:12,810 --> 00:22:20,170
+الـAlpha عبارة عن الأسس موجبة والـP مرتبة P1 P2 P3
+
+195
+00:22:20,170 --> 00:22:24,310
+زي ما أحنا شايفين و هكذايبقى اي عدد يجي في بالك ان
+
+196
+00:22:24,310 --> 00:22:28,910
+شاء الله يكون الف وان شاء الله يكون خمسين الف جدا
+
+197
+00:22:28,910 --> 00:22:32,770
+الرقم اللي يجي في بالك بتقدر تكتبه كله على حاصل
+
+198
+00:22:32,770 --> 00:22:36,330
+ضرباش ال price مخدها بالتدريج يعني انا بقدرش اشوف
+
+199
+00:22:36,330 --> 00:22:40,730
+اكم اتنين فيها اكم تلاتة فيها اكم خمسة اكم سبعة
+
+200
+00:22:40,730 --> 00:22:46,990
+الى اخرين تمام؟ يبقى هذا المقصود بهذا نجي لتعريف
+
+201
+00:22:46,990 --> 00:22:51,870
+جديد حاجة اسمه المضاعف المشترك الأصغرهذا اللي بيجي
+
+202
+00:22:51,870 --> 00:22:57,110
+ناخده لما نوحد المقامات في المرحلة الابتدائية و
+
+203
+00:22:57,110 --> 00:23:01,270
+الاعدادية مش خدناه هذا لما يكون عندك رقامين أو
+
+204
+00:23:01,270 --> 00:23:05,070
+كاسرين بيبقى توحد المقامات و تشوف القاسرين قد إيش
+
+205
+00:23:05,070 --> 00:23:08,970
+بتساوي يبقى هنعطي التعريف التالي اللي هو
+
+206
+00:23:08,970 --> 00:23:15,950
+definition the least common multiple the least
+
+207
+00:23:15,950 --> 00:23:19,790
+common multiple
+
+208
+00:23:22,680 --> 00:23:29,420
+least common multiple of two
+
+209
+00:23:29,420 --> 00:23:41,200
+non-zero integers a and b
+
+210
+00:23:41,200 --> 00:23:44,720
+is the smallest
+
+211
+00:23:51,050 --> 00:23:58,930
+positive integer positive
+
+212
+00:23:58,930 --> 00:24:12,090
+integer that is multiple of
+
+213
+00:24:12,090 --> 00:24:19,270
+both a and b
+
+214
+00:24:23,210 --> 00:24:35,310
+we do not add by least common multiple لل a والb
+
+215
+00:24:54,470 --> 00:25:00,410
+common مشترك least أقل multiple مضاعفة يبقى مسمى
+
+216
+00:25:00,410 --> 00:25:06,450
+المضاعف المشترك الأصغر يعني بدي أشوف أصغر رقم
+
+217
+00:25:06,450 --> 00:25:11,610
+بيقسم كل من الرقمين اللي عندنايبقى the least
+
+218
+00:25:11,610 --> 00:25:19,390
+common multiple أصغر رقم يقسم non-zero integers a
+
+219
+00:25:19,390 --> 00:25:25,870
+والb يبقى of two non-zero integers a and b
+
+220
+00:25:30,190 --> 00:25:36,490
+is the smallest positive integer أصغر عدد صحيح
+
+221
+00:25:36,490 --> 00:25:41,850
+موجب that is a multiple of both a and b يبقى أصغر
+
+222
+00:25:41,850 --> 00:25:47,940
+عدد يكون مضاعفات ال a والb في آن واحدwe denote it
+
+223
+00:25:47,940 --> 00:25:55,440
+by اللي هو main a و b يبقى هذا هندله الرمز least
+
+224
+00:25:55,440 --> 00:25:59,700
+common multiple of a و b زي مجرسيس common divisor
+
+225
+00:25:59,700 --> 00:26:05,080
+قدنا g,c,d هنا least common multiple يبقى l,c,m هو
+
+226
+00:26:05,080 --> 00:26:09,300
+اختصار لل least common multiple نعطي مثال مثلا
+
+227
+00:26:09,300 --> 00:26:10,020
+example
+
+228
+00:26:14,420 --> 00:26:19,020
+لو دي اتنين من واحد بدي ال least common multiple
+
+229
+00:26:19,020 --> 00:26:26,920
+مثلا لست و اتناش ايش اول رقم بيقابلني بيقسم كله من
+
+230
+00:26:26,920 --> 00:26:40,600
+الست و اتناش الواحد اتنين تلاتة بدي اول رقم اتنين
+
+231
+00:26:40,600 --> 00:26:45,580
+هدول بيقسموه في انا واحدأيوة ممتاز جدا يبقى هنا
+
+232
+00:26:45,580 --> 00:26:50,740
+هذا بدى يساوي كده اش او اتناش يبقى اتناش هو اول
+
+233
+00:26:50,740 --> 00:26:54,860
+رقم بيقابلني الست بيقدر يقسمه و اتناش يعني هذا
+
+234
+00:26:54,860 --> 00:27:00,080
+المضاعف المشترك الأصغر للاتنين طبعا طيب لو جيت
+
+235
+00:27:00,080 --> 00:27:07,300
+قولتك بدي ال least common multiple للاربعة والست
+
+236
+00:27:07,300 --> 00:27:09,200
+اتنين
+
+237
+00:27:12,570 --> 00:27:17,970
+الاربعة بتقسم اتنين بقولك اول رقم بيجابلك بحيث
+
+238
+00:27:17,970 --> 00:27:20,510
+هالرقمين بدهم يقسموا هذا الرقم
+
+239
+00:27:26,370 --> 00:27:32,690
+يبقى 12 هذا أول رقم بيقسم الأربعة والستة طبعا في
+
+240
+00:27:32,690 --> 00:27:38,150
+أرقام بعده كتير في بعده لكن هذا هو أصغر رقم اللي
+
+241
+00:27:38,150 --> 00:27:42,310
+.. اللي .. اللي اتنين هدول بيجسموه مثلا الأربعة
+
+242
+00:27:42,310 --> 00:27:46,240
+والستة بتجسم الأربعة وعشرينلكن في أصغر من ال 24
+
+243
+00:27:46,240 --> 00:27:51,240
+ليومين اللي هو ال 12 و هكذا طيب لو بد ال least
+
+244
+00:27:51,240 --> 00:27:57,940
+common multiple ل التلاتة و السبعة
+
+245
+00:28:09,050 --> 00:28:17,090
+لو بدي ال least common multiple لستة والعشرة
+
+246
+00:28:21,130 --> 00:28:25,110
+تلاتين تلاتين قبل الستين تلاتين بتقسم الستة
+
+247
+00:28:25,110 --> 00:28:31,690
+وبتقسمين وبتقسم العشرة يبقى هذا بده يساوي تلاتين
+
+248
+00:28:31,690 --> 00:28:36,110
+طب لو جيت قولتلك بد ال least common multiple
+
+249
+00:28:36,110 --> 00:28:39,650
+للعشرة والاطمعاش
+
+250
+00:28:42,730 --> 00:28:49,110
+ستين يبقى هنا ستين يبقى الستين بتقسم العشرة وفي
+
+251
+00:28:49,110 --> 00:28:52,610
+نفس الوقت بتقسم الأتنان يعني شوف الإبتدائي المضاعف
+
+252
+00:28:52,610 --> 00:28:56,130
+المشترك لرقامين بس انت كان عندك في الإبتدائي علشان
+
+253
+00:28:56,130 --> 00:28:58,970
+شاك القصور بشوف المضاعفات للقصور
+
+254
+00:29:01,120 --> 00:29:05,080
+وهكذا يعني قد يكون الاسكم وال multiple الاثنين
+
+255
+00:29:05,080 --> 00:29:10,240
+واحد فيهم مثل هيك لكن بعد هيك لازم يكون اكبر من
+
+256
+00:29:10,240 --> 00:29:16,000
+الاثنين اكبر من الرقمين في انواع تطلع هنا اكبر من
+
+257
+00:29:16,000 --> 00:29:19,640
+الأربعة و اكبر من الستة اكبر من التلاتة و اكبر من
+
+258
+00:29:19,640 --> 00:29:22,840
+السبعة اكبر من الستة و اكبر من العشرة اكبر من
+
+259
+00:29:22,840 --> 00:29:27,600
+العشرة و من الاطناش و هكذايعني أقل حاجة لازم يسوي
+
+260
+00:29:27,600 --> 00:29:33,200
+واحد فيهم ولا يمكن ينزل عن أي واحد فيهم يعني مش
+
+261
+00:29:33,200 --> 00:29:38,560
+ممكن يكون أقل من أي رقم راه وإنما أقل لما ننزل
+
+262
+00:29:38,560 --> 00:29:42,340
+خلاص بدي يسوي مين بدي يسوي واحد فيهم يبقى هذا مين
+
+263
+00:29:42,340 --> 00:29:47,000
+ال least common multiple في ملاحظة بدنا نقولها لك
+
+264
+00:29:47,000 --> 00:29:50,460
+هنا ضرورة تكون ملمقة بها remark
+
+265
+00:29:52,920 --> 00:29:57,940
+أنا عندي رقامين يا شباب ممكن أجيب ال list common
+
+266
+00:29:57,940 --> 00:30:02,400
+multiple و ممكن أجيب ال grids common divisor لهم
+
+267
+00:30:02,400 --> 00:30:09,020
+لو ضربت اتنين في بعض باطيني حصل ضربة الرقامين يبقى
+
+268
+00:30:09,020 --> 00:30:13,730
+هنا باجي بقول الملاحظة ده بتقولLegacies common
+
+269
+00:30:13,730 --> 00:30:18,730
+divisor للـA والـB مضروبة في ال list common
+
+270
+00:30:18,730 --> 00:30:25,350
+multiple ل الأي والبي بدي سوى حصل ضرب الأي في البي
+
+271
+00:30:25,350 --> 00:30:26,830
+for example
+
+272
+00:30:31,240 --> 00:30:35,420
+لو بدنا نعطي مثالين او مثال على الكلام اللي احنا
+
+273
+00:30:35,420 --> 00:30:41,580
+بقوله بدنا نيجي ناخد اي رقامين a و b فمثلا لو بدي
+
+274
+00:30:41,580 --> 00:30:46,940
+لجريسيس common divisor لمان اختار اللي بدكي المرة
+
+275
+00:30:46,940 --> 00:30:53,100
+فيه كده شخدناها مثلا خليها 12 و 10 هذه اللي عندنا
+
+276
+00:30:53,100 --> 00:31:00,590
+هي عشرة و اتناشقواسم الاتنين اللي هو الواحد و
+
+277
+00:31:00,590 --> 00:31:04,730
+اتنين في غيرهم لأ يبقى ال aggressors come and
+
+278
+00:31:04,730 --> 00:31:09,610
+devise قداش بيكون اتنين يبقى هذا الكلام بده يساوي
+
+279
+00:31:09,610 --> 00:31:17,790
+اتنين andالليست كومون ملتبل للعشرة والاتناش هي و
+
+280
+00:31:17,790 --> 00:31:24,090
+قلنا قداش ستين يبقى انا بتروح اضرب لجريس كومون
+
+281
+00:31:24,090 --> 00:31:30,310
+ديفازر للعشرة والاتناشر ضرب ال least common
+
+282
+00:31:30,310 --> 00:31:35,660
+multiple للعشرة والاتناشراللي جلس ال common
+
+283
+00:31:35,660 --> 00:31:40,920
+divisor قداش اتنين واللي اس common multiple هو
+
+284
+00:31:40,920 --> 00:31:48,640
+قداش ستين قداش النتج مية وعشرين مية وعشرين هي حصل
+
+285
+00:31:48,640 --> 00:31:55,530
+ضرب عشرة في اتناشيبقى هذه تساوي حاصل ضرب العشرة في
+
+286
+00:31:55,530 --> 00:32:00,530
+الاطمعاش يبقى أي رقمين تاخدهم ال least common
+
+287
+00:32:00,530 --> 00:32:02,970
+multiple او ضربه في ال degree's least common
+
+288
+00:32:02,970 --> 00:32:07,230
+divisor بيعطيك حاصل ضرب الرقمين هذه في الكتاب
+
+289
+00:32:07,230 --> 00:32:11,620
+موجودة عندك على شكل سؤاللكن انا بدأ اخدها قاعدة
+
+290
+00:32:11,620 --> 00:32:17,700
+يمكن تلزمني قدام وستلزم ان شاء الله في بعض مسائل
+
+291
+00:32:17,700 --> 00:32:22,820
+الجبر قدام ومن هنا اعطيتلك carry mark وليس كسؤال
+
+292
+00:32:22,820 --> 00:32:29,480
+حتى نستخدمها متى لازم الأمر يبقى بدنا نيجي للنقطة
+
+293
+00:32:29,480 --> 00:32:33,060
+الثانية من هذا ال section كل حكينا في اللي فات كله
+
+294
+00:32:33,060 --> 00:32:37,880
+حول ال integers بدنا نيجي لحجم اسمها modular
+
+295
+00:32:51,930 --> 00:32:59,810
+اريثماتيك نعطي definition let
+
+296
+00:32:59,810 --> 00:33:03,430
+n
+
+297
+00:33:03,430 --> 00:33:07,950
+be a fixed positive
+
+298
+00:33:18,660 --> 00:33:28,100
+integer for any integers a
+
+299
+00:33:28,100 --> 00:33:33,460
+and b for
+
+300
+00:33:33,460 --> 00:33:38,620
+any integer a and b ال
+
+301
+00:33:38,620 --> 00:33:50,090
+a زائدي ال bالـ a زائد ال b modulo n modulo n is
+
+302
+00:33:50,090 --> 00:33:59,770
+the remainder is the remainder is upon dividing
+
+303
+00:33:59,770 --> 00:34:17,380
+upon dividing upon dividing aزائد ال V by N ال
+
+304
+00:34:17,380 --> 00:34:29,800
+A ضد B modulo N is the remainder upon dividing AB
+
+305
+00:34:29,800 --> 00:34:31,960
+by N
+
+306
+00:34:53,330 --> 00:34:56,790
+يبقى احنا رافعين عنوان modular arithmetic
+
+307
+00:34:56,790 --> 00:35:01,470
+arithmetic اللي هو علم الحساب modular الشغلات
+
+308
+00:35:01,470 --> 00:35:07,170
+الدورية لكن الترجمة الحقيقية بنقول الحساب باستخدام
+
+309
+00:35:07,170 --> 00:35:11,850
+المقاييس انا بدي اخد مقياس معين و بدي ابدأ اجيط
+
+310
+00:35:11,850 --> 00:35:17,010
+الست اللي عندي هذه كلها بهذا المقياس يبقى الحساب
+
+311
+00:35:17,010 --> 00:35:22,390
+باستخدام المقايس نعطي تعريف ل modular arithmetic
+
+312
+00:35:23,020 --> 00:35:29,020
+يقول افترض ان عدد موجب وهذا عدد ثابت موجب ثابت
+
+313
+00:35:29,020 --> 00:35:33,300
+ثبتنا
+
+314
+00:35:33,300 --> 00:35:37,860
+بنقول سمي هذا المقياس تلاتة ماشي اتنين ماشي عشرة
+
+315
+00:35:37,860 --> 00:35:42,970
+عشرين قمص عشقود المقياس اللي بدكيه تمامبقول for
+
+316
+00:35:42,970 --> 00:35:49,430
+any integers لأي رقمين a و b a زائد b modulo n ايش
+
+317
+00:35:49,430 --> 00:35:55,090
+معناها معناها is the remainder الباقي upon
+
+318
+00:35:55,090 --> 00:36:02,330
+dividing نتيجة لقسم a زائد b by m يعني كيف يعني
+
+319
+00:36:02,330 --> 00:36:07,120
+انا باجي بجمع العددين a و b بطلع رقام كبيريعني
+
+320
+00:36:07,120 --> 00:36:14,240
+افترض هذا ال N أخدها بعشرة واخد ال A و ال B واحد
+
+321
+00:36:14,240 --> 00:36:19,180
+سبعة و واحد تسعة سبعة و تسعة كده؟ ستة عشر مديل و
+
+322
+00:36:19,180 --> 00:36:24,040
+عشرة يعني بتهمل العشرة و بتاخد اللي بيظل كدهش بيظل
+
+323
+00:36:24,040 --> 00:36:24,360
+سبعة
+
+324
+00:36:29,050 --> 00:36:34,470
+يبقى التسعة زي التمانية modulo عشرة هو عبارة عن ال
+
+325
+00:36:34,470 --> 00:36:38,950
+remainder اللي هو سبعة يعني اهم للعشرات زي ما اقول
+
+326
+00:36:38,950 --> 00:36:45,920
+عندي الف درجةيبقى بدي احمل كل 360 واخد من اللي
+
+327
+00:36:45,920 --> 00:36:49,980
+بيظل عندنا تبقى هذه تساوي الزاوية الحقيقية هذه
+
+328
+00:36:49,980 --> 00:36:56,760
+يبقى هذا المقياس لكن لو كان الرقم اللي عندي بيقسم
+
+329
+00:36:56,760 --> 00:37:03,700
+على هذا المقياس ال reminder كداش؟ كداش؟ Zero تمام
+
+330
+00:37:03,700 --> 00:37:11,980
+يبقى مثلا لو جيت قلتلك هنا 6 modulo 2ستة modulo
+
+331
+00:37:11,980 --> 00:37:17,460
+اتنين يبقى انا اخدت المقياس قداش اتنين الستة بتقسم
+
+332
+00:37:17,460 --> 00:37:22,260
+على اتنين ولا لا ستة بتقسم على اتنين صحيح ولا لا
+
+333
+00:37:22,260 --> 00:37:27,820
+يبقى قداش النتج هنا بده يكونبدى يكون zero يعني يا
+
+334
+00:37:27,820 --> 00:37:34,080
+شباب لما اقولي ال remainder بقوله because الستة
+
+335
+00:37:34,080 --> 00:37:40,060
+هذه يسوى اتنين عندنا مضروبة في تلاتة زائد zero ليش
+
+336
+00:37:40,060 --> 00:37:42,800
+هنا بيجينا نقول المرة اللى فاتت في ال division
+
+337
+00:37:42,800 --> 00:37:48,520
+algorithmأى رقم هنا بقدر أكتبه بدلالة الرقم هذا
+
+338
+00:37:48,520 --> 00:37:53,800
+زائد R الـ R هذا أكبر من أو يسوى Zero وأقل من أو
+
+339
+00:37:53,800 --> 00:37:59,240
+يسوى من اتنين يبقى ال remainder هنا بقداش ب Zero
+
+340
+00:37:59,240 --> 00:38:06,400
+طيب لو جيت قلتلك على سبيل المثال هنا عاشرة مثلا
+
+341
+00:38:06,400 --> 00:38:13,330
+module تلاتةواحد تمام كل التلاتات بدي احمله تلات
+
+342
+00:38:13,330 --> 00:38:19,310
+تلاتات بتسعة بيظل قديش اب واحد شو السبب لإن العشرة
+
+343
+00:38:19,310 --> 00:38:24,750
+بدي يساوي تلاتة مضروبة في تلاتة زائد من واحد يبقى
+
+344
+00:38:24,750 --> 00:38:29,310
+ال remainder اب واحد لما اقول عشرة مديله تلاتة
+
+345
+00:38:29,310 --> 00:38:33,510
+يساوي الواحد اللي عندنا لإن ال remainder هنا يساوي
+
+346
+00:38:33,510 --> 00:38:40,270
+قديش واحد طيب يا شباب لما اقولنقص ثلاثة modulo
+
+347
+00:38:40,270 --> 00:38:45,370
+سبعة كيف
+
+348
+00:38:45,370 --> 00:38:53,020
+أسويبكل بساطة ضيف لل سالب تلاتة سبعة اللي هو مقدار
+
+349
+00:38:53,020 --> 00:38:57,340
+المقياس سالب تلاتة سبعة بيضال قداش اربعة يبقى
+
+350
+00:38:57,340 --> 00:39:04,720
+النتيجة تساوي اربعة بكوز سالب تلاتة يساوي سبعة في
+
+351
+00:39:04,720 --> 00:39:11,280
+أبصر قداش زائد الأربعة اللي طلعت عندنا هذهتمام
+
+352
+00:39:11,280 --> 00:39:17,100
+يبقى سبعة في قداش مشان يطلع أربعة سبعة في كام في
+
+353
+00:39:17,100 --> 00:39:21,500
+سالب واحد سالب سبعة زائد أربعة اللي هي سالب تلاتة
+
+354
+00:39:21,500 --> 00:39:24,780
+يبقى ال remainder اتفجنا المرة اللي فات قولنا
+
+355
+00:39:24,780 --> 00:39:30,320
+ممنوع يكون قيمة سالبة دائما و أبدا بناخده قيمة
+
+356
+00:39:30,320 --> 00:39:37,000
+موجب و هكذا طيب لو جيت قولتلك هنا ستة زائد سبعة
+
+357
+00:39:37,000 --> 00:39:48,310
+modulo خمسةيساوي ستة و سبعة تلتاشر modulo خمسة
+
+358
+00:39:48,310 --> 00:39:54,490
+يبقى النتيجة يساوي تلتة و هكذا طيب لو جيت قولتلك
+
+359
+00:39:54,490 --> 00:40:02,830
+ستة في سبعة modulo خمسةستة فى سبعة ستة فى سبعة
+
+360
+00:40:02,830 --> 00:40:07,950
+باتنين واربعين شيل الخمسات لغة اربعين بتطلع اتنين
+
+361
+00:40:07,950 --> 00:40:17,550
+يبقى هذه اتنين واربعين modulo modulo خمسة ويسوى
+
+362
+00:40:17,550 --> 00:40:25,860
+جداش ويسوى اتنين طيب قد يكون الرقم اللى عندناأقل
+
+363
+00:40:25,860 --> 00:40:32,380
+من المقياس اقل من المقياس يعني لما انا اجي اقولك
+
+364
+00:40:32,380 --> 00:40:40,500
+مثلا تلاتة modulo تمانية بتساوي تلاتة على طول الخط
+
+365
+00:40:40,500 --> 00:40:46,120
+تلاتة modulo تمانية بتساوي تلاتة كل رقم أصغر من
+
+366
+00:40:46,120 --> 00:40:51,180
+المقياس بيبقى المقياس فيهيعني واحد مضله تمانية
+
+367
+00:40:51,180 --> 00:40:54,480
+بواحد اتنين مضله تمانية بواحد خمسة مضله تمانية
+
+368
+00:40:54,480 --> 00:41:00,960
+بخمسة ستة مضله تمانيةبستة سبعة modulo تمانية طيب
+
+369
+00:41:00,960 --> 00:41:06,440
+تمانية modulo تمانية صفر صفر على طول الخطوة طيب
+
+370
+00:41:06,440 --> 00:41:11,620
+تسعة modulo تمانية واحد وها كده يبقى فهمنا عملية
+
+371
+00:41:11,620 --> 00:41:15,680
+الحسابات دي ربالة كده very important هتلعب معانا
+
+372
+00:41:15,680 --> 00:41:19,100
+شغل كتير في علم الجبر تبعنا
+
+373
+00:41:39,200 --> 00:41:46,120
+ودي التعريف definition
+
+374
+00:41:46,120 --> 00:41:51,400
+let
+
+375
+00:41:51,400 --> 00:42:06,620
+ال a والb والn be integers with n greater than
+
+376
+00:42:06,620 --> 00:42:26,500
+zerothen ال A modulo N بدرساوي B modulo N if they
+
+377
+00:42:26,500 --> 00:42:31,860
+have
+
+378
+00:42:31,860 --> 00:42:37,820
+the same remainder
+
+379
+00:42:40,440 --> 00:42:49,820
+if they have the same remainder upon dividing
+
+380
+00:42:49,820 --> 00:43:06,900
+نتيجة لقسمة each one of a and b by n نتيجة لقسمة
+
+381
+00:43:06,900 --> 00:43:09,920
+كل واحد فيهم by n
+
+382
+00:43:20,050 --> 00:43:25,130
+تعريف مرة تانية بيقول لي في عندي تلت أعداد صحيحة a
+
+383
+00:43:25,130 --> 00:43:30,490
+و b و n و ال n greater than zero يبقى هذا عدد موجب
+
+384
+00:43:30,490 --> 00:43:36,090
+دائما و أبدا بيقول لي اذا ان ال a modulo n بتساوي
+
+385
+00:43:36,090 --> 00:43:42,230
+b modulo n شو معناها هذه؟ معناها ان لو قسمت ال a
+
+386
+00:43:42,230 --> 00:43:47,870
+على ال n بيظل ال remainder لو قسمت ال ال الالـ B
+
+387
+00:43:47,870 --> 00:43:50,630
+على N بيبقى لـ remainder يبقى الـ remainder هنا
+
+388
+00:43:50,630 --> 00:43:54,270
+لازم يسوي main الـ remainder اللي هنا بيقول if
+
+389
+00:43:54,270 --> 00:43:58,950
+they have the same remainder نفس الباقي نتيجة
+
+390
+00:43:58,950 --> 00:44:04,270
+لقسمة كل واحد من A وB بيبقى على main على N مثال و
+
+391
+00:44:04,270 --> 00:44:12,350
+ذلكلو جاي تقولش لك مثلا سبعتاشر modulo ستة قداش
+
+392
+00:44:12,350 --> 00:44:17,670
+بده يساوي هذا؟ خمسة، ستة و ستة و اتناش من سبعتاشر
+
+393
+00:44:17,670 --> 00:44:19,150
+بيظل خمسة
+
+394
+00:44:21,240 --> 00:44:28,140
+لو جيت قولتلك مثلا تسعة وعشرين موديولو ستة برضه
+
+395
+00:44:28,140 --> 00:44:34,480
+خمسة يبقى بناء عليه ايش بقدر استنتج انه السبعتاشر
+
+396
+00:44:34,480 --> 00:44:41,550
+موديولو ستة بتساوي تسعة وعشرين موديولو ستةيبقى
+
+397
+00:44:41,550 --> 00:44:45,570
+هدول الرقمين بيسووا بقى يعني الرمين درهينة بدي
+
+398
+00:44:45,570 --> 00:44:50,830
+يسوى مين بدي يسوى الرمين درهينة نفسه بدون تغيير
+
+399
+00:44:50,830 --> 00:44:55,090
+طيب في عندنا سؤال في الكتاب السؤال بدي أعطيه لك
+
+400
+00:44:55,090 --> 00:45:00,250
+كمثال سؤال رقم تسعة من الكتاب بدي أكتبه على شكل
+
+401
+00:45:00,250 --> 00:45:05,010
+example مربوط مع الكلام اللي احنا بنقوله هذا
+
+402
+00:45:05,010 --> 00:45:13,460
+السؤال تسعة من الكتاب بيقولي F ال Aand ال B are
+
+403
+00:45:13,460 --> 00:45:25,320
+integers اعداد صحيحة and ال N is a positive
+
+404
+00:45:25,320 --> 00:45:38,070
+integer positive integer prove that اثبت انهProof
+
+405
+00:45:38,070 --> 00:45:48,130
+that ال A modulo N بدو
+
+406
+00:45:48,130 --> 00:45:59,270
+يساوي B modulo N if and only if ال N divides ال A
+
+407
+00:45:59,270 --> 00:46:00,310
+minus ال B
+
+408
+00:46:28,860 --> 00:46:35,040
+مرة تانية بقول لي عندي رقمين a و b أعداد صحيحة ال
+
+409
+00:46:35,040 --> 00:46:40,540
+n هو positive integer قال لي اثبتلي ان ال a modulo
+
+410
+00:46:40,540 --> 00:46:44,620
+n بدي سوى ال b modulo n يعني ال remainder تبع ال a
+
+411
+00:46:44,620 --> 00:46:48,300
+لما نجي اسمه على n بسوى ال remainder تبع ال b لما
+
+412
+00:46:48,300 --> 00:46:52,000
+نجي اسمه على n if and only if ال n تقسم الفرق ما
+
+413
+00:46:52,000 --> 00:46:57,480
+بين ال a و ال b if and only if تعني ان الحال بدي
+
+414
+00:46:57,480 --> 00:47:02,990
+يحصل wellفى اتجاهين بس لو if لحالها يبقى لحال اللى
+
+415
+00:47:02,990 --> 00:47:06,430
+بدى نصير فى اتجاه واحد يبقى if and only if كأن
+
+416
+00:47:06,430 --> 00:47:12,150
+المسألة عبارة عن مسألتين يبقى بناخد ال term الأول
+
+417
+00:47:12,150 --> 00:47:16,470
+كما أعطيته بنحاول نثبت ال term التانى بعدك العملية
+
+418
+00:47:16,470 --> 00:47:20,470
+العكسية بناخد هذه كما أعطيتها بنحاول نثبت تمام ال
+
+419
+00:47:20,470 --> 00:47:24,970
+term الأول يبقى بداجى أقول assume
+
+420
+00:47:27,060 --> 00:47:35,820
+that افترض ان ال a modulo n بده يساوي ال b modulo
+
+421
+00:47:35,820 --> 00:47:45,980
+n طيب كويس من ال division algorithm ال a هادي يبقى
+
+422
+00:47:45,980 --> 00:47:54,750
+هذا بده يعطينا ما يأتي ان ال aوالله خلينا نقول
+
+423
+00:47:54,750 --> 00:48:09,230
+there exist مثلا q1 و r1 في z such that بحيث أن
+
+424
+00:48:10,850 --> 00:48:15,570
+والله جيبها مرة واحدة كلها بلاش نقعد نفصل فيها
+
+425
+00:48:15,570 --> 00:48:24,330
+اكتر يبقى there exist a q1 و q2 و r1 و r2 and z
+
+426
+00:48:24,330 --> 00:48:29,210
+such that ال
+
+427
+00:48:29,210 --> 00:48:43,290
+a بده يساوي q1n زائد r1 andطبعا ال R1 هذه اكبر
+
+428
+00:48:43,290 --> 00:48:50,470
+من أو تساوي ال zero و اقل من مين انوفي نفس الوقت
+
+429
+00:48:50,470 --> 00:49:01,130
+ال B يبقى Q2N زائد R2 وR2 أكبر من أو تساوي 0 أقل
+
+430
+00:49:01,130 --> 00:49:08,810
+من ال N يبقى هذول كخوارزمية القسمة إيش الفرض اللي
+
+431
+00:49:08,810 --> 00:49:14,070
+عنده هنا بيقول افترض هذول بيسووا بعض يبقى معناته
+
+432
+00:49:14,070 --> 00:49:18,070
+ال remainder هنا بيسووا ال remainder هنا يعني إيش؟
+
+433
+00:49:18,390 --> 00:49:23,930
+ار واحد تساوي ار اتنين يبقى باجي بقوله بما ان
+
+434
+00:49:23,930 --> 00:49:34,310
+since ال a modulo n بده يساوي ال b modulo n we
+
+435
+00:49:34,310 --> 00:49:35,370
+have
+
+436
+00:49:42,050 --> 00:49:47,810
+يظهر ان الان بتقسم ال a ناقص ال b اذا حاجة اطرح ال
+
+437
+00:49:47,810 --> 00:49:56,090
+a ناقص ال b يبقى بصير ان ال a ناقص ال b يساوي ال a
+
+438
+00:49:56,090 --> 00:50:08,980
+هو q1n زائد r1التانية يبقى ناقص Q2N ناقص R2 تمام
+
+439
+00:50:08,980 --> 00:50:18,620
+هذا الكلام بده يساوي Q1 ناقص Q2 كله في N زائد مش
+
+440
+00:50:18,620 --> 00:50:25,860
+R1 تساوي R2 صح ولا لأ يبقى هذه مع هذه الله سهل
+
+441
+00:50:25,860 --> 00:50:32,290
+عليهايبقى انتهينا هذه لان انا قلت R1 تسوي R2 هذه
+
+442
+00:50:32,290 --> 00:50:37,510
+موجب و هذه سلبة مع السلامة و هدولة خدنا منهم ال N
+
+443
+00:50:37,510 --> 00:50:44,930
+عامل مشرك صار ال A ناقص ال B ال A ناقص ال B يسوي
+
+444
+00:50:44,930 --> 00:50:53,890
+Q1 ناقص Q2 كله في .. ايش تفسيرك لهذا ان ال N بيقسم
+
+445
+00:50:53,890 --> 00:51:01,480
+ال A minus ال Bيبقى هذا معناه ان ال N divide ال A
+
+446
+00:51:01,480 --> 00:51:07,900
+ناقص ال B وهو المطلوب الأول الآن بدنا نمشي بالعكس
+
+447
+00:51:07,900 --> 00:51:13,440
+لما نمشي بالعكس بقوله conversely
+
+448
+00:51:13,440 --> 00:51:21,380
+يبقى conversely على العكس assume افترض ان ال N
+
+449
+00:51:21,380 --> 00:51:27,740
+divide ال A minus ال Bوبدى احاول اثبت ان ال a
+
+450
+00:51:27,740 --> 00:51:33,900
+modulo n بدر سوى ال b modulo n يبجى هذا معناه ايه
+
+451
+00:51:33,900 --> 00:51:42,480
+ان ال a نقص ال b بدر سوى ال aq في n وال aq موجودة
+
+452
+00:51:42,480 --> 00:51:51,230
+وين في z في remainderمافيش remainder لإن هذه
+
+453
+00:51:51,230 --> 00:51:56,090
+بتقسمها يبقى ال remainder هذا كم بده يساوي؟ Zero
+
+454
+00:51:56,090 --> 00:52:03,750
+يبقى هنا بقوله and ال R1 ناقص R2 بده يساوي Zero
+
+455
+00:52:03,750 --> 00:52:07,750
+لإن انا طرح اتنين من بعض يبقى الفرق ما بين ال two
+
+456
+00:52:07,750 --> 00:52:13,580
+remainders لإنه فرض الأول هيو وهي التانيإذا لما
+
+457
+00:52:13,580 --> 00:52:20,520
+انطرحتم بيصير R1 ناقص R2 يبقى ال R1 ناقص R2 بقداش
+
+458
+00:52:20,520 --> 00:52:27,640
+ب Zero هذا معناه ايه ان ال R1 بيساوي ميهم يعني ال
+
+459
+00:52:27,640 --> 00:52:32,720
+remainder للأول بيساوي ال remainder للثاني يبقى
+
+460
+00:52:32,720 --> 00:52:39,620
+هذا معناهإن ال A modulo N بده ساوي ال B modulo N
+
+461
+00:52:39,620 --> 00:52:44,480
+اللي هو ال remainder وهو المطلوب يبقى الاتجاه
+
+462
+00:52:44,480 --> 00:52:49,000
+التاني أبسط من من الاتجاه الأول يعطيكوا العافية
+
+463
+00:52:49,000 --> 00:52:52,340
+بنكمل ان شاء الله المرة القادمة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..284a212471fe9a78d5e2e51690f679cdb1a70191
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.json
@@ -0,0 +1 @@
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"probability": 0.989501953125}, {"start": 351.24, "end": 352.12, "word": " أخدت", "probability": 0.9254150390625}, {"start": 352.12, "end": 352.66, "word": " الطرق", "probability": 0.8317057291666666}, {"start": 352.66, "end": 354.24, "word": " المختلفة", "probability": 0.9957275390625}, {"start": 354.24, "end": 355.44, "word": " للبراهين", "probability": 0.966064453125}, {"start": 355.44, "end": 356.04, "word": " ولذلك", "probability": 0.8299153645833334}, {"start": 356.04, "end": 356.38, "word": " الشغل", "probability": 0.86328125}, {"start": 356.38, "end": 356.78, "word": " هيكون", "probability": 0.8505859375}, {"start": 356.78, "end": 357.38, "word": " مليان", "probability": 0.9884440104166666}, {"start": 357.38, "end": 358.24, "word": " براهين", "probability": 0.9769287109375}], "temperature": 1.0}, {"id": 16, "seek": 38002, "start": 358.52, "end": 380.02, "text": "براهين كتيرة و كلها مطلوبة لإن انت انسان متخصص و بعد سنة او سنتين بدك توقف تشرح للطلاب لذلك ضروري تكون تعرف تبرهن حتى تستطيع تبرهن بعد سنة او سنتين للطلاب سواء كان في المدارس الاعدادية او المدارس الثانوية او ربما", "tokens": [26890, 40294, 9957, 9122, 2655, 48923, 4032, 28242, 11296, 3714, 9566, 1211, 37746, 3660, 5296, 28814, 1863, 16472, 2655, 16472, 3794, 7649, 44650, 9778, 9381, 9381, 4032, 39182, 8608, 1863, 3660, 1975, 2407, 8608, 29399, 9957, 47525, 4117, 6055, 30543, 5172, 6055, 46309, 5016, 24976, 9566, 15040, 3555, 5296, 8848, 23275, 48812, 2288, 13063, 1829, 6055, 30544, 37279, 28480, 6055, 26890, 3224, 1863, 11331, 49975, 6055, 14851, 9566, 40228, 6055, 26890, 3224, 1863, 39182, 8608, 1863, 3660, 1975, 2407, 8608, 29399, 9957, 24976, 9566, 15040, 3555, 8608, 2407, 16606, 25961, 8978, 9673, 3215, 9640, 3794, 42963, 22488, 18513, 10632, 1975, 2407, 9673, 3215, 9640, 3794, 6024, 104, 7649, 2407, 10632, 1975, 2407, 12602, 3555, 15042], "avg_logprob": -0.09933997876942158, "compression_ratio": 1.9896373056994818, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 358.52, "end": 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"end": 1379.91, "word": " عالمين", "probability": 0.95703125}, {"start": 1379.91, "end": 1380.29, "word": " لل", "probability": 0.837890625}, {"start": 1380.29, "end": 1380.71, "word": " groups", "probability": 0.70654296875}, {"start": 1380.71, "end": 1381.01, "word": " زي", "probability": 0.853759765625}, {"start": 1381.01, "end": 1381.25, "word": " ايش", "probability": 0.7802734375}, {"start": 1381.25, "end": 1381.65, "word": " مثلا", "probability": 0.96435546875}], "temperature": 1.0}, {"id": 62, "seek": 140115, "start": 1382.71, "end": 1401.15, "text": "كل group لدينا حاجة اسمه عنصر محايد identity element وفي عندنا كل عنصر له معكوس inverse element هل ال inverse هذا وحيد و لا ممكن ألاقي العنصر له أكتر من معكوس", "tokens": [28820, 1594, 5296, 16254, 8315, 11331, 26108, 3660, 24525, 2304, 3224, 18871, 9381, 2288, 3714, 5016, 995, 25708, 6575, 4478, 4032, 41185, 43242, 8315, 28242, 18871, 9381, 2288, 46740, 20449, 4117, 41779, 17340, 4478, 8032, 1211, 2423, 17340, 23758, 4032, 5016, 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1670.03, "word": " كام", "probability": 0.576416015625}, {"start": 1670.03, "end": 1670.83, "word": " تبديلة", "probability": 0.80963134765625}, {"start": 1670.83, "end": 1671.59, "word": " بقدر", "probability": 0.9449869791666666}, {"start": 1671.59, "end": 1672.45, "word": " اسوي", "probability": 0.729736328125}, {"start": 1672.45, "end": 1673.13, "word": " منهم", "probability": 0.974609375}, {"start": 1673.13, "end": 1674.37, "word": " بحيث", "probability": 0.9656982421875}, {"start": 1674.37, "end": 1674.65, "word": " ولا", "probability": 0.7841796875}, {"start": 1674.65, "end": 1674.97, "word": " واحد", "probability": 0.988525390625}, {"start": 1674.97, "end": 1675.41, "word": " هتكون", "probability": 0.9378255208333334}, {"start": 1675.41, "end": 1675.75, "word": " زي", "probability": 0.934326171875}, {"start": 1675.75, "end": 1676.71, "word": " التانية", "probability": 0.90869140625}, {"start": 1676.71, "end": 1677.19, "word": " يعني", "probability": 0.866943359375}, {"start": 1677.19, "end": 1677.73, "word": " مثلا", "probability": 0.987548828125}, {"start": 1677.73, "end": 1678.41, "word": " لو", "probability": 0.87841796875}, {"start": 1678.41, "end": 1678.71, "word": " جينا", "probability": 0.9830729166666666}, {"start": 1678.71, "end": 1679.19, "word": " قولنا", "probability": 0.712646484375}, {"start": 1679.19, "end": 1679.63, "word": " واحد", "probability": 0.96142578125}, {"start": 1679.63, "end": 1680.11, "word": " واثنين", "probability": 0.867236328125}, {"start": 1680.11, "end": 1680.97, "word": " وتلاتة", "probability": 0.869140625}, {"start": 1680.97, "end": 1681.35, "word": " يبقى", "probability": 0.824462890625}, {"start": 1681.35, "end": 1681.59, "word": " هذي", "probability": 0.6464029947916666}, {"start": 1681.59, "end": 1682.27, "word": " بسميها", "probability": 0.971923828125}, {"start": 1682.27, "end": 1683.59, "word": " تبديلة", "probability": 0.814697265625}, {"start": 1683.59, "end": 1683.81, "word": " من", "probability": 0.94921875}, {"start": 1683.81, "end": 1684.63, "word": " التبديلة", "probability": 0.9447021484375}, {"start": 1684.63, "end": 1684.97, "word": " هذي", "probability": 0.8626302083333334}, {"start": 1684.97, "end": 1685.37, "word": " بقدر", "probability": 0.9930013020833334}, {"start": 1685.37, "end": 1686.07, "word": " اخلق", "probability": 0.7442626953125}, {"start": 1686.07, "end": 1686.89, "word": " مجموعة", "probability": 0.9595703125}, {"start": 1686.89, "end": 1687.39, "word": " من", "probability": 0.9921875}, {"start": 1687.39, "end": 1689.07, "word": " التبديلات", "probability": 0.9637451171875}, {"start": 1689.07, "end": 1689.73, "word": " تعرف", "probability": 0.8583984375}, {"start": 1689.73, "end": 1690.15, "word": " كم", "probability": 0.58642578125}, {"start": 1690.15, "end": 1690.37, "word": " من", "probability": 0.8955078125}, {"start": 1690.37, "end": 1690.73, "word": " التلات", "probability": 0.9454752604166666}, {"start": 1690.73, "end": 1691.25, "word": " عناصر", "probability": 0.99365234375}, {"start": 1691.25, "end": 1691.69, "word": " بتقدر", "probability": 0.88720703125}, {"start": 1691.69, "end": 1692.05, "word": " تسوي", "probability": 0.9396158854166666}, {"start": 1692.05, "end": 1693.05, "word": " تبديلات", "probability": 0.97705078125}, {"start": 1693.05, "end": 1694.05, "word": " مرت", "probability": 0.708740234375}, {"start": 1694.05, "end": 1694.45, "word": " عليكم", "probability": 0.9541015625}, {"start": 1694.45, "end": 1694.75, "word": " بدأ", "probability": 0.3839111328125}, {"start": 1694.75, "end": 1695.41, "word": " الرياضيات", "probability": 0.81806640625}, {"start": 1695.41, "end": 1696.19, "word": " كم", "probability": 0.85107421875}, {"start": 1696.19, "end": 1696.75, "word": " يعني؟", "probability": 0.8634440104166666}], "temperature": 1.0}, {"id": 75, "seek": 172245, "start": 1697.45, "end": 1722.45, "text": "مضروب تلاتة مضروب تلاتة يبقى تلاتة في اتنين في واحد يبقى عندي ست تبديلات ممكن اخلق من هذه التبديلات احنا بدنا ننشي جروب على التبديلات اللي عندنا هذه وندرس بعض المعلومات على هذه التبديلات وهل التبديلات بتبقى even ولا odd", "tokens": [2304, 11242, 32887, 3555, 6055, 1211, 9307, 3660, 3714, 11242, 32887, 3555, 6055, 1211, 9307, 3660, 7251, 3555, 4587, 7578, 6055, 1211, 9307, 3660, 8978, 1975, 2655, 1863, 9957, 8978, 36764, 24401, 7251, 3555, 4587, 7578, 18871, 16254, 8608, 2655, 6055, 3555, 16254, 1211, 9307, 3714, 43020, 1975, 9778, 1211, 4587, 9154, 29538, 16712, 3555, 16254, 1211, 9307, 1975, 5016, 8315, 47525, 8315, 8717, 1863, 8592, 1829, 10874, 32887, 3555, 15844, 16712, 3555, 16254, 1211, 9307, 13672, 1829, 43242, 8315, 29538, 4032, 41260, 2288, 3794, 45030, 11242, 9673, 30241, 20498, 9307, 15844, 29538, 16712, 3555, 16254, 1211, 9307, 37037, 1211, 16712, 3555, 16254, 1211, 9307, 39894, 3555, 4587, 7578, 754, 49429, 7401], "avg_logprob": -0.1566648272286474, "compression_ratio": 2.202247191011236, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1697.45, "end": 1698.19, "word": "مضروب", "probability": 0.794921875}, {"start": 1698.19, "end": 1699.15, "word": " تلاتة", "probability": 0.877685546875}, {"start": 1699.15, "end": 1700.13, "word": " مضروب", "probability": 0.758453369140625}, {"start": 1700.13, "end": 1700.69, "word": " تلاتة", "probability": 0.978271484375}, {"start": 1700.69, "end": 1700.93, "word": " يبقى", "probability": 0.8223876953125}, {"start": 1700.93, "end": 1701.39, "word": " تلاتة", "probability": 0.979736328125}, {"start": 1701.39, "end": 1701.47, "word": " في", "probability": 0.75244140625}, {"start": 1701.47, "end": 1701.99, "word": " اتنين", "probability": 0.9317626953125}, {"start": 1701.99, "end": 1702.41, "word": " في", "probability": 0.677734375}, {"start": 1702.41, "end": 1702.73, "word": " واحد", "probability": 0.961181640625}, {"start": 1702.73, "end": 1702.97, "word": " يبقى", "probability": 0.9605712890625}, {"start": 1702.97, "end": 1703.31, "word": " عندي", "probability": 0.75048828125}, {"start": 1703.31, "end": 1703.97, "word": " ست", "probability": 0.662109375}, {"start": 1703.97, "end": 1705.11, "word": " تبديلات", "probability": 0.851513671875}, {"start": 1705.11, "end": 1705.61, "word": " ممكن", "probability": 0.984130859375}, {"start": 1705.61, "end": 1706.15, "word": " اخلق", "probability": 0.80517578125}, {"start": 1706.15, "end": 1706.35, "word": " من", "probability": 0.9892578125}, {"start": 1706.35, "end": 1706.67, "word": " هذه", "probability": 0.94091796875}, {"start": 1706.67, "end": 1709.17, "word": " التبديلات", "probability": 0.797265625}, {"start": 1709.17, "end": 1710.09, "word": " احنا", "probability": 0.953125}, {"start": 1710.09, "end": 1710.57, "word": " بدنا", "probability": 0.938232421875}, {"start": 1710.57, "end": 1711.05, "word": " ننشي", "probability": 0.8612060546875}, {"start": 1711.05, "end": 1711.51, "word": " جروب", "probability": 0.8079427083333334}, {"start": 1711.51, "end": 1711.97, "word": " على", "probability": 0.8251953125}, {"start": 1711.97, "end": 1713.47, "word": " التبديلات", "probability": 0.959375}, {"start": 1713.47, "end": 1713.85, "word": " اللي", "probability": 0.839599609375}, {"start": 1713.85, "end": 1714.41, "word": " عندنا", "probability": 0.994140625}, {"start": 1714.41, "end": 1714.87, "word": " هذه", "probability": 0.72412109375}, {"start": 1714.87, "end": 1715.95, "word": " وندرس", "probability": 0.860595703125}, {"start": 1715.95, "end": 1716.29, "word": " بعض", "probability": 0.9833984375}, {"start": 1716.29, "end": 1717.39, "word": " المعلومات", "probability": 0.9931640625}, {"start": 1717.39, "end": 1717.99, "word": " على", "probability": 0.72119140625}, {"start": 1717.99, "end": 1718.33, "word": " هذه", "probability": 0.9677734375}, {"start": 1718.33, "end": 1719.37, "word": " التبديلات", "probability": 0.97822265625}, {"start": 1719.37, "end": 1719.69, "word": " وهل", "probability": 0.714599609375}, {"start": 1719.69, "end": 1720.35, "word": " التبديلات", "probability": 0.8970703125}, {"start": 1720.35, "end": 1720.85, "word": " بتبقى", "probability": 0.918701171875}, {"start": 1720.85, "end": 1721.17, "word": " even", "probability": 0.8818359375}, {"start": 1721.17, "end": 1721.87, "word": " ولا", "probability": 0.441650390625}, {"start": 1721.87, "end": 1722.45, "word": " odd", "probability": 0.95703125}], "temperature": 1.0}, {"id": 76, "seek": 174472, "start": 1722.72, "end": 1744.72, "text": "وقداش رتبت هذه التبديلة وقداش وقداش الاخرى يبقى هذا شغلنا اللي يكون وين اللي هيكون في هذا الشبطق اللي هو ال permutation group يبقى permutation تبديلة permutation group اللي هي مجموعة التبديلات او زمرة التبديلات", "tokens": [2407, 28543, 33599, 12602, 2655, 3555, 2655, 29538, 16712, 3555, 16254, 37977, 4032, 28543, 33599, 4032, 28543, 33599, 2423, 47283, 2288, 7578, 7251, 3555, 4587, 7578, 23758, 13412, 17082, 1211, 8315, 13672, 1829, 7251, 30544, 4032, 9957, 13672, 1829, 39896, 30544, 8978, 23758, 25124, 3555, 9566, 4587, 13672, 1829, 31439, 2423, 4784, 11380, 1594, 7251, 3555, 4587, 7578, 4784, 11380, 6055, 44510, 26895, 3660, 4784, 11380, 1594, 13672, 1829, 39896, 3714, 7435, 2304, 2407, 27884, 16712, 44510, 26895, 9307, 1975, 2407, 30767, 2304, 25720, 16712, 44510, 26895, 9307], "avg_logprob": -0.2122542081254252, "compression_ratio": 2.0176470588235293, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1722.72, "end": 1723.6, "word": "وقداش", "probability": 0.6315104166666666}, {"start": 1723.6, "end": 1724.24, "word": " رتبت", "probability": 0.52166748046875}, {"start": 1724.24, "end": 1724.58, "word": " هذه", "probability": 0.74853515625}, {"start": 1724.58, "end": 1725.48, "word": " التبديلة", "probability": 0.8177490234375}, {"start": 1725.48, "end": 1726.18, "word": " وقداش", "probability": 0.9189453125}, {"start": 1726.18, "end": 1726.94, "word": " وقداش", "probability": 0.9601236979166666}, {"start": 1726.94, "end": 1727.82, "word": " الاخرى", "probability": 0.62481689453125}, {"start": 1727.82, "end": 1728.5, "word": " يبقى", "probability": 0.952880859375}, {"start": 1728.5, "end": 1728.78, "word": " هذا", "probability": 0.802734375}, {"start": 1728.78, "end": 1729.28, "word": " شغلنا", "probability": 0.7735595703125}, {"start": 1729.28, "end": 1729.44, "word": " اللي", "probability": 0.7197265625}, {"start": 1729.44, "end": 1729.66, "word": " يكون", "probability": 0.90966796875}, {"start": 1729.66, "end": 1730.0, "word": " وين", "probability": 0.435791015625}, {"start": 1730.0, "end": 1730.5, "word": " اللي", "probability": 0.9150390625}, {"start": 1730.5, "end": 1731.02, "word": " هيكون", "probability": 0.789306640625}, {"start": 1731.02, "end": 1731.22, "word": " في", "probability": 0.93212890625}, {"start": 1731.22, "end": 1731.52, "word": " هذا", "probability": 0.8955078125}, {"start": 1731.52, "end": 1732.18, "word": " الشبطق", "probability": 0.863037109375}, {"start": 1732.18, "end": 1732.86, "word": " اللي", "probability": 0.94970703125}, {"start": 1732.86, "end": 1733.08, "word": " هو", "probability": 0.943359375}, {"start": 1733.08, "end": 1733.24, "word": " ال", "probability": 0.84814453125}, {"start": 1733.24, "end": 1734.24, "word": " permutation", "probability": 0.883056640625}, {"start": 1734.24, "end": 1735.4, "word": " group", "probability": 0.374755859375}, {"start": 1735.4, "end": 1736.22, "word": " يبقى", "probability": 0.9381103515625}, {"start": 1736.22, "end": 1736.9, "word": " permutation", "probability": 0.98046875}, {"start": 1736.9, "end": 1737.94, "word": " تبديلة", "probability": 0.830078125}, {"start": 1737.94, "end": 1738.94, "word": " permutation", "probability": 0.788330078125}, {"start": 1738.94, "end": 1739.62, "word": " group", "probability": 0.93701171875}, {"start": 1739.62, "end": 1740.18, "word": " اللي", "probability": 0.96630859375}, {"start": 1740.18, "end": 1740.6, "word": " هي", "probability": 0.8935546875}, {"start": 1740.6, "end": 1741.6, "word": " مجموعة", "probability": 0.97236328125}, {"start": 1741.6, "end": 1742.54, "word": " التبديلات", "probability": 0.9154052734375}, {"start": 1742.54, "end": 1743.04, "word": " او", "probability": 0.772216796875}, {"start": 1743.04, "end": 1743.58, "word": " زمرة", "probability": 0.8829752604166666}, {"start": 1743.58, "end": 1744.72, "word": " التبديلات", "probability": 0.9583740234375}], "temperature": 1.0}, {"id": 77, "seek": 176647, "start": 1745.23, "end": 1766.47, "text": "بنجي لحاجة هنا اسمها isomorphisms isomorphisms و كذلك ال atomorphisms طيب", "tokens": [3555, 1863, 7435, 1829, 5296, 5016, 26108, 3660, 34105, 24525, 2304, 11296, 307, 32702, 13539, 307, 32702, 13539, 4032, 9122, 8848, 23275, 2423, 412, 32702, 13539, 23032, 1829, 3555], "avg_logprob": -0.24947915375232696, "compression_ratio": 1.1764705882352942, "no_speech_prob": 0.0, "words": [{"start": 1745.23, "end": 1745.77, "word": "بنجي", "probability": 0.72039794921875}, {"start": 1745.77, "end": 1746.33, "word": " لحاجة", "probability": 0.9329833984375}, {"start": 1746.33, "end": 1746.69, "word": " هنا", "probability": 0.6787109375}, {"start": 1746.69, "end": 1747.31, "word": " اسمها", "probability": 0.9752604166666666}, {"start": 1747.31, "end": 1749.21, "word": " isomorphisms", "probability": 0.6953938802083334}, {"start": 1749.21, "end": 1754.57, "word": " isomorphisms", "probability": 0.685302734375}, {"start": 1754.57, "end": 1755.69, "word": " و", "probability": 0.95166015625}, {"start": 1755.69, "end": 1756.59, "word": " كذلك", "probability": 0.8120930989583334}, {"start": 1756.59, "end": 1757.13, "word": " ال", "probability": 0.94384765625}, {"start": 1757.13, "end": 1760.43, "word": " atomorphisms", "probability": 0.68310546875}, {"start": 1760.43, "end": 1766.47, "word": " طيب", "probability": 0.9661458333333334}], "temperature": 1.0}, {"id": 78, "seek": 177919, "start": 1773.13, "end": 1779.19, "text": "الترجمة العربية بتقول التشكل النمطي أو التشابه النمطي", "tokens": [6027, 2655, 47341, 46007, 18863, 25513, 10632, 39894, 39648, 16712, 8592, 28820, 28239, 2304, 9566, 1829, 34051, 16712, 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فيه تشابه مابليه؟ ايش كيف يعني تشابه؟ يعني هذا و هذا و هذا بنعم هذا؟ لأ مش هيك في عندنا شروط الشروط لو تحققت على ال two groups بقول ان هم دول اتنين فيهم تشابه نمطين تعرفوا زي ايش مثلا؟", "tokens": [2304, 45636, 995, 37495, 22653, 6055, 8592, 16758, 3224, 16070, 1863, 2304, 9566, 22807, 37495, 22653, 1975, 8315, 18871, 16254, 1594, 4032, 3615, 1863, 16254, 1594, 6055, 7649, 10632, 1975, 2655, 1863, 9957, 8978, 3224, 6055, 8592, 16758, 3224, 3714, 16758, 20292, 3224, 22807, 1975, 1829, 8592, 9122, 33911, 37495, 22653, 6055, 8592, 16758, 3224, 22807, 37495, 22653, 23758, 4032, 23758, 4032, 23758, 44945, 25957, 23758, 22807, 5296, 10721, 37893, 39896, 4117, 8978, 43242, 8315, 13412, 32887, 9566, 25124, 32887, 9566, 45164, 6055, 5016, 4587, 38149, 15844, 2423, 732, 3935, 4724, 39648, 16472, 8032, 2304, 11778, 12610, 1975, 2655, 1863, 9957, 8978, 16095, 6055, 8592, 16758, 3224, 8717, 2304, 9566, 9957, 37279, 28480, 14407, 30767, 1829, 1975, 1829, 8592, 50113, 15040, 22807], "avg_logprob": 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16254, 41891, 15844, 29910, 23275, 46599, 3615, 11242, 28239, 19913, 16572, 9307, 9673, 2655, 30241, 28671, 4724, 11296], "avg_logprob": -0.24734043948193815, "compression_ratio": 1.3008130081300813, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2100.78, "end": 2101.4, "word": "وهذه", "probability": 0.4903971354166667}, {"start": 2101.4, "end": 2101.56, "word": " من", "probability": 0.72265625}, {"start": 2101.56, "end": 2101.76, "word": " ال", "probability": 0.35400390625}, {"start": 2101.76, "end": 2102.14, "word": " group", "probability": 0.7216796875}, {"start": 2102.14, "end": 2102.62, "word": " G", "probability": 0.66357421875}, {"start": 2102.62, "end": 2102.9, "word": " إلى", "probability": 0.81591796875}, {"start": 2102.9, "end": 2103.12, "word": " ال", "probability": 0.7724609375}, {"start": 2103.12, "end": 2103.48, "word": " group", "probability": 0.970703125}, {"start": 2103.48, "end": 2103.88, "word": " G", "probability": 0.759765625}, {"start": 2103.88, "end": 2104.38, "word": " bar", "probability": 0.5068359375}, {"start": 2104.38, "end": 2105.94, "word": " طبعاً", "probability": 0.797802734375}, {"start": 2105.94, "end": 2106.44, "word": " وحنعطي", "probability": 0.6600341796875}, {"start": 2106.44, "end": 2106.96, "word": " أمثلة", "probability": 0.9219970703125}, {"start": 2106.96, "end": 2107.56, "word": " عديدة", "probability": 0.9651692708333334}, {"start": 2107.56, "end": 2107.76, "word": " على", "probability": 0.814453125}, {"start": 2107.76, "end": 2108.16, "word": " ذلك", "probability": 0.994140625}, {"start": 2108.16, "end": 2108.56, "word": " وبعض", "probability": 0.90283203125}, {"start": 2108.56, "end": 2109.28, "word": " النظريات", "probability": 0.977294921875}, {"start": 2109.28, "end": 2110.22, "word": " المتعلقة", "probability": 0.984375}, {"start": 2110.22, "end": 2110.6, "word": " بها", "probability": 0.95263671875}], "temperature": 1.0}, {"id": 94, "seek": 213159, "start": 2110.99, "end": 2131.59, "text": "بنجي لل atomorphism شو يعني atomorphism هو function فاي بس من جي إلى جي itself مش لوحدة تانية هنا جي و هنا جي بربوا اختلفوا عن بعض تماما هاي شجة و هاي شجة تانية و ليهم مش علاقة ببعض ولا بقرب ولا بعض ولا غيره", "tokens": [3555, 1863, 7435, 1829, 24976, 12018, 18191, 1434, 13412, 2407, 37495, 22653, 12018, 18191, 1434, 31439, 2445, 6156, 47302, 4724, 3794, 9154, 10874, 1829, 30731, 10874, 1829, 2564, 37893, 45164, 24401, 3660, 6055, 7649, 10632, 34105, 10874, 1829, 4032, 34105, 10874, 1829, 4724, 25513, 14407, 1975, 46456, 46538, 14407, 18871, 45030, 11242, 46811, 10943, 995, 8032, 47302, 13412, 7435, 3660, 4032, 8032, 47302, 13412, 7435, 3660, 6055, 7649, 10632, 4032, 32239, 16095, 37893, 11203, 995, 28671, 4724, 3555, 3615, 11242, 49429, 4724, 4587, 25513, 49429, 45030, 11242, 49429, 32771, 13546, 3224], "avg_logprob": -0.3247282488838486, "compression_ratio": 1.7578947368421052, "no_speech_prob": 0.0, "words": [{"start": 2110.99, "end": 2111.73, "word": "بنجي", "probability": 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"probability": 0.8560791015625}, {"start": 2125.05, "end": 2125.21, "word": " عن", "probability": 0.9716796875}, {"start": 2125.21, "end": 2125.63, "word": " بعض", "probability": 0.989501953125}, {"start": 2125.63, "end": 2126.63, "word": " تماما", "probability": 0.98583984375}, {"start": 2126.63, "end": 2127.33, "word": " هاي", "probability": 0.42431640625}, {"start": 2127.33, "end": 2127.75, "word": " شجة", "probability": 0.9217122395833334}, {"start": 2127.75, "end": 2127.83, "word": " و", "probability": 0.64892578125}, {"start": 2127.83, "end": 2127.97, "word": " هاي", "probability": 0.787109375}, {"start": 2127.97, "end": 2128.31, "word": " شجة", "probability": 0.9967447916666666}, {"start": 2128.31, "end": 2128.55, "word": " تانية", "probability": 0.8961588541666666}, {"start": 2128.55, "end": 2128.65, "word": " و", "probability": 0.313720703125}, {"start": 2128.65, "end": 2128.79, "word": " ليهم", "probability": 0.5321044921875}, {"start": 2128.79, "end": 2128.91, "word": " مش", "probability": 0.9052734375}, {"start": 2128.91, "end": 2129.29, "word": " علاقة", "probability": 0.9689127604166666}, {"start": 2129.29, "end": 2129.77, "word": " ببعض", "probability": 0.78302001953125}, {"start": 2129.77, "end": 2129.99, "word": " ولا", "probability": 0.70166015625}, {"start": 2129.99, "end": 2130.43, "word": " بقرب", "probability": 0.9392903645833334}, {"start": 2130.43, "end": 2130.61, "word": " ولا", "probability": 0.496337890625}, {"start": 2130.61, "end": 2130.93, "word": " بعض", "probability": 0.884521484375}, {"start": 2130.93, "end": 2131.13, "word": " ولا", "probability": 0.92822265625}, {"start": 2131.13, "end": 2131.59, "word": " غيره", "probability": 0.8966471354166666}], "temperature": 1.0}, {"id": 95, "seek": 214734, "start": 2131.9, "end": 2147.34, "text": "لكن عندما أقول من ال group G إلى ال group G itself ال isomorphism هذا بسميه ايه؟ بسميه atomorphism يبقى كأن ال atomorphism هو حالة خاصة من مهم", "tokens": [1211, 19452, 43242, 15042, 5551, 39648, 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{"start": 2134.0, "end": 2134.4, "word": " إلى", "probability": 0.88232421875}, {"start": 2134.4, "end": 2134.68, "word": " ال", "probability": 0.73974609375}, {"start": 2134.68, "end": 2135.02, "word": " group", "probability": 0.9013671875}, {"start": 2135.02, "end": 2135.54, "word": " G", "probability": 0.6630859375}, {"start": 2135.54, "end": 2136.38, "word": " itself", "probability": 0.690704345703125}, {"start": 2136.38, "end": 2136.92, "word": " ال", "probability": 0.2025146484375}, {"start": 2136.92, "end": 2138.14, "word": " isomorphism", "probability": 0.783447265625}, {"start": 2138.14, "end": 2138.46, "word": " هذا", "probability": 0.611328125}, {"start": 2138.46, "end": 2139.22, "word": " بسميه", "probability": 0.8140869140625}, {"start": 2139.22, "end": 2139.64, "word": " ايه؟", "probability": 0.7830810546875}, {"start": 2139.64, "end": 2140.4, "word": " بسميه", "probability": 0.972900390625}, {"start": 2140.4, "end": 2142.02, "word": " atomorphism", "probability": 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بحقق لمين الخاصية اللي عندنا هذه إن حدث ذلك يبقى هذا بسميه atomorphism وسنحسب بعض ال atomorphisms لمين لبعض ال group بعد ذلك بنجي ل chapter 7", "tokens": [27842, 307, 32702, 1434, 2423, 307, 32702, 1434, 9154, 1594, 5296, 1594, 6055, 7649, 10632, 44381, 2423, 12018, 18191, 1434, 9154, 2423, 1594, 5296, 1863, 36178, 2135, 5296, 1863, 36178, 1594, 37037, 2407, 307, 32702, 1434, 472, 281, 472, 4032, 7649, 2655, 14407, 4032, 4724, 5016, 4587, 4587, 32767, 9957, 33962, 33546, 10632, 13672, 1829, 43242, 8315, 29538, 36145, 11331, 3215, 12984, 29910, 23275, 7251, 3555, 4587, 7578, 23758, 4724, 38251, 1829, 3224, 12018, 18191, 1434, 46952, 1863, 5016, 35457, 45030, 11242, 2423, 12018, 18191, 13539, 32767, 9957, 5296, 3555, 3615, 11242, 2423, 1594, 39182, 29910, 23275, 44945, 7435, 1829, 5296, 7187, 1614], "avg_logprob": -0.22430889680981636, "compression_ratio": 1.8867924528301887, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2148.22, "end": 2148.5, "word": "من", 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وانتوا", "probability": 0.74462890625}, {"start": 2160.42, "end": 2160.78, "word": " و", "probability": 0.6552734375}, {"start": 2160.78, "end": 2161.38, "word": " بحقق", "probability": 0.79107666015625}, {"start": 2161.38, "end": 2161.72, "word": " لمين", "probability": 0.784423828125}, {"start": 2161.72, "end": 2162.4, "word": " الخاصية", "probability": 0.9669596354166666}, {"start": 2162.4, "end": 2162.58, "word": " اللي", "probability": 0.727294921875}, {"start": 2162.58, "end": 2162.98, "word": " عندنا", "probability": 0.64501953125}, {"start": 2162.98, "end": 2163.26, "word": " هذه", "probability": 0.56201171875}, {"start": 2163.26, "end": 2163.62, "word": " إن", "probability": 0.3515625}, {"start": 2163.62, "end": 2163.98, "word": " حدث", "probability": 0.99267578125}, {"start": 2163.98, "end": 2164.46, "word": " ذلك", "probability": 0.9765625}, {"start": 2164.46, "end": 2164.96, "word": " يبقى", "probability": 0.828369140625}, {"start": 2164.96, "end": 2165.18, "word": " هذا", 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ذلك", "probability": 0.6298828125}, {"start": 2174.02, "end": 2174.78, "word": " بنجي", "probability": 0.7744140625}, {"start": 2174.78, "end": 2175.34, "word": " ل", "probability": 0.9111328125}, {"start": 2175.34, "end": 2176.12, "word": " chapter", "probability": 0.90185546875}, {"start": 2176.12, "end": 2176.76, "word": " 7", "probability": 0.4072265625}], "temperature": 1.0}, {"id": 97, "seek": 220469, "start": 2178.85, "end": 2204.69, "text": "سابعة بنا نيجي ناخد حاجة اسمها cosets and Lagrange theorem coset كلمة جديدة هنا set اللي فيها او مجموعة co مرافق", "tokens": [3794, 16758, 27884, 4724, 8315, 8717, 1829, 7435, 1829, 8717, 47283, 3215, 11331, 26108, 3660, 24525, 2304, 11296, 3792, 1385, 293, 24886, 14521, 20904, 3792, 302, 9122, 19528, 3660, 10874, 16254, 41891, 34105, 992, 13672, 1829, 8978, 11296, 1975, 2407, 3714, 7435, 2304, 2407, 27884, 598, 3714, 23557, 5172, 4587], "avg_logprob": -0.33700980392156865, "compression_ratio": 1.2781954887218046, "no_speech_prob": 0.0, 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"probability": 0.900390625}, {"start": 2199.47, "end": 2199.91, "word": " جديدة", "probability": 0.9889322916666666}, {"start": 2199.91, "end": 2200.39, "word": " هنا", "probability": 0.302978515625}, {"start": 2200.39, "end": 2201.37, "word": " set", "probability": 0.361083984375}, {"start": 2201.37, "end": 2201.61, "word": " اللي", "probability": 0.9345703125}, {"start": 2201.61, "end": 2202.27, "word": " فيها", "probability": 0.7137451171875}, {"start": 2202.27, "end": 2202.99, "word": " او", "probability": 0.773193359375}, {"start": 2202.99, "end": 2203.57, "word": " مجموعة", "probability": 0.94921875}, {"start": 2203.57, "end": 2203.93, "word": " co", "probability": 0.238037109375}, {"start": 2203.93, "end": 2204.69, "word": " مرافق", "probability": 0.883544921875}], "temperature": 1.0}, {"id": 98, "seek": 223477, "start": 2205.07, "end": 2234.77, "text": "يبقى هى الست جديدة وولدناها من شيء ما شو شيء ما؟ شايف عندى هذه ال subgroup أخدت عنصر من برا ال subgroup لكن من نفس ال group 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بالضرورة ان تكون subgroup من ال group الأصلية ما علينا يبقى احنا", "tokens": [6027, 4117, 41779, 36081, 8032, 8848, 1829, 7251, 43020, 6055, 9566, 1211, 3615, 1422, 17377, 4032, 32640, 19452, 19446, 6055, 9566, 1211, 3615, 8592, 1422, 17377, 7251, 3555, 4587, 7578, 294, 2674, 2423, 1411, 9122, 41779, 36081, 1975, 2407, 2423, 558, 9122, 41779, 36081, 32239, 3794, 20666, 11242, 2288, 13063, 3660, 16472, 6055, 30544, 1422, 17377, 9154, 2423, 1594, 16247, 36520, 10632, 19446, 25894, 8315, 7251, 3555, 4587, 7578, 1975, 5016, 8315], "avg_logprob": -0.26626713635170296, "compression_ratio": 1.6603773584905661, "no_speech_prob": 0.0, "words": [{"start": 2235.01, "end": 2236.09, "word": "الكوسيت", "probability": 0.537353515625}, {"start": 2236.09, "end": 2236.69, "word": " هذي", "probability": 0.3736979166666667}, {"start": 2236.69, "end": 2237.45, "word": " يمكن", "probability": 0.887939453125}, {"start": 2237.45, "end": 2238.17, "word": " تطلع", "probability": 0.937744140625}, {"start": 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أحمد المبحوح تمام؟ لكن اذا مسجل الماديتين مع بعض مافيش مشكلة لكن ما انتش مسجل اديك، cancel الموضوع خلاص، حد بدي أسأل تاني؟ ننتظركوا الساعة اتناشر ان شاء الله في هذا المكان", "tokens": [2655, 28543, 2288, 8592, 6055, 2655, 35571, 1211, 1975, 1829, 3224, 21542, 42213, 22807, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 4724, 1829, 39648, 4117, 1975, 15730, 37893, 3714, 47283, 3215, 12602, 2407, 5016, 24525, 5016, 3555, 9673, 18513, 3660, 4032, 32887, 5016, 6055, 3794, 7435, 1211, 3714, 3555, 18513, 19986, 12602, 1829, 46958, 1829, 9307, 5296, 28814, 1863, 11296, 8717, 31377, 37977, 21542, 9957, 20449, 32748, 4117, 2655, 13063, 5551, 35571, 3215, 9673, 49628, 2407, 5016, 46811, 10943, 22807, 44381, 1975, 15730, 47524, 7435, 1211, 9673, 18513, 36081, 9957, 20449, 45030, 11242, 19446, 41185, 8592, 37893, 28820, 3660, 44381, 19446, 16472, 2655, 8592, 47524, 7435, 1211, 1975, 16254, 4117, 12399, 10373, 9673, 2407, 11242, 45367, 16490, 1211, 33546, 12399, 11331, 3215, 4724, 16254, 5551, 3794, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fbd9c61ec0bcc66e53460e74e68bfa4f3cd42512
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/fpxaZ9Pv2HM_raw.srt
@@ -0,0 +1,2012 @@
+1
+00:00:20,790 --> 00:00:25,630
+بسم الله الرحمن الرحيم محاضرتنا اليوم ان شاء الله
+
+2
+00:00:25,630 --> 00:00:33,770
+تعالى هي في جبر حديث واحد طبعا ان بتعرفوا ان مادة
+
+3
+00:00:33,770 --> 00:00:38,930
+جبر الحديث الواحد وكذلك مادة تحليل حقيقي واحد
+
+4
+00:00:38,930 --> 00:00:43,010
+ومادة ال topology هي اثقل ثلاث مواد بالنسبة
+
+5
+00:00:43,010 --> 00:00:47,990
+للرياضيات اللي أخدتول كالكلصادة ما هو الا بسكوتة
+
+6
+00:00:47,990 --> 00:00:53,040
+الرياضياتيعني بسيط جدا إذا قيص بالجبر أو التحليل
+
+7
+00:00:53,040 --> 00:00:56,720
+أو ال topology لكن ان شاء الله من خلال دراستنا
+
+8
+00:00:56,720 --> 00:01:01,520
+هلاقي المادة بسيطة لإنه سنحاول أن نبسطها إلى أبعد
+
+9
+00:01:01,520 --> 00:01:07,940
+الحدود بحيث تستوعبها وتفهمها تمامالكن قبل ان ابدأ
+
+10
+00:01:07,940 --> 00:01:13,340
+بدي كل واحد جوال يكون مجفول تحاول تلتزم بالحضور
+
+11
+00:01:13,340 --> 00:01:17,000
+الساعة تسعة يعني الساعة تسعة تماما طبعا احنا
+
+12
+00:01:17,000 --> 00:01:20,840
+اتخرنا خمس دقايق لان اذهبت الى المبنى الثاني و
+
+13
+00:01:20,840 --> 00:01:25,620
+كتبت انتقلة المحاضرة الى قاعة التصوير فالاربع
+
+14
+00:01:25,620 --> 00:01:30,640
+ساعات بدنا ندومهم هنا المادة اربع ساعات وليس ثلاث
+
+15
+00:01:30,640 --> 00:01:34,960
+ساعات كما كانت من قبل قبل كانت ثلاث ساعات وساعات
+
+16
+00:01:34,960 --> 00:01:40,060
+مناقشأربع ساعات اللي هي من ضمنهم المناقشة المدرس
+
+17
+00:01:40,060 --> 00:01:44,860
+هو اللذي سيناقش معاك المسائل مش المعيد كما كان في
+
+18
+00:01:44,860 --> 00:01:50,280
+الأعوام السابقة اليوم عندنا محاضرتين المحاضرة
+
+19
+00:01:50,280 --> 00:01:55,680
+الأولى هذه سنتكلم فيها الخطوط العريضة للمنهج
+
+20
+00:01:55,680 --> 00:01:58,920
+والمحاضرة الثانية اللي بتبدأ الساعة اتناشر ان شاء
+
+21
+00:01:58,920 --> 00:02:06,570
+الله سندخل في صميم المقررطيب قبل ان نبدأ احب ان
+
+22
+00:02:06,570 --> 00:02:12,830
+اركز على كيفية فهم المادة مشان تفهم المادة يجب ان
+
+23
+00:02:12,830 --> 00:02:17,910
+تحرص على الحضور مبكرا الساعة تسعة يمكن تسعة لدقيقة
+
+24
+00:02:17,910 --> 00:02:21,650
+تلاقيني هنا ان اتأخرت دقيقة بكون بس في الأسانسية
+
+25
+00:02:22,190 --> 00:02:26,230
+لكن الساعة تسعة بدي الكل .. و لو كنت تسعة العشرة
+
+26
+00:02:26,230 --> 00:02:30,210
+بكون أحسن انا بعرف بدك تنتقل من مبنى إلى مبنى من
+
+27
+00:02:30,210 --> 00:02:34,450
+قاعة إلى قاعة ياخدلك خمس دقايق المهم الساعة تسعة
+
+28
+00:02:34,450 --> 00:02:40,070
+بدك تجبع قاعة ايه جاعد هنا في مقعدك تنتظر اللي هو
+
+29
+00:02:40,070 --> 00:02:46,530
+ما سيشرح أمامك حتى تستطيع أن تستوعبالمادة مشان
+
+30
+00:02:46,530 --> 00:02:52,150
+تفهمها لازم تروح تجرى المحاضرة بمجرد ما تاخدها
+
+31
+00:02:52,150 --> 00:02:57,190
+خلال المحاضرة بطلع على ذهنك سؤال بتحب تناقش بترفع
+
+32
+00:02:57,190 --> 00:03:02,370
+عيدك بنقولك اتفضل وماعنديش إجابة جماعية الإجابة
+
+33
+00:03:02,370 --> 00:03:05,470
+الفردية اللي هو السؤال فشان بترفع عيدك بنقولك
+
+34
+00:03:05,470 --> 00:03:10,890
+اتفضل حتى تكون الفائدة عامة للجميع بلا استثناء
+
+35
+00:03:11,240 --> 00:03:16,200
+وأحنا كلامنا قصير ما نحبش اما يعني نجرش الكلام
+
+36
+00:03:16,200 --> 00:03:23,500
+لكتير لأن أفضل الكلام يعني ما قلة عدده هو كثرة
+
+37
+00:03:23,500 --> 00:03:29,200
+معانيت ولذلك علمنا في معاني كثيرة ان شاء الله
+
+38
+00:03:29,200 --> 00:03:35,360
+سنتعرض لها من خلال دراستنا لمساق الجبر الحديث واحد
+
+39
+00:03:35,830 --> 00:03:40,250
+طيب روحنا على البيت الدراسة ليست انك تقرأ المحاضرة
+
+40
+00:03:40,250 --> 00:03:45,070
+و تقرأ الأمثلة صحيح ان هذا ضروري جدا لكن حل
+
+41
+00:03:45,070 --> 00:03:52,710
+الأسئلة له ضرورة كبيرة جدا في فهم منالموضوع يعني
+
+42
+00:03:52,710 --> 00:03:57,310
+ال definition النظرية اللي مليه الفرضية المساعدة
+
+43
+00:03:57,310 --> 00:04:01,390
+النتيجة اللي موجودة على النظرية كلها قد تجد عليها
+
+44
+00:04:01,390 --> 00:04:05,270
+على كل واحدة فيها مجموعة من الأسئلة في التمرين
+
+45
+00:04:05,270 --> 00:04:11,000
+والحمد لله كتابنا مليانبالتمرين التطبيقي قد تكون
+
+46
+00:04:11,000 --> 00:04:17,600
+عددية وقد تكون نظرية طيب السؤال هو ما هو المساق
+
+47
+00:04:17,600 --> 00:04:23,140
+السابق الذي يعتمد عليه هذا المساق طبعا سؤال وجيه
+
+48
+00:04:23,140 --> 00:04:27,780
+جدا وكتير منكم كان بإمكانه أو يدور في خلده أن يسأل
+
+49
+00:04:27,780 --> 00:04:33,190
+هذا السؤالالمادة الأساسية اللي لازمان لهذه المادة
+
+50
+00:04:33,190 --> 00:04:38,410
+هي مادة مبادئ الرياضيات principle of mathematics
+
+51
+00:04:38,410 --> 00:04:42,910
+طبعا و لذلك ال chapter الأول عندنا في هذا الكتاب
+
+52
+00:04:42,910 --> 00:04:48,310
+يعتبر مراجعة لما سبقت دراسته في مبادئ الرياضيات
+
+53
+00:04:48,310 --> 00:04:54,610
+الأعداد الصحية الأعداد الطبيعية الأعداد الجذرية
+
+54
+00:04:54,610 --> 00:05:00,740
+مجموعة الأعداد الحقيقية مجموعة الأعدادالتخيلية هذا
+
+55
+00:05:00,740 --> 00:05:06,520
+الأساس أو الخمس مجموعات هذه هو الذي أُسس عليها علم
+
+56
+00:05:06,520 --> 00:05:11,670
+الجبر اللي بين إيديناهي لزمنا بعض الشغلات البسيطة
+
+57
+00:05:11,670 --> 00:05:16,150
+مش كتير من مادة ال number theory نظرية الاعداد
+
+58
+00:05:16,150 --> 00:05:22,130
+ستكون في المقدمة ولذلك كل الأشياء الضرورية خلال
+
+59
+00:05:22,130 --> 00:05:26,150
+دراستنا في موضوع الجبرة الحديث سنضعها لك في
+
+60
+00:05:26,150 --> 00:05:32,130
+chapter المقدمة وبعد هيك كل شويه يطلعان واحدة منهم
+
+61
+00:05:32,130 --> 00:05:37,380
+يكون ايه ملمين قبهاأو ذكرنا بها في بداية دراستنا
+
+62
+00:05:37,380 --> 00:05:43,440
+هنا يبقى مبادئ الرياضيات أساسية جدا لفهم الجبر
+
+63
+00:05:43,440 --> 00:05:47,640
+والتحليل والتوبوليجي كله بيعتمد على مادة مبادئ
+
+64
+00:05:47,640 --> 00:05:51,240
+الرياضيات وانت في مبادئ الرياضيات في الشتر الأول
+
+65
+00:05:51,240 --> 00:05:56,780
+أخدت الطرق المختلفة للبراهين ولذلك الشغل هيكون
+
+66
+00:05:56,780 --> 00:06:01,480
+مليان براهينبراهين كتيرة و كلها مطلوبة لإن انت
+
+67
+00:06:01,480 --> 00:06:06,540
+انسان متخصص و بعد سنة او سنتين بدك توقف تشرح
+
+68
+00:06:06,540 --> 00:06:12,300
+للطلاب لذلك ضروري تكون تعرف تبرهن حتى تستطيع تبرهن
+
+69
+00:06:12,300 --> 00:06:15,900
+بعد سنة او سنتين للطلاب سواء كان في المدارس
+
+70
+00:06:15,900 --> 00:06:21,580
+الاعدادية او المدارس الثانوية او ربمايكون بعضكم
+
+71
+00:06:21,580 --> 00:06:26,460
+معيدا عندنا في الكلية ويطور نفسه وبعض ذلك يصبح
+
+72
+00:06:26,460 --> 00:06:32,160
+زميل لنا كما كثير منه الزملاء هم خريجي الجامعة
+
+73
+00:06:32,160 --> 00:06:37,100
+الإسلامية من عندنا واتدرسناهم والأن هايهم زملاء
+
+74
+00:06:37,100 --> 00:06:41,660
+لنا في القسم بل رئيس القسم الدكتور أحمد بابحوح هو
+
+75
+00:06:41,660 --> 00:06:46,400
+أحد خريجي الجامعة الإسلامية الدكتور الرائد قبله
+
+76
+00:06:46,400 --> 00:06:51,850
+برضه خريجي الجامعة الإسلاميةو هكذا فيعني تستجلش
+
+77
+00:06:51,850 --> 00:06:55,670
+بنفسك لكن اللي بيشتغل هو اللي بيقدم اللي بيشتغلش
+
+78
+00:06:55,670 --> 00:06:59,030
+بيبقى قاعد و عمره مابيقدم بيصير حط على الكم زي
+
+79
+00:06:59,030 --> 00:07:03,470
+باقى الناس لكن اللي بيشغل مخ و بيشتغل هذا هو اللي
+
+80
+00:07:03,470 --> 00:07:07,870
+بيقدم انت لان في المستوى التالت يبقى احرص على ان
+
+81
+00:07:07,870 --> 00:07:12,950
+المستوى التالت والرابع ترفع معدلك حتى تتمكن من
+
+82
+00:07:12,950 --> 00:07:19,670
+العمل او اكمال دراستك بعد ذلكيبقى هذه الأشياء
+
+83
+00:07:19,670 --> 00:07:23,770
+ضرورية نقرأ المحاضرة أن أن نفهم المحاضرة بقدر
+
+84
+00:07:23,770 --> 00:07:28,330
+الإمكان صيب عليك شغل بتسألني بتروح على الدار بتقرا
+
+85
+00:07:28,330 --> 00:07:32,130
+المحاضرة من جديد بتقرا الأمثلة بتبدأها اتحل
+
+86
+00:07:32,130 --> 00:07:36,570
+الأسئلة و في نهاية كل section بنخلي المحاضرة
+
+87
+00:07:36,570 --> 00:07:42,490
+للمناقشة خصوصاللأصل اللى هنعطيك أرقامها بحيث تكون
+
+88
+00:07:42,490 --> 00:07:47,990
+مجهز حالك لحل هذه المسائل هذا بالنسبة للدراسة أما
+
+89
+00:07:47,990 --> 00:07:52,270
+بالنسبة للامتحانات فعندنا امتحانين أعمال فصل
+
+90
+00:07:52,270 --> 00:07:56,050
+الامتحان الأول بيكون حوالي أربعين يوم من بدء
+
+91
+00:07:56,050 --> 00:08:00,370
+الدراسة يعني اليوم السابعة تسعة اتوقع حوالي عشرين
+
+92
+00:08:00,370 --> 00:08:05,000
+عشرة قبله بيوم يومين أو بعده بيوم يومين تلاتةهيكون
+
+93
+00:08:05,000 --> 00:08:08,860
+عندك الامتحان الأول كل امتحان عليه خمسة و عشرين
+
+94
+00:08:08,860 --> 00:08:14,660
+درجة يبقى امتحانين بخمسين درجة يبقى النهاية بقداش
+
+95
+00:08:14,660 --> 00:08:20,380
+بخمسين درجة طيب هذا بالنسبة لكيفية الدراسة و بنفسي
+
+96
+00:08:20,380 --> 00:08:26,070
+ولا الامتحان الحضور عندي أساسيو ساخد حضور و غياب
+
+97
+00:08:26,070 --> 00:08:30,030
+اول أسبوعين مشان السحب والاضافة باخدش حضور و غياب
+
+98
+00:08:30,030 --> 00:08:34,810
+ابتدا من اليوم الأول في الأسبوع التالت باخد حضور و
+
+99
+00:08:34,810 --> 00:08:38,830
+غياب لو غيبت عندي خمسة و عشرين في المية اعتبر حالك
+
+100
+00:08:38,830 --> 00:08:43,770
+مفصول على ذو الخط بنلغي تسجيلك لكن بنبلغك هذا انا
+
+101
+00:08:43,770 --> 00:08:49,960
+ببلغ من اليومالحضور عندى .. الحضور بد يكون لو غبط
+
+102
+00:08:49,960 --> 00:08:53,520
+خمسة و عشرين في المئة اعتبر حالك مفصول، مفصول من
+
+103
+00:08:53,520 --> 00:08:57,620
+المادة على طول القطب، منشطب تسجيلكم يقولك انت مع
+
+104
+00:08:57,620 --> 00:09:02,540
+السلام بلزمكش تكون حاضر عن هنا، لإن الحضور أساسى،
+
+105
+00:09:02,540 --> 00:09:07,380
+طبعا سيدعي بعض يكونان انا بحضرها على التصوير ما هي
+
+106
+00:09:07,380 --> 00:09:11,820
+مصورة بالفيديو بتيجي بالصوت و الصورة بقولك صحيح
+
+107
+00:09:11,820 --> 00:09:17,840
+الصورة ليست كالاصل يعني انت حاضر هنا تطلع لنظرة
+
+108
+00:09:17,840 --> 00:09:23,220
+العين حركات الإيدينالمناقش اللى بيصير بينه و بين
+
+109
+00:09:23,220 --> 00:09:27,420
+الغالب غالب كلها هادي بتفيدك لكن يمكن ما تسمعهاش
+
+110
+00:09:27,420 --> 00:09:31,640
+كويس في بيتكوا يمكن تقطيعات الوجه ماتظهرش تماما
+
+111
+00:09:31,640 --> 00:09:36,000
+أثناء السؤال و الإجابة عليه فكل هذا له تأثير في
+
+112
+00:09:36,000 --> 00:09:42,410
+فهمين في فهم المساق يبقى الحضور عندي أساسيأول
+
+113
+00:09:42,410 --> 00:09:46,370
+أسبوعين أنا مسامحك لكن ابدا من الأسبوع التالت حابد
+
+114
+00:09:46,370 --> 00:09:53,090
+أخد الحضور والغياب إذا وصل غيابك ل 25% بنبلغك أنك
+
+115
+00:09:53,090 --> 00:09:58,150
+مفصول حتى وإن كنت مقدم لمتحان النصفيتمام يبقى
+
+116
+00:09:58,150 --> 00:10:02,250
+الحضور أساسي هذا بالنسبة للحضور وبالنسبة لمن
+
+117
+00:10:02,250 --> 00:10:10,450
+وبالنسبة للدرجات وكذلك بالنسبة لطريقة الدراسة الآن
+
+118
+00:10:10,450 --> 00:10:15,580
+قبل أن أبدأ فيها أن حاجة اسمها ساعات مكتبيةالساعات
+
+119
+00:10:15,580 --> 00:10:18,920
+المكتبية بتجدني قاعد في المكتب بس تنسيتك تيجي
+
+120
+00:10:18,920 --> 00:10:24,640
+تسألني سؤال حلو حاجة ماانتش فاهمها نشرح حالك أي
+
+121
+00:10:24,640 --> 00:10:30,040
+تساؤل حول المساق نحاول انفيدك فيه بقدر الإمكان انا
+
+122
+00:10:30,040 --> 00:10:35,460
+متواجد في المكتب من الساعة واحدة لساعتين سبت اتنين
+
+123
+00:10:35,460 --> 00:10:43,330
+اربعةوكذلك متواجد في المكتب من الأحداش لأتناش برضه
+
+124
+00:10:43,330 --> 00:10:49,030
+سبت اتنين اربع حسب جدول الطلاب والطالبات الوقت
+
+125
+00:10:49,030 --> 00:10:53,750
+المناسب بالنسبالك اتفضل احنا في انتظارك بس بعتقد
+
+126
+00:10:53,750 --> 00:10:58,330
+المناسب اللي هو من الأحداش لأتناش مش هيك من
+
+127
+00:10:58,330 --> 00:11:05,330
+الأحداش لأتناش في المكتب تمام؟يبقى هذا بالنسبة
+
+128
+00:11:05,330 --> 00:11:09,850
+لمين للساعات المكتبية، رقم المكتب تلاتمية و تلاتة
+
+129
+00:11:09,850 --> 00:11:16,370
+و عشريناللي هي كلية العلوم الطابق الثالث الغرفة
+
+130
+00:11:16,370 --> 00:11:23,030
+رقمها 323 في ال corridor التليفون الداخلي 2619
+
+131
+00:11:23,030 --> 00:11:28,930
+يعني بإمكانك من أي تليفون هنا تصل على 2619 تعرف
+
+132
+00:11:28,930 --> 00:11:32,770
+انه متواجد في المكتب و الله مش متواجد حتى لو كان
+
+133
+00:11:32,770 --> 00:11:39,210
+في غير الساعات المكتبية واضح كلامي؟طيب نجي الآن
+
+134
+00:11:39,210 --> 00:11:45,590
+للموضوع موضوع الجبرا الحديث الكتاب المقرر اسمه
+
+135
+00:11:45,590 --> 00:11:50,170
+contemporary abstract algebra هكتب هلك الآن هذا
+
+136
+00:11:50,170 --> 00:11:55,570
+شكل الكتاب موجود الآن في مكتبة الطالب الجامعي
+
+137
+00:11:55,570 --> 00:12:00,660
+بتاعه ممكن تشتريه بعد نهاية المحاضرة تماماو موجود
+
+138
+00:12:00,660 --> 00:12:05,340
+كمان في المكتبات اللي قدام الجامعة الإسلامية في
+
+139
+00:12:05,340 --> 00:12:09,560
+أحد المكتبات موجود فيها كمان نسخ اللي يريحك اشتريه
+
+140
+00:12:09,560 --> 00:12:14,760
+و اللي تلاقيه أرخص اشتريه الكتاب هو Contemporary
+
+141
+00:12:14,760 --> 00:12:20,240
+Abstract Algebra المؤلف اسمه Joseph Galliam الطبعة
+
+142
+00:12:20,240 --> 00:12:27,770
+السابعة طبعا احنا دخلنا هذا الكتابوقررنا منذ سنوات
+
+143
+00:12:27,770 --> 00:12:32,490
+منذ الطبعة الثانية لأن حسب ما شوفنا كتب جبر كثيرة
+
+144
+00:12:32,490 --> 00:12:38,590
+لجينا أن هذا أنسب كتاب بالنسبة للطالب وفيه عدد لا
+
+145
+00:12:38,590 --> 00:12:44,450
+بأس به من الأسئلة في التمرين الواحد ونصفها محلول
+
+146
+00:12:44,450 --> 00:12:49,530
+يعني حل بس حل مختصرا وانواعيا في نهاية الكتاب
+
+147
+00:12:49,530 --> 00:12:55,020
+الأسئلة الفردية غالبها محلولةوبالتالي بيساعدك على
+
+148
+00:12:55,020 --> 00:13:00,720
+فهم المساق فهما صحيا يبقى اسم الكتاب Contemporary
+
+149
+00:13:00,720 --> 00:13:02,280
+Abstract Algebra
+
+150
+00:13:25,630 --> 00:13:39,950
+اسم المؤلف جوزيف جوزيف
+
+151
+00:13:39,950 --> 00:13:49,210
+جاليان الطابعة السابعة بجهة seven edition
+
+152
+00:13:57,810 --> 00:14:03,230
+again شوفتش شكل الكتاب وهذا الاسم المساكن
+
+153
+00:14:03,230 --> 00:14:06,230
+temporary abstract algebra الاسم اللي موجود على
+
+154
+00:14:06,230 --> 00:14:11,390
+الكتاب المؤلف اسمه Joseph Gallien الطابعة السابعة
+
+155
+00:14:11,390 --> 00:14:15,270
+احنا بنتعامل مع الكتاب منذ الطابعة الثانية والان
+
+156
+00:14:15,270 --> 00:14:19,150
+وصلنا إلى الطابعة السابعة كل ما يصير تغيير بنتابع
+
+157
+00:14:19,150 --> 00:14:24,370
+هذا التغيير لإن العلم يتطور يومياوالعقل البشري كل
+
+158
+00:14:24,370 --> 00:14:29,110
+يوم يهتدي لشيء في الكون لم يكن قد اكتشفه من قبل
+
+159
+00:14:29,110 --> 00:14:35,210
+وهذه طبيعة البشر وطبيعة الكون اللذي نحن فيه الا
+
+160
+00:14:35,210 --> 00:14:38,850
+ابن نيجي ما هي الموضوعات اللتي سندرسها من هذا
+
+161
+00:14:38,850 --> 00:14:43,730
+الكتاب هذا الكتاب لجبر حديث واحد وجبر حديث اتنين
+
+162
+00:14:43,730 --> 00:14:49,950
+طبعا كلاب كلية العلوم مقرر عليهم المساقينضلاب كلية
+
+163
+00:14:49,950 --> 00:14:53,650
+التربية مقرر عليهم جبر حديث واحد جبر اتنين
+
+164
+00:14:53,650 --> 00:14:58,030
+optional اختياري تاخدها اهلا وسهلا بدكش بلاش لكن
+
+165
+00:14:58,030 --> 00:15:01,970
+العلوم اجباري عليهم جبر حديث اتنين
+
+166
+00:15:04,990 --> 00:15:11,750
+هذا الكتاب سندرس منه ten chapters يبقى عشر شباتر
+
+167
+00:15:11,750 --> 00:15:20,210
+سندرس من هذا الكتاب أول شبتر هو شبتر المقدمة
+
+168
+00:15:20,750 --> 00:15:27,010
+المقدمة اللى هناطفى مراجعة لما سبقت دراسته في
+
+169
+00:15:27,010 --> 00:15:33,630
+مبادئ الرياضية زى ايش مثلا يبقى الشبتر الاول بتكلم
+
+170
+00:15:33,630 --> 00:15:35,650
+عن ال integers
+
+171
+00:15:37,860 --> 00:15:41,960
+اللي هو من مجموعة الأعداد الصحية طبعا احنا اول ما
+
+172
+00:15:41,960 --> 00:15:47,080
+نبدأ هنبدأ بنفسنا ال number نعرفلك إياه المجموعة
+
+173
+00:15:47,080 --> 00:15:50,220
+ال six of integers مجموعة ال rational number ال
+
+174
+00:15:50,220 --> 00:15:54,020
+real number ال complex number الخمسة هدول اللي
+
+175
+00:15:54,020 --> 00:15:57,820
+علمنا في الجبرق ان بنا عليهم اللي هي الأساسيات
+
+176
+00:15:57,820 --> 00:16:03,430
+الأساسيةبعد ذلك نقوم بالإنتجار ناخد الـ prime
+
+177
+00:16:03,430 --> 00:16:07,730
+numbers الأعداد الأولية ال division algorithm
+
+178
+00:16:07,730 --> 00:16:14,590
+خوارزمية القسمة modular arithmetic الحسابات بمقياس
+
+179
+00:16:14,590 --> 00:16:19,970
+معين ال mathematical induction اللي هو الاستنتاج
+
+180
+00:16:19,970 --> 00:16:25,470
+الرياضي أو الاستقراء الرياضيالـ equivalence
+
+181
+00:16:25,470 --> 00:16:29,350
+relations اللي هي علاقات التكافؤ وبعدها الـ
+
+182
+00:16:29,350 --> 00:16:33,770
+functions يبقى هذه الملامح الأساسية لمين لل
+
+183
+00:16:33,770 --> 00:16:38,250
+chapter اللي عندنا يبقى في ال integers بدنا ندرس ل
+
+184
+00:16:38,250 --> 00:16:41,970
+prime ال
+
+185
+00:16:41,970 --> 00:16:50,070
+division اللي هو القسمة او ال division algorithm
+
+186
+00:16:50,070 --> 00:16:52,050
+خوارزمية القسمة
+
+187
+00:16:56,430 --> 00:17:00,430
+خوارزمية القسمة بناخد حاجة اسمها modular
+
+188
+00:17:00,430 --> 00:17:03,730
+arithmetic
+
+189
+00:17:03,730 --> 00:17:10,710
+اللي
+
+190
+00:17:10,710 --> 00:17:18,130
+هو الحسابات الدورية بمقياس معين بعد ال modular
+
+191
+00:17:18,130 --> 00:17:21,250
+بناخد حاجة اسمة mathematical induction
+
+192
+00:17:29,030 --> 00:17:34,570
+استنتاج او الاستقرار الرياضي بعد الاستنتاج الرياضي
+
+193
+00:17:34,570 --> 00:17:44,610
+بنجي لحاجة اسمها ال equivalence relations علاقات
+
+194
+00:17:44,610 --> 00:17:52,590
+التكافؤ اخر حاجة and functions اللي هم من الدولة
+
+195
+00:17:53,960 --> 00:17:59,360
+طبعا كل هذا مر عليك في مبادئ الرياضية يعني هذا
+
+196
+00:17:59,360 --> 00:18:03,200
+الشفطة يعتبر مراجعة طبعا بتعرفوا مجموعة الأعداد
+
+197
+00:18:03,200 --> 00:18:08,360
+الصحيحة بتعرفوا الأعداد الأولية ال prime numbers
+
+198
+00:18:08,360 --> 00:18:13,660
+بتعرفوا الخوارزمية القسمة كيف نكتب عددين بدلالة
+
+199
+00:18:13,660 --> 00:18:20,480
+بعض واحد بدلالة التاني مضاعفات وزايد شيء معين علم
+
+200
+00:18:20,480 --> 00:18:26,110
+قياس زي إيش مثلازي العدد اتناش اظن كل اتناش ساعة
+
+201
+00:18:26,110 --> 00:18:29,650
+بتبدأ الساعة من جديد في الليل و النهار الساعة ..
+
+202
+00:18:29,650 --> 00:18:32,450
+بنبدأ من الساعة واحدة لغاية الساعة اتناش بعد
+
+203
+00:18:32,450 --> 00:18:34,610
+الساعة اتناش مايقولش الساعة تلاتاش مايقولش الساعة
+
+204
+00:18:34,610 --> 00:18:38,810
+واحدة و هكذا يبقى كل اتناش ساعة بتتدعت من هنا
+
+205
+00:18:38,810 --> 00:18:43,450
+الدورة من جديد طبعا المقياس هنا كان12 ممكن تكون
+
+206
+00:18:43,450 --> 00:18:47,370
+المقاس تلاتة ممكن عشرة ممكن سبعة ممكن خمسة زي ما
+
+207
+00:18:47,370 --> 00:18:51,450
+بدك زي ما بدنا بناخد مقاسات وبناء عليه بنشغل
+
+208
+00:18:51,450 --> 00:18:56,110
+هالشغل هذي بعدين الاستنتاج الرياضي برضه هدرسنا في
+
+209
+00:18:56,110 --> 00:19:00,770
+مبادئ الرياضياتباختصار بجينا نقول نفرض انه او
+
+210
+00:19:00,770 --> 00:19:05,370
+نحاول نثبت انه العدد صحيح عند ال .. القاعدة
+
+211
+00:19:05,370 --> 00:19:09,270
+لمطالية صحية عند N تسوى واحد ثم نحاول .. نفرض
+
+212
+00:19:09,270 --> 00:19:14,770
+صحيتها عند N ونحاول اثبتها عند مين عند N زيد واحد
+
+213
+00:19:14,770 --> 00:19:19,180
+وها كدهيبقى هذا ال mathematical induction ال
+
+214
+00:19:19,180 --> 00:19:23,420
+equivalence relation يقول ان ال relation عدة أنواع
+
+215
+00:19:23,420 --> 00:19:27,000
+بقول عن ال relation انها equivalence relation إذا
+
+216
+00:19:27,000 --> 00:19:32,160
+حققت لي كام شرط ثلاثة شرط الشرط الأول تبقى
+
+217
+00:19:32,160 --> 00:19:37,320
+relation reflexive العنصر مرتبط مع نفسهتبقى
+
+218
+00:19:37,320 --> 00:19:41,360
+symmetric إذا الـ A مرتبطة مع الـ B يبقى الـ B
+
+219
+00:19:41,360 --> 00:19:45,120
+بتكون مرتبطة مع الـ A بال relation اللي عندنا
+
+220
+00:19:45,120 --> 00:19:49,640
+الأمر الثالث اللي هو ال transitive لو ال element A
+
+221
+00:19:49,640 --> 00:19:53,980
+مربوط مع B و B مربوط مع C إذا الـ A مربوط مع C أو
+
+222
+00:19:53,980 --> 00:20:00,100
+في relation ما بين الإذا تحققت الشروط التلاتة في
+
+223
+00:20:00,100 --> 00:20:02,700
+ال relation بقول ال relation اللي عندنا is an
+
+224
+00:20:02,700 --> 00:20:06,400
+equivalence relation بعد هيك بدنا نروح لمين لل
+
+225
+00:20:06,400 --> 00:20:09,980
+functions طبعا هنا في ال calculus أخدنا ال
+
+226
+00:20:09,980 --> 00:20:12,720
+functions وفي مبادئ الرياضية أخدنا ال functions
+
+227
+00:20:12,720 --> 00:20:17,200
+هنرجع نذكرتعريف ال function ال one to one function
+
+228
+00:20:17,200 --> 00:20:22,540
+ال on to function هدول ضروريات جدا خلال دراستنا في
+
+229
+00:20:22,540 --> 00:20:26,420
+مساق الجبر يعني بدك تعرف شو ال identity function
+
+230
+00:20:26,420 --> 00:20:29,300
+ايش ال one to one function ايش ال on to function
+
+231
+00:20:29,300 --> 00:20:32,780
+ال composition ما بين ال two functions لو كان one
+
+232
+00:20:32,780 --> 00:20:35,920
+to one هل الناتج one to one ولا لأ؟لو كانوا
+
+233
+00:20:35,920 --> 00:20:39,120
+التنتين انتوا هل الناتج انتوا ولا كل هذا الكلام
+
+234
+00:20:39,120 --> 00:20:44,440
+سنعرفه من خلال من؟ من خلال هذا ال chapter ومن خلال
+
+235
+00:20:44,440 --> 00:20:48,360
+الجزء تبع من؟ تبع ال functions يبقى هذه هي
+
+236
+00:20:48,360 --> 00:20:52,580
+المقدمات اللي عندنا بنجي لل chapter الثاني ال
+
+237
+00:20:52,580 --> 00:20:58,880
+chapter الثاني بناخد فيه ال groups ال groups اللي
+
+238
+00:20:58,880 --> 00:21:02,500
+هي المجموعات أو الترجمة الحقيقية حسب اللغة العربية
+
+239
+00:21:02,500 --> 00:21:09,470
+بنسميها الزمرالزمر اللي هي جمع .. جمع ايش؟ زمرة
+
+240
+00:21:09,470 --> 00:21:14,830
+الزمر هذه موجودة في القرآن الكريم؟ موجودة يعني في
+
+241
+00:21:14,830 --> 00:21:21,810
+صورة ايش؟ في صورة الزمر طيب و يعني قرآننا يشير إلى
+
+242
+00:21:21,810 --> 00:21:28,290
+هذا الموضوعومش زمرتين في آخر ياتي صورة الزمر بيقول
+
+243
+00:21:28,290 --> 00:21:34,210
+ربنا سبحانه وتعالى وسيقى الذين كفروا إلى جهنم زمرة
+
+244
+00:21:34,210 --> 00:21:39,490
+يعني على شكل مجموعات وبعدها بيقول وسيقى الذين
+
+245
+00:21:39,490 --> 00:21:45,170
+اتقوا ربهم إلى الجنة زمرة كذلك على شكل مجموعات شكل
+
+246
+00:21:45,170 --> 00:21:51,490
+مجموعات ليه؟لأنه جهنم دركات فالمجرمين اللي أكثر
+
+247
+00:21:51,490 --> 00:21:55,530
+جرمهم المنافقين بيكونوا في الدرك الأسفل من النار و
+
+248
+00:21:55,530 --> 00:22:00,950
+هدول عذابهم شديدة لفوق وخف لفوق وخف لفوق وخف لكن
+
+249
+00:22:00,950 --> 00:22:04,870
+الجنة بالعكس درجات الدرجة العليا هي اللي فوق
+
+250
+00:22:04,870 --> 00:22:09,990
+الفردوس الأعلىإذا سألتم الله سبحانه وتعالى فاسألوه
+
+251
+00:22:09,990 --> 00:22:15,170
+الفردوس الأعلى يعني مثل ما أعمال الناس بتكون على
+
+252
+00:22:15,170 --> 00:22:19,810
+شكل اللي هو زمر أو مجموعات ويساقوا طبقا لهذه
+
+253
+00:22:19,810 --> 00:22:25,170
+الأعمال إلى الجنة أو إلى النار فكذلك ال group إنها
+
+254
+00:22:25,170 --> 00:22:30,740
+عبارة عن مجموعة لها صفات معينةفي أن ثلاثة شروط
+
+255
+00:22:30,740 --> 00:22:35,660
+بنحط على الـ set بالإضافة إلى العملية الثنائية على
+
+256
+00:22:35,660 --> 00:22:40,980
+ال set بتصير عند group ويعني عند groups كثيرة كل
+
+257
+00:22:40,980 --> 00:22:45,420
+واحدة إلها صفات معينة لكن كلهم بدهم يشتركوا في
+
+258
+00:22:45,420 --> 00:22:49,720
+الشروط التلاتة الأساسية اللي هنعرفها في حينها يبقى
+
+259
+00:22:49,720 --> 00:22:55,350
+في هذا ال chapterهنعطي ال groups و أمثلة عالمين
+
+260
+00:22:55,350 --> 00:23:01,250
+على ال groups و بعض الخواص عالمين لل groups زي ايش
+
+261
+00:23:01,250 --> 00:23:08,930
+مثلاكل group لدينا حاجة اسمه عنصر محايد identity
+
+262
+00:23:08,930 --> 00:23:15,450
+element وفي عندنا كل عنصر له معكوس inverse element
+
+263
+00:23:15,450 --> 00:23:19,730
+هل ال inverse هذا وحيد و لا ممكن ألاقي العنصر له
+
+264
+00:23:19,730 --> 00:23:24,140
+أكتر من معكوسطبعا مافيش الا واحد وهذا مثلا يعني هو
+
+265
+00:23:24,140 --> 00:23:27,760
+نثبته فيه حيني ال identity element ماعنديش الا
+
+266
+00:23:27,760 --> 00:23:31,120
+identity واحد في ال group لو وجود اتنين بدهم
+
+267
+00:23:31,120 --> 00:23:35,820
+يكونوا اتنين are equivalent اتنين نفس الشيء تمام
+
+268
+00:23:35,820 --> 00:23:39,260
+يبقى هذا بالنسبة ال identity element و هكذا يعني
+
+269
+00:23:39,260 --> 00:23:45,820
+احنا هنعطيتعريف لل group ثم نعطي بعض الأمثلة على
+
+270
+00:23:45,820 --> 00:23:51,040
+ال group هذا وبعض الخصائص البسيطة لمن لل group هذا
+
+271
+00:23:51,040 --> 00:23:57,240
+ما سيكون في هذا الشبتر الشبتر تلاتة بدنا نيجي
+
+272
+00:23:57,240 --> 00:23:59,800
+لحاجة اسمها subgroups
+
+273
+00:24:03,000 --> 00:24:07,320
+subgroups يبقى أنا لجروب اللي عندى هذه يعنى مثلا
+
+274
+00:24:07,320 --> 00:24:11,980
+كيف لو جيت قولت للطلاب اللى فى القاعة هدول يمثلولى
+
+275
+00:24:11,980 --> 00:24:17,300
+لجروب طبعا خدت شوية منهم اخدت الشجة هذه السبعة
+
+276
+00:24:17,300 --> 00:24:23,740
+هدول هل هدول بيصيروا ايه جروب تحت نفس العملية اللى
+
+277
+00:24:23,740 --> 00:24:28,130
+موجودة على الجروب الاصلية ولا لأبمعنى السبعة هذول
+
+278
+00:24:28,130 --> 00:24:33,750
+فيهم ال identity element وفيهم كل عنصر له معكوس
+
+279
+00:24:33,750 --> 00:24:37,630
+ولا لأ وعملية ال associativity ان شاء الله هنشرحها
+
+280
+00:24:37,630 --> 00:24:41,550
+فيه هنا إذا انطبقت عليهم هذه اللي بقول هذول مثل ال
+
+281
+00:24:41,550 --> 00:24:46,210
+subgroup لو اختل واحد من الشروط هذه بقول بطل يصير
+
+282
+00:24:46,210 --> 00:24:51,250
+subgroup هاي إيش بتصير؟ بتصير subset مجموعة يزيية
+
+283
+00:24:51,250 --> 00:24:56,680
+لكنها ليست subgroup إذا ال subgroup هذههي مجموعة
+
+284
+00:24:56,680 --> 00:25:01,920
+جزئية من ال group اللي عندنا هذه وبدها ضالها group
+
+285
+00:25:01,920 --> 00:25:07,120
+تحت نفس العملية الرياضية المعرفة على ال group
+
+286
+00:25:07,120 --> 00:25:12,380
+الأصلية ان حدث ذلك بقول هذه subgroup ما حدث يبقى
+
+287
+00:25:12,380 --> 00:25:17,200
+انسى الموضوع هذه الست عادية وخلاصنا وليست subgroup
+
+288
+00:25:17,200 --> 00:25:22,340
+بدنا نيجي ل chapter أربع حاجة اسمها ال cyclic
+
+289
+00:25:22,340 --> 00:25:24,480
+groups
+
+290
+00:25:35,510 --> 00:25:42,650
+cyclic group يعني الزمرة الدائرية generator يعني
+
+291
+00:25:42,650 --> 00:25:49,010
+مولدمولد يعني بيولدلي جميع عناصر main جميع عناصر
+
+292
+00:25:49,010 --> 00:25:52,810
+ال group Cyclic group يعني إيش المقصود بالcyclic
+
+293
+00:25:52,810 --> 00:25:57,990
+group؟ group عادية هذه بس تحقق فيها شرط، إيش
+
+294
+00:25:57,990 --> 00:26:03,790
+الشرط؟ أخدت عنصر منها، العنصر هذا ربعته، قعدته، و
+
+295
+00:26:03,790 --> 00:26:07,230
+أس أربعة و أس خمسة و أس ستة و أس سبعة و أس عشرة و
+
+296
+00:26:07,230 --> 00:26:11,360
+انه جابلي جميع العناصر اللي موجودة في ال groupإن
+
+297
+00:26:11,360 --> 00:26:16,920
+حدث ذلك بقول هذا العنصر هو generator للجروب يبقى
+
+298
+00:26:16,920 --> 00:26:21,140
+هذا العنصر هو اللي بولدلي جميع عناصر الجروب بلا
+
+299
+00:26:21,140 --> 00:26:26,440
+استثناء يبقى إن حدث ذلك بقول هذا generator طب بدي
+
+300
+00:26:26,440 --> 00:26:31,220
+أسأل واحد يعني لو كانت الجروب cyclic كل عنصر بنفع
+
+301
+00:26:31,220 --> 00:26:38,350
+يكون generator الإجابة نعم ولا لا؟ لايعني ممكن
+
+302
+00:26:38,350 --> 00:26:44,530
+تلاقي two generators فيها يعني أي group فيها أكتر
+
+303
+00:26:44,530 --> 00:26:49,910
+من عنصره على الأقل فيها two generators مين هم ال
+
+304
+00:26:49,910 --> 00:26:54,790
+generators هدول؟ العنصر و معكوسهيمكن الجروب الواحد
+
+305
+00:26:54,790 --> 00:26:59,190
+اللي أجيه فيها إياش مولدين يمكن أربعة يمكن ستة
+
+306
+00:26:59,190 --> 00:27:03,930
+يبقى يمكن تمانية بس ماتبقاش ال trivial subgroup ال
+
+307
+00:27:03,930 --> 00:27:07,630
+trivial subgroup اللي مش فيها إلا أنصر واحد اللي
+
+308
+00:27:07,630 --> 00:27:11,970
+هو main أنصر الواحدة تمام؟ يبقى هاي المقصود
+
+309
+00:27:11,970 --> 00:27:17,090
+بالcyclic group وكذلك ال generators بعد الcyclic
+
+310
+00:27:17,090 --> 00:27:21,430
+group نجي لحاجة اسمة ال permutation group يبقى
+
+311
+00:27:21,430 --> 00:27:37,150
+chapter خمسةالحاجة اسمها ال permutation group ايش
+
+312
+00:27:37,150 --> 00:27:43,070
+ال permutation هذه يبقى احنا بنيجي على set وفيها
+
+313
+00:27:43,070 --> 00:27:47,130
+مجموعة من العناصر افترض في عندي مثلا تلت عناصر
+
+314
+00:27:47,790 --> 00:27:54,650
+التلات عناصر كام تبديلة بقدر اسوي منهم بحيث ولا
+
+315
+00:27:54,650 --> 00:27:59,630
+واحد هتكون زي التانية يعني مثلا لو جينا قولنا واحد
+
+316
+00:27:59,630 --> 00:28:04,630
+واثنين وتلاتة يبقى هذي بسميها تبديلة من التبديلة
+
+317
+00:28:04,630 --> 00:28:10,370
+هذي بقدر اخلق مجموعة من التبديلات تعرف كم من
+
+318
+00:28:10,370 --> 00:28:14,750
+التلات عناصر بتقدر تسوي تبديلات مرت عليكم بدأ
+
+319
+00:28:14,750 --> 00:28:20,930
+الرياضيات كم يعني؟مضروب تلاتة مضروب تلاتة يبقى
+
+320
+00:28:20,930 --> 00:28:25,610
+تلاتة في اتنين في واحد يبقى عندي ست تبديلات ممكن
+
+321
+00:28:25,610 --> 00:28:31,970
+اخلق من هذه التبديلات احنا بدنا ننشي جروب على
+
+322
+00:28:31,970 --> 00:28:37,990
+التبديلات اللي عندنا هذه وندرس بعض المعلومات على
+
+323
+00:28:37,990 --> 00:28:42,450
+هذه التبديلات وهل التبديلات بتبقى even ولا odd
+
+324
+00:28:42,720 --> 00:28:48,500
+وقداش رتبت هذه التبديلة وقداش وقداش الاخرى يبقى
+
+325
+00:28:48,500 --> 00:28:52,180
+هذا شغلنا اللي يكون وين اللي هيكون في هذا الشبطق
+
+326
+00:28:52,180 --> 00:28:56,900
+اللي هو ال permutation group يبقى permutation
+
+327
+00:28:56,900 --> 00:29:02,540
+تبديلة permutation group اللي هي مجموعة التبديلات
+
+328
+00:29:02,540 --> 00:29:09,210
+او زمرة التبديلاتبنجي لحاجة هنا اسمها isomorphisms
+
+329
+00:29:09,210 --> 00:29:14,570
+isomorphisms
+
+330
+00:29:14,570 --> 00:29:20,430
+و كذلك ال atomorphisms
+
+331
+00:29:20,430 --> 00:29:26,470
+طيب
+
+332
+00:29:33,130 --> 00:29:38,230
+الترجمة العربية بتقول التشكل النمطي أو التشابه
+
+333
+00:29:38,230 --> 00:29:42,990
+النمطيماذا يعني تشابه والنمط؟ يعني انا عندي group
+
+334
+00:29:42,990 --> 00:29:48,270
+وعندي group تانية اتنين فيه تشابه مابليه؟ ايش كيف
+
+335
+00:29:48,270 --> 00:29:52,790
+يعني تشابه؟ يعني هذا و هذا و هذا بنعم هذا؟ لأ مش
+
+336
+00:29:52,790 --> 00:29:57,590
+هيك في عندنا شروط الشروط لو تحققت على ال two
+
+337
+00:29:57,590 --> 00:30:02,550
+groups بقول ان هم دول اتنين فيهم تشابه نمطين
+
+338
+00:30:02,550 --> 00:30:07,530
+تعرفوا زي ايش مثلا؟يبقى لو جيت قولت هذه فيها سبعة
+
+339
+00:30:07,530 --> 00:30:13,710
+يبقى هذه فيها سبعة نفس العدد رتبة أي عنصر هنا زي
+
+340
+00:30:13,710 --> 00:30:19,390
+رتبة أي عنصر هنا عدد العناصر رتبتهم مثلا ستة جد
+
+341
+00:30:19,390 --> 00:30:23,250
+عدد العناصر اللي رتبتهم ستة عدد العناصر اللي
+
+342
+00:30:23,250 --> 00:30:27,830
+رتبتهم اتنين جد عدد العناصر اللي رتبتهم اتنينعدد
+
+343
+00:30:27,830 --> 00:30:31,450
+ال subgroups هنا جد عدد ال subgroups هنا ده اسمه
+
+344
+00:30:31,450 --> 00:30:37,230
+تشابه نمطي أو تشاكل نمطي طيب يبقى ايش يعني
+
+345
+00:30:37,230 --> 00:30:41,450
+isomorphism ان احنا شرحنا كلام بلدي لك رياضيا
+
+346
+00:30:41,450 --> 00:30:47,990
+بنقول ال isomorphism هو function ما بين two groups
+
+347
+00:30:47,990 --> 00:30:55,300
+يبقى لو جهتي قلتلك افترض عندي فيفانكشن من الجروب
+
+348
+00:30:55,300 --> 00:31:02,280
+جي إلى الجروب جي بار مثلا كويس يبقى هذا عشان يكون
+
+349
+00:31:02,280 --> 00:31:07,000
+ايزو مورفزم تتحقق بعض الشروط اول شي هي function
+
+350
+00:31:08,740 --> 00:31:15,860
+تلاتة تبقى one to one تلاتة تبقى onto ان حدث ذلك
+
+351
+00:31:15,860 --> 00:31:20,840
+بقول هذه ال function one to one and onto كمان في
+
+352
+00:31:20,840 --> 00:31:27,860
+خاصية لازم اتحقها وهي في تأثيرها على ال X Y في
+
+353
+00:31:27,860 --> 00:31:34,160
+تأثيرها على عنصر X في Y بتساوي في of X في of Y
+
+354
+00:31:35,360 --> 00:31:40,700
+تمام؟ هنا في عملية ما بين العنصرين ضرب جمع طرح
+
+355
+00:31:40,700 --> 00:31:45,920
+الجسم أخدوس حسب ما هي معرفة على G هنا كمان في
+
+356
+00:31:45,920 --> 00:31:49,520
+عملية ما بين العنصر هذا والعنصر هذا هي العملية
+
+357
+00:31:49,520 --> 00:31:54,480
+المعرفة على G bar والتي قد تكون تاعة العملية G وقد
+
+358
+00:31:54,480 --> 00:32:00,470
+تكون غيرها وفي الغالب غيرهايبقى هذا الشرط مع ال
+
+359
+00:32:00,470 --> 00:32:05,490
+one to one and one to two إذا حدث ذلك تحققت الشروط
+
+360
+00:32:05,490 --> 00:32:11,370
+التلاتة بقول الفاية عندي هذه isomorphism وبالتالي
+
+361
+00:32:11,370 --> 00:32:17,320
+بقول الجي والجي بار are isomorphicأيزو مورفك يعني
+
+362
+00:32:17,320 --> 00:32:22,280
+في ايزو مورفزم ما بين من؟ ما بين ال two groups
+
+363
+00:32:22,280 --> 00:32:26,600
+يبقى معنا هذا الكلام لما جينا قولنالكوا هنا بدنا
+
+364
+00:32:26,600 --> 00:32:30,980
+نتكلم على ال functions و نذكر بين one to one and
+
+365
+00:32:30,980 --> 00:32:35,310
+untoمش بلاش من ذاكره يبقى هذه الأساسيات اللي
+
+366
+00:32:35,310 --> 00:32:38,770
+بتلزمنا للي قدام روح نعطيها لك في ال chapter اول
+
+367
+00:32:38,770 --> 00:32:43,350
+يبقى لما ناجي اقولك automatic phi is one to one
+
+368
+00:32:43,350 --> 00:32:46,450
+يبقى فيه one to one function يبقى كنت ماخد ال one
+
+369
+00:32:46,450 --> 00:32:50,410
+to one function في اول chapter في المقدمة ان قلت
+
+370
+00:32:50,410 --> 00:32:55,250
+لك phi is onto يبقى هنا فهمتك ما معنى onto
+
+371
+00:32:55,250 --> 00:32:58,590
+functionلو جيت سؤال تعالى واحد يقولش يعني onto
+
+372
+00:32:58,590 --> 00:33:01,550
+function بيقول يعني ده الفوقية بيقول له ده ترجمة
+
+373
+00:33:01,550 --> 00:33:06,150
+عربية انا موديش ترجمة عربية انا بدي ترجمة رياضية
+
+374
+00:33:06,150 --> 00:33:13,150
+حد فيكم يتذكر ايش يعني معنى onto function دي اللي
+
+375
+00:33:13,150 --> 00:33:18,310
+درسيه مبادئ onto function ايش معناها رياضيا؟ قولي
+
+376
+00:33:18,310 --> 00:33:21,350
+اللي انت فاهم وموديش حافظ نص عن غيرك، بتفضل
+
+377
+00:33:28,820 --> 00:33:34,880
+انا عندى ست a وست b فى من a إلى b is a function
+
+378
+00:33:34,880 --> 00:33:37,200
+وقتش هدى بقول عليها أنتوا
+
+379
+00:33:40,780 --> 00:33:46,420
+مية المية اذا جيت اخدت اي عنصر من الست بي لجيته
+
+380
+00:33:46,420 --> 00:33:50,620
+اصل وين في ايه يعني ماعنها كلام ان ال function دي
+
+381
+00:33:50,620 --> 00:33:56,500
+غطت جميع عناصر بي لستنها لان ال function يا شباب
+
+382
+00:33:56,500 --> 00:34:01,940
+من الست اي لست بي ليس بالضرورة تغطي لجميع عناصر بي
+
+383
+00:34:01,940 --> 00:34:05,840
+لكن بتغطي اجبار جميع عناصر اي لان ال اي هو ال
+
+384
+00:34:05,840 --> 00:34:11,150
+domain تبعها تمام اذا مش هتكون انتوابدي يكون ال
+
+385
+00:34:11,150 --> 00:34:14,870
+range تبع هذه ال function هو نفس ال code main
+
+386
+00:34:14,870 --> 00:34:19,990
+بالضبط يعني جميع عناصر B كلهم بدهم يظهروا كصور
+
+387
+00:34:19,990 --> 00:34:25,130
+لعناصر A بلاست اتناء هذا ال onto ال one to one
+
+388
+00:34:25,130 --> 00:34:29,690
+زواج كاتوليكي الواحد مالوش الا واحدة جوزه بس غير
+
+389
+00:34:29,690 --> 00:34:34,810
+هي كده ممنوع عندنا المسعية اه مش عندنايبقى العنصر
+
+390
+00:34:34,810 --> 00:34:39,430
+الواحد له صورة واحدة ولا واحد بيشاركوا فيها مش
+
+391
+00:34:39,430 --> 00:34:43,010
+عنصرين بيشتركوا في نفس الصورة إذا اشترك عنصرا في
+
+392
+00:34:43,010 --> 00:34:47,290
+نفس الصورة يبقى في هذه الحالة ال function ليست one
+
+393
+00:34:47,290 --> 00:34:51,310
+to one طب إذا العنصر طالع لصفتان يبقى ماهياش
+
+394
+00:34:51,310 --> 00:34:56,790
+function من الأساس يبقى ال five function بدأت حقق
+
+395
+00:34:56,790 --> 00:35:01,760
+الخاصية هذه بتبقى one to one and untoوهذه من ال
+
+396
+00:35:01,760 --> 00:35:06,960
+group G إلى ال group G bar طبعاً وحنعطي أمثلة
+
+397
+00:35:06,960 --> 00:35:11,950
+عديدة على ذلك وبعض النظريات المتعلقة بهابنجي لل
+
+398
+00:35:11,950 --> 00:35:18,470
+atomorphism شو يعني atomorphism هو function فاي بس
+
+399
+00:35:18,470 --> 00:35:24,230
+من جي إلى جي itself مش لوحدة تانية هنا جي و هنا جي
+
+400
+00:35:24,230 --> 00:35:28,550
+بربوا اختلفوا عن بعض تماما هاي شجة و هاي شجة تانية
+
+401
+00:35:28,550 --> 00:35:32,300
+و ليهم مش علاقة ببعض ولا بقرب ولا بعض ولا غيرهلكن
+
+402
+00:35:32,300 --> 00:35:36,920
+عندما أقول من ال group G إلى ال group G itself ال
+
+403
+00:35:36,920 --> 00:35:43,240
+isomorphism هذا بسميه ايه؟ بسميه atomorphism يبقى
+
+404
+00:35:43,240 --> 00:35:48,500
+كأن ال atomorphism هو حالة خاصة من مهممن
+
+405
+00:35:48,500 --> 00:35:53,080
+isomorphism ال isomorphism من group ل group تانية
+
+406
+00:35:53,080 --> 00:35:56,940
+لكن ال atomorphism من ال group لنفس main لنفس
+
+407
+00:35:56,940 --> 00:36:01,380
+group وهو isomorphism one to one وانتوا و بحقق
+
+408
+00:36:01,380 --> 00:36:05,180
+لمين الخاصية اللي عندنا هذه إن حدث ذلك يبقى هذا
+
+409
+00:36:05,180 --> 00:36:11,140
+بسميه atomorphism وسنحسب بعض ال atomorphisms لمين
+
+410
+00:36:11,140 --> 00:36:19,550
+لبعض ال group بعد ذلك بنجي ل chapter 7سابعة بنا
+
+411
+00:36:19,550 --> 00:36:26,210
+نيجي ناخد حاجة اسمها cosets and Lagrange theorem
+
+412
+00:36:26,210 --> 00:36:38,670
+coset
+
+413
+00:36:38,670 --> 00:36:44,690
+كلمة جديدة هنا set اللي فيها او مجموعة co مرافق
+
+414
+00:36:45,070 --> 00:36:51,750
+يبقى هى الست جديدة وولدناها من شيء ما شو شيء ما؟
+
+415
+00:36:51,750 --> 00:36:57,710
+شايف عندى هذه ال subgroup أخدت عنصر من برا ال
+
+416
+00:36:57,710 --> 00:37:02,150
+subgroup لكن من نفس ال group ضربته في هذه ال
+
+417
+00:37:02,150 --> 00:37:06,590
+subgroup من جهة اليمين او من جهة الشمال ان كان
+
+418
+00:37:06,590 --> 00:37:10,930
+الضرب من جهة الشمال بسميه left corset وان كان
+
+419
+00:37:10,930 --> 00:37:16,690
+الضرب من جهة اليمين بسميها right corsetالكوسيت هذي
+
+420
+00:37:16,690 --> 00:37:22,110
+يمكن تطلع subgroup ويمكن ما تطلعش subgroup يبقى in
+
+421
+00:37:22,110 --> 00:37:25,710
+general ال left كوسيت او ال right كوسيت ليس
+
+422
+00:37:25,710 --> 00:37:31,430
+بالضرورة ان تكون subgroup من ال group الأصلية ما
+
+423
+00:37:31,430 --> 00:37:36,600
+علينا يبقى احناجبنا حاجة جديدة اسمها كوسيت ال
+
+424
+00:37:36,600 --> 00:37:40,620
+group الأصلية أخد جزء من أسر subgroup ال subgroup
+
+425
+00:37:40,620 --> 00:37:45,580
+جبت عنصر ضربته فيه عناصرها كلهم طلع عندهمين اللي
+
+426
+00:37:45,580 --> 00:37:52,280
+هو الكوسيت كويس يبقى الكوسيت هذي جبت عنصر تاني
+
+427
+00:37:52,280 --> 00:37:55,560
+طلعت كوسيت تانية جبت عنصر تانية ضربته فيه طلع
+
+428
+00:37:55,560 --> 00:38:00,010
+كوسيت تانية و هكذاطبعا يبقى هذا مفهوم ال process
+
+429
+00:38:00,010 --> 00:38:04,190
+and Lagrange theory بنظرية Lagrange هذه بتلعب دور
+
+430
+00:38:04,190 --> 00:38:10,690
+كبير جديد في علم الجبر بالبلد هيك باختصار بيقول ال
+
+431
+00:38:10,690 --> 00:38:13,370
+order لصبي جروبي بيجسم
+
+432
+00:38:19,410 --> 00:38:25,290
+العدد العناصر في ال subgroup يقسم عدد العناصر في
+
+433
+00:38:25,290 --> 00:38:30,790
+ال group إذا كان العدد اللي هو finite عددا محدودا
+
+434
+00:38:30,790 --> 00:38:35,170
+يبقى هذه اللي بتقوله من؟ هذه اللي بتقوله نظرية
+
+435
+00:38:35,170 --> 00:38:40,180
+Lagrangeهذه عمود فقري في علم الجبرو خاصة بالنسبة
+
+436
+00:38:40,180 --> 00:38:45,400
+لموضوع main بالنسبة لموضوع gross هذا بالنسبة ل
+
+437
+00:38:45,400 --> 00:38:49,420
+main لنظرية Lagrange ابنجي بعد ذلك حاجة اسم ال
+
+438
+00:38:49,420 --> 00:38:53,120
+external indirect product يبقى ال chapter تمانية
+
+439
+00:38:53,120 --> 00:39:01,320
+حاجة اسمها ال external direct product
+
+440
+00:39:01,320 --> 00:39:08,310
+ايش ال external direct productيبقى أنا بدي أكوّن
+
+441
+00:39:08,310 --> 00:39:13,730
+group جديدة من two groups موجودة، هذه group وهذه
+
+442
+00:39:13,730 --> 00:39:18,970
+group تانية، ثانيا منهم بدي أكوّن group جديدة عن
+
+443
+00:39:18,970 --> 00:39:24,210
+طريق حاجة اسمه حاصل الضرب الخارجي external خارجي
+
+444
+00:39:24,470 --> 00:39:29,750
+كيف يعني؟ بصير العنصر، بدأ أقول هذه group G1 وهذه
+
+445
+00:39:29,750 --> 00:39:35,270
+group G2 يبقى G1 cross G2، هذا بدأ أرمز إلى مين؟
+
+446
+00:39:35,270 --> 00:39:40,810
+للضرب الخارج، يمين عناصر وكل عنصر ordered pair زوج
+
+447
+00:39:40,810 --> 00:39:45,150
+مرتب، عنصر هنا مع عنصر هنا، اتنين تأور ضرب الكقص،
+
+448
+00:39:45,150 --> 00:39:49,070
+بقول هذا عنصر واحد في مين؟ فال group الجديدة يعني
+
+449
+00:39:49,070 --> 00:39:55,690
+أنا بدي أنشئ group جديدة من two groupsموجودة طيب
+
+450
+00:39:55,690 --> 00:40:00,570
+هذا هو حاصل الضرب الخارجي في حاصل ضرب داخلي اه في
+
+451
+00:40:00,570 --> 00:40:06,030
+حاصل ضرب داخلي وهذا مثلا نشير اليه بعد قليل يبقى
+
+452
+00:40:06,030 --> 00:40:10,910
+هذا هو ال external direct product بدنا نيجي لتسعة
+
+453
+00:40:10,910 --> 00:40:15,730
+حاجة اسمها normal subgroups يبقى هنا normal
+
+454
+00:40:15,730 --> 00:40:19,350
+subgroups
+
+455
+00:40:21,580 --> 00:40:27,080
+هذه يا شباب أهم أنواع ال subgroups و بتلعب دور
+
+456
+00:40:27,080 --> 00:40:33,300
+كبير جدا في موضوع اللي هو ال groups إذا حصلت على
+
+457
+00:40:33,300 --> 00:40:38,880
+normal subgroup بقدر أنشئ group جديدة المن المين
+
+458
+00:40:38,880 --> 00:40:42,820
+من كلمة اللي هو ال cosets اللي عندنا بقدر أعمل
+
+459
+00:40:42,820 --> 00:40:48,440
+cosets و ال cosets يعملولي group جديدة بسميها ال
+
+460
+00:40:48,440 --> 00:40:56,210
+factor groupfactor group وزيادة
+
+461
+00:40:56,210 --> 00:41:00,670
+على ذلك باجي كمان نقطة اخرى internal direct
+
+462
+00:41:00,670 --> 00:41:08,530
+product و كذلك internal direct product
+
+463
+00:41:11,440 --> 00:41:15,580
+بس ال internal غير ال external external بجيب group
+
+464
+00:41:15,580 --> 00:41:19,100
+مع group تانية ال internal لأ داخل ال group
+
+465
+00:41:19,100 --> 00:41:23,640
+الواحدة بجيب sub group و بجيب sub group تانية طبعا
+
+466
+00:41:23,640 --> 00:41:29,120
+ال two sub groups هذول بروح بدربهم في بعض لو كان
+
+467
+00:41:29,120 --> 00:41:33,480
+حاصل ضربهم يعطوني ال group الأساسية و التقاطهم
+
+468
+00:41:33,480 --> 00:41:37,910
+يعطوني بس عنصر واحدة بسمي هذاinternal direct
+
+469
+00:41:37,910 --> 00:41:42,870
+product يعني احنا بنشتغل داخل ال group الواحدة
+
+470
+00:41:42,870 --> 00:41:48,250
+بطلع منها ال internal direct product تمام اخر
+
+471
+00:41:48,250 --> 00:41:56,550
+section عاشرة حاجة اسمها ال homomorphism
+
+472
+00:41:56,550 --> 00:42:04,200
+ايش ال homomorphismهو عبارة عن الـ function هذه
+
+473
+00:42:04,200 --> 00:42:10,940
+Phi من G إلى G bar بس هذه مش لازم تكون one to one
+
+474
+00:42:10,940 --> 00:42:17,320
+ولو انتوا بس تحققلي الشرط هنا اللهم إلا فقط لغاية
+
+475
+00:42:17,320 --> 00:42:25,950
+يبقى هنا Phi of XY بدل سوى Phi of X في Phi of Yإذا
+
+476
+00:42:25,950 --> 00:42:31,590
+تحقق هذا الشرق بقول هذا هو homomorphism و برضه
+
+477
+00:42:31,590 --> 00:42:35,490
+عليه مجموعة من نظريات لباسية بها و section طويل
+
+478
+00:42:35,490 --> 00:42:39,670
+شوية يعني في مجموعة من البراهين و مجموعة من نظريات
+
+479
+00:42:39,670 --> 00:42:45,520
+و مجموعة من الشغلات يعنيهذا اللي قدامك هو الإطار
+
+480
+00:42:45,520 --> 00:42:50,500
+العام لمين لال مقرر في جبر حديث واحد كل الشغلات
+
+481
+00:42:50,500 --> 00:42:56,000
+اللتي سندرسها في اللي هو جبر حديث واحد بعد هيك
+
+482
+00:42:56,000 --> 00:43:00,940
+بيجينا جبر حديث اتنين للفصل الثاني وهذا مش الكل في
+
+483
+00:43:00,940 --> 00:43:06,280
+كوه قبل اخر الان حد فيكم بيحب يسأل اي سؤال بالنسبة
+
+484
+00:43:06,280 --> 00:43:10,460
+للي سمعه اليوم في المحاضرة او اي سؤال بيدور في
+
+485
+00:43:10,460 --> 00:43:11,180
+دماغك
+
+486
+00:43:19,140 --> 00:43:24,860
+والله عمود في قرية هذه كلها براهين وانت أخدت في
+
+487
+00:43:24,860 --> 00:43:27,540
+المبادئ الرياضية اللي ما أخدش فيها حد يسمع ال
+
+488
+00:43:27,540 --> 00:43:32,040
+direct proof برهان مباشر في proof بال
+
+489
+00:43:32,040 --> 00:43:37,440
+contrapositiveتمشي تمشي العكس في لا التناقض اسمه
+
+490
+00:43:37,440 --> 00:43:40,780
+ال contradiction طريقة تالتة اللي هي طريقة ال
+
+491
+00:43:40,780 --> 00:43:44,440
+contradiction إذا مش ماخد مبادر رياضيات لا يمكن
+
+492
+00:43:44,440 --> 00:43:49,500
+أنك تفهم حاجة معانا هنا لإن شغلنا كله يعني قول
+
+493
+00:43:49,500 --> 00:43:55,780
+بنسبة 70% براهينكلها براهيم، مبادر رياضية بتعلمك
+
+494
+00:43:55,780 --> 00:44:00,220
+كيف تبرم، بتعلمك هي ال logic، المنطقة الرياضية،
+
+495
+00:44:00,220 --> 00:44:03,920
+كيف يصير عندك منطقة رياضية تفهم و أنت ستطيع تبرم،
+
+496
+00:44:03,920 --> 00:44:07,640
+ما أنتش ماخد مبادر رياضيات، يبقى أنت جاي على عمارة
+
+497
+00:44:07,640 --> 00:44:13,290
+بلا أساسات، بس تطلع شوية بتهيلتقدرش تتحمل ايه
+
+498
+00:44:13,290 --> 00:44:16,430
+الحمل؟ يبقى احنا بيقولك اذا مش ماخد روح اسحب
+
+499
+00:44:16,430 --> 00:44:20,570
+المادة وروح تسجل مبادئ رياضيات لإنها نازلة الحين
+
+500
+00:44:20,570 --> 00:44:26,110
+مع الدكتور أحمد المبحوح تمام؟ لكن اذا مسجل
+
+501
+00:44:26,110 --> 00:44:29,790
+الماديتين مع بعض مافيش مشكلة لكن ما انتش مسجل
+
+502
+00:44:29,790 --> 00:44:34,130
+اديك، cancel الموضوع خلاص، حد بدي أسأل تاني؟
+
+503
+00:44:34,130 --> 00:44:38,230
+ننتظركوا الساعة اتناشر ان شاء الله في هذا المكان
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8e7805578a52cfc57bc82ccf2aaa3b81b7161018
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_postprocess.srt
@@ -0,0 +1,1728 @@
+1
+00:00:21,350 --> 00:00:26,170
+السلام عليكم اسمي الله أحمد محليم هنعرج على ال ..
+
+2
+00:00:26,170 --> 00:00:29,010
+هنكمل ان شاء الله اليوم في خمس أسئلة تبقتنا من ال
+
+3
+00:00:29,010 --> 00:00:35,290
+chapter الأخير الشخصية ال 56, 58, 59, 64 و 65 كم
+
+4
+00:00:35,290 --> 00:00:39,410
+هنحلهم مش كلهم بس نعرج على أفكار لحل الأسئلة بعدين
+
+5
+00:00:39,410 --> 00:00:41,350
+هنفوت في ال chapter الخامس اللي هو chapter
+
+6
+00:00:41,350 --> 00:00:46,100
+permutation in groups بالنسبة لسؤال 56مرة الماضية
+
+7
+00:00:46,100 --> 00:00:50,240
+انتهينا فيه وماكملنهوش السؤال ستة و خمسين بيقول
+
+8
+00:00:50,240 --> 00:00:58,360
+اثبت ان U تنين N is not cyclic طيب، بالنسبة لعناصر
+
+9
+00:00:58,360 --> 00:01:06,180
+ال U تنين N هي عبارة عن كل .. كل إيش؟ العناصر اللي
+
+10
+00:01:06,180 --> 00:01:09,720
+بتكون relative لبعض مع تنين N مين هي؟ هي كل الأد
+
+11
+00:01:11,500 --> 00:01:14,740
+انت جارز اللي ما بين الواحد والتنين ان كيف بتثبت
+
+12
+00:01:14,740 --> 00:01:18,860
+انها مش cyclic عشان
+
+13
+00:01:18,860 --> 00:01:22,540
+تكون not cyclic معناته انا بتثبت ان لكل a ينتمي ل
+
+14
+00:01:22,540 --> 00:01:30,360
+u تنين ان a ال order لل a أقل من تنين ان تنين نفسي
+
+15
+00:01:30,360 --> 00:01:33,520
+صح؟
+
+16
+00:01:33,520 --> 00:01:36,340
+لأ أقل من في تنين ان
+
+17
+00:01:39,850 --> 00:01:49,310
+لأن ال order ل U2N عبارة عن فاية تنين N جداش فاية
+
+18
+00:01:49,310 --> 00:01:58,110
+تنين N هي تنين plus N minus واحد طبعا أنا بشغل N
+
+19
+00:01:58,110 --> 00:02:08,890
+أكبر أو يساوي تلاتة فانا شغال بدء من U8 U16 U32
+
+20
+00:02:08,890 --> 00:02:15,190
+إلى خارجطيب عشان برضه نذكر ال U تنين N عبارة عن
+
+21
+00:02:15,190 --> 00:02:24,170
+واحد تلاتة خمسة سبعة لان تنينوس N ماينس واحد كيف
+
+22
+00:02:24,170 --> 00:02:30,230
+بتثبت ان هذا ال group not cyclic؟زي ما قلتلك فوق،
+
+23
+00:02:30,230 --> 00:02:35,990
+لازم أثبت أنه أقدر أي عنصر أقل من 2 أُس N لو أنا
+
+24
+00:02:35,990 --> 00:02:40,330
+أخدت ال A، ينتمي ل U2N، معناته ال degrees common
+
+25
+00:02:40,330 --> 00:02:48,210
+divisor ل A و 2N، إيش بتتساوي؟ واحد، هذا معناته أن
+
+26
+00:02:48,210 --> 00:02:55,150
+ال degrees common divisor ل A و 2، إيش مالها؟
+
+27
+00:02:55,150 --> 00:02:58,070
+واحد، إيش يعني؟
+
+28
+00:03:03,050 --> 00:03:09,730
+ماذا يعني اجريز common divisor ل a و 2 و دي ساوي
+
+29
+00:03:09,730 --> 00:03:16,050
+واحد انا
+
+30
+00:03:16,050 --> 00:03:22,290
+في ال number 3 غيش بقول دي انه تنين و صفاي ال a
+
+31
+00:03:22,290 --> 00:03:26,410
+congruent ل واحد مدمين
+
+32
+00:03:32,430 --> 00:03:38,910
+أو congruent ل واحد mod a في
+
+33
+00:03:38,910 --> 00:03:42,810
+نظرية احنا اخدنا اسمها نظرية firmات في لتعميم
+
+34
+00:03:42,810 --> 00:03:47,290
+اسمها Euler theorem ايش نظرية firmات بتقول الاجيز
+
+35
+00:03:47,290 --> 00:03:52,650
+common divisor ل a و b ساو واحد ف a أسفل p minus
+
+36
+00:03:52,650 --> 00:04:00,450
+واحد congruent ل واحد mod mod مين mod a مش عارف
+
+37
+00:04:00,450 --> 00:04:01,910
+ايه البلسيتها دي ايه و الله ان
+
+38
+00:04:04,990 --> 00:04:11,790
+يجي بس أتأكد Mod
+
+39
+00:04:11,790 --> 00:04:17,510
+P طيب
+
+40
+00:04:17,510 --> 00:04:21,630
+فانا لما بدي أجي أشغل هانت نينوس التعميم تبعها
+
+41
+00:04:21,630 --> 00:04:26,210
+اللي هي ال Euler theorem لو اتطلعت على شبتر سبعة
+
+42
+00:04:26,210 --> 00:04:30,430
+في نظرية الأعداد اللي أخد أو ما أخد عبارة عن النص
+
+43
+00:04:30,430 --> 00:04:31,050
+التالي
+
+44
+00:04:37,660 --> 00:04:48,420
+اللي هي a أصفاء الان congment لواحد مد
+
+45
+00:04:48,420 --> 00:04:54,540
+ان لأ هو أنا مش محتاج هذي
+
+46
+00:04:54,540 --> 00:04:57,820
+طيب
+
+47
+00:04:57,820 --> 00:05:09,440
+هذا معناته هبدل ان a أصفاء الاتنين انconjuant ل 1
+
+48
+00:05:09,440 --> 00:05:27,440
+mod 2n ايش يعني a2n-1 conjuant ل 1 mod 2n يعني a2n
+
+49
+00:05:27,440 --> 00:05:33,500
+-1 بتساوي 1 on u2n
+
+50
+00:05:34,340 --> 00:05:40,160
+يعني a أس تنين أس n مينوس واحد نقص الواحد بيسوي
+
+51
+00:05:40,160 --> 00:05:53,080
+واحد on او نقص الواحد بيسوي zero on u تنين n طيب
+
+52
+00:05:53,080 --> 00:05:58,320
+تقدر تحلل؟
+
+53
+00:05:58,320 --> 00:06:07,890
+تقدر تحلل؟ هذا يا حبيبي العدد زوجيمعناته 2 a أُس 2
+
+54
+00:06:07,890 --> 00:06:13,730
+هو 2 أُس n minus 1 عبارة عن 2 في 2 أُس n minus 2
+
+55
+00:06:13,730 --> 00:06:19,570
+وأنا بشتغل n شمالها أكبر وساوية تلاتة معناته a أُس
+
+56
+00:06:19,570 --> 00:06:22,930
+2 أُس n minus 1 نقص الواحد اللي هي بتساوي zero
+
+57
+00:06:22,930 --> 00:06:27,990
+عبارة عن a أُس 2 في 2 أُس n minus 2
+
+58
+00:06:34,970 --> 00:06:38,610
+نقص الواحد اللي عبارة عن ايه اتنين أس ان ماينوس
+
+59
+00:06:38,610 --> 00:06:47,790
+اتنين الكل تربيع نقص الواحد حلل هذه عبارة عن اتنين
+
+60
+00:06:47,790 --> 00:06:55,050
+أس اتنين أس ان ماينوس اتو نقص الواحد في اتنين أس
+
+61
+00:06:55,050 --> 00:07:00,210
+اتنين أس ان ماينوس اتو زاد الواحد بس هذه ايه
+
+62
+00:07:04,370 --> 00:07:13,150
+هذا ايش بيساوي؟ Zero اش يعني؟ يعني ان a أس 2 أس n
+
+63
+00:07:13,150 --> 00:07:19,810
+minus 2 بيساوي 1 or 2 أس 2 أس n minus 2 بيساوي
+
+64
+00:07:19,810 --> 00:07:24,950
+سالب 1 طبعا
+
+65
+00:07:24,950 --> 00:07:31,570
+انا باشتغل وين؟بشتغل في U2N لما بقول A أوس اتنين
+
+66
+00:07:31,570 --> 00:07:35,110
+أوس N minus اتنين مش يساوي واحد معناه to order ال
+
+67
+00:07:35,110 --> 00:07:40,130
+A اقل او يساوي تنين أوس N minus اتنين اقل من تنين
+
+68
+00:07:40,130 --> 00:07:46,630
+أوس N minus واحد اللي هو بدي ساوي order ال U2N or
+
+69
+00:07:46,630 --> 00:07:54,910
+ال A اتنين أوس N minus two ايش بدي ساوي
+
+70
+00:07:58,740 --> 00:08:07,060
+السالب واحد لأ أنا مابديش أربّه مافرجتش كتير هذي
+
+71
+00:08:07,060 --> 00:08:13,060
+لما بدي أربّه هيعطيني في النهاية A أُس 2 أُس N-1 و
+
+72
+00:08:13,060 --> 00:08:18,680
+هذي بحتاجهاش لكن أنا مين هحتاج؟ هذي علاقة صحيحة أه
+
+73
+00:08:18,680 --> 00:08:23,650
+لكن بلزمهاش بلزم مين؟انه انا هذه اللي بدور عليها
+
+74
+00:08:23,650 --> 00:08:28,990
+معناته كل عنصر في U تنين N ال order اللي هو جال من
+
+75
+00:08:28,990 --> 00:08:37,650
+مين؟ من U من order U تنين N هذه المعلومة لو ربعت
+
+76
+00:08:37,650 --> 00:08:41,070
+هحصل على مين؟ هرجع للأصل اللي مابتلزمنيش أصلا
+
+77
+00:08:41,070 --> 00:08:48,130
+وبالتاليمدام ال order لل A أقل من ال order لل U
+
+78
+00:08:48,130 --> 00:08:54,370
+تنين N معناته generated by ال A لا يساوي ال U تنين
+
+79
+00:08:54,370 --> 00:09:02,190
+N لكل A ينتمي ل U تنين N هذا معناته U تنين N not
+
+80
+00:09:02,190 --> 00:09:11,230
+cycling بس مشكلة انا احتجت ايش هادي باي اغلر
+
+81
+00:09:11,230 --> 00:09:18,430
+ثيرنظرية ايرلر الموجودة في نظرية الاعداد اعيد
+
+82
+00:09:18,430 --> 00:09:24,830
+بسرعة انا عناصر ال U N ال U تنانوس N هي كل ال odd
+
+83
+00:09:24,830 --> 00:09:30,690
+انتجار اللي جاب لل تنين N او تنانوس N اخدت اي عنصر
+
+84
+00:09:30,690 --> 00:09:34,770
+في هذه ال groupهيكون ال guess common divisor ايه
+
+85
+00:09:34,770 --> 00:09:39,050
+له مع 2 أُس N؟ ايش بيساوي؟ واحد حسب نظرية ايرلر
+
+86
+00:09:39,050 --> 00:09:44,210
+هتكون A أُس FI 2 أُس N congruent ل 1 مُد 2 أُس N
+
+87
+00:09:44,210 --> 00:09:50,050
+طيب FI 2 أُس N يعني A أُس 2 أُس N minus 1
+
+88
+00:09:50,050 --> 00:09:55,210
+congruent ل 1 مُد 2 أُس Nأفكار دي أنا ممكن أسترني
+
+89
+00:09:55,210 --> 00:10:00,870
+عنها لما أخد نظرية Error في chapter 7 أنه أنا باخش
+
+90
+00:10:00,870 --> 00:10:04,090
+أشتغل على عنصر في ال group فال order إيه اللي
+
+91
+00:10:04,090 --> 00:10:07,510
+بيقسم ال order لل group تنساش أن ال 2 أس N minus 1
+
+92
+00:10:07,510 --> 00:10:11,330
+هو order مين؟ اللي يوتي نين N فأنا ممكن لو أنا
+
+93
+00:10:11,330 --> 00:10:16,070
+أدرس نظرية 7 محتاجش نظرية ال Error theorem تبع
+
+94
+00:10:16,070 --> 00:10:21,730
+نظرية الأعداد طيب A أس 2 أس N minus 1كون ground ل
+
+95
+00:10:21,730 --> 00:10:29,140
+1 وين؟مد 2N أو 2 نص N يعني ال A أُس 2 نص N ماينس
+
+96
+00:10:29,140 --> 00:10:35,320
+واحد بيساوي واحد وين؟ في ال group U2N، لا تنساش أن
+
+97
+00:10:35,320 --> 00:10:39,520
+U2N هي عبارة عن الدرب، العملية اللي عليها هي الدرب
+
+98
+00:10:39,520 --> 00:10:45,360
+مد مين؟ 2 نص N طبعا A أُس 2 نص N ماينس واحد نقص
+
+99
+00:10:45,360 --> 00:10:50,570
+الواحد بيساوي صفر، حللهاهتسيب معايا a أُس 2 أُس n
+
+100
+00:10:50,570 --> 00:10:55,710
+-2 نقص الواحد في a أُس 2 أُس n-2 زاد الواحد فرق
+
+101
+00:10:55,710 --> 00:11:01,030
+بين المربعين طبعا هذي بتسوى صفر أو هذي بتسوى صفر
+
+102
+00:11:01,030 --> 00:11:06,010
+يعني a أُس 2 أُس n-2 بيساوي واحد او a أُس 2 أُس n
+
+103
+00:11:06,010 --> 00:11:10,940
+-2 بيساوي سالب واحد هذه المعلومة زي ما قلتحقيقية
+
+104
+00:11:10,940 --> 00:11:14,540
+لكن محتاجهاش لأن فعليا انا مابدأ اقول a اص 2 اص n
+
+105
+00:11:14,540 --> 00:11:19,860
+minus 2 بيساوي سالب واحد السالب واحد في 2 اص n او
+
+106
+00:11:19,860 --> 00:11:26,460
+في fight a few 2 اص n هي عبارة عن 2 اص n نقص
+
+107
+00:11:26,460 --> 00:11:32,460
+الواحد طبعا مش محتاجها انا كتيرأنا محتاج مين؟ أن
+
+108
+00:11:32,460 --> 00:11:37,540
+الـ A أُس 2 أُس N-2 يسوى 1 وبالتالي أُردر الـ A
+
+109
+00:11:37,540 --> 00:11:43,140
+أقل أو يسوى 2 أُس N-2 اللي هو أقل من 2 أُس N-1
+
+110
+00:11:43,140 --> 00:11:46,560
+اللي هو أُردر الـ U 2 N
+
+111
+00:11:50,840 --> 00:11:55,140
+أقل من order الـ U تنانوس N يجب أكيد الـ A لا يولد
+
+112
+00:11:55,140 --> 00:11:58,800
+هذه ال group مدام كل .. انت لا تنسى ان انا اخدت ال
+
+113
+00:11:58,800 --> 00:12:03,060
+A arbitrary لكل A في ال group كل عنصر في هذه ال
+
+114
+00:12:03,060 --> 00:12:06,600
+group ال order له لا يصل ل order ال group يجب لا
+
+115
+00:12:06,600 --> 00:12:11,840
+يولدها يجب ليست صحيك لك واضحة؟
+
+116
+00:12:25,190 --> 00:12:28,450
+هذه تانية نص واحد في تانية نص ن minus اتنين يعني
+
+117
+00:12:28,450 --> 00:12:31,050
+تانية نص ن minus اتنين زي اد واحد تانية نص ن minus
+
+118
+00:12:31,050 --> 00:12:31,510
+اتنين
+
+119
+00:12:38,610 --> 00:12:42,550
+هنا هاد المعلومة اللي هان ماروح نقول يا هذا بدي
+
+120
+00:12:42,550 --> 00:12:46,150
+يساوي صفر يا هذا بدي يساوي صفر هاد المعلومة هتقول
+
+121
+00:12:46,150 --> 00:12:49,370
+اتنين ا اثنين نص ان ماينوس واحد بدي أساوي واحد
+
+122
+00:12:49,370 --> 00:12:55,810
+موجودة لكن بحتاج رشد يعني أنا مستفدش منها اشي او
+
+123
+00:12:55,810 --> 00:12:59,390
+مش هي اللي هتعمللي الاشكالية او اللي انا بديها
+
+124
+00:12:59,390 --> 00:13:04,970
+عشان اثبت ان ال order ال ا لايساوي order واضح؟
+
+125
+00:13:06,980 --> 00:13:12,280
+واضح شباب؟ السؤال
+
+126
+00:13:12,280 --> 00:13:17,020
+اللي بعده السؤال تمانية .. تمانية و خمسين prove
+
+127
+00:13:17,020 --> 00:13:21,140
+that zn has an even number of generator if n أكبر
+
+128
+00:13:21,140 --> 00:13:26,740
+من اتنين what does this tell you about file n طيب
+
+129
+00:13:26,740 --> 00:13:34,560
+تمانية و خمسين لو ال n أكبر من اتنين فzn
+
+130
+00:13:59,150 --> 00:14:05,870
+FZN مولدة بإيه؟ والان أكبر من تنين دينبس هفيد شغلة
+
+131
+00:14:05,870 --> 00:14:11,810
+تانية شغلة الاولى ان زن مولدة ب a مولدة ب a
+
+132
+00:14:11,810 --> 00:14:15,830
+inverse شغلة
+
+133
+00:14:15,830 --> 00:14:19,590
+التانية ان
+
+134
+00:14:19,590 --> 00:14:25,650
+order ال a بديساوي n اكبر من 2 معناته a تغبيه لا
+
+135
+00:14:25,650 --> 00:14:30,900
+يساوي ال identity طب ال identity في zn الشوةالصفر
+
+136
+00:14:30,900 --> 00:14:37,540
+يعني A لا يساوي A inverse طبعا انت بتشغل في ZN فA
+
+137
+00:14:37,540 --> 00:14:43,600
+inverse مش بيساوي سالب A عشان العملية جامعة اذا A
+
+138
+00:14:43,600 --> 00:14:53,840
+لا يساوي سالب A ايش
+
+139
+00:14:53,840 --> 00:14:57,580
+يعني شباب يعني
+
+140
+00:14:57,580 --> 00:15:05,020
+ZNمولدة بعناصر ممكن انا اكتب علي شكل العنصر و
+
+141
+00:15:05,020 --> 00:15:17,360
+معكوسه هذا معناته The generators of Z and R A1
+
+142
+00:15:17,360 --> 00:15:28,630
+سالب A1 A2 سالب A2 لعند Aفايل ان على اتنين سالب ا
+
+143
+00:15:28,630 --> 00:15:35,390
+فايل ان على اتنين فايل
+
+144
+00:15:35,390 --> 00:15:45,770
+ان على اتنين فايل ان على اتنين فايل
+
+145
+00:15:45,770 --> 00:15:53,670
+ان على اتنين فايل ان على اتنين فايل ان على اتنين
+
+146
+00:15:53,670 --> 00:16:01,590
+فايل ان على اتنينfixed n has even number of
+
+147
+00:16:01,590 --> 00:16:15,530
+generators and file n نفسه is even هذه
+
+148
+00:16:15,530 --> 00:16:19,270
+نظرية موجودة برضه في نظرية الاعداد لكن اثباتها
+
+149
+00:16:19,270 --> 00:16:20,390
+بشكل مختلف
+
+150
+00:16:25,280 --> 00:16:29,540
+فايل ان على اتنين و سالب ا فايل ان على اتنين و
+
+151
+00:16:29,540 --> 00:16:32,540
+سالب ا فايل ان على اتنين فايل ان على اتنين عداد
+
+152
+00:16:32,540 --> 00:16:39,760
+يعني مش عامل يضرب الشغل من وين نهجر على اللومتين
+
+153
+00:16:39,760 --> 00:16:44,520
+نستفدتهم هن ال generator لزد ان لو ال a generator
+
+154
+00:16:44,520 --> 00:16:48,980
+فالسالب تبعه generator يعني انا بقدر اكتب ال
+
+155
+00:16:48,980 --> 00:16:54,240
+generators عبارة عن ثنائياتالـ A و سالب الـ A طبعا
+
+156
+00:16:54,240 --> 00:16:56,560
+الـ A واحد و سالب الـ A واحد الـ A تنين و سالب الـ
+
+157
+00:16:56,560 --> 00:17:00,340
+A تنين لأن آخر واحد هو السالب تبعه طبعا اللي خلاني
+
+158
+00:17:00,340 --> 00:17:05,080
+أقدر أكتب الكلام هذا أيضا ان ولا واحد بيساوي سالبه
+
+159
+00:17:05,080 --> 00:17:10,320
+يعني هدول مش مكررات هدول دستنقت عشان ماحدش يقولي
+
+160
+00:17:10,320 --> 00:17:15,160
+طب ما هدول ممكن تساوي لأ مابتساوش لو كان ال
+
+161
+00:17:15,160 --> 00:17:21,380
+generator لزد N فطبعا عشان ال N أكبر من 2فال a لا
+
+162
+00:17:21,380 --> 00:17:29,340
+يساوي سالب ال a طيب
+
+163
+00:17:29,340 --> 00:17:32,880
+سؤال
+
+164
+00:17:32,880 --> 00:17:39,020
+اللي بعده تسعة و خمسين لو
+
+165
+00:17:39,020 --> 00:17:42,540
+ال or لو ال or ضغط a أس خمسة بيسوا اتناشر
+
+166
+00:17:56,470 --> 00:18:02,370
+فعلا موجودين في تنائية 59
+
+167
+00:18:02,370 --> 00:18:08,010
+بيقول ال order ل a أُس 5 بيديه يساوي 12 ايش ال
+
+168
+00:18:08,010 --> 00:18:13,270
+possibilities ل order ال a مع ال order ل a أُس 5
+
+169
+00:18:13,270 --> 00:18:18,250
+بيديه يساوي 12 معناته a أُس 5 أُس 12 بيساوي ال
+
+170
+00:18:18,250 --> 00:18:25,800
+identityيعني اهو الستين بيساوي ال identity بيقسم
+
+171
+00:18:25,800 --> 00:18:34,420
+الستين بأردر ال a اش بيساوي واحد اتنين تلاتة اربعة
+
+172
+00:18:34,420 --> 00:18:44,300
+خمسة ستة لأ سبعة مفعش هي ستة عشرة اتناش خمستاش
+
+173
+00:18:44,300 --> 00:18:54,830
+تلاتين في اشعين و تلاتينو ستين هيك ما خلصناش هيك
+
+174
+00:18:54,830 --> 00:19:02,910
+ما خلصناش في بعض الحاجات هننفيها F لو
+
+175
+00:19:02,910 --> 00:19:08,710
+كان order ال A بساوي واحد معناته order ال A أس
+
+176
+00:19:08,710 --> 00:19:13,990
+خمسة بيساوي إيش؟ واحد لإن order ال A بيساوي واحد
+
+177
+00:19:13,990 --> 00:19:19,830
+معناته ال A هي ال identity طبعا هذا لأ هننفيهذا
+
+178
+00:19:19,830 --> 00:19:27,790
+ممنوع طيب لو order ال
+
+179
+00:19:27,790 --> 00:19:33,030
+a بدي ساوي اتنين معناته
+
+180
+00:19:33,030 --> 00:19:41,850
+a تربيه بدي ساوي ايش ال identity طيب
+
+181
+00:19:41,850 --> 00:19:46,770
+ايش يعني ال
+
+182
+00:19:46,770 --> 00:19:53,810
+order ال a بدي ساويال identity تنساش ان ال order ل
+
+183
+00:19:53,810 --> 00:19:58,170
+a أُس خمسة شو بدي ساوي اتناش هذا معناته ان a أُس
+
+184
+00:19:58,170 --> 00:20:03,430
+خمسة عبارة عن a تربيه تربيه في a اللي هو شو بدي
+
+185
+00:20:03,430 --> 00:20:10,190
+ساوي a اتناش اللي هو order ال a أُس خمسة اللي هو
+
+186
+00:20:10,190 --> 00:20:15,110
+order ال a اللي هو اتناش
+
+187
+00:20:15,110 --> 00:20:17,970
+اللي هو order ال a اللي هو order ال a اللي هو
+
+188
+00:20:17,970 --> 00:20:23,140
+اللي هو order الال A أُس خمسة عشان ال A تربيع بده
+
+189
+00:20:23,140 --> 00:20:26,900
+يساوي ال identity شيه ال A تربيع و كمان A تربيعاش
+
+190
+00:20:26,900 --> 00:20:32,360
+بده يظل ال A ف A أُس خمسة إيش بتساوي ال A هداش
+
+191
+00:20:32,360 --> 00:20:35,680
+معناته معناته ال 12 اللي هو order ال A أُس خمسة
+
+192
+00:20:35,680 --> 00:20:42,600
+إيش بده يساوي اتنين و هذا ممنوع هنتناقض و هنتناقض
+
+193
+00:20:42,600 --> 00:20:53,070
+اجبى التنين لأ طيب كمال؟لو أُردر ال A بدي يساوي
+
+194
+00:20:53,070 --> 00:21:01,210
+تلاتة معناته A تكييب بدي يساوي ال identity معناته
+
+195
+00:21:01,210 --> 00:21:11,770
+ال A والخمسة إبارة عن ال A تربيه طيب ال A بدي
+
+196
+00:21:11,770 --> 00:21:21,330
+يساوي ال A والستة قبل شويه بسمش هنخلص لأن هذا طويل
+
+197
+00:21:21,330 --> 00:21:27,350
+شوية السؤال قلت A أُس خمسة ايش بتتساوي A تربيع A
+
+198
+00:21:27,350 --> 00:21:36,910
+أُس خمسة بتتساوي A تربيع شوية
+
+199
+00:21:36,910 --> 00:21:40,270
+بس
+
+200
+00:21:40,270 --> 00:21:46,430
+معناته
+
+201
+00:21:46,430 --> 00:21:55,110
+اتناشبدي ساوي order الـ a و 5 بدي ساوي order ال a
+
+202
+00:21:55,110 --> 00:22:00,910
+تربيع معناته اتناش
+
+203
+00:22:00,910 --> 00:22:05,730
+بدي ساوي order ال
+
+204
+00:22:05,730 --> 00:22:14,510
+a تربيع طيب
+
+205
+00:22:14,510 --> 00:22:16,050
+في بنعمل شغل هنا
+
+206
+00:22:23,930 --> 00:22:33,110
+كيف الاربع و عشرين لا تقسم الستين شوية بس
+
+207
+00:22:33,110 --> 00:22:37,750
+ال
+
+208
+00:22:37,750 --> 00:22:44,550
+بقية اص أربع و عشرين ممكن يساوي ال identity but a
+
+209
+00:22:44,550 --> 00:22:51,270
+اص ستين ممكن يساوي ال identityهنصل في المحصلة ان a
+
+210
+00:22:51,270 --> 00:22:57,890
+أُس 12 دي ساو ال identity بطل
+
+211
+00:22:57,890 --> 00:23:10,950
+لأ هاد a أُس سالعة في النهاية هي اصلا
+
+212
+00:23:10,950 --> 00:23:13,410
+اقدر ال a دي ساو ال identity مقدرش اصل التناقض
+
+213
+00:23:13,410 --> 00:23:13,870
+مباشرة
+
+214
+00:23:27,570 --> 00:23:33,530
+طيب انا مش هعرف شوية و بعدين حصل حتى مش منطقى دلنا
+
+215
+00:23:33,530 --> 00:23:39,210
+اكمل بعد الاسلوب طب
+
+216
+00:23:39,210 --> 00:23:44,390
+خلينا نفكر باسلوب يعنى شوية بس assume خلينا نفكر
+
+217
+00:23:44,390 --> 00:23:50,690
+باسلوب يعنى ان order ال a بدي ساوي n اجبه order ال
+
+218
+00:23:50,690 --> 00:23:58,640
+a أُس خمسةبدي ساوي N على جريس common divisor لخمسة
+
+219
+00:23:58,640 --> 00:24:05,000
+و N إجبال 12 بدي ساوي N على جريس common divisor
+
+220
+00:24:05,000 --> 00:24:11,340
+لخمسة و N إجبال N بدي ساوي 12 في الجريس common
+
+221
+00:24:11,340 --> 00:24:18,240
+divisor لخمسة و N معناته 12 بدي اقسم order بدي
+
+222
+00:24:18,240 --> 00:24:22,610
+اقسم ال N اللي هو order ال Aما دام 12 بدي اقسم
+
+223
+00:24:22,610 --> 00:24:27,730
+order ال A هنلغي التلاتة هنلغي الأربعة هنلغي
+
+224
+00:24:27,730 --> 00:24:31,110
+الخمسة هنلغي الستة هنلغي العشرة هنلغي الخمس عشرة
+
+225
+00:24:31,110 --> 00:24:38,910
+هنلغي العشرين هنلغي التلاتين ايش هذا لأن دي يا 12
+
+226
+00:24:38,910 --> 00:24:49,190
+يا 60 وبالتالي اما order ال A بدي يسوا 12 او
+
+227
+00:24:50,870 --> 00:24:55,270
+وهو اخضر ال A و D ساعة و ستة و متانية ده افضل ليه
+
+228
+00:24:55,270 --> 00:24:59,710
+من ان انا اقعد امسك واحد واحد و اصل لتناقضات فهذا
+
+229
+00:24:59,710 --> 00:25:04,930
+الحل اسهل من الحل الاول يعنى فاضح؟
+
+230
+00:25:04,930 --> 00:25:13,960
+والله بتدعي عادة تبدينا باسلوب1,2,3,4,5,6,7,8,9,10
+
+231
+00:25:13,960 --> 00:25:18,060
+,11,12 كان مطلوب مني أروح أفحص 12 احتمال و أدلغي
+
+232
+00:25:18,060 --> 00:25:21,440
+لغتي الأول لغتي التانية جيت أدلغي التالت ماعرفتش
+
+233
+00:25:21,440 --> 00:25:25,980
+أكمل فجيت فكرت بسلوب جديد أنه لو كان ال order لل A
+
+234
+00:25:25,980 --> 00:25:30,860
+بدي ساوي N ف order ال A أُس 5 بدي ساوي N على الجيس
+
+235
+00:25:30,860 --> 00:25:35,500
+common divisor ل 5 و N طبعا هذا 12 إيش بـ 12 في
+
+236
+00:25:35,500 --> 00:25:42,280
+الجيس common divisor ل 5 و N بدي ساوي إيشيقبل 12
+
+237
+00:25:42,280 --> 00:25:47,020
+بيقسم ال N بس انساش ان ال N واحد من ال 12 الخيار
+
+238
+00:25:47,020 --> 00:25:55,520
+هدول شطب كل ال 12 بيقسمهمش، مين هيضل؟ ال 12 او ال
+
+239
+00:25:55,520 --> 00:25:59,840
+60، يقبل order ال ايه؟ يا 12 يا 60
+
+240
+00:26:10,220 --> 00:26:15,780
+سؤال 64 لأ
+
+241
+00:26:15,780 --> 00:26:21,180
+حلته انت ممكن هذا تلغي يعني هذا ممكن ماتحتاجوش
+
+242
+00:26:21,180 --> 00:26:24,800
+خلاص
+
+243
+00:26:24,800 --> 00:26:28,880
+يا 12 يا 60 تقدر تحدد بالظبط لأ لو انت بتشتغل في
+
+244
+00:26:28,880 --> 00:26:36,620
+Z12 فال order 12 مثلا في Z12اللي هو الـ A 5 عبارة
+
+245
+00:26:36,620 --> 00:26:40,220
+عن خمسة ال order لها 12 و ال order ل ال A 12 في Z
+
+246
+00:26:40,220 --> 00:26:48,940
+60 ال order ل ال A 60 لكن ال order ل الخمسة 12 طيب
+
+247
+00:26:48,940 --> 00:26:55,100
+السؤال 64 ال
+
+248
+00:26:55,100 --> 00:27:06,080
+H عبارة عن واحد and Zero واحد حيث انمطلوب اثبت
+
+249
+00:27:06,080 --> 00:27:11,440
+انها Cyclic subgroup of GL2R طبعا عشان ما انا اجعش
+
+250
+00:27:11,440 --> 00:27:15,600
+في اشكالية و بجهود اثبت انها subgroup و بعدين ادور
+
+251
+00:27:15,600 --> 00:27:19,620
+لها generator ممكن مباشرة اثبت انها generated by
+
+252
+00:27:19,620 --> 00:27:22,720
+some element و بعدين ماداما generated by some
+
+253
+00:27:22,720 --> 00:27:27,920
+element من GL2R بتكون مباشرة هي subgroup انا هقولك
+
+254
+00:27:27,920 --> 00:27:28,380
+اكلام
+
+255
+00:27:31,440 --> 00:27:41,160
+الـ H generated by 1101 تعالي
+
+256
+00:27:41,160 --> 00:27:49,700
+نتبت لت
+
+257
+00:27:49,700 --> 00:27:58,620
+A ينتمي لـ H هذا معناته الـ A بدأ تساوي 1101
+
+258
+00:27:58,620 --> 00:28:08,050
+و الـ N من أين؟ من ال 6بدي أثبت إنه ال A عبارة عن
+
+259
+00:28:08,050 --> 00:28:12,110
+power فن
+
+260
+00:28:12,110 --> 00:28:22,110
+بيبقى تساوي 0 معناته ال A بيبقى تساوي 1001
+
+261
+00:28:22,110 --> 00:28:27,050
+عبارة عن 1101
+
+262
+00:28:27,050 --> 00:28:34,100
+أُس 0أو انا خدنا في الجابر الخاطئ ان اي مصفوفة أُس
+
+263
+00:28:34,100 --> 00:28:44,680
+زي روش بيعضيناها ال identity if
+
+264
+00:28:44,680 --> 00:28:50,400
+n أكبر من الصفر ال n ينتمي لمين ده ال initial
+
+265
+00:28:50,400 --> 00:28:57,040
+number we will use mathematical
+
+266
+00:28:57,040 --> 00:29:00,300
+induction for
+
+267
+00:29:01,850 --> 00:29:08,170
+أن بيسوي واحد واحد واحد واحد واحد اللي هي واحد
+
+268
+00:29:08,170 --> 00:29:17,170
+عبارة عن واحد واحد واحد واحد اص واحد assume for
+
+269
+00:29:17,170 --> 00:29:25,950
+أن بيسوي ك ذات واحد كزيرو كزيرو واحد عبارة عن واحد
+
+270
+00:29:25,950 --> 00:29:30,370
+واحد واحد واحد اص ك then
+
+271
+00:29:32,820 --> 00:29:40,660
+ورقان بيساوي كزاد الواحد واحد واحد زير واحد قص
+
+272
+00:29:40,660 --> 00:29:46,900
+كزاد الواحد عبارة عن واحد واحد زير واحد قص ك في
+
+273
+00:29:46,900 --> 00:29:52,140
+واحد واحد زير واحد حسب المعطل عندي هذا معناه واحد
+
+274
+00:29:52,140 --> 00:30:00,280
+كزير واحد في واحد واحد زير واحد اضرب واحد في واحد
+
+275
+00:30:00,280 --> 00:30:05,160
+واحد ك في صفر صفر واحد1 في 1 و 1 و K في 1 و K و 1
+
+276
+00:30:05,160 --> 00:30:13,120
+و K و K زاد ال 1 و هو المطلوب طبعا المطلوب في ال
+
+277
+00:30:13,120 --> 00:30:18,880
+induction يعني
+
+278
+00:30:18,880 --> 00:30:26,000
+ان موجب
+
+279
+00:30:28,000 --> 00:30:34,140
+1 and 01 عبارة عن واحد واحد زي رو واحد اشف ضال
+
+280
+00:30:34,140 --> 00:30:38,020
+عندي ده
+
+281
+00:30:38,020 --> 00:30:47,120
+السالب four and اقل من الصفر ده داش معناته معناته
+
+282
+00:30:47,120 --> 00:30:54,460
+سالب and موجب معناته
+
+283
+00:30:54,460 --> 00:30:57,000
+سالب and موجب طيب
+
+284
+00:30:58,540 --> 00:31:06,580
+واحد واحد واحد واحد والسالب n هكون واحد سالب n زير
+
+285
+00:31:06,580 --> 00:31:12,220
+واحد حسب
+
+286
+00:31:12,220 --> 00:31:21,760
+مين؟ by part n أكبر من zero طبعا مابديش واحد سالب
+
+287
+00:31:21,760 --> 00:31:29,580
+n زير واحد بدي واحد n زير واحد إيش هنعمل؟اخد
+
+288
+00:31:29,580 --> 00:31:34,940
+inverse الطرفين يا شباب هذا معناته واحد واحد zero
+
+289
+00:31:34,940 --> 00:31:43,960
+واحد inverse أس N عبارة عن واحد سالب N zero واحد
+
+290
+00:31:43,960 --> 00:31:52,700
+أنا بشتغل جبر خطي هنا بس أغير هدول عشان ما نخبطش
+
+291
+00:31:52,700 --> 00:31:59,340
+في الجبر الخطي الأس و ال inverse شبهلهمببدله هذا
+
+292
+00:31:59,340 --> 00:32:08,720
+عيسى معايا 1101 أس أن انفرس بدي ساوي 1 سالم ان 01
+
+293
+00:32:08,720 --> 00:32:20,600
+معناته 1101 أس أن بدي ساوي هذا انفرس احسب الانفرس
+
+294
+00:32:20,600 --> 00:32:26,680
+بعد ما تحسبه بالجبر الخطي هيعطيك 1101
+
+295
+00:32:28,820 --> 00:32:36,380
+هذا معناته في كل الأحوال اي عبارة عن 1 n 0 1 اللي
+
+296
+00:32:36,380 --> 00:32:52,460
+عبارة عن 1 1 0 1 plus n المحصرة النهائية ان ال
+
+297
+00:32:52,460 --> 00:32:55,220
+H generated by
+
+298
+00:33:00,530 --> 00:33:03,710
+طب انا مفترض في جزء تاني يا شباب انه هذا subset
+
+299
+00:33:03,710 --> 00:33:07,350
+انه هذا هيخليني اقول ان ال H subset من هذا و بعدين
+
+300
+00:33:07,350 --> 00:33:12,090
+اقول ان هذا subset من ال H بس مادام 1101 موجود في
+
+301
+00:33:12,090 --> 00:33:17,230
+ال H فأكيد ال generated من هذا الأنصار subset من
+
+302
+00:33:17,230 --> 00:33:25,030
+ال H وبتالي صارت ال H اشمالها Cyclic Subject واضح؟
+
+303
+00:33:25,030 --> 00:33:31,340
+واضح يا شباب؟دكتور كيف المصيبة من الوسكي صارت
+
+304
+00:33:31,340 --> 00:33:39,020
+مصيبة هذه؟ كيف انفكت هيك؟ حسب القاعدة هذه عشان
+
+305
+00:33:39,020 --> 00:33:54,120
+أقولك أسيوم أنه هذي بيساوي هذي 65
+
+306
+00:33:54,120 --> 00:33:58,040
+و آخر سؤال معانا أفندم كيف انفكت إلى إيه؟ مصيبة
+
+307
+00:33:58,040 --> 00:34:05,900
+تانيةكيف؟ هطيين ال generator تاني هذه sub group
+
+308
+00:34:05,900 --> 00:34:10,880
+infinite infinite sub group كم generator لها؟ تنين
+
+309
+00:34:10,880 --> 00:34:17,940
+واحد واحد صفر واحد واحد سالب واحد صفر واحد 65
+
+310
+00:34:23,610 --> 00:34:27,510
+الـ order للـ A بدي يساوي 12 ال order لل B بدي
+
+311
+00:34:27,510 --> 00:34:34,250
+يساوي 22 و generated by ال A فقاطع generated by ال
+
+312
+00:34:34,250 --> 00:34:42,590
+B لا يساوي ال identity أثبت أن A أُس 6 بدي يساوي A
+
+313
+00:34:42,590 --> 00:34:43,350
+أُس 11
+
+314
+00:35:11,660 --> 00:35:17,560
+عشرة يعني a-12 يساوي ال identity و b-22 يساوي ال
+
+315
+00:35:17,560 --> 00:35:23,440
+identity a-12 يساوي b-22 يساوي ال identity a-12
+
+316
+00:35:23,440 --> 00:35:25,640
+يساوي b-22 يساوي ال identity a-12 يساوي b-22 يساوي
+
+317
+00:35:25,640 --> 00:35:29,780
+ال identity a-12 يساوي b-22 يساوي ال identity a-12
+
+318
+00:35:29,780 --> 00:35:31,520
+يساوي b-22 يساوي ال identity a-12 يساوي b-22 يساوي
+
+319
+00:35:31,520 --> 00:35:31,940
+ال identity a-12 يساوي b-22 يساوي b-22 يساوي b-22
+
+320
+00:35:31,940 --> 00:35:32,220
+يساوي b-22 يساوي b-22 يساوي b-22 يساوي b-22 يساوي
+
+321
+00:35:35,610 --> 00:35:40,410
+معناته في أنصر مشترك ال X في generated by A وال X
+
+322
+00:35:40,410 --> 00:35:45,150
+في generated by B مدام هو في generated by A يكبر
+
+323
+00:35:45,150 --> 00:35:49,390
+ال order اله بيقسم order ال A بيساوي 12 ف order ال
+
+324
+00:35:49,390 --> 00:35:56,530
+X بيقسم 12 و بيقسم أيضا ال 22 يكبر X قص 12 بيساوي
+
+325
+00:35:56,530 --> 00:35:57,010
+X
+
+326
+00:35:59,930 --> 00:36:03,750
+أو ال order له بيقسم ال 12 و بيقسم ال 22 ف order
+
+327
+00:36:03,750 --> 00:36:08,510
+ال x بيقسم لجريس common divisor لل 12 و 22 ايش
+
+328
+00:36:08,510 --> 00:36:14,190
+يعني؟ يعني x تربيع او x هيقسم لجريس common divisor
+
+329
+00:36:14,190 --> 00:36:19,350
+لل 22 كده؟ اتنين، معناته يا اما ال x بيسوي ال
+
+330
+00:36:19,350 --> 00:36:25,830
+identity يا اما ال order لل x مش بيسويإتنين طيب
+
+331
+00:36:25,830 --> 00:36:29,230
+انسى ال identity خد x ال order اللي هو بيساوي
+
+332
+00:36:29,230 --> 00:36:36,710
+اتنين ايش يعني ال
+
+333
+00:36:36,710 --> 00:36:42,830
+order ال x بيساوي اتنين ايش يعني
+
+334
+00:36:42,830 --> 00:36:46,930
+مين
+
+335
+00:36:46,930 --> 00:36:51,270
+هو العنصر اللي ال order له اتنين في generated by a
+
+336
+00:36:54,370 --> 00:37:00,030
+هو الـ A أُس 6 من العنصر اللي الـ O ضر إله 2 في B
+
+337
+00:37:00,030 --> 00:37:04,530
+أُس 2 في generated by الـ B B أُس 11 يجب الإكس هو
+
+338
+00:37:04,530 --> 00:37:09,470
+نفسه الـ A أُس 6 هو نفسه الـ B أُس 11 هذا هو الحل
+
+339
+00:37:09,470 --> 00:37:15,910
+let X لا يساوي ال identity and X ينتمي لgenerated
+
+340
+00:37:15,910 --> 00:37:21,820
+by A تقاطع generated by B معناته ال Xينتمي
+
+341
+00:37:21,820 --> 00:37:26,160
+لgenerated by a and ال x ينتمي لgenerated by b
+
+342
+00:37:26,160 --> 00:37:31,640
+معناته order ال x بيقسم order ال a and order ال x
+
+343
+00:37:31,640 --> 00:37:36,280
+بيقسم order ال b معناته order ال x بيقسم لgreased
+
+344
+00:37:36,280 --> 00:37:42,520
+common divisor ل order ال a order ال b order ال x
+
+345
+00:37:42,520 --> 00:37:47,400
+بيقسم لgreased common divisor ل 12 و 22 و 9 و 2
+
+346
+00:37:48,370 --> 00:37:55,570
+order of x هو اتنين but يقسم الاتنين ال x لا يساوي
+
+347
+00:37:55,570 --> 00:38:05,390
+ال identity order of x هو اتنين ال
+
+348
+00:38:05,390 --> 00:38:10,170
+element of
+
+349
+00:38:10,170 --> 00:38:19,350
+order اتنين generated by a هو a6أو بلاش اقول the
+
+350
+00:38:19,350 --> 00:38:25,550
+element كمان the only element فش في a أُس
+
+351
+00:38:25,550 --> 00:38:28,950
+generated by ال a اللي هي ال order إلها اتناش غير
+
+352
+00:38:28,950 --> 00:38:32,510
+عنصر واحد ال order إله اتنين ليش أنا بشغل في
+
+353
+00:38:32,510 --> 00:38:36,230
+cyclic group أكم عنصر ال order إله اتنين في ال
+
+354
+00:38:36,230 --> 00:38:42,310
+cyclic group فيه اتنين فيه اتنين جديش واحد أنا
+
+355
+00:38:42,310 --> 00:38:43,470
+بشغل في finite يا حبيبي
+
+356
+00:38:48,860 --> 00:38:51,280
+القاعدة الـ Phi للـ finite أصلا مش لل Infinite
+
+357
+00:38:51,280 --> 00:38:55,160
+قاعدة
+
+358
+00:38:55,160 --> 00:39:02,160
+ال Phi للـ finite مش لل Infinite واضحة؟
+
+359
+00:39:02,160 --> 00:39:07,300
+الوحدة الوحيدة
+
+360
+00:39:07,300 --> 00:39:08,120
+الوحيدة الوحيدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+361
+00:39:08,120 --> 00:39:08,920
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+362
+00:39:13,980 --> 00:39:19,440
+P أُس 11 يكبر X هي نفس ال P أُس 11 و هي نفس ال A
+
+363
+00:39:19,440 --> 00:39:26,600
+أُس 6 يكبر A أُس 6 بيساوي P أُس 11 و هي كده end of
+
+364
+00:39:26,600 --> 00:39:37,540
+chapter 4 واضح؟
+
+365
+00:39:37,540 --> 00:39:42,490
+و بالنهاية ضيعنا المحاضرة في خمس أسئلةكان مفترض
+
+366
+00:39:42,490 --> 00:39:49,610
+اننا ندخل في الشبتر الخامس ال generator لل a بسوة
+
+367
+00:39:49,610 --> 00:39:53,890
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+368
+00:39:53,890 --> 00:39:54,710
+ال generator لل a بسوة وستة a والستة ال generator
+
+369
+00:39:54,710 --> 00:39:56,310
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+370
+00:39:56,310 --> 00:39:59,310
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+371
+00:39:59,310 --> 00:39:59,390
+ال generator لل a بسوة وستة a والستة ال generator
+
+372
+00:39:59,390 --> 00:39:59,410
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+373
+00:39:59,410 --> 00:39:59,950
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+374
+00:39:59,950 --> 00:40:00,530
+ال generator لل a بسوة وستة a والستة ال generator
+
+375
+00:40:00,530 --> 00:40:04,850
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+376
+00:40:04,850 --> 00:40:11,610
+وستة a والستة ال generator لل a بسوة وست12 هدى الـ
+
+377
+00:40:11,610 --> 00:40:17,870
+Cyclic group التنين تقسم ال order لل A يكبر يوجد
+
+378
+00:40:17,870 --> 00:40:22,170
+عناصر داخل ال generated by A ال order لتنين جدش
+
+379
+00:40:22,170 --> 00:40:29,870
+عددهم؟ five تنين يكبر يوجد عنصر واحد مين هو؟ ال A
+
+380
+00:40:29,870 --> 00:40:34,470
+و ال 6 نفس الفكرة هنا في generated by B ال order
+
+381
+00:40:34,470 --> 00:40:40,710
+لل B بيساوي 22تنين بيخسم 22 فيوجد عناصر ال order
+
+382
+00:40:40,710 --> 00:40:44,910
+اللي هتنين في generated by P عدد ده بيساوي five
+
+383
+00:40:44,910 --> 00:40:48,250
+تنين بيساوي واحد ماقلتلك هال the only the only
+
+384
+00:40:48,250 --> 00:40:51,730
+element واضحة
+
+385
+00:40:51,730 --> 00:40:57,650
+وخاضرة اللي هناخدها او الكان المفترض انه نبدأ فيها
+
+386
+00:40:57,650 --> 00:41:05,110
+اليوم هو chapter خمسة اللي
+
+387
+00:41:05,110 --> 00:41:05,930
+هو permutation
+
+388
+00:41:09,230 --> 00:41:14,530
+الـ groups او
+
+389
+00:41:14,530 --> 00:41:19,530
+الزمر
+
+390
+00:41:19,530 --> 00:41:31,790
+.. الزمر ايش؟ تبادلية .. تبدلية لأ مش يعني
+
+391
+00:41:31,790 --> 00:41:38,050
+permutation زمر التبادل زمر
+
+392
+00:41:39,560 --> 00:41:45,200
+طبعا الفكرة كانت تالية يا شباب عشان نكون جاهزين
+
+393
+00:41:45,200 --> 00:41:51,760
+للمحاضرة الجاية انا بستعمل group G و بعرف عليها
+
+394
+00:41:51,760 --> 00:41:57,920
+عمليات هتلاحظ ان معظم العمليات اللي عرفناها في
+
+395
+00:41:57,920 --> 00:42:05,390
+الشباتر اللي فاتت لو بتعامل مع groupsمش مجرد يعني
+
+396
+00:42:05,390 --> 00:42:09,410
+عناصرها محسوسة بتقدر تتعامل معاها زي ال Z زي ال R
+
+397
+00:42:09,410 --> 00:42:12,290
+زي ال N زي ال matrices زي ال polynomial الاخرين
+
+398
+00:42:12,290 --> 00:42:17,370
+كانت معظم العمليات تركز على الجمع العادي الجمع
+
+399
+00:42:17,370 --> 00:42:21,590
+التقليدي أو الدرب التقليدي حتى لو كان في الجمع و
+
+400
+00:42:21,590 --> 00:42:27,290
+الدرب مد N معين او درب او جمع matrices انه في
+
+401
+00:42:27,290 --> 00:42:32,080
+النهاية هيرجع للجمع العادي و الدرب العاديإذا بتذكر
+
+402
+00:42:32,080 --> 00:42:40,200
+أخدنا groups كان فيها functions مع
+
+403
+00:42:40,200 --> 00:42:43,980
+الجامعة مع
+
+404
+00:42:43,980 --> 00:42:47,520
+ال multiplication فيه إشكالية لل group لإنه انا
+
+405
+00:42:47,520 --> 00:42:52,480
+بدي اشتغل على واحد على F لما اتعامل مع واحد على F
+
+406
+00:42:52,480 --> 00:42:57,080
+لازم ال F ما تكونش Zero ببدي انا انا بدي اخد ال
+
+407
+00:42:57,080 --> 00:43:02,730
+non-zero functions بقدر أعرفطيب بتجمعوا الضرب جدًا
+
+408
+00:43:02,730 --> 00:43:08,870
+تحلوا مشكلتهم لو أنا بدي أعرف groups group مثلا هي
+
+409
+00:43:08,870 --> 00:43:16,190
+X و بدي أشغل على function من X جولة نفسها و تكون
+
+410
+00:43:16,190 --> 00:43:22,030
+عناصرها دي هو ال group بس
+
+411
+00:43:22,030 --> 00:43:28,790
+بدي أشغل على عملية ال composition Circle Jماذا
+
+412
+00:43:28,790 --> 00:43:33,750
+لازم الشروط اللي انا اشتغل فيها هنا؟ ماتنساش انا
+
+413
+00:43:33,750 --> 00:43:38,730
+بده اعمل معاشر مع associative ال composition
+
+414
+00:43:38,730 --> 00:43:43,510
+associative بتعامل مع وجود identity فيه بقدر الاقي
+
+415
+00:43:43,510 --> 00:43:45,730
+identity مع ال composition هو ال identity function
+
+416
+00:43:45,730 --> 00:43:52,570
+انا بشتغل من المجموعة لنفسها بظل closed و ال
+
+417
+00:43:52,570 --> 00:43:56,570
+composition لو انا بشتغل من X ل Xوبدأ اجيب كمان
+
+418
+00:43:56,570 --> 00:44:02,110
+function من X ل X اللي closed موجود بظالمين شرط ال
+
+419
+00:44:02,110 --> 00:44:07,790
+inverse انا مش inverse طرح ولا inverse ضرب اني
+
+420
+00:44:07,790 --> 00:44:10,270
+اقول سالب ال function او واحد على ال function لأ
+
+421
+00:44:10,270 --> 00:44:13,730
+inverse composition وبالتالي بدأش انا مع أف
+
+422
+00:44:13,730 --> 00:44:21,530
+inverse من X ل Xعشان اقدر نعرف ال F inverse لازم
+
+423
+00:44:21,530 --> 00:44:25,870
+ال F نفسه اش تكون one to one ايه بقى لازم
+
+424
+00:44:25,870 --> 00:44:30,470
+الاقترابات اللي باخدها اش تكون مش بس one to one ال
+
+425
+00:44:30,470 --> 00:44:35,770
+inverse بدي يكون function من المجموع على نفسها بدي
+
+426
+00:44:35,770 --> 00:44:41,890
+تكون برضه on to فلازم تكون ال function ايه شمالها؟
+
+427
+00:44:41,890 --> 00:44:44,150
+one to one correspondence يعني πي جيكشن
+
+428
+00:44:46,980 --> 00:44:51,200
+بيجيكشن على الـ finite يكفي نشرط واحد عشان اوجده
+
+429
+00:44:51,200 --> 00:44:56,200
+وبتالي هكتفي بال one to one عشان احش على finite
+
+430
+00:44:56,200 --> 00:44:59,540
+set ال X تكون finite هذه هسميها permutation
+
+431
+00:44:59,540 --> 00:45:02,440
+هناخدها في المخادرة التانية ان شاء الله يعطيكوا
+
+432
+00:45:02,440 --> 00:45:02,760
+العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..cc55151791f6f112c2b37c4c4dde1859546fae41
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.json
@@ -0,0 +1 @@
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"text": "بدي ساوي N على جريس common divisor لخمسة و N إجبال 12 بدي ساوي N على جريس common divisor لخمسة و N إجبال N بدي ساوي 12 في الجريس common divisor لخمسة و N معناته 12 بدي اقسم order بدي اقسم ال N اللي هو order ال A", "tokens": [3555, 16254, 8608, 995, 45865, 426, 15844, 10874, 16572, 3794, 2689, 25974, 284, 5296, 9778, 2304, 3794, 3660, 4032, 426, 11933, 7435, 3555, 6027, 2272, 4724, 16254, 8608, 995, 45865, 426, 15844, 10874, 16572, 3794, 2689, 25974, 284, 5296, 9778, 2304, 3794, 3660, 4032, 426, 11933, 7435, 3555, 6027, 426, 4724, 16254, 8608, 995, 45865, 2272, 8978, 25724, 16572, 3794, 2689, 25974, 284, 5296, 9778, 2304, 3794, 3660, 4032, 426, 20449, 8315, 47395, 2272, 4724, 16254, 1975, 4587, 38251, 1668, 4724, 16254, 1975, 4587, 38251, 2423, 426, 13672, 1829, 31439, 1668, 2423, 316], "avg_logprob": -0.2029587746934688, "compression_ratio": 2.1818181818181817, "no_speech_prob": 0.0, "words": [{"start": 1433.48, "end": 1433.84, "word": "بدي", "probability": 0.450897216796875}, 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"probability": 0.81982421875}, {"start": 2696.2, "end": 2696.54, "word": " set", "probability": 0.962890625}, {"start": 2696.54, "end": 2696.92, "word": " ال", "probability": 0.75927734375}, {"start": 2696.92, "end": 2697.08, "word": " X", "probability": 0.60693359375}, {"start": 2697.08, "end": 2697.34, "word": " تكون", "probability": 0.971435546875}, {"start": 2697.34, "end": 2697.76, "word": " finite", "probability": 0.97705078125}, {"start": 2697.76, "end": 2698.54, "word": " هذه", "probability": 0.259765625}, {"start": 2698.54, "end": 2698.94, "word": " هسميها", "probability": 0.9107666015625}, {"start": 2698.94, "end": 2699.54, "word": " permutation", "probability": 0.978759765625}, {"start": 2699.54, "end": 2700.44, "word": " هناخدها", "probability": 0.80771484375}, {"start": 2700.44, "end": 2700.54, "word": " في", "probability": 0.93115234375}, {"start": 2700.54, "end": 2701.04, "word": " المخادرة", "probability": 0.8287353515625}, {"start": 2701.04, "end": 2701.56, "word": " التانية", "probability": 0.9791666666666666}, {"start": 2701.56, "end": 2701.68, "word": " ان", "probability": 0.8134765625}, {"start": 2701.68, "end": 2701.86, "word": " شاء", "probability": 0.946533203125}, {"start": 2701.86, "end": 2701.96, "word": " الله", "probability": 0.95654296875}, {"start": 2701.96, "end": 2702.44, "word": " يعطيكوا", "probability": 0.8556640625}, {"start": 2702.44, "end": 2702.76, "word": " العافية", "probability": 0.6619466145833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2704.196, "duration_after_vad": 2507.0331249999913}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2ec6ee9b80a16e4a49c80815c451527d8b465d99
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/hBlmUqqCXws_raw.srt
@@ -0,0 +1,1768 @@
+1
+00:00:21,350 --> 00:00:26,170
+السلام عليكم اسمي الله أحمد محليم هنعرج على ال ..
+
+2
+00:00:26,170 --> 00:00:29,010
+هنكمل ان شاء الله اليوم في خمس أسئلة تبقتنا من ال
+
+3
+00:00:29,010 --> 00:00:35,290
+chapter الأخير الشخصية ال 56, 58, 59, 64 و 65 كم
+
+4
+00:00:35,290 --> 00:00:39,410
+هنحلهم مش كلهم بس نعرج على أفكار لحل الأسئلة بعدين
+
+5
+00:00:39,410 --> 00:00:41,350
+هنفوت في ال chapter الخامس اللي هو chapter
+
+6
+00:00:41,350 --> 00:00:46,100
+permutation in groups بالنسبة لسؤال 56مرة الماضية
+
+7
+00:00:46,100 --> 00:00:50,240
+انتهينا فيه وماكملنهوش السؤال ستة و خمسين بيقول
+
+8
+00:00:50,240 --> 00:00:58,360
+اثبت ان U تنين N is not cyclic طيب، بالنسبة لعناصر
+
+9
+00:00:58,360 --> 00:01:06,180
+ال U تنين N هي عبارة عن كل .. كل إيش؟ العناصر اللي
+
+10
+00:01:06,180 --> 00:01:09,720
+بتكون relative لبعض مع تنين N مين هي؟ هي كل الأد
+
+11
+00:01:11,500 --> 00:01:14,740
+انت جارز اللي ما بين الواحد والتنين ان كيف بتثبت
+
+12
+00:01:14,740 --> 00:01:18,860
+انها مش cyclic عشان
+
+13
+00:01:18,860 --> 00:01:22,540
+تكون not cyclic معناته انا بتثبت ان لكل a ينتمي ل
+
+14
+00:01:22,540 --> 00:01:30,360
+u تنين ان a ال order لل a أقل من تنين ان تنين نفسي
+
+15
+00:01:30,360 --> 00:01:33,520
+صح؟
+
+16
+00:01:33,520 --> 00:01:36,340
+لأ أقل من في تنين ان
+
+17
+00:01:39,850 --> 00:01:49,310
+لأن ال order ل U2N عبارة عن فاية تنين N جداش فاية
+
+18
+00:01:49,310 --> 00:01:58,110
+تنين N هي تنين plus N minus واحد طبعا أنا بشغل N
+
+19
+00:01:58,110 --> 00:02:08,890
+أكبر أو يساوي تلاتة فانا شغال بدء من U8 U16 U32
+
+20
+00:02:08,890 --> 00:02:15,190
+إلى خارجطيب عشان برضه نذكر ال U تنين N عبارة عن
+
+21
+00:02:15,190 --> 00:02:24,170
+واحد تلاتة خمسة سبعة لان تنينوس N ماينس واحد كيف
+
+22
+00:02:24,170 --> 00:02:30,230
+بتثبت ان هذا ال group not cyclic؟زي ما قلتلك فوق،
+
+23
+00:02:30,230 --> 00:02:35,990
+لازم أثبت أنه أقدر أي عنصر أقل من 2 أُس N لو أنا
+
+24
+00:02:35,990 --> 00:02:40,330
+أخدت ال A، ينتمي ل U2N، معناته ال degrees common
+
+25
+00:02:40,330 --> 00:02:48,210
+divisor ل A و 2N، إيش بتتساوي؟ واحد، هذا معناته أن
+
+26
+00:02:48,210 --> 00:02:55,150
+ال degrees common divisor ل A و 2، إيش مالها؟
+
+27
+00:02:55,150 --> 00:02:58,070
+واحد، إيش يعني؟
+
+28
+00:03:03,050 --> 00:03:09,730
+ماذا يعني اجريز common divisor ل a و 2 و دي ساوي
+
+29
+00:03:09,730 --> 00:03:16,050
+واحد انا
+
+30
+00:03:16,050 --> 00:03:22,290
+في ال number 3 غيش بقول دي انه تنين و صفاي ال a
+
+31
+00:03:22,290 --> 00:03:26,410
+congruent ل واحد مدمين
+
+32
+00:03:32,430 --> 00:03:38,910
+أو congruent ل واحد mod a في
+
+33
+00:03:38,910 --> 00:03:42,810
+نظرية احنا اخدنا اسمها نظرية firmات في لتعميم
+
+34
+00:03:42,810 --> 00:03:47,290
+اسمها Euler theorem ايش نظرية firmات بتقول الاجيز
+
+35
+00:03:47,290 --> 00:03:52,650
+common divisor ل a و b ساو واحد ف a أسفل p minus
+
+36
+00:03:52,650 --> 00:04:00,450
+واحد congruent ل واحد mod mod مين mod a مش عارف
+
+37
+00:04:00,450 --> 00:04:01,910
+ايه البلسيتها دي ايه و الله ان
+
+38
+00:04:04,990 --> 00:04:11,790
+يجي بس أتأكد Mod
+
+39
+00:04:11,790 --> 00:04:17,510
+P طيب
+
+40
+00:04:17,510 --> 00:04:21,630
+فانا لما بدي أجي أشغل هانت نينوس التعميم تبعها
+
+41
+00:04:21,630 --> 00:04:26,210
+اللي هي ال Euler theorem لو اتطلعت على شبتر سبعة
+
+42
+00:04:26,210 --> 00:04:30,430
+في نظرية الأعداد اللي أخد أو ما أخد عبارة عن النص
+
+43
+00:04:30,430 --> 00:04:31,050
+التالي
+
+44
+00:04:37,660 --> 00:04:48,420
+اللي هي a أصفاء الان congment لواحد مد
+
+45
+00:04:48,420 --> 00:04:54,540
+ان لأ هو أنا مش محتاج هذي
+
+46
+00:04:54,540 --> 00:04:57,820
+طيب
+
+47
+00:04:57,820 --> 00:05:09,440
+هذا معناته هبدل ان a أصفاء الاتنين انconjuant ل 1
+
+48
+00:05:09,440 --> 00:05:27,440
+mod 2n ايش يعني a2n-1 conjuant ل 1 mod 2n يعني a2n
+
+49
+00:05:27,440 --> 00:05:33,500
+-1 بتساوي 1 on u2n
+
+50
+00:05:34,340 --> 00:05:40,160
+يعني a أس تنين أس n مينوس واحد نقص الواحد بيسوي
+
+51
+00:05:40,160 --> 00:05:53,080
+واحد on او نقص الواحد بيسوي zero on u تنين n طيب
+
+52
+00:05:53,080 --> 00:05:58,320
+تقدر تحلل؟
+
+53
+00:05:58,320 --> 00:06:07,890
+تقدر تحلل؟ هذا يا حبيبي العدد زوجيمعناته 2 a أُس 2
+
+54
+00:06:07,890 --> 00:06:13,730
+هو 2 أُس n minus 1 عبارة عن 2 في 2 أُس n minus 2
+
+55
+00:06:13,730 --> 00:06:19,570
+وأنا بشتغل n شمالها أكبر وساوية تلاتة معناته a أُس
+
+56
+00:06:19,570 --> 00:06:22,930
+2 أُس n minus 1 نقص الواحد اللي هي بتساوي zero
+
+57
+00:06:22,930 --> 00:06:27,990
+عبارة عن a أُس 2 في 2 أُس n minus 2
+
+58
+00:06:34,970 --> 00:06:38,610
+نقص الواحد اللي عبارة عن ايه اتنين أس ان ماينوس
+
+59
+00:06:38,610 --> 00:06:47,790
+اتنين الكل تربيع نقص الواحد حلل هذه عبارة عن اتنين
+
+60
+00:06:47,790 --> 00:06:55,050
+أس اتنين أس ان ماينوس اتو نقص الواحد في اتنين أس
+
+61
+00:06:55,050 --> 00:07:00,210
+اتنين أس ان ماينوس اتو زاد الواحد بس هذه ايه
+
+62
+00:07:04,370 --> 00:07:13,150
+هذا ايش بيساوي؟ Zero اش يعني؟ يعني ان a أس 2 أس n
+
+63
+00:07:13,150 --> 00:07:19,810
+minus 2 بيساوي 1 or 2 أس 2 أس n minus 2 بيساوي
+
+64
+00:07:19,810 --> 00:07:24,950
+سالب 1 طبعا
+
+65
+00:07:24,950 --> 00:07:31,570
+انا باشتغل وين؟بشتغل في U2N لما بقول A أوس اتنين
+
+66
+00:07:31,570 --> 00:07:35,110
+أوس N minus اتنين مش يساوي واحد معناه to order ال
+
+67
+00:07:35,110 --> 00:07:40,130
+A اقل او يساوي تنين أوس N minus اتنين اقل من تنين
+
+68
+00:07:40,130 --> 00:07:46,630
+أوس N minus واحد اللي هو بدي ساوي order ال U2N or
+
+69
+00:07:46,630 --> 00:07:54,910
+ال A اتنين أوس N minus two ايش بدي ساوي
+
+70
+00:07:58,740 --> 00:08:07,060
+السالب واحد لأ أنا مابديش أربّه مافرجتش كتير هذي
+
+71
+00:08:07,060 --> 00:08:13,060
+لما بدي أربّه هيعطيني في النهاية A أُس 2 أُس N-1 و
+
+72
+00:08:13,060 --> 00:08:18,680
+هذي بحتاجهاش لكن أنا مين هحتاج؟ هذي علاقة صحيحة أه
+
+73
+00:08:18,680 --> 00:08:23,650
+لكن بلزمهاش بلزم مين؟انه انا هذه اللي بدور عليها
+
+74
+00:08:23,650 --> 00:08:28,990
+معناته كل عنصر في U تنين N ال order اللي هو جال من
+
+75
+00:08:28,990 --> 00:08:37,650
+مين؟ من U من order U تنين N هذه المعلومة لو ربعت
+
+76
+00:08:37,650 --> 00:08:41,070
+هحصل على مين؟ هرجع للأصل اللي مابتلزمنيش أصلا
+
+77
+00:08:41,070 --> 00:08:48,130
+وبالتاليمدام ال order لل A أقل من ال order لل U
+
+78
+00:08:48,130 --> 00:08:54,370
+تنين N معناته generated by ال A لا يساوي ال U تنين
+
+79
+00:08:54,370 --> 00:09:02,190
+N لكل A ينتمي ل U تنين N هذا معناته U تنين N not
+
+80
+00:09:02,190 --> 00:09:11,230
+cycling بس مشكلة انا احتجت ايش هادي باي اغلر
+
+81
+00:09:11,230 --> 00:09:18,430
+ثيرنظرية ايرلر الموجودة في نظرية الاعداد اعيد
+
+82
+00:09:18,430 --> 00:09:24,830
+بسرعة انا عناصر ال U N ال U تنانوس N هي كل ال odd
+
+83
+00:09:24,830 --> 00:09:30,690
+انتجار اللي جاب لل تنين N او تنانوس N اخدت اي عنصر
+
+84
+00:09:30,690 --> 00:09:34,770
+في هذه ال groupهيكون ال guess common divisor ايه
+
+85
+00:09:34,770 --> 00:09:39,050
+له مع 2 أُس N؟ ايش بيساوي؟ واحد حسب نظرية ايرلر
+
+86
+00:09:39,050 --> 00:09:44,210
+هتكون A أُس FI 2 أُس N congruent ل 1 مُد 2 أُس N
+
+87
+00:09:44,210 --> 00:09:50,050
+طيب FI 2 أُس N يعني A أُس 2 أُس N minus 1
+
+88
+00:09:50,050 --> 00:09:55,210
+congruent ل 1 مُد 2 أُس Nأفكار دي أنا ممكن أسترني
+
+89
+00:09:55,210 --> 00:10:00,870
+عنها لما أخد نظرية Error في chapter 7 أنه أنا باخش
+
+90
+00:10:00,870 --> 00:10:04,090
+أشتغل على عنصر في ال group فال order إيه اللي
+
+91
+00:10:04,090 --> 00:10:07,510
+بيقسم ال order لل group تنساش أن ال 2 أس N minus 1
+
+92
+00:10:07,510 --> 00:10:11,330
+هو order مين؟ اللي يوتي نين N فأنا ممكن لو أنا
+
+93
+00:10:11,330 --> 00:10:16,070
+أدرس نظرية 7 محتاجش نظرية ال Error theorem تبع
+
+94
+00:10:16,070 --> 00:10:21,730
+نظرية الأعداد طيب A أس 2 أس N minus 1كون ground ل
+
+95
+00:10:21,730 --> 00:10:29,140
+1 وين؟مد 2N أو 2 نص N يعني ال A أُس 2 نص N ماينس
+
+96
+00:10:29,140 --> 00:10:35,320
+واحد بيساوي واحد وين؟ في ال group U2N، لا تنساش أن
+
+97
+00:10:35,320 --> 00:10:39,520
+U2N هي عبارة عن الدرب، العملية اللي عليها هي الدرب
+
+98
+00:10:39,520 --> 00:10:45,360
+مد مين؟ 2 نص N طبعا A أُس 2 نص N ماينس واحد نقص
+
+99
+00:10:45,360 --> 00:10:50,570
+الواحد بيساوي صفر، حللهاهتسيب معايا a أُس 2 أُس n
+
+100
+00:10:50,570 --> 00:10:55,710
+-2 نقص الواحد في a أُس 2 أُس n-2 زاد الواحد فرق
+
+101
+00:10:55,710 --> 00:11:01,030
+بين المربعين طبعا هذي بتسوى صفر أو هذي بتسوى صفر
+
+102
+00:11:01,030 --> 00:11:06,010
+يعني a أُس 2 أُس n-2 بيساوي واحد او a أُس 2 أُس n
+
+103
+00:11:06,010 --> 00:11:10,940
+-2 بيساوي سالب واحد هذه المعلومة زي ما قلتحقيقية
+
+104
+00:11:10,940 --> 00:11:14,540
+لكن محتاجهاش لأن فعليا انا مابدأ اقول a اص 2 اص n
+
+105
+00:11:14,540 --> 00:11:19,860
+minus 2 بيساوي سالب واحد السالب واحد في 2 اص n او
+
+106
+00:11:19,860 --> 00:11:26,460
+في fight a few 2 اص n هي عبارة عن 2 اص n نقص
+
+107
+00:11:26,460 --> 00:11:32,460
+الواحد طبعا مش محتاجها انا كتيرأنا محتاج مين؟ أن
+
+108
+00:11:32,460 --> 00:11:37,540
+الـ A أُس 2 أُس N-2 يسوى 1 وبالتالي أُردر الـ A
+
+109
+00:11:37,540 --> 00:11:43,140
+أقل أو يسوى 2 أُس N-2 اللي هو أقل من 2 أُس N-1
+
+110
+00:11:43,140 --> 00:11:46,560
+اللي هو أُردر الـ U 2 N
+
+111
+00:11:50,840 --> 00:11:55,140
+أقل من order الـ U تنانوس N يجب أكيد الـ A لا يولد
+
+112
+00:11:55,140 --> 00:11:58,800
+هذه ال group مدام كل .. انت لا تنسى ان انا اخدت ال
+
+113
+00:11:58,800 --> 00:12:03,060
+A arbitrary لكل A في ال group كل عنصر في هذه ال
+
+114
+00:12:03,060 --> 00:12:06,600
+group ال order له لا يصل ل order ال group يجب لا
+
+115
+00:12:06,600 --> 00:12:11,840
+يولدها يجب ليست صحيك لك واضحة؟
+
+116
+00:12:25,190 --> 00:12:28,450
+هذه تانية نص واحد في تانية نص ن minus اتنين يعني
+
+117
+00:12:28,450 --> 00:12:31,050
+تانية نص ن minus اتنين زي اد واحد تانية نص ن minus
+
+118
+00:12:31,050 --> 00:12:31,510
+اتنين
+
+119
+00:12:38,610 --> 00:12:42,550
+هنا هاد المعلومة اللي هان ماروح نقول يا هذا بدي
+
+120
+00:12:42,550 --> 00:12:46,150
+يساوي صفر يا هذا بدي يساوي صفر هاد المعلومة هتقول
+
+121
+00:12:46,150 --> 00:12:49,370
+اتنين ا اثنين نص ان ماينوس واحد بدي أساوي واحد
+
+122
+00:12:49,370 --> 00:12:55,810
+موجودة لكن بحتاج رشد يعني أنا مستفدش منها اشي او
+
+123
+00:12:55,810 --> 00:12:59,390
+مش هي اللي هتعمللي الاشكالية او اللي انا بديها
+
+124
+00:12:59,390 --> 00:13:04,970
+عشان اثبت ان ال order ال ا لايساوي order واضح؟
+
+125
+00:13:06,980 --> 00:13:12,280
+واضح شباب؟ السؤال
+
+126
+00:13:12,280 --> 00:13:17,020
+اللي بعده السؤال تمانية .. تمانية و خمسين prove
+
+127
+00:13:17,020 --> 00:13:21,140
+that zn has an even number of generator if n أكبر
+
+128
+00:13:21,140 --> 00:13:26,740
+من اتنين what does this tell you about file n طيب
+
+129
+00:13:26,740 --> 00:13:34,560
+تمانية و خمسين لو ال n أكبر من اتنين فzn
+
+130
+00:13:59,150 --> 00:14:05,870
+FZN مولدة بإيه؟ والان أكبر من تنين دينبس هفيد شغلة
+
+131
+00:14:05,870 --> 00:14:11,810
+تانية شغلة الاولى ان زن مولدة ب a مولدة ب a
+
+132
+00:14:11,810 --> 00:14:15,830
+inverse شغلة
+
+133
+00:14:15,830 --> 00:14:19,590
+التانية ان
+
+134
+00:14:19,590 --> 00:14:25,650
+order ال a بديساوي n اكبر من 2 معناته a تغبيه لا
+
+135
+00:14:25,650 --> 00:14:30,900
+يساوي ال identity طب ال identity في zn الشوةالصفر
+
+136
+00:14:30,900 --> 00:14:37,540
+يعني A لا يساوي A inverse طبعا انت بتشغل في ZN فA
+
+137
+00:14:37,540 --> 00:14:43,600
+inverse مش بيساوي سالب A عشان العملية جامعة اذا A
+
+138
+00:14:43,600 --> 00:14:53,840
+لا يساوي سالب A ايش
+
+139
+00:14:53,840 --> 00:14:57,580
+يعني شباب يعني
+
+140
+00:14:57,580 --> 00:15:05,020
+ZNمولدة بعناصر ممكن انا اكتب علي شكل العنصر و
+
+141
+00:15:05,020 --> 00:15:17,360
+معكوسه هذا معناته The generators of Z and R A1
+
+142
+00:15:17,360 --> 00:15:28,630
+سالب A1 A2 سالب A2 لعند Aفايل ان على اتنين سالب ا
+
+143
+00:15:28,630 --> 00:15:35,390
+فايل ان على اتنين فايل
+
+144
+00:15:35,390 --> 00:15:45,770
+ان على اتنين فايل ان على اتنين فايل
+
+145
+00:15:45,770 --> 00:15:53,670
+ان على اتنين فايل ان على اتنين فايل ان على اتنين
+
+146
+00:15:53,670 --> 00:16:01,590
+فايل ان على اتنينfixed n has even number of
+
+147
+00:16:01,590 --> 00:16:15,530
+generators and file n نفسه is even هذه
+
+148
+00:16:15,530 --> 00:16:19,270
+نظرية موجودة برضه في نظرية الاعداد لكن اثباتها
+
+149
+00:16:19,270 --> 00:16:20,390
+بشكل مختلف
+
+150
+00:16:25,280 --> 00:16:29,540
+فايل ان على اتنين و سالب ا فايل ان على اتنين و
+
+151
+00:16:29,540 --> 00:16:32,540
+سالب ا فايل ان على اتنين فايل ان على اتنين عداد
+
+152
+00:16:32,540 --> 00:16:39,760
+يعني مش عامل يضرب الشغل من وين نهجر على اللومتين
+
+153
+00:16:39,760 --> 00:16:44,520
+نستفدتهم هن ال generator لزد ان لو ال a generator
+
+154
+00:16:44,520 --> 00:16:48,980
+فالسالب تبعه generator يعني انا بقدر اكتب ال
+
+155
+00:16:48,980 --> 00:16:54,240
+generators عبارة عن ثنائياتالـ A و سالب الـ A طبعا
+
+156
+00:16:54,240 --> 00:16:56,560
+الـ A واحد و سالب الـ A واحد الـ A تنين و سالب الـ
+
+157
+00:16:56,560 --> 00:17:00,340
+A تنين لأن آخر واحد هو السالب تبعه طبعا اللي خلاني
+
+158
+00:17:00,340 --> 00:17:05,080
+أقدر أكتب الكلام هذا أيضا ان ولا واحد بيساوي سالبه
+
+159
+00:17:05,080 --> 00:17:10,320
+يعني هدول مش مكررات هدول دستنقت عشان ماحدش يقولي
+
+160
+00:17:10,320 --> 00:17:15,160
+طب ما هدول ممكن تساوي لأ مابتساوش لو كان ال
+
+161
+00:17:15,160 --> 00:17:21,380
+generator لزد N فطبعا عشان ال N أكبر من 2فال a لا
+
+162
+00:17:21,380 --> 00:17:29,340
+يساوي سالب ال a طيب
+
+163
+00:17:29,340 --> 00:17:32,880
+سؤال
+
+164
+00:17:32,880 --> 00:17:39,020
+اللي بعده تسعة و خمسين لو
+
+165
+00:17:39,020 --> 00:17:42,540
+ال or لو ال or ضغط a أس خمسة بيسوا اتناشر
+
+166
+00:17:56,470 --> 00:18:02,370
+فعلا موجودين في تنائية 59
+
+167
+00:18:02,370 --> 00:18:08,010
+بيقول ال order ل a أُس 5 بيديه يساوي 12 ايش ال
+
+168
+00:18:08,010 --> 00:18:13,270
+possibilities ل order ال a مع ال order ل a أُس 5
+
+169
+00:18:13,270 --> 00:18:18,250
+بيديه يساوي 12 معناته a أُس 5 أُس 12 بيساوي ال
+
+170
+00:18:18,250 --> 00:18:25,800
+identityيعني اهو الستين بيساوي ال identity بيقسم
+
+171
+00:18:25,800 --> 00:18:34,420
+الستين بأردر ال a اش بيساوي واحد اتنين تلاتة اربعة
+
+172
+00:18:34,420 --> 00:18:44,300
+خمسة ستة لأ سبعة مفعش هي ستة عشرة اتناش خمستاش
+
+173
+00:18:44,300 --> 00:18:54,830
+تلاتين في اشعين و تلاتينو ستين هيك ما خلصناش هيك
+
+174
+00:18:54,830 --> 00:19:02,910
+ما خلصناش في بعض الحاجات هننفيها F لو
+
+175
+00:19:02,910 --> 00:19:08,710
+كان order ال A بساوي واحد معناته order ال A أس
+
+176
+00:19:08,710 --> 00:19:13,990
+خمسة بيساوي إيش؟ واحد لإن order ال A بيساوي واحد
+
+177
+00:19:13,990 --> 00:19:19,830
+معناته ال A هي ال identity طبعا هذا لأ هننفيهذا
+
+178
+00:19:19,830 --> 00:19:27,790
+ممنوع طيب لو order ال
+
+179
+00:19:27,790 --> 00:19:33,030
+a بدي ساوي اتنين معناته
+
+180
+00:19:33,030 --> 00:19:41,850
+a تربيه بدي ساوي ايش ال identity طيب
+
+181
+00:19:41,850 --> 00:19:46,770
+ايش يعني ال
+
+182
+00:19:46,770 --> 00:19:53,810
+order ال a بدي ساويال identity تنساش ان ال order ل
+
+183
+00:19:53,810 --> 00:19:58,170
+a أُس خمسة شو بدي ساوي اتناش هذا معناته ان a أُس
+
+184
+00:19:58,170 --> 00:20:03,430
+خمسة عبارة عن a تربيه تربيه في a اللي هو شو بدي
+
+185
+00:20:03,430 --> 00:20:10,190
+ساوي a اتناش اللي هو order ال a أُس خمسة اللي هو
+
+186
+00:20:10,190 --> 00:20:15,110
+order ال a اللي هو اتناش
+
+187
+00:20:15,110 --> 00:20:17,970
+اللي هو order ال a اللي هو order ال a اللي هو
+
+188
+00:20:17,970 --> 00:20:17,970
+order ال a اللي هو order ال a اللي هو order ال a
+
+189
+00:20:17,970 --> 00:20:17,970
+اللي هو order ال a اللي هو order ال a اللي هو
+
+190
+00:20:17,970 --> 00:20:17,970
+order ال a اللي هو order ال a اللي هو order ال a
+
+191
+00:20:17,970 --> 00:20:17,970
+اللي هو order ال a اللي هو order ال a اللي هو
+
+192
+00:20:17,970 --> 00:20:17,970
+order ال a اللي هو order ال a اللي هو order ال a
+
+193
+00:20:17,970 --> 00:20:17,970
+اللي هو order ال a اللي هو order ال a اللي هو
+
+194
+00:20:17,970 --> 00:20:17,970
+order ال a اللي هو order ال a اللي هو order ال a
+
+195
+00:20:17,970 --> 00:20:23,140
+اللي هو order الال A أُس خمسة عشان ال A تربيع بده
+
+196
+00:20:23,140 --> 00:20:26,900
+يساوي ال identity شيه ال A تربيع و كمان A تربيعاش
+
+197
+00:20:26,900 --> 00:20:32,360
+بده يظل ال A ف A أُس خمسة إيش بتساوي ال A هداش
+
+198
+00:20:32,360 --> 00:20:35,680
+معناته معناته ال 12 اللي هو order ال A أُس خمسة
+
+199
+00:20:35,680 --> 00:20:42,600
+إيش بده يساوي اتنين و هذا ممنوع هنتناقض و هنتناقض
+
+200
+00:20:42,600 --> 00:20:53,070
+اجبى التنين لأ طيب كمال؟لو أُردر ال A بدي يساوي
+
+201
+00:20:53,070 --> 00:21:01,210
+تلاتة معناته A تكييب بدي يساوي ال identity معناته
+
+202
+00:21:01,210 --> 00:21:11,770
+ال A والخمسة إبارة عن ال A تربيه طيب ال A بدي
+
+203
+00:21:11,770 --> 00:21:21,330
+يساوي ال A والستة قبل شويه بسمش هنخلص لأن هذا طويل
+
+204
+00:21:21,330 --> 00:21:27,350
+شوية السؤال قلت A أُس خمسة ايش بتتساوي A تربيع A
+
+205
+00:21:27,350 --> 00:21:36,910
+أُس خمسة بتتساوي A تربيع شوية
+
+206
+00:21:36,910 --> 00:21:40,270
+بس
+
+207
+00:21:40,270 --> 00:21:46,430
+معناته
+
+208
+00:21:46,430 --> 00:21:55,110
+اتناشبدي ساوي order الـ a و 5 بدي ساوي order ال a
+
+209
+00:21:55,110 --> 00:22:00,910
+تربيع معناته اتناش
+
+210
+00:22:00,910 --> 00:22:05,730
+بدي ساوي order ال
+
+211
+00:22:05,730 --> 00:22:14,510
+a تربيع طيب
+
+212
+00:22:14,510 --> 00:22:16,050
+في بنعمل شغل هنا
+
+213
+00:22:23,930 --> 00:22:33,110
+كيف الاربع و عشرين لا تقسم الستين شوية بس
+
+214
+00:22:33,110 --> 00:22:37,750
+ال
+
+215
+00:22:37,750 --> 00:22:44,550
+بقية اص أربع و عشرين ممكن يساوي ال identity but a
+
+216
+00:22:44,550 --> 00:22:51,270
+اص ستين ممكن يساوي ال identityهنصل في المحصلة ان a
+
+217
+00:22:51,270 --> 00:22:57,890
+أُس 12 دي ساو ال identity بطل
+
+218
+00:22:57,890 --> 00:23:10,950
+لأ هاد a أُس سالعة في النهاية هي اصلا
+
+219
+00:23:10,950 --> 00:23:13,410
+اقدر ال a دي ساو ال identity مقدرش اصل التناقض
+
+220
+00:23:13,410 --> 00:23:13,870
+مباشرة
+
+221
+00:23:27,570 --> 00:23:33,530
+طيب انا مش هعرف شوية و بعدين حصل حتى مش منطقى دلنا
+
+222
+00:23:33,530 --> 00:23:39,210
+اكمل بعد الاسلوب طب
+
+223
+00:23:39,210 --> 00:23:44,390
+خلينا نفكر باسلوب يعنى شوية بس assume خلينا نفكر
+
+224
+00:23:44,390 --> 00:23:50,690
+باسلوب يعنى ان order ال a بدي ساوي n اجبه order ال
+
+225
+00:23:50,690 --> 00:23:58,640
+a أُس خمسةبدي ساوي N على جريس common divisor لخمسة
+
+226
+00:23:58,640 --> 00:24:05,000
+و N إجبال 12 بدي ساوي N على جريس common divisor
+
+227
+00:24:05,000 --> 00:24:11,340
+لخمسة و N إجبال N بدي ساوي 12 في الجريس common
+
+228
+00:24:11,340 --> 00:24:18,240
+divisor لخمسة و N معناته 12 بدي اقسم order بدي
+
+229
+00:24:18,240 --> 00:24:22,610
+اقسم ال N اللي هو order ال Aما دام 12 بدي اقسم
+
+230
+00:24:22,610 --> 00:24:27,730
+order ال A هنلغي التلاتة هنلغي الأربعة هنلغي
+
+231
+00:24:27,730 --> 00:24:31,110
+الخمسة هنلغي الستة هنلغي العشرة هنلغي الخمس عشرة
+
+232
+00:24:31,110 --> 00:24:38,910
+هنلغي العشرين هنلغي التلاتين ايش هذا لأن دي يا 12
+
+233
+00:24:38,910 --> 00:24:49,190
+يا 60 وبالتالي اما order ال A بدي يسوا 12 او
+
+234
+00:24:50,870 --> 00:24:55,270
+وهو اخضر ال A و D ساعة و ستة و متانية ده افضل ليه
+
+235
+00:24:55,270 --> 00:24:59,710
+من ان انا اقعد امسك واحد واحد و اصل لتناقضات فهذا
+
+236
+00:24:59,710 --> 00:25:04,930
+الحل اسهل من الحل الاول يعنى فاضح؟
+
+237
+00:25:04,930 --> 00:25:13,960
+والله بتدعي عادة تبدينا باسلوب1,2,3,4,5,6,7,8,9,10
+
+238
+00:25:13,960 --> 00:25:18,060
+,11,12 كان مطلوب مني أروح أفحص 12 احتمال و أدلغي
+
+239
+00:25:18,060 --> 00:25:21,440
+لغتي الأول لغتي التانية جيت أدلغي التالت ماعرفتش
+
+240
+00:25:21,440 --> 00:25:25,980
+أكمل فجيت فكرت بسلوب جديد أنه لو كان ال order لل A
+
+241
+00:25:25,980 --> 00:25:30,860
+بدي ساوي N ف order ال A أُس 5 بدي ساوي N على الجيس
+
+242
+00:25:30,860 --> 00:25:35,500
+common divisor ل 5 و N طبعا هذا 12 إيش بـ 12 في
+
+243
+00:25:35,500 --> 00:25:42,280
+الجيس common divisor ل 5 و N بدي ساوي إيشيقبل 12
+
+244
+00:25:42,280 --> 00:25:47,020
+بيقسم ال N بس انساش ان ال N واحد من ال 12 الخيار
+
+245
+00:25:47,020 --> 00:25:55,520
+هدول شطب كل ال 12 بيقسمهمش، مين هيضل؟ ال 12 او ال
+
+246
+00:25:55,520 --> 00:25:59,840
+60، يقبل order ال ايه؟ يا 12 يا 60
+
+247
+00:26:10,220 --> 00:26:15,780
+سؤال 64 لأ
+
+248
+00:26:15,780 --> 00:26:21,180
+حلته انت ممكن هذا تلغي يعني هذا ممكن ماتحتاجوش
+
+249
+00:26:21,180 --> 00:26:24,800
+خلاص
+
+250
+00:26:24,800 --> 00:26:28,880
+يا 12 يا 60 تقدر تحدد بالظبط لأ لو انت بتشتغل في
+
+251
+00:26:28,880 --> 00:26:36,620
+Z12 فال order 12 مثلا في Z12اللي هو الـ A 5 عبارة
+
+252
+00:26:36,620 --> 00:26:40,220
+عن خمسة ال order لها 12 و ال order ل ال A 12 في Z
+
+253
+00:26:40,220 --> 00:26:48,940
+60 ال order ل ال A 60 لكن ال order ل الخمسة 12 طيب
+
+254
+00:26:48,940 --> 00:26:55,100
+السؤال 64 ال
+
+255
+00:26:55,100 --> 00:27:06,080
+H عبارة عن واحد and Zero واحد حيث انمطلوب اثبت
+
+256
+00:27:06,080 --> 00:27:11,440
+انها Cyclic subgroup of GL2R طبعا عشان ما انا اجعش
+
+257
+00:27:11,440 --> 00:27:15,600
+في اشكالية و بجهود اثبت انها subgroup و بعدين ادور
+
+258
+00:27:15,600 --> 00:27:19,620
+لها generator ممكن مباشرة اثبت انها generated by
+
+259
+00:27:19,620 --> 00:27:22,720
+some element و بعدين ماداما generated by some
+
+260
+00:27:22,720 --> 00:27:27,920
+element من GL2R بتكون مباشرة هي subgroup انا هقولك
+
+261
+00:27:27,920 --> 00:27:28,380
+اكلام
+
+262
+00:27:31,440 --> 00:27:41,160
+الـ H generated by 1101 تعالي
+
+263
+00:27:41,160 --> 00:27:49,700
+نتبت لت
+
+264
+00:27:49,700 --> 00:27:58,620
+A ينتمي لـ H هذا معناته الـ A بدأ تساوي 1101
+
+265
+00:27:58,620 --> 00:28:08,050
+و الـ N من أين؟ من ال 6بدي أثبت إنه ال A عبارة عن
+
+266
+00:28:08,050 --> 00:28:12,110
+power فن
+
+267
+00:28:12,110 --> 00:28:22,110
+بيبقى تساوي 0 معناته ال A بيبقى تساوي 1001
+
+268
+00:28:22,110 --> 00:28:27,050
+عبارة عن 1101
+
+269
+00:28:27,050 --> 00:28:34,100
+أُس 0أو انا خدنا في الجابر الخاطئ ان اي مصفوفة أُس
+
+270
+00:28:34,100 --> 00:28:44,680
+زي روش بيعضيناها ال identity if
+
+271
+00:28:44,680 --> 00:28:50,400
+n أكبر من الصفر ال n ينتمي لمين ده ال initial
+
+272
+00:28:50,400 --> 00:28:57,040
+number we will use mathematical
+
+273
+00:28:57,040 --> 00:29:00,300
+induction for
+
+274
+00:29:01,850 --> 00:29:08,170
+أن بيسوي واحد واحد واحد واحد واحد اللي هي واحد
+
+275
+00:29:08,170 --> 00:29:17,170
+عبارة عن واحد واحد واحد واحد اص واحد assume for
+
+276
+00:29:17,170 --> 00:29:25,950
+أن بيسوي ك ذات واحد كزيرو كزيرو واحد عبارة عن واحد
+
+277
+00:29:25,950 --> 00:29:30,370
+واحد واحد واحد اص ك then
+
+278
+00:29:32,820 --> 00:29:40,660
+ورقان بيساوي كزاد الواحد واحد واحد زير واحد قص
+
+279
+00:29:40,660 --> 00:29:46,900
+كزاد الواحد عبارة عن واحد واحد زير واحد قص ك في
+
+280
+00:29:46,900 --> 00:29:52,140
+واحد واحد زير واحد حسب المعطل عندي هذا معناه واحد
+
+281
+00:29:52,140 --> 00:30:00,280
+كزير واحد في واحد واحد زير واحد اضرب واحد في واحد
+
+282
+00:30:00,280 --> 00:30:05,160
+واحد ك في صفر صفر واحد1 في 1 و 1 و K في 1 و K و 1
+
+283
+00:30:05,160 --> 00:30:13,120
+و K و K زاد ال 1 و هو المطلوب طبعا المطلوب في ال
+
+284
+00:30:13,120 --> 00:30:18,880
+induction يعني
+
+285
+00:30:18,880 --> 00:30:26,000
+ان موجب
+
+286
+00:30:28,000 --> 00:30:34,140
+1 and 01 عبارة عن واحد واحد زي رو واحد اشف ضال
+
+287
+00:30:34,140 --> 00:30:38,020
+عندي ده
+
+288
+00:30:38,020 --> 00:30:47,120
+السالب four and اقل من الصفر ده داش معناته معناته
+
+289
+00:30:47,120 --> 00:30:54,460
+سالب and موجب معناته
+
+290
+00:30:54,460 --> 00:30:57,000
+سالب and موجب طيب
+
+291
+00:30:58,540 --> 00:31:06,580
+واحد واحد واحد واحد والسالب n هكون واحد سالب n زير
+
+292
+00:31:06,580 --> 00:31:12,220
+واحد حسب
+
+293
+00:31:12,220 --> 00:31:21,760
+مين؟ by part n أكبر من zero طبعا مابديش واحد سالب
+
+294
+00:31:21,760 --> 00:31:29,580
+n زير واحد بدي واحد n زير واحد إيش هنعمل؟اخد
+
+295
+00:31:29,580 --> 00:31:34,940
+inverse الطرفين يا شباب هذا معناته واحد واحد zero
+
+296
+00:31:34,940 --> 00:31:43,960
+واحد inverse أس N عبارة عن واحد سالب N zero واحد
+
+297
+00:31:43,960 --> 00:31:52,700
+أنا بشتغل جبر خطي هنا بس أغير هدول عشان ما نخبطش
+
+298
+00:31:52,700 --> 00:31:59,340
+في الجبر الخطي الأس و ال inverse شبهلهمببدله هذا
+
+299
+00:31:59,340 --> 00:32:08,720
+عيسى معايا 1101 أس أن انفرس بدي ساوي 1 سالم ان 01
+
+300
+00:32:08,720 --> 00:32:20,600
+معناته 1101 أس أن بدي ساوي هذا انفرس احسب الانفرس
+
+301
+00:32:20,600 --> 00:32:26,680
+بعد ما تحسبه بالجبر الخطي هيعطيك 1101
+
+302
+00:32:28,820 --> 00:32:36,380
+هذا معناته في كل الأحوال اي عبارة عن 1 n 0 1 اللي
+
+303
+00:32:36,380 --> 00:32:52,460
+عبارة عن 1 1 0 1 plus n المحصرة النهائية ان ال
+
+304
+00:32:52,460 --> 00:32:55,220
+H generated by
+
+305
+00:33:00,530 --> 00:33:03,710
+طب انا مفترض في جزء تاني يا شباب انه هذا subset
+
+306
+00:33:03,710 --> 00:33:07,350
+انه هذا هيخليني اقول ان ال H subset من هذا و بعدين
+
+307
+00:33:07,350 --> 00:33:12,090
+اقول ان هذا subset من ال H بس مادام 1101 موجود في
+
+308
+00:33:12,090 --> 00:33:17,230
+ال H فأكيد ال generated من هذا الأنصار subset من
+
+309
+00:33:17,230 --> 00:33:25,030
+ال H وبتالي صارت ال H اشمالها Cyclic Subject واضح؟
+
+310
+00:33:25,030 --> 00:33:31,340
+واضح يا شباب؟دكتور كيف المصيبة من الوسكي صارت
+
+311
+00:33:31,340 --> 00:33:39,020
+مصيبة هذه؟ كيف انفكت هيك؟ حسب القاعدة هذه عشان
+
+312
+00:33:39,020 --> 00:33:54,120
+أقولك أسيوم أنه هذي بيساوي هذي 65
+
+313
+00:33:54,120 --> 00:33:58,040
+و آخر سؤال معانا أفندم كيف انفكت إلى إيه؟ مصيبة
+
+314
+00:33:58,040 --> 00:34:05,900
+تانيةكيف؟ هطيين ال generator تاني هذه sub group
+
+315
+00:34:05,900 --> 00:34:10,880
+infinite infinite sub group كم generator لها؟ تنين
+
+316
+00:34:10,880 --> 00:34:17,940
+واحد واحد صفر واحد واحد سالب واحد صفر واحد 65
+
+317
+00:34:23,610 --> 00:34:27,510
+الـ order للـ A بدي يساوي 12 ال order لل B بدي
+
+318
+00:34:27,510 --> 00:34:34,250
+يساوي 22 و generated by ال A فقاطع generated by ال
+
+319
+00:34:34,250 --> 00:34:42,590
+B لا يساوي ال identity أثبت أن A أُس 6 بدي يساوي A
+
+320
+00:34:42,590 --> 00:34:43,350
+أُس 11
+
+321
+00:35:11,660 --> 00:35:17,560
+عشرة يعني a-12 يساوي ال identity و b-22 يساوي ال
+
+322
+00:35:17,560 --> 00:35:23,440
+identity a-12 يساوي b-22 يساوي ال identity a-12
+
+323
+00:35:23,440 --> 00:35:25,640
+يساوي b-22 يساوي ال identity a-12 يساوي b-22 يساوي
+
+324
+00:35:25,640 --> 00:35:29,780
+ال identity a-12 يساوي b-22 يساوي ال identity a-12
+
+325
+00:35:29,780 --> 00:35:31,520
+يساوي b-22 يساوي ال identity a-12 يساوي b-22 يساوي
+
+326
+00:35:31,520 --> 00:35:31,940
+ال identity a-12 يساوي b-22 يساوي b-22 يساوي b-22
+
+327
+00:35:31,940 --> 00:35:32,220
+يساوي b-22 يساوي b-22 يساوي b-22 يساوي b-22 يساوي
+
+328
+00:35:32,220 --> 00:35:32,220
+b-22 يساوي b-22 يساوي b-22 يساوي b-22 يساوي b-22
+
+329
+00:35:32,220 --> 00:35:32,220
+يساوي b-22 يساوي b-22 يسا
+
+330
+00:35:35,610 --> 00:35:40,410
+معناته في أنصر مشترك ال X في generated by A وال X
+
+331
+00:35:40,410 --> 00:35:45,150
+في generated by B مدام هو في generated by A يكبر
+
+332
+00:35:45,150 --> 00:35:49,390
+ال order اله بيقسم order ال A بيساوي 12 ف order ال
+
+333
+00:35:49,390 --> 00:35:56,530
+X بيقسم 12 و بيقسم أيضا ال 22 يكبر X قص 12 بيساوي
+
+334
+00:35:56,530 --> 00:35:57,010
+X
+
+335
+00:35:59,930 --> 00:36:03,750
+أو ال order له بيقسم ال 12 و بيقسم ال 22 ف order
+
+336
+00:36:03,750 --> 00:36:08,510
+ال x بيقسم لجريس common divisor لل 12 و 22 ايش
+
+337
+00:36:08,510 --> 00:36:14,190
+يعني؟ يعني x تربيع او x هيقسم لجريس common divisor
+
+338
+00:36:14,190 --> 00:36:19,350
+لل 22 كده؟ اتنين، معناته يا اما ال x بيسوي ال
+
+339
+00:36:19,350 --> 00:36:25,830
+identity يا اما ال order لل x مش بيسويإتنين طيب
+
+340
+00:36:25,830 --> 00:36:29,230
+انسى ال identity خد x ال order اللي هو بيساوي
+
+341
+00:36:29,230 --> 00:36:36,710
+اتنين ايش يعني ال
+
+342
+00:36:36,710 --> 00:36:42,830
+order ال x بيساوي اتنين ايش يعني
+
+343
+00:36:42,830 --> 00:36:46,930
+مين
+
+344
+00:36:46,930 --> 00:36:51,270
+هو العنصر اللي ال order له اتنين في generated by a
+
+345
+00:36:54,370 --> 00:37:00,030
+هو الـ A أُس 6 من العنصر اللي الـ O ضر إله 2 في B
+
+346
+00:37:00,030 --> 00:37:04,530
+أُس 2 في generated by الـ B B أُس 11 يجب الإكس هو
+
+347
+00:37:04,530 --> 00:37:09,470
+نفسه الـ A أُس 6 هو نفسه الـ B أُس 11 هذا هو الحل
+
+348
+00:37:09,470 --> 00:37:15,910
+let X لا يساوي ال identity and X ينتمي لgenerated
+
+349
+00:37:15,910 --> 00:37:21,820
+by A تقاطع generated by B معناته ال Xينتمي
+
+350
+00:37:21,820 --> 00:37:26,160
+لgenerated by a and ال x ينتمي لgenerated by b
+
+351
+00:37:26,160 --> 00:37:31,640
+معناته order ال x بيقسم order ال a and order ال x
+
+352
+00:37:31,640 --> 00:37:36,280
+بيقسم order ال b معناته order ال x بيقسم لgreased
+
+353
+00:37:36,280 --> 00:37:42,520
+common divisor ل order ال a order ال b order ال x
+
+354
+00:37:42,520 --> 00:37:47,400
+بيقسم لgreased common divisor ل 12 و 22 و 9 و 2
+
+355
+00:37:48,370 --> 00:37:55,570
+order of x هو اتنين but يقسم الاتنين ال x لا يساوي
+
+356
+00:37:55,570 --> 00:38:05,390
+ال identity order of x هو اتنين ال
+
+357
+00:38:05,390 --> 00:38:10,170
+element of
+
+358
+00:38:10,170 --> 00:38:19,350
+order اتنين generated by a هو a6أو بلاش اقول the
+
+359
+00:38:19,350 --> 00:38:25,550
+element كمان the only element فش في a أُس
+
+360
+00:38:25,550 --> 00:38:28,950
+generated by ال a اللي هي ال order إلها اتناش غير
+
+361
+00:38:28,950 --> 00:38:32,510
+عنصر واحد ال order إله اتنين ليش أنا بشغل في
+
+362
+00:38:32,510 --> 00:38:36,230
+cyclic group أكم عنصر ال order إله اتنين في ال
+
+363
+00:38:36,230 --> 00:38:42,310
+cyclic group فيه اتنين فيه اتنين جديش واحد أنا
+
+364
+00:38:42,310 --> 00:38:43,470
+بشغل في finite يا حبيبي
+
+365
+00:38:48,860 --> 00:38:51,280
+القاعدة الـ Phi للـ finite أصلا مش لل Infinite
+
+366
+00:38:51,280 --> 00:38:55,160
+قاعدة
+
+367
+00:38:55,160 --> 00:39:02,160
+ال Phi للـ finite مش لل Infinite واضحة؟
+
+368
+00:39:02,160 --> 00:39:07,300
+الوحدة الوحيدة
+
+369
+00:39:07,300 --> 00:39:08,120
+الوحيدة الوحيدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+370
+00:39:08,120 --> 00:39:08,920
+الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة الوحدة
+
+371
+00:39:08,920 --> 00:39:08,920
+الوحدة
+
+372
+00:39:13,980 --> 00:39:19,440
+P أُس 11 يكبر X هي نفس ال P أُس 11 و هي نفس ال A
+
+373
+00:39:19,440 --> 00:39:26,600
+أُس 6 يكبر A أُس 6 بيساوي P أُس 11 و هي كده end of
+
+374
+00:39:26,600 --> 00:39:37,540
+chapter 4 واضح؟
+
+375
+00:39:37,540 --> 00:39:42,490
+و بالنهاية ضيعنا المحاضرة في خمس أسئلةكان مفترض
+
+376
+00:39:42,490 --> 00:39:49,610
+اننا ندخل في الشبتر الخامس ال generator لل a بسوة
+
+377
+00:39:49,610 --> 00:39:53,890
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+378
+00:39:53,890 --> 00:39:54,710
+ال generator لل a بسوة وستة a والستة ال generator
+
+379
+00:39:54,710 --> 00:39:56,310
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+380
+00:39:56,310 --> 00:39:59,310
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+381
+00:39:59,310 --> 00:39:59,390
+ال generator لل a بسوة وستة a والستة ال generator
+
+382
+00:39:59,390 --> 00:39:59,410
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+383
+00:39:59,410 --> 00:39:59,950
+وستة a والستة ال generator لل a بسوة وستة a والستة
+
+384
+00:39:59,950 --> 00:40:00,530
+ال generator لل a بسوة وستة a والستة ال generator
+
+385
+00:40:00,530 --> 00:40:04,850
+لل a بسوة وستة a والستة ال generator لل a بسوة
+
+386
+00:40:04,850 --> 00:40:11,610
+وستة a والستة ال generator لل a بسوة وست12 هدى الـ
+
+387
+00:40:11,610 --> 00:40:17,870
+Cyclic group التنين تقسم ال order لل A يكبر يوجد
+
+388
+00:40:17,870 --> 00:40:22,170
+عناصر داخل ال generated by A ال order لتنين جدش
+
+389
+00:40:22,170 --> 00:40:29,870
+عددهم؟ five تنين يكبر يوجد عنصر واحد مين هو؟ ال A
+
+390
+00:40:29,870 --> 00:40:34,470
+و ال 6 نفس الفكرة هنا في generated by B ال order
+
+391
+00:40:34,470 --> 00:40:40,710
+لل B بيساوي 22تنين بيخسم 22 فيوجد عناصر ال order
+
+392
+00:40:40,710 --> 00:40:44,910
+اللي هتنين في generated by P عدد ده بيساوي five
+
+393
+00:40:44,910 --> 00:40:48,250
+تنين بيساوي واحد ماقلتلك هال the only the only
+
+394
+00:40:48,250 --> 00:40:51,730
+element واضحة
+
+395
+00:40:51,730 --> 00:40:57,650
+وخاضرة اللي هناخدها او الكان المفترض انه نبدأ فيها
+
+396
+00:40:57,650 --> 00:41:05,110
+اليوم هو chapter خمسة اللي
+
+397
+00:41:05,110 --> 00:41:05,930
+هو permutation
+
+398
+00:41:09,230 --> 00:41:14,530
+الـ groups او
+
+399
+00:41:14,530 --> 00:41:19,530
+الزمر
+
+400
+00:41:19,530 --> 00:41:31,790
+.. الزمر ايش؟ تبادلية .. تبدلية لأ مش يعني
+
+401
+00:41:31,790 --> 00:41:38,050
+permutation زمر التبادل زمر
+
+402
+00:41:39,560 --> 00:41:45,200
+طبعا الفكرة كانت تالية يا شباب عشان نكون جاهزين
+
+403
+00:41:45,200 --> 00:41:51,760
+للمحاضرة الجاية انا بستعمل group G و بعرف عليها
+
+404
+00:41:51,760 --> 00:41:57,920
+عمليات هتلاحظ ان معظم العمليات اللي عرفناها في
+
+405
+00:41:57,920 --> 00:42:05,390
+الشباتر اللي فاتت لو بتعامل مع groupsمش مجرد يعني
+
+406
+00:42:05,390 --> 00:42:09,410
+عناصرها محسوسة بتقدر تتعامل معاها زي ال Z زي ال R
+
+407
+00:42:09,410 --> 00:42:12,290
+زي ال N زي ال matrices زي ال polynomial الاخرين
+
+408
+00:42:12,290 --> 00:42:17,370
+كانت معظم العمليات تركز على الجمع العادي الجمع
+
+409
+00:42:17,370 --> 00:42:21,590
+التقليدي أو الدرب التقليدي حتى لو كان في الجمع و
+
+410
+00:42:21,590 --> 00:42:27,290
+الدرب مد N معين او درب او جمع matrices انه في
+
+411
+00:42:27,290 --> 00:42:32,080
+النهاية هيرجع للجمع العادي و الدرب العاديإذا بتذكر
+
+412
+00:42:32,080 --> 00:42:40,200
+أخدنا groups كان فيها functions مع
+
+413
+00:42:40,200 --> 00:42:43,980
+الجامعة مع
+
+414
+00:42:43,980 --> 00:42:47,520
+ال multiplication فيه إشكالية لل group لإنه انا
+
+415
+00:42:47,520 --> 00:42:52,480
+بدي اشتغل على واحد على F لما اتعامل مع واحد على F
+
+416
+00:42:52,480 --> 00:42:57,080
+لازم ال F ما تكونش Zero ببدي انا انا بدي اخد ال
+
+417
+00:42:57,080 --> 00:43:02,730
+non-zero functions بقدر أعرفطيب بتجمعوا الضرب جدًا
+
+418
+00:43:02,730 --> 00:43:08,870
+تحلوا مشكلتهم لو أنا بدي أعرف groups group مثلا هي
+
+419
+00:43:08,870 --> 00:43:16,190
+X و بدي أشغل على function من X جولة نفسها و تكون
+
+420
+00:43:16,190 --> 00:43:22,030
+عناصرها دي هو ال group بس
+
+421
+00:43:22,030 --> 00:43:28,790
+بدي أشغل على عملية ال composition Circle Jماذا
+
+422
+00:43:28,790 --> 00:43:33,750
+لازم الشروط اللي انا اشتغل فيها هنا؟ ماتنساش انا
+
+423
+00:43:33,750 --> 00:43:38,730
+بده اعمل معاشر مع associative ال composition
+
+424
+00:43:38,730 --> 00:43:43,510
+associative بتعامل مع وجود identity فيه بقدر الاقي
+
+425
+00:43:43,510 --> 00:43:45,730
+identity مع ال composition هو ال identity function
+
+426
+00:43:45,730 --> 00:43:52,570
+انا بشتغل من المجموعة لنفسها بظل closed و ال
+
+427
+00:43:52,570 --> 00:43:56,570
+composition لو انا بشتغل من X ل Xوبدأ اجيب كمان
+
+428
+00:43:56,570 --> 00:44:02,110
+function من X ل X اللي closed موجود بظالمين شرط ال
+
+429
+00:44:02,110 --> 00:44:07,790
+inverse انا مش inverse طرح ولا inverse ضرب اني
+
+430
+00:44:07,790 --> 00:44:10,270
+اقول سالب ال function او واحد على ال function لأ
+
+431
+00:44:10,270 --> 00:44:13,730
+inverse composition وبالتالي بدأش انا مع أف
+
+432
+00:44:13,730 --> 00:44:21,530
+inverse من X ل Xعشان اقدر نعرف ال F inverse لازم
+
+433
+00:44:21,530 --> 00:44:25,870
+ال F نفسه اش تكون one to one ايه بقى لازم
+
+434
+00:44:25,870 --> 00:44:30,470
+الاقترابات اللي باخدها اش تكون مش بس one to one ال
+
+435
+00:44:30,470 --> 00:44:35,770
+inverse بدي يكون function من المجموع على نفسها بدي
+
+436
+00:44:35,770 --> 00:44:41,890
+تكون برضه on to فلازم تكون ال function ايه شمالها؟
+
+437
+00:44:41,890 --> 00:44:44,150
+one to one correspondence يعني πي جيكشن
+
+438
+00:44:46,980 --> 00:44:51,200
+بيجيكشن على الـ finite يكفي نشرط واحد عشان اوجده
+
+439
+00:44:51,200 --> 00:44:56,200
+وبتالي هكتفي بال one to one عشان احش على finite
+
+440
+00:44:56,200 --> 00:44:59,540
+set ال X تكون finite هذه هسميها permutation
+
+441
+00:44:59,540 --> 00:45:02,440
+هناخدها في المخادرة التانية ان شاء الله يعطيكوا
+
+442
+00:45:02,440 --> 00:45:02,760
+العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..875d7f0a7ee72a0610054e287067d3de80a88da3
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/iL2JhRM8vU8_raw.srt
@@ -0,0 +1,1748 @@
+1
+00:00:21,280 --> 00:00:24,820
+بسم الله الرحمن الرحيم المرة اللى فاتت و اللى
+
+2
+00:00:24,820 --> 00:00:29,380
+قبلها أخدنا تعريف ل group و بدأنا ناخد أمثلة على
+
+3
+00:00:29,380 --> 00:00:35,340
+ذلك و أخدنا عشرة من الأمثلة و الآن بنكمل برضه بدل
+
+4
+00:00:35,340 --> 00:00:39,360
+المثال اتنين على نفس الموضوع المثال الرقم أحداشر
+
+5
+00:00:39,360 --> 00:00:47,210
+بيقول افترض جي كل ال X اللى موجودة في ال Qفي ال
+
+6
+00:00:47,210 --> 00:00:52,010
+set of rational numbers وليس فقط كل ال X الموجودة
+
+7
+00:00:52,010 --> 00:00:57,390
+في ال IQ بحيث ال X لا تساوي واحد يبقى احنا عندنا
+
+8
+00:00:57,390 --> 00:01:04,070
+اعداد نسبية موجبة وسالبة وصفر ما عدا الواحد الصحيح
+
+9
+00:01:04,800 --> 00:01:08,880
+عرفنا binary operation star يبقى أنا أعطيتك أنها
+
+10
+00:01:08,880 --> 00:01:13,540
+binary operation بالشكل أن a star b يسوى a زائد b
+
+11
+00:01:13,540 --> 00:01:19,500
+ناقص ال a b يبقى مجموع العددين ناقص حاصل ضربهم
+
+12
+00:01:19,500 --> 00:01:23,500
+كلها على بعضها هذه بدي أسميها ال operation star
+
+13
+00:01:23,500 --> 00:01:30,860
+لكل ال a و b الموجودة في gهل الـ G و الـ Star هدى
+
+14
+00:01:30,860 --> 00:01:36,260
+اي group ولا لأ يبقى انا بروح بسبحة ثمانة الثلاثة
+
+15
+00:01:36,260 --> 00:01:40,320
+شروط لإعطانيها binary operation بدي أشوف هل الـ
+
+16
+00:01:40,320 --> 00:01:44,380
+Star هدى associative هل ال identity element موجود
+
+17
+00:01:44,380 --> 00:01:50,320
+هل المعكوس لكل عنصر موجود ام لأ يبقى solution
+
+18
+00:01:53,940 --> 00:01:58,880
+النقطة الأولى هل العملية هذه associative ولا لأ
+
+19
+00:01:58,880 --> 00:02:04,740
+إذا بتروح أخد تلت عناصر موجودة في ال group G يبقى
+
+20
+00:02:04,740 --> 00:02:10,280
+بداجي أقوله let ال A والB والC موجودة في G then
+
+21
+00:02:11,170 --> 00:02:18,770
+بتروح اخد a star b star c اشوف كده شو ساوي بدي اجي
+
+22
+00:02:18,770 --> 00:02:23,950
+الان ل a star b a star b هي معرفة يبقى بدي اشيلها
+
+23
+00:02:23,950 --> 00:02:29,950
+و احط اللي هي القيمة تبعتها يبقى a زائد ال b ناقص
+
+24
+00:02:29,950 --> 00:02:38,060
+ال a b هي ال star و هي cالان هذا كله صار عنصر جديد
+
+25
+00:02:38,060 --> 00:02:44,940
+في ال group اللي عندنا جي او في الست اللي عندنا جي
+
+26
+00:02:44,940 --> 00:02:50,280
+يبقى هذا العنصر بدي اعمله star مع c ال star بين
+
+27
+00:02:50,280 --> 00:02:54,960
+two عنصر يمكن اقول الاول زائد التاني ناقص حصل ضرب
+
+28
+00:02:54,960 --> 00:03:00,900
+الاول في الثاني اذا هذا بدي يساوي الاول زائد b
+
+29
+00:03:00,900 --> 00:03:09,000
+ناقص الabزائد الثاني اللي هو C تمام ناقص حاصل
+
+30
+00:03:09,000 --> 00:03:15,900
+ضربهما يبقى ناقص A زائد B ناقص ال A و ال B كله في
+
+31
+00:03:15,900 --> 00:03:20,540
+مين؟ في ال C يبقى هاي طبق لل start طبق لل
+
+32
+00:03:20,540 --> 00:03:25,370
+definition اللي فوقبدي اشوف هذا شو بيساوي يبقى هذا
+
+33
+00:03:25,370 --> 00:03:37,230
+بدي يساوي a زائد b زائد c ناقص ab ناقص ca عفوا
+
+34
+00:03:37,230 --> 00:03:49,420
+ناقص ac ac بالترتيب ناقص bc زائد abcهذا ال term
+
+35
+00:03:49,420 --> 00:03:55,520
+الأول بده أشوف ال term التاني بده أشوف ال a star b
+
+36
+00:03:55,520 --> 00:04:01,670
+star c شو بده يعطينييبقى بدروح أحسبله بي ستار سي
+
+37
+00:04:01,670 --> 00:04:08,410
+يبقى هذا ال a اللي برا وهذا ال star وهيجوز بي زائد
+
+38
+00:04:08,410 --> 00:04:15,690
+سي ناقص بي سي طبق ال definition اللي عرفناها ال
+
+39
+00:04:15,690 --> 00:04:20,100
+operation أو ال binary operation اللي عندنابتطبق
+
+40
+00:04:20,100 --> 00:04:24,680
+ال binary operation كمان مرة يبقى الأول زائد
+
+41
+00:04:24,680 --> 00:04:29,600
+التاني ناقص حاصل ضرب الأول في الثاني يبقى هذا
+
+42
+00:04:29,600 --> 00:04:38,720
+الأول زائد التاني بزائد c ناقص bc ناقص حاصل ضرب
+
+43
+00:04:38,720 --> 00:04:48,280
+الأول في الثاني بزائد c ناقص bc هذا الكلام يساوي a
+
+44
+00:04:49,470 --> 00:05:02,190
+A زائد B زائد C ناقص BC ناقص AB ناقص AC زائد ABC
+
+45
+00:05:02,190 --> 00:05:10,430
+طلعلي هذه رقم واحد وهذه رقم اتنينتعالى نطلع على
+
+46
+00:05:10,430 --> 00:05:14,370
+رقم واحد و رقم اتنين هل اتنين نفس الشيء ولا
+
+47
+00:05:14,370 --> 00:05:20,530
+باختلفوا a زائد b زائد c a زائد b زائد c ناقص ab
+
+48
+00:05:20,530 --> 00:05:28,430
+ناقص ac ناقص bc يبقى ناقص bc ناقص ab ناقص ac
+
+49
+00:05:28,430 --> 00:05:32,970
+التلاتة دول هم هما زائد حصل ضرب التلاتة زائد حصل
+
+50
+00:05:32,970 --> 00:05:38,950
+ضرب التلاتةيبقى بناء علي اتنين هذول مالهم بيسووا
+
+51
+00:05:38,950 --> 00:05:47,930
+بعض يبقى بروح بقوله هنا from واحد and اتنين we
+
+52
+00:05:47,930 --> 00:06:00,720
+have ان ال a star bstar c بده يساوي a star b star
+
+53
+00:06:00,720 --> 00:06:06,600
+c يبقى هذا معناته ان ال star مالها is associative
+
+54
+00:06:06,600 --> 00:06:18,360
+يبقى هنا so ال star is an associative
+
+55
+00:06:18,360 --> 00:06:21,140
+binary operation
+
+56
+00:06:28,360 --> 00:06:32,280
+يبقى خلّصنا النقطة الأولى بدي أجل النقطة التانية
+
+57
+00:06:32,280 --> 00:06:40,240
+بدي أثبت أنه في عندي identity element وطبقا لهذه
+
+58
+00:06:40,240 --> 00:06:44,040
+العملية بدي أعرفش إيه شكل هذا ال identity element
+
+59
+00:06:44,040 --> 00:06:50,120
+إذا أنا هفترض أن عندي identity element E وشوف ال E
+
+60
+00:06:50,120 --> 00:06:54,450
+بقدر أجيب له قيمة ولا بقدرشإذا قدرنا نجيب له قيمة
+
+61
+00:06:54,450 --> 00:06:58,330
+معناته موجود ماقدرنا معناته مش موجود فرضي مش صحيح
+
+62
+00:06:58,330 --> 00:07:07,430
+يبقى بناء عليه بداية أقول له assume أفترض that أن
+
+63
+00:07:07,430 --> 00:07:19,170
+ال E is the identity element of
+
+64
+00:07:19,170 --> 00:07:26,450
+Gافترض ان ايه ال identity element في g افترض كمان
+
+65
+00:07:26,450 --> 00:07:42,690
+ان ال a موجود في g يبقى then ال e star a بدي اعرف
+
+66
+00:07:42,690 --> 00:07:50,190
+ايه شكل ال e هذي لذلك بروح اخد اي واحدة من هذولأذا
+
+67
+00:07:50,190 --> 00:07:58,010
+لو أخدت ال E star ايه يسوى ايه امبليزه؟ بدي أطبخ
+
+68
+00:07:58,010 --> 00:08:02,250
+تعريف ال star اللي عندنا هذه على الجزء اللي عندنا
+
+69
+00:08:02,250 --> 00:08:10,290
+هذا يبقى الأول زائدي الثاني ناقص حاصل ضرب الأول في
+
+70
+00:08:10,290 --> 00:08:18,590
+الثاني كل هذا بده سوى مين؟ بده سوى ال A itselfطيب
+
+71
+00:08:18,590 --> 00:08:24,110
+احنا بنشتغل في مين؟ في rational numbers اعداد
+
+72
+00:08:24,110 --> 00:08:30,770
+جذرية عادية اذا هذا لو جبت عند هذا بروح اذا هذا
+
+73
+00:08:30,770 --> 00:08:37,490
+هيعطيني ما يأتي ان ال E نقص ال E في ايه؟ بيكون سوى
+
+74
+00:08:37,490 --> 00:08:39,490
+كده؟ بيكون سوى Zero
+
+75
+00:08:45,960 --> 00:08:52,440
+يبقى هذا معناه ان ال E في واحد ناقص ال A يبقى يسوى
+
+76
+00:08:52,440 --> 00:08:57,320
+Zero يبقى هذا معناه ان ال E يسوى Zero على واحد
+
+77
+00:08:57,320 --> 00:08:58,440
+ناقص ال A
+
+78
+00:09:02,280 --> 00:09:08,840
+لأن لو كان الواحد موجود لأصبح الـ E Undefined يبقى
+
+79
+00:09:08,840 --> 00:09:17,900
+هذا معناته كم؟ Zero يبقى هنا سواء الـ E Identity
+
+80
+00:09:17,900 --> 00:09:31,780
+Element of GS الـ E بده يساوي Zeroطيب يبقى صار ال
+
+81
+00:09:31,780 --> 00:09:36,700
+identity element exist الان بدنا نثبت ان ال
+
+82
+00:09:36,700 --> 00:09:43,100
+inverse element كذلك ماله exist لذلك بداجي اقول
+
+83
+00:09:43,100 --> 00:09:53,060
+هنا النقطة الثالثة والاخيرة let B be the inverse
+
+84
+00:09:53,060 --> 00:09:57,780
+element of
+
+85
+00:09:58,350 --> 00:10:08,190
+أي اللي موجودة في g then a star b يسوى b star a
+
+86
+00:10:08,190 --> 00:10:13,990
+يسوى ال identity element اللي هو مين ال zero هاخد
+
+87
+00:10:13,990 --> 00:10:22,910
+أي واحدة فيهميبقى a star بي بدي ساوي a زائد بي
+
+88
+00:10:22,910 --> 00:10:29,430
+ناقص ال a بي بدي ساوي قداش بدي ساوي zero طلعلي
+
+89
+00:10:29,430 --> 00:10:35,510
+لهذه أنا ببحث عن مين عن بي إذا بدي أخلي بي في
+
+90
+00:10:35,510 --> 00:10:40,180
+ناحية والباقي كله في ناحية تانيةيبقى هذه ايش
+
+91
+00:10:40,180 --> 00:10:48,890
+هتعطيني هتعطيني ان ال a يساوي a في b ناقص bأو الـ
+
+92
+00:10:48,890 --> 00:10:56,590
+A بدي ساوي اللي هو A ناقص واحد في B أو الـ B بدي
+
+93
+00:10:56,590 --> 00:11:03,390
+ساوي A على A ناقص واحد يبقى هذا الشكل ال inverse
+
+94
+00:11:03,390 --> 00:11:12,150
+element يبقى B تساوي A على A ناقص واحد is the
+
+95
+00:11:12,150 --> 00:11:15,330
+inverse element
+
+96
+00:11:17,140 --> 00:11:26,860
+of a اللي موجود في main في g طب ايش رأيك انا جبت
+
+97
+00:11:26,860 --> 00:11:31,160
+ال zero element و جبت ال inverse element حابب
+
+98
+00:11:31,160 --> 00:11:37,220
+اتأكد شغلي هذا صح ولا لأ انا بدعي انه صح 100% لكن
+
+99
+00:11:37,220 --> 00:11:43,020
+حابب اتأكد حابب اتأكد كيف لو جبت a star zero لازم
+
+100
+00:11:43,020 --> 00:11:48,470
+يعطيني mainالـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+101
+00:11:48,470 --> 00:11:48,690
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+102
+00:11:48,690 --> 00:11:50,030
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+103
+00:11:50,030 --> 00:11:53,870
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+104
+00:11:53,870 --> 00:11:53,870
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+105
+00:11:53,870 --> 00:11:53,870
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+106
+00:11:53,870 --> 00:11:53,970
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+107
+00:11:53,970 --> 00:11:57,170
+أصح أو لا؟ الـ A أصح أو لا؟ الـ A أصح أو لا؟ الـ A
+
+108
+00:11:57,170 --> 00:12:01,620
+أصح أو لا؟ الـ A أصح أو لايبقى أنا بناء عليه بقدر
+
+109
+00:12:01,620 --> 00:12:11,480
+أقول رص و هكذا ال g و ال star is a group لكن لو
+
+110
+00:12:11,480 --> 00:12:16,280
+جيت في ال ه مش هيك بدأ أتأكد من صحة كلامي بداجي
+
+111
+00:12:16,280 --> 00:12:23,600
+أخد a star is zeroهذا لازم يطلع جداش a مشانيك
+
+112
+00:12:23,600 --> 00:12:29,500
+بالكلام الصحيح يبقى هذا الكلام بده يساوي a زائد
+
+113
+00:12:29,500 --> 00:12:37,320
+zero ناقص a في zeroطبعا هدف zero و هدف zero يبقى
+
+114
+00:12:37,320 --> 00:12:42,660
+الجواب قداش يبقى الجواب a وهو المطلوب بالمثل
+
+115
+00:12:42,660 --> 00:12:50,860
+similarly similarly ال zero star a بده يساوي ال a
+
+116
+00:12:50,860 --> 00:12:59,860
+and بده اخد a star bأنا ادعيت ان ب هو معكوس ال a
+
+117
+00:12:59,860 --> 00:13:03,740
+يبقى لما انا اعمل star في مابينهما لازم يطلع ال
+
+118
+00:13:03,740 --> 00:13:08,100
+identity element اللي هو mean ال zero يبقى هذا
+
+119
+00:13:08,100 --> 00:13:15,820
+الكلام بده يساوي a star ب هي موجودة عندى a على a
+
+120
+00:13:15,820 --> 00:13:21,800
+minus ال oneيبقى حسب التعريف تبع الـ star هذا بده
+
+121
+00:13:21,800 --> 00:13:29,900
+يساوي العدد الأول زائد العدد الثاني ناقص حاصل
+
+122
+00:13:29,900 --> 00:13:39,370
+ضربهما تمام؟ طيب هذا الكلام يساويلو حتى المقامات
+
+123
+00:13:39,370 --> 00:13:46,370
+للكل بصير a ناقص واحد بصير هنا a في a ناقص واحد
+
+124
+00:13:46,370 --> 00:13:55,280
+زائد ال a ناقص ال a تربيةهذه لو فكيتها بيصير a
+
+125
+00:13:55,280 --> 00:14:03,580
+تربيع ناقص ال a زائد ال a ناقص ال a تربيع كله على
+
+126
+00:14:03,580 --> 00:14:12,340
+a ناقص واحد أظن كده البسط هذا بيطلع0 على a-1 يبقى
+
+127
+00:14:12,340 --> 00:14:17,560
+يساوي 0 يبقى فعلا هذا هو معكوس ال element اللي
+
+128
+00:14:17,560 --> 00:14:21,800
+موجود هنا طبعا لم ناخد في الأمثلة السابقة العشرة
+
+129
+00:14:21,800 --> 00:14:27,020
+أمثلة السابقة ولا مثال أخدنا بهذا الشكل لأن كان من
+
+130
+00:14:27,020 --> 00:14:30,720
+السهل أو بكل بساطةكان ممكن نجيب ال identity
+
+131
+00:14:30,720 --> 00:14:34,700
+element و ال inverse element بس لما صارت ال
+
+132
+00:14:34,700 --> 00:14:39,480
+operation هذا فيها نوع من التعقيد صارت عملية
+
+133
+00:14:39,480 --> 00:14:44,540
+الحسابات بهذا الشكل دقيقة يبقى بناء عليه لو أعطاك
+
+134
+00:14:44,540 --> 00:14:48,600
+أي binary operation بعد ذلك فيها تعقيد بدك تمشي
+
+135
+00:14:48,600 --> 00:14:51,680
+بنفس ال tacticبعد ذلك تفترض ان عندك ال identity
+
+136
+00:14:51,680 --> 00:14:56,400
+element تستنتج ما هو شكله بعد ذلك تفترض ان عندك
+
+137
+00:14:56,400 --> 00:15:01,760
+inverse element وتستنتج ما هو شكل هذا ال inverse
+
+138
+00:15:01,760 --> 00:15:09,480
+element إذا هذا المثال هو نوع جديد من التفكير لكنه
+
+139
+00:15:09,480 --> 00:15:17,700
+تطبيق مباشر عالميا على هذه الخاصةالان بنعطي مثال
+
+140
+00:15:17,700 --> 00:15:24,040
+اخر على ال groups لكن هذا المثال very important كل
+
+141
+00:15:24,040 --> 00:15:28,500
+section هتلاقي طالع لك main سؤال على هذا المثال او
+
+142
+00:15:28,500 --> 00:15:32,840
+معلومة على هذا المثال او ما إلى ذلك المثال هذا
+
+143
+00:15:32,840 --> 00:15:40,320
+بنسميه symmetry of a square او dihedral group يبقى
+
+144
+00:15:40,320 --> 00:15:41,920
+المثال الثاني عشر
+
+145
+00:16:07,260 --> 00:16:15,580
+الكتب بتسميها the dihedral
+
+146
+00:16:18,660 --> 00:16:29,480
+the dihedral group of order اتنين في اربعة اللي هو
+
+147
+00:16:29,480 --> 00:16:30,800
+بده يسوى تمانية
+
+148
+00:16:38,290 --> 00:16:42,490
+نجي للتسمية اللي احنا كاتبينها لـ group D4 لـ
+
+149
+00:16:42,490 --> 00:16:49,790
+symmetries of A² تماثل المربع تماثل المربع هذا خاص
+
+150
+00:16:49,790 --> 00:16:59,430
+بـ D4 لكن in general لو كان D2 D3 D4 D5 D6 DN
+
+151
+00:16:59,430 --> 00:17:06,420
+بسميها الـ dihydral group of order 2Nيعني الرقم
+
+152
+00:17:06,420 --> 00:17:11,140
+اللي عندك هدا دائما و قبلها بتضربه في كده؟ في
+
+153
+00:17:11,140 --> 00:17:16,080
+اتنين اللي انا بدنا نشوف ليش سمناها symmetries of
+
+154
+00:17:16,080 --> 00:17:22,380
+a² هذي ال group انت نشأ نتيجة لحركة مين؟ لحركة
+
+155
+00:17:22,380 --> 00:17:30,680
+مربع طب ايش معنى ايش معنى دايهدرال بالعربي؟
+
+156
+00:17:30,680 --> 00:17:37,480
+دايهدرال يعني ثناء السطوحيعني إله وجهين أو إله
+
+157
+00:17:37,480 --> 00:17:43,340
+سطحين كما ستراونا بعد قليل من خلال الشغل شوف يا
+
+158
+00:17:43,340 --> 00:17:49,340
+سيدي أنا بدي أخد مربع المربع هذا بالشكل اللي عندنا
+
+159
+00:17:49,340 --> 00:17:54,140
+هنا و بدي أعطيه تسميات مشان نتقيد بالتسمية اللي
+
+160
+00:17:54,140 --> 00:17:59,820
+بالكتاب مشان ماصيرش مشاكل بيننا وبينه يبقى P وهنا
+
+161
+00:17:59,820 --> 00:18:03,300
+G وهنا B
+
+162
+00:18:09,690 --> 00:18:16,690
+هذا المربع بدى اعمل فيه دورانات يعني انت قدامك وجه
+
+163
+00:18:16,690 --> 00:18:21,890
+مظبوط لكن الوجه في ناحية التانية احيانا بدى اخلي
+
+164
+00:18:21,890 --> 00:18:26,590
+هذا الوجه يبين و احيانا بدى اخلي الوجه الثاني و
+
+165
+00:18:26,590 --> 00:18:34,100
+احيانا بدى اخلي نفس الوجه بس بدى اغير مواقعيبقى
+
+166
+00:18:34,100 --> 00:18:40,860
+هنا لو جيت قلت عملت rotation بزاوية مقدرها zero
+
+167
+00:18:40,860 --> 00:18:48,720
+درجة هل سيتغير وضع هذا المربع؟ لأ يبقى بداجي أسمي
+
+168
+00:18:48,720 --> 00:18:57,140
+حاجة عندي R node روتيشن
+
+169
+00:18:57,140 --> 00:19:05,570
+of zero درجةrotation of zero درجة يبقى دوران بزيرو
+
+170
+00:19:05,570 --> 00:19:11,390
+درجة يبقى هنا بده أسميها no change in position
+
+171
+00:19:11,390 --> 00:19:19,630
+مافيش تغيير في المكان no change in position مافيش
+
+172
+00:19:19,630 --> 00:19:24,850
+تغيير في وضع المربع يبقى المربع هيصير عندنا بالشكل
+
+173
+00:19:24,850 --> 00:19:34,480
+اللي عندنا هذا هذا P هذا Gهذا P وهذا W وهذا R نوت
+
+174
+00:19:34,480 --> 00:19:39,200
+يعني ماصارش دوران يبقى بدي أسبب هذا الوضع الأساسي
+
+175
+00:19:39,200 --> 00:19:47,400
+طيب بدي أجي ل R تسعين R تسعين درجة هو rotation of
+
+176
+00:19:47,400 --> 00:19:53,380
+تسعين درجة بس تسعين ممكن مع أقارب الساعة وممكن ضد
+
+177
+00:19:53,380 --> 00:19:58,980
+أقارب الساعة أنا بدي أمشي counter clockwiseيبقى
+
+178
+00:19:58,980 --> 00:20:06,460
+هنا هذا counter clockwise
+
+179
+00:20:06,460 --> 00:20:15,340
+ضد عقارب الساعة يبقى هذا وضع المربع هذا P وهذا G
+
+180
+00:20:15,340 --> 00:20:23,920
+وهذا P وهذا W وهنا اتحركتبزاوية تسعين درجة يبقى
+
+181
+00:20:23,920 --> 00:20:29,940
+الشكل المربع هيصير على الشكل اللي عندنا ال P هتيجي
+
+182
+00:20:29,940 --> 00:20:36,780
+مكان G و G هتيجي مكان P و P مكان ال W و ال W مكان
+
+183
+00:20:36,780 --> 00:20:42,500
+مين مكان ال P يبقى ال P هتيجي هنا و ال G هتيجي هنا
+
+184
+00:20:42,500 --> 00:20:49,650
+و ال P هتيجي هنا و ال W هتيجي هنايبقى هاي دوران
+
+185
+00:20:49,650 --> 00:20:57,070
+rotation بزاوية 90 درجة طب لو خلت الدوران R 180
+
+186
+00:20:57,070 --> 00:21:02,770
+درجة يبقى rotation of 180 درجة برضه counter
+
+187
+00:21:02,770 --> 00:21:08,690
+clockwise اللي هو ضد عقارب الساعة يبقى هذه حضريها
+
+188
+00:21:08,690 --> 00:21:13,690
+الرمزي التالي هذا المربع الأصلي اللي عندنا هذا P
+
+189
+00:21:13,690 --> 00:21:21,430
+وهذا G وهذا ال Bو هذه ال W وهنا Rotation بزاوية
+
+190
+00:21:21,430 --> 00:21:29,090
+مقدرها 180 درجة بدي اجي عند المربع التالي من هنا
+
+191
+00:21:29,090 --> 00:21:33,170
+لهنا قولنا بقداش تسعين اذا بدي امشي كمان من هنا
+
+192
+00:21:33,170 --> 00:21:39,370
+كمان تسعين اذا P بدي اتيجي هنا تمام؟ الان P بدي
+
+193
+00:21:39,370 --> 00:21:45,070
+اتيجي هنا يبقى G بعد ال P يبقى ال G بدي اتيجي هنا
+
+194
+00:21:45,520 --> 00:21:52,040
+الـ P بدها تيجي هنا الـ W بدها تيجي هنا تمام؟ يبقى
+
+195
+00:21:52,040 --> 00:21:59,700
+هذا دوران بزاوية مقدرها 180 درجة بدها GR 270 درجة
+
+196
+00:21:59,700 --> 00:22:05,680
+روتيشن ب 270 counter clockwise يبقى هذا المربع
+
+197
+00:22:05,680 --> 00:22:14,850
+اللي عندنا الأصلي هذا P وهذا Gوهذا P وهذا W يصير
+
+198
+00:22:14,850 --> 00:22:25,090
+بالشكل اللي عندنا هذا نتيجة لل R 270 درجة P لما جت
+
+199
+00:22:25,090 --> 00:22:31,310
+هنا كان 180 270 بدنا ايه؟ كمان واحدة إذا ال P بدها
+
+200
+00:22:31,310 --> 00:22:35,970
+تيجي هناالـ G لما جت هنا كان مية و تمانية يبقى
+
+201
+00:22:35,970 --> 00:22:41,450
+بتيجي مكان ال P يبقى هنا بده يجين ال G و هنا بده
+
+202
+00:22:41,450 --> 00:22:48,470
+يجين ال P ال P و هنا ال W يبقى هاي ال متين
+
+203
+00:22:48,470 --> 00:22:53,710
+والسبعين درجة طب لو تلتنية و ستين درجة برجع كما
+
+204
+00:22:53,710 --> 00:23:00,740
+كنت مظبوطيبقى بتطلع الارنود اللى فوق طب انا بدى
+
+205
+00:23:00,740 --> 00:23:08,160
+اعمل شغل تانى بدى الان اخد دوران حول خط أفقى
+
+206
+00:23:08,160 --> 00:23:14,840
+ودوران حول خط رأسى ودوران حول من؟ حول الأقطار
+
+207
+00:23:32,710 --> 00:23:40,710
+واللي بقى لكن الان بدي أخد H اللي هو عبارة عن
+
+208
+00:23:40,710 --> 00:23:45,510
+rotation about
+
+209
+00:23:45,510 --> 00:23:49,770
+a
+
+210
+00:23:49,770 --> 00:24:00,270
+horizontal line about a horizontal line
+
+211
+00:24:01,580 --> 00:24:08,960
+حوالين خط مستقيم هذا المربع اللي عندك وهذه P وهذه
+
+212
+00:24:08,960 --> 00:24:20,260
+G وهذه P وهذه W هنا هذه الهيمين ال H بدي أجيك
+
+213
+00:24:20,260 --> 00:24:26,490
+المربع اللي عندك هناخلّي بالك هنا انا بدي ادخلي
+
+214
+00:24:26,490 --> 00:24:32,050
+الدوران افو الدوران horizontal حوالين الخط الأحمر
+
+215
+00:24:32,050 --> 00:24:39,690
+هذا بزاوية قداش rotation مية و تمانين درجة مية و
+
+216
+00:24:39,690 --> 00:24:45,250
+تمانين درجة about a horizontal line يبقى انا لما
+
+217
+00:24:45,250 --> 00:24:50,630
+اجي مية و تمانين درجة ال G وين بتصير مكان ال P و
+
+218
+00:24:50,630 --> 00:24:58,330
+ال B و ال Wيعني بده يظهر الوجه الآخر للمربع السطح
+
+219
+00:24:58,330 --> 00:25:01,470
+اللي اقبلنا هذا بده يصير هذا في الناحية التانية و
+
+220
+00:25:01,470 --> 00:25:04,550
+اللي كان الناحية التانية بده يصير في وجهنا هو من
+
+221
+00:25:04,550 --> 00:25:10,210
+هنا سمناه dihydral ثنائي السطوح السطح اللي كان مش
+
+222
+00:25:10,210 --> 00:25:13,570
+ظاهر بده يصير هو الظاهر والسطح اللي كان ظاهر بده
+
+223
+00:25:13,570 --> 00:25:18,620
+يصير ماله مش ظاهر سمناه من هنا ثنائي السطوحيبقى
+
+224
+00:25:18,620 --> 00:25:23,780
+دوران حوال الخط بده يصير عندنا مين؟ بده يصير هذه G
+
+225
+00:25:23,780 --> 00:25:35,000
+وتحت هنا P وهنا B وهنا W طيب مافيش أحسن حد من حد
+
+226
+00:25:35,000 --> 00:25:40,140
+مدام صورة دوران أفق بده يخلي دوران حوال الخط
+
+227
+00:25:40,140 --> 00:25:45,880
+الرأسي يبقى لو جيت سميت ال verticalاللي هو
+
+228
+00:25:45,880 --> 00:25:55,740
+rotation بمية و تمانين درجة about a vertical line
+
+229
+00:25:55,740 --> 00:26:01,980
+حوالين الخط الرأسي يبقى هذا المربع اللي عندنا هذا
+
+230
+00:26:01,980 --> 00:26:12,860
+P هذا G هذا W هذا P وهذا هو الخط الرأسيالـ
+
+231
+00:26:12,860 --> 00:26:19,200
+vertical يبقى بناء عليه بدي يصبح عندنا المربع على
+
+232
+00:26:19,200 --> 00:26:24,740
+الشكل التالي هذا V بدي يصير المربع بالشكل اللي
+
+233
+00:26:24,740 --> 00:26:30,120
+عندنا هنا ال P بدي تيجي مكان ال W و ال W مكان ال P
+
+234
+00:26:30,120 --> 00:26:35,820
+يعني بدي نجلي برأسي تمام؟ يعني زي ما تقول هاي هذا
+
+235
+00:26:35,820 --> 00:26:40,860
+المربع لما نجلي برأسي حوالين نص بدي أصير دوران فوق
+
+236
+00:26:40,860 --> 00:26:44,670
+و تحتقبل كان دوران اللي قبل هي أمين و أشمال لكن هي
+
+237
+00:26:44,670 --> 00:26:49,510
+منذ عامة الدوران فوق أو تحت معناته ال P بده تيجي
+
+238
+00:26:49,510 --> 00:26:58,590
+مكان ال W و ال W مكان ال P تمام؟ و ال B بده تيجي
+
+239
+00:26:58,590 --> 00:27:04,930
+مكان ال G و ال G مكان ال B يبقى هذا اسمه vertical
+
+240
+00:27:04,930 --> 00:27:12,390
+rotation ب180 درجةطيب بدي أخلي دوران حوالين القطر
+
+241
+00:27:12,390 --> 00:27:19,210
+الرئيسي يبقى الحالة السابعة بدي أسميها اللي هي دي
+
+242
+00:27:19,210 --> 00:27:24,990
+يبقى هذه rotation 180
+
+243
+00:27:24,990 --> 00:27:33,910
+درجة about the mean diagonal
+
+244
+00:27:36,260 --> 00:27:45,160
+حوالين القطر الرئيسي main main
+
+245
+00:27:45,160 --> 00:27:50,960
+diagonal حوالين القطر الرئيسي تمام يبقى المربع كان
+
+246
+00:27:50,960 --> 00:27:58,080
+بالشكل اللي عندنا هذا وهذه الرموز كما هي هنا P هنا
+
+247
+00:27:58,080 --> 00:28:08,270
+G هنا Bهنا اللي هو W هذه بده يسميها اللي هو الرمز
+
+248
+00:28:08,270 --> 00:28:13,450
+D يبقى بده يصير المربع اللي عندنا على الشكل التالي
+
+249
+00:28:13,450 --> 00:28:20,610
+لما أقول يا شباب هذا هو القطر الرئيسي يبقى عندي
+
+250
+00:28:20,610 --> 00:28:26,110
+الدوران هل P و B بيحصل لهم حاجة يبقى هدول بيبقوا
+
+251
+00:28:26,110 --> 00:28:33,620
+ثوابت زي ما هميبقى هذه بيبقى P و هذه بي كما هي
+
+252
+00:28:33,620 --> 00:28:39,920
+مافيش تغيير هالتغيير بيصير بين مين ومين يبقى ال W
+
+253
+00:28:39,920 --> 00:28:45,300
+بتيجي هنا و ال G بتيجي هنا طيب بدنا نيجي أخر حاجة
+
+254
+00:28:45,300 --> 00:28:50,660
+اللي هي D prime اللي هو ال rotation about the
+
+255
+00:28:50,660 --> 00:28:59,000
+other diagonal على القطر الآخريبقى باجي بقوله هذا
+
+256
+00:28:59,000 --> 00:29:09,540
+المربع و هذا ال P G P G و هنا اللي هي ال P و هنا
+
+257
+00:29:09,540 --> 00:29:16,440
+من ال W يبقى هذه اللي هو D Prime المربع سيأخذ
+
+258
+00:29:16,440 --> 00:29:23,180
+الشكل التالي الدوران حوالين القطر الأخر اللي هو
+
+259
+00:29:23,180 --> 00:29:30,070
+القطر اللي عندنا هذا يبقى ال Gو ال P و ال W عند
+
+260
+00:29:30,070 --> 00:29:36,130
+الدوران تبقى كما هي اللى بده يتغير بس مين ال P و
+
+261
+00:29:36,130 --> 00:29:42,750
+ال B يبقى بده يصير ال P و هنا مين و هنا ال P
+
+262
+00:29:42,750 --> 00:29:49,410
+العناصر اللى شايفهم قدامك بيكونولي ال dihydral
+
+263
+00:29:49,410 --> 00:29:55,610
+group D4 و زى ما انت شايف فيها ستة و اتنين ثمانية
+
+264
+00:29:55,610 --> 00:30:03,440
+عناصريبقى الان الديهيدرالي جروب D4 عناصرها ال
+
+265
+00:30:03,440 --> 00:30:11,240
+identity element اللي حدله الرمز R0 و بعدها R90 و
+
+266
+00:30:11,240 --> 00:30:12,560
+R180
+
+267
+00:30:16,180 --> 00:30:25,640
+وR2O70 وH وV وD وD prime هي ثمانية عناصر تبعات D4
+
+268
+00:30:25,640 --> 00:30:31,140
+طيب D3 يا شباب كام عنصر فيها ستة كله ضرب في اتنين
+
+269
+00:30:31,140 --> 00:30:36,020
+دي عشرة فيها عشرين عنصر دي تلاتين فيها ستين عنصر و
+
+270
+00:30:36,020 --> 00:30:42,040
+هكذا تمام يبقى هذه ايه هذه ال group اللي هي D4
+
+271
+00:30:42,530 --> 00:30:49,710
+تعالى نبدأ ببعض الملاحظات على هذه الـ group خلّينا
+
+272
+00:30:49,710 --> 00:30:55,470
+نبدأ بالاكتشاف هذا ال identity element R تسعين هذي
+
+273
+00:30:55,470 --> 00:31:01,870
+بدي اعمل كم مرة بهذه الطريقة حتى ارجع للاصل اربع
+
+274
+00:31:01,870 --> 00:31:07,050
+مرات يبقى هذه معناته R أس أربع عارف تسعين أس أربع
+
+275
+00:31:07,050 --> 00:31:14,610
+بدي أساوي من ال identityطيب و الـ 270 برضه كمان
+
+276
+00:31:14,610 --> 00:31:22,170
+أربع مرات يبقى هنا باجي بقوله some properties
+
+277
+00:31:22,170 --> 00:31:26,310
+of default
+
+278
+00:31:28,510 --> 00:31:35,910
+الخاصية الأولى ان R تسعين أس أربعة هي R ميتين
+
+279
+00:31:35,910 --> 00:31:40,850
+وسبعين أس أربعة اللي تساوي ال identity اللي هو
+
+280
+00:31:40,850 --> 00:31:49,790
+main R node الخاصية الثانية R مية و تمانين تربيع
+
+281
+00:31:54,620 --> 00:31:59,400
+أرنود الأصلية اتش
+
+282
+00:31:59,400 --> 00:32:07,020
+تربيع ارنود الأصلية برضه الرد بترجع كما كانت مظبوط
+
+283
+00:32:07,020 --> 00:32:14,520
+طيب ادي تربيع ال V تربيع نفسها
+
+284
+00:32:14,520 --> 00:32:22,480
+ال identity طب ادي تربيع طيب ادي prime تربيع
+
+285
+00:32:25,950 --> 00:32:29,690
+يبقى الار مية و تمانية تربيع هي ال identity اللى
+
+286
+00:32:29,690 --> 00:32:35,790
+قلت بديش اعطيها ايه بدي اسميها ارنود تمام طيب و ال
+
+287
+00:32:35,790 --> 00:32:39,610
+H تربيع بتسوي ارنود و ال V تربيع ليش ان لو لفيت
+
+288
+00:32:39,610 --> 00:32:44,390
+المربع كمان مرة برجع كمان كنت مظبوط يبقى من هنا
+
+289
+00:32:44,390 --> 00:32:51,510
+هذه كلها بالارنود طيب ايش رايكلو جيت قلت ال R مية
+
+290
+00:32:51,510 --> 00:32:57,190
+و تمانين تربية بده يساوي ال identity وضربت الطرفين
+
+291
+00:32:57,190 --> 00:33:03,190
+في R مية و تمانين inverse قداش بطلع يعني لما أقول
+
+292
+00:33:03,190 --> 00:33:08,950
+G تربية يساوي E يبقى لو ضربت inverse الطرفين بصير
+
+293
+00:33:08,950 --> 00:33:14,780
+الطرف اليمين G inverse و الطرف الشمالجي واحدة بس
+
+294
+00:33:14,780 --> 00:33:18,700
+يبقى بصير جي يساوي جي انفرست معناته ال element
+
+295
+00:33:18,700 --> 00:33:24,540
+يساوي مين؟ يساوي معكوسه إذا للعناصر اللي عندك واحد
+
+296
+00:33:24,540 --> 00:33:29,780
+اتنين تلاتة اربعة خمسة كل عنصر يساوي ايه؟ يساوي
+
+297
+00:33:29,780 --> 00:33:38,580
+معكوسه يبقى هذا معناه ان ال R مية و تمانينيساوي
+
+298
+00:33:38,580 --> 00:33:44,700
+الار مية و تمانين inverse واللي بعدها ال H بده
+
+299
+00:33:44,700 --> 00:33:50,720
+يساوي ال H inverse و ال V بده يساوي ال V inverse و
+
+300
+00:33:50,720 --> 00:33:55,280
+ال D بده يساوي ال D inverse و ال D prime بده يساوي
+
+301
+00:33:55,280 --> 00:34:02,820
+D prime inverse هذا
+
+302
+00:34:02,820 --> 00:34:07,760
+كويسهذه المعلومات ديلوا بالك منها ان شاء الله ال
+
+303
+00:34:07,760 --> 00:34:11,580
+section جاي نبدأ ال order لل element و ال order لل
+
+304
+00:34:11,580 --> 00:34:17,300
+group ال order لل element أقل رقم بيرفعه عدد صحيح
+
+305
+00:34:17,300 --> 00:34:21,260
+موجة بيرفعه نقص بيعطيني ال identity يعني معناته
+
+306
+00:34:21,260 --> 00:34:25,340
+بعد قليل المحاضرة القادمة يمكن ندخلها و يمكن لأ
+
+307
+00:34:39,090 --> 00:34:47,530
+طيب بدنا نروح لخاصية تالتة غير هذه الخواصلو ضربت
+
+308
+00:34:47,530 --> 00:34:52,470
+او قبل ان اضرب ايش رأيك هدول الاربع واحد اتنين
+
+309
+00:34:52,470 --> 00:34:57,470
+تلات اربع اليست هذه حركة دورانية counter clockwise
+
+310
+00:34:57,470 --> 00:35:08,310
+يبقى هدول الاربع حالات كلهم بسميهم rotation دوران
+
+311
+00:35:09,580 --> 00:35:14,720
+و ممكن اختصارا اديهم الرمز R طب والاربع حالات اللي
+
+312
+00:35:14,720 --> 00:35:21,300
+بعدهم الاتنين هدول و الاتنين هدول اسم من عكاس
+
+313
+00:35:21,300 --> 00:35:29,140
+reflection يبقى هدول بسميهم reflection و هدول
+
+314
+00:35:29,140 --> 00:35:36,760
+اتنين كمان reflection تمام
+
+315
+00:35:36,760 --> 00:35:45,190
+تمام طيبعشان نختار دوران مع reflection اشوف ايه
+
+316
+00:35:45,190 --> 00:35:49,750
+يعطينا دوران يعني حاصل ضرب اي دوران من الدورانات
+
+317
+00:35:49,750 --> 00:35:53,790
+هدول في اي reflection من ال reflections الأربعة
+
+318
+00:35:53,790 --> 00:35:58,990
+اشوف ايه يعطينا دوران هل بيعطينا rotation دوران و
+
+319
+00:35:58,990 --> 00:36:04,730
+الله بيعطينا reflection تعالي ناخد اختارلك اي رقم
+
+320
+00:36:04,730 --> 00:36:08,970
+من الدورانات اللي عندناو بدي اختار اي reflection
+
+321
+00:36:08,970 --> 00:36:14,210
+منهم و اضرب اتنين في بعض ابسط الحالات لو اخد ر
+
+322
+00:36:14,210 --> 00:36:19,230
+تسعين بدي
+
+323
+00:36:19,230 --> 00:36:25,480
+اضربها مثلا في Hفي أول دوران أشوف إيش بيعطينا وين
+
+324
+00:36:25,480 --> 00:36:31,320
+ال H اللي عندي طلع لل H هي ال H يبقى هذه ال H اللي
+
+325
+00:36:31,320 --> 00:36:35,880
+عندنا هذه إيش بدي أعمل لها بدي أعمل لها دوران
+
+326
+00:36:35,880 --> 00:36:41,760
+بتسعين درجة أشوف إيش هتعطينا هذه يبقى هذه ال H هه
+
+327
+00:36:41,760 --> 00:36:48,780
+بدي أسوي لها دوران بتسعين درجة لما أسوي لها دوران
+
+328
+00:36:48,780 --> 00:36:53,790
+بتسعين درجة يبقى هنا بدها TGGوهنا بدها تجيني P
+
+329
+00:36:53,790 --> 00:36:59,930
+وهنا بدها تجي W وهنا بدها تجي تجيني B صحيح ولا لا
+
+330
+00:36:59,930 --> 00:37:06,410
+طيب بده أشوف هذه مين منهم تعالي نطلع نشوف نشوف
+
+331
+00:37:06,410 --> 00:37:12,590
+تعالي ال D هذي هيها ولا لا هي؟ لأ هي هذي؟ اه هاي
+
+332
+00:37:12,590 --> 00:37:18,590
+GPW مية المية يبقى حاصل الضرب هذا بده يسوي قداش D
+
+333
+00:37:18,590 --> 00:37:26,640
+Prime تمام؟طيب واحد يقول ليه طيب لو أخدت R تسعين
+
+334
+00:37:26,640 --> 00:37:32,100
+بدل ما أخدت ال H خدلي ال V هشوف إيش بده يعطيني هذا
+
+335
+00:37:32,100 --> 00:37:37,180
+حاصل الضرب بقوله أه وين ال V هاي ال V اللي عندي
+
+336
+00:37:37,180 --> 00:37:45,610
+تمام؟ال V هذه بدي اهي ال V بدي اعملها دوران بمقدار
+
+337
+00:37:45,610 --> 00:37:51,930
+الواحد فقط لا غير يعني دوران تسعين يبقى هذه هتاخد
+
+338
+00:37:51,930 --> 00:38:00,770
+الشكل التالف هذه ال B وهذه ال G وهذه ال P اعلي فوق
+
+339
+00:38:00,770 --> 00:38:06,530
+استنى استنى استنى استنى يا شيخ استنى
+
+340
+00:38:09,060 --> 00:38:15,500
+احنا بدنا V وين ال V هاي ال V تمام يبقى هاد ال V
+
+341
+00:38:15,500 --> 00:38:20,080
+بده أشوف إيش بده يصير لها يبقى هاد بده أصير بالشكل
+
+342
+00:38:20,080 --> 00:38:23,820
+اللي عندنا هنا بده أعملها دوران تسعين يبقى ال W
+
+343
+00:38:23,820 --> 00:38:30,020
+هتيجي هنا و ال P هتيجي هنا و ال G هتيجي هنا و ال P
+
+344
+00:38:30,020 --> 00:38:36,880
+هتيجي هنا بده أشوف هاد مين منهم ديوارينا نشوف يبقى
+
+345
+00:38:36,880 --> 00:38:42,140
+و ب هي تحت و P و G مظبوط يبقى هذا حصلت ضرب بده
+
+346
+00:38:42,140 --> 00:38:46,660
+يعطينا D يبقى هذا reflection و هذا كمان reflection
+
+347
+00:38:46,660 --> 00:38:55,740
+طيب لو جيت أخدت ال R تسعين في من في ال D هذه بده
+
+348
+00:38:55,740 --> 00:39:01,440
+يساوي يبقى وين ال D هيها كويس؟بدي أعمل لها لفة
+
+349
+00:39:01,440 --> 00:39:08,600
+بمقدار تسعين يبقى هذه هتاخد الشكل التالي هنا P
+
+350
+00:39:08,600 --> 00:39:20,240
+وهنا W وهنا P وهنا Gوين ال P و ال W يبقى H ممتاز
+
+351
+00:39:20,240 --> 00:39:25,540
+يدن يبقى هذا ال P W و G P مظبوط يبقى هذا الكلام
+
+352
+00:39:25,540 --> 00:39:32,420
+بده يساوي H بده يساوي H طيب لو جيت قولتلك N R
+
+353
+00:39:32,420 --> 00:39:39,160
+تسعين في D Primeراحة ال H و راحة ال D و هتظلش إلا
+
+354
+00:39:39,160 --> 00:39:44,300
+ال V مظبوط يبقى ده هتلاقيه بده ساوي V يبقى الآن
+
+355
+00:39:44,300 --> 00:39:48,540
+حاصل ضرب rotation ف reflection بيعطينا reflection
+
+356
+00:39:48,540 --> 00:39:53,740
+و أنت بتجري وهي كله دليل عدالة قدامك حتى لو أخدت
+
+357
+00:39:53,740 --> 00:39:59,640
+ال R مية و تمانين برضه بنفس الشيء يبقى هنا باجي
+
+358
+00:39:59,640 --> 00:40:03,840
+بقوله إيش يبقى
+
+359
+00:40:03,840 --> 00:40:04,280
+remark
+
+360
+00:40:07,860 --> 00:40:15,900
+any rotation ضد
+
+361
+00:40:15,900 --> 00:40:26,180
+any reflection بد
+
+362
+00:40:26,180 --> 00:40:27,580
+يساوي reflection
+
+363
+00:40:32,020 --> 00:40:41,980
+طب مدام هيك شفوي شفوي هذا تربيع كده شو ساوي؟
+
+364
+00:40:41,980 --> 00:40:47,260
+ايوة هذا تربيع كدهش؟
+
+365
+00:40:47,260 --> 00:40:52,760
+ارنول مش هذا reflection صار reflection يعني قد اده
+
+366
+00:40:52,760 --> 00:40:56,040
+D prime D prime تربيع بال identity على طول الخط
+
+367
+00:40:56,340 --> 00:40:59,960
+يبقى هذا تربيه بال identity هذا تربيه بال identity
+
+368
+00:40:59,960 --> 00:41:03,580
+هذا تربيه بال identity هذا تربيه بال identity على
+
+369
+00:41:03,580 --> 00:41:07,900
+طول الخط و انت بتجيبها كده يعني هذه هنطلع منها اشي
+
+370
+00:41:07,900 --> 00:41:12,800
+كتير لسه احنا هذه بس نكشات بسيطة مشان تعرف يعني لو
+
+371
+00:41:12,800 --> 00:41:18,880
+قلتلك اي بدي اجي اضرب مثلا R270 في D مثلا كيف بدي
+
+372
+00:41:18,880 --> 00:41:22,950
+اضرب R270 في D؟ بنروح على ال Dو انا دى هى دى
+
+373
+00:41:22,950 --> 00:41:26,910
+ارمتين و سبعين بتخليها تلف اللى هو التلت اماكن و
+
+374
+00:41:26,910 --> 00:41:30,670
+انا بتوصل بشوف مين من هدول بكون جبت الجواب دورى
+
+375
+00:41:30,670 --> 00:41:35,870
+على اى حال هادى راح عمل ليه فيها جدول فى صفحه واحد
+
+376
+00:41:35,870 --> 00:41:39,600
+و تلاتينهدا فيكم معاه كتاب اللى معاه كتاب يفتحلى
+
+377
+00:41:39,600 --> 00:41:43,220
+على صفحة واحد و تلاتين اللى قبل ما ندخل في ال
+
+378
+00:41:43,220 --> 00:41:46,120
+group الشابتر اللى مرضيش هجيبلكم سيطة و أقولكم
+
+379
+00:41:46,120 --> 00:41:49,920
+هعطيكميها من خلال الشابتر القادر يعني مش خليه
+
+380
+00:41:49,920 --> 00:41:54,700
+أفصله لحاله يبقى هذا هو ايه هذا هو من الشابتر
+
+381
+00:41:54,700 --> 00:41:58,610
+السابقلإن ال chapter اللى قبله ماكناش ماخدين حاجة
+
+382
+00:41:58,610 --> 00:42:03,390
+اسم مجروم لكن الأن أخدت هذه كحالة اللى من ال
+
+383
+00:42:03,390 --> 00:42:06,750
+holography جدول عندك في صفحه تواعى و تلاتين حطت
+
+384
+00:42:06,750 --> 00:42:12,110
+التمن عناصر و التمن عناصر و حاصل ضربهم كله يبقى يا
+
+385
+00:42:12,110 --> 00:42:15,730
+ريت هذا تطلعلي على الجدول اللى بتعرف النتائج الدرب
+
+386
+00:42:15,730 --> 00:42:22,870
+كلها بلا استثناء يبقى بداجة أقولك هنا lock the
+
+387
+00:42:22,870 --> 00:42:24,430
+table
+
+388
+00:42:30,080 --> 00:42:36,940
+تعرف باقى الضربيات و كل الشغلات هذه حد
+
+389
+00:42:36,940 --> 00:42:40,800
+بتسأل لي سؤال هنا يا شباب لازلنا في نفس ال section
+
+390
+00:42:40,800 --> 00:42:44,920
+بس بدنا نخش على بعض الشغلات التي تهم خاص ال group
+
+391
+00:42:44,920 --> 00:42:48,980
+لحد هنا بدنا نوقف بالنسبة لمين للأمثلة
+
+392
+00:43:27,730 --> 00:43:34,330
+بنجي لحاجة اسمها ال elementary properties
+
+393
+00:43:34,330 --> 00:43:39,490
+of
+
+394
+00:43:39,490 --> 00:43:47,530
+groups هنعقد
+
+395
+00:43:47,530 --> 00:43:54,670
+اعطي نقاط فيها النقطة الأولى ن هي group g
+
+396
+00:43:58,910 --> 00:44:21,370
+there is only one identity element احنا
+
+397
+00:44:21,370 --> 00:44:25,460
+المرة اللي فاتت لما عرفنا ال groupقلنا لجروب فيها
+
+398
+00:44:25,460 --> 00:44:29,240
+identity element لكن ماقلناش هما اتنين هو تلاتة هو
+
+399
+00:44:29,240 --> 00:44:33,760
+واحد الاخري تمام يبقى الخاصية الأولى من خاصة
+
+400
+00:44:33,760 --> 00:44:38,060
+الجروب بتقولي ال identity element في الجروب يكون
+
+401
+00:44:38,060 --> 00:44:42,490
+وحيدايعني ال group الواحدة لا يوجد فيها الا
+
+402
+00:44:42,490 --> 00:44:47,350
+identity element واحد in a group G there is only
+
+403
+00:44:47,350 --> 00:44:52,490
+one واحد فقط اللي هو identity element طب بدنا نثبت
+
+404
+00:44:52,490 --> 00:44:56,850
+صحة تاذا الكلام مشان نثبت صحة تاذا الكلام مفرض انه
+
+405
+00:44:56,850 --> 00:45:01,410
+عنده ايش اتنين و بثبت ان اتنين هدول مالهم are
+
+406
+00:45:01,410 --> 00:45:10,330
+equal يبقى هنا بداجي اقول assume افترض thatإن الـ
+
+407
+00:45:10,330 --> 00:45:25,050
+E and الـ E prime are two identity elements of
+
+408
+00:45:25,050 --> 00:45:29,930
+the group G then
+
+409
+00:45:29,930 --> 00:45:33,830
+ال
+
+410
+00:45:33,830 --> 00:45:42,880
+A star Eبتساوي الـ A لكل الـ A الموجودة في G
+
+411
+00:45:42,880 --> 00:45:46,300
+مظبوط؟
+
+412
+00:45:46,300 --> 00:45:53,020
+طيب هذا الشيء بيعطيك الان الـ A أسطري أنا حتى الـ
+
+413
+00:45:53,020 --> 00:45:57,860
+E هو ال identity element هنا مظبوط؟ إذا الـ E
+
+414
+00:45:57,860 --> 00:46:02,740
+prime بيكون element عادي صح ولا لأ؟ بالنسبة لأني
+
+415
+00:46:02,740 --> 00:46:05,820
+إذا كان هذا هو ال identity elementيبقى الـ E'
+
+416
+00:46:06,200 --> 00:46:10,620
+بيكون element عادي يبقى بناء على اللي بدي يكون E'
+
+417
+00:46:11,440 --> 00:46:18,420
+أستار E بدي يساوي الـ E' يعني كأنه الـ E' حطيتها
+
+418
+00:46:18,420 --> 00:46:25,620
+مكان مين؟ مكان الـ E الأن لو افترت أن الـ E' هو
+
+419
+00:46:25,620 --> 00:46:36,400
+identity element يبقى and الـ E' أستارلأ لأ بدنا
+
+420
+00:46:36,400 --> 00:46:41,700
+نغيّر هذه يبقى
+
+421
+00:46:41,700 --> 00:46:48,420
+and ال and بدأ ياخد ال a star هو ال identity
+
+422
+00:46:48,420 --> 00:46:55,160
+element يبقى بدأ ياخد a star ال star a بده يسوي
+
+423
+00:46:55,160 --> 00:47:00,440
+من؟ بده يسوي ال a itself يعني هنا أخدت ال a
+
+424
+00:47:00,440 --> 00:47:04,620
+identity element وهنا أخدت ال e prime identity
+
+425
+00:47:04,620 --> 00:47:11,850
+elementيبقى هذا بده يعطينا ايه لكل اللي موجودة في
+
+426
+00:47:11,850 --> 00:47:19,090
+فيجيالأن ال element E موجود في G إذا ينطبق عليه
+
+427
+00:47:19,090 --> 00:47:26,550
+هذه الخاصية يبقى معناته إن ال E prime star E بده
+
+428
+00:47:26,550 --> 00:47:32,530
+يساوي ال E itself طب اتنين هذول الطرف الشمال مش هو
+
+429
+00:47:32,530 --> 00:47:38,210
+نفسه إذا الطرف اليمين هو نفسه إذا هذا بده يعطيلك
+
+430
+00:47:38,210 --> 00:47:45,400
+إن ال E تساوي مينالـ E' هو المطلوب إذا من الآن
+
+431
+00:47:45,400 --> 00:47:49,960
+فصاعدا ال identity element في ال group G يكون
+
+432
+00:47:49,960 --> 00:47:54,680
+وحيدا مافيش غيره إن قلت هو ال zero هو ال identity
+
+433
+00:47:54,680 --> 00:47:58,590
+element إذا لا يوجد غير هذا الصفرإن جدش ال group
+
+434
+00:47:58,590 --> 00:48:02,230
+فيها الواحد ال identity element يبقى الواحد مافيش
+
+435
+00:48:02,230 --> 00:48:09,170
+غيره و هكذا تمام؟ في كمان نقطة تانية ممكن نتعرض
+
+436
+00:48:09,170 --> 00:48:13,590
+إلى الآن بس بتاخد وقت شوية إذا نكتفي بهذا القدر
+
+437
+00:48:13,590 --> 00:48:19,070
+اليوم و نكمل المحاضرة القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c021689b39f2851385b49c9fb113a22f6db1d4d9
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jT-3W_Othuo.srt
@@ -0,0 +1,1503 @@
+1
+00:00:21,720 --> 00:00:25,900
+السلام عليكم شباب إن شاء الله هنكمل الـ .. بعد
+
+2
+00:00:25,900 --> 00:00:30,780
+أستاذ إسماعيل أصدر في مساق جبر الحديث طبعا زي ما
+
+3
+00:00:30,780 --> 00:00:33,060
+أنا عارف و أنتم عارفين أنه أستاذ إسماعيل وصل
+
+4
+00:00:33,060 --> 00:00:37,220
+لسؤال سبعة عشر مناقشة الوحدة الثالثة اللي بتتكلم عن
+
+5
+00:00:37,220 --> 00:00:44,160
+finite group أو subgroups و السؤال 18 الـ finite group
+
+6
+00:00:44,160 --> 00:00:48,020
+زي ما أنت شايف قدامك if H and K are subgroups يعني
+
+7
+00:00:48,020 --> 00:00:52,860
+أي two subgroups من الـ G، H subgroup من الـ G، الـ
+
+8
+00:00:52,860 --> 00:00:56,640
+K subgroup من الـ G المطلوب في السؤال اثبت أن
+
+9
+00:00:56,640 --> 00:01:01,360
+تقاطعه عبارة عن subgroup، معطياتي أن الـ two
+
+10
+00:01:01,360 --> 00:01:04,900
+subgroups H و K مطلوب اثبت أن تقاطعه، ولا الـ two
+
+11
+00:01:04,900 --> 00:01:13,400
+subgroup بيعطيني أيضا subgroup، لو بنرجع للطرق
+
+12
+00:01:13,400 --> 00:01:16,160
+اللي من خلالها بأثبت أنه مجموعة ما عبارة عن
+
+13
+00:01:16,160 --> 00:01:19,940
+subgroup من group، هبدأ بالوضع التقليدي أن اثبت
+
+14
+00:01:19,940 --> 00:01:24,440
+أنه group تحت نفس العملية المعرفة على الـ J اللي
+
+15
+00:01:24,440 --> 00:01:29,240
+هو التعريف، بعد ذلك أخذنا ثلاث طرق الـ one step و الـ
+
+16
+00:01:29,240 --> 00:01:33,120
+two step و الـ finite subgroup test، الـ one step كان
+
+17
+00:01:33,120 --> 00:01:37,300
+بيعتمد على إثبات أن a-b في حالة الجامعة أو a b
+
+18
+00:01:37,300 --> 00:01:41,160
+inverse في حالة ما تكون العملية عملية ضرب، اثبت أن
+
+19
+00:01:41,160 --> 00:01:46,320
+لو الـ a و الـ b موجودين في المجموعة الجزئية أن a-b
+
+20
+00:01:46,320 --> 00:01:51,580
+أو a b inverse موجودة فيها، الـ two step كان يعتمد
+
+21
+00:01:51,580 --> 00:01:57,300
+علي إثبات إن هذه المجموعة مغلقة على العملية
+
+22
+00:01:57,300 --> 00:02:05,200
+وعلى المعكوس طبعا، في شغلة مهمة لازم يكون المجموعة
+
+23
+00:02:05,200 --> 00:02:09,600
+الجزئية اللي أنا بأثبتها هي مجموعة غير خالية لأن
+
+24
+00:02:09,600 --> 00:02:12,420
+ما أقدرش أثبت إن مجموعة خالية هي عبارة عن subgroup
+
+25
+00:02:12,420 --> 00:02:14,360
+بالنسبة للـ finite
+
+26
+00:02:17,930 --> 00:02:22,550
+Test كنا نثبت فيه شرط واحد وهو أن المجموعة مغلقة
+
+27
+00:02:22,550 --> 00:02:28,970
+على العملية، هل بإمكاني استعمل الطريقة الأولى و
+
+28
+00:02:28,970 --> 00:02:35,890
+الطريقة الثانية، First الـ E ينتمي للـ H، الـ E ينتمي
+
+29
+00:02:35,890 --> 00:02:39,990
+للـ K صح ولا لأ، المحايد موجود في الـ H والمحايد
+
+30
+00:02:39,990 --> 00:02:44,670
+موجود في الـ K النتيجة أن E موجود في التقاطع
+
+31
+00:02:44,670 --> 00:02:51,180
+وبالتالي التقاطع الـ two subgroups لا يساوي five
+
+32
+00:02:51,180 --> 00:03:02,500
+اختصارا للوقت هنستعمل الـ one step، now let a و b
+
+33
+00:03:02,500 --> 00:03:08,660
+ينتمي للتقاطع، هذا معناه حسب قوانين الـ set
+
+34
+00:03:08,660 --> 00:03:14,800
+theory أن الـ a و الـ b ينتمي للـ h and الـ a و الـ b
+
+35
+00:03:14,800 --> 00:03:19,820
+ينتمي لمين؟ للـ K، تنساش أن الـ H subgroup و الـ K
+
+36
+00:03:19,820 --> 00:03:27,460
+subgroup، معناه الـ A B inverse موجودة وين في الـ H
+
+37
+00:03:27,460 --> 00:03:33,200
+و موجودة وين في الـ K، الـ A B inverse في الـ H و الـ A
+
+38
+00:03:33,200 --> 00:03:36,260
+B inverse في الـ K، ايه بالـ A B inverse وين موجود
+
+39
+00:03:36,260 --> 00:03:43,490
+موجود في التقاطع، وبالتالي تقاطع مجموعة غير خالية
+
+40
+00:03:43,490 --> 00:03:50,170
+وفي نفس الوقت بتحقق شروط نظرية الـ one step، النتيجة
+
+41
+00:03:50,170 --> 00:04:01,590
+H تقاطع الـ K sub group من الـ G، واضحة هذه؟ واضحة، و
+
+42
+00:04:01,590 --> 00:04:02,470
+الله، بدأت أوضح؟
+
+43
+00:04:05,290 --> 00:04:09,770
+ما أثبتش أن الـ B inverse، الـ H sub group و الـ A و
+
+44
+00:04:09,770 --> 00:04:13,590
+الـ B في الـ H، فـ A B inverse في الـ H، بالـ one step
+
+45
+00:04:13,590 --> 00:04:21,970
+ننتقل لسؤال 20، سؤال 20 يقول اثبت أنه centralizer الـ
+
+46
+00:04:21,970 --> 00:04:28,200
+A هو centralizer الـ A inverse، هذا السؤال ممكن تستعمل
+
+47
+00:04:28,200 --> 00:04:32,240
+أسلوبين للحل، الأسلوب المباشر أن تكتب تعريف
+
+48
+00:04:32,240 --> 00:04:35,400
+المجموعة الأولى و تصل منها لتعريف المجموعة الثانية
+
+49
+00:04:35,400 --> 00:04:39,880
+أو الأسلوب الثاني الخاص بيثبت أنه الـ centralizer A
+
+50
+00:04:39,880 --> 00:04:42,640
+subset من الـ centralizer A inverse و
+
+51
+00:04:42,640 --> 00:04:45,500
+الـ centralizer A inverse subset من الـ centralizer
+
+52
+00:04:45,500 --> 00:04:51,500
+A، أنا بفضل الأسلوب هذا، Centralizer الـ A حسب
+
+53
+00:04:51,500 --> 00:04:56,200
+التعريف هذا عبارة عن كل الـ X في J اللي بيكون
+
+54
+00:04:56,200 --> 00:05:04,460
+commute مع مين؟ مع الـ A، يعني AX بيساوي XA، نشغل على
+
+55
+00:05:04,460 --> 00:05:09,940
+المجموعة نفسها، هذا عبارة عن كل الـ X في الـ J، أضرب
+
+56
+00:05:09,940 --> 00:05:24,620
+ضربًا في المساواة في a inverse، اشتغلت
+
+57
+00:05:24,620 --> 00:05:29,200
+أنا على المساواة اللي جوا ضربت في a inverse من
+
+58
+00:05:29,200 --> 00:05:35,950
+الجهتين، هذا حاسيب معايا كل الـ X في J حيث X A
+
+59
+00:05:35,950 --> 00:05:43,430
+Inverse بدي يساوي A Inverse X، اجرأ تعريف المجموعة
+
+60
+00:05:43,430 --> 00:05:48,010
+هذا يشوف ايش بتاني لك، هو كل الـ X اللي في الـ J اللي
+
+61
+00:05:48,010 --> 00:05:52,790
+بيكون commute مع مين؟ مع الـ A Inverse، وبالتالي هذا
+
+62
+00:05:52,790 --> 00:05:55,910
+عبارة عن Centralizer الـ A Inverse
+
+63
+00:05:59,060 --> 00:06:04,400
+بإمكانك تفصل فيها و X في الأول، فـ X في الثاني بعدين
+
+64
+00:06:04,400 --> 00:06:09,200
+X في الثاني ثم X في الأول و تصل للمطلوب إثباته
+
+65
+00:06:09,200 --> 00:06:14,160
+واضح سؤال
+
+66
+00:06:14,160 --> 00:06:18,300
+23 سنحله
+
+67
+00:06:18,300 --> 00:06:26,030
+قدامك على الشاشة البيضاء هذه، عندي أو هو زي ما أنت
+
+68
+00:06:26,030 --> 00:06:30,730
+شايف معطيني جدول الضرب لـ group J فيها العناصر من
+
+69
+00:06:30,730 --> 00:06:37,610
+واحد لثمانية في عملية معرفة بغض النظر ايش التعريف
+
+70
+00:06:37,610 --> 00:06:42,790
+تبعها أو القول تبعت العملية، أنا بهمني جدول الضرب
+
+71
+00:06:42,790 --> 00:06:46,750
+الموجود قدامي، من خلال هذا الجدول بدي أجيب الـ
+
+72
+00:06:46,750 --> 00:06:52,380
+centralizer لكل عنصر، بدي أجيب الـ center تبع الـ
+
+73
+00:06:52,380 --> 00:06:57,420
+group و بدي أجيب الـ order لكل عنصر، هذا السؤال
+
+74
+00:06:57,420 --> 00:07:02,340
+مهم جدا و كثير من الطلاب كانوا يغلطوا فيه، نبدأ
+
+75
+00:07:02,340 --> 00:07:08,100
+بالفرع الأول find centralizer of each member of G
+
+76
+00:07:08,100 --> 00:07:12,660
+هنبدأ في البداية في الـ identity، من الـ identity؟
+
+77
+00:07:13,910 --> 00:07:17,750
+واضح بالنسبة لي الواحد لإنه واحد مع أي عنصر
+
+78
+00:07:17,750 --> 00:07:25,510
+بيعطيني نفس العنصر، طبعا centerizer الواحد عبارة عن
+
+79
+00:07:25,510 --> 00:07:34,910
+مين؟ الـ group كله، طبعا أنا هستغل شغلة درستها في سؤال
+
+80
+00:07:34,910 --> 00:07:37,930
+الـ 20، يعني أنا لو جبت الـ centralizer الاتنين
+
+81
+00:07:41,820 --> 00:07:46,700
+وعرفت الـ inverse للاتنين، فبكون نفس الـ centralizer
+
+82
+00:07:46,700 --> 00:07:55,740
+نبدأ بالاتنين، هاي الاتنين نبدأ
+
+83
+00:07:55,740 --> 00:08:02,060
+me commute مع الاتنين، أكيد الـ identity والاتنين
+
+84
+00:08:02,060 --> 00:08:08,340
+نفسه لأن العنصر commute مع نفسه، نبدأ الاتنين مع
+
+85
+00:08:08,340 --> 00:08:13,020
+التلاتة، اتنين مع التلاتة كده؟ طيب تلاتة مع الاتنين
+
+86
+00:08:13,020 --> 00:08:19,280
+يكبر، تلاتة مع الأربعة، اتنين مع الأربعة سبعة، و
+
+87
+00:08:19,280 --> 00:08:25,920
+أربعة مع الاتنين، مش موجود، مع الخمسة، اتنين مع الخمسة، و
+
+88
+00:08:25,920 --> 00:08:32,200
+خمسة مع الاتنين، ستة، يكبر، الستة موجود أو الخمسة، طيب
+
+89
+00:08:33,200 --> 00:08:39,100
+الاتنين مع الستة .. الاتنين مع الستة كده؟ خمسة ..
+
+90
+00:08:39,100 --> 00:08:43,700
+الاتنين مع الستة خمسة .. طيب .. ستة مع الاتنين ..
+
+91
+00:08:43,700 --> 00:08:48,060
+ايه بقى برضه الستة موجود .. طيب .. اتنين مع السبعة
+
+92
+00:08:48,060 --> 00:08:52,640
+.. السبعة مع الاتنين .. ما نفعش .. اتنين مع التمانية
+
+93
+00:08:52,640 --> 00:08:57,300
+.. تلاتة .. اتنين أو تمانية مع الاتنين .. ايه بقى
+
+94
+00:08:57,300 --> 00:08:57,880
+بسكرها
+
+95
+00:09:01,430 --> 00:09:06,870
+تعال نشوف مين العنصر اللي بدربه في الاتنين بيعطينا
+
+96
+00:09:06,870 --> 00:09:11,310
+الـ identity، الاتنين يكبر، الـ centralizer الاتنين بدي
+
+97
+00:09:11,310 --> 00:09:14,170
+يساوي الـ centralizer الاتنين inversely ليا، اتنين مش
+
+98
+00:09:14,170 --> 00:09:18,470
+هستفيد من الخاصية هذه، ننتقل على التلاتة
+
+99
+00:09:23,130 --> 00:09:27,810
+أول حاجة الواحد موجود، والتلاتة، حد هيقول ليش
+
+100
+00:09:27,810 --> 00:09:32,450
+ما تعاملتش مع الاتنين، التلاتة مش موجودة في الـ
+
+101
+00:09:32,450 --> 00:09:37,090
+Centralizer الاتنين فأكيد الاتنين مش موجودة في الـ
+
+102
+00:09:37,090 --> 00:09:40,870
+Centralizer التلاتة، طيب يجب الواحد والاتنين
+
+103
+00:09:40,870 --> 00:09:45,430
+التلاتة، خلصناهم، التلاتة مع الأربعة ستة، الأربعة مع
+
+104
+00:09:45,430 --> 00:09:49,130
+التلاتة، تلاتة ما نفعش أو الأربعة مع التلاتة اتنين
+
+105
+00:09:49,130 --> 00:09:56,240
+ما نفعش، التلاتة مع الخمسة سبعة، الخمسة مع التلاتة ..
+
+106
+00:09:56,240 --> 00:10:01,860
+سبعة .. ايه بس؟ الخمسة موجود مع الستة .. تلاتة مع
+
+107
+00:10:01,860 --> 00:10:06,640
+الستة .. تمانية، ستة مع التلاتة .. أربعة .. لأ
+
+108
+00:10:06,640 --> 00:10:11,580
+التلاتة مع السبعة .. واحد، السبعة مع التلاتة .. ايه
+
+109
+00:10:11,580 --> 00:10:15,180
+بس؟ السبعة موجود طبعا والتمانية لأ بنفس الطريقة
+
+110
+00:10:15,180 --> 00:10:20,580
+هدف دي ساوي .. Centralize و التلاتة inverse مين
+
+111
+00:10:20,580 --> 00:10:26,710
+التلاتة inverse؟ السبعة، ليش؟ لأنه تلاتة في سبعة
+
+112
+00:10:26,710 --> 00:10:33,170
+واحد و سبعة في تلاتة واحد، طيب خلصنا الواحد والاتنين
+
+113
+00:10:33,170 --> 00:10:40,230
+والتلاتة والسبعة، على الأربعة، الأربعة
+
+114
+00:10:40,230 --> 00:10:47,490
+كميوت مع مين؟ نبدأ بالواحد، والأربعة، اتنين، والتلاتة
+
+115
+00:10:47,490 --> 00:10:52,840
+لأ، لأن الأربعة لم توجد في الـ Centralizer 2 ولم
+
+116
+00:10:52,840 --> 00:10:57,720
+توجد في الـ Centralizer 3، نجرب مع الخمسة، أربعة مع
+
+117
+00:10:57,720 --> 00:11:02,380
+الخمسة تمانية، خمسة مع الأربعة تمانية، إجبار الخمسة
+
+118
+00:11:02,380 --> 00:11:09,400
+موجود، طيب الأربعة مع الستة سبعة، و الستة مع الأربعة
+
+119
+00:11:09,400 --> 00:11:15,900
+تلاتة، لأ، الأربعة مع السبعة ستة، و السبعة مع الأربعة
+
+120
+00:11:16,850 --> 00:11:21,530
+اتنين، لأ، الأربعة مع التمانية خمسة، و التمانية مع
+
+121
+00:11:21,530 --> 00:11:26,130
+الأربعة يكبر، تمانية، هذا بني ساوز centralize و
+
+122
+00:11:26,130 --> 00:11:31,050
+الأربع inverse مين؟ الأربع inverse، الأربع مع نفسه
+
+123
+00:11:31,050 --> 00:11:37,050
+ما استفدناش، اشيه centralize و الخمسة، هلاحظ أن الواحد
+
+124
+00:11:37,050 --> 00:11:44,590
+و الاتنين، الخمسة موجودة، و التلاتة و الأربعة و الخمسة
+
+125
+00:11:45,740 --> 00:11:50,580
+نجرب مع الستة، خمسة مع الستة اتنين، ستة مع الخمسة 
+
+126
+00:11:50,580 --> 00:11:55,540
+اتنين طبعا الستة والسبعة والتمانية هذا بيساوي مين
+
+127
+00:11:55,540 --> 00:12:01,080
+الـ J بتظهر عندك الـ Centralizer الستة و
+
+128
+00:12:01,080 --> 00:12:05,640
+Centralizer التمانية هيتساوى بنفس الطريقة هيصبح
+
+129
+00:12:05,640 --> 00:12:15,160
+معاك واحد خمسة وستة وتمانية شوية بسهولة التمانية
+
+130
+00:12:15,160 --> 00:12:19,800
+والستة الـ inverse لهم زي بعض ستة في التمانية لأ لأ
+
+131
+00:12:19,800 --> 00:12:29,380
+لأ هنا حاسب معايا واحد خمسة و ستة و تمانية إن
+
+132
+00:12:29,380 --> 00:12:39,960
+الستة مع التمانية سبعة اتنين طيب
+
+133
+00:12:39,960 --> 00:12:47,630
+Centralizer بالتمانية واحد وخمسة و تمانية و أربعة
+
+134
+00:12:47,630 --> 00:12:50,730
+واضح
+
+135
+00:12:50,730 --> 00:12:54,070
+كيف
+
+136
+00:12:54,070 --> 00:12:57,910
+الواحد
+
+137
+00:12:57,910 --> 00:13:02,400
+محايد بس الخمسة لأ من الـ generator احنا أصلا
+
+138
+00:13:02,400 --> 00:13:06,760
+ما بنتكلمش عن Cyclic group الخمسة commute مع الجميع
+
+139
+00:13:06,760 --> 00:13:11,780
+فلما نيجي نتكلم عن ثرع B زد الجيه مين العناصر
+
+140
+00:13:11,780 --> 00:13:18,140
+المشتركة في الكل واحد وخمسة الواحد و الخمسة هم
+
+141
+00:13:18,140 --> 00:13:27,280
+عناصر الـ center يظل مين الـ order الـ order للواحد
+
+142
+00:13:27,280 --> 00:13:35,420
+كده؟ هذه سهلة طيب الـ order للاتنين هبدأ
+
+143
+00:13:35,420 --> 00:13:42,800
+بالاتنين اتنين × اتنين اتنين في اتنين كده؟ لا يا عم
+
+144
+00:13:42,800 --> 00:13:50,320
+مش أربعة اتنين في اتنين واحد يكبر الـ order الاتنين بدي
+
+145
+00:13:50,320 --> 00:13:51,140
+يساوي اتنين
+
+146
+00:13:56,000 --> 00:14:00,320
+شوف مدام أنا مش عارف إيه العملية تحديدا من هي بشر
+
+147
+00:14:00,320 --> 00:14:06,640
+على الـ general و هو يا إش الضرب طيب الـ order للتلاتة
+
+148
+00:14:06,640 --> 00:14:15,660
+تلاتة × اتنين جديش تلاتة في تلاتة جديش خمسة طيب
+
+149
+00:14:15,660 --> 00:14:20,440
+تلاتة × تلاتة عبارة عن تلاتة في تلاتة في تلاتة
+
+150
+00:14:20,440 --> 00:14:31,740
+خمسة في تلاتة جديش خمسة في تلاتة سبعة طيب نكمل يبقى
+
+151
+00:14:31,740 --> 00:14:39,660
+الـ order مش اتنين و مش تلاتة نجرب أربعة تلاتة ×
+
+152
+00:14:39,660 --> 00:14:45,080
+أربعة تلاتة في تلاتة في تلاتة في تلاتة هنا خمسة و
+
+153
+00:14:45,080 --> 00:14:52,460
+هنا خمسة خمسة في خمسة Order الاربعة هيساوي أربعة
+
+154
+00:14:52,460 --> 00:14:58,400
+Order الخامسة
+
+155
+00:14:58,400 --> 00:15:04,800
+هيساوي اتنين Order الستة هيساوي اتنين Order السبعة
+
+156
+00:15:04,800 --> 00:15:11,360
+هيساوي أربعة Order التمانية هيساوي اتنين بنفس
+
+157
+00:15:11,360 --> 00:15:16,980
+الطريقة تطلع الـ orders زي ما أنت شايف واضح؟
+
+158
+00:15:18,100 --> 00:15:22,760
+واضح ولا ما في حاجة محتاجة توضيح؟
+
+159
+00:15:22,760 --> 00:15:26,360
+مالو؟
+
+160
+00:15:26,360 --> 00:15:30,460
+how are these order are thematically related to
+
+161
+00:15:30,460 --> 00:15:32,880
+the order of the group؟ إيش الـ orders اللي طلعت
+
+162
+00:15:32,880 --> 00:15:36,740
+معاك؟ واحد واتنين وأربعة بيقسموا التمانية في
+
+163
+00:15:36,740 --> 00:15:40,740
+chapter سبعة هناخد نظرية بتقول إن order أي عنصر في
+
+164
+00:15:40,740 --> 00:15:45,000
+الـ finite group بيقسم الـ order تبع الـ group نفسه
+
+165
+00:15:45,000 --> 00:15:47,000
+هذه نظرية اسمها نظرية Lagrang
+
+166
+00:15:50,850 --> 00:15:56,250
+طيب نيجي لسؤال 26 26
+
+167
+00:15:56,250 --> 00:16:01,990
+بيعمم
+
+168
+00:16:01,990 --> 00:16:07,970
+تعريف Centralizer العنصر و بينتقل منه ل
+
+169
+00:16:07,970 --> 00:16:13,430
+Centralizer المجموعة فلو كان عندي sub group من ال
+
+170
+00:16:13,430 --> 00:16:19,690
+J ف الـ centralizer الـ H عبارة عن الـ X في الـ J
+
+171
+00:16:19,690 --> 00:16:25,210
+اللي بيكون commute مع مين؟ مع كل عناصر الـ H يعني
+
+172
+00:16:25,210 --> 00:16:35,150
+XH بيساوي HX لكل H في H مطلوب من يثبت هنا أن الـ
+
+173
+00:16:35,150 --> 00:16:40,050
+centralizer للـ H عبارة عن subgroup
+
+174
+00:16:47,010 --> 00:16:52,610
+طيب في البداية لازم نثبت إن هذه المجموعة فيها
+
+175
+00:16:52,610 --> 00:17:03,250
+عناصر first الـ E  أو الـ E إيه؟ إيه؟ إيه؟ إيه؟
+
+176
+00:17:03,250 --> 00:17:05,110
+إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟
+
+177
+00:17:05,110 --> 00:17:09,290
+إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟ إيه؟
+
+178
+00:17:09,290 --> 00:17:14,990
+إيه؟ إيه؟ إيه؟
+
+179
+00:17:15,820 --> 00:17:19,460
+يعني ينتمي لـ Centralizer الـ H وهذا يعني
+
+180
+00:17:19,460 --> 00:17:29,180
+Centralizer الـ H not empty كيف؟
+
+181
+00:17:29,180 --> 00:17:37,420
+H في H، A في J أنا فاهم، بس أنا بنتقل من إنه محايد
+
+182
+00:17:37,420 --> 00:17:39,560
+لكل الـ J فمحايد للجزء
+
+183
+00:17:46,120 --> 00:17:51,940
+طيب احنا بنشتغل إن الـ X من الـ H ولا من الـ J طيب
+
+184
+00:17:51,940 --> 00:17:59,900
+انتقالي من هنا لهنا إن هو محيط للكل فمحيط للجزء
+
+185
+00:17:59,900 --> 00:18:03,660
+الجزئية
+
+186
+00:18:03,660 --> 00:18:12,280
+التانية لـ A و B ينتمي لـ Centralizer الـ H هذا
+
+187
+00:18:12,280 --> 00:18:21,310
+معناتهمعناته ax بدي يساوي اك .. أو h بدي يساوي ha ph
+
+188
+00:18:21,310 --> 00:18:30,250
+بدي يساوي hb لكل h small في h capital طيب .. هذا
+
+189
+00:18:30,250 --> 00:18:33,330
+هيخليني أقول إن aH
+
+190
+00:18:36,200 --> 00:18:41,760
+أو هنا هنتقل منها بي انفرس بي اتش بي انفرس بدي
+
+191
+00:18:41,760 --> 00:18:51,180
+يساوي بي انفرس اتش بي بي انفرس حاسب معايا بي
+
+192
+00:18:51,180 --> 00:18:58,420
+انفرس اتش بي انفرس بي انفرس اتش
+
+193
+00:19:00,880 --> 00:19:04,040
+علشان الـ a b inverse يكون في الـ centralizer و الـ h
+
+194
+00:19:04,040 --> 00:19:11,140
+لازم الـ a b inverse في h يساوي h a b inverse a b
+
+195
+00:19:11,140 --> 00:19:19,420
+inverse الـ h عبارة عن a b inverse الـ h اللي عبارة
+
+196
+00:19:19,420 --> 00:19:30,750
+عن a h b inverse يعني a h في b inverse يعني h a في
+
+197
+00:19:30,750 --> 00:19:38,550
+B inverse أو H AB inverse هذا معناه إنه AB
+
+198
+00:19:38,550 --> 00:19:43,210
+inverse ينتمي لـ centralizer الـH وبالتالي
+
+199
+00:19:43,210 --> 00:19:50,950
+centralizer الـH subgroup من الـG طبعا مش من
+
+200
+00:19:50,950 --> 00:19:55,690
+الضرورة إن عناصر centralizer الـH تكون في الـH
+
+201
+00:19:55,690 --> 00:20:02,430
+نفسها مش ضروري إن عناصر الـ centralizer الـ H تكون
+
+202
+00:20:02,430 --> 00:20:09,950
+في الـ H نفسها يعني
+
+203
+00:20:09,950 --> 00:20:13,910
+حتى ممكن يكون الـ centralizer عدد عناصره أكثر من
+
+204
+00:20:13,910 --> 00:20:19,630
+الـ H centralizer الـ subgroup يكون فيه عناصر أكثر
+
+205
+00:20:19,630 --> 00:20:25,970
+من الـ subgroup نفسها وين؟
+
+206
+00:20:28,090 --> 00:20:36,690
+رد يا مهر أقولك إيه أنت ما لقيتش اتجاه
+
+207
+00:20:36,690 --> 00:20:42,230
+هذه عناصر الصندوق لازم من وين من J بس لازم تكون
+
+208
+00:20:42,230 --> 00:20:45,670
+تتبدل مع كل عناصر H طب هي احنا انتقلنا من هتتبدل
+
+209
+00:20:45,670 --> 00:20:49,190
+مع كل عناصر J يعني مثلا العنصر بتتبدل مع كل
+
+210
+00:20:49,190 --> 00:20:52,590
+عناصر القاعة هيتبدل مع عناصر جيها ولا لأ
+
+211
+00:21:00,940 --> 00:21:06,040
+كيف ده اكتب هذه مش حاجة ده اكتب مباشرة لما انتقل
+
+212
+00:21:06,040 --> 00:21:14,040
+من معلومة أنا متأكد منها 29 let J be an abelian
+
+213
+00:21:14,040 --> 00:21:17,000
+group with identity E and let N be some fixed
+
+214
+00:21:17,000 --> 00:21:19,800
+integer, both are the set of all elements of J
+
+215
+00:21:19,800 --> 00:21:26,040
+that satisfy the equation J
+
+216
+00:21:26,040 --> 00:21:26,740
+abelian
+
+217
+00:21:34,850 --> 00:21:42,210
+و الـ N ينتمي للـ national number أو حتى ينتمي للـ
+
+218
+00:21:42,210 --> 00:21:49,930
+Z بشكل عام The set of all elements in J يعني ال
+
+219
+00:21:49,930 --> 00:21:55,990
+set هذه خلّيني أعتبر عنها بغمز T هي كل الـ X في J
+
+220
+00:21:55,990 --> 00:22:01,150
+اللي X أس N بدي تساوي الـ identity مطلوب أثبت إنه T
+
+221
+00:22:02,420 --> 00:22:08,400
+subgroup من الـ j مطلوب أثبت أن مجموعة حل معادلة
+
+222
+00:22:08,400 --> 00:22:13,400
+ما في group
+
+223
+00:22:13,400 --> 00:22:18,980
+بس بشغل أنها تكون abelian بيعطيني الـ subgroup ماشي
+
+224
+00:22:18,980 --> 00:22:24,380
+proof طبعا السؤال اللي لتكمله إنه لو شيلنا كلمة
+
+225
+00:22:24,380 --> 00:22:31,760
+abelian بيبطل كلام هذا صحيح first الـ team ده عنصر
+
+226
+00:22:33,560 --> 00:22:39,200
+الـ A أُس N بدي يساوي إيه؟ إجباليا تملة T وبالتالي
+
+227
+00:22:39,200 --> 00:22:48,520
+T ليست مجموعة خالية تقل الخطوة التانية لـ A و B
+
+228
+00:22:48,520 --> 00:22:55,860
+تملة T إيش يعني؟ A أُس N بدي يساوي الـ identity B
+
+229
+00:22:55,860 --> 00:23:02,260
+أُس N بدي يساوي الـ identity طيب الـ A الـ B أُس N
+
+230
+00:23:02,260 --> 00:23:06,860
+بدي يساوي الـ identity بـ B أُس N inverse بدي
+
+231
+00:23:06,860 --> 00:23:11,960
+يساوي الـ identity inverse بدي يساوي إيش الـ
+
+232
+00:23:11,960 --> 00:23:20,300
+identity بس هذه عبارة عن B inverse لكل أُس N ده
+
+233
+00:23:20,300 --> 00:23:27,540
+تساوي الـ identity طيب احنا هنا بنجهز معلومة معينة
+
+234
+00:23:27,540 --> 00:23:32,700
+نسميها الغرس علشان نستعملها في الإثبات التالي Now
+
+235
+00:23:32,700 --> 00:23:40,100
+A P inverse لكل أُس N تنساش إن الـ J is abelian هذا
+
+236
+00:23:40,100 --> 00:23:50,980
+عبارة عن A أُس N P inverse أُس N هذا ليش؟ J is abelian
+
+237
+00:23:50,980 --> 00:23:56,450
+طب الـ A أُس N إيش بتساوي؟ الـ Identity والـ B inverse
+
+238
+00:23:56,450 --> 00:24:02,890
+أُس N برضه الـ Identity Identity في Identity يساوي
+
+239
+00:24:02,890 --> 00:24:08,530
+الـ Identity وبالتالي A B inverse أُس N يساوي الـ E
+
+240
+00:24:08,530 --> 00:24:17,970
+A B inverse يعني تامي للـ T تامي للـ T subgroup
+
+241
+00:24:17,970 --> 00:24:24,380
+من الـ G T صارت subgroup لاحظ إن هذا الأسلوب
+
+242
+00:24:24,380 --> 00:24:29,620
+استعملته ثلاث مرات اليوم باستعمال الـ first step
+
+243
+00:24:29,620 --> 00:24:35,600
+تكملت السؤال إيش بيقول ليه Give an example of a
+
+244
+00:24:35,600 --> 00:24:39,940
+group J in which the set of all elements of J that
+
+245
+00:24:39,940 --> 00:24:44,300
+satisfy the equation X تربيع بدي يساوي E doesn't
+
+246
+00:24:44,300 --> 00:24:49,220
+form a subgroup of J شوف
+
+247
+00:24:52,250 --> 00:24:56,550
+طلع المعطيات اللي أعطانيها المعطى اللي بيخص ال
+
+248
+00:24:56,550 --> 00:25:00,830
+group نفسه إن هي إيش abelian فلو كانت الـ group
+
+249
+00:25:00,830 --> 00:25:05,090
+abelian أكيد الـ T subgroup يعني بقى لما تدّيش تدور
+
+250
+00:25:05,090 --> 00:25:09,590
+على example تروحش تدور في الـ abelian group هتدور 
+
+251
+00:25:09,590 --> 00:25:13,730
+وين؟ في الـ non abelian كم non abelian sub group
+
+252
+00:25:13,730 --> 00:25:19,130
+أخدت حتى الآن واحدة واحدة بس طبعا هو في non
+
+253
+00:25:19,130 --> 00:25:25,250
+abelian sub group غيرها أخدت طبعا واحدة non-abelian
+
+254
+00:25:25,250 --> 00:25:31,630
+اللي هي JL2R أو SL2R لكن هنا حاجة صعبة في حال
+
+255
+00:25:31,630 --> 00:25:37,330
+المعادلات في الـ matrices عملية
+
+256
+00:25:37,330 --> 00:25:43,570
+الطرح بتعمليش جوب أصلا مع الـ Z طيب
+
+257
+00:25:43,570 --> 00:25:52,170
+شوية بس الطرح لأ بتعملي جوب بتعملي جوب في الـ ان لأ
+
+258
+00:25:53,410 --> 00:26:00,470
+هناخد الـ J عبارة عن الـ D4 لما يجي نشتغل T عبارة
+
+259
+00:26:00,470 --> 00:26:04,830
+عن كل الـ X في الـ D4 اللي X تقريبا بيساوي الـ
+
+260
+00:26:04,830 --> 00:26:09,170
+identity ارجع الـ multiplication table للـ D4 هدي
+
+261
+00:26:09,170 --> 00:26:16,790
+هيعطيك الـ R0 الـ R رمية
+
+262
+00:26:16,790 --> 00:26:27,630
+و تمانينو الـ H و الـ V و الـ D و الـ D شغطة وهذه ليست
+
+263
+00:26:27,630 --> 00:26:32,610
+subgroup of
+
+264
+00:26:32,610 --> 00:26:38,070
+D4 هذه مستحيلة تكون subgroup للـ D4 ليش؟ شوية بس
+
+265
+00:26:38,070 --> 00:26:44,570
+ليش مش هتكون subgroup من الـ D4؟
+
+266
+00:26:44,570 --> 00:26:44,990
+اه
+
+267
+00:26:48,050 --> 00:26:52,430
+كل عنصر موجود هو معكوسه الـ inverse exist لكن هل
+
+268
+00:26:52,430 --> 00:27:02,430
+المجموعة مغلقة فلو ضربت الـ D في D شرطة شو هيعطيك D
+
+269
+00:27:02,430 --> 00:27:08,910
+في D شرطة هيعطيك يا R 90 يا R 270 حسب اتجاه الضرب
+
+270
+00:27:11,810 --> 00:27:14,330
+يعني في النهاية انت لو ضربت انتين من هدول في بعض
+
+271
+00:27:14,330 --> 00:27:18,870
+هعطيك الـ R90 والـ R90 مش موجودة في الـ T قبل T نطسة
+
+272
+00:27:18,870 --> 00:27:37,810
+بالجروب من الـ D فافضل صحيح
+
+273
+00:27:37,810 --> 00:27:41,430
+طيب
+
+274
+00:27:43,770 --> 00:27:51,670
+مش في بعدها تلاتين طيب
+
+275
+00:27:51,670 --> 00:27:54,850
+سؤال تلاتين بيقول لصبوز a belong to the group الـ
+
+276
+00:27:54,850 --> 00:28:01,130
+order ل الـ a بيساوي خمسة الـ
+
+277
+00:28:01,130 --> 00:28:07,350
+a في الـ j و order ل الـ a بيساوي خمسة center
+
+278
+00:28:07,350 --> 00:28:12,870
+centralizer ل الـ a بيساوي centralizer
+
+279
+00:28:19,750 --> 00:28:25,490
+من عنده فكرة على السؤال هذا من عنده فكرة على
+
+280
+00:28:25,490 --> 00:28:27,930
+السؤال هذا من عنده فكرة على السؤال هذا من عنده
+
+281
+00:28:27,930 --> 00:28:28,630
+فكرة على السؤال هذا من عنده فكرة على السؤال هذا من
+
+282
+00:28:28,630 --> 00:28:28,790
+عنده فكرة على السؤال هذا من عنده فكرة على السؤال
+
+283
+00:28:28,790 --> 00:28:32,070
+هذا من عنده فكرة على السؤال هذا من عنده فكرة على
+
+284
+00:28:32,070 --> 00:28:39,090
+السؤال هذا من عنده فكرة على السؤال هذا من
+
+285
+00:28:39,090 --> 00:28:40,370
+عنده فكرة على السؤال هذا من عنده فكرة على السؤال
+
+286
+00:28:40,370 --> 00:28:40,970
+هذا من عنده فكرة على السؤال هذا من عنده فكرة على
+
+287
+00:28:40,970 --> 00:28:44,990
+السؤال order للـ inverse طيب بس ايش هتستفيد ان
+
+288
+00:28:44,990 --> 00:29:04,130
+هالكلام ايش هتستفيد تعالوا
+
+289
+00:29:04,130 --> 00:29:06,350
+نضبطها بالواضح لسلوب التقليدي انه
+
+290
+00:29:10,270 --> 00:29:15,410
+الـ order ل الـ A خمسة مش واحد ايش ده بتستفيد منها
+
+291
+00:29:15,410 --> 00:29:23,290
+تعلم ده بالاتجاه الأول أو
+
+292
+00:29:23,290 --> 00:29:33,090
+خلينا اتجاه الأسل لين X ينتمي لـ Centralizer A ده
+
+293
+00:29:33,090 --> 00:29:42,780
+اش معناته معناته AX بدي يساوي إيش؟ XA وبالتالي لما
+
+294
+00:29:42,780 --> 00:29:48,860
+نيجي نقول A تكييب X عبارة عن الـ A في A في A في X A
+
+295
+00:29:48,860 --> 00:29:57,240
+في A في X في A A في X في A في A X في A في A في A X
+
+296
+00:29:57,240 --> 00:30:02,460
+A تكييب وين صارت الـ X؟ في Centralizer الـ A تكييب
+
+297
+00:30:03,400 --> 00:30:10,700
+وبتالي الـ Centralizer الـ A بيكون Subset من
+
+298
+00:30:10,700 --> 00:30:20,020
+Centralizer الـ A تكعيب وبتالي
+
+299
+00:30:20,020 --> 00:30:26,700
+خلصنا الاتجاه الأول انه Centralizer الـ A Subset
+
+300
+00:30:26,700 --> 00:30:35,290
+من Centralizer الـ A تكعيب مين عنده قدرة ان يثبت
+
+301
+00:30:35,290 --> 00:30:42,290
+للاتجاه الثاني؟
+
+302
+00:30:42,290 --> 00:30:55,370
+اه
+
+303
+00:30:55,370 --> 00:30:59,850
+يا شباب فضل تطلعتوا كتاب؟
+
+304
+00:31:15,150 --> 00:31:17,630
+كبّي خطك و فمّا يجيب عليك
+
+305
+00:31:44,040 --> 00:31:49,720
+شوية بس .. شوية حاجات انت ضربت في الاتجاه اللي
+
+306
+00:31:49,720 --> 00:31:55,040
+نحيتي من اتجاه هذا لما ده تضرب هنا ده تضرب على نفس
+
+307
+00:31:55,040 --> 00:31:55,600
+الاتجاه
+
+308
+00:32:22,050 --> 00:32:30,630
+طيب، إيش سؤال؟ كان
+
+309
+00:32:30,630 --> 00:32:32,070
+سنجي اللي هو مش بروح لبنان
+
+310
+00:33:02,030 --> 00:33:05,650
+طب انت لما بدك تحطه ماناجك تستفيد انت بدك تنجل
+
+311
+00:33:05,650 --> 00:33:08,630
+تنتين ماتقدرش تنجل تنتين تنجل التلاتة لما تنجل
+
+312
+00:33:08,630 --> 00:33:14,450
+التلاتة هتصير X سواء X هتكمل
+
+313
+00:33:14,450 --> 00:33:21,950
+انا وانت بتحل وقعد في خطاين الخطأ الأول مابدتش صح
+
+314
+00:33:22,760 --> 00:33:25,200
+أنت لما بدك تيجي تبدأ وتثبت أن مجموعة بيساوي
+
+315
+00:33:25,200 --> 00:33:29,760
+مجموعة لازم تاخد عنصر من المجموعة هذه هتقول let X
+
+316
+00:33:29,760 --> 00:33:35,760
+ينتمي لـ centralizer الـ A تكعيب الخطأ الثاني و أنت
+
+317
+00:33:35,760 --> 00:33:40,780
+بتشتغل مافكرتش تستعمل الـ order أنت كتبت أن A X
+
+318
+00:33:40,780 --> 00:33:49,260
+تكعيب بيساوي A X A تكعيب بهذا
+
+319
+00:33:49,260 --> 00:33:49,620
+الشكل
+
+320
+00:33:53,180 --> 00:34:04,480
+طيب اضغط في X تكييب جهة في اي تكييب؟
+
+321
+00:34:04,480 --> 00:34:11,240
+هاي الـ X ايش
+
+322
+00:34:11,240 --> 00:34:21,670
+حاسسي معاك هان؟ A6 X بدي يساوي A3 X A3 الـ A أُس
+
+323
+00:34:21,670 --> 00:34:22,830
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+324
+00:34:22,830 --> 00:34:25,470
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+325
+00:34:25,470 --> 00:34:26,070
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+326
+00:34:26,070 --> 00:34:30,010
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+327
+00:34:30,010 --> 00:34:34,410
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+328
+00:34:34,410 --> 00:34:38,810
+ثلاثة الـ A أُس ثلاثة الـ A أُس ثلاثة الـ A أُس
+
+329
+00:34:38,810 --> 00:34:49,910
+ثلاثة الـ A أُس ثلاثة الـ
+
+330
+00:34:49,910 --> 00:34:56,040
+A أيجب اكس في Centralizer الـ A Centralizer الـ A
+
+331
+00:34:56,040 --> 00:35:03,020
+تكييب subset من Centralizer الـ A اعطيها 2 1 و 2
+
+332
+00:35:03,020 --> 00:35:08,680
+هيصير Centralizer الـ A بيساوي Centralizer الـ A
+
+333
+00:35:08,680 --> 00:35:17,240
+تكييب وهو المفروض واضح؟ واضح؟
+
+334
+00:35:17,240 --> 00:35:24,320
+واضح يا شباب؟ لو كان الـ order ل الـ a سواء عشرة نفس
+
+335
+00:35:24,320 --> 00:35:28,080
+الكلمة كيف مش فاهم لو كان الـ order ل الـ a سواء عشرة
+
+336
+00:35:28,080 --> 00:35:32,600
+كيف ده توصلها يعني الـ order ل الـ a برضه متساوي
+
+337
+00:35:32,600 --> 00:35:36,680
+خمسة من جالك الـ order ل الـ a بيساوي عشرة بتستعمل
+
+338
+00:35:36,680 --> 00:35:41,920
+ان الـ a plus خمسة بيساوي identity تقدرش كل اللي
+
+339
+00:35:41,920 --> 00:35:47,460
+بتقدر تثبته لو الـ order ل الـ a بيساوي عشرة انه الـ
+
+340
+00:35:47,460 --> 00:35:50,380
+centralizer ل a تربيع أو الـ centralizer ل a تكعيب
+
+341
+00:35:50,380 --> 00:35:50,900
+متساوي
+
+342
+00:35:55,050 --> 00:36:00,210
+الـ A و الـ A تكعيب جاجر طبعا ممكن منها توصل
+
+343
+00:36:00,210 --> 00:36:02,550
+الاستغلال صغير الـ A بساهم الاستغلال صغير الـ A تكعيب
+
+344
+00:36:02,550 --> 00:36:06,130
+ممكن لكن ماقدرش انا اجزملك على هذا الكلام صحيح ولا
+
+345
+00:36:06,130 --> 00:36:12,890
+خطأ طيب
+
+346
+00:36:12,890 --> 00:36:22,860
+السؤال تلاتة و تلاتين اللي تكمل السؤال صحيح find an
+
+347
+00:36:22,860 --> 00:36:26,180
+element a from subgroup such that in order الـ a
+
+348
+00:36:26,180 --> 00:36:29,900
+بيساوي 6 لكن الـ centralizer الـ a لا يساوي الـ
+
+349
+00:36:29,900 --> 00:36:37,960
+centralizer الـ a تكعيب هات
+
+350
+00:36:37,960 --> 00:36:43,260
+مثال مدام
+
+351
+00:36:43,260 --> 00:36:46,820
+تشتغل على الـ centralizer و بدكش مساواة اوعيك تجيب
+
+352
+00:36:46,820 --> 00:36:52,860
+مثال على abelian اوعيك تجيب مثالعلى abelian ايك
+
+353
+00:36:52,860 --> 00:36:57,240
+بدور على مين على مثال non abelian بعدين في الموضوع
+
+354
+00:36:57,240 --> 00:37:03,080
+الأردغ بدي يساوي 6 في
+
+355
+00:37:03,080 --> 00:37:09,920
+الـ D3 في عنصر الأردغ له 6 لأ ايك بشر على D6 خد الـ
+
+356
+00:37:09,920 --> 00:37:22,490
+J بدي يساوي D6 D6 عبارة عن R0 R 360 على 6 60 120
+
+357
+00:37:22,490 --> 00:37:38,710
+180 240 و 300 و عندك 6 دورانات و 6 انعكاسات كلها
+
+358
+00:37:38,710 --> 00:37:46,950
+R1 R2 R3 R4 R5 R6
+
+359
+00:37:50,560 --> 00:37:58,340
+عطينا عمصر الـ order له 6 خد الـ A بدي يساوي R120 الـ
+
+360
+00:37:58,340 --> 00:38:04,740
+order للـ A أو R60 الـ order للـ A ايش بدي يساوي؟ 6
+
+361
+00:38:04,740 --> 00:38:19,620
+Centralizer الـ A ايش بتساوي؟ R0 R60 R120 لعند R300
+
+362
+00:38:21,440 --> 00:38:25,180
+لكن الـ Centralizer الـ A تكعيب يعني الـ
+
+363
+00:38:25,180 --> 00:38:31,020
+Centralizer الـ R 180 عبارة عن الـ D6 كلها في
+
+364
+00:38:31,020 --> 00:38:35,100
+قاعدة أخدتها في قبل chapter أنه لو كانت الـ D N و
+
+365
+00:38:35,100 --> 00:38:39,760
+الـ N even فالـ Z تبع الـ group أو الـ Center تبع
+
+366
+00:38:39,760 --> 00:38:47,300
+الـ group عبارة عن R 0 و R 180 يعني بس Centralizer
+
+367
+00:38:47,300 --> 00:38:50,880
+الـ A لا يساوي الـ Centralizer الـ A تكعيب
+
+368
+00:38:54,910 --> 00:39:03,250
+واضح؟ اه مهما فضل
+
+369
+00:39:03,250 --> 00:39:08,770
+الارض
+
+370
+00:39:08,770 --> 00:39:14,970
+لر ستين ر ستين مش ر ستة هذا حط ر ستين
+
+371
+00:39:21,640 --> 00:39:29,280
+مش كل المجموعة من R0
+
+372
+00:39:29,280 --> 00:39:34,820
+ل R300 R1
+
+373
+00:39:34,820 --> 00:39:45,040
+و R2 و R3 خليني اكتب بالسرد عشان اريحك بس
+
+374
+00:39:45,040 --> 00:39:50,520
+الدورانات مش الانعكاسات الدورانات ده فجأة واحدة
+
+375
+00:39:52,320 --> 00:39:55,000
+ماشي بقى بيعطيكوا العافية طبعا عشان الوقت انتهى
+
+376
+00:39:55,000 --> 00:39:57,380
+هنكمل السؤال والحصة القادمة 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1e1326e011633d7ba271d90d152ab55be4d08280
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg.srt
@@ -0,0 +1,1303 @@
+1
+00:00:22,050 --> 00:00:26,010
+السلام عليكم ورحمة الله وبركاته طبعا اليوم
+
+2
+00:00:26,010 --> 00:00:28,250
+هناخد إن شاء الله المحاضرة الأخيرة اللي هكون 
+
+3
+00:00:28,250 --> 00:00:31,910
+متواجد معاكم فيها، المحاضرة القادمة هيكون أستاذ 
+
+4
+00:00:31,910 --> 00:00:36,090
+إسماعيل، أصل هناخد بعض الأسئلة على الوحدة الخامسة 
+
+5
+00:00:36,090 --> 00:00:38,970
+permutation group بس قبل ما أفوض في الأسئلة، بدأ
+
+6
+00:00:38,970 --> 00:00:41,930
+أذكر للناس اللي ما كانوا موجودين المحاضرة الماضية 
+
+7
+00:00:41,930 --> 00:00:48,410
+بقواعد حساب ال orders في ال permutations. أول شغلة 
+
+8
+00:00:48,410 --> 00:00:52,970
+لو كان عندي permutation بهذا الشكل a1, a2 اللي عند 
+
+9
+00:00:52,970 --> 00:01:02,370
+an فال order لل alpha بدي يساوي n. الشغلة 
+
+10
+00:01:02,370 --> 00:01:08,200
+التانية لو كانت ال alpha مثلا عبارة عن alpha 1 و 
+
+11
+00:01:08,200 --> 00:01:13,980
+alpha 2 لعند alpha k، وهدول عبارة عن cycles فال 
+
+12
+00:01:13,980 --> 00:01:17,700
+order لل alpha عبارة عن ال least common multiple ل
+
+13
+00:01:17,700 --> 00:01:23,020
+order ال alpha 1، order ال alpha 2، order ال alpha k.
+
+14
+00:01:23,020 --> 00:01:31,880
+تلاتة لو كانت ال alpha عبارة عن a1 a2 لعند an فال
+
+15
+00:01:31,880 --> 00:01:38,960
+alpha inverse هيكون a n، a n minus واحد، a تنين، a واحد.
+
+16
+00:01:38,960 --> 00:01:43,820
+ليش كتبت هنا تلات قواعد؟ هادول لإن السؤال 
+
+17
+00:01:43,820 --> 00:01:47,500
+الأول والسؤال التاني والسؤال التالت الموجودين
+
+18
+00:01:47,500 --> 00:01:53,040
+قدامك يتم التعامل معاهم بناء على الشغل اللي عندك.
+
+19
+00:01:53,040 --> 00:01:58,420
+موجود جاب لما نحلهم، هحل سؤال موجود في التلخيص وهو
+
+20
+00:01:59,420 --> 00:02:07,380
+Exercise على اعتقاد رقم 3 بيقول في ال S7 إيش 
+
+21
+00:02:07,380 --> 00:02:12,240
+احتمالات ال order؟
+
+22
+00:02:12,240 --> 00:02:22,040
+يعني عناصر ال S7 إيش ال orders الممكنين عندك؟ هبدأ
+
+23
+00:02:22,040 --> 00:02:27,260
+بأشكال العناصر في ال S7. أول شكل ممكن يكون زي هيك
+
+24
+00:02:32,870 --> 00:02:38,250
+و هذا ال order إيه اللي وجدناه؟ سبعة. ممكن أحصل 
+
+25
+00:02:38,250 --> 00:02:44,370
+على عنصر بهذا الشكل a1, a2, a6، و ال order 6 بنفس 
+
+26
+00:02:44,370 --> 00:02:49,370
+الطريقة أنا ممكن أحصل على ال order خمسة و أربعة و 
+
+27
+00:02:49,370 --> 00:02:54,040
+تلاتة و اتنين و واحدة. هاخد cycle فيها خمس عناصر
+
+28
+00:02:54,040 --> 00:02:59,000
+cycle فيها أربع عناصر، cycle فيها تلت عناصر، cycle 
+
+29
+00:02:59,000 --> 00:03:03,200
+فيها عنصرين، و cycle اللي هو ال identity مافيش فيها
+
+30
+00:03:03,200 --> 00:03:07,940
+ولا عنصر. ييك بقى الأرقام من واحد لسبعة دائما
+
+31
+00:03:07,940 --> 00:03:15,000
+موجودين كاحتمالات orders هنا. في شغلة مهمة، عناصر ال
+
+32
+00:03:15,000 --> 00:03:17,960
+S7 كده، عددهم؟
+
+33
+00:03:25,350 --> 00:03:29,190
+سبعة في ستة فاكتوريال، سبعة في سبعمائة عشرين وخمس
+
+34
+00:03:29,190 --> 00:03:30,070
+سلاف وأربعين.
+
+35
+00:03:40,100 --> 00:03:42,920
+خلال الأسئلة اللي هنشرحهم سواء أنا وصلتله أو 
+
+36
+00:03:42,920 --> 00:03:47,080
+الأستاذ إسماعيل، هيجي سؤال جداش عدد العناصر اللي من
+
+37
+00:03:47,080 --> 00:03:53,940
+order كذا في ال S7 و S8. طيب هيك اتخلصنا كل 
+
+38
+00:03:53,940 --> 00:03:58,500
+الاحتمالات، يكون عندي cycle واحدة، ناخد احتمالات 
+
+39
+00:03:58,500 --> 00:04:04,920
+يكون عندي two cycles مع بعض، يعني مثلا لو جينا A1, 
+
+40
+00:04:05,200 --> 00:04:14,590
+A2, A3, A4, A5, A6 لما بدي أكملها هيكون A7، طبعا هذا 
+
+41
+00:04:14,590 --> 00:04:20,970
+بيروح، فانخجعت لمين؟ لهذه إيه؟ يبقى هذه مالهاش لازمة.
+
+42
+00:04:20,970 --> 00:04:27,290
+نشيل A6 و نشتغل على A5 اللي تكملة تبعتها، يا cycles
+
+43
+00:04:27,290 --> 00:04:34,810
+زي هيك، وبالتالي مالهمش لازمة، يا cycle زي هيك في
+
+44
+00:04:34,810 --> 00:04:39,990
+هذه الحالة ال order بقى عن ال least common multiple
+
+45
+00:04:39,990 --> 00:04:46,710
+لمين؟ لخمسة و اتنين، كم؟ عشرة. إيه احتمال ان يكون 
+
+46
+00:04:46,710 --> 00:04:52,610
+عنده عنصر ال order ال عشرة، إشماله موجود. طب لو 
+
+47
+00:04:52,610 --> 00:04:57,690
+أخدنا مثلا Alpha، خلصنا الخمسة cycle، ناخد أربع
+
+48
+00:04:57,690 --> 00:05:04,570
+cycle A1, A2, A3, A4 بيضلوا تلت واحدات، يا إما 
+
+49
+00:05:04,570 --> 00:05:05,590
+بعملهم زي هيك
+
+50
+00:05:09,470 --> 00:05:14,590
+طبعا على الفاضي، تلات واحدات واحد واحد واحد ما بنفعش.
+
+51
+00:05:14,590 --> 00:05:23,210
+يا اما a5 a6 a7، وهدا بشيله و بيصير ال order ل ال
+
+52
+00:05:23,210 --> 00:05:25,830
+alpha عبارة عن ال least common multiple لاربعة و
+
+53
+00:05:25,830 --> 00:05:33,530
+اتنين، أربعة. أو ممكن يصير عندي الاحتمال هدا بدل ما
+
+54
+00:05:33,530 --> 00:05:38,720
+يكون لتنتين يكونوا تلاتة، وال order للألف عبارة عن 
+
+55
+00:05:38,720 --> 00:05:43,120
+ال least common multiple للأربعة والتلاتة، جديش؟
+
+56
+00:05:43,120 --> 00:05:49,380
+اتناش. طبعا الأربعة موجود مسبقا اصلا فمالوش أهمية. 
+
+57
+00:05:49,380 --> 00:05:53,220
+حاجات، لما أريد أخلص أنا ال cycle الأولانية فيها أربعة.
+
+58
+00:05:53,220 --> 00:06:00,100
+نيجي لما يريد يكون فيها جديش؟ تلاتة، اي واحد اي تنين
+
+59
+00:06:00,100 --> 00:06:06,330
+اي تلاتة، التكملات يا اما واحدة فيها أربعة زي هذه أو 
+
+60
+00:06:06,330 --> 00:06:10,990
+أربعة فيهم واحدة بلاش لازمة لأن في النهاية دول 
+
+61
+00:06:10,990 --> 00:06:18,530
+بيكونوا identity، يا إما واحدة فيهم تنتين والباقي 
+
+62
+00:06:18,530 --> 00:06:29,030
+تنتين فيهم واحدة أو واحدة زي هيك سواء هذه أو 
+
+63
+00:06:29,030 --> 00:06:32,480
+هذه اللي من نفس ال order لأن حاسيب معايا ال order 
+
+64
+00:06:32,480 --> 00:06:35,460
+للألفة يبقى on least common multiple اللي التلاتة
+
+65
+00:06:35,460 --> 00:06:40,860
+والاتنين بيعطينا ستة، والست أصلا موجود. طبعا اللي 
+
+66
+00:06:40,860 --> 00:06:44,540
+بعد هي كده، إذا أخد واحدة فيها تنتين، يا بكمل بخمسة
+
+67
+00:06:44,540 --> 00:06:49,960
+يا بكمل بأربعة وواحد، يا بكمل بتلاتة واتنين، يا بكمل 
+
+68
+00:06:49,960 --> 00:06:54,160
+بخمس واحدات، في النهاية هحصل على orders موجودين
+
+69
+00:06:54,160 --> 00:07:00,840
+مسبقا، باحتمالات ال orders واحد واتنين وتلاتة و 4 و 
+
+70
+00:07:00,840 --> 00:07:10,960
+5 و 6 و 7 و 10 و 12. يعني بأي عنصر داخل ال S7 ال
+
+71
+00:07:10,960 --> 00:07:17,300
+order إله واحد من هذه الأرقام. لاحقا هناخد طريقة
+
+72
+00:07:17,300 --> 00:07:23,440
+كيف نعرف ال order ال 12 كم عنصر موجود منه.
+
+73
+00:07:27,110 --> 00:07:32,070
+العناصر السبعة، ال orders لها بتاخد الأرقام
+
+74
+00:07:35,000 --> 00:07:38,080
+طيب نيجي للأسئلة الواحد والاتنين والتلاتة 
+
+75
+00:07:38,080 --> 00:07:41,280
+الموجودين قدامك، find the order of each element
+
+76
+00:07:41,280 --> 00:07:45,460
+طبعا هذا هطبق مباشرة على القاعدة الأولى، ال order
+
+77
+00:07:45,460 --> 00:07:49,340
+اتنين، ال order تلاتة، ال order خمسة، ال order K
+
+78
+00:07:49,340 --> 00:07:54,420
+اتنين. هطبق على مين؟ القاعدة التانية، ال least common 
+
+79
+00:07:54,420 --> 00:07:57,420
+multiple للاربع والتلاتة، اتن عاشر. ال least common
+
+80
+00:07:57,420 --> 00:08:00,520
+multiple للخمسة والاتنين والخمسة عشرة. ال least 
+
+81
+00:08:00,520 --> 00:08:07,630
+common multiple للاتنين والاتنين والتلاتة ستة، صح؟
+
+82
+00:08:07,630 --> 00:08:16,330
+صح لأ غلط. هدول لازم يكونوا إيش؟ disjoint، لازم هدول
+
+83
+00:08:16,330 --> 00:08:21,770
+يكونوا إيش؟ لازم أحولهم ليش؟ ل disjoint لازم أضغط
+
+84
+00:08:21,770 --> 00:08:26,310
+وأعملهم disjoint وبعدين أشتغل عليه، ال least 
+
+85
+00:08:26,310 --> 00:08:29,910
+common multiple. هبدأ بالواحد، واحد للتلاتة، وتلاتة
+
+86
+00:08:29,910 --> 00:08:34,790
+للخمسة يكبر، واحد للخمسة، خمسة للخمسة، وخمسة للواحد
+
+87
+00:08:34,790 --> 00:08:39,930
+سكرها على التنين، تنين للتنين، وتنين للتلاتة يكبر
+
+88
+00:08:39,930 --> 00:08:46,990
+تنين للتلاتة، تلاتة للاربع، واربع للاربع، واش ال
+
+89
+00:08:46,990 --> 00:08:51,310
+order، least common multiple للتنين و التلاتة كم؟ 
+
+90
+00:08:51,310 --> 00:08:57,050
+ستة. طبعا تجيش مرة واحدة وتقول least common 
+
+91
+00:08:57,050 --> 00:08:59,110
+multiple زي ما كنا .. زي ما عملنا في الأول، لإن
+
+92
+00:08:59,110 --> 00:09:02,490
+هدول إيش مالهم؟ مش disjoint فلازم يكونوا disjoint
+
+93
+00:09:02,490 --> 00:09:07,350
+حسب النظرية، هانا في P، هدى لمّا بدك تشتغلها ابدا 
+
+94
+00:09:07,350 --> 00:09:12,270
+بالواحد، واحد لاتنين، للتلاتة، للتنين يكبر واحد
+
+95
+00:09:12,270 --> 00:09:17,290
+لاتنين، تنين للاربعة، أربعة للاربعة، واربعة للاربعة
+
+96
+00:09:17,290 --> 00:09:21,670
+يكبر، تنين للاربعة، أربعة للستة، ستة للستة، وستة
+
+97
+00:09:21,670 --> 00:09:28,710
+للواحد وسكركمّل، تلاتة لنفسها، تلاتة للتنين، وتنين
+
+98
+00:09:28,710 --> 00:09:34,430
+للتلاتة، طيب،
+
+99
+00:09:34,430 --> 00:09:40,190
+أربعة خلصناها، خمسة، خمسة للواحد، واحد لنفسه، واحد
+
+100
+00:09:40,190 --> 00:09:46,470
+للتلاتة، يبقى في خلل لنا هنا، نرجع 
+
+101
+00:09:46,470 --> 00:09:52,210
+للتلاتة، تلاتة لنفسها، التلاتة للتنين، والتنين للخمسة
+
+102
+00:09:52,210 --> 00:09:57,490
+صحيح، اجبار التلاتة للخمسة، وخمسة للواحد، واحد للواحد
+
+103
+00:09:57,490 --> 00:10:01,390
+وواحد للتلاتة، سكر، اجبار أكيد الستة زي ما هي، ال
+
+104
+00:10:01,390 --> 00:10:06,490
+least common multiple كم؟ ستة. ال least common
+
+105
+00:10:06,490 --> 00:10:13,810
+multiple ستة. آخر واحدة، واحد للاربع، أربع للاربع
+
+106
+00:10:13,810 --> 00:10:18,600
+للاربع، للاربع، اجبار واحد للاربع، أربعة للتانين، تانين
+
+107
+00:10:18,600 --> 00:10:21,880
+للتلاتة، تلاتة للواحد، واحد للتانين يكبر، أربعة
+
+108
+00:10:21,880 --> 00:10:27,720
+للتانين، تانين للواحد، واحد للواحد، واحد للتلاتة
+
+109
+00:10:27,720 --> 00:10:34,620
+تلاتة للتلاتة، مين بيضل عنده؟ خلصه، اللي مافيش
+
+110
+00:10:34,620 --> 00:10:40,760
+خمسة، هيكبهاش، ال order what 
+
+111
+00:10:40,760 --> 00:10:45,360
+is the order؟ write each of the following
+
+112
+00:10:45,360 --> 00:10:50,800
+permutation، مش مشكلة، what is the order of each of
+
+113
+00:10:50,800 --> 00:10:53,840
+the following permutation، هنا بتطبق قاعدة least
+
+114
+00:10:53,840 --> 00:10:58,760
+common multiple، بعد ما إيش طبعا هدول disjoint، هدي
+
+115
+00:10:58,760 --> 00:11:05,560
+disjoint، هدي disjoint، هدي لأ وهدي لأ، بتكتبهم زي ما
+
+116
+00:11:05,560 --> 00:11:10,060
+عملنا هنا، وبعدين بتاخد مين؟ ال least common 
+
+117
+00:11:10,060 --> 00:11:18,730
+multiple، واضح؟ واضح يا شباب؟ هو احنا قرأنا السؤال
+
+118
+00:11:18,730 --> 00:11:21,570
+خطأ، المفترض أنه فقط نكتبهم زي هيك، ما نحسبش ال
+
+119
+00:11:21,570 --> 00:11:24,990
+order، سؤال ال order هو اللي تحت، لكن قدر الله أنه
+
+120
+00:11:24,990 --> 00:11:30,290
+نحسب ال order مع مين؟ مع نكتبهم على شكل disjoint
+
+121
+00:11:30,290 --> 00:11:37,830
+cycles، تلاتة
+
+122
+00:11:37,830 --> 00:11:42,850
+إيه؟ تلاتة مع تلاتة، إيش اللي يكون multiple تلاتة، أقبل 
+
+123
+00:11:42,850 --> 00:11:46,750
+أردر تلاتة، ال least common multiple هي تلاتة و 
+
+124
+00:11:46,750 --> 00:11:55,370
+اربعة، اتناش، تلاتة و اتنين، تلاتة و ستة، ستة، أربعة و 
+
+125
+00:11:55,370 --> 00:12:00,710
+خمسة، بس هدول بدهم يكونوا، بدك تشتغلهم سرعة اللي 
+
+126
+00:12:00,710 --> 00:12:01,250
+أنا همسح
+
+127
+00:12:21,220 --> 00:12:25,080
+طيب what is the order of each of the following 
+
+128
+00:12:25,080 --> 00:12:31,060
+permutations؟ طبعًا إيش هنعمل؟ هنكتبهم cycles نبدأ
+
+129
+00:12:31,060 --> 00:12:37,740
+بالواحد للثنين، الثنين للواحد، ونسكر، ثلاثة للخمسة، و
+
+130
+00:12:37,740 --> 00:12:41,300
+خمسة للستة، وستة للثلاثة، وأربعة، إيش الـ least common
+
+131
+00:12:41,300 --> 00:12:49,090
+multiple؟ ستة، هنا واحد للسبعة، سبعة للخمسة، خمسة 
+
+132
+00:12:49,090 --> 00:12:55,530
+للثلاثة، ثلاثة للواحد، ونسكر، كمل، اثنين للستة، وستة
+
+133
+00:12:55,530 --> 00:13:01,830
+للأربعة، الـ least common multiple قد ايش؟ اثنا عشر، الـ
+
+134
+00:13:01,830 --> 00:13:04,870
+least common multiple للأربعة والثلاثة عبارة عن
+
+135
+00:13:04,870 --> 00:13:09,110
+اثنا عشر، what is the order of product of a pair of
+
+136
+00:13:09,110 --> 00:13:13,450
+disjoint cycles of length أربعة وستة، الـ least
+
+137
+00:13:13,450 --> 00:13:15,870
+common multiple لأربعة وستة قد ايش؟
+
+138
+00:13:19,450 --> 00:13:23,770
+Show that A8 contains an element of order 15
+
+139
+00:13:28,770 --> 00:13:32,250
+عشان يكون عندك order خمسة عشر، الخمسة عشر لازم تكون 
+
+140
+00:13:32,250 --> 00:13:37,430
+least common multiple لعددين، يا واحد وخمسة عشر
+
+141
+00:13:37,430 --> 00:13:41,470
+ما أقدرش أحصل على طول خمسة عشر، فيه ثمانية، يجب ثلاثة
+
+142
+00:13:41,470 --> 00:13:45,890
+أو خمسة، يجب مين؟ هناخد واحد، اثنين، ثلاثة، أربعة، خمسة،
+
+143
+00:13:45,890 --> 00:13:53,510
+ستة، سبعة، ثمانية، وهذه الـ order لها قد ايش؟ What are
+
+144
+00:13:53,510 --> 00:14:06,810
+the possible orders for the elements of S6 and A6؟
+
+145
+00:14:15,160 --> 00:14:20,780
+طيب، حسب نفس الأسلوب، الـ orders واحد، واثنين، وثلاثة،
+
+146
+00:14:20,780 --> 00:14:28,900
+وأربعة، وخمسة، وستة، يمالهم exist الـ orders هدول
+
+147
+00:14:28,900 --> 00:14:33,780
+موجودين، permutation فيها عنصر واحد، عنصرين، ثلاثة،
+
+148
+00:14:33,780 --> 00:14:41,310
+أربعة، خمسة، ستة، هنجي نشوف التشكيلات، تشكيلات لـ
+
+149
+00:14:41,310 --> 00:14:44,970
+permutation طولها ستة، يا إما بيكون عندي واحد اللي هو
+
+150
+00:14:44,970 --> 00:14:56,190
+a1, a2, a3, a4 طبعًا، أو a5 مع a6، بنشيل الـ a6 وبنرجع 
+
+151
+00:14:56,190 --> 00:15:04,010
+لمين؟ لخمسة، بنشيلها مع a5 و a6، القوة ده قد ايش؟ أربعة،
+
+152
+00:15:04,010 --> 00:15:13,820
+موجود، أو تشكيلات بهذا الشكل، ثلاثة، ثلاثة، أو 
+
+153
+00:15:13,820 --> 00:15:23,420
+ثلاثة، اثنين، هنا الـ order ثلاثة موجود، وهنا الـ order 
+
+154
+00:15:23,420 --> 00:15:28,840
+ستة موجود، لو بتتكلم عن تشكيلات الـ orders فيها
+
+155
+00:15:28,840 --> 00:15:35,720
+اثنين، أ واحد، اثنين، أ ثلاثة، أ أربعة، أو أ واحد، اثنين،
+
+156
+00:15:35,720 --> 00:15:43,270
+أ ثلاثة، أ أربعة، A5، A6، وهنا الـ order اثنين موجود،
+
+157
+00:15:43,270 --> 00:15:50,910
+وهنا الـ order اثنين موجود، يقبل orders في A6 فقط، الـ
+
+158
+00:15:50,910 --> 00:15:58,890
+orders in A6 are من
+
+159
+00:15:58,890 --> 00:16:07,550
+واحدة لستة، طيب، في A6، E6 للناس اللي ما كانوش موجودين
+
+160
+00:16:07,550 --> 00:16:13,750
+هي الـ even permutation لـ
+
+161
+00:16:13,750 --> 00:16:21,490
+الـ even permutation عشان أقول إنه الـ alpha بكتبها
+
+162
+00:16:21,490 --> 00:16:26,610
+Alpha 1، Alpha 2 لعند Alpha N، حيث Alpha I is two
+
+163
+00:16:26,610 --> 00:16:33,050
+cycle، إيش يعني two cycle؟ Alpha I عبارة عن AI 1، AI
+
+164
+00:16:33,050 --> 00:16:40,290
+2، يعني الـ .. الـ permutation بروح بكتبه على شكل حاصل
+
+165
+00:16:40,290 --> 00:16:46,070
+ضرب cycles، كل واحدة منهم الطول قد ايش؟ اثنين، هنّا
+
+166
+00:16:46,070 --> 00:16:52,410
+ما بفرجش معايا الـ disjoint، طبعًا لو الـ N even بقولي
+
+167
+00:16:52,410 --> 00:16:57,890
+الـ alpha even، لو الـ N odd بقولي الـ alpha odd،
+
+168
+00:17:01,290 --> 00:17:07,430
+لو بدي أجي هنّا، أول حاجة الـ identity even، يعني الـ
+
+169
+00:17:07,430 --> 00:17:16,430
+identity في أي ستة، يجب الـ order واحد موجود، طيب،
+
+170
+00:17:16,430 --> 00:17:21,970
+الـ order اثنين، هل بقدر ألاقي عنصر الـ order اثنين في
+
+171
+00:17:21,970 --> 00:17:29,430
+أي ستة؟ بلاقي واحد، اثنين، ثلاثة، أربعة ينتمي لـ إي ستة،
+
+172
+00:17:30,690 --> 00:17:37,630
+يجب الـ order اثنين، إيش ماله؟ برضه موجود، ليش هذا
+
+173
+00:17:37,630 --> 00:17:44,550
+العنصر زوجي يا شباب؟ ليش هذا زوجي؟ لأنه عبارة عن
+
+174
+00:17:44,550 --> 00:17:48,710
+عدد زوجي من الـ two cycles، هذا بنسميه two cycle، و
+
+175
+00:17:48,710 --> 00:17:51,530
+هذا بنسميه two cycle، في عندك اثنتين من الـ two 
+
+176
+00:17:51,530 --> 00:17:57,370
+cycle؟ ما حدش يجي يقول لي ماهي الـ order اثنين وقد
+
+177
+00:17:57,370 --> 00:18:03,630
+لا، أنت من أيه ستة؟ لا، يكفيني عنصر واحد الـ order له
+
+178
+00:18:03,630 --> 00:18:09,110
+الـ 2 في الـ a6 عشان أقول إنه يوجد عنصر الـ order له الـ 2
+
+179
+00:18:09,110 --> 00:18:13,690
+في الـ a6، أو الـ order 2 موجود ضمن الـ orders لعناصر
+
+180
+00:18:13,690 --> 00:18:24,090
+الـ a6، طيب، الـ order 3، 123، هل هو في a6؟ لا، في a6 هذا 
+
+181
+00:18:24,090 --> 00:18:27,970
+عبارة عن 1312
+
+182
+00:18:30,900 --> 00:18:35,500
+هذه الـ permutation بتُكتب بهذا الشكل، وهذا أنصف
+
+183
+00:18:35,500 --> 00:18:43,240
+أيه ستة؟ هذا أنصف كيف؟
+
+184
+00:18:43,240 --> 00:18:47,940
+لا، هذه غير هذه، هذه الـ order اثنين، لكن أنا الـ order
+
+185
+00:18:47,940 --> 00:18:52,400
+ثلاثة، هذولا مش disjoint يا شباب، هذولا الـ two
+
+186
+00:18:52,400 --> 00:18:59,110
+permutation مش disjoint، العنصر هذا اللي الـ order 
+
+187
+00:18:59,110 --> 00:19:03,690
+إله الثلاثة موجود في S ده، خدها قاعدة، كل cycle
+
+188
+00:19:03,690 --> 00:19:10,830
+طولها فردي بتكون permutation زوجية، كل cycle طولها
+
+189
+00:19:10,830 --> 00:19:16,590
+فردي، إيش يعني طولها؟ طبعًا بتكلم عن cycle واحدة، مش
+
+190
+00:19:16,590 --> 00:19:23,430
+حاصل ضرب cycles، طولها فردي بتكون عنصر وين؟ في A6، أو
+
+191
+00:19:23,430 --> 00:19:29,490
+في AN يعني، طب إن الـ order ثلاثة exist، طب الـ order
+
+192
+00:19:29,490 --> 00:19:39,590
+أربعة، هذه لا تنتمي لـ A6، هل هذا يعني إن مافيش order
+
+193
+00:19:39,590 --> 00:19:48,250
+أربعة في عناصر الـ A6؟ لا، هذا العنصر ينتمي
+
+194
+00:19:48,250 --> 00:19:54,170
+لـ A6، ليش؟ لأن هذا بدي أساوي واحد، أربعة، واحد، ثلاثة،
+
+195
+00:19:54,170 --> 00:20:00,690
+واحد، اثنين، خمسة، ستة، واحد، اثنين، ثلاثة، أربعة، كم two
+
+196
+00:20:00,690 --> 00:20:06,690
+cycle عندك؟ أربعة من الـ two cycles، يعني أربعة
+
+197
+00:20:06,690 --> 00:20:11,210
+permutations جزئيات من الـ alpha، طول كل واحدة منهم
+
+198
+00:20:11,210 --> 00:20:17,090
+إيش؟ اثنين، disjoint أو مش disjoint، ما يهمنيش، يكبر
+
+199
+00:20:17,090 --> 00:20:19,530
+الـ order أربعة موجود ولا مش موجود؟
+
+200
+00:20:24,980 --> 00:20:34,900
+موجود، طيب، ماشي، أركز
+
+201
+00:20:34,900 --> 00:20:41,540
+معايا، أضع القلم، أركز معايا، أضع القلم، قلت لك الـ
+
+202
+00:20:41,540 --> 00:20:46,510
+permutation، أي permutation في الدنيا، بأجي بكتبها
+
+203
+00:20:46,510 --> 00:20:49,770
+على شكل two cycles، يعني لو الـ ألفا عبارة عن الـ a
+
+204
+00:20:49,770 --> 00:21:01,950
+واحد، اثنين لعند الـ an، هتكتب زي هيك الأول
+
+205
+00:21:01,950 --> 00:21:05,690
+مع الآخر، ما جاب لي الآخر، قبل قبل الآخر، لعند
+
+206
+00:21:05,690 --> 00:21:13,010
+الثاني، هنجي هد، لو عددهم زوجي،
+
+207
+00:21:13,010 --> 00:21:20,760
+بنقول عنها، شلو عددهم فردي، نقول
+
+208
+00:21:20,760 --> 00:21:27,520
+الـ alpha is odd، حاجة الـ AN بياخد كل الـ alpha في
+
+209
+00:21:27,520 --> 00:21:33,660
+SN حيث الـ alpha is even، وهذه أثبتنا إنها group، و
+
+210
+00:21:33,660 --> 00:21:39,940
+الـ order لـ AN بيساوي N factorial على 2، آخر نظرية
+
+211
+00:21:39,940 --> 00:21:46,660
+في الشبطة، هنجي، المطلوب مني في الـ A6 أشوف إيش الـ
+
+212
+00:21:46,660 --> 00:21:51,680
+orders للعناصر تبع الـ A6، هنجي لما أنا حسبت الـ A6
+
+213
+00:21:51,680 --> 00:21:56,040
+إيش احتمالات الـ order؟ واحد، اثنين، ثلاثة، أربعة، خمسة،
+
+214
+00:21:56,040 --> 00:22:01,420
+ستة، لما بنتقل على الـ A6 بنشوف مين من هذه الـ orders
+
+215
+00:22:01,420 --> 00:22:06,450
+موجودين في الـ A6، عشان يكون الـ order موجود كـ order
+
+216
+00:22:06,450 --> 00:22:10,890
+لعنصر في الـ a6 لازم أوجد عنصر يكون زوجي، والـ order
+
+217
+00:22:10,890 --> 00:22:15,090
+له حسب الرقم اللي اللي بدشر عليه، لو بدأت برقم واحد،
+
+218
+00:22:15,090 --> 00:22:20,130
+الـ identity permutation زوجية، identity تُكتب بهذا
+
+219
+00:22:20,130 --> 00:22:29,570
+الشكل، واحد، اثنين، اثنين، واحد، هذه زوجية، فـ الـ
+
+220
+00:22:29,570 --> 00:22:34,820
+identity even، يجب إن الـ order واحد شمالهم موجود، هنجي
+
+221
+00:22:34,820 --> 00:22:38,820
+نيجي على الـ order اثنين، عشان أتكلم عن order اثنين،
+
+222
+00:22:38,820 --> 00:22:43,040
+بدي permutation الـ order اللي لها اثنين، وتكون
+
+223
+00:22:43,040 --> 00:22:46,040
+even، هد الـ order اللي لها اثنين، الـ least common
+
+224
+00:22:46,040 --> 00:22:49,460
+multiple اللي لها اثنين واثنين مش بيساوي اثنين، هل
+
+225
+00:22:49,460 --> 00:22:55,700
+هي even؟ نعم، even، كم جوز من الـ two cycle موجود؟
+
+226
+00:22:55,700 --> 00:23:01,560
+جوزين، يجب الـ order اثنين شمالهم موجود كـ order لعنصر
+
+227
+00:23:01,560 --> 00:23:07,060
+في الـ a6، الأردر ثلاثة، هذه الـ permutation واحد، اثنين،
+
+228
+00:23:07,060 --> 00:23:12,400
+ثلاثة، الـ order لا يجديش ثلاثة، الـ order ثلاثة وهي
+
+229
+00:23:12,400 --> 00:23:17,000
+permutation زوجية، ليش؟ واحد مع ثلاثة، واحد مع اثنين،
+
+230
+00:23:17,000 --> 00:23:22,180
+كم جوز اثنين؟ زوجي، يعني بهذه الـ permutation زوجية،
+
+231
+00:23:22,180 --> 00:23:25,800
+والـ order الـ .. ما بيخسرنيش، أنا هنا يكون .. هدول
+
+232
+00:23:25,800 --> 00:23:30,390
+أكيد مش disjoint، هدول أكيد .. شوف الـ disjoint مهمني
+
+233
+00:23:30,390 --> 00:23:34,570
+عند الضرب، عند حساب الـ inverse، عند حساب الطول، لكن
+
+234
+00:23:34,570 --> 00:23:38,830
+لما أنا بدي أجي أتكلم عن even أو odd، بتكلمش على
+
+235
+00:23:38,830 --> 00:23:45,480
+disjoint، هنا واضح؟ طيب، أخلصها، الـ order ثلاثة، الـ
+
+236
+00:23:45,480 --> 00:23:50,800
+order أربعة، الـ order أربعة، هذا العنصر 1234 مش في
+
+237
+00:23:50,800 --> 00:23:58,520
+الـ a6، ليش؟ لما أنا بفرغ لـ two cycle، 141312
+
+238
+00:23:58,520 --> 00:24:03,560
+كده، العدد هنا ثلاثة، هذا ليه يعني إنه نجح في عناصر
+
+239
+00:24:03,560 --> 00:24:08,050
+ثانية الـ order لها أربعة من هذا الشكل، هذا لو فررتك 
+
+240
+00:24:08,050 --> 00:24:12,610
+two cycles، واحد، اثنين، ثلاثة، أربعة، كم two cycle
+
+241
+00:24:12,610 --> 00:24:17,930
+عندك؟ أربعة، زوجي ولا فردي؟ زوجي، إيه بقى هذه الـ
+
+242
+00:24:17,930 --> 00:24:23,570
+permutation زوجية، الـ order اللي هنجد ايش؟ أربعة، إيه بقى
+
+243
+00:24:23,570 --> 00:24:27,790
+الـ order أربعة موجود في asset ولا لأ؟ موجود، نيجي للـ
+
+244
+00:24:27,790 --> 00:24:28,690
+order خمسة،
+
+245
+00:24:35,360 --> 00:24:44,320
+هذا الـ permutation 1 2 3 4 5 .. 1 5 .. 1 4 .. 1 2 .. 1
+
+246
+00:24:44,320 --> 00:24:48,940
+3 1 2 .. موجودة في
+
+247
+00:24:48,940 --> 00:24:55,840
+A6 .. لماذا؟ .. 1 2 3 4 .. كم two cycle عندك؟
+
+248
+00:24:55,840 --> 00:25:00,100
+أربعة two cycles .. هذا الـ permutation even ولا odd ..
+
+249
+00:25:00,100 --> 00:25:01,520
+even، قد ايش طولها؟
+
+250
+00:25:13,790 --> 00:25:19,010
+عشان يكون عندك عنصر الـ order له 6 في A6 يا إما 
+
+251
+00:25:19,010 --> 00:25:25,510
+هياخد الخيار هذا وبالتالي
+
+252
+00:25:25,510 --> 00:25:26,530
+لما تيجي تكتبه
+
+253
+00:25:33,580 --> 00:25:40,420
+كداش عددهم هدول؟ هل هذا لا ينتمي إلى ستة؟ ليش؟ لأنه
+
+254
+00:25:40,420 --> 00:25:52,100
+فردي أو الشكل هل عناصر
+
+255
+00:25:52,100 --> 00:25:58,000
+للـ order إلى ستة في ستة؟ يا cycles طولها ستة يا
+
+256
+00:25:58,000 --> 00:26:03,750
+two cycles واحدة ثلاثة والثانية اثنين طبعا كمل A1,
+
+257
+00:26:03,970 --> 00:26:14,290
+A3, A1, A2, A4, A5 هل هذا ينتمي إلى A6؟ لا لا 
+
+258
+00:26:14,290 --> 00:26:20,310
+ينتمي إلى A6 هل الـ order 6 موجود؟ الـ order 6 does
+
+259
+00:26:20,310 --> 00:26:36,770
+not exist الـ orders in A6 1 و2 و3 و4 و5 هذه
+
+260
+00:26:36,770 --> 00:26:43,050
+احتمالات الـ orders لعناصر الـ a6 طبعا لو أنا بشغل
+
+261
+00:26:43,050 --> 00:26:50,110
+في a7 نفس الأسلوب استعمله لكن القيم قد تكون مختلفة
+
+262
+00:26:50,110 --> 00:26:56,890
+يعني في a7 ممكن أجد الـ order 6 لأ
+
+263
+00:26:56,890 --> 00:27:03,870
+هاجي الـ order 7 في A7 هلاجي الـ order واحد هلاجي الـ
+
+264
+00:27:03,870 --> 00:27:08,610
+order اثنين في الـ A7 الـ order واحد الـ order اثنين
+
+265
+00:27:08,610 --> 00:27:12,330
+الـ order ثلاثة الـ order أربعة الـ order خمسة و الـ
+
+266
+00:27:12,330 --> 00:27:21,990
+order ستة و الـ order سبعة و الـ order عشرة لأ الـ
+
+267
+00:27:21,990 --> 00:27:24,530
+order اثني عشر على الأرجح لأ برضه
+
+268
+00:27:27,840 --> 00:27:31,080
+ما هو الـ .. السبعة في الـ order واحد و اثنين و
+
+269
+00:27:31,080 --> 00:27:34,560
+ثلاثة و أربعة و خمسة و ستة و سبعة و عشرة و اثنين و
+
+270
+00:27:34,560 --> 00:27:35,520
+اثنين و اثنين و اثنين و اثنين و اثنين و اثنين و
+
+271
+00:27:35,520 --> 00:27:38,100
+اثنين و اثنين و اثنين و اثنين و اثنين و اثنين و
+
+272
+00:27:38,100 --> 00:27:41,440
+اثنين و اثنين و اثنين و اثنين و اثنين و اثنين و
+
+273
+00:27:41,440 --> 00:27:41,960
+اثنين و اثنين و اثنين و اثنين و اثنين و اثنين و
+
+274
+00:27:41,960 --> 00:27:44,560
+اثنين و اثنين و اثنين و اثنين و اثنين و اثنين و
+
+275
+00:27:44,560 --> 00:27:47,980
+اثنين
+
+276
+00:27:47,980 --> 00:27:57,490
+و اثنين و اثنين و اثنين و اثنين ومافيش احتمالات الـ
+
+277
+00:27:57,490 --> 00:28:01,150
+order اثنين في A6 يا cycle واحدة طول .. يا cycle
+
+278
+00:28:01,150 --> 00:28:06,450
+واحدة طولها اثنين زي هيك خلينا نكتبها هنا 1
+
+279
+00:28:06,450 --> 00:28:13,830
+2 يا 1 2 3 4 يا 1 2
+
+280
+00:28:13,830 --> 00:28:21,190
+3 4 5 6 هذه احتمالات العناصر للـ
+
+281
+00:28:21,190 --> 00:28:25,850
+order الاثنين في A6 هذا فردي وهذا فردي بس هذا زوجي
+
+282
+00:28:28,170 --> 00:28:40,110
+هذا فردي وهذا فردي لكن هذا إيه؟ زوجي طيب
+
+283
+00:28:40,110 --> 00:28:44,290
+what about إيه سبعة؟ جاوبناها 1 2 3
+
+284
+00:28:44,290 --> 00:28:48,570
+4 5 6 7 10 لا هجيت الـ order 12
+
+285
+00:28:48,570 --> 00:28:55,430
+بيحصل زي هيك يعني عنصر زي هيك هذا فردي لا ينتمي
+
+286
+00:28:55,430 --> 00:29:00,220
+لأي سبعة يكبر فقط الـ orders هدول 1 و 2 و
+
+287
+00:29:00,220 --> 00:29:07,520
+3 4 و 5 و 6 و 7 what
+
+288
+00:29:07,520 --> 00:29:12,660
+is the maximum order of any element in A عشرة إيش
+
+289
+00:29:12,660 --> 00:29:19,500
+أكبر least common multiple ممكن أحصل عليه من أرقام
+
+290
+00:29:19,500 --> 00:29:25,560
+مجموعة عشرة أو المجموعة الأكبر تبع عشرة تعال نجرب
+
+291
+00:29:26,540 --> 00:29:31,460
+في A10 أنا لو أخدت .. طبعا أنا حاول أخد رقم ..
+
+292
+00:29:31,460 --> 00:29:37,480
+عشان أنت تزيد الـ least common multiple خد أرقام
+
+293
+00:29:37,480 --> 00:29:42,480
+كبار شوية فلو أخدت أنت الأربعة مع الستة كداش؟
+
+294
+00:29:42,480 --> 00:29:48,500
+12 الثلاثة مع السبعة 21 الخمسة مع
+
+295
+00:29:48,500 --> 00:29:57,010
+الخمسة least common multiple خمسة طيب الاثنين مع
+
+296
+00:29:57,010 --> 00:30:01,650
+الثمانية ثمانية الواحد مع التسعة تسعة طيب في
+
+297
+00:30:01,650 --> 00:30:16,950
+احتمالات ثانية في احتمالات ثانية اثنين
+
+298
+00:30:16,950 --> 00:30:19,930
+مع الثلاثة مع خمسة إيش الـ least common multiple
+
+299
+00:30:23,460 --> 00:30:33,740
+جديش؟ أعلى order في الـ S عشرة 30 هل هذا العنصر
+
+300
+00:30:33,740 --> 00:30:40,860
+موجود في أي عشرة؟ لا، هذا فردي طيب، لو شن هذا
+
+301
+00:30:40,860 --> 00:30:46,700
+بيصير زوجي، هو بيحصل على مين؟ على 15 طبعا، هذا
+
+302
+00:30:46,700 --> 00:30:53,470
+طول فردي، وفردي مع بعض بيطلع زوجي هنا زوجي مع زوجي
+
+303
+00:30:53,470 --> 00:30:57,470
+هيطلع الجواب جديش 21 لإنه هاخد عنصر زي
+
+304
+00:30:57,470 --> 00:31:05,870
+هيك يعني هزود 1 2 3 4 5 6 7
+
+305
+00:31:05,870 --> 00:31:12,900
+8 9 10 هذا عنصر الـ order إله جديش 21 هو
+
+306
+00:31:12,900 --> 00:31:24,660
+even لأن هذا بنكتب 1 3 1 2 4 10 4 9 4 8 4 7 4 6 4
+
+307
+00:31:24,660 --> 00:31:32,440
+5 1 2 3 4 5 6 7 8 وهذا العنصر زوجي ينتمي لـ a 10 و
+
+308
+00:31:32,440 --> 00:31:38,020
+الـ order الـ 21 نجونا اللي بعد الـ 21 30 ما بيكونش
+
+309
+00:31:38,020 --> 00:31:45,090
+زوجي يكبر مين الأقل منه 21 طيب الـ determine
+
+310
+00:31:45,090 --> 00:31:47,450
+whether the following permutation are even or odd
+
+311
+00:31:47,450 --> 00:31:59,850
+هذه 1 5 سؤال 9 even ولا odd طبعا هذا 1
+
+312
+00:31:59,850 --> 00:32:06,590
+5 1 3 زوجي ولا فردي زوجي 1 3 5
+
+313
+00:32:06,590 --> 00:32:09,990
+6 1 6 1 5 1 3
+
+314
+00:32:13,620 --> 00:32:18,320
+لو طول فردي فهي زوجية لو طول زوجي فهي فردية بس لو
+
+315
+00:32:18,320 --> 00:32:25,380
+كانوا زي هيك هذا بدك تروح تعمل زي مين وتعد طبعا
+
+316
+00:32:25,380 --> 00:32:34,240
+هذا even هذا odd even odd even even odd ده تنعمل
+
+317
+00:32:34,240 --> 00:32:45,050
+زي هيك 1 2 و 1 4 و 1 3 و 1
+
+318
+00:32:45,050 --> 00:32:54,870
+2 و 1 5 كم عددها هدول خمسة كيف عملتم
+
+319
+00:32:54,870 --> 00:32:59,530
+على طول اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+320
+00:32:59,530 --> 00:32:59,670
+اد اد اد اد اد اد اد اد اد اد اد اد اد 
+
+321
+00:32:59,670 --> 00:32:59,830
+اد اد اد اد اد اد اد اد اد اد اد اد اد 
+
+322
+00:32:59,830 --> 00:32:59,850
+اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+323
+00:32:59,850 --> 00:33:04,130
+اد اد اد اد اد
+
+324
+00:33:04,130 --> 00:33:09,830
+اد طبعا في تكملة للسؤال هو إيه؟ المحاضرة القادمة إن
+
+325
+00:33:09,830 --> 00:33:15,230
+شاء الله سأسمعيه بكملكوا بداية السؤال عشرة يعطيكوا
+
+326
+00:33:15,230 --> 00:33:15,590
+العافية
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..3efced594025f84876f975375e9c13090767e5db
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/jsNOtE-lgcg_postprocess.srt
@@ -0,0 +1,1304 @@
+1
+00:00:22,050 --> 00:00:26,010
+السلام عليكم اسمي الله الرحمن الرحيم طبعا اليوم
+
+2
+00:00:26,010 --> 00:00:28,250
+هناخد ان شاء الله المحاضرة الأخيرة اللي هكون
+
+3
+00:00:28,250 --> 00:00:31,910
+متواجد معاكم فيها المحاضرة القادمة هيكون أستاذ
+
+4
+00:00:31,910 --> 00:00:36,090
+إسماعيل أصل هناخد بعض الأسئلة على الوحدة الخامسة
+
+5
+00:00:36,090 --> 00:00:38,970
+permutation group بس قبل ما أفوض في الأسئلة بدأ
+
+6
+00:00:38,970 --> 00:00:41,930
+أذكر للناس اللي ما كانوا موجودين المحاضرة الماضية
+
+7
+00:00:41,930 --> 00:00:48,410
+بقواعد حساب ال orders في ال permutationsأول شغلة
+
+8
+00:00:48,410 --> 00:00:52,970
+لو كان عندي permutation بهذا الشكل a1, a2 اللي عند
+
+9
+00:00:52,970 --> 00:01:02,370
+an فال order لل alpha بدي ساوي n الشغلة
+
+10
+00:01:02,370 --> 00:01:08,200
+التانيةلو كانت ال alpha مثلا عبارة عن alpha 1 و
+
+11
+00:01:08,200 --> 00:01:13,980
+alpha 2 لعند alpha k و هدولة عبارة عن cycles فال
+
+12
+00:01:13,980 --> 00:01:17,700
+order لل alpha عبارة عن ال least common multiple ل
+
+13
+00:01:17,700 --> 00:01:23,020
+order ال alpha 1 order ال alpha 2 order ال alpha k
+
+14
+00:01:23,020 --> 00:01:31,880
+تلاتة لو كانت ال alpha عبارة عن a1 a2 لعند anفال
+
+15
+00:01:31,880 --> 00:01:38,960
+alpha inverse هيكون a n a n minus واحد a تنين nine
+
+16
+00:01:38,960 --> 00:01:43,820
+a واحد ليش كتابت هنا تلات قواعد هادول لإن السؤال
+
+17
+00:01:43,820 --> 00:01:47,500
+الأول والسؤال التاني والسؤال التالت الموجودين
+
+18
+00:01:47,500 --> 00:01:53,040
+قدامك يتم التعامل معاهم بناء على الشغل اللي عندك
+
+19
+00:01:53,040 --> 00:01:58,420
+موجود جاب لما نحلهم هحل سؤال موجود في التلخيص وهو
+
+20
+00:01:59,420 --> 00:02:07,380
+Exercise على معتقد رقم 3 بيقول في ال S7 إيش
+
+21
+00:02:07,380 --> 00:02:12,240
+احتمالات ال order؟
+
+22
+00:02:12,240 --> 00:02:22,040
+يعني عناصر ال S7 إيش ال orders الممكنين عندك؟ هبدأ
+
+23
+00:02:22,040 --> 00:02:27,260
+بأشكال العناصر في ال S7 أول شكل ممكن يكون زي هيك
+
+24
+00:02:32,870 --> 00:02:38,250
+و هذا ال order إيه اللي و جدياش؟ سبعة ممكن أحصل
+
+25
+00:02:38,250 --> 00:02:44,370
+على عنصر بهذا الشكل a1, a2, a6 و ال order 6 بنفس
+
+26
+00:02:44,370 --> 00:02:49,370
+الطريقة أنا ممكن أحصل على ال order خمسة و أربعة و
+
+27
+00:02:49,370 --> 00:02:54,040
+تلاتة و اتنين و واحدةهاخد cycle فيها خمس عناصر
+
+28
+00:02:54,040 --> 00:02:59,000
+cycle فيها أربع عناصر cycle فيها تلت عناصر cycle
+
+29
+00:02:59,000 --> 00:03:03,200
+فيها عنصرين وcycle اللي هو ال identity مافيش فيها
+
+30
+00:03:03,200 --> 00:03:07,940
+ولا عنصر ييك بقى الأرقام من واحد لسبعة دائما
+
+31
+00:03:07,940 --> 00:03:15,000
+موجودين كاحتمالات orders هنا في شغلة مهمة عناصر ال
+
+32
+00:03:15,000 --> 00:03:17,960
+S7 كدهش عددهم؟
+
+33
+00:03:25,350 --> 00:03:29,190
+سبعة في ستة فاكتوريال سبعة في سبعمائه عشرين خمس
+
+34
+00:03:29,190 --> 00:03:30,070
+سلاف واربعين
+
+35
+00:03:40,100 --> 00:03:42,920
+خلال الأسئلة اللى هنشرحهم سواء أنا وصلتله أو
+
+36
+00:03:42,920 --> 00:03:47,080
+الأستاذ اسماعيل هيجي سؤال جداش عدد العناصر اللى من
+
+37
+00:03:47,080 --> 00:03:53,940
+order كذا في ال S7 و S8 طيب هيك اتخلصنا كل
+
+38
+00:03:53,940 --> 00:03:58,500
+الاحتمالات يكون عندي cycle واحدة ناخد احتمالات
+
+39
+00:03:58,500 --> 00:04:04,920
+يكون عندي two cycles مع بعض يعني مثلا لو جلنا A1,
+
+40
+00:04:05,200 --> 00:04:14,590
+A2, A3, A4, A5, A6لما بدي اكملها هيكون A7 طبعا هذا
+
+41
+00:04:14,590 --> 00:04:20,970
+بروح فانخجعت لمين لهذه ايه يبقى هذه مالهاش لازمة
+
+42
+00:04:20,970 --> 00:04:27,290
+نشيل A6 و نشتر على A5 اللي تكملة تبعتها يا cycles
+
+43
+00:04:27,290 --> 00:04:34,810
+زي هيك وبالتالي مالهمش لازمة يا cycle زي هيك في
+
+44
+00:04:34,810 --> 00:04:39,990
+هذه الحالة ال orderبقى عن ال least common multiple
+
+45
+00:04:39,990 --> 00:04:46,710
+لمن؟ لخمسة و اتنين كم؟ عشرة ايه باحتمال ان يكون
+
+46
+00:04:46,710 --> 00:04:52,610
+عنده عنصر ال order الو عشرة اشماله موجود طب لو
+
+47
+00:04:52,610 --> 00:04:57,690
+أخدنا مثلا Alpha خلصنا الخمسة cycle ناخد أربع
+
+48
+00:04:57,690 --> 00:05:04,570
+cycle A1, A2, A3, A4 بيضلوا تلت واحدات يا إما
+
+49
+00:05:04,570 --> 00:05:05,590
+بعملهم زي هيك
+
+50
+00:05:09,470 --> 00:05:14,590
+طبعا على الفاضي تلات واحدات واحد واحد واحد مابنفعش
+
+51
+00:05:14,590 --> 00:05:23,210
+يا اما a5 a6 a7 و هدا بشيله و بيصير ال order ل ال
+
+52
+00:05:23,210 --> 00:05:25,830
+alpha عبارة عن ال least common multiple لاربعة و
+
+53
+00:05:25,830 --> 00:05:33,530
+اتنين اربعة او ممكن يصير عندى الاحتمال هدا بدل ما
+
+54
+00:05:33,530 --> 00:05:38,720
+يكون لتنتينيكونوا تلاتة وال order للألف عبارة عن
+
+55
+00:05:38,720 --> 00:05:43,120
+ال least common multiple للأربعة والتلاتة جديش
+
+56
+00:05:43,120 --> 00:05:49,380
+اتناش طبعا الأربعة موجود مسبقا اصلا فمالوش اهمية
+
+57
+00:05:49,380 --> 00:05:53,220
+حاجات لما اريد اخلص انا icon الأولانية فيها أربعة
+
+58
+00:05:53,220 --> 00:06:00,100
+نيجي لما يريد يكون فيها جديش تلاتة اي واحد اي تنين
+
+59
+00:06:00,100 --> 00:06:06,330
+اي تلاتة التكملات يا اما واحدة فيها أربعة زي هذهأو
+
+60
+00:06:06,330 --> 00:06:10,990
+أربعة فيهم واحدة بلاش لازمة لأن في النهاية دول
+
+61
+00:06:10,990 --> 00:06:18,530
+بيكونوا identity يا إما واحدة فيهم تنتين والباقي
+
+62
+00:06:18,530 --> 00:06:29,030
+تنتين فيهم واحدة أو واحدة زي هيك سواء هذه أو
+
+63
+00:06:29,030 --> 00:06:32,480
+هذه اللي من نفس ال orderلأن حاسيب معايا ال order
+
+64
+00:06:32,480 --> 00:06:35,460
+للألفة يبقى on least common multiple اللي التلاتة
+
+65
+00:06:35,460 --> 00:06:40,860
+والاتنين بيعطينا ستة والست أصلا موجود طبعا اللي
+
+66
+00:06:40,860 --> 00:06:44,540
+بعد هي كده إذا أخد واحدة فيها تنتين يا بكمل بخمسة
+
+67
+00:06:44,540 --> 00:06:49,960
+يا بكمل باربعة وواحد يا بكمل بتلاتة واتنين يا بكمل
+
+68
+00:06:49,960 --> 00:06:54,160
+بخمس واحدات في النهاية هحصل على orders موجودين
+
+69
+00:06:54,160 --> 00:07:00,840
+مسبقا باحتمالات ال orders واحد واتنين وتلاتةو 4 و
+
+70
+00:07:00,840 --> 00:07:10,960
+5 و 6 و 7 و 10 و 12 يعني بأي عنصر داخل ال S7 ال
+
+71
+00:07:10,960 --> 00:07:17,300
+order إله واحد من هذه الأرقام لاحقا هناخد طريقة
+
+72
+00:07:17,300 --> 00:07:23,440
+كيف نعرف ال order ال 12 أكم عنصر موجود منه
+
+73
+00:07:27,110 --> 00:07:32,070
+اليناصر السبعة ال orders لها بتاخد الأرقام
+
+74
+00:07:35,000 --> 00:07:38,080
+طيب نيجي للأسئلة الواحد والاتنين والتلاتة
+
+75
+00:07:38,080 --> 00:07:41,280
+الموجودين قدامك find the order of each element
+
+76
+00:07:41,280 --> 00:07:45,460
+طبعا هذا هطبق مباشرة على القاعدة الأولى ال order
+
+77
+00:07:45,460 --> 00:07:49,340
+اتنين ال order تلاتة ال order خمسة ال order K
+
+78
+00:07:49,340 --> 00:07:54,420
+اتنين هطبق على مين القاعدة التانية ال least common
+
+79
+00:07:54,420 --> 00:07:57,420
+multiple للاربع والتلاتة اتن عاشر ال least common
+
+80
+00:07:57,420 --> 00:08:00,520
+multiple للخمسة والاتنين والخمسة عشرة ال least
+
+81
+00:08:00,520 --> 00:08:07,630
+common multiple للاتنين والاتنين والتلاتةستة صح؟
+
+82
+00:08:07,630 --> 00:08:16,330
+صح لأ غلط هدول لازم يكونوا ايش؟ disjoint لازم هدول
+
+83
+00:08:16,330 --> 00:08:21,770
+يكونوا ايش؟ لازم احولهم ليش؟ ل disjoint لازم اضغط
+
+84
+00:08:21,770 --> 00:08:26,310
+و اعملهم disjoint و بعدين اشتغل عليهالـ least
+
+85
+00:08:26,310 --> 00:08:29,910
+common multiple هبدأ بالواحد واحد للتلاتة و تلاتة
+
+86
+00:08:29,910 --> 00:08:34,790
+للخمسة يكبر واحد للخمسة خمسة للخمسة و خمسة للواحد
+
+87
+00:08:34,790 --> 00:08:39,930
+سكرها على التنين تنين للتنين و تنين للتلاتة يكبر
+
+88
+00:08:39,930 --> 00:08:46,990
+تنين للتلاتة تلاتة للاربع واربع للاربع واش ال
+
+89
+00:08:46,990 --> 00:08:51,310
+order least common multiple للتنين و التلاتة كم؟
+
+90
+00:08:51,310 --> 00:08:57,050
+ستةطبعا تجيش مرة واحدة و تقول least common
+
+91
+00:08:57,050 --> 00:08:59,110
+multiple زي ما كنا .. زي ما عملنا في الأول لإن
+
+92
+00:08:59,110 --> 00:09:02,490
+هدول إيش معلهم مش disjoint فلازم يكونوا disjoint
+
+93
+00:09:02,490 --> 00:09:07,350
+حسب النظرية هانا في P هدى لمّا بدك تشتغلها ابدا
+
+94
+00:09:07,350 --> 00:09:12,270
+بالواحد واحد لاتنين للتلاتة للتنين يكبر واحد
+
+95
+00:09:12,270 --> 00:09:17,290
+لاتنين تنين للاربعة اربعة للاربعة واربعة للاربعة
+
+96
+00:09:17,290 --> 00:09:21,670
+يكبر تنين للاربعة اربعة للستة ستة للستة وستة
+
+97
+00:09:21,670 --> 00:09:28,710
+للواحد وسكركمّل، تلاتة لنفسها، تلاتة للتنين، وتنين
+
+98
+00:09:28,710 --> 00:09:34,430
+للتلاتة طيب،
+
+99
+00:09:34,430 --> 00:09:40,190
+أربعة خلصناها، خمسة، خمسة للواحد، واحد لنفسه، واحد
+
+100
+00:09:40,190 --> 00:09:46,470
+للتلاتة، يبقى في خلل لنا هنا نرجع
+
+101
+00:09:46,470 --> 00:09:52,210
+للتلاتة، تلاتة لنفسهاالتلاتة للتنين والتنين للخمسة
+
+102
+00:09:52,210 --> 00:09:57,490
+صحيح اجبار التلاتة للخمسة وخمسة للواحد واحد للواحد
+
+103
+00:09:57,490 --> 00:10:01,390
+وواحد للتلاتة سكر اجبار اكيد الستة زي ما هي ال
+
+104
+00:10:01,390 --> 00:10:06,490
+least common multiple كم؟ ستة ال least common
+
+105
+00:10:06,490 --> 00:10:13,810
+multiple ستة اخر واحدة واحد للاربع اربع للاربع
+
+106
+00:10:13,810 --> 00:10:18,600
+للاربع للاربع اجبار واحد للاربعأربعة للتانين تانين
+
+107
+00:10:18,600 --> 00:10:21,880
+للتلاتة تلاتة للواحد واحد للتانين يكبر أربعة
+
+108
+00:10:21,880 --> 00:10:27,720
+للتانين تانين للواحد واحد للواحد واحد للتلاتة
+
+109
+00:10:27,720 --> 00:10:34,620
+تلاتة للتلاتة مين بيضل عنده؟ خلصه، اللي مافيش
+
+110
+00:10:34,620 --> 00:10:40,760
+خمسة، هيكبهاش ال order what
+
+111
+00:10:40,760 --> 00:10:45,360
+is the order؟write each of the following
+
+112
+00:10:45,360 --> 00:10:50,800
+permutation مش مشكلة what is the order of each of
+
+113
+00:10:50,800 --> 00:10:53,840
+the following permutation هنا بتطبق قاعدة least
+
+114
+00:10:53,840 --> 00:10:58,760
+common multiple بعد ما إياش طبعا هدول disjoint هدي
+
+115
+00:10:58,760 --> 00:11:05,560
+disjoint هدي disjoint هدي لأ وهدي لأ بتكتبهم زي ما
+
+116
+00:11:05,560 --> 00:11:10,060
+عملنا هنا و بعدين بتاخد مين ال least common
+
+117
+00:11:10,060 --> 00:11:18,730
+multiple واضح؟واضح يا شباب؟ هو احنا قرأنا السؤال
+
+118
+00:11:18,730 --> 00:11:21,570
+خطأ المفترض انه فقط نكتبهم زي هيك ما نحسبش ال
+
+119
+00:11:21,570 --> 00:11:24,990
+order سؤال ال order هو اللي تحت لكن قدر الله انه
+
+120
+00:11:24,990 --> 00:11:30,290
+نحسب ال order مع مين مع نكتبهم على شكل disjoint
+
+121
+00:11:30,290 --> 00:11:37,830
+cycles تلاتة
+
+122
+00:11:37,830 --> 00:11:42,850
+ايه؟ تلاتة مع تلاتاش اللي يكون multipleتلاتة اقبل
+
+123
+00:11:42,850 --> 00:11:46,750
+اردر تلاتة ال least common multiple هي تلاتة و
+
+124
+00:11:46,750 --> 00:11:55,370
+اربعة اتناش تلاتة و اتنين تلاتة و ستة ستة اربعة و
+
+125
+00:11:55,370 --> 00:12:00,710
+خمسة بس هدولة بدهم يكونوا بدك تشتغلهم سرعة اللي
+
+126
+00:12:00,710 --> 00:12:01,250
+انا همسح
+
+127
+00:12:21,220 --> 00:12:25,080
+طيب what is the order of each of the following
+
+128
+00:12:25,080 --> 00:12:31,060
+permutations؟ طبعا ايش هنعمل؟ هنكتبهم cycles نبدأ
+
+129
+00:12:31,060 --> 00:12:37,740
+بالواحد للتنين التنين للواحد و سكر تلاتة للخمسة و
+
+130
+00:12:37,740 --> 00:12:41,300
+خمسة للستة وستة للتلاتة واربع ايش ال least common
+
+131
+00:12:41,300 --> 00:12:49,090
+multiple؟ ستة هناواحد للسبعة، سبعة للخمسة، خمسة
+
+132
+00:12:49,090 --> 00:12:55,530
+للتلاتة، تلاتة للواحد وسكر كمل اتنين للستة وستة
+
+133
+00:12:55,530 --> 00:13:01,830
+للاربع ال least common multiple جديش اتناش ال
+
+134
+00:13:01,830 --> 00:13:04,870
+least common multiple للاربع والتلاتة عبارة عن
+
+135
+00:13:04,870 --> 00:13:09,110
+اتناش what is the order of product of a pair of
+
+136
+00:13:09,110 --> 00:13:13,450
+disjoint cycles of length اربع وستة ال least
+
+137
+00:13:13,450 --> 00:13:15,870
+common multiple لاربع وستة جديش
+
+138
+00:13:19,450 --> 00:13:23,770
+Show that A8 contains an element of order 15
+
+139
+00:13:28,770 --> 00:13:32,250
+عشان يكون عندك order خمسة عشر الخمسة عشر لازم تكون
+
+140
+00:13:32,250 --> 00:13:37,430
+least common multiple لعددين يا واحد و خمسة عشر
+
+141
+00:13:37,430 --> 00:13:41,470
+مقدرش احصل على طول خمسة عشر فيه تمانية يجب تلاتة
+
+142
+00:13:41,470 --> 00:13:45,890
+او خمسة يجب مين هناخد واحد اتنين تلاتة اربعة خمسة
+
+143
+00:13:45,890 --> 00:13:53,510
+ستة سبعة تمانية و هذه ال order لها جديشWhat are
+
+144
+00:13:53,510 --> 00:14:06,810
+the possible orders for the elements of S6 and A6؟
+
+145
+00:14:15,160 --> 00:14:20,780
+طيب حسب نفس الأسلوب ال orders واحد واثنين وتلاتة
+
+146
+00:14:20,780 --> 00:14:28,900
+واربعة وخمسة وستة يمالهم exist ال orders هدول
+
+147
+00:14:28,900 --> 00:14:33,780
+موجودين permutation فيها عنصر واحد عنصرين تلاتة
+
+148
+00:14:33,780 --> 00:14:41,310
+اربعة خمسة ستة هجيت نشوف التشكيلاتتشكيلات لـ
+
+149
+00:14:41,310 --> 00:14:44,970
+permutation طولة 6 يا إما بيكون عندي واحد اللي هو
+
+150
+00:14:44,970 --> 00:14:56,190
+a1, a2, a3, a4 طبعا او a5 مع a6 بنشيل ال a6 وبترجع
+
+151
+00:14:56,190 --> 00:15:04,010
+لمين؟ لخمسة بشيلها مع a5 و a6 القوة ده قداش 4
+
+152
+00:15:04,010 --> 00:15:13,820
+موجود أو تشكيلات بهذا الشكلتلاتة تلاتة او
+
+153
+00:15:13,820 --> 00:15:23,420
+تلاتة اتنين هنا ال order تلاتة موجود وهنا ال order
+
+154
+00:15:23,420 --> 00:15:28,840
+ستة موجود لو بتتكلم عن تشكيلات ال orders فيها
+
+155
+00:15:28,840 --> 00:15:35,720
+اتنين ا واحد اتنين ا تلاتة ا اربعة او ا واحد اتنين
+
+156
+00:15:35,720 --> 00:15:43,270
+ا تلاتة ا اربعةA5 A6 وهنا ال order اتنين موجود
+
+157
+00:15:43,270 --> 00:15:50,910
+وهنا ال order اتنين موجود يقبل orders في A6 فقط ال
+
+158
+00:15:50,910 --> 00:15:58,890
+orders in A6 are من
+
+159
+00:15:58,890 --> 00:16:07,550
+واحدة ستة طيب في A6E6 للناس اللي ماكانوش موجودين
+
+160
+00:16:07,550 --> 00:16:13,750
+هي ال even permutation لأ
+
+161
+00:16:13,750 --> 00:16:21,490
+ال even permutation عشان اقول انه ال alpha بكتبها
+
+162
+00:16:21,490 --> 00:16:26,610
+Alpha 1 Alpha 2 لعند Alpha N حيث Alpha I is two
+
+163
+00:16:26,610 --> 00:16:33,050
+cycle ايش يعني two cycle Alpha I عبارة عن AI 1 AI
+
+164
+00:16:33,050 --> 00:16:40,290
+2يعني ال .. ال permutation بروح بكتبه على شكل حاصل
+
+165
+00:16:40,290 --> 00:16:46,070
+ضرب cycles كل واحدة منهم الطولة جدياش اتنين هانا
+
+166
+00:16:46,070 --> 00:16:52,410
+مابفرجش معايا ال disjoint طبعا لو ال N even بقولي
+
+167
+00:16:52,410 --> 00:16:57,890
+ال alpha even لو ال N odd بقولي ال alpha ash
+
+168
+00:17:01,290 --> 00:17:07,430
+لو بدي اجي هان اول حاجة ال identity even يعني ال
+
+169
+00:17:07,430 --> 00:17:16,430
+identity في اي ستة يجب ال order واحد موجود طيب
+
+170
+00:17:16,430 --> 00:17:21,970
+ال order تنين هل بقدر الاقي عنصر ال order تنين في
+
+171
+00:17:21,970 --> 00:17:29,430
+اي ستة بلاقي واحد اتنين تلاتة اربعة ينتمي لإي ستة
+
+172
+00:17:30,690 --> 00:17:37,630
+يجب ال order اتنين ايش ماله؟ برضه موجود ليش هذا
+
+173
+00:17:37,630 --> 00:17:44,550
+العنصر زوجي يا شباب؟ ليش هذا زوجي؟ لأنه عبارة عن
+
+174
+00:17:44,550 --> 00:17:48,710
+عدد زوجي من ال two cycles هذا بنسميها two cycle و
+
+175
+00:17:48,710 --> 00:17:51,530
+هذا بنسميها two cycle في عندك تنتين من ال two
+
+176
+00:17:51,530 --> 00:17:57,370
+cycle؟ ماحدش يجيجي يقولني ماهي ال order اتنين و قد
+
+177
+00:17:57,370 --> 00:18:03,630
+لا انت من ايه ستة؟لأ يكفيني 1 عنصر 1 ال order اله
+
+178
+00:18:03,630 --> 00:18:09,110
+2 في ال a6 علشان اقول انه يوجد عنصر ال order اله 2
+
+179
+00:18:09,110 --> 00:18:13,690
+في ال a6 او ال order 2 موجود ضمن ال orders لعناصر
+
+180
+00:18:13,690 --> 00:18:24,090
+ال a6 طيب ال order 3 123 هل هو في a6 لأ في a6 هذا
+
+181
+00:18:24,090 --> 00:18:27,970
+عبارة عن 1312
+
+182
+00:18:30,900 --> 00:18:35,500
+هذه الـ permutation بتنكتب بهذا الشكل وهذا أنصف
+
+183
+00:18:35,500 --> 00:18:43,240
+ايه ستة؟ هذا أنصف كيف؟
+
+184
+00:18:43,240 --> 00:18:47,940
+لأ هذه غير هذه هذه الأردر اتنين لكن انا الأردر
+
+185
+00:18:47,940 --> 00:18:52,400
+تلاتة هذولا مش this joint يا شباب هذولا ال two
+
+186
+00:18:52,400 --> 00:18:59,110
+permutation مش this jointالعنصر هذا اللي ال order
+
+187
+00:18:59,110 --> 00:19:03,690
+إله التلاتة موجود في S ده خدها قاعدة كل cycle
+
+188
+00:19:03,690 --> 00:19:10,830
+طولها فردي بتكون permutation زوجية كل cycle طولها
+
+189
+00:19:10,830 --> 00:19:16,590
+فردي اش يعني طولها طبعا بتكلم عن cycle واحدة مش
+
+190
+00:19:16,590 --> 00:19:23,430
+حاصل ضرب cycles طولها فردي بتكون عنصر وين؟في A6 او
+
+191
+00:19:23,430 --> 00:19:29,490
+في AN يعني طب ان ال order تلاتة exist طب ال order
+
+192
+00:19:29,490 --> 00:19:39,590
+أربعة هذه لا ينتمي ل A6 هل هذا يعني ان مافيش order
+
+193
+00:19:39,590 --> 00:19:48,250
+أربعة في عناصر ال A6 لأ هذا العنصر ينتمي
+
+194
+00:19:48,250 --> 00:19:54,170
+ل A6ليش؟ لأن هذا بدي ساوي واحد اربعة واحد تلاتة
+
+195
+00:19:54,170 --> 00:20:00,690
+واحد اتنين خمسة ستة واحد اتنين تلاتة اربع اكم two
+
+196
+00:20:00,690 --> 00:20:06,690
+cycle عندك؟ اربع من ال two cycles يعني اربع
+
+197
+00:20:06,690 --> 00:20:11,210
+permutations جزئيات من ال alpha طول كل واحدة منهم
+
+198
+00:20:11,210 --> 00:20:17,090
+ايش؟ اتنين disjoint او مش disjoint مابهمنيش يكبر
+
+199
+00:20:17,090 --> 00:20:19,530
+ال order اربع موجود ولا مش موجود؟
+
+200
+00:20:24,980 --> 00:20:34,900
+موجود طيب ماشي اركز
+
+201
+00:20:34,900 --> 00:20:41,540
+معايا اضع القلم اركز معايا اضع القلم قلتلك ال
+
+202
+00:20:41,540 --> 00:20:46,510
+permutation اي permutation في الدنياباجي بكتبها
+
+203
+00:20:46,510 --> 00:20:49,770
+على شكل two cycles يعني لو الالفة عبارة عن ال a
+
+204
+00:20:49,770 --> 00:21:01,950
+واحد اتنين لعند ال an هد تكتب زي هيك الأول
+
+205
+00:21:01,950 --> 00:21:05,690
+مع الأخر، ما جابلي الأخر، قبل قبل الأخر، لعند
+
+206
+00:21:05,690 --> 00:21:13,010
+التاني هجت هد لو عددهم زودي،
+
+207
+00:21:13,010 --> 00:21:20,760
+بنقول عنهاشلو عددهم فردي نقول
+
+208
+00:21:20,760 --> 00:21:27,520
+الـ alpha is good حاجة ال AN بياخد كل ال alpha في
+
+209
+00:21:27,520 --> 00:21:33,660
+SN حيث ال alpha is even و هذه أثبتنا إنها group و
+
+210
+00:21:33,660 --> 00:21:39,940
+ال order ل AN بيساوي N factorial على 2 أخر نظرية
+
+211
+00:21:39,940 --> 00:21:46,660
+في الشبطةهجيت المطلوب مني في ال A6 أشوف أيش ال
+
+212
+00:21:46,660 --> 00:21:51,680
+orders للعناصر تبع ال A6 هجيت لما أنا حسبت ال A6
+
+213
+00:21:51,680 --> 00:21:56,040
+أيش احتمالات ال order؟ واحد اتنين تلاتة اربعة خمسة
+
+214
+00:21:56,040 --> 00:22:01,420
+ستة لما بنتقل على ال A6 بنشوف مين من هذه ال orders
+
+215
+00:22:01,420 --> 00:22:06,450
+موجودين في ال A6عشان يكون ال order موجود ك order
+
+216
+00:22:06,450 --> 00:22:10,890
+لعنصر في ال a6 لازم اوجد عنصر يكون زوجي وال order
+
+217
+00:22:10,890 --> 00:22:15,090
+له حسب الرقم اللي اللي بدشر عليه لو بدأت برقم واحد
+
+218
+00:22:15,090 --> 00:22:20,130
+ال identity permutation زوجية identity تكتب بهذا
+
+219
+00:22:20,130 --> 00:22:29,570
+الشكل واحد اتنين اتنين واحد هذه زوجية ف ال
+
+220
+00:22:29,570 --> 00:22:34,820
+identity even يجب ان ال order واحد شمالهموجود هجت
+
+221
+00:22:34,820 --> 00:22:38,820
+نيجي على ال order اتنين عشان اتكلم عن order اتنين
+
+222
+00:22:38,820 --> 00:22:43,040
+بدي permutation ال order اللي لها اتنين و تكون
+
+223
+00:22:43,040 --> 00:22:46,040
+even هد ال order اللي لها اتنين ال least common
+
+224
+00:22:46,040 --> 00:22:49,460
+multiple اللي لها اتنين و اتنين مش بيساوي اتنين هل
+
+225
+00:22:49,460 --> 00:22:55,700
+هي even نعم even هكم جوز من ال two cycle موجود؟
+
+226
+00:22:55,700 --> 00:23:01,560
+جوزين يجب ال order اتنين شماله موجود ك order لعنصر
+
+227
+00:23:01,560 --> 00:23:07,060
+في ال a6الأردر تلاتة هذه ال permutation واحد اتنين
+
+228
+00:23:07,060 --> 00:23:12,400
+تلاتة ال order لا يجديش تلاتة ال order تلاتة وهي
+
+229
+00:23:12,400 --> 00:23:17,000
+permutation زوجية ليش؟ واحد مع تلاتة واحد مع اتنين
+
+230
+00:23:17,000 --> 00:23:22,180
+اكم جوس اتنين زوجي يعني بهذه ال permutation زوجية
+
+231
+00:23:22,180 --> 00:23:25,800
+وال order ال ..ما بيخسنيش انا هنا يكون .. هدول
+
+232
+00:23:25,800 --> 00:23:30,390
+اكيد مش disjointهدول أكيد .. شوف ال disjoint مهمني
+
+233
+00:23:30,390 --> 00:23:34,570
+عند الضرب عند حساب ال inverse عند حساب الطول لكن
+
+234
+00:23:34,570 --> 00:23:38,830
+لما أنا بدي أجي أتكلم عن even أو odd بتكلمش على
+
+235
+00:23:38,830 --> 00:23:45,480
+disjoint هنا واضح؟ طيبخلصها ال order تلاتة ال
+
+236
+00:23:45,480 --> 00:23:50,800
+order أربعة ال order أربعة هذا العنصر 1234 مش في
+
+237
+00:23:50,800 --> 00:23:58,520
+ال a6 ليش لما أنا بفرغ ل two cycle 141312
+
+238
+00:23:58,520 --> 00:24:03,560
+كدهش العدد هنا تلاتة هذا ليه يعني انه نجح في عناصر
+
+239
+00:24:03,560 --> 00:24:08,050
+تانية ال order لها أربعة من هذا الشكلهذا لو فررتك
+
+240
+00:24:08,050 --> 00:24:12,610
+two cycles واحد اتنين تلاتة اربع كام two cycle
+
+241
+00:24:12,610 --> 00:24:17,930
+عندك اربع زوجي ولا فردي زوجي ايه بقى هذه ال
+
+242
+00:24:17,930 --> 00:24:23,570
+permutation زوجية ال order اللي هجداش اربع ايه بقى
+
+243
+00:24:23,570 --> 00:24:27,790
+ال order اربع موجود في asset ولا لأ موجود نجي لل
+
+244
+00:24:27,790 --> 00:24:28,690
+order خمسة
+
+245
+00:24:35,360 --> 00:24:44,320
+هذا البرموتيشن 1 2 3 4 5 .. 1 5 .. 1 4 .. 1 2 .. 1
+
+246
+00:24:44,320 --> 00:24:48,940
+3 1 2 .. موجودة في
+
+247
+00:24:48,940 --> 00:24:55,840
+A6 .. لماذا؟ .. 1 2 3 4 .. هكم two cycle عندك؟
+
+248
+00:24:55,840 --> 00:25:00,100
+اربعة two cycles .. هذا البرموتيشن even ولا odd ..
+
+249
+00:25:00,100 --> 00:25:01,520
+even قداش طولها؟
+
+250
+00:25:13,790 --> 00:25:19,010
+عشان يكون عندك انصر ال order له 6 في A6 يا اما
+
+251
+00:25:19,010 --> 00:25:25,510
+هياخد الخيار هذا وبالتالي
+
+252
+00:25:25,510 --> 00:25:26,530
+لما تيجي تكتبه
+
+253
+00:25:33,580 --> 00:25:40,420
+كداش عددهم هدول؟ هدى لا ينتمي لإيه ستة؟ ليش؟ لأنه
+
+254
+00:25:40,420 --> 00:25:52,100
+فردي أو الشكل هدى العناصر
+
+255
+00:25:52,100 --> 00:25:58,000
+لل order إلى ستة في إيه ستة؟ يا cycles طولة ستة يا
+
+256
+00:25:58,000 --> 00:26:03,750
+two cycles واحدة تلاتة والتانية اتنين طبعا كملA1,
+
+257
+00:26:03,970 --> 00:26:14,290
+A3, A1, A2, A4, A5 هل هذا ينتمي إلى A6؟ لأ لا
+
+258
+00:26:14,290 --> 00:26:20,310
+ينتمي إلى A6 هل ال order 6 موجود؟ ال order 6 does
+
+259
+00:26:20,310 --> 00:26:36,770
+not exist ال orders in A61 و2 و3 و4 و5 هذه
+
+260
+00:26:36,770 --> 00:26:43,050
+احتمالات ال orders لعناصر ال a6 طبعا لو انا بشغل
+
+261
+00:26:43,050 --> 00:26:50,110
+في a7 نفس الأسلوب استعمله لكن القيم قد تكون مختلفة
+
+262
+00:26:50,110 --> 00:26:56,890
+يعني في a7 ممكن اجد ال order 6 لأ
+
+263
+00:26:56,890 --> 00:27:03,870
+هاجي ال order 7في A7 هلاجي ال order واحد هلاجي ال
+
+264
+00:27:03,870 --> 00:27:08,610
+order اتنين في ال A7 ال order واحد ال order اتنين
+
+265
+00:27:08,610 --> 00:27:12,330
+ال order تلاتة ال order اربعة ال order خمسة و ال
+
+266
+00:27:12,330 --> 00:27:21,990
+order ستة و ال order سبعة و ال order عشرة لأ ال
+
+267
+00:27:21,990 --> 00:27:24,530
+order اتناشر على الأرجح لأ برضه
+
+268
+00:27:27,840 --> 00:27:31,080
+ما هو ال .. السبعة في ال order واحد و اتنين و
+
+269
+00:27:31,080 --> 00:27:34,560
+تلاتة و أربعة و خمسة و ستة و سبعة و عشرة و اتنين و
+
+270
+00:27:34,560 --> 00:27:35,520
+أتنين و أتنين و أتنين و أتنين و أتنين و أتنين و
+
+271
+00:27:35,520 --> 00:27:38,100
+أتنين و أتنين و أتنين و أتنين و أتنين و أتنين و
+
+272
+00:27:38,100 --> 00:27:41,440
+أتنين و أتنين و أتنين و أتنين و أتنين و أتنين و
+
+273
+00:27:41,440 --> 00:27:41,960
+أتنين و أتنين و أتنين و أتنين و أتنين و أتنين و
+
+274
+00:27:41,960 --> 00:27:44,560
+أتنين و أتنين و أتنين و أتنين و أتنين و أتنين و
+
+275
+00:27:44,560 --> 00:27:47,980
+أتنين
+
+276
+00:27:47,980 --> 00:27:57,490
+و أتنين و أتنين و أتنين و أتنين وماواش احتمالات ال
+
+277
+00:27:57,490 --> 00:28:01,150
+order اتنين في A6 يا cycle واحدة طول .. يا cycle
+
+278
+00:28:01,150 --> 00:28:06,450
+واحدة طولها اتنين زي هيك خلينا نكتبها هان اواحد
+
+279
+00:28:06,450 --> 00:28:13,830
+اتنين يا اواحد اتنين اتلاتة ااربعة يا اواحد اتنين
+
+280
+00:28:13,830 --> 00:28:21,190
+اتلاتة ااربعة اخمسة استة هذه احتمالات العناصر لل
+
+281
+00:28:21,190 --> 00:28:25,850
+order الاتنين في A6 هذا فردي وهذا فردي بس هذا زوجي
+
+282
+00:28:28,170 --> 00:28:40,110
+هذا فردي وهذا فردي لكن هذا ايه؟ زوجي طيب
+
+283
+00:28:40,110 --> 00:28:44,290
+what about ايه سبعة؟ جاوبناها واحد اتنين تلاتة
+
+284
+00:28:44,290 --> 00:28:48,570
+اربعة خمسة ستة سبعة عشرة لأ هجيت ال order اتناشر
+
+285
+00:28:48,570 --> 00:28:55,430
+بيحصل زي هيك يعني عنصر زي هيك هذا فردي لا ينتمي
+
+286
+00:28:55,430 --> 00:29:00,220
+لأي سبعةيكبر فقط ال orders هدول واحد و اتنين و
+
+287
+00:29:00,220 --> 00:29:07,520
+تلاتة اربع و خمسة و ستة و سبعة what
+
+288
+00:29:07,520 --> 00:29:12,660
+is the maximum order of any element in A عشرة ايش
+
+289
+00:29:12,660 --> 00:29:19,500
+اكبر least common multiple ممكن احصله من ارقام
+
+290
+00:29:19,500 --> 00:29:25,560
+مجموعة عشرة او المجموعة الاكبر تبع عشرة تعالى نجرب
+
+291
+00:29:26,540 --> 00:29:31,460
+في A10 انا لو اخدت .. طبعا انا حاول اخد رقم ..
+
+292
+00:29:31,460 --> 00:29:37,480
+عشان انت تزيد ال least common multiple خد ارقام
+
+293
+00:29:37,480 --> 00:29:42,480
+كبار شوية فلو اخدت انت الأربعة مع الستة كداش؟
+
+294
+00:29:42,480 --> 00:29:48,500
+اتناش التلاتة مع السبعة واحد وعشرين الخمسة مع
+
+295
+00:29:48,500 --> 00:29:57,010
+الخمسة least common multiple خمسةطيب التنين مع
+
+296
+00:29:57,010 --> 00:30:01,650
+التمانية تمانية الواحد مع التسعة تسعة طيب في
+
+297
+00:30:01,650 --> 00:30:16,950
+احتمالات تانية في احتمالات تانية اتنين
+
+298
+00:30:16,950 --> 00:30:19,930
+مع التلاتة مع خمسة ايش ال least common multiple
+
+299
+00:30:23,460 --> 00:30:33,740
+جديش؟ اعلى order في ال S عشرة تلاتين هل هذا العنصر
+
+300
+00:30:33,740 --> 00:30:40,860
+موجود في اي عشرة؟ لأ، هذا فردي طيب، لو شن هذا
+
+301
+00:30:40,860 --> 00:30:46,700
+بيصير زوجي، هو بحصل على مين؟ على خمس عشر طبعا، هذا
+
+302
+00:30:46,700 --> 00:30:53,470
+طول فردي، وفردي مع بعض بيطلع زوجيهنا زوجي مع زوجي
+
+303
+00:30:53,470 --> 00:30:57,470
+هيطلع الجواب جديش واحد و عشرين لإنه هاخد عنصر زي
+
+304
+00:30:57,470 --> 00:31:05,870
+هيك يعني هزود واحد اتنين تلاتة اربعة خمسة ستة سبعة
+
+305
+00:31:05,870 --> 00:31:12,900
+تمانية تسعة عشرة هذا عنصر ال order إله جديش21 هو
+
+306
+00:31:12,900 --> 00:31:24,660
+even لأن هذا بنكتب 1 3 1 2 4 10 4 9 4 8 4 7 4 6 4
+
+307
+00:31:24,660 --> 00:31:32,440
+5 1 2 3 4 5 6 7 8 و هذا الانصر زوجي ينتمي ل a 10 و
+
+308
+00:31:32,440 --> 00:31:38,020
+ال order ال 21 نجونا اللي بعد ال 21 30 مابكونش
+
+309
+00:31:38,020 --> 00:31:45,090
+زوجي يكبر مين الأقل منهواحد عشري طيب الtermine
+
+310
+00:31:45,090 --> 00:31:47,450
+whether the following permutation are even or odd
+
+311
+00:31:47,450 --> 00:31:59,850
+هذه واحد خمسة سؤال تسعة even ولا odd طبعا هذا واحد
+
+312
+00:31:59,850 --> 00:32:06,590
+خمسة واحد تلاتة زوجي ولا فردي زوجي واحد تلاتة خمسة
+
+313
+00:32:06,590 --> 00:32:09,990
+ستة واحد ستة واحد خمسة واحد تلاتة
+
+314
+00:32:13,620 --> 00:32:18,320
+لو طول فردي فهي زوجية لو طول زوجي فهي فردية بس لو
+
+315
+00:32:18,320 --> 00:32:25,380
+كانوا زي هيك هذا بدك تروح تعمل زي مين و تعد طبعا
+
+316
+00:32:25,380 --> 00:32:34,240
+هذا even هذا odd even odd even even odd ده تنعمل
+
+317
+00:32:34,240 --> 00:32:45,050
+زي هيك واحد اتنينواحد أربعة وواحد تلاتة وواحد
+
+318
+00:32:45,050 --> 00:32:54,870
+اتنين وواحد خمسة كماش عددهم هدول خمسة كيف عملتم
+
+319
+00:32:54,870 --> 00:32:59,530
+على طول اد اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+320
+00:32:59,530 --> 00:32:59,670
+اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+321
+00:32:59,670 --> 00:32:59,830
+اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+322
+00:32:59,830 --> 00:32:59,850
+اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد اد
+
+323
+00:32:59,850 --> 00:33:04,130
+اد اد اد اد اد
+
+324
+00:33:04,130 --> 00:33:09,830
+ادطبعا في تكملة للسؤال هو ايه؟ المحاضرة القادمة ان
+
+325
+00:33:09,830 --> 00:33:15,230
+شاء الله ساسمعيه بكملكوا بدءا السؤال عشرة يعطيكوا
+
+326
+00:33:15,230 --> 00:33:15,590
+العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9c12034c74c99999caf7418815978ad77e8e3ab4
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY.srt
@@ -0,0 +1,1467 @@
+1
+00:00:21,160 --> 00:00:23,740
+السلام عليكم ورحمة الله وبركاته إن شاء الله
+
+2
+00:00:23,740 --> 00:00:27,320
+اليوم هناخد الجزء الثالث من الوحدة الرابعة اللي
+
+3
+00:00:27,320 --> 00:00:31,860
+بتتكلم فيها عن ال cyclic groups اللي ذاكر أو كان 
+
+4
+00:00:31,860 --> 00:00:36,540
+معانا في أول محاضرتين اتكلمنا عن شغلتين أساسيتين
+
+5
+00:00:36,540 --> 00:00:40,680
+الشغلة الأولى متعلقة بخصائص أو بعض الخصائص  للـ 
+
+6
+00:00:40,680 --> 00:00:44,460
+cyclic subgroup بعدين أخدناها في المحاضرة الأولى
+
+7
+00:00:44,460 --> 00:00:47,700
+ضمن التعريف والأمثلة، المحاضرة الثانية اللي
+
+8
+00:00:47,700 --> 00:00:52,590
+أخدناها اليوم الصبح اتكلمنا عن النظرية التي تتعلق بخصائص
+
+9
+00:00:52,590 --> 00:00:58,930
+العنصر وما يولده، مجموعات العناصر داخل ال cyclic
+
+10
+00:00:58,930 --> 00:01:04,230
+group، اليوم هنتكلم عن نظرية الأساسية لل cyclic
+
+11
+00:01:04,230 --> 00:01:06,870
+subgroup،  the fundamental theorem of cyclic subgroup
+
+12
+00:01:06,870 --> 00:01:12,710
+اللي من خلالها بتناول التركيبات الداخلية داخل ال
+
+13
+00:01:12,710 --> 00:01:17,110
+cyclic group المتعلقة بال subgroup نفسها وليست 
+
+14
+00:01:17,110 --> 00:01:21,310
+بالعناصر، نص النظرية اللي هي نظرية 4.3 هيقول
+
+15
+00:01:21,310 --> 00:01:30,030
+التالي، the fundamental theorem 
+
+16
+00:01:30,030 --> 00:01:34,070
+theorem
+
+17
+00:01:34,070 --> 00:01:39,630
+of cyclic groups
+
+18
+00:01:44,620 --> 00:01:47,900
+هنجسم نص النظرية الموجودة في الكتاب لـ 3 أجزاء
+
+19
+00:01:47,900 --> 00:01:54,500
+الجزء الأول، every subgroup
+
+20
+00:01:54,500 --> 00:01:58,360
+of
+
+21
+00:01:58,360 --> 00:02:03,500
+a cyclic group
+
+22
+00:02:03,500 --> 00:02:10,310
+is cyclic، يعني أي subgroup أنا باخدها جوا الـ
+
+23
+00:02:10,310 --> 00:02:17,210
+cyclic group هتكون أيضًا cyclic، الجزء الثاني، if j
+
+24
+00:02:17,210 --> 00:02:28,930
+is generated by some a and the order of a بيساوي n with h
+
+25
+00:02:28,930 --> 00:02:37,210
+a subgroup of j then the order of h يقسم n، مش بس ال
+
+26
+00:02:37,210 --> 00:02:41,270
+subgroup هذه cyclic لأ، و ال order لها بيقسم ال
+
+27
+00:02:41,270 --> 00:02:45,170
+order لل group، لو كنت أنا بتكلم في ال finite case
+
+28
+00:02:45,170 --> 00:02:51,730
+الثالث، اتجاه الثاني للجزء الثاني، احنا قلنا عن أي
+
+29
+00:02:51,730 --> 00:02:57,150
+subgroup ال order لها بيقسم ال order لل group، هجيت 
+
+30
+00:02:57,150 --> 00:03:04,070
+السؤال هل كل قاسم لـ order بلاقي subgroup ال
+
+31
+00:03:04,070 --> 00:03:09,240
+order لها بيساوي هذا القاسم؟ هذا كلام بيكون صحيح فقط 
+
+32
+00:03:09,240 --> 00:03:19,200
+لو بتكلم عن cyclic، الجواب، if k يقسم n then is
+
+33
+00:03:19,200 --> 00:03:24,780
+any positive divisor
+
+34
+00:03:24,780 --> 00:03:33,500
+of n then there
+
+35
+00:03:36,920 --> 00:03:51,020
+exists a unique subgroup of
+
+36
+00:03:51,020 --> 00:04:03,880
+is generated by a، namely تحديدًا h بيساوي generated by 
+
+37
+00:04:03,880 --> 00:04:13,860
+a to n على k، و ال order لـ h بيساوي k، بالعربي
+
+38
+00:04:13,860 --> 00:04:23,240
+أنه لأي قاسم لل order لل finite cyclic group أنا
+
+39
+00:04:23,240 --> 00:04:28,380
+بقدر ألاقي cyclic subgroup، و ال order لهذه ال
+
+40
+00:04:28,380 --> 00:04:33,120
+cyclic subgroup بيساوي القاسم اللي عندي، نيجي
+
+41
+00:04:37,950 --> 00:04:46,630
+فضّل طيب، بالعربي، الجزء الأول كل مجموعة جزئية أو
+
+42
+00:04:46,630 --> 00:04:52,810
+كل زمرة جزئية من زمرة دوارة هي زمرة دوارة، يعني ال
+
+43
+00:04:52,810 --> 00:04:59,230
+cyclic group عبارة عن زمرة دوارة، الجزء الثاني لو
+
+44
+00:04:59,230 --> 00:05:03,350
+كان الزمرة اللي أنت بتشتغل عليها دوارة
+
+45
+00:05:05,570 --> 00:05:11,550
+ال order لها finite، يعني زمرة دوارة محدودة، فال sub
+
+46
+00:05:11,550 --> 00:05:15,850
+group الزمرة الجزئية منها، ال order لهذه الزمرة
+
+47
+00:05:15,850 --> 00:05:22,890
+الجزئية بتقسم ال order للزمرة الأساسية، جزء ثالث 
+
+48
+00:05:22,890 --> 00:05:33,490
+لأي قاسم موجب لـ order الزمرة الدوارة بقدر ألاقي
+
+49
+00:05:33,490 --> 00:05:40,270
+زمرة جزئية group أو subgroup، ال order لهذه الزمرة
+
+50
+00:05:40,270 --> 00:05:45,370
+الجزئية بيساوي هذا القاسم، مش بس هيك، هذه الزمرة
+
+51
+00:05:45,370 --> 00:05:51,230
+تحديدًا هي ال generated by a to n على k، نيجي نثبت
+
+52
+00:05:51,230 --> 00:05:56,190
+نثبت الجزء الأول، every
+
+53
+00:05:56,190 --> 00:06:01,950
+subgroup of a cyclic group is cyclic، let j be
+
+54
+00:06:01,950 --> 00:06:07,950
+generated by a and h subgroup من الجيل، إيش اللي
+
+55
+00:06:07,950 --> 00:06:15,330
+لازم أثبته؟ بدي أثبت أنا إن الـ h cyclic subgroup
+
+56
+00:06:15,330 --> 00:06:18,930
+عشان تكون cyclic subgroup إيش لازم أنا أجيب لها؟
+
+57
+00:06:18,930 --> 00:06:25,990
+generator، في الحالة الأولية if الـ h فيه عنصر واحد
+
+58
+00:06:25,990 --> 00:06:32,480
+وهو ال identity فالـ h generated by مين؟ by ال
+
+59
+00:06:32,480 --> 00:06:37,640
+identity، فهي cyclic، لو الـ h مافيش فيه غير ال
+
+60
+00:06:37,640 --> 00:06:45,420
+identity، معناته الـ h generated by ال identity، if h
+
+61
+00:06:45,420 --> 00:06:56,960
+لا يساوي ال identity، هذا معناته there is at
+
+62
+00:06:56,960 --> 00:07:01,020
+least one element
+
+63
+00:07:02,430 --> 00:07:12,550
+in h with one element x، يعني terminal h and x لا
+
+64
+00:07:12,550 --> 00:07:21,010
+يساوي ال identity، طيب now فضل ماشي
+
+65
+00:07:21,010 --> 00:07:24,970
+بس لو كانت هي ال identity و بس فهي cyclic، طيب لو
+
+66
+00:07:24,970 --> 00:07:29,870
+فيها حاجة غير ال identity، طب احنا بنثبت هذا الكلام
+
+67
+00:07:31,190 --> 00:07:37,250
+بتقدر تثبت اللي هي هيك بط بط
+
+68
+00:07:37,250 --> 00:07:41,250
+x ينتمي لل h اللي هي ال subgroup من الجيل
+
+69
+00:07:41,250 --> 00:07:46,870
+generated by a، يكبر x عبارة عن إيش power لل a 
+
+70
+00:07:46,870 --> 00:07:52,410
+فليكن a أُس، اختار a لأكيد هنحتاج، هنستعملها بعد
+
+71
+00:07:52,410 --> 00:07:56,430
+هيكد a أُس r، و ال r ينتمي لل z
+
+72
+00:08:00,950 --> 00:08:07,530
+طيب أو a of t for
+
+73
+00:08:07,530 --> 00:08:12,810
+t، عندك two cases there
+
+74
+00:08:12,810 --> 00:08:27,370
+is two cases for t، ال case الأولانية إن t أكبر أو
+
+75
+00:08:27,370 --> 00:08:34,940
+يساوي الواحد، ال t مش صفر، فيا إما من الواحد وفوق
+
+76
+00:08:34,940 --> 00:08:44,460
+يا إما إيش؟ case 2، t أقل من الصفر، في ال case الثاني
+
+77
+00:08:44,460 --> 00:08:49,840
+in the second case
+
+78
+00:08:49,840 --> 00:08:55,760
+سالب
+
+79
+00:08:55,760 --> 00:08:55,980
+t
+
+80
+00:08:58,940 --> 00:09:09,780
+أكبر من الصفر، now x inverse بدي يساوي x t أو a to
+
+81
+00:09:09,780 --> 00:09:16,980
+t inverse اللي هي a أو سالب t ينتمي لل h with سالب
+
+82
+00:09:16,980 --> 00:09:23,780
+t أكبر من الصفر، طبعًا ال case الأولاني و ال case
+
+83
+00:09:23,780 --> 00:09:32,320
+الثاني بيعطون الحقيقة التالية، case one and two give
+
+84
+00:09:32,320 --> 00:09:46,060
+us that there is at least one element in h with
+
+85
+00:09:46,060 --> 00:09:57,240
+positive which is a positive power
+
+86
+00:09:59,630 --> 00:10:08,290
+of a، يعني دائمًا بأضمن وجود عنصر جوه ال h ال or أو
+
+87
+00:10:08,290 --> 00:10:14,310
+ال power له إيش؟ positive، بأضمن دائمًا وجود عنصر جوه
+
+88
+00:10:14,310 --> 00:10:20,510
+ال h، و ال power له أو العنصر هذا عبارة عن power
+
+89
+00:10:20,510 --> 00:10:23,830
+موجب لمين؟ لل a
+
+90
+00:10:29,010 --> 00:10:33,430
+ناخد m والله إيش؟
+
+91
+00:10:33,430 --> 00:10:48,550
+let m be the smallest positive power of a in h
+
+92
+00:10:48,550 --> 00:10:56,430
+ناخد ال m هو أصغر أُس موجب لل a في ال h، that is
+
+93
+00:11:00,110 --> 00:11:09,990
+a to m ينتمي لل h، and if a to t ينتمي لل h with t
+
+94
+00:11:09,990 --> 00:11:19,550
+أكبر من الصفر then m أقل أو يساوي t، ال m
+
+95
+00:11:19,550 --> 00:11:32,960
+هو أصغر power موجب لل a جوا مين؟ جوا h، claim ادعاء
+
+96
+00:11:32,960 --> 00:11:41,560
+ال h generated by a to m، طبعًا أنا هي كنت بكون
+
+97
+00:11:41,560 --> 00:11:46,680
+خلصت خطوتين، خطوة الأولى أثبت إن ال h is cyclic
+
+98
+00:11:46,680 --> 00:11:54,560
+خطوة الثانية جبت ال generator لل h، اتحولت شغل ليه
+
+99
+00:11:54,560 --> 00:12:03,070
+يا شانا؟ لـ set theory نظرية مجموعة، since a to m
+
+100
+00:12:03,070 --> 00:12:08,850
+ينتمي لل h، معناته generated by a to m subgroup من
+
+101
+00:12:08,850 --> 00:12:21,810
+ال h، وعطيها إيش؟ واحد، let x ينتمي لل h، since
+
+102
+00:12:23,760 --> 00:12:30,180
+h subgroup من generated by a، معناته ال x هتساوي a
+
+103
+00:12:30,180 --> 00:12:40,460
+to r for some r ينتمي لمن؟ لل z، مدام ال h subset
+
+104
+00:12:40,460 --> 00:12:47,260
+من generated by a فكل عناصر ال h عبارة عن إيش؟
+
+105
+00:12:47,260 --> 00:12:53,940
+عبارة عن إيش؟ powers لل a، فليكن a to r، هجيت بال
+
+106
+00:12:53,940 --> 00:13:05,260
+division algorithm، ال 
+
+107
+00:13:05,260 --> 00:13:11,000
+r أو بلش ال r خدها لإن ال r هستعملها، هجيت ك
+
+108
+00:13:11,000 --> 00:13:14,640
+remainder، استعمل غمز ثاني، فليكن k
+
+109
+00:13:18,460 --> 00:13:25,040
+ال k لو أنا بدي أجسمها على ال m عبارة عن qm زائد
+
+110
+00:13:25,040 --> 00:13:33,100
+ال r، و ال r ما بين ال m و ال
+
+111
+00:13:33,100 --> 00:13:36,480
+0، طيب
+
+112
+00:13:36,480 --> 00:13:43,160
+now a
+
+113
+00:13:50,330 --> 00:14:00,310
+ال a to r عبارة عن a to k minus qm اللي عبارة عن
+
+114
+00:14:00,310 --> 00:14:10,090
+a to k في a minus qm اللي عبارة عن x في a to m
+
+115
+00:14:10,090 --> 00:14:21,870
+أس سالب q، و هذا العنصر وين موجود؟ موجود وين؟ في ال h
+
+116
+00:14:21,870 --> 00:14:28,250
+ليش؟ x في ال h، a to m في ال h، فأي power لل a to m
+
+117
+00:14:28,250 --> 00:14:35,750
+هيكون وين؟ جوا ال h، طيب هنخل الجزء هذا مكتوب ونكمل
+
+118
+00:14:35,750 --> 00:14:40,150
+إثباتًا لسه
+
+119
+00:14:40,150 --> 00:14:45,750
+إثبات الجزء الأول هذا، هذا 
+
+120
+00:14:45,750 --> 00:14:58,440
+معناته إن a to r ينتمي لمين؟ لـ h، حاجة if r لا
+
+121
+00:14:58,440 --> 00:15:11,020
+يساوي zero then r is a positive power of a such
+
+122
+00:15:11,020 --> 00:15:16,720
+that a to r وين؟ في h
+
+123
+00:15:20,580 --> 00:15:26,900
+لو ال r مش صفر معناته يصير ال r موجب هو أُس موجب لل
+
+124
+00:15:26,900 --> 00:15:31,960
+a بيخلي ال a تقار وين؟ في ال h، نرجع لل m، ال m هو
+
+125
+00:15:31,960 --> 00:15:37,420
+مين؟ هو أصغر positive power لل a في ال h، هذا 
+
+126
+00:15:37,420 --> 00:15:44,440
+معناته أنه لازم الـ M يكون أقل أو يساوي الـ R but الـ R
+
+127
+00:15:44,440 --> 00:15:49,000
+أقل من الـ M نفس الـ contradiction اللي كان في
+
+128
+00:15:49,000 --> 00:15:52,500
+المحاضرة السابقة هذا مع هذا عبارة عن ايش
+
+129
+00:15:52,500 --> 00:16:01,180
+contradiction معناته ايش الخطأ اللي أنا فرضته إن
+
+130
+00:16:01,180 --> 00:16:14,320
+R لا يساوي زيرو so R بيساوي زيرو و نرجع 
+
+131
+00:16:14,320 --> 00:16:17,820
+للـ division algorithm R بيساوي زيرو  كياش بيساوي
+
+132
+00:16:18,850 --> 00:16:35,610
+aQ + mQ
+
+133
+00:16:35,610 --> 00:16:40,990
+aQ m
+
+134
+00:16:40,990 --> 00:16:41,250
+aQ m aQ m aQ m aQ m aQ m aQ m
+
+135
+00:16:41,250 --> 00:16:45,660
+aQ m by a to m وين في الـ H و أنا أصلا هنا ماخد
+
+136
+00:16:45,660 --> 00:16:50,440
+الـ X من الـ H صار الـ X من generated لأ أنا
+
+137
+00:16:50,440 --> 00:16:55,020
+generated by a to m شباب أنا
+
+138
+00:16:55,020 --> 00:16:59,900
+ماخد الـ X من الـ H صار في generated by a to m
+
+139
+00:16:59,900 --> 00:17:05,800
+معناته الـ H sub group من generated by a to m و
+
+140
+00:17:05,800 --> 00:17:12,210
+أعطيها 2 , 1 و 2 هتخليك تقول إن الـ H بيساوي generated
+
+141
+00:17:12,210 --> 00:17:22,710
+by a تقام و الـ H شمالها الـ Cyclic وهو المطلوب وهي
+
+142
+00:17:22,710 --> 00:17:29,950
+كده أثبتنا الجزء الأول إنه أخدت subgroup من الـ
+
+143
+00:17:29,950 --> 00:17:33,130
+Cyclic group اللي بأشتغل عليها و طلعت الـ subgroup
+
+144
+00:17:33,130 --> 00:17:41,090
+هديش Cyclic مش Cyclic بس generated by أصغر أو by a
+
+145
+00:17:41,090 --> 00:17:47,090
+أصغر positive power داخل الله تفضل بس أنا هربطه
+
+146
+00:17:47,090 --> 00:17:50,170
+معاك في بعض أنا أعمل هذا عشان الدنيا هو بالظبط الـ
+
+147
+00:17:50,170 --> 00:17:54,610
+claim لأ إنكسوا واحد و اتنين إن أنت صار بتاعة أكبر
+
+148
+00:17:54,610 --> 00:17:59,510
+من صفرها داخلها دع القلم تعال أقولك الخطوات اللي
+
+149
+00:17:59,510 --> 00:18:04,500
+اتبعت بعتك التالي في الـ case الأولاني تبع إن الـ H
+
+150
+00:18:04,500 --> 00:18:08,220
+بيساوي الـ identity هذا صف في نعجن بينهم trivial
+
+151
+00:18:08,220 --> 00:18:12,460
+فاشتغلنا على الـ H اللي فيه عنصر غير الـ identity
+
+152
+00:18:12,460 --> 00:18:18,040
+هيجي الـ case الأول و التاني هنا بدي أخلص منه باب
+
+153
+00:18:18,040 --> 00:18:25,180
+عراض إنه دائما بقدر ألاقي positive power للـ A جوا
+
+154
+00:18:25,180 --> 00:18:29,570
+الـ H عشري الـ case الأول و التاني اشتغلت أنا على الـ A
+
+155
+00:18:29,570 --> 00:18:34,030
+to T الـ A to T الـ T قدامي خيارين يا موجبة باور تاني
+
+156
+00:18:34,030 --> 00:18:38,150
+اللي بدي أخلصه فيه positive power للـ A جوا الـ H يا
+
+157
+00:18:38,150 --> 00:18:42,910
+الـ T سالبة بس أنا بأشتغل جوا sub group الـ inverse
+
+158
+00:18:42,910 --> 00:18:48,970
+تبع العنصر اللي أنا بدأت منه اللي هو X موجود طبعا
+
+159
+00:18:48,970 --> 00:18:53,750
+الـ X هو A to T فـ X inverse A to سالب T الـ T سالبة
+
+160
+00:18:53,750 --> 00:18:58,690
+فسالب T موجبة يكبى في الـ case التاني برضه أجدت
+
+161
+00:18:58,690 --> 00:19:02,370
+الآجي عنصر الـ positive أو الـ power له positive
+
+162
+00:19:02,370 --> 00:19:08,290
+يكبى دائما بأضمن إنه يوجد positive power جوا مين؟
+
+163
+00:19:08,290 --> 00:19:12,010
+positive power للـ A جوا؟ الـ H مدام دائما في
+
+164
+00:19:12,010 --> 00:19:16,910
+positive هأخد أصغر واحد طبعا ما تنساش إنه أنا بأشتغل
+
+165
+00:19:16,910 --> 00:19:21,800
+في الـ Z و الـ Z لما أنا بأشتغل على الـ positive
+
+166
+00:19:21,800 --> 00:19:25,980
+integer فانتقلت من الـ z لـ الـ n في الـ natural
+
+167
+00:19:25,980 --> 00:19:33,240
+number أي مجموعة جزئية من الـ natural number غير
+
+168
+00:19:33,240 --> 00:19:39,780
+خالية الها ايش؟ الها minimum أو minimal at least
+
+169
+00:19:39,780 --> 00:19:43,280
+اللي هو الـ least one أو least number ف أنا أخدت الـ
+
+170
+00:19:43,280 --> 00:19:46,340
+least أو الـ smallest positive power للـ H و الـ H
+
+171
+00:19:46,340 --> 00:19:52,140
+فليكن هو M انسى كل القصص الأولى اللي في الآخر اللي
+
+172
+00:19:52,140 --> 00:19:56,160
+أخذناها توي و بنمسك في الـ A تقامها ده و نثبت إنه
+
+173
+00:19:56,160 --> 00:20:01,620
+بيولد الـ H طب ليش جبنا صغير واحد يعني؟ ليش جبنا
+
+174
+00:20:01,620 --> 00:20:05,100
+أصغر واحد؟ طالع معايا يعني هي ممكن هذه الفلسفة
+
+175
+00:20:05,100 --> 00:20:10,660
+موجودة في كثير من الشغلات المتعلقة في الجبر أنا
+
+176
+00:20:10,660 --> 00:20:15,780
+لما بدي أدور على عنصر هو يولد الباقي فليه بصغير
+
+177
+00:20:15,780 --> 00:20:21,170
+واحد؟ الكبير مش هيولد الصغير لأن الكبير لما تعطيه
+
+178
+00:20:21,170 --> 00:20:25,490
+قوة و مطلوب إنه يرجع لبور صغير بدك تشتغل على إن
+
+179
+00:20:25,490 --> 00:20:29,970
+القوة بتكبر في لحظة معينة و بتختصر منها و بتنزل
+
+180
+00:20:29,970 --> 00:20:34,530
+فمن الأسهل إن أنا بأخد أصغر واحد و أصنع الباقي من
+
+181
+00:20:34,530 --> 00:20:43,750
+خلاله واضح؟ واضح
+
+182
+00:20:43,750 --> 00:20:50,740
+الجزء هذا؟ واضح الجزء الأول يا شباب؟ نيجي نثبت
+
+183
+00:20:50,740 --> 00:20:58,460
+الجزء الثاني ذاكرين
+
+184
+00:20:58,460 --> 00:21:08,920
+ايش الجزء الثاني؟ طب يحكوه واحد جاره يفسر الجزء
+
+185
+00:21:08,920 --> 00:21:12,700
+الثاني من الاثبات احنا اثبتنا فقط مين الـ part
+
+186
+00:21:12,700 --> 00:21:13,360
+الأولاني 
+
+187
+00:21:20,680 --> 00:21:27,840
+طيب تعال نتكلم عنه الجزء الثاني let J generated
+
+188
+00:21:27,840 --> 00:21:35,920
+by الـ A و الـ order للـ A بدي يساوي N given أو take
+
+189
+00:21:35,920 --> 00:21:50,530
+H subgroup من مين؟ من الـ J we must أو since J is
+
+190
+00:21:50,530 --> 00:21:58,370
+Cyclic ايش مقدر أقول أنا عن الـ H H is Cyclic
+
+191
+00:21:58,370 --> 00:22:06,030
+Cyclic
+
+192
+00:22:06,030 --> 00:22:12,990
+يجوبش يعني هذا
+
+193
+00:22:12,990 --> 00:22:20,930
+معناته الـ H generated by some A to M الـ H
+
+194
+00:22:20,930 --> 00:22:28,050
+generated by some .. طب الـ order للـ H هو الـ order
+
+195
+00:22:28,050 --> 00:22:33,730
+generated by a to m اللي هو عبارة عن مين؟ الـ order
+
+196
+00:22:33,730 --> 00:22:39,410
+لـ a to m اللي هو عبارة عن ايش؟ n على الـ gcd
+
+197
+00:22:39,410 --> 00:22:45,410
+common divisor لـ m و n agreed common divisor لـ m و
+
+198
+00:22:45,410 --> 00:22:53,580
+n عبارة عن ايش؟ بغض النظر ايش بيساوي إذا order الـ H
+
+199
+00:22:53,580 --> 00:23:00,500
+بدي يساوي N على الـ gcd common divisor لـ M و N هذا
+
+200
+00:23:00,500 --> 00:23:08,420
+رقم ايش ماله؟ ايش ماله؟ بيقسم الـ N أنا مطلوب من
+
+201
+00:23:08,420 --> 00:23:12,200
+يثبت إنما order الـ H بيقسم الـ N و هذا N على عدد
+
+202
+00:23:12,200 --> 00:23:19,820
+صحيح و هو عدد صحيح إذا order الـ H بيقسم N الآن خلصنا
+
+203
+00:23:19,820 --> 00:23:24,100
+الجزء الثاني جزء
+
+204
+00:23:24,100 --> 00:23:31,900
+الثالث في الجزء الثالث هجيء أي subgroup الـ order
+
+205
+00:23:31,900 --> 00:23:35,580
+لها بيقسم الـ order لـ الـ group نفسه في حالة الـ finite
+
+206
+00:23:35,580 --> 00:23:43,340
+case طبعا هجيء كل قاسم بيجي له subgroup ولا لا طلع
+
+207
+00:23:43,340 --> 00:23:51,370
+على الجزء الثالث let k يقسم الـ N given أو let الـ
+
+208
+00:23:51,370 --> 00:23:57,430
+J بده تساوي generated by a و الـ order للـ a بده
+
+209
+00:23:57,430 --> 00:24:01,430
+يساوي N يعني ايش المطلوب هنا شباب مطلوب بنلاقي
+
+210
+00:24:01,430 --> 00:24:05,490
+subgroup الـ order اللي لها k subgroup من وين من
+
+211
+00:24:05,490 --> 00:24:10,250
+الـ J بس هو أنا ريحني في النص ايش قال لي قال لي
+
+212
+00:24:10,250 --> 00:24:16,220
+الـ subgroup المطلوبة مين هي generated by a to n على
+
+213
+00:24:16,220 --> 00:24:21,560
+k أنا همسك هذه بحسب التلات شغلات إن هي subgroup
+
+214
+00:24:21,560 --> 00:24:25,380
+سهلة إنه generated by any element subgroup شغلت
+
+215
+00:24:25,380 --> 00:24:28,440
+ثاني الـ order لها بيساوي k و هذه هتكون برضه شغلة
+
+216
+00:24:28,440 --> 00:24:36,460
+سهلة شغلت تالتة ايش إن هي unique ما فيش غيرها إن هي
+
+217
+00:24:36,460 --> 00:24:38,780
+unique أو ما فيش غيرها
+
+218
+00:24:41,860 --> 00:24:53,340
+we first show that order بدأت
+
+219
+00:24:53,340 --> 00:25:03,160
+ساوي كام هذه سهلة which
+
+220
+00:25:03,160 --> 00:25:06,420
+is
+
+221
+00:25:06,420 --> 00:25:14,740
+trivial الـ order generated by n على k بدي أساوي الـ
+
+222
+00:25:14,740 --> 00:25:22,840
+order لـ a أقصر n على k و هي عبارة عن n على gcd
+
+223
+00:25:22,840 --> 00:25:28,640
+common divisor لـ n و n على k شباب gcd common
+
+224
+00:25:28,640 --> 00:25:32,160
+divisor لـ n و لـ n على k ايش بيساوي أو لـ n و n على
+
+225
+00:25:32,160 --> 00:25:37,880
+k بدي أساوي n على n
+
+226
+00:25:37,880 --> 00:25:45,360
+على k اللي عبارة عن k أكبر order لـ generated by a
+
+227
+00:25:45,360 --> 00:25:49,080
+أُس n على k أكبر أكبر أكبر أكبر أكبر
+
+228
+00:25:49,080 --> 00:25:51,460
+أكبر أكبر أكبر أكبر أكبر أكبر أكبر
+
+229
+00:25:51,460 --> 00:25:55,080
+أكبر أكبر أكبر أكبر أكبر أكبر أكبر
+
+230
+00:25:55,080 --> 00:26:07,260
+أكبر أكبر أكبر أكبر أكبر أكبر أكبر
+
+231
+00:26:17,300 --> 00:26:21,500
+كيف أثبت الـ Uniqueness يا شباب؟ بأفترض إن هناك
+
+232
+00:26:21,500 --> 00:26:28,920
+واحدة ثانية و بأثبت المساواة let A مثلا أختار الهؤوس
+
+233
+00:26:28,920 --> 00:26:35,240
+خليني أتماشى مع الكتاب A to M subgroup
+
+234
+00:26:35,240 --> 00:26:41,000
+من الـ J و الـ order that generated by A to M بدي
+
+235
+00:26:41,000 --> 00:26:42,500
+يساوي ايش؟ فضل
+
+236
+00:26:48,140 --> 00:26:56,780
+a unique subgroup of generated by a namely طيب
+
+237
+00:26:56,780 --> 00:27:05,320
+كيف بدأ أثبت؟ كيف بدأ أثبت إن هدول زي بعض؟ أنا
+
+238
+00:27:05,320 --> 00:27:09,840
+شباب بالدفتر موجود قدامي بس مش عارف أجري مين يطلع
+
+239
+00:27:09,840 --> 00:27:13,260
+يفكر معايا؟
+
+240
+00:27:13,260 --> 00:27:16,520
+يعني ماشي بيبنيك أشوش real sound
+
+241
+00:27:25,370 --> 00:27:31,710
+أنا مش كل مرة هأثبت لحالي أنا يا شباب دي أثبت إنه
+
+242
+00:27:31,710 --> 00:27:38,630
+هذه هي نفسها هذه يعني generated by a to m و
+
+243
+00:27:38,630 --> 00:27:44,490
+generated by a to n على k زي بعض
+
+244
+00:27:48,920 --> 00:27:56,580
+أستفيد من إن الـ M بتحقق خاصيتها دي with M is the
+
+245
+00:27:56,580 --> 00:28:07,700
+smallest positive power of
+
+246
+00:28:07,700 --> 00:28:16,810
+A in generated by A to M هاي كمان مساعدة الـ M عشان
+
+247
+00:28:16,810 --> 00:28:21,230
+ما يجردش يلاقي Mات كتيرة هو أصغر positive power للـ
+
+248
+00:28:21,230 --> 00:28:24,750
+A دي هو الـ generated by A تقريبا هاجت على .. هذا
+
+249
+00:28:24,750 --> 00:28:29,430
+صار العنصر بالنسبة لهدي unique و هذا العنصر بالنسبة
+
+250
+00:28:29,430 --> 00:28:33,750
+لهدي ما هو الـ N على K unique ما فيش منه اتنين فلو 
+
+251
+00:28:33,750 --> 00:28:38,650
+أنا أثبتت أنه A على N A أس N على K هو نفسه A أس
+
+252
+00:28:38,650 --> 00:28:44,990
+M بكون خلصت ما كنتش مقدرة بتهدي كلامه لو كان الـ M و
+
+253
+00:28:44,990 --> 00:28:51,010
+الـ N على K شمالهم متساويين يكبر أنت قلت لي أن N على
+
+254
+00:28:51,010 --> 00:28:56,690
+K بيساوي M اه
+
+255
+00:28:56,690 --> 00:29:01,250
+طيب
+
+256
+00:29:01,250 --> 00:29:07,430
+مساعدة ثانية هذه
+
+257
+00:29:07,430 --> 00:29:14,000
+الـ order إلها K الـ K بيقسم الـ N حطها على جانب الـ
+
+258
+00:29:14,000 --> 00:29:18,280
+order اللي generated by A to M إيش بيساوي الـ order
+
+259
+00:29:18,280 --> 00:29:25,280
+لـ A to M إيش الـ order لـ A to M N على الجريس common
+
+260
+00:29:25,280 --> 00:29:33,200
+divisor لمين؟ للـ M و للـ N اللي هو إيش بيساوي؟ فضل
+
+261
+00:29:33,200 --> 00:29:38,220
+مهمش الـ M بتساوي على كلمة نفسك طيب يبقى الـ M
+
+262
+00:29:38,220 --> 00:29:39,160
+هتساوي ك M
+
+263
+00:29:42,120 --> 00:29:48,260
+هذا المقوم إثباته طيب
+
+264
+00:29:48,260 --> 00:29:53,700
+الـ M رتبة هذه طيب
+
+265
+00:29:53,700 --> 00:29:57,900
+رتبة
+
+266
+00:29:57,900 --> 00:29:58,740
+العنصر
+
+267
+00:30:01,460 --> 00:30:05,480
+رتبة العنصر بتقسم .. رتبة العنصر بتقسم رتبة العنصر
+
+268
+00:30:05,480 --> 00:30:10,520
+طيب طيب طيب طب الـ .. الـ M هي رتبة العنصر شوية بس
+
+269
+00:30:10,520 --> 00:30:18,400
+الـ M رتبة العنصر ولا power العنصر فارج power power
+
+270
+00:30:18,400 --> 00:30:23,700
+مش رتبة الرتبة هو عبارة عن N على الجيزكم و divisor
+
+271
+00:30:23,700 --> 00:30:25,720
+لـ N و M
+
+272
+00:30:36,130 --> 00:30:40,950
+فكه عشان .. طيب أعطيك مساعدة أثبت أن الأم بتجسم
+
+273
+00:30:40,950 --> 00:30:47,910
+العنصر أه
+
+274
+00:30:47,910 --> 00:30:57,190
+.. فكه
+
+275
+00:30:57,190 --> 00:31:00,470
+أنا مش عارف أفجر من الدفتر
+
+276
+00:31:04,480 --> 00:31:16,560
+هيا يا شباب هيعطيك كل المساعدات الممكنة الـ
+
+277
+00:31:16,560 --> 00:31:20,440
+order
+
+278
+00:31:20,440 --> 00:31:23,040
+لـ الـ a و الـ m هي عبارة عن n على الـ a's common
+
+279
+00:31:23,040 --> 00:31:26,840
+divisor لـ m و n أنت لو أثبتت أن الـ m بتجسم الـ m
+
+280
+00:31:26,840 --> 00:31:31,050
+خلص إثبات بالمساعدات اللي أعطيتك إياها الـ K بيساوي
+
+281
+00:31:31,050 --> 00:31:37,010
+order generated by A to M الـ وبد يساوي الـ N على
+
+282
+00:31:37,010 --> 00:31:40,870
+الجيزكم و الـ divisor لـ M و N لو أثبتت أن الـ M
+
+283
+00:31:40,870 --> 00:31:47,390
+بيقسم الـ N خلصت الإثبات كله وجف على إيش؟ أن الـ M
+
+284
+00:31:47,390 --> 00:31:58,970
+بيقسم الـ N آه
+
+285
+00:31:58,970 --> 00:31:59,290
+شباب
+
+286
+00:32:07,580 --> 00:32:15,140
+العنصر بتقسم شوية العنصر
+
+287
+00:32:15,140 --> 00:32:18,880
+بتقسم إيه؟
+
+288
+00:32:18,880 --> 00:32:25,960
+كيف؟ طيب
+
+289
+00:32:25,960 --> 00:32:30,240
+طب إحنا قولنا الكلام هذا و هذا الأخضر إيه اللي و
+
+290
+00:32:30,240 --> 00:32:34,360
+جديش كيف؟
+
+291
+00:32:34,360 --> 00:32:37,060
+كمل تكملة
+
+292
+00:32:45,260 --> 00:32:50,820
+طيب طالع معايا هجيت
+
+293
+00:32:50,820 --> 00:32:55,120
+K بدي يساوي الـ order that generated by A to M اللي
+
+294
+00:32:55,120 --> 00:33:03,060
+هو الـ order لمين؟ لـ A to M إيش يعني؟ يعني A to M أس K
+
+295
+00:33:03,060 --> 00:33:13,580
+إيش بدي يساوي الـ identity يعني A to MK بدي يساوي الـ
+
+296
+00:33:13,580 --> 00:33:14,340
+identity طيب
+
+297
+00:33:17,540 --> 00:33:24,040
+هذا إيش بيساوي؟ هذا بيساوي a to n إيش يعني؟ الـ n
+
+298
+00:33:24,040 --> 00:33:30,240
+تقسم الـ .. الـ n تقسم الـ .. الـ n تقسم الـ .. الـ n
+
+299
+00:33:30,240 --> 00:33:34,660
+على k بيساوي الـ n مين جالك؟ الـ n بيساوي الـ n في k
+
+300
+00:33:34,660 --> 00:33:41,340
+طبعًا يمكن الـ mk أكبر من الـ n يمكن
+
+301
+00:33:41,340 --> 00:33:49,290
+الـ mk يكون أكبر من الـ n الـ N بدها تكون تقسم الـ MK
+
+302
+00:33:49,290 --> 00:33:54,870
+لأن هذا هيعطيني على جانب أن N بتقسم الـ N ناقص الـ
+
+303
+00:33:54,870 --> 00:34:00,890
+MK يجب أن N تقسم الـ MK اه
+
+304
+00:34:00,890 --> 00:34:06,650
+تقسم ولا تساوي؟ تساوي لأنه عيب إذا تساوت المقادير
+
+305
+00:34:06,650 --> 00:34:11,170
+ليش تقسم؟ ليش تتساوي؟ ممكن يكون أكبر فكروا
+
+306
+00:34:16,760 --> 00:34:24,660
+اه اجرح اجرح ما مكتوب عندي ايوه
+
+307
+00:34:24,660 --> 00:34:28,420
+حاجة
+
+308
+00:34:28,420 --> 00:34:35,260
+الـ K إيش بدها تساوي order الـ A تقم حيدها اللي عبارة
+
+309
+00:34:35,260 --> 00:34:44,840
+عن N على الجريس common divisor لمن؟ لـ M و N يعني كما
+
+310
+00:34:44,840 --> 00:34:50,920
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+311
+00:34:50,920 --> 00:34:56,880
+تسمح كما تسمح كما تسمح كما
+
+312
+00:34:56,880 --> 00:34:57,400
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+313
+00:34:57,400 --> 00:34:57,520
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+314
+00:34:57,520 --> 00:34:57,540
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+315
+00:34:57,540 --> 00:34:59,280
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+316
+00:34:59,280 --> 00:35:01,460
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+317
+00:35:01,460 --> 00:35:13,520
+تسمح كما تسمح كما تسمح كما
+
+318
+00:35:14,990 --> 00:35:20,770
+شباب من عشر دقائق في شغلة افترض أن أنا أعطيتك كل
+
+319
+00:35:20,770 --> 00:35:27,030
+المساعدات اللي هي مكتوبة حتى كتبت مساعدات على اللوح
+
+320
+00:35:27,030 --> 00:35:33,830
+هذه كيف بتساوي أما كيف أنه زوجها أزهار أزهار أزهار
+
+321
+00:35:33,830 --> 00:35:40,810
+أزهار أزهار
+
+322
+00:35:55,820 --> 00:36:02,960
+طيب فكروا طيب
+
+323
+00:36:02,960 --> 00:36:11,960
+هفكر أنا طيب since شغل سهل الـ H generated by الـ A
+
+324
+00:36:11,960 --> 00:36:13,660
+term فضل
+
+325
+00:36:21,180 --> 00:36:24,320
+العنصر على K بيقسم العنصر و العنصر على K بيقسم العنصر
+
+326
+00:36:24,320 --> 00:36:31,740
+صحيح هذا
+
+327
+00:36:31,740 --> 00:36:36,680
+معناته أن N على K بتقسم مين؟ العنصر دي ما لها لازمة
+
+328
+00:36:36,680 --> 00:36:40,580
+العنصر على K بتقسم مين؟ العنصر إيش يعني؟
+
+329
+00:36:43,400 --> 00:36:46,280
+العنصر على K بتقسم الـ M؟ مش حتى فادت العنصر بيقسم
+
+330
+00:36:46,280 --> 00:36:57,140
+الـ M K؟ العنصر بيقسم الـ M K؟ طيب بعد هيك؟ لأ أنا
+
+331
+00:36:57,140 --> 00:37:04,560
+مستنتجة منها سيبك من الخربشات هذه كلها خليني ألتزم
+
+332
+00:37:04,560 --> 00:37:07,460
+بشغل الكتاب طلع معايا
+
+333
+00:37:10,720 --> 00:37:16,060
+let generated by الـ a to m هو في النهاية مش هنعمل
+
+334
+00:37:16,060 --> 00:37:25,020
+هيك دي يعني لأ ضايق الوجه حجرة
+
+335
+00:37:25,020 --> 00:37:29,440
+الـ h generated by الـ a to m سبقوا من الـ j الـ order
+
+336
+00:37:29,440 --> 00:37:32,900
+لـ a to m دي ساوية k with m is the smallest positive
+
+337
+00:37:32,900 --> 00:37:35,520
+power of a in أو أنا وصلت هنا
+
+338
+00:37:48,600 --> 00:37:53,740
+طيب هجيت الـ K بدها تساوي generated by A to M اللي هو
+
+339
+00:37:53,740 --> 00:37:59,580
+N على الجريس common divisor لـ M على N هذا بدها تساوي
+
+340
+00:37:59,580 --> 00:38:06,300
+N على M تمام النتيجة أن M بدها تساوي N على K
+
+341
+00:38:06,880 --> 00:38:11,100
+وبالتالي generated by a to m يستوي generated by a
+
+342
+00:38:11,100 --> 00:38:23,460
+to n على k وهو المطلوب يعني h is .. اه صحيح صحيح
+
+343
+00:38:23,460 --> 00:38:31,360
+نهدر
+
+344
+00:38:31,360 --> 00:38:37,200
+يا عدنا نخربش فيها نص ساعة عشان نفهم اللي هي هذه
+
+345
+00:38:37,200 --> 00:38:43,120
+أنها هذه متساوية بناء على أن M هي الـ smallest
+
+346
+00:38:43,120 --> 00:38:48,400
+positive power للـ A في الـ generated part معناه
+
+347
+00:38:48,400 --> 00:38:53,580
+حاجة هنا الـ A to M دي ساوى الـ identity و الـ A to MK
+
+348
+00:38:53,580 --> 00:38:58,080
+دي ساوى الـ identity المفروض في علاقة بين الـ N و الـ
+
+349
+00:38:58,080 --> 00:39:03,460
+MK هجيت الـ N أصغر واحد المفروض أن الـ N تقسم الـ MK
+
+350
+00:39:03,460 --> 00:39:11,760
+هجيت بإمكاني بطريقة لو فرضت أن الـ MK أكبر من الـ N
+
+351
+00:39:11,760 --> 00:39:16,660
+يعني
+
+352
+00:39:16,660 --> 00:39:21,700
+هذه المفتاح على الأقل هذه بتكون إيش؟ الـ N تقسم الـ
+
+353
+00:39:21,700 --> 00:39:28,170
+MK تمام؟ و الـ M K أكبر لو كانت أكبر من الـ N فهي على
+
+354
+00:39:28,170 --> 00:39:38,050
+الـ M K أكبر أو سواش 2N هنا تنساش أن الـ K بتقسم فالـ
+
+355
+00:39:38,050 --> 00:39:43,110
+K هتكون عبارة عن حاجة أصغر من الـ N معناته علشان
+
+356
+00:39:43,110 --> 00:39:46,790
+تكون الـ K أصغر من الـ N و لما أضربها في الـ M يعطيني
+
+357
+00:39:46,790 --> 00:39:50,410
+عدد أكبر أو يساوي 2N الـ M بدها تكون أكبر من الـ N
+
+358
+00:39:53,920 --> 00:40:02,080
+هجيت الـ K بتقسم الـ N فالـ K أقل من مين؟ من الـ N هجيت
+
+359
+00:40:02,080 --> 00:40:07,060
+عشان يكون الـ M K اللي هي أقل من M N وهذه بدها تكون
+
+360
+00:40:07,060 --> 00:40:15,450
+أكبر أو يساوي 2 N المفروض أن الـ M هو الـ M K هتضرب
+
+361
+00:40:15,450 --> 00:40:18,810
+الـ M في عدد أقل من الـ N هيعطيك أكبر من اتنين N
+
+362
+00:40:18,810 --> 00:40:23,950
+فلازم الـ M يكون أكبر من الـ N وهذا بيعطيك تناقض لأن
+
+363
+00:40:23,950 --> 00:40:29,250
+أصلًا الـ M أصغر positive power بيخلي الـ A to M جوا
+
+364
+00:40:29,250 --> 00:40:34,830
+الـ A بس الـ A to N بساوي الـ identity ينتمي للـ H فكيف
+
+365
+00:40:34,830 --> 00:40:39,470
+الـ M أكبر من الـ N و الـ N هو positive power للـ A
+
+366
+00:40:39,470 --> 00:40:42,710
+بيخلي الـ A to N جوا الـ H فهذا هيكون التناقض
+
+367
+00:40:46,230 --> 00:40:48,230
+واضح؟ وبالتالي ساعة الـ H is 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b35a0d537885ba03dc81bb395020ef86b4c15548
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_postprocess.srt
@@ -0,0 +1,1468 @@
+1
+00:00:21,160 --> 00:00:23,740
+السلام عليكم بسم الله الرحمن الرحيم ان شاء الله
+
+2
+00:00:23,740 --> 00:00:27,320
+اليوم هناخد الجزء التالت من الوحدة الرابعة اللي
+
+3
+00:00:27,320 --> 00:00:31,860
+بتتكلم فيها عن ال cyclic groups اللي ذاكر أو كان
+
+4
+00:00:31,860 --> 00:00:36,540
+معانا في أول محاضرتين اتكلمنا عن شغلتين أساسيتين
+
+5
+00:00:36,540 --> 00:00:40,680
+الشغلة الأولى متعلقة بخصائص أو بعض الخصائص ل ال
+
+6
+00:00:40,680 --> 00:00:44,460
+cyclic subgroup بعدين أخدناها في المحاضرة الأولى
+
+7
+00:00:44,460 --> 00:00:47,700
+ضمن التعريف و الأمثلة المحاضرة التانية اللي
+
+8
+00:00:47,700 --> 00:00:52,590
+أخدناها اليوم الصبح اتكلمنا عنالنظرية تتعلق بخصائص
+
+9
+00:00:52,590 --> 00:00:58,930
+العنصر وما يولده مجموعات العناصر داخل ال cyclic
+
+10
+00:00:58,930 --> 00:01:04,230
+group اليوم هنتكلم عن نظرية الأساسية لل cyclic
+
+11
+00:01:04,230 --> 00:01:06,870
+subgroup ال fundamental theorem of cyclic subgroup
+
+12
+00:01:06,870 --> 00:01:12,710
+اللي من خلالها بتناول التركيبات الداخلية داخل ال
+
+13
+00:01:12,710 --> 00:01:17,110
+cyclic group المتعلقة بال subgroup نفسها و ليست
+
+14
+00:01:17,110 --> 00:01:21,310
+بالعناصرنص النظرية اللي هي نظرية اربعة تلاتة هيقول
+
+15
+00:01:21,310 --> 00:01:30,030
+التالي theorem fundamental
+
+16
+00:01:30,030 --> 00:01:34,070
+theorem
+
+17
+00:01:34,070 --> 00:01:39,630
+of cyclic groups
+
+18
+00:01:44,620 --> 00:01:47,900
+هنجسم النص النظرية الموجودة في الكتاب ل 3 أجزاء
+
+19
+00:01:47,900 --> 00:01:54,500
+الجزء الأول every subgroup
+
+20
+00:01:54,500 --> 00:01:58,360
+of
+
+21
+00:01:58,360 --> 00:02:03,500
+a cyclic group
+
+22
+00:02:03,500 --> 00:02:10,310
+is cyclicيعني اي subgroup انا باخدها جوا الـ
+
+23
+00:02:10,310 --> 00:02:17,210
+cyclic group هتكون ايضا cyclic الجزء التاني if j
+
+24
+00:02:17,210 --> 00:02:28,930
+generated by some a and order ال a بيساوي n with h
+
+25
+00:02:28,930 --> 00:02:37,210
+subgroup من ال j then order ال h يقسم ال nمش بس ال
+
+26
+00:02:37,210 --> 00:02:41,270
+subgroup هذي cyclic لأ و ال order لها بيقسم ال
+
+27
+00:02:41,270 --> 00:02:45,170
+order لل group لو كنت أنا بتكلم في ال finite case
+
+28
+00:02:45,170 --> 00:02:51,730
+تلاتة اتجاه التاني للجزء اتنين احنا قولنا عن اي
+
+29
+00:02:51,730 --> 00:02:57,150
+subgroup ال order لها بيقسم ال order ل group هجيت
+
+30
+00:02:57,150 --> 00:03:04,070
+السؤال هل كل قاسم ل ال order بلاقي subgroup ال
+
+31
+00:03:04,070 --> 00:03:09,240
+order لهابساوي هذا القاسم هذا كلام بيكون صحيح فقط
+
+32
+00:03:09,240 --> 00:03:19,200
+لو بتكلم عن cyclic الجواب if K يقسم ال N then is
+
+33
+00:03:19,200 --> 00:03:24,780
+any positive divisor
+
+34
+00:03:24,780 --> 00:03:33,500
+of N then there
+
+35
+00:03:36,920 --> 00:03:51,020
+exist a unique subgroup of
+
+36
+00:03:51,020 --> 00:04:03,880
+generated by A namely تحديدًا H بساوي generated by
+
+37
+00:04:03,880 --> 00:04:13,860
+A to N على Kand ال order ل h بيساوي كيه بالعربي
+
+38
+00:04:13,860 --> 00:04:23,240
+انه لأي قاسم لل order ل ال finite cyclic group أنا
+
+39
+00:04:23,240 --> 00:04:28,380
+بقدر ألاقي cyclic sub group و ال order لهذه ال
+
+40
+00:04:28,380 --> 00:04:33,120
+cyclic sub group بيساوي القاسم اللي عندي نيجي
+
+41
+00:04:37,950 --> 00:04:46,630
+فضّال طيب بالعربي الجزء الأول كل مجموعة جزئية او
+
+42
+00:04:46,630 --> 00:04:52,810
+كل زمرة جزئية من زمرة دوارة هي زمرة دوارة يعني ال
+
+43
+00:04:52,810 --> 00:04:59,230
+cyclic group عبارة عن زمرة دوارة الجزء التاني لو
+
+44
+00:04:59,230 --> 00:05:03,350
+كان الزمرة اللي انت بتشتغل عليها دوارة
+
+45
+00:05:05,570 --> 00:05:11,550
+order لها finite يعني زمرة دوارة محدودة فال sub
+
+46
+00:05:11,550 --> 00:05:15,850
+group الزمرة الجزئية منها ال order لهذه الزمرة
+
+47
+00:05:15,850 --> 00:05:22,890
+الجزئية بتقسم ال order للزمرة الأساسية جزء تالت
+
+48
+00:05:22,890 --> 00:05:33,490
+لأي قاسم موجب ل order الزمرة الدوارةبقدر ألاقي
+
+49
+00:05:33,490 --> 00:05:40,270
+زمرة جزئية group أو subgroup ال order لهذه الزمرة
+
+50
+00:05:40,270 --> 00:05:45,370
+الجزئية بساوي هذا القاسم مش بس هيك هذه الزمرة
+
+51
+00:05:45,370 --> 00:05:51,230
+تحديدا هي ال generated by a to n على k نجي نثبت
+
+52
+00:05:51,230 --> 00:05:56,190
+نثبت الجزء الأول every
+
+53
+00:05:56,190 --> 00:06:01,950
+subgroup of a cyclic group is cyclic let jbe
+
+54
+00:06:01,950 --> 00:06:07,950
+generated by a and h subgroup من الجيل ايش اللي
+
+55
+00:06:07,950 --> 00:06:15,330
+لازم اثبته؟ بدي اثبت انا ان الـ H Cyclic Subgroup
+
+56
+00:06:15,330 --> 00:06:18,930
+عشان تكون Cyclic Subgroup ايش لازم انا اجيلها؟
+
+57
+00:06:18,930 --> 00:06:25,990
+generator في الحالة الأولية if الـ H في أنصر واحد
+
+58
+00:06:25,990 --> 00:06:32,480
+وهو ال identity فالـ H generated by مين؟by ال
+
+59
+00:06:32,480 --> 00:06:37,640
+identity فهي Cyclic لو ال H مافيش فيه غير ال
+
+60
+00:06:37,640 --> 00:06:45,420
+identity معناته ال H generated by ال identity if H
+
+61
+00:06:45,420 --> 00:06:56,960
+لا يساوي ال identity هذا معناته there is at
+
+62
+00:06:56,960 --> 00:07:01,020
+least one element
+
+63
+00:07:02,430 --> 00:07:12,550
+in H with one element X يعني terminal H and X لا
+
+64
+00:07:12,550 --> 00:07:21,010
+يساوي ال identity طيب now فضل ماشي
+
+65
+00:07:21,010 --> 00:07:24,970
+بس لو كانت هي ال identity و بس فهي psychic اگه لو
+
+66
+00:07:24,970 --> 00:07:29,870
+فيها حاجة غير ال identity طب احنا بنثبت هذا الكلام
+
+67
+00:07:31,190 --> 00:07:37,250
+بتقدر تثبت اللي هي هيك بط بط
+
+68
+00:07:37,250 --> 00:07:41,250
+X ينتمي لل H اللي هي ال sub group من الجلية
+
+69
+00:07:41,250 --> 00:07:46,870
+generated by A يكبر X عبارة عن ايش power لل A
+
+70
+00:07:46,870 --> 00:07:52,410
+فليكن A أُس اختار A لأكيد هنحتاج هنستعملها بعد
+
+71
+00:07:52,410 --> 00:07:56,430
+هيكد A أُس R وال R ينتمي لل Z
+
+72
+00:08:00,950 --> 00:08:07,530
+طيب او a of t for
+
+73
+00:08:07,530 --> 00:08:12,810
+t عندك two cases there
+
+74
+00:08:12,810 --> 00:08:27,370
+is two cases for t ال case الاولانية ان t اكبر او
+
+75
+00:08:27,370 --> 00:08:34,940
+يساوي الواحدالـ T مش صفر فيا إما من الواحد و فوق
+
+76
+00:08:34,940 --> 00:08:44,460
+يا إما إيش case 2 T أقل من الصفر في ال case التاني
+
+77
+00:08:44,460 --> 00:08:49,840
+in the second case
+
+78
+00:08:49,840 --> 00:08:55,760
+سالب
+
+79
+00:08:55,760 --> 00:08:55,980
+T
+
+80
+00:08:58,940 --> 00:09:09,780
+أكبر من الصفر Now X inverse بدي يساوي X T أو A to
+
+81
+00:09:09,780 --> 00:09:16,980
+T inverse اللي هي A أو سالب T ينتمي لل H with سالب
+
+82
+00:09:16,980 --> 00:09:23,780
+T أكبر من الصفر طبعا ال case الأولاني و ال case
+
+83
+00:09:23,780 --> 00:09:32,320
+التاني بيعطون الحقيقة التالية Case oneand to give
+
+84
+00:09:32,320 --> 00:09:46,060
+us that there is at least one element in H with
+
+85
+00:09:46,060 --> 00:09:57,240
+positive which is a positive power
+
+86
+00:09:59,630 --> 00:10:08,290
+of A يعني دائما بأضمن وجود عنصر جوه ال H ال or أو
+
+87
+00:10:08,290 --> 00:10:14,310
+ال power له إيش positive بأضمن دائما وجود عنصر جوه
+
+88
+00:10:14,310 --> 00:10:20,510
+ال H و ال power له أو العنصر هذا عبارة عن power
+
+89
+00:10:20,510 --> 00:10:23,830
+موجب لمين لل إيه
+
+90
+00:10:29,010 --> 00:10:33,430
+ناخد M والله ايش؟
+
+91
+00:10:33,430 --> 00:10:48,550
+Let M Be The Smallest Positive Power Of A In H
+
+92
+00:10:48,550 --> 00:10:56,430
+ناخد الـ M هو أصغر أُس موجب للـ A في الـ H That is
+
+93
+00:11:00,110 --> 00:11:09,990
+A to M ينتمي للـH and if A to T ينتمي للـH with T
+
+94
+00:11:09,990 --> 00:11:19,550
+أكبر من الصفر then M أقل أو يساوي T الـM
+
+95
+00:11:19,550 --> 00:11:32,960
+هو أصغر power موجب للـA جوا مينDual H claim ادعاء
+
+96
+00:11:32,960 --> 00:11:41,560
+الـ H generated by A to M طبعا انا هي كنت بكون
+
+97
+00:11:41,560 --> 00:11:46,680
+خلصت خطوتين خطوة الاولى اثبت ان الـ H is cyclic
+
+98
+00:11:46,680 --> 00:11:54,560
+خطوة التانية جبت ال generator الـ H اتحولت شغل ليه
+
+99
+00:11:54,560 --> 00:12:03,070
+يا شانا؟لـ set theory نظرية مجموعة since a to m
+
+100
+00:12:03,070 --> 00:12:08,850
+ينتمي لل H معناته generated by a to m sub group من
+
+101
+00:12:08,850 --> 00:12:21,810
+ال H وعطيها إيش؟ واحد let x ينتمي لل H since
+
+102
+00:12:23,760 --> 00:12:30,180
+H subgroup من generated by A معناته الـ X هتساوي A
+
+103
+00:12:30,180 --> 00:12:40,460
+to R for some R ينتمي لمن؟ لـ Z مدام الـ H subset
+
+104
+00:12:40,460 --> 00:12:47,260
+من generated by A فكل عناصر الـ H عبارة عن إيش؟
+
+105
+00:12:47,260 --> 00:12:53,940
+عبارة عن إيش Powers للـ Aفليكن A to R هجيت بال
+
+106
+00:12:53,940 --> 00:13:05,260
+division algorithm ال
+
+107
+00:13:05,260 --> 00:13:11,000
+R أو بلش ال R خدها لإن ال R هستعملها هجيت ك
+
+108
+00:13:11,000 --> 00:13:14,640
+remainder استعمل غمز تاني فليكن K
+
+109
+00:13:18,460 --> 00:13:25,040
+الـ K لو أنا بدي أجسمها على ال M عبارة عن QM زاد
+
+110
+00:13:25,040 --> 00:13:33,100
+ال R والـ R ما بين ال M والـ
+
+111
+00:13:33,100 --> 00:13:36,480
+0 طيب
+
+112
+00:13:36,480 --> 00:13:43,160
+Now A
+
+113
+00:13:50,330 --> 00:14:00,310
+الـ a to r عبارة عن a to k minus qm اللي عبارة عن
+
+114
+00:14:00,310 --> 00:14:10,090
+a to k في a minus qm اللي عبارة عن x في a to m
+
+115
+00:14:10,090 --> 00:14:21,870
+أسالب q و هذا العنصر وين موجود؟ موجود وين؟في ال H
+
+116
+00:14:21,870 --> 00:14:28,250
+ليش X في ال H A to M في ال H فأي power لل A to M
+
+117
+00:14:28,250 --> 00:14:35,750
+هيكون وين جوا ال H طيب هنخل الجزء هذا مكتوب و نكمل
+
+118
+00:14:35,750 --> 00:14:40,150
+اثباتا لسه
+
+119
+00:14:40,150 --> 00:14:45,750
+اثبات الجزء الأول هذا هذا
+
+120
+00:14:45,750 --> 00:14:58,440
+معناته ان A to Rينتمي لمين؟ لـ Latch حاجة if R لا
+
+121
+00:14:58,440 --> 00:15:11,020
+يساوي Zero then R is a positive power of A such
+
+122
+00:15:11,020 --> 00:15:16,720
+that A to R وين؟ في Latch
+
+123
+00:15:20,580 --> 00:15:26,900
+لو ال R مش صفر معناه يصار ال R موجب هو أُس موجب لل
+
+124
+00:15:26,900 --> 00:15:31,960
+A بيخلي ال A تقار وين؟ في ال H نرجع لل M ال M هو
+
+125
+00:15:31,960 --> 00:15:37,420
+مين؟ هو أصغر positive power لل A في ال H هذا
+
+126
+00:15:37,420 --> 00:15:44,440
+معناته أنه لازم ال M يكون أقل أو يساوي R but ال R
+
+127
+00:15:44,440 --> 00:15:49,000
+أقل من ال M نفس ال contradiction الليكان في
+
+128
+00:15:49,000 --> 00:15:52,500
+المحاضرة السابقة هذا مع هذا عبارة عن ايش
+
+129
+00:15:52,500 --> 00:16:01,180
+contradiction معناته ايش الخطأ الفاضل انا فرضه ان
+
+130
+00:16:01,180 --> 00:16:14,320
+ر لا يساوي زيرو so ر بيساوي زيرو and نرجع
+
+131
+00:16:14,320 --> 00:16:17,820
+لل division algorithm ر بيساوي زيرو كياش بيساوي
+
+132
+00:16:18,850 --> 00:16:35,610
+اكيو ام اكيو
+
+133
+00:16:35,610 --> 00:16:40,990
+ام اكيو
+
+134
+00:16:40,990 --> 00:16:41,250
+ام اكيو ام اكيو ام اكيو ام اكيو ام اكيو ام اكيو ام
+
+135
+00:16:41,250 --> 00:16:45,660
+اكيو امby a to m وين في ال H و انا اصلا هنا ماخد
+
+136
+00:16:45,660 --> 00:16:50,440
+ال X من ال H صار ال X من generated لأ انا
+
+137
+00:16:50,440 --> 00:16:55,020
+generated by a to m شباب انا
+
+138
+00:16:55,020 --> 00:16:59,900
+ماخد ال X من ال H صار في generated by a to m
+
+139
+00:16:59,900 --> 00:17:05,800
+معناته ال H sub group من generated by a to m و
+
+140
+00:17:05,800 --> 00:17:12,210
+اعطيها 2 1 و 2هتخليك تقول ان ال H بيساوي generated
+
+141
+00:17:12,210 --> 00:17:22,710
+by a تقام و ال H اشمالها ال Cyclic وهو المطلوب وهي
+
+142
+00:17:22,710 --> 00:17:29,950
+كده أثبتنيش الجزء الأول انه أخدت subgroup من ال
+
+143
+00:17:29,950 --> 00:17:33,130
+Cyclic group اللي باشتغل عليها و طلعت ال subgroup
+
+144
+00:17:33,130 --> 00:17:41,090
+هديش Cyclic مش Cyclic بس generated by أصغرأو by a
+
+145
+00:17:41,090 --> 00:17:47,090
+أصغر positive power داخل الله تفضل بس انا هربطه
+
+146
+00:17:47,090 --> 00:17:50,170
+معاك في بعض انا أعمل هذا عشان الدنيا هو بالظبط ال
+
+147
+00:17:50,170 --> 00:17:54,610
+claim لأ انكسوا واحد و اتنين ان انت صار بتاعة أكبر
+
+148
+00:17:54,610 --> 00:17:59,510
+من صفرها داخلها دع القلم تعالي أقولك الخطوات اللي
+
+149
+00:17:59,510 --> 00:18:04,500
+اتبعت بعتك التاليفي ال case الأولاني تبع أن ال H
+
+150
+00:18:04,500 --> 00:18:08,220
+بيساوي ال identity هذا صف في نعجن بينهم trivial
+
+151
+00:18:08,220 --> 00:18:12,460
+فاشتغلنا على ال H اللي في عنصر غير ال identity
+
+152
+00:18:12,460 --> 00:18:18,040
+هيجيت ال case الأول والتاني هنا بدي أخلص منه باب
+
+153
+00:18:18,040 --> 00:18:25,180
+عرا أنه دائما بقدر ألاقي positive power لل A جوا
+
+154
+00:18:25,180 --> 00:18:29,570
+ال Hعشري ال case الأول والتاني اشتغلت انا على ال A
+
+155
+00:18:29,570 --> 00:18:34,030
+to T ال A to T ال T قدامي خيارين يا موجة باور تاني
+
+156
+00:18:34,030 --> 00:18:38,150
+اللي بدي اخلصه فيه positive power لل A جوا ال H يا
+
+157
+00:18:38,150 --> 00:18:42,910
+ال T سالبة بس انا بشغل جوا sub group ال inverse
+
+158
+00:18:42,910 --> 00:18:48,970
+تبع العنصر اللي انا بدأت منه اللي هو X موجود طبعا
+
+159
+00:18:48,970 --> 00:18:53,750
+ال X هو A to T ف X inverse A to سالب T ال T سالبة
+
+160
+00:18:53,750 --> 00:18:58,690
+فسالب Tموجبة يكبى في ال case التاني برضه اجدرت
+
+161
+00:18:58,690 --> 00:19:02,370
+الاجي عنصر ال positive او ال power له positive
+
+162
+00:19:02,370 --> 00:19:08,290
+يكبى دائما بضمن انه يوجد positive power جوا مين؟
+
+163
+00:19:08,290 --> 00:19:12,010
+positive power لل ايه جوا؟ ال H مدام دائما في
+
+164
+00:19:12,010 --> 00:19:16,910
+positive هاخد اصغر واحد طبعا ماتنساش انه انا بشتغل
+
+165
+00:19:16,910 --> 00:19:21,800
+في ال Z وال Zلما انا بتشتغل على ال positive
+
+166
+00:19:21,800 --> 00:19:25,980
+integer فانتقلت من ال z ل ال n في ال natural
+
+167
+00:19:25,980 --> 00:19:33,240
+number اي مجموعة جزئية من ال natural number غير
+
+168
+00:19:33,240 --> 00:19:39,780
+خالية الها ايش؟ الها minimum او minimal at least
+
+169
+00:19:39,780 --> 00:19:43,280
+اللي هو ال least one او least number فانا أخدت ال
+
+170
+00:19:43,280 --> 00:19:46,340
+least او ال smallest positive power لل H والH
+
+171
+00:19:46,340 --> 00:19:52,140
+فليكن هو Mانسى كل القصص الأولى اللى فى الآخر اللى
+
+172
+00:19:52,140 --> 00:19:56,160
+أخدناها توى و بنمسك فى الـA تقامها ده و نثبت أنه
+
+173
+00:19:56,160 --> 00:20:01,620
+بولد الـH طب ليش جبنى صغير واحد يعنى؟ ليش جبنى
+
+174
+00:20:01,620 --> 00:20:05,100
+أصغر واحد؟ طالع معايا يعني هي ممكن هذه الفلسفة
+
+175
+00:20:05,100 --> 00:20:10,660
+موجودة فى كتير من الشغلات المتعلقة فى الجبر أنا
+
+176
+00:20:10,660 --> 00:20:15,780
+لما بدى أدور على عنصر هو يولد الباقي فليه بصغير
+
+177
+00:20:15,780 --> 00:20:21,170
+واحد؟ الكبير مش هيولد الصغيرلأن الكبير لما تعطيه
+
+178
+00:20:21,170 --> 00:20:25,490
+قوة ومطلوب انه يرجع لبور صغير بدك تشتغل على ان
+
+179
+00:20:25,490 --> 00:20:29,970
+القوة بتكبر في لحظة معينة و بتختصر منها و بتنزل
+
+180
+00:20:29,970 --> 00:20:34,530
+فمن الأسهل ان انا باخد أصغر واحد و أصنع الباقي من
+
+181
+00:20:34,530 --> 00:20:43,750
+خلاله واضح؟ واضح
+
+182
+00:20:43,750 --> 00:20:50,740
+الجزء هذا؟ واضح الجزء الأول يا شباب؟نيجي نثبت
+
+183
+00:20:50,740 --> 00:20:58,460
+الجزء التاني ذاكين
+
+184
+00:20:58,460 --> 00:21:08,920
+ايش الجزء التاني؟ طب يحكوه واحد جاره يفسر الجزء
+
+185
+00:21:08,920 --> 00:21:12,700
+التاني من الاثبات احنا اثبتنا فقط مين ال part
+
+186
+00:21:12,700 --> 00:21:13,360
+الأولاني
+
+187
+00:21:20,680 --> 00:21:27,840
+طيب تعالى نتكلم عنه الجزء التانى let J generated
+
+188
+00:21:27,840 --> 00:21:35,920
+by ال A و ال order لل A بدى يساوي N given او take
+
+189
+00:21:35,920 --> 00:21:50,530
+H subgroup من مين؟ من الجيه we must or sinceJ is
+
+190
+00:21:50,530 --> 00:21:58,370
+Cyclic إيش مقدر أقول أنا عن ال H H is Cyclic
+
+191
+00:21:58,370 --> 00:22:06,030
+Cyclic
+
+192
+00:22:06,030 --> 00:22:12,990
+يجوبش يعني هذا
+
+193
+00:22:12,990 --> 00:22:20,930
+معناته ال H generated by some A to Mالـ H
+
+194
+00:22:20,930 --> 00:22:28,050
+generated by some .. طب ال order للـ H هو ال order
+
+195
+00:22:28,050 --> 00:22:33,730
+generated by a to m اللي هو عبارة عن مين؟ ال order
+
+196
+00:22:33,730 --> 00:22:39,410
+ل a to m اللي هو عبارة عن إيش؟ n على ال agreed
+
+197
+00:22:39,410 --> 00:22:45,410
+common divisor ل m و n agreed common divisor ل m و
+
+198
+00:22:45,410 --> 00:22:53,580
+n عبارة عن إيش؟بغض النظر إيش بيساوي إذا أردر ال H
+
+199
+00:22:53,580 --> 00:23:00,500
+بدي يساوي N على الجريس common divisor ل M و N هذا
+
+200
+00:23:00,500 --> 00:23:08,420
+رقم إيش ماله؟ إيش ماله؟ بيقسم ال N أنا مطلوب من
+
+201
+00:23:08,420 --> 00:23:12,200
+يثبت إنما أردر ال H بيقسم ال N و هذا N على عدد
+
+202
+00:23:12,200 --> 00:23:19,820
+صحيح و هو عدد صحيح إذا أردر ال Hبيجسمين الان خلصوا
+
+203
+00:23:19,820 --> 00:23:24,100
+الجزء التاني جزء
+
+204
+00:23:24,100 --> 00:23:31,900
+التالت في الجزء التالت هجيه اي subgroup ال order
+
+205
+00:23:31,900 --> 00:23:35,580
+لبيقسم ال order ل ال group نفسه في حالة ال finite
+
+206
+00:23:35,580 --> 00:23:43,340
+case طبعا هجيه كل قاسم بيجيله subgroup ولا لا طلع
+
+207
+00:23:43,340 --> 00:23:51,370
+على الجزء التالت letك يقسم الان given او let ال
+
+208
+00:23:51,370 --> 00:23:57,430
+جيه بده تساوي generated by a وال order لل ايه بده
+
+209
+00:23:57,430 --> 00:24:01,430
+يساوي يعنى ايش المطلوب هنا شباب مطلوب بنلاقي
+
+210
+00:24:01,430 --> 00:24:05,490
+subgroup ال order اللي لها كيه subgroup من وين من
+
+211
+00:24:05,490 --> 00:24:10,250
+ال جيه بس هو أنا ريحني في النص ايش قال ليه قاللي
+
+212
+00:24:10,250 --> 00:24:16,220
+ال subgroup المطلوبة مين هيgenerated by a to n على
+
+213
+00:24:16,220 --> 00:24:21,560
+k انا همسك هذه بحسب التلات شغلات انها subgroup
+
+214
+00:24:21,560 --> 00:24:25,380
+سهلة انه generated by any element subgroup شغلت
+
+215
+00:24:25,380 --> 00:24:28,440
+تاني ال order الها بيساوي k وهذه هتكون برضه شغلة
+
+216
+00:24:28,440 --> 00:24:36,460
+سهلة شغلت تالتة ايش انها unique مافيش غيرها انها
+
+217
+00:24:36,460 --> 00:24:38,780
+unique او مافيش غيرها
+
+218
+00:24:41,860 --> 00:24:53,340
+we first show that order بدت
+
+219
+00:24:53,340 --> 00:25:03,160
+ساوة كام هذه سهلة which
+
+220
+00:25:03,160 --> 00:25:06,420
+is
+
+221
+00:25:06,420 --> 00:25:14,740
+trivialالـ order generated by n على k بدي أسوأ ال
+
+222
+00:25:14,740 --> 00:25:22,840
+order ل a أقصر n على k وهي عبارة عن n على لجريس
+
+223
+00:25:22,840 --> 00:25:28,640
+common divisor ل n و n على k شباب لجريس common
+
+224
+00:25:28,640 --> 00:25:32,160
+divisor ل n و ل n على k ايش بيساوي او ل n و n على
+
+225
+00:25:32,160 --> 00:25:37,880
+k بدي أسوأ n على n
+
+226
+00:25:37,880 --> 00:25:45,360
+على kاللي عبارة عن كيكبار ال order لgenerated by a
+
+227
+00:25:45,360 --> 00:25:49,080
+أُس n على كيكبار كيكبار كيكبار كيكبار كيكبار
+
+228
+00:25:49,080 --> 00:25:51,460
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+229
+00:25:51,460 --> 00:25:55,080
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+230
+00:25:55,080 --> 00:26:07,260
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+231
+00:26:17,300 --> 00:26:21,500
+كيف اثبت الـ Uniqueness يا شباب؟ بفترض ان هناك
+
+232
+00:26:21,500 --> 00:26:28,920
+واحدة تانية وبثبت المساواة let A مثلا اختار الهؤوس
+
+233
+00:26:28,920 --> 00:26:35,240
+خليني اتماشى مع الكتاب A to M subgroup
+
+234
+00:26:35,240 --> 00:26:41,000
+من الـ J و ال order that generated by A to M بدي
+
+235
+00:26:41,000 --> 00:26:42,500
+ساوي ايش؟ فضل
+
+236
+00:26:48,140 --> 00:26:56,780
+a unique subgroup of generated by a namely طيب
+
+237
+00:26:56,780 --> 00:27:05,320
+كيف بدا أثبت؟ كيف بدا أثبت أن هدوله زي بعض؟ أنا
+
+238
+00:27:05,320 --> 00:27:09,840
+شابة بالدفتر موجود قدامي بس مش عارف أجرى مين يطلع
+
+239
+00:27:09,840 --> 00:27:13,260
+يفكر معايا؟
+
+240
+00:27:13,260 --> 00:27:16,520
+يعني ماشي بيبنيك أشوش real sound
+
+241
+00:27:25,370 --> 00:27:31,710
+أنا مش كل مرة هثبت لحالي أنا يا شباب دي أثبت أنه
+
+242
+00:27:31,710 --> 00:27:38,630
+هذه هي نفسها هذه يعني generated by a to m و
+
+243
+00:27:38,630 --> 00:27:44,490
+generated by a to n على k زي بعض
+
+244
+00:27:48,920 --> 00:27:56,580
+استفيد من ان ال M بتحقق خاصيتها دي with M is the
+
+245
+00:27:56,580 --> 00:28:07,700
+smallest positive power of
+
+246
+00:28:07,700 --> 00:28:16,810
+A in generated by A to M هاي كمان مساعدةال M عشان
+
+247
+00:28:16,810 --> 00:28:21,230
+ما يجردش يلاقي Mات كتيرة هو أصغر positive power لل
+
+248
+00:28:21,230 --> 00:28:24,750
+A دي هو ال generated by A تقريبا هاجت على .. هذا
+
+249
+00:28:24,750 --> 00:28:29,430
+صار العنصر بالنسبة لهدي unique وهذا العنصر بالنسبة
+
+250
+00:28:29,430 --> 00:28:33,750
+لهدي ما هو ال N على K unique مافيش منه اتنين فلو
+
+251
+00:28:33,750 --> 00:28:38,650
+أنا اثبتت انه A على N A أُس N على K هو نفسه A أُس
+
+252
+00:28:38,650 --> 00:28:44,990
+M بكون خلصت ماكنتش مقدرت بتهدي كلاملو كان ال M و
+
+253
+00:28:44,990 --> 00:28:51,010
+ال N على K شمالهم متساوين يكبر انت قبطلي ان N على
+
+254
+00:28:51,010 --> 00:28:56,690
+K بيساوي M اه
+
+255
+00:28:56,690 --> 00:29:01,250
+طيب
+
+256
+00:29:01,250 --> 00:29:07,430
+مساعدة تانية هذه
+
+257
+00:29:07,430 --> 00:29:14,000
+ال order إلها Kال K بيقسم ال N حطها ع جانب ال
+
+258
+00:29:14,000 --> 00:29:18,280
+order اللي generated by A to M ايش بيساوي ال order
+
+259
+00:29:18,280 --> 00:29:25,280
+ل A to M ايش ال order ل A to M N على الجريس common
+
+260
+00:29:25,280 --> 00:29:33,200
+divisor لمين لل M و لل N اللي هو ايش بيساوي فضل
+
+261
+00:29:33,200 --> 00:29:38,220
+مهمش ال M بتساوي على كلمة نفسك طيب يبقى ال M
+
+262
+00:29:38,220 --> 00:29:39,160
+هتساوي ك M
+
+263
+00:29:42,120 --> 00:29:48,260
+هذا المقوم اثباته طيب
+
+264
+00:29:48,260 --> 00:29:53,700
+ال M رتبة هذه طيب
+
+265
+00:29:53,700 --> 00:29:57,900
+رتبة
+
+266
+00:29:57,900 --> 00:29:58,740
+الأنصة
+
+267
+00:30:01,460 --> 00:30:05,480
+رتبة العنصر بتقسم .. رتبة العنصر بتقسم رتبة العنصر
+
+268
+00:30:05,480 --> 00:30:10,520
+طيب طيب طيب طب ال .. ال M هي رتبة العنصر شوية بس
+
+269
+00:30:10,520 --> 00:30:18,400
+ال M رتبة العنصر ولا power العنصر فارج power power
+
+270
+00:30:18,400 --> 00:30:23,700
+مش رتبة الرتبة هو عبارة عن N على الجيزكم و divisor
+
+271
+00:30:23,700 --> 00:30:25,720
+ل N و M
+
+272
+00:30:36,130 --> 00:30:40,950
+فكه عشان .. طيب أعطيك مساعدة أثبت أن الأم بتجسم
+
+273
+00:30:40,950 --> 00:30:47,910
+الأن أه
+
+274
+00:30:47,910 --> 00:30:57,190
+.. فكه
+
+275
+00:30:57,190 --> 00:31:00,470
+أنا مش عارف أفجر من الدفتر
+
+276
+00:31:04,480 --> 00:31:16,560
+ه يا شباب هيعطيك كل المساعدات الممكنة ال
+
+277
+00:31:16,560 --> 00:31:20,440
+order
+
+278
+00:31:20,440 --> 00:31:23,040
+ل ال a و ال m هي عبارة عن n على ال a's common
+
+279
+00:31:23,040 --> 00:31:26,840
+divisor ل m و n انت لو اثبتت ان ال m بتجسم ال m
+
+280
+00:31:26,840 --> 00:31:31,050
+خلص اثبات بالمساعدات اللي اعطيتك إياهاالـ K بيسوي
+
+281
+00:31:31,050 --> 00:31:37,010
+order generated by A to M الوبد يساوي ال N على
+
+282
+00:31:37,010 --> 00:31:40,870
+الجيزكم و ال divisor ل M و N لو أثبتت أن ال M
+
+283
+00:31:40,870 --> 00:31:47,390
+بيقسم ال N خلصت الأثبات كله وجف على إيش أن ال M
+
+284
+00:31:47,390 --> 00:31:58,970
+بيقسم ال N آه
+
+285
+00:31:58,970 --> 00:31:59,290
+شباب
+
+286
+00:32:07,580 --> 00:32:15,140
+الان بتقسم الشوة الان
+
+287
+00:32:15,140 --> 00:32:18,880
+بتقسم مى؟
+
+288
+00:32:18,880 --> 00:32:25,960
+كيف؟ طيب
+
+289
+00:32:25,960 --> 00:32:30,240
+طب احنا جولنا الكلام هذا و هذا الأخضر إيه اللي و
+
+290
+00:32:30,240 --> 00:32:34,360
+جديش كيف؟
+
+291
+00:32:34,360 --> 00:32:37,060
+كمل تك دالة
+
+292
+00:32:45,260 --> 00:32:50,820
+طيب طالع معايا هلجيت
+
+293
+00:32:50,820 --> 00:32:55,120
+K بدي ساوي ال order that generated by A to M اللي
+
+294
+00:32:55,120 --> 00:33:03,060
+هو ال order لمين ل A to M اش يعني يعني A to M أس K
+
+295
+00:33:03,060 --> 00:33:13,580
+اش بدي ساوي ال identity يعني A to MK بدي ساوي ال
+
+296
+00:33:13,580 --> 00:33:14,340
+identity طيب
+
+297
+00:33:17,540 --> 00:33:24,040
+هذا شو بيساوي؟ هذا بيساوي a to n اش يعني؟ ال n
+
+298
+00:33:24,040 --> 00:33:30,240
+تقسم ال .. ال n تقسم ال .. ال n تقسم ال .. ال n
+
+299
+00:33:30,240 --> 00:33:34,660
+على k بيساوي ال n مين جالك؟ ال n بيساوي ال n في k
+
+300
+00:33:34,660 --> 00:33:41,340
+طبعا يمكن ال mk أكبر من ال n يمكن
+
+301
+00:33:41,340 --> 00:33:49,290
+ال mk يكون أكبر من ال nال N بدا تكون تقسم ال MK
+
+302
+00:33:49,290 --> 00:33:54,870
+لأن هذا هيعطيني على جانب أن N بتقسم ال N minus ال
+
+303
+00:33:54,870 --> 00:34:00,890
+MK يجب أن N تقسم ال MK اه
+
+304
+00:34:00,890 --> 00:34:06,650
+تقسم ولا تساوي؟ تساوي لأنه عيب اذا تساوت المقادرة
+
+305
+00:34:06,650 --> 00:34:11,170
+ليش تقسم؟ ليش تتساوي؟ ممكن يكون أكبر فكروا
+
+306
+00:34:16,760 --> 00:34:24,660
+اه اجرح اجرح ماكتوب عندى ايوة
+
+307
+00:34:24,660 --> 00:34:28,420
+حاجة
+
+308
+00:34:28,420 --> 00:34:35,260
+ال K ايش بدى يساوي order ال A تقم حيدها اللى عبارة
+
+309
+00:34:35,260 --> 00:34:44,840
+عن N على الجريس common divisor لمن ل M و Nيعني كما
+
+310
+00:34:44,840 --> 00:34:50,920
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+311
+00:34:50,920 --> 00:34:56,880
+تسمح كما تسمح كما تسمح كما
+
+312
+00:34:56,880 --> 00:34:57,400
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+313
+00:34:57,400 --> 00:34:57,520
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+314
+00:34:57,520 --> 00:34:57,540
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+315
+00:34:57,540 --> 00:34:59,280
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+316
+00:34:59,280 --> 00:35:01,460
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+317
+00:35:01,460 --> 00:35:13,520
+تسمح كما تسمح كما تسمح كما
+
+318
+00:35:14,990 --> 00:35:20,770
+شباب من عشر دقيق فى شغله انفترض ان انا اعطيتك كل
+
+319
+00:35:20,770 --> 00:35:27,030
+المساعدات اللى هى كتبت حتى كتبت مساعدات على اللوح
+
+320
+00:35:27,030 --> 00:35:33,830
+هذى كيف بتساوي اما كيف انه زوجه ازهر ازهر ازهر
+
+321
+00:35:33,830 --> 00:35:40,810
+ازهر ازهر
+
+322
+00:35:55,820 --> 00:36:02,960
+طيب فكروا طيب
+
+323
+00:36:02,960 --> 00:36:11,960
+هفكر انا طيب since شغل سهل ال H generated by ال A
+
+324
+00:36:11,960 --> 00:36:13,660
+term فضل
+
+325
+00:36:21,180 --> 00:36:24,320
+الان على كيب بيقسم الان و الان على كيب بيقسم الان
+
+326
+00:36:24,320 --> 00:36:31,740
+صحيح هذا
+
+327
+00:36:31,740 --> 00:36:36,680
+معناته ان ان على كيب تقسم مين الان دي مالك لازمة
+
+328
+00:36:36,680 --> 00:36:40,580
+الان على كيب تقسم مين الان اش يعني
+
+329
+00:36:43,400 --> 00:36:46,280
+الان علي كيف تقسم الام؟ مش حتى فادت الان بيقسم
+
+330
+00:36:46,280 --> 00:36:57,140
+الام كيه؟ الان بيقسم الام كيه؟ طيب بعد هيك؟ لأ أنا
+
+331
+00:36:57,140 --> 00:37:04,560
+مستنتجة منها سيبك من الخربشات هذه كلها خليني أتزم
+
+332
+00:37:04,560 --> 00:37:07,460
+بشغل الكتاب طلع معايا
+
+333
+00:37:10,720 --> 00:37:16,060
+let generated by ال a to m هو في النهاية مش هنعمل
+
+334
+00:37:16,060 --> 00:37:25,020
+هيك دي يعني لأ ضايق الوجه حجرة
+
+335
+00:37:25,020 --> 00:37:29,440
+ال h generated by ال a to m سبقوا من ال j ال order
+
+336
+00:37:29,440 --> 00:37:32,900
+ل a to m دي ساوة k with m is the smallest positive
+
+337
+00:37:32,900 --> 00:37:35,520
+power of a in او انا وصلت هنا
+
+338
+00:37:48,600 --> 00:37:53,740
+طيب هجت ال K بدي ساوي generated by A to M اللي هو
+
+339
+00:37:53,740 --> 00:37:59,580
+N على الجريس common divisor ل M على N هذا بدي ساوي
+
+340
+00:37:59,580 --> 00:38:06,300
+N على M تمام النتيجة ان M بدي تساوي N على K
+
+341
+00:38:06,880 --> 00:38:11,100
+وبالتالي generated by a to m يستوي generated by a
+
+342
+00:38:11,100 --> 00:38:23,460
+to n على k وهو المطلوب يعني h is .. اه صحيح صحيح
+
+343
+00:38:23,460 --> 00:38:31,360
+نهدر
+
+344
+00:38:31,360 --> 00:38:37,200
+يا عدنا نخربش فيها نص ساعة عشان نفهماللي هي هذه
+
+345
+00:38:37,200 --> 00:38:43,120
+انها هذه متساوية بناء على ان M هي ال smallest
+
+346
+00:38:43,120 --> 00:38:48,400
+positive power لل A في ال generated part معناه
+
+347
+00:38:48,400 --> 00:38:53,580
+حاجة هنا ال A to M دي سوى ال identity وال A to MK
+
+348
+00:38:53,580 --> 00:38:58,080
+دي سوى ال identityالمفروض في علاقة بين ال N و ال
+
+349
+00:38:58,080 --> 00:39:03,460
+MK هجيت ال N أصغر واحد المفروض ان ال N تقسم ال MK
+
+350
+00:39:03,460 --> 00:39:11,760
+هجيت بإمكاني بطريقة لو فرضت ان ال MK أكبر من ال N
+
+351
+00:39:11,760 --> 00:39:16,660
+يعني
+
+352
+00:39:16,660 --> 00:39:21,700
+هذه المفتاح على الأقل هذه بتكون ايش ال N تقسم ال
+
+353
+00:39:21,700 --> 00:39:28,170
+MKتمام؟ و ال M K أكبر لو كانت أكبر من ال N فهي على
+
+354
+00:39:28,170 --> 00:39:38,050
+ال M K أكبر أو سواش 2N هنا تنساش أن ال K تقسم فال
+
+355
+00:39:38,050 --> 00:39:43,110
+K هتكون عبارة عن حاجة أصغر من ال N معناته علشان
+
+356
+00:39:43,110 --> 00:39:46,790
+تكون ال K أصغر من ال N و لما أضربها في ال M يعطيني
+
+357
+00:39:46,790 --> 00:39:50,410
+عدد أكبر أو سوى 2N ال M بدأ تكون أكبر من ال N
+
+358
+00:39:53,920 --> 00:40:02,080
+هجيت ال K تقسم ال N فال K أقل من مين؟ من ال N هجيت
+
+359
+00:40:02,080 --> 00:40:07,060
+عشان يكون ال M K اللي هي أقل من M N وهذه بدأت تكون
+
+360
+00:40:07,060 --> 00:40:15,450
+أكبر أو يساوي 2 N المفروض أن ال Mهو ال M K هتضرب
+
+361
+00:40:15,450 --> 00:40:18,810
+ال M في عدد أقل من ال N هيعطيك أكبر من اتنين N
+
+362
+00:40:18,810 --> 00:40:23,950
+فلازم ال M يكون أكبر من ال N وهذا بيعطيك تناقض لأن
+
+363
+00:40:23,950 --> 00:40:29,250
+أصلا ال M أصغر positive power بيخلي ال A to M جوا
+
+364
+00:40:29,250 --> 00:40:34,830
+ال A بس ال A to N بسوا ال identity ينتمي لل H فكيف
+
+365
+00:40:34,830 --> 00:40:39,470
+ال M أكبر من ال N و ال N هو positive power لل A
+
+366
+00:40:39,470 --> 00:40:42,710
+بيخلي ال A to N جوا ال H فهذا هيكون التناقض
+
+367
+00:40:46,230 --> 00:40:48,230
+واضح؟ وبالتالي ساعة ال H is
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..167b690d517eebdf8501ae5fcee7a35bfd1d431d
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4954, "start": 21.16, "end": 49.54, "text": "السلام عليكم بسم الله الرحمن الرحيم ان شاء الله اليوم هناخد الجزء التالت من الوحدة الرابعة اللي بتتكلم فيها عن ال cyclic groups اللي ذاكر أو كان معانا في أول محاضرتين اتكلمنا عن شغلتين أساسيتين الشغلة الأولى متعلقة بخصائص أو بعض الخصائص ل ال cyclic subgroup بعدين أخدناها في المحاضرة الأولى ضمن التعريف و الأمثلة المحاضرة التانية اللي أخدناها اليوم الصبح اتكلمنا عن", "tokens": [6027, 3794, 37440, 25894, 24793, 4724, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 16472, 13412, 16606, 21984, 45595, 20498, 8032, 1863, 47283, 3215, 25724, 11622, 38207, 16712, 6027, 2655, 9154, 2423, 2407, 24401, 3660, 34892, 16758, 27884, 13672, 1829, 39894, 2655, 4117, 19528, 8978, 11296, 18871, 2423, 38154, 1050, 3935, 13672, 1829, 29910, 995, 37983, 34051, 25961, 20449, 7649, 995, 8978, 5551, 12610, 3714, 5016, 46958, 43500, 9957, 1975, 2655, 4117, 19528, 8315, 18871, 13412, 17082, 1211, 2655, 9957, 5551, 3794, 32277, 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"end": 1076.47, "word": " القلم", "probability": 0.750244140625}, {"start": 1076.47, "end": 1078.51, "word": " تعالي", "probability": 0.809814453125}, {"start": 1078.51, "end": 1078.89, "word": " أقولك", "probability": 0.9034830729166666}, {"start": 1078.89, "end": 1079.37, "word": " الخطوات", "probability": 0.976318359375}, {"start": 1079.37, "end": 1079.51, "word": " اللي", "probability": 0.849853515625}, {"start": 1079.51, "end": 1079.79, "word": " اتبعت", "probability": 0.878173828125}, {"start": 1079.79, "end": 1080.17, "word": " بعتك", "probability": 0.6278483072916666}, {"start": 1080.17, "end": 1080.51, "word": " التالي", "probability": 0.9208984375}], "temperature": 1.0}, {"id": 38, "seek": 110554, "start": 1082.06, "end": 1105.54, "text": "في ال case الأولاني تبع أن ال H بيساوي ال identity هذا صف في نعجن بينهم trivial فاشتغلنا على ال H اللي في عنصر غير ال identity هيجيت ال case الأول والتاني هنا بدي أخلص منه باب عرا أنه دائما بقدر ألاقي positive power لل A جوا ال H", "tokens": [41185, 2423, 1389, 16247, 12610, 7649, 1829, 6055, 3555, 3615, 14739, 2423, 389, 4724, 1829, 3794, 995, 45865, 2423, 6575, 23758, 20328, 5172, 8978, 8717, 3615, 7435, 1863, 49374, 16095, 26703, 6156, 33599, 2655, 17082, 1211, 8315, 15844, 2423, 389, 13672, 1829, 8978, 18871, 9381, 2288, 32771, 13546, 2423, 6575, 8032, 1829, 7435, 36081, 2423, 1389, 16247, 12610, 16070, 2655, 7649, 1829, 34105, 4724, 16254, 5551, 9778, 1211, 9381, 9154, 3224, 4724, 16758, 6225, 23557, 14739, 3224, 11778, 16373, 15042, 4724, 28543, 2288, 5551, 15040, 38436, 3353, 1347, 24976, 316, 10874, 14407, 2423, 389], "avg_logprob": -0.27828947368421053, "compression_ratio": 1.6605504587155964, "no_speech_prob": 0.0, "words": [{"start": 1082.06, "end": 1082.3, "word": "في", "probability": 0.6708984375}, {"start": 1082.3, "end": 1082.46, "word": " ال", "probability": 0.62060546875}, {"start": 1082.46, "end": 1082.7, "word": " case", "probability": 0.8056640625}, {"start": 1082.7, "end": 1083.58, "word": " 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"probability": 0.9373372395833334}, {"start": 1100.18, "end": 1101.48, "word": " بقدر", "probability": 0.9899088541666666}, {"start": 1101.48, "end": 1102.08, "word": " ألاقي", "probability": 0.7775065104166666}, {"start": 1102.08, "end": 1103.02, "word": " positive", "probability": 0.9296875}, {"start": 1103.02, "end": 1103.82, "word": " power", "probability": 0.93505859375}, {"start": 1103.82, "end": 1104.72, "word": " لل", "probability": 0.74853515625}, {"start": 1104.72, "end": 1105.02, "word": " A", "probability": 0.342041015625}, {"start": 1105.02, "end": 1105.18, "word": " جوا", "probability": 0.4913330078125}, {"start": 1105.18, "end": 1105.28, "word": " ال", "probability": 0.94580078125}, {"start": 1105.28, "end": 1105.54, "word": " H", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 39, "seek": 113489, "start": 1106.63, "end": 1134.89, "text": "عشري ال case الأول والتاني اشتغلت انا على ال A to T ال A to T ال T قدامي خيارين يا موجة باور تاني اللي بدي اخلصه فيه positive power لل A جوا ال H يا ال T سالبة بس انا بشغل جوا sub group ال inverse تبع العنصر اللي انا بدأت منه اللي هو X موجود طبعا ال X هو A to T ف X inverse A to سالب T ال T سالبة فسالب T", "tokens": [3615, 8592, 16572, 2423, 1389, 16247, 12610, 16070, 2655, 7649, 1829, 1975, 8592, 2655, 17082, 1211, 2655, 1975, 8315, 15844, 2423, 316, 281, 314, 2423, 316, 281, 314, 2423, 314, 12174, 3215, 10943, 1829, 16490, 1829, 9640, 9957, 35186, 3714, 29245, 3660, 4724, 995, 13063, 6055, 7649, 1829, 13672, 1829, 4724, 16254, 1975, 9778, 1211, 9381, 3224, 8978, 3224, 3353, 1347, 24976, 316, 10874, 14407, 2423, 389, 35186, 2423, 314, 8608, 6027, 49401, 4724, 3794, 1975, 8315, 4724, 8592, 17082, 1211, 10874, 14407, 1422, 1594, 2423, 17340, 6055, 3555, 3615, 18863, 1863, 9381, 2288, 13672, 1829, 1975, 8315, 47525, 10721, 2655, 9154, 3224, 13672, 1829, 31439, 1783, 3714, 29245, 23328, 23032, 3555, 3615, 995, 2423, 1783, 31439, 316, 281, 314, 6156, 1783, 17340, 316, 281, 8608, 6027, 3555, 314, 2423, 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" H", "probability": 0.95654296875}, {"start": 1117.47, "end": 1118.15, "word": " يا", "probability": 0.7392578125}, {"start": 1118.15, "end": 1118.53, "word": " ال", "probability": 0.9296875}, {"start": 1118.53, "end": 1118.69, "word": " T", "probability": 0.96240234375}, {"start": 1118.69, "end": 1119.29, "word": " سالبة", "probability": 0.8776041666666666}, {"start": 1119.29, "end": 1120.03, "word": " بس", "probability": 0.9267578125}, {"start": 1120.03, "end": 1120.19, "word": " انا", "probability": 0.754150390625}, {"start": 1120.19, "end": 1120.57, "word": " بشغل", "probability": 0.91943359375}, {"start": 1120.57, "end": 1120.77, "word": " جوا", "probability": 0.946533203125}, {"start": 1120.77, "end": 1120.97, "word": " sub", "probability": 0.8125}, {"start": 1120.97, "end": 1121.45, "word": " group", "probability": 0.499755859375}, {"start": 1121.45, "end": 1122.29, "word": " ال", "probability": 0.13671875}, {"start": 1122.29, "end": 1122.91, "word": " inverse", "probability": 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0.978515625}, {"start": 1129.11, "end": 1129.49, "word": " X", "probability": 0.98974609375}, {"start": 1129.49, "end": 1129.79, "word": " هو", "probability": 0.97412109375}, {"start": 1129.79, "end": 1130.03, "word": " A", "probability": 0.9775390625}, {"start": 1130.03, "end": 1130.11, "word": " to", "probability": 0.943359375}, {"start": 1130.11, "end": 1130.31, "word": " T", "probability": 0.98583984375}, {"start": 1130.31, "end": 1130.63, "word": " ف", "probability": 0.9404296875}, {"start": 1130.63, "end": 1130.83, "word": " X", "probability": 0.448486328125}, {"start": 1130.83, "end": 1131.37, "word": " inverse", "probability": 0.85205078125}, {"start": 1131.37, "end": 1131.75, "word": " A", "probability": 0.85791015625}, {"start": 1131.75, "end": 1131.87, "word": " to", "probability": 0.7421875}, {"start": 1131.87, "end": 1132.25, "word": " سالب", "probability": 0.737060546875}, {"start": 1132.25, "end": 1132.41, "word": " T", "probability": 0.97021484375}, {"start": 1132.41, 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1450.31, "end": 1450.73, "word": " subgroup", "probability": 0.937744140625}, {"start": 1450.73, "end": 1451.39, "word": " المطلوبة", "probability": 0.93388671875}, {"start": 1451.39, "end": 1451.53, "word": " مين", "probability": 0.91552734375}, {"start": 1451.53, "end": 1451.77, "word": " هي", "probability": 0.88134765625}], "temperature": 1.0}, {"id": 51, "seek": 147878, "start": 1452.82, "end": 1478.78, "text": "generated by a to n على k انا همسك هذه بحسب التلات شغلات انها subgroup سهلة انه generated by any element subgroup شغلت تاني ال order الها بيساوي k وهذه هتكون برضه شغلة سهلة شغلت تالتة ايش انها unique مافيش غيرها انها unique او مافيش غيرها", "tokens": [21848, 770, 538, 257, 281, 297, 15844, 350, 1975, 8315, 8032, 2304, 3794, 4117, 29538, 4724, 5016, 35457, 16712, 1211, 9307, 13412, 17082, 1211, 9307, 16472, 11296, 1422, 17377, 8608, 3224, 37977, 16472, 3224, 10833, 538, 604, 4478, 1422, 17377, 13412, 17082, 1211, 2655, 6055, 7649, 1829, 2423, 1668, 2423, 11296, 4724, 1829, 3794, 995, 45865, 350, 37037, 24192, 8032, 2655, 30544, 4724, 43042, 3224, 13412, 17082, 37977, 8608, 3224, 37977, 13412, 17082, 1211, 2655, 6055, 6027, 2655, 3660, 1975, 1829, 8592, 16472, 11296, 3845, 19446, 41185, 8592, 32771, 13546, 11296, 16472, 11296, 3845, 1975, 2407, 19446, 41185, 8592, 32771, 13546, 11296], "avg_logprob": -0.25530946601941745, "compression_ratio": 1.8274111675126903, "no_speech_prob": 6.556510925292969e-07, "words": [{"start": 1452.82, "end": 1453.5, "word": "generated", "probability": 0.6512451171875}, {"start": 1453.5, "end": 1453.98, "word": " by", "probability": 0.97265625}, {"start": 1453.98, "end": 1455.22, "word": " a", "probability": 0.572265625}, {"start": 1455.22, "end": 1455.72, "word": " to", "probability": 0.5751953125}, {"start": 1455.72, "end": 1456.0, "word": " n", "probability": 0.8623046875}, {"start": 1456.0, "end": 1456.22, "word": " على", "probability": 0.556640625}, {"start": 1456.22, "end": 1456.5, "word": " k", "probability": 0.859375}, {"start": 1456.5, "end": 1457.54, "word": " انا", "probability": 0.4967041015625}, {"start": 1457.54, "end": 1457.98, "word": " همسك", "probability": 0.8297119140625}, {"start": 1457.98, "end": 1458.28, "word": " هذه", "probability": 0.80419921875}, {"start": 1458.28, "end": 1458.86, "word": " بحسب", "probability": 0.6714680989583334}, {"start": 1458.86, "end": 1459.22, "word": " التلات", "probability": 0.6781412760416666}, {"start": 1459.22, "end": 1459.78, "word": " شغلات", "probability": 0.8970947265625}, {"start": 1459.78, "end": 1461.12, "word": " انها", "probability": 0.867919921875}, {"start": 1461.12, "end": 1461.56, "word": " subgroup", "probability": 0.787109375}, {"start": 1461.56, "end": 1462.04, "word": " سهلة", "probability": 0.9619140625}, {"start": 1462.04, "end": 1462.76, "word": " انه", "probability": 0.53759765625}, {"start": 1462.76, "end": 1463.14, "word": " generated", "probability": 0.78955078125}, {"start": 1463.14, "end": 1463.4, "word": " by", "probability": 0.9736328125}, {"start": 1463.4, "end": 1463.7, "word": " any", "probability": 0.89990234375}, {"start": 1463.7, "end": 1464.04, "word": " element", "probability": 0.85595703125}, {"start": 1464.04, "end": 1464.58, "word": " subgroup", "probability": 0.92236328125}, {"start": 1464.58, "end": 1465.38, "word": " شغلت", "probability": 0.68048095703125}, {"start": 1465.38, "end": 1465.6, "word": " تاني", "probability": 0.8963216145833334}, {"start": 1465.6, "end": 1465.72, "word": " ال", "probability": 0.84912109375}, {"start": 1465.72, "end": 1466.04, "word": " order", "probability": 0.9150390625}, {"start": 1466.04, "end": 1466.42, "word": " الها", "probability": 0.4775390625}, {"start": 1466.42, "end": 1466.82, "word": " بيساوي", "probability": 0.8796875}, {"start": 1466.82, "end": 1467.16, "word": " k", "probability": 0.55810546875}, {"start": 1467.16, "end": 1467.58, "word": " وهذه", "probability": 0.4200439453125}, {"start": 1467.58, "end": 1467.88, "word": " هتكون", "probability": 0.83984375}, {"start": 1467.88, "end": 1468.14, "word": " برضه", "probability": 0.751220703125}, {"start": 1468.14, "end": 1468.44, "word": " شغلة", "probability": 0.8668619791666666}, {"start": 1468.44, "end": 1468.82, "word": " سهلة", "probability": 0.986328125}, {"start": 1468.82, "end": 1469.6, "word": " شغلت", "probability": 0.9576416015625}, {"start": 1469.6, "end": 1469.92, "word": " تالتة", "probability": 0.74102783203125}, {"start": 1469.92, "end": 1471.12, "word": " ايش", "probability": 0.8271484375}, {"start": 1471.12, "end": 1472.66, "word": " انها", "probability": 0.92138671875}, {"start": 1472.66, "end": 1473.18, "word": " unique", "probability": 0.91748046875}, {"start": 1473.18, "end": 1474.36, "word": " مافيش", "probability": 0.7679036458333334}, {"start": 1474.36, "end": 1474.88, "word": " غيرها", "probability": 0.9952799479166666}, {"start": 1474.88, "end": 1476.46, "word": " انها", "probability": 0.965576171875}, {"start": 1476.46, "end": 1477.08, "word": " unique", "probability": 0.92578125}, {"start": 1477.08, "end": 1477.58, "word": " او", "probability": 0.941650390625}, {"start": 1477.58, "end": 1478.2, "word": " مافيش", "probability": 0.94287109375}, {"start": 1478.2, "end": 1478.78, "word": " غيرها", "probability": 0.99658203125}], "temperature": 1.0}, {"id": 52, "seek": 150714, "start": 1481.86, "end": 1507.14, "text": "we first show that order بدت ساوة كام هذه سهلة which is trivial", "tokens": [826, 700, 855, 300, 1668, 47525, 2655, 8608, 995, 2407, 3660, 9122, 10943, 29538, 8608, 3224, 37977, 597, 307, 26703], "avg_logprob": -0.44717260769435335, "compression_ratio": 0.963855421686747, "no_speech_prob": 0.0, "words": [{"start": 1481.86, "end": 1482.24, "word": "we", "probability": 0.1654052734375}, {"start": 1482.24, "end": 1483.6, "word": " first", "probability": 0.86279296875}, {"start": 1483.6, "end": 1486.14, "word": " show", "probability": 0.92822265625}, {"start": 1486.14, "end": 1487.18, "word": " that", "probability": 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على k ايش بيساوي او ل n و n على k بدي أسوأ n على n على k", "tokens": [6027, 39184, 1668, 10833, 538, 297, 15844, 350, 4724, 16254, 5551, 3794, 2407, 10721, 2423, 1668, 5296, 257, 5551, 4587, 9381, 2288, 297, 15844, 350, 37037, 1829, 6225, 3555, 9640, 3660, 18871, 297, 15844, 5296, 7435, 16572, 3794, 2689, 25974, 284, 5296, 297, 4032, 297, 15844, 350, 13412, 3555, 16758, 5296, 7435, 16572, 3794, 2689, 25974, 284, 5296, 297, 4032, 5296, 297, 15844, 350, 1975, 1829, 8592, 4724, 1829, 3794, 995, 45865, 1975, 2407, 5296, 297, 4032, 297, 15844, 350, 4724, 16254, 5551, 3794, 2407, 10721, 297, 15844, 297, 15844, 350], "avg_logprob": -0.31182066675113596, "compression_ratio": 1.89937106918239, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1509.38, "end": 1509.76, "word": "الـ", "probability": 0.26385498046875}, {"start": 1509.76, "end": 1510.12, "word": " order", "probability": 0.5615234375}, {"start": 1510.12, "end": 1510.78, "word": " generated", "probability": 0.467041015625}, 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"word": " و", "probability": 0.9169921875}, {"start": 1526.46, "end": 1526.64, "word": " n", "probability": 0.38330078125}, {"start": 1526.64, "end": 1526.84, "word": " على", "probability": 0.912109375}, {"start": 1526.84, "end": 1527.08, "word": " k", "probability": 0.96728515625}, {"start": 1527.08, "end": 1528.1, "word": " شباب", "probability": 0.8509114583333334}, {"start": 1528.1, "end": 1528.44, "word": " لجريس", "probability": 0.9407958984375}, {"start": 1528.44, "end": 1528.64, "word": " common", "probability": 0.96337890625}, {"start": 1528.64, "end": 1529.16, "word": " divisor", "probability": 0.94140625}, {"start": 1529.16, "end": 1529.3, "word": " ل", "probability": 0.96826171875}, {"start": 1529.3, "end": 1529.48, "word": " n", "probability": 0.85888671875}, {"start": 1529.48, "end": 1529.58, "word": " و", "probability": 0.8623046875}, {"start": 1529.58, "end": 1529.66, "word": " ل", "probability": 0.79150390625}, {"start": 1529.66, "end": 1529.86, "word": " n", 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{"start": 1533.54, "end": 1533.88, "word": " أسوأ", "probability": 0.908447265625}, {"start": 1533.88, "end": 1534.32, "word": " n", "probability": 0.5302734375}, {"start": 1534.32, "end": 1534.82, "word": " على", "probability": 0.93701171875}, {"start": 1534.82, "end": 1537.88, "word": " n", "probability": 0.75341796875}, {"start": 1537.88, "end": 1538.1, "word": " على", "probability": 0.93603515625}, {"start": 1538.1, "end": 1538.38, "word": " k", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 54, "seek": 156726, "start": 1539.66, "end": 1567.26, "text": "اللي عبارة عن كيكبار ال order لgenerated by a أُس n على كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار", "tokens": [6027, 20292, 6225, 3555, 9640, 3660, 18871, 9122, 1829, 4117, 3555, 9640, 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1587.3, "end": 1587.76, "word": " مثلا", "probability": 0.849853515625}, {"start": 1587.76, "end": 1588.32, "word": " اختار", "probability": 0.8790690104166666}, {"start": 1588.32, "end": 1588.92, "word": " الهؤوس", "probability": 0.51080322265625}, {"start": 1588.92, "end": 1589.44, "word": " خليني", "probability": 0.72430419921875}, {"start": 1589.44, "end": 1589.88, "word": " اتماشى", "probability": 0.67242431640625}, {"start": 1589.88, "end": 1589.98, "word": " مع", "probability": 0.92529296875}, {"start": 1589.98, "end": 1590.52, "word": " الكتاب", "probability": 0.9775390625}, {"start": 1590.52, "end": 1591.32, "word": " A", "probability": 0.67578125}, {"start": 1591.32, "end": 1591.42, "word": " to", "probability": 0.6611328125}, {"start": 1591.42, "end": 1591.76, "word": " M", "probability": 0.9765625}, {"start": 1591.76, "end": 1595.24, "word": " subgroup", "probability": 0.687744140625}, {"start": 1595.24, "end": 1595.5, "word": " من", "probability": 0.97021484375}, {"start": 1595.5, "end": 1595.72, "word": " الـ", "probability": 0.69580078125}, {"start": 1595.72, "end": 1595.96, "word": " J", "probability": 0.4736328125}, {"start": 1595.96, "end": 1596.74, "word": " و", "probability": 0.3876953125}, {"start": 1596.74, "end": 1596.9, "word": " ال", "probability": 0.417724609375}, {"start": 1596.9, "end": 1597.34, "word": " order", "probability": 0.9072265625}, {"start": 1597.34, "end": 1597.76, "word": " that", "probability": 0.285888671875}, {"start": 1597.76, "end": 1598.3, "word": " generated", "probability": 0.52099609375}, {"start": 1598.3, "end": 1598.72, "word": " by", "probability": 0.91015625}, {"start": 1598.72, "end": 1599.04, "word": " A", "probability": 0.94970703125}, {"start": 1599.04, "end": 1599.18, "word": " to", "probability": 0.94677734375}, {"start": 1599.18, "end": 1599.58, "word": " M", "probability": 0.99609375}, {"start": 1599.58, "end": 1601.0, "word": " بدي", "probability": 0.4808349609375}, {"start": 1601.0, "end": 1601.34, "word": " ساوي", "probability": 0.779296875}, {"start": 1601.34, "end": 1602.08, "word": " ايش؟", "probability": 0.68450927734375}, {"start": 1602.08, "end": 1602.5, "word": " فضل", "probability": 0.7840169270833334}], "temperature": 1.0}, {"id": 56, "seek": 163652, "start": 1608.14, "end": 1636.52, "text": "a unique subgroup of generated by a namely طيب كيف بدا أثبت؟ كيف بدا أثبت أن هدوله زي بعض؟ أنا شابة بالدفتر موجود قدامي بس مش عارف أجرى مين يطلع يفكر معايا؟ يعني ماشي بيبنيك أشوش real sound", "tokens": [64, 3845, 1422, 17377, 295, 10833, 538, 257, 20926, 23032, 1829, 3555, 9122, 33911, 4724, 28259, 5551, 12984, 3555, 2655, 22807, 9122, 33911, 4724, 28259, 5551, 12984, 3555, 2655, 14739, 8032, 3215, 12610, 3224, 30767, 1829, 45030, 11242, 22807, 41850, 13412, 16758, 3660, 20666, 3215, 5172, 2655, 2288, 3714, 29245, 23328, 12174, 3215, 10943, 1829, 4724, 3794, 37893, 6225, 9640, 5172, 5551, 7435, 2288, 7578, 3714, 9957, 7251, 9566, 1211, 3615, 7251, 5172, 37983, 20449, 995, 25528, 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"end": 1618.18, "word": " كيف", "probability": 0.785400390625}, {"start": 1618.18, "end": 1618.36, "word": " بدا", "probability": 0.4312744140625}, {"start": 1618.36, "end": 1620.62, "word": " أثبت؟", "probability": 0.811328125}, {"start": 1620.62, "end": 1622.28, "word": " كيف", "probability": 0.932861328125}, {"start": 1622.28, "end": 1622.44, "word": " بدا", "probability": 0.95166015625}, {"start": 1622.44, "end": 1622.66, "word": " أثبت", "probability": 0.99560546875}, {"start": 1622.66, "end": 1622.78, "word": " أن", "probability": 0.57177734375}, {"start": 1622.78, "end": 1623.06, "word": " هدوله", "probability": 0.66375732421875}, {"start": 1623.06, "end": 1623.24, "word": " زي", "probability": 0.972412109375}, {"start": 1623.24, "end": 1625.16, "word": " بعض؟", "probability": 0.8470052083333334}, {"start": 1625.16, "end": 1625.32, "word": " أنا", "probability": 0.931640625}, {"start": 1625.32, "end": 1625.66, "word": " شابة", "probability": 0.5641276041666666}, {"start": 1625.66, "end": 1626.02, "word": " بالدفتر", "probability": 0.72744140625}, {"start": 1626.02, "end": 1626.28, "word": " موجود", "probability": 0.9899088541666666}, {"start": 1626.28, "end": 1626.6, "word": " قدامي", "probability": 0.879638671875}, {"start": 1626.6, "end": 1626.72, "word": " بس", "probability": 0.920654296875}, {"start": 1626.72, "end": 1626.84, "word": " مش", "probability": 0.98828125}, {"start": 1626.84, "end": 1627.04, "word": " عارف", "probability": 0.9964192708333334}, {"start": 1627.04, "end": 1627.46, "word": " أجرى", "probability": 0.7886962890625}, {"start": 1627.46, "end": 1629.52, "word": " مين", "probability": 0.81396484375}, {"start": 1629.52, "end": 1629.84, "word": " يطلع", "probability": 0.993408203125}, {"start": 1629.84, "end": 1630.22, "word": " يفكر", "probability": 0.9853515625}, {"start": 1630.22, "end": 1633.26, "word": " معايا؟", "probability": 0.9197998046875}, {"start": 1633.26, "end": 1633.54, "word": " يعني", "probability": 0.767822265625}, {"start": 1633.54, "end": 1633.92, "word": " ماشي", "probability": 0.6405029296875}, {"start": 1633.92, "end": 1634.56, "word": " بيبنيك", "probability": 0.58076171875}, {"start": 1634.56, "end": 1635.64, "word": " أشوش", "probability": 0.5826416015625}, {"start": 1635.64, "end": 1636.04, "word": " real", "probability": 0.09185791015625}, {"start": 1636.04, "end": 1636.52, "word": " sound", "probability": 0.6826171875}], "temperature": 1.0}, {"id": 57, "seek": 166449, "start": 1645.37, "end": 1664.49, "text": "أنا مش كل مرة هثبت لحالي أنا يا شباب دي أثبت أنه هذه هي نفسها هذه يعني generated by a to m و generated by a to n على k زي بعض", "tokens": [10721, 8315, 37893, 28242, 3714, 25720, 8032, 12984, 3555, 2655, 5296, 5016, 6027, 1829, 41850, 35186, 13412, 3555, 16758, 11778, 1829, 5551, 12984, 3555, 2655, 14739, 3224, 29538, 39896, 8717, 36178, 11296, 29538, 37495, 22653, 10833, 538, 257, 281, 275, 4032, 10833, 538, 257, 281, 297, 15844, 350, 30767, 1829, 45030, 11242], "avg_logprob": 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{"start": 2413.53, "end": 2413.63, "word": " ال", "probability": 0.7890625}, {"start": 2413.63, "end": 2413.77, "word": " M", "probability": 0.32177734375}, {"start": 2413.77, "end": 2414.11, "word": " K", "probability": 0.55029296875}, {"start": 2414.11, "end": 2415.45, "word": " هتضرب", "probability": 0.8956298828125}, {"start": 2415.45, "end": 2415.63, "word": " ال", "probability": 0.87158203125}, {"start": 2415.63, "end": 2415.83, "word": " M", "probability": 0.94580078125}, {"start": 2415.83, "end": 2416.01, "word": " في", "probability": 0.78125}, {"start": 2416.01, "end": 2416.33, "word": " عدد", "probability": 0.9676106770833334}, {"start": 2416.33, "end": 2416.71, "word": " أقل", "probability": 0.8966471354166666}, {"start": 2416.71, "end": 2416.87, "word": " من", "probability": 0.99072265625}, {"start": 2416.87, "end": 2417.01, "word": " ال", "probability": 0.92578125}, {"start": 2417.01, "end": 2417.15, "word": " N", "probability": 0.9521484375}, {"start": 2417.15, "end": 2417.65, "word": " هيعطيك", "probability": 0.882421875}, {"start": 2417.65, "end": 2418.05, "word": " أكبر", "probability": 0.9274088541666666}, {"start": 2418.05, "end": 2418.21, "word": " من", "probability": 0.99365234375}, {"start": 2418.21, "end": 2418.55, "word": " اتنين", "probability": 0.80218505859375}, {"start": 2418.55, "end": 2418.81, "word": " N", "probability": 0.91357421875}, {"start": 2418.81, "end": 2419.69, "word": " فلازم", "probability": 0.9427490234375}, {"start": 2419.69, "end": 2419.83, "word": " ال", "probability": 0.97412109375}, {"start": 2419.83, "end": 2419.97, "word": " M", "probability": 0.9755859375}, {"start": 2419.97, "end": 2420.25, "word": " يكون", "probability": 0.986083984375}, {"start": 2420.25, "end": 2420.65, "word": " أكبر", "probability": 0.9326171875}, {"start": 2420.65, "end": 2420.81, "word": " من", "probability": 0.9951171875}, {"start": 2420.81, "end": 2420.93, "word": " ال", "probability": 0.9873046875}, {"start": 2420.93, "end": 2421.13, 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"word": " ال", "probability": 0.94091796875}, {"start": 2427.59, "end": 2427.89, "word": " A", "probability": 0.87060546875}, {"start": 2427.89, "end": 2428.79, "word": " to", "probability": 0.6826171875}, {"start": 2428.79, "end": 2428.99, "word": " M", "probability": 0.97265625}, {"start": 2428.99, "end": 2429.25, "word": " جوا", "probability": 0.80615234375}, {"start": 2429.25, "end": 2429.41, "word": " ال", "probability": 0.90380859375}, {"start": 2429.41, "end": 2429.59, "word": " A", "probability": 0.9775390625}, {"start": 2429.59, "end": 2430.33, "word": " بس", "probability": 0.97314453125}, {"start": 2430.33, "end": 2430.53, "word": " ال", "probability": 0.98876953125}, {"start": 2430.53, "end": 2430.77, "word": " A", "probability": 0.9755859375}, {"start": 2430.77, "end": 2430.95, "word": " to", "probability": 0.96630859375}, {"start": 2430.95, "end": 2431.33, "word": " N", "probability": 0.97021484375}, {"start": 2431.33, "end": 2432.21, "word": " بسوا", "probability": 0.5958658854166666}, {"start": 2432.21, "end": 2432.29, "word": " ال", "probability": 0.98583984375}, {"start": 2432.29, "end": 2432.77, "word": " identity", "probability": 0.81201171875}, {"start": 2432.77, "end": 2433.27, "word": " ينتمي", "probability": 0.9537353515625}, {"start": 2433.27, "end": 2433.43, "word": " لل", "probability": 0.76904296875}, {"start": 2433.43, "end": 2433.81, "word": " H", "probability": 0.94140625}, {"start": 2433.81, "end": 2434.83, "word": " فكيف", "probability": 0.9781901041666666}, {"start": 2434.83, "end": 2435.01, "word": " ال", "probability": 0.97412109375}, {"start": 2435.01, "end": 2435.21, "word": " M", "probability": 0.82763671875}, {"start": 2435.21, "end": 2436.07, "word": " أكبر", "probability": 0.9690755208333334}, {"start": 2436.07, "end": 2436.21, "word": " من", "probability": 0.9921875}, {"start": 2436.21, "end": 2436.35, "word": " ال", "probability": 0.953125}, {"start": 2436.35, "end": 2436.61, "word": " N", "probability": 0.80517578125}, {"start": 2436.61, "end": 2437.25, "word": " و", "probability": 0.8125}, {"start": 2437.25, "end": 2437.41, "word": " ال", "probability": 0.84619140625}, {"start": 2437.41, "end": 2437.75, "word": " N", "probability": 0.92236328125}, {"start": 2437.75, "end": 2438.27, "word": " هو", "probability": 0.96435546875}, {"start": 2438.27, "end": 2438.77, "word": " positive", "probability": 0.9306640625}, {"start": 2438.77, "end": 2439.17, "word": " power", "probability": 0.9306640625}, {"start": 2439.17, "end": 2439.35, "word": " لل", "probability": 0.74951171875}, {"start": 2439.35, "end": 2439.47, "word": " A", "probability": 0.98486328125}, {"start": 2439.47, "end": 2439.91, "word": " بيخلي", "probability": 0.94287109375}, {"start": 2439.91, "end": 2440.07, "word": " ال", "probability": 0.97412109375}, {"start": 2440.07, "end": 2440.27, "word": " A", "probability": 0.990234375}, {"start": 2440.27, "end": 2440.39, "word": " to", "probability": 0.9794921875}, {"start": 2440.39, "end": 2440.63, "word": " N", "probability": 0.953125}, {"start": 2440.63, "end": 2440.93, "word": " جوا", "probability": 0.950927734375}, {"start": 2440.93, "end": 2441.07, "word": " ال", "probability": 0.9765625}, {"start": 2441.07, "end": 2441.33, "word": " H", "probability": 0.990234375}, {"start": 2441.33, "end": 2441.83, "word": " فهذا", "probability": 0.9239908854166666}, {"start": 2441.83, "end": 2442.13, "word": " هيكون", "probability": 0.79833984375}, {"start": 2442.13, "end": 2442.71, "word": " التناقض", "probability": 0.9918212890625}], "temperature": 1.0}, {"id": 85, "seek": 244823, "start": 2446.23, "end": 2448.23, "text": "واضح؟ وبالتالي ساعة ال H is", "tokens": [2407, 46958, 5016, 22807, 46599, 6027, 2655, 6027, 1829, 8608, 995, 27884, 2423, 389, 307], "avg_logprob": -0.3005371056497097, "compression_ratio": 0.9019607843137255, "no_speech_prob": 0.0, "words": [{"start": 2446.23, "end": 2446.83, "word": "واضح؟", "probability": 0.84100341796875}, {"start": 2446.83, "end": 2447.29, "word": " وبالتالي", "probability": 0.92841796875}, {"start": 2447.29, "end": 2447.59, "word": " ساعة", "probability": 0.684326171875}, {"start": 2447.59, "end": 2447.73, "word": " ال", "probability": 0.95068359375}, {"start": 2447.73, "end": 2447.93, "word": " H", "probability": 0.496337890625}, {"start": 2447.93, "end": 2448.23, "word": " is", "probability": 0.5849609375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2452.30575, "duration_after_vad": 2263.613749999994}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..276cf3f8c2a7095f57be103173ccc7bbe8f4feb2
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/njB-DM5hiPY_raw.srt
@@ -0,0 +1,1480 @@
+1
+00:00:21,160 --> 00:00:23,740
+السلام عليكم بسم الله الرحمن الرحيم ان شاء الله
+
+2
+00:00:23,740 --> 00:00:27,320
+اليوم هناخد الجزء التالت من الوحدة الرابعة اللي
+
+3
+00:00:27,320 --> 00:00:31,860
+بتتكلم فيها عن ال cyclic groups اللي ذاكر أو كان
+
+4
+00:00:31,860 --> 00:00:36,540
+معانا في أول محاضرتين اتكلمنا عن شغلتين أساسيتين
+
+5
+00:00:36,540 --> 00:00:40,680
+الشغلة الأولى متعلقة بخصائص أو بعض الخصائص ل ال
+
+6
+00:00:40,680 --> 00:00:44,460
+cyclic subgroup بعدين أخدناها في المحاضرة الأولى
+
+7
+00:00:44,460 --> 00:00:47,700
+ضمن التعريف و الأمثلة المحاضرة التانية اللي
+
+8
+00:00:47,700 --> 00:00:52,590
+أخدناها اليوم الصبح اتكلمنا عنالنظرية تتعلق بخصائص
+
+9
+00:00:52,590 --> 00:00:58,930
+العنصر وما يولده مجموعات العناصر داخل ال cyclic
+
+10
+00:00:58,930 --> 00:01:04,230
+group اليوم هنتكلم عن نظرية الأساسية لل cyclic
+
+11
+00:01:04,230 --> 00:01:06,870
+subgroup ال fundamental theorem of cyclic subgroup
+
+12
+00:01:06,870 --> 00:01:12,710
+اللي من خلالها بتناول التركيبات الداخلية داخل ال
+
+13
+00:01:12,710 --> 00:01:17,110
+cyclic group المتعلقة بال subgroup نفسها و ليست
+
+14
+00:01:17,110 --> 00:01:21,310
+بالعناصرنص النظرية اللي هي نظرية اربعة تلاتة هيقول
+
+15
+00:01:21,310 --> 00:01:30,030
+التالي theorem fundamental
+
+16
+00:01:30,030 --> 00:01:34,070
+theorem
+
+17
+00:01:34,070 --> 00:01:39,630
+of cyclic groups
+
+18
+00:01:44,620 --> 00:01:47,900
+هنجسم النص النظرية الموجودة في الكتاب ل 3 أجزاء
+
+19
+00:01:47,900 --> 00:01:54,500
+الجزء الأول every subgroup
+
+20
+00:01:54,500 --> 00:01:58,360
+of
+
+21
+00:01:58,360 --> 00:02:03,500
+a cyclic group
+
+22
+00:02:03,500 --> 00:02:10,310
+is cyclicيعني اي subgroup انا باخدها جوا الـ
+
+23
+00:02:10,310 --> 00:02:17,210
+cyclic group هتكون ايضا cyclic الجزء التاني if j
+
+24
+00:02:17,210 --> 00:02:28,930
+generated by some a and order ال a بيساوي n with h
+
+25
+00:02:28,930 --> 00:02:37,210
+subgroup من ال j then order ال h يقسم ال nمش بس ال
+
+26
+00:02:37,210 --> 00:02:41,270
+subgroup هذي cyclic لأ و ال order لها بيقسم ال
+
+27
+00:02:41,270 --> 00:02:45,170
+order لل group لو كنت أنا بتكلم في ال finite case
+
+28
+00:02:45,170 --> 00:02:51,730
+تلاتة اتجاه التاني للجزء اتنين احنا قولنا عن اي
+
+29
+00:02:51,730 --> 00:02:57,150
+subgroup ال order لها بيقسم ال order ل group هجيت
+
+30
+00:02:57,150 --> 00:03:04,070
+السؤال هل كل قاسم ل ال order بلاقي subgroup ال
+
+31
+00:03:04,070 --> 00:03:09,240
+order لهابساوي هذا القاسم هذا كلام بيكون صحيح فقط
+
+32
+00:03:09,240 --> 00:03:19,200
+لو بتكلم عن cyclic الجواب if K يقسم ال N then is
+
+33
+00:03:19,200 --> 00:03:24,780
+any positive divisor
+
+34
+00:03:24,780 --> 00:03:33,500
+of N then there
+
+35
+00:03:36,920 --> 00:03:51,020
+exist a unique subgroup of
+
+36
+00:03:51,020 --> 00:04:03,880
+generated by A namely تحديدًا H بساوي generated by
+
+37
+00:04:03,880 --> 00:04:13,860
+A to N على Kand ال order ل h بيساوي كيه بالعربي
+
+38
+00:04:13,860 --> 00:04:23,240
+انه لأي قاسم لل order ل ال finite cyclic group أنا
+
+39
+00:04:23,240 --> 00:04:28,380
+بقدر ألاقي cyclic sub group و ال order لهذه ال
+
+40
+00:04:28,380 --> 00:04:33,120
+cyclic sub group بيساوي القاسم اللي عندي نيجي
+
+41
+00:04:37,950 --> 00:04:46,630
+فضّال طيب بالعربي الجزء الأول كل مجموعة جزئية او
+
+42
+00:04:46,630 --> 00:04:52,810
+كل زمرة جزئية من زمرة دوارة هي زمرة دوارة يعني ال
+
+43
+00:04:52,810 --> 00:04:59,230
+cyclic group عبارة عن زمرة دوارة الجزء التاني لو
+
+44
+00:04:59,230 --> 00:05:03,350
+كان الزمرة اللي انت بتشتغل عليها دوارة
+
+45
+00:05:05,570 --> 00:05:11,550
+order لها finite يعني زمرة دوارة محدودة فال sub
+
+46
+00:05:11,550 --> 00:05:15,850
+group الزمرة الجزئية منها ال order لهذه الزمرة
+
+47
+00:05:15,850 --> 00:05:22,890
+الجزئية بتقسم ال order للزمرة الأساسية جزء تالت
+
+48
+00:05:22,890 --> 00:05:33,490
+لأي قاسم موجب ل order الزمرة الدوارةبقدر ألاقي
+
+49
+00:05:33,490 --> 00:05:40,270
+زمرة جزئية group أو subgroup ال order لهذه الزمرة
+
+50
+00:05:40,270 --> 00:05:45,370
+الجزئية بساوي هذا القاسم مش بس هيك هذه الزمرة
+
+51
+00:05:45,370 --> 00:05:51,230
+تحديدا هي ال generated by a to n على k نجي نثبت
+
+52
+00:05:51,230 --> 00:05:56,190
+نثبت الجزء الأول every
+
+53
+00:05:56,190 --> 00:06:01,950
+subgroup of a cyclic group is cyclic let jbe
+
+54
+00:06:01,950 --> 00:06:07,950
+generated by a and h subgroup من الجيل ايش اللي
+
+55
+00:06:07,950 --> 00:06:15,330
+لازم اثبته؟ بدي اثبت انا ان الـ H Cyclic Subgroup
+
+56
+00:06:15,330 --> 00:06:18,930
+عشان تكون Cyclic Subgroup ايش لازم انا اجيلها؟
+
+57
+00:06:18,930 --> 00:06:25,990
+generator في الحالة الأولية if الـ H في أنصر واحد
+
+58
+00:06:25,990 --> 00:06:32,480
+وهو ال identity فالـ H generated by مين؟by ال
+
+59
+00:06:32,480 --> 00:06:37,640
+identity فهي Cyclic لو ال H مافيش فيه غير ال
+
+60
+00:06:37,640 --> 00:06:45,420
+identity معناته ال H generated by ال identity if H
+
+61
+00:06:45,420 --> 00:06:56,960
+لا يساوي ال identity هذا معناته there is at
+
+62
+00:06:56,960 --> 00:07:01,020
+least one element
+
+63
+00:07:02,430 --> 00:07:12,550
+in H with one element X يعني terminal H and X لا
+
+64
+00:07:12,550 --> 00:07:21,010
+يساوي ال identity طيب now فضل ماشي
+
+65
+00:07:21,010 --> 00:07:24,970
+بس لو كانت هي ال identity و بس فهي psychic اگه لو
+
+66
+00:07:24,970 --> 00:07:29,870
+فيها حاجة غير ال identity طب احنا بنثبت هذا الكلام
+
+67
+00:07:31,190 --> 00:07:37,250
+بتقدر تثبت اللي هي هيك بط بط
+
+68
+00:07:37,250 --> 00:07:41,250
+X ينتمي لل H اللي هي ال sub group من الجلية
+
+69
+00:07:41,250 --> 00:07:46,870
+generated by A يكبر X عبارة عن ايش power لل A
+
+70
+00:07:46,870 --> 00:07:52,410
+فليكن A أُس اختار A لأكيد هنحتاج هنستعملها بعد
+
+71
+00:07:52,410 --> 00:07:56,430
+هيكد A أُس R وال R ينتمي لل Z
+
+72
+00:08:00,950 --> 00:08:07,530
+طيب او a of t for
+
+73
+00:08:07,530 --> 00:08:12,810
+t عندك two cases there
+
+74
+00:08:12,810 --> 00:08:27,370
+is two cases for t ال case الاولانية ان t اكبر او
+
+75
+00:08:27,370 --> 00:08:34,940
+يساوي الواحدالـ T مش صفر فيا إما من الواحد و فوق
+
+76
+00:08:34,940 --> 00:08:44,460
+يا إما إيش case 2 T أقل من الصفر في ال case التاني
+
+77
+00:08:44,460 --> 00:08:49,840
+in the second case
+
+78
+00:08:49,840 --> 00:08:55,760
+سالب
+
+79
+00:08:55,760 --> 00:08:55,980
+T
+
+80
+00:08:58,940 --> 00:09:09,780
+أكبر من الصفر Now X inverse بدي يساوي X T أو A to
+
+81
+00:09:09,780 --> 00:09:16,980
+T inverse اللي هي A أو سالب T ينتمي لل H with سالب
+
+82
+00:09:16,980 --> 00:09:23,780
+T أكبر من الصفر طبعا ال case الأولاني و ال case
+
+83
+00:09:23,780 --> 00:09:32,320
+التاني بيعطون الحقيقة التالية Case oneand to give
+
+84
+00:09:32,320 --> 00:09:46,060
+us that there is at least one element in H with
+
+85
+00:09:46,060 --> 00:09:57,240
+positive which is a positive power
+
+86
+00:09:59,630 --> 00:10:08,290
+of A يعني دائما بأضمن وجود عنصر جوه ال H ال or أو
+
+87
+00:10:08,290 --> 00:10:14,310
+ال power له إيش positive بأضمن دائما وجود عنصر جوه
+
+88
+00:10:14,310 --> 00:10:20,510
+ال H و ال power له أو العنصر هذا عبارة عن power
+
+89
+00:10:20,510 --> 00:10:23,830
+موجب لمين لل إيه
+
+90
+00:10:29,010 --> 00:10:33,430
+ناخد M والله ايش؟
+
+91
+00:10:33,430 --> 00:10:48,550
+Let M Be The Smallest Positive Power Of A In H
+
+92
+00:10:48,550 --> 00:10:56,430
+ناخد الـ M هو أصغر أُس موجب للـ A في الـ H That is
+
+93
+00:11:00,110 --> 00:11:09,990
+A to M ينتمي للـH and if A to T ينتمي للـH with T
+
+94
+00:11:09,990 --> 00:11:19,550
+أكبر من الصفر then M أقل أو يساوي T الـM
+
+95
+00:11:19,550 --> 00:11:32,960
+هو أصغر power موجب للـA جوا مينDual H claim ادعاء
+
+96
+00:11:32,960 --> 00:11:41,560
+الـ H generated by A to M طبعا انا هي كنت بكون
+
+97
+00:11:41,560 --> 00:11:46,680
+خلصت خطوتين خطوة الاولى اثبت ان الـ H is cyclic
+
+98
+00:11:46,680 --> 00:11:54,560
+خطوة التانية جبت ال generator الـ H اتحولت شغل ليه
+
+99
+00:11:54,560 --> 00:12:03,070
+يا شانا؟لـ set theory نظرية مجموعة since a to m
+
+100
+00:12:03,070 --> 00:12:08,850
+ينتمي لل H معناته generated by a to m sub group من
+
+101
+00:12:08,850 --> 00:12:21,810
+ال H وعطيها إيش؟ واحد let x ينتمي لل H since
+
+102
+00:12:23,760 --> 00:12:30,180
+H subgroup من generated by A معناته الـ X هتساوي A
+
+103
+00:12:30,180 --> 00:12:40,460
+to R for some R ينتمي لمن؟ لـ Z مدام الـ H subset
+
+104
+00:12:40,460 --> 00:12:47,260
+من generated by A فكل عناصر الـ H عبارة عن إيش؟
+
+105
+00:12:47,260 --> 00:12:53,940
+عبارة عن إيش Powers للـ Aفليكن A to R هجيت بال
+
+106
+00:12:53,940 --> 00:13:05,260
+division algorithm ال
+
+107
+00:13:05,260 --> 00:13:11,000
+R أو بلش ال R خدها لإن ال R هستعملها هجيت ك
+
+108
+00:13:11,000 --> 00:13:14,640
+remainder استعمل غمز تاني فليكن K
+
+109
+00:13:18,460 --> 00:13:25,040
+الـ K لو أنا بدي أجسمها على ال M عبارة عن QM زاد
+
+110
+00:13:25,040 --> 00:13:33,100
+ال R والـ R ما بين ال M والـ
+
+111
+00:13:33,100 --> 00:13:36,480
+0 طيب
+
+112
+00:13:36,480 --> 00:13:43,160
+Now A
+
+113
+00:13:50,330 --> 00:14:00,310
+الـ a to r عبارة عن a to k minus qm اللي عبارة عن
+
+114
+00:14:00,310 --> 00:14:10,090
+a to k في a minus qm اللي عبارة عن x في a to m
+
+115
+00:14:10,090 --> 00:14:21,870
+أسالب q و هذا العنصر وين موجود؟ موجود وين؟في ال H
+
+116
+00:14:21,870 --> 00:14:28,250
+ليش X في ال H A to M في ال H فأي power لل A to M
+
+117
+00:14:28,250 --> 00:14:35,750
+هيكون وين جوا ال H طيب هنخل الجزء هذا مكتوب و نكمل
+
+118
+00:14:35,750 --> 00:14:40,150
+اثباتا لسه
+
+119
+00:14:40,150 --> 00:14:45,750
+اثبات الجزء الأول هذا هذا
+
+120
+00:14:45,750 --> 00:14:58,440
+معناته ان A to Rينتمي لمين؟ لـ Latch حاجة if R لا
+
+121
+00:14:58,440 --> 00:15:11,020
+يساوي Zero then R is a positive power of A such
+
+122
+00:15:11,020 --> 00:15:16,720
+that A to R وين؟ في Latch
+
+123
+00:15:20,580 --> 00:15:26,900
+لو ال R مش صفر معناه يصار ال R موجب هو أُس موجب لل
+
+124
+00:15:26,900 --> 00:15:31,960
+A بيخلي ال A تقار وين؟ في ال H نرجع لل M ال M هو
+
+125
+00:15:31,960 --> 00:15:37,420
+مين؟ هو أصغر positive power لل A في ال H هذا
+
+126
+00:15:37,420 --> 00:15:44,440
+معناته أنه لازم ال M يكون أقل أو يساوي R but ال R
+
+127
+00:15:44,440 --> 00:15:49,000
+أقل من ال M نفس ال contradiction الليكان في
+
+128
+00:15:49,000 --> 00:15:52,500
+المحاضرة السابقة هذا مع هذا عبارة عن ايش
+
+129
+00:15:52,500 --> 00:16:01,180
+contradiction معناته ايش الخطأ الفاضل انا فرضه ان
+
+130
+00:16:01,180 --> 00:16:14,320
+ر لا يساوي زيرو so ر بيساوي زيرو and نرجع
+
+131
+00:16:14,320 --> 00:16:17,820
+لل division algorithm ر بيساوي زيرو كياش بيساوي
+
+132
+00:16:18,850 --> 00:16:35,610
+اكيو ام اكيو
+
+133
+00:16:35,610 --> 00:16:40,990
+ام اكيو
+
+134
+00:16:40,990 --> 00:16:41,250
+ام اكيو ام اكيو ام اكيو ام اكيو ام اكيو ام اكيو ام
+
+135
+00:16:41,250 --> 00:16:45,660
+اكيو امby a to m وين في ال H و انا اصلا هنا ماخد
+
+136
+00:16:45,660 --> 00:16:50,440
+ال X من ال H صار ال X من generated لأ انا
+
+137
+00:16:50,440 --> 00:16:55,020
+generated by a to m شباب انا
+
+138
+00:16:55,020 --> 00:16:59,900
+ماخد ال X من ال H صار في generated by a to m
+
+139
+00:16:59,900 --> 00:17:05,800
+معناته ال H sub group من generated by a to m و
+
+140
+00:17:05,800 --> 00:17:12,210
+اعطيها 2 1 و 2هتخليك تقول ان ال H بيساوي generated
+
+141
+00:17:12,210 --> 00:17:22,710
+by a تقام و ال H اشمالها ال Cyclic وهو المطلوب وهي
+
+142
+00:17:22,710 --> 00:17:29,950
+كده أثبتنيش الجزء الأول انه أخدت subgroup من ال
+
+143
+00:17:29,950 --> 00:17:33,130
+Cyclic group اللي باشتغل عليها و طلعت ال subgroup
+
+144
+00:17:33,130 --> 00:17:41,090
+هديش Cyclic مش Cyclic بس generated by أصغرأو by a
+
+145
+00:17:41,090 --> 00:17:47,090
+أصغر positive power داخل الله تفضل بس انا هربطه
+
+146
+00:17:47,090 --> 00:17:50,170
+معاك في بعض انا أعمل هذا عشان الدنيا هو بالظبط ال
+
+147
+00:17:50,170 --> 00:17:54,610
+claim لأ انكسوا واحد و اتنين ان انت صار بتاعة أكبر
+
+148
+00:17:54,610 --> 00:17:59,510
+من صفرها داخلها دع القلم تعالي أقولك الخطوات اللي
+
+149
+00:17:59,510 --> 00:18:04,500
+اتبعت بعتك التاليفي ال case الأولاني تبع أن ال H
+
+150
+00:18:04,500 --> 00:18:08,220
+بيساوي ال identity هذا صف في نعجن بينهم trivial
+
+151
+00:18:08,220 --> 00:18:12,460
+فاشتغلنا على ال H اللي في عنصر غير ال identity
+
+152
+00:18:12,460 --> 00:18:18,040
+هيجيت ال case الأول والتاني هنا بدي أخلص منه باب
+
+153
+00:18:18,040 --> 00:18:25,180
+عرا أنه دائما بقدر ألاقي positive power لل A جوا
+
+154
+00:18:25,180 --> 00:18:29,570
+ال Hعشري ال case الأول والتاني اشتغلت انا على ال A
+
+155
+00:18:29,570 --> 00:18:34,030
+to T ال A to T ال T قدامي خيارين يا موجة باور تاني
+
+156
+00:18:34,030 --> 00:18:38,150
+اللي بدي اخلصه فيه positive power لل A جوا ال H يا
+
+157
+00:18:38,150 --> 00:18:42,910
+ال T سالبة بس انا بشغل جوا sub group ال inverse
+
+158
+00:18:42,910 --> 00:18:48,970
+تبع العنصر اللي انا بدأت منه اللي هو X موجود طبعا
+
+159
+00:18:48,970 --> 00:18:53,750
+ال X هو A to T ف X inverse A to سالب T ال T سالبة
+
+160
+00:18:53,750 --> 00:18:58,690
+فسالب Tموجبة يكبى في ال case التاني برضه اجدرت
+
+161
+00:18:58,690 --> 00:19:02,370
+الاجي عنصر ال positive او ال power له positive
+
+162
+00:19:02,370 --> 00:19:08,290
+يكبى دائما بضمن انه يوجد positive power جوا مين؟
+
+163
+00:19:08,290 --> 00:19:12,010
+positive power لل ايه جوا؟ ال H مدام دائما في
+
+164
+00:19:12,010 --> 00:19:16,910
+positive هاخد اصغر واحد طبعا ماتنساش انه انا بشتغل
+
+165
+00:19:16,910 --> 00:19:21,800
+في ال Z وال Zلما انا بتشتغل على ال positive
+
+166
+00:19:21,800 --> 00:19:25,980
+integer فانتقلت من ال z ل ال n في ال natural
+
+167
+00:19:25,980 --> 00:19:33,240
+number اي مجموعة جزئية من ال natural number غير
+
+168
+00:19:33,240 --> 00:19:39,780
+خالية الها ايش؟ الها minimum او minimal at least
+
+169
+00:19:39,780 --> 00:19:43,280
+اللي هو ال least one او least number فانا أخدت ال
+
+170
+00:19:43,280 --> 00:19:46,340
+least او ال smallest positive power لل H والH
+
+171
+00:19:46,340 --> 00:19:52,140
+فليكن هو Mانسى كل القصص الأولى اللى فى الآخر اللى
+
+172
+00:19:52,140 --> 00:19:56,160
+أخدناها توى و بنمسك فى الـA تقامها ده و نثبت أنه
+
+173
+00:19:56,160 --> 00:20:01,620
+بولد الـH طب ليش جبنى صغير واحد يعنى؟ ليش جبنى
+
+174
+00:20:01,620 --> 00:20:05,100
+أصغر واحد؟ طالع معايا يعني هي ممكن هذه الفلسفة
+
+175
+00:20:05,100 --> 00:20:10,660
+موجودة فى كتير من الشغلات المتعلقة فى الجبر أنا
+
+176
+00:20:10,660 --> 00:20:15,780
+لما بدى أدور على عنصر هو يولد الباقي فليه بصغير
+
+177
+00:20:15,780 --> 00:20:21,170
+واحد؟ الكبير مش هيولد الصغيرلأن الكبير لما تعطيه
+
+178
+00:20:21,170 --> 00:20:25,490
+قوة ومطلوب انه يرجع لبور صغير بدك تشتغل على ان
+
+179
+00:20:25,490 --> 00:20:29,970
+القوة بتكبر في لحظة معينة و بتختصر منها و بتنزل
+
+180
+00:20:29,970 --> 00:20:34,530
+فمن الأسهل ان انا باخد أصغر واحد و أصنع الباقي من
+
+181
+00:20:34,530 --> 00:20:43,750
+خلاله واضح؟ واضح
+
+182
+00:20:43,750 --> 00:20:50,740
+الجزء هذا؟ واضح الجزء الأول يا شباب؟نيجي نثبت
+
+183
+00:20:50,740 --> 00:20:58,460
+الجزء التاني ذاكين
+
+184
+00:20:58,460 --> 00:21:08,920
+ايش الجزء التاني؟ طب يحكوه واحد جاره يفسر الجزء
+
+185
+00:21:08,920 --> 00:21:12,700
+التاني من الاثبات احنا اثبتنا فقط مين ال part
+
+186
+00:21:12,700 --> 00:21:13,360
+الأولاني
+
+187
+00:21:20,680 --> 00:21:27,840
+طيب تعالى نتكلم عنه الجزء التانى let J generated
+
+188
+00:21:27,840 --> 00:21:35,920
+by ال A و ال order لل A بدى يساوي N given او take
+
+189
+00:21:35,920 --> 00:21:50,530
+H subgroup من مين؟ من الجيه we must or sinceJ is
+
+190
+00:21:50,530 --> 00:21:58,370
+Cyclic إيش مقدر أقول أنا عن ال H H is Cyclic
+
+191
+00:21:58,370 --> 00:22:06,030
+Cyclic
+
+192
+00:22:06,030 --> 00:22:12,990
+يجوبش يعني هذا
+
+193
+00:22:12,990 --> 00:22:20,930
+معناته ال H generated by some A to Mالـ H
+
+194
+00:22:20,930 --> 00:22:28,050
+generated by some .. طب ال order للـ H هو ال order
+
+195
+00:22:28,050 --> 00:22:33,730
+generated by a to m اللي هو عبارة عن مين؟ ال order
+
+196
+00:22:33,730 --> 00:22:39,410
+ل a to m اللي هو عبارة عن إيش؟ n على ال agreed
+
+197
+00:22:39,410 --> 00:22:45,410
+common divisor ل m و n agreed common divisor ل m و
+
+198
+00:22:45,410 --> 00:22:53,580
+n عبارة عن إيش؟بغض النظر إيش بيساوي إذا أردر ال H
+
+199
+00:22:53,580 --> 00:23:00,500
+بدي يساوي N على الجريس common divisor ل M و N هذا
+
+200
+00:23:00,500 --> 00:23:08,420
+رقم إيش ماله؟ إيش ماله؟ بيقسم ال N أنا مطلوب من
+
+201
+00:23:08,420 --> 00:23:12,200
+يثبت إنما أردر ال H بيقسم ال N و هذا N على عدد
+
+202
+00:23:12,200 --> 00:23:19,820
+صحيح و هو عدد صحيح إذا أردر ال Hبيجسمين الان خلصوا
+
+203
+00:23:19,820 --> 00:23:24,100
+الجزء التاني جزء
+
+204
+00:23:24,100 --> 00:23:31,900
+التالت في الجزء التالت هجيه اي subgroup ال order
+
+205
+00:23:31,900 --> 00:23:35,580
+لبيقسم ال order ل ال group نفسه في حالة ال finite
+
+206
+00:23:35,580 --> 00:23:43,340
+case طبعا هجيه كل قاسم بيجيله subgroup ولا لا طلع
+
+207
+00:23:43,340 --> 00:23:51,370
+على الجزء التالت letك يقسم الان given او let ال
+
+208
+00:23:51,370 --> 00:23:57,430
+جيه بده تساوي generated by a وال order لل ايه بده
+
+209
+00:23:57,430 --> 00:24:01,430
+يساوي يعنى ايش المطلوب هنا شباب مطلوب بنلاقي
+
+210
+00:24:01,430 --> 00:24:05,490
+subgroup ال order اللي لها كيه subgroup من وين من
+
+211
+00:24:05,490 --> 00:24:10,250
+ال جيه بس هو أنا ريحني في النص ايش قال ليه قاللي
+
+212
+00:24:10,250 --> 00:24:16,220
+ال subgroup المطلوبة مين هيgenerated by a to n على
+
+213
+00:24:16,220 --> 00:24:21,560
+k انا همسك هذه بحسب التلات شغلات انها subgroup
+
+214
+00:24:21,560 --> 00:24:25,380
+سهلة انه generated by any element subgroup شغلت
+
+215
+00:24:25,380 --> 00:24:28,440
+تاني ال order الها بيساوي k وهذه هتكون برضه شغلة
+
+216
+00:24:28,440 --> 00:24:36,460
+سهلة شغلت تالتة ايش انها unique مافيش غيرها انها
+
+217
+00:24:36,460 --> 00:24:38,780
+unique او مافيش غيرها
+
+218
+00:24:41,860 --> 00:24:53,340
+we first show that order بدت
+
+219
+00:24:53,340 --> 00:25:03,160
+ساوة كام هذه سهلة which
+
+220
+00:25:03,160 --> 00:25:06,420
+is
+
+221
+00:25:06,420 --> 00:25:14,740
+trivialالـ order generated by n على k بدي أسوأ ال
+
+222
+00:25:14,740 --> 00:25:22,840
+order ل a أقصر n على k وهي عبارة عن n على لجريس
+
+223
+00:25:22,840 --> 00:25:28,640
+common divisor ل n و n على k شباب لجريس common
+
+224
+00:25:28,640 --> 00:25:32,160
+divisor ل n و ل n على k ايش بيساوي او ل n و n على
+
+225
+00:25:32,160 --> 00:25:37,880
+k بدي أسوأ n على n
+
+226
+00:25:37,880 --> 00:25:45,360
+على kاللي عبارة عن كيكبار ال order لgenerated by a
+
+227
+00:25:45,360 --> 00:25:49,080
+أُس n على كيكبار كيكبار كيكبار كيكبار كيكبار
+
+228
+00:25:49,080 --> 00:25:51,460
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+229
+00:25:51,460 --> 00:25:55,080
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+230
+00:25:55,080 --> 00:25:55,080
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+231
+00:25:55,080 --> 00:25:55,080
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+232
+00:25:55,080 --> 00:26:07,260
+كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار كيكبار
+
+233
+00:26:17,300 --> 00:26:21,500
+كيف اثبت الـ Uniqueness يا شباب؟ بفترض ان هناك
+
+234
+00:26:21,500 --> 00:26:28,920
+واحدة تانية وبثبت المساواة let A مثلا اختار الهؤوس
+
+235
+00:26:28,920 --> 00:26:35,240
+خليني اتماشى مع الكتاب A to M subgroup
+
+236
+00:26:35,240 --> 00:26:41,000
+من الـ J و ال order that generated by A to M بدي
+
+237
+00:26:41,000 --> 00:26:42,500
+ساوي ايش؟ فضل
+
+238
+00:26:48,140 --> 00:26:56,780
+a unique subgroup of generated by a namely طيب
+
+239
+00:26:56,780 --> 00:27:05,320
+كيف بدا أثبت؟ كيف بدا أثبت أن هدوله زي بعض؟ أنا
+
+240
+00:27:05,320 --> 00:27:09,840
+شابة بالدفتر موجود قدامي بس مش عارف أجرى مين يطلع
+
+241
+00:27:09,840 --> 00:27:13,260
+يفكر معايا؟
+
+242
+00:27:13,260 --> 00:27:16,520
+يعني ماشي بيبنيك أشوش real sound
+
+243
+00:27:25,370 --> 00:27:31,710
+أنا مش كل مرة هثبت لحالي أنا يا شباب دي أثبت أنه
+
+244
+00:27:31,710 --> 00:27:38,630
+هذه هي نفسها هذه يعني generated by a to m و
+
+245
+00:27:38,630 --> 00:27:44,490
+generated by a to n على k زي بعض
+
+246
+00:27:48,920 --> 00:27:56,580
+استفيد من ان ال M بتحقق خاصيتها دي with M is the
+
+247
+00:27:56,580 --> 00:28:07,700
+smallest positive power of
+
+248
+00:28:07,700 --> 00:28:16,810
+A in generated by A to M هاي كمان مساعدةال M عشان
+
+249
+00:28:16,810 --> 00:28:21,230
+ما يجردش يلاقي Mات كتيرة هو أصغر positive power لل
+
+250
+00:28:21,230 --> 00:28:24,750
+A دي هو ال generated by A تقريبا هاجت على .. هذا
+
+251
+00:28:24,750 --> 00:28:29,430
+صار العنصر بالنسبة لهدي unique وهذا العنصر بالنسبة
+
+252
+00:28:29,430 --> 00:28:33,750
+لهدي ما هو ال N على K unique مافيش منه اتنين فلو
+
+253
+00:28:33,750 --> 00:28:38,650
+أنا اثبتت انه A على N A أُس N على K هو نفسه A أُس
+
+254
+00:28:38,650 --> 00:28:44,990
+M بكون خلصت ماكنتش مقدرت بتهدي كلاملو كان ال M و
+
+255
+00:28:44,990 --> 00:28:51,010
+ال N على K شمالهم متساوين يكبر انت قبطلي ان N على
+
+256
+00:28:51,010 --> 00:28:56,690
+K بيساوي M اه
+
+257
+00:28:56,690 --> 00:29:01,250
+طيب
+
+258
+00:29:01,250 --> 00:29:07,430
+مساعدة تانية هذه
+
+259
+00:29:07,430 --> 00:29:14,000
+ال order إلها Kال K بيقسم ال N حطها ع جانب ال
+
+260
+00:29:14,000 --> 00:29:18,280
+order اللي generated by A to M ايش بيساوي ال order
+
+261
+00:29:18,280 --> 00:29:25,280
+ل A to M ايش ال order ل A to M N على الجريس common
+
+262
+00:29:25,280 --> 00:29:33,200
+divisor لمين لل M و لل N اللي هو ايش بيساوي فضل
+
+263
+00:29:33,200 --> 00:29:38,220
+مهمش ال M بتساوي على كلمة نفسك طيب يبقى ال M
+
+264
+00:29:38,220 --> 00:29:39,160
+هتساوي ك M
+
+265
+00:29:42,120 --> 00:29:48,260
+هذا المقوم اثباته طيب
+
+266
+00:29:48,260 --> 00:29:53,700
+ال M رتبة هذه طيب
+
+267
+00:29:53,700 --> 00:29:57,900
+رتبة
+
+268
+00:29:57,900 --> 00:29:58,740
+الأنصة
+
+269
+00:30:01,460 --> 00:30:05,480
+رتبة العنصر بتقسم .. رتبة العنصر بتقسم رتبة العنصر
+
+270
+00:30:05,480 --> 00:30:10,520
+طيب طيب طيب طب ال .. ال M هي رتبة العنصر شوية بس
+
+271
+00:30:10,520 --> 00:30:18,400
+ال M رتبة العنصر ولا power العنصر فارج power power
+
+272
+00:30:18,400 --> 00:30:23,700
+مش رتبة الرتبة هو عبارة عن N على الجيزكم و divisor
+
+273
+00:30:23,700 --> 00:30:25,720
+ل N و M
+
+274
+00:30:36,130 --> 00:30:40,950
+فكه عشان .. طيب أعطيك مساعدة أثبت أن الأم بتجسم
+
+275
+00:30:40,950 --> 00:30:47,910
+الأن أه
+
+276
+00:30:47,910 --> 00:30:57,190
+.. فكه
+
+277
+00:30:57,190 --> 00:31:00,470
+أنا مش عارف أفجر من الدفتر
+
+278
+00:31:04,480 --> 00:31:16,560
+ه يا شباب هيعطيك كل المساعدات الممكنة ال
+
+279
+00:31:16,560 --> 00:31:20,440
+order
+
+280
+00:31:20,440 --> 00:31:23,040
+ل ال a و ال m هي عبارة عن n على ال a's common
+
+281
+00:31:23,040 --> 00:31:26,840
+divisor ل m و n انت لو اثبتت ان ال m بتجسم ال m
+
+282
+00:31:26,840 --> 00:31:31,050
+خلص اثبات بالمساعدات اللي اعطيتك إياهاالـ K بيسوي
+
+283
+00:31:31,050 --> 00:31:37,010
+order generated by A to M الوبد يساوي ال N على
+
+284
+00:31:37,010 --> 00:31:40,870
+الجيزكم و ال divisor ل M و N لو أثبتت أن ال M
+
+285
+00:31:40,870 --> 00:31:47,390
+بيقسم ال N خلصت الأثبات كله وجف على إيش أن ال M
+
+286
+00:31:47,390 --> 00:31:58,970
+بيقسم ال N آه
+
+287
+00:31:58,970 --> 00:31:59,290
+شباب
+
+288
+00:32:07,580 --> 00:32:15,140
+الان بتقسم الشوة الان
+
+289
+00:32:15,140 --> 00:32:18,880
+بتقسم مى؟
+
+290
+00:32:18,880 --> 00:32:25,960
+كيف؟ طيب
+
+291
+00:32:25,960 --> 00:32:30,240
+طب احنا جولنا الكلام هذا و هذا الأخضر إيه اللي و
+
+292
+00:32:30,240 --> 00:32:34,360
+جديش كيف؟
+
+293
+00:32:34,360 --> 00:32:37,060
+كمل تك دالة
+
+294
+00:32:45,260 --> 00:32:50,820
+طيب طالع معايا هلجيت
+
+295
+00:32:50,820 --> 00:32:55,120
+K بدي ساوي ال order that generated by A to M اللي
+
+296
+00:32:55,120 --> 00:33:03,060
+هو ال order لمين ل A to M اش يعني يعني A to M أس K
+
+297
+00:33:03,060 --> 00:33:13,580
+اش بدي ساوي ال identity يعني A to MK بدي ساوي ال
+
+298
+00:33:13,580 --> 00:33:14,340
+identity طيب
+
+299
+00:33:17,540 --> 00:33:24,040
+هذا شو بيساوي؟ هذا بيساوي a to n اش يعني؟ ال n
+
+300
+00:33:24,040 --> 00:33:30,240
+تقسم ال .. ال n تقسم ال .. ال n تقسم ال .. ال n
+
+301
+00:33:30,240 --> 00:33:34,660
+على k بيساوي ال n مين جالك؟ ال n بيساوي ال n في k
+
+302
+00:33:34,660 --> 00:33:41,340
+طبعا يمكن ال mk أكبر من ال n يمكن
+
+303
+00:33:41,340 --> 00:33:49,290
+ال mk يكون أكبر من ال nال N بدا تكون تقسم ال MK
+
+304
+00:33:49,290 --> 00:33:54,870
+لأن هذا هيعطيني على جانب أن N بتقسم ال N minus ال
+
+305
+00:33:54,870 --> 00:34:00,890
+MK يجب أن N تقسم ال MK اه
+
+306
+00:34:00,890 --> 00:34:06,650
+تقسم ولا تساوي؟ تساوي لأنه عيب اذا تساوت المقادرة
+
+307
+00:34:06,650 --> 00:34:11,170
+ليش تقسم؟ ليش تتساوي؟ ممكن يكون أكبر فكروا
+
+308
+00:34:16,760 --> 00:34:24,660
+اه اجرح اجرح ماكتوب عندى ايوة
+
+309
+00:34:24,660 --> 00:34:28,420
+حاجة
+
+310
+00:34:28,420 --> 00:34:35,260
+ال K ايش بدى يساوي order ال A تقم حيدها اللى عبارة
+
+311
+00:34:35,260 --> 00:34:44,840
+عن N على الجريس common divisor لمن ل M و Nيعني كما
+
+312
+00:34:44,840 --> 00:34:50,920
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+313
+00:34:50,920 --> 00:34:56,880
+تسمح كما تسمح كما تسمح كما
+
+314
+00:34:56,880 --> 00:34:57,400
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+315
+00:34:57,400 --> 00:34:57,400
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+316
+00:34:57,400 --> 00:34:57,520
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+317
+00:34:57,520 --> 00:34:57,540
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+318
+00:34:57,540 --> 00:34:59,280
+تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح
+
+319
+00:34:59,280 --> 00:35:01,460
+كما تسمح كما تسمح كما تسمح كما تسمح كما تسمح كما
+
+320
+00:35:01,460 --> 00:35:13,520
+تسمح كما تسمح كما تسمح كما
+
+321
+00:35:14,990 --> 00:35:20,770
+شباب من عشر دقيق فى شغله انفترض ان انا اعطيتك كل
+
+322
+00:35:20,770 --> 00:35:27,030
+المساعدات اللى هى كتبت حتى كتبت مساعدات على اللوح
+
+323
+00:35:27,030 --> 00:35:33,830
+هذى كيف بتساوي اما كيف انه زوجه ازهر ازهر ازهر
+
+324
+00:35:33,830 --> 00:35:40,810
+ازهر ازهر
+
+325
+00:35:55,820 --> 00:36:02,960
+طيب فكروا طيب
+
+326
+00:36:02,960 --> 00:36:11,960
+هفكر انا طيب since شغل سهل ال H generated by ال A
+
+327
+00:36:11,960 --> 00:36:13,660
+term فضل
+
+328
+00:36:21,180 --> 00:36:24,320
+الان على كيب بيقسم الان و الان على كيب بيقسم الان
+
+329
+00:36:24,320 --> 00:36:31,740
+صحيح هذا
+
+330
+00:36:31,740 --> 00:36:36,680
+معناته ان ان على كيب تقسم مين الان دي مالك لازمة
+
+331
+00:36:36,680 --> 00:36:40,580
+الان على كيب تقسم مين الان اش يعني
+
+332
+00:36:43,400 --> 00:36:46,280
+الان علي كيف تقسم الام؟ مش حتى فادت الان بيقسم
+
+333
+00:36:46,280 --> 00:36:57,140
+الام كيه؟ الان بيقسم الام كيه؟ طيب بعد هيك؟ لأ أنا
+
+334
+00:36:57,140 --> 00:37:04,560
+مستنتجة منها سيبك من الخربشات هذه كلها خليني أتزم
+
+335
+00:37:04,560 --> 00:37:07,460
+بشغل الكتاب طلع معايا
+
+336
+00:37:10,720 --> 00:37:16,060
+let generated by ال a to m هو في النهاية مش هنعمل
+
+337
+00:37:16,060 --> 00:37:25,020
+هيك دي يعني لأ ضايق الوجه حجرة
+
+338
+00:37:25,020 --> 00:37:29,440
+ال h generated by ال a to m سبقوا من ال j ال order
+
+339
+00:37:29,440 --> 00:37:32,900
+ل a to m دي ساوة k with m is the smallest positive
+
+340
+00:37:32,900 --> 00:37:35,520
+power of a in او انا وصلت هنا
+
+341
+00:37:48,600 --> 00:37:53,740
+طيب هجت ال K بدي ساوي generated by A to M اللي هو
+
+342
+00:37:53,740 --> 00:37:59,580
+N على الجريس common divisor ل M على N هذا بدي ساوي
+
+343
+00:37:59,580 --> 00:38:06,300
+N على M تمام النتيجة ان M بدي تساوي N على K
+
+344
+00:38:06,880 --> 00:38:11,100
+وبالتالي generated by a to m يستوي generated by a
+
+345
+00:38:11,100 --> 00:38:23,460
+to n على k وهو المطلوب يعني h is .. اه صحيح صحيح
+
+346
+00:38:23,460 --> 00:38:31,360
+نهدر
+
+347
+00:38:31,360 --> 00:38:37,200
+يا عدنا نخربش فيها نص ساعة عشان نفهماللي هي هذه
+
+348
+00:38:37,200 --> 00:38:43,120
+انها هذه متساوية بناء على ان M هي ال smallest
+
+349
+00:38:43,120 --> 00:38:48,400
+positive power لل A في ال generated part معناه
+
+350
+00:38:48,400 --> 00:38:53,580
+حاجة هنا ال A to M دي سوى ال identity وال A to MK
+
+351
+00:38:53,580 --> 00:38:58,080
+دي سوى ال identityالمفروض في علاقة بين ال N و ال
+
+352
+00:38:58,080 --> 00:39:03,460
+MK هجيت ال N أصغر واحد المفروض ان ال N تقسم ال MK
+
+353
+00:39:03,460 --> 00:39:11,760
+هجيت بإمكاني بطريقة لو فرضت ان ال MK أكبر من ال N
+
+354
+00:39:11,760 --> 00:39:16,660
+يعني
+
+355
+00:39:16,660 --> 00:39:21,700
+هذه المفتاح على الأقل هذه بتكون ايش ال N تقسم ال
+
+356
+00:39:21,700 --> 00:39:28,170
+MKتمام؟ و ال M K أكبر لو كانت أكبر من ال N فهي على
+
+357
+00:39:28,170 --> 00:39:38,050
+ال M K أكبر أو سواش 2N هنا تنساش أن ال K تقسم فال
+
+358
+00:39:38,050 --> 00:39:43,110
+K هتكون عبارة عن حاجة أصغر من ال N معناته علشان
+
+359
+00:39:43,110 --> 00:39:46,790
+تكون ال K أصغر من ال N و لما أضربها في ال M يعطيني
+
+360
+00:39:46,790 --> 00:39:50,410
+عدد أكبر أو سوى 2N ال M بدأ تكون أكبر من ال N
+
+361
+00:39:53,920 --> 00:40:02,080
+هجيت ال K تقسم ال N فال K أقل من مين؟ من ال N هجيت
+
+362
+00:40:02,080 --> 00:40:07,060
+عشان يكون ال M K اللي هي أقل من M N وهذه بدأت تكون
+
+363
+00:40:07,060 --> 00:40:15,450
+أكبر أو يساوي 2 N المفروض أن ال Mهو ال M K هتضرب
+
+364
+00:40:15,450 --> 00:40:18,810
+ال M في عدد أقل من ال N هيعطيك أكبر من اتنين N
+
+365
+00:40:18,810 --> 00:40:23,950
+فلازم ال M يكون أكبر من ال N وهذا بيعطيك تناقض لأن
+
+366
+00:40:23,950 --> 00:40:29,250
+أصلا ال M أصغر positive power بيخلي ال A to M جوا
+
+367
+00:40:29,250 --> 00:40:34,830
+ال A بس ال A to N بسوا ال identity ينتمي لل H فكيف
+
+368
+00:40:34,830 --> 00:40:39,470
+ال M أكبر من ال N و ال N هو positive power لل A
+
+369
+00:40:39,470 --> 00:40:42,710
+بيخلي ال A to N جوا ال H فهذا هيكون التناقض
+
+370
+00:40:46,230 --> 00:40:48,230
+واضح؟ وبالتالي ساعة ال H is
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..91e2883120210836c3330279bd5af7609bfd99a1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/nvh2dOLwT_0.srt
@@ -0,0 +1,1825 @@
+1
+00:00:21,510 --> 00:00:25,030
+بسم الله الرحمن الرحيم انتهينا في المرة الماضية من
+
+2
+00:00:25,030 --> 00:00:29,070
+شبتر تسعة والآن بدنا نعمل discussion حول هذا
+
+3
+00:00:29,070 --> 00:00:35,390
+الشبتر بيقول إيش بيقول لو كان عندي ال cyclic group
+
+4
+00:00:35,390 --> 00:00:41,630
+G يبقى any factor group for this cyclic group is
+
+5
+00:00:41,630 --> 00:00:45,930
+cyclic يعني إيه؟ يعني لما نقول لو افترضنا G is a
+
+6
+00:00:45,930 --> 00:00:51,300
+cyclic group generated by A، وإفترضنا  مشان يكون عندي
+
+7
+00:00:51,300 --> 00:00:55,020
+factor group لازم يكون عندي normal subgroup رغم
+
+8
+00:00:55,020 --> 00:00:59,320
+أنه ما قالش كل اللي قالوا show that any factor
+
+9
+00:00:59,320 --> 00:01:03,020
+group of a cyclic group is cyclic بس هي كل الكلام
+
+10
+00:01:03,020 --> 00:01:07,120
+اللي قالوا يبقى معنى هذا الكلام أنه لو كانت G ال
+
+11
+00:01:07,120 --> 00:01:11,340
+cyclic group وكانت each normal subgroup معناته
+
+12
+00:01:11,340 --> 00:01:15,480
+بقدر أكون اللي هو ال factor group أو ال quotient
+
+13
+00:01:15,480 --> 00:01:19,530
+group اللي قدامنا هذا، هيبقى لو كان الـ G cyclic بدي
+
+14
+00:01:19,530 --> 00:01:24,550
+أثبت إنه هذا إيه Cyclic بمعنى آخر بدي أحاول أثبت
+
+15
+00:01:24,550 --> 00:01:28,470
+إنه هذه إلها generator إذا قررنا نثبت إنها
+
+16
+00:01:28,470 --> 00:01:31,570
+generator يبقى بصير هذه الـcyclic، وإذا كان يكون
+
+17
+00:01:31,570 --> 00:01:36,610
+وصلنا إيه للمطلوب اللي احنا بدنا يعني يبقى 
+
+18
+00:01:36,610 --> 00:01:45,390
+solution بدي أقوله افترض إن عندي element موجود
+
+19
+00:01:45,390 --> 00:01:52,010
+وليكن مثلًا اللي هو H والله سميّه اللي بدك إيه
+
+20
+00:01:52,010 --> 00:01:58,450
+سمّيه والله قبل ال BH بدي أقول إن أثبت ما يأتي
+
+21
+00:01:58,450 --> 00:02:08,300
+want to show that، to show that نحاول نبين أن الـ G
+
+22
+00:02:08,300 --> 00:02:14,400
+modulo H هي عبارة عن subgroup generated by any
+
+23
+00:02:14,400 --> 00:02:19,140
+element من مكان يكون الـ element هذا وليكن على
+
+24
+00:02:19,140 --> 00:02:26,900
+سبيل المثال AH كويس
+
+25
+00:02:28,400 --> 00:02:33,480
+مِشان هيك بدنا هذا تساوي لو قدرت أثبت أن هذه subset
+
+26
+00:02:33,480 --> 00:02:38,700
+من هذه، وهذه subset من هذه بيتم المطلوب تمام؟ الآن
+
+27
+00:02:38,700 --> 00:02:45,140
+السؤال هو هل الـAH هذه موجودة في الـG modulo H ولا
+
+28
+00:02:45,140 --> 00:02:51,860
+لأ؟ تمام يعني ال subgroup generated by AH بدها
+
+29
+00:02:51,860 --> 00:02:58,330
+تبقى subset من من subset من الـG modulo H مظبوط
+
+30
+00:02:58,330 --> 00:03:02,110
+هكذا ال element موجود في ال group يبقى ال sub
+
+31
+00:03:02,110 --> 00:03:07,390
+group المتكونة بهذا ال element بتبقى ال subset من
+
+32
+00:03:07,390 --> 00:03:13,550
+من ال group الأساسية ويعتبر إن هذه رقم واحد بدنا
+
+33
+00:03:13,550 --> 00:03:18,050
+نعمل العملية العكسية بدنا ناخد element هنا ونحاول
+
+34
+00:03:18,050 --> 00:03:26,060
+نثبت إنه موجود هنا، إذا لو روحت quote let الـ BH
+
+35
+00:03:26,060 --> 00:03:33,220
+موجودة في الـ G modulo H إذا قدرت أثبت إن الـ BH
+
+36
+00:03:33,220 --> 00:03:39,800
+موجودة هنا بيتم المطلوب طيب كويس الآن احنا عندنا B
+
+37
+00:03:39,800 --> 00:03:48,870
+موجودة في الـ G مظبوط ولا لا؟ B موجودة في الـ G أي
+
+38
+00:03:48,870 --> 00:03:54,510
+element أخدته من جهة يبقى شكل هذا ال element يعني
+
+39
+00:03:54,510 --> 00:04:04,580
+بيبدو يساوي ال a<sup>i</sup> for some i الموجودة في Z ليش؟
+
+40
+00:04:04,580 --> 00:04:09,080
+لأنه G الـCyclic يبقى أي element فيها بدي يكون
+
+41
+00:04:09,080 --> 00:04:17,760
+على شكل الـA ليش هذا الكلام؟ هذا الكلام لأن G
+
+42
+00:04:17,760 --> 00:04:22,500
+بدي تساوي ال subgroup generated by A مِشان هيك
+
+43
+00:04:22,500 --> 00:04:26,760
+كتبناها على الشكل اللي عندنا هذا إذا بناء عليه
+
+44
+00:04:26,760 --> 00:04:36,410
+الـBH هذا بدي يساوي الـB عندي بقداش؟ بA<sup>i</sup> يبقى A<sup>i</sup> في
+
+45
+00:04:36,410 --> 00:04:45,990
+ال H A<sup>i</sup> في H عبارة عن A H A H A H i من المرات أو
+
+46
+00:04:45,990 --> 00:04:55,940
+بمعنى آخر هذه بدها تساوي A H كله to the power i إذا
+
+47
+00:04:55,940 --> 00:05:05,240
+هذه ال elements صار صورة من من ال AH بالشكل اللي
+
+48
+00:05:05,240 --> 00:05:05,920
+عندنا هنا
+
+49
+00:05:09,300 --> 00:05:14,740
+واضح يبقى الآن أخدت element موجود في ال GH وجدته
+
+50
+00:05:14,740 --> 00:05:21,160
+في ال AH يبقى هذه النقطة رقم اثنين إذا من واحد
+
+51
+00:05:21,160 --> 00:05:25,880
+واتنين from واحد and اثنين
+
+52
+00:05:27,780 --> 00:05:33,580
+إن الـ G modulo H اللي بدها تساوي ال subgroup
+
+53
+00:05:33,580 --> 00:05:43,500
+generated by AH يبقى هنا so ال G modulo H is cyclic
+
+54
+00:05:43,500 --> 00:05:51,820
+وانتهينا من السؤال إذا لو كانت G Cyclic وعملنا منها
+
+55
+00:05:51,820 --> 00:05:55,340
+أي quotient group فهذه ال quotient group كذلك
+
+56
+00:05:55,340 --> 00:05:59,220
+ستكون Cyclic group طبعًا السؤال السابع اللي جابله
+
+57
+00:05:59,220 --> 00:06:06,760
+حلّناه كمثال من خلال الأمثلة خذ سؤال زي سؤال 14
+
+58
+00:06:06,760 --> 00:06:09,980
+سؤال
+
+59
+00:06:09,980 --> 00:06:16,910
+14 بيقول what is the order of بدنا ال order تبع 14
+
+60
+00:06:16,910 --> 00:06:23,750
+زائد ال sub group generated by ثمانية وهذا الكلام
+
+61
+00:06:23,750 --> 00:06:34,550
+في ال group اللي هو Z 24 and Z 24 module sub group
+
+62
+00:06:34,550 --> 00:06:36,290
+generated by ثمانية
+
+63
+00:06:39,060 --> 00:06:44,380
+بنعرف قداش ال order لهذا ال element طبعًا ليس
+
+64
+00:06:44,380 --> 00:06:48,180
+بالضرورة أن تبدأ أنت تربع دغري وتكعب لغاية ما
+
+65
+00:06:48,180 --> 00:06:54,660
+توصل لل identity لكن بنظرة بسيطة ال 14 هذه بقدر
+
+66
+00:06:54,660 --> 00:07:01,520
+أكتبها بدلالة ال 8 يبقى باجي بقول الحل كتالي
+
+67
+00:07:01,520 --> 00:07:02,400
+solution
+
+68
+00:07:06,380 --> 00:07:10,620
+الاربعتاشر زي ال subgroup generated by ثمانية
+
+69
+00:07:10,620 --> 00:07:17,020
+يساوي ستة زائد ثمانية زي ال subgroup generated by
+
+70
+00:07:17,020 --> 00:07:25,100
+ثمانية ال element هذا موجود هنا ولا لا يبقى هدول
+
+71
+00:07:25,100 --> 00:07:30,050
+إيش بدهم يعطوني؟Subgroup generated by ثمانية
+
+72
+00:07:51,400 --> 00:07:57,160
+لو قلت الكلام هذا أستربية يعني معناته اثنين في ستة
+
+73
+00:07:57,160 --> 00:08:02,180
+اثنين في ستة لأن أخذنا ال factor group ال AH في
+
+74
+00:08:02,180 --> 00:08:07,600
+BH بدّه يساوي A في BH يعني H بتظهر لثابتة والدرَب
+
+75
+00:08:07,600 --> 00:08:12,040
+يكون لمين؟ للعنصر الآن عندنا جمع يبقى لو جمعت ستة و
+
+76
+00:08:12,040 --> 00:08:18,170
+ستة اثنا عشر تعطيني قداش؟ تعطيني أربعة طب لو قلت ثلاثة
+
+77
+00:08:18,170 --> 00:08:22,790
+في الستة بيبقى ثمان عشر شيل منها ستة عشر بيبقى اثنين
+
+78
+00:08:22,790 --> 00:08:27,270
+لو قلت أربعة في الستة أربعة وعشرين اللي هي ثلاثة
+
+79
+00:08:27,270 --> 00:08:30,470
+وثمانية تبقى هذا بدّه يعطيني الثمانية إذا ال order
+
+80
+00:08:30,470 --> 00:08:36,330
+لهذا ال element يساوي قداش؟ يساوي أربعة يبقى ال
+
+81
+00:08:36,330 --> 00:08:42,850
+order لل 14 زائد ال subgroup generated by 8 يبقى
+
+82
+00:08:42,850 --> 00:08:48,950
+ال order لل 6 زائد ال subgroup generated by 8 يبقى
+
+83
+00:08:48,950 --> 00:08:51,030
+ال order لل 6 زائد ال subgroup generated by 8 يبقى
+
+84
+00:08:51,030 --> 00:08:54,830
+ال order لل 6 زائد ال subgroup generated by 8
+
+85
+00:08:54,870 --> 00:09:00,830
+الأربعة في ستة زائد ال subgroup generated by ثمانية
+
+86
+00:09:00,830 --> 00:09:05,530
+يساوي أربعة وعشرين زائد ال subgroup generated by
+
+87
+00:09:05,530 --> 00:09:09,330
+ثمانية يساوي ال subgroup generated by ثمانية ال
+
+88
+00:09:09,330 --> 00:09:16,530
+identity element لذلك ال order يساوي أربعة
+
+89
+00:09:23,000 --> 00:09:29,120
+طب أروح لسؤال زي سؤال أربعة وعشرين هي سؤال أربعة
+
+90
+00:09:29,120 --> 00:09:38,800
+وعشرين بيقول في ال group اللي هو Z أربعة external
+
+91
+00:09:38,800 --> 00:09:44,640
+product مع مين؟ مع Z اثنا عشر module ال sub group
+
+92
+00:09:44,640 --> 00:09:49,740
+generated by اثنين واثنين بالشكل اللي عندنا هذا
+
+93
+00:09:50,520 --> 00:09:57,540
+الجروب هذا isomorphic لواحدة من isomorphic لزد
+
+94
+00:09:57,540 --> 00:10:04,240
+ثمانية والله زد أربعة external direct product مع زد
+
+95
+00:10:04,240 --> 00:10:10,260
+اثنين والله مع زد اثنين external direct product مع
+
+96
+00:10:10,260 --> 00:10:11,320
+زد اثنين
+
+97
+00:10:14,890 --> 00:10:19,630
+بسأل هل ال group هذه isomorphic لواحدة من هذول أم
+
+98
+00:10:19,630 --> 00:10:24,910
+لا، و determine which one by elimination يعني بدك
+
+99
+00:10:24,910 --> 00:10:29,270
+تحاول تحذف اللي هو الاثنتين وبالتالي تثبت عندك مين
+
+100
+00:10:29,270 --> 00:10:34,670
+تثبت عندك واحدة هي ال solution
+
+101
+00:10:40,640 --> 00:10:44,400
+الحين بدي أعرف هذه ال group فيها كام عنصر وبعد هيك
+
+102
+00:10:44,400 --> 00:10:49,940
+نتفهم على الباقي الآن لو جيت سمّيت ال H هي ال
+
+103
+00:10:49,940 --> 00:10:56,400
+subgroup generated by 2 و2 وبدي أشوف العناصر
+
+104
+00:10:56,400 --> 00:11:02,640
+تبع هذه ال subgroup يبقى ال element الأول 00 ال
+
+105
+00:11:02,640 --> 00:11:08,620
+element الثاني اللي هو 2 و2 الـ Element الثالث
+
+106
+00:11:08,620 --> 00:11:19,580
+يبقى هذا تربيع يبقى 4 و4 4 في زد 4 تعني 0 فديك
+
+107
+00:11:19,580 --> 00:11:26,190
+في زد 12 تعني 4 كما هي الآن تكييب يعني اضرب في
+
+108
+00:11:26,190 --> 00:11:32,230
+ثلاثة بيصير ثلاثة في اثنين يبقى ستة وستة الستة في
+
+109
+00:11:32,230 --> 00:11:38,770
+الزد أربعة باثنين وهذيك ستة كما هي هذا تكييب لو
+
+110
+00:11:38,770 --> 00:11:45,600
+جيت أس أربعة بدّه يعطيني هذا zero وهذا ثمانية الآن
+
+111
+00:11:45,600 --> 00:11:51,180
+لو جيت أس خمسة بدّه يعطيني عشرة وعشرة يبقى خمسة
+
+112
+00:11:51,180 --> 00:11:57,780
+هذه بيعطيني اثنين وعشرة يبقى أس ستة بيعطيني اثنا عشر
+
+113
+00:11:57,780 --> 00:12:02,580
+واثنا عشر اللي هو ال identity وال identity هي هيبقى
+
+114
+00:12:02,580 --> 00:12:07,920
+على هك انتهت من انتهت هذه ال subgroup يبقى زي ما
+
+115
+00:12:07,920 --> 00:12:12,380
+أنت ملاحظ في عندي ال order اللي يساوي قداش؟ يساوي
+
+116
+00:12:12,380 --> 00:12:18,480
+ستة عناصر إذا لما بدي أجي لل factor group هذه ال
+
+117
+00:12:18,480 --> 00:12:24,760
+factor group external product لزد اثنا عشر module ال
+
+118
+00:12:24,760 --> 00:12:30,050
+subgroup generated by اثنين واثنين الـ Order لها
+
+119
+00:12:30,050 --> 00:12:35,990
+أربعة في اثنا عشر بتمانية وأربعين على ستة يبقى فيها
+
+120
+00:12:35,990 --> 00:12:41,450
+قداش؟ فيها ثمانية الآن هذه ال group فيها ثمانية
+
+121
+00:12:41,450 --> 00:12:46,890
+عناصر بدنا نتعرف على هذه العناصر الثمانية اللي
+
+122
+00:12:46,890 --> 00:12:53,630
+عندنا يبقى ال group اللي عندنا اللي هي Z4 external
+
+123
+00:12:53,630 --> 00:13:00,990
+product مع Z12 modulo H بدها تساوي ما بدّيش أكتبه
+
+124
+00:13:00,990 --> 00:13:08,380
+بالشكل هذا H أخف في الكتابة يبقى هذا H zero وواحد
+
+125
+00:13:08,380 --> 00:13:14,980
+اللي هو zero وواحد زائد ال H من operation عملية 
+
+
+
+126
+00:13:14,980 --> 00:13:22,520
+جامعة واحد و صفر زائد الـ H واحد و واحد زائد الـ H
+
+127
+00:13:23,920 --> 00:13:29,640
+واحد و اثنين زائد 
+
+128
+00:13:29,640 --> 00:13:39,280
+الـ H اللي هو اثنين و واحد زائد الـ H واحد و ثلاثة
+
+129
+00:13:39,280 --> 00:13:49,160
+زائد الـ H وكذلك اللي هو صفر و اثنين زائد الـ H يبقى
+
+130
+00:13:49,160 --> 00:13:53,900
+هذه العناصر واحد اثنين ثلاثة أربعة خمسة ستة سبعة
+
+131
+00:13:53,900 --> 00:13:59,300
+ثمانية عناصر يبقى هذه ثمانية عناصر عندنا تبعت الـ
+
+132
+00:13:59,300 --> 00:14:04,860
+group هذه طبعا كيف عرفتها؟ بدنا ناخد العناصر تبعات
+
+133
+00:14:04,860 --> 00:14:10,110
+الـ group اللي عندنا و نبدأ نضربهم في سالب الـ H
+
+134
+00:14:10,110 --> 00:14:15,550
+طبعا هيطلعوا بعضهم يساوي بعض أو هيطلعوا الستة منهم 
+
+135
+00:14:15,550 --> 00:14:20,750
+كل ستة بيساوي بعض فبيصف عنا مين؟ بيصف عنا الثمانية
+
+136
+00:14:20,750 --> 00:14:25,310
+اللي قدامنا هدول يبقى هدول عناصر الـ group اللي
+
+137
+00:14:25,310 --> 00:14:30,270
+عندك كان سؤال هو هذه isomorphic لمين؟ هل أزد
+
+138
+00:14:30,270 --> 00:14:35,880
+ثمانية؟ والله لهذه والله لهذه تعالوا نشوف لو أخدت
+
+139
+00:14:35,880 --> 00:14:41,100
+عشوائيا أي element من هدول هتلاقي الـ order له يا 
+
+140
+00:14:41,100 --> 00:14:46,980
+واحد ثلاثة أنسى الموضوع ثلاثة لأن هذه فيها ثمانية
+
+141
+00:14:46,980 --> 00:14:50,300
+عناصر الـ order للـ element بدي أجسم الـ order للـ
+
+142
+00:14:50,300 --> 00:14:54,220
+group يا واحد يا اثنين يا أربعة يا ثمانية مظبوط
+
+143
+00:14:54,220 --> 00:15:00,400
+السؤال هو هل هناك element الـ order له يساوي ثمانية
+
+144
+00:15:02,030 --> 00:15:10,770
+الله أعلم كل اللي بقوله أنا each of these elements
+
+145
+00:15:15,310 --> 00:15:20,770
+this element has
+
+146
+00:15:20,770 --> 00:15:28,110
+orders يا ما واحد، يا ما اثنين، يا ما أربعة فقط، لا
+
+147
+00:15:28,110 --> 00:15:32,550
+غير نجرب؟
+
+148
+00:15:32,550 --> 00:15:36,990
+حسب السؤال هذا كتير مش cycle أنت مستخدم يكون
+
+149
+00:15:36,990 --> 00:15:43,280
+جنّينك بتاعك cycle ما أنت عشوائيابس في فن شوية هنا
+
+150
+00:15:43,280 --> 00:15:47,980
+عشوائيا خد لك أي element و تعالى نحسب الـ order تبعه
+
+151
+00:15:47,980 --> 00:15:52,080
+تمام؟ و أنت بعد هيك بدك تجرب الـ order تبع الباقي
+
+152
+00:15:52,080 --> 00:15:55,700
+براحتك في البيت أو احنا باقي المحاضرة نقعد نحسب الـ
+
+153
+00:15:55,700 --> 00:16:01,240
+order كلهم لأ تعالى خد أنتقل لك أي واحد من هدول واحد
+
+154
+00:16:01,240 --> 00:16:05,440
+و ثلاثة وين واحد و ثلاثة هاي؟ يبقى بيروح يدور على
+
+155
+00:16:05,440 --> 00:16:11,660
+الـ order تبعه يبقى تربيع جداش بيكون اثنين و ستة
+
+156
+00:16:11,660 --> 00:16:16,920
+تمام اثنين و ستة هل موجود هنا اثنين و ستة؟ اه ايه هنا
+
+157
+00:16:16,920 --> 00:16:21,830
+يبقى الـ order له جداش باثنين طبعا هذا الواحد
+
+158
+00:16:21,830 --> 00:16:24,310
+و الثالث و الثاني و الستين هذين موجودين في الـ H
+
+159
+00:16:24,310 --> 00:16:28,370
+موجود في الـ H يبقى الـ order له بس يساوي اثنين يعني
+
+160
+00:16:28,370 --> 00:16:32,970
+حصلت ضرب هذا التربيع بدي يعطيني الـ H itself لأن
+
+161
+00:16:32,970 --> 00:16:36,350
+هذين أعطاني الـ element اثنين و الستين و غيره يبقى
+
+162
+00:16:36,350 --> 00:16:41,730
+هذا الـ order له يساوي اثنين يلا طالك كمان عنصر
+
+163
+00:16:41,730 --> 00:16:46,730
+ثاني اه ليه عجبك؟ أي واحد فيهم عشوائي اللي بدك
+
+164
+00:16:46,730 --> 00:16:53,480
+إياه قداش؟ اثنين و واحد طيب اثنين و واحد يبقى بدي
+
+165
+00:16:53,480 --> 00:16:59,920
+أقوله تربيع بصير أربعة و اثنين، مظبوط؟ أربعة و
+
+166
+00:16:59,920 --> 00:17:05,360
+اثنين تعني صفر و اثنين، صفر و اثنين، و راح صفر
+
+167
+00:17:05,360 --> 00:17:11,180
+أقل، مش موجود، يبقى تربيع بجيبليش صفر و اثنين،
+
+168
+00:17:11,180 --> 00:17:16,020
+تمام؟ بجيبليش صفر و اثنين، تمام، يبقى تكعيب، يبقى
+
+169
+00:17:16,020 --> 00:17:24,060
+بصير ستة و ثلاثة، بس كيف؟ ممتاز جدا يبقى الساعة
+
+170
+00:17:24,060 --> 00:17:27,880
+اثنين حطينا على الهشك يبقى وصلنا للـ أربعة يبقى هنا
+
+171
+00:17:27,880 --> 00:17:32,460
+أربعة في اثنين في ثمانية و هنا أربعة يعني صفر
+
+172
+00:17:32,460 --> 00:17:36,760
+و أربعة صفر و أربعة هي موجودة يبقى الـ order يساوي
+
+173
+00:17:36,760 --> 00:17:42,250
+كده؟ يساوي أربعة و هكذا يبقى أي element من هدول الـ
+
+174
+00:17:42,250 --> 00:17:46,730
+order يقولوا يا واحد يا اثنين يا أربعة إذا هل ممكن
+
+175
+00:17:46,730 --> 00:17:50,950
+تبقى الـ group هذه isomorphic لـ Z ثمانية؟ في
+
+176
+00:17:50,950 --> 00:17:54,430
+الشمكانية لأن Z ثمانية فيها الـ order ثمانية هذه
+
+177
+00:17:54,430 --> 00:17:59,110
+فيهاش يبقى لا يمكن تبقى isomorphic لمين؟ لـ Z ثمانية
+
+178
+00:17:59,110 --> 00:18:05,270
+طيب هذه أقصى order فيها جداش اثنين يبقى هذه أربعة
+
+179
+00:18:05,270 --> 00:18:09,510
+يبقى لا يمكن تكون isomorphic لهذه يبقى بضل إجباري
+
+180
+00:18:09,510 --> 0:18:14,530
+isomorphic لمين؟ لـ زد أربعة external product مع زد
+
+181
+00:18:14,530 --> 00:18:22,870
+اثنين يبقى هذا بده يعطيني الـ group اللي عندنا هو Z4
+
+182
+00:18:22,870 --> 00:18:31,510
+Xenodyic product لـ Z12 is not isomorphic لـ Z8
+
+183
+00:18:31,510 --> 00:18:36,590
+لأن Z8 فيها elements الـ order لهم يسوى ثمانية
+
+184
+00:18:39,300 --> 00:18:49,880
+الـ z4 external product مع z12 طبعا modulo h يا
+
+185
+00:18:49,880 --> 00:18:56,480
+شباب و هنا كمان modulo h لا يمكن تبقى isomorphic
+
+186
+00:18:56,480 --> 00:19:03,800
+إلى z2 external product مع z2 external product مع
+
+187
+00:19:03,800 --> 00:19:05,800
+z2 because
+
+188
+00:19:09,360 --> 00:19:24,180
+the last group has orders of .. والله has elements
+
+189
+00:19:24,180 --> 00:19:28,940
+of
+
+190
+00:19:28,940 --> 00:19:37,700
+orders واحد و اثنين فقط يبقى بناء عليه بقول له thus
+
+191
+00:19:37,700 --> 00:19:46,180
+و هكذا z for external byproduct مع z12 modulo h is
+
+192
+00:19:46,180 --> 00:19:53,940
+isomorphic الى z4 external byproduct مع z2 يعني
+
+193
+00:19:53,940 --> 00:19:59,880
+حذفنا two groups ولاجناها isomorphic لواحدة من الـ
+
+194
+00:19:59,880 --> 00:20:02,100
+groups الأخرى
+
+195
+00:20:16,060 --> 00:20:27,640
+هذا كان سؤال 24 خد لي سؤال 28 سؤال 28 حول نفس
+
+196
+00:20:27,640 --> 00:20:36,940
+الموضوع بيقول بيقول جي تساوي زد أربعة جي تساوي زد
+
+197
+00:20:36,940 --> 00:20:46,440
+أربعة external product مع زد أربعة و الـ H ما عطينيها
+
+198
+00:20:46,440 --> 00:20:55,020
+هي صفر و صفر و صفر و اثنين و اثنين و صفر و
+
+199
+00:20:55,020 --> 00:21:01,360
+اثنين و صفر و كذلك اثنين و اثنين بالشكل اللي
+
+200
+00:21:01,360 --> 00:21:09,480
+عندنا هذا و ما عطيني K هي الـ sub group generated by
+
+201
+00:21:09,480 --> 00:21:16,650
+واحد من عناصرها مش ما عطيني لكن أنا بقدر أجيب عناصر
+
+202
+00:21:16,650 --> 00:21:23,210
+تبعتها يبقى أول شي هيكون صفر و صفر لأنها الـ sub
+
+203
+00:21:23,210 --> 00:21:27,970
+group اللي بعده واحد و اثنين زي ما هو اللي بعده
+
+204
+00:21:27,970 --> 00:21:34,190
+تربيع بصير اثنين و أربعة اثنين و أربعة تعني ايه؟
+
+205
+00:21:34,190 --> 00:21:40,020
+تعني اثنين و صفر يبقى تقريبا تقريبا تقريبا تقريبا
+
+206
+00:21:40,020 --> 00:21:48,580
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+207
+00:21:48,580 --> 00:21:54,040
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+208
+00:21:54,040 --> 00:21:54,840
+تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا تقريبا
+
+209
+00:21:54,840 --> 00:21:58,320
+تقريبا تقريبا تقريبا تقريبا تقريبا
+
+210
+00:22:04,820 --> 00:22:12,480
+is g modulo
+
+211
+00:22:12,480 --> 00:22:22,080
+h isomorphic لمين؟ لـ زد أربعة؟ لـ زد أربعة و الله لـ زد
+
+212
+00:22:22,080 --> 00:22:31,370
+اثنين external product مع زد اثنين نمر باه هل الـ جي
+
+213
+00:22:31,370 --> 00:22:40,230
+موديولوكا is الجي موديولوكا isomorphic لـ زد أربعة
+
+214
+00:22:40,230 --> 00:22:46,810
+و الله لـ زد اثنين external like product مع زد اثنين
+
+215
+00:22:46,810 --> 00:22:50,270
+كذلك يعني مع هذه بالضبط تماما
+
+216
+00:22:58,060 --> 00:23:04,680
+تعالى نشوف هذا الكلام solution يبقى
+
+217
+00:23:04,680 --> 00:23:09,720
+احنا عندنا group فيها 16 element و عندنا الـ H فيها
+
+218
+00:23:09,720 --> 00:23:16,140
+أربعة element يبقى هذه فيها كام عنصر؟ أربعة عناصر
+
+219
+00:23:16,140 --> 00:23:25,630
+يبقى بناء عليه بادئ بقول هنا الـ order لـ جي modulo H
+
+220
+00:23:25,630 --> 00:23:30,810
+بديه يسوى الـ order لـ جي على الـ order للـ H و اللي هو
+
+221
+00:23:30,810 --> 00:23:36,510
+بديه يسوى 16 على 4 بديه يسوى كده؟ بديه يسوى 4
+
+222
+00:23:36,510 --> 00:23:44,330
+عناصر يبقى الجي modulo H عناصرها هي 00 اللي هو الـ
+
+223
+00:23:44,330 --> 00:23:50,820
+identity element في عندك هنا zero واحد واحد و zero
+
+224
+00:23:50,820 --> 00:24:00,130
+و هنا واحد و واحد كله زائد H يبقى هذه الأولى اللي
+
+225
+00:24:00,130 --> 00:24:08,970
+هي H 00 اللي هي H itself و بعدها 01 زائد الـ H
+
+226
+00:24:08,970 --> 00:24:18,070
+و الثانية 100 زائد الـ H و الرابعة اللي هي 11 زائد الـ H
+
+227
+00:24:18,070 --> 00:24:23,480
+بالشكل اللي عندنا هنا هذه حداد العناصر الباقي
+
+228
+00:24:23,480 --> 00:24:27,760
+العناصر ايش ما تضرب هتطلع واحدة من الأربعة هدول
+
+229
+00:24:27,760 --> 00:24:33,500
+طيب يعني كل أربعة left cosets هيطلعوا are equal
+
+230
+00:24:33,500 --> 00:24:38,950
+بيساووا بعض ليش؟ إن هذه العناصر عندي هنا أربعة؟ طب
+
+231
+00:24:38,950 --> 00:24:43,910
+كويس الآن لو جيت لهذه بدي أشوف ايزو مورفك لـ زد
+
+232
+00:24:43,910 --> 00:24:48,810
+أربعة ولا لـ زد اثنين إذا بدي اروح أدور على مين؟ للـ
+
+233
+00:24:48,810 --> 00:24:54,750
+orders لهذه الـ elements تعالى نشوف الـ order لأي
+
+234
+00:24:54,750 --> 00:25:01,830
+element من هدول كده بيكون نقدر نشوفهم كلهم سيبك إنّه
+
+235
+00:25:01,830 --> 00:25:06,790
+ليه اتش هذه الـ identity هذه ههه لو قلت تربيع بصير
+
+236
+00:25:06,790 --> 00:25:18,510
+الـ 02 02 زائد الـ H 02 02 موجودة هذه كل تربيع تعطي
+
+237
+00:25:18,510 --> 00:25:27,450
+الـ H نفسها هذي لما أربعها بصير صفر و اثنين زائد
+
+238
+00:25:27,450 --> 00:25:33,050
+الـ H صفر و اثنين موجودة في الـ H إذا بتعطيني H
+
+239
+00:25:33,050 --> 00:25:38,740
+يبقى الـ order له بس قداش؟ اثنين نمسك الثاني، لو قلت
+
+240
+00:25:38,740 --> 00:25:46,540
+تربيع بيصير 2 و 0 زائد الـ H 2 و 0 موجودة في الـ H
+
+241
+00:25:46,540 --> 00:25:50,220
+يبقى هذا كمان هيعطيني من؟ هيعطيني الـ H يبقى الـ
+
+242
+00:25:50,220 --> 00:25:58,880
+order إله يساوي 2 لو جينا لهذه 2 و 2 يبقى كل non
+
+243
+00:25:58,880 --> 00:26:04,960
+identity element has order قداش؟ 2 يبقى الـ orders
+
+244
+00:26:04,960 --> 00:26:08,880
+للـ element يا إما واحد يا إما اثنين يعني ما يقول
+
+245
+00:26:08,880 --> 00:26:14,140
+تبقى isomorphic لـ زد أربعة؟ لأ مش ممكنية لـ زد أربعة
+
+246
+00:26:14,140 --> 00:26:21,160
+الـ order واحد اثنين أربعة يبقى باجي بقول each of
+
+247
+00:26:21,160 --> 00:26:35,330
+this element has order اللي هو واحد or اثنين for
+
+248
+00:26:35,330 --> 00:26:40,950
+example كتوضيح for example لو بدنا نوضح الكلام
+
+249
+00:26:40,950 --> 00:26:49,330
+تبعنا خد لي أي واحد فيهم يبقى واحد و صفر زائد H لكل
+
+250
+00:26:49,330 --> 00:26:58,310
+تربيع يبقى هذا بيصير اثنين في واحد و صفر زائد الـ H 
+
+251
+00:26:58,310 --> 00:27:06,370
+و يساوي اثنين و صفر زائد الـ H يبقى
+
+252
+00:27:06,370 --> 00:27:15,170
+ال order له يكون اثنين و صفر زائد الـ H يساوي
+
+253
+00:27:15,170 --> 00:27:23,890
+اثنين يبقى هنا الـ G modulo H isomorphic لـ Z2
+
+254
+00:27:23,890 --> 00:27:30,610
+external product لـ Z2 لأن أي element فيها is of
+
+255
+00:27:30,610 --> 00:27:37,670
+order 1 أو 2 طيب
+
+256
+00:27:37,670 --> 00:27:38,610
+نشوف الثانية
+
+257
+00:27:47,280 --> 00:27:54,400
+بنشوف الثانية اللي هي الـ G modulo K الآن برضه ال
+
+258
+00:27:54,400 --> 00:28:01,760
+order للـ G modulo K modulo K بده يساوي اللي هو
+
+259
+00:28:01,760 --> 00:28:07,320
+الستة عشر على أربعة ويساوي كمان أربعة بدنا نشوف
+
+260
+00:28:07,320 --> 00:28:14,770
+عناصرها إذا الـ G modulo K لو روحت دورت على عناصرها
+
+261
+00:28:14,770 --> 00:28:26,730
+هتلاقيها Zero و Zero و واحد و .. قصدي K يبقى
+
+262
+00:28:26,730 --> 00:28:35,910
+K و اللي هو واحد و واحد زائد K اثنين و اثنين زائد
+
+263
+00:28:35,910 --> 00:28:44,770
+K ثلاثة و ثلاثة زائد K الآن لو فكتهم ولا واحدة
+
+264
+00:28:44,770 --> 00:28:49,450
+عناصرها زي الثانية يبقى كلهم الأربعة هذول are
+
+265
+00:28:49,450 --> 00:28:54,810
+disjoint وبالتالي بقية 12 left cosets هيكون هنا
+
+266
+00:28:54,810 --> 00:28:59,470
+واحدة من الأربع اللي عندك كل واحدة هتساوي واحدة
+
+267
+00:28:59,470 --> 00:29:04,430
+طيب على أي حال الآن بدي أدور على ال orders لبين
+
+268
+00:29:04,430 --> 00:29:10,470
+لأي element موجود هنا لو جيت لل element هذا كداشه
+
+269
+00:29:10,470 --> 00:29:11,350
+ال order له
+
+270
+00:29:14,660 --> 00:29:19,300
+الـ order ال order ال order له اثنين لأنه يعطيني
+
+271
+00:29:19,300 --> 00:29:24,560
+أربعة و أربعة واحنا بنشتغل هنا وهنا على زد أربعة
+
+272
+00:29:24,560 --> 00:29:29,560
+يبقى هذا ال order له يساوي اثنين طيب ايش العلاقة
+
+273
+00:29:29,560 --> 00:29:34,690
+بين اثنين هدول واحد معكوس للثاني يبقى ال order
+
+274
+00:29:34,690 --> 00:29:38,910
+للأول بده يساوي ال order للثاني قداش ال order لهذا
+
+275
+00:29:38,910 --> 00:29:43,530
+أربعة يبقى لا يمكن يجب isomorphic لـ Z2 × Z2
+
+276
+00:29:43,530 --> 00:29:49,290
+Z2 وإنما isomorphic لمين؟ لـ Z4 يبقى هنا
+
+277
+00:29:49,290 --> 00:29:55,870
+ال order للواحد وواحد زائد K بده يساوي ال order
+
+278
+00:29:56,320 --> 00:30:02,440
+لثلاثة و ثلاثة زائد K وهذا الكلام كله بده يساوي
+
+279
+00:30:02,440 --> 00:30:08,720
+قداش؟ بده يساوي أربعة هذا automatic بده يعطينا أن
+
+280
+00:30:08,720 --> 00:30:15,600
+ال group اللي عندنا G modulo K is isomorphic إلى Z
+
+281
+00:30:15,600 --> 00:30:21,000
+أربعة وليس إلى Z2 external product مع Z2
+
+282
+00:30:21,000 --> 00:30:21,860
+كيف؟
+
+283
+00:30:28,010 --> 00:30:35,010
+طيب هذا كان سؤال ثمانية و عشرين شوف لي سؤال سبعة و
+
+284
+00:30:35,010 --> 00:30:43,910
+ثلاثين سؤال سبعة و ثلاثين بيقول ياخد الـ G group و
+
+285
+00:30:43,910 --> 00:30:49,410
+الـ H normal subgroup يبقى الـ H normal subgroup من
+
+286
+00:30:49,410 --> 00:30:57,290
+G prove that ال order لل element GH prove أن ال
+
+287
+00:30:57,290 --> 00:31:04,850
+order لل element GH divides ال order لمين؟ ال
+
+288
+00:31:04,850 --> 00:31:05,850
+order لـ G
+
+289
+00:31:09,110 --> 00:31:14,030
+عظمنا لما كنا نقول isomorphism بقينا نقول ال order
+
+290
+00:31:14,030 --> 00:31:18,550
+لل element يساوي ال order للصورة، مظبوط؟ يبقى هذا
+
+291
+00:31:18,550 --> 00:31:23,330
+في حالة مين؟ ال isomorphism هنا بيختلف الكلام كليًا
+
+292
+00:31:23,330 --> 00:31:28,510
+عندنا بيقول ال order لل left coset بده يقسم ال
+
+293
+00:31:28,510 --> 00:31:33,490
+order لمين؟ ال order لل element بدنا نروح نثبت صحة
+
+294
+00:31:33,490 --> 00:31:37,350
+هذا الكلام يبقى ال proof
+
+295
+00:31:43,840 --> 00:31:49,140
+لما قال الـ H normal subgroup من G يعني معناته
+
+296
+00:31:49,140 --> 00:31:54,840
+صارت الـ G modulo H اللي هذا أحد عناصرها exist
+
+297
+00:31:54,840 --> 00:31:57,920
+يعني ال factor group أو ال quotient group exist
+
+298
+00:31:57,920 --> 00:32:04,120
+وبالتالي هذا هو أحد العناصر اللي موجود فيها بنثبت
+
+299
+00:32:04,120 --> 00:32:10,220
+أن هذا ال element ال order اللي بده يقسم ال order
+
+300
+00:32:10,220 --> 00:32:15,960
+تبع ال element الثاني يعني ال order لل element في
+
+301
+00:32:15,960 --> 00:32:20,400
+ال quotient group بده يقسم ال order تبع ال element
+
+302
+00:32:20,400 --> 00:32:26,880
+اللي موجود في ال group بنقوله كويس احنا لو روحنا
+
+303
+00:32:26,880 --> 00:32:33,720
+جينا وقلنا as you افترض أن ال order للـ G بده يساوي
+
+304
+00:32:33,720 --> 00:32:40,780
+الـ N that is أي أن الـ G to the power N بده يساوي
+
+305
+00:32:40,780 --> 00:32:47,840
+مين؟ بده يساوي ال identity طيب لو روحنا وقلنا خد لي
+
+306
+00:32:47,840 --> 00:32:57,730
+GH كله to the power N يبقى هذا الكلام بده يساوي GN
+
+307
+00:32:57,730 --> 00:33:05,610
+في الـ H الـ GN هي بالـ Identity Element في H بده
+
+308
+00:33:05,610 --> 00:33:11,610
+يساوي من؟ بده يساوي الـ H إذا الـ Order تبع الـ GH
+
+309
+00:33:11,610 --> 00:33:17,890
+شو علاقته بالـ N؟ يعني يقسم من؟ يقسم الـ N وقد
+
+310
+00:33:17,890 --> 00:33:22,950
+يساويها لو سواها كمان بيقسموا هذا معناته إن الـ
+
+311
+00:33:22,950 --> 00:33:31,990
+Order للـ GH Divides الـ N هذا معناته أن ال order
+
+312
+00:33:31,990 --> 00:33:40,720
+لل GH divides من الـ N هذه الـ order تبع الـ G يبقى
+
+313
+00:33:40,720 --> 00:33:45,820
+ال order تبع الـ G وهو المطلوب يبقى من الآن فصاعد
+
+314
+00:33:45,820 --> 00:33:50,180
+لما تحط في دماغك لما يكون عندك normal subgroup
+
+315
+00:33:50,180 --> 00:33:55,340
+وكوننا ال factor group ال order لأي element في ال
+
+316
+00:33:55,340 --> 00:34:01,280
+factor group بيقسم نظيره من ال element اللي موجود
+
+317
+00:34:01,280 --> 00:34:04,740
+في ال group الأصلية
+
+318
+00:34:06,620 --> 00:34:13,180
+هذا كان سؤال سبعة و ثلاثين بدنا نروح لسؤال أربعة و
+
+319
+00:34:13,180 --> 00:34:19,380
+أربعين بيقول يبيني أن دي ثلاث عشرة isomorphic لل inner
+
+320
+00:34:19,380 --> 00:34:24,340
+atomorphism اللي دي ثلاث عشرة يبقى السؤال أربعة و
+
+321
+00:34:24,340 --> 00:34:36,640
+أربعين show that أن الـ D13 isomorphic للـ Inner
+
+322
+00:34:36,640 --> 00:34:45,500
+Atomorphism لـ D13 أول
+
+323
+00:34:45,500 --> 00:34:50,220
+مرة نشوف سؤال زي هيك يعني ال Inner Atomorphism للي
+
+324
+00:34:50,220 --> 00:34:57,460
+جروب بدي يكون isomorphic للي جروب itself طيب ممتاز
+
+325
+00:34:58,830 --> 00:35:03,650
+بنحاول نبرهن هذا الكلام من خلال الجزء النظري الذي
+
+326
+00:35:03,650 --> 00:35:11,190
+تعرضنا له في المحاضرات السابقة يبقى solution مرت
+
+327
+00:35:11,190 --> 00:35:16,050
+علينا نظرية فيها isomorphic لل inner atomorphism
+
+328
+00:35:16,050 --> 00:35:23,470
+للـ G حد ماذا ذكرها يعني هيك؟ الـ G-modulus center
+
+329
+00:35:23,470 --> 00:35:30,110
+isomorphic للـ Inner Atomorphism للـ D4 صحيح يبقى
+
+330
+00:35:30,110 --> 00:35:37,590
+احنا أخذنا نظرية بتقول ايش؟ بتقول أن الـ G-modulus
+
+331
+00:35:37,590 --> 00:35:44,230
+center تبع الـ G isomorphic لل Inner Atomorphism
+
+332
+00:35:44,230 --> 00:35:53,800
+لمين؟ للـ G هذا معناه أن دي ثلاث عشرة modulo جداش ال
+
+333
+00:35:53,800 --> 00:36:02,140
+center تبع ال identity فقط مش السبب ثلاث عشرة odd لأن
+
+334
+00:36:02,140 --> 00:36:07,460
+ال center تبع الـ D إن لا يوجد فيه إلا two elements
+
+335
+00:36:07,460 --> 00:36:12,220
+إن كان الـ N even أو element واحد اللي هو ال
+
+336
+00:36:12,220 --> 00:36:20,750
+trivial إن كان الـ N is odd يبقى هذا معناه أن الـ D13
+
+337
+00:36:20,750 --> 00:36:29,650
+modulo R node isomorphic لأن هذا ال center لمن؟ لل
+
+338
+00:36:29,650 --> 00:36:38,720
+inner atom morphism لـ D13 السبب because أن الـ
+
+339
+00:36:38,720 --> 00:36:45,920
+Center تبع الـ D13 لا يوجد فيه إلا الـ R node
+
+340
+00:36:45,920 --> 00:36:56,360
+since الـ D13 is odd ممتاز جدًا يبقى صار D13 modulo
+
+341
+00:36:56,360 --> 00:37:02,260
+الـ R node ما لها isomorphic للـ Inner Atomorphism
+
+342
+00:37:02,260 --> 00:37:09,180
+لمين؟ لـ G طيب أنا الآن لو قدرت أثبت أن G
+
+343
+00:37:09,180 --> 00:37:14,880
+isomorphic لهذه ال group بصير G الأصلية
+
+344
+00:37:14,880 --> 00:37:19,900
+isomorphic لمين؟ للـ Inner Atomorphism لـ G وبالتالي
+
+345
+00:37:19,900 --> 00:37:25,360
+بيكون خلصنا يبقى if we show that أنه D13
+
+346
+00:37:25,360 --> 00:37:31,920
+isomorphic لـ D13 modulo R node then we have the
+
+347
+00:37:31,920 --> 00:37:36,330
+result بيكون حصلنا على من؟ على النتيجة طيب كيف
+
+348
+00:37:36,330 --> 00:37:41,210
+بتسويها هذه؟ بسيط اعرف function و أثبت أنها one to
+
+349
+00:37:41,210 --> 00:37:46,050
+one and on two و تخدم خاصية ال isomorphism و وصلنا
+
+350
+00:37:46,050 --> 00:37:55,190
+للمطلوب بسهولة كيف؟ ولا في أسهل منها هذا يعني
+
+351
+00:37:55,190 --> 00:37:56,590
+define
+
+352
+00:38:01,200 --> 00:38:11,960
+فاي من D13 إلى D13 modulo R0
+
+353
+00:38:17,460 --> 00:38:23,080
+5 of X بدي آخذ X موجود في D13 مين ما يكون شكله
+
+354
+00:38:23,080 --> 00:38:28,760
+يكون هذا بدي أوديه وين في ال group هذه يبقى هذه
+
+355
+00:38:28,760 --> 00:38:34,020
+كعنصرها كلهم left cosets طبعًا هذه مش subgroup
+
+356
+00:38:34,020 --> 00:38:39,040
+generated by R node قلت لها generated والله بس ال
+
+357
+00:38:39,040 --> 00:38:44,720
+R node ماهيها ما فيش غيرها ما فيش غير هالأنصار هذا
+
+358
+00:38:44,720 --> 00:38:50,420
+تمام؟ بدي أعرفه يبقى ما بدي أقول له left corsets يبقى
+
+359
+00:38:50,420 --> 00:38:57,440
+X في مين؟ في الـ R node ايش رأيك في التعريف؟ صعب ولا
+
+360
+00:38:57,440 --> 00:39:04,990
+سهل؟ ما فيش هتفهم إنه صحيح؟ ليش؟ لأن الـ R node هذه
+
+361
+00:39:04,990 --> 00:39:09,450
+ما فيش إلا عنصر واحد اللي هو ال identity element في
+
+362
+00:39:09,450 --> 00:39:15,350
+ال group لكن لو في عناصر ثانية بصير هنا فيها كلام
+
+363
+00:39:17,300 --> 00:39:21,100
+طيب عرفنا ال function هذه بدي أثبت له أن ال
+
+364
+00:39:21,100 --> 00:39:27,600
+function هذه فاي is one to one يبقى بدي آخذ صورتين
+
+365
+00:39:27,600 --> 00:39:34,480
+متساويتين فاي X بده يساوي فاي Y وبده أحاول
+
+366
+00:39:34,480 --> 00:39:40,680
+أثبت له أن الـ X يساوي Y يبقى هذا معناه أن الـ X في R
+
+367
+00:39:40,680 --> 00:39:47,970
+node بده يساوي الـ Y في R node هذا الكلام يساوي لما
+
+368
+00:39:47,970 --> 00:39:54,170
+أنت ضربت الـ X في R node من بيعطيك X itself هذا بده
+
+369
+00:39:54,170 --> 00:39:59,830
+يعطينا هذه
+
+370
+00:39:59,830 --> 00:40:05,530
+تعطيك ال set اللي هي Y set ما فيش فيها غير عنصر و set
+
+371
+00:40:05,530 --> 00:40:10,610
+ما فيش فيها غير عنصر يبقى اثنين متساويتين يبقى الـ X
+
+372
+00:40:10,610 --> 00:40:15,580
+بالساوي Y وبالتالي ال Phi one to one نجي فاي is
+
+373
+00:40:15,580 --> 00:40:20,900
+onto هذه well defined لو كان فيها عناصر لكن ما فيش
+
+374
+00:40:20,900 --> 00:40:24,960
+غير ال identity كيف؟ مظلوم ما فيش غير هو وبالتالي مش
+
+375
+00:40:24,960 --> 00:40:27,940
+محتاجة well defined أما لو كان فيها مجموعة عناصر 
+
+376
+00:40:27,940 --> 00:40:37,920
+كلامك صحيح طيب الآن فاي is onto فايوز أنتو يبقى
+
+377
+00:40:37,920 --> 00:40:46,120
+بتروح آخذ اللي هو element يبقى let الـ element مثلا
+
+378
+00:40:46,120 --> 00:40:56,060
+X R node هذا هيك موجود في مين؟ موجود في الـ D
+
+379
+00:40:56,060 --> 00:41:01,900
+ثلاثة عشر modulo اللي هو الـ R node
+
+380
+00:41:04,910 --> 00:41:09,010
+يبقى افترض أن هذا الـ element موجود هنا
+
+381
+00:41:12,640 --> 00:41:19,120
+الـ X في الـ R node حسب التعريف تبع الـ function هو
+
+382
+00:41:19,120 --> 00:41:25,220
+بيعطينا image فاي of X يبقى هذا بيعطينا الـ image
+
+383
+00:41:25,220 --> 00:41:31,540
+فاي of X يبقى بناء عليه فاي is onto ضالة النقطة
+
+384
+00:41:31,540 --> 00:41:39,320
+الأخيرة فاي is an isomorphism يبقى بده أروح آخذ
+
+385
+00:41:39,320 --> 00:41:48,180
+فاي of XY يبقى هذا الكلام دي يساوي XY في الـ R node R
+
+386
+00:41:48,180 --> 00:41:53,180
+node هو الـ identity element يعني بقدر أقول الـ X في
+
+387
+00:41:53,180 --> 00:41:58,500
+الـ R node و في الـ Y في الـ R node بالشكل اللي عندنا
+
+388
+00:41:58,500 --> 00:42:03,280
+هنا و بقدر أشيل الـ R node بالمرة كمان هذه لأن هو الـ
+
+389
+00:42:03,280 --> 00:42:08,700
+identity element تبع الـ D13 طيب هذه بدها تعطينا
+
+390
+00:42:08,700 --> 00:42:14,440
+مين؟ فاي of X وهذه بدها تعطينا فاي of Y لذلك صورة
+
+391
+00:42:14,440 --> 00:42:23,810
+isomorphism يبقى صورة D13 ايزو مورفك لـ D13 موديولو
+
+392
+00:42:23,810 --> 00:42:33,290
+R node وهذه ايزو مورفك للانر أوتومورفزم لمن؟ للـ D13
+
+393
+00:42:33,290 --> 00:42:41,370
+وهذا سيعطيك أن D13 ايزو مورفك للانر أوتومورفزم
+
+394
+00:42:41,370 --> 00:42:43,470
+لـ D13
+
+395
+00:42:46,940 --> 00:42:50,780
+طبعا لو جاءك هذا السؤال في الامتحان وأنا جيتها مرة
+
+396
+00:42:50,780 --> 00:42:56,960
+بتسألني سؤاله لما؟ أقول لجروب يبقى isomorphism أو
+
+397
+00:42:56,960 --> 00:43:02,140
+isomorphic لا الـ inner-automorphism ما احنا بنقول
+
+398
+00:43:02,140 --> 00:43:06,360
+ها هتسألي السؤال أنا بقول لك اه ممكن هاي مثال يوضح
+
+399
+00:43:06,360 --> 00:43:12,460
+أن هذا الكلام ممكن يبقى هذا كان سؤال اللي هو أربعة
+
+400
+00:43:12,460 --> 00:43:13,840
+وأربعين
+
+401
+00:43:16,470 --> 00:43:21,150
+سؤال 46 ستة
+
+402
+00:43:21,150 --> 00:43:29,050
+وأربعين بيقول لو كان جي a group والـ index بتابع
+
+403
+00:43:29,050 --> 00:43:36,070
+الـ G الـ index بتابع الـ G في الـ center بتابع الـ G
+
+404
+00:43:36,070 --> 00:43:44,410
+بده يساوي قداش أربعة وكذلك كان prove that prove
+
+405
+00:43:44,410 --> 00:43:54,010
+that برهلي أن الـ G موديولوسينتر بتبع الـ G ايزو
+
+406
+00:43:54,010 --> 00:44:03,570
+مورفك لمن؟ لـ Z2 external product مع من؟ مع Z2
+
+407
+00:44:36,980 --> 00:44:43,400
+خلّي بالقناة السؤال مرة ثانية بيقول الـ index تبع
+
+408
+00:44:43,400 --> 00:44:46,620
+الـ center في الـ group G هو أربعة يعني عندي كام
+
+409
+00:44:46,620 --> 00:44:51,200
+left coset؟ أربعة أ prove that أن الـ G موديل الـ
+
+410
+00:44:51,200 --> 00:44:56,380
+center isomorphic لـ Z2 external product مع مين؟ مع
+
+411
+00:44:56,380 --> 00:45:03,420
+Z2 الآن لما أجي أقول الـ order لـ Z of G بده يساوي
+
+412
+00:45:03,420 --> 00:45:11,120
+أربعة هذا معناته أن الـ order لـ جي موديولوس سنتر
+
+413
+00:45:11,120 --> 00:45:16,460
+بتابع الجي بده يساوي قداش؟ أربعة يبقى فيها أربعة
+
+414
+00:45:16,460 --> 00:45:24,300
+عناصر هذا معناه أن الجي موديولوس سنتر بتابع الجي
+
+415
+00:45:24,300 --> 00:45:31,800
+isomorphic يا إما لزد أربعة يا إما لزد اثنين
+
+416
+00:45:31,800 --> 00:45:37,610
+external product مع زد اثنين هذه فيها أربعة وهذه
+
+417
+00:45:37,610 --> 00:45:47,250
+فيها أربعة إذا هذه isomorphic لهذه أو لهذه كيف؟
+
+418
+00:45:47,250 --> 00:45:52,710
+يعني
+
+419
+00:45:52,710 --> 00:45:53,430
+زد أربعة
+
+420
+00:45:57,510 --> 00:46:01,710
+ماشي ماشي لكن أنت لما تيجي تبقى أزواج مرتبة مظبوط
+
+421
+00:46:01,710 --> 00:46:07,110
+يعني إيه؟ ما ينطبق عليها ينطبق علي Z4 صح ولا لا
+
+422
+00:46:07,110 --> 00:46:11,710
+حرفيا حتى لو حطيت الـ zero في الأول والـ Z في الآخر
+
+423
+00:46:11,710 --> 00:46:17,150
+أربعة نفسها يبقى هدول التنتين هادي وهادي فقط لغير
+
+424
+00:46:17,150 --> 00:46:22,110
+هادي isomorphic للـ Z4 كسينوديكا product مع الـ zero
+
+425
+00:46:22,110 --> 00:46:27,310
+و أثبتنا اصابق Robonormal قبل هيك كمان طيب يبقى يا
+
+426
+00:46:27,310 --> 00:46:31,750
+إما ايزومورفك لهذه ويا إما ايزومورفك لهذه لو
+
+427
+00:46:31,750 --> 00:46:38,010
+استبعدنا Z4 بصير ايزومورفك لمين؟ لـ Z2 external
+
+428
+00:46:38,010 --> 00:46:45,140
+product مع Z2 تعال نشوف هل ممكن نستبعد هذه والله
+
+429
+00:46:45,140 --> 00:46:51,080
+مش ممكن يعني بدي أستبعد أن الـ G modula Z تبقى
+
+430
+00:46:51,080 --> 00:46:55,600
+isomorphic لمين لـ Z أربعة والله ما احنا عارفين
+
+431
+00:46:55,600 --> 00:47:03,360
+نجرب يلا اقترح علينا نشوف إيش ممكن نسوي في هذه
+
+432
+00:47:05,650 --> 00:47:09,550
+يعني بدي أفترض أنها ماهياش isomorphic لزت اثنين
+
+433
+00:47:09,550 --> 00:47:12,410
+اكستران ضعية كبيرة لزت اثنين يبقى بيصير isomorphic
+
+434
+00:47:12,410 --> 00:47:19,150
+لمان لزت أربعة صحيح ولا لأ طيب بدنا نجي نشوف قداش
+
+435
+00:47:19,150 --> 00:47:25,350
+أو إيش ممكن نستنتج من هذا الكلام نشوف الكلام أن هذا
+
+436
+00:47:25,350 --> 00:47:34,590
+بيطلع صح ولا غلط طيب لو جيت قلت assume افترض أن
+
+437
+00:47:34,590 --> 00:47:40,930
+الـ G modulus center بتبع الـ G isomorphically زد
+
+438
+00:47:40,930 --> 00:47:45,750
+4 كويس؟
+
+439
+00:47:46,420 --> 00:47:52,160
+إذا عدد العناصر هنا بيساوي عدد العناصر هنا صحيح
+
+440
+00:47:52,160 --> 00:48:00,780
+ولا لا؟ طيب، الآن باجي بقوله إذا الـ order لمن؟ للـ
+
+441
+00:48:00,780 --> 00:48:08,060
+G modulo Z of G بيساوي الـ order للـ G على الـ order
+
+442
+00:48:08,060 --> 00:48:14,100
+للـ center بتابع الـ G قداش الـ order بتابع الـ G؟
+
+443
+00:48:22,080 --> 00:48:27,860
+كل الـ order لها يساوي أربعة هذا الكلام يعني كله
+
+444
+00:48:27,860 --> 00:48:31,460
+على بعض الـ order لها يساوي أربعة
+
+445
+00:48:33,420 --> 00:48:37,680
+يبقى هذا كل القيمة بتساوي أربعة يعني معنى هذا
+
+446
+00:48:37,680 --> 00:48:43,680
+الكلام أن الـ order لـ G اللي أنا مش عارفه على الـ
+
+447
+00:48:43,680 --> 00:48:50,280
+center بتابع الـ G الـ G هذي قال الـ order اه ما قالش
+
+448
+00:48:50,280 --> 00:48:56,160
+هذي G زد يعني كل اللي بدي أقوله أن الـ order لـ الـ
+
+449
+00:48:56,160 --> 00:49:04,810
+center اه مش عارفينه قد ايش استنى شوية استنى شوية طيب
+
+450
+00:49:04,810 --> 00:49:12,130
+احنا عندنا نظرية بتقول ما يأتي هذا الآن الـ G
+
+451
+00:49:12,130 --> 00:49:17,930
+modulus center يبقى isomorphic للـ inner تبع من؟
+
+452
+00:49:17,930 --> 00:49:24,710
+تبع الـ group G اللي عندنا صح؟ أخذنا نظرية اللي
+
+453
+00:49:24,710 --> 00:49:31,870
+توكننا من الحل عليها اللي هو الـ G-modulo الـ G
+
+454
+00:49:31,870 --> 00:49:35,690
+-modulo is center isomorphic للإنر أوتومورفزم
+
+455
+00:49:35,690 --> 00:49:41,150
+لمين؟ لـ G طيب على أي حال ايزال بدنا نحل هذا
+
+456
+00:49:41,150 --> 00:49:44,330
+السؤال وكمان سؤالين قادمات إن شاء الله
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4e155737178bdc6922b38e7d13613ed7726268cf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/oqLU1qa1owQ_postprocess.srt
@@ -0,0 +1,2120 @@
+1
+00:00:20,690 --> 00:00:26,090
+بسم الله الرحمن الرحيم نرجع ثانية إلى المحاضرة
+
+2
+00:00:26,090 --> 00:00:32,020
+الماضية و نكمل ما ابتدأنا به المرة الماضيةأخر حاجة
+
+3
+00:00:32,020 --> 00:00:36,520
+أعطناها المرة الماضية كان تعريف الـcentralizer لـ
+
+4
+00:00:36,520 --> 00:00:40,900
+element موجود في الـ group وعرفنا الـ centralizer
+
+5
+00:00:40,900 --> 00:00:44,960
+لـ element A الموجود في الـ group على إن كل الـ G
+
+6
+00:00:44,960 --> 00:00:50,620
+اللي موجودة في G بحيث GA يساوي AG مكتوب معاكم
+
+7
+00:00:50,620 --> 00:00:54,240
+المرة الماضية مش الجديد وحتى نص النظرية مكتوب
+
+8
+00:00:54,240 --> 00:00:57,380
+معاكم المرة الماضية يبقى حابيت أذكر لإنه بدنا نروح
+
+9
+00:00:57,380 --> 00:01:02,530
+نبرهن النظريةالنظرية بدنا نبرهن و نتابعها للمرة
+
+10
+00:01:02,530 --> 00:01:09,130
+القادمة يبقى الـcentralizer لـA هو كل العناصر اللي
+
+11
+00:01:09,130 --> 00:01:14,670
+موجودة في G و اللي بتبقى commutes مع A كل الـG
+
+12
+00:01:14,670 --> 00:01:20,320
+اللي موجودة في G بيعني الـG of A يساوي الـAGالان
+
+13
+00:01:20,320 --> 00:01:24,780
+بنا نثبت تبقى لهذه النظرية لو خت element A موجود
+
+14
+00:01:24,780 --> 00:01:29,300
+في ال group G بدي ال centralizer ل A يبقى بدي أثبت
+
+15
+00:01:29,300 --> 00:01:35,570
+ان ال centralizer ل A is a subgroup of G يعنيبدي
+
+16
+00:01:35,570 --> 00:01:39,430
+أحاول أثبت النقطتين تبعات الـ subgroup تبعات أول
+
+17
+00:01:39,430 --> 00:01:44,190
+نظرية وهو إن الـ centralizer لا A is non-empty
+
+18
+00:01:44,190 --> 00:01:48,130
+اتنين لو أخدت two elements في ال centralizer بدي
+
+19
+00:01:48,130 --> 00:01:51,970
+أحاول أثبت أن الأول في معكوس الثاني موجود في ال
+
+20
+00:01:51,970 --> 00:01:55,830
+centralizer لا A وبالتالي بيصبح ال centralizer لا
+
+21
+00:01:55,830 --> 00:02:02,500
+A is a subgroup of Gيبقى بيني ان انا اجي ال proof
+
+22
+00:02:02,500 --> 00:02:07,000
+اللي موجودة عندنا يبقى النقطة الأولى بدي اقوله ال
+
+23
+00:02:07,000 --> 00:02:14,400
+centralizer لإيه is non-empty non-empty ليش لإن
+
+24
+00:02:14,400 --> 00:02:19,940
+انا بدي احاول اجيبه ولو اللي هو element واحد موجود
+
+25
+00:02:19,940 --> 00:02:24,320
+في ال centralizer لإيه مشان ادلل على هذا الكلام
+
+26
+00:02:24,320 --> 00:02:28,800
+اللي عندي يبقى ال centralizer لإيه is non-empty
+
+27
+00:02:28,800 --> 00:02:37,700
+senseالـ E موجود في الـ centralizer لـ A شو السبب؟
+
+28
+00:02:37,700 --> 00:02:45,040
+because ان الـ E A بدر يساوي الـ A في الـ E ال
+
+29
+00:02:45,040 --> 00:02:49,380
+identity element لو ضربناه في أي element يبقى من
+
+30
+00:02:49,380 --> 00:02:52,680
+اليمين او من الشمال بطلع نفس ال element اللي هو
+
+31
+00:02:52,680 --> 00:02:56,540
+الـ A يبقى الـ E صارت موجودة في ال centralizer لـ
+
+32
+00:02:56,540 --> 00:03:00,120
+A يبقى ال centralizer لـ A is non-empty
+
+33
+00:03:04,840 --> 00:03:10,660
+عنصرين XY موجودة في الـ Centralizer لـ A
+
+34
+00:03:29,260 --> 00:03:34,560
+إذا بدي أحاول أستخدم خاصية الـcentralizer اللي ايه
+
+35
+00:03:34,560 --> 00:03:39,980
+اللي فوق لمين الـtwo elements x و y يبقى بناء عليه
+
+36
+00:03:39,980 --> 00:03:46,980
+بدي يصير x a بدي يساوي ax and اللي هو y a بدي
+
+37
+00:03:46,980 --> 00:03:52,800
+يساوي ay طبق اللي تعرف من الـcentralizer لإن أخد
+
+38
+00:03:52,800 --> 00:03:57,350
+two elements موجودات في الـcentralizerهذا هارجعله
+
+39
+00:03:57,350 --> 00:04:03,970
+بعد قليل هذا هحاول أستفيد منه مشان أستفيد منه بدي
+
+40
+00:04:03,970 --> 00:04:10,110
+أروح أضرب في A inverse من جهة الشمال و كذلك من جهة
+
+41
+00:04:10,110 --> 00:04:14,630
+اليمين إذا لو ضربنا من جهة الشمال في A inverse
+
+42
+00:04:14,630 --> 00:04:23,570
+بيصير عند A inverse YA بده يساوي Yماذا فعلت؟ ضربت
+
+43
+00:04:23,570 --> 00:04:29,350
+من جهة الشمال في مين في A inverse الان بادرح اضرب
+
+44
+00:04:29,350 --> 00:04:33,950
+في جهة اليامين برضه في ال A inverse مش الدرب
+
+45
+00:04:33,950 --> 00:04:36,950
+العادى اللى احنا عارفينه لما اقول اضرب يعني بدي
+
+46
+00:04:36,950 --> 00:04:40,870
+اطبق ال binary operation اللى موجودة على جهة ضرب
+
+47
+00:04:40,870 --> 00:04:45,580
+جمع الجسم المهم ال operation اللى موجودةيبقى هذا
+
+48
+00:04:45,580 --> 00:04:52,720
+بده يعطينا انه a inverse y يساوي y a inverse ضربنا
+
+49
+00:04:52,720 --> 00:04:57,680
+من جهة اليمين في مين في ال a inverse بصير عندي a a
+
+50
+00:04:57,680 --> 00:05:01,520
+inverse اللي هو بال identity بضلش الا ال element
+
+51
+00:05:01,520 --> 00:05:06,800
+هذا يبقى a inverse y بده يساوي y inverse ايش
+
+52
+00:05:06,800 --> 00:05:12,940
+تفسيركوا للعبارة الأخيرة اللي وصلنا لها ديلأ مش
+
+53
+00:05:12,940 --> 00:05:16,360
+هذا اللي بدنا نقوله لأ احنا أخدنا y في ال
+
+54
+00:05:16,360 --> 00:05:23,760
+centralizer ل a يعني طلع a y يسوى y a وصلنا إلى a
+
+55
+00:05:23,760 --> 00:05:30,500
+inverse y يسوى y a inverse يبقى ال y موجود في ال
+
+56
+00:05:30,500 --> 00:05:35,630
+centralizer ل a inverseيبقى بناء عليه لو كان الـ
+
+57
+00:05:35,630 --> 00:05:39,750
+Element موجود في الـ Centralizer لـ A هذا الـ
+
+58
+00:05:39,750 --> 00:05:44,470
+Element لازم يكون موجود في الـ Centralizer لمعكوس
+
+59
+00:05:44,470 --> 00:05:45,210
+الـ A
+
+60
+00:05:50,200 --> 00:05:54,980
+Y هذه I الموجودة في الـ Centralizer لـ A هذا معناه
+
+61
+00:05:54,980 --> 00:06:01,420
+أن Y موجودة في الـ Centralizer لـ A وبالتالي يصبح
+
+62
+00:06:01,420 --> 00:06:05,160
+الـ Centralizer لـ A الـ subset من الـ Centralizer
+
+63
+00:06:05,160 --> 00:06:08,560
+لـ A inverse دعوني أخبرك أن هناك سؤال في الكتاب
+
+64
+00:06:08,560 --> 00:06:11,580
+يقول أثبت أن الـ Centralizer لـ A
+
+65
+00:06:15,290 --> 00:06:20,370
+يبقى هذا نص البرهان والاتجاه التاني هو النص الثاني
+
+66
+00:06:20,370 --> 00:06:25,370
+لما نيجي لسؤال رقم عشرين او ما بعرف جد ايش المهم
+
+67
+00:06:26,570 --> 00:06:31,130
+يبقى تفسيرنا لهذه العبارة أنه إذا كان ال element
+
+68
+00:06:31,130 --> 00:06:36,890
+موجود في ال centralizer لإيه فإن هذا ال element
+
+69
+00:06:36,890 --> 00:06:41,930
+يكون موجود في ال centralizer لإيه inverse مجرد
+
+70
+00:06:41,930 --> 00:06:47,850
+استنتاج استنتجناه الآن بس مجرد إشارة شرط له لكن
+
+71
+00:06:47,850 --> 00:06:52,270
+لازم هنا مش لازم للكلام اللي أنا بقوله طيب انا ليش
+
+72
+00:06:52,270 --> 00:06:58,490
+اللي بدياه بدي ادي اخد الآناللي هو مين بده ياخد
+
+73
+00:06:58,490 --> 00:07:09,150
+الـ X Y inverse في مين؟ في الـ Aإذا قدرت أثبت أن
+
+74
+00:07:09,150 --> 00:07:14,770
+هذا يسوي الـA في الـXY inverse بتم المطلوب لأنه
+
+75
+00:07:14,770 --> 00:07:20,850
+بيصير الأول في معكوس الثاني إذا قدرت أثبت أن الـXY
+
+76
+00:07:20,850 --> 00:07:25,290
+inverse A يسوي الـA XY inverse بيصير ال element XY
+
+77
+00:07:25,290 --> 00:07:28,750
+inverse موجود في الـcentralizer لـA وبالتالي
+
+78
+00:07:28,750 --> 00:07:34,760
+الـcentralizer لـA بيصير subgroup طيب ممتاز جداأيش
+
+79
+00:07:34,760 --> 00:07:42,160
+رايك هذي بقدر اكتبها x y inverse a inverse inverse
+
+80
+00:07:42,160 --> 00:07:48,680
+خدناها قبل ذلك وبرهناهاطب ايش رأيك في الـ two
+
+81
+00:07:48,680 --> 00:07:54,860
+elements دول بدي اجمعهم ب inverse واحد بدي اخلّيهم
+
+82
+00:07:54,860 --> 00:07:58,460
+بدل ما في inverse و inverse بدي اخلّيهم inverse
+
+83
+00:07:58,460 --> 00:08:03,620
+واحد يبقى حسب معلوماتنا في الشبتر الماضي هذا بدي
+
+84
+00:08:03,620 --> 00:08:10,040
+يصير مين؟ بدي يصير a inverse while كل inverse
+
+85
+00:08:10,040 --> 00:08:18,170
+مظبوط؟طيب لكن ايش عندنا هنا احنا a inverse y هو
+
+86
+00:08:18,170 --> 00:08:22,750
+بواي a inverse يبقى بقدر اشيل a inverse y و احط
+
+87
+00:08:22,750 --> 00:08:28,230
+بدالها مين سميلي هذا على النقطة رقم واحد عشان
+
+88
+00:08:28,230 --> 00:08:34,870
+نستفيد منها يبقى هذا الكلام بده يساوي x y a
+
+89
+00:08:34,870 --> 00:08:42,400
+inverse لكل inverse هذا من وين from oneمن العلاقة
+
+90
+00:08:42,400 --> 00:08:48,670
+الأولى اللى عندناطيب ممتاز بدى افك ال inverse هذا
+
+91
+00:08:48,670 --> 00:08:54,110
+مرة تانية يبقى هذا ايش بيعطينا هذا بيعطينا هاي ال
+
+92
+00:08:54,110 --> 00:08:59,670
+X اللي برا وهذا بيعطينا A inverse inverse Y
+
+93
+00:08:59,670 --> 00:09:06,110
+inverse هذا بدي يعطينا X A Y inverse الشكل اللي
+
+94
+00:09:06,110 --> 00:09:11,870
+عندنا هنا لكن في معلومة حتى الآن لم نستفد منها شيء
+
+95
+00:09:11,870 --> 00:09:16,850
+المعلومة اللي هي المعلومة اللي عندنا هذهإن الـ X
+
+96
+00:09:16,850 --> 00:09:21,190
+موجود في الـ Centralizer لـ A مدام الـ X موجود
+
+97
+00:09:21,190 --> 00:09:26,310
+يبقى الـ X A بده يساوي A X إذا بنقدر نبدل الأثنين
+
+98
+00:09:26,310 --> 00:09:33,150
+هذول مكان بعض يبقى هذا الكلام بده يساوي A X Y
+
+99
+00:09:33,150 --> 00:09:38,670
+inverse ليش هذا الكلام؟ since ال X موجود في ال
+
+100
+00:09:38,670 --> 00:09:50,240
+Centralizer ل Aهذا الكلام سيصبح A X Y Inverseيبقى
+
+101
+00:09:50,240 --> 00:09:56,740
+انا بدأت هنا بال X Y inverse في A لقيته يسوى ال A
+
+102
+00:09:56,740 --> 00:10:01,400
+في ال X Y inverse ايش معنى هذا الكلام ان ال X Y
+
+103
+00:10:01,400 --> 00:10:06,400
+inverse موجود في ال centralizer ل A يبقى بدي بقوله
+
+104
+00:10:06,400 --> 00:10:13,440
+Sir ال X Y inverse belongs لل centralizer ل A يبقى
+
+105
+00:10:13,440 --> 00:10:17,940
+تحقق ال condition الأول تحقق ال condition التاني
+
+106
+00:10:17,940 --> 00:10:18,460
+by
+
+107
+00:10:25,940 --> 00:10:33,000
+بنظرية سابقة الـ Centralizer لـ A is a subgroup من
+
+108
+00:10:33,000 --> 00:10:40,310
+G وهو المطلوبيبقى الآن اثبتنا ان الـcentre للجروب
+
+109
+00:10:40,310 --> 00:10:45,590
+هو الـsubgroup واثبتنا الـcentralizer لأي element
+
+110
+00:10:45,590 --> 00:10:50,930
+كذلك هو subgroup من مين من الجروب الأساسية لحد هنا
+
+111
+00:10:50,930 --> 00:10:55,910
+stop انتهى الجزء النظري تبع ال section ننتقل الآن
+
+112
+00:10:55,910 --> 00:11:00,210
+إلى الأسئلة والمرة اللى فاتت اعطيتكوا أرقام
+
+113
+00:11:00,210 --> 00:11:01,330
+المسائل مش هيك
+
+114
+00:11:09,830 --> 00:11:16,450
+طبعا كان مطلوب من ضمن الأسئلة اول سؤال بيقول هاتلي
+
+115
+00:11:16,450 --> 00:11:21,330
+ال order لل group و ال order لكل element موجود في
+
+116
+00:11:21,330 --> 00:11:26,090
+ال group و ما شاء الله عليهم يعطينا خمس groups لكن
+
+117
+00:11:26,090 --> 00:11:29,930
+اول تنتهي انزلت اتناشوي و عشر هذه المحلولات معاك
+
+118
+00:11:29,930 --> 00:11:35,300
+كامثلةيبقى احنا ممكن نتعرض واحدة من ال TNT اللي هي
+
+119
+00:11:35,300 --> 00:11:39,860
+واطماشي ويه عشرين واحدة منهم اللي بدك إياها و دي
+
+120
+00:11:39,860 --> 00:11:47,860
+فار معانا مشكلة فيها يه عشرين يه عشرين يا سيني
+
+121
+00:11:47,860 --> 00:11:51,440
+يبقى
+
+122
+00:11:51,440 --> 00:11:57,340
+السؤال الأول يه عشرين من اللي قال بديه عشرين فيكون
+
+123
+00:11:57,340 --> 00:12:07,730
+شوفأنت طب اعطيني العناصر تبعك واحد ثلاثة سبعة تسعة
+
+124
+00:12:07,730 --> 00:12:09,090
+اتناشر
+
+125
+00:12:11,330 --> 00:12:17,290
+أربعة تاش، خمس تاش، ستة تاش، سبعة تاش، تمانتاش،
+
+126
+00:12:17,290 --> 00:12:22,150
+تسعة تاش الان واحد، اتنين، تلاتة، اربعة، خمسة،
+
+127
+00:12:22,150 --> 00:12:27,450
+ستة، سبعة، تمانية يبقى المطلوب الأول ال order ليه
+
+128
+00:12:27,450 --> 00:12:34,030
+عشرين هو قداش تمانية الان بدك ال order لكل element
+
+129
+00:12:34,030 --> 00:12:38,960
+موجود في ال groupعشان اقول ال order للواحد كده؟
+
+130
+00:12:38,960 --> 00:12:44,180
+واحد لإنه ال identity element بعدين اريد ال order
+
+131
+00:12:44,180 --> 00:12:48,440
+لثلاثة كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+132
+00:12:48,440 --> 00:12:48,680
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+133
+00:12:48,680 --> 00:12:53,360
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟
+
+134
+00:12:53,360 --> 00:12:56,830
+كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟ كده؟تلاتة
+
+135
+00:12:56,830 --> 00:13:04,010
+تربيع بتسعة موجود تلاتة في سبعة تلاتة اقصد تلاتة
+
+136
+00:13:04,010 --> 00:13:09,530
+تربيع تلاتة تكيب سبعة وعشرين شيل منهم بيضل قداش
+
+137
+00:13:09,530 --> 00:13:16,250
+سبعة في تلاتة بواحدة وعشرين اللي هو ال identity
+
+138
+00:13:16,250 --> 00:13:22,190
+يبقى قداش الأرض لتلاتة أربعة يبقى هذا الكلام طب
+
+139
+00:13:22,190 --> 00:13:23,770
+مين معكوس التلاتة؟
+
+140
+00:13:26,720 --> 00:13:31,080
+تلاتة بيبقى معكوسة من اللي لو ضربت فيها بطلع ال
+
+141
+00:13:31,080 --> 00:13:37,260
+identity يبقى ال order لسبعة كمان أربعة يبقى يساوي
+
+142
+00:13:37,260 --> 00:13:42,380
+ال order لسبعة اللي هو مين اللي هو أربعة طيب تعالى
+
+143
+00:13:42,380 --> 00:13:52,480
+تسعة قداش ال order إلها اتنين تلاتة اختلفت
+
+144
+00:13:52,480 --> 00:13:57,120
+الروايات هو تسعة في تسعة بقداشواقع تمانين شيل اربع
+
+145
+00:13:57,120 --> 00:14:03,180
+عشرينات بظل واحد يبقى ال order ل ستة اتنين يبقى ال
+
+146
+00:14:03,180 --> 00:14:08,680
+order لتسعة يساوي اتنين مين معكوس التسعة تسعة
+
+147
+00:14:08,680 --> 00:14:14,000
+نفسها صحيح يبقى خلاصنا بدي بعد هيك ال order لليحدى
+
+148
+00:14:14,000 --> 00:14:20,460
+هذا كمان يساوي ال order لليحدى عشان موافقين هيكمن
+
+149
+00:14:20,460 --> 00:14:25,480
+11 فى 11 مية واحد وعشرين شيل ست عشرينات بظل واحد
+
+150
+00:14:25,480 --> 00:14:31,960
+ال identity يبقى ال order الى يساوى اتنين التلتاشر
+
+151
+00:14:31,960 --> 00:14:35,000
+اريحك
+
+152
+00:14:35,000 --> 00:14:42,060
+شوية التلتاشر modulo عشرين لو اضفتلها سالب عشرين
+
+153
+00:14:42,060 --> 00:14:47,360
+بطلع جداشر يعني كانوا زى الشغل تبع سالب سبعة تمام
+
+154
+00:14:47,360 --> 00:14:53,870
+اذالما أقوله تلتاشر ترابية كأنه سالب سبعة ترابية
+
+155
+00:14:53,870 --> 00:15:00,330
+سالب سبعة ترابية مجداش تسعة واربعين يعني تسعة تسعة
+
+156
+00:15:00,330 --> 00:15:05,850
+فيه سالب سبعة اللي هو بسالب تلاتة وستين بيظل سالب
+
+157
+00:15:05,850 --> 00:15:09,690
+تلاتة تسعة سبعة بسالب واحد وعشرين يبقى ال order
+
+158
+00:15:09,690 --> 00:15:15,970
+أربعة تمام؟ يبقى كمان هذا بده يساوي ال order
+
+159
+00:15:15,970 --> 00:15:18,030
+لتلتاشر
+
+160
+00:15:20,900 --> 00:15:27,320
+و بالمثل ال order ل 17 و 19 بنفس الطريقة و أسهل
+
+161
+00:15:27,320 --> 00:15:32,960
+بصير لأن ال 17 مرة عن سالف تلاتة تمام؟ يبقى ال
+
+162
+00:15:32,960 --> 00:15:40,380
+order احنا بقداش؟ باربعةيبقى كمان هذا بده يساوي ال
+
+163
+00:15:40,380 --> 00:15:47,520
+order ل 17 ال 19 عبارة عن ايه؟ سالب واحد يبقى ال
+
+164
+00:15:47,520 --> 00:15:53,180
+order لها بس اتنين يبقى هذا بده يساوي ال order ل
+
+165
+00:15:53,180 --> 00:15:57,900
+19 خلصنا ماشي؟
+
+166
+00:15:57,900 --> 00:16:01,980
+طيب هاي خلصنا بالنسبة لل group الأولى نيجي لل
+
+167
+00:16:01,980 --> 00:16:04,860
+group التانية اللي هو D4
+
+168
+00:16:07,490 --> 00:16:21,470
+D4 عناصرها اللي هي R0 وR90 وR180 وR270 وH وV وD
+
+169
+00:16:21,470 --> 00:16:30,730
+وD' طبعا كتبنالكوا قبل ذلك ان R أس 4 تساوي R270
+
+170
+00:16:30,730 --> 00:16:36,570
+تساوي ال identity يعني لو مسكنهم بالدور هذا بده
+
+171
+00:16:36,570 --> 00:16:43,850
+يعطيكإن ال order ل دي four بده يسوي تمانية هنا ال
+
+172
+00:16:43,850 --> 00:16:49,670
+order لل R note بده يسوي واحد ال order لل R تسعين
+
+173
+00:16:49,670 --> 00:16:56,250
+هو ال order لمعكوسة R ميتين وسبعين هو أربعة الباقي
+
+174
+00:16:56,250 --> 00:17:02,310
+ال order ل R مية و تمانين هو ال order لل H هو ال
+
+175
+00:17:02,310 --> 00:17:07,980
+order لل Vهو ال order لديه هو ال order لديه prime
+
+176
+00:17:07,980 --> 00:17:12,120
+هو اتنين مش هالول قولنا كل واحد تربية بيعطينا ال
+
+177
+00:17:12,120 --> 00:17:17,440
+identity إذا ال order لهم يساوي اتنين يبقى كلام
+
+178
+00:17:17,440 --> 00:17:22,400
+كتبناه معاك سابقا مجرد تحصيل حاصل هذا بالنسبة
+
+179
+00:17:22,400 --> 00:17:27,440
+للسؤال الأول بالنسبة للسؤال الرابع بقول prove that
+
+180
+00:17:27,440 --> 00:17:31,840
+in any group an element and its inverse have the
+
+181
+00:17:31,840 --> 00:17:33,260
+same order
+
+182
+00:17:36,320 --> 00:17:44,000
+يبقى السؤال الرابع بيقول لي show ان ال order لل A
+
+183
+00:17:44,000 --> 00:17:51,160
+هو ال order لل A inverse شايف السؤال هكذا؟ طيب،
+
+184
+00:17:51,160 --> 00:17:58,060
+الان بدي افترض ان هذا ال order له رقم و هذا رقم
+
+185
+00:17:58,060 --> 00:18:05,760
+تاني و احاول اثبت ان الرقمين متساويان، تمام؟ فمثلا
+
+186
+00:18:06,190 --> 00:18:13,150
+لو قلت let ال order لل A بده يسوي ال N and ال
+
+187
+00:18:13,150 --> 00:18:21,970
+order لل A inverse بده يسوي ال M شوف
+
+188
+00:18:21,970 --> 00:18:30,030
+يا سيدالان بدي اضافه لـ A itself بدي اضافه كأس ل M
+
+189
+00:18:30,030 --> 00:18:35,230
+او بدي اضافه M أس له و بدي اذهب لل A inverse و
+
+190
+00:18:35,230 --> 00:18:40,490
+اضافه هذا الأس N و اشوف اين اتوجه الدنيا اذا انا
+
+191
+00:18:40,490 --> 00:18:50,060
+لو بدأت ب A inverse اللي هو أس Nيبجى هذا إيش معناه
+
+192
+00:18:50,060 --> 00:18:59,080
+أنه a أُس minus ال n مظبوط طيب هذا معناه a n
+
+193
+00:18:59,080 --> 00:19:07,710
+inverse طيب ال a n بجد إيش؟الـ Identity مش الـ
+
+194
+00:19:07,710 --> 00:19:13,210
+Order لـ A بده يسوي N يعني أقل عدد صحيح موجب بحط
+
+195
+00:19:13,210 --> 00:19:18,630
+أصل A بيعطيني الـ Identity اللي هو مين؟ N يبقى هذا
+
+196
+00:19:18,630 --> 00:19:24,650
+الكلام بده يسوي E inverse اللي هو مين؟ الـ E إيش
+
+197
+00:19:24,650 --> 00:19:30,470
+تفسيرك لهذا الكلام؟ إن الـ Order للـ A inverse يا
+
+198
+00:19:30,470 --> 00:19:37,150
+إما N يا إما أقل من الـ Nصحيح ولا لا؟ ليش؟ لأن أنا
+
+199
+00:19:37,150 --> 00:19:42,370
+بعرفش إن هذا هو أصغر رقم ولا فيه أصغر منه أنا
+
+200
+00:19:42,370 --> 00:19:47,550
+مفترض إن ال order لهذا main اللي هو M يبقى هذا
+
+201
+00:19:47,550 --> 00:19:53,670
+معناه إن ال order لل A inverse أقل من أو يسوى ال N
+
+202
+00:19:53,670 --> 00:20:01,760
+قد يكون ال N و قد يكون أقل منهطيب ال order ل A
+
+203
+00:20:01,760 --> 00:20:08,440
+inverse N عيش فرضه M يبقى صار ال M أقل من أو يسوى
+
+204
+00:20:08,440 --> 00:20:15,560
+ال N و دي المعادلة رقم واحد طيب تعالى شوف للتجاه
+
+205
+00:20:15,560 --> 00:20:22,060
+الثاني يبقى لو جيت برضه أخد ال A أس M
+
+206
+00:20:25,070 --> 00:20:31,670
+يعني انا حطيت الاص تبع ال A inverse لل A وحطيت ال
+
+207
+00:20:31,670 --> 00:20:37,230
+order تبع ال A لل A inverse وشوف وين بدنا نوصل
+
+208
+00:20:37,230 --> 00:20:44,590
+يبقى هذا الكلام بقدر اقول A inverse inverse كله اص
+
+209
+00:20:44,590 --> 00:20:48,270
+M او
+
+210
+00:20:48,270 --> 00:21:03,060
+ان شئتم فقولوا A inverse لسالب Mاو يساوي a-m لل a
+
+211
+00:21:03,060 --> 00:21:06,960
+inverse او
+
+212
+00:21:06,960 --> 00:21:19,920
+بقدر اقول a m a m يبقى
+
+213
+00:21:19,920 --> 00:21:30,020
+هذه a-m inverseيبقى هذه a m و هنا inverse و هنا
+
+214
+00:21:30,020 --> 00:21:38,620
+inverse تمام ال a m مابجدهش عند هنا ال a a لأ a
+
+215
+00:21:38,620 --> 00:21:44,940
+inverse m هذه استنى شوية استنى شوية هذه بدي اخليها
+
+216
+00:21:44,940 --> 00:21:51,160
+a inverse و هنا m تمام
+
+217
+00:21:51,760 --> 00:21:57,440
+يبقى هذا اللي بين جثيني بقداش بال identity يبقى
+
+218
+00:21:57,440 --> 00:22:04,060
+هذا يعطيني E inverse اللي هو بال E يبقى A لما رفعت
+
+219
+00:22:04,060 --> 00:22:10,660
+لل أس M اعطتني العدد E يبقى هذا معناته ايش ان ال
+
+220
+00:22:10,660 --> 00:22:18,700
+order لل A أقل من أو يسوى ال M طيب ال order ل A
+
+221
+00:22:18,700 --> 00:22:25,970
+جداش Nيبقى الان أقل من او يساوي الام وهذه المعادلة
+
+222
+00:22:25,970 --> 00:22:32,050
+رقام اتنين نرجع لمبادئ الرياضيات لما أثبت أن هذا
+
+223
+00:22:32,050 --> 00:22:37,670
+أقل من هذا و المقلوب صحيح ان أقل من هذا يبقى
+
+224
+00:22:37,670 --> 00:22:43,090
+معاناة اتنين ماله ا equal يبقى هنا باجي بقوله from
+
+225
+00:22:43,090 --> 00:22:52,150
+واحد andأتنين يبقى ال N بده يساوي ال M هذا معناته
+
+226
+00:22:52,150 --> 00:22:57,350
+ان ال order ل A بده يساوي ال order ل A inverse وهو
+
+227
+00:22:57,350 --> 00:22:58,070
+المطلوب
+
+228
+00:23:04,320 --> 00:23:09,480
+يبقى شباب في الجبرال هنا احنا بنحاول نستخدم كل
+
+229
+00:23:09,480 --> 00:23:15,220
+المعلومات اللي درسناها في مبادئ الرياضيات متى لازم
+
+230
+00:23:15,220 --> 00:23:20,480
+الأمر و أين بنلزم بنروح نستخدمها يبقى هذا كان
+
+231
+00:23:20,480 --> 00:23:27,840
+السؤال رقم أربع معانا الآن السؤال رقم ستة يبقى ستة
+
+232
+00:23:27,840 --> 00:23:36,100
+بيقول ايه element موجود في ال groupو A6 يساوي ال
+
+233
+00:23:36,100 --> 00:23:43,300
+identity element و what are the possible orders
+
+234
+00:23:43,300 --> 00:23:49,160
+for order A و قول لي ليش هذا بده يعطينا ان ال
+
+235
+00:23:49,160 --> 00:23:56,300
+order ل A الله أعلم بده
+
+236
+00:23:56,300 --> 00:24:04,160
+ال order ل A قد إيش ممكن يكون الله أعلمطيب الحين
+
+237
+00:24:04,160 --> 00:24:10,020
+قد يكون ال a هذا هو ال identity element بقدر أقول
+
+238
+00:24:10,020 --> 00:24:15,900
+ال order يساوي ستة؟ قد يكون لكن ماقدرش أكد بقولي
+
+239
+00:24:15,900 --> 00:24:22,840
+ما هي الاحتمالات الممكنة لل order تبع ال a شو
+
+240
+00:24:22,840 --> 00:24:27,470
+الاحتمالات الممكنة لل order تبع ال aبقول له يمكن
+
+241
+00:24:27,470 --> 00:24:31,810
+يكون الـA هو ال identity إليه إذا ال order لا يبقى
+
+242
+00:24:31,810 --> 00:24:38,170
+جديش واحد اتنين قد يكون ال order ل A هو اتنين
+
+243
+00:24:38,170 --> 00:24:41,510
+معقول
+
+244
+00:24:41,510 --> 00:24:46,830
+ولا لا بصير اتنين تكيب ال identity إذا الاحتمال
+
+245
+00:24:46,830 --> 00:24:53,810
+وارد قد يكون ال order ل A تلاتة وارد
+
+246
+00:24:54,210 --> 00:25:01,310
+قد يكون ال order لإيه؟ أربعة خمسة ممكن؟ غير ممكن
+
+247
+00:25:01,310 --> 00:25:07,590
+على الإطلاق يبقى بيظل ستة أغششك شغلة سنثبتها كمان
+
+248
+00:25:07,590 --> 00:25:14,990
+جدام شويةدائما و أبدا لو كان عندك order ل element
+
+249
+00:25:14,990 --> 00:25:20,670
+و اللي حطيت أس تاني ل ال element هذا طلع ال
+
+250
+00:25:20,670 --> 00:25:25,630
+identity لازم ال order ل ال element يقسم هذا الرقم
+
+251
+00:25:25,630 --> 00:25:32,750
+يعني كل الاحتمالات الممكنة هو divisor الست يبقى
+
+252
+00:25:32,750 --> 00:25:38,240
+بصير ال identity هو واحدوالـ A تربيع اللي هو اتنين
+
+253
+00:25:38,240 --> 00:25:41,940
+والـ A تكيب اللي هو تلاتة والـ A والستة يبقى
+
+254
+00:25:41,940 --> 00:25:45,520
+الواحد والاتنين والتلاتة والستة هما ال possible
+
+255
+00:25:45,520 --> 00:25:52,900
+orders فقط لا غير يبقى باجي بقوله هنا the possible
+
+256
+00:25:52,900 --> 00:26:03,540
+orders areواحد و اتنين و تلاتة و ستة only فقط
+
+257
+00:26:03,540 --> 00:26:08,660
+مافيش غيرهم يعني لا بقدر أقول أربعة ولا بقدر أقول
+
+258
+00:26:08,660 --> 00:26:15,140
+خمسة ولا غيره كل هذه الأرقام بستطيعش أقولها أبدا
+
+259
+00:26:35,110 --> 00:26:41,430
+طيب ننتقل لسؤال تمانية سؤال تمانية بيقول ال X
+
+260
+00:26:41,430 --> 00:26:52,070
+موجود في group G و X تربيع لا
+
+261
+00:26:52,070 --> 00:26:53,170
+يساوي
+
+262
+00:26:57,150 --> 00:27:01,590
+و X6 يساوي E
+
+263
+00:27:10,650 --> 00:27:16,910
+هذا بده يعطينا ان ال X أس أربعة لا يمكن أن تساوي
+
+264
+00:27:16,910 --> 00:27:25,990
+ال E and ال X أس خمسة لا يمكن أن تساوي ال identity
+
+265
+00:27:25,990 --> 00:27:30,930
+element what can you say about the order of X بدي
+
+266
+00:27:30,930 --> 00:27:35,890
+كمان ال order ل X يساوي جداش عندنا
+
+267
+00:27:41,670 --> 00:27:48,450
+الان المعطيات كالتالي هدول اتنين معطيات وهدول
+
+268
+00:27:48,450 --> 00:27:53,290
+التلاتة مطلوب يبقى انا بدي احاول استخدام المعطيات
+
+269
+00:27:53,290 --> 00:27:58,870
+بقدر الامكان مشان اوصل للمطلوب يبقى ال X تربيع لا
+
+270
+00:27:58,870 --> 00:28:03,270
+يمكن ان يساوي ال identity element السؤال هو هل
+
+271
+00:28:03,270 --> 00:28:08,800
+يمكن لل X ان يكون ال identity؟هو مستبعد تماما لأن
+
+272
+00:28:08,800 --> 00:28:12,560
+كل اندرز يبقى مربع ويعطينا ال identity وهذا مستبعد
+
+273
+00:28:12,560 --> 00:28:15,940
+يبقى استبعدنا ال identity element ان X يساوي ال
+
+274
+00:28:15,940 --> 00:28:20,100
+identity واستبعدنا كذلك ال X تربية يساوي مايعنى ال
+
+275
+00:28:20,100 --> 00:28:24,480
+identity يعطينا بعد ذلك ان X والستة يساوي ال
+
+276
+00:28:24,480 --> 00:28:30,400
+identity هل بقدر اقول ان ال order لل X يساوي 6لأ
+
+277
+00:28:30,400 --> 00:28:34,820
+طيب خلّي ال order للاخر بس نثبت هذو قاللي اثبتلي
+
+278
+00:28:34,820 --> 00:28:39,820
+ان ال X أص 4 لا يمكن أن يسوى ال identity ولا حتى
+
+279
+00:28:39,820 --> 00:28:45,180
+ال X أص 6 ولا ال X أص 5 بدت سوى ماين ال identity
+
+280
+00:28:45,180 --> 00:28:50,320
+درجة لطرق ال pros اللي اتعلمناها في مبادئ الرياضية
+
+281
+00:28:51,270 --> 00:28:54,930
+يا إما direct proof باخد المعطيات اللى عندى و امشي
+
+282
+00:28:54,930 --> 00:28:59,450
+بها مباشرة يا إما بمشي بال contradiction يا إما
+
+283
+00:28:59,450 --> 00:29:05,550
+بال contrapositive تمام الحين هو بقولي اثبت هذا طب
+
+284
+00:29:05,550 --> 00:29:11,070
+أنا بدي بدي أنفي هذا و لما أنفي هذا بدي أشوف
+
+285
+00:29:11,070 --> 00:29:16,030
+المسار هذا وين بدي يوصلني تمام يبقى بالدهجة أقوله
+
+286
+00:29:16,030 --> 00:29:16,570
+solution
+
+287
+00:29:21,500 --> 00:29:29,460
+assume أفترض أن X أُس 4 يسوى ال identity إذا قدني
+
+288
+00:29:29,460 --> 00:29:35,300
+هذا الكلام إلى تناقض معناته فرضي غلط وعكسه هو الصح
+
+289
+00:29:35,300 --> 00:29:44,160
+طيب then إيش رأيك لو قلت X أُس 4 تربيع مش يسوى ال
+
+290
+00:29:44,160 --> 00:29:49,260
+identity تربيع اللي هو بال identityطيب هذا معناه
+
+291
+00:29:49,260 --> 00:29:56,240
+ايه؟ معناته ان x أُس 8 يساوي ال identity طيب ال x
+
+292
+00:29:56,240 --> 00:30:01,820
+أُس 8 مش هي عبارة عن x أُس 6 في x تربيع يساوي ال
+
+293
+00:30:01,820 --> 00:30:09,030
+identity؟الـ X أُس 6 مُعطَى بالـ Identity في الـ X
+
+294
+00:30:09,030 --> 00:30:13,370
+تربيع بدّي يسوى الـ Identity هذا بدّي يعطيك إن X
+
+295
+00:30:13,370 --> 00:30:19,370
+تربيع بدّي يسوى الـ Identity يبقى سارة ناقم يبقى
+
+296
+00:30:19,370 --> 00:30:26,490
+this is contradict او contradiction
+
+297
+00:30:29,570 --> 00:30:36,910
+for الاكس تربية لا يسوى ال identity فردي
+
+298
+00:30:36,910 --> 00:30:44,350
+غلط وعكسه هو الصح يبقى so الاكس أُص أربعة لا يمكن
+
+299
+00:30:44,350 --> 00:30:49,950
+أن تسوى ال identity على الإطلاق هذا نفس الطريقة
+
+300
+00:31:14,130 --> 00:31:18,230
+يبقى الهدف اللي اتالج exercise
+
+301
+00:31:20,500 --> 00:31:26,020
+بعدها جالي هتل ال order لل X بقوله والله كويس الآن
+
+302
+00:31:26,020 --> 00:31:31,600
+ال X تربيه لا يسوى ال identity وال X أص أربعة لا
+
+303
+00:31:31,600 --> 00:31:35,300
+يسوى ال identity وال X أص خمسة لا يسوى ال identity
+
+304
+00:31:35,300 --> 00:31:38,380
+وال X أص ستة لا يسوى ال identity إذا ما هي
+
+305
+00:31:38,380 --> 00:31:43,310
+الاحتمالات الممكنة لل orderيا تلاتة يا ستة فيش
+
+306
+00:31:43,310 --> 00:31:47,070
+غيرهم حتى لو كان تلاتة بصير اكسته كيف يسوى ال
+
+307
+00:31:47,070 --> 00:31:51,570
+identity وبالتالي مربعه يسوى اكسه الستة اللي هو
+
+308
+00:31:51,570 --> 00:31:56,550
+بال identity وقلت لك قبل قليل ال order لل element
+
+309
+00:31:56,550 --> 00:32:02,010
+بجسم الرقم اللي بتحطه سبعتين من ال identity اذا
+
+310
+00:32:02,010 --> 00:32:05,390
+بجي بقوله the possible
+
+311
+00:32:07,960 --> 00:32:19,260
+orders for x is تلاتة or ستة غير هيك يبعتلك الله
+
+312
+00:32:19,260 --> 00:32:26,560
+طيب هذا كان السؤال رقم تمانية لبعض السؤال يحداش
+
+313
+00:32:26,560 --> 00:32:36,040
+show that يبقى احداش بيقوللي showthat ان ال U كده
+
+314
+00:32:36,040 --> 00:32:40,340
+اش عشرة ولا عشرين وانسة ولا احداشر بيقولي ان ال U
+
+315
+00:32:40,340 --> 00:32:52,080
+عشرين لا يمكن اني الاجيها تولد بعنصر واحد K و ال K
+
+316
+00:32:52,080 --> 00:32:59,940
+هذا for any K موجود في ال U عشرين for any K اللي
+
+317
+00:32:59,940 --> 00:33:01,600
+موجود في ال U عشرين
+
+318
+00:33:06,720 --> 00:33:11,420
+طيب الان بدي اعرف مين هي ال U عشرين بدي نقفها قبل
+
+319
+00:33:11,420 --> 00:33:16,960
+شوية و اماسحناها ال U عشرين قولنا هي واحد و تلاتة
+
+320
+00:33:16,960 --> 00:33:23,260
+و سبعة خمسة لا يا ابني انا سبعة و تسعة و الاحداشر
+
+321
+00:33:23,260 --> 00:33:29,780
+و تلتاشر و سبعة و تاشر و تسعة و تاشرأو حسبنا لهم
+
+322
+00:33:29,780 --> 00:33:35,540
+ال orders قبل قليل مظبوط ال order كان يا إما واحد
+
+323
+00:33:35,540 --> 00:33:41,080
+يا إما اتنين يا إما أربعة فى غير هي كده إذا أى
+
+324
+00:33:41,080 --> 00:33:45,660
+واحد أعلى أس بتحطهله اللى هو أربعة بيعطينا ال
+
+325
+00:33:45,660 --> 00:33:50,800
+identity element بعد ذلك يبقى اللى هدول كام واحد
+
+326
+00:33:50,800 --> 00:33:56,940
+هدول تمانية يعني ماعنديش ولا element ال order اللى
+
+327
+00:33:56,940 --> 00:34:01,830
+يسوى تمانيةلو كان ال order له تمانية فهو يجيب لي
+
+328
+00:34:01,830 --> 00:34:06,750
+كل عناصر ال group اللي عندنا هنا يبقى باجي بقول له
+
+329
+00:34:06,750 --> 00:34:14,150
+هذه ال U عشرين لا يمكن أن تساوي ال subgroup
+
+330
+00:34:14,150 --> 00:34:21,870
+generated by K والك موجود في U عشرين السبب because
+
+331
+00:34:21,870 --> 00:34:36,840
+any element inالـ U عشرين has ordered الهمان طب
+
+332
+00:34:36,840 --> 00:34:47,060
+أنا بقولك عمل هذا و هذا كيف ال U عشرين لا يساوي
+
+333
+00:34:47,060 --> 00:34:51,100
+صحيح يبقى ال U عشرين لا يساوي الكي والكي because
+
+334
+00:34:51,100 --> 00:34:56,540
+any element من عند كلمة because هذا هو البرهانيبقى
+
+335
+00:34:56,540 --> 00:35:02,140
+because any element in Uعشرين has order واحد او
+
+336
+00:35:02,140 --> 00:35:09,340
+اتنين او اربعة او اربعة غير هيك ماعنديش مشان ال
+
+337
+00:35:09,340 --> 00:35:13,920
+element يجيب ل group كلهامشان يجيب الجروب كلها و
+
+338
+00:35:13,920 --> 00:35:19,500
+تبقى Cyclic ال orders اللى بدك ترفع هنا بدي يكون
+
+339
+00:35:19,500 --> 00:35:23,880
+تمانية بدي يساوي ال order لل group مشان يجيب كل
+
+340
+00:35:23,880 --> 00:35:27,760
+عناصر ال group غير هيك بعتلك الله يعني زى ما شوفنا
+
+341
+00:35:27,760 --> 00:35:30,720
+توسعة كل واحد بيجيب ليها عنصر يعنصرين يعني أربع
+
+342
+00:35:30,720 --> 00:35:35,280
+عناصر بس لا يوجد element من ال Z20 بيجيب ليه كل
+
+343
+00:35:35,280 --> 00:35:40,380
+عناصر ال Z20 وبالتالي هذه لا يمكن أن تكون Cyclic
+
+344
+00:35:41,300 --> 00:35:46,280
+طيب روحنا الأن لخمستاش خمستاش بيقول الـH proper
+
+345
+00:35:46,280 --> 00:35:52,260
+subgroup من Z under addition تحت عملية الجامعة
+
+346
+00:35:52,260 --> 00:36:03,800
+يبقى سؤال خمستاش الـH subgroup من Z تحت عملية
+
+347
+00:36:03,800 --> 00:36:10,660
+الجامعة العادية under addition and الـH contains و
+
+348
+00:36:11,150 --> 00:36:20,170
+عند مين اتناشر وتلاتين واربعة وخمسين كلهم موجودات
+
+349
+00:36:20,170 --> 00:36:26,070
+هدول وين في ال H بيقولي what are the possibilities
+
+350
+00:36:26,070 --> 00:36:35,930
+for H ما هي إمكانيات ان ال H يكون شكلها ايه حد
+
+351
+00:36:35,930 --> 00:36:41,390
+فيكم بيقدر يجيبليأي شكل من أشكال H طبعا عدة أشكال
+
+352
+00:36:41,390 --> 00:36:46,090
+دي واحد يجيبلي بس شكل واحد السؤال مرة تانية أنا
+
+353
+00:36:46,090 --> 00:36:51,650
+عند مجموعة اللي أدد صحيحة ومعرف عليها الجامعة أخدت
+
+354
+00:36:51,650 --> 00:36:57,390
+H هذه ال sub group منها ال H لجيت فيها العناصر 12
+
+355
+00:36:57,390 --> 00:37:03,350
+و34 و50 بيقول لي احتمال H تكون mean هذه
+
+356
+00:37:07,670 --> 00:37:13,390
+يجب أن يتجمع كل واحد صفر صفر ممكن ال H تبقى zero
+
+357
+00:37:13,390 --> 00:37:17,250
+يعني ليه trivial subgroup لا يعني صفر واحد ممكن
+
+358
+00:37:17,250 --> 00:37:21,550
+تبقى صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+359
+00:37:21,550 --> 00:37:24,970
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+360
+00:37:24,970 --> 00:37:30,050
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+361
+00:37:30,050 --> 00:37:32,150
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر
+
+362
+00:37:32,150 --> 00:37:37,360
+صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفر صفطبعا
+
+363
+00:37:37,360 --> 00:37:42,180
+كتير بلاجة مش واحد و واحد ايه
+
+364
+00:37:42,180 --> 00:37:45,220
+التاجمة
+
+365
+00:37:45,220 --> 00:37:48,580
+هتجيبله معكوس كله لازم تجيبه تقدر تجيبلي واحدة
+
+366
+00:37:48,580 --> 00:37:56,840
+ايوة ستة تلاتة تلاتة ماشي طب و اتنين عملية جمع
+
+367
+00:37:56,840 --> 00:38:00,260
+اتنين اربعة ستة تمانية بتجي على التلاتين و تجي على
+
+368
+00:38:00,260 --> 00:38:05,140
+اربعة خمسين ولا لاطيب ممتاز طيب التلاتة تلاتة ستة
+
+369
+00:38:05,140 --> 00:38:07,760
+تسعة اطلع تجي على التلاتين والاربعة والخمسين الستة
+
+370
+00:38:07,760 --> 00:38:13,460
+كمان يعني ايش يعني كأن انا بجيب لجريس ال common
+
+371
+00:38:13,460 --> 00:38:19,600
+divisors ما بين التلاتين والاربعة والخمسين جيب
+
+372
+00:38:19,600 --> 00:38:23,920
+لجريس ال common مش لجريس كل ال common divisor كل
+
+373
+00:38:23,920 --> 00:38:28,880
+ال common divisor المشتركان بتلاقيهم هم تبعت من؟
+
+374
+00:38:29,090 --> 00:38:35,590
+يبقى هنا بقوله يبقى ال H بدها تساوي subgroup
+
+375
+00:38:35,590 --> 00:38:42,050
+generated by 2 4 6 8 10 12 14 30 32 34 لغاية توصل
+
+376
+00:38:42,050 --> 00:38:48,170
+ل 4 5 و تبقى ماشيوالاحتمال الاخر ممكن تكون الـ H
+
+377
+00:38:48,170 --> 00:38:52,590
+في يمين ال subgroup generated by 3 والاحتمال
+
+378
+00:38:52,590 --> 00:38:56,810
+الثالث تبقى ال subgroup generated by 6 كلها بتجيب
+
+379
+00:38:56,810 --> 00:39:03,730
+لثلاثة أرقام ما خل ذلكتلاقيش تمام فش .. إذا فضت
+
+380
+00:39:03,730 --> 00:39:07,710
+الستة إذا فضت ستة مافيش إمكانية بصير أكتر من
+
+381
+00:39:07,710 --> 00:39:12,650
+أطمعاش مرتين أين؟ لذلك ماعنديش إلا التلاتة هذول كل
+
+382
+00:39:12,650 --> 00:39:18,750
+الاحتمالات الممكنة لل cyclic subgroups اللي بدي
+
+383
+00:39:18,750 --> 00:39:22,630
+يكون العناصر التلاتة هذول موجودات فيها كيف؟ الواحد
+
+384
+00:39:22,630 --> 00:39:27,790
+الواحد بيجيبها يا راجل الجامعة الواحد أه بيجيبها
+
+385
+00:39:27,790 --> 00:39:34,950
+ليش ما ..بجيبها واحد و الواحد كمان زيادة على ذلك
+
+386
+00:39:34,950 --> 00:39:40,010
+لإن ال identity هنا هو ال zero والواحد برضه وال H
+
+387
+00:39:40,010 --> 00:39:45,810
+برضه احتمال يكون الواحد كل اللي بتجيبها تمام؟ لكن
+
+388
+00:39:45,810 --> 00:39:49,050
+أبسط الحاجة اتنين تلتة ستة هذه لأول واحد ال
+
+389
+00:39:49,050 --> 00:39:53,710
+divisor بيجيبوا كل الباقى لإن كل واحد من التلاتة
+
+390
+00:39:53,710 --> 00:39:59,010
+عبارة عن ال divisor مضروب في رقم بيجيبوا دغريو
+
+391
+00:39:59,010 --> 00:40:04,890
+الواحد اللي هي بتجيب الكل طيب الان
+
+392
+00:40:04,890 --> 00:40:11,070
+سؤال سبعتاش سؤال سبعتاش اه هذا very important لأن
+
+393
+00:40:11,070 --> 00:40:25,830
+في معلومة جديدة سؤال
+
+394
+00:40:25,830 --> 00:40:26,610
+سبعتاش
+
+395
+00:40:31,010 --> 00:40:37,430
+سؤال سبعتاشر يا شباب بيقول لأني divisor K of N
+
+396
+00:40:37,430 --> 00:40:49,630
+يبقى K بتقسم ال N ولات ال UKN هي من؟ هي كل العناصر
+
+397
+00:40:49,630 --> 00:40:57,920
+X اللي موجودة في ال UNبحيث ان
+
+398
+00:40:57,920 --> 00:41:06,320
+الـ x modulo k بده يساوي الواحدة الصحية بقول for
+
+399
+00:41:06,320 --> 00:41:10,480
+example بيعطيني u تلاتة تساوي كذا و u سبعة تساوي
+
+400
+00:41:10,480 --> 00:41:18,900
+كذا list the elements of
+
+401
+00:41:18,900 --> 00:41:22,100
+u
+
+402
+00:41:22,100 --> 00:41:31,630
+أربعة عشرينيو أربعة عشرين و يو خمسة عشرين يو خمسة
+
+403
+00:41:31,630 --> 00:41:41,330
+عشرين و يو خمسة تلاتين يو خمسة تلاتين و كذلك يو
+
+404
+00:41:41,330 --> 00:41:49,750
+عشرة تلاتين يو عشرة تلاتين هذا المطلوب الأول هذا
+
+405
+00:41:49,750 --> 00:41:55,960
+نمر ايه؟بعدها نمرة B بيقول prove that هذي ال sub
+
+406
+00:41:55,960 --> 00:42:06,160
+group نمرة B prove ان U KN sub group من ال UN وبعد
+
+407
+00:42:06,160 --> 00:42:15,420
+ذلك خد ال H نمرة C ال H تساوي كل العناصر X كل
+
+408
+00:42:15,420 --> 00:42:23,910
+العناصر X اللي موجودة في U عشرةبحيث ان ال X modulo
+
+409
+00:42:23,910 --> 00:42:29,090
+تلاتة تساوي واحد X modulo تلاتة تساوي واحد بيقول
+
+410
+00:42:29,090 --> 00:42:38,050
+هل ال H subgroup من عشرة ام لا is ال H subgroup من
+
+411
+00:42:38,050 --> 00:42:45,910
+U عشرة ام لا هي السؤال يبقى في عندي ثلاث نقاط بدي
+
+412
+00:42:45,910 --> 00:42:49,590
+ابدا مع كل نقطة من النقاط الثلاثة
+
+413
+00:43:08,860 --> 00:43:16,400
+عندي K تقسم ال N وعندي ال U K N كل العناصر اللي
+
+414
+00:43:16,400 --> 00:43:22,700
+موجود في U N اللي بتحقق X modulo K يساوي واحد يعني
+
+415
+00:43:22,700 --> 00:43:30,800
+الفرق ما بين ال X وما بين ال 1 هو مضاعفات ال Kبقول
+
+416
+00:43:30,800 --> 00:43:33,420
+لي هاتل ال elements طبعا هو ميعطيني تنتين و
+
+417
+00:43:33,420 --> 00:43:37,520
+حسبهملي و بعدين يقولي يلا احسب ال U أربع عشرين و
+
+418
+00:43:37,520 --> 00:43:41,720
+ال U خمسة عشرين و ال U خمسة تلاتين و ال U عشرة
+
+419
+00:43:41,720 --> 00:43:46,180
+تلاتين و ما إلى ذلك بقوله كويس اذا بدي اجي للنقطة
+
+420
+00:43:46,180 --> 00:43:50,520
+الأولى مشان هيك بدي اجيب له U عشرين في الأول لإن
+
+421
+00:43:50,520 --> 00:43:55,010
+الشغل بدي أكون عليهايبقى بدي اجي الى النقطة الاولى
+
+422
+00:43:55,010 --> 00:44:00,470
+بدي اجيب له U عشرين ودى حسبناها قبل قليل واحد
+
+423
+00:44:00,470 --> 00:44:07,930
+تلاتة سبعة تسعة احداشر تلاتاشر سبعتاشر تسعة تاشر
+
+424
+00:44:07,930 --> 00:44:12,190
+واحد اتنين تلاتة اربعة وكمان اربعة تمانية مظبوط
+
+425
+00:44:12,190 --> 00:44:18,610
+طيب الان بدي اجي اجيب له U اربعة عشرين يبقى U
+
+426
+00:44:18,610 --> 00:44:20,090
+اربعة
+
+427
+00:44:24,580 --> 00:44:32,400
+عشرين يساوي تعالى التعريف بيقول U K N كل اللي
+
+428
+00:44:32,400 --> 00:44:37,580
+موجودات في UN بحيث يكون الفرق بينها و بينها هو
+
+429
+00:44:37,580 --> 00:44:42,220
+مضاعفات ال K يبقى بدي أشوف الأرقام اللي عندي من
+
+430
+00:44:42,220 --> 00:44:47,340
+الفرق بينه و بين الواحد هو مضاعفات الأربعة طبعا
+
+431
+00:44:47,340 --> 00:44:51,760
+الواحد لأن الفرق بينهم Zero مضاعفات الأربعة طيب
+
+432
+00:44:51,760 --> 00:44:56,810
+هاي واحدالتلاتة اطرح من واحد وصير اتنين هي مضاعفات
+
+433
+00:44:56,810 --> 00:45:00,330
+الأربعة لأ السابعة اطرح من واحد ستة مضاعفات
+
+434
+00:45:00,330 --> 00:45:04,170
+الأربعة لأ تسعة اطرح من واحد بضل قداش تمانية
+
+435
+00:45:04,170 --> 00:45:10,030
+مضاعفات الأربعة يبقى هذه التسعة الان احداش انسى
+
+436
+00:45:10,030 --> 00:45:15,900
+تلتاش اه صحيحيبقى تلتاش اطرح منها واحد اتناش
+
+437
+00:45:15,900 --> 00:45:22,420
+مضاعفات الأربعة سبعتاش نفس القصة يبقى و السبعتاش و
+
+438
+00:45:22,420 --> 00:45:28,000
+التسعتاش بلاش منها تمام يبقى هذه U أربعة عشرين
+
+439
+00:45:28,000 --> 00:45:32,980
+جيبناها و بعدين قاللي هذه U خمسة عشرين النقطة
+
+440
+00:45:32,980 --> 00:45:41,100
+الثانية بدنا U خمسة عشرين و يساوي الواحد و نجي
+
+441
+00:45:41,100 --> 00:45:45,810
+ندورالواحد والاحداشر الواحد والاحداشر الواحد
+
+442
+00:45:45,810 --> 00:45:46,150
+الواحد الواحد الواحد الواحد الواحد الواحد الواحد
+
+443
+00:45:46,150 --> 00:45:47,430
+الواحد الواحد الواحد الواحد الواحد الواحد الواحد
+
+444
+00:45:47,430 --> 00:45:47,670
+الواحد الواحد الواحد الواحد الواحد الواحد الواحد
+
+445
+00:45:47,670 --> 00:45:51,070
+الواحد الواحد الواحد
+
+446
+00:45:51,070 --> 00:45:54,670
+الواحد
+
+447
+00:45:54,670 --> 00:45:55,190
+الواحد الواحد الواحد الواحد الواحد الواحد الواحد
+
+448
+00:45:55,190 --> 00:46:04,890
+الواحد الواحد الواحد الواحد الواحد الواحد الواحد
+
+449
+00:46:04,890 --> 00:46:08,450
+الواحد ال
+
+450
+00:46:09,610 --> 00:46:16,590
+و بعدين تمانية تسعة عشرة احداش تلتاش اربعتاش
+
+451
+00:46:16,590 --> 00:46:25,150
+خمستاش ستاش سبعتاش وحط تسعة عشر عشرين واحدة وعشرين
+
+452
+00:46:25,150 --> 00:46:30,530
+اتنين وعشرين تلاتة وعشرين اربعة وعشرين خمسة وعشرين
+
+453
+00:46:30,530 --> 00:46:36,730
+ستة وعشرين سبعة وعشرين تمانية وعشرين تسعة وعشرين
+
+454
+00:46:36,730 --> 00:46:41,210
+تبقى هذه جبت له U تلاتينقال لي هاتلي يو خمسة
+
+455
+00:46:41,210 --> 00:46:48,510
+تلاتين يو خمسة تلاتين يو ساوي الواحد منهم وبدأ
+
+456
+00:46:48,510 --> 00:46:57,270
+أروح أدور يبقى قداش احداش في غيرها اتناش، ستاش،
+
+457
+00:46:57,270 --> 00:47:01,370
+تمانتاش، اتنين وعشرين، تمانية وعشرين ولا واحدة
+
+458
+00:47:01,370 --> 00:47:05,250
+بتكسب على خمسة تمام؟ يبقى ماعنديش الا الواحد
+
+459
+00:47:05,250 --> 00:47:10,250
+والاحداشبعدها تقول ياتي يو عشرة تلاتين يو عشرة
+
+460
+00:47:10,250 --> 00:47:17,610
+تلاتين موجودة يو عشرة تلاتين اللي هي برضه واحد و
+
+461
+00:47:17,610 --> 00:47:19,070
+واحدة عشرة مافيش غير
+
+462
+00:47:22,780 --> 00:47:28,740
+هذه و هذه كلها مختلفة لكن النتيجة واحدة لكن كل
+
+463
+00:47:28,740 --> 00:47:35,380
+واحدة في موقع في set مختلفة عن التانية هذه يو خمسة
+
+464
+00:47:35,380 --> 00:47:40,420
+عشرين جزء من ال يو عشرين هذه يو خمسة تلاتين جزء من
+
+465
+00:47:40,420 --> 00:47:44,980
+ال يو تلاتين يو عشرة تلاتين جزء من ال يو تلاتين
+
+466
+00:47:45,220 --> 00:47:49,940
+يبقى بقدرش اقول انه هذه كل اللي بقدر اقوله انه هذه
+
+467
+00:47:49,940 --> 00:47:53,380
+ال subgroup هي ال subgroup هذه هذا بعد ما اثبتنا
+
+468
+00:47:53,380 --> 00:47:57,340
+subgroup لسه ما اثبتناش هذا احنا جيبنا لسه المطلوب
+
+469
+00:47:57,340 --> 00:48:01,180
+الاول المطلوب التالي يقول اثبتلي انه هذه ال
+
+470
+00:48:01,180 --> 00:48:09,580
+subgroup بقوله بصيفة باجلن امرميه اول شيء ال UKN
+
+471
+00:48:09,580 --> 00:48:15,900
+is non-emptyفيها العنصر زي ما انتشب و احنا بنحسب
+
+472
+00:48:15,900 --> 00:48:20,160
+كل واحد واحد واحد لإنه اطرح منه يصير مضعفة الرقم
+
+473
+00:48:20,160 --> 00:48:24,920
+اللي عندك مين مكان يكون UK is non-empty since
+
+474
+00:48:24,920 --> 00:48:28,940
+الواحد موجود في UKN
+
+475
+00:48:30,920 --> 00:48:38,460
+طيب الان بدي افترض هذه النقطة الاولى بدي اخد list
+
+476
+00:48:38,460 --> 00:48:46,280
+بدي اخد رقامين ال a مثلا او ال x و ال y موجودات في
+
+477
+00:48:46,280 --> 00:48:50,800
+ال UK then
+
+478
+00:48:50,800 --> 00:48:53,920
+ال
+
+479
+00:48:53,920 --> 00:49:02,990
+x modulo كيف بدي اسمه كده؟و ال y modulo k يسوى كم؟
+
+480
+00:49:02,990 --> 00:49:11,630
+كمان واحد طيب هذا معناه ايش؟ مش معناه ان ال x يسوى
+
+481
+00:49:11,630 --> 00:49:21,430
+q واحد k زائد واحد؟ مظبوط طيب و ال y اي q اتنين k
+
+482
+00:49:21,430 --> 00:49:29,030
+زائد واحد؟والـ Q1 موجودة في Z integer و الـ Q2
+
+483
+00:49:29,030 --> 00:49:34,990
+موجودة في Z integer طيب أنا بدي أشوف هل حاصل ضربهم
+
+484
+00:49:34,990 --> 00:49:41,750
+موجود في الـ U K ولا لأ بجي بقوله الآن بدي أخد ال
+
+485
+00:49:41,750 --> 00:49:51,450
+X في Y يساوي Q1 K زائد 1 في Q2 K زائد 1هذا سوف
+
+486
+00:49:51,450 --> 00:49:59,870
+يعطيك ان ال X Y يساوي نضرب يا شباب يبقى Q1 Q2 K
+
+487
+00:49:59,870 --> 00:50:11,990
+تربيع زائد Q1 K زائد Q2 K زائد واحد طيب هذا معناه
+
+488
+00:50:11,990 --> 00:50:17,990
+ان ال X Y يساوي شرايك هذول التلاتة بدي اخد منهم K
+
+489
+00:50:17,990 --> 00:50:24,380
+عامل مشتركيبقى لو أخد كي عمل مشترك بيصير كي واحد
+
+490
+00:50:24,380 --> 00:50:31,620
+اكي و اتنين كي زائد كي واحد زائد كي و اتنين في كي
+
+491
+00:50:31,620 --> 00:50:40,840
+زائد واحد ايش معنى هذا الكلام انه x y موجودة او ال
+
+492
+00:50:40,840 --> 00:50:49,360
+x y modulo k بدى يسوي جداشإذا هذا معناه ان ال X Y
+
+493
+00:50:49,360 --> 00:50:57,080
+موديولو K بدل سوى الواحد هذا معناه ان ال X Y موجود
+
+494
+00:50:57,080 --> 00:50:59,120
+في ال U KN
+
+495
+00:51:02,490 --> 00:51:07,690
+طب احنا الأصل نثبت الأول في معكوسي الثاني موجود
+
+496
+00:51:07,690 --> 00:51:11,690
+لكن هذا إذا بدنا النظرية الأولى لكن أخدنا نظرية
+
+497
+00:51:11,690 --> 00:51:17,930
+تانية السؤال هو هل ال UK infinite ولا ما هوش
+
+498
+00:51:17,930 --> 00:51:23,150
+finite finite لإن ال UN أصلا finite انت الحد ال N
+
+499
+00:51:23,150 --> 00:51:30,550
+ناقص واحد بتوقف تبقى باجي بقولهالان ال U K N is
+
+500
+00:51:30,550 --> 00:51:41,410
+finite السبب finite because ال U N is finite
+
+501
+00:51:44,370 --> 00:51:50,490
+طيب هى الست اللى أخدناها non-empty واحد اتنين
+
+502
+00:51:50,490 --> 00:51:54,310
+أخدته elements اللى جت حاصل ضرب الأول موجود فيها
+
+503
+00:51:54,310 --> 00:52:00,030
+تلاتة ال subset هذه مالها finite خلصنا مش في نظرية
+
+504
+00:52:00,030 --> 00:52:03,930
+بتقول هيك لأ non-empty finite subset و بكتابت
+
+505
+00:52:03,930 --> 00:52:06,430
+البيت لو أخدت عنصرين موجودات فيها أثبتنا يبقى
+
+506
+00:52:06,430 --> 00:52:12,030
+خلصنا يبقى بناء عليه ال UK is a subgroup يبقى بروح
+
+507
+00:52:12,030 --> 00:52:13,310
+بقوله bye
+
+508
+00:52:24,590 --> 00:52:34,000
+الـ UKN is a subgroup من من ال UNخلاص المطلوب بيه
+
+509
+00:52:34,000 --> 00:52:38,760
+بدنا نروح للمطلوب C المطلوب C بيقول ال X كل
+
+510
+00:52:38,760 --> 00:52:43,560
+العناصر اللي موجودة في عشرة في U عشرة اذا بدروح
+
+511
+00:52:43,560 --> 00:52:50,860
+احسب له من U عشرة عناصره ليه واحد وثلاثة وسبعة
+
+512
+00:52:50,860 --> 00:52:56,980
+وتسعة مظبوط هيك؟يبقى بيقول ال X اللى موجودة فيه
+
+513
+00:52:56,980 --> 00:53:03,340
+عشرة بحيث ال X modulo تلاتة بده ساوى مين بده ساوى
+
+514
+00:53:03,340 --> 00:53:09,480
+واحد طيب هذا بده يعطينا انه H تساوي الواحد منهم
+
+515
+00:53:10,050 --> 00:53:14,330
+اندور على التاني ثلاثة لو شيلنا واحد بيصير اتنين
+
+516
+00:53:14,330 --> 00:53:18,210
+ماهياش مضاعفات التلاتة سبعة شيلنا واحد بيصير ستة
+
+517
+00:53:18,210 --> 00:53:25,230
+اه سبعة منهم ستعة لأ هدئتش الان هل لئتش subgroup
+
+518
+00:53:25,230 --> 00:53:32,060
+ام لا قولوا الله أعلمتعالى شوف الواحد فشه مشكلة لو
+
+519
+00:53:32,060 --> 00:53:37,640
+ضربت السبعة في نفسه لو كانت ال subgroup السبعة
+
+520
+00:53:37,640 --> 00:53:42,620
+هيكون هو المعكوس لنفسه يعني السبعة تربيها بتعطيني
+
+521
+00:53:42,620 --> 00:53:48,120
+main ال identity element لكن سبعة في سبعة تسعة
+
+522
+00:53:48,120 --> 00:53:54,060
+واربعين شيل اربع عشرات بيظل تسعة هل التسعة هذا
+
+523
+00:53:54,060 --> 00:54:00,280
+موجود فيكش؟مش موجود في هاتش يبقى أخدت element في h
+
+524
+00:54:00,280 --> 00:54:04,460
+ضربته نفسي طوله يعني ال h is not closed under the
+
+525
+00:54:04,460 --> 00:54:10,340
+operation يبقى هل هذه subgroup يبقى هذا بده يعطيلك
+
+526
+00:54:10,340 --> 00:54:18,000
+ان ال h is not a subgroup من ال u عشرة من ال u
+
+527
+00:54:18,000 --> 00:54:19,060
+عشرة because
+
+528
+00:54:21,670 --> 00:54:33,690
+إن الـ H is not closed under the
+
+529
+00:54:33,690 --> 00:54:40,210
+operation on
+
+530
+00:54:40,210 --> 00:54:42,050
+ال U عشرة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..609878a3c2f33441b1b144b42e9dabee5aeb4cf1
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/rqvs3Awtmos_raw.srt
@@ -0,0 +1,2116 @@
+1
+00:00:20,990 --> 00:00:25,090
+بسم الله الرحمن الرحيم الان نبدأ في الموضوع اللي
+
+2
+00:00:25,090 --> 00:00:30,190
+أشارناه الصبح وهو ال chapter المقدمة اللي بتحدث عن
+
+3
+00:00:30,190 --> 00:00:35,210
+تذكير ببعض ما درس في مبادئ الرياضيات و اللي هنأسس
+
+4
+00:00:35,210 --> 00:00:40,850
+عليه دراستنا في علم algebra قبل أن نبدأ بأي نقطة
+
+5
+00:00:40,850 --> 00:00:45,230
+في هذا ال chapter بحب نذكر بمجموعة ال sets اللي
+
+6
+00:00:45,230 --> 00:00:49,350
+عليها بدنا نبني دراستنا ان شاء الله تبارك وتعالى
+
+7
+00:00:49,860 --> 00:00:55,140
+أول set من هذه ال sets يبقى مضاجي أقول اللي هو ال
+
+8
+00:00:55,140 --> 00:01:00,760
+sets المجموعات أول set من هذه ال sets اللي هو the
+
+9
+00:01:00,760 --> 00:01:04,560
+set of
+
+10
+00:01:04,560 --> 00:01:14,560
+natural numbers هذا هديها الرمز capital N
+
+11
+00:01:23,950 --> 00:01:33,190
+النقطة التانية هي the set ofIntegers مجموعة
+
+12
+00:01:33,190 --> 00:01:41,910
+الاعداد الصحيحة اللي هديها الرمز Z عناصرها هي نقط
+
+13
+00:01:41,910 --> 00:01:49,370
+سالب تلاتة سالب اتنين سالب واحد زيرو واحد اتنين
+
+14
+00:01:49,370 --> 00:01:56,070
+تلاتة الى اخرىيبقى مجموعة الأعداد الصحيحة الموجبة
+
+15
+00:01:56,070 --> 00:02:01,910
+والسالبة والصفر بنسميها the set of integers يبقى
+
+16
+00:02:01,910 --> 00:02:08,400
+اللي فوق أشهر بسميها شبابthe set of positive
+
+17
+00:02:08,400 --> 00:02:16,200
+integers يعني ممكن اقول هذه هي z plus z plus يبقى
+
+18
+00:02:16,200 --> 00:02:20,720
+the set of positive integers يعني معناته مجموعة
+
+19
+00:02:20,720 --> 00:02:26,360
+الأعداد الصحيحة الموجبة اللي بتاخد الأعداد من هنا
+
+20
+00:02:26,360 --> 00:02:34,720
+و لغاية الخلف تمام المجموعة التالتة the setof
+
+21
+00:02:34,720 --> 00:02:44,680
+rational numbers مجموعة الأعداد النسبية او مجموعة
+
+22
+00:02:44,680 --> 00:02:49,620
+الأعداد الجذرية هنديلها رمز و الرمز هذا هيظل معانا
+
+23
+00:02:49,620 --> 00:02:54,680
+موجود في الكتابة على طول الخط الرمز هذا كاب تالي
+
+24
+00:02:54,680 --> 00:03:00,910
+كيوEqually the set of all elements A على B such
+
+25
+00:03:00,910 --> 00:03:07,570
+that الـ A والـ B belongs to Z and وفي نفس الوقت
+
+26
+00:03:07,570 --> 00:03:13,310
+الـ B ممنوع تساوي Zero على الإطلاقلأن لو ال بيه
+
+27
+00:03:13,310 --> 00:03:19,470
+سوى Zero بصير إيه ماهياش معرفة يبقى كل الأعداد
+
+28
+00:03:19,470 --> 00:03:24,590
+اللي على الشكل أعلى بيه بحيث أهوا بأعداد صحيحة وفي
+
+29
+00:03:24,590 --> 00:03:30,910
+نفس الوقت بيه ممنوع يساوي Zero الست الرابع اللي هي
+
+30
+00:03:30,910 --> 00:03:36,150
+the set of real numbers
+
+31
+00:03:38,600 --> 00:03:44,020
+اللي هي مجموعة الأعداد الحقيقية يبقى لو جيت قولت
+
+32
+00:03:44,020 --> 00:03:50,220
+هذا ال real life يبقى هنا zero و هنا واحد و هنا
+
+33
+00:03:50,220 --> 00:03:55,240
+اتنين الاخره و سالب واحد سالب اتنين و الأعداد اللي
+
+34
+00:03:55,240 --> 00:04:01,010
+موجودة كذلك بينهماكل ال rational و ال irrational
+
+35
+00:04:01,010 --> 00:04:06,890
+number يعني ال set of real numbers هذه حديها الرمز
+
+36
+00:04:06,890 --> 00:04:12,330
+capital Rيبقى من حد ما نشوف capital R في الكتاب
+
+37
+00:04:12,330 --> 00:04:15,630
+اللي عندنا يبقى the set of real numbers مجموعة
+
+38
+00:04:15,630 --> 00:04:21,650
+الأعداد الحقيقية الصحيحة و غير الصحيحة نسبية و غير
+
+39
+00:04:21,650 --> 00:04:28,810
+النسبية بيجينا بعد هيك الأخيرة اللي هو the set of
+
+40
+00:04:28,810 --> 00:04:36,920
+complex numbers complex numbersمجموعة الأعداد
+
+41
+00:04:36,920 --> 00:04:43,240
+المركبة أو مجموعة الأعداد التخيلية يبقى هذه the
+
+42
+00:04:43,240 --> 00:04:51,500
+set of all elements a زائد bi بحيث أن ال a وال b
+
+43
+00:04:51,500 --> 00:04:58,660
+موجودة في R وفي نفس الوقت ال I يسوى الجذر التربيع
+
+44
+00:04:58,660 --> 00:05:05,360
+لمين لسالب واحديبقى بيان اقول زمان في الثانوية
+
+45
+00:05:05,360 --> 00:05:11,420
+العامة العدو الموركة بالـC زائد صاد T حيث T اللي
+
+46
+00:05:11,420 --> 00:05:16,800
+هو الحرف الأول من كلمة تخيلي واحنا هنا A زائد Bi
+
+47
+00:05:16,800 --> 00:05:23,840
+حيث I العدد للحرف الأول من كلمة imaginary تخيلي
+
+48
+00:05:23,840 --> 00:05:30,490
+تمام يبقى ال I هذا هو ال square root زمان-1 يبقى
+
+49
+00:05:30,490 --> 00:05:35,750
+هو الجدرى التربية إلى أمام لـ-1 إيش بتلاحظوا على
+
+50
+00:05:35,750 --> 00:05:40,930
+ال 6 الخمسة اللي عندنا هذه شو العلاقة بين N و Z
+
+51
+00:05:40,930 --> 00:05:49,490
+ده؟ممتاز يبقى N subset من Z طب Z ماعليك يوم subset
+
+52
+00:05:49,490 --> 00:05:56,330
+منها لإنه أي integer هو عبارة عن مين عبارة عن اللي
+
+53
+00:05:56,330 --> 00:06:01,950
+هو rational number زي ايش مثلا زي خمسة الخمسة بقدر
+
+54
+00:06:01,950 --> 00:06:06,530
+كتب خمسة على واحد يبقى صرت على الشكل A على B
+
+55
+00:06:06,530 --> 00:06:10,510
+الخمسة والواحد موجودة في Z والمقام لا يساوي Zero
+
+56
+00:06:10,510 --> 00:06:15,200
+اللي هو واحديبقى any integer is a rational number
+
+57
+00:06:15,200 --> 00:06:19,420
+but the converse is not necessarily true ليس
+
+58
+00:06:19,420 --> 00:06:26,160
+بالضرورة صحيحا بعد هيك ال Q هذا subset من R ولا لا
+
+59
+00:06:26,160 --> 00:06:31,820
+اي عدد نسبي هو عبارة عن عدد حقيقي لكن العكس ليس
+
+60
+00:06:31,820 --> 00:06:37,310
+بالضرورة صحيحا يعني مثلا زي جدر تلاتةعدد غير نسبي
+
+61
+00:06:37,310 --> 00:06:42,330
+هذا زي باي عدد غير نسبي زي العدد ايه اللي هو اتنين
+
+62
+00:06:42,330 --> 00:06:47,010
+وسبعة من حشرة وحط كصور إلى مال نهاية يبجي هذه كلها
+
+63
+00:06:47,010 --> 00:06:53,940
+أعداد irrational number أعداد غير نسبيةطيب الآن ال
+
+64
+00:06:53,940 --> 00:06:58,840
+R هي subset من مين؟ من ال 6 of complex numbers
+
+65
+00:06:58,840 --> 00:07:04,360
+يعني any real number is a complex number بس ال
+
+66
+00:07:04,360 --> 00:07:08,480
+converse is not necessarily true مثال و ذلك لو جيت
+
+67
+00:07:08,480 --> 00:07:09,580
+قولتلك نص
+
+68
+00:07:12,360 --> 00:07:18,960
+بقدر اكتب نص زائد زيرو في I يبقى النص وزيرو
+
+69
+00:07:18,960 --> 00:07:23,740
+موجودات في R وال I يسوى الجدر التربية إلى سالب
+
+70
+00:07:23,740 --> 00:07:30,510
+واحديبقى أي عدد حقيقي هو عدد تخيلي أو هو عدد مركب
+
+71
+00:07:30,510 --> 00:07:36,010
+لكن العكس ليس بالضرورة صحيحا يبقى بناء عليه بروح
+
+72
+00:07:36,010 --> 00:07:44,050
+بقوله ال N هذه هي subset من Z و Z هذه subset من ال
+
+73
+00:07:44,050 --> 00:07:51,610
+Q و ال Q subset من R و ال R subset من 6 of complex
+
+74
+00:07:51,610 --> 00:07:56,050
+numberيبقى هذه ما كتبناش رمزة بديها الرمز capital
+
+75
+00:07:56,050 --> 00:08:02,850
+من capital C يبقى N subset من Z, Z subset من ال Q,
+
+76
+00:08:02,990 --> 00:08:06,730
+ال Q subset من R, ال R subset من Z و complex
+
+77
+00:08:06,730 --> 00:08:12,680
+number كابتل Cيبقى هذه ال six الخامسة اللي وان ما
+
+78
+00:08:12,680 --> 00:08:16,400
+نيجي و احنا خلال دراستنا في الجبر بيطلعولك ال six
+
+79
+00:08:16,400 --> 00:08:21,060
+دول يطلع واحدة يطلع سنتين يطلع تلاتة في كل مرة
+
+80
+00:08:21,060 --> 00:08:25,340
+بتطلع بعض ال six اللي عندنا هذا بدنا نيجي ل مين
+
+81
+00:08:25,340 --> 00:08:29,320
+للف reporties of انتجارز
+
+82
+00:08:30,870 --> 00:08:36,410
+يبقى بدنا نيجي لأول definition عندنا هنا بالنسبة
+
+83
+00:08:36,410 --> 00:08:44,610
+لل integers فبجي بقول a non zero a non zero
+
+84
+00:08:44,610 --> 00:08:52,190
+integer a
+
+85
+00:08:52,190 --> 00:09:03,460
+non zero integer T is a divisoris a divisor of an
+
+86
+00:09:03,460 --> 00:09:23,060
+integer s if there is an integer u if there is an
+
+87
+00:09:23,060 --> 00:09:26,880
+integer u
+
+88
+00:09:29,260 --> 00:09:33,960
+such that
+
+89
+00:09:33,960 --> 00:09:47,580
+بحيث ان ال S بده يساوي T في ال U we
+
+90
+00:09:47,580 --> 00:09:56,680
+are right بروح نكتب ان T divides ال S
+
+91
+00:10:00,660 --> 00:10:07,440
+if T does
+
+92
+00:10:07,440 --> 00:10:21,010
+not divide ال S لو ال T مقسمتش ال S we writeبنروح
+
+93
+00:10:21,010 --> 00:10:30,850
+نكتب ان الـ T does not divide ال S definition تاني
+
+94
+00:10:30,850 --> 00:10:34,050
+a
+
+95
+00:10:34,050 --> 00:10:41,290
+prime number P is
+
+96
+00:10:41,290 --> 00:10:44,970
+a positive integer
+
+97
+00:10:50,690 --> 00:10:58,950
+integer greater than
+
+98
+00:10:58,950 --> 00:11:07,830
+one أكبر من الواحد الصحيح who's only
+
+99
+00:11:07,830 --> 00:11:12,350
+positive divisors are
+
+100
+00:11:19,590 --> 00:11:30,810
+اللي هو main one and be itself be itself ال
+
+101
+00:11:30,810 --> 00:11:37,670
+definition الثالث والأخير في هذه المجموعة an
+
+102
+00:11:37,670 --> 00:11:41,690
+integer S
+
+103
+00:11:41,690 --> 00:11:56,360
+is a multiplea multiple of is
+
+104
+00:11:56,360 --> 00:12:09,760
+a multiple of an integer T if there is if there is
+
+105
+00:12:09,760 --> 00:12:13,740
+if
+
+106
+00:12:13,740 --> 00:12:14,460
+there is
+
+107
+00:12:17,990 --> 00:12:32,950
+and integer U such that بحيث ان ال S بدها تساوي T
+
+108
+00:12:32,950 --> 00:12:33,690
+في ال U
+
+109
+00:12:55,300 --> 00:12:59,960
+هنا نجي لبعض الخواص على مين على مجموعة الأعداد
+
+110
+00:12:59,960 --> 00:13:05,020
+الصحيحة الثانية اللي هي المجموعة Z في عندنا three
+
+111
+00:13:05,020 --> 00:13:10,120
+definitions هذه three definitions أساسية لها ما
+
+112
+00:13:10,120 --> 00:13:16,630
+بعدها أثناء دراستنابنجي للتعريف الأول بدنا نعرف
+
+113
+00:13:16,630 --> 00:13:21,850
+العدد الذي يقسم عدد أخر شو معناه رياضيا التعريف
+
+114
+00:13:21,850 --> 00:13:25,890
+التاني بتكلم عن الأعداد الأولية التعريف التالف
+
+115
+00:13:25,890 --> 00:13:31,350
+يتكلم عن مضاعفات الأعداد اللي هو في شبه بينه بين
+
+116
+00:13:31,350 --> 00:13:36,680
+التعريف الأول إلى حد مافبجي بقول a non zero
+
+117
+00:13:36,680 --> 00:13:42,880
+integer T is a divisor of an integer S يبقى T وS
+
+118
+00:13:42,880 --> 00:13:50,760
+أعداد صحيحة يبقى كلهم موجودات في Z فبجي بقول T هو
+
+119
+00:13:50,760 --> 00:13:57,850
+قاسم للعدد S يعني بيقسم لعدد Sإذا جدرت انا لاجي
+
+120
+00:13:57,850 --> 00:14:01,870
+integer U
+
+121
+00:14:01,870 --> 00:14:10,030
+بحيث ان ال S بده يسوى من T في U يعني ال T بيقسم ال
+
+122
+00:14:10,030 --> 00:14:15,500
+Sإذا جدرت لاجي رقم تاني اضربه في T يطلع من؟ يطلع
+
+123
+00:14:15,500 --> 00:14:21,440
+ال S إن حدث ذلك بروح بكتب T تقسم ال S يبقى هذه
+
+124
+00:14:21,440 --> 00:14:29,410
+الإشارة معناها Divide يقسم هذه معناها Divideيبقى
+
+125
+00:14:29,410 --> 00:14:36,590
+هنا T قاسم ال S او T بيقسم ال S مثال و ذلك لو جهت
+
+126
+00:14:36,590 --> 00:14:45,410
+تقولك اربعة divide اللي هو من العشرين ليش؟ because
+
+127
+00:14:45,410 --> 00:14:49,390
+العشرين
+
+128
+00:14:49,390 --> 00:14:55,130
+هذه بدها تساوي اربعة في عدد تاني ابصرية تطلع من؟
+
+129
+00:14:55,130 --> 00:14:57,350
+من يطلع؟ خمسة
+
+130
+00:15:00,230 --> 00:15:04,030
+يبقى اربعة في خمسة تساوي كده؟ تساوي عشرين انا بدي
+
+131
+00:15:04,030 --> 00:15:07,250
+احط الخمسة بين قصين حتى ما تقوليش هذه اربعة و نص
+
+132
+00:15:07,250 --> 00:15:15,730
+لأ المقصود هنا ضرب تمام زي مثلا لو جيت قولتلك مثلا
+
+133
+00:15:15,730 --> 00:15:22,490
+ناقص تلاتين ناقص تلاتين او بديش اقول ناقص تلاتين
+
+134
+00:15:22,490 --> 00:15:32,540
+بدي اقول الستة divides ناقص تلاتينالستة تقسم ناقص
+
+135
+00:15:32,540 --> 00:15:41,700
+تلاتين لماذا؟ لأن ناقص تلاتين ساوي ستة أبصر في مين
+
+136
+00:15:41,700 --> 00:15:47,960
+ما هو الرقم اللي نرغب أن يكون في ستة سالب تلاتين
+
+137
+00:15:47,960 --> 00:15:55,150
+واضح أنه سالب خمسة كذلكطيب يبقى في هذه الحالة بروح
+
+138
+00:15:55,150 --> 00:16:02,610
+نكتب انه ستة بتقسم التلاتين لكن هل الستة بتقسم
+
+139
+00:16:02,610 --> 00:16:06,950
+مثلا اللي هو ستة وعشرين مثلا؟
+
+140
+00:16:09,690 --> 00:16:15,650
+تقسمه؟ لأ يبقى برف أكتب الستة لا تقسم اللي هو من
+
+141
+00:16:15,650 --> 00:16:21,470
+الستة وعشرين لإنه لا يمكن ألاقي انتجار عدد صحيح
+
+142
+00:16:21,470 --> 00:16:26,430
+أضربه في الستة يطلع الجواب قد ستة وعشرين مافيش
+
+143
+00:16:26,430 --> 00:16:29,310
+عندى بالمرة في هذه الحالة طيب
+
+144
+00:16:34,000 --> 00:16:38,960
+العدد الأول P هو عبارة عن positive integer greater
+
+145
+00:16:38,960 --> 00:16:43,780
+than one يبقى العدد الأول هو عدد الخصية الأولى
+
+146
+00:16:43,780 --> 00:16:48,900
+أكبر من الواحد الصحيحالخاصية الثانية بيقول who is
+
+147
+00:16:48,900 --> 00:16:54,820
+only positive divisors القواسم المشتركة لهذا العدد
+
+148
+00:16:54,820 --> 00:17:00,580
+الصحيح اتنين بس رقمين مين هما الواحد الصحيح هو
+
+149
+00:17:00,580 --> 00:17:06,660
+العدد في itself نفسه يبقى لا يوجد قواسم لهذا العدد
+
+150
+00:17:06,660 --> 00:17:12,000
+إلا العدد نفسه وكذلك مين الواحد الصحيح طيب ببناء
+
+151
+00:17:12,000 --> 00:17:17,880
+عليه هل اتنين يا شباب prime numberتنين عدد أولى؟
+
+152
+00:17:17,880 --> 00:17:23,060
+أه لأن هذا الصحية أكبر من الواحد الصحية و لا يقسم
+
+153
+00:17:23,060 --> 00:17:27,580
+إلا الواحد و الاتنين طب التلاتة prime number؟ أه
+
+154
+00:17:27,580 --> 00:17:31,060
+طب الأربعة؟ لأ ماهواش prime number لأن الأربعة
+
+155
+00:17:31,060 --> 00:17:35,300
+بتيجي اسمه اتنين غير حكاية الأربعة طب الخامسة؟
+
+156
+00:17:35,300 --> 00:17:42,790
+prime number؟ ستة؟ سبعة؟صحيح تمانية لأ تسعة لأ
+
+157
+00:17:42,790 --> 00:17:48,090
+برضه و لو انه فردي تمام يبقى ال prime number هم
+
+158
+00:17:48,090 --> 00:17:53,570
+واحد اتنين صحيح غلط الواحد لا استفد واحد لازم يكون
+
+159
+00:17:53,570 --> 00:17:58,140
+اكبر واحد يبقى ببدأ من ويمحط لي معلومتك ان اتنين
+
+160
+00:17:58,140 --> 00:18:03,860
+هو الرقم الزوجي الوحيد اللي هو prime number لو طلع
+
+161
+00:18:03,860 --> 00:18:08,040
+بعدك اربعة ستة تمانية كلها بتقسم على اتنين تمام
+
+162
+00:18:08,040 --> 00:18:11,540
+يبقى العدد الزوجي الوحيد اللي هو prime number
+
+163
+00:18:11,540 --> 00:18:16,040
+مافيش غير اتنين والباجي كلها اعداد فردية بس مش كل
+
+164
+00:18:16,040 --> 00:18:20,280
+الاعداد الفردية يبقى الاعداد ال prime number اتنين
+
+165
+00:18:20,280 --> 00:18:31,540
+تلاتة خمسة سبعة احداشر تلتاشرسبعتاش تسعتاش تلاتة و
+
+166
+00:18:31,540 --> 00:18:39,040
+عشرين تسعة و عشرين واحد و تلاتين و هكذا يبقى سبعة
+
+167
+00:18:39,040 --> 00:18:44,570
+و تلاتين يبقى كلها هذه ال numberيبقى العدد الأولي
+
+168
+00:18:44,570 --> 00:18:48,630
+هو العدد اللذي لا يقسم إلا على نفسه وعلى الواحد
+
+169
+00:18:48,630 --> 00:18:54,210
+الصحيح تمام؟ يبقى هادمين دير بالك هتلعب دور كبير
+
+170
+00:18:54,210 --> 00:18:58,010
+عندنا لما نخش على الشبطر التاني وشبطر ال groups
+
+171
+00:18:58,010 --> 00:19:03,570
+يبقى هنجيب groups الأعداد تبعها أعداد أولية دير
+
+172
+00:19:03,570 --> 00:19:08,250
+بالك يبقى صح صح من الآن هذه very important خلال
+
+173
+00:19:08,250 --> 00:19:14,960
+دراستنا طيبنجد تانية أن integer S is a multiple of
+
+174
+00:19:14,960 --> 00:19:23,160
+an integer T يبقى ال S هو مضاعفات العدد T وقت إذا
+
+175
+00:19:23,160 --> 00:19:28,480
+جدرت لاجي عدد تاني U بحيث ال S بدأ تسوى 100 T في U
+
+176
+00:19:28,480 --> 00:19:33,540
+أظن نفس الكلام اللي عندنا هنا صح ولا لا؟يبقى
+
+177
+00:19:33,540 --> 00:19:39,320
+مضاعفات الأعداد الـ
+
+178
+00:19:39,320 --> 00:19:45,860
+S ومضاعفات العدد T إذا قدرت ألجن تجارب U بحيث الـ
+
+179
+00:19:45,860 --> 00:19:46,060
+S
+
+180
+00:19:49,810 --> 00:19:55,010
+العشرين هو مضاعفات الأربعة، لماذا؟ لأن العشرين
+
+181
+00:19:55,010 --> 00:20:00,730
+سيكونوا أربعة في رقم كان الخمسة، العدد ناقص تلاتين
+
+182
+00:20:00,730 --> 00:20:05,810
+هو مضاعفات الستة، لماذا؟ لأن ناقص تلاتين هو ستة في
+
+183
+00:20:05,810 --> 00:20:10,070
+من؟ في ناقص خمسة، يبقى العدد يطلع موجة، والله سلم،
+
+184
+00:20:10,070 --> 00:20:14,770
+لا تفرج عندي، يبقى هذا معنى مضاعفات العدديبقى
+
+185
+00:20:14,770 --> 00:20:18,630
+المعادلة تبعت مضاعفات العدد والمعادلة تبعت القسم
+
+186
+00:20:18,630 --> 00:20:24,110
+التنتين زي بعض بس كل واحدة إلها مفهوم هنا T بتقسم
+
+187
+00:20:24,110 --> 00:20:29,550
+العدد S يعني إيش؟ يعني لو قسمت S على T الناتج هو
+
+188
+00:20:29,550 --> 00:20:37,070
+عدد صحيح اسمه U هنا ال S هو مضاعفات ال T إذا جدرت
+
+189
+00:20:37,070 --> 00:20:41,630
+ألاقي رقم تاني أضربه في T يطلع من عنده يطلع عند S
+
+190
+00:20:41,630 --> 00:20:50,200
+و هكذايبقى هذا المثال اللي عندنا طيب إيش رأيك؟ أي
+
+191
+00:20:50,200 --> 00:20:52,640
+عدد عندى بيقسم ال zero ولا لأ؟
+
+192
+00:20:55,840 --> 00:21:00,340
+الخمسين بتقسم Zero ولا لا؟ Zero على خمسين بتسوى
+
+193
+00:21:00,340 --> 00:21:06,240
+Zero إذا أي رقم عندي صحيح بيقسم مين؟ بيقسم Zero
+
+194
+00:21:06,240 --> 00:21:10,240
+صحيح ولا غير صحيح حتى لو كان real number لكن مادام
+
+195
+00:21:10,240 --> 00:21:15,300
+نتكلم في integers يبقى كلامنا على ال integers يبقى
+
+196
+00:21:15,300 --> 00:21:20,640
+اتنين هنا بقدر اقول every non zero integer every
+
+197
+00:21:20,640 --> 00:21:24,340
+non zero
+
+198
+00:21:26,530 --> 00:21:39,190
+integer وليكن n divides ال zero because السبب لإن
+
+199
+00:21:39,190 --> 00:21:48,010
+ال zero بده يساوي ال n في ال zero itself also
+
+200
+00:21:48,010 --> 00:22:01,540
+وكذلك ال واحد بيقسم ال nلش؟ because ال N تساوي
+
+201
+00:22:01,540 --> 00:22:16,020
+واحد ضرب ال N يعني
+
+202
+00:22:16,020 --> 00:22:19,500
+كل حاجة بنقدر نحطها على شكل المعادلة اللي عندنا
+
+203
+00:22:19,500 --> 00:22:23,360
+هذه و خلاص بيصير كلامنا صحيح
+
+204
+00:22:31,330 --> 00:22:35,710
+ننتقل إلى نقطة مهمة جدا و هي ال will ordering
+
+205
+00:22:35,710 --> 00:22:44,970
+principle حاجة اسمها ال will ordering principle
+
+206
+00:22:44,970 --> 00:22:50,670
+بتقول
+
+207
+00:22:50,670 --> 00:22:57,390
+ما ياتي every non zero every
+
+208
+00:22:57,390 --> 00:23:16,050
+non zero setof positive integers contains
+
+209
+00:23:16,050 --> 00:23:25,090
+a smallest member
+
+210
+00:23:39,830 --> 00:23:46,230
+قاعدة الترتيب الجيد لو
+
+211
+00:23:46,230 --> 00:23:52,250
+جينا قولنا بدنا ناخد set بس ال set هذي بيبقى non
+
+212
+00:23:52,250 --> 00:23:57,070
+-zero of positive integers يبقى انا بدي اعداد
+
+213
+00:23:57,070 --> 00:24:02,520
+صحيحة كلها موجبة ولا يوجد فيها صفرلو أخدت هذه
+
+214
+00:24:02,520 --> 00:24:07,440
+المجموعة مثلا لو جيت مجموعة الشباب اللي هنا جيت
+
+215
+00:24:07,440 --> 00:24:12,720
+أخدت أعمارهم بقيت ولا واحد عمره زي التاني وأخدتهم
+
+216
+00:24:12,720 --> 00:24:18,440
+مثلا بدي أخد شهور أو أيام أو سنين ليه السهولة بدي
+
+217
+00:24:18,440 --> 00:24:22,800
+أخد سنين طبعا كلهم نفس السنة تقريبا لكن أنا جدا
+
+218
+00:24:22,800 --> 00:24:26,840
+اللي بدي أسمي حالي لأ عمرهم مش زي بعض يبقى لجيت
+
+219
+00:24:26,840 --> 00:24:31,470
+واحد عمره مثلا اللي هو سبعتاشر سنةواحد تمانتاشر
+
+220
+00:24:31,470 --> 00:24:34,310
+سنة وواحد تسعة عشر سنة وواحد عشرين وواحد واتنين
+
+221
+00:24:34,310 --> 00:24:37,990
+وعشرين يبقى هذه المجموعة اللى خدتها لازم ألاقي
+
+222
+00:24:37,990 --> 00:24:44,310
+واحد فيهم عمره أقل ما يمكن بالنسبة لمين للآخرين
+
+223
+00:24:44,310 --> 00:24:47,470
+يبقى أي مجموعة من الأعداد تاخدها بالترتيب والله
+
+224
+00:24:47,470 --> 00:24:51,170
+عشوائي لو أخدت خمسين وثلاثاشر واربع وعشرين واتنين
+
+225
+00:24:51,170 --> 00:24:55,440
+وتلاتين وواحد وستين ومية وواحد وعشرينيبقى هذه
+
+226
+00:24:55,440 --> 00:24:59,000
+مجموعة الأرقام كلها non-zero انتجة لازم ألاقي واحد
+
+227
+00:24:59,000 --> 00:25:03,560
+فيهم بيكون أقل من باقي مين من باقي الأرقام هذه
+
+228
+00:25:03,560 --> 00:25:08,380
+الترتيب وبالتالي ممكن أرتبهم فعلا ترتيب جيد أو
+
+229
+00:25:08,380 --> 00:25:12,700
+ترتيب حسب واحد بعد التاني حسب الأقل من اللي بعده
+
+230
+00:25:12,700 --> 00:25:16,200
+اللي بعده أقل من اللي بعده اللي بعده أقل من مين من
+
+231
+00:25:16,200 --> 00:25:20,760
+اللي بعده يبقى هذه المقصود فيهاevery non-zero set
+
+232
+00:25:20,760 --> 00:25:24,020
+of positive integers contains a smallest member
+
+233
+00:25:24,020 --> 00:25:28,300
+يبقى فيها عوضه أو فيها عنصر بيكون ماله أقل ما يمكن
+
+234
+00:25:28,300 --> 00:25:34,380
+من نفسه لمهم للعناصر الأخرى ننتقل الآن لنقطة مهمة
+
+235
+00:25:34,380 --> 00:25:38,400
+جدا خلال دراستنا في الجابرة لزمان أكتر من اللي
+
+236
+00:25:38,400 --> 00:25:42,360
+قدامنا هذه كثيرة جدا اللي هي division algorithm
+
+237
+00:25:42,360 --> 00:25:48,740
+خوارزمية القسمةنشوف ايش بتقول و نعطي بعض التطبيقات
+
+238
+00:25:48,740 --> 00:25:56,320
+عليها يبقى بدنا نيجي لل division algorithm
+
+239
+00:25:56,320 --> 00:26:01,480
+خوارزمية
+
+240
+00:26:01,480 --> 00:26:10,660
+القسمة بتقول لمية الات ال a and ال b
+
+241
+00:26:34,100 --> 00:26:37,780
+يوجد ايونيك انتجار
+
+242
+00:26:45,640 --> 00:26:58,240
+a unique integers اللي هو Q and ال R Q and ال R
+
+243
+00:26:58,240 --> 00:27:02,540
+with property
+
+244
+00:27:02,540 --> 00:27:15,170
+ذات with property ذات ان ال Aبتساوي ال بي كيو زائد
+
+245
+00:27:15,170 --> 00:27:24,150
+ال R where حيث ال R أكبر من أو تساوي ال zero أقل
+
+246
+00:27:24,150 --> 00:27:34,870
+من مين و أقل من بي نقطة مهمة جدا هنا if ال بي
+
+247
+00:27:34,870 --> 00:27:47,720
+بتقسم ال a thenالـ R بدا تساوي Zero That is I N ال
+
+248
+00:27:47,720 --> 00:27:52,240
+A بدا تساوي BQ في هذه الحالة
+
+249
+00:28:29,960 --> 00:28:37,500
+كلمة خوارزمية منسوبة إلى مؤسس علم الجبر اللى هو
+
+250
+00:28:37,500 --> 00:28:43,620
+مين؟ إيش اسمه؟ مين؟ اسمه محمد بن موسى الخوارزمى
+
+251
+00:28:43,620 --> 00:28:49,080
+اللى عاش في العصر العباسى واللى وضع كثير من قوانين
+
+252
+00:28:49,080 --> 00:28:55,200
+رياضيات اللى تدرس من ذلك الوقت وإلى يومنا هذاخاصة
+
+253
+00:28:55,200 --> 00:29:00,100
+في calculus ايه وفي الجبر تبع التنمية والاعدادية
+
+254
+00:29:00,100 --> 00:29:04,440
+وفي الهندسة يعني اللي هو خاصة حساب المثلثات هذه
+
+255
+00:29:04,440 --> 00:29:08,960
+الجوا الجتا هو اول من وضعها في التاريخ يبقى لما
+
+256
+00:29:08,960 --> 00:29:12,240
+اقول division algorithm خوارزمية القسم اقول لو
+
+257
+00:29:12,240 --> 00:29:18,440
+اخدت اي عددين a وb بعد تبقى اعداد صحيحة وb دائما
+
+258
+00:29:18,440 --> 00:29:24,450
+وابدا مالهأكبر من الـ zero يبقى أخدت أعداد صحية ب
+
+259
+00:29:24,450 --> 00:29:29,250
+أكبر من ال zero هل اشترت a أكبر من ال zero ليس
+
+260
+00:29:29,250 --> 00:29:33,830
+بالضرورة ممكن يكون ال a بالسالم لكن بي بديها
+
+261
+00:29:33,830 --> 00:29:37,930
+بالموجة then there will exist a unique integers
+
+262
+00:29:37,930 --> 00:29:44,420
+هلاجي عددين وحيدين مافيش غيرهممرتبطين مع a وb كيف
+
+263
+00:29:44,420 --> 00:29:50,580
+اللي هم الخاصية التالية ان ال a تساوي b في ال q
+
+264
+00:29:50,580 --> 00:29:57,720
+يعني مضاعفات ال b زائد r حيث ر هذي اكبر من او
+
+265
+00:29:57,720 --> 00:30:03,840
+تساوي zero اقل من b لو ال r تساوي zero يبقى ايه
+
+266
+00:30:03,840 --> 00:30:10,350
+ايش بتساويB في Q صحيح ولا لأ الار تسوى Zero يبقى
+
+267
+00:30:10,350 --> 00:30:16,430
+ال A يسوى ال B في ال Q معناه هذا الكلام ان ال A هي
+
+268
+00:30:16,430 --> 00:30:24,240
+مضعفات من ال B او ال B تقسم من تقسم ال Aيبقى يا
+
+269
+00:30:24,240 --> 00:30:28,980
+شباب هذا ال condition ضروري جدا very important
+
+270
+00:30:28,980 --> 00:30:34,900
+دايما يا بده يساوي zero يا أكبر من zero إذا سوى
+
+271
+00:30:34,900 --> 00:30:40,380
+zero معناته ال B بتقسم ال A أو ال A هي مضاعفات ال
+
+272
+00:30:40,380 --> 00:30:47,060
+Bإذا كان الـ A الـ B لا تقسيم الـ A يبقى الـ R بدي
+
+273
+00:30:47,060 --> 00:30:52,260
+أخذ قيمة أكبر من الـ 0 لكن دائما و أبدا مالها أقل
+
+274
+00:30:52,260 --> 00:30:55,500
+من الـ B لأن لو سوى الـ B بصير الـ R بـ 0 على طول
+
+275
+00:30:55,500 --> 00:30:59,940
+الخط يبقى الـ R دائما و أبدا محصورة ما بين الـ 0 و
+
+276
+00:30:59,940 --> 00:31:05,280
+بين الـ B اليومين العدد الثاني اللي عندنا تمام؟
+
+277
+00:31:05,280 --> 00:31:09,820
+يبقى هذه خوارزمية القسمة نعطي أمثلة examples
+
+278
+00:31:13,630 --> 00:31:18,670
+أول مثال بدي أخد a برقم و أخد b برقم و نشوف كيف
+
+279
+00:31:18,670 --> 00:31:24,430
+نسوي خوارزمية القسمة لو كان مثلا ال a بده يساوي
+
+280
+00:31:24,430 --> 00:31:34,410
+تسعة عشر and ال b كان مثلا بده يساوي خمسة يبقى
+
+281
+00:31:34,410 --> 00:31:39,750
+باجي بقوله the division algorithm
+
+282
+00:31:46,430 --> 00:31:53,370
+التسعة عشر هذه بدى اكتبها بدلالة مين بدلالة الخمسة
+
+283
+00:31:53,370 --> 00:32:00,010
+يبقى هذه بده تساوي الخمسة مضروبة أبصر في مين زائد
+
+284
+00:32:00,010 --> 00:32:05,510
+رقم تاني السؤال هو هل الخمسة بتقسم التسعة عشرإذا
+
+285
+00:32:05,510 --> 00:32:09,470
+الـR اللي عندها لا يمكن أن تساوي 0 وإنما أكبر من
+
+286
+00:32:09,470 --> 00:32:17,270
+الـ0 أقل من الـB لخمسة ممتاز جدا يبقى خمسة في قداش
+
+287
+00:32:17,270 --> 00:32:22,850
+بده يطلع أقل من تسعة عشر خمسة في تلاتةيبقى خمسة في
+
+288
+00:32:22,850 --> 00:32:28,930
+تلاتة بخمستاشر يبقى اربعة يبقى بقوله زائد اربعة
+
+289
+00:32:28,930 --> 00:32:33,350
+والاربعة زي ما انتوا شايفين اكبر من او تساوي zero
+
+290
+00:32:33,350 --> 00:32:39,030
+اقل من المئة و اقل من الخمسة اللي عندنا يبقى ضروري
+
+291
+00:32:39,030 --> 00:32:45,010
+ينطبق الشرطين في قارن واحد مش ينطبق شرطه التاني لأ
+
+292
+00:32:45,010 --> 00:32:53,530
+نعطيك مثال اخر مثال اتنينمثال اتنين لو أخدت ال a
+
+293
+00:32:53,530 --> 00:33:01,130
+تساوي ناقص تسعة عشر and ال b تساوي تلتة على سبيل
+
+294
+00:33:01,130 --> 00:33:12,870
+المثال يبقى the division algorithm is
+
+295
+00:33:12,870 --> 00:33:16,070
+ناقص
+
+296
+00:33:16,070 --> 00:33:23,340
+تسعة عشربدو يساوي اللي هو تلاتة أبصر في قداش زاد
+
+297
+00:33:23,340 --> 00:33:28,840
+أبصر قداش بدي
+
+298
+00:33:28,840 --> 00:33:35,510
+ناقص سنتاشر تلاتة في قداش ممكن تعطينيسالب سبعة
+
+299
+00:33:35,510 --> 00:33:41,850
+سالب سبعة طيب لو قلت سالب سبعة يبقى بيصير قداش
+
+300
+00:33:41,850 --> 00:33:46,630
+سالب واحد وعشرين يبقى بدي اضيفلها قداش مشان يطلع
+
+301
+00:33:46,630 --> 00:33:53,670
+سالب تسعة عشر اتنين يبقى زائد اتنين والاتنين هذه
+
+302
+00:33:53,670 --> 00:34:00,770
+اكبر من او تساوي zero اقل من مين اقل من تلاتة طيب
+
+303
+00:34:01,270 --> 00:34:05,950
+هذا الكلام مئة بالمئة انطبقه الشرطين في آن المؤهد
+
+304
+00:34:05,950 --> 00:34:11,910
+يبقى بداجي اقوله ايش رايك في ناقص تسعة واطعش ها
+
+305
+00:34:11,910 --> 00:34:17,330
+ديها ناقص تسعة واطعش بدي اكتبها بدل ما اقول تلاتة
+
+306
+00:34:17,330 --> 00:34:24,470
+في ناقص سبعة بدي اقول تلاتة في ناقص ستة تلاتة في
+
+307
+00:34:24,470 --> 00:34:30,210
+ناقص ستة في قدر؟ الوصف عليه بتمانطعي زائد ناقص
+
+308
+00:34:30,210 --> 00:34:30,550
+واحد
+
+309
+00:34:33,520 --> 00:34:41,000
+مش هدول احنا بطلع سلب تسعة عشر بس يبقى هذه not
+
+310
+00:34:41,000 --> 00:34:46,760
+division يبقى
+
+311
+00:34:46,760 --> 00:34:51,360
+كتاب اللي هنا but ولكن نقص تسعة ونصف division
+
+312
+00:34:51,360 --> 00:35:01,050
+algorithm السبب becauseايوة شو اللي اختل عندى
+
+313
+00:35:01,050 --> 00:35:07,630
+السالب واحد السالب واحد هذا ماهواش اكبر من او
+
+314
+00:35:07,630 --> 00:35:15,300
+يساوي zero لكن فعلا اقل من تلاتةمظبوط أقل من تلاتة
+
+315
+00:35:15,300 --> 00:35:20,780
+صحيح لكن سالب واحد ماهواش أكبر من سوى Zero وإنما
+
+316
+00:35:20,780 --> 00:35:27,540
+أقل من Zero إذا صارت تناقض لهذه الخاصية مع مين؟ مع
+
+317
+00:35:27,540 --> 00:35:32,300
+الخاصية اللي عندنا هذه تمام؟ يبقى هذه الأولى
+
+318
+00:35:32,300 --> 00:35:36,510
+الصحيحة والتانية مالها؟هذه خطأ ليست division
+
+319
+00:35:36,510 --> 00:35:41,610
+algorithm يعني يا شباب الزيادة لازم تكون بإشارة
+
+320
+00:35:41,610 --> 00:35:47,010
+موجبة وليست بإشارة سلبة ديربالك من النقطة هذه اللي
+
+321
+00:35:47,010 --> 00:35:50,770
+عندنا طيب بدنا نيجي لحاجة اسم ال greatest common
+
+322
+00:35:50,770 --> 00:35:57,690
+divisor definition the greatest common divisor the
+
+323
+00:35:57,690 --> 00:36:01,970
+greatest common
+
+324
+00:36:03,320 --> 00:36:16,100
+divisor القاسم المشترك الأعظم you
+
+325
+00:36:16,100 --> 00:36:24,840
+got the greatest common divisor of two non-zero
+
+326
+00:36:24,840 --> 00:36:26,560
+integers
+
+327
+00:36:38,640 --> 00:36:46,300
+is the largest
+
+328
+00:36:46,300 --> 00:37:00,580
+of all common divisors of all common divisors of
+
+329
+00:37:01,740 --> 00:37:13,560
+الـ A and ال B and denoted by هنعطيهم
+
+330
+00:37:13,560 --> 00:37:24,800
+الرمز GCD للـ A و ال B when
+
+331
+00:37:24,800 --> 00:37:27,840
+عندما
+
+332
+00:37:29,150 --> 00:37:34,250
+the greatest common divisor لل A والB يبدو يساوي
+
+333
+00:37:34,250 --> 00:37:45,370
+واحد we say that .. we say that بروح نقول ان ال A
+
+334
+00:37:45,370 --> 00:37:54,310
+and ال B are relatively prime
+
+335
+00:37:58,290 --> 00:38:03,070
+relatively prime examples
+
+336
+00:38:22,960 --> 00:38:27,360
+طبعا هنا عندي شغلتين الشغلة الأولى الجريس ال
+
+337
+00:38:27,360 --> 00:38:30,900
+common divisor الشغلة التانية لو كجريس ال common
+
+338
+00:38:30,900 --> 00:38:37,760
+divisor يساوي واحد شو تسمي هذه؟تعريف الأول بقول
+
+339
+00:38:37,760 --> 00:38:42,360
+the greatest common divisors القاسم المشترك الأعظم
+
+340
+00:38:42,360 --> 00:38:47,460
+divisor قاسم common مشترك greatest اللي هو الأكبر
+
+341
+00:38:47,460 --> 00:38:51,520
+أو الأعظم يبقى القاسم المشترك الأعظم of two non
+
+342
+00:38:51,520 --> 00:38:57,440
+zero integers لعددين صحيحين غير صفريين a و b is
+
+343
+00:38:57,440 --> 00:39:03,500
+the largest أكبر واحد of all common divisors of a
+
+344
+00:39:03,500 --> 00:39:08,720
+and bيعني انا عندي رقامين لقيت رقم بيقسم لإثنين
+
+345
+00:39:08,720 --> 00:39:12,260
+لقيت كمان رقم بيقسم لإثنين لقيت كمان رقم .. لقيت
+
+346
+00:39:12,260 --> 00:39:16,780
+كمان رقم بيقسم لإثنين أكبر واحد في هدول القواسم
+
+347
+00:39:16,780 --> 00:39:21,160
+بسميهمين الـ greatest common divisor و هعطيله
+
+348
+00:39:21,160 --> 00:39:28,660
+الرمز GCDG greatest C جاء من common with B divisor
+
+349
+00:39:28,840 --> 00:39:31,860
+يبقى بدل ما أقول الـ greatest common divisor
+
+350
+00:39:31,860 --> 00:39:37,820
+هأختصرهم إلى مين الثلاثة أحرف و أحط العددين A وB
+
+351
+00:39:37,820 --> 00:39:43,060
+تمام تمام يبقى ال greatest common divisor هو أكبر
+
+352
+00:39:43,060 --> 00:39:48,540
+قاسم للعددين يعني عندي عدة قواسم للعددين أكبر واحد
+
+353
+00:39:48,540 --> 00:39:53,420
+فيهم بسميه ال greatest common divisor ممكن يحصل أن
+
+354
+00:39:53,420 --> 00:39:56,380
+ال greatest common divisor بين العددين يكون
+
+355
+00:39:56,380 --> 00:40:02,490
+ماعنديش إلا مينإلا الواحد الصحيح إن حدث ذلك بقول
+
+356
+00:40:02,490 --> 00:40:09,750
+يبقى العددين a وb are relatively prime طيب كلمة
+
+357
+00:40:09,750 --> 00:40:14,510
+relatively prime يعني prime عدد أولي بس relatively
+
+358
+00:40:14,510 --> 00:40:19,960
+يعني نسبييعني اتنين الـprimes بالنسبة لبعض مش
+
+359
+00:40:19,960 --> 00:40:24,640
+اتنين الـprimes اكيد العدد هذا والعدد هذا يعتبر
+
+360
+00:40:24,640 --> 00:40:29,840
+بالنسبة لبعض الـprimes هي المقصود فيها مش كل واحد
+
+361
+00:40:29,840 --> 00:40:35,600
+فيهم لازم يكون الـprime لأ ليس بالضرورة تمام نعطي
+
+362
+00:40:35,600 --> 00:40:40,540
+توضيح لكل واحد من الكلام اللي عندنا هذا بأمثلة
+
+363
+00:40:40,540 --> 00:40:48,620
+عدديةالان لو جيت قولتلك خلط ال a تساوي مثلا ستاش
+
+364
+00:40:48,620 --> 00:40:58,240
+and ال b تساوي الأربعة و عشرين then الواحد divide
+
+365
+00:40:58,240 --> 00:41:01,580
+الستاش
+
+366
+00:41:01,580 --> 00:41:07,380
+and الأربعة و عشرين صح ولا لأ؟ ايش بيجي بعد الواحد
+
+367
+00:41:07,380 --> 00:41:13,970
+بيقسم اتنين؟ اتنينإتنين الـ device الستاش و
+
+368
+00:41:13,970 --> 00:41:21,830
+الأربعة و عشرين بعد إتنين التلاتة لأ الأربعة بتقسم
+
+369
+00:41:21,830 --> 00:41:29,790
+الستاش و الأربعة و عشرين الخامسة الستة السبعة
+
+370
+00:41:29,790 --> 00:41:40,650
+التمانية آه تمانيةبتقسم ال 16 و كذلك ال 24 في اكتر
+
+371
+00:41:40,650 --> 00:41:45,650
+من هيك فشل لإنه تمانية هو نص العدد 16 من حد ما
+
+372
+00:41:45,650 --> 00:41:50,250
+توصل لنص العدد stop بوجة تمشيش ولا خطوة قدام لإنه
+
+373
+00:41:50,250 --> 00:41:54,050
+إذا زاد عن نصف لا يمكن أن يقسم العدد و يطلع عنده
+
+374
+00:41:54,050 --> 00:42:01,650
+عدد صحيح يبجأ كم قاسم صار عنده هنااربع اكبر واحد
+
+375
+00:42:01,650 --> 00:42:05,450
+فيهم بيقول هو الجريس ال common divisor يبقى الجريس
+
+376
+00:42:05,450 --> 00:42:08,390
+ال common divisor للستاشر والاربع عشرين مين هو
+
+377
+00:42:08,390 --> 00:42:14,650
+تمانية من هذا الكلام بقدر اقول يبقى الجريس ال
+
+378
+00:42:14,650 --> 00:42:20,710
+common divisor للستاشر والاربع عشرين هو العدد مين؟
+
+379
+00:42:20,710 --> 00:42:28,190
+العدد تمانية طيب هذا المثال الأول بدأجي لمثال ثاني
+
+380
+00:42:29,950 --> 00:42:34,790
+بدي أجيبلك على حكاية إيه relatively prime لو جيت
+
+381
+00:42:34,790 --> 00:42:41,430
+قولتلك الآن ل greatest common divisor لتلاتة وسبعة
+
+382
+00:42:41,430 --> 00:42:49,810
+قد إيش؟في غيره؟ في غيره؟ لأ يبقى هذا يساوي الواحد
+
+383
+00:42:49,810 --> 00:42:58,910
+because التلاتة and السبعة are primes مش
+
+384
+00:42:58,910 --> 00:43:05,930
+relatively primes تمام؟ but ولكن ال aggressives
+
+385
+00:43:05,930 --> 00:43:12,650
+common divisors للأربعة والسبعة مثلا كدهش؟في شغيره
+
+386
+00:43:12,650 --> 00:43:17,410
+هو الواحد الوحيد اللي بيقسم العددين الاتنين هدول
+
+387
+00:43:17,410 --> 00:43:22,330
+يبقى يساوي واحد هل الأربعة prime number لكن
+
+388
+00:43:22,330 --> 00:43:26,010
+الأربعة والسبعة بالنسبة لبعض يعتبروا ايش prime
+
+389
+00:43:26,010 --> 00:43:33,960
+يبقى are relatively prime يبقى هنا becauseالسبعة
+
+390
+00:43:33,960 --> 00:43:39,640
+and الأربعة are والله الأربعة and السبعة خلينا
+
+391
+00:43:39,640 --> 00:43:45,820
+بالترتيب ماشيين and السبعة are relatively
+
+392
+00:43:45,820 --> 00:43:49,240
+relatively
+
+393
+00:43:49,240 --> 00:43:53,960
+primes يبقى
+
+394
+00:43:53,960 --> 00:43:56,980
+شايف الفرق ما بين ال prime و relatively prime ايش
+
+395
+00:43:56,980 --> 00:43:57,520
+هتفضل
+
+396
+00:44:03,250 --> 00:44:08,970
+طب ما هي .. شوف في .. في غير الواحد؟
+
+397
+00:44:08,970 --> 00:44:15,580
+طب هو العوامل اللي هو .. هو السنةممتاز جدا لك
+
+398
+00:44:15,580 --> 00:44:19,900
+الاربعة والسبعة في اكتر طيب مافيش غيره يعني انا
+
+399
+00:44:19,900 --> 00:44:24,080
+بعطي مثال relatively prime لك المثال اللي جابله
+
+400
+00:44:24,080 --> 00:44:27,580
+جبت ال grasses common divisor لأي عدنى بس ماطلعش
+
+401
+00:44:27,580 --> 00:44:31,540
+واحد طلع قداش طلع تمانية جبت الواحد والاتنين
+
+402
+00:44:31,540 --> 00:44:35,640
+والاربعة والتمانية أخدت الكبير فيهم طبقا للتعريف
+
+403
+00:44:35,640 --> 00:44:39,300
+تمام هنا ال grasses common divisor قد يكون واحد قد
+
+404
+00:44:39,300 --> 00:44:42,840
+يكون واحد في كام حالةبدل الحالة حالتين الحالة
+
+405
+00:44:42,840 --> 00:44:46,700
+الأولى لو كانوا اتنين primes وفي هذه الحالة بقول
+
+406
+00:44:46,700 --> 00:44:50,520
+اتنين primes مثلا بقول relatively prime relatively
+
+407
+00:44:50,520 --> 00:44:55,120
+يعني في بنسب واحد بالنسبة للتانية أخدت الأربعة
+
+408
+00:44:55,120 --> 00:45:01,460
+والسبعة أخدت الأحداشر والخمسمية مثلامثلا تسعة و
+
+409
+00:45:01,460 --> 00:45:05,520
+عشرة are relatively prime كلام صحيح يبقى انا خدت
+
+410
+00:45:05,520 --> 00:45:08,420
+احداشر و اخدت الخمسمية مافيش قواصم بينهم الا
+
+411
+00:45:08,420 --> 00:45:13,200
+الواحد الصحيح و هكذا تفضل كيف؟
+
+412
+00:45:14,710 --> 00:45:19,070
+automatic relatively prime لكن العكس ليس صحيحا
+
+413
+00:45:19,070 --> 00:45:25,190
+يبقى زميكوف يقول هدول لما يكونوا are primes ما
+
+414
+00:45:25,190 --> 00:45:29,250
+بقدر أقول عليهم relatively primes لكن العكس ليس
+
+415
+00:45:29,250 --> 00:45:34,830
+صحيحا يبقى هذه الأمثلة على ال grasses common
+
+416
+00:45:34,830 --> 00:45:40,250
+divisors وعلى main وrelatively primes
+
+417
+00:46:07,100 --> 00:46:14,340
+طيب خد لها الملاحظة if
+
+418
+00:46:14,340 --> 00:46:23,880
+ال N is an integer and
+
+419
+00:46:23,880 --> 00:46:34,570
+ال N greater than zeroثم لجرس ال common divisor لل
+
+420
+00:46:34,570 --> 00:46:39,210
+N وال0 كده يا شباب؟
+
+421
+00:46:41,350 --> 00:46:49,330
+ان الواحد تقسم الان و تقسم ال zero الان اتنين تقسم
+
+422
+00:46:49,330 --> 00:46:53,430
+ال zero بس مضمون تقسم ال ان لا مش مضمون ايه
+
+423
+00:46:53,430 --> 00:46:59,010
+التلاتة الأربعة ال ان ال ان اكبر رقم بيقسم ال ان و
+
+424
+00:46:59,010 --> 00:47:04,550
+بيقسم ال zero يبقى هنا هذا الكلام بدو يساوي ال in
+
+425
+00:47:04,550 --> 00:47:10,250
+because ال in is the
+
+426
+00:47:32,560 --> 00:47:45,550
+بقسم الاتنين في النظرية بتقول ما يأتيtheorem for
+
+427
+00:47:45,550 --> 00:47:57,810
+any none zero integers a
+
+428
+00:47:57,810 --> 00:48:08,830
+and b there exist integers
+
+429
+00:48:11,450 --> 00:48:24,130
+بلاقي أعداد صحيحة S and A T such that such that ان
+
+430
+00:48:24,130 --> 00:48:30,030
+ال aggressive common divisor لل A و ال B بدي ساوي
+
+431
+00:48:30,030 --> 00:48:39,610
+ال A في S زائد ال B في T moreover
+
+432
+00:48:40,520 --> 00:48:48,920
+و أكثر من ذلك moreover the greatest common divisor
+
+433
+00:48:48,920 --> 00:48:55,080
+لل a والb is the smallest positive integer is the
+
+434
+00:48:55,080 --> 00:49:02,900
+smallest positive integer
+
+435
+00:49:02,900 --> 00:49:06,040
+smallest
+
+436
+00:49:06,040 --> 00:49:17,910
+positive integer ofreform على الشكل as زائد bt
+
+437
+00:49:17,910 --> 00:49:21,450
+quaternary
+
+438
+00:49:21,450 --> 00:49:24,950
+نتيجة
+
+439
+00:49:24,950 --> 00:49:38,030
+if ال a and ال b are relatively prime
+
+440
+00:49:39,750 --> 00:49:49,590
+relatively prime then there exist then there exist
+
+441
+00:49:49,590 --> 00:49:55,610
+integers s
+
+442
+00:49:55,610 --> 00:50:07,150
+and t s and t such that بحيث
+
+443
+00:50:07,150 --> 00:50:16,780
+أنالـ AS زائد ال BT يساوي كده؟ يساوي واحد
+
+444
+00:51:06,130 --> 00:51:10,410
+طيب نرجع لنص النظرية بيقول for any non zero
+
+445
+00:51:10,410 --> 00:51:15,770
+integers a و b يبقى انا عندي عددين صحيحين a و b
+
+446
+00:51:15,770 --> 00:51:21,250
+there exist integers لازم الاقي عددين اخرين s and
+
+447
+00:51:21,250 --> 00:51:25,250
+t such that the greatest common divisor لل a و ال
+
+448
+00:51:25,250 --> 00:51:31,820
+b بدى يسوى a في ال s زائد bt ايش يعني؟بقول هنا
+
+449
+00:51:31,820 --> 00:51:36,440
+لجلس ال common divisor بتقدر تكتبه على صيغة linear
+
+450
+00:51:36,440 --> 00:51:42,600
+combination من العددين A وB يعني بقدر ألاقي عدد
+
+451
+00:51:42,600 --> 00:51:47,120
+أضربه في A وعدد تاني أضربه في B أجمع يطلع له لجلس
+
+452
+00:51:47,120 --> 00:51:52,460
+ال common divisorهل حطيت قيود على ال S و T؟
+
+453
+00:51:52,460 --> 00:51:56,160
+ماحطيتش، يعني يمكن يطلعوا اتنين سالب، يمكن واحد
+
+454
+00:51:56,160 --> 00:52:00,100
+موجب وواحد سالب المهم ان الهدف الصحيح بيهمنيش موجب
+
+455
+00:52:00,100 --> 00:52:05,320
+سالب غيره لكن بيهمنياش انه فعلا يكون the greatest
+
+456
+00:52:05,320 --> 00:52:09,560
+common divisor هو linear combination من الرقمين
+
+457
+00:52:09,560 --> 00:52:15,350
+اللي عندي من A وB moreoverGreece's Common Divisor
+
+458
+00:52:15,350 --> 00:52:21,530
+هو أصغر رقم بقدر أكتفه على صيغة Linear Combination
+
+459
+00:52:21,530 --> 00:52:29,970
+AS زائد BTطيب النتيجة بتقول ليش؟ لو كان ال a وال b
+
+460
+00:52:29,970 --> 00:52:34,290
+relatively prime زي الأربعة والسبعة اللي قبل قليل
+
+461
+00:52:34,290 --> 00:52:38,750
+مثلا يبقى then there exists an integer S و T such
+
+462
+00:52:38,750 --> 00:52:43,450
+that يعني قصده يقول لك linear combination هذي ال
+
+463
+00:52:43,450 --> 00:52:47,390
+aggressives common ده يغزلوا بقداشيبقى الواحد back
+
+464
+00:52:47,390 --> 00:52:53,730
+to record وعلى شكل AS بزاقة BT طبعا انها تامثل لكل
+
+465
+00:52:53,730 --> 00:52:58,580
+من النظرية وكل مناللي هو .. و كذلك الـ Crawler الـ
+
+466
+00:52:58,580 --> 00:53:02,480
+Crawler يعني نتيجة شباب على نظره يعني كانها حالة
+
+467
+00:53:02,480 --> 00:53:05,280
+خاصة الحالة الخاصة لو كان ال greatest common
+
+468
+00:53:05,280 --> 00:53:09,480
+divisor هدف واحد يبقى أقدر أكتب الواحد على صيغة
+
+469
+00:53:09,480 --> 00:53:13,680
+لينا ال combination من مين؟ من الاتنين، هدول نعطي
+
+470
+00:53:13,680 --> 00:53:19,240
+أول مثال على ذلك يبقى example one لو كان ال
+
+471
+00:53:19,240 --> 00:53:25,860
+greatest common divisor لمين؟ للأتناشر والتلاتين
+
+472
+00:53:26,910 --> 00:53:31,140
+قداش ال classes كانوا يلبسوا ال 12 وال 30ستة
+
+473
+00:53:31,140 --> 00:53:38,200
+ممتازة يبقى الستة هذا أكبر رقم بيقسم كل من الاتنين
+
+474
+00:53:38,200 --> 00:53:43,740
+في آن واحد الستة هذا بدأ كتبه على صيغة linear
+
+475
+00:53:43,740 --> 00:53:49,120
+combination من مين؟ من الاتناشر والتلاتين بقوله آه
+
+476
+00:53:49,120 --> 00:53:55,880
+يبقى هذا بيسوء اتناشر في رقم زائد تلاتين في رقم
+
+477
+00:53:55,880 --> 00:54:05,330
+آخرطيب اتناش هذه لو ضربتها في سالب اتنين مثلا بصير
+
+478
+00:54:05,330 --> 00:54:11,240
+كدهش؟سالب اربعة وعشرين يبقى الفرق بينهم بين
+
+479
+00:54:11,240 --> 00:54:15,960
+التلاتين جداش هو الستة تبعتنا يبقى بروح بضرب هنا
+
+480
+00:54:15,960 --> 00:54:22,380
+جداش يواحد يبقى هذا الرقم هو عبارة عن اس وهذا
+
+481
+00:54:22,380 --> 00:54:28,160
+الرقم هو عبارة عن مين هو عبارة عن تي يبقى للرقمين
+
+482
+00:54:28,160 --> 00:54:33,460
+اتناشر وتلاتين لجيت اس بسلب اتنين و لجيت تي تساوي
+
+483
+00:54:33,460 --> 00:54:37,090
+واحدبحيث اتناشر في السلبي اتنين زي التلاتين في
+
+484
+00:54:37,090 --> 00:54:40,810
+واحد يعطينا main الرقم ست الأولي greatest common
+
+485
+00:54:40,810 --> 00:54:46,590
+divisor لاتناشر وmain والتلاتين خد لي كمان مثال
+
+486
+00:54:46,590 --> 00:54:54,480
+آخريبقى لو جيت قلت المثال ارقم اتنين لو جيت ال
+
+487
+00:54:54,480 --> 00:55:00,840
+greatest common divisor لمن؟ للاربعة والسبعتاش
+
+488
+00:55:00,840 --> 00:55:06,880
+هدول ما لهم? rentable price صحيح ولا لأ؟ يبقى دول
+
+489
+00:55:06,880 --> 00:55:13,110
+بده يساوي واحدمش زي اللي هناك يساوي ستة يبقى هذا
+
+490
+00:55:13,110 --> 00:55:19,310
+بده يساوي أربعة في أبصر قداش زائد سبعتاشر في أبصر
+
+491
+00:55:19,310 --> 00:55:28,070
+قداش كذلك سالب أربعة قصير قداش سالب ستاش واني عندى
+
+492
+00:55:28,070 --> 00:55:32,750
+هنا قداش يبقى السبعتاشر بدها قداش واحد ليس
+
+493
+00:55:32,750 --> 00:55:36,210
+بالضرورة دايما يطلع واحد ممكن يطلع أي رقم آخر يعني
+
+494
+00:55:36,210 --> 00:55:42,820
+بقدر الله المرة هذه طلعيبقى هذا يمثل الـ S وهذا
+
+495
+00:55:42,820 --> 00:55:48,760
+يمثل الـ T يبقى هاي اتنين are relatively prime
+
+496
+00:55:48,760 --> 00:55:53,020
+قدرت اكتب الواحد على الشكل الأربعة مضروبة في
+
+497
+00:55:53,020 --> 00:55:57,040
+integer زاد سبعتاشر مضروبة في integer طبق اللي مين
+
+498
+00:55:57,040 --> 00:56:01,370
+لكرولري اللي عندى هذهوبالتالي ماعندي مشكلة في هذه
+
+499
+00:56:01,370 --> 00:56:07,790
+الحالة طيب يا شباب لو جيت قلت رقم تلاتة لو بد ال
+
+500
+00:56:07,790 --> 00:56:14,270
+degree is common divisor لمن؟ لليتنين تربيع في
+
+501
+00:56:14,270 --> 00:56:22,450
+تلاتة تربيع في خمسة كل هذا ضرب والرقم التاني اتنين
+
+502
+00:56:22,450 --> 00:56:27,150
+في تلاتة تربيع في سبعة تربيع
+
+503
+00:56:29,290 --> 00:56:34,450
+رقمين كبار يبقى لو كان عندى رقم كبير بحلله الى
+
+504
+00:56:34,450 --> 00:56:38,010
+أبسط العوامل بشوف فيه اكم اتنين و بعدين اكم تلاتة
+
+505
+00:56:38,010 --> 00:56:44,390
+و اكم خمسة و اكم سبعة و هكذا طيب لو بدى اجيب الجنس
+
+506
+00:56:44,390 --> 00:56:49,510
+ال common divisor للاتنين هدول عشان احسب هذا بجيب
+
+507
+00:56:49,510 --> 00:56:54,350
+قدش الجنس ال common divisor لتنين تربيع و اتنين
+
+508
+00:56:55,280 --> 00:57:03,200
+أكبر رقم بيقسم الاتنين هو الاتنين اتنين مقدش لجريس
+
+509
+00:57:03,200 --> 00:57:07,520
+ال common divisor للثلاثة تربيه والتلاتة تربيه
+
+510
+00:57:08,190 --> 00:57:14,710
+التسعة يعني تلاتة تربية يبقى هذا تلاتة تربية جداش
+
+511
+00:57:14,710 --> 00:57:18,870
+اللي جرس ال common divisor للخمسة والسبعة تربية
+
+512
+00:57:18,870 --> 00:57:23,070
+سبعة يعني تسعة واربعين مع خمسة اتنين are
+
+513
+00:57:23,070 --> 00:57:27,810
+relatively primed بجداشواحد يبقى الجرس ال common
+
+514
+00:57:27,810 --> 00:57:31,710
+divisor لهم اللي هو يساوي واحد تسعة في اتنين في
+
+515
+00:57:31,710 --> 00:57:36,570
+تمانتاش يبقى الجرس ال common divisor لهذين العددين
+
+516
+00:57:36,570 --> 00:57:41,630
+يساوي جداش تمانتاش و هكذا يبقى الجرس ال common
+
+517
+00:57:41,630 --> 00:57:44,670
+divisor لو كان مجموعة من الاعداد و عندي مجموعة من
+
+518
+00:57:44,670 --> 00:57:49,000
+الاعداد بقارن كل واحد بالاجبالهو بطلع جديش لجريس
+
+519
+00:57:49,000 --> 00:57:52,420
+ال common divisor لكل اتنين متنظرين وبعدين بضربهم
+
+520
+00:57:52,420 --> 00:57:57,060
+في بعض بطلع جديش لجريس ال common divisor لمين؟ لكل
+
+521
+00:57:57,060 --> 00:58:01,420
+الأعداد يبقى لحد هنا ا stop المرة الجاية ان شاء
+
+522
+00:58:01,420 --> 00:58:06,120
+الله بنكمل يوم الأتنين و هجيك المرة الجاية هبدأ
+
+523
+00:58:06,410 --> 00:58:11,090
+بلمة وبرهين نبدأ بنقول احنا حتى لا مابورهناش ولا
+
+524
+00:58:11,090 --> 00:58:14,730
+حاجة بنعطي بعض المعلومات الأساسية و بنحاول نثبت
+
+525
+00:58:14,730 --> 00:58:19,990
+هالمعلومة بواسطة من؟ بواسطة أمثلة مختلفة يمكن
+
+526
+00:58:19,990 --> 00:58:23,530
+الكلام اللي بقوله كثير منه تفتحت لك بتلاقيش أمثلة
+
+527
+00:58:23,530 --> 00:58:27,290
+لكن أنا بعطيك أمثلة مش هنثبت المعلومة عندك لإن
+
+528
+00:58:27,290 --> 00:58:31,010
+المعلومة القديمة عندك بس بنحاول نثبتها من خلال
+
+529
+00:58:31,010 --> 00:58:33,130
+الأمثلة يعطيكوا العافية
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c0902e755e09da21bc070a7d51871c1a82a3d456
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0.srt
@@ -0,0 +1,1852 @@
+1
+00:00:21,670 --> 00:00:27,730
+الآن بنرجع مرة ثانية لما بدأنا به صباحًا وهو إكمال
+
+2
+00:00:27,730 --> 00:00:31,950
+مناقشة مسائل الـ permutations إن هنا سؤال تسعة و
+
+3
+00:00:31,950 --> 00:00:37,010
+عشرين في الفترة الصباحية وقلنا لكم احسبوا اضربوا
+
+4
+00:00:37,010 --> 00:00:40,850
+فينا الـ sigma اللي طلعناها ضربًا في نفسها ثلاث مرات
+
+5
+00:00:40,850 --> 00:00:44,690
+sigma تكعيب تلاقيه على حاصل ضرب اللي هو الـ three
+
+6
+00:00:44,690 --> 00:00:48,760
+cycles اللي موجودة عندكم بالفعل بعضكم قالوا 
+
+7
+00:00:48,760 --> 00:00:52,620
+عملناها وطلعت زيه كما قلت تمامًا قلنا ماشي إذا 
+
+8
+00:00:52,620 --> 00:00:57,500
+بنتنقل الآن إلى السؤال واحد و ثلاثين واحد و ثلاثين
+
+9
+00:00:57,500 --> 00:01:02,980
+عرف لي ست جديدة سماها الـ stabilizer لـ a وهي كل الـ
+
+10
+00:01:02,980 --> 00:01:07,800
+alpha اللي موجودة فيه بحيث أن alpha of a بدها تساوي
+
+11
+00:01:07,800 --> 00:01:12,710
+الـ a لما يقول alpha موجودة في G alpha is a
+
+12
+00:01:12,710 --> 00:01:17,070
+permutation فلما يقول alpha of a بدها تساوي a
+
+13
+00:01:17,070 --> 00:01:22,370
+معناته لسه لازم تلاقي كل الـ permutations اللي
+
+14
+00:01:22,370 --> 00:01:27,110
+بيكون فيهم الـ a fixed ايش يعني fixed يعني الـ
+
+15
+00:01:27,110 --> 00:01:32,940
+element هو صورة لنفسه alpha of a بدها تساوي a أنا
+
+16
+00:01:32,940 --> 00:01:39,140
+بدي أذهب وأبحث في الـ SG على كل الـ Permutations
+
+17
+00:01:39,140 --> 00:01:44,640
+التي تثبت منها العنصر a بدي أذهب وأثبت أن هذا الـ
+
+18
+00:01:44,640 --> 00:01:48,280
+list لازم الـ a هو عبارة عن subgroup من الـ group
+
+19
+00:01:48,280 --> 00:01:53,760
+الأساسية اللي هي G بالرجوع إلى ذاكرتنا إلى شابتر 3
+
+20
+00:01:53,760 --> 00:01:58,460
+بجينا الـ subset من الـ group نثبتها subgroup إذا
+
+21
+00:01:58,460 --> 00:02:02,660
+أثبتنا تو conditions الـ condition الأول أن الـ
+
+22
+00:02:02,660 --> 00:02:06,500
+stabilizer لـ a is non-empty يعني على الأقل فيها و
+
+23
+00:02:06,500 --> 00:02:10,220
+لو عنصر واحد الأمر الثاني لو أخذت عنصرين في الـ
+
+24
+00:02:10,220 --> 00:02:13,700
+stabilizer بدي أثبت أن الأول في معكوسة الثاني
+
+25
+00:02:13,700 --> 00:02:18,040
+موجود في الـ stabilizer أن أثبتنا ذلك بيكون الـ
+
+26
+00:02:18,040 --> 00:02:22,480
+stabilizer لـ a هي subgroup من من من الـ group G
+
+27
+00:02:23,030 --> 00:02:27,910
+يبقى النقطة الأولى في الحل هو إثبات أن الـ
+
+28
+00:02:27,910 --> 00:02:32,590
+stabilizer لـ a is non-empty أنا أدعي أن الـ
+
+29
+00:02:32,590 --> 00:02:42,170
+stabilizer لـ a is non-empty ليش؟ because الـ
+
+30
+00:02:42,170 --> 00:02:48,810
+identity permutation موجودة في الـ stabilizer لـ الـ
+
+31
+00:02:48,810 --> 00:02:55,070
+a  الآن الـ identity permutation بيثبت اللي هو
+
+32
+00:02:55,070 --> 00:03:01,070
+بس هو اللي بيثبت كل العناصر كل العناصر بيثبت ...
+
+33
+00:03:01,070 --> 00:03:05,060
+إذا من باب هو اللي بيثبت اللي هي يبقى هنا non
+
+34
+00:03:05,060 --> 00:03:08,660
+-empty لأن الـ E موجودة في الـ stabilizer since الـ
+
+35
+00:03:08,660 --> 00:03:12,760
+identity permutation لما تأثر على الـ element A
+
+36
+00:03:12,760 --> 00:03:19,060
+بتعطينا منه الـ A itself ومن ثم صار الـ stabilizer لـ
+
+37
+00:03:19,060 --> 00:03:25,760
+A فيها على الأقل الـ identity permutation الآن هذه
+
+38
+00:03:25,760 --> 00:03:31,490
+هي الخطوة الأولى الخطوة الثانية بداية أقول إن الـ
+
+39
+00:03:31,490 --> 00:03:36,350
+alpha والـ beta موجودة في الـ stabilizer للـ element
+
+40
+00:03:36,350 --> 00:03:44,110
+a تمام؟ إذا بناء عليه بقدر أقول له then الـ alpha
+
+41
+00:03:44,110 --> 00:03:49,570
+لما تأثر على العنصر a بتعطينا العنصر a itself and
+
+42
+00:03:49,570 --> 00:03:54,550
+الـ beta لما تأثر على العنصر a بتعطينا العنصر a
+
+43
+00:03:54,550 --> 00:04:01,640
+itself أنا هاروح آخذ المعلومة هذه وأستنتج منها شغلة
+
+44
+00:04:01,640 --> 00:04:07,920
+ثانية هذه ايش معناها لو جيت أثرت على الطرفين بالـ
+
+45
+00:04:07,920 --> 00:04:17,150
+beta inverse يبقى بيصير beta inverse لـ beta of a يساوي
+
+46
+00:04:17,150 --> 00:04:26,150
+beta inverse of a أو beta inverse لـ beta كلها لما تأثر
+
+47
+00:04:26,150 --> 00:04:32,170
+على a بدها تساوي beta inverse of a الـ composition بين
+
+48
+00:04:32,170 --> 00:04:36,430
+الـ permutation ومعكوسها شو بعطينا الـ identity
+
+49
+00:04:36,430 --> 00:04:40,650
+element لما تأثر على الـ element بعطيني نفس الـ
+
+50
+00:04:40,650 --> 00:04:46,430
+element يبقى هذا يعطينا الـ beta inverse of a هذا
+
+51
+00:04:46,430 --> 00:04:53,070
+ايش معناه؟ ايش تفسيرك لهذه العبارة طبقا للتعريف
+
+52
+00:04:53,070 --> 00:04:57,710
+اللي احنا قلناه؟ موجود كويس يبقى alpha inverse
+
+53
+00:04:57,710 --> 00:05:01,550
+موجودة في الـ stabilizer لـ a؟ هاي معناها ليش إنها
+
+54
+00:05:01,550 --> 00:05:08,560
+بتثبت العنصر a يبقى هذا معناه الـ beta inverse
+
+55
+00:05:08,560 --> 00:05:16,420
+موجودة في الـ stabilizer لمن؟ لـ a الآن consider خذ
+
+56
+00:05:16,420 --> 00:05:22,060
+لمن؟ خذ للـ alpha beta inverse of a
+
+57
+00:05:25,670 --> 00:05:31,270
+يبقى أنا أخذت العنصرين alpha و beta في موجودة في
+
+58
+00:05:31,270 --> 00:05:36,030
+الـ stabilizer بدي أشوف هل الـ alpha في beta inverse
+
+59
+00:05:36,030 --> 00:05:40,250
+بتثبت اللي إن ثبته خلاص موجودة في الـ stabilizer و
+
+60
+00:05:40,250 --> 00:05:44,710
+التالي الـ stabilizer عبارة عن subgroup يبقى هذا
+
+61
+00:05:44,710 --> 00:05:51,950
+الكلام بدها يساوي alpha of beta inverse of a ويساوي
+
+62
+00:05:51,950 --> 00:05:57,830
+alpha of beta inverse of a عبارة عن ما؟ عبارة عن a
+
+63
+00:05:57,830 --> 00:06:04,530
+itself مدام عبارة عن a itself يبقى هذا a لكن أنا
+
+64
+00:06:04,530 --> 00:06:08,610
+عند هنا alpha موجودة في الـ stabilizer يبقى alpha
+
+65
+00:06:08,610 --> 00:06:14,750
+of a بتعطيني ما؟ a إذا صار تأثير Alpha Beta Inverse
+
+66
+00:06:14,750 --> 00:06:18,230
+عليها سيكون الـ a itself، ما هو معناه هذا الكلام؟
+
+67
+00:06:18,230 --> 00:06:24,730
+أن Alpha Beta Inverse يبقى هذا معناه أن Alpha Beta
+
+68
+00:06:24,730 --> 00:06:30,430
+Inverse موجودة في الـ stabilizer للـ a معنى هذا
+
+69
+00:06:30,430 --> 00:06:36,010
+الكلام الـ stabilizer لـ a عبارة عن subgroup من G
+
+70
+00:06:36,010 --> 00:06:44,490
+يبقى الـ stabilizer لمن؟ الـ stabilizer للـ a
+
+71
+00:06:44,490 --> 00:06:50,250
+subgroup من G وهو المطلوب ايه لخاطر أعطيك مثال
+
+72
+00:06:50,250 --> 00:06:54,910
+عملي ولو إنه مش طالب ولا حاطب مثال عملي يوضح لك
+
+73
+00:06:54,910 --> 00:06:59,170
+ايش المقصود منه هذا فمثلاً يعني for example
+
+74
+00:07:03,800 --> 00:07:11,560
+لو أخذت الـ G تساوي S3 S3 هي كم عنصر فيها يا شباب؟
+
+75
+00:07:11,560 --> 00:07:17,600
+ست عناصر اللي هو الأول اللي هو الـ identity يبقى الـ
+
+76
+00:07:17,600 --> 00:07:24,400
+identity والثاني اللي هو واحد اثنين ثلاثة وبعد هيك
+
+77
+00:07:24,400 --> 00:07:31,000
+واحد اثنين وبعد هيك واحد ثلاثة اثنين وبعد هيك واحد
+
+78
+00:07:31,000 --> 00:07:38,460
+ثلاثة وبعد هيك اثنين ثلاثة يبقى هي عناصر S3 كلهم
+
+79
+00:07:38,460 --> 00:07:45,010
+ستة عناصر S6 عناصر يعني هاي الستة permutations اللي
+
+80
+00:07:45,010 --> 00:07:50,170
+موجودة وإن في S3 الآن بدأ أجيب الـ stabilizer
+
+81
+00:07:50,170 --> 00:07:55,970
+للواحد والـ stabilizer للثنين والـ stabilizer للتلاتة هاي
+
+82
+00:07:55,970 --> 00:08:00,790
+العناصر اللي موجودة في أي permutation الآن بدأ آجي
+
+83
+00:08:00,790 --> 00:08:08,120
+آخذ له الـ stabilizer لمن للواحد تساوي من المقصود
+
+84
+00:08:08,120 --> 00:08:12,560
+بالـ stabilizer للواحد يعني كل الـ permutation اللي
+
+85
+00:08:12,560 --> 00:08:17,160
+فيهم الواحد fixed يعني صورة الواحد هي الواحد
+
+86
+00:08:17,160 --> 00:08:21,660
+itself ماشي
+
+87
+00:08:21,660 --> 00:08:25,600
+هو واحد اثنين ثلاثة الـ identity والـ identity بتكون
+
+88
+00:08:25,600 --> 00:08:29,560
+واحد بين قوسين أو اثنين بين قوسين أو ثلاثة بين قوسين
+
+89
+00:08:29,560 --> 00:08:34,920
+هذه الـ order اللي هيسوي ثلاثة وبالتالي كيف خلتها
+
+90
+00:08:34,920 --> 00:08:39,820
+الـ identity؟ أما لو كنت واحد اثنين ثلاثة واحد اثنين
+
+91
+00:08:39,820 --> 00:08:43,440
+ثلاثة بيقول لك هذا كلامك صح بس هذه معناته إن الواحد
+
+92
+00:08:43,440 --> 00:08:46,500
+صرت اثنين والاثنين صرت ثلاثة والثلاثة صرت واحد
+
+93
+00:08:46,500 --> 00:08:50,000
+يبقى هذه ليست الـ identity يبقى كتبنا الـ identity
+
+94
+00:08:50,000 --> 00:08:56,110
+لحال كان بإمكاني أقول لك هذه وأسكت بدل الـ E كان
+
+95
+00:08:56,110 --> 00:09:00,350
+ممكن أقول لك اثنين وأسكت ثلاثة وأسكت stop بقولش
+
+96
+00:09:00,350 --> 00:09:05,910
+أربعة وأسكت ليش؟ لأن الـ S3 باس معمولة على ستم
+
+97
+00:09:05,910 --> 00:09:10,130
+ثلاثة عناصر واحد اثنين ثلاثة تمام؟ الآن بدي أجيب
+
+98
+00:09:10,130 --> 00:09:13,950
+الـ stabilizer اللي هو يعني مين هم الـ permutation
+
+99
+00:09:13,950 --> 00:09:18,370
+اللي فيهم الواحد fixed يعني اللي الواحد صورته واحد
+
+100
+00:09:18,370 --> 00:09:23,400
+باجي الـ identity هذه منهم اه لأن بيثبت الواحد
+
+101
+00:09:23,400 --> 00:09:27,100
+والاثنين والثلاثة مش عايزين الواحد يبقى باجي بقوله
+
+102
+00:09:27,100 --> 00:09:32,220
+الـ identity permutation اشتغلنا هذي بيثبت الواحد هذي
+
+103
+00:09:32,220 --> 00:09:38,100
+بيثبت الواحد هذي بيثبت الواحد هذي يبقى ايش اثنين
+
+104
+00:09:38,100 --> 00:09:42,820
+ثلاثة هذي اللي فيها الواحد fixed مظهرليش يبقى هنا
+
+105
+00:09:42,820 --> 00:09:50,570
+اثنين وثلاثة تمام في غيرهم؟ لا طب لو بدي الـ
+
+106
+00:09:50,570 --> 00:09:56,250
+stabilizer للثنين كل الـ permutations المثبتة
+
+107
+00:09:56,250 --> 00:10:01,290
+للثنين الـ identity واحدة وبداجة دول هذه اثنين
+
+108
+00:10:01,290 --> 00:10:05,590
+صورتها واحد وهذه اثنين صورتها واحد وهذه اثنين صورتها
+
+109
+00:10:05,590 --> 00:10:06,290
+واحد وهذه اثنين صورتها واحد وهذه اثنين صورتها واحد
+
+110
+00:10:06,290 --> 00:10:07,010
+وهذه اثنين صورتها واحد وهذه اثنين صورتها واحد وهذه
+
+111
+00:10:07,010 --> 00:10:07,070
+واحد وهذه اثنين صورتها واحد وهذه اثنين صورتها واحد
+
+112
+00:10:07,070 --> 00:10:07,610
+وهذه اثنين صورتها واحد وهذه اثنين صورتها واحد وهذه
+
+113
+00:10:07,610 --> 00:10:12,070
+اثنين صورتها واحد وهذه اثنين صورتها واحد وهذه
+
+114
+00:10:12,070 --> 00:10:20,610
+اثنين
+
+115
+00:10:20,610 --> 00:10:23,030
+صورة
+
+116
+00:10:26,470 --> 00:10:31,930
+هذه لا تثبت هذه لا تثبت هذه لا تثبت الثلاثة يبقى
+
+117
+00:10:31,930 --> 00:10:36,750
+مافيش غيرهم يبقى عرفنا ايش المقصود بالـ stabilizer
+
+118
+00:10:36,750 --> 00:10:42,170
+للـ element يعني كل الـ permutations اللي موجودة في
+
+119
+00:10:42,170 --> 00:10:46,210
+الـ group اللي هنا بحيث هذه الـ parameter يكون الـ a
+
+120
+00:10:46,210 --> 00:10:51,470
+هذا رقم ثابت يعني fixed صورته هو نفسه فهمنا ايش
+
+121
+00:10:51,470 --> 00:10:56,590
+معنى stabilizer لـ a؟ طيب ننتقل الآن إلى السؤال
+
+122
+00:10:56,590 --> 00:11:05,610
+الذي يليه اللي هو 32 سؤال 32 بيقول ما يأتي أخذنا
+
+123
+00:11:05,610 --> 00:11:12,390
+beta تساوي واحد ثلاثة خمسة سبعة تسعة ثمانية ستة
+
+124
+00:11:24,410 --> 00:11:32,160
+مضروبة في اثنين أربعة عشرة 2 4 10 بالشكل اللي عن
+
+125
+00:11:32,160 --> 00:11:36,560
+هنا بقول what is the smallest positive integer n
+
+126
+00:11:36,560 --> 00:11:47,440
+for which بحيث أن بيتا أس n يساوي بيتا أس ناقص خمسة
+
+127
+00:11:57,540 --> 00:12:02,820
+نرجع لسؤالنا مرة ثانية ماتينا permutation beta
+
+128
+00:12:02,820 --> 00:12:09,680
+عبارة عن product of two disjoint cycles تمام و
+
+129
+00:12:09,680 --> 00:12:13,920
+واحد حطينا فواصل مرة هذه فواصل ليش مش هنا الرقم
+
+130
+00:12:13,920 --> 00:12:18,870
+عشرة أرقام بلاش تقول هذا أربعة يعني طوله أربعة وهذا 
+
+131
+00:12:18,870 --> 00:12:22,790
+طوله جد ما يكون بقولها يبقى حاطين الفواصل مش
+
+132
+00:12:22,790 --> 00:12:27,570
+هنقولك أن العشرة عبارة عن عشرة عنصر واحد ما علينا مش
+
+133
+00:12:27,570 --> 00:12:35,990
+مشكلة بقولي ما هو أصغر رقم N بحط أس ل Beta بده
+
+134
+00:12:35,990 --> 00:12:42,450
+يعطيني Beta أس سالب خمسة يعني حددتلك أصغر رقم ها
+
+135
+00:12:42,450 --> 00:12:47,970
+مش حيال لا أرقام تمام بقولي بدي قديش قيمة N هذه
+
+136
+00:12:47,970 --> 00:12:53,190
+بقول و الله كويسة الآن احنا لو جينا لل order للـ 
+
+137
+00:12:53,190 --> 00:12:53,570
+B
+
+138
+00:13:01,200 --> 00:13:07,960
+هل في بينهم عنصر مشترك يبقى ال order ل beta هو ال
+
+139
+00:13:07,960 --> 00:13:12,660
+least common multiple ما بين طول الأولى اثنين
+
+140
+00:13:12,660 --> 00:13:19,260
+أربعة ستة سبعة وطول الثانية كده ثلاثة يبقى ال
+
+141
+00:13:19,260 --> 00:13:24,540
+least common multiple لهم كده واحد وعشرين معناته
+
+142
+00:13:24,540 --> 00:13:29,700
+ال order ل beta بدي نسوي واحد وعشرين هذا معناه أن
+
+143
+00:13:29,700 --> 00:13:35,360
+beta أس واحد وعشرين يساوي ال identity والواحد
+
+144
+00:13:35,360 --> 00:13:41,200
+وعشرين هو أصغر الرقم حطيته لل أس بيتا اتانى مين
+
+145
+00:13:41,200 --> 00:13:46,160
+أتاني ال identity طيب ايش بيقول لي في السؤال ما هو
+
+146
+00:13:46,160 --> 00:13:52,880
+أصغر رقم ان بتحطه أس لبيتا بتطلع بيتا أس خمسة
+
+147
+00:13:52,880 --> 00:14:02,370
+بقوله آه الآن باجي بقوله ولكن ال beta أُس n بدها
+
+148
+00:14:02,370 --> 00:14:09,130
+تساوي beta أُس سالب خمسة implies شو رايك لو ضربت
+
+149
+00:14:09,130 --> 00:14:15,130
+الطرفين في beta أُس خمسة بس فيدي عندي هنا beta أُس
+
+150
+00:14:15,130 --> 00:14:21,990
+n زائد خمسة بده يساوي مين ال identity لما أطلع في
+
+151
+00:14:21,990 --> 00:14:27,840
+هذه هيك وأطلع في هذه هيك وقال لي في السؤال بيتا
+
+152
+00:14:27,840 --> 00:14:34,660
+الآن هذا أصغر رقم حاطيته كأس لبيتا طلع بيتا أس
+
+153
+00:14:34,660 --> 00:14:39,320
+سالب خمسة إذا ما هي العلاقة بين الرقمين الاثنين
+
+154
+00:14:39,320 --> 00:14:48,160
+هدول بيك اسمه والله بيساويه بيساويه لأنه أصغر رقم
+
+155
+00:14:48,160 --> 00:14:53,800
+لكن قال لي الآن هذا رقم حيال الله بقوله إذا ال 21
+
+156
+00:14:53,800 --> 00:14:58,580
+لازم تجسم من الرقم اللي عندنا هذا لكن كونه قال لي
+
+157
+00:14:58,580 --> 00:15:04,740
+أن أصغر الرقم وأنّي أثبت أن ال order ل beta هو 21
+
+158
+00:15:05,480 --> 00:15:11,400
+إذا هذا الرقم من الاثنين هدول مع بعض بستنتج أن ال
+
+159
+00:15:11,400 --> 00:15:17,360
+N زائد خمسة يساوي واحد وعشرين يبقى ال N تساوي كده؟
+
+160
+00:15:17,360 --> 00:15:26,840
+ستة عشر إذا أصغر رقم بحط أس ل Beta بيطلع لي Beta أس
+
+161
+00:15:26,840 --> 00:15:33,880
+لخمسة هو الرقم أين؟ الرقم اللي هو ستة عشر طيب السؤال
+
+162
+00:15:33,880 --> 00:15:40,940
+اللي بعده نفس الفكرة بس ما قالش أصغر رقم هذا اثنين و
+
+163
+00:15:40,940 --> 00:15:47,250
+ثلاثين ثلاثة وثلاثين ما أعطيني Alpha ثلاثة يبقى هذه
+
+164
+00:15:47,250 --> 00:15:52,250
+ثلاثة وثلاثين ما أعطيني Alpha تساوي اللي هو واحد
+
+165
+00:15:52,250 --> 00:15:58,730
+ثلاثة خمسة سبعة تسعة واحد ثلاثة خمسة سبعة تسعة
+
+166
+00:15:58,730 --> 00:16:03,350
+بالشكل اللي عندنا هذا وهذه مضروبة في اثنين أربعة
+
+167
+00:16:03,350 --> 00:16:10,970
+ستة اثنين أربعة ستة وهذه مضروبة كمان في ثمانية و
+
+168
+00:16:10,970 --> 00:16:16,870
+عشرة ثمانية وعشرة بالشكل اللي عندنا هذا وبقول ليش
+
+169
+00:16:16,870 --> 00:16:27,330
+إذا كان ال A أُس M is a خمسة cycle is a خمسة cycle
+
+170
+00:16:27,330 --> 00:16:37,210
+يعني ال cycle طولها خمسة خمسة cycle what can you
+
+171
+00:16:37,210 --> 00:16:42,870
+say about M what
+
+172
+00:16:42,870 --> 00:16:53,220
+اللي هو what can you say
+
+173
+00:16:53,220 --> 00:17:00,840
+about M السؤال
+
+174
+00:17:00,840 --> 00:17:05,080
+هذا زي ما أنت بلاحظ هو السؤال اللي جاوب له مع الفارق
+
+175
+00:17:05,080 --> 00:17:12,120
+شو الفارق هناك قال لك أن أصغر رقم مظبوط هنا ما جاء ليش M
+
+176
+00:17:12,120 --> 00:17:18,900
+كل اللي قالوه ليش جرح قال لي الام خمسة cycle يعني
+
+177
+00:17:18,900 --> 00:17:25,920
+ال order له يساوي كده؟ ال order لـ M خمسة تمام لأنه
+
+178
+00:17:25,920 --> 00:17:29,840
+قال له ال cycle طوله خمسة مدام طوله خمسة إذا ال
+
+179
+00:17:29,840 --> 00:17:35,180
+order لهذه ال cycle يساوي خمسة يعني a أس m أس خمسة
+
+180
+00:17:35,180 --> 00:17:40,590
+لازم يعطينا مين؟ ال identity الألفة بالشكل اللي عندها
+
+181
+00:17:40,590 --> 00:17:44,870
+ده باذي بتطلع في three cycles ولا عنصر مشترك
+
+182
+00:17:44,870 --> 00:17:49,760
+فيه ما بينهما إذا على طول الخطاب بروح بقوله ال order
+
+183
+00:17:49,760 --> 00:17:55,600
+لل alpha بده يساوي ال least common multiple لمن؟
+
+184
+00:17:55,600 --> 00:18:00,500
+لطول الأولى خمسة وطول الثانية ثلاثة وطول الأخيرة
+
+185
+00:18:00,500 --> 00:18:05,460
+اثنين يبقى الرقم الذي يقسم على أو الرقم اللي
+
+186
+00:18:05,460 --> 00:18:10,560
+بيقسمه الثلاثة في أنا واحد هو الرقم كم؟ ثلاثين
+
+187
+00:18:10,560 --> 00:18:15,780
+ممتاز جدا يبقى ال order ل alpha بده يساوي ثلاثين
+
+188
+00:18:15,780 --> 00:18:20,800
+بيبقى ال alpha أس ثلاثين بده يساوي من ال identity
+
+189
+00:18:20,800 --> 00:18:26,200
+هذا معناه أن ال alpha أس ثلاثين بده يساوي ال
+
+190
+00:18:26,200 --> 00:18:32,240
+identity element والثلاثين أصغر رقم بحط أس ل alpha
+
+191
+00:18:32,240 --> 00:18:36,850
+بيطل من ال identity اللي أنا إيش قال له قال لي لو
+
+192
+00:18:36,850 --> 00:18:45,790
+كان ال AM is A خمسة cycle يعني ال AM لو جيت قلت له
+
+193
+00:18:45,790 --> 00:18:51,930
+مين هم الخمسة cycle قلت A B C D E هاي خمسة cycle
+
+194
+00:18:52,340 --> 00:18:59,020
+معناته أن ال order ل ال AM بده يساوي كده؟ بده يساوي
+
+195
+00:18:59,020 --> 00:19:06,880
+خمسة معناته أن ال AM أُس خمسة بده يعطي نمين ال
+
+196
+00:19:06,880 --> 00:19:13,280
+identity يعني معنى هذا الكلام أن A خمسة M بده يساوي
+
+197
+00:19:13,280 --> 00:19:19,740
+نمين ال identity element هل حطينا قيود أو شروط على
+
+198
+00:19:19,740 --> 00:19:26,680
+M لا ما حطيناش على M ولا قيد ولا شرط اللهم إلا قلنا
+
+199
+00:19:26,680 --> 00:19:31,180
+Alpha أس M عبارة عن خمسة cycle يعني ال cycle طولها
+
+200
+00:19:31,180 --> 00:19:36,540
+يساوي خمسة طيب ما قالش زي السؤال اللي جاوب له إن ال N
+
+201
+00:19:36,540 --> 00:19:41,910
+أصغر أرقام لا ما حطيتش قيود على M بناء عليه لما يكون
+
+202
+00:19:41,910 --> 00:19:46,670
+عندي alpha أس ثلاثين والثلاثين هو أصغر رقم بدي
+
+203
+00:19:46,670 --> 00:19:50,970
+يعطينا ال identity وال A أس خمسة M يساوي ال
+
+204
+00:19:50,970 --> 00:19:56,070
+identity إذا ما هي العلاقة ما بين الثلاثين والخمسة
+
+205
+00:19:56,070 --> 00:20:05,910
+M ثلاثين تقسم الخمسة M أو الخمسة M مضاعفات الثلاثين
+
+206
+00:20:05,910 --> 00:20:10,390
+هذه وهذه اثنين نفس الصورة إذا من الاثنين هدول بس
+
+207
+00:20:10,390 --> 00:20:18,990
+تنتج أن ثلاثين تقسم خمسة M مين
+
+208
+00:20:18,990 --> 00:20:24,790
+اللي بيحكي؟ أيوة إيش بتقول؟ ال A بتساوي ال Alpha؟ و
+
+209
+00:20:24,790 --> 00:20:30,210
+مين ال A هذه؟ ال A أنا قلته يساوي Alpha؟ أنا ما قلتش
+
+210
+00:20:30,210 --> 00:20:35,490
+أنا الكلام هو قال لي a أُس m is a خمسة كلمة معناته
+
+211
+00:20:35,490 --> 00:20:40,610
+permutation والله alpha أُس m قال alpha أُس m هو
+
+212
+00:20:40,610 --> 00:20:46,720
+سؤال طب إذا alpha أُس m مظبوط المقصود اللي قلت لك
+
+213
+00:20:46,720 --> 00:20:51,000
+إيه والله اللي هيبقى هذا Alpha أس M خمسة cycle
+
+214
+00:20:51,000 --> 00:20:56,020
+على أي حال حتى لو قلنا A أس M يساوي خمسة cycle
+
+215
+00:20:56,020 --> 00:21:02,380
+معناته ال A permutation صح
+
+216
+00:21:02,380 --> 00:21:08,000
+هذه احنا عدلناها ألفة أس M is A خمسة cycle معناته
+
+217
+00:21:08,000 --> 00:21:16,440
+هذه Alpha أس M معناته هذه Alpha هذه Alpha يبقى هذه
+
+218
+00:21:16,440 --> 00:21:23,760
+alpha يبقى الثلاثين الثلاثين بتقسم الخمسة M لو
+
+219
+00:21:23,760 --> 00:21:31,540
+جسمنا كله على خمسة بيظل عندنا ستة تقسم ال M إذا ال
+
+220
+00:21:31,540 --> 00:21:39,900
+M شو علاقتها بستة مضاعفاتها يبقى هنا ال M is a
+
+221
+00:21:39,900 --> 00:21:48,100
+multiple of 6 يبقى الام اللي عندنا هذه هي مضاعفات
+
+222
+00:21:48,100 --> 00:21:53,260
+مين؟ مضاعفات العدد ستة شوف السؤال اللي جاوب له وقلنا
+
+223
+00:21:53,260 --> 00:21:59,920
+لأ تساوي مثلا ستة دوري بس هنا مضاعفاته ليش؟ لأنه
+
+224
+00:21:59,920 --> 00:22:05,440
+لهناك هو أصغر رقم يعني يدخل في ال order بس احنا
+
+225
+00:22:05,440 --> 00:22:10,160
+عندنا في هذا السؤال ال order ثلاثين يبقى أي رقم
+
+226
+00:22:10,160 --> 00:22:16,570
+آخر الثلاثين بتجسم مين؟ تجسم هذا الرقم هذا كان سؤال
+
+227
+00:22:16,570 --> 00:22:22,610
+ثلاثة وثلاثين سؤال ستة وثلاثين قال لي في S4 بدنا
+
+228
+00:22:22,610 --> 00:22:28,010
+Cyclic subgroup of order أربعة و non-cyclic of
+
+229
+00:22:28,010 --> 00:22:38,230
+order أربعة سؤال ستة وثلاثين سؤال ستة وثلاثين بدنا
+
+230
+00:22:38,230 --> 00:22:51,580
+Cyclic group of order أربعة in S4 وبدنا non-cyclic
+
+231
+00:22:51,580 --> 00:23:02,660
+group of order أربعة برضه in S4 solution S4
+
+232
+00:23:02,660 --> 00:23:09,500
+أكام عنصر فيها شباب بس ثمانية وعشرين عنصر
+
+233
+00:23:09,500 --> 00:23:14,380
+اللي قال ثمانية بتقدر تجيب لي ال sub group من ال S
+
+234
+00:23:14,380 --> 00:23:18,220
+أربعة ال order اللي هيساوي ثمانية يعني ما فيش فيها
+
+235
+00:23:18,220 --> 00:23:25,660
+إلا ثمان عناصر وقد D4 صحيح الكلام صحيح يبقى D4 هي
+
+236
+00:23:25,660 --> 00:23:31,560
+ال sub group من ال S4 وال order اللي هيساوي ثمانية
+
+237
+00:23:31,560 --> 00:23:38,610
+تمام أي subgroup من ال D4 هي subgroup من ال S4 يبقى
+
+238
+00:23:38,610 --> 00:23:43,570
+إذا بتجيب لي من ال D4 Cyclic group ال order اللي
+
+239
+00:23:43,570 --> 00:23:50,470
+هيساوي أربعة بكل قدّيت الواجب يلا هيغششناك من D4
+
+240
+00:23:50,470 --> 00:23:53,730
+بتقدر تجيب لي ال subgroup ال order اللي هيساوي
+
+241
+00:23:53,730 --> 00:23:54,350
+أربعة
+
+242
+00:24:07,840 --> 00:24:11,460
+D4 D4 R0 R90 R180 R270 HV D' ممتاز جدا يبقى ال rotation
+
+243
+00:24:11,460 --> 00:24:18,080
+واحدة R290 الأردر لها يساوي أربعة وتساوي ال
+
+244
+00:24:18,080 --> 00:24:22,100
+subgroup generated by R مئتين وسبعين لأن ال R
+
+245
+00:24:22,100 --> 00:24:26,080
+مئتين وسبعين هي ال inverse لمين يبقى احنا بدنا
+
+246
+00:24:26,080 --> 00:24:29,040
+واحدة بدناش اثنين بس اثنين واحدة والله يعطيك
+
+247
+00:24:29,040 --> 00:24:37,860
+العافية يبقى باجي بقوله الآن the cyclic subgroup
+
+248
+00:24:37,860 --> 00:24:47,620
+اللي هي مين الـ R تسعين اللي عناصرها R نوت و R
+
+249
+00:24:47,620 --> 00:24:58,200
+تسعين و R مئة وثمانين و R مئتين وسبعين هذه is of
+
+250
+00:24:58,200 --> 00:25:04,980
+order اللي هو أربعة إذا 
+
+251
+00:25:04,980 --> 00:25:12,960
+بدك تكتبها على شكل cycle يبقى عندك الارت السعيد هي
+
+252
+00:25:12,960 --> 00:25:18,820
+عبارة عن واحد اثنين ثلاثة أربعة يبقى هي ال cycle
+
+253
+00:25:18,820 --> 00:25:24,140
+اللي عندنا هنا تمام يبقى هذه هي الارت السعيد هذا 
+
+254
+00:25:24,140 --> 00:25:28,120
+لو حبيت تشتغل ال cycles حبيت مباشرة تشتغل مع الناس
+
+255
+00:25:28,120 --> 00:25:37,110
+مشكلة طيب بدنا non-cyclic يبقى دي non-cyclic
+
+256
+00:25:37,110 --> 00:25:45,170
+group of order أربعة أحيانا تقدر تجيب أكثر من واحدة
+
+257
+00:25:45,170 --> 00:25:50,970
+ال sub group تحتوي على ال identity الحين بقدر
+
+258
+00:25:50,970 --> 00:25:57,850
+أقولك ال identity are not وكمان are مئة وثمانين
+
+259
+00:25:59,600 --> 00:26:08,640
+وحط عليهم H والـ R مئة وثمانين فيه H الشكل اللي
+
+260
+00:26:08,640 --> 00:26:17,130
+عندنا هنا هذه non-cyclic لأن الـR180S² بتعطيك ال
+
+261
+00:26:17,130 --> 00:26:21,470
+identity يبقى ماهيَش generator هذه بتعطيك ال
+
+262
+00:26:21,470 --> 00:26:26,170
+identity التربية بتعطيك ال identity وهذه التربية
+
+263
+00:26:26,170 --> 00:26:30,730
+برضه بتعطيك ال identity طبعا هذه لو رجعت للجدول
+
+264
+00:26:30,730 --> 00:26:35,850
+صفحة 31 يبقى R0 وR180
+
+265
+00:26:38,670 --> 00:26:42,510
+وهذه لو فتحنا الجدول في صفحة مئة وواحد وتبقى في
+
+266
+00:26:42,510 --> 00:26:49,150
+صفحة واحد وثلاثين وطبعا حسبناها قبل كده اللي هو ال
+
+267
+00:26:49,150 --> 00:26:55,250
+R مئة وثمانين في H R مئة وثمانين R مئة وثمانين
+
+268
+00:26:55,250 --> 00:27:07,200
+في H بتعطيك V يبقى V طبعا لو حطيت إيش حط ما احنا
+
+269
+00:27:07,200 --> 00:27:11,260
+بقوله فيه كمان واحدة ثانية يعني أول اثنين خليهم زي
+
+270
+00:27:11,260 --> 00:27:12,900
+ما هو ده اللي بتحطهم بنفع
+
+271
+00:27:16,940 --> 00:27:22,520
+احنا أعطيتك كمثال بسيط يعني أنت .. أنت .. أنت ..
+
+272
+00:27:22,520 --> 00:27:26,780
+بس لما تجيب عناصر بدك تتأكد أنه لو رفعتها لأي أس
+
+273
+00:27:26,780 --> 00:27:30,280
+بدي يكون موجود ولو ضربت اثنين في بعض بدي يكون
+
+274
+00:27:30,280 --> 00:27:34,100
+موجود فيها عشان تتأكد أن هذه فعلا subgroup ليها
+
+275
+00:27:34,100 --> 00:27:37,740
+closed under the operation أنا اخترت من D4 لأنه
+
+276
+00:27:37,740 --> 00:27:41,400
+أسهل ليه؟ لأن D4 أنا زهجت وأنا بشرح فيها ويمكن
+
+277
+00:27:41,400 --> 00:27:45,520
+يعطينا عليها مثال بدل مثال عشرة يبقى أصبحت محفوظة
+
+278
+00:27:45,520 --> 00:27:51,150
+بالنسبة لنا ومن هنا نجب لك هذا كمثال بسيط منها على 
+
+279
+00:27:51,150 --> 00:27:57,310
+أي حال هذا كان سؤال اللي هو ستة وثلاثين بعده عندك
+
+280
+00:27:57,310 --> 00:28:04,430
+سبعة وأربعين وما أدراك ما سبعة وأربعين سؤال سبعة و
+
+281
+00:28:04,430 --> 00:28:11,010
+أربعين بيقول ما يلي show that every element  الـ alpha
+
+282
+00:28:11,010 --> 00:28:19,370
+الموجودة في الـ An أي element في الـ An can be
+
+283
+00:28:19,370 --> 00:28:23,930
+expressed as a three cycle or product of a three
+
+284
+00:28:23,930 --> 00:28:35,310
+cycle يبقى is written as a three cycle or product
+
+285
+00:28:35,310 --> 00:28:39,450
+of a three cycles
+
+286
+00:28:43,140 --> 00:28:48,560
+فكر معايا كويس السؤال ليس سهلا لكن بده تفكير
+
+287
+00:28:48,560 --> 00:28:56,400
+الحقيقة ومن خلال التفكير قد نصل إلى النتيجة حد
+
+288
+00:28:56,400 --> 00:29:01,800
+فيكم حلوا الدار هذا إيه أو جاب فكرة يعني طبعا
+
+289
+00:29:01,800 --> 00:29:06,160
+هيقول لي السؤال مش هذا دي؟ اه مش هذا دي صحيح رغم
+
+290
+00:29:06,160 --> 00:29:09,540
+أنه فردي لكن ما يعطيك hint في الكتاب لكن hint لن
+
+291
+00:29:09,540 --> 00:29:14,880
+تستفيد منها شيئا مش هتعرف تشغلها طيب على أي حال
+
+292
+00:29:14,880 --> 00:29:21,200
+السؤال مرة ثانية بيقولي أي even permutation أو أي
+
+293
+00:29:21,200 --> 00:29:25,580
+element موجود في An is written يابني يمكن نكتبه
+
+294
+00:29:25,580 --> 00:29:29,800
+على شكل three cycle يعني ما product of three
+
+295
+00:29:29,800 --> 00:29:40,960
+cycles طيب يبقى الحل كالتالي solution let
+
+296
+00:29:40,960 --> 00:29:52,510
+alpha موجودة في An الـ alpha is an even
+
+297
+00:29:52,510 --> 00:29:58,490
+permutation تمام؟
+
+298
+00:29:58,490 --> 00:30:03,530
+لما أقول لك even permutation يعني يمكن حصل ضرب two
+
+299
+00:30:03,530 --> 00:30:09,890
+transpositions صح؟ يمكن أربع transpositions مش
+
+300
+00:30:09,890 --> 00:30:15,210
+ثلاثة أنت لازم تصير good يمكن ستة transpositions
+
+301
+00:30:15,210 --> 00:30:20,790
+يمكن ثمانية قد ما يكون يكون أيوة يبقى هنا ال alpha
+
+302
+00:30:20,790 --> 00:30:26,750
+بكتبها على شكل أزواج من إيه؟ من ال transpositions
+
+303
+00:30:26,750 --> 00:30:33,630
+يبقى باجي بقوله هذا بده يعطينا أن ال alpha is
+
+304
+00:30:33,630 --> 00:30:42,050
+written as a product of
+
+305
+00:30:43,150 --> 00:30:49,410
+pairs أزواج of two cycles أو transpositions
+
+306
+00:30:54,380 --> 00:31:00,520
+طيب بدي أخد زوج من هذه الأزواج يعني بدي أخد اثنين
+
+307
+00:31:00,520 --> 00:31:05,660
+transpositions وأشوف هل بقدر أكتبهم على شكل three
+
+308
+00:31:05,660 --> 00:31:11,020
+cycles ولا لأ؟ لأنه كان كل زوج بنقدر نكتبه على شكل
+
+309
+00:31:11,020 --> 00:31:15,480
+three cycles يبقى ال alpha فيها اثنين ولا أربعة ولا
+
+310
+00:31:15,480 --> 00:31:22,220
+ستة ولا ثمانية كلها بقدر أكتبها على شكل عشان هنا
+
+311
+00:31:22,220 --> 00:31:26,540
+قلت alpha بقدر أكتبها على شكل of pairs of two
+
+312
+00:31:26,540 --> 00:31:32,140
+cycle يعني الزوج يعني اثنين transpositions يبقى
+
+313
+00:31:32,140 --> 00:31:42,180
+هنا لو جيت قلت if ال a والـ b والـ c والـ d are distinct
+
+314
+00:31:42,180 --> 00:31:44,880
+then
+
+315
+00:31:46,690 --> 00:31:52,130
+this pair has
+
+316
+00:31:52,130 --> 00:32:02,670
+the following cases
+
+317
+00:32:02,670 --> 00:32:07,310
+أنا
+
+318
+00:32:07,310 --> 00:32:13,270
+عندي أربعة عناصر مختلفة والزوج هذا يعني even
+
+319
+00:32:13,270 --> 00:32:21,520
+permutation إذا الاحتمال الأول أنه يكون على شكل AB
+
+320
+00:32:21,520 --> 00:32:32,060
+في AB يعني أول عنصر مكرر AB زي CD CD CD CD زي A
+
+321
+00:32:32,060 --> 00:32:40,060
+B A B طب هدول حصل ضرب مش بيطينا مين ال
+
+322
+00:32:40,060 --> 00:32:43,320
+parameter one اثنين واحد اثنين لو ضربت في بعضهاش
+
+323
+00:32:43,320 --> 00:32:51,730
+بتعطيله بتعطيك واحد اثنين؟ بتعطيلك مين؟ identity
+
+324
+00:32:51,730 --> 00:32:55,510
+permutation مش قلنا ال identity permutation نستطيع
+
+325
+00:32:55,510 --> 00:32:59,450
+نسكبها على شكل زوجي ومكتوبة عندك في الكتاب واحد
+
+326
+00:32:59,450 --> 00:33:02,970
+اثنين واحد اثنين أو واحد اثنين واحد اثنين ثلاثة
+
+327
+00:33:02,970 --> 00:33:06,590
+أربعة ثلاثة أربعة أو خمسة ستة خمسة يعني بقدر
+
+328
+00:33:06,590 --> 00:33:11,350
+أكتبها على شكل زوج إذا هذه تعطينا اللي هو الاحتمال
+
+329
+00:33:11,350 --> 00:33:17,050
+الأول أنه E لأن ال E is an even permutation
+
+330
+00:33:17,050 --> 00:33:26,910
+الاحتمال الثاني أنه تبقى على الشكل ABC صح ولا لأ
+
+331
+00:33:26,910 --> 00:33:32,370
+لإحتمال الثالث يكون فش عنصر فيما بينهما لإحتمال
+
+332
+00:33:32,370 --> 00:33:38,570
+الثالث والأخير أن يكون على الشكل ABCD
+
+333
+00:33:38,570 --> 00:33:45,750
+في غير هيك؟ طيب في كل حالة من الحالات الثلاث أنا
+
+334
+00:33:45,750 --> 00:33:50,070
+بدي أبين لك أنه بنكتبها على شكل product of three
+
+335
+00:33:50,070 --> 00:33:55,050
+cycles أو three cycle واحدة تمام خلّينا نمسك
+
+336
+00:33:55,050 --> 00:34:01,710
+الحالة الأولى يبقى الحالة الأولى اللي هي a b a b
+
+337
+00:34:01,710 --> 00:34:08,930
+اللي هي ال identity permutation تمام أليست ال
+
+338
+00:34:08,930 --> 00:34:16,470
+identity permutation هي عبارة عن ال a,b,c الكل
+
+339
+00:34:16,470 --> 00:34:22,970
+تكعيب؟ مش هذه طولها ثلاثة يبقى ال order اللي هي
+
+340
+00:34:22,970 --> 00:34:27,530
+ثلاثة يبقى مكعبها بدي يعطينا ال identity يبقى كأنه
+
+341
+00:34:27,530 --> 00:34:32,230
+ضارب ال cycle ABC في ABC في ABC يبقى product of
+
+342
+00:34:32,230 --> 00:34:36,450
+three cycles مظبوط ولا لا؟ حد بيقدر يعترض على هذا
+
+343
+00:34:36,450 --> 00:34:41,330
+الكلام اللي عنده اعتراض يحكي حتى نفند هذا الاعتراض
+
+344
+00:34:41,330 --> 00:34:52,750
+يبقى هذا اسمه product of three cycles تمام؟ يبقى
+
+345
+00:34:52,750 --> 00:34:56,890
+خلاصة من النقطة الأولى شوف النقطة الأولى اعتمدت
+
+346
+00:34:56,890 --> 00:35:01,530
+على فهمك فلو أنت فاهم فعلا أن ال identity variation
+
+347
+00:35:01,530 --> 00:35:07,270
+is an even وكيف كتبناها لما صارت even طبعا مكتوب
+
+348
+00:35:07,270 --> 00:35:11,110
+عندك على التواب وشرحها لك الأستاذ محمود طيب نيجي
+
+349
+00:35:11,110 --> 00:35:17,040
+للنقطة الثانية النقطة الثانية اللي همّنا اللي هي ال
+
+350
+00:35:17,040 --> 00:35:24,140
+A B A C كويس بدي أجيب ال composition ما بين
+
+351
+00:35:24,140 --> 00:35:28,720
+الاثنين لأنه في عنصر مشترك في ما بينهما إذا هذول
+
+352
+00:35:28,720 --> 00:35:34,080
+are not disjoint بدي أخليهم disjoint يبقى لو جيت
+
+353
+00:35:34,080 --> 00:35:41,560
+قلت لك العنصر الأول هو AA ثورتها مين؟ الـC الـC ثورتها
+
+354
+00:35:41,560 --> 00:35:49,720
+مين؟ C لأن الـC هنا مقفل، C بعد ذلك الـC ثورتها A
+
+355
+00:35:49,720 --> 00:35:57,120
+والـA ثورتها B بعد ذلك الـB مقفل ثورتها B والـB
+
+356
+00:35:57,120 --> 00:36:03,060
+ثورتها موجودة يبقى قفلة يبقى ال composition ما بين
+
+357
+00:36:03,060 --> 00:36:10,640
+اثنين هذول هي three cycle أول اثنين بساطة
+
+358
+00:36:10,640 --> 00:36:19,100
+المشكلة في الثالثة يبقى الثالثة نهاية الثالثة عندنا A
+
+359
+00:36:19,100 --> 00:36:29,400
+B C D يوسام هذه الخبرة بتلعب دور كبير هل بقدر أكتب
+
+360
+00:36:29,400 --> 00:36:36,710
+هدول على شكل product of three cycles هذا السؤال حتى
+
+361
+00:36:36,710 --> 00:36:40,370
+ولو كان في بينهم عناصر مشتركة ما عنديش مشكلة المهم
+
+362
+00:36:40,370 --> 00:36:46,050
+أن أقدر أكتبها على شكل three cycles أنا أزعم أنه
+
+363
+00:36:46,050 --> 00:36:53,430
+بقدر بقدر أقوله a وهنا d و b والتاني بدي أخد a d
+
+364
+00:36:53,430 --> 00:36:59,890
+c طب زعمك هذا صحيح والله ما يصحيح بقوله تعال خد ال
+
+365
+00:36:59,890 --> 00:37:03,270
+composition ما بين الاثنين M طلع الطرف هذا يبقى
+
+366
+00:37:03,270 --> 00:37:08,230
+كتابتي صح ما طلعش يبقى كتابتي غلط تمام؟ بقولك كويس
+
+367
+00:37:08,230 --> 00:37:14,070
+تعال ناخد ال M بدي أبدأ بالعنصر A ال A صورتها وال
+
+368
+00:37:14,070 --> 00:37:20,070
+D صورتها هذا ال B ما جفلت شهر لسه بالداجة هنا ال B
+
+369
+00:37:20,070 --> 00:37:22,430
+صورتها B
+
+370
+00:37:24,280 --> 00:37:32,180
+الـ B صورتها B والـ B صورتها إيش؟ جفنة تمام خلصت
+
+371
+00:37:32,180 --> 00:37:36,970
+ال A وال B بده يروح لل C الآن هاي كتبت الـC الـC
+
+372
+00:37:36,970 --> 00:37:42,890
+صورتها A والـA صورتها D هذا الـD بدي أمسك الـD
+
+373
+00:37:42,890 --> 00:37:49,330
+الـD صورتها C والـC صورتها هاي يبقى قفلا يبقى
+
+374
+00:37:49,330 --> 00:37:54,750
+معناته فعلا هذول كتبناهم على شكل product of three
+
+375
+00:37:54,750 --> 00:38:07,030
+cycles يبقى هذا product of three cycles إذا الزوج 
+
+376
+00:38:07,030 --> 00:38:12,810
+تبع Transposition مهما كان شكله قدرت أكتبه يا إما
+
+377
+00:38:12,810 --> 00:38:17,630
+على شكل a 3-cycle يا product of three cycles
+
+378
+00:38:17,630 --> 00:38:21,030
+السؤال سهل مع هذه النقطة الأخيرة النقطة الأخيرة
+
+379
+00:38:21,030 --> 00:38:24,950
+بيبقى تقعد تفكر كيف تكتب بحيث الـ composition فيما
+
+380
+00:38:24,950 --> 00:38:30,660
+بينهما يعطيك مين؟ يعطيك الـ two transpositions و هذه
+
+381
+00:38:30,660 --> 00:38:34,740
+عملية ليست سهلة أما الباقي مباشرة اتنين الأولانين
+
+382
+00:38:34,740 --> 00:38:42,320
+تمام؟ يبقى هنا لما ناخد كل اتنين كل زوج من الـ two
+
+383
+00:38:42,320 --> 00:38:46,910
+transpositions كل واحد بقدر أكتبه على شكل مين؟ 3-cycle
+
+384
+00:38:46,910 --> 00:38:50,430
+cycle خد الزوج اللي بعده والزوج اللي بعده واللي
+
+385
+00:38:50,430 --> 00:38:54,910
+بعده قد ما بدك كله بتكتب ويش على شكل three cycles
+
+386
+00:38:54,910 --> 00:39:01,490
+لذلك أي element α موجود في الـ A<sub>n</sub> is a three
+
+387
+00:39:01,490 --> 00:39:04,890
+cycle or a product of a three cycle أي التانية
+
+388
+00:39:04,890 --> 00:39:08,910
+كانت a three cycle الأولى والتالتة product of a
+
+389
+00:39:08,910 --> 00:39:11,770
+three cycle يبقى هنا
+
+390
+00:39:15,780 --> 00:39:24,260
+الخطوة الأولى اللي موجودة في A<sub>n</sub> is a three
+
+391
+00:39:24,260 --> 00:39:32,960
+cycle or product of a three cycles
+
+392
+00:39:36,830 --> 00:39:41,170
+السؤال على درجة من الأهمية لكن لو تركتك لحالك اللي
+
+393
+00:39:41,170 --> 00:39:44,130
+يوم تقدر تحلله يمكن تجيب الأولى والتانية بس
+
+394
+00:39:44,130 --> 00:39:48,930
+التالتة لا يمكن أن تأتي بها يبقى هاي بساطة حالك
+
+395
+00:39:48,930 --> 00:39:55,590
+الآن نروح لسؤال 56 سؤال 56
+
+396
+00:39:57,800 --> 00:40:02,060
+يقول ليش هذا عدد يا صاحب نشوف قال يقبل α و
+
+397
+00:40:02,060 --> 00:40:07,580
+β موجودة في S<sub>4</sub> α و β ولا γ و β
+
+398
+00:40:07,580 --> 00:40:14,940
+يبقى β و γ β و γ التنتين هذول ال
+
+399
+00:40:14,940 --> 00:40:21,940
+permutations موجودات في S<sub>4</sub> وفي نفس الوقت β γ
+
+400
+00:40:22,340 --> 00:40:29,000
+β γ β تساوي (1 4 3 2) (1
+
+401
+00:40:29,000 --> 00:40:36,860
+4 3 2) وγ β تساوي وγ β (1
+
+402
+00:40:36,860 --> 00:40:43,600
+2 4 3) (1 2 4 3) وزيادة على
+
+403
+00:40:43,600 --> 00:40:48,540
+ذلك β of 1 يساوي الـ 4 و β لما تأثرت
+
+404
+00:40:48,540 --> 00:40:54,600
+على الـ 1 بده يساوي الـ 4 قال لي determine حدد
+
+405
+00:40:54,600 --> 00:41:01,440
+determine اللي هو β and γ بدي أعرف إيه شكل
+
+406
+00:41:01,440 --> 00:41:08,290
+الـ β وكذلك γ بمعنى آخر أكتبها لي على شكل
+
+407
+00:41:08,290 --> 00:41:13,470
+الـ cycle زي ما هؤلاء المكتوبات على شكل الـ cycle حد
+
+408
+00:41:13,470 --> 00:41:20,010
+فيكوا حل السؤال هذا؟ يلا يا أبو الأعدادات اللي
+
+409
+00:41:20,010 --> 00:41:21,670
+بتكلم بالأعداد
+
+410
+00:41:31,120 --> 00:41:37,720
+هو زوّق؟ طيب حد فيكوا حل السؤال هذا في البيت؟ none
+
+411
+00:41:37,720 --> 00:41:44,100
+علماً أنه very easy بس أنت شغل مخك والشيء هيو
+
+412
+00:41:44,100 --> 00:41:49,140
+قدامك الحل لا بد تفكير ولا هاجر بدنا نشتغل الشغل
+
+413
+00:41:49,140 --> 00:41:55,450
+الروتيني أنت عندك α و β و γ في S<sub>4</sub> وال
+
+414
+00:41:55,450 --> 00:41:59,190
+composition ما بين اتنين من اليمين والشمال هيو على
+
+415
+00:41:59,190 --> 00:42:03,430
+شكل الـ cycle وما طيك تأثير الـ β على الـ 1 يساوي
+
+416
+00:42:03,430 --> 00:42:08,190
+الـ 4 قليتلي شكل الـ β وشكل الـ γ يعني بدي
+
+417
+00:42:08,190 --> 00:42:10,790
+أشوف تأثير الـ β على 1 إيش بيعطينا و β على
+
+418
+00:42:10,790 --> 00:42:13,170
+2 و β على 3 و β على 4 وγ على
+
+419
+00:42:13,170 --> 00:42:15,050
+1 وγ على 2 وγ على 3 وγ على
+
+420
+00:42:15,050 --> 00:42:18,890
+4 القصة بسيطة جداً هذه solution
+
+421
+00:42:21,960 --> 00:42:27,100
+المعلومة اللي عندي أن β of 1 بده يساوي
+
+422
+00:42:27,100 --> 00:42:34,780
+4 بنقدر نجيب γ of 4 جداش تساوي γ
+
+423
+00:42:34,780 --> 00:42:43,020
+of 4 نقدر يبقى أثر على الطرفين بـ γ صح ولا لا
+
+424
+00:42:43,380 --> 00:42:48,700
+إذاً لو أثرت على الطرفين بـ γ هذا بده يصبح على
+
+425
+00:42:48,700 --> 00:42:55,400
+الشكل ده γ β of 1 يساوي γ of 4
+
+426
+00:42:58,010 --> 00:43:02,930
+طيب γ β of 1 وين γ β هذه؟ γ β
+
+427
+00:43:02,930 --> 00:43:09,910
+of 1 صورتها إيش؟ 2 يبقى هذا معناه أنه 2
+
+428
+00:43:09,910 --> 00:43:17,550
+يساوي γ of 4 هذه كانت معلومة جديدة طيب سؤال
+
+429
+00:43:17,550 --> 00:43:23,760
+بنقدر نجيب β of 2 أثر على الطرفين بـ β
+
+430
+00:43:23,760 --> 00:43:30,400
+يبقى لو جينا يقولنا هنا β of 2 يساوي β
+
+431
+00:43:30,400 --> 00:43:36,900
+γ of 4 يبقى معنى هذا الكلام أن β of
+
+432
+00:43:36,900 --> 00:43:43,380
+2 يساوي β γ of 4 بتعطينا مين؟ 3
+
+433
+00:43:43,380 --> 00:43:56,220
+يبقى أي 3 الآن بدنا γ of 3 يبقى
+
+434
+00:43:56,220 --> 00:44:02,540
+هذه صارت γ β of 2 بده يساوي γ of
+
+435
+00:44:02,540 --> 00:44:09,770
+3 تمام هذا معناه أن γ β of 2 γ
+
+436
+00:44:09,770 --> 00:44:14,050
+β of 2 بيعطينا مين؟ بيعطينا 4 يبقى
+
+437
+00:44:14,050 --> 00:44:21,210
+4 بده يساوي γ of 3 طيب ده أثر عليهم ب
+
+438
+00:44:21,210 --> 00:44:29,430
+β يبقى بيصير β of 4 بده يساوي β γ
+
+439
+00:44:29,430 --> 00:44:37,780
+of 3 هذا سيعطيك β of 4 يساوي β γ
+
+440
+00:44:37,780 --> 00:44:47,420
+of 3 بيعطيك 2 طيب هذا سيعطيك β γ of
+
+441
+00:44:47,420 --> 00:44:55,300
+4 يساوي γ of 2 γ β of 4
+
+442
+00:44:55,300 --> 00:45:08,290
+بيعطينا يبقى 3 يبقى 3 يبقى يبقى يبقى
+
+443
+00:45:08,290 --> 00:45:21,590
+يبقى يبقى
+
+444
+00:45:21,590 --> 00:45:24,830
+يبقى
+
+445
+00:45:24,830 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+446
+00:45:26,130 --> 00:45:30,390
+يبقى يبقى يبقى يبقى يبقى طيب هذا لو أثرت عليه ب
+
+447
+00:45:30,390 --> 00:45:38,010
+γ بيصير γ β of 3 يساوي γ of
+
+448
+00:45:38,010 --> 00:45:44,830
+1 هذا بده يعطيلك أن γ β of 3 γ
+
+449
+00:45:44,830 --> 00:45:51,200
+β of 3 بيعطيك 1 يبقى الـ 1 يساوي γ
+
+450
+00:45:51,200 --> 00:45:55,300
+of 1 خلصنا هيك γ of 1، γ of 2، γ
+
+451
+00:45:55,300 --> 00:45:59,820
+of 3، γ of 4، خلصنا الـ βات هي هم كلهم يبقى
+
+452
+00:45:59,820 --> 00:46:05,240
+بناءً عليه بقدر أكتب له β وγ يبقى β
+
+453
+00:46:05,240 --> 00:46:13,360
+بدها تساوي (1 4 2 3) لو أثرت على الـ 1 إيش صورتها؟
+
+454
+00:46:13,360 --> 00:46:21,150
+4 طيب β لو أثرت على الـ 4 إيش بتعطيك؟ 2 طيب
+
+455
+00:46:21,150 --> 00:46:26,570
+β لو أثرت على الـ 2 بتعطيك 3 طيب β لو
+
+456
+00:46:26,570 --> 00:46:36,150
+أثرت على الـ 3 بتعطيك 1 قفلة تمام؟ يبقى أنداء ال
+
+457
+00:46:36,150 --> 00:46:43,520
+α تساوي بدي أخد الـ 1 الحين γ لو أثرت على
+
+458
+00:46:43,520 --> 00:46:51,660
+الـ 1 بتعطينا مين؟ يبقى (1)، تمام؟ بعدها بتاخد
+
+459
+00:46:51,660 --> 00:46:58,360
+الـ 2 γ لو أثرت على الـ 2 بتعطيني 3 γ
+
+460
+00:46:58,360 --> 00:47:03,100
+لو أثرت على الـ 3 بتعطيني 4 γ لو أثرت على
+
+461
+00:47:03,100 --> 00:47:07,340
+الـ 4 بتعطيني 2، قفلة، يبقى هي الـ cycle
+
+462
+00:47:07,340 --> 00:47:11,500
+(2 3 4)، واللي بيظهرش بيكون fixed
+
+463
+00:47:11,500 --> 00:47:19,100
+صعبنا الشغل هذه؟ طيب، لحد هنا stop، انتهينا؟
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..9abe4e0f37d278fef2be673984ba8e63b47386b8
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sAFIBnw6VV0_postprocess.srt
@@ -0,0 +1,1852 @@
+1
+00:00:21,670 --> 00:00:27,730
+الان بنرجع مرة ثانية لما بدأنا بيه صباحا وهو اكمال
+
+2
+00:00:27,730 --> 00:00:31,950
+مناقشة مسائل ال permutations ان هنا سؤال تسعة و
+
+3
+00:00:31,950 --> 00:00:37,010
+عشرين في الفترة الصباحية وقلنالكوا احسبوا اضربوا
+
+4
+00:00:37,010 --> 00:00:40,850
+فينا ال sigma اللى طلعناها ضربة في نفسها تلت مرات
+
+5
+00:00:40,850 --> 00:00:44,690
+sigma تكيب تلاقيه على حاصل ضرب اللى هو ال three
+
+6
+00:00:44,690 --> 00:00:48,760
+cycles اللى موجودة عندكو بالفعل بعضكم قالوا
+
+7
+00:00:48,760 --> 00:00:52,620
+عملناها و طلعت زيه كما قلت تماما قلنا ماشي إذا
+
+8
+00:00:52,620 --> 00:00:57,500
+بننتقل الآن إلى السؤال واحد و تلاتين واحد و تلاتين
+
+9
+00:00:57,500 --> 00:01:02,980
+عرفلي ست جديدة سماها ال stabilizer لإيه و هي كل ال
+
+10
+00:01:02,980 --> 00:01:07,800
+alpha اللي موجودة فيه بحيث ان alpha of a بدي ساوي
+
+11
+00:01:07,800 --> 00:01:12,710
+ال aلما يقول الفا موجودة في جي الفا is a
+
+12
+00:01:12,710 --> 00:01:17,070
+permutation فلما يقول الفا of a بده يساوي ايه
+
+13
+00:01:17,070 --> 00:01:22,370
+معناته لسه بلازم تلاقي كل ال permutations اللي
+
+14
+00:01:22,370 --> 00:01:27,110
+بيكون فيهم ال a fixed ايش يعني fixed يعني ال
+
+15
+00:01:27,110 --> 00:01:32,940
+element هو صورة لنفسي الفا of a بده يساوي ايهأنا
+
+16
+00:01:32,940 --> 00:01:39,140
+بدي اذهب و ابحث في الـ SG على كل الـPermutations
+
+17
+00:01:39,140 --> 00:01:44,640
+التي تثبت منهم الانصار A بدي اذهب و اثبت ان هذا ال
+
+18
+00:01:44,640 --> 00:01:48,280
+list بلازر الـA هو عبارة عن subgroup من ال group
+
+19
+00:01:48,280 --> 00:01:53,760
+الأساسية اللي هي G بالرجوع إلى ذاكره إلى شبطر 3
+
+20
+00:01:53,760 --> 00:01:58,460
+بجينا ال subset من ال group نثبتها subgroup إذا
+
+21
+00:01:58,460 --> 00:02:02,660
+أثبتناتو conditions ال condition الأول أن ال
+
+22
+00:02:02,660 --> 00:02:06,500
+stabilizer لإيه is non-empty يعني على الأقل فيها و
+
+23
+00:02:06,500 --> 00:02:10,220
+لو عنصر واحد الأمر الثاني لو أخدت عنصرين في ال
+
+24
+00:02:10,220 --> 00:02:13,700
+stabilizer بدي أثبت أن الأول في معقولتي الثاني
+
+25
+00:02:13,700 --> 00:02:18,040
+موجود في ال stabilizer أن أثبتنا ذلك بيكون ال
+
+26
+00:02:18,040 --> 00:02:22,480
+stabilizer لإيه هي subgroup من من من ال group G
+
+27
+00:02:23,030 --> 00:02:27,910
+يبقى النقطة الأولى في الحل هو اثبات ان ال
+
+28
+00:02:27,910 --> 00:02:32,590
+stabilizer ل a is non-empty انا ادعي ان ال
+
+29
+00:02:32,590 --> 00:02:42,170
+stabilizer ل a is non-empty ليش؟ because ال
+
+30
+00:02:42,170 --> 00:02:48,810
+identity permutation موجودة في ال stabilizer ل ال
+
+31
+00:02:48,810 --> 00:02:55,070
+a senseالان ال identity permutation بيثبت اللي هو
+
+32
+00:02:55,070 --> 00:03:01,070
+بس هو اللي بيثبت كل العناصر كل العناصر بيثبت ..
+
+33
+00:03:01,070 --> 00:03:05,060
+اذا من بابا هو اللي بيثبت اللي هييبقى هنا non
+
+34
+00:03:05,060 --> 00:03:08,660
+-empty لأن الـ E موجودة في الاستبلايزر since ال
+
+35
+00:03:08,660 --> 00:03:12,760
+identity permutation لما اتأثر على ال element A
+
+36
+00:03:12,760 --> 00:03:19,060
+بتعطينا منه الـ A itself ومن ثم صار الاستبلايزر لـ
+
+37
+00:03:19,060 --> 00:03:25,760
+A فيها على الأقل ال identity permutation الان هذه
+
+38
+00:03:25,760 --> 00:03:31,490
+هي الخطوة الأولى الخطوة الثانيةبداية اقول ان ال
+
+39
+00:03:31,490 --> 00:03:36,350
+alpha و ال beta موجودة في ال stabilizer لل element
+
+40
+00:03:36,350 --> 00:03:44,110
+a تمام؟ اذا بناء عليه بقدر اقول له then ال alpha
+
+41
+00:03:44,110 --> 00:03:49,570
+لما تأثر على العنصر a بتعطينا العنصر a itself and
+
+42
+00:03:49,570 --> 00:03:54,550
+ال beta لما تأثر على العنصر a بتعطينا العنصر a
+
+43
+00:03:54,550 --> 00:04:01,640
+itselfأنا هاروح أخد المعلومة هذه واستنتج منها شغلة
+
+44
+00:04:01,640 --> 00:04:07,920
+تانية هذه ايش معناها لو جيت أثرت على الطرفين بال
+
+45
+00:04:07,920 --> 00:04:17,150
+beta inverse يبقى بيصيربيتا انفرس لبيتا of a يسوى
+
+46
+00:04:17,150 --> 00:04:26,150
+بيتا انفرس of a او بيتا انفرس لبيتا كلها لما اتأثر
+
+47
+00:04:26,150 --> 00:04:32,170
+على a بدها تسوى بيتا انفرس of a ال composition بين
+
+48
+00:04:32,170 --> 00:04:36,430
+ال permutation و معكوسة شو بعطينا ال identity
+
+49
+00:04:36,430 --> 00:04:40,650
+element لما اتأثر على ال element بعطيني نفس ال
+
+50
+00:04:40,650 --> 00:04:46,430
+elementيبقى هذا يطينا الـ beta inverse of a هذا
+
+51
+00:04:46,430 --> 00:04:53,070
+ايش معناه؟ ايش تفسيرك لهذه العبارة طبقا للتعريف
+
+52
+00:04:53,070 --> 00:04:57,710
+اللي احنا قيلينه؟ موجود كويس يبقى alpha inverse
+
+53
+00:04:57,710 --> 00:05:01,550
+موجودة في ال stabilizer لإيه؟ هاي معناها ليش انها
+
+54
+00:05:01,550 --> 00:05:08,560
+بتثبت العنصر a يبقى هذا معناهالـ beta inverse
+
+55
+00:05:08,560 --> 00:05:16,420
+موجودة في ال stabilizer لمن؟ لـ A الان consider خد
+
+56
+00:05:16,420 --> 00:05:22,060
+لمن؟ خد لل alpha beta inverse of A
+
+57
+00:05:25,670 --> 00:05:31,270
+يبقى انا اخدت العنصرين alpha و beta في موجودة في
+
+58
+00:05:31,270 --> 00:05:36,030
+ال stabilizer بدي اشوف هل ال alpha في beta inverse
+
+59
+00:05:36,030 --> 00:05:40,250
+بتثبت اللي ان ثبته خلاص موجودة في ال stabilizer و
+
+60
+00:05:40,250 --> 00:05:44,710
+التالي ال stabilizer عبارة عن subgroupيبقى هذا
+
+61
+00:05:44,710 --> 00:05:51,950
+الكلام بده يساوي alpha of beta inverse of a ويساوي
+
+62
+00:05:51,950 --> 00:05:57,830
+alpha of beta inverse of a عبارة عن ما؟ عبارة عن a
+
+63
+00:05:57,830 --> 00:06:04,530
+itself مدام عبارة عن a itself يبقى هذا a لكن أنا
+
+64
+00:06:04,530 --> 00:06:08,610
+عند هنا alpha موجودة في ال stabilizer يبقى alpha
+
+65
+00:06:08,610 --> 00:06:14,750
+of a بتعطيني ما؟ aإذا صار تأثير Alpha Beta Inverse
+
+66
+00:06:14,750 --> 00:06:18,230
+عليها سيكون الـ A itself، ما هو معناه هذا الكلام؟
+
+67
+00:06:18,230 --> 00:06:24,730
+أن Alpha Beta Inverse يبقى هذا معناه أن Alpha Beta
+
+68
+00:06:24,730 --> 00:06:30,430
+Inverse موجودة في ال stabilizer للـ Aمعنى هذا
+
+69
+00:06:30,430 --> 00:06:36,010
+الكلب ال stabilizer لإيه عبارة عن subgroup من G
+
+70
+00:06:36,010 --> 00:06:44,490
+يبقى ال stabilizer لمن؟ ال stabilizer لل a
+
+71
+00:06:44,490 --> 00:06:50,250
+subgroup من G و هو المطلوب إيه لخاطر أعطيك مثال
+
+72
+00:06:50,250 --> 00:06:54,910
+عملي و لو انه مش طالب و لا حاطب مثال عملي يوضح لك
+
+73
+00:06:54,910 --> 00:06:59,170
+إيش المقصود منه هذا فمثلا يعني for example
+
+74
+00:07:03,800 --> 00:07:11,560
+لو أخدت الـ G تساوي S3 S3 هي كم عنصر فيها يا شباب؟
+
+75
+00:07:11,560 --> 00:07:17,600
+ست عناصر اللي هو الأول اللي هو ال identity يبقى ال
+
+76
+00:07:17,600 --> 00:07:24,400
+identity والتاني اللي هو واحد اتنين تلاتة وبعد هيك
+
+77
+00:07:24,400 --> 00:07:31,000
+واحد اتنينوبعد هيك واحد تلاتة اتنين وبعد هيك واحد
+
+78
+00:07:31,000 --> 00:07:38,460
+تلاتة وبعد هيك اتنين تلاتة يبجي هي عناصر S3 كلهم
+
+79
+00:07:38,460 --> 00:07:45,010
+ستة عناصر S6 عناصريعني هاي الستة permutations اللي
+
+80
+00:07:45,010 --> 00:07:50,170
+موجودة وان في S3 الآن بدأ اجيب ال stabilizer
+
+81
+00:07:50,170 --> 00:07:55,970
+للواحد والستابليزر للاتنين والستابليزر للتلاتة هاي
+
+82
+00:07:55,970 --> 00:08:00,790
+العناصر اللي موجودة في اي permutation الان بدأ اجي
+
+83
+00:08:00,790 --> 00:08:08,120
+أخدله ال stabilizer لمن للواحد تساوي منالمقصود
+
+84
+00:08:08,120 --> 00:08:12,560
+بالـstabilizer للواحد يعني كل ال permutation اللي
+
+85
+00:08:12,560 --> 00:08:17,160
+فيهم الواحد fixed يعني صورة الواحد هي الواحد
+
+86
+00:08:17,160 --> 00:08:21,660
+itself ماشي
+
+87
+00:08:21,660 --> 00:08:25,600
+هو واحد اتنين تلاتة ال identity وال identity بتكون
+
+88
+00:08:25,600 --> 00:08:29,560
+واحد بين جثين او اتنين بين جثين او تلاتة بين جثين
+
+89
+00:08:29,560 --> 00:08:34,920
+هذه ال order اللي هيسوي تلاتة وبالتالي كيف خلتها
+
+90
+00:08:34,920 --> 00:08:39,820
+ال identity؟أما لو كنت واحد اتنين تلاتة واحد اتنين
+
+91
+00:08:39,820 --> 00:08:43,440
+تلاتة بيقولك هذا كلامك صح بس هذه معناته ان الواحد
+
+92
+00:08:43,440 --> 00:08:46,500
+صرت اتنين والاتنين صرت تلاتة والتلاتة صرت واحد
+
+93
+00:08:46,500 --> 00:08:50,000
+يبقى هذه ليست ال identity يبقى كتبناك ال identity
+
+94
+00:08:50,000 --> 00:08:56,110
+لحالك كان بإمكاني أقولك هذهو أسكت بدل ال E كان
+
+95
+00:08:56,110 --> 00:09:00,350
+ممكن أقولك اتنين و أسكت تلاتة و أسكت stop بقولش
+
+96
+00:09:00,350 --> 00:09:05,910
+أربعة و أسكت ليش؟ لأن ال S3 باس معمولة على ستم
+
+97
+00:09:05,910 --> 00:09:10,130
+تلاتة عناصر واحد اتنين تلاتة تمام؟ الان بدي أجيب
+
+98
+00:09:10,130 --> 00:09:13,950
+ال stabilizer اللي هو يعني مين هم ال permutation
+
+99
+00:09:13,950 --> 00:09:18,370
+اللي فيهم الواحد fixed يعني اللي الواحد صورته واحد
+
+100
+00:09:18,370 --> 00:09:23,400
+باجي ال identity هذهمنهم اه لان بيثبت الواحد
+
+101
+00:09:23,400 --> 00:09:27,100
+والاتنين والتلاتة مش ع جد الواحد يبقى باجي بقوله
+
+102
+00:09:27,100 --> 00:09:32,220
+ال identity pyramid اشتنام هذي بيثبت الواحد هذي
+
+103
+00:09:32,220 --> 00:09:38,100
+بيثبت الواحد هذي بيثبت الواحد هذي يبقى ايش اتنين
+
+104
+00:09:38,100 --> 00:09:42,820
+تلاتة هذي اللي فيها الواحد fixed مظهرليش يبقى هنا
+
+105
+00:09:42,820 --> 00:09:50,570
+اتنين وتلاتة تمامفي غيرهم؟ لأ طب لو بدي ال
+
+106
+00:09:50,570 --> 00:09:56,250
+stabilizer للي اتنين كل ال permitations المثبتة
+
+107
+00:09:56,250 --> 00:10:01,290
+للي اتنين ال identity واحدة و بداجة دولهذه اتنين
+
+108
+00:10:01,290 --> 00:10:05,590
+صورتة واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة
+
+109
+00:10:05,590 --> 00:10:06,290
+واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد
+
+110
+00:10:06,290 --> 00:10:07,010
+وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+111
+00:10:07,010 --> 00:10:07,070
+واحد وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد
+
+112
+00:10:07,070 --> 00:10:07,610
+وهذه اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+113
+00:10:07,610 --> 00:10:12,070
+اتنين صورتة واحد وهذه اتنين صورتة واحد وهذه
+
+114
+00:10:12,070 --> 00:10:20,610
+اتنين
+
+115
+00:10:20,610 --> 00:10:23,030
+صور
+
+116
+00:10:26,470 --> 00:10:31,930
+هذه لا تثبت هذه لا تثبت هذه لا تثبت التلاتة يبقى
+
+117
+00:10:31,930 --> 00:10:36,750
+مافيش غيرهم يبقى عرفنا أيش المقصود بال stabilizer
+
+118
+00:10:36,750 --> 00:10:42,170
+لل element يعني كل ال permutations اللي موجودة في
+
+119
+00:10:42,170 --> 00:10:46,210
+ال group اللي هنا بحيثهذه ال parameter يكون ال a
+
+120
+00:10:46,210 --> 00:10:51,470
+هذا رقم ثابت يعني fixed صورته هو نفسه فهمنا إيش
+
+121
+00:10:51,470 --> 00:10:56,590
+معنى stabilizer لإيه؟ طيب ننتقل الآن إلى السؤال
+
+122
+00:10:56,590 --> 00:11:05,610
+الذي يليه اللي هو 32 سؤال 32 بيقول ما يأتي أخدنا
+
+123
+00:11:05,610 --> 00:11:12,390
+beta تساوي واحد تلاتة خمسة سبعة تسعة تمانية ستة
+
+124
+00:11:24,410 --> 00:11:32,160
+مضروبة في اتنين اربع عاشرة2 4 10 بالشكل اللي عن
+
+125
+00:11:32,160 --> 00:11:36,560
+هنا بقول what is the smallest positive integer n
+
+126
+00:11:36,560 --> 00:11:47,440
+for which بحيث أن بيتا أس n يسوى بيتا أس ناقص خمسة
+
+127
+00:11:57,540 --> 00:12:02,820
+نرجع لسؤالنا مرة تانية ماتينا permutation beta
+
+128
+00:12:02,820 --> 00:12:09,680
+عبارة عن product of two disjoint cycles تمام و
+
+129
+00:12:09,680 --> 00:12:13,920
+واحد حطينا فواصل مرة هذه فواصل ليش مش هنا الرقم
+
+130
+00:12:13,920 --> 00:12:18,870
+عشرةرقمين بلاش تقول هذا اربع يعني طوله اربع وهذا
+
+131
+00:12:18,870 --> 00:12:22,790
+طوله جد ما يكون بقولها يبقى حاطين الفواصل مش
+
+132
+00:12:22,790 --> 00:12:27,570
+هنقولك ان العشرة عبارة عناش عنصر واحد ما علينا مش
+
+133
+00:12:27,570 --> 00:12:35,990
+مشكلةبقولي ما هو أصغر رقم N بحط اس ل Beta بده
+
+134
+00:12:35,990 --> 00:12:42,450
+يعطيني Beta أس سالب خمسة يعني حددتلك أصغر رقم ها
+
+135
+00:12:42,450 --> 00:12:47,970
+مش حيال لا رقام تمام بقولي بدي قديش قيمة N هذه
+
+136
+00:12:47,970 --> 00:12:53,190
+بقول و الله كويسة الآن احنا لو جينا لل order كبار
+
+137
+00:12:53,190 --> 00:12:53,570
+ال B
+
+138
+00:13:01,200 --> 00:13:07,960
+هل في بينهم عنصر مشتركيبقى ال order ل beta هو ال
+
+139
+00:13:07,960 --> 00:13:12,660
+least common multiple ما بين طول الأولى اتنين
+
+140
+00:13:12,660 --> 00:13:19,260
+اربعة ستة سبعة و طول التانية كده تلاتة يبقى ال
+
+141
+00:13:19,260 --> 00:13:24,540
+least common multiple لهم كده واحد وعشرين معناته
+
+142
+00:13:24,540 --> 00:13:29,700
+ال order ل beta بدي نسوي واحد وعشرين هذا معناه ان
+
+143
+00:13:29,700 --> 00:13:35,360
+beta أس واحد وعشرينيساوي ال identity والواحد
+
+144
+00:13:35,360 --> 00:13:41,200
+وعشرين هو أصغر الرقم حطيته لل أس بيتا اتانى مين
+
+145
+00:13:41,200 --> 00:13:46,160
+اتانى ال identity طيب ايش بيقولى فى السؤال ما هو
+
+146
+00:13:46,160 --> 00:13:52,880
+أصغر رقم ان بتحطه أس لبيتا بتطلع بيتا أس خمسة
+
+147
+00:13:52,880 --> 00:14:02,370
+بقوله آه الآنباجي بقوله ولكن ال beta أُس n بدها
+
+148
+00:14:02,370 --> 00:14:09,130
+تساوي beta أُس سالب خمسة implies شو رايك لو ضربت
+
+149
+00:14:09,130 --> 00:14:15,130
+الطرفين في beta أُس خمسة بس فيدي عندى هنا beta أُس
+
+150
+00:14:15,130 --> 00:14:21,990
+n زائد خمسة بده يساوي مين ال identity لما اطلع في
+
+151
+00:14:21,990 --> 00:14:27,840
+هذه هيك واطلع في هذه هيكو قال لي في السؤال بيتا
+
+152
+00:14:27,840 --> 00:14:34,660
+الان هذا أصغر رقم حاطيته كأس لبيتا طلع بيتا أس
+
+153
+00:14:34,660 --> 00:14:39,320
+سالب خمسة إذا ما هي العلاقة بين الرقمين الاتنين
+
+154
+00:14:39,320 --> 00:14:48,160
+هدول بيك اسمه والله بيسويه بيسويه لأنه أصغر رقم
+
+155
+00:14:48,160 --> 00:14:53,800
+لكن قال لي الان هذا رقم حيال اللهبقوله إذا ال 21
+
+156
+00:14:53,800 --> 00:14:58,580
+لازم تجسم من الرقم اللي عندنا هذا لكن كونه قاللي
+
+157
+00:14:58,580 --> 00:15:04,740
+إن أصغر الرقم و أني أثبت ان ال order ل beta هو 21
+
+158
+00:15:05,480 --> 00:15:11,400
+إذا هذا الرقم من الاتنين هدول مع بعض بستنتج ان ال
+
+159
+00:15:11,400 --> 00:15:17,360
+N زائد خمسة يساوي واحد وعشرين يبقى ال N تساوي كده؟
+
+160
+00:15:17,360 --> 00:15:26,840
+ستاشر إذا أصغر رقم بحط أس ل Beta بيطلع لي Beta أس
+
+161
+00:15:26,840 --> 00:15:33,880
+لخمسة هو الرقم اين؟ الرقماللي هو ستاشر طيب السؤال
+
+162
+00:15:33,880 --> 00:15:40,940
+اللي بعده نفس الفكرة بس ماقلش أصغر رقم هذا اتنين و
+
+163
+00:15:40,940 --> 00:15:47,250
+تلاتين تلاتة و تلاتين ماعطيني Alpha كتالةيبقى هذه
+
+164
+00:15:47,250 --> 00:15:52,250
+تلاتة و تلاتين ماتيني Alpha تساوي اللي هو واحد
+
+165
+00:15:52,250 --> 00:15:58,730
+تلاتة خمسة سبعة تسعة واحد تلاتة خمسة سبعة تسعة
+
+166
+00:15:58,730 --> 00:16:03,350
+بالشكل اللي عندنا هذا وهذه مضروبة في اتنين اربعة
+
+167
+00:16:03,350 --> 00:16:10,970
+ستة اتنين اربعة ستة وهذه مضروبة كمان في تمانية و
+
+168
+00:16:10,970 --> 00:16:16,870
+عشرة تمانية و عشرة بالشكل اللي عندنا هذاو بقول ليش
+
+169
+00:16:16,870 --> 00:16:27,330
+إذا كان ال A أُس M is a خمسة cycle is a خمسة cycle
+
+170
+00:16:27,330 --> 00:16:37,210
+يعني ال cycle طولها خمسة خمسة cycle what can you
+
+171
+00:16:37,210 --> 00:16:42,870
+say about M what
+
+172
+00:16:42,870 --> 00:16:53,220
+اللي هوwhat can you say
+
+173
+00:16:53,220 --> 00:17:00,840
+about M السؤال
+
+174
+00:17:00,840 --> 00:17:05,080
+هذا زي ما انت بلاحظ هو السؤال اللى جابله مع الفارق
+
+175
+00:17:05,080 --> 00:17:12,120
+شو الفارق هناك قالك ان أصغر رقم مظبوط هنا ماجليش M
+
+176
+00:17:12,120 --> 00:17:18,900
+كل اللى قالوه ليشجرح قال لي الام خمسة cycle يعني
+
+177
+00:17:18,900 --> 00:17:25,920
+ال order له يسوي كده؟ ال order لام خمسة تمام لإنه
+
+178
+00:17:25,920 --> 00:17:29,840
+قال له ال cycle طولة خمسة مدام طولة خمسة إذا ال
+
+179
+00:17:29,840 --> 00:17:35,180
+order لهذه ال cycle يسوي خمسة يعني a أس m أس خمسة
+
+180
+00:17:35,180 --> 00:17:40,590
+لازم يعطينا مين؟ ال islandالألفة بالشكل اللي عندها
+
+181
+00:17:40,590 --> 00:17:44,870
+ده باذي بتطلع في three cycles ولا element مشترك
+
+182
+00:17:44,870 --> 00:17:49,760
+فيه ما بينهماإذا على طول الخطب بروح بقوله ال order
+
+183
+00:17:49,760 --> 00:17:55,600
+لل alpha بده يساوي ال least common multiple لمن؟
+
+184
+00:17:55,600 --> 00:18:00,500
+لطول الأولى خمسة وطول الثانية تلاتة وطول الأخيرة
+
+185
+00:18:00,500 --> 00:18:05,460
+اتنين يبقى الرقم اللذي يقسم على او الرقم اللي
+
+186
+00:18:05,460 --> 00:18:10,560
+بيقسمه التلاتة في انا نواحد هو الرقم كم؟ تلاتين
+
+187
+00:18:10,560 --> 00:18:15,780
+ممتاز جدايبقى ال order ل alpha بده يسوى تلاتين
+
+188
+00:18:15,780 --> 00:18:20,800
+بيبقى ال alpha أس تلاتين بده يسوى من ال identity
+
+189
+00:18:20,800 --> 00:18:26,200
+هذا معناه ان ال alpha أس تلاتين بده يسوى ال
+
+190
+00:18:26,200 --> 00:18:32,240
+identity element والتلاتين أصغر رقم بحط أس ل alpha
+
+191
+00:18:32,240 --> 00:18:36,850
+بيطل من ال identity اللي أنا اشي قال ليهقال لي لو
+
+192
+00:18:36,850 --> 00:18:45,790
+كان ال AM is A خمسة cycle يعني ال AM لو جيت قلت له
+
+193
+00:18:45,790 --> 00:18:51,930
+مين هم الخمسة cycle قلت A B C D E هاي خمسة cycle
+
+194
+00:18:52,340 --> 00:18:59,020
+معناته ان ال order ل ال AM بده يسوي كده؟ بده يسوي
+
+195
+00:18:59,020 --> 00:19:06,880
+خمسة معناته ان ال AM أُس خمسة بده يعطي نمين ال
+
+196
+00:19:06,880 --> 00:19:13,280
+identity يعني معنى هذا الكلام أن A خمسة M بده يسوي
+
+197
+00:19:13,280 --> 00:19:19,740
+نمين ال identity elementهل حطينا قيود أو شروط على
+
+198
+00:19:19,740 --> 00:19:26,680
+M لا ماحطيناش على M ولا قيد ولا شرط اللهم إلا قلنا
+
+199
+00:19:26,680 --> 00:19:31,180
+Alpha أس M عبارة عن خمسة cycle يعني ال cycle طولها
+
+200
+00:19:31,180 --> 00:19:36,540
+يساوي خمسة طيب ماقلتش زي السؤال اللي جابله إن ال N
+
+201
+00:19:36,540 --> 00:19:41,910
+أصغر رقام لا ماحطيتش قيود على M بناء عليهلما يكون
+
+202
+00:19:41,910 --> 00:19:46,670
+عندى alpha أس تلاتين والتلاتين هو أصغر رقم بدي
+
+203
+00:19:46,670 --> 00:19:50,970
+يعطينا ال identity وال A أس خمسة M يساوي ال
+
+204
+00:19:50,970 --> 00:19:56,070
+identity إذا ما هي العلاقة ما بين التلاتين والخمسة
+
+205
+00:19:56,070 --> 00:20:05,910
+M تلاتين تقسم الخمسة M أو الخمسة M مضعفات التلاتين
+
+206
+00:20:05,910 --> 00:20:10,390
+هذه و هذه اتنين نفس الصورةاذا من الاتنين هدول بس
+
+207
+00:20:10,390 --> 00:20:18,990
+تنتج انه تلاتين تقسم خمسة M مين
+
+208
+00:20:18,990 --> 00:20:24,790
+اللي بيحكي؟ ايوة ايش بتقول؟ ال A بتسوي ال Alpha؟ و
+
+209
+00:20:24,790 --> 00:20:30,210
+مين ال A هذه؟ ال A أنا قلته سوي Alpha؟أنا ماقلتش
+
+210
+00:20:30,210 --> 00:20:35,490
+أنا الكلام هو قال لي a أُس m is a خمسة كلمة معناته
+
+211
+00:20:35,490 --> 00:20:40,610
+permutation والله alpha أُس m قال alpha أُس m هو
+
+212
+00:20:40,610 --> 00:20:46,720
+سؤال طب إذا alpha أُس m مظبوطالمقصود اللي قلتلك
+
+213
+00:20:46,720 --> 00:20:51,000
+ايه و الله اللي هيبقى هذا Alpha أس M خمسة cycle
+
+214
+00:20:51,000 --> 00:20:56,020
+على أي حال حتى لو قلنا A أس M يسوى خمسة cycle
+
+215
+00:20:56,020 --> 00:21:02,380
+معناته ال A permutation صح
+
+216
+00:21:02,380 --> 00:21:08,000
+هذه احنا عدلناها ألفة أس M is A خمسة cycle معناته
+
+217
+00:21:08,000 --> 00:21:16,440
+هذه Alpha أس M معناته هذه Alpha هذه Alphaيبقى هذه
+
+218
+00:21:16,440 --> 00:21:23,760
+alpha يبقى التلاتين التلاتين بتقسم الخمسة M لو
+
+219
+00:21:23,760 --> 00:21:31,540
+جسمنا كله على خمسة بيظل عناش ستة تقسم ال M إذا ال
+
+220
+00:21:31,540 --> 00:21:39,900
+M شو علاقتها بستة مضاعفاتها يبقى هنا ال M is a
+
+221
+00:21:39,900 --> 00:21:48,100
+multiple of 6يبقى الام اللي عندنا هذه هي مضاعفات
+
+222
+00:21:48,100 --> 00:21:53,260
+مين؟ مضاعفات العدد ستة شوف السؤال اللي جابله وقلنا
+
+223
+00:21:53,260 --> 00:21:59,920
+لأ تساوي مثلا ستة دوري بس هنا مضاعفاته ليش؟ لأنه
+
+224
+00:21:59,920 --> 00:22:05,440
+لهناك هو أصغر رقم يعني يدخل في ال order بس احنا
+
+225
+00:22:05,440 --> 00:22:10,160
+عندنا في هذا السؤال ال order تلاتين يبقى أي رقم
+
+226
+00:22:10,160 --> 00:22:16,570
+آخر التلاتين بتجسم مين؟تجسم هذا الرقم هذا كان سؤال
+
+227
+00:22:16,570 --> 00:22:22,610
+تلاتة وتلاتين سؤال ستة وتلاتين قال لي في S4 بدنا
+
+228
+00:22:22,610 --> 00:22:28,010
+Cyclic subgroup of order أربعة و non-cyclic of
+
+229
+00:22:28,010 --> 00:22:38,230
+order أربعة سؤال ستة وتلاتين سؤال ستة وتلاتين بدنا
+
+230
+00:22:38,230 --> 00:22:51,580
+Cyclic groupof order أربعة in S4 وبدنا non-cyclic
+
+231
+00:22:51,580 --> 00:23:02,660
+group of order أربعة برضه in S4 solution S4
+
+232
+00:23:02,660 --> 00:23:09,500
+أكام عنصر فيها شباببس تمانية اس اربعة وعشرين عنصر
+
+233
+00:23:09,500 --> 00:23:14,380
+اللي قال تمانية بتقدر تجيبلي ال sub group من ال S
+
+234
+00:23:14,380 --> 00:23:18,220
+أربعة ال order اللي هيساوي تمانية يعني مافيش فيها
+
+235
+00:23:18,220 --> 00:23:25,660
+إلا تمان عناصر وقد D4 صحيح الكلام صحيح يبقى D4 هي
+
+236
+00:23:25,660 --> 00:23:31,560
+ال sub group من ال S4 وال order اللي هيساوي تمانية
+
+237
+00:23:31,560 --> 00:23:38,610
+تمامأي subgroup من ال D4 هي subgroup من ال S4 يبقى
+
+238
+00:23:38,610 --> 00:23:43,570
+إذا بتجيبلي من ال D4 Cyclic group ال order اللي
+
+239
+00:23:43,570 --> 00:23:50,470
+هيساوي أربعة بكل قدّيت الواجب يلا هيغششناك من D4
+
+240
+00:23:50,470 --> 00:23:53,730
+بتقدر تجيبلي ال subgroup ال order اللي هيساوي
+
+241
+00:23:53,730 --> 00:23:54,350
+أربعة
+
+242
+00:24:07,840 --> 00:24:11,460
+D4D4R0R90R180R270HVDD' ممتاز جدا يبقى ال rotation
+
+243
+00:24:11,460 --> 00:24:18,080
+واحدة R290الأردر لها يساوي أربعة وتساوي ال
+
+244
+00:24:18,080 --> 00:24:22,100
+subgroup generated by R ميتين وسبعين لأن ال R
+
+245
+00:24:22,100 --> 00:24:26,080
+ميتين وسبعين هي ال inverse لمين يبقى احنا بدنا
+
+246
+00:24:26,080 --> 00:24:29,040
+واحدة بدناش تنتين بس تنتين واحدة والله يعطيك
+
+247
+00:24:29,040 --> 00:24:37,860
+العافية يبقى باجي بقوله الان the cyclic subgroup
+
+248
+00:24:37,860 --> 00:24:47,620
+اللي هي مينالـ R تسعين اللي عناصرها R نوت و R
+
+249
+00:24:47,620 --> 00:24:58,200
+تسعين و R مية و تمانين و R ميتين و سبعين هذه is of
+
+250
+00:24:58,200 --> 00:25:04,980
+order اللي هو أربعة إذا
+
+251
+00:25:04,980 --> 00:25:12,960
+بدك تكتبها على شكل cycle يبقى عندكالارت السعيد هي
+
+252
+00:25:12,960 --> 00:25:18,820
+عبارة عن واحد اتنين تلاتة اربع يبقى هي ال cycle
+
+253
+00:25:18,820 --> 00:25:24,140
+اللي عندنا هنا تمام يبقى هذه هي الارت السعيد هذا
+
+254
+00:25:24,140 --> 00:25:28,120
+لو حبيت تشتغل ال cycles حبيت مباشرة تشتغل مع الناس
+
+255
+00:25:28,120 --> 00:25:37,110
+مشكلة طيب بدنا non-cyclic يبقى دي non-cyclica
+
+256
+00:25:37,110 --> 00:25:45,170
+group of order أربعة أزم تقدر تجيب أكتر من واحدة
+
+257
+00:25:45,170 --> 00:25:50,970
+ال sub group تحتوي على ال identity الحين بقدر
+
+258
+00:25:50,970 --> 00:25:57,850
+أقولك ال identity are not وكمان are مية و تمانين
+
+259
+00:25:59,600 --> 00:26:08,640
+وحط عليهم H والر مية و تمانين فيه H الشكل اللي
+
+260
+00:26:08,640 --> 00:26:17,130
+عندنا هناهذه non-cyclic لأن الـR180S² بتعطيك ال
+
+261
+00:26:17,130 --> 00:26:21,470
+identity يبقى ماهياش generator هذه بتعطيك ال
+
+262
+00:26:21,470 --> 00:26:26,170
+identity التربية بتعطيك ال identity وهذه التربية
+
+263
+00:26:26,170 --> 00:26:30,730
+برضه بتعطيك ال identity طبعا هذه لو رجعت للجدول
+
+264
+00:26:30,730 --> 00:26:35,850
+صفة 31 يبقى R0 وR180
+
+265
+00:26:38,670 --> 00:26:42,510
+وهذه لو فتحنا الجدول في صفحة مية و واحد و تبقى في
+
+266
+00:26:42,510 --> 00:26:49,150
+صفحة واحد و تلاتين و طبعا حسبناها قبلك اللي هو ال
+
+267
+00:26:49,150 --> 00:26:55,250
+R مية و تمانين في H R مية و تمانين R مية و تمانين
+
+268
+00:26:55,250 --> 00:27:07,200
+في H بتعطيك V يبقى V طبعا لو حطيت ايشحط ما احنا
+
+269
+00:27:07,200 --> 00:27:11,260
+بقوله فيه كمان واحدة تانية يعني اول اتنين خليهم زي
+
+270
+00:27:11,260 --> 00:27:12,900
+ما هو ده اللي بتحطهم بنفع
+
+271
+00:27:16,940 --> 00:27:22,520
+أحنا أعطيتك كمثال بسيط يعني انت .. انت .. انت ..
+
+272
+00:27:22,520 --> 00:27:26,780
+بس لما تجيب عناصر بدك تتأكد انه لو وفعته لأي أس
+
+273
+00:27:26,780 --> 00:27:30,280
+بدي يكون موجود و لو ضربت اثنين في بعض بدي يكون
+
+274
+00:27:30,280 --> 00:27:34,100
+موجود فيها عشان تتأكد ان هذه فعلا subgroup ليها
+
+275
+00:27:34,100 --> 00:27:37,740
+closed under the operation أنا اختارت من D4 لإنه
+
+276
+00:27:37,740 --> 00:27:41,400
+أسهل ليه لإن D4 أنا ازهجت و أنا بشرح فيها و يمكن
+
+277
+00:27:41,400 --> 00:27:45,520
+يعطينا عليها مثال بدل مثال عشرة يبقى أصبحت محفوظة
+
+278
+00:27:45,520 --> 00:27:51,150
+بالنسبة لناومن هنا نجب لك هذا كمثال بسيط منها على
+
+279
+00:27:51,150 --> 00:27:57,310
+أي حال هذا كان سؤال اللي هو ستة و تلاتين بعده عندك
+
+280
+00:27:57,310 --> 00:28:04,430
+سبعة و أربعين وما أدراك سبعة و أربعين سؤال سبعة و
+
+281
+00:28:04,430 --> 00:28:11,010
+أربعين بيقول ما ياتي show that every elementالفة
+
+282
+00:28:11,010 --> 00:28:19,370
+الموجودة في الان أي element في الان can be
+
+283
+00:28:19,370 --> 00:28:23,930
+expressed as a three cycle or product of a three
+
+284
+00:28:23,930 --> 00:28:35,310
+cycle يبقى is written as a three cycle or product
+
+285
+00:28:35,310 --> 00:28:39,450
+of a three cycles
+
+286
+00:28:43,140 --> 00:28:48,560
+فكر معايا كويس السؤال ليس سهلا لكن بده تفكير
+
+287
+00:28:48,560 --> 00:28:56,400
+الحقيقة ومن خلال التفكير قد نصل الى النتيجة حد
+
+288
+00:28:56,400 --> 00:29:01,800
+فيكوا حلوا الدار هذا ايه او جاب فكرة يعنيطبعا
+
+289
+00:29:01,800 --> 00:29:06,160
+هيقول لي السؤال مش هذا دي؟ اه مش هذا دي صحيح رغم
+
+290
+00:29:06,160 --> 00:29:09,540
+انه فردي لكن مايعطيك hint في الكتاب لكن hint لن
+
+291
+00:29:09,540 --> 00:29:14,880
+تستفيد منها شيئا مش هتعرف تشغلها طيب على اي حال
+
+292
+00:29:14,880 --> 00:29:21,200
+السؤال مرة تانية بيقولي اي even permutation او اي
+
+293
+00:29:21,200 --> 00:29:25,580
+element موجود في a,nis written يابنك يمكن نكتبه
+
+294
+00:29:25,580 --> 00:29:29,800
+على شكل three cycle يعني ما product of three
+
+295
+00:29:29,800 --> 00:29:40,960
+cycles طيب يبقى الحل كتالي solution let
+
+296
+00:29:40,960 --> 00:29:52,510
+alpha موجودة في الثم الـ alpha is an even
+
+297
+00:29:52,510 --> 00:29:58,490
+permutation تمام؟
+
+298
+00:29:58,490 --> 00:30:03,530
+لما أقول لك even permutation يعني يمكن حصل ضرب two
+
+299
+00:30:03,530 --> 00:30:09,890
+transpositions صح؟ يمكن أربع transpositions مش
+
+300
+00:30:09,890 --> 00:30:15,210
+تلاتة انت لازم تصير goodيمكن ستة transpositions
+
+301
+00:30:15,210 --> 00:30:20,790
+يمكن تمانية قد ما يكون يكون أيوة يبقى هنا ال alpha
+
+302
+00:30:20,790 --> 00:30:26,750
+بكتبها على شكل أزواج من ايه من ال transpositions
+
+303
+00:30:26,750 --> 00:30:33,630
+يبقى باجي بقوله هذا بده يعطينا ان ال alpha is
+
+304
+00:30:33,630 --> 00:30:42,050
+written as a product of
+
+305
+00:30:43,150 --> 00:30:49,410
+pairs أزواج of two cycles أو transpositions
+
+306
+00:30:54,380 --> 00:31:00,520
+طيب بدي اخد زوج من هذه الأزواج يعني بدي اخد اتنين
+
+307
+00:31:00,520 --> 00:31:05,660
+transpositions واشوف هل بقدر اكتبهم على شكل three
+
+308
+00:31:05,660 --> 00:31:11,020
+cycles ولا لأ انه كان كل زوج بنقدر نكتبه على شكل
+
+309
+00:31:11,020 --> 00:31:15,480
+three cycles يبقى ال alpha فيها اتنين ولا اربع ولا
+
+310
+00:31:15,480 --> 00:31:22,220
+ستة ولا تمانية كلها بقدر اكتبها على شكلمشان هنا
+
+311
+00:31:22,220 --> 00:31:26,540
+قلت alpha بقدر اكتبها على شكل of pairs of two
+
+312
+00:31:26,540 --> 00:31:32,140
+cycle يعني الزوج يعني اتنين transpositions يبقى
+
+313
+00:31:32,140 --> 00:31:42,180
+هنا لو جيت قلت if ال a والb والc والd are distinct
+
+314
+00:31:42,180 --> 00:31:44,880
+then
+
+315
+00:31:46,690 --> 00:31:52,130
+this pair has
+
+316
+00:31:52,130 --> 00:32:02,670
+the following cases
+
+317
+00:32:02,670 --> 00:32:07,310
+أنا
+
+318
+00:32:07,310 --> 00:32:13,270
+عندي أربع عناصر مختلفة والزوج هذا يعني even
+
+319
+00:32:13,270 --> 00:32:21,520
+permutationإذا الاحتمال الأول انه يكون على شكل AB
+
+320
+00:32:21,520 --> 00:32:32,060
+في AB يعني أول عنصر مكررات AB زي CD CD CD CD زي A
+
+321
+00:32:32,060 --> 00:32:40,060
+B A B طب هدول حصل ضرب مش بيطينا مين ال
+
+322
+00:32:40,060 --> 00:32:43,320
+parameter one اتنين واحد اتنين لو ضربت في عضاش
+
+323
+00:32:43,320 --> 00:32:51,730
+بتعطيلهبتعطيك واحد اتنين؟ بتعطيلك مين؟identity
+
+324
+00:32:51,730 --> 00:32:55,510
+permutation مش قلنا ال identity permutation نستطيع
+
+325
+00:32:55,510 --> 00:32:59,450
+نسكبها على شكل زوجي ومكتوبة عندك في الكتاب واحد
+
+326
+00:32:59,450 --> 00:33:02,970
+اتنين واحد اتنين او واحد اتنين واحد اتنين تلاتة
+
+327
+00:33:02,970 --> 00:33:06,590
+اربعة تلاتة اربعة او خمسة ستة خمسة يعني بقدر
+
+328
+00:33:06,590 --> 00:33:11,350
+اكتبها على شكل زوج اذا هذه تعطينا اللي هو الاحتمال
+
+329
+00:33:11,350 --> 00:33:17,050
+الاول انه E لان ال E is an even permutation
+
+330
+00:33:17,050 --> 00:33:26,910
+الاحتمال الثانيإنه تبقى على الشكل ABC صح ولا لأ
+
+331
+00:33:26,910 --> 00:33:32,370
+لإحتمال التالت يكون فش عنصر فيما بينهما لإحتمال
+
+332
+00:33:32,370 --> 00:33:38,570
+الثالث والاخير ان يكون على الشكل ABCD
+
+333
+00:33:38,570 --> 00:33:45,750
+في غير هيك؟طيب في كل حالة من الحالات الثلاث انا
+
+334
+00:33:45,750 --> 00:33:50,070
+بدي أبيّلك انه بنكتبها على شكل product of three
+
+335
+00:33:50,070 --> 00:33:55,050
+cycles او three cycle واحدة تمام خلّينا نمسك
+
+336
+00:33:55,050 --> 00:34:01,710
+الحالة الأولى يبقى الحالة الأولى اللي هي a b a b
+
+337
+00:34:01,710 --> 00:34:08,930
+اللي هي ال identity permutation تمامأليست ال
+
+338
+00:34:08,930 --> 00:34:16,470
+identity permutation هي عبارة عن ال a,b,c الكل
+
+339
+00:34:16,470 --> 00:34:22,970
+تكييف؟مش هذه طولها تلاتة يبقى ال order اللي هي
+
+340
+00:34:22,970 --> 00:34:27,530
+تلاتة يبقى مكعبها بدي يعطينا ال identity يبقى كأنه
+
+341
+00:34:27,530 --> 00:34:32,230
+ضارب ال cycle ABC في ABC في ABC يبقى product of
+
+342
+00:34:32,230 --> 00:34:36,450
+three cycles مظبوط ولا لا؟ حد بيقدر يعترض على هذا
+
+343
+00:34:36,450 --> 00:34:41,330
+الكلام اللي عنده اعتراض يحكي حتى نفند هذا الاعتراض
+
+344
+00:34:41,330 --> 00:34:52,750
+يبقى هذا اسمه productof three cycles تمام؟ يبقى
+
+345
+00:34:52,750 --> 00:34:56,890
+خلاصه من النقطة الأولى شوف النقطة الأولى اعتمدت
+
+346
+00:34:56,890 --> 00:35:01,530
+على فهمك فلانت فاهم فعلا ان ال identity variation
+
+347
+00:35:01,530 --> 00:35:07,270
+is an even وكيف كتبناها لما صارت even طبعا مكتوب
+
+348
+00:35:07,270 --> 00:35:11,110
+عندك على التواب وشرحالكه لأستاذ محمود طيب نيجي
+
+349
+00:35:11,110 --> 00:35:17,040
+للنقطة الثانيةالنقطة الثانية اللى همين اللى هى ال
+
+350
+00:35:17,040 --> 00:35:24,140
+A B A C كويس بدي أجيب ال composition ما بين
+
+351
+00:35:24,140 --> 00:35:28,720
+الاتنين لإنه فى عنصر مشترك فى ما بينهما إذا هذول
+
+352
+00:35:28,720 --> 00:35:34,080
+are not disjoint بدي أخليهم disjoint يبقى لو جيت
+
+353
+00:35:34,080 --> 00:35:41,560
+قلتلك العنصر الأول هو AA ثورت مين؟ C الـC ثورتها
+
+354
+00:35:41,560 --> 00:35:49,720
+مين؟ C لأن الـC هنا مقفل، C بعد ذلك الـC ثورتها A
+
+355
+00:35:49,720 --> 00:35:57,120
+والـA ثورتها B بعد ذلك الـB مقفل ثورتها B والـB
+
+356
+00:35:57,120 --> 00:36:03,060
+ثورتها موجودة يبقى قفلة يبقى ال composition ما بين
+
+357
+00:36:03,060 --> 00:36:10,640
+اتنين هذول هي three cycleأولتين اتنين بساطة
+
+358
+00:36:10,640 --> 00:36:19,100
+المشكلة في التالتة يبقى التالتة هاية التالتة عنا A
+
+359
+00:36:19,100 --> 00:36:29,400
+B C D يوسام هذه الخبرة بتلعب دور كبير هل بقدر اكتب
+
+360
+00:36:29,400 --> 00:36:36,710
+هدولعلى شكل product of three cycles هذا السؤال حتى
+
+361
+00:36:36,710 --> 00:36:40,370
+و لو كان في بينهم عناصر مشتركة ماعنديش مشكلة المهم
+
+362
+00:36:40,370 --> 00:36:46,050
+ان اقدر اكتبها على شكل three cycles انا ازعم انه
+
+363
+00:36:46,050 --> 00:36:53,430
+بقدر بقدر اقوله a و هنا d و b و التاني بدي اخد a d
+
+364
+00:36:53,430 --> 00:36:59,890
+cطب زعمك هذا صحيح و الله ما يصحيح بقوله تعال خد ال
+
+365
+00:36:59,890 --> 00:37:03,270
+composition ما بين الأتنين M طلع الطرف هذا يبقى
+
+366
+00:37:03,270 --> 00:37:08,230
+كتابتي صح ماطلعش يبقى كتابتي غلط تمام؟ بقولك كويس
+
+367
+00:37:08,230 --> 00:37:14,070
+تعال ناخد ال M بدي أبدأ بالعنصر A ال A صورته و ال
+
+368
+00:37:14,070 --> 00:37:20,070
+D صورته هذا ال B ماجفلت شهر لسه بالداجة هنا ال B
+
+369
+00:37:20,070 --> 00:37:22,430
+صورتها B
+
+370
+00:37:24,280 --> 00:37:32,180
+الـ B صورتها B والـ B صورتها ايش؟ جفنة تمام خلصت
+
+371
+00:37:32,180 --> 00:37:36,970
+ال A و ال B بده روح لل Cالان هاي كتبت الـC الـC
+
+372
+00:37:36,970 --> 00:37:42,890
+صورتها A والـA صورتها D هذا الـD بدي أمسك الـD
+
+373
+00:37:42,890 --> 00:37:49,330
+الـD صورتها C والـC صورتها هاي يبقى قفلا يبقى
+
+374
+00:37:49,330 --> 00:37:54,750
+معناته فعلا هذول كتبتم على شكل product of three
+
+375
+00:37:54,750 --> 00:38:07,030
+cycles يبقى هذا productof three cycles إذا الزوج
+
+376
+00:38:07,030 --> 00:38:12,810
+تبع Transposition مهما كان شكله قدرت أكتبه يا إما
+
+377
+00:38:12,810 --> 00:38:17,630
+على شكل every cycle يا product of three cycles
+
+378
+00:38:17,630 --> 00:38:21,030
+السؤال سهل مع هذا النقطة الأخيرة النقطة الأخيرة
+
+379
+00:38:21,030 --> 00:38:24,950
+بيبقى تقعد تفكر كيف تكتب بحيث ال composition فيما
+
+380
+00:38:24,950 --> 00:38:30,660
+بينهمايعطيك مين؟ يعطيك الـ two transposition و هذه
+
+381
+00:38:30,660 --> 00:38:34,740
+عملية ليست سهلة أما الباقى مباشرة اتنين الأولانين
+
+382
+00:38:34,740 --> 00:38:42,320
+تمام؟ يبقى هنا لما ناخد كل اتنين كل زوج من ال two
+
+383
+00:38:42,320 --> 00:38:46,910
+transposition كل واحد بقدر اكتب على شكل مين؟3
+
+384
+00:38:46,910 --> 00:38:50,430
+cycle خد الزوج اللي بعده والزوج اللي بعده واللي
+
+385
+00:38:50,430 --> 00:38:54,910
+بعده قد ما بدك كله بتكتب ويش على شكل three cycles
+
+386
+00:38:54,910 --> 00:39:01,490
+لذلك أي element alpha موجود في الان is a three
+
+387
+00:39:01,490 --> 00:39:04,890
+cycle or a product of a three cycle أي التانية
+
+388
+00:39:04,890 --> 00:39:08,910
+كانت a three cycle الأولى والتالتة product of a
+
+389
+00:39:08,910 --> 00:39:11,770
+three cycle يبقى هنا
+
+390
+00:39:15,780 --> 00:39:24,260
+الخطوة الأولى اللى موجودة في a and is a three
+
+391
+00:39:24,260 --> 00:39:32,960
+cycle or product of a three cycles
+
+392
+00:39:36,830 --> 00:39:41,170
+السؤال على درجة من الأهمية لكن لو تركتك لحالك اللي
+
+393
+00:39:41,170 --> 00:39:44,130
+يوم تقدر تحلله يمكن تجيب الأولى والتانية بس
+
+394
+00:39:44,130 --> 00:39:48,930
+التالتة لا يمكن ان تأتي بيها يبقى هاي بساطنا حالك
+
+395
+00:39:48,930 --> 00:39:55,590
+الان نروح لسؤال ستة وخمسين سؤال ستة وخمسين
+
+396
+00:39:57,800 --> 00:40:02,060
+يقول ليش هذا عدد يا صاحب نشوف قال يقبل Alpha و
+
+397
+00:40:02,060 --> 00:40:07,580
+Beta موجودة في S4 Alpha و Beta ولا Jama و Beta
+
+398
+00:40:07,580 --> 00:40:14,940
+يبقى Beta و Jama Beta و Jama التنتين هذول ال
+
+399
+00:40:14,940 --> 00:40:21,940
+permutations موجودات في S4 وفي نفس الوقت Beta Jama
+
+400
+00:40:22,340 --> 00:40:29,000
+بيتا جاما بيتا تساوي واحد اربعة تلاتة اتنين واحد
+
+401
+00:40:29,000 --> 00:40:36,860
+اربعة تلاتة اتنين وجاما بيتا تساوي وجاما بيتا واحد
+
+402
+00:40:36,860 --> 00:40:43,600
+اتنين اربعة تلاتة واحد اتنينأربعة تلاتة وزيادة على
+
+403
+00:40:43,600 --> 00:40:48,540
+ذلك beta of واحد يساوي الأربعة و beta لما اتأثر
+
+404
+00:40:48,540 --> 00:40:54,600
+على الواحد بده يساوي الأربعة قال لي determine حدد
+
+405
+00:40:54,600 --> 00:41:01,440
+determine اللي هو beta and gamma بدي أعرف أيه شكل
+
+406
+00:41:01,440 --> 00:41:08,290
+ال beta و كذلك gammaبمعنى أخر أكتبها لي على شكل
+
+407
+00:41:08,290 --> 00:41:13,470
+الـcycle زي ما هؤلاء المكتوبات على شكل الـcycle حد
+
+408
+00:41:13,470 --> 00:41:20,010
+فيكوا حل السؤال هذا ؟ يالا يا أبو الأعدادات اللي
+
+409
+00:41:20,010 --> 00:41:21,670
+بتكلم بالأعداد
+
+410
+00:41:31,120 --> 00:41:37,720
+هو زوّق؟ طيب حد فيكوا حل السؤال هذا في البيت؟ none
+
+411
+00:41:37,720 --> 00:41:44,100
+علما انه very easy بس انت شغل مخك و الشيء هيو
+
+412
+00:41:44,100 --> 00:41:49,140
+قدامك الحل لا بد تفكير ولا هاجر بدنا نشتغل الشغل
+
+413
+00:41:49,140 --> 00:41:55,450
+روتينيانت عندك alpha و beta و جامعة في S4 و ال
+
+414
+00:41:55,450 --> 00:41:59,190
+composition ما بين اتنين من اليمين والشمال هيو على
+
+415
+00:41:59,190 --> 00:42:03,430
+شكل الcycle و ماطيك تأثير ال beta على الواحد يساوي
+
+416
+00:42:03,430 --> 00:42:08,190
+الأربعة قليهتلي شكل ال beta و شكل الجامعة يعني بدي
+
+417
+00:42:08,190 --> 00:42:10,790
+اشوف تأثير ال beta على واحد ايش بيعطينا و beta على
+
+418
+00:42:10,790 --> 00:42:13,170
+اتنين و beta على تلاتة و beta على اربعة وجامعة على
+
+419
+00:42:13,170 --> 00:42:15,050
+واحد وجامعة على اتنين وجامعة على تلاتة وجامعة على
+
+420
+00:42:15,050 --> 00:42:18,890
+اربعة القصة بسيطة جدا هاي solution
+
+421
+00:42:21,960 --> 00:42:27,100
+المعلومة اللى عندى ان ال beta of واحد بده ساوي
+
+422
+00:42:27,100 --> 00:42:34,780
+أربعة بنقدر نجيب gamma of أربعة جداش تساوي gamma
+
+423
+00:42:34,780 --> 00:42:43,020
+of أربعة نقدر يبقى أثر على الطرفين بجانب صح ولا لا
+
+424
+00:42:43,380 --> 00:42:48,700
+إذا لو أثرت على الطرفين بجامعة هذا بده يصبح على
+
+425
+00:42:48,700 --> 00:42:55,400
+الشكل ده جامعة beta of واحد يساوي جامعة of أربع
+
+426
+00:42:58,010 --> 00:43:02,930
+طيب جامة beta of واحد وين جامة beta هاي؟ جامة beta
+
+427
+00:43:02,930 --> 00:43:09,910
+of واحد صورتها ايش؟ اتنين يبقى هذا معناه انه اتنين
+
+428
+00:43:09,910 --> 00:43:17,550
+يساوي جامة of اربع هاي كان معلوم جديدة طيب سؤال
+
+429
+00:43:17,550 --> 00:43:23,760
+بنقدر نجيب beta of اتنينأثر على الطرفين بـ Beta
+
+430
+00:43:23,760 --> 00:43:30,400
+يبقى لو جينا يقولنا هنا Beta of اتنين يساوي Beta
+
+431
+00:43:30,400 --> 00:43:36,900
+Gamma of أربع يبقى معنى هذا الكلام أن ال Beta of
+
+432
+00:43:36,900 --> 00:43:43,380
+اتنين يساوي Beta Gamma of أربع بتعطينا مين؟ تلاتة
+
+433
+00:43:43,380 --> 00:43:56,220
+يبقى آي تلاتةالان بدنا جامع اوف تلاتة يبقى
+
+434
+00:43:56,220 --> 00:44:02,540
+هذه صارت جامع بيتا اوفي اتنين بده يسوي جامع اوف
+
+435
+00:44:02,540 --> 00:44:09,770
+تلاتة تمام هذا معناهان الجامعة beta of اتنين جامعة
+
+436
+00:44:09,770 --> 00:44:14,050
+beta of اتنين بيعطينا مين؟ بيعطينا أربعة يبقى
+
+437
+00:44:14,050 --> 00:44:21,210
+أربعة بده يساوي جامعة of تلاتة طيب ده أثر عليهم ب
+
+438
+00:44:21,210 --> 00:44:29,430
+beta يبقى بيصير beta of أربعة بده يساوي beta jama
+
+439
+00:44:29,430 --> 00:44:37,780
+of تلاتةهذا سيعطيك بيتا of أربعة يساوي بيتا جامعة
+
+440
+00:44:37,780 --> 00:44:47,420
+of ثلاثة بيعطيك اتنين طيب هذا سيعطيك بيتا جامعة of
+
+441
+00:44:47,420 --> 00:44:55,300
+أربعة يساوي جامعة of اتنين جامعة بيتا of أربعة
+
+442
+00:44:55,300 --> 00:45:08,290
+بيعطينايبقى تلاتة يبقى تلاتة يبقى يبقى يبقى يبقى
+
+443
+00:45:08,290 --> 00:45:21,590
+يبقى يبقى
+
+444
+00:45:21,590 --> 00:45:24,830
+يبقى
+
+445
+00:45:24,830 --> 00:45:26,130
+يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى يبقى
+
+446
+00:45:26,130 --> 00:45:30,390
+يبقى يبقى يبقى يبقى يبقىطيب هذا لو أثرت عليه ب
+
+447
+00:45:30,390 --> 00:45:38,010
+جامعة بيصير جامعة beta of تلاتة يساوي جامعة of
+
+448
+00:45:38,010 --> 00:45:44,830
+واحد هذا بده يعطيلك انه جامعة beta of تلاتة جامعة
+
+449
+00:45:44,830 --> 00:45:51,200
+beta of تلاتة بيعطيك واحديبقى الواحد يساوي جامعه
+
+450
+00:45:51,200 --> 00:45:55,300
+بواحد خلصنا هيك جامعه بواحد، جامعه باتنين، جامعه
+
+451
+00:45:55,300 --> 00:45:59,820
+بثلاثة، جامعه باربع، خلصنا البيتات هي هم كلهم يبقى
+
+452
+00:45:59,820 --> 00:46:05,240
+بناء العليا بقدر اكتب له بيته وجامعه يبقى بيته
+
+453
+00:46:05,240 --> 00:46:13,360
+بيدها تساوي بيته لو أثرت على الواحد ايش صورته؟
+
+454
+00:46:13,360 --> 00:46:21,150
+اربعطيب بيتا لو أثرت على الأربعاش تعطيك إتنين طيب
+
+455
+00:46:21,150 --> 00:46:26,570
+بيتا لو أثرت على الإتنين بتعطيك تلاتة طيب بيتا لو
+
+456
+00:46:26,570 --> 00:46:36,150
+أثرت على التلاتة بتعطيك قفلة تمام؟ يبقى أنداء ال
+
+457
+00:46:36,150 --> 00:46:43,520
+alpha تساوي بدي أخد الواحدالحين جامعة لو أثرت على
+
+458
+00:46:43,520 --> 00:46:51,660
+الواحد بتعطينا مين؟ يبقى قفلة، تمام؟ بعدها بتاخد
+
+459
+00:46:51,660 --> 00:46:58,360
+الاتنينجامع لو أثرت على الأتنين بتعطيني تلاتة جامع
+
+460
+00:46:58,360 --> 00:47:03,100
+لو أثرت على التلاتة بتعطيني أربعة جامع لو أثرت على
+
+461
+00:47:03,100 --> 00:47:07,340
+الأربعة بتعطيني اتنين، قفلة، يبقى هي ال cycle
+
+462
+00:47:07,340 --> 00:47:11,500
+اتنين، تلاتة، أربعة، واللي بيظهرش بيكون fixed
+
+463
+00:47:11,500 --> 00:47:19,100
+صعبها الشغل هذه؟ طيب، لحد هنا stop، انتهينا؟
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sITeKhKUP3A_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sITeKhKUP3A_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f881d83bec9ace5c04d7ca83d69c22ddd84dbb0e
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/sITeKhKUP3A_postprocess.srt
@@ -0,0 +1,1908 @@
+1
+00:00:21,680 --> 00:00:25,760
+بسم الله الرحمن الرحيم المرة اللي فاتبا جينا
+
+2
+00:00:25,760 --> 00:00:31,020
+بنعملنا discussion على chapter 9ووصلنا الى سؤال 46
+
+3
+00:00:31,020 --> 00:00:36,000
+ودخل علينا الوقت وطلعنا وخلنا لليوم ان شاء الله و
+
+4
+00:00:36,000 --> 00:00:39,220
+تعالى طبعا هنحل كمان سؤالين غيره ان شاء الله و
+
+5
+00:00:39,220 --> 00:00:44,000
+بعدين ندخل فى الشابتر الجديد اللى هو شابتر 10 على
+
+6
+00:00:44,000 --> 00:00:46,960
+اي حال السؤال كان بيقولى لو كان ال index تبع ال
+
+7
+00:00:46,960 --> 00:00:50,860
+center تبع ال group G فى ال G هو عبارة عن اربعة
+
+8
+00:00:50,860 --> 00:00:56,140
+بييلى ان ال G modulo ال center isomorphic ال Z to
+
+9
+00:00:56,140 --> 00:01:05,460
+X product مع مينمع z2 المرة اللى فاتت قولنا ال
+
+10
+00:01:05,460 --> 00:01:13,790
+order لل g لل z of g بدى يساوي اربعة impliesما
+
+11
+00:01:13,790 --> 00:01:18,190
+يأتي انه عدد ال left cosets هو عبارة عن ماين عن
+
+12
+00:01:18,190 --> 00:01:23,290
+أربعة left cosets وبالتالي هذا بيخلي ال group اللي
+
+13
+00:01:23,290 --> 00:01:30,610
+عندنا اللي هي G modulus center بتابع ال G Z of G
+
+14
+00:01:30,610 --> 00:01:36,650
+isomorphic يا إما لزد أربعة يا إما لزد اتنين
+
+15
+00:01:36,650 --> 00:01:41,710
+external like product مع ماين مع زد اتنين مع هذه
+
+16
+00:01:41,710 --> 00:01:47,280
+أو هذهالان قال لي اثبت ان هذا ايزو مورفك لزد اتنين
+
+17
+00:01:47,280 --> 00:01:51,880
+اكسيرون ضايكابرودك زد اتنين يجب ان نحاول نستبعد زد
+
+18
+00:01:51,880 --> 00:01:56,340
+اربعة ان استبعدنا زد اربعة بيفضل عندنا اللي هو زد
+
+19
+00:01:56,340 --> 00:02:01,200
+اتنين اكسيرون ضايكابرودك مع مين مع زد اتنين طيب
+
+20
+00:02:01,200 --> 00:02:07,960
+باجي بقول لو كان اللي هو الجي موديولوس سينتر بتابع
+
+21
+00:02:07,960 --> 00:02:14,820
+الجي ايزو مورفك لزد اربعة دمزد اربعة هذي Cyclic
+
+22
+00:02:14,820 --> 00:02:20,660
+إذا هذي ال group بصير ما لها Cyclic يبقى then ال G
+
+23
+00:02:20,660 --> 00:02:27,280
+module ال center بتابع ال G is Cyclicمدام Cyclic
+
+24
+00:02:27,280 --> 00:02:34,060
+بالنظرية اللى أخدناها في هذا الشبطر يبقى
+
+25
+00:02:34,060 --> 00:02:42,000
+الـ G is abelian طيب مدام الـ G is abelian يبقى في
+
+26
+00:02:42,000 --> 00:02:46,750
+هذه الحالةأي جروب .. والله لا مش في ال normal هذه
+
+27
+00:02:46,750 --> 00:02:52,550
+يبقى .. يبقى اي .. اي جروب في هذه الحلقة بتبقى ..
+
+28
+00:02:52,550 --> 00:02:58,790
+بتبقى normal subgroup تمام؟ مدام جي is abelian
+
+29
+00:02:58,790 --> 00:03:04,710
+يبقى معنى هذا الكلام انه ايش؟ ان ال center بتابع
+
+30
+00:03:04,710 --> 00:03:10,190
+لجروب جي بده يساوي جي itself كله مدام الجي abelian
+
+31
+00:03:11,240 --> 00:03:16,880
+يبقى معنى هذا الكلام ان ال index بتابع ال center
+
+32
+00:03:16,880 --> 00:03:23,440
+of G ال center تابع ال G بده يساوي ال order تابع
+
+33
+00:03:23,440 --> 00:03:28,360
+ال G على ال order تابع ال Z of G اللي هو ال order
+
+34
+00:03:28,360 --> 00:03:32,340
+بتابع ال G على ال order بتابع ال G يساوي كده؟
+
+35
+00:03:32,340 --> 00:03:38,200
+يساوي واحد طب هو جايلي ال index كده؟كداش ال index
+
+36
+00:03:38,200 --> 00:03:44,100
+ماطة؟ أربعة طلع كداش أن واحد معناته اللي أخدنا خطأ
+
+37
+00:03:44,100 --> 00:03:51,220
+وعكسه هو من الصح يبقى هذا this is contradiction
+
+38
+00:03:52,760 --> 00:03:57,820
+يبقى هذا تناقض ليش؟ لأن ال index فوق يبقى داش؟
+
+39
+00:03:57,820 --> 00:04:03,100
+يبقى أربعة معناته اللي أخدنا هذا ليس صحيحا والآخر
+
+40
+00:04:03,100 --> 00:04:08,500
+هو الصحيح يعني معنى هذا الكلام أن ال G modulus
+
+41
+00:04:08,500 --> 00:04:14,660
+center of G is not isomorphic لمين إلى زد أربعة
+
+42
+00:04:14,660 --> 00:04:24,160
+يبقى it remainsذات يبقى انه الـ G-modulus center
+
+43
+00:04:24,160 --> 00:04:30,380
+بتبع الـ G-isomorphic لمن؟ لزد اتنين Extended
+
+44
+00:04:30,380 --> 00:04:34,020
+product مع من؟ مع زد اتنين
+
+45
+00:04:36,750 --> 00:04:40,670
+هذا اللي كان اخر سؤال كتبناه المرة اللي فاتت ولم
+
+46
+00:04:40,670 --> 00:04:47,390
+نتمكن من حله بسبب ضيق الوقت ننتقل الى سؤال اخر
+
+47
+00:04:47,390 --> 00:04:54,670
+وليكن سؤال ستة وخمسين سؤال ستة وخمسين بيقول ما
+
+48
+00:04:54,670 --> 00:05:00,600
+ياتي انه m normal subgroupsالـ N normal subgroup
+
+49
+00:05:00,600 --> 00:05:08,220
+من G والـ M normal subgroup من G prove that انه
+
+50
+00:05:08,220 --> 00:05:17,160
+هادي normal subgroup prove ان ال N في M is a
+
+51
+00:05:17,160 --> 00:05:23,810
+normal subgroup من G هاد اللي عايزين نثبتهخلّي
+
+52
+00:05:23,810 --> 00:05:29,770
+بالك هنا قال لي N normal subgroup من G و M normal
+
+53
+00:05:29,770 --> 00:05:35,390
+subgroup من G اثبتلي ان حاصل ضرب ال N في M هو
+
+54
+00:05:35,390 --> 00:05:40,850
+normal subgroup من Gإذا إحنا هنا بدنا نثبت شغلتين
+
+55
+00:05:40,850 --> 00:05:45,170
+الشغل الأولى بدنا نثبت إنه حصل الضرب هذا ال
+
+56
+00:05:45,170 --> 00:05:49,690
+subgroup قبل كل شيء لإنه مامرش علينا قبل هيك أن
+
+57
+00:05:49,690 --> 00:05:54,370
+حصل ضرب two subgroups is a subgroup وطبعا in
+
+58
+00:05:54,370 --> 00:05:55,830
+general ماهوش subgroup
+
+59
+00:06:05,300 --> 00:06:13,660
+الخطوة الأولى يبقى firstlyWe show that
+
+60
+00:06:13,660 --> 00:06:20,000
+ان الـ N في M is a subgroup من G هذا اللي عزيزي
+
+61
+00:06:20,000 --> 00:06:25,920
+نثبته في الأول انها subgroup من G لذلك، بدا اقول
+
+62
+00:06:25,920 --> 00:06:35,440
+النقطة الأولى الـ N في M is non-empty ليش؟ since
+
+63
+00:06:35,440 --> 00:06:43,620
+او becauseالـ E موجودة في الـ N والـ E نفسها كمان
+
+64
+00:06:43,620 --> 00:06:49,860
+موجودة في الـ M إذا هذا الكلام بده يساوي E موجودة
+
+65
+00:06:49,860 --> 00:06:57,300
+في N Mيبقى الـ N Subgroup و الـ M Subgroup يبقى كل
+
+66
+00:06:57,300 --> 00:07:01,280
+واحدة فيهم تحتوي على الـ Identity Element حاصل
+
+67
+00:07:01,280 --> 00:07:05,560
+ضارهم بالـ Identity يبقى هذا موجود وان في الـ N M
+
+68
+00:07:05,560 --> 00:07:10,360
+الان بدي اروح اثبت ان هذا الـ Subgroup يبقى بداجي
+
+69
+00:07:10,360 --> 00:07:21,290
+اقوله let ال X و ال Y موجودة في الـ N M thenالـ X
+
+70
+00:07:21,290 --> 00:07:27,750
+هذه بدها تساوي N1 M1 على شكل حاصل ضرب Element من N
+
+71
+00:07:27,750 --> 00:07:37,170
+و Element من M و كذلك ال Y هتساوي عنصر تاني N2 M2
+
+72
+00:07:38,140 --> 00:07:42,860
+طب انا ايش بده اثبت؟ بده اثبت ان ال X Y inverse
+
+73
+00:07:42,860 --> 00:07:48,880
+موجود في ال N M لو استطعت ذلك لأصبحت ال N M عبارة
+
+74
+00:07:48,880 --> 00:07:56,340
+عن subgroup اذا بدهاجي اخد ال X Y inverse ال X N 1
+
+75
+00:07:56,340 --> 00:08:04,530
+M 1هذا الانفرس
+
+76
+00:08:04,530 --> 00:08:13,530
+يبقى M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2
+
+77
+00:08:13,530 --> 00:08:16,150
+M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M1 M2 M2 M1 M2 M2 M1
+
+78
+00:08:16,150 --> 00:08:18,870
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+79
+00:08:18,870 --> 00:08:19,070
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+80
+00:08:19,070 --> 00:08:19,190
+M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2 M2
+
+81
+00:08:19,190 --> 00:08:27,900
+M2 M2 M2 M2 M2 M2 Mفي M إذا بدأت تبدأ اللي هم
+
+82
+00:08:27,900 --> 00:08:36,220
+بعنصر تالت يبقى لو جيت قلت هذا الكلام دي سوى N1 M3
+
+83
+00:08:36,220 --> 00:08:46,160
+N2 inverse و ال M3 اللي هي عبارة عن M1 M2 inverse
+
+84
+00:08:46,400 --> 00:08:51,180
+الشكل اللي عندنا هنا اذا انا استبدلت العنصر اللي
+
+85
+00:08:51,180 --> 00:08:57,480
+اتنين هدول بعنصر بدالهم من من من اللي هو ال M يبقى
+
+86
+00:08:57,480 --> 00:09:01,700
+أصبحت على الشكل اللي عندنا هنا طيب كويس استأنى
+
+87
+00:09:01,700 --> 00:09:07,320
+شويةبتذكروا أول ما أخدنا ال normal subgroup لما
+
+88
+00:09:07,320 --> 00:09:10,420
+أخدنا ال normal subgroup أخدنا التعريف تبعها جون
+
+89
+00:09:10,420 --> 00:09:14,760
+ال left coset يسوى ال right coset جون هذا لا يعني
+
+90
+00:09:14,760 --> 00:09:20,400
+أن ال a في h بدي يسوى ال h في a كsmall لكن هذا
+
+91
+00:09:20,400 --> 00:09:27,440
+يعني أن ال a h one بدي يسوى h two في a يبقى إذا
+
+92
+00:09:27,440 --> 00:09:35,890
+هذا الكلام بقدر أقول يساوييساوي N1 زي ما هى هدها
+
+93
+00:09:35,890 --> 00:09:41,490
+ها بدي استبدله برقم اخر و اعمله تبديل مع مين مع ال
+
+94
+00:09:41,490 --> 00:09:50,910
+M يبقى هذا بدي يعطيني N3 M3 ليش هذا الكلام because
+
+95
+00:09:50,910 --> 00:09:59,380
+اللي هو ال N is a normal subgroup من Gمن تعريف الـ
+
+96
+00:09:59,380 --> 00:10:03,860
+Normality لما تبقى ال N Normal هذا element موجود
+
+97
+00:10:03,860 --> 00:10:07,540
+في G يبقى هذا ال element في هذا ال element بقدر
+
+98
+00:10:07,540 --> 00:10:12,140
+استبدله ب element تاني من هذا و هذا زي ما هو و
+
+99
+00:10:12,140 --> 00:10:18,940
+بنجلب وضعهم يبقى قلت N تلاتة M تلاتة ليش؟ لأن ال N
+
+100
+00:10:18,940 --> 00:10:23,780
+عبارة عن Normal Subgroup من G طب N واحد في N تلاتة
+
+101
+00:10:23,780 --> 00:10:30,040
+وين موجود؟وهذا الوضع موجود في الـM ويبقى هذا الوضع
+
+102
+00:10:30,040 --> 00:10:38,560
+كله موجود في الـNM مدام موجود في الـNM أخد عنصرين
+
+103
+00:10:38,560 --> 00:10:42,200
+موجودات في الـNM واخدت الأول في المعكس التاني
+
+104
+00:10:42,200 --> 00:10:49,700
+وجدته موجود في الـNM يبقى سائل الـNM is a subgroup
+
+105
+00:10:49,700 --> 00:10:56,890
+من Gبقى الآن نثبت خاصية ال normality يبقى باجي
+
+106
+00:10:56,890 --> 00:11:07,010
+بقوله هنا if ال G موجود في G and ال X موجود في ال
+
+107
+00:11:07,010 --> 00:11:15,760
+N M او بقدر اقول دغري هكذا ولا X ولا غيره thenعلى
+
+108
+00:11:15,760 --> 00:11:23,800
+طول الخط IG في N M إذا قلت أثبت إن هذا يسوي N M في
+
+109
+00:11:23,800 --> 00:11:29,980
+G بتم المطلوب طب الكلام هذا بده يساوي بقدر أقول
+
+110
+00:11:29,980 --> 00:11:32,480
+هذا NGM
+
+111
+00:11:34,870 --> 00:11:42,310
+نقدر؟ ليش؟ لأن N is normal يبقى هذا because ال N
+
+112
+00:11:42,310 --> 00:11:47,550
+is a normal subgroup من G طب بدأجي للاتنين هدول
+
+113
+00:11:47,550 --> 00:11:53,370
+يبقى هذا الكلام هاي ال N زي ما هيهذه الـ M في G
+
+114
+00:11:53,370 --> 00:11:58,410
+لأن الـ M مجلد عام من جهة جديدة من جهة جديدة من
+
+115
+00:11:58,410 --> 00:11:59,470
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+116
+00:11:59,470 --> 00:12:01,390
+من جهة جديدة من جهة جديدة من جهة جديدة من جهة
+
+117
+00:12:01,390 --> 00:12:01,850
+جديدة من جهة جديدة من جهة جديدة من جهة جديدة من
+
+118
+00:12:01,850 --> 00:12:03,790
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+119
+00:12:03,790 --> 00:12:07,930
+جديدة من جهة جديدة من جهة جديدة من جهة جديدة من
+
+120
+00:12:07,930 --> 00:12:11,250
+جهة جديدة من جهة جديدة من جهة جديدة من جهة جديدة
+
+121
+00:12:11,250 --> 00:12:15,170
+من جهة جديدة من جهيعني يبقى يا شباب لما يقولك خدلي
+
+122
+00:12:15,170 --> 00:12:18,830
+هست و اثبتلي انها normal subgroup بدك تثبت اولا
+
+123
+00:12:18,830 --> 00:12:24,550
+انها subgroup و بعدين بتثبت انها normal وبالتالي
+
+124
+00:12:24,550 --> 00:12:28,890
+بيكون اجبت سؤالك اجابة كاملة يعني يمكن لو طلبت
+
+125
+00:12:28,890 --> 00:12:31,470
+سؤال زي هيك اقولك show that نمرا واحد انها
+
+126
+00:12:31,470 --> 00:12:36,790
+subgroup نمرا اتنين انها normal subgroup من main
+
+127
+00:12:36,790 --> 00:12:45,780
+من Gكمان سؤال أخر يبقى سؤال تسعة وستين سؤال تسعة
+
+128
+00:12:45,780 --> 00:12:50,200
+وستين بيقول لي لو كان ال order ل G بده يساوي
+
+129
+00:12:50,200 --> 00:12:56,440
+تلاتين و ال order لل center بتابع ال G بده يساوي
+
+130
+00:12:56,440 --> 00:13:04,480
+خمسة بيقول لي what is the structure
+
+131
+00:13:11,390 --> 00:13:19,620
+Structure of LG Modulus Center بتابع LGأريد أن
+
+132
+00:13:19,620 --> 00:13:24,380
+أعرف جيه موديلوس سنتر بتابع الجيه عبارة عن مين أو
+
+133
+00:13:24,380 --> 00:13:30,320
+أي قدرة تتطلع ان ايزو مورفك لمين بتم المطلب يبقى
+
+134
+00:13:30,320 --> 00:13:34,600
+عندنا ال order لجيه تلاتين وال order للسنتر يسوى
+
+135
+00:13:34,600 --> 00:13:39,260
+خمسة بقولوا شو ال structure هذا تابع مين تابع ال
+
+136
+00:13:39,260 --> 00:13:46,930
+center اللي عندنا طب كويس قال لي بلا كدهالحين احنا
+
+137
+00:13:46,930 --> 00:13:51,670
+لو جينا كونا ال factor group اللى عندنا اللى هى ال
+
+138
+00:13:51,670 --> 00:13:58,250
+G موديولو ال center بتبع ال G وروحت اخدت ال order
+
+139
+00:13:58,250 --> 00:14:03,510
+لها يبقى هذا بدى يساوي ال order لل G على ال order
+
+140
+00:14:03,510 --> 00:14:11,090
+لمين ل ال center بتبع ال Gهذا بده يعطيني تلاتين
+
+141
+00:14:11,090 --> 00:14:17,970
+على خمسة ويسوى كدهاش؟ ستة طب الستة أليست اتنين في
+
+142
+00:14:17,970 --> 00:14:27,130
+تلاتة؟ يعني كأنها ايش؟ كأنها اتنين P وال P أكبر من
+
+143
+00:14:27,130 --> 00:14:27,650
+اتنين
+
+144
+00:14:30,510 --> 00:14:38,530
+في عنا نظرية في صفحة 144 النظرية في صفحة 144 بتقول
+
+145
+00:14:38,530 --> 00:14:44,930
+إذا كان ال order لجروب 2P يبقى هذي الجروب اللي
+
+146
+00:14:44,930 --> 00:14:59,330
+عندنا Z of G isomorphic لزد 2P او لD او لDP
+
+147
+00:15:01,780 --> 00:15:04,920
+طبعا نظرية هذه اعطيناها لكم بس مابرهنهاش اقول لكم
+
+148
+00:15:04,920 --> 00:15:10,320
+مابندهاش البرهان تمام يبقى الجي موديولوس سنتر اذا
+
+149
+00:15:10,320 --> 00:15:15,620
+امرك لزد اتنين P او ل دي P طبعا ال P عندنا بقداش
+
+150
+00:15:15,620 --> 00:15:22,680
+تلاتة طب كويس اذا استبعدنا هذه بيكون حصلنا على هذه
+
+151
+00:15:22,680 --> 00:15:29,570
+او اذا استبعدنا هذه بيكون حصلنا على هذهيعني هذه
+
+152
+00:15:29,570 --> 00:15:35,720
+اتنين في تلاتة وهذه دي تلاتةلأننا قلنا ال P عندنا
+
+153
+00:15:35,720 --> 00:15:41,260
+هذه اللي هي F تلاتة كويس يبقى هذه لو كانت
+
+154
+00:15:41,260 --> 00:15:49,260
+isomorphic لل 2 في 3 يعني 6 يبقى هنا F ال G
+
+155
+00:15:49,260 --> 00:15:55,740
+modulus center بتابع ال G isomorphic ل Z 2 في 3
+
+156
+00:15:55,740 --> 00:16:02,760
+يعني اللي هي Z 6 then ال G modulus center ايش
+
+157
+00:16:02,760 --> 00:16:11,990
+بتكونCyclic مدام Cyclic يبقى G مالها Abelian مدام
+
+158
+00:16:11,990 --> 00:16:17,650
+Abelian يعني ال center تبع ال group بده يساوي ال
+
+159
+00:16:17,650 --> 00:16:24,280
+group itselfيعني ال order لل group بده يساوي ال
+
+160
+00:16:24,280 --> 00:16:29,800
+order لل center هذا بده يعطيك ان ال order لل
+
+161
+00:16:29,800 --> 00:16:34,920
+center بده يساوي ال order لل G لكن احنا المعطى
+
+162
+00:16:34,920 --> 00:16:40,510
+عندنا عاشرتلاتين وخمس هل التلاتين بتساوي الخمسة؟
+
+163
+00:16:40,510 --> 00:16:45,910
+لا يمكن هذا الكلام this is يعني that is التلاتين
+
+164
+00:16:45,910 --> 00:16:54,270
+بتساوي الخمسة يبقى this is impossible أو هذا تناقض
+
+165
+00:16:54,270 --> 00:17:00,670
+غير ممكنمدام غير ممكن إذا بنستبعد هذا بضالمين يبقى
+
+166
+00:17:00,670 --> 00:17:07,110
+هنا ساعة ال G يعني نفس سكرة السؤال ذاك تقريبا G
+
+167
+00:17:07,110 --> 00:17:14,510
+modulus center بتابع ال G isomorphic ل D3
+
+168
+00:17:17,120 --> 00:17:21,980
+إذا الـ structure تبع ال group اللي عندنا هو نفس
+
+169
+00:17:21,980 --> 00:17:27,320
+ال structure تبع مين؟ تبع ال D3 وD3 فيها كم عنصر؟
+
+170
+00:17:27,320 --> 00:17:33,700
+ستة عناصر ضعف الرقم اللي عندنا دائما و أبدا
+
+171
+00:17:43,650 --> 00:17:48,090
+ننتقل لآخر chapter اللي هو chapter عشرة اللي هو
+
+172
+00:17:48,090 --> 00:17:55,130
+group homomorphism
+
+173
+00:17:55,130 --> 00:17:59,570
+بدنا
+
+174
+00:17:59,570 --> 00:18:05,030
+نعطي تعريف لل group homomorphism وبعد ذلك نبدأ
+
+175
+00:18:05,030 --> 00:18:10,950
+ناخد بعض الأمثلة المتعلقة بيهم يبقى definition
+
+176
+00:18:13,450 --> 00:18:18,670
+a homomorphism a homomorphism
+
+177
+00:18:18,670 --> 00:18:27,870
+في من الـ g إلى الـ g bar is a mapping is a
+
+178
+00:18:27,870 --> 00:18:36,070
+mapping يبقى هو عبارة عن دل أو function from from
+
+179
+00:18:36,070 --> 00:18:41,130
+the group g
+
+180
+00:18:43,030 --> 00:18:49,590
+توزع جروب جي
+
+181
+00:18:49,590 --> 00:19:01,050
+بارthat satisfies that satisfies the condition
+
+182
+00:19:01,050 --> 00:19:06,070
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+183
+00:19:06,070 --> 00:19:06,550
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+184
+00:19:06,550 --> 00:19:08,550
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+185
+00:19:08,550 --> 00:19:09,610
+التي تحقق الشرط التي تحقق الشرط التي تحقق الشرط
+
+186
+00:19:09,610 --> 00:19:09,850
+اللي تحقق الشرط اللي تحقق الشرط اللي تحقق الشرط
+
+187
+00:19:09,850 --> 00:19:15,270
+اللي تحقق الشرط اللي تحقق
+
+188
+00:19:18,520 --> 00:19:26,580
+اللي موجودات في جي كمان definition آخر the kernel
+
+189
+00:19:26,580 --> 00:19:31,980
+of
+
+190
+00:19:31,980 --> 00:19:47,660
+a homomorphism في from جي from a groupG from a
+
+191
+00:19:47,660 --> 00:20:02,700
+group G to a group G bar is the set is the set
+
+192
+00:20:05,710 --> 00:20:11,090
+هديلة اختصرها الى care الـ Phi كل العناصر اللي
+
+193
+00:20:11,090 --> 00:20:18,250
+موجودة في جيه بحيث Phi of X بده يساوي ال identity
+
+194
+00:20:18,250 --> 00:20:21,050
+بتابع من ال جيه بقى
+
+195
+00:20:42,690 --> 00:20:47,990
+نرجع لتعريفين اللي كتبناه حاول نفهم كل تعريف ما هو
+
+196
+00:20:47,990 --> 00:20:55,930
+المقصود منه a homomorphism phi من g إلى g bar is a
+
+197
+00:20:55,930 --> 00:21:00,720
+mapping a يبقى عبارة عن functionمن الـ group G إلى
+
+198
+00:21:00,720 --> 00:21:06,020
+الـ group G bar والذي يحقق ال condition Phi of A
+
+199
+00:21:06,020 --> 00:21:11,140
+بيبقى سوى Phi of A في Phi of B لكل الـ A والـ B
+
+200
+00:21:11,140 --> 00:21:16,970
+اللي موجودة في الـ Gعملية جامع يبقى باجي بقوله في
+
+201
+00:21:16,970 --> 00:21:23,530
+of a زائد ال b بيسوي في of a زائد ال في of b إذا
+
+202
+00:21:23,530 --> 00:21:26,690
+كانت ال operation زائد على ال group التانى وإذا
+
+203
+00:21:26,690 --> 00:21:33,090
+كان ضرب بيكون في of a في في of bيعني يا شباب هذا
+
+204
+00:21:33,090 --> 00:21:38,270
+حاصل ضربته elements في الـG بار بس هذا اللي بنقصين
+
+205
+00:21:38,270 --> 00:21:43,290
+حاصل ضربته elements موجود في G يبقى كل elements
+
+206
+00:21:43,290 --> 00:21:46,850
+وين موقعهم يخضعوا للعملية اللي على من؟ اللي على ال
+
+207
+00:21:46,850 --> 00:21:50,290
+group السؤال اللي بدأ أسأله بما ياتي احنا أخدنا
+
+208
+00:21:50,290 --> 00:21:54,590
+isomorphism قبل هيك وال isomorphism كان فيه ثلاث
+
+209
+00:21:54,590 --> 00:22:01,300
+خواصة اظن هذه الخاصية التالتةبناء عليه اي ايزو
+
+210
+00:22:01,300 --> 00:22:07,240
+مورفزم هو هومو مورفزم لكن العكس صحيح العكس ليس
+
+211
+00:22:07,240 --> 00:22:12,600
+صحيحا ليس بدرورة ان يكون كل هومو مورفزم هو ايزو
+
+212
+00:22:12,600 --> 00:22:16,520
+مورفزم لانه لسه بدي one to one and on to نحققوا
+
+213
+00:22:16,520 --> 00:22:19,910
+تلات شروط عشان نصير ايزو مورفزميبقى any
+
+214
+00:22:19,910 --> 00:22:24,830
+isomorphism is a homomorphism but the converse is
+
+215
+00:22:24,830 --> 00:22:29,410
+not necessarily تقول ليس بضرورته صحيحة هذه واحدة
+
+216
+00:22:29,410 --> 00:22:33,710
+نروح لل definition التاني الان بدأ يجي لقلب ال
+
+217
+00:22:33,710 --> 00:22:39,650
+homomorphism ال kern ofthe homomorphism في من جي
+
+218
+00:22:39,650 --> 00:22:44,510
+إلى جي بار باعرفه بالشكل التالي كيرنل هاختصلها إلى
+
+219
+00:22:44,510 --> 00:22:50,050
+كير و ال homomorphism هقول كيرنل للفي حسب التعريف
+
+220
+00:22:50,050 --> 00:22:55,230
+بيقولي كل ال X في اللي موجودة في جي بي حيث صورتها
+
+221
+00:22:55,230 --> 00:22:59,370
+بده تعطيني ال identity element تبع من ال جي بار
+
+222
+00:22:59,370 --> 00:23:06,540
+هذا بده يخليني أطرح أكثر من سؤال السؤال الأوللما
+
+223
+00:23:06,540 --> 00:23:10,840
+أقول كيرنا لفاي كل ال X اللي موجودة في G بحيث فاي
+
+224
+00:23:10,840 --> 00:23:16,320
+of X يساوي ال identity element هل هذا يعني ان
+
+225
+00:23:16,320 --> 00:23:21,680
+الكيرنا لفاي هو ال identity element تبع ال G bar؟
+
+226
+00:23:21,680 --> 00:23:30,540
+يعني كلام غلط هذا الكلام اللي أنا بقوله واحد
+
+227
+00:23:30,540 --> 00:23:32,060
+واحد يعني كيف؟
+
+228
+00:23:35,390 --> 00:23:40,930
+يعني .. يعني أنا قصدت هل ال kernel هو ال identity
+
+229
+00:23:40,930 --> 00:23:46,710
+تبع ال G bar؟ لأ الإجابة خطأ، طيب السؤال الثاني هل
+
+230
+00:23:46,710 --> 00:23:53,040
+ال kernel subset من ال G bar؟ برضه لألأ لإيش؟ لأن
+
+231
+00:23:53,040 --> 00:23:59,240
+كل ال X اللي موجودة في G يعني ال kernel subset من
+
+232
+00:23:59,240 --> 00:24:03,540
+من من ال G وليس من ال G bar بس مين ال subset؟ كل
+
+233
+00:24:03,540 --> 00:24:12,130
+العناصر اللي موجودة في G اللي صورتهمهذا يجعلني
+
+234
+00:24:12,130 --> 00:24:18,170
+أطرح كمان تساؤل لو كان عندي isomorphism فتح كويس
+
+235
+00:24:18,170 --> 00:24:22,010
+معايا ايزو مورفزم وبدي ال kernel لهذا ال
+
+236
+00:24:22,010 --> 00:24:27,470
+isomorphism اكم عنصر بقدر اللاجي فيهوحد بس ليش
+
+237
+00:24:27,470 --> 00:24:31,110
+حكاية ال one to one مافيش عنصرين بيشتركوا في نفس
+
+238
+00:24:31,110 --> 00:24:34,870
+الصورة لكن لما انا اقول ال kernel ال phi كل ال x
+
+239
+00:24:34,870 --> 00:24:38,390
+اللي في بحيث ال phi of x بدها تساوي ال identity
+
+240
+00:24:38,390 --> 00:24:43,010
+معناته عندي عدة عناصر بيشتركوا في نفس الصورة اللي
+
+241
+00:24:43,010 --> 00:24:46,810
+هي ال identity تبعي ال G bar يرجى ال kernel هو
+
+242
+00:24:46,810 --> 00:24:51,290
+حضرة العناصر اللي عندي هدول اللي من G واضح؟يبقى
+
+243
+00:24:51,290 --> 00:24:55,970
+بدك تفهم شغل احطهالي في دماغك ان الكيرنل تبع الفاي
+
+244
+00:24:55,970 --> 00:25:02,350
+هو ال subset من جي وليس من جي بار مين هم هدول هم
+
+245
+00:25:02,350 --> 00:25:06,590
+العناصر اللي موجودات في جي و اللي صرتهم بتكون ال
+
+246
+00:25:06,590 --> 00:25:12,990
+identity تبع من تبع الجي بار تمام نبدأ ناخد امثلة
+
+247
+00:25:12,990 --> 00:25:14,690
+يبقى examples
+
+248
+00:25:19,440 --> 00:25:25,180
+أول مثال بدي أطرحه اللي هو الـ isomorphism يبقى
+
+249
+00:25:25,180 --> 00:25:35,440
+any isomorphism في من جي إلى جي بار is a
+
+250
+00:25:35,440 --> 00:25:40,680
+homomorphism بدون لشته ولا حاجة لإنه فاهمين
+
+251
+00:25:40,680 --> 00:25:46,760
+isomorphism يعني ثلاثة شروط andلو قلنا لك هات لي
+
+252
+00:25:46,760 --> 00:25:53,060
+مين؟ هات لي ال kernel تبع هذا ال isomorphism ال
+
+253
+00:25:53,060 --> 00:26:00,680
+kernel بتبع ال Phi يساوي مين؟ ال identity تبع ال G
+
+254
+00:26:00,680 --> 00:26:08,720
+bar ولا تبع ال G؟تبع الـ G فقط لغير ليش because
+
+255
+00:26:08,720 --> 00:26:15,360
+أنه five is one to one ولو واحد هيشترك مع ال
+
+256
+00:26:15,360 --> 00:26:18,880
+identity element تبع ال G في الصورة يبقى ال kernel
+
+257
+00:26:18,880 --> 00:26:24,000
+في هذه الحالة يساوي ال identity يبقى هذا أبسط
+
+258
+00:26:24,000 --> 00:26:29,260
+أنواع الأمثلة أروح لمثال ثاني مثال ثاني بيقول
+
+259
+00:26:29,260 --> 00:26:29,900
+define
+
+260
+00:26:32,490 --> 00:26:38,790
+A function فاي من
+
+261
+00:26:38,790 --> 00:26:42,830
+ال general linear group of two by two matrices
+
+262
+00:26:42,830 --> 00:26:49,470
+over R لمن لست of real numbers لما أشيل منها ال
+
+263
+00:26:49,470 --> 00:26:57,830
+zero تحت عملية الضرب by فاي of A بدو سوى ال
+
+264
+00:26:57,830 --> 00:27:05,610
+determinant لل Aيبقى show that show المطلوب الأول
+
+265
+00:27:05,610 --> 00:27:12,950
+نمره a show that phi is homomorphism هذا المطلوب
+
+266
+00:27:12,950 --> 00:27:21,470
+الأول المطلوب التاني نمره b find الكيرن ال main لل
+
+267
+00:27:21,470 --> 00:27:21,890
+phi
+
+268
+00:27:30,810 --> 00:27:37,750
+خلّي بالا كدا الان مرة ثانية عرفنا function من ال
+
+269
+00:27:37,750 --> 00:27:41,430
+general linear group of two by two matrices over R
+
+270
+00:27:41,430 --> 00:27:45,470
+لل R minus Zero مجموعة الاعداد الحقيقية شيلت منها
+
+271
+00:27:45,470 --> 00:27:49,490
+الصفر وعرفنا عليها عملية الضرب سابقا اثبتنا انها
+
+272
+00:27:49,490 --> 00:27:55,010
+group by Phi of A يسوى ال determinant لل A الان ال
+
+273
+00:27:55,010 --> 00:28:00,880
+A هى عبارة عن مين؟مصوفة نظامها 2 في 2 ومحددها لا
+
+274
+00:28:00,880 --> 00:28:05,920
+يساوي الصفر رقم جد ما يكون يكون بعد ذلك ودناها
+
+275
+00:28:05,920 --> 00:28:10,320
+لوان determinant ليها داري ال number يبقى
+
+276
+00:28:10,320 --> 00:28:15,160
+determinant لأ موجود في ال R ناقص ال zero يبقى
+
+277
+00:28:15,160 --> 00:28:19,420
+determinant لل A بحيث هذا ال determinant بدي
+
+278
+00:28:19,420 --> 00:28:24,880
+يعطيني رقم غير من الصفر لأن الصفر هنا ماله مستبعد
+
+279
+00:28:25,200 --> 00:28:28,560
+قال يثبت لي أن فاي هذا هو هذا هو عبارة عن
+
+280
+00:28:28,560 --> 00:28:33,400
+homomorphism بقوله كويس إذا بدي أروح أطبق الخاصية
+
+281
+00:28:33,400 --> 00:28:38,640
+اللي فوق عندنا هنا يبقى بدي أخد فاي لحاصل ضرب
+
+282
+00:28:38,640 --> 00:28:44,640
+مصفوف تينأريد أن أثبت أن هذا الكلام يسوى فاي of a
+
+283
+00:28:44,640 --> 00:28:49,300
+في فاي of b يبقى حسب ال definition هذا ال
+
+284
+00:28:49,300 --> 00:28:55,360
+determinant لل a في ال b من ال linear algebra هذا
+
+285
+00:28:55,360 --> 00:28:57,300
+عبارة عن ال determinant
+
+286
+00:29:23,250 --> 00:29:30,030
+يبقى معناه كيف؟ما هو الهيزمورفزم كانت تلت شغلات و
+
+287
+00:29:30,030 --> 00:29:37,230
+ده شغلة واحدة فقط لا غير يبقى أصبح ال Phi of A بي
+
+288
+00:29:37,230 --> 00:29:40,670
+هي Phi of A في Phi of B لكل ال A و ال B اللي
+
+289
+00:29:40,670 --> 00:29:43,550
+موجودة في ال general linear group of two by two
+
+290
+00:29:43,550 --> 00:29:48,570
+matrices over R يبقى Phi عبارة عن همومورفزمنمرا بي
+
+291
+00:29:48,570 --> 00:29:53,250
+قال لي هاتلي ال kernel يبقى بداجي أطبقله التعريف
+
+292
+00:29:53,250 --> 00:29:58,850
+تبع ال kernel يبقى باجي بقوله ال kernel ل الفاي هو
+
+293
+00:29:58,850 --> 00:30:03,690
+كل المصفوفات اللي موجودة في ال general linear
+
+294
+00:30:03,690 --> 00:30:09,490
+group of two by two matrices over Rsuch that ان
+
+295
+00:30:09,490 --> 00:30:16,990
+الـ Phi of A بده يساوي ال identity تبع ال R minus
+
+296
+00:30:16,990 --> 00:30:24,450
+ال 0 ال R minus ال 0 تمام؟
+
+297
+00:30:30,650 --> 00:30:35,590
+مرة تانية بقول الان انا كتبت تعريف ال kernel الذي
+
+298
+00:30:35,590 --> 00:30:40,490
+يناسب وضع المثلة كل المصففات اللي موجودة في ال
+
+299
+00:30:40,490 --> 00:30:43,690
+general linear group of two by two matrices over R
+
+300
+00:30:43,690 --> 00:30:50,840
+بحيث ال Phi of A بده يسوى من ال I identityطيب الان
+
+301
+00:30:50,840 --> 00:30:56,580
+لما اقول هذا الكلام كل المصفوفات اللى موجودة في ال
+
+302
+00:30:56,580 --> 00:31:00,920
+general linear group of two by two matrices over R
+
+303
+00:31:00,920 --> 00:31:06,760
+such that الـ Phi of A هو مين ال determinant لل A
+
+304
+00:31:07,370 --> 00:31:14,710
+بدو يساوي ال identity في هذا ال human الواحد طيب
+
+305
+00:31:14,710 --> 00:31:18,950
+المصطفات ال determinant اللي هي عبارة عن مين ال
+
+306
+00:31:18,950 --> 00:31:24,550
+special يبقى هذا الكلام بيساوي ال special linear
+
+307
+00:31:24,550 --> 00:31:32,290
+group of two by two matrices over Rيبقى أصبح الـ
+
+308
+00:31:32,290 --> 00:31:38,550
+Kern كل المصرفات المحددة يساوي كم؟ يساوي الواحد
+
+309
+00:31:38,550 --> 00:31:49,630
+الصحيح مثال رقم تلاتة بيقول define برضه a function
+
+310
+00:31:49,630 --> 00:31:57,420
+في منالـ set of real numbers ناقص الـ zero تحت
+
+311
+00:31:57,420 --> 00:32:03,340
+عملية الضرب الى نفس ال group الى ال set of real
+
+312
+00:32:03,340 --> 00:32:09,160
+numbers ناقص ال zero تحت عملية الضرب بالضبط تماما
+
+313
+00:32:09,160 --> 00:32:19,170
+نهيها by فاي of X بده يسوي absolute value ل Xبرضه
+
+314
+00:32:19,170 --> 00:32:26,810
+بدي اعمل نفس اللي مطلوب هنا نمرة a show that phi
+
+315
+00:32:26,810 --> 00:32:36,470
+is a homomorphism نمرة b find الكيرن اللي من للphi
+
+316
+00:32:36,470 --> 00:32:40,050
+شكل اللي عندنا هنا الان solution
+
+317
+00:32:45,300 --> 00:32:51,380
+العملية عملية ضرب يبقى بيقول XY حسب التعريف يبقى
+
+318
+00:32:51,380 --> 00:32:56,860
+absolute value لل X في Y لو راجعنا إلى ال calculus
+
+319
+00:32:56,860 --> 00:33:00,640
+هذا absolute value لل X في ال absolute value
+
+320
+00:33:00,640 --> 00:33:06,180
+لماذا؟للـ Y الـ absolute value لل X هي Phi of X
+
+321
+00:33:06,180 --> 00:33:11,500
+والـ absolute value لل Y Phi of Y هذا لكل ال X
+
+322
+00:33:11,500 --> 00:33:17,440
+والـ Y اللي موجودة في الـ R ناقص الـ Zero لذلك Phi
+
+323
+00:33:17,440 --> 00:33:22,360
+is a homomorphism يبقى هذه النقطة الأولى بداجة
+
+324
+00:33:22,360 --> 00:33:29,040
+للنقطة الثانية بدنا الكيرن للـ Phiيبقى كل العناصر
+
+325
+00:33:29,040 --> 00:33:35,040
+اللي موجودة في الـR ناقص الـ0 بحيث Phi of X بده
+
+326
+00:33:35,040 --> 00:33:39,840
+يساوي مين؟ بده يساوي الـ0 ولا الـ1؟ بده يساوي
+
+327
+00:33:39,840 --> 00:33:45,340
+الـ1، تمام يعني كل العناصر X اللي موجودة في الـR
+
+328
+00:33:45,340 --> 00:33:51,080
+ناقص الـ0، وصتتش ذات Absolute value للـX بده يساوي
+
+329
+00:33:51,080 --> 00:33:57,460
+1 طب مين العناصر هنا الـAbsolute فيها يساوي 1؟بس
+
+330
+00:33:57,460 --> 00:34:01,020
+واحد و سالب واحد في غيرهم يبقى الكيرن اللي لا
+
+331
+00:34:01,020 --> 00:34:06,420
+يحتوي إلا على two elements اللي هي سالب واحد واحد
+
+332
+00:34:06,420 --> 00:34:09,800
+فقط لغاية ال absolute value للواحد هي بواحد ال
+
+333
+00:34:09,800 --> 00:34:15,660
+absolute value لسالب واحد هي اللي هي بواحد طب مثال
+
+334
+00:34:15,660 --> 00:34:25,310
+رقم أربع بيقول define a mappingبدنا نعرف كمان
+
+335
+00:34:25,310 --> 00:34:34,470
+function فاي من ال R وعليها عملية الجامعة الى ال R
+
+336
+00:34:34,470 --> 00:34:40,630
+plus وعليها عملية الضرب يبقى اختلفت العمليتين بين
+
+337
+00:34:40,630 --> 00:34:50,190
+المجمعتين by فاي of X يساوي ال E أس X لكل ال X
+
+338
+00:34:50,190 --> 00:34:56,890
+اللي موجودة في Rيبقى برضه نفس المطلوب نمرا a show
+
+339
+00:34:56,890 --> 00:35:05,030
+that بييل لي أن فاي is homomorphism نمرا بي find
+
+340
+00:35:05,030 --> 00:35:09,190
+ال kern ال mainly الفاي
+
+341
+00:35:13,790 --> 00:35:20,870
+فكر في الموضوع كويس و بدنا نيجي نثبت أو نوجد له
+
+342
+00:35:20,870 --> 00:35:29,110
+المطلبين اللي طلبهم في هذه المسألة طبعا لما درسنا
+
+343
+00:35:29,110 --> 00:35:33,750
+ال isomorphism ماجيبناش سيرة ال kernel على الإطلاق
+
+344
+00:35:33,750 --> 00:35:37,530
+لكن أجلنا لل homomorphism كيف؟
+
+345
+00:35:40,170 --> 00:35:45,650
+لانه فش غير عنصر واحد طيب الان بدى نبين ان هذا هو
+
+346
+00:35:45,650 --> 00:35:51,650
+homomorphism فباجى بقوله بدي اخد في of بدي اشوف x
+
+347
+00:35:51,650 --> 00:36:02,080
+زائد y والله x في yيبقى عملية جامعة فاي اف اكس
+
+348
+00:36:02,080 --> 00:36:03,320
+زائد واي
+
+349
+00:36:17,560 --> 00:36:24,240
+هذا يعني إن الـ E أُس X في الـ E أُس Y عند الضرب
+
+350
+00:36:24,240 --> 00:36:29,600
+تجمع من الأسس معلومات Calculus تمام؟ هذا الكلام
+
+351
+00:36:29,600 --> 00:36:37,240
+يساوي Phi of X وهذا Phi of Y وهذا كله صحيح لكل الـ
+
+352
+00:36:37,240 --> 00:36:42,250
+X والـ Y اللي موجودة ويناللي موجودة في الـR يبقى
+
+353
+00:36:42,250 --> 00:36:47,870
+هي أثبتناله في عبارة عن homomorphism نمرأ بيه بدنا
+
+354
+00:36:47,870 --> 00:36:54,070
+نجيب ال kernel للـFi ال kernel للـFi كل ال X اللي
+
+355
+00:36:54,070 --> 00:37:03,040
+موجودة في الـRالـ Phi of X بده يساوي ال identity
+
+356
+00:37:03,040 --> 00:37:09,760
+element
+
+357
+00:37:09,760 --> 00:37:18,820
+تبع ال R plusبقوله كويس كل ال X اللي موجودة في R
+
+358
+00:37:18,820 --> 00:37:25,780
+بحيث ان Phi of X هي مين إيقص X تمام؟ وهذا ال
+
+359
+00:37:25,780 --> 00:37:33,570
+identity element اللي هو واحد صحيح في غيره؟ممتاز
+
+360
+00:37:33,570 --> 00:37:40,790
+جدا يبقى هذه هها بدها تساوي Zero فقط يعني X التي
+
+361
+00:37:40,790 --> 00:37:46,130
+تساوي Zero اللي موجودة في R هي حل المعادلة هذه
+
+362
+00:37:46,130 --> 00:37:54,430
+because X تساوي Zero
+
+363
+00:37:54,430 --> 00:38:09,740
+isthe only solution of the equation EO6 تساوي مين؟
+
+364
+00:38:09,740 --> 00:38:15,340
+تساوي واحد هذا هو الحل الوحيد اللي ماعناش غيره
+
+365
+00:38:15,340 --> 00:38:23,900
+نعطي كمان مثال خمسة نمرة A بيقول define
+
+366
+00:38:47,220 --> 00:38:58,890
+السؤال هوفاي a homomorphism والإجابة نعم او لا بدك
+
+367
+00:38:58,890 --> 00:39:11,950
+تقولي why نمر بي define a function في من زد اتناش
+
+368
+00:39:12,610 --> 00:39:21,230
+الى زد اتناش بي فاي of اكس بده يساوي تلاتة اكس
+
+369
+00:39:21,230 --> 00:39:32,490
+show that show that فاي is homomorphism
+
+370
+00:39:32,490 --> 00:39:38,990
+and find ال kernel للفاي
+
+371
+00:39:50,090 --> 00:39:56,690
+المعارف function φي من الار بلس وعليها عملية الضرب
+
+372
+00:39:56,690 --> 00:40:00,070
+لار بلس وعليها عملية الضرب يبقى من مجموعة العدد
+
+373
+00:40:00,070 --> 00:40:04,750
+الحقيقية الموجبة إلى مجموعة العدد الحقيقية الموجبة
+
+374
+00:40:04,750 --> 00:40:08,430
+by five of x سوى التلاتة اكس ويقول هل هذه
+
+375
+00:40:08,430 --> 00:40:13,010
+homomorphism ولا لأ إن كان نعم لماذا وإن كان لا
+
+376
+00:40:13,010 --> 00:40:19,200
+لماذاوالله ما احنا عارفين بنجيجي نشوف في of x في y
+
+377
+00:40:19,200 --> 00:40:25,300
+يبقى عملية ضرب فاخدت في of x في y حسب التعريف
+
+378
+00:40:25,300 --> 00:40:33,900
+تلاتة x y يعني هذه تلاتة x في مين في ال y في of x
+
+379
+00:40:33,900 --> 00:40:43,030
+في ال y وليس في في of yطيب خدلي الان في of x في في
+
+380
+00:40:43,030 --> 00:40:49,850
+of y اللي هي تلاتة x في تلاتة y يعني قدشته ساوي
+
+381
+00:40:49,850 --> 00:40:57,490
+تسعة x y المعنى هذا الكلام ان ال في of x y لا
+
+382
+00:40:57,490 --> 00:41:07,810
+يساوي في of x في في of y يبقى هنا ال في is not
+
+383
+00:41:09,550 --> 00:41:15,850
+Homomorphism تعال خدلي نمر بيه نمر بيه بنفس
+
+384
+00:41:15,850 --> 00:41:23,330
+الطريقة بس ال operation هنا شباباشجمع يبقى في of x
+
+385
+00:41:23,330 --> 00:41:30,270
+زائد ال y يسوى تلاتة في x زائد y يبقى تلاتة x زائد
+
+386
+00:41:30,270 --> 00:41:38,270
+تلاتة y يبقى في of x زائد في of y هذا كله صحيح لكل
+
+387
+00:41:38,270 --> 00:41:43,970
+ال x و ال y اللي موجودة في z main اتناش يبقى هنا
+
+388
+00:41:43,970 --> 00:41:53,530
+في is a homomorphismجالي هاتلي ال kernel يبقى
+
+389
+00:41:53,530 --> 00:42:00,670
+بالداجي اقوله ال kernel بتبع ال five كل ال X اللي
+
+390
+00:42:00,670 --> 00:42:07,130
+موجودة في Z12 بحيث ال five of X بديه يسوى ال
+
+391
+00:42:07,130 --> 00:42:15,130
+identity تبع Z12 اللي هم هنا شباب ال zero تمام؟طيب
+
+392
+00:42:15,130 --> 00:42:21,330
+بدا اتي اشوف تحت تأثير ال homomorphism اللي هو
+
+393
+00:42:21,330 --> 00:42:28,570
+five of x بده يساوي تلاتة x من ال elements اللي
+
+394
+00:42:28,570 --> 00:42:33,330
+صورتها دائما و أبدا ال zero اللي عندها طبعا أكيد
+
+395
+00:42:33,330 --> 00:42:38,230
+ال zero لإنه تلاتة في zero ب zero طبعا طب من كمان؟
+
+396
+00:42:38,500 --> 00:42:43,420
+والاربعة لان تلاتة في اربعة باطناش تعني مين؟ تعني
+
+397
+00:42:43,420 --> 00:42:50,580
+Zero في كمان تمانية تمانية في تلاتة باربعة وعشرين
+
+398
+00:42:50,580 --> 00:42:56,900
+جد اتناش مرتين يبقى تمانية في غيرهم؟ لأ يبقى الكرن
+
+399
+00:42:56,900 --> 00:43:01,200
+اللي فيه تلاتة اللي من الصفر اربعة تمانية فقط لا
+
+400
+00:43:01,200 --> 00:43:01,820
+غير
+
+401
+00:43:18,750 --> 00:43:26,610
+طب اننا نجي لأول نظرية على هذا ال isomorphism وهذه
+
+402
+00:43:26,610 --> 00:43:32,890
+تتحدث عن علاقة ال isomorphism بال elements يبقى
+
+403
+00:43:32,890 --> 00:43:37,770
+هنا theorem اللي
+
+404
+00:43:37,770 --> 00:43:48,130
+هي ال properties of elements under
+
+405
+00:43:59,930 --> 00:44:08,430
+homomorphisms نظرية بتقول let في من جي إلى جي بار
+
+406
+00:44:08,430 --> 00:44:14,790
+بأقرب
+
+407
+00:44:14,790 --> 00:44:17,370
+homomorphism
+
+408
+00:44:18,770 --> 00:44:24,550
+a group homomorphism let and
+
+409
+00:44:24,550 --> 00:44:36,390
+let الجي موجودة في الجي then النقطة الأولى اللي هي
+
+410
+00:44:36,390 --> 00:44:41,530
+five of ال identity element تبع الجي قد يقين ال
+
+411
+00:44:41,530 --> 00:44:47,180
+identity element تبع الجي بقىالنقطة الثانية يبقى
+
+412
+00:44:47,180 --> 00:44:53,860
+هذه هي النقطة الأولى النقطة الثانية five of g to
+
+413
+00:44:53,860 --> 00:45:02,700
+the power n يسوى five of g to the power n for all
+
+414
+00:45:02,700 --> 00:45:09,140
+in اللي موجودة في زد يعني أعداد صحيحةالنقطة
+
+415
+00:45:09,140 --> 00:45:18,380
+الثالثة if ال order لل G is finite لو كان هذا
+
+416
+00:45:18,380 --> 00:45:26,840
+finite then ال order لل phi of G divides ال order
+
+417
+00:45:26,840 --> 00:45:37,080
+لمين ال order ل G النقطة الرابعة ال kernelللـ Phi
+
+418
+00:45:37,080 --> 00:45:47,520
+is a subgroup من مين؟ من G النقطة الخامسة Phi of A
+
+419
+00:45:47,520 --> 00:45:56,240
+بده يساوي Phi of B if and only if ال A في الكيرن
+
+420
+00:45:56,240 --> 00:46:05,940
+للـ Phi بده يساوي ال Bالنقطة السادسة والاخيرة if
+
+421
+00:46:05,940 --> 00:46:13,400
+الـ phi of G بدي ساوي الـ G prime then الـ phi
+
+422
+00:46:13,400 --> 00:46:19,200
+inverse of G primeفاينفرس في جي برايم اللي هو كل
+
+423
+00:46:19,200 --> 00:46:26,520
+ال X اللي موجودة في جي بحيث ان فاي اف X بدر ساوي
+
+424
+00:46:26,520 --> 00:46:32,180
+جي برايم واللي هي بدها تساوي جي في كيرن للفاي
+
+425
+00:46:58,070 --> 00:47:02,290
+أظن الأولى والتانية برهنهم في حالة ال isomorphism
+
+426
+00:47:02,290 --> 00:47:07,210
+وبالتالي انبرهانات مافيش مالناشن ضايع فيه يقوموا
+
+427
+00:47:07,210 --> 00:47:13,170
+.. يبقى واحد and اتنين و approved
+
+428
+00:47:17,210 --> 00:47:25,250
+Rowed in chapter سبعة أظن ستة in chapter ستة يبقى
+
+429
+00:47:25,250 --> 00:47:32,110
+بترجعهم نفس البرهان حرفية بنجي لتلاتة تلاتة بيقول
+
+430
+00:47:32,110 --> 00:47:36,170
+لو كان ال order اللي جي يبقى بالداجة أقوله assume
+
+431
+00:47:36,170 --> 00:47:44,170
+ان ال order اللي جي بده يساوي n و ال n is finite
+
+432
+00:47:46,550 --> 00:47:54,210
+that is يعني ان الـG to the power N بده ساوى من؟
+
+433
+00:47:54,210 --> 00:48:00,330
+بده ساوى ال identity بدي اثبت ان ال order للصورة
+
+434
+00:48:00,330 --> 00:48:05,400
+تبعت ال G بيقسم ال order تبع من ال Gإحنا أثبتنا
+
+435
+00:48:05,400 --> 00:48:10,340
+هذا الكلام في حالة الـ isomorphism إنه 2 are equal
+
+436
+00:48:10,340 --> 00:48:14,200
+ال order للصورة بيعطينا ال order للأصل نفسه ال
+
+437
+00:48:14,200 --> 00:48:18,440
+order لل G هو ال order لل Phi of G هذا في حالة لو
+
+438
+00:48:18,440 --> 00:48:22,580
+كانت Phi isomorphism لكن هنا homomorphism بدي أثبت
+
+439
+00:48:22,580 --> 00:48:27,280
+ان ال order للصورة بيقسم من ال order تبع الأصل
+
+440
+00:48:27,280 --> 00:48:32,140
+بقوله بسيطة فرضنا ال order اللي G بده يساوي N يعني
+
+441
+00:48:32,140 --> 00:48:40,490
+finiteيعني G أُس N بده يسوي ال identity بده يقسم
+
+442
+00:48:40,490 --> 00:48:50,430
+ال N لذلك لو جيت قلت لخدلي ال Phi خدلي ال Phi of G
+
+443
+00:48:50,430 --> 00:48:58,360
+كله to the power Nحسب الخصية رقم اتنين هذا بدي
+
+444
+00:48:58,360 --> 00:49:06,240
+يعطيني في of GN طيب في of GN اللي هي عبارة عن ال
+
+445
+00:49:06,240 --> 00:49:13,430
+identity element بتابعي ال Gفاي لما اتأثر على الـ
+
+446
+00:49:13,430 --> 00:49:16,770
+identity element تبع الـG من النقطة الأولى بدي
+
+447
+00:49:16,770 --> 00:49:21,710
+اعطينا من الـ identity element تبع الـG بقى اذا
+
+448
+00:49:21,710 --> 00:49:27,210
+انا في of G رفعتها كأسل عدد طالع ال identity يبقى
+
+449
+00:49:27,210 --> 00:49:34,370
+ال order تبعهايا بيكون N يا أقل من N ويقسمين ويقسم
+
+450
+00:49:34,370 --> 00:49:38,810
+ال N على كل الأمرين ال N بتقسم نفسها صحيح لو كان
+
+451
+00:49:38,810 --> 00:49:44,670
+أصغر منها برضه بدي أقسم منها ال N يبقى هذا يعني أن
+
+452
+00:49:44,670 --> 00:49:54,260
+ال order تبع ال Phi of G ماله divide ال Nأظن
+
+453
+00:49:54,260 --> 00:50:00,220
+كرولري على Lagrange theorem طيب هذا الكلام يعني ان
+
+454
+00:50:00,220 --> 00:50:06,480
+ال order ل phi of G divide ال order ل G وهو
+
+455
+00:50:06,480 --> 00:50:12,240
+المطلوبهذه النقطة التالتة النقطة الرابعة ال kernel
+
+456
+00:50:12,240 --> 00:50:17,920
+subgroup هذه النقطة الرابعة اول شي ال kernel
+
+457
+00:50:25,280 --> 00:50:29,780
+اللي هو الـ Phi of الـ Identity بتابع الـ G بدي
+
+458
+00:50:29,780 --> 00:50:34,060
+أسوأ الـ Identity تابع الـ G bar هذا يعني أن الـ
+
+459
+00:50:34,060 --> 00:50:38,560
+Identity تابع الـ G موجودة في الـ Kernel للـ Phi
+
+460
+00:50:38,560 --> 00:50:46,720
+الآن لو قلت لك خدلي XY موجودة في الـ Kernel للـ
+
+461
+00:50:46,720 --> 00:50:52,850
+Phi thenالـ Phi of X بده يساوي الـ Identity تبع
+
+462
+00:50:52,850 --> 00:50:58,690
+الـ G bar وفي نفس الوقت الـ Phi of Y بده يساوي الـ
+
+463
+00:50:58,690 --> 00:51:05,580
+Identity Element تبع الـ G bar هذا بده يعنيإن
+
+464
+00:51:05,580 --> 00:51:13,260
+الـPhi of Y الكل انفرس اللي هو عبارة عن Phi of Y
+
+465
+00:51:13,260 --> 00:51:19,640
+انفرس بدر يساوي ال identity element تبع الـG bar
+
+466
+00:51:19,640 --> 00:51:25,040
+انفرس اللي هو الـG barطب انا بدي اثبت ان ال X في
+
+467
+00:51:25,040 --> 00:51:34,220
+ال Y انفرس موجود في الكيرنل لذلك بدي اخد الان فاي
+
+468
+00:51:34,220 --> 00:51:40,660
+اف X Y انفرسوالله إذا طلع يسوى ال identity يبقى
+
+469
+00:51:40,660 --> 00:51:47,160
+هذا موجود يبقى هذا الكلام بدي يعطيني في of X في في
+
+470
+00:51:47,160 --> 00:51:52,800
+of Y inverse في of X عندي بقداش بال identity
+
+471
+00:51:52,800 --> 00:51:58,640
+element تبع ال G bar وفي of Y inverse كمان بمين
+
+472
+00:51:58,640 --> 00:52:04,120
+بال identity تبع ال G bar يبقى هذا الكلام بدي سوى
+
+473
+00:52:04,120 --> 00:52:09,530
+ال identity تبع مينتبع الـ G bar مدام هيك معناته
+
+474
+00:52:09,530 --> 00:52:14,930
+الـ X Y inverse موجود في الكيرن اللي الفاي هذا
+
+475
+00:52:14,930 --> 00:52:20,910
+معناه ان الكيرن اللي الفاي is a subgroup من مين؟
+
+476
+00:52:20,910 --> 00:52:28,230
+من G وبعد شوية هنتبهتلك هي انه normal للمحاضرة
+
+477
+00:52:28,230 --> 00:52:30,910
+القادمة ان شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..68ad5af8d3d2f8dc307272928af5c6103c2f7eda
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk.srt
@@ -0,0 +1,1631 @@
+1
+00:00:21,750 --> 00:00:23,890
+بسم الله الرحمن الرحيم إن شاء الله يا شباب اليوم
+
+2
+00:00:23,890 --> 00:00:27,910
+هنكمل اللي بدنا إياه في المحاضرة الماضية من مناقشة
+
+3
+00:00:27,910 --> 00:00:31,610
+اللي هو الوحدة الثالثة المتعلقة بالـ subgroup طبعا
+
+4
+00:00:31,610 --> 00:00:35,230
+لذا وقفنا المرة الماضية عند سؤال 33
+
+5
+00:00:35,230 --> 00:00:40,030
+كتبناه وما حليناه نرجع نكتب السؤال، السؤال بيقول
+
+6
+00:00:40,030 --> 00:00:46,710
+التالي: إن لو كان عندي group وفيها two elements a وb
+
+7
+00:00:46,710 --> 00:00:51,170
+الـ order لـ الـ a بدو يساوي أربعة، الـ order لـ الـ b بدو 
+
+8
+00:00:51,170 --> 00:00:55,490
+يساوي اثنين، وعندي علاقة بتربط الـ a والـ b بتقول إن
+
+9
+00:00:55,490 --> 00:01:02,450
+الـ a تكعيب b بتساوي p في a، المطلوب في السؤال find
+
+10
+00:01:02,450 --> 00:01:05,390
+order الـ a,b
+
+11
+00:01:08,360 --> 00:01:11,440
+الطريقة اللي احنا بنتبعها لحساب الـ order تبع أي
+
+12
+00:01:11,440 --> 00:01:16,500
+عنصر هو إن أنا أشتغل على العنصر هذا وأعطيه powers
+
+13
+00:01:16,500 --> 00:01:21,480
+اثنين، ثلاثة، أربعة، خمسة، لما أصل لأقل أو لأول عدد
+
+14
+00:01:21,480 --> 00:01:26,780
+صحيح موجب بيعطيني الـ identity، في البداية أنا بدي
+
+15
+00:01:26,780 --> 00:01:32,420
+أثبت إن الـ order لا يساوي واحد، a b لا يساوي الـ
+
+16
+00:01:32,420 --> 00:01:36,360
+identity، claim هنحطها كـ claim
+
+17
+00:01:41,470 --> 00:01:48,170
+تعالوا نثبتها، Assume على النقيض that إن a,b بدو
+
+18
+00:01:48,170 --> 00:01:54,850
+يساوي الـ identity، هذا معناه إن a بدو يساوي b
+
+19
+00:01:54,850 --> 00:02:00,110
+inverse، وبالتالي order الـ a بدو يساوي order الـ b
+
+20
+00:02:00,110 --> 00:02:04,770
+inverse، طبعا order الـ b inverse هو إيش order الـ b
+
+21
+00:02:04,770 --> 00:02:10,410
+وبالتالي الأربعة بدو يساوي اثنين وهذا إيش تناقض
+
+22
+00:02:11,450 --> 00:02:15,750
+صار عندي تناقض وبالتالي so الـ a b لا يساوي الـ
+
+23
+00:02:15,750 --> 00:02:21,550
+identity، وبالتالي الـ order لا يساوي واحد، حد
+
+24
+00:02:21,550 --> 00:02:29,050
+هيسألني ليش أنا كتبت هذا الشغل؟ لأن أنا لما أكمل حل
+
+25
+00:02:29,050 --> 00:02:33,200
+الصورة اللي جيت هنكتشف إن الـ order هيساوي اثنين لأن
+
+26
+00:02:33,200 --> 00:02:38,640
+a b تربيع هيعطينا الـ identity، فالسؤال إن مادام الـ
+
+27
+00:02:38,640 --> 00:02:42,440
+a b تربيع هيعطينا الـ identity، فالـ order هيكون يا
+
+28
+00:02:42,440 --> 00:02:45,980
+اثنين يا واحد، أنا بنفي هيكد إن يكون الـ order
+
+29
+00:02:45,980 --> 00:02:54,820
+بيساوي واحد، now لو قلنا a b الكل تربيع عبارة عن إيش
+
+30
+00:02:54,820 --> 00:03:03,200
+عبارة عن a b a b، زي ما احنا عارفين الـ operation
+
+31
+00:03:03,200 --> 00:03:13,220
+بتحقق خاصية التجميع، هذا هي يساوي a في b a في b حسب
+
+32
+00:03:13,220 --> 00:03:19,080
+الخاصية لأن b إيش بتساوي a في a تكعيب في b في b
+
+33
+00:03:19,080 --> 00:03:24,700
+يعني a قوس 4 في b تربيع، الـ identity في الـ identity
+
+34
+00:03:24,700 --> 00:03:31,100
+بدو يساوي الـ identity، هذا معناه إن order الـ a b أقل
+
+35
+00:03:31,100 --> 00:03:44,160
+أو يساوي اثنين، but order الـ a b لا يساوي واحد، واضح
+
+36
+00:03:44,160 --> 00:03:49,020
+هذا يا شباب، أنا نفقت إن الـ order يكون واحد، وقلت إن
+
+37
+00:03:49,020 --> 00:03:52,360
+الـ order هيبدأ من الاثنين وينزل، فيا الاثنين يا
+
+38
+00:03:52,360 --> 00:03:57,400
+الواحد، والواحد لأ هيظل عند مين؟ الاثنين لأ لأ مش
+
+39
+00:03:57,400 --> 00:04:02,900
+تجريب، أنت لما تيجي تتعامل مع الـ order التعريف تبعه
+
+40
+00:04:02,900 --> 00:04:11,850
+أصغر عدد طبيعي لما بترفع العنصر إله بيعطيك الـ
+
+41
+00:04:11,850 --> 00:04:15,970
+identity، أنا بدأت بالواحد ما نفعش، الاثنين زبط
+
+42
+00:04:15,970 --> 00:04:20,210
+بالتجريب، هو الأغلب بالتجريب إلا لو كان في عندك
+
+43
+00:04:20,210 --> 00:04:33,690
+شغلات مساعدة أخرى أشفهم
+
+44
+00:04:35,740 --> 00:04:40,000
+هي a b طيب
+
+45
+00:04:40,000 --> 00:04:52,180
+وحطه
+
+46
+00:04:52,180 --> 00:04:56,740
+بهذا الشكل وشوف، عشان اللي أنا عملته لأ بدل التحذير
+
+47
+00:04:56,740 --> 00:04:59,340
+يعني أنا مش .. أنا ما عملتش .. ما عملتش تحذير أنت
+
+48
+00:04:59,340 --> 00:05:03,240
+هتصل في النهاية إن إيه؟ الـ result بيبقى بيساوي الـ
+
+49
+00:05:03,240 --> 00:05:06,580
+identity تمام؟ يبقى الـ order يا اثنين يا واحد
+
+50
+00:05:06,580 --> 00:05:09,500
+هتيجي تنفي الواحد وبالتالي أنت هو كأنك بدأت من
+
+51
+00:05:09,500 --> 00:05:13,800
+هان بعدين حلت هذا هي هي بدل التحذير اه في النهاية
+
+52
+00:05:13,800 --> 00:05:17,840
+ده برضه تحذير إيش ضامنك إنك هتصل لهذا؟ نفس الضمان
+
+53
+00:05:17,840 --> 00:05:19,500
+اللي موجود هنا هو الضمان اللي موجود هنا
+
+54
+00:05:24,100 --> 00:05:29,300
+طيب إيش فيه سؤال بعده؟ سؤال
+
+55
+00:05:29,300 --> 00:05:35,520
+أربعة و ثلاثين، suppose
+
+56
+00:05:35,520 --> 00:05:39,220
+a and p are group elements such that order a بدو
+
+57
+00:05:39,220 --> 00:05:42,240
+يساوي اثنين، الـ b لا يساوي الـ identity، هو a p a بدو
+
+58
+00:05:42,240 --> 00:05:48,200
+يساوي p تربيع، find order الـ b
+
+59
+00:05:52,030 --> 00:05:57,350
+الـ order للـ A بدو يساوي اثنين، الـ B لا يساوي الـ
+
+60
+00:05:57,350 --> 00:06:00,390
+identity، طبعا هو رايحني من الجثة اللي أنا عملتها
+
+61
+00:06:00,390 --> 00:06:05,910
+الـ B لا يساوي الـ identity يعني order الـ B لا يساوي
+
+62
+00:06:05,910 --> 00:06:13,430
+الواحد، وعندي العلاقة التالية إن A P A بدو تساوي A
+
+63
+00:06:13,430 --> 00:06:18,430
+تربيع، مين عنده أفكار لحل السؤال ده يا شباب؟ مين
+
+64
+00:06:18,430 --> 00:06:19,110
+عنده أفكار؟
+
+65
+00:06:22,520 --> 00:06:28,460
+هنفكر طبعا بنفس الاسلوب اللي هان أفيدونا
+
+66
+00:06:28,460 --> 00:06:33,340
+أفادكم الله عشرة
+
+67
+00:06:33,340 --> 00:06:42,760
+أكثر طيب
+
+68
+00:06:42,760 --> 00:06:46,700
+A
+
+69
+00:06:46,700 --> 00:06:51,160
+تربيع P A بيساوي طيب بعد إيه؟
+
+70
+00:06:54,360 --> 00:07:00,360
+تعالى نخربش، تعمل a b a بدو يساوي b تربيع، هتضرب
+
+71
+00:07:00,360 --> 00:07:05,500
+الطرفين في a، هصير a تربيع b a بدو يساوي a b
+
+72
+00:07:05,500 --> 00:07:07,800
+تربيع، الـ a تربيع اللي على الناحية هذه بدها إيه؟
+
+73
+00:07:07,800 --> 00:07:19,680
+تروح، بدو صار عندي b a a b تربيع، طيب إيش
+
+74
+00:07:19,680 --> 00:07:20,600
+ممكن يسي بعد هيك؟
+
+75
+00:07:24,000 --> 00:07:27,620
+تجرب تضغط على الثانية هصير b a تربيع
+
+76
+00:07:27,620 --> 00:07:33,780
+بتساوي a b تربيع a اللي هي b بتساوي a b
+
+77
+00:07:33,780 --> 00:07:45,740
+تربيع a، طيب اه كمان فكرة بس فكرة واحدة ضايلة وين
+
+78
+00:07:45,740 --> 00:07:54,770
+طب بدك تستفيد لأ هذه عبارة عن a b b a صح ولا لأ؟ اللي
+
+79
+00:07:54,770 --> 00:08:03,450
+عبارة عن a b identity b a، اللي عبارة عن a b a
+
+80
+00:08:03,450 --> 00:08:09,350
+تربيع b
+
+81
+00:08:09,350 --> 00:08:15,830
+إيه؟ هذي عبارة عن a b a a b a، اللي a b a لكل تربيع
+
+82
+00:08:15,830 --> 00:08:24,980
+اللي عبارة عن b تربيع تربيع يعني b قوس أربعة يعني
+
+83
+00:08:24,980 --> 00:08:30,800
+أنت وصلت إن p بيساو p قوس 4، الـ p لا يساوي الـ
+
+84
+00:08:30,800 --> 00:08:35,940
+identity، بالـ cancellation law، p تكعيب بيساوي الـ
+
+85
+00:08:35,940 --> 00:08:44,440
+identity وبالتالي هيصير الـ order لـ p يا
+
+86
+00:08:44,440 --> 00:08:52,790
+واحد يا اثنين يا ثلاثة، هذا مرفوض، p مظلتانين في
+
+87
+00:08:52,790 --> 00:09:04,130
+الاثنين كنت هاي فكرة السؤال، تعالى نغطبها، الـ
+
+88
+00:09:04,130 --> 00:09:14,050
+b تربيع تربيع أنا هبدأ بالعكس عبارة عن a b a الكل
+
+89
+00:09:14,050 --> 00:09:29,640
+تربيع، عبارة عن إيش؟ عن a b a a p a a p a، الـ a إيش
+
+90
+00:09:29,640 --> 00:09:33,100
+بتساوي؟
+
+91
+00:09:33,100 --> 00:09:42,640
+إيش بتساوي؟ a p a تربيع p a يعني a p identity p a
+
+92
+00:09:42,640 --> 00:09:51,500
+يعني a b تربيع a، إيش الـ b تربيع بتساوي؟ هذا هتساوي
+
+93
+00:09:51,500 --> 00:09:58,180
+a في a p a a a تربيع b إيه تربيع بدو يساوي b
+
+94
+00:09:58,180 --> 00:10:04,340
+المحصلة إن b قوس أربعة بدو تساوي b، وبالتالي b تك
+
+95
+00:10:04,340 --> 00:10:10,520
+عيب بدو تساوي الـ identity، معناه to order الـ b يا
+
+96
+00:10:10,520 --> 00:10:19,100
+واحد يا اثنين يا ثلاثة، but order الـ b لا يساوي
+
+97
+00:10:19,100 --> 00:10:26,440
+واحد، ليش؟ لأن b لا يساوي الـ identity، بيضايق قدامي
+
+98
+00:10:26,440 --> 00:10:35,040
+خيارين يا الاثنين يا الثلاثة، كيف ده ننفيه؟
+
+99
+00:10:35,040 --> 00:10:42,580
+if order الـ b بدو يساوي اثنين، معناه b تربيع الـ
+
+100
+00:10:42,580 --> 00:10:47,960
+identity، بيساوي b تربيع اللي إيش بيساوي؟ بيساوي
+
+101
+00:10:47,960 --> 00:11:01,970
+إيه؟ p a يعني e بدو يساوي a p a، وبالتالي a تربيع
+
+102
+00:11:01,970 --> 00:11:07,270
+بدو يساوي a p a، مش الـ identity بيساوي a تربيع، يعني a
+
+103
+00:11:07,270 --> 00:11:13,110
+في a بدو يساوي a p a، المحصلة بعد ما تعمل
+
+104
+00:11:13,110 --> 00:11:19,410
+cancellation، الـ identity بدو يساوي p وهذا إيش؟ تناقض
+
+105
+00:11:19,410 --> 00:11:24,490
+النتيجة order الـ b لا يساوي اثنين، المحصلة إن order
+
+106
+00:11:24,490 --> 00:11:36,010
+الـ b إيش بتساوي؟ تساوي ثلاثة، واضح؟ واضح؟
+
+107
+00:11:36,010 --> 00:11:39,110
+مين عنده أي شك أو أي نقطة غير مفهومة؟
+
+108
+00:11:53,980 --> 00:11:59,260
+مش الـ b تربيع بس هو a p a، شيل الـ b تربيع وحط الـ a p a
+
+109
+00:11:59,260 --> 00:12:06,980
+طيب
+
+110
+00:12:06,980 --> 00:12:10,460
+بالنسبة للسؤال ثمانية و ثلاثين أنا هسيبه عليك يعني
+
+111
+00:12:10,460 --> 00:12:15,480
+هو هتحلوا بالسماء للـ induction، ثمانية
+
+112
+00:12:15,480 --> 00:12:22,290
+وثلاثين، مطلوب تثبت العلاقة هذه في sl2r إن cos θ
+
+113
+00:12:22,290 --> 00:12:28,850
+ناقص sin θ sin θ cos θ أس n بيساوي cos nθ سالب sin
+
+114
+00:12:28,850 --> 00:12:34,710
+nθ sin nθ cos nθ بيستعمل الـ induction بإمكانك
+
+115
+00:12:34,710 --> 00:12:39,290
+تثبته، أثبت صحتها لما n بيساوي 2، بعدين افترض صحتها
+
+116
+00:12:39,290 --> 00:12:44,150
+لما n بيساوي k، وأثبت صحتها بعدين لما n بيساوي k
+
+117
+00:12:44,150 --> 00:12:45,870
+زائد الـ 1 using
+
+118
+00:12:47,910 --> 00:12:53,750
+mathematical induction، فضل
+
+119
+00:12:53,750 --> 00:13:02,670
+الآن على الطبيعي positive integer، هو إيش جالك
+
+120
+00:13:02,670 --> 00:13:10,330
+positive integer، طبعا هل هذه المصفوفة لها inverse
+
+121
+00:13:13,260 --> 00:13:18,780
+cos θ سالب sin θ لها inverse لأن المحدد تبعها واحد
+
+122
+00:13:18,780 --> 00:13:22,000
+فأنت ممكن ترفع لأس سالب، بس لما ترفع لأس سالب
+
+123
+00:13:22,000 --> 00:13:29,240
+هتتعامل مع مين؟ مع معكوس المصفوفة، واضح؟ 41
+
+124
+00:13:29,240 --> 00:13:36,900
+D4
+
+125
+00:13:36,900 --> 00:13:42,140
+has seven cyclic subgroups list them، هذا سؤال سهل
+
+126
+00:13:45,960 --> 00:13:52,180
+generated by R0 generated by R90 هو نفس ال
+
+127
+00:13:52,180 --> 00:13:57,440
+generated by R270 ال generated by R180 ال
+
+128
+00:13:57,440 --> 00:14:02,300
+generated by H ال generated by V ال generated by D
+
+129
+00:14:02,300 --> 00:14:07,820
+ال generated by D شرطة هم ال seven واحد اثنان
+
+130
+00:14:07,820 --> 00:14:12,640
+ثلاثة أربعة خمسة ستة سبعة seven cyclic subgroup
+
+131
+00:14:26,150 --> 00:14:34,330
+طيب سؤال اثنين و أربعين اثنين و أربعين like سؤال
+
+132
+00:14:34,330 --> 00:14:42,450
+واحد و أربعين اللي هو خمسة عشر مين فيها عناصر واحد
+
+133
+00:14:42,450 --> 00:14:49,810
+اثنين أربعة سبعة ثمانية أحد عشر وثلاثة عشر وأربعة عشر
+
+134
+00:14:49,810 --> 00:14:58,260
+اثنا عشر طيب سؤال أربعة و أربعين suppose j is a
+
+135
+00:14:58,260 --> 00:15:01,820
+group that has exactly eight elements of order
+
+136
+00:15:01,820 --> 00:15:05,720
+ثلاثة how many subgroups of order ثلاثة does j has
+
+137
+00:15:05,720 --> 00:15:14,940
+أو have هذا السؤال حلو فيه أفكار عند group j have
+
+138
+00:15:14,940 --> 00:15:19,060
+أو has عشان نكون ماشيين صح
+
+139
+00:15:22,470 --> 00:15:30,030
+exactly ثمان element x with order x بدي تساوي
+
+140
+00:15:30,030 --> 00:15:39,690
+ثلاثة say من هما x واحد x اثنان x ثلاثة x أربعة x
+
+141
+00:15:39,690 --> 00:15:44,990
+خمسة x ستة x سبعة و x ثمانية
+
+142
+00:15:47,730 --> 00:15:53,230
+وال order ل X I يكون ثلاثة لكل I أقل أو يساوي
+
+143
+00:15:53,230 --> 00:16:01,330
+ثمانية بقول ليه how many H
+
+144
+00:16:01,330 --> 00:16:12,070
+subgroup من ال J with H cyclic and ال order ل H
+
+145
+00:16:12,070 --> 00:16:15,070
+يكون ثلاثة
+
+146
+00:16:18,850 --> 00:16:25,870
+أكم جروب من هدولة أو subgroup من الـ Cyclic واللي 
+
+147
+00:16:25,870 --> 00:16:31,190
+الأرضة غيرهم ثلاثة موجودين في ERG قدام هناخد نظرية
+
+148
+00:16:31,190 --> 00:16:37,810
+تربط في chapter 4 أو chapter 7 بتحللك الأشكالية
+
+149
+00:16:37,810 --> 00:16:42,270
+هذه أنه بتقدر تحسبهم مباشرة بدون ما تقعد تتحذر زي
+
+150
+00:16:42,270 --> 00:16:48,400
+ما هنعمل هال game الحلقة التالية let H subgroup من
+
+151
+00:16:48,400 --> 00:16:54,020
+الـ J ال order لل H بدي يساوي ثلاثة and H is
+
+152
+00:16:54,020 --> 00:17:00,660
+cyclic عشان أعرف كم واحدة من هدول ال subgroup
+
+153
+00:17:00,660 --> 00:17:04,460
+المطلوبات هاخد واحدة منهم وأتكلم عن الهيكلية
+
+154
+00:17:04,460 --> 00:17:09,280
+الداخلية تبعها هذا معناه أن ال H generated by
+
+155
+00:17:09,280 --> 00:17:14,470
+some A وال a ينتمي لل J وال order لل a يبدو
+
+156
+00:17:14,470 --> 00:17:21,250
+يساوي ثلاثة هذا معناه أن ال h أكم عنصر فيها في
+
+157
+00:17:21,250 --> 00:17:27,570
+البداية ال identity وال a تربيع اللي هو عبارة عن
+
+158
+00:17:27,570 --> 00:17:35,810
+ال a inverse مش
+
+159
+00:17:35,810 --> 00:17:41,240
+هذه sub group مغلقة على ال inverse ولا لأ الـ A
+
+160
+00:17:41,240 --> 00:17:49,500
+موجودة والـ E موجودة و since طبعا هذه تفسيرها لأن
+
+161
+00:17:49,500 --> 00:17:54,380
+ال order ال A بدي يساوي ثلاثة معناه A تكعيب بدي
+
+162
+00:17:54,380 --> 00:17:57,660
+يساوي ال identity معناه A تربيع بدي يساوي ال A
+
+163
+00:17:57,660 --> 00:18:06,830
+inverse تمام؟ also A لا يساوي الـ A inverse since
+
+164
+00:18:06,830 --> 00:18:15,630
+ال order لـ A يساوي ثلاثة مدام
+
+165
+00:18:15,630 --> 00:18:23,810
+ال A وال A inverse موجودين هذا معناه ال order ل
+
+166
+00:18:23,810 --> 00:18:32,870
+A يساوي ثلاثة يقبل A يساوي some xi صح
+
+167
+00:18:32,870 --> 00:18:33,310
+ولا لأ؟
+
+168
+00:18:36,060 --> 00:18:40,360
+ال order لل a inverse بدي يساوي ثلاثة وال a لا
+
+169
+00:18:40,360 --> 00:18:45,920
+يساوي ال a inverse يكبر ال a inverse بدي يساوي xj وال
+
+170
+00:18:45,920 --> 00:18:51,940
+j لا يساوي i هدول
+
+171
+00:18:51,940 --> 00:18:57,060
+معناه كل واحدة من اللي زي h أكم عنصر ال order له
+
+172
+00:18:57,060 --> 00:19:03,680
+ثلاثة موجود فيها يكبر every such
+
+173
+00:19:04,710 --> 00:19:11,370
+H contains two
+
+174
+00:19:11,370 --> 00:19:21,290
+elements of order ثلاثة مش contain two ممكن أقول
+
+175
+00:19:21,290 --> 00:19:24,010
+احنا كمان contain exactly
+
+176
+00:19:30,600 --> 00:19:33,540
+كل واحدة من الـ H اللي أنا بدور عليهم فيها اثنين
+
+177
+00:19:33,540 --> 00:19:38,760
+طب هم مجددش كلهم هم
+
+178
+00:19:38,760 --> 00:19:44,240
+ثمانية هذا
+
+179
+00:19:44,240 --> 00:19:52,040
+معناه يوجد ثمانية على اثنين بيساوي أربعة such H
+
+180
+00:19:52,040 --> 00:19:58,960
+كم واحدة موجودة؟ أربعة
+
+181
+00:20:02,170 --> 00:20:08,790
+الـ Identity اللي هو ضغط له ثلاثة ماشي
+
+182
+00:20:08,790 --> 00:20:15,130
+طالع معايا هم هيكون أربع group من ال H X واحد و X
+
+183
+00:20:15,130 --> 00:20:19,890
+واحد inverse مع ال identity X2 و X2 inverse مع ال
+
+184
+00:20:19,890 --> 00:20:25,810
+identity X3 و X3 inverse مع ال identity و X4 و X4
+
+185
+00:20:25,810 --> 00:20:29,190
+inverse مع ال identity هتقولي هدول ثمانية مما هي
+
+186
+00:20:29,190 --> 00:20:34,650
+أول أربعة والأربعة الثانية مين ال inverse تبعهم
+
+187
+00:20:34,650 --> 00:20:38,290
+44 45
+
+188
+00:20:49,630 --> 00:20:55,850
+طيب خمسة و أربعين بسؤال
+
+189
+00:20:55,850 --> 00:21:01,190
+خمسة و أربعين H subgroup من ال J وال J finite
+
+190
+00:21:01,190 --> 00:21:04,310
+suppose
+
+191
+00:21:04,310 --> 00:21:14,930
+J تنتمي لل J و N is the smallest positive
+
+192
+00:21:25,380 --> 00:21:31,220
+مطلوب اثبت ان انت تقسم order ج
+
+193
+00:21:39,260 --> 00:21:43,940
+شباب أول ما نيجي نحل أسئلة من نوعية ال .. خصوصا في
+
+194
+00:21:43,940 --> 00:21:48,260
+الجبر الحديث أهم حاجة لازم أعرفها وأقدر أتعامل
+
+195
+00:21:48,260 --> 00:21:52,260
+معاها هو تفسيري للمواضيع اللي عندي إذا ما قدرت
+
+196
+00:21:52,260 --> 00:21:56,460
+أفهم إيش المواضيع اللي في السؤال تتوقعش مني أعرف
+
+197
+00:21:56,460 --> 00:22:01,680
+أجيب المطلوب تتوقعش مني أعرف أجيب المطلوب
+
+198
+00:22:04,400 --> 00:22:08,180
+السؤال المعطيات اللغوية السهلة الـ H subgroup
+
+199
+00:22:08,180 --> 00:22:11,560
+والـ J finite عشان أقدر أتعامل مع ال orders يوجد
+
+200
+00:22:11,560 --> 00:22:20,200
+عنصر في الـ J لكل عنصر من هذا النوع أصغر عدد طبيعي
+
+201
+00:22:20,200 --> 00:22:25,800
+بيخلي الـ J أس N جوا الـ H هو N مطلوب أثبت أنه
+
+202
+00:22:25,800 --> 00:22:31,020
+الـ N تقسم ال order للـ J طيب تعالوا نشوف
+
+203
+00:22:35,740 --> 00:22:43,180
+let order j اختار له رقم خمسة
+
+204
+00:22:43,180 --> 00:22:53,000
+لأ أخي يعني أعطيه رمز خد دي دي ولا M المطلوب من
+
+205
+00:22:53,000 --> 00:23:02,060
+السؤال let n بدي يساوي ال smallest positive
+
+206
+00:23:03,860 --> 00:23:13,080
+Integral with J أس N ينتمي للـ H المطلوب أن N تقسم
+
+207
+00:23:13,080 --> 00:23:17,660
+الـ M ارجع
+
+208
+00:23:17,660 --> 00:23:21,700
+شوية بالذاكرة لنظرية الأعداد اللي أخدها كيف أثبت
+
+209
+00:23:21,700 --> 00:23:28,290
+أن N بيقسم الـ M اسلوبين يا بلاجي عدد صحيح بضربه في
+
+210
+00:23:28,290 --> 00:23:32,550
+ال N بيعطيني ال M يا بثبت انه remainder عند عملية
+
+211
+00:23:32,550 --> 00:23:40,810
+القسمة يساوي صفر using division algorithm
+
+212
+00:23:40,810 --> 00:23:51,190
+let M بدها تساوي QN زائد ال R ال R أقل من ال N وأصغر
+
+213
+00:23:51,190 --> 00:23:53,250
+من ال 0
+
+214
+00:23:57,090 --> 00:24:02,390
+الآن الـ J to M بدي يساوي ال identity ينتمي لل H
+
+215
+00:24:02,390 --> 00:24:09,430
+الـ J to N ينتمي لل H هيخليني أقول أن الـ J to N
+
+216
+00:24:09,430 --> 00:24:16,530
+أس كيو ينتمي لل H عشان الـ H subgroup فهي مغلقة على
+
+217
+00:24:16,530 --> 00:24:19,850
+العملية هذا معناه J
+
+218
+00:24:23,090 --> 00:24:35,110
+QN ينتمي للـ H مش بس هيك يا شباب J أس QN inverse
+
+219
+00:24:35,110 --> 00:24:44,750
+ينتمي للـ H J أس QN inverse عبارة عن أيش؟ J أس
+
+220
+00:24:44,750 --> 00:24:50,710
+سالب QN ينتمي للـ H أعطي هذا واحد وأعطي هذا اثنين
+
+221
+00:24:53,340 --> 00:24:59,920
+من واحد واثنين عنصرين في ال H وال H subgroup
+
+222
+00:24:59,920 --> 00:25:06,600
+حصل ضرب و مون هيكون في ال H حاصل معايا J أس M في
+
+223
+00:25:06,600 --> 00:25:15,920
+J سالب Q N هو عنصر من وين عنصر من ال H عند الضرب
+
+224
+00:25:15,920 --> 00:25:23,770
+إيش بيصير في الأسس؟ تجمع الأسس حاصل معايا J أس M
+
+225
+00:25:23,770 --> 00:25:35,510
+minus Q N ينتمي لمن؟ للـ H اطلح J أس R ينتمي لمن؟
+
+226
+00:25:35,510 --> 00:25:43,270
+للـ H هذا معناه N أقل أو يساوي R by the definition
+
+227
+00:25:43,270 --> 00:25:51,740
+of N تعريف ال N بيقول لي أن ال N هو أصغر عدد طبيعي
+
+228
+00:25:51,740 --> 00:25:57,880
+أو positive integer بيخلي ال J أس N جوه ال R فأي
+
+229
+00:25:57,880 --> 00:26:03,080
+أس ثاني لل J .. جوه ال H أي أس ثاني لل J بيكون
+
+230
+00:26:03,080 --> 00:26:07,620
+جوه ال H لازم هذا الأس يكون إشماله أكبر من ال N
+
+231
+00:26:07,620 --> 00:26:16,020
+but R أقل من ال N قارن لأ
+
+232
+00:26:17,470 --> 00:26:25,070
+هنا أقل وهنا أقل أو يساوي كيف دي يكون ال R أقل من
+
+233
+00:26:25,070 --> 00:26:29,650
+الآن؟ هذه نقيض هذه يعني النفي تبعها هذا هيعطيني هذا
+
+234
+00:26:29,650 --> 00:26:41,210
+فصارت الجملة ونفيها contradiction so .. so إيش؟
+
+235
+00:26:41,210 --> 00:26:46,490
+ال R يساوي
+
+236
+00:26:46,490 --> 00:26:56,610
+صفر وين الخلل في الإثبات؟ فيه سطر لازم نضيفه فيه
+
+237
+00:26:56,610 --> 00:27:04,750
+سطر في البداية نضيفه بيصير الحل سليم حاجة
+
+238
+00:27:04,750 --> 00:27:09,750
+هنا وأقول assume that
+
+239
+00:27:09,750 --> 00:27:17,750
+M أو N لا تقسم ال M هنا هنشيل هذه
+
+240
+00:27:23,100 --> 00:27:27,960
+لما نضيف N تقسم ال M معناه remainder مستحيل
+
+241
+00:27:27,960 --> 00:27:32,500
+يكون صفر واضح
+
+242
+00:27:32,500 --> 00:27:39,640
+يا عادي؟ واضح يا شباب؟ اللي ضفته؟
+
+243
+00:27:42,790 --> 00:27:48,270
+ليش فيه تناقض؟ طالع معايا ال N هو أصغر واحد بيحقق
+
+244
+00:27:48,270 --> 00:27:52,110
+العلاقة فأي واحد بيحقق العلاقة لازم يكون إشماله
+
+245
+00:27:52,110 --> 00:27:56,930
+أكبر منه ال R صار يحقق فصار ال R أكبر أو يساوي ال
+
+246
+00:27:56,930 --> 00:28:01,590
+N بس أنا أصلا بعرف أن ال R أصغر من ال N صار عندي
+
+247
+00:28:01,590 --> 00:28:02,090
+تناقض
+
+248
+00:28:14,570 --> 00:28:18,170
+كيف؟ وأنا لما شيلت الشرق .. لما ضفت أن ال N لا
+
+249
+00:28:18,170 --> 00:28:24,810
+يقسم ال M صار remainder ليه يساوي صفر هلجيت؟ لما
+
+250
+00:28:24,810 --> 00:28:28,570
+أنا أقول .. لما يصير تناقض يجب لازم يكون remainder
+
+251
+00:28:28,570 --> 00:28:31,430
+صفر والمحصلة اللي احنا بدنا إياها مش أنه قعد
+
+252
+00:28:31,430 --> 00:28:36,510
+بساوة صفر لأ إنّ الان تقسم الأم هذا المطلوب مش أنه
+
+253
+00:28:36,510 --> 00:28:37,730
+قعد بساوة صفر
+
+254
+00:28:42,020 --> 00:28:49,160
+طيب سؤال سبعة وأربعين خمسة وأربعين مطلوب مطلوب
+
+255
+00:28:49,160 --> 00:28:53,500
+خمسة وأربعين خمسة وأربعين حلناها سبعة وأربعين R
+
+256
+00:28:53,500 --> 00:28:59,320
+R* be the group of non zero real number under
+
+257
+00:28:59,320 --> 00:29:07,500
+multiplication R* يا شباب عبارة عن R معدوم Zero
+
+258
+00:29:07,500 --> 00:29:12,960
+والعملية عملية ضرب H عبارة عن كل X في R*) X تربيع
+
+259
+00:29:12,960 --> 00:29:20,020
+is rational يثبت أن H subgroup of R* H عبارة عن كل
+
+260
+00:29:20,020 --> 00:29:27,520
+X في R*) X تربيع ينتمي لـ Q المطلوب إثبات أن H 
+
+261
+00:29:27,520 --> 00:29:36,050
+subgroup من R*) عارف إنّ السؤال هذا حلنا واحد زيه
+
+262
+00:29:36,050 --> 00:29:42,970
+مخضر الماضية لما قلنا عندي abelian group وهاد ال
+
+263
+00:29:42,970 --> 00:29:48,650
+R*) مع ضرب abelian فكل الـ Xات اللي بيحقّق له إنّ X
+
+264
+00:29:48,650 --> 00:29:54,630
+أس N بساوي الـ identity بيعملوا له سبق الـ group هذا
+
+265
+00:29:54,630 --> 00:29:59,750
+السؤال شبيه فيه بس ما قالش إنّ x تربيع بيساوي الـ
+
+266
+00:29:59,750 --> 00:30:03,330
+identity لأ هان بقول إنّ x تربيع عبارة عن إيش
+
+267
+00:30:03,330 --> 00:30:09,550
+rational number أول شيء الـ
+
+268
+00:30:09,550 --> 00:30:18,170
+H لا يساوي فيه since واحد ينتمي لـ H now if
+
+269
+00:30:22,520 --> 00:30:32,320
+A وB ينتمي للـ H A تربيع ينتمي للـ Q وB تربيع ينتمي
+
+270
+00:30:32,320 --> 00:30:44,440
+للـ Q طيب ال A P inverse تربيع عبارة عن إيش عن A على
+
+271
+00:30:44,440 --> 00:30:48,740
+B لكل تربيع ليش أنا عملت A على B
+
+272
+00:30:51,710 --> 00:30:55,510
+لأنّ أنا بشتغل مع العداد الحقيقية فالـ inverse لضرب
+
+273
+00:30:55,510 --> 00:31:04,470
+ماله تواحد على حسين على a تربيع على b تربيع وهذا
+
+274
+00:31:04,470 --> 00:31:10,050
+ينتمي لـ الـ Q ليش ينتمي لـ الـ Q عدد نسبي على عدد
+
+275
+00:31:10,050 --> 00:31:15,610
+نسبي عدد نسبي لأنّه أصلاً عملية القسمة أو عملية
+
+276
+00:31:15,610 --> 00:31:17,630
+الضرب مغلقة في الـ Q
+
+277
+00:31:31,690 --> 00:31:37,870
+هل ممكن نبدّل الاثنين بأي عدد صحيح
+
+278
+00:31:37,870 --> 00:31:38,590
+آخر؟
+
+279
+00:31:44,660 --> 00:31:49,620
+شيل اثنين واحط أي رقم أو أي قيمة بالعداد الصحيح
+
+280
+00:31:49,620 --> 00:31:55,680
+الموجبة تكييب هتظل تكييب قص 17 هتظل قص 17 وهنا
+
+281
+00:31:55,680 --> 00:32:10,600
+ما فيش مشكلة بقدر أستبدل اثنين بعدد نسبي ليش بقدرش
+
+282
+00:32:10,600 --> 00:32:18,980
+أتعامل مع السؤال هنا بقدر yes we can replace
+
+283
+00:32:18,980 --> 00:32:29,540
+اثنين by any natural number بقدر أبدّل اثنين بأي
+
+284
+00:32:29,540 --> 00:32:37,680
+عدد طبيعي سبعة
+
+285
+00:32:37,680 --> 00:32:39,020
+وأربعين اثنين وخمسين
+
+286
+00:32:49,060 --> 00:32:58,000
+طب 52 ما أعتقد أنه فيه مشكلة يعني 52 و53 سهلين سي
+
+287
+00:32:58,000 --> 00:33:05,840
+سؤال 47 حلين
+
+288
+00:33:05,840 --> 00:33:10,060
+أكتر من سؤال على حتى المحاضرة الماضية حلت تقريباً
+
+289
+00:33:10,060 --> 00:33:15,500
+ثلت أسئلة على موضوع subgroup 56 و57
+
+290
+00:33:18,570 --> 00:33:25,290
+تعال نشوفهم 56 بيقول A زي P I حيث ال A P Positive
+
+291
+00:33:25,290 --> 00:33:35,270
+هل
+
+292
+00:33:35,270 --> 00:33:41,130
+هذا هل الـ H سابقه مع الـ C والجامع
+
+293
+00:33:47,210 --> 00:33:52,410
+هل الـ arch subgroup من الـ C عشان أميزه أحط له شرطا
+
+294
+00:33:52,410 --> 00:33:57,190
+مع الجامعة إيش رأيك؟
+
+295
+00:33:57,190 --> 00:34:06,250
+آه إيش رأيك؟
+
+296
+00:34:06,250 --> 00:34:16,540
+هل هذه subgroup من الـ C مع الجامعة؟ آه فاكرها أول
+
+297
+00:34:16,540 --> 00:34:22,120
+حاجة الـ identity موجود identity تبع الجامعة موجود
+
+298
+00:34:22,120 --> 00:34:27,740
+هيك
+
+299
+00:34:27,740 --> 00:34:33,740
+بقى مغلقة على وجود الـ identity العملية associative
+
+300
+00:34:33,740 --> 00:34:41,840
+ولا لأ associative طب الـ inverse موجود
+
+301
+00:34:42,610 --> 00:34:48,630
+لو الـ A P موجب يعني A زائد P I في الـ H سالب A سالب
+
+302
+00:34:48,630 --> 00:34:52,530
+P I برضه في الـ H لإنه A P موجب فسالب A في سالب P
+
+303
+00:34:52,530 --> 00:34:57,910
+برضه موجب يجب أولي الخلل اللي ممكن يكون معانا في
+
+304
+00:34:57,910 --> 00:35:03,450
+إنّ العملية تكون مغلقة أصلاً هلاحظ الشغل التالي سالب
+
+305
+00:35:03,450 --> 00:35:11,950
+واحد أو واحد زائد اثنين I تامين الـ H تمام؟
+
+306
+00:35:14,440 --> 00:35:24,880
+وسالب ثلاثة ناقص I برضه في الاتش خلي هذا A وهذا B
+
+307
+00:35:24,880 --> 00:35:31,840
+طيب A زائد الـ B عبارة عن إيش سالب اثنين زائد الـ I
+
+308
+00:35:31,840 --> 00:35:37,580
+هذا مش في الاتش وبالتالي
+
+309
+00:35:37,580 --> 00:35:42,860
+العملية مش مغلقة هنا ما فيش إغلاق للعملية جوا الاتش
+
+310
+00:35:42,860 --> 00:35:49,630
+وبالتالي H not subgroup
+
+311
+00:35:49,630 --> 00:36:02,810
+of C والجمهور مش subgroup لأنّه
+
+312
+00:36:02,810 --> 00:36:06,850
+لو أنت ضربت الـ F أنا هالخطأ إنّ أخدت A وB حط ليها
+
+313
+00:36:06,850 --> 00:36:13,010
+X وY تعالوا
+
+314
+00:36:13,010 --> 00:36:18,400
+اضرب هدف يعني سالب 2 في 1 سالب اثنين هل السالب اثنين
+
+315
+00:36:18,400 --> 00:36:24,380
+موجب أو أكبر أو يساوي الصفر سبعة وخمسين على نفس
+
+316
+00:36:24,380 --> 00:36:31,420
+المنطقة برضه بشترط على الـ C مع الـ multiplication
+
+317
+00:36:31,420 --> 00:36:39,720
+طبعاً
+
+318
+00:36:39,720 --> 00:36:45,270
+هذه المجموعة شباب عبارة عن إيش؟ A زي a+bi حيث
+
+319
+00:36:45,270 --> 00:36:49,350
+a تربيع +b تربيع بيساوي واحد هذه بيسميها الـ
+
+320
+00:36:49,350 --> 00:36:54,670
+unit circle دائرة الوحدة تمّ عظمها أخذ complex هل
+
+321
+00:36:54,670 --> 00:36:59,930
+هذه sub group مع طبعاً احنا هيك أجبنا على الجزء
+
+322
+00:36:59,930 --> 00:37:02,410
+الثاني من السؤال describe the element of H
+
+323
+00:37:02,410 --> 00:37:10,470
+geometrically دائرة الوحدة الـ unit circle
+
+324
+00:37:10,470 --> 00:37:21,540
+هل هذه sub group أنا بتعامل مع مين؟ مع الضرب أول شيء
+
+325
+00:37:21,540 --> 00:37:29,800
+المحايد هنا طبعاً C* عبارة عن C مع ده مين؟ الـ
+
+326
+00:37:29,800 --> 00:37:37,060
+Zero الـ identity موجود مين الـ identity هنا؟ الـ A
+
+327
+00:37:37,060 --> 00:37:41,000
+بتساوي واحد زائد Zero I بتساوي واحد هذا ينتمي
+
+328
+00:37:41,000 --> 00:37:47,220
+للـ H يقبل أش لا يساوي فيه اثنين الـ identity موجود ولا
+
+329
+00:37:47,220 --> 00:37:55,340
+يساوي فيه associative موجود طبعاً لأنّه جزء من الكبير
+
+330
+00:37:55,340 --> 00:38:07,420
+أش فيه ضالة شروط الـ inverse ومين كمان الـ inverse و
+
+331
+00:38:07,420 --> 00:38:12,970
+الـ close الـ inverse موجود يا شباب لو الـ A زي الـ P I
+
+332
+00:38:12,970 --> 00:38:17,950
+ينتمي للـ H فـ A تربيع زي الـ P تربيع بساوي واحد طب الـ
+
+333
+00:38:17,950 --> 00:38:22,610
+A زي الـ P I inverse هذا عبارة عن A ناقص الـ P I
+
+334
+00:38:22,610 --> 00:38:29,110
+على A تربيع زي الـ P تربيع اللي هو عبارة عن A على A
+
+335
+00:38:29,110 --> 00:38:33,830
+تربيع زي الـ P تربيع ناقص الـ P I على A تربيع زي الـ P
+
+336
+00:38:33,830 --> 00:38:37,450
+تربيع بس هي أنا تحت الجزر
+
+337
+00:38:45,640 --> 00:38:54,960
+شوية بس ما فيش جزايا طب
+
+338
+00:38:54,960 --> 00:38:59,480
+ما تنساش إنّ هذا إيش بيساوي واحد يكبر هذا عبارة عن
+
+339
+00:38:59,480 --> 00:39:04,300
+الـ a ناقص bi والـ a تربيع زائد سالب الـ b تربيع
+
+340
+00:39:04,300 --> 00:39:08,340
+بيساوي a تربيع زائد الـ b تربيع بيساوي واحد يكبر a
+
+341
+00:39:08,340 --> 00:39:16,930
+زائد الـ bi inverse ينتمي للـ h أول تلات شروط تحققوا
+
+342
+00:39:16,930 --> 00:39:21,490
+طب أنا هنا مش راضي أستعمل ليه الـ notation تبعت الـ
+
+343
+00:39:21,490 --> 00:39:25,290
+C أو تبعت الـ complex analysis إنّ بعضهم هيقول أنا
+
+344
+00:39:25,290 --> 00:39:31,610
+ما أخذتش تحليل مُركّب أربعة لو أنا قلت الـ X بيساوي
+
+345
+00:39:31,610 --> 00:39:36,450
+A زائد الـ P I والـ Y بيساوي الـ C زائد الـ D I هدول
+
+346
+00:39:36,450 --> 00:39:43,020
+ينتموا للـ H معناته A تربيع زائد الـ B تربيع بدي يساوي
+
+347
+00:39:43,020 --> 00:39:49,360
+واحد بدي يساوي C تربيع زائد الـ D تربيع لو أنا جيت
+
+348
+00:39:49,360 --> 00:39:58,720
+أشتغل على XY XY عبارة عن إيش هذا
+
+349
+00:39:58,720 --> 00:40:10,380
+عبارة عن AC ناقص BD زائد DI في C زائد
+
+350
+00:40:11,860 --> 00:40:18,240
+تخربطوني هيك يا شباب A في D زائد
+
+351
+00:40:18,240 --> 00:40:23,440
+BC بي في CI تعال نشوف هذا تربيع زائد هذا تربيع
+
+352
+00:40:23,440 --> 00:40:30,580
+إيش بيساوي AC ناقص الـ BD تربيع زائد الـ AD زائد الـ
+
+353
+00:40:30,580 --> 00:40:36,000
+BC تربيع إيش بيساوي A تربيع C تربيع ناقص اثنين AC
+
+354
+00:40:36,000 --> 00:40:45,060
+BD زائد الـ B تربيع D تربيع زائد A تربيع D تربيع زائد
+
+355
+00:40:45,060 --> 00:40:51,340
+اثنين ACPD زائد B تربيع C تربيع هذا مع هذا بيطير
+
+356
+00:40:51,340 --> 00:40:58,580
+بيظل عندي A تربيع في C تربيع زائد الـ D تربيع زائد B
+
+357
+00:40:58,580 --> 00:41:04,520
+تربيع في C تربيع زائد الـ D تربيع هذا واحد وهذا واحد
+
+358
+00:41:04,520 --> 00:41:10,020
+هيصيب معايا A تربيع زائد الـ B تربيع مش بيساوي هذا
+
+359
+00:41:10,020 --> 00:41:17,720
+معناته إنّ XY جوا الـ H Identity موجود Associative
+
+360
+00:41:17,720 --> 00:41:25,480
+متحقق مغلقة على الـ inverse مغلقة على العملية نفسها
+
+361
+00:41:25,480 --> 00:41:29,840
+يكبر H subgroup من C
+
+362
+00:41:35,920 --> 00:41:40,960
+أخذت complex analysis أخذت العدد المركب في
+
+363
+00:41:40,960 --> 00:41:45,280
+الثانوية ولا لأ كيف أجيب معكوس لعدد المركب بضغط في
+
+364
+00:41:45,280 --> 00:41:52,900
+المرافق فوق وتحت هو الـ A زائد الـ I B inverse هذا
+
+365
+00:41:52,900 --> 00:41:59,500
+عبارة عن واحد على A زائد الـ I B واحد ناقص الـ .. و
+
+366
+00:41:59,500 --> 00:42:03,120
+بكمل قاضي
+
+367
+00:42:05,490 --> 00:42:15,010
+إيش بيظل عندي يا شباب؟ تسعة وخمسين جي
+
+368
+00:42:15,010 --> 00:42:19,910
+قلت
+
+369
+00:42:19,910 --> 00:42:33,990
+وآه؟ هذا سؤال فيه خربشة كثير طيب
+
+370
+00:42:35,180 --> 00:42:42,220
+تسعة وخمسين اختار سؤال مثلاً إيه بدك الـ center أو
+
+371
+00:42:42,220 --> 00:42:50,800
+الـ centralizer لـ 1110 حسب التعريف هذا عبارة عن كل
+
+372
+00:42:50,800 --> 00:43:03,430
+الـ A في الـ GL to R اللي A 1110 بيساوي 1110 في A لو
+
+373
+00:43:03,430 --> 00:43:11,450
+أنا أخذت الـ a عبارة عن a,b,c,d وجيت اشتغلت a,b,c,d
+
+374
+00:43:11,450 --> 00:43:25,150
+1110 هذا المفروض يساوي 1110 في a,b,c,d اضرب a زائد
+
+375
+00:43:25,150 --> 00:43:25,570
+الـ b
+
+376
+00:43:29,260 --> 00:43:40,080
+C زائد D C  هذا بـ D يساوي A زائد C واحد
+
+377
+00:43:40,080 --> 00:43:45,400
+واحد في B B زائد D A
+
+378
+00:43:45,400 --> 00:43:52,960
+B A
+
+379
+00:43:52,960 --> 00:43:57,580
+زائد C B زائد D A وB اعمل مساواة
+
+380
+00:44:24,230 --> 00:44:27,690
+هتستفيد من هذه و هذه شغلة واحدة أن ال B بيساوي ال
+
+381
+00:44:27,690 --> 00:44:27,830
+C
+
+382
+00:44:33,170 --> 00:44:38,950
+طب وهذه وهذه نفس
+
+383
+00:44:38,950 --> 00:44:44,230
+الفكرة لما تساوي a بساوي b زائد دي و a بساوي c زائد 
+
+384
+00:44:44,230 --> 00:44:49,150
+دي طير دي من الطرفين مش هيظل عندك فقط المعلومة
+
+385
+00:44:49,150 --> 00:44:53,110
+الوحيدة اللي أنت بتقدر تستفيدها هيش أن ال b و ال
+
+386
+00:44:53,110 --> 00:45:03,870
+c متساوين وبالتالي ال centralizer لواحد واحد واحد
+
+387
+00:45:03,870 --> 00:45:16,710
+صفر عبارة عن كل ال a,b,b,d حيث a,b,d ينتموا لمين
+
+388
+00:45:16,710 --> 00:45:21,750
+هي كل
+
+389
+00:45:21,750 --> 00:45:29,290
+المصفوفات اللي ال b و ال c فيهم متساوية طبعا الفرع
+
+390
+00:45:29,290 --> 00:45:37,510
+b like الفرع a هيكون أسهل شوية طيب
+
+391
+00:45:37,510 --> 00:45:44,650
+الفرضية
+
+392
+00:45:44,650 --> 00:45:52,270
+ال center تبع JL2R
+
+393
+00:45:52,270 --> 00:45:59,230
+مين
+
+394
+00:45:59,230 --> 00:46:00,170
+بيقدر يعرفهم؟
+
+395
+00:46:03,410 --> 00:46:15,970
+من بيقدر يعرفه بس بس
+
+396
+00:46:15,970 --> 00:46:20,750
+بعد
+
+397
+00:46:20,750 --> 00:46:28,590
+شوية حسابات هنكتشف أن هذا عبارة عن كل a 00a حيث a
+
+398
+00:46:28,590 --> 00:46:29,030
+في r
+
+399
+00:46:32,520 --> 00:46:39,880
+هذا التوقعي بحاول المرة الجاية أكدلك إياه أعتقد
+
+400
+00:46:39,880 --> 00:46:43,380
+أن هذا كلام صحيح اللي لو كان في أمثلة أخرى خليني
+
+401
+00:46:43,380 --> 00:46:47,580
+أنا برضه أنه ييجي على بالي شغلة معينة ممكن تتحقق
+
+402
+00:46:47,580 --> 00:46:57,860
+كلام اللي بنحكي واضح؟ هذا اللي التأكد بأكيده
+
+403
+00:46:57,860 --> 00:47:02,630
+المرة الجاية لأنه ما يظلش وجهة عندنا نناقش تفاصيلها 
+
+404
+00:47:02,630 --> 00:47:07,590
+طب بنعطيكوا العافية محاضرة جاية إن شاء الله بنفوت
+
+405
+00:47:07,590 --> 00:47:12,890
+في الوحدة الرابعة بنتكلم فيها عن ال cyclic group و
+
+406
+00:47:12,890 --> 00:47:16,890
+بنتكلم فيها عن الهيكلية الداخلية لكل ال cyclic
+
+407
+00:47:16,890 --> 00:47:20,450
+group و التفاصيل الخاصة في هذا الموضوع بنعطيكوا
+
+408
+00:47:20,450 --> 00:47:21,850
+العافية السلام عليكم
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..93846c71468f003321a40dc25839ab8f039ff617
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/seOBSENCxlk_postprocess.srt
@@ -0,0 +1,1632 @@
+1
+00:00:21,750 --> 00:00:23,890
+بسم الله الرحمن الرحيم ان شاء الله يا شباب اليوم
+
+2
+00:00:23,890 --> 00:00:27,910
+هنكمل اللي بدناها في المحاضرة الماضية من مناقشة
+
+3
+00:00:27,910 --> 00:00:31,610
+اللي هو الوحدة التالتة المتعلقة بال subgroup طبعا
+
+4
+00:00:31,610 --> 00:00:35,230
+لذا وقفنا المرة الماضية عن سؤال تلاتة و تلاتين
+
+5
+00:00:35,230 --> 00:00:40,030
+كتبناه و ما حلناه نرجع نكتب السؤال السؤال بيقول
+
+6
+00:00:40,030 --> 00:00:46,710
+التاليإن لو كان عندي group وفيها two elements a وb
+
+7
+00:00:46,710 --> 00:00:51,170
+ال order ل ال a بدو يساوي اربع ال order ل ال b بدو
+
+8
+00:00:51,170 --> 00:00:55,490
+يساوي اتنين وعندي علاقة بتربط ال a و ال b بتقول ان
+
+9
+00:00:55,490 --> 00:01:02,450
+ال a تكايب بي بتساوي p في a المطلوب في السؤال find
+
+10
+00:01:02,450 --> 00:01:05,390
+order ال a,b
+
+11
+00:01:08,360 --> 00:01:11,440
+الطريقة اللى احنا بنتبعها لحساب ال order تبع أي
+
+12
+00:01:11,440 --> 00:01:16,500
+أنصر هو ان انا اشتغل على الانصر هذا و اعطيه powers
+
+13
+00:01:16,500 --> 00:01:21,480
+تنين تلاتة اربعة خمسة لما اصل لأقل او لأول عدد
+
+14
+00:01:21,480 --> 00:01:26,780
+صحيح موجب بيعطيني ال identity في البداية انا بدي
+
+15
+00:01:26,780 --> 00:01:32,420
+اثبت ان ال order لا يساوي واحد ا بي لا يساوي ال
+
+16
+00:01:32,420 --> 00:01:36,360
+identity claim هنحطها ك claim
+
+17
+00:01:41,470 --> 00:01:48,170
+تعالوا نثبتها Assume على النقيض that ان a,b بديوا
+
+18
+00:01:48,170 --> 00:01:54,850
+يساوي ال identity هذا معناته ان a بديت ساوي b
+
+19
+00:01:54,850 --> 00:02:00,110
+inverse وبالتالي order ال a بديه يساوي order ال b
+
+20
+00:02:00,110 --> 00:02:04,770
+inverse طبعا order ال b inverse هو ايش order ال b
+
+21
+00:02:04,770 --> 00:02:10,410
+وبالتالي الأربعة بديه يساوي اتنين وهذا ايش تنقدرة
+
+22
+00:02:11,450 --> 00:02:15,750
+صار عندى تناقض وبالتالي so ال a b لا يساوي ال
+
+23
+00:02:15,750 --> 00:02:21,550
+identity وبالتالي ال order لا يساوي واحد حد
+
+24
+00:02:21,550 --> 00:02:29,050
+هيسألني ليش انا كتبت هذا الشغل لان انا لما اكمل حل
+
+25
+00:02:29,050 --> 00:02:33,200
+الصورة اللى جيت هنكتشف ان ال order هيساوي اتنينلأن
+
+26
+00:02:33,200 --> 00:02:38,640
+AP تربية هيعطينا ال identity فالسؤال ان مادام ال
+
+27
+00:02:38,640 --> 00:02:42,440
+AP تربية هيعطينا ال identity فال order هيكون يا
+
+28
+00:02:42,440 --> 00:02:45,980
+اتنين يا واحد انا بأنفي هيكد ان يكون ال order
+
+29
+00:02:45,980 --> 00:02:54,820
+بيساوي واحد now لو قلنا AP الكل تربية عبارة عن ايش
+
+30
+00:02:54,820 --> 00:03:03,200
+عبارة عن AP AP زي ما احنا عارفين الدربأو العملية
+
+31
+00:03:03,200 --> 00:03:13,220
+بتحقيق خاصية التجميع هذا هي ساوي a في b a في b حسب
+
+32
+00:03:13,220 --> 00:03:19,080
+الخاصية لان بي اياش بتساويA في A تكيب في B في B
+
+33
+00:03:19,080 --> 00:03:24,700
+يعني A قص 4 في B تربيع ال identity في ال identity
+
+34
+00:03:24,700 --> 00:03:31,100
+بدي ساوي ال identity هذا معناته ان order ال AB أقل
+
+35
+00:03:31,100 --> 00:03:44,160
+او يساوي اتنين but order ال AB لا يساوي واحد واضح
+
+36
+00:03:44,160 --> 00:03:49,020
+هذا يا شبابأنا نفقت إن ال order يكون واحد و قلت إن
+
+37
+00:03:49,020 --> 00:03:52,360
+ال order هيبدأ من التنين و ينزل فيا التنين يا
+
+38
+00:03:52,360 --> 00:03:57,400
+الواحد و الواحد لأ هيظل عند مين؟ التنين لأ لأ مش
+
+39
+00:03:57,400 --> 00:04:02,900
+تجريب انت لما تيجي تتعامل مع ال order التعريف تبعه
+
+40
+00:04:02,900 --> 00:04:11,850
+أصغر عددطبيعي لما بترفع العنصر إله بيعطيك ال
+
+41
+00:04:11,850 --> 00:04:15,970
+identity انا بدأت بالواحد مانفعش الاتنين زبط
+
+42
+00:04:15,970 --> 00:04:20,210
+بالتجريب هو الأغلب بالتجريب إلا لو كان في عندك
+
+43
+00:04:20,210 --> 00:04:33,690
+شغلات مساعدة أخرى اشفهم
+
+44
+00:04:35,740 --> 00:04:40,000
+هي AB طيب
+
+45
+00:04:40,000 --> 00:04:52,180
+وحطه
+
+46
+00:04:52,180 --> 00:04:56,740
+بهذا الشكل وشوف عشان اللي انا عملتهلأ بدل التحذير
+
+47
+00:04:56,740 --> 00:04:59,340
+يعني انا مش .. انا ماعملتش .. ماعملتش تحذير انت
+
+48
+00:04:59,340 --> 00:05:03,240
+هتصل في النهاية ان ايه ال culture بيبقى بيساوي ال
+
+49
+00:05:03,240 --> 00:05:06,580
+identity تمام؟ يبقى ال order يا اتنين يا واحد
+
+50
+00:05:06,580 --> 00:05:09,500
+هتيجي تن في الواحد وبالتالي انت هو كأنك بدأت من
+
+51
+00:05:09,500 --> 00:05:13,800
+هان بعدين حلت هذا هي هي بدل التحذير اه في النهاية
+
+52
+00:05:13,800 --> 00:05:17,840
+ده برضه تحذير اش ضمنك انك هتصل لهذا نفس الضمان
+
+53
+00:05:17,840 --> 00:05:19,500
+اللي موجود هنا هو الضمان اللي موجود هنا
+
+54
+00:05:24,100 --> 00:05:29,300
+طيب ايش فيه سؤال بعده سؤال
+
+55
+00:05:29,300 --> 00:05:35,520
+اربعة و تلاتين suppose
+
+56
+00:05:35,520 --> 00:05:39,220
+a and p are group elements such that order a بدي
+
+57
+00:05:39,220 --> 00:05:42,240
+ساوي اتنين ال b لا يساوي ال identity هو a p a بدي
+
+58
+00:05:42,240 --> 00:05:48,200
+ساوي p تربيه find order ال b
+
+59
+00:05:52,030 --> 00:05:57,350
+ال order لل A بدي يساوي تنين ال B لا يساوي ال
+
+60
+00:05:57,350 --> 00:06:00,390
+identity طبعا هو رايحني من الجثة اللي انا عملتها
+
+61
+00:06:00,390 --> 00:06:05,910
+ال B لا يساوي ال identity يعني order ال B لا يساوي
+
+62
+00:06:05,910 --> 00:06:13,430
+ال واحد و عند ال علاقة التالية ان A PA بدي تساوي A
+
+63
+00:06:13,430 --> 00:06:18,430
+تربيع مين عنده أفكار لحل السؤال ده يا شباب مين
+
+64
+00:06:18,430 --> 00:06:19,110
+عنده أفكار
+
+65
+00:06:22,520 --> 00:06:28,460
+هنفكر طبعا بنفس الاسطوب اللي هان أفيدونا
+
+66
+00:06:28,460 --> 00:06:33,340
+أفادكم الله عشرة
+
+67
+00:06:33,340 --> 00:06:42,760
+أكتر طيب
+
+68
+00:06:42,760 --> 00:06:46,700
+A
+
+69
+00:06:46,700 --> 00:06:51,160
+تربية PA بيساوي طيب بعد ايه
+
+70
+00:06:54,360 --> 00:07:00,360
+تعالى نخربش تعمل ا بي ا بدي يساوي بي تربية هتضرب
+
+71
+00:07:00,360 --> 00:07:05,500
+الطرفين في a هصير a تربية بي ا بدي يساوي ا بي
+
+72
+00:07:05,500 --> 00:07:07,800
+تربية ال a تربية اللى على الناحية هذه بدها ايه
+
+73
+00:07:07,800 --> 00:07:19,680
+اتوح بدي صار عندى بي ا ا بي تربية طيب اش
+
+74
+00:07:19,680 --> 00:07:20,600
+ممكن يسي بعد هيك
+
+75
+00:07:24,000 --> 00:07:27,620
+تجرب تضغط على الشاشة التانية هصير بي ايه تربية
+
+76
+00:07:27,620 --> 00:07:33,780
+بتساوي ايه بي تربية ايه اللي هي بي بتساوي ايه بي
+
+77
+00:07:33,780 --> 00:07:45,740
+تربية ايه طيب اه كمان فكرة بس فكرة واحدة ضايلة وين
+
+78
+00:07:45,740 --> 00:07:54,770
+طب بدك تسفيد لأ هذه عبارة عن a b b a صح ولا لأاللي
+
+79
+00:07:54,770 --> 00:08:03,450
+عبارة عن a b identity b a اللي عبارة عن a b a
+
+80
+00:08:03,450 --> 00:08:09,350
+تربية بي
+
+81
+00:08:09,350 --> 00:08:15,830
+إيه هذي عبارة عن a b a a b a اللي a b a لكل تربية
+
+82
+00:08:15,830 --> 00:08:24,980
+اللي عبارة عن بي تربية تربية يعني بي قص أربعةيعني
+
+83
+00:08:24,980 --> 00:08:30,800
+انت وصلت ان P بيساو P وص 4 ال P لا يساو ال
+
+84
+00:08:30,800 --> 00:08:35,940
+identity بال cancellation law P تكئيب بيساو ال
+
+85
+00:08:35,940 --> 00:08:44,440
+identity وبالتالي هيصير ال order ل P يا
+
+86
+00:08:44,440 --> 00:08:52,790
+واحد يا اتنين يا تلاتة هذا مرفوض P مظلتانين في
+
+87
+00:08:52,790 --> 00:09:04,130
+التانين كنت هاي فكرة السؤال تعالى نغطبها ال
+
+88
+00:09:04,130 --> 00:09:14,050
+B تربية تربية انا هبدأ بالعكس عبارة عن A B A الكل
+
+89
+00:09:14,050 --> 00:09:29,640
+تربية عبارة عن ايش عن A B AA PA A PA الـ A إيش
+
+90
+00:09:29,640 --> 00:09:33,100
+بتساوي؟
+
+91
+00:09:33,100 --> 00:09:42,640
+إيش بتساوي؟ A P A تربيع PA يعني A P Identity PA
+
+92
+00:09:42,640 --> 00:09:51,500
+يعني A B تربيع A إيش ال B تربيع بتساوي؟هذا هتساوي
+
+93
+00:09:51,500 --> 00:09:58,180
+a في a p a a a تربية بي اي تربية بدي يساوي بي
+
+94
+00:09:58,180 --> 00:10:04,340
+المحصلة ان بي قص اربعة بدي تساوي بي وبالتالي بي تك
+
+95
+00:10:04,340 --> 00:10:10,520
+ايه بدي تساوي ال identity معناه to order ال بي يا
+
+96
+00:10:10,520 --> 00:10:19,100
+واحد يا اتنين يا تلاتة but order ال بي لا يساوي
+
+97
+00:10:19,100 --> 00:10:26,440
+واحدليش؟ لأن بي لا يساوي ال identity بيضايق قدامي
+
+98
+00:10:26,440 --> 00:10:35,040
+خيارين يا التنين يا التلاتة كيف ده ننفيه؟
+
+99
+00:10:35,040 --> 00:10:42,580
+if order ال بي بدت ساوي اتنين معناته بي تربيع ال
+
+100
+00:10:42,580 --> 00:10:47,960
+identity بيساوي بي تربيع اللي واش بيساوي بيساوي
+
+101
+00:10:47,960 --> 00:11:01,970
+ايه؟P A يعني E بدت ساوي A PA وبالتالي A تربيع
+
+102
+00:11:01,970 --> 00:11:07,270
+بدت ساوي A PA مش ال identity بيساوي A تربيع يعني A
+
+103
+00:11:07,270 --> 00:11:13,110
+في A بدت ساوي A PA المحصلة بعد ما تعمل
+
+104
+00:11:13,110 --> 00:11:19,410
+cancellation ال identity بدت ساوي P وهذا إيشتناقض
+
+105
+00:11:19,410 --> 00:11:24,490
+النتيجة order ال B لا يساوي اتنين المحصلة ان order
+
+106
+00:11:24,490 --> 00:11:36,010
+ال B ايش بتساوي تساوي تلاتة واضح؟ واضح؟
+
+107
+00:11:36,010 --> 00:11:39,110
+مين عنده اي شك او اي نقطة غير مفهومة؟
+
+108
+00:11:53,980 --> 00:11:59,260
+مش ال B تربيه بس هو APA شين ال B تربيه وحط ال APA
+
+109
+00:11:59,260 --> 00:12:06,980
+طيب
+
+110
+00:12:06,980 --> 00:12:10,460
+بالنسبة للسؤال تمانية و تلاتين انا هسيبه عليك يعني
+
+111
+00:12:10,460 --> 00:12:15,480
+هو هتحلوا بالسماء لل induction تمانية
+
+112
+00:12:15,480 --> 00:12:22,290
+و تلاتينمطلوب تثبت العلاقة هذه في SL2R ان cos θ
+
+113
+00:12:22,290 --> 00:12:28,850
+نقص sin θ sin θ cos θ أس N بيساوي cos Nθ سالب sin
+
+114
+00:12:28,850 --> 00:12:34,710
+Nθ sin Nθ cos Nθ بيستعمل ال induction بإمكانك
+
+115
+00:12:34,710 --> 00:12:39,290
+تثبته أثبت صحتها لما N بيساوي 2 بعدين افترض صحتها
+
+116
+00:12:39,290 --> 00:12:44,150
+لما N بيساوي K و أثبت صحتها بعدين لما N بيساوي K
+
+117
+00:12:44,150 --> 00:12:45,870
+زاد ال 1 using
+
+118
+00:12:47,910 --> 00:12:53,750
+mathematical induction فضل
+
+119
+00:12:53,750 --> 00:13:02,670
+الان على الطبيعي positive integer هو ايش جالك
+
+120
+00:13:02,670 --> 00:13:10,330
+positive integer طبعا هل هذه المصفوفة لها inverse
+
+121
+00:13:13,260 --> 00:13:18,780
+Cos θ سلب sin θ لها inverse لأن المحدد تبعها واحد
+
+122
+00:13:18,780 --> 00:13:22,000
+فانت ممكن ترفع لأس سالب بس لما ترفع لأس سالب
+
+123
+00:13:22,000 --> 00:13:29,240
+هتتعامل مع مين مع معكس المصفوفة واضح 41
+
+124
+00:13:29,240 --> 00:13:36,900
+D4
+
+125
+00:13:36,900 --> 00:13:42,140
+has seven cyclic subgroups list them هذا سؤال سهل
+
+126
+00:13:45,960 --> 00:13:52,180
+generated by R0 generated by R90 هو نفس ال
+
+127
+00:13:52,180 --> 00:13:57,440
+generated by R270 ال generated by R180 ال
+
+128
+00:13:57,440 --> 00:14:02,300
+generated by H ال generated by V ال generated by D
+
+129
+00:14:02,300 --> 00:14:07,820
+ال generated by D شرطة هم ال seven واحد اتنين
+
+130
+00:14:07,820 --> 00:14:12,640
+تلاتة اربعة خمسة ستة سبعة seven cyclic subgroup
+
+131
+00:14:26,150 --> 00:14:34,330
+طيب سؤال تنين و أربعين تنين و أربعين like سؤال
+
+132
+00:14:34,330 --> 00:14:42,450
+واحد و أربعين اللي هو خمسة عشر مين فيها عناصر واحد
+
+133
+00:14:42,450 --> 00:14:49,810
+اتنين اربع سبعة تمانية احداشر و تلتاشر و اربعة عشر
+
+134
+00:14:49,810 --> 00:14:58,260
+اتناشر لاطيب سؤال اربع و اربعين suppose j is a
+
+135
+00:14:58,260 --> 00:15:01,820
+group that has exactly eight elements of order
+
+136
+00:15:01,820 --> 00:15:05,720
+تلاتة how many subgroups of order تلاتة does j has
+
+137
+00:15:05,720 --> 00:15:14,940
+او have هذا السؤال حلو فيه أفكار عند group j have
+
+138
+00:15:14,940 --> 00:15:19,060
+او has عشان نكون ماشيين صح
+
+139
+00:15:22,470 --> 00:15:30,030
+exactly تمان element x with order x بدي تساوي
+
+140
+00:15:30,030 --> 00:15:39,690
+تلاتة say من هما x واحد x اتنين x تلاتة x اربع x
+
+141
+00:15:39,690 --> 00:15:44,990
+خمسة x ستة x سبعة و x تمانية
+
+142
+00:15:47,730 --> 00:15:53,230
+وال order ل X I يكون ثلاثة لكل I أقل أو يسوى
+
+143
+00:15:53,230 --> 00:16:01,330
+تمانية بقول ليه how many H
+
+144
+00:16:01,330 --> 00:16:12,070
+subgroup من ال J with H cyclic and ال order ل H
+
+145
+00:16:12,070 --> 00:16:15,070
+يكون ثلاثة
+
+146
+00:16:18,850 --> 00:16:25,870
+أكام جروب من هدولة أو subgroup من الـ Cyclic واللي
+
+147
+00:16:25,870 --> 00:16:31,190
+الأرضة غيرهم تلاتة موجودين في ERG قدام هناخد نظرية
+
+148
+00:16:31,190 --> 00:16:37,810
+تربط في chapter 4 أو chapter 7 بتحللك الأشكالية
+
+149
+00:16:37,810 --> 00:16:42,270
+هذه أنه بتقدر تحسبهم مباشرة بدون ما تقعد يتحذر زي
+
+150
+00:16:42,270 --> 00:16:48,400
+ما هنعمل هال game الحلقة التالية let Hsubgroup من
+
+151
+00:16:48,400 --> 00:16:54,020
+الجيه ال order لل H بدي يساوي تلاتة and H is
+
+152
+00:16:54,020 --> 00:17:00,660
+cyclic عشان اعرف كم واحدة من هدولة ال subgroup
+
+153
+00:17:00,660 --> 00:17:04,460
+المطلوبات هاخد واحدة منهم و اتكلم عن الهيكلية
+
+154
+00:17:04,460 --> 00:17:09,280
+الداخلية تبعتها هذا معناته ان ال H generated by
+
+155
+00:17:09,280 --> 00:17:14,470
+some Aو ال a ينتمي لل جيه و ال order لل a يبدو
+
+156
+00:17:14,470 --> 00:17:21,250
+يساوي تلاتة هذا معناته ان ال h أكم انصر فيها في
+
+157
+00:17:21,250 --> 00:17:27,570
+البداية ال identity و ال a تربيع اللي هو عبارة عن
+
+158
+00:17:27,570 --> 00:17:35,810
+ال a inverse مش
+
+159
+00:17:35,810 --> 00:17:41,240
+هذه sub group مغلقة على ال inverse ولا لأالـ A
+
+160
+00:17:41,240 --> 00:17:49,500
+موجودة والـ E موجودة و since طبعا هذه تفسيرها لإن
+
+161
+00:17:49,500 --> 00:17:54,380
+ال order ال A بدي ساوي تلاتة معناته A تكاري بدي
+
+162
+00:17:54,380 --> 00:17:57,660
+ساوي ال identity معناته A تغبيه بدي ساوي ال A
+
+163
+00:17:57,660 --> 00:18:06,830
+inverse تمام؟ alsoA لا يساوي الـ A inverse since
+
+164
+00:18:06,830 --> 00:18:15,630
+ال order لـ A يساوي ثلاثة مدام
+
+165
+00:18:15,630 --> 00:18:23,810
+ال A و ال A inverse موجودين هذا معناته ال order ل
+
+166
+00:18:23,810 --> 00:18:32,870
+A يساوي ثلاثة يقبل A يساوي some xi صح
+
+167
+00:18:32,870 --> 00:18:33,310
+ولا لأ؟
+
+168
+00:18:36,060 --> 00:18:40,360
+ال order لل a inverse بدي يساوي تلاتة و ال a لا
+
+169
+00:18:40,360 --> 00:18:45,920
+يساوي ال a inverse يكبر ال a inverse بدت ساوي xj و
+
+170
+00:18:45,920 --> 00:18:51,940
+ال j لا يساوي i هداش
+
+171
+00:18:51,940 --> 00:18:57,060
+معناته كل واحدة من اللي زي h أكمل أنصر ال order له
+
+172
+00:18:57,060 --> 00:19:03,680
+تلاتة موجود فيها يكبر every such
+
+173
+00:19:04,710 --> 00:19:11,370
+H contains two
+
+174
+00:19:11,370 --> 00:19:21,290
+elements of order تلاتة مش contain two ممكن اقول
+
+175
+00:19:21,290 --> 00:19:24,010
+احنا كمان contain exactly
+
+176
+00:19:30,600 --> 00:19:33,540
+كل واحدة من الـ H اللي أنا بدور عليهم فيها تنتين
+
+177
+00:19:33,540 --> 00:19:38,760
+طب هم مجددش كلهم هم
+
+178
+00:19:38,760 --> 00:19:44,240
+تمانية هذا
+
+179
+00:19:44,240 --> 00:19:52,040
+معناته يوجد تمانية على اتنين بيساوي اربعة such H
+
+180
+00:19:52,040 --> 00:19:58,960
+كم واحدة موجودة؟ اربعة
+
+181
+00:20:02,170 --> 00:20:08,790
+الـ Identity اللي هو ضغط له تلاتة ماشي
+
+182
+00:20:08,790 --> 00:20:15,130
+طالع معايا هم هيكون أربع group من ال H X واحد و X
+
+183
+00:20:15,130 --> 00:20:19,890
+واحد inverse مع ال identityX2 و X2 inverse مع ال
+
+184
+00:20:19,890 --> 00:20:25,810
+identity X3 و X3 inverse مع ال identity و X4 و X4
+
+185
+00:20:25,810 --> 00:20:29,190
+inverse مع ال identity هتقولي هدول تمانية مما هي
+
+186
+00:20:29,190 --> 00:20:34,650
+أول أربعة و الأربعة التانية مين ال inverse تبعهم
+
+187
+00:20:34,650 --> 00:20:38,290
+44 45
+
+188
+00:20:49,630 --> 00:20:55,850
+طيب خمسة و اربعين بسؤال
+
+189
+00:20:55,850 --> 00:21:01,190
+خمسة و اربعين H sub group من ال J و ال J finite
+
+190
+00:21:01,190 --> 00:21:04,310
+suppose
+
+191
+00:21:04,310 --> 00:21:14,930
+J تنتمي لل J و N is the smallest positive
+
+192
+00:21:25,380 --> 00:21:31,220
+مطلوب اثبت ان انت تقسم order ج
+
+193
+00:21:39,260 --> 00:21:43,940
+شباب أول ما نيجي نحل أسئلة من نوعية ال .. خصوصا في
+
+194
+00:21:43,940 --> 00:21:48,260
+الجبر الحديث أهم حاجة لازم أعرفها و أقدر أتعامل
+
+195
+00:21:48,260 --> 00:21:52,260
+معاها هو تفسيري للمواضيات اللي عندي إذا ما أقدرت
+
+196
+00:21:52,260 --> 00:21:56,460
+أفهم إيش المواضيات اللي في السؤال تتوقعش مني أعرف
+
+197
+00:21:56,460 --> 00:22:01,680
+أجيب المطلوب تتوقعش مني أعرف أجيب المطلوب
+
+198
+00:22:04,400 --> 00:22:08,180
+السؤال المعطلية اللوانية السهلات الـ H sub group
+
+199
+00:22:08,180 --> 00:22:11,560
+والـ J finite عشان أقدر أتعامل مع ال orders يوجد
+
+200
+00:22:11,560 --> 00:22:20,200
+عنصر في الـ J لكل عنصر من هذا النوع أصغر عدد طبيعي
+
+201
+00:22:20,200 --> 00:22:25,800
+بيخلي الـ J أُس N جوا الـ H هو N مطلوب أثبت أنه
+
+202
+00:22:25,800 --> 00:22:31,020
+الـ N تقسم ال order للـ J طيب تعالوا نشوف
+
+203
+00:22:35,740 --> 00:22:43,180
+let order j اختار له رقم خمسة
+
+204
+00:22:43,180 --> 00:22:53,000
+لأ اخي يعني اعطيه رمز خد دي دي و لا M المطلوب من
+
+205
+00:22:53,000 --> 00:23:02,060
+السؤال let n بدي يسوي ال smallest positive
+
+206
+00:23:03,860 --> 00:23:13,080
+Integral with J أس N ينتمي للـH المطلوب أن N تقسم
+
+207
+00:23:13,080 --> 00:23:17,660
+الـM ارجع
+
+208
+00:23:17,660 --> 00:23:21,700
+شوية بالذاكرة لنظرية الأعداد اللي أخدها كيف أثبت
+
+209
+00:23:21,700 --> 00:23:28,290
+أن N بيقسم الـMاسلوبين يا بلاجي عدد صحيح بضربه في
+
+210
+00:23:28,290 --> 00:23:32,550
+ال N بيعطيين ال M يا بثبت انه remainder عند عملية
+
+211
+00:23:32,550 --> 00:23:40,810
+القسمة يساوي صفر using division algorithm
+
+212
+00:23:40,810 --> 00:23:51,190
+let M بده تساوي QN زاد ال R ال R أقل من ال N وأصغر
+
+213
+00:23:51,190 --> 00:23:53,250
+من ال 0
+
+214
+00:23:57,090 --> 00:24:02,390
+الان الـ J to M بدي ساوي ال identity ينتمي لل H
+
+215
+00:24:02,390 --> 00:24:09,430
+الـ J to N ينتمي لل H هيخليني اقول ان الـ J to N
+
+216
+00:24:09,430 --> 00:24:16,530
+أس كيو ينتمي لل H عشان الـ H صب جوب فهي مغلقة على
+
+217
+00:24:16,530 --> 00:24:19,850
+العملية هذا معناته J
+
+218
+00:24:23,090 --> 00:24:35,110
+QN ينتمي للـH مش بس هيك يا شباب J قصة QN inverse
+
+219
+00:24:35,110 --> 00:24:44,750
+ينتمي للـH J قصة QN inverse عبارة عن أيش؟ J قصة
+
+220
+00:24:44,750 --> 00:24:50,710
+سالب QN ينتمي للـH أعطي هذا واحد و أعطي هذا اتنين
+
+221
+00:24:53,340 --> 00:24:59,920
+من واحد و اتنين عنصرين في ال H و ال H sub group
+
+222
+00:24:59,920 --> 00:25:06,600
+حصل ضرب و مون هيكون في ال H حاسيب معايا J أس M في
+
+223
+00:25:06,600 --> 00:25:15,920
+J سالب Q N هو عنصر من وين عنصر من ال H عند الضرب
+
+224
+00:25:15,920 --> 00:25:23,770
+ايش بيصير في الأسستجمع الأسس هاسي معايا J أُس M
+
+225
+00:25:23,770 --> 00:25:35,510
+minus Q N ينتمي لمن؟ للـH اطلح J أُس R ينتمي لمن؟
+
+226
+00:25:35,510 --> 00:25:43,270
+للـH هذا معناته N أقل أو يسوى R by the definition
+
+227
+00:25:43,270 --> 00:25:51,740
+of Nتعريف ال N بيقوللي أن ال N هو أصغر عدد طبيعي
+
+228
+00:25:51,740 --> 00:25:57,880
+أو positive integer بيخللي ال J أُس N جوه ال R فأي
+
+229
+00:25:57,880 --> 00:26:03,080
+أُس تاني لل J .. جوه ال H أي أُس تاني لل J بيكون
+
+230
+00:26:03,080 --> 00:26:07,620
+جوه ال H لازم هذا الأُس يكون أشماله أكبر من ال N
+
+231
+00:26:07,620 --> 00:26:16,020
+but R أقل من ال N قارن لأ
+
+232
+00:26:17,470 --> 00:26:25,070
+هنا أقل وهنا أقل أو يساوي كيف دي يكون الار أقل من
+
+233
+00:26:25,070 --> 00:26:29,650
+الان؟ هذه نقيض هذه يعني النفي تبقى هذا هيعطيني هذا
+
+234
+00:26:29,650 --> 00:26:41,210
+فصارت الجملة و نفيها contradiction so .. so إيش؟
+
+235
+00:26:41,210 --> 00:26:46,490
+الار يساوي
+
+236
+00:26:46,490 --> 00:26:56,610
+ستةوين الخلل في الإثبات؟ فيه سطر لازم نضيفه فيه
+
+237
+00:26:56,610 --> 00:27:04,750
+سطر في البداية بنضيفه بصير الحل سليم حاجة
+
+238
+00:27:04,750 --> 00:27:09,750
+هنا و اقول assume that
+
+239
+00:27:09,750 --> 00:27:17,750
+M أو N لا تقسم ال M هنا هنشيل هذه
+
+240
+00:27:23,100 --> 00:27:27,960
+لما نضيف أنا تقسم ال M معناته remainder مستحيل
+
+241
+00:27:27,960 --> 00:27:32,500
+يكون صفر واضح
+
+242
+00:27:32,500 --> 00:27:39,640
+يا عادي؟ واضح يا شباب؟ اللي ضفته؟
+
+243
+00:27:42,790 --> 00:27:48,270
+ليش فيه تناقض؟ طالع معايا ال N هو أصغر واحد بيحقق
+
+244
+00:27:48,270 --> 00:27:52,110
+العلاقة فأي واحد بيحقق العلاقة لازم يكون إشماله
+
+245
+00:27:52,110 --> 00:27:56,930
+أكبر منه ال R صار يحقق فصار ال R أكبر أو يساوي ال
+
+246
+00:27:56,930 --> 00:28:01,590
+N بس أنا أصلا بعرف أن ال R أصغر من ال N صار عندي
+
+247
+00:28:01,590 --> 00:28:02,090
+تناقض
+
+248
+00:28:14,570 --> 00:28:18,170
+كيف؟ و انا لما شيلت الشرق .. لما ضفت ان الان لا
+
+249
+00:28:18,170 --> 00:28:24,810
+يقسم الام صار remainder ليه ساوة صفر هلجيت؟ لما
+
+250
+00:28:24,810 --> 00:28:28,570
+انا اقول .. لما يصير تناقض يجب لازم يكون remainder
+
+251
+00:28:28,570 --> 00:28:31,430
+صفر و المحاصلة اللي احنا بدنا إياها مش انه قعد
+
+252
+00:28:31,430 --> 00:28:36,510
+بساوة صفر لأ ان الان تقسم الام هذا المطلوب مش انه
+
+253
+00:28:36,510 --> 00:28:37,730
+قعد بساوة صفر
+
+254
+00:28:42,020 --> 00:28:49,160
+طيب سؤال سبعة و أربعين خمسة و أربعين مطلوب مطلوب
+
+255
+00:28:49,160 --> 00:28:53,500
+خمسة و أربعين خمسة و أربعين حلناها سبعة و أربعين R
+
+256
+00:28:53,500 --> 00:28:59,320
+star be the group of non zero real number under
+
+257
+00:28:59,320 --> 00:29:07,500
+multiplication R star يا شباب عبارة عن Rمعدد Zero
+
+258
+00:29:07,500 --> 00:29:12,960
+والعملية عملية ضرب H عبارة عن كل X في R*) X تربيه
+
+259
+00:29:12,960 --> 00:29:20,020
+is rational يثبت أن H subgroup of R H عبارة عن كل
+
+260
+00:29:20,020 --> 00:29:27,520
+X في R*) X تربيه ينتمي ل Q المطلوب اثبات أن H
+
+261
+00:29:27,520 --> 00:29:36,050
+subgroup من R*)عارف ان السؤال هذا حلنا واحد زيه
+
+262
+00:29:36,050 --> 00:29:42,970
+مخضر الماضية لما قلنا عندي abelian group و هاد ال
+
+263
+00:29:42,970 --> 00:29:48,650
+R*) مع ضرب abelian فكل ال Xات اللي بيحققوله ان X
+
+264
+00:29:48,650 --> 00:29:54,630
+أس N بساوي ال identity بيعملوا له سبق ال group هذا
+
+265
+00:29:54,630 --> 00:29:59,750
+السؤال شبيه فيهبس ماجولش انه x تربيه بيسوي ال
+
+266
+00:29:59,750 --> 00:30:03,330
+identity لأ هان بقول انه x تربيه عبارة عن ايش
+
+267
+00:30:03,330 --> 00:30:09,550
+rational number اول شي ال
+
+268
+00:30:09,550 --> 00:30:18,170
+H لا يسوي فيه since واحد ينتمي لل H now if
+
+269
+00:30:22,520 --> 00:30:32,320
+A وB ينتمي للـH A تربيع ينتمي للـQ وB تربيع ينتمي
+
+270
+00:30:32,320 --> 00:30:44,440
+للـQ طيب ال AP inverse تربيع عبارة عن ايش عن A على
+
+271
+00:30:44,440 --> 00:30:48,740
+B لكل تربيع ليش انا عملت A على B
+
+272
+00:30:51,710 --> 00:30:55,510
+لان انا بشتغل مع العداد الحقيقية فال inverse لضرب
+
+273
+00:30:55,510 --> 00:31:04,470
+ماله تواحد على حسين على a تربيع على b تربيع وهذا
+
+274
+00:31:04,470 --> 00:31:10,050
+ينتمي ل ال Q ليش ينتمي ل ال Q عدد نسبي على عدد
+
+275
+00:31:10,050 --> 00:31:15,610
+نسبي عدد نسبي لانه اصلا عملية القسمة او عملية
+
+276
+00:31:15,610 --> 00:31:17,630
+الضرب مغلقة في ال Q
+
+277
+00:31:31,690 --> 00:31:37,870
+هل ممكن نبدل التنين بأي عدد صحيح
+
+278
+00:31:37,870 --> 00:31:38,590
+أخر؟
+
+279
+00:31:44,660 --> 00:31:49,620
+شيل اتنين و احط اي رقم او اي قيمة بالعداد الصحيح
+
+280
+00:31:49,620 --> 00:31:55,680
+الموجبه تكييب هتظل تكييب قص 17 هتظل قص 17 وهنا
+
+281
+00:31:55,680 --> 00:32:10,600
+مافيش مشكلة بقدر استبدل اتنين بعدد نسبي ليش بقدرش
+
+282
+00:32:10,600 --> 00:32:18,980
+اتعامل مع السوالبانا هنا بقدر yes we can replace
+
+283
+00:32:18,980 --> 00:32:29,540
+اتنين by any natural number بقدر ابدل اتنين بأي
+
+284
+00:32:29,540 --> 00:32:37,680
+عدد طبيعي سبعة
+
+285
+00:32:37,680 --> 00:32:39,020
+واربعين اتنين وخمسين
+
+286
+00:32:49,060 --> 00:32:58,000
+طب 52 ما أعتقد أنه فيه مشكلة يعني 52 و 53 سهلين سي
+
+287
+00:32:58,000 --> 00:33:05,840
+سؤال 47 حلين
+
+288
+00:33:05,840 --> 00:33:10,060
+أكتر من سؤال على حتى المحاضرة الماضية حلت تقريبا
+
+289
+00:33:10,060 --> 00:33:15,500
+تلت أسئلة على موضوع subgroup 56 و 57
+
+290
+00:33:18,570 --> 00:33:25,290
+تعالى نشوفهم 56 بيقول A زي P I حيث ال A P Positive
+
+291
+00:33:25,290 --> 00:33:35,270
+هل
+
+292
+00:33:35,270 --> 00:33:41,130
+هذا هل ال H سابقه مع ال C و الجامع
+
+293
+00:33:47,210 --> 00:33:52,410
+هل ال arch subgroup من ال C عشان اميزه احطله شرطا
+
+294
+00:33:52,410 --> 00:33:57,190
+مع الجامعة ايش رأيك؟
+
+295
+00:33:57,190 --> 00:34:06,250
+اه ايش رأيك؟
+
+296
+00:34:06,250 --> 00:34:16,540
+هل هذه subgroup من ال C مع الجامعة؟ اه فاكرهأول
+
+297
+00:34:16,540 --> 00:34:22,120
+حاجة ال identity موجود identity تبع الجامعة موجود
+
+298
+00:34:22,120 --> 00:34:27,740
+هيك
+
+299
+00:34:27,740 --> 00:34:33,740
+بقى مغلقة على وجود ال identity العملية associative
+
+300
+00:34:33,740 --> 00:34:41,840
+ولا لأ associative طب ال inverse موجود
+
+301
+00:34:42,610 --> 00:34:48,630
+لو ال A P موجب يعني A زاد P I في ال H سالب A سالب
+
+302
+00:34:48,630 --> 00:34:52,530
+P I برضه في ال H لإنه A P موجب فسالب A في سالب P
+
+303
+00:34:52,530 --> 00:34:57,910
+برضه موجب يجب أولي الخلل اللي ممكن يكون معانا في
+
+304
+00:34:57,910 --> 00:35:03,450
+إن العملية تكون مغلقة أصلا هلاحظ الشغل التالي سالب
+
+305
+00:35:03,450 --> 00:35:11,950
+واحد او واحد زاد اتنين I تامين ال H تمام؟
+
+306
+00:35:14,440 --> 00:35:24,880
+و سالب ثلاثة ناقص I برضه في الاتش خلي هذا A وهذا B
+
+307
+00:35:24,880 --> 00:35:31,840
+طيب A زاد ال B عبارة عن ايش سالب اتنين زاد ال I
+
+308
+00:35:31,840 --> 00:35:37,580
+هذا مش في الاتش وبالتالي
+
+309
+00:35:37,580 --> 00:35:42,860
+العملية مش مغلقة هنا مافيش اغلاق للعملية جوا الاتش
+
+310
+00:35:42,860 --> 00:35:49,630
+وبالتاليH not subgroup
+
+311
+00:35:49,630 --> 00:36:02,810
+of C و الجمهور مش subgroup لأنه
+
+312
+00:36:02,810 --> 00:36:06,850
+لو انت ضربت ال F انا هالخطأ ان اخدت A و B حطيليها
+
+313
+00:36:06,850 --> 00:36:13,010
+X و Y تعالوا
+
+314
+00:36:13,010 --> 00:36:18,400
+ضرب هدف يعني سلب 2 في 1سالف اتنين هل السالف اتنين
+
+315
+00:36:18,400 --> 00:36:24,380
+موجب او اكبر أو سوى الصفر سبعة و خمسين على نفس
+
+316
+00:36:24,380 --> 00:36:31,420
+المنطقة برضه بشتر على ال C مع ال multiplication
+
+317
+00:36:31,420 --> 00:36:39,720
+طبعا
+
+318
+00:36:39,720 --> 00:36:45,270
+هذه المجموعة شباب عبارة عن ايش؟A زي ات بي I حيث
+
+319
+00:36:45,270 --> 00:36:49,350
+ايه تر بي زي بي تر بي بيسوا واحد هذه بيسميها ال
+
+320
+00:36:49,350 --> 00:36:54,670
+unit circle دائرة الوحدة تم عظمها أخد complex هل
+
+321
+00:36:54,670 --> 00:36:59,930
+هذه sub group مع طبعا احنا هيك اتجاوبنا على الجزء
+
+322
+00:36:59,930 --> 00:37:02,410
+التاني من السؤال describe the element of H
+
+323
+00:37:02,410 --> 00:37:10,470
+geometrically دائرة الوحدة ال unit circle
+
+324
+00:37:10,470 --> 00:37:21,540
+هل هذه sub groupأنا بتعامل مع مين؟ مع الضنب أولش
+
+325
+00:37:21,540 --> 00:37:29,800
+المحايد هنا طبعا C Star عبارة عن C مع ده مين؟ الـ
+
+326
+00:37:29,800 --> 00:37:37,060
+Zero ال identity موجود مين ال identity هنا؟ ال A
+
+327
+00:37:37,060 --> 00:37:41,000
+بتتساوي واحد زي ال Zero I بتتساوي واحد هذا ينتمي
+
+328
+00:37:41,000 --> 00:37:47,220
+لل Hيقبل أش لا تساو فيه تنين ال identity موجود ولا
+
+329
+00:37:47,220 --> 00:37:55,340
+تساو فيه associative موجود طبعا لأنه جزء من الكبير
+
+330
+00:37:55,340 --> 00:38:07,420
+أش فيه ضالة شروط ال inverse ومي كمان ال inverse و
+
+331
+00:38:07,420 --> 00:38:12,970
+ال close ال inverse موجود يا شبابلو ال A زي ال P I
+
+332
+00:38:12,970 --> 00:38:17,950
+ينتمي لل H ف A تربيع زي ال P تربيع بسوء واحد طب ال
+
+333
+00:38:17,950 --> 00:38:22,610
+A زي ال P I inverse هذا عبارة عن A minus ال P I
+
+334
+00:38:22,610 --> 00:38:29,110
+على A تربيع زي ال P تربيع اللي هو عبارة عن A على A
+
+335
+00:38:29,110 --> 00:38:33,830
+تربيع زي ال P تربيع نقص ال P I على A تربيع زي ال P
+
+336
+00:38:33,830 --> 00:38:37,450
+تربيع بس هي أنا تحت الجزر
+
+337
+00:38:45,640 --> 00:38:54,960
+شوية بس مافيش جزايا طب
+
+338
+00:38:54,960 --> 00:38:59,480
+ماتنساش ان هذا ايش بيساوي واحد يكبر هذا عبارة عن
+
+339
+00:38:59,480 --> 00:39:04,300
+ال a minus bi و ال a تربيه زاد سالب ال b تربيه
+
+340
+00:39:04,300 --> 00:39:08,340
+بيساوي a تربيه زاد ال b تربيه بيساوي واحد يكبر a
+
+341
+00:39:08,340 --> 00:39:16,930
+زاد ال bi inverse ينتمي للhأول تلات شروط اتحققوا
+
+342
+00:39:16,930 --> 00:39:21,490
+طب أنا هنا مش راضي استعمل ليه ال notation تبعت ال
+
+343
+00:39:21,490 --> 00:39:25,290
+C أو تبعت ال complex analysis ان بعضهم هيقول انا
+
+344
+00:39:25,290 --> 00:39:31,610
+مااخدتش تحليل مُركّب اربعة لو أنا قولت ال X بيساوي
+
+345
+00:39:31,610 --> 00:39:36,450
+A زاد ال P I و ال Y بيساوي ال C زاد ال D I هدول
+
+346
+00:39:36,450 --> 00:39:43,020
+ينتموا لل H معناته A تربية زادالـ B تربيع بدي أسوأ
+
+347
+00:39:43,020 --> 00:39:49,360
+واحد بدي أسوأ C تربيع زاد ال D تربيع لو أنا جيت
+
+348
+00:39:49,360 --> 00:39:58,720
+أشتغل على XY XY عبارة عن إيش هذا
+
+349
+00:39:58,720 --> 00:40:10,380
+عبارة عن AC نقص BD زائد D في C زائد
+
+350
+00:40:11,860 --> 00:40:18,240
+تخربطوني هيك يا شباب A في D زائد
+
+351
+00:40:18,240 --> 00:40:23,440
+BC بي في CI تعالى نشوف هذا تربية زائد هذا تربية
+
+352
+00:40:23,440 --> 00:40:30,580
+ايش بيساوي AC نقص ال BD تربية زائد ال AD زائد ال
+
+353
+00:40:30,580 --> 00:40:36,000
+BC تربية ايش بيساوي A تربية C تربية نقص اتنين AC
+
+354
+00:40:36,000 --> 00:40:45,060
+BD زائد ال B تربية D تربية زائدA تربيع D تربيع زاد
+
+355
+00:40:45,060 --> 00:40:51,340
+اتنين ACPD زاد B تربيع C تربيع هذا مع هذا بيطير
+
+356
+00:40:51,340 --> 00:40:58,580
+بيظل عندي A تربيع في C تربيع زاد ال D تربيع زاد B
+
+357
+00:40:58,580 --> 00:41:04,520
+تربيع في C تربيع زاد ال D تربيع هذا واحد وهذا واحد
+
+358
+00:41:04,520 --> 00:41:10,020
+هيصيب معايا A تربيع زاد ال B تربيع مش بيساويهذا
+
+359
+00:41:10,020 --> 00:41:17,720
+معناته انه XY جوا ال H Identity موجود Associative
+
+360
+00:41:17,720 --> 00:41:25,480
+متحقق مغلقة على ال inverse مغلقة على العملية نفسها
+
+361
+00:41:25,480 --> 00:41:29,840
+يكبر H subgroup من C
+
+362
+00:41:35,920 --> 00:41:40,960
+أخدت complex analysis أخدت العدد المركب في
+
+363
+00:41:40,960 --> 00:41:45,280
+الثانوية ولا لأ كيف أجيب معكوس لعدد المركب بضغط في
+
+364
+00:41:45,280 --> 00:41:52,900
+المرافق فوق و تحت هو ال A زاد ال I B inverse هذا
+
+365
+00:41:52,900 --> 00:41:59,500
+عبارة عن واحد على A زاد ال I B واحد نقص ال .. و
+
+366
+00:41:59,500 --> 00:42:03,120
+بكمل قاضي
+
+367
+00:42:05,490 --> 00:42:15,010
+إيش بيظلاندي يا شباب؟ تسعة و خمسين جي
+
+368
+00:42:15,010 --> 00:42:19,910
+قلت
+
+369
+00:42:19,910 --> 00:42:33,990
+و اه؟ هذا سؤال فيه خربش كتير طيب
+
+370
+00:42:35,180 --> 00:42:42,220
+تسعة و خمسين اختار سؤال مثلا ايه بدك ال center او
+
+371
+00:42:42,220 --> 00:42:50,800
+ال centralizer ل 1110 حسب التعريف هذا عبارة عن كل
+
+372
+00:42:50,800 --> 00:43:03,430
+ال A في ال GL to R اللي A 1110 بيساوي 1110 في Aلو
+
+373
+00:43:03,430 --> 00:43:11,450
+انا خدت ال a عبارة عن a,b,c,d و جيت اشتغلت a,b,c,d
+
+374
+00:43:11,450 --> 00:43:25,150
+1110 هذا المفروض يساوي 1110 في a,b,c,d اضرب a زائد
+
+375
+00:43:25,150 --> 00:43:25,570
+ال b
+
+376
+00:43:29,260 --> 00:43:40,080
+C زائد D C هذا بـ D ساوي A زائد C واحد
+
+377
+00:43:40,080 --> 00:43:45,400
+واحد في B B زائد D A
+
+378
+00:43:45,400 --> 00:43:52,960
+B A
+
+379
+00:43:52,960 --> 00:43:57,580
+زائد C B زائد D A وB اعمل مساواة
+
+380
+00:44:24,230 --> 00:44:27,690
+هتستفيد من هذه و هذه شغلة واحدة ان ال B بيساوي ال
+
+381
+00:44:27,690 --> 00:44:27,830
+C
+
+382
+00:44:33,170 --> 00:44:38,950
+طب وهذه وهذه نفس
+
+383
+00:44:38,950 --> 00:44:44,230
+الفكرة لما تساوي a بساوي b زاد دي و a بساوي c زاد
+
+384
+00:44:44,230 --> 00:44:49,150
+دي طير دي من الطرفين مش هيظل عندك فقط المعلومة
+
+385
+00:44:49,150 --> 00:44:53,110
+الوحيدة اللي انت بتقدر تستفيدها نهيش ان ال b و ال
+
+386
+00:44:53,110 --> 00:45:03,870
+c متساوين وبالتالي ال centralizer لواحد واحدواحد
+
+387
+00:45:03,870 --> 00:45:16,710
+صفر عبارة عن كل ال a,b,b,d حيث a,b,d ينتموا لمين
+
+388
+00:45:16,710 --> 00:45:21,750
+هي كل
+
+389
+00:45:21,750 --> 00:45:29,290
+المصفوفات اللي ال b و ال c فيهم متساوية طبعا الفرع
+
+390
+00:45:29,290 --> 00:45:37,510
+b like الفرع aهيكون أسهل شوية طيب
+
+391
+00:45:37,510 --> 00:45:44,650
+الفرصية
+
+392
+00:45:44,650 --> 00:45:52,270
+ال center تبع JL2R
+
+393
+00:45:52,270 --> 00:45:59,230
+مين
+
+394
+00:45:59,230 --> 00:46:00,170
+بيقدر يعرفهم؟
+
+395
+00:46:03,410 --> 00:46:15,970
+من بيقدر يعرفه بس بس
+
+396
+00:46:15,970 --> 00:46:20,750
+بعد
+
+397
+00:46:20,750 --> 00:46:28,590
+شوية حسابات هنكتشف ان هذا عبارة عن كل a 00a حيث a
+
+398
+00:46:28,590 --> 00:46:29,030
+في r
+
+399
+00:46:32,520 --> 00:46:39,880
+هذا التوقعي بحاول المرة الجاية أكيدلك إياه أعتقد
+
+400
+00:46:39,880 --> 00:46:43,380
+أن هذا كلام صحي اللي لو كان في أمثلة أخرى خليني
+
+401
+00:46:43,380 --> 00:46:47,580
+أنا برضه أنه إيجي على بالي شغلة معينة ممكن تتحقق
+
+402
+00:46:47,580 --> 00:46:57,860
+كلام اللي بنحكي واضح؟ هذا اللي التأكد بأكيدها
+
+403
+00:46:57,860 --> 00:47:02,630
+المرة الجاية لأنه مايظلش وجهة عنديمناخش تفاصيلها
+
+404
+00:47:02,630 --> 00:47:07,590
+طب بنعطيكوا العافية محاضرة جاية ان شاء الله بنفوت
+
+405
+00:47:07,590 --> 00:47:12,890
+في الوحدة الرابعة بنتكلم فيها عن ال cyclic group و
+
+406
+00:47:12,890 --> 00:47:16,890
+بنتكلم فيها عن الهيكلية الداخلية لكل ال cyclic
+
+407
+00:47:16,890 --> 00:47:20,450
+group و التفاصيل الخاصة في هذا الموضوع بنعطيكوا
+
+408
+00:47:20,450 --> 00:47:21,850
+العافية السلام عليكم
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7f96cceb9ec6722904e00eda842ea187bf46bc31
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w.srt
@@ -0,0 +1,1815 @@
+1
+00:00:20,990 --> 00:00:24,830
+بسم الله الرحمن الرحيم نرجع لمحاضرة ابتدأناها في
+
+2
+00:00:24,830 --> 00:00:29,010
+الفترة الصباحية وهو أنه بدأنا في chapter 3 اللي 
+
+3
+00:00:29,010 --> 00:00:38,030
+بتحدث عن ال subgroups طبعا أعطينا تعريف لل order
+
+4
+00:00:38,030 --> 00:00:42,370
+لل group و order لل element اللي موجود داخل ال
+
+5
+00:00:42,370 --> 00:00:46,120
+group وعرفنا أن ال order لل group هو عدد العناصر في
+
+6
+00:00:46,120 --> 00:00:49,900
+ال group و ال order لل element هو أصغر عدد صحيح 
+
+7
+00:00:49,900 --> 00:00:53,000
+موجب أحط ال cos لل element بيعطينا ال main 
+
+8
+00:00:53,000 --> 00:00:56,980
+identity element و أخدنا على ذلك مثالا واحدة وهي
+
+9
+00:00:56,980 --> 00:01:02,020
+قدامنا المثال رقم اثنين يبقى لو أخدت g هي ال z
+
+10
+00:01:02,020 --> 00:01:06,900
+ثمانية لما أحط زائد في دائرة صغيرة ليست عملية 
+
+11
+00:01:06,900 --> 00:01:11,140
+الضرب العادية لو كان عملية الضرب العادية بحط زائد
+
+12
+00:01:11,140 --> 00:01:15,200
+بدون دائرة حولها يبقى هذا المقصود أن الجامعة
+
+13
+00:01:15,200 --> 00:01:20,720
+modulo 8 هي المقصود العملية هذه يبقى زائد في دائرة
+
+14
+00:01:20,720 --> 00:01:25,000
+حسب الرقم اللي عندي بيكون هذا modulo هذا ال main هذا
+
+15
+00:01:25,000 --> 00:01:29,780
+الرقم يعني z ثمانية وعليها عملية الجمع modulo
+
+16
+00:01:29,780 --> 00:01:34,620
+ثمانية عناصرها من صفر لغاية سبعة يبقى بناء عليه ال
+
+17
+00:01:34,620 --> 00:01:39,240
+order اللي جاي كده شو يساوي ثمانية فيها ثمان عناصر 
+
+18
+00:01:39,240 --> 00:01:45,900
+الصفر من ضمنهم يبقى then ال order اللي جاي بده
+
+19
+00:01:45,900 --> 00:01:51,990
+يساوي ثمانية زيرو هو ال identity element لما نضيف
+
+20
+00:01:51,990 --> 00:01:55,250
+زيرو لأي element modulo ثمانية بيبقى نفس ال element 
+
+21
+00:01:55,250 --> 00:02:00,450
+يبقى zero هو ال identity element الآن لو بدأنا ال
+
+22
+00:02:00,450 --> 00:02:09,890
+order مثلا للواحد كده ال order للواحد تحت عملية
+
+23
+00:02:09,890 --> 00:02:15,230
+الجمع يعني واحد تربيع يعني واحد زائد واحد modulo
+
+24
+00:02:15,230 --> 00:02:20,030
+ثماني بنجد اثنين زائد واحد زائد واحد يعني بنجد
+
+25
+00:02:20,030 --> 00:02:27,870
+ال order له ثلاثة سبعة ودي يطلع ال zero ها ال
+
+26
+00:02:27,870 --> 00:02:32,210
+zero هو ال identity ثمانية طيب يجي ال order للواحد
+
+27
+00:02:32,210 --> 00:02:36,950
+بده يساوي ثمانية طيب ال order لثلاثة
+
+28
+00:02:40,210 --> 00:02:47,450
+ثلاثة ثلاثة وثلاثة ستة وثلاثة تسعة وثلاثة اثنا عشر 
+
+29
+00:02:47,450 --> 00:02:54,390
+وثلاثة خمسة عشر وثلاثة ثمانية عشر وثلاثة واحد وعشرين 
+
+30
+00:02:54,390 --> 00:03:00,190
+وثلاثة يبقى هذا ال zero يبقى كده ثمانية 
+
+31
+00:03:00,190 --> 00:03:07,910
+كذلك يبقى هذا هو ال order كمان لثلاثة طيب أليس هو
+
+32
+00:03:07,910 --> 00:03:09,710
+ال order كمان لخمسة 
+
+33
+00:03:12,610 --> 00:03:19,170
+خمسة وخمسة عشرة هيبقى اثنين وكمان خمسة سبعة وكمان
+
+34
+00:03:19,170 --> 00:03:25,210
+خمسة بصير اثنا عشر وكمان خمسة سبعة طيب هتلاقي كمان
+
+35
+00:03:25,210 --> 00:03:30,750
+ثمانية وال order لسبعة كمان هو ثمانية يبقى هذا 
+
+36
+00:03:30,750 --> 00:03:35,790
+يساوي كمان ال order لسبعة كل هذا الكلام بده 
+
+37
+00:03:35,790 --> 00:03:41,790
+يساوي قداش ثمانية طب لو جيت ال order لل zero قداش
+
+38
+00:03:41,790 --> 00:03:47,230
+يا شباب واحد لأن هو ال identity element طب ال order
+
+39
+00:03:47,230 --> 00:03:53,070
+لاثنين اثنين 
+
+40
+00:03:53,070 --> 00:03:57,230
+زائد اثنين زائد اثنين زائد اثنين ب zero يبقى أربعة
+
+41
+00:03:57,230 --> 00:04:02,250
+يبقى ال order ل اثنين بده يساوي أربعة طيب لو بده
+
+42
+00:04:02,250 --> 00:04:08,130
+يقولك ال order لأربعة اثنين طب ال order لستة 
+
+43
+00:04:12,200 --> 00:04:16,980
+أربعة بالضبط صحيح ستة وستة اثنا عشر كمان ستة ثمانية عشر 
+
+44
+00:04:16,980 --> 00:04:20,920
+كمان ستة أربعة وعشرين اللي هو تلف ثمانية يبقى هذا
+
+45
+00:04:20,920 --> 00:04:26,200
+بده يساوي الأربعة يبقى بناء عليه جبنا ال order لل
+
+46
+00:04:26,200 --> 00:04:30,950
+group G اللي هو ثمانية وجبنا ال order لكل element
+
+47
+00:04:30,950 --> 00:04:34,090
+موجود في ال group ال order لل identity element هو
+
+48
+00:04:34,090 --> 00:04:39,530
+بواحد صحيح الباقي بعضهم يساوي ثمانية وبعضهم يساوي
+
+49
+00:04:39,530 --> 00:04:42,950
+اثنين زي ما طلع لنا الأربعة والباقي ال order لهم
+
+50
+00:04:42,950 --> 00:04:48,010
+يساوي كده أربعة طيب خليني أسأل سؤال كده إيش
+
+51
+00:04:48,010 --> 00:04:51,670
+بتلاحظوا عن ال order تبع ال element وال order تبع 
+
+52
+00:04:51,670 --> 00:04:54,870
+ال group في علاقة بينهم
+
+53
+00:04:58,210 --> 00:05:04,790
+معلومة ثانية مضاعف ال order لل element دائما لو
+
+54
+00:05:04,790 --> 00:05:10,270
+أبدأ بيكسب ال order لل group كله ال group finite
+
+55
+00:05:10,270 --> 00:05:14,830
+إذا ال order لل element هتلاقي السؤال هذا بس قدامي
+
+56
+00:05:14,830 --> 00:05:18,510
+شوية مش الحين كويس يبقى ال order للإيمين دائما و
+
+57
+00:05:18,510 --> 00:05:22,850
+أبدأ بيجسم ال order لل group وكمان هتلاقي كمان أن
+
+58
+00:05:22,850 --> 00:05:27,290
+ال order لل sub group بيجسم ال order لل group بس
+
+59
+00:05:27,290 --> 00:05:31,730
+لقدامي شوية بس معلومة هيك على الله مش هادر طيب نجي
+
+60
+00:05:31,730 --> 00:05:38,430
+ناخد كمان مثال ثلاثة يبقى مثال ثلاثة يقول خدلي 
+
+61
+00:05:38,430 --> 00:05:47,320
+الآن the group اللي هو the group R star من ال R 
+
+62
+00:05:47,320 --> 00:05:52,460
+star هي عبارة عن ال R بدي أشيل منها ال zero وبدي
+
+63
+00:05:52,460 --> 00:05:58,940
+أخد عليها عملية الضرب قداش ال order هذه اللي هي يا 
+
+64
+00:05:58,940 --> 00:06:09,360
+شباب تمام يبقى هذه is of infinite order 
+
+65
+00:06:11,050 --> 00:06:16,010
+هذا ال order لها سيكون كمية ما لا نهاية السؤال هو
+
+66
+00:06:16,010 --> 00:06:21,690
+إذا أخذت أي عنصر فيها مثل 2 مثل 3 مثل نصف مثل خمسة 
+
+67
+00:06:21,690 --> 00:06:26,730
+مثل سدس مثل جذر ثلاثة مثلا كمية ال order لهذه
+
+68
+00:06:26,730 --> 00:06:36,630
+العناصر هل يعرف ال order مثلا لاثنين هل أجد رقم
+
+69
+00:06:36,630 --> 00:06:40,610
+أضعه كأس للاثنين يظهر ال identity اللي هو واحد
+
+70
+00:06:48,260 --> 00:06:55,360
+is of infinite order يعني إذا ما لقيتش رقم أحطه
+
+71
+00:06:55,360 --> 00:06:59,760
+كأس لهذا العدد يطلع ال identity element يبقى في
+
+72
+00:06:59,760 --> 00:07:04,420
+هذه الحالة order لهذا ال element يساوي infinite
+
+73
+00:07:04,420 --> 00:07:10,750
+طيب السؤال هو ال zero مافيش سيبلي الواحد والسالب
+
+74
+00:07:10,750 --> 00:07:16,850
+واحد امسك بعد الواحد وقبل السالب واحد وما بين
+
+75
+00:07:16,850 --> 00:07:20,830
+الزيرو والواحد وما بين الزيرو والسالب واحد خدلي أي
+
+76
+00:07:20,830 --> 00:07:25,690
+رقم عمرك بتلاقي عدد أن تحطه كأسئلة ويطلع الواحد
+
+77
+00:07:25,690 --> 00:07:31,740
+الصحيح أي رقم ينجز صحيح كثري إيراشيونال إيراشيونال 
+
+78
+00:07:31,740 --> 00:07:35,720
+بدكية تربيتك أي بوس خمسة واس عشرة واس مانيا اوس
+
+79
+00:07:35,720 --> 00:07:41,180
+مليون كذا الأخرى عمره بيطلع واحد صحيح ساكتيه
+
+80
+00:07:41,180 --> 00:07:46,940
+الولادة خد أي رقم وربع شوفه بيزيد ولا بينجس مثل
+
+81
+00:07:46,940 --> 00:07:51,220
+افترض أنه عدد صحيح زي ما قلت لك اثنين بقدر ألاقي
+
+82
+00:07:51,220 --> 00:07:54,820
+أو أن عدد صحيح أحطه له يطلع ال identity اللي هو 
+
+83
+00:07:54,820 --> 00:07:59,070
+واحد صحيح يعني بقدر اثنين أضربها في نفسها من
+
+84
+00:07:59,070 --> 00:08:03,290
+المرات يطلع واحد صحيح عمره شو بيحصل يبقى اثنين of
+
+85
+00:08:03,290 --> 00:08:05,570
+of of of of of of of of of of of of of of of of of
+
+86
+00:08:05,570 --> 00:08:07,050
+of of of of of of of of of of of of of of of of
+
+87
+00:08:07,050 --> 00:08:07,130
+of of of of of of of of of of of of of of of of
+
+88
+00:08:07,130 --> 00:08:07,490
+of of of of of of of of of of of of of of of of
+
+89
+00:08:07,490 --> 00:08:07,610
+of of of of of of of of of of of of of of of of
+
+90
+00:08:07,610 --> 00:08:08,110
+of of of of of of of of of of of of of of of of
+
+91
+00:08:08,110 --> 00:08:08,130
+of of of of of of of of of of of of of of of of
+
+92
+00:08:08,130 --> 00:08:15,390
+of
+
+93
+00:08:15,390 --> 00:08:15,850
+of of of
+
+94
+00:08:24,530 --> 00:08:30,170
+ألاقي شيء بالكسور هذه are of infinite order من
+
+95
+00:08:30,170 --> 00:08:33,750
+ضايق اللي عندي الواحد والسالب الواحد all order
+
+96
+00:08:33,750 --> 00:08:37,290
+وقداش واحد لأن هو ال identity element طب والسالب
+
+97
+00:08:37,290 --> 00:08:42,450
+واحد اثنين اثنين في شغلنا هدول اثنين فقط في ال
+
+98
+00:08:42,450 --> 00:08:48,130
+group هذه هم لل order أنهم finite أما ما عدا ذلك كل 
+
+99
+00:08:48,130 --> 00:08:51,630
+ال elements اللي باقي ال order أنهم is infinite
+
+100
+00:08:51,630 --> 00:08:56,090
+تمام أحد يقول لي طب هذا متناقض مع كلمة اللي تو
+
+101
+00:08:56,090 --> 00:08:59,830
+إيش كلمة اللي تو أنا قلت ال order لل element بيقسم
+
+102
+00:08:59,830 --> 00:09:05,010
+ال order للي group بشرط أن ال group تبقى finite
+
+103
+00:09:05,010 --> 00:09:09,930
+order مش infinite هذا ال order ما يتقدش infinity ل
+
+104
+00:09:09,930 --> 00:09:20,000
+group تمام يبقى باجي بقوله الواحد and الواحد and 
+
+105
+00:09:20,000 --> 00:09:28,680
+الواحد and سالب واحد are of finite order 
+
+106
+00:09:34,140 --> 00:09:39,760
+ال order للواحد يساوي الواحد and ال order لسالب
+
+107
+00:09:39,760 --> 00:09:43,660
+واحد يساوي اثنين لأن السالب واحد تربيع ثاني و
+
+108
+00:09:43,660 --> 00:09:46,480
+السالب واحد بسالب واحد اللي هو بال identity بواحد
+
+109
+00:09:46,480 --> 00:09:50,180
+يبقى ال order اللي يساوي اثنين يبقى بروح بقوله
+
+110
+00:09:50,180 --> 00:09:57,280
+the other elements of 
+
+111
+00:09:58,740 --> 00:10:07,860
+R star are of infinite order 
+
+112
+00:10:07,860 --> 00:10:12,120
+يبقى هذول ال order اللي بقى ال element كله ب
+
+113
+00:10:12,120 --> 00:10:19,360
+infinite خدلي هذا المثال وتعالى نشوف اللي هو إيش
+
+114
+00:10:19,360 --> 00:10:23,300
+الموضوع بالظبط الآن مثال رقم أربعة 
+
+115
+00:10:27,260 --> 00:10:31,240
+الآن لو أخدت ال order لل general linear group of
+
+116
+00:10:31,240 --> 00:10:34,220
+two by two matrices over R
+
+117
+00:10:40,910 --> 00:10:46,670
+أكم مصفوفة عندي بيطلع محددهم لا يساوي zero نظامهم
+
+118
+00:10:46,670 --> 00:10:51,850
+اثنين في اثنين كده ثمانية كده ما بدك تاخد
+
+119
+00:10:51,850 --> 00:10:56,690
+مصفوفة تغير الأرقام زي ما بدك لأن الأرقام عددهم
+
+120
+00:10:56,690 --> 00:11:01,270
+لنهاية set of real number بقدر أخلي الأربع أرقام
+
+121
+00:11:01,270 --> 00:11:05,360
+زي بعضها وشوف أكم مصفوفة يطلع كيف لما أغيرهم يبقى 
+
+122
+00:11:05,360 --> 00:11:09,560
+infinity يبقى ال order لهذه اللي هو بده يساوي 
+
+123
+00:11:09,560 --> 00:11:15,100
+infinity طب بتاخد فيها بعض ال elements وشوف قداش
+
+124
+00:11:15,100 --> 00:11:22,320
+ال order لهم يبقى هذا ال order infinity but ال
+
+125
+00:11:22,320 --> 00:11:29,440
+a تساوي اللي هو zero واحد وسالب واحد وسالب واحد 
+
+126
+00:11:29,440 --> 00:11:42,080
+and  والتانية هي الـ main مصوفة ب تساوي ب تساوي
+
+127
+00:11:42,080 --> 00:11:48,840
+الـ zero والسالب واحد واحد و zero هذه موجودة في
+
+128
+00:11:48,840 --> 00:11:51,380
+الـ general group
+
+129
+00:11:54,820 --> 00:12:00,480
+ليش موجودة؟ لأن محددها لا يساوي Zero Zero زائد
+
+130
+00:12:00,480 --> 00:12:05,080
+واحد بيطلع واحد موجودة فيها هذه Zero زائد واحد
+
+131
+00:12:05,080 --> 00:12:08,560
+بيطلع واحد يبقى موجودة فيها يبقى اتنين موجودات في
+
+132
+00:12:08,560 --> 00:12:11,080
+ال general linear group of two by two matrices
+
+133
+00:12:11,080 --> 00:12:16,540
+over R بدي أدور على ال order تبع ال A يبقى بدي
+
+134
+00:12:16,540 --> 00:12:22,430
+أروح أقوله ال A تربيع يبقى الـ A تربيع الـ 0 1 سالب 
+
+135
+00:12:22,430 --> 00:12:28,050
+واحد سالب واحد 0 1 سالب واحد سالب واحد و يساوي
+
+136
+00:12:37,780 --> 00:12:43,100
+الصف الأول في العمود الثاني هو zero وبطلع هنا كمان
+
+137
+00:12:43,100 --> 00:12:47,620
+سالب واحد طب الصف الثاني في العمود الأول بطلع واحد
+
+138
+00:12:47,620 --> 00:12:53,060
+الصف الثاني في العمود الثاني سالب واحد وهنا زائد
+
+139
+00:12:53,060 --> 00:12:57,680
+واحد بطلع كم؟ بطلع zero لا يساوي ال identity
+
+140
+00:12:57,680 --> 00:13:03,560
+element طيب إيش رأيك لو روحت ضربت كمان في ايه بصير
+
+141
+00:13:03,560 --> 00:13:09,390
+عندي كم؟ اتكيب طيب لو جيت قولت هذا بده يعطينا انه
+
+142
+00:13:09,390 --> 00:13:15,810
+ايه تكييب بده يساوي اللي هو من Zero و واحد و سالب
+
+143
+00:13:15,810 --> 00:13:22,370
+واحد و سالب واحد في سالب واحد سالب واحد واحد Zero
+
+144
+00:13:22,370 --> 00:13:27,650
+و يساوي الصف الأول في العمود الأول يبقى Zero و هنا
+
+145
+00:13:27,650 --> 00:13:35,060
+واحد هنا Zero و هنا Zero اللي هو ب Zero تمامهنا هي
+
+146
+00:13:35,060 --> 00:13:40,080
+واحد وهنا سالب واحد يبقى zero الصف هذا في هذا
+
+147
+00:13:40,080 --> 00:13:45,820
+بيطلع واحد وهنا واحد فقط لا غير يبقى ال order
+
+148
+00:13:45,820 --> 00:13:50,980
+لإيه؟ تلاتة لإن هذه ال identity matrix يبقى
+
+149
+00:13:50,980 --> 00:13:59,970
+similarly بنفس الطريقة similarly ال
+
+150
+00:13:59,970 --> 00:14:07,070
+b square يساوي ال b square يبقى بدأ اضرب zero سالب
+
+151
+00:14:07,070 --> 00:14:14,310
+واحد واحد zero في zero سالب واحد واحد zero ويساوي
+
+152
+00:14:14,310 --> 00:14:18,330
+الصف الأول في العامل الأول zero سالب واحد بسالب
+
+153
+00:14:18,330 --> 00:14:25,950
+واحد زيرو وزيرو أب زيرو صف التاني زيرو وزيرو أب
+
+154
+00:14:25,950 --> 00:14:31,750
+زيرو و هنا سالب واحد شكلنا ماطلعش ال identity
+
+155
+00:14:31,750 --> 00:14:38,650
+element لكن الشافوي طلعلي هذه لو ضربت في نفسي مين
+
+156
+00:14:38,650 --> 00:14:45,770
+بطلع مين تتوقع يطلع الـ Identity Matrix على طول
+
+157
+00:14:45,770 --> 00:14:52,350
+الخط يبقى لو روحت جبت ال بي أس أربع اوتوماتيك
+
+158
+00:14:52,350 --> 00:14:57,800
+هيطلع واحد زيرو زيرو واحد بناء ان عليه هذا بدي
+
+159
+00:14:57,800 --> 00:15:04,520
+يقولك ان ال order ل a بدي ساوي تلاتة and ال order
+
+160
+00:15:04,520 --> 00:15:10,160
+ل b بدي ساوي كده اربعة طيب ايش رايك لو ضربت
+
+161
+00:15:10,160 --> 00:15:14,420
+التنتين في بعض و بدي اشوف ال order ايه الشطعة تبعه
+
+162
+00:15:14,420 --> 00:15:21,790
+الا لو اخدت اللي هو ال A في B يساوي وين ال A اللي
+
+163
+00:15:21,790 --> 00:15:27,270
+عندنا هذا ال A اللي هي Zero واحد سالب واحد سالب
+
+164
+00:15:27,270 --> 00:15:32,710
+واحد في B اللي هي Zero سالب واحد واحد Zero بده
+
+165
+00:15:32,710 --> 00:15:37,280
+يشوف كده يصنع الصف الأول في العمود الأول بيطلع
+
+166
+00:15:37,280 --> 00:15:44,580
+بواحد الصف الأول في العمود الثاني بيطلع zero الصف
+
+167
+00:15:44,580 --> 00:15:49,700
+الثاني في العمود الأول بيطلع سالب واحد الصف الثاني
+
+168
+00:15:49,700 --> 00:15:55,380
+في العمود الثاني بيطلع له كمان قداش اللي هو واحد
+
+169
+00:15:55,380 --> 00:16:00,680
+بالشكل اللي عندنا هذا ال a في b الآن لو ال a في b
+
+170
+00:16:00,680 --> 00:16:06,260
+تضربها في نفسها مائة مرة لا يمكن يطلع ال identity
+
+171
+00:16:06,260 --> 00:16:13,120
+مثال و ذلك لو روحت أخدت ال a بي الكل ترمية يبقى
+
+172
+00:16:13,120 --> 00:16:22,360
+واحد زيرو سالب واحد واحد هذا الكلام يساوي في واحد
+
+173
+00:16:22,360 --> 00:16:27,620
+زيرو سالب واحد واحد ويساوي الصف الأول في العمود
+
+174
+00:16:27,620 --> 00:16:33,860
+الأول بواحد الصف الأول في العمود الثاني بزيرو الصف
+
+175
+00:16:33,860 --> 00:16:38,960
+الثاني في العمود الأول بسالب اتنين الصف الثاني في
+
+176
+00:16:38,960 --> 00:16:43,650
+العمود الثاني بواحد ايش اللى تغير عن حصل الضرب
+
+177
+00:16:43,650 --> 00:16:49,630
+المصوفة الأصلية؟ ثلاثة عناصر هدول هما يتغيرون بس
+
+178
+00:16:49,630 --> 00:16:55,150
+السالب واحد صار باتنين يبقى بناء عليه لو جيت قلتلك
+
+179
+00:16:55,150 --> 00:17:01,630
+يبقى ال a b to the power n ايش بيتقولي واحد زير و
+
+180
+00:17:01,630 --> 00:17:09,010
+واحد و هنا كده؟ سالب M طيب بتقدر تلاقي رقم تحطه ك
+
+181
+00:17:09,010 --> 00:17:14,310
+أس ل a,b يطلع ال identity؟ مفيش إمكانية يبقى ال a
+
+182
+00:17:14,310 --> 00:17:19,310
+,b كده ف ال order اللي لها infinity يبقى هذا بده
+
+183
+00:17:19,310 --> 00:17:27,390
+يعطيلي ان ال a,b is of infinite order
+
+184
+00:17:28,710 --> 00:17:34,670
+يبقى هذا مثال جميل جدا لو سألك قالك انت عندك group
+
+185
+00:17:34,670 --> 00:17:39,630
+فيها two elements كل واحد بفيهم finite order هل
+
+186
+00:17:39,630 --> 00:17:44,890
+حاصل الضرب بديكون finite ولا infinite لاحتمالين
+
+187
+00:17:44,890 --> 00:17:49,210
+وردات قد يكون حاصل الضرب finite وقد يكون حاصل
+
+188
+00:17:49,210 --> 00:17:54,690
+الضرب infinite هي طلع ال order لكل واحدة فيهم
+
+189
+00:17:54,690 --> 00:17:58,790
+finite لكن ال order لحاصل الدربع التاني infinite
+
+190
+00:18:00,400 --> 00:18:06,500
+هذا مثال جميل جدا حكيتلكوا الصبح عنه و نحنا قد
+
+191
+00:18:06,500 --> 00:18:11,780
+أعطيناكم هذا المثال طب بدنا نخش الأن للموضوع اللي
+
+192
+00:18:11,780 --> 00:18:15,040
+احنا كنا رافعينه اللي هو انتبعنا اللي لسه
+
+193
+00:18:15,040 --> 00:18:20,880
+ماتحدثناش فيه لغمين ال subgroups المجموعات الجزئية
+
+194
+00:18:20,880 --> 00:18:26,550
+لمجموعة ما الـ definition بيقول ما يأتي definition
+
+195
+00:18:26,550 --> 00:18:40,650
+let الـ H be a subset of G الـ
+
+196
+00:18:40,650 --> 00:18:53,780
+H is called هذي بنسميها a subgroup of G subgroup من
+
+197
+00:18:53,780 --> 00:19:09,380
+G F L H is a group is a group under the same
+
+198
+00:19:09,380 --> 00:19:19,540
+operation under the same operation of
+
+199
+00:19:20,800 --> 00:19:33,080
+G We write بروح نكتب ان ال H هي ال sub group من جي
+
+200
+00:19:33,080 --> 00:19:37,460
+بالشكل اللي عندنا Notes
+
+201
+00:19:37,460 --> 00:19:49,740
+بعض الملاحظات اول ملاحظة F ال H لا تساوي G We
+
+202
+00:19:49,740 --> 00:20:03,150
+write بنروح نكتب ان ال H subgroup من G and ال H is
+
+203
+00:20:03,150 --> 00:20:11,290
+called بنروح نسميها a proper
+
+204
+00:20:11,290 --> 00:20:18,330
+subgroup نقطة
+
+205
+00:20:18,330 --> 00:20:19,070
+ثانية
+
+206
+00:20:21,440 --> 00:20:32,180
+ست إي فقط لغير is called a
+
+207
+00:20:32,180 --> 00:20:38,960
+trivial subgroup of
+
+208
+00:20:38,960 --> 00:20:40,300
+G
+
+209
+00:20:47,700 --> 00:20:56,780
+the others and the other subgroups
+
+210
+00:20:56,780 --> 00:21:03,400
+are called
+
+211
+00:21:03,400 --> 00:21:07,860
+the
+
+212
+00:21:07,860 --> 00:21:11,340
+non
+
+213
+00:21:11,340 --> 00:21:15,740
+-trivial subgroups
+
+214
+00:21:22,890 --> 00:21:24,670
+R G
+
+215
+00:22:07,520 --> 00:22:10,640
+نرجع للتعريف اللي احنا كنا نقوله تعريف ال subgroup
+
+216
+00:22:10,640 --> 00:22:16,120
+فباجي بقول لو كانت ال H هي ال subset من G بس مش
+
+217
+00:22:16,120 --> 00:22:20,820
+حيالها subset في شغلة بتتحقق عليها يبقى ال H is
+
+218
+00:22:20,820 --> 00:22:25,380
+called subgroup من G إذا كانت ال H باقية هي group
+
+219
+00:22:25,380 --> 00:22:31,980
+under the same operation of G يعني اعتبر الطلاب
+
+220
+00:22:31,980 --> 00:22:36,060
+اللي عندي في هذه القاعة كلهم group لو أخدت هذه
+
+221
+00:22:36,060 --> 00:22:41,080
+المجموعة منهم يبقى هذه بسميها ال subgroup إذا طلعت
+
+222
+00:22:41,080 --> 00:22:45,400
+هذه group تحت نفسي العملية المعرفة عليه ال group
+
+223
+00:22:45,400 --> 00:22:49,780
+الأصلية إيش يعني group؟ يعني هذه فيهم ال identity
+
+224
+00:22:49,780 --> 00:22:55,440
+element وعناصرهم associative مع بعضهم وكل عنصر له
+
+225
+00:22:55,440 --> 00:23:00,500
+معكوس يبقى ان حدث ذلك بقول يبقى هذه الجديدة group
+
+226
+00:23:00,500 --> 00:23:05,040
+ان حد ذلك يبقى بقول هذه ال sub group من من من ال
+
+227
+00:23:05,040 --> 00:23:09,240
+group الأصلية يبقى ال H sub group من ال group
+
+228
+00:23:09,240 --> 00:23:13,980
+الأصلية إذا كانت هي group تحت نفس العملية وبدل
+
+229
+00:23:13,980 --> 00:23:18,040
+مكتوب sub group من الأنفا ساعدا هكتب ال sub group
+
+230
+00:23:18,040 --> 00:23:23,220
+H is a sub group من جيه مش H أقل من أو يساوي جيه
+
+231
+00:23:23,580 --> 00:23:27,200
+هذا أقل من سوى للاعداد العادية بس هذا رمز عندنا
+
+232
+00:23:27,200 --> 00:23:31,860
+يدل طيلة الكتاب على ميم على ال subgroup بيبقى كلمة
+
+233
+00:23:31,860 --> 00:23:36,520
+subgroup بدي أختصرها إلى الرمز اللي عندنا هذا و
+
+234
+00:23:36,520 --> 00:23:42,590
+تقرأ subgroup اتش subgroup من G الـ H هذه يا شباب
+
+235
+00:23:42,590 --> 00:23:48,450
+ممكن تساوي جي وممكن ما تساويش الجي إذا الـ H هذه
+
+236
+00:23:48,450 --> 00:23:53,410
+ما سواتش الجي بنكتب H subgroup من جي وبنشيل
+
+237
+00:23:53,410 --> 00:23:55,210
+اليساوي اللي عندنا
+
+238
+00:23:57,730 --> 00:24:01,550
+الـ H في هذه الحالة بسميها proper subgroup يعني
+
+239
+00:24:01,550 --> 00:24:06,370
+انا لو أخدت subgroup و لاقيتها لا تساوي لجروب
+
+240
+00:24:06,370 --> 00:24:10,750
+الأصلية لأنه بناعرف احنا any set is a subset of
+
+241
+00:24:10,750 --> 00:24:16,730
+itself صحيح ولا لأ؟ هي مجموعة جزئية من نفسها طلعت
+
+242
+00:24:16,730 --> 00:24:21,750
+المجموعة هذه الجزئية أقل من نفسه الاتساوي الأصلية
+
+243
+00:24:21,750 --> 00:24:28,170
+يبقى في هذه الحالة بسميها proper subgroup طبعا طيب
+
+244
+00:24:28,170 --> 00:24:32,050
+طب لو كده تلاقيتش تساوي جيه طبعا تلاقيتش جد الجيه
+
+245
+00:24:32,050 --> 00:24:37,630
+بالضبط تماما يبقى بسميها بسميها improper subgroup
+
+246
+00:24:37,630 --> 00:24:42,670
+هذه اسمها improper بقوم بلغيها زي ما نقول إن هذا
+
+247
+00:24:42,670 --> 00:24:48,240
+possible ممكن ننفيها بنقول impossible غير ممكن يبقى
+
+248
+00:24:48,240 --> 00:24:55,380
+هذي ممكن احطها لك ملاحظة رقم تلاتة if ال H تساوي G
+
+249
+00:24:55,380 --> 00:25:09,380
+then ال H is called improper subgroup
+
+250
+00:25:09,380 --> 00:25:13,020
+يبقى 
+
+251
+00:25:13,020 --> 00:25:17,810
+هذه مسميها improper subgroup لو رحت أخدت ال
+
+252
+00:25:17,810 --> 00:25:23,630
+identity وحدها لحالها و حطيته داخل set يبقى السعر
+
+253
+00:25:23,630 --> 00:25:28,610
+عندي set لا يوجد فيها إلا ال identity element هل
+
+254
+00:25:28,610 --> 00:25:33,570
+هذه ال subgroup في الأول؟ subgroup ليش؟ لأن ال
+
+255
+00:25:33,570 --> 00:25:37,870
+identity موجود لو ضربت ال identity في نفسه بيطلع ال
+
+256
+00:25:37,870 --> 00:25:42,690
+identity موجود معكوس ال identity هو ال identity
+
+257
+00:25:42,690 --> 00:25:48,010
+نفسه إذا موجود يبقى هذا صارت subgroup إن حدث ذلك
+
+258
+00:25:48,010 --> 00:25:52,310
+يبقى بسميها هذا ال subgroup ال trivial subgroup
+
+259
+00:25:52,600 --> 00:25:58,140
+يعني المجموعة الجزئية البدية أو التافهة أبسط أنواع
+
+260
+00:25:58,140 --> 00:26:02,720
+ال subgroups يبقى هذه ال set عبارة عن subgroup من
+
+261
+00:26:02,720 --> 00:26:06,580
+من ال group الأصلي بسميها ال trivial subgroup
+
+262
+00:26:06,580 --> 00:26:11,220
+نسيبنا هذه وروح ناخد كل ال subgroups الباقية كلهم
+
+263
+00:26:11,220 --> 00:26:15,840
+بسميهم non trivial subgroups يبقى هنا and the
+
+264
+00:26:15,840 --> 00:26:19,160
+other subgroups are called the non trivial
+
+265
+00:26:19,160 --> 00:26:25,080
+subgroups of G يبقى صار  undeterminable subgroup, non
+
+266
+00:26:25,080 --> 00:26:28,360
+-determinable subgroup, proper subgroup, improper
+
+267
+00:26:28,360 --> 00:26:34,640
+subgroup, improper يبقى 
+
+268
+00:26:34,640 --> 00:26:39,260
+أقل من الأصلية بشوية طبعا جد ما يكون يكون إن شاء
+
+269
+00:26:39,260 --> 00:26:45,560
+الله يكون عنصرين طب خليني أسألك طب هذه بنفع أقول
+
+270
+00:26:45,560 --> 00:26:51,210
+عليها proper بنفع proper على كل خط بس لدرجة إنّها
+
+271
+00:26:51,210 --> 00:26:54,570
+مسمية trivial subgroup وبالتالي مقولش عليها proper
+
+272
+00:26:54,570 --> 00:26:59,710
+subgroup بدأ ناخذ بعض الأمثلة التوضيحية على ذلك
+
+273
+00:26:59,710 --> 00:27:09,730
+قبل أن ندخل إلى أول نظرية يبقى examples أول
+
+274
+00:27:09,730 --> 00:27:16,510
+مثل بيقول Z under
+
+275
+00:27:19,250 --> 00:27:28,150
+addition modulo n اللي هي توسعة رمز نالها بالرمز Z 
+
+276
+00:27:28,150 --> 00:27:36,250
+under وعليها عملية الجمع modulo n هذه ماالها is not a
+
+277
+00:27:36,250 --> 00:27:44,090
+subgroup of
+
+278
+00:27:44,090 --> 00:27:45,890
+Z
+
+279
+00:27:47,150 --> 00:27:53,850
+هو عليها عملية الجمع العادية هذه
+
+280
+00:27:53,850 --> 00:27:58,990
+مش subgroup طب Z n عناصرها zero واحد واثنين
+
+281
+00:27:58,990 --> 00:28:04,210
+وثلاثة لغاية n ناقص واحد زد هذه الموجب والسالب
+
+282
+00:28:04,210 --> 00:28:09,830
+والصفر يبقى Zn هي subset من من؟ subset من Z
+
+283
+00:28:09,830 --> 00:28:14,090
+بيتداعي هنا بيقول ماهياش subgroup حد بيقول لي ليش؟
+
+284
+00:28:14,090 --> 00:28:20,350
+أيوة أيوة اختلفت العملية حسب التعريف اللي كتبناه
+
+285
+00:28:20,350 --> 00:28:23,650
+لازم تبقى العملية على ال group الأصلية هي نفس
+
+286
+00:28:23,650 --> 00:28:28,390
+العملية على من؟ على ال subset يبقى هنا Z under
+
+287
+00:28:28,390 --> 00:28:38,730
+that is not a subgroup because the two operations
+
+288
+00:28:41,770 --> 00:28:50,570
+on Z under and الـ Z are different تختلف عن
+
+289
+00:28:50,570 --> 00:28:55,170
+التانية ولا واحدة فيهم زي التانية يبقى هذا نقض
+
+290
+00:28:55,170 --> 00:29:02,650
+التعريف لذلك هذا ماهياش subgroup خدلي مثال ثاني
+
+291
+00:29:02,650 --> 00:29:11,070
+خدلي الـ G هي عبارة عن Q و عليها عملية الجمع
+
+292
+00:29:11,910 --> 00:29:20,830
+and الـ H هي عبارة عن الـ Z و عليها عملية الجمع
+
+293
+00:29:20,830 --> 00:29:29,670
+السؤال هو هل هذه subset من هذه صحيح لأن any integer
+
+294
+00:29:29,670 --> 00:29:33,210
+is a rational number ال operation نفس ال
+
+295
+00:29:33,210 --> 00:29:40,450
+operation ال identity هنا مين؟ هنا نفس ال identity
+
+296
+00:29:40,450 --> 00:29:45,490
+element المعكوس لل element هنا a عبارة عن مين؟
+
+297
+00:29:45,490 --> 00:29:49,850
+سالب a، المعكوس لهنا، مثل نفس الشيء، إذا هذه
+
+298
+00:29:49,850 --> 00:29:56,110
+subgroup من مين؟ من هنا، يبقى let G and then ال H
+
+299
+00:29:56,110 --> 00:30:02,710
+is a subgroup من G على طول الخط، مافيش أي تناقض ما
+
+300
+00:30:02,710 --> 00:30:08,590
+بين الأثنين لا عملية ولا identity ولا معكوس طيب
+
+301
+00:30:08,590 --> 00:30:16,550
+السؤال الثالث لو أخدت ال Q plus تحت عملية الضرب
+
+302
+00:30:16,550 --> 00:30:27,810
+العادية and ال Q تحت عملية الجمع groups and all
+
+303
+00:30:29,450 --> 00:30:34,470
+group صحيح بس هل هذه subgroup من هذه أو العكس هل
+
+304
+00:30:34,470 --> 00:30:40,070
+هذه subgroup من هذه برضه لأ ليش لإنه ال operation
+
+305
+00:30:40,070 --> 00:30:47,050
+هنا ضرب وهناك جمع تختلف كليا and then
+
+306
+00:30:48,500 --> 00:30:56,320
+الـ Q plus تحت عملية الجمع is not a subgroup من
+
+307
+00:30:56,320 --> 00:31:07,900
+ال Q plus because السبب the two operations
+
+308
+00:31:07,900 --> 00:31:20,340
+العمليتين on ال Q and الـ Q plus are different ولا
+
+309
+00:31:20,340 --> 00:31:27,780
+واحدة فيهم زي التانية طيب نبدأ في أول نظرية أظن إن
+
+310
+00:31:27,780 --> 00:31:32,160
+كان كل مرة بدنا نقعد نفحص إن هذه ال subgroup
+
+311
+00:31:32,160 --> 00:31:37,240
+العملية نفس العملية قصتنا هذه طويلة لكن نحاول ناخد
+
+312
+00:31:37,240 --> 00:31:41,940
+نظرية بواسطتها نقدر نحكم على ال subset اللي أخدنا
+
+313
+00:31:41,940 --> 00:31:47,480
+منه هل هو subgroup أم لا بطريقة أسهل يبقى بإذن
+
+314
+00:31:47,480 --> 00:31:52,460
+الله نأتي لأول نظرية very important على ال
+
+315
+00:31:52,460 --> 00:32:02,300
+subgroup فالنظرية بتقول ما يأتي let الـ H بـ a non
+
+316
+00:32:02,300 --> 00:32:10,120
+empty subset of
+
+317
+00:32:10,120 --> 00:32:14,760
+a group G
+
+318
+00:32:20,070 --> 00:32:24,270
+الـ H is
+
+319
+00:32:24,270 --> 00:32:33,330
+a subgroup of G
+
+320
+00:32:33,330 --> 00:32:36,710
+إذا 
+
+321
+00:32:36,710 --> 00:32:43,970
+A B inverse belongs to H whenever
+
+322
+00:32:47,020 --> 00:32:54,920
+عندما ال A and ال B are in H
+
+323
+00:33:19,250 --> 00:33:26,150
+مرة ثانية أنا عندي group أخدت منها subset ال
+
+324
+00:33:26,150 --> 00:33:31,770
+subset هذا وقتش بقدر أقول عنه subgroup إذا تحقق
+
+325
+00:33:31,770 --> 00:33:37,630
+شرطين الشرط الأول إن ال H اللي أخدت هذا تبقى non
+
+326
+00:33:37,630 --> 00:33:43,290
+-empty subset of G الشرط الثاني لو أخدت عنصرين
+
+327
+00:33:43,290 --> 00:33:48,370
+موجودات في H بدي أكون حاصل ضرب الأول في معكوس
+
+328
+00:33:48,370 --> 00:33:53,370
+الثاني موجود في H إن حدث ذلك تبقى ال H هذه بقول
+
+329
+00:33:53,370 --> 00:33:58,870
+عليها subgroup تمام طب قبل ما أبرهن بدي أبرهن صحة
+
+330
+00:33:58,870 --> 00:34:03,590
+هذا الكلام مش حأحيل الله ال a b inverse هذه موجودة
+
+331
+00:34:03,590 --> 00:34:08,330
+في H لو كان شباب ال operation اللي على G عملية
+
+332
+00:34:08,330 --> 00:34:16,930
+الجمع هذا الشرط كيف بكتبه a ناقص b موجود في H
+
+333
+00:34:16,930 --> 00:34:27,950
+يبقى هنا هذه كملاحظة بس يبقى if the operation if
+
+334
+00:34:27,950 --> 00:34:28,990
+the operation
+
+335
+00:34:35,690 --> 00:34:50,090
+on G is addition then ال a b inverse belongs to H
+
+336
+00:34:50,090 --> 00:34:56,130
+is written is
+
+337
+00:34:56,130 --> 00:35:03,620
+written as a minus b كل هذا موجود في H كل ال
+
+338
+00:35:03,620 --> 00:35:10,880
+elements هذا موجود في ال proof مرة
+
+339
+00:35:10,880 --> 00:35:17,280
+ثانية بقول لو كان ال H هي ال non-empty subset of a
+
+340
+00:35:17,280 --> 00:35:22,300
+group G، هذه ال condition الأول، then ال H is a
+
+341
+00:35:22,300 --> 00:35:27,100
+subgroup of G if ال A, B inverse موجود في H
+
+342
+00:35:27,100 --> 00:35:32,540
+whenever A و B are in H يبقى حسب التعريف ال subset
+
+343
+00:35:32,540 --> 00:35:39,480
+اللي أخدت بتبقى subgroup لو بقيت group تحت نفس
+
+344
+00:35:39,480 --> 00:35:44,330
+العملية تعال نشوف هل هذا الكلام بيحقق خاصية ال
+
+345
+00:35:44,330 --> 00:35:48,530
+group تحت نفس العملية ولا لأ؟ الآن ال H هذه ال
+
+346
+00:35:48,530 --> 00:35:53,510
+subset من مين؟ من G و ال operation اللي على G
+
+347
+00:35:53,510 --> 00:35:58,490
+associative binary operation صح ولا لأ؟ يبقى هل
+
+348
+00:35:58,490 --> 00:36:02,390
+اختلفوا عناصر H؟ يعني صار على رأسهم ريشة لما
+
+349
+00:36:02,390 --> 00:36:06,910
+أخذناهم من G؟ لأ ما ينطبق على عناصر G ينطبق عليهم
+
+350
+00:36:07,270 --> 00:36:12,230
+إذا ال operation على H is associative binary
+
+351
+00:36:12,230 --> 00:36:17,330
+operation تمام ليش؟ لأن H هي ال subset من G يعني
+
+352
+00:36:17,330 --> 00:36:22,950
+ما ينطبق على عناصر G ينطبق تماما على عناصر من؟ على
+
+353
+00:36:22,950 --> 00:36:28,700
+عناصر H لكن هل ال identity هو نفسه؟ الله أعلم هل
+
+354
+00:36:28,700 --> 00:36:33,780
+معكوس العنصر اللي بده ياخده من H بده يكون في H
+
+355
+00:36:33,780 --> 00:36:39,280
+ولا برا الله أعلم هل لو أخدت عنصرين من H وضربتهم
+
+356
+00:36:39,280 --> 00:36:44,300
+في بعض بده يكون داخل H ولا لأ إن تحققت خواص
+
+357
+00:36:44,300 --> 00:36:48,080
+التلاتة دي بيصير هذه ال subgroup لو ما تحقق واحد
+
+358
+00:36:48,080 --> 00:36:52,360
+منهم يبقى برا بتبطل يصير subgroup يبقى هو حاطط ل
+
+359
+00:36:52,360 --> 00:36:57,660
+condition بدي أحاول أستفيد منه يبقى البرهان النقطة
+
+360
+00:36:57,660 --> 00:37:13,280
+الأولى الآن the operation on H is an associative
+
+361
+00:37:13,280 --> 00:37:15,480
+binary
+
+362
+00:37:25,220 --> 00:37:31,680
+بسبب إن ال H مالها subset من G
+
+363
+00:37:37,990 --> 00:37:41,710
+يبقى هذه ال associative binary operation متحققة
+
+364
+00:37:41,710 --> 00:37:46,890
+بالنسبة للخاصية الثانية الخاصية الثانية بتقول أنت
+
+365
+00:37:46,890 --> 00:37:51,670
+كل اللي عندي إن لو أخدت عنصرين من H بدي يكون حاصل
+
+366
+00:37:51,670 --> 00:38:00,090
+ضرب الأول فيه الثاني موجود في H صح ولا لا الآن let
+
+367
+00:38:00,090 --> 00:38:11,010
+ال A و ال B موجودة في ال H then ال A B inverse موجود
+
+368
+00:38:11,010 --> 00:38:19,350
+في ال H هذا in general هذا مقطع من نص النظرية طب
+
+369
+00:38:19,350 --> 00:38:26,240
+إيش رأيك؟ بنفع آخد A تساوي B؟ بنفع ولا ما بنفعش؟ هذا
+
+370
+00:38:26,240 --> 00:38:33,520
+ينفع لجميع العناصر إن A ممنوع يساوي B فيه أنا
+
+371
+00:38:33,520 --> 00:38:36,180
+ممكن آخد أي عناصر إذا أنا ممكن آخد أي عناصر إذا
+
+372
+00:38:36,180 --> 00:38:36,320
+أنا ممكن آخد أي عناصر إذا أنا ممكن آخد أي عناصر
+
+373
+00:38:36,320 --> 00:38:38,200
+إذا أنا ممكن آخد أي عناصر إذا أنا ممكن آخد
+
+374
+00:38:38,200 --> 00:38:38,540
+عناصر إذا أنا ممكن آخد أي عناصر إذا أنا ممكن 
+
+375
+00:38:38,540 --> 00:38:41,580
+أي عناصر إذا أنا ممكن آخد أي عناصر إذا أنا ممكن 
+
+376
+00:38:41,580 --> 00:38:43,340
+أخذ أي أنصار إذا أنا ممكن أخذ أي أنصار إذا أنا
+
+377
+00:38:43,340 --> 00:38:48,420
+ممكن أخذ أي أنصار إذا أنا ممكن أخذ أي أنصار إذا
+
+378
+00:38:48,420 --> 00:38:51,660
+أنا ممكن أخذ أي أنصار 
+
+379
+00:38:53,490 --> 00:38:59,210
+الـ A B Inverse بدي أساوي ال X في ال X Inverse
+
+380
+00:38:59,210 --> 00:39:00,290
+موجودة في H
+
+381
+00:39:08,810 --> 00:39:15,790
+هذا يعني أن الـ E موجود في الـ H يبقى الـ H فيها 
+
+382
+00:39:15,790 --> 00:39:20,070
+الـ identity element تبع من؟ تبع الـ group الأصلي
+
+383
+00:39:20,070 --> 00:39:23,490
+صار الـ identity في الـ group الأصلي اللي هو E
+
+384
+00:39:23,490 --> 00:39:29,310
+نفسه هو هو موجود في من؟ في ال subset اللي هي H حتى
+
+385
+00:39:29,310 --> 00:39:33,610
+لما أقول subset ما أقول subgroup موجود هو هو يبقى
+
+386
+00:39:33,610 --> 00:39:38,110
+ال X X inverse هذا موجود في G و هذا موجود في G إذا
+
+387
+00:39:38,110 --> 00:39:42,410
+ال element هذا صار موجود في H لأنه حصل ضربه ما
+
+388
+00:39:42,410 --> 00:39:46,450
+موجود في H ال identity هذا هو تبع G الأصلية
+
+389
+00:39:46,450 --> 00:39:55,470
+ما غيرتها طيب بدنا نيجي لل condition الثالث F
+
+390
+00:40:06,200 --> 00:40:12,120
+معكوس العنصر هذا موجود لأنه في G بس موجود في H
+
+391
+00:40:12,120 --> 00:40:17,980
+والله برة H أنا مش عارف أنا بدي أثبت أن معكوس هذا
+
+392
+00:40:17,980 --> 00:40:20,640
+العنصر موجود في H
+
+393
+00:40:24,680 --> 00:40:30,080
+الآن إيه شفنا هنا يا شباب أن ال E موجود في H بدي
+
+394
+00:40:30,080 --> 00:40:38,180
+أخذ هذا ال E هو A و ال B inverse يبقى هنا A في ال
+
+395
+00:40:38,180 --> 00:40:45,760
+B inverse موجود في H implies بدي أخدي ال A في ال B
+
+396
+00:40:45,760 --> 00:40:50,140
+inverse بدي أكون موجود في H صح ولا لا طبق لل
+
+397
+00:40:50,140 --> 00:40:56,510
+condition اللي عندي كويس يبقى هذا إيش معناه أن ال P
+
+398
+00:40:56,510 --> 00:41:01,430
+inverse موجود في H هل ال P اللي أخدته في H عليه
+
+399
+00:41:01,430 --> 00:41:06,250
+قيود والله أي عنصر موجود في H أي عنصر موجود في H
+
+400
+00:41:06,250 --> 00:41:11,650
+يبقى أي عنصر موجود في H اللي جات المعكوث تبعه 
+
+401
+00:41:11,650 --> 00:41:16,650
+موجود وين؟ موجود في H يبقى ضايق لنا بس النقطة
+
+402
+00:41:16,650 --> 00:41:17,490
+الأخيرة
+
+403
+00:41:20,560 --> 00:41:26,300
+إن لو أخدت عنصرين من H بدي أثبت أن حاصل ضربهما 
+
+404
+00:41:26,300 --> 00:41:32,500
+موجود في H بس هاي كل اللي بدي إياها إن تم ذلك بصير
+
+405
+00:41:32,500 --> 00:41:37,200
+عندنا هذا الـ H is a subgroup وبصير نستخدم هذه
+
+406
+00:41:37,200 --> 00:41:41,120
+النظرية في الحكم على ال subsets المختلفة هل هي
+
+407
+00:41:41,120 --> 00:41:47,860
+subgroup أم لا أنا بدي أخذ عنصرين موجودات في H و
+
+408
+00:41:47,860 --> 00:41:56,060
+بدي أثبت أن حاصل ضربه موجود في H يبقى هنا F A و B
+
+409
+00:41:56,060 --> 00:42:01,580
+موجودات في H let
+
+410
+00:42:01,580 --> 00:42:12,480
+A تساوي X و B تساوي Y inverse مثلا واخذ الـ P يبدو
+
+411
+00:42:12,480 --> 00:42:19,040
+يساوي Y inverse then إيش 
+
+412
+00:42:19,040 --> 00:42:22,120
+رأيك لو أخدت ال X في Y؟
+
+413
+00:42:24,710 --> 00:42:30,250
+الـ X في Y أشوف إيش بيساوي هنا X وهنا B تساوي Y
+
+414
+00:42:30,250 --> 00:42:36,510
+inverse يعني ال Y هذه موجودة في G موجودة في G بدي
+
+415
+00:42:36,510 --> 00:42:44,550
+أخذ ال X في Y مين ال X؟ أو ملاش يساوي X في ال Y
+
+416
+00:42:44,550 --> 00:42:50,850
+بقدر أكتبها Y inverse inverse مظبوط؟
+
+417
+00:42:51,360 --> 00:42:57,100
+هذا الكلام يستوي ال X أنا أفرضها بقداش؟ ب A وال Y
+
+418
+00:42:57,100 --> 00:42:59,600
+inverse ب مين؟ ب B
+
+419
+00:43:03,070 --> 00:43:09,370
+يبقى هذا موجود في h طبقا لل condition يعني حاصل
+
+420
+00:43:09,370 --> 00:43:14,930
+ضرب any two elements موجودة وين؟ في h يبقى هذا
+
+421
+00:43:14,930 --> 00:43:21,650
+بيعطينا أن x و y موجود في h for all x و y اللي
+
+422
+00:43:21,650 --> 00:43:27,000
+موجودة وين؟ موجودة في H يعني ال H is closed under
+
+423
+00:43:27,000 --> 00:43:31,020
+multiplication يبقى تحققت أو هذه اللي كنا نسميها
+
+424
+00:43:31,020 --> 00:43:35,700
+binary operation أنه تاخد two elements أثر واحد
+
+425
+00:43:35,700 --> 00:43:39,120
+على التاني يعطيك عنصر جديد هذا العنصر موجود في من؟
+
+426
+00:43:39,120 --> 00:43:45,920
+في H يبقى بناء عليه بروح بقوله thus وهكذا ال H is
+
+427
+00:43:45,920 --> 00:43:51,740
+a subgroup من G وبالتالي برهن النظرية اللي موجودة
+
+428
+00:43:51,740 --> 00:43:57,960
+عندنا من الأنفة الصاعدة يا شباب لو أعطاني group
+
+429
+00:43:57,960 --> 00:44:03,280
+وأعطاني set من ال group وقال يثبت لي أن ال set هذه
+
+430
+00:44:03,280 --> 00:44:10,210
+is a sub group بدي أعمله خطوتين لثلاثة لهما الخطوة
+
+431
+00:44:10,210 --> 00:44:18,790
+الأولى هي أن أثبت له أن الـH هي non-empty يبقى هذه
+
+432
+00:44:18,790 --> 00:44:23,830
+فيها عناصر ولو تثبت أن فيها عنصر واحد يكفي منك 
+
+433
+00:44:23,830 --> 00:44:26,870
+الله يعطيك العفو بس أثبت أن فيها عنصر واحد يبقى
+
+434
+00:44:26,870 --> 00:44:30,030
+non-empty خلصنا من ال condition الأولى الـ
+
+435
+00:44:30,030 --> 00:44:34,830
+condition الثاني لو رحت أخذت أي two elements في
+
+436
+00:44:34,830 --> 00:44:40,430
+هذه ال subset وقدرت تثبت أن الأول في معكوس الثاني
+
+437
+00:44:40,430 --> 00:44:45,510
+موجود في h double h subgroup خلصنا يبقى من الآن
+
+438
+00:44:45,510 --> 00:44:52,670
+فصاعدا لو أخذ subset من group G ال subset هذا بدي
+
+439
+00:44:52,670 --> 00:44:58,510
+أثبت أنه subgroup معطوب منك تثبت شرطين إذا أثبتهم
+
+440
+00:44:58,510 --> 00:45:04,210
+صحيح بيصير هذا subgroup كيف؟ يعني بيكتثبت أولا أن 
+
+441
+00:45:04,210 --> 00:45:08,970
+ال subset اللي أخدتها non-empty على الأقل يجب أن
+
+442
+00:45:08,970 --> 00:45:14,270
+تظهر أن هناك عنصر موجود في هذه الـ subset اثنين لو
+
+443
+00:45:14,270 --> 00:45:17,250
+أخذت أي أحد من الـ two elements في هذا الـ subset
+
+444
+00:45:17,250 --> 00:45:21,350
+يجب أن تثبت أنه حصل ضرب الأول في معكوس الثاني
+
+445
+00:45:21,350 --> 00:45:25,330
+موجود فيه إذا أثبتت ذلك يبقى هذا سيصبح معناه
+
+446
+00:45:25,330 --> 00:45:31,070
+subgroup يعني شغلنا بعد ذلك في الأمثلة يجب أن
+
+447
+00:45:31,070 --> 00:45:35,030
+يعطيني group يعطيني ال subset من هنا يقول يثبت أن
+
+448
+00:45:35,030 --> 00:45:38,940
+هذه subgroup أو ما هيش السابقروب يعني ما قلت ماهياش 
+
+449
+00:45:38,940 --> 00:45:43,180
+ساب قروب بدك تجيب له counter example قلت له group
+
+450
+00:45:43,180 --> 00:45:47,800
+بدك تروح إيش اتبرهنها والله بنفع أجيب example بس 
+
+451
+00:45:47,800 --> 00:45:50,920
+كده عدد يثبت أن هي group .. أن هي سابقروب بالفعل
+
+452
+00:45:50,920 --> 00:45:54,460
+بنفعش لكن counter example اه بيثبت أنه ماهيش
+
+453
+00:45:54,460 --> 00:46:00,180
+ساب قروب بس ديك لازم اتبرهنها برهانة طيب الآن ما ضلش
+
+454
+00:46:00,180 --> 00:46:04,780
+وقت الحقيقة كان أخذنا الآن بعض الأمثلة
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7992e843c642346d7d6a4e15579f6b17f833c3dc
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/tRJru8L1_5w_postprocess.srt
@@ -0,0 +1,1816 @@
+1
+00:00:20,990 --> 00:00:24,830
+بسم الله الرحمن الرحيم نرجع لمحاضرة ابتدناها في
+
+2
+00:00:24,830 --> 00:00:29,010
+الفترة الصباحية و هو أنه بدأنا في chapter 3 اللي
+
+3
+00:00:29,010 --> 00:00:38,030
+بتحدث عن ال subgroups طبعا أعطينا تعريف لل order
+
+4
+00:00:38,030 --> 00:00:42,370
+لل group و order لل element اللي موجود داخل ال
+
+5
+00:00:42,370 --> 00:00:46,120
+groupوعرفنا ان ال order لل group هو عدد العناصر في
+
+6
+00:00:46,120 --> 00:00:49,900
+ال group و ال order لل element هو أصغر عدد صحيح
+
+7
+00:00:49,900 --> 00:00:53,000
+موجب أحط ال cos لل element بيعطينا main ال
+
+8
+00:00:53,000 --> 00:00:56,980
+identity element و أخدنا على ذلك مثالا واحدة وهي
+
+9
+00:00:56,980 --> 00:01:02,020
+قدامنا المثالة رقم اتنين يبقى لو أخدت g هي ال z
+
+10
+00:01:02,020 --> 00:01:06,900
+تمانية لما أحط زائد في دائرة صغيرة ليست عملية
+
+11
+00:01:06,900 --> 00:01:11,140
+الضرب العاديةلو كان عملية الضرب العادية بحط زائد
+
+12
+00:01:11,140 --> 00:01:15,200
+بدون دائرة حول الناس يبقى هذا المقصود ان الجامعه
+
+13
+00:01:15,200 --> 00:01:20,720
+modulo 8 هي المقصود العملية هذه يبقى زاده في دائرة
+
+14
+00:01:20,720 --> 00:01:25,000
+حسب الرقم اللي عندى بكون هذا modulo هذا main هذا
+
+15
+00:01:25,000 --> 00:01:29,780
+الرقميعني زد تمانية وعليها عملية الجمع مدينة
+
+16
+00:01:29,780 --> 00:01:34,620
+تمانية عناصرها من صفر لغاية سبعة يبقى بناء عليه ال
+
+17
+00:01:34,620 --> 00:01:39,240
+order اللي جيه كده شو ساوي تمانية فيها تمان عناصر
+
+18
+00:01:39,240 --> 00:01:45,900
+الصفر من ضمنهم يبقى then ال order اللي جيه بده
+
+19
+00:01:45,900 --> 00:01:51,990
+يساوي تمانيةزيرو هو ال identity element لما نضيف
+
+20
+00:01:51,990 --> 00:01:55,250
+زيرو لأي element مديره تمانية بيبقى نفس ال element
+
+21
+00:01:55,250 --> 00:02:00,450
+يبقى zero هو ال identity element الان لو بد ال
+
+22
+00:02:00,450 --> 00:02:09,890
+order مثلا للواحد كده ال order للواحدتحت عملية
+
+23
+00:02:09,890 --> 00:02:15,230
+الجمعة يعني واحد تربيع يعني واحد زائد واحد موديله
+
+24
+00:02:15,230 --> 00:02:20,030
+تمانى له جداش اتنين زائد واحد زائد واحد يعني جداش
+
+25
+00:02:20,030 --> 00:02:27,870
+ال order ايه له تلاتة سبعة ودي يطلع ال zero ها ال
+
+26
+00:02:27,870 --> 00:02:32,210
+zero هو ال identity تمانية طيب يجي ال order للواحد
+
+27
+00:02:32,210 --> 00:02:36,950
+بده يساوي تمانية طيب ال order ليه تلاتة
+
+28
+00:02:40,210 --> 00:02:47,450
+تلاتة تلاتة و تلاتة ستة و تلاتة تسعة و تلاتة اتناش
+
+29
+00:02:47,450 --> 00:02:54,390
+و تلاتة خمستاش و تلاتة تمانتاش و تلاتة واحد و
+
+30
+00:02:54,390 --> 00:03:00,190
+عشرين و تلاتة يبقى هذا ال zero يبقى كدهش تمانية
+
+31
+00:03:00,190 --> 00:03:07,910
+كذلك يبقى هذا هو ال order كمان لتلاتة طيب أليس هو
+
+32
+00:03:07,910 --> 00:03:09,710
+ال order كمان لخمسة
+
+33
+00:03:12,610 --> 00:03:19,170
+خمسة وخمسة عشر هبقى اتنين وكمان خمسة سبعة وكمان
+
+34
+00:03:19,170 --> 00:03:25,210
+خمسة بصير اتناشر وكمان خمسة سبعة طيب هتلاقي كمان
+
+35
+00:03:25,210 --> 00:03:30,750
+تمانية و ال order ليه سبعة كمان هو تمانية يبقى هذا
+
+36
+00:03:30,750 --> 00:03:35,790
+يساوي كمان ال order ليه سبعة كل هذا الكلام بده
+
+37
+00:03:35,790 --> 00:03:41,790
+يساوي قداش تمانية طب لو جيت ال order لل zero قداش
+
+38
+00:03:41,790 --> 00:03:47,230
+يا شبابواحد لأن هو ال identity element طب ال order
+
+39
+00:03:47,230 --> 00:03:53,070
+للي اتنين اتنين
+
+40
+00:03:53,070 --> 00:03:57,230
+زيدي اتنين زيدي اتنين زيدي اتنين ب zero يبقى اربعة
+
+41
+00:03:57,230 --> 00:04:02,250
+يبقى ال order ل اتنين بده يساوي اربعة طيب لو بده
+
+42
+00:04:02,250 --> 00:04:08,130
+يقولك ال order ل الأربعة اتنين طب ال order لستة
+
+43
+00:04:12,200 --> 00:04:16,980
+أربعة بالضبط صحيح ستة و ستة اتناش كمان ستة تمانتاش
+
+44
+00:04:16,980 --> 00:04:20,920
+كمان ستة اربع عشرين اللي هو تلف تمانية يبقى هذا
+
+45
+00:04:20,920 --> 00:04:26,200
+بده يساوي الأربعة يبقى بناء عليه جيبنا ال order لل
+
+46
+00:04:26,200 --> 00:04:30,950
+group G اللي هو تمانيةوجبنا ال order لكل element
+
+47
+00:04:30,950 --> 00:04:34,090
+موجود في ال group ال order لل identity element هو
+
+48
+00:04:34,090 --> 00:04:39,530
+بواحد صحيح الباقي بعضهم يساوي تمانية وبعضهم يساوي
+
+49
+00:04:39,530 --> 00:04:42,950
+اتنين زي ما طلع لنا الأربعة و الباقي ال order لهم
+
+50
+00:04:42,950 --> 00:04:48,010
+يساوي كده؟ أربعة طيب خليني أسأل سؤال كامشي ايش
+
+51
+00:04:48,010 --> 00:04:51,670
+بتلاحظوا عن ال order تبع ال element و ال order تبع
+
+52
+00:04:51,670 --> 00:04:54,870
+ال group؟ في علاقة بينهم؟
+
+53
+00:04:58,210 --> 00:05:04,790
+معلومة تانية مضاعفة ال order لل element دائما لو
+
+54
+00:05:04,790 --> 00:05:10,270
+أبدا بيكسب ال order لل group كله ال group finite
+
+55
+00:05:10,270 --> 00:05:14,830
+إذا ال order لل elementهتلاقي السؤال هذا بس قدامي
+
+56
+00:05:14,830 --> 00:05:18,510
+شوية مش الحين كويس يبقى ال order للإيمين دائما و
+
+57
+00:05:18,510 --> 00:05:22,850
+أبدا بيجسم ال order لل group وكمان هتلاقي كمان ان
+
+58
+00:05:22,850 --> 00:05:27,290
+ال order لل sub group بيجسم ال order لل group بس
+
+59
+00:05:27,290 --> 00:05:31,730
+لقدامي شوية بس معلومة هيك على الله مش هادر طيب نجي
+
+60
+00:05:31,730 --> 00:05:38,430
+ناخد كمان مثال تلاتة يبقى مثال تلاتة يقول خدلي
+
+61
+00:05:38,430 --> 00:05:47,320
+الأن the groupاللي هو the group R star من ال R
+
+62
+00:05:47,320 --> 00:05:52,460
+star هي عبارة عن ال R بدي أشيل منها ال zero و بدي
+
+63
+00:05:52,460 --> 00:05:58,940
+أخد عليها عملية الضرب قداش ال order هذه اللي هي يا
+
+64
+00:05:58,940 --> 00:06:09,360
+شباب تمام يبقى هذه is of infinite order
+
+65
+00:06:11,050 --> 00:06:16,010
+هذا الـ order لها سيكون كمية ما لا نهاية السؤال هو
+
+66
+00:06:16,010 --> 00:06:21,690
+إذا أخذت أي عنصر فيها مثل 2 مثل 3 مثل نص مثل قمس
+
+67
+00:06:21,690 --> 00:06:26,730
+مثل سدس مثل جذر تلاتة مثلا كمية ال order لهذه
+
+68
+00:06:26,730 --> 00:06:36,630
+العناص؟ هل يعرف؟ ال order مثلا لإتنين هل أجد رقم
+
+69
+00:06:36,630 --> 00:06:40,610
+أضعه كأس لإتنين يظهر ال identity اللي هو واحد؟
+
+70
+00:06:48,260 --> 00:06:55,360
+is of infinite order يعني إذا ما لقيتش رقم أحطه
+
+71
+00:06:55,360 --> 00:06:59,760
+كأس لهذا العدد يطلع ال identity element يبقى في
+
+72
+00:06:59,760 --> 00:07:04,420
+هذه الحالة order لهذا ال element يساوي infinite
+
+73
+00:07:04,420 --> 00:07:10,750
+طيب السؤال هوالزيرو مافيش سيبلي الواحد والسالب
+
+74
+00:07:10,750 --> 00:07:16,850
+واحد امسك بعد الواحد وقبل السالب واحد وما بين
+
+75
+00:07:16,850 --> 00:07:20,830
+الزيرو والواحد وما بين الزيرو والسالب واحد خدلي اي
+
+76
+00:07:20,830 --> 00:07:25,690
+رقم عمرك بتلاقي عدد ان تحطه كأسئلة ويطلع الواحد
+
+77
+00:07:25,690 --> 00:07:31,740
+الصحيحأي رقم ينجز صحيح كثري ايراشيونال ايراشيونال
+
+78
+00:07:31,740 --> 00:07:35,720
+بدكية تربيتك اي بوس خمسة واس عشرة واس مانيا اوس
+
+79
+00:07:35,720 --> 00:07:41,180
+مليون كذا الاخرى عمره بطلع واحد صحيح ساكتيه
+
+80
+00:07:41,180 --> 00:07:46,940
+الولادة خد اي رقم وربع شوفه بزيد ولا بينجس مثل
+
+81
+00:07:46,940 --> 00:07:51,220
+افترض انه عدد صحيح زي ما قلتلك اتنين بقدر الاقي
+
+82
+00:07:51,220 --> 00:07:54,820
+اوس ان عدد صحيح احطه له يطلع ال identity اللي هو
+
+83
+00:07:54,820 --> 00:07:59,070
+واحد صحيحيعني بقدر اتنين اضربها في نفسه ان من
+
+84
+00:07:59,070 --> 00:08:03,290
+المرات يطلع واحد صحيح عمره شو بيحصل يبقى اتنين of
+
+85
+00:08:03,290 --> 00:08:05,570
+of of of of of of of of of of of of of of of of of
+
+86
+00:08:05,570 --> 00:08:07,050
+of of of of of of of of of of of of of of of of of
+
+87
+00:08:07,050 --> 00:08:07,130
+of of of of of of of of of of of of of of of of of
+
+88
+00:08:07,130 --> 00:08:07,490
+of of of of of of of of of of of of of of of of of
+
+89
+00:08:07,490 --> 00:08:07,610
+of of of of of of of of of of of of of of of of of
+
+90
+00:08:07,610 --> 00:08:08,110
+of of of of of of of of of of of of of of of of of
+
+91
+00:08:08,110 --> 00:08:08,130
+of of of of of of of of of of of of of of of of of
+
+92
+00:08:08,130 --> 00:08:15,390
+of
+
+93
+00:08:15,390 --> 00:08:15,850
+of of of
+
+94
+00:08:24,530 --> 00:08:30,170
+ألاقي اشي بالكسور هذه are of infinite order مين
+
+95
+00:08:30,170 --> 00:08:33,750
+ضايق اللي عندى؟ الواحد والسالب الواحد all order
+
+96
+00:08:33,750 --> 00:08:37,290
+وقداش واحد لأن هو ال identity element طب والسالب
+
+97
+00:08:37,290 --> 00:08:42,450
+واحد اتنين اتنين في شغلنا هدول اتنين فقط في ال
+
+98
+00:08:42,450 --> 00:08:48,130
+group هذه هم لل order انهم finite اما ما خل ذلك كل
+
+99
+00:08:48,130 --> 00:08:51,630
+ال elements اللي باقي ال order انهم is infinite
+
+100
+00:08:51,630 --> 00:08:56,090
+تمام؟وأحد يقول لي طب هذا متناقض مع كلمة اللي تو
+
+101
+00:08:56,090 --> 00:08:59,830
+ايش كلمة اللي تو انا قلت ال order لل element بيقسم
+
+102
+00:08:59,830 --> 00:09:05,010
+ال order للي group بشرط ان ال group تبقى finite
+
+103
+00:09:05,010 --> 00:09:09,930
+order مش infinite هذا ال order يتقدش infinity ل
+
+104
+00:09:09,930 --> 00:09:20,000
+group تمام يبقى باجي بقوله الواحد andالواحد and
+
+105
+00:09:20,000 --> 00:09:28,680
+الواحد and سلب واحد are of finite order
+
+106
+00:09:34,140 --> 00:09:39,760
+الـ order للواحد يساوي الواحد and ال order لسالب
+
+107
+00:09:39,760 --> 00:09:43,660
+واحد يساوي اتنين لأن السالب واحد تربيه تاني و
+
+108
+00:09:43,660 --> 00:09:46,480
+السالب واحد يسالي واحد اللي هو بال identity بواحد
+
+109
+00:09:46,480 --> 00:09:50,180
+يبقى ال order اللي يساوي اتنين يبقى باروح بقوله
+
+110
+00:09:50,180 --> 00:09:57,280
+the other elements of
+
+111
+00:09:58,740 --> 00:10:07,860
+R star are of infinite order
+
+112
+00:10:07,860 --> 00:10:12,120
+يبقى هذول ال order اللي بقى ال element كله ب
+
+113
+00:10:12,120 --> 00:10:19,360
+infinite خدلي هذا المثال وتعالى نشوف اللي هو ايش
+
+114
+00:10:19,360 --> 00:10:23,300
+الموضوع بالظبط الان مثالة رقم أربعة
+
+115
+00:10:27,260 --> 00:10:31,240
+الآن لو أخدت ال order لل general linear group of
+
+116
+00:10:31,240 --> 00:10:34,220
+two by two matrices over R
+
+117
+00:10:40,910 --> 00:10:46,670
+أكم مصفوفة عندى بيطلع محددهم لا يساوي zero نظامهم
+
+118
+00:10:46,670 --> 00:10:51,850
+اتنين في اتنين كدهش infinity كده ما بدك تاخد
+
+119
+00:10:51,850 --> 00:10:56,690
+مصفوفة تغير الأرقام زى ما بدك لإن الأرقام عددهما
+
+120
+00:10:56,690 --> 00:11:01,270
+لنهاية set of real number بقدر أخلي الأربع أرقام
+
+121
+00:11:01,270 --> 00:11:05,360
+زى بعضها وشوف أكم مصفوفة يطلع كيف لما أغيرهميبقى
+
+122
+00:11:05,360 --> 00:11:09,560
+infinity يبقى ال order لهذه اللي هو بده يساوي
+
+123
+00:11:09,560 --> 00:11:15,100
+infinity طب بتاخد فيها بعض ال elements وشوف قداش
+
+124
+00:11:15,100 --> 00:11:22,320
+ال order لهم يبقى هذا ال order infinity but ال
+
+125
+00:11:22,320 --> 00:11:29,440
+a تساوي اللي هو zero واحد و سالب واحد و سالب واحد
+
+126
+00:11:29,440 --> 00:11:42,080
+andوالتانية هي الـ main المصوفة بي تساوي بي تساوي
+
+127
+00:11:42,080 --> 00:11:48,840
+الـ zero والسالب واحد واحد و zero هذه موجودة في
+
+128
+00:11:48,840 --> 00:11:51,380
+الـ general group
+
+129
+00:11:54,820 --> 00:12:00,480
+ليش موجودة؟ لأن محددها لا يساوي Zero Zero زائد
+
+130
+00:12:00,480 --> 00:12:05,080
+واحد بيطلع واحد موجودة فيها هذه Zero زائد واحد
+
+131
+00:12:05,080 --> 00:12:08,560
+بيطلع واحد يبقى موجودة فيها يبقى اتنين موجودات في
+
+132
+00:12:08,560 --> 00:12:11,080
+ال general linear group of two by two matrices
+
+133
+00:12:11,080 --> 00:12:16,540
+over R بدي أدور على ال order تبع ال A يبقى بدي
+
+134
+00:12:16,540 --> 00:12:22,430
+أروح أقوله ال A تربيعيبقى الـ A تربيع الـ 0 1 سالب
+
+135
+00:12:22,430 --> 00:12:28,050
+واحد سالب واحد 0 1 سالب واحد سالب واحد و يسوى
+
+136
+00:12:37,780 --> 00:12:43,100
+الصف الأول في العمود الثاني هو zero وبطلع هنا كمان
+
+137
+00:12:43,100 --> 00:12:47,620
+سالب واحد طب الصف الثاني في العمود الأول بطلع واحد
+
+138
+00:12:47,620 --> 00:12:53,060
+الصف الثاني في العمود الثاني سالب واحد وهنا زائد
+
+139
+00:12:53,060 --> 00:12:57,680
+واحد بطلع كم؟ بطلع zero لا يسوى ال identity
+
+140
+00:12:57,680 --> 00:13:03,560
+element طيب إيش رأيك لو روحت ضربت كمان في ايه بصير
+
+141
+00:13:03,560 --> 00:13:09,390
+عندي كم؟ اتكيبطيب لو جيت قولت هذا بده يعطينا انه
+
+142
+00:13:09,390 --> 00:13:15,810
+ايه تكييب بده يساوي اللي هو من Zero و واحد و سالب
+
+143
+00:13:15,810 --> 00:13:22,370
+واحد و سالب واحد في سالب واحد سالب واحد واحد Zero
+
+144
+00:13:22,370 --> 00:13:27,650
+و يساوي الصف الأول في العمود الأول يبقى Zero و هنا
+
+145
+00:13:27,650 --> 00:13:35,060
+واحد هنا Zero و هنا Zero اللي هو ب Zero تمامهنا هي
+
+146
+00:13:35,060 --> 00:13:40,080
+واحد وهنا سالب واحد يبقى zero الصف هذا في هذا
+
+147
+00:13:40,080 --> 00:13:45,820
+بيطلع واحد وهنا واحد فقط لا غير يبقى ال order
+
+148
+00:13:45,820 --> 00:13:50,980
+لإيه؟ تلاتة لإن هذه ال identity matrix يبقى
+
+149
+00:13:50,980 --> 00:13:59,970
+similarlyبنفس الطريقة similarly ال
+
+150
+00:13:59,970 --> 00:14:07,070
+b square يساوي ال b square يبقى بدأ اضرب zero سالب
+
+151
+00:14:07,070 --> 00:14:14,310
+واحد واحد zero في zero سالب واحد واحد zero ويساوي
+
+152
+00:14:14,310 --> 00:14:18,330
+الصف الأول في العامل الأول zero سالب واحد بسالب
+
+153
+00:14:18,330 --> 00:14:25,950
+واحدزيرو وزيرو أب زيرو صف التاني زيرو وزيرو أب
+
+154
+00:14:25,950 --> 00:14:31,750
+زيرو و هنا سالب واحد شكلنا ماطلعش ال identity
+
+155
+00:14:31,750 --> 00:14:38,650
+element لكن الشافوي طلعلي هذه لو ضربت في نفسي مين
+
+156
+00:14:38,650 --> 00:14:45,770
+بطلع مين تتوقع يطلعالـ Identity Matrix على طول
+
+157
+00:14:45,770 --> 00:14:52,350
+الخط يبقى لو روحت جبت ال بي أس أربع اوتوماتيك
+
+158
+00:14:52,350 --> 00:14:57,800
+هيطلع واحد زيرو زيرو واحدبناء ان عليه هذا بدي
+
+159
+00:14:57,800 --> 00:15:04,520
+يقولك ان ال order ل a بدي ساوي تلاتة and ال order
+
+160
+00:15:04,520 --> 00:15:10,160
+ل b بدي ساوي كده اربعة طيب ايش رايك لو ضربت
+
+161
+00:15:10,160 --> 00:15:14,420
+التنتين في بعض و بدي اشوف ال order ايه الشطعة تبعه
+
+162
+00:15:14,420 --> 00:15:21,790
+الا لو اخدتاللي هو ال A في B يساوي وين ال A اللي
+
+163
+00:15:21,790 --> 00:15:27,270
+عندنا هذا ال A اللي هي Zero واحد سالب واحد سالب
+
+164
+00:15:27,270 --> 00:15:32,710
+واحد في B اللي هي Zero سالب واحد واحد Zero بده
+
+165
+00:15:32,710 --> 00:15:37,280
+يشوف كده يصنعالصف الأول في العمود الأول بيطلع
+
+166
+00:15:37,280 --> 00:15:44,580
+بواحد الصف الأول في العمود الثاني بيطلع zero الصف
+
+167
+00:15:44,580 --> 00:15:49,700
+الثاني في العمود الأول بيطلع سالب واحد الصف الثاني
+
+168
+00:15:49,700 --> 00:15:55,380
+في العمود الثاني بيطلع له كمان قداش اللي هو واحد
+
+169
+00:15:55,380 --> 00:16:00,680
+بالشكل اللي عندنا هذا ال a في bالأن لو ال a في b
+
+170
+00:16:00,680 --> 00:16:06,260
+تضربها في نفسها مائة مرة لا يمكن يطلع ال identity
+
+171
+00:16:06,260 --> 00:16:13,120
+مثال و ذلك لو روحت أخدت ال a بي الكل ترميةيبقى
+
+172
+00:16:13,120 --> 00:16:22,360
+واحد زيرو سالب واحد واحد هذا الكلام يساوي في واحد
+
+173
+00:16:22,360 --> 00:16:27,620
+زيرو سالب واحد واحد ويساوي الصف الأول في العمود
+
+174
+00:16:27,620 --> 00:16:33,860
+الأول بواحد الصف الأول في العمود الثاني بزيرو الصف
+
+175
+00:16:33,860 --> 00:16:38,960
+الثاني في العمود الأول بسالب اتنين الصف الثاني في
+
+176
+00:16:38,960 --> 00:16:43,650
+العمود الثاني بواحدأيش اللى تغير عن حصل الضرب
+
+177
+00:16:43,650 --> 00:16:49,630
+المصوفة الأصلية ؟ ثلاثة عناصر هدول هما يتغيرون بس
+
+178
+00:16:49,630 --> 00:16:55,150
+السالب واحد صار باتنين يبقى بناء عليه لو جيت قلتلك
+
+179
+00:16:55,150 --> 00:17:01,630
+يبقى ال a b to the power nأيش بيتقولي واحد زير و
+
+180
+00:17:01,630 --> 00:17:09,010
+واحد و هنا كده؟ سالب M طيب بتقدر تلاقي رقم تحطه ك
+
+181
+00:17:09,010 --> 00:17:14,310
+أس ل a,b يطلع ال identity؟ مفيش إمكانية يبقى ال a
+
+182
+00:17:14,310 --> 00:17:19,310
+,b كدهش ال order اللي لها infinity يبقى هذا بده
+
+183
+00:17:19,310 --> 00:17:27,390
+يعطيلي ان ال a,b is of infinite order
+
+184
+00:17:28,710 --> 00:17:34,670
+يبقى هذا مثال جميل جدا لو سألك قالك انت عندك group
+
+185
+00:17:34,670 --> 00:17:39,630
+فيها two elements كل واحد بفيهم finite order هل
+
+186
+00:17:39,630 --> 00:17:44,890
+حاصل الضرب بديكون finite ولا infinite لاحتمالين
+
+187
+00:17:44,890 --> 00:17:49,210
+وردات قد يكون حاصل الضرب finite وقد يكون حاصل
+
+188
+00:17:49,210 --> 00:17:54,690
+الضرب infiniteهي طلع ال order لكل واحدة فيهم
+
+189
+00:17:54,690 --> 00:17:58,790
+finite لكن ال order لحاصل الدربع التاني infinite
+
+190
+00:18:00,400 --> 00:18:06,500
+هذا مثال جميل جدا حكيتلكوا الصبح عنه و نحنا قد
+
+191
+00:18:06,500 --> 00:18:11,780
+أعطيناكم هذا المثال طب بدنا نخش الأن للموضوع اللي
+
+192
+00:18:11,780 --> 00:18:15,040
+احنا كنا رافعينه اللي هو انتبعنا اللي لسه
+
+193
+00:18:15,040 --> 00:18:20,880
+ماتحدثناش فيه لغمين ال subgroups المجموعات الجزئية
+
+194
+00:18:20,880 --> 00:18:26,550
+لمجموعة ماالـ definition بيقول ما يأتي definition
+
+195
+00:18:26,550 --> 00:18:40,650
+let الـ H be a subset of G الـ
+
+196
+00:18:40,650 --> 00:18:53,780
+H is called هذي بنسميها a subgroup ofG subgroup من
+
+197
+00:18:53,780 --> 00:19:09,380
+G F L H is a group is a group under the same
+
+198
+00:19:09,380 --> 00:19:19,540
+operation under the same operation of
+
+199
+00:19:20,800 --> 00:19:33,080
+G We write بروح نكتب ان ال H هي ال sub group من جي
+
+200
+00:19:33,080 --> 00:19:37,460
+بالشكل اللي عندنا Notes
+
+201
+00:19:37,460 --> 00:19:49,740
+بعض الملاحظات اول ملاحظة F ال H لا تساوي G We
+
+202
+00:19:49,740 --> 00:20:03,150
+writeبنروح نكتب ان ال H subgroup من G and ال H is
+
+203
+00:20:03,150 --> 00:20:11,290
+called بنروح نسميها a proper
+
+204
+00:20:11,290 --> 00:20:18,330
+subgroup نقطة
+
+205
+00:20:18,330 --> 00:20:19,070
+ثانية
+
+206
+00:20:21,440 --> 00:20:32,180
+ست إي فقط لغير is called a
+
+207
+00:20:32,180 --> 00:20:38,960
+trivial subgroup of
+
+208
+00:20:38,960 --> 00:20:40,300
+G
+
+209
+00:20:47,700 --> 00:20:56,780
+the others and the other subgroups
+
+210
+00:20:56,780 --> 00:21:03,400
+are called
+
+211
+00:21:03,400 --> 00:21:07,860
+the
+
+212
+00:21:07,860 --> 00:21:11,340
+non
+
+213
+00:21:11,340 --> 00:21:15,740
+-atrivial subgroups
+
+214
+00:21:22,890 --> 00:21:24,670
+R G
+
+215
+00:22:07,520 --> 00:22:10,640
+نرجع للتعريف اللى احنا كنا نقوله تعريف ال subgroup
+
+216
+00:22:10,640 --> 00:22:16,120
+فباجي بقول لو كانت ال H هي ال subset من G بس مش
+
+217
+00:22:16,120 --> 00:22:20,820
+حيالها subset في شغلة بتتحقق عليها يبقى ال H is
+
+218
+00:22:20,820 --> 00:22:25,380
+called subgroup من G إذا كانت ال H باقية هي group
+
+219
+00:22:25,380 --> 00:22:31,980
+under the same operation of G يعني اعتبر الطلاب
+
+220
+00:22:31,980 --> 00:22:36,060
+اللى عندي في هذه القاعة كلهم groupلو أخدت هذه
+
+221
+00:22:36,060 --> 00:22:41,080
+المجموعة منهم يبقى هذه بسميها ال subgroup إذا طلعت
+
+222
+00:22:41,080 --> 00:22:45,400
+هذه group تحت نفسي العملية المعرفة عليه ال group
+
+223
+00:22:45,400 --> 00:22:49,780
+الأصلية إيش يعني group؟ يعني هذه فيهم ال identity
+
+224
+00:22:49,780 --> 00:22:55,440
+element وعناصرهم associative مع بعضهم وكل عنصر له
+
+225
+00:22:55,440 --> 00:23:00,500
+معكوسيبقى ان حدث ذلك بقول يبقى هذه الجديدة group
+
+226
+00:23:00,500 --> 00:23:05,040
+ان حد ذلك يبقى بقول هذه ال sub group من من من ال
+
+227
+00:23:05,040 --> 00:23:09,240
+group الأصلية يبقى ال H sub group من ال group
+
+228
+00:23:09,240 --> 00:23:13,980
+الأصلية إذا كانت هي group تحت نفس العملية وبدل
+
+229
+00:23:13,980 --> 00:23:18,040
+مكتوب sub group من الأنفا ساعدا هكتب ال sub group
+
+230
+00:23:18,040 --> 00:23:23,220
+H is a sub group من جيه مش H أقل من أو يساوي جيه
+
+231
+00:23:23,580 --> 00:23:27,200
+هذا أقل من سوى للاعداد العادية بس هذا رمز عندنا
+
+232
+00:23:27,200 --> 00:23:31,860
+يدل طيلة الكتاب على ميم على ال subgroup بيبقى كلمة
+
+233
+00:23:31,860 --> 00:23:36,520
+subgroup بدي أختصرها إلى الرمز اللي عندنا هذا و
+
+234
+00:23:36,520 --> 00:23:42,590
+تقرأ subgroup اتش subgroup من Gالـ H هذه يا شباب
+
+235
+00:23:42,590 --> 00:23:48,450
+ممكن تساوي جي وممكن ما تساويش الجي إذا الـ H هذه
+
+236
+00:23:48,450 --> 00:23:53,410
+ما سواتش الجي بنكتب H subgroup من جي وبنشيل
+
+237
+00:23:53,410 --> 00:23:55,210
+اليساوي اللي عندنا
+
+238
+00:23:57,730 --> 00:24:01,550
+الـ HP في هذه الحالة بسميها proper subgroup يعني
+
+239
+00:24:01,550 --> 00:24:06,370
+انا لو أخدت subgroup و لاقيتها لا تساوي لجروب
+
+240
+00:24:06,370 --> 00:24:10,750
+الأصلية لأنه بناعرف احنا any set is a subset of
+
+241
+00:24:10,750 --> 00:24:16,730
+itself صحيح ولا لأ؟ هي مجموعة جزئية من نفسها طلعت
+
+242
+00:24:16,730 --> 00:24:21,750
+المجموعة هذه الجزئية أقل من نفسهالاتساوي الأصلية
+
+243
+00:24:21,750 --> 00:24:28,170
+يبقى في هذه الحالة بسميها proper subgroup طبعا طيب
+
+244
+00:24:28,170 --> 00:24:32,050
+طب لو كده تلاقيتش تساوي جيه طبعا تلاقيتش جد الجيه
+
+245
+00:24:32,050 --> 00:24:37,630
+بالضبط تماما يبقى بسميها بسميها improper subgroup
+
+246
+00:24:37,630 --> 00:24:42,670
+هذه اسمها improper بقوم بلغيها زي ما نقول إن هذا
+
+247
+00:24:42,670 --> 00:24:48,240
+possible ممكن ننفيها بنقول impossible غير ممكنيبقى
+
+248
+00:24:48,240 --> 00:24:55,380
+هذي ممكن احطها لك ملاحظة رقم تلاتة if ال H تساوي G
+
+249
+00:24:55,380 --> 00:25:09,380
+then ال H is called improper subgroup
+
+250
+00:25:09,380 --> 00:25:13,020
+يبقى
+
+251
+00:25:13,020 --> 00:25:17,810
+هذي مسميها improper subgroupلو رحت أخدت ال
+
+252
+00:25:17,810 --> 00:25:23,630
+identity وحدة لحاله و حطيته داخل set يبقى السعر
+
+253
+00:25:23,630 --> 00:25:28,610
+عندي set لا يوجد فيها إلا ال identity element هل
+
+254
+00:25:28,610 --> 00:25:33,570
+هذه ال subgroup في الأول؟ subgroup ليش؟ لأن ال
+
+255
+00:25:33,570 --> 00:25:37,870
+identity موجودلو ضربت ال identity في نفسه بيطلع ال
+
+256
+00:25:37,870 --> 00:25:42,690
+identity موجود معكس ال identity هو ال identity
+
+257
+00:25:42,690 --> 00:25:48,010
+نفسه إذا موجود يبقى هذا صارت subgroup إن حدث ذلك
+
+258
+00:25:48,010 --> 00:25:52,310
+يبقى بسميها هذا ال subgroup ال trivial subgroup
+
+259
+00:25:52,600 --> 00:25:58,140
+يعني المجموع الجزئي البدي هي أو التافية أبسط أنواع
+
+260
+00:25:58,140 --> 00:26:02,720
+ال subgroups يبقى هذه ال set عبارة عن subgroup من
+
+261
+00:26:02,720 --> 00:26:06,580
+من من ال group الأصلي بسميها ال trivial subgroup
+
+262
+00:26:06,580 --> 00:26:11,220
+سيبنا هذه وروح تاخد كل ال subgroups الباقية كلهم
+
+263
+00:26:11,220 --> 00:26:15,840
+بسميهم non trivial subgroups يبقى هنا and the
+
+264
+00:26:15,840 --> 00:26:19,160
+other subgroups are called the non trivial
+
+265
+00:26:19,160 --> 00:26:25,080
+subgroupsof g يبقى صار undetriable subgroup, non
+
+266
+00:26:25,080 --> 00:26:28,360
+-detriable subgroup, proper subgroup, improper
+
+267
+00:26:28,360 --> 00:26:34,640
+subgroup, improper يبقى
+
+268
+00:26:34,640 --> 00:26:39,260
+أقل من الأصلية بشوية طبعا جد ما يكون يكون ان شاء
+
+269
+00:26:39,260 --> 00:26:45,560
+الله يكون عنصرين طب خليني أسألك طب هذه بنفع أقول
+
+270
+00:26:45,560 --> 00:26:51,210
+عليها properبنفع proper على كل خط بس لدرجة انها
+
+271
+00:26:51,210 --> 00:26:54,570
+مسمية trivial subgroup وبالتالي مقولش عليها proper
+
+272
+00:26:54,570 --> 00:26:59,710
+subgroup بدأ ناخد بعض الأمثلة التوضيحية على ذلك
+
+273
+00:26:59,710 --> 00:27:09,730
+قبل أن ندخل إلى أول نظرية يبقى examples أول
+
+274
+00:27:09,730 --> 00:27:16,510
+مثل بيقول z in under
+
+275
+00:27:19,250 --> 00:27:28,150
+addition modulo n اللي هي توسعة رمز نالها بالرمز z
+
+276
+00:27:28,150 --> 00:27:36,250
+in وعليها عملية الجمع modulo n هذه ماالها is not a
+
+277
+00:27:36,250 --> 00:27:44,090
+subgroup of
+
+278
+00:27:44,090 --> 00:27:45,890
+z
+
+279
+00:27:47,150 --> 00:27:53,850
+هو عليها عملية الجمع العادية هذه
+
+280
+00:27:53,850 --> 00:27:58,990
+مش subgroup طب زد n عناصرها zero واحد واثنين
+
+281
+00:27:58,990 --> 00:28:04,210
+وتلاتة لغاية n ناقص واحد زد هذه الموجب والسالب
+
+282
+00:28:04,210 --> 00:28:09,830
+والصفر يبقى zn هي subset من من؟ subset من z
+
+283
+00:28:09,830 --> 00:28:14,090
+بيتداعي هنا بيقول ماهياش subgroup حد بيقول لي ليش؟
+
+284
+00:28:14,090 --> 00:28:20,350
+ايوةأيوة اختلفت العملية حسب التعريف اللي كتبناه
+
+285
+00:28:20,350 --> 00:28:23,650
+لازم تبقى العملية على ال group الأصلية هي نفس
+
+286
+00:28:23,650 --> 00:28:28,390
+العملية على من؟ على ال subset يبقى هنا Z under
+
+287
+00:28:28,390 --> 00:28:38,730
+that is not a subgroup because the two operations
+
+288
+00:28:41,770 --> 00:28:50,570
+on zed in and الـ zed are different تختلف عن
+
+289
+00:28:50,570 --> 00:28:55,170
+التانية ولا واحدة فيهم زي التانية يبقى هذا نقض
+
+290
+00:28:55,170 --> 00:29:02,650
+التعريف لذلك هذا ماهياش subgroup خدلي مثال ثاني
+
+291
+00:29:02,650 --> 00:29:11,070
+خدلي الـ G هي عبارة عن ليكيو و عليها عملية الجمع
+
+292
+00:29:11,910 --> 00:29:20,830
+and ال h هي عبارة عن ال z و عليها عملية الجمع
+
+293
+00:29:20,830 --> 00:29:29,670
+السؤال هو هل هذه صبست من هذه صحيح لأن any integer
+
+294
+00:29:29,670 --> 00:29:33,210
+is a rational number ال operation نفسي ال
+
+295
+00:29:33,210 --> 00:29:40,450
+operation ال identity هنا مينوهنا نفس الـ identity
+
+296
+00:29:40,450 --> 00:29:45,490
+element المعكوس لل element هنا a عبارة عن مين؟
+
+297
+00:29:45,490 --> 00:29:49,850
+سالب a، المعكوس لهنا، مثل نفس الشيء، إذا هذه
+
+298
+00:29:49,850 --> 00:29:56,110
+subgroup من مين؟ من هنا، يبقى let g and then ال H
+
+299
+00:29:56,110 --> 00:30:02,710
+is a subgroup من g على طول الخط، مافيش أي تناقضما
+
+300
+00:30:02,710 --> 00:30:08,590
+بين الأثنين لا عملية ولا identity ولا معكوس طيب
+
+301
+00:30:08,590 --> 00:30:16,550
+السؤال الثالث لو أخدت ال Q plus تحت عملية الضرب
+
+302
+00:30:16,550 --> 00:30:27,810
+العادية and ال Q تحت عملية الجمع groups and all
+
+303
+00:30:29,450 --> 00:30:34,470
+group صحيح بس هل هذه subgroup من هذه أو العكس هل
+
+304
+00:30:34,470 --> 00:30:40,070
+هذه subgroup من هذه برضه لأ ليش لإنه ال operation
+
+305
+00:30:40,070 --> 00:30:47,050
+هنا ضربه هناك جامعة تختلف كليا and then
+
+306
+00:30:48,500 --> 00:30:56,320
+الـ q plus تحت عملية الجامعة is not a subgroup من
+
+307
+00:30:56,320 --> 00:31:07,900
+ال q و ال plus because السبب the two operations
+
+308
+00:31:07,900 --> 00:31:20,340
+العمليتين on ال q andالـ Q plus are different ولا
+
+309
+00:31:20,340 --> 00:31:27,780
+واحدة فيهم زي التانية طيب نبدأ في أول نظرية اظن ان
+
+310
+00:31:27,780 --> 00:31:32,160
+كان كل مرة بدنا نقعد نفحص ان هذه ال subgroup
+
+311
+00:31:32,160 --> 00:31:37,240
+العملية نفس العملية قصتنا هذه طويلةلكن نحاول ناخد
+
+312
+00:31:37,240 --> 00:31:41,940
+نظرية بواسطها نقدر نحكم على ال subset اللى أخدنا
+
+313
+00:31:41,940 --> 00:31:47,480
+منه هل هو subgroup أم لا بطريقة أسهل يبقى بإذن
+
+314
+00:31:47,480 --> 00:31:52,460
+الله نأتي لأول نظرية very important على ال
+
+315
+00:31:52,460 --> 00:32:02,300
+subgroup فالنظرية بتقول ما يأتي letالـ H بـ A non
+
+316
+00:32:02,300 --> 00:32:10,120
+empty subset of
+
+317
+00:32:10,120 --> 00:32:14,760
+a group G
+
+318
+00:32:20,070 --> 00:32:24,270
+الـ H is
+
+319
+00:32:24,270 --> 00:32:33,330
+a subgroup من G
+
+320
+00:32:33,330 --> 00:32:36,710
+الـ
+
+321
+00:32:36,710 --> 00:32:43,970
+A B inverse belongs to H whenever
+
+322
+00:32:47,020 --> 00:32:54,920
+عندما ال A and ال B are in H
+
+323
+00:33:19,250 --> 00:33:26,150
+مرة تانية انا عندى group اخدت منها subset ال
+
+324
+00:33:26,150 --> 00:33:31,770
+subset هذا وقتش بقدر اقول عنه subgroup اذا تحقق
+
+325
+00:33:31,770 --> 00:33:37,630
+شرطا الشرط الاول ان ال H اللي اخدت هذا تبقى non
+
+326
+00:33:37,630 --> 00:33:43,290
+-empty subset من Gالشرط التاني لو أخدت عمصرين
+
+327
+00:33:43,290 --> 00:33:48,370
+موجودات في H بدي أكون حاصل ضرب الأول في معكوس
+
+328
+00:33:48,370 --> 00:33:53,370
+الثاني موجود في H ان حد ذلك تبقى ال H هذه بقول
+
+329
+00:33:53,370 --> 00:33:58,870
+عليها subgroup تمام طب قبل ما برهن بدي أبرهن صحة
+
+330
+00:33:58,870 --> 00:34:03,590
+هذا الكلام مش حيال اللهالـ a b inverse هذه موجودة
+
+331
+00:34:03,590 --> 00:34:08,330
+في اتش لو كان شباب ال operation اللي على g عملية
+
+332
+00:34:08,330 --> 00:34:16,930
+الجامعة هذا الشرط كيف بكتبه a ناقص b موجود في اتش
+
+333
+00:34:16,930 --> 00:34:27,950
+يبقى هنا هذه كملاحظة بس يبقى if the operation if
+
+334
+00:34:27,950 --> 00:34:28,990
+the operation
+
+335
+00:34:35,690 --> 00:34:50,090
+on g is addition then الو a b inverse belongs to h
+
+336
+00:34:50,090 --> 00:34:56,130
+is written is
+
+337
+00:34:56,130 --> 00:35:03,620
+written as a minus b كل هذا موجود في hكل ال
+
+338
+00:35:03,620 --> 00:35:10,880
+element هذا موجود في ال proof مرة
+
+339
+00:35:10,880 --> 00:35:17,280
+تانيةبقول لو كان الـH هي الـnon-empty subset of A
+
+340
+00:35:17,280 --> 00:35:22,300
+group G، هاي ال condition الأول، then الـH is a
+
+341
+00:35:22,300 --> 00:35:27,100
+subgroup of G if الـA, B inverse موجود في H
+
+342
+00:35:27,100 --> 00:35:32,540
+whenever A وB are in H يبقى حسب التعريف الـsubset
+
+343
+00:35:32,540 --> 00:35:39,480
+اللي خدت بتبقى subgroup لو بقيت group تحت نفس
+
+344
+00:35:39,480 --> 00:35:44,330
+العمليةتعالى نشوف هل هذا الكلام بيحقق خاصية ال
+
+345
+00:35:44,330 --> 00:35:48,530
+group تحت نفس العملية ولا لأ؟ الآن ال H هذه ال
+
+346
+00:35:48,530 --> 00:35:53,510
+subset من مين؟ من G و ال operation اللي ع G
+
+347
+00:35:53,510 --> 00:35:58,490
+associative binary operation صح ولا لأ؟ يبقى هل
+
+348
+00:35:58,490 --> 00:36:02,390
+اختلفوا عناصر H؟ يعني صار على رأسهم ريشة لما
+
+349
+00:36:02,390 --> 00:36:06,910
+أخدناهم من G؟ لأ ما ينطبق على عناصر G ينطبق عليهم
+
+350
+00:36:07,270 --> 00:36:12,230
+إذا ال operation على H is associative binary
+
+351
+00:36:12,230 --> 00:36:17,330
+operation تمام ليش؟ لأن H هي ال subset من G يعني
+
+352
+00:36:17,330 --> 00:36:22,950
+ما ينطبق على عناصر G ينطبق تماما على عناصر من؟ على
+
+353
+00:36:22,950 --> 00:36:28,700
+عناصر H لكن هل ال identity هو نفسه؟ الله أعلمهل
+
+354
+00:36:28,700 --> 00:36:33,780
+معكوس العنصر اللى بده ياخده من إتش بده يكون في إتش
+
+355
+00:36:33,780 --> 00:36:39,280
+ولا برا الله أعلم هل لو أخدت عنصرين من إتش وضربتهم
+
+356
+00:36:39,280 --> 00:36:44,300
+في بعض بده يكون داخل إتش ولا لأ إن تحققت خواصة
+
+357
+00:36:44,300 --> 00:36:48,080
+التلاتة دي بيصير هذه الصعبة بالرومما تحقق واحد
+
+358
+00:36:48,080 --> 00:36:52,360
+منهم يبقى برا بتبطل يصير subgroup يبقى هو حاط ل
+
+359
+00:36:52,360 --> 00:36:57,660
+condition بدي أحاول أستفيد منه يبقى البرهان النقطة
+
+360
+00:36:57,660 --> 00:37:13,280
+الأولى الان the operation on H is an associative
+
+361
+00:37:13,280 --> 00:37:15,480
+binary
+
+362
+00:37:25,220 --> 00:37:31,680
+بسبب ان الـ H مالها subset من G
+
+363
+00:37:37,990 --> 00:37:41,710
+يبقى هذه ال associative binary operation متحققة
+
+364
+00:37:41,710 --> 00:37:46,890
+بالنسبة للخاصية الثانية الخاصية التانية بتقول انت
+
+365
+00:37:46,890 --> 00:37:51,670
+كل اللي عندي ان لو أخدت أنصرين من H بدي يكون حاصل
+
+366
+00:37:51,670 --> 00:38:00,090
+ضرب الأول فيه الثاني موجود في H صح ولا لا الان let
+
+367
+00:38:00,090 --> 00:38:11,010
+ال A و ال B موجودة في ال H thenالـ A B إنفرس موجود
+
+368
+00:38:11,010 --> 00:38:19,350
+في الـ H هذا in general هذا مواطع من نص النظرية طب
+
+369
+00:38:19,350 --> 00:38:26,240
+إيش رايك؟ بنفع أخد A تساوي B؟ بنفع ولا مانفعش؟هذا
+
+370
+00:38:26,240 --> 00:38:33,520
+ينفع لجميع الانصار ان ايه ممنوع يساوي بيه فانا
+
+371
+00:38:33,520 --> 00:38:36,180
+ممكن اخد اي انصار اذا انا ممكن اخد اي انصار اذا
+
+372
+00:38:36,180 --> 00:38:36,320
+انا ممكن اخد اي انصار اذا انا ممكن اخد اي انصار
+
+373
+00:38:36,320 --> 00:38:38,200
+اذا انا ممكن اخد اي انصار اذا انا ممكن اخد اي
+
+374
+00:38:38,200 --> 00:38:38,540
+انصار اذا انا ممكن اخد اي انصار اذا انا ممكن اخد
+
+375
+00:38:38,540 --> 00:38:41,580
+اي انصار اذا انا ممكن اخد اي انصار اذا انا ممكن
+
+376
+00:38:41,580 --> 00:38:43,340
+اخد اي انصار اذا انا ممكن اخد اي انصار اذا انا
+
+377
+00:38:43,340 --> 00:38:48,420
+ممكن اخد اي انصار اذا انا ممكن اخد اي انصار اذا
+
+378
+00:38:48,420 --> 00:38:51,660
+انا ممكن اخد اي انصار ا
+
+379
+00:38:53,490 --> 00:38:59,210
+الـ A B Inverse بدي ساوي ال X في ال X Inverse
+
+380
+00:38:59,210 --> 00:39:00,290
+موجودة في H
+
+381
+00:39:08,810 --> 00:39:15,790
+هذا يعني أن الـ E موجود في الـ H يبقى الـ H فيها
+
+382
+00:39:15,790 --> 00:39:20,070
+الـ identity element تبع من؟ تبع الـ group الأصلي
+
+383
+00:39:20,070 --> 00:39:23,490
+صار الـ identity في الـ group الأصلي اللي هو E
+
+384
+00:39:23,490 --> 00:39:29,310
+نفسه هو هو موجود في من؟ في ال subset اللي هي H حتى
+
+385
+00:39:29,310 --> 00:39:33,610
+لما أقول subset ما أقول subgroupموجود هو هو يبقى
+
+386
+00:39:33,610 --> 00:39:38,110
+ال X X inverse هذا موجود في G و هذا موجود في G إذا
+
+387
+00:39:38,110 --> 00:39:42,410
+ال element هذا صار موجود في H لإنه حصل ضاربه ما
+
+388
+00:39:42,410 --> 00:39:46,450
+موجود في H ال identity هذا هو تبع G الأصلية
+
+389
+00:39:46,450 --> 00:39:55,470
+ماغيرتشها طيب بدنا نيجي لل condition التالت F
+
+390
+00:40:06,200 --> 00:40:12,120
+معكوس العنصر هذا موجود لأنه في جيه بس موجود في H
+
+391
+00:40:12,120 --> 00:40:17,980
+والله برة H انا مش عارف انا بدي اثبت ان معكوس هذا
+
+392
+00:40:17,980 --> 00:40:20,640
+العنصر موجود في H
+
+393
+00:40:24,680 --> 00:40:30,080
+الان ايه شفتنا هنا يا شباب ان ال E موجود في H بدي
+
+394
+00:40:30,080 --> 00:40:38,180
+اخد هذا ال E هو A و ال B inverse يبقى هنا A في ال
+
+395
+00:40:38,180 --> 00:40:45,760
+B inverse موجود في H implies بدي اخدي ال A في ال B
+
+396
+00:40:45,760 --> 00:40:50,140
+inverse بدي اكون موجود في H صح ولا لا طبق لل
+
+397
+00:40:50,140 --> 00:40:56,510
+condition اللي عندي كويسيبقى هذا ايش معناه ان ال P
+
+398
+00:40:56,510 --> 00:41:01,430
+inverse موجود في H هل ال P اللي أخدته في H عليه
+
+399
+00:41:01,430 --> 00:41:06,250
+قيود والله اي عنصر موجود في H اي عنصر موجود في H
+
+400
+00:41:06,250 --> 00:41:11,650
+يبقى اي عنصر موجود في H اللي جات المعكوث تبعه
+
+401
+00:41:11,650 --> 00:41:16,650
+موجود وين موجود في H يبقى ضايق لنا بس النقطة
+
+402
+00:41:16,650 --> 00:41:17,490
+الأخيرة
+
+403
+00:41:20,560 --> 00:41:26,300
+إن لو أخدت عنصرين من H بدي أثبت أن حاصل ضربهما
+
+404
+00:41:26,300 --> 00:41:32,500
+موجود في H بس هاي كل اللي بديها ان تم ذلك بصير
+
+405
+00:41:32,500 --> 00:41:37,200
+عندنا هذا الـ H is a subgroup وبصير نستخدم هذه
+
+406
+00:41:37,200 --> 00:41:41,120
+النظرية في الحكم على ال subsets المختلفة هل هي
+
+407
+00:41:41,120 --> 00:41:47,860
+subgroup ام لاأنا بدي أخد عنصرين موجودات في H و
+
+408
+00:41:47,860 --> 00:41:56,060
+بدي أثبت أن حاصل ضربه موجود في H يبقى هنا F A و B
+
+409
+00:41:56,060 --> 00:42:01,580
+موجودات في H let
+
+410
+00:42:01,580 --> 00:42:12,480
+A تساوي X و B تساوي Y inverse مثلاوخد الـ P يبدو
+
+411
+00:42:12,480 --> 00:42:19,040
+يساوي Y inverse then ايش
+
+412
+00:42:19,040 --> 00:42:22,120
+رأيك لو اخدت ال X في Y؟
+
+413
+00:42:24,710 --> 00:42:30,250
+الـ X في Y أشوف إيش بيساوي هنا X وهنا B تساوي Y
+
+414
+00:42:30,250 --> 00:42:36,510
+inverse يعني ال Y هذه موجودة في G موجودة في G بدي
+
+415
+00:42:36,510 --> 00:42:44,550
+أخد ال X في Y مين ال X؟ أو ملاش يساوي X في ال Y
+
+416
+00:42:44,550 --> 00:42:50,850
+بقدر أكتبها Y inverse inverse مظبوط؟
+
+417
+00:42:51,360 --> 00:42:57,100
+هذا الكلام يستوي ال X انا افرضها بقداش؟ ب A وال Y
+
+418
+00:42:57,100 --> 00:42:59,600
+inverse ب مين؟ ب B
+
+419
+00:43:03,070 --> 00:43:09,370
+يبقى هذا موجود في h طبقا لل condition يعني حاصل
+
+420
+00:43:09,370 --> 00:43:14,930
+ضرب any two elements موجودة وين في h يبقى هذا
+
+421
+00:43:14,930 --> 00:43:21,650
+بيعطينا ان x و y موجود في h for all x و y اللي
+
+422
+00:43:21,650 --> 00:43:27,000
+موجودة وينموجودة في H يعني ال H is closed under
+
+423
+00:43:27,000 --> 00:43:31,020
+multiplication يبقى تحققت أو هذه اللي كنا نسميها
+
+424
+00:43:31,020 --> 00:43:35,700
+binary operation أنه تاخد two elements أثر واحد
+
+425
+00:43:35,700 --> 00:43:39,120
+على التاني يعطيك عنصر يديد هذا العنصر موجود في من؟
+
+426
+00:43:39,120 --> 00:43:45,920
+في H يبقى بناء عليه بروح بقوله thus و هكذا ال H is
+
+427
+00:43:45,920 --> 00:43:51,740
+a subgroup من G وبالتالي برهن النظرية اللي موجودة
+
+428
+00:43:51,740 --> 00:43:57,960
+عندنامن الانفة الصاعدة يا شباب لو اعطاني group
+
+429
+00:43:57,960 --> 00:44:03,280
+واعطاني set من ال group وقال يثبتلي ان ال set هذه
+
+430
+00:44:03,280 --> 00:44:10,210
+is a sub group بدي اعمله خطوتين لثالثة لهماالخطوة
+
+431
+00:44:10,210 --> 00:44:18,790
+الأولى هي أن أثبت له أن الـH هي non-empty يبقى هذه
+
+432
+00:44:18,790 --> 00:44:23,830
+فيها عناصر و لو تثبت أن فيها عنصر واحد يكفي منك
+
+433
+00:44:23,830 --> 00:44:26,870
+الله يعطيك العفو بس أثبت أن فيها عنصر واحد يبقى
+
+434
+00:44:26,870 --> 00:44:30,030
+non-empty خلصنا من ال condition الأولىالـ
+
+435
+00:44:30,030 --> 00:44:34,830
+condition الثاني لو رحت أخدت أي two elements في
+
+436
+00:44:34,830 --> 00:44:40,430
+هذه ال subset وقدرت تثبت أن الأول في معكوس الثاني
+
+437
+00:44:40,430 --> 00:44:45,510
+موجود في h double h subgroupخلصنا يبقى من الآن
+
+438
+00:44:45,510 --> 00:44:52,670
+فصاعدا لو أخد subset من group G ال subset هذا بدي
+
+439
+00:44:52,670 --> 00:44:58,510
+أثبت أنه subgroup معطوب منك تثبت شرطين إذا أثبتهم
+
+440
+00:44:58,510 --> 00:45:04,210
+صحيح بيصير هذا subgroup كيف؟ يعني بيكتثبت أولا أن
+
+441
+00:45:04,210 --> 00:45:08,970
+ال subset اللي أخدتها non-empty على الأقليجب أن
+
+442
+00:45:08,970 --> 00:45:14,270
+تظهر أن هناك عنصر موجود في هذه الـ subset اثنين لو
+
+443
+00:45:14,270 --> 00:45:17,250
+أخذت أي احد من الـ two elements في هذا الـ subset
+
+444
+00:45:17,250 --> 00:45:21,350
+يجب أن تثبت أنه حصل ضرب الأول في معكوس الثاني
+
+445
+00:45:21,350 --> 00:45:25,330
+موجود فيه إذا أثبتت ذلك يبقى هذا سيصبح معناه
+
+446
+00:45:25,330 --> 00:45:31,070
+subgroup يعني شغلنا بعد ذلك في الأمثلة يجب أن
+
+447
+00:45:31,070 --> 00:45:35,030
+يعطيني group يعطيني ال subset من هنا يقول يثبت أن
+
+448
+00:45:35,030 --> 00:45:38,940
+هذه subgroup أو ما هيشالسابقروب يعني ما قلت ماهياش
+
+449
+00:45:38,940 --> 00:45:43,180
+سابقروب بدك تجيبله counter example قلت له group
+
+450
+00:45:43,180 --> 00:45:47,800
+بدك تروح اياش اتبرهنها والله بنفع اجيب example بس
+
+451
+00:45:47,800 --> 00:45:50,920
+كده عدد يثبت انها group .. انها سابقروب بالفعل
+
+452
+00:45:50,920 --> 00:45:54,460
+بنفعش لكن counter example اه بثبت انه ماهيش
+
+453
+00:45:54,460 --> 00:46:00,180
+سابقروب بس ديك لازم اتبرهنها برهانة طيب الآن ماضلش
+
+454
+00:46:00,180 --> 00:46:04,780
+وقت الحقيقة كان أخدنا الآن بعض الأمثلة
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6b3c9ac2addd529cdaccd1d76a1c213ebc3773d3
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4663, "start": 20.67, "end": 46.63, "text": "المحاضرة الصباحية حين دخلنا على ال chapter التاسع اللى بتحدث عن ال normal subgroups and factor groups بدأنا بتعريف ال normal subgroup وقلنا اللى لو عندى H subgroup من G بقول عنها normal لو كان ال left coset يساوي ال right coset لأى element موجود في ال group", "tokens": [45340, 5016, 46958, 25720, 31767, 3555, 39319, 10632, 11331, 9957, 11778, 9778, 1211, 8315, 15844, 2423, 7187, 16712, 32277, 3615, 13672, 7578, 39894, 24401, 12984, 18871, 2423, 2710, 1422, 17377, 82, 293, 5952, 3935, 4724, 3215, 10721, 8315, 39894, 3615, 16572, 5172, 2423, 2710, 1422, 17377, 4032, 4587, 1211, 8315, 13672, 7578, 45164, 43242, 7578, 389, 1422, 17377, 9154, 460, 4724, 39648, 18871, 11296, 2710, 45164, 25961, 2423, 1411, 3792, 302, 7251, 3794, 995, 45865, 2423, 558, 3792, 302, 5296, 10721, 7578, 4478, 3714, 29245, 23328, 8978, 2423, 1594], "avg_logprob": -0.14314235829644734, "compression_ratio": 1.6473214285714286, "no_speech_prob": 1.9669532775878906e-06, "words": [{"start": 20.670000000000005, "end": 21.590000000000003, "word": "المحاضرة", "probability": 0.939697265625}, {"start": 21.590000000000003, "end": 22.51, "word": " الصباحية", "probability": 0.9302978515625}, {"start": 22.51, "end": 23.73, "word": " حين", "probability": 0.9794921875}, {"start": 23.73, "end": 24.35, "word": " دخلنا", "probability": 0.9908447265625}, {"start": 24.35, "end": 24.71, "word": " على", "probability": 0.8544921875}, {"start": 24.71, "end": 25.03, "word": " ال", "probability": 0.740234375}, {"start": 25.03, "end": 25.45, "word": " chapter", "probability": 0.95458984375}, {"start": 25.45, "end": 26.47, "word": " التاسع", "probability": 0.9855143229166666}, {"start": 26.47, "end": 27.25, "word": " اللى", "probability": 0.76171875}, {"start": 27.25, "end": 27.79, "word": " بتحدث", "probability": 0.9554036458333334}, {"start": 27.79, "end": 28.01, "word": " عن", "probability": 0.9765625}, {"start": 28.01, "end": 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التلاتة لانها دول بقول الـH هي normal subgroup من G الان الـG و الـH التنتينة groups قال اثبت ان الـexternal byproduct ما بين الـG و الـidentity element تبع الـH هو normal subgroup من الـexternal byproduct ما بين الـG و الـH طبعا في الأمثلة التابعة الصبح", "tokens": [28814, 1863, 11331, 3215, 12984, 29910, 23275, 36632, 36764, 24401, 3660, 9154, 21542, 6027, 9307, 16712, 1211, 9307, 3660, 5296, 7649, 11296, 11778, 12610, 4724, 39648, 2423, 39184, 39, 39896, 2710, 1422, 17377, 9154, 460, 2423, 7649, 2423, 39184, 38, 4032, 2423, 39184, 39, 16712, 29399, 9957, 3660, 3935, 50239, 1975, 12984, 3555, 2655, 16472, 2423, 39184, 3121, 7481, 538, 33244, 19446, 49374, 2423, 39184, 38, 4032, 2423, 39184, 1078, 507, 4478, 6055, 3555, 3615, 2423, 39184, 39, 31439, 2710, 1422, 17377, 9154, 2423, 39184, 3121, 7481, 538, 33244, 19446, 49374, 2423, 39184, 38, 4032, 2423, 39184, 39, 23032, 3555, 3615, 995, 8978, 16247, 2304, 12984, 37977, 16712, 16758, 27884, 31767, 49628], "avg_logprob": 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"probability": 0.29541015625}, {"start": 83.2, "end": 83.84, "word": " اثبت", "probability": 0.875244140625}, {"start": 83.84, "end": 84.04, "word": " ان", "probability": 0.73974609375}, {"start": 84.04, "end": 84.72, "word": " الـexternal", "probability": 0.60723876953125}, {"start": 84.72, "end": 85.36, "word": " byproduct", "probability": 0.4373779296875}, {"start": 85.36, "end": 85.78, "word": " ما", "probability": 0.869140625}, {"start": 85.78, "end": 86.12, "word": " بين", "probability": 0.98681640625}, {"start": 86.12, "end": 86.94, "word": " الـG", "probability": 0.9466145833333334}, {"start": 86.94, "end": 87.16, "word": " و", "probability": 0.459228515625}, {"start": 87.16, "end": 88.1, "word": " الـidentity", "probability": 0.7200927734375}, {"start": 88.1, "end": 88.7, "word": " element", "probability": 0.96533203125}, {"start": 88.7, "end": 89.26, "word": " تبع", "probability": 0.9498697916666666}, {"start": 89.26, "end": 89.8, "word": " الـH", "probability": 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"end": 95.34, "word": " في", "probability": 0.857421875}, {"start": 95.34, "end": 95.76, "word": " الأمثلة", "probability": 0.9732666015625}, {"start": 95.76, "end": 96.16, "word": " التابعة", "probability": 0.7491048177083334}, {"start": 96.16, "end": 96.64, "word": " الصبح", "probability": 0.92431640625}], "temperature": 1.0}, {"id": 4, "seek": 12581, "start": 97.99, "end": 125.81, "text": "قلنا الـcenter أثبتناها قبل ذلك subgroup الـspecial linear group of two by two matrices over R أثبتناها قبل ذلك subgroup ولذلك اعتمدنا على ما أخدناه سابقا و أثبتناه بس حكاية ال normality لكن هذه هل أثبتناها أنها subgroup قبل ذلك؟ طبعا لا يبقى هنا بكتير ما الخطوطين الخطوة الأولى بدي أثبت أن هذه subgroup أولا ثم بعد ذلك نثبت أنها normal subgroup", "tokens": [4587, 1211, 8315, 2423, 39184, 50085, 5551, 12984, 3555, 2655, 8315, 11296, 12174, 36150, 29910, 23275, 1422, 17377, 2423, 39184, 7053, 1013, 8213, 1594, 295, 732, 538, 732, 32284, 670, 497, 5551, 12984, 3555, 2655, 8315, 11296, 12174, 36150, 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{"start": 194.97, "end": 196.51, "word": " يبقى", "probability": 0.80145263671875}, {"start": 196.51, "end": 196.83, "word": " مرة", "probability": 0.958251953125}, {"start": 196.83, "end": 197.25, "word": " تانية", "probability": 0.9744466145833334}, {"start": 197.25, "end": 197.55, "word": " انا", "probability": 0.82080078125}, {"start": 197.55, "end": 197.75, "word": " عند", "probability": 0.70947265625}, {"start": 197.75, "end": 198.19, "word": " توجه", "probability": 0.6328938802083334}, {"start": 198.19, "end": 198.61, "word": " H", "probability": 0.50830078125}, {"start": 198.61, "end": 199.45, "word": " بدي", "probability": 0.857177734375}, {"start": 199.45, "end": 200.09, "word": " اثبت", "probability": 0.9564208984375}, {"start": 200.09, "end": 200.57, "word": " ان", "probability": 0.94384765625}, {"start": 200.57, "end": 201.21, "word": " ال", "probability": 0.7255859375}, {"start": 201.21, "end": 201.69, "word": " external", "probability": 0.72802734375}, {"start": 201.69, 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205.92, "end": 222.24, "text": "هو سبع جروب من الجيك السينادكي product ال H جينا قولنا الجروب اللي عندنا هذي is non-empty because ال identity اللي متبع ال G و ال identity اللي متبع ال H هو ال identity element لمن للجروب اللي عندنا هذا يبقى", "tokens": [3224, 2407, 8608, 3555, 3615, 10874, 32887, 3555, 9154, 25724, 1829, 4117, 21136, 1829, 8315, 3215, 4117, 1829, 1674, 2423, 389, 10874, 1829, 8315, 12174, 12610, 8315, 25724, 32887, 3555, 13672, 1829, 43242, 8315, 8032, 8848, 1829, 307, 2107, 12, 4543, 88, 570, 2423, 6575, 13672, 1829, 44650, 3555, 3615, 2423, 460, 4032, 2423, 6575, 13672, 1829, 44650, 3555, 3615, 2423, 389, 31439, 2423, 6575, 4478, 5296, 27842, 24976, 7435, 32887, 3555, 13672, 1829, 43242, 8315, 23758, 7251, 3555, 4587, 7578], "avg_logprob": -0.32774389844115187, "compression_ratio": 1.8421052631578947, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 205.92, "end": 206.44, "word": "هو", "probability": 0.7978515625}, {"start": 206.44, "end": 206.8, "word": 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H inverse بال E H itself يعني ال identity element هو معكوس لنفسه يبقى هذا في ال identity element تبع ال H من خلاص عملية الضرب يبقى هذا بده يعطيني X Y inverse وال E H في ال E H بال E H itself", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 28820, 10943, 47525, 3224, 7251, 3794, 995, 45865, 2423, 39184, 1783, 2423, 6575, 6055, 3555, 3615, 2423, 389, 3714, 11242, 32887, 3555, 8978, 2423, 398, 17340, 31439, 2423, 462, 389, 17340, 20666, 462, 389, 2564, 37495, 22653, 2423, 6575, 4478, 31439, 20449, 4117, 41779, 5296, 1863, 36178, 3224, 7251, 3555, 4587, 7578, 23758, 8978, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 389, 9154, 16490, 1211, 33546, 6225, 42213, 10632, 6024, 114, 25513, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 7251, 3615, 9566, 9957, 1829, 1783, 398, 17340, 16070, 462, 389, 8978, 2423, 462, 389, 20666, 462, 389, 2564], "avg_logprob": -0.21324404194241478, "compression_ratio": 1.98, "no_speech_prob": 0.0, "words": [{"start": 249.41, "end": 249.91, "word": "يبقى", 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{"start": 609.54, "end": 609.94, "word": " يساوي", "probability": 0.829345703125}, {"start": 609.94, "end": 610.4, "word": " اتنين", "probability": 0.842529296875}, {"start": 610.4, "end": 610.78, "word": " يبقى", "probability": 0.958984375}, {"start": 610.78, "end": 610.94, "word": " في", "probability": 0.9423828125}, {"start": 610.94, "end": 611.26, "word": " هذه", "probability": 0.90966796875}, {"start": 611.26, "end": 611.7, "word": " الحالة", "probability": 0.9827473958333334}, {"start": 611.7, "end": 611.84, "word": " ال", "probability": 0.9541015625}, {"start": 611.84, "end": 612.08, "word": " H", "probability": 0.953125}, {"start": 612.08, "end": 612.8, "word": " بتبقى", "probability": 0.939697265625}, {"start": 612.8, "end": 613.38, "word": " normal", "probability": 0.6630859375}, {"start": 613.38, "end": 614.14, "word": " subgroup", "probability": 0.929931640625}, {"start": 614.14, "end": 614.38, "word": " من", "probability": 0.98388671875}, {"start": 614.38, "end": 614.82, 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"تنتين left cassettes only واحدة فيهم بتكون الـH itself والتانية and والتانية امسك اي element من ال group واضربه في من من ال group هذه", "tokens": [2655, 29399, 9957, 1411, 21943, 16049, 787, 36764, 24401, 3660, 8978, 16095, 39894, 30544, 2423, 39184, 39, 309, 405, 75, 69, 16070, 2655, 7649, 10632, 293, 16070, 2655, 7649, 10632, 1975, 2304, 3794, 4117, 1975, 1829, 4478, 9154, 2423, 1594, 4032, 46958, 25513, 3224, 8978, 9154, 9154, 2423, 1594, 29538], "avg_logprob": -0.43290441527086143, "compression_ratio": 1.4042553191489362, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 646.45, "end": 647.27, "word": "تنتين", "probability": 0.6697184244791666}, {"start": 647.27, "end": 648.29, "word": " left", "probability": 0.5068359375}, {"start": 648.29, "end": 651.01, "word": " cassettes", "probability": 0.608642578125}, {"start": 651.01, "end": 656.13, "word": " only", "probability": 0.79248046875}, {"start": 656.13, "end": 657.53, "word": " واحدة", "probability": 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0.52685546875}, {"start": 668.31, "end": 668.57, "word": " group", "probability": 0.82177734375}, {"start": 668.57, "end": 669.25, "word": " واضربه", "probability": 0.84228515625}, {"start": 669.25, "end": 669.39, "word": " في", "probability": 0.92333984375}, {"start": 669.39, "end": 669.69, "word": " من", "probability": 0.37646484375}, {"start": 669.69, "end": 670.17, "word": " من", "probability": 0.5}, {"start": 670.17, "end": 670.33, "word": " ال", "probability": 0.69091796875}, {"start": 670.33, "end": 670.63, "word": " group", "probability": 0.9130859375}, {"start": 670.63, "end": 671.01, "word": " هذه", "probability": 0.306884765625}], "temperature": 1.0}, {"id": 28, "seek": 67709, "start": 671.47, "end": 677.09, "text": "طيب أنا بدي الدعوة التانية هي G ناقص ال H بنفع", "tokens": [9566, 1829, 3555, 41850, 4724, 16254, 32748, 3615, 2407, 3660, 16712, 7649, 10632, 39896, 460, 8717, 995, 4587, 9381, 2423, 389, 44945, 5172, 3615], "avg_logprob": -0.3825, "compression_ratio": 1.0810810810810811, "no_speech_prob": 0.0, "words": [{"start": 671.47, "end": 671.85, "word": "طيب", "probability": 0.5846354166666666}, {"start": 671.85, "end": 672.13, "word": " أنا", "probability": 0.51025390625}, {"start": 672.13, "end": 672.51, "word": " بدي", "probability": 0.5972900390625}, {"start": 672.51, "end": 673.13, "word": " الدعوة", "probability": 0.791748046875}, {"start": 673.13, "end": 673.69, "word": " التانية", "probability": 0.8828125}, {"start": 673.69, "end": 674.13, "word": " هي", "probability": 0.8310546875}, {"start": 674.13, "end": 674.75, "word": " G", "probability": 0.35498046875}, {"start": 674.75, "end": 675.67, "word": " ناقص", "probability": 0.881591796875}, {"start": 675.67, "end": 675.83, "word": " ال", "probability": 0.91650390625}, {"start": 675.83, "end": 676.23, "word": " H", "probability": 0.78466796875}, {"start": 676.23, "end": 677.09, "word": " بنفع", "probability": 0.6832682291666666}], "temperature": 1.0}, {"id": 29, "seek": 70629, "start": 680.09, "end": 706.29, "text": "لما ناخد الـ H كل العناصر اللي بيظلوا هي G نقص الـ H ليش؟ لأن الـ two cosets يبقى يا MR coincide التنتين بنطبقوا يعني التنتين بيساوي يعني ال intersection تبعهم مش بيساوي فاي يعني ال left distant cosets بيعملوا partition على ال group G إذا لما ناخد الـ H اللي بيظل بيكون هم ال left cosets", "tokens": [1211, 15042, 8717, 47283, 3215, 2423, 39184, 389, 28242, 18863, 8315, 9381, 2288, 13672, 1829, 4724, 1829, 19913, 1211, 14407, 39896, 460, 8717, 4587, 9381, 2423, 39184, 389, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 732, 3792, 1385, 7251, 3555, 4587, 7578, 35186, 9808, 13001, 482, 2423, 2655, 29399, 9957, 44945, 9566, 3555, 4587, 14407, 37495, 22653, 16712, 29399, 9957, 4724, 1829, 3794, 995, 45865, 37495, 22653, 2423, 15236, 6055, 3555, 3615, 16095, 37893, 4724, 1829, 3794, 995, 45865, 6156, 47302, 37495, 22653, 2423, 1411, 17275, 3792, 1385, 4724, 1829, 25957, 1211, 14407, 24808, 15844, 2423, 1594, 460, 11933, 15730, 5296, 15042, 8717, 47283, 3215, 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"end": 936.06, "word": " G", "probability": 0.81396484375}], "temperature": 1.0}, {"id": 38, "seek": 95711, "start": 941.83, "end": 957.11, "text": "يبقى هذا الان من الآن فصاعدا اي subgroup ال index ايه اللي هيساوي اتنين من ال group الأصلية بتكون ال subgroup هذي normal subgroup من ال main من ال group الأصلية", "tokens": [1829, 3555, 4587, 7578, 23758, 2423, 7649, 9154, 6024, 48506, 6156, 9381, 995, 22488, 995, 1975, 1829, 1422, 17377, 2423, 8186, 1975, 1829, 3224, 13672, 1829, 39896, 3794, 995, 45865, 1975, 2655, 1863, 9957, 9154, 2423, 1594, 16247, 36520, 10632, 39894, 30544, 2423, 1422, 17377, 8032, 8848, 1829, 2710, 1422, 17377, 9154, 2423, 2135, 9154, 2423, 1594, 16247, 36520, 10632], "avg_logprob": -0.3122438661387709, "compression_ratio": 1.6971830985915493, "no_speech_prob": 0.0, "words": [{"start": 941.83, "end": 942.29, "word": "يبقى", "probability": 0.8162841796875}, {"start": 942.29, "end": 942.67, "word": " هذا", "probability": 0.70458984375}, {"start": 942.67, "end": 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من", "probability": 0.79296875}, {"start": 949.37, "end": 949.47, "word": " ال", "probability": 0.73779296875}, {"start": 949.47, "end": 949.73, "word": " group", "probability": 0.927734375}, {"start": 949.73, "end": 950.47, "word": " الأصلية", "probability": 0.7701009114583334}, {"start": 950.47, "end": 951.27, "word": " بتكون", "probability": 0.86767578125}, {"start": 951.27, "end": 951.41, "word": " ال", "probability": 0.8115234375}, {"start": 951.41, "end": 951.99, "word": " subgroup", "probability": 0.91455078125}, {"start": 951.99, "end": 952.43, "word": " هذي", "probability": 0.568115234375}, {"start": 952.43, "end": 952.87, "word": " normal", "probability": 0.634765625}, {"start": 952.87, "end": 953.65, "word": " subgroup", "probability": 0.918701171875}, {"start": 953.65, "end": 953.83, "word": " من", "probability": 0.98828125}, {"start": 953.83, "end": 954.05, "word": " ال", "probability": 0.58642578125}, {"start": 954.05, "end": 954.25, "word": " main", "probability": 0.68359375}, {"start": 954.25, "end": 954.87, "word": " من", "probability": 0.5537109375}, {"start": 954.87, "end": 955.07, "word": " ال", "probability": 0.94921875}, {"start": 955.07, "end": 955.67, "word": " group", "probability": 0.98681640625}, {"start": 955.67, "end": 957.11, "word": " الأصلية", "probability": 0.8258463541666666}], "temperature": 1.0}, {"id": 39, "seek": 99105, "start": 962.33, "end": 991.05, "text": "يعني يمكن استخدام هذه او هذا المثال في حل بعض المسائل بعد ذلك او على طول الخط انجلك ال index اتنين بدك تفهم ان هذي normal subgroup من ال group الأساسية اللي هي G نمرة سبعة مثال رقم سبعة you is they", "tokens": [40228, 22653, 7251, 43020, 44713, 9778, 3215, 10943, 29538, 1975, 2407, 23758, 9673, 12984, 6027, 8978, 11331, 1211, 45030, 11242, 9673, 3794, 16373, 1211, 39182, 29910, 23275, 1975, 2407, 15844, 23032, 12610, 33962, 9566, 16472, 7435, 23275, 2423, 8186, 1975, 2655, 1863, 9957, 47525, 4117, 6055, 5172, 16095, 16472, 8032, 8848, 1829, 2710, 1422, 17377, 9154, 2423, 1594, 16247, 3794, 32277, 10632, 13672, 1829, 39896, 460, 8717, 2304, 25720, 8608, 3555, 27884, 50113, 6027, 12602, 4587, 2304, 8608, 3555, 27884, 291, 307, 436], "avg_logprob": -0.2587425730058125, "compression_ratio": 1.5637254901960784, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 962.33, "end": 962.71, "word": "يعني", "probability": 0.800537109375}, {"start": 962.71, "end": 963.21, "word": " يمكن", "probability": 0.965576171875}, {"start": 963.21, "end": 964.17, "word": " استخدام", "probability": 0.9688720703125}, {"start": 964.17, "end": 964.87, "word": " هذه", "probability": 0.9267578125}, {"start": 964.87, "end": 965.75, "word": " او", "probability": 0.798583984375}, {"start": 965.75, "end": 966.09, "word": " هذا", "probability": 0.9267578125}, {"start": 966.09, "end": 966.87, "word": " المثال", "probability": 0.9757486979166666}, {"start": 966.87, "end": 967.51, "word": " في", "probability": 0.77392578125}, {"start": 967.51, "end": 968.03, "word": " حل", "probability": 0.967529296875}, {"start": 968.03, "end": 968.43, "word": " بعض", "probability": 0.994140625}, {"start": 968.43, "end": 969.23, "word": " المسائل", "probability": 0.958740234375}, {"start": 969.23, "end": 969.59, "word": " بعد", "probability": 0.96142578125}, {"start": 969.59, "end": 970.13, "word": " ذلك", "probability": 0.994873046875}, {"start": 970.13, "end": 971.01, "word": " او", "probability": 0.901123046875}, {"start": 971.01, "end": 971.21, "word": " على", "probability": 0.251708984375}, {"start": 971.21, "end": 971.33, "word": " طول", "probability": 0.956787109375}, {"start": 971.33, "end": 971.65, "word": " الخط", "probability": 0.6519775390625}, {"start": 971.65, "end": 972.13, "word": " انجلك", "probability": 0.67626953125}, {"start": 972.13, "end": 972.33, "word": " ال", "probability": 0.96435546875}, {"start": 972.33, "end": 972.69, "word": " index", "probability": 0.72216796875}, {"start": 972.69, "end": 973.25, "word": " اتنين", "probability": 0.8057861328125}, {"start": 973.25, "end": 973.91, "word": " بدك", "probability": 0.76953125}, {"start": 973.91, "end": 974.31, "word": " تفهم", "probability": 0.98681640625}, {"start": 974.31, "end": 974.51, "word": " ان", "probability": 0.88525390625}, {"start": 974.51, "end": 974.93, "word": " هذي", "probability": 0.4836832682291667}, {"start": 974.93, "end": 975.45, "word": " normal", "probability": 0.5947265625}, {"start": 975.45, "end": 976.41, "word": " subgroup", "probability": 0.6962890625}, {"start": 976.41, "end": 977.01, "word": " من", "probability": 0.81494140625}, {"start": 977.01, "end": 977.15, "word": " ال", "probability": 0.59033203125}, {"start": 977.15, "end": 977.41, "word": " group", "probability": 0.92138671875}, {"start": 977.41, "end": 978.51, "word": " الأساسية", "probability": 0.9033203125}, {"start": 978.51, "end": 978.93, "word": " اللي", "probability": 0.82080078125}, {"start": 978.93, "end": 980.63, "word": " هي", "probability": 0.87451171875}, {"start": 980.63, "end": 981.19, "word": " G", "probability": 0.212890625}, {"start": 981.19, "end": 985.47, "word": " نمرة", "probability": 0.47119140625}, {"start": 985.47, "end": 986.05, "word": " سبعة", "probability": 0.9178059895833334}, {"start": 986.05, "end": 986.89, "word": " مثال", "probability": 0.759765625}, {"start": 986.89, "end": 987.41, "word": " رقم", "probability": 0.9482421875}, {"start": 987.41, "end": 988.05, "word": " سبعة", "probability": 0.93505859375}, {"start": 988.05, "end": 989.21, "word": " you", "probability": 0.56591796875}, {"start": 989.21, "end": 989.85, "word": " is", "probability": 0.402099609375}, {"start": 989.85, "end": 991.05, "word": " they", "probability": 0.482421875}], "temperature": 1.0}, {"id": 40, "seek": 101286, "start": 991.78, "end": 1012.86, "text": "above example بناخد المثال أعلاه to show that مشان نثبت ان ال subgroup generated by R90 is a normal subgroup من من ال D4", "tokens": [455, 1682, 1365, 4724, 1863, 47283, 3215, 9673, 12984, 6027, 5551, 3615, 15040, 3224, 281, 855, 300, 37893, 7649, 8717, 12984, 3555, 2655, 16472, 2423, 1422, 17377, 10833, 538, 497, 7771, 307, 257, 2710, 1422, 17377, 9154, 9154, 2423, 413, 19], "avg_logprob": -0.32979911991528105, "compression_ratio": 1.1407407407407408, "no_speech_prob": 0.0, "words": [{"start": 991.78, "end": 992.62, "word": "above", "probability": 0.59356689453125}, {"start": 992.62, "end": 994.42, "word": " example", "probability": 0.8330078125}, {"start": 994.42, "end": 996.06, "word": " بناخد", "probability": 0.610687255859375}, {"start": 996.06, "end": 996.68, "word": " المثال", "probability": 0.9488932291666666}, {"start": 996.68, "end": 997.66, "word": " أعلاه", "probability": 0.802734375}, {"start": 997.66, "end": 998.24, "word": " to", "probability": 0.75}, {"start": 998.24, "end": 998.6, "word": " show", "probability": 0.9599609375}, {"start": 998.6, "end": 1002.58, "word": " that", "probability": 0.935546875}, {"start": 1002.58, "end": 1003.54, "word": " مشان", "probability": 0.4073486328125}, {"start": 1003.54, "end": 1004.12, "word": " نثبت", "probability": 0.9896240234375}, {"start": 1004.12, "end": 1004.8, "word": " ان", "probability": 0.55615234375}, {"start": 1004.8, "end": 1005.06, "word": " ال", "probability": 0.78173828125}, {"start": 1005.06, "end": 1005.72, "word": " subgroup", "probability": 0.619140625}, {"start": 1005.72, "end": 1006.48, "word": " generated", "probability": 0.70654296875}, {"start": 1006.48, "end": 1007.02, "word": " by", "probability": 0.92724609375}, {"start": 1007.02, "end": 1008.14, "word": " R90", "probability": 0.65234375}, {"start": 1008.14, "end": 1009.08, "word": " is", "probability": 0.84814453125}, {"start": 1009.08, "end": 1009.5, "word": " a", "probability": 0.9365234375}, {"start": 1009.5, "end": 1010.0, "word": " normal", "probability": 0.76171875}, {"start": 1010.0, "end": 1010.82, "word": " subgroup", "probability": 0.93115234375}, {"start": 1010.82, "end": 1011.06, "word": " من", "probability": 0.9892578125}, {"start": 1011.06, "end": 1011.36, "word": " من", "probability": 0.369873046875}, {"start": 1011.36, "end": 1012.22, "word": " ال", "probability": 0.4306640625}, {"start": 1012.22, "end": 1012.86, "word": " D4", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 41, "seek": 104936, "start": 1030.09, "end": 1049.37, "text": "هي عبارة عن الـ identity element اللي هو الـ R نود والـ R تسعين والـ R مية و تمانين والـ R متين و سبعين", "tokens": [3224, 1829, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 6575, 4478, 13672, 1829, 31439, 2423, 39184, 497, 8717, 23328, 16070, 39184, 497, 6055, 3794, 3615, 9957, 16070, 39184, 497, 3714, 10632, 4032, 46811, 7649, 9957, 16070, 39184, 497, 44650, 9957, 4032, 8608, 3555, 3615, 9957], "avg_logprob": -0.318783981644589, "compression_ratio": 1.490909090909091, "no_speech_prob": 0.0, "words": [{"start": 1030.0900000000001, "end": 1031.15, "word": "هي", "probability": 0.1961669921875}, {"start": 1031.15, "end": 1032.21, "word": " عبارة", "probability": 0.96533203125}, {"start": 1032.21, "end": 1038.17, "word": " عن", "probability": 0.99560546875}, {"start": 1038.17, "end": 1038.73, "word": " الـ", "probability": 0.5693359375}, {"start": 1038.73, "end": 1039.33, "word": " identity", "probability": 0.4599609375}, {"start": 1039.33, "end": 1040.31, "word": " element", "probability": 0.84033203125}, {"start": 1040.31, "end": 1040.59, "word": " اللي", "probability": 0.5887451171875}, {"start": 1040.59, "end": 1040.71, "word": " هو", "probability": 0.919921875}, {"start": 1040.71, "end": 1040.87, "word": " الـ", "probability": 0.795166015625}, {"start": 1040.87, "end": 1041.19, "word": " R", "probability": 0.5654296875}, {"start": 1041.19, "end": 1041.61, "word": " نود", "probability": 0.3916015625}, {"start": 1041.61, "end": 1042.77, "word": " والـ", "probability": 0.65869140625}, {"start": 1042.77, "end": 1043.07, "word": " R", "probability": 0.76416015625}, {"start": 1043.07, "end": 1043.85, "word": " تسعين", "probability": 0.9635009765625}, {"start": 1043.85, "end": 1044.85, "word": " والـ", "probability": 0.928466796875}, {"start": 1044.85, "end": 1045.11, "word": " R", "probability": 0.91357421875}, {"start": 1045.11, "end": 1045.41, "word": " مية", "probability": 0.86376953125}, {"start": 1045.41, "end": 1045.63, "word": " و", "probability": 0.62060546875}, {"start": 1045.63, "end": 1046.43, "word": " تمانين", "probability": 0.95947265625}, {"start": 1046.43, "end": 1047.39, "word": " والـ", "probability": 0.9345703125}, {"start": 1047.39, "end": 1047.69, "word": " R", "probability": 0.9033203125}, {"start": 1047.69, "end": 1048.71, "word": " متين", "probability": 0.674560546875}, {"start": 1048.71, "end": 1048.87, "word": " و", "probability": 0.98486328125}, {"start": 1048.87, "end": 1049.37, "word": " سبعين", "probability": 0.852783203125}], "temperature": 1.0}, {"id": 42, "seek": 105923, "start": 1050.53, "end": 1059.23, "text": "يبقى هذا يعني ان ال order لل R تسعين بدي ساوي كده؟ بدي ساوي أربعة", "tokens": [1829, 3555, 4587, 7578, 23758, 37495, 22653, 16472, 2423, 1668, 24976, 497, 6055, 3794, 3615, 9957, 4724, 16254, 8608, 995, 45865, 9122, 3215, 3224, 22807, 4724, 16254, 8608, 995, 45865, 5551, 25513, 27884], "avg_logprob": -0.3586856740362504, "compression_ratio": 1.2222222222222223, "no_speech_prob": 0.0, "words": [{"start": 1050.53, "end": 1051.09, "word": "يبقى", "probability": 0.8092041015625}, {"start": 1051.09, "end": 1051.45, "word": " هذا", "probability": 0.90478515625}, {"start": 1051.45, "end": 1052.43, "word": " يعني", "probability": 0.9072265625}, {"start": 1052.43, "end": 1052.81, "word": " ان", "probability": 0.498779296875}, {"start": 1052.81, "end": 1053.01, "word": " ال", "probability": 0.68310546875}, {"start": 1053.01, "end": 1053.61, "word": " order", "probability": 0.81689453125}, {"start": 1053.61, "end": 1054.51, "word": " لل", "probability": 0.64013671875}, {"start": 1054.51, "end": 1055.09, "word": " R", "probability": 0.1417236328125}, {"start": 1055.09, "end": 1056.11, "word": " تسعين", "probability": 0.8243408203125}, {"start": 1056.11, "end": 1056.71, "word": " بدي", "probability": 0.2667236328125}, {"start": 1056.71, "end": 1056.97, "word": " ساوي", "probability": 0.7908528645833334}, {"start": 1056.97, "end": 1057.77, "word": " كده؟", "probability": 0.72119140625}, {"start": 1057.77, "end": 1058.29, "word": " بدي", "probability": 0.873779296875}, {"start": 1058.29, "end": 1058.71, "word": " ساوي", "probability": 0.9484049479166666}, {"start": 1058.71, "end": 1059.23, "word": " أربعة", "probability": 0.7610677083333334}], "temperature": 1.0}, {"id": 43, "seek": 108018, "start": 1059.88, "end": 1080.18, "text": "الان اذا اريت ان اجهزة الاندكس بتابع الـ subgroup generated by R90 فالجروب D4 سيسوء ال order لـ D4 مقسوما على ال order لل subgroup generated by R90", "tokens": [6027, 7649, 1975, 15730, 1975, 16572, 2655, 16472, 1975, 7435, 3224, 11622, 3660, 2423, 7649, 3215, 4117, 3794, 39894, 16758, 3615, 2423, 39184, 1422, 17377, 10833, 538, 497, 7771, 6156, 6027, 7435, 32887, 3555, 413, 19, 8608, 1829, 3794, 2407, 38207, 2423, 1668, 5296, 39184, 413, 19, 3714, 4587, 3794, 2407, 15042, 15844, 2423, 1668, 24976, 1422, 17377, 10833, 538, 497, 7771], "avg_logprob": -0.5734126794905889, "compression_ratio": 1.4413793103448276, "no_speech_prob": 0.0, "words": [{"start": 1059.88, "end": 1060.48, "word": "الان", "probability": 0.5645751953125}, {"start": 1060.48, "end": 1060.64, "word": " اذا", "probability": 0.60235595703125}, {"start": 1060.64, "end": 1060.9, "word": " اريت", "probability": 0.5849609375}, {"start": 1060.9, "end": 1060.98, "word": " ان", "probability": 0.60400390625}, {"start": 1060.98, "end": 1061.5, "word": " اجهزة", "probability": 0.55615234375}, {"start": 1061.5, "end": 1062.42, "word": " الاندكس", "probability": 0.516552734375}, {"start": 1062.42, "end": 1063.66, "word": " بتابع", "probability": 0.4902750651041667}, {"start": 1063.66, "end": 1064.7, "word": " الـ", "probability": 0.28485107421875}, {"start": 1064.7, "end": 1065.8, "word": " subgroup", "probability": 0.647705078125}, {"start": 1065.8, "end": 1066.48, "word": " generated", "probability": 0.5556640625}, {"start": 1066.48, "end": 1066.94, "word": " by", "probability": 0.96435546875}, {"start": 1066.94, "end": 1068.02, "word": " R90", "probability": 0.71240234375}, {"start": 1068.02, "end": 1069.34, "word": " فالجروب", "probability": 0.694482421875}, {"start": 1069.34, "end": 1070.14, "word": " D4", "probability": 0.910400390625}, {"start": 1070.14, "end": 1071.38, "word": " سيسوء", "probability": 0.39293212890625}, {"start": 1071.38, "end": 1071.44, "word": " ال", "probability": 0.46484375}, {"start": 1071.44, "end": 1071.98, "word": " order", "probability": 0.4140625}, {"start": 1071.98, "end": 1072.4, "word": " لـ", "probability": 0.381103515625}, {"start": 1072.4, "end": 1073.22, "word": " D4", "probability": 0.85986328125}, {"start": 1073.22, "end": 1074.58, "word": " مقسوما", "probability": 0.753125}, {"start": 1074.58, "end": 1074.94, "word": " على", "probability": 0.8623046875}, {"start": 1074.94, "end": 1075.12, "word": " ال", "probability": 0.8740234375}, {"start": 1075.12, "end": 1075.68, "word": " order", "probability": 0.8125}, {"start": 1075.68, "end": 1076.4, "word": " لل", "probability": 0.720703125}, {"start": 1076.4, "end": 1077.28, "word": " subgroup", "probability": 0.906005859375}, {"start": 1077.28, "end": 1078.04, "word": " generated", "probability": 0.86328125}, {"start": 1078.04, "end": 1078.74, "word": " by", "probability": 0.9873046875}, {"start": 1078.74, "end": 1080.18, "word": " R90", "probability": 0.979736328125}], "temperature": 1.0}, {"id": 44, "seek": 111100, "start": 1082.88, "end": 1111.0, "text": "الأولى ال order اللى هيساوي تمانية والتانية ال order اللى هيساوي أربعة يبقى ال index كده اتنين يبقى هذا بده يعطينا ان ال index تبع ال subgroup generated by R90 in D4 بده يساوي اتنين بروح بقوله by the above example", "tokens": [6027, 10721, 12610, 7578, 2423, 1668, 13672, 7578, 39896, 3794, 995, 45865, 46811, 7649, 10632, 16070, 2655, 7649, 10632, 2423, 1668, 13672, 7578, 39896, 3794, 995, 45865, 5551, 25513, 27884, 7251, 3555, 4587, 7578, 2423, 8186, 9122, 3215, 3224, 1975, 2655, 1863, 9957, 7251, 3555, 4587, 7578, 23758, 47525, 3224, 37495, 9566, 1829, 8315, 16472, 2423, 8186, 6055, 3555, 3615, 2423, 1422, 17377, 10833, 538, 497, 7771, 294, 413, 19, 47525, 3224, 7251, 3794, 995, 45865, 1975, 2655, 1863, 9957, 4724, 32887, 5016, 4724, 39648, 3224, 538, 264, 3673, 1365], "avg_logprob": -0.188701922421927, "compression_ratio": 1.6649484536082475, "no_speech_prob": 0.0, "words": [{"start": 1082.88, "end": 1083.7, "word": "الأولى", "probability": 0.795654296875}, {"start": 1083.7, "end": 1084.12, "word": " ال", "probability": 0.54541015625}, {"start": 1084.12, "end": 1084.46, "word": " order", "probability": 0.6416015625}, {"start": 1084.46, "end": 1084.74, "word": " اللى", "probability": 0.5787353515625}, {"start": 1084.74, "end": 1085.34, "word": " هيساوي", "probability": 0.738525390625}, {"start": 1085.34, "end": 1086.04, "word": " تمانية", "probability": 0.8042805989583334}, {"start": 1086.04, "end": 1086.92, "word": " والتانية", "probability": 0.7889404296875}, {"start": 1086.92, "end": 1087.08, "word": " ال", "probability": 0.84521484375}, {"start": 1087.08, "end": 1087.44, "word": " order", "probability": 0.96533203125}, {"start": 1087.44, "end": 1087.76, "word": " اللى", "probability": 0.97412109375}, {"start": 1087.76, "end": 1088.38, "word": " هيساوي", "probability": 0.975830078125}, {"start": 1088.38, "end": 1088.82, "word": " أربعة", "probability": 0.8167317708333334}, {"start": 1088.82, "end": 1089.12, "word": " يبقى", "probability": 0.9383544921875}, {"start": 1089.12, "end": 1089.26, "word": " ال", "probability": 0.96533203125}, {"start": 1089.26, "end": 1089.64, "word": " index", "probability": 0.91455078125}, {"start": 1089.64, "end": 1090.2, "word": " كده", "probability": 0.8504231770833334}, {"start": 1090.2, "end": 1091.78, "word": " اتنين", "probability": 0.80023193359375}, {"start": 1091.78, "end": 1092.78, "word": " يبقى", "probability": 0.9189453125}, {"start": 1092.78, "end": 1093.12, "word": " هذا", "probability": 0.9169921875}, {"start": 1093.12, "end": 1093.56, "word": " بده", "probability": 0.549072265625}, {"start": 1093.56, "end": 1094.3, "word": " يعطينا", "probability": 0.9439697265625}, {"start": 1094.3, "end": 1094.98, "word": " ان", "probability": 0.84814453125}, {"start": 1094.98, "end": 1095.22, "word": " ال", "probability": 0.90087890625}, {"start": 1095.22, "end": 1095.9, "word": " index", "probability": 0.89208984375}, {"start": 1095.9, "end": 1096.52, "word": " تبع", "probability": 0.8919270833333334}, {"start": 1096.52, "end": 1097.1, "word": " ال", "probability": 0.880859375}, {"start": 1097.1, "end": 1097.76, "word": " subgroup", "probability": 0.6170654296875}, {"start": 1097.76, "end": 1098.44, "word": " generated", "probability": 0.7958984375}, 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"probability": 0.316650390625}, {"start": 1148.99, "end": 1149.53, "word": " عضو", "probability": 0.470703125}, {"start": 1149.53, "end": 1149.95, "word": " عادل", "probability": 0.459716796875}, {"start": 1149.95, "end": 1151.73, "word": " من", "probability": 0.67724609375}, {"start": 1151.73, "end": 1152.11, "word": " G", "probability": 0.3056640625}, {"start": 1152.11, "end": 1156.29, "word": " ثم", "probability": 0.657470703125}, {"start": 1156.29, "end": 1156.61, "word": " الـ", "probability": 0.175537109375}, {"start": 1156.61, "end": 1158.25, "word": " set", "probability": 0.315673828125}, {"start": 1158.25, "end": 1161.53, "word": " of", "probability": 0.1685791015625}, {"start": 1161.53, "end": 1163.19, "word": " left", "probability": 0.6650390625}, {"start": 1163.19, "end": 1164.99, "word": " أو", "probability": 0.5859375}, {"start": 1164.99, "end": 1165.57, "word": " right", "probability": 0.92041015625}, {"start": 1165.57, "end": 1166.65, "word": " هدى", "probability": 0.4813639322916667}, {"start": 1166.65, "end": 1166.87, "word": " أو", "probability": 0.734375}, {"start": 1166.87, "end": 1167.47, "word": " هدى", "probability": 0.9695638020833334}, {"start": 1167.47, "end": 1168.69, "word": " left", "probability": 0.58203125}, {"start": 1168.69, "end": 1169.29, "word": " أو", "probability": 0.419677734375}, {"start": 1169.29, "end": 1169.91, "word": " right", "probability": 0.953125}], "temperature": 1.0}, {"id": 47, "seek": 120164, "start": 1174.84, "end": 1201.64, "text": "cossets of HNG is called is called the factor group is called the factor group of", "tokens": [66, 772, 1385, 295, 389, 30237, 307, 1219, 307, 1219, 264, 5952, 1594, 307, 1219, 264, 5952, 1594, 295], "avg_logprob": -0.32031249552965163, "compression_ratio": 1.5, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1174.84, "end": 1176.24, "word": "cossets", "probability": 0.5702107747395834}, {"start": 1176.24, "end": 1177.64, "word": " of", "probability": 0.939453125}, 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1199.94, "end": 1200.54, "word": " group", "probability": 0.97607421875}, {"start": 1200.54, "end": 1201.64, "word": " of", "probability": 0.98828125}], "temperature": 1.0}, {"id": 48, "seek": 123013, "start": 1202.71, "end": 1230.13, "text": "جي باي اتش or the quotient or the quotient group of جي باي اتش and we write", "tokens": [7435, 1829, 4724, 47302, 1975, 2655, 8592, 420, 264, 9641, 1196, 420, 264, 9641, 1196, 1594, 295, 10874, 1829, 4724, 47302, 1975, 2655, 8592, 293, 321, 2464], "avg_logprob": -0.3549107110926083, "compression_ratio": 1.3582089552238805, "no_speech_prob": 0.0, "words": [{"start": 1202.71, "end": 1203.51, "word": "جي", "probability": 0.558837890625}, {"start": 1203.51, "end": 1205.25, "word": " باي", "probability": 0.65771484375}, {"start": 1205.25, "end": 1206.23, "word": " اتش", "probability": 0.86376953125}, {"start": 1206.23, "end": 1209.39, "word": " or", "probability": 0.09136962890625}, {"start": 1209.39, "end": 1211.17, "word": " the", "probability": 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0.939453125}], "temperature": 1.0}, {"id": 49, "seek": 126213, "start": 1236.97, "end": 1262.13, "text": "و نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب", "tokens": [2407, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555, 8717, 4117, 2655, 3555], "avg_logprob": -0.31093749046325686, "compression_ratio": 5.0, "no_speech_prob": 0.0, "words": [{"start": 1236.97, "end": 1237.51, "word": "و", "probability": 0.66357421875}, {"start": 1237.51, "end": 1238.09, "word": " نكتب", "probability": 0.71209716796875}, {"start": 1238.09, "end": 1246.03, "word": " نكتب", "probability": 0.8358154296875}, {"start": 1246.03, "end": 1246.81, "word": " نكتب", "probability": 0.738250732421875}, {"start": 1246.81, "end": 1249.11, "word": " نكتب", "probability": 0.7541961669921875}, 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اتنين", "probability": 0.93359375}, {"start": 1349.14, "end": 1350.14, "word": " بنفس", "probability": 0.97314453125}, {"start": 1350.14, "end": 1350.88, "word": " المعنى", "probability": 0.9906005859375}], "temperature": 1.0}, {"id": 54, "seek": 136895, "start": 1351.47, "end": 1368.95, "text": "and we write the factor group as g modulo h أو g by h هي كل ال elements اللي على شكل left cosets بحيث ال g موجودة في g", "tokens": [474, 321, 2464, 264, 5952, 1594, 382, 290, 1072, 13455, 276, 34051, 290, 538, 276, 39896, 28242, 2423, 4959, 13672, 1829, 15844, 13412, 28820, 1411, 3792, 1385, 4724, 5016, 1829, 12984, 2423, 290, 3714, 29245, 23328, 3660, 8978, 290], "avg_logprob": -0.30644531920552254, "compression_ratio": 1.171875, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1351.47, "end": 1351.83, "word": "and", "probability": 0.060028076171875}, {"start": 1351.83, "end": 1352.07, "word": " we", "probability": 0.82275390625}, {"start": 1352.07, "end": 1352.47, "word": " write", "probability": 0.9033203125}, {"start": 1352.47, "end": 1352.71, "word": " the", "probability": 0.62060546875}, {"start": 1352.71, "end": 1353.03, "word": " factor", "probability": 0.59326171875}, {"start": 1353.03, "end": 1353.51, "word": " group", "probability": 0.9453125}, {"start": 1353.51, "end": 1356.43, "word": " as", "probability": 0.93505859375}, {"start": 1356.43, "end": 1357.19, "word": " g", "probability": 0.199462890625}, {"start": 1357.19, "end": 1358.07, "word": " modulo", "probability": 0.898193359375}, {"start": 1358.07, "end": 1358.55, "word": " h", "probability": 0.89404296875}, {"start": 1358.55, "end": 1359.03, "word": " أو", "probability": 0.54541015625}, {"start": 1359.03, "end": 1359.37, "word": " g", "probability": 0.9267578125}, {"start": 1359.37, "end": 1359.77, "word": " by", "probability": 0.74853515625}, {"start": 1359.77, "end": 1360.37, "word": " h", "probability": 0.97265625}, {"start": 1360.37, "end": 1361.61, "word": " هي", "probability": 0.6728515625}, {"start": 1361.61, "end": 1362.39, "word": " كل", "probability": 0.8544921875}, {"start": 1362.39, "end": 1362.69, "word": " ال", "probability": 0.8310546875}, {"start": 1362.69, "end": 1363.41, "word": " elements", "probability": 0.81005859375}, {"start": 1363.41, "end": 1363.79, "word": " اللي", "probability": 0.862548828125}, {"start": 1363.79, "end": 1363.99, "word": " على", "probability": 0.89794921875}, {"start": 1363.99, "end": 1364.47, "word": " شكل", "probability": 0.9814453125}, {"start": 1364.47, "end": 1364.79, "word": " left", "probability": 0.7275390625}, {"start": 1364.79, "end": 1365.49, "word": " cosets", "probability": 0.83349609375}, {"start": 1365.49, "end": 1366.19, "word": " بحيث", "probability": 0.96923828125}, {"start": 1366.19, "end": 1366.37, "word": " ال", "probability": 0.6923828125}, {"start": 1366.37, "end": 1366.59, "word": " g", "probability": 0.6982421875}, {"start": 1366.59, "end": 1367.31, "word": " موجودة", "probability": 0.981689453125}, {"start": 1367.31, "end": 1368.11, "word": " في", "probability": 0.771484375}, {"start": 1368.11, "end": 1368.95, "word": " g", "probability": 0.381103515625}], "temperature": 1.0}, {"id": 55, "seek": 138485, "start": 1371.77, "end": 1384.85, "text": "انت قلتلنا اول ما خدنا ال cosets ان ال coset هذه ليست group ليست subgroup طبعا قلتلك يمكن ان تكون subgroup ويمكن ان لا تكون subgroup", "tokens": [7649, 2655, 12174, 1211, 2655, 1211, 8315, 1975, 12610, 19446, 16490, 3215, 8315, 2423, 3792, 1385, 16472, 2423, 3792, 302, 29538, 32239, 14851, 1594, 32239, 14851, 1422, 17377, 23032, 3555, 3615, 995, 12174, 1211, 2655, 23275, 7251, 43020, 16472, 6055, 30544, 1422, 17377, 4032, 32640, 19452, 16472, 20193, 6055, 30544, 1422, 17377], "avg_logprob": -0.2418926830561656, "compression_ratio": 1.6722689075630253, "no_speech_prob": 0.0, "words": [{"start": 1371.77, "end": 1372.19, "word": "انت", "probability": 0.54718017578125}, {"start": 1372.19, "end": 1372.75, "word": " قلتلنا", "probability": 0.759716796875}, {"start": 1372.75, "end": 1373.11, "word": " اول", "probability": 0.857177734375}, {"start": 1373.11, "end": 1373.29, "word": " ما", "probability": 0.85400390625}, {"start": 1373.29, "end": 1373.69, "word": " خدنا", "probability": 0.92822265625}, {"start": 1373.69, "end": 1373.83, "word": " ال", "probability": 0.8662109375}, {"start": 1373.83, "end": 1374.45, "word": " cosets", "probability": 0.4670867919921875}, {"start": 1374.45, "end": 1374.89, "word": " ان", "probability": 0.82421875}, {"start": 1374.89, "end": 1375.11, "word": " ال", "probability": 0.7763671875}, {"start": 1375.11, "end": 1375.93, "word": " coset", "probability": 0.835205078125}, {"start": 1375.93, "end": 1376.53, "word": " هذه", "probability": 0.5322265625}, {"start": 1376.53, "end": 1377.29, "word": " ليست", "probability": 0.988037109375}, {"start": 1377.29, "end": 1377.69, "word": " group", "probability": 0.85595703125}, {"start": 1377.69, "end": 1378.33, "word": " ليست", "probability": 0.923828125}, {"start": 1378.33, "end": 1378.93, "word": " subgroup", "probability": 0.771728515625}, {"start": 1378.93, "end": 1379.87, "word": " طبعا", "probability": 0.9794921875}, {"start": 1379.87, "end": 1380.39, "word": " قلتلك", "probability": 0.8526611328125}, {"start": 1380.39, "end": 1380.95, "word": " يمكن", "probability": 0.98681640625}, {"start": 1380.95, "end": 1381.23, "word": " ان", "probability": 0.66015625}, {"start": 1381.23, "end": 1381.61, "word": " تكون", "probability": 0.992431640625}, {"start": 1381.61, "end": 1382.31, "word": " subgroup", "probability": 0.963623046875}, {"start": 1382.31, "end": 1382.99, "word": " ويمكن", "probability": 0.9337565104166666}, {"start": 1382.99, "end": 1383.37, "word": " ان", "probability": 0.44140625}, {"start": 1383.37, "end": 1383.51, "word": " لا", "probability": 0.87158203125}, {"start": 1383.51, "end": 1384.11, "word": " تكون", "probability": 0.988037109375}, {"start": 1384.11, "end": 1384.85, "word": " subgroup", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 56, "seek": 140749, "start": 1385.39, "end": 1407.49, "text": "يوم هم ماكناش ماخدينا normal subgroup لكن قلنا إذا ال element اللي ضربنا فيه ال subgroup كان من نفس ال subgroup بيطلع الناتج ال left coset هي ال subgroup الآن احنا جبنا شغلة جديدة ايش الشغلة الجديدة ان لو كانت ال H هذه normal subgroup", "tokens": [1829, 20498, 8032, 2304, 19446, 19452, 33599, 3714, 47283, 3215, 9957, 995, 2710, 1422, 17377, 44381, 12174, 1211, 8315, 11933, 15730, 2423, 4478, 13672, 1829, 48812, 25513, 8315, 8978, 3224, 2423, 1422, 17377, 25961, 9154, 8717, 36178, 2423, 1422, 17377, 4724, 1829, 9566, 1211, 3615, 28239, 9307, 7435, 2423, 1411, 3792, 302, 39896, 2423, 1422, 17377, 6024, 48506, 1975, 5016, 8315, 10874, 3555, 8315, 13412, 17082, 37977, 10874, 16254, 41891, 1975, 1829, 8592, 25124, 17082, 37977, 25724, 16254, 41891, 16472, 45164, 25961, 2655, 2423, 389, 29538, 2710, 1422, 17377], "avg_logprob": -0.23715277281072406, 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0.7994791666666666}, {"start": 1395.79, "end": 1396.05, "word": " ال", "probability": 0.79833984375}, {"start": 1396.05, "end": 1396.27, "word": " left", "probability": 0.83984375}, {"start": 1396.27, "end": 1396.85, "word": " coset", "probability": 0.6436767578125}, {"start": 1396.85, "end": 1397.11, "word": " هي", "probability": 0.8935546875}, {"start": 1397.11, "end": 1397.35, "word": " ال", "probability": 0.583984375}, {"start": 1397.35, "end": 1397.93, "word": " subgroup", "probability": 0.96923828125}, {"start": 1397.93, "end": 1398.59, "word": " الآن", "probability": 0.597900390625}, {"start": 1398.59, "end": 1399.71, "word": " احنا", "probability": 0.9142252604166666}, {"start": 1399.71, "end": 1400.15, "word": " جبنا", "probability": 0.86962890625}, {"start": 1400.15, "end": 1400.67, "word": " شغلة", "probability": 0.8304036458333334}, {"start": 1400.67, "end": 1400.99, "word": " جديدة", "probability": 0.9845377604166666}, {"start": 1400.99, "end": 1401.21, "word": " ايش", "probability": 0.6456705729166666}, {"start": 1401.21, "end": 1401.71, "word": " الشغلة", "probability": 0.9459635416666666}, {"start": 1401.71, "end": 1402.45, "word": " الجديدة", "probability": 0.9811197916666666}, {"start": 1402.45, "end": 1403.09, "word": " ان", "probability": 0.662109375}, {"start": 1403.09, "end": 1403.39, "word": " لو", "probability": 0.8525390625}, {"start": 1403.39, "end": 1404.27, "word": " كانت", "probability": 0.963623046875}, {"start": 1404.27, "end": 1404.57, "word": " ال", "probability": 0.9541015625}, {"start": 1404.57, "end": 1404.91, "word": " H", "probability": 0.7333984375}, {"start": 1404.91, "end": 1405.31, "word": " هذه", "probability": 0.361328125}, {"start": 1405.31, "end": 1406.19, "word": " normal", "probability": 0.67138671875}, {"start": 1406.19, "end": 1407.49, "word": " subgroup", "probability": 0.972412109375}], "temperature": 1.0}, {"id": 57, "seek": 143317, "start": 1407.95, "end": 1433.17, "text": "فكل الـ left cosets اللي عندي او ال destined left cosets بيكونولي جروب جديد اسمها ال factor group او ال quotient group وهذه ماكنتش قبل ذلك يبقى ال factor group او ال quotient group عناصرها كلهم left cosets او كلهم right cosets يا هذه امين يا هذه", "tokens": [5172, 28820, 2423, 39184, 1411, 3792, 1385, 13672, 1829, 18871, 16254, 1975, 2407, 2423, 33169, 1411, 3792, 1385, 4724, 1829, 30544, 12610, 1829, 10874, 32887, 3555, 10874, 16254, 3215, 24525, 2304, 11296, 2423, 5952, 1594, 1975, 2407, 2423, 9641, 1196, 1594, 37037, 24192, 19446, 19452, 2655, 8592, 12174, 36150, 29910, 23275, 7251, 3555, 4587, 7578, 2423, 5952, 1594, 1975, 2407, 2423, 9641, 1196, 1594, 18871, 33546, 2288, 11296, 28242, 16095, 1411, 3792, 1385, 1975, 2407, 28242, 16095, 558, 3792, 1385, 35186, 29538, 1975, 2304, 9957, 35186, 29538], "avg_logprob": -0.2604758400808681, "compression_ratio": 1.8457446808510638, "no_speech_prob": 0.0, "words": [{"start": 1407.95, "end": 1408.67, "word": "فكل", "probability": 0.5966796875}, {"start": 1408.67, "end": 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1414.09, "end": 1414.55, "word": " جديد", "probability": 0.92333984375}, {"start": 1414.55, "end": 1415.11, "word": " اسمها", "probability": 0.8294270833333334}, {"start": 1415.11, "end": 1415.23, "word": " ال", "probability": 0.62939453125}, {"start": 1415.23, "end": 1415.59, "word": " factor", "probability": 0.837890625}, {"start": 1415.59, "end": 1416.11, "word": " group", "probability": 0.91259765625}, {"start": 1416.11, "end": 1416.67, "word": " او", "probability": 0.810546875}, {"start": 1416.67, "end": 1416.99, "word": " ال", "probability": 0.814453125}, {"start": 1416.99, "end": 1418.07, "word": " quotient", "probability": 0.934326171875}, {"start": 1418.07, "end": 1418.77, "word": " group", "probability": 0.98876953125}, {"start": 1418.77, "end": 1419.67, "word": " وهذه", "probability": 0.710205078125}, {"start": 1419.67, "end": 1420.35, "word": " ماكنتش", "probability": 0.787353515625}, {"start": 1420.35, "end": 1420.85, "word": " قبل", "probability": 0.981689453125}, {"start": 1420.85, "end": 1421.73, "word": " ذلك", "probability": 0.993408203125}, {"start": 1421.73, "end": 1422.81, "word": " يبقى", "probability": 0.952392578125}, {"start": 1422.81, "end": 1422.93, "word": " ال", "probability": 0.81884765625}, {"start": 1422.93, "end": 1423.35, "word": " factor", "probability": 0.943359375}, {"start": 1423.35, "end": 1423.87, "word": " group", "probability": 0.98583984375}, {"start": 1423.87, "end": 1424.17, "word": " او", "probability": 0.939208984375}, {"start": 1424.17, "end": 1424.39, "word": " ال", "probability": 0.88916015625}, {"start": 1424.39, "end": 1424.99, "word": " quotient", "probability": 0.9892578125}, {"start": 1424.99, "end": 1425.45, "word": " group", "probability": 0.990234375}, {"start": 1425.45, "end": 1426.71, "word": " عناصرها", "probability": 0.7825927734375}, {"start": 1426.71, "end": 1427.61, "word": " كلهم", "probability": 0.9599609375}, {"start": 1427.61, "end": 1427.97, "word": " left", "probability": 0.96875}, {"start": 1427.97, "end": 1428.57, "word": " cosets", "probability": 0.97607421875}, {"start": 1428.57, "end": 1428.91, "word": " او", "probability": 0.947509765625}, {"start": 1428.91, "end": 1429.59, "word": " كلهم", "probability": 0.968017578125}, {"start": 1429.59, "end": 1430.23, "word": " right", "probability": 0.96728515625}, {"start": 1430.23, "end": 1430.79, "word": " cosets", "probability": 0.980224609375}, {"start": 1430.79, "end": 1431.05, "word": " يا", "probability": 0.55859375}, {"start": 1431.05, "end": 1431.35, "word": " هذه", "probability": 0.607421875}, {"start": 1431.35, "end": 1431.83, "word": " امين", "probability": 0.5021158854166666}, {"start": 1431.83, "end": 1432.55, "word": " يا", "probability": 0.52734375}, {"start": 1432.55, "end": 1433.17, "word": " هذه", "probability": 0.88818359375}], "temperature": 1.0}, {"id": 58, "seek": 144761, "start": 1433.63, "end": 1447.61, "text": "طيب، الان هذا اللي احنا بنقوله، الان انا ايش قلت؟ قلت الـ G modulo H is a group 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b", "probability": 0.947265625}, {"start": 1703.27, "end": 1704.13, "word": " prime", "probability": 0.9189453125}, {"start": 1704.13, "end": 1704.73, "word": " h", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 68, "seek": 172907, "start": 1708.61, "end": 1729.07, "text": "مشان أثبت عملية الضرب بدأ أضرب الأول هنا في الأول هنا و أثبت أنه يساوي حاصل ضرب الثاني في الثاني من هنا ان طلع الكلام هذا صحيح يبقى ال operation تبقى معرفة تعريفا صحيحا يبقى انا افترضت ان اتنين هذول ما لهم", "tokens": [2304, 8592, 7649, 5551, 12984, 3555, 2655, 6225, 42213, 10632, 6024, 114, 25513, 47525, 10721, 5551, 11242, 25513, 16247, 12610, 34105, 8978, 16247, 12610, 34105, 4032, 5551, 12984, 3555, 2655, 14739, 3224, 7251, 3794, 995, 45865, 11331, 33546, 1211, 48812, 25513, 6024, 104, 7649, 1829, 8978, 6024, 104, 7649, 1829, 9154, 34105, 16472, 23032, 1211, 3615, 2423, 28820, 10943, 23758, 20328, 5016, 1829, 5016, 7251, 3555, 4587, 7578, 2423, 6916, 6055, 3555, 4587, 7578, 20449, 28480, 3660, 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معرفة", "probability": 0.682373046875}, {"start": 1724.23, "end": 1725.13, "word": " تعريفا", "probability": 0.974365234375}, {"start": 1725.13, "end": 1726.07, "word": " صحيحا", "probability": 0.96611328125}, {"start": 1726.07, "end": 1726.85, "word": " يبقى", "probability": 0.939208984375}, {"start": 1726.85, "end": 1727.03, "word": " انا", "probability": 0.800048828125}, {"start": 1727.03, "end": 1727.59, "word": " افترضت", "probability": 0.8865234375}, {"start": 1727.59, "end": 1727.71, "word": " ان", "probability": 0.7783203125}, {"start": 1727.71, "end": 1728.15, "word": " اتنين", "probability": 0.9388427734375}, {"start": 1728.15, "end": 1728.49, "word": " هذول", "probability": 0.6986490885416666}, {"start": 1728.49, "end": 1728.71, "word": " ما", "probability": 0.88134765625}, {"start": 1728.71, "end": 1729.07, "word": " لهم", "probability": 0.817138671875}], "temperature": 1.0}, {"id": 69, "seek": 175673, "start": 1729.69, "end": 1756.73, "text": "هذا بيسوي هذا و التاني بيسوي هذا طيب من خلال هذه المعلومات دي احاول اثبت ان ال A BH بدي اسوي A prime B prime H بس قبل هذا الكلام تعالوا ناخد معلومة نستفيد بها في البرهان اللي بعدها الآن شباب ال A prime موجودة في ال A prime H", "tokens": [3224, 15730, 4724, 1829, 3794, 45865, 23758, 4032, 16712, 7649, 1829, 4724, 1829, 3794, 45865, 23758, 23032, 1829, 3555, 9154, 16490, 1211, 6027, 29538, 9673, 30241, 20498, 9307, 11778, 1829, 1975, 5016, 995, 12610, 1975, 12984, 3555, 2655, 16472, 2423, 316, 40342, 4724, 16254, 24525, 45865, 316, 5835, 363, 5835, 389, 4724, 3794, 12174, 36150, 23758, 2423, 28820, 10943, 37279, 6027, 14407, 8717, 47283, 3215, 20449, 1211, 20498, 3660, 8717, 14851, 5172, 25708, 4724, 11296, 8978, 2423, 26890, 3224, 7649, 13672, 1829, 39182, 11296, 6024, 48506, 13412, 3555, 16758, 2423, 316, 5835, 3714, 29245, 23328, 3660, 8978, 2423, 316, 5835, 389], "avg_logprob": -0.1930147036910057, "compression_ratio": 1.8137254901960784, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 1729.69, 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" prime", "probability": 0.86279296875}, {"start": 1743.23, "end": 1743.63, "word": " H", "probability": 0.95849609375}, {"start": 1743.63, "end": 1744.33, "word": " بس", "probability": 0.9599609375}, {"start": 1744.33, "end": 1744.67, "word": " قبل", "probability": 0.974609375}, {"start": 1744.67, "end": 1744.97, "word": " هذا", "probability": 0.90087890625}, {"start": 1744.97, "end": 1745.51, "word": " الكلام", "probability": 0.95654296875}, {"start": 1745.51, "end": 1746.49, "word": " تعالوا", "probability": 0.9453125}, {"start": 1746.49, "end": 1746.93, "word": " ناخد", "probability": 0.9793294270833334}, {"start": 1746.93, "end": 1747.65, "word": " معلومة", "probability": 0.9866943359375}, {"start": 1747.65, "end": 1748.57, "word": " نستفيد", "probability": 0.97216796875}, {"start": 1748.57, "end": 1748.85, "word": " بها", "probability": 0.87841796875}, {"start": 1748.85, "end": 1749.03, "word": " في", "probability": 0.8134765625}, {"start": 1749.03, "end": 1749.81, "word": " البرهان", "probability": 0.873779296875}, {"start": 1749.81, "end": 1750.27, "word": " اللي", "probability": 0.935791015625}, {"start": 1750.27, "end": 1751.15, "word": " بعدها", "probability": 0.6177978515625}, {"start": 1751.15, "end": 1751.75, "word": " الآن", "probability": 0.60186767578125}, {"start": 1751.75, "end": 1752.23, "word": " شباب", "probability": 0.8361002604166666}, {"start": 1752.23, "end": 1752.47, "word": " ال", "probability": 0.96875}, {"start": 1752.47, "end": 1753.05, "word": " A", "probability": 0.962890625}, {"start": 1753.05, "end": 1753.73, "word": " prime", "probability": 0.802734375}, {"start": 1753.73, "end": 1754.75, "word": " موجودة", "probability": 0.986083984375}, {"start": 1754.75, "end": 1754.95, "word": " في", "probability": 0.931640625}, {"start": 1754.95, "end": 1755.23, "word": " ال", "probability": 0.93408203125}, {"start": 1755.23, "end": 1755.57, "word": " A", "probability": 0.98193359375}, {"start": 1755.57, "end": 1756.19, "word": " prime", 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since الـH is a normal subgroup من مين؟ من G وبالتالي حصل الضرب اللي عندها ده سواء حصل الضرب اللي عندها ده يبقى ال operation معرفة تعريفا سليما مافيش فيها أي شيء طبعا إيش بده أثبات؟", "tokens": [20292, 8592, 22807, 2423, 39184, 39, 33, 12602, 7435, 34268, 11296, 30731, 3714, 9957, 22807, 30731, 40342, 23758, 28242, 10943, 20328, 5016, 1829, 5016, 1670, 2423, 39184, 39, 307, 257, 2710, 1422, 17377, 9154, 3714, 9957, 22807, 9154, 460, 46599, 6027, 2655, 6027, 1829, 11331, 36520, 6024, 114, 25513, 13672, 1829, 43242, 11296, 11778, 3224, 8608, 2407, 16606, 11331, 36520, 6024, 114, 25513, 13672, 1829, 43242, 11296, 11778, 3224, 7251, 3555, 4587, 7578, 2423, 6916, 20449, 28480, 3660, 37279, 16572, 5172, 995, 8608, 20292, 15042, 19446, 41185, 8592, 8978, 11296, 36632, 44049, 38207, 23032, 3555, 3615, 995, 11933, 1829, 8592, 47525, 3224, 5551, 12984, 3555, 9307, 22807], "avg_logprob": -0.22395833650672878, "compression_ratio": 1.6491228070175439, "no_speech_prob": 0.0, "words": [{"start": 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"word": " تعريفا", "probability": 0.9732666015625}, {"start": 1981.2, "end": 1981.8, "word": " سليما", "probability": 0.9541015625}, {"start": 1981.8, "end": 1982.7, "word": " مافيش", "probability": 0.8756510416666666}, {"start": 1982.7, "end": 1983.22, "word": " فيها", "probability": 0.99169921875}, {"start": 1983.22, "end": 1983.74, "word": " أي", "probability": 0.70068359375}, {"start": 1983.74, "end": 1984.84, "word": " شيء", "probability": 0.81103515625}, {"start": 1984.84, "end": 1985.22, "word": " طبعا", "probability": 0.77423095703125}, {"start": 1985.22, "end": 1985.4, "word": " إيش", "probability": 0.7657877604166666}, {"start": 1985.4, "end": 1985.74, "word": " بده", "probability": 0.5372314453125}, {"start": 1985.74, "end": 1986.6, "word": " أثبات؟", "probability": 0.9095703125}], "temperature": 1.0}, {"id": 80, "seek": 201403, "start": 1987.05, "end": 2014.03, "text": "بدي أثبت أن هذه عبارة عن مين؟ عن group يبقى بد ال identity element و ال inverse element و ال associativity بقوله بسيطة بدالي الحكاية ال associativity let ال a h و ال b h و ال c h موجودة في ال g modulo h let then", "tokens": [3555, 16254, 5551, 12984, 3555, 2655, 14739, 29538, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 18871, 1594, 7251, 3555, 4587, 7578, 47525, 2423, 6575, 4478, 4032, 2423, 17340, 4478, 4032, 2423, 4180, 30142, 4724, 39648, 3224, 4724, 3794, 1829, 9566, 3660, 47525, 6027, 1829, 21542, 4117, 995, 10632, 2423, 4180, 30142, 718, 2423, 257, 276, 4032, 2423, 272, 276, 4032, 2423, 269, 276, 3714, 29245, 23328, 3660, 8978, 2423, 290, 1072, 13455, 276, 718, 550], "avg_logprob": -0.27008929964783907, "compression_ratio": 1.5783783783783785, "no_speech_prob": 0.0, "words": [{"start": 1987.05, "end": 1987.47, "word": "بدي", "probability": 0.39715576171875}, {"start": 1987.47, "end": 1988.01, "word": " أثبت", "probability": 0.9202880859375}, {"start": 1988.01, "end": 1988.23, "word": " أن", "probability": 0.357666015625}, {"start": 1988.23, "end": 1988.63, "word": 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{"start": 2117.74, "end": 2118.34, "word": " c", "probability": 0.4990234375}, {"start": 2118.34, "end": 2118.92, "word": " h", "probability": 0.57177734375}, {"start": 2118.92, "end": 2119.8, "word": " بشكل", "probability": 0.8177083333333334}, {"start": 2119.8, "end": 2120.14, "word": " لأن", "probability": 0.4564208984375}, {"start": 2120.14, "end": 2120.56, "word": " هذا", "probability": 0.92529296875}, {"start": 2120.56, "end": 2121.24, "word": " يبقى", "probability": 0.922607421875}, {"start": 2121.24, "end": 2121.94, "word": " خاصية", "probability": 0.9347330729166666}, {"start": 2121.94, "end": 2122.12, "word": " ال", "probability": 0.95703125}, {"start": 2122.12, "end": 2122.98, "word": " associativity", "probability": 0.810791015625}, {"start": 2122.98, "end": 2123.98, "word": " عليها", "probability": 0.976806640625}, {"start": 2123.98, "end": 2124.88, "word": " خاصية", "probability": 0.9733072916666666}, {"start": 2124.88, "end": 2125.56, "word": " صحية", "probability": 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generated by أربعة هذه كنا نسميها زمان في chapter أربعة و chapter تلاتة هي ال sub group generated by أربعة بس احنا الأن بنقول أربعة زد", "tokens": [11622, 3215, 5551, 25513, 27884, 15844, 30767, 3215, 16070, 43761, 2423, 1422, 1594, 10833, 538, 5551, 25513, 27884, 3714, 19913, 3555, 2407, 9566, 7251, 3555, 4587, 7578, 16247, 25513, 27884, 30767, 3215, 39896, 6225, 3555, 9640, 3660, 18871, 2423, 1422, 1594, 10833, 538, 5551, 25513, 27884, 29538, 9122, 8315, 8717, 38251, 1829, 11296, 30767, 2304, 7649, 8978, 7187, 5551, 25513, 27884, 4032, 7187, 6055, 1211, 9307, 3660, 39896, 2423, 1422, 1594, 10833, 538, 5551, 25513, 27884, 4724, 3794, 1975, 5016, 8315, 16247, 1863, 44945, 39648, 5551, 25513, 27884, 30767, 3215], "avg_logprob": -0.164577603995145, "compression_ratio": 1.9943502824858756, "no_speech_prob": 1.0132789611816406e-06, "words": [{"start": 2578.89, "end": 2579.29, "word": "زد", "probability": 0.568115234375}, {"start": 2579.29, "end": 2579.65, "word": " أربعة", "probability": 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خطوة تانية جل الأربعة زد normal في زد زد ال operation اللي عليها هي عملية عملية الجمع عملية الجمع abelian ولا لا", "tokens": [2655, 15042, 2304, 23032, 1829, 3555, 16247, 25513, 27884, 30767, 3215, 29538, 13672, 1829, 39896, 2423, 1422, 17377, 4032, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 11296, 29538, 2423, 1422, 17377, 9154, 30767, 3215, 7251, 10943, 995, 1975, 12984, 3555, 2655, 8315, 11296, 46811, 10943, 7251, 3555, 4587, 7578, 16490, 1211, 9381, 8315, 33962, 9566, 2407, 3660, 16247, 12610, 7578, 16490, 9566, 2407, 3660, 6055, 7649, 10632, 10874, 1211, 16247, 25513, 27884, 30767, 3215, 2710, 8978, 30767, 3215, 30767, 3215, 2423, 6916, 13672, 1829, 25894, 11296, 39896, 6225, 42213, 10632, 6225, 42213, 10632, 25724, 2304, 3615, 6225, 42213, 10632, 25724, 2304, 3615, 410, 338, 952, 49429, 20193], "avg_logprob": -0.24827981432643506, "compression_ratio": 1.9043062200956937, "no_speech_prob": 7.152557373046875e-07, "words": [{"start": 2601.58, "end": 2602.2, "word": "تمام", 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subgroup of an abelian group is normal يبقى هذه يبقى باجي بيقول since اللي هو z is abelian يبقى الأربعة z is a normal subgroup من مين subgroup من g", "tokens": [9566, 3555, 5551, 12610, 50113, 6027, 5551, 9778, 3215, 8315, 45595, 20498, 604, 1422, 17377, 295, 364, 410, 338, 952, 1594, 307, 2710, 7251, 3555, 4587, 7578, 29538, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 1829, 39648, 1670, 13672, 1829, 31439, 710, 307, 410, 338, 952, 7251, 3555, 4587, 7578, 16247, 25513, 27884, 710, 307, 257, 2710, 1422, 17377, 9154, 3714, 9957, 1422, 17377, 9154, 290], "avg_logprob": -0.19347426843117266, "compression_ratio": 1.5354838709677419, "no_speech_prob": 0.0, "words": [{"start": 2627.4, "end": 2627.84, "word": "طب", "probability": 0.861328125}, {"start": 2627.84, "end": 2628.32, "word": " أول", "probability": 0.73681640625}, {"start": 2628.32, "end": 2628.74, "word": " مثال", "probability": 0.96923828125}, {"start": 2628.74, "end": 2629.26, "word": " أخدنا", "probability": 0.927734375}, 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"end": 2989.05, "word": " بده", "probability": 0.9599609375}, {"start": 2989.05, "end": 2989.33, "word": " يساوي", "probability": 0.984130859375}, {"start": 2989.33, "end": 2990.01, "word": " مين؟", "probability": 0.95361328125}, {"start": 2990.01, "end": 2990.37, "word": " بده", "probability": 0.960205078125}, {"start": 2990.37, "end": 2990.99, "word": " يساوي", "probability": 0.9842529296875}, {"start": 2990.99, "end": 2991.53, "word": " أربعة", "probability": 0.9620768229166666}, {"start": 2991.53, "end": 2992.03, "word": " طيب", "probability": 0.9599609375}, {"start": 2992.03, "end": 2993.93, "word": " مدام", "probability": 0.8346354166666666}, {"start": 2993.93, "end": 2994.35, "word": " هيك", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 117, "seek": 301540, "start": 2994.84, "end": 3015.4, "text": "إذا هذه قولنا فيها أكم element إذا بقدر أقول إنها Cyclic وهذا generator تمام؟ مش حاجات هيك الواحد زائد أربعة زد generator والتلاتة زائد أربعة زد برضه generator", "tokens": [28814, 15730, 29538, 12174, 12610, 8315, 8978, 11296, 5551, 24793, 4478, 11933, 15730, 4724, 28543, 2288, 5551, 39648, 36145, 11296, 10295, 66, 1050, 37037, 15730, 19265, 46811, 10943, 22807, 37893, 11331, 26108, 9307, 39896, 4117, 2423, 14407, 24401, 30767, 16373, 3215, 5551, 25513, 27884, 30767, 3215, 19265, 16070, 2655, 1211, 9307, 3660, 30767, 16373, 3215, 5551, 25513, 27884, 30767, 3215, 4724, 43042, 3224, 19265], "avg_logprob": -0.27908653846153847, "compression_ratio": 1.494047619047619, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2994.84, "end": 2995.36, "word": "إذا", "probability": 0.5452880859375}, {"start": 2995.36, "end": 2997.4, "word": " هذه", "probability": 0.224853515625}, {"start": 2997.4, "end": 2997.78, "word": " قولنا", "probability": 0.70068359375}, {"start": 2997.78, "end": 2998.38, "word": " فيها", "probability": 0.9765625}, {"start": 2998.38, "end": 2999.0, "word": " أكم", "probability": 0.643310546875}, {"start": 2999.0, "end": 2999.86, "word": " element", "probability": 0.72021484375}, {"start": 2999.86, "end": 3000.96, "word": " إذا", "probability": 0.6905517578125}, {"start": 3000.96, "end": 3001.76, "word": " بقدر", "probability": 0.9803059895833334}, {"start": 3001.76, "end": 3002.36, "word": " أقول", "probability": 0.868408203125}, {"start": 3002.36, "end": 3002.88, "word": " إنها", "probability": 0.839111328125}, {"start": 3002.88, "end": 3003.56, "word": " Cyclic", "probability": 0.67236328125}, {"start": 3003.56, "end": 3004.0, "word": " وهذا", "probability": 0.7978515625}, {"start": 3004.0, "end": 3004.84, "word": " generator", "probability": 0.69873046875}, {"start": 3004.84, "end": 3006.4, "word": " تمام؟", "probability": 0.6554361979166666}, {"start": 3006.4, "end": 3006.58, "word": " مش", "probability": 0.9267578125}, {"start": 3006.58, "end": 3006.98, "word": " حاجات", "probability": 0.7908528645833334}, {"start": 3006.98, "end": 3007.54, "word": " هيك", "probability": 0.626708984375}, {"start": 3007.54, "end": 3008.64, "word": " الواحد", "probability": 0.93994140625}, {"start": 3008.64, "end": 3009.36, "word": " زائد", "probability": 0.9296875}, {"start": 3009.36, "end": 3010.28, "word": " أربعة", "probability": 0.8111979166666666}, {"start": 3010.28, "end": 3010.48, "word": " زد", "probability": 0.4482421875}, {"start": 3010.48, "end": 3011.24, "word": " generator", "probability": 0.8779296875}, {"start": 3011.24, "end": 3012.56, "word": " والتلاتة", "probability": 0.89873046875}, {"start": 3012.56, "end": 3013.0, "word": " زائد", "probability": 0.9420572916666666}, {"start": 3013.0, "end": 3013.54, "word": " أربعة", "probability": 0.9202473958333334}, {"start": 3013.54, "end": 3013.94, "word": " زد", "probability": 0.97314453125}, {"start": 3013.94, "end": 3014.54, "word": " برضه", "probability": 0.8533528645833334}, {"start": 3014.54, "end": 3015.4, "word": " generator", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 118, "seek": 304625, "start": 3017.69, "end": 3046.25, "text": "يبقى هنا باجي بقول له so تلاتة زائد اربعة زد is a generator is a generator for اللي هو z modulo اربعة زد هذا بدي يعطيلك ان زد modulo اربعة زد is cyclic", "tokens": [1829, 3555, 4587, 7578, 34105, 4724, 26108, 1829, 4724, 39648, 46740, 370, 6055, 1211, 9307, 3660, 30767, 16373, 3215, 1975, 25513, 27884, 30767, 3215, 307, 257, 19265, 307, 257, 19265, 337, 13672, 1829, 31439, 710, 1072, 13455, 1975, 25513, 27884, 30767, 3215, 23758, 4724, 16254, 37495, 9566, 1829, 23275, 16472, 30767, 3215, 1072, 13455, 1975, 25513, 27884, 30767, 3215, 307, 38154, 1050], "avg_logprob": -0.2120535671710968, "compression_ratio": 1.5602836879432624, "no_speech_prob": 0.0, "words": [{"start": 3017.69, "end": 3018.21, "word": "يبقى", "probability": 0.9093017578125}, {"start": 3018.21, "end": 3018.53, "word": " هنا", "probability": 0.9443359375}, {"start": 3018.53, "end": 3018.91, "word": " باجي", "probability": 0.7329915364583334}, {"start": 3018.91, "end": 3019.41, "word": " بقول", "probability": 0.93994140625}, {"start": 3019.41, "end": 3019.85, "word": " له", "probability": 0.5302734375}, {"start": 3019.85, "end": 3020.61, "word": " so", "probability": 0.403564453125}, {"start": 3020.61, "end": 3021.87, "word": " تلاتة", "probability": 0.9217529296875}, {"start": 3021.87, "end": 3022.45, "word": " زائد", "probability": 0.9267578125}, {"start": 3022.45, "end": 3023.15, "word": " اربعة", "probability": 0.7605794270833334}, {"start": 3023.15, "end": 3023.87, "word": " زد", "probability": 0.55712890625}, {"start": 3023.87, "end": 3024.81, "word": " is", "probability": 0.8251953125}, {"start": 3024.81, "end": 3025.49, "word": " a", "probability": 0.9599609375}, {"start": 3025.49, "end": 3027.17, "word": " generator", "probability": 0.97705078125}, {"start": 3027.17, "end": 3029.85, "word": " is", "probability": 0.56640625}, {"start": 3029.85, "end": 3030.29, "word": " a", "probability": 0.9736328125}, {"start": 3030.29, "end": 3031.31, "word": " generator", "probability": 0.97314453125}, {"start": 3031.31, "end": 3032.87, "word": " for", "probability": 0.91064453125}, {"start": 3032.87, "end": 3033.85, "word": " اللي", "probability": 0.940673828125}, {"start": 3033.85, "end": 3034.33, "word": " هو", "probability": 0.9814453125}, {"start": 3034.33, "end": 3035.49, "word": " z", "probability": 0.56494140625}, {"start": 3035.49, "end": 3036.99, "word": " modulo", "probability": 0.845703125}, {"start": 3036.99, "end": 3038.29, "word": " اربعة", "probability": 0.8600260416666666}, {"start": 3038.29, "end": 3038.87, "word": " زد", "probability": 0.908935546875}, {"start": 3038.87, "end": 3039.49, "word": " هذا", "probability": 0.90673828125}, {"start": 3039.49, "end": 3039.85, "word": " بدي", "probability": 0.717529296875}, {"start": 3039.85, "end": 3040.37, "word": " يعطيلك", "probability": 0.73150634765625}, {"start": 3040.37, "end": 3040.63, "word": " ان", "probability": 0.85400390625}, {"start": 3040.63, "end": 3041.45, "word": " زد", "probability": 0.5791015625}, {"start": 3041.45, "end": 3042.39, "word": " modulo", "probability": 0.866943359375}, {"start": 3042.39, "end": 3043.17, "word": " اربعة", "probability": 0.90673828125}, {"start": 3043.17, "end": 3044.11, "word": " زد", "probability": 0.990966796875}, {"start": 3044.11, "end": 3044.97, "word": " is", "probability": 0.9638671875}, {"start": 3044.97, "end": 3046.25, "word": " cyclic", "probability": 0.84033203125}], "temperature": 1.0}, {"id": 119, "seek": 306465, "start": 3046.81, "end": 3064.65, "text": "مش عاجزكوا بس يبقى هنا also اللي هو z modulo 4z ايزو مورفك لمين ل z 4 طب لو عمّمت و اروح اقول", "tokens": [2304, 8592, 6225, 26108, 11622, 4117, 14407, 4724, 3794, 7251, 3555, 4587, 7578, 34105, 611, 13672, 1829, 31439, 710, 1072, 13455, 1017, 89, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 4117, 32767, 9957, 5296, 710, 1017, 23032, 3555, 45164, 6225, 2304, 11703, 2304, 2655, 4032, 1975, 32887, 5016, 1975, 39648], "avg_logprob": -0.2731311262822619, "compression_ratio": 1.1825396825396826, "no_speech_prob": 0.0, "words": [{"start": 3046.81, "end": 3047.13, "word": "مش", "probability": 0.91455078125}, {"start": 3047.13, "end": 3047.83, "word": " عاجزكوا", "probability": 0.663916015625}, {"start": 3047.83, "end": 3048.33, "word": " بس", "probability": 0.972900390625}, {"start": 3048.33, "end": 3049.43, "word": " يبقى", "probability": 0.9287109375}, {"start": 3049.43, "end": 3049.85, "word": " هنا", "probability": 0.984375}, {"start": 3049.85, "end": 3050.71, "word": " also", "probability": 0.77197265625}, {"start": 3050.71, "end": 3052.39, "word": " اللي", "probability": 0.92578125}, {"start": 3052.39, "end": 3052.57, "word": " هو", "probability": 0.9619140625}, {"start": 3052.57, "end": 3053.11, "word": " z", "probability": 0.33544921875}, {"start": 3053.11, "end": 3054.45, "word": " modulo", "probability": 0.823974609375}, {"start": 3054.45, "end": 3056.23, "word": " 4z", "probability": 0.6220703125}, {"start": 3056.23, "end": 3057.37, "word": " ايزو", "probability": 0.76959228515625}, {"start": 3057.37, "end": 3058.03, "word": " مورفك", "probability": 0.8173828125}, {"start": 3058.03, "end": 3058.53, "word": " لمين", "probability": 0.66259765625}, {"start": 3058.53, "end": 3059.15, "word": " ل", "probability": 0.68408203125}, {"start": 3059.15, "end": 3059.65, "word": " z", "probability": 0.369384765625}, {"start": 3059.65, "end": 3060.49, "word": " 4", "probability": 0.363037109375}, {"start": 3060.49, "end": 3061.17, "word": " طب", "probability": 0.88671875}, {"start": 3061.17, "end": 3061.39, "word": " لو", "probability": 0.99560546875}, {"start": 3061.39, "end": 3062.27, "word": " عمّمت", "probability": 0.843603515625}, {"start": 3062.27, "end": 3063.65, "word": " و", "probability": 0.8935546875}, {"start": 3063.65, "end": 3064.03, "word": " اروح", "probability": 0.798583984375}, {"start": 3064.03, "end": 3064.65, "word": " اقول", "probability": 0.948486328125}], "temperature": 1.0}, {"id": 120, "seek": 309199, "start": 3065.09, "end": 3091.99, "text": "in general وعلى وجه العموم z modulo n في z عايز أمرك لمين يا شباب ل z n من الأن فصاعدا يبقى هذا المثال استفدنا منه شغلات كثيرة جدا يعطيكوا العافية ونكمل ان شاء الله يوم الأثنين", "tokens": [259, 2674, 4032, 3615, 23942, 49610, 3224, 18863, 2304, 20498, 710, 1072, 13455, 297, 8978, 710, 6225, 47302, 11622, 5551, 29973, 4117, 32767, 9957, 35186, 13412, 3555, 16758, 5296, 710, 297, 9154, 16247, 1863, 6156, 9381, 995, 22488, 995, 7251, 3555, 4587, 7578, 23758, 9673, 12984, 6027, 44713, 5172, 3215, 8315, 9154, 3224, 13412, 17082, 1211, 9307, 9122, 12984, 48923, 10874, 28259, 37495, 9566, 1829, 4117, 14407, 18863, 31845, 10632, 4032, 1863, 24793, 1211, 16472, 13412, 16606, 21984, 7251, 20498, 16247, 12984, 1863, 9957], "avg_logprob": -0.211397062329685, "compression_ratio": 1.4874371859296482, "no_speech_prob": 3.0994415283203125e-06, "words": [{"start": 3065.09, "end": 3065.79, "word": "in", "probability": 0.299560546875}, {"start": 3065.79, "end": 3067.03, "word": " general", "probability": 0.91552734375}, {"start": 3067.03, "end": 3068.51, "word": " وعلى", "probability": 0.8723958333333334}, {"start": 3068.51, "end": 3069.07, "word": " وجه", "probability": 0.968505859375}, {"start": 3069.07, "end": 3069.71, "word": " العموم", "probability": 0.9697265625}, {"start": 3069.71, "end": 3071.03, "word": " z", "probability": 0.576171875}, {"start": 3071.03, "end": 3072.75, "word": " modulo", "probability": 0.9501953125}, {"start": 3072.75, "end": 3073.75, "word": " n", "probability": 0.7431640625}, {"start": 3073.75, "end": 3074.09, "word": " في", "probability": 0.896484375}, {"start": 3074.09, "end": 3074.77, "word": " z", "probability": 0.96240234375}, {"start": 3074.77, "end": 3075.57, "word": " عايز", "probability": 0.689208984375}, {"start": 3075.57, "end": 3076.01, "word": " أمرك", "probability": 0.8008626302083334}, {"start": 3076.01, "end": 3076.37, "word": " لمين", "probability": 0.771728515625}, {"start": 3076.37, "end": 3076.47, "word": " يا", "probability": 0.9873046875}, {"start": 3076.47, "end": 3077.01, "word": " شباب", "probability": 0.986328125}, {"start": 3077.01, "end": 3078.25, "word": " ل", "probability": 0.580078125}, {"start": 3078.25, "end": 3078.87, "word": " z", "probability": 0.82373046875}, {"start": 3078.87, "end": 3079.61, "word": " n", "probability": 0.278564453125}, {"start": 3079.61, "end": 3080.69, "word": " من", "probability": 0.81396484375}, {"start": 3080.69, "end": 3081.13, "word": " الأن", "probability": 0.725341796875}, {"start": 3081.13, "end": 3081.95, "word": " فصاعدا", "probability": 0.75439453125}, {"start": 3081.95, "end": 3082.79, "word": " يبقى", "probability": 0.931884765625}, {"start": 3082.79, "end": 3083.03, "word": " هذا", "probability": 0.95849609375}, {"start": 3083.03, "end": 3083.63, "word": " المثال", "probability": 0.9737955729166666}, {"start": 3083.63, "end": 3084.55, "word": " استفدنا", "probability": 0.82958984375}, {"start": 3084.55, "end": 3084.97, "word": " منه", "probability": 0.980224609375}, {"start": 3084.97, "end": 3086.23, "word": " شغلات", "probability": 0.982177734375}, {"start": 3086.23, "end": 3087.07, "word": " كثيرة", "probability": 0.9611002604166666}, {"start": 3087.07, "end": 3087.79, "word": " جدا", "probability": 0.98583984375}, {"start": 3087.79, "end": 3088.75, "word": " يعطيكوا", "probability": 0.769287109375}, {"start": 3088.75, "end": 3089.13, "word": " العافية", "probability": 0.9226888020833334}, {"start": 3089.13, "end": 3089.73, "word": " ونكمل", "probability": 0.701416015625}, {"start": 3089.73, "end": 3089.91, "word": " ان", "probability": 0.677734375}, {"start": 3089.91, "end": 3090.21, "word": " شاء", "probability": 0.973876953125}, {"start": 3090.21, "end": 3090.31, "word": " الله", "probability": 0.9560546875}, {"start": 3090.31, "end": 3091.09, "word": " يوم", "probability": 0.987060546875}, {"start": 3091.09, "end": 3091.99, "word": " الأثنين", "probability": 0.6712646484375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3093.641, "duration_after_vad": 2840.1337499999886}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b3d8d45aea7f542450b20b797b6b9f7f267536dc
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uLiOio_FRc0_raw.srt
@@ -0,0 +1,1880 @@
+1
+00:00:20,670 --> 00:00:26,470
+المحاضرة الصباحية حين دخلنا على ال chapter التاسع
+
+2
+00:00:26,470 --> 00:00:30,670
+اللى بتحدث عن ال normal subgroups and factor
+
+3
+00:00:30,670 --> 00:00:37,150
+groups بدأنا بتعريف ال normal subgroup وقلنا اللى
+
+4
+00:00:37,150 --> 00:00:41,910
+لو عندى H subgroup من G بقول عنها normal لو كان ال
+
+5
+00:00:41,910 --> 00:00:45,610
+left coset يساوي ال right coset لأى element موجود
+
+6
+00:00:45,610 --> 00:00:50,620
+في ال groupوبعد ذلك ذهبنا إلى نظرية وقلنا بتبقى
+
+7
+00:00:50,620 --> 00:00:54,780
+normal subgroup إذا كان ال X H X inverse subset من
+
+8
+00:00:54,780 --> 00:00:59,920
+H لكل ال X اللي موجود في ال group G وبعد ذلك قلنا
+
+9
+00:00:59,920 --> 00:01:03,760
+ممكن نجيبها عن طريق ال elements لو خط ال A موجود
+
+10
+00:01:03,760 --> 00:01:09,320
+في G وخط ال H موجود في H لأن A H A inverse بدي
+
+11
+00:01:09,320 --> 00:01:13,340
+يكون belonging to main two Hإن حدث ذلك أي واحدة من
+
+12
+00:01:13,340 --> 00:01:16,600
+الحالات التلاتة لانها دول بقول الـH هي normal
+
+13
+00:01:16,600 --> 00:01:23,200
+subgroup من G الان الـG و الـH التنتينة groups قال
+
+14
+00:01:23,200 --> 00:01:27,160
+اثبت ان الـexternal byproduct ما بين الـG و
+
+15
+00:01:27,160 --> 00:01:31,840
+الـidentity element تبع الـH هو normal subgroup من
+
+16
+00:01:31,840 --> 00:01:35,340
+الـexternal byproduct ما بين الـG و الـH طبعا في
+
+17
+00:01:35,340 --> 00:01:40,130
+الأمثلة التابعة الصبحقلنا الـcenter أثبتناها قبل
+
+18
+00:01:40,130 --> 00:01:42,990
+ذلك subgroup الـspecial linear group of two by two
+
+19
+00:01:42,990 --> 00:01:46,530
+matrices over R أثبتناها قبل ذلك subgroup ولذلك
+
+20
+00:01:46,530 --> 00:01:50,750
+اعتمدنا على ما أخدناه سابقا و أثبتناه بس حكاية ال
+
+21
+00:01:50,750 --> 00:01:55,050
+normality لكن هذه هل أثبتناها أنها subgroup قبل
+
+22
+00:01:55,050 --> 00:01:59,310
+ذلك؟ طبعا لا يبقى هنا بكتير ما الخطوطين الخطوة
+
+23
+00:01:59,310 --> 00:02:03,530
+الأولى بدي أثبت أن هذه subgroup أولا ثم بعد ذلك
+
+24
+00:02:03,530 --> 00:02:08,130
+نثبت أنها normal subgroupمشان يكبر كلامنا صحيح
+
+25
+00:02:08,130 --> 00:02:13,330
+يبقى الخطوة الأولى بدي أقوله الـ G external like a
+
+26
+00:02:13,330 --> 00:02:18,530
+product مع ال identity element تبع ال H is not
+
+27
+00:02:18,530 --> 00:02:26,670
+empty ولا non-empty is non-empty السؤال ليش؟
+
+28
+00:02:26,670 --> 00:02:33,330
+becauseإن ال identity element تبع ال G و ال
+
+29
+00:02:33,330 --> 00:02:38,970
+identity element تبع ال H لإتنين هدول كلهم موجودات
+
+30
+00:02:38,970 --> 00:02:44,150
+في ال G ال external direct product مع من مع ال
+
+31
+00:02:44,150 --> 00:02:52,770
+identity لل H بالشكل اللي عندنا هنا تمام في اللي
+
+32
+00:02:52,770 --> 00:02:58,050
+هو ال group اللي عندنا تمامهذه الخطوه اللي هو
+
+33
+00:02:58,050 --> 00:03:04,970
+الخطوه التانية بدي اخد عنصرين لت مثلا X و ال
+
+34
+00:03:04,970 --> 00:03:10,110
+identity element تبع ال H و ال Y و ال identity
+
+35
+00:03:10,110 --> 00:03:14,970
+element تبع ال H موجودات في ال G external product
+
+36
+00:03:14,970 --> 00:03:21,210
+يبقى مرة تانية انا عند توجه H بدي اثبت ان ال
+
+37
+00:03:21,210 --> 00:03:24,990
+external product ما بين ال G و ال identity element
+
+38
+00:03:24,990 --> 00:03:28,940
+تبع ال Hهو سبع جروب من الجيك السينادكي product ال
+
+39
+00:03:28,940 --> 00:03:33,540
+H جينا قولنا الجروب اللي عندنا هذي is non-empty
+
+40
+00:03:33,540 --> 00:03:36,720
+because ال identity اللي متبع ال G و ال identity
+
+41
+00:03:36,720 --> 00:03:41,140
+اللي متبع ال H هو ال identity element لمن للجروب
+
+42
+00:03:41,140 --> 00:03:45,100
+اللي عندنا هذا يبقىأو الـ 6 اللي عندنا هذه الـ non
+
+43
+00:03:45,100 --> 00:03:50,420
+-empty بعدين أخدت عمصرين موجودات في من في هذه الـ
+
+44
+00:03:50,420 --> 00:03:55,000
+6 بدي أحاول أثبت أن الأول في معكوس الثاني موجود في
+
+45
+00:03:55,000 --> 00:04:01,680
+هذه الـ 6 يعني لو جيت أخدت ال X مع ال identity
+
+46
+00:04:01,680 --> 00:04:07,120
+element بتابع ال H مضروب في ال Y ال identity تابع
+
+47
+00:04:07,120 --> 00:04:12,670
+ال H inverseيبقى هذا الكلام بده يساوي الـ X ال
+
+48
+00:04:12,670 --> 00:04:18,970
+identity تبع ال H مضروب في ال Y inverse هو ال E H
+
+49
+00:04:18,970 --> 00:04:22,830
+inverse بال E H itself يعني ال identity element هو
+
+50
+00:04:22,830 --> 00:04:28,870
+معكوس لنفسه يبقى هذا في ال identity element تبع ال
+
+51
+00:04:28,870 --> 00:04:34,090
+H من خلاص عملية الضرب يبقى هذا بده يعطيني X Y
+
+52
+00:04:34,090 --> 00:04:41,620
+inverse وال E H في ال E H بال E H itselfالان الـ X
+
+53
+00:04:42,740 --> 00:04:48,860
+الـ X و الـ Y كل واحدة فيهم موجودة في جي و الـ X و
+
+54
+00:04:48,860 --> 00:04:53,740
+الـ Y في جي جي جروب يبقى هذا موجود على طول الخط في
+
+55
+00:04:53,740 --> 00:05:00,200
+الجروب جي external direct product مع مين مع اللي
+
+56
+00:05:00,200 --> 00:05:05,020
+هو ال identity element تبع الجروب H يبقى بناء على
+
+57
+00:05:05,020 --> 00:05:08,680
+المعلومة الأثنين هذول بصير هذه ال sub group من
+
+58
+00:05:08,680 --> 00:05:14,930
+مين؟ من جييبقى هنا sir ال g external like product
+
+59
+00:05:14,930 --> 00:05:20,090
+مع ال identity element تبع ال h is a subgroup من
+
+60
+00:05:20,090 --> 00:05:25,990
+ال g external like product مع ال h يبقى لغاية الان
+
+61
+00:05:25,990 --> 00:05:30,470
+انا اثبت ايشأثبت أنها subgroup داي اللي بده يروح
+
+62
+00:05:30,470 --> 00:05:34,910
+أثبته ال normality يبقى بده ياخد عنصر في ال group
+
+63
+00:05:34,910 --> 00:05:38,630
+الأساسية اللي هي جيك سنة ضايق product معاتش وأخد
+
+64
+00:05:38,630 --> 00:05:42,390
+element من ال set أو من ال subgroup اللي عندنا
+
+65
+00:05:42,390 --> 00:05:49,430
+واخد حاصل الدرب وشوف كده بده يعطيه إذا لو جيت قلت
+
+66
+00:05:49,430 --> 00:05:57,260
+هنا Fال X و ال identity element تبع ال H موجود في
+
+67
+00:05:57,260 --> 00:06:07,020
+ال G extended product تبع ال H and ال G و ال E H
+
+68
+00:06:07,020 --> 00:06:13,060
+موجود في ال G extended product مع ال identity
+
+69
+00:06:13,060 --> 00:06:20,800
+element تبع ال H then بدي أخد ال Xالـ Identity
+
+70
+00:06:20,800 --> 00:06:25,860
+element تبع الـ H في G والـ Identity element تبع
+
+71
+00:06:25,860 --> 00:06:31,440
+الـ H في Mان في الـ X والـ Identity element تبع
+
+72
+00:06:31,440 --> 00:06:38,180
+الـ H لكل Inverseيبقى بناء عليه هذا الكلام بده
+
+73
+00:06:38,180 --> 00:06:44,060
+يساوي هدول بده ضربهم ضرب عادي component wise يبقى
+
+74
+00:06:44,060 --> 00:06:50,000
+X في G وهنا ال identity element تبع ال HV هذا ال
+
+75
+00:06:50,000 --> 00:06:56,300
+inverse بينزل على كل منهايبقى هذا هو عبارة عن الـ
+
+76
+00:06:56,300 --> 00:07:00,940
+X inverse في ال identity element تبع ال H inverse
+
+77
+00:07:00,940 --> 00:07:06,160
+يعني نفس ال identity element يبقى هذا الكلام بده
+
+78
+00:07:06,160 --> 00:07:12,820
+يساوي XGX inverse وهذا ال identity element تبع
+
+79
+00:07:12,820 --> 00:07:17,480
+مين؟ تبع ال H هذول الأنواع الموجودة
+
+80
+00:07:20,110 --> 00:07:26,110
+XG X inverse في G لأن X في G وجي موجودة في G
+
+81
+00:07:26,110 --> 00:07:28,490
+وبالتالي X inverse موجودة في G
+
+82
+00:07:35,120 --> 00:07:43,200
+external product مع ميم مع ال EH لذلك أخدت عنصر في
+
+83
+00:07:43,200 --> 00:07:47,780
+عنصر من ال subset او من ال subgroup في عنصر من ال
+
+84
+00:07:47,780 --> 00:07:51,440
+group وضربت التلاتة مع بعض اللي جبت موجودة في ال
+
+85
+00:07:51,440 --> 00:07:56,530
+subgroup اللي عندنا معنا هذا الكلام انالـ G
+
+86
+00:07:56,530 --> 00:08:02,290
+Extended Product مع الـ Identity H is a normal
+
+87
+00:08:02,290 --> 00:08:09,330
+subgroup من الـ G Extended Product مع H فلخطر
+
+88
+00:08:09,330 --> 00:08:18,170
+أخريك تمرن إيدك يبقى exercise show that بيّل
+
+89
+00:08:18,170 --> 00:08:24,940
+إنهالـ Identity element تبع الـ G external like
+
+90
+00:08:24,940 --> 00:08:33,900
+product مع H is a normal subgroup من
+
+91
+00:08:33,900 --> 00:08:40,740
+الـ G external like product مع Hيعني بدل ما أخد
+
+92
+00:08:40,740 --> 00:08:44,060
+الـ G External Product ما أخدش لأ بدي أخد ال
+
+93
+00:08:44,060 --> 00:08:49,260
+identity تبع الـ G ماعلش و أحاول أثبت أنه Normal
+
+94
+00:08:49,260 --> 00:09:00,680
+Subgroup من الـ G External Product لمين لـ H مثال
+
+95
+00:09:00,680 --> 00:09:04,720
+ستة مثال ستة بقول
+
+96
+00:09:07,320 --> 00:09:14,640
+الـ H is a subgroup من G الـ H is a subgroup of G
+
+97
+00:09:14,640 --> 00:09:24,560
+and if وإذا كان ال index بتابع الـ H in G يساوي 2
+
+98
+00:09:24,560 --> 00:09:31,300
+then الـ H is a normal subgroup من G
+
+99
+00:09:45,880 --> 00:09:50,160
+هذا يعطينا معلومة جديدة المعلومة الجديدة ماكناش
+
+100
+00:09:50,160 --> 00:09:54,320
+بنعرفها قبل هيك بس المعلومة هذه بصير عندنا حقيقة
+
+101
+00:09:54,320 --> 00:09:59,160
+بعد ما انبرهنها بقول إيش لو كان عندك ال H subgroup
+
+102
+00:09:59,160 --> 00:10:03,740
+من G و ال index تبع ال subgroup إيش يعني ال index
+
+103
+00:10:03,740 --> 00:10:09,540
+يعني عدد ال left cosets أو عدد ال right cosets بدو
+
+104
+00:10:09,540 --> 00:10:13,380
+يساوي اتنين يبقى في هذه الحالة ال H بتبقى normal
+
+105
+00:10:13,380 --> 00:10:20,370
+subgroup من مالهامن جي يبقى ده جي اقوله assume
+
+106
+00:10:20,370 --> 00:10:28,410
+افترض ان ال H is a subgroup من G and ال index
+
+107
+00:10:28,410 --> 00:10:36,130
+بتابع من اللي هو ال H ان جي بده يساوي من اتنين هذا
+
+108
+00:10:36,130 --> 00:10:44,210
+بده يعطينا we have two distinct
+
+109
+00:10:46,450 --> 00:10:56,130
+تنتين left cassettes only
+
+110
+00:10:56,130 --> 00:11:06,290
+واحدة فيهم بتكون الـH itself والتانية and والتانية
+
+111
+00:11:06,290 --> 00:11:10,330
+امسك اي element من ال group واضربه في من من ال
+
+112
+00:11:10,330 --> 00:11:16,230
+group هذهطيب أنا بدي الدعوة التانية هي G ناقص ال H
+
+113
+00:11:16,230 --> 00:11:17,090
+بنفع
+
+114
+00:11:20,090 --> 00:11:24,290
+لما ناخد الـ H كل العناصر اللي بيظلوا هي G نقص الـ
+
+115
+00:11:24,290 --> 00:11:30,110
+H ليش؟ لأن الـ two cosets يبقى يا MR coincide
+
+116
+00:11:30,110 --> 00:11:32,670
+التنتين بنطبقوا يعني التنتين بيساوي يعني ال
+
+117
+00:11:32,670 --> 00:11:36,210
+intersection تبعهم مش بيساوي فاي يعني ال left
+
+118
+00:11:36,210 --> 00:11:41,290
+distant cosets بيعملوا partition على ال group G
+
+119
+00:11:41,290 --> 00:11:45,590
+إذا لما ناخد الـ H اللي بيظل بيكون هم ال left
+
+120
+00:11:45,590 --> 00:11:51,210
+cosetsاللي هو الـ G ناقص الـ H طب G ناقص الـ H هذه
+
+121
+00:11:51,210 --> 00:11:57,190
+بدها تبقى على شكل element اللي هو مضروم في مين؟
+
+122
+00:11:57,190 --> 00:12:03,750
+مضروم في H والـ A هذه موجودة وين؟ موجودة في G يبقى
+
+123
+00:12:03,750 --> 00:12:07,670
+هاي ال left cosets اللي عندنا زي ما هي ال left
+
+124
+00:12:07,670 --> 00:12:11,650
+cosets كذلك زي ما هي ال right cosets يبقى باجي
+
+125
+00:12:11,650 --> 00:12:18,790
+بقول sense نظرا لأن ال indexتبع ال HNG بده يساوي
+
+126
+00:12:18,790 --> 00:12:33,850
+اتنين we have also كذلك two distinct right facets
+
+127
+00:12:33,850 --> 00:12:37,150
+of
+
+128
+00:12:37,150 --> 00:12:51,740
+HNG that isالأولى H والتانية برضه G ناقص ال H اللى
+
+129
+00:12:51,740 --> 00:13:00,420
+بده تساوي HA إذا
+
+130
+00:13:00,420 --> 00:13:11,120
+أصبحت ال G هي عبارة H وAH وفي المقابل G هي H وHA
+
+131
+00:13:11,120 --> 00:13:20,390
+الإثنان نفس الشيءيبقى هنا الـ G العناصر بتابعتها
+
+132
+00:13:20,390 --> 00:13:30,710
+أو الـ G هي عبارة عن مين؟ عن ال H اتحاد H وكذلك
+
+133
+00:13:30,710 --> 00:13:40,450
+بدها الساوي اللي هو .. هذه كلها كاسيت الـ G وكمان
+
+134
+00:13:40,450 --> 00:13:50,230
+هذه مين؟اللي هي الـ H إتحاد HA طيب
+
+135
+00:13:50,230 --> 00:13:52,890
+الـ Left Destinate Coexists اللي قلنا بتعمل
+
+136
+00:13:52,890 --> 00:13:58,130
+partition لمين لسنس
+
+137
+00:13:58,130 --> 00:14:04,410
+ال left or
+
+138
+00:14:04,410 --> 00:14:08,810
+ال right or
+
+139
+00:14:08,810 --> 00:14:10,010
+ال right
+
+140
+00:14:15,110 --> 00:14:36,210
+destined cosets make a partition of G we have ان
+
+141
+00:14:36,210 --> 00:14:49,620
+ال Hاتحاد اللي هو LAH بده يساوي من LH اتحاد اللي
+
+142
+00:14:49,620 --> 00:14:53,700
+هو ال H
+
+143
+00:14:53,700 --> 00:15:02,560
+يتحاد ال AH يساوي H اتحاد ال HA طب هذا نفس ال
+
+144
+00:15:02,560 --> 00:15:05,320
+element and
+
+145
+00:15:06,980 --> 00:15:15,640
+الـ H intersection AH بده يساوي فاي و ال H
+
+146
+00:15:15,640 --> 00:15:20,360
+intersection HA بده يساوي main فاي لأنه partition
+
+147
+00:15:20,360 --> 00:15:26,280
+كويس يبقى هذا ايش بده يعطينا بده يعطينا ان ال AH
+
+148
+00:15:26,280 --> 00:15:32,960
+بده يساوي ال HA هذا بده يعطيلك ان ال H is a normal
+
+149
+00:15:32,960 --> 00:15:36,060
+subgroup من main من G
+
+150
+00:15:41,830 --> 00:15:47,330
+يبقى هذا الان من الآن فصاعدا اي subgroup ال index
+
+151
+00:15:47,330 --> 00:15:51,410
+ايه اللي هيساوي اتنين من ال group الأصلية بتكون ال
+
+152
+00:15:51,410 --> 00:15:55,070
+subgroup هذي normal subgroup من ال main من ال
+
+153
+00:15:55,070 --> 00:15:57,110
+group الأصلية
+
+154
+00:16:02,330 --> 00:16:08,430
+يعني يمكن استخدام هذه او هذا المثال في حل بعض
+
+155
+00:16:08,430 --> 00:16:12,690
+المسائل بعد ذلك او على طول الخط انجلك ال index
+
+156
+00:16:12,690 --> 00:16:17,410
+اتنين بدك تفهم ان هذي normal subgroup من ال group
+
+157
+00:16:17,410 --> 00:16:25,470
+الأساسية اللي هي G نمرة
+
+158
+00:16:25,470 --> 00:16:36,060
+سبعة مثال رقم سبعة you is theyabove example بناخد
+
+159
+00:16:36,060 --> 00:16:42,580
+المثال أعلاه to show that
+
+160
+00:16:42,580 --> 00:16:49,500
+مشان نثبت ان ال subgroup generated by R90 is a
+
+161
+00:16:49,500 --> 00:16:52,860
+normal subgroup من من ال D4
+
+162
+00:17:10,090 --> 00:17:18,170
+هي عبارة عن
+
+163
+00:17:18,170 --> 00:17:23,070
+الـ identity element اللي هو الـ R نود والـ R
+
+164
+00:17:23,070 --> 00:17:31,090
+تسعين والـ R مية و تمانين والـ R متين و سبعينيبقى
+
+165
+00:17:31,090 --> 00:17:38,290
+هذا يعني ان ال order لل R تسعين بدي ساوي كده؟ بدي
+
+166
+00:17:38,290 --> 00:17:44,700
+ساوي أربعةالان اذا اريت ان اجهزة الاندكس بتابع الـ
+
+167
+00:17:44,700 --> 00:17:51,440
+subgroup generated by R90 فالجروب D4 سيسوء ال
+
+168
+00:17:51,440 --> 00:17:57,280
+order لـ D4 مقسوما على ال order لل subgroup
+
+169
+00:17:57,280 --> 00:18:00,180
+generated by R90
+
+170
+00:18:02,880 --> 00:18:07,080
+الأولى ال order اللى هيساوي تمانية والتانية ال
+
+171
+00:18:07,080 --> 00:18:11,780
+order اللى هيساوي أربعة يبقى ال index كده اتنين
+
+172
+00:18:11,780 --> 00:18:17,760
+يبقى هذا بده يعطينا ان ال index تبع ال subgroup
+
+173
+00:18:17,760 --> 00:18:24,820
+generated by R90 in D4 بده يساوي اتنين بروح بقوله
+
+174
+00:18:24,820 --> 00:18:31,000
+by the above example
+
+175
+00:18:32,430 --> 00:18:39,590
+المثال أعلى هو we have ان ال subgroup generated by
+
+176
+00:18:39,590 --> 00:18:46,570
+R تسعين is a normal subgroup في main في D4
+
+177
+00:18:46,570 --> 00:18:57,670
+وبالتالي انتهت هذه المثلة نجي
+
+178
+00:18:57,670 --> 00:19:01,270
+ل definition جديد definition
+
+179
+00:19:05,150 --> 00:19:16,290
+إذا الـ H هو عضو عادل من G ثم
+
+180
+00:19:16,290 --> 00:19:21,530
+الـ set of
+
+181
+00:19:21,530 --> 00:19:29,910
+left أو right هدى أو هدى left أو right
+
+182
+00:19:34,840 --> 00:19:50,480
+cossets of HNG is called is called the
+
+183
+00:19:50,480 --> 00:19:59,040
+factor group is
+
+184
+00:19:59,040 --> 00:20:09,390
+called the factor group ofجي باي اتش or
+
+185
+00:20:09,390 --> 00:20:23,050
+the quotient or the quotient group of جي باي اتش
+
+186
+00:20:23,050 --> 00:20:27,430
+and
+
+187
+00:20:27,430 --> 00:20:30,130
+we write
+
+188
+00:20:36,970 --> 00:20:46,030
+و نكتب نكتب
+
+189
+00:20:46,030 --> 00:20:55,430
+نكتب نكتب نكتب نكتب نكتب نكتب نكتب نكتب
+
+190
+00:20:55,430 --> 00:21:02,130
+نكتب نكتب
+
+191
+00:21:02,640 --> 00:21:11,360
+بدها تساوي كل الـ gh such that الجي belongs to جي
+
+192
+00:21:11,360 --> 00:21:15,360
+خد
+
+193
+00:21:15,360 --> 00:21:21,130
+برا كده الان بدنا نعطي تعريفجديد هذا التعريف طبعا
+
+194
+00:21:21,130 --> 00:21:25,410
+لأول مرة وفي كلامنا نحكي على هذا التعريف العنوان
+
+195
+00:21:25,410 --> 00:21:29,690
+تبع هذا ال chapter كله كان normal subgroups and
+
+196
+00:21:29,690 --> 00:21:34,450
+factor groups كل اللي اتكلمنا عنه سابقا كان عن ال
+
+197
+00:21:34,450 --> 00:21:39,030
+normal subgroups والان بدنا نيجي لل normal
+
+198
+00:21:39,030 --> 00:21:40,410
+subgroups
+
+199
+00:21:42,540 --> 00:21:45,980
+اللي هنبتدى نيجي لل factor of growth نقول لو كانت
+
+200
+00:21:45,980 --> 00:21:50,740
+ال H هي ال normal sub group من G then the set of
+
+201
+00:21:50,740 --> 00:21:55,760
+left او right cosets of H in G is called the
+
+202
+00:21:55,760 --> 00:22:00,440
+factor A group يبقى كل ال left cosets او ال right
+
+203
+00:22:00,440 --> 00:22:06,500
+cosets لمين؟ لجروب معين عندناأيش بسميها بسميها ال
+
+204
+00:22:06,500 --> 00:22:12,160
+factor group of G by H أو بسميها ال quotient group
+
+205
+00:22:12,160 --> 00:22:16,960
+of G by H سواء قلنا ال factor group او ال quotient
+
+206
+00:22:16,960 --> 00:22:21,160
+group كله الاتنين بنفس المعنى يعني ممكن بعض الكتب
+
+207
+00:22:21,160 --> 00:22:25,180
+تكتب ال factor group و بعض الكتب تكتب ال quotient
+
+208
+00:22:25,180 --> 00:22:28,480
+group سي اللي جيت quotient group و اللي جيت factor
+
+209
+00:22:28,480 --> 00:22:36,430
+اتنين بنفس المعنىand we write the factor group as
+
+210
+00:22:36,430 --> 00:22:43,990
+g modulo h أو g by h هي كل ال elements اللي على
+
+211
+00:22:43,990 --> 00:22:48,950
+شكل left cosets بحيث ال g موجودة في g
+
+212
+00:22:51,770 --> 00:22:56,530
+انت قلتلنا اول ما خدنا ال cosets ان ال coset هذه
+
+213
+00:22:56,530 --> 00:23:01,610
+ليست group ليست subgroup طبعا قلتلك يمكن ان تكون
+
+214
+00:23:01,610 --> 00:23:06,390
+subgroup ويمكن ان لا تكون subgroupيوم هم ماكناش
+
+215
+00:23:06,390 --> 00:23:10,150
+ماخدينا normal subgroup لكن قلنا إذا ال element
+
+216
+00:23:10,150 --> 00:23:14,450
+اللي ضربنا فيه ال subgroup كان من نفس ال subgroup
+
+217
+00:23:14,450 --> 00:23:18,590
+بيطلع الناتج ال left coset هي ال subgroup الآن
+
+218
+00:23:18,590 --> 00:23:24,270
+احنا جبنا شغلة جديدة ايش الشغلة الجديدة ان لو كانت
+
+219
+00:23:24,270 --> 00:23:30,370
+ال H هذه normal subgroupفكل الـ left cosets اللي
+
+220
+00:23:30,370 --> 00:23:34,550
+عندي او ال destined left cosets بيكونولي جروب جديد
+
+221
+00:23:34,550 --> 00:23:39,670
+اسمها ال factor group او ال quotient group وهذه
+
+222
+00:23:39,670 --> 00:23:44,990
+ماكنتش قبل ذلك يبقى ال factor group او ال quotient
+
+223
+00:23:44,990 --> 00:23:50,230
+group عناصرها كلهم left cosets او كلهم right
+
+224
+00:23:50,230 --> 00:23:55,850
+cosets يا هذه امين يا هذهطيب، الان هذا اللي احنا
+
+225
+00:23:55,850 --> 00:24:01,110
+بنقوله، الان انا ايش قلت؟ قلت الـ G modulo H is a
+
+226
+00:24:01,110 --> 00:24:06,410
+group مظبوط، مدام group السؤال هو مين ال operation
+
+227
+00:24:06,410 --> 00:24:11,730
+اللي عليها؟ما هو شكل الـ identity element؟ ما هو
+
+228
+00:24:11,730 --> 00:24:16,370
+الشكل المعكوس لكل element؟ وهل ال associativity إن
+
+229
+00:24:16,370 --> 00:24:20,990
+كان جروب يقول associativity كمظهر صحيح عليها؟ يبقى
+
+230
+00:24:20,990 --> 00:24:24,950
+الدور الآن علينا أن نثبت أن هذه عبارة عن إيش،
+
+231
+00:24:24,950 --> 00:24:28,370
+عبارة عن جروب لأننا نطبق من التعريف ونقول إنها
+
+232
+00:24:28,370 --> 00:24:34,150
+جروب مدام جروب برهنها لكي نقول من الآن فصاعدا هذه
+
+233
+00:24:34,150 --> 00:24:38,440
+عبارة عن إيش، عبارة عن جروبطبعاً برهنة على شكل
+
+234
+00:24:38,440 --> 00:24:45,140
+نظرية، النظرية بتقول ما يأتي to your M النظرية
+
+235
+00:24:45,140 --> 00:24:52,060
+بتقول let ال G be a group أخدنا ال G عبارة عن
+
+236
+00:24:52,060 --> 00:25:00,120
+group and let ال H وافترش be a normal subgroup
+
+237
+00:25:08,450 --> 00:25:20,010
+normal subgroup of G then the
+
+238
+00:25:20,010 --> 00:25:28,870
+set اللي هي الـ G modulo H هي عبارة عن كل العناصر
+
+239
+00:25:28,870 --> 00:25:35,390
+A H بحيث ان A موجود في G is
+
+240
+00:25:37,610 --> 00:25:52,350
+A group is a group under the operation تحت العملية
+
+241
+00:25:52,350 --> 00:26:03,750
+اللي هو AH في BH بدي ساوي ABH بالشكل اللي عندنا
+
+242
+00:26:03,750 --> 00:26:03,930
+هنا
+
+243
+00:26:24,050 --> 00:26:29,090
+يبقى الأن في عندى شغل تانى الشغل الأولى انه ال H
+
+244
+00:26:29,090 --> 00:26:34,510
+normal sub group من مين؟ من G ال factor group هذه
+
+245
+00:26:34,510 --> 00:26:38,510
+عرفت عليها operation ال operation اللى أول مرة
+
+246
+00:26:38,510 --> 00:26:43,450
+بنشوفها انه ال left coset في ال left coset بدرب ال
+
+247
+00:26:43,450 --> 00:26:46,990
+A ال element في ال element و كله مضروف في مين؟ في
+
+248
+00:26:46,990 --> 00:26:51,510
+ال subset اللى عندنا تحت العملية هذه و ال H normal
+
+249
+00:26:51,510 --> 00:26:57,830
+يبقى ال Gعلى H أو ال quotient group G by H بنسميها
+
+250
+00:26:57,830 --> 00:27:05,600
+عبارة عن groupيبقى أول شغلة بدي أثبتها بدي أثبت أن
+
+251
+00:27:05,600 --> 00:27:12,360
+هذا التعريف حقيقي يعني ال operation هذه is well
+
+252
+00:27:12,360 --> 00:27:16,320
+defined بدي أن أثبتها أولا وبعد هيك نروح لل
+
+253
+00:27:16,320 --> 00:27:19,900
+associativity و ال identity element و ال inverse
+
+254
+00:27:19,900 --> 00:27:22,900
+element يبقى هنا firstly
+
+255
+00:27:33,920 --> 00:27:48,960
+want to show بنروح نبين انه the given operation is
+
+256
+00:27:48,960 --> 00:28:00,320
+well defined يبقى بنثبت ان هذه معرفة تعريفا صحيحا
+
+257
+00:28:02,330 --> 00:28:12,970
+بقول له assume ان ال a prime h او ال a h بده ساوي
+
+258
+00:28:12,970 --> 00:28:16,370
+a
+
+259
+00:28:16,370 --> 00:28:24,730
+prime h and ال b h بده ساوي b prime h
+
+260
+00:28:28,610 --> 00:28:33,950
+مشان أثبت عملية الضرب بدأ أضرب الأول هنا في الأول
+
+261
+00:28:33,950 --> 00:28:38,790
+هنا و أثبت أنه يساوي حاصل ضرب الثاني في الثاني من
+
+262
+00:28:38,790 --> 00:28:42,570
+هنا ان طلع الكلام هذا صحيح يبقى ال operation تبقى
+
+263
+00:28:42,570 --> 00:28:48,490
+معرفة تعريفا صحيحا يبقى انا افترضت ان اتنين هذول
+
+264
+00:28:48,490 --> 00:28:54,670
+ما لهمهذا بيسوي هذا و التاني بيسوي هذا طيب من خلال
+
+265
+00:28:54,670 --> 00:29:01,650
+هذه المعلومات دي احاول اثبت ان ال A BH بدي اسوي A
+
+266
+00:29:01,650 --> 00:29:06,930
+prime B prime H بس قبل هذا الكلام تعالوا ناخد
+
+267
+00:29:06,930 --> 00:29:12,230
+معلومة نستفيد بها في البرهان اللي بعدها الآن شباب
+
+268
+00:29:12,230 --> 00:29:19,140
+ال A prime موجودة في ال A prime Hهنا a prime
+
+269
+00:29:19,140 --> 00:29:27,600
+موجودة من هنا طب هذه بيساوي هذه and ال a prime h
+
+270
+00:29:27,600 --> 00:29:34,740
+بيساوي a h هذا بيعطينا ان ال a prime موجودة في ال
+
+271
+00:29:34,740 --> 00:29:46,260
+a hهذا سيعطينا ان الـ A' بيساوي AH1 for some H1
+
+272
+00:29:46,260 --> 00:29:54,980
+اللي موجودة في H بنفس الطريقة similarly ال
+
+273
+00:29:54,980 --> 00:30:05,900
+B' موجودة في ال B'H andالـB'H بيقوم بإعطائنا
+
+274
+00:30:05,900 --> 00:30:10,420
+الـB' موجودة في الـ BH
+
+275
+00:30:21,060 --> 00:30:26,400
+طب بدالي اخدله a prime b prime h اشوف وين بده
+
+276
+00:30:26,400 --> 00:30:33,280
+اتوصل اذا وصلتلي الى a b
+
+277
+00:30:33,280 --> 00:30:37,980
+في h بصيلة العملية معرفة تعريفا صحيحا يبقى ضرب
+
+278
+00:30:37,980 --> 00:30:41,500
+العناصر هنا يساوي ضرب العناصر هنا وبالتالي ال
+
+279
+00:30:41,500 --> 00:30:47,800
+operation هذه بتكون صحيحةطيب بداجي ال a prime هو
+
+280
+00:30:47,800 --> 00:30:56,440
+عبارة عن a h1 يبقى هذا a h1 ال b prime اللي هو b
+
+281
+00:30:56,440 --> 00:31:04,060
+h2 يبقى b اللي هو h2 بالشكل اللي عندنا هذا وهذا ال
+
+282
+00:31:04,060 --> 00:31:09,570
+h اللي هي من التانية اللي عندنايبقى اشيلت الـ A'
+
+283
+00:31:09,990 --> 00:31:15,170
+والـ B' وحطيت قيمة كل منها يبقى هذا الكلام بده
+
+284
+00:31:15,170 --> 00:31:24,810
+يساوي A H1 BH والـ H2 طارت لإن الـ H2 موجودة وين؟
+
+285
+00:31:24,810 --> 00:31:31,750
+فاتش يبقى هذا صحيح since الـ H2 موجودة وين؟ موجودة
+
+286
+00:31:31,750 --> 00:31:42,080
+فاتشطب هذا الكلام بده يساوي a h1 في hb بي
+
+287
+00:31:42,080 --> 00:31:48,420
+في اتش حطيت مدلمين اتش بي طيب ليش؟
+
+288
+00:31:48,420 --> 00:31:56,160
+لانه قال ال itch normal subgroup يبقى هذا sense ال
+
+289
+00:31:56,160 --> 00:32:01,820
+itch is a normal subgroup من gلأن الـ H أخدنا أول
+
+290
+00:32:01,820 --> 00:32:06,280
+تعريف للـ normality أنه لو كان ال بيه H بده يساوي
+
+291
+00:32:06,280 --> 00:32:10,120
+HP لو كل ال بيه اللي موجودة في القرم يبقى هي
+
+292
+00:32:10,120 --> 00:32:14,380
+normal مدام أعطانيها normal إذا هذه الخاصية خاصية
+
+293
+00:32:14,380 --> 00:32:20,770
+ما لها محققة طب هذا الكلام بده يساويهدى فى هدى،
+
+294
+00:32:20,770 --> 00:32:28,250
+إيش هتعطينا؟ H يبقى هدى بتعطينا A H B since نظرا
+
+295
+00:32:28,250 --> 00:32:35,530
+لإن ال H one موجود وين فى H كويس هذا الكلام بده
+
+296
+00:32:35,530 --> 00:32:45,220
+يساوي A فى BHليش؟ الـHB رجعتها إلى مين؟ إلى BH هذا
+
+297
+00:32:45,220 --> 00:32:51,500
+كلام صحيح since الـH is a normal subgroup من مين؟
+
+298
+00:32:51,500 --> 00:32:56,520
+من G وبالتالي حصل الضرب اللي عندها ده سواء حصل
+
+299
+00:32:56,520 --> 00:33:01,200
+الضرب اللي عندها ده يبقى ال operation معرفة تعريفا
+
+300
+00:33:01,200 --> 00:33:07,470
+سليما مافيش فيها أي شيء طبعا إيش بده أثبات؟بدي
+
+301
+00:33:07,470 --> 00:33:12,130
+أثبت أن هذه عبارة عن مين؟ عن group يبقى بد ال
+
+302
+00:33:12,130 --> 00:33:15,170
+identity element و ال inverse element و ال
+
+303
+00:33:15,170 --> 00:33:19,690
+associativity بقوله بسيطة بدالي الحكاية ال
+
+304
+00:33:19,690 --> 00:33:28,290
+associativity let ال a h و ال b h و ال c h موجودة
+
+305
+00:33:28,290 --> 00:33:34,030
+في ال g modulo h let then
+
+306
+00:33:42,850 --> 00:33:48,930
+مش هنثبت خاصية ال associativity حسب ال definition
+
+307
+00:33:48,930 --> 00:33:57,170
+تبع ال operation يبقى هذا بده يساوي abh في main في
+
+308
+00:33:57,170 --> 00:34:04,960
+chحسب التعريف نفسه كمان مرة يبقى هذا الكلام بديه
+
+309
+00:34:04,960 --> 00:34:13,020
+يساوي ايه بديه يساوي A B كله في C في H طب السؤال
+
+310
+00:34:13,020 --> 00:34:20,980
+هوالان ال a و ال b و ال c عناصر موجودة في جي مش في
+
+311
+00:34:20,980 --> 00:34:26,420
+هتش ال a و ال b و ال c left cosets لما تقول ال h
+
+312
+00:34:26,420 --> 00:34:30,440
+يبقى ال a جايبه من جي و ال h هي عبارة عن ال sub
+
+313
+00:34:30,440 --> 00:34:34,640
+group يبقى هذول ال elements التلاتة موجودة في ال
+
+314
+00:34:34,640 --> 00:34:39,570
+group جيG group يبقى ال associative عليها خاصية
+
+315
+00:34:39,570 --> 00:34:45,070
+صحيحة مدام خاصية صحيحة إذا بقدر أقول هذا الكلام
+
+316
+00:34:45,070 --> 00:34:52,630
+بده يساوي A في ال BCH الشكل اللي عندنا هذا طيب
+
+317
+00:34:52,630 --> 00:35:02,660
+كويس هذا يعني ايه هذا يعني انههذا يعني ان ال a h
+
+318
+00:35:02,660 --> 00:35:11,680
+في مين في ال b c h هذا بيسوي هذا نرجعها الى أصلها
+
+319
+00:35:11,680 --> 00:35:19,800
+هذا a h في هذا بقدر اقول بي اتش في مين في c h بشكل
+
+320
+00:35:19,800 --> 00:35:24,880
+لأن هذا يبقى خاصية ال associativity عليها خاصية
+
+321
+00:35:24,880 --> 00:35:32,800
+صحيةطب الآن بدنا نجي لمين؟ لل identity element و
+
+322
+00:35:32,800 --> 00:35:39,120
+المعكوس تبع ال element مين تتوقع يكون ال identity
+
+323
+00:35:39,120 --> 00:35:46,060
+element تبع هذه ال group؟
+
+324
+00:35:46,060 --> 00:35:53,900
+ما دي كل عناصرها left coset ال E يعني ال H نفسها
+
+325
+00:35:53,900 --> 00:35:58,940
+ال H نفسها ال H يتسلببدك تجيب element من جيه بجيب
+
+326
+00:35:58,940 --> 00:36:02,600
+ال identity element و بضربه في مين في h اللي هو
+
+327
+00:36:02,600 --> 00:36:09,400
+بيعطينا ال h itself يبقى هنا بجيب اقوله ال h او ال
+
+328
+00:36:09,400 --> 00:36:17,840
+e h اللي هو بده يساوي h is the identity element
+
+329
+00:36:17,840 --> 00:36:29,470
+طبعا سهلة كمان هذه becauseلأن الـ E H في الـ A H
+
+330
+00:36:29,470 --> 00:36:38,510
+بده يساوي الـ E A H اللي هو بده يساوي الـ A H لكل
+
+331
+00:36:38,510 --> 00:36:43,670
+الـ A اللي موجودة في ال group G يجب ان اعطاني نفس
+
+332
+00:36:43,670 --> 00:36:49,190
+ال element و بالمثل كمان Similarly
+
+333
+00:36:51,670 --> 00:37:00,750
+بنفس الطريقة ال a h في مين في ال e h بده يساوي ال
+
+334
+00:37:00,750 --> 00:37:07,030
+a h لكل ال a اللي موجودة
+
+335
+00:37:07,030 --> 00:37:13,310
+في جيه طب إننا نيجي الأن لل inverse element يبقى
+
+336
+00:37:13,310 --> 00:37:16,970
+the inverse of
+
+337
+00:37:30,630 --> 00:37:37,250
+الإنفارس ينزل عالمين على الـ element و الـ H تبقى
+
+338
+00:37:37,250 --> 00:37:38,110
+كذلك
+
+339
+00:37:42,950 --> 00:37:51,800
+لو جيه تقولش لك A inverse H في الـ Hأنا قلت ان هذا
+
+340
+00:37:51,800 --> 00:37:56,400
+ال element معكوس انطلع الناتج يسوى ال identity
+
+341
+00:37:56,400 --> 00:38:00,700
+element اللي هو ال H بتما المطلوب يبقى بقدر أقول
+
+342
+00:38:00,700 --> 00:38:05,620
+حسب ال definition اللي عندي هذا هذا بده يسوى A
+
+343
+00:38:05,620 --> 00:38:11,760
+inverse AH يعني AH اللي هو ال H ال identity
+
+344
+00:38:11,760 --> 00:38:15,920
+element بالمثل similarly
+
+345
+00:38:18,410 --> 00:38:25,630
+اللي هو main A H في ال A inverse H بده يساوي A A
+
+346
+00:38:25,630 --> 00:38:32,590
+inverse H اللي هو ال H يبقى بناء عليه معكوس ال A H
+
+347
+00:38:32,590 --> 00:38:37,330
+هو ال A inverse H يبقى ال identity موجود والمعكوس
+
+348
+00:38:37,330 --> 00:38:42,190
+موجود وال associativity موجودة وزيادة على ذلك
+
+349
+00:38:42,190 --> 00:38:48,070
+العملية معرفةيبقى بناء عليه الـ G modulo H is a
+
+350
+00:38:48,070 --> 00:38:59,490
+group يبقى داصر وهكذا الـ G modulo H is a group
+
+351
+00:38:59,490 --> 00:39:11,070
+under the operation تحت العملية AH في BH بده يساوي
+
+352
+00:39:11,070 --> 00:39:13,170
+ABH
+
+353
+00:39:16,370 --> 00:39:23,570
+طب لو كانت العملية عملية جامعة، ايش بيصير هذه؟ a
+
+354
+00:39:23,570 --> 00:39:31,510
+بي زائد .. اه جزء اه زائد بي اتش بيسوي a زائد بي
+
+355
+00:39:31,510 --> 00:39:37,470
+كله زائد اتش ال a و ال b ك elements مع بعضهم جامعة
+
+356
+00:39:37,470 --> 00:39:41,550
+و بيصير زائد main زائد ال subgroup اللي هي اتش كنت
+
+357
+00:39:41,550 --> 00:39:42,150
+باكتشف سهل
+
+358
+00:39:48,100 --> 00:39:53,820
+ممتاز جدا، الحين هذه إيش معناها؟ مش حاصل ضربة، هو
+
+359
+00:39:53,820 --> 00:39:59,360
+left corset، سياطتني left corset، يبقى closedلأ لأ
+
+360
+00:39:59,360 --> 00:40:03,560
+هى ماطينة يعني هى ماطينة حاصلة بتوع left cosets و
+
+361
+00:40:03,560 --> 00:40:08,060
+left cosets أثبت بس صاروا شوية أثبت ان هذه العملية
+
+362
+00:40:08,060 --> 00:40:12,620
+عملية معرفة مدى معرفة كأنه ثبتت له ال binary
+
+363
+00:40:12,620 --> 00:40:16,020
+operation على طول الخط انه حاصل ضرب two left
+
+364
+00:40:16,020 --> 00:40:19,940
+cosets بتساوي نفس حاصلة ضرب two left cosets اللى
+
+365
+00:40:19,940 --> 00:40:25,290
+بيسويها يعني هو معرفة و بتعطيهبالضبط كإنه function
+
+366
+00:40:25,290 --> 00:40:31,970
+بالضبط تمام حد أيه لقى اي تساوى لآخر بدنا نبدأ
+
+367
+00:40:31,970 --> 00:40:34,270
+ناخد أمثلة على ذلك
+
+368
+00:41:59,470 --> 00:42:04,590
+أول شيء جل الأربعة زد هي subgroup من زد وبعد ذلك
+
+369
+00:42:04,590 --> 00:42:10,550
+جل الأربعة زد هي normal subgroup من من من زد كذلك
+
+370
+00:42:10,550 --> 00:42:17,370
+السبب ليش؟ أول شيء بنعرف مين هي الأربعة زد الأربعة
+
+371
+00:42:17,370 --> 00:42:26,470
+زد اللي هي مين؟ اللي على سرها أظن zero هيك واربعة
+
+372
+00:42:26,470 --> 00:42:30,350
+و تمانيةو 12 و تبقى مازال مازال مازال مازال مازال
+
+373
+00:42:30,350 --> 00:42:31,250
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+374
+00:42:31,250 --> 00:42:34,570
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+375
+00:42:34,570 --> 00:42:34,630
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+376
+00:42:34,630 --> 00:42:35,590
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+377
+00:42:35,590 --> 00:42:37,510
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+378
+00:42:37,510 --> 00:42:38,610
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+379
+00:42:38,610 --> 00:42:38,910
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+380
+00:42:38,910 --> 00:42:41,510
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+381
+00:42:41,510 --> 00:42:46,010
+مازال
+
+382
+00:42:46,010 --> 00:42:54,230
+مازال مازال
+
+383
+00:42:54,230 --> 00:42:56,030
+م
+
+384
+00:42:58,890 --> 00:43:03,130
+زد أربعة على زد والله ال sub group generated by
+
+385
+00:43:03,130 --> 00:43:09,110
+أربعة مظبوط يبقى الأربعة زد هي عبارة عن ال sub
+
+386
+00:43:09,110 --> 00:43:13,670
+group generated by أربعة هذه كنا نسميها زمان في
+
+387
+00:43:13,670 --> 00:43:17,390
+chapter أربعة و chapter تلاتة هي ال sub group
+
+388
+00:43:17,390 --> 00:43:22,200
+generated by أربعة بس احنا الأن بنقول أربعة زدتمام
+
+389
+00:43:22,200 --> 00:43:26,780
+طيب الأربعة زد هذه اللي هي ال subgroup و احنا
+
+390
+00:43:26,780 --> 00:43:31,420
+عارفين انها هذه ال subgroup من زد ياما اثبتناها
+
+391
+00:43:31,420 --> 00:43:36,120
+تمام يبقى خلصنا الخطوة الأولى خطوة تانية جل
+
+392
+00:43:36,120 --> 00:43:41,860
+الأربعة زد normal في زد زد ال operation اللي عليها
+
+393
+00:43:41,860 --> 00:43:47,840
+هي عملية عملية الجمع عملية الجمع abelian ولا لاطب
+
+394
+00:43:47,840 --> 00:43:51,900
+أول مثال أخدنا اليوم any subgroup of an abelian
+
+395
+00:43:51,900 --> 00:43:59,140
+group is normal يبقى هذه يبقى باجي بيقول since
+
+396
+00:43:59,140 --> 00:44:07,840
+اللي هو z is abelian يبقى
+
+397
+00:44:07,840 --> 00:44:14,820
+الأربعة z is a normal subgroup من مين subgroup من
+
+398
+00:44:14,820 --> 00:44:20,340
+gطيب مدام normal subgroup اذا بقدر اكوّن ال
+
+399
+00:44:20,340 --> 00:44:24,780
+quotient a group او ال factor a group يبقى باجي
+
+400
+00:44:24,780 --> 00:44:37,900
+بقوله هنا the factor a group is بروح بحط له z وهي
+
+401
+00:44:37,900 --> 00:44:46,040
+الشرطة وهي اربعة zوبداجي اكتب العناصر العناصر هي
+
+402
+00:44:46,040 --> 00:44:52,700
+كلها left cosets تمام اول عنصر حد بيقدر يعطيني اول
+
+403
+00:44:52,700 --> 00:44:56,780
+عنصر من هو اللي هو ال identity element اربعة زد
+
+404
+00:44:56,780 --> 00:45:02,660
+يعني ال zero زائد اربعة زد انسى ال zero يبقى اربعة
+
+405
+00:45:02,660 --> 00:45:10,020
+زدبدي ايجي بعده مين؟ واحد زائد أربعة زد طبعا لما
+
+406
+00:45:10,020 --> 00:45:14,220
+اقول زائد لإن ال operation اللي عندنا هي عملية مين
+
+407
+00:45:14,220 --> 00:45:18,360
+عملية الجامعة وقد أشرته إلى ذلك قبل اقل يقولنا إذا
+
+408
+00:45:18,360 --> 00:45:22,820
+العملية عملية جامعة يبقى مكتوبها واحد زائد أربعة
+
+409
+00:45:22,820 --> 00:45:29,940
+زد اللي بعده اتنين زائد أربعة زد اللي بعده تلاتة
+
+410
+00:45:29,940 --> 00:45:32,560
+زائد أربعة زد أمشي كمان؟
+
+411
+00:45:36,030 --> 00:45:40,790
+ليش مكتوب اربعة زي اربعة زي اربعة زي اربعة زي
+
+412
+00:45:40,790 --> 00:45:42,570
+اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة
+
+413
+00:45:42,570 --> 00:45:45,850
+زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي
+
+414
+00:45:45,850 --> 00:45:47,350
+اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة
+
+415
+00:45:47,350 --> 00:45:47,770
+زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي
+
+416
+00:45:47,770 --> 00:45:50,610
+اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة
+
+417
+00:45:50,610 --> 00:45:51,610
+زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي
+
+418
+00:45:51,610 --> 00:45:54,630
+اربعة زي اربعة زي اربعة زي اربعة زي اربعة زي اربعة
+
+419
+00:45:54,630 --> 00:46:04,150
+زي
+
+420
+00:46:04,150 --> 00:46:09,660
+اربعةفبنقول الآن نظرا لإن زد أبيليان هادي نورمال
+
+421
+00:46:09,660 --> 00:46:13,640
+subgroup إذا بقدر أكوّن ال quotient group اللي هي
+
+422
+00:46:13,640 --> 00:46:17,880
+زد مضيله أربعة زد اللي عناصرها أربعة زد واحد زائد
+
+423
+00:46:17,880 --> 00:46:21,880
+أربعة زد اتنين زائد أربعة زد تلاتة زائد أربعة زد
+
+424
+00:46:21,880 --> 00:46:28,600
+الآن لو بدنا نجيب مجموع عنصرين يعني بمعنى أخر حاصل
+
+425
+00:46:28,600 --> 00:46:32,500
+ضرب عنصرين إذا كان عملية عملية ضرب كيه بده أعملهم
+
+426
+00:46:32,500 --> 00:46:37,750
+هدول؟العمل اللي كانت عندنا باجي بقول a h في b h
+
+427
+00:46:37,750 --> 00:46:43,230
+يساوي a في b في h لكن العملية عملية جامع إذا باجي
+
+428
+00:46:43,230 --> 00:46:49,070
+بقول اللي قال لو بدي اجي اخدي اتنين زائد اربعة زد
+
+429
+00:46:49,070 --> 00:46:56,110
+كل هذا ك element زائد له تلاتة زائد اربعة زد
+
+430
+00:46:56,110 --> 00:47:03,100
+بالشكل اللي عندنا هذايبقى هذا يسوى اتنين زائد
+
+431
+00:47:03,100 --> 00:47:08,620
+تلاتة زائد اربعة زد يبقى هذا اتنين زائد تلاتة مع
+
+432
+00:47:08,620 --> 00:47:13,760
+بعض زائد اربعة زد مش بقول اربعة زد واربعة زد اتنين
+
+433
+00:47:13,760 --> 00:47:18,020
+فاربعة زد يعني تمانية زد مافيش حاجة اسمة زيك أبدا
+
+434
+00:47:18,020 --> 00:47:23,880
+ليش انه قولنا a h في bh يسوى a في b في h فهو h
+
+435
+00:47:23,880 --> 00:47:29,700
+واحدةتمام اتنين و تلاتة خمسة في اربعة زد يعطيني
+
+436
+00:47:29,700 --> 00:47:37,120
+كدهش واحد زائد اربعة زد يبقى هذا يعطيني خمسة زائد
+
+437
+00:47:37,120 --> 00:47:44,140
+اربعة زد وهنا اللي هي عبارة عن واحد زائد اربعة زد
+
+438
+00:47:44,140 --> 00:47:52,460
+طب لو بدى اجي اقول مثلا تلاتة زائد اربعة زدهذا
+
+439
+00:47:52,460 --> 00:47:58,120
+الكل تكيب مثلا
+
+440
+00:47:58,120 --> 00:48:04,100
+يعني هذا باعتباره الجوز زائد الجوز زائد الجوز تلات
+
+441
+00:48:04,100 --> 00:48:09,100
+مرات يعني كأنه احنا بنضرب اين نضرب في تلاتة يبقى
+
+442
+00:48:09,100 --> 00:48:15,160
+بالضبط هذا هو تسعة زائد اربعة زد مش هقول اربعة زد
+
+443
+00:48:15,160 --> 00:48:21,730
+في تلاتةلأن الجميع الـ z هذه أربعة z ثابتة التسعة
+
+444
+00:48:21,730 --> 00:48:27,930
+هذه عبارة عن جدات عبارة عن واحد زائد أربعة زد و
+
+445
+00:48:27,930 --> 00:48:36,920
+هكذا طيب لو بدى أجيب أس أربعةيبقى تلاتة زائد أربعة
+
+446
+00:48:36,920 --> 00:48:43,400
+زد أس أربعة اللي هي عبارة عن تلاتة زائد أربعة زد
+
+447
+00:48:43,400 --> 00:48:49,240
+الكل تكيب زائد واحد زائد أربعة زد اللي حصلنا عليها
+
+448
+00:48:49,240 --> 00:48:54,240
+أو لو من البداية ضربنا في أربعة بتفرجش عنا يبقى
+
+449
+00:48:54,240 --> 00:49:01,890
+هذه عبارة عن تسعة زائد أربعة زد زائداللي هو من ..
+
+450
+00:49:01,890 --> 00:49:08,810
+زائد تلاتة مش واحد هذه الكل تكيب هذه اللي هي بقى
+
+451
+00:49:08,810 --> 00:49:13,530
+هذه تلاتة زائد هذه عبارة عن مين عبارة عن واحد زائد
+
+452
+00:49:13,530 --> 00:49:21,570
+أربعة زيد هي طلعت فوق وهو هذه زائد له تلاتة زائد
+
+453
+00:49:21,570 --> 00:49:27,770
+أربعة زيد ويساوي Zero زائد أربعة زيد تلاتة واحد
+
+454
+00:49:28,230 --> 00:49:34,150
+أربعة هذه بتعطينا مين؟ أربعة زد يبقى بناء عليه
+
+455
+00:49:34,150 --> 00:49:41,450
+بقدر أقول ال order لتلاتة زائد أربعة زد هذا كله
+
+456
+00:49:41,450 --> 00:49:47,750
+بده يساوي قداش؟ بده يساوي أربعة يبقى ال order لهذا
+
+457
+00:49:47,750 --> 00:49:52,030
+ال element كله بده يساوي مين؟ بده يساوي أربعة طيب
+
+458
+00:49:52,030 --> 00:50:01,760
+مدام هيكإذا هذه قولنا فيها أكم element إذا بقدر
+
+459
+00:50:01,760 --> 00:50:07,540
+أقول إنها Cyclic وهذا generator تمام؟ مش حاجات هيك
+
+460
+00:50:07,540 --> 00:50:13,540
+الواحد زائد أربعة زد generator والتلاتة زائد أربعة
+
+461
+00:50:13,540 --> 00:50:15,400
+زد برضه generator
+
+462
+00:50:17,690 --> 00:50:25,490
+يبقى هنا باجي بقول له so تلاتة زائد اربعة زد is a
+
+463
+00:50:25,490 --> 00:50:36,990
+generator is a generator for اللي هو z modulo
+
+464
+00:50:36,990 --> 00:50:44,970
+اربعة زد هذا بدي يعطيلك ان زد modulo اربعة زد is
+
+465
+00:50:44,970 --> 00:50:54,450
+cyclicمش عاجزكوا بس يبقى هنا also اللي هو z modulo
+
+466
+00:50:54,450 --> 00:51:05,790
+4z ايزو مورفك لمين ل z 4 طب لو عمّمت و اروح اقولin
+
+467
+00:51:05,790 --> 00:51:16,010
+general وعلى وجه العموم z modulo n في z عايز أمرك
+
+468
+00:51:16,010 --> 00:51:23,630
+لمين يا شباب ل z n من الأن فصاعدا يبقى هذا المثال
+
+469
+00:51:23,630 --> 00:51:29,730
+استفدنا منه شغلات كثيرة جدا يعطيكوا العافية ونكمل
+
+470
+00:51:29,730 --> 00:51:31,990
+ان شاء الله يوم الأثنين
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_postprocess.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c016e011ab4591d1209b8c4cbda84c6918eeb49f
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/uNgZXyIcVM8_postprocess.srt
@@ -0,0 +1,1604 @@
+1
+00:00:20,970 --> 00:00:26,550
+بسم الله الرحمن الرحيم لازلنا في نفس ال chapter
+
+2
+00:00:26,550 --> 00:00:31,750
+الأول اللي هو بتحدث عن أساسيات لمساق الجبرة اللي
+
+3
+00:00:31,750 --> 00:00:36,670
+سندرسه و اليوم ان شاء الله سنتعرض الى ال
+
+4
+00:00:36,670 --> 00:00:41,190
+equivalence relations والتي سبقت دراستها في مبادئ
+
+5
+00:00:41,190 --> 00:00:46,100
+الرياضيةهنعطي تعريف نعرف شو يعني معنى equivalence
+
+6
+00:00:46,100 --> 00:00:51,080
+relation نعطي مثال نعرف شو يعني equivalence class
+
+7
+00:00:51,080 --> 00:00:55,660
+نعرف ما هو ال partition على ال set يعني هذا جمال
+
+8
+00:00:55,660 --> 00:01:00,000
+ما سندرسه في هذه المحاضرة ان شاء الله بنبدأ بال
+
+9
+00:01:00,000 --> 00:01:04,140
+equivalence relations اللي على أولاقات التكافؤ
+
+10
+00:01:04,140 --> 00:01:08,630
+بدنا نعرف أولاق التكافؤو بعدين انا اخد مثال و
+
+11
+00:01:08,630 --> 00:01:13,310
+اوضيها عليها بقول little s ب a6 يبقى اخدنا s
+
+12
+00:01:13,310 --> 00:01:19,970
+كمجموعة جالي a subset R of s cross ال s يبقى انا
+
+13
+00:01:19,970 --> 00:01:25,150
+على ال 6s بدي اعمل direct product ما بين ال s و ال
+
+14
+00:01:25,150 --> 00:01:29,910
+s itself بصير كل element في ال s cross ال s عبارة
+
+15
+00:01:29,910 --> 00:01:36,620
+عن order pair زوج مرتبيبقى ال R هي subset من ال S
+
+16
+00:01:36,620 --> 00:01:41,860
+cross ال S وهذه بسميها equivalence relation on S
+
+17
+00:01:41,860 --> 00:01:47,740
+إذا تحققت ثلاث خواص الخاصية الأولى هي خاصية
+
+18
+00:01:47,740 --> 00:01:51,520
+reflexive التانية ال symmetric التالتة هي ال
+
+19
+00:01:51,520 --> 00:01:55,020
+transitiveتعالى نشوف شو يعني معنى reflexive
+
+20
+00:01:55,020 --> 00:02:00,400
+property بيقول ال a و ال a موجودة في R يعني لو
+
+21
+00:02:00,400 --> 00:02:05,900
+أخدت a موجود في S لازم يكون ال element a و a ك
+
+22
+00:02:05,900 --> 00:02:11,340
+order pair موجود وام موجود في R يعني العنصر مرتبط
+
+23
+00:02:11,340 --> 00:02:17,520
+مع مين؟ مع نفسه بهذه ال relationيقبل الـ A والـ A
+
+24
+00:02:17,520 --> 00:02:22,080
+موجودة في الـ R لكل الـ A الموجودة في الـ Main في
+
+25
+00:02:22,080 --> 00:02:26,640
+الـ S يعني لو أخدت أي element من الـ6S يكون هذا
+
+26
+00:02:26,640 --> 00:02:31,460
+الـ element مربوط مع نفسه بالعلاقة من الـ R وهذا
+
+27
+00:02:31,460 --> 00:02:37,860
+اللي نسميها العلاقة العاكسة reflexive property
+
+28
+00:02:37,860 --> 00:02:44,300
+العلاقة العاكسة أو القصية العاكسةالشرط التاني او
+
+29
+00:02:44,300 --> 00:02:49,960
+الخاصية التانية لو كان عندي زوج مرتب a و b موجود
+
+30
+00:02:49,960 --> 00:02:55,500
+في R لازم يكون المقلب اللي هو b و a موجودة في R
+
+31
+00:02:55,730 --> 00:02:59,790
+يبقى هذا يعطيك يعني المركبة التانية بيصير الأولى
+
+32
+00:02:59,790 --> 00:03:03,650
+والأولى بيصير التانية وهذا ال element لازم يكون
+
+33
+00:03:03,650 --> 00:03:08,050
+موجود في R يعني إن كان A وB موجود في R لازم يكون B
+
+34
+00:03:08,050 --> 00:03:13,870
+وA كذلك موجود في R لكل ال A وB اللي موجودة في اسم
+
+35
+00:03:13,870 --> 00:03:19,610
+وهذه بسميها علاقة التماثل symmetric property أو
+
+36
+00:03:19,610 --> 00:03:25,510
+خاصية التماثلالأمر الثالث والأخير لو كان ال order
+
+37
+00:03:25,510 --> 00:03:30,410
+pair A وB موجود في R و ال B و C موجود في R لاحظ
+
+38
+00:03:30,410 --> 00:03:34,910
+المركبة الثانية هنا هي المركبة الأولى هنا لو كانوا
+
+39
+00:03:34,910 --> 00:03:39,710
+اتنين موجودات في R لازم يكون ال A و ال C موجود وان
+
+40
+00:03:39,710 --> 00:03:45,350
+موجود في R وهذه بسميها Transitive Property خاصية
+
+41
+00:03:45,350 --> 00:03:50,090
+النقل أو العلاقة التي حقق هذه الخاصية بسميها علاقة
+
+42
+00:03:50,090 --> 00:03:54,240
+ناقلةإذا الـ equivalence relation هي عبارة عن
+
+43
+00:03:54,240 --> 00:03:59,180
+علاقة عاكسة وفي نفس الوقت علاقة متماثلة وفي نفس
+
+44
+00:03:59,180 --> 00:04:03,860
+الوقت علاقة ناقلة إذا تحققت هذه الخواص الثلاثة
+
+45
+00:04:03,860 --> 00:04:08,240
+بقول ال relation اللي عندنا is an equivalence
+
+46
+00:04:08,240 --> 00:04:14,570
+relationهذا equivalence relation بنعبر عنها بصيغة
+
+47
+00:04:14,570 --> 00:04:18,730
+رياضية بعد ما كنا بنقول عليها جملة أدبية يعني
+
+48
+00:04:18,730 --> 00:04:22,710
+equivalence relation بدنا نعطيها رمز وهذا الرمز
+
+49
+00:04:22,710 --> 00:04:27,750
+بدي يصير متعرف عليها طبعا أن أكثر من رمز يمكن أن
+
+50
+00:04:27,750 --> 00:04:31,610
+نرمز بهي ال equivalence relation لكن الدرجة الغالب
+
+51
+00:04:31,610 --> 00:04:37,240
+هو رمز واحدمثال و ذلك لو قلنا ال R هي equivalence
+
+52
+00:04:37,240 --> 00:04:43,360
+relation على ال 6S بالروح نكتب ان ال A are related
+
+53
+00:04:43,360 --> 00:04:47,980
+with B هذي مش ال set of real numbers هذي R اللي هي
+
+54
+00:04:47,980 --> 00:04:52,920
+العلاقة اللي عندي يعني بقول ان ال A و ال B مرتبطات
+
+55
+00:04:52,920 --> 00:04:58,430
+مع بعض بالعلاقة R instead of بدلا مقولإن الراجل
+
+56
+00:04:58,430 --> 00:05:02,810
+مرتب a و b موجود في الارض بقول لأ ال a مرتبط مع
+
+57
+00:05:02,810 --> 00:05:08,310
+مين مع بي يعني a are b يبقى a are related with b
+
+58
+00:05:08,310 --> 00:05:13,410
+مرتبط تماما مع مين مع بي أو ممكن نعبر عنها بالصيغة
+
+59
+00:05:13,410 --> 00:05:18,750
+هذه a are related with b و أحيانا بيعبروا بحكاية
+
+60
+00:05:18,750 --> 00:05:23,490
+اليساوي و أحيانا بثلاثةاللي هي زي التكافو أو ما
+
+61
+00:05:23,490 --> 00:05:27,050
+إلى ذلك على أي حال لكن الدرج عندنا في كتابنا
+
+62
+00:05:27,050 --> 00:05:31,970
+بيحاول يستخدم him اللي هو الرمز اللي عندنا يبقى
+
+63
+00:05:31,970 --> 00:05:37,730
+هذا الرمز هو عبارة عن رمز يرمز لعلاقة التكافو اللي
+
+64
+00:05:37,730 --> 00:05:43,680
+هي reflexive و symmetric and transitiveطيب العلاقة
+
+65
+00:05:43,680 --> 00:05:48,080
+اللى عندنا هذه لما نجى على الست اللى عندنا هذه
+
+66
+00:05:48,080 --> 00:05:52,640
+ونقول عندنا العلاقة هذه العلاقة هذه بتعملى مجموعة
+
+67
+00:05:52,640 --> 00:05:57,780
+من ال equivalence classes اللي همين فصولي التكافئة
+
+68
+00:05:57,780 --> 00:06:02,660
+ايه قصة فصولي التكافئة هذا تعالي تشوفي دىلو كان ان
+
+69
+00:06:02,660 --> 00:06:06,300
+ال relation هذه عبارة عن equivalent relation على
+
+70
+00:06:06,300 --> 00:06:13,480
+ال 6S وخت أي عنصر موجود في ال 6S وليكن عنصر A
+
+71
+00:06:13,480 --> 00:06:19,940
+فبروح بعرف ال equivalence class لل 6A وكل العناصر
+
+72
+00:06:19,940 --> 00:06:24,340
+اللي موجودة في ال 6S و اللي بتكون مربوطة مع هذا
+
+73
+00:06:24,340 --> 00:06:28,800
+العنصر فقط وماليش دعوة في الباقييعني أنا طبقا
+
+74
+00:06:28,800 --> 00:06:33,080
+لتأثير ال relation أو تحت أثير ال relation هذه في
+
+75
+00:06:33,080 --> 00:06:38,440
+عندي عناصر بتكون مرتبطة مع العناصر هدول بيكونولي
+
+76
+00:06:38,440 --> 00:06:42,040
+مجموعة لمجموعة هذه اللي بيسميها equivalence class
+
+77
+00:06:42,040 --> 00:06:47,970
+فصل التكافئ لهذا الألميبقى لما نشوف element a
+
+78
+00:06:47,970 --> 00:06:53,390
+ومحطوط بين قسينك باربك تفهم هذا معناه equivalency
+
+79
+00:06:53,390 --> 00:06:56,490
+class نتيجة ال equivalency relation اللي موجودة
+
+80
+00:06:56,490 --> 00:07:01,190
+على ال S شو تعريفه؟ كل العناصر اللي موجودة في S و
+
+81
+00:07:01,190 --> 00:07:05,230
+اللي بتكون مرتبطة مع نفس العنصر هذا اللي هو A اللي
+
+82
+00:07:05,230 --> 00:07:08,690
+أخدته طبعا بعد قليل هعطيك مثال كيف بنجيب هذه
+
+83
+00:07:08,690 --> 00:07:13,210
+العناصر؟يبقى هذا ال element بنسميه ال equivalence
+
+84
+00:07:13,210 --> 00:07:18,830
+class تبع ال 6S that contains A يعني ال
+
+85
+00:07:18,830 --> 00:07:23,550
+equivalence class لل element لازم يحتوي على مين؟
+
+86
+00:07:23,550 --> 00:07:28,510
+يحتوي على ال element itself بالاضافة إلى مجموعة من
+
+87
+00:07:28,510 --> 00:07:33,120
+العناصر الأخرىنعطي مثال على ال equivalence
+
+88
+00:07:33,120 --> 00:07:36,140
+relation
+
+89
+00:07:36,140 --> 00:07:40,520
+و بعد ذلك نذهب نجيب ال equivalence class لأي
+
+90
+00:07:40,520 --> 00:07:45,960
+element موجود داخل ال set اللى بدنا ناخدها بقول لو
+
+91
+00:07:45,960 --> 00:07:52,000
+أخدت ال set of integers يبقى ال S هدفين ليه ال Z
+
+92
+00:07:52,000 --> 00:07:56,740
+مجموعة الأعداد الصحية الموجبة والسالمة والصفريعني
+
+93
+00:07:56,740 --> 00:08:02,620
+هذه صارت يا مين هي ال 6z اللى عرفنالكوا في أول
+
+94
+00:08:02,620 --> 00:08:07,860
+محاضرة قولنالكوا ال 6 اللى 6 of integer لت ال n
+
+95
+00:08:07,860 --> 00:08:12,660
+بيه positive integer أخدت ال n أي عدد صحيح موجه ب2
+
+96
+00:08:12,660 --> 00:08:19,800
+3 10 20 قد ما يكون تمامبناخد عنصرين موجودة في الست
+
+97
+00:08:19,800 --> 00:08:23,840
+S يعني ال A و ال B انتجرز يمكن يكونوا اتنين
+
+98
+00:08:23,840 --> 00:08:26,020
+بالموجة يمكن يكونوا اتنين بالسالي يمكن يكونوا واحد
+
+99
+00:08:26,020 --> 00:08:30,220
+موجة و واحد سالي مهمنيش ماليهمش قيود بدنا نروح و
+
+100
+00:08:30,220 --> 00:08:35,970
+نعرف ان ال A مرتبط مع ال B إذا كانالـ A modulo N
+
+101
+00:08:35,970 --> 00:08:41,030
+بيساوي ال B modulo N توجه لك ال relation يابن
+
+102
+00:08:41,030 --> 00:08:45,870
+أعطيها الرمز هذا يابن أعطيها الرمز هذا يابن أعطيها
+
+103
+00:08:45,870 --> 00:08:49,130
+الرمز هذا يابن أعطيها الرمز هذا هو راح أعطاها
+
+104
+00:08:49,130 --> 00:08:53,710
+الرمز اللي عندنا اللي هو رمز اليساوييعني الـ
+
+105
+00:08:53,710 --> 00:08:57,110
+remainder تبع الـ A يبقى يساوي الـ remainder تبع
+
+106
+00:08:57,110 --> 00:09:02,670
+الباقي نتيجة لقسمة الـ A على M نفس الباقي لو قسمنا
+
+107
+00:09:02,670 --> 00:09:08,850
+الـ B على M that is بدي أترجم هذا الكلام بصياغة
+
+108
+00:09:08,850 --> 00:09:15,730
+أخرىبعدين بقول ال A مرتبطة مع بي اف هذا أخدنا صيغة
+
+109
+00:09:15,730 --> 00:09:20,410
+مكافئة إلو و هي N بدأ تقسم الفرق ما بين ال A و
+
+110
+00:09:20,410 --> 00:09:24,070
+اللي بياخدناه المرة الماضية مظبوط إذا الصيغة بدل
+
+111
+00:09:24,070 --> 00:09:27,430
+ما صرت X صارت الصيغة اللي عندنا يعني بقول this
+
+112
+00:09:27,430 --> 00:09:32,140
+relation is an equivalence relation ليش؟يبقى قال
+
+113
+00:09:32,140 --> 00:09:35,880
+لي هذه equivalence relation بدنا نقيم الدليل على
+
+114
+00:09:35,880 --> 00:09:39,060
+إن هذا ال relation اللي عرفناها بهذا الشكل هي
+
+115
+00:09:39,060 --> 00:09:43,440
+عبارة عن equivalence relation بمعنى آخر بدي أروح
+
+116
+00:09:43,440 --> 00:09:47,260
+أحقق الشروط التلاتة أو الخواص التلاتة اللي عندنا
+
+117
+00:09:47,260 --> 00:09:51,160
+إذا تحققت الخواص التلاتة على ال relation هذي بيصير
+
+118
+00:09:51,160 --> 00:09:56,120
+هذه equivalence relation تمام؟ بنقوله كويس بدنا
+
+119
+00:09:56,120 --> 00:10:02,080
+نيجي للخاصية الأولىأنا بدي العنصر يكون مرتبط مع
+
+120
+00:10:02,080 --> 00:10:07,180
+نفسه كيف يعني مرتبط مع نفسه يعني لو طرحتي اتنين من
+
+121
+00:10:07,180 --> 00:10:13,460
+بعض الان بده تقسمين الفرق في ما بينهما يبقى بدي
+
+122
+00:10:13,460 --> 00:10:20,300
+اخد اول حاجة خاصية ال reflex يبقى باجي بقوله بدي
+
+123
+00:10:20,300 --> 00:10:25,760
+اجي اقوله الآن ال ا are related مع ا مرتبط مع ا شو
+
+124
+00:10:25,760 --> 00:10:34,380
+السبب becauseان ال N بتقسم ال A ناقص ال A يعني
+
+125
+00:10:34,380 --> 00:10:40,800
+مكان ال B حطينا مين حطينا بيه يعني ايش sense لإن
+
+126
+00:10:40,800 --> 00:10:46,660
+ال N بتقسم ال zero صحيح ولا لأمش ال N بتقسم ال
+
+127
+00:10:46,660 --> 00:10:50,960
+Zero ال Zero على N جدش يساوي Zero او لأن Zero
+
+128
+00:10:50,960 --> 00:10:56,300
+يساوي N في Zero عملناها برضه المرة اللي فاتت يبقى
+
+129
+00:10:56,300 --> 00:11:00,400
+لأن ال N بتقسم ال Zero يبقى هذا العنصر مرتبط مع
+
+130
+00:11:00,400 --> 00:11:07,960
+نفسه وهذه اللي سمنها reflexive property طيب نيجي
+
+131
+00:11:07,960 --> 00:11:11,620
+للخاصية التانية F
+
+132
+00:11:21,910 --> 00:11:33,070
+لما نقول ان ال N بدأ تقسم ال A minus ال B هذا
+
+133
+00:11:33,070 --> 00:11:40,070
+معناه ان ال A ناقص ال B بده يساوي ال N في ال Q
+
+134
+00:11:44,970 --> 00:11:51,910
+طب ايش رايك لو ضربت الطرفين في اشارة سالب انفك و
+
+135
+00:11:51,910 --> 00:11:56,350
+لو ضربت اتنين في اشارة سالب ايش بديصير؟ بيصير ال B
+
+136
+00:11:56,350 --> 00:12:03,030
+بالموجب و ال A بالسالب يبقى هذا بيصير B سالب ال A
+
+137
+00:12:03,030 --> 00:12:10,640
+هنا بقدر اقول انف ناقص Qماذا يعني هذا الكلام؟
+
+138
+00:12:10,640 --> 00:12:17,940
+معناته ان بتقسم من؟ ال b ناقص ال a هذا معناه ان ال
+
+139
+00:12:17,940 --> 00:12:24,000
+n بتقسم ال b ناقص ال a مدام هيك يبقى هذا معناه ان
+
+140
+00:12:24,000 --> 00:12:30,340
+ال b are related with a وهذا اللي بسميها symmetric
+
+141
+00:12:30,340 --> 00:12:32,880
+property
+
+142
+00:12:35,780 --> 00:12:40,340
+طيب كويس يبقى الأن تحققت الخاصية الثانية بتروح
+
+143
+00:12:40,340 --> 00:12:46,760
+لمين للخاصية التالتة يبقى بالداجة للخاصية التالتة
+
+144
+00:12:46,760 --> 00:12:55,280
+assume أفترض أن ال a are related with b and ال b
+
+145
+00:12:55,280 --> 00:13:02,940
+are related with c و ال a و ال b و ال c موجودات في
+
+146
+00:13:02,940 --> 00:13:12,090
+ال z اللي هو integersthen بقدر اقول ان ال N
+
+147
+00:13:12,090 --> 00:13:22,110
+divides ال A ناقص ال B and ال N divides ال B ناقص
+
+148
+00:13:22,110 --> 00:13:22,650
+ال C
+
+149
+00:13:25,490 --> 00:13:28,110
+مش هيك تعريف ال equivalence relation أو ال
+
+150
+00:13:28,110 --> 00:13:32,310
+relation اللي عندنا يبقى ال N بتقسم ال A ناقص ال B
+
+151
+00:13:32,310 --> 00:13:38,270
+وفي نفس الوقت ال N بتقسم ال B ناقص ال C هذا معناه
+
+152
+00:13:38,270 --> 00:13:53,680
+ان هناك Q1 و Q2 موجودة في Z such that بحيث انالـ A
+
+153
+00:13:53,680 --> 00:14:03,600
+minus ال B يساوي Q واحد في N and ال B ناقص ال C
+
+154
+00:14:03,600 --> 00:14:07,720
+بدر ساوي AQ اتنين في N
+
+155
+00:14:11,650 --> 00:14:18,370
+طيب انا ايش بدي؟ بدي الخاصية التالتة بدي A مرتبطة
+
+156
+00:14:18,370 --> 00:14:23,310
+مع مين؟ مع ال C يبقى بدي ال A تكون مرتبطة مع ال C
+
+157
+00:14:23,310 --> 00:14:28,220
+باجي بقول كويسة بدي اتطلع في هذه و هذهأظن لو جمعنا
+
+158
+00:14:28,220 --> 00:14:34,060
+الاتنين بيبقى من عنده ال A و ال C يبقى هذا يعطيك
+
+159
+00:14:34,060 --> 00:14:41,700
+لو جنا جمعنا هدول بيصير عند ال A ناقص ال C يساوي Q
+
+160
+00:14:41,700 --> 00:14:47,880
+واحد زائد Q اتنين كله مضروم في مين؟ مضروم في اين؟
+
+161
+00:14:48,090 --> 00:14:55,310
+معنى هذا الكلام ان ال N بتقسم ال A نقص ال C هذا
+
+162
+00:14:55,310 --> 00:15:04,300
+معناه ان ال N تقسم ال A نقص ال Cمدام الـ N مقاومة
+
+163
+00:15:04,300 --> 00:15:06,720
+الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ C
+
+164
+00:15:06,720 --> 00:15:08,960
+مقاومة الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ
+
+165
+00:15:08,960 --> 00:15:10,680
+C مقاومة الـ A مقاومة الـ C مقاومة الـ C مقاومة
+
+166
+00:15:10,680 --> 00:15:16,940
+الـ A مقاومة الـ C مقاومة الـ A مقاومة الـ C
+
+167
+00:15:16,940 --> 00:15:20,500
+مقاومة الـ C مقاومة الـ C مقاومة الـ C مقاومة الـ
+
+168
+00:15:20,500 --> 00:15:23,220
+C مقاومة الـ C مقاومة الـ C مقاومة الـ C مقاومة
+
+169
+00:15:23,220 --> 00:15:24,400
+الـ C مقاومة الـ C مقاومة الـ C مقاومة الـ C
+
+170
+00:15:24,400 --> 00:15:29,300
+مقاومة الـ C مقإذا تحققت الشروط التلاتة اللي عندنا
+
+171
+00:15:29,300 --> 00:15:33,400
+يبقى ال relation هذي مالها is an equivalence
+
+172
+00:15:33,400 --> 00:15:39,280
+relation يبقى بقى دي بقوله ده و هكذا ان ال
+
+173
+00:15:39,280 --> 00:15:46,960
+relation اللي عندنا هذي is an equivalence relation
+
+174
+00:15:53,890 --> 00:15:58,170
+طب كويس يبقى يعطينا مثال على ال equivalence
+
+175
+00:15:58,170 --> 00:16:03,390
+relation بدنا نيجي نحسب ال equivalence class لأي
+
+176
+00:16:03,390 --> 00:16:09,610
+element موجود عندنا يعني بدي أروح أخد عنصر من Z و
+
+177
+00:16:09,610 --> 00:16:14,770
+أجيب كل العناصر اللي مرتبطة مع هذا العنصر طبق ال
+
+178
+00:16:14,770 --> 00:16:19,930
+main طبق ال definition اللي احنا معطينه طيب الآن
+
+179
+00:16:19,930 --> 00:16:22,750
+بدي أجي أطبق هذا التعريف
+
+180
+00:16:37,630 --> 00:16:41,530
+خلّيني أقول لكم هنا إحنا عندنا ال equivalence
+
+181
+00:16:41,530 --> 00:16:46,490
+class A كل العناصر X اللي موجودة في S يعني موجودة
+
+182
+00:16:46,490 --> 00:16:55,310
+في Z بحيث أن ال X are related with A طيب
+
+183
+00:16:55,310 --> 00:17:00,140
+احنا أخدنا هنا لما جينا أعرفنا ديقلنا إن الـ A
+
+184
+00:17:00,140 --> 00:17:06,840
+مرتبطة مع B إذا كانت الـ N تقسم الـ A نقص الـ B
+
+185
+00:17:06,840 --> 00:17:13,140
+يبقى الـ N بدي أخده كم قياس Modulo N بدي أخد
+
+186
+00:17:13,140 --> 00:17:18,740
+الأرقام هذه كلها Modulo M بس إن هذا رقم شايع بياخد
+
+187
+00:17:18,740 --> 00:17:23,880
+مالة نهاية من القيام أنا بقدر أحسب لرقم محدد اختار
+
+188
+00:17:23,880 --> 00:17:30,430
+لك رقم يجي في بالكقداش؟ خمسة ممتاز جدا يبقى صاحبنا
+
+189
+00:17:30,430 --> 00:17:38,570
+أخد الرقم خمسة بقوله آه يبقى الخمسة هذا طبقا لهذا
+
+190
+00:17:38,570 --> 00:17:43,950
+التعريف هو كل العناصر X اللي موجودة في S such ذات
+
+191
+00:17:43,950 --> 00:17:50,830
+ال X مرتبط مع مين؟ مع الخمسةطب كويس يعني هذا كل
+
+192
+00:17:50,830 --> 00:17:57,370
+العناصر X اللي موجودة في Z such that ال X بده
+
+193
+00:17:57,370 --> 00:18:02,930
+يساوي انت حتى المقياس خمسة والله المقياس كدهش؟
+
+194
+00:18:02,930 --> 00:18:06,690
+خمسة برضه؟ لأ إذا بناخد المقياس خمسة بده ناخد رقم
+
+195
+00:18:06,690 --> 00:18:10,690
+تاني مثلا بدي أخد تسعة
+
+196
+00:18:19,870 --> 00:18:31,330
+يبقى تسعة كل العناصر X بحيث X مرتبطة مع 9 يبقى كل
+
+197
+00:18:31,330 --> 00:18:41,550
+ال X الموجودة في Z بحيث X ساوي 9 زائدالرقم مضروب
+
+198
+00:18:41,550 --> 00:18:47,270
+في خمسة قد ما يكون يكون تمام يبقى بالداجي اقول Q
+
+199
+00:18:47,270 --> 00:18:55,080
+مضروب في خمسةيبقى هذا بجيبلي كل العناصر من أول ال
+
+200
+00:18:55,080 --> 00:18:59,660
+Z إلى آخرها اللي مرتبطة مع مين؟ مع التسعة طب انا
+
+201
+00:18:59,660 --> 00:19:05,120
+بدي شغل عملي الشغل العملي كالتالي باجي بقول هي
+
+202
+00:19:05,120 --> 00:19:09,060
+الست اللي عندنا و باجي بحط الرقم اللي عندنا اللي
+
+203
+00:19:09,060 --> 00:19:14,060
+هو تسعة في المصر و بصير اضيفله خمسات و اطرح منه
+
+204
+00:19:14,060 --> 00:19:22,370
+خمسات لإنه قلت تسعة زي ما هي زائد ل Q في خمسةليه Q
+
+205
+00:19:22,370 --> 00:19:29,130
+موجودة في Z يعني Q انتجر باجي بقوله لو التسعة
+
+206
+00:19:29,130 --> 00:19:37,420
+حاطتله خمسة قداش بصير اربعتاش وكمان خمسةوكمان خمسة
+
+207
+00:19:37,420 --> 00:19:42,600
+بيصير تسعة عشر وكمان خمسة بيصير أربعة وعشرين وكمان
+
+208
+00:19:42,600 --> 00:19:47,140
+خمسة بيصير تسعة وعشرين إلى ما شاء الله زي ما ضفت
+
+209
+00:19:47,140 --> 00:19:52,300
+خمسات بتطرح خمسات لو طرحت خمسة بيظل هنا جداش أربعة
+
+210
+00:19:52,300 --> 00:19:58,220
+بيظل سالب واحد بيظل سالب ستة بيظل سالب يحداش وهكذا
+
+211
+00:19:58,780 --> 00:20:04,160
+يبقى هي عناصر ال equivalency class كل العناصر هذول
+
+212
+00:20:04,160 --> 00:20:09,740
+أخدوا جزء من الست و الونتجر بس مش كلها أخدوا جزء
+
+213
+00:20:09,740 --> 00:20:13,880
+منها هذا الجزء أو هذه المجموعة هي اللي بنسميها ال
+
+214
+00:20:13,880 --> 00:20:18,540
+equivalency class يبقى ال equivalency class تبع
+
+215
+00:20:18,540 --> 00:20:24,340
+التسعة يحتوي على مجموعة من العناصر بس مش كل عناصر
+
+216
+00:20:24,340 --> 00:20:30,690
+z شوية منهمطيب إيش رايك ال equivalence relation
+
+217
+00:20:30,690 --> 00:20:36,730
+بتعملي partition للست اللي عندها أو للزد اللي
+
+218
+00:20:36,730 --> 00:20:41,310
+عندنا، إيش يعني partitionلو رجعنا لمبادئ رياضات
+
+219
+00:20:41,310 --> 00:20:46,390
+بقول لو عندي set و عليها partition partition يعني
+
+220
+00:20:46,390 --> 00:20:53,390
+مجموعة من ال subset اللي بتحقق شرطين الشرط الأول
+
+221
+00:20:53,390 --> 00:20:58,810
+لو أخدت ال union على كل ال subsets هذي بيطلع main
+
+222
+00:20:58,810 --> 00:21:04,510
+set الأصل يتنام لو عملت intersection على كل ال
+
+223
+00:21:04,510 --> 00:21:10,590
+subsets هذي بيطلع mainخلّيني اذكر بتعريف ال
+
+224
+00:21:10,590 --> 00:21:16,370
+partition و بعد هيك نحسبه للبعض يبقى بدنا نيجي
+
+225
+00:21:16,370 --> 00:21:21,450
+لحاجة اسمها اللي هو ال partition
+
+226
+00:21:46,380 --> 00:21:57,340
+هيبقى definition a
+
+227
+00:21:57,340 --> 00:22:05,040
+partition of
+
+228
+00:22:05,040 --> 00:22:11,500
+a set S is a collection
+
+229
+00:22:17,390 --> 00:22:25,970
+collection of non-empty
+
+230
+00:22:25,970 --> 00:22:29,050
+disjoint
+
+231
+00:22:29,050 --> 00:22:36,270
+subsets
+
+232
+00:22:36,270 --> 00:22:43,990
+of
+
+233
+00:22:43,990 --> 00:22:54,040
+Swhose union is
+
+234
+00:22:54,040 --> 00:23:00,620
+S itself طب
+
+235
+00:23:00,620 --> 00:23:07,220
+كويس تعالى نوضح هذا المفهوم افترض ان انا عندى ال 6
+
+236
+00:23:07,220 --> 00:23:13,940
+وال6 بالشكل هذا هذا ال 6S قسمتها الى مجموعة من ال
+
+237
+00:23:13,940 --> 00:23:19,920
+subsets وهذه واحدة وهذه واحدة وهذه واحدة وهذه
+
+238
+00:23:19,920 --> 00:23:30,220
+واحدة.و هكذا تمام سميتها S1 S2 S3 وظلت ماشي
+
+239
+00:23:30,220 --> 00:23:38,100
+للاخيرة اللي هي ال S N تمام يبقى ال partition
+
+240
+00:23:38,100 --> 00:23:45,660
+هديله الرمز بيه هو عبارة عن مجموعة S S1 و S2 و
+
+241
+00:23:45,660 --> 00:23:55,070
+لغاية S N بس بشرططالعش بيقول الـ Partition of non
+
+242
+00:23:55,070 --> 00:24:02,710
+-empty disjoint subsets يبقى كل واحدة فيها مجموعة
+
+243
+00:24:02,710 --> 00:24:06,910
+من العناصر يبقى هنا في عندي عناصر و هنا في عندي
+
+244
+00:24:06,910 --> 00:24:11,470
+عناصر و هنا في عناصر و هنا في عناصر و هكذا يبقى كل
+
+245
+00:24:11,470 --> 00:24:15,970
+مجموعة لازم يكون على الأقل فيها ولوعنصر واحد تمام
+
+246
+00:24:15,970 --> 00:24:21,350
+هذا المقصود non-empty this joint مافيش تقاطع فيما
+
+247
+00:24:21,350 --> 00:24:26,470
+بينهما تمام يبقى الشرط الأول مشان يكون هذا
+
+248
+00:24:26,470 --> 00:24:32,150
+partition الشرط الأولاني بدي يكون ال intersection
+
+249
+00:24:32,150 --> 00:24:39,650
+على ال S I و I تساوي واحد لغاية ال N بدي يساوي
+
+250
+00:24:39,650 --> 00:24:44,920
+قداشفاي ولا two subsets بتقاطعوا مع بعض مافيش
+
+251
+00:24:44,920 --> 00:24:51,720
+تنتين بتقاطعوا مع بعض على الإطلاق الشرط الثاني بدي
+
+252
+00:24:51,720 --> 00:24:57,860
+يكون ال union من I تساوي واحد لغاية ال N لل S I
+
+253
+00:24:57,860 --> 00:25:03,320
+بدي يساوي ال S itself ان حدث ذلك يبقى بقول هذا
+
+254
+00:25:03,320 --> 00:25:11,890
+بسمي partition على مين على Sيبقى ال partition على
+
+255
+00:25:11,890 --> 00:25:16,810
+set معينة هو تجزيه ال set هذه إلى مجموعة من ال
+
+256
+00:25:16,810 --> 00:25:21,210
+subsets بحيث ال subsets هدول بدوني محقولي شرطين
+
+257
+00:25:21,210 --> 00:25:25,670
+مافيش تداخل بين اي subset و التانية يعني ال
+
+258
+00:25:25,670 --> 00:25:30,410
+intersection بين اي subset و التانية بده يسوى قداش
+
+259
+00:25:30,410 --> 00:25:36,310
+fiveإذا خدت ال union عليهم كلهم بدي يعطينا نفس ال
+
+260
+00:25:36,310 --> 00:25:41,590
+6S لا بيزيد عليها ولا بينقص عنها مافي إمكانية إن
+
+261
+00:25:41,590 --> 00:25:47,790
+حدث ذلك يبقى هذا بسمي partition لمين لل 6S اللي
+
+262
+00:25:47,790 --> 00:25:57,230
+عندنا طيب خلينا .. خلينا نيجي الآن نعطي شغل عملية
+
+263
+00:25:57,230 --> 00:26:02,400
+على حكاية ال partition بس قبل هيكبدنا نعطي النقطة
+
+264
+00:26:02,400 --> 00:26:07,820
+الأخيرة قبل ما ناخد المثال العملي على ذلك في نظرية
+
+265
+00:26:07,820 --> 00:26:15,740
+بتقول لما يأتي theorem the
+
+266
+00:26:15,740 --> 00:26:18,700
+equivalence classes of an equivalence relation
+
+267
+00:26:18,700 --> 00:26:22,420
+equivalence
+
+268
+00:26:22,420 --> 00:26:30,000
+classes of an
+
+269
+00:26:37,750 --> 00:26:44,250
+equivalence classes of an equivalence relation on
+
+270
+00:26:44,250 --> 00:26:48,010
+a
+
+271
+00:26:48,010 --> 00:26:54,850
+set S على المجموعة S constitute a partition
+
+272
+00:27:21,730 --> 00:27:24,690
+العملية العكسية conversely
+
+273
+00:27:29,740 --> 00:27:39,920
+conversely for any partition
+
+274
+00:27:39,920 --> 00:27:46,160
+P
+
+275
+00:27:46,160 --> 00:27:49,880
+of
+
+276
+00:27:49,880 --> 00:27:54,460
+S there is
+
+277
+00:28:00,280 --> 00:28:15,400
+an equivalence relation there is
+
+278
+00:28:15,400 --> 00:28:24,760
+an equivalence relation on S على S whose
+
+279
+00:28:24,760 --> 00:28:26,300
+equivalence classes
+
+280
+00:28:32,590 --> 00:28:43,150
+equivalent classes فصول التكافئة تبعتها are the
+
+281
+00:28:43,150 --> 00:28:49,050
+elements of P
+
+282
+00:29:05,430 --> 00:29:10,810
+يبقى مرة تانية بنرجع الكلام اللى قلناه بنقول ال
+
+283
+00:29:10,810 --> 00:29:16,170
+partition على الست S هو collection of non-empty
+
+284
+00:29:16,170 --> 00:29:20,570
+disjoint subset لمين لل S اللي ال union تبعهم بدي
+
+285
+00:29:20,570 --> 00:29:25,030
+سوى مين S بالبلد هيك ال intersection على كل ال
+
+286
+00:29:25,030 --> 00:29:28,750
+subsets بدي سوى Phi و ال union بدي سوى ال S itself
+
+287
+00:29:29,700 --> 00:29:33,940
+النظرية بتقول لو كان ال equivalence classes اللي
+
+288
+00:29:33,940 --> 00:29:38,700
+نشأوا عن equivalence relation على ال 6S هدول
+
+289
+00:29:38,700 --> 00:29:44,420
+بيكونولي partition لمن؟ لل S يبقى مجموعة ال
+
+290
+00:29:44,420 --> 00:29:48,360
+equivalence classes اللي نتجوا عن ال equivalence
+
+291
+00:29:48,360 --> 00:29:52,540
+relation بيكونولي partition على ال 6S العملية
+
+292
+00:29:52,540 --> 00:29:57,950
+العكسية قال لي converselyلأي partition P على ست S
+
+293
+00:29:57,950 --> 00:30:03,210
+هما
+
+294
+00:30:03,210 --> 00:30:07,230
+عناصر الـ equivalence classes يبقى ال equivalence
+
+295
+00:30:07,230 --> 00:30:12,830
+class بتعمل partition على ست وعكسه صحيةلو كان عندى
+
+296
+00:30:12,830 --> 00:30:16,730
+partition على الست يبقى هذا ال partition بينشئ
+
+297
+00:30:16,730 --> 00:30:22,390
+equivalence classes كل equivalence class هو عضو من
+
+298
+00:30:22,390 --> 00:30:26,570
+أعضاء من ال partition أو هو عنصر من عناصر ال
+
+299
+00:30:26,570 --> 00:30:31,110
+partition على الست اللى عندناالان الي خاطر اوضح
+
+300
+00:30:31,110 --> 00:30:35,770
+هذا الكلام عمليا عمليا من وين انا اخد ال relation
+
+301
+00:30:35,770 --> 00:30:40,410
+اللى عندنا احنا اخدنا اللى هو قولنا العمصر تسعة
+
+302
+00:30:40,410 --> 00:30:45,490
+واخدنا المقياس مين اللى هو خمسة طب انا لما اخد
+
+303
+00:30:45,490 --> 00:30:50,800
+المقياس خمسةلما نأخد المقياس خمسة يبقى العناصر
+
+304
+00:30:50,800 --> 00:30:56,820
+Zero واحد واتنين وتلاتة واربعة خمسة بترجع مين؟
+
+305
+00:30:56,820 --> 00:31:01,960
+Zero ستة بترجع واحد سبعة بترجع اتنين تمانية بترجع
+
+306
+00:31:01,960 --> 00:31:07,520
+تلاتة تسعة بترجع اربعة وهكذا نوضح هذا الكلام يبقى
+
+307
+00:31:07,520 --> 00:31:20,450
+for example كمثال على ذلك from theabove example
+
+308
+00:31:20,450 --> 00:31:26,130
+where ال
+
+309
+00:31:26,130 --> 00:31:38,670
+S بدها تساوي Z وال N او and ال N بدها تساوي خمسة
+
+310
+00:31:38,670 --> 00:31:43,930
+يبقى بجي بقوله هنا the equivalence
+
+311
+00:31:45,620 --> 00:31:55,780
+A classes are اللي هو الـ Zero والواحد والاتنين
+
+312
+00:31:55,780 --> 00:32:05,240
+والتلاتة والاربعة فقط لغيرهم
+
+313
+00:32:05,240 --> 00:32:12,500
+where حيثهم بدنا نعرف مين هو الـ Zero ال
+
+314
+00:32:12,500 --> 00:32:17,840
+equivalence class تبع الـ Zeroبجي بقول هي ال zero
+
+315
+00:32:17,840 --> 00:32:25,460
+حط ال zero ضيفله خمسات يبقاش بصير خمسة عشرة خمستاش
+
+316
+00:32:25,460 --> 00:32:32,700
+و تضلك ماشي سالب خمسة سالب عشرة سالب خمستاش و تضلك
+
+317
+00:32:32,700 --> 00:32:37,910
+ماشيبعد ذلك يبدأ ال equivalence class للواحد يبقى
+
+318
+00:32:37,910 --> 00:32:43,290
+بالدرجة اقول له هذه واحد وخمسة ستة وخمسة احداشر
+
+319
+00:32:43,290 --> 00:32:46,670
+وخمسة ستة عشر وتبقى مازال مازال مازال مازال مازال
+
+320
+00:32:46,670 --> 00:32:47,490
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+321
+00:32:47,490 --> 00:32:48,110
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+322
+00:32:48,110 --> 00:32:48,970
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+323
+00:32:48,970 --> 00:32:50,350
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+324
+00:32:50,350 --> 00:32:50,970
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+325
+00:32:50,970 --> 00:32:55,850
+مازال مازال مازال مازال مازال مازال مازال مازال
+
+326
+00:32:55,850 --> 00:33:04,460
+مازال مازتمام؟ طيب لو بد ال equivalence class للي
+
+327
+00:33:04,460 --> 00:33:12,000
+اتنين هو عبارة عن اتنين و خمسة سبعة اتناش سبعتاش
+
+328
+00:33:12,000 --> 00:33:17,700
+إلى ما شاء الله اضيف سالب خمسة بصير سالب تلاتة
+
+329
+00:33:17,700 --> 00:33:23,880
+سالب تمانية سالب تلتاش إلى ما شاء الله بد ال
+
+330
+00:33:23,880 --> 00:33:29,260
+equivalence class لمن؟ لتلاتةيبقى باجي بقول له هذه
+
+331
+00:33:29,260 --> 00:33:36,380
+التلاتة وخمسة تمانية تلتاش تمانتاش إلى ما شاء الله
+
+332
+00:33:36,380 --> 00:33:42,020
+و هنا نضيف سالب خمسة بصير السالب اتنين و هنا سالب
+
+333
+00:33:42,020 --> 00:33:47,700
+سبعة و هنا سالب اتناش إلى ما شاء الله بنوصل للعنصر
+
+334
+00:33:47,700 --> 00:33:52,510
+اللي هو مين؟ أربعيبقى العمصر أربعة، يبقى هذه
+
+335
+00:33:52,510 --> 00:33:59,150
+الأربعة وخمسة، تسعة، أربعتاشر، تسعتاشر إلى ما شاء
+
+336
+00:33:59,150 --> 00:34:06,210
+الله نرجع نضيف سالب خمسة وكمان سالب خمسة وكمان
+
+337
+00:34:06,210 --> 00:34:12,860
+سالب خمسة وهكذاطيب هذه العناصر اللي حطيتها من قبل
+
+338
+00:34:12,860 --> 00:34:17,680
+طيب بده اجي لخمسة يبقى بده احط خمسة يبقى بده احط
+
+339
+00:34:17,680 --> 00:34:26,380
+خمسة وخمسة وخمسة هي هذهو سالب خمسة زيرو و سالب
+
+340
+00:34:26,380 --> 00:34:30,260
+خمسة و سالب عشرة هى هذى ولا لا طيب لو جيت بعد
+
+341
+00:34:30,260 --> 00:34:36,260
+الخمسة بتاخدى الستة يبقى بتبدأ بستة و خمسة احداشر
+
+342
+00:34:36,260 --> 00:34:41,260
+هى ستة و خمسة احداشر وكمان خمسة بيطلع هذى يبقى
+
+343
+00:34:41,260 --> 00:34:46,000
+الستة هتطلع الواحد و السبعة هتطلع اتنين و التمانية
+
+344
+00:34:46,000 --> 00:34:50,660
+هتطلع التلاتة و التسعة تطلع الأربعة و العشرة ترجع
+
+345
+00:34:50,660 --> 00:34:57,410
+لزيرو و هكذاطيب يبقى هدول equivalency classes يبقى
+
+346
+00:34:57,410 --> 00:35:03,650
+هدول all equivalency
+
+347
+00:35:03,650 --> 00:35:09,270
+classes لو
+
+348
+00:35:09,270 --> 00:35:13,810
+جبتلي أي equivalency class أخر لأن الـ z فيها
+
+349
+00:35:13,810 --> 00:35:18,570
+ملنية من العناصر أي واحد فيهم هيطلع واحد من هدول
+
+350
+00:35:19,130 --> 00:35:24,790
+يبقى ماعنديش إلا مين إلا الخمسة هدول فقط لغية في
+
+351
+00:35:24,790 --> 00:35:31,190
+علم الجبره خلّي بالك في علم الجبره هذه الست مجموعة
+
+352
+00:35:31,190 --> 00:35:40,050
+العناصر هنقول عليها Z خمسة Z خمسة اللي هي عناصرها
+
+353
+00:35:40,050 --> 00:35:48,440
+Zero وواحد واتنين وتلاتة واربعة دائما وابنانطيب زد
+
+354
+00:35:48,440 --> 00:35:57,740
+خمسة ايش تمثلي بالنسبة لزد الأصلية ال partition
+
+355
+00:35:57,740 --> 00:36:05,220
+ممتاز جدا هلحين اي رقم يجي في بالك من الزد هتلاقيه
+
+356
+00:36:05,220 --> 00:36:08,880
+موجود في واحد من الخمسة هدول اي رقم يطلع على بالك
+
+357
+00:36:09,110 --> 00:36:14,950
+لازم تجد موجود في واحد من هدول هذه واحدة اثنين لن
+
+358
+00:36:14,950 --> 00:36:19,230
+تجد اي عنصر في اي equivalency class موجود في
+
+359
+00:36:19,230 --> 00:36:24,910
+التاني مافيش بالمرة طب لو عملت union عليهم كلهم
+
+360
+00:36:24,910 --> 00:36:30,400
+بيعطيني الذد الأصلي طلعهي عندك هنا كده ال zero هي
+
+361
+00:36:30,400 --> 00:36:35,080
+واحد اتنين تلاتة اربعة و هيجي خمسة ستة سبعة تمانية
+
+362
+00:36:35,080 --> 00:36:40,000
+بعدين بترجع مين وين التسعة في عنها هي التسعة و
+
+363
+00:36:40,000 --> 00:36:42,440
+عندك هنا هي العشرة و هي الاحداشر و هي اتناشر
+
+364
+00:36:42,440 --> 00:36:46,860
+تلاتاشر اربعتاشر خمساشر و السالب زيه يبقى هتلاقي
+
+365
+00:36:46,860 --> 00:36:52,720
+كل الأرقام هده لو أخدتلهم ال union بيعطيني مينالزد
+
+366
+00:36:52,720 --> 00:36:58,700
+الأصلي يتنين لا يوجد أي عنصر مشترك بين أي set و
+
+367
+00:36:58,700 --> 00:37:04,440
+أخرى من هذه ال sets يعني لا يوجد أي عنصر مشترك ما
+
+368
+00:37:04,440 --> 00:37:07,760
+بين ال equivalence classes طلع لما روحنا عرفنا ال
+
+369
+00:37:07,760 --> 00:37:12,320
+equivalence class هناهو ال equivalence class يقول
+
+370
+00:37:12,320 --> 00:37:17,200
+كل العناصر اللي بتبقى بس مرتبطة مع ايه تحت ال
+
+371
+00:37:17,200 --> 00:37:21,080
+relation اللي هي modulo خمسة يبقى انا جيبت بس
+
+372
+00:37:21,080 --> 00:37:24,100
+العنصر مرتبطة مع مين مع العنصر اللي بقى يعني انا
+
+373
+00:37:24,100 --> 00:37:29,570
+لما اقول zeroبدّى العناصر المرتبطة مع الـ zero تحت
+
+374
+00:37:29,570 --> 00:37:33,130
+أثير ال relation الهيموديولو خمسة غير هيك ماليش
+
+375
+00:37:33,130 --> 00:37:37,270
+علاقة فيه الواحد بدي أجيب كل العناصر المرتبطة مع
+
+376
+00:37:37,270 --> 00:37:41,610
+الواحد تحت أثير ال relation الهيموديولو خمسة وهكذا
+
+377
+00:37:41,610 --> 00:37:46,230
+بالنسبة للباقية إذا ال union عليهم كلهم بدي يعطيني
+
+378
+00:37:46,230 --> 00:37:52,570
+ال z بالكامل اتنينلا يوجد أي عنصر مشترك بين أي
+
+379
+00:37:52,570 --> 00:37:56,790
+equivalency class والثاني على الإطلاق مافيش بالمرة
+
+380
+00:37:56,790 --> 00:38:01,770
+يبقى فاهمني أيش معنى ال partition يبقى بناء عليه
+
+381
+00:38:01,770 --> 00:38:07,330
+هدول بيكونولي partition على من؟ على ال z يبقى باجي
+
+382
+00:38:07,330 --> 00:38:11,290
+بقول so the partition
+
+383
+00:38:13,850 --> 00:38:22,750
+of z is the six هي الست اللي حديلها الرمز capital
+
+384
+00:38:22,750 --> 00:38:28,890
+P و اللي هما ال class بتبع ال zero و ال class بتبع
+
+385
+00:38:28,890 --> 00:38:33,310
+ال واحد و ال class بتبع ال اتنين و ال class بتبع
+
+386
+00:38:33,310 --> 00:38:38,590
+التلاتة و ال class بتبع الاربعة غير هيك ماعنديش
+
+387
+00:38:38,590 --> 00:38:41,150
+طيب
+
+388
+00:38:41,900 --> 00:38:46,620
+لو روحت غيرت الموديولو الخامسة خليتها الموديولو
+
+389
+00:38:46,620 --> 00:38:53,260
+سبعة مثلا أكم عنصر هيطلع عندى؟ سبع عناصر أولى واحد
+
+390
+00:38:53,260 --> 00:38:56,990
+في اشتراك بينه وبين التانى واليولن انتبعهمالـ
+
+391
+00:38:56,990 --> 00:39:02,930
+union تبعهم بيساوي z itself و هكذا وهذا هيعطينا
+
+392
+00:39:02,930 --> 00:39:06,850
+group هسميها مستقبل ان شاء الله في الشبتر الجاي
+
+393
+00:39:06,850 --> 00:39:12,730
+هسميها z سبعة زي ما روحت سميتها لك هنا z خمسة يبقى
+
+394
+00:39:12,730 --> 00:39:15,530
+z خمسة على أسرها ال zero والواحد انا اختصارا
+
+395
+00:39:15,530 --> 00:39:18,630
+مكتوبهم زي هيك اما هي الاصل ال equivalence class
+
+396
+00:39:18,630 --> 00:39:20,850
+تبع ال zero ال equivalence class تبع ال واحد
+
+397
+00:39:20,850 --> 00:39:23,820
+والاثنين والتلاتة و هكذاهذه الجروب ان شاء الله
+
+398
+00:39:23,820 --> 00:39:27,820
+هتلعب دور كبير عندنا في ال chapter القادم ان شاء
+
+399
+00:39:27,820 --> 00:39:31,640
+الله و تعالى طبعا الان وصلنا لموضوع ال functions
+
+400
+00:39:31,640 --> 00:39:36,540
+في المحاضرة القادمة يوم السبت بناخد الموضوع ال
+
+401
+00:39:36,540 --> 00:39:37,000
+functions
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5be11795888fcf4f7a2502440295e91b766cc552
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vFbYWlDoUF4.srt
@@ -0,0 +1,1759 @@
+1
+00:00:21,550 --> 00:00:26,090
+بسم الله الرحمن الرحيم ننتقل الآن إلى الـ chapter
+
+2
+00:00:26,090 --> 00:00:30,290
+الثامن الـ chapter الثامن بتحدث عن الـ external
+
+3
+00:00:30,290 --> 00:00:35,390
+direct products external طبعًا خارجي direct product
+
+4
+00:00:35,390 --> 00:00:41,010
+ضرب product ضرب direct مباشر يبقى الضرب المباشر
+
+5
+00:00:41,010 --> 00:00:45,450
+الخارجي لمجموعة من الـ groups سواء كانوا اثنين اثنين
+
+6
+00:00:45,450 --> 00:00:52,030
+ثلاثة أربعة جد ما يكونوا المهم أن عددهم محدود فبأجي
+
+7
+00:00:52,030 --> 00:00:56,890
+بقول افترض أنه في عندنا groups من جي واحد لغاية جي
+
+8
+00:00:56,890 --> 00:01:03,770
+إن وكل واحدة فيهم finite تمام يبقى بيقول let الـ
+
+9
+00:01:03,770 --> 00:01:08,030
+groups be finite collection of groups يبقى مجموعة
+
+10
+00:01:08,030 --> 00:01:12,610
+محدودة من الـ groups the external direct product
+
+11
+00:01:12,610 --> 00:01:16,270
+الضرب الخارجي لهذه الـ groups من جي واحد لغاية جي
+
+12
+00:01:16,270 --> 00:01:22,310
+إنبعنّه نعرفه كالتالي طبعًا إذا كتبنا كلمة external
+
+13
+00:01:22,310 --> 00:01:29,190
+product زائد وداخل دائرة تمام؟ لكن المقصود بمين؟
+
+14
+00:01:29,190 --> 00:01:34,330
+الـ external direct product يبقى هذا رمز يدل على الـ
+
+15
+00:01:34,330 --> 00:01:38,830
+external direct product لمين؟ لهذه المجموعة من الـ
+
+16
+00:01:38,830 --> 00:01:45,460
+group هذا رمز لكن عمليًا كيف بدي أعرف؟ هو كل العناصر
+
+17
+00:01:45,460 --> 00:01:50,960
+اللي على شكل N-tuple بحيث المركبة الأولى جاية من
+
+18
+00:01:50,960 --> 00:01:53,980
+الـ group الأولى المركبة الثانية جاية من الـ group
+
+19
+00:01:53,980 --> 00:01:59,900
+الثانية وهكذا المركبة النونية جاية من الـ group رقم
+
+20
+00:01:59,900 --> 00:02:04,920
+n حيث جي موجودة في جي اي يعني جي واحد موجودة في
+
+21
+00:02:04,920 --> 00:02:08,020
+جي واحد جي اثنين موجودة في جي اثنين لغاية جي ان
+
+22
+00:02:08,020 --> 00:02:13,500
+موجودة وين؟ في جي ان إذا من الآن فصاعدًا الـ external
+
+23
+00:02:13,500 --> 00:02:18,760
+product لمجموعة من الـ groups هي عبارة عن set جديدة
+
+24
+00:02:18,760 --> 00:02:23,600
+هذه الـ set بعد قليل سنّشاهد أنّها group كل عنصر من
+
+25
+00:02:23,600 --> 00:02:29,300
+عناصر هذه الـ group يتكون من n-tuple من الـ
+
+26
+00:02:29,300 --> 00:02:34,210
+elements يبقى كل element في الـ group على شكل N
+
+27
+00:02:34,210 --> 00:02:39,950
+-tuple يعني جوز مكوّن من مجموعة من المركبات الـ
+
+28
+00:02:39,950 --> 00:02:44,010
+remark بتقول الـ external product كله أن هذا is a
+
+29
+00:02:44,010 --> 00:02:48,450
+group under the following operation يبقى بدنا نعرف
+
+30
+00:02:48,450 --> 00:02:54,080
+binary operation على هذه الـ set بحيث فعلًا يصبح هذه
+
+31
+00:02:54,080 --> 00:02:58,960
+اللي عندنا group كيف الـ binary operation بدي اخذ
+
+32
+00:02:58,960 --> 00:03:03,540
+حاصل ضرب قوسين بالشكل اللي عندنا حاصل ضرب قوسين
+
+33
+00:03:03,540 --> 00:03:09,120
+اللي عندنا بدي اضرب component wise كل مركبة في
+
+34
+00:03:09,120 --> 00:03:14,440
+نظيرتها يبقى بدّي يصير حاصل ضرب الشكل اللي
+
+35
+00:03:14,440 --> 00:03:18,800
+عنها بدي اضرب جي واحد في جي واحد برايم فاصلة جي
+
+36
+00:03:18,800 --> 00:03:21,580
+اثنين في جي اثنين برايم و هكذا لغاية ما نوصل
+
+37
+00:03:21,580 --> 00:03:26,660
+إلى جي ان بجي ان برايم زي ما أنت شايف طلع element
+
+38
+00:03:26,660 --> 00:03:31,120
+موجود وأن في الـ external direct product يبقى هذه
+
+39
+00:03:31,120 --> 00:03:35,140
+binary operation ضل عليك تعمل تشيك هل هي
+
+40
+00:03:35,140 --> 00:03:40,750
+associative ولا لأ والـ identity element تبعها يتكون
+
+41
+00:03:40,750 --> 00:03:45,130
+من الـ identity element لكل group من الـ groups اللي
+
+42
+00:03:45,130 --> 00:03:50,070
+عندنا يعني الـ A1 هو الـ identity element لـ G1 الـ A2
+
+43
+00:03:50,070 --> 00:03:54,390
+هو الـ identity element لـ G2 الـ GN هو الـ identity
+
+44
+00:03:54,390 --> 00:04:00,250
+element لمين؟ للـ GN ويرجل الـ Ei is the identity
+
+45
+00:04:00,250 --> 00:04:06,070
+element of Gi وهي بتأخذ من الـ واحد لغاية مين؟ لغاية
+
+46
+00:04:06,070 --> 00:04:12,140
+الـ N المعكوس تبع هذا الوضع هو المعكوس inverse
+
+47
+00:04:12,140 --> 00:04:17,700
+المعكوس inverse يدخل على كل مركبة من هذه المركبات
+
+48
+00:04:17,700 --> 00:04:22,480
+يبقى بصير عندنا جي ون انفرست جو تي وانفرست جي انفرست
+
+49
+00:04:22,480 --> 00:04:27,900
+يعني المركبة تبقى في مكانها بس بنزلها الـ inverse
+
+50
+00:04:27,900 --> 00:04:32,290
+عليه لكن عندما كان لدي cycle يا جماعة وكنت اقول
+
+51
+00:04:32,290 --> 00:04:35,390
+أنني أريد أن أتبع الـ inverse قرار من أين تبع هذه
+
+52
+00:04:35,390 --> 00:04:40,890
+الـ cycle بجيت أجلب وأضع اتجاه من الـ cycle أو لو عندي
+
+53
+00:04:40,890 --> 00:04:45,750
+حصل ضرب عنصرين وبجيت اخذ الـ inverse قرار وبجيت أجلب
+
+54
+00:04:46,230 --> 00:04:50,930
+العنصر الأخير في الأول وهكذا لكن هنا لأ بيبقى
+
+55
+00:04:50,930 --> 00:04:54,990
+العنصر في مكانه بس بنزل الـ main الـ inverse عليه
+
+56
+00:04:54,990 --> 00:04:59,750
+نبدأ نأخذ أمثلة عملية على ذلك أول مثال جالي هاتلي
+
+57
+00:04:59,750 --> 00:05:05,890
+شكل لـ group U8 وU10 بقول قبل أن أجيب شكل أنا بدي
+
+58
+00:05:05,890 --> 00:05:11,830
+أعرف مين عناصر الـ U8 ومين عناصر الـ U10 فلو جيت
+
+59
+00:05:11,830 --> 00:05:17,370
+قلت له الـ U8 اللي هي عناصرها كل الأعداد اللي
+
+60
+00:05:17,370 --> 00:05:21,690
+relatively prime مع main مع ثمانية اللي هو واحد،
+
+61
+00:05:21,690 --> 00:05:27,810
+ثلاثة، خمسة، مين؟ سبعة بدي الـ U عشرة كذلك كل
+
+62
+00:05:27,810 --> 00:05:32,470
+العناصر اللي relatively prime مع مين؟ مع العشرة اللي هو
+
+63
+00:05:32,470 --> 00:05:39,360
+واحد وثلاثة وسبعة وتسعة من الـ two groups هذول
+
+64
+00:05:39,360 --> 00:05:43,620
+بدي أكون الـ product ما بين الـ two groups يبقى
+
+65
+00:05:43,620 --> 00:05:48,740
+بالعادة أقوله الآن بدي الـ U8 يا external product
+
+66
+00:05:48,740 --> 00:05:57,180
+مع مين؟ مع U10 مع مين مركبة يبقى كل عنصر من عناصر
+
+67
+00:05:57,180 --> 00:06:02,120
+الـ external product يتكون عنصر من الجروب الأولى مع
+
+68
+00:06:02,120 --> 00:06:05,880
+عنصر من من من الجروب الثاني يعني كل element هو
+
+69
+00:06:05,880 --> 00:06:12,200
+ordered pair بعد ذلك أقول له يبقى بدي اخذ الواحد مع
+
+70
+00:06:12,200 --> 00:06:17,660
+مين؟ مع أول رقم أقبله اللي هو واحد بعد هيك بدي اخذ
+
+71
+00:06:17,660 --> 00:06:23,460
+الواحد مع باقي الأرقام والواحد مع الثلاثة وبعدها
+
+72
+00:06:23,460 --> 00:06:29,580
+الواحد مع السبعة والواحد مع مين؟ مع التسعة يبقى هاي
+
+73
+00:06:29,580 --> 00:06:34,040
+الأربع احتمالات الممكنة بعد هيك اللي عملت الواحد
+
+74
+00:06:34,040 --> 00:06:38,920
+بدي أعمله للثلاثة يبقى بأجي بقوله و ثلاثة مع واحد
+
+75
+00:06:38,920 --> 00:06:43,740
+.. ثلاثة مع مين؟ مع واحد بالشكل اللي عندنا و
+
+76
+00:06:43,740 --> 00:06:50,420
+الثلاثة مع الثلاثة و الثلاثة مع الخمسة أظن والله
+
+77
+00:06:50,420 --> 00:06:57,220
+إيه؟ و الثلاثة مع السبعة و الثلاثة مع التسعة اللي
+
+78
+00:06:57,220 --> 00:07:02,160
+عملته للثلاثة اروح اعمله كمان مع مين؟ مع الخمسة
+
+79
+00:07:02,160 --> 00:07:07,180
+مع الواحد نكمل في السطر الثاني اخذنا الخمسة مع
+
+80
+00:07:07,180 --> 00:07:13,860
+الواحد يبقى الخمسة مع الثلاثة و الخمسة مع السبعة و
+
+81
+00:07:13,860 --> 00:07:19,020
+الخمسة مع مين؟ مع التسعة خلصنا بديت ضلّ عندنا السبعة
+
+82
+00:07:19,470 --> 00:07:25,190
+يبقى هنا السابعة مع الواحد وهنا السابعة مع الثلاثة
+
+83
+00:07:25,190 --> 00:07:33,610
+وهنا السابعة مع السابعة وبعدها مين؟ السابعة مع مين؟
+
+84
+00:07:33,610 --> 00:07:40,430
+مع التسعة خلصنا أكمل صورة هدول يا جماعة ستة عشر عنصر
+
+85
+00:07:40,430 --> 00:07:45,130
+يبقى هذه فيها أربع elements وهذه أربع elements الـ
+
+86
+00:07:45,130 --> 00:07:49,850
+external directly بتطلع ستة عشر elements وكأنه ضربت
+
+87
+00:07:49,850 --> 00:07:53,210
+الـ order للـ group الأولى في من؟ في الـ order للـ
+
+88
+00:07:53,210 --> 00:07:57,930
+group الثانية طب السؤال هو لو بدي أضرب عنصرين في
+
+89
+00:07:57,930 --> 00:08:02,150
+بعض بدي يطلع الناتج داخل الـ group هذه لأن احنا
+
+90
+00:08:02,150 --> 00:08:06,990
+بنقول هذه group السؤال هو كيف بدأت تتم عملية الضرب؟
+
+91
+00:08:07,280 --> 00:08:11,700
+يبقى بدي اختار لرقمين كبار هيك واضربهم في بعض
+
+92
+00:08:11,700 --> 00:08:17,720
+واشوف كده الناتج فمثلاً سبعة وتسعة هاي سبعة وتسعة
+
+93
+00:08:17,720 --> 00:08:21,760
+ناخذهم مع خمسة وثمانية مثلاً و الله خمسة وسبعة
+
+94
+00:08:21,760 --> 00:08:26,100
+ما أدهاش خمسة وثمانية يبقى أنا لو بدي أشوف كيف بدأت
+
+95
+00:08:26,100 --> 00:08:31,020
+تتم عملية الضرب فبأجي بقوله بدي اخذ خمسة وسبعة
+
+96
+00:08:31,020 --> 00:08:39,010
+مثلاً مع سبعة وتسعة واشوف كده الناتج الضرب بين
+
+97
+00:08:39,010 --> 00:08:44,310
+الرقم الأول والرقم الثاني طبقًا لتعريف الضرب اللي
+
+98
+00:08:44,310 --> 00:08:49,630
+عندي بيكون module لـ group الأولى والضرب الثاني هذا
+
+99
+00:08:49,630 --> 00:08:54,970
+مع هذا بيكون module لـ group الثانية يبقى هذا
+
+100
+00:08:54,970 --> 00:08:59,790
+الكلام عبارة عن خمسة في سبعة في جدّاش؟ خمسة و
+
+101
+00:08:59,790 --> 00:09:04,770
+ثلاثين modulo ثمانية لأن الضرب هذا في الـ group
+
+102
+00:09:04,770 --> 00:09:08,010
+الأولى والضرب الثاني في الـ group الثانية سبعة في
+
+103
+00:09:08,010 --> 00:09:13,970
+تسعة في جدّاش؟ بثلاثة وستين modulo عشرة بالشكل
+
+104
+00:09:13,970 --> 00:09:14,570
+اللي عندنا
+
+105
+00:09:24,310 --> 00:09:28,750
+بثلاثة تطلع لهذه الثلاثة وثلاثة موجودة اه نعم
+
+106
+00:09:28,750 --> 00:09:33,310
+موجودة تمام يبقى أيش ما تضرب تضرب العنصر في نفسه
+
+107
+00:09:33,310 --> 00:09:37,090
+تضربه في عنصر ثاني كيف ما يكون بدي يطلع الناتج
+
+108
+00:09:37,090 --> 00:09:41,150
+داخلها لأن قلنا عليها binary operation binary
+
+109
+00:09:41,150 --> 00:09:45,150
+operation لو أخذت two elements ضربتهم في بعض بدي
+
+110
+00:09:45,150 --> 00:09:49,990
+يكون الناتج داخل الـ main داخل الـ group نعطي كمان
+
+111
+00:09:49,990 --> 00:10:01,270
+مثال آخر يبقى example two find
+
+112
+00:10:01,270 --> 00:10:06,990
+خلّي المعلومة اللي سألتك عنها كم عنصر هذا كنت لـ 16
+
+113
+00:10:06,990 --> 00:10:10,150
+خلّيها عندك لزمالك بعد قليل
+
+114
+00:10:16,860 --> 00:10:22,900
+جليهات للـ External Direct Product لمين؟ لـ Z2 مع
+
+115
+00:10:22,900 --> 00:10:31,020
+Z3 فقط يبقى أنا بدي أعرف عناصر Z2 وعناصر Z3 وبعد
+
+116
+00:10:31,020 --> 00:10:35,160
+هيك بدي أشوف كيف بدنا نشتغل الشغل تبعهم الآن يا
+
+117
+00:10:35,160 --> 00:10:43,230
+شباب Z2 هي عبارة عن مين؟ هي عبارة عن 0 1 الآن Z
+
+118
+00:10:43,230 --> 00:10:50,510
+ثلاثة هي عبارة عن Zero وواحد واثنين تمام؟ بدي
+
+119
+00:10:50,510 --> 00:10:53,370
+أجيب الـ product product تبعهم أو الـ external
+
+120
+00:10:53,370 --> 00:10:59,850
+product product Z two external Z three ويوسعه كم
+
+121
+00:10:59,850 --> 00:11:06,250
+عنصر تتوقع يكون هنا ستة عناصر يبقى بدي اخذ الـ zero
+
+122
+00:11:06,250 --> 00:11:13,690
+مع الـ zero تمام؟ الـ zero مع الواحد zero مع اثنين
+
+123
+00:11:13,690 --> 00:11:21,950
+بعدين خلصنا الواحد مع الـ zero والواحد مع الواحد
+
+124
+00:11:21,950 --> 00:11:28,430
+والواحد مع اثنين بالشكل هذا يجيب كل العناصر اللي
+
+125
+00:11:28,430 --> 00:11:34,270
+عندنا هذه زي ما أنت شايف يبقى هذه عناصر الـ group
+
+126
+00:11:34,270 --> 00:11:40,150
+هذه تعالى بس نوقف شوية نبدأ بعض الملاحظات على
+
+127
+00:11:40,150 --> 00:11:45,170
+الكلام اللي احنا جايلينه طب ايش الملاحظات هذه
+
+128
+00:11:45,170 --> 00:11:50,590
+تعالى نشوف السؤال هو هل z2 external dynamic
+
+129
+00:11:50,590 --> 00:11:56,490
+product مع z3 هل هي cyclic نقول الله أعلم تعالى
+
+130
+00:11:56,490 --> 00:12:00,970
+نشوف إذا قدرنا نلاقي generator يبقى كان بيهام
+
+131
+00:12:00,970 --> 00:12:05,270
+ما قدرنا يبقى انسى الموضوع لو مسكت أي واحد اللي
+
+132
+00:12:05,270 --> 00:12:10,270
+مقدمتهم أو فيهم أصفار هدول هل ممكن يكون generator
+
+133
+00:12:10,270 --> 00:12:16,730
+يعني مش ممكن يبقى مدام فيه zero في المركبة الأولى
+
+134
+00:12:16,730 --> 00:12:21,710
+أو zero في المركبة الثانية فيش طيب إذا ممكن يكون
+
+135
+00:12:21,710 --> 00:12:25,850
+واحد من هدول generator تعالى نشوف هل هذا الكلام
+
+136
+00:12:25,850 --> 00:12:31,250
+ممكن؟ والله ليس ممكن يجب أن آخذ واحد و واحد أس
+
+137
+00:12:31,250 --> 00:12:35,930
+زيرو اللي هو بال identity zero zero طب لو كان أس
+
+138
+00:12:35,930 --> 00:12:41,910
+واحد يبقى بنفسه طب لو كان اثنين العملية اللي عزيزي
+
+139
+00:12:41,910 --> 00:12:47,550
+عملتها جامعة يعني هذا الكلام يجب أن يساوي اثنين في
+
+140
+00:12:47,550 --> 00:12:51,650
+واحد و واحد يعني اثنين و اثنين اللي هو يجب أن
+
+141
+00:12:51,650 --> 00:12:56,790
+يساوي الاثنين الأولى موجودة في زد اثنين والاثنين في
+
+142
+00:12:56,790 --> 00:13:02,750
+زد اثنين تعني كم؟ Zero يبقى هذا Zero لكن اثنين هذه تعني
+
+143
+00:13:02,750 --> 00:13:09,410
+اثنين كما هي طيب لو روحنا أخذنا واحد واحد تكعيب
+
+144
+00:13:09,410 --> 00:13:16,170
+يعني هذه تساوي ثلاثة و ثلاثة يبقى هذه تساوي ثلاثة في
+
+145
+00:13:16,170 --> 00:13:22,670
+the group الأولى تعني ايه؟ تعني واحد تمام يعني واحد
+
+146
+00:13:22,670 --> 00:13:27,210
+ثلاثة في the group الثانية تعني كده؟ Zero ما طلعش ال
+
+147
+00:13:27,210 --> 00:13:33,730
+identity طيب لو أخذنا واحد واحد أس أربعة يبقى هذه
+
+148
+00:13:33,730 --> 00:13:39,710
+تعني أربعة وأربعة وتساوي الأربعة في زيد اثنين تعني
+
+149
+00:13:39,710 --> 00:13:44,920
+Zero والاربعة في زيد ثلاثة تعني ايه؟ ما طلعش ال
+
+150
+00:13:44,920 --> 00:13:51,000
+identity طب خد الخمسة الخمسة الآن في واحد و واحد
+
+151
+00:13:51,000 --> 00:13:58,790
+تعني خمسة و خمسة خمسة و خمسة تعني واحد و اثنين طيب
+
+152
+00:13:58,790 --> 00:14:07,090
+لو روحنا أخذنا واحد و واحد أس ستة تعني ستة و ستة
+
+153
+00:14:07,090 --> 00:14:11,530
+اللي هو مين؟ Zero Zero اللي هو ال identity element
+
+154
+00:14:11,530 --> 00:14:17,530
+إذا بتقدر تقول أن ال order للواحد و واحد قداش ستة
+
+155
+00:14:18,330 --> 00:14:24,670
+يبقى هذا بده يعطينا أن ال order ل الواحد و الواحد
+
+156
+00:14:24,670 --> 00:14:29,170
+بده يساوي كده؟ بده يساوي ستة طب و ال order لل
+
+157
+00:14:29,170 --> 00:14:37,520
+group؟ يبقى and الـ order لزد اثنين external
+
+158
+00:14:37,520 --> 00:14:47,180
+product مع زد ثلاثة هذا بده يساوي ستة الواحد واحد
+
+159
+00:14:47,180 --> 00:14:51,260
+is a generator
+
+160
+00:14:53,290 --> 00:15:01,350
+generator for زد اثنين external product مع زد
+
+161
+00:15:01,350 --> 00:15:08,610
+ثلاثة يبقى طلعت هذه معاها cyclic يبقى هذا يعطينا
+
+162
+00:15:08,610 --> 00:15:16,050
+أن زد اثنين external product مع زد ثلاثة is cyclic
+
+163
+00:15:18,200 --> 00:15:21,460
+يبقى طلعت ال group اللي عندها هذه مالها اللي هو
+
+164
+00:15:21,460 --> 00:15:26,760
+الـ cyclic group وبالتالي مدام ال cyclic وعدد
+
+165
+00:15:26,760 --> 00:15:32,780
+العناصر لها ستة بنقدر نقول أن هذه isomorphic لزد
+
+166
+00:15:32,780 --> 00:15:41,470
+ستة أكيد؟ طيب بقول زميل الكهاد أبو بدر بقول طبعا
+
+167
+00:15:41,470 --> 00:15:48,050
+يبقى أنا بقوله and وفي نفس الوقت z2 external
+
+168
+00:15:48,050 --> 00:15:55,390
+direct product ل z3 is isomorphic ل z6 طب أنا طالع
+
+169
+00:15:55,390 --> 00:15:59,870
+أتعني z2 external direct product مع z3 is cyclic
+
+170
+00:15:59,870 --> 00:16:07,290
+هل z6 is cyclic؟ صحيح و ال order لأي عنصر فيها بدي
+
+171
+00:16:07,290 --> 00:16:11,290
+يساوي ال order لأي عنصر مناظر له في مين في Z
+
+172
+00:16:11,290 --> 00:16:14,810
+التانية X تانية نضعيه ك product ل Z الثلاثة يبقى
+
+173
+00:16:14,810 --> 00:16:19,730
+بناء عليه اثنين هدول are isomorphic بدي أطرح كمان
+
+174
+00:16:19,730 --> 00:16:24,610
+سؤال احنا أثبتنا أن واحد و واحد هو عبارة عن
+
+175
+00:16:24,610 --> 00:16:29,210
+generator وبالتالي هذه الجروب صارت Cycle مدام
+
+176
+00:16:29,210 --> 00:16:35,090
+Cycle كمان قبيلية تمام السؤال هو هل فيها generator
+
+177
+00:16:35,090 --> 00:16:47,430
+آخر ولا خلصنا .. أكيد؟ اللي هو مين؟ طيب
+
+178
+00:16:47,430 --> 00:16:51,590
+احنا أخذنا واحد و واحد generator يبقى فيش غيره
+
+179
+00:16:51,590 --> 00:16:58,780
+بيقول أبو غدر؟ المعترضين يقولون فيه ما بنعرفش نجرب
+
+180
+00:16:58,780 --> 00:17:05,200
+بمجرد النظر أكثر مرة سمعت منه لو عندك element و
+
+181
+00:17:05,200 --> 00:17:11,180
+بيكون generator فمعكسه هو generator وقلنا أي group
+
+182
+00:17:11,180 --> 00:17:15,880
+إذا فيها generator واحد معناته فيه كمان واحد يعني
+
+183
+00:17:15,880 --> 00:17:20,080
+ال generator يظهر على شكل الأزواج إلا إذا كانت ل
+
+184
+00:17:20,080 --> 00:17:21,220
+three subgroup
+
+185
+00:17:31,150 --> 00:17:37,190
+السؤال هو من ذاك ال element اللي لو ضربته في
+
+186
+00:17:37,190 --> 00:17:39,870
+الواحد و واحد بيعطيني zero zero
+
+187
+00:17:42,200 --> 00:17:45,580
+و اثنين و واحد و اثنين ليش هنا مش ضرب احنا بنجي
+
+188
+00:17:45,580 --> 00:17:52,320
+مع الجامعة واحد و واحد زيرو اثنين و واحد زيرو يبقى
+
+189
+00:17:52,320 --> 00:17:57,300
+صار واحد و اثنين is a generator يبقى باجي بقوله
+
+190
+00:17:57,300 --> 00:18:07,440
+هنا also و كذلك اللي هو واحد و اثنين is other
+
+191
+00:18:07,440 --> 00:18:09,680
+generator
+
+192
+00:18:12,330 --> 00:18:18,210
+يبقى هذا كمان generator آخر غير الواحد الواحد يبقى
+
+193
+00:18:18,210 --> 00:18:22,250
+دائما هو خط في دماغك قاعدة لو قال لك أتلقي كل ال
+
+194
+00:18:22,250 --> 00:18:27,170
+generator في group بدك تروح تدور عليه أي element
+
+195
+00:18:27,170 --> 00:18:32,270
+لقيته على طول الخط اتدورش عليه أي واحد ثاني بتروح
+
+196
+00:18:32,270 --> 00:18:36,830
+على معكوسه automatic لقيت معكوسه بيكون هو ال
+
+197
+00:18:36,830 --> 00:18:42,570
+generator الآخر وهكذا تمام؟ طيب هذا كان المثال
+
+198
+00:18:42,570 --> 00:18:49,260
+رقم اثنين بدنا نروح لمثال رقم ثلاثة يبقى example
+
+199
+00:18:49,260 --> 00:18:59,100
+three example
+
+200
+00:18:59,100 --> 00:19:10,180
+three بيقول a group of order أربعة a group of
+
+201
+00:19:10,180 --> 00:19:14,440
+order أربعة is isomorphic
+
+202
+00:19:18,440 --> 00:19:27,420
+زد أربعة أو زد اثنين اكستير نضعيه ك product مع زد
+
+203
+00:19:27,420 --> 00:19:27,880
+اثنين
+
+204
+00:19:32,540 --> 00:19:36,600
+جاب المبدأ الشغل في هذه الشغلة بدأ يسأل السؤال
+
+205
+00:19:36,600 --> 00:19:41,060
+التالي بقول أي group من ما كانت تكون مدام ال order
+
+206
+00:19:41,060 --> 00:19:45,980
+لها أربعة يبقى يا isomorphic إلى z أربعة يا
+
+207
+00:19:45,980 --> 00:19:50,560
+isomorphic إلى z اثنين external like product مع z
+
+208
+00:19:50,560 --> 00:19:58,550
+اثنين السؤال ليش خيرني بين هذه و هذه؟ أيوة Z4 هذه
+
+209
+00:19:58,550 --> 00:20:03,870
+cyclic تمام Z2 external dielectric product مع Z2
+
+210
+00:20:03,870 --> 00:20:08,710
+هذه is not cyclic بقدرش ألاقي فيها ولا generator
+
+211
+00:20:08,710 --> 00:20:13,010
+إذا لو كانت ال group اللي ال order لها يساوي 4
+
+212
+00:20:13,010 --> 00:20:18,500
+cyclic يبقى isomorphic لمين ل Z4 وإذا كانت non
+
+213
+00:20:18,500 --> 00:20:22,540
+-cyclic يبقى isomorphic لزد اثنين external product
+
+214
+00:20:22,540 --> 00:20:28,800
+مع main مع زد اثنين عرفنا ما هو السبب يعني ليش هذه
+
+215
+00:20:28,800 --> 00:20:34,540
+أو هذه لأن واحدة فيهم cyclic والثانية لأ وبالتالي
+
+216
+00:20:34,540 --> 00:20:39,320
+ال order ال group اللي هيساوي ال order اللي هيساوي
+
+217
+00:20:39,320 --> 00:20:48,170
+أربعة بيكون isomorphic لهذه أو تلك خد الأندليل على
+
+218
+00:20:48,170 --> 00:20:55,870
+ذلك لت الجي عناصر E و A و B و AV
+
+219
+00:21:04,340 --> 00:21:11,260
+أربعة بدي أسأل يا تورا هذه isomorphic لزيد أربعة و
+
+220
+00:21:11,260 --> 00:21:15,180
+الله لزيد two external direct product لزيد two
+
+221
+00:21:15,180 --> 00:21:19,440
+تعالى نشوف هل هي cyclic ولا ماهي cyclic لزيد أربعة
+
+222
+00:21:19,440 --> 00:21:29,180
+أنها cyclic صحيح ولا لا الآن لو جيت قلت أن هذه طيب
+
+223
+00:21:31,160 --> 00:21:42,800
+يبقى little g تساوي كذا وهي non-cyclic group non
+
+224
+00:21:42,800 --> 00:21:47,750
+-cyclic group then شوفوا عشان اللي بده يصير لأن لو
+
+225
+00:21:47,750 --> 00:21:52,630
+cyclic بدي أخد لها generator يبقى بدي تطلع لمين؟ ل
+
+226
+00:21:52,630 --> 00:21:56,730
+Z4، أنا بدي أشيلها ل Z4، أنا بدي لموضوعنا اللي هو
+
+227
+00:21:56,730 --> 00:21:59,550
+mainly external direct product بدي أخليها
+
+228
+00:21:59,550 --> 00:22:05,730
+isomorphic لمين؟ ل Z2 في Z2 طب هذه non-cyclic يعني
+
+229
+00:22:05,730 --> 00:22:10,690
+ما فيش فيها ولا generator طيب مدام ما فيش فيها ولا
+
+230
+00:22:10,690 --> 00:22:15,870
+generator بدي أسأل السؤال التالي قداش ال order ل
+
+231
+00:22:15,870 --> 00:22:25,270
+ايه؟ ممتاز و يقسم يعني ايش لو كان الواحد لكان ال a
+
+232
+00:22:25,270 --> 00:22:30,270
+هي ال a صح وإذا لا يمكن ال a تساوي من ال a لأنه
+
+233
+00:22:30,270 --> 00:22:33,310
+في ال set بكتبش عنصرين متساويين عنصرين متساويين يعني
+
+234
+00:22:33,310 --> 00:22:37,430
+عنصر واحد تمام يبقى ال order ل a باثنين طب ال
+
+235
+00:22:37,430 --> 00:22:42,960
+order ل b نفس القصة طب ال order ل a باثنين برضه
+
+236
+00:22:42,960 --> 00:22:48,100
+إجباري يبقى ال order لكل واحد فيهم ما له يساوي
+
+237
+00:22:48,100 --> 00:22:52,740
+اثنين لأنه قايل non cyclic غير اثنين بقى تقولي
+
+238
+00:22:52,740 --> 00:22:57,200
+أربعة يبقى تصير cyclic تصير contradiction تمام يبقى
+
+239
+00:22:57,200 --> 00:23:04,740
+هنا then ال order ل a بده يساوي ال order ل b بده
+
+240
+00:23:04,740 --> 00:23:08,960
+يساوي ال order ل a بيه بده يساوي من اثنين
+
+241
+00:23:18,720 --> 00:23:23,400
+طيب و في هذه الحالة ايش العلاقة ما بين ال element و
+
+242
+00:23:23,400 --> 00:23:29,820
+معكوسه؟ يعني اضرب الطرفين في a inverse بصير ال a
+
+243
+00:23:29,820 --> 00:23:34,560
+بده يساوي a inverse يبقى ال a بده يساوي a inverse
+
+244
+00:23:34,560 --> 00:23:42,780
+لكل ال a اللي موجود في مين اللي موجود في g طيب هذه
+
+245
+00:23:42,780 --> 00:23:47,280
+non cyclic يبقى طبقا للكلام اللي احنا جاي نجيه هو
+
+246
+00:23:47,280 --> 00:23:53,940
+هتكون isomorphic لمين لزد اثنين external product مع
+
+247
+00:23:53,940 --> 00:23:58,320
+زد اثنين طب مين هي زد اثنين زد اثنين طب احنا بنعرف
+
+248
+00:23:58,320 --> 00:24:06,500
+أن زد اثنين هي Zero و واحد و زد اثنين كذلك هي Zero
+
+249
+00:24:06,500 --> 00:24:10,280
+و واحد إذا أنا بده اروح اجيب ال external product
+
+250
+00:24:10,280 --> 00:24:18,540
+لزد اثنين مع زد اثنين بده العناصر تبعتهم يبقى Zero 
+
+251
+00:24:18,540 --> 00:24:25,960
+و Zero وبعد هيك Zero و واحد وبعد هيك الواحد و
+
+252
+00:24:25,960 --> 00:24:33,100
+Zero و واحد و واحد طيب
+
+253
+00:24:33,100 --> 00:24:38,380
+هل هذه Cyclic ولا لا أنا مش عارف تعال تقدر تلاقي
+
+254
+00:24:38,380 --> 00:24:45,980
+فيها generator طيب أنا أدعي أن every non identity
+
+255
+00:24:45,980 --> 00:24:53,390
+element has order to صح؟ لأن هنا جمع هذه تربيع
+
+256
+00:24:53,390 --> 00:24:58,190
+بتضرب في اثنين بيصير Zero وهنا اثنين Zero Zero هذه
+
+257
+00:24:58,190 --> 00:25:02,330
+تربيع برضه اثنين و Zero بيصير Zero Zero هذه اثنين
+
+258
+00:25:02,330 --> 00:25:06,670
+بيصير اثنين و اثنين Zero Zero يبقى أي element من
+
+259
+00:25:06,670 --> 00:25:11,430
+هناها الـ order له يساوي اثنين يعني زي مين زي
+
+260
+00:25:11,430 --> 00:25:15,830
+الكلام اللي قلناه هذا بالضبط تماما وهذول أربعة
+
+261
+00:25:15,830 --> 00:25:20,590
+عناصر وهذول أربعة عناصر طب إيش رأيك؟ بدي أعرف
+
+262
+00:25:20,590 --> 00:25:24,230
+function ما بين الاثنين وأثبت أنها one to one أن
+
+263
+00:25:24,230 --> 00:25:27,530
+أنتم وبالتالي بصير الجروب اللي عندنا ده
+
+264
+00:25:27,530 --> 00:25:32,590
+isomorphic لمين؟ لـ Z اثنين external direct product
+
+265
+00:25:32,590 --> 00:25:39,500
+لـ Z اثنين يبقى باجي بقول له ملاحظة بسيطة جدا أن Z اثنين
+
+266
+00:25:39,500 --> 00:25:50,060
+external لـ Z اثنين is not cyclic because any
+
+267
+00:25:50,060 --> 00:25:56,400
+element والله any non identity element
+
+268
+00:26:06,220 --> 00:26:14,260
+of Z اثنين has order
+
+269
+00:26:14,260 --> 00:26:19,000
+two أيوة أحد الـ order اللي بيساوي اثنين هو تربيع
+
+270
+00:26:19,000 --> 00:26:23,260
+تربيع تربيع تربيع تربيع كله بيطلع من الـ identity
+
+271
+00:26:23,260 --> 00:26:31,030
+يعني طيب لو جيت قلت لك define إيه الـ function؟ فاي
+
+272
+00:26:31,030 --> 00:26:38,850
+من الـ G إلى Z ده to stay in a like product لـ Z ده
+
+273
+00:26:38,850 --> 00:26:45,970
+to buy بدي أخلي الـ فاي تأثر على الـ identity element 
+
+274
+00:26:45,970 --> 00:26:53,730
+بشكل فاي وبالـ identity كده أتوقع صورتها ده؟ إجباري
+
+275
+00:26:53,730 --> 00:26:58,350
+مش بخاطر كمان تمام ليش إن صوت الـ identity element
+
+276
+00:26:58,350 --> 00:27:01,810
+في الـ group الأولى مش هنكون isomorphism بده يكون
+
+277
+00:27:01,810 --> 00:27:06,750
+الـ identity element فيه الثانية يبقى هذا بده يصير
+
+278
+00:27:06,750 --> 00:27:11,190
+Zero و Zero الآن Phi of A
+
+279
+00:27:29,720 --> 00:27:35,500
+السؤال هو هل هذه one to one 
+
+280
+00:27:38,420 --> 00:27:43,620
+غطّط كل العناصر تمام يبقى ده الخاصية الـ isomorphism
+
+281
+00:27:43,620 --> 00:27:48,880
+سهل إثباتها عن طريق الجمع يبقى في هذه isomorphism
+
+282
+00:27:48,880 --> 00:27:55,520
+يبقى من هذه المعلومات بقدر أقول سا اللي هو الـ G
+
+283
+00:27:55,520 --> 00:28:02,440
+هذه isomorphic إلى Z اثنين external direct product مع
+
+284
+00:28:02,440 --> 00:28:04,820
+مين؟ مع Z اثنين
+
+285
+00:28:07,820 --> 00:28:13,240
+طلع لي بالصورة شوية، طلع لي عليها دي اللي بسيط خالص،
+
+286
+00:28:13,240 --> 00:28:19,240
+not cyclic، لكن Z اثنين في Z ثلاثة cyclic تمام طب
+
+287
+00:28:19,240 --> 00:28:24,240
+قد إيش عدد العناصر هنا أربعة Z اثنين في Z ثلاثة
+
+288
+00:28:24,240 --> 00:28:29,580
+طلع ستة اللي قبلها أربعة وأربعة طلع ستة عشر إذا بقدر
+
+289
+00:28:29,580 --> 00:28:35,280
+أجيب قد إيش الـ order لـ الـ external direct أفرضك لـ two
+
+290
+00:28:35,280 --> 00:28:40,860
+groups من خلال الـ order لمين؟ لـ الـ groups لذا بروح
+
+291
+00:28:40,860 --> 00:28:43,820
+بقول له هذه ملاحظة بسيطة اللي هي remark
+
+292
+00:28:47,610 --> 00:28:55,940
+In general على وجه العموم الـ order للـ G واحد
+
+293
+00:28:55,940 --> 00:29:04,280
+external للـ order للـ G اثنين external ونظل ماشيين
+
+294
+00:29:04,280 --> 00:29:10,060
+external لغاية الـ G n بدل يساوي الـ order للـ G
+
+295
+00:29:10,060 --> 00:29:16,260
+واحد مضروب في الـ order للـ G اثنين مضروب مضروب في
+
+296
+00:29:16,260 --> 00:29:23,800
+الـ order للـ G n بهذا الشكل يبقى بدك تعرف كم عنصر
+
+297
+00:29:23,800 --> 00:29:29,740
+في الـ group أو قد إيش الـ order ما عليك إلا إيه؟ تجيب
+
+298
+00:29:29,740 --> 00:29:33,520
+الـ order لكل group وتضربه في مين؟ تضربه في الـ
+
+299
+00:29:33,520 --> 00:29:38,560
+group الثانية بيطلع لك اللي هو قد إيش عدد العناصر في
+
+300
+00:29:38,560 --> 00:29:43,500
+الـ external product أو بيطلع لك قد إيش الـ order للـ
+
+301
+00:29:43,500 --> 00:29:49,640
+external product لمين؟ لهذه الـ groups تمام؟ آه أيضا
+
+302
+00:29:55,180 --> 00:29:59,520
+هي اللي بده يحصل طبعا هذا تشكلك براحتك تشتغلها في
+
+303
+00:29:59,520 --> 00:30:07,540
+الدار عشان ما نضيع وقت فيها، ماشي؟ طيب بدنا نجي لشغلة
+
+304
+00:30:07,540 --> 00:30:13,140
+مهمة هنا جدا example
+
+305
+00:30:21,100 --> 00:30:25,400
+لو بدنا .. بدنا نحسب بدل ما هو two groups لو
+
+306
+00:30:25,400 --> 00:30:31,460
+خليتهم ثلاثة كيف بدنا نحسب الشغلة هذه؟ الآن نقيس
+
+307
+00:30:31,460 --> 00:30:34,940
+عليها لو صاروا ثلاثة أو أربعة أو ما إلى ذلك
+
+308
+00:30:34,940 --> 00:30:40,880
+example يعني example على مين؟ على هذه الـ remark
+
+309
+00:30:40,880 --> 00:30:49,420
+بيقول find the number of elements find the number
+
+310
+00:30:54,570 --> 00:31:02,550
+number of elements of group
+
+311
+00:31:02,550 --> 00:31:07,070
+U4
+
+312
+00:31:07,070 --> 00:31:16,030
+with U6 with Z3
+
+313
+00:31:18,150 --> 00:31:22,550
+يعني في حالة الـ external ليس بالضرورة تبقى الـ
+
+314
+00:31:22,550 --> 00:31:25,310
+operation اللي على الأولى هي الـ operation اللي على
+
+315
+00:31:25,310 --> 00:31:29,390
+الثانية هي اللي على الثالثة لأ كل group قائمة بالـ
+
+316
+00:31:29,390 --> 00:31:34,010
+operation الخاصة بيه اطلع هنا الـ operation عملية
+
+317
+00:31:34,010 --> 00:31:38,650
+ضرب هنا عملية ضرب هنا عملية إيش؟ هنا عملية جمع
+
+318
+00:31:38,650 --> 00:31:45,590
+بيقول لي كم رقم بيكون أو وجد إيش عدد العناصر في الـ
+
+319
+00:31:45,590 --> 00:31:50,300
+group اللي عندنا هذه اللي هو الـ order بناء عليه لو
+
+320
+00:31:50,300 --> 00:31:58,040
+أنا جيت قلت له الـ order لـ U4 External Direct
+
+321
+00:31:58,040 --> 00:32:05,420
+Product مع الـ U6 External Direct Product مع Z3
+
+322
+00:32:05,420 --> 00:32:11,820
+يبقى بده يساوي الـ order لـ الـ U4 في مين؟ في الـ order
+
+323
+00:32:11,820 --> 00:32:19,680
+لـ الـ U6 في الـ order لـ Z3 هو يساوي الـ U4 فيها كم
+
+324
+00:32:19,680 --> 00:32:27,680
+عنصر؟ اثنين والـ U6 اثنين والـ Z ثلاثة يبقى كم
+
+325
+00:32:27,680 --> 00:32:34,180
+عنصر عندي؟ عشر عناصر بدنا نحسب لو حبيت أعرف عليه
+
+326
+00:32:34,180 --> 00:32:40,130
+شكلهم آه بتيجي تقول لي ما يأتي هاي أنت عندك اللي هو
+
+327
+00:32:40,130 --> 00:32:48,790
+U4 U4 فيها عنصرين اللي هو واحد وثلاثة عندك U6 فيها
+
+328
+00:32:48,790 --> 00:32:57,510
+عنصرين واحد وخمسة زي Z ثلاثة اللي هو فيها ثلاثة
+
+329
+00:32:57,510 --> 00:33:06,660
+عناصر Zero واحد واثنين طيب لو بدي أجيب الآن U4
+
+330
+00:33:06,660 --> 00:33:13,080
+External Product مع U6 External Product مع مين؟ مع
+
+331
+00:33:13,080 --> 00:33:19,140
+Z3 يساوي يبقى كل عنصر مكون من كم مركبة؟ من ثلاث
+
+332
+00:33:19,140 --> 00:33:24,180
+مكونات بدي أروح أخد العنصر الأول في الـ group
+
+333
+00:33:24,180 --> 00:33:28,300
+الأولى مع العنصر الأول في الـ group الثانية مع
+
+334
+00:33:28,300 --> 00:33:33,100
+العنصر الأول في الـ group الثالثة بعدين الأول مع
+
+335
+00:33:33,100 --> 00:33:40,710
+الأول مع الثاني بعدين الأول مع الأول مع الثالث يبقى
+
+336
+00:33:40,710 --> 00:33:47,010
+ثبت الأول وثبت الأول وحركت الثلاثة الأهم بدي
+
+337
+00:33:47,010 --> 00:33:52,850
+أقول له بدي أثبت الأول زي ما هو وبدل ما أخد الأول
+
+338
+00:33:52,850 --> 00:33:58,830
+هنا بدي أخد من الخامس وبدي أبدأ مع من؟ مع الـ Zero
+
+339
+00:33:59,210 --> 00:34:07,330
+يبقى واحد خمسة واحد وهذه قفلنا يبقى هنا واحد وخمسة
+
+340
+00:34:07,330 --> 00:34:11,650
+واثنين وهذه قفلنا يبقى حتى لو أنا أخدت العنصر
+
+341
+00:34:11,650 --> 00:34:17,910
+الأول مع الأول مع الثلاثة بعدين الأول مع الثاني مع
+
+342
+00:34:17,910 --> 00:34:22,650
+الثلاثة طيب الآن خلصنا معناته بحكاية العنصر الأول
+
+343
+00:34:22,650 --> 00:34:27,530
+تبعناه يبقى بدي أبدأ العنصر main الثاني العنصر
+
+344
+00:34:27,530 --> 00:34:32,750
+الثاني بدي يكون اللي هو الثلاثة مع العنصر الأول
+
+345
+00:34:32,750 --> 00:34:39,510
+اللي هو واحد مع الـ Zero والثلاثة مع الواحد مع
+
+346
+00:34:39,510 --> 00:34:46,520
+الواحد والثلاثة مع الواحد مع اثنين يبقى أخدت العنصر
+
+347
+00:34:46,520 --> 00:34:51,780
+الثاني مع الأول مع الثلاثة العنصر الثاني مع الثاني
+
+348
+00:34:51,780 --> 00:34:57,160
+بدي أبدأ مع الثلاثة العنصر الثاني اللي هو ثلاثة مع
+
+349
+00:34:57,160 --> 00:35:04,040
+العنصر خمسة مع Zero يبقى ثلاثة وخمسة وواحد ثلاثة
+
+350
+00:35:04,040 --> 00:35:10,420
+وخمسة واثنين بالشكل يعني هذا أي عنصر يجي في بالك
+
+351
+00:35:10,420 --> 00:35:15,990
+هتلاقي واحد من هدول هدول قد إيش عددهم؟ ستة عشر عنصر زي
+
+352
+00:35:15,990 --> 00:35:20,290
+ما تشوف هاي ستة فوق وهي ستة تحت يبقى هذول ستة عشر
+
+353
+00:35:20,290 --> 00:35:25,130
+عنصر اللي موجودات عندنا بدنا نجي لأول نظرية على
+
+354
+00:35:25,130 --> 00:35:27,470
+هذا الموضوع
+
+355
+00:35:30,100 --> 00:35:35,580
+النظرية على هذا الموضوع بتتحدث عن الـ order للـ
+
+356
+00:35:35,580 --> 00:35:39,540
+element اللي موجود في الـ external direct product
+
+357
+00:35:39,540 --> 00:35:46,560
+وهذا ما نشر إليه من قريب أو بعيد فجأة بدنا نيجي
+
+358
+00:35:46,560 --> 00:35:53,280
+لنص النظرية اللي بيقول ما يأتي اللي هو the order
+
+359
+00:35:53,280 --> 00:36:07,530
+of an element an element رتبة العنصر in a direct
+
+360
+00:36:07,530 --> 00:36:14,150
+product of
+
+361
+00:36:14,150 --> 00:36:27,370
+a finite of a finite number of
+
+362
+00:36:27,370 --> 00:36:28,970
+finite
+
+363
+00:36:31,050 --> 00:36:36,950
+groups finite groups is the least common multiple
+
+364
+00:36:36,950 --> 00:36:50,930
+of the
+
+365
+00:36:50,930 --> 00:36:53,370
+orders of
+
+366
+00:37:01,120 --> 00:37:10,180
+of the orders of the components of
+
+367
+00:37:10,180 --> 00:37:19,700
+the components of the element that
+
+368
+00:37:19,700 --> 00:37:24,940
+is الـ
+
+369
+00:37:24,940 --> 00:37:32,370
+order لل element G واحد وG اثنين ولغاية GN بدي
+
+370
+00:37:32,370 --> 00:37:38,690
+أساوي least common multiple لل order تبع الـ G1 والـ
+
+371
+00:37:38,690 --> 00:37:45,910
+order تبع الـ G2 والـ order تبع الـ GN بالشكل اللي
+
+372
+00:37:45,910 --> 00:37:46,510
+عندنا هذا
+
+373
+00:38:10,850 --> 00:38:16,470
+نرجع للنص مرة ثانية أنا عندك product بدي الـ order
+
+374
+00:38:16,470 --> 00:38:19,610
+لأي element الـ order للـ element يساوي least
+
+375
+00:38:19,610 --> 00:38:23,770
+common multiple للـ order لكل مركبة على حده يعني 
+
+376
+00:38:23,770 --> 00:38:28,690
+بدي أجيب ال order للعنصر الأول في الـ N tuple ال
+
+377
+00:38:28,690 --> 00:38:32,070
+order للعنصر الثاني في الـ N tuple ال order في
+
+378
+00:38:32,070 --> 00:38:35,370
+التالت ال order للرابع صار عندي مجموعة من ال order
+
+379
+00:38:35,370 --> 00:38:38,790
+بتجيب ال least common multiple لهم كلهم بيكون هو
+
+380
+00:38:39,450 --> 00:38:45,150
+يكون هو ال order لانتوبل كلها اللي عندها يبقى 
+
+381
+00:38:45,150 --> 00:38:50,050
+بيقول the order of an element in a direct product
+
+382
+00:38:50,050 --> 00:38:55,470
+of a finite number of finite groups يبقى أنا عندي
+
+383
+00:38:55,470 --> 00:38:59,910
+كل group من ال groups هذه finite يعني فيها عدد
+
+384
+00:38:59,910 --> 00:39:06,170
+محدود من العناصر كويس، اتنين أخدت عدد محدود من ال
+
+385
+00:39:06,170 --> 00:39:10,710
+groups هي المقصود فيها عدد محدود من ال groups كل
+
+386
+00:39:10,710 --> 00:39:14,650
+group فيها عدد محدود من مهم من العناصر هو ال least
+
+387
+00:39:14,650 --> 00:39:18,370
+common multiple of the orders of the components of
+
+388
+00:39:18,370 --> 00:39:22,650
+the elements يعني بدي أترجم هذا الكلام أترجم عملية
+
+389
+00:39:22,650 --> 00:39:28,610
+فباجي بقول ال order لل element كل اللي موجود في ال
+
+390
+00:39:28,610 --> 00:39:34,670
+product external ال order للمركبة
+
+391
+00:39:34,670 --> 00:39:38,170
+الأولى و ال order للتانية و ال order للتالتة و ال
+
+392
+00:39:38,170 --> 00:39:43,910
+order للرابعة و هكذا، تمام، لفروف بسيط يبقى بداجي
+
+393
+00:39:43,910 --> 00:39:51,010
+أقوله افترض أن G1 و G2 و لغاية GN موجود
+
+394
+00:39:51,010 --> 00:39:55,370
+في الـ External Direct Product اللي عندنا .. الشكل
+
+395
+00:39:55,370 --> 00:40:01,810
+اللي عندنا هذا لغاية الـ GN الآن
+
+396
+00:40:01,810 --> 00:40:11,430
+أ assume افترض أن ال order للـ G1 و G2 و لغاية ال
+
+397
+00:40:11,430 --> 00:40:20,890
+GN بده يساوي T والـ S هو الـ least common
+
+398
+00:40:20,890 --> 00:40:26,550
+multiple للـ order تبع الـ G1 والـ order تبع الـ
+
+399
+00:40:26,550 --> 00:40:35,210
+G2 والـ order تبع الـ GN بالشكل اللي عندنا، إذا
+
+400
+00:40:35,210 --> 00:40:39,410
+قررت أثبت أن الـ S بساوي الـ T بتم المطلوب بس هي
+
+401
+00:40:39,410 --> 00:40:44,610
+كل الفكرة، مش أنا أفرض أن ال order لهذا يساوي T و ال
+
+402
+00:40:44,610 --> 00:40:48,790
+multiple يساوي S، إذا قلت اثبت أن الـ S و T بيساوا
+
+403
+00:40:48,790 --> 00:40:54,010
+بعض بيكون إيه؟ أنت هنا من الموضوع، طيب الآن لو جيت
+
+404
+00:40:54,010 --> 00:41:00,650
+قلت لك consider خد لي اللي هو الـ G واحد والـ G اتنين
+
+405
+00:41:00,650 --> 00:41:11,500
+و لغاية الـ GN هذا الكلام
+
+406
+00:41:11,500 --> 00:41:19,760
+يسمى G1 أس S G2 أس S و لغاية Gn أس
+
+407
+00:41:19,760 --> 00:41:28,130
+S طيب تعال نشوف هذا الكلام إيش بده يساوي، كده إيش
+
+408
+00:41:28,130 --> 00:41:32,150
+بده يساوي؟ الأعلى، لإيش؟ لأن الـ S هي اللي يسكم ال
+
+409
+00:41:32,150 --> 00:41:36,890
+multiple لل others، لكل واحد فيهم، يبقى هذا الكلام
+
+410
+00:41:36,890 --> 00:41:44,090
+ذاتني واحد و E2 و لغاية EN يبقى هذا ال element
+
+411
+00:41:44,090 --> 00:41:49,430
+رفعته إلى S وجدته يساوي ال identity طب قداش ال
+
+412
+00:41:49,430 --> 00:41:55,510
+order لهذا يبقى T بدي يقسم الـ S صح ولا لأ؟ يبقى هنا
+
+413
+00:41:55,510 --> 00:42:00,570
+so by the grand theorem أو كرول اللي على ال grand
+
+414
+00:42:00,570 --> 00:42:06,530
+theorem الـ T الـ T divides
+
+415
+00:42:08,360 --> 00:42:14,600
+الـ S يعني معناه هذا الكلام أن T أقل من أو تساوي S
+
+416
+00:42:14,600 --> 00:42:20,820
+واعتبر المعادلة هذه رقم واحد، الآن بدل ما أخدت هكذا
+
+417
+00:42:20,820 --> 00:42:29,180
+أخد G1 أس T G2 أس T و لغاية GN أس T
+
+418
+00:42:33,020 --> 00:42:37,140
+هذا لو أردت أن أرجعه يعني أن الـ S أُس T برا صح
+
+419
+00:42:37,140 --> 00:42:43,920
+ولا لأ؟ يبقى هذا معناته G1 G2 و لغاية G
+
+420
+00:42:43,920 --> 00:42:50,040
+N أس T أنا فرضت أن ال order لهذا ال element قداشر
+
+421
+00:42:50,040 --> 00:42:55,000
+T إذا هذا قداشر بدي أعطيه إيه ال identity يبقى هذا
+
+422
+00:42:55,000 --> 00:43:00,080
+بدي أعطيه الـ E واحد و الـ E اتنين و لغاية الـ E N
+
+423
+00:43:01,640 --> 00:43:06,780
+يبقى صار عندك G1 أس T بدأ ثاني مين ال
+
+424
+00:43:06,780 --> 00:43:11,560
+identity يبقى ال order لهذا ال element بدأ يقسم
+
+425
+00:43:11,560 --> 00:43:16,640
+مين؟ بدأ يقسم الـ T يبقى صار ال order لـ G1
+
+426
+00:43:16,640 --> 00:43:28,150
+divides الـ T و ال order لـ G2 divides الـ T وهو
+
+427
+00:43:28,150 --> 00:43:35,410
+ال order اللي GN كمان divides اللي هو main الـ T
+
+428
+00:43:35,410 --> 00:43:41,610
+طيب، إيه كويس يبقى معنى هذا الكلام أن الـ T هو
+
+429
+00:43:41,610 --> 00:43:47,510
+عبارة عن common multiples لكل ال orders صح؟ يبقى
+
+430
+00:43:47,510 --> 00:43:59,790
+هنا this means that أن الـ T is a
+
+431
+00:43:59,790 --> 00:44:12,490
+common multiple of ال order للـ G1 وال order للـ G2
+
+432
+00:44:12,490 --> 00:44:18,890
+و ال order لل GM طب أنا عندي least common multiple
+
+433
+00:44:18,890 --> 00:44:27,370
+كدهش يبقى T مالها؟ أكبر من S أو S أقل من أو يساوي T
+
+434
+00:44:27,370 --> 00:44:38,090
+but ولكن S is the least common multiple
+
+435
+00:44:41,330 --> 00:44:49,050
+هذا سيعطيك أن الـ S أقل من أو يساوي الـ T ومعدل رقم
+
+436
+00:44:49,050 --> 00:44:55,190
+2 يبقى باشر بقول from واحد
+
+437
+00:44:57,120 --> 00:45:03,280
+والاتنين يبقى T تساوي كده؟ الـ S طب الـ S هنا فرضه
+
+438
+00:45:03,280 --> 00:45:06,840
+هو least common multiple و T هي الأقل يبقى اتنين
+
+439
+00:45:06,840 --> 00:45:12,560
+ماله are equal و هو المفتوح يبقى بناء عليك بنكون
+
+440
+00:45:12,560 --> 00:45:17,940
+برهنة النظرية و المرة جاها إن شاء الله بنكمل 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ccc2d9b92c1b65e801d6197a83fa79b396eb20da
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA.srt
@@ -0,0 +1,1683 @@
+1
+00:00:21,210 --> 00:00:24,770
+بسم الله الرحمن الرحيم السلام عليكم يا شباب إن شاء
+
+2
+00:00:24,770 --> 00:00:28,310
+الله اليوم هناخد الجزء الثاني من محاضرات خاصة
+
+3
+00:00:28,310 --> 00:00:31,670
+بالوحدة الرابعة اللي بنتكلم فيها عن ال cyclic
+
+4
+00:00:31,670 --> 00:00:35,670
+subgroups أو ال cyclic groups اللي كان معنا
+
+5
+00:00:35,670 --> 00:00:40,110
+المحاضرة الماضية بيتذكر أنه بدأنا في شغلات تتعلق
+
+6
+00:00:40,110 --> 00:00:48,750
+بتعميم تعريف درسناه في الوحدة الثالثة بتعلق بتوليد
+
+7
+00:00:48,750 --> 00:00:53,710
+subgroup عن طريق عناصر ما داخل الجروب معينة بعدين
+
+8
+00:00:53,710 --> 00:00:58,530
+حاولنا نأخذ هذا الكلام ونطبقه على الجروب نفسه حيث
+
+9
+00:00:58,530 --> 00:01:02,590
+نقول الجروب كلها مولدة من هذا العنصر طلع معنا
+
+10
+00:01:02,590 --> 00:01:07,790
+تعريف ال cyclic اتكلمنا عن التعريف أخذنا أشهر أمثلة
+
+11
+00:01:07,790 --> 00:01:12,130
+Cyclic group سواء كانت ال infinite هو المتعلقة بال
+
+12
+00:01:12,130 --> 00:01:16,270
+Z integers تحت عملية الجمع هنكتشف لاحقا أن أي 
+
+13
+00:01:16,270 --> 00:01:20,790
+Cyclic group ال order لها ما له نهاية هي عبارة عن
+
+14
+00:01:20,790 --> 00:01:26,150
+نسخة من ال Z أيضا اتكلمنا عن ال Cyclic groups ال
+
+15
+00:01:26,150 --> 00:01:33,600
+finite اللي نشملها تحت إطار ال ZN برضه لاحقا هنكتشف
+
+16
+00:01:33,600 --> 00:01:37,960
+أن أي cyclic الجروب و finite هتكون نسخة من some ZN
+
+17
+00:01:37,960 --> 00:01:43,640
+أخذنا مثالين على UN واحدة كانت cyclic والتانية كانت
+
+18
+00:01:43,640 --> 00:01:47,060
+non أو not cyclic وبالتالي ال UN بقدرش أنا أطلق
+
+19
+00:01:47,060 --> 00:01:52,440
+عليها تعميم أن ايه all UN cyclic أو all UN not
+
+20
+00:01:52,440 --> 00:01:56,780
+cyclic برضه لاحقا هنفهم وقت أيش ال UN بتكون cyclic
+
+21
+00:01:56,780 --> 00:02:01,400
+ووقت أيش ال UN بتكونش not cyclic هناخد اليوم الجزء
+
+22
+00:02:01,400 --> 00:02:06,500
+التالي من النظريات المتعلقة بهذا الموضوع هنبدأ
+
+23
+00:02:06,500 --> 00:02:13,660
+بنظرية 4.2 اللي بتتكلم عن order العنصر داخل الـ
+
+24
+00:02:13,660 --> 00:02:23,780
+cyclic group theorem 4.2 طيب
+
+25
+00:02:23,780 --> 00:02:26,260
+هنبدل الجلم
+
+26
+00:02:47,340 --> 00:02:50,140
+النقطة الأولى
+
+27
+00:03:02,110 --> 00:03:07,770
+Generated by A to K هي
+
+28
+00:03:07,770 --> 00:03:14,170
+ساوي Generated by A لأن
+
+29
+00:03:14,170 --> 00:03:24,950
+و K P ال order ل A to K هي ساوي N على ال common
+
+30
+00:03:24,950 --> 00:03:28,810
+divisor لن و K
+
+31
+00:03:32,240 --> 00:03:35,540
+قبل أن ندخل في الظروف سنفهم أيش أهمية هذه النظرية
+
+32
+00:03:35,540 --> 00:03:39,740
+ومذا تقولنيها الشق
+
+33
+00:03:39,740 --> 00:03:46,460
+الأول منها يتعلق بالتالي طبعا نرجع لشغل الجي ليست
+
+34
+00:03:46,460 --> 00:03:50,000
+بضوء تكون Cyclic أنا بتكلم على جزء من الجي اللي هو
+
+35
+00:03:50,000 --> 00:03:55,430
+generated by A اللي بيكون Cyclic ومش تشغل داخلهالـ
+
+36
+00:03:55,430 --> 00:03:59,670
+generated by A to K بيساوي الـ generated by A وقص
+
+37
+00:03:59,670 --> 00:04:02,030
+الـ greatest common divisor لأن و K ومن المعروف أن
+
+38
+00:04:02,030 --> 00:04:05,890
+الـ greatest common divisor لأن و K دائما وأبدا
+
+39
+00:04:05,890 --> 00:04:11,250
+أقل أو يساوي K الهدف هنا أنه أنا أدور على عنصر
+
+40
+00:04:11,250 --> 00:04:18,030
+القص تبعه أقل من ال K ويولد نفس ال subgroup الجزء
+
+41
+00:04:18,030 --> 00:04:23,900
+الثاني ال order ل power لل A أيش علاقته؟ في ال
+
+42
+00:04:23,900 --> 00:04:29,500
+order لل A نفسه هندف الإثبات للجزء الأول هقول
+
+43
+00:04:29,500 --> 00:04:34,580
+الثالث جاب المعنى أفوت في التفاصيل هعطي تسميات let
+
+44
+00:04:34,580 --> 00:04:42,640
+D بساوة ل greatest common divisor لأن و K بتحول الإثبات
+
+45
+00:04:42,640 --> 00:04:47,160
+أنه أنا بدي أثبت أنه generated by A to K بدي أثبت
+
+46
+00:04:47,160 --> 00:04:55,690
+أنه generated by A to D وش ننتقل للمفهوم لمفهوم set
+
+47
+00:04:55,690 --> 00:05:02,010
+theory نظرية مجموعات أثبت أن ال two sets أيش مالهم
+
+48
+00:05:02,010 --> 00:05:08,290
+متساويات هاخد عنصر من هنا وأثبت أنه يعني كل عنصر
+
+49
+00:05:08,290 --> 00:05:13,750
+موجود هنا هثبت أنه موجود هنا طبعا والعكس صحيح
+
+50
+00:05:13,750 --> 00:05:21,610
+since دي بدت ساوة ل greatest common divisor لأن و كيه
+
+51
+00:05:21,610 --> 00:05:27,250
+أيَش اللي مقدر أستفيد منه هنا إن دي تقسم ال N و دي
+
+52
+00:05:27,250 --> 00:05:41,570
+تقسم ال K دي تقسم ال N و دي هتقسم ال K أيضا نشتغل
+
+53
+00:05:41,570 --> 00:05:48,550
+على دي تقسم ال N يعني ال D أو N بدت ساوة D في T و
+
+54
+00:05:48,550 --> 00:05:52,990
+ال K بدت ساوة D في R
+
+55
+00:05:55,990 --> 00:06:00,650
+كيف بدي أثبت هذا الكلام؟ كيف بدي أثبت أنه كل عنصر
+
+56
+00:06:00,650 --> 00:06:08,130
+هنا هو عنصر موجود هنا؟ هلاحظ التالي أن ال a to k
+
+57
+00:06:08,130 --> 00:06:17,110
+عبارة عن أيش؟ عن a to dr اللي هو عبارة عن مين؟ عن
+
+58
+00:06:17,110 --> 00:06:25,510
+a to d to r وهذا عنصر موجود هذا عنصر موجود هذا
+
+59
+00:06:25,510 --> 00:06:32,230
+العنصر موجود في generated by a to d أيش يعني يعني a
+
+60
+00:06:32,230 --> 00:06:41,110
+to k موجود وين في generated by a to d عنصر موجود
+
+61
+00:06:41,110 --> 00:06:49,190
+في group فال subgroup للعنصر هذا بيولدها ويل
+
+62
+00:06:49,190 --> 00:06:55,850
+هتكون جزء من الجروب هذه وبالتالي generated by a to
+
+63
+00:06:55,850 --> 00:07:04,730
+k subset من generated by a to d و أعطيها واحدة
+
+64
+00:07:04,730 --> 00:07:09,290
+نعيد بسرعة أنا حولت السؤال ل set theory نظرية
+
+65
+00:07:09,290 --> 00:07:14,450
+مجموعات بدي أثبت أن مجموعة بتساوي مجموعة بدي أستفيد
+
+66
+00:07:14,450 --> 00:07:18,850
+من خصائص أنه أنا بشغل في ال group theory لو كان
+
+67
+00:07:18,850 --> 00:07:22,090
+العنصر موجود في المجموعة فال generated من هذا
+
+68
+00:07:22,090 --> 00:07:26,770
+العنصر برضه موجود داخل ال group أخدت ال D عبارة عن
+
+69
+00:07:26,770 --> 00:07:30,110
+ال greatest common divisor ل N و K ال D بتقسم ال N ال D
+
+70
+00:07:30,110 --> 00:07:35,390
+بتقسم ال K فال K عبارة عن DR ال A to K عبارة عن A
+
+71
+00:07:35,390 --> 00:07:40,530
+to DR يعني عبارة عن A to D الكل أس R وهذا عنصر
+
+72
+00:07:40,530 --> 00:07:41,070
+موجود
+
+73
+00:08:01,470 --> 00:08:06,530
+الجزء الثاني أو
+
+74
+00:08:06,530 --> 00:08:12,220
+D بدأ تساوي لـ greatest common divisor لن و K معناتها
+
+75
+00:08:12,220 --> 00:08:19,980
+D بيبدأ تساوي N في X زي ك في Y for some integers Y من
+
+76
+00:08:19,980 --> 00:08:27,120
+وين؟ من ال Z number three ال greatest common divisor
+
+77
+00:08:27,120 --> 00:08:33,320
+ لعددين عبارة عن تركيبة خطية من مين؟ من العددين
+
+78
+00:08:33,320 --> 00:08:42,670
+هدول طيب يقبل A to D عبارة عن a to n x زائد ky اللي
+
+79
+00:08:42,670 --> 00:08:52,810
+هو بديه يساوي a to n plus x في a to k to y ال a to
+
+80
+00:08:52,810 --> 00:09:00,750
+n أيش بيساوي ال a to n ال order ل a بيساوي n أيش
+
+81
+00:09:00,750 --> 00:09:05,010
+بقى a to n أيش بيساوي identity أيش بده عبارة عن ال
+
+82
+00:09:05,010 --> 00:09:09,450
+identity to x مش E أس X يعني أنا متكلمش شغال احنا
+
+83
+00:09:09,450 --> 00:09:14,770
+في الجبر مش في ال calculus و A to K أس Y اللي هو
+
+84
+00:09:14,770 --> 00:09:21,190
+عبارة عن A to K أس Y وهذا عنصر موجود في
+
+85
+00:09:21,190 --> 00:09:27,770
+generated by A to K لأن ال power ل A to K صار ال A
+
+86
+00:09:27,770 --> 00:09:34,190
+to D ينتمي ل generated by A to K نفس الأسلوب اللي
+
+87
+00:09:34,190 --> 00:09:41,500
+في الأول حاسيب معايا A to D subset من generated by
+
+88
+00:09:41,500 --> 00:09:45,700
+A to K و أعطيها اثنين واحد و اثنين هيعطيني التالي
+
+89
+00:09:45,700 --> 00:09:52,640
+واحد و اثنين هيعطيني أنه generated by A to D
+
+90
+00:09:52,640 --> 00:09:58,360
+بيتساوى generated by A to K طبعا هو اللي احنا
+
+91
+00:09:58,360 --> 00:10:04,220
+مطلوب نثبته واضحة
+
+92
+00:10:04,220 --> 00:10:09,610
+ولا محتاجة توضيح آخر generated by a to d بيساوي
+
+93
+00:10:09,610 --> 00:10:14,170
+generated by a to k وبالتالي generated by a to k
+
+94
+00:10:14,170 --> 00:10:19,630
+بيساوي generated by a ل greatest common divisor ل N
+
+95
+00:10:19,630 --> 00:10:22,990
+اكتب
+
+96
+00:10:22,990 --> 00:10:29,350
+بس بسرعة E
+
+97
+00:10:29,350 --> 00:10:34,190
+أس X مش ال A اللي أخضر يلو N ف E أس N مش بيساوي
+
+98
+00:10:35,780 --> 00:10:39,240
+أيه أسئلة مش هيساوي ال identity ال identity و أي
+
+99
+00:10:39,240 --> 00:10:48,960
+حاجة بيبقى ال identity كيف هذه number three نظرية
+
+100
+00:10:48,960 --> 00:10:52,840
+الأعداد ال greatest common divisor لأي عددين تركيبها
+
+101
+00:10:52,840 --> 00:10:56,940
+خطية من العددين شبكة واحدة في الكتاب أو لو رجعت
+
+102
+00:10:56,940 --> 00:11:01,360
+لكتاب نظرية الأعداد موجودة في section 2 3
+
+103
+00:11:12,420 --> 00:11:18,400
+عيد عيد بس بصراحة أي أس كي أس واي بس هو power
+
+104
+00:11:18,400 --> 00:11:22,620
+لقيت okay؟ وهو موجود في generated by a to k لأن
+
+105
+00:11:22,620 --> 00:11:27,780
+وعيش ال generated by a to k هي جميع الأسس الممكنة
+
+106
+00:11:27,780 --> 00:11:31,340
+من هذا العنصر شرحناها المحاضرة الماضية وجون ال
+
+107
+00:11:31,340 --> 00:11:35,520
+generated by a to n لو ال order لل a في a infinite
+
+108
+00:11:35,520 --> 00:11:40,040
+بيظل عبارة عن e, a, a تربيع, a تكعيب إلى آخره لكن
+
+109
+00:11:40,040 --> 00:11:44,260
+لو ال order finite e, a, a تربيع وصولها إلى a to n
+
+110
+00:11:44,260 --> 00:11:50,210
+minus 1 الجزء الثاني من الإثبات يا شباب بنثبت أن ال
+
+111
+00:11:50,210 --> 00:11:55,870
+order ل a to k عبارة عن n على ال greatest common divisor ل
+
+112
+00:11:55,870 --> 00:12:01,590
+n و d أنا مش هبدأ ب a to k هبدأ ب a to d وأثبت أن
+
+113
+00:12:01,590 --> 00:12:06,010
+ال order ل a to d بيساوي n على d يعني ال greatest common
+
+114
+00:12:06,010 --> 00:12:11,550
+divisor ل n و k وبعدين عن طريق أن هذه ال subgroup
+
+115
+00:12:11,550 --> 00:12:17,590
+بتساوي هذه ال subgroup فال order اللي هم واحد حسب
+
+116
+00:12:17,590 --> 00:12:20,790
+قاعدة السابقة ال order لل generator هيكون واحد
+
+117
+00:12:20,790 --> 00:12:24,010
+يكبر ال order ل a to k و ال order ل a to d
+
+118
+00:12:24,010 --> 00:12:28,630
+متساويين فلو كان ال order ل a to d بيساوي n على d
+
+119
+00:12:28,630 --> 00:12:36,990
+هصير ال order ل a to k برضه n على d دي
+
+120
+00:12:36,990 --> 00:12:44,730
+بدت ساوة ال greatest common divisor ل n و k و n
+
+121
+00:12:44,730 --> 00:12:54,110
+بدت ساوة dt حسب الجزء الأول أو D تتساوي أو T تتساوي
+
+122
+00:12:54,110 --> 00:13:05,310
+N على D Now A to D أس T عبارة عن A to D أس N على
+
+123
+00:13:05,310 --> 00:13:09,810
+D هي عبارة عن A أس N بدي تساوي ال identity
+
+124
+00:13:09,810 --> 00:13:16,870
+وبالتالي A to D أس T بيعطيني ال identity يقبل
+
+125
+00:13:16,870 --> 00:13:21,730
+order ل A to D أقل 
+
+126
+00:13:21,730 --> 00:13:29,710
+أو يساوي T طيب أنا بدأت أثبت أنه يساوي هأفترض العكس
+
+127
+00:13:29,710 --> 00:13:40,750
+أنه أقل من الـ T assume that الـ order لـ A to D بدأ
+
+128
+00:13:40,750 --> 00:13:49,020
+تساوي I و I أقل من T اللي هي بتساوي N على D هذا إيش
+
+129
+00:13:49,020 --> 00:13:57,180
+معناته؟ معناته الـ A to D أُس I بدي تساوي الـ
+
+130
+00:13:57,180 --> 00:14:03,520
+identity وبالتالي الـ A to D I بدي تساوي الـ identity
+
+131
+00:14:03,520 --> 00:14:11,860
+هذا معناته أن N أقل أو يساوي DI لإن الـ order للـ A 
+
+132
+00:14:11,860 --> 00:14:22,370
+بساوي الـ N but I أقل من الـ T ليه بتساوي N على D D I
+
+133
+00:14:22,370 --> 00:14:29,870
+أقل من الـ N إيش في بين الجمعتين هدول الـ N أقل أو
+
+134
+00:14:29,870 --> 00:14:35,750
+يساوي DI و الـ DI أقل من مين؟ من الـ N صحيح عندك
+
+135
+00:14:35,750 --> 00:14:36,370
+تناقض
+
+136
+00:14:41,450 --> 00:14:46,670
+تناقض كيف بقول أنه الرقم هذا اللي هو N أقل أو يساوي
+
+137
+00:14:46,670 --> 00:14:51,230
+DI وفي نفس الوقت هو أكبر منه مادام فيه تناقض يجب
+
+138
+00:14:51,230 --> 00:14:57,390
+فيه فرض أنا فرضتُه خاطئ يجب الـ order لـ A to D بدأت
+
+139
+00:14:57,390 --> 00:15:05,630
+تساوى T بدأت تساوي N على D الـ order لـ a to k عبارة عن الـ
+
+140
+00:15:05,630 --> 00:15:09,730
+order generated by a to k اللي هي نفس الـ order
+
+141
+00:15:09,730 --> 00:15:13,750
+generated by a to d طبعا هذه أخذناها المحاضرة
+
+142
+00:15:13,750 --> 00:15:18,570
+الماضية هذه هي موجودة قدامك توي أثبتناها الـ order
+
+143
+00:15:18,570 --> 00:15:26,570
+لـ a to d عبارة عن الـ order لـ a to d بـ d تساوي n على d
+
+144
+00:15:26,570 --> 00:15:33,650
+وبالتالي الـ order لـ a to k بدي تساوي N على D اللي هو
+
+145
+00:15:33,650 --> 00:15:40,290
+N على الـ greatest common divisor لـ N و K وهو المطلوب
+
+146
+00:15:40,290 --> 00:15:43,970
+فاضح؟
+
+147
+00:15:43,970 --> 00:15:50,710
+أي جزئية بالظبط طيب أنت مش فيعمل contradiction الله
+
+148
+00:15:50,710 --> 00:15:57,490
+اللي بقى ده طيب ماشي هجيت احنا بنثبت إن الـ order لـ
+
+149
+00:15:57,490 --> 00:16:02,590
+A to K بدي تساوي الـ N على D أنا ما بدأت بـ A to K بدأت
+
+150
+00:16:02,590 --> 00:16:08,850
+بـ A to D الـ A to D بنشوف الـ order اللي هنجدها حسب
+
+151
+00:16:08,850 --> 00:16:14,190
+اللي أنا كتبته هنا إن الـ N بيساوي D في T الـ T بدي
+
+152
+00:16:14,190 --> 00:16:21,300
+تساوي N على D رفعت الـ A to D أس T صارت a to d أس n
+
+153
+00:16:21,300 --> 00:16:28,400
+على d اللي عبارة عن a to n a to n مش بتساوي ليش الـ
+
+154
+00:16:28,400 --> 00:16:33,340
+order لـ a جديش بيساوي يعني يكبر الـ order لـ a to d
+
+155
+00:16:33,340 --> 00:16:39,500
+هيكون أقل أو يساوي t لإن مدام أنت رفعت الأنصر لـ
+
+156
+00:16:39,500 --> 00:16:43,840
+power و أعطاك identity يكبر order للأنصر أقل من الـ
+
+157
+00:16:43,840 --> 00:16:48,130
+power هذا أو يساوي حاجات أنا بدي N في المساواة عشان
+
+158
+00:16:48,130 --> 00:16:52,290
+أصل لتناقض فرضتُ أن الـ order أقل مش أقل أو يساوي
+
+159
+00:16:52,290 --> 00:16:59,110
+يعني أخذته I و أقل من T حاجات الـ order I فـ A to D
+
+160
+00:16:59,110 --> 00:17:04,990
+الكل أُس I المفروض يعطيني identity فـ A to D I بدي
+
+161
+00:17:04,990 --> 00:17:07,970
+يساوي identity حاجات أنا بعرف إن الـ order الـ A
+
+162
+00:17:07,970 --> 00:17:13,710
+بيساوي N لما بدي أرفع الـ A لـ power ويعطيك identity
+
+163
+00:17:13,710 --> 00:17:18,530
+هذا البرر يبدو يساوي صفريا إما إذا كان موجب يكون
+
+164
+00:17:18,530 --> 00:17:22,770
+أكبر من الـ N أنا بتشتغل على الـ D موجب والـ I موجب
+
+165
+00:17:22,770 --> 00:17:27,790
+يكبر الـ DI أكبر من الـ N لكن أنا حسب ما هو موجود
+
+166
+00:17:27,790 --> 00:17:32,710
+عندي I أقل من الـ D بتساوي N على D فـ ID أقل من الـ
+
+167
+00:17:32,710 --> 00:17:37,230
+N كيف ID أكبر أو يساوي الـ N و ID في نفس الوقت
+
+168
+00:17:37,230 --> 00:17:42,490
+أصغر من الـ N صار تناقض تناقض هذا هيرجعك ويقولك أن
+
+169
+00:17:42,490 --> 00:17:45,670
+الفرض اللي أنت فرضته خاطئ مين هو الفرض اللي أنت
+
+170
+00:17:45,670 --> 00:17:52,370
+فرضته إنه I أقل من T؟ إيش الصواب؟ إنه يساوي إنه
+
+171
+00:17:52,370 --> 00:17:55,590
+يساوي الـ T وبالتالي الـ order لـ A to D بدي تساوي
+
+172
+00:17:55,590 --> 00:17:59,670
+الـ T طبعا هذه السلسلة معروفة هتلاقي المحاضرة
+
+173
+00:17:59,670 --> 00:18:03,530
+الماضية إن order العنصر بيساوي order generated
+
+174
+00:18:03,530 --> 00:18:08,550
+للعنصر أو بالسماع للعنصر هذه توي أثبتناها إنه
+
+175
+00:18:08,550 --> 00:18:11,090
+generated by A to K بيساوي generated by A to D
+
+176
+00:18:11,090 --> 00:18:15,150
+ارجع لمحاضرة المرة الماضية وهذه توي جبناها إن
+
+177
+00:18:15,150 --> 00:18:20,450
+على D خد الأول مع الأخير بيكون المطلوب عندك إن وجد
+
+178
+00:18:20,450 --> 00:18:21,370
+واضح؟
+
+179
+00:18:27,050 --> 00:18:34,150
+واضح؟ طبعا معايا كم تساوي الـ greatest common divisor لأن
+
+180
+00:18:34,150 --> 00:18:38,310
+و K حسب التعريف تبع الـ greatest common divisor الـ greatest
+
+181
+00:18:38,310 --> 00:18:42,930
+common divisor لازم يكون positive لازم يكون
+
+182
+00:18:42,930 --> 00:18:50,210
+positive في على هذه النظرية تلاتة corollaries
+
+183
+00:18:50,210 --> 00:18:51,470
+ثلاثة
+
+184
+00:18:53,530 --> 00:19:01,850
+ملاحظات هنبدأ بالملاحظة الأولى وكتيش بيتساوى الـ
+
+185
+00:19:01,850 --> 00:19:09,370
+generated لـ two powers لـ الـ a كولر
+
+186
+00:19:09,370 --> 00:19:13,970
+واحد نص
+
+187
+00:19:13,970 --> 00:19:20,270
+الكولر بيقول التالي let order الـ a بدي يساوي n
+
+188
+00:19:20,270 --> 00:19:22,090
+then
+
+189
+00:19:23,780 --> 00:19:30,840
+generated by a to i بتساوي generated by a to j if
+
+190
+00:19:30,840 --> 00:19:35,220
+and only if لـ greatest common divisor لأن i بيساوي
+
+191
+00:19:35,220 --> 00:19:43,080
+لـ greatest common divisor لأن j two
+
+192
+00:19:43,080 --> 00:19:49,210
+powers للـ a والدول نفس الـ subgroup إذا كانت two
+
+193
+00:19:49,210 --> 00:19:54,330
+parallels هدول لـ greatest common divisors لـهم مع الـ N
+
+194
+00:19:54,330 --> 00:20:09,230
+متساويين طيب from theorem 4.2 generated by a to i
+
+195
+00:20:09,230 --> 00:20:12,470
+إيش بتساوي؟
+
+196
+00:20:12,470 --> 00:20:19,380
+إيش بتساوي؟ generated by a greatest common divisor
+
+197
+00:20:19,380 --> 00:20:27,680
+لأنواع a صح ولا لأ؟ و generated by a to j عبارة عن
+
+198
+00:20:27,680 --> 00:20:34,760
+generated by a greatest common divisor لأنواع j طيب
+
+199
+00:20:34,760 --> 00:20:42,720
+هذه تمهيد نجي للاتجاه الأول assume
+
+200
+00:20:50,820 --> 00:20:55,460
+generated by a to i بيساوي generated by a to j
+
+201
+00:20:55,460 --> 00:21:06,660
+هذا
+
+202
+00:21:06,660 --> 00:21:13,440
+معناته معناته generated by a greatest common divisor
+
+203
+00:21:13,440 --> 00:21:21,480
+لأن و I بيساوي generated by a و أصلا greatest common
+
+204
+00:21:21,480 --> 00:21:25,800
+divisor لأنواع j
+
+205
+00:21:25,800 --> 00:21:29,680
+متساويين،
+
+206
+00:21:29,680 --> 00:21:39,100
+إيش يعني؟ معناته الـ order اللي لهم متساوي
+
+207
+00:21:39,100 --> 00:21:45,660
+طيب
+
+208
+00:21:45,660 --> 00:21:46,760
+إيش الـ order لها دي؟
+
+209
+00:21:51,470 --> 00:21:56,370
+أنت على فكرة أنا ممكن يعني أسهل عليك الأمور يعني
+
+210
+00:21:56,370 --> 00:22:01,530
+أتجاوز المرحلة دي وأقول لك إن هذه الخطوة ما بتلزَمْش
+
+211
+00:22:01,530 --> 00:22:06,810
+واستبدلك إياها بـ I و J وهي كده بيطلع معك أسهل
+
+212
+00:22:06,810 --> 00:22:11,970
+الإثبات هجيت الـ order that is generated by A to I
+
+213
+00:22:11,970 --> 00:22:20,610
+جديش و على الـ greatest common divisor لـ N و I لأن ما
+
+214
+00:22:20,610 --> 00:22:26,390
+مسحناهش generated by a to j عبارة عن n على الـ
+
+215
+00:22:26,390 --> 00:22:32,950
+greatest common divisor لـ n و j طيّر الـ n من
+
+216
+00:22:32,950 --> 00:22:35,890
+الطرفين وضع الطرفين في وسطين حيث يكون معايا
+
+217
+00:22:35,890 --> 00:22:39,830
+greatest common divisor لـ n و j عبارة عن
+
+218
+00:22:39,830 --> 00:22:45,010
+greatest common divisor لـ n و i هذا الجزء الأول
+
+219
+00:22:45,010 --> 00:22:48,810
+الجزء الثاني f
+
+220
+00:22:49,980 --> 00:22:54,960
+الـ greatest common divisor لأن و j لأن و i
+
+221
+00:22:54,960 --> 00:22:59,680
+بيساوي الـ greatest common divisor لأن و j معناته
+
+222
+00:22:59,680 --> 00:23:09,340
+الـ generated by A لأن و i بيساوي الـ greatest
+
+223
+00:23:09,340 --> 00:23:15,200
+common divisor لأن و j معناته الـ generated by A
+
+224
+00:23:15,200 --> 00:23:21,390
+to I بيساوي الـ generated by A to j وهو المطلوب
+
+225
+00:23:21,390 --> 00:23:24,410
+واضحة
+
+226
+00:23:24,410 --> 00:23:34,630
+و الله محتاج إعادة شرح واضحة و الله بدنا إياها تمد
+
+227
+00:23:34,630 --> 00:23:39,590
+على الخاصية هذه ف الـ generated .. مدام هذا بيساوي
+
+228
+00:23:39,590 --> 00:23:42,150
+هذا الأس بيساوي الأس فالـ generated بيساوي الـ
+
+229
+00:23:42,150 --> 00:23:45,090
+generated هذا بيساوي هذا وهذا بيساوي هذا
+
+230
+00:23:51,220 --> 00:24:06,300
+طيب كولر الثانية كولر
+
+231
+00:24:06,300 --> 00:24:13,620
+الثانية بتقول لك وقت إيش power للـ a بيولد الـ
+
+232
+00:24:13,620 --> 00:24:17,120
+generated by a يعني أنا لو اشتغلت على group J
+
+233
+00:24:17,120 --> 00:24:23,280
+generated by some A مين هي الأسس تبعت الـ A الغير
+
+234
+00:24:23,280 --> 00:24:30,540
+الواحد اللي بتولد الـ J؟ let J generated by A
+
+235
+00:24:37,640 --> 00:24:43,100
+الـ j بتكون generated by a to k if and only if
+
+236
+00:24:43,100 --> 00:24:50,980
+لـ greatest common divisor لـ n و k بدي يساوي الواحد
+
+237
+00:24:50,980 --> 00:24:57,240
+proof بعدها
+
+238
+00:24:57,240 --> 00:24:59,140
+دي سهلة هيتمل الكولر اللي جابلها
+
+239
+00:25:04,470 --> 00:25:09,470
+الـ j بيساوي generated by a to k if and only if
+
+240
+00:25:09,470 --> 00:25:17,050
+generated by a بيساوي generated by a to k ليش؟
+
+241
+00:25:17,050 --> 00:25:23,410
+ليش؟ لأن الـ j generated by a شيل الـ j وحط مدلة
+
+242
+00:25:23,410 --> 00:25:29,230
+generated by a هذا الكلام ما قدش يكون صحيح if and
+
+243
+00:25:29,230 --> 00:25:35,250
+only if لـ greatest common divisor لإنو 1 طبعا أنا
+
+244
+00:25:35,250 --> 00:25:41,790
+المفترض أضيف الجملة هذه with order للـ A بدي تساوي
+
+245
+00:25:41,790 --> 00:25:46,010
+الـ N if
+
+246
+00:25:46,010 --> 00:25:50,110
+and only if الـ greatest common divisor لـ N و 1 بيساوي
+
+247
+00:25:50,110 --> 00:25:56,790
+الـ greatest common divisor لـ N و K ما هو A to 1 و A to
+
+248
+00:25:56,790 --> 00:26:03,910
+K الـ 1 I و الـ K أحطها J وأطبق القاعدة هذه طيب greatest
+
+249
+00:26:03,910 --> 00:26:11,950
+common divisor لـ n و 1 جديش؟ واحد لإن واحد بدي
+
+250
+00:26:11,950 --> 00:26:16,330
+تساوي greatest common divisor لـ n و k يعني if and only 
+
+251
+00:26:16,330 --> 00:26:21,630
+if gcd ل n و k بتساوي واحد
+
+252
+00:26:49,080 --> 00:26:54,060
+كورلاري التالتة هي عبارة عن تطبيق الكورلاري التانية
+
+253
+00:26:54,060 --> 00:27:03,160
+لكن على Z to N أو Z to N كورلاري ايه؟
+
+254
+00:27:03,160 --> 00:27:09,500
+تلاتة An
+
+255
+00:27:09,500 --> 00:27:13,460
+integral K
+
+256
+00:27:13,460 --> 00:27:15,860
+N
+
+257
+00:27:17,600 --> 00:27:29,020
+Zn is a generator of Zn if and only if gcd
+
+258
+00:27:29,020 --> 00:27:38,930
+لن وk بتساوي واحد العنصر k اللي
+
+259
+00:27:38,930 --> 00:27:42,110
+موجود في gcd ل z و n بيكون
+
+260
+00:27:42,110 --> 00:27:46,650
+generator ل Z to N if and only if في gcd
+
+261
+00:27:46,650 --> 00:27:59,970
+ل n و k بتساوي واحد برهان سهل Zn
+
+262
+00:27:59,970 --> 00:28:07,730
+بيساوي generated by k if and only if generated by
+
+263
+00:28:07,730 --> 00:28:14,430
+واحد بيكون generated by واحد to k if and only if
+
+264
+00:28:14,430 --> 00:28:21,150
+ل gcd ل n و k بيساوي واحد ما هو ال Z
+
+265
+00:28:21,150 --> 00:28:26,330
+ان generated by واحد لما أقول generated by k في Z
+
+266
+00:28:26,330 --> 00:28:30,830
+ان ال k عبارة عن ايش؟ عن k في واحد k في واحد مع
+
+267
+00:28:30,830 --> 00:28:41,670
+الجمع هي عبارة عن ايش؟ واحد آسف ناخد مثال بس
+
+268
+00:28:41,670 --> 00:28:53,210
+مش على Z to N ونبدأ
+
+269
+00:28:53,210 --> 00:29:02,170
+ب Z to N four Z .. نختار رقم Z كده ايش بدك؟ سبعة
+
+270
+00:29:02,170 --> 00:29:14,000
+صغيرة زي الثلاثين the generators of
+
+271
+00:29:14,000 --> 00:29:24,700
+Z30 are the integers k تنتمي ل Z30 with
+
+272
+00:29:24,700 --> 00:29:32,490
+gcd ل k و 30 مش بيساوي صفر يا شباب
+
+273
+00:29:32,490 --> 00:29:36,430
+العناصر اللي بتكون أقل من N و relatively prime
+
+274
+00:29:36,430 --> 00:29:44,410
+مع N  فين بنحطها؟
+
+275
+00:29:44,410 --> 00:29:50,230
+لا فين بنحطها؟ في ال U و كنا نعدها باقتران في
+
+276
+00:29:50,230 --> 00:29:56,450
+نظرية العدد، ايش اسمه؟ اللي أخذ باقتران اسمه ال
+
+277
+00:29:56,450 --> 00:30:01,180
+Phi ايه ال Phi function؟ طبعا مين يالي gcd كم on
+
+278
+00:30:01,180 --> 00:30:05,000
+divisor اللي مع ال 30 بيعطيني واحد k هيساوي
+
+279
+00:30:05,000 --> 00:30:10,120
+واحد؟ مين بعد ال واحد؟ اثنين لا، ثلاثة لا، أربعة
+
+280
+00:30:10,120 --> 00:30:17,020
+لا، خمسة لا، ستة لا، سبعة، أحد عشر، ثلاثة عشر، سبعة عشر،
+
+281
+00:30:17,020 --> 00:30:24,200
+تسعة عشر، ثلاثة و عشرين، تسعة و عشرين يقبل
+
+282
+00:30:24,200 --> 00:30:31,400
+generators ل Z30 عبارة عن مين؟  ده أرقامها دول
+
+283
+00:30:31,400 --> 00:30:39,340
+لو بنعمم ال generators of
+
+284
+00:30:39,340 --> 00:30:50,280
+Zn are the integers k اللي بينتموا ل Zn with
+
+285
+00:30:50,280 --> 00:30:58,260
+gcd ل k و n بتساوي واحد these
+
+286
+00:30:58,260 --> 00:31:00,140
+integers
+
+287
+00:31:02,860 --> 00:31:10,840
+are the members of
+
+288
+00:31:10,840 --> 00:31:15,280
+U N
+
+289
+00:31:15,280 --> 00:31:18,700
+are
+
+290
+00:31:18,700 --> 00:31:23,940
+the elements of
+
+291
+00:31:23,940 --> 00:31:31,240
+U N يعني ال generators بتوع ال Z N هم عناصر مين؟
+
+292
+00:31:31,240 --> 00:31:42,390
+عناصر مين؟ ال U30 find
+
+293
+00:31:42,390 --> 00:31:51,730
+the generators of U50
+
+294
+00:31:51,730 --> 00:31:59,410
+هنجيب
+
+295
+00:31:59,410 --> 00:32:02,050
+مولدات ال U50
+
+296
+00:32:06,680 --> 00:32:14,700
+لا هذه قاعدة لل ZN مش لل U N أصلا
+
+297
+00:32:14,700 --> 00:32:19,320
+ال UN مش ضروري تكون Cyclic فلازم تكون Cyclic في
+
+298
+00:32:19,320 --> 00:32:24,940
+الأول قبل ما تدور على مين على ال generator بتوعها
+
+299
+00:32:24,940 --> 00:32:29,020
+solution أول
+
+300
+00:32:29,020 --> 00:32:36,360
+خطوة list the elements in U50
+
+301
+00:32:38,880 --> 00:32:47,820
+مين عناصر ال U50؟ لو قلنا U50، ايش بتساوي؟ واحد،
+
+302
+00:32:47,820 --> 00:32:51,740
+ثلاثة،
+
+303
+00:32:51,740 --> 00:32:58,960
+سبعة، تسعة، أحد عشر، ثلاثة عشر، سبعة عشر، تسعة
+
+304
+00:32:58,960 --> 00:33:06,040
+عشر، ثلاثة وعشرين، سبعة وعشرين، تسعة وعشرين، في
+
+305
+00:33:06,040 --> 00:33:11,470
+أصغر من الخمسين، واحد وعشرين وأحد وثلاثين ثلاثة و
+
+306
+00:33:11,470 --> 00:33:14,830
+ثلاثين سبعة و ثلاثين تسعة و ثلاثين واحد و أربعين
+
+307
+00:33:14,830 --> 00:33:24,650
+ثلاثة و أربعين سبعة و أربعين تسعة و أربعين تمام
+
+308
+00:33:24,650 --> 00:33:38,350
+الخطوة الثانية find a generator of U50 تعطينا
+
+309
+00:33:38,350 --> 00:33:47,470
+عنصر بيولد ال U50 الواحد لا احنا
+
+310
+00:33:47,470 --> 00:33:51,190
+هنا بنشتغل على ضغط مش على جمع عشان أنت تقدر تجيب
+
+311
+00:33:51,190 --> 00:33:58,470
+جنرال ال U50 الأخضر لها جنرال عده
+
+312
+00:33:58,470 --> 00:34:00,330
+دول 4 في 25
+
+313
+00:34:06,220 --> 00:34:12,360
+أربعة و أكمل أربعة منهم هاي أربعة، هاي كمان واحدة
+
+314
+00:34:12,360 --> 00:34:14,880
+و هاي كمان واحدة و هاي كمان واحدة و كمان واحدة
+
+315
+00:34:14,880 --> 00:34:23,080
+عشرين عنصر We must find .. find
+
+316
+00:34:23,080 --> 00:34:30,080
+an element in U50 with order
+
+317
+00:34:41,180 --> 00:34:53,740
+عشان ما نضيعش وقت we can show that 3 is
+
+318
+00:34:53,740 --> 00:35:00,380
+or satisfy this
+
+319
+00:35:00,380 --> 00:35:01,820
+property
+
+320
+00:35:04,360 --> 00:35:08,300
+مش هنضيع وقت الثلاثه بتحقق هذا الكلام عشان أثبت
+
+321
+00:35:08,300 --> 00:35:12,160
+لازم أضرب الثلاثه في نفسها لعندي عشرين وكل مرة
+
+322
+00:35:12,160 --> 00:35:16,400
+بتولد نفسك لما بيجيبلك سؤال في الامتحان مش هجيبلك
+
+323
+00:35:16,400 --> 00:35:20,600
+يومية مثلا تقعد تضرب أربعين مرة أو أو اشتغل عشان
+
+324
+00:35:20,600 --> 00:35:23,920
+تضمن
+
+325
+00:35:23,920 --> 00:35:29,020
+عناصر يعني هتضرب كم مرة هذا cannot cycle اصلا
+
+326
+00:35:29,020 --> 00:35:31,960
+يعني طيب
+
+327
+00:35:33,840 --> 00:35:40,360
+يعني اللي وصلنا له أنه ال U50 generated
+
+328
+00:35:40,360 --> 00:35:49,120
+by مين؟ by ثلاثة هل جيت؟ وقتش ال U50 بتكون
+
+329
+00:35:49,120 --> 00:35:56,660
+generated by عنصر تاني power للثلاثة لما يكون ال
+
+330
+00:35:56,660 --> 00:35:59,880
+power هذا relatively prime مع مين؟
+
+331
+00:36:03,120 --> 00:36:09,300
+مع ال order ل U50 مش مع الخمسين خطوة تالتة
+
+332
+00:36:09,300 --> 00:36:20,460
+since ال U50 generated by ثلاثة then ال U50
+
+333
+00:36:20,460 --> 00:36:25,280
+generated by ثلاثة أس K if and only if gcd
+
+334
+00:36:25,280 --> 00:36:30,280
+common divisor لل
+
+335
+00:36:30,280 --> 00:36:37,540
+order ل U50 و ال K بتساوي واحد يعني هذا if and on
+
+336
+00:36:37,540 --> 00:36:44,580
+if gcd ل ال 20 و ال K بيساوي واحد
+
+337
+00:36:44,580 --> 00:36:56,750
+النتيجة we must find the elements K أقل من العشرين
+
+338
+00:36:56,750 --> 00:37:01,710
+أكبر أو يساوي واحد with gcd common divisor
+
+339
+00:37:01,710 --> 00:37:10,210
+العشرين و K بيساوي واحد مين هذه العناصر؟ واحد،
+
+340
+00:37:10,210 --> 00:37:16,090
+ثلاثة، سبعة، تسعة، أحد عشر، ثلاثة عشر، سبعة عشر،
+
+341
+00:37:16,090 --> 00:37:20,450
+تسعة عشر، شوية يا شباب مش هذه العناصر اللي بتولد ال
+
+342
+00:37:20,450 --> 00:37:25,390
+U50 لا هذه ال powers اللي بدي أرفع الثلاثه الها
+
+343
+00:37:25,390 --> 00:37:31,730
+عشان تجيبلي عناصر تولد ال U50 هذا معناه الخطوة
+
+344
+00:37:31,730 --> 00:37:35,650
+الأخيرة ال
+
+345
+00:37:35,650 --> 00:37:44,050
+U50 generated by ثلاثة generated by ثلاثة أس ثلاثة
+
+346
+00:37:44,050 --> 00:37:51,460
+ثلاثة أس سبعة ثلاثة أس تسعة وصولا لثلاثة أس تسعة
+
+347
+00:37:51,460 --> 00:37:58,440
+وتسعة عشر طيب ثلاثة أس واحد معروفة ثلاثة أس ثلاثة
+
+348
+00:37:58,440 --> 00:38:04,300
+عبارة عن ثلاثة في نفسها ثلاثة في ثلاثة في ثلاثة جد
+
+349
+00:38:04,300 --> 00:38:15,980
+ايش؟ سبعة وعشرين طيب ثلاثة أس سبعة عبارة عن ايش؟
+
+350
+00:38:17,340 --> 00:38:23,800
+ثلاثة في نفسها كم مرة؟
+
+351
+00:38:23,800 --> 00:38:27,240
+شيل
+
+352
+00:38:27,240 --> 00:38:35,040
+منها الخمسينات كم هيبقى؟ 2187 هيبقى
+
+353
+00:38:35,040 --> 00:38:43,800
+37 شيل الخمسينات طيب ثلاثة أس تسعة عبارة
+
+354
+00:38:43,800 --> 00:38:44,380
+عن مين؟
+
+355
+00:38:51,300 --> 00:39:08,360
+اضرب ثلاثة في ثلاثة في سبعة و ثلاثين ثلاثة
+
+356
+00:39:08,360 --> 00:39:13,440
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+357
+00:39:13,440 --> 00:39:13,600
+ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة ثلاثة
+
+358
+00:39:13,600 --> 00:39:19,440
+ثلاثة هيبقى ثلاثة و ثلاثين بقى
+
+359
+00:39:19,440 --> 00:39:26,200
+لعندي كمان أربعة عناصر ثلاثة أس أحد عشر أقرب عن تسعة
+
+360
+00:39:26,200 --> 00:39:35,480
+في ثلاثة و ثلاثين كم؟ 297 شيل
+
+361
+00:39:35,480 --> 00:39:45,050
+الخمسينات 47 ثلاثة أس ثلاثة عشر أقرب عن تسعة في سبعة
+
+362
+00:39:45,050 --> 00:39:54,150
+و أربعين كم يا شباب؟ 433 هيبقى
+
+363
+00:39:54,150 --> 00:40:01,750
+ثلاثة و عشرين ثلاثة أس سبعة عشر عبارة عن واحد و
+
+364
+00:40:01,750 --> 00:40:10,310
+ثمانين في ثلاثة و عشرين كم؟ شيل
+
+365
+00:40:10,310 --> 00:40:18,840
+ال ..ألف وثمانية و ثلاثين و ستين ثلاثة عشر أخر حاجة
+
+366
+00:40:18,840 --> 00:40:24,460
+ثلاثة أس تسعة عشر عبارة عن تسعة في ثلاثة عشر تسعة في
+
+367
+00:40:24,460 --> 00:40:32,400
+ثلاثة عشر كم؟ 177 هيبقى 7 عشر يكبر the
+
+368
+00:40:32,400 --> 00:40:36,840
+generators of
+
+369
+00:40:36,840 --> 00:40:46,130
+U50 اه ابدأ ثلاثة سبعة و عشرين سبعة و ثلاثين
+
+370
+00:40:46,130 --> 00:40:49,210
+ثلاثة
+
+371
+00:40:49,210 --> 00:40:57,450
+و ثلاثين سبعة و أربعين ثلاثة و عشرين ثلاثة عشر سبعة
+
+372
+00:40:57,450 --> 00:41:03,330
+واحد تمانية
+
+373
+00:41:03,330 --> 00:41:08,150
+generators هناخد
+
+374
+00:41:08,150 --> 00:41:15,040
+نظرية قدام إن لو كانت عندك group ال order لها n و
+
+375
+00:41:15,040 --> 00:41:20,480
+ال Cyclic فعدد ال generator بيساوي فاي n اللي 
+
+376
+00:41:20,480 --> 00:41:29,780
+فاي بقى عن الإغلاق فاي function أنا مغاري طيب
+
+377
+00:41:29,780 --> 00:41:34,800
+ايش المشكلة طيب
+
+378
+00:41:34,800 --> 00:41:37,380
+ايش المشكلة طيب ايش المشكلة طيب ايش المشكلة طيب
+
+379
+00:41:37,380 --> 00:41:40,700
+ايش المشكلة؟ ماشي المشكلة يا عزيزي؟ المشكلة هي أن في
+
+380
+00:41:40,700 --> 00:41:44,040
+كمان واحد مليون وخمسين يقول الصحابي .. وقول في خلل
+
+381
+00:41:44,040 --> 00:41:48,280
+في الحساب هنا فقط واحد مفروض .. واحد مفروض سبعة
+
+382
+00:41:48,280 --> 00:41:57,580
+عشر هذا هو .. هذي سبعة عشر مش سبعة كلامك
+
+383
+00:41:57,580 --> 00:42:06,260
+صحيح أي سؤال ثاني يا شباب؟ أي معلومة ثانية مطلوبة؟
+
+384
+00:42:06,260 --> 00:42:13,930
+أي نقطة مش مفهومة في الدرس اليوم؟ فضلاً .. .. .. ..
+
+385
+00:42:13,930 --> 00:42:19,710
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+386
+00:42:19,710 --> 00:42:21,130
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+387
+00:42:21,130 --> 00:42:25,090
+.. .. .. .. ..
+
+388
+00:42:25,090 --> 00:42:25,870
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+389
+00:42:25,870 --> 00:42:25,890
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+390
+00:42:25,890 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+391
+00:42:26,650 --> 00:42:27,070
+.. .. .. .. .. .. ..
+
+392
+00:42:37,660 --> 00:42:41,440
+الـ groups نظرية أربعة ثلاثة طبعا طويلة شوية هي
+
+393
+00:42:41,440 --> 00:42:48,420
+ثلاثة أفرع هناخد فيها أن كل subgroup من cyclic
+
+394
+00:42:48,420 --> 00:42:55,920
+group هتكون cyclic هناخد علاقة ل .. لو كان عندي ال
+
+395
+00:42:55,920 --> 00:43:02,120
+cyclic subgroup ال generator تبعه ايش تفاصيله شغلة
+
+396
+00:43:02,120 --> 00:43:06,410
+ثالثة طبعا هنجي تقولنا أن ال order لو كان عندي
+
+397
+00:43:06,410 --> 00:43:10,330
+subgroup من cyclic فهي cyclic هنتبه أن ال order
+
+398
+00:43:10,330 --> 00:43:14,930
+اللي هيقسم ال order لل group لو كان finite والعكس
+
+399
+00:43:14,930 --> 00:43:18,990
+أن لو كان عندي قاسم ل order ل group فانا بقدر
+
+400
+00:43:18,990 --> 00:43:23,590
+ألاقي subgroup لها نفس ال order هتطول شوية معنى
+
+401
+00:43:23,590 --> 00:43:28,690
+النظرية يعني هناخدها في المحاضرة القادمة تفضل
+
+402
+00:43:31,020 --> 00:43:36,880
+الخمسين جيبنا ال order قبل نشوف جيبنا أن التلاتة
+
+403
+00:43:36,880 --> 00:43:41,540
+مولد ل ال U خمسين بعدين إذا جيبنا ال MK اللي بتكون ال
+
+404
+00:43:41,540 --> 00:43:45,140
+.. ال bride مع ال order ل ال U خمسين اه مش .. مش ل
+
+405
+00:43:45,140 --> 00:43:48,940
+الخمسين بس جيبنا ال MK بالظبط بعدين برفع التلاتة لها
+
+406
+00:43:48,940 --> 00:43:51,760
+عشان تعطينا ال U خمسين بالظبط بس لازم في الأول
+
+407
+00:43:51,760 --> 00:43:56,410
+اجيبه جيب generator .. أنا لو ايش .. ايش سفدت لو
+
+408
+00:43:56,410 --> 00:43:58,410
+جيبت relative ل Brian مع ال order و أنا ما فيش عندي
+
+409
+00:43:58,410 --> 00:44:02,590
+generator؟ يمكن ما تكونش Cyclic أصلا طب السؤال إذا
+
+410
+00:44:02,590 --> 00:44:07,510
+أجيبش السبع عشر in versus .. هي موجودة السبع عشر
+
+411
+00:44:07,510 --> 00:44:10,790
+.. مين ال .. اللي جنبك توي سألته أنا فاهم .. يعني
+
+412
+00:44:10,790 --> 00:44:13,430
+لو أنت عاملت مع السبع عشر طب أنت قاعد تجيب التلاتة
+
+413
+00:44:13,430 --> 00:44:17,960
+و السبع عشر و الباقية ال جيب اثنين و ال ستة .. و
+
+414
+00:44:17,960 --> 00:44:21,100
+على الأقل اثنين عشان تجرب الساعة تبدأ بك واحد
+
+415
+00:44:21,100 --> 00:44:24,000
+generator عشان تكون .. هل جيتك .. تبدأ كل المولدات
+
+416
+00:44:24,000 --> 00:44:27,420
+يعني .. بلأ معايا أنت عشان تثبت أن ال group cyclic
+
+417
+00:44:27,420 --> 00:44:31,660
+بيكفيك generator واحد مش دور ال جيب اثنين هذي
+
+418
+00:44:31,660 --> 00:44:33,520
+الشغلة، الشغلة الثانية ليش ما شغلناش على السبع
+
+419
+00:44:33,520 --> 00:44:37,680
+عشر؟ مين أسهل؟ تضرب التلتات ولا تضرب السبع عشر ات؟
+
+420
+00:44:37,680 --> 00:44:41,640
+تلتات أو تلتات .. بالظبط يعطيكم العافية، تكمل
+
+421
+00:44:41,640 --> 00:44:42,480
+محاضرة جاهزة الله 
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..23a06f336bee3d09899c3a6100d93692b1be4268
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4141, "start": 21.21, "end": 41.41, "text": "بسم الله الرحمن الرحيم السلام عليكم يا شباب ان شاء الله اليوم هناخد الجزء التاني من محاضرات خاصة بالوحدة الرابعة اللي بنتكلم فيها عن ال cyclic subgroups أو ال cyclic groups اللي كان معانا المحاضرة الماضية بيتذكر انه بدأنا في شغلات تتعلق بتعميم", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 21136, 37440, 25894, 24793, 35186, 13412, 3555, 16758, 16472, 13412, 16606, 21984, 45595, 20498, 8032, 1863, 47283, 3215, 25724, 11622, 38207, 16712, 7649, 1829, 9154, 3714, 5016, 46958, 2288, 9307, 16490, 33546, 3660, 20666, 2407, 24401, 3660, 34892, 16758, 27884, 13672, 1829, 44945, 2655, 4117, 19528, 8978, 11296, 18871, 2423, 38154, 1050, 1422, 17377, 82, 34051, 2423, 38154, 1050, 3935, 13672, 1829, 25961, 20449, 7649, 995, 9673, 5016, 46958, 25720, 9673, 46958, 10632, 4724, 36081, 8848, 37983, 16472, 3224, 47525, 10721, 8315, 8978, 13412, 17082, 1211, 9307, 6055, 2655, 30241, 4587, 39894, 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أن أي Cyclic group ال order لها مالة نهاية هي عبارة عن كوبي من ال Z أيضا اتكلمنا عن ال Cyclic groups ال finite اللي نشملها تحت إطار ال ZN", "tokens": [10721, 2655, 4117, 19528, 8315, 18871, 16712, 3615, 16572, 5172, 5551, 9778, 3215, 8315, 5551, 8592, 3224, 2288, 5551, 2304, 12984, 37977, 10295, 66, 1050, 1594, 8608, 2407, 16606, 25961, 2655, 2423, 13785, 31439, 9673, 2655, 30241, 28671, 20666, 1176, 2423, 7649, 2655, 7435, 2288, 11622, 6055, 33753, 6225, 42213, 47395, 25724, 10943, 27884, 8032, 1863, 4117, 2655, 8592, 5172, 20193, 5016, 4587, 995, 14739, 36632, 10295, 66, 1050, 1594, 2423, 1668, 5296, 11296, 3714, 6027, 3660, 8717, 11296, 10632, 39896, 6225, 3555, 9640, 3660, 18871, 9122, 37746, 1829, 9154, 2423, 1176, 36632, 11242, 995, 1975, 2655, 4117, 19528, 8315, 18871, 2423, 10295, 66, 1050, 3935, 2423, 19362, 13672, 1829, 8717, 8592, 42213, 11296, 6055, 33753, 11933, 9566, 9640, 2423, 1176, 45], "avg_logprob": -0.25558944397825534, "compression_ratio": 1.7096774193548387, 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327.75, "end": 327.97, "word": " ال", "probability": 0.86376953125}, {"start": 327.97, "end": 328.19, "word": " K", "probability": 0.9287109375}, {"start": 328.19, "end": 330.97, "word": " دي", "probability": 0.80078125}, {"start": 330.97, "end": 331.31, "word": " تقسم", "probability": 0.98583984375}, {"start": 331.31, "end": 331.49, "word": " ال", "probability": 0.95751953125}, {"start": 331.49, "end": 331.71, "word": " N", "probability": 0.9697265625}, {"start": 331.71, "end": 332.55, "word": " و", "probability": 0.943359375}, {"start": 332.55, "end": 332.91, "word": " دي", "probability": 0.928955078125}, {"start": 332.91, "end": 334.05, "word": " هتقسم", "probability": 0.79791259765625}, {"start": 334.05, "end": 334.43, "word": " ال", "probability": 0.8896484375}, {"start": 334.43, "end": 334.63, "word": " K", "probability": 0.97216796875}, {"start": 334.63, "end": 335.37, "word": " أيضا", "probability": 0.91650390625}, {"start": 335.37, "end": 341.57, "word": " نشتغل", "probability": 0.928125}, {"start": 341.57, "end": 341.95, "word": " على", "probability": 0.9208984375}, {"start": 341.95, "end": 342.39, "word": " دي", "probability": 0.847900390625}, {"start": 342.39, "end": 342.77, "word": " تقسم", "probability": 0.9903971354166666}, {"start": 342.77, "end": 342.93, "word": " ال", "probability": 0.96826171875}, {"start": 342.93, "end": 343.15, "word": " N", "probability": 0.982421875}, {"start": 343.15, "end": 343.75, "word": " يعني", "probability": 0.834716796875}, {"start": 343.75, "end": 343.89, "word": " ال", "probability": 0.349853515625}, {"start": 343.89, "end": 344.09, "word": " D", "probability": 0.90576171875}, {"start": 344.09, "end": 345.19, "word": " أو", "probability": 0.86865234375}, {"start": 345.19, "end": 345.63, "word": " N", "probability": 0.525390625}, {"start": 345.63, "end": 346.55, "word": " بدت", "probability": 0.43316650390625}, {"start": 346.55, "end": 346.91, "word": " ساوة", "probability": 0.77789306640625}, {"start": 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عنصر موجود هنا؟ هلاحظ التالي ان ال a to k عبارة عن ايش؟ عن a to dr اللي هو عبارة عن مين؟ عن a to d to r وهذا عنصر موجود هذا عنصر موجود", "tokens": [4117, 33911, 4724, 16254, 5551, 12984, 3555, 2655, 23758, 2423, 28820, 10943, 22807, 9122, 33911, 4724, 16254, 5551, 12984, 3555, 2655, 16472, 3224, 28242, 18871, 9381, 2288, 34105, 31439, 18871, 9381, 2288, 3714, 29245, 23328, 34105, 22807, 8032, 15040, 5016, 19913, 16712, 6027, 1829, 16472, 2423, 257, 281, 350, 6225, 3555, 9640, 3660, 18871, 1975, 1829, 8592, 22807, 18871, 257, 281, 1224, 13672, 1829, 31439, 6225, 3555, 9640, 3660, 18871, 3714, 9957, 22807, 18871, 257, 281, 274, 281, 367, 37037, 15730, 18871, 9381, 2288, 3714, 29245, 23328, 23758, 18871, 9381, 2288, 3714, 29245, 23328], "avg_logprob": -0.1344572415477351, "compression_ratio": 2.0, "no_speech_prob": 0.0, "words": [{"start": 355.99, "end": 356.41, "word": "كيف", "probability": 0.9384765625}, {"start": 356.41, "end": 356.67, "word": " بدي", "probability": 0.724853515625}, 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"probability": 0.85791015625}, {"start": 371.45, "end": 371.89, "word": " a", "probability": 0.9560546875}, {"start": 371.89, "end": 372.95, "word": " to", "probability": 0.955078125}, {"start": 372.95, "end": 373.45, "word": " dr", "probability": 0.642578125}, {"start": 373.45, "end": 374.99, "word": " اللي", "probability": 0.95458984375}, {"start": 374.99, "end": 375.11, "word": " هو", "probability": 0.705078125}, {"start": 375.11, "end": 375.43, "word": " عبارة", "probability": 0.9971923828125}, {"start": 375.43, "end": 375.61, "word": " عن", "probability": 0.98779296875}, {"start": 375.61, "end": 376.87, "word": " مين؟", "probability": 0.92236328125}, {"start": 376.87, "end": 377.11, "word": " عن", "probability": 0.93310546875}, {"start": 377.11, "end": 377.43, "word": " a", "probability": 0.98681640625}, {"start": 377.43, "end": 377.59, "word": " to", "probability": 0.98486328125}, {"start": 377.59, "end": 377.95, "word": " d", "probability": 0.9921875}, {"start": 377.95, "end": 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"probability": 0.96923828125}, {"start": 787.55, "end": 787.95, "word": " N", "probability": 0.99267578125}, {"start": 787.95, "end": 788.97, "word": " بدي", "probability": 0.4803466796875}, {"start": 788.97, "end": 789.23, "word": " تساوي", "probability": 0.79876708984375}, {"start": 789.23, "end": 789.33, "word": " ال", "probability": 0.96728515625}, {"start": 789.33, "end": 789.81, "word": " identity", "probability": 0.7744140625}, {"start": 789.81, "end": 791.09, "word": " وبالتالي", "probability": 0.94638671875}, {"start": 791.09, "end": 791.45, "word": " A", "probability": 0.95947265625}, {"start": 791.45, "end": 791.63, "word": " to", "probability": 0.9755859375}, {"start": 791.63, "end": 791.95, "word": " D", "probability": 0.9970703125}, {"start": 791.95, "end": 793.15, "word": " أُس", "probability": 0.9759114583333334}, {"start": 793.15, "end": 793.53, "word": " T", "probability": 0.98779296875}, {"start": 793.53, "end": 794.97, "word": " بيعطيني", "probability": 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"probability": 0.91650390625}, {"start": 850.3, "end": 850.62, "word": " لإن", "probability": 0.7837727864583334}, {"start": 850.62, "end": 850.78, "word": " ال", "probability": 0.84033203125}, {"start": 850.78, "end": 851.12, "word": " order", "probability": 0.94189453125}, {"start": 851.12, "end": 851.48, "word": " لل", "probability": 0.6640625}, {"start": 851.48, "end": 851.86, "word": " A", "probability": 0.8310546875}, {"start": 851.86, "end": 853.38, "word": " بساوي", "probability": 0.904052734375}, {"start": 853.38, "end": 853.48, "word": " ال", "probability": 0.86865234375}, {"start": 853.48, "end": 853.68, "word": " N", "probability": 0.95849609375}, {"start": 853.68, "end": 854.54, "word": " but", "probability": 0.6396484375}], "temperature": 1.0}, {"id": 31, "seek": 87637, "start": 856.57, "end": 876.37, "text": "I أقل من ال T ليه بتساوي N على D D I أقل من ال N إيش في بين الجمعتين هدول ال N أقل أو يساوي D I و ال D I أقل من مين من ال N صحيح عندك تناقض", "tokens": [40, 5551, 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{"start": 1165.68, "end": 1168.26, "word": " بتساوي", "probability": 0.6466064453125}, {"start": 1168.26, "end": 1168.88, "word": " generated", "probability": 0.73779296875}, {"start": 1168.88, "end": 1169.18, "word": " by", "probability": 0.9814453125}, {"start": 1169.18, "end": 1169.42, "word": " a", "probability": 0.978515625}, {"start": 1169.42, "end": 1169.58, "word": " to", "probability": 0.9775390625}, {"start": 1169.58, "end": 1169.94, "word": " j", "probability": 0.9384765625}, {"start": 1169.94, "end": 1170.84, "word": " if", "probability": 0.8505859375}, {"start": 1170.84, "end": 1171.14, "word": " and", "probability": 0.94873046875}, {"start": 1171.14, "end": 1171.52, "word": " only", "probability": 0.91162109375}, {"start": 1171.52, "end": 1171.78, "word": " if", "probability": 0.98046875}, {"start": 1171.78, "end": 1172.36, "word": " لجريس", "probability": 0.651611328125}, {"start": 1172.36, "end": 1172.62, "word": " common", "probability": 0.7255859375}, {"start": 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"end": 1467.5, "word": " let", "probability": 0.49072265625}, {"start": 1467.5, "end": 1468.78, "word": " J", "probability": 0.75439453125}, {"start": 1468.78, "end": 1469.88, "word": " generated", "probability": 0.8388671875}, {"start": 1469.88, "end": 1470.24, "word": " by", "probability": 0.98828125}, {"start": 1470.24, "end": 1470.54, "word": " A", "probability": 0.98828125}], "temperature": 1.0}, {"id": 55, "seek": 149914, "start": 1477.64, "end": 1499.14, "text": "الـ j بتكون generated by a to k if and only if لجريست common divisor ل n و k بده يساوي الواحد proof بعدها دي سهل هيتمل الكورلر اللي جابلها", "tokens": [6027, 39184, 361, 39894, 30544, 10833, 538, 257, 281, 350, 498, 293, 787, 498, 5296, 7435, 16572, 14851, 2689, 25974, 284, 5296, 297, 4032, 350, 47525, 3224, 7251, 3794, 995, 45865, 2423, 14407, 24401, 8177, 39182, 11296, 11778, 1829, 8608, 3224, 1211, 39896, 39237, 1211, 33251, 13063, 1211, 2288, 13672, 1829, 10874, 16758, 1211, 11296], "avg_logprob": -0.3275669738650322, "compression_ratio": 1.2987012987012987, "no_speech_prob": 0.0, "words": [{"start": 1477.64, "end": 1478.0, "word": "الـ", "probability": 0.87548828125}, {"start": 1478.0, "end": 1478.26, "word": " j", "probability": 0.36962890625}, {"start": 1478.26, "end": 1479.28, "word": " بتكون", "probability": 0.8203125}, {"start": 1479.28, "end": 1479.76, "word": " generated", "probability": 0.5419921875}, {"start": 1479.76, "end": 1480.08, "word": " by", "probability": 0.818359375}, {"start": 1480.08, "end": 1480.4, "word": " a", "probability": 0.810546875}, {"start": 1480.4, "end": 1480.54, "word": " to", "probability": 0.53271484375}, {"start": 1480.54, "end": 1480.96, "word": " k", "probability": 0.97412109375}, {"start": 1480.96, "end": 1481.96, "word": " if", "probability": 0.81005859375}, {"start": 1481.96, "end": 1482.3, "word": " and", "probability": 0.919921875}, {"start": 1482.3, "end": 1482.64, "word": " only", "probability": 0.9140625}, {"start": 1482.64, "end": 1483.1, "word": " if", "probability": 0.970703125}, {"start": 1483.1, "end": 1484.5, "word": " لجريست", "probability": 0.62286376953125}, {"start": 1484.5, "end": 1485.04, "word": " common", "probability": 0.9248046875}, {"start": 1485.04, "end": 1485.96, "word": " divisor", "probability": 0.865478515625}, {"start": 1485.96, "end": 1487.24, "word": " ل", "probability": 0.943359375}, {"start": 1487.24, "end": 1487.58, "word": " n", "probability": 0.35693359375}, {"start": 1487.58, "end": 1488.14, "word": " و", "probability": 0.96484375}, {"start": 1488.14, "end": 1488.6, "word": " k", "probability": 0.677734375}, {"start": 1488.6, "end": 1490.24, "word": " بده", "probability": 0.3511962890625}, {"start": 1490.24, "end": 1490.5, "word": " يساوي", "probability": 0.8936767578125}, {"start": 1490.5, "end": 1490.98, "word": " الواحد", "probability": 0.8738606770833334}, {"start": 1490.98, "end": 1493.22, "word": " proof", "probability": 0.413818359375}, {"start": 1493.22, "end": 1497.24, "word": " بعدها", "probability": 0.42437744140625}, {"start": 1497.24, "end": 1497.38, "word": " دي", "probability": 0.68359375}, {"start": 1497.38, "end": 1497.66, "word": " سهل", "probability": 0.9925130208333334}, {"start": 1497.66, "end": 1498.14, "word": " هيتمل", "probability": 0.649169921875}, {"start": 1498.14, "end": 1498.58, "word": " الكورلر", "probability": 0.793701171875}, {"start": 1498.58, "end": 1498.72, "word": " اللي", "probability": 0.89501953125}, {"start": 1498.72, "end": 1499.14, "word": " جابلها", "probability": 0.789794921875}], "temperature": 1.0}, {"id": 56, "seek": 153243, "start": 1504.47, "end": 1532.43, "text": "الـ j بيساوي generated by a to k if and only if generated by a بيساوي generated by a to k ليش؟ ليش؟ لأن الـ j generated by a شيل الـ j و حط مدلة generated by a هذا الكلام ماقدش يكون صحيح if and only if لجريس common divisor لان", "tokens": [6027, 39184, 361, 4724, 1829, 3794, 995, 45865, 10833, 538, 257, 281, 350, 498, 293, 787, 498, 10833, 538, 257, 4724, 1829, 3794, 995, 45865, 10833, 538, 257, 281, 350, 32239, 8592, 22807, 32239, 8592, 22807, 5296, 33456, 2423, 39184, 361, 10833, 538, 257, 13412, 26895, 2423, 39184, 361, 4032, 11331, 9566, 3714, 3215, 37977, 10833, 538, 257, 23758, 2423, 28820, 10943, 19446, 28543, 8592, 7251, 30544, 20328, 5016, 1829, 5016, 498, 293, 787, 498, 5296, 7435, 16572, 3794, 2689, 25974, 284, 5296, 7649], "avg_logprob": -0.25551470307742846, "compression_ratio": 1.7951807228915662, "no_speech_prob": 0.0, "words": [{"start": 1504.47, "end": 1505.15, "word": "الـ", "probability": 0.64208984375}, {"start": 1505.15, "end": 1505.27, "word": " j", "probability": 0.1392822265625}, {"start": 1505.27, "end": 1505.71, "word": " بيساوي", "probability": 0.664306640625}, {"start": 1505.71, "end": 1506.21, "word": " generated", "probability": 0.7783203125}, {"start": 1506.21, "end": 1506.49, "word": " by", "probability": 0.9521484375}, {"start": 1506.49, "end": 1506.77, "word": " a", "probability": 0.83984375}, {"start": 1506.77, "end": 1506.91, "word": " to", "probability": 0.78466796875}, {"start": 1506.91, "end": 1507.17, "word": " k", "probability": 0.9599609375}, {"start": 1507.17, "end": 1508.31, "word": " if", "probability": 0.73388671875}, {"start": 1508.31, "end": 1508.75, "word": " and", "probability": 0.95703125}, {"start": 1508.75, "end": 1509.09, "word": " only", "probability": 0.89501953125}, {"start": 1509.09, "end": 1509.47, "word": " if", "probability": 0.9765625}, {"start": 1509.47, "end": 1511.67, "word": " generated", "probability": 0.73828125}, {"start": 1511.67, "end": 1512.15, "word": " by", "probability": 0.9853515625}, {"start": 1512.15, "end": 1512.59, "word": " a", "probability": 0.97314453125}, {"start": 1512.59, "end": 1513.65, "word": " بيساوي", "probability": 0.94248046875}, {"start": 1513.65, "end": 1514.19, "word": " generated", "probability": 0.890625}, {"start": 1514.19, "end": 1514.53, "word": " by", "probability": 0.984375}, {"start": 1514.53, "end": 1514.81, "word": " a", "probability": 0.9931640625}, {"start": 1514.81, "end": 1514.93, "word": " to", "probability": 0.9140625}, {"start": 1514.93, "end": 1515.19, "word": " k", "probability": 0.98291015625}, {"start": 1515.19, "end": 1517.05, "word": " ليش؟", "probability": 0.6759440104166666}, {"start": 1517.05, "end": 1519.45, "word": " ليش؟", "probability": 0.807373046875}, {"start": 1519.45, "end": 1519.71, "word": " لأن", "probability": 0.812744140625}, {"start": 1519.71, "end": 1519.89, "word": " الـ", "probability": 0.812255859375}, {"start": 1519.89, "end": 1519.99, "word": " j", "probability": 0.67431640625}, {"start": 1519.99, "end": 1520.43, "word": " generated", "probability": 0.51416015625}, {"start": 1520.43, "end": 1520.73, "word": " by", "probability": 0.990234375}, {"start": 1520.73, "end": 1521.05, "word": " a", "probability": 0.9892578125}, {"start": 1521.05, "end": 1522.19, "word": " شيل", "probability": 0.795654296875}, {"start": 1522.19, "end": 1522.39, "word": " الـ", "probability": 0.814697265625}, {"start": 1522.39, "end": 1522.53, "word": " j", "probability": 0.7666015625}, {"start": 1522.53, "end": 1522.71, "word": " و", "probability": 0.93359375}, {"start": 1522.71, "end": 1523.09, "word": " حط", "probability": 0.6766357421875}, {"start": 1523.09, "end": 1523.41, "word": " مدلة", "probability": 0.8271484375}, {"start": 1523.41, "end": 1523.99, "word": " generated", "probability": 0.88037109375}, {"start": 1523.99, "end": 1525.59, "word": " by", "probability": 0.92138671875}, {"start": 1525.59, "end": 1525.85, "word": " a", "probability": 0.99072265625}, {"start": 1525.85, "end": 1526.51, "word": " هذا", "probability": 0.76806640625}, {"start": 1526.51, "end": 1526.83, "word": " الكلام", "probability": 0.9064127604166666}, {"start": 1526.83, "end": 1527.11, "word": " ماقدش", "probability": 0.6142171223958334}, {"start": 1527.11, "end": 1527.35, "word": " يكون", "probability": 0.81298828125}, {"start": 1527.35, "end": 1527.89, "word": " صحيح", "probability": 0.9951171875}, {"start": 1527.89, "end": 1528.89, "word": " if", "probability": 0.9140625}, {"start": 1528.89, "end": 1529.23, "word": " and", "probability": 0.966796875}, {"start": 1529.23, "end": 1529.55, "word": " only", "probability": 0.91845703125}, {"start": 1529.55, "end": 1529.75, "word": " if", "probability": 0.96630859375}, {"start": 1529.75, "end": 1530.25, "word": " لجريس", "probability": 0.50225830078125}, {"start": 1530.25, "end": 1530.51, "word": " common", "probability": 0.413330078125}, {"start": 1530.51, "end": 1531.83, "word": " divisor", "probability": 0.956787109375}, {"start": 1531.83, "end": 1532.43, "word": " لان", "probability": 0.87109375}], "temperature": 1.0}, {"id": 57, "seek": 156203, "start": 1533.83, "end": 1562.03, "text": "و 1 طبعا انا المفترض اضيف الجملة هذه with order لل A بدي ساوي ال N if and only if ال G is common divisor ل N و 1 بيساوي ال G is common divisor ل N و K ما هو A to 1 و A to K ال 1 I و ال K احطها J و اطبق القاعدة هذه", "tokens": [2407, 502, 23032, 3555, 3615, 995, 1975, 8315, 9673, 5172, 2655, 43042, 1975, 11242, 33911, 25724, 2304, 37977, 29538, 365, 1668, 24976, 316, 4724, 16254, 8608, 995, 45865, 2423, 426, 498, 293, 787, 498, 2423, 460, 307, 2689, 25974, 284, 5296, 426, 4032, 502, 4724, 1829, 3794, 995, 45865, 2423, 460, 307, 2689, 25974, 284, 5296, 426, 4032, 591, 19446, 31439, 316, 281, 502, 4032, 316, 281, 591, 2423, 502, 286, 4032, 2423, 591, 1975, 5016, 9566, 11296, 508, 4032, 1975, 9566, 3555, 4587, 25062, 995, 22488, 3660, 29538], "avg_logprob": -0.2998264021343655, "compression_ratio": 1.574468085106383, "no_speech_prob": 0.0, "words": [{"start": 1533.83, "end": 1534.07, "word": "و", "probability": 0.454345703125}, {"start": 1534.07, "end": 1534.57, "word": " 1", "probability": 0.316162109375}, {"start": 1534.57, "end": 1535.11, "word": " طبعا", "probability": 0.77679443359375}, {"start": 1535.11, "end": 1535.25, "word": " انا", "probability": 0.7452392578125}, {"start": 1535.25, "end": 1535.77, "word": " المفترض", "probability": 0.9503173828125}, {"start": 1535.77, "end": 1537.27, "word": " اضيف", "probability": 0.72314453125}, {"start": 1537.27, "end": 1537.71, "word": " الجملة", "probability": 0.8982747395833334}, {"start": 1537.71, "end": 1538.07, "word": " هذه", "probability": 0.493408203125}, {"start": 1538.07, "end": 1539.01, "word": " with", "probability": 0.64111328125}, {"start": 1539.01, "end": 1539.61, "word": " order", "probability": 0.9609375}, {"start": 1539.61, "end": 1539.93, "word": " لل", "probability": 0.5078125}, {"start": 1539.93, "end": 1540.31, "word": " A", "probability": 0.275634765625}, {"start": 1540.31, "end": 1541.47, "word": " بدي", "probability": 0.44561767578125}, {"start": 1541.47, "end": 1541.79, "word": " ساوي", "probability": 0.5608723958333334}, {"start": 1541.79, "end": 1541.91, "word": " ال", "probability": 0.75244140625}, {"start": 1541.91, "end": 1542.13, "word": " N", "probability": 0.81787109375}, {"start": 1542.13, "end": 1546.01, "word": " if", "probability": 0.845703125}, {"start": 1546.01, "end": 1546.29, "word": " and", "probability": 0.9599609375}, {"start": 1546.29, "end": 1546.63, "word": " only", "probability": 0.93603515625}, {"start": 1546.63, "end": 1546.83, "word": " if", "probability": 0.83935546875}, {"start": 1546.83, "end": 1546.97, "word": " ال", "probability": 0.492431640625}, {"start": 1546.97, "end": 1547.09, "word": " G", "probability": 0.58349609375}, {"start": 1547.09, "end": 1547.25, "word": " is", "probability": 0.446044921875}, {"start": 1547.25, "end": 1547.45, "word": " common", "probability": 0.787109375}, {"start": 1547.45, "end": 1548.03, "word": " divisor", "probability": 0.980712890625}, {"start": 1548.03, "end": 1548.17, "word": " ل", "probability": 0.94970703125}, {"start": 1548.17, "end": 1548.41, "word": " N", "probability": 0.51416015625}, {"start": 1548.41, "end": 1548.57, "word": " و", "probability": 0.88427734375}, {"start": 1548.57, "end": 1549.07, "word": " 1", "probability": 0.90576171875}, {"start": 1549.07, "end": 1550.11, "word": " بيساوي", "probability": 0.809375}, {"start": 1550.11, "end": 1550.27, "word": " ال", "probability": 0.6865234375}, {"start": 1550.27, "end": 1550.49, "word": " G", "probability": 0.98193359375}, {"start": 1550.49, "end": 1550.65, "word": " is", "probability": 0.865234375}, {"start": 1550.65, "end": 1550.87, "word": " common", "probability": 0.923828125}, {"start": 1550.87, "end": 1552.63, "word": " divisor", "probability": 0.95654296875}, {"start": 1552.63, "end": 1553.13, "word": " ل", "probability": 0.96484375}, {"start": 1553.13, "end": 1553.31, "word": " N", "probability": 0.93115234375}, {"start": 1553.31, "end": 1553.47, "word": " و", "probability": 0.98583984375}, {"start": 1553.47, "end": 1553.69, "word": " K", "probability": 0.90576171875}, {"start": 1553.69, "end": 1555.49, "word": " ما", "probability": 0.1099853515625}, {"start": 1555.49, "end": 1555.63, "word": " هو", "probability": 0.974609375}, {"start": 1555.63, "end": 1555.91, "word": " A", "probability": 0.8896484375}, {"start": 1555.91, "end": 1555.99, "word": " to", "probability": 0.5078125}, {"start": 1555.99, "end": 1556.33, "word": " 1", "probability": 0.890625}, {"start": 1556.33, "end": 1556.51, "word": " و", "probability": 0.947265625}, {"start": 1556.51, "end": 1556.69, "word": " A", "probability": 0.88720703125}, {"start": 1556.69, "end": 1556.79, "word": " to", "probability": 0.974609375}, {"start": 1556.79, "end": 1557.09, "word": " K", "probability": 0.97314453125}, {"start": 1557.09, "end": 1557.97, "word": " ال", "probability": 0.91064453125}, {"start": 1557.97, "end": 1558.21, "word": " 1", "probability": 0.578125}, {"start": 1558.21, "end": 1558.59, "word": " I", "probability": 0.8193359375}, {"start": 1558.59, "end": 1558.73, "word": " و", "probability": 0.8662109375}, {"start": 1558.73, "end": 1559.45, "word": " ال", "probability": 0.54052734375}, {"start": 1559.45, "end": 1559.67, "word": " K", "probability": 0.947265625}, {"start": 1559.67, "end": 1560.15, "word": " احطها", "probability": 0.7357177734375}, {"start": 1560.15, "end": 1560.41, "word": " J", "probability": 0.6201171875}, {"start": 1560.41, "end": 1560.95, "word": " و", "probability": 0.80078125}, {"start": 1560.95, "end": 1561.25, "word": " اطبق", "probability": 0.79754638671875}, {"start": 1561.25, "end": 1561.75, "word": " القاعدة", "probability": 0.98974609375}, {"start": 1561.75, "end": 1562.03, "word": " هذه", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 58, "seek": 158163, "start": 1563.15, "end": 1581.63, "text": "طيب لجيز common divisor ل n و 1 جديش؟ واحد لإن واحد بدا تساوي لجيز common divisor ل n و k يعني if and only if لجيز common divisor ل n و k بتساوي واحد", "tokens": [9566, 1829, 3555, 5296, 7435, 1829, 11622, 2689, 25974, 284, 5296, 297, 4032, 502, 10874, 16254, 8592, 22807, 36764, 24401, 5296, 28814, 1863, 36764, 24401, 4724, 28259, 6055, 3794, 995, 45865, 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1567.65, "word": " جديش؟", "probability": 0.55267333984375}, {"start": 1567.65, "end": 1568.85, "word": " واحد", "probability": 0.7091064453125}, {"start": 1568.85, "end": 1569.65, "word": " لإن", "probability": 0.5889485677083334}, {"start": 1569.65, "end": 1570.35, "word": " واحد", "probability": 0.736328125}, {"start": 1570.35, "end": 1571.95, "word": " بدا", "probability": 0.4364013671875}, {"start": 1571.95, "end": 1572.33, "word": " تساوي", "probability": 0.865966796875}, {"start": 1572.33, "end": 1572.81, "word": " لجيز", "probability": 0.93115234375}, {"start": 1572.81, "end": 1573.15, "word": " common", "probability": 0.9765625}, {"start": 1573.15, "end": 1573.81, "word": " divisor", "probability": 0.950439453125}, {"start": 1573.81, "end": 1573.99, "word": " ل", "probability": 0.97509765625}, {"start": 1573.99, "end": 1574.21, "word": " n", "probability": 0.9033203125}, {"start": 1574.21, "end": 1574.43, "word": " و", "probability": 0.966796875}, {"start": 1574.43, "end": 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تلاتة", "probability": 0.7464599609375}, {"start": 2143.68, "end": 2144.98, "word": " هل", "probability": 0.695556640625}, {"start": 2144.98, "end": 2147.16, "word": " جيت؟", "probability": 0.795166015625}, {"start": 2147.16, "end": 2147.76, "word": " وقتش", "probability": 0.725830078125}, {"start": 2147.76, "end": 2147.9, "word": " ال", "probability": 0.94775390625}, {"start": 2147.9, "end": 2148.7, "word": " U50", "probability": 0.968994140625}, {"start": 2148.7, "end": 2149.12, "word": " بتكون", "probability": 0.974609375}, {"start": 2149.12, "end": 2149.64, "word": " generated", "probability": 0.85205078125}, {"start": 2149.64, "end": 2149.96, "word": " by", "probability": 0.94921875}, {"start": 2149.96, "end": 2150.54, "word": " عنصر", "probability": 0.935546875}, {"start": 2150.54, "end": 2151.92, "word": " تاني", "probability": 0.9671223958333334}, {"start": 2151.92, "end": 2153.8, "word": " power", "probability": 0.45458984375}, {"start": 2153.8, "end": 2155.0, "word": " للتلاتة", "probability": 0.8931640625}, {"start": 2155.0, "end": 2156.28, "word": " لما", "probability": 0.84912109375}, {"start": 2156.28, "end": 2156.5, "word": " يكون", "probability": 0.9921875}, {"start": 2156.5, "end": 2156.66, "word": " ال", "probability": 0.986328125}, {"start": 2156.66, "end": 2156.94, "word": " power", "probability": 0.837890625}, {"start": 2156.94, "end": 2157.5, "word": " هذا", "probability": 0.7314453125}, {"start": 2157.5, "end": 2158.52, "word": " relative", "probability": 0.93994140625}, {"start": 2158.52, "end": 2158.8, "word": " ال", "probability": 0.3671875}, {"start": 2158.8, "end": 2159.06, "word": " prime", "probability": 0.50927734375}, {"start": 2159.06, "end": 2159.26, "word": " مع", "probability": 0.939453125}, {"start": 2159.26, "end": 2159.88, "word": " مين؟", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 78, "seek": 219173, "start": 2163.12, "end": 2191.74, "text": "مع ال order ل ال U50 مش مع الخمسين قطوة تالتة since ال U50 generated by تلاتة then ال U50 generated by تلاتة أُس K if and only if لجريس كومون Divisor لل order ل U50", "tokens": [2304, 3615, 2423, 1668, 5296, 2423, 624, 2803, 37893, 20449, 33962, 2304, 3794, 9957, 12174, 9566, 2407, 3660, 6055, 6027, 2655, 3660, 1670, 2423, 624, 2803, 10833, 538, 6055, 1211, 9307, 3660, 550, 2423, 624, 2803, 10833, 538, 6055, 1211, 9307, 3660, 5551, 10859, 3794, 591, 498, 293, 787, 498, 5296, 7435, 16572, 3794, 9122, 20498, 11536, 9886, 271, 284, 5296, 1211, 1668, 5296, 624, 2803], "avg_logprob": -0.33535446604686, "compression_ratio": 1.4350649350649352, "no_speech_prob": 0.0, "words": [{"start": 2163.12, "end": 2163.44, "word": "مع", "probability": 0.7012939453125}, {"start": 2163.44, "end": 2163.6, "word": " ال", "probability": 0.736328125}, {"start": 2163.6, "end": 2164.16, "word": " order", "probability": 0.7900390625}, {"start": 2164.16, "end": 2164.4, "word": " ل", "probability": 0.6552734375}, {"start": 2164.4, "end": 2164.5, "word": " ال", "probability": 0.433837890625}, {"start": 2164.5, "end": 2165.0, "word": " U50", "probability": 0.56982421875}, {"start": 2165.0, "end": 2165.18, "word": " مش", "probability": 0.2208251953125}, {"start": 2165.18, "end": 2165.32, "word": " مع", "probability": 0.849609375}, {"start": 2165.32, "end": 2165.82, "word": " الخمسين", "probability": 0.84759521484375}, {"start": 2165.82, "end": 2167.82, "word": " قطوة", "probability": 0.67498779296875}, {"start": 2167.82, "end": 2169.3, "word": " تالتة", "probability": 0.8822021484375}, {"start": 2169.3, "end": 2171.28, "word": " since", "probability": 0.473388671875}, {"start": 2171.28, "end": 2173.98, "word": " ال", "probability": 0.80810546875}, {"start": 2173.98, "end": 2174.96, "word": " U50", "probability": 0.945556640625}, {"start": 2174.96, "end": 2177.0, "word": " generated", "probability": 0.7587890625}, {"start": 2177.0, "end": 2177.34, "word": " by", "probability": 0.95458984375}, {"start": 2177.34, "end": 2178.0, "word": " تلاتة", "probability": 0.8519287109375}, {"start": 2178.0, "end": 2178.38, "word": " then", "probability": 0.68115234375}, {"start": 2178.38, "end": 2179.64, "word": " ال", "probability": 0.90673828125}, {"start": 2179.64, "end": 2180.46, "word": " U50", "probability": 0.97802734375}, {"start": 2180.46, "end": 2181.6, "word": " generated", "probability": 0.84814453125}, {"start": 2181.6, "end": 2181.92, "word": " by", "probability": 0.98681640625}, {"start": 2181.92, "end": 2182.42, "word": " تلاتة", "probability": 0.964111328125}, {"start": 2182.42, "end": 2182.68, "word": " أُس", "probability": 0.455322265625}, {"start": 2182.68, "end": 2182.98, "word": " K", "probability": 0.80126953125}, {"start": 2182.98, "end": 2183.86, "word": " if", "probability": 0.90380859375}, {"start": 2183.86, "end": 2184.16, "word": " and", "probability": 0.95166015625}, {"start": 2184.16, "end": 2184.56, "word": " only", "probability": 0.92919921875}, {"start": 2184.56, "end": 2184.76, "word": " if", "probability": 0.9609375}, {"start": 2184.76, "end": 2185.28, "word": " لجريس", "probability": 0.7164306640625}, {"start": 2185.28, "end": 2185.56, "word": " كومون", "probability": 0.6337890625}, {"start": 2185.56, "end": 2186.98, "word": " Divisor", "probability": 0.685546875}, {"start": 2186.98, "end": 2190.28, "word": " لل", "probability": 0.4654541015625}, {"start": 2190.28, "end": 2190.68, "word": " order", "probability": 0.96630859375}, {"start": 2190.68, "end": 2190.92, "word": " ل", "probability": 0.958984375}, {"start": 2190.92, "end": 2191.74, "word": " U50", "probability": 0.963623046875}], "temperature": 1.0}, {"id": 79, "seek": 221212, "start": 2193.36, "end": 2212.12, "text": "و ال K بدي سوى واحد يعني هذا if and on if لجريمز common divisor ل ال 20 و ال K بيسوى واحد النتيجة we must find the elements", "tokens": [2407, 2423, 591, 4724, 16254, 8608, 2407, 7578, 36764, 24401, 37495, 22653, 23758, 498, 293, 322, 498, 5296, 7435, 16572, 2304, 11622, 2689, 25974, 284, 5296, 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2196.88, "end": 2197.2, "word": " and", "probability": 0.88330078125}, {"start": 2197.2, "end": 2197.54, "word": " on", "probability": 0.68701171875}, {"start": 2197.54, "end": 2197.96, "word": " if", "probability": 0.935546875}, {"start": 2197.96, "end": 2199.14, "word": " لجريمز", "probability": 0.574169921875}, {"start": 2199.14, "end": 2199.38, "word": " common", "probability": 0.6201171875}, {"start": 2199.38, "end": 2200.12, "word": " divisor", "probability": 0.96484375}, {"start": 2200.12, "end": 2200.72, "word": " ل", "probability": 0.58447265625}, {"start": 2200.72, "end": 2200.84, "word": " ال", "probability": 0.381103515625}, {"start": 2200.84, "end": 2201.32, "word": " 20", "probability": 0.62646484375}, {"start": 2201.32, "end": 2203.56, "word": " و", "probability": 0.60400390625}, {"start": 2203.56, "end": 2203.68, "word": " ال", "probability": 0.70751953125}, {"start": 2203.68, "end": 2203.82, "word": " K", "probability": 0.9228515625}, {"start": 2203.82, "end": 2204.16, "word": " بيسوى", "probability": 0.816552734375}, {"start": 2204.16, "end": 2204.58, "word": " واحد", "probability": 0.95849609375}, {"start": 2204.58, "end": 2205.8, "word": " النتيجة", "probability": 0.9246826171875}, {"start": 2205.8, "end": 2207.1, "word": " we", "probability": 0.302734375}, {"start": 2207.1, "end": 2207.96, "word": " must", "probability": 0.90869140625}, {"start": 2207.96, "end": 2209.78, "word": " find", "probability": 0.94140625}, {"start": 2209.78, "end": 2211.36, "word": " the", "probability": 0.89208984375}, {"start": 2211.36, "end": 2212.12, "word": " elements", "probability": 0.88916015625}], "temperature": 1.0}, {"id": 80, "seek": 223779, "start": 2213.59, "end": 2237.79, "text": "K أقل من العشرين أكبر ويساوي واحد with degrees common divisor العشرين وK بيساوي واحد مين هذه العناصر؟ واحد، تلاتة، سبعة، تسعة، احداشر، تلتاشر، سبعتاشر، تسعتاشر، شوية يا شباب", "tokens": [42, 5551, 4587, 1211, 9154, 18863, 46309, 9957, 5551, 4117, 26890, 4032, 1829, 3794, 995, 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"probability": 0.9069010416666666}, {"start": 2217.73, "end": 2218.19, "word": " ويساوي", "probability": 0.690380859375}, {"start": 2218.19, "end": 2218.83, "word": " واحد", "probability": 0.955322265625}, {"start": 2218.83, "end": 2219.77, "word": " with", "probability": 0.334716796875}, {"start": 2219.77, "end": 2220.75, "word": " degrees", "probability": 0.27392578125}, {"start": 2220.75, "end": 2221.05, "word": " common", "probability": 0.5302734375}, {"start": 2221.05, "end": 2221.71, "word": " divisor", "probability": 0.749267578125}, {"start": 2221.71, "end": 2222.33, "word": " العشرين", "probability": 0.8028157552083334}, {"start": 2222.33, "end": 2222.77, "word": " وK", "probability": 0.7470703125}, {"start": 2222.77, "end": 2224.01, "word": " بيساوي", "probability": 0.89306640625}, {"start": 2224.01, "end": 2224.33, "word": " واحد", "probability": 0.989501953125}, {"start": 2224.33, "end": 2225.09, "word": " مين", "probability": 0.716064453125}, {"start": 2225.09, "end": 2225.35, "word": " هذه", "probability": 0.96630859375}, {"start": 2225.35, "end": 2227.15, "word": " العناصر؟", "probability": 0.844921875}, {"start": 2227.15, "end": 2230.21, "word": " واحد،", "probability": 0.6808268229166666}, {"start": 2230.21, "end": 2231.61, "word": " تلاتة،", "probability": 0.912109375}, {"start": 2231.61, "end": 2232.87, "word": " سبعة،", "probability": 0.945556640625}, {"start": 2232.87, "end": 2233.97, "word": " تسعة،", "probability": 0.981689453125}, {"start": 2233.97, "end": 2234.67, "word": " احداشر،", "probability": 0.7814453125}, {"start": 2234.67, "end": 2235.51, "word": " تلتاشر،", "probability": 0.8978678385416666}, {"start": 2235.51, "end": 2236.09, "word": " سبعتاشر،", "probability": 0.9056803385416666}, {"start": 2236.09, "end": 2237.11, "word": " تسعتاشر،", "probability": 0.8054606119791666}, {"start": 2237.11, "end": 2237.39, "word": " شوية", "probability": 0.9422200520833334}, {"start": 2237.39, "end": 2237.59, "word": " يا", "probability": 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2657.02, "word": "ال", "probability": 0.87060546875}, {"start": 2657.02, "end": 2657.14, "word": " جيب", "probability": 0.651611328125}, {"start": 2657.14, "end": 2657.52, "word": " اثنين", "probability": 0.80859375}, {"start": 2657.52, "end": 2657.82, "word": " و", "probability": 0.51416015625}, {"start": 2657.82, "end": 2657.94, "word": " ال", "probability": 0.305419921875}, {"start": 2657.94, "end": 2657.94, "word": " ستة", "probability": 0.686767578125}, {"start": 2657.94, "end": 2657.96, "word": " ..", "probability": 0.307861328125}, {"start": 2657.96, "end": 2657.96, "word": " و", "probability": 0.45947265625}, {"start": 2657.96, "end": 2658.04, "word": " على", "probability": 0.84375}, {"start": 2658.04, "end": 2658.36, "word": " الأقل", "probability": 0.9231770833333334}, {"start": 2658.36, "end": 2658.7, "word": " اثنين", "probability": 0.8641357421875}, {"start": 2658.7, "end": 2658.9, "word": " عشان", "probability": 0.90478515625}, {"start": 2658.9, "end": 2659.12, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..4a7943dbde22bd1b144c8204510d0ac32c1df147
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vTv-S_KlsSA_raw.srt
@@ -0,0 +1,1728 @@
+1
+00:00:21,210 --> 00:00:24,770
+بسم الله الرحمن الرحيم السلام عليكم يا شباب ان شاء
+
+2
+00:00:24,770 --> 00:00:28,310
+الله اليوم هناخد الجزء التاني من محاضرات خاصة
+
+3
+00:00:28,310 --> 00:00:31,670
+بالوحدة الرابعة اللي بنتكلم فيها عن ال cyclic
+
+4
+00:00:31,670 --> 00:00:35,670
+subgroups أو ال cyclic groups اللي كان معانا
+
+5
+00:00:35,670 --> 00:00:40,110
+المحاضرة الماضية بيتذكر انه بدأنا في شغلات تتعلق
+
+6
+00:00:40,110 --> 00:00:48,750
+بتعميملتعريف درسناه في الوحدة التالتة بتعلق بتوليد
+
+7
+00:00:48,750 --> 00:00:53,710
+subgroup عن طريق أنصر ما داخل الجروب معينة بعدين
+
+8
+00:00:53,710 --> 00:00:58,530
+حاولنا ناخد هذا الكلام و نطبقه على الجروب نفسه حيث
+
+9
+00:00:58,530 --> 00:01:02,590
+نقول الجروب كلها مولدة من هذا الأنصر طلع معنا
+
+10
+00:01:02,590 --> 00:01:07,790
+تعريف ال cyclicأتكلمنا عن التعريف أخدنا أشهر أمثلة
+
+11
+00:01:07,790 --> 00:01:12,130
+Cyclic group سواء كانت ال infinite هو المتعلقة بال
+
+12
+00:01:12,130 --> 00:01:16,270
+Z الانتجرز تحت عملته الجامعة هنكتشف لاحقا أن أي
+
+13
+00:01:16,270 --> 00:01:20,790
+Cyclic group ال order لها مالة نهاية هي عبارة عن
+
+14
+00:01:20,790 --> 00:01:26,150
+كوبي من ال Z أيضا اتكلمنا عن ال Cyclic groups ال
+
+15
+00:01:26,150 --> 00:01:33,600
+finite اللي نشملها تحت إطار ال ZNبرضه لاحقا هنكتشف
+
+16
+00:01:33,600 --> 00:01:37,960
+ان اي cyclic الجروب و finite هتكون كب من some ZN
+
+17
+00:01:37,960 --> 00:01:43,640
+خدنا مثالين على UN واحدة كانت cyclic والتانية كانت
+
+18
+00:01:43,640 --> 00:01:47,060
+non أو not cyclic وبالتالي ال UN بقدرش انا اطلق
+
+19
+00:01:47,060 --> 00:01:52,440
+عليها تعميم ان ايه all UN cyclic او all UN not
+
+20
+00:01:52,440 --> 00:01:56,780
+cyclic برضه لاحقا هنفهم وقت ايش ال UN بتكون cyclic
+
+21
+00:01:56,780 --> 00:02:01,400
+ووقت ايش ال UN بتكونش not cyclicهناخد اليوم الجزء
+
+22
+00:02:01,400 --> 00:02:06,500
+التالي من النظريات المتعلقة بهذا الموضوع هنبدأ
+
+23
+00:02:06,500 --> 00:02:13,660
+بنظرية 4.2 اللى بتتكلم عن order العمصر داخل الـ
+
+24
+00:02:13,660 --> 00:02:23,780
+cyclic group theorem 4.2 طيب
+
+25
+00:02:23,780 --> 00:02:26,260
+هنبدل الجلم
+
+26
+00:02:47,340 --> 00:02:50,140
+النقطة الأولى
+
+27
+00:03:02,110 --> 00:03:07,770
+Generated by A to K هي
+
+28
+00:03:07,770 --> 00:03:14,170
+ساوي Generated by A لإن
+
+29
+00:03:14,170 --> 00:03:24,950
+و K P ال order ل A to K هي ساوي N على ال common
+
+30
+00:03:24,950 --> 00:03:28,810
+divisor لن و K
+
+31
+00:03:32,240 --> 00:03:35,540
+قبل أن ندخل في الظروف سنفهم ايش اهمية هذه النظرية
+
+32
+00:03:35,540 --> 00:03:39,740
+وماذا تقولنيها الشق
+
+33
+00:03:39,740 --> 00:03:46,460
+الأول منها يتعلق بالتالي طبعا نرجع لشغل الجي ليست
+
+34
+00:03:46,460 --> 00:03:50,000
+بضوء تكون Cyclic انا بتكلم على جزء من الجي اللي هو
+
+35
+00:03:50,000 --> 00:03:55,430
+generated by A اللي بيكون Cyclic ومش تشغل داخلهالـ
+
+36
+00:03:55,430 --> 00:03:59,670
+generated by A to K بيساوي الـ generated by A وقص
+
+37
+00:03:59,670 --> 00:04:02,030
+الـ greased common divisor لأن و K ومن المعروف أن
+
+38
+00:04:02,030 --> 00:04:05,890
+الـ greased common divisor لأن و K دائما و أبدا
+
+39
+00:04:05,890 --> 00:04:11,250
+أقل لو يساوي K الهدف هنا أنه أنا أدور على عنصر
+
+40
+00:04:11,250 --> 00:04:18,030
+القص تبعه أقل من ال K ويولد نفس ال subgroup الجزء
+
+41
+00:04:18,030 --> 00:04:23,900
+التاني ال order ل power لل A إيش علاقته؟في ال
+
+42
+00:04:23,900 --> 00:04:29,500
+order لل A نفسه هندف الاثبات للجزء الاول هقول
+
+43
+00:04:29,500 --> 00:04:34,580
+التالت جاب المعنى افوت في التفاصيل هعطي تسميات let
+
+44
+00:04:34,580 --> 00:04:42,640
+D بساوة لجريس common divisor لان و K بتحول الاثبات
+
+45
+00:04:42,640 --> 00:04:47,160
+انه انا بدي اثبت انه generated by A to K بدي اثبت
+
+46
+00:04:47,160 --> 00:04:55,690
+انه generated by A to D وش ننتقلالمفهوم لمفهوم set
+
+47
+00:04:55,690 --> 00:05:02,010
+theory نظرية مجموعات اثبت ان ال two sets ايش مالهم
+
+48
+00:05:02,010 --> 00:05:08,290
+متساويات هاخد عنصر من هنا و اثبت انه يعني كل عنصر
+
+49
+00:05:08,290 --> 00:05:13,750
+موجود هنا هثبت انه موجود هنا طبعا و العكس صحيح
+
+50
+00:05:13,750 --> 00:05:21,610
+since دي بدت ساوي للجريس common divisor لان و كيه
+
+51
+00:05:21,610 --> 00:05:27,250
+ايش اللي مقدر استفيد منه هناإن دي تقسم ال N و دي
+
+52
+00:05:27,250 --> 00:05:41,570
+تقسم ال K دي تقسم ال N و دي هتقسم ال K أيضا نشتغل
+
+53
+00:05:41,570 --> 00:05:48,550
+على دي تقسم ال N يعني ال D أو N بدت ساوة D في T و
+
+54
+00:05:48,550 --> 00:05:52,990
+ال K بدت ساوة D في R
+
+55
+00:05:55,990 --> 00:06:00,650
+كيف بدي أثبت هذا الكلام؟ كيف بدي أثبت انه كل عنصر
+
+56
+00:06:00,650 --> 00:06:08,130
+هنا هو عنصر موجود هنا؟ هلاحظ التالي ان ال a to k
+
+57
+00:06:08,130 --> 00:06:17,110
+عبارة عن ايش؟ عن a to dr اللي هو عبارة عن مين؟ عن
+
+58
+00:06:17,110 --> 00:06:25,510
+a to d to r وهذا عنصر موجود هذا عنصر موجودهذا
+
+59
+00:06:25,510 --> 00:06:32,230
+العنصر موجود في generated by a to d اش يعني يعني a
+
+60
+00:06:32,230 --> 00:06:41,110
+to k موجود وين في generated by a to d عنصر موجود
+
+61
+00:06:41,110 --> 00:06:49,190
+في group فال sub group للعنصر هذا بيولدها ويل
+
+62
+00:06:49,190 --> 00:06:55,850
+هتكونجزء من الجروب هذه وبالتالي generated by a to
+
+63
+00:06:55,850 --> 00:07:04,730
+k subset من generated by a to d و اعطيها واحدة
+
+64
+00:07:04,730 --> 00:07:09,290
+نعيد بسرعة انا حولت السؤال ل set theory نظرية
+
+65
+00:07:09,290 --> 00:07:14,450
+مجموعات بدي اثبت ان مجموعة بتساوي مجموعةبدي أستفيد
+
+66
+00:07:14,450 --> 00:07:18,850
+من خصائص أنه أنا بشغل في ال group theory لو كان
+
+67
+00:07:18,850 --> 00:07:22,090
+العنصر موجود في المجموعة فال generated من هذا
+
+68
+00:07:22,090 --> 00:07:26,770
+العنصر برضه موجود داخل ال group أخدت ال D عبارة عن
+
+69
+00:07:26,770 --> 00:07:30,110
+ال Geoscomal Divisor ل N و K ال D بتقسم ال N ال D
+
+70
+00:07:30,110 --> 00:07:35,390
+بتقسم ال K فال K عبارة عن DR ال A to K عبارة عن A
+
+71
+00:07:35,390 --> 00:07:40,530
+to DR يعني عبارة عن A to D الكل أُس R وهذا عنصر
+
+72
+00:07:40,530 --> 00:07:41,070
+موجود
+
+73
+00:08:01,470 --> 00:08:06,530
+الجزء التاني او
+
+74
+00:08:06,530 --> 00:08:12,220
+D بدأ تساوي لـ Greece Common Divisor لان و Kمعناته
+
+75
+00:08:12,220 --> 00:08:19,980
+D بيبدأ تساوي N في X زي ك في Y for some extra Y من
+
+76
+00:08:19,980 --> 00:08:27,120
+وين؟ من الـ Z number three الجريس common divisor
+
+77
+00:08:27,120 --> 00:08:33,320
+لعددين عبارة عن تركيبة خطية من مين؟ من العددين
+
+78
+00:08:33,320 --> 00:08:42,670
+هدول طيب يقبل A to Dعبارة عن a to n x زائد ky اللي
+
+79
+00:08:42,670 --> 00:08:52,810
+هو بديه يساوي a to n plus x في a to k to y ال a to
+
+80
+00:08:52,810 --> 00:09:00,750
+n ايش بيساوي ال a to n ال order ل a بيساوي n ايش
+
+81
+00:09:00,750 --> 00:09:05,010
+بقى a to n ايش بيساوي identity ايش بده عبارة عن ال
+
+82
+00:09:05,010 --> 00:09:09,450
+identity to xمش E أُس X يعني أنا متكلمش شغال احنا
+
+83
+00:09:09,450 --> 00:09:14,770
+في الجابر مش في ال calculus و A to K أُس Y اللي هو
+
+84
+00:09:14,770 --> 00:09:21,190
+عبارة عن A to K أُس Y و هذا أنص وان موجود في
+
+85
+00:09:21,190 --> 00:09:27,770
+generated by A to K لإن ال power ل A to K صار ال A
+
+86
+00:09:27,770 --> 00:09:34,190
+to D ينتمي لgenerated by A to K نفس الأسلوب اللي
+
+87
+00:09:34,190 --> 00:09:41,500
+في الأول حاسيب معاياA to D subset من generated by
+
+88
+00:09:41,500 --> 00:09:45,700
+A to K و اعطيها اتنين واحد و اتنين هيعطيني التالي
+
+89
+00:09:45,700 --> 00:09:52,640
+واحد و اتنين هيعطيني انه generated by A to D
+
+90
+00:09:52,640 --> 00:09:58,360
+بيتساوى generated by A to K طبعا هو اللي احنا
+
+91
+00:09:58,360 --> 00:10:04,220
+مطلوب نثبته واضحة
+
+92
+00:10:04,220 --> 00:10:09,610
+ولا محتاجة توضيح اخرgenerated by a to d بيساوي
+
+93
+00:10:09,610 --> 00:10:14,170
+generated by a to k وبالتالي generated by a to k
+
+94
+00:10:14,170 --> 00:10:19,630
+بيساوي generated by a لجريس common divisor ل N
+
+95
+00:10:19,630 --> 00:10:22,990
+اكتب
+
+96
+00:10:22,990 --> 00:10:29,350
+بس بسرعة E
+
+97
+00:10:29,350 --> 00:10:34,190
+أُس X مش ال A اللي أخضر يلو N فE أُس N مش بيساوي
+
+98
+00:10:35,780 --> 00:10:39,240
+أيه أسئلة مش هيساوي ال identity ال identity وس أي
+
+99
+00:10:39,240 --> 00:10:48,960
+حاجة بيبقى ال identity كيف هذه number three نظرية
+
+100
+00:10:48,960 --> 00:10:52,840
+الأعداد ال grace common divisor لأي عددين تركيبها
+
+101
+00:10:52,840 --> 00:10:56,940
+خاطية من العددين شبكة واحدة في الكتاب أو لو رجعت
+
+102
+00:10:56,940 --> 00:11:01,360
+لكتاب نظرية الأعداد موجودة في section 2 3
+
+103
+00:11:12,420 --> 00:11:18,400
+عيد عيد بس بصراحة اي اوس كي اوس واي بس هو power
+
+104
+00:11:18,400 --> 00:11:22,620
+لقيت okay؟وهو موجود في generated by a to k لأن
+
+105
+00:11:22,620 --> 00:11:27,780
+وعيش ال generated by a to k هي جميع الأسس الممكنة
+
+106
+00:11:27,780 --> 00:11:31,340
+من هذا العنصر شرحناها المحاضرة الماضية وجون ال
+
+107
+00:11:31,340 --> 00:11:35,520
+generated by a to n لو ال order لل a في a infinite
+
+108
+00:11:35,520 --> 00:11:40,040
+بيظل عبارة عن e, a, a تربية, a تكييب إلى آخره لكن
+
+109
+00:11:40,040 --> 00:11:44,260
+لو ال order finite e, a, a تربية وصولها إلى a to n
+
+110
+00:11:44,260 --> 00:11:50,210
+minus 1الجزء التاني من الاثبات يا شباب بنثبت ان ال
+
+111
+00:11:50,210 --> 00:11:55,870
+order ل a to k عبارة عن n على الجيس كومون ديفازر ل
+
+112
+00:11:55,870 --> 00:12:01,590
+n و d انا مش هبدأ ب a to k هبدأ ب a to d و اثبت ان
+
+113
+00:12:01,590 --> 00:12:06,010
+ال order ل a to d بيساوي n على d يعني الجيس كومون
+
+114
+00:12:06,010 --> 00:12:11,550
+ديفازر ل n و k و بعدين عن طريق ان هذه ال sub group
+
+115
+00:12:11,550 --> 00:12:17,590
+بتساوي هذه ال sub group فال order اللي هم واحدحسب
+
+116
+00:12:17,590 --> 00:12:20,790
+قاعدة السابقة ال order لل generator هيكون واحد
+
+117
+00:12:20,790 --> 00:12:24,010
+يكبر ال order ل a to k و ال order ل a to d
+
+118
+00:12:24,010 --> 00:12:28,630
+متساويين فلو كان ال order ل a to d بيساوي n على d
+
+119
+00:12:28,630 --> 00:12:36,990
+هصير ال order ل a to k برضه n على d دي
+
+120
+00:12:36,990 --> 00:12:44,730
+بدت ساوي ال grease common divisor ل n و k and n
+
+121
+00:12:44,730 --> 00:12:54,110
+بدت ساوي dtحسب الجزء الأول او D تتساوي او T تتساوي
+
+122
+00:12:54,110 --> 00:13:05,310
+N على D Now A to D أُس T عبارة عن A to D أُس N على
+
+123
+00:13:05,310 --> 00:13:09,810
+D هي عبارة عن A أُس N بدي تساوي ال identity
+
+124
+00:13:09,810 --> 00:13:16,870
+وبالتالي A to D أُس T بيعطيني ال identityيقبل
+
+125
+00:13:16,870 --> 00:13:21,730
+order ل A to D أقل
+
+126
+00:13:21,730 --> 00:13:29,710
+أو يساوي T طيب أنا بدأ أثبت أنه يساوي هفترض العكس
+
+127
+00:13:29,710 --> 00:13:40,750
+أنه أقل من ال T assume that ال order ل A to D بدأ
+
+128
+00:13:40,750 --> 00:13:49,020
+تساوي I و I أقل من T اللي هي بتساوي Nعلى D هذا إيش
+
+129
+00:13:49,020 --> 00:13:57,180
+معناته؟ معناته ال A to D أُص I بدي تساوي ال
+
+130
+00:13:57,180 --> 00:14:03,520
+identity وبالتالي ال A to DI بدي تساوي ال identity
+
+131
+00:14:03,520 --> 00:14:11,860
+هذا معناته أن N أقل أو يساوي DI لإن ال order لل A
+
+132
+00:14:11,860 --> 00:14:22,370
+بساوي ال N butI أقل من ال T ليه بتساوي N على D D I
+
+133
+00:14:22,370 --> 00:14:29,870
+أقل من ال N إيش في بين الجمعتين هدول ال N أقل أو
+
+134
+00:14:29,870 --> 00:14:35,750
+يساوي D I و ال D I أقل من مين من ال N صحيح عندك
+
+135
+00:14:35,750 --> 00:14:36,370
+تناقض
+
+136
+00:14:41,450 --> 00:14:46,670
+تناقض كيف بقول أنه الرقم هذا اللي هو N أقل أو سوى
+
+137
+00:14:46,670 --> 00:14:51,230
+DI وفي نفس الوقت هو أكبر منه مادام فيه تناقض يجب
+
+138
+00:14:51,230 --> 00:14:57,390
+فيه فرض أنا فرض وخاطئ يجب ال order ل A to D بدت
+
+139
+00:14:57,390 --> 00:15:05,630
+سوى T بدت سوى N على Dال order ل a to k عبارة عن ال
+
+140
+00:15:05,630 --> 00:15:09,730
+order generated by a to k اللي هي نفس ال order
+
+141
+00:15:09,730 --> 00:15:13,750
+generated by a to d طبعا هذه أخدناها المحاضرة
+
+142
+00:15:13,750 --> 00:15:18,570
+الماضية هذه هي موجودة قدامك توي أثبتناها ال order
+
+143
+00:15:18,570 --> 00:15:26,570
+ل a to d عبارة عن ال order ل a to d بd سوى n على d
+
+144
+00:15:26,570 --> 00:15:33,650
+وبالتالي ال order ل a to kبدي ساوي N على D اللي هو
+
+145
+00:15:33,650 --> 00:15:40,290
+N على الجريست common divisor ل N و K وهو المطلوب
+
+146
+00:15:40,290 --> 00:15:43,970
+فاضح؟
+
+147
+00:15:43,970 --> 00:15:50,710
+أي جزية بالظبط طيب انت مش فيعمل contradiction الله
+
+148
+00:15:50,710 --> 00:15:57,490
+اللي بقى دهطيب ماشي هجيت احنا بنثبت ان ال order ل
+
+149
+00:15:57,490 --> 00:16:02,590
+A to K بدي ساوي ال N على D انا ما بدت ب A to K بدت
+
+150
+00:16:02,590 --> 00:16:08,850
+ب A to D ال A to D بنشوف ال order اللي هجداش حسب
+
+151
+00:16:08,850 --> 00:16:14,190
+اللي انا كتبته هنا ان ال N بيساوي D في T ال T بدي
+
+152
+00:16:14,190 --> 00:16:21,300
+تساوي N على D رفعت ال A to D أس Tصارت a to d أس n
+
+153
+00:16:21,300 --> 00:16:28,400
+على d اللي عبارة عن a to n a to n مش بتساوي ليش ال
+
+154
+00:16:28,400 --> 00:16:33,340
+order ل a جديش بيساوي يعني يكبر ال order ل a to d
+
+155
+00:16:33,340 --> 00:16:39,500
+هيكون أقل أو يساوي t لإن مدام انت رفعت الأنصر ل
+
+156
+00:16:39,500 --> 00:16:43,840
+power و أعطاك identity يكبر order للأنصر أقل من ال
+
+157
+00:16:43,840 --> 00:16:48,130
+power هذاأو يساوي حاجات انا بدي N في المساوية عشان
+
+158
+00:16:48,130 --> 00:16:52,290
+اصل لتناقض فرضت ان ال order أقل مش أقل أو يساوي
+
+159
+00:16:52,290 --> 00:16:59,110
+يعني أخدته I و أقل من T حاجات ال order I ف A to D
+
+160
+00:16:59,110 --> 00:17:04,990
+الكل أُس I المفروض يعطيني identity ف A to D I بيده
+
+161
+00:17:04,990 --> 00:17:07,970
+يساوي identity حاجات انا بعرف ان ال order ال A
+
+162
+00:17:07,970 --> 00:17:13,710
+بيساوي N لما بدي ارفع ال A ل powerويعطيك identity
+
+163
+00:17:13,710 --> 00:17:18,530
+هذا البرر يبدو يساوي صفريا إما إذا كان موجب يكون
+
+164
+00:17:18,530 --> 00:17:22,770
+أكبر من ال N أنا بتشتغل على ال D موجب وال I موجب
+
+165
+00:17:22,770 --> 00:17:27,790
+يكبر ال D I أكبر من ال N لكن أنا حسب ما هو موجود
+
+166
+00:17:27,790 --> 00:17:32,710
+عندي I أقل من ال D بتساوي N على D ف I D أقل من ال
+
+167
+00:17:32,710 --> 00:17:37,230
+N كيف I D أكبر أو يساوي ال N و I D في نفس الوقت
+
+168
+00:17:37,230 --> 00:17:42,490
+أصغر من ال N صار تناقض تناقض هذا هيرجعك ويقولك أن
+
+169
+00:17:42,490 --> 00:17:45,670
+الفرض اللي انت فرضه خاطئمين هو الفائض اللي انت
+
+170
+00:17:45,670 --> 00:17:52,370
+فرضته انه I أقل من T؟ ايش الصواب؟ انه يساويإنه
+
+171
+00:17:52,370 --> 00:17:55,590
+يساوي الـ T وبالتالي ال order ل A to D بيبدأ تساوي
+
+172
+00:17:55,590 --> 00:17:59,670
+ال T طبعا هذه السلسلة معروفة هتلاقى المحاضرة
+
+173
+00:17:59,670 --> 00:18:03,530
+الماضية أن order العنصر بيساوي order generated
+
+174
+00:18:03,530 --> 00:18:08,550
+للعنصر أو بالسماع للعنصر هذه تاوي أثبتناها أنه
+
+175
+00:18:08,550 --> 00:18:11,090
+generated by A to K بيساوي generated by A to D
+
+176
+00:18:11,090 --> 00:18:15,150
+ارجع لمحاضرة المرة الماضية وهذه تاوي جيبناها أن
+
+177
+00:18:15,150 --> 00:18:20,450
+على D خد الأول مع الأخير بيكون المطلوب عندك ان وجد
+
+178
+00:18:20,450 --> 00:18:21,370
+واضح؟
+
+179
+00:18:27,050 --> 00:18:34,150
+واضح؟ طبعا معايا كم تساوي الجيز common divisor لان
+
+180
+00:18:34,150 --> 00:18:38,310
+و كيه حسب التعريف تبع الجيز common divisor الجيز
+
+181
+00:18:38,310 --> 00:18:42,930
+common divisor لازم يكون positive لازم يكون
+
+182
+00:18:42,930 --> 00:18:50,210
+positive في على هذه النظرية تلاتة corollaries
+
+183
+00:18:50,210 --> 00:18:51,470
+تلاتة
+
+184
+00:18:53,530 --> 00:19:01,850
+ملاحظات هنبدأ بالملاحظة الأولى وكتيش بيتساوى ال
+
+185
+00:19:01,850 --> 00:19:09,370
+generated ل two powers ل ال a كولر
+
+186
+00:19:09,370 --> 00:19:13,970
+واحد نص
+
+187
+00:19:13,970 --> 00:19:20,270
+الكولر بيقول التالي let order ال a بدو يساوي n
+
+188
+00:19:20,270 --> 00:19:22,090
+then
+
+189
+00:19:23,780 --> 00:19:30,840
+generated by a to i بتساوي generated by a to j if
+
+190
+00:19:30,840 --> 00:19:35,220
+and only if لجريس common divisor لأنه i بيساوي
+
+191
+00:19:35,220 --> 00:19:43,080
+لجريس common divisor لأنه j two
+
+192
+00:19:43,080 --> 00:19:49,210
+powers لل aبوالدول نفس ال subgroup إذا كانت two
+
+193
+00:19:49,210 --> 00:19:54,330
+parallels هدول لجهيز common divisors Lهم مع ال N
+
+194
+00:19:54,330 --> 00:20:09,230
+متساويين طيب from theorem 4.2 generated by a to i
+
+195
+00:20:09,230 --> 00:20:12,470
+إيش بتساوي؟
+
+196
+00:20:12,470 --> 00:20:19,380
+إيش بتساوي؟generated by a grace common divisor
+
+197
+00:20:19,380 --> 00:20:27,680
+لأنواع a صح ولا لأ؟ و generated by a to j عبارة عن
+
+198
+00:20:27,680 --> 00:20:34,760
+generated by a grace common divisor لأنواع j طيب
+
+199
+00:20:34,760 --> 00:20:42,720
+هذه تمهيد نجي للاتجاه الأول assume
+
+200
+00:20:50,820 --> 00:20:55,460
+generated by a to i بيساوي generated by a to g
+
+201
+00:20:55,460 --> 00:21:06,660
+هاداش
+
+202
+00:21:06,660 --> 00:21:13,440
+معناته معناته generated by a agreed common divisor
+
+203
+00:21:13,440 --> 00:21:21,480
+لأن و I بيساوي generated by aواصل جريسكم من
+
+204
+00:21:21,480 --> 00:21:25,800
+divisor لأنواجين
+
+205
+00:21:25,800 --> 00:21:29,680
+متساوين،
+
+206
+00:21:29,680 --> 00:21:39,100
+إيش يعني؟ معناته ال order اللي لهم متساوي
+
+207
+00:21:39,100 --> 00:21:45,660
+طيب
+
+208
+00:21:45,660 --> 00:21:46,760
+إيش ال order لها دي؟
+
+209
+00:21:51,470 --> 00:21:56,370
+انت على فكرة انا ممكن يعني اسهل عليك الأمور يعني
+
+210
+00:21:56,370 --> 00:22:01,530
+اتجاوز المرحلة دي و اقولك انه هذه الخطوة مابتلزمش
+
+211
+00:22:01,530 --> 00:22:06,810
+واستبدلك إياها ب I و J و هي كده بيطلع معاك أسهل
+
+212
+00:22:06,810 --> 00:22:11,970
+الإثبات هجيت ال order that is generated by A to I
+
+213
+00:22:11,970 --> 00:22:20,610
+جديش and على الجريس common divisor ل N و Iلان ما
+
+214
+00:22:20,610 --> 00:22:26,390
+مسحناهش generated by a to j عبارة عن n على ال
+
+215
+00:22:26,390 --> 00:22:32,950
+agreeable common divisor ل n و j طيّر ال n من
+
+216
+00:22:32,950 --> 00:22:35,890
+الطرفين وضع الطرفين في وسطين حيث يكون معايا
+
+217
+00:22:35,890 --> 00:22:39,830
+agreeable common divisor ل n و j عبارة عن
+
+218
+00:22:39,830 --> 00:22:45,010
+agreeable common divisor ل n و i هذا الجزء الأول
+
+219
+00:22:45,010 --> 00:22:48,810
+الجزء التاني f
+
+220
+00:22:49,980 --> 00:22:54,960
+الـ Greece Common Divisor لان و جيه لان و ايه
+
+221
+00:22:54,960 --> 00:22:59,680
+بيساوي الـ Greece Common Divisor لان و جيه معناته
+
+222
+00:22:59,680 --> 00:23:09,340
+الـ Generated by A لان و ايه بيساوي الـ Greece
+
+223
+00:23:09,340 --> 00:23:15,200
+Common Divisor لان و جيه معناته الـ Generated by A
+
+224
+00:23:15,200 --> 00:23:21,390
+to I بيساوي الـ Generated by A to Gوهو المطلوب
+
+225
+00:23:21,390 --> 00:23:24,410
+واضحة
+
+226
+00:23:24,410 --> 00:23:34,630
+و الله محتاج اعادة شرح واضحة و الله بدنا ايدها تمد
+
+227
+00:23:34,630 --> 00:23:39,590
+على الخاصية هذه ف ال generated .. مدام هذا بيساوي
+
+228
+00:23:39,590 --> 00:23:42,150
+هذا الأس بيساوي الأس فال generated بيساوي ال
+
+229
+00:23:42,150 --> 00:23:45,090
+generated هذا بيساوي هذا و هذا بيساوي هذا
+
+230
+00:23:51,220 --> 00:24:06,300
+طيب كوالر التانية كوالر
+
+231
+00:24:06,300 --> 00:24:13,620
+التانية بتقولك وقت ايش power لل a بيولد ال
+
+232
+00:24:13,620 --> 00:24:17,120
+generated by aيعني انا لو اشتغلت علي group J
+
+233
+00:24:17,120 --> 00:24:23,280
+generated by some A مين هي الأسس تبعت الـ A الغير
+
+234
+00:24:23,280 --> 00:24:30,540
+الواحد اللي بتولد الـ J؟ let J generated by A
+
+235
+00:24:37,640 --> 00:24:43,100
+الـ j بتكون generated by a to k if and only if
+
+236
+00:24:43,100 --> 00:24:50,980
+لجريست common divisor ل n و k بده يساوي الواحد
+
+237
+00:24:50,980 --> 00:24:57,240
+proof بعدها
+
+238
+00:24:57,240 --> 00:24:59,140
+دي سهل هيتمل الكورلر اللي جابلها
+
+239
+00:25:04,470 --> 00:25:09,470
+الـ j بيساوي generated by a to k if and only if
+
+240
+00:25:09,470 --> 00:25:17,050
+generated by a بيساوي generated by a to k ليش؟
+
+241
+00:25:17,050 --> 00:25:23,410
+ليش؟ لأن الـ j generated by a شيل الـ j و حط مدلة
+
+242
+00:25:23,410 --> 00:25:29,230
+generated by a هذا الكلام ماقدش يكون صحيح if and
+
+243
+00:25:29,230 --> 00:25:35,250
+only if لجريس common divisor لانو 1 طبعا انا
+
+244
+00:25:35,250 --> 00:25:41,790
+المفترض اضيف الجملة هذه with order لل A بدي ساوي
+
+245
+00:25:41,790 --> 00:25:46,010
+ال N if
+
+246
+00:25:46,010 --> 00:25:50,110
+and only if ال G is common divisor ل N و 1 بيساوي
+
+247
+00:25:50,110 --> 00:25:56,790
+ال G is common divisor ل N و K ما هو A to 1 و A to
+
+248
+00:25:56,790 --> 00:26:03,910
+K ال 1 I و ال K احطها J و اطبق القاعدة هذهطيب لجيز
+
+249
+00:26:03,910 --> 00:26:11,950
+common divisor ل n و 1 جديش؟ واحد لإن واحد بدا
+
+250
+00:26:11,950 --> 00:26:16,330
+تساوي لجيز common divisor ل n و k يعني if and only
+
+251
+00:26:16,330 --> 00:26:21,630
+if لجيز common divisor ل n و k بتساوي واحد
+
+252
+00:26:49,080 --> 00:26:54,060
+كورلر التالتة هي عبارة عن تطبيق الكورلر التانية
+
+253
+00:26:54,060 --> 00:27:03,160
+لكن على Z to N او Z to N كورلر ايه؟
+
+254
+00:27:03,160 --> 00:27:09,500
+تلاتة An
+
+255
+00:27:09,500 --> 00:27:13,460
+integral K
+
+256
+00:27:13,460 --> 00:27:15,860
+N
+
+257
+00:27:17,600 --> 00:27:29,020
+زن is a generator of zn if and only if degrees
+
+258
+00:27:29,020 --> 00:27:38,930
+common divisor لن وk بدي سوى واحدالعنصر k اللي
+
+259
+00:27:38,930 --> 00:27:42,110
+موجود في الجيز common divisor ل z و n بيكون
+
+260
+00:27:42,110 --> 00:27:46,650
+generator ل z to n if and only في الجيز common
+
+261
+00:27:46,650 --> 00:27:59,970
+divisor ل n و k بيستوي واحد بروف سهل zn
+
+262
+00:27:59,970 --> 00:28:07,730
+بيستوي generated by kif and only if generated by
+
+263
+00:28:07,730 --> 00:28:14,430
+واحد بيكون generated by واحد to k if and only if
+
+264
+00:28:14,430 --> 00:28:21,150
+لجهزكم ال divisor لان و كي بيسوي واحد ما هو ال z
+
+265
+00:28:21,150 --> 00:28:26,330
+ان generated by واحد لما اقول generated by كي في z
+
+266
+00:28:26,330 --> 00:28:30,830
+ان الكي عبارة عن ايش عن كي في واحد كي في واحد مع
+
+267
+00:28:30,830 --> 00:28:41,670
+الجامعة هي عبارة عن ايش واحدأسكت ناخد مثال بس
+
+268
+00:28:41,670 --> 00:28:53,210
+مش على زدان ونبدأ
+
+269
+00:28:53,210 --> 00:29:02,170
+بزدان four زد .. اختار رقم زد كده إيش بدك؟ سبعة
+
+270
+00:29:02,170 --> 00:29:14,000
+صغيرةزي التلاتين the generators of
+
+271
+00:29:14,000 --> 00:29:24,700
+z 30 are the integers k أنتمي لزي التلاتين with
+
+272
+00:29:24,700 --> 00:29:32,490
+لجريس common divisor ل k والتلاتين مش بيساويشباب
+
+273
+00:29:32,490 --> 00:29:36,430
+العناصر اللي بتكون أجل من ال N و relative ال prime
+
+274
+00:29:36,430 --> 00:29:44,410
+مع ال N و أين بنحطها؟
+
+275
+00:29:44,410 --> 00:29:50,230
+لأ و أين بنحطها؟ في ال U و كنا نعدها باقتران في
+
+276
+00:29:50,230 --> 00:29:56,450
+نظرية العدد، إيش اسمه؟ اللي أخد باقتران اسمه ال
+
+277
+00:29:56,450 --> 00:30:01,180
+Phi ايه ال Phi function؟طبعا مين يالي جيزكم on
+
+278
+00:30:01,180 --> 00:30:05,000
+divisor اللي مع ال 30 بيعطيني واحد كيه هيساوي
+
+279
+00:30:05,000 --> 00:30:10,120
+واحد؟ مين بعد ال واحد؟ اتنين لأ، تلاتة لأ، اربع
+
+280
+00:30:10,120 --> 00:30:17,020
+لأ، خمسة لأ، ستة لأ، سبعة، احداش، تلاتاش، سبعتاش،
+
+281
+00:30:17,020 --> 00:30:24,200
+تسعة عشر، تلاتة و عشرين، تسعة و عشرين يقبل
+
+282
+00:30:24,200 --> 00:30:31,400
+generators لزد تلاتين عبارة عن مين؟ده أقامها دول
+
+283
+00:30:31,400 --> 00:30:39,340
+لو بننعمم ال generators of
+
+284
+00:30:39,340 --> 00:30:50,280
+zn are the integrals k اللي بينتموا ل zn with
+
+285
+00:30:50,280 --> 00:30:58,260
+لجريس common divisor ل k و n بده يسوى واحد these
+
+286
+00:30:58,260 --> 00:31:00,140
+integrals
+
+287
+00:31:02,860 --> 00:31:10,840
+are the members of
+
+288
+00:31:10,840 --> 00:31:15,280
+UN
+
+289
+00:31:15,280 --> 00:31:18,700
+are
+
+290
+00:31:18,700 --> 00:31:23,940
+the elements of
+
+291
+00:31:23,940 --> 00:31:31,240
+UN يعني ال generators تبعون ال ZN هم عناصر مين؟
+
+292
+00:31:31,240 --> 00:31:42,390
+عناصر مين؟الـ U1 تلاتة find
+
+293
+00:31:42,390 --> 00:31:51,730
+the generators of U50
+
+294
+00:31:51,730 --> 00:31:59,410
+هنجيب
+
+295
+00:31:59,410 --> 00:32:02,050
+مولدات الـ U50
+
+296
+00:32:06,680 --> 00:32:14,700
+لأ هذه قاعدة لل ZN مش لل UN أصلا
+
+297
+00:32:14,700 --> 00:32:19,320
+ال UN مش ضرور تكون Cyclic فلازم تكون Cyclic في
+
+298
+00:32:19,320 --> 00:32:24,940
+الأول قبل ما تدور على مين على ال generator تبعونها
+
+299
+00:32:24,940 --> 00:32:29,020
+solution أول
+
+300
+00:32:29,020 --> 00:32:36,360
+خطوة list the elements in U50
+
+301
+00:32:38,880 --> 00:32:47,820
+مين عراسي ال U50؟ لو قولنا U50، إيش بتساوي؟ واحد،
+
+302
+00:32:47,820 --> 00:32:51,740
+تلاتة،
+
+303
+00:32:51,740 --> 00:32:58,960
+سبعة، تسعة، إحدى عشر، تلاتة عشر، سبعة عشر، تسعة
+
+304
+00:32:58,960 --> 00:33:06,040
+عشر، تلاتة وعشرين، سبعة وعشرين، تسعة وعشرين، في
+
+305
+00:33:06,040 --> 00:33:11,470
+أنصر الصناعة، واحد وعشرينوأحد و تلاتين تلاتة و
+
+306
+00:33:11,470 --> 00:33:14,830
+تلاتين سبعة و تلاتين تسعة و تلاتين واحد و أربعين
+
+307
+00:33:14,830 --> 00:33:24,650
+تلاتة و أربعين سبعة و أربعين تسعة و أربعين تمام
+
+308
+00:33:24,650 --> 00:33:38,350
+الخطوة التانية find a generator of you خمسينعطينا
+
+309
+00:33:38,350 --> 00:33:47,470
+عنصر بيولد ال U50 الواحد لأ احنا
+
+310
+00:33:47,470 --> 00:33:51,190
+هانا بنشغل على ضغط مش على جامعة عشان انت تقدر تجيب
+
+311
+00:33:51,190 --> 00:33:58,470
+جنايته ال U50 الأخضر لها جداش عده
+
+312
+00:33:58,470 --> 00:34:00,330
+دول 4 في 25
+
+313
+00:34:06,220 --> 00:34:12,360
+أربعات و أكمل أربعة منهم هاي أربعة، هاي كمان واحدة
+
+314
+00:34:12,360 --> 00:34:14,880
+و هاي كمان واحدة و هاي كمان واحدة و كمان واحدة
+
+315
+00:34:14,880 --> 00:34:23,080
+عشرين أنصار We must find .. find
+
+316
+00:34:23,080 --> 00:34:30,080
+an element in U خمسين with order
+
+317
+00:34:41,180 --> 00:34:53,740
+عشان ماضيعش وجهة we can show that x بسوء تلاتة is
+
+318
+00:34:53,740 --> 00:35:00,380
+or satisfy this
+
+319
+00:35:00,380 --> 00:35:01,820
+property
+
+320
+00:35:04,360 --> 00:35:08,300
+مش هضيع وجد التلاتة بتحقق هذا الكلام عشان اثبت
+
+321
+00:35:08,300 --> 00:35:12,160
+لازم اضرب التلاتة في نفس سنة لعندي عشرين وكل مرة
+
+322
+00:35:12,160 --> 00:35:16,400
+بتولد نفسك لما بيجيبلك سؤال في الامتحان مش هجيبلك
+
+323
+00:35:16,400 --> 00:35:20,600
+يومية مثلا تقعد تضرب اربعين مرة او او اشتغل عشان
+
+324
+00:35:20,600 --> 00:35:23,920
+تمن
+
+325
+00:35:23,920 --> 00:35:29,020
+عناصر يعني هتضرب كم مرة هذا can not cycle اصلا
+
+326
+00:35:29,020 --> 00:35:31,960
+يعني طيب
+
+327
+00:35:33,840 --> 00:35:40,360
+يعني اللي وصلنا له انه ال U50 generated
+
+328
+00:35:40,360 --> 00:35:49,120
+by مين؟ by تلاتة هل جيت؟ وقتش ال U50 بتكون
+
+329
+00:35:49,120 --> 00:35:56,660
+generated by عنصر تاني power للتلاتة لما يكون ال
+
+330
+00:35:56,660 --> 00:35:59,880
+power هذا relative ال prime مع مين؟
+
+331
+00:36:03,120 --> 00:36:09,300
+مع ال order ل ال U50 مش مع الخمسين قطوة تالتة
+
+332
+00:36:09,300 --> 00:36:20,460
+since ال U50 generated by تلاتة then ال U50
+
+333
+00:36:20,460 --> 00:36:25,280
+generated by تلاتة أُس K if and only if لجريس
+
+334
+00:36:25,280 --> 00:36:30,280
+كومون Divisor لل
+
+335
+00:36:30,280 --> 00:36:37,540
+order ل U50و ال K بدي سوى واحد يعني هذا if and on
+
+336
+00:36:37,540 --> 00:36:44,580
+if لجريمز common divisor ل ال 20 و ال K بيسوى واحد
+
+337
+00:36:44,580 --> 00:36:56,750
+النتيجة we must find the elementsK أقل من العشرين
+
+338
+00:36:56,750 --> 00:37:01,710
+أكبر ويساوي واحد with degrees common divisor
+
+339
+00:37:01,710 --> 00:37:10,210
+العشرين وK بيساوي واحد مين هذه العناصر؟ واحد،
+
+340
+00:37:10,210 --> 00:37:16,090
+تلاتة، سبعة، تسعة، احداشر، تلتاشر، سبعتاشر،
+
+341
+00:37:16,090 --> 00:37:20,450
+تسعتاشر، شوية يا شبابمش هذه العناصر اللي بتولد ال
+
+342
+00:37:20,450 --> 00:37:25,390
+U50 لأ هذه ال powers اللي بدي أرفع التلاتة إلها
+
+343
+00:37:25,390 --> 00:37:31,730
+عشان تجيبلي عناصر تولد ال U50 هذا معناته الخطوة
+
+344
+00:37:31,730 --> 00:37:35,650
+الأخيرة ال
+
+345
+00:37:35,650 --> 00:37:44,050
+U50 generated by تلاتة generated by تلاتة أس تلاتة
+
+346
+00:37:44,050 --> 00:37:51,460
+تلاتة أس سبعةتلاتة أُس تسعة وصولة لتلاتة أُس تسعة
+
+347
+00:37:51,460 --> 00:37:58,440
+واتعاش طيب تلاتة أُس واحد معروفة تلاتة أُس ثلاثة
+
+348
+00:37:58,440 --> 00:38:04,300
+عبارة عن تلاتة في نفسها تلاتة في تلاتة في تلاتة جد
+
+349
+00:38:04,300 --> 00:38:15,980
+أيش؟ سبعة وعشرين طيب تلاتة أُس سبعة عبارة عن أيش؟
+
+350
+00:38:17,340 --> 00:38:23,800
+تلاتة في نفسها جمرة جديش؟
+
+351
+00:38:23,800 --> 00:38:27,240
+شيل
+
+352
+00:38:27,240 --> 00:38:35,040
+منها الخمسينات جديش هيضل؟ 2187 هيضل
+
+353
+00:38:35,040 --> 00:38:43,800
+37 شيل الخمسينات طيب تلاتة أس تسعة عبارة
+
+354
+00:38:43,800 --> 00:38:44,380
+عن مين؟
+
+355
+00:38:51,300 --> 00:39:08,360
+أضغط تلاتة في تلاتة في سبعة و تلاتين تلاتة
+
+356
+00:39:08,360 --> 00:39:13,440
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+357
+00:39:13,440 --> 00:39:13,600
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+358
+00:39:13,600 --> 00:39:13,600
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+359
+00:39:13,600 --> 00:39:13,600
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+360
+00:39:13,600 --> 00:39:13,600
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+361
+00:39:13,600 --> 00:39:13,600
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+362
+00:39:13,600 --> 00:39:19,440
+تلاتة تلبيظل تلاتة و تلاتين بقى
+
+363
+00:39:19,440 --> 00:39:26,200
+لعندي كمان أربع ناصر تلاتة قصة احداشر اقرب عن تسعة
+
+364
+00:39:26,200 --> 00:39:35,480
+في تلاتة و تلاتين جديش 297 شيل
+
+365
+00:39:35,480 --> 00:39:45,050
+الخمسينات 47 تلاتة قصة تلاتاشر اقرب عن تسعةفي سبعة
+
+366
+00:39:45,050 --> 00:39:54,150
+واربعين جديش يا شباب اربعمية تلاتة و عشرين بيضل
+
+367
+00:39:54,150 --> 00:40:01,750
+تلاتة و عشرين تلاتة اص سبعة عشر عبارة عن واحد و
+
+368
+00:40:01,750 --> 00:40:10,310
+تمانين في تلاتة و عشرين جديش شيل
+
+369
+00:40:10,310 --> 00:40:18,840
+ال ..الف وتمنية و تلاتة و ستين تلت عش اخر حاجة
+
+370
+00:40:18,840 --> 00:40:24,460
+تلاتة و ست تسعة عش عبارة عن تسعة في تلت عش تسعة في
+
+371
+00:40:24,460 --> 00:40:32,400
+تلت عش جداش مية و سبعة عش بيضل سبعة عش يكبر the
+
+372
+00:40:32,400 --> 00:40:36,840
+generators of
+
+373
+00:40:36,840 --> 00:40:46,130
+you خمسين اه ابدأ تلاتةسبعة و عشرين سبعة و تلاتين
+
+374
+00:40:46,130 --> 00:40:49,210
+تلاتة
+
+375
+00:40:49,210 --> 00:40:57,450
+و تلاتين سبعة و أربعين تلاتة و عشرين تلتاش سبعة
+
+376
+00:40:57,450 --> 00:41:03,330
+واضح تمانية
+
+377
+00:41:03,330 --> 00:41:08,150
+generators هناخد
+
+378
+00:41:08,150 --> 00:41:15,040
+نظرية جدام ان لو كانت عندك groupالـ order لها n و
+
+379
+00:41:15,040 --> 00:41:20,480
+الـ Cyclic فعدد ال generator بيساوي فاي لان اللي
+
+380
+00:41:20,480 --> 00:41:29,780
+فاي بقى عن الإغلاق فاي function انا مغاري طيب
+
+381
+00:41:29,780 --> 00:41:34,800
+ايش المشكلة طيب
+
+382
+00:41:34,800 --> 00:41:37,380
+ايش المشكلة طيب ايش المشكلة طيب ايش المشكلة طيب
+
+383
+00:41:37,380 --> 00:41:40,700
+ايش المشكلةماشي المشكلة يا عزيزي؟ المشكلة هي ان في
+
+384
+00:41:40,700 --> 00:41:44,040
+كمان واحد مليون وخمسين يقول الصحابي .. وقول في خلل
+
+385
+00:41:44,040 --> 00:41:48,280
+في الحساب هنا فقط واحد مفروض .. واحد مفروض سبعت
+
+386
+00:41:48,280 --> 00:41:57,580
+عشر هذا هو .. هذي سبعت عشر مش سبعة كلامك
+
+387
+00:41:57,580 --> 00:42:06,260
+صحيح أي سؤال تاني يا شباب؟ أي معلومة تانية مطلوبة؟
+
+388
+00:42:06,260 --> 00:42:13,930
+أي نقطة مش مفهومة في دارس اليوم؟فضّال .. .. .. ..
+
+389
+00:42:13,930 --> 00:42:19,710
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+390
+00:42:19,710 --> 00:42:21,130
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+391
+00:42:21,130 --> 00:42:25,090
+.. .. .. .. ..
+
+392
+00:42:25,090 --> 00:42:25,870
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+393
+00:42:25,870 --> 00:42:25,890
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+394
+00:42:25,890 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+395
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+396
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+397
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+398
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+399
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+400
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+401
+00:42:26,650 --> 00:42:26,650
+.. .. .. .. .. .. .. .. .. .. .. .. .. .. .. .. ..
+
+402
+00:42:26,650 --> 00:42:27,070
+.. .. .. .. .. .. ..
+
+403
+00:42:37,660 --> 00:42:41,440
+الـ groups نظرية اربعة تلاتة طبعا طويلة شوية هي
+
+404
+00:42:41,440 --> 00:42:48,420
+تلت افرع هناخد فيها انه كل subgroup من cyclic
+
+405
+00:42:48,420 --> 00:42:55,920
+group هتكون cyclic هناخد علاقة ل .. لو كان عندي ال
+
+406
+00:42:55,920 --> 00:43:02,120
+cyclic subgroup ال generator تبعه ايش تفاصيله شغلة
+
+407
+00:43:02,120 --> 00:43:06,410
+تالتةطبعا هنجي تقولنا ان ال order لو كان عندي
+
+408
+00:43:06,410 --> 00:43:10,330
+subgroup من cyclic فهي cyclic هنتبه ان ال order
+
+409
+00:43:10,330 --> 00:43:14,930
+اللي هيقسم ال order لل group لو كان finite و العكس
+
+410
+00:43:14,930 --> 00:43:18,990
+ان لو كان عندي قاسم ل order ل group فانا بقدر
+
+411
+00:43:18,990 --> 00:43:23,590
+ألاقي subgroup لها نفس ال order هتطول شوية معنى
+
+412
+00:43:23,590 --> 00:43:28,690
+النظرية يعني هناخدها في المحاضرة القادمة تفضل
+
+413
+00:43:31,020 --> 00:43:36,880
+الخمسين جيبنا ال order قبل نشوف جيبنا انه التلاتة
+
+414
+00:43:36,880 --> 00:43:41,540
+مولد ل ال U خمسين بعدين اذا جيبكي MK اللي بتكون ال
+
+415
+00:43:41,540 --> 00:43:45,140
+.. ال bride مع ال order ل ال U خمسين اه مش .. مش ل
+
+416
+00:43:45,140 --> 00:43:48,940
+الخمسين بس جيبكي MK بالظبط بعدين برفع التلاتة لها
+
+417
+00:43:48,940 --> 00:43:51,760
+عشان تعطينا ال U خمسين بالظبط بس لازم في الأول
+
+418
+00:43:51,760 --> 00:43:56,410
+اجيبهجيب generator .. انا لو ايش .. ايش سفدت لو
+
+419
+00:43:56,410 --> 00:43:58,410
+جيبت relative ل Brian مع ال order و أنا مافيش عندي
+
+420
+00:43:58,410 --> 00:44:02,590
+generator؟ يمكن ما تكونش Cyclic أصلا طب السؤال اذا
+
+421
+00:44:02,590 --> 00:44:07,510
+أجيبش السبت عشر in versus .. هي موجودة السبت عشر
+
+422
+00:44:07,510 --> 00:44:10,790
+.. مين ال .. اللي جنبك توي سألة أنا فاهم .. يعني
+
+423
+00:44:10,790 --> 00:44:13,430
+لو انت عاملت مع السبت عشر طب انت قاعد يجيب التلاتة
+
+424
+00:44:13,430 --> 00:44:17,960
+و السبت عشر و الباقيةال جيب اثنين و ال ستة .. و
+
+425
+00:44:17,960 --> 00:44:21,100
+على الأقل اثنين عشان تجرب ال ساعة تبدأك واحد
+
+426
+00:44:21,100 --> 00:44:24,000
+generator عشان تكون .. هل جيتك .. تبدأ كل المولدات
+
+427
+00:44:24,000 --> 00:44:27,420
+يعني .. بلأ معايا انت عشان تثبت ان ال group cyclic
+
+428
+00:44:27,420 --> 00:44:31,660
+بيكفيك generator واحد مش دور ال جيب اثنين هذي
+
+429
+00:44:31,660 --> 00:44:33,520
+الشغلة، الشغلة التانية ليش ما شغلناش على السبع
+
+430
+00:44:33,520 --> 00:44:37,680
+دعش؟ مين أسهل؟ تضرب التلتات ولا تضرب السبع دعشات؟
+
+431
+00:44:37,680 --> 00:44:41,640
+تلتات أو تلتات .. بالظبط يعطيكوا العافية، تكمل
+
+432
+00:44:41,640 --> 00:44:42,480
+محاضرة جاهزة الله
+
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.json b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..d48d5369a8b578e1877e1dac0b15746280ede272
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/vg_8OS-lDhg_raw.json
@@ -0,0 +1 @@
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"start": 78.03, "end": 87.97, "text": "مانأمتى ليش since او بدل since نقول because .. because", "tokens": [2304, 7649, 10721, 2304, 49975, 32239, 8592, 1670, 1975, 2407, 47525, 1211, 1670, 8717, 39648, 570, 4386, 570], "avg_logprob": -0.314144724293759, "compression_ratio": 1.042857142857143, "no_speech_prob": 0.0, "words": [{"start": 78.03, "end": 79.25, "word": "مانأمتى", "probability": 0.663525390625}, {"start": 79.25, "end": 79.85, "word": " ليش", "probability": 0.922607421875}, {"start": 79.85, "end": 80.79, "word": " since", "probability": 0.47998046875}, {"start": 80.79, "end": 83.73, "word": " او", "probability": 0.758056640625}, {"start": 83.73, "end": 84.11, "word": " بدل", "probability": 0.9697265625}, {"start": 84.11, "end": 84.51, "word": " since", "probability": 0.9033203125}, {"start": 84.51, "end": 84.97, "word": " نقول", "probability": 0.86669921875}, {"start": 84.97, "end": 85.91, "word": " because", "probability": 0.958984375}, {"start": 85.91, "end": 87.43, "word": " ..", "probability": 0.464111328125}, {"start": 87.43, "end": 87.97, "word": " because", "probability": 0.9052734375}], "temperature": 1.0}, {"id": 4, "seek": 11640, "start": 91.28, "end": 116.4, "text": "الـ Phi of الـ Identity G بدل ساوي الـ Identity تبع الـ G bar معناه هذا الكلام أن الـ Identity تبع الـ G بدل ساوي Phi Inverse of الـ Identity Element تبع الـ G bar وهذا الـ Element موجود في الجروب اللي عندنا هذا", "tokens": [6027, 39184, 41435, 295, 2423, 39184, 25905, 507, 460, 47525, 1211, 8608, 995, 45865, 2423, 39184, 25905, 507, 6055, 3555, 3615, 2423, 39184, 460, 2159, 20449, 8315, 3224, 23758, 2423, 28820, 10943, 14739, 2423, 39184, 25905, 507, 6055, 3555, 3615, 2423, 39184, 460, 47525, 1211, 8608, 995, 45865, 41435, 682, 4308, 295, 2423, 39184, 25905, 507, 20900, 6055, 3555, 3615, 2423, 39184, 460, 2159, 37037, 15730, 2423, 39184, 20900, 3714, 29245, 23328, 8978, 25724, 32887, 3555, 13672, 1829, 43242, 8315, 23758], "avg_logprob": -0.3025914670490637, "compression_ratio": 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132.54, "end": 133.08, "word": " Phi", "probability": 0.9052734375}, {"start": 133.08, "end": 134.04, "word": " inverse", "probability": 0.86083984375}, {"start": 134.04, "end": 134.52, "word": " of", "probability": 0.97705078125}, {"start": 134.52, "end": 134.86, "word": " K", "probability": 0.9638671875}, {"start": 134.86, "end": 135.6, "word": " bar", "probability": 0.87548828125}, {"start": 135.6, "end": 136.74, "word": " يبقى", "probability": 0.89892578125}, {"start": 136.74, "end": 137.12, "word": " then", "probability": 0.480224609375}], "temperature": 1.0}, {"id": 6, "seek": 15144, "start": 138.04, "end": 151.44, "text": "الـ X هذي بيبقى تسوى في في انفرس of K1 for some K1 اللي موجودة في K bar", "tokens": [6027, 39184, 1783, 8032, 8848, 1829, 4724, 1829, 3555, 4587, 7578, 6055, 3794, 2407, 7578, 8978, 8978, 16472, 5172, 2288, 3794, 295, 591, 16, 337, 512, 591, 16, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 591, 2159], "avg_logprob": -0.5020559210526315, "compression_ratio": 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175.57, "end": 176.27, "word": " موجودة", "probability": 0.990478515625}, {"start": 176.27, "end": 176.45, "word": " في", "probability": 0.982421875}, {"start": 176.45, "end": 176.81, "word": " k", "probability": 0.95703125}, {"start": 176.81, "end": 177.15, "word": " bar", "probability": 0.896484375}, {"start": 177.15, "end": 178.13, "word": " and", "probability": 0.91748046875}], "temperature": 1.0}, {"id": 8, "seek": 18765, "start": 179.21, "end": 187.65, "text": "فاي واي بدها تساوي كتو اللي موجودة في ك بار", "tokens": [5172, 47302, 4032, 47302, 47525, 11296, 6055, 3794, 995, 45865, 9122, 2655, 2407, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 9122, 4724, 9640], "avg_logprob": -0.3782552145421505, "compression_ratio": 1.1666666666666667, "no_speech_prob": 0.0, "words": [{"start": 179.21, "end": 180.17, "word": "فاي", "probability": 0.35150146484375}, {"start": 180.17, "end": 181.25, "word": " واي", "probability": 0.72412109375}, {"start": 181.25, "end": 182.09, "word": " بدها", 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"probability": 0.55078125}, {"start": 386.71, "end": 387.01, "word": " five", "probability": 0.1622314453125}, {"start": 387.01, "end": 387.31, "word": " of", "probability": 0.92138671875}, {"start": 387.31, "end": 387.55, "word": " x", "probability": 0.76171875}, {"start": 387.55, "end": 388.13, "word": " موجودة", "probability": 0.9866943359375}, {"start": 388.13, "end": 388.57, "word": " في", "probability": 0.63330078125}, {"start": 388.57, "end": 390.37, "word": " كي", "probability": 0.569091796875}, {"start": 390.37, "end": 390.71, "word": " بار", "probability": 0.9365234375}, {"start": 390.71, "end": 391.51, "word": " و", "probability": 0.4892578125}, {"start": 391.51, "end": 391.99, "word": " هذه", "probability": 0.66748046875}, {"start": 391.99, "end": 393.17, "word": " موجودة", "probability": 0.955810546875}, {"start": 393.17, "end": 393.75, "word": " في", "probability": 0.9775390625}, {"start": 393.75, "end": 395.21, "word": " كي", "probability": 0.6954345703125}, {"start": 395.21, "end": 396.03, "word": " بار", "probability": 0.99072265625}, {"start": 396.03, "end": 396.67, "word": " بالشكل", "probability": 0.9200846354166666}, {"start": 396.67, "end": 396.83, "word": " اللي", "probability": 0.927001953125}, {"start": 396.83, "end": 397.19, "word": " عندنا", "probability": 0.866455078125}], "temperature": 1.0}, {"id": 18, "seek": 41690, "start": 400.1, "end": 416.9, "text": "طيب و هذه وين موجودة؟ موجودة كذلك في جي با طيب ال K bar هذه أصلا normal subgroup معطاة مدام normal subgroup إذا كل هذا الكلام ماله وين موجود؟", "tokens": [9566, 1829, 3555, 4032, 29538, 4032, 9957, 3714, 29245, 23328, 3660, 22807, 3714, 29245, 23328, 3660, 9122, 8848, 23275, 8978, 10874, 1829, 4724, 995, 23032, 1829, 3555, 2423, 591, 2159, 29538, 5551, 9381, 15040, 2710, 1422, 17377, 20449, 9566, 995, 3660, 3714, 3215, 10943, 2710, 1422, 17377, 11933, 15730, 28242, 23758, 2423, 28820, 10943, 3714, 6027, 3224, 4032, 9957, 3714, 29245, 23328, 22807], "avg_logprob": -0.268310550134629, "compression_ratio": 1.5310344827586206, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 400.1, "end": 400.62, "word": "طيب", "probability": 0.6888020833333334}, {"start": 400.62, "end": 400.96, "word": " و", "probability": 0.458984375}, {"start": 400.96, "end": 401.22, "word": " هذه", "probability": 0.49853515625}, {"start": 401.22, "end": 401.46, "word": " وين", "probability": 0.5682373046875}, {"start": 401.46, "end": 402.78, "word": " موجودة؟", "probability": 0.8677734375}, {"start": 402.78, "end": 403.78, "word": " موجودة", "probability": 0.93359375}, {"start": 403.78, "end": 404.48, "word": " كذلك", "probability": 0.9754231770833334}, {"start": 404.48, "end": 404.78, "word": " في", "probability": 0.93359375}, {"start": 404.78, "end": 405.5, "word": " جي", "probability": 0.7490234375}, {"start": 405.5, "end": 406.0, "word": " با", "probability": 0.825927734375}, {"start": 406.0, "end": 407.1, "word": " طيب", "probability": 0.88134765625}, {"start": 407.1, "end": 407.32, "word": " ال", "probability": 0.931640625}, {"start": 407.32, "end": 407.54, "word": " K", "probability": 0.56005859375}, {"start": 407.54, "end": 407.92, "word": " bar", "probability": 0.53564453125}, {"start": 407.92, "end": 408.32, "word": " هذه", "probability": 0.51904296875}, {"start": 408.32, "end": 408.74, "word": " أصلا", "probability": 0.8282877604166666}, {"start": 408.74, "end": 409.18, "word": " normal", "probability": 0.381591796875}, {"start": 409.18, "end": 409.86, "word": " subgroup", "probability": 0.7109375}, {"start": 409.86, "end": 411.06, "word": " معطاة", "probability": 0.7547607421875}, {"start": 411.06, "end": 411.78, "word": " مدام", "probability": 0.78955078125}, {"start": 411.78, "end": 412.28, "word": " normal", "probability": 0.77392578125}, {"start": 412.28, "end": 413.26, "word": " subgroup", "probability": 0.966064453125}, {"start": 413.26, "end": 413.7, "word": " إذا", "probability": 0.722412109375}, {"start": 413.7, "end": 414.3, "word": " كل", "probability": 0.9375}, {"start": 414.3, "end": 414.84, "word": " هذا", "probability": 0.97314453125}, {"start": 414.84, "end": 415.5, "word": " الكلام", "probability": 0.9549153645833334}, {"start": 415.5, "end": 415.84, "word": " ماله", "probability": 0.6007486979166666}, {"start": 415.84, "end": 416.06, "word": " وين", "probability": 0.992919921875}, {"start": 416.06, "end": 416.9, "word": " موجود؟", "probability": 0.9752197265625}], "temperature": 1.0}, {"id": 19, "seek": 43286, "start": 417.28, "end": 432.86, "text": "موجود في K bar بالشكل لأن هذا ليش؟ sense لإن ال K bar عبارة عن subgroup من ال G bar مع طياب", "tokens": [2304, 29245, 23328, 8978, 591, 2159, 20666, 8592, 28820, 5296, 33456, 23758, 32239, 8592, 22807, 2020, 5296, 28814, 1863, 2423, 591, 2159, 6225, 3555, 9640, 3660, 18871, 1422, 17377, 9154, 2423, 460, 2159, 20449, 23032, 1829, 16758], "avg_logprob": -0.27857729165177597, "compression_ratio": 1.1623931623931625, "no_speech_prob": 5.960464477539063e-08, "words": 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bar", "probability": 0.86328125}, {"start": 428.36, "end": 429.16, "word": " عبارة", "probability": 0.9874267578125}, {"start": 429.16, "end": 429.42, "word": " عن", "probability": 0.99755859375}, {"start": 429.42, "end": 430.42, "word": " subgroup", "probability": 0.684814453125}, {"start": 430.42, "end": 431.0, "word": " من", "probability": 0.98779296875}, {"start": 431.0, "end": 431.26, "word": " ال", "probability": 0.76318359375}, {"start": 431.26, "end": 431.46, "word": " G", "probability": 0.89892578125}, {"start": 431.46, "end": 431.84, "word": " bar", "probability": 0.91015625}, {"start": 431.84, "end": 432.18, "word": " مع", "probability": 0.93408203125}, {"start": 432.18, "end": 432.86, "word": " طياب", "probability": 0.6412760416666666}], "temperature": 1.0}, {"id": 20, "seek": 45626, "start": 433.72, "end": 456.26, "text": "إذا بناء عليه أصبح عنده إيه؟ اللي هو الـPhi of G X G inverse موجود في الـK bar معنى هذا الكلام إن الـG X G inverse موجود في الـPhi inverse of K bar", 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"end": 437.6, "word": " اللي", "probability": 0.71435546875}, {"start": 437.6, "end": 438.02, "word": " هو", "probability": 0.9873046875}, {"start": 438.02, "end": 439.3, "word": " الـPhi", "probability": 0.633392333984375}, {"start": 439.3, "end": 440.0, "word": " of", "probability": 0.7841796875}, {"start": 440.0, "end": 440.44, "word": " G", "probability": 0.85009765625}, {"start": 440.44, "end": 441.2, "word": " X", "probability": 0.342041015625}, {"start": 441.2, "end": 441.98, "word": " G", "probability": 0.6259765625}, {"start": 441.98, "end": 442.68, "word": " inverse", "probability": 0.53271484375}, {"start": 442.68, "end": 444.22, "word": " موجود", "probability": 0.97998046875}, {"start": 444.22, "end": 444.52, "word": " في", "probability": 0.97216796875}, {"start": 444.52, "end": 445.06, "word": " الـK", "probability": 0.78125}, {"start": 445.06, "end": 445.52, "word": " bar", "probability": 0.66845703125}, {"start": 445.52, "end": 446.5, "word": " معنى", "probability": 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"end": 455.52, "word": " K", "probability": 0.955078125}, {"start": 455.52, "end": 456.26, "word": " bar", "probability": 0.8759765625}], "temperature": 1.0}, {"id": 21, "seek": 47049, "start": 456.89, "end": 470.49, "text": "يبقى بناء عليه أصبح أن الـ Phi inverse of K bar is a normal subgroup من G وانتهينا من هذه النقطة", "tokens": [1829, 3555, 4587, 7578, 44945, 16606, 47356, 5551, 9381, 49628, 14739, 2423, 39184, 41435, 17340, 295, 591, 2159, 307, 257, 2710, 1422, 17377, 9154, 460, 4032, 7649, 47395, 1829, 8315, 9154, 29538, 28239, 47432, 3660], "avg_logprob": -0.2792968642380502, "compression_ratio": 1.078125, "no_speech_prob": 0.0, "words": [{"start": 456.89, "end": 457.45, "word": "يبقى", "probability": 0.8328857421875}, {"start": 457.45, "end": 457.77, "word": " بناء", "probability": 0.754638671875}, {"start": 457.77, "end": 458.33, "word": " عليه", "probability": 0.81201171875}, {"start": 458.33, "end": 459.39, "word": " أصبح", "probability": 0.7850748697916666}, {"start": 459.39, "end": 459.83, "word": " أن", "probability": 0.46923828125}, {"start": 459.83, "end": 460.77, "word": " الـ", "probability": 0.6611328125}, {"start": 460.77, "end": 461.09, "word": " Phi", "probability": 0.2015380859375}, {"start": 461.09, "end": 462.03, "word": " inverse", "probability": 0.7158203125}, {"start": 462.03, "end": 462.91, "word": " of", "probability": 0.94580078125}, {"start": 462.91, "end": 463.39, "word": " K", "probability": 0.62109375}, {"start": 463.39, "end": 463.97, "word": " bar", "probability": 0.67626953125}, {"start": 463.97, "end": 464.79, "word": " is", "probability": 0.6455078125}, {"start": 464.79, "end": 465.21, "word": " a", "probability": 0.96337890625}, {"start": 465.21, "end": 465.91, "word": " normal", "probability": 0.70263671875}, {"start": 465.91, "end": 467.13, "word": " subgroup", "probability": 0.73828125}, {"start": 467.13, "end": 467.45, "word": " من", "probability": 0.9365234375}, {"start": 467.45, "end": 467.69, "word": " G", "probability": 0.7626953125}, {"start": 467.69, "end": 468.45, "word": " وانتهينا", "probability": 0.8927734375}, {"start": 468.45, "end": 468.67, "word": " من", "probability": 0.96875}, {"start": 468.67, "end": 469.17, "word": " هذه", "probability": 0.78564453125}, {"start": 469.17, "end": 470.49, "word": " النقطة", "probability": 0.9900716145833334}], "temperature": 1.0}, {"id": 22, "seek": 49714, "start": 470.96, "end": 497.14, "text": "يبقى ده مقتصر النقطة السابعة والثامنة مرة ثانية بدأ نيجي للنقطة التاسعة النقطة التاسعة بتقول لي ما يأتي لو كانت في is unto في is unto والكرن للفي بده يساوي ال identity element", "tokens": [1829, 3555, 4587, 7578, 11778, 3224, 3714, 38149, 9381, 2288, 28239, 47432, 3660, 21136, 16758, 27884, 16070, 12984, 10943, 1863, 3660, 3714, 25720, 38637, 7649, 10632, 47525, 10721, 8717, 1829, 7435, 1829, 24976, 1863, 47432, 3660, 16712, 32277, 27884, 28239, 47432, 3660, 16712, 32277, 27884, 39894, 39648, 32239, 19446, 7251, 10721, 31371, 45164, 25961, 2655, 8978, 307, 16521, 8978, 307, 16521, 16070, 37983, 1863, 24976, 41185, 47525, 3224, 7251, 3794, 995, 45865, 2423, 6575, 4478], "avg_logprob": -0.22779605596473343, "compression_ratio": 1.7017543859649122, "no_speech_prob": 0.0, "words": [{"start": 470.96, "end": 471.54, "word": "يبقى", "probability": 0.765869140625}, {"start": 471.54, "end": 471.8, "word": " ده", "probability": 0.35009765625}, {"start": 471.8, "end": 472.36, "word": " مقتصر", "probability": 0.9163818359375}, {"start": 472.36, "end": 472.8, "word": " النقطة", "probability": 0.93896484375}, {"start": 472.8, "end": 473.3, "word": " السابعة", "probability": 0.9182942708333334}, {"start": 473.3, "end": 474.34, "word": " والثامنة", "probability": 0.8486328125}, {"start": 474.34, "end": 475.34, "word": " مرة", "probability": 0.97412109375}, {"start": 475.34, "end": 477.04, "word": " ثانية", "probability": 0.984375}, {"start": 477.04, "end": 478.28, "word": " بدأ", "probability": 0.451416015625}, {"start": 478.28, "end": 478.56, "word": " نيجي", "probability": 0.9078369140625}, {"start": 478.56, "end": 479.56, "word": " للنقطة", "probability": 0.959228515625}, {"start": 479.56, "end": 480.78, "word": " التاسعة", "probability": 0.9856770833333334}, {"start": 480.78, "end": 482.04, "word": " النقطة", "probability": 0.9435221354166666}, {"start": 482.04, "end": 482.72, "word": " التاسعة", "probability": 0.9921875}, {"start": 482.72, "end": 483.3, "word": " بتقول", "probability": 0.94677734375}, {"start": 483.3, "end": 483.46, "word": " لي", "probability": 0.36669921875}, {"start": 483.46, "end": 483.7, "word": " ما", "probability": 0.89794921875}, {"start": 483.7, "end": 484.32, "word": " يأتي", "probability": 0.947265625}, {"start": 484.32, "end": 485.12, "word": " لو", "probability": 0.91064453125}, {"start": 485.12, "end": 485.76, "word": " كانت", "probability": 0.9140625}, {"start": 485.76, "end": 486.2, "word": " في", "probability": 0.276611328125}, {"start": 486.2, "end": 486.8, "word": " is", "probability": 0.6748046875}, {"start": 486.8, "end": 487.56, "word": " unto", "probability": 0.39111328125}, {"start": 487.56, "end": 488.94, "word": " في", "probability": 0.37939453125}, {"start": 488.94, "end": 489.54, "word": " is", "probability": 0.9013671875}, {"start": 489.54, "end": 490.22, "word": " unto", "probability": 0.861328125}, {"start": 490.22, "end": 492.16, "word": " والكرن", "probability": 0.6420084635416666}, {"start": 492.16, "end": 493.46, "word": " للفي", "probability": 0.6552734375}, {"start": 493.46, "end": 494.5, "word": " بده", "probability": 0.6195068359375}, {"start": 494.5, "end": 495.06, "word": " يساوي", "probability": 0.94384765625}, {"start": 495.06, "end": 495.3, "word": " ال", "probability": 0.9599609375}, {"start": 495.3, "end": 496.08, "word": " identity", "probability": 0.783203125}, {"start": 496.08, "end": 497.14, "word": " element", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 23, "seek": 50912, "start": 498.28, "end": 509.12, "text": "ثم فاي هو ايزو مورفزم من الـG إلى الـG بار", "tokens": [12984, 2304, 6156, 47302, 31439, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 11622, 2304, 9154, 2423, 39184, 38, 30731, 2423, 39184, 38, 4724, 9640], "avg_logprob": -0.6975, "compression_ratio": 1.123076923076923, "no_speech_prob": 0.0, "words": [{"start": 498.28, "end": 498.88, "word": "ثم", "probability": 0.5535888671875}, {"start": 498.88, "end": 499.36, "word": " فاي", "probability": 0.24261474609375}, {"start": 499.36, "end": 499.62, "word": " هو", "probability": 0.41552734375}, {"start": 499.62, "end": 500.4, "word": " ايزو", "probability": 0.5704345703125}, {"start": 500.4, "end": 501.04, "word": " مورفزم", "probability": 0.79990234375}, {"start": 501.04, "end": 504.68, "word": " من", "probability": 0.2374267578125}, {"start": 504.68, "end": 507.82, "word": " الـG", "probability": 0.3894856770833333}, {"start": 507.82, "end": 508.34, "word": " إلى", "probability": 0.472900390625}, {"start": 508.34, "end": 508.76, "word": " الـG", "probability": 0.8203125}, {"start": 508.76, "end": 509.12, "word": " بار", "probability": 0.620361328125}], "temperature": 1.0}, {"id": 24, "seek": 54064, "start": 511.72, "end": 540.64, "text": "أنا لكي أثبت في ايزو مورفزم بدي أثبت ثلاثة شروط one to one وانتوا وخاصية ال homomorphism بقوله كويسة انتوا هيوم اعطينيها تمام الفي قلي عنها من البداية هي homomorphism مش بقاش dial علي اثبات fight one to one يبقى باجي بقول if we show that", "tokens": [10721, 8315, 5296, 4117, 1829, 5551, 12984, 3555, 2655, 8978, 1975, 1829, 11622, 2407, 3714, 13063, 5172, 11622, 2304, 4724, 16254, 5551, 12984, 3555, 2655, 38637, 1211, 5718, 104, 3660, 13412, 32887, 9566, 472, 281, 472, 4032, 7649, 2655, 14407, 4032, 9778, 33546, 10632, 2423, 3655, 32702, 1434, 4724, 39648, 3224, 9122, 45865, 3794, 3660, 16472, 2655, 14407, 39896, 20498, 1975, 3615, 9566, 9957, 1829, 11296, 46811, 10943, 27188, 1829, 12174, 20292, 18871, 11296, 9154, 29739, 28259, 10632, 39896, 3655, 32702, 1434, 37893, 4724, 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0.9091796875}, {"start": 515.94, "end": 516.5, "word": " شروط", "probability": 0.9114583333333334}, {"start": 516.5, "end": 516.88, "word": " one", "probability": 0.401123046875}, {"start": 516.88, "end": 517.18, "word": " to", "probability": 0.85009765625}, {"start": 517.18, "end": 517.46, "word": " one", "probability": 0.9560546875}, {"start": 517.46, "end": 518.64, "word": " وانتوا", "probability": 0.57916259765625}, {"start": 518.64, "end": 519.56, "word": " وخاصية", "probability": 0.9429931640625}, {"start": 519.56, "end": 519.82, "word": " ال", "probability": 0.974609375}, {"start": 519.82, "end": 520.84, "word": " homomorphism", "probability": 0.8330078125}, {"start": 520.84, "end": 521.98, "word": " بقوله", "probability": 0.66943359375}, {"start": 521.98, "end": 522.54, "word": " كويسة", "probability": 0.91748046875}, {"start": 522.54, "end": 523.16, "word": " انتوا", "probability": 0.8248697916666666}, {"start": 523.16, "end": 523.6, "word": " هيوم", "probability": 0.82861328125}, {"start": 523.6, "end": 524.78, "word": " اعطينيها", "probability": 0.8423258463541666}, {"start": 524.78, "end": 525.82, "word": " تمام", "probability": 0.718994140625}, {"start": 525.82, "end": 527.1, "word": " الفي", "probability": 0.5235595703125}, {"start": 527.1, "end": 527.58, "word": " قلي", "probability": 0.675537109375}, {"start": 527.58, "end": 528.08, "word": " عنها", "probability": 0.993896484375}, {"start": 528.08, "end": 528.38, "word": " من", "probability": 0.9873046875}, {"start": 528.38, "end": 529.24, "word": " البداية", "probability": 0.9788411458333334}, {"start": 529.24, "end": 529.54, "word": " هي", "probability": 0.8759765625}, {"start": 529.54, "end": 530.6, "word": " homomorphism", "probability": 0.939453125}, {"start": 530.6, "end": 530.8, "word": " مش", "probability": 0.17236328125}, {"start": 530.8, "end": 531.02, "word": " بقاش", "probability": 0.6009114583333334}, {"start": 531.02, "end": 531.28, "word": " dial", "probability": 0.163330078125}, {"start": 531.28, "end": 531.52, "word": " علي", "probability": 0.607421875}, {"start": 531.52, "end": 532.2, "word": " اثبات", "probability": 0.87109375}, {"start": 532.2, "end": 533.62, "word": " fight", "probability": 0.1424560546875}, {"start": 533.62, "end": 533.92, "word": " one", "probability": 0.94189453125}, {"start": 533.92, "end": 534.14, "word": " to", "probability": 0.955078125}, {"start": 534.14, "end": 534.42, "word": " one", "probability": 0.9501953125}, {"start": 534.42, "end": 535.08, "word": " يبقى", "probability": 0.9058837890625}, {"start": 535.08, "end": 535.44, "word": " باجي", "probability": 0.857421875}, {"start": 535.44, "end": 535.9, "word": " بقول", "probability": 0.964599609375}, {"start": 535.9, "end": 536.54, "word": " if", "probability": 0.87060546875}, {"start": 536.54, "end": 538.0, "word": " we", "probability": 0.9150390625}, {"start": 538.0, "end": 539.28, "word": " show", "probability": 0.95849609375}, {"start": 539.28, "end": 540.64, "word": " that", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 25, "seek": 55165, "start": 541.79, "end": 551.65, "text": "اللي هو five is one to one then we have the result", "tokens": [6027, 20292, 31439, 1732, 307, 472, 281, 472, 550, 321, 362, 264, 1874], "avg_logprob": -0.17047991071428573, "compression_ratio": 1.018181818181818, "no_speech_prob": 0.0, "words": [{"start": 541.79, "end": 542.29, "word": "اللي", "probability": 0.94384765625}, {"start": 542.29, "end": 542.51, "word": " هو", "probability": 0.98486328125}, {"start": 542.51, "end": 543.13, "word": " five", "probability": 0.2744140625}, {"start": 543.13, "end": 543.93, "word": " is", "probability": 0.87939453125}, {"start": 543.93, "end": 544.71, "word": " one", "probability": 0.96728515625}, {"start": 544.71, "end": 545.09, "word": " to", "probability": 0.92138671875}, {"start": 545.09, "end": 545.47, "word": " one", "probability": 0.95751953125}, {"start": 545.47, "end": 546.51, "word": " then", "probability": 0.68310546875}, {"start": 546.51, "end": 547.83, "word": " we", "probability": 0.95458984375}, {"start": 547.83, "end": 549.45, "word": " have", "probability": 0.97216796875}, {"start": 549.45, "end": 550.57, "word": " the", "probability": 0.9052734375}, {"start": 550.57, "end": 551.65, "word": " result", "probability": 0.96044921875}], "temperature": 1.0}, {"id": 26, "seek": 57713, "start": 553.65, "end": 577.13, "text": "يبقى لو أثبت أنه في one to one بكون وصلت إلى النتيجة إذا بدأ أروح أخد صورتين متساويتين لأنصرين وأثبت أن أصلهم متساوين يبقى بناء عليه بالداجة أقول له assume أنه في of X بده يساوي في of Y", "tokens": [1829, 3555, 4587, 7578, 45164, 5551, 12984, 3555, 2655, 14739, 3224, 8978, 472, 281, 472, 4724, 30544, 4032, 36520, 2655, 30731, 28239, 31371, 7435, 3660, 11933, 15730, 47525, 10721, 5551, 32887, 5016, 5551, 9778, 3215, 20328, 13063, 2655, 9957, 44650, 3794, 995, 45865, 2655, 9957, 5296, 33456, 9381, 2288, 9957, 36725, 12984, 3555, 2655, 14739, 5551, 36520, 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999.84, "word": " والـ", "probability": 0.4296875}, {"start": 999.84, "end": 1001.02, "word": " Crawlery", "probability": 0.509765625}, {"start": 1001.02, "end": 1002.86, "word": " والنظرية", "probability": 0.9326171875}, {"start": 1002.86, "end": 1003.04, "word": " اللي", "probability": 0.88330078125}, {"start": 1003.04, "end": 1003.5, "word": " جابلها", "probability": 0.8470458984375}, {"start": 1003.5, "end": 1004.58, "word": " معاهم", "probability": 0.80224609375}, {"start": 1004.58, "end": 1006.1, "word": " بيقول", "probability": 0.74609375}, {"start": 1006.1, "end": 1006.74, "word": " define", "probability": 0.48046875}], "temperature": 1.0}, {"id": 44, "seek": 103249, "start": 1009.95, "end": 1032.49, "text": "فانكشن فاي من زد تمانتاشر إلى زد تمانتاش باي فاي او اكس يساوي تلاتة اكس النقطة الأولى show that", "tokens": [5172, 7649, 4117, 8592, 1863, 6156, 47302, 9154, 30767, 3215, 46811, 7649, 2655, 33599, 2288, 30731, 30767, 3215, 46811, 7649, 2655, 33599, 4724, 47302, 6156, 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[6027, 1863, 47432, 3660, 6024, 104, 7649, 10632], "avg_logprob": -0.5954861111111112, "compression_ratio": 0.7941176470588235, "no_speech_prob": 0.0, "words": [{"start": 1040.6699999999998, "end": 1042.07, "word": "النقطة", "probability": 0.702972412109375}, {"start": 1042.07, "end": 1043.43, "word": " الثانية", "probability": 0.9273681640625}], "temperature": 1.0}, {"id": 46, "seek": 107380, "start": 1047.5, "end": 1073.8, "text": "الـ Kernel للـ Phi and show that وبيلنا ان الـ Phi is a تلاتة تون تلاتة تون تلاتة تون function", "tokens": [6027, 39184, 40224, 338, 24976, 39184, 41435, 293, 855, 300, 4032, 21292, 1211, 8315, 16472, 2423, 39184, 41435, 307, 257, 6055, 1211, 9307, 3660, 6055, 11536, 6055, 1211, 9307, 3660, 6055, 11536, 6055, 1211, 9307, 3660, 6055, 11536, 2445], "avg_logprob": -0.3886718854308128, "compression_ratio": 1.4210526315789473, "no_speech_prob": 0.0, "words": [{"start": 1047.5, "end": 1047.94, "word": "الـ", "probability": 0.50732421875}, {"start": 1047.94, 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يبقى باجي بقوله الكيرنل للفاي كل ال X اللي موجودة في ال Z 18 بحيث ان في of X بدي سوى ال identity element تبع ال Z 18 اللي همين", "tokens": [1829, 3555, 4587, 7578, 29538, 39896, 28239, 47432, 3660, 16247, 12610, 7578, 8717, 24192, 3555, 24976, 1863, 47432, 3660, 6024, 104, 7649, 10632, 10874, 6027, 1829, 3224, 9307, 5296, 23275, 13546, 1863, 1211, 7251, 3555, 4587, 7578, 4724, 26108, 1829, 4724, 39648, 3224, 33251, 13546, 1863, 1211, 24976, 5172, 47302, 28242, 2423, 1783, 13672, 1829, 3714, 29245, 23328, 3660, 8978, 2423, 1176, 2443, 4724, 5016, 1829, 12984, 16472, 8978, 295, 1783, 4724, 16254, 8608, 2407, 7578, 2423, 6575, 4478, 6055, 3555, 3615, 2423, 1176, 2443, 13672, 1829, 8032, 2304, 9957], "avg_logprob": -0.3705357097007416, "compression_ratio": 1.6864864864864866, "no_speech_prob": 0.0, "words": [{"start": 1232.9, "end": 1233.4, "word": "يبقى", "probability": 0.745849609375}, {"start": 1233.4, "end": 1233.74, "word": " هذه", "probability": 0.787109375}, {"start": 1233.74, 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1317.51, "word": " عناصر", "probability": 0.9803059895833334}, {"start": 1317.51, "end": 1318.17, "word": " ايش", "probability": 0.6521402994791666}, {"start": 1318.17, "end": 1319.05, "word": " صورتهم؟", "probability": 0.8921875}, {"start": 1319.05, "end": 1320.09, "word": " Zero", "probability": 0.7294921875}, {"start": 1320.09, "end": 1320.29, "word": " ال", "probability": 0.361083984375}, {"start": 1320.29, "end": 1320.73, "word": " identity", "probability": 0.37060546875}, {"start": 1320.73, "end": 1320.97, "word": " و", "probability": 0.7333984375}, {"start": 1320.97, "end": 1321.13, "word": " من", "probability": 0.63134765625}, {"start": 1321.13, "end": 1321.35, "word": " هنا", "probability": 0.96484375}, {"start": 1321.35, "end": 1321.55, "word": " ال", "probability": 0.96630859375}, {"start": 1321.55, "end": 1322.01, "word": " function", "probability": 0.87646484375}, {"start": 1322.01, "end": 1322.71, "word": " هي", "probability": 0.90771484375}, {"start": 1322.71, "end": 1323.73, "word": " تلتة", "probability": 0.8719482421875}, {"start": 1323.73, "end": 1324.05, "word": " to", "probability": 0.92236328125}, {"start": 1324.05, "end": 1324.51, "word": " one", "probability": 0.94775390625}, {"start": 1324.51, "end": 1325.55, "word": " يبقى", "probability": 0.98291015625}, {"start": 1325.55, "end": 1325.95, "word": " هذا", "probability": 0.9541015625}, {"start": 1325.95, "end": 1326.47, "word": " بده", "probability": 0.459228515625}, {"start": 1326.47, "end": 1327.23, "word": " يعطيلك", "probability": 0.861572265625}, {"start": 1327.23, "end": 1327.99, "word": " ان", "probability": 0.81689453125}, {"start": 1327.99, "end": 1328.39, "word": " ال", "probability": 0.77099609375}, {"start": 1328.39, "end": 1329.11, "word": " Phi", "probability": 0.52978515625}, {"start": 1329.11, "end": 1330.37, "word": " is", "probability": 0.8798828125}, {"start": 1330.37, "end": 1331.55, "word": " a", "probability": 0.78564453125}, {"start": 1331.55, "end": 1332.73, "word": " تلتة", "probability": 0.9776611328125}, {"start": 1332.73, "end": 1333.49, "word": " to", "probability": 0.9560546875}, {"start": 1333.49, "end": 1334.87, "word": " one", "probability": 0.95068359375}, {"start": 1334.87, "end": 1336.17, "word": " function", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 59, "seek": 134727, "start": 1338.39, "end": 1347.27, "text": "خلصنا النقطة الثانية النقطة التالتة النقطة التالتة بيقول فاين فاينفرس of ستة", "tokens": [9778, 1211, 9381, 8315, 28239, 47432, 3660, 6024, 104, 7649, 10632, 28239, 47432, 3660, 16712, 6027, 2655, 3660, 28239, 47432, 3660, 16712, 6027, 2655, 3660, 4724, 1829, 39648, 6156, 995, 9957, 6156, 995, 9957, 5172, 2288, 3794, 295, 8608, 2655, 3660], "avg_logprob": -0.32403273454734255, "compression_ratio": 1.6951219512195121, "no_speech_prob": 0.0, "words": [{"start": 1338.3899999999999, "end": 1339.57, "word": "خلصنا", "probability": 0.72308349609375}, {"start": 1339.57, "end": 1340.01, "word": " النقطة", "probability": 0.9293619791666666}, {"start": 1340.01, "end": 1340.37, "word": " الثانية", "probability": 0.82379150390625}, {"start": 1340.37, "end": 1340.93, "word": " النقطة", "probability": 0.8483072916666666}, {"start": 1340.93, "end": 1341.63, "word": " التالتة", "probability": 0.9664306640625}, {"start": 1341.63, "end": 1343.43, "word": " النقطة", "probability": 0.7336018880208334}, {"start": 1343.43, "end": 1343.93, "word": " التالتة", "probability": 0.983154296875}, {"start": 1343.93, "end": 1344.25, "word": " بيقول", "probability": 0.7237955729166666}, {"start": 1344.25, "end": 1345.15, "word": " فاين", "probability": 0.3649088541666667}, {"start": 1345.15, "end": 1346.39, "word": " فاينفرس", "probability": 0.7638346354166666}, {"start": 1346.39, "end": 1346.65, "word": " of", "probability": 0.3916015625}, {"start": 1346.65, "end": 1347.27, "word": " ستة", "probability": 0.900390625}], "temperature": 1.0}, {"id": 60, "seek": 136833, "start": 1348.73, "end": 1368.33, "text": "أول امبارح اخدنا النقطة السادسة في النظرية الأولى بيجينا نقول انه في انفرس لو كان في اف جي بده يساوي ال جي برايم النقطة السادسة عندك يبقى في انفرس اف جي برايم هو ال جي في ال kernel", "tokens": [10721, 12610, 1975, 2304, 3555, 9640, 5016, 1975, 9778, 3215, 8315, 28239, 47432, 3660, 21136, 18513, 3794, 3660, 8978, 28239, 19913, 2288, 10632, 16247, 12610, 7578, 4724, 1829, 7435, 1829, 8315, 8717, 39648, 16472, 3224, 8978, 16472, 5172, 2288, 3794, 45164, 25961, 8978, 1975, 5172, 10874, 1829, 47525, 3224, 7251, 3794, 995, 45865, 2423, 10874, 1829, 4724, 23557, 32640, 28239, 47432, 3660, 21136, 18513, 3794, 3660, 43242, 4117, 7251, 3555, 4587, 7578, 8978, 16472, 5172, 2288, 3794, 1975, 5172, 10874, 1829, 4724, 23557, 32640, 31439, 2423, 10874, 1829, 8978, 2423, 28256], "avg_logprob": -0.3033287991648135, "compression_ratio": 1.968944099378882, "no_speech_prob": 0.0, "words": [{"start": 1348.73, "end": 1349.69, "word": "أول", "probability": 0.4149169921875}, {"start": 1349.69, "end": 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{"start": 1367.77, "end": 1368.33, "word": " kernel", "probability": 0.5859375}], "temperature": 1.0}, {"id": 61, "seek": 139432, "start": 1368.96, "end": 1394.32, "text": "أو بلغتنا هنا الجامعة يبقى يقول جي زائد ال kernel بس بدنا نعرف مين هي جي هذه يبقى احنا عندنا الفاي inverse of ستة الفاي inverse of ستة تعني اللي هو ال X زائد ال kernel للفاي تمام؟", "tokens": [10721, 2407, 4724, 1211, 17082, 2655, 8315, 34105, 25724, 10943, 27884, 7251, 3555, 4587, 7578, 7251, 39648, 10874, 1829, 30767, 16373, 3215, 2423, 28256, 4724, 3794, 47525, 8315, 8717, 3615, 28480, 3714, 9957, 39896, 10874, 1829, 29538, 7251, 3555, 4587, 7578, 1975, 5016, 8315, 43242, 8315, 27188, 47302, 17340, 295, 8608, 2655, 3660, 27188, 47302, 17340, 295, 8608, 2655, 3660, 37279, 22653, 13672, 1829, 31439, 2423, 1783, 30767, 16373, 3215, 2423, 28256, 24976, 5172, 47302, 46811, 10943, 22807], "avg_logprob": -0.21439873794966105, "compression_ratio": 1.7159763313609468, "no_speech_prob": 0.0, "words": [{"start": 1368.96, 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of G في الـ kernel للـ Phi بدي ساوي الـ Phi of G يبقى هذا كله بدي ساوي الـ Phi of G is an isomorphism that is ان الـ G", "tokens": [2600, 72, 295, 460, 8978, 2423, 39184, 28256, 24976, 39184, 41435, 4724, 16254, 8608, 995, 45865, 2423, 39184, 41435, 295, 460, 7251, 3555, 4587, 7578, 23758, 28242, 3224, 4724, 16254, 8608, 995, 45865, 2423, 39184, 41435, 295, 460, 307, 364, 307, 32702, 1434, 300, 307, 16472, 2423, 39184, 460], "avg_logprob": -0.27843750596046446, "compression_ratio": 1.4821428571428572, "no_speech_prob": 0.0, "words": [{"start": 1867.74, "end": 1868.78, "word": "ipsi", "probability": 0.560791015625}, {"start": 1868.78, "end": 1869.7, "word": " of", "probability": 0.8408203125}, {"start": 1869.7, "end": 1870.14, "word": " G", "probability": 0.39892578125}, {"start": 1870.14, "end": 1870.66, "word": " في", "probability": 0.87841796875}, {"start": 1870.66, "end": 1870.94, "word": " الـ", "probability": 0.63623046875}, {"start": 1870.94, "end": 1871.52, "word": " kernel", 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"probability": 0.876953125}, {"start": 1965.64, "end": 1966.38, "word": " بتقول", "probability": 0.940673828125}, {"start": 1966.38, "end": 1966.68, "word": " لي", "probability": 0.1790771484375}, {"start": 1966.68, "end": 1967.62, "word": " لو", "probability": 0.83154296875}, {"start": 1967.62, "end": 1968.12, "word": " كان", "probability": 0.994140625}, {"start": 1968.12, "end": 1970.48, "word": " عندنا", "probability": 0.939697265625}, {"start": 1970.48, "end": 1972.08, "word": " five", "probability": 0.161376953125}, {"start": 1972.08, "end": 1973.1, "word": " a", "probability": 0.1683349609375}, {"start": 1973.1, "end": 1973.54, "word": " group", "probability": 0.8955078125}, {"start": 1973.54, "end": 1974.84, "word": " homomorphism", "probability": 0.9215494791666666}, {"start": 1974.84, "end": 1975.3, "word": " from", "probability": 0.80078125}, {"start": 1975.3, "end": 1975.68, "word": " G", "probability": 0.50390625}, {"start": 1975.68, "end": 1975.88, "word": " ل", "probability": 0.75341796875}, {"start": 1975.88, "end": 1976.2, "word": " G", "probability": 0.425048828125}, {"start": 1976.2, "end": 1976.44, "word": " bar", "probability": 0.4580078125}, {"start": 1976.44, "end": 1977.98, "word": " ماقلش", "probability": 0.6058349609375}, {"start": 1977.98, "end": 1978.26, "word": " G", "probability": 0.59521484375}, {"start": 1978.26, "end": 1978.4, "word": " و", "probability": 0.95849609375}, {"start": 1978.4, "end": 1978.58, "word": " G", "probability": 0.76123046875}, {"start": 1978.58, "end": 1978.8, "word": " bar", "probability": 0.5703125}, {"start": 1978.8, "end": 1979.28, "word": " groups", "probability": 0.689453125}, {"start": 1979.28, "end": 1979.82, "word": " هدول", "probability": 0.8953450520833334}, {"start": 1979.82, "end": 1980.42, "word": " لكن", "probability": 0.8291015625}, {"start": 1980.42, "end": 1980.9, "word": " أنا", "probability": 0.7568359375}, {"start": 1980.9, "end": 1981.36, "word": " بفهم", "probability": 0.94287109375}, {"start": 1981.36, "end": 1981.74, "word": " انه", "probability": 0.758056640625}, {"start": 1981.74, "end": 1982.18, "word": " groups", "probability": 0.87548828125}, {"start": 1982.18, "end": 1982.84, "word": " من", "probability": 0.986328125}, {"start": 1982.84, "end": 1983.16, "word": " خلال", "probability": 0.9845377604166666}, {"start": 1983.16, "end": 1983.54, "word": " قللي", "probability": 0.5165201822916666}, {"start": 1983.54, "end": 1984.14, "word": " group", "probability": 0.92041015625}, {"start": 1984.14, "end": 1985.4, "word": " homomorphism", "probability": 0.9763997395833334}, {"start": 1985.4, "end": 1986.1, "word": " يعني", "probability": 0.963134765625}, {"start": 1986.1, "end": 1986.38, "word": " مش", "probability": 0.96728515625}, {"start": 1986.38, "end": 1986.72, "word": " function", "probability": 0.18994140625}, {"start": 1986.72, "end": 1987.12, "word": " بين", "probability": 0.64453125}, {"start": 1987.12, "end": 1987.4, "word": " two", "probability": 0.9267578125}, {"start": 1987.4, "end": 1987.96, "word": " sets،", "probability": 0.453857421875}, {"start": 1987.96, "end": 1988.2, "word": " بين", "probability": 0.865234375}, {"start": 1988.2, "end": 1988.68, "word": " two", "probability": 0.93701171875}, {"start": 1988.68, "end": 1989.14, "word": " groups", "probability": 0.96142578125}], "temperature": 1.0}, {"id": 84, "seek": 201702, "start": 1989.48, "end": 2017.02, "text": "يبقى لو قللت الـPhi بـA جروب همومورفزم من G لـG bar أو قللت Phi بـA همومورفزم from the group G to the group G bar اتنين نفس النص تمام؟ يبقى then the mapping ابصى من الـG kernel Phi للـPhi of G معرفة بـPhi of الـleft coset الجي في ال kernel للـPhi بده يساوي Phi of G is an isomorphism", "tokens": [1829, 3555, 4587, 7578, 45164, 12174, 1211, 1211, 2655, 2423, 39184, 47, 4954, 4724, 39184, 32, 10874, 32887, 3555, 8032, 2304, 20498, 13063, 5172, 11622, 2304, 9154, 460, 5296, 39184, 38, 2159, 34051, 12174, 1211, 1211, 2655, 41435, 4724, 39184, 32, 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114, "seek": 275316, "start": 2732.58, "end": 2753.16, "text": "مقسوما على ال order تبع الكرنل للفاي بدي ساوي ال order للفاي of G بالشكل اللي عندنا طيب لو ضربناها بصير عندنا مين بصير عندنا ان ال order لل G", "tokens": [2304, 4587, 3794, 2407, 15042, 15844, 2423, 1668, 6055, 3555, 3615, 33251, 2288, 1863, 1211, 24976, 5172, 47302, 4724, 16254, 8608, 995, 45865, 2423, 1668, 24976, 5172, 47302, 295, 460, 20666, 8592, 28820, 13672, 1829, 43242, 8315, 23032, 1829, 3555, 45164, 48812, 25513, 8315, 11296, 4724, 9381, 13546, 43242, 8315, 3714, 9957, 4724, 9381, 13546, 43242, 8315, 16472, 2423, 1668, 24976, 460], "avg_logprob": -0.32812498770062887, "compression_ratio": 1.7080291970802919, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2732.58, "end": 2733.78, "word": "مقسوما", "probability": 0.658154296875}, {"start": 2733.78, "end": 2734.16, "word": " على", "probability": 0.77734375}, {"start": 2734.16, "end": 2734.38, "word": " ال", "probability": 0.2208251953125}, {"start": 2734.38, "end": 2734.8, "word": " order", "probability": 0.333740234375}, {"start": 2734.8, "end": 2735.38, "word": " تبع", "probability": 0.7024739583333334}, {"start": 2735.38, "end": 2736.18, "word": " الكرنل", "probability": 0.659912109375}, {"start": 2736.18, "end": 2736.88, "word": " للفاي", "probability": 0.5478515625}, {"start": 2736.88, "end": 2737.8, "word": " بدي", "probability": 0.27764892578125}, {"start": 2737.8, "end": 2738.3, "word": " ساوي", "probability": 0.7320963541666666}, {"start": 2738.3, "end": 2738.48, "word": " ال", "probability": 0.91650390625}, {"start": 2738.48, "end": 2739.1, "word": " order", "probability": 0.966796875}, {"start": 2739.1, "end": 2740.86, "word": " للفاي", "probability": 0.6666666666666666}, {"start": 2740.86, "end": 2741.84, "word": " of", "probability": 0.91748046875}, {"start": 2741.84, "end": 2742.56, "word": " G", "probability": 0.52734375}, {"start": 2742.56, "end": 2743.9, "word": " بالشكل", "probability": 0.8759765625}, {"start": 2743.9, "end": 2744.06, "word": " اللي", "probability": 0.92138671875}, {"start": 2744.06, "end": 2744.42, "word": " عندنا", "probability": 0.948974609375}, {"start": 2744.42, "end": 2745.48, "word": " طيب", "probability": 0.7953287760416666}, {"start": 2745.48, "end": 2746.04, "word": " لو", "probability": 0.92041015625}, {"start": 2746.04, "end": 2747.36, "word": " ضربناها", "probability": 0.9879150390625}, {"start": 2747.36, "end": 2748.08, "word": " بصير", "probability": 0.9532877604166666}, {"start": 2748.08, "end": 2748.5, "word": " عندنا", "probability": 0.980712890625}, {"start": 2748.5, "end": 2748.82, "word": " مين", "probability": 0.7027587890625}, {"start": 2748.82, "end": 2749.7, "word": " بصير", "probability": 0.8221842447916666}, {"start": 2749.7, "end": 2750.36, "word": " عندنا", "probability": 0.975341796875}, {"start": 2750.36, "end": 2751.0, "word": " ان", "probability": 0.7783203125}, {"start": 2751.0, "end": 2751.26, "word": " ال", "probability": 0.98583984375}, {"start": 2751.26, "end": 2752.04, "word": " order", "probability": 0.9814453125}, {"start": 2752.04, "end": 2752.7, "word": " لل", "probability": 0.91650390625}, {"start": 2752.7, "end": 2753.16, "word": " G", "probability": 0.7646484375}], "temperature": 1.0}, {"id": 115, "seek": 277302, "start": 2753.54, "end": 2773.02, "text": "بدي ساوي ال order للكرن للـ Phi في ال order للـ Phi of G هذا معناه ان ال order للـ Phi of G divide ال order لـ G وهو المطلوب", "tokens": [3555, 16254, 8608, 995, 45865, 2423, 1668, 5296, 23275, 2288, 1863, 24976, 39184, 41435, 8978, 2423, 1668, 24976, 39184, 41435, 295, 460, 23758, 20449, 8315, 3224, 16472, 2423, 1668, 24976, 39184, 41435, 295, 460, 9845, 2423, 1668, 5296, 39184, 460, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.37533244300395885, "compression_ratio": 1.6238532110091743, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2753.54, "end": 2754.04, "word": "بدي", "probability": 0.369903564453125}, {"start": 2754.04, "end": 2754.76, "word": " ساوي", "probability": 0.7423502604166666}, {"start": 2754.76, "end": 2754.94, "word": " ال", "probability": 0.6005859375}, {"start": 2754.94, "end": 2755.48, "word": " order", "probability": 0.90185546875}, {"start": 2755.48, "end": 2756.84, "word": " للكرن", "probability": 0.66497802734375}, {"start": 2756.84, "end": 2757.6, "word": " للـ", "probability": 0.4632568359375}, {"start": 2757.6, "end": 2758.04, "word": " Phi", "probability": 0.08721923828125}, {"start": 2758.04, "end": 2758.66, "word": " في", "probability": 0.654296875}, {"start": 2758.66, "end": 2758.92, "word": " ال", "probability": 0.89990234375}, {"start": 2758.92, "end": 2759.64, "word": " order", "probability": 0.953125}, {"start": 2759.64, "end": 2760.62, "word": " للـ", "probability": 0.59765625}, {"start": 2760.62, "end": 2761.44, "word": " Phi", "probability": 0.7841796875}, {"start": 2761.44, "end": 2762.56, "word": " of", "probability": 0.9248046875}, {"start": 2762.56, "end": 2763.26, "word": " G", "probability": 0.923828125}, {"start": 2763.26, "end": 2764.28, "word": " هذا", "probability": 0.87255859375}, {"start": 2764.28, "end": 2765.08, "word": " معناه", "probability": 0.9864908854166666}, {"start": 2765.08, "end": 2765.88, "word": " ان", "probability": 0.728515625}, {"start": 2765.88, "end": 2766.16, "word": " ال", "probability": 0.97265625}, {"start": 2766.16, "end": 2766.78, "word": " order", "probability": 0.9755859375}, {"start": 2766.78, "end": 2767.42, "word": " للـ", "probability": 0.540771484375}, {"start": 2767.42, "end": 2767.82, "word": " Phi", "probability": 0.861328125}, {"start": 2767.82, "end": 2768.52, "word": " of", "probability": 0.95947265625}, {"start": 2768.52, "end": 2768.96, "word": " G", "probability": 0.98974609375}, {"start": 2768.96, "end": 2770.02, "word": " divide", "probability": 0.2432861328125}, {"start": 2770.02, "end": 2771.04, "word": " ال", "probability": 0.95263671875}, {"start": 2771.04, "end": 2771.62, "word": " order", "probability": 0.970703125}, {"start": 2771.62, "end": 2771.98, "word": " لـ", "probability": 0.658203125}, {"start": 2771.98, "end": 2772.12, "word": " G", "probability": 0.80517578125}, {"start": 2772.12, "end": 2772.5, "word": " وهو", "probability": 0.755859375}, {"start": 2772.5, "end": 2773.02, "word": " المطلوب", "probability": 0.931884765625}], "temperature": 1.0}, {"id": 116, "seek": 279346, "start": 2776.8, "end": 2793.46, "text": "يبقى أحاول أن أثبت الكرولري من خلال main من خلال النتيجة يوم الأربعاء ان شاء الله بتكون المحاضرة الأخيرة التي بها ننهي هذا section وحنحاول نحل أكثر من سؤال على شكل أمثلة", "tokens": [1829, 3555, 4587, 7578, 5551, 5016, 995, 12610, 14739, 5551, 12984, 3555, 2655, 33251, 2288, 12610, 16572, 9154, 16490, 1211, 6027, 2135, 9154, 16490, 1211, 6027, 28239, 31371, 7435, 3660, 7251, 20498, 16247, 25513, 3615, 16606, 16472, 13412, 16606, 21984, 39894, 30544, 9673, 5016, 46958, 25720, 16247, 9778, 48923, 38392, 4724, 11296, 8717, 1863, 3224, 1829, 23758, 3541, 4032, 5016, 1863, 5016, 995, 12610, 8717, 5016, 1211, 5551, 4117, 49115, 9154, 8608, 33604, 6027, 15844, 13412, 28820, 5551, 2304, 12984, 37977], "avg_logprob": -0.2143673845907537, "compression_ratio": 1.6353591160220995, "no_speech_prob": 7.271766662597656e-06, "words": [{"start": 2776.8, "end": 2777.14, "word": "يبقى", "probability": 0.63824462890625}, {"start": 2777.14, "end": 2777.46, "word": " أحاول", "probability": 0.83428955078125}, {"start": 2777.46, "end": 2777.6, "word": " أن", "probability": 0.564453125}, {"start": 2777.6, "end": 2777.96, "word": " أثبت", "probability": 0.957275390625}, {"start": 2777.96, "end": 2778.66, "word": " الكرولري", "probability": 0.6500244140625}, {"start": 2778.66, "end": 2779.32, "word": " من", "probability": 0.9326171875}, {"start": 2779.32, "end": 2779.74, "word": " خلال", "probability": 0.994140625}, {"start": 2779.74, "end": 2780.1, "word": " main", "probability": 0.1717529296875}, {"start": 2780.1, "end": 2780.42, "word": " من", "probability": 0.51123046875}, {"start": 2780.42, "end": 2781.1, "word": " خلال", "probability": 0.99462890625}, {"start": 2781.1, "end": 2782.0, "word": " النتيجة", "probability": 0.8751220703125}, {"start": 2782.0, "end": 2782.52, "word": " يوم", "probability": 0.840576171875}, {"start": 2782.52, "end": 2782.98, "word": " الأربعاء", "probability": 0.8924560546875}, {"start": 2782.98, "end": 2783.12, "word": " ان", "probability": 0.724609375}, {"start": 2783.12, "end": 2783.32, "word": " شاء", "probability": 0.9697265625}, {"start": 2783.32, "end": 2783.38, "word": " الله", "probability": 0.94189453125}, {"start": 2783.38, "end": 2783.78, "word": " بتكون", "probability": 0.8310546875}, {"start": 2783.78, "end": 2784.56, "word": " المحاضرة", "probability": 0.989990234375}, {"start": 2784.56, "end": 2785.78, "word": " الأخيرة", "probability": 0.9337565104166666}, {"start": 2785.78, "end": 2786.16, "word": " التي", "probability": 0.6728515625}, {"start": 2786.16, "end": 2786.64, "word": " بها", "probability": 0.71630859375}, {"start": 2786.64, "end": 2787.08, "word": " ننهي", "probability": 0.962646484375}, {"start": 2787.08, "end": 2787.38, "word": " هذا", "probability": 0.87939453125}, {"start": 2787.38, "end": 2787.92, "word": " section", "probability": 0.521484375}, {"start": 2787.92, "end": 2789.14, "word": " وحنحاول", "probability": 0.8849690755208334}, {"start": 2789.14, "end": 2789.72, "word": " نحل", "probability": 0.9417317708333334}, {"start": 2789.72, "end": 2790.68, "word": " أكثر", "probability": 0.87255859375}, {"start": 2790.68, "end": 2790.92, "word": " من", "probability": 0.98974609375}, {"start": 2790.92, "end": 2791.36, "word": " سؤال", "probability": 0.9920247395833334}, {"start": 2791.36, "end": 2791.6, "word": " على", "probability": 0.86962890625}, {"start": 2791.6, "end": 2792.5, "word": " شكل", "probability": 0.88720703125}, {"start": 2792.5, "end": 2793.46, "word": " أمثلة", "probability": 0.9581298828125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2795.21825, "duration_after_vad": 2616.208749999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1600c817b496a2d7389ed8a97a8239b5be81cddf
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/xcu62wzN56k.srt
@@ -0,0 +1,1823 @@
+1
+00:00:21,700 --> 00:00:26,740
+بسم الله الرحمن الرحيم عودة على بدء المرة الماضية
+
+2
+00:00:27,120 --> 00:00:31,700
+عطينا تعريف للـ isomorphism وعطينا بعض الأمثلة على
+
+3
+00:00:31,700 --> 00:00:37,640
+الـ isomorphism ثم برهننا نظرية وهي أي group
+
+4
+00:00:37,640 --> 00:00:41,680
+isomorphic إلى الـ group of permutations وعطينا
+
+5
+00:00:41,680 --> 00:00:46,920
+مثالًا واحدًا المرة الماضية ووصلنا إلى خواص
+
+6
+00:00:46,920 --> 00:00:51,280
+الـ isomorphism يبقى أنا كاتب عنوان properties of
+
+7
+00:00:51,280 --> 00:00:57,970
+isomorphism بخواص التشكل النمطية نقسم هذه الخواص 
+
+8
+00:00:57,970 --> 00:01:03,350
+إلى جزءين الجزء الأول الخواص حين يعمل الـ
+
+9
+00:01:03,350 --> 00:01:08,970
+isomorphism على عناصر الـ group والخاصية الثانية
+
+10
+00:01:08,970 --> 00:01:13,170
+حينما يعمل الـ isomorphism على الشكل العام للـ group
+
+11
+00:01:13,170 --> 00:01:17,630
+وبالتالي سيكون عندنا نظريتين هذه النظرية الأولى
+
+12
+00:01:17,630 --> 00:01:22,890
+مكونة من سبع نقاط والنظرية الثانية مكونة من أربع
+
+13
+00:01:22,890 --> 00:01:28,320
+نقاط إن شاء الله تعالى نبدأ بالنظرية الأولى وهي الـ
+
+14
+00:01:28,320 --> 00:01:33,160
+properties of isomorphism acting on elements يبقى
+
+15
+00:01:33,160 --> 00:01:39,600
+خواص الـ isomorphism إن كان يعمل عالميًا على العناصر
+
+16
+00:01:39,600 --> 00:01:43,990
+الموجودة في الـ group بقول يفترض أن الـ Phi عبارة
+
+17
+00:01:43,990 --> 00:01:48,250
+عن isomorphism من الآن فصاعدًا سأختصر كلمة
+
+18
+00:01:48,250 --> 00:01:53,770
+isomorphism إلى ISO اللي هي أول ثلاث حروف من كلمة
+
+19
+00:01:53,770 --> 00:01:59,290
+isomorphism يبقى Phi isomorphism من الـ group G onto
+
+20
+00:01:59,290 --> 00:02:04,970
+to G bar يبقى one to one و on to ويختصم الخاصية اللي
+
+21
+00:02:04,970 --> 00:02:08,310
+هو الـ isomorphism بالإضافة إلى أن الـ Phi عبارة عن
+
+22
+00:02:08,310 --> 00:02:15,150
+function يبقى then phi of EG يساوي الـ EG bar يعني
+
+23
+00:02:15,150 --> 00:02:19,610
+فيه لما تؤثر على الـ identity element تبع الـ group
+
+24
+00:02:19,610 --> 00:02:25,450
+G ستخلي صورته من الـ identity تبع الـ group G bar
+
+25
+00:02:25,450 --> 00:02:29,070
+يعني صورة الـ identity في الـ group الأولى هو الـ
+
+26
+00:02:29,070 --> 00:02:34,910
+identity تبع الـ group الثاني النقطة الثانية لو أخذت
+
+27
+00:02:34,910 --> 00:02:40,570
+أي عدد صحيح موجب أو سالب أو صفر موجود في Z وأخذت
+
+28
+00:02:40,570 --> 00:02:45,510
+أي element a موجود في g فـ phi لم تؤثر على a to the
+
+29
+00:02:45,510 --> 00:02:51,340
+power n بدها تساوي phi of a كله to the power n لاحظوا
+
+30
+00:02:51,340 --> 00:02:56,440
+أن الـ a إنّها دي موجودة في g لأن a موجودة في g بس
+
+31
+00:02:56,440 --> 00:03:02,000
+الـ phi of a موجودة في G bar يبقى هذا element موجود
+
+32
+00:03:02,000 --> 00:03:07,620
+في G bar النقطة الثالثة فرعان a و b موجودة في g
+
+33
+00:03:07,620 --> 00:03:13,660
+الـ a ب تبدأ تساوي b أي بي اي فندع phi of a في phi
+
+34
+00:03:13,660 --> 00:03:19,950
+of b وساوي phi of b في phi of a بمعنى آخر لو كان هذا
+
+35
+00:03:19,950 --> 00:03:24,430
+الكلام لأي two elements لو كانت الـ G أبيليان يبقى
+
+36
+00:03:24,430 --> 00:03:28,990
+الـ G bar بتصير أبيليان كذلك هذا معنى الـ two
+
+37
+00:03:28,990 --> 00:03:33,690
+elements لو تطوّرها على مجموع العناصر كلها النقطة
+
+38
+00:03:33,690 --> 00:03:38,440
+الرابعة الـ G بدأت تساوي الـ group generated by A
+
+39
+00:03:38,440 --> 00:03:44,000
+فندع الـ G bar generated by Phi of A يعني يا
+
+40
+00:03:44,000 --> 00:03:48,280
+شباب الـ generator في الـ group الأولى صورتها بتبقى
+
+41
+00:03:48,280 --> 00:03:54,080
+generator لمين؟ للـ group الثانية يبقى أنا عندي A
+
+42
+00:03:54,080 --> 00:03:59,140
+هو generator للـ group G صارت صورتها Phi of A هي
+
+43
+00:03:59,140 --> 00:04:04,560
+generator لمين؟ للـ group G bar النقطة الخامسة الـ
+
+44
+00:04:04,560 --> 00:04:09,220
+order لـ A بدها تساوي الـ order للـ Phi of A الـ order
+
+45
+00:04:09,220 --> 00:04:13,820
+للـ element A اللي موجود في الـ group G يساوي الـ
+
+46
+00:04:13,820 --> 00:04:18,340
+order لصورته تبع هذا الـ element اللي موجود وين؟ في
+
+47
+00:04:18,340 --> 00:04:22,010
+الـ group G bar وإذا بتذكروا المرة الماضية لما
+
+48
+00:04:22,010 --> 00:04:26,630
+تكلّمنا عن معنى الـ isomorphism قلنا الخواص جميعها
+
+49
+00:04:26,630 --> 00:04:30,150
+اللي موجودة على الـ group الأولى هي نفس الخواص اللي
+
+50
+00:04:30,150 --> 00:04:34,350
+موجودة على الـ group الثانية ومن هنا فالـ order للـ a
+
+51
+00:04:34,350 --> 00:04:40,660
+هو الـ order للـ phi of a بالضبط تمامًا النقطة السادسة
+
+52
+00:04:40,660 --> 00:04:45,240
+for any fixed integer k يعني لو أخذت عدد صحيح
+
+53
+00:04:45,240 --> 00:04:51,060
+سمّيته k و fixed element b in g وكانت عندك المعادلة
+
+54
+00:04:51,060 --> 00:04:57,400
+x<sup>k</sup> تساوي b يبقى هذه المعادلة لها نفس العدد من
+
+55
+00:04:57,400 --> 00:05:01,860
+الحلول مثل حل المعادلة x<sup>k</sup> بدها تساوي
+
+56
+00:05:01,860 --> 00:05:07,940
+phi of b in G bar الأولى في G والثانية وين؟ في G
+
+57
+00:05:07,940 --> 00:05:12,420
+bar حلول المعادلة لو كان عشرة حلول إذا المعادلة
+
+58
+00:05:12,420 --> 00:05:17,480
+الثانية لها عشرة حلول بالضبط تمامًا النقطة السادسة
+
+59
+00:05:17,480 --> 00:05:21,920
+السابعة والأخيرة لو كانت الـ G finite يبقى الـ order
+
+60
+00:05:21,920 --> 00:05:25,880
+للـ G بدها تساوي من؟ الـ order للـ G bar طب لو
+
+61
+00:05:25,880 --> 00:05:31,620
+كانوا اثنان N finite يبقى الـ order للأولى يساوي الـ
+
+62
+00:05:31,620 --> 00:05:36,680
+order للثانية يساوي infinite لكن المشكلة تبقى لو
+
+63
+00:05:36,680 --> 00:05:41,640
+كانوا finite هل العدد هنا هو نفس العدد هنا الإجابة
+
+64
+00:05:41,640 --> 00:05:47,410
+نعم لماذا هذا ما سنعرفه بعد قليل يبقى بعد أن فهمنا
+
+65
+00:05:47,410 --> 00:05:52,070
+هذه النقاط السبع نريد أن نبرهن على صحة هذه
+
+66
+00:05:52,070 --> 00:05:58,270
+النقاط ونبدأ بالنقطة الأولى بدي أثبت أن صورة الـ
+
+67
+00:05:58,270 --> 00:06:02,430
+identity element اللي موجود في G هو الـ identity
+
+68
+00:06:02,430 --> 00:06:07,860
+element اللي موجود وين؟ مش يعني هيك، إيش رأيك في
+
+69
+00:06:07,860 --> 00:06:13,120
+هالشغلة؟ لو جئت أخذت الـ identity تبع الـ G وضربته
+
+70
+00:06:13,120 --> 00:06:18,100
+في الـ identity تبع الـ G، شو بيعطيني هذا؟ الـ
+
+71
+00:06:18,100 --> 00:06:23,720
+identity تبع الـ G هو نفسه طب إيش رأيك بدي أؤثر في
+
+72
+00:06:23,720 --> 00:06:30,160
+على الطرفين مادام طرفين متساويين هذا يعني أن phi of
+
+73
+00:06:30,160 --> 00:06:35,080
+الـ identity تبع الـ G في الـ identity تبع الـ G بدها
+
+74
+00:06:35,080 --> 00:06:41,780
+تساوي phi of الـ identity تبع الـ G الآن نحن جالين
+
+75
+00:06:41,780 --> 00:06:47,150
+في عبارة عن إيش؟ isomorphism إذا أستطيع أدخل الـ Phi
+
+76
+00:06:47,150 --> 00:06:52,130
+على كل element من هذه الـ elements يبقى هذا بدها
+
+77
+00:06:52,130 --> 00:06:57,850
+يعطينا أن Phi of الـ identity تبع الـ G في Phi of الـ
+
+78
+00:06:57,850 --> 00:07:03,730
+identity تبع الـ G بدها تساوي Phi of الـ identity تبع
+
+79
+00:07:03,730 --> 00:07:08,910
+الـ G ليش؟ لأن Phi عبارة عن isomorphism وبالتالي
+
+80
+00:07:08,910 --> 00:07:14,440
+دخلت الـ Phi على كل element من الـ two elements طب في
+
+81
+00:07:14,440 --> 00:07:19,460
+أو في عنصر موجود وين هذا في أي group في G طب
+
+82
+00:07:19,460 --> 00:07:23,140
+G إيش قلنا عليها؟ group العنصر معناته إيه؟ له
+
+83
+00:07:23,140 --> 00:07:27,700
+معكوس معناته هذا العنصر اللي هو معكوس في G bar
+
+84
+00:07:27,700 --> 00:07:32,920
+بدي أروح أضرب الطرفين في هذا المعكوس يبقى لو روحت
+
+85
+00:07:32,920 --> 00:07:36,820
+ضربت الطرفين في هذا المعكوس بيصير phi of الـ
+
+86
+00:07:36,820 --> 00:07:42,860
+identity تبع الـ G في phi of الـ identity تبع الـ G في
+
+87
+00:07:42,860 --> 00:07:49,290
+phi of الـ identity تبع الـ G بس الكل inverse بدها تساوي
+
+88
+00:07:49,290 --> 00:07:53,830
+الـ Phi of الـ identity تبع الـ G في Phi of الـ
+
+89
+00:07:53,830 --> 00:08:01,190
+identity تبع الـ G الكل inverse يبقى ضربت المعادلة
+
+90
+00:08:01,190 --> 00:08:06,010
+اللي عندنا هذه من جهتي اليمين في الـ element Phi of
+
+91
+00:08:06,010 --> 00:08:11,590
+G inverse طب الـ element هذا في هذا مش هذا الـ
+
+92
+00:08:11,590 --> 00:08:16,970
+element ومعكوسه؟ قد إيش بيعطيني؟ تبع مين؟ تبع الـ G
+
+93
+00:08:16,970 --> 00:08:25,110
+bar في الـ Phi of EG بيعطيني مين؟ لا بيعطيني Phi
+
+94
+00:08:25,110 --> 00:08:30,810
+of EG دغري لأن Phi of EG element في G bar ويعني هذا
+
+95
+00:08:30,810 --> 00:08:35,590
+بدها تعطيني مين؟ بدها تعطيني الـ Phi of الـ identity
+
+96
+00:08:35,590 --> 00:08:40,550
+تبع الـ G في الـ identity element تبع الـ G bar وهذا
+
+97
+00:08:40,550 --> 00:08:45,410
+بدها تعطيني الـ identity element تبع مين؟ تبع الـ G
+
+98
+00:08:45,410 --> 00:08:51,220
+bar طب هذا element في G bar لأن صورة الـ identity
+
+99
+00:08:51,220 --> 00:08:55,340
+element تبع الـ G وهذا الـ identity element تبع الـ
+
+100
+00:08:55,340 --> 00:09:01,640
+G bar حصل ضربهم شو بيعطيني؟ الـ phi of EG نفسه لأن
+
+101
+00:09:01,640 --> 00:09:04,660
+الـ identity element أضربه في أي عنصر في الـ group
+
+102
+00:09:04,660 --> 00:09:10,650
+بيعطيني نفس العنصر إذا بناء عليه هذا بدها تعطيني أن
+
+103
+00:09:10,650 --> 00:09:17,570
+الـ Phi of الـ EG بدها تساوي الـ Identity Element تبع
+
+104
+00:09:17,570 --> 00:09:24,170
+الـ G bar أظن وهو المطلوب يبقى هَيْ أثبتنا له أن
+
+105
+00:09:24,170 --> 00:09:28,130
+صورة الـ Identity Element تبع الـ G هو الـ Identity
+
+106
+00:09:28,130 --> 00:09:34,110
+Element تبع الـ G bar طيب، كويس نجي للنقطة
+
+107
+00:09:34,110 --> 00:09:39,930
+الثانية النقطة الثانية بيقول for any n belongs to Z
+
+108
+00:09:39,930 --> 00:09:45,930
+وما قال ليّش positive integer قال ليّ n موجود في Z إذا
+
+109
+00:09:45,930 --> 00:09:51,630
+احتمال n أن يكون صفر واحتمال أن يكون عدد موجب
+
+110
+00:09:51,630 --> 00:09:56,910
+واحتمال أن يكون عدد سالب مش كل الاحتمالات واردة إذا
+
+111
+00:09:56,910 --> 00:10:02,230
+لازم أدرس كل هذه الاحتمالات على العلاقة اللي عندنا
+
+112
+00:10:02,230 --> 00:10:07,040
+هذه يبقى أنا بدي أثبت صحيحة في حالة إنّ السالبة وإنّ
+
+113
+00:10:07,040 --> 00:10:12,380
+الموجبة وإنّ الصفرية كل الاحتمالات لازم أدرسها حتى
+
+114
+00:10:12,380 --> 00:10:18,640
+تبقى العلاقة عندي صحيحة على طول بعد ذلك الآن بنجي
+
+115
+00:10:18,640 --> 00:10:26,220
+بيقولوا لو كانت الـ n تساوي zero then ماذا يحصل هنا
+
+116
+00:10:26,220 --> 00:10:34,840
+يا عزيزي؟ phi of a<sup>0</sup> يساوي phi of a<sup>0</sup> كله<sup>0</sup>
+
+117
+00:10:34,840 --> 00:10:41,780
+هذا يريد أن يعطينا إذا a<sup>0</sup> عبارة عن مين؟ تبع الـ G
+
+118
+00:10:41,780 --> 00:10:46,680
+يبقى هذا يريد أن يعطينا الـ phi identity element تبع
+
+119
+00:10:46,680 --> 00:10:48,500
+الـ G وهذا يريد أن يعطينا مين؟
+
+120
+00:10:54,190 --> 00:10:58,150
+النقطة الأولى اللي عندنا هذا بالضبط تمامًا يبقى
+
+121
+00:10:58,150 --> 00:11:03,350
+معناته الـ statement صحيحة في حالة n تساوي zero
+
+122
+00:11:03,350 --> 00:11:12,640
+يبقى هذا بدها تعطينا in the statement hall يبقى
+
+123
+00:11:12,640 --> 00:11:17,600
+الجملة اللي عندنا هذه مالها؟ صحيحة في حالة n تساوي
+
+124
+00:11:17,600 --> 00:11:22,640
+zero طب لو كانت الـ n تساوي واحد then
+
+125
+00:11:32,890 --> 00:11:38,630
+يبقى الجملة صحيحة في حالة الـ n تساوي واحد هذا 
+
+126
+00:11:38,630 --> 00:11:43,130
+سيعطينا أن ال statement صحيح في حالة الـ n تساوي
+
+127
+00:11:43,130 --> 00:11:48,240
+واحد، الآن بدي استخدم الـ induction، بدي أفترض أنَّها 
+
+128
+00:11:48,240 --> 00:11:53,780
+صحيحة في حالة الـ n تساوي k الموجبة، وأثبت أنَّها صحيحة
+
+129
+00:11:53,780 --> 00:11:59,180
+في حالة الـ n تساوي k زائد واحد، يبقى بدي أقول له
+
+130
+00:11:59,180 --> 00:12:08,240
+assume that أن Phi of a to the power k بتساوي five
+
+131
+00:12:08,240 --> 00:12:16,200
+of a كله to the power k، والـ K هذي أكبر منين؟ من
+
+132
+00:12:16,200 --> 00:12:22,440
+الواحد، لأن الواحد استخدمناها، حُطها على طول طيب،
+
+133
+00:12:22,440 --> 00:12:30,160
+بدأ أروح أقول الـ Phi of K plus one ويساوي يبقى
+
+134
+00:12:30,160 --> 00:12:38,120
+هذه بقدر تبع Phi of K في A أس واحد، لو جمعته، نجمع
+
+135
+00:12:38,120 --> 00:12:40,520
+الأسس، نجمعها، يبقى صحيحة
+
+136
+00:12:45,990 --> 00:12:57,130
+فاي عبارة عن isomorphism لأن فاي
+
+137
+00:12:57,130 --> 00:13:00,370
+عبارة عن isomorphism لأن فاي عبارة عن isomorphism
+
+138
+00:13:00,370 --> 00:13:05,750
+لأن فاي عبارة عن isomorphism لأن
+
+139
+00:13:05,750 --> 00:13:13,670
+فاي عبارة عن isomorphism، يبقى بقدر أكتب هذه في of a
+
+140
+00:13:13,670 --> 00:13:20,590
+كله to the power كيف؟ في of a من وين؟ من الفرض اللي
+
+141
+00:13:20,590 --> 00:13:32,540
+فوق اللي عندنا هذا، يبقى هذا الكلام from above
+
+142
+00:13:32,540 --> 00:13:40,940
+assumption، من الفرض اللي فرضناه، يبقى صارت العبارة
+
+143
+00:13:40,940 --> 00:13:47,180
+صحيحة، فرضنا صحتها عند n تساوي k، وأثبتنا صحتها عند n 
+
+144
+00:13:47,180 --> 00:13:53,400
+تساوي k plus one، إذا العبارة صحيحة لكل الـ n اللي
+
+145
+00:13:53,400 --> 00:14:00,300
+أكبر من أو تساوي zero، يبقى هنا so the statement
+
+146
+00:14:02,650 --> 00:14:10,110
+hold، صحيحة for all ان اللي أكبر من أو تساوي zero
+
+147
+00:14:10,110 --> 00:14:15,410
+ايش ضايل عندي؟ أقل من الـ zero، يبقى باجي بقوله بعد
+
+148
+00:14:15,410 --> 00:14:21,150
+ما أخذنا F(n)، وهنا لو كانت N تساوي K، يبقى بدي أجي
+
+149
+00:14:21,150 --> 00:14:29,620
+يأخذ، لو كانت N أقل من الـ zero then، الـ N تساوي
+
+150
+00:14:29,620 --> 00:14:38,100
+الناقص M، والـ M أكبر من الـ Zero، يبقى أنا فارض أن
+
+151
+00:14:38,100 --> 00:14:44,340
+إن n تساوي ناقص M، وM أكبر من الـ zero، مسبوقة بإشارة
+
+152
+00:14:44,340 --> 00:14:48,840
+سالب، إذا هذه السالبة على طول، يبقى مضمون كلامي صحيح
+
+153
+00:14:48,840 --> 00:14:55,240
+مية بالمئة، يبقى لو كانت الـ M الآن موجبة، أكبر من الـ
+
+154
+00:14:55,240 --> 00:14:59,580
+zero، ضربت في إشارة سالب، مش بيصير اللي هي n، يبقى
+
+155
+00:14:59,580 --> 00:15:05,620
+مضمون هيك أن سالبة مائة بالمئة تمام، يبقى بدك تحط
+
+156
+00:15:05,620 --> 00:15:10,940
+في دماغك أن M موجبة، سوقت بإشارة سالبة، وصارت ايه؟
+
+157
+00:15:10,940 --> 00:15:17,860
+سالبة، يبقى هذا بده يعطيلك أن الـ N زائد الـ M قداش؟
+
+158
+00:15:17,860 --> 00:15:23,860
+بده يساوي زيرو، نجلناها على شجة ثانية، يساوي زيرو طيب،
+
+159
+00:15:23,860 --> 00:15:32,620
+الآن لو جيت أخذت A N زائد الـ M، مش بده يساوي الـ A أو
+
+160
+00:15:32,620 --> 00:15:43,420
+الـ Zero؟ فَهِمْتُ؟ تمام؟ طيب، أليس تهادي A N في A M، بده
+
+161
+00:15:43,420 --> 00:15:50,840
+يساوي الـ identity element تبع الـ G؟ مظبوط؟ طيب،
+
+162
+00:15:50,840 --> 00:15:55,930
+ايش رأيك؟ بده يأثر على الطرفين بـ Fi، لأن في ايزو
+
+163
+00:15:55,930 --> 00:16:04,630
+مورفزم، هذا بدي يعطيك أن Phi of a n في Phi of a m، بدي يساوي
+
+164
+00:16:04,630 --> 00:16:11,010
+Phi of الـ identity element تبع الـ G، الآن في ايزو
+
+165
+00:16:11,010 --> 00:16:18,910
+مورفزم، معناه هذا الكلام أن Phi of a n في Phi of a m
+
+166
+00:16:18,910 --> 00:16:25,890
+بدي يساوي الـ identity element تبع الـ G بار، طب الـ M
+
+167
+00:16:25,890 --> 00:16:31,320
+موجبة، الله سالمة، بقى طب، واحنا أثبتنا أن هذه
+
+168
+00:16:31,320 --> 00:16:37,040
+الصحيحة لـ K الموجبة، إذا بالنسبة لـ n بقدر أكتب Phi
+
+169
+00:16:37,040 --> 00:16:46,560
+of A لكل أس M، مظبوط؟ يبقى هذا بده يعطيلك أن Phi of A
+
+170
+00:16:46,560 --> 00:16:54,860
+N في Phi of A كل أس M، بده يساوي الـ identity element
+
+171
+00:16:54,860 --> 00:17:03,390
+تبع الـ G بار، ليش هذا؟ هذا الكلام from the .. حطها
+
+172
+00:17:03,390 --> 00:17:12,330
+ليه بين قوسين؟ above approved since ال M greater
+
+173
+00:17:12,330 --> 00:17:19,300
+than zero، يعني نظرًا لأن الـ M أكبر من الـ zero، قدرت
+
+174
+00:17:19,300 --> 00:17:25,520
+أرفع الأس من هنا على A، وأحطه على Phi of A كله، لكن
+
+175
+00:17:25,520 --> 00:17:31,380
+تبع الـ N لسه مش قادر، كويس؟ ايش رأيك؟ بدي أضرب فيه
+
+176
+00:17:31,380 --> 00:17:43,060
+معكوس هذا العنصر، يبقى هذا يعطيك أن Phi of m في Phi of m
+
+177
+00:17:43,060 --> 00:17:51,320
+في Phi of m في Phi of m في Phi of m في Phi of m في Phi of m في
+
+178
+00:17:51,320 --> 00:17:51,520
+m في Phi of m في Phi of m في Phi of m في Phi of m في Phi of m في
+
+179
+00:17:51,520 --> 00:17:52,300
+m في Phi of m في Phi of m في Phi of m في Phi of m في Phi of m في
+
+180
+00:17:52,300 --> 00:17:52,400
+m في Phi of m في Phi of m في Phi of m في Phi of m في Phi of m في
+
+181
+00:17:52,400 --> 00:18:01,860
+m في Phi of m في Phi of m في Phi of m في Phi of m في Phi of m في
+
+182
+00:18:01,860 --> 00:18:03,940
+Phi of m
+
+183
+00:18:05,750 --> 00:18:11,830
+طب ايش رأيك في العنصر هذا وهذا؟ مش واحد معكوس
+
+184
+00:18:11,830 --> 00:18:16,670
+الثاني؟ إذا هذا بيعطيني الـ identity element تبع
+
+185
+00:18:16,670 --> 00:18:23,290
+من؟ الـ G بار، بيقدروا في Phi of An، يبقى هذا بيقدر
+
+186
+00:18:23,290 --> 00:18:30,730
+يعطيني Phi of An، بيقدر يساوي هذا أس مركب
+
+187
+00:18:30,730 --> 00:18:35,030
+باعتباره، يبقى تضرب الأسس في بعضها في الـ identity
+
+188
+00:18:35,030 --> 00:18:42,470
+بيطلع نفس الـ main، نفس الـ element، يبقى هذا Phi of L
+
+189
+00:18:42,470 --> 00:18:52,050
+ناقص M، تمام؟ طيب، ناقص M هي مين عندنا هنا؟ N، يبقى بده
+
+190
+00:18:52,050 --> 00:18:58,310
+يشيلها ويكتب بدلها N، يبقى هذا بده يعطينا Phi of A
+
+191
+00:18:58,310 --> 00:19:06,370
+N، بده يساوي Phi of A كله to the power N، وهو المطلوب
+
+192
+00:19:07,110 --> 00:19:12,670
+إذا أثبتنا هذه الخاصية رقم اثنين، لأن Zero إن بواحد
+
+193
+00:19:12,670 --> 00:19:18,530
+وإن عدد موجب، وإن عدد سالب، إذا صحيحة لكل الـ n اللي
+
+194
+00:19:18,530 --> 00:19:27,850
+موجودة في Z، يبقى هنا So Phi of A N بدرساوي Phi of
+
+195
+00:19:27,850 --> 00:19:34,430
+A كله to the power N، لكل n اللي موجود في Z بلا
+
+196
+00:19:34,430 --> 00:19:39,600
+استثناء، حد بيحب يسألني سؤال هنا في النقطة الثانية
+
+197
+00:19:39,600 --> 00:19:46,720
+قبل أن نذهب إلى الثالثة، حد بيحب يسألني سؤال؟ اقرأ
+
+198
+00:19:46,720 --> 00:19:50,860
+زين مرة علينا شغل زي هيك مرة، وفصلناها بهذا
+
+199
+00:19:50,860 --> 00:19:56,140
+التفصيل، وبالـ induction، من حد ما يقول لك n في Z، بدك
+
+200
+00:19:56,140 --> 00:20:01,880
+تسوي التفصيل هذا كله، لكن لو جاك n موجودة في N
+
+201
+00:20:01,880 --> 00:20:06,100
+capital، يعني set of natural number، يبقى بكفيني الـ
+
+202
+00:20:06,100 --> 00:20:09,920
+zero أو حتى الـ zero مش لازم، ليه؟ بكفيني الـ واحد والـ
+
+203
+00:20:09,920 --> 00:20:15,390
+k، خلاص، اللي هو الجزء الأول من الـ proof، نعود
+
+204
+00:20:15,390 --> 00:20:21,830
+للنقطة الثالثة، النقطة الثالثة بيقول for any a وb
+
+205
+00:20:21,830 --> 00:20:26,750
+اللي موجود في G، a بيبقى بيبقى بي، بيبقى a، بيبقى a
+
+206
+00:20:26,750 --> 00:20:27,010
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+207
+00:20:27,010 --> 00:20:28,170
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+208
+00:20:28,170 --> 00:20:29,750
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+209
+00:20:29,750 --> 00:20:33,550
+بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a بيبقى a
+
+210
+00:20:33,550 --> 00:20:39,320
+بيبقى a بيبقى a بيبقى a بيA وB اللي موجودة في G، ب
+
+211
+00:20:39,320 --> 00:20:49,000
+الـ A بيبدا يساووا بي A، if and only if تأثير الفاي على
+
+212
+00:20:49,000 --> 00:20:56,060
+الأولى بيبدا يساووا تأثير الفاي على الثانية، مش هدول
+
+213
+00:20:56,060 --> 00:21:00,640
+عنصرين متساويين، وعندي isomorphism، إذا تأثير الـ
+
+214
+00:21:00,640 --> 00:21:03,480
+Phi على الـ element الأول هو نفس تأثير الـ Phi
+
+215
+00:21:03,480 --> 00:21:07,500
+عالميا على الـ element الثاني، لأنه one to one and
+
+216
+00:21:07,500 --> 00:21:14,110
+onto، طيب الكلام هذا صحيح if and only if الـ Phi
+
+217
+00:21:14,110 --> 00:21:18,470
+هذه عبارة عن ايزو مورفزم، إذا بدي أفك هذي وأفك هذي
+
+218
+00:21:18,470 --> 00:21:26,070
+إذا الـ Phi of A في Phi of B بده يساوي، ده أفك هذي
+
+219
+00:21:26,070 --> 00:21:35,590
+يبقى Phi of B في Phi of A، طبعًا يبقى ايه؟ صارت عندنا
+
+220
+00:21:35,590 --> 00:21:40,550
+بالشكل هذا، وهو المطلوب، يبقى وهو المطلوب، نجي
+
+221
+00:21:40,550 --> 00:21:42,350
+للنقطة الرابعة
+
+222
+00:21:44,760 --> 00:21:52,100
+بنمسح الشجة دي كلها، طب وش بتستنوا يالا؟ ما فيش وقت
+
+223
+00:21:52,100 --> 00:21:55,560
+مش هنجي للشجة دي، يعني خلصنا نقطة ثالثة، بنروح
+
+224
+00:21:55,560 --> 00:22:00,820
+للرابعة، الآن بدنا نجي للنقطة الرابعة، واضح أنه G
+
+225
+00:22:01,880 --> 00:22:07,040
+بيقول هي الـ group generated by a أو الـ group
+
+226
+00:22:07,040 --> 00:22:12,780
+generated by a if and only if الـ G bar هي الـ group
+
+227
+00:22:12,780 --> 00:22:19,740
+generated by Phi of a، وكأنه بمعنى آخر بيقول صورة
+
+228
+00:22:19,910 --> 00:22:26,750
+الجنريتر في G هو جنريتر لمين؟ لـ G بار، بعبارة
+
+229
+00:22:26,750 --> 00:22:33,830
+أخرى بيقول الجنريتر تبع لـ group G صورته هو
+
+230
+00:22:33,830 --> 00:22:38,710
+الجنريتر لمين؟ لـ group G بار، معناه أن أنا بقول هذا
+
+231
+00:22:38,710 --> 00:22:43,090
+من ناحية الفهم، لكن احنا بدنا نروح نبرهن، أنا عندي
+
+232
+00:22:43,090 --> 00:22:48,010
+عبارتين مربوطات بـ if and only if، يبقى البرهان بده
+
+233
+00:22:48,010 --> 00:22:55,350
+يصير في اتجاهين، يبقى بدي أجي أقوله assume، افترض
+
+234
+00:22:55,350 --> 00:23:00,710
+العبارة الأولى، أن G هو الـ cyclic group generated
+
+235
+00:23:00,710 --> 00:23:07,320
+by A، ماذا بدنا نثبت؟ بدنا نثبت أن G بار هي الـ
+
+236
+00:23:07,320 --> 00:23:12,880
+group generated by Phi of a، بمعنى آخر لو رجعت إلى
+
+237
+00:23:12,880 --> 00:23:19,240
+مبادئ الرياضيات وقدرت أثبت أن G بار subset من الـ
+
+238
+00:23:19,240 --> 00:23:23,920
+subgroup generated by Phi of a، وبعد ذلك استطعت أن
+
+239
+00:23:23,920 --> 00:23:29,220
+أثبت أن الـ subgroup من الـ G بار، يبقى اثنين are
+
+240
+00:23:29,220 --> 00:23:33,080
+equal، يبقى هذه الاستراتيجية في البرهان بدأت تحدث
+
+241
+00:23:33,080 --> 00:23:38,820
+بالشكل اللي عندنا هذا، طيب نمشي الآن، أنا بدأ أثبت
+
+242
+00:23:38,820 --> 00:23:45,280
+الاثنين هذول are equal، كويس؟ الآن assume، فرضنا هذا
+
+243
+00:23:45,280 --> 00:23:54,460
+الآن الـ A موجودة في G، هذا معناه أن الـ Phi of A
+
+244
+00:23:54,460 --> 00:24:03,000
+موجود في الـ G bar، تمام؟ الـ Phi A موجود في الـ G
+
+245
+00:24:03,000 --> 00:24:10,480
+bar، هذا معناه أن الـ subgroup generated by Phi of
+
+246
+00:24:10,480 --> 00:24:16,280
+A subset من الـ G bar، صح ولا لا؟ هذا الـ element
+
+247
+00:24:16,280 --> 00:24:21,380
+موجود في ايه؟ يبقى صورته موجودة في G بار، مادام الـ
+
+248
+00:24:21,380 --> 00:24:25,380
+element هذا موجود في G بار، يبقى هيك كل الـ
+
+249
+00:24:25,380 --> 00:24:30,560
+subgroup generated by Phi of a يمكن قد الـ G bar
+
+250
+00:24:30,560 --> 00:24:35,420
+بالكامل، ويمكن أقل شوية، لكن عنها ما يزيدش بالمرة، 
+
+251
+00:24:35,420 --> 00:24:38,280
+مظبوط؟ يبقى هذا معناه 
+
+252
+00:24:45,310 --> 00:24:51,570
+العلاقة هذه رقم star الآن
+
+253
+00:24:51,570 --> 00:24:57,390
+نأخذ العملية العكسية افترض
+
+254
+00:24:57,390 --> 00:25:06,780
+أن P موجودة في G باراليل فاي is onto يبقى P
+
+255
+00:25:06,780 --> 00:25:14,520
+اللي موجودة في G بار لها أصل في G يبقى هنا
+
+256
+00:25:14,520 --> 00:25:24,780
+since بما أن الفاي is onto  الـP هذه لازم تسوي لي
+
+257
+00:25:24,780 --> 00:25:34,470
+فاي of  A يبقى الـP اللي أخدته في G أنا فرضت من؟
+
+258
+00:25:34,470 --> 00:25:39,790
+فرضت هذه هيك بالشكل هذا يعني فرضتها الـCyclic group
+
+259
+00:25:39,790 --> 00:25:44,230
+generated by A إذا الـElement P يبدو يساوي
+
+260
+00:25:44,230 --> 00:25:49,070
+الـElement موجود هنا إيه شكل الـElement؟ شكله A
+
+261
+00:25:49,070 --> 00:25:54,130
+أس K يبقى الـElement P اللي موجود في G برصوته Phi
+
+262
+00:25:54,130 --> 00:26:01,530
+of AK طيب لما أقول فاي of a k الـk هادي positive ولا 
+
+263
+00:26:01,530 --> 00:26:05,410
+negative ولا zero؟ positive و negative و zero
+
+264
+00:26:05,410 --> 00:26:15,270
+معقول؟ طلع هنا 0 ممكن 1,2,3,4 لغاية الـN يبقى لا
+
+265
+00:26:15,270 --> 00:26:21,610
+يمكن تبقى negative بالمرة على الإطلاق حتى لو كانت
+
+266
+00:26:21,610 --> 00:26:29,010
+negative فهذه بدها تساوي فاي of A كله to the power K
+
+267
+00:26:29,010 --> 00:26:36,850
+from part 2 طبعا negative مش ممكن لكن احنا بنقول حتى
+
+268
+00:26:36,850 --> 00:26:42,630
+لو كانت يبقى هذه صحيحة بقدر أحط الـK من الـA إلى
+
+269
+00:26:42,630 --> 00:26:49,090
+الـPhi of A K كلها هذا طيب هذا الـelement موجود في
+
+270
+00:26:49,090 --> 00:26:54,780
+الـsubgroup generated by Phi of A ولا لا؟ صح؟ سكت
+
+271
+00:26:54,780 --> 00:26:59,540
+الشعب شخصيات الـcyclic group chapter أربع يبقى الـ
+
+272
+00:26:59,540 --> 00:27:03,740
+element اللي موجود في الـcyclic group generated by a
+
+273
+00:27:03,740 --> 00:27:08,380
+بيكون a أس رقم يبقى الـsub group generated by five
+
+274
+00:27:08,380 --> 00:27:14,740
+of a بيكون فاي of a أس رقم صحيح موجب يبقى معنى
+
+275
+00:27:14,740 --> 00:27:20,660
+هذا الكلام أن الـb تساوي هذه وهذه وإن موجودة هذه
+
+276
+00:27:20,660 --> 00:27:26,760
+موجودة في الـsubgroup generated by phi of a طب
+
+277
+00:27:26,760 --> 00:27:33,090
+أتطلع أخذنا b وين موجودة؟ في G بار وين لقينا b
+
+278
+00:27:33,090 --> 00:27:37,810
+موجودة في فاي of a subgroup generated by فاي of
+
+279
+00:27:37,810 --> 00:27:43,970
+a يبقى معنى هذا الكلام أن G بار هذي الـsubset من
+
+280
+00:27:43,970 --> 00:27:48,950
+الـsubgroup generated by فاي of a وهذه اللي هي
+
+281
+00:27:48,950 --> 00:27:53,370
+double star أطلع لي في الـstar و أطلع لي في الـ
+
+282
+00:27:53,370 --> 00:27:58,350
+double star إيش بنستنتج؟ يبقى باجي بقوله هنا from
+
+283
+00:28:06,130 --> 00:28:13,010
+G بار بيساوي الـsubgroup generated by Phi of A
+
+284
+00:28:13,010 --> 00:28:16,870
+نمشي
+
+285
+00:28:16,870 --> 00:28:25,170
+العملية العكسية يبقى باجي بقوله conversely assume
+
+286
+00:28:25,170 --> 00:28:27,510
+that
+
+287
+00:28:28,610 --> 00:28:34,710
+الـG بار هي الـsubgroup generated by Phi of A
+
+288
+00:28:34,710 --> 00:28:38,850
+مرة
+
+289
+00:28:38,850 --> 00:28:44,870
+ثانية احنا أثبتنا الاتجاه افترضنا الاتجاه الأول و
+
+290
+00:28:44,870 --> 00:28:48,750
+أثبتنا الاتجاه الثاني الآن بدي أفترض الاتجاه
+
+291
+00:28:48,750 --> 00:28:55,540
+الثاني و بدي أحاول أثبت من الاتجاه الأول طب كويس
+
+292
+00:28:55,540 --> 00:29:01,120
+أنا فرضت أن G بار تساوي فاي of a بدي أحاول أثبت أن
+
+293
+00:29:01,120 --> 00:29:07,060
+الـG هي الـsubgroup generated by a اللي صورته من؟
+
+294
+00:29:07,060 --> 00:29:15,300
+صورته فاي of a طب كويس الآن لو جئت أخذت العنصر اللي
+
+295
+00:29:15,300 --> 00:29:19,340
+موجود في G مين ما يكون يكون يبقى لو جئت يقول لك
+
+296
+00:29:19,340 --> 00:29:23,660
+little a belongs to g then
+
+297
+00:29:26,000 --> 00:29:32,660
+الـA K موجود في G ولا لا؟ لأنه G جروب اضربه نفسه
+
+298
+00:29:32,660 --> 00:29:35,600
+إن شاء الله مليون مرة بيكون موجود فيه G لأن G
+
+299
+00:29:35,600 --> 00:29:40,660
+closed under the operation يبقى A K موجود فيه G
+
+300
+00:29:40,660 --> 00:29:48,980
+طيب، الآن لو جئت أخذت هذا بدي أخذ لك إنه الـPhi أو
+
+301
+00:29:48,980 --> 00:29:52,800
+في الأول أستنى، أستنى، لحظة شوية، لحظة شوية والله
+
+302
+00:29:52,800 --> 00:29:59,630
+يا شباب استعجلنا احنا هذه a موجودة في G يبقى تمام
+
+303
+00:29:59,630 --> 00:30:05,890
+معنى هذا الكلام أن الـsubgroup generated by a sub
+
+304
+00:30:05,890 --> 00:30:12,570
+set من G يبقى صح ولا لا؟ يبقى هذه الـsubset من من G
+
+305
+00:30:12,570 --> 00:30:19,550
+وهذه النقطة الأولى اللي بدي أسميها شرطة واحدة تمام
+
+306
+00:30:19,550 --> 00:30:23,970
+يبقى أنا صار subgroup by subset من دي لأن بدي
+
+307
+00:30:23,970 --> 00:30:31,210
+أعمل العملية العكسية يبقى بدأت أقول let الـa
+
+308
+00:30:31,210 --> 00:30:37,990
+belongs to g then الـ
+
+309
+00:30:37,990 --> 00:30:43,630
+a k belongs to g تمام
+
+310
+00:30:44,690 --> 00:30:51,890
+طيب هذا معناه إيش؟ أن الـPhi of A K وين موجودة يا
+
+311
+00:30:51,890 --> 00:30:59,310
+شباب؟ G بار G بار طب و G بار مين هي؟ subgroup
+
+312
+00:30:59,310 --> 00:31:08,170
+generated by Phi of A معناه هذا الكلام أن Phi of A
+
+313
+00:31:08,170 --> 00:31:12,270
+K بده يساوي هنا Phi
+
+314
+00:31:15,180 --> 00:31:25,420
+هذا فاي بيساوي فاي of a اللي هو كله to the power k
+
+315
+00:31:25,420 --> 00:31:33,060
+هذا من أين جبتها؟ من الخاصية رقم اثنين يبقى هذه
+
+316
+00:31:33,060 --> 00:31:42,430
+from اللي هو الخاصية رقم اثنين طيب، الآن صار عندي
+
+317
+00:31:42,430 --> 00:31:49,870
+مين؟ صار عندي Phi of A K بدها تساوي Phi of A كله to
+
+318
+00:31:49,870 --> 00:31:55,770
+the power K طيب، هذا يعتبر element وين موجود؟
+
+319
+00:31:55,770 --> 00:32:02,530
+موجود، فاهمين؟ هذا كله element موجود في الـ
+
+320
+00:32:02,530 --> 00:32:10,650
+subgroup generated by Phi of A لحظة شوية a K موجودة
+
+321
+00:32:10,650 --> 00:32:15,090
+في G فاي أو a K موجودة في P بار G بار احنا
+
+322
+00:32:15,090 --> 00:32:23,350
+فرضينها تساوي هيك اه طيب طيب
+
+323
+00:32:23,350 --> 00:32:28,830
+هذه العبارة لحظة شوية شباب هذه بدي أشيلها a موجودة
+
+324
+00:32:28,830 --> 00:32:40,670
+في G a موجودة في G هذا بده يعطيني أن فاي أو a
+
+325
+00:32:40,670 --> 00:32:45,670
+موجودة
+
+326
+00:32:45,670 --> 00:32:54,390
+في G بار تمام و G بار هي التي تساوي من تساوي فاي
+
+327
+00:32:54,390 --> 00:33:01,930
+أو a طيب
+
+328
+00:33:01,930 --> 00:33:08,650
+يبقى أصبحت عندي بس بديش أخليها يا طيب هذا خطأ A
+
+329
+00:33:08,650 --> 00:33:14,550
+موجود في G يبقى Phi of A موجود في G بار تمام موجود
+
+330
+00:33:14,550 --> 00:33:25,470
+في G بار يبقى Phi of A بدها تساوي استنشف
+
+331
+00:33:25,470 --> 00:33:30,330
+بدي آخذ خلي لي HDB مشان ما يصيرش بس لبس في الموضوع
+
+332
+00:33:30,330 --> 00:33:37,090
+HDB و HDB يبقى بدي أفترض أن P موجود في G يبقى فاي
+
+333
+00:33:37,090 --> 00:33:46,170
+of P موجود في G بار فاي of a هذا بده يعطيني أن فاي
+
+334
+00:33:46,170 --> 00:33:58,820
+of P بده يساوي فاي of a كله to the power of k فاي
+
+335
+00:33:58,820 --> 00:34:06,420
+أو a كله to the power k هذا اللي هو بده يساوي فاي
+
+336
+00:34:06,420 --> 00:34:16,240
+أو a to the power k طبعا فاي إيزو مورفيزم يعني
+
+337
+00:34:16,240 --> 00:34:24,940
+الفاي إيش is one to one يبقى هنا but فاي is one to
+
+338
+00:34:24,940 --> 00:34:31,390
+one ما دام one to one صورتين متساويتين يبقى أصلهم
+
+339
+00:34:31,390 --> 00:34:37,510
+مش بده يكون متساوي يبقى فاي is one to one هذا بده
+
+340
+00:34:37,510 --> 00:34:46,190
+يعطيلك أن P بدها تساوي a to the power k مدام a
+
+341
+00:34:46,190 --> 00:34:50,550
+to the power k يبقى الـa to the power k موجودة في
+
+342
+00:34:50,550 --> 00:34:55,780
+الـsubgroup generated by a ممتاز إذا أخذنا P
+
+343
+00:34:55,780 --> 00:35:01,160
+موجود في G أثبتنا أن P موجود في subgroup
+
+344
+00:35:01,160 --> 00:35:07,680
+generated by a هذا معناه أن G is a subset
+
+345
+00:35:07,680 --> 00:35:14,700
+milligroup generated by a أطلع لي للأولى و أطلع لي
+
+346
+00:35:14,700 --> 00:35:20,630
+للتانية هذه هي اللي هو التانية بالشكل اللي عندنا
+
+347
+00:35:20,630 --> 00:35:26,130
+هنا يبقى بقدر أقول الآن
+
+348
+00:35:26,130 --> 00:35:35,030
+بقدر
+
+349
+00:35:35,030 --> 00:35:43,290
+أقول from اللي هو الـstar الأولى الـstar التانية
+
+350
+00:35:43,290 --> 00:35:52,100
+we have إن الـG بيكون ساوي لـgroup generated by
+
+351
+00:35:52,100 --> 00:35:55,940
+A يبقى
+
+352
+00:35:55,940 --> 00:36:01,560
+هي أثبتنا A اللي هو النظرية يعني يبقى بناء عليه
+
+353
+00:36:01,560 --> 00:36:04,960
+الـG بيكون ساوي لـsubgroup generated by A if
+
+354
+00:36:04,960 --> 00:36:08,340
+and only if الـG برة و الـsubgroup generated by
+
+355
+00:36:08,340 --> 00:36:12,680
+Phi of A بيبقى تفهيمي من الآن فصاعدا إن الـ
+
+356
+00:36:12,680 --> 00:36:17,540
+generator لجروب الأولى الصورة هتولد أو يكون
+
+357
+00:36:17,540 --> 00:36:22,840
+generator لمين؟ للجروب الثاني يبقى هذا النقطة
+
+358
+00:36:22,840 --> 00:36:29,390
+الرابعة بدنا نروح للنقطة الخامسة النقطة الخامسة
+
+359
+00:36:29,390 --> 00:36:34,350
+بتقول أن الـorder لـa بده يساوي الـorder لـفاي of a
+
+360
+00:36:34,350 --> 00:36:39,870
+لكل الـa اللي موجود في G يبقى بقى دا جي أقول له
+
+361
+00:36:39,870 --> 00:36:50,390
+assume أن الـorder لـa بده يساوي m و الـm is
+
+362
+00:36:50,390 --> 00:36:53,750
+finite and
+
+363
+00:36:55,110 --> 00:37:07,890
+الـOrder لـPhi of A بدل سوء الـN مثلا مرة
+
+364
+00:37:07,890 --> 00:37:12,350
+ثانية مطلوب أني أثبت أن الـOrder لـA بدل سوء الـ
+
+365
+00:37:12,350 --> 00:37:18,850
+Order لـPhi A في حالة إذا كان Phi isomorphism يبقى
+
+366
+00:37:18,850 --> 00:37:22,650
+باجي بقول افترض أن الـorder ليه يساوي m و الـm
+
+367
+00:37:22,650 --> 00:37:27,670
+finite لأن الـorder قد يكون infinite يبقى أنا بدأ
+
+368
+00:37:27,670 --> 00:37:32,790
+أخذ حالة الـfinite الـm is finite و أخذت الـorder
+
+369
+00:37:32,790 --> 00:37:37,950
+لفاي يو فيه يساوي الـn إيش بدي أثبت؟ أن الـm بدها
+
+370
+00:37:37,950 --> 00:37:44,630
+ساوي الـn إذا وجدت أثبت أن الـm أقل من أو يساوي الـn
+
+371
+00:37:44,630 --> 00:37:51,000
+و الـn أقل من أو يساوي الـm  أركل بلغة مبادئ
+
+372
+00:37:51,000 --> 00:38:00,480
+الرياضية كويس بأجي بقوله consider خد لي الـPhi of A
+
+373
+00:38:00,480 --> 00:38:12,160
+كله اسم يساوي هذا عبارة عن Phi of A M من أين جبت
+
+374
+00:38:12,160 --> 00:38:18,040
+المعلومة هذه؟ من part two من الجزء الأول يبقى هذه
+
+375
+00:38:18,040 --> 00:38:27,980
+from part two هذا الكلام يساوي فاي of أنا فرضت ال 
+
+376
+00:38:27,980 --> 00:38:36,280
+m هو الأردر تبع الـ a يبقى a أس m ما بجدّش a أس m a
+
+377
+00:38:36,280 --> 00:38:43,790
+أس m بمين؟ بالـ Identity تبع من؟ تبع الـ G وليس الـ 
+
+378
+00:38:43,790 --> 00:38:49,490
+G bar يبقى الـ Identity element تبع الـ G هذا كله
+
+379
+00:38:49,490 --> 00:38:54,790
+يساوي الـ Identity element تبع الـ G bar طيب، أنا
+
+380
+00:38:54,790 --> 00:39:01,530
+فرضت أن ال order لـ Phi of A يساوي الـ N لجيت رقم
+
+381
+00:39:01,530 --> 00:39:06,870
+ثاني رفعته للـ M ساوى الـ Identity شو العلاقة ما
+
+382
+00:39:06,870 --> 00:39:14,940
+بين الـ N و الـ M؟ يبقى ال N أقل من M لأن ال N أصغر
+
+383
+00:39:14,940 --> 00:39:20,480
+عدد صحيح موجب بارفع أس له وبيعطينا ال identity يبقى
+
+384
+00:39:20,480 --> 00:39:27,200
+هنا هذا بده يعطينا أن ال N أقل من أو يساوي ال M
+
+385
+00:39:27,200 --> 00:39:36,100
+وهذا اعتبر هالي هنا Star أغششك أكثر؟ لو كان عندك
+
+386
+00:39:36,100 --> 00:39:42,420
+ال order لإيه هو N ولو وجدت M وضعته أس ساوى ال
+
+387
+00:39:42,420 --> 00:39:49,640
+identity يبقى لازم ال N تقسم ال M دائماً وأبداً
+
+388
+00:39:49,640 --> 00:39:55,700
+يعني ال order لل element أقل أس بحطه للعدد بيعطيني
+
+389
+00:39:55,700 --> 00:40:00,720
+ال identity لو لجيت عدد غيره وضعته أس اللي يعطاني 
+
+390
+00:40:00,720 --> 00:40:04,080
+ال identity يبقى ال order لل element هذا يقسم
+
+391
+00:40:04,080 --> 00:40:09,330
+الرقم الجديد أنا عارف أن هناك Chapter أربعة بس أنا
+
+392
+00:40:09,330 --> 00:40:13,630
+بتذكره بتذكير لأنها بتلزمنا كثير واحنا بنحل مسائل
+
+393
+00:40:13,630 --> 00:40:19,470
+هذه طيب يبقى ال N أقل من أو يساوي من أقل من أو
+
+394
+00:40:19,470 --> 00:40:25,510
+يساوي ال M الآن بدنا نعمل العملية العكسية بدي أثبت
+
+395
+00:40:25,510 --> 00:40:32,380
+أن ال M أقل من أو يساوي ال M أنا فارض هنا ال order
+
+396
+00:40:32,380 --> 00:40:38,880
+لـ ال a يساوي ال m و ال m is finite افترض أن ال n is 
+
+397
+00:40:38,880 --> 00:40:50,420
+finite يبقى هنا if ال n is finite if
+
+398
+00:40:50,420 --> 00:40:59,930
+ال n is finite then بدي اخذ Phi of a أس n يبقى من
+
+399
+00:40:59,930 --> 00:41:07,340
+part two هذا Phi of a كله to the power n طب أنا افترض
+
+400
+00:41:07,340 --> 00:41:11,500
+أن ال order له كله بده يساوي ال N يبقى هذا مين بده
+
+401
+00:41:11,500 --> 00:41:17,120
+يساوي؟ بده يساوي ال Identity element تبع مين؟ تبع 
+
+402
+00:41:17,120 --> 00:41:23,320
+ال G bar ال Identity element تبع ال G bar اللي هو
+
+403
+00:41:23,320 --> 00:41:28,920
+عبارة عن مين؟ عبارة عن صورة ال Identity element
+
+404
+00:41:28,920 --> 00:41:34,020
+تبع ال G هذا الكلام من وين؟ من part one من النقطة
+
+405
+00:41:34,020 --> 00:41:40,740
+الأولى طيب في one to one ولا لا؟ لو كانت one to one
+
+406
+00:41:40,740 --> 00:41:46,180
+و الصورتين متساويتين يبقى الأصل متساوي
+
+407
+00:41:46,180 --> 00:41:53,020
+يبقى هذا بده يعطينا أن ال n بده يساوي ال Identity
+
+408
+00:41:53,020 --> 00:42:00,000
+since Phi is one to one  نظرًا لأن Phi is one to
+
+409
+00:42:00,000 --> 00:42:06,010
+one طيب يبقى إيه؟ لجيت أس حتة طويلة اعطانا ال
+
+410
+00:42:06,010 --> 00:42:13,630
+identity وأنا فرضت ال order له قداش؟ M يبقى إيش العلاقة
+
+411
+00:42:13,630 --> 00:42:22,370
+M ب N أصغر منه بتقسمه كذلك يبقى باجي بقوله so ال M
+
+412
+00:42:22,370 --> 00:42:30,080
+أقل من أو تساوي ال N وهذه double star الثانية يبقى
+
+413
+00:42:30,080 --> 00:42:34,900
+أنا أثبت له في الحالة الأولى أن N أقل من أو تساوي
+
+414
+00:42:34,900 --> 00:42:40,220
+M وأثبت له أن ال M أقل من أو تساوي N من الاثنين
+
+415
+00:42:40,220 --> 00:42:44,800
+مع بعض هدول يبقى الاثنين are equal يبقى باجي بقوله
+
+416
+00:42:44,800 --> 00:42:54,490
+هنا from Star and Double Star ال N بدها تساوي ال M
+
+417
+00:42:54,490 --> 00:43:00,250
+هذا معناه أن ال order لل element A بده يساوي ال
+
+418
+00:43:00,250 --> 00:43:05,770
+order لـ Phi of A لكل ال element A اللي belongs لـ
+
+419
+00:43:05,770 --> 00:43:11,350
+group main لـ group G وهو المطلوب أحد بده يسألني سؤال
+
+420
+00:43:11,350 --> 00:43:18,930
+في هذه النقطة الخامسة كذلك اه النقطة السادسة
+
+421
+00:43:18,930 --> 00:43:22,830
+والسابعة على السريع في ثلاث دقائق إن شاء الله
+
+422
+00:43:32,770 --> 00:43:35,470
+النقطة الصعبة بالنسبة لي هي إذا قمت باستخدام Integer
+
+423
+00:43:35,470 --> 00:43:38,050
+K وقمت باستخدام Group Element P موجود في الـ
+
+424
+00:43:38,050 --> 00:43:46,210
+Equation يبقى بداجي أقوله افترض أن A اللي موجود في
+
+425
+00:43:46,210 --> 00:43:56,890
+G is a solution of ال X to the power K بدو يساوي
+
+426
+00:43:56,890 --> 00:44:04,650
+الـ B ما دام أنا افترضت حل هذه المعادلة إذا تحقق هذه
+
+427
+00:44:04,650 --> 00:44:09,630
+المعادلة يبقى بصيلة أن a to the power of k بده
+
+428
+00:44:09,630 --> 00:44:16,110
+يساوي من؟ بده يساوي B الآن اثرلي على الطرفين بـ Phi
+
+429
+00:44:16,110 --> 00:44:23,980
+يبقى Phi of a k بده يساوي Phi of B من الجزء اثنين
+
+430
+00:44:23,980 --> 00:44:29,580
+من النظرية يبقى Phi of a كله to the power k بده
+
+431
+00:44:29,580 --> 00:44:35,540
+يساوي Phi of B شوف لي هذا الجزء الثاني ولا لأ هو
+
+432
+00:44:35,540 --> 00:44:42,760
+هذا يبقى Phi of a حققت لمين المعادلة الثانية يبقى 
+
+433
+00:44:42,760 --> 00:44:48,000
+Phi of a عبارة عن Solution يبقى هذا بده يقين أن
+
+434
+00:44:48,000 --> 00:44:55,880
+Phi of a is a solution of x to the power k بده
+
+435
+00:44:55,880 --> 00:45:05,660
+يساوي Phi of B معناته أي Solution للمعادلة يبقى
+
+436
+00:45:05,660 --> 00:45:15,860
+هنا Sir any solution of the equation x to the
+
+437
+00:45:15,860 --> 00:45:20,500
+power k is corresponding
+
+438
+00:45:38,700 --> 00:45:46,740
+وهو المطلوب يعني أي حل للمعادلة الأولى سنجد نظيره
+
+439
+00:45:46,740 --> 00:45:51,680
+له Phi of A حل من للمعادلة الثانية وبالتالي عدد
+
+440
+00:45:51,680 --> 00:45:55,580
+الحلول للمعادلة الأولى يساوي عدد الحلول للمعادلة
+
+441
+00:45:55,580 --> 00:45:58,300
+الثانية سبعة تحصيل حاصل
+
+442
+00:46:13,270 --> 00:46:17,730
+ذن ال order اللي أجيبه دي يساوي ال order اللي أجيبه
+
+443
+00:46:17,730 --> 00:46:28,120
+ليش؟ because Phi is one to one and onto يبقى عدد
+
+444
+00:46:28,120 --> 00:46:31,880
+العناصر هنا بيكون جد عدد عدد عدد عدد عدد عدد عدد
+
+445
+00:46:31,880 --> 00:46:34,380
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+446
+00:46:34,380 --> 00:46:38,280
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+447
+00:46:38,280 --> 00:46:38,820
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+448
+00:46:38,820 --> 00:46:40,460
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+449
+00:46:40,460 --> 00:46:41,940
+عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد عدد
+
+450
+00:46:41,940 --> 00:46:45,420
+عدد عدد
+
+451
+00:46:49,600 --> 00:46:53,300
+يبقى من بابا ولا مالها نهاية جد مالها نهاية يعني
+
+452
+00:46:53,300 --> 00:47:05,260
+يبقى if G is finite also if ال G is infinite then
+
+453
+00:47:05,260 --> 00:47:16,620
+ال G bar is infinite because برضه ال Phi is one
+
+454
+00:47:16,620 --> 00:47:18,880
+to one and onto 
+
+455
+00:47:23,720 --> 00:47:29,800
+طيب لا يزال في خاصية أخيرة للمرة القادمة إن شاء
+
+456
+00:47:29,800 --> 00:47:31,060
+الله يعطيكم العافية
diff --git a/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060.srt b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1a4d90dc57bb9de1874acf0ad94cbe8c02bc4d09
--- /dev/null
+++ b/PL9fwy3NUQKwZKOpj354PRgwYPWWgxchnI/yo2JdR6s060.srt
@@ -0,0 +1,2001 @@
+1
+00:00:20,700 --> 00:00:26,660
+بسم الله الرحمن الرحيم المرة الماضية كانت المحاضرة
+
+2
+00:00:26,660 --> 00:00:32,010
+discussion ونقشنا الأسئلة المطلوبة وبقى سؤالان
+
+3
+00:00:32,010 --> 00:00:40,070
+سؤال 35 وسؤال 39 سؤال 35 يقول اثبت أن لو كانت جي
+
+4
+00:00:40,070 --> 00:00:45,350
+جروب وعليها خاصية الخاصية بتقول the square of
+
+5
+00:00:45,350 --> 00:00:52,930
+every element is the identity then g is abelian
+
+6
+00:00:52,930 --> 00:01:02,730
+يبقى سؤال 35 بقول ما يأتي لو كانت الـ G كل العناصر X
+
+7
+00:01:02,730 --> 00:01:10,070
+بحيث أن X تربيع يساوي الـ identity بدي أثبت هذا هو
+
+8
+00:01:10,070 --> 00:01:18,370
+المطلوب أن G is abelian هذا هو المطلوب طبعا إذا
+
+9
+00:01:18,370 --> 00:01:25,510
+بيقول لي لو كانت الـ group G فيها خاصية هذه الخاصية
+
+10
+00:01:25,860 --> 00:01:31,460
+بتقول أنه أي element x لو رفعته للأس اثنين بدي
+
+11
+00:01:31,460 --> 00:01:36,660
+يعطيني الـ identity بدي أثبت أن هذه هي abelian
+
+12
+00:01:36,660 --> 00:01:41,440
+group abelian group لو أخذت any two elements فيها
+
+13
+00:01:41,440 --> 00:01:46,520
+معناته أن الـ a في b بدي أساويه بي في a for all a و b
+
+14
+00:01:46,520 --> 00:01:53,080
+اللي belongs to g يبقى لأثبت أنه g abelian يبقى
+
+15
+00:01:53,080 --> 00:02:05,010
+هنا fالـ A والـ B موجودة في G و shall shall ذات
+
+16
+00:02:05,010 --> 00:02:11,910
+بدنا نحاول نثبت أن الـ A في B بده يساوي B في A لكل الـ
+
+17
+00:02:11,910 --> 00:02:17,290
+A و B اللي belongs تماما لـ G يعني أبقى بقالي بقوله
+
+18
+00:02:17,290 --> 00:02:18,850
+الحل كتالي
+
+19
+00:02:23,490 --> 00:02:28,890
+مطلوب لإثبات تحت هذا الـ condition أن G أبليان a
+
+20
+00:02:28,890 --> 00:02:34,850
+group فبتروح تأخذ two elements موجودات في G يبقى لو
+
+21
+00:02:34,850 --> 00:02:41,130
+كان الـ A والـ B موجودة في G then مربع أي واحد فيهم
+
+22
+00:02:41,130 --> 00:02:46,990
+أو a star a اللي هي main اللي هي a تربيع بده يساوي
+
+23
+00:02:46,990 --> 00:02:52,290
+الـ identity و الـ b تربيع بده يساوي الـ identity
+
+24
+00:02:52,290 --> 00:02:57,690
+طبق لمين؟ طبق للمعطيات اللي موجودة عندنا هنا طب
+
+25
+00:02:57,690 --> 00:03:02,690
+خليني أسأل السؤال التالي طب لو كان a في b لكل
+
+26
+00:03:02,690 --> 00:03:07,980
+تربيع كده إيش بده يعطينا؟ برضه الـ identity لأن الـ a
+
+27
+00:03:07,980 --> 00:03:11,920
+في b هو element موجود في الـ group لأن الـ group is
+
+28
+00:03:11,920 --> 00:03:16,040
+closed under the given operation يبقى بناء عليه
+
+29
+00:03:16,040 --> 00:03:21,840
+هذا كمان هيعطينا الـ identity element طب الآن لو
+
+30
+00:03:21,840 --> 00:03:29,420
+جيت الـ a تربيع هذه أليست هي a في a يعني عند الـ a
+
+31
+00:03:29,420 --> 00:03:35,820
+تربيع هذا معناه أن الـ A تربيع بي تربيع بدي يساوي A
+
+32
+00:03:35,820 --> 00:03:39,520
+بي الكل تربيع اللي هو الـ identity هذا بيساوي الـ
+
+33
+00:03:39,520 --> 00:03:42,180
+identity وهذا بيساوي الـ identity وهذا بيساوي الـ
+
+34
+00:03:42,180 --> 00:03:47,820
+identity يبقى بناء عليه هذا كله بدي يعطيني الـ
+
+35
+00:03:47,820 --> 00:03:54,860
+identity element لكن الـ A تربيع هذه هي عبارة عن A
+
+36
+00:03:54,860 --> 00:04:01,090
+في A والـ B اللي هي عبارة عن B في B والـ AB تربيع
+
+37
+00:04:01,090 --> 00:04:07,710
+اللي هي عبارة عن AB في AB مظبوط أخذنا احنا الـ
+
+38
+00:04:07,710 --> 00:04:10,770
+right cancellation law والـ left cancellation law
+
+39
+00:04:10,770 --> 00:04:16,970
+مظبوط يعني معنى هذا الكلام أنه ممكن أضرب من جهة
+
+40
+00:04:16,970 --> 00:04:21,630
+الشمال في A inverse وأضرب من جهة اليمين في B
+
+41
+00:04:21,630 --> 00:04:26,730
+inverse ولن تكون هناك أي مشكلة بس بدك ترى الدقة
+
+42
+00:04:26,730 --> 00:04:31,570
+عندما تضرب من جهة الشمال في الـ a inverse يبقى a
+
+43
+00:04:31,570 --> 00:04:38,910
+inverse a a b كمان b بدي أضربها في الـ b inverse
+
+44
+00:04:38,910 --> 00:04:43,570
+بدي أساويه زي ما ضربت في الـ a inverse من جهة الشمال
+
+45
+00:04:43,570 --> 00:04:49,530
+يبقى بدي أضرب في الـ a inverse من جهة الشمال a b a
+
+46
+00:04:49,530 --> 00:04:54,650
+b كمان في الـ b inverse من جهة الشمال طيب تمام هذا
+
+47
+00:04:54,650 --> 00:05:00,980
+كده ش بيعطينا الـ identity هذا كم يعطينا الـ identity
+
+48
+00:05:00,980 --> 00:05:04,260
+وهذا كم يعطينا الـ identity وهذا كم يعطينا الـ
+
+49
+00:05:04,260 --> 00:05:04,640
+identity وهذا كم يعطينا الـ identity وهذا كم يعطينا
+
+50
+00:05:04,640 --> 00:05:05,440
+الـ identity وهذا كم يعطينا الـ identity وهذا كم
+
+51
+00:05:05,440 --> 00:05:08,080
+يعطينا الـ identity وهذا كم يعطينا الـ identity وهذا
+
+52
+00:05:08,080 --> 00:05:11,200
+كم يعطينا الـ identity وهذا كم يعطينا الـ identity
+
+53
+00:05:11,200 --> 00:05:13,740
+وهذا كم يعطينا الـ identity وهذا كم يعطينا الـ
+
+54
+00:05:13,740 --> 00:05:13,760
+identity وهذا كم يعطينا الـ identity وهذا كم يعطينا
+
+55
+00:05:13,760 --> 00:05:14,520
+الـ identity وهذا كم يعطينا الـ identity وهذا كم
+
+56
+00:05:14,520 --> 00:05:16,880
+كم يعطينا الـ identity وهذا كم يعطينا الـ identity
+
+57
+00:05:16,880 --> 00:05:18,540
+وهذا كم يعطينا الـ identity وهذا كم يعطينا الـ
+
+58
+00:05:18,540 --> 00:05:25,360
+identity وهذا كم يعطينا 
+
+59
+00:05:25,360 --> 00:05:31,160
+الـ identity وهذا كم بـ A شو تفسير كل هذا؟ Abelian
+
+60
+00:05:31,160 --> 00:05:36,580
+طبعا هذا كلام صحيح لأن ما أخذتش عنصرين محددين بعينهم
+
+61
+00:05:36,580 --> 00:05:41,940
+أو إني ما أخذت any two elements يعني اختياري يبقى
+
+62
+00:05:41,940 --> 00:05:46,780
+هذا معناه صحيح لكل الـ A والـ B اللي موجودة في G
+
+63
+00:05:46,780 --> 00:05:55,320
+هذا بدي أقول لك أن G is abelian وهو المطلوب سؤال تسعة
+
+64
+00:05:55,320 --> 00:05:55,980
+وثلاثين
+
+65
+00:05:58,680 --> 00:06:06,100
+سؤال تسعة وثلاثين بيقول ما يأتي خد لي الـ G كل
+
+66
+00:06:06,100 --> 00:06:14,060
+المصفوفات يبقى خد لي G هي عبارة عن كل المصفوفات
+
+67
+00:06:14,060 --> 00:06:22,360
+اللي على الشكل التالي A A Aأيه بحيث الـ A موجود في
+
+68
+00:06:22,360 --> 00:06:27,640
+الـ R Star مظبوط هيك بحيث الـ G موجود ولا موجودة
+
+69
+00:06:27,640 --> 00:06:32,400
+في R A موجودة في R و A لا تساوي Zero يعني A موجودة
+
+70
+00:06:32,400 --> 00:06:37,320
+في R Star يعني لا يمكن أن تساوي Zero سواء قلنا
+
+71
+00:06:37,320 --> 00:06:43,030
+الصيغة هذه أو قلنا أن A موجودة في R والـ A لا يساوي
+
+72
+00:06:43,030 --> 00:06:48,450
+0 إذا ممنوع الـ A يساوي الـ 0 يبقى كل المصوفات
+
+73
+00:06:48,450 --> 00:06:52,910
+اللي على الشكل اللي عندنا هذا بيقول يبين الـ G is
+
+74
+00:06:52,910 --> 00:06:57,910
+a group under matrix multiplication X plan Y each
+
+75
+00:06:57,910 --> 00:07:02,710
+element of G has an inverse رغم كذا كذا طيب على أي
+
+76
+00:07:02,710 --> 00:07:08,210
+حال الآن هذه مجموعة المصحفات اللي على الشكل هذا
+
+77
+00:07:08,210 --> 00:07:12,870
+يعني اللي جميع العناصر الأربعة في الـ two by two
+
+78
+00:07:12,870 --> 00:07:17,650
+matrix are equal 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+79
+00:07:17,650 --> 00:07:19,870
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+80
+00:07:19,870 --> 00:07:23,510
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+81
+00:07:23,510 --> 00:07:25,090
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+82
+00:07:25,090 --> 00:07:29,950
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+83
+00:07:29,950 --> 00:07:30,430
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+84
+00:07:30,430 --> 00:07:31,070
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+85
+00:07:31,070 --> 00:07:32,830
+1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
+
+86
+00:07:32,830 --> 00:07:39,930
+1 1 1 1
+
+87
+00:07:39,930 --> 00:07:44,210
+1 1 1 عبارة عن مجموعة تحت عملية ضرب المصوفات احنا
+
+88
+00:07:44,210 --> 00:07:47,850
+بنعرف أن عملية ضرب المصوفات لأي أنواع المصوفات
+
+89
+00:07:47,850 --> 00:07:52,410
+عبارة عن associative binary operation يعني لو ضربت
+
+90
+00:07:52,410 --> 00:07:56,150
+مصوفتين اثنين في اثنين في بعض بيطلع نفس النظام له
+
+91
+00:07:56,150 --> 00:08:01,350
+اثنين في اثنين غير هيك عملية الضرب عملية إدماجية
+
+92
+00:08:01,350 --> 00:08:05,290
+يبقى باجي بقوله solution و
+
+93
+00:08:09,510 --> 00:08:18,350
+know that بنعرف أن الـ matrix multiplication
+
+94
+00:08:18,350 --> 00:08:23,470
+is
+
+95
+00:08:23,470 --> 00:08:32,990
+an associative binary
+
+96
+00:08:32,990 --> 00:08:33,770
+operation
+
+97
+00:08:41,390 --> 00:08:46,050
+يبقى هذه هي النقطة الأولى بدنا نيجي للنقطة الثانية
+
+98
+00:08:46,050 --> 00:08:53,310
+النقطة الثانية بدنا نثبت أن هذه المصوفات لها عنصر
+
+99
+00:08:53,310 --> 00:08:58,790
+واحد طبعا كيف عنصر واحد بحيث هذا العنصر لو ضربته
+
+100
+00:08:58,790 --> 00:09:03,190
+في أي مصوفة بدي يطلع من نفس المصوفة أنا شو شكله
+
+101
+00:09:03,190 --> 00:09:08,770
+أنا مش عارف لذلك هعطيها رمز روح اطلع شو شكل هذا
+
+102
+00:09:08,770 --> 00:09:20,890
+الرمز فبجي بقول assume افترض أن الـ B بي بي بي is
+
+103
+00:09:20,890 --> 00:09:32,130
+the identity element طبعا يا شباب الـ B هنا مالها
+
+104
+00:09:33,180 --> 00:09:37,840
+لا تساوي الـ zero لأن كلها موجودة في الـ R plus
+
+105
+00:09:37,840 --> 00:09:45,040
+افترض أن هذا هو الـ identity element الـ identity
+
+106
+00:09:45,040 --> 00:09:54,000
+element بي بي بي بي لو ضربته في a a a بيطلع نفس الـ
+
+107
+00:09:54,000 --> 00:09:59,920
+element اللي هو a a a بالشكل عن ضربت من اليمين و
+
+108
+00:09:59,920 --> 00:10:04,080
+الشمال للاثنين are the same لأنه مادام identity
+
+109
+00:10:04,080 --> 00:10:07,180
+element إذا ضربت من اليمين ولا ضربت من الشمال كله
+
+110
+00:10:07,180 --> 00:10:11,980
+سيؤدي إلى نفس النتيجة يبقى هذا إيش بيعطينا هذا
+
+111
+00:10:11,980 --> 00:10:15,600
+بيعطينا مثلا بدي أضرب الصف الأول في العمود الأول
+
+112
+00:10:15,600 --> 00:10:24,720
+يبقى BA وهنا BA يبقى اثنين BA يبقى هذا اثنين BA و
+
+113
+00:10:24,720 --> 00:10:31,450
+هنا اثنين BA اثنين بي إيه اثنين بي إيه كله بده يساوي
+
+114
+00:10:31,450 --> 00:10:38,410
+الـ a في الـ a في الـ a طبعا عندي مصفتين بيساووا بعض
+
+115
+00:10:38,410 --> 00:10:45,490
+إذا العناصر المتناظرة مالها؟ متساوية يبقى هذا معناه
+
+116
+00:10:45,490 --> 00:10:53,170
+إيه؟ معناته أنه اثنين بي إيه بده يساوي الـ a itself
+
+117
+00:10:54,340 --> 00:10:59,320
+بنقدر نجسم الطرفين على a نجسم الطرفين على a أو بالـ
+
+118
+00:10:59,320 --> 00:11:03,380
+right cancellation لأن الـ a والـ b هدول real
+
+119
+00:11:03,380 --> 00:11:08,500
+numbers بس لا يساووا صفرا يبقى الـ a لا يساوي zero
+
+120
+00:11:08,500 --> 00:11:12,740
+إذا معناته هذا الكلام أنه اثنين بي بده يساوي جداش
+
+121
+00:11:12,740 --> 00:11:20,160
+واحد هذا معناه أنه بيساوي نص يبقى أصبح اللي هو الـ
+
+122
+00:11:20,160 --> 00:11:21,860
+identity element
+
+123
+00:11:24,530 --> 00:11:36,770
+identity element is نص نص نص نص نص نص
+
+124
+00:11:36,770 --> 00:11:40,070
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+125
+00:11:40,070 --> 00:11:40,490
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+126
+00:11:40,490 --> 00:11:40,610
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+127
+00:11:40,610 --> 00:11:41,790
+نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص نص
+
+128
+00:11:41,790 --> 00:11:44,930
+نص نص
+
+129
+00:11:47,890 --> 00:11:53,890
+بدي افترض أن عندي مصفوفة وهذه المصوفة هي معكوس
+
+130
+00:11:53,890 --> 00:12:02,890
+المصفوفة a a a يبقى هنا باجي بقول assume افترض أن c
+
+131
+00:12:02,890 --> 00:12:12,290
+c c c is the inverse element of
+
+132
+00:12:15,130 --> 00:12:23,770
+اللي موجودة في جيل أصلي افترض أن هذا ال element هو
+
+133
+00:12:23,770 --> 00:12:28,290
+المعكوس إذا الحاصل ضربهما سواء من اليمين أو من اليسار
+
+134
+00:12:28,290 --> 00:12:32,650
+بده يعطيني الـ identity element اللي هو
+
+135
+00:12:32,650 --> 00:12:40,050
+المصفوفة نص نص نص يبقى باجي بقوله إذا ال C C بالشكل
+
+136
+00:12:40,050 --> 00:12:45,370
+اللي عندنا هذا مضروبة في ال A A A كل هذا الكلام
+
+137
+00:12:45,370 --> 00:12:51,870
+بده يساوي نص نص نص طيب
+
+138
+00:12:51,870 --> 00:12:57,390
+هذا الكلام بده يساوي الآن بدي اضرب المصفوفات هدول ضرب
+
+139
+00:12:57,390 --> 00:13:08,310
+في بعض يبقى CA و CA ب 2 CA يبقى هنا اثنين CA اثنين
+
+140
+00:13:08,310 --> 00:13:15,890
+CA اثنين CA اثنين CA اثنين CA اثنين CA اثنين CA
+
+141
+00:13:15,890 --> 00:13:21,350
+اثنين CA اثنين CA اثنين CA اثنين CA اثنين CA اثنين
+
+142
+00:13:21,350 --> 00:13:22,250
+CA اثنين CA اثنين CA اثنين CA اثنين CA اثنين CA
+
+143
+00:13:22,250 --> 00:13:24,090
+اثنين CA اثنين CA اثنين CA اثنين CA اثنين CA اثنين
+
+144
+00:13:24,090 --> 00:13:24,390
+CA اثنين CA اثنين CA اثنين CA اثنين CA اثنين CA
+
+145
+00:13:24,390 --> 00:13:26,420
+CA اثنين CA اثنين CA اثنين CA يبقى لو قررنا العناصر
+
+146
+00:13:26,420 --> 00:13:32,480
+المتطابقة في الطرفين بصير عندي اثنين CA بده يساوي
+
+147
+00:13:32,480 --> 00:13:38,480
+قداش؟ واحد والباقي كله بنفس الطريقة أنا عندي المجهول
+
+148
+00:13:38,480 --> 00:13:45,980
+مين؟ C يبقى C بده يساوي واحد على أربعة A يبقى باجي
+
+149
+00:13:45,980 --> 00:13:55,600
+بقوله هذا بده يعطينا the inverse of اللي هو a و a و
+
+150
+00:13:55,600 --> 00:14:05,140
+a is واحد على أربعة a واحد على أربعة a واحد على
+
+151
+00:14:05,140 --> 00:14:11,640
+أربعة a واحد على أربعة a بهذا الشكل هذا هو المعكوس
+
+152
+00:14:11,640 --> 00:14:15,040
+لمصفوفة اللي عندنا
+
+153
+00:14:17,940 --> 00:14:23,620
+إذا صار كل element له معكوس والـ identity موجود و
+
+154
+00:14:23,620 --> 00:14:28,300
+binary أو associative binary operation يبقى تحققت
+
+155
+00:14:28,300 --> 00:14:33,260
+كل الشروط اللي عندنا معناته جماعة دمالها group يبقى
+
+156
+00:14:33,260 --> 00:14:39,620
+باجي بقوله thus وهكذا that's it اللي عندنا هذه
+
+157
+00:14:39,620 --> 00:14:46,320
+اللي على الشكل اللي عندنا هذا بحيث أن الـ A موجود
+
+158
+00:14:46,320 --> 00:14:55,260
+في الـ (R*) هذي is a group اللي خاطري أتناقش هنا
+
+159
+00:14:55,260 --> 00:15:00,560
+وياكوا في هذا السؤال هذا بعض المناقشات البسيطة
+
+160
+00:15:00,560 --> 00:15:05,580
+السؤال الأول هل الـ group اللي احنا هذي قايلينها
+
+161
+00:15:05,580 --> 00:15:09,640
+موجودة في الـ general linear group of two by two
+
+162
+00:15:09,640 --> 00:15:18,690
+matrices over R؟ مش ممكنية هذه المحددة لا تساوي 0
+
+163
+00:15:18,690 --> 00:15:23,530
+هل هي في الـ special linear group of 2x2 matrices
+
+164
+00:15:23,530 --> 00:15:28,310
+over R؟ لأ لأن هذه المحددة لا تساوي 1
+
+165
+00:15:35,700 --> 00:15:41,900
+إذا المعكوس تبع المصفوفة العادية بيختلف عن المعكوس
+
+166
+00:15:41,900 --> 00:15:45,860
+في حالة من؟ في حالة الجروب، مش يعني دائماً زي ما هو
+
+167
+00:15:45,860 --> 00:15:49,280
+مطلوع في دماغنا واحد، zero, zero, zero، لا، لا،
+
+168
+00:15:49,280 --> 00:15:52,940
+لا، لا، بتختلف، دلوقت هذا السؤال أنا جبته في إحدى
+
+169
+00:15:52,940 --> 00:15:58,880
+الامتحانات قبل خمسة عشر سنة، آه، اللي جيته في كتاب
+
+170
+00:15:58,880 --> 00:16:01,240
+هندي، ما كانش موجود في كتابنا، موجود في الطبعة
+
+171
+00:16:01,240 --> 00:16:05,160
+الجديدة بس، زمان ما كانش موجود في هذه الطبعة لا
+
+172
+00:16:05,160 --> 00:16:10,380
+الأولى ولا الثانية ولا حتى الثالثة طبعاً فلجيت
+
+173
+00:16:10,380 --> 00:16:15,180
+السؤال فكر فيه عجبني الفكرة فجم جايبه إيه؟ جايبه
+
+174
+00:16:15,180 --> 00:16:19,420
+في الامتحان طبعاً ليه؟ عشان إنه طالع هيستغرب لأول و
+
+175
+00:16:19,420 --> 00:16:23,000
+هيقول لك محددة لا تساوي صفر محددة تساوي صفر ويبقى
+
+176
+00:16:23,000 --> 00:16:27,220
+ما فيش لكن اللي بيقولوا اثبت أن هذه group يعني رصبا
+
+177
+00:16:27,220 --> 00:16:30,360
+عنك بدك تجيب الـ identity element أو بدك تجيب الـ
+
+178
+00:16:30,360 --> 00:16:32,180
+inverse element لكن الـ associative binary
+
+179
+00:16:32,180 --> 00:16:35,430
+operation هذه مشهورة على المصفوفات و احنا في التنويه
+
+180
+00:16:35,430 --> 00:16:40,190
+قبل ما نجي على الجامعة تمام لحد هنا stop بدنا نروح
+
+181
+00:16:40,190 --> 00:16:46,170
+نكمل محاضرات كما كنا في المحاضرة قبل الماضي في
+
+182
+00:16:46,170 --> 00:16:52,090
+المحاضرة قبل الماضي بدأنا بموضوع الـ subgroups و قبل
+
+183
+00:16:52,090 --> 00:16:56,450
+أن نبدأ بالـ subgroups روحنا جيبنا عرفنا الـ
+
+184
+00:16:56,450 --> 00:17:01,350
+identity للـ group و الـ identity للـ element اللي في
+
+185
+00:17:01,350 --> 00:17:09,330
+الـ group وبعد ذلك روحنا لمين؟ إلى الـ subgroups الآن
+
+186
+00:17:09,330 --> 00:17:15,470
+بدأ أُلخص شفهي هيك ما درسناه في الشابتر الجديد حتى
+
+187
+00:17:15,470 --> 00:17:22,170
+نكمل عليه معلوماتنا شوف يا سيد في الجزء النظري
+
+188
+00:17:22,170 --> 00:17:27,070
+اللي أخذناه في الشابتر ثلاثة هذا ذكرنا الـ order للـ
+
+189
+00:17:27,070 --> 00:17:32,370
+group وقلنا الـ order للـ group هو عبارة عن عن إيش؟
+
+190
+00:17:32,370 --> 00:17:37,350
+حد بيعرف؟ عدد العناصر اللي موجودة في الـ group طب
+
+191
+00:17:37,350 --> 00:17:40,730
+كويس هذا التعريف الأول التعريف الثاني بدنا الـ
+
+192
+00:17:40,730 --> 00:17:47,150
+order للعنصر اللي موجود في الـ group ها حد بيعرف الـ
+
+193
+00:17:47,150 --> 00:17:48,210
+order للعنصر
+
+194
+00:17:53,330 --> 00:17:58,430
+بالشرط يكون أصغر أس يبقى هو the smallest positive
+
+195
+00:17:58,430 --> 00:18:03,410
+integer such that الـ G to the power n بدو يساوي الـ
+
+196
+00:18:03,410 --> 00:18:09,310
+identity يبقى الـ n هذه بقول عليها هي الـ order لمين؟
+
+197
+00:18:09,310 --> 00:18:15,800
+هي الـ order للـ element تمام يبقى الـ order للـ element
+
+198
+00:18:15,800 --> 00:18:22,520
+هو أصغر عدد موجب برفعه كأس لمن؟ برفعه كأس للـ
+
+199
+00:18:22,520 --> 00:18:26,580
+element بيعطيني الـ identity وممكن ألاقي غيره أكبر
+
+200
+00:18:26,580 --> 00:18:29,380
+منه برضه بيعطيني الـ identity لكن بهمنيش أنا بهمني
+
+201
+00:18:29,380 --> 00:18:34,860
+أصغر أس بحطه للـ element بيعطيني من الـ identity
+
+202
+00:18:34,860 --> 00:18:38,770
+يبقى هذا الفرق ما بين الـ order للـ group والـ order
+
+203
+00:18:38,770 --> 00:18:42,490
+للـ element اللي موجود في الـ group وأخذنا على ذلك
+
+204
+00:18:42,490 --> 00:18:47,870
+بعض الأمثلة ثم دخلنا إلى موضوع الـ subgroup وقلنا
+
+205
+00:18:47,870 --> 00:18:52,490
+لو أخدت subset من الـ group الـ subset دي اللي
+
+206
+00:18:52,490 --> 00:18:57,010
+أخدتها من الـ group بقول عليها الـ subgroup إذا لجأت
+
+207
+00:18:57,010 --> 00:19:02,010
+الـ subset دي بقيت group جديدة تحت نفس العملية تبع
+
+208
+00:19:02,010 --> 00:19:06,590
+الـ group الأصلية مش هاجو بعدين قولنا هذه قصة طويلة
+
+209
+00:19:06,590 --> 00:19:12,110
+روحنا أخذنا عليها نظرية النظرية بتقول لو أخدت الـ H
+
+210
+00:19:12,110 --> 00:19:16,050
+subset من الـ group يبقى هذه الـ H بقول على الـ
+
+211
+00:19:16,050 --> 00:19:21,590
+subgroup إذا تحقق شرطان الشرط الأول إنه H non
+
+212
+00:19:21,590 --> 00:19:27,050
+-empty والشرط الثاني لو أخدت عنصرين موجودات في H
+
+213
+00:19:27,050 --> 00:19:31,950
+فحصل ضرب الأول في معكوس الثاني بيكون وين؟ في H
+
+214
+00:19:31,950 --> 00:19:34,630
+هذه آخر حاجة أخذناها المرة الماضية لكن ما أخذناش
+
+215
+00:19:34,630 --> 00:19:39,380
+أمثلة مظبوط؟ ولا أخذنا .. إذا نجي ناخد أمثلة تطبيق
+
+216
+00:19:39,380 --> 00:19:45,020
+على هذه النظرية يبقى باختصار جاب المبدأ مشان تبقى
+
+217
+00:19:45,020 --> 00:19:53,820
+الـ H subgroup من G لازم يتحقق شرطين الشرط الأولاني
+
+218
+00:19:53,820 --> 00:19:59,780
+أن الـ H لا تساوي Φ أو non-empty يابا نقول عليها
+
+219
+00:19:59,780 --> 00:20:05,730
+non-empty يا ابن قول عليها الـ H لا تساوي Φ هذا
+
+220
+00:20:05,730 --> 00:20:11,870
+الأمر الأول الأمر الثاني لو كان الـ A و الـ B
+
+221
+00:20:11,870 --> 00:20:18,150
+موجودات في الـ H then الـ A B inverse موجود في الـ H
+
+222
+00:20:18,150 --> 00:20:24,050
+يبقى هذه آخر نظرية أخذناها المرة الماضية بدنا الآن
+
+223
+00:20:24,050 --> 00:20:29,230
+على هذه النظرية نعطي عليها مجموعة من الأمثلة
+
+224
+00:20:29,230 --> 00:20:40,750
+التطبيقية أول مثال يبقى example أول مثال بيقول let
+
+225
+00:20:40,750 --> 00:20:47,870
+الـ G be an abelian group let الـ G be an abelian
+
+226
+00:20:47,870 --> 00:20:52,710
+group define
+
+227
+00:20:52,710 --> 00:21:01,170
+عرف الـ H Define الـ H بدها تساوي كل العناصر X اللي
+
+228
+00:21:01,170 --> 00:21:06,610
+موجودة في الـ group G بحيث أن الـ X تربيع بده
+
+229
+00:21:06,610 --> 00:21:12,290
+يساوي الـ identity element السؤال هو هل الـ H هذه
+
+230
+00:21:12,290 --> 00:21:19,570
+الـ subgroup أو ماهياش subgroup يبقى prove or
+
+231
+00:21:19,570 --> 00:21:21,550
+disapprove
+
+232
+00:21:23,500 --> 00:21:30,680
+الـ H هي الـ subgroup من هنا يمكن أن تثبت أن الـ H
+
+233
+00:21:30,680 --> 00:21:33,960
+هي subgroup أو يمكن أن تثبت أن الـ H ليس موجودة في
+
+234
+00:21:33,960 --> 00:21:40,860
+الـ subgroup يمكن أن تثبت أن الـ H هي subgroup من
+
+235
+00:21:40,860 --> 00:21:41,060
+هنا
+
+236
+00:21:45,720 --> 00:21:50,320
+باجي بقوله والله إذا تحقق الشرطان اللي فوق يبقى
+
+237
+00:21:50,320 --> 00:21:55,040
+الـ H subgroup تحقق واحد والتاني لأ يبقى ماهياش
+
+238
+00:21:55,040 --> 00:22:00,160
+subgroup أو ينجيب counter example إن أمكنها ذلك
+
+239
+00:22:00,160 --> 00:22:04,360
+يبقى بدنا نجي نشوف نقول له الـ H هل هي empty ولا non
+
+240
+00:22:04,360 --> 00:22:12,080
+-empty أنا أزعم أن الـ H is non-empty non-empty
+
+241
+00:22:12,080 --> 00:22:20,980
+ليه؟ لأنه بيقول لي عناصر H هما كل العناصر اللي مربعهم
+
+242
+00:22:20,980 --> 00:22:25,480
+بيساوي من؟ الـ identity طب الـ identity نفسه مربع
+
+243
+00:22:25,480 --> 00:22:31,460
+وقداش؟ الـ identity يبقى الـ H is non-empty since
+
+244
+00:22:31,460 --> 00:22:42,150
+حيث الـ E هو الـ E تربيع وهذا موجود في H أي subgroup
+
+245
+00:22:42,150 --> 00:22:44,530
+من المرة الماضية يقول إنه لازم يكون الـ identity
+
+246
+00:22:44,530 --> 00:22:48,690
+element و الـ inverse element موجود يبقى سرعتنا
+
+247
+00:22:48,690 --> 00:22:53,570
+ننفي إذا تحقق الـ condition الأول يبقى هذا الـ
+
+248
+00:22:53,570 --> 00:22:57,510
+condition الأول بدي أجي للـ condition الثاني بدي
+
+249
+00:22:57,510 --> 00:23:07,410
+أخد عنصرين موجودات في H then مربع
+
+250
+00:23:07,410 --> 00:23:14,480
+الأول كده؟ والتاني؟ الـ identity يبقى then A تربيع
+
+251
+00:23:14,480 --> 00:23:19,320
+بده يساوي ال identity، و الـ b تربيع بده يساوي الـ
+
+252
+00:23:19,320 --> 00:23:26,500
+identity. طيب لو جيت قلت لك طيب قداش الـ a والـ b كل
+
+253
+00:23:26,500 --> 00:23:37,720
+تربيع قداش برضه بالـ identity؟ ليش؟ لأنه because إنه 
+
+254
+00:23:37,720 --> 00:23:46,540
+الـ... لأن الـ X تربيع ساوية الـ E لكل X الموجودة في
+
+255
+00:23:46,540 --> 00:23:51,980
+الـ H. طيب 
+
+256
+00:23:51,980 --> 00:23:56,120
+هذا الآن بيساوي ال identity، وهذا الآن بيساوي الـ
+
+257
+00:23:56,120 --> 00:24:03,960
+identity. لو ضربت الـ A تربيع في الـ B تربيع كده إيش
+
+258
+00:24:03,960 --> 00:24:10,440
+بيطلع؟ E في E اللي هو بالـ identity. يبقى هذا الكلام
+
+259
+00:24:10,440 --> 00:24:17,080
+بده يساوي A B كذلك لكل تربيع اللي كل واحد فيهم
+
+260
+00:24:17,080 --> 00:24:22,700
+بيساوي ال identity element. طيب هذا الكلام بده
+
+261
+00:24:22,700 --> 00:24:27,600
+يعطينا إن الـ
+
+262
+00:24:27,600 --> 00:24:36,360
+A في الـ A في الـ B في الـ B بده يساوي A B في الـ A B
+
+263
+00:24:39,230 --> 00:24:43,090
+لكن احنا إيش بدنا؟ بدنا الـ A B inverse ولا لا؟ اه
+
+264
+00:24:43,090 --> 00:24:47,350
+ثانية شوية. يبقى خلينا نجيب الـ A B بلاش الخطوة هذه
+
+265
+00:24:47,350 --> 00:24:52,970
+نيجي ناخد الـ A B inverse. طيب مدام هيك أنا ماخد الـ
+
+266
+00:24:52,970 --> 00:24:57,230
+A والـ B موجودة في H، then الـ A تربيع بده يساوي B
+
+267
+00:24:57,230 --> 00:25:03,110
+تربيع بده يساوي الـ A. لو أخدت من... لو أخدت من...
+
+268
+00:25:03,110 --> 00:25:09,400
+بده ياخد الـ... الـ B inverse. خلي بالك معايا تاني
+
+269
+00:25:09,400 --> 00:25:13,400
+خلي بالك معايا تاني والله بس نعيد الخطوة هذه من
+
+270
+00:25:13,400 --> 00:25:18,460
+جديد. أنا ماخد الـ A والـ B موجودة في H، يبقى A تربيع
+
+271
+00:25:18,460 --> 00:25:21,400
+بده يساوي ال identity، والـ B تربيع بده يساوي الـ
+
+272
+00:25:21,400 --> 00:25:30,200
+identity. طيب لو جيت أخدت هنا من معكوس الـ B، يبقى لو
+
+273
+00:25:30,200 --> 00:25:39,540
+كان f الـ A بده يساوي الـ X، and الـ B بده يساوي Y
+
+274
+00:25:39,540 --> 00:25:44,000
+inverse. على سبيل المثال الـ Y بده يساوي B inverse
+
+275
+00:25:44,000 --> 00:25:49,400
+على سبيل المثال، والـ Y بده يساوي B inverse على
+
+276
+00:25:49,400 --> 00:25:56,920
+سبيل المثال. يبقى أخدت الـ A بده يساوي الـ X، والـ Y بده
+
+277
+00:25:56,920 --> 00:26:02,660
+يساوي B inverse مثلاً. أنا عايز أثبت إن الـ A B
+
+278
+00:26:02,660 --> 00:26:08,160
+inverse موجود وين؟ موجود في H، مظبوط؟ طيب إذا لو
+
+279
+00:26:08,160 --> 00:26:16,840
+جيت أخد الـ A B inverse الكل
+
+280
+00:26:16,840 --> 00:26:22,910
+تربيع، يبقى هذا الكلام يبدو يساوي A B inverse في الـ
+
+281
+00:26:22,910 --> 00:26:31,470
+A B inverse. مظبوط؟ طيب هذا الكلام بدي يكون ماله؟ بدي
+
+282
+00:26:31,470 --> 00:26:37,510
+يكون موجود في H، لإن هذا بدي يساوي ال identity. هذا
+
+283
+00:26:37,510 --> 00:26:43,920
+بدي يساوي من ال identity. طيب كويس. يبقى أنا بدي أحاول
+
+284
+00:26:43,920 --> 00:26:50,320
+هذا بدي يساوي ال identity. لأنه كمية لأ أنا بدي أثبت
+
+285
+00:26:50,320 --> 00:26:54,540
+إنه بدي يساوي ال identity. مش هيك؟ لأ أنا بدي أثبت
+
+286
+00:26:54,540 --> 00:26:58,980
+إنّه بدي يساوي ال identity element، لأن مربع الـ
+
+287
+00:26:58,980 --> 00:27:03,560
+element بده يكون وين موجود؟ بده يكون موجود في it. إذا
+
+288
+00:27:03,560 --> 00:27:08,740
+لما أقول A B inverse في الـ A B inverse، بدي أثبت إن
+
+289
+00:27:08,740 --> 00:27:13,620
+هذا يساوي من ال identity element. كويسة. الحين يا
+
+290
+00:27:13,620 --> 00:27:17,060
+جماعة لما أقول الـ A تربيع بده يساوي الـ E، والـ B
+
+291
+00:27:17,060 --> 00:27:22,160
+تربيع كمان بده يساوي من... بده يساوي الـ E. طب أنا
+
+292
+00:27:22,160 --> 00:27:30,140
+أخدت الـ X في Y، يبقى الـ X Y تربيع
+
+293
+00:27:34,120 --> 00:27:42,080
+ثانية ثانية شوية. لو أخدت أنا بدي أثبت إيش؟ بدي أثبت بدي
+
+294
+00:27:42,080 --> 00:27:47,200
+أثبت لا جي أبيليان. اه صحيح. مواطع أنا نفسي مش شايف
+
+295
+00:27:47,200 --> 00:27:52,480
+إن جي هدي is abelian. جي أبيليان جروب وعرفنا بدي
+
+296
+00:27:52,480 --> 00:27:56,100
+أثبت هذا إنّها subgroup. اه ثانية خلصنا حلت مشكلتنا
+
+297
+00:27:57,080 --> 00:28:01,340
+انحلت المشكلة، يبقى مش ماخد بالله بالي إن جي is
+
+298
+00:28:01,340 --> 00:28:06,140
+أبيليان، خلي بالك يعني، خلاص خلاص خلاص، انحلت خلاص،
+
+299
+00:28:06,140 --> 00:28:10,440
+فرطت كل شيء. يبقى صارت إيه؟ صارت A تربيع بده يساوي
+
+300
+00:28:10,440 --> 00:28:12,720
+ال identity، والـ B تربيع بده يساوي ال identity. أنا
+
+301
+00:28:12,720 --> 00:28:18,640
+بدي أثبت إن الـ A B inverse بده يساوي الـ كل تربيع
+
+302
+00:28:18,640 --> 00:28:22,880
+بده يساوي إيه؟ إن أثبت ذلك، يبقى على طول الخط بصير
+
+303
+00:28:22,880 --> 00:28:26,520
+إيه؟ بصير الـ A B inverse موجودة في H، والتالي الـ H
+
+304
+00:28:26,520 --> 00:28:30,880
+subgroup. تبقى لمين؟ ده الكلام اللي عندنا هذا، يبقى
+
+305
+00:28:30,880 --> 00:28:38,560
+بضعكي آخد A B inverse الكل تربيع. هذا الكلام بده
+
+306
+00:28:38,560 --> 00:28:48,820
+يساوي A B inverse في الـ A B inverse. هذا الكلام
+
+307
+00:28:48,820 --> 00:28:59,420
+بده يساوي A B inverse في A في الـ B inverse في الـ B 
+
+308
+00:28:59,420 --> 00:29:00,180
+inverse
+
+309
+00:29:02,610 --> 00:29:08,770
+يبقى هذا الكلام بده يساوي A تربيع B inverse تربيع.
+
+310
+00:29:08,770 --> 00:29:20,030
+هذا الكلام بده يساوي A تربيع B أس سالب اثنين، أو هذا
+
+311
+00:29:20,030 --> 00:29:27,350
+الكلام بده يساوي A تربيع B تربيع inverse. الشكل
+
+312
+00:29:27,350 --> 00:29:33,450
+اللي عندنا هذا. أخدنا G to the power of M N هي G M N
+
+313
+00:29:33,450 --> 00:29:38,490
+جلبناهم، يبقى هي تطبيق مباشر الآن. هذا بيعطينا من الـ
+
+314
+00:29:38,490 --> 00:29:43,490
+identity، والبين جثين بيعطينا ال identity، وهي الـ
+
+315
+00:29:43,490 --> 00:29:47,650
+inverse اللي برا، يبقى هذا إيش معناه؟ معناه الـ
+
+316
+00:29:47,650 --> 00:29:55,310
+identity itself. بناء عليه الـ A B inverse موجود وين
+
+317
+00:29:55,310 --> 00:30:01,140
+في الـ H. هذا بدي يعطيك إن الـ H is a subgroup من الـ
+
+318
+00:30:01,140 --> 00:30:09,160
+main من الجروب إنّها حققت الشرطين. طب نعطي مثالا رقم
+
+319
+00:30:09,160 --> 00:30:16,460
+اثنين. example two
+
+320
+00:30:16,460 --> 00:30:22,960
+بيقول
+
+321
+00:30:22,960 --> 00:30:33,080
+الـ G be an abelian group. برضه هذه abelian group
+
+322
+00:30:33,080 --> 00:30:46,120
+و let الـ H بدها تساوي كل العناصر X تربيع بحيث إن X
+
+323
+00:30:46,120 --> 00:30:51,420
+موجودة في G. show
+
+324
+00:30:51,420 --> 00:31:01,910
+that بيّلني إن الـ H is a subgroup من G
+
+325
+00:31:01,910 --> 00:31:12,170
+جي
+
+326
+00:31:12,170 --> 00:31:20,620
+أبيليان. أخدنا ست منها H، مين هي هذه الـ H؟ كل X 
+
+327
+00:31:20,620 --> 00:31:25,140
+تربيع بحيث X موجودة في جي. يعني أنا بدي آجي على
+
+328
+00:31:25,140 --> 00:31:30,020
+عناصر جي، بدي أمسك كل عنصر وأربعه، إيش بيطلع؟ بدي
+
+329
+00:31:30,020 --> 00:31:35,980
+موجودة دوان بـ H. بدي أثبت إن الـ H هو subgroup. يبقى
+
+330
+00:31:35,980 --> 00:31:44,060
+بدي آجي للخطوة الأولى، الـ H is non-empty. حد بيقدر
+
+331
+00:31:44,060 --> 00:31:52,480
+يجيب لي فيها answer؟ اه ليش؟ because الـ E موجودة في
+
+332
+00:31:52,480 --> 00:32:00,380
+G. الـ E موجودة في G، and الـ E بيساوي الـ E تربيع
+
+333
+00:32:00,380 --> 00:32:07,160
+اللي موجودة في H، لأن مربع الـ E هو E تربيع، وأنا كل
+
+334
+00:32:07,160 --> 00:32:11,440
+العناصر تبعت الـ H اللي هو العناصر المربعة تبعت
+
+335
+00:32:11,440 --> 00:32:18,510
+الـ G. بيبقى G non-empty. بعد ذلك بدي أفترض إن الـ A والـ
+
+336
+00:32:18,510 --> 00:32:27,610
+B موجودة في الـ H، ثم كل واحد فيهم بيكون على شكل
+
+337
+00:32:27,610 --> 00:32:33,970
+A على شكل كمية مردعة. يبقى باجي بقول الـ A والـ B
+
+338
+00:32:33,970 --> 00:32:41,810
+then الـ X هذا بدي يكون الـ A بدي يكون على شكل X
+
+339
+00:32:41,810 --> 00:32:52,610
+تربيع، and الـ B بدي يكون على شكل Y تربيع for some X
+
+340
+00:32:52,610 --> 00:33:03,480
+و Y اللي موجودة في G. مرة ثانية. مرة ثانية أنا خدت A
+
+341
+00:33:03,480 --> 00:33:10,020
+و B موجودات في H، يبقى كل واحد هنا بدي يكون شكله يا
+
+342
+00:33:10,020 --> 00:33:14,840
+إما X تربيع يا إما Y تربيع، لأن كل عنصر في H هو
+
+343
+00:33:14,840 --> 00:33:19,540
+مربعات main مربعات الـ G. أنا ماخد هدول في H، إذا
+
+344
+00:33:19,540 --> 00:33:25,640
+أصلًا هدول موجودات في G، إذا كل واحد فيهم على الشكل
+
+345
+00:33:25,640 --> 00:33:31,630
+اللي عندنا هذا. الآن بدي آجي آخد A B inverse. إن قدرت
+
+346
+00:33:31,630 --> 00:33:37,890
+أثبت إن موجود موجود في H بتتم المطلوب، يبقى بدي آجي
+
+347
+00:33:37,890 --> 00:33:45,490
+آخد هنا الـ A B inverse. يبقى هذا الكلام الـ A هي X
+
+348
+00:33:45,490 --> 00:33:53,010
+تربيع، والـ B اللي هي Y تربيع، وهذا الـ inverse فوق
+
+349
+00:33:56,320 --> 00:34:05,800
+هذا الكلام يساوي X تربيع في Y سالب اثنين. هذا
+
+350
+00:34:05,800 --> 00:34:08,800
+الكلام
+
+351
+00:34:08,800 --> 00:34:18,000
+يساوي X تربيع Y inverse الكل تربيع.
+
+352
+00:34:23,270 --> 00:34:29,410
+مدام abelian إذا هذا بقدر أقول X Y inverse الكل
+
+353
+00:34:29,410 --> 00:34:34,990
+تربيع بدون مشاكل، لأنك لو ماكنتش abelian بدي أجلب
+
+354
+00:34:34,990 --> 00:34:40,430
+مكان واحد الواحد مكان الثاني، يبقى هذا الكلام بتكتب
+
+355
+00:34:40,430 --> 00:34:46,150
+ليه جنبه because يعني كتبناه بهذا الشكل. G is
+
+356
+00:34:46,150 --> 00:34:54,240
+abelian. طيب السؤال هو هذا موجود في H ولا لا؟ موجود
+
+357
+00:34:54,240 --> 00:35:01,160
+في H، لأنه على شكل كمية مربعة لعنصر من مين؟ من G
+
+358
+00:35:01,160 --> 00:35:06,260
+يبقى مدام صار كمية مربعة، إذا هذا موجود في H، معناه
+
+359
+00:35:06,260 --> 00:35:14,800
+هذا الكلام إنّه A B inverse belongs to H. بإنفرس هذه
+
+360
+00:35:14,800 --> 00:35:21,320
+اللي طلعناها مربع هذا العنصر موجود في H، إذا تحققت
+
+361
+00:35:21,320 --> 00:35:26,360
+الخاصية الثانية من خواص ال subgroup. non-empty أخدت
+
+362
+00:35:26,360 --> 00:35:32,320
+عنصرين من H، أثبت إن حاصل ضرب الأول في معكوس الثاني
+
+363
+00:35:32,320 --> 00:35:38,500
+موجود في H، طبقا للنظرية. هذا معناه إن الـ H is a
+
+364
+00:35:38,500 --> 00:35:41,640
+subgroup من G
+
+365
+00:35:42,940 --> 00:35:47,580
+يعني المقصود من ذلك إحنا بدنا نحقق الخاصية اللي
+
+366
+00:35:47,580 --> 00:35:53,240
+اثنين تبعها ال subgroup بأي وسيلة رياضية صحيحة. طيب
+
+367
+00:35:53,240 --> 00:36:04,780
+المثال الثالث بيقول show that. show that بيّلني إن
+
+368
+00:36:04,780 --> 00:36:08,920
+ال special linear group of two by two matrices
+
+369
+00:36:08,920 --> 00:36:15,020
+over R عبارة عن subgroup من ال general linear
+
+370
+00:36:15,020 --> 00:36:19,140
+group of two by two matrices over R
+
+371
+00:36:23,240 --> 00:36:28,420
+بيّلني لي إن ال special linear group هي sub group من
+
+372
+00:36:28,420 --> 00:36:31,420
+ال general linear group. طبعًا المرة الماضية إحنا و
+
+373
+00:36:31,420 --> 00:36:34,300
+إحنا بناخد أمثلة مش الماضية اللي جبلها واللي 
+
+374
+00:36:34,300 --> 00:36:38,860
+جبلها. أثبتنا إن ال general linear group هي عبارة
+
+375
+00:36:38,860 --> 00:36:42,880
+عن group، وأثبتنا كذلك إن ال special linear group 
+
+376
+00:36:42,880 --> 00:36:46,960
+هي عبارة عن group اليوم بنثبت أن الـ special هي 
+
+377
+00:36:46,960 --> 00:36:51,780
+subset من الـ general ما الفرق ما بين الاتنين
+
+378
+00:36:52,400 --> 00:36:56,480
+إتنين مصفوفة ومربعة نظامها إتنين في إتنين لكن في
+
+379
+00:36:56,480 --> 00:37:01,200
+حالة الـ general المحدد لا يساوي zero مهما يكون
+
+380
+00:37:01,200 --> 00:37:05,820
+الرقم يكون لكن في الثانية المحدد يساوي كده؟ واحد
+
+381
+00:37:05,820 --> 00:37:11,180
+صحيح، أيه الفرق ما بين الاتنين؟ يعني احنا الـ special
+
+382
+00:37:11,180 --> 00:37:14,440
+linear group solution
+
+383
+00:37:16,210 --> 00:37:20,990
+الـ Special Linear Group of 2x2 matrices over R كل
+
+384
+00:37:20,990 --> 00:37:32,550
+المصفات A وB وC وD بحيث أن الـ A وB وC وD موجودة
+
+385
+00:37:32,550 --> 00:37:37,230
+في set of real numbers والـ A D ناقص الـ B C موجودة
+
+386
+00:37:37,230 --> 00:37:42,020
+في set of real numbers هذه اللي هي شغلة عندنا
+
+387
+00:37:42,020 --> 00:37:47,680
+مكان الـ H بدي أثبت أن هذه الـ sub group الآن أنا
+
+388
+00:37:47,680 --> 00:37:54,600
+أدعي أن هذه non-empty، non-empty ليش؟ لأن على الأقل
+
+389
+00:37:54,600 --> 00:37:59,570
+فيها من؟ مصفوفة الوحدة، المحدد تبعها يساوي واحد
+
+390
+00:37:59,570 --> 00:38:05,250
+صحيح، يبقى باجي بقوله النقطة الأولى الـ special
+
+391
+00:38:05,250 --> 00:38:11,110
+linear group of two by two matrices over R is non
+
+392
+00:38:11,110 --> 00:38:20,590
+empty السبب because اللي هو واحد زيرو زيرو واحد
+
+393
+00:38:20,590 --> 00:38:25,810
+موجودة في الـ special linear group of two by two
+
+394
+00:38:25,810 --> 00:38:34,750
+matrices over R since الـ
+
+395
+00:38:34,750 --> 00:38:39,310
+determinant لواحد زيرو زيرو واحد بده يساوي من
+
+396
+00:38:39,310 --> 00:38:47,230
+الواحد بعد ذلك اختار مصففتين موجودة في الـ special ل
+
+397
+00:38:47,230 --> 00:38:52,530
+الـ a والـ b موجودة في الـ special linear group of
+
+398
+00:38:52,530 --> 00:38:59,490
+two by two matrices over R ثم كم محدد الأولى يا 
+
+399
+00:38:59,490 --> 00:39:05,650
+شباب؟ واحد، وكم محدد الثانية؟
+
+400
+00:39:07,830 --> 00:39:13,010
+يساوي واحد، طب أنا بدي أثبت إنه الأولى في معكوس
+
+401
+00:39:13,010 --> 00:39:18,410
+الثانية موجودة في الـ special بمعنى آخر بدي أثبت
+
+402
+00:39:18,410 --> 00:39:23,250
+إنه محدد الأولى في معكوس الثانية يساوي واحد، إن كنت
+
+403
+00:39:23,250 --> 00:39:27,710
+أثبت واحد معناته حصل الضرب هذا موجود و A موجود في
+
+404
+00:39:27,710 --> 00:39:30,730
+الـ special وبالتالي الـ special صارت sub group من
+
+405
+00:39:30,730 --> 00:39:33,990
+الـ main group من الـ group الأساسي اللي هي الـ
+
+406
+00:39:33,990 --> 00:39:39,360
+general linear group على أي حال لو جيت قلت لك بالله
+
+407
+00:39:39,360 --> 00:39:47,320
+قداش الـ determinant للـ A B inverse ورجعنا بذاكرتنا
+
+408
+00:39:47,320 --> 00:39:52,280
+إلى الوراء إلى الجبري الخطي، يبقى هذا بدي يعطينا
+
+409
+00:39:52,280 --> 00:39:58,240
+الـ determinant للـ A في الـ determinant للـ B inverse
+
+410
+00:39:58,240 --> 00:40:02,800
+طب أنا الـ determinant للـ B inverse ماهو عندي
+
+411
+00:40:02,800 --> 00:40:07,970
+ما أعرفوش لكن بنقدر نعرفه قداش يساوي 1 على
+
+412
+00:40:07,970 --> 00:40:14,610
+determinant للـ a من أين جبتها؟ اه لو ضربنا المصوفة
+
+413
+00:40:14,610 --> 00:40:19,130
+في معكوسها بيعطينا مصفوفة الوحدة، قداش محدد
+
+414
+00:40:19,130 --> 00:40:23,570
+مصفوفة الوحدة؟ واحد، الـ determinant للـ B B inverse
+
+415
+00:40:23,570 --> 00:40:26,890
+يساوي واحد، يبقى صار الـ determinant للـ B في الـ
+
+416
+00:40:26,890 --> 00:40:29,890
+determinant للـ B inverse يساوي واحد، إذا الـ
+
+417
+00:40:29,890 --> 00:40:32,630
+determinant للـ B inverse يساوي واحد على الـ
+
+418
+00:40:32,630 --> 00:40:38,440
+determinant للـ B إذا هذا الكلام بدي يساوي
+
+419
+00:40:38,440 --> 00:40:49,220
+determinant للـ A في واحد على determinant للـ B الآن
+
+420
+00:40:49,220 --> 00:40:53,560
+determinant للـ A بواحد وهذا واحد على واحد يبقى
+
+421
+00:40:53,560 --> 00:40:58,380
+النتيجة كده ايش؟ النتيجة واحدة، صحيح، ايش تفسيرك لهذا
+
+422
+00:40:58,380 --> 00:41:03,300
+الكلام؟ أن الـ A B inverse belong للـ special linear
+
+423
+00:41:03,300 --> 00:41:11,250
+group يبقى هنا إذن الـ A B inverse belongs للـ
+
+424
+00:41:11,250 --> 00:41:16,410
+special linear group of two by two matrices over R
+
+425
+00:41:16,410 --> 00:41:22,610
+وبالتالي تحقق الـ two conditions يبقى باجي بقول له
+
+426
+00:41:22,610 --> 00:41:27,170
+هذه من هنا هي النقطة الثانية يا شباب، من هنا بدأت
+
+427
+00:41:27,170 --> 00:41:32,950
+النقطة الثانية، يبقى إذن الـ special linear group of
+
+428
+00:41:32,950 --> 00:41:38,230
+two by two matrices over R عبارة عن subgroup من الـ
+
+429
+00:41:38,230 --> 00:41:44,150
+general linear group of two by two matrices over R
+
+430
+00:41:44,150 --> 00:41:53,550
+حد عنده أي سؤال هنا؟ بالنسبة ليه؟ أيوة، ماله هذا؟
+
+431
+00:41:54,660 --> 00:42:02,440
+أخذ دراسة جبر خطي ولا لا؟ زمان بسأل درست ولا لا؟
+
+432
+00:42:02,440 --> 00:42:08,160
+درست درست درست، يعني طار بفعل زمان؟ شوف يا سيد
+
+433
+00:42:08,160 --> 00:42:15,360
+الحين المصوفة B في المصوفة B inverse كده ايش
+
+434
+00:42:15,360 --> 00:42:21,940
+بتعطيك؟ مصفوفة الوحدة صح؟ طيب مصفوفة الوحدة
+
+435
+00:42:21,940 --> 00:42:27,000
+أخذ المحدد للاتنين Determinant للـ B طبعا كله
+
+436
+00:42:27,000 --> 00:42:30,380
+نظامه إتنين في إتنين، Determinant للـ B في
+
+437
+00:42:30,380 --> 00:42:36,260
+Determinant للـ B inverse يساوي Determinant لمصفوفة
+
+438
+00:42:36,260 --> 00:42:40,940
+الواحدة، يبقى قداش Determinant لمصفوفة الواحدة؟ هي
+
+439
+00:42:40,940 --> 00:42:48,560
+واحد، يبقى هذا بواحد، يبقى بصير Determinant للـ B
+
+440
+00:42:48,560 --> 00:42:53,180
+inverse يساوي واحد على Determinant
+
+441
+00:43:11,200 --> 00:43:21,240
+المثال الرقم 4 بيقول
+
+442
+00:43:24,060 --> 00:43:32,080
+الـ G هي الـ general linear group of two by two
+
+443
+00:43:32,080 --> 00:43:42,220
+matrices over R and let الـ H تساوي كل المصفوفات
+
+444
+00:43:42,220 --> 00:43:52,450
+اللي على الصيغة اللي هي A, 0, 0, B بحيث أن الـ a والـ
+
+445
+00:43:52,450 --> 00:44:01,450
+b موجودة في الـ R*، تاع بقول prove or
+
+446
+00:44:01,450 --> 00:44:09,970
+disprove، prove or disprove that أن الـ h هي الـ sub
+
+447
+00:44:09,970 --> 00:44:14,810
+group من مين؟ sub group من G، هذا من الكتاب السؤال
+
+448
+00:44:14,810 --> 00:44:18,590
+من الكتاب رقمه اللي هو خمسة وخمسين
+
+449
+00:44:24,260 --> 00:44:28,220
+مرة ثانية، ما يعطينا الـ general linear group اللي هي
+
+450
+00:44:28,220 --> 00:44:33,810
+كل المصفات اللي محددها لا يساوي zero، بعد ذلك أخد H
+
+451
+00:44:33,810 --> 00:44:40,530
+كل المصفوفة للقطر الرئيسي عناصرها لا تساوي أصفارا
+
+452
+00:44:40,530 --> 00:44:45,790
+جالي الـ A والـ B موجودة في R*)، R*) هي R minus Zero
+
+453
+00:44:45,790 --> 00:44:50,950
+يعني لا يمكن لـ A تساوي Zero ولا يمكن لـ B تساوي
+
+454
+00:44:50,950 --> 00:44:58,160
+Zero لكن للقطر الثانوي كل عناصره أصفارا، يبقى هدول
+
+455
+00:44:58,160 --> 00:45:03,440
+لا يمكن في أي يوم من الأيام أن يكون أصفارا، لكن هدول
+
+456
+00:45:03,440 --> 00:45:07,760
+أصفارا على طول، الخطب بيقول لي شوف لي بالله الـ H
+
+457
+00:45:07,760 --> 00:45:11,640
+هذه ممكن تكون subgroup والله ممكن ما تكونش
+
+458
+00:45:11,640 --> 00:45:17,180
+subgroup، السؤال هو هل هذي non-empty تقدر تجيب لي
+
+459
+00:45:17,180 --> 00:45:22,000
+عنصر فيها؟ identity matrix الرئيسي واحد واحد لا يساوي
+
+460
+00:45:22,000 --> 00:45:30,310
+أصفارا والباقي أصفارا، يبقى لقربهو الـ solution الـ H
+
+461
+00:45:30,310 --> 00:45:43,950
+is non-empty because السبب because مصفوفة
+
+462
+00:45:43,950 --> 00:45:52,430
+الوحدة اللي هي 1001 موجودة في H تمام، يبقى هذه non
+
+463
+00:45:52,430 --> 00:46:00,780
+-empty، الآن أخد مصففتين موجودات هنا واضرب الأولى في
+
+464
+00:46:00,780 --> 00:46:05,020
+معكوس الثانية، والله إن طلع على الشكل هذا تبع الـ H
+
+465
+00:46:05,020 --> 00:46:08,600
+يقول خلاص كلامنا صحيح وهذي صح بجروح، ما طلع
+
+466
+00:46:08,600 --> 00:46:15,880
+بجمهياش صح بجروح، يبقى بدنا نجي نقول له الـ H، الـ A والـ
+
+467
+00:46:15,880 --> 00:46:21,920
+B مصففتين موجودات في H then ايه الشكل الـ A يا شباب
+
+468
+00:46:25,230 --> 00:46:31,410
+A00B والـ B تساوي ها بدنا نغيرها، ليس بالضرورة أنّه
+
+469
+00:46:31,410 --> 00:46:34,850
+ممكن C00D
+
+470
+00:46:34,850 --> 00:46:40,090
+والـ A والـ B والـ C والـ D كلهم موجودات وين؟ في R
+
+471
+00:46:40,090 --> 00:46:46,910
+Star، طيب مشان هيك بدروح أجيب معكوس المصوفة B يبقى
+
+472
+00:46:46,910 --> 00:46:54,750
+بدي أروح له أجيب له الـ B Inverse تساوي واحد على محدد
+
+473
+00:46:54,750 --> 00:47:03,990
+المصفوفة، قداش المحدد تبعها؟ CD، يبقى واحد على CD و
+
+474
+00:47:03,990 --> 00:47:08,530
+باجي على المصوفة دي و ببدل عناصر القطر الثانوي
+
+475
+00:47:08,530 --> 00:47:14,050
+مكان بعض وبغير إشارات عناصر القطر الرئيسي، يبقى لو
+
+476
+00:47:14,050 --> 00:47:23,090
+جيت قلت هنا D وهنا C وهنا Zero وهنا Zero، بمشكلة
+
+477
+00:47:23,090 --> 00:47:27,050
+فاش مشكلة؟ تمام، الرئيسي ما هو الـ zero، والله سالب
+
+478
+00:47:27,050 --> 00:47:30,790
+zero هو بـ zero، يبقى اتغير ولا ما تغير ولا كل شيء زي
+
+479
+00:47:30,790 --> 00:47:36,000
+ما هو؟ طيب بدنا نشوف ايه الشكل هذه بالضبط، هذا يعتبر
+
+480
+00:47:36,000 --> 00:47:40,840
+real number مضروب في المصوفة، إذا مضروب في كل عنصر
+
+481
+00:47:40,840 --> 00:47:47,880
+من عناصر المصوفة، إذا لو ضربناها هذا سيصبح D على CD
+
+482
+00:47:58,200 --> 00:48:03,800
+هذا الكلام ممكن اختصر D مع D ويظهر كده 1 على C وهنا
+
+483
+00:48:03,800 --> 00:48:09,220
+Zero زي ما هي وهنا زي ما هي وهنا واحد على D
+
+484
+00:48:09,220 --> 00:48:15,020
+هذا من الـ B inverse، الآن أنا بدي أشوف الـ A في الـ B
+
+485
+00:48:15,020 --> 00:48:20,000
+inverse هل هو موجود في H ولا لأ، يبقى بتروح أخد له
+
+486
+00:48:20,000 --> 00:48:26,950
+الـ A B inverse الـ A عندنا اللي هي A 00B والـ B
+
+487
+00:48:26,950 --> 00:48:36,590
+inverse واحد على C 001 على D ويساوي الصف الأول في
+
+488
+00:48:36,590 --> 00:48:42,530
+العمود الأول يبقى A على C زائد Zero، الصف الأول في
+
+489
+00:48:42,530 --> 00:48:47,630
+العمود الثاني بـ Zero، الصف الثاني في العمود الأول
+
+490
+00:48:47,630 --> 00:48:54,730
+بـ Zero، الصف الثاني في العمود الثاني B على D، يبقى
+
+491
+00:48:54,730 --> 00:48:59,590
+هي القطر الرئيسي لا يساوي أصفارا والقطر الثانوي
+
+492
+00:48:59,590 --> 00:49:07,480
+بأصفار، يبقى كل هذا موجود في H، بناء عليه تحققت
+
+493
+00:49:07,480 --> 00:49:11,740
+الخاصية، من أين؟ من هنا تبدأ الخاصية الثانية من هنا
+
+494
+00:49:11,740 --> 00:49:16,920
+تبدأ الخاصية الثانية وهذه هي الخاصية الأولى، إذا
+
+495
+00:49:16,920 --> 00:49:21,460
+تبقى النظرية اللي عندنا تحققت الخاصيتين الاثنين أو
+
+496
+00:49:21,460 --> 00:49:25,100
+المعطيات الاثنين تبع النظرية، يبقى بناء عليه
+
+497
+00:49:25,100 --> 00:49:30,400
+المصفوفة الموطنة هي subgroup من الـ general linear 
+
+498
+00:49:30,400 --> 00:49:32,500
+group، يبقى هنا by
+
+499
+00:49:39,830 --> 00:49:45,910
+بالنظرية السابقة الـ H is a subgroup من الـ general
+
+500
+00:49:45,910 --> 00:49:50,610
+linear group of two by two matrices over R
+
+Okay, provide the lecture transcript and I will correct any typos and grammatical errors as per your instructions. I will ensure that the original Arabic and English text, dialect, grammar, and meaning are preserved, and the output will be in the same format as your input.