diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_postprocess.srt
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+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_postprocess.srt
@@ -0,0 +1,1648 @@
+1
+00:00:20,870 --> 00:00:25,910
+المرة اللى فاتت او في المحاضرة للصادفة عرفنا ال
+
+2
+00:00:25,910 --> 00:00:31,410
+cluster point و أخدنا أمثلة كيف نجيب ال cluster
+
+3
+00:00:31,410 --> 00:00:39,710
+points لمجموعة معينة و وجفنا عند المثال التالت
+
+4
+00:00:59,030 --> 00:01:05,110
+المثال التالت show that
+
+5
+00:01:05,110 --> 00:01:12,070
+zero is the only cluster
+
+6
+00:01:12,070 --> 00:01:18,290
+point of
+
+7
+00:01:18,290 --> 00:01:23,570
+the set A7
+
+8
+00:01:26,690 --> 00:01:31,870
+كل واحد على N حيث و N that's a number دكتور هذا
+
+9
+00:01:31,870 --> 00:01:37,210
+مثال تاني أخدناها ده؟ لأ لأ اللي أخدناه اللي هو ال
+
+10
+00:01:37,210 --> 00:01:48,030
+.. هناخدها هناخدها هناخدها ف .. هنا هنا .. هنا
+
+11
+00:01:48,030 --> 00:01:55,250
+هنا اتنين
+
+12
+00:01:59,360 --> 00:02:11,580
+إن Zero is a cluster point تلت
+
+13
+00:02:11,580 --> 00:02:22,720
+Delta أكبر من السفل Be given by Archimedean
+
+14
+00:02:22,720 --> 00:02:25,880
+property
+
+15
+00:02:30,960 --> 00:02:40,920
+يوجد capital N ينتمي إلى N بحيث انه واحد على N
+
+16
+00:02:40,920 --> 00:02:54,340
+أصغر من نفسه hence
+
+17
+00:03:01,430 --> 00:03:09,270
+الدلتا نيبر هو zero لو
+
+18
+00:03:09,270 --> 00:03:25,690
+أخدت xN هو واحد على ن فهذا ينتمي إلى
+
+19
+00:03:25,690 --> 00:03:39,580
+المجموعة Aوانت ليه لا ال delta number هون ل ..
+
+20
+00:03:39,580 --> 00:03:44,040
+او ال x هذا المفروض delta ال delta number هو ده
+
+21
+00:03:44,040 --> 00:03:47,860
+اسمه
+
+22
+00:03:47,860 --> 00:03:56,940
+أسوأ؟ إذن
+
+23
+00:03:56,940 --> 00:03:58,460
+هذا لا أي سؤال خالد
+
+24
+00:04:06,200 --> 00:04:10,700
+الدلتا نبقى رهود للسفر اللي هي الفترة المفتوحة من
+
+25
+00:04:10,700 --> 00:04:16,100
+سالب دلتا إلى دلتا
+
+26
+00:04:16,100 --> 00:04:21,960
+فهي عندي واحد على N أصغر من دلتا وطبعا أكبر من سفر
+
+27
+00:04:24,160 --> 00:04:27,620
+فواحد على أن ينتمي للـDelta neighborhood للسفر
+
+28
+00:04:27,620 --> 00:04:32,400
+وواحد على أن ينتمي للمجموعة A وبالتالي يجب أن نكون
+
+29
+00:04:32,400 --> 00:04:38,580
+أثبتنا أنه لأي Delta أكبر من السفر أو أي Delta
+
+30
+00:04:38,580 --> 00:04:44,680
+neighborhood للسفر يتقاطع مع A في نقطة مختلفة عن
+
+31
+00:04:44,680 --> 00:04:49,000
+السفر ال
+
+32
+00:04:49,000 --> 00:04:56,810
+X انها جلدها تساوي سفرلاتسار السفر وبالتالي إذا
+
+33
+00:04:56,810 --> 00:05:05,470
+هذا بثبت السفر is a cluster point of
+
+34
+00:05:05,470 --> 00:05:12,310
+الست إذا هذا بثبت ال claim الآن ليه مايكون فيه
+
+35
+00:05:12,310 --> 00:05:14,130
+cluster points أخرى؟
+
+36
+00:05:30,490 --> 00:05:41,150
+إذا كانت X لا تساوي سفر، فهي ليست مجموعة من A
+
+37
+00:05:41,150 --> 00:05:46,390
+فحاسيبكم
+
+38
+00:05:46,390 --> 00:05:47,630
+أنتم تكتبوا البرهان
+
+39
+00:05:50,290 --> 00:06:02,390
+هي سفر وهي واحد وهي نص وهي تلت وهي واحد على N وهي
+
+40
+00:06:02,390 --> 00:06:05,390
+واحد على N زائد واحد وهكذا
+
+41
+00:06:16,430 --> 00:06:25,930
+فهنا تاندي two cases case one ان x تنتمي الى a و
+
+42
+00:06:25,930 --> 00:06:34,690
+الحلقة التانية case two ان x لا تنتمي الى a ال x
+
+43
+00:06:34,690 --> 00:06:39,530
+دي مستويش السفر احنا already اثبتنا ان السفر
+
+44
+00:06:39,530 --> 00:06:43,850
+cluster pointطيب افرض X مستويش سفر إذا X ممكن
+
+45
+00:06:43,850 --> 00:06:48,170
+تساوي واحد أو نص أو تلت أو واحد على N for some N
+
+46
+00:06:48,170 --> 00:06:53,250
+صح؟ ممكن ماتساويش ولا عنصر ممكن ماتكونش تم تمل أيه
+
+47
+00:06:53,250 --> 00:06:58,070
+فلو كانت ال X واحد من العناصر هدول واحد من العناصر
+
+48
+00:06:58,070 --> 00:07:04,630
+الست فبقدر ألاقي أن يوجد بقدر ألاقي delta
+
+49
+00:07:04,630 --> 00:07:08,990
+neighborhood للعنصر مثلا التلت بقدر ألاقي delta
+
+50
+00:07:08,990 --> 00:07:09,490
+neighborhood
+
+51
+00:07:13,860 --> 00:07:19,840
+الأنصر اللي بعد هذا هيكون ربع فباخد المسافة الأصغر
+
+52
+00:07:19,840 --> 00:07:26,560
+بين تلت ربع تلت و نص و باخد نص المسافة ديلتا فبصير
+
+53
+00:07:26,560 --> 00:07:30,920
+عند هنا ديلتا نبرهود للتلت و بتقاطعش مع المجموعة A
+
+54
+00:07:30,920 --> 00:07:38,120
+بالمرة أو في نقطة مختلفة عن التلتوبالتالي لو كانت
+
+55
+00:07:38,120 --> 00:07:44,880
+ال X موجودة في A زي التلت مثلا فال X ليست cluster
+
+56
+00:07:44,880 --> 00:07:49,860
+point الآن ال X لا تنتمي ل أيه؟ ال X لا تنتمي ل
+
+57
+00:07:49,860 --> 00:07:55,920
+أيه؟ معناته هي عنصر هنا زي هذا X أزرق من سفر أو X
+
+58
+00:07:55,920 --> 00:08:01,540
+ممكن تكون جاية بين عنصرين فباخد المسافة بين X و
+
+59
+00:08:01,540 --> 00:08:04,840
+أقرب عنصر إلها من اليمين و أقرب عنصر إلها من
+
+60
+00:08:04,840 --> 00:08:11,140
+اليسارو باخد نص المسافة ديلتا او ابسلان و بكوّن
+
+61
+00:08:11,140 --> 00:08:17,480
+دلتا نبرود ل X هذا دلتا نبرود مش هيتقاطع مع ال 6 و
+
+62
+00:08:17,480 --> 00:08:20,700
+بالتالي النقطة هذه عمرها ما بتكون cluster point
+
+63
+00:08:20,700 --> 00:08:26,020
+ممكن كمان النقطة هذه ال X مش موجودة فيها ممكن تكون
+
+64
+00:08:26,020 --> 00:08:31,260
+على شمال السفر او على يمين الواحدفلو كانت على يمين
+
+65
+00:08:31,260 --> 00:08:35,560
+الواحد خد نص المسافة هي دلتا إذا هي دلتا نبقى
+
+66
+00:08:35,560 --> 00:08:39,420
+روحود ل X مابتخطعش معاه بالمرة بالتالي X مابت
+
+67
+00:08:39,420 --> 00:08:44,440
+cluster هنا لو كانت X أصغر من سفر فخد نص المسافة
+
+68
+00:08:44,440 --> 00:08:48,960
+بين X و 0 على إنها دلتاوبالتالي كونة delta
+
+69
+00:08:48,960 --> 00:08:52,460
+neighborhood ل X هذا delta neighborhood بتقاطعش مع
+
+70
+00:08:52,460 --> 00:08:56,240
+A بالمرة وبالتالي X ليست cluster point إذا في كل
+
+71
+00:08:56,240 --> 00:09:01,860
+الأحوال X ليست cluster point سواء كانت في A أو مش
+
+72
+00:09:01,860 --> 00:09:05,420
+موجودة إذا كانت X مختلفة عن الصفر فليست cluster
+
+73
+00:09:05,420 --> 00:09:14,930
+point okay إذا zero is the only نقطة الوحيدةمافيش
+
+74
+00:09:14,930 --> 00:09:18,990
+نقطة غيرها بتكون cluster point بالمثل ممكن نثبت
+
+75
+00:09:18,990 --> 00:09:29,650
+مثال أخر f
+
+76
+00:09:29,650 --> 00:09:35,710
+i بساوي ال
+
+77
+00:09:35,710 --> 00:09:39,830
+unit technological interval and
+
+78
+00:09:51,210 --> 00:10:02,710
+IQ بساوي I تقاطع ال rational numbers then
+
+79
+00:10:02,710 --> 00:10:13,170
+every x تنهي ل I is a cluster point a cluster
+
+80
+00:10:13,170 --> 00:10:15,250
+point of IQ
+
+81
+00:10:18,800 --> 00:10:26,900
+إذا I هي الفترة المغلقة من صفر لواحد IQ هي كل
+
+82
+00:10:26,900 --> 00:10:31,800
+الأعداد المسبية الموجودة في الفترة المغلقة من صفر
+
+83
+00:10:31,800 --> 00:10:38,340
+لواحد ممكن إثبات إن كل X في الفترة المغلقة I هي
+
+84
+00:10:38,340 --> 00:10:45,940
+cluster point للمجموعة IQ وذلك باستخدام ال density
+
+85
+00:10:45,940 --> 00:10:52,060
+theoremproof use
+
+86
+00:10:52,060 --> 00:11:06,500
+the density theorem فحاسيبكم
+
+87
+00:11:06,500 --> 00:11:15,920
+انتوا تكتبوا البرهان خدي أي x في I واخدتي انه أي
+
+88
+00:11:17,780 --> 00:11:22,140
+أعملكم برهان هكذا بدون أن أكتب أي شيء هذه الفترة I
+
+89
+00:11:22,140 --> 00:11:29,720
+من صفر إلى واحد هذه الفترة المغلقة من ملفة أن كل X
+
+90
+00:11:29,720 --> 00:11:35,800
+كل X فيها هو cluster point لمجموعة الأعداد المسمية
+
+91
+00:11:35,800 --> 00:11:42,520
+في I ففي عندي تلت حالات MX هتكون أكبر من صفر أصغر
+
+92
+00:11:42,520 --> 00:11:48,060
+من واحد يعني نقطة داخليها ليست نقطة طرفو طبعا هي
+
+93
+00:11:48,060 --> 00:11:52,460
+لو أخدت أي delta عدد موجب و كوّنت delta
+
+94
+00:11:52,460 --> 00:11:57,380
+neighborhood لل X فال delta neighborhood هذا
+
+95
+00:11:57,380 --> 00:12:05,920
+هيتقاطع مع المجموعة A IQ حسب نظرية الكثافة أي فترة
+
+96
+00:12:05,920 --> 00:12:11,520
+مفتوحة زي هذه تحتوي rational number صح؟وبالتالي اي
+
+97
+00:12:11,520 --> 00:12:16,600
+delta neighborhood ل ال X هيتقاطع مع المجموعة IQ
+
+98
+00:12:16,600 --> 00:12:24,160
+في نقطة R مختلفة عن ال X حسب نظرية الكثارة
+
+99
+00:12:24,160 --> 00:12:28,040
+وبالتالي حسب التعريف اذا ال X هذه اللي هي نقطة
+
+100
+00:12:28,040 --> 00:12:33,700
+داخلية is a cluster point لمن؟
+
+101
+00:12:33,700 --> 00:12:40,260
+للمجموعة IQلو كانت ال .. ال .. ال x هي نقطة الطرف
+
+102
+00:12:40,260 --> 00:12:46,960
+الحلقة التانية لما x تكون هي سفر لما x تكون بساوي
+
+103
+00:12:46,960 --> 00:12:52,160
+سفر وخدي أي delta neighborhood لأن هاي سالب delta
+
+104
+00:12:52,160 --> 00:12:56,560
+موجب delta فالفترة
+
+105
+00:12:56,560 --> 00:13:01,200
+هذه تتقطع يعني
+
+106
+00:13:01,200 --> 00:13:07,230
+هاي delta هادي delta و هادي نقطة سفرالان الفترة
+
+107
+00:13:07,230 --> 00:13:12,870
+هذه بقدر الاقي فيها rational number حسب مباريك
+
+108
+00:13:12,870 --> 00:13:16,970
+الكفافة موجود بين سفر و دلتا و ال rational number
+
+109
+00:13:16,970 --> 00:13:23,550
+هذا موجود في ال unit closed intervalوبالتالي كل
+
+110
+00:13:23,550 --> 00:13:28,450
+delta neighborhood للصفر يتقاطع
+
+111
+00:13:28,450 --> 00:13:33,670
+مع المجموع IQ في نقطة R مختلفة عن الصفر وبالتالي
+
+112
+00:13:33,670 --> 00:13:37,910
+الصفر هو cluster point بالمثل ممكن تباتل بالواحد
+
+113
+00:13:37,910 --> 00:13:41,970
+cluster point لأن اي delta neighborhood للواحد
+
+114
+00:13:43,720 --> 00:13:48,560
+هيحتوي حسب نظرية الكثافة لو هذا كان واحد ثالث دلتا
+
+115
+00:13:48,560 --> 00:13:54,510
+في النقطة هذه وهذه واحد فبنقدر نلاقي Rrational
+
+116
+00:13:54,510 --> 00:13:58,650
+number حسب مجرد كدفة بين واحد سالب دلتا وواحد
+
+117
+00:13:58,650 --> 00:14:03,710
+وبالتالي ال delta neighborhood هذا المركزه واحد و
+
+118
+00:14:03,710 --> 00:14:08,490
+نصف خطره دلتا هيتقاطع مع ال IQ في نقطة مختلفة عن
+
+119
+00:14:08,490 --> 00:14:13,250
+الواحد وبالتالي واحد cluster point الان لان هسيبكم
+
+120
+00:14:13,250 --> 00:14:15,650
+تكتبوا البرهان بالتفصيل
+
+121
+00:14:19,850 --> 00:14:25,250
+Okay إذاً هيك يعني عندنا عدة أمثلة على ال cluster
+
+122
+00:14:25,250 --> 00:14:32,490
+points نرجع لمفهوم ال limit ل ال function اللي هو
+
+123
+00:14:32,490 --> 00:14:47,650
+كان عنوان ال section تبعنا اذا
+
+124
+00:14:47,650 --> 00:14:48,750
+هنا definition
+
+125
+00:14:55,450 --> 00:15:07,150
+دع الـ f يكون مفعولًا من a إلى r مفعولًا
+
+126
+00:15:07,150 --> 00:15:19,710
+في أين a مجزرة من r و c مجزرة من الـ
+
+127
+00:15:19,710 --> 00:15:22,090
+set A
+
+128
+00:15:26,660 --> 00:15:35,260
+المعنى number L هو مقال
+
+129
+00:15:35,260 --> 00:15:39,440
+للمعنى
+
+130
+00:15:39,440 --> 00:15:44,440
+f at
+
+131
+00:15:44,440 --> 00:15:59,020
+xبس you see إذا تحقق الشرط التالي for any epsilon
+
+132
+00:15:59,020 --> 00:16:05,340
+أكبر من سفر يوجد delta تعتمد على epsilon عدد موجد
+
+133
+00:16:05,340 --> 00:16:14,690
+بحيث أنه لكل x ينتمي إلى aو المسافة بين .. و ال X
+
+134
+00:16:14,690 --> 00:16:23,090
+هذا يختلف عن ال C و المسافة بينها و بين ال C أصغر
+
+135
+00:16:23,090 --> 00:16:30,030
+من Delta لازم هذا يضمن أن absolute F of X minus L
+
+136
+00:16:30,030 --> 00:16:41,010
+أصغر من Delta إذن هذا شرط .. هذا شرط أو بسميهأنا
+
+137
+00:16:41,010 --> 00:16:49,470
+بسميه ابسلون دلتا definition ابسلون دلتا
+
+138
+00:16:49,470 --> 00:16:54,310
+definition of limit لل
+
+139
+00:16:54,310 --> 00:16:58,550
+limit of a functionالـ Limit لـ function f of x
+
+140
+00:16:58,550 --> 00:17:03,590
+بالساوي أو L هي عبارة عن Limit لـ function f of x
+
+141
+00:17:03,590 --> 00:17:09,970
+and x بالساوي C إذا لو أعطتوني أي إبسلون عدد موجب
+
+142
+00:17:09,970 --> 00:17:15,570
+لازم أنا أرد عليها Delta عدد موجب آخر يعتمد على
+
+143
+00:17:15,570 --> 00:17:20,750
+إبسلون بحيث أنه لكل X في المجموعة A اللي هو ال
+
+144
+00:17:20,750 --> 00:17:27,300
+domain تبع ال functionو X هذه مختلفة لا تساوي C
+
+145
+00:17:27,300 --> 00:17:33,360
+يعني المتباين هذه معناها X لا تساوي Cإذاً لكل x في
+
+146
+00:17:33,360 --> 00:17:38,200
+a مختلفة عن الـc والمسافة بينها وبين الـc أصغر من
+
+147
+00:17:38,200 --> 00:17:42,580
+دلتا لازم تطلع المسافة بين f of x و L أصغر من
+
+148
+00:17:42,580 --> 00:17:47,220
+إبسلون هذا الكلام اتحقق لكل إبسلون أكبر من الصفر
+
+149
+00:17:47,220 --> 00:17:51,640
+فبنقول إن العدد L is a limit of the function f عند
+
+150
+00:17:51,640 --> 00:17:52,360
+النقطة c
+
+151
+00:17:59,170 --> 00:18:07,710
+من هذا التعريف بينتج على طول اه طيب in this case
+
+152
+00:18:07,710 --> 00:18:13,930
+in this case we
+
+153
+00:18:13,930 --> 00:18:26,600
+say انه if converges if convergesto the number L
+
+154
+00:18:26,600 --> 00:18:39,520
+at X بساوي C and we write ونكتب الحالة هذه limit ل
+
+155
+00:18:39,520 --> 00:18:46,940
+F of X لما X تقول إلى C بساوي L أو ممكن نكتب limit
+
+156
+00:18:46,940 --> 00:18:54,260
+F as X tends to C بساوي L أو ممكن نكتب
+
+157
+00:19:01,220 --> 00:19:11,260
+أو ممكن نكتب f of x tends to L as x tends to c كل
+
+158
+00:19:11,260 --> 00:19:16,360
+هدول معناهم أن العدد L limit لل function f and x
+
+159
+00:19:16,360 --> 00:19:17,360
+سوى c
+
+160
+00:19:22,850 --> 00:19:30,090
+ف limit f of x as x tends to c does not exist،
+
+161
+00:19:30,090 --> 00:19:37,430
+يعني مافيش عدد L زي هذا، we say ان ال function f
+
+162
+00:19:37,430 --> 00:19:45,590
+diverges، diverges at x less than c
+
+163
+00:19:50,120 --> 00:19:55,320
+الان نستطيع ان نثبت ان ال limit لل function هذه
+
+164
+00:19:55,320 --> 00:20:00,040
+النقطة لو كانت موجودة لو كان ال function لها limit
+
+165
+00:20:00,040 --> 00:20:07,120
+فlimit هذه لازم تكون unique ال
+
+166
+00:20:07,120 --> 00:20:19,320
+function if from A to R can have only
+
+167
+00:20:39,940 --> 00:20:44,760
+والبرهان شبه البرهان الـ uniqueness of the limit
+
+168
+00:20:44,760 --> 00:20:50,700
+of a sequence we use epsilon over two argument
+
+169
+00:20:51,860 --> 00:20:54,780
+استنتاج epsilon على اتنين او برهان epsilon على
+
+170
+00:20:54,780 --> 00:21:01,020
+اتنين هنشوف مع بعض هاي برهان تروح left epsilon
+
+171
+00:21:01,020 --> 00:21:04,300
+اكبر
+
+172
+00:21:04,300 --> 00:21:11,720
+من السفر ب given since
+
+173
+00:21:11,720 --> 00:21:19,120
+طب
+
+174
+00:21:19,120 --> 00:21:25,040
+خليني الأوللبرهانة النظرية هذه بدي أفرض أنه فيه
+
+175
+00:21:25,040 --> 00:21:34,640
+two limits assume أن ال limit ل f of x as x tends
+
+176
+00:21:34,640 --> 00:21:44,340
+to c بساوي عدد الواحد and limit أيضا ل f of x as x
+
+177
+00:21:44,340 --> 00:21:50,340
+tends to c بساوي عدد تاني الاتنينوعشان أثبت
+
+178
+00:21:50,340 --> 00:21:57,860
+النظرية لازم أثبت الإدعاء التالي إن ال1 بساوي ال4
+
+179
+00:21:57,860 --> 00:22:07,720
+فلبرهان ذلك let epsilon أكبر من السفر be given
+
+180
+00:22:07,720 --> 00:22:19,500
+since مما أننا فرضين أن ال limitلأف as x tends to
+
+181
+00:22:19,500 --> 00:22:28,420
+c بالساوي الواحد then by definition by epsilon
+
+182
+00:22:28,420 --> 00:22:33,180
+delta definition of limit there exists delta one
+
+183
+00:22:33,180 --> 00:22:39,830
+depends on epsilon positive numberبحيث أنه لو كان
+
+184
+00:22:39,830 --> 00:22:46,150
+x ينتمي إلى a و absolute x minus c أصغر من delta
+
+185
+00:22:46,150 --> 00:22:54,850
+one أكبر من سفر فهذا بيقدي أن absolute f of x
+
+186
+00:22:54,850 --> 00:23:02,530
+minus l one أصغر من epsilon عتنين عشان الاستنتاج
+
+187
+00:23:02,530 --> 00:23:05,510
+هذا واحد
+
+188
+00:23:08,770 --> 00:23:13,810
+Also ايضا احنا
+
+189
+00:23:13,810 --> 00:23:20,610
+فرضين من ال limit لل function f of x as x tends to
+
+190
+00:23:20,610 --> 00:23:27,990
+c بساوي عدد تاني ال اتنين then
+
+191
+00:23:27,990 --> 00:23:35,650
+for the same for same epsilon اكبر من ستة نفس ال
+
+192
+00:23:35,650 --> 00:23:43,140
+epsilon يعنيلنفس الـ Epsilon بما أن limit ل F of X
+
+193
+00:23:43,140 --> 00:23:48,940
+and X بساوية C بساوية L2 نجد Delta 2 تعتمد على
+
+194
+00:23:48,940 --> 00:23:53,940
+Epsilon على 2 وبالتالي على Epsilon عدد موجد بحيث
+
+195
+00:23:53,940 --> 00:24:00,300
+أنه لو كان X ينتمي إلى A و Absolute X minus C أصغر
+
+196
+00:24:00,300 --> 00:24:07,350
+من Delta 2 أكبر من 0فهذا أكيد بيقدّي أنه absolute
+
+197
+00:24:07,350 --> 00:24:14,510
+f of x minus L2 أصغر من epsilon على 2 ال sum ال
+
+198
+00:24:14,510 --> 00:24:22,030
+implication هي D2 الآن بناخد .. بنعرف delta ل L
+
+199
+00:24:22,030 --> 00:24:31,230
+Delta بتساوي ال minimum ل delta واحد و delta اتنين
+
+200
+00:24:32,560 --> 00:24:37,340
+طبعا هذا بيطلع عدد
+
+201
+00:24:37,340 --> 00:24:43,200
+موجب لإن دلتا واحد ودلتا اتنين عدد موجب وكذلك دلتا
+
+202
+00:24:43,200 --> 00:24:46,200
+دي تعتمد على ابسلون لإن دلتا واحد ودلتا اتنين
+
+203
+00:24:46,200 --> 00:24:52,720
+يعتمدوا على ابسلون then
+
+204
+00:24:52,720 --> 00:24:55,860
+by
+
+205
+00:24:55,860 --> 00:25:07,520
+واحد and اتنيننحصل على التالي، لو كان x ينتقل إلى
+
+206
+00:25:07,520 --> 00:25:14,980
+a و absolute x minus c أصغر من delta أكبر من سفر
+
+207
+00:25:14,980 --> 00:25:26,590
+فهذا هيقدر أن absolute L1 minus L2بساوي absolute
+
+208
+00:25:26,590 --> 00:25:39,610
+L1 minus F of X زائد F of X minus L2 إذا انطلعت
+
+209
+00:25:39,610 --> 00:25:46,590
+أنا F of X ورجعتها فكأني ما جيرتش حاجة وهذا بيطلع
+
+210
+00:25:46,590 --> 00:25:50,460
+باستخدام ال triangle inequalityبالترائنجل الـ
+
+211
+00:25:50,460 --> 00:25:54,900
+equality لـ absolute value لمجموعة حاجتين أصغر من
+
+212
+00:25:54,900 --> 00:26:00,920
+لو يساوي absolute L1 minus F of X ذات absolute F
+
+213
+00:26:00,920 --> 00:26:07,980
+of X minus L2 الآن
+
+214
+00:26:07,980 --> 00:26:13,340
+باستخدام ال implication واحد، اللحظة أن الـ delta
+
+215
+00:26:13,340 --> 00:26:17,960
+هي ال minimum لـ delta واحد و delta اتنينوبالتالي
+
+216
+00:26:17,960 --> 00:26:24,340
+الـ delta هذه أصغر من delta واحد فحسب ال
+
+217
+00:26:24,340 --> 00:26:28,600
+implication واحد لما يكون x ينتمي ل a و absolute x
+
+218
+00:26:28,600 --> 00:26:33,800
+minus c أصغر من delta واحد فانا بقدم ال absolute
+
+219
+00:26:33,800 --> 00:26:40,460
+value هذه أصغر من y على 2 كذلك باستخدام ال
+
+220
+00:26:40,460 --> 00:26:45,060
+implication 2أنا عندي الـ delta هذه هي الـ minimum
+
+221
+00:26:45,060 --> 00:26:51,760
+لـ delta 1 و delta 2 وبالتالي أصغر من delta 2 فبال
+
+222
+00:26:51,760 --> 00:26:55,680
+implication 2 بتقول لو كان x ينتمي ل a و absolute
+
+223
+00:26:55,680 --> 00:27:00,320
+x minus c أصغر من delta 2 فال absolute value ل f
+
+224
+00:27:00,320 --> 00:27:07,500
+of x minus l2 less than epsilon over 2 هذا بيساوي
+
+225
+00:27:07,500 --> 00:27:16,080
+epsilonإذا أنا طلع عندي أثبتت أن absolute L1 minus
+
+226
+00:27:16,080 --> 00:27:22,540
+L2 أكبر من أبسلون طبعا أكيد أكبر من أو ساوى سفر و
+
+227
+00:27:22,540 --> 00:27:28,600
+الأن هذا صحيح لكل أبسلون أكبر من السفر لأن one
+
+228
+00:27:28,600 --> 00:27:34,500
+hand هنا ال epsilon was arbitrary givenالإبسلون
+
+229
+00:27:34,500 --> 00:27:38,660
+was arbitrarily يعني نقول since this holds for
+
+230
+00:27:38,660 --> 00:27:43,160
+every إبسلون في لمّة أخدناها في بداية ال course
+
+231
+00:27:43,160 --> 00:27:48,820
+بتقول لو في عندي عدد حفيفي a أكبر من أو ساوي سفر و
+
+232
+00:27:48,820 --> 00:27:53,940
+أصغر من إبسلون فإن إبسلون أكبر من السفر فهذا بيقدي
+
+233
+00:27:53,940 --> 00:28:00,160
+أن a بيساوي سفرأخد ايه هنا الـ absolute value ل L1
+
+234
+00:28:00,160 --> 00:28:09,140
+minus L2 فحسب النمة هذه هيطلع عندى هذا بقدر اللي
+
+235
+00:28:09,140 --> 00:28:15,600
+قدر انه absolute L1 minus L2 بالساوية سفر وبالتالي
+
+236
+00:28:15,600 --> 00:28:24,600
+بطلع عندى L1 بساوية L2 وهو المطلوبإذا أنا فرقت إن
+
+237
+00:28:24,600 --> 00:28:28,860
+الـ function إلها two limits عن نقطة فطلع الـ two
+
+238
+00:28:28,860 --> 00:28:32,680
+limits متساوياتين وبالتالي لو كانت الـ function
+
+239
+00:28:32,680 --> 00:28:37,240
+إلها limit عن نقطة فال limit تطلع وحيدة unique،
+
+240
+00:28:37,240 --> 00:28:43,200
+بقى ده؟ في أي سؤال أو أي سؤال على البرهانة؟
+
+241
+00:29:02,290 --> 00:29:15,590
+ناخد ملاحظة هنا الـ
+
+242
+00:29:15,590 --> 00:29:27,330
+epsilon delta definition of limit of a function f
+
+243
+00:29:27,330 --> 00:29:29,270
+from a to r
+
+244
+00:29:32,670 --> 00:29:40,250
+the inequality المتباينة
+
+245
+00:29:40,250 --> 00:29:48,030
+اللي هي absolute x minus c أكبر من سفر أصغر من
+
+246
+00:29:48,030 --> 00:29:58,470
+دولتان means حاجتين الجزء هذا معناه أن absolute x
+
+247
+00:29:58,470 --> 00:30:09,330
+minus c لا يساوى سفروبالتالي X لا يساوي C إذاً هذا
+
+248
+00:30:09,330 --> 00:30:17,870
+يعني أن X لا تساوي C المتباينة
+
+249
+00:30:17,870 --> 00:30:23,410
+التانية اللي هي absolute X minus C أصغر من Delta
+
+250
+00:30:23,410 --> 00:30:31,170
+هذه بتكافئ أن X minus C أصغر من Delta أكبر من ثالث
+
+251
+00:30:31,170 --> 00:30:39,850
+Delta صح؟وهذه بتكافئ أن X أكبر من C Negative Delta
+
+252
+00:30:39,850 --> 00:30:47,870
+أصغر من C زائد Delta وهذا معناه أن X تنتمي لـ
+
+253
+00:30:47,870 --> 00:30:56,450
+Delta Neverhood لـ C اللي هو الفترة اللي اتروها من
+
+254
+00:30:56,450 --> 00:30:59,410
+C Minus Delta ل C Plus Delta
+
+255
+00:31:06,690 --> 00:31:12,550
+إذا المتباينة دي معناها x لا تساوي c and x تنتمي
+
+256
+00:31:12,550 --> 00:31:18,190
+لل delta اللي برجود لل c اللي هو الفترة المفتوحة
+
+257
+00:31:18,190 --> 00:31:25,170
+من c سالم negative delta إلى c plus delta كذلك
+
+258
+00:31:25,170 --> 00:31:29,570
+المتباينة also
+
+259
+00:31:33,070 --> 00:31:37,490
+الإي نكواليتي المتباينة
+
+260
+00:31:37,490 --> 00:31:43,450
+اللي هي absolute f of x minus L أصغر من إبسلون
+
+261
+00:31:43,450 --> 00:31:46,490
+means
+
+262
+00:31:46,490 --> 00:31:52,830
+لو جينا الحل المتباينة هذه في f of x
+
+263
+00:32:05,840 --> 00:32:11,920
+فهي عندي f of x minus L أصغر من إبسلون أكبر من
+
+264
+00:32:11,920 --> 00:32:17,480
+سالم إبسلون حل المتباينة هذه في f of x اجمع L على
+
+265
+00:32:17,480 --> 00:32:24,880
+كل أطراف فبطلع f of x أصغر من L زاد إبسلون أكبر من
+
+266
+00:32:24,880 --> 00:32:33,940
+L ميجا تل إبسلون فهذا معناه أن f of xbelongs to
+
+267
+00:32:33,940 --> 00:32:38,520
+the epsilon neighborhood للعدد L اللي هو الفترة
+
+268
+00:32:38,520 --> 00:32:44,040
+المفتوحة from L negative epsilon إلى L plus
+
+269
+00:32:44,040 --> 00:32:57,040
+epsilon مظبوط؟ صحيح؟ وبالتالي إن هذا بيقود إلى
+
+270
+00:32:57,040 --> 00:32:59,780
+المتيجة التالية
+
+271
+00:33:06,460 --> 00:33:20,660
+دع الـ F تعمل من A إلى R وC مقاومة مقاومة من A
+
+272
+00:33:20,660 --> 00:33:32,220
+ثم التقالير ممتازة التقالير ممتازة
+
+273
+00:33:36,480 --> 00:33:43,660
+Limit f of x as x tends to c بساوية عدد delta اللي
+
+274
+00:33:43,660 --> 00:33:51,460
+هو تعريف epsilon delta هذا معناه أنه لكل epsilon
+
+275
+00:33:51,460 --> 00:33:57,640
+أكبر من السفر يوجد delta تعتمد على epsilon عدد
+
+276
+00:33:57,640 --> 00:33:58,180
+موجد
+
+277
+00:34:03,020 --> 00:34:10,300
+Such that لو كان x ينتمي ل a و absolute x minus c
+
+278
+00:34:10,300 --> 00:34:16,340
+أصغر من delta أكبر من ستر فهذا لازم يتضمن أن
+
+279
+00:34:16,340 --> 00:34:23,580
+absolute f of x minus L أصغر من أصغر يعني معنى أخر
+
+280
+00:34:23,580 --> 00:34:29,200
+L هي limit لل function f of x هو بتالي تعريف
+
+281
+00:34:29,200 --> 00:34:33,300
+epsilon delta متحقفالان هذا تعريف epsilon دلتا
+
+282
+00:34:33,300 --> 00:34:42,000
+بكاذب ال neverhood definition ال
+
+283
+00:34:42,000 --> 00:34:54,940
+neverhood definition of limit وهو
+
+284
+00:34:54,940 --> 00:34:57,720
+ان for every
+
+285
+00:35:02,320 --> 00:35:06,700
+for every epsilon
+
+286
+00:35:06,700 --> 00:35:12,480
+neighborhood V
+
+287
+00:35:12,480 --> 00:35:22,920
+epsilon of L there exists delta neighborhood V
+
+288
+00:35:22,920 --> 00:35:30,280
+delta of C بحيث
+
+289
+00:35:32,120 --> 00:35:46,700
+إن لو كانت X تنتمي إلى A ومختلفة عن الـC وموجودة
+
+290
+00:35:46,700 --> 00:35:53,200
+أيضًا في الـDelta نبرهود لـC فلازم هذا يقدر إن
+
+291
+00:35:53,200 --> 00:36:01,600
+صورة X لازم تنتمي للـY نبرهود لـA
+
+292
+00:36:06,140 --> 00:36:13,440
+و هذا بالظبط عملنا اخر remark، prove it
+
+293
+00:36:13,440 --> 00:36:19,240
+follows from
+
+294
+00:36:19,240 --> 00:36:32,800
+above remark write
+
+295
+00:36:32,800 --> 00:36:33,380
+it down
+
+296
+00:36:40,630 --> 00:36:44,690
+حاولوا تكتبوا البرهان، البرهان فسرناها هنا
+
+297
+00:36:44,690 --> 00:37:00,590
+واضحناها من ال remark خلينا نشوف خلينا
+
+298
+00:37:00,590 --> 00:37:10,530
+نرسم رسمها في المحور Xنحو الـ y وهي ال origin وخفض
+
+299
+00:37:10,530 --> 00:37:16,270
+انه يوجد function مثل هذه فهذا بالحقيقة function y
+
+300
+00:37:16,270 --> 00:37:23,070
+بسهولة f of x وهي c نقطة في المجال تبع الدالة او
+
+301
+00:37:23,070 --> 00:37:34,330
+حتى لو ماكنتش موجودة c is the cluster point وهي
+
+302
+00:37:34,330 --> 00:37:35,870
+هذا عدد حقيقي
+
+303
+00:37:38,510 --> 00:37:44,570
+فده عدد حقيقي فمعنى
+
+304
+00:37:44,570 --> 00:37:50,770
+ان limit لل F and X بالساوية C بالساوية L معناه
+
+305
+00:37:50,770 --> 00:37:57,210
+لأي أبسلون أكبر من السفر أي لأي أبسلون أكبر من
+
+306
+00:37:57,210 --> 00:38:24,500
+السفر ممكن أناأكول epsilon neighborhood لأي
+
+307
+00:38:24,500 --> 00:38:33,180
+epsilon أكبر من 0 يعني بقدر أكوّنإبسلون نبرهود
+
+308
+00:38:33,180 --> 00:38:37,660
+بإبسلون
+
+309
+00:38:37,660 --> 00:38:44,180
+لإل فلو كان هذا given given إبسلون يعني given
+
+310
+00:38:44,180 --> 00:38:52,920
+إبسلون نبرهود لإل بقدر أجيل
+
+311
+00:38:52,920 --> 00:38:56,200
+أرد عليه
+
+312
+00:39:01,810 --> 00:39:07,770
+الدلتا دلتا neighborhood هذا عبارة عن delta
+
+313
+00:39:07,770 --> 00:39:15,250
+neighborhood ل C إذا انا أخدت اعطتوني إبسلون بقدر
+
+314
+00:39:15,250 --> 00:39:20,570
+أكون إبسلون neighborhood ل L فبقدر أرد عليه ال
+
+315
+00:39:20,570 --> 00:39:24,110
+delta neighborhood ل C في الفترة المفتوحة هذه
+
+316
+00:39:25,810 --> 00:39:31,550
+بالتالي، إذا كان هناك مجتمع إبسلن لـL، فهناك مجتمع
+
+317
+00:39:31,550 --> 00:39:38,230
+Delta لـC أو هناك مجتمع Delta عدد موجب بحيث إن لو
+
+318
+00:39:38,230 --> 00:39:42,930
+كانت الـX موجودة في A، و المتباين هذا تتحقق، طب X
+
+319
+00:39:42,930 --> 00:39:47,550
+موجودة في A، و المتباين هذا تتحقق، معناته X موجودة
+
+320
+00:39:47,550 --> 00:39:51,990
+في A و مختلفة عن الـC، و X موجودة في الـDelta
+
+321
+00:39:51,990 --> 00:39:57,400
+neighborhoodهذه معناته X تنتمي لـA ومختلفة عن الـC
+
+322
+00:39:57,400 --> 00:40:02,480
+و X موجودة في الـDelta نبرهود هذا الشرط هذا بيقدّي
+
+323
+00:40:02,480 --> 00:40:08,760
+أن المتباين هذا تتحقق المتباين هذا تتحقق معناه أن
+
+324
+00:40:08,760 --> 00:40:14,840
+ال F of X صورة X تنتمي للـY نبرهود لـB فهو واضح أن
+
+325
+00:40:14,840 --> 00:40:20,020
+هذا التعريف بيقدّي للتعريف هذا باستخدام تفسير ال
+
+326
+00:40:20,020 --> 00:40:31,340
+remarkو العكس طبعا صحيح .. صحيح okay تمام؟ اذا هذا
+
+327
+00:40:31,340 --> 00:40:36,270
+بنسميه ال .. هذا التعريفبنسمي الـ neighborhood
+
+328
+00:40:36,270 --> 00:40:40,630
+definition للـ limit of a function والتعريف دا أو
+
+329
+00:40:40,630 --> 00:40:45,810
+هذا بنسمي الـ epsilon delta definition
+
+330
+00:40:45,810 --> 00:40:52,930
+of the limit of a function تمام؟ وهذا طبعا زي ال
+
+331
+00:40:52,930 --> 00:40:57,490
+epsilon capital N definition للlimit of a sequence
+
+332
+00:40:57,490 --> 00:41:00,870
+وبعد هي فكرين أعرفنا ال neighborhood definition
+
+333
+00:41:00,870 --> 00:41:05,640
+للlimit of a sequenceهذا يعني يكافئ الكلام اللي
+
+334
+00:41:05,640 --> 00:41:09,720
+هنا إذا الأن في عندي تعريفين لل limit of a
+
+335
+00:41:09,720 --> 00:41:14,060
+function at a point أو at a cluster point الدارش
+
+336
+00:41:14,060 --> 00:41:17,080
+التعريف اللي هنستخدمه أكتر هو epsilon delta
+
+337
+00:41:17,080 --> 00:41:23,580
+definition of the limit أكتر من ال neighborhood
+
+338
+00:41:23,580 --> 00:41:26,920
+definition لكن أنا ممنعش أن أنا في أوقات معينة
+
+339
+00:41:26,920 --> 00:41:30,560
+أستخدم ال neighborhood definition طيب ناخد بعض
+
+340
+00:41:30,560 --> 00:41:38,200
+الأمثلةعلى كيفية إثبات إن الـ limit لـ certain
+
+341
+00:41:38,200 --> 00:41:43,980
+function is a certain number by
+
+342
+00:41:43,980 --> 00:41:49,020
+using epsilon delta definition نشوف مع بعض، وهذا
+
+343
+00:41:49,020 --> 00:41:54,100
+يعني بوازي الكلام اللي عملناه بالنسبة لل limits of
+
+344
+00:41:54,100 --> 00:42:00,240
+sequencesفإذا هنا في الامثلة في كل الامثلة التالية
+
+345
+00:42:00,240 --> 00:42:04,500
+عايزين نستخدم ال definition of أو epsilon delta
+
+346
+00:42:04,500 --> 00:42:07,520
+definition أو ال neighborhood definition لل limit
+
+347
+00:42:07,520 --> 00:42:10,720
+of a function to prove إنه limit عن نقطة محددة
+
+348
+00:42:10,720 --> 00:42:18,760
+بساوي عدد محدد فمثلا إن نثبت إنه limit لدالة ثابت
+
+349
+00:42:18,760 --> 00:42:22,240
+B لما X تقولها C بساوي B
+
+350
+00:42:25,710 --> 00:42:30,410
+فلت هنا عندي فان الـ function تبعتي f of x بالساوي
+
+351
+00:42:30,410 --> 00:42:38,130
+ثابت بي لكل x تنتمي إلى R فان الـ function تبعتي
+
+352
+00:42:38,130 --> 00:42:43,130
+ده اللي ثابتة وبالتالي اذا هنا لثبات ان ال limit
+
+353
+00:42:43,130 --> 00:42:45,290
+تبعتها بالساوي بي
+
+354
+00:42:48,460 --> 00:42:50,340
+أكبر من السفر أكبر من السفر أكبر من السفر أكبر من
+
+355
+00:42:50,340 --> 00:42:50,500
+أكبر من السفر أكبر من السفر أكبر من السفر أكبر من
+
+356
+00:42:50,500 --> 00:42:51,200
+السفر أكبر من السفر أكبر من السفر أكبر من السفر
+
+357
+00:42:51,200 --> 00:42:52,980
+أكبر من السفر أكبر من السفر أكبر من السفر أكبر من
+
+358
+00:42:52,980 --> 00:42:53,500
+السفر أكبر من السفر أكبر من السفر أكبر من السفر
+
+359
+00:42:53,500 --> 00:42:54,560
+أكبر من السفر أكبر من السفر أكبر من السفر أكبر من
+
+360
+00:42:54,560 --> 00:42:55,760
+السفر أكبر من السفر أكبر من السفر أكبر من السفر
+
+361
+00:42:55,760 --> 00:43:05,680
+أكبر من السفر أكبر من السفر أكبر من السفر أكبر
+
+362
+00:43:05,680 --> 00:43:06,180
+من السفر
+
+363
+00:43:18,680 --> 00:43:23,060
+تعالى نشوف ال implication ال delta هذه works ولا
+
+364
+00:43:23,060 --> 00:43:27,560
+لأ فانا عندي ان لو كانت ال X تنتمي ل A طبعا ال A
+
+365
+00:43:27,560 --> 00:43:31,700
+مجال الدالة هنا هو كل العدالة الحقيقية و absolute
+
+366
+00:43:31,700 --> 00:43:38,610
+X minus C أكبر من 0 أصغر من Deltaهل هذا بيقدر
+
+367
+00:43:38,610 --> 00:43:43,910
+لأبسليوت f of x minus b أصغر من إبسلون بالتأكيد
+
+368
+00:43:43,910 --> 00:43:48,910
+أنا عندي f of x بالساوي بيه سالب ال limit اللي هي
+
+369
+00:43:48,910 --> 00:43:55,090
+بيه فهذا بيطلع أبسليوت السفر بيطلع سفر والسفر هذا
+
+370
+00:43:55,090 --> 00:44:02,040
+أصغر من أي إبسلون موجةإذا حصلت تعريف Epsilon Delta
+
+371
+00:44:02,040 --> 00:44:06,560
+يعني أثبتت أنه لأي Epsilon أي Delta موجبة works
+
+372
+00:44:06,560 --> 00:44:10,580
+تعمل تعطيل ال implication وبالتالي by definition
+
+373
+00:44:10,580 --> 00:44:20,140
+limit F of X as X tends to C بساوي D طيب
+
+374
+00:44:20,140 --> 00:44:27,120
+ناخد كمان مثال لو أخدت ال identity function
+
+375
+00:44:34,810 --> 00:44:40,290
+بنثبت ان limit ده identity function لما x تقول الى
+
+376
+00:44:40,290 --> 00:44:47,110
+اي عدد حقيقى c بساوي c نستخدم
+
+377
+00:44:47,110 --> 00:44:52,310
+تعريف epsilon delta let epsilon أكبر من السفر be
+
+378
+00:44:52,310 --> 00:44:59,370
+given المرة هذه بدي ارد على ال epsilon هذه ال
+
+379
+00:44:59,370 --> 00:45:05,230
+delta تعتمد عليها هختار ال deltaبساول ابسلون
+
+380
+00:45:05,230 --> 00:45:10,430
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+381
+00:45:10,430 --> 00:45:10,530
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+382
+00:45:10,530 --> 00:45:12,470
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+383
+00:45:12,470 --> 00:45:17,090
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+384
+00:45:17,090 --> 00:45:19,890
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+385
+00:45:19,890 --> 00:45:23,450
+بيختار دلتا بساول ابسلون بيختار دلتا بساول ابسلون
+
+386
+00:45:23,450 --> 00:45:29,320
+بيختار دلتا بساول ابسلون بيختار دلتهي عبارة عن ال
+
+387
+00:45:29,320 --> 00:45:33,500
+identity function لكل X المجال تبعها كل الأعداد
+
+388
+00:45:33,500 --> 00:45:40,060
+الحقيقية فلو كانت X تنتمي ل A اللي هي R و Absolute
+
+389
+00:45:40,060 --> 00:45:46,100
+X minus C أكبر من Zero أصغر من Delta فخلينا نشوف
+
+390
+00:45:46,100 --> 00:45:52,880
+هل بيطلع Absolute F of X minus ال L اللي هو C أصغر
+
+391
+00:45:52,880 --> 00:45:56,240
+من Epsilon هنشوف
+
+392
+00:45:57,800 --> 00:46:04,860
+طيب نعوض عن F of X بالساوي X minus C طب أنا عند ال
+
+393
+00:46:04,860 --> 00:46:10,320
+X هذه موجودة في R و المسافة بينها و مختلفة عن ال C
+
+394
+00:46:10,320 --> 00:46:13,880
+و المسافة بينهم أصغر من Delta اللي أنا باخدها
+
+395
+00:46:13,880 --> 00:46:19,420
+بالساوي Y إذا ال absolute X minus C من هنا أصغر من
+
+396
+00:46:19,420 --> 00:46:27,090
+Delta اللي هي Yوبالتالي درهين أثبتت أنه لأي إبسلون
+
+397
+00:46:27,090 --> 00:46:32,990
+يوجد دلتا اللي هي إبسلون نفسها بحيث لكل x في a إذا
+
+398
+00:46:32,990 --> 00:46:36,570
+كان absolute x minus c أكبر من صفر أصغر من دلتا
+
+399
+00:46:36,570 --> 00:46:40,490
+هذا بيقدر أن absolute f of x minus l أصغر من
+
+400
+00:46:40,490 --> 00:46:47,650
+إبسلون since إبسلون أكبر من الصفر was arbitrary
+
+401
+00:46:52,350 --> 00:47:00,830
+we get from the definition هذا الكلام صحيح لكل
+
+402
+00:47:00,830 --> 00:47:06,690
+epsilon وبالتالي by definition بطلع عندي limit ال
+
+403
+00:47:06,690 --> 00:47:10,430
+function f of x اللي هي ال identity function لما x
+
+404
+00:47:10,430 --> 00:47:19,750
+تقوى ل c بساوي c وهو المطلوب تمام okay إذا المرة
+
+405
+00:47:19,750 --> 00:47:27,480
+الجايةهنثبت ان limited ده لتربعية لما x او ل c
+
+406
+00:47:27,480 --> 00:47:33,280
+بساوي c تربية وهذا موجود طبعا في الكتاب وفي كمان
+
+407
+00:47:33,280 --> 00:47:37,780
+أمثلة أخرى فارجو أنكم تقرؤوا الأمثلة هذه من الكتاب
+
+408
+00:47:37,780 --> 00:47:44,350
+و تحضروها للمحاضرة الجايةوتشوفوا كيف تم استخدام
+
+409
+00:47:44,350 --> 00:47:49,410
+تعريف epsilon delta في اثبات ان ال limit لدالة زهر
+
+410
+00:47:49,410 --> 00:47:53,530
+الدالة التربعية بساوي C تربية عند اي نقطة C okay
+
+411
+00:47:53,530 --> 00:47:58,270
+تمام؟ في اي سؤال او افسار؟ اذا نكتفي بهذا القدر
+
+412
+00:47:58,270 --> 00:48:02,410
+وان شاء الله اللي انا تكمله في المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..2a668c0ef5065f592a9d396e2fd6dbaf543d3373
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/6FDcUXR9Pqo_raw.json
@@ -0,0 +1 @@
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11933, 15730, 23758, 4724, 12984, 3555, 2655, 2423, 3932, 6024, 48506, 32239, 3224, 19446, 1829, 30544, 8978, 3224, 13630, 2793, 5551, 34740, 7578, 22807], "avg_logprob": -0.3559658971699801, "compression_ratio": 1.5461538461538462, "no_speech_prob": 0.0, "words": [{"start": 292.61, "end": 293.59, "word": "لاتسار", "probability": 0.51513671875}, {"start": 293.59, "end": 294.01, "word": " السفر", "probability": 0.8665364583333334}, {"start": 294.01, "end": 296.49, "word": " وبالتالي", "probability": 0.7202809651692709}, {"start": 296.49, "end": 296.81, "word": " إذا", "probability": 0.489715576171875}, {"start": 296.81, "end": 297.11, "word": " هذا", "probability": 0.67822265625}, {"start": 297.11, "end": 297.69, "word": " بثبت", "probability": 0.8934326171875}, {"start": 297.69, "end": 299.41, "word": " السفر", "probability": 0.8525390625}, {"start": 299.41, "end": 299.93, "word": " is", "probability": 0.78369140625}, {"start": 299.93, "end": 300.29, "word": " a", "probability": 0.90234375}, {"start": 300.29, "end": 300.71, "word": " cluster", "probability": 0.92822265625}, {"start": 300.71, "end": 301.37, "word": " point", "probability": 0.96923828125}, {"start": 301.37, "end": 305.47, "word": " of", "probability": 0.277099609375}, {"start": 305.47, "end": 306.49, "word": " الست", "probability": 0.529541015625}, {"start": 306.49, "end": 307.91, "word": " إذا", "probability": 0.635009765625}, {"start": 307.91, "end": 308.17, "word": " هذا", "probability": 0.83642578125}, {"start": 308.17, "end": 308.69, "word": " بثبت", "probability": 0.9696044921875}, {"start": 308.69, "end": 308.81, "word": " ال", "probability": 0.84375}, {"start": 308.81, "end": 309.15, "word": " claim", "probability": 0.83740234375}, {"start": 309.15, "end": 310.07, "word": " الآن", "probability": 0.6729736328125}, {"start": 310.07, "end": 311.41, "word": " ليه", "probability": 0.955322265625}, {"start": 311.41, "end": 312.09, "word": " مايكون", "probability": 0.7880859375}, {"start": 312.09, "end": 312.31, "word": " فيه", "probability": 0.759033203125}, {"start": 312.31, "end": 312.65, "word": " cluster", "probability": 0.95751953125}, {"start": 312.65, "end": 313.25, "word": " points", "probability": 0.93603515625}, {"start": 313.25, "end": 314.13, "word": " أخرى؟", "probability": 0.9578857421875}], "temperature": 1.0}, {"id": 11, "seek": 34763, "start": 330.49, "end": 347.63, "text": "إذا كانت X لا تساوي سفر، فهي ليست مجموعة من A فحاسيبكم أنتم تكتبوا البرهان", "tokens": [28814, 15730, 25961, 2655, 1783, 20193, 6055, 3794, 995, 45865, 8608, 5172, 2288, 12399, 6156, 3224, 1829, 32239, 14851, 3714, 7435, 2304, 2407, 27884, 9154, 316, 6156, 5016, 32277, 1829, 3555, 24793, 14739, 39237, 6055, 4117, 2655, 3555, 14407, 2423, 26890, 3224, 7649], "avg_logprob": -0.5557528219439767, "compression_ratio": 1.233644859813084, "no_speech_prob": 0.0, "words": [{"start": 330.49, "end": 331.33000000000004, "word": "إذا", "probability": 0.283172607421875}, {"start": 331.33000000000004, "end": 332.17, "word": " كانت", "probability": 0.7763671875}, {"start": 332.17, "end": 332.39, "word": " X", "probability": 0.275634765625}, {"start": 332.39, "end": 332.61, "word": " لا", "probability": 0.63427734375}, {"start": 332.61, "end": 333.09, "word": " تساوي", "probability": 0.8519287109375}, {"start": 333.09, "end": 333.47, "word": " سفر،", "probability": 0.59808349609375}, {"start": 333.47, "end": 333.79, "word": " فهي", "probability": 0.6863606770833334}, {"start": 333.79, "end": 334.07, "word": " ليست", "probability": 0.81005859375}, {"start": 334.07, "end": 334.71, "word": " مجموعة", "probability": 0.5892333984375}, {"start": 334.71, "end": 335.13, "word": " من", "probability": 0.08087158203125}, {"start": 335.13, "end": 341.15, "word": " A", "probability": 0.450927734375}, {"start": 341.15, "end": 346.39, "word": " فحاسيبكم", "probability": 0.7115885416666666}, {"start": 346.39, "end": 346.65, "word": " أنتم", "probability": 0.521728515625}, {"start": 346.65, "end": 347.07, "word": " تكتبوا", "probability": 0.97919921875}, {"start": 347.07, "end": 347.63, "word": " البرهان", "probability": 0.69744873046875}], "temperature": 1.0}, {"id": 12, "seek": 36539, "start": 350.29, "end": 365.39, "text": "هي سفر وهي واحد وهي نص وهي تلت وهي واحد على N وهي واحد على N زائد واحد وهكذا", "tokens": [3224, 1829, 8608, 5172, 2288, 37037, 1829, 36764, 24401, 37037, 1829, 8717, 9381, 37037, 1829, 6055, 1211, 2655, 37037, 1829, 36764, 24401, 15844, 426, 37037, 1829, 36764, 24401, 15844, 426, 30767, 16373, 3215, 36764, 24401, 37037, 4117, 15730], "avg_logprob": -0.22556089361508688, "compression_ratio": 1.736842105263158, "no_speech_prob": 0.0, "words": [{"start": 350.29, "end": 350.63, "word": "هي", "probability": 0.5052490234375}, {"start": 350.63, "end": 351.11, "word": " سفر", "probability": 0.7296549479166666}, {"start": 351.11, "end": 351.43, "word": " وهي", "probability": 0.7412109375}, {"start": 351.43, "end": 352.01, "word": " واحد", "probability": 0.986328125}, {"start": 352.01, "end": 353.31, "word": " وهي", "probability": 0.877197265625}, {"start": 353.31, "end": 353.77, "word": " نص", "probability": 0.987060546875}, {"start": 353.77, "end": 355.85, "word": " وهي", "probability": 0.81982421875}, {"start": 355.85, "end": 356.45, "word": " تلت", "probability": 0.9313151041666666}, {"start": 356.45, "end": 359.03, "word": " وهي", "probability": 0.9248046875}, {"start": 359.03, "end": 359.67, "word": " واحد", "probability": 0.98876953125}, {"start": 359.67, "end": 359.95, "word": " على", "probability": 0.5859375}, {"start": 359.95, "end": 360.39, "word": " N", "probability": 0.201904296875}, {"start": 360.39, "end": 362.39, "word": " وهي", "probability": 0.784423828125}, {"start": 362.39, "end": 362.89, "word": " واحد", "probability": 0.98974609375}, {"start": 362.89, "end": 363.11, "word": " على", "probability": 0.810546875}, {"start": 363.11, "end": 363.57, "word": " N", "probability": 0.87646484375}, {"start": 363.57, "end": 364.25, "word": " زائد", "probability": 0.8780924479166666}, {"start": 364.25, "end": 364.77, "word": " واحد", "probability": 0.980712890625}, {"start": 364.77, "end": 365.39, "word": " وهكذا", "probability": 0.80419921875}], "temperature": 1.0}, {"id": 13, "seek": 40035, "start": 376.43, "end": 400.35, "text": "فهنا تاندي two cases case one ان x تنتمي الى a و الحلقة التانية case two ان x لا تنتمي الى a ال x دي مستويش السفر احنا already اثبتنا ان السفر cluster point", "tokens": [5172, 3224, 8315, 6055, 7649, 16254, 732, 3331, 1389, 472, 16472, 2031, 6055, 29399, 2304, 1829, 2423, 7578, 257, 4032, 21542, 1211, 28671, 16712, 7649, 10632, 1389, 732, 16472, 2031, 20193, 6055, 29399, 2304, 1829, 2423, 7578, 257, 2423, 2031, 11778, 1829, 3714, 14851, 45865, 8592, 21136, 5172, 2288, 1975, 5016, 8315, 1217, 1975, 12984, 3555, 2655, 8315, 16472, 21136, 5172, 2288, 13630, 935], "avg_logprob": -0.3894230769230769, "compression_ratio": 1.563758389261745, "no_speech_prob": 0.0, "words": [{"start": 376.43, "end": 376.95, "word": "فهنا", "probability": 0.6041666666666666}, {"start": 376.95, "end": 377.53, "word": " تاندي", "probability": 0.2945963541666667}, {"start": 377.53, "end": 377.83, "word": " two", "probability": 0.460693359375}, {"start": 377.83, "end": 378.45, "word": " cases", "probability": 0.9384765625}, {"start": 378.45, "end": 379.59, "word": " case", "probability": 0.485107421875}, {"start": 379.59, "end": 380.01, "word": " one", "probability": 0.7177734375}, {"start": 380.01, "end": 380.87, "word": " ان", "probability": 0.435546875}, {"start": 380.87, "end": 381.27, "word": " x", "probability": 0.3193359375}, {"start": 381.27, "end": 382.03, "word": " تنتمي", "probability": 0.8489990234375}, {"start": 382.03, "end": 382.81, "word": " الى", "probability": 0.6524658203125}, {"start": 382.81, "end": 383.15, "word": " a", "probability": 0.81884765625}, {"start": 383.15, "end": 385.93, "word": " و", "probability": 0.4228515625}, {"start": 385.93, "end": 386.41, "word": " الحلقة", "probability": 0.7900390625}, {"start": 386.41, "end": 386.97, "word": " التانية", "probability": 0.87939453125}, {"start": 386.97, "end": 387.91, "word": " case", "probability": 0.83203125}, {"start": 387.91, "end": 388.35, "word": " two", "probability": 0.8671875}, {"start": 388.35, "end": 389.77, "word": " ان", "probability": 0.73095703125}, {"start": 389.77, "end": 390.19, "word": " x", "probability": 0.62060546875}, {"start": 390.19, "end": 390.41, "word": " لا", "probability": 0.82275390625}, {"start": 390.41, "end": 391.07, "word": " تنتمي", "probability": 0.9161376953125}, {"start": 391.07, "end": 391.21, "word": " الى", "probability": 0.754150390625}, {"start": 391.21, "end": 391.87, "word": " a", "probability": 0.853515625}, {"start": 391.87, "end": 394.41, "word": " ال", "probability": 0.68115234375}, {"start": 394.41, "end": 394.69, "word": " x", "probability": 0.462890625}, {"start": 394.69, "end": 394.91, "word": " دي", "probability": 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كانت ال X واحد من العناصر هدول واحد من العناصر الست فبقدر ألاقي أن يوجد بقدر ألاقي delta neighborhood للعنصر مثلا التلت بقدر ألاقي delta neighborhood", "tokens": [9566, 1829, 3555, 1975, 5172, 43042, 1783, 3714, 14851, 45865, 8592, 8608, 5172, 2288, 11933, 15730, 1783, 3714, 43020, 6055, 3794, 995, 45865, 36764, 24401, 34051, 8717, 9381, 34051, 6055, 1211, 2655, 34051, 36764, 24401, 15844, 426, 337, 512, 426, 20328, 5016, 22807, 3714, 43020, 3714, 9307, 3794, 995, 45865, 8592, 49429, 18871, 9381, 2288, 3714, 43020, 3714, 9307, 30544, 8592, 46811, 46811, 1211, 36632, 3224, 6156, 1211, 2407, 25961, 2655, 2423, 1783, 36764, 24401, 9154, 18863, 1863, 33546, 2288, 8032, 3215, 12610, 36764, 24401, 9154, 18863, 1863, 33546, 2288, 2423, 14851, 6156, 3555, 28543, 2288, 5551, 15040, 38436, 14739, 7251, 29245, 3215, 4724, 28543, 2288, 5551, 15040, 38436, 8289, 7630, 24976, 3615, 1863, 9381, 2288, 50113, 15040, 16712, 1211, 2655, 4724, 28543, 2288, 5551, 15040, 38436, 8289, 7630], "avg_logprob": 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"probability": 0.7705485026041666}, {"start": 410.81, "end": 411.01, "word": " ولا", "probability": 0.955078125}, {"start": 411.01, "end": 411.43, "word": " عنصر", "probability": 0.98388671875}, {"start": 411.43, "end": 411.93, "word": " ممكن", "probability": 0.805419921875}, {"start": 411.93, "end": 412.37, "word": " ماتكونش", "probability": 0.9139404296875}, {"start": 412.37, "end": 412.53, "word": " تم", "probability": 0.544921875}, {"start": 412.53, "end": 412.97, "word": " تمل", "probability": 0.481353759765625}, {"start": 412.97, "end": 413.25, "word": " أيه", "probability": 0.868408203125}, {"start": 413.25, "end": 414.33, "word": " فلو", "probability": 0.96044921875}, {"start": 414.33, "end": 414.63, "word": " كانت", "probability": 0.944091796875}, {"start": 414.63, "end": 414.75, "word": " ال", "probability": 0.77392578125}, {"start": 414.75, "end": 414.93, "word": " X", "probability": 0.9521484375}, {"start": 414.93, "end": 415.29, "word": " واحد", "probability": 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{"start": 423.91, "end": 424.25, "word": " ألاقي", "probability": 0.9690755208333334}, {"start": 424.25, "end": 424.63, "word": " delta", "probability": 0.391357421875}, {"start": 424.63, "end": 425.11, "word": " neighborhood", "probability": 0.7861328125}, {"start": 425.11, "end": 426.97, "word": " للعنصر", "probability": 0.933203125}, {"start": 426.97, "end": 427.45, "word": " مثلا", "probability": 0.96533203125}, {"start": 427.45, "end": 427.99, "word": " التلت", "probability": 0.9158528645833334}, {"start": 427.99, "end": 428.33, "word": " بقدر", "probability": 0.9742838541666666}, {"start": 428.33, "end": 428.61, "word": " ألاقي", "probability": 0.9851888020833334}, {"start": 428.61, "end": 428.99, "word": " delta", "probability": 0.8359375}, {"start": 428.99, "end": 429.49, "word": " neighborhood", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 15, "seek": 45418, "start": 433.86, "end": 454.18, "text": "الأنصر اللي بعد هذا هيكون ربع فباخد المسافة الأصغر بين تلت ربع 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0.82421875}, {"start": 1009.99, "end": 1010.47, "word": " of", "probability": 0.89453125}, {"start": 1010.47, "end": 1010.93, "word": " limit", "probability": 0.9482421875}, {"start": 1010.93, "end": 1014.31, "word": " لل", "probability": 0.273193359375}, {"start": 1014.31, "end": 1014.63, "word": " limit", "probability": 0.77490234375}, {"start": 1014.63, "end": 1014.89, "word": " of", "probability": 0.96630859375}, {"start": 1014.89, "end": 1015.05, "word": " a", "probability": 0.794921875}, {"start": 1015.05, "end": 1015.45, "word": " function", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 38, "seek": 104205, "start": 1016.63, "end": 1042.05, "text": "الـ Limit لـ function f of x بالساوي أو L هي عبارة عن Limit لـ function f of x and x بالساوي C إذا لو أعطتوني أي إبسلون عدد موجب لازم أنا أرد عليها Delta عدد موجب آخر يعتمد على إبسلون بحيث أنه لكل X في المجموعة A اللي هو ال domain تبع ال function", "tokens": [6027, 39184, 16406, 270, 5296, 39184, 2445, 283, 295, 2031, 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{"start": 1017.37, "end": 1017.81, "word": " function", "probability": 0.48828125}, {"start": 1017.81, "end": 1018.09, "word": " f", "probability": 0.712890625}, {"start": 1018.09, "end": 1018.31, "word": " of", "probability": 0.3583984375}, {"start": 1018.31, "end": 1018.55, "word": " x", "probability": 0.849609375}, {"start": 1018.55, "end": 1019.29, "word": " بالساوي", "probability": 0.635589599609375}, {"start": 1019.29, "end": 1020.59, "word": " أو", "probability": 0.439453125}, {"start": 1020.59, "end": 1020.89, "word": " L", "probability": 0.434326171875}, {"start": 1020.89, "end": 1021.17, "word": " هي", "probability": 0.88330078125}, {"start": 1021.17, "end": 1021.57, "word": " عبارة", "probability": 0.9764404296875}, {"start": 1021.57, "end": 1021.73, "word": " عن", "probability": 0.9609375}, {"start": 1021.73, "end": 1022.13, "word": " Limit", "probability": 0.82666015625}, {"start": 1022.13, "end": 1022.33, "word": " لـ", "probability": 0.770263671875}, {"start": 1022.33, "end": 1022.67, "word": " function", "probability": 0.79736328125}, {"start": 1022.67, "end": 1023.05, "word": " f", "probability": 0.90283203125}, {"start": 1023.05, "end": 1023.25, "word": " of", "probability": 0.888671875}, {"start": 1023.25, "end": 1023.59, "word": " x", "probability": 0.95166015625}, {"start": 1023.59, "end": 1023.93, "word": " and", "probability": 0.755859375}, {"start": 1023.93, "end": 1024.15, "word": " x", "probability": 0.81103515625}, {"start": 1024.15, "end": 1024.65, "word": " بالساوي", "probability": 0.9312744140625}, {"start": 1024.65, "end": 1024.97, "word": " C", "probability": 0.303466796875}, {"start": 1024.97, "end": 1026.13, "word": " إذا", "probability": 0.853271484375}, {"start": 1026.13, "end": 1027.89, "word": " لو", "probability": 0.75732421875}, {"start": 1027.89, "end": 1028.57, "word": " أعطتوني", "probability": 0.8391927083333334}, {"start": 1028.57, "end": 1028.77, "word": " أي", "probability": 0.89013671875}, {"start": 1028.77, "end": 1029.27, "word": " إبسلون", "probability": 0.6882080078125}, {"start": 1029.27, "end": 1029.55, "word": " عدد", "probability": 0.9552408854166666}, {"start": 1029.55, "end": 1029.97, "word": " موجب", "probability": 0.9680989583333334}, {"start": 1029.97, "end": 1030.41, "word": " لازم", "probability": 0.92724609375}, {"start": 1030.41, "end": 1030.63, "word": " أنا", "probability": 0.69384765625}, {"start": 1030.63, "end": 1031.35, "word": " أرد", "probability": 0.9051106770833334}, {"start": 1031.35, "end": 1031.89, "word": " عليها", "probability": 0.980712890625}, {"start": 1031.89, "end": 1032.45, "word": " Delta", "probability": 0.45751953125}, {"start": 1032.45, "end": 1033.93, "word": " عدد", "probability": 0.9708658854166666}, {"start": 1033.93, "end": 1034.35, "word": " موجب", "probability": 0.9943033854166666}, {"start": 1034.35, "end": 1034.81, "word": " آخر", "probability": 0.752685546875}, {"start": 1034.81, "end": 1035.39, "word": " يعتمد", "probability": 0.7747395833333334}, {"start": 1035.39, "end": 1035.57, "word": " على", "probability": 0.90380859375}, {"start": 1035.57, "end": 1036.19, "word": " إبسلون", "probability": 0.96787109375}, {"start": 1036.19, "end": 1036.81, "word": " بحيث", "probability": 0.894287109375}, {"start": 1036.81, "end": 1037.31, "word": " أنه", "probability": 0.790771484375}, {"start": 1037.31, "end": 1038.63, "word": " لكل", "probability": 0.984130859375}, {"start": 1038.63, "end": 1039.07, "word": " X", "probability": 0.48388671875}, {"start": 1039.07, "end": 1039.41, "word": " في", "probability": 0.96923828125}, {"start": 1039.41, "end": 1040.09, "word": " المجموعة", "probability": 0.91484375}, {"start": 1040.09, "end": 1040.31, "word": " A", "probability": 0.8232421875}, {"start": 1040.31, "end": 1040.45, "word": " اللي", "probability": 0.93017578125}, {"start": 1040.45, "end": 1040.61, "word": " هو", "probability": 0.990234375}, {"start": 1040.61, "end": 1040.75, "word": " ال", "probability": 0.8486328125}, {"start": 1040.75, "end": 1041.09, "word": " domain", "probability": 0.84619140625}, {"start": 1041.09, "end": 1041.45, "word": " تبع", "probability": 0.9112955729166666}, {"start": 1041.45, "end": 1041.59, "word": " ال", "probability": 0.9208984375}, {"start": 1041.59, "end": 1042.05, "word": " function", "probability": 0.85400390625}], "temperature": 1.0}, {"id": 39, "seek": 105061, "start": 1044.38, "end": 1050.62, "text": "و X هذه مختلفة لا تساوي C يعني المتباين هذه معناها X لا تساوي C", "tokens": [2407, 1783, 29538, 3714, 46456, 46538, 3660, 20193, 6055, 3794, 995, 45865, 383, 37495, 22653, 9673, 2655, 3555, 995, 9957, 29538, 20449, 8315, 11296, 1783, 20193, 6055, 3794, 995, 45865, 383], "avg_logprob": -0.32397459633648396, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1044.38, "end": 1044.68, "word": "و", "probability": 0.62451171875}, {"start": 1044.68, "end": 1045.3, "word": " X", "probability": 0.416259765625}, {"start": 1045.3, "end": 1045.72, "word": " هذه", "probability": 0.47216796875}, {"start": 1045.72, "end": 1046.48, "word": " مختلفة", "probability": 0.9007568359375}, {"start": 1046.48, "end": 1046.48, "word": " لا", "probability": 0.2413330078125}, {"start": 1046.48, "end": 1047.08, "word": " تساوي", "probability": 0.866943359375}, {"start": 1047.08, "end": 1047.3, "word": " C", "probability": 0.7333984375}, {"start": 1047.3, "end": 1047.84, "word": " يعني", "probability": 0.5997314453125}, {"start": 1047.84, "end": 1048.52, "word": " المتباين", "probability": 0.869677734375}, {"start": 1048.52, "end": 1048.78, "word": " هذه", "probability": 0.2939453125}, {"start": 1048.78, "end": 1049.28, "word": " معناها", "probability": 0.7410481770833334}, {"start": 1049.28, "end": 1049.58, "word": " X", "probability": 0.919921875}, {"start": 1049.58, "end": 1049.8, "word": " لا", "probability": 0.95361328125}, {"start": 1049.8, "end": 1050.42, "word": " تساوي", "probability": 0.9776611328125}, {"start": 1050.42, "end": 1050.62, "word": " C", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 40, "seek": 107235, "start": 1052.14, "end": 1072.36, "text": "إذاً لكل x في a مختلفة عن الـc والمسافة بينها وبين الـc أصغر من دلتا لازم تطلع المسافة بين f of x و L أصغر من إبسلون هذا الكلام اتحقق لكل إبسلون أكبر من الصفر فبنقول إن العدد L is a limit of the function f عند النقطة c", "tokens": [28814, 15730, 14111, 5296, 28820, 2031, 8978, 257, 3714, 46456, 46538, 3660, 18871, 2423, 39184, 66, 4032, 45340, 3794, 31845, 3660, 49374, 11296, 46599, 9957, 2423, 39184, 66, 5551, 9381, 17082, 2288, 9154, 11778, 1211, 2655, 995, 5296, 31377, 2304, 6055, 9566, 1211, 3615, 9673, 3794, 31845, 3660, 49374, 283, 295, 2031, 4032, 441, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 23758, 2423, 28820, 10943, 1975, 2655, 5016, 4587, 4587, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 6156, 3555, 1863, 39648, 36145, 18863, 3215, 3215, 441, 307, 257, 4948, 295, 264, 2445, 283, 43242, 28239, 47432, 3660, 269], "avg_logprob": -0.24197248417303102, "compression_ratio": 1.6511627906976745, "no_speech_prob": 0.0, "words": [{"start": 1052.14, "end": 1052.56, "word": "إذاً", "probability": 0.4373982747395833}, {"start": 1052.56, "end": 1052.9, "word": " لكل", "probability": 0.960205078125}, {"start": 1052.9, "end": 1053.16, "word": " x", "probability": 0.6748046875}, {"start": 1053.16, "end": 1053.36, "word": " في", "probability": 0.85205078125}, {"start": 1053.36, "end": 1053.5, "word": " a", "probability": 0.69775390625}, {"start": 1053.5, "end": 1054.3, "word": " مختلفة", "probability": 0.9827880859375}, {"start": 1054.3, "end": 1054.44, "word": " عن", "probability": 0.9794921875}, {"start": 1054.44, "end": 1054.86, "word": " الـc", "probability": 0.5435384114583334}, {"start": 1054.86, "end": 1056.32, "word": " والمسافة", "probability": 0.8373046875}, {"start": 1056.32, "end": 1056.74, "word": " بينها", "probability": 0.978759765625}, {"start": 1056.74, "end": 1057.18, "word": " وبين", "probability": 0.70654296875}, {"start": 1057.18, "end": 1057.56, "word": " الـc", "probability": 0.9332682291666666}, {"start": 1057.56, "end": 1058.02, "word": " أصغر", "probability": 0.9854736328125}, {"start": 1058.02, "end": 1058.2, "word": " من", "probability": 0.9951171875}, {"start": 1058.2, "end": 1058.68, "word": " دلتا", "probability": 0.7401123046875}, {"start": 1058.68, "end": 1059.58, "word": " لازم", "probability": 0.8406575520833334}, {"start": 1059.58, "end": 1059.96, "word": " تطلع", "probability": 0.959716796875}, {"start": 1059.96, "end": 1060.58, "word": " المسافة", "probability": 0.9869384765625}, {"start": 1060.58, "end": 1060.8, "word": " بين", "probability": 0.90966796875}, {"start": 1060.8, "end": 1061.04, "word": " f", "probability": 0.88427734375}, {"start": 1061.04, "end": 1061.2, "word": " of", "probability": 0.7646484375}, {"start": 1061.2, "end": 1061.46, "word": " x", "probability": 0.9853515625}, {"start": 1061.46, "end": 1061.62, "word": " و", "probability": 0.87841796875}, {"start": 1061.62, "end": 1061.82, "word": " L", "probability": 0.42578125}, {"start": 1061.82, "end": 1062.42, "word": " أصغر", "probability": 0.98828125}, {"start": 1062.42, "end": 1062.58, "word": " من", "probability": 0.99169921875}, {"start": 1062.58, "end": 1063.06, "word": " إبسلون", "probability": 0.7048583984375}, {"start": 1063.06, "end": 1063.64, "word": " هذا", "probability": 0.171142578125}, {"start": 1063.64, "end": 1064.04, "word": " الكلام", "probability": 0.7639973958333334}, {"start": 1064.04, "end": 1064.56, "word": " اتحقق", "probability": 0.92431640625}, {"start": 1064.56, "end": 1064.98, "word": " لكل", "probability": 0.98193359375}, {"start": 1064.98, "end": 1065.5, "word": " إبسلون", "probability": 0.96455078125}, {"start": 1065.5, "end": 1065.86, "word": " أكبر", "probability": 0.9680989583333334}, {"start": 1065.86, "end": 1066.12, "word": " من", "probability": 0.9912109375}, {"start": 1066.12, "end": 1067.22, "word": " الصفر", "probability": 0.7017415364583334}, {"start": 1067.22, "end": 1067.74, "word": " فبنقول", "probability": 0.844970703125}, {"start": 1067.74, "end": 1067.9, "word": " إن", "probability": 0.525390625}, {"start": 1067.9, "end": 1068.36, "word": " العدد", "probability": 0.8977864583333334}, {"start": 1068.36, "end": 1068.7, "word": " L", "probability": 0.85546875}, {"start": 1068.7, "end": 1069.18, "word": " is", "probability": 0.8154296875}, {"start": 1069.18, "end": 1069.88, "word": " a", "probability": 0.75537109375}, {"start": 1069.88, "end": 1070.18, "word": " limit", "probability": 0.96923828125}, {"start": 1070.18, "end": 1070.46, "word": " of", "probability": 0.95947265625}, {"start": 1070.46, "end": 1070.62, "word": " the", "probability": 0.85986328125}, {"start": 1070.62, "end": 1071.0, "word": " function", "probability": 0.96875}, {"start": 1071.0, "end": 1071.3, "word": " f", "probability": 0.8525390625}, {"start": 1071.3, "end": 1071.64, "word": " عند", "probability": 0.74560546875}, {"start": 1071.64, "end": 1072.14, "word": " النقطة", "probability": 0.74951171875}, {"start": 1072.14, "end": 1072.36, "word": " c", "probability": 0.65283203125}], "temperature": 1.0}, {"id": 41, "seek": 110373, "start": 1079.17, "end": 1103.73, "text": "من هذا التعريف بينتج على طول اه طيب in this case in this case we say انه if converges if converges", "tokens": [27842, 23758, 16712, 3615, 16572, 5172, 4724, 9957, 2655, 7435, 15844, 23032, 12610, 1975, 3224, 23032, 1829, 3555, 294, 341, 1389, 294, 341, 1389, 321, 584, 16472, 3224, 498, 9652, 2880, 498, 9652, 2880], "avg_logprob": -0.18962053741727555, "compression_ratio": 1.2403846153846154, "no_speech_prob": 0.0, "words": [{"start": 1079.17, "end": 1079.57, "word": "من", "probability": 0.84765625}, {"start": 1079.57, "end": 1079.85, "word": " هذا", "probability": 0.86962890625}, {"start": 1079.85, "end": 1080.59, "word": " التعريف", "probability": 0.991455078125}, {"start": 1080.59, "end": 1081.39, "word": " بينتج", "probability": 0.7801513671875}, {"start": 1081.39, "end": 1081.59, "word": " على", "probability": 0.8056640625}, {"start": 1081.59, "end": 1082.17, "word": " طول", "probability": 0.993896484375}, {"start": 1082.17, "end": 1084.31, "word": " اه", "probability": 0.615966796875}, {"start": 1084.31, "end": 1084.75, "word": " طيب", "probability": 0.9697265625}, {"start": 1084.75, "end": 1086.15, "word": " in", "probability": 0.72119140625}, {"start": 1086.15, "end": 1086.49, "word": " this", "probability": 0.97314453125}, {"start": 1086.49, "end": 1087.71, "word": " case", "probability": 0.95068359375}, {"start": 1087.71, "end": 1089.69, "word": " in", "probability": 0.52978515625}, {"start": 1089.69, "end": 1090.03, "word": " this", "probability": 0.970703125}, {"start": 1090.03, "end": 1090.63, "word": " case", "probability": 0.94873046875}, {"start": 1090.63, "end": 1093.93, "word": " we", "probability": 0.73974609375}, {"start": 1093.93, "end": 1096.05, "word": " say", "probability": 0.9765625}, {"start": 1096.05, "end": 1096.89, "word": " انه", "probability": 0.887451171875}, {"start": 1096.89, "end": 1097.67, "word": " if", "probability": 0.54443359375}, {"start": 1097.67, "end": 1100.09, "word": " converges", "probability": 0.64208984375}, {"start": 1100.09, "end": 1102.71, "word": " if", "probability": 0.859375}, {"start": 1102.71, "end": 1103.73, "word": " converges", "probability": 0.972900390625}], "temperature": 1.0}, {"id": 42, "seek": 113426, "start": 1105.18, "end": 1134.26, "text": "to the number L at X بساوي C and we write ونكتب الحالة هذه limit ل F of X لما X تقول إلى C بساوي L أو ممكن نكتب limit F as X tends to C بساوي L أو ممكن نكتب", "tokens": [1353, 264, 1230, 441, 412, 1783, 4724, 3794, 995, 45865, 383, 293, 321, 2464, 4032, 1863, 4117, 2655, 3555, 21542, 6027, 3660, 29538, 4948, 5296, 479, 295, 1783, 5296, 15042, 1783, 6055, 39648, 30731, 383, 4724, 3794, 995, 45865, 441, 34051, 3714, 43020, 8717, 4117, 2655, 3555, 4948, 479, 382, 1783, 12258, 281, 383, 4724, 3794, 995, 45865, 441, 34051, 3714, 43020, 8717, 4117, 2655, 3555], "avg_logprob": -0.18435168310777464, "compression_ratio": 1.469387755102041, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1105.18, "end": 1105.44, "word": "to", "probability": 0.1646728515625}, {"start": 1105.44, "end": 1105.6, "word": " the", "probability": 0.693359375}, {"start": 1105.6, "end": 1106.12, "word": " number", "probability": 0.97265625}, {"start": 1106.12, "end": 1106.6, "word": " L", "probability": 0.685546875}, {"start": 1106.6, "end": 1108.44, "word": " at", "probability": 0.763671875}, {"start": 1108.44, "end": 1110.16, "word": " X", "probability": 0.6845703125}, {"start": 1110.16, "end": 1111.02, "word": " بساوي", "probability": 0.69976806640625}, {"start": 1111.02, "end": 1111.52, "word": " C", "probability": 0.8916015625}, {"start": 1111.52, "end": 1112.78, "word": " and", "probability": 0.76318359375}, {"start": 1112.78, "end": 1113.16, "word": " we", "probability": 0.7021484375}, {"start": 1113.16, "end": 1113.72, "word": " write", "probability": 0.939453125}, {"start": 1113.72, "end": 1114.6, "word": " ونكتب", "probability": 0.82412109375}, {"start": 1114.6, "end": 1116.5, "word": " الحالة", "probability": 0.83837890625}, {"start": 1116.5, "end": 1116.84, "word": " هذه", "probability": 0.853515625}, {"start": 1116.84, "end": 1117.4, "word": " limit", "probability": 0.2183837890625}, {"start": 1117.4, "end": 1119.52, "word": " ل", "probability": 0.7109375}, {"start": 1119.52, "end": 1119.92, "word": " F", "probability": 0.5751953125}, {"start": 1119.92, "end": 1120.18, "word": " of", "probability": 0.8505859375}, {"start": 1120.18, "end": 1120.56, "word": " X", "probability": 0.9814453125}, {"start": 1120.56, "end": 1120.92, "word": " لما", "probability": 0.76416015625}, {"start": 1120.92, "end": 1121.24, "word": " X", "probability": 0.974609375}, {"start": 1121.24, "end": 1121.84, "word": " تقول", "probability": 0.90087890625}, {"start": 1121.84, "end": 1122.24, "word": " إلى", "probability": 0.63232421875}, {"start": 1122.24, "end": 1122.6, "word": " C", "probability": 0.9541015625}, {"start": 1122.6, "end": 1123.4, "word": " بساوي", "probability": 0.9530029296875}, {"start": 1123.4, "end": 1123.82, "word": " L", "probability": 0.98779296875}, {"start": 1123.82, "end": 1125.12, "word": " أو", "probability": 0.64794921875}, {"start": 1125.12, "end": 1126.08, "word": " ممكن", "probability": 0.979248046875}, {"start": 1126.08, "end": 1126.52, "word": " نكتب", "probability": 0.9954833984375}, {"start": 1126.52, "end": 1126.94, "word": " limit", "probability": 0.9423828125}, {"start": 1126.94, "end": 1128.56, "word": " F", "probability": 0.85888671875}, {"start": 1128.56, "end": 1129.14, "word": " as", "probability": 0.89111328125}, {"start": 1129.14, "end": 1129.56, "word": " X", "probability": 0.9892578125}, {"start": 1129.56, "end": 1129.92, "word": " tends", "probability": 0.82177734375}, {"start": 1129.92, "end": 1130.08, "word": " to", "probability": 0.97314453125}, {"start": 1130.08, "end": 1130.38, "word": " C", "probability": 0.9736328125}, {"start": 1130.38, "end": 1131.18, "word": " بساوي", "probability": 0.9593505859375}, {"start": 1131.18, "end": 1131.64, "word": " L", "probability": 0.99365234375}, {"start": 1131.64, "end": 1132.38, "word": " أو", "probability": 0.7548828125}, {"start": 1132.38, "end": 1133.62, "word": " ممكن", "probability": 0.9921875}, {"start": 1133.62, "end": 1134.26, "word": " نكتب", "probability": 0.998291015625}], "temperature": 1.0}, {"id": 43, "seek": 115735, "start": 1141.22, "end": 1157.36, "text": "أو ممكن نكتب f of x tends to L as x tends to c كل هدول معناهم أن العدد L limit لل function f and x سوى c", "tokens": [10721, 2407, 3714, 43020, 8717, 4117, 2655, 3555, 283, 295, 2031, 12258, 281, 441, 382, 2031, 12258, 281, 269, 28242, 8032, 3215, 12610, 20449, 8315, 16095, 14739, 18863, 3215, 3215, 441, 4948, 24976, 2445, 283, 293, 2031, 8608, 2407, 7578, 269], "avg_logprob": -0.25093006023338865, "compression_ratio": 1.1596638655462186, "no_speech_prob": 0.0, "words": [{"start": 1141.22, "end": 1141.62, "word": "أو", "probability": 0.7427978515625}, {"start": 1141.62, "end": 1142.02, "word": " ممكن", "probability": 0.810791015625}, {"start": 1142.02, "end": 1142.7, "word": " نكتب", "probability": 0.9903564453125}, {"start": 1142.7, "end": 1143.48, "word": " f", "probability": 0.2445068359375}, {"start": 1143.48, "end": 1143.76, "word": " of", "probability": 0.215576171875}, {"start": 1143.76, "end": 1144.22, "word": " x", "probability": 0.91162109375}, {"start": 1144.22, "end": 1145.86, "word": " tends", "probability": 0.65673828125}, {"start": 1145.86, "end": 1146.5, "word": " to", "probability": 0.98291015625}, {"start": 1146.5, "end": 1146.88, "word": " L", "probability": 0.73583984375}, {"start": 1146.88, "end": 1148.32, "word": " as", "probability": 0.92236328125}, {"start": 1148.32, "end": 1148.7, "word": " x", "probability": 0.890625}, {"start": 1148.7, "end": 1149.1, "word": " tends", "probability": 0.85205078125}, {"start": 1149.1, "end": 1149.3, "word": " to", "probability": 0.98486328125}, {"start": 1149.3, "end": 1149.7, "word": " c", "probability": 0.61572265625}, {"start": 1149.7, "end": 1151.26, "word": " كل", "probability": 0.7666015625}, {"start": 1151.26, "end": 1151.54, "word": " هدول", "probability": 0.8077799479166666}, {"start": 1151.54, "end": 1152.12, "word": " معناهم", "probability": 0.9612630208333334}, {"start": 1152.12, "end": 1152.38, "word": " أن", "probability": 0.45166015625}, {"start": 1152.38, "end": 1152.88, "word": " العدد", "probability": 0.9256184895833334}, {"start": 1152.88, "end": 1153.22, "word": " L", "probability": 0.7333984375}, {"start": 1153.22, "end": 1154.6, "word": " limit", "probability": 0.7119140625}, {"start": 1154.6, "end": 1154.84, "word": " لل", "probability": 0.765625}, {"start": 1154.84, "end": 1155.22, "word": " function", "probability": 0.43310546875}, {"start": 1155.22, "end": 1155.62, "word": " f", "probability": 0.81396484375}, {"start": 1155.62, "end": 1156.0, "word": " and", "probability": 0.85595703125}, {"start": 1156.0, "end": 1156.36, "word": " x", "probability": 0.93603515625}, {"start": 1156.36, "end": 1157.0, "word": " سوى", "probability": 0.5263671875}, {"start": 1157.0, "end": 1157.36, "word": " c", "probability": 0.7744140625}], "temperature": 1.0}, {"id": 44, "seek": 118558, "start": 1162.85, "end": 1185.59, "text": "ف limit f of x as x tends to c does not exist، يعني مافيش عدد L زي هذا، we say ان ال function f diverges، diverges at x less than c", "tokens": [5172, 4948, 283, 295, 2031, 382, 2031, 12258, 281, 269, 775, 406, 2514, 12399, 37495, 22653, 19446, 41185, 8592, 6225, 3215, 3215, 441, 30767, 1829, 23758, 12399, 321, 584, 16472, 2423, 2445, 283, 18558, 2880, 12399, 18558, 2880, 412, 2031, 1570, 813, 269], "avg_logprob": -0.31196733631870965, "compression_ratio": 1.1729323308270676, "no_speech_prob": 0.0, "words": [{"start": 1162.85, "end": 1163.33, "word": "ف", "probability": 0.35595703125}, {"start": 1163.33, "end": 1163.89, "word": " limit", "probability": 0.424072265625}, {"start": 1163.89, "end": 1165.59, "word": " f", "probability": 0.5439453125}, {"start": 1165.59, "end": 1165.87, "word": " of", "probability": 0.40869140625}, {"start": 1165.87, "end": 1166.27, "word": " x", "probability": 0.94580078125}, {"start": 1166.27, "end": 1166.81, "word": " as", "probability": 0.87744140625}, {"start": 1166.81, "end": 1167.27, "word": " x", "probability": 0.97314453125}, {"start": 1167.27, "end": 1167.61, "word": " tends", "probability": 0.79931640625}, {"start": 1167.61, "end": 1167.75, "word": " to", "probability": 0.98681640625}, {"start": 1167.75, "end": 1168.11, "word": " c", "probability": 0.80029296875}, {"start": 1168.11, "end": 1169.19, "word": " does", "probability": 0.49951171875}, {"start": 1169.19, "end": 1169.47, "word": " not", "probability": 0.9638671875}, {"start": 1169.47, "end": 1170.09, "word": " exist،", "probability": 0.56781005859375}, {"start": 1170.09, "end": 1170.31, "word": " يعني", "probability": 0.90234375}, {"start": 1170.31, "end": 1170.73, "word": " مافيش", "probability": 0.9339192708333334}, {"start": 1170.73, "end": 1171.11, "word": " عدد", "probability": 0.9793294270833334}, {"start": 1171.11, "end": 1171.45, "word": " L", "probability": 0.517578125}, {"start": 1171.45, "end": 1172.93, "word": " زي", "probability": 0.94580078125}, {"start": 1172.93, "end": 1174.07, "word": " هذا،", "probability": 0.717529296875}, {"start": 1174.07, "end": 1175.55, "word": " we", "probability": 0.67236328125}, {"start": 1175.55, "end": 1176.09, "word": " say", "probability": 0.9619140625}, {"start": 1176.09, "end": 1176.35, "word": " ان", "probability": 0.433349609375}, {"start": 1176.35, "end": 1176.55, "word": " ال", "probability": 0.94677734375}, {"start": 1176.55, "end": 1176.95, "word": " function", "probability": 0.81884765625}, {"start": 1176.95, "end": 1177.43, "word": " f", "probability": 0.78369140625}, {"start": 1177.43, "end": 1180.11, "word": " diverges،", "probability": 0.6888020833333334}, {"start": 1180.11, "end": 1182.99, "word": " diverges", "probability": 0.754150390625}, {"start": 1182.99, "end": 1183.51, "word": " at", "probability": 0.97900390625}, {"start": 1183.51, "end": 1184.13, "word": " x", "probability": 0.9794921875}, {"start": 1184.13, "end": 1184.57, "word": " less", "probability": 0.1143798828125}, {"start": 1184.57, "end": 1185.13, "word": " than", "probability": 0.955078125}, {"start": 1185.13, "end": 1185.59, "word": " c", "probability": 0.8427734375}], "temperature": 1.0}, {"id": 45, "seek": 121932, "start": 1190.12, "end": 1219.32, "text": "الان نستطيع ان نثبت ان ال limit لل function هذه النقطة لو كانت موجودة لو كان ال function لها limit فlimit هذه لازم تكون unique ال function if from A to R can have only", "tokens": [6027, 7649, 8717, 14851, 9566, 40228, 16472, 8717, 12984, 3555, 2655, 16472, 2423, 4948, 24976, 2445, 29538, 28239, 47432, 3660, 45164, 25961, 2655, 3714, 29245, 23328, 3660, 45164, 25961, 2423, 2445, 5296, 11296, 4948, 6156, 4197, 270, 29538, 5296, 31377, 2304, 6055, 30544, 3845, 2423, 2445, 498, 490, 316, 281, 497, 393, 362, 787], "avg_logprob": -0.3420454664663835, "compression_ratio": 1.4904458598726114, "no_speech_prob": 0.0, "words": [{"start": 1190.12, "end": 1190.74, "word": "الان", "probability": 0.7587890625}, {"start": 1190.74, "end": 1191.6, "word": " نستطيع", "probability": 0.808349609375}, {"start": 1191.6, "end": 1192.14, "word": " ان", "probability": 0.297119140625}, {"start": 1192.14, "end": 1192.66, "word": " نثبت", "probability": 0.9427490234375}, {"start": 1192.66, "end": 1192.9, "word": " ان", "probability": 0.8447265625}, {"start": 1192.9, "end": 1193.1, "word": " ال", "probability": 0.424560546875}, {"start": 1193.1, "end": 1193.5, "word": " limit", "probability": 0.705078125}, {"start": 1193.5, "end": 1194.62, "word": " لل", "probability": 0.3779296875}, {"start": 1194.62, "end": 1195.06, "word": " function", "probability": 0.72607421875}, {"start": 1195.06, "end": 1195.32, "word": " هذه", "probability": 0.083740234375}, {"start": 1195.32, "end": 1195.92, "word": " النقطة", "probability": 0.9601236979166666}, {"start": 1195.92, "end": 1197.2, "word": " لو", "probability": 0.7626953125}, {"start": 1197.2, "end": 1197.58, "word": " كانت", "probability": 0.960205078125}, {"start": 1197.58, "end": 1198.22, "word": " موجودة", "probability": 0.95703125}, {"start": 1198.22, "end": 1198.44, "word": " لو", "probability": 0.387451171875}, {"start": 1198.44, "end": 1198.7, "word": " كان", "probability": 0.9599609375}, {"start": 1198.7, "end": 1198.82, "word": " ال", "probability": 0.5068359375}, {"start": 1198.82, "end": 1199.1, "word": " function", "probability": 0.89306640625}, {"start": 1199.1, "end": 1199.46, "word": " لها", "probability": 0.8564453125}, {"start": 1199.46, "end": 1200.04, "word": " limit", "probability": 0.95361328125}, {"start": 1200.04, "end": 1200.62, "word": " فlimit", "probability": 0.7334798177083334}, {"start": 1200.62, "end": 1200.8, "word": " هذه", "probability": 0.1702880859375}, {"start": 1200.8, "end": 1201.14, "word": " لازم", "probability": 0.892578125}, {"start": 1201.14, "end": 1201.46, "word": " تكون", "probability": 0.87060546875}, {"start": 1201.46, "end": 1201.88, "word": " unique", "probability": 0.26904296875}, {"start": 1201.88, "end": 1207.12, "word": " ال", "probability": 0.5029296875}, {"start": 1207.12, "end": 1207.52, "word": " function", "probability": 0.90283203125}, {"start": 1207.52, "end": 1208.04, "word": " if", "probability": 0.5615234375}, {"start": 1208.04, "end": 1209.44, "word": " from", "probability": 0.85546875}, {"start": 1209.44, "end": 1209.96, "word": " A", "probability": 0.46630859375}, {"start": 1209.96, "end": 1210.18, "word": " to", "probability": 0.9619140625}, {"start": 1210.18, "end": 1210.72, "word": " R", "probability": 0.98974609375}, {"start": 1210.72, "end": 1213.2, "word": " can", "probability": 0.85595703125}, {"start": 1213.2, "end": 1214.22, "word": " have", "probability": 0.95361328125}, {"start": 1214.22, "end": 1219.32, "word": " only", "probability": 0.8828125}], "temperature": 1.0}, {"id": 46, "seek": 125070, "start": 1239.94, "end": 1250.7, "text": "والبرهان شبه البرهان الـ uniqueness of the limit of a sequence we use epsilon over two argument", "tokens": [2407, 6027, 26890, 3224, 7649, 13412, 3555, 3224, 2423, 26890, 3224, 7649, 2423, 39184, 48294, 295, 264, 4948, 295, 257, 8310, 321, 764, 17889, 670, 732, 6770], "avg_logprob": -0.39481025614908766, "compression_ratio": 1.2210526315789474, "no_speech_prob": 0.0, "words": [{"start": 1239.94, "end": 1241.02, "word": "والبرهان", "probability": 0.706884765625}, {"start": 1241.02, "end": 1241.56, "word": " شبه", "probability": 0.7420247395833334}, {"start": 1241.56, "end": 1242.42, "word": " البرهان", "probability": 0.8414306640625}, {"start": 1242.42, "end": 1243.2, "word": " الـ", "probability": 0.3974609375}, {"start": 1243.2, "end": 1243.56, "word": " uniqueness", "probability": 0.95166015625}, {"start": 1243.56, "end": 1244.16, "word": " of", "probability": 0.8994140625}, {"start": 1244.16, "end": 1244.36, "word": " the", "probability": 0.46435546875}, {"start": 1244.36, "end": 1244.76, "word": " limit", "probability": 0.8427734375}, {"start": 1244.76, "end": 1245.3, "word": " of", "probability": 0.9296875}, {"start": 1245.3, "end": 1245.84, "word": " a", "probability": 0.8935546875}, {"start": 1245.84, "end": 1246.38, "word": " sequence", "probability": 0.9638671875}, {"start": 1246.38, "end": 1248.56, "word": " we", "probability": 0.264404296875}, {"start": 1248.56, "end": 1248.98, "word": " use", "probability": 0.8896484375}, {"start": 1248.98, "end": 1249.46, "word": " epsilon", "probability": 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{"start": 1400.17, "end": 1400.47, "word": " tends", "probability": 0.470458984375}, {"start": 1400.47, "end": 1400.61, "word": " to", "probability": 0.96875}, {"start": 1400.61, "end": 1400.85, "word": " c", "probability": 0.814453125}, {"start": 1400.85, "end": 1401.43, "word": " بساوي", "probability": 0.71270751953125}, {"start": 1401.43, "end": 1401.89, "word": " عدد", "probability": 0.9287109375}, {"start": 1401.89, "end": 1402.25, "word": " تاني", "probability": 0.9651692708333334}, {"start": 1402.25, "end": 1402.45, "word": " ال", "probability": 0.44677734375}, {"start": 1402.45, "end": 1402.99, "word": " اتنين", "probability": 0.81463623046875}, {"start": 1402.99, "end": 1407.99, "word": " then", "probability": 0.374267578125}, {"start": 1407.99, "end": 1408.65, "word": " for", "probability": 0.96142578125}, {"start": 1408.65, "end": 1409.37, "word": " the", "probability": 0.90380859375}, {"start": 1409.37, "end": 1409.89, "word": " same", "probability": 0.92138671875}, 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تعتمد على Epsilon على 2 وبالتالي على Epsilon عدد موجد بحيث أنه لو كان X ينتمي إلى A و Absolute X minus C أصغر من Delta 2 أكبر من 0", "tokens": [1211, 1863, 36178, 2423, 39184, 462, 16592, 4724, 15042, 14739, 4948, 5296, 479, 295, 1783, 293, 1783, 4724, 3794, 995, 2407, 10632, 383, 4724, 3794, 995, 2407, 10632, 441, 17, 8717, 7435, 3215, 18183, 568, 6055, 34268, 2304, 3215, 15844, 462, 16592, 15844, 568, 46599, 6027, 2655, 6027, 1829, 15844, 462, 16592, 6225, 3215, 3215, 3714, 29245, 3215, 4724, 5016, 1829, 12984, 14739, 3224, 45164, 25961, 1783, 7251, 29399, 2304, 1829, 30731, 316, 4032, 43965, 1169, 1783, 3175, 383, 5551, 9381, 17082, 2288, 9154, 18183, 568, 5551, 4117, 26890, 9154, 1958], "avg_logprob": -0.3077445726679719, "compression_ratio": 1.4653465346534653, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1418.54, "end": 1419.1, "word": "لنفس", "probability": 0.7055257161458334}, {"start": 1419.1, "end": 1419.34, "word": " الـ", "probability": 0.8193359375}, 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absolute value ل L1 minus L2 فحسب النمة هذه هيطلع عندى هذا بقدر اللي قدر انه absolute L1 minus L2 بالساوية سفر وبالتالي بطلع عندى L1 بساوية L2 وهو المطلوب", "tokens": [10721, 9778, 3215, 1975, 1829, 3224, 34105, 2423, 39184, 8236, 2158, 5296, 441, 16, 3175, 441, 17, 6156, 5016, 35457, 28239, 2304, 3660, 29538, 8032, 1829, 9566, 1211, 3615, 43242, 7578, 23758, 4724, 28543, 2288, 13672, 1829, 12174, 3215, 2288, 16472, 3224, 8236, 441, 16, 3175, 441, 17, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 4724, 9566, 1211, 3615, 43242, 7578, 441, 16, 4724, 3794, 995, 2407, 10632, 441, 17, 37037, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.37255270150770625, "compression_ratio": 1.5808383233532934, "no_speech_prob": 0.0, "words": [{"start": 1676.36, "end": 1676.94, "word": "أخد", "probability": 0.443115234375}, {"start": 1676.94, "end": 1677.2, "word": " ايه", "probability": 0.56787109375}, {"start": 1677.2, "end": 1677.5, "word": " هنا", "probability": 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1742.29, "end": 1769.27, "text": "ناخد ملاحظة هنا الـ epsilon delta definition of limit of a function f from a to r", "tokens": [1863, 47283, 3215, 3714, 15040, 5016, 19913, 3660, 34105, 2423, 39184, 17889, 8289, 7123, 295, 4948, 295, 257, 2445, 283, 490, 257, 281, 367], "avg_logprob": -0.29593749046325685, "compression_ratio": 1.065934065934066, "no_speech_prob": 0.0, "words": [{"start": 1742.29, "end": 1742.83, "word": "ناخد", "probability": 0.77294921875}, {"start": 1742.83, "end": 1743.45, "word": " ملاحظة", "probability": 0.97578125}, {"start": 1743.45, "end": 1744.73, "word": " هنا", "probability": 0.86474609375}, {"start": 1744.73, "end": 1755.59, "word": " الـ", "probability": 0.558349609375}, {"start": 1755.59, "end": 1755.83, "word": " epsilon", "probability": 0.5283203125}, {"start": 1755.83, "end": 1756.39, "word": " delta", "probability": 0.2235107421875}, {"start": 1756.39, "end": 1758.43, "word": " definition", "probability": 0.8125}, {"start": 1758.43, "end": 1761.13, 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سفر", "tokens": [3322, 16970, 9673, 2655, 3555, 995, 9957, 3660, 13672, 1829, 39896, 8236, 2031, 3175, 269, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 11778, 12610, 2655, 7649, 1355, 11331, 26108, 2655, 9957, 25724, 11622, 38207, 23758, 20449, 8315, 3224, 14739, 8236, 2031, 3175, 269, 20193, 7251, 3794, 995, 2407, 7578, 8608, 5172, 2288], "avg_logprob": -0.31519396397574195, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 1772.6699999999998, "end": 1774.07, "word": "the", "probability": 0.1690673828125}, {"start": 1774.07, "end": 1775.47, "word": " inequality", "probability": 0.9287109375}, {"start": 1775.47, "end": 1780.25, "word": " المتباينة", "probability": 0.7985432942708334}, {"start": 1780.25, "end": 1781.39, "word": " اللي", "probability": 0.472381591796875}, {"start": 1781.39, "end": 1781.95, "word": " هي", "probability": 0.95068359375}, {"start": 1781.95, "end": 1782.97, "word": " absolute", "probability": 0.81591796875}, 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لل", "probability": 0.5322265625}, {"start": 2266.25, "end": 2266.59, "word": " F", "probability": 0.47802734375}, {"start": 2266.59, "end": 2266.95, "word": " and", "probability": 0.50390625}, {"start": 2266.95, "end": 2267.55, "word": " X", "probability": 0.95556640625}, {"start": 2267.55, "end": 2268.07, "word": " بالساوية", "probability": 0.7779296875}, {"start": 2268.07, "end": 2268.33, "word": " C", "probability": 0.66455078125}, {"start": 2268.33, "end": 2269.03, "word": " بالساوية", "probability": 0.9794921875}, {"start": 2269.03, "end": 2269.31, "word": " L", "probability": 0.79736328125}, {"start": 2269.31, "end": 2270.77, "word": " معناه", "probability": 0.88525390625}, {"start": 2270.77, "end": 2271.23, "word": " لأي", "probability": 0.8616536458333334}, {"start": 2271.23, "end": 2271.91, "word": " أبسلون", "probability": 0.772216796875}, {"start": 2271.91, "end": 2272.35, "word": " أكبر", "probability": 0.9567057291666666}, {"start": 2272.35, "end": 2272.53, "word": " من", 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نبرهود", "probability": 0.971923828125}, {"start": 2325.1, "end": 2325.56, "word": " لإل", "probability": 0.9207356770833334}, {"start": 2325.56, "end": 2326.94, "word": " بقدر", "probability": 0.96337890625}, {"start": 2326.94, "end": 2332.92, "word": " أجيل", "probability": 0.8728841145833334}, {"start": 2332.92, "end": 2335.76, "word": " أرد", "probability": 0.9095052083333334}, {"start": 2335.76, "end": 2336.2, "word": " عليه", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 85, "seek": 236411, "start": 2341.81, "end": 2364.11, "text": "الدلتا دلتا neighborhood هذا عبارة عن delta neighborhood ل C إذا انا أخدت اعطتوني إبسلون بقدر أكون إبسلون neighborhood ل L فبقدر أرد عليه ال delta neighborhood ل C في الفترة المفتوحة هذه", "tokens": [6027, 3215, 1211, 2655, 995, 11778, 1211, 2655, 995, 7630, 23758, 6225, 3555, 9640, 3660, 18871, 8289, 7630, 5296, 383, 11933, 15730, 1975, 8315, 5551, 9778, 3215, 2655, 1975, 3615, 9566, 2655, 11536, 1829, 11933, 3555, 3794, 1211, 11536, 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"probability": 0.967529296875}, {"start": 2774.32, "end": 2774.64, "word": " Y", "probability": 0.580078125}, {"start": 2774.64, "end": 2775.82, "word": " إذا", "probability": 0.4354248046875}, {"start": 2775.82, "end": 2775.98, "word": " ال", "probability": 0.84912109375}, {"start": 2775.98, "end": 2776.32, "word": " absolute", "probability": 0.77197265625}, {"start": 2776.32, "end": 2776.68, "word": " X", "probability": 0.93994140625}, {"start": 2776.68, "end": 2777.46, "word": " minus", "probability": 0.96826171875}, {"start": 2777.46, "end": 2777.82, "word": " C", "probability": 0.9853515625}, {"start": 2777.82, "end": 2778.06, "word": " من", "probability": 0.98779296875}, {"start": 2778.06, "end": 2778.34, "word": " هنا", "probability": 0.9970703125}, {"start": 2778.34, "end": 2779.08, "word": " أصغر", "probability": 0.9949951171875}, {"start": 2779.08, "end": 2779.42, "word": " من", "probability": 0.99560546875}, {"start": 2779.42, "end": 2780.6, "word": " Delta", "probability": 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"word": " أن", "probability": 0.595703125}, {"start": 2797.81, "end": 2798.17, "word": " absolute", "probability": 0.7734375}, {"start": 2798.17, "end": 2798.57, "word": " f", "probability": 0.7587890625}, {"start": 2798.57, "end": 2798.75, "word": " of", "probability": 0.77001953125}, {"start": 2798.75, "end": 2798.99, "word": " x", "probability": 0.990234375}, {"start": 2798.99, "end": 2799.45, "word": " minus", "probability": 0.97119140625}, {"start": 2799.45, "end": 2799.77, "word": " l", "probability": 0.59814453125}, {"start": 2799.77, "end": 2800.33, "word": " أصغر", "probability": 0.99169921875}, {"start": 2800.33, "end": 2800.49, "word": " من", "probability": 0.994140625}, {"start": 2800.49, "end": 2801.73, "word": " إبسلون", "probability": 0.97587890625}, {"start": 2801.73, "end": 2802.33, "word": " since", "probability": 0.533203125}, {"start": 2802.33, "end": 2804.83, "word": " إبسلون", "probability": 0.894677734375}, {"start": 2804.83, "end": 2805.25, "word": " أكبر", 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"end": 2833.07, "word": " وهو", "probability": 0.5979817708333334}, {"start": 2833.07, "end": 2833.99, "word": " المطلوب", "probability": 0.830078125}, {"start": 2833.99, "end": 2836.31, "word": " تمام", "probability": 0.6444091796875}, {"start": 2836.31, "end": 2837.99, "word": " okay", "probability": 0.215576171875}, {"start": 2837.99, "end": 2838.31, "word": " إذا", "probability": 0.698974609375}, {"start": 2838.31, "end": 2839.75, "word": " المرة", "probability": 0.85009765625}, {"start": 2839.75, "end": 2840.29, "word": " الجاية", "probability": 0.9189453125}], "temperature": 1.0}, {"id": 104, "seek": 286108, "start": 2842.16, "end": 2861.08, "text": "هنثبت ان limited ده لتربعية لما x او ل c بساوي c تربية وهذا موجود طبعا في الكتاب وفي كمان أمثلة أخرى فارجو أنكم تقرؤوا الأمثلة هذه من الكتاب و تحضروها للمحاضرة الجاية", "tokens": [3224, 1863, 12984, 3555, 2655, 16472, 5567, 11778, 3224, 5296, 2655, 25513, 3615, 10632, 5296, 15042, 2031, 1975, 2407, 5296, 269, 4724, 3794, 995, 45865, 269, 6055, 25513, 10632, 37037, 15730, 3714, 29245, 23328, 23032, 3555, 3615, 995, 8978, 33251, 2655, 16758, 4032, 41185, 9122, 2304, 7649, 5551, 2304, 12984, 37977, 5551, 34740, 7578, 6156, 9640, 7435, 2407, 14739, 24793, 6055, 4587, 2288, 33604, 14407, 16247, 2304, 12984, 37977, 29538, 9154, 33251, 2655, 16758, 4032, 6055, 5016, 11242, 32887, 11296, 5296, 19528, 5016, 46958, 25720, 25724, 995, 10632], "avg_logprob": -0.2034761302926567, "compression_ratio": 1.6477272727272727, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2842.16, "end": 2843.08, "word": "هنثبت", "probability": 0.89453125}, {"start": 2843.08, "end": 2844.0, "word": " ان", "probability": 0.61376953125}, {"start": 2844.0, "end": 2844.48, "word": " limited", "probability": 0.34033203125}, {"start": 2844.48, "end": 2844.82, "word": " ده", "probability": 0.81103515625}, {"start": 2844.82, "end": 2845.8, "word": " لتربعية", "probability": 0.69130859375}, {"start": 2845.8, "end": 2846.14, "word": " لما", "probability": 0.847412109375}, {"start": 2846.14, "end": 2846.42, "word": " x", "probability": 0.54248046875}, {"start": 2846.42, "end": 2846.84, "word": " او", "probability": 0.41046142578125}, {"start": 2846.84, "end": 2846.98, "word": " ل", "probability": 0.60302734375}, {"start": 2846.98, "end": 2847.48, "word": " c", "probability": 0.76025390625}, {"start": 2847.48, "end": 2849.18, "word": " بساوي", "probability": 0.864501953125}, {"start": 2849.18, "end": 2849.48, "word": " c", "probability": 0.8388671875}, {"start": 2849.48, "end": 2850.12, "word": " تربية", "probability": 0.7880859375}, {"start": 2850.12, "end": 2850.5, "word": " وهذا", "probability": 0.554443359375}, {"start": 2850.5, "end": 2850.88, "word": " موجود", "probability": 0.98193359375}, {"start": 2850.88, "end": 2851.22, "word": " طبعا", "probability": 0.9482421875}, {"start": 2851.22, "end": 2851.36, "word": " في", "probability": 0.72412109375}, {"start": 2851.36, "end": 2852.08, "word": " الكتاب", "probability": 0.9886067708333334}, {"start": 2852.08, "end": 2852.82, "word": " وفي", "probability": 0.75927734375}, {"start": 2852.82, "end": 2853.28, "word": " كمان", "probability": 0.9130859375}, {"start": 2853.28, "end": 2853.74, "word": " أمثلة", "probability": 0.9217529296875}, {"start": 2853.74, "end": 2854.78, "word": " أخرى", "probability": 0.962890625}, {"start": 2854.78, "end": 2855.56, "word": " فارجو", "probability": 0.835205078125}, {"start": 2855.56, "end": 2855.82, "word": " أنكم", "probability": 0.66455078125}, {"start": 2855.82, "end": 2856.28, "word": " تقرؤوا", "probability": 0.85830078125}, {"start": 2856.28, "end": 2856.76, "word": " الأمثلة", "probability": 0.9884033203125}, {"start": 2856.76, "end": 2857.14, "word": " هذه", "probability": 0.8427734375}, {"start": 2857.14, "end": 2857.34, "word": " من", "probability": 0.9853515625}, {"start": 2857.34, "end": 2857.78, "word": " الكتاب", "probability": 0.9908854166666666}, {"start": 2857.78, "end": 2857.9, "word": " و", "probability": 0.6953125}, {"start": 2857.9, "end": 2858.62, "word": " تحضروها", "probability": 0.823828125}, {"start": 2858.62, "end": 2860.26, "word": " للمحاضرة", "probability": 0.95390625}, {"start": 2860.26, "end": 2861.08, "word": " الجاية", "probability": 0.78173828125}], "temperature": 1.0}, {"id": 105, "seek": 288241, "start": 2861.75, "end": 2882.41, "text": "وتشوفوا كيف تم استخدام تعريف epsilon delta في اثبات ان ال limit لدالة زهر الدالة التربعية بساوي C تربية عند اي نقطة C okay تمام؟ في اي سؤال او افسار؟ اذا نكتفي بهذا القدر وان شاء الله اللي انا تكمله في المحاضرة القادمة", "tokens": [35473, 8592, 38688, 14407, 9122, 33911, 46811, 44713, 9778, 3215, 10943, 37279, 16572, 5172, 17889, 8289, 8978, 1975, 12984, 3555, 9307, 16472, 2423, 4948, 5296, 3215, 6027, 3660, 30767, 3224, 2288, 32748, 6027, 3660, 16712, 25513, 3615, 10632, 4724, 3794, 995, 45865, 383, 6055, 25513, 10632, 43242, 1975, 1829, 8717, 47432, 3660, 383, 1392, 46811, 10943, 22807, 8978, 1975, 1829, 8608, 33604, 6027, 1975, 2407, 1975, 36178, 9640, 22807, 1975, 15730, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 4032, 7649, 13412, 16606, 21984, 13672, 1829, 1975, 8315, 6055, 24793, 43761, 8978, 9673, 5016, 46958, 25720, 25062, 18513, 46007], "avg_logprob": -0.2057549534457745, "compression_ratio": 1.6271929824561404, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2861.75, "end": 2862.43, "word": "وتشوفوا", "probability": 0.856689453125}, {"start": 2862.43, "end": 2862.77, "word": " كيف", "probability": 0.971923828125}, {"start": 2862.77, "end": 2863.73, "word": " تم", "probability": 0.978515625}, {"start": 2863.73, "end": 2864.35, "word": " استخدام", "probability": 0.9757080078125}, {"start": 2864.35, "end": 2864.79, "word": " تعريف", "probability": 0.986328125}, {"start": 2864.79, "end": 2865.25, "word": " epsilon", "probability": 0.59765625}, {"start": 2865.25, "end": 2866.17, "word": " delta", "probability": 0.30859375}, {"start": 2866.17, "end": 2866.83, "word": " في", "probability": 0.86474609375}, {"start": 2866.83, "end": 2867.45, "word": " اثبات", "probability": 0.846923828125}, {"start": 2867.45, "end": 2867.65, "word": " ان", "probability": 0.66259765625}, {"start": 2867.65, "end": 2867.79, "word": " ال", "probability": 0.8046875}, {"start": 2867.79, "end": 2868.11, "word": " limit", "probability": 0.8427734375}, {"start": 2868.11, "end": 2869.07, "word": " لدالة", "probability": 0.8809814453125}, {"start": 2869.07, "end": 2869.41, "word": " زهر", "probability": 0.6512044270833334}, {"start": 2869.41, "end": 2869.85, "word": " الدالة", "probability": 0.9384765625}, {"start": 2869.85, "end": 2870.43, "word": " التربعية", "probability": 0.8756103515625}, {"start": 2870.43, "end": 2870.91, "word": " بساوي", "probability": 0.840087890625}, {"start": 2870.91, "end": 2871.15, "word": " C", "probability": 0.36376953125}, {"start": 2871.15, "end": 2871.59, "word": " تربية", "probability": 0.7911783854166666}, {"start": 2871.59, "end": 2871.83, "word": " عند", "probability": 0.93798828125}, {"start": 2871.83, "end": 2871.97, "word": " اي", "probability": 0.72509765625}, {"start": 2871.97, "end": 2872.29, "word": " نقطة", "probability": 0.9830729166666666}, {"start": 2872.29, "end": 2872.59, "word": " C", "probability": 0.70361328125}, {"start": 2872.59, "end": 2873.53, "word": " okay", "probability": 0.140380859375}, {"start": 2873.53, "end": 2874.29, "word": " تمام؟", "probability": 0.81005859375}, {"start": 2874.29, "end": 2874.81, "word": " في", "probability": 0.74853515625}, {"start": 2874.81, "end": 2874.95, "word": " اي", "probability": 0.7890625}, {"start": 2874.95, "end": 2875.29, "word": " سؤال", "probability": 0.943359375}, {"start": 2875.29, "end": 2875.45, "word": " او", "probability": 0.7705078125}, {"start": 2875.45, "end": 2876.65, "word": " افسار؟", "probability": 0.666351318359375}, {"start": 2876.65, "end": 2876.95, "word": " اذا", "probability": 0.83544921875}, {"start": 2876.95, "end": 2877.45, "word": " نكتفي", "probability": 0.9620361328125}, {"start": 2877.45, "end": 2877.77, "word": " بهذا", "probability": 0.945556640625}, {"start": 2877.77, "end": 2878.27, "word": " القدر", "probability": 0.98193359375}, {"start": 2878.27, "end": 2878.69, "word": " وان", "probability": 0.8525390625}, {"start": 2878.69, "end": 2878.97, "word": " شاء", "probability": 0.971923828125}, {"start": 2878.97, "end": 2879.11, "word": " الله", "probability": 0.93505859375}, {"start": 2879.11, "end": 2879.39, "word": " اللي", "probability": 0.946533203125}, {"start": 2879.39, "end": 2879.55, "word": " انا", "probability": 0.863037109375}, {"start": 2879.55, "end": 2880.27, "word": " تكمله", "probability": 0.6455891927083334}, {"start": 2880.27, "end": 2881.03, "word": " في", "probability": 0.73193359375}, {"start": 2881.03, "end": 2881.69, "word": " المحاضرة", "probability": 0.9732666015625}, {"start": 2881.69, "end": 2882.41, "word": " القادمة", "probability": 0.9900716145833334}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2883.036, "duration_after_vad": 2608.8912499999883}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..851e71e14d72b41a284d188c7626c675d81362d8
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs.srt
@@ -0,0 +1,1443 @@
+1
+00:00:21,410 --> 00:00:29,070
+السلام عليكم، اليوم في اللقاء الأول هناخد مناقشة و
+
+2
+00:00:29,070 --> 00:00:36,710
+أعتقد أن احنا في المناقشة السابقة وصلنا لـ section 
+
+3
+00:00:36,710 --> 00:00:46,810
+ثلاثة خمسة، أصبع؟ فممكن
+
+4
+00:00:46,810 --> 00:01:07,930
+اليوم هنناقش section ثلاثة ستة أو ثلاثة سبعة في
+
+5
+00:01:07,930 --> 00:01:14,710
+أي أسئلة عندكم في section ثلاثة خمسة أو section
+
+6
+00:01:14,710 --> 00:01:25,230
+ثلاثة ستة، السؤال ستة، أي سؤال؟ سؤال ثلاثة ستة
+
+7
+00:01:25,230 --> 00:01:35,470
+سؤال 
+
+8
+00:01:35,470 --> 00:01:37,650
+ستة، section ثلاثة ستة
+
+9
+00:01:46,160 --> 00:01:58,020
+Let x<sub>n</sub>, let the sequence x<sub>n</sub> be properly divergent
+
+10
+00:01:58,020 --> 00:02:05,920
+there, and let
+
+11
+00:02:05,920 --> 00:02:24,780
+and let y<sub>n</sub> be such that limit x<sub>n</sub> ضرب y<sub>n</sub> limit
+
+12
+00:02:24,780 --> 00:02:31,980
+حاصل الضرب لما n تؤول لـ infinity يساوي
+
+13
+00:02:31,980 --> 00:02:40,620
+L ينتمي إلى R، يعني exists in R، شو 
+
+14
+00:02:40,620 --> 00:02:54,410
+مطلوب ثم اثبت، أظهر أن سيكوينس y<sub>n</sub> يتعامل
+
+15
+00:02:54,410 --> 00:03:10,230
+بالصفر، حل
+
+16
+00:03:10,230 --> 00:03:17,950
+السؤال هذا بيعتمد على سؤال سابق، اللي هو سؤال ثلاثة
+
+17
+00:03:17,950 --> 00:03:27,190
+فالسؤال
+
+18
+00:03:27,190 --> 00:03:32,430
+هذا بيقول أن f
+
+19
+00:03:32,430 --> 00:03:50,310
+x<sub>n</sub> أكبر من صفر لكل n عدد طبيعي، then
+
+20
+00:03:50,310 --> 00:04:03,990
+limit x<sub>n</sub> بساوي zero if and only if limit واحد على
+
+21
+00:04:03,990 --> 00:04:10,350
+x<sub>n</sub> as n tends to infinity بساوي plus infinity
+
+22
+00:04:20,790 --> 00:04:27,670
+Okay، لأن في سؤال طلعتها إذا كانت x<sub>n</sub> حدود sequence 
+
+23
+00:04:27,670 --> 00:04:36,290
+حدودها موجبة، و ف limit ال sequence x<sub>n</sub> بساوي صفر
+
+24
+00:04:36,290 --> 00:04:41,350
+if and only if limit مقلوب ال sequence x<sub>n</sub> بساوي 
+
+25
+00:04:41,350 --> 00:04:42,190
+plus infinity
+
+26
+00:04:46,230 --> 00:04:52,690
+وطبعًا في كمان ممكن نثبت أن لو كانت الـ x<sub>n</sub> حدودها 
+
+27
+00:04:52,690 --> 00:05:00,950
+سالبة، ف limit x<sub>n</sub> بساوي صفر if and only if limit واحد 
+
+28
+00:05:00,950 --> 00:05:03,970
+على x<sub>n</sub> بساوي negative infinity
+
+29
+00:05:15,220 --> 00:05:24,480
+بما أن x<sub>n</sub> هو بشكل صحيح ديفرجينت
+
+30
+00:05:24,480 --> 00:05:39,580
+ثم قيمة x<sub>n</sub> بساوي إنفينتي أو قيمة x<sub>n</sub> بساوي نيجاتيف 
+
+31
+00:05:39,580 --> 00:05:40,180
+إنفينتي
+
+32
+00:05:45,460 --> 00:05:52,220
+case one، ناخد الحالة الأولى اللي فيها limit x<sub>m</sub>
+
+33
+00:05:52,220 --> 00:05:59,860
+بساوي infinity by 
+
+34
+00:05:59,860 --> 00:06:03,560
+exercise 
+
+35
+00:06:03,560 --> 00:06:15,020
+رقم ثلاثة، section ثلاثة ستة، والـ exercise اللي فوق 
+
+36
+00:06:15,020 --> 00:06:18,100
+هذا
+
+37
+00:06:18,100 --> 00:06:27,160
+معناه أنه we have هيطلع أنه limit المطلوب ال
+
+38
+00:06:27,160 --> 00:06:38,000
+sequence x<sub>n</sub> as n tends to infinity بيطلع صفر، يعني
+
+39
+00:06:38,000 --> 00:06:44,710
+اعتبري هذه هي x<sub>n</sub>، تعتبر الـ 1 على x<sub>n</sub> هي x<sub>n</sub>، فإذا كان
+
+40
+00:06:44,710 --> 00:06:49,510
+limit x<sub>n</sub> بساوي infinity، فlimit مقلوب الـ x<sub>n</sub> اللي
+
+41
+00:06:49,510 --> 00:06:57,530
+هنا، مقلوب اللي هو إيه؟ بتطلع صفر ولا عكس؟ يعني هنا
+
+42
+00:06:57,530 --> 00:07:03,850
+نفس الـ exercise بس بدل x<sub>n</sub> بـ 1 على x<sub>n</sub>، فهذه 
+
+43
+00:07:03,850 --> 00:07:08,690
+نتيجة صحيحة تمام، hence
+
+44
+00:07:13,030 --> 00:07:16,810
+الـ limit لـ
+
+45
+00:07:16,810 --> 00:07:29,290
+y<sub>n</sub> as n tends to infinity بساوي الـ limit الـ
+
+46
+00:07:29,290 --> 00:07:38,110
+y<sub>n</sub>، ممكن كتبتها على صورة على 
+
+47
+00:07:38,110 --> 00:07:39,310
+صورة
+
+48
+00:07:46,210 --> 00:07:55,770
+x<sub>n</sub> في y<sub>n</sub> ضرب 1 
+
+49
+00:07:55,770 --> 00:08:01,290
+على x<sub>n</sub> صح؟
+
+50
+00:08:01,290 --> 00:08:09,850
+نظبط هيك، الـ y<sub>n</sub> هي عبارة عن x<sub>n</sub> في y<sub>n</sub> في 1 على x<sub>n</sub>
+
+51
+00:08:12,880 --> 00:08:18,360
+الآن الـ limit هذه لحد الأول exist، و limit لـ 1 
+
+52
+00:08:18,360 --> 00:08:22,660
+على x<sub>n</sub> برضه exist، إذا الـ limit حاصل الضرب بساوي حاصل 
+
+53
+00:08:22,660 --> 00:08:27,540
+ضرب الـ limits، بقدر استخدم القانون هذا، هطبق أنه
+
+54
+00:08:27,540 --> 00:08:32,360
+limit حاصل ضرب two sequences بساوي limit الأولى
+
+55
+00:08:32,360 --> 00:08:41,100
+اللي هي حاصل ضرب x<sub>n</sub> y<sub>n</sub>، ضرب limit الـ sequence
+
+56
+00:08:41,100 --> 00:08:48,180
+التانية هي 1 على x<sub>n</sub> as n tends to infinity، و
+
+57
+00:08:48,180 --> 00:08:53,940
+الـ limit الأولى مش ساميناها عدد L لما exist ضرب الـ
+
+58
+00:08:53,940 --> 00:09:01,600
+limit التانية صفر، فبيطلع عندي صفر وهو المطلوب، فهنا
+
+59
+00:09:01,600 --> 00:09:05,920
+أثبتنا في الحالة التانية، case two
+
+60
+00:09:10,140 --> 00:09:24,200
+لو كانت الـ limit لـ x<sub>n</sub> بساوي negative infinity، ففي
+
+61
+00:09:24,200 --> 00:09:29,580
+الحالة هذه بيطلع عندي برضه by exercise ثلاثة
+
+62
+00:09:29,580 --> 00:09:36,020
+section ثلاثة ستة، بس هنا مع التعديل هيطلع أن الـ
+
+63
+00:09:36,020 --> 00:09:44,910
+limit لـ 1 على x<sub>n</sub> مثلًا صفر، وباقي البرهان
+
+64
+00:09:44,910 --> 00:09:58,730
+and the rest of the proof is similar to 
+
+65
+00:09:58,730 --> 00:09:59,450
+case one
+
+66
+00:10:03,650 --> 00:10:09,850
+Okay تمام، إذا هذا اللي هو البرهان أن الادعاء
+
+67
+00:10:09,850 --> 00:10:15,870
+يعتمد على exercise ثلاثة المهم وهو أن limit لـ
+
+68
+00:10:15,870 --> 00:10:19,750
+sequence بيساوي infinity if and only if limit 
+
+69
+00:10:19,750 --> 00:10:24,810
+مقلوب ال sequence بيساوي صفر أو العكس تمام، وهذا
+
+70
+00:10:34,460 --> 00:10:39,400
+في عنكم أسئلة ثانية؟
+
+71
+00:10:39,400 --> 00:10:45,260
+في
+
+72
+00:10:45,260 --> 00:10:49,220
+أسئلة ثانية، section ثلاثة ستة الفرق بيه من سؤال 
+
+73
+00:10:49,220 --> 00:10:49,680
+تسعة
+
+74
+00:11:33,220 --> 00:11:41,380
+نحاول نكتب السؤال وبعدين السؤال
+
+75
+00:11:41,380 --> 00:11:43,600
+تسعة، section ثلاثة ستة
+
+76
+00:11:53,320 --> 00:12:04,400
+لت x<sub>n</sub> و y<sub>n</sub> بيكونوا عاملين من عاملين من عاملين من
+
+77
+00:12:04,400 --> 00:12:06,860
+عاملين من عاملين من عاملين من عاملين من عاملين من
+
+78
+00:12:06,860 --> 00:12:09,100
+عاملين من عاملين من عاملين من عاملين من عاملين من
+
+79
+00:12:09,100 --> 00:12:22,440
+عاملين من عاملين
+
+80
+00:12:31,890 --> 00:12:44,270
+مطلوب الأول هو show if limit y<sub>n</sub> بساوي infinity 
+
+81
+00:12:44,270 --> 00:12:51,370
+then limit
+
+82
+00:12:51,370 --> 00:12:53,590
+x<sub>n</sub> بساوي infinity
+
+83
+00:12:56,820 --> 00:13:10,660
+والجزء الثاني show if x<sub>n</sub> is bounded then 
+
+84
+00:13:10,660 --> 00:13:15,680
+limit
+
+85
+00:13:15,680 --> 00:13:25,600
+y<sub>n</sub> is serviceable طبعًا
+
+86
+00:13:30,880 --> 00:13:39,520
+في برهانين للـ
+
+87
+00:13:39,520 --> 00:13:47,540
+للـ exercise هذا، البرهان الأول باستخدام
+
+88
+00:13:47,540 --> 00:13:55,580
+exercise 7 اللي جابله، يعني هنا since
+
+89
+00:13:55,580 --> 00:14:04,790
+من الفرض لما إنه limit x<sub>n</sub> على y<sub>n</sub> as n tends to 
+
+90
+00:14:04,790 --> 00:14:15,150
+infinity بساوي plus infinity then by exercise
+
+91
+00:14:15,150 --> 00:14:24,790
+ثلاثة، section ثلاثة ستة، if limit sequence بساوي
+
+92
+00:14:24,790 --> 00:14:30,780
+infinity بيطلع limit مقلوب الـ sequence اللي هو y<sub>n</sub> 
+
+93
+00:14:30,780 --> 00:14:40,920
+على x<sub>n</sub> as n tends to infinity بساوي صفر، now
+
+94
+00:14:40,920 --> 00:14:44,480
+apply
+
+95
+00:14:44,480 --> 00:14:47,900
+exercise
+
+96
+00:14:47,900 --> 00:14:55,940
+رقم سبعة، section ثلاثة ستة، to 
+
+97
+00:14:55,940 --> 00:14:56,340
+get
+
+98
+00:14:59,870 --> 00:15:13,950
+the results in a and b، وهذا بيعطيني المطلوب، لو بصيت ولا
+
+99
+00:15:13,950 --> 00:15:18,950
+لا الـ exercise
+
+100
+00:15:18,950 --> 00:15:25,070
+سبعة في الـ exercise سبعة بيقول ده كانت الـ limit للـ
+
+101
+00:15:25,070 --> 00:15:30,880
+quotient للـ quotient زي هذا بساوي صفر، و x<sub>n</sub> و y<sub>n</sub>
+
+102
+00:15:30,880 --> 00:15:37,200
+حدودهم موجبة، ففي الحالة هذه إذا كانت limit الـ
+
+103
+00:15:37,200 --> 00:15:47,200
+sequence اللي تحت convergent إذا
+
+104
+00:15:47,200 --> 00:15:50,240
+كانت limit الـ sequence اللي تحت 
+
+105
+00:15:56,100 --> 00:16:01,960
+لأ limit الـ sequence اللي فوق اللي هي y<sub>n</sub> هنا
+
+106
+00:16:01,960 --> 00:16:06,040
+infinity فبيطلع limit x<sub>n</sub> بالـ infinity اللي هو جزء
+
+107
+00:16:06,040 --> 00:16:12,980
+الاول، وكمان إذا كانت الـ sequence اللي في المقام
+
+108
+00:16:12,980 --> 00:16:16,520
+bounded اللي هي x<sub>n</sub> هنا طبعًا في المقام bounded 
+
+109
+00:16:16,520 --> 00:16:21,500
+فرقة الـ sequence اللي في الـ bust تطلع يساوي 0، وهذا
+
+110
+00:16:21,500 --> 00:16:25,740
+هو الجزء الثاني، هذا حسب هذا لو بدنا نستخدم
+
+111
+00:16:25,740 --> 00:16:33,610
+exercise رقم 7 وطبعًا لازم نبرهنه، لكن ممكن نعطي
+
+112
+00:16:33,610 --> 00:16:39,710
+برهان مباشر بدون ما يستخدم exercise السابعة
+
+113
+00:16:39,710 --> 00:16:49,670
+وبالتالي إذا في حال ثاني أو برهان ثاني باستخدام
+
+114
+00:16:49,670 --> 00:16:57,900
+التعريفات وال comparison tests، باستخدام التعريفات
+
+115
+00:16:57,900 --> 00:17:01,820
+زائد ال comparison tests، اختبارات المقارنة، الـ
+
+116
+00:17:01,820 --> 00:17:09,240
+proof رقم اثنين، since
+
+117
+00:17:09,240 --> 00:17:16,820
+إننا ننسى هذا القران، أنا عندي هذه الفرض since limit 
+
+118
+00:17:16,820 --> 00:17:24,630
+لـ x<sub>n</sub> over y<sub>n</sub> هذا عبارة عن sequence، لأن الـ limit
+
+119
+00:17:24,630 --> 00:17:33,410
+إلى بالصفر plus infinity، then given Alpha أي real
+
+120
+00:17:33,410 --> 00:17:41,610
+number Alpha من تعريف الـ improper convergence 
+
+121
+00:17:41,610 --> 00:17:50,030
+لأي Alpha there exists capital N يعتمد على Alpha 
+
+122
+00:17:50,030 --> 00:17:56,450
+عدد طبيعي بحيث إنه يكون M أكبر من أو يساوي الـ capital N
+
+123
+00:17:56,450 --> 00:18:12,950
+بيطلع عندي x<sub>m</sub> على y<sub>m</sub> أكبر من Alpha، طبعًا
+
+124
+00:18:12,950 --> 00:18:20,480
+وهذا بيقودِ أن x<sub>m</sub> أكبر من Alpha في y<sub>m</sub>، لما عندي y<sub>n</sub>
+
+125
+00:18:20,480 --> 00:18:26,120
+هنا موجبة، لما أضرب الطرفين في y<sub>n</sub>، التباين إشارتها 
+
+126
+00:18:26,120 --> 00:18:32,340
+تبقى كما هي، إذا
+
+127
+00:18:32,340 --> 00:18:40,880
+أنا عندي الآن الكلام هذا صحيح لكل n أكبر من أو يساوي 
+
+128
+00:18:40,880 --> 00:18:46,540
+كابتن، الآن الآن
+
+129
+00:18:46,540 --> 00:18:47,360
+by
+
+130
+00:18:49,930 --> 00:18:56,930
+بمعنى الـ Direct Comparison Test، بما
+
+131
+00:18:56,930 --> 00:19:02,970
+إنه limit y<sub>n</sub>
+
+132
+00:19:02,970 --> 00:19:04,130
+بساوي infinity
+
+133
+00:19:25,130 --> 00:19:33,010
+ناخد Alpha في 1 ممكن
+
+134
+00:19:33,010 --> 00:19:37,750
+آه ناخد Alpha في 1 صح، دي من الـ Alpha دي ثاني
+
+135
+00:19:37,750 --> 00:19:49,320
+واحد يعني ثاني الـ R مظبوط، فده واحد وثاني واحد، بما
+
+136
+00:19:49,320 --> 00:19:54,600
+أن الـ limit لـ y<sub>n</sub>
+
+137
+00:19:54,600 --> 00:20:02,180
+بساوي infinity، نحن نحصل على limit لـ x<sub>n</sub> بساوي 
+
+138
+00:20:02,180 --> 00:20:06,640
+infinity، لأن هذا بيثبت الجزء الأول، أنت بدك الجزء
+
+139
+00:20:06,640 --> 00:20:08,160
+الثاني صح؟ طيب
+
+140
+00:20:15,760 --> 00:20:19,840
+بنشوف الجزء الثاني، إذا كانت الـ sequence x<sub>n</sub> 
+
+141
+00:20:19,840 --> 00:20:27,400
+bounded فبالتالي y in بسرعة نصف طيب
+
+142
+00:20:27,400 --> 00:20:32,420
+الجزء
+
+143
+00:20:32,420 --> 00:20:43,340
+دي since x is bounded إذن
+
+144
+00:20:43,340 --> 00:20:48,760
+في عدد موجب There exists a positive number بحيث أنه
+
+145
+00:20:48,760 --> 00:20:57,360
+absolute value of x<sub>n</sub> أصغر من أو يساوي m لكل n في هذا من
+
+146
+00:20:57,360 --> 00:21:05,280
+تعريف الboundary نفسه طيب بالمنطلق بتاعنا إيه؟ أن
+
+147
+00:21:05,280 --> 00:21:16,480
+ال limit ل y<sub>n</sub>  عند صفر طيب to show limit y<sub>n</sub> يساوي
+
+148
+00:21:16,480 --> 00:21:23,260
+zero let epsilon بنستخدم تعريف epsilon و capital M
+
+149
+00:21:23,260 --> 00:21:32,060
+لإن هي let epsilon أكبر من الصفر be given من
+
+150
+00:21:32,060 --> 00:21:39,100
+epsilon على M بيطلع عدد موجب من
+
+151
+00:21:41,390 --> 00:21:52,910
+العدد الموجب يعتمد
+
+152
+00:21:52,910 --> 00:21:58,830
+على إبسلون على M يعتبر
+
+153
+00:21:58,830 --> 00:22:01,590
+إبسلون على M
+
+154
+00:22:16,450 --> 00:22:24,150
+أنا عندي إيش عندي بدي
+
+155
+00:22:24,150 --> 00:22:31,170
+أثبت أن limit y<sub>n</sub> يساوي صفر فخلينا نشوف
+
+156
+00:22:43,720 --> 00:22:54,900
+طيب أنا لازم أستخدم .. آه لازم أستخدم ..
+
+157
+00:22:54,900 --> 00:23:01,840
+طيب since ..
+
+158
+00:23:01,840 --> 00:23:06,820
+طيب بس هنا يعني خليني أقول since
+
+159
+00:23:11,850 --> 00:23:20,390
+بما أن ال limit ل y<sub>n</sub> على x<sub>n</sub> as n tends to infinity
+
+160
+00:23:20,390 --> 00:23:24,410
+أنا عندي المقلوب هذا ال limit تبعته infinity، هذا
+
+161
+00:23:24,410 --> 00:23:29,890
+ال limit تبعته صفر وهي عندي epsilon على m عدد موجب 
+
+162
+00:23:29,890 --> 00:23:36,150
+given، there exists capital M يعتمد على epsilon
+
+163
+00:23:36,150 --> 00:23:47,110
+على m عدد طبيعي لحيث أنه لكل n أكبر من أو يساوي ال
+
+164
+00:23:47,110 --> 00:23:56,850
+capital N بيطلع عندي absolute value of y<sub>n</sub> على x<sub>n</sub> ناقص ال
+
+165
+00:23:56,850 --> 00:24:05,850
+zero أصغر من epsilon على m تمام؟
+
+166
+00:24:07,690 --> 00:24:27,750
+طب ما هذا بيقودني فإنا 
+
+167
+00:24:27,750 --> 00:24:32,910
+بدي أثبت أن limit y<sub>n</sub> يساوي صفر يعني بدي أثبت أن
+
+168
+00:24:32,910 --> 00:24:38,980
+ال absolute value لو كان n أكبر من أو يساوي capital
+
+169
+00:24:38,980 --> 00:24:44,920
+N بتثبت أن ال absolute value ل y<sub>n</sub> ناقص 0 أصغر
+
+170
+00:24:44,920 --> 00:24:50,020
+من epsilon عشان أثبت أن ال limit ل y<sub>n</sub> يساوي صفر
+
+171
+00:24:50,020 --> 00:24:55,520
+بتثبت أن ال absolute value ل y<sub>n</sub> ناقص 0 أصغر من
+
+172
+00:24:55,520 --> 00:25:00,500
+ال given epsilon طيب
+
+173
+00:25:00,500 --> 00:25:12,970
+هذا يساوي absolute value of Y<sub>n</sub> يساوي absolute value of X<sub>n</sub> ضرب Y<sub>n</sub>
+
+174
+00:25:12,970 --> 00:25:26,270
+على X<sub>n</sub> ناقص zero و هذا يساوي absolute value of X<sub>n</sub> في
+
+175
+00:25:26,270 --> 00:25:30,170
+absolute value of Y<sub>n</sub> على X<sub>n</sub>
+
+176
+00:25:37,650 --> 00:25:44,410
+بتكون موضوع ممكن نحط  zero هنا طيب
+
+177
+00:25:44,410 --> 00:25:51,510
+هذا لكل N هذا أصغر من أو يساوي M و ال absolute
+
+178
+00:25:51,510 --> 00:25:56,570
+value هذه لكل N أكبر من أو يساوي capital N هذا
+
+179
+00:25:56,570 --> 00:26:05,270
+أصغر من إبسلون على M إبسلون على M مش هيبقى M مع N
+
+180
+00:26:05,270 --> 00:26:14,790
+بقى اللي عندي إبسلون طبعا؟ طيب since أكبر من الصفر
+
+181
+00:26:14,790 --> 00:26:25,310
+was arbitrarily we get أن limit ل y<sub>n</sub> as n tends
+
+182
+00:26:25,310 --> 00:26:29,650
+to infinity يساوي zero و هو المفروض يعني هذا بيكمل
+
+183
+00:26:29,650 --> 00:26:35,380
+برهان الجزء بيه okay طبعا؟ هذا على اعتبار أن احنا
+
+184
+00:26:35,380 --> 00:26:41,300
+exercise سبعة ما بنعرفوش بس في كل الأحوال احنا
+
+185
+00:26:41,300 --> 00:26:47,300
+استخدمنا exercise ثلاثة طبعا
+
+186
+00:26:47,300 --> 00:26:54,400
+هكذا بنثبت تسعة و سبعة بالمناسبة زيه بنفس الطريقة
+
+187
+00:26:54,400 --> 00:27:01,020
+بأفكار مشابهة ممكن إثباته بنفس السلوب بنفس النمط
+
+188
+00:27:03,510 --> 00:27:09,270
+كمان في أي أسئلة تانية في section ثلاثة سبعة؟ إذا
+
+189
+00:27:09,270 --> 00:27:15,430
+مافيش خلينا ننتقل ل section ثلاثة سبعة تبع
+
+190
+00:27:15,430 --> 00:27:20,110
+ال series هذا في
+
+191
+00:27:20,110 --> 00:27:24,550
+عندكم أي أسئلة في section ثلاثة سبعة؟ ثلاثة خمسة؟
+
+192
+00:27:24,550 --> 00:27:25,750
+ثلاثة سبعة؟
+
+193
+00:27:44,990 --> 00:27:54,110
+في أي أسئلة في section ثلاثة سبعة أو ثلاثة ستة
+
+194
+00:27:54,110 --> 00:28:07,910
+مافيش؟
+
+195
+00:28:07,910 --> 00:28:13,700
+السؤال ثلاثة فرع ثلاثة سبعة السؤال الثالث الفرع 
+
+196
+00:28:13,700 --> 00:28:14,320
+السيه؟
+
+197
+00:28:28,470 --> 00:28:33,570
+استخدمت ال partial fractions؟ آه بس مش .. مش كله
+
+198
+00:28:33,570 --> 00:28:37,990
+بالغاية طلعت قيم A و C بيطلعوا نص و نص و B بيطلعوا
+
+199
+00:28:37,990 --> 00:28:43,770
+سالب واحد و بعد ما جيت أكمل مش كل الحدود بيطلعوا
+
+200
+00:28:43,770 --> 00:28:48,790
+بالطبع معايا زي قمتي لو سألني الجامعة آه عشان
+
+201
+00:28:48,790 --> 00:28:52,310
+هيكون ثلاثة كسور يعني آه
+
+202
+00:28:54,820 --> 00:29:09,900
+بس لازم يكون فيه يعني تلاشي و فيه
+
+203
+00:29:09,900 --> 00:29:18,020
+.. نشوف
+
+204
+00:29:18,020 --> 00:29:22,040
+يعني مافيش تلاشي جيبت الارتباط برشا الصمت .. فيه
+
+205
+00:29:22,040 --> 00:29:26,940
+تلاشي بس فيه بيضغط آه بخلينا نشوف خليني أجرب
+
+206
+00:29:26,940 --> 00:29:44,520
+السؤال
+
+207
+00:29:44,520 --> 00:29:47,580
+ثلاثة الفرع C سيكشن ثلاثة سبعة
+
+208
+00:29:54,860 --> 00:29:59,300
+استخدمت ال partial fractions
+
+209
+00:29:59,300 --> 00:30:03,020
+لإظهار
+
+210
+00:30:03,020 --> 00:30:11,100
+أن عدد الـ infinite series سيجما من ن يعني واحد
+
+211
+00:30:11,100 --> 00:30:21,320
+لما لا نهاية الواحد على n في n زائد واحد في n زائد
+
+212
+00:30:21,320 --> 00:30:23,600
+اثنين يساوي واحد على أربعة
+
+213
+00:30:32,200 --> 00:30:37,060
+فبدنا نكتب هذا بتحلل و باستخدام ال partial
+
+214
+00:30:37,060 --> 00:30:43,740
+fractions إلى ثلاثة كسور فوجدت
+
+215
+00:30:43,740 --> 00:30:48,080
+فرعة التواردة كانت دي؟ كان الأولى A بتساوي نص يعني
+
+216
+00:30:48,080 --> 00:30:57,340
+نص على n الثانية سالب واحد سالب أو زائد سالب واحد على
+
+217
+00:30:57,340 --> 00:31:09,270
+n زائد واحد والأخيرة نص على n زائد اثنين تعال
+
+218
+00:31:09,270 --> 00:31:18,590
+نحسب ال nth partial sum s<sub>n</sub> يساوي سيجما من k يساوي
+
+219
+00:31:18,590 --> 00:31:31,370
+واحد إلى n ل x<sub>k</sub> اللي هو واحد على k في k زائد واحد
+
+220
+00:31:31,370 --> 00:31:40,190
+في k زائد اثنين بنبدل n بال k وبعدين
+
+221
+00:31:40,190 --> 00:31:54,030
+هذا عبارة عن سيجما من k يساوي واحد إلى n و بنكتب
+
+222
+00:31:54,030 --> 00:31:57,350
+هذا واحد على
+
+223
+00:32:00,560 --> 00:32:07,980
+2k ناقص واحد
+
+224
+00:32:07,980 --> 00:32:16,740
+على k زائد واحد موجب خلينا
+
+225
+00:32:16,740 --> 00:32:21,800
+نحط الحاجات الموجبة مع بعض يعني زائد واحد على
+
+226
+00:32:21,800 --> 00:32:26,360
+2k زائد أربعة
+
+227
+00:32:28,860 --> 00:32:36,700
+ناقص واحد على K ناقص واحد و
+
+228
+00:32:36,700 --> 00:32:42,140
+بعدين نكتب أول شوية حدود مهم جدا اللي كل ثوابت هذه
+
+229
+00:32:42,140 --> 00:32:48,080
+صح يعني في حد ثاني جابهم متأكد من صحتهم لأن لو
+
+230
+00:32:48,080 --> 00:32:50,680
+فيهم خطأ مش هنقبلهم ونطلع الجواب
+
+231
+00:33:03,670 --> 00:33:08,910
+فنكتب أول حد هي .. أول حد هيكون لما k يساوي
+
+232
+00:33:08,910 --> 00:33:17,090
+واحد .. نص .. هيطلع نص زائد واحد على .. ثمانية ..
+
+233
+00:33:17,090 --> 00:33:24,090
+اثنين .. لأ واحد على ستة .. واحد على ستة صح ناقص
+
+234
+00:33:24,090 --> 00:33:26,110
+نص .. سالب نص
+
+235
+00:33:31,480 --> 00:33:38,960
+زائد لحد الثاني واحد على ثلاثة زائد
+
+236
+00:33:38,960 --> 00:33:41,520
+.. واحد على أربعة .. واحد على أربعة .. أربعة .. الأول
+
+237
+00:33:41,520 --> 00:33:48,800
+واحد على أربعة أو واحد على أربعة الأول وبعدين واحد
+
+238
+00:33:48,800 --> 00:33:53,040
+على .. ثمانية .. واحد على ثمانية .. ثمانية ناقص
+
+239
+00:33:53,040 --> 00:34:03,060
+ثُلث ناقص ثُلث طيب قول لي بعده واحد على ستة واحد على
+
+240
+00:34:03,060 --> 00:34:09,380
+ستة واحد على إيه؟ على ستة واحد على عشرة اثنين في
+
+241
+00:34:09,380 --> 00:34:14,500
+ثلاثة بستة آه واحد على ستة زائد واحد على عشرة زائد
+
+242
+00:34:14,500 --> 00:34:25,360
+واحد على عشرة ناقص ربع ناقص ربع زائد
+
+243
+00:34:25,360 --> 00:34:39,020
+وهكذا الآخر حد هيكون واحد على 2n زائد واحد على 2n زائد 4
+
+244
+00:34:39,020 --> 00:34:55,940
+مع بعض وبعدين الثاني واحد على n زائد 1 فنشوف
+
+245
+00:34:55,940 --> 00:35:01,570
+إيش اللي بيتلاشى وإيش اللي بيطلع يعني نص هنا راح مع
+
+246
+00:35:01,570 --> 00:35:07,190
+نص و
+
+247
+00:35:07,190 --> 00:35:20,090
+ربع هنا راح مع الربع هنا قلت
+
+248
+00:35:20,090 --> 00:35:26,030
+لك هذا مش هيروح مع حد صح؟ هذا يبقى
+
+249
+00:35:30,600 --> 00:35:36,960
+لكن الثمن هيروح والثُلث هيروح لأن الثُلث في مجموعة
+
+250
+00:35:36,960 --> 00:35:42,560
+ليه ثُلث والثمن هيجمع ليه الثمن بس برضه هييجي
+
+251
+00:35:42,560 --> 00:35:46,620
+ناقص واحد على ثمانية وهيظل واحد على ثمانية فيه؟
+
+252
+00:35:46,620 --> 00:35:51,220
+آه لما نقعد بالقيمة سوى سبعة هيطلع إننا ناقص واحد
+
+253
+00:35:51,220 --> 00:35:54,040
+على ثمانية آه شيء ناقص واحد على ثمانية
+
+254
+00:35:56,980 --> 00:36:01,600
+وممكن كمان برضه واحد على ستة أو في برضه واحد على
+
+255
+00:36:01,600 --> 00:36:08,020
+ستة سيطلع سالب واحد على ستة لأن بيساوي خمسة سيطلع
+
+256
+00:36:08,020 --> 00:36:14,700
+ثاندي سالب واحد على ستة فمين اللي بيضل على المحدود
+
+257
+00:36:14,700 --> 00:36:21,140
+يعني
+
+258
+00:36:21,140 --> 00:36:33,420
+بتاعي هذا ستس هيبقى هذا هيروحوا هذا هيروح يعني
+
+259
+00:36:33,420 --> 00:36:39,600
+شو اللي بضل في الآخر يعني
+
+260
+00:36:39,600 --> 00:36:46,060
+أنا بتاعي اللي هيضل في الآخر اللي هو يمكن الثُلث
+
+261
+00:36:46,060 --> 00:36:53,860
+الثُلث ناقص ثُلث وهنا
+
+262
+00:36:58,270 --> 00:37:05,290
+كل حد بيروح مع آدم فوضوح يروح مع اللي بعده فمش
+
+263
+00:37:05,290 --> 00:37:15,870
+هيروح مع حد فهيبقى واحد على اثنين يعني و
+
+264
+00:37:15,870 --> 00:37:19,030
+.. إيش هيبقى كمان؟
+
+265
+00:37:30,970 --> 00:37:36,990
+هذا هيروح هيبقى له اثنين هدول اثنين إيه مظلوم زاد
+
+266
+00:37:36,990 --> 00:37:51,870
+واحد على اثنين ام زائد أربعة سُدُس
+
+267
+00:37:51,870 --> 00:37:59,410
+ناقص ثُلث تطلع ناقص سُدُس وهذا ما يروح من صفر مش مظلوم
+
+268
+00:38:08,750 --> 00:38:15,650
+المفروض ال limit تطلع ربعها بالتالي
+
+269
+00:38:15,650 --> 00:38:19,710
+لازم احنا نكتب المزيد من الحدود عشان نشوف كيف النمط
+
+270
+00:38:19,710 --> 00:38:22,150
+.. كيف النمط هيصير
+
+271
+00:38:27,470 --> 00:38:34,430
+فبدأ عملية grouping للحدود تجميع ويعني الحصول على علامات
+
+272
+00:38:34,430 --> 00:38:41,310
+معينة مش عارف أنا مش متأكد أن هذا هتكون صح يمكن
+
+273
+00:38:41,310 --> 00:38:55,770
+في شغلات ثانية بتبقى واحنا ما ذكرناش فال
+
+274
+00:38:55,770 --> 00:38:56,090
+..
+
+275
+00:38:59,080 --> 00:39:04,640
+ذا بده فحص آه فخلينا نقول try it again try it
+
+276
+00:39:04,640 --> 00:39:07,780
+again
+
+277
+00:39:07,780 --> 00:39:17,200
+خلينا نحاول فيه مرة ثانية ونحاول يعني نقدر نخلي
+
+278
+00:39:17,200 --> 00:39:22,740
+يعني هذا يساوي ربع أو يساوي حاجة ال limit بتاعتها في
+
+279
+00:39:22,740 --> 00:39:26,480
+النهاية هتطلع ربع وبالتالي ال limit لل sequence of
+
+280
+00:39:26,480 --> 00:39:29,180
+partial sums هيطلع ربعه وبالتالي ال series
+
+281
+00:39:29,180 --> 00:39:33,000
+conversion مجموعة بساوي ال limit لل partial sums
+
+282
+00:39:33,000 --> 00:39:38,700
+فهذا يعني مشكوك فيه شكله مش صح نحاول مرة ثانية فيه
+
+283
+00:39:38,700 --> 00:39:43,100
+وبعدين نشوف يعني كيف مين اللي بيصل للجواب الصح
+
+284
+00:39:43,100 --> 00:39:48,720
+نحاول نكتبه مرة ثانية okay تمام لكن يعني ماهو 
+
+285
+00:39:48,720 --> 00:39:53,570
+مستحيل أو ماهو يعني صعب ممكن أي واحد يتوصل إليه
+
+286
+00:39:53,570 --> 00:39:58,990
+بس بده إيه مزيد من الحدود والاستنتاج نمط معين
+
+287
+00:39:58,990 --> 00:40:04,370
+فخلينا نسيبكم تفكروا فيه كمان مرة في أسئلة ثانية
+
+288
+00:40:04,370 --> 00:40:08,990
+في ال section هذا فحاولوا
+
+289
+00:40:08,990 --> 00:40:11,170
+تفكروا فيه في أسئلة ثانية
+
+290
+00:40:17,700 --> 00:40:21,980
+في أسئلة ثانية في section ثلاثة سبعة أو ال sections
+
+291
+00:40:21,980 --> 00:40:32,680
+السابقة اللي تسبقه ثلاثة ستة ثلاثة خمسة في
+
+292
+00:40:32,680 --> 00:40:38,140
+كتير أسئلة يعني مطلوبة منكم واضح أن أنتم مش محضرين 
+
+293
+00:40:38,140 --> 00:40:42,420
+ولا دارسين الموضوع وبالتالي ما عندكم مش أسئلة
+
+294
+00:40:46,220 --> 00:40:54,880
+فإلى أن يكون عندكم أسئلة بنكمل المناقشة يوم السبت 
+
+295
+00:40:54,880 --> 00:40:59,860
+الجاي أو تحضروا المناقشة مع الشعبة الثانية يوم
+
+296
+00:40:59,860 --> 00:41:05,140
+الأربعاء خلينا
+
+297
+00:41:05,140 --> 00:41:14,690
+نرجع لل limits of functions وناخد المثال الأخير في 
+
+298
+00:41:14,690 --> 00:41:16,930
+ال section هذاك
+
+299
+00:41:46,290 --> 00:41:50,970
+المرة الجاية دخلنا أثبتنا
+
+300
+00:41:50,970 --> 00:42:02,310
+أن ال limit أثبتنا
+
+301
+00:42:02,310 --> 00:42:05,450
+أن ال limit  أنتِ مثال رقم 2
+
+302
+00:42:08,630 --> 00:42:15,350
+لسفر function ل X لما X تقول لسفر does not exist
+
+303
+00:42:15,350 --> 00:42:19,270
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+304
+00:42:19,270 --> 00:42:21,290
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+305
+00:42:21,290 --> 00:42:21,570
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+306
+00:42:21,570 --> 00:42:21,890
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+307
+00:42:21,890 --> 00:42:22,210
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+308
+00:42:22,210 --> 00:42:22,610
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+309
+00:42:22,610 --> 00:42:25,970
+أخذنا هذا و أخذنا هذا و أخذنا هذا و أخذنا هذا و
+
+310
+00:42:25,970 --> 00:42:33,830
+أخذنا هذا و أخذنا 
+
+311
+00:42:33,830 --> 00:42:46,640
+هذا و أوحد على X لما X تقول لسفر does not exist in
+
+312
+00:42:46,640 --> 00:42:50,400
+R فلبرحان
+
+313
+00:42:50,400 --> 00:42:56,700
+ذلك let
+
+314
+00:42:56,700 --> 00:43:04,380
+F of X تساوي sign واحد على X و X لا تساوي صفر
+
+315
+00:43:10,730 --> 00:43:16,210
+وبعدين we consider two
+
+316
+00:43:16,210 --> 00:43:20,870
+sequences واحدة
+
+317
+00:43:20,870 --> 00:43:33,750
+xn الحد العام تبعها عبارة عن واحد على واحد
+
+318
+00:43:33,750 --> 00:43:38,030
+على n πاي و n ينتمي ل Z
+
+319
+00:43:41,720 --> 00:43:47,620
+و Yn الحد العام تبعها واحد على πاي على ثمانين زائد
+
+320
+00:43:47,620 --> 00:43:56,020
+اثنين N πاي و N ينتمي إلى Z هذا عبارة عن Sequences
+
+321
+00:43:56,020 --> 00:44:01,300
+of positive numbers
+
+322
+00:44:04,950 --> 00:44:12,130
+واضح أن ال limit ل xn as n tends to infinity بساوي
+
+323
+00:44:12,130 --> 00:44:20,290
+0 وكذلك ال limit ل yn لما n تقول infinity برضه
+
+324
+00:44:20,290 --> 00:44:24,730
+بساوي 0 لأن المقام لما n تقول infinity المقام
+
+325
+00:44:24,730 --> 00:44:32,090
+بيروح ل infinity طيب
+
+326
+00:44:32,090 --> 00:44:33,690
+الآن ال limit
+
+327
+00:44:37,860 --> 00:44:42,420
+الـ image لـ sequence xn لما n تقول الانفينيتي
+
+328
+00:44:42,420 --> 00:44:55,500
+بساوي ال limit ل sign xn لما n تقول الانفينيتي وهذا
+
+329
+00:44:55,500 --> 00:45:05,620
+بساوي ال limit ل sign n في pi لما n تقول الانفينيتي
+
+330
+00:45:06,340 --> 00:45:16,300
+Sin N في Pi بساوي واحد بساوي صفر لكل N وبالتالي
+
+331
+00:45:16,300 --> 00:45:21,640
+هذا بساوي limit ال sequence صفر لما N تؤول
+
+332
+00:45:21,640 --> 00:45:32,600
+infinity بساوي صفر and limit
+
+333
+00:45:33,900 --> 00:45:41,360
+الإمج للسيكوينس YM لما N تقول انفينيتي بساوي limit
+
+334
+00:46:08,450 --> 00:46:16,370
+وهذا المفروض يكون sign
+
+335
+00:46:16,370 --> 00:46:24,840
+1 على xn وهذا المفروض يكون sign 1 على yn مقلوب y in
+
+336
+00:46:24,840 --> 00:46:34,540
+بيطلع بساوي πاية اتنين ازايد اتنين in πاية وهذا
+
+337
+00:46:34,540 --> 00:46:44,040
+المقدار دائما بساوي واحد لكل in إذا أنا في عندي 
+
+338
+00:46:44,040 --> 00:46:51,770
+limit لل sequence بالحد العام تبعها واحد السيكوانس
+
+339
+00:46:51,770 --> 00:46:57,670
+تابعة واحد وهذا بساوي واحد إن إن أنا في عندي 
+
+340
+00:46:57,670 --> 00:47:03,710
+two sequences Xm تؤول صفر و limit صورتها 
+
+341
+00:47:03,710 --> 00:47:09,050
+بساوي صفر و في عندي سيكوانس ثانية Ym ال limit
+
+342
+00:47:09,050 --> 00:47:13,650
+تبعها أيضا بساوي صفر لكن limit صورتها بساوي 
+
+343
+00:47:13,650 --> 00:47:17,310
+واحد وبالتالي
+
+344
+00:47:20,360 --> 00:47:28,340
+by sequential criterion ال
+
+345
+00:47:28,340 --> 00:47:35,480
+limit لل function f of x لما x تقول ل0 does not
+
+346
+00:47:35,480 --> 00:47:46,440
+exist in R مش ممكن تكون موجودة في R لأن
+
+347
+00:47:46,440 --> 00:47:53,900
+لو كانت ال limit هذه موجودة فالمفروض limit صورة xn
+
+348
+00:47:53,900 --> 00:48:02,060
+بما أن xn تؤول للسفر نكتب
+
+349
+00:48:02,060 --> 00:48:07,180
+since otherwise لأن
+
+350
+00:48:07,180 --> 00:48:14,780
+لو كلاك ذلك لو كانت هذه موجودة if limit
+
+351
+00:48:20,170 --> 00:48:25,210
+في limit ل F of X لما X تؤول ل صفر exist
+
+352
+00:48:32,710 --> 00:48:39,990
+then المفروض ال limit ل f of x n لما n تؤول 
+
+353
+00:48:39,990 --> 00:48:47,270
+infinity بتساوي ال limit ل f of y n as n tends to
+
+354
+00:48:47,270 --> 00:48:57,070
+infinity وهذا مستحيل which is impossible وهذا زي
+
+355
+00:48:57,070 --> 00:49:03,150
+ما شوفنا مستحيل impossible لأن طولها limit f of x
+
+356
+00:49:03,150 --> 00:49:09,390
+in بساوي صفر و limit f of y in بساوي واحد إذن
+
+357
+00:49:09,390 --> 00:49:13,470
+هنا استخدمنا sequential criterion في إثبات إن ال
+
+358
+00:49:13,470 --> 00:49:17,330
+limit لل function f of x بساوي sign واحد على x
+
+359
+00:49:17,330 --> 00:49:24,490
+غير موجودة عند الصفر طيب
+
+360
+00:49:24,490 --> 00:49:30,120
+هناخد break خمس دقائق وبعدين نواصل المحاضرة
+
+361
+00:49:30,120 --> 00:49:31,840
+الثانية
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c94b3cb12b029df42e570a2335413ba0361557de
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/7K-d4aAzbLs_postprocess.srt
@@ -0,0 +1,1444 @@
+1
+00:00:21,410 --> 00:00:29,070
+السلام عليكم اليوم في اللقاء الأول هناخد مناقشة و
+
+2
+00:00:29,070 --> 00:00:36,710
+اعتقد ان احنا في المناقشة السابقة وصلنا ل section
+
+3
+00:00:36,710 --> 00:00:46,810
+تلاتة خمسة، أصبع؟ فممكن
+
+4
+00:00:46,810 --> 00:01:07,930
+اليومبنناقش section تلاتة ستة أو تلاتة سبعة في
+
+5
+00:01:07,930 --> 00:01:14,710
+أي أسل عندكم في section تلاتة خمسة أو section
+
+6
+00:01:14,710 --> 00:01:25,230
+تلاتة ستةثلاثة ستة السؤال ستة أي سؤال سؤال ستة ستة
+
+7
+00:01:25,230 --> 00:01:35,470
+سؤال
+
+8
+00:01:35,470 --> 00:01:37,650
+ستة section تلاتة ستة
+
+9
+00:01:46,160 --> 00:01:58,020
+let x in let the sequence x in be properly die
+
+10
+00:01:58,020 --> 00:02:05,920
+there and let
+
+11
+00:02:05,920 --> 00:02:24,780
+and let y inب such that limit x in ضرب y in limit
+
+12
+00:02:24,780 --> 00:02:31,980
+حصل ضرب لما n تقول لinfinity الساوي
+
+13
+00:02:31,980 --> 00:02:40,620
+L ينتمي إلى R يعني exists in R شو
+
+14
+00:02:40,620 --> 00:02:54,410
+مطلوبثم اثبت اظهر ان سيكوينس ين يتعامل
+
+15
+00:02:54,410 --> 00:03:10,230
+بالزيرو حل
+
+16
+00:03:10,230 --> 00:03:17,950
+السؤال هذا بعتمدعلى سؤال سابق اللي هو سؤال تلاتة
+
+17
+00:03:17,950 --> 00:03:27,190
+فالسؤال
+
+18
+00:03:27,190 --> 00:03:32,430
+هذا بيقول ان f
+
+19
+00:03:32,430 --> 00:03:50,310
+x n أكبر من سفر لكل n عدد طبيعيو ال then
+
+20
+00:03:50,310 --> 00:04:03,990
+limit xn بساوي zero if and only if limit واحد على
+
+21
+00:04:03,990 --> 00:04:10,350
+xn as n tends to infinity بساوي plus infinity
+
+22
+00:04:20,790 --> 00:04:27,670
+Okay لأن في سؤال طلعتها إذا كانت xn حدود sequence
+
+23
+00:04:27,670 --> 00:04:36,290
+حدودها موجة بقى و ف limit ال sequence xn بساوي سفر
+
+24
+00:04:36,290 --> 00:04:41,350
+if and only if limit مقلوب ال sequence xn بساوي
+
+25
+00:04:41,350 --> 00:04:42,190
+plus infinity
+
+26
+00:04:46,230 --> 00:04:52,690
+و طبعا في كمان ممكن نثبت ان لو كانت ال Xn حدودها
+
+27
+00:04:52,690 --> 00:05:00,950
+سالبة ف limit Xn بساوي صفر F and only F limit واحد
+
+28
+00:05:00,950 --> 00:05:03,970
+على Xn بساوي negative infinity
+
+29
+00:05:15,220 --> 00:05:24,480
+بما أن xn هو بشكل صحيح ديبيرزينت
+
+30
+00:05:24,480 --> 00:05:39,580
+ثم قيمة xn بساوي إفينتي أو قيمة xn بساوي نيجاتيف
+
+31
+00:05:39,580 --> 00:05:40,180
+إفينتي
+
+32
+00:05:45,460 --> 00:05:52,220
+case one ناخد الحالة الأولى اللى فيها limit xm
+
+33
+00:05:52,220 --> 00:05:59,860
+بساوي infinity by
+
+34
+00:05:59,860 --> 00:06:03,560
+exercise
+
+35
+00:06:03,560 --> 00:06:15,020
+رقم تلاتة section تلاتة ستةوالـ exercise اللى فوق
+
+36
+00:06:15,020 --> 00:06:18,100
+هذا
+
+37
+00:06:18,100 --> 00:06:27,160
+معناه انه we have هيطلع انه limit مطلوب ال
+
+38
+00:06:27,160 --> 00:06:38,000
+sequence xn as n tends to infinity بفلع صفر يعني
+
+39
+00:06:38,000 --> 00:06:44,710
+اعتبرى هذه هي xnتعتبر ال 1 على xn هي xn فإذا كان
+
+40
+00:06:44,710 --> 00:06:49,510
+limit xn بساوي infinity فlimit مقلوب ال xn اللي
+
+41
+00:06:49,510 --> 00:06:57,530
+هنا مقلوب اللي هو ايه بتطلع سفر ولا عكس يعني هنا
+
+42
+00:06:57,530 --> 00:07:03,850
+نفس ال exercise بس badly xn بواحد على xn فهذه
+
+43
+00:07:03,850 --> 00:07:08,690
+نتيجة صحية تمام hence
+
+44
+00:07:13,030 --> 00:07:16,810
+الـ limit ل
+
+45
+00:07:16,810 --> 00:07:29,290
+YN as intense infinity بساوي ال limit ال
+
+46
+00:07:29,290 --> 00:07:38,110
+YN ممكن كتبتها على صورة على
+
+47
+00:07:38,110 --> 00:07:39,310
+صورة
+
+48
+00:07:46,210 --> 00:07:55,770
+xn في yn ضرب 1
+
+49
+00:07:55,770 --> 00:08:01,290
+على xn صح
+
+50
+00:08:01,290 --> 00:08:09,850
+نظبط هيك ال yn هي عبارة عن xn في yn في 1 على xn
+
+51
+00:08:12,880 --> 00:08:18,360
+الان ال limit هذه لحد الأول exist و limit ل واحد
+
+52
+00:08:18,360 --> 00:08:22,660
+على xn برضه exist اذا ال limit حاصل ضرب بساوي حاصل
+
+53
+00:08:22,660 --> 00:08:27,540
+ضرب ال limits بقدر استخدم القانون هذا هطبق انه
+
+54
+00:08:27,540 --> 00:08:32,360
+limit حاصل ضرب two sequences بساوي limit الأولى
+
+55
+00:08:32,360 --> 00:08:41,100
+اللي هي حاصل ضرب xn ynدرب limit الـ sequence
+
+56
+00:08:41,100 --> 00:08:48,180
+التانية هي واحد على X end as n tends to infinity و
+
+57
+00:08:48,180 --> 00:08:53,940
+ال limit الأولى مش سامناها عدد L لما exist ضرب ال
+
+58
+00:08:53,940 --> 00:09:01,600
+limit التانية سفر فبطلع عندي سفر و هو المطلوب فهنا
+
+59
+00:09:01,600 --> 00:09:05,920
+أثبتنا في الحالة التانية case two
+
+60
+00:09:10,140 --> 00:09:24,200
+لو كانت ال limit لـ xn بساوي negative infinity ففي
+
+61
+00:09:24,200 --> 00:09:29,580
+الحالة هذه بيطلع عندي برضه by exercise تلاتة
+
+62
+00:09:29,580 --> 00:09:36,020
+section تلاتة ستة بس هنا مع التعديل هيطلع ان ال
+
+63
+00:09:36,020 --> 00:09:44,910
+limitلا واحد على اكس ان مثلا سفر و باقي البرهان
+
+64
+00:09:44,910 --> 00:09:58,730
+and the rest of the proof is similar to
+
+65
+00:09:58,730 --> 00:09:59,450
+case one
+
+66
+00:10:03,650 --> 00:10:09,850
+Okay تمام اذا هذا اللي هو البرهام ان الادكارة
+
+67
+00:10:09,850 --> 00:10:15,870
+تعتمد على exercise ثلاثة المهم وهو ان limit ل
+
+68
+00:10:15,870 --> 00:10:19,750
+sequence بيساوي infinity if and only if limit
+
+69
+00:10:19,750 --> 00:10:24,810
+مقلوب ال sequence بيساوي سفر او لعكس تمام و هذا
+
+70
+00:10:34,460 --> 00:10:39,400
+في عنكم أسئلة تانية؟
+
+71
+00:10:39,400 --> 00:10:45,260
+في
+
+72
+00:10:45,260 --> 00:10:49,220
+أسئلة تانية section تلاتة ستة الفرق بيه من سؤال
+
+73
+00:10:49,220 --> 00:10:49,680
+تسعة
+
+74
+00:11:33,220 --> 00:11:41,380
+حاول نكتب السؤال و بعدين السؤال
+
+75
+00:11:41,380 --> 00:11:43,600
+تسعة section تلاتة ع ستة
+
+76
+00:11:53,320 --> 00:12:04,400
+لت XIN و YIN بيكونوا عاملين من عاملين من عاملين من
+
+77
+00:12:04,400 --> 00:12:06,860
+عاملين من عاملين من عاملين من عاملين من عاملين من
+
+78
+00:12:06,860 --> 00:12:09,100
+عاملين من عاملين من عاملين من عاملين من عاملين من
+
+79
+00:12:09,100 --> 00:12:22,440
+عاملين من عاملين
+
+80
+00:12:31,890 --> 00:12:44,270
+مطلوب الأول هو show if limit yn بساوي infinity
+
+81
+00:12:44,270 --> 00:12:51,370
+then limit
+
+82
+00:12:51,370 --> 00:12:53,590
+xn بساوي infinity
+
+83
+00:12:56,820 --> 00:13:10,660
+والجزء التاني show if x in is bounded then
+
+84
+00:13:10,660 --> 00:13:15,680
+limit
+
+85
+00:13:15,680 --> 00:13:25,600
+y in is serviceable طبعا
+
+86
+00:13:30,880 --> 00:13:39,520
+في برهانين لل ..
+
+87
+00:13:39,520 --> 00:13:47,540
+لل exercise هذا البرهان الأول باستخدام
+
+88
+00:13:47,540 --> 00:13:55,580
+exercise 7 اللي جابله يعني هنا since
+
+89
+00:13:55,580 --> 00:14:04,790
+من الفرض لما انه limitxn على yn as n tends to
+
+90
+00:14:04,790 --> 00:14:15,150
+infinity بساوي plus infinity then by exercise
+
+91
+00:14:15,150 --> 00:14:24,790
+تلاتة section تلاتة ستة if limit sequence بساوي
+
+92
+00:14:24,790 --> 00:14:30,780
+infinityبطلع limit مقلوب الـ sequence اللي هو y in
+
+93
+00:14:30,780 --> 00:14:40,920
+على x and as n tends to infinity بساوي سبعة now
+
+94
+00:14:40,920 --> 00:14:44,480
+apply
+
+95
+00:14:44,480 --> 00:14:47,900
+exercise
+
+96
+00:14:47,900 --> 00:14:55,940
+رقم سبعة section تلاتة ستة to
+
+97
+00:14:55,940 --> 00:14:56,340
+get
+
+98
+00:14:59,870 --> 00:15:13,950
+the results in a and b وهذا بيعطيني مرغب لو بصيت و
+
+99
+00:15:13,950 --> 00:15:18,950
+لا ال exercise
+
+100
+00:15:18,950 --> 00:15:25,070
+سبعة في ال exercise سبعة بيقول ده كانت ال limit لل
+
+101
+00:15:25,070 --> 00:15:30,880
+quotientلـ quotient زي هذا بساوي صفر و x in و y in
+
+102
+00:15:30,880 --> 00:15:37,200
+حدودهم موجبة ففي الحالة هذه إذا كانت limit ال
+
+103
+00:15:37,200 --> 00:15:47,200
+sequence اللي تحت convergent إذا
+
+104
+00:15:47,200 --> 00:15:50,240
+كانت limit ال sequence اللي تحت
+
+105
+00:15:56,100 --> 00:16:01,960
+لأ limit ال sequence اللي فوق اللي هي yn هنا
+
+106
+00:16:01,960 --> 00:16:06,040
+infinity فبطلع limit xn بال 7 infinity اللي هو جزء
+
+107
+00:16:06,040 --> 00:16:12,980
+11وكمان اذا كانت ال sequence اللى فى المقام
+
+108
+00:16:12,980 --> 00:16:16,520
+bounded اللى هى x in هنا طبعا فى المقام bounded
+
+109
+00:16:16,520 --> 00:16:21,500
+فرقة ال sequence اللى فى ال bust تطلع يساوي 0 وهذا
+
+110
+00:16:21,500 --> 00:16:25,740
+هو الجزء التانى هذا حسب هذا لو بدنا نستخدم
+
+111
+00:16:25,740 --> 00:16:33,610
+exercise رقم 7 وطبعا لازم نبرهنهلكن ممكن نعطي
+
+112
+00:16:33,610 --> 00:16:39,710
+برهان مباشر بدون ما يستخدم exercise السابعة
+
+113
+00:16:39,710 --> 00:16:49,670
+وبالتالي إذا في حال تاني أو برهان تاني باستخدام
+
+114
+00:16:49,670 --> 00:16:57,900
+التعريفات وال comparison testsباستخدام التعريفات
+
+115
+00:16:57,900 --> 00:17:01,820
+زايد ال comparison tests اختبارات المقارنة ال
+
+116
+00:17:01,820 --> 00:17:09,240
+proof رقم اتنين since
+
+117
+00:17:09,240 --> 00:17:16,820
+اننا ننسى هذا القرآن انا عند هذه الفرض since limit
+
+118
+00:17:16,820 --> 00:17:24,630
+ل xn over yn هذا عبارة عن sequenceلأن الـ limit
+
+119
+00:17:24,630 --> 00:17:33,410
+إلا بالساقر plus infinity then given Alpha أي real
+
+120
+00:17:33,410 --> 00:17:41,610
+number Alpha من تعريف الـ improper convergence
+
+121
+00:17:41,610 --> 00:17:50,030
+لأي Alpha there exists capital N يعتمد على Alpha
+
+122
+00:17:50,030 --> 00:17:56,450
+عدد قضيةبحيث انه يكون M أكبر من أوسع ال capital M
+
+123
+00:17:56,450 --> 00:18:12,950
+بطلع عندي XM على YM أكبر من Alpha طبعا
+
+124
+00:18:12,950 --> 00:18:20,480
+وهذا بيقدي ان XM أكبر من Alpha في YMلما عندي yn
+
+125
+00:18:20,480 --> 00:18:26,120
+هنا موجبة لما أضرب الطرفين في yn التباينة إشارتها
+
+126
+00:18:26,120 --> 00:18:32,340
+تبقى كما هي إذا
+
+127
+00:18:32,340 --> 00:18:40,880
+أنا عندي الان الكلام هذا صحيح لكل n أكبر من أوسع
+
+128
+00:18:40,880 --> 00:18:46,540
+كابتن الان الان
+
+129
+00:18:46,540 --> 00:18:47,360
+by
+
+130
+00:18:49,930 --> 00:18:56,930
+بمعنى الـ Direct Comparison Test بما
+
+131
+00:18:56,930 --> 00:19:02,970
+انه limit yn
+
+132
+00:19:02,970 --> 00:19:04,130
+بالساوي infinity
+
+133
+00:19:25,130 --> 00:19:33,010
+ناخد alpha في واحد ممكن
+
+134
+00:19:33,010 --> 00:19:37,750
+اه ناخد alpha في واحد صح دي من ال alpha دي ثاني
+
+135
+00:19:37,750 --> 00:19:49,320
+واحد يعني ثاني ال R مظبوط فده واحد وبتاني واحدبما
+
+136
+00:19:49,320 --> 00:19:54,600
+ان ال limit ل yn
+
+137
+00:19:54,600 --> 00:20:02,180
+بساوي infinity نحن نحصل على limit ل xn بساوي
+
+138
+00:20:02,180 --> 00:20:06,640
+infinity لان هذا بثبت الجزء الأول انت بدك الجزء
+
+139
+00:20:06,640 --> 00:20:08,160
+التاني صح؟ طيب
+
+140
+00:20:15,760 --> 00:20:19,840
+بنشوف الجزء التاني إذا كانت ال sequence x in
+
+141
+00:20:19,840 --> 00:20:27,400
+bounded فبنلمط y in بسرعه نصف طيب
+
+142
+00:20:27,400 --> 00:20:32,420
+الجزء
+
+143
+00:20:32,420 --> 00:20:43,340
+دي since x in is bounded إذن
+
+144
+00:20:43,340 --> 00:20:48,760
+في عدد موجبThere exists m positive number بحيث انه
+
+145
+00:20:48,760 --> 00:20:57,360
+absolute xm أصغر من أو ساوي m لكل m في n هذا من
+
+146
+00:20:57,360 --> 00:21:05,280
+تعريف الboundary نفسي طيب بالمنفذ بتاعنا ايه؟ ان
+
+147
+00:21:05,280 --> 00:21:16,480
+ال limit ل ym بساعة صفر طيب to showlimit yn بساوي
+
+148
+00:21:16,480 --> 00:21:23,260
+zero let epsilon بنستخدم تعريف epsilon capital M
+
+149
+00:21:23,260 --> 00:21:32,060
+لإن هي let epsilon أكبر من الصفر be given من
+
+150
+00:21:32,060 --> 00:21:39,100
+epsilon على M بيطلع عدد موجب من
+
+151
+00:21:41,390 --> 00:21:52,910
+العدد الموجب يعتمد
+
+152
+00:21:52,910 --> 00:21:58,830
+على إبسلون على م يعتبر
+
+153
+00:21:58,830 --> 00:22:01,590
+إبسلون على م
+
+154
+00:22:16,450 --> 00:22:24,150
+أنا عندي ايش عندي بدي
+
+155
+00:22:24,150 --> 00:22:31,170
+أثبت ان limit yn بالساوي سفر فخلينا نشوف
+
+156
+00:22:43,720 --> 00:22:54,900
+طيب أنا لازم أستخدم .. آه لازم أستخدم ..
+
+157
+00:22:54,900 --> 00:23:01,840
+طيب since ..
+
+158
+00:23:01,840 --> 00:23:06,820
+طيب بس هنا يعني خليني أقول since
+
+159
+00:23:11,850 --> 00:23:20,390
+بما أن ال limit ل yn على xn as n tends to infinity
+
+160
+00:23:20,390 --> 00:23:24,410
+أنا عندي المقلوب هذا ال limit تبعته infinity، هذا
+
+161
+00:23:24,410 --> 00:23:29,890
+ال limit تبعته سفر وهي عندي epsilon على m عدد موجة
+
+162
+00:23:29,890 --> 00:23:36,150
+given، there exists capital M يعتمد على epsilon
+
+163
+00:23:36,150 --> 00:23:47,110
+على mعدد طبيعي لحيث انه لكل n أكبر من أوسع ال
+
+164
+00:23:47,110 --> 00:23:56,850
+capital N بيطلع عندي absolute yn على xn minus ال
+
+165
+00:23:56,850 --> 00:24:05,850
+zero أصغر من epsilon على n تمام؟
+
+166
+00:24:07,690 --> 00:24:27,750
+طب ما هذا بيقدي فانا
+
+167
+00:24:27,750 --> 00:24:32,910
+بدي اثبت انه limit yn بالساو ستر يعني بدي اثبت انه
+
+168
+00:24:32,910 --> 00:24:38,980
+ال absolute valueلو كان n أكبر من أو ساوي capital
+
+169
+00:24:38,980 --> 00:24:44,920
+N بتثبت أن ال absolute value ل y in minus 0 أصغر
+
+170
+00:24:44,920 --> 00:24:50,020
+من epsilon عشان أثبت أن ال limit ل y in بساوي سفر
+
+171
+00:24:50,020 --> 00:24:55,520
+بتثبت أن ال absolute value ل y in minus 0 أصغر من
+
+172
+00:24:55,520 --> 00:25:00,500
+ال given epsilon طيب
+
+173
+00:25:00,500 --> 00:25:12,970
+هذا بساوي absoluteYn بيساوي أبقى عن Xn ضرب Yn
+
+174
+00:25:12,970 --> 00:25:26,270
+على Xn minus zero و هذا بيساوي absolute Xn في
+
+175
+00:25:26,270 --> 00:25:30,170
+absolute Yn على Xn
+
+176
+00:25:37,650 --> 00:25:44,410
+بتكون موضوع ممكن نحط سارة zero هنا طيب
+
+177
+00:25:44,410 --> 00:25:51,510
+هذا لكل N هذا أصغر من أو يساوي M وال absolute
+
+178
+00:25:51,510 --> 00:25:56,570
+value هذه لكل N أكبر من أو يساوي capital N هذا
+
+179
+00:25:56,570 --> 00:26:05,270
+أصغر من إبسلون على M إبسلون على M مش هبقى M مع N
+
+180
+00:26:05,270 --> 00:26:14,790
+بقى اللي عندي إبسلونطبعا؟ طيب since أكبر من السفر
+
+181
+00:26:14,790 --> 00:26:25,310
+was arbitrarily we get انه limit ل y in as in tens
+
+182
+00:26:25,310 --> 00:26:29,650
+of infinity بساوي zero و هو المفروض يعني هذا بيكمل
+
+183
+00:26:29,650 --> 00:26:35,380
+برعان الجزء بيه okay طبعا؟هذا على اعتبار ان احنا
+
+184
+00:26:35,380 --> 00:26:41,300
+exercise سبعة ما بنعرفوش بس في كل الأحوال احنا
+
+185
+00:26:41,300 --> 00:26:47,300
+استخدمنا exercise ثلاثة طبعا
+
+186
+00:26:47,300 --> 00:26:54,400
+هكذا بنثبت تسعة و سبعة بالمناسبة زيه بنفس الطريقة
+
+187
+00:26:54,400 --> 00:27:01,020
+بافكار مشابه ممكن اثباته بنفس السلوب بنفس النمط
+
+188
+00:27:03,510 --> 00:27:09,270
+كمان في أي أسئلة تانية في section تلاتة سبعة؟ إذا
+
+189
+00:27:09,270 --> 00:27:15,430
+مافيش خلينا ننتقل ل section تلاتة سبعة تبع
+
+190
+00:27:15,430 --> 00:27:20,110
+ال series هذا في
+
+191
+00:27:20,110 --> 00:27:24,550
+عندكم أي أسئلة في section تلاتة سبعة؟ تلاتة خمسة؟
+
+192
+00:27:24,550 --> 00:27:25,750
+تلاتة سبعة؟
+
+193
+00:27:44,990 --> 00:27:54,110
+في أي أسلة في section تلاتة سبعة أو تلاتة ستة
+
+194
+00:27:54,110 --> 00:28:07,910
+مافيش؟
+
+195
+00:28:07,910 --> 00:28:13,700
+السؤال تلاتة فرصة تلاتة سبعةالسؤال التالت الفارقة
+
+196
+00:28:13,700 --> 00:28:14,320
+السيه؟
+
+197
+00:28:28,470 --> 00:28:33,570
+استخدمت ال partial fractions؟ اه بس مش .. مش كله
+
+198
+00:28:33,570 --> 00:28:37,990
+بالغاية طلعت قيم A و C بيطلعوا نص و نص و B بيطلعوا
+
+199
+00:28:37,990 --> 00:28:43,770
+سالم واحد و بعد ما جيت اكمل مش كل الحدود بيطلعوا
+
+200
+00:28:43,770 --> 00:28:48,790
+بالطب معايا زي قمتي لو سؤاليني للجامعة اه عشان
+
+201
+00:28:48,790 --> 00:28:52,310
+هيكون تلات قصور يعني اه
+
+202
+00:28:54,820 --> 00:29:09,900
+بس لازم يكون فيه يعني تلاشي و فيه
+
+203
+00:29:09,900 --> 00:29:18,020
+.. نشوف
+
+204
+00:29:18,020 --> 00:29:22,040
+يعني مافيش تلاشي جيبت الارت برشا الصمت .. فيه
+
+205
+00:29:22,040 --> 00:29:26,940
+تلاشي بس فيه بيضغط اه بخلينا نشوفخلّيني أجرب
+
+206
+00:29:26,940 --> 00:29:44,520
+السؤال
+
+207
+00:29:44,520 --> 00:29:47,580
+تلاتة الفرق C سكتشن تلاتة سبعة
+
+208
+00:29:54,860 --> 00:29:59,300
+استخدم الـ partial fractions
+
+209
+00:29:59,300 --> 00:30:03,020
+لإظهار
+
+210
+00:30:03,020 --> 00:30:11,100
+أن عدد الـ infinite series sigma من ن يعني واحد
+
+211
+00:30:11,100 --> 00:30:21,320
+لإنفينيتي الواحد عشان ن في ن اضافة واحد لان اضافة
+
+212
+00:30:21,320 --> 00:30:23,600
+اثنين بساوي واحد اربعة
+
+213
+00:30:32,200 --> 00:30:37,060
+فبدنا نكتب هذا بتحلل و باستخدام ال partial
+
+214
+00:30:37,060 --> 00:30:43,740
+fractions إلى تلت قصور فجدتش
+
+215
+00:30:43,740 --> 00:30:48,080
+فرعة التواردة كانت دي؟ كان الأولى a بتسوي نص يعني
+
+216
+00:30:48,080 --> 00:30:57,340
+نص على n تانية سالب واحد سالب او زاد سالب واحد على
+
+217
+00:30:57,340 --> 00:31:09,270
+n plus one والاخيرة نصنص على n plus two تعالى
+
+218
+00:31:09,270 --> 00:31:18,590
+نحسب ال inf partial sum sn بسعر sigma من k بسعر
+
+219
+00:31:18,590 --> 00:31:31,370
+واحد الى n ل xk اللى هو واحد علىك في ك زائد واحد
+
+220
+00:31:31,370 --> 00:31:40,190
+في ك زائد اتنين بنبدل ن بالك وبعدين
+
+221
+00:31:40,190 --> 00:31:54,030
+هذا عبارة عن سيجما من ك بيسار واحد إلى ن و بنكتب
+
+222
+00:31:54,030 --> 00:31:57,350
+هذا واحد على
+
+223
+00:32:00,560 --> 00:32:07,980
+2k سالب واحد
+
+224
+00:32:07,980 --> 00:32:16,740
+على ك زائد واحد موجب خلينا
+
+225
+00:32:16,740 --> 00:32:21,800
+نحط الحاجات الموجبة مع بعض يعني زائد واحد على
+
+226
+00:32:21,800 --> 00:32:26,360
+اتنين ك زائد اربعة
+
+227
+00:32:28,860 --> 00:32:36,700
+-1 على K-1 و
+
+228
+00:32:36,700 --> 00:32:42,140
+بعدين نكتب أول شوية حدوث مهم جدا اللي كل ثوابت هذه
+
+229
+00:32:42,140 --> 00:32:48,080
+صح يعني في حد تاني جابهم متأكد من صحتهم لإن لو
+
+230
+00:32:48,080 --> 00:32:50,680
+فيهم خطأ مش هنقبلهم و نطلع الجواب
+
+231
+00:33:03,670 --> 00:33:08,910
+فنكتب أول حد هي .. أول حد هيكون لما كيب الساعة
+
+232
+00:33:08,910 --> 00:33:17,090
+واحد .. نص .. هيطلع نص زائد واحد على .. تمانية ..
+
+233
+00:33:17,090 --> 00:33:24,090
+اتنين .. لأ واحد على ستة .. واحد على ستة صح ناقص
+
+234
+00:33:24,090 --> 00:33:26,110
+نص .. سالب نص
+
+235
+00:33:31,480 --> 00:33:38,960
+زاد لحد التاني واحد على تلاتة زاد
+
+236
+00:33:38,960 --> 00:33:41,520
+.. واحد على اربع .. واحد على اربع .. اربع .. الاول
+
+237
+00:33:41,520 --> 00:33:48,800
+واحد على اربع او واحد على اربع الاول و بعدين واحد
+
+238
+00:33:48,800 --> 00:33:53,040
+على .. تمانية .. واحد على تمانية .. تمانية ناقص
+
+239
+00:33:53,040 --> 00:34:03,060
+تلت مايناس تلت طيب قولي بعدهواحد على ستة واحد على
+
+240
+00:34:03,060 --> 00:34:09,380
+ستة واحد على ايه؟ على ستة واحد على عشرة اتنين في
+
+241
+00:34:09,380 --> 00:34:14,500
+تلاتة بستة اه واحد على ستة زائد واحد على عشرة زائد
+
+242
+00:34:14,500 --> 00:34:25,360
+واحد على عشرة minus ربع minus ربع زائد
+
+243
+00:34:25,360 --> 00:34:39,020
+و هكذا الاخر حد هيكون1 على 2n زائد 1 على 2n زائد 4
+
+244
+00:34:39,020 --> 00:34:55,940
+مع بعض و بعدين الثاني 1 على n زائد 1 فنشوف
+
+245
+00:34:55,940 --> 00:35:01,570
+أيش اللي بتلاعش و أيش اللي بيطلععين نص هنا راح عين
+
+246
+00:35:01,570 --> 00:35:07,190
+نص و
+
+247
+00:35:07,190 --> 00:35:20,090
+ربع هنا راح مع الربع هنا قلت
+
+248
+00:35:20,090 --> 00:35:26,030
+لك هذا مش هيروح مع حد صح؟ هذا يبقى
+
+249
+00:35:30,600 --> 00:35:36,960
+لكن الطمن هيروح والصدرس هيروح لإن الصدرس في مجموعة
+
+250
+00:35:36,960 --> 00:35:42,560
+ليه صدرس و الطمن هيجمع ليه الطمن بس برضه هييجي
+
+251
+00:35:42,560 --> 00:35:46,620
+ناقص واحد على تمانية و هيظل واحد على تمانية فيه؟
+
+252
+00:35:46,620 --> 00:35:51,220
+اه لما نقعد بالقمة سوى سبعة هيطلع اننا ناقص واحد
+
+253
+00:35:51,220 --> 00:35:54,040
+على تمانية اه اشي ناقص واحد على تمانية
+
+254
+00:35:56,980 --> 00:36:01,600
+و ممكن كمان برز واحد على ستة او في برز واحد على
+
+255
+00:36:01,600 --> 00:36:08,020
+ستة سيطلع سالب واحد على ستة لإن بيساوي خمسة سيطلع
+
+256
+00:36:08,020 --> 00:36:14,700
+ثاندي سالب واحد على ستة فمين اللي بيضل على المحدود
+
+257
+00:36:14,700 --> 00:36:21,140
+يعني
+
+258
+00:36:21,140 --> 00:36:33,420
+بتاعي هذا ستس هيبقى هذا هيروحو هذا هيروحك يعني
+
+259
+00:36:33,420 --> 00:36:39,600
+شو اللي بضلف الآخر يعني
+
+260
+00:36:39,600 --> 00:36:46,060
+انا بتاعي اللي هيضلف الآخر اللي هو يمكن السدر
+
+261
+00:36:46,060 --> 00:36:53,860
+السادى ناقص تلت ناقص تلت و هنا
+
+262
+00:36:58,270 --> 00:37:05,290
+كل حد بيروح مع ادم فوضوح يروح مع اللي بعده فمش
+
+263
+00:37:05,290 --> 00:37:15,870
+هيروح مع حد فهيبقى واحد على اتنين يعني و
+
+264
+00:37:15,870 --> 00:37:19,030
+.. ايش هبقى كمان؟
+
+265
+00:37:30,970 --> 00:37:36,990
+هذا هيروح هيبقى له اتنين هدول اتالي ايه مظلوم زاد
+
+266
+00:37:36,990 --> 00:37:51,870
+واحد على اتنين ام زاد اربع سدس
+
+267
+00:37:51,870 --> 00:37:59,410
+minus تلت تطلع minus سدس وهذا مروح من صفر مش مظلوم
+
+268
+00:38:08,750 --> 00:38:15,650
+المفروض ال limit تطلع ربعها بالتالي
+
+269
+00:38:15,650 --> 00:38:19,710
+لازم احنا نكتب مزيد من الحدود عشان نشوف كيف النمط
+
+270
+00:38:19,710 --> 00:38:22,150
+.. كيف النمط هيصير
+
+271
+00:38:27,470 --> 00:38:34,430
+فبدأ عملية grouping للحدود تجميع ويعني حصول علامات
+
+272
+00:38:34,430 --> 00:38:41,310
+معينة مش عارف انا مش متأكد ان هذا هتكون صح يمكن
+
+273
+00:38:41,310 --> 00:38:55,770
+في شغلات تانية بتبقى واحنا ماذكرناش فال
+
+274
+00:38:55,770 --> 00:38:56,090
+..
+
+275
+00:38:59,080 --> 00:39:04,640
+ذا بده فحص اه فخلينا نقول try it again try it
+
+276
+00:39:04,640 --> 00:39:07,780
+again
+
+277
+00:39:07,780 --> 00:39:17,200
+خلينا نحاول فيه مرة تانية و نحاول يعني نقدر نخلي
+
+278
+00:39:17,200 --> 00:39:22,740
+يعني هذا يساوي ربع او يساوي حاجة ال limit بقتها في
+
+279
+00:39:22,740 --> 00:39:26,480
+النهاية هتطلع ربعوبالتالي ال limit لل sequence of
+
+280
+00:39:26,480 --> 00:39:29,180
+partial sums هيطلع ربعه وبالتالي ال series
+
+281
+00:39:29,180 --> 00:39:33,000
+conversion مجموعة بساوي ال limit لل partial sums
+
+282
+00:39:33,000 --> 00:39:38,700
+فهذا يعني مشكوك فيه شكله مش صح نحاول مرة تانية فيه
+
+283
+00:39:38,700 --> 00:39:43,100
+و بعدين نشوف يعني كيف مين اللي بصل للجواب الصح
+
+284
+00:39:43,100 --> 00:39:48,720
+نحاول نكتبه مرة تانية okay تمام لكن يعني ماهواش
+
+285
+00:39:48,720 --> 00:39:53,570
+مستحيل أو ماهواش يعني صعبممكن اي واحد يتواصل اليه
+
+286
+00:39:53,570 --> 00:39:58,990
+بس بده ايه مزيد من الحدود والاستنتاج نمط معين
+
+287
+00:39:58,990 --> 00:40:04,370
+فخلينا نسيبكم تفكروا فيه كمان مرة في اسئلة تانية
+
+288
+00:40:04,370 --> 00:40:08,990
+في ال section هذا فحاولوا
+
+289
+00:40:08,990 --> 00:40:11,170
+تفكروا فيه في اسئلة تانية
+
+290
+00:40:17,700 --> 00:40:21,980
+في أسئلة تانية في section تلاتة سبعة أو السكاشن
+
+291
+00:40:21,980 --> 00:40:32,680
+السابقة اللى تسبقه تلاتة ستة تلاتة خمسة في
+
+292
+00:40:32,680 --> 00:40:38,140
+كتير أسئلة يعني مطلوبة منكم واضح أن انتم مش محضرين
+
+293
+00:40:38,140 --> 00:40:42,420
+ولا دارسين الموضوع وبالتالي ماعندكم مش أسئلة
+
+294
+00:40:46,220 --> 00:40:54,880
+فإلى أن يكون عندكم أسئلة بنكمل المناقشة يوم السبت
+
+295
+00:40:54,880 --> 00:40:59,860
+الجاي أو تحضروا المناقشة مع الشعبة التانية يوم
+
+296
+00:40:59,860 --> 00:41:05,140
+الأربع خلينا
+
+297
+00:41:05,140 --> 00:41:14,690
+نرجع لل limits of functions وناخد المثال الأخيرفي
+
+298
+00:41:14,690 --> 00:41:16,930
+ال section هداك
+
+299
+00:41:46,290 --> 00:41:50,970
+المرة الجاية دخلنا اثبتنا
+
+300
+00:41:50,970 --> 00:42:02,310
+ان ال limit اثبتنا
+
+301
+00:42:02,310 --> 00:42:05,450
+ان ال candy انتي مثال رقم 2
+
+302
+00:42:08,630 --> 00:42:15,350
+لسفر function ل X لما X تقول لسفر does not exist
+
+303
+00:42:15,350 --> 00:42:19,270
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+304
+00:42:19,270 --> 00:42:21,290
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+305
+00:42:21,290 --> 00:42:21,570
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+306
+00:42:21,570 --> 00:42:21,890
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+307
+00:42:21,890 --> 00:42:22,210
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+308
+00:42:22,210 --> 00:42:22,610
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+309
+00:42:22,610 --> 00:42:25,970
+أخدنا هذا و أخدنا هذا و أخدنا هذا و أخدنا هذا و
+
+310
+00:42:25,970 --> 00:42:33,830
+أخدنا هذا و أخدنا
+
+311
+00:42:33,830 --> 00:42:46,640
+هذا و أوحد على X لما X تقول لسفر does not exist in
+
+312
+00:42:46,640 --> 00:42:50,400
+R فلبرحان
+
+313
+00:42:50,400 --> 00:42:56,700
+ذلك let
+
+314
+00:42:56,700 --> 00:43:04,380
+F of X تساوي صين واحد على X و X لا تساوي سفر
+
+315
+00:43:10,730 --> 00:43:16,210
+و بعدين we consider two
+
+316
+00:43:16,210 --> 00:43:20,870
+sequences واحدة
+
+317
+00:43:20,870 --> 00:43:33,750
+xn الحد لعام تبعها أدارة عن واحد على واحد
+
+318
+00:43:33,750 --> 00:43:38,030
+على n πاي و n ينتمي ل z
+
+319
+00:43:41,720 --> 00:43:47,620
+و Yn لحد الآن تبعها واحد على πاي على تمين زاد
+
+320
+00:43:47,620 --> 00:43:56,020
+اتنين N πاي و N ينتمي الى Z هذا عبارة عن Sequences
+
+321
+00:43:56,020 --> 00:44:01,300
+of positive numbers
+
+322
+00:44:04,950 --> 00:44:12,130
+واضح ان ال limit ل xn as n tends to infinity بساوي
+
+323
+00:44:12,130 --> 00:44:20,290
+0 وكذلك ال limit ل yn لما n تقول infinity برضه
+
+324
+00:44:20,290 --> 00:44:24,730
+بساوي 0 لان المقان لما n تقول infinity المقان
+
+325
+00:44:24,730 --> 00:44:32,090
+بيروح ل infinity طيب
+
+326
+00:44:32,090 --> 00:44:33,690
+الآن ال limit
+
+327
+00:44:37,860 --> 00:44:42,420
+الـ image لـ sequence xn لما n تقول الانفلتين
+
+328
+00:44:42,420 --> 00:44:55,500
+بساوي ال limit ل sign xn لما n تقول الانفلتين وهذا
+
+329
+00:44:55,500 --> 00:45:05,620
+بساوي ال limit ل sign n في pi لما n تقول الانفلتين
+
+330
+00:45:06,340 --> 00:45:16,300
+Sin N في Pi بساوي واحد بساوي سفر لكل N وبالتالي
+
+331
+00:45:16,300 --> 00:45:21,640
+هذا بساوي limit ال sequence سفر لما N طولة
+
+332
+00:45:21,640 --> 00:45:32,600
+infinity بساوي سفر and limit
+
+333
+00:45:33,900 --> 00:45:41,360
+الإمج للسيكوينس YM لما N تقول انفينيتي بساوي limit
+
+334
+00:46:08,450 --> 00:46:16,370
+وهذا المفروض يكون sign
+
+335
+00:46:16,370 --> 00:46:24,840
+1 على xn وهذا المفروض يكون sign 1 على ynمقلوب y in
+
+336
+00:46:24,840 --> 00:46:34,540
+بيطلع بساوي πاية اتنين ازايد اتنين in πاية وهذا
+
+337
+00:46:34,540 --> 00:46:44,040
+المقدار دايما بساوي واحد لكل in اذا انا في عندي
+
+338
+00:46:44,040 --> 00:46:51,770
+limit لل sequence بالحد العام تبعها واحدالسيكوانس
+
+339
+00:46:51,770 --> 00:46:57,670
+تابعة واحد وهذا بالساوية واحد ان ان انا في عندي
+
+340
+00:46:57,670 --> 00:47:03,710
+two sequences Xm تقولها سفر و limit صورتها
+
+341
+00:47:03,710 --> 00:47:09,050
+بالساوية سفر و في عندي سيكوانس تانية Ym ال limit
+
+342
+00:47:09,050 --> 00:47:13,650
+تبعتها ايضا بالساوية سفر لكن limit صورتها بالساوية
+
+343
+00:47:13,650 --> 00:47:17,310
+واحد وبالتالي
+
+344
+00:47:20,360 --> 00:47:28,340
+by sequential criterion ال
+
+345
+00:47:28,340 --> 00:47:35,480
+limit لل function f of x لما x تقول ل0 does not
+
+346
+00:47:35,480 --> 00:47:46,440
+exist in R مش ممكن تكون موجودة في R لأن
+
+347
+00:47:46,440 --> 00:47:53,900
+لو كانت ال limit هذه موجودةفالمفروض limit صورة xn
+
+348
+00:47:53,900 --> 00:48:02,060
+بما أن xn تقول السفر نكتب
+
+349
+00:48:02,060 --> 00:48:07,180
+since otherwise لأن
+
+350
+00:48:07,180 --> 00:48:14,780
+لو كلاك ذلك لو كانت هذه موجودة if limit
+
+351
+00:48:20,170 --> 00:48:25,210
+فى limit ل F of X لما X تقول لسة exist
+
+352
+00:48:32,710 --> 00:48:39,990
+then المفروض ال limit ل f of x n لما n تقول
+
+353
+00:48:39,990 --> 00:48:47,270
+infinity بتساوي ال limit ل f of y n as n tends to
+
+354
+00:48:47,270 --> 00:48:57,070
+infinity وهذا مستحيل which is impossible وهذا زي
+
+355
+00:48:57,070 --> 00:49:03,150
+ما شوفنا مستحيل impossibleلأن طولها limit f of x
+
+356
+00:49:03,150 --> 00:49:09,390
+in بالساوي سفر و limit f of y in بالساوي واحد إذن
+
+357
+00:49:09,390 --> 00:49:13,470
+هنا استخدمنا sequential criterion في إثبات إن ال
+
+358
+00:49:13,470 --> 00:49:17,330
+limit لل function f of x بالساوي صين واحد على x
+
+359
+00:49:17,330 --> 00:49:24,490
+غير موجودة عند السفر طيب
+
+360
+00:49:24,490 --> 00:49:30,120
+هناخد break خمس دقايق و بعدين نواصلالمحاضرة
+
+361
+00:49:30,120 --> 00:49:31,840
+التانية
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/8Xs3EWM1_9g_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/8Xs3EWM1_9g_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e611318aa053aee6e767730ecf81d8fef433fd01
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/8Xs3EWM1_9g_raw.srt
@@ -0,0 +1,896 @@
+1
+00:00:21,620 --> 00:00:25,660
+طيب ناخد أمثلة
+
+2
+00:00:25,660 --> 00:00:31,280
+كيف نجيب ال supremum و ال infimum لمجموعات جزئية
+
+3
+00:00:31,280 --> 00:00:36,300
+من مجموعة الأعداد الحقيقية فلو أخدت الفترة المغلقة
+
+4
+00:00:36,300 --> 00:00:42,660
+من سفر لواحد فعايز أفبت claim هنا ادعي ان ال
+
+5
+00:00:42,660 --> 00:00:48,540
+supremum لست اسم سار واحدلبرهان ذلك حسب تعريف ال
+
+6
+00:00:48,540 --> 00:00:53,320
+supremum اللي هو least upper bound لازم أثبت شرطين
+
+7
+00:00:53,320 --> 00:00:59,140
+أول شي الواحد upper bound ل S وهذا صحيح واضح واحد
+
+8
+00:00:59,140 --> 00:01:03,860
+is upper bound لمجموع S لأن الواحد أكبر من أو
+
+9
+00:01:03,860 --> 00:01:08,930
+يساوي كل العناصر اللي في الفترة صح؟إذاً واحد upper
+
+10
+00:01:08,930 --> 00:01:13,170
+bound الآن لإثبات أن واحد هو أصغر upper bound ال
+
+11
+00:01:13,170 --> 00:01:16,950
+supremum يعني لازم أثبته أن واحد أصغر من أو ساوي
+
+12
+00:01:16,950 --> 00:01:25,170
+أي upper bound فلو خدنا V V any upper bound فال V
+
+13
+00:01:25,170 --> 00:01:28,310
+أكبر من أو ساوي كل العناصر اللي هنا من ضمنها
+
+14
+00:01:28,310 --> 00:01:33,530
+الواحدإذن ال V أكبر من أو ساوي ال واحد الان واحد
+
+15
+00:01:33,530 --> 00:01:38,230
+upper bound والواحد أصغر من أو ساوي أي upper bound
+
+16
+00:01:38,230 --> 00:01:43,910
+V إذن ال واحد هو ال supremum إذن هيك أثبتنا إن
+
+17
+00:01:43,910 --> 00:01:49,390
+واحد هو ال supremum بالمثل ممكن أثبات إن العنصر أو
+
+18
+00:01:49,390 --> 00:01:54,170
+العدد سفر هو ال infimum للفترة المغلقة من سفر إلى
+
+19
+00:01:54,170 --> 00:02:00,850
+واحدطيب مثال تاني لو أخدت T هي الفترة المفتوحة من
+
+20
+00:02:00,850 --> 00:02:11,950
+0 ل1 فبرضه كمان لو
+
+21
+00:02:11,950 --> 00:02:18,030
+أخدت T هي الفترة المفتوحة من 0 ل1 فممكن أثبات أن
+
+22
+00:02:18,030 --> 00:02:23,970
+ال supremum ل T هو 1واضح ان الواحد upper bound
+
+23
+00:02:23,970 --> 00:02:29,030
+للست للفترة المفتوحة لأن واحد أكبر من أو ساوي كل
+
+24
+00:02:29,030 --> 00:02:34,390
+ال X اللي هنا هذا واضح الان لإثبات أن الواحد هذا
+
+25
+00:02:34,390 --> 00:02:37,310
+هو ال supremum في لمّة واحد اتناش خدناها المرة
+
+26
+00:02:37,310 --> 00:02:42,070
+اللي فاتت بتقول عشان ال upper bound واحد يكون هو
+
+27
+00:02:42,070 --> 00:02:47,310
+ال supremum لازم أثبت أنه في شرط لكل ابسلون أكبر
+
+28
+00:02:47,310 --> 00:02:56,120
+من السفر يوجدعنصر S Y في السفر S أو T هنا بحيث أنه
+
+29
+00:02:56,120 --> 00:03:02,300
+واحد سالب ال epsilon أصغر من S epsilon فهنثبت
+
+30
+00:03:02,300 --> 00:03:07,900
+الكلام هذا إذن هنا هينبدأ let epsilon أكبر من
+
+31
+00:03:07,900 --> 00:03:11,940
+السفر be given لأن ال epsilon هذا ممكن يكون أصغر
+
+32
+00:03:11,940 --> 00:03:17,980
+من أو ساوي الواحد أو أكبر من أو أكبر من الواحد
+
+33
+00:03:20,030 --> 00:03:22,970
+الإبسلون هذا عدد موجب ممكن جدا يكون أصغر من أو
+
+34
+00:03:22,970 --> 00:03:26,170
+ساوي الواحد أو أكبر من واحد ناخد الحالة الأولى، لو
+
+35
+00:03:26,170 --> 00:03:30,770
+إبسلون أصغر من أو ساوي الواحد فحاخد S إبسلون، أعرف
+
+36
+00:03:30,770 --> 00:03:36,330
+S إبسلون واحد سالب إبسلون على اتنين هذا العدد
+
+37
+00:03:36,330 --> 00:03:41,350
+بيطلع عدد أكبر من سفر وأصغر من واحد وبالتالي ينتمي
+
+38
+00:03:41,350 --> 00:03:45,510
+لتين الآن
+
+39
+00:03:45,510 --> 00:03:53,380
+لو أخدت واحد وطرحت منها إبسلونفهذا بيطلع أصغر يعني
+
+40
+00:03:53,380 --> 00:03:59,840
+لو أخدت واحد و طرحت منها epsilon فهذا أصغر من واحد
+
+41
+00:03:59,840 --> 00:04:06,500
+سالب epsilon ع اتنين هذا طرحت منه عدد أكبر من هذا
+
+42
+00:04:06,500 --> 00:04:17,080
+لذا هذا أصغر من التاني و بعدين ليش يقصر؟ طب
+
+43
+00:04:17,080 --> 00:04:25,100
+ما هذا هو S epsilonهذا هو سإبسلون إذا
+
+44
+00:04:25,100 --> 00:04:30,160
+في الحالة هذه لأي إبسلون أكبر من السفر هين أثبتت
+
+45
+00:04:30,160 --> 00:04:36,740
+إن يوجد سإبسلون في T وهذا الـ S إبسلون أكبر من
+
+46
+00:04:36,740 --> 00:04:40,600
+واحد سالب إبسلون أو واحد سالب إبسلون أصغر من S
+
+47
+00:04:40,600 --> 00:04:47,480
+إبسلون هذا هو الشرط اللي في لمبة واحد اتناش هينتقل
+
+48
+00:04:48,090 --> 00:04:52,170
+الحالة التانية، لو كان إمسنان أكبر من واحد فأكيد
+
+49
+00:04:52,170 --> 00:04:56,050
+واحد سالب إمسنان هيطلع عدد سالب، يعني أصغر من سفر،
+
+50
+00:04:56,050 --> 00:05:01,930
+وال X هذا .. ال X هذا لو أخدت أي X في T فأي X في T
+
+51
+00:05:01,930 --> 00:05:06,300
+موجب، أي X في T موجبإذن هين أثبتنا في الحالة
+
+52
+00:05:06,300 --> 00:05:13,160
+التانية إنه لو كان epsilon أكبر من واحد فبطلع مش
+
+53
+00:05:13,160 --> 00:05:18,620
+يوجد S epsilon واحد في T كل عناصر ال T بتحقق إنه
+
+54
+00:05:18,620 --> 00:05:24,120
+واحد سالب epsilon أصغر من S أو S epsilon وبالتالي
+
+55
+00:05:24,120 --> 00:05:28,420
+في كلتال حالتين ال both cases الشرط تبع لما واحد
+
+56
+00:05:28,420 --> 00:05:33,490
+اتناشر تبع ال supremum اللي بكافئ ال supremumمتحقق
+
+57
+00:05:33,490 --> 00:05:39,810
+وبالتالي واحد هو ال supremum لتين مثال
+
+58
+00:05:39,810 --> 00:05:46,710
+تالت احنا شفنا قبل شوية في بداية المحاضرة ان كل
+
+59
+00:05:46,710 --> 00:05:51,510
+عدد حقيقي هو upper bound و كذلك lower bound
+
+60
+00:05:51,510 --> 00:05:57,070
+للمجموع الخالي Phi و بناء على ذلك Phi does not
+
+61
+00:05:57,070 --> 00:06:00,730
+have a supremum ولا infimum
+
+62
+00:06:03,600 --> 00:06:14,960
+هي برهان فاي has no .. فاي has no supremum البرهان
+
+63
+00:06:14,960 --> 00:06:19,380
+proof assume
+
+64
+00:06:19,380 --> 00:06:24,240
+you
+
+65
+00:06:24,240 --> 00:06:32,620
+belong to R is supremum فاي ال least upper bound
+
+66
+00:06:32,620 --> 00:06:33,120
+لفاي
+
+67
+00:06:40,890 --> 00:06:53,830
+then u سالب واحد أصغر من u and u سالب واحد هاد عدد
+
+68
+00:06:53,830 --> 00:07:00,610
+حقيقي is upper bound
+
+69
+00:07:00,610 --> 00:07:13,110
+of ال fiveكمان مرة نفرض ان U جد U نفرض
+
+70
+00:07:13,110 --> 00:07:21,590
+ان U جد U جد U بالنمط R و هو Supremum ل Phi طيب U
+
+71
+00:07:21,590 --> 00:07:27,000
+سالب واحد أصغر من Uو قبل شوية كنا ملاحظة ان اي عدد
+
+72
+00:07:27,000 --> 00:07:32,440
+حقيقي زي هذا عبارة عن upper bound لفائي ف K في ال
+
+73
+00:07:32,440 --> 00:07:37,080
+U .. K في ال U هو ال supremum K في ال U هو ال
+
+74
+00:07:37,080 --> 00:07:40,580
+supremum هو أصغر upper bound و في upper bound أصغر
+
+75
+00:07:40,580 --> 00:07:47,260
+منه هذا بدي تناقض which
+
+76
+00:07:47,260 --> 00:07:52,340
+.. which is a contradiction
+
+77
+00:07:59,520 --> 00:08:04,320
+إن هذا بدّيني تناقض وبالتالي هذا أثبات أن الـ Fi
+
+78
+00:08:04,320 --> 00:08:10,700
+مالهاش Supremum بالمثل ممكن أثبات أن الـ Fi أو
+
+79
+00:08:10,700 --> 00:08:20,420
+المجموعة الخالية ليس لها Supremum طيب
+
+80
+00:08:20,420 --> 00:08:22,620
+نيجي لل completeness property
+
+81
+00:08:29,610 --> 00:08:34,370
+الـ completeness property of R بتنص على إنه كل
+
+82
+00:08:34,370 --> 00:08:40,990
+مجموعة غير خالية .. كل مجموعة غير خالية S من R و
+
+83
+00:08:40,990 --> 00:08:45,010
+bounded above .. و bounded above محدودة من أعلى
+
+84
+00:08:45,010 --> 00:08:50,430
+has supremum لازم يكون فيه لها supremum يعني مثال
+
+85
+00:08:50,430 --> 00:08:57,580
+على ذلك لو أخدنا S بسبب الفترة المغلقة 01 أوالفترة
+
+86
+00:08:57,580 --> 00:09:04,960
+مفتوحة من صفر واحد فهي هذي set و bounded above اذا
+
+87
+00:09:04,960 --> 00:09:10,960
+ال property بتقولي بتضمنلي تضمن ان هذي ال set لها
+
+88
+00:09:10,960 --> 00:09:15,840
+soprano اللي هو الواحد اللي اثبتناه قبل شوية اذا
+
+89
+00:09:15,840 --> 00:09:19,700
+ال property بتضمن وجود soprano لكن ما بتجيبليها
+
+90
+00:09:19,700 --> 00:09:26,050
+ولا بتقوليإيش هو؟ عشان نجيبه لازم نعمل برهان زي ما
+
+91
+00:09:26,050 --> 00:09:30,310
+شوفنا في الأمثلة السابقة هد هي ال supremum أو ال
+
+92
+00:09:30,310 --> 00:09:33,790
+completeness property خاصية التمام للأعداد
+
+93
+00:09:33,790 --> 00:09:38,510
+الحقيقية الآن زي ما قلتلكم قبل هيك في توقع ما بين
+
+94
+00:09:38,510 --> 00:09:42,130
+ال upper bounds و ال lower bounds ال supremums و
+
+95
+00:09:42,130 --> 00:09:52,510
+ال infimumsفال .. ال .. اي خاصية صحيحة لل supreme
+
+96
+00:09:52,510 --> 00:09:58,170
+بتكون في بقابلها خاصية صحيحة لل infimum ففي نتيجة
+
+97
+00:09:58,170 --> 00:10:03,640
+هنا على completeness property corollaryبنسميها الـ
+
+98
+00:10:03,640 --> 00:10:07,580
+infimum property of R لإن في supremum property of
+
+99
+00:10:07,580 --> 00:10:12,260
+R وفي بقبلها infimum property of R فال infimum
+
+100
+00:10:12,260 --> 00:10:16,160
+property of R بتقول ان every non-empty subset S of
+
+101
+00:10:16,160 --> 00:10:21,160
+R which is bounded below has an infimum يعني كل
+
+102
+00:10:21,160 --> 00:10:26,440
+مجموعة غير خالية من العداد الحقيقية ومحصورة من
+
+103
+00:10:26,440 --> 00:10:30,460
+أسفل لازم يكون لها infimum أو أكبر حد أدنى
+
+104
+00:10:38,820 --> 00:10:45,060
+وهي البرهان .. نشوف البرهان تبع ال .. ال corollary
+
+105
+00:10:45,060 --> 00:10:54,520
+أو النتيجة هذه بنعرف set .. بنعرف ال set E علي
+
+106
+00:10:54,520 --> 00:10:59,120
+أنها كل العناصر W اللي بتكون lower bound للمجموعة
+
+107
+00:10:59,120 --> 00:11:06,510
+S طيب by hypothesis حسب الفرضالـ E مجموعة غير
+
+108
+00:11:06,510 --> 00:11:09,610
+خالية، يعني فيها على الأقل عنصر، ليه؟ لإن احنا
+
+109
+00:11:09,610 --> 00:11:16,090
+فرضين إن المجموعة S، المجموعة S هذه bounded below،
+
+110
+00:11:16,090 --> 00:11:19,710
+يعني إلها lower bound وبالتالي إذا في على الأقل
+
+111
+00:11:19,710 --> 00:11:24,350
+عنصر واحد، W في E، إذا الـ E مجموعة غير خالية،
+
+112
+00:11:24,350 --> 00:11:25,990
+تمام؟ هذا من الفرض
+
+113
+00:11:29,380 --> 00:11:34,720
+كذلك من الفرض أي X في S ثبار عن upper bound لـ E
+
+114
+00:11:34,720 --> 00:11:49,760
+لو كان X ينتمي إلى S فهذا بيقدّي انه W أصغر من أو
+
+115
+00:11:49,760 --> 00:11:56,160
+يساوي X لكل W في E
+
+116
+00:12:04,760 --> 00:12:11,300
+ليش هذا الكلام صحيح؟ لأن كل W في E عبارة عن lower
+
+117
+00:12:11,300 --> 00:12:17,300
+bound ل S وبما أن W lower bound ل S فأي أنصر في S
+
+118
+00:12:17,300 --> 00:12:23,480
+بيكون أكبر من أو ساوي ال lower bound، صح؟ إذن هذا
+
+119
+00:12:23,480 --> 00:12:28,360
+معناه إن X upper bound هي X أكبر من أو ساوي كل
+
+120
+00:12:28,360 --> 00:12:33,820
+عناصر ال E وبالتالي أي X في S هو عبارة عن
+
+121
+00:12:40,550 --> 00:12:45,910
+أي x في s هو upper bound للست
+
+122
+00:12:51,680 --> 00:12:57,900
+خاصية التمام، إذا ال .. ال set E هذه is bounded
+
+123
+00:12:57,900 --> 00:13:02,580
+above وبالتالي يوجد إلها suprem، ال suprem تبعها
+
+124
+00:13:02,580 --> 00:13:08,100
+لو سميته small s exists in R هذا .. وجود ال suprem
+
+125
+00:13:08,100 --> 00:13:14,560
+مضمون باستخدام ال suprem propertyالان بدنا نثبت ان
+
+126
+00:13:14,560 --> 00:13:21,000
+هذا العدد small s هو الـ infimum هو الـ infimum
+
+127
+00:13:21,000 --> 00:13:27,100
+للست S وهيك بنكون كملنا البرهان إذا الإثبات
+
+128
+00:13:27,100 --> 00:13:33,580
+للادعاء هذا ان عندي ال S هنا بساوي supremum E
+
+129
+00:13:33,580 --> 00:13:40,780
+وبالتالي ال S هذا upper bound ل E يعني S أكبر من
+
+130
+00:13:40,780 --> 00:13:42,340
+أو ساوي كل ال X في E
+
+131
+00:13:46,050 --> 00:13:52,070
+الأن بناء على المتباينة هذه أو الجملة هذه لإثبات
+
+132
+00:13:52,070 --> 00:13:58,610
+أن S هي الـ infimum لcapital S يبقى إثبات أن S
+
+133
+00:13:58,610 --> 00:14:06,830
+عبارة عن lower bound S is a lower bound of S ليش
+
+134
+00:14:06,830 --> 00:14:11,350
+هذا يكفي لإثبات أن S هو الinfimum لS؟
+
+135
+00:14:15,610 --> 00:14:20,590
+تعالى نشوف ليش هذا يكفي يكفي
+
+136
+00:14:20,590 --> 00:14:28,850
+اثبات ان ال S is a lower bound لل 6S يعني بدنا
+
+137
+00:14:28,850 --> 00:14:34,830
+نثبت ان ال X عفوا
+
+138
+00:14:34,830 --> 00:14:43,410
+ال S أصغر من أو ساوي كل العناصر Y
+
+139
+00:14:58,200 --> 00:15:03,540
+يعني بدنا نثبت أن S ينتمي
+
+140
+00:15:03,540 --> 00:15:09,980
+للset E يعني
+
+141
+00:15:09,980 --> 00:15:17,320
+لإثبات أن S is the lower bound of S معناه بد أثبت
+
+142
+00:15:17,320 --> 00:15:20,560
+أن S عنصر في E لأن E is the set of all lower
+
+143
+00:15:20,560 --> 00:15:25,380
+bounds of S صح؟ فلو أثبتت أن S تنتمي إلى E
+
+144
+00:15:34,100 --> 00:15:41,300
+فالمفروض هذا معناه ان ال S .. اه هايه .. لو هذا ال
+
+145
+00:15:41,300 --> 00:15:47,680
+S .. لو هذا ال S أثبتت انه .. لو أثبتت ان ال S هذا
+
+146
+00:15:47,680 --> 00:15:49,380
+ينتمي إلى ايه؟
+
+147
+00:15:52,900 --> 00:15:58,420
+فمعناه ان كل العناصر اللي في E أصغر من أو يساوي ال
+
+148
+00:15:58,420 --> 00:16:04,900
+S طيب كل العناصر X اللي في E هي عبارة عن lower
+
+149
+00:16:04,900 --> 00:16:11,330
+bounds ل Sواذا كان S موجود في E بيكون أيضا lower
+
+150
+00:16:11,330 --> 00:16:17,350
+bound ل S لكن ال S هذا بتمتع بالخاصية أنه أكبر من
+
+151
+00:16:17,350 --> 00:16:22,970
+أو ساوي كل عناصر ال set A إذا هو أكبر lower bound
+
+152
+00:16:22,970 --> 00:16:29,560
+يعني هو ال infimum صح؟ تمام؟مرة تانية احنا وصلنا
+
+153
+00:16:29,560 --> 00:16:35,780
+ان ال X كل العناصر X في E اصغر من او ساوي S الان
+
+154
+00:16:35,780 --> 00:16:42,800
+لو اثبتت ان ال S هذا ينتمي ل E يعني lower bound ل
+
+155
+00:16:42,800 --> 00:16:50,130
+Sمعناته ال S هدى اكبر من او ساوي كل عناصر ال 6E
+
+156
+00:16:50,130 --> 00:16:54,890
+وبالتالي هو اكبر lower
+
+157
+00:16:54,890 --> 00:17:02,450
+bound يعني هو ال infimum اذا فعلا يكفي او يبقى
+
+158
+00:17:02,450 --> 00:17:06,990
+اثبات ان ال S اسمه ال S lower bound لل 6S فلبرهان
+
+159
+00:17:06,990 --> 00:17:11,770
+ذلك بنعمل برهان بالتناقض افرضى انه اللي احنا
+
+160
+00:17:11,770 --> 00:17:18,960
+بنلثبته خطأيعني اسمه ال S ليس lower bound للست S
+
+161
+00:17:18,960 --> 00:17:23,500
+هذا معناه بقدر ألاجي أنصر Y في S و هذا ال Y أصغر
+
+162
+00:17:23,500 --> 00:17:30,600
+من S لأن S ليس lower bound فهذا بيقدي .. لاحظوا أن
+
+163
+00:17:30,600 --> 00:17:35,400
+ال S هو ال supremum ل E .. S هو ال supremum ل E و
+
+164
+00:17:35,400 --> 00:17:42,980
+Y أصغر منه إذن Y هذا مش ممكن يكون upper bound للست
+
+165
+00:17:42,980 --> 00:17:49,920
+Eال Y أصغر من S و S بساوي supremum E إذا Y مش ممكن
+
+166
+00:17:49,920 --> 00:17:54,740
+يكون upper bound ل E لأنه بجوزش هذا يكون upper
+
+167
+00:17:54,740 --> 00:18:00,320
+bound ل E و هذا أصغر upper bound ل E صح؟ طيب إذا
+
+168
+00:18:00,320 --> 00:18:05,980
+ال Y مش ممكن يكون upper bound ل E إذا بقدر ألاقي X
+
+169
+00:18:05,980 --> 00:18:12,160
+في E و هذا ال X أكبر من ال Y هذه المتباينة بتعطيني
+
+170
+00:18:12,160 --> 00:18:12,840
+تناقض
+
+171
+00:18:16,450 --> 00:18:23,870
+تتناقض مع تعريف ال set E كيف X تنتمي ل E كيف ال X
+
+172
+00:18:23,870 --> 00:18:29,510
+تنتمي ل E و في نفس الوجهة X أكبر من عنصر ما اللي
+
+173
+00:18:29,510 --> 00:18:35,010
+هو Y في S يعني ال X هذا ليس lower bound هذا تناقض
+
+174
+00:18:35,010 --> 00:18:40,130
+okay إذا نصل إلى تناقض وبالتالي هذا التناقض بيقول
+
+175
+00:18:40,130 --> 00:18:42,990
+لي أن الفرض الفرض تبعنا هذا
+
+176
+00:18:45,580 --> 00:18:50,800
+إن small s is not lower bound كان فرض خطأ إذا لازم
+
+177
+00:18:50,800 --> 00:19:01,520
+يكون s lower bound وهذا بيكمل برهان ال claim تمام؟
+
+178
+00:19:01,520 --> 00:19:08,040
+في
+
+179
+00:19:08,040 --> 00:19:09,500
+ال section القادم
+
+180
+00:19:12,270 --> 00:19:18,530
+هناخد تطبيقات على الـ supreme property و ال infame
+
+181
+00:19:18,530 --> 00:19:24,410
+property فالتطبيقات
+
+182
+00:19:24,410 --> 00:19:35,230
+هذه هتكون على شكل أمثلة فمثلا
+
+183
+00:19:35,230 --> 00:19:43,410
+أول تطبيقلو أخدت أي subset من R و bounded above و
+
+184
+00:19:43,410 --> 00:19:49,510
+A أي عدد حقيقي فمنعرف A زائد capital S على أنه
+
+185
+00:19:49,510 --> 00:19:54,110
+مجموعة كل العناصر على الصورة A plus X حيث X ينتمي
+
+186
+00:19:54,110 --> 00:20:00,890
+لS الآن ممكن أثبت أن ال supremum للمجموعة هذه هو
+
+187
+00:20:00,890 --> 00:20:04,870
+عبارة عن A زائد ال supremum لS
+
+188
+00:20:07,460 --> 00:20:16,840
+و هذا يعني البرهان مش صعب أيه بسيط وسهل نشوف مع
+
+189
+00:20:16,840 --> 00:20:22,540
+بعض نفرض ان U هو ال suprem ل S ال set S is bounded
+
+190
+00:20:22,540 --> 00:20:28,980
+above، إذن إلها suprem هذا مضمون حسب ال suprem
+
+191
+00:20:28,980 --> 00:20:33,920
+propertyوبالتالي الـ U هذا اللي هو ال supreme هو
+
+192
+00:20:33,920 --> 00:20:38,520
+upper bound ل S إذا U أكبر من أو ساوي كل عناصر ال
+
+193
+00:20:38,520 --> 00:20:45,800
+S إذا لو ضفت A على الطرفين فبطلع A زاد X أصغر من
+
+194
+00:20:45,800 --> 00:20:54,270
+أو ساوي A زاد U لكل X في S وبالتالي العدد هذاعبارة
+
+195
+00:20:54,270 --> 00:20:59,830
+عن upper bound لمن؟ لست a زاد s اللي عرفناها قبل
+
+196
+00:20:59,830 --> 00:21:04,310
+شوية لأن هذا العدد أكبر من أو ساوي كل عناصر الست
+
+197
+00:21:04,310 --> 00:21:08,850
+هذه اللي على الصورة a زاد x لذلك هي اللي أثبتت أن
+
+198
+00:21:08,850 --> 00:21:13,110
+a زاد u is upper bound للست هذه لأن نريد أن نثبت
+
+199
+00:21:13,110 --> 00:21:18,510
+أن a زاد u هو أصغر upper bound للست هذه فبناخد أي
+
+200
+00:21:18,510 --> 00:21:24,550
+upper bound آخر للست a plus sفطبعا ال V Upper
+
+201
+00:21:24,550 --> 00:21:30,410
+Bound للست هي U أكبر من أو ساوي كل عناصرها الان
+
+202
+00:21:30,410 --> 00:21:34,430
+انجل ال A عن ناحية التانية فبصير X أصغر من أو ساوي
+
+203
+00:21:34,430 --> 00:21:40,710
+V minus A لكل X في S طيب
+
+204
+00:21:40,710 --> 00:21:47,410
+الان احنا عندنا ال U هو ال supremum ل S ال U هو ال
+
+205
+00:21:47,410 --> 00:21:52,800
+supremum ل S والان هذا العددهذا عبارة عن upper
+
+206
+00:21:52,800 --> 00:22:00,200
+bound of S لأن U أكبر من أو ساوي كل عناصر الـ S
+
+207
+00:22:00,200 --> 00:22:07,400
+وهذا أصغر upper bound لـ S إذن ال superman بيطلع
+
+208
+00:22:07,400 --> 00:22:13,240
+أصغر من أو ساوي ال upper bound V minus A ل S إذن
+
+209
+00:22:13,240 --> 00:22:16,080
+بيطلع عند U أصغر من أو ساوي
+
+210
+00:22:19,910 --> 00:22:26,350
+إن أنا بطلع عندي U أصغر من أو ساوي V minus A ودي A
+
+211
+00:22:26,350 --> 00:22:30,290
+عن ناحية التانية فبصير A زاد U أصغر من أو ساوي V
+
+212
+00:22:30,290 --> 00:22:35,870
+إذا هين أثبتنا حاجتين أول شيء إنه العدد هذا upper
+
+213
+00:22:35,870 --> 00:22:40,590
+bound للست هذه أخدنا أي upper bound عشوائي للست
+
+214
+00:22:40,590 --> 00:22:47,640
+هذهفطلع العدد a زاد u اصغر من او ساوي اي upper
+
+215
+00:22:47,640 --> 00:22:52,880
+bound لست a زاد s اذا من تعريف ال supremum بطلع ال
+
+216
+00:22:52,880 --> 00:23:00,520
+supremum لست a زاد s exist و بساوي a زاد uأن الـ
+
+217
+00:23:00,520 --> 00:23:05,380
+supremum للست هذي هو a زيد u وبالتالي و هذا بساوي
+
+218
+00:23:05,380 --> 00:23:08,720
+a و ال u هي ال supremum ل S أننا هيك بنكون أثبتنا
+
+219
+00:23:08,720 --> 00:23:15,900
+أن supremum الست a زيد s هو a زاد supremum S،
+
+220
+00:23:15,900 --> 00:23:21,540
+تمام؟ لو كانت الست هذي bounded below فممكن أيضا
+
+221
+00:23:21,540 --> 00:23:26,960
+نثبت أن ال infimum ل a زاد s بساوي a زاد infimum
+
+222
+00:23:26,960 --> 00:23:33,430
+S، تمام؟طبعا في أمثلة أخرى هنا ممكن تقرؤوها و
+
+223
+00:23:33,430 --> 00:23:39,650
+تحضروها و نوقف هنا نكتفي بهذا القدر و بنكمل ان شاء
+
+224
+00:23:39,650 --> 00:23:42,170
+الله يوم السبت المحاضرة القادمة
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2459a0ac82b111b9507da3f06a4e228bb121da37
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII.srt
@@ -0,0 +1,1275 @@
+1
+00:00:21,430 --> 00:00:27,610
+بسم الله الرحمن الرحيم أول شيء بنحب يعني نرحب فيكم
+
+2
+00:00:27,610 --> 00:00:31,770
+بمناسبة 
+
+3
+00:00:31,770 --> 00:00:38,690
+بداية العام الدراسي الجديد ونسأل الله تعالى أنه
+
+4
+00:00:38,690 --> 00:00:46,510
+يكون الفصل هذا فصل يعني متميز و يعني فيه إن شاء 
+
+5
+00:00:46,510 --> 00:00:51,860
+الله الخير الكثير لكم خاصة بعد أجواء الحرب اللي
+
+6
+00:00:51,860 --> 00:00:57,020
+عشناها في الفترة اللي فاتت وربنا
+
+7
+00:00:57,020 --> 00:01:03,860
+يعني يكلل جهدكم بالـ .. بالنجاح والتفوق يمكن
+
+8
+00:01:03,860 --> 00:01:09,640
+أول مرة يمكن تشوفوني أو يمكن ما درستكمش قبل هيك
+
+9
+00:01:09,640 --> 00:01:14,260
+فإذا ما بتعرفوش مين أنا فأنا الدكتور أيمن اللي
+
+10
+00:01:14,260 --> 00:01:18,840
+هيبيلي طبعا كان المفروض أن الدكتور Asad .. Asad هو
+
+11
+00:01:18,840 --> 00:01:23,280
+اللي درسكم الـ course هذا لكن حصل في يعني الجداول
+
+12
+00:01:23,280 --> 00:01:26,020
+زي ما أنتم عارفين في .. بيصير فيها تغيرات في آخر
+
+13
+00:01:26,020 --> 00:01:35,060
+لحظة فانا إن شاء الله اللي هيدرسكم المادة هذه ف ..
+
+14
+00:01:35,060 --> 00:01:38,380
+يعني ال .. 
+
+15
+00:01:41,030 --> 00:01:46,430
+أهم حاجة في المادة هذه وفي كل مواد الرياضيات أن
+
+16
+00:01:46,430 --> 00:01:55,150
+الطالب يعني يواظب على الحضور يحاول يحضر المحاضرات
+
+17
+00:01:55,150 --> 00:02:02,710
+ي .. يقرأ المحاضرات أول بأول يحاول يشتغل في الـ
+
+18
+00:02:02,710 --> 00:02:07,770
+homework برضه أول بأول ما يجزلش الـ .. الدراسة أو حل 
+
+19
+00:02:07,770 --> 00:02:16,610
+المسائل وما تتركمش عليه كمان يعني زي أي مادة في 
+
+20
+00:02:16,610 --> 00:02:20,150
+الرياضيات عشان الواحد يفهمها ويقدر يعني يستوعبها
+
+21
+00:02:20,150 --> 00:02:25,730
+لازم يحاول يحل أكبر عدد ممكن من المسائل أو بنسمي
+
+22
+00:02:25,730 --> 00:02:30,690
+الـ homework assignment طبعا احنا هنعطيكم syllabus
+
+23
+00:02:30,690 --> 00:02:37,010
+زي هذا فيه كل البيانات اللازمة اللي هو بنسميه
+
+24
+00:02:37,010 --> 00:02:45,490
+course outline أو ملخص لـ course و syllabus فيه كل
+
+25
+00:02:45,490 --> 00:02:50,130
+المعلومات عن المدرس عن المساق عن الـ textbook عن
+
+26
+00:02:50,130 --> 00:02:54,190
+كتاب المقرر عن المراجع الإضافية اللي ممكن يستعان
+
+27
+00:02:54,190 --> 00:03:00,630
+بيها بالإضافة للمرجع الأساسي أيه المادة العلمية
+
+28
+00:03:00,630 --> 00:03:08,940
+اللي هناخدها وكيف توزيعها على أسابيع أو على الـ ..
+
+29
+00:03:08,940 --> 00:03:16,560
+آه ممكن توزيعها على أسابيع توزيع 
+
+30
+00:03:16,560 --> 00:03:20,220
+الدرجات الـ evaluation policy أو تقييم الـ course
+
+31
+00:03:20,220 --> 00:03:27,720
+برضه هذا بيكون موجود عادة في الـ syllabus وفي
+
+32
+00:03:27,720 --> 00:03:32,320
+النهاية بنضع اللي هو الـ homework assignments اللي
+
+33
+00:03:32,320 --> 00:03:36,680
+هو مسائل الـ homework اللي المفروض تحلوها من الكتاب
+
+34
+00:03:36,680 --> 00:03:42,340
+ففي نهاية كل section هيكون في عدد من المسائل وهذه 
+
+35
+00:03:42,340 --> 00:03:46,200
+المسائل احنا بنختار يعني جزء منها مش كلها على أساس
+
+36
+00:03:46,200 --> 00:03:51,860
+الطالب بيحاول يحلها المسائل طبعا يعني الطالبة اللي
+
+37
+00:03:51,860 --> 00:03:57,500
+يعني مستواها متواضع أو متوسط المفروض تحاول تحل
+
+38
+00:03:57,500 --> 00:04:01,680
+يعني مش أقل من خمسين إلى سبعين في المية من المسائل
+
+39
+00:04:01,680 --> 00:04:05,940
+لوحدها إذا حضرت المحاضرة ودرست المحاضرة كويس
+
+40
+00:04:05,940 --> 00:04:09,640
+المفروض أنّهـا يعني يكون عندك مقدرة أنّهـا تحل على 
+
+41
+00:04:09,640 --> 00:04:13,580
+الأقل بين خمسين إلى سبعين في المية إذا ما كانش أكثر
+
+42
+00:04:14,270 --> 00:04:17,750
+الـ .. طبعا باقي المسائل الصعبة بيكون في أما بيكون 
+
+43
+00:04:17,750 --> 00:04:21,630
+في .. بيكون دائماً بنحاول نحلها في أو نحل بعضها 
+
+44
+00:04:21,630 --> 00:04:28,510
+المسائل الصعبة من خلال مناقشة فبنعمل مناقشة المادة
+
+45
+00:04:28,510 --> 00:04:32,690
+دي فيها أربع ساعات ممكن نخصص ثلاث ساعات محاضرة و
+
+46
+00:04:32,690 --> 00:04:38,650
+ساعة مناقشة أو حسب يعني الـ .. تطور الـ course لكن
+
+47
+00:04:38,650 --> 00:04:42,660
+في عندنا يعني الساعة من الوقت ممكن أن احنا يعني
+
+48
+00:04:42,660 --> 00:04:47,280
+أخصص أنا من وقت لآخر ساعة مناقشة ونتفق عليها يعني
+
+49
+00:04:47,280 --> 00:04:52,760
+قبل ما ناخدها، فعشان هيك الحضور يعني كثير ضروري
+
+50
+00:04:52,760 --> 00:04:54,640
+جداً و ..
+
+51
+00:04:56,630 --> 00:05:00,370
+طبعاً بمكانكم منكم أنتم يعني تستغلوا الساعات
+
+52
+00:05:00,370 --> 00:05:06,330
+المكتبية وأي واحد عنده استفسار، سؤال، أي شيء يعني
+
+53
+00:05:06,330 --> 00:05:12,350
+بتعلق بالمادة ممكن تجيلي على المكتب وتتناقش معاه،
+
+54
+00:05:12,350 --> 00:05:19,010
+تسألني وممكن أساعدها ممكن برضه تسأل المدرسين أو
+
+55
+00:05:19,010 --> 00:05:24,050
+المعيدات، الأخوات اللي هنا عندكم، ما بعرفش .. ضايلين 
+
+56
+00:05:24,050 --> 00:05:29,530
+مكان هم اللي غيروابرضه كمان هذا يعني وسيلة ثانية
+
+57
+00:05:29,530 --> 00:05:33,270
+للمساعدة ممكن تستعينوا بالمراجعة اللي احنا بنكتبها
+
+58
+00:05:33,270 --> 00:05:37,450
+في الـ syllabus هذه برضه بتساعدكم ممكن تستعملوا الـ
+
+59
+00:05:37,450 --> 00:05:41,910
+internet ممكن تستعملوا المكتبة يعني في وسائل
+
+60
+00:05:41,910 --> 00:05:45,670
+مساعدة كثيرة لكن يعني أهم شيء .. أهم شيء في المادة 
+
+61
+00:05:45,670 --> 00:05:51,010
+هذه بتحضروا المحاضرة وتحاولوا تحلوا المسائل و
+
+62
+00:05:51,010 --> 00:05:55,910
+تتناقشوا مع المدرس أكثر .. أكثر واحد بفيدكم مدرس 
+
+63
+00:05:55,910 --> 00:06:00,660
+المادة واحنا مش هنبخل عليكم يعني في أن احنا نجاوب
+
+64
+00:06:00,660 --> 00:06:05,520
+على أسئلتكم واستفساراتكم سواء .. سواء الأسئلة دي
+
+65
+00:06:05,520 --> 00:06:10,800
+أو الاستفسارات كانت بتتعلق بالـ homework أو بالمادة
+
+66
+00:06:10,800 --> 00:06:17,640
+الـ material اللي احنا هناخدها okay تمام؟ عشان شوية
+
+67
+00:06:17,640 --> 00:06:24,860
+هيك احنا يعني حالنا زي حال الـ .. الـ .. البلد الـ ..
+
+68
+00:06:24,860 --> 00:06:27,880
+انتم عارفين مكاتبنا كلها كانت مبنى الإدارة و
+
+69
+00:06:27,880 --> 00:06:33,980
+بالتالي مكاتبنا يعني في عملية نزوح أو نقل من
+
+70
+00:06:33,980 --> 00:06:39,940
+المبنى الإدارة لمبنى جديد فلسه مكاتبنا يعني ما
+
+71
+00:06:39,940 --> 00:06:43,900
+استقرناش ف .. لكن أنا بحاول إن شاء الله مرة جاية
+
+72
+00:06:43,900 --> 00:06:49,040
+أجهزلكم الـ syllabus تبع الـ course وهحطه على 
+
+73
+00:06:49,040 --> 00:06:53,990
+الصفحة تبعتي بالتالي ممكن أنكم تاخدوا نسخة منه ..
+
+74
+00:06:53,990 --> 00:07:01,310
+من الصفحة كذلك بإمكانكم تروحوا على صفحة المدرس في 
+
+75
+00:07:01,310 --> 00:07:05,450
+الامتحانات أنا بضعها نصفية سابقة وامتحانات نهائية
+
+76
+00:07:05,450 --> 00:07:10,970
+برضه ممكن تلاقوها على صفحة المدرس ممكن لو في حاجات 
+
+77
+00:07:10,970 --> 00:07:15,230
+معينة مهمة ممكن أدرس .. أ .. أنزلها على الصفحة و
+
+78
+00:07:15,230 --> 00:07:19,190
+بعدين أنتم يعني تعملولها copy و paste وإش زي ذلك
+
+79
+00:07:20,970 --> 00:07:26,830
+إذا عشان احنا يعني ما نضيعش الوقت كثير خليني بس
+
+80
+00:07:26,830 --> 00:07:34,410
+أكتبلكم الـ .. الـ .. الـ .. موقع الصفحة تبعتي عشان
+
+81
+00:07:34,410 --> 00:07:38,750
+إذا حد يعني .. وهترب ممكن برضه تخشوا على كلية 
+
+82
+00:07:38,750 --> 00:07:43,080
+العلوم خاصة الرياضيات والمدرسين وتطلع الصفحة أو
+
+83
+00:07:43,080 --> 00:07:55,920
+إذا كان ممكن تستخدمه بالرابط اللي هو http://www
+
+84
+00:07:55,920 --> 00:08:00,440
+.iogaza
+
+85
+00:08:00,440 --> 00:08:04,800
+.edu
+
+86
+00:08:04,800 --> 00:08:09,400
+.ps
+
+87
+00:08:14,490 --> 00:08:20,790
+backslash employee habil
+
+88
+00:08:20,790 --> 00:08:26,830
+الكتاب
+
+89
+00:08:26,830 --> 00:08:35,790
+المقرر اللي هو introduction text الكتاب المقرر هو 
+
+90
+00:08:35,790 --> 00:08:38,590
+عبارة عن introduction
+
+91
+00:08:43,370 --> 00:08:54,990
+introduction to real analysis by
+
+92
+00:08:54,990 --> 00:09:01,770
+bartel sherbert
+
+93
+00:09:01,770 --> 00:09:08,830
+or bartel and
+
+94
+00:09:08,830 --> 00:09:09,590
+sherbert
+
+95
+00:09:13,410 --> 00:09:22,990
+وهذا الطبع الثالثة third edition إذا 
+
+96
+00:09:22,990 --> 00:09:27,270
+هذا الكتاب المقرر اللي احنا هنعتمد عليه طبعاً هذا
+
+97
+00:09:27,270 --> 00:09:30,670
+الكتاب موجود في مكتبة الطالب أو الطالبة ويمكنكم 
+
+98
+00:09:30,670 --> 00:09:32,610
+يعني تشتروه
+
+99
+00:09:34,470 --> 00:09:39,090
+Okay إذا يعني هذه معظم الشغلات، احنا الـ بالنسبة
+
+100
+00:09:39,090 --> 00:09:44,970
+للـ .. للـ course يعني ممكن احنا حسب ما الـ .. الكلية
+
+101
+00:09:44,970 --> 00:09:48,690
+شوية غيرت سياستها، كنا في الأول نعطي امتحانين 
+
+102
+00:09:48,690 --> 00:09:53,950
+نصفيين وامتحان نهائي لكن إذا الكلية غيرت ورجعت 
+
+103
+00:09:53,950 --> 00:09:59,450
+لامتحان نصف واحد ونهائي فهنحكيلكم
+
+104
+00:09:59,450 --> 00:10:04,270
+المرة الجاية يعني إنّه نحدد بالضبط بعدين الدكتور عشان 
+
+105
+00:10:04,270 --> 00:10:07,350
+أسعد أنا وياه وبدرس الطلاب وأنا بدرسكم فعشان
+
+106
+00:10:07,350 --> 00:10:11,990
+نعمل امتحانات موحدة فلازم السياسة تكون موحدة فيعني
+
+107
+00:10:11,990 --> 00:10:16,390
+يوم المحاضرة الجاية نتفق على قليل يعني عدد
+
+108
+00:10:16,390 --> 00:10:20,610
+الامتحانات وتوزيعها والدرجات هنتفق عليه إن شاء الله 
+
+109
+00:10:20,610 --> 00:10:26,270
+المرة الجاية أنا يعني عامل زي ما أنتم شايفين ملخص
+
+110
+00:10:26,270 --> 00:10:29,890
+يعني طبعاً هذا الملخص لا يغني عن الكتاب المقرر يعني 
+
+111
+00:10:29,890 --> 00:10:34,510
+المفروض الطالب ي .. أو الطالبة يعني .. يعني تفلي 
+
+112
+00:10:34,510 --> 00:10:38,210
+الكتاب المقرر أو يعني تدرس من الكتاب المقرر أو
+
+113
+00:10:38,210 --> 00:10:43,870
+تشوفه لكن أنا بحاول يعني الكتاب المقرر بحاول يعني 
+
+114
+00:10:43,870 --> 00:10:49,770
+أنا آخذ الصفوة تبعته وأحاول ألخص يعني الـ material
+
+115
+00:10:49,770 --> 00:10:53,690
+بالطريقة وبالأسلوب تبعي أنا .. أنا اللي بقرا ..
+
+116
+00:10:53,690 --> 00:10:58,550
+بقرا مناسب فبرضه لو اعتمدتم على الملخص هذا أو
+
+117
+00:10:58,550 --> 00:11:02,130
+حليتم المسائل برضه هذا شيء يعني كثير كويس وطيب جداً
+
+118
+00:11:04,800 --> 00:11:11,100
+أنا هحاول أن أشوف هل يعني عن طريق العرض زي هيك،
+
+119
+00:11:11,100 --> 00:11:15,880
+هشتغلكم كل شيء، إذا في أي شيء مش واضح أو مش
+
+120
+00:11:15,880 --> 00:11:21,640
+فاهمينه ممكن نحاول نكتب ونوضحه بالكتابة، لكن أنا
+
+121
+00:11:21,640 --> 00:11:28,280
+مش هـ .. مش هـ .. مش هـ .. يعني مش هعدي عن نقطة من
+
+122
+00:11:28,280 --> 00:11:31,880
+نقطة لنقطة ثانية إلا إذا كانت أقل من أنتم
+
+123
+00:11:31,880 --> 00:11:37,440
+فاهمينها المادة هذه يعني حساسة وفيها عمق رياضي
+
+124
+00:11:37,440 --> 00:11:43,200
+ومادة كثير مهمة ما عناش نقول صعبة مش صعبة لكن بدها 
+
+125
+00:11:43,200 --> 00:11:48,500
+يعني تركيز وبدها اهتمام وبدها جهود فهنحاول أن 
+
+126
+00:11:48,500 --> 00:11:50,840
+نساعدكم إن شاء الله تفهموها بقدر الممكن
+
+127
+00:11:53,810 --> 00:11:58,050
+أنا بحب دائماً أعطي يعني material أو أعطي محاضرة من
+
+128
+00:11:58,050 --> 00:12:03,170
+أول يوم فهنبدأ نشرح وبعدين المحاضرة جاية بنحكي 
+
+129
+00:12:03,170 --> 00:12:06,730
+شوية عن الـ evaluation وعن الامتحانات والعلامات
+
+130
+00:12:06,730 --> 00:12:12,630
+ماشي الحال فيمكن أنتم مش مستعدين لكن أنا مستعد أن 
+
+131
+00:12:12,630 --> 00:12:19,570
+أنا يعني ناخذ شوية ولو أنه وقت كثير يعني نراها لأ
+
+132
+00:12:19,570 --> 00:12:24,620
+في معانا وقت إن احنا ناخذ شوية Okay فيعني هذا يعني 
+
+133
+00:12:24,620 --> 00:12:31,880
+مش يعني سيء ومش غلط فهنبدأ 
+
+134
+00:12:31,880 --> 00:12:39,120
+.. احنا هناخد أربع فصول في المادة هذه لكن الفصول 
+
+135
+00:12:39,120 --> 00:12:45,080
+مش متساوية الفصل الأول بيتحدث عن الـ real number
+
+136
+00:12:45,080 --> 00:12:50,570
+system أو نظام الأعداد الحقيقية وهذا أساس حاجات
+
+137
+00:12:50,570 --> 00:12:58,390
+كثيرة في الرياضيات فأول شيء بنا أن نتحدث
+
+138
+00:12:58,390 --> 00:13:01,450
+في أول band في الفصل هذا أو في أول section
+
+139
+00:13:01,450 --> 00:13:05,890
+بنا نتحدث عن الـ algebraic properties of R أو
+
+140
+00:13:05,890 --> 00:13:12,070
+الصفات الجبرية لنظام الأعداد الحقيقية فما هو نظام 
+
+141
+00:13:12,070 --> 00:13:19,180
+الأعداد الحقيقية؟ نرمزه بالرمز هذا real number
+
+142
+00:13:19,180 --> 00:13:22,940
+system أو نظام الأعداد الحقيقية نرمزه بالرمز **bold** R
+
+143
+00:13:22,940 --> 00:13:30,440
+في ℝ اللي هو الرمز هذا، هذا يرمز لمجموعة الأعداد 
+
+144
+00:13:30,440 --> 00:13:34,160
+الحقيقية. الآن هذه مجموعة الأعداد الحقيقية بنعرف 
+
+145
+00:13:34,160 --> 00:13:38,380
+عليها عمليتين جبريتين two algebraic operations
+
+146
+00:13:39,430 --> 00:13:43,270
+عملية جمع، يعني بأخذ عددين حقيقيين، زوج مرتب من
+
+147
+00:13:43,270 --> 00:13:47,530
+الأعداد الحقيقية، وبعرف عملية الجمع على... على
+
+148
+00:13:47,530 --> 00:13:53,050
+الزوج هذا. فعملية الجمع بتجمعهم، بعرف عملية ثانية
+
+149
+00:13:53,050 --> 00:13:57,570
+binary operation جديدة، بأخذ عددين حقيقيين أو زوج
+
+150
+00:13:57,570 --> 00:14:01,910
+مرتب من الأعداد الحقيقية، و بحاول أعرف عليهم عملية
+
+151
+00:14:01,910 --> 00:14:07,630
+جديدة، عملية ضرب أو multiplication. فهذا يعتبر
+
+152
+00:14:07,630 --> 00:14:10,830
+function وهذا يعتبر function من الـ Cartesian
+
+153
+00:14:10,830 --> 00:14:15,490
+product  الـ ℝ مع نفسها إلى ℝ. فهدول بنسميهم binary
+
+154
+00:14:15,490 --> 00:14:20,210
+operations. الآن نظام الأعداد الحقيقية هو مجموعة
+
+155
+00:14:20,210 --> 00:14:24,190
+الأعداد الحقيقية ℝ، boldface R، هذه الـ R الكبيرة
+
+156
+00:14:24,190 --> 00:14:30,370
+المُغَمَّخة مع العمليتين الجبريتين هدول. الآن العمليات 
+
+157
+00:14:30,370 --> 00:14:34,510
+هذه لازم تحقق خمس خواص
+
+158
+00:14:37,700 --> 00:14:43,380
+فالخواص هذه الخمسة، أول خاصية فيهم هي الـ
+
+159
+00:14:43,380 --> 00:14:47,200
+commutative laws، قوانين الإبدال، يعني عملية الجمع
+
+160
+00:14:47,200 --> 00:14:51,580
+اللي اتحدثنا عنها قبل شوية هي عملية إبدالية، بقدر 
+
+161
+00:14:51,580 --> 00:14:57,180
+أبدل الأعداد الحقيقية في الجمع. كذلك عملية الضرب
+
+162
+00:14:58,760 --> 00:15:04,100
+برضه عملية إبدالية commutative. فإذاً عملية عمليات
+
+163
+00:15:04,100 --> 00:15:09,640
+الجمع والضرب هي عمليات إبدالية. كذلك العمليات
+
+164
+00:15:09,640 --> 00:15:15,960
+الجمع والضرب عمليات associative laws، قوانين
+
+165
+00:15:15,960 --> 00:15:21,460
+الدمج، يعني الأقواس. عملية الجمع عملية دمج
+
+166
+00:15:21,460 --> 00:15:26,710
+associative. يعني بقدر لما أجمع X و Y و Z ثلاث أعداد 
+
+167
+00:15:26,710 --> 00:15:31,410
+حقيقية، بقدر أحط الأقواس حوالين هنا، أو ممكن أحطهم
+
+168
+00:15:31,410 --> 00:15:35,870
+هنا، سيان ما بتفرقش. هاي عملية الدمج أو الـ associative
+
+169
+00:15:35,870 --> 00:15:44,050
+law. نفس الحاجة، نفس الشيء عملية الضرب عملية دمج
+
+170
+00:15:44,050 --> 00:15:45,170
+associative.
+
+171
+00:15:48,760 --> 00:15:53,220
+الخاصية الثالثة، الـ distributive laws أو قوانين
+
+172
+00:15:53,220 --> 00:16:02,130
+التوزيع. عملية الضرب تتوزع على عملية الجمع. هذه X
+
+173
+00:16:02,130 --> 00:16:09,170
+لما أضربها في مجموعة Y و Z، فبوزع الضرب X على Y و
+
+174
+00:16:09,170 --> 00:16:15,470
+بوزع X على Z. نفس الشيء برضه في قانون توزيع لما
+
+175
+00:16:15,470 --> 00:16:20,330
+أضرب من اليسار برضه بوزع الضرب على المجموعة من
+
+176
+00:16:20,330 --> 00:16:23,590
+اليسار. إذاً أنا دول القانونين بسميهم distributive
+
+177
+00:16:23,590 --> 00:16:27,830
+laws أو قوانين التوزيع. عملية الضرب توزيعية على
+
+178
+00:16:27,830 --> 00:16:32,830
+عملية الجمع. فيه برضه خاصية رابعة، الـ identity
+
+179
+00:16:32,830 --> 00:16:39,310
+elements، وجود العناصر المحايدة. ففي الأعداد
+
+180
+00:16:39,310 --> 00:16:40,110
+الحقيقية
+
+181
+00:16:42,360 --> 00:16:47,040
+في عددين أو عنصرين، واحد نرمزه بالـ 0، وواحد
+
+182
+00:16:47,040 --> 00:16:51,760
+نرمزه بالرمز 1. وطبعاً هدول عنصرين مختلفين، غير 
+
+183
+00:16:51,760 --> 00:16:58,660
+متساويين. إذاً هنا نفترض أن في يوجد عنصرين متميزين في
+
+184
+00:16:58,660 --> 00:17:05,280
+ℝ في مجموعة الأعداد الحقيقية بحيث أن العنصر الأول
+
+185
+00:17:05,280 --> 00:17:10,340
+هذا المتميز لما أجمعه على أي عدد حقيقي X بيعطيه X
+
+186
+00:17:12,550 --> 00:17:16,290
+فهذا بنسميه العنصر صفر. هذا بنسميه الـ additive
+
+187
+00:17:16,290 --> 00:17:25,750
+identity أو المحايد الجمعي. كذلك 1 ضرب X، لو ضربت
+
+188
+00:17:25,750 --> 00:17:30,370
+هذا العنصر المتميز في أي عدد حقيقي X هيطلع عندي
+
+189
+00:17:30,370 --> 00:17:35,290
+النتيجة X، نفس العنصر. هذا صحيح لكل عدد حقيقي. إذاً 
+
+190
+00:17:35,290 --> 00:17:39,470
+هنا بنسمي الواحد multiplicative identity أو 
+
+191
+00:17:39,470 --> 00:17:45,070
+المحايد الضربي. okay، إذاً هي أربع خواص. في كمان خاصية
+
+192
+00:17:45,070 --> 00:17:46,890
+خامسة.
+
+193
+00:17:52,510 --> 00:17:59,710
+اللي هي وجود العناصر أو 
+
+194
+00:17:59,710 --> 00:18:04,590
+الـ inverse... وجود الـ inverse elements أو اللي هو
+
+195
+00:18:04,590 --> 00:18:12,220
+بيسموها النظائر أو العناصر المعاكسة. فلأي عدد حقيقي 
+
+196
+00:18:12,220 --> 00:18:17,620
+X يوجد
+
+197
+00:18:17,620 --> 00:18:25,860
+عنصر وحيد -X ينتمي لـ ℝ بحيث لو جمعت X مع سالبه
+
+198
+00:18:25,860 --> 00:18:32,040
+بيطلع المحايد الجمعي 0. في الحالة هذه بنسمي -X
+
+199
+00:18:32,040 --> 00:18:37,680
+هذا العنصر -X بنسميه الـ additive inverse لـ
+
+200
+00:18:37,680 --> 00:18:45,900
+X، الـ additive inverse، النظير الجمعي لـ X. كذلك
+
+201
+00:18:45,900 --> 00:18:53,400
+في حالة الضرب، في حالة الضرب مش كل عنصر له نظير
+
+202
+00:18:53,400 --> 00:18:57,320
+ضربي. عشان X يكون له نظير ضربي لازم يكون مختلف عن
+
+203
+00:18:57,320 --> 00:19:03,630
+الصفر. يعني الصفر مستثنى، الصفر. إذا كان X غير، لا مختلف
+
+204
+00:19:03,630 --> 00:19:08,390
+عن الصفر، ففي عنصر واحد there exist unique element
+
+205
+00:19:08,390 --> 00:19:13,390
+نرمزه بالرمز X⁻¹ ينتمي لـ ℝ بحيث لو
+
+206
+00:19:13,390 --> 00:19:18,530
+ضربت الـ X هذا مع العنصر هذا بيطلع عندي المحايد
+
+207
+00:19:18,530 --> 00:19:23,450
+الضربي أو multiplicative identity
+
+208
+00:19:26,280 --> 00:19:33,100
+العنصر هذا بنسميه النظير الضربي أو multiplicative
+
+209
+00:19:33,100 --> 00:19:33,800
+inverse
+
+210
+00:19:36,420 --> 00:19:41,260
+إذاً ما هو الـ real number system؟ هو عبارة عن مجموعة 
+
+211
+00:19:41,260 --> 00:19:46,260
+الأعداد الحقيقية هذه، معرف عليها two binary 
+
+212
+00:19:46,260 --> 00:19:50,880
+operations، عمليتين جبريتين. واحدة بنسميها الجمع،
+
+213
+00:19:50,880 --> 00:19:55,400
+واحدة بنسميها الضرب. والعمليتين هدول بيحققوا خمس
+
+214
+00:19:55,400 --> 00:20:00,660
+خواص مهمة، اللي هي الخمس خواص اللي سردناها قبل شوية
+
+215
+00:20:02,340 --> 00:20:07,060
+Okay، تمام. هذا هو نظام الأعداد الحقيقية. احنا الآن
+
+216
+00:20:07,060 --> 00:20:16,660
+بدنا ندرس خواص الأعداد الحقيقية هذه. فأول
+
+217
+00:20:16,660 --> 00:20:22,320
+خاصية، وهذه الخواص كلها خواص طبيعية ومعروفة، وانتوا 
+
+218
+00:20:22,320 --> 00:20:26,340
+عارفينها قبل هيك، بس ما حدا كان بيعطيها أسماءها.
+
+219
+00:20:26,340 --> 00:20:30,660
+الآن بدنا نسمي الأشياء، بنعطي الأشياء أسماء أو 
+
+220
+00:20:30,660 --> 00:20:38,100
+مسميات. فأول نظرية في الـ section هذا بتعطيني 
+
+221
+00:20:38,100 --> 00:20:43,340
+cancellation laws أو قوانين الحذف. قوانين الحذف إيه
+
+222
+00:20:43,340 --> 00:20:46,580
+يعني؟ قوانين الحذف النظرية هذه بتقول لو كان في عندي
+
+223
+00:20:46,580 --> 00:20:51,880
+X و Y و Z و W أعداد حقيقية، و W مختلف عن الصفر،
+
+224
+00:20:51,880 --> 00:20:55,320
+فالنتائج 
+
+225
+00:20:55,320 --> 00:21:03,040
+التالية بتكون صحيحة. لو كان X + Z = Y + Z
+
+226
+00:21:03,040 --> 00:21:11,540
+فبقدر أنا أجيب الـ Z وأشطب الـ Z مع الـ Z وأقول
+
+227
+00:21:11,540 --> 00:21:15,220
+أستنتج أن X لازم تطلع = Y. إذاً أنا إيش عملت؟
+
+228
+00:21:15,220 --> 00:21:20,020
+حذفت. فهذا cancellation، أحد الـ cancellation laws.
+
+229
+00:21:20,020 --> 00:21:24,730
+أحد قوانين الحذف. القانون الثاني بيقول لو كان عندي
+
+230
+00:21:24,730 --> 00:21:31,150
+X × W = Y × W، فممكن وطبعاً لازم W ما يساويش 
+
+231
+00:21:31,150 --> 00:21:37,070
+0 عشان القسمة على 0 غير معرفة. فبقدر أنا أقسم على W أو
+
+232
+00:21:37,070 --> 00:21:43,350
+أشطب W أو cancelling W، وأقول إنه لو كان هذا صحيح 
+
+233
+00:21:43,350 --> 00:21:48,890
+فأكيد لازم يطلع X = Y، بشرط أن W ما يساويش 0. أما
+
+234
+00:21:48,890 --> 00:21:55,290
+لو W = 0 فهذا الكلام nonsense، يعني هراء، ليس له
+
+235
+00:21:55,290 --> 00:22:02,610
+أساس رياضي. طيب هذه القوانين بدنا نثبتها، شو عرفناها
+
+236
+00:22:02,610 --> 00:22:08,990
+صح؟ فبدنا نستخدم الآن تعريف نظام الأعداد الحقيقية
+
+237
+00:22:08,990 --> 00:22:15,810
+أنه عبارة عن مجموعة ℝ وعمليتين جبريتين بيحققوا خمس
+
+238
+00:22:15,810 --> 00:22:22,060
+خواص. من خلال الخمس خواص دول بدي أحاول أثبت 
+
+239
+00:22:22,060 --> 00:22:25,760
+صحة القوانين هذه اللي هي cancellation laws. أنا
+
+240
+00:22:25,760 --> 00:22:29,260
+أخترت لكم أثبت الثاني لأنه الأول أسهل دائماً.
+
+241
+00:22:29,260 --> 00:22:35,710
+ال التعامل مع الجمع أسهل من الضرب. فنشوف برهان الجزء
+
+242
+00:22:35,710 --> 00:22:39,090
+الثاني، وطبعاً برهان الجزء الأول هيكون بالمثل، مماثل.
+
+243
+00:22:39,090 --> 00:22:43,110
+فاحنا في رياضيات ما بنحب التكرار والحكي كثير لما
+
+244
+00:22:43,110 --> 00:22:47,570
+يكون في حاجة مماثلة، فنقول ممكن برهانها بالمثل، و
+
+245
+00:22:47,570 --> 00:22:52,950
+بنسيب الطالب يتدرب عليها أو يعني يحاول يتمرن عليها
+
+246
+00:22:52,950 --> 00:22:57,970
+أو يثبتها بنفسه لأنها هتكون مماثلة ونفس الفكرة. و
+
+247
+00:22:57,970 --> 00:23:00,210
+في الرياضيات، أنتم عارفين الأفكار، إذا احنا عرفنا
+
+248
+00:23:00,210 --> 00:23:07,380
+الأفكار، يعني ملكنا الحل. Okay، نشوف برهان الجزء
+
+249
+00:23:07,380 --> 00:23:11,640
+الثاني. أنا بدي أثبت إيش الـ... إيش الفرض؟ أنتم كلكم
+
+250
+00:23:11,640 --> 00:23:15,720
+درستم مبادئ رياضيات، هذا conditional statement، هي
+
+251
+00:23:15,720 --> 00:23:20,860
+المقدم، وهي التالي، هي الفرض، وهي النتيجة. فبنفرض إنه
+
+252
+00:23:20,860 --> 00:23:25,860
+الفرض هذا صحيح، يعني هذا صح. الآن بنثبت النتيجة، بنعمل
+
+253
+00:23:25,860 --> 00:23:30,880
+direct proof، برهان مباشر، صح؟ يعني بدي أثبت النتيجة
+
+254
+00:23:30,880 --> 00:23:35,560
+فهي النتيجة بدي أثبت X = Y، هي الـ X. الآن الـ X
+
+255
+00:23:35,560 --> 00:23:39,840
+هذه من الخواص الخمسة، ممكن أبدل X بـ 1 × X لأن
+
+256
+00:23:39,840 --> 00:23:45,620
+1 × X عبارة عن X. الآن هذه عملية الضرب
+
+257
+00:23:45,620 --> 00:23:51,060
+commutative، إبدالية. فممكن أبدل. الآن هذا الواحد 
+
+258
+00:23:51,060 --> 00:24:00,470
+هبدهله W × W⁻¹. وهذا صحيح. طيب الآن أنا في عندي
+
+259
+00:24:00,470 --> 00:24:04,490
+عملية ضرب، عملية associative، فبحاول أن أنا إيه
+
+260
+00:24:04,490 --> 00:24:11,230
+أستخدم الـ associative law. هين استخدمته. الآن XW من
+
+261
+00:24:11,230 --> 00:24:15,550
+المعطيات، أنا عندي X × W = Y × W. إذاً أنا
+
+262
+00:24:15,550 --> 00:24:23,640
+هشيل XW وأضع مكانها YW. وبالتالي صار عندي الكلام
+
+263
+00:24:23,640 --> 00:24:28,360
+هذا، لأن بستخدم الـ associative law، تغير ترتيب
+
+264
+00:24:28,360 --> 00:24:33,180
+الأقواس. وهذا برجعه = 1، وبستخدم الـ 
+
+265
+00:24:33,180 --> 00:24:37,240
+commutative law، فبيطلع عندي في النهاية Y. إذن هين
+
+266
+00:24:37,240 --> 00:24:45,200
+أثبتت إن X = Y. وهنا في البرهان استخدمت بعض
+
+267
+00:24:45,200 --> 00:24:49,170
+الخواص الخمسة تبقى. الـ real number system أو نظام 
+
+268
+00:24:49,170 --> 00:24:54,350
+الأعداد الحقيقية بظبط زاد الـ logic، المنطق، أو 
+
+269
+00:24:54,350 --> 00:24:59,010
+أساسيات الرياضيات. إذاً هذا هو إيه البرهان؟ برهان
+
+270
+00:24:59,010 --> 00:25:03,050
+الجزء الأول مماثل، فهي اللي كتبلكم exercise، يعني
+
+271
+00:25:03,050 --> 00:25:07,290
+اتمرنوا عليه، اتمرنوا عليه، يعني حاولوا تكتبوه بنفس
+
+272
+00:25:07,290 --> 00:25:12,250
+الطريقة. تمام، واضح البرهان؟ واضح. في أي سؤال؟ 
+
+273
+00:25:14,950 --> 00:25:19,530
+Okay، تمام. طيب نشوف كمان نظرية ثانية، نظريات لسه
+
+274
+00:25:19,530 --> 00:25:25,270
+حاجات بسيطة. نشوف النص تبع النظرية، أنا عندي ضايل
+
+275
+00:25:25,270 --> 00:25:30,910
+دقيقتين. ممكن احنا تبعين رياضيات، يعني بنحب نستغل
+
+276
+00:25:30,910 --> 00:25:38,470
+وقتنا كثير، وكل دقيقة أنا اه... هذه نظرية طويلة. طيب مش
+
+277
+00:25:38,470 --> 00:25:43,530
+مش لازم بس، هنحاول نشوف النص تبعها، وبعدين المرة
+
+278
+00:25:43,530 --> 00:25:49,920
+الجاية بنبرهنها. هذه النظرية فيها عشر أجزاء. النظرية 
+
+279
+00:25:49,920 --> 00:25:55,180
+هذه بتقول إذا أخذت أي أربع أعداد حقيقية XYZW، وإذا 
+
+280
+00:25:55,180 --> 00:26:00,960
+كان الـ Z والـ W مختلفين عن الصفر، فالخواص 
+
+281
+00:26:00,960 --> 00:26:06,650
+التالية كلها صحيحة وهي أول خاصية لو ضربت أي عدد
+
+282
+00:26:06,650 --> 00:26:10,030
+حقيقي في صفر المفروض يطلع لعدد الصفر ال additive
+
+283
+00:26:10,030 --> 00:26:16,050
+ال additive identity الآن هذا ال additive inverse
+
+284
+00:26:16,050 --> 00:26:21,510
+لـ X لما آخذ ال additive inverse لـ X مرتين كأن إيه
+
+285
+00:26:21,510 --> 00:26:25,390
+رجعت لـ X زي المصفوفة آخذ ال inverse للمصفوفة
+
+286
+00:26:25,390 --> 00:26:30,980
+مرتين تطلع المصفوفة نفسها شبيهة فيها صحيح؟ طيب برضه 
+
+287
+00:26:30,980 --> 00:26:35,360
+نفس الحاجة لما آخذ ال multiplicative inverse مرتين
+
+288
+00:26:35,360 --> 00:26:39,940
+هذا بيساوي العنصر نفسه هذا صحيح طبعًا هنا بشرط w
+
+289
+00:26:39,940 --> 00:26:45,080
+مايساويش صفر في الضرب دائمًا بنكون ... نحاول نكون
+
+290
+00:26:45,080 --> 00:26:48,440
+careful حريصين أنه إيه الحاجة اللي بدنا نجيبلها
+
+291
+00:26:48,440 --> 00:26:52,910
+multiplicative inverse ما تكونش بتساوي صفر لو ضربت
+
+292
+00:26:52,910 --> 00:26:56,430
+العدد سالب واحد هذا real number في X كأن ضربت X في
+
+293
+00:26:56,430 --> 00:27:02,790
+سالب فهذا نفس الشيء لو ضربت X في سالب Y نفس الشيء
+
+294
+00:27:02,790 --> 00:27:07,030
+كما لو أني ضربت X في Y وضربت الكل في سالب واحد أو
+
+295
+00:27:07,030 --> 00:27:12,850
+هيك كل هذا صح لو أخذت negative X و جمعتها على
+
+296
+00:27:12,850 --> 00:27:18,470
+negative Y كأن أخذت X زائد Y وضربت في سالب هذا كله
+
+297
+00:27:18,470 --> 00:27:23,680
+صح طيب لو ضربت negative x في negative y كأنني ضربت
+
+298
+00:27:23,680 --> 00:27:31,880
+x في y هذا برضه صحيح لو جمعت x على z و y على w و
+
+299
+00:27:31,880 --> 00:27:42,120
+جمعتهم فهيطلع عندي ال ... من واحد المقامات و
+
+300
+00:27:42,120 --> 00:27:47,350
+العملية الجبرية هذه المعروفة أخيرًا الخاصية الأخيرة
+
+301
+00:27:47,350 --> 00:27:51,990
+هذه لو أنا فيها عندي عددين حقيقيين كان حصل ضربهم
+
+302
+00:27:51,990 --> 00:27:58,090
+بيساوى صفر فلازم واحد على الأقل منهم بيساوى صفر فإما x
+
+303
+00:27:58,090 --> 00:28:02,830
+بيساوى صفر أو y بيساوى صفر وهذه ممكن مرت معكم في
+
+304
+00:28:02,830 --> 00:28:08,430
+المبادئ عفوًا هذا أكيد مرت معكم في المبادئ كمثال
+
+305
+00:28:08,430 --> 00:28:15,100
+على indirect proof على برهان غير مباشر حاولوا أنكم
+
+306
+00:28:15,100 --> 00:28:21,660
+أنتم تفكروا في براهين الحاجات هذه والمرة الجاية
+
+307
+00:28:21,660 --> 00:28:28,520
+إن شاء الله نحاول نبرهن بعض الأجزاء okay تمام ال
+
+308
+00:28:28,520 --> 00:28:34,310
+... ال material هذه هأحطها على الصفحة بتاعتكم ممكنكم
+
+309
+00:28:34,310 --> 00:28:39,670
+أنكم تنسخوها و تأخذوها و تشوفوها فبالتالي مافيش
+
+310
+00:28:39,670 --> 00:28:44,670
+ داعي أنكم تكتبوا لأن ممكن تنسخوها و تحطوها على ال
+
+311
+00:28:44,670 --> 00:28:49,250
+laptop تبعكم أو على ال computer okay تمام هنوقف
+
+312
+00:28:49,250 --> 00:28:53,090
+هنا وإن شاء الله المرة الجاية بنكمل وبنجيب لكم
+
+313
+00:28:53,090 --> 00:28:56,710
+معلومات جديدة عن توزيع الدرجات والامتحانات في حد
+
+314
+00:28:56,710 --> 00:28:58,090
+عنده أي سؤال أو استفسار
+
+315
+00:29:03,220 --> 00:29:06,820
+اه من ... هنحط لكم يعني اه هنحط لكم يعني إن شاء الله
+
+316
+00:29:06,820 --> 00:29:12,660
+يعني كام كبير له يعني يكون يكفيكِ من هالشهر okay
+
+317
+00:29:12,660 --> 00:29:16,980
+تمام؟ في أي سؤال ثاني؟ okay شكرًا لكم وإن شاء الله
+
+318
+00:29:16,980 --> 00:29:22,500
+نشوفكم المرة الجاية ونلتقي يوم الاثنين إن شاء
+
+319
+00:29:22,500 --> 00:29:22,600
+الله 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..76e56f6766a6e2e1014ef201a0a07eaa97a61a0d
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/BdWUrxEOLII_postprocess.srt
@@ -0,0 +1,1276 @@
+1
+00:00:21,430 --> 00:00:27,610
+بسم الله الرحمن الرحيم أول شي بنحب يعني نرحب فيكم
+
+2
+00:00:27,610 --> 00:00:31,770
+بمناسبة
+
+3
+00:00:31,770 --> 00:00:38,690
+بداية العالم الدراسي الجديد و نسأل الله تعالى أنه
+
+4
+00:00:38,690 --> 00:00:46,510
+يكون الفصل هذا فصل يعني متميز و يعني فيه ان شاء
+
+5
+00:00:46,510 --> 00:00:51,860
+الله الخير الكتيرلكم خاصة بعد أجواء الحرب اللى
+
+6
+00:00:51,860 --> 00:00:57,020
+عشناها فى الفترة اللى فاتت وربنا
+
+7
+00:00:57,020 --> 00:01:03,860
+يعني يكلل جهدكم بال .. بالنجاح والتفوق يمكن
+
+8
+00:01:03,860 --> 00:01:09,640
+أول مرة يمكن تشوفونى او يمكن ما درستكم مش قبل هيك
+
+9
+00:01:09,640 --> 00:01:14,260
+فإذا مابتعرفوش مين أنا فأنا الدكتور أيسى اللى
+
+10
+00:01:14,260 --> 00:01:18,840
+هبيلىطبعا كان المفروض ان الدكتور Asad .. Asad هو
+
+11
+00:01:18,840 --> 00:01:23,280
+اللي درسكم ال course هذا لكن حصل في يعني الجداول
+
+12
+00:01:23,280 --> 00:01:26,020
+زي ما انتوا عارفين في .. بيصير فيها تغيرات في آخر
+
+13
+00:01:26,020 --> 00:01:35,060
+لحظة فانا ان شاء الله اللي هدرسكم المادة هذه ف ..
+
+14
+00:01:35,060 --> 00:01:38,380
+يعني ال ..
+
+15
+00:01:41,030 --> 00:01:46,430
+أهم حاجة في المادة هذه و في كل مواد رياضيات أن
+
+16
+00:01:46,430 --> 00:01:55,150
+الطالب يعني يواظب على الحضور يحاول يحضر المحاضرات
+
+17
+00:01:55,150 --> 00:02:02,710
+ي .. يقرأ المحاضرات أول بأول يحاول يشتغل في ال
+
+18
+00:02:02,710 --> 00:02:07,770
+homework برضه أول بأول مايجزلش ال .. الدراسة أو حل
+
+19
+00:02:07,770 --> 00:02:16,610
+المثالوما تتركمش عليه كمان يعني زي أي مادة في
+
+20
+00:02:16,610 --> 00:02:20,150
+رياضيات عشان الواحد يفهمها ويقدر يعني يستوعبها
+
+21
+00:02:20,150 --> 00:02:25,730
+لازم يحاول يحل أكبر عدد ممكن من المسائل أو بنسمي
+
+22
+00:02:25,730 --> 00:02:30,690
+ال homework assignment طبعا احنا هنعطيلكم syllabus
+
+23
+00:02:30,690 --> 00:02:37,010
+زي هذافيه كل البيانات اللازمة اللي هو بنسميه
+
+24
+00:02:37,010 --> 00:02:45,490
+course outline أو ملخص لcourse و syllabus فيه كل
+
+25
+00:02:45,490 --> 00:02:50,130
+المعلومات عن المدرس عن المساقة عن ال textbook عن
+
+26
+00:02:50,130 --> 00:02:54,190
+كتاب المقرر عن المراجع الإضافية اللي ممكن لاستعانى
+
+27
+00:02:54,190 --> 00:03:00,630
+بيها بالإضافة للمرجع الأساسي أيه المادة العلمية
+
+28
+00:03:00,630 --> 00:03:08,940
+اللي هناخدهاو كيف توزيعها على أسابيع أو على ال ..
+
+29
+00:03:08,940 --> 00:03:16,560
+اه ممكن توزيعها على أسابيع توزيع
+
+30
+00:03:16,560 --> 00:03:20,220
+الدرجات ال evaluation policy أو تقييم ال course
+
+31
+00:03:20,220 --> 00:03:27,720
+برضه هذا بيكون موجود عادة في ال syllabusو في
+
+32
+00:03:27,720 --> 00:03:32,320
+النهاية بنضع اللي هو ال homework assignments اللي
+
+33
+00:03:32,320 --> 00:03:36,680
+هو مسائل ال homework اللي المفروض تحلوها من الكتاب
+
+34
+00:03:36,680 --> 00:03:42,340
+ففي نهاية كل section هيكون في عدد من المسائل و هذه
+
+35
+00:03:42,340 --> 00:03:46,200
+المسائل احنا بنختار يعني جزء منها مش كلها على أساس
+
+36
+00:03:46,200 --> 00:03:51,860
+الطالب بيحاول يحلهاالمسائل طبعا يعني الطالبة اللي
+
+37
+00:03:51,860 --> 00:03:57,500
+يعني مستواها متواضع او متوسط المفروض تحاول تحل
+
+38
+00:03:57,500 --> 00:04:01,680
+يعني مش اقل من خمسين الى سبعين في المية من المسائل
+
+39
+00:04:01,680 --> 00:04:05,940
+لوحدها اذا حضرت المحاضرة ودرست المحاضرة كويس
+
+40
+00:04:05,940 --> 00:04:09,640
+المفروض انها يعني يكون عندك مقدرة انها تحل على
+
+41
+00:04:09,640 --> 00:04:13,580
+الاقل بين خمسين الى سبعين في المية اذا ماكانش اكتر
+
+42
+00:04:14,270 --> 00:04:17,750
+ال .. طبعا باقي المسائل الصعبة بيكون في اما بيكون
+
+43
+00:04:17,750 --> 00:04:21,630
+في .. بيكون دايما بنحاول نحلها في او نحل بعضها
+
+44
+00:04:21,630 --> 00:04:28,510
+المسائل الصعبة من خلال مناقشة فبنعمل مناقشة المادة
+
+45
+00:04:28,510 --> 00:04:32,690
+دي فيها اربع ساعات ممكن نخصص تلت ساعات محاضرة و
+
+46
+00:04:32,690 --> 00:04:38,650
+ساعة مناقشة او حسب يعني ال .. تطور ال course لكن
+
+47
+00:04:38,650 --> 00:04:42,660
+في عندنا يعني الساعة من الوقت ممكن ان احنايعني
+
+48
+00:04:42,660 --> 00:04:47,280
+أخصص أنا من وقت لآخر ساعة مناقشة و نتفق عليها يعني
+
+49
+00:04:47,280 --> 00:04:52,760
+قبل ما ناخدها، فعشان هيك الحضور يعني كتير ضروري
+
+50
+00:04:52,760 --> 00:04:54,640
+جدا و ..
+
+51
+00:04:56,630 --> 00:05:00,370
+طبعا بمكانكم منكم أنتوا يعني تستغلوا الساعات
+
+52
+00:05:00,370 --> 00:05:06,330
+المكتبية و أي واحد عنده استفسار، سؤال، أي شيء يعني
+
+53
+00:05:06,330 --> 00:05:12,350
+بتعلق بالمادة ممكن تجيلي على المكتب و تتناقش معاه،
+
+54
+00:05:12,350 --> 00:05:19,010
+تسألني و ممكن أساعدها ممكن برضه تسأل المهدين أو
+
+55
+00:05:19,010 --> 00:05:24,050
+المعيدات، الأخوات اللي هنا عندكم، ماعرفش .. ضايلين
+
+56
+00:05:24,050 --> 00:05:29,530
+مكان هم اللي غيروابرضه كمان هذا يعني وسيلة تانية
+
+57
+00:05:29,530 --> 00:05:33,270
+للمساعدة ممكن تستعينوا بالمراجعة اللي احنا بنكتبها
+
+58
+00:05:33,270 --> 00:05:37,450
+في ال syllabusهذه برضه بتساعدكم ممكن تستعملوا ال
+
+59
+00:05:37,450 --> 00:05:41,910
+internet ممكن تستعملوا المكتبة يعني في وسائل
+
+60
+00:05:41,910 --> 00:05:45,670
+مساعدة كتيرة لكن يعني أهم شيء .. أهم شيء في المادة
+
+61
+00:05:45,670 --> 00:05:51,010
+هذه بتحضروا المحاضرة و تحاولوا تحلوا المسائل و
+
+62
+00:05:51,010 --> 00:05:55,910
+تتناقشوا مع المدرس أكتر .. أكتر واحد بفيدكم مدرس
+
+63
+00:05:55,910 --> 00:06:00,660
+المادةو احنا مش هنبخل عليكم يعني في ان احنا نجاوب
+
+64
+00:06:00,660 --> 00:06:05,520
+على أسئلتكم و الصفصاراتكم سواء .. سواء الأسئلة ده
+
+65
+00:06:05,520 --> 00:06:10,800
+أو الصفصارات كانت بتتعلق بال homework أو بالمادة
+
+66
+00:06:10,800 --> 00:06:17,640
+ال material اللي احنا هناخدها okay تمام؟ عشان شوية
+
+67
+00:06:17,640 --> 00:06:24,860
+هيك احنا يعني حالنا زي حال ال ..ال .. البلد ال ..
+
+68
+00:06:24,860 --> 00:06:27,880
+انتوا عارفين مكاتبنا كلها كانت مبنى الإدارة و
+
+69
+00:06:27,880 --> 00:06:33,980
+بالتالي مكاتبنا يعني في عملية نزوح او نقل من
+
+70
+00:06:33,980 --> 00:06:39,940
+المبنى الإدارة لمبنى جديد فلسه مكاتبنا يعني ما
+
+71
+00:06:39,940 --> 00:06:43,900
+استقرناش ف .. لكن انا بحاول ان شاء الله مرة جاية
+
+72
+00:06:43,900 --> 00:06:49,040
+اجهزلكم ال syllabus تبع ال course و هحطه على
+
+73
+00:06:49,040 --> 00:06:53,990
+الصفحه تبعتيو بالتالي ممكن أنكم تاخدوا نسخة منه ..
+
+74
+00:06:53,990 --> 00:07:01,310
+من الصفحة كذلك بإمكانكم تروحوا على صفحة المدرس في
+
+75
+00:07:01,310 --> 00:07:05,450
+امتحانات أنا بضعها نصفية سابقة و امتحانات نهائية
+
+76
+00:07:05,450 --> 00:07:10,970
+برضه ممكن تلاجوا على صفحة المدرس ممكن لو في حاجات
+
+77
+00:07:10,970 --> 00:07:15,230
+معينة مهمة ممكن ادرس .. ا .. انزلها على الصفحة و
+
+78
+00:07:15,230 --> 00:07:19,190
+بعدين انتوا يعني تعملولها copy و paste و إش زي ذلك
+
+79
+00:07:20,970 --> 00:07:26,830
+إذا عشان احنا يعني ما نضيعش الوجد كتير خليني بس
+
+80
+00:07:26,830 --> 00:07:34,410
+أكتبلكم ال .. ال .. ال .. موقع الصفحة تبعتي عشان
+
+81
+00:07:34,410 --> 00:07:38,750
+إذا حد يعني .. و هترب ممكن برضه تخشوا على كلية
+
+82
+00:07:38,750 --> 00:07:43,080
+العلوم خاصة الرياضيات و المدرسين و تطلع الصفحةأو
+
+83
+00:07:43,080 --> 00:07:55,920
+إذا كان ممكن تستخدمه بالرابط اللي هو http://www
+
+84
+00:07:55,920 --> 00:08:00,440
+.iogaza
+
+85
+00:08:00,440 --> 00:08:04,800
+.edu
+
+86
+00:08:04,800 --> 00:08:09,400
+.ps
+
+87
+00:08:14,490 --> 00:08:20,790
+backslash employee habil
+
+88
+00:08:20,790 --> 00:08:26,830
+الكتاب
+
+89
+00:08:26,830 --> 00:08:35,790
+المقرر اللي هو introduction text الكتاب المقرر هو
+
+90
+00:08:35,790 --> 00:08:38,590
+عبارة عن introduction
+
+91
+00:08:43,370 --> 00:08:54,990
+introduction to real analysis by
+
+92
+00:08:54,990 --> 00:09:01,770
+bartel sherbert
+
+93
+00:09:01,770 --> 00:09:08,830
+or bartel and
+
+94
+00:09:08,830 --> 00:09:09,590
+sherbert
+
+95
+00:09:13,410 --> 00:09:22,990
+وهذا الطبع التالتة third edition اذا
+
+96
+00:09:22,990 --> 00:09:27,270
+هذا الكتاب المخرر اللي احنا هنعتمد عليه طبعا هذا
+
+97
+00:09:27,270 --> 00:09:30,670
+الكتاب موجود في مكتبة الطالب او الطالبة ويمكنكم
+
+98
+00:09:30,670 --> 00:09:32,610
+يعني تشتروا
+
+99
+00:09:34,470 --> 00:09:39,090
+Okay إذا يعني هذه معظم الشغلات، احنا ال .. بالنسبة
+
+100
+00:09:39,090 --> 00:09:44,970
+لل .. لل course يعني ممكن احنا حسب ما ال .. الكلية
+
+101
+00:09:44,970 --> 00:09:48,690
+شوية غيرت سياستها، كنا في الأول نعطي امتحانين
+
+102
+00:09:48,690 --> 00:09:53,950
+نصفيين و امتحان نهائيلكن إذا الكلية غيرت و رجعت
+
+103
+00:09:53,950 --> 00:09:59,450
+لامتحان نصف واحد و نهائي فهنحكيلكم
+
+104
+00:09:59,450 --> 00:10:04,270
+المرة الجاية يعني انحدد بالظبط بعدين الدكتور عشان
+
+105
+00:10:04,270 --> 00:10:07,350
+أسعد أنا وياه و ببدرس الطلاب و أنا بدرسكم فعشان
+
+106
+00:10:07,350 --> 00:10:11,990
+نعمل امتحانات موحدة فلازم السياسة تكون موحدة فيعني
+
+107
+00:10:11,990 --> 00:10:16,390
+يوم المحاضرة الجاية نتفق على قليل يعني عدد
+
+108
+00:10:16,390 --> 00:10:20,610
+الامتحانات و توزيها الدرجات هنتفق عليه ان شاء الله
+
+109
+00:10:20,610 --> 00:10:26,270
+المرة الجايةأنا يعني عامل زي ما أنتوا شايفين ملخص
+
+110
+00:10:26,270 --> 00:10:29,890
+يعني طبعا هذا الملخص لا يغني عن الكتاب المقرر يعني
+
+111
+00:10:29,890 --> 00:10:34,510
+المفروض الطالب ي .. أو الطالبة يعني .. يعني تفلي
+
+112
+00:10:34,510 --> 00:10:38,210
+الكتاب المقرر أو يعني تدرس من الكتاب المقرر أو
+
+113
+00:10:38,210 --> 00:10:43,870
+تشوفهلكن انا بحاول يعني الكتاب المقرر بحاول يعني
+
+114
+00:10:43,870 --> 00:10:49,770
+انا اخد الصفوة تبعته و احاول ألخص يعني ال material
+
+115
+00:10:49,770 --> 00:10:53,690
+بالطريقة و بالاسلوب تبعي انا .. انا اللي بقرا ..
+
+116
+00:10:53,690 --> 00:10:58,550
+بقرا مناسب فبرضه لو اعتمدتوا على الملخص هذا او
+
+117
+00:10:58,550 --> 00:11:02,130
+حليته المسائل برضه هذا شئ يعني كتير كويس وطيب جدا
+
+118
+00:11:04,800 --> 00:11:11,100
+أنا هحاول أن أشوف هل يعني عن طريق العرض زي هيك،
+
+119
+00:11:11,100 --> 00:11:15,880
+هشتغلكم كل شيء، إذا في أي شيء مش واضح أو مش
+
+120
+00:11:15,880 --> 00:11:21,640
+فاهمينه ممكن نحاول نكتب و نوضحه بالكتابة، لكن أنا
+
+121
+00:11:21,640 --> 00:11:28,280
+مش ه .. مش ه .. مش ه .. يعني مش هعديعن نقطة من
+
+122
+00:11:28,280 --> 00:11:31,880
+نقطة لنقطة تانية إلا إذا كانت أقل من انتوا
+
+123
+00:11:31,880 --> 00:11:37,440
+فاهمينها المادة هذه يعني حساسة وفيها عمق رياضي
+
+124
+00:11:37,440 --> 00:11:43,200
+ومادة كتير مهمة ماعناش نقول صعبة مش صعبة لكن بدها
+
+125
+00:11:43,200 --> 00:11:48,500
+يعني تركيز وبدها اهتمام وبدها جهود فحنحاول ان
+
+126
+00:11:48,500 --> 00:11:50,840
+ساعدكم ان شاء الله تفهموها بقدر الممكن
+
+127
+00:11:53,810 --> 00:11:58,050
+انا بحب دائما اعطي يعني material او اعطي محاضرة من
+
+128
+00:11:58,050 --> 00:12:03,170
+اول يوم فهنبدأ نشرح و بعدين المحاضرة جاية بنحكي
+
+129
+00:12:03,170 --> 00:12:06,730
+شوية عن ال evaluation و عن الامتحانات و العلامات
+
+130
+00:12:06,730 --> 00:12:12,630
+ماشي الحال فيمكن انتوا مش مستعدين لكن انا مستعد ان
+
+131
+00:12:12,630 --> 00:12:19,570
+انا يعني ناخد شوية ولو انه وجدت كتير يعني نراها لأ
+
+132
+00:12:19,570 --> 00:12:24,620
+في معانا وجدت ان احنا ناخد شويةOkay فيعني هذا يعني
+
+133
+00:12:24,620 --> 00:12:31,880
+مش يعني سيء ومش غلط فهنبدأ
+
+134
+00:12:31,880 --> 00:12:39,120
+.. احنا هناخد أربع شباتر في المادة هذه لكن الشباتر
+
+135
+00:12:39,120 --> 00:12:45,080
+مش متساوية الشبتر الأول بتحدث عن ال real number
+
+136
+00:12:45,080 --> 00:12:50,570
+system أو نظام الأعداد الحقيقيةوهذا أساس حاجات
+
+137
+00:12:50,570 --> 00:12:58,390
+كتيرة في رياضيات فأول شيء بنا ان نتحدث
+
+138
+00:12:58,390 --> 00:13:01,450
+في أول band في ال chapter هذا أو في أول section
+
+139
+00:13:01,450 --> 00:13:05,890
+بنا نتحدث عن ال algebraic properties of R أو
+
+140
+00:13:05,890 --> 00:13:12,070
+الصفات الجابرية لنظام الأعداد الحقيقية فما هو نظام
+
+141
+00:13:12,070 --> 00:13:19,180
+الأعداد الحقيقية؟نرمزه بالرمز هذا real number
+
+142
+00:13:19,180 --> 00:13:22,940
+system أو نظام الأعداد الحقيقية نرمزه بالرمز bold
+
+143
+00:13:22,940 --> 00:13:30,440
+في SR اللي هو الرمز هذا هذا يرمز لمجموعة الأعداد
+
+144
+00:13:30,440 --> 00:13:34,160
+الحقيقية الآن هذه مجموعة الأعداد الحقيقية بنعرف
+
+145
+00:13:34,160 --> 00:13:38,380
+عليها عمليتين جبريتين two algebraic operations
+
+146
+00:13:39,430 --> 00:13:43,270
+عملية جمع يعني باخد عددين حقيقيين زوج مرتب من
+
+147
+00:13:43,270 --> 00:13:47,530
+العداد الحقيقية و بعرف عملية الجمع على .. على
+
+148
+00:13:47,530 --> 00:13:53,050
+الزوج هذا فعملية الجمع بتجمعهم بعرف عملية تانية
+
+149
+00:13:53,050 --> 00:13:57,570
+binary operation جديدة باخد عددين حقيقيين او زوج
+
+150
+00:13:57,570 --> 00:14:01,910
+مرتب من العداد الحقيقية و بحاول اعرف عليهم عملية
+
+151
+00:14:01,910 --> 00:14:07,630
+جديدة عملية ضرب او multiplicationفهذا يعتبر
+
+152
+00:14:07,630 --> 00:14:10,830
+function هذا وهذا يعتبر function من الـ Cartesian
+
+153
+00:14:10,830 --> 00:14:15,490
+product الـ R مع نفسها إلى R فهدول بنسميهم binary
+
+154
+00:14:15,490 --> 00:14:20,210
+operations الان نظام العداد الحقيقية هو مجموعة
+
+155
+00:14:20,210 --> 00:14:24,190
+العداد الحقيقية R boldface R هذه الـ R الكبيرة
+
+156
+00:14:24,190 --> 00:14:30,370
+المغمخة مع العمليتين الجبرياتين هدول الان العمليات
+
+157
+00:14:30,370 --> 00:14:34,510
+هذه لازم تحقق خمس قواص
+
+158
+00:14:37,700 --> 00:14:43,380
+فالخواص هذه الخمسة أول خاصية فيهم هي ال
+
+159
+00:14:43,380 --> 00:14:47,200
+commutative laws قوانين الإبدال يعني عملية الجامعة
+
+160
+00:14:47,200 --> 00:14:51,580
+اللي اتحدثنا عنها قبل شوية هي عملية إبدالية بقدر
+
+161
+00:14:51,580 --> 00:14:57,180
+أبدل العناد الحقيقية في الجامعة كذلك عملية الضرب
+
+162
+00:14:58,760 --> 00:15:04,100
+برضه عملية إبدالية competitive فإذا عملية عمليات
+
+163
+00:15:04,100 --> 00:15:09,640
+الجامعة والضرب هي عمليات إبدالية كذلك العمليات
+
+164
+00:15:09,640 --> 00:15:15,960
+الجامعة والضرب عمليات ال associative laws قوانين
+
+165
+00:15:15,960 --> 00:15:21,460
+الدمج يعني الأقواص عملية الجامعة عملية دمج
+
+166
+00:15:21,460 --> 00:15:26,710
+associativeيعني بقدر لما أجمع X و Y و Z تلت أعداد
+
+167
+00:15:26,710 --> 00:15:31,410
+حقيقية بقدر أحط القواس حوالين هنا أو ممكن أحطهم
+
+168
+00:15:31,410 --> 00:15:35,870
+هنا سيا مابتفرجش هاي عملية الدمج أو ال associative
+
+169
+00:15:35,870 --> 00:15:44,050
+law نفس الحاجة نفس الشيء عملية الضرب عملية دمج
+
+170
+00:15:44,050 --> 00:15:45,170
+associative
+
+171
+00:15:48,760 --> 00:15:53,220
+الخاصية التالتة الـ distributive laws أو قوانين
+
+172
+00:15:53,220 --> 00:16:02,130
+التوزيع عملية الضرب تتوزع على عملية الجامعةهذه X
+
+173
+00:16:02,130 --> 00:16:09,170
+لما أضربها في مجموعة Y و Z فبوزع الضرب X على Y و
+
+174
+00:16:09,170 --> 00:16:15,470
+بوزع X على Z نفس الشيء برضه في قانون توزيع لما
+
+175
+00:16:15,470 --> 00:16:20,330
+أضرب من اليسار برضه بوزع الضرب على المجموعة من
+
+176
+00:16:20,330 --> 00:16:23,590
+اليسار إذا أنا دول القانونين بسميهم distributive
+
+177
+00:16:23,590 --> 00:16:27,830
+laws أو قوانين التوزيع عملية الضرب توزيعية على
+
+178
+00:16:27,830 --> 00:16:32,830
+عملية الجمعفيه برضه خاصية رابعة ال identity
+
+179
+00:16:32,830 --> 00:16:39,310
+elements وجود العناصر المحايدة ففي الأعداد
+
+180
+00:16:39,310 --> 00:16:40,110
+الحقيقية
+
+181
+00:16:42,360 --> 00:16:47,040
+في عددين او عنصرين واحد نرمزله بالـ 0 و واحد
+
+182
+00:16:47,040 --> 00:16:51,760
+نرمزله بالرمز 1 و طبعا هدول عنصرين مختلفين غير
+
+183
+00:16:51,760 --> 00:16:58,660
+متساوين اذا هنا نفترض ان في يوجد عنصرين متميزين في
+
+184
+00:16:58,660 --> 00:17:05,280
+R في مجموعة الاعداد الحقيقية بحيث ان الانصر السفر
+
+185
+00:17:05,280 --> 00:17:10,340
+هذا المتميز لما اجمعه على اي عدد حقيقي X بيعطيه X
+
+186
+00:17:12,550 --> 00:17:16,290
+فهذا بنسميه الانصار صفر هذا بنسميه ال additive
+
+187
+00:17:16,290 --> 00:17:25,750
+identity أو المحايد الجامعيكذلك واحد ضرب X لو ضربت
+
+188
+00:17:25,750 --> 00:17:30,370
+هذا العنصر المتميز في أي عدد حقيقي X هيطلع عندي
+
+189
+00:17:30,370 --> 00:17:35,290
+الناتج X نفس العنصر هذا صحيح لكل عداد الحقيقية اذا
+
+190
+00:17:35,290 --> 00:17:39,470
+هنا بنسمي الواحد multiplicative identity او
+
+191
+00:17:39,470 --> 00:17:45,070
+المحايد الضربي okay اذا هي اربع خواص في كمان خاصية
+
+192
+00:17:45,070 --> 00:17:46,890
+خامسة
+
+193
+00:17:52,510 --> 00:17:59,710
+اللي هي وجود العناصر أو
+
+194
+00:17:59,710 --> 00:18:04,590
+ال inverse .. وجود ال inverse elements أو اللي هو
+
+195
+00:18:04,590 --> 00:18:12,220
+بيسموها النظارة أو العناصر المعاكسةفلأي عدد حقيقي
+
+196
+00:18:12,220 --> 00:18:17,620
+X يوجد
+
+197
+00:18:17,620 --> 00:18:25,860
+أنصر وحيد سالب X ينتمي ل R بحيث لو جمعت X مع سالبه
+
+198
+00:18:25,860 --> 00:18:32,040
+بيطلع المحايد يجمع 0في الحالة هذه بنسمي negative x
+
+199
+00:18:32,040 --> 00:18:37,680
+هذا العنصر negative x بنسميه ال additive inverse ل
+
+200
+00:18:37,680 --> 00:18:45,900
+x ال additive inverse النظير الجمعي ل x كذلك
+
+201
+00:18:45,900 --> 00:18:53,400
+في حالة الضرب في حالة الضرب مش كل عنصر له نظير
+
+202
+00:18:53,400 --> 00:18:57,320
+ضربي عشان x يكون له نظير ضربي لازم يكون مختلف عن
+
+203
+00:18:57,320 --> 00:19:03,630
+السفريعني السفر مستفن السفر إذا كان X غير لا مختلف
+
+204
+00:19:03,630 --> 00:19:08,390
+عن السفر ففي عنصر واحد there exist unique element
+
+205
+00:19:08,390 --> 00:19:13,390
+نرمزه بالرمز X to negative one ينتمي لR بحيث لو
+
+206
+00:19:13,390 --> 00:19:18,530
+ضربت ال X هذا مع العنصر هذا بيطلع عندي المظير
+
+207
+00:19:18,530 --> 00:19:23,450
+الضربي او multiplicative identity
+
+208
+00:19:26,280 --> 00:19:33,100
+العنصر هذا بنسميه النظير الضربي أو multiplicative
+
+209
+00:19:33,100 --> 00:19:33,800
+inverse
+
+210
+00:19:36,420 --> 00:19:41,260
+إذا ما هو ال real number system هو عبارة عن مجموعة
+
+211
+00:19:41,260 --> 00:19:46,260
+الأعداد الحقيقية هذه امعرف عليها two binary
+
+212
+00:19:46,260 --> 00:19:50,880
+operations عمليتين جبريتين واحدة بنسميها الجامعة
+
+213
+00:19:50,880 --> 00:19:55,400
+واحدة بنسميها الضرب والعمليتين هدول بيحققوا خمس
+
+214
+00:19:55,400 --> 00:20:00,660
+خواص مهمة اللي هي الخمس خواص اللي سردناها قبل شويه
+
+215
+00:20:02,340 --> 00:20:07,060
+Okay تمام هذا هو نظام الأعداد الحقيقية احنا الآن
+
+216
+00:20:07,060 --> 00:20:16,660
+بدنا ندرس خواص الأعداد الحقيقية هذه فأول
+
+217
+00:20:16,660 --> 00:20:22,320
+خاصية وهذه الخواص كلها خواص طبيعية ومعروفة وانتوا
+
+218
+00:20:22,320 --> 00:20:26,340
+عارفينها قبل هيك بس ماحدش كان بيعطيلها أسماءها
+
+219
+00:20:26,340 --> 00:20:30,660
+الآن بدنا نسمي الأشياءبنعطي الأشياء أسماء أو
+
+220
+00:20:30,660 --> 00:20:38,100
+مسميات فأول نظرية في ال section هذا بتعطيني
+
+221
+00:20:38,100 --> 00:20:43,340
+cancellation laws او قوانين الحذف قوانين الحذف ايه
+
+222
+00:20:43,340 --> 00:20:46,580
+يعني قوانين الحذف النظرية هذه بتقول لو كان في عندي
+
+223
+00:20:46,580 --> 00:20:51,880
+x و y و z و w أعداد حقيقية و w مختلف عن الصفر
+
+224
+00:20:51,880 --> 00:20:55,320
+فالنتائج
+
+225
+00:20:55,320 --> 00:21:03,040
+التالية بتكون صحيحةلو كان x زائد z بساوي y plus z
+
+226
+00:21:03,040 --> 00:21:11,540
+فبقدر أنا أجيب الجلم و أشطب ال z مع ال z و أقول
+
+227
+00:21:11,540 --> 00:21:15,220
+أستنتج أن x لازم تطلع بالساوي y إذا أنا إيش عملت
+
+228
+00:21:15,220 --> 00:21:20,020
+حدفت فهذا cancellation أحد ال cancellation الوزر
+
+229
+00:21:20,020 --> 00:21:24,730
+أحد قوانين الحدفةالخانون التاني بيقول لو كان عندي
+
+230
+00:21:24,730 --> 00:21:31,150
+X ضرب W بساوي Y ضرب W فممكن و طبعا لازم W مايسويش
+
+231
+00:21:31,150 --> 00:21:37,070
+0 عشان القسم على 0 غير معرفة فبقدر انا اجسم ع W او
+
+232
+00:21:37,070 --> 00:21:43,350
+اشطب W او cancelling W و اقول انه لو كان هذا صحيح
+
+233
+00:21:43,350 --> 00:21:48,890
+فاكيد لازم يطلع X بساوي Y بشرط ان W مايسويش 0 اما
+
+234
+00:21:48,890 --> 00:21:55,290
+لو W بساوي 0 فهذا الكلامnonsense يعني هراء ليس له
+
+235
+00:21:55,290 --> 00:22:02,610
+أساس رياضي طيب هذه القوانين بدنا نثبتها شو عرفناها
+
+236
+00:22:02,610 --> 00:22:08,990
+صح فبدأ استخدم الآن تعريف نظام الأعداد الحقيقية
+
+237
+00:22:08,990 --> 00:22:15,810
+انه عبارة عن مجموعة R وعمليتين جبريتين بحقق خمس
+
+238
+00:22:15,810 --> 00:22:22,060
+قواصمن خلال الخمس خواصة دول بدي أسهل أحاول أثبت
+
+239
+00:22:22,060 --> 00:22:25,760
+صحة القوانين هذه اللي هي cancellation laws أنا
+
+240
+00:22:25,760 --> 00:22:29,260
+أختارتلكم أثبت التاني لأنه الأول أسهل دايما
+
+241
+00:22:29,260 --> 00:22:35,710
+التعامل مع الجامعة أسهل من الضربفنشوف برهان الجزء
+
+242
+00:22:35,710 --> 00:22:39,090
+التاني و طبعا برهان الجزء الأول هيكون بالمثل مماثل
+
+243
+00:22:39,090 --> 00:22:43,110
+فاحنا في رياضيات ما نحبش اتقرار و الحكي كتير لما
+
+244
+00:22:43,110 --> 00:22:47,570
+يكون في حاجة مماثلة فنقول ممكن برهانها بالمثل و
+
+245
+00:22:47,570 --> 00:22:52,950
+بنسيب الطالب يتدرب عليها او يعني يحاول يتمرن عليها
+
+246
+00:22:52,950 --> 00:22:57,970
+او يثبتها بنفسه لأنها هتكون مماثلة و نفس الفكرة و
+
+247
+00:22:57,970 --> 00:23:00,210
+في الرياضيات انت عارفين افكار اذا احنا عارفنا
+
+248
+00:23:00,210 --> 00:23:07,380
+الأفكار يعني ملكنا الحلOkay نشوف برهان الجزء
+
+249
+00:23:07,380 --> 00:23:11,640
+التاني انا بدي اثبت ايش ال .. ايش الفرض انتوا كلكم
+
+250
+00:23:11,640 --> 00:23:15,720
+درستوا مبادئ رياضيات هذا conditional statement هي
+
+251
+00:23:15,720 --> 00:23:20,860
+المقدم وهي التالي هي الفرض وهي النتيجة فبنفرض انه
+
+252
+00:23:20,860 --> 00:23:25,860
+الفرض هذا صحيح يعني هذا صح الان بنثبت النتيجة نعمل
+
+253
+00:23:25,860 --> 00:23:30,880
+direct proof برهان مباشر صح؟ يعني بدي اثبت النتيجة
+
+254
+00:23:30,880 --> 00:23:35,560
+فهي النتيجة بدي اثبت X بساوي Y هي ال Xالان ال X
+
+255
+00:23:35,560 --> 00:23:39,840
+هذه من الخواص الخمسة ممكن ابدل X بواحد في X لان
+
+256
+00:23:39,840 --> 00:23:45,620
+واحد في X عبارة عن X الان هذا عملية الضرب
+
+257
+00:23:45,620 --> 00:23:51,060
+commutative ابدالية فممكن ابدل الان هذا الواحد
+
+258
+00:23:51,060 --> 00:24:00,470
+هبدله W ضرب W انفرس وهذا صحيحطيب الان انا في عند
+
+259
+00:24:00,470 --> 00:24:04,490
+عملية ضرب عملية associative فبحاول ان انا ايه
+
+260
+00:24:04,490 --> 00:24:11,230
+استخدم ال associative law هين استخدمته الان xw من
+
+261
+00:24:11,230 --> 00:24:15,550
+المعطيات انا عندي x ضرب w بساوي y ضرب w اذا انا
+
+262
+00:24:15,550 --> 00:24:23,640
+هشيل xw و اضع مكانها ywوبالتالي صار عندي الكلام
+
+263
+00:24:23,640 --> 00:24:28,360
+هذا لان بستخدم ال associative law تغير ترتيب
+
+264
+00:24:28,360 --> 00:24:33,180
+الأقواص وهذا برجعه بساوي واحد و بستخدم ال
+
+265
+00:24:33,180 --> 00:24:37,240
+commutative law فبطلع عندي في النهاية Y إذن هين
+
+266
+00:24:37,240 --> 00:24:45,200
+أثبتت إن X بساوي Y و هنا في البرهان استخدمت بعض
+
+267
+00:24:45,200 --> 00:24:49,170
+الخواص الخمسة تبقىالـ real number system أو نظام
+
+268
+00:24:49,170 --> 00:24:54,350
+الأعداد الحقيقية بظبط زاد ال logic المنطق أو
+
+269
+00:24:54,350 --> 00:24:59,010
+أساسيات الرياضيات إذا هذا هو إيه البرهان برهان
+
+270
+00:24:59,010 --> 00:25:03,050
+الجزء الأول مماثل فهي اللي كتبلكم exercise يعني
+
+271
+00:25:03,050 --> 00:25:07,290
+اتمرنوا عليه اتمرنوا عليه يعني حاولوا تكتبوه بنفس
+
+272
+00:25:07,290 --> 00:25:12,250
+الطريقة تمام واضح البرهان واضح في أي سؤال
+
+273
+00:25:14,950 --> 00:25:19,530
+Okay تمام طيب نشوف كمان نظرية تانية نظريات لسه
+
+274
+00:25:19,530 --> 00:25:25,270
+حاجات بسيطة نشوف النص تبع النظرية انا عندي ضايل
+
+275
+00:25:25,270 --> 00:25:30,910
+دقيقتين ممكن احنا تبعين رياضيات يعني بنحب نستغل
+
+276
+00:25:30,910 --> 00:25:38,470
+وجتنا كتير وكل دقيقة انا اه هذه نظرية طويلة طيب مش
+
+277
+00:25:38,470 --> 00:25:43,530
+مشلا بس هنحاول نشوف النص تبعها و بعدين المرة
+
+278
+00:25:43,530 --> 00:25:49,920
+الجاية بنبرهنهاهذه النظرية فيها عشر أجزاء النظرية
+
+279
+00:25:49,920 --> 00:25:55,180
+هذه بتقول إذا أخدت أي أربع عداد حقيقية XYZW وإذا
+
+280
+00:25:55,180 --> 00:26:00,960
+كان ال Z و ال W مختلفين عن السفر فالخواص
+
+281
+00:26:00,960 --> 00:26:06,650
+التالية كلها صحيحةو هي اول خاصية لو ضربت اي عدد
+
+282
+00:26:06,650 --> 00:26:10,030
+حقيقي في سفر المفروض يطلع لعدد السفر ال additive
+
+283
+00:26:10,030 --> 00:26:16,050
+ال additive identity الان هذا ال additive inverse
+
+284
+00:26:16,050 --> 00:26:21,510
+ل X لما اخد ال additive inverse ل X مرتين كأن ايه
+
+285
+00:26:21,510 --> 00:26:25,390
+ارجعت ل X زي المصفوفة خد ال inverse ل المصفوفة
+
+286
+00:26:25,390 --> 00:26:30,980
+مرتين تطلع المصفوفة نفسها شبيها فيها صحيح؟طيب برضه
+
+287
+00:26:30,980 --> 00:26:35,360
+نفس الحاجة لما أخد ال multiplicative inverse مرتين
+
+288
+00:26:35,360 --> 00:26:39,940
+هذا بيساوي العنصر نفسه هذا صحيح طبعا هنا بشرط w
+
+289
+00:26:39,940 --> 00:26:45,080
+مايساويش سفر في الضرب دايما بنكون .. حاول نكون
+
+290
+00:26:45,080 --> 00:26:48,440
+careful حريصين أنه إيه الحاجة اللي بدنا نجيبلها
+
+291
+00:26:48,440 --> 00:26:52,910
+multiplicative inverse ماتكونش بتساوي سفرلو ضربت
+
+292
+00:26:52,910 --> 00:26:56,430
+العدد سالب واحد هذا real number في X كأن ضربت X في
+
+293
+00:26:56,430 --> 00:27:02,790
+سالب فهذا نفس الشيء لو ضربت X في سالب Y نفس الشيء
+
+294
+00:27:02,790 --> 00:27:07,030
+كما لو أني ضربت X في Y وضربت الكل في سالب واحد أو
+
+295
+00:27:07,030 --> 00:27:12,850
+هيك كل هذا صح لو أخدت negative X و جمعتها على
+
+296
+00:27:12,850 --> 00:27:18,470
+negative Y كأن أخدت X زاد Y وضربت في سالب هذا كله
+
+297
+00:27:18,470 --> 00:27:23,680
+صحطيب لو ضربت negative x في negative y كأنني ضربت
+
+298
+00:27:23,680 --> 00:27:31,880
+x في y هذا برضه صحيح لو جسمت x على z و y على w و
+
+299
+00:27:31,880 --> 00:27:42,120
+جمعتهم فهيطلع عندى ال .. من واحد المقامات و
+
+300
+00:27:42,120 --> 00:27:47,350
+العملية الجبرية هذه المعروفةأخيرا الخاصية الأخيرة
+
+301
+00:27:47,350 --> 00:27:51,990
+هذه لو أنا فيها عندي عددين حقيقيين كان حصل ضربهم
+
+302
+00:27:51,990 --> 00:27:58,090
+بساوي سفر فلازم واحد على أقل منهم بساوي سفر فاما x
+
+303
+00:27:58,090 --> 00:28:02,830
+بساوي سفر او y بساوي سفر وهذه ممكن مرت معاكم في
+
+304
+00:28:02,830 --> 00:28:08,430
+المبادئ عفوا هذا أكيد مرت معاكم في المبادئ كمثال
+
+305
+00:28:08,430 --> 00:28:15,100
+على indirect proofعلى برهان غير مباشر حاولوا انكم
+
+306
+00:28:15,100 --> 00:28:21,660
+انتوا تفكروا في براهين الحاجات هذه و المرة الجاية
+
+307
+00:28:21,660 --> 00:28:28,520
+ان شاء الله نحاول نبرهن بعض الأجزاء okay تمام ال
+
+308
+00:28:28,520 --> 00:28:34,310
+.. ال material هذه هحطها على الصفحه تبعتيو ممكنكم
+
+309
+00:28:34,310 --> 00:28:39,670
+أنكم تنسخوها و تاخدوها و تشوفوها فبالتالي مافيش
+
+310
+00:28:39,670 --> 00:28:44,670
+داعي أنكم تكتبوا لإن ممكن تنسخوها و تحطوها على ال
+
+311
+00:28:44,670 --> 00:28:49,250
+laptop تبعكم أو على ال computer okay تمام هنوقف
+
+312
+00:28:49,250 --> 00:28:53,090
+هنا و ان شاء الله المرة الجاية بنكمل و بنجيبلكم
+
+313
+00:28:53,090 --> 00:28:56,710
+معلومات جديدة عن توزيع الدرجات و الامتحانات فى حد
+
+314
+00:28:56,710 --> 00:28:58,090
+عنده اي سؤال او استفسار
+
+315
+00:29:03,220 --> 00:29:06,820
+اه من .. منحطلكم يعني اه منحطلكم يعني ان شاء الله
+
+316
+00:29:06,820 --> 00:29:12,660
+يعني كام كبير ليه يعني يكون يكفيكي من هالشهر okay
+
+317
+00:29:12,660 --> 00:29:16,980
+تمام؟ في اي سؤال تاني؟ okay شكرا لكم و ان شاء الله
+
+318
+00:29:16,980 --> 00:29:22,500
+نشوفكم المرة الجاية و نلتقي يوم الأتنين ان شاء
+
+319
+00:29:22,500 --> 00:29:22,600
+الله
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/CRzAwh3Ypto_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/CRzAwh3Ypto_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..498a73dcfab7727eed31eceb464ac765b266afdc
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/CRzAwh3Ypto_postprocess.srt
@@ -0,0 +1,1704 @@
+1
+00:00:21,580 --> 00:00:26,600
+بسم الله الرحمن الرحيم ان شاء الله اليوم هناخد
+
+2
+00:00:26,600 --> 00:00:31,760
+section خمسة اتنين اللي عنوانه combination of
+
+3
+00:00:31,760 --> 00:00:38,560
+continuous functions قبل ما ناخد اول نظريةعن الـ
+
+4
+00:00:38,560 --> 00:00:41,860
+combination of continuous functions نستذكر أو
+
+5
+00:00:41,860 --> 00:00:45,300
+نسترجع مع بعض تعريف ال continuous ال continuity
+
+6
+00:00:45,300 --> 00:00:49,300
+عند نقطة ف a function f from a to r is continuous
+
+7
+00:00:49,300 --> 00:00:55,620
+at c نقطة c تنتمي ل a f and only f لكل إبسلون في
+
+8
+00:00:55,620 --> 00:00:59,740
+دلتا تعتمد على إبسلون عدد موجة بهات لكل x في a
+
+9
+00:01:00,390 --> 00:01:03,710
+المسافة بينها وبين الـC أصغر من دلتا لازم هذا
+
+10
+00:01:03,710 --> 00:01:08,610
+يتضمن أن absolute F of X minus F of C أصغر من
+
+11
+00:01:08,610 --> 00:01:13,270
+إبسلون طبعا شوفنا أن هذا التعريف بيكافئ التعريف
+
+12
+00:01:13,270 --> 00:01:18,970
+اللي أخدناه في calculus A هو الشرط
+
+13
+00:01:18,970 --> 00:01:23,980
+اللي هو بتاوي تلت شروطوهو ان limit f عن c تكون
+
+14
+00:01:23,980 --> 00:01:30,900
+موجودة و f عن c موجودة و اتنين بسوء نفس القيمة
+
+15
+00:01:30,900 --> 00:01:43,420
+الان لو فى عندي تلت دولة f و g و h بيه functions
+
+16
+00:01:43,420 --> 00:01:48,700
+from a to r بيه
+
+17
+00:01:48,700 --> 00:01:49,460
+functions
+
+18
+00:01:54,460 --> 00:02:06,860
+و c تنتمي إلى a و b real number ال
+
+19
+00:02:06,860 --> 00:02:17,440
+functions
+
+20
+00:02:17,440 --> 00:02:23,820
+are continuous at c
+
+21
+00:02:28,450 --> 00:02:34,350
+إذا الدوالة التلاتة F وG وH كلهم متصلين عند النقطة
+
+22
+00:02:34,350 --> 00:02:44,150
+C اللي بتنتمي إليها النتيجة F plus أو minus G F
+
+23
+00:02:44,150 --> 00:02:53,630
+ضرب G B ضرب F are continuous at C
+
+24
+00:02:55,230 --> 00:03:11,750
+B إذا كان H H of X لا تساوي سفر لكل X في A then F
+
+25
+00:03:11,750 --> 00:03:19,710
+على H الدالة F على H is continuous is continuous
+
+26
+00:03:19,710 --> 00:03:20,950
+at C
+
+27
+00:03:25,450 --> 00:03:38,190
+وهي البرهان proof to
+
+28
+00:03:38,190 --> 00:03:48,530
+show مثلا ال function fg is continuous at c
+
+29
+00:03:51,910 --> 00:04:02,370
+We have لدينا التالي بتثبت
+
+30
+00:04:02,370 --> 00:04:09,010
+ان ال F حصل ضرب الدالتين F و G متصل اخترار متصل
+
+31
+00:04:09,010 --> 00:04:14,990
+and C فالاثبات دالك بتثبت ان الشرط هذا تبع الاتصال
+
+32
+00:04:14,990 --> 00:04:23,830
+على النقطة بتحقق فتعالى نشوف high limit F ضرب Gعند
+
+33
+00:04:23,830 --> 00:04:33,190
+X لما X تقول لـC بنثبت أن هذا بيساوي FG عند C فهذا
+
+34
+00:04:33,190 --> 00:04:42,190
+بيساوي limit F of X ضرب G of X as X tends to C هذا
+
+35
+00:04:42,190 --> 00:04:48,610
+من تعريف حصل ضرب اخترانين وهذا بيساوي أنا عندي
+
+36
+00:04:48,610 --> 00:04:56,150
+limit F of X لما X تقول لـC existو limit ال
+
+37
+00:04:56,150 --> 00:05:02,250
+function g of x لما x تقول ل c exist لأن ال
+
+38
+00:05:02,250 --> 00:05:05,110
+function f continuous عند ال c و ال function g
+
+39
+00:05:05,110 --> 00:05:11,250
+احنا فرضينها continuous عند cمش هيكو بس ومن اتصال
+
+40
+00:05:11,250 --> 00:05:17,410
+ده ل F عن C ال limit هذه بيساوي قيمة F عن C وكذلك
+
+41
+00:05:17,410 --> 00:05:20,810
+من اتصال ال function G عن C ال limit هذه بتطلع
+
+42
+00:05:20,810 --> 00:05:30,610
+بيساوي G عن C وهذا بيساوي F ضرب G of C إذن هاي
+
+43
+00:05:30,610 --> 00:05:36,480
+الشرطتبع الاتصال عن نقطة متحقق لل function f ضارب
+
+44
+00:05:36,480 --> 00:05:42,720
+g وبالتالي therefore by definition ال function f g
+
+45
+00:05:42,720 --> 00:05:59,940
+is continuous at c تمام ال proof ال proof of the
+
+46
+00:05:59,940 --> 00:06:00,580
+other
+
+47
+00:06:05,540 --> 00:06:14,200
+parts is similar مشابه للبرهان اللي احنا لسه
+
+48
+00:06:14,200 --> 00:06:19,180
+ماخدينه يعني لإثبات ان مثلا مجموعة دلتين
+
+49
+00:06:19,180 --> 00:06:24,660
+continuous برضه ممكن اثبات ان limit f زائد g لما x
+
+50
+00:06:24,660 --> 00:06:31,220
+تقول ل c بساوي f زائد g and cلو بدنا نثبت ان limit
+
+51
+00:06:31,220 --> 00:06:39,480
+f على g او f على h continuous عن c فبناخد limit f
+
+52
+00:06:39,480 --> 00:06:47,420
+على h عن c وهذا بيطلع بساوي limit f of x على h of
+
+53
+00:06:47,420 --> 00:06:53,810
+x ومع ان limit المقاملأ يساوي سفر لأن H ب X لأ
+
+54
+00:06:53,810 --> 00:07:00,210
+يساوي سفر لكل X في A فممكن نوزع ال limit نقول
+
+55
+00:07:00,210 --> 00:07:02,910
+limit خارج كسمها بيساوي limit ال bus علي limit
+
+56
+00:07:02,910 --> 00:07:06,770
+المقام و limit ال bus بيساوي F عن C لأن F
+
+57
+00:07:06,770 --> 00:07:13,070
+continuous عن C و limit المقام عن C اللي هو H عن C
+
+58
+00:07:13,070 --> 00:07:15,950
+بيساوي قيمة الدالة H عن C لإن أنا متصل عن C
+
+59
+00:07:16,620 --> 00:07:21,880
+وبالتالي بيطلع limit f على h لما x تقول ل c بس هو
+
+60
+00:07:21,880 --> 00:07:27,660
+قيمة الدالة f على h and c okay إذا البرهين
+
+61
+00:07:27,660 --> 00:07:34,860
+المتبقية ممكن يعني أعطاها بنفس الطريقة okay تمام
+
+62
+00:07:34,860 --> 00:07:38,720
+النظرية
+
+63
+00:07:38,720 --> 00:07:40,640
+هذه ممكن تعميمها
+
+64
+00:07:43,880 --> 00:07:51,460
+يعني بدل لو كانت الدالة F و G و H متصلين are
+
+65
+00:07:51,460 --> 00:07:56,640
+continuous are
+
+66
+00:07:56,640 --> 00:08:08,380
+continuous على كل المجموعة A على كل المجال على
+
+67
+00:08:08,380 --> 00:08:15,140
+كل المجال Aالـ F والـ G والـ H المجال المشترك
+
+68
+00:08:15,140 --> 00:08:18,800
+تبعهم المجموعة A فلو كانت الدوالة اتا كلهم
+
+69
+00:08:18,800 --> 00:08:30,280
+continuous على كل المجموعة A ف .. then فبتطلع
+
+70
+00:08:30,280 --> 00:08:36,520
+كل الدوالة هذه متصلة على كل المجموعة Aعلى كل
+
+71
+00:08:36,520 --> 00:08:51,320
+المجموع A يعني هذا بيصير on A وهذه on .. on A فلو
+
+72
+00:08:51,320 --> 00:08:52,380
+بدي أبرهن
+
+73
+00:08:58,870 --> 00:09:03,330
+أي واحدة من الدوايا الهادئة continuous على كل ال A
+
+74
+00:09:03,330 --> 00:09:15,770
+فإيش بعمل بقول fix C تنتمي إلى A and
+
+75
+00:09:15,770 --> 00:09:21,870
+then by
+
+76
+00:09:21,870 --> 00:09:23,090
+above theorem
+
+77
+00:09:28,740 --> 00:09:35,220
+by above theorem أنا
+
+78
+00:09:35,220 --> 00:09:40,520
+الأن عندي كل واحدة من الدوال هدولة continuous على
+
+79
+00:09:40,520 --> 00:09:45,240
+المجموعة a وبالتالي
+
+80
+00:09:45,240 --> 00:09:47,040
+then
+
+81
+00:09:48,850 --> 00:09:52,490
+بما أنه F و G و H continuous على كل المجموعة A فهي
+
+82
+00:09:52,490 --> 00:09:55,870
+continuous عند أي نقطة مش هيك تعرف الاتصال على
+
+83
+00:09:55,870 --> 00:10:08,510
+مجموعة اذا F و G و H are continuous at C وبالتالي
+
+84
+00:10:08,510 --> 00:10:10,130
+حسب النظرية السابقة
+
+85
+00:10:19,920 --> 00:10:26,160
+So by above theorem
+
+86
+00:10:26,160 --> 00:10:32,600
+all functions in
+
+87
+00:10:32,600 --> 00:10:36,660
+parts A
+
+88
+00:10:36,660 --> 00:10:45,920
+and B are continuous at C مش هي كثبتنا احنا في
+
+89
+00:10:45,920 --> 00:10:48,120
+النظرية السابقة هذه اللي جاب ال head اللي انا
+
+90
+00:10:48,120 --> 00:10:52,520
+عدلتهالو كان في عندي تلت دوال و كلهم متصلين عن
+
+91
+00:10:52,520 --> 00:10:57,040
+النقطة فكل الدول الموجودة في الفرق a و الدول
+
+92
+00:10:57,040 --> 00:11:01,300
+الموجودة في الفرق b كلهم بيطلعوا continuous عن نفس
+
+93
+00:11:01,300 --> 00:11:09,660
+النقطة الان بما أن النقطة c was arbitrary since c
+
+94
+00:11:09,660 --> 00:11:17,880
+belonged to a was arbitrary the above
+
+95
+00:11:25,240 --> 00:11:32,060
+All functions in A
+
+96
+00:11:32,060 --> 00:11:37,260
+and B are
+
+97
+00:11:37,260 --> 00:11:39,580
+continuous
+
+98
+00:11:41,100 --> 00:11:46,400
+على كل المجموعة A لأن كل واحدة منهم continuous على
+
+99
+00:11:46,400 --> 00:11:51,060
+أي و كل نقطة C في A وبالتالي هذا يكون برنامج
+
+100
+00:11:51,060 --> 00:11:56,540
+النظرية إذا النظرية هذه تنتج مباشرة من نظرية
+
+101
+00:11:56,540 --> 00:12:04,020
+السابقتها وذلك بتثبيت C عنصر في A وطبعا النظرية
+
+102
+00:12:04,020 --> 00:12:08,300
+السابقة بتقول عند أي عنصرC بما أن التلات دوال
+
+103
+00:12:08,300 --> 00:12:12,440
+متصلة إذا كل ال combinations هدولة بطلعوا متصلين
+
+104
+00:12:12,440 --> 00:12:17,220
+عن نفس النقطة هذا صحيح لأي نقطة ل C وبالتالي كلهم
+
+105
+00:12:17,220 --> 00:12:21,840
+متصلين على كل المجال تباعهم اللي هو المجموعة A
+
+106
+00:12:21,840 --> 00:12:28,040
+تمام ناخد
+
+107
+00:12:28,040 --> 00:12:29,100
+بعض الأمثلة
+
+108
+00:12:40,050 --> 00:12:46,710
+every polynomial .. every polynomial function على
+
+109
+00:12:46,710 --> 00:12:56,190
+الصورة P of X بيساوي A N في X to N plus A N minus
+
+110
+00:12:56,190 --> 00:13:03,290
+one في X to N minus one زائد .. زائد A one في X
+
+111
+00:13:03,290 --> 00:13:08,330
+زائد A zero is continuous
+
+112
+00:13:10,930 --> 00:13:15,470
+on R proof
+
+113
+00:13:15,470 --> 00:13:20,310
+fix
+
+114
+00:13:20,310 --> 00:13:23,750
+fix
+
+115
+00:13:23,750 --> 00:13:29,150
+C ينتمي ل R و بد أثبت أن ال polynomial function P
+
+116
+00:13:29,150 --> 00:13:36,470
+هذه متصلة عند النقطة C طيب we should أثبتنا في
+
+117
+00:13:36,470 --> 00:13:45,400
+chapter 4 we shouldin chapter in chapter four that
+
+118
+00:13:45,400 --> 00:13:48,960
+لو
+
+119
+00:13:48,960 --> 00:13:53,420
+في عندي polynomial P
+
+120
+00:13:53,420 --> 00:13:57,660
+polynomial في X فأثبتنا أن ال limit لل polynomial
+
+121
+00:13:57,660 --> 00:14:03,280
+P عند أي real number
+
+122
+00:14:03,280 --> 00:14:11,430
+C بسوء قيمتها عن C thereforeحسب تعريف تبع الاتصال
+
+123
+00:14:11,430 --> 00:14:22,830
+النقطة إذا P is continuous at C بما أن الـ C was
+
+124
+00:14:22,830 --> 00:14:28,510
+arbitrary element
+
+125
+00:14:28,510 --> 00:14:35,610
+إذا P continuous عند كل الـ C في R وبالتالي P is
+
+126
+00:14:35,610 --> 00:14:43,190
+continuousعلى كل المجموعة R هنا ال A اللي هي R
+
+127
+00:14:43,190 --> 00:14:49,190
+تمام مثال
+
+128
+00:14:49,190 --> 00:15:04,390
+تاني if R بتساوي P على Q P على Q where P
+
+129
+00:15:04,390 --> 00:15:05,930
+و Q R
+
+130
+00:15:08,300 --> 00:15:19,440
+Polynomials are كثيرات حدود then R is continuous
+
+131
+00:15:19,440 --> 00:15:29,720
+on الست اللي هي R كل الأعداد الحقيقية معدى أسفار
+
+132
+00:15:29,720 --> 00:15:36,720
+المقام كل ال X حيث Q of X بتساوي سفر
+
+133
+00:15:50,720 --> 00:15:56,680
+Proof برضه Fix C
+
+134
+00:15:56,680 --> 00:16:08,860
+تنتمي الى R معدى كل ال X حيث Q of X بتساوي سفر
+
+135
+00:16:08,860 --> 00:16:18,260
+معدى أسفار ال function Q إذن Q and C لا يساوي سفر
+
+136
+00:16:20,990 --> 00:16:30,050
+So by chapter .. By chapter four احنا أثبتنا انه
+
+137
+00:16:30,050 --> 00:16:37,310
+في الحالة هذه ال limit ل R of X as X tends to C
+
+138
+00:16:37,310 --> 00:16:48,030
+بساوي R of C وبالتالي therefore R is continuous
+
+139
+00:16:50,660 --> 00:16:58,640
+at C ولمّا كانت الـ C موجودة في R minus أسفار
+
+140
+00:16:58,640 --> 00:17:04,520
+المقام was arbitrarily إذن الـ R continuous على كل
+
+141
+00:17:04,520 --> 00:17:18,080
+الـ A الست هذه okay دي الأبارع بنكتبها طيب
+
+142
+00:17:18,080 --> 00:17:19,900
+في الدول المثلثية
+
+143
+00:17:25,880 --> 00:17:41,480
+في الدوان المثلثية زي الدالة مثلا sign مثال
+
+144
+00:17:41,480 --> 00:17:52,660
+رقم تلاتة f of x بساوي sign x is continuous
+
+145
+00:17:56,130 --> 00:18:07,970
+on R مبتصل على جميع الأعداد الحقيقية proof we
+
+146
+00:18:07,970 --> 00:18:08,650
+use
+
+147
+00:18:13,350 --> 00:18:21,010
+هنستخدم الحقائق التالية absolute sign z أصغر من أو
+
+148
+00:18:21,010 --> 00:18:30,290
+ساوى واحد لكل z في R هذا معروف من الرسمة تبعت ال
+
+149
+00:18:30,290 --> 00:18:33,690
+sign function ال sign function أكبر قيمة إلها ال
+
+150
+00:18:33,690 --> 00:18:38,190
+maximum value واحد وال absolute minimum سالب واحد
+
+151
+00:18:38,190 --> 00:18:43,220
+إذا قيمها محصورة بينهمإذن هذه واضحة من الرسم أو من
+
+152
+00:18:43,220 --> 00:18:50,960
+تعريف ال function كذلك في اندي كمان absolute
+
+153
+00:18:50,960 --> 00:18:59,040
+sin z أصغر من أو ساوي absolute z for all z في R
+
+154
+00:18:59,040 --> 00:19:02,240
+إذن
+
+155
+00:19:02,240 --> 00:19:08,260
+هذه موجود برهانها في chapter chapter
+
+156
+00:19:08,260 --> 00:19:16,030
+8الناس اللي هياخدوا تحليل حقيقة 2 هيشوفوا البرهان
+
+157
+00:19:16,030 --> 00:19:20,890
+والناس اللي مش هياخدوا تحليل حقيقة 2 ممكن يقرؤوا
+
+158
+00:19:20,890 --> 00:19:27,890
+البرهان من chapter 8 حتى تعرفوا يعني ايه تتحققوا
+
+159
+00:19:27,890 --> 00:19:35,870
+ان هذه فعلا المتباينة الصحيحة كذلكمن حساب المثلثات
+
+160
+00:19:35,870 --> 00:19:39,970
+من الـ trigonometry اللي درسناها في calculus A أو
+
+161
+00:19:39,970 --> 00:19:45,030
+ما حتى في الثانوية العامة كان في متطابقات مثلثية و
+
+162
+00:19:45,030 --> 00:19:54,690
+من المتطابقات هذه ممكن نستنتج ان sign x minus sign
+
+163
+00:19:54,690 --> 00:20:11,220
+c بساوي اتنين في signنص في x minus c ضرب
+
+164
+00:20:11,220 --> 00:20:23,100
+cosine نص
+
+165
+00:20:23,100 --> 00:20:26,200
+في
+
+166
+00:20:26,200 --> 00:20:27,680
+x زاد c
+
+167
+00:20:37,480 --> 00:20:46,140
+إذن هذه المتطابقة ممكن أثبتها كيف نثبتها sign
+
+168
+00:20:46,140 --> 00:20:51,900
+الفرق x ع 2 سالب c ع 2 sign الفرق بيسوي sign
+
+169
+00:20:51,900 --> 00:21:00,860
+cosine سالب cosine sign و cosine المجموعة بيسوي
+
+170
+00:21:00,860 --> 00:21:04,420
+cosine cosine سالب sine sine و بعدين نجمعهم و
+
+171
+00:21:04,420 --> 00:21:09,160
+نضربهموفي اتنين فهيطلع في الآخر بتتصف عليه okay
+
+172
+00:21:12,120 --> 00:21:16,040
+بالمناسبة في برضه كمان هندي مش absolute sine z
+
+173
+00:21:16,040 --> 00:21:22,100
+أصغر من أو ساوي الواحد وكذلك في هندي absolute
+
+174
+00:21:22,100 --> 00:21:28,820
+cosine z برضه أصغر من أو ساوي واحد لكل z في R لأنه
+
+175
+00:21:28,820 --> 00:21:32,260
+برضه ال cosine ال absolute مجزمة منها واحد وال
+
+176
+00:21:32,260 --> 00:21:35,600
+absolute minimum سالب واحد وبالتالي قيمة محصورة
+
+177
+00:21:35,600 --> 00:21:40,020
+بين سالب واحد واحد الآن خلينا ناخد ال ..
+
+178
+00:21:42,890 --> 00:21:46,090
+من المعادلة الأخيرة
+
+179
+00:21:56,720 --> 00:21:59,960
+من المعادلة الأخيرة بطلع عندي لو أخدت ال absolute
+
+180
+00:21:59,960 --> 00:22:05,840
+value للطرفين فبطلع عندي absolute sin x minus sin
+
+181
+00:22:05,840 --> 00:22:12,700
+c طبعا هذا الكلام كله صحيح لكل x و c أعداد حقيقية
+
+182
+00:22:14,590 --> 00:22:20,190
+فهذا بيطلع بساوي او اصغر من او ساوي اتنين في
+
+183
+00:22:20,190 --> 00:22:28,230
+absolute sin z absolute sin z اصغر من او ساوي
+
+184
+00:22:28,230 --> 00:22:35,070
+absolute z اللي هو نص في absolute x minus z ضرب
+
+185
+00:22:35,070 --> 00:22:41,650
+absolute cosine z اصغر من او ساوي الواحد اصغر من
+
+186
+00:22:41,650 --> 00:22:52,580
+او ساوي الواحدتمام؟ و هذا صحيح لكل x و c في R طبعا
+
+187
+00:22:52,580 --> 00:23:00,660
+هذا بيساوي absolute x minus c و
+
+188
+00:23:00,660 --> 00:23:06,260
+من المتباين هذي بينتج ان ده ل sign متصل عن c okay؟
+
+189
+00:23:06,260 --> 00:23:20,770
+اذا to show fix c belong to Rto show أن f of x
+
+190
+00:23:20,770 --> 00:23:32,290
+بساوي sin x is continuous at c let epsilon أكبر من
+
+191
+00:23:32,290 --> 00:23:37,050
+السفر be given it shows
+
+192
+00:23:40,310 --> 00:23:44,950
+دلتا بساوي إبسلون أكبر من الصفر إذا هيوجد دلتا
+
+193
+00:23:44,950 --> 00:23:51,430
+تعتمد على إبسلون عدد موجب فلهذه الدلتا لو كان X
+
+194
+00:23:51,430 --> 00:23:56,950
+بينتمي إلى R اللي هو مجال الدالة A و absolute X
+
+195
+00:23:56,950 --> 00:24:04,070
+minus C أصغر من دلتا فهذا بتضمن أنه absolute F of
+
+196
+00:24:04,070 --> 00:24:15,190
+X-f of c اللي هو absolute sin x minus sin c شوفنا
+
+197
+00:24:15,190 --> 00:24:21,870
+هذا أصغر من أو ساوي absolute x minus c من هنا الآن
+
+198
+00:24:21,870 --> 00:24:25,530
+ال x هذه ماخدها أنا بحيث المسافة بينها وبين ال c
+
+199
+00:24:25,530 --> 00:24:30,410
+أصغرمن delta وانا اختار ال delta تساوي epsilon
+
+200
+00:24:30,410 --> 00:24:34,810
+عشان يطلع absolute الفرق بين f of x وf of z أصغر
+
+201
+00:24:34,810 --> 00:24:39,370
+من epsilon إذا هاي شرط epsilon delta لتعريف ال
+
+202
+00:24:39,370 --> 00:24:44,910
+continuity و النقطة المتحققةبما ان ابسلون was
+
+203
+00:24:44,910 --> 00:24:51,090
+arbitrary since ابسلون اكبر من السفر was arbitrary
+
+204
+00:24:51,090 --> 00:24:56,550
+اذا حسب تعريف ابسلون دلتا للاتصال بيطلع عندي ال
+
+205
+00:24:56,550 --> 00:25:05,710
+function f of x بتساوي sin x is continuous at c
+
+206
+00:25:05,710 --> 00:25:11,130
+وبما ان ال c was arbitrary since
+
+207
+00:25:14,280 --> 00:25:22,700
+C belonged to R since C belonged to R was
+
+208
+00:25:22,700 --> 00:25:29,940
+arbitrary وهين أثبتنا أن ال F continuous at C فF
+
+209
+00:25:29,940 --> 00:25:36,980
+is continuous على كل ال R وهو المطلوب
+
+210
+00:25:40,210 --> 00:25:43,290
+ان الـ sine function continuous على كل الـ R
+
+211
+00:25:43,290 --> 00:25:52,970
+بالمثل ممكن اثبات ان ال function g of x بساوي
+
+212
+00:25:52,970 --> 00:26:01,630
+cosine x ايضا continuous on R هنستخدم ال ..
+
+213
+00:26:01,630 --> 00:26:10,410
+هنستخدم يعني الحاجات هذه او اتنين منهم و ..بدل ال
+
+214
+00:26:10,410 --> 00:26:16,710
+sign هنستخدم معادلة أو متطابقة زي هذه بس نبدل ال
+
+215
+00:26:16,710 --> 00:26:27,010
+sign ب cosine فهنا
+
+216
+00:26:27,010 --> 00:26:34,800
+هيصير في عندي اختلاف هذا هصير سالب اتنينبدل اتنين
+
+217
+00:26:34,800 --> 00:26:43,640
+و هيكون عند هنا sign نص sign نص المجموعة ضرب sign
+
+218
+00:26:43,640 --> 00:26:48,820
+نص الفرق تمام؟
+
+219
+00:26:48,820 --> 00:26:54,040
+و طبعا هناخد ال absolute value للطرفين
+
+220
+00:26:56,180 --> 00:26:59,400
+فهذا بيساوي ال absolute value للطرف التاني
+
+221
+00:26:59,400 --> 00:27:06,700
+وباستخدام المتطابقات هذه فهذا هيطلع أصغر من
+
+222
+00:27:06,700 --> 00:27:11,380
+absolute سالب اتنين بيطلع اتنين وهذا أصغر من
+
+223
+00:27:11,380 --> 00:27:17,000
+absolute sine of z أصغر من أو ساوي الواحد و
+
+224
+00:27:17,000 --> 00:27:18,960
+absolute cosine of z
+
+225
+00:27:30,570 --> 00:27:37,920
+لأ هذه مش cosine هذه sinهذه الـ sine فهي sine الـ
+
+226
+00:27:37,920 --> 00:27:40,800
+z ال absolute value لها أصغر من أو يساوي الواحد
+
+227
+00:27:40,800 --> 00:27:47,800
+وهي كمان sine أو absolute value ل sine ال z أصغر
+
+228
+00:27:47,800 --> 00:27:53,360
+من أو يساوي absolute ال z ال z هنا اللي هو نص في x
+
+229
+00:27:53,360 --> 00:28:00,620
+minus z فبطلع نص في absolute في absolute x minus z
+
+230
+00:28:00,620 --> 00:28:06,150
+بطلع هذا بساوي absolute x minus zو باقي البرهان زي
+
+231
+00:28:06,150 --> 00:28:10,110
+ما عملنا هنا okay تمام لأي epsilon أكبر من السفر
+
+232
+00:28:10,110 --> 00:28:15,130
+choose delta بساوي epsilon ف this delta will work
+
+233
+00:28:15,130 --> 00:28:22,370
+تمام إذا باقي البرهان كما عملنا في حالة ال sine
+
+234
+00:28:22,370 --> 00:28:29,210
+إذا هذا المثال الرابع شوفنا فيه كيف نثبت إن ال
+
+235
+00:28:29,210 --> 00:28:33,870
+cosine function is continuous تمام واضح
+
+236
+00:28:37,340 --> 00:28:48,220
+الان ممكن اثبات بعد هيك انه ال tangent function
+
+237
+00:28:48,220 --> 00:28:58,040
+tangent x اللي هي بساوي sin x على cos x is
+
+238
+00:28:58,040 --> 00:28:58,800
+continuous
+
+239
+00:29:01,890 --> 00:29:06,770
+الصين مستمر على الار والكوسين مستمر على الار هذه
+
+240
+00:29:06,770 --> 00:29:10,670
+راشيونال فانتشار فانتشار راشيونال فانتشار مستمر
+
+241
+00:29:10,670 --> 00:29:14,370
+على الار ما عدا عند أسفار المخام ما هي أسفار
+
+242
+00:29:14,370 --> 00:29:19,910
+الكوسين المضاعفات
+
+243
+00:29:19,910 --> 00:29:27,970
+الفردية لا πاية اتنين مستمر على الار ما عدا
+
+244
+00:29:31,580 --> 00:29:42,960
+تنين n زياد واحد في πاي على اتنين حيث ان عدد صحيح
+
+245
+00:29:42,960 --> 00:29:46,040
+صح؟
+
+246
+00:29:46,040 --> 00:29:49,100
+هيك
+
+247
+00:29:49,100 --> 00:29:57,940
+بقطين المضاعفات الفردية لπاي على اتنينو كذلك cot x
+
+248
+00:29:57,940 --> 00:30:06,200
+بيساوي cosine x على sin x is continuous على r مادة
+
+249
+00:30:06,200 --> 00:30:14,260
+أسفار المقام اللي هي مضاعفات الـ pi مضاعفات الـ pi
+
+250
+00:30:14,260 --> 00:30:21,160
+مادة n pi حيث ان عدد صحيح
+
+251
+00:30:27,460 --> 00:30:32,160
+و كذلك بالمثل
+
+252
+00:30:32,160 --> 00:30:39,460
+ال .. ال .. ال secant .. لأ ال cosecant x اللي
+
+253
+00:30:39,460 --> 00:30:45,240
+بيساوي واحد على sign ال x متصل على R معدى عند
+
+254
+00:30:45,240 --> 00:30:52,570
+أسفار المقان، اذا زيها زيالـ cotangent و ال secant
+
+255
+00:30:52,570 --> 00:30:58,430
+x اللي هي واحد على cos برضه متصلة زيها زي ال
+
+256
+00:30:58,430 --> 00:31:02,690
+tangent على R بعد المضاعفات الفردية ل πاية اتنين
+
+257
+00:31:02,690 --> 00:31:10,190
+okay تمام طيب
+
+258
+00:31:10,190 --> 00:31:10,790
+ناخد
+
+259
+00:31:28,820 --> 00:31:39,340
+ناخد النظرية التالية let f
+
+260
+00:31:39,340 --> 00:31:43,440
+be a function from A to R
+
+261
+00:31:56,070 --> 00:32:09,810
+وحد if if is continuous if if is continuous at c
+
+262
+00:32:09,810 --> 00:32:14,370
+تنتمي إلى a then absolute if
+
+263
+00:32:17,670 --> 00:32:27,990
+is continuous at c then if if is continuous on a
+
+264
+00:32:27,990 --> 00:32:41,190
+then absolute if is continuous on a proof
+
+265
+00:32:41,190 --> 00:32:44,230
+we
+
+266
+00:32:44,230 --> 00:32:44,850
+use
+
+267
+00:32:47,240 --> 00:32:51,480
+we use exercise
+
+268
+00:32:51,480 --> 00:32:54,760
+exercise
+
+269
+00:32:54,760 --> 00:33:00,600
+رقم تلتاش
+
+270
+00:33:00,600 --> 00:33:09,220
+في section أربعة اتنين نرجع لل exercise هذا و
+
+271
+00:33:09,220 --> 00:33:09,900
+نكتبه
+
+272
+00:33:16,290 --> 00:33:29,470
+الـ exercise هذا بيقول if
+
+273
+00:33:29,470 --> 00:33:38,790
+ال limit ل ال function f of x لما x تقول إلى c
+
+274
+00:33:38,790 --> 00:33:41,470
+exists
+
+275
+00:33:47,480 --> 00:33:57,760
+then ال limit ل absolute f of x لما x تقول إلى c
+
+276
+00:33:57,760 --> 00:34:04,600
+exist
+
+277
+00:34:04,600 --> 00:34:11,180
+and equals absolute limit absolute
+
+278
+00:34:11,180 --> 00:34:16,900
+limit f of x لما x تقول إلى c
+
+279
+00:34:22,160 --> 00:34:26,760
+طبعاً و هنا C is cluster point الـ C هنا cluster
+
+280
+00:34:26,760 --> 00:34:30,700
+point cluster
+
+281
+00:34:30,700 --> 00:34:41,220
+point of A و طبعاً F function من A إلى R فهذا
+
+282
+00:34:41,220 --> 00:34:46,480
+التمرين موجود في section 4-2 لو كانت ال function F
+
+283
+00:34:46,480 --> 00:34:54,090
+ال limit تبعتها عن C موجودةف limit absolute f and
+
+284
+00:34:54,090 --> 00:34:58,170
+c برضه بتكون موجودة و بساوي قيمتها ال absolute
+
+285
+00:34:58,170 --> 00:35:02,350
+value ل limit f of x and z يعني مقدر نبدل ال
+
+286
+00:35:02,350 --> 00:35:06,170
+absolute value مع ال limit الآن باستخدام هذا ال
+
+287
+00:35:06,170 --> 00:35:18,290
+exercise ممكن نبره هنا النظرية السابقة إذا
+
+288
+00:35:18,290 --> 00:35:18,690
+هنا
+
+289
+00:35:23,870 --> 00:35:30,210
+لبرهان الجزء الأول to
+
+290
+00:35:30,210 --> 00:35:36,410
+show if
+
+291
+00:35:36,410 --> 00:35:44,890
+is .. to show absolute if is
+
+292
+00:35:44,890 --> 00:35:51,710
+continuous at c تنتمي ل a
+
+293
+00:36:03,810 --> 00:36:09,350
+لدينا اتصالين اتصال
+
+294
+00:36:09,350 --> 00:36:16,650
+اتصال اتصال اتصال اتصال اتصال اتصال اتصال اتصال
+
+295
+00:36:23,200 --> 00:36:26,500
+فشوفنا ان لو كانت الـ C ماهياش cluster point
+
+296
+00:36:26,500 --> 00:36:31,780
+فالاتصال عندها بيطلع متحقق اوتوماتيكي شوفنا في
+
+297
+00:36:31,780 --> 00:36:40,600
+التعريف then the continuity of
+
+298
+00:36:40,600 --> 00:36:47,700
+absolute if at C is automatic
+
+299
+00:36:47,700 --> 00:36:49,560
+اوتوماتيكي
+
+300
+00:36:50,790 --> 00:36:56,590
+إذا احنا بنهتم بالحالة التانية انه C is a cluster
+
+301
+00:36:56,590 --> 00:37:12,550
+point of A ففي الحالة هذه by exercise تلتاش
+
+302
+00:37:12,550 --> 00:37:19,170
+of section اربعة
+
+303
+00:37:19,170 --> 00:37:19,930
+اتنين
+
+304
+00:37:28,440 --> 00:37:37,660
+بما أنه limit ل f of x as x tends to c بيساوي c
+
+305
+00:37:37,660 --> 00:37:46,940
+احنا فرضين ان f continuous by continuity of f at c
+
+306
+00:37:48,200 --> 00:37:51,740
+بما ان f continuous at c احنا فرضين ان f is
+
+307
+00:37:51,740 --> 00:37:55,920
+continuous at c فبالتالي
+
+308
+00:37:55,920 --> 00:38:01,020
+limit f of x لما x تقول ل c بيساوي f of c اذا هاي
+
+309
+00:38:01,020 --> 00:38:05,320
+في عندي limit f of x لما x تقول ل c exist و بيساوي
+
+310
+00:38:05,320 --> 00:38:13,860
+f of c اذا by exercise 13 بطلع عندي limit
+
+311
+00:38:16,480 --> 00:38:25,460
+absolute f of x as x tends to c موجودة وبساوي
+
+312
+00:38:25,460 --> 00:38:37,480
+absolute limit ل f of x لما x تقول ل c اللي هي
+
+313
+00:38:37,480 --> 00:38:45,580
+بتطلع بساوي absolute f of cاللي هي عبارة عن
+
+314
+00:38:45,580 --> 00:38:50,780
+absolute f محسوب عن c إذا هي شرط الاتصال لل
+
+315
+00:38:50,780 --> 00:38:55,980
+function absolute f عند النقطة c متحقق وبالتالي
+
+316
+00:38:55,980 --> 00:39:04,620
+therefore absolute f is continuous at c إذا هذا
+
+317
+00:39:04,620 --> 00:39:09,020
+بثبت الجزء الأول الجزء التاني corollary على الجزء
+
+318
+00:39:09,020 --> 00:39:14,920
+الأول نتيجة الجزء الأوللأن إذا كانت الدالة F
+
+319
+00:39:14,920 --> 00:39:20,640
+continuous على كل الـ A معناته F continuous عند كل
+
+320
+00:39:20,640 --> 00:39:26,600
+C في A وبالتالي بيطلع absolute F متصل عند كل C في
+
+321
+00:39:26,600 --> 00:39:34,680
+A صح؟ إذن هذا إيه برهن النظرية إذن التاني نتيجة
+
+322
+00:39:34,680 --> 00:39:40,900
+على الجزء الأول في كمان نظرية أخرى مشابهة زي هذه
+
+323
+00:39:43,790 --> 00:39:50,770
+لكن بدل absolute f ففي عندى هنا let f be function
+
+324
+00:39:50,770 --> 00:39:57,510
+from a to r such that f of x أكبر من أو يساوي سفر
+
+325
+00:39:57,510 --> 00:40:05,170
+لكل x في a يعني هنا ال dialer قيمها غير سالبة فلو
+
+326
+00:40:05,170 --> 00:40:14,660
+كانت f continuous at c فال square root ل fبطلع
+
+327
+00:40:14,660 --> 00:40:21,580
+continuous at C كذلك لو كانت F continuous on A ف
+
+328
+00:40:21,580 --> 00:40:29,760
+ال square root ل F is continuous على كل ال A و
+
+329
+00:40:29,760 --> 00:40:34,500
+المرة هذه البرهان بستخدم exercise ثاني في section
+
+330
+00:40:34,500 --> 00:40:40,090
+42 اللي هو exercise 14الـ exercise هذا بيقول إذا
+
+331
+00:40:40,090 --> 00:40:44,510
+كانت ال limit للدالة هذه، يعني C موجودة، then ال
+
+332
+00:40:44,510 --> 00:40:49,030
+limit للـ square .. لل function اللي هي square
+
+333
+00:40:49,030 --> 00:40:56,970
+root of F عند الـ C موجودة وبتساوي ال square root
+
+334
+00:40:56,970 --> 00:41:04,110
+وبتساوي جذر التربيع أيه؟ ال limit لل square root
+
+335
+00:41:05,350 --> 00:41:09,530
+يعني بمعنى اخر انا ممكن ابدل ال limit مع ال square
+
+336
+00:41:09,530 --> 00:41:15,750
+root و البرهان زي برهان النظرية السابقة
+
+337
+00:41:34,960 --> 00:41:37,360
+الحالة التانية اللي هي المهمة لو كانت C cluster
+
+338
+00:41:37,360 --> 00:41:44,180
+point ل A فحسب exercise 14من سكتشن أربعة اتنين
+
+339
+00:41:44,180 --> 00:41:49,120
+اللي هو كتبناه هناك بما أنه ال limit بما أنه ال
+
+340
+00:41:49,120 --> 00:41:54,160
+function if continuous at c إذا ال limit f of x من
+
+341
+00:41:54,160 --> 00:41:58,900
+x تقوى ل c exist و بساوي f of c الآن من exercise
+
+342
+00:41:58,900 --> 00:42:03,400
+أربعة عشر إذا
+
+343
+00:42:03,400 --> 00:42:07,680
+ال limit هي عند ال limit ل f of x من x تقوى ل c
+
+344
+00:42:07,680 --> 00:42:10,440
+exist إذا by exercise
+
+345
+00:42:14,160 --> 00:42:19,740
+أربعتاش limit ال square root لل function f لما X
+
+346
+00:42:19,740 --> 00:42:27,200
+تقول ل C exist و بساوي ال square root لل limit of
+
+347
+00:42:27,200 --> 00:42:31,460
+the function يعني C وهذا بساوي
+
+348
+00:42:33,950 --> 00:42:37,990
+الـ square root أنا عندي limit f of x عند c exist
+
+349
+00:42:37,990 --> 00:42:44,870
+و بتساوي f of c إذن هذا بيطلع بساوي ال square root
+
+350
+00:42:44,870 --> 00:42:50,870
+ل f هذه ك function محسوبة عن c إذن أنا في عند ال
+
+351
+00:42:50,870 --> 00:42:57,510
+function جدر ال f بالمناسبة جدر f and x كيف
+
+352
+00:42:57,510 --> 00:43:02,430
+بنعرفها؟ بيه عبارة عن الجدر التربيهي ل f of x
+
+353
+00:43:05,740 --> 00:43:11,800
+فإذا أنا عندي الدالة تبعتي جذر F هي دي function ال
+
+354
+00:43:11,800 --> 00:43:16,920
+function هي حسبنا ال limit اللي عند C طلعت موجودة
+
+355
+00:43:16,920 --> 00:43:24,140
+و بتساوي قيمتها عند C إذا ال square root ل F ك
+
+356
+00:43:24,140 --> 00:43:29,560
+function is continuous at C تمام؟ إذا هذا بثبت
+
+357
+00:43:29,560 --> 00:43:33,980
+الجزء الأول من النظرية هذه الآن الجزء التاني
+
+358
+00:43:33,980 --> 00:43:41,050
+Corollaryto the first part نتيجة على الجزء الأول
+
+359
+00:43:41,050 --> 00:43:45,510
+لأنه إذا كانت إذا
+
+360
+00:43:45,510 --> 00:43:52,210
+كانت ال F continuous على كل ال A فهي continuous
+
+361
+00:43:52,210 --> 00:43:56,370
+عند كل C في A وبالتالي ال square root من الجزء
+
+362
+00:43:56,370 --> 00:44:01,250
+الأول إلها continuous عند ال C وهذا ال C هذا طبعا
+
+363
+00:44:01,250 --> 00:44:04,170
+ال C was arbitrary إذا ال square root continuous
+
+364
+00:44:04,170 --> 00:44:15,650
+على كل ال Aتمام؟ إذن هذه الحاجات .. هذا هو برهانها
+
+365
+00:44:15,650 --> 00:44:24,030
+ال exercise 13 و 14 هدول نظريات فالمفروض أن احنا
+
+366
+00:44:24,030 --> 00:44:31,910
+يعني إيه .. ان .. نبرهنهم فلو
+
+367
+00:44:31,910 --> 00:44:52,750
+بدنا نبرهن مثلاالجزء الأخير هذا فممكن
+
+368
+00:44:52,750 --> 00:45:02,030
+نستخدم ال sequential criterion يعني
+
+369
+00:45:02,030 --> 00:45:03,070
+مثلا ال proof
+
+370
+00:45:06,120 --> 00:45:25,180
+of exercise أربعة طعش section أربعة اتنين we
+
+371
+00:45:25,180 --> 00:45:28,920
+use sequential
+
+372
+00:45:28,920 --> 00:45:29,920
+criterion
+
+373
+00:45:32,750 --> 00:45:37,670
+أنا بتثبت أن عندي limit f of x عن c exist و بتثبت
+
+374
+00:45:37,670 --> 00:45:42,450
+limit الجذر ال f عن c exist و بساوي الجذر تربية ال
+
+375
+00:45:42,450 --> 00:45:55,150
+unlimited ف let x in be sequence طبعا
+
+376
+00:45:55,150 --> 00:45:56,530
+في مجال الدالة
+
+377
+00:46:01,100 --> 00:46:10,900
+b sequence in a such that limit xn بساوي c تمام
+
+378
+00:46:10,900 --> 00:46:18,060
+then xn
+
+379
+00:46:18,060 --> 00:46:24,120
+أكبر من أو يساوي سفر لأ قيمة الدالة
+
+380
+00:46:43,880 --> 00:46:53,240
+طيب اذا ال function عندي f of x اذا
+
+381
+00:46:53,240 --> 00:47:01,820
+since limit f of x as x tends to c exist هذا
+
+382
+00:47:01,820 --> 00:47:09,850
+بيقدّي انه ال limitالـ f of x in as n tends to
+
+383
+00:47:09,850 --> 00:47:14,530
+infinity موجودة
+
+384
+00:47:14,530 --> 00:47:21,010
+exist و
+
+385
+00:47:21,010 --> 00:47:29,270
+بتساوي and مثلا equals عدد L كويس هذا by
+
+386
+00:47:29,270 --> 00:47:32,810
+sequential criterion
+
+387
+00:47:35,150 --> 00:47:39,110
+الـ function لها limit عن c إذا كان لكل sequence x
+
+388
+00:47:39,110 --> 00:47:46,570
+in تتقارب ل c نهاية صورتها موجودة وبتساوي عدد معين
+
+389
+00:47:46,570 --> 00:47:55,910
+الأن أنا عندي sense f of x in أكبر من أو ساوى 0
+
+390
+00:47:55,910 --> 00:48:01,350
+لكل in لأن الدالة قيمها موجبة الدالة هذه قيمها
+
+391
+00:48:01,350 --> 00:48:10,190
+موجبةفالـ limit فالـ L اللي هي limit f
+
+392
+00:48:10,190 --> 00:48:14,510
+of x in تطلع موجب ايضا اكبر من أو ساوي سفر
+
+393
+00:48:14,510 --> 00:48:21,610
+وبالتالي
+
+394
+00:48:21,610 --> 00:48:26,410
+ال limit وفي
+
+395
+00:48:26,410 --> 00:48:30,310
+عندي انا الآن ال sequence هذه by
+
+396
+00:48:32,240 --> 00:48:41,100
+في مثال أخدناه سابقا او نظرية by theorem تلاتة
+
+397
+00:48:41,100 --> 00:48:46,260
+اتنين عشرة في الكتاب بتقول لو في عندي sequence زي
+
+398
+00:48:46,260 --> 00:48:55,330
+هذه حدودها غير سالبة فال limitللـ square root ل F
+
+399
+00:48:55,330 --> 00:49:05,390
+of X N as N tends to infinity تطلع موجودة
+
+400
+00:49:05,390 --> 00:49:11,610
+و
+
+401
+00:49:11,610 --> 00:49:16,970
+بالساوي جذر ال Lحسب النظرية هذه إذا كان في end
+
+402
+00:49:16,970 --> 00:49:22,170
+sequence حدودها غير سالبة ومتقاربة إذا ال limit
+
+403
+00:49:22,170 --> 00:49:25,630
+square root لحدودها بساوي square root ل limit
+
+404
+00:49:25,630 --> 00:49:29,330
+تبعتها طبما ال square root ل L هي عبارة عن ال
+
+405
+00:49:29,330 --> 00:49:37,150
+square root ل limit f of x in
+
+406
+00:49:41,810 --> 00:49:47,030
+من هنا الـ square root لإيه اللي بيساوي ال square
+
+407
+00:49:47,030 --> 00:49:56,990
+root لlimit f of x n لما n طول لإنفينتيز اذا
+
+408
+00:49:56,990 --> 00:50:04,550
+انا هيطلع عندي ال limit وهذه عبارة عن limit
+
+409
+00:50:07,530 --> 00:50:15,030
+للـ square root ل F of XN لما N تقول infinity اذا
+
+410
+00:50:15,030 --> 00:50:19,650
+انا بدأت ب XN sequence contained in A ونهايتها C
+
+411
+00:50:19,650 --> 00:50:25,330
+فطلع نهايت نهايت
+
+412
+00:50:25,330 --> 00:50:30,250
+صورتها صورة ال sequence موجودة وبساوي ال square
+
+413
+00:50:30,250 --> 00:50:35,010
+root ل L موجودة وبالتالي therefore by sequential
+
+414
+00:50:39,060 --> 00:50:47,080
+criterion ال limit لل square root ل F of X لما X
+
+415
+00:50:47,080 --> 00:50:55,780
+تقول إلى C بساوي exist و بساوي ال square root ل F
+
+416
+00:50:55,780 --> 00:51:00,980
+and C أو
+
+417
+00:51:00,980 --> 00:51:03,820
+اللي هو اللي بساوي .. لأ بساوي اللي هو
+
+418
+00:51:09,800 --> 00:51:20,620
+السكوير روت ال L اللي هو برضه اللي هو
+
+419
+00:51:20,620 --> 00:51:23,100
+نعم نعم
+
+420
+00:51:31,480 --> 00:51:37,500
+يعني هاد ممكن هاد يسميها L من الأول فإذا بطلع عندي
+
+421
+00:51:37,500 --> 00:51:40,940
+ال square root function لها limit، limit عن سي
+
+422
+00:51:40,940 --> 00:51:46,260
+موجودة بساوي square root ل L إذا هاد بكمل البرهن
+
+423
+00:51:46,260 --> 00:51:52,320
+بالمثل ممكن نبرهن exercise اللي جابله 13
+
+424
+00:51:57,010 --> 00:52:01,530
+فحاولوا يكونوا تبرهنوا exercise 13 بنفس الطريقة،
+
+425
+00:52:01,530 --> 00:52:07,570
+في أي سؤال أو استفسار؟ okay إذا المرة الجاية بال
+
+426
+00:52:07,570 --> 00:52:08,070
+campbell
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ehj01gka7EU.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ehj01gka7EU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..463fd2b901a445a1c9fb4ceee7508cab65b436d7
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ehj01gka7EU.srt
@@ -0,0 +1,1739 @@
+1
+00:00:19,740 --> 00:00:27,020
+بسم الله الرحمن الرحيم هنواصل اليوم تغطية section 
+
+2
+00:00:27,020 --> 00:00:34,550
+5-3 اللي بتعلق ب .. موضوع ال continuous functions
+
+3
+00:00:34,550 --> 00:00:40,590
+على ال intervals على الفترات احنا بدينا ال ..
+
+4
+00:00:40,590 --> 00:00:46,690
+بدينا الموضوع هذا المحاضرة السابقة و كان آخر نظرية
+
+5
+00:00:46,690 --> 00:00:50,890
+أخدناها اللي هي ال maximum .. maximum minimum
+
+6
+00:00:50,890 --> 00:00:56,870
+theorem نعود نستذكر بس نظرية الأخيرة هذه ال
+
+7
+00:00:56,870 --> 00:00:57,670
+maximum
+
+8
+00:01:12,090 --> 00:01:21,410
+ال maximum minimum theorem
+
+9
+00:01:21,410 --> 00:01:28,050
+يقول
+
+10
+00:01:28,050 --> 00:01:36,050
+إذا كانت if I is a closed and bounded interval 
+
+11
+00:01:36,050 --> 00:01:40,290
+closed and bounded
+
+12
+00:01:46,350 --> 00:01:56,730
+وإذا كانت الدالة من I إلى R مستمرة
+
+13
+00:01:56,730 --> 00:02:01,270
+على
+
+14
+00:02:01,270 --> 00:02:02,470
+الفترة I
+
+15
+00:02:07,590 --> 00:02:20,690
+there exist x lower star و x upper star عناصر في I
+
+16
+00:02:20,690 --> 00:02:22,070
+بحيث أن
+
+17
+00:02:24,550 --> 00:02:32,550
+f of x lower star بساوي ال minimum ل range ال
+
+18
+00:02:32,550 --> 00:02:41,450
+function f and f of x super star بساوي ال supremum
+
+19
+00:02:41,450 --> 00:02:49,410
+ل range ال function f وبالتالي هذه بسميها ال
+
+20
+00:02:49,410 --> 00:02:52,930
+absolute maximum
+
+21
+00:02:54,540 --> 00:03:03,820
+value والقيمة هتبسميها ال absolute minimum
+
+22
+00:03:03,820 --> 00:03:06,900
+value
+
+23
+00:03:06,900 --> 00:03:15,920
+لل function f على الفترة I طبعا okay okay في اليوم
+
+24
+00:03:15,920 --> 00:03:22,580
+هناخد نظريات برضه خاصة باتصال الدوال على الفترات
+
+25
+00:03:23,810 --> 00:03:30,090
+فأول نظرية هتكون location location
+
+26
+00:03:30,090 --> 00:03:36,970
+of roots theorem
+
+27
+00:03:36,970 --> 00:03:45,570
+نظرية تحديد ال roots فنفس
+
+28
+00:03:45,570 --> 00:03:46,790
+الحاجة let
+
+29
+00:03:49,750 --> 00:03:57,890
+I be closed and bounded interval على الصورة AB and
+
+30
+00:03:57,890 --> 00:04:06,190
+let f be a function from I to R be continuous
+
+31
+00:04:06,190 --> 00:04:09,790
+function
+
+32
+00:04:09,790 --> 00:04:15,390
+على الفترة المغلقة والمحدودة I if
+
+33
+00:04:17,630 --> 00:04:29,370
+لو كان f of a أصغر من صفر أصغر من f of b أو f of b
+
+34
+00:04:29,370 --> 00:04:38,610
+أصغر من صفر أصغر من f of a then
+
+35
+00:04:38,610 --> 00:04:48,980
+there exist c ينتمي للفترة المفتوحة من a إلى b بحيث
+
+36
+00:04:48,980 --> 00:04:57,540
+أن f of c بيساوي صفر فالنظرية
+
+37
+00:04:57,540 --> 00:05:08,100
+هذه ممكن أن نلخصها بالرسمة التالية محاور
+
+38
+00:05:08,100 --> 00:05:13,280
+الإحداثيات وممكن يكون في ending حاجة زي هذه
+
+39
+00:05:22,650 --> 00:05:28,930
+فهي function هذه عبارة عن ال graph y بساوي f of x
+
+40
+00:05:28,930 --> 00:05:37,750
+ال function هذه متصلة على الفترة المغلقة من a ل d
+
+41
+00:05:37,750 --> 00:05:42,890
+وهي 
+
+42
+00:05:42,890 --> 00:05:51,450
+عندي f of a أصغر من صفر وهي عندي
+
+43
+00:05:59,190 --> 00:06:02,510
+النظرية بتقول لو كان في دالة متصلة زي هذه على
+
+44
+00:06:02,510 --> 00:06:07,830
+فترة مغلقة من a ل b وكان f of a أصغر من الصفر و
+
+45
+00:06:07,830 --> 00:06:16,370
+الصفر أصغر من f of b لابد أن نجد نقطة C بين A و B
+
+46
+00:06:16,370 --> 00:06:21,030
+بحيث أن قيمة الـ function عندها بيساوي صفر وواضح
+
+47
+00:06:21,030 --> 00:06:26,270
+أن نقطة C هي قيمة الـ function عندها بيساوي صفر
+
+48
+00:06:26,270 --> 00:06:30,830
+ممكن برضه يكون العكس يعني الملحوظة هذه يكون شكلها
+
+49
+00:06:30,830 --> 00:06:31,430
+زي هيك
+
+50
+00:06:35,680 --> 00:06:41,700
+فيكون يعني عندي هنا ال F of B هي السالبة بقى وهي
+
+51
+00:06:41,700 --> 00:06:46,580
+عند ال A فال F of B هي الموجبة بقى برضه نفس النتيجة
+
+52
+00:06:46,580 --> 00:06:47,620
+okay تمام؟
+
+53
+00:06:55,410 --> 00:06:59,790
+البرهان النظرية هذه يعني it's زي ما بيقولوا it's
+
+54
+00:06:59,790 --> 00:07:06,630
+quite technical يعني فيه شوية تفاصيل تقنية زيادة أنه 
+
+55
+00:07:06,630 --> 00:07:13,090
+طويل شوية فاحنا عشان بصدر نهاية الفصل ما بنحبش ناخد
+
+56
+00:07:13,090 --> 00:07:16,330
+.. ناخد .. ناخد في الـ proofs الطويلة فهنسيبكم تقرأوا
+
+57
+00:07:16,330 --> 00:07:19,530
+البرهان إذا see the textbook
+
+58
+00:07:25,030 --> 00:07:32,130
+إذا ممكن بدؤوكم يمكن تقرأوا البرهان من الكتاب و
+
+59
+00:07:32,130 --> 00:07:36,770
+تحاولوا تفهموه طبعا البرهان طويل ما بنجيبش طبعا
+
+60
+00:07:36,770 --> 00:07:41,990
+ال proofs الطويلة في هدف الامتحانات okay فهذا بالنسبة
+
+61
+00:07:41,990 --> 00:07:46,930
+للبرهان الآن هاي مثال مثلا مثال example
+
+62
+00:07:54,050 --> 00:07:58,270
+Show that the
+
+63
+00:07:58,270 --> 00:08:03,470
+equation f
+
+64
+00:08:03,470 --> 00:08:11,510
+of x بتساوي x في e أس x سالب اتنين بتساوي صفر has
+
+65
+00:08:11,510 --> 00:08:14,210
+a root
+
+66
+00:08:20,420 --> 00:08:29,980
+in الـ interval من صفر لواحد لنثبت
+
+67
+00:08:29,980 --> 00:08:35,200
+أن المعادلة f of x بيساوي صفر عشان f of x بيساوي
+
+68
+00:08:35,200 --> 00:08:43,100
+الدالة هذه لها جذور يعني بنقدر نلاقي أي
+
+69
+00:08:43,100 --> 00:08:54,460
+هذا يعني show أن يوجد C ينتمي للفترة المغلقة من صفر
+
+70
+00:08:54,460 --> 00:09:01,900
+لواحد بحيث أن f of C بيساوي صفر ففي الحالة اللي
+
+71
+00:09:01,900 --> 00:09:07,360
+بنقول أن C root جذر للمعادلة أو C zero لل
+
+72
+00:09:07,360 --> 00:09:14,900
+function F فبنثبت الكلام هذا فحسب النظرية هذه
+
+73
+00:09:27,630 --> 00:09:35,370
+F of X بيساوي X في E to X سالب اتنين is continuous
+
+74
+00:09:35,370 --> 00:09:40,650
+متصلة على الفترة المغلقة من صفر لواحد
+
+75
+00:09:47,890 --> 00:09:51,510
+لأن X في E to X هي دالة متصلة طرحنا منها ثابت
+
+76
+00:09:51,510 --> 00:09:56,750
+دالة متصلة على R كذلك
+
+77
+00:09:56,750 --> 00:10:06,460
+أنا عندي F of صفر بيساوي سالب اتنين أصغر من صفر و F
+
+78
+00:10:06,460 --> 00:10:15,300
+of واحد بيساوي E ثاني اتنين وال E معروف أنه عدد
+
+79
+00:10:15,300 --> 00:10:21,100
+أكبر من اتنين فهذا أكبر من صفر إذا هاي شروط ال
+
+80
+00:10:21,100 --> 00:10:28,500
+location of roots theorem كلها متحققة hence by
+
+81
+00:10:28,500 --> 00:10:33,700
+location of roots theorem
+
+82
+00:10:36,360 --> 00:10:42,300
+يوجد C ينتمي للفترة المغلقة من صفر إلى واحد بحيث
+
+83
+00:10:42,300 --> 00:10:55,640
+أن F of C بيساوي صفر إذا هنا اثبتنا أن C is a root
+
+84
+00:10:55,640 --> 00:11:01,400
+of equation F of X
+
+85
+00:11:04,080 --> 00:11:09,640
+بيساوي X في E أس X minus اتنين بيساوي صفر وهو
+
+86
+00:11:09,640 --> 00:11:16,360
+المطلوب إذا هنا اثبتنا أن فعلا المعادلة هذه لها
+
+87
+00:11:16,360 --> 00:11:22,720
+جذر في الفترة هذا الجذر يقع هو عدد C يقع في الفترة
+
+88
+00:11:22,720 --> 00:11:28,180
+من صفر لواحد عدد من صفر لواحد طبعا ممكن هذا العدد
+
+89
+00:11:28,180 --> 00:11:35,450
+C نعمله تقريب إلى أقرب يعني بحيث يكون النسبة الخطأ
+
+90
+00:11:35,450 --> 00:11:41,470
+من القيمة الحقيقية تبقى تكون أقل من واحد على ألف
+
+91
+00:11:41,470 --> 00:11:46,210
+أو واحد على مية أو واحد على عشر ألف فالكتاب موضح
+
+92
+00:11:46,210 --> 00:11:51,610
+لكم هي هنا في المثال كيف نجيب تقريب نحصل على العدد
+
+93
+00:11:51,610 --> 00:11:55,730
+صفر بحيث نطلع تقريبا قريب من القيمة الحقيقية
+
+94
+00:11:55,730 --> 00:11:59,030
+والفرق بينها ومن القيمة الحقيقية واللي هنحصل عليها في
+
+95
+00:11:59,030 --> 00:12:05,240
+المثال تكون أقل من واحد على ألف أو شيء زيها فممكن تقرأ
+
+96
+00:12:05,240 --> 00:12:09,960
+وتشوف الكلام هذا في الكتاب لكن احنا اللي يهمنا أن
+
+97
+00:12:09,960 --> 00:12:15,460
+ال equation هذه ضمننا أن في لها root في الفترة
+
+98
+00:12:15,460 --> 00:12:18,740
+هذه حسب ال location of roots في الفترة الباقية
+
+99
+00:12:18,740 --> 00:12:24,520
+كانت تخلي ال root هذا يعني تجيب له قيمة قريبة جدا
+
+100
+00:12:24,520 --> 00:12:30,020
+من القيمة الحقيقية هذه مجرد يعني تفاصيل حسابية
+
+101
+00:12:30,020 --> 00:12:36,320
+okay فحاولوا تقرأوها من الكتاب لو سمحتوا الآن هذه
+
+102
+00:12:36,320 --> 00:12:47,540
+النظرية بتقود إلى نظرية ثانية وهي
+
+103
+00:12:47,540 --> 00:12:55,380
+Bolzano's
+
+104
+00:12:55,380 --> 00:12:57,140
+intermediate
+
+105
+00:13:04,990 --> 00:13:25,730
+value theorem let
+
+106
+00:13:25,730 --> 00:13:29,210
+I be any interval
+
+107
+00:13:36,870 --> 00:13:50,310
+and f from I to R be continuous على
+
+108
+00:13:50,310 --> 00:14:00,830
+الفترة I إذا كان A و B أعداد في الفترة I and
+
+109
+00:14:03,830 --> 00:14:16,170
+K عدد حقيقي such that F of A أصغر من K أصغر من F
+
+110
+00:14:16,170 --> 00:14:20,150
+of B then
+
+111
+00:14:20,150 --> 00:14:31,610
+النتيجة أنه يوجد C ينتمي للفترة I وهذا العدد C يقع
+
+112
+00:14:31,610 --> 00:14:32,010
+بين
+
+113
+00:14:38,340 --> 00:14:48,280
+between a and b such that بحيث أن f of c تطلع
+
+114
+00:14:48,280 --> 00:14:56,720
+بيساوي قيمة k لنعمل
+
+115
+00:14:56,720 --> 00:14:58,740
+رسمة قبل أن أظهر المظهر
+
+116
+00:15:17,560 --> 00:15:37,280
+فممكن يكون في عندي function زي هذه مثلا فهي
+
+117
+00:15:37,280 --> 00:15:43,320
+في عندي فترة I الدالة معرفة ومتصلة عليها
+
+118
+00:15:45,810 --> 00:15:52,110
+يعني هذه الفترة من هنا إلى هنا I وممكن يكون في
+
+119
+00:15:52,110 --> 00:15:59,510
+عندي أعداد A و B فممكن يكون مثلا هذه ال A وهذه ال B
+
+120
+00:15:59,510 --> 00:16:04,630
+فهذه
+
+121
+00:16:04,630 --> 00:16:10,450
+F of A فهذه
+
+122
+00:16:10,450 --> 00:16:11,430
+F of A
+
+123
+00:16:16,610 --> 00:16:22,070
+وهي F of B فلو
+
+124
+00:16:22,070 --> 00:16:25,290
+كان
+
+125
+00:16:25,290 --> 00:16:38,180
+K عدد بين F of A و F of B فهي F of B وهي F of A فـ K
+
+126
+00:16:38,180 --> 00:16:45,220
+عدد بين F of A و F of B فلهذا العدد نقدر نلاقي C
+
+127
+00:16:45,220 --> 00:16:49,420
+عدد C عدد
+
+128
+00:16:49,420 --> 00:16:53,960
+C بين A و B وبالتالي ينتمي للفترة I
+
+129
+00:16:57,560 --> 00:17:06,760
+إذا C بين A و B وينتمي للفترة I بحيث أن صورة C
+
+130
+00:17:06,760 --> 00:17:12,380
+هي صورة الـ C بيساوي العدد K هذا هو بولزانو
+
+131
+00:17:12,380 --> 00:17:16,560
+intermediate value theorem نظرية القيمة الوسيطية
+
+132
+00:17:16,560 --> 00:17:22,740
+نظرية القيمة الوسيطية لبولزانو ملاحظة نظرية هذه مش
+
+133
+00:17:22,740 --> 00:17:23,880
+صعبة سهلة
+
+134
+00:17:43,340 --> 00:17:48,440
+Proof البرهان بيعتمد على ال maximum minimum theorem
+
+135
+00:17:48,440 --> 00:17:55,160
+وعلى اللي هو location of roots theorem ففي عندي
+
+136
+00:17:55,160 --> 00:17:58,740
+هنا حلتين لاحظوا أن a و b أعداد حقيقية
+
+137
+00:18:19,180 --> 00:18:25,800
+النتيجة بتكون واضحة لو كان a بيساوي b فـ f of a
+
+138
+00:18:25,800 --> 00:18:31,470
+بتطلع بيساوي f of b وبالتالي أي k بين f of a وf of b
+
+139
+00:18:31,470 --> 00:18:35,690
+هيساوي واحدة منهم وبالتالي ال k بيساوي f of a خذ
+
+140
+00:18:35,690 --> 00:18:40,790
+ال c بيساوي a أو b فالنتيجة إيه واضحة بديهية يعني
+
+141
+00:18:40,790 --> 00:18:49,030
+متحققات القائمة so assume أن 
+
+142
+00:18:49,030 --> 00:18:52,630
+a لا يساوي b then
+
+143
+00:18:54,390 --> 00:18:58,750
+by tricotomy property إذا كان في عددين لا يساويان بعض
+
+144
+00:18:58,750 --> 00:19:06,610
+فبطلع a أصغر من b أو b أصغر من a فنأخذ الحالة
+
+145
+00:19:06,610 --> 00:19:14,850
+الأولى case one لو كان a أصغر من b ففي الحالة هذه
+
+146
+00:19:21,390 --> 00:19:29,810
+لو كان الـ a أصغر من b فبدي أعرف define
+
+147
+00:19:29,810 --> 00:19:39,130
+في الحالة هذه define g of x على أنها الدالة
+
+148
+00:19:39,130 --> 00:19:43,990
+اللي هي بالساوي f 
+
+149
+00:19:43,990 --> 00:19:47,990
+of x ناقص 
+
+150
+00:19:47,990 --> 00:19:48,470
+k
+
+151
+00:19:51,460 --> 00:19:56,340
+فطبعًا الـ function g الـ function f متصل على
+
+152
+00:19:56,340 --> 00:20:01,680
+الفترة I هو متصل على الفترة المغلقة من a إلى b
+
+153
+00:20:01,680 --> 00:20:07,080
+اللي هي جزء من الفترة I فالـ function g اللي 
+
+154
+00:20:07,080 --> 00:20:11,760
+بتساوي f ناقص ثابت مثلها متصل على نفس الفترة إذا g 
+
+155
+00:20:11,760 --> 00:20:18,450
+is continuous على الفترة المغلقة من a إلى b اللي هي
+
+156
+00:20:18,450 --> 00:20:22,130
+بالمناسبة مجموعة جزئية من I لأن الـ A و الـ B
+
+157
+00:20:22,130 --> 00:20:26,530
+موجودين في I و
+
+158
+00:20:26,530 --> 00:20:35,210
+كذلك لاحظوا أن G of A بيساوي F of A ناقص K وهذا من
+
+159
+00:20:35,210 --> 00:20:44,570
+هنا من الفرض هذا بيطلع أصغر من صفر وهذا أصغر من F
+
+160
+00:20:44,570 --> 00:20:52,070
+of B ناقص K F of B ناقص K بيطلع موجب اللي هو
+
+161
+00:20:52,070 --> 00:20:58,110
+بيساوي G of B إذا هذه شروط ال location of roots ال
+
+162
+00:20:58,110 --> 00:21:01,990
+theorem كلها متحققة هي و اندي فانش جي متصلة على فترة
+
+163
+00:21:01,990 --> 00:21:06,560
+مغلقة ومحدودة وقيمة الـ G عند الـ left endpoint
+
+164
+00:21:06,560 --> 00:21:11,980
+سلبية وقيمة الـ G عند ال right endpoint موجبة and
+
+165
+00:21:11,980 --> 00:21:16,220
+then by then 
+
+166
+00:21:16,220 --> 00:21:28,020
+by location of roots theorem يوجد
+
+167
+00:21:28,020 --> 00:21:37,570
+C ينتمي للفترة I يعني يوجد C ينتمي للفترة
+
+168
+00:21:37,570 --> 00:21:46,150
+المفتوحة من A و B اللي هي subset من I بحيث أن صورة
+
+169
+00:21:46,150 --> 00:21:54,170
+الـ C عندها بيساوي صفر لكن أنا عندي G of C من تعريف 
+
+170
+00:21:54,170 --> 00:22:02,490
+الـ function G G of C بيساوي F of C ناقص K حل
+
+171
+00:22:02,490 --> 00:22:09,850
+المعادلة هذه في F of C فبطلع F of C بيساوي K كما هو
+
+172
+00:22:09,850 --> 00:22:15,270
+مطلوب زي ما هو مطلوب أن هيك بتكون برهانة نظرية بس
+
+173
+00:22:15,270 --> 00:22:20,540
+في الحالة اللي فيها بتكون A أصغر من B يبقى ندرين
+
+174
+00:22:20,540 --> 00:22:25,300
+النظرية في الحالة التالية case 2 اللي فيها الـ b
+
+175
+00:22:25,300 --> 00:22:29,920
+أصغر من a ففي
+
+176
+00:22:29,920 --> 00:22:37,080
+الحالة هذه خلّيني أعرف المرة هذه function h على
+
+177
+00:22:37,080 --> 00:22:45,820
+أنها بتساوي K ناقص f of x فواضح clearly 
+
+178
+00:22:48,290 --> 00:22:57,210
+واضح أن الـ H زيها زي الـ F متصلة is continuous على
+
+179
+00:22:57,210 --> 00:23:06,690
+الفترة المغلقة والمحدودة من A لـ B and H 
+
+180
+00:23:06,690 --> 00:23:15,910
+of A بيساوي K ناقص K ناقص F of A بيطلع سالب K
+
+181
+00:23:15,910 --> 00:23:23,460
+ناقص F of A ومن الفرض هذا بيطلع سالب وهذا أصغر من 
+
+182
+00:23:23,460 --> 00:23:36,300
+K ناقص f of b اللي هو بيطلع h of b كذلك K لو 
+
+183
+00:23:36,300 --> 00:23:41,600
+طرحت من الـ k f of b فبيطلع موجب الفرق إذا الآن في 
+
+184
+00:23:41,600 --> 00:23:45,200
+هذه function h continuous على فترة مغلقة ومحدودة 
+
+185
+00:23:45,970 --> 00:23:49,610
+وقيمتها عند الـ left endpoint سالبة وعند الـ right
+
+186
+00:23:49,610 --> 00:23:58,170
+point موجبة إذا كل شروط ال location of roots في 
+
+187
+00:23:58,170 --> 00:24:04,550
+المتحققة so by
+
+188
+00:24:04,550 --> 00:24:12,790
+location of roots theorem يوجد
+
+189
+00:24:12,790 --> 00:24:23,950
+C ينتمي إلى الفترة مظبوط هيك؟ كده كده كده كده كده
+
+190
+00:24:23,950 --> 00:24:30,130
+كده كده كده كده
+
+191
+00:24:30,130 --> 00:24:31,150
+كده كده كده كده كده
+
+192
+00:24:36,660 --> 00:24:43,600
+هيك صح K ناقص F of B بيطلع سالب و هنا هاد المفروض 
+
+193
+00:24:43,600 --> 00:24:53,120
+تكون A و هاد A صحيح، بظبط، صح، إذا H of A اللي هي
+
+194
+00:24:53,120 --> 00:24:58,180
+K ناقص F of A هي K اطرح منها F of A بيطلع موجب 
+
+195
+00:24:58,940 --> 00:25:03,460
+بينما K ناقص F of B بيطلع سالب، مظبوط هيك، إذا U
+
+196
+00:25:03,460 --> 00:25:10,920
+يوجد C بين B و A وهي طبعًا فترة contained in R بحيث
+
+197
+00:25:10,920 --> 00:25:19,420
+أن H of C بيساوي صفر، لكن H of C من تعريفها هي 
+
+198
+00:25:19,420 --> 00:25:24,400
+عبارة عن K ناقص F of C وبالتالي هذا بيقدر حل
+
+199
+00:25:24,400 --> 00:25:30,190
+المعادلة هذه في F of C فبطلع F of C بيساوي K وهو
+
+200
+00:25:30,190 --> 00:25:35,010
+المطلوب إذا في الحالتين أثبتنا أن يوجد C في الفترة
+
+201
+00:25:35,010 --> 00:25:43,510
+I بين A و B وقيمتها عند C بيساوي K إذا هيك بيكون
+
+202
+00:25:43,510 --> 00:25:47,930
+برهاننا Bolzano's Intermediate Value
+
+203
+00:25:55,030 --> 00:26:03,170
+الآن هذه النظرية في عليها نتيجة مهمة
+
+204
+00:26:20,170 --> 00:26:26,910
+let I بيساوي closed and bounded interval and if the 
+
+205
+00:26:26,910 --> 00:26:37,070
+function from I to R be continuous ومتصلة على
+
+206
+00:26:37,070 --> 00:26:42,590
+الفترة I تمام؟
+
+207
+00:26:42,590 --> 00:26:45,910
+لو كان
+
+208
+00:26:48,570 --> 00:27:01,130
+K عدد حقيقي satisfies
+
+209
+00:27:01,130 --> 00:27:08,250
+بيحقق الشرط التالي أن K .. العدد K هذا أكبر من أو
+
+210
+00:27:08,250 --> 00:27:16,090
+ساوي ال infimum لـ set f of I اللي هو range الـ F اللي 
+
+211
+00:27:16,090 --> 00:27:20,590
+هي القيمة الصغيرة المطلقة لـ F على I وأصغر من أو يساوي
+
+212
+00:27:20,590 --> 00:27:24,890
+ال supremum لـ range الـ F اللي هي ال absolute 
+
+213
+00:27:24,890 --> 00:27:29,850
+maximum value لـ الـ function F على I ففي الحالة هذه
+
+214
+00:27:29,850 --> 00:27:42,260
+من نقدر نلاقي C there exist C ينتمي للفترة I بحيث
+
+215
+00:27:42,260 --> 00:27:51,400
+أن F of C بيساوي العدد K وبرهان
+
+216
+00:27:51,400 --> 00:28:00,440
+النظرية هذه سهل By
+
+217
+00:28:00,440 --> 00:28:05,440
+maximum minimum theorem
+
+218
+00:28:11,040 --> 00:28:14,040
+الـ maximum minimum theorem بتقول لو كان في هذه
+
+219
+00:28:14,040 --> 00:28:18,640
+function متصلة على فترة مغلقة ومحدودة فالـ
+
+220
+00:28:18,640 --> 00:28:24,020
+function هذه بتأخذ قيمتها العظمى المطلقة وقيمتها
+
+221
+00:28:24,020 --> 00:28:29,360
+الصغرى المطلقة وقيمتها العظمى المطلقة على الفترة I
+
+222
+00:28:29,360 --> 00:28:34,920
+يعني في أعداد في الفترة I عندها الـ function بتأخذ
+
+223
+00:28:34,920 --> 00:28:37,760
+قيمتها العظمى المطلقة وقيمتها الصغرى المطلقة
+
+224
+00:28:40,910 --> 00:28:51,330
+إذاً there exist x lower star و x super star عناصر
+
+225
+00:28:51,330 --> 00:29:00,870
+في I بحيث أن الـ F of x lower star بيساوي infimum
+
+226
+00:29:01,750 --> 00:29:10,230
+لسيت f of i and f of x super star بيساوي الـ
+
+227
+00:29:10,230 --> 00:29:15,050
+supremum لسيت
+
+228
+00:29:15,050 --> 00:29:26,270
+f of i تمام
+
+229
+00:29:26,270 --> 00:29:27,750
+hence
+
+230
+00:29:31,910 --> 00:29:41,670
+by حسب ال hypothesis ال hypothesis star من الفرض
+
+231
+00:29:41,670 --> 00:29:44,750
+ال star اللي هو إحنا فرضين أن الـ key عدد K هذا
+
+232
+00:29:44,750 --> 00:29:55,670
+بيحقق المتباينة يعني we have لدينا الـ k أكبر من أو
+
+233
+00:29:55,670 --> 00:30:06,970
+ساوي f of x lower star أصغر من أو يساوي f
+
+234
+00:30:06,970 --> 00:30:15,370
+of x upper star و 
+
+235
+00:30:15,370 --> 00:30:21,630
+الـ function and if is continuous على الفترة المغلقة
+
+236
+00:30:21,630 --> 00:30:33,690
+من x lower star إلى x super star أو
+
+237
+00:30:33,690 --> 00:30:41,650
+لعكس ممكن يكونوا متبادلة ثانية أو x super star x
+
+238
+00:30:41,650 --> 00:30:46,320
+lower star تعتمد على مين اللي أصغر من الثانية إذا
+
+239
+00:30:46,320 --> 00:30:50,760
+كانت هذه أصغر من هذه فهذه تطلع فترة داخل I و F 
+
+240
+00:30:50,760 --> 00:30:54,340
+continuous على I أيضًا continuous على أي فترة جزئية
+
+241
+00:30:54,340 --> 00:30:58,060
+منها وإذا كان ال X Superstar أصغر من X Lower Star 
+
+242
+00:30:58,060 --> 00:30:59,380
+فنأخذ الفترة أيضًا
+
+243
+00:31:03,410 --> 00:31:08,850
+شروط بولزانو فيروس تراسي فيرم هاي في عندي نقطتين A
+
+244
+00:31:08,850 --> 00:31:16,070
+و B بينتموا للفترة I و F continuous على I
+
+245
+00:31:28,770 --> 00:31:35,190
+وعندي a و b بينتموا للفترة I وعندي K أكبر من أو 
+
+246
+00:31:35,190 --> 00:31:47,070
+ساوي F of A أصغر من أو يساوي F of B so by Bolzano's
+
+247
+00:31:57,180 --> 00:32:09,500
+يوجد C ينتمي للفترة I بين X
+
+248
+00:32:09,500 --> 00:32:21,000
+lower star و X super star بحيث أن f of c بيساوي
+
+249
+00:32:21,000 --> 00:32:25,580
+العدد K وهذا
+
+250
+00:32:25,580 --> 00:32:30,820
+اللي بدنا نقوله يعني أثبتنا يوجد c ينتمي للفترة I
+
+251
+00:32:30,820 --> 00:32:38,800
+وصورة c بيساوي العدد K وهو المطلوب إذا هذه النتيجة
+
+252
+00:32:38,800 --> 00:32:44,440
+على بلزانو intermediate valley theorem برهنها بكل
+
+253
+00:32:44,440 --> 00:32:51,920
+بساطة وبكل أريحية واضح البرهان في أي استفسار أن 
+
+254
+00:32:51,920 --> 00:32:55,420
+البرهان هنا تبع النظرية هذه بعتمد على maximum 
+
+255
+00:32:55,420 --> 00:32:59,680
+minimum maximum minimum theorem نظرية القيم
+
+256
+00:32:59,680 --> 00:33:03,360
+القصوى أخذناها المحاضرة اللي فاتت وعلى Bolzano
+
+257
+00:33:03,360 --> 00:33:11,040
+intermediate value theorem okay
+
+258
+00:33:11,040 --> 00:33:11,480
+تمام
+
+259
+00:33:15,690 --> 00:33:23,230
+طيب الـ ..
+
+260
+00:33:23,230 --> 00:33:29,290
+نأخذ نظرية
+
+261
+00:33:29,290 --> 00:33:38,950
+يمكن
+
+262
+00:33:38,950 --> 00:33:43,350
+ما نحتاجش هدول نمسح
+
+263
+00:33:43,350 --> 00:33:44,010
+اللوح هذا
+
+264
+00:34:03,530 --> 00:34:11,490
+فيرم let I بيساوي closed bounded interval be closed
+
+265
+00:34:11,490 --> 00:34:25,090
+and bounded closed and bounded interval and let f
+
+266
+00:34:25,090 --> 00:34:49,240
+from I to R دي continuous متصلة على الفترة I then
+
+267
+00:34:49,240 --> 00:34:57,280
+النتيجة أن الـ set أو الـ range الـ range للـ
+
+268
+00:34:57,280 --> 00:35:08,740
+function I is a closed and bounded closed and
+
+269
+00:35:08,740 --> 00:35:17,460
+bounded interval that
+
+270
+00:35:17,460 --> 00:35:18,920
+is هذا يعني 
+
+271
+00:35:21,810 --> 00:35:26,930
+هذا يعني .. يعني النص أو نتيجة النظرية دي من كلها 
+
+272
+00:35:26,930 --> 00:35:33,850
+مختصرة في عبارة واحدة وهي أن a continuous function
+
+273
+00:35:33,850 --> 00:35:44,230
+a continuous function preserves .. preserves
+
+274
+00:35:44,230 --> 00:35:49,610
+بتحافظ closed 
+
+275
+00:35:51,530 --> 00:35:56,510
+and bounded intervals
+
+276
+00:35:56,510 --> 00:36:00,870
+الدوال
+
+277
+00:36:00,870 --> 00:36:05,130
+المتصلة بتحافظ على الـ closed و الـ bounded interval
+
+278
+00:36:05,130 --> 00:36:10,350
+يعني الـ function f بتأخذ I اللي هي closed bounded
+
+279
+00:36:10,350 --> 00:36:13,610
+interval بتعطيني صورتها closed bounded interval
+
+280
+00:36:13,610 --> 00:36:19,410
+زيها من نفس الصنف من نفس النوع لبرهان ذلك 
+
+281
+00:36:29,060 --> 00:36:44,440
+ف let M يساوي الـ infimum لـ range الـ F و
+
+282
+00:36:44,440 --> 00:36:50,720
+capital M يساوي الـ supremum لـ range الـ F
+
+283
+00:36:56,430 --> 00:37:11,770
+both M and N exist in R by maximum 
+
+284
+00:37:11,770 --> 00:37:15,290
+minimum theorem
+
+285
+00:37:19,900 --> 00:37:25,120
+نظرية القيمة القصوى بتقول إنه إذا كانت f function
+
+286
+00:37:25,120 --> 00:37:30,180
+متصلة على closed bounded interval فالـ .. الـ .. الـ
+
+287
+00:37:30,180 --> 00:37:34,560
+function إلها قيمة صغرى مطلقة و إلها قيمة عظمى
+
+288
+00:37:34,560 --> 00:37:39,300
+مطلقة سمها قيمة صغرى مطلقة M و قيمة العظمى
+
+289
+00:37:39,300 --> 00:37:44,760
+المطلقة capital M تمام؟
+
+290
+00:37:44,760 --> 00:37:47,580
+clearly
+
+291
+00:37:54,210 --> 00:38:02,370
+F of X أكبر من أو يساوي M أصغر من أو يساوي م لكل X
+
+292
+00:38:02,370 --> 00:38:10,630
+في I قيمة الدالة عند أي X في المجال تبعها أصغر من
+
+293
+00:38:10,630 --> 00:38:15,090
+أو يساوي قيمة العظمى المطلقة و أكبر في نفس المجال
+
+294
+00:38:15,090 --> 00:38:17,370
+أكبر من أو يساوي قيمة الصغرى المطلقة
+
+295
+00:38:21,460 --> 00:38:26,040
+فهذا بيؤدي which
+
+296
+00:38:26,040 --> 00:38:40,440
+implies هذا بيؤدي أنه الـ .. أنه f of I contained
+
+297
+00:38:40,440 --> 00:38:47,680
+في الفترة المغلقة من small m لـ capital M المتبادلة
+
+298
+00:38:47,680 --> 00:38:53,400
+الأخيرة هذه تثبت أن الـ set هذه subset من هذه لأنه
+
+299
+00:38:53,400 --> 00:38:59,880
+خذوا أي عنصر هنا فأي عنصر هنا عبارة عن f of x for
+
+300
+00:38:59,880 --> 00:39:07,100
+some x ينتمي لـ I صح فأي f of x for some x ينتمي لـ
+
+301
+00:39:07,100 --> 00:39:12,730
+I هيمحصور من small m و capital M وبالتالي ينتمي
+
+302
+00:39:12,730 --> 00:39:16,610
+للفترة المغلقة هذه، لأن كل عنصر أنا هو عنصر في
+
+303
+00:39:16,610 --> 00:39:22,490
+الفترة المغلقة، لأن هذا الاحتواء صحيح، تمام؟ الآن
+
+304
+00:39:22,490 --> 00:39:24,770
+احنا بنثبت المساواة
+
+305
+00:39:30,090 --> 00:39:36,190
+إن الـ range للـ function f يساوي كل الفترة المغلقة
+
+306
+00:39:36,190 --> 00:39:44,150
+من small m لـ capital M فلإثبات
+
+307
+00:39:44,150 --> 00:39:55,350
+ذلك هي عندي أنا to prove this it
+
+308
+00:39:55,350 --> 00:39:56,090
+remains
+
+309
+00:39:59,390 --> 00:40:07,930
+it remains to show يبقى إثبات دا في إثبات إن احنا
+
+310
+00:40:07,930 --> 00:40:12,370
+لثبت الاحتواء المعاكس the reverse inclusion
+
+311
+00:40:18,550 --> 00:40:28,670
+إذا يبقى إثبات إن الفترة المغلقة من small m to
+
+312
+00:40:28,670 --> 00:40:35,970
+capital M contained in F of I فكيف نثبت إحنا set
+
+313
+00:40:35,970 --> 00:40:41,570
+subset من الأخرى نسميه
+
+314
+00:40:41,570 --> 00:40:45,950
+برهان بإيه بتتبع العناصر يعني بناخد عنصر في
+
+315
+00:40:45,950 --> 00:40:49,540
+المجموعة الأولى نثبت العناصر في المجموعة الثانية
+
+316
+00:40:49,540 --> 00:40:53,080
+هذا بيسموه في رياضيات الـ chasing of elements
+
+317
+00:40:53,080 --> 00:41:03,880
+argument برهان بتتبع العناصر فقالت why ينتمي
+
+318
+00:41:03,880 --> 00:41:12,580
+للفترة المغلقة من small m لـ capital M طيب هذا
+
+319
+00:41:12,580 --> 00:41:19,540
+بيؤدي الـ y أكبر من أو يساوي small m أصغر من أو
+
+320
+00:41:19,540 --> 00:41:31,720
+يساوي capital M وهذا عبارة عن الـ infimum لـ range
+
+321
+00:41:31,720 --> 00:41:39,460
+الـ function f وهذا يساوي الـ supremum لـ range
+
+322
+00:41:39,460 --> 00:41:40,500
+الـ function f
+
+323
+00:41:47,540 --> 00:41:57,540
+وعندي الـ .. إذا حسب الـ .. الـ corollary تبع النظرية
+
+324
+00:41:57,540 --> 00:42:04,060
+هذه فإن عندي الـ function if continuous على الفترة
+
+325
+00:42:04,060 --> 00:42:10,520
+المغلقة a,b فعندي if continuous على الفترة المغلقة
+
+326
+00:42:10,520 --> 00:42:18,800
+a,b وعندي k اللي هو y عدد محصور بين الـ infimum لـ f
+
+327
+00:42:18,800 --> 00:42:28,520
+of i و الـ supremum لـ f of i by
+
+328
+00:42:28,520 --> 00:42:36,090
+above corollaryالقرن اللي لـ Bolzano Intermediate
+
+329
+00:42:36,090 --> 00:42:43,390
+Value Theorem يقول إن يوجد C ينتمي للفترة I بحيث
+
+330
+00:42:43,390 --> 00:42:50,090
+أن F of C يساوي
+
+331
+00:42:50,090 --> 00:42:58,170
+العدد Y اللي هو قابل الـ K في نص النظرية الـ C ينتمي
+
+332
+00:42:58,170 --> 00:43:05,170
+لـ I إذاً F of C تنتمي لـ F للست F of I إذاً أنا
+
+333
+00:43:05,170 --> 00:43:09,410
+بدأت بـ Y ينتمي للفترة المغلقة طلع Y ينتمي لـ F of
+
+334
+00:43:09,410 --> 00:43:17,570
+I Therefore Hence هيك
+
+335
+00:43:17,570 --> 00:43:20,750
+منكون أثبتنا أن الفترة المغلقة من small m
+
+336
+00:43:20,750 --> 00:43:31,990
+لـ capital M is contained في الـ set f of i هذا
+
+337
+00:43:31,990 --> 00:43:37,490
+بيبرهن الـ claim و النظرية لأن هيك بيكون برهننا الـ
+
+338
+00:43:37,490 --> 00:43:42,010
+claim وبالتالي برهننا النظرية لأن هيك هي أثبتت أن
+
+339
+00:43:42,010 --> 00:43:45,950
+الـ image لـ الـ closed bounded interval I طلعت
+
+340
+00:43:45,950 --> 00:43:49,970
+closed bounded interval صح و هو المطلوب
+
+341
+00:43:53,870 --> 00:44:00,730
+Okay واضح البرهان؟ في أي استفسار على البرهان؟
+
+342
+00:44:00,730 --> 00:44:08,030
+في هنا تحذير warning تحذير
+
+343
+00:44:08,030 --> 00:44:15,070
+in
+
+344
+00:44:15,070 --> 00:44:30,000
+the above theorem we had F of I التي هي F للفترة
+
+345
+00:44:30,000 --> 00:44:35,320
+المغلقة من A لـ B طلعت
+
+346
+00:44:35,320 --> 00:44:39,900
+بالساوي الفترة المغلقة من small m لـ capital M حيث
+
+347
+00:44:39,900 --> 00:44:43,980
+small m is the absolute minimum value و capital M
+
+348
+00:44:43,980 --> 00:44:47,140
+is the absolute maximum value of the function F on
+
+349
+00:44:47,140 --> 00:44:54,980
+the interval I و هذا ليس بالضرورة مش شرط هذه الفترة
+
+350
+00:44:54,980 --> 00:45:03,750
+تكون الفترة من F of A لـ F of B هذه الفترة ماحدش قال
+
+351
+00:45:03,750 --> 00:45:08,370
+أو مقدر يزم أن تكون الفترة المغلقة من F of A لـ F of B
+
+352
+00:45:08,370 --> 00:45:13,750
+هذا مش صحيح okay النظرية ما بتقولش الكلام هذا
+
+353
+00:45:13,750 --> 00:45:18,490
+بتقولش الكلام هذا فقط هذا غلط مش شرط الـ image
+
+354
+00:45:18,490 --> 00:45:23,050
+للفترة I بالساوي الفترة المغلقة من F of A لـ F of B
+
+355
+00:45:23,050 --> 00:45:30,640
+فخذوا بالكم من إيه من التحذير هذا Okay إذاً هن
+
+356
+00:45:30,640 --> 00:45:34,720
+أثبتنا إن لو كانت الـ function تبعتي متصلة على فترة
+
+357
+00:45:34,720 --> 00:45:39,420
+مغلقة أو محدودة فصورتها بتطلع مغلقة أو محدودة
+
+358
+00:45:39,420 --> 00:45:45,280
+وبالتالي الـ function preserves الـ .. الـ .. الـ
+
+359
+00:45:45,280 --> 00:45:50,640
+intervals طيب
+
+360
+00:45:50,640 --> 00:45:53,940
+الـ .. النظرية دي إلها تعميم
+
+361
+00:46:03,890 --> 00:46:10,730
+preservation of intervals
+
+362
+00:46:10,730 --> 00:46:14,770
+theorem لو
+
+363
+00:46:14,770 --> 00:46:21,050
+كانت الفترة let I be any interval مش شرط تكون ..
+
+364
+00:46:21,050 --> 00:46:28,070
+مش شرط تكون close about it .. be any interval and
+
+365
+00:46:28,070 --> 00:46:43,200
+let إذاً من I إلى R يكون مستمر على الفترة I ثم
+
+366
+00:46:43,200 --> 00:46:49,260
+ستة F من I هي معرفة
+
+367
+00:46:53,620 --> 00:46:57,220
+النظرية هذه بتقول لو كانت f دالة متصلة مجال
+
+368
+00:46:57,220 --> 00:47:03,960
+تبعها أي فترة مغلقة، محدودة، مش محدودة، half-open،
+
+369
+00:47:03,960 --> 00:47:06,580
+open-half-open interval اللي لقاش، أي لوحة من الـ
+
+370
+00:47:06,580 --> 00:47:11,820
+intervals اللي شفناهم في chapter واحد فصورتها أيضا
+
+371
+00:47:11,820 --> 00:47:15,500
+لازم تطلع interval وبالتالي الـ continuous function
+
+372
+00:47:15,500 --> 00:47:19,880
+بتحافظ على الفترة، على الفترات يعني بتأخذ فترة في
+
+373
+00:47:19,880 --> 00:47:24,780
+مجالها بتعطيل صورتها فترة هذه الفترة ما بنعرفش كيف
+
+374
+00:47:24,780 --> 00:47:29,620
+نوعها لكن اللي بنقدر نظمه في النظرية السابقة أنه
+
+375
+00:47:29,620 --> 00:47:33,300
+لو كانت الفترة I هذه closed bounded فصورتها هتطلع
+
+376
+00:47:33,300 --> 00:47:36,960
+closed bounded أما لو كانت من نوع آخر فصورتها مش
+
+377
+00:47:36,960 --> 00:47:42,200
+شرط تكون من نفس النوع ماحدش قال الكلام هذا فلبرهان
+
+378
+00:47:42,200 --> 00:47:47,780
+ذلك لبرهان
+
+379
+00:47:47,780 --> 00:47:48,260
+ذلك
+
+380
+00:47:53,440 --> 00:48:01,040
+خلينا ناخد let alpha و beta belong to except f of
+
+381
+00:48:01,040 --> 00:48:14,580
+I with alpha أصغر من beta خلينا
+
+382
+00:48:14,580 --> 00:48:15,640
+نستذكر بس
+
+383
+00:48:22,460 --> 00:48:27,560
+في نظرية أخدناها قبل هيك الـ theorem اتنين خمسة
+
+384
+00:48:27,560 --> 00:48:44,300
+واحد بتقول if S subset of R contains at least two
+
+385
+00:48:44,300 --> 00:48:48,500
+elements and satisfies
+
+386
+00:48:52,530 --> 00:48:58,810
+Satisfies الخاصية واحد إن لو كان X و Y تنتمي لـ S و
+
+387
+00:48:58,810 --> 00:49:04,850
+X أصغر من Y هذا بيؤدي إن الفترة من X إلى Y
+
+388
+00:49:04,850 --> 00:49:10,670
+contained in S then
+
+389
+00:49:10,670 --> 00:49:13,790
+set S is an interval
+
+390
+00:49:17,430 --> 00:49:19,470
+إن إن هذه النظرية أخدناها في الـ chapter .. في الـ
+
+391
+00:49:19,470 --> 00:49:23,830
+chapter الأول بتقول لو كان في عندي set subset
+
+392
+00:49:23,830 --> 00:49:29,520
+من R فيها على الأقل عنصرين وبتحقق الـ set هذه بتحقق
+
+393
+00:49:29,520 --> 00:49:33,580
+الخاصية واحد property one أنه لأي x و y في الـ set
+
+394
+00:49:33,580 --> 00:49:39,300
+و x أصغر من y الفترة من x لـ y بتكون موجودة داخل الـ
+
+395
+00:49:39,300 --> 00:49:43,880
+set في الحالة هذه الـ set نفسها S تطلع interval إذا
+
+396
+00:49:43,880 --> 00:49:50,820
+أنا بدي أثبت to show طيب
+
+397
+00:49:50,820 --> 00:49:51,780
+أنا عندي
+
+398
+00:49:54,280 --> 00:50:00,060
+هذه أخذت نقطتين في الـ set هذه هي الـ set الـ set S
+
+399
+00:50:00,060 --> 00:50:04,600
+هذه أخذت نقطتين و Alpha أصغر من Beta و بتثبت أنها
+
+400
+00:50:04,600 --> 00:50:08,700
+بتحقق الخاصية واحد عشان أثبت أنها interval أنا
+
+401
+00:50:08,700 --> 00:50:13,160
+عندي Alpha و Beta تنتمي لـ F of I لأن Alpha تساوي
+
+402
+00:50:13,160 --> 00:50:22,570
+F of A for some a تنتمي إلى I و Beta تساوي F of B
+
+403
+00:50:22,570 --> 00:50:30,330
+for some B تنتمي إلى I وبالتالي
+
+404
+00:50:30,330 --> 00:50:36,950
+..
+
+405
+00:50:36,950 --> 00:50:39,790
+بالتالي ..
+
+406
+00:50:47,200 --> 00:50:59,180
+أنا عندي الـ Bolzano طيب طيب to show to
+
+407
+00:50:59,180 --> 00:51:09,420
+show f of I is an interval we
+
+408
+00:51:09,420 --> 00:51:20,550
+need to show أن الـ set f of i satisfies property
+
+409
+00:51:20,550 --> 00:51:23,830
+واحد
+
+410
+00:51:23,830 --> 00:51:33,430
+of theorem اتنين خمسة واحد فهي
+
+411
+00:51:33,430 --> 00:51:36,830
+عندي alpha و beta تنتمي لـ f of i و alpha أصغر من
+
+412
+00:51:36,830 --> 00:51:40,690
+beta ف
+
+413
+00:51:40,690 --> 00:51:42,290
+to show
+
+414
+00:51:44,880 --> 00:51:56,020
+الفترة من Alpha إلى Beta contained in F of I let K
+
+415
+00:51:56,020 --> 00:52:00,300
+ينتمي إلى الفترة المغلقة من Alpha إلى Beta
+
+416
+00:52:04,220 --> 00:52:11,680
+أكبر من أو يساوي alpha هي تساوي f of a وأصغر من
+
+417
+00:52:11,680 --> 00:52:21,460
+أو يساوي beta هي تساوي f of b وبالتالي so by
+
+418
+00:52:21,460 --> 00:52:26,440
+Bolzano's
+
+419
+00:52:26,440 --> 00:52:31,120
+intermediate
+
+420
+00:52:31,120 --> 00:52:32,940
+value theorem
+
+421
+00:52:35,620 --> 00:52:48,960
+يوجد C ينتمي إلى I between Alpha
+
+422
+00:52:48,960 --> 00:52:59,400
+و Beta بحيث أن F of C يساوي K أو
+
+423
+00:52:59,400 --> 00:53:08,640
+K يساوي F of C  طبقا لما إذا ال C تنتمي لـ I إذا F of C تنتمي
+
+424
+00:53:08,640 --> 00:53:13,380
+لـ F of I إذا 
+
+425
+00:53:13,380 --> 00:53:18,200
+هاني أثبتت إنه كل K في الفترة المغلقة من Alpha إلى
+
+426
+00:53:18,200 --> 00:53:25,850
+Beta طلع ينتمي لـ F of I وبالتالي إذن بيطلع عند
+
+427
+00:53:25,850 --> 00:53:31,270
+الفترة المغلقة من Alpha إلى Beta  الـ subset من F of
+
+428
+00:53:31,270 --> 00:53:38,830
+I وبالتالي إذا الـ set F of I بتحقق الـ property 
+
+429
+00:53:38,830 --> 00:53:46,810
+واحد إذا by theorem .. by theorem اثنين خمسة واحد
+
+430
+00:53:46,810 --> 00:53:53,650
+الـ set F of I بتطلع interval is an interval
+
+431
+00:53:56,670 --> 00:54:03,570
+و هذا بيكمل النظرية إذا هذا بيكمل البرهان هيك
+
+432
+00:54:03,570 --> 00:54:10,630
+بنكون خلصنا الـ section خمسة تلاتة و باقي عننا
+
+433
+00:54:10,630 --> 00:54:16,190
+section خمسة أربعة هناخده في المحاضرة الجاية نحاول
+
+434
+00:54:16,190 --> 00:54:24,130
+نشوف زمنا نخلصه ولا لأفال .. شكرا لحسن إصغائكم و
+
+435
+00:54:24,130 --> 00:54:26,910
+يعطيكم العافية و نشوفكم إن شاء الله المرة الجاية
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index 0000000000000000000000000000000000000000..13b02f39ef2d8eba970805ddf08915cccb95195a
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@@ -0,0 +1,1547 @@
+1
+00:00:20,920 --> 00:00:24,640
+بسم الله الرحمن الرحيم هنبدأ في المحاضرة هذه
+
+2
+00:00:24,640 --> 00:00:29,600
+chapter جديد وهو chapter أربعة في الكتاب المقرر
+
+3
+00:00:29,600 --> 00:00:35,280
+عنوان الـ chapter limits of functions  و هنبدأ أول
+
+4
+00:00:35,280 --> 00:00:39,540
+section في الـ chapter هذا و برضه عنوان الـ section
+
+5
+00:00:39,540 --> 00:00:44,180
+الأول هو نفس عنوان الـ chapter limits of functions
+
+6
+00:00:44,180 --> 00:00:52,780
+فقبل ما نعرف limit of a function بدنا نتعرف على
+
+7
+00:00:52,780 --> 00:01:00,060
+مصطلح جديد وهو cluster point of a set نقطة تراكم
+
+8
+00:01:00,060 --> 00:01:04,780
+الـ cluster point أو بعض الكتب بيسموها accumulation 
+
+9
+00:01:04,780 --> 00:01:12,120
+point و كتب أخرى بيسميها limit point فلو في عندي
+
+10
+00:01:12,120 --> 00:01:18,200
+set A subset من R set of real numbers و C real
+
+11
+00:01:18,200 --> 00:01:23,190
+number فالـ real number هذا بنسميه cluster point
+
+12
+00:01:23,190 --> 00:01:28,030
+للست a if and only if the following condition is
+
+13
+00:01:28,030 --> 00:01:33,770
+satisfied for every delta عدد موجب نقدر نجد x
+
+14
+00:01:33,770 --> 00:01:39,650
+ينتمي إلى المجموعة a و الـ x هذه مختلفة عن النقطة c
+
+15
+00:01:39,650 --> 00:01:45,330
+بحيث ان المسافة بين x و c تكون أصغر من delta هذا
+
+16
+00:01:45,330 --> 00:01:49,410
+الشرط هذا
+
+17
+00:01:49,410 --> 00:01:54,020
+الشرط is equivalent to saying بكافئ ان انا اقول
+
+18
+00:01:54,020 --> 00:01:59,160
+every delta neighborhood every delta neighborhood
+
+19
+00:01:59,160 --> 00:02:03,940
+لنقطة c اللى هو الفترة المفتوحة اللى مركزها c ونص
+
+20
+00:02:03,940 --> 00:02:11,500
+قطرة delta every delta neighborhood of c يتقاطع مع
+
+21
+00:02:11,500 --> 00:02:18,200
+المجموعة a في نقطة واحدة على الأقل x مختلفة عن الـ
+
+22
+00:02:18,200 --> 00:02:25,720
+c يعني بمعنى أخر بقدر ألاقي في التقاطع هذا نقطة x
+
+23
+00:02:25,720 --> 00:02:32,440
+يعني التقاطع هذا لا يساوي five okay
+
+24
+00:02:32,440 --> 00:02:37,990
+كمان مرة النقطة C هذه بتكون cluster point للمجموعة
+
+25
+00:02:37,990 --> 00:02:44,370
+A إذا أي delta neighborhood للنقطة C بيتقاطع مع
+
+26
+00:02:44,370 --> 00:02:52,690
+المجموعة A في نقطة X مختلفة عن الـC بس لازم
+
+27
+00:02:52,690 --> 00:02:58,060
+كل delta neighborhood لـC يتقاطع مع المجموعة A في
+
+28
+00:02:58,060 --> 00:03:02,720
+نقطة X مختلفة عن الـC طب عشان اثبت ان الـC ليست
+
+29
+00:03:02,720 --> 00:03:09,000
+cluster point بنفي الشرط هذا يكفي ان اقول there
+
+30
+00:03:09,000 --> 00:03:14,520
+exist بدل for every delta او every delta
+
+31
+00:03:14,520 --> 00:03:18,860
+neighborhood يكفى ان اجيب there exists delta
+
+32
+00:03:18,860 --> 00:03:24,720
+neighborhood واحد ل C و التقاطع هذا بساوي فاي يعني
+
+33
+00:03:24,720 --> 00:03:30,540
+بحيث ان الـ delta neighborhood لا يتقاطع مع اي
+
+34
+00:03:30,540 --> 00:03:39,180
+مشيول منها C بالمرة ناخد نظرية الأول الـ definition
+
+35
+00:03:39,180 --> 00:03:43,180
+هذا بيكافئ النظرية التانية بتقول ان
+
+36
+00:03:46,060 --> 00:03:53,140
+الـ condition هذا تبع التعريف بكافئ شرط تاني اذا
+
+37
+00:03:53,140 --> 00:04:06,140
+هنا let A subset من R و C real number C
+
+38
+00:04:06,140 --> 00:04:16,740
+is a cluster is a cluster point of the set A if and
+
+39
+00:04:16,740 --> 00:04:22,400
+only if the following condition is satisfied there
+
+40
+00:04:22,400 --> 00:04:26,600
+exist a
+
+41
+00:04:26,600 --> 00:04:38,640
+sequence a n contained in A وكل عناصرها مختلفة
+
+42
+00:04:38,640 --> 00:04:52,650
+عن ال C such that limit a n بساوي c اذا هذا الشرط
+
+43
+00:04:52,650 --> 00:04:59,310
+بكافئ الشرط اللي هناك الشرط هذا او اللي بكافه
+
+44
+00:04:59,310 --> 00:05:06,290
+فلبرهان ذلك اذا كمان مرة انا عشان اثبت ان c is a
+
+45
+00:05:06,290 --> 00:05:10,610
+cluster point للمجموع يعني يكفي ان اثبت ان يوجد
+
+46
+00:05:12,310 --> 00:05:17,950
+سيكوانس في المجموعة A وكل على سرها مختلفة لاتساوي
+
+47
+00:05:17,950 --> 00:05:23,370
+C وانهيتها بالساوي لعدد C فتعالى نبرهن النظرية هذه
+
+48
+00:05:23,370 --> 00:05:28,850
+نبرهن الـ only if part الأول فالـ only if part يعني
+
+49
+00:05:28,850 --> 00:05:36,910
+الـ assumption assume ان C is a cluster is
+
+50
+00:05:36,910 --> 00:05:39,230
+a cluster point
+
+51
+00:05:40,700 --> 00:05:49,140
+of a then
+
+52
+00:05:49,140 --> 00:06:00,080
+for every n ينتمي إلى n لكل عدد طبيعي n take delta
+
+53
+00:06:00,080 --> 00:06:08,110
+بساوي واحد على n عدد موجب بما انه C is a cluster
+
+54
+00:06:08,110 --> 00:06:11,230
+point ل A then by definition of a cluster point
+
+55
+00:06:11,230 --> 00:06:14,410
+then
+
+56
+00:06:14,410 --> 00:06:23,770
+by definition there exist a N ينتمي إلى A مختلف عن
+
+57
+00:06:23,770 --> 00:06:28,210
+ال C such that
+
+58
+00:06:28,210 --> 00:06:31,070
+ال ..
+
+59
+00:06:34,910 --> 00:06:42,950
+الـ AN هذا ينتمي للـ Delta neighborhood للـ
+
+60
+00:06:42,950 --> 00:06:56,090
+C وطبعا ينتمي إلى A negative C هعمل
+
+61
+00:06:56,090 --> 00:07:02,810
+التعريف هذالما انه الـ C is a cluster point لأي
+
+62
+00:07:02,810 --> 00:07:09,410
+Delta أكبر من السفر خد Delta بساوي واحد على N لكل
+
+63
+00:07:09,410 --> 00:07:13,290
+عدد طبيعي N هذا بيطلع عدد موجب لذلك لـ Delta بساوي
+
+64
+00:07:13,290 --> 00:07:18,470
+واحد على N بقدر ألاجني عنصر X اللي هو ساميه An
+
+65
+00:07:18,470 --> 00:07:24,470
+يعتمد على الـ Delta وهذا العنصر موجود في A مختلف
+
+66
+00:07:24,470 --> 00:07:30,570
+عن الـ Cو أيضا موجود في الـ delta neighborhood لـ
+
+67
+00:07:30,570 --> 00:07:38,370
+C طيب
+
+68
+00:07:38,370 --> 00:07:42,610
+إذا و
+
+69
+00:07:42,610 --> 00:07:51,230
+واضح هنا من الـ AN ينتمي ل الـ
+
+70
+00:07:51,230 --> 00:07:56,150
+AN ينتمي ل DN الـ
+
+71
+00:07:56,150 --> 00:08:01,970
+delta أو الـ 1 على N neighborhood للـ C اللي هو C
+
+72
+00:08:01,970 --> 00:08:09,750
+سالب واحد على N C موجب واحد على N وهذا صحيح لكل N
+
+73
+00:08:09,750 --> 00:08:16,270
+بيقدي انه بيقدي
+
+74
+00:08:16,270 --> 00:08:20,890
+انه C سالم A N أو
+
+75
+00:08:24,630 --> 00:08:31,950
+absolute a n سالب c أصغر من واحد على n وهذا صحيح
+
+76
+00:08:31,950 --> 00:08:36,370
+لكل n هزبوت؟
+
+77
+00:08:36,370 --> 00:08:40,750
+هاي a n أكبر من c سالب واحد على n أصغر من c زاد
+
+78
+00:08:40,750 --> 00:08:45,310
+واحد على n هذا معناه absolute a n minus c أصغر من
+
+79
+00:08:45,310 --> 00:08:48,790
+واحد على n لكل n هذا صحيح لكل n
+
+80
+00:08:52,390 --> 00:08:56,990
+إذا هاي فيها sequence إذا هاي أثبتنا مايوجد
+
+81
+00:08:56,990 --> 00:09:09,350
+sequence إذا am is a sequence in a وكل حدودها
+
+82
+00:09:09,350 --> 00:09:16,610
+مختلفة عن ال c and by theorem اتنين اربعة الشهيرة
+
+83
+00:09:18,560 --> 00:09:21,560
+أنا عندي الـ absolute value هذي أصغر من واحد على N
+
+84
+00:09:21,560 --> 00:09:26,480
+لكل N limit واحد على N بالساوي سفر خد C بالساوي
+
+85
+00:09:26,480 --> 00:09:33,760
+واحد عدن موجب لأن بيطلع limit الـ sequence A N as N
+
+86
+00:09:33,760 --> 00:09:39,300
+tends to infinity بساوي S C إذن هين أثبتنا إنه لو
+
+87
+00:09:39,300 --> 00:09:44,920
+كانت C cluster point فأثبتنا إنه يوجد sequence A N
+
+88
+00:09:44,920 --> 00:09:51,380
+في المجموعة A وكل عناصرها مختلفة عن الـ C ونهايتها
+
+89
+00:09:51,380 --> 00:09:59,080
+بساوي الـ C إذا هذا بثبت جزء الـ only if part الآن
+
+90
+00:09:59,080 --> 00:10:04,220
+لثبت العكس لإثبات
+
+91
+00:10:04,220 --> 00:10:04,920
+العكس
+
+92
+00:10:21,910 --> 00:10:28,090
+assume أن الشرط اللي حصل بتتحقق
+
+93
+00:10:28,090 --> 00:10:41,250
+assume الـ condition اللي حصل holds يعني بتتحقق to
+
+94
+00:10:41,250 --> 00:10:48,890
+show c is a cluster point of
+
+95
+00:10:48,890 --> 00:11:03,360
+a let delta أكبر من السفر is given since
+
+96
+00:11:03,360 --> 00:11:15,160
+by star من الشرط star لدي limit لان بساوي c و
+
+97
+00:11:15,160 --> 00:11:19,260
+delta أكبر من السفر is given إذا من تعريف delta
+
+98
+00:11:19,260 --> 00:11:25,560
+capital N للـ limit لأي delta أو إبسلون عدد موجب
+
+99
+00:11:25,560 --> 00:11:31,320
+there exist n يعتمد على delta natural number دحيث
+
+100
+00:11:31,320 --> 00:11:40,140
+أنه لكل n أكبر من أو سوى capital N هذا بيقدي أنه
+
+101
+00:11:40,140 --> 00:11:47,000
+absolute a n minus c أصغر من delta
+
+102
+00:11:50,570 --> 00:11:57,870
+إذاً هذا بيقدّي إنه هيعندي am
+
+103
+00:12:02,990 --> 00:12:08,910
+طبعا هدف قلبي أن a n أصغر
+
+104
+00:12:08,910 --> 00:12:15,370
+من c زائد delta أكبر من c negative delta يعني a n
+
+105
+00:12:15,370 --> 00:12:22,630
+تنتمي إلى v delta of c وتنتمي طبعا من الـ condition
+
+106
+00:12:22,630 --> 00:12:32,780
+star تنتمي إلى a difference c وهذا صحيح لكل n أكبر
+
+107
+00:12:32,780 --> 00:12:38,660
+من أو ساوي capital N إذا هاي كل delta neighborhood
+
+108
+00:12:38,660 --> 00:12:50,240
+ل C بيتقاطع مع A في عدد لانهائي من النقاط المختلفة
+
+109
+00:12:50,240 --> 00:12:57,420
+عن ال C وبالتالي الشرط تبع الـ definition هيتحققو
+
+110
+00:12:57,420 --> 00:13:05,660
+then by definition .. by definition C is a cluster
+
+111
+00:13:05,660 --> 00:13:14,000
+point of the set A و هدا بكمل الـ F part and
+
+112
+00:13:14,000 --> 00:13:19,140
+therefore completes the proof of the theorem okay
+
+113
+00:13:19,140 --> 00:13:20,000
+تمام؟
+
+114
+00:13:25,140 --> 00:13:27,540
+Fine خلّينا ناخد بعض الأمثلة
+
+115
+00:13:49,070 --> 00:14:05,410
+تشير إلى أن كل X ينتمي إلى مقفل مقفل مقفل
+
+116
+00:14:05,410 --> 00:14:16,770
+مقفل
+
+117
+00:14:23,120 --> 00:14:29,460
+of set A1 بساوي الفترة
+
+118
+00:14:29,460 --> 00:14:40,780
+المفتوحة من سفر إلى واحد من
+
+119
+00:14:40,780 --> 00:14:45,460
+هنا يثبت إن كل X الفترة المغلقة من سفر إلى واحد هي
+
+120
+00:14:45,460 --> 00:14:50,480
+cluster point للفترة المفتوحة من سفر إلى واحد
+
+121
+00:15:01,360 --> 00:15:09,580
+ففي الأول بدي أثبت أنه كل نقطة داخل الفترة المغلقة
+
+122
+00:15:09,580 --> 00:15:14,460
+هي cluster point للمجموع عادي و بعدين في المرحلة
+
+123
+00:15:14,460 --> 00:15:19,840
+التانية حتة من نقاط الأطراف اللي هي 01 تطلع أيضا
+
+124
+00:15:19,840 --> 00:15:26,620
+cluster point لست A1 فنشوف مع بعض ان الـ claim 1
+
+125
+00:15:34,010 --> 00:15:45,190
+بنثبت ان كل X ينتمي للفترة المفتوحة is a cluster
+
+126
+00:15:45,190 --> 00:15:50,410
+point of
+
+127
+00:15:50,410 --> 00:15:58,730
+set A1 اللي هي الفترة المفتوحة نفسها لبرهان ذلك to
+
+128
+00:15:58,730 --> 00:16:09,390
+see this البرهن ذلك fix ينتمي
+
+129
+00:16:09,390 --> 00:16:17,470
+للفترة المفتوحة ونثبت ان cluster point للمجموعة a1
+
+130
+00:16:17,470 --> 00:16:29,940
+اذا fix x and let delta أكبر من السفر be given نبدأ
+
+131
+00:16:29,940 --> 00:16:35,900
+بالـ delta أكبر من 0 ونثبت أن كل delta
+
+132
+00:16:35,900 --> 00:16:42,820
+neighborhood للنقطة X بيتقاطع مع المجموعة A1 في
+
+133
+00:16:42,820 --> 00:16:49,400
+نقطة مختلفة عن X وبالتالي الـ X هتطلع cluster
+
+134
+00:16:49,400 --> 00:16:55,960
+point حسب التعريف طيب نحن
+
+135
+00:16:55,960 --> 00:16:56,920
+لدينا اتصالين
+
+136
+00:17:01,270 --> 00:17:07,090
+two cases حالتين الحالة
+
+137
+00:17:07,090 --> 00:17:10,270
+الأولى ان الـ delta هذه اللى انا اخترتها العشوائية
+
+138
+00:17:10,270 --> 00:17:17,310
+الـ delta اللى انا اخترتها ممكن تكون اصغر من ..
+
+139
+00:17:17,310 --> 00:17:23,590
+طبعا موجبة هي ممكن تكون اصغر من واحد ف in this
+
+140
+00:17:23,590 --> 00:17:27,930
+case in 
+
+141
+00:17:27,930 --> 00:17:30,050
+in this case في هذه الحالة
+
+142
+00:17:35,000 --> 00:17:49,440
+لدينا in this
+
+143
+00:17:49,440 --> 00:17:58,680
+case  الـ delta neighborhood لـ X اللي هو X minus
+
+144
+00:17:58,680 --> 00:18:06,650
+Delta X  موجب Delta بنلاحظ أنه تقاطع مع المجموعة A
+
+145
+00:18:06,650 --> 00:18:14,050
+اللي هي الفترة اللي مفتوحة من صفر لواحد بيطلع
+
+146
+00:18:14,050 --> 00:18:23,080
+واحد من الخيارات التالية: إما الفترة المفتوحة x
+
+147
+00:18:23,080 --> 00:18:28,820
+negative delta x positive delta أو الفترة المفتوحة
+
+148
+00:18:28,820 --> 00:18:36,420
+من صفر إلى x positive delta أو الفترة 
+
+149
+00:18:36,420 --> 00:18:40,340
+المفتوحة من x negative delta إلى واحد أو الفترة
+
+150
+00:18:40,340 --> 00:18:42,920
+المفتوحة من صفر إلى واحد
+
+151
+00:18:48,470 --> 00:18:55,310
+حسب قيمة الـ Delta يعني أنا
+
+152
+00:18:55,310 --> 00:19:03,030
+عندي الفترة المفتوحة من 0 إلى 1 هذه الفترة 
+
+153
+00:19:03,030 --> 00:19:12,350
+المفتوحة تبعتي اللي هي A1 هذا الـ set A1 وأنا عندي 
+
+154
+00:19:12,350 --> 00:19:20,080
+الـ Delta عدد موجب أصغر من 1 والـ X هذه تنتمي .. الـ
+
+155
+00:19:20,080 --> 00:19:27,300
+X هذه نقطة ما في الفترة
+
+156
+00:19:27,300 --> 00:19:38,320
+fixed number بين 0 و 1 الآن
+
+157
+00:19:38,320 --> 00:19:41,160
+أنا عندي الـ delta neighborhood لـ X هذا هو ممكن 
+
+158
+00:19:41,160 --> 00:19:46,510
+يكون زي هيك شكله وبالتالي تقاطع تقاطعه مع الفترة 
+
+159
+00:19:46,510 --> 00:19:53,310
+المفتوحة هو نفسه، صح؟ إذا كان زي هيك أو ممكن يكون
+
+160
+00:19:53,310 --> 00:19:57,250
+الـ delta neighborhood للـ X يكون شكله زي هيك
+
+161
+00:19:57,250 --> 00:20:01,430
+وبالتالي
+
+162
+00:20:01,430 --> 00:20:06,150
+تقاطعه مع الفترة .. مع الـ set واحد، هيكون الفترة
+
+163
+00:20:06,150 --> 00:20:10,830
+المفتوحة من صفر إلى X زي الـ Delta اللي هي الثانية
+
+164
+00:20:10,830 --> 00:20:17,310
+يعني صح وممكن يكون الـ
+
+165
+00:20:17,310 --> 00:20:21,810
+delta neighborhood الـ X تكون قريبة من الواحد زي
+
+166
+00:20:21,810 --> 00:20:26,410
+هيك والـ delta neighborhood حوالين الـ X يكون زي
+
+167
+00:20:26,410 --> 00:20:34,190
+هيك شكله هاي x negative delta x positive delta 
+
+168
+00:20:35,200 --> 00:20:39,440
+وبالتالي تقاطع مع الفترة من صفر إلى واحد هيعطيني
+
+169
+00:20:39,440 --> 00:20:44,700
+الجزء هذا اللي هو فترة مفتوحة من X سالب Delta إلى
+
+170
+00:20:44,700 --> 00:20:48,360
+واحد وممكن
+
+171
+00:20:48,360 --> 00:20:56,170
+الـ Delta neighborhood الـ X تكون قريبة من المنتصف والـ
+
+172
+00:20:56,170 --> 00:20:59,250
+Delta تكون قريبة من الواحد قيمتها أصغر من واحد لكن
+
+173
+00:20:59,250 --> 00:21:04,250
+قريبة من واحد وبالتالي الـ Delta neighborhood للـ X
+
+174
+00:21:04,250 --> 00:21:09,150
+يكون زي هيك وبالتالي تقاطعه مع المجموعة A واحد
+
+175
+00:21:09,150 --> 00:21:12,970
+بيطلع المجموعة A واحد نفسها، صحيح؟ إن هذه كل
+
+176
+00:21:12,970 --> 00:21:20,590
+الاحتمالات وفي كل الأحوال التقاطع هذا بيطلع infinite
+
+177
+00:21:20,590 --> 00:21:22,090
+is infinite
+
+178
+00:21:25,670 --> 00:21:29,890
+تقاطع المجموعتين هذول بيطلع فترة والفترة أي فترة 
+
+179
+00:21:29,890 --> 00:21:33,330
+مفتوحة الـ cardinal number تبعها بيساوي الـ cardinal
+
+180
+00:21:33,330 --> 00:21:36,310
+number تبع الـ real numbers اللي هي uncountable set
+
+181
+00:21:36,310 --> 00:21:41,270
+وبالتالي infinite إذا التقاطع هذا infinite وهذا
+
+182
+00:21:41,270 --> 00:21:46,410
+بيقود إلى أن الـ V
+
+183
+00:21:46,410 --> 00:21:57,490
+Delta of X تقاطع الـ a1 منزوعة منها الـ X هيطلع 
+
+184
+00:21:57,490 --> 00:22:03,390
+بالتأكيد لا يساوي في لأن التقاطع هذا بيطلع
+
+185
+00:22:03,390 --> 00:22:07,630
+infinite وبالتالي هيك بيكون أثبتنا أن كل Delta
+
+186
+00:22:07,630 --> 00:22:13,370
+neighborhood لـ X بيتقاطع مع a1 في نقطة مختلفة عن X
+
+187
+00:22:23,000 --> 00:22:31,840
+الحالة الثانية case two أن الـ Delta هذه تكون أكبر
+
+188
+00:22:31,840 --> 00:22:36,670
+من أو يساوي واحد برضه في الحالة دي بنأتي نثبت أنه كل
+
+189
+00:22:36,670 --> 00:22:41,170
+delta neighborhood لـ X بتقاطع مع A واحد في نقطة
+
+190
+00:22:41,170 --> 00:22:49,730
+مختلفة عن الـ X نشوف مع بعض in this case in
+
+191
+00:22:49,730 --> 00:22:57,310
+this case الـ X negative أو الـ negative delta X
+
+192
+00:22:57,310 --> 00:23:01,310
+موجب delta هذا اللي هو الـ delta neighborhood لـ X
+
+193
+00:23:01,310 --> 00:23:06,620
+تقاطع المجموعة A1 اللي هي الفترة المفتوحة من 0 إلى
+
+194
+00:23:06,620 --> 00:23:17,040
+1 هيطلع بيساوي الفترة المفتوحة من 0 إلى 1 لأن الـ
+
+195
+00:23:17,040 --> 00:23:24,780
+Delta هنا أكبر من أو يساوي الواحد يعني هي عندي من 0
+
+196
+00:23:24,780 --> 00:23:36,180
+إلى 1 هذه اللي هي المجموعة A وهي X نقطة ما داخل
+
+197
+00:23:36,180 --> 00:23:42,300
+الفترة فلما يكون X زائد الـ Delta لما تكون الـ Delta
+
+198
+00:23:42,300 --> 00:23:49,160
+تبعتي أكبر من واحد فـ X زائد الـ Delta هتكون هنا و X
+
+199
+00:23:49,160 --> 00:23:55,880
+سالب الـ Delta بالتأكيد هتكون هنا وبالتالي الـ Delta
+
+200
+00:23:55,880 --> 00:24:01,640
+neighborhood لـ X هيحتوي المجموعة A واحد وبالتالي
+
+201
+00:24:01,640 --> 00:24:06,760
+تقاطع معاها تطلع المجموعة A واحد وهذا is infinite
+
+202
+00:24:06,760 --> 00:24:11,680
+وبالتالي
+
+203
+00:24:11,680 --> 00:24:18,060
+إذا الـ delta neighborhood هذا تقاطع الفترة
+
+204
+00:24:18,060 --> 00:24:20,460
+المفتوحة minus X
+
+205
+00:24:23,650 --> 00:24:29,910
+لا أكيد بتأكيد لا يساوي five okay تمام إذا في 
+
+206
+00:24:29,910 --> 00:24:34,470
+الحالتين الـ condition تبع الـ cluster point تتحقق
+
+207
+00:24:34,470 --> 00:24:44,730
+therefore by definition X is cluster point is 
+
+208
+00:24:44,730 --> 00:24:50,780
+cluster point of الـ set A واحد اللي هي الفترة 
+
+209
+00:24:50,780 --> 00:24:56,280
+المفتوحة من صفر إلى واحد طبعاً إذا هذا بيثبت الـ
+
+210
+00:24:56,280 --> 00:25:09,140
+claim الأولاني طبعاً الآن هأثبت claim ثاني الـ claim
+
+211
+00:25:09,140 --> 00:25:09,880
+الثاني
+
+212
+00:25:16,660 --> 00:25:25,180
+النقطة 0 is a cluster point 
+
+213
+00:25:25,180 --> 00:25:36,460
+of set A1 الفترة مفتوحة من 0 إلى 1 لإثبات
+
+214
+00:25:36,460 --> 00:25:37,020
+ذلك
+
+215
+00:25:47,440 --> 00:25:55,860
+to see this let نبدأ let Delta أكبر من الصفر be 
+
+216
+00:25:55,860 --> 00:26:03,120
+given فهنا
+
+217
+00:26:03,120 --> 00:26:11,380
+لأي Delta الـ Delta
+
+218
+00:26:11,380 --> 00:26:16,140
+neighborhood للصفر اللي هو هيطلع
+
+219
+00:26:18,570 --> 00:26:28,630
+سالب Delta زائد صفر وموجب Delta زائد صفر فتقاطع هذا مع 
+
+220
+00:26:28,630 --> 00:26:35,150
+الفترة المفتوحة من صفر إلى واحد بيساوي
+
+221
+00:26:36,900 --> 00:26:44,360
+في خيارين إما الفترة المفتوحة من صفر إلى Delta إذا
+
+222
+00:26:44,360 --> 00:26:52,680
+كانت الـ Delta أصغر من واحد طبعاً أكبر من صفر وبساوي
+
+223
+00:26:52,680 --> 00:26:57,600
+الفترة المفتوحة من صفر إلى واحد إذا كان الـ Delta
+
+224
+00:26:57,600 --> 00:27:04,220
+أكبر من أو يساوي الواحد زي ما شوفنا في برهان الكلام
+
+225
+00:27:04,220 --> 00:27:12,240
+الأولاني مظبوط هاي الاندي الفترة من صفر إلى واحد
+
+226
+00:27:12,240 --> 00:27:19,520
+هذه المجموعة A1 وهي 
+
+227
+00:27:19,520 --> 00:27:27,700
+X نقطة .. لأ هاي الصفر بالدفتر أن الصفر cluster
+
+228
+00:27:27,700 --> 00:27:34,660
+point للمجموعة A1 فأخذت أي Delta أكبر من الصفر الآن 
+
+229
+00:27:34,660 --> 00:27:38,260
+الـ Delta هذه لو كانت الـ Delta هذه إذا هي سالب 
+
+230
+00:27:38,260 --> 00:27:42,720
+Delta موجب Delta لو كانت الـ Delta هذه أصغر من واحد
+
+231
+00:27:42,720 --> 00:27:47,120
+فتقاطع الـ Delta neighborhood مع الـ A واحد هيكون
+
+232
+00:27:47,120 --> 00:27:51,140
+الجزء هذا اللي هو الفترة المفتوحة من صفر لـ Delta 
+
+233
+00:27:51,140 --> 00:27:57,100
+صح؟ ولو كانت الـ Delta هذه أكبر من واحد لو كانت الـ
+
+234
+00:27:57,100 --> 00:27:58,940
+Delta هذه أكبر من واحد
+
+235
+00:28:01,680 --> 00:28:11,060
+فالـ .. فـ Delta هتكون هاي Delta أكبر من واحد وسالب
+
+236
+00:28:11,060 --> 00:28:15,120
+Delta هتكون هنا وبالتالي الـ Delta neighborhood هذا 
+
+237
+00:28:15,120 --> 00:28:24,220
+تقاطع مع A واحد بيساوي A واحد مظبوط صح؟ تمام؟ وفي 
+
+238
+00:28:24,220 --> 00:28:27,840
+كل الأحوال التقاطع هذا بيطلع infinite is infinite
+
+239
+00:28:27,840 --> 00:28:31,000
+infinite set لأنه open interval
+
+240
+00:28:38,080 --> 00:28:46,040
+تقاطع A-A1 هو
+
+241
+00:28:46,040 --> 00:28:53,940
+نفس تقاطع A1
+
+242
+00:29:00,690 --> 00:29:03,830
+إذن هي اللي أثبتت إن كل Delta neighborhood للصفر
+
+243
+00:29:03,830 --> 00:29:09,590
+يتقاطع مع المجموعة A1 في نقطة مختلفة عن الصفر في
+
+244
+00:29:09,590 --> 00:29:14,070
+حقيقة الأمر في حقيقة الأمر كل Delta neighborhood 
+
+245
+00:29:14,070 --> 00:29:19,250
+للصفر بتقاطع مع A1 في عدد لانهائي من النقاط اللي
+
+246
+00:29:19,250 --> 00:29:24,350
+موجودة في A1 ومختلفة عن الصفر إذن by definition
+
+247
+00:29:24,350 --> 00:29:27,610
+zero is a cluster
+
+248
+00:29:30,120 --> 00:29:36,540
+point of A1 اللي هي الفترة مفتوحة من صفر لواحد
+
+249
+00:29:36,540 --> 00:29:43,720
+يبقى لإكمال البرهان يمكن أن يظهر الكليم الثالث
+
+250
+00:29:43,720 --> 00:29:55,560
+باقي أُثبت أن الواحد is a cluster point of set A1
+
+251
+00:29:55,560 --> 00:30:02,300
+اللي هي الفترة المفتوحة من صفر لواحد وبرهان الـ claim
+
+252
+00:30:02,300 --> 00:30:07,360
+الثالث زي .. similar لبرهان الـ claim الثالث إذا 
+
+253
+00:30:07,360 --> 00:30:19,280
+هنا the proof its proof is similar to
+
+254
+00:30:19,280 --> 00:30:20,260
+claim to
+
+255
+00:30:23,650 --> 00:30:27,990
+فحاسيبكم أنتم تكتبوا وبالتالي هيك بيكون أثبتنا
+
+256
+00:30:27,990 --> 00:30:32,250
+أن كل نقطة في الفترة المغلقة سواء كانت نقطة الطرف
+
+257
+00:30:32,250 --> 00:30:37,570
+اللي هي 0 أو 1 أو نقطة داخلية interior point نقطة 
+
+258
+00:30:37,570 --> 00:30:41,290
+داخل الفترة المغلقة كل النقاط هذه بتطلع cluster
+
+259
+00:30:41,290 --> 00:30:47,970
+points لمجموعة A1 اللي هي الفترة المفتوحة تمام؟
+
+260
+00:30:52,450 --> 00:31:05,790
+بالمثل ممكن إثبات أن 
+
+261
+00:31:05,790 --> 00:31:09,250
+كل نقطة في الفترة المغلقة is cluster point
+
+262
+00:31:09,250 --> 00:31:16,990
+للمجموعة A2 اللي هي الفترة المغلقة من 0 إلى 1
+
+263
+00:31:16,990 --> 00:31:20,390
+والبرهان
+
+264
+00:31:20,390 --> 00:31:28,770
+هو نفسه بنعمل three claims وفي كل برهان هيكون الفرق
+
+265
+00:31:28,770 --> 00:31:35,430
+أنه عندي أنا A بدل A1 هيكون A2 فهتكون اللي هو
+
+266
+00:31:35,430 --> 00:31:41,370
+الفترات هذه فترة مغلقة من صفر إلى واحد وبالتالي
+
+267
+00:31:41,370 --> 00:31:47,910
+بيصير هذه الفترة من هنا مغلقة عند الصفر ومغلقة عند
+
+268
+00:31:47,910 --> 00:31:54,070
+الصفر ومغلقة عند الواحد وهكذا نفس البرهان نسخ لصق
+
+269
+00:31:54,070 --> 00:31:59,790
+مع التعديلات البسيطة أن A واحد الآن أصبحت بدل ما
+
+270
+00:31:59,790 --> 00:32:03,270
+كانت فترة مفتوحة من صفر لواحد أصبحت فترة مغلقة
+
+271
+00:32:03,270 --> 00:32:06,830
+وبالتالي في التقاطعات الحسابات نغلق اللي هو
+
+272
+00:32:06,830 --> 00:32:13,590
+الفترات and الحاجة المطلوبة okay وبالتالي نفس
+
+273
+00:32:13,590 --> 00:32:18,910
+البرهان will go through هيمشي بالتمام والكمال Okay
+
+274
+00:32:18,910 --> 00:32:24,270
+تمام؟ إذا هذا البرهان مشابه لبرهان المثال الأول
+
+275
+00:32:24,270 --> 00:32:34,010
+نأخذ كمان مثال آخر مثال
+
+276
+00:32:34,010 --> 00:32:43,770
+ثالث every every
+
+277
+00:32:43,770 --> 00:32:44,310
+finite
+
+278
+00:32:46,970 --> 00:32:59,350
+set A contained in R has no
+
+279
+00:32:59,350 --> 00:33:03,070
+cluster
+
+280
+00:33:03,070 --> 00:33:09,730
+points 
+
+281
+00:33:09,730 --> 00:33:19,970
+كل finite set ما لهاش ولا cluster point والبرهان سهل
+
+282
+00:33:19,970 --> 00:33:24,950
+proof say
+
+283
+00:33:24,950 --> 00:33:35,030
+دعنا الـ set a نسمي عناصرها a1, a2 إلى an هدف مش
+
+284
+00:33:35,030 --> 00:33:39,950
+هدف finite set إذا عناصرهم ممكن أعملهم list a1, a2
+
+285
+00:33:39,950 --> 00:33:47,530
+إلى an و ممكن أعملهم order أرتبهم حسب المؤشر تبعهم
+
+286
+00:33:47,530 --> 00:33:57,450
+يعني a1 أصغر من a2 أصغر من a3 أصغر من أصغر من an
+
+287
+00:33:57,450 --> 00:34:03,570
+ممكن نعمل كلمة من هذا ولا لأ ممكن by the ordering
+
+288
+00:34:03,570 --> 00:34:04,370
+principle
+
+289
+00:34:11,360 --> 00:34:20,780
+أو باستخدام الـ ordering تبع الـ real numbers إذا
+
+290
+00:34:20,780 --> 00:34:30,880
+هي عندي الـ set A تبعتي هي خط العداد وهي A1 وهي A2 وهي
+
+291
+00:34:30,880 --> 00:34:36,160
+A3 مش شرط المسافة بين كل أنصار والتاني تكون
+
+292
+00:34:36,160 --> 00:34:46,230
+متساوية وهكذا إلى أخر عنصر AN ف
+
+293
+00:34:46,230 --> 00:34:49,910
+fix X
+
+294
+00:34:49,910 --> 00:35:01,190
+ينتمي إلى R و بدي أثبت أن claim X is not a cluster
+
+295
+00:35:01,190 --> 00:35:01,910
+point
+
+296
+00:35:09,790 --> 00:35:12,850
+بالتالي المجموعة A ليس لديه أي cluster point
+
+297
+00:35:12,850 --> 00:35:16,770
+بالتالي المجموعة A ليس لديه أي cluster point
+
+298
+00:35:16,770 --> 00:35:16,790
+بالتالي المجموعة A ليس لديه أي cluster point
+
+299
+00:35:16,790 --> 00:35:17,530
+بالتالي المجموعة A ليس لديه أي cluster point
+
+300
+00:35:17,530 --> 00:35:17,750
+بالتالي المجموعة A ليس لديه أي cluster point
+
+301
+00:35:17,750 --> 00:35:18,430
+بالتالي المجموعة A ليس لديه أي cluster point
+
+302
+00:35:18,430 --> 00:35:19,070
+بالتالي المجموعة A ليس لديه أي cluster point
+
+303
+00:35:19,070 --> 00:35:19,690
+بالتالي المجموعة A ليس لديه أي cluster point
+
+304
+00:35:19,690 --> 00:35:25,170
+بالتالي المجموعة A ليس لديه أي cluster point
+
+305
+00:35:25,170 --> 00:35:28,870
+بالتالي المجموعة A ليس لديه أي cluster point
+
+306
+00:35:28,870 --> 00:35:33,950
+بالتالي المجم
+
+307
+00:35:37,690 --> 00:35:44,410
+إما X تنتمي إلى A أو X تنتمي إلى الـ complement
+
+308
+00:35:44,410 --> 00:35:50,530
+يعني لا تنتمي إلى A صح؟
+
+309
+00:35:50,530 --> 00:35:59,870
+ففي الحالة الأولى case واحد أثر من X تنتمي إلى A
+
+310
+00:35:59,870 --> 00:36:03,970
+وبالدفع تثبت إن X ليست cluster point
+
+311
+00:36:10,180 --> 00:36:18,560
+say x بساوي a m for some m أكبر من أو ساوي واحد
+
+312
+00:36:18,560 --> 00:36:24,180
+أصغر من أو ساوي مش هذا الـ x موجود في a و a على
+
+313
+00:36:24,180 --> 00:36:29,460
+سرها a واحد إلى a n إذا هذا الـ x هو a m for some m
+
+314
+00:36:29,460 --> 00:36:36,300
+بين واحد و n طيب let
+
+315
+00:36:37,980 --> 00:36:48,860
+delta بساوي نص المسافة الـ minimum المسافة
+
+316
+00:36:48,860 --> 00:37:04,760
+بين am minus am minus واحد وam زائد واحد minus am
+
+317
+00:37:11,460 --> 00:37:21,160
+يعني هاي الـ X هاي الـ M هاي AM وهاي AM زاد واحد
+
+318
+00:37:21,160 --> 00:37:30,960
+والأنصر اللي جاب لها AM minus واحد احنا قلنا الـ X
+
+319
+00:37:30,960 --> 00:37:39,850
+سبعتي الـ X سبعتي هي الـ AM الآن باخد المسافة هذه
+
+320
+00:37:39,850 --> 00:37:46,030
+اللي هي بين a m زي دول اللي هي المسافة هذه و باخد
+
+321
+00:37:46,030 --> 00:37:51,150
+المسافة هذه بين a m و a m سالب واحد لازم واحدة
+
+322
+00:37:51,150 --> 00:37:55,730
+تكون أصغر من أو يساوي التانية باخدها الـ minimum الـ
+
+323
+00:37:55,730 --> 00:37:57,730
+minimum .. الـ minimum بين المسافتين .. الأصغر بين
+
+324
+00:37:57,730 --> 00:38:02,650
+المسافتين هدول و باخد نصها و باخد نصها بسميها
+
+325
+00:38:02,650 --> 00:38:08,720
+delta فنص .. لو قلنا الأصغر لو قلنا مثلا الأصغر
+
+326
+00:38:08,720 --> 00:38:15,400
+اللي هي هذه فنص الدلتا هذا هي فإذا الـ delta هتكون
+
+327
+00:38:15,400 --> 00:38:21,040
+المسافة هذه و بكوّن delta neighborhood حوالين الـ X
+
+328
+00:38:21,040 --> 00:38:29,720
+الآن الـ delta neighborhood هذا then verify
+
+329
+00:38:29,720 --> 00:38:34,860
+ممكنكم تتحققوا verify that
+
+330
+00:38:37,340 --> 00:38:43,600
+الـ Delta neighborhood V Delta ل A M اللي هي الـ X
+
+331
+00:38:43,600 --> 00:38:46,760
+تقاطع
+
+332
+00:38:46,760 --> 00:38:55,280
+الـ set A فاي منزوعة منها A M هيطلع بساوي الفاي
+
+333
+00:38:55,280 --> 00:39:01,980
+مافيش تقاطع بينهم وبالتالي therefore by definition
+
+334
+00:39:04,480 --> 00:39:13,200
+ام اكس بساوي ام is not a
+
+335
+00:39:13,200 --> 00:39:22,360
+cluster point of set A لأن عشان تكون ما تكونيش
+
+336
+00:39:22,360 --> 00:39:28,040
+cluster point لمجموعة A لازم أثبت إنه يوجد there
+
+337
+00:39:28,040 --> 00:39:35,840
+exist delta neighborhood للـ X تبعت اللي هي AM بحيث
+
+338
+00:39:35,840 --> 00:39:42,980
+إنه الـ delta neighborhood هذا ما يتقطعش مع الـ set A في
+
+339
+00:39:42,980 --> 00:39:50,440
+أي نقطة مختلفة عن النقطة X وهذا حصل Okay تمام إذا
+
+340
+00:39:50,440 --> 00:39:56,140
+هذا في حالة لما الـ X تكون موجودة في A الحالة
+
+341
+00:39:56,140 --> 00:40:03,340
+التانية ان الـ case 2 case
+
+342
+00:40:03,340 --> 00:40:13,040
+2 ان الـ X لا تنتمي الـ الـ set A ففي الحالة هذه
+
+343
+00:40:14,910 --> 00:40:20,590
+معناته x مابتساويش ولا واحد من العناصر هذه فالحالة
+
+344
+00:40:20,590 --> 00:40:26,690
+هذه ممكن أجزيها إلى تلت حالات الحالة
+
+345
+00:40:26,690 --> 00:40:32,750
+الأولى ان الـ x تبعتي تكون أصغر من a واحد وبالتالي
+
+346
+00:40:32,750 --> 00:40:37,010
+واضح ان المسافة بين X و A واحد كبيرة وباخد نص
+
+347
+00:40:37,010 --> 00:40:43,930
+المسافة دلتا إذا هيوجد دلتا نبرود ل X ومابتقطعش
+
+348
+00:40:43,930 --> 00:40:47,650
+مع المجموعة A بالمرة وبالتالي X is not cluster
+
+349
+00:40:47,650 --> 00:40:54,250
+point ممكن الحالة التانية أن X تكون أكبر من الـ AM
+
+350
+00:40:54,250 --> 00:40:59,470
+برضه باخد المسافة دي بجيبها و باخد نصها على انه
+
+351
+00:40:59,470 --> 00:41:03,670
+Delta و بكون Delta neighborhood حوالين الـ X هذا الـ
+
+352
+00:41:03,670 --> 00:41:06,530
+Delta neighborhood واضح انه مابتقطعش مع الـ set A
+
+353
+00:41:06,530 --> 00:41:11,910
+بالمرة وبالتالي إذا X في الحالة دي ليست cluster
+
+354
+00:41:11,910 --> 00:41:20,190
+point الحالة التالتة ان X تكون واقعة بين عنصرين من
+
+355
+00:41:20,190 --> 00:41:25,170
+عناصر الـ set فباخد اللي هو المسافة الأصغر من
+
+356
+00:41:25,170 --> 00:41:29,310
+المسافتين هدول و هي تكون هادي و باخد نصها delta و
+
+357
+00:41:29,310 --> 00:41:32,890
+بكون delta neighborhood حواليها هذا الـ delta
+
+358
+00:41:32,890 --> 00:41:36,510
+neighborhood بتقطعش مع المجموعة هاد المرة وبالتالي
+
+359
+00:41:36,510 --> 00:41:38,990
+حسب التعريف x ليست cluster point
+
+360
+00:41:43,100 --> 00:41:46,360
+ما احنا قلنا إذا كانت X تنتمي لأيه هي برهانة MA لا
+
+361
+00:41:46,360 --> 00:41:52,640
+تنتمي لأ تنتمي اه ليش قدامها بين تنتمي و لا تنتمي
+
+362
+00:41:52,640 --> 00:41:58,420
+ما هي الـ X ما تنتميش لأيه فممكن تكون بين عنصرين من
+
+363
+00:41:58,420 --> 00:42:03,360
+عنصرهم هي تنتمي لـ R ما تنتميش لأيه فممكن تكون
+
+364
+00:42:03,360 --> 00:42:09,640
+موجودة بين A2 و A3 صح أو بين A1 و A2 أو بين A3 أو
+
+365
+00:42:09,640 --> 00:42:16,530
+A و هكذا أو ممكن تكون الـ X على يمين الـ AN أو حالة
+
+366
+00:42:16,530 --> 00:42:20,190
+تالتة X تكون على يسار الـ A واحد وشوفنا في كل
+
+367
+00:42:20,190 --> 00:42:24,310
+الحالات هذه التلاتة أنه بقدر ألاقي delta
+
+368
+00:42:24,310 --> 00:42:27,990
+neighborhood حوالين الـ X لا يتقاطع مع المجموعة A
+
+369
+00:42:27,990 --> 00:42:32,330
+بالمرة وبالتالي X ليست cluster point إذا الكلام
+
+370
+00:42:32,330 --> 00:42:37,110
+هذا واضح حاولوا تكتبوه بطريقة يعني منطقية okay
+
+371
+00:42:37,110 --> 00:42:37,810
+تمام؟
+
+372
+00:42:42,120 --> 00:42:46,900
+أنا متخيلة الـ A عبارة عن set دائر مثلا أنا هيك
+
+373
+00:42:46,900 --> 00:42:50,340
+متخيلة و أنه مثلا الـ cluster point هي عبارة عن
+
+374
+00:42:50,340 --> 00:42:54,820
+نقطة .. لأ الـ A ماتتخيليش الـ A عند الـ set الـ A هي
+
+375
+00:42:54,820 --> 00:43:01,140
+جزء من الأعداد الحقيقية subset من R و R خط لازم
+
+376
+00:43:01,140 --> 00:43:04,200
+يعني تتخيل الحاجات زمان على الـ interior point و الـ
+
+377
+00:43:04,200 --> 00:43:08,260
+boundary هذا في الـ topology حاجة تانية هي زي ات
+
+378
+00:43:08,260 --> 00:43:11,140
+شبهها يعني ممكن نفهمها بهذا الطريقة بس ممكن اه
+
+379
+00:43:11,140 --> 00:43:13,860
+ممكن بس احنا هنا على الـ real line يعني خليني احنا
+
+380
+00:43:13,860 --> 00:43:18,820
+نتقيد بالـ sets اللي موجودة على الـ real line أما هو
+
+381
+00:43:18,820 --> 00:43:24,080
+طبعا في تعني من الكلام هذا في حاجات أعم و فرغات
+
+382
+00:43:24,080 --> 00:43:28,550
+أعم من الـ .. الـ real number اللي هو الـ topological
+
+383
+00:43:28,550 --> 00:43:36,030
+spaces و هذا موضوع طبعا متشعب و بده يعني تدرس الـ
+
+384
+00:43:36,030 --> 00:43:40,530
+topology عشان تفهم كل شيء okay فى أي أسئلة تاني؟
+
+385
+00:43:40,530 --> 00:43:44,430
+okay لنكتفي بهذا القدر و إن شاء الله بنكمل
+
+386
+00:43:44,430 --> 00:43:52,670
+المحاضرة الجاية الموضوع و بنخش بتعريف الـ limit للـ
+
+387
+00:43:52,670 --> 00:43:53,110
+functions
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Gx7j9GpXuiI.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Gx7j9GpXuiI.srt
new file mode 100644
index 0000000000000000000000000000000000000000..646d90ea5c842ce1d71b50f25269045509424f7e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Gx7j9GpXuiI.srt
@@ -0,0 +1,1779 @@
+1
+00:00:21,580 --> 00:00:26,880
+بسم الله الرحمن الرحيم اليوم إن شاء الله هنبدأ
+
+2
+00:00:26,880 --> 00:00:34,000
+chapter خمسة وهذا آخر chapter هناخده في الـ course
+
+3
+00:00:34,000 --> 00:00:50,080
+فأنواع الـ chapter هذا continuous
+
+4
+00:00:53,880 --> 00:01:01,820
+functions الدوال المتصلة و
+
+5
+00:01:01,820 --> 00:01:08,460
+أول section برضه section خمسة واحد في هذا الـ
+
+6
+00:01:08,460 --> 00:01:16,320
+chapter برضه عنوانه continuous functions
+
+7
+00:01:24,100 --> 00:01:29,280
+الدالة المتصلة فنعرف شو معنى الدالة تكون متصلة عن
+
+8
+00:01:29,280 --> 00:01:35,160
+نقطة definition let
+
+9
+00:01:35,160 --> 00:01:49,280
+f be a function from a to r and c be an element of a we
+
+10
+00:01:49,280 --> 00:02:00,630
+say إنه الـ function if is continuous if
+
+11
+00:02:00,630 --> 00:02:05,770
+is continuous at
+
+12
+00:02:05,770 --> 00:02:18,950
+x بساوي c if إذا تحقق الشرط التالي for
+
+13
+00:02:18,950 --> 00:02:20,470
+every
+
+14
+00:02:22,680 --> 00:02:29,400
+إبسيلون أكبر من الصفر نقدر نرد عليها دلتا تعتمد
+
+15
+00:02:29,400 --> 00:02:37,840
+على إبسيلون positive number بحيث أنه لكل X لكل
+
+16
+00:02:37,840 --> 00:02:44,090
+X في A و الـ absolute value لـ x minus c أصغر من
+
+17
+00:02:44,090 --> 00:02:52,170
+دلتا فهذا بتضمن ان absolute f of x minus f of c
+
+18
+00:02:52,170 --> 00:03:01,630
+أصغر من الـ إبسيلون فهذا
+
+19
+00:03:01,630 --> 00:03:13,010
+بنسميه this is called this is called epsilon delta
+
+20
+00:03:13,010 --> 00:03:18,770
+definition of
+
+21
+00:03:18,770 --> 00:03:31,170
+continuity لأن 
+
+22
+00:03:31,170 --> 00:03:36,790
+هذا تعريف إبسيلون دلتا للاتصال لحظو هذا التعريف
+
+23
+00:03:36,790 --> 00:03:44,530
+تقريبا هو هو تعريف أن limit الـ function f of x لما
+
+24
+00:03:44,530 --> 00:03:52,310
+x تقول c بساوي f of c هذد
+
+25
+00:03:52,310 --> 00:04:07,210
+كانت c is a cluster point طب
+
+26
+00:04:07,210 --> 00:04:13,930
+لحظة أنت لما عرفنا احنا ما معناه ان الـ limit لـ
+
+27
+00:04:13,930 --> 00:04:18,710
+function and x بيساوي c و c cluster point للمجموعة
+
+28
+00:04:18,710 --> 00:04:24,570
+a بيساوي عدد l بدلنا l هنا بـ f و c صح؟ معناه كان
+
+29
+00:04:24,570 --> 00:04:30,290
+لكل إبسيلون فيه دلتا بحيث لكل x في a و الـ x هذه
+
+30
+00:04:30,290 --> 00:04:37,540
+كانت مختلفة لا تساوي c فكنا نحط هنا أكبر من 0 فإذا
+
+31
+00:04:37,540 --> 00:04:41,480
+كانت المسافة هذه أصغر من دلتا تطلع المسافة من f of
+
+32
+00:04:41,480 --> 00:04:46,040
+x والـ l اللي هي الـ limit هنا طبعا احنا بدلنا الـ l
+
+33
+00:04:46,040 --> 00:04:50,940
+بـ f of c فبين هذا يطلع أصغر من x هنا تقريبا نفس
+
+34
+00:04:50,940 --> 00:04:56,480
+التعريف if
+
+35
+00:04:56,480 --> 00:05:00,460
+if
+
+36
+00:05:00,460 --> 00:05:09,090
+is not continuous لو كانت الـ f ليست متصلة عند
+
+37
+00:05:09,090 --> 00:05:14,910
+النقطة c فبنقول if
+
+38
+00:05:14,910 --> 00:05:31,810
+f fails to be continuous at c we say أن f is
+
+39
+00:05:31,810 --> 00:05:32,990
+discontinuous
+
+40
+00:05:38,310 --> 00:05:46,350
+discontinuous at c إذا لو كانت الدالة مش متصلة عن
+
+41
+00:05:46,350 --> 00:05:52,710
+c يعني شرط الاتصال هذا مش متحقق فبنقول أن الدالة
+
+42
+00:05:52,710 --> 00:05:57,610
+discontinuous منفصلة عند النقطة c okay تمام
+
+43
+00:06:09,660 --> 00:06:17,360
+بنلاحظ أن الـ .. زي ما شوفنا في section 4-1 تعريف
+
+44
+00:06:17,360 --> 00:06:21,840
+إبسيلون دلتا للـ limits of functions في بكافة
+
+45
+00:06:21,840 --> 00:06:26,600
+neighborhood definition وهنا برضه تعريف الـ إبسيلون
+
+46
+00:06:26,600 --> 00:06:31,760
+دلتا definition للاتصال عن النقطة في بكافة
+
+47
+00:06:31,760 --> 00:06:36,400
+neighborhood definition فنكتب الـ neighborhood
+
+48
+00:06:36,400 --> 00:06:37,340
+definition هذا
+
+49
+00:06:46,200 --> 00:06:53,400
+لت if دي function from a to r و c belong to a then
+
+50
+00:06:53,400 --> 00:07:02,480
+the following statements are equivalent واحد
+
+51
+00:07:02,480 --> 00:07:11,180
+الـ function if is continuous is continuous at x
+
+52
+00:07:11,180 --> 00:07:12,540
+بساوي z
+
+53
+00:07:20,900 --> 00:07:26,360
+إثنين هذا طبعا إثنين نسميه in labor hood
+
+54
+00:07:26,360 --> 00:07:31,940
+definition of continuity
+
+55
+00:07:45,120 --> 00:07:48,580
+الـ neighborhood definition للـ continuity ايش
+
+56
+00:07:48,580 --> 00:07:57,920
+بيقول لكل for every epsilon neighborhood v epsilon
+
+57
+00:07:57,920 --> 00:08:05,700
+لنقطة f of c there
+
+58
+00:08:05,700 --> 00:08:18,440
+exist delta neighborhood v delta of c لنقطة c طبعا
+
+59
+00:08:18,440 --> 00:08:26,200
+هذا إبسيلون neighborhood لـ f of c يوجد دلتا
+
+60
+00:08:26,200 --> 00:08:38,660
+neighborhood v دلتا of c بحيث أن لكل x تنتمي إلى
+
+61
+00:08:38,660 --> 00:08:47,830
+a تقاطع الـ دلتا neighborhood لـ c لازم هذا يضمن ان
+
+62
+00:08:47,830 --> 00:08:53,050
+صورة الـ x تنتمي
+
+63
+00:08:53,050 --> 00:09:04,590
+إلى دلتا إبسيلون لـ f of c that
+
+64
+00:09:04,590 --> 00:09:08,630
+is that
+
+65
+00:09:08,630 --> 00:09:11,910
+is هذا يعني أن الـ
+
+66
+00:09:14,980 --> 00:09:23,060
+الـ image للست a تقاطع v دلتا of c is contained
+
+67
+00:09:23,060 --> 00:09:34,140
+in الـ إبسيلون neighbourhood لـ f of c
+
+68
+00:09:34,140 --> 00:09:40,100
+هاي
+
+69
+00:09:40,100 --> 00:09:47,330
+كان في عنديزي هيك مثلا يكون في اندي فانكشن زي هذه
+
+70
+00:09:47,330 --> 00:09:57,210
+y بساوي f of x وقلنا
+
+71
+00:09:57,210 --> 00:10:03,810
+أن لو كانت x أو c c
+
+72
+00:10:03,810 --> 00:10:07,670
+نقطة الـ dial عندها متصلة هي f of c
+
+73
+00:10:11,410 --> 00:10:17,830
+ما معناه ان الدالة متصلة عند x بساوي c معناه لو
+
+74
+00:10:17,830 --> 00:10:23,770
+أخدت لأي
+
+75
+00:10:23,770 --> 00:10:30,850
+إبسيلون أكبر من الصفر فيه دلتا أو لو أخدت أي إبسيلون
+
+76
+00:10:30,850 --> 00:10:31,290
+neighborhood
+
+77
+00:10:34,530 --> 00:10:38,270
+يعني النقطة هذه f of c زائد إبسيلون النقطة هذه
+
+78
+00:10:38,270 --> 00:10:48,430
+المسافة هذه إبسيلون فهذه f of c سالب إبسيلون فهذه
+
+79
+00:10:48,430 --> 00:10:53,610
+الفترة المفتوحة عبارة عن إبسيلون neighborhood لـ f
+
+80
+00:10:53,610 --> 00:10:54,150
+of c
+
+81
+00:10:57,200 --> 00:11:01,620
+فلأي إبسيلون أكبر من الصفر ممكن أكون إبسيلون
+
+82
+00:11:01,620 --> 00:11:06,420
+neighborhood لـ f of c وبالتالي بقدر أرد على الـ
+
+83
+00:11:06,420 --> 00:11:14,580
+إبسيلون neighborhood هذا بـ دلتا يعني
+
+84
+00:11:14,580 --> 00:11:20,980
+أكون دلتا neighborhood هنا c minus دلتا c موجة
+
+85
+00:11:20,980 --> 00:11:21,460
+بـ دلتا
+
+86
+00:11:26,200 --> 00:11:37,060
+إذاً هذا عبارة عن v دلتا v دلتا لـ c إذاً
+
+87
+00:11:37,060 --> 00:11:43,200
+لأي إبسيلون لأي إبسيلون neighborhood لـ f of c بقدر
+
+88
+00:11:43,200 --> 00:11:52,720
+ألاقي دلتا neighborhood للنقطة c بحيث أن لكل x لو
+
+89
+00:11:52,720 --> 00:12:01,620
+أخدت x نقطة في الـ دلتا neighborhood فصورتها f of
+
+90
+00:12:01,620 --> 00:12:09,060
+x هتطلع تنتمي للـ إبسيلون neighborhood للـ f of c
+
+91
+00:12:09,060 --> 00:12:17,140
+okay تمام فهذا هو نفسه هذا بكفي التعريف هذا بكفي
+
+92
+00:12:17,140 --> 00:12:20,660
+التعريف الـ إبسيلون دلتا definition للـ continuity
+
+93
+00:12:24,390 --> 00:12:29,850
+هي لكل إبسيلون لكل إبسيلون أكبر من الصفر يعني كأني
+
+94
+00:12:29,850 --> 00:12:36,450
+بقول لكل إبسيلون نبرهود لـ f و c يوجد دلتا عدد موجب
+
+95
+00:12:36,450 --> 00:12:44,290
+فهذا معناه يوجد دلتا نبرهود للـ c بحيث أن لكل x
+
+96
+00:12:44,290 --> 00:12:50,560
+المسافر لكل x تنتمي لكل x في a و x بالتحقق
+
+97
+00:12:50,560 --> 00:12:55,980
+المتباينة دي معناته x سنتمي المسافة بين x و c أصغر
+
+98
+00:12:55,980 --> 00:12:56,380
+من دلتا
+
+99
+00:13:02,120 --> 00:13:07,000
+فهذا بيقدي أن المسافة بين f of x و f of c هي f of
+
+100
+00:13:07,000 --> 00:13:12,160
+x و f of c أصغر من إبسيلون يعني الـ f of x هذه
+
+101
+00:13:12,160 --> 00:13:17,900
+تنتمي للـ إبسيلون برهود لـ f of c إذن التعريفين هذول
+
+102
+00:13:17,900 --> 00:13:24,800
+متكافئين وهذا واضح من الرسم وبالتالي البرهان جاهز
+
+103
+00:13:24,800 --> 00:13:32,000
+من .. بس ترجمته الحاجات هذه إلى لغة الـ neighborhood
+
+104
+00:13:32,000 --> 00:13:39,600
+إذا في لان تعريفين للاتصال على النقطة واحد إبسيلون
+
+105
+00:13:39,600 --> 00:13:45,400
+دلتا definition والتاني اللي بكافه neighborhood
+
+106
+00:13:45,400 --> 00:13:50,360
+definition طيب
+
+107
+00:13:50,360 --> 00:13:55,260
+ناخد بعض الملاحظات على تعريف الاتصال
+
+108
+00:14:16,000 --> 00:14:22,640
+إذا c هو مقاومة مقاومة
+
+109
+00:14:22,640 --> 00:14:30,180
+a ثم
+
+110
+00:14:30,180 --> 00:14:38,200
+f مستمر في x بساوي
+
+111
+00:14:42,830 --> 00:14:47,530
+لو كانت الـ c هذه cluster point فالاتصال ان c
+
+112
+00:14:47,530 --> 00:14:55,730
+بكافئ بكافئ ان الـ limit لـ f of x من تعريف الـ
+
+113
+00:14:55,730 --> 00:15:03,570
+limits ان c بساوي f of c وهذا
+
+114
+00:15:03,570 --> 00:15:06,790
+طبعاً
+
+115
+00:15:06,790 --> 00:15:09,090
+this condition
+
+116
+00:15:12,780 --> 00:15:19,680
+is three in
+
+117
+00:15:19,680 --> 00:15:24,800
+one الـ
+
+118
+00:15:24,800 --> 00:15:30,480
+definition هذا بكافئ ثلاثة أو الشرط هذا بكافئ ثلاثة
+
+119
+00:15:30,480 --> 00:15:37,600
+شروط أو هو ثلاثة شروط في واحد أول شرط ان الـ function
+
+120
+00:15:37,600 --> 00:15:39,540
+f and c is defined
+
+121
+00:15:43,900 --> 00:15:49,540
+يعني هذا عبارة عن عدد حقيقي name الـ limit لـ f of x
+
+122
+00:15:49,540 --> 00:15:56,180
+لما x تقول إلى c exist يعني عدد حقيقي والشرط
+
+123
+00:15:56,180 --> 00:16:04,880
+الثالث أنه لازم الـ limit للـ function f and c بساوي
+
+124
+00:16:04,880 --> 00:16:09,980
+قيمة الدالة and c يعني عشان الدالة تكون متصلة عند
+
+125
+00:16:09,980 --> 00:16:16,020
+النقطة c في مجالها و لو كانت الـ c هي cluster point
+
+126
+00:16:16,020 --> 00:16:21,790
+طبعاً أو حتى لو ما كانتش cluster point فلازم الثلاثة
+
+127
+00:16:21,790 --> 00:16:25,250
+صوروطها تتحقق الدالة معرفة عن c طبعا هذا لأن c
+
+128
+00:16:25,250 --> 00:16:30,450
+نقطة في مجال الدالة فلازم تكون معرفة عن ده لازم الـ
+
+129
+00:16:30,450 --> 00:16:34,830
+limit لـ f عن c تكون موجودة وقيمة الـ limit بساوي
+
+130
+00:16:34,830 --> 00:16:39,290
+قيمة الدالة عند النقطة c لو أي واحد ما ليش صوروط
+
+131
+00:16:39,290 --> 00:16:43,830
+الثلاثة هدول اختل فبنقول أن الـ function مش متصلة
+
+132
+00:16:43,830 --> 00:16:49,410
+عند النقطة c okay تمام واضح إذا لو كانت الـ c هي دي
+
+133
+00:16:49,410 --> 00:16:53,510
+cluster point فتعريف الاتصال النقطة هو بالظبط
+
+134
+00:16:53,510 --> 00:16:58,470
+تعريف أن limited دالة ان c تكون موجودة و بتساوي
+
+135
+00:16:58,470 --> 00:17:02,570
+قيمتها ان c وهذا الشرط هو ثلاثة شروط و الـ c في الـ a
+
+136
+00:17:02,570 --> 00:17:09,510
+نعم الـ c تنتمي لـ a اه طبعا الـ c تنتمي لـ a الـ c
+
+137
+00:17:09,510 --> 00:17:11,130
+دائما تنتمي لـ a
+
+138
+00:17:17,100 --> 00:17:22,120
+طب لو ما كناش الـ c cluster point الملاحظة الثانية
+
+139
+00:17:22,120 --> 00:17:29,440
+if c is not يعني لو كان الـ c تنتمي طبعا دائما الـ c
+
+140
+00:17:29,440 --> 00:17:40,980
+تنتمي لـ a is not a cluster point is 
+
+141
+00:17:40,980 --> 00:17:44,100
+not a cluster point of a
+
+142
+00:17:48,950 --> 00:17:54,070
+then من تعريف الـ cluster point لازم نلاقي delta
+
+143
+00:17:54,070 --> 00:18:05,430
+أكبر من صفر such that a تقاطع v delta of c بساوي
+
+144
+00:18:05,430 --> 00:18:06,850
+singleton c
+
+145
+00:18:11,300 --> 00:18:14,580
+ما معناه أن النقطة C الموجودة في A مايعنيش 
+
+146
+00:18:14,580 --> 00:18:18,460
+cluster point أو ما معناه أن C تنتمي لـ A cluster
+
+147
+00:18:18,460 --> 00:18:24,380
+point معناها أن كل delta neighborhood للـ C بيتقاطع
+
+148
+00:18:24,380 --> 00:18:30,400
+مع A في نقطة مختلفة عن الـ C على الأقل، معناه أن الـ
+
+149
+00:18:30,400 --> 00:18:34,040
+C ما تكونش cluster point معناه أن يوجد delta
+
+150
+00:18:34,040 --> 00:18:37,040
+neighborhood واحد، يعني يوجد delta عدد موجب
+
+151
+00:18:37,040 --> 00:18:40,780
+وبالتالي يوجد على الأقل delta neighborhood للـ C
+
+152
+00:18:40,780 --> 00:18:46,620
+وهذا الـ delta neighborhood مابتقاطعش مع a في أي
+
+153
+00:18:46,620 --> 00:18:50,660
+نقطة مختلفة عن الـ c، يعني التقاطع هذا بس في نقطة
+
+154
+00:18:50,660 --> 00:18:55,300
+واحدة c لأن الـ c هي مركز الـ neighborhood و c تنتمي
+
+155
+00:18:55,300 --> 00:19:03,320
+لـ a فالتقاطع هذا مافيش فيه أي x مختلفة عن الـ c في
+
+156
+00:19:03,320 --> 00:19:09,740
+الحالة هذه، in this case, in 
+
+157
+00:19:09,740 --> 00:19:10,580
+this case
+
+158
+00:19:14,230 --> 00:19:23,970
+if f is automatically continuous
+
+159
+00:19:23,970 --> 00:19:34,940
+at c، الدالة في الحالة هذه بتكون متصلة تلقائيًا عند
+
+160
+00:19:34,940 --> 00:19:39,360
+النقطة C، أو التعريف متحقق تلقائيًا ليه؟ لأنه
+
+161
+00:19:39,360 --> 00:19:44,060
+تعالوا نرجع للتعريف، ما معناه أن F تكون متصلة عند
+
+162
+00:19:44,060 --> 00:19:49,660
+النقطة C، معناه لأي epsilon neighborhood لـ F و C
+
+163
+00:19:49,660 --> 00:19:53,680
+نقدر
+
+164
+00:19:53,680 --> 00:19:57,020
+نلاقي يوجد delta neighborhood لـ C، فخد الـ delta 
+
+165
+00:19:57,020 --> 00:20:00,040
+neighborhood في التعريف هذا، خد الـ delta
+
+166
+00:20:00,040 --> 00:20:07,900
+neighborhood هو هذا، ففي الحالة هذه لكل x تنتمي إلى
+
+167
+00:20:07,900 --> 00:20:12,340
+a تقاطع v delta و c، ما التقاطع هذا مافيش فيه إلا
+
+168
+00:20:12,340 --> 00:20:17,100
+نقطة واحدة اللي هي c، صح؟ فلكل x موجود في التقاطع
+
+169
+00:20:17,100 --> 00:20:21,950
+هذا، مافيش إلا x بساوي c، فصورة الـ X هذه هي صورة
+
+170
+00:20:21,950 --> 00:20:28,210
+الـ C، وبالتالي صورة الـ X هذه هي صورة الـ C، فهذه أكيد
+
+171
+00:20:28,210 --> 00:20:33,310
+تنتمي لـ epsilon neighborhood لـ F of C، لأن الـ F of C هي
+
+172
+00:20:33,310 --> 00:20:38,850
+المركز تبع الفترة هذه، صح؟ فهذا شرط متحقق trivially
+
+173
+00:20:38,850 --> 00:20:44,870
+تلقائيًا، وبالتالي إذا سواء
+
+174
+00:20:46,570 --> 00:20:49,730
+سواء الـ C هنا كانت cluster point أو ماكنتش
+
+175
+00:20:49,730 --> 00:20:55,630
+cluster point، فممكن نعتبر أن التعريف لاتصال النقطة
+
+176
+00:20:55,630 --> 00:21:00,450
+هو التعريف هذا، لأن لو كانت الـ C cluster point
+
+177
+00:21:00,450 --> 00:21:04,190
+فتعريف لاتصال النقطة هو هذا التعريف، لو كانت الـ C
+
+178
+00:21:04,190 --> 00:21:07,750
+ماهياش cluster point فهذا التعريف متحقق trivially
+
+179
+00:21:07,750 --> 00:21:12,380
+اللي بدهي، وبالتالي مافيش داعي إن احنا نقول .. لما
+
+180
+00:21:12,380 --> 00:21:14,840
+نيجي نفحص الاتصال على النقطة C، نقول هل الـ C
+
+181
+00:21:14,840 --> 00:21:18,840
+cluster point أو مش cluster point، سواء كانت
+
+182
+00:21:18,840 --> 00:21:24,380
+cluster point أو ماكانتش cluster point، فالاتصال
+
+183
+00:21:24,380 --> 00:21:33,020
+عن الـ C بيصير هو .. يعني هل هذا شرط بتحقق أو لا
+
+184
+00:21:41,130 --> 00:21:44,890
+طبعًا زي ما أخدنا احنا أيام ما أخدنا دراسنا الـ
+
+185
+00:21:44,890 --> 00:21:54,950
+limits للـ functions فكان
+
+186
+00:21:54,950 --> 00:21:57,590
+في عندي sequential criterion for limits
+
+187
+00:22:02,270 --> 00:22:06,810
+بنفس الطريقة، في هنا sequential criterion for
+
+188
+00:22:06,810 --> 00:22:15,990
+continuity للاتصال، إذا في عندي هنا sequential
+
+189
+00:22:15,990 --> 00:22:21,130
+criterion
+
+190
+00:22:21,130 --> 00:22:24,150
+for
+
+191
+00:22:24,150 --> 00:22:25,110
+continuity
+
+192
+00:22:35,670 --> 00:22:44,430
+let f be a function from a to r، و c نقطة في a، then
+
+193
+00:22:44,430 --> 00:22:56,170
+the following statements are equivalent، واحد
+
+194
+00:22:56,170 --> 00:23:08,010
+f is continuous at c، f is continuous at c for
+
+195
+00:23:08,010 --> 00:23:11,910
+every، for
+
+196
+00:23:11,910 --> 00:23:22,050
+every sequence x n contained in a with
+
+197
+00:23:22,050 --> 00:23:25,370
+limit
+
+198
+00:23:25,370 --> 00:23:41,270
+x n بساوي c، نحن لدينا أن الـ limit لـ f of x n as n 
+
+199
+00:23:41,270 --> 00:23:45,790
+tends to infinity بساوي f of c
+
+200
+00:23:51,740 --> 00:23:54,940
+الآن الـ sequential criterion for continuity بتقول
+
+201
+00:23:54,940 --> 00:24:00,380
+عشان أثبت أن الدالة F continuous عند نقطة، يكفي أن
+
+202
+00:24:00,380 --> 00:24:04,900
+أنا أثبت أن لو أخدت أي sequence نهايتها أي
+
+203
+00:24:04,900 --> 00:24:07,660
+sequence في مجال الدالة، طبعًا كنا في الـ limits
+
+204
+00:24:07,660 --> 00:24:13,020
+نُشترط أن X n كل عنصر في الـ sequence مختلف عن الـ C
+
+205
+00:24:13,020 --> 00:24:17,200
+هنا لأ، ممكن يساوي الـ C، مش مشكلة، هاي الاختلاف بس
+
+206
+00:24:17,200 --> 00:24:21,430
+بين الـ sequential criterion for limits و Sequential
+
+207
+00:24:21,430 --> 00:24:26,030
+criterion for continuity إنه لكل sequence x n في
+
+208
+00:24:26,030 --> 00:24:32,550
+مجال الدالة، ونهايتها بتساوي c، لازم يطلع عندي
+
+209
+00:24:32,550 --> 00:24:37,990
+نهاية الـ image تبعت الـ sequence x n بتساوي العدد
+
+210
+00:24:37,990 --> 00:24:42,860
+f و c، وبرهان النظرية هذه زي برهان sequential
+
+211
+00:24:42,860 --> 00:24:49,120
+criterion for limits مع تعديلات طفيفة، مع التعديلات
+
+212
+00:24:49,120 --> 00:24:58,580
+الطفيفة في التعريفين أو في التعريف تبع الاتصال إذا
+
+213
+00:24:58,580 --> 00:25:11,090
+الـ proof similar to proof of sequential criterion
+
+214
+00:25:11,090 --> 00:25:19,570
+for limits for limits، sequential criterion for
+
+215
+00:25:19,570 --> 00:25:34,190
+limits of functions in section أربعة واحد with
+
+216
+00:25:34,190 --> 00:25:38,030
+slight modification
+
+217
+00:25:45,120 --> 00:25:51,780
+مع تعديل بسيط، مع تعديل بسيط، التعديل هنا إنه الـ هنا
+
+218
+00:25:51,780 --> 00:25:58,180
+كنا نطلب الـ X لا تساوي C، وكمان كنا هناك نطلب إنه C
+
+219
+00:25:58,180 --> 00:26:02,740
+تكون cluster point، لكن شفنا حتى لو C ماكنتش
+
+220
+00:26:02,740 --> 00:26:10,940
+cluster point، فهذا برضه متحقق تلقائيًا، برضه
+
+221
+00:26:10,940 --> 00:26:11,700
+أخدنا
+
+222
+00:26:14,550 --> 00:26:18,230
+بعد ما أخدنا الـ sequential criterion for limits
+
+223
+00:26:18,230 --> 00:26:22,410
+of functions في section 4-1، أخدنا بعدها على طول
+
+224
+00:26:22,410 --> 00:26:29,850
+مباشرة divergence criterion for limits، فهنا بقابل
+
+225
+00:26:29,850 --> 00:26:38,190
+الـ divergence criterion اللي هو
+
+226
+00:26:38,190 --> 00:26:39,910
+discontinuity criterion
+
+227
+00:26:46,180 --> 00:26:48,980
+discontinuity criterion
+
+228
+00:27:00,500 --> 00:27:10,940
+let f be a function from a to r، و c نقطة في a، و d
+
+229
+00:27:10,940 --> 00:27:15,440
+then the
+
+230
+00:27:15,440 --> 00:27:23,000
+following statements are equivalent، واحد، if f is
+
+231
+00:27:23,000 --> 00:27:24,160
+discontinuous
+
+232
+00:27:26,370 --> 00:27:36,730
+إذا كان الـ f discontinuous at x بساوي c، ثم يوجد
+
+233
+00:27:36,730 --> 00:27:49,070
+sequence x n contained in a with limit x n بساوي
+
+234
+00:27:49,070 --> 00:27:49,610
+c
+
+235
+00:27:53,460 --> 00:28:01,180
+but limit الـ image للـ sequence x n لا يساوي f
+
+236
+00:28:01,180 --> 00:28:08,260
+of c، وبرهان
+
+237
+00:28:08,260 --> 00:28:13,100
+النظرية هذه بيجي من النظرية الـ sequential
+
+238
+00:28:13,100 --> 00:28:16,980
+criterion، أنا 
+
+239
+00:28:16,980 --> 00:28:21,400
+عندي واحد one يكفي اتنين one if and only if two
+
+240
+00:28:24,600 --> 00:28:29,660
+وبالتالي not one نفي one يكافئ نفي two، طيب تعالى
+
+241
+00:28:29,660 --> 00:28:35,400
+نشوف نفي one، if f is discontinuous at c، نفي two، for
+
+242
+00:28:35,400 --> 00:28:40,420
+every sequence بتحقق الشرط هذا، نهايت صورتها بساوي
+
+243
+00:28:40,420 --> 00:28:45,160
+f of c، إن في الشرط العبارة هذه، فبصير there exist a
+
+244
+00:28:45,160 --> 00:28:50,380
+sequence x n contained in a ونهايتها c، لكن نهايت
+
+245
+00:28:50,380 --> 00:28:56,550
+صورتها لا تساوي f of c، Okay تمام، إذا البرهان نظرية
+
+246
+00:28:56,550 --> 00:29:05,170
+هذه جاي من نفي أو ينتج من النظرية السابقة، طب
+
+247
+00:29:05,170 --> 00:29:15,350
+نرجع ناخد، قبل ما ناخد أمثلة، بدنا ناخد بس تعريف
+
+248
+00:29:15,350 --> 00:29:20,170
+الاتصال على مجموعة، definition
+
+249
+00:29:24,990 --> 00:29:32,690
+استخدم الفرصة، let f be a function from a to r and
+
+250
+00:29:32,690 --> 00:29:38,050
+let
+
+251
+00:29:38,050 --> 00:29:47,090
+b be a subset of a، نقول
+
+252
+00:29:47,090 --> 00:29:50,890
+أن الفرصة f is continuous
+
+253
+00:29:54,760 --> 00:30:05,060
+if f is continuous on the set B، on the
+
+254
+00:30:05,060 --> 00:30:16,640
+set B، if f is continuous on the set B، if if f is
+
+255
+00:30:16,640 --> 00:30:32,720
+continuous at every، at every x ينتمي إلى B، إذا 
+
+256
+00:30:32,720 --> 00:30:38,880
+الاتصال على مجموعة معناه إن الدالة تكون متصلة عند
+
+257
+00:30:38,880 --> 00:30:47,520
+كل نقطة في المجموعة، عند كل نقطة في المجموعة، طيب
+
+258
+00:30:47,520 --> 00:30:49,080
+ناخد بعض الأمثلة
+
+259
+00:31:06,780 --> 00:31:17,520
+الـ function f of x بتساوي k، و
+
+260
+00:31:17,520 --> 00:31:30,460
+x belong to R is continuous on R، الدالة 
+
+261
+00:31:30,460 --> 00:31:43,300
+ثابت k continuous على كل الـ R، احنا شفنا proof، fix
+
+262
+00:31:43,300 --> 00:31:46,240
+c تنتمي لـ R
+
+263
+00:31:51,650 --> 00:32:02,150
+Since limit لـ F of X as X tends to C بساوي K، احنا
+
+264
+00:32:02,150 --> 00:32:07,850
+أثبتنا قبلين أن limit أي ده لثابته بساوي ثابت K
+
+265
+00:32:07,850 --> 00:32:15,690
+وهذا بساوي F of C، فالـ
+
+266
+00:32:15,690 --> 00:32:29,850
+F is continuous at every c تنتمي إلى r، فاكرين
+
+267
+00:32:29,850 --> 00:32:34,430
+احنا هدفنا كان باستخدام تعريف epsilon delta، قولنا
+
+268
+00:32:34,430 --> 00:32:39,930
+لأي epsilon أكبر من صفر، choose أي delta أكبر من
+
+269
+00:32:39,930 --> 00:32:43,690
+الصفر، فتعريف
+
+270
+00:32:43,690 --> 00:32:47,670
+الـ limit بتحقق
+
+271
+00:32:47,670 --> 00:32:48,790
+وهنا نفس الحاجة
+
+272
+00:33:16,050 --> 00:33:25,330
+طيب المثال تاني، لو أخدت f of x بساوي x لكل x ينتمي
+
+273
+00:33:25,330 --> 00:33:31,570
+إلى R، الـ identity function، فبرضه 
+
+274
+00:33:31,570 --> 00:33:39,350
+أثبتنا احنا إن الـ function هذه is continuous، if f is
+
+275
+00:33:39,350 --> 00:33:44,290
+continuous على مجموعة الأعداد الحقيقية
+
+276
+00:34:07,950 --> 00:34:17,850
+فممكن أن نثبت، C تنتمي إلى R، و أثبتنا احنا في
+
+277
+00:34:17,850 --> 00:34:24,390
+section أربعة واحد، إن limit F of X لما X تقول C
+
+278
+00:34:24,390 --> 00:34:32,530
+طلعت بساوي C، صح؟ وهذا عبارة عن F of C، فالـ F is
+
+279
+00:34:32,530 --> 00:34:35,610
+continuous at C
+
+280
+00:34:39,860 --> 00:34:48,180
+وبما إنه c arbitrary element، إذا 
+
+281
+00:34:48,180 --> 00:34:55,720
+الـf يكون continuous at every c ينتمي إلى R
+
+282
+00:34:55,720 --> 00:35:03,220
+وبالتالي continuous على كل الـR ممكن
+
+283
+00:35:03,220 --> 00:35:08,760
+برضه نستخدم تعريف epsilon دلتا مباشرة بلاش نقول إن
+
+284
+00:35:08,760 --> 00:35:13,440
+احنا أثبتنا إن الـlimit لـ الـfunction f عند c
+
+285
+00:35:13,440 --> 00:35:17,020
+بالساوية c في section أربعة واحد أنا ممكن أُثبت
+
+286
+00:35:17,020 --> 00:35:22,520
+يعني نستخدم تعريف epsilon دلتا مباشرة ونقول let
+
+287
+00:35:22,520 --> 00:35:32,180
+if fix أول حاجة fix c تنتمي إلى R to show if it is
+
+288
+00:35:32,180 --> 00:35:39,820
+continuous at c let epsilon أكبر من الصفر be given
+
+289
+00:35:39,820 --> 00:35:44,720
+it 
+
+290
+00:35:44,720 --> 00:35:49,540
+shows... زي ما عملنا في الـlimits it shows delta
+
+291
+00:35:49,540 --> 00:35:54,640
+بساوي epsilon إذن
+
+292
+00:35:54,640 --> 00:36:00,160
+هَيوجد دلتا تعتمد على epsilon Then لهذه الـDelta
+
+293
+00:36:00,160 --> 00:36:06,600
+لو كان x ينتمي إلى A، A هنا اللي هي R و |x|
+
+294
+00:36:06,600 --> 00:36:12,360
+- C أصغر من دلتا فهذا بيضمن إنه |f of
+
+295
+00:36:12,360 --> 00:36:20,080
+x| |f of x - f of C| هذا بيطلع بساوي 
+
+296
+00:36:20,080 --> 00:36:28,590
+|x - f of x| بساوي x و f of c بساوي c
+
+297
+00:36:28,590 --> 00:36:33,010
+وهذا أصغر من دلتا، ماخدين المسافة هذه أصغر من
+
+298
+00:36:33,010 --> 00:36:38,250
+دلتا وأنا اخترت دلتا بساوي Epsilon إذن هذه 
+
+299
+00:36:38,250 --> 00:36:42,110
+أثبتت لكل Epsilon يوجد Delta تعتمد على Epsilon
+
+300
+00:36:42,110 --> 00:36:46,150
+بحيث لكل x في مجال الدالة المسافة بينها وبين c
+
+301
+00:36:46,150 --> 00:36:50,650
+أصغر من دلتا طلع المسافة بين f of x و f of c أصغر
+
+302
+00:36:50,650 --> 00:36:58,390
+من Epsilon إذن هذا معناه إن f is continuous at c
+
+303
+00:36:58,390 --> 00:37:06,010
+since c تنتمي إلى R was arbitrary إذن f is
+
+304
+00:37:06,010 --> 00:37:12,750
+continuous على كل الأعداد الحقيقية تمام؟ إذن هذا
+
+305
+00:37:12,750 --> 00:37:15,890
+ممكن نستخدم تعريف Epsilon Delta مباشرة 
+
+306
+00:37:19,990 --> 00:37:23,390
+دون الاعتماد على النتائج اللي عملناها تابعة
+
+307
+00:37:23,390 --> 00:37:28,390
+النهاية في section أربعة واحد بالمثل ممكن مثال زي
+
+308
+00:37:28,390 --> 00:37:35,290
+هذا برضه الـfunction f
+
+309
+00:37:35,290 --> 00:37:43,790
+of x بساوي x سلبية is continuous على كل الأعداد
+
+310
+00:37:43,790 --> 00:37:44,570
+الحقيقية
+
+311
+00:38:05,350 --> 00:38:08,350
+الدالة متصلة عند النقطة c
+
+312
+00:38:13,110 --> 00:38:18,330
+نفس تعريف epsilon دلتا زي ما عملنا في إثبات إن الـ
+
+313
+00:38:18,330 --> 00:38:24,490
+limit للـfunction f of x عند x بساوي c بساوي c
+
+314
+00:38:24,490 --> 00:38:30,110
+تربيع اللي هو f of c وذلك
+
+315
+00:38:30,110 --> 00:38:35,710
+بياخد أي epsilon أكبر من صفر وبنجيب دلتا زي ما
+
+316
+00:38:35,710 --> 00:38:38,510
+عملنا في section أربعة واحد دلتا بساوي الـminimum
+
+317
+00:38:38,510 --> 00:38:45,380
+لقيمتين نثبت إنه لكل x المسافة بينها وبين الـc
+
+318
+00:38:45,380 --> 00:38:47,960
+أصغر من الـدلتا بيطلع المسافة هذه أصغر من الـc
+
+319
+00:38:47,960 --> 00:38:53,120
+نعيد يعني إيش نفس البرمجة، إذن هذا لو طلب منكم
+
+320
+00:38:53,120 --> 00:38:56,460
+استخدام تعريف epsilon delta لإثبات إن الدالة هذه
+
+321
+00:38:56,460 --> 00:39:00,420
+مقتصرة على R فبتقول لأي epsilon أكبر من الصفر
+
+322
+00:39:00,420 --> 00:39:05,060
+choose delta زي ما عملنا في section 4-1 في إثبات
+
+323
+00:39:05,060 --> 00:39:08,900
+إن limit للدالة هذه عند c بساوي c تربيع
+
+324
+00:39:12,370 --> 00:39:18,470
+أو ممكن تقولي we should إذا ما طلبش منك تستخدم
+
+325
+00:39:18,470 --> 00:39:23,590
+التعريف epsilon دلتا فبتقولي we should أثبتنا in
+
+326
+00:39:23,590 --> 00:39:33,970
+section أربعة واحد that limit لـf of x لما x تقول
+
+327
+00:39:33,970 --> 00:39:42,230
+إلى c بساوي c تربيع اللي هي f of c حسب تعريف
+
+328
+00:39:42,230 --> 00:39:45,470
+الاتصال على النقطة بيطلع أي شرط تلاتة في واحد
+
+329
+00:39:45,470 --> 00:39:54,190
+متحقق وبالتالي if it is continuous at c okay تمام
+
+330
+00:39:57,190 --> 00:40:00,230
+وطبعًا بما إن الـc تنتمي إلى R was arbitrary إذن
+
+331
+00:40:00,230 --> 00:40:03,970
+الدالة f continuous على كل الـR okay إذا دامت
+
+332
+00:40:03,970 --> 00:40:11,050
+يا إما نستخدم نتائج section 4-1 أو نعيد البرهان
+
+333
+00:40:11,050 --> 00:40:15,250
+باستخدام تعريف epsilon Delta زي ما عملنا في المثال
+
+334
+00:40:15,250 --> 00:40:22,770
+الأخير أو زي ما عملنا في section 4-1 الدالة كمان
+
+335
+00:40:22,770 --> 00:40:23,930
+عندي الدالة
+
+336
+00:40:32,140 --> 00:40:41,000
+لو أخدت phi of x بساوي 1 على x فهذه الدالة is 
+
+337
+00:40:41,000 --> 00:40:46,280
+continuous on الـset A
+
+338
+00:40:58,940 --> 00:41:04,860
+اللي هي كل الـx ينتمي إلى R حيث x أكبر من الصفر
+
+339
+00:41:04,860 --> 00:41:11,380
+فاحنا
+
+340
+00:41:11,380 --> 00:41:20,880
+أثبتنا في x c تنتمي إلى A هذا بقدر إنه c أكبر من
+
+341
+00:41:20,880 --> 00:41:23,280
+الصفر وأثبتنا
+
+342
+00:41:28,820 --> 00:41:35,560
+in section أربعة
+
+343
+00:41:35,560 --> 00:41:44,320
+واحد ذات limit لـfunction phi of x لما x تقول إلى
+
+344
+00:41:44,320 --> 00:41:52,240
+c بساوي 1 على c بساوي phi of c باستخدام تعريف
+
+345
+00:41:52,240 --> 00:41:58,070
+epsilon دلتا يا إما نعيد البرهان هذاك لأي epsilon في
+
+346
+00:41:58,070 --> 00:42:03,450
+دلتا بساوي minimum لقيمتين أو نقول إن احنا أثبتنا
+
+347
+00:42:03,450 --> 00:42:06,890
+إن limit للدالة هذه عند أي عدد c موجود بساوي 1
+
+348
+00:42:06,890 --> 00:42:12,590
+على c اللي هو قيمة الدالة عند c وبالتالي إذا الدالة 
+
+349
+00:42:12,590 --> 00:42:19,830
+في is continuous at c بما إن الـc تنتمي إلى a was
+
+350
+00:42:19,830 --> 00:42:26,450
+arbitrary إذن الـفي continuous على المجموعة A
+
+351
+00:42:26,450 --> 00:42:30,370
+بالمثل
+
+352
+00:42:30,370 --> 00:42:35,050
+ممكن نثبت إن الدالة دي continuous كمان على
+
+353
+00:42:35,050 --> 00:42:44,530
+المجموعة B اللي هي كل الـx ينتمي إلى R حيث x أصغر من
+
+354
+00:42:44,530 --> 00:42:48,990
+0 الدالة
+
+355
+00:42:48,990 --> 00:42:54,190
+دي متصلة عند كل الأعداد الحقيقية ما عدا عدد 0 فهي متصلة
+
+356
+00:42:54,190 --> 00:42:57,610
+عند الأعداد الحقيقية الموجبة وعند الأعداد الحقيقية 
+
+357
+00:42:57,610 --> 00:43:07,950
+السالبة طيب
+
+358
+00:43:07,950 --> 00:43:13,370
+الدالة phi
+
+359
+00:43:13,370 --> 00:43:19,950
+of x نفسها برضه بساوي 1 على x is not is
+
+360
+00:43:19,950 --> 00:43:33,190
+discontinuous is discontinuous at c بساوي 0 proof
+
+361
+00:43:33,190 --> 00:43:39,090
+one الدالة
+
+362
+00:43:39,090 --> 00:43:44,530
+هذه ليست متصلة عند الصفر فالبرهان ذلك ممكن نقول
+
+363
+00:43:44,530 --> 00:43:49,610
+أنه في phi
+
+364
+00:43:52,850 --> 00:43:59,250
+is undefined is undefined is undefined is 
+
+365
+00:43:59,250 --> 00:44:05,090
+undefined is undefined is undefined is undefined
+
+366
+00:44:05,090 --> 00:44:05,970
+undefined is undefined is undefined is undefined
+
+367
+00:44:05,970 --> 00:44:07,390
+is undefined is undefined is undefined is 
+
+368
+00:44:07,390 --> 00:44:07,470
+undefined is undefined is undefined is undefined
+
+369
+00:44:07,470 --> 00:44:07,830
+is undefined is undefined is undefined is
+
+370
+00:44:07,830 --> 00:44:09,950
+is undefined is undefined is undefined is
+
+371
+00:44:09,950 --> 00:44:16,950
+undefined is undefined is undefined is undefined
+
+372
+00:44:18,990 --> 00:44:25,170
+can't be continuous at x بساوي 0 لأن عشان هي
+
+373
+00:44:25,170 --> 00:44:28,550
+تكون متصلة عند 0 لازم تلات شروط يتحققوا إنها
+
+374
+00:44:28,550 --> 00:44:32,790
+تكون أول شرط معرفة عند الصفر فده هي مش معرفة عند
+
+375
+00:44:32,790 --> 00:44:38,390
+الصفر فكيف تلات شروط هيتحققوا هذا برهان تاني برهان
+
+376
+00:44:38,390 --> 00:44:45,850
+آخر إن ما احنا شوفنا we should
+
+377
+00:44:48,290 --> 00:44:52,870
+in section أربعة
+
+378
+00:44:52,870 --> 00:44:57,990
+واحد أو أربعة اتنين that
+
+379
+00:44:57,990 --> 00:45:08,290
+limit لـphi of x as x tends to zero does not exist
+
+380
+00:45:08,290 --> 00:45:12,850
+أثبتنا إن الـfunction هذه ما لهاش limit عند الصفر
+
+381
+00:45:15,830 --> 00:45:21,510
+فاستخدمنا الـdivergence criterion وشوفنا إن هناك
+
+382
+00:45:21,510 --> 00:45:27,450
+sequence اللي هي 1 على n converge للصفر but
+
+383
+00:45:27,450 --> 00:45:34,690
+limit الـimage للـsequence 1 على n as n tends
+
+384
+00:45:34,690 --> 00:45:40,170
+to infinity بساوي limit n بساوي infinity does not
+
+385
+00:45:40,170 --> 00:45:47,950
+exist in R وبالتالي by divergence criterion الـ
+
+386
+00:45:47,950 --> 00:45:51,270
+function هذه ما لهاش limit وبالتالي مش ممكن تكون
+
+387
+00:45:51,270 --> 00:46:02,990
+continuous so if it can't be continuous at x بساوي
+
+388
+00:46:02,990 --> 00:46:09,510
+0 تمام؟ لأن واحد من الشروط التلاتة تبعت الاتصال
+
+389
+00:46:09,510 --> 00:46:12,650
+عن نقطة غير متحققة تمام؟
+
+390
+00:46:22,580 --> 00:46:28,520
+في كمان مثال أخذناه في section
+
+391
+00:46:28,520 --> 00:46:36,020
+4-1 الـ
+
+392
+00:46:36,020 --> 00:46:42,220
+signum function اللي
+
+393
+00:46:42,220 --> 00:46:52,050
+كان تعريفها بساوي 0 if x بساوي 0 و x على
+
+394
+00:46:52,050 --> 00:47:00,370
+|x| إذا كان x لا يساوي 0 is discontinuous
+
+395
+00:47:00,370 --> 00:47:09,170
+is discontinuous at x بساوي 0 why
+
+396
+00:47:18,170 --> 00:47:23,550
+لأنه أثبتنا احنا في section أربعة واحد إنه limit لـ
+
+397
+00:47:23,550 --> 00:47:31,490
+signum x لما x تقول إلى 0 does not exist
+
+398
+00:47:40,560 --> 00:47:43,240
+اللي هي إن الـlimit للـsignal function عند الصفر
+
+399
+00:47:43,240 --> 00:47:46,580
+does not exist شوفنا إن الـlimit من اليمين 1
+
+400
+00:47:46,580 --> 00:47:50,020
+عند الصفر والـlimit والـlimit عند الصفر من اليسار
+
+401
+00:47:50,020 --> 00:47:53,340
+بساوي -1 وبالتالي مش متساويين الاثنين إذن الـ
+
+402
+00:47:53,340 --> 00:48:00,000
+limit عند الصفر does not exist okay تمام إذن الـالـ
+
+403
+00:48:00,000 --> 00:48:04,700
+function هذه ما هيّاش متصلة عند الصفر لعدم نظرا لعدم
+
+404
+00:48:04,700 --> 00:48:10,970
+وجود الـlimit عند الصفر رغم إن الدالة هذه معرفة عند
+
+405
+00:48:10,970 --> 00:48:17,310
+الصفر، الـSignum للصفر هي معرفة عند الصفر بساوي
+
+406
+00:48:17,310 --> 00:48:24,930
+0 تمام؟
+
+407
+00:48:24,930 --> 00:48:30,710
+طيب، لكن ممكن إثبات إن الـSignum function متصلة
+
+408
+00:48:30,710 --> 00:48:32,850
+عند كل x لا يساوي 0
+
+409
+00:48:45,100 --> 00:48:52,440
+However، الـsignum الـsignum function is 
+
+410
+00:48:52,440 --> 00:48:59,280
+continuous at 
+
+411
+00:48:59,280 --> 00:49:09,460
+every x لا يساوي 0 لأنه
+
+412
+00:49:22,230 --> 00:49:42,610
+proof fix c لا تنتمي إلى R و c لا يساوي 0 تمام then
+
+413
+00:49:42,610 --> 00:49:53,460
+|signum x - signum الـc| بساوي |
+
+414
+00:49:53,460 --> 00:49:57,420
+x
+
+415
+00:49:57,420 --> 00:50:14,640
+على |x| أو
+
+416
+00:50:14,640 --> 00:50:15,160
+بلاش
+
+417
+00:50:19,850 --> 00:50:26,730
+then الـlimit لـsigma x 
+
+418
+00:50:26,730 --> 00:50:34,390
+لما x تقول إلى c بساوي
+
+419
+00:50:34,390 --> 00:50:37,990
+لما
+
+420
+00:50:37,990 --> 00:50:43,670
+x تقول إلى c فهذا عبارة عن limit x على |x| 
+
+421
+00:50:43,670 --> 00:50:45,630
+لما x تقول إلى c
+
+422
+00:51:03,050 --> 00:51:08,750
+فده كانت ال X لا تساوي صفر فإما ال X موجبة بقى أو
+
+423
+00:51:08,750 --> 00:51:12,890
+سلبية بقى
+
+424
+00:51:12,890 --> 00:51:18,010
+then C أكبر من الصفر or C أصغر من صفر
+
+425
+00:51:23,040 --> 00:51:27,120
+الـ C هتكون أكبر من الصفر الـ C هنا لا تساوي صفر
+
+426
+00:51:27,120 --> 00:51:33,240
+إذا إما C أكبر من الصفر أو أصغر من الصفر case one
+
+427
+00:51:33,240 --> 00:51:41,000
+لو كانت C أكبر من صفر فهذا بيعني أنه limit signum X
+
+428
+00:51:41,000 --> 00:51:50,980
+as X tends to C بيساوي limit X على absolute X
+
+429
+00:51:59,940 --> 00:52:05,660
+و طبعا ال X أكبر من ال
+
+430
+00:52:05,660 --> 00:52:11,860
+C أكبر من الصفر ف absolute .. فهذا بيساوي واحد
+
+431
+00:52:11,860 --> 00:52:21,440
+بيساوي limit واحد as X tends to C بيساوي واحد
+
+432
+00:52:21,440 --> 00:52:32,490
+بيساوي F of C أو signum C لأن
+
+433
+00:52:32,490 --> 00:52:40,050
+ال C موجبة فلما ال C تكون موجبة ف absolute ال C
+
+434
+00:52:40,050 --> 00:52:47,250
+بيساوي ال C بيطلع القيمة المطلقة هذه بيطلع واحد وبالتالي إذا
+
+435
+00:52:47,250 --> 00:52:57,970
+ال signal x is continuous at c case 2 إذا كانت ال
+
+436
+00:52:57,970 --> 00:53:11,210
+c أصغر من صفر ف similar to case 1 في
+
+437
+00:53:11,210 --> 00:53:17,600
+الحالة هذه قيمة ال function هتطلع سالب واحد عند c و
+
+438
+00:53:17,600 --> 00:53:22,820
+limit عند c هتطلع سالب واحد وبالتالي في اتصال عند
+
+439
+00:53:22,820 --> 00:53:26,320
+ال c إذا ال sign and function مش متصلة عند الصفر
+
+440
+00:53:26,320 --> 00:53:30,800
+لكنها متصلة عند كل الأعداد الحقيقية المختلفة عن
+
+441
+00:53:30,800 --> 00:53:37,910
+الصفر Okay بنكتفي بهذا القدر و بنكمل طبعا إن شاء
+
+442
+00:53:37,910 --> 00:53:44,390
+الله في المحاضرة القادمة هنعطيكم إن شاء الله break
+
+443
+00:53:44,390 --> 00:53:49,350
+خمس دقائق وبعدين نواصل المحاضرة التانية اللي
+
+444
+00:53:49,350 --> 00:53:56,090
+هناخد فيها discussion أو مناقشة لل chapter أربعة
+
+445
+00:53:56,090 --> 00:53:58,350
+section أربعة واحد وأربعة اتنين 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..fce74bcb0a27d485ce1ae5bc7730a203e237e9f8
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Ij2H9eVnog4_raw.json
@@ -0,0 +1 @@
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تنتمي إلى r إذا ال function هذه اللي معرفها بالطريقة كما هو موضح على هذه ال function بتكون discontinuous ليست متصلة عند أي x في R ليه برهان ذلك proof", "tokens": [21825, 2031, 6055, 29399, 2304, 1829, 30731, 367, 11933, 15730, 2423, 2445, 29538, 13672, 1829, 20449, 28480, 11296, 20666, 9566, 16572, 28671, 9122, 15042, 31439, 3714, 2407, 11242, 5016, 15844, 29538, 2423, 2445, 39894, 30544, 31420, 12549, 32239, 14851, 44650, 36520, 3660, 43242, 36632, 2031, 8978, 497, 32239, 3224, 4724, 2288, 3224, 7649, 29910, 23275, 8177], "avg_logprob": -0.2815241102586713, "compression_ratio": 1.3793103448275863, "no_speech_prob": 0.0, "words": [{"start": 133.63, "end": 134.63, "word": "every", "probability": 0.328125}, {"start": 134.63, "end": 135.63, "word": " x", "probability": 0.83203125}, {"start": 135.63, "end": 137.17, "word": " تنتمي", "probability": 0.7652587890625}, {"start": 137.17, "end": 137.47, "word": " إلى", "probability": 0.791015625}, {"start": 137.47, "end": 137.93, "word": " r", 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153.45, "end": 153.89, "word": " برهان", "probability": 0.861572265625}, {"start": 153.89, "end": 154.37, "word": " ذلك", "probability": 0.99560546875}, {"start": 154.37, "end": 154.93, "word": " proof", "probability": 0.395751953125}], "temperature": 1.0}, {"id": 6, "seek": 18332, "start": 162.42, "end": 183.32, "text": "fix C تنتمي إلى R then فما احنا عارفين ان ال real numbers عبارة عن ال union disjoint union لل rational numbers وال irrational numbers", "tokens": [69, 970, 383, 6055, 29399, 2304, 1829, 30731, 497, 550, 6156, 15042, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 2423, 957, 3547, 6225, 3555, 9640, 3660, 18871, 2423, 11671, 717, 48613, 11671, 24976, 15090, 3547, 16070, 39914, 3547], "avg_logprob": -0.3433593772351742, "compression_ratio": 1.376, "no_speech_prob": 0.0, "words": [{"start": 162.42000000000002, "end": 163.58, "word": "fix", "probability": 0.58001708984375}, {"start": 163.58, "end": 164.74, "word": " C", "probability": 0.160888671875}, {"start": 164.74, 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"probability": 0.9970703125}, {"start": 178.48, "end": 178.62, "word": " ال", "probability": 0.873046875}, {"start": 178.62, "end": 179.06, "word": " union", "probability": 0.93115234375}, {"start": 179.06, "end": 179.66, "word": " disjoint", "probability": 0.5986328125}, {"start": 179.66, "end": 180.32, "word": " union", "probability": 0.91552734375}, {"start": 180.32, "end": 180.98, "word": " لل", "probability": 0.8857421875}, {"start": 180.98, "end": 181.4, "word": " rational", "probability": 0.900390625}, {"start": 181.4, "end": 182.0, "word": " numbers", "probability": 0.47705078125}, {"start": 182.0, "end": 182.22, "word": " وال", "probability": 0.5654296875}, {"start": 182.22, "end": 182.64, "word": " irrational", "probability": 0.57275390625}, {"start": 182.64, "end": 183.32, "word": " numbers", "probability": 0.8916015625}], "temperature": 1.0}, {"id": 7, "seek": 21318, "start": 189.68, "end": 213.18, "text": "then X أو C تنتمي إلى Q أو C تنتمي إلى R minus Q إذا الـ C هذا إما هتكون rational number أو irrational number الحالة الأولى case one لو كانت C rational number", "tokens": [19096, 1783, 34051, 383, 6055, 29399, 2304, 1829, 30731, 1249, 34051, 383, 6055, 29399, 2304, 1829, 30731, 497, 3175, 1249, 11933, 15730, 2423, 39184, 383, 23758, 11933, 15042, 8032, 2655, 30544, 15090, 1230, 34051, 39914, 1230, 21542, 6027, 3660, 16247, 12610, 7578, 1389, 472, 45164, 25961, 2655, 383, 15090, 1230], "avg_logprob": -0.2499999953251259, "compression_ratio": 1.5579710144927537, "no_speech_prob": 0.0, "words": [{"start": 189.68, "end": 190.72, "word": "then", "probability": 0.219970703125}, {"start": 190.72, "end": 191.76, "word": " X", "probability": 0.33935546875}, {"start": 191.76, "end": 192.42, "word": " أو", "probability": 0.7255859375}, {"start": 192.42, "end": 192.76, "word": " C", "probability": 0.90478515625}, {"start": 192.76, "end": 193.56, "word": " تنتمي", "probability": 0.961181640625}, {"start": 193.56, "end": 195.88, "word": " إلى", "probability": 0.72119140625}, {"start": 195.88, "end": 196.38, "word": " Q", "probability": 0.91064453125}, {"start": 196.38, "end": 197.08, "word": " أو", "probability": 0.482177734375}, {"start": 197.08, "end": 198.38, "word": " C", "probability": 0.751953125}, {"start": 198.38, "end": 199.28, "word": " تنتمي", "probability": 0.985107421875}, {"start": 199.28, "end": 199.62, "word": " إلى", "probability": 0.92626953125}, {"start": 199.62, "end": 201.6, "word": " R", "probability": 0.83349609375}, {"start": 201.6, "end": 202.08, "word": " minus", "probability": 0.30224609375}, {"start": 202.08, "end": 202.5, "word": " Q", "probability": 0.91943359375}, {"start": 202.5, "end": 203.14, "word": " إذا", "probability": 0.5811767578125}, {"start": 203.14, "end": 203.42, "word": " الـ", "probability": 0.666015625}, {"start": 203.42, "end": 203.62, "word": " C", "probability": 0.66357421875}, {"start": 203.62, "end": 203.86, "word": " هذا", "probability": 0.358154296875}, {"start": 203.86, "end": 204.06, "word": " إما", "probability": 0.80419921875}, {"start": 204.06, "end": 204.44, "word": " هتكون", "probability": 0.7763671875}, {"start": 204.44, "end": 204.8, "word": " rational", "probability": 0.8818359375}, {"start": 204.8, "end": 205.32, "word": " number", "probability": 0.98388671875}, {"start": 205.32, "end": 205.68, "word": " أو", "probability": 0.95068359375}, {"start": 205.68, "end": 206.7, "word": " irrational", "probability": 0.469482421875}, {"start": 206.7, "end": 207.24, "word": " number", "probability": 0.96533203125}, {"start": 207.24, "end": 207.76, "word": " الحالة", "probability": 0.9778645833333334}, {"start": 207.76, "end": 208.8, "word": " الأولى", "probability": 0.9755859375}, {"start": 208.8, "end": 210.06, "word": " case", "probability": 0.7939453125}, {"start": 210.06, "end": 210.48, "word": " one", "probability": 0.64892578125}, {"start": 210.48, "end": 211.4, "word": " لو", "probability": 0.9306640625}, {"start": 211.4, "end": 211.92, "word": " كانت", "probability": 0.972900390625}, {"start": 211.92, "end": 212.16, "word": " C", "probability": 0.943359375}, {"start": 212.16, "end": 212.6, "word": " rational", "probability": 0.9326171875}, {"start": 212.6, "end": 213.18, "word": " number", "probability": 0.9794921875}], "temperature": 1.0}, {"id": 8, "seek": 24663, "start": 217.87, "end": 246.63, "text": "استخدم الـ Corollary to Density Theorem لتختار سيكوينس XN من أعداد غير عقلية", "tokens": [995, 14851, 9778, 3215, 2304, 2423, 39184, 3925, 1833, 822, 281, 413, 6859, 440, 37956, 5296, 2655, 46456, 9640, 8608, 1829, 4117, 2407, 9957, 3794, 1783, 45, 9154, 5551, 22488, 18513, 32771, 13546, 6225, 4587, 1211, 10632], "avg_logprob": -0.687500010979803, "compression_ratio": 0.9826086956521739, "no_speech_prob": 0.0, "words": [{"start": 217.87, "end": 218.63, "word": "استخدم", "probability": 0.627587890625}, {"start": 218.63, "end": 220.51, "word": " الـ", "probability": 0.284912109375}, {"start": 220.51, "end": 221.37, "word": " Corollary", "probability": 0.8486328125}, {"start": 221.37, "end": 223.45, "word": " to", "probability": 0.52294921875}, {"start": 223.45, "end": 229.73, "word": " Density", "probability": 0.7105712890625}, {"start": 229.73, "end": 230.35, "word": " Theorem", "probability": 0.768798828125}, {"start": 230.35, "end": 238.31, "word": " لتختار", "probability": 0.57525634765625}, {"start": 238.31, "end": 241.83, "word": " سيكوينس", "probability": 0.5501505533854166}, {"start": 241.83, "end": 243.83, "word": " XN", "probability": 0.5848388671875}, {"start": 243.83, "end": 245.67, "word": " من", "probability": 0.31884765625}, {"start": 245.67, "end": 246.01, "word": " أعداد", "probability": 0.3336995442708333}, {"start": 246.01, "end": 246.05, "word": " غير", "probability": 0.8408203125}, {"start": 246.05, "end": 246.63, "word": " عقلية", "probability": 0.496368408203125}], "temperature": 1.0}, {"id": 9, "seek": 26356, "start": 259.74, "end": 263.56, "text": "اعتقد ان احنا اثبتنا حاجة زي هذه سابقا", "tokens": [995, 34268, 28543, 16472, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 11331, 26108, 3660, 30767, 1829, 29538, 8608, 16758, 4587, 995], "avg_logprob": -0.3614130408867546, "compression_ratio": 1.0454545454545454, "no_speech_prob": 0.0, "words": [{"start": 259.73999999999995, "end": 260.46, "word": "اعتقد", "probability": 0.524169921875}, {"start": 260.46, "end": 260.56, "word": " ان", "probability": 0.8271484375}, {"start": 260.56, "end": 260.74, "word": " احنا", "probability": 0.7574869791666666}, {"start": 260.74, "end": 261.3, "word": " اثبتنا", "probability": 0.923046875}, {"start": 261.3, "end": 261.64, "word": " حاجة", "probability": 0.9083658854166666}, {"start": 261.64, "end": 261.88, "word": " زي", "probability": 0.917236328125}, {"start": 261.88, "end": 262.26, "word": " هذه", "probability": 0.85791015625}, {"start": 262.26, "end": 263.56, "word": " سابقا", "probability": 0.9810791015625}], "temperature": 1.0}, {"id": 10, "seek": 28149, "start": 268.77, "end": 281.49, "text": "حتى لو كان rational فby ال corollary النتيجة تبع ال density theorem ممكن اثبات ان يوجد sequence of irrationals ونهيتها العدد c", "tokens": [33753, 7578, 45164, 25961, 15090, 6156, 2322, 2423, 1181, 1833, 822, 28239, 31371, 7435, 3660, 6055, 3555, 3615, 2423, 10305, 20904, 3714, 43020, 1975, 12984, 3555, 9307, 16472, 7251, 29245, 3215, 8310, 295, 3418, 2405, 1124, 4032, 1863, 3224, 36081, 11296, 18863, 3215, 3215, 269], "avg_logprob": -0.27904212798761285, "compression_ratio": 1.2571428571428571, "no_speech_prob": 0.0, "words": [{"start": 268.77, "end": 269.19, "word": "حتى", "probability": 0.6533203125}, {"start": 269.19, "end": 269.31, "word": " لو", "probability": 0.97119140625}, {"start": 269.31, "end": 269.57, "word": " كان", "probability": 0.9833984375}, {"start": 269.57, "end": 270.07, "word": " rational", "probability": 0.88037109375}, {"start": 270.07, "end": 272.31, "word": " فby", "probability": 0.40966796875}, {"start": 272.31, "end": 272.67, "word": " ال", "probability": 0.49609375}, {"start": 272.67, "end": 273.15, "word": " corollary", "probability": 0.6872965494791666}, {"start": 273.15, "end": 273.55, "word": " النتيجة", "probability": 0.8851318359375}, {"start": 273.55, "end": 273.75, "word": " تبع", "probability": 0.7532552083333334}, {"start": 273.75, "end": 273.89, "word": " ال", "probability": 0.75830078125}, {"start": 273.89, "end": 274.27, "word": " density", "probability": 0.94580078125}, {"start": 274.27, "end": 274.77, "word": " theorem", "probability": 0.9140625}, {"start": 274.77, "end": 275.99, "word": " ممكن", "probability": 0.962158203125}, {"start": 275.99, "end": 276.63, "word": " اثبات", "probability": 0.88037109375}, {"start": 276.63, "end": 276.91, "word": " ان", "probability": 0.75830078125}, {"start": 276.91, "end": 277.59, "word": " يوجد", "probability": 0.9060872395833334}, {"start": 277.59, "end": 278.19, "word": " sequence", "probability": 0.9609375}, {"start": 278.19, "end": 278.63, "word": " of", 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326.07, "end": 327.03, "word": " صحيح", "probability": 0.9835205078125}, {"start": 327.03, "end": 327.53, "word": " لكل", "probability": 0.98095703125}, {"start": 327.53, "end": 327.89, "word": " n", "probability": 0.81396484375}, {"start": 327.89, "end": 328.83, "word": " هذا", "probability": 0.9482421875}, {"start": 328.83, "end": 329.45, "word": " بيقدي", "probability": 0.71685791015625}, {"start": 329.45, "end": 330.31, "word": " ان", "probability": 0.9091796875}, {"start": 330.31, "end": 330.47, "word": " ال", "probability": 0.6455078125}, {"start": 330.47, "end": 330.87, "word": " limit", "probability": 0.9794921875}, {"start": 330.87, "end": 333.41, "word": " ل", "probability": 0.8798828125}, {"start": 333.41, "end": 333.71, "word": " f", "probability": 0.54638671875}, {"start": 333.71, "end": 333.97, "word": " of", "probability": 0.7197265625}, {"start": 333.97, "end": 334.99, "word": " xn", "probability": 0.973876953125}, {"start": 334.99, "end": 336.95, "word": " as", "probability": 0.91650390625}, {"start": 336.95, "end": 337.51, "word": " n", "probability": 0.92333984375}, {"start": 337.51, "end": 337.87, "word": " tends", "probability": 0.82568359375}, {"start": 337.87, "end": 338.13, "word": " to", "probability": 0.95703125}, {"start": 338.13, "end": 338.69, "word": " infinity", "probability": 0.9013671875}], "temperature": 1.0}, {"id": 13, "seek": 34414, "start": 340.1, "end": 344.14, "text": "بساوي limit ثابت سفر بساوي سفر", "tokens": [3555, 3794, 995, 45865, 4948, 38637, 16758, 2655, 8608, 5172, 2288, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.2878289505055076, "compression_ratio": 1.0416666666666667, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 340.1, "end": 341.2, "word": "بساوي", "probability": 0.7178955078125}, {"start": 341.2, "end": 341.82, "word": " limit", "probability": 0.78759765625}, {"start": 341.82, "end": 342.78, "word": " ثابت", "probability": 0.89501953125}, {"start": 342.78, "end": 343.16, "word": " سفر", "probability": 0.7308756510416666}, {"start": 343.16, "end": 343.62, "word": " بساوي", "probability": 0.8507080078125}, {"start": 343.62, "end": 344.14, "word": " سفر", "probability": 0.9296875}], "temperature": 1.0}, {"id": 14, "seek": 37806, "start": 349.06, "end": 378.06, "text": "وهذا لا يساوي واحد اللي هو f of c ال c rational number ف f and c بيساوي واحد اذا هاي اندي انا اثبتت ان يوجد sequence xn في المجال تبع الدولة اللي هو R و ال sequence هذه converge ل c لكن ال limit لل image لل sequence لا تساوي f of c اذا by divergence criterion", "tokens": [2407, 3224, 15730, 20193, 7251, 3794, 995, 45865, 36764, 24401, 13672, 1829, 31439, 283, 295, 269, 2423, 269, 15090, 1230, 6156, 283, 293, 269, 4724, 1829, 3794, 995, 45865, 36764, 24401, 1975, 15730, 8032, 47302, 16472, 16254, 1975, 8315, 1975, 12984, 3555, 2655, 2655, 16472, 7251, 29245, 3215, 8310, 2031, 77, 8978, 9673, 7435, 6027, 6055, 3555, 3615, 32748, 12610, 3660, 13672, 1829, 31439, 497, 4032, 2423, 8310, 29538, 41881, 5296, 269, 44381, 2423, 4948, 24976, 3256, 24976, 8310, 20193, 6055, 3794, 995, 45865, 283, 295, 269, 1975, 15730, 538, 47387, 46691], "avg_logprob": -0.21690188620680123, "compression_ratio": 1.7264150943396226, "no_speech_prob": 0.0, "words": [{"start": 349.06, "end": 349.7, "word": "وهذا", "probability": 0.7633463541666666}, {"start": 349.7, "end": 349.9, "word": " لا", "probability": 0.7568359375}, {"start": 349.9, "end": 350.66, "word": " يساوي", "probability": 0.936767578125}, {"start": 350.66, "end": 351.26, "word": " واحد", "probability": 0.884033203125}, {"start": 351.26, "end": 351.48, "word": " اللي", "probability": 0.718017578125}, {"start": 351.48, "end": 351.8, "word": " هو", "probability": 0.98046875}, {"start": 351.8, "end": 352.2, "word": " f", "probability": 0.4609375}, {"start": 352.2, "end": 353.36, "word": " of", "probability": 0.64501953125}, {"start": 353.36, "end": 353.7, "word": " c", "probability": 0.76904296875}, {"start": 353.7, "end": 354.5, "word": " ال", "probability": 0.80615234375}, {"start": 354.5, "end": 354.78, "word": " c", "probability": 0.401611328125}, {"start": 354.78, "end": 355.48, "word": " rational", "probability": 0.4443359375}, {"start": 355.48, "end": 356.08, "word": " number", "probability": 0.97314453125}, {"start": 356.08, "end": 356.86, "word": " ف", "probability": 0.947265625}, {"start": 356.86, "end": 357.12, "word": " f", "probability": 0.27734375}, {"start": 357.12, "end": 357.36, "word": " and", "probability": 0.787109375}, {"start": 357.36, "end": 357.62, "word": " c", "probability": 0.95947265625}, {"start": 357.62, "end": 358.08, "word": " بيساوي", "probability": 0.830810546875}, {"start": 358.08, "end": 358.48, "word": " واحد", "probability": 0.992919921875}, {"start": 358.48, "end": 359.5, "word": " اذا", "probability": 0.70458984375}, {"start": 359.5, "end": 359.74, "word": " هاي", "probability": 0.599609375}, {"start": 359.74, "end": 360.06, "word": " اندي", "probability": 0.5897216796875}, {"start": 360.06, "end": 360.36, "word": " انا", "probability": 0.942138671875}, {"start": 360.36, "end": 361.08, "word": " اثبتت", "probability": 0.96015625}, {"start": 361.08, "end": 361.22, "word": " ان", "probability": 0.92822265625}, {"start": 361.22, "end": 361.8, "word": " يوجد", "probability": 0.8528645833333334}, {"start": 361.8, "end": 362.46, "word": " sequence", "probability": 0.94775390625}, {"start": 362.46, "end": 363.92, "word": " xn", "probability": 0.5916748046875}, {"start": 363.92, "end": 364.64, "word": " في", "probability": 0.87646484375}, {"start": 364.64, "end": 365.14, "word": " المجال", "probability": 0.9700520833333334}, {"start": 365.14, "end": 365.44, "word": " تبع", "probability": 0.8434244791666666}, {"start": 365.44, "end": 365.94, "word": " الدولة", "probability": 0.8899739583333334}, {"start": 365.94, "end": 366.1, "word": " اللي", "probability": 0.973876953125}, {"start": 366.1, "end": 366.36, "word": " هو", "probability": 0.95703125}, {"start": 366.36, "end": 366.74, "word": " R", "probability": 0.59814453125}, {"start": 366.74, "end": 367.86, "word": " و", "probability": 0.44873046875}, {"start": 367.86, "end": 368.02, "word": " ال", "probability": 0.69580078125}, {"start": 368.02, "end": 368.36, "word": " sequence", "probability": 0.98681640625}, {"start": 368.36, "end": 368.68, "word": " هذه", "probability": 0.33642578125}, {"start": 368.68, "end": 369.26, "word": " converge", "probability": 0.8994140625}, {"start": 369.26, "end": 369.44, "word": " ل", "probability": 0.9384765625}, {"start": 369.44, "end": 369.8, "word": " c", "probability": 0.477294921875}, {"start": 369.8, "end": 370.86, "word": " لكن", "probability": 0.900390625}, {"start": 370.86, "end": 371.34, "word": " ال", "probability": 0.74462890625}, {"start": 371.34, "end": 371.64, "word": " limit", "probability": 0.97265625}, {"start": 371.64, "end": 371.88, "word": " لل", "probability": 0.88916015625}, {"start": 371.88, "end": 372.18, "word": " image", "probability": 0.80908203125}, {"start": 372.18, "end": 372.42, "word": " لل", "probability": 0.75439453125}, {"start": 372.42, "end": 373.04, "word": " sequence", "probability": 0.984375}, {"start": 373.04, "end": 373.74, "word": " لا", "probability": 0.7099609375}, {"start": 373.74, "end": 374.5, "word": " تساوي", "probability": 0.974853515625}, {"start": 374.5, "end": 374.86, "word": " f", "probability": 0.892578125}, {"start": 374.86, "end": 375.08, "word": " of", "probability": 0.95751953125}, {"start": 375.08, "end": 375.38, "word": " c", "probability": 0.95751953125}, {"start": 375.38, "end": 376.3, "word": " اذا", "probability": 0.876953125}, {"start": 376.3, "end": 376.66, "word": " by", "probability": 0.93994140625}, {"start": 376.66, "end": 377.36, "word": " divergence", "probability": 0.94482421875}, {"start": 377.36, "end": 378.06, "word": " criterion", "probability": 0.951171875}], "temperature": 1.0}, {"id": 15, "seek": 40775, "start": 379.69, "end": 407.75, "text": "أو by discontinuity criterion اذا by discontinuity criterion if is discontinuous is discontinuous at C في الحالة اللي هي C rational number في الحالة التانية", "tokens": [10721, 2407, 538, 31420, 21757, 46691, 1975, 15730, 538, 31420, 21757, 46691, 498, 307, 31420, 12549, 307, 31420, 12549, 412, 383, 8978, 21542, 6027, 3660, 13672, 1829, 39896, 383, 15090, 1230, 8978, 21542, 6027, 3660, 16712, 7649, 10632], "avg_logprob": -0.19310897817978492, "compression_ratio": 1.6379310344827587, "no_speech_prob": 0.0, "words": [{"start": 379.69, "end": 380.53, "word": "أو", "probability": 0.61590576171875}, {"start": 380.53, "end": 380.81, "word": " by", "probability": 0.75146484375}, {"start": 380.81, "end": 381.81, "word": " discontinuity", "probability": 0.921630859375}, {"start": 381.81, "end": 382.49, "word": " criterion", "probability": 0.95263671875}, {"start": 382.49, "end": 382.97, "word": " اذا", "probability": 0.6707763671875}, {"start": 382.97, "end": 384.89, "word": " by", "probability": 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0.79638671875}, {"start": 404.13, "end": 404.41, "word": " هي", "probability": 0.869140625}, {"start": 404.41, "end": 404.71, "word": " C", "probability": 0.794921875}, {"start": 404.71, "end": 405.15, "word": " rational", "probability": 0.8916015625}, {"start": 405.15, "end": 405.67, "word": " number", "probability": 0.984375}, {"start": 405.67, "end": 406.89, "word": " في", "probability": 0.72021484375}, {"start": 406.89, "end": 407.29, "word": " الحالة", "probability": 0.98486328125}, {"start": 407.29, "end": 407.75, "word": " التانية", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 16, "seek": 43815, "start": 412.27, "end": 438.15, "text": "لو كان الـ c irrational number فممكن نستخدم ال density theorem نفسها use density theorem to choose a sequence x in contained", "tokens": [1211, 2407, 25961, 2423, 39184, 269, 39914, 1230, 6156, 2304, 43020, 8717, 14851, 9778, 40448, 2423, 10305, 20904, 8717, 36178, 11296, 764, 10305, 20904, 281, 2826, 257, 8310, 2031, 294, 16212], "avg_logprob": -0.23901366768404841, "compression_ratio": 1.2195121951219512, "no_speech_prob": 0.0, "words": [{"start": 412.27, "end": 412.67, "word": "لو", "probability": 0.7578125}, {"start": 412.67, "end": 413.03, "word": " كان", "probability": 0.98388671875}, {"start": 413.03, "end": 413.35, "word": " الـ", "probability": 0.78125}, {"start": 413.35, "end": 413.61, "word": " c", "probability": 0.210205078125}, {"start": 413.61, "end": 414.19, "word": " irrational", "probability": 0.407470703125}, {"start": 414.19, "end": 414.93, "word": " number", "probability": 0.96484375}, {"start": 414.93, "end": 421.11, "word": " فممكن", "probability": 0.9114583333333334}, {"start": 421.11, "end": 421.97, "word": " نستخدم", "probability": 0.97119140625}, {"start": 421.97, "end": 422.27, "word": " ال", "probability": 0.88134765625}, {"start": 422.27, "end": 422.85, "word": " density", "probability": 0.58203125}, {"start": 422.85, "end": 423.51, "word": " theorem", "probability": 0.875}, {"start": 423.51, "end": 424.23, "word": " نفسها", "probability": 0.8836263020833334}, {"start": 424.23, "end": 424.67, "word": " use", "probability": 0.6240234375}, {"start": 424.67, "end": 425.33, "word": " density", "probability": 0.931640625}, {"start": 425.33, "end": 426.03, "word": " theorem", "probability": 0.85546875}, {"start": 426.03, "end": 429.13, "word": " to", "probability": 0.92431640625}, {"start": 429.13, "end": 430.05, "word": " choose", "probability": 0.93603515625}, {"start": 430.05, "end": 433.71, "word": " a", "probability": 0.9306640625}, {"start": 433.71, "end": 434.49, "word": " sequence", "probability": 0.98388671875}, {"start": 434.49, "end": 436.43, "word": " x", "probability": 0.75146484375}, {"start": 436.43, "end": 436.97, "word": " in", "probability": 0.45263671875}, {"start": 436.97, "end": 438.15, "word": " contained", "probability": 0.54443359375}], "temperature": 1.0}, {"id": 17, "seek": 46392, "start": 439.76, "end": 463.92, "text": "of rational numbers contained in Q يعني ال sequence هذه عناصرها rational numbers بحيث انه ال limit لل sequence x in as n tends to infinity بساوي c هذا أثبتناه في المحاضرة السابقة وبالتالي so", "tokens": [2670, 15090, 3547, 16212, 294, 1249, 37495, 22653, 2423, 8310, 29538, 18871, 33546, 2288, 11296, 15090, 3547, 4724, 5016, 1829, 12984, 16472, 3224, 2423, 4948, 24976, 8310, 2031, 294, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 269, 23758, 5551, 12984, 3555, 2655, 8315, 3224, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 46599, 6027, 2655, 6027, 1829, 370], "avg_logprob": -0.24244364167823165, "compression_ratio": 1.4357541899441342, "no_speech_prob": 0.0, "words": [{"start": 439.76, "end": 440.1, "word": "of", "probability": 0.4912109375}, {"start": 440.1, "end": 440.58, "word": " rational", "probability": 0.85107421875}, {"start": 440.58, "end": 441.28, "word": " numbers", "probability": 0.8486328125}, {"start": 441.28, "end": 441.7, "word": " contained", "probability": 0.6005859375}, {"start": 441.7, "end": 442.12, "word": " in", "probability": 0.962890625}, {"start": 442.12, "end": 442.38, "word": " Q", "probability": 0.60595703125}, {"start": 442.38, "end": 442.62, "word": " يعني", "probability": 0.6754150390625}, {"start": 442.62, "end": 442.76, "word": " ال", "probability": 0.6005859375}, {"start": 442.76, "end": 442.98, "word": " sequence", "probability": 0.57763671875}, {"start": 442.98, "end": 443.26, "word": " هذه", "probability": 0.8212890625}, {"start": 443.26, "end": 443.76, "word": " عناصرها", "probability": 0.86767578125}, {"start": 443.76, "end": 444.0, "word": " rational", "probability": 0.8955078125}, {"start": 444.0, "end": 444.66, "word": " numbers", "probability": 0.60498046875}, {"start": 444.66, "end": 446.0, "word": " بحيث", "probability": 0.9620361328125}, {"start": 446.0, "end": 446.62, "word": " انه", "probability": 0.665283203125}, {"start": 446.62, "end": 447.4, "word": " ال", "probability": 0.56494140625}, {"start": 447.4, "end": 447.8, "word": " limit", "probability": 0.939453125}, {"start": 447.8, "end": 449.32, "word": " لل", "probability": 0.23046875}, {"start": 449.32, "end": 450.02, "word": " sequence", "probability": 0.96533203125}, {"start": 450.02, "end": 450.44, "word": " x", "probability": 0.61572265625}, {"start": 450.44, "end": 451.02, "word": " in", "probability": 0.476806640625}, {"start": 451.02, "end": 451.56, "word": " as", "probability": 0.82470703125}, {"start": 451.56, "end": 451.88, "word": " n", "probability": 0.626953125}, {"start": 451.88, "end": 452.14, "word": " tends", "probability": 0.73876953125}, {"start": 452.14, "end": 452.28, "word": " to", "probability": 0.857421875}, {"start": 452.28, "end": 452.86, "word": " infinity", "probability": 0.88134765625}, {"start": 452.86, "end": 453.8, "word": " بساوي", "probability": 0.8826904296875}, {"start": 453.8, "end": 454.24, "word": " c", "probability": 0.487060546875}, {"start": 454.24, "end": 454.84, "word": " هذا", "probability": 0.82080078125}, {"start": 454.84, "end": 455.96, "word": " أثبتناه", "probability": 0.8940022786458334}, {"start": 455.96, "end": 456.26, "word": " في", "probability": 0.9599609375}, {"start": 456.26, "end": 456.78, "word": " المحاضرة", "probability": 0.9085693359375}, {"start": 456.78, "end": 457.38, "word": " السابقة", "probability": 0.9855143229166666}, {"start": 457.38, "end": 462.48, "word": " وبالتالي", "probability": 0.890283203125}, {"start": 462.48, "end": 463.92, "word": " so", "probability": 0.814453125}], "temperature": 1.0}, {"id": 18, "seek": 48120, "start": 466.98, "end": 481.2, "text": "أنا عندي بما أنه ال Xn rationals ف F of Xn بتساوي واحد لكل N هذا بيقدي انه limit ل F of Xn as N tends to infinity", "tokens": [10721, 8315, 18871, 16254, 4724, 15042, 14739, 3224, 2423, 1783, 77, 24258, 1124, 6156, 479, 295, 1783, 77, 39894, 3794, 995, 45865, 36764, 24401, 5296, 28820, 426, 23758, 4724, 1829, 4587, 16254, 16472, 3224, 4948, 5296, 479, 295, 1783, 77, 382, 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"word": " انا", "probability": 0.654541015625}, {"start": 499.17, "end": 499.45, "word": " هنا", "probability": 0.59228515625}, {"start": 499.45, "end": 500.77, "word": " اثبتت", "probability": 0.96630859375}, {"start": 500.77, "end": 500.93, "word": " ان", "probability": 0.853515625}, {"start": 500.93, "end": 501.73, "word": " يوجد", "probability": 0.8723958333333334}, {"start": 501.73, "end": 503.61, "word": " sequence", "probability": 0.368896484375}], "temperature": 1.0}, {"id": 20, "seek": 53015, "start": 505.71, "end": 530.15, "text": "في مجال الدالة نهايتها c لكن نهاية صورتها لا تساوي صورة ال c كمان مرة hence by discontinuity by discontinuity criterion", "tokens": [41185, 3714, 7435, 6027, 32748, 6027, 3660, 8717, 11296, 36081, 11296, 269, 44381, 8717, 11296, 10632, 20328, 13063, 2655, 11296, 20193, 6055, 3794, 995, 45865, 20328, 13063, 3660, 2423, 269, 9122, 2304, 7649, 3714, 25720, 16678, 538, 31420, 21757, 538, 31420, 21757, 46691], "avg_logprob": -0.12579900195652788, 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number c طبعا في الحالتين لأن هذا بكمل البرهانة لأن هذه ال function هي function من R لR", "tokens": [6027, 39184, 2445, 283, 307, 31420, 12549, 412, 269, 5296, 33456, 4724, 15042, 14739, 269, 390, 23211, 6156, 6027, 39184, 2445, 307, 31420, 12549, 18871, 28242, 957, 1230, 269, 23032, 3555, 3615, 995, 8978, 21542, 6027, 2655, 9957, 5296, 33456, 23758, 4724, 24793, 1211, 2423, 26890, 3224, 7649, 3660, 5296, 33456, 29538, 2423, 2445, 39896, 2445, 9154, 497, 5296, 49], "avg_logprob": -0.31762294104841887, "compression_ratio": 1.5297619047619047, "no_speech_prob": 0.0, "words": [{"start": 532.89, "end": 533.23, "word": "الـ", "probability": 0.5560302734375}, {"start": 533.23, "end": 533.63, "word": " function", "probability": 0.74755859375}, {"start": 533.63, "end": 534.13, "word": " f", "probability": 0.455078125}, {"start": 534.13, "end": 534.77, "word": " is", "probability": 0.87060546875}, {"start": 534.77, "end": 536.83, "word": " discontinuous", "probability": 0.876220703125}, 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566.77, "word": " هذه", "probability": 0.53369140625}, {"start": 566.77, "end": 566.95, "word": " ال", "probability": 0.95654296875}, {"start": 566.95, "end": 567.25, "word": " function", "probability": 0.75146484375}, {"start": 567.25, "end": 567.63, "word": " لها", "probability": 0.6385498046875}, {"start": 567.63, "end": 568.01, "word": " اسم", "probability": 0.90380859375}, {"start": 568.01, "end": 568.73, "word": " ومشهورة", "probability": 0.800048828125}, {"start": 568.73, "end": 569.67, "word": " ومعروفة", "probability": 0.9884440104166666}, {"start": 569.67, "end": 570.45, "word": " اسمها", "probability": 0.97119140625}, {"start": 570.45, "end": 571.03, "word": " Dirichlet", "probability": 0.93408203125}, {"start": 571.03, "end": 572.13, "word": " function", "probability": 0.89892578125}, {"start": 572.13, "end": 575.21, "word": " اذا", "probability": 0.516265869140625}, {"start": 575.21, "end": 575.63, "word": " ال", "probability": 0.84619140625}, {"start": 575.63, "end": 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function بتكونش continuous and النقطة c ف sometimes the function can be discontinuous at x بساوي c because", "tokens": [6027, 7649, 45164, 1975, 1829, 36764, 24401, 9154, 16712, 1211, 9307, 25124, 32887, 9566, 8032, 3215, 12610, 1975, 46456, 1211, 6156, 6027, 2445, 39894, 30544, 8592, 10957, 293, 28239, 47432, 3660, 269, 6156, 2171, 264, 2445, 393, 312, 31420, 12549, 412, 2031, 4724, 3794, 995, 45865, 269, 570], "avg_logprob": -0.24346301020408162, "compression_ratio": 1.368421052631579, "no_speech_prob": 0.0, "words": [{"start": 744.59, "end": 745.25, "word": "الان", "probability": 0.705322265625}, {"start": 745.25, "end": 746.25, "word": " لو", "probability": 0.68212890625}, {"start": 746.25, "end": 746.53, "word": " اي", "probability": 0.81689453125}, {"start": 746.53, "end": 746.83, "word": " واحد", "probability": 0.99169921875}, {"start": 746.83, "end": 747.01, "word": " من", "probability": 0.99169921875}, {"start": 747.01, "end": 747.39, "word": " التلات", "probability": 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however", "tokens": [351, 307, 674, 5666, 2001, 307, 674, 5666, 2001, 412, 383, 44381, 5551, 5016, 1829, 7649, 995, 5551, 34740, 7578, 4032, 41185, 21542, 6027, 3660, 13672, 1829, 4724, 28543, 2288, 8592, 5551, 25957, 1211, 11331, 26108, 3660, 4724, 28543, 2288, 8592, 5551, 25957, 1211, 11331, 26108, 3660, 4461], "avg_logprob": -0.15369898445752203, "compression_ratio": 1.3893805309734513, "no_speech_prob": 0.0, "words": [{"start": 769.45, "end": 769.99, "word": "if", "probability": 0.3583984375}, {"start": 769.99, "end": 770.65, "word": " is", "probability": 0.921875}, {"start": 770.65, "end": 771.67, "word": " undefined", "probability": 0.8650716145833334}, {"start": 771.67, "end": 773.45, "word": " is", "probability": 0.7373046875}, {"start": 773.45, "end": 775.21, "word": " undefined", "probability": 0.8880208333333334}, {"start": 775.21, "end": 776.11, "word": " at", "probability": 0.9013671875}, {"start": 776.11, "end": 777.85, "word": " C", "probability": 0.53857421875}, 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إذا لو كانت الدالة مش معرفة لو كانت small f مش معرفة عن c لكن نهايتها عن c موجودة وبالساوي عدد L فبقدر أعرف دالة جديدة capital F اللي هي توسعة extension ل small f و ال extension الدالة هذه اللي هي توسعة", "tokens": [39237, 10943, 22807, 11933, 15730, 29538, 5551, 12610, 3714, 15040, 5016, 19913, 3660, 11933, 15730, 45164, 25961, 2655, 32748, 6027, 3660, 37893, 20449, 28480, 3660, 45164, 25961, 2655, 1359, 283, 37893, 20449, 28480, 3660, 18871, 269, 44381, 8717, 11296, 36081, 11296, 18871, 269, 3714, 29245, 23328, 3660, 46599, 6027, 3794, 995, 45865, 6225, 3215, 3215, 441, 6156, 3555, 28543, 2288, 5551, 3615, 28480, 11778, 6027, 3660, 10874, 16254, 41891, 4238, 479, 13672, 1829, 39896, 33427, 3794, 27884, 10320, 5296, 1359, 283, 4032, 2423, 10320, 32748, 6027, 3660, 29538, 13672, 1829, 39896, 33427, 3794, 27884], "avg_logprob": -0.16957237124443053, "compression_ratio": 1.7766990291262137, "no_speech_prob": 0.0, "words": [{"start": 1079.22, "end": 1080.08, "word": "تمام؟", 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1119.62, "text": "بتكون متصلة عند الـ C اننا ناخد قيمتها عند الـ C بساوي قيمة ال limit و عند النقاط ال A هي نفس small if لكن الملاحظة التانية", "tokens": [3555, 2655, 30544, 44650, 36520, 3660, 43242, 2423, 39184, 383, 16472, 8315, 8717, 47283, 3215, 12174, 32640, 2655, 11296, 43242, 2423, 39184, 383, 4724, 3794, 995, 45865, 12174, 32640, 3660, 2423, 4948, 4032, 43242, 28239, 4587, 41193, 2423, 316, 39896, 8717, 36178, 1359, 498, 44381, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632], "avg_logprob": -0.24262153219293664, "compression_ratio": 1.4539007092198581, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1103.2, "end": 1103.8, "word": "بتكون", "probability": 0.8118489583333334}, {"start": 1103.8, "end": 1104.48, "word": " متصلة", "probability": 0.9034830729166666}, {"start": 1104.48, "end": 1104.64, "word": " عند", "probability": 0.90234375}, {"start": 1104.64, "end": 1104.82, "word": " الـ", "probability": 0.5206298828125}, {"start": 1104.82, "end": 1104.98, 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معرفة عن C يعني هنا sometimes a function g is discontinuous a function g from A to R is discontinuous at C", "tokens": [1211, 2407, 25961, 2655, 2423, 18513, 6027, 3660, 4386, 3714, 43020, 6055, 30544, 2423, 18513, 6027, 3660, 20449, 28480, 3660, 18871, 383, 37495, 22653, 34105, 2171, 257, 2445, 290, 307, 31420, 12549, 257, 2445, 290, 490, 316, 281, 497, 307, 31420, 12549, 412, 383], "avg_logprob": -0.2031250066227383, "compression_ratio": 1.3909774436090225, "no_speech_prob": 0.0, "words": [{"start": 1131.35, "end": 1131.77, "word": "لو", "probability": 0.60491943359375}, {"start": 1131.77, "end": 1132.39, "word": " كانت", "probability": 0.9658203125}, {"start": 1132.39, "end": 1133.35, "word": " الادالة", "probability": 0.75732421875}, {"start": 1133.35, "end": 1133.35, "word": " ..", "probability": 0.357177734375}, {"start": 1133.35, "end": 1133.65, "word": " ممكن", "probability": 0.891357421875}, {"start": 1133.65, "end": 1133.89, "word": " تكون", "probability": 0.981201171875}, 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{"start": 1442.99, "end": 1443.17, "word": " عند", "probability": 0.9345703125}, {"start": 1443.17, "end": 1443.73, "word": " النقطة", "probability": 0.9873046875}, {"start": 1443.73, "end": 1444.91, "word": " فماقدرش", "probability": 0.8609375}, {"start": 1444.91, "end": 1445.51, "word": " أعرف", "probability": 0.7882486979166666}, {"start": 1445.51, "end": 1446.83, "word": " continuous", "probability": 0.9541015625}, {"start": 1446.83, "end": 1447.85, "word": " extension", "probability": 0.97021484375}, {"start": 1447.85, "end": 1449.49, "word": " لدالة", "probability": 0.831787109375}, {"start": 1449.49, "end": 1451.19, "word": " and", "probability": 0.6494140625}, {"start": 1451.19, "end": 1451.99, "word": " النقطة", "probability": 0.9651692708333334}, {"start": 1451.99, "end": 1452.19, "word": " C", "probability": 0.67138671875}], "temperature": 1.0}, {"id": 54, "seek": 148057, "start": 1453.43, "end": 1480.57, "text": "لأن هنا فرضنا أن هناك extension هذا ال extension مش ممكن يكون continuous عند النقطة C لأنه لو كان continuous عند النقطة C سيقدر ان الملمت الدالة small g and c exist وهذا يتناقض مع الفرض تمام، هذا النوع من ال discontinuity لما تكون الدالة discontinuous لعدم", "tokens": [1211, 33456, 34105, 6156, 43042, 8315, 14739, 34105, 4117, 10320, 23758, 2423, 10320, 37893, 3714, 43020, 7251, 30544, 10957, 43242, 28239, 47432, 3660, 383, 5296, 33456, 3224, 45164, 25961, 10957, 43242, 28239, 47432, 3660, 383, 8608, 1829, 4587, 3215, 2288, 16472, 9673, 19528, 2655, 32748, 6027, 3660, 1359, 290, 293, 269, 2514, 37037, 15730, 7251, 2655, 8315, 4587, 11242, 20449, 27188, 43042, 46811, 10943, 12399, 23758, 28239, 45367, 9154, 2423, 31420, 21757, 5296, 15042, 6055, 30544, 32748, 6027, 3660, 31420, 12549, 5296, 22488, 2304], "avg_logprob": -0.36268380950478946, "compression_ratio": 1.8246445497630333, "no_speech_prob": 0.0, "words": [{"start": 1453.43, "end": 1453.85, "word": "لأن", "probability": 0.50653076171875}, {"start": 1453.85, "end": 1454.05, "word": " هنا", "probability": 0.5576171875}, {"start": 1454.05, "end": 1454.53, "word": " فرضنا", "probability": 0.94384765625}, {"start": 1454.53, "end": 1455.23, "word": " أن", "probability": 0.315673828125}, {"start": 1455.23, "end": 1455.61, "word": " هناك", "probability": 0.6806640625}, {"start": 1455.61, "end": 1456.19, "word": " extension", "probability": 0.89501953125}, {"start": 1456.19, "end": 1456.99, "word": " هذا", "probability": 0.244140625}, {"start": 1456.99, "end": 1457.17, "word": " ال", "probability": 0.6826171875}, {"start": 1457.17, "end": 1457.53, "word": " extension", "probability": 0.83984375}, {"start": 1457.53, "end": 1457.85, "word": " مش", "probability": 0.421875}, {"start": 1457.85, "end": 1458.11, "word": " ممكن", "probability": 0.98095703125}, {"start": 1458.11, "end": 1458.39, "word": " يكون", "probability": 0.96337890625}, {"start": 1458.39, "end": 1459.03, "word": " continuous", "probability": 0.94580078125}, {"start": 1459.03, "end": 1459.87, "word": " عند", "probability": 0.861328125}, {"start": 1459.87, "end": 1460.31, "word": " النقطة", "probability": 0.8684895833333334}, {"start": 1460.31, "end": 1460.45, "word": " C", "probability": 0.479248046875}, {"start": 1460.45, "end": 1461.29, "word": " لأنه", "probability": 0.7955729166666666}, {"start": 1461.29, "end": 1461.41, "word": " لو", "probability": 0.85498046875}, {"start": 1461.41, "end": 1461.63, "word": " كان", "probability": 0.9912109375}, {"start": 1461.63, "end": 1462.05, "word": " continuous", "probability": 0.9580078125}, {"start": 1462.05, "end": 1462.35, "word": " عند", "probability": 0.990234375}, {"start": 1462.35, "end": 1462.77, "word": " النقطة", "probability": 0.9783528645833334}, {"start": 1462.77, "end": 1463.05, "word": " C", "probability": 0.921875}, {"start": 1463.05, "end": 1463.97, "word": " سيقدر", "probability": 0.544677734375}, {"start": 1463.97, "end": 1464.09, "word": " ان", "probability": 0.430419921875}, {"start": 1464.09, "end": 1464.51, "word": " الملمت", "probability": 0.4155680338541667}, {"start": 1464.51, "end": 1465.05, "word": " الدالة", "probability": 0.6997884114583334}, {"start": 1465.05, "end": 1465.35, "word": " small", "probability": 0.61962890625}, {"start": 1465.35, "end": 1465.63, "word": " g", "probability": 0.7333984375}, {"start": 1465.63, "end": 1465.87, "word": " and", "probability": 0.2310791015625}, {"start": 1465.87, "end": 1466.15, "word": " c", "probability": 0.81494140625}, {"start": 1466.15, "end": 1466.75, "word": " exist", "probability": 0.490234375}, {"start": 1466.75, "end": 1467.75, "word": " وهذا", "probability": 0.863525390625}, {"start": 1467.75, "end": 1468.49, "word": " يتناقض", "probability": 0.805322265625}, {"start": 1468.49, "end": 1468.77, "word": " مع", "probability": 0.9306640625}, {"start": 1468.77, "end": 1469.55, "word": " الفرض", "probability": 0.81298828125}, {"start": 1469.55, "end": 1471.71, "word": " تمام،", "probability": 0.5166829427083334}, {"start": 1471.71, "end": 1473.21, "word": " هذا", "probability": 0.55859375}, {"start": 1473.21, "end": 1473.73, "word": " النوع", "probability": 0.967529296875}, {"start": 1473.73, "end": 1474.13, "word": " من", "probability": 0.97265625}, {"start": 1474.13, "end": 1474.83, "word": " ال", "probability": 0.9169921875}, {"start": 1474.83, "end": 1475.91, "word": " discontinuity", "probability": 0.932373046875}, {"start": 1475.91, "end": 1477.61, "word": " لما", "probability": 0.701416015625}, {"start": 1477.61, "end": 1477.87, "word": " تكون", "probability": 0.980224609375}, {"start": 1477.87, "end": 1478.35, "word": " الدالة", "probability": 0.98876953125}, {"start": 1478.35, "end": 1479.35, "word": " discontinuous", "probability": 0.93505859375}, {"start": 1479.35, "end": 1480.57, "word": " لعدم", "probability": 0.9308268229166666}], "temperature": 1.0}, {"id": 55, "seek": 148392, "start": 1482.16, "end": 1483.92, "text": "لما تكون الدالة discontinuous", "tokens": [1211, 15042, 6055, 30544, 32748, 6027, 3660, 31420, 12549], "avg_logprob": -0.1455078139901161, "compression_ratio": 0.875, "no_speech_prob": 0.0, "words": [{"start": 1482.16, "end": 1482.5, "word": "لما", "probability": 0.740966796875}, {"start": 1482.5, "end": 1482.74, "word": " تكون", "probability": 0.97119140625}, {"start": 1482.74, "end": 1483.12, "word": " الدالة", "probability": 0.8795572916666666}, {"start": 1483.12, "end": 1483.92, "word": " discontinuous", "probability": 0.9248046875}], "temperature": 1.0}, {"id": 56, "seek": 151196, "start": 1486.76, "end": 1511.96, "text": "السبب في ذلك أنها مش معرفة عند النقطة C لكن نهيتها موجودة عند الـ C فهذا النوع من ال discontinuity من عدم الاتصال بنسميه removable يعني ممكن إزالته أو التخلص منه وهي فعلا اتخلصنا من عدم الاتصال للدالة small f and c بتعريف دالة capital F بالطريقة هذه وشوفنا أن الدالة الجديدة continuous عند ال C", "tokens": [6027, 35457, 3555, 8978, 29910, 23275, 14739, 11296, 37893, 20449, 28480, 3660, 43242, 28239, 47432, 3660, 383, 44381, 8717, 3224, 36081, 11296, 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0.9853515625}, {"start": 1487.94, "end": 1488.2, "word": " أنها", "probability": 0.718017578125}, {"start": 1488.2, "end": 1488.44, "word": " مش", "probability": 0.4208984375}, {"start": 1488.44, "end": 1489.08, "word": " معرفة", "probability": 0.8572591145833334}, {"start": 1489.08, "end": 1489.32, "word": " عند", "probability": 0.98193359375}, {"start": 1489.32, "end": 1489.8, "word": " النقطة", "probability": 0.7515462239583334}, {"start": 1489.8, "end": 1490.0, "word": " C", "probability": 0.5888671875}, {"start": 1490.0, "end": 1490.86, "word": " لكن", "probability": 0.81982421875}, {"start": 1490.86, "end": 1491.5, "word": " نهيتها", "probability": 0.8189697265625}, {"start": 1491.5, "end": 1492.14, "word": " موجودة", "probability": 0.9796142578125}, {"start": 1492.14, "end": 1492.36, "word": " عند", "probability": 0.98046875}, {"start": 1492.36, "end": 1492.56, "word": " الـ", "probability": 0.693603515625}, {"start": 1492.56, "end": 1492.72, "word": " C", "probability": 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"probability": 0.981689453125}, {"start": 1498.98, "end": 1499.66, "word": " إزالته", "probability": 0.86407470703125}, {"start": 1499.66, "end": 1500.36, "word": " أو", "probability": 0.87548828125}, {"start": 1500.36, "end": 1500.96, "word": " التخلص", "probability": 0.982666015625}, {"start": 1500.96, "end": 1501.28, "word": " منه", "probability": 0.995849609375}, {"start": 1501.28, "end": 1501.46, "word": " وهي", "probability": 0.517578125}, {"start": 1501.46, "end": 1501.84, "word": " فعلا", "probability": 0.9412434895833334}, {"start": 1501.84, "end": 1503.0, "word": " اتخلصنا", "probability": 0.9759114583333334}, {"start": 1503.0, "end": 1503.16, "word": " من", "probability": 0.99267578125}, {"start": 1503.16, "end": 1503.5, "word": " عدم", "probability": 0.989990234375}, {"start": 1503.5, "end": 1504.28, "word": " الاتصال", "probability": 0.9453125}, {"start": 1504.28, "end": 1505.3, "word": " للدالة", "probability": 0.73358154296875}, {"start": 1505.3, "end": 1505.64, "word": " small", "probability": 0.68994140625}, {"start": 1505.64, "end": 1505.92, "word": " f", "probability": 0.7314453125}, {"start": 1505.92, "end": 1506.18, "word": " and", "probability": 0.76171875}, {"start": 1506.18, "end": 1506.46, "word": " c", "probability": 0.79150390625}, {"start": 1506.46, "end": 1507.12, "word": " بتعريف", "probability": 0.9593505859375}, {"start": 1507.12, "end": 1507.5, "word": " دالة", "probability": 0.78955078125}, {"start": 1507.5, "end": 1507.86, "word": " capital", "probability": 0.740234375}, {"start": 1507.86, "end": 1508.22, "word": " F", "probability": 0.9296875}, {"start": 1508.22, "end": 1509.22, "word": " بالطريقة", "probability": 0.948486328125}, {"start": 1509.22, "end": 1509.48, "word": " هذه", "probability": 0.798828125}, {"start": 1509.48, "end": 1509.88, "word": " وشوفنا", "probability": 0.9234619140625}, {"start": 1509.88, "end": 1510.0, "word": " أن", "probability": 0.59765625}, {"start": 1510.0, "end": 1510.38, "word": " الدالة", "probability": 0.9811197916666666}, {"start": 1510.38, "end": 1510.8, "word": " الجديدة", "probability": 0.9641927083333334}, {"start": 1510.8, "end": 1511.24, "word": " continuous", "probability": 0.92333984375}, {"start": 1511.24, "end": 1511.66, "word": " عند", "probability": 0.78076171875}, {"start": 1511.66, "end": 1511.84, "word": " ال", "probability": 0.68212890625}, {"start": 1511.84, "end": 1511.96, "word": " C", "probability": 0.490478515625}], "temperature": 1.0}, {"id": 57, "seek": 153743, "start": 1512.45, "end": 1537.43, "text": "إذا هذا النوع من عدم الاتصال أو ال discontinuity is called removable يمكن إزالته يمكن تخلص منه أما إذا كانت الدالة discontinuous عند النقطة C لأن نهايتها in C مش موجودة فهذا النوع من عدم الاتصال بنسميه essential يعني أساسي لا يمكن تخلص منه زي ما شفنا في التحليل التحت okay تمام", "tokens": [28814, 15730, 23758, 28239, 45367, 9154, 6225, 40448, 2423, 9307, 9381, 6027, 34051, 2423, 31420, 21757, 307, 1219, 44060, 7251, 43020, 11933, 11622, 6027, 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0.92333984375}, {"start": 1763.02, "end": 1763.34, "word": " limit", "probability": 0.66357421875}, {"start": 1763.34, "end": 1763.54, "word": " لل", "probability": 0.75390625}, {"start": 1763.54, "end": 1763.9, "word": " function", "probability": 0.65625}, {"start": 1763.9, "end": 1764.14, "word": " عند", "probability": 0.939453125}, {"start": 1764.14, "end": 1764.74, "word": " السفر", "probability": 0.9462890625}, {"start": 1764.74, "end": 1765.6, "word": " إذا", "probability": 0.78515625}, {"start": 1765.6, "end": 1766.04, "word": " كان", "probability": 0.99560546875}, {"start": 1766.04, "end": 1766.36, "word": " ال", "probability": 0.89111328125}, {"start": 1766.36, "end": 1766.74, "word": " X", "probability": 0.90087890625}, {"start": 1766.74, "end": 1767.72, "word": " بساوى", "probability": 0.94033203125}, {"start": 1767.72, "end": 1768.18, "word": " السفر", "probability": 0.88330078125}, {"start": 1768.18, "end": 1769.04, "word": " و", "probability": 0.421875}, {"start": 1769.04, "end": 1769.56, "word": " بالساوى", "probability": 0.9080078125}, {"start": 1769.56, "end": 1770.02, "word": " small", "probability": 0.912109375}, {"start": 1770.02, "end": 1770.36, "word": " f", "probability": 0.57958984375}, {"start": 1770.36, "end": 1770.62, "word": " of", "probability": 0.9443359375}, {"start": 1770.62, "end": 1771.02, "word": " X", "probability": 0.9384765625}, {"start": 1771.02, "end": 1772.42, "word": " إذا", "probability": 0.939453125}, {"start": 1772.42, "end": 1772.94, "word": " كان", "probability": 0.9951171875}, {"start": 1772.94, "end": 1774.96, "word": " X", "probability": 0.9736328125}, {"start": 1774.96, "end": 1776.28, "word": " تنتمي", "probability": 0.83978271484375}, {"start": 1776.28, "end": 1776.38, "word": " ل", "probability": 0.97216796875}, {"start": 1776.38, "end": 1776.66, "word": " domain", "probability": 0.72509765625}, {"start": 1776.66, "end": 1777.44, "word": " الدالة", "probability": 0.9319661458333334}, {"start": 1777.44, 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"probability": 0.810791015625}, {"start": 2178.71, "end": 2180.11, "word": " لأ", "probability": 0.47235107421875}, {"start": 2180.11, "end": 2180.43, "word": " لأ", "probability": 0.89111328125}, {"start": 2180.43, "end": 2181.13, "word": " منجمعوش", "probability": 0.8367106119791666}, {"start": 2181.13, "end": 2182.01, "word": " الناس", "probability": 0.5591227213541666}, {"start": 2182.01, "end": 2188.71, "word": " ما", "probability": 0.6064453125}, {"start": 2188.71, "end": 2189.45, "word": " بنجمعهم", "probability": 0.948046875}], "temperature": 1.0}, {"id": 81, "seek": 221053, "start": 2197.41, "end": 2210.53, "text": "ما بنجمع مش عاملة اتجمع الان في اندي انا لحظة انت عندك من الفرض xn أكبر من أو سوى سفر لكل n في n", "tokens": [15042, 44945, 7435, 2304, 3615, 37893, 6225, 10943, 37977, 1975, 2655, 7435, 2304, 3615, 2423, 7649, 8978, 16472, 16254, 1975, 8315, 5296, 5016, 19913, 3660, 16472, 2655, 43242, 4117, 9154, 27188, 43042, 2031, 77, 5551, 4117, 26890, 9154, 34051, 8608, 2407, 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2202.67, "end": 2202.95, "word": " انت", "probability": 0.679443359375}, {"start": 2202.95, "end": 2203.95, "word": " عندك", "probability": 0.973876953125}, {"start": 2203.95, "end": 2205.13, "word": " من", "probability": 0.96337890625}, {"start": 2205.13, "end": 2205.71, "word": " الفرض", "probability": 0.92138671875}, {"start": 2205.71, "end": 2207.27, "word": " xn", "probability": 0.463134765625}, {"start": 2207.27, "end": 2207.99, "word": " أكبر", "probability": 0.84423828125}, {"start": 2207.99, "end": 2208.21, "word": " من", "probability": 0.96435546875}, {"start": 2208.21, "end": 2208.41, "word": " أو", "probability": 0.828125}, {"start": 2208.41, "end": 2208.85, "word": " سوى", "probability": 0.7776692708333334}, {"start": 2208.85, "end": 2209.27, "word": " سفر", "probability": 0.8196614583333334}, {"start": 2209.27, "end": 2209.81, "word": " لكل", "probability": 0.984375}, {"start": 2209.81, "end": 2210.15, "word": " n", "probability": 0.5927734375}, {"start": 2210.15, "end": 2210.33, "word": " في", "probability": 0.91162109375}, {"start": 2210.33, "end": 2210.53, "word": " n", "probability": 0.1585693359375}], "temperature": 1.0}, {"id": 82, "seek": 224312, "start": 2215.48, "end": 2243.12, "text": "فبالتالي إذا x2n سالب واحد أكبر من أوسعه سفر لكل n وكذلك x2n برضه أكبر من أوسعه سفر لكل n صح؟ أصبت؟ وبالتالي إذا ال limit ل x2n سالب واحد تطلع أكبر من أوسعه سفر", "tokens": [5172, 3555, 6027, 2655, 6027, 1829, 11933, 15730, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288, 5296, 28820, 297, 4032, 4117, 8848, 23275, 2031, 17, 77, 4724, 43042, 3224, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288, 5296, 28820, 297, 20328, 5016, 22807, 5551, 9381, 3555, 2655, 22807, 46599, 6027, 2655, 6027, 1829, 11933, 15730, 2423, 4948, 5296, 2031, 17, 77, 8608, 6027, 3555, 36764, 24401, 6055, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288], "avg_logprob": 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0.77783203125}, {"start": 2223.28, "end": 2225.04, "word": " وكذلك", "probability": 0.923828125}, {"start": 2225.04, "end": 2226.58, "word": " x2n", "probability": 0.9830729166666666}, {"start": 2226.58, "end": 2228.12, "word": " برضه", "probability": 0.9296875}, {"start": 2228.12, "end": 2229.12, "word": " أكبر", "probability": 0.9768880208333334}, {"start": 2229.12, "end": 2229.34, "word": " من", "probability": 0.99658203125}, {"start": 2229.34, "end": 2229.9, "word": " أوسعه", "probability": 0.9757080078125}, {"start": 2229.9, "end": 2230.3, "word": " سفر", "probability": 0.9925130208333334}, {"start": 2230.3, "end": 2230.74, "word": " لكل", "probability": 0.990478515625}, {"start": 2230.74, "end": 2231.12, "word": " n", "probability": 0.97216796875}, {"start": 2231.12, "end": 2233.6, "word": " صح؟", "probability": 0.7501627604166666}, {"start": 2233.6, "end": 2235.82, "word": " أصبت؟", "probability": 0.743603515625}, {"start": 2235.82, "end": 2236.84, "word": " وبالتالي", 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{"start": 2412.1099999999997, "end": 2412.91, "word": " مش", "probability": 0.986328125}, {"start": 2412.91, "end": 2413.19, "word": " عارف", "probability": 0.9952799479166666}, {"start": 2413.19, "end": 2413.41, "word": " أنا", "probability": 0.359375}, {"start": 2413.41, "end": 2413.85, "word": " ليش", "probability": 0.94482421875}, {"start": 2413.85, "end": 2414.47, "word": " رفضت", "probability": 0.8397216796875}, {"start": 2414.47, "end": 2414.59, "word": " اللي", "probability": 0.57696533203125}, {"start": 2414.59, "end": 2414.93, "word": " نجمع", "probability": 0.9375}, {"start": 2414.93, "end": 2415.17, "word": " مش", "probability": 0.7958984375}, {"start": 2415.17, "end": 2415.39, "word": " هو", "probability": 0.94580078125}, {"start": 2415.39, "end": 2415.79, "word": " عبارة", "probability": 0.9832763671875}, {"start": 2415.79, "end": 2415.93, "word": " ال", "probability": 0.478515625}, {"start": 2415.93, "end": 2416.43, "word": " XN", "probability": 0.4752197265625}, 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b69552aba6ec2539f03af1df54d69b6c41a5f10f
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA.srt
@@ -0,0 +1,1859 @@
+1
+00:00:20,220 --> 00:00:25,360
+بسم الله الرحمن الرحيم هندرس اليوم إن شاء الله مع
+
+2
+00:00:25,360 --> 00:00:32,000
+بعض الـ section خمسة أربعة اللي بيتحدث عن موضوع الـ
+
+3
+00:00:32,000 --> 00:00:36,720
+uniform continuity أو الاتصال المنظم للدوال
+
+4
+00:00:36,720 --> 00:00:40,600
+هنحاول ناخد أكبر جزء ممكن من الـ section الجزء
+
+5
+00:00:40,600 --> 00:00:44,860
+المتبقي ممكن نكمله في المحاضرة الجاية يوم الأثنين
+
+6
+00:00:44,860 --> 00:00:49,820
+فالـ
+
+7
+00:00:49,820 --> 00:00:54,540
+.. خلّينا الأول نراجع .. نراجع تعريف الاتصال 
+
+8
+00:00:54,540 --> 00:00:59,270
+العادي الـ continuity على مجموعة فلو كان في handy
+
+9
+00:00:59,270 --> 00:01:04,170
+function f من a لـ r فالعبارات التالية بتكون
+
+10
+00:01:04,170 --> 00:01:13,410
+متكافئة if f is continuous at every u ينتمي إلى a اللي هو مجال الدالة
+
+11
+00:01:13,410 --> 00:01:20,810
+every u ينتمي إلى a اللي هو مجال الدالة
+
+12
+00:01:20,810 --> 00:01:24,370
+العبارة الثانية given
+
+13
+00:01:27,500 --> 00:01:36,300
+epsilon أكبر من الصفر and given u ينتمي إلى a يوجد
+
+14
+00:01:36,300 --> 00:01:41,160
+.. بيقدر نلاقي delta و الـ delta هذه تعتمد على الـ
+
+15
+00:01:41,160 --> 00:01:51,590
+epsilon و على الـ u عدد موجب بحيث أنه لكل x ينتمي
+
+16
+00:01:51,590 --> 00:01:59,250
+إلى a و |x - u| أصغر من delta فهذا
+
+17
+00:01:59,250 --> 00:02:07,830
+بتضمن إلى |f(x) - f(u)| أصغر من 
+
+18
+00:02:07,830 --> 00:02:08,310
+epsilon
+
+19
+00:02:19,690 --> 00:02:30,650
+خلّينا بس ناخد المثال التالي consider
+
+20
+00:02:30,650 --> 00:02:41,910
+الـ function f(x) بتساوي 1/X و X ينتمي لأيه
+
+21
+00:02:41,910 --> 00:02:45,890
+اللي هي الفترة
+
+22
+00:02:45,890 --> 00:02:56,270
+كل الـ X في R حيث X أكبر من الصفر إذا الـ function F
+
+23
+00:02:56,270 --> 00:03:02,770
+معرفة على كل الأعداد الموجبة احنا
+
+24
+00:03:02,770 --> 00:03:05,770
+أثبتنا قبل هيك و proved
+
+25
+00:03:10,640 --> 00:03:14,920
+earlier فيما سبق في دراساتنا السابقة في section
+
+26
+00:03:14,920 --> 00:03:21,540
+اربعة خمسة ثلاثة أو خمسة اثنين اثبتنا أن الـ
+
+27
+00:03:21,540 --> 00:03:30,700
+function f is continuous على المجموعة a وخلنا
+
+28
+00:03:30,700 --> 00:03:36,580
+نراجع مع بعض أن مع بعض نراجع البرهان fix
+
+29
+00:03:39,080 --> 00:03:46,920
+fix u ينتمي إلى a given إبصر
+
+30
+00:03:46,920 --> 00:03:49,760
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+31
+00:03:49,760 --> 00:03:50,560
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+32
+00:03:50,560 --> 00:03:53,060
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+33
+00:03:53,060 --> 00:03:56,600
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+34
+00:03:56,600 --> 00:03:57,260
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+35
+00:03:57,260 --> 00:03:57,360
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+36
+00:03:57,360 --> 00:04:00,020
+أكبر من صفر أكبر من صفر أكبر من صفر أكبر من صفر
+
+37
+00:04:00,020 --> 00:04:06,790
+أكبر من صفر أكبر من صفربتطبيق تعريف epsilon delta
+
+38
+00:04:06,790 --> 00:04:12,110
+للاتصال أن نقطة given epsilon إذا بيطلع ارجعه we
+
+39
+00:04:12,110 --> 00:04:19,350
+found delta و الـ delta هذه كانت الـ minimum لقيمتين
+
+40
+00:04:19,350 --> 00:04:24,470
+u/2 أو كانت هناك c/2 بدل u كانت النقطة
+
+41
+00:04:24,470 --> 00:04:33,350
+بيسميها c فعندي u/2 و u²/2 في
+
+42
+00:04:33,350 --> 00:04:40,450
+epsilon طبعاً هذا عدد موجب واضح أن الـ delta هذه عدد
+
+43
+00:04:40,450 --> 00:04:44,530
+موجب لأن هذا عدد موجب و هذا عدد موجب و بعدين الـ
+
+44
+00:04:44,530 --> 00:04:50,530
+delta لاحظوا أنّهـا بتعتمد على الـ epsilon و على الـ U
+
+45
+00:04:52,480 --> 00:04:55,840
+الـ Delta بتعتمد على الـ Epsilon وعلى الـ U مش بس
+
+46
+00:04:55,840 --> 00:04:58,280
+على الـ Epsilon وعلى النقطة U اللي احنا بدنا نفحص
+
+47
+00:04:58,280 --> 00:05:05,020
+عندها الاتصال فشوفنا بعد هيك أنّهـ .. إذا for this
+
+48
+00:05:05,020 --> 00:05:11,880
+Delta إذا لو أخدنا X ينتمي إلى A و |X
+
+49
+00:05:11,880 --> 00:05:19,560
+- U| أصغر من Delta فطبعاً هذا قدهذا أدى أن الـ
+
+50
+00:05:19,560 --> 00:05:26,240
+delta هنا أصغر من أو يساوي U/2 وبالتالي هذا
+
+51
+00:05:26,240 --> 00:05:35,600
+بيقدر أن X أصغر من 3U/2 أكبر من U/2 لما نحل
+
+52
+00:05:35,600 --> 00:05:42,720
+المعادلة المتباينة هذه في U وهذا
+
+53
+00:05:42,720 --> 00:05:44,520
+بيقدر بدوره
+
+54
+00:05:46,640 --> 00:05:59,580
+|f(x) - f(u)| طالع بيساوي |1
+
+55
+00:05:59,580 --> 00:06:06,580
+/x - 1/u| هذا بيساوي |u - x|
+
+56
+00:06:06,580 --> 00:06:13,390
+/xu المفروض أحط هنا |xu| لكن الـ X
+
+57
+00:06:13,390 --> 00:06:17,290
+و الـ U عناصر في A و A عناصرها كل أعداد موجبة فلا
+
+58
+00:06:17,290 --> 00:06:21,950
+داعي الـ | | الأن absolute أنا عندي هنا
+
+59
+00:06:21,950 --> 00:06:31,390
+من المتباينة هذه بيطلع عندي المفروض أنه أنا عندي
+
+60
+00:06:31,390 --> 00:06:43,100
+بيطلع U/2 أصغر من X صح فهذا بيقودى أنّهـ X في أضرب
+
+61
+00:06:43,100 --> 00:06:47,420
+في U، U عدد موجب فبيطلع U²/2 أصغر من X
+
+62
+00:06:47,420 --> 00:06:55,520
+وبالتالي 1/XU بيطلع أصغر من 2/U
+
+63
+00:06:55,520 --> 00:07:02,200
+تربيع إذا 1/XU أصغر من 2/U² في
+
+64
+00:07:02,200 --> 00:07:08,790
+|U - X| و هذي أصغر من دلتا إذاً هذي أصغر
+
+65
+00:07:08,790 --> 00:07:13,830
+من 2/U² في دلتا طيب الـ delta أنا
+
+66
+00:07:13,830 --> 00:07:18,390
+اخترتها الـ minimum للقيمة هذه وهذه فبالتالي الـ delta
+
+67
+00:07:18,390 --> 00:07:22,890
+هذه تطلع أصغر من أو ساوي القيمة الثانية إذن 2
+
+68
+00:07:22,890 --> 00:07:28,850
+/U² ضرب U²/2 في Epsilon و
+
+69
+00:07:28,850 --> 00:07:33,490
+طبعاً هذولا بيروحوا مع بعض و بيظل Epsilon وبالتالي
+
+70
+00:07:33,490 --> 00:07:38,290
+بما أن Epsilon was arbitrary إذا الـ F is
+
+71
+00:07:38,290 --> 00:07:48,110
+continuous at U ولما كانت U arbitrary since U
+
+72
+00:07:48,110 --> 00:07:49,770
+belonged to A was
+
+73
+00:07:52,720 --> 00:08:00,980
+arbitrary f is continuous على كل المجموعة A هذا
+
+74
+00:08:00,980 --> 00:08:05,740
+كان برهاننا خلناها قبل هيك طيب ما الغرض مش إيش
+
+75
+00:08:05,740 --> 00:08:10,200
+النقطة أن احنا نعيد البرهان النقطة هي عايزين نفهم
+
+76
+00:08:10,200 --> 00:08:16,160
+أو نأكد أنّهـ في إثبات الاتصال عند النقطة U لاحظنا
+
+77
+00:08:16,160 --> 00:08:20,330
+أن الـ delta بتعتمد على الـ epsilon و على الـ U هذا
+
+78
+00:08:20,330 --> 00:08:24,510
+معناه أن الـ delta بتتغير قيمتها مع تغير الـ U
+
+79
+00:08:24,510 --> 00:08:28,070
+فمثلاً
+
+80
+00:08:28,070 --> 00:08:40,890
+لو جينا نعمل هاي الدالة دي لو جينا رسمناها هاي
+
+81
+00:08:40,890 --> 00:08:47,730
+الدالة 1/X لو جيت اخدت أنا X لو كان هذا
+
+82
+00:08:47,730 --> 00:08:59,250
+واحد هذا اثنين و هذا نصف لو كانت الـ U تبعتي لو كانت
+
+83
+00:08:59,250 --> 00:09:07,750
+الـ U بتساوي نصف ف
+
+84
+00:09:07,750 --> 00:09:17,810
+f لنصف بتساوي هيطلع اثنين هذا بتساوي f لنصف طب لو جيت
+
+85
+00:09:17,810 --> 00:09:25,470
+أخدت epsilon neighborhood للاثنين إذا هذا عبارة عن بي
+
+86
+00:09:25,470 --> 00:09:32,310
+epsilon للاثنين اللي هو صورة النصف فهذا الـ epsilon
+
+87
+00:09:32,310 --> 00:09:38,130
+neighborhood هيقابله delta
+
+88
+00:09:38,130 --> 00:09:43,350
+neighborhood هيقابله
+
+89
+00:09:43,350 --> 00:09:44,150
+delta
+
+90
+00:09:50,400 --> 00:09:59,440
+هذا عبارة عن delta neighborhood للنصف باللاحظ هنا
+
+91
+00:09:59,440 --> 00:10:02,680
+أن الـ delta هي قيمتها
+
+92
+00:10:20,550 --> 00:10:25,830
+هذه اثنين لو أخدت U بتساوي اثنين لو أخدت U بتساوي
+
+93
+00:10:25,830 --> 00:10:30,230
+اثنين احنا اثبتنا أن الدالة متصلة على الاثنين وهذه
+
+94
+00:10:30,230 --> 00:10:37,730
+الـ function شكلها هيكون زي هيك يعني
+
+95
+00:10:37,730 --> 00:10:41,770
+هون فـ f للاثنين
+
+96
+00:10:44,810 --> 00:10:49,990
+بتساوي نصف أو صورة الاثنين بيطلع نصف اللي هي صورة
+
+97
+00:10:49,990 --> 00:10:54,470
+الاثنين الآن لو أنا أخدت قيمة epsilon
+
+98
+00:10:54,470 --> 00:11:01,750
+neighborhood لنقطة نصف هذه الـ epsilon هنا نفس قيمة
+
+99
+00:11:01,750 --> 00:11:06,890
+الـ epsilon اللي هنا نفس القيمة وبالتالي الآن إذا
+
+100
+00:11:06,890 --> 00:11:13,680
+في عندي أنا دي epsilon للنصف طبعاً لكل epsilon
+
+101
+00:11:13,680 --> 00:11:16,480
+neighborhood للنصف بما أن الدالة متصلة عند اثنين
+
+102
+00:11:16,480 --> 00:11:22,480
+هيوجد v delta يوجد
+
+103
+00:11:22,480 --> 00:11:28,800
+v delta okay
+
+104
+00:11:28,800 --> 00:11:32,960
+هذا هيكون v delta
+
+105
+00:11:39,350 --> 00:11:43,010
+هذا عبارة عن v delta أو delta neighborhood للاثنين
+
+106
+00:11:43,010 --> 00:11:48,190
+فبلاحظ أنّهـ رغم أن الـ epsilon هنا نفس قيمة الـ
+
+107
+00:11:48,190 --> 00:11:52,890
+epsilon هنا إلا أن الـ delta هنا شوف قد إيش صغيرة
+
+108
+00:11:52,890 --> 00:12:00,400
+بينما الـ delta هنا شايفين ما أكبرها؟ تغيرت مين اللي
+
+109
+00:12:00,400 --> 00:12:05,220
+غير الـ delta الـ U لما الـ U كانت نصف الـ delta كانت
+
+110
+00:12:05,220 --> 00:12:11,340
+صغيرة لما الـ U كانت اثنين الـ U كبرت إذا الـ delta
+
+111
+00:12:11,340 --> 00:12:15,600
+هنا أو الـ delta neighborhood بيعتمد على الـ epsilon أو الـ
+
+112
+00:12:15,600 --> 00:12:19,200
+delta بتعتمد على الـ مش بس على الـ epsilon و على الـ
+
+113
+00:12:19,200 --> 00:12:23,840
+U و على النقطة نفسها okay واضح إذا هنا الـ delta
+
+114
+00:12:23,840 --> 00:12:31,210
+تغيرت مع تغير الـ U Okay تمام وبالتالي الـ delta لأي
+
+115
+00:12:31,210 --> 00:12:34,470
+epsilon الـ delta ده بتعتمد على الـ u على الـ epsilon
+
+116
+00:12:34,470 --> 00:12:39,410
+أو على النقطة وعلى الـ epsilon تمام واضحة النقطة
+
+117
+00:12:39,410 --> 00:12:45,370
+هذه طيب احنا خلّينا نقول ناشية ده المثال خلّينا ناخد
+
+118
+00:12:45,370 --> 00:12:54,770
+مثال ثاني example
+
+119
+00:12:54,770 --> 00:12:56,210
+2
+
+120
+00:12:59,420 --> 00:13:09,840
+خلّينا ناخد الـ function f(x) بتساوي 2x و x ينتمي
+
+121
+00:13:09,840 --> 00:13:13,780
+إلى R Note
+
+122
+00:13:13,780 --> 00:13:20,620
+that .. خلّينا نلاحظ أولاً أن |f(x) -
+
+123
+00:13:20,620 --> 00:13:29,440
+f(u)| بتساوي |2X - 2U| بتساوي
+
+124
+00:13:29,440 --> 00:13:38,420
+2 في |X - U| لكل X و U ينتمي لـ R
+
+125
+00:13:38,420 --> 00:13:44,880
+مظبوط هيك؟ طيب
+
+126
+00:13:44,880 --> 00:13:51,760
+الدالة هذه معروفة أنّهـا متصلة على R المجال تبعها
+
+127
+00:13:51,760 --> 00:13:52,200
+صح؟
+
+128
+00:14:03,920 --> 00:14:13,000
+على الـ set R فكيف بنعمل fix بنثبت U في R بنثبت أن
+
+129
+00:14:13,000 --> 00:14:22,180
+F متصل عند الـ U صح؟ and let epsilon أكبر من الصفر be
+
+130
+00:14:22,180 --> 00:14:22,780
+given
+
+131
+00:14:28,810 --> 00:14:36,250
+نختار دلتا نختار دلتا بتساوي epsilon/2 أكبر من
+
+132
+00:14:36,250 --> 00:14:45,010
+الصفر فلهذه الـ delta then لو كان x ينتمي إلى الـ a
+
+133
+00:14:45,010 --> 00:14:51,490
+اللي هي r و |x - u| أصغر من الـ delta فهذا
+
+134
+00:14:51,490 --> 00:14:58,840
+هيديني |f(x) - f(u)| بتقول أن هذا
+
+135
+00:14:58,840 --> 00:15:03,440
+بيطلع بتساوي أصغر من أو يساوي 2 في |x
+
+136
+00:15:03,440 --> 00:15:09,940
+- u| أو بتساوي بالأعلى، صح؟ طيب ما إحنا الـ X هذه
+
+137
+00:15:09,940 --> 00:15:14,660
+ماخدينها بحيث أن |x - u| أصغر من الـ
+
+138
+00:15:14,660 --> 00:15:20,160
+delta، صح؟ عشان ذلك إحنا اخترنا delta بتساوي epsilon/
+
+139
+00:15:20,160 --> 00:15:24,500
+2 اه شوفت إيش أخدنا delta بتساوي epsilon/2
+
+140
+00:15:24,500 --> 00:15:30,740
+طيب و هذا بتساوي epsilon حسب اختيارنا للـ delta 
+
+141
+00:15:30,740 --> 00:15:37,460
+وبالتالي هيك إذا الـ function بما أن epsilon was
+
+142
+00:15:37,460 --> 00:15:44,800
+arbitrarily إذا f is continuous at الـ U وبما أن U
+
+143
+00:15:44,800 --> 00:15:48,060
+belongs to R وزر فبتره إذا if continuous على كل ال
+
+144
+00:15:48,060 --> 00:15:55,240
+R كمان مرة النقطة هنا اللي عايزين أن أكد عليها هو
+
+145
+00:15:55,240 --> 00:16:01,520
+إن الـ Delta لأي إبسلون و لأي U و لأي إبسلون ال
+
+146
+00:16:01,520 --> 00:16:06,160
+Delta هنا تعتمد على إبسلون فقط مالهاش دعوة في الـ U
+
+147
+00:16:06,160 --> 00:16:11,790
+بمعنى آخر لو أنا الـ U هذه غيرتها أخذت U تانية لو
+
+148
+00:16:11,790 --> 00:16:14,670
+كانت تانية مثلا U بالساعة و سفر او واحد او اتنين
+
+149
+00:16:14,670 --> 00:16:19,310
+أو تلاتة او اي عدد حقيقي فكل مرة الـ delta نفس ال
+
+150
+00:16:19,310 --> 00:16:25,800
+delta F2 will work للـ U لكل U لأي إبسن خدي نفس ال
+
+151
+00:16:25,800 --> 00:16:28,340
+delta إبسن على اتنين هتعطيهم إيه الـ implication
+
+152
+00:16:28,340 --> 00:16:33,640
+هذه بغض النظر عن الـ U okay؟ وبالتالي هنا في ال ..
+
+153
+00:16:33,640 --> 00:16:37,320
+في ال .. في الاتصال هذا الـ delta هنا تعتمد على
+
+154
+00:16:37,320 --> 00:16:40,540
+إبسن فقط و لا تعتمد على U بينما في المثال السابق
+
+155
+00:16:40,540 --> 00:16:45,240
+شوفنا الـ delta بتعتمد على U هذا النوع من الاتصال
+
+156
+00:16:45,240 --> 00:16:48,860
+بنسميه اتصال منتظم اللي فيه الـ delta تعتمد على
+
+157
+00:16:48,860 --> 00:16:52,760
+epsilon فقط اتصال منتظم او uniform continuity
+
+158
+00:16:52,760 --> 00:16:55,540
+اتصال اللي جابله اللي الـ delta تعتمد على ال
+
+159
+00:16:55,540 --> 00:17:00,510
+epsilon و على النقطة U هذا نسميه continuity عادية
+
+160
+00:17:00,510 --> 00:17:04,230
+أو نقول continuity اتصال اما هذا uniform
+
+161
+00:17:04,230 --> 00:17:08,770
+continuity هنشوف الـ gate من التعريف ان الـ uniform
+
+162
+00:17:08,770 --> 00:17:13,990
+continuity اقوى و اشمل من الـ continuity العادية
+
+163
+00:17:13,990 --> 00:17:22,670
+okay تمام اذا خليني اضع تعريف الـ uniform
+
+164
+00:17:22,670 --> 00:17:25,590
+continuity definition
+
+165
+00:17:28,670 --> 00:17:40,970
+فنشطة f من a الى r هي عامة عامة
+
+166
+00:17:40,970 --> 00:17:49,130
+مستمرة عامة مستمرة عامة عامة عامة عامة عامة عامة
+
+167
+00:17:49,130 --> 00:17:49,170
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+168
+00:17:49,170 --> 00:17:54,610
+عامة عامة عامة عامة عامة عامة عامة عامة
+
+169
+00:17:54,610 --> 00:17:55,930
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+170
+00:17:55,930 --> 00:17:55,950
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+171
+00:17:55,950 --> 00:17:56,070
+عامة عامة عامة عامة عامة عامة عامة عامة عامة
+
+172
+00:18:00,400 --> 00:18:06,760
+لأي إبسلون أكبر من الصفر يوجد Delta تعتمد على إبسلون
+
+173
+00:18:06,760 --> 00:18:13,920
+فقط، عدد موجب بحيث أنه لكل X و U تنتمي إلى A
+
+174
+00:18:13,920 --> 00:18:20,620
+و absolute X minus U أصغر من Delta هذا بتضمن أن
+
+175
+00:18:20,620 --> 00:18:29,420
+absolute F of X minus F of U أصغر من الإبسلون
+
+176
+00:18:31,760 --> 00:18:35,660
+إذا هنا لأي أبسلون أكبر من الصفر في دلتة واحدة
+
+177
+00:18:35,660 --> 00:18:40,100
+تعتمد على أبسلون فقط والدلتة هذه تلف على كل الـ X
+
+178
+00:18:40,100 --> 00:18:44,620
+و كل الـ U أو لكل الـ U مرة واحدة فهنا لكل X و لأي U
+
+179
+00:18:44,620 --> 00:18:48,300
+إذا المسافة بينهم أصغر من الدلتة فالمسافة بين
+
+180
+00:18:48,300 --> 00:18:54,140
+أصغرهم أصغر من X تمام؟ الآن واضح من التعريفات
+
+181
+00:18:58,880 --> 00:19:05,820
+remarks الملاحظة الأولى uniform
+
+182
+00:19:05,820 --> 00:19:13,760
+continuity
+
+183
+00:19:13,760 --> 00:19:23,440
+uniform continuity implies continuity
+
+184
+00:19:27,240 --> 00:19:35,720
+الاتصال المنتظم بيؤدي للاتصال العادي و البرهان
+
+185
+00:19:35,720 --> 00:19:39,960
+واضح يعني بمعنى آخر لو في عندي function f from a
+
+186
+00:19:39,960 --> 00:19:46,460
+to r و الـ function كانت uniformly continuous فهذا
+
+187
+00:19:46,460 --> 00:19:54,350
+بيؤدي ان f continuous فالبرهان ذلك افرضي أن F
+
+188
+00:19:54,350 --> 00:20:00,770
+uniformly continuous إذا اشترتها تتحقق تبع الـ
+
+189
+00:20:00,770 --> 00:20:05,750
+Uniform Continuous الآن لإثبات أن F continuous على
+
+190
+00:20:05,750 --> 00:20:11,210
+A بتثبت أن F continuous at every U ينتمي لـ A يعني
+
+191
+00:20:11,210 --> 00:20:17,090
+بتثبت أنه لأي epsilon و لأي U فـ let epsilon be
+
+192
+00:20:17,090 --> 00:20:20,030
+given و let U be fixed element في A
+
+193
+00:20:22,930 --> 00:20:26,390
+من هنا لهذه الـ Epsilon من هنا بما أن هذا الشرط
+
+194
+00:20:26,390 --> 00:20:32,670
+متحقق لأن خد الـ Delta لأي الـ Epsilon هادي given خد
+
+195
+00:20:32,670 --> 00:20:34,950
+الـ Delta اللي هي هذه موجودة في الـ uniform
+
+196
+00:20:34,950 --> 00:20:38,650
+continuous اللي بتعتمد على Epsilon فقط خديها هي ال
+
+197
+00:20:38,650 --> 00:20:43,730
+Delta هذه فطبعا هذه الـ Delta بتخلي الـ implication
+
+198
+00:20:43,730 --> 00:20:51,850
+هذه تتحقق نظرت؟ لو هذه متحققة فهذه متحققة إذن هيك
+
+199
+00:20:51,850 --> 00:20:55,270
+واضح إن الـ uniform continuous إذا الواحدة بيقدر أن
+
+200
+00:20:55,270 --> 00:20:58,930
+f continuous and u لما أن u واظهر بترة إذا f
+
+201
+00:20:58,930 --> 00:21:05,310
+continuous and كل على كل المجموعية لكن
+
+202
+00:21:05,310 --> 00:21:11,690
+العكس مش صحيح إذا العكس المواحدة التانية العكس مش
+
+203
+00:21:11,690 --> 00:21:17,570
+صحيح but not conversely
+
+204
+00:21:22,160 --> 00:21:26,380
+العكس مش صحيح، يعني الـ continuity لا تؤدي إلى ال
+
+205
+00:21:26,380 --> 00:21:37,360
+uniform continuity و على سبيل المثال for
+
+206
+00:21:37,360 --> 00:21:39,220
+example على سبيل المثال
+
+207
+00:21:46,610 --> 00:21:51,610
+احنا شوفنا قبل شوية في بداية المحاضرة الـ function
+
+208
+00:21:51,610 --> 00:21:56,870
+f of x بساوي واحد على x و x ينتمي إلى a اللي هي
+
+209
+00:21:56,870 --> 00:22:03,870
+الفترة مفتوحة من صفر لما لا نهاية is continuous on
+
+210
+00:22:03,870 --> 00:22:11,550
+a أثبتت أنها continuous على المجموعة a but
+
+211
+00:22:15,440 --> 00:22:28,480
+but it is not uniformly continuous on a as we
+
+212
+00:22:28,480 --> 00:22:34,140
+shall see in
+
+213
+00:22:34,140 --> 00:22:39,100
+a few minutes
+
+214
+00:22:39,100 --> 00:22:46,160
+كما سنرى بعد لحظات الدالة هذه ليست متصلة اتصالا
+
+215
+00:22:46,160 --> 00:22:52,940
+منتظم هنأخر المرحلة دي شوية و هنبرهنه فلكن في
+
+216
+00:22:52,940 --> 00:22:59,560
+الأول خلينا من التعريف تبع الـ uniform continuity
+
+217
+00:22:59,560 --> 00:23:09,720
+نستنتج non uniform continuity criterion من
+
+218
+00:23:09,720 --> 00:23:13,120
+هنا non uniform
+
+219
+00:23:15,380 --> 00:23:22,560
+non uniform continuity criteria
+
+220
+00:23:22,560 --> 00:23:33,940
+let
+
+221
+00:23:33,940 --> 00:23:41,240
+f from a to r be a function then
+
+222
+00:23:44,150 --> 00:23:53,730
+the following statements are equivalent واحد if f is
+
+223
+00:23:53,730 --> 00:23:58,810
+not uniformly
+
+224
+00:23:58,810 --> 00:24:09,510
+continuous على المجال تبعها نين there exists
+
+225
+00:24:09,510 --> 00:24:17,380
+epsilon zero أكبر من الصفر such that for every
+
+226
+00:24:17,380 --> 00:24:26,620
+delta أكبر من الصفر يوجد x delta و u delta عناصر
+
+227
+00:24:26,620 --> 00:24:36,220
+في a such that absolute x delta minus u delta أصغر
+
+228
+00:24:36,220 --> 00:24:45,160
+من delta and absolute f of x delta-f of u دلتا
+
+229
+00:24:45,160 --> 00:24:53,160
+أكبر من أو يساوي epsilon zero الرابعة
+
+230
+00:24:53,160 --> 00:25:00,020
+الثالثة there exist epsilon zero أكبر من الصفر and
+
+231
+00:25:00,020 --> 00:25:06,200
+two sequences متتاليتين xn
+
+232
+00:25:07,630 --> 00:25:14,930
+و un موجودين في مجال الدالة a such that بحيث أن
+
+233
+00:25:14,930 --> 00:25:23,910
+limit xn minus un بساوي صفر as n tends to infinity
+
+234
+00:25:23,910 --> 00:25:25,690
+and
+
+235
+00:25:27,050 --> 00:25:35,910
+absolute f of xn minus f of un أكبر من أو يساوي
+
+236
+00:25:35,910 --> 00:25:42,350
+epsilon zero هذا صحيح لكل n ينتمي للأعداد الطبيعية
+
+237
+00:25:42,350 --> 00:25:51,070
+okay تمام طيب نشوف البرهان تبع النظرية هذه البرهان
+
+238
+00:25:51,070 --> 00:25:55,440
+تبع النظرية هذه ينتج مباشرة من تعريف الـ uniform
+
+239
+00:25:55,440 --> 00:26:01,980
+continuity تعال نشوف واحد بكافئ اتنين طيب ما
+
+240
+00:26:01,980 --> 00:26:07,300
+معناه if uniform continuous على المجموعة ايه؟
+
+241
+00:26:07,300 --> 00:26:12,920
+معناه الشرط هذا بيتحقق طيب ما معناه ان if not
+
+242
+00:26:12,920 --> 00:26:16,540
+uniform continuous على ايه؟ معناه الـ negation تبع
+
+243
+00:26:16,540 --> 00:26:19,720
+العبارة دي بتحقق تعال ننفذ العبارة انفذ العبارة
+
+244
+00:26:20,730 --> 00:26:25,250
+بدل لكل epsilon يوجد epsilon zero بدل يوجد delta
+
+245
+00:26:25,250 --> 00:26:31,550
+لكل delta موجبة بدل لكل x و u يوجد x و u يعتمد كل
+
+246
+00:26:31,550 --> 00:26:36,730
+واحد منهم يعتمد على الـ delta بحيث لو كان هذا أصغر
+
+247
+00:26:36,730 --> 00:26:41,950
+من delta فلازم هذا يقدر انه الأصغر هذا أكبر من أو
+
+248
+00:26:41,950 --> 00:26:45,910
+يساوي الـ epsilon zero لأن واضح أن العبارة الأولى
+
+249
+00:26:45,910 --> 00:26:50,330
+بتكافئ التانية لأنه نفي التعريف بكافئ العبارة
+
+250
+00:26:50,330 --> 00:26:55,570
+التانية طيب التانية بتكافئ التالتة وهذا برضه صح
+
+251
+00:26:55,570 --> 00:27:01,650
+افرض أن التانية صحيحة تعني نثبت أن التالتة صحيحة
+
+252
+00:27:01,650 --> 00:27:05,170
+طيب هي التانية يوجد epsilon zero يوجد و هكذا
+
+253
+00:27:12,050 --> 00:27:16,770
+بحيث لكل delta خدي delta بالساوية واحد على n يعني
+
+254
+00:27:16,770 --> 00:27:21,370
+بمعنى آخر لكل n يوجد delta بالساوية واحد على n عدد
+
+255
+00:27:21,370 --> 00:27:26,730
+موجب وبالتالي يوجد X يعتمد على الـ Delta اللي هي
+
+256
+00:27:26,730 --> 00:27:31,670
+واحد على N اللي بتعتمد على N إذا لكل N لكل N يوجد
+
+257
+00:27:31,670 --> 00:27:37,310
+XN و UN صح؟ وبالتالي يوجد two sequences و الـ two
+
+258
+00:27:37,310 --> 00:27:41,470
+sequences هدول بيحققوا أن absolute X واحدة XN
+
+259
+00:27:41,470 --> 00:27:46,310
+minus UN أصغر من واحد على N اللي هي الـ Delta و هذا
+
+260
+00:27:46,310 --> 00:27:52,660
+صحيح لكل N إذا الـ limit إذا كان هذا أصغر من واحد
+
+261
+00:27:52,660 --> 00:27:55,900
+على xn minus un على absolute أصغر من واحد على n
+
+262
+00:27:55,900 --> 00:28:00,020
+حسب نظرية اتنين أربعة هذا معناه limit xn minus un
+
+263
+00:28:00,020 --> 00:28:06,420
+بساوي صفر وهذا هي absolute f of xn minus f of un
+
+264
+00:28:06,420 --> 00:28:12,180
+أكبر من أو يساوي epsilon zero okay فهو واضح وطبعا العكس نفس الحاجة
+
+265
+00:28:12,180 --> 00:28:16,020
+إذن البرهان النظرية هذه ينتج مباشرة من ال
+
+266
+00:28:16,020 --> 00:28:20,340
+definition تبع الـ uniform continuity
+
+267
+00:28:22,600 --> 00:28:27,400
+الآن دعونا نرجع للمثال
+
+268
+00:28:27,400 --> 00:28:38,560
+هذا إذا هنا example to
+
+269
+00:28:38,560 --> 00:28:46,710
+show ان الـ function f of x بساوي واحد على x is
+
+270
+00:28:46,710 --> 00:28:51,190
+not uniformly
+
+271
+00:28:51,190 --> 00:28:58,750
+continuous على المجموعة a اللي هي الفافرة مفتوحة
+
+272
+00:28:58,750 --> 00:29:07,010
+من صفر لما لا نهاية we use non
+
+273
+00:29:07,010 --> 00:29:09,270
+uniform
+
+274
+00:29:11,050 --> 00:29:16,390
+Non-uniform continuity
+
+275
+00:29:16,390 --> 00:29:21,890
+criteria
+
+276
+00:29:37,150 --> 00:29:47,310
+يوجد ابسلون زيرو يوجد
+
+277
+00:29:47,310 --> 00:29:49,870
+عدد ابسلون زيرو موجود
+
+278
+00:30:07,550 --> 00:30:16,570
+تختار خيار Xm بساوي واحد على ان اكيد هذه ال
+
+279
+00:30:16,570 --> 00:30:19,630
+sequence contain في الفترة المفتوحة من صفر للملا
+
+280
+00:30:19,630 --> 00:30:28,210
+نهاية صح؟ and كمان تختار خيار ثاني UN بساوي واحد على ان زائد واحد
+
+281
+00:30:28,210 --> 00:30:33,370
+على أن زايد واحد برضه هذه الـ sequence حدودها كلها 
+
+282
+00:30:33,370 --> 00:30:37,730
+موزّبة وبالتالي مجموعة جزئية من الفترة المفتوحة من
+
+283
+00:30:37,730 --> 00:30:41,830
+صفر لملانها Clearly
+
+284
+00:30:41,830 --> 00:30:45,290
+واضح
+
+285
+00:30:45,290 --> 00:30:54,330
+أن الـ limit لـ xn ناقص un as n times infinity
+
+286
+00:30:54,330 --> 00:31:04,720
+بساوي limit 1 على n ناقص 1 على n زائد 1 as n equals
+
+287
+00:31:04,720 --> 00:31:11,660
+infinity فـ limit الأولى ساوي صفر limit الـ sequence
+
+288
+00:31:11,660 --> 00:31:18,200
+الثانية صفر وبالتالي بيطلع صفر لأن هنا حققت كل
+
+289
+00:31:18,200 --> 00:31:24,020
+الشروط ضايل بس المتباينة هادي also
+
+290
+00:31:28,610 --> 00:31:38,510
+أنا عندي absolute f of x n ناقص f of u n هذا
+
+291
+00:31:38,510 --> 00:31:46,990
+المفروض بيطلع بيساوي absolute n ناقص n زائد واحد،
+
+292
+00:31:46,990 --> 00:31:53,430
+أزبوتك؟ وهذا بيساوي واحد، واحد أصغر من أو يساوي، بيساوي
+
+293
+00:31:53,430 --> 00:32:00,000
+واحد اللي هو epsilon zero وهذا صحيح لكل n في n
+
+294
+00:32:00,000 --> 00:32:08,940
+أصبوت هنا هاني أنا ايش عملت الـ criterion رقم ثلاثة 
+
+295
+00:32:08,940 --> 00:32:15,660
+تحققّتها تحقّقت أنّه متحققة ها يوجد epsilon zero
+
+296
+00:32:15,660 --> 00:32:21,600
+واحد لاحظوا الواحد علشان أنا اختارت واحد ممكن آخذ
+
+297
+00:32:21,600 --> 00:32:25,040
+برضه epsilon zero بساوي اثنين لأن الواحد أصغر من
+
+298
+00:32:25,040 --> 00:32:29,380
+الاثنين ما في مشكلة بس مش أقل من واحد يعني نصف من
+
+299
+00:32:29,380 --> 00:32:32,840
+فعشان لأن هي أثبتت يوجد epsilon zero عدد موجب
+
+300
+00:32:32,840 --> 00:32:36,280
+ويوجد two sequences أنا اخترتّهم أنا أوجدتهم بنفسي
+
+301
+00:32:36,280 --> 00:32:39,780
+واحد على n واحد على n زيادة واحد كلهم موجودين في
+
+302
+00:32:39,780 --> 00:32:45,380
+مجال الدالة ايه و limit الفرق بينهم صفر لكن
+
+303
+00:32:45,380 --> 00:32:52,960
+absolute الفرق بين صورهم مش أقوى هذا هيكون بيساوي
+
+304
+00:32:52,960 --> 00:32:59,860
+واحد أكبر من أو يساوي .. مش أصغر من أو يساوي بدي
+
+305
+00:32:59,860 --> 00:33:06,140
+أكبر من أو يساوي واحد اللي هو epsilon خليني
+
+306
+00:33:06,140 --> 00:33:09,760
+أنا أسحب الكلام اللي حكيته سابقا وأقول هنا ممكن
+
+307
+00:33:09,760 --> 00:33:13,140
+آخذ الـ epsilon zero بساوي واحد أو أي حاجة أصغر
+
+308
+00:33:13,140 --> 00:33:19,750
+يعني نصف بنفع يعني أبسلون زيرو بساوي نصف بنفع لكن أي
+
+309
+00:33:19,750 --> 00:33:23,630
+شيء أكبر من واحد منفعش لأن أنا بدي واحد يكون أكبر
+
+310
+00:33:23,630 --> 00:33:28,270
+من أو يساوي أبسلون زيرو تمام؟ إذا هذه أثبتنا
+
+311
+00:33:28,270 --> 00:33:31,750
+وبالتالي حسب الـ non-uniform continuity criterion
+
+312
+00:33:31,750 --> 00:33:35,710
+الـ .. الـ function هذه is not uniform لـ continuous
+
+313
+00:33:35,710 --> 00:33:42,250
+تمام؟ لكن أثبتنا سابقا جابليك أنها is continuous
+
+314
+00:33:42,250 --> 00:33:48,150
+على المجال تبعها إذا لو قلنا لكم prove or disprove
+
+315
+00:33:48,150 --> 00:33:51,330
+continuity
+
+316
+00:33:51,330 --> 00:33:55,010
+implies continuity .. الـ uniform .. continuity
+
+317
+00:33:55,010 --> 00:33:58,970
+implies uniform continuity هتقولي هذا الـ statement
+
+318
+00:33:58,970 --> 00:34:04,150
+false والـ counter example هو هذا هذا مثال على
+
+319
+00:34:04,150 --> 00:34:07,570
+function continuous لكن ليست uniformly continuous
+
+320
+00:34:07,570 --> 00:34:17,820
+تمام؟ طيب، كويس خلينا الآن نثبت بعض النظريات
+
+321
+00:34:17,820 --> 00:34:24,300
+المهمة اللي بتخص uniform continuity ومن أهم
+
+322
+00:34:24,300 --> 00:34:32,680
+النظريات التي هي النظرية التالية theorem اسمها
+
+323
+00:34:32,680 --> 00:34:36,660
+uniform continuity
+
+324
+00:34:36,660 --> 00:34:40,160
+continuity theorem
+
+325
+00:34:49,430 --> 00:34:56,770
+let I بساوي be
+
+326
+00:34:56,770 --> 00:35:05,570
+a closed and bounded interval
+
+327
+00:35:05,570 --> 00:35:09,350
+إذا
+
+328
+00:35:09,350 --> 00:35:17,360
+I عبارة عن closed and bounded interval لو كان لو
+
+329
+00:35:17,360 --> 00:35:22,980
+كانت الـ function f continuous، if f from I to R
+
+330
+00:35:22,980 --> 00:35:34,040
+is continuous on I، then f is uniformly ..
+
+331
+00:35:34,040 --> 00:35:43,060
+uniformly continuous on
+
+332
+00:35:43,060 --> 00:35:43,620
+I
+
+333
+00:35:46,190 --> 00:35:51,870
+والبرهان السهل prove by contradiction إذا أنّ بكلّ
+
+334
+00:35:51,870 --> 00:35:57,070
+بساطة نظرية هذه رغم بساطة بساطة الـ statement تبعها
+
+335
+00:35:57,070 --> 00:36:01,710
+اللي أنا من أهم النظريات بكل بساطة النظرية اللي
+
+336
+00:36:01,710 --> 00:36:04,850
+بيقول لو كان في عندك function متصل على المجال
+
+337
+00:36:04,850 --> 00:36:08,550
+تبعها والمجال تبعها closed bounded interval إذا
+
+338
+00:36:08,550 --> 00:36:13,970
+الاتصال العادي يصبح اتصال منتظم إنّ إنّ هذه الحالة
+
+339
+00:36:13,970 --> 00:36:18,030
+الوحيدة اللي أو يعني أحد الحالات اللي فيها بيكون
+
+340
+00:36:18,030 --> 00:36:22,650
+الاتصال العادي بقدر الاتصال المنتظم إنّ احنا أضفنا
+
+341
+00:36:22,650 --> 00:36:26,630
+شرط أن مجال تبع الدالة ما يكونش أي set لازم يكون
+
+342
+00:36:26,630 --> 00:36:31,090
+closed bounded interval لبرهان ذلك بال
+
+343
+00:36:31,090 --> 00:36:39,670
+contradiction assume on contrary that
+
+344
+00:36:41,290 --> 00:36:55,010
+if is not uniformly continuous on I then by non
+
+345
+00:36:55,010 --> 00:37:03,550
+uniform continuity criteria النظرية
+
+346
+00:37:03,550 --> 00:37:10,620
+اللي فوق يوجد إبسلون زيرو أكبر من الصفر و two
+
+347
+00:37:10,620 --> 00:37:15,620
+sequences and
+
+348
+00:37:15,620 --> 00:37:25,040
+two sequences واحدة نسميها x n والثانية u n
+
+349
+00:37:25,040 --> 00:37:37,510
+contained in I بحيث أنّ absolute x n ناقص u n أصغر
+
+350
+00:37:37,510 --> 00:37:46,390
+من واحد على n لكل n and absolute f of x n ناقص f
+
+351
+00:37:46,390 --> 00:37:56,420
+of u n أكبر من أو يساوي epsilon zero لكل n في n كلّ
+
+352
+00:37:56,420 --> 00:38:01,300
+هذا نأخذه من الـ non uniform continuity criterion
+
+353
+00:38:01,300 --> 00:38:11,500
+الآن بدنا نصل لتناقض طيب
+
+354
+00:38:11,500 --> 00:38:15,980
+عشان نصل لتناقض since
+
+355
+00:38:18,370 --> 00:38:25,750
+I is bounded الفترة دي احنا فرضين أنها bounded و
+
+356
+00:38:25,750 --> 00:38:32,550
+الـ sequence x n contained in I then الـ sequence x
+
+357
+00:38:32,550 --> 00:38:35,450
+n is bounded
+
+358
+00:38:41,210 --> 00:38:57,810
+هنا باستخدام حسب Bolzano
+
+359
+00:38:57,810 --> 00:39:01,890
+Weierstrass
+
+360
+00:39:01,890 --> 00:39:02,350
+firm
+
+361
+00:39:11,180 --> 00:39:23,360
+السيكوينس هناك سبسيكوينس سميها x n k of x n such that
+
+362
+00:39:23,360 --> 00:39:28,740
+السيكوينس had a convergence limit x n k as k tends
+
+363
+00:39:28,740 --> 00:39:33,840
+to infinity as
+
+364
+00:39:33,840 --> 00:39:40,030
+k tends to infinity بساوي z ينتمي إلى r بالنسبة لـ
+
+365
+00:39:40,030 --> 00:39:45,090
+some z and some r Bolzano Weierstrass كلّ sequence
+
+366
+00:39:45,090 --> 00:39:48,570
+لها convergence subsequence سمّي الـ subsequence هكذا
+
+367
+00:39:48,570 --> 00:39:50,330
+وسمّي الـ limit تبعتها هكذا
+
+368
+00:39:54,530 --> 00:40:00,450
+الـ sub-sequence X n K contained in I التي هي
+
+369
+00:40:00,450 --> 00:40:05,450
+الفترة المغلقة من A إلى B فأحنا أخذنا نظرية تقول
+
+370
+00:40:05,450 --> 00:40:08,290
+أن لو كان هناك sequence حدودها محصورة بين A وB
+
+371
+00:40:08,290 --> 00:40:13,230
+ومتقاربة فنهايتها أيضًا محصورة بين A وB فهذا سيؤدي
+
+372
+00:40:13,230 --> 00:40:18,230
+إلى أن Z تنتمي إلى الفترة المغلقة من A إلى B التي
+
+373
+00:40:18,230 --> 00:40:18,890
+هي I
+
+374
+00:40:24,140 --> 00:40:28,340
+الذي يدفع الاتصال
+
+375
+00:40:28,340 --> 00:40:31,620
+الاتصال
+
+376
+00:40:31,620 --> 00:40:34,420
+الاتصال الاتصال الاتصال الاتصال الاتصال الاتصال
+
+377
+00:40:34,420 --> 00:40:44,240
+الاتصال الاتصال
+
+378
+00:40:51,890 --> 00:41:02,550
+موجودين في I موجودين في I موجودين
+
+379
+00:41:02,550 --> 00:41:12,990
+في I موجودين في I الـ subsequence U n برضه لها
+
+380
+00:41:12,990 --> 00:41:16,970
+subsequence مشابهة و convergent لنفس الـ Z هذا مش
+
+381
+00:41:16,970 --> 00:41:25,390
+واضح لثبته لثباته to see this to see this note
+
+382
+00:41:25,390 --> 00:41:28,250
+that
+
+383
+00:41:31,680 --> 00:41:37,040
+بنقدر نخلّي الفرق بين
+
+384
+00:41:37,040 --> 00:41:47,580
+u n k و z أصغر من أي epsilon فهذا
+
+385
+00:41:47,580 --> 00:41:58,020
+أصغر من أو يساوي u n k ناقص x n k زائد absolute x n k
+
+386
+00:41:58,020 --> 00:42:03,380
+ناقص z هو في الأصل أنّ أنا المفروض أكتب أنا أشعر
+
+387
+00:42:03,380 --> 00:42:07,840
+بالإضطراب x n k ورجعتها واستخدمت الـ triangle
+
+388
+00:42:07,840 --> 00:42:18,420
+inequality طيب هذا صحيح لكل k ينتمي إلى n طيب أنا
+
+389
+00:42:18,420 --> 00:42:22,220
+عندي limit
+
+390
+00:42:22,220 --> 00:42:30,290
+x n ناقص u n بساوي صفر لأن هذا صحيح لكل n فـ
+
+391
+00:42:30,290 --> 00:42:36,130
+limit u n k ناقص x n k برضه بيساوي صفر فهذا
+
+392
+00:42:36,130 --> 00:42:43,750
+بيروح لصفر as k tends to infinity وعندي أنا برضه u
+
+393
+00:42:43,750 --> 00:42:50,290
+الـ x n k جلنا تقول إلى z فبالتالي الـ absolute
+
+394
+00:42:50,290 --> 00:42:56,630
+value هذه بتروح لصفر as k tends to infinity وهذا
+
+395
+00:42:56,630 --> 00:43:08,170
+أكبر من صفر، إذن by squeeze theorem الـ sequence
+
+396
+00:43:08,170 --> 00:43:13,030
+هذه محصورة بين الـ sequence هذه بالصفر ومجموعة two
+
+397
+00:43:13,030 --> 00:43:18,270
+sequences بيقولوا للصفر إذا من الـ limit لـ absolute
+
+398
+00:43:18,270 --> 00:43:25,570
+u n k ناقص z as k tends to infinity بساوي صفر و
+
+399
+00:43:25,570 --> 00:43:31,270
+منها بطلع الـ limit u n k as k tends to infinity
+
+400
+00:43:31,270 --> 00:43:38,230
+بساوي z وبالتالي هذا بيثبت الـ claim تمام؟ إذا هنا
+
+401
+00:43:38,230 --> 00:43:43,830
+أثبتنا الـ claim الآن بعد ما أثبتنا الـ claim
+
+402
+00:43:57,160 --> 00:44:04,320
+طيب طيب now أنا
+
+403
+00:44:04,320 --> 00:44:12,300
+بدّي أقول لكم اثبتنا أنه النقطة z تنتمي .. z تنتمي لـ
+
+404
+00:44:12,300 --> 00:44:16,880
+I الـ limit تبعت الـ subsequence تنتمي لـ I والـ f
+
+405
+00:44:16,880 --> 00:44:17,460
+continuous
+
+406
+00:44:21,950 --> 00:44:25,850
+إنّ الهدف بقدم if is continuous لأن if continuous
+
+407
+00:44:25,850 --> 00:44:32,210
+على I وبالتالي continuous عند أي نقطة في الـ I ولا
+
+408
+00:44:32,210 --> 00:44:36,990
+تكن الـ Z hence
+
+409
+00:44:36,990 --> 00:44:40,730
+by
+
+410
+00:44:40,730 --> 00:44:46,510
+sequential criterion by sequential criterion for
+
+411
+00:44:46,510 --> 00:44:50,500
+continuous function الـ function continuous عند
+
+412
+00:44:50,500 --> 00:44:54,640
+النقطة z وفي عندي sequence x n k converged لـ z
+
+413
+00:44:54,640 --> 00:45:01,260
+إذا الـ limit لصورة الـ sequence أو الـ subsequence
+
+414
+00:45:01,260 --> 00:45:10,180
+لما كتره لـ infinity بساوي f of z وكذلك أيضًا And
+
+415
+00:45:10,180 --> 00:45:13,760
+برضه الـ limit أنا عندي برضه الـ sequence هذي
+
+416
+00:45:13,760 --> 00:45:20,220
+converge لـ z فنهاية صورة الـ subsequence u n k as
+
+417
+00:45:20,220 --> 00:45:27,260
+k tends to infinity برضه بيساوي f of z تمام
+
+418
+00:45:27,260 --> 00:45:31,520
+طيب
+
+419
+00:45:31,520 --> 00:45:35,000
+لكن
+
+420
+00:45:35,000 --> 00:45:43,090
+أنا عندي أنا عندي المتباينة الـ but أنا عندي 
+
+421
+00:45:43,090 --> 00:45:47,170
+absolute f of x in
+
+422
+00:45:55,850 --> 00:46:01,570
+من الفرض هيها من الفرض أن ال function not
+
+423
+00:46:01,570 --> 00:46:07,070
+uniformly continuous أنا عندي هذا أكبر من أو يساوي
+
+424
+00:46:07,070 --> 00:46:10,050
+epsilon zero لكل n لكل حدود ال sequences
+
+425
+00:46:14,300 --> 00:46:20,060
+فهذا بيقدّي .. هذا بدوره بيقدّي أن epsilon zero
+
+426
+00:46:20,060 --> 00:46:27,180
+هي epsilon zero أصغر من أو يساوي absolute f of x in
+
+427
+00:46:27,180 --> 00:46:36,220
+k minus f of u in k تمام؟
+
+428
+00:46:37,840 --> 00:46:41,720
+هذا صحيح لـ sequence x in و لـ sequence u in إذا
+
+429
+00:46:41,720 --> 00:46:46,200
+صحيح للـ subsequence للـ subsequences إذا هذه جاية
+
+430
+00:46:46,200 --> 00:46:50,620
+من هنا طيب و by triangle inequality by triangle
+
+431
+00:46:50,620 --> 00:46:56,760
+inequality ممكن أخلي هذا أصغر من أو يساوي f of x nk
+
+432
+00:46:56,760 --> 00:47:10,090
+minus f of z زائد absolute f of z-F of U in K أنا
+
+433
+00:47:10,090 --> 00:47:14,610
+شو أنا عاملة اتراحت من هنا F of Z و رجعتها اه و
+
+434
+00:47:14,610 --> 00:47:17,810
+استخدمت ال triangle equality فصار عندي اصلا مجموعة
+
+435
+00:47:17,810 --> 00:47:24,070
+two absolute values طيب
+
+436
+00:47:24,070 --> 00:47:30,660
+ما أنا ممكن أخليأنا عندي limit ال sequence هذه
+
+437
+00:47:30,660 --> 00:47:36,800
+بساوي f of z فلأي given epsilon أكبر من الصفر ممكن
+
+438
+00:47:36,800 --> 00:47:42,300
+أخلي absolute الفرخ هذا أصغر من epsilon على 2 ونفس
+
+439
+00:47:42,300 --> 00:47:47,260
+الحاجة أنا عندي ال sequence f of u and k converged
+
+440
+00:47:47,260 --> 00:47:51,840
+ل f of z إذا ممكن أخلي ال absolute value للفرخ هذه
+
+441
+00:47:51,840 --> 00:47:59,540
+أصغر من epsilon على 2وبالتالي بيطلع المجموعة
+
+442
+00:47:59,540 --> 00:48:06,420
+epsilon هذا صحيح لكل K أكبر من أو يساوي كابتل K أو
+
+443
+00:48:06,420 --> 00:48:12,360
+كابتل N واضح تمام؟ يعني لا أي epsilon أكبر من صفر
+
+444
+00:48:12,360 --> 00:48:15,820
+أو لا عفو أن ال epsilon نفس ال epsilon zero هذه ال
+
+445
+00:48:15,820 --> 00:48:19,380
+epsilon هي نفس ال epsilon zeroهي عندي الـ Epsilon
+
+446
+00:48:19,380 --> 00:48:23,780
+Zero given لما أن ال sequence هي ال converge إذا
+
+447
+00:48:23,780 --> 00:48:28,400
+يوجد capital N واحد يعتمد على Epsilon Zero بحيث أن
+
+448
+00:48:28,400 --> 00:48:33,580
+أبسلوت الفرق هذا أصغر من أو يساوي Epsilon على اتنين
+
+449
+00:48:33,580 --> 00:48:37,140
+لكل K أكبر من أو يساوي capital K واحد أو capital N
+
+450
+00:48:37,140 --> 00:48:42,560
+واحد ونفس الحاجة لنفس ال Epsilon Zero يوجد N اتنين
+
+451
+00:48:43,830 --> 00:48:47,730
+بحيث أن بما أن هذه ال sequence converge إذا
+
+452
+00:48:47,730 --> 00:48:52,310
+الفرخة ده بقدر أخليه لكل n أكبر من أو لكل k أكبر
+
+453
+00:48:52,310 --> 00:48:56,630
+من أو يساوي n اتنين أصغر من ابسلون اتنين الآن خدي n
+
+454
+00:48:56,630 --> 00:49:05,410
+بساوي ال maximum ل n واحد و n اتنين فبقدر
+
+455
+00:49:05,410 --> 00:49:11,930
+أخلي هذا أصغر من ابسلون زيرو لكل k أكبر من أو يساوي
+
+456
+00:49:11,930 --> 00:49:16,590
+nففي النهاية بيطلع عندي epsilon zero أقل من
+
+457
+00:49:16,590 --> 00:49:19,650
+epsilon أصغر من epsilon zero هذا مديني
+
+458
+00:49:19,650 --> 00:49:23,590
+contradiction لأن هذا التناقض بيقول لي أن ال
+
+459
+00:49:23,590 --> 00:49:28,150
+assumption تبعنا أن ال function not uniformly
+
+460
+00:49:28,150 --> 00:49:32,050
+continuous كان assumption خطأ لأن الصح أن ال F
+
+461
+00:49:32,050 --> 00:49:37,810
+تكون uniformly continuous okay تمام واضح؟Okay إذا
+
+462
+00:49:37,810 --> 00:49:44,230
+بنوقف إن شاء الله هنا عند نهاية البرهان هذا و
+
+463
+00:49:44,230 --> 00:49:51,690
+بيكون هيك احنا يعني خلصنا جزء مش بسيط في section
+
+464
+00:49:51,690 --> 00:49:56,730
+خمسة أربعة و نكتفي بهذا القدر و يعطيكم ألف عافية و
+
+465
+00:49:56,730 --> 00:49:58,590
+شكرا لحسن أصغائكم 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..5eb0c3b53e2abe3ab8ee01d68b730903cd1f196d
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/JXFFuyzuuqA_raw.json
@@ -0,0 +1 @@
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24.74, "end": 24.92, "word": " ان", "probability": 0.42138671875}, {"start": 24.92, "end": 25.08, "word": " شاء", "probability": 0.966796875}, {"start": 25.08, "end": 25.16, "word": " الله", "probability": 0.9609375}, {"start": 25.16, "end": 25.36, "word": " مع", "probability": 0.9765625}, {"start": 25.36, "end": 25.78, "word": " بعض", "probability": 0.990234375}, {"start": 25.78, "end": 26.8, "word": " ال", "probability": 0.642578125}, {"start": 26.8, "end": 27.48, "word": " section", "probability": 0.85205078125}, {"start": 27.48, "end": 27.96, "word": " خمسة", "probability": 0.79583740234375}, {"start": 27.96, "end": 28.36, "word": " أربعة", "probability": 0.7877604166666666}], "temperature": 1.0}, {"id": 2, "seek": 5508, "start": 29.18, "end": 55.08, "text": "اللي بيتحدث عن موضوع ال uniform continuity أو الاتصال المنظم للدوال هحنحاول ناخد أكبر جزء ممكن من ال section الجزء المتبقي ممكن نكمله في المحاضرة الجاية يوم الأتنين فال .. خلّينا الأول نراجع .. نراجع تعريف الاتصال العادي", 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" اللي", "probability": 0.944580078125}, {"start": 662.47, "end": 662.77, "word": " هنا", "probability": 0.466064453125}, {"start": 662.77, "end": 664.19, "word": " نفس", "probability": 0.92333984375}, {"start": 664.19, "end": 665.23, "word": " القيمة", "probability": 0.97998046875}, {"start": 665.23, "end": 666.31, "word": " وبالتالي", "probability": 0.92041015625}, {"start": 666.31, "end": 666.67, "word": " الان", "probability": 0.798828125}, {"start": 666.67, "end": 666.89, "word": " اذا", "probability": 0.646484375}, {"start": 666.89, "end": 667.09, "word": " في", "probability": 0.80859375}, {"start": 667.09, "end": 667.39, "word": " عندي", "probability": 0.821533203125}, {"start": 667.39, "end": 668.03, "word": " انا", "probability": 0.800048828125}, {"start": 668.03, "end": 668.37, "word": " دي", "probability": 0.753173828125}, {"start": 668.37, "end": 668.97, "word": " epsilon", "probability": 0.958984375}, {"start": 668.97, "end": 670.95, "word": " لن", "probability": 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ال u على ال epsilon أو على النقطة وعلى ال epsilon تمام واضحة النقطة هذه طيب احنا خلينا نقبل ناشية ده المثال خلينا ناخد مثال تاني example 2", "tokens": [8297, 46811, 10943, 46599, 6027, 2655, 6027, 1829, 2423, 8289, 5296, 10721, 1829, 17889, 2423, 8289, 11778, 3224, 39894, 34268, 2304, 3215, 15844, 2423, 344, 15844, 2423, 17889, 34051, 15844, 28239, 47432, 3660, 4032, 3615, 23942, 2423, 17889, 46811, 10943, 4032, 46958, 5016, 3660, 28239, 47432, 3660, 29538, 23032, 1829, 3555, 1975, 5016, 8315, 16490, 1211, 9957, 995, 8717, 4587, 36150, 8717, 33599, 10632, 11778, 3224, 9673, 12984, 6027, 16490, 1211, 9957, 995, 8717, 47283, 3215, 50113, 6027, 6055, 7649, 1829, 1365, 568], "avg_logprob": -0.2563244005044301, "compression_ratio": 1.7921348314606742, "no_speech_prob": 0.0, "words": [{"start": 748.81, "end": 749.25, "word": "Okay", "probability": 0.3779296875}, {"start": 749.25, "end": 749.69, "word": " تمام", "probability": 0.911376953125}, {"start": 749.69, "end": 750.39, "word": " 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uniform", "probability": 0.42431640625}, {"start": 1145.82, "end": 1153.76, "word": " continuity", "probability": 0.82861328125}, {"start": 1153.76, "end": 1156.28, "word": " uniform", "probability": 0.5009765625}, {"start": 1156.28, "end": 1157.8, "word": " continuity", "probability": 0.91064453125}, {"start": 1157.8, "end": 1159.88, "word": " implies", "probability": 0.853515625}, {"start": 1159.88, "end": 1163.44, "word": " continuity", "probability": 0.861328125}], "temperature": 1.0}, {"id": 45, "seek": 119194, "start": 1167.24, "end": 1191.94, "text": "الاتصال المنتظر بيؤدي للاتصال العادى و البرهان واضح يعني بمعنى اخر لو في عندي function f from a to r و ال function كانت uniformly continuous فهذا بيؤدي ان f continuous فالبرهان ذلك", "tokens": [6027, 9307, 9381, 6027, 9673, 29399, 19913, 2288, 4724, 1829, 33604, 16254, 24976, 9307, 9381, 6027, 18863, 18513, 7578, 4032, 2423, 26890, 3224, 7649, 4032, 46958, 5016, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 1975, 34740, 45164, 8978, 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{"start": 1241.97, "end": 1242.23, "word": " هذه", "probability": 0.5224609375}, {"start": 1242.23, "end": 1242.37, "word": " ال", "probability": 0.96240234375}, {"start": 1242.37, "end": 1242.57, "word": " Delta", "probability": 0.91943359375}, {"start": 1242.57, "end": 1243.15, "word": " بتخلي", "probability": 0.9005533854166666}, {"start": 1243.15, "end": 1243.31, "word": " ال", "probability": 0.9697265625}, {"start": 1243.31, "end": 1243.73, "word": " implication", "probability": 0.98828125}, {"start": 1243.73, "end": 1244.09, "word": " هذه", "probability": 0.486083984375}, {"start": 1244.09, "end": 1244.89, "word": " تتحقق", "probability": 0.8908203125}, {"start": 1244.89, "end": 1246.95, "word": " نظرت؟", "probability": 0.594757080078125}, {"start": 1246.95, "end": 1247.93, "word": " لو", "probability": 0.8876953125}, {"start": 1247.93, "end": 1248.15, "word": " هذه", "probability": 0.61767578125}, {"start": 1248.15, "end": 1248.77, "word": " متحققة", "probability": 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uniform continuity criterion من هنا non uniform", "tokens": [28814, 2655, 9381, 6027, 995, 9154, 2655, 19913, 2304, 8032, 1863, 10721, 34740, 9673, 2288, 5016, 37977, 11778, 3224, 13412, 2407, 10632, 4032, 8032, 1863, 26890, 3224, 1863, 3224, 6156, 1211, 19452, 8978, 16247, 12610, 16490, 1211, 9957, 995, 9154, 16712, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 9452, 23807, 8717, 14851, 29399, 7435, 2107, 9452, 23807, 46691, 9154, 34105, 2107, 9452], "avg_logprob": -0.22445436366020688, "compression_ratio": 1.515923566878981, "no_speech_prob": 0.0, "words": [{"start": 1365.3, "end": 1366.16, "word": "إتصالا", "probability": 0.764013671875}, {"start": 1366.16, "end": 1366.72, "word": " منتظم", "probability": 0.7056884765625}, {"start": 1366.72, "end": 1367.48, "word": " هنأخر", "probability": 0.712188720703125}, {"start": 1367.48, "end": 1367.94, "word": " المرحلة", "probability": 0.732177734375}, {"start": 1367.94, "end": 1368.12, "word": " ده", "probability": 0.968505859375}, {"start": 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"tokens": [30092, 9452, 23807, 11101, 718, 283, 490, 257, 281, 367, 312, 257, 2445, 550], "avg_logprob": -0.44583332935969033, "compression_ratio": 1.0793650793650793, "no_speech_prob": 0.0, "words": [{"start": 1395.38, "end": 1395.82, "word": "non", "probability": 0.0750732421875}, {"start": 1395.82, "end": 1396.32, "word": " uniform", "probability": 0.50537109375}, {"start": 1396.32, "end": 1397.84, "word": " continuity", "probability": 0.7119140625}, {"start": 1397.84, "end": 1402.56, "word": " criteria", "probability": 0.79345703125}, {"start": 1402.56, "end": 1413.94, "word": " let", "probability": 0.28759765625}, {"start": 1413.94, "end": 1414.44, "word": " f", "probability": 0.64111328125}, {"start": 1414.44, "end": 1416.3, "word": " from", "probability": 0.880859375}, {"start": 1416.3, "end": 1416.76, "word": " a", "probability": 0.6513671875}, {"start": 1416.76, "end": 1416.96, "word": " to", "probability": 0.9697265625}, {"start": 1416.96, "end": 1417.44, "word": " r", "probability": 0.92333984375}, {"start": 1417.44, "end": 1418.82, "word": " be", "probability": 0.88818359375}, {"start": 1418.82, "end": 1419.1, "word": " a", "probability": 0.93603515625}, {"start": 1419.1, "end": 1419.62, "word": " function", "probability": 0.9794921875}, {"start": 1419.62, "end": 1421.24, "word": " then", "probability": 0.84716796875}], "temperature": 1.0}, {"id": 54, "seek": 145221, "start": 1424.15, "end": 1452.21, "text": "the following statements are equivalent واحد if is not uniformly continuous على المجال تبعها نين there exists epsilon zero أكبر من السفر", "tokens": [3322, 3480, 12363, 366, 10344, 36764, 24401, 498, 307, 406, 48806, 10957, 15844, 9673, 7435, 6027, 6055, 3555, 3615, 11296, 8717, 9957, 456, 8198, 17889, 4018, 5551, 4117, 26890, 9154, 21136, 5172, 2288], "avg_logprob": -0.23965992208789377, "compression_ratio": 1.1586206896551725, "no_speech_prob": 0.0, "words": [{"start": 1424.15, "end": 1424.55, "word": "the", "probability": 0.1131591796875}, {"start": 1424.55, "end": 1425.29, "word": " following", "probability": 0.86865234375}, {"start": 1425.29, "end": 1426.31, "word": " statements", "probability": 0.8818359375}, {"start": 1426.31, "end": 1426.91, "word": " are", "probability": 0.9638671875}, {"start": 1426.91, "end": 1428.87, "word": " equivalent", "probability": 0.9501953125}, {"start": 1428.87, "end": 1431.01, "word": " واحد", "probability": 0.89013671875}, {"start": 1431.01, "end": 1432.95, "word": " if", "probability": 0.62158203125}, {"start": 1432.95, "end": 1433.73, "word": " is", "probability": 0.89111328125}, {"start": 1433.73, "end": 1435.77, "word": " not", "probability": 0.9521484375}, {"start": 1435.77, "end": 1438.81, "word": " uniformly", "probability": 0.9609375}, {"start": 1438.81, "end": 1440.39, "word": " continuous", "probability": 0.88232421875}, {"start": 1440.39, "end": 1442.93, "word": " على", "probability": 0.818359375}, {"start": 1442.93, "end": 1443.77, "word": " المجال", "probability": 0.97119140625}, {"start": 1443.77, "end": 1444.93, "word": " تبعها", "probability": 0.9598388671875}, {"start": 1444.93, "end": 1447.09, "word": " نين", "probability": 0.5706787109375}, {"start": 1447.09, "end": 1448.85, "word": " there", "probability": 0.88720703125}, {"start": 1448.85, "end": 1449.51, "word": " exists", "probability": 0.450439453125}, {"start": 1449.51, "end": 1450.37, "word": " epsilon", "probability": 0.56982421875}, {"start": 1450.37, "end": 1450.89, "word": " zero", "probability": 0.79443359375}, {"start": 1450.89, "end": 1451.39, "word": " أكبر", "probability": 0.923828125}, {"start": 1451.39, "end": 1451.63, "word": " من", "probability": 0.98681640625}, {"start": 1451.63, "end": 1452.21, "word": " السفر", "probability": 0.8181966145833334}], "temperature": 1.0}, {"id": 55, "seek": 148120, "start": 1454.4, "end": 1481.2, "text": "such that for every delta أكبر من السفر يوجد x delta و u delta أناصر في a such that absolute x delta minus u delta أصغر من delta and absolute f of x delta", "tokens": [39974, 300, 337, 633, 8289, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 7251, 29245, 3215, 2031, 8289, 4032, 344, 8289, 14739, 33546, 2288, 8978, 257, 1270, 300, 8236, 2031, 8289, 3175, 344, 8289, 5551, 9381, 17082, 2288, 9154, 8289, 293, 8236, 283, 295, 2031, 8289], "avg_logprob": -0.19344429606976715, "compression_ratio": 1.4409448818897639, "no_speech_prob": 0.0, "words": [{"start": 1454.4, "end": 1455.04, "word": "such", "probability": 0.25341796875}, {"start": 1455.04, "end": 1455.66, "word": " that", "probability": 0.95556640625}, {"start": 1455.66, "end": 1456.84, "word": " for", "probability": 0.91845703125}, {"start": 1456.84, "end": 1457.38, "word": " every", "probability": 0.79248046875}, {"start": 1457.38, "end": 1458.04, "word": " delta", "probability": 0.470703125}, {"start": 1458.04, "end": 1459.6, "word": " أكبر", "probability": 0.923828125}, {"start": 1459.6, "end": 1459.88, "word": " من", "probability": 0.9951171875}, {"start": 1459.88, "end": 1460.68, "word": " السفر", "probability": 0.84326171875}, {"start": 1460.68, "end": 1462.36, "word": " يوجد", "probability": 0.96484375}, {"start": 1462.36, "end": 1462.7, "word": " x", "probability": 0.55908203125}, {"start": 1462.7, "end": 1463.28, "word": " delta", "probability": 0.47265625}, {"start": 1463.28, "end": 1464.72, "word": " و", "probability": 0.9609375}, {"start": 1464.72, "end": 1465.0, "word": " u", "probability": 0.5537109375}, {"start": 1465.0, "end": 1465.54, "word": " delta", "probability": 0.8349609375}, {"start": 1465.54, "end": 1466.62, "word": " أناصر", "probability": 0.760498046875}, {"start": 1466.62, "end": 1468.04, "word": " في", "probability": 0.92333984375}, {"start": 1468.04, "end": 1468.62, "word": " a", "probability": 0.6044921875}, {"start": 1468.62, "end": 1470.32, "word": " such", "probability": 0.95166015625}, {"start": 1470.32, "end": 1470.96, "word": " that", "probability": 0.95361328125}, {"start": 1470.96, "end": 1471.84, "word": " absolute", "probability": 0.84033203125}, {"start": 1471.84, "end": 1472.54, "word": " x", "probability": 0.98876953125}, {"start": 1472.54, "end": 1473.14, "word": " delta", "probability": 0.9287109375}, {"start": 1473.14, "end": 1473.8, "word": " minus", "probability": 0.9541015625}, {"start": 1473.8, "end": 1475.06, "word": " u", "probability": 0.98095703125}, {"start": 1475.06, "end": 1475.62, "word": " delta", "probability": 0.943359375}, {"start": 1475.62, "end": 1476.22, "word": " أصغر", "probability": 0.9866943359375}, {"start": 1476.22, "end": 1476.42, "word": " من", "probability": 0.99462890625}, {"start": 1476.42, "end": 1476.82, "word": " delta", "probability": 0.40576171875}, {"start": 1476.82, "end": 1478.32, "word": " and", "probability": 0.92626953125}, {"start": 1478.32, "end": 1479.08, "word": " absolute", "probability": 0.93505859375}, {"start": 1479.08, "end": 1479.86, "word": " f", "probability": 0.7333984375}, {"start": 1479.86, "end": 1480.16, "word": " of", "probability": 0.912109375}, {"start": 1480.16, "end": 1480.62, "word": " x", "probability": 0.9931640625}, {"start": 1480.62, "end": 1481.2, "word": " delta", "probability": 0.9423828125}], "temperature": 1.0}, {"id": 56, "seek": 150620, "start": 1482.3, "end": 1506.2, "text": "-f of u دلتا أكبر من أو يساوي epsilon zero الأبارع التالتة there exist epsilon zero أكبر من الصفر and two sequences متتاليتين xn", "tokens": [12, 69, 295, 344, 11778, 1211, 2655, 995, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 17889, 4018, 16247, 3555, 9640, 3615, 16712, 6027, 2655, 3660, 456, 2514, 17889, 4018, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 293, 732, 22978, 44650, 2655, 6027, 36081, 9957, 2031, 77], "avg_logprob": -0.3026148056497379, "compression_ratio": 1.2971014492753623, "no_speech_prob": 0.0, "words": [{"start": 1482.3, "end": 1483.56, "word": "-f", "probability": 0.2142333984375}, {"start": 1483.56, "end": 1483.98, "word": " of", "probability": 0.52587890625}, {"start": 1483.98, "end": 1484.38, "word": " u", "probability": 0.779296875}, {"start": 1484.38, "end": 1485.16, "word": " دلتا", "probability": 0.72760009765625}, {"start": 1485.16, "end": 1486.72, "word": " أكبر", "probability": 0.8855794270833334}, {"start": 1486.72, "end": 1486.96, "word": " من", "probability": 0.8525390625}, {"start": 1486.96, "end": 1487.22, "word": " أو", "probability": 0.966796875}, {"start": 1487.22, "end": 1488.06, "word": " يساوي", "probability": 0.8670654296875}, {"start": 1488.06, "end": 1488.54, "word": " epsilon", "probability": 0.216064453125}, {"start": 1488.54, "end": 1489.12, "word": " zero", "probability": 0.5966796875}, {"start": 1489.12, "end": 1493.16, "word": " الأبارع", "probability": 0.74273681640625}, {"start": 1493.16, "end": 1493.9, "word": " التالتة", "probability": 0.903076171875}, {"start": 1493.9, "end": 1494.32, "word": " there", "probability": 0.513671875}, {"start": 1494.32, "end": 1494.88, "word": " exist", "probability": 0.63671875}, {"start": 1494.88, "end": 1496.72, "word": " epsilon", "probability": 0.72509765625}, {"start": 1496.72, "end": 1497.28, "word": " zero", "probability": 0.88427734375}, {"start": 1497.28, "end": 1497.68, "word": " أكبر", "probability": 0.9723307291666666}, {"start": 1497.68, "end": 1497.86, "word": " من", "probability": 0.92138671875}, {"start": 1497.86, "end": 1498.48, "word": " الصفر", "probability": 0.6974283854166666}, {"start": 1498.48, "end": 1500.02, "word": " and", "probability": 0.71923828125}, {"start": 1500.02, "end": 1500.66, "word": " two", "probability": 0.91455078125}, {"start": 1500.66, "end": 1502.18, "word": " sequences", "probability": 0.93359375}, {"start": 1502.18, "end": 1504.12, "word": " متتاليتين", "probability": 0.91083984375}, {"start": 1504.12, "end": 1506.2, "word": " xn", "probability": 0.61376953125}], "temperature": 1.0}, {"id": 57, "seek": 152569, "start": 1507.63, "end": 1525.69, "text": "و un موجودين في مجال الدالة a such that بحيث ان limit xn minus un بساوي سفر as n tends to infinity and", "tokens": [2407, 517, 3714, 29245, 23328, 9957, 8978, 3714, 7435, 6027, 32748, 6027, 3660, 257, 1270, 300, 4724, 5016, 1829, 12984, 16472, 4948, 2031, 77, 3175, 517, 4724, 3794, 995, 45865, 8608, 5172, 2288, 382, 297, 12258, 281, 13202, 293], "avg_logprob": -0.34316405430436137, "compression_ratio": 1.152542372881356, "no_speech_prob": 0.0, "words": [{"start": 1507.63, "end": 1508.01, "word": "و", "probability": 0.30859375}, {"start": 1508.01, "end": 1508.83, "word": " un", "probability": 0.08709716796875}, {"start": 1508.83, "end": 1510.91, "word": " موجودين", "probability": 0.9041748046875}, {"start": 1510.91, "end": 1511.07, "word": " في", "probability": 0.93359375}, {"start": 1511.07, "end": 1511.51, "word": " مجال", "probability": 0.9837239583333334}, {"start": 1511.51, "end": 1512.09, "word": " الدالة", "probability": 0.7981770833333334}, {"start": 1512.09, "end": 1512.45, "word": " a", "probability": 0.41796875}, {"start": 1512.45, 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1721.96, "word": " ال", "probability": 0.75341796875}, {"start": 1721.96, "end": 1722.48, "word": " function", "probability": 0.7333984375}], "temperature": 1.0}, {"id": 66, "seek": 174927, "start": 1723.61, "end": 1749.27, "text": "f of x بالساوي واحد على x is not uniformly continuous على المجموعة a اللي هي الفافرة مفتوحة من صفر لما لا نهاية we use non uniform", "tokens": [69, 295, 2031, 20666, 3794, 995, 45865, 36764, 24401, 15844, 2031, 307, 406, 48806, 10957, 15844, 9673, 7435, 2304, 2407, 27884, 257, 13672, 1829, 39896, 27188, 31845, 25720, 3714, 5172, 2655, 2407, 5016, 3660, 9154, 20328, 5172, 2288, 5296, 15042, 20193, 8717, 11296, 10632, 321, 764, 2107, 9452], "avg_logprob": -0.31521045918367346, "compression_ratio": 1.3309859154929577, "no_speech_prob": 0.0, "words": [{"start": 1723.61, "end": 1723.97, "word": "f", "probability": 0.1800537109375}, {"start": 1723.97, "end": 1724.23, "word": " of", "probability": 0.630859375}, {"start": 1724.23, "end": 1724.57, "word": " x", "probability": 0.95166015625}, {"start": 1724.57, "end": 1725.33, "word": " بالساوي", "probability": 0.642578125}, {"start": 1725.33, "end": 1725.83, "word": " واحد", "probability": 0.827392578125}, {"start": 1725.83, "end": 1725.97, "word": " على", "probability": 0.363037109375}, {"start": 1725.97, "end": 1726.31, "word": " x", "probability": 0.387939453125}, {"start": 1726.31, "end": 1726.71, "word": " is", "probability": 0.8583984375}, {"start": 1726.71, "end": 1727.13, "word": " not", "probability": 0.96044921875}, {"start": 1727.13, "end": 1731.19, "word": " uniformly", "probability": 0.8115234375}, {"start": 1731.19, "end": 1732.95, "word": " continuous", "probability": 0.90673828125}, {"start": 1732.95, "end": 1734.67, "word": " على", "probability": 0.72119140625}, {"start": 1734.67, "end": 1736.83, "word": " المجموعة", "probability": 0.9498046875}, {"start": 1736.83, "end": 1737.15, "word": " a", "probability": 0.65478515625}, {"start": 1737.15, "end": 1737.51, "word": " اللي", "probability": 0.5379638671875}, {"start": 1737.51, "end": 1737.75, "word": " هي", "probability": 0.82275390625}, {"start": 1737.75, "end": 1738.19, "word": " الفافرة", "probability": 0.9090169270833334}, {"start": 1738.19, "end": 1738.75, "word": " مفتوحة", "probability": 0.9805501302083334}, {"start": 1738.75, "end": 1738.93, "word": " من", "probability": 0.9775390625}, {"start": 1738.93, "end": 1739.35, "word": " صفر", "probability": 0.7818196614583334}, {"start": 1739.35, "end": 1739.63, "word": " لما", "probability": 0.41455078125}, {"start": 1739.63, "end": 1739.75, "word": " لا", "probability": 0.459228515625}, {"start": 1739.75, "end": 1740.43, "word": " نهاية", "probability": 0.8460286458333334}, {"start": 1740.43, "end": 1741.75, "word": " we", "probability": 0.63232421875}, {"start": 1741.75, "end": 1742.29, "word": " use", "probability": 0.90185546875}, {"start": 1742.29, "end": 1747.01, "word": " non", "probability": 0.482666015625}, {"start": 1747.01, "end": 1749.27, "word": " uniform", "probability": 0.6455078125}], "temperature": 1.0}, {"id": 67, "seek": 176189, "start": 1751.05, "end": 1761.89, "text": "Non-uniform continuity criteria", "tokens": [47914, 12, 409, 8629, 23807, 11101], "avg_logprob": -0.6696428571428571, "compression_ratio": 0.7948717948717948, "no_speech_prob": 0.0, "words": [{"start": 1751.05, "end": 1751.53, "word": "Non", "probability": 0.2325439453125}, {"start": 1751.53, "end": 1752.35, "word": "-uniform", "probability": 0.7232259114583334}, {"start": 1752.35, "end": 1756.39, "word": " continuity", "probability": 0.6533203125}, {"start": 1756.39, "end": 1761.89, "word": " criteria", "probability": 0.8134765625}], "temperature": 1.0}, {"id": 68, "seek": 178987, "start": 1777.15, "end": 1789.87, "text": "يوجد أبسلون زيرو يوجد عدد أبسلون زيرو موجد", "tokens": [1829, 29245, 3215, 5551, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 7251, 29245, 3215, 6225, 3215, 3215, 5551, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 3714, 29245, 3215], "avg_logprob": -0.41729527095268515, "compression_ratio": 1.4528301886792452, "no_speech_prob": 0.0, "words": [{"start": 1777.15, "end": 1778.25, "word": "يوجد", "probability": 0.705322265625}, {"start": 1778.25, "end": 1778.71, "word": " أبسلون", "probability": 0.7775390625}, {"start": 1778.71, "end": 1779.21, "word": " زيرو", "probability": 0.725341796875}, {"start": 1779.21, "end": 1787.31, "word": " يوجد", "probability": 0.4886881510416667}, {"start": 1787.31, "end": 1788.41, "word": " عدد", "probability": 0.85107421875}, {"start": 1788.41, "end": 1788.97, "word": " أبسلون", "probability": 0.90126953125}, {"start": 1788.97, "end": 1789.33, "word": " زيرو", "probability": 0.87060546875}, {"start": 1789.33, "end": 1789.87, "word": " موجد", "probability": 0.727783203125}], "temperature": 1.0}, {"id": 69, "seek": 182965, "start": 1807.55, "end": 1829.65, "text": "تختار خيار Xm بساوي واحد على ان اكيد هذه ال sequence contain في الفترة المفتوحة من سفر للملا نهاية صح؟ and كمان تختار خيار ثاني UN بساوي واحد على ان زايد واحد", "tokens": [2655, 46456, 9640, 16490, 1829, 9640, 1783, 76, 4724, 3794, 995, 45865, 36764, 24401, 15844, 16472, 1975, 4117, 25708, 29538, 2423, 8310, 5304, 8978, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 19528, 15040, 8717, 11296, 10632, 20328, 5016, 22807, 293, 9122, 2304, 7649, 6055, 46456, 9640, 16490, 1829, 9640, 38637, 7649, 1829, 8229, 4724, 3794, 995, 45865, 36764, 24401, 15844, 16472, 30767, 995, 25708, 36764, 24401], "avg_logprob": -0.441300668023728, "compression_ratio": 1.6134969325153374, "no_speech_prob": 0.0, "words": [{"start": 1807.55, "end": 1808.53, "word": "تختار", "probability": 0.5718180338541666}, {"start": 1808.53, "end": 1809.51, "word": " خيار", "probability": 0.607421875}, {"start": 1809.51, "end": 1810.65, "word": " Xm", "probability": 0.26171875}, {"start": 1810.65, "end": 1813.09, "word": " بساوي", "probability": 0.4987640380859375}, {"start": 1813.09, "end": 1813.63, 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1819.31, "word": " سفر", "probability": 0.7841796875}, {"start": 1819.31, "end": 1819.63, "word": " للملا", "probability": 0.5801595052083334}, {"start": 1819.63, "end": 1820.19, "word": " نهاية", "probability": 0.9000651041666666}, {"start": 1820.19, "end": 1821.41, "word": " صح؟", "probability": 0.6200358072916666}, {"start": 1821.41, "end": 1823.11, "word": " and", "probability": 0.218994140625}, {"start": 1823.11, "end": 1823.59, "word": " كمان", "probability": 0.7522786458333334}, {"start": 1823.59, "end": 1824.23, "word": " تختار", "probability": 0.8356119791666666}, {"start": 1824.23, "end": 1824.79, "word": " خيار", "probability": 0.779541015625}, {"start": 1824.79, "end": 1825.35, "word": " ثاني", "probability": 0.72265625}, {"start": 1825.35, "end": 1825.85, "word": " UN", "probability": 0.1611328125}, {"start": 1825.85, "end": 1827.03, "word": " بساوي", "probability": 0.928466796875}, {"start": 1827.03, "end": 1828.21, "word": " واحد", "probability": 0.96826171875}, {"start": 1828.21, "end": 1828.41, "word": " على", "probability": 0.7802734375}, {"start": 1828.41, "end": 1828.77, "word": " ان", "probability": 0.84033203125}, {"start": 1828.77, "end": 1829.23, "word": " زايد", "probability": 0.754638671875}, {"start": 1829.23, "end": 1829.65, "word": " واحد", "probability": 0.989013671875}], "temperature": 1.0}, {"id": 70, "seek": 185747, "start": 1831.19, "end": 1857.47, "text": "برضه هذه ال sequence حدودها كلها موزبة وبالتالي مجموعة جزئية من الفترة المفتوحة من سفر لملنغا Clearly واضح ان ال limit ل xn minus un as n times infinity بساوي limit", "tokens": [3555, 43042, 3224, 29538, 2423, 8310, 11331, 3215, 23328, 11296, 28242, 11296, 3714, 2407, 11622, 49401, 46599, 6027, 2655, 6027, 1829, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 9154, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 5172, 2288, 5296, 42213, 1863, 17082, 995, 24120, 4032, 46958, 5016, 16472, 2423, 4948, 5296, 2031, 77, 3175, 517, 382, 297, 1413, 13202, 4724, 3794, 995, 45865, 4948], "avg_logprob": -0.27662853539829524, "compression_ratio": 1.3932584269662922, "no_speech_prob": 0.0, "words": [{"start": 1831.19, "end": 1831.71, "word": "برضه", "probability": 0.5643717447916666}, {"start": 1831.71, "end": 1832.03, "word": " هذه", "probability": 0.6416015625}, {"start": 1832.03, "end": 1832.13, "word": " ال", "probability": 0.8212890625}, {"start": 1832.13, "end": 1832.39, "word": " sequence", "probability": 0.396240234375}, {"start": 1832.39, "end": 1833.01, "word": " حدودها", "probability": 0.9847412109375}, {"start": 1833.01, "end": 1833.37, "word": " كلها", "probability": 0.954833984375}, {"start": 1833.37, "end": 1833.81, "word": " موزبة", "probability": 0.6605224609375}, {"start": 1833.81, "end": 1834.47, "word": " وبالتالي", "probability": 0.91318359375}, {"start": 1834.47, "end": 1834.93, "word": " مجموعة", "probability": 0.91416015625}, {"start": 1834.93, "end": 1835.63, "word": " جزئية", "probability": 0.9580078125}, {"start": 1835.63, "end": 1836.57, "word": " من", "probability": 0.95068359375}, {"start": 1836.57, "end": 1837.07, "word": " الفترة", "probability": 0.9892578125}, {"start": 1837.07, "end": 1837.57, "word": " المفتوحة", "probability": 0.97216796875}, {"start": 1837.57, "end": 1837.73, "word": " من", "probability": 0.9599609375}, {"start": 1837.73, "end": 1838.07, "word": " سفر", "probability": 0.7200520833333334}, {"start": 1838.07, "end": 1838.73, "word": " لملنغا", "probability": 0.630126953125}, {"start": 1838.73, "end": 1841.83, "word": " Clearly", "probability": 0.1761474609375}, {"start": 1841.83, "end": 1845.29, "word": " واضح", "probability": 0.9562174479166666}, {"start": 1845.29, "end": 1846.49, "word": " ان", "probability": 0.57568359375}, {"start": 1846.49, "end": 1846.65, "word": " ال", "probability": 0.5}, {"start": 1846.65, "end": 1847.01, "word": " limit", "probability": 0.9462890625}, {"start": 1847.01, "end": 1848.81, "word": " ل", "probability": 0.84375}, {"start": 1848.81, "end": 1849.65, "word": " xn", "probability": 0.44677734375}, {"start": 1849.65, "end": 1850.43, "word": " minus", "probability": 0.666015625}, {"start": 1850.43, "end": 1851.43, "word": " un", "probability": 0.78369140625}, {"start": 1851.43, "end": 1852.95, "word": " as", "probability": 0.791015625}, {"start": 1852.95, "end": 1853.31, "word": " n", "probability": 0.5205078125}, {"start": 1853.31, "end": 1853.57, "word": " times", "probability": 0.28955078125}, {"start": 1853.57, "end": 1854.33, "word": " infinity", "probability": 0.71728515625}, {"start": 1854.33, "end": 1856.91, "word": " بساوي", "probability": 0.781005859375}, {"start": 1856.91, "end": 1857.47, "word": " limit", "probability": 0.939453125}], "temperature": 1.0}, {"id": 71, "seek": 188402, "start": 1859.02, "end": 1884.02, "text": "1 على n minus 1 على n زاد 1 as n equals infinity ف limit الأولى ساوي سفر limit ال sequence التانية سفر وبالتالي بيطلع سفر لأن هنا حققت كل شروط ضايل بس المتبينة هادية also", "tokens": [16, 15844, 297, 3175, 502, 15844, 297, 30767, 18513, 502, 382, 297, 6915, 13202, 6156, 4948, 16247, 12610, 7578, 8608, 995, 45865, 8608, 5172, 2288, 4948, 2423, 8310, 16712, 7649, 10632, 8608, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 4724, 1829, 9566, 1211, 3615, 8608, 5172, 2288, 5296, 33456, 34105, 11331, 4587, 38149, 28242, 13412, 32887, 9566, 48812, 995, 26895, 4724, 3794, 9673, 2655, 3555, 9957, 3660, 8032, 18513, 10632, 611], "avg_logprob": -0.3383246531916989, "compression_ratio": 1.4628571428571429, "no_speech_prob": 0.0, "words": [{"start": 1859.02, "end": 1859.54, "word": "1", "probability": 0.07965087890625}, {"start": 1859.54, "end": 1859.92, "word": " على", "probability": 0.324951171875}, {"start": 1859.92, "end": 1860.2, "word": " n", "probability": 0.36181640625}, {"start": 1860.2, "end": 1860.76, "word": " minus", "probability": 0.244384765625}, {"start": 1860.76, "end": 1861.3, "word": " 1", "probability": 0.74560546875}, {"start": 1861.3, "end": 1862.58, "word": " على", "probability": 0.57958984375}, {"start": 1862.58, "end": 1862.84, "word": " n", "probability": 0.83740234375}, {"start": 1862.84, "end": 1863.2, "word": " زاد", "probability": 0.736083984375}, {"start": 1863.2, "end": 1863.6, "word": " 1", "probability": 0.80078125}, {"start": 1863.6, "end": 1864.1, "word": " as", "probability": 0.455322265625}, {"start": 1864.1, "end": 1864.42, "word": " n", "probability": 0.79541015625}, {"start": 1864.42, "end": 1864.72, "word": " equals", "probability": 0.1982421875}, {"start": 1864.72, "end": 1865.36, "word": " infinity", "probability": 0.86279296875}, {"start": 1865.36, "end": 1866.42, "word": " ف", "probability": 0.80712890625}, {"start": 1866.42, "end": 1866.7, "word": " limit", "probability": 0.57666015625}, {"start": 1866.7, "end": 1868.22, "word": " الأولى", "probability": 0.9557291666666666}, {"start": 1868.22, "end": 1869.18, "word": " ساوي", "probability": 0.5824381510416666}, {"start": 1869.18, "end": 1869.74, "word": " 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I", "probability": 0.5234375}, {"start": 2453.73, "end": 2455.39, "word": " موجودين", "probability": 0.6328582763671875}, {"start": 2455.39, "end": 2455.53, "word": " في", "probability": 0.73095703125}, {"start": 2455.53, "end": 2457.43, "word": " I", "probability": 0.260986328125}, {"start": 2457.43, "end": 2462.55, "word": " موجودين", "probability": 0.7930908203125}, {"start": 2462.55, "end": 2462.55, "word": " في", "probability": 0.89453125}, {"start": 2462.55, "end": 2462.55, "word": " I", "probability": 0.8955078125}, {"start": 2462.55, "end": 2464.19, "word": " موجودين", "probability": 0.8460693359375}, {"start": 2464.19, "end": 2465.71, "word": " في", "probability": 0.98291015625}, {"start": 2465.71, "end": 2467.79, "word": " I", "probability": 0.98046875}], "temperature": 1.0}, {"id": 94, "seek": 248825, "start": 2468.63, "end": 2488.25, "text": "الـ subsequence UN برضه لها subsequence مشابهة وconvergent لنفس الـ Z هذا مش واضح لثبته لثباته to see this to see this note that", 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"probability": 0.7666015625}, {"start": 2574.15, "end": 2574.31, "word": " to", "probability": 0.9736328125}, {"start": 2574.31, "end": 2574.71, "word": " infinity", "probability": 0.892578125}], "temperature": 1.0}, {"id": 98, "seek": 259477, "start": 2576.09, "end": 2594.77, "text": "وهذا أكبر من سفر، إذن by squeeze theorem ال sequence هذه محصورة بين ال sequence هذه بالسفر ومجموعة two sequences بيقولوا للسفر", "tokens": [2407, 3224, 15730, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 12399, 11933, 8848, 1863, 538, 13578, 20904, 2423, 8310, 29538, 3714, 5016, 9381, 13063, 3660, 49374, 2423, 8310, 29538, 20666, 3794, 5172, 2288, 4032, 2304, 7435, 2304, 2407, 27884, 732, 22978, 4724, 1829, 39648, 14407, 24976, 3794, 5172, 2288], "avg_logprob": -0.256718755364418, "compression_ratio": 1.3955223880597014, "no_speech_prob": 0.0, "words": [{"start": 2576.09, "end": 2576.63, "word": "وهذا", "probability": 0.6790364583333334}, {"start": 2576.63, "end": 2577.11, "word": " أكبر", "probability": 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"probability": 0.47314453125}, {"start": 2963.45, "end": 2963.59, "word": " ال", "probability": 0.9287109375}, {"start": 2963.59, "end": 2964.15, "word": " assumption", "probability": 0.94189453125}, {"start": 2964.15, "end": 2964.97, "word": " تبعنا", "probability": 0.9351806640625}, {"start": 2964.97, "end": 2966.31, "word": " أن", "probability": 0.5234375}, {"start": 2966.31, "end": 2966.47, "word": " ال", "probability": 0.97900390625}, {"start": 2966.47, "end": 2967.01, "word": " function", "probability": 0.9345703125}, {"start": 2967.01, "end": 2967.43, "word": " not", "probability": 0.7958984375}, {"start": 2967.43, "end": 2968.15, "word": " uniformly", "probability": 0.92724609375}, {"start": 2968.15, "end": 2968.79, "word": " continuous", "probability": 0.87548828125}, {"start": 2968.79, "end": 2969.37, "word": " كان", "probability": 0.7763671875}, {"start": 2969.37, "end": 2970.43, "word": " assumption", "probability": 0.525390625}, {"start": 2970.43, "end": 2970.95, "word": " خطأ", "probability": 0.8958333333333334}, {"start": 2970.95, "end": 2971.21, "word": " لأن", "probability": 0.4219970703125}, {"start": 2971.21, "end": 2971.65, "word": " الصح", "probability": 0.899658203125}, {"start": 2971.65, "end": 2971.83, "word": " أن", "probability": 0.440673828125}, {"start": 2971.83, "end": 2971.87, "word": " ال", "probability": 0.5419921875}, {"start": 2971.87, "end": 2972.05, "word": " F", "probability": 0.5078125}, {"start": 2972.05, "end": 2972.55, "word": " تكون", "probability": 0.970947265625}, {"start": 2972.55, "end": 2973.67, "word": " uniformly", "probability": 0.978515625}, {"start": 2973.67, "end": 2974.59, "word": " continuous", "probability": 0.9150390625}, {"start": 2974.59, "end": 2975.07, "word": " okay", "probability": 0.31396484375}, {"start": 2975.07, "end": 2975.59, "word": " تمام", "probability": 0.931396484375}, {"start": 2975.59, "end": 2976.73, "word": " واضح؟", "probability": 0.9007568359375}], "temperature": 1.0}, {"id": 114, "seek": 299859, "start": 2977.05, "end": 2998.59, "text": "Okay إذا بنوقف ان شاء الله هنا عند نهاية البرهان هذا و بيكون هيك احنا يعني خلصنا جزء مش بسيط في section خمسة أربعة و نكتفي بهذا القدر و يعطيكم ألف عافية و شكرا لحصن أصغائكم", "tokens": [8297, 11933, 15730, 44945, 30543, 5172, 16472, 13412, 16606, 21984, 34105, 43242, 8717, 11296, 10632, 2423, 26890, 3224, 7649, 23758, 4032, 4724, 1829, 30544, 39896, 4117, 1975, 5016, 8315, 37495, 22653, 16490, 1211, 9381, 8315, 10874, 11622, 38207, 37893, 4724, 3794, 1829, 9566, 8978, 3541, 16490, 2304, 3794, 3660, 5551, 25513, 27884, 4032, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288, 4032, 37495, 9566, 1829, 24793, 5551, 46538, 6225, 31845, 10632, 4032, 13412, 4117, 23557, 5296, 5016, 9381, 1863, 5551, 9381, 17082, 16373, 24793], "avg_logprob": -0.14089752941630607, "compression_ratio": 1.544041450777202, "no_speech_prob": 0.0, "words": [{"start": 2977.05, "end": 2977.53, "word": "Okay", "probability": 0.91162109375}, {"start": 2977.53, "end": 2977.81, "word": " إذا", "probability": 0.7275390625}, {"start": 2977.81, "end": 2978.91, "word": " بنوقف", "probability": 0.8439127604166666}, {"start": 2978.91, "end": 2979.05, "word": " ان", "probability": 0.5244140625}, {"start": 2979.05, "end": 2979.27, "word": " شاء", "probability": 0.983642578125}, {"start": 2979.27, "end": 2979.35, "word": " الله", "probability": 0.9609375}, {"start": 2979.35, "end": 2980.05, "word": " هنا", "probability": 0.96435546875}, {"start": 2980.05, "end": 2981.05, "word": " عند", "probability": 0.93994140625}, {"start": 2981.05, "end": 2982.11, "word": " نهاية", "probability": 0.97607421875}, {"start": 2982.11, "end": 2982.65, "word": " البرهان", "probability": 0.8861083984375}, {"start": 2982.65, "end": 2983.13, "word": " هذا", "probability": 0.65673828125}, {"start": 2983.13, "end": 2984.23, "word": " و", "probability": 0.861328125}, {"start": 2984.23, "end": 2985.05, "word": " بيكون", "probability": 0.87451171875}, {"start": 2985.05, "end": 2985.35, "word": " هيك", "probability": 0.58819580078125}, {"start": 2985.35, "end": 2985.61, "word": " احنا", "probability": 0.8902994791666666}, {"start": 2985.61, "end": 2986.13, "word": " يعني", "probability": 0.9267578125}, {"start": 2986.13, "end": 2987.23, "word": " خلصنا", "probability": 0.9927978515625}, {"start": 2987.23, "end": 2988.23, "word": " جزء", "probability": 0.94287109375}, {"start": 2988.23, "end": 2989.39, "word": " مش", "probability": 0.9970703125}, {"start": 2989.39, "end": 2990.65, "word": " بسيط", "probability": 0.99755859375}, {"start": 2990.65, "end": 2991.39, "word": " في", "probability": 0.85888671875}, {"start": 2991.39, "end": 2991.69, "word": " section", "probability": 0.82763671875}, {"start": 2991.69, "end": 2992.15, "word": " خمسة", "probability": 0.8548583984375}, {"start": 2992.15, "end": 2992.63, "word": " أربعة", "probability": 0.8828125}, {"start": 2992.63, "end": 2993.01, "word": " و", "probability": 0.982421875}, {"start": 2993.01, "end": 2993.73, "word": " نكتفي", "probability": 0.849609375}, {"start": 2993.73, "end": 2994.03, "word": " بهذا", "probability": 0.963134765625}, {"start": 2994.03, "end": 2994.49, "word": " القدر", "probability": 0.9951171875}, {"start": 2994.49, "end": 2994.59, "word": " و", "probability": 0.91357421875}, {"start": 2994.59, "end": 2995.03, "word": " يعطيكم", "probability": 0.93310546875}, {"start": 2995.03, "end": 2995.29, "word": " ألف", "probability": 0.703857421875}, {"start": 2995.29, "end": 2995.75, "word": " عافية", "probability": 0.9669596354166666}, {"start": 2995.75, "end": 2996.73, "word": " و", "probability": 0.98583984375}, {"start": 2996.73, "end": 2997.17, "word": " شكرا", "probability": 0.9391276041666666}, {"start": 2997.17, "end": 2997.97, "word": " لحصن", "probability": 0.834228515625}, {"start": 2997.97, "end": 2998.59, "word": " أصغائكم", "probability": 0.8009765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2999.55375, "duration_after_vad": 2793.5409687499914}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d80def903c6ad0e18a70f04ea69b7b6f8a4d6fdb
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk.srt
@@ -0,0 +1,1616 @@
+1
+00:00:20,650 --> 00:00:26,490
+طبعًا إحنا زي ما اتفقنا معاكم هنعمل
+
+2
+00:00:26,490 --> 00:00:36,030
+مناقشة للـ course  و هنبدأ طبعًا بـ chapter  اتنين اللي 
+
+3
+00:00:36,030 --> 00:00:42,270
+هو أول chapter درسناه و هنبدأ بـ section اتنين واحد
+
+4
+00:00:42,270 --> 00:00:46,270
+و إذا في واجب طبعًا هنحاول نجاوب على أسئلة في
+
+5
+00:00:46,270 --> 00:00:47,190
+section اتنين اتنين
+
+6
+00:00:50,880 --> 00:00:55,480
+أطمئن عليكم أنه يعني طبعًا الأسئلة عددها كبير و مش 
+
+7
+00:00:55,480 --> 00:01:00,980
+هنلحق نحل كل المسائل لكن أطمئن عليكم إنكم تسألوا
+
+8
+00:01:00,980 --> 00:01:06,020
+الأسئلة اللي أنتو يعني وجدتوا فيها صعوبة في حالها
+
+9
+00:01:06,020 --> 00:01:10,000
+حتى 
+
+10
+00:01:10,000 --> 00:01:17,240
+تكون يعني الفائدة تعمق أكثر فنبدأ بـ section 2 1 هل
+
+11
+00:01:17,240 --> 00:01:23,860
+في أي سؤال في section 2 1 حاولتوا تحلوه ما عرفتووش 
+
+12
+00:01:23,860 --> 00:01:33,540
+تحلوه أو وجدته صعوبة في حاله ففي
+
+13
+00:01:33,540 --> 00:01:36,640
+أي سؤال من الأسئلة اللي إحنا حددناها في الـ
+
+14
+00:01:36,640 --> 00:01:42,080
+syllabus و قولنا لكم حلوها في أي سؤال في section 2
+
+15
+00:01:42,080 --> 00:01:49,810
+و 1 تحبوا تسألوا عنه؟ أستاذ ممكن نسأل .. نشرح ..
+
+16
+00:01:49,810 --> 00:01:54,650
+نشرح .. نظرية ما .. ما نثبتش .. مش عارف كيف نثبت
+
+17
+00:01:54,650 --> 00:02:02,090
+ما هي عامة exercise اه إيش هي دي؟ X على Z زي Y على
+
+18
+00:02:02,090 --> 00:02:07,930
+W يوم ساوي X Z زي Z Y على Z W كيف نستخدم .. كيف
+
+19
+00:02:07,930 --> 00:02:09,430
+نبدأ فيها؟ مش عارف
+
+20
+00:02:17,430 --> 00:02:21,510
+يعني الخواص اللي .. مش هادى خاصيه من الخواص اللي
+
+21
+00:02:21,510 --> 00:02:27,210
+خدناها حاول تشوف يعني كيف إحنا برهنا الخواص الأخرى
+
+22
+00:02:27,210 --> 00:02:37,050
+و تستفيدي منها و .. و تحاولي تبرهنها يعني ممكن
+
+23
+00:02:37,050 --> 00:02:41,310
+كمان تبصي في الكتاب المقرر و تشوفي يعني هل هو حلها 
+
+24
+00:02:41,310 --> 00:02:47,940
+أو محلهاش لكن أنا يعني الخواص اللي إحنا ما برهناهاش
+
+25
+00:02:47,940 --> 00:02:53,700
+يعني .. يعني كان برهانها سهل و ممكن تتبرهنيها بنفس
+
+26
+00:02:53,700 --> 00:03:00,280
+الأسلوب اللي إحنا برهنا فيه الخصائص الأخرى فخليني 
+
+27
+00:03:00,280 --> 00:03:03,900
+أترك الإجابة على السؤال هذا إليكي تحاولي فيه مرة 
+
+28
+00:03:03,900 --> 00:03:08,360
+ثانية و إذا ما عرفتيش ممكن تجيلي على المكتب و ممكن
+
+29
+00:03:08,360 --> 00:03:09,280
+نتناقش
+
+30
+00:03:11,940 --> 00:03:16,180
+يا ريت تسألوني أسئلة من التمرين من الـ exercises إذا
+
+31
+00:03:16,180 --> 00:03:26,140
+سمحتوا، تفضلي السؤال الرابع في section السابع في
+
+32
+00:03:26,140 --> 00:03:30,360
+section اتنين واحد، حاضر
+
+33
+00:03:39,140 --> 00:03:50,140
+إذا حل السؤال سبعة section اتنين واحد modify
+
+34
+00:03:50,140 --> 00:03:53,360
+the proof of theorem اتنين واحد أربعة في الكتاب
+
+35
+00:03:53,360 --> 00:03:59,200
+المقرر to show that there
+
+36
+00:03:59,200 --> 00:04:05,640
+does not exist لا يوجد there does not exist
+
+37
+00:04:08,790 --> 00:04:19,170
+T ينتمي للـ Q بحيث أن T تربيع بساوي تلاتة بمعنى 
+
+38
+00:04:19,170 --> 00:04:23,770
+آخر يعني الجذر التلاتة بنا نثبت أنه جذر التلاتة
+
+39
+00:04:23,770 --> 00:04:28,730
+ليس عدد نسبي فالمفروض
+
+40
+00:04:28,730 --> 00:04:33,010
+أنكم يعني تفهموا و تحاولوا تفهموا البرهان تبع
+
+41
+00:04:33,010 --> 00:04:37,810
+إثبات أنه جذر اتنين ليس عدد نسبي وتحاولوا تعملوا
+
+42
+00:04:37,810 --> 00:04:45,910
+برهان مشابه في أسلوب براهين للسؤال هذا فأحد البراهين
+
+43
+00:04:45,910 --> 00:04:52,590
+شبه البرهان اللي أخدنا بتاع جذر الاتنين ليس عدد
+
+44
+00:04:52,590 --> 00:04:59,330
+نسبي فخلينا نشوفه مع بعض خلينا نشوف إذن البرهان 
+
+45
+00:04:59,330 --> 00:05:04,810
+prove طبعًا البرهان بالتناقض assume
+
+46
+00:05:07,480 --> 00:05:18,180
+on contrary نفرض على النقيض there exist T بساوي A 
+
+47
+00:05:18,180 --> 00:05:29,420
+على B عدد نسبي بحيث أنه الـ greatest common divisor
+
+48
+00:05:29,420 --> 00:05:34,760
+للـ A والـ B بساوي واحد and
+
+49
+00:05:37,230 --> 00:05:43,970
+T تربيع اللي هو بساوي A على B الكل تربيع بساوي 
+
+50
+00:05:43,970 --> 00:05:52,030
+تلاتة إذا هذا النقيض أو النفي تبع يوجد عدد نسبي 
+
+51
+00:05:52,030 --> 00:06:00,050
+مربعه بساوي تلاتة النفي تبعه يوجد عدد نسبي مربعه
+
+52
+00:06:00,050 --> 00:06:05,840
+بساوي تلاتة وطبعًا ممكن نفرض إنه العدد النسبي الـ
+
+53
+00:06:05,840 --> 00:06:10,160
+greatest common divisor للـ بسط والمقام تبعه بساوي 
+
+54
+00:06:10,160 --> 00:06:17,300
+واحد زي ما عملنا في حالة الـ square root of two طيب
+
+55
+00:06:17,300 --> 00:06:22,740
+then في الحالة هذه لو ربع .. لو هنا من المعادلة
+
+56
+00:06:22,740 --> 00:06:32,820
+هذه بنحصل على A تربيع بساوي تلاتة B تربيع وهذا
+
+57
+00:06:32,820 --> 00:06:42,870
+بيقودى إن الـ B تقسم A تربيع الـ
+
+58
+00:06:42,870 --> 00:06:48,170
+B تقسم A تربيع أو A تربيع اللي هي تلاتة B تربيع 
+
+59
+00:06:48,170 --> 00:06:54,810
+تقبل القسمة على B بدون باقي طيب
+
+60
+00:06:54,810 --> 00:07:03,250
+الـ  و في الحالة هذه بقدر
+
+61
+00:07:04,790 --> 00:07:10,850
+أفصل حالتين العدد بي هذا ممكن .. هذا طبعًا عدد .. 
+
+62
+00:07:10,850 --> 00:07:20,430
+عدد صحيح ممكن يكون أكبر من الواحد و ممكن يكون 
+
+63
+00:07:20,430 --> 00:07:28,990
+بساوي واحد فنفرض أن الـ بي أكبر من واحد then في 
+
+64
+00:07:28,990 --> 00:07:32,770
+الحالة هذه بي can be written
+
+65
+00:07:37,720 --> 00:07:45,000
+as product of
+
+66
+00:07:45,000 --> 00:07:49,640
+primes الـ
+
+67
+00:07:49,640 --> 00:07:54,820
+بيه ده عدد صحيح أكبر من واحد فممكن نكتبه على صورة
+
+68
+00:07:55,540 --> 00:08:01,280
+حاصل ضرب أعداد أولية أي عدد صحيح أكبر من واحد ممكن
+
+69
+00:08:01,280 --> 00:08:06,180
+كتابته على صورة حاصل ضرب أعداد أولية product of
+
+70
+00:08:06,180 --> 00:08:12,100
+primes prime عدد أولي هذا حقيقة معروفة في نظرية
+
+71
+00:08:12,100 --> 00:08:17,020
+الأعداد وبالتالي
+
+72
+00:08:17,020 --> 00:08:20,240
+hence وبالتالي 
+
+73
+00:08:22,840 --> 00:08:33,180
+يوجد a prime يوجد عدد أولي a prime P بحيث أن هذا
+
+74
+00:08:33,180 --> 00:08:39,120
+الـ P يقسم الـ B يعني
+
+75
+00:08:39,120 --> 00:08:44,880
+أنا الـ B هذا هي product of primes ممكن يكون بساوي
+
+76
+00:08:44,880 --> 00:08:50,840
+P1 ضرب P2 ضرب PN
+
+77
+00:08:52,290 --> 00:08:59,710
+حيث و P1 و P2 و PN كلهم Primes أعداد أولية فأكيد
+
+78
+00:08:59,710 --> 00:09:07,390
+لو أخدت أي واحد منهم فهذا بيقسم بي أو بيقبل قسم
+
+79
+00:09:07,390 --> 00:09:16,530
+عليه بس إذا يوجد يوجد Prime سمي P يقسم بي أو بيقبل
+
+80
+00:09:16,530 --> 00:09:20,710
+قسم عليه فهذا
+
+81
+00:09:20,710 --> 00:09:33,050
+بيؤدي هذا بيقودى أن P يقسم الـ A تربيع لأن أنا عندي P
+
+82
+00:09:33,050 --> 00:09:40,570
+يقسم A تربيع و P يقسم B إذا
+
+83
+00:09:40,570 --> 00:09:51,030
+الـ P هذا يقسم A تربيع okay تمام طيب و منها هذا 
+
+84
+00:09:51,030 --> 00:09:57,970
+بيقودى أن P يقسم A إذا P يقسم A تربيع فممكن إثبات
+
+85
+00:09:57,970 --> 00:10:08,830
+أن P يقسم العدد الصحيح A وهكذا أثبتنا الـ
+
+86
+00:10:08,830 --> 00:10:20,170
+greatest common divisor لـ A وB أكبر من أو يساوي P و
+
+87
+00:10:20,170 --> 00:10:27,090
+P هذا طبعًا أكبر من واحد لأن
+
+88
+00:10:27,090 --> 00:10:39,430
+الـ P يقسم الـ A و P يقسم الـ B فمعناته
+
+89
+00:10:39,430 --> 00:10:46,350
+في عامل مشترك في common divisor اللي هو P بين a و b
+
+90
+00:10:46,350 --> 00:10:50,050
+لأن الـ greatest common divisor سيكون على الأقل p
+
+91
+00:10:50,050 --> 00:10:53,770
+ويمكن أن يكون أكبر وبالتالي greatest common
+
+92
+00:10:53,770 --> 00:10:59,070
+divisor ل a و b أكبر من واحد وهذا بتناقض مع فرضنا
+
+93
+00:10:59,070 --> 00:11:02,650
+أن greatest common divisor ل a و b بساوي واحد
+
+94
+00:11:02,650 --> 00:11:07,850
+which is
+
+95
+00:11:07,850 --> 00:11:08,870
+a contradiction
+
+96
+00:11:15,680 --> 00:11:23,960
+وهذا التناقض بيكمل البرهان يعني
+
+97
+00:11:23,960 --> 00:11:30,740
+فرضنا هذا أنه في عدد نسبي مربعه بساوي تلاتة كان فرض
+
+98
+00:11:30,740 --> 00:11:36,780
+خطأ الصح أنه لا يوجد عدد نسبي مربعه بساوي تلاتة Okay
+
+99
+00:11:36,780 --> 00:11:39,740
+تمام إذا هذا برهان وفيه طبعًا براهين أخرى ممكن
+
+100
+00:11:39,740 --> 00:11:43,460
+تلاقوها تجدوها في كتب الـ real analysis لكن هذا أحد
+
+101
+00:11:43,460 --> 00:11:52,580
+البراهين تمام؟ مين عنده سؤال تاني؟ في أي سؤال 
+
+102
+00:11:52,580 --> 00:12:03,220
+تاني؟ في section 2.1 أو 2.2؟
+
+103
+00:12:03,220 --> 00:12:04,680
+نعم
+
+104
+00:12:06,770 --> 00:12:10,590
+لا نفس السؤال مش في أكثر من حالة ولا بس بأخذ الـ D
+
+105
+00:12:10,590 --> 00:12:15,390
+أكثر من حالة؟ اه في كمان حالة صحيح الـ case الثانية
+
+106
+00:12:15,390 --> 00:12:23,290
+مظبوط الـ case الثانية خليني أكتبها هناك صحيح في
+
+107
+00:12:23,290 --> 00:12:24,030
+حالة ثانية
+
+108
+00:12:42,990 --> 00:12:48,270
+case اتنين الـ بي بيساوي واحد لو كانت الـ بي 
+
+109
+00:12:48,270 --> 00:12:55,330
+بيساوي واحد فهذا بيقودى أنا عندي A تربيع من هنا
+
+110
+00:12:55,330 --> 00:13:00,270
+في عندي A تربيع بيساوي تلاتة B تربيع فلو الـ بي
+
+111
+00:13:00,270 --> 00:13:08,730
+بيساوي واحد معناه A تربيع تطلع بيساوي تلاتة و
+
+112
+00:13:08,730 --> 00:13:20,170
+هذا يعني مستحيل which is impossible هذا
+
+113
+00:13:20,170 --> 00:13:28,690
+مستحيل لأنه لأنه ما فيش عدد صحيح عدد صحيح مربعه
+
+114
+00:13:28,690 --> 00:13:34,130
+بيساوي تلاتة since there does not exist integer
+
+115
+00:13:34,130 --> 00:13:36,950
+integer
+
+116
+00:13:38,790 --> 00:13:46,690
+a such that a تربيع بيساوي تلاتة إذا في الحالة هذه
+
+117
+00:13:46,690 --> 00:13:54,510
+حصلنا على حاجة impossible يعني تناقض وهنا
+
+118
+00:13:54,510 --> 00:14:01,510
+كمان حصلنا على تناقض أن الـ assumption تبعنا أنه
+
+119
+00:14:01,510 --> 00:14:06,550
+يوجد عدد نسبي مربعه بساوي تلاتة كان فرض خاطئ وهذا
+
+120
+00:14:06,550 --> 00:14:08,090
+بيكمل البرهان في الحالتين
+
+121
+00:14:10,890 --> 00:14:17,630
+في أي سؤال تاني؟ في 
+
+122
+00:14:17,630 --> 00:14:25,890
+أسئلة تانية في الـ section 2 1 أو 2 2 أنا
+
+123
+00:14:25,890 --> 00:14:30,190
+كنت متوقع أن يكون عندكم أسئلة كتيرة واضح جدا إنكم
+
+124
+00:14:30,190 --> 00:14:35,150
+أنتم ما حاولين تحلوا الأسئلة وبالتالي ما عندكمش
+
+125
+00:14:35,150 --> 00:14:38,550
+يعني استفسارات
+
+126
+00:14:40,490 --> 00:14:42,690
+طبعًا ستة و عشرين
+
+127
+00:15:13,320 --> 00:15:20,080
+سؤال ستة و عشرين سكتشن اتنين واحد show
+
+128
+00:15:20,080 --> 00:15:28,560
+by induction that
+
+129
+00:15:28,560 --> 00:15:36,860
+لو
+
+130
+00:15:36,860 --> 00:15:46,900
+كان A ينتمي لـ R و M و N أعداد طبيعية فهذا بيقودى أن
+
+131
+00:15:46,900 --> 00:15:52,480
+A to M
+
+132
+00:15:52,480 --> 00:16:04,080
+plus N بيساوي A to M في A to N نريد
+
+133
+00:16:04,080 --> 00:16:10,300
+أن نثبت أن استخدام الـ induction إنه لأي عدد حقيقي A
+
+134
+00:16:10,300 --> 00:16:15,640
+و لأي عدد طبيعي M و N A to M زائد N بيساوي A to M
+
+135
+00:16:15,640 --> 00:16:24,800
+ضرب A to N هذا أحد قوانين الأسس فطبعًا
+
+136
+00:16:24,800 --> 00:16:29,420
+هنعمل induction أو بيسموه double induction على M و
+
+137
+00:16:29,420 --> 00:16:32,860
+N في نفس الوقت فالحالة الأولى
+
+138
+00:16:36,700 --> 00:16:40,780
+فـ M بيساوي N بيساوي واحد لو كان الـ M والـ N كلها
+
+139
+00:16:40,780 --> 00:16:46,040
+بيساوي واحد then
+
+140
+00:16:46,040 --> 00:16:56,900
+a to m زي الـ N بيساوي a to واحد زي الواحد بيساوي a 
+
+141
+00:16:56,900 --> 00:17:06,340
+A to M ضرب A to N يساوي A to 1 ضرب A to 
+
+142
+00:17:06,340 --> 00:17:13,780
+1 يساوي A تلبي  وبالتالي الطرفين المعادلة هذه
+
+143
+00:17:13,780 --> 00:17:21,200
+متحققة لأن الطرفين يساوي نفس المقدار A تلبي 
+
+144
+00:17:21,200 --> 00:17:26,300
+إذا إذا 
+
+145
+00:17:26,300 --> 00:17:27,680
+star holds
+
+146
+00:17:30,970 --> 00:17:39,310
+in case M يساوي M يساوي 1 المعادلة star متحققة في
+
+147
+00:17:39,310 --> 00:17:43,610
+حالة M يساوي M يساوي 1 الآن ال induction
+
+148
+00:17:43,610 --> 00:17:48,370
+hypothesis ان هذا induction عادي بس يعني بدل من
+
+149
+00:17:48,370 --> 00:17:53,530
+قيام على M يكون على M و M ال induction hypothesis
+
+150
+00:17:53,530 --> 00:17:59,270
+الفرض تبع ال induction بنفرض assume
+
+151
+00:18:03,340 --> 00:18:09,860
+assume star holds المعادلة
+
+152
+00:18:09,860 --> 00:18:18,760
+star صحيحة for m يساوي k أكبر من واحد and n يساوي
+
+153
+00:18:18,760 --> 00:18:28,940
+j أكبر من واحد this
+
+154
+00:18:28,940 --> 00:18:42,170
+means هذا معناه ان a to k plus j يساوي a to k ضرب a
+
+155
+00:18:42,170 --> 00:18:48,710
+to j إذا احنا فرضنا صحة المعادلة هذه عندما m يساوي
+
+156
+00:18:48,710 --> 00:18:57,560
+k و عندما n يساوي j الآن نريد اثبات صحتها عندما M
+
+157
+00:18:57,560 --> 00:19:01,440
+يساوي K زائد واحد وعندما N يساوي G زائد واحد
+
+158
+00:19:01,440 --> 00:19:08,840
+تعال نثبت صحتها في الحالة يعني إذا now A نأخذ A
+
+159
+00:19:08,840 --> 00:19:16,320
+to K زائد واحد زائد G زائد واحد
+
+160
+00:19:20,610 --> 00:19:25,150
+ان نتبع صحة المعادلة star عندما M يساوي K زائد
+
+161
+00:19:25,150 --> 00:19:29,370
+واحد و N يساوي G زائد واحد في الحالة هذه الطرف
+
+162
+00:19:29,370 --> 00:19:37,310
+اليسار لـ star يساوي الكلام هذا وهذا ممكن نجزئه إلى A
+
+163
+00:19:37,310 --> 00:19:49,290
+to K زائد G زائد واحد زائد واحد الأُس هذا ممكن نقعد
+
+164
+00:19:49,290 --> 00:19:53,450
+الكتابة على صورة ك زائد جي زائد واحد مع بعض زائد
+
+165
+00:19:53,450 --> 00:20:01,550
+واحد وهذا يساوي a to ك زائد جي زائد واحد ضرب a
+
+166
+00:20:01,550 --> 00:20:06,090
+إذن
+
+167
+00:20:06,090 --> 00:20:13,630
+a أُس الكلام هذا ضرب a أُس واحد صح؟ وهذا يساوي
+
+168
+00:20:15,990 --> 00:20:20,710
+A أُس K زائد J زائد واحد عبارة عن A أُس K زائد J
+
+169
+00:20:20,710 --> 00:20:30,370
+ضرب A إذن الجزء هذا A أُس K زائد J زائد واحد عبارة
+
+170
+00:20:30,370 --> 00:20:34,850
+عن A أُس K زائد J ضرب A وفي أندم الأول ضرب A
+
+171
+00:20:34,850 --> 00:20:39,410
+باستخدام
+
+172
+00:20:39,410 --> 00:20:44,690
+ال induction hypothesis الفرض طبع ال induction احنا
+
+173
+00:20:44,690 --> 00:20:52,950
+فرضنا ان a to k زي j يساوي a to k ضرب a ضرب a to j
+
+174
+00:20:52,950 --> 00:21:03,390
+وفي عندي من الأول a في a إذا
+
+175
+00:21:03,390 --> 00:21:06,910
+هذا
+
+176
+00:21:06,910 --> 00:21:15,050
+يساوي a to k ضرب a مع بعض ممكن أخدهم مع بعض ضرب a
+
+177
+00:21:15,050 --> 00:21:22,670
+to j في a مع بعض لأن هنا استخدمنا ال fact ان عملية
+
+178
+00:21:22,670 --> 00:21:30,430
+ضرب الأعداد الحقيقية associative الآن a to k ضرب a
+
+179
+00:21:30,430 --> 00:21:38,650
+يساوي a to k زائد واحد و a to j ضرب a يساوي a to j
+
+180
+00:21:38,650 --> 00:21:48,390
+زائد واحد وهذا هو المطلوب إذاً هذا يثبت إذاً
+
+181
+00:21:48,390 --> 00:21:54,090
+هنا أثبتنا صحة ال star هاي الطرف الشمال لـ star
+
+182
+00:21:54,090 --> 00:22:00,110
+عندما M يساوي K زائد واحد و M يساوي K زائد واحد و
+
+183
+00:22:00,110 --> 00:22:04,010
+هذا هو الطرف اليمين لـ star عندما M يساوي K زائد
+
+184
+00:22:04,010 --> 00:22:09,430
+واحد و M يساوي G زائد واحد إذاً star holds
+
+185
+00:22:12,700 --> 00:22:27,220
+N يساوي ك زائد واحد and N يساوي جي زائد واحد this
+
+186
+00:22:27,220 --> 00:22:32,620
+completes the
+
+187
+00:22:32,620 --> 00:22:33,140
+induction
+
+188
+00:22:38,010 --> 00:22:43,590
+إن ان هذا يكمل البرهان by induction تمام واضح؟ في
+
+189
+00:22:43,590 --> 00:22:51,510
+أي سؤال؟ مفهوم؟ في أسئلة ثانية؟ أي أسئلة ثانية؟
+
+190
+00:23:15,480 --> 00:23:20,400
+سؤال 14؟ بس نجيب example لنا اسمها بس نجيب
+
+191
+00:23:20,400 --> 00:23:21,980
+example لنا اسمها بس نجيب example لنا اسمها بس
+
+192
+00:23:21,980 --> 00:23:24,560
+نجيب example لنا اسمها بس نجيب example لنا اسمها
+
+193
+00:23:24,560 --> 00:23:25,020
+بس نجيب example لنا اسمها بس نجيب example لنا
+
+194
+00:23:25,020 --> 00:23:28,740
+اسمها بس نجيب example لنا اسمها بس نجيب example
+
+195
+00:23:28,740 --> 00:23:29,260
+لنا اسمها بس نجيب example لنا اسمها بس نجيب
+
+196
+00:23:29,260 --> 00:23:29,440
+example لنا اسمها بس نجيب example لنا اسمها بس
+
+197
+00:23:29,440 --> 00:23:29,680
+نجيب example لنا اسمها بس نجيب example لنا اسمها
+
+198
+00:23:29,680 --> 00:23:29,900
+بس نجيب example لنا اسمها بس نجيب example لنا
+
+199
+00:23:29,900 --> 00:23:33,360
+اسمها بس نجيب example لنا اسمها بس نجيب example
+
+200
+00:23:33,360 --> 00:23:37,520
+لنا
+
+201
+00:23:37,520 --> 00:23:37,620
+اسمها
+
+202
+00:23:42,390 --> 00:23:45,070
+الجزء الأول ولا الثاني؟ الأول
+
+203
+00:24:16,920 --> 00:24:25,800
+إذا الجزء الأول مسألة 14 F zero
+
+204
+00:24:25,800 --> 00:24:36,560
+less than or equal a less than b show أثبتي أنه a
+
+205
+00:24:36,560 --> 00:24:43,160
+تربيع أصغر من أو يساوي a في b أصغر من b تربيع
+
+206
+00:25:01,170 --> 00:25:07,290
+proof case واحد a يساوي واحد أنتو ان ال a أكبر من
+
+207
+00:25:07,290 --> 00:25:12,430
+أو يساوي صفر فناخد الأول a يساوي صفر وبعدين a أكبر
+
+208
+00:25:12,430 --> 00:25:21,050
+من صفر فلو كان a يساوي صفر هذا يودي أنه
+
+209
+00:25:21,050 --> 00:25:32,740
+a تربيع اللي هي بتساوي صفر أصغر من أو يساوي A في B
+
+210
+00:25:32,740 --> 00:25:39,740
+اللي هو صفر و
+
+211
+00:25:39,740 --> 00:25:44,180
+طبعا ال B في الحالة هذه أكبر من A يعني أكبر من صفر
+
+212
+00:25:44,180 --> 00:25:47,760
+لأن هذا أصغر من B
+
+213
+00:25:56,410 --> 00:26:01,650
+و أصغر من B تربيع لأن
+
+214
+00:26:01,650 --> 00:26:12,050
+هذا يساوي صفر و B تربيع و B أكبر من صفر B أكبر من
+
+215
+00:26:12,050 --> 00:26:17,190
+A اللي هو يساوي صفر يعني B أكبر من صفر يعني B
+
+216
+00:26:17,190 --> 00:26:22,370
+تربيع أكبر من صفر إذا المتباينة متحققة
+
+217
+00:26:27,190 --> 00:26:38,030
+إذا المتباينة اللي احنا عايزين نثبتها نسميها
+
+218
+00:26:38,030 --> 00:26:48,770
+star إذا star holds in this case الحالة
+
+219
+00:26:48,770 --> 00:27:01,890
+الثانية أن a أكبر من صفر لو كانت a أكبر من صفر by
+
+220
+00:27:01,890 --> 00:27:08,270
+hypothesis من الفرض أنا عندي الآن a أكبر من صفر
+
+221
+00:27:08,270 --> 00:27:13,230
+أصغر من b فنضرب
+
+222
+00:27:13,230 --> 00:27:17,590
+multiply multiply
+
+223
+00:27:17,590 --> 00:27:18,970
+by
+
+224
+00:27:20,970 --> 00:27:28,150
+أو multiply by صحيح by a أكبر من صفر لما أضرب
+
+225
+00:27:28,150 --> 00:27:32,450
+متباينة في عدد موجب  بشريفتها طابقة زي ما هي فهذا
+
+226
+00:27:32,450 --> 00:27:40,710
+يودي فهذا يودي أنه صفر في a بيطلع صفر أصغر
+
+227
+00:27:40,710 --> 00:27:47,550
+من a تربيع أصغر من a في b وهذا اللي بدنا يعني
+
+228
+00:27:51,030 --> 00:28:02,650
+لأ هذا .. هذا شيء كمان and then بعد هيك multiply
+
+229
+00:28:02,650 --> 00:28:08,890
+.. multiply by
+
+230
+00:28:08,890 --> 00:28:14,730
+B اللي هو أكبر من صفر أيضاً لإن ال B أكبر من A أكبر
+
+231
+00:28:14,730 --> 00:28:20,340
+من صفر صح؟ فلو ضربنا المتباينة هذه في بي اللي هو
+
+232
+00:28:20,340 --> 00:28:25,980
+عدد موجب برضه إشارتها هتبقى زي ما هي إذن هذا
+
+233
+00:28:25,980 --> 00:28:31,760
+يودي لما أضرب المتباينة هذه في بي عدد موجب
+
+234
+00:28:31,760 --> 00:28:37,020
+فهيطلع عند صفر أصغر من a في بي أصغر من b تربيع
+
+235
+00:28:37,020 --> 00:28:47,280
+نسمي هذه 1 والمتباينة هذه 2 الآن 1 عندي
+
+236
+00:28:47,280 --> 00:28:51,760
+2 يديان يعني
+
+237
+00:28:51,760 --> 00:29:00,540
+عندي a تربيع أكبر من صفر أصغر من a بيه وعندي a بيه
+
+238
+00:29:00,540 --> 00:29:05,120
+أصغر من b تربيع وهذه هي ال star
+
+239
+00:29:16,200 --> 00:29:22,040
+إذا in both cases
+
+240
+00:29:22,040 --> 00:29:30,280
+في الحالة الأولى والثانية we have أثبتنا أن a
+
+241
+00:29:30,280 --> 00:29:34,680
+تربيع أصغر
+
+242
+00:29:34,680 --> 00:29:40,760
+أو يساوي ab و
+
+243
+00:29:40,760 --> 00:29:47,120
+ab في الحالتين أصغر من b تربيع كمان مرة في الحالة
+
+244
+00:29:47,120 --> 00:29:53,080
+الأولى a تربيع أصغر من أو يساوي a b في الحالة
+
+245
+00:29:53,080 --> 00:29:58,020
+الثانية a تربيع أصغر من a b إذا في الحالتين a
+
+246
+00:29:58,020 --> 00:30:02,420
+تربيع أصغر من أو يساوي a b في الحالة الأولى a b
+
+247
+00:30:02,420 --> 00:30:05,680
+أصغر من b تربيع وفي الحالة الثانية a b أصغر من b
+
+248
+00:30:05,680 --> 00:30:10,300
+تربيع إذا في الحالتين a b أصغر من b تربيع و هذا
+
+249
+00:30:10,300 --> 00:30:13,820
+اللي احنا عايزين نثبته تمام إذا هيك بتكون أثبتنا
+
+250
+00:30:13,820 --> 00:30:21,140
+الجزء الأول من السؤال الجزء
+
+251
+00:30:21,140 --> 00:30:27,960
+الثاني بيقول انه احنا ما نقدرش المتباينة هذه star
+
+252
+00:30:27,960 --> 00:30:38,500
+نبدلها 
+ال
+
+253
+00:30:38,500 --> 00:30:43,760
+star can't be replaced
+
+254
+00:30:46,040 --> 00:30:53,660
+replaced by a تربيع أصغر من a بيه أصغر من بي تربيع
+
+255
+00:30:53,660 --> 00:31:01,140
+يعني هنا ال inequality هذه أصغر من أو يساوي ما نقدرش
+
+256
+00:31:01,140 --> 00:31:08,260
+نبدلها بأصغر من strictly أصغر من فبنوضح ذلك بمثال
+
+257
+00:31:08,260 --> 00:31:15,280
+فأخذنا a يساوي صفر و b أي عدد example
+
+258
+00:31:37,110 --> 00:31:39,170
+زي ما عملنا في الحلقة الأولى
+
+259
+00:31:43,550 --> 00:31:50,550
+فهيطلع عندي هذه مساوية وليست .. وليست أكبر من ..
+
+260
+00:31:50,550 --> 00:32:01,390
+اه؟ okay في أسئلة ثانية؟ مين عند السؤال الثاني؟
+
+261
+00:32:01,390 --> 00:32:05,050
+section اثنين اثنين؟ في أي أسئلة في section اثنين
+
+262
+00:32:05,050 --> 00:32:08,910
+اثنين؟ section اثنين واحد اثنين اثنين
+
+263
+00:32:12,890 --> 00:32:21,830
+في أسئلة كثيرة حلوة section
+
+264
+00:32:21,830 --> 00:32:37,450
+1122 فينا مجموعة كبيرة من الأسئلة الناس
+
+265
+00:32:37,450 --> 00:32:39,270
+بتدرس الناس بتحل مثال
+
+266
+00:32:42,490 --> 00:32:46,430
+حليتوا كل المسائل؟ مش عندكم أسئلة؟ ال section
+
+267
+00:32:46,430 --> 00:32:56,890
+اثنين واحد و اثنين اثنين؟
+
+268
+00:32:56,890 --> 00:33:03,850
+ما لديها سؤال؟ السؤال اثنين في section اثنين
+
+269
+00:33:03,850 --> 00:33:10,710
+اثنين حاضر اثنين اثنين اثنين نكتب النص تبع السؤال
+
+270
+00:33:14,400 --> 00:33:25,960
+if a و b are real numbers show ifpty أنه
+
+271
+00:33:25,960 --> 00:33:35,160
+absolute a زائد b يساوي absolute a زائد absolute b
+
+272
+00:33:35,160 --> 00:33:47,110
+if and only if a في b أكبر من أو يساوي صفر هيك
+
+273
+00:33:47,110 --> 00:33:59,610
+مكتوب طيب
+
+274
+00:33:59,610 --> 00:34:07,590
+البرهان ال proof لاحظوا هذا if and only if
+
+275
+00:34:07,590 --> 00:34:11,730
+statement فخلينا
+
+276
+00:34:11,730 --> 00:34:21,730
+الأول نثبت ال claim الأول claim one للدعاء الأول أن
+
+277
+00:34:21,730 --> 00:34:28,350
+a ضرب b أكبر من أو يساوي صفر if and only if
+
+278
+00:34:28,350 --> 00:34:36,290
+absolute a ضرب b يساوي a في b
+
+279
+00:34:43,590 --> 00:34:47,970
+هل هذا واضح هذا
+
+280
+00:34:47,970 --> 00:35:01,250
+واضح من تعريف that this is clear by definition of 
+
+281
+00:35:01,250 --> 00:35:09,370
+absolute value طيب
+
+282
+00:35:09,370 --> 00:35:10,490
+الكلام الثاني
+
+283
+00:35:16,440 --> 00:35:24,700
+الكلام الثاني absolute a plus absolute b الكل
+
+284
+00:35:24,700 --> 00:35:35,560
+تربيع بساوي a زائد b الكل تربيع if
+
+285
+00:35:35,560 --> 00:35:43,500
+and only if absolute a ضرب b بساوي a في b
+
+286
+00:35:49,120 --> 00:35:56,920
+برهان للـ claim هذا ها لو أخدت absolute a زائد
+
+287
+00:35:56,920 --> 00:36:04,520
+absolute b وربعت فهذا المفروض يساوي absolute a
+
+288
+00:36:04,520 --> 00:36:12,780
+الكل تربيع زائد absolute b الكل تربيع زائد 2
+
+289
+00:36:12,780 --> 00:36:19,600
+absolute a في absolute b وهذا بساوي absolute a
+
+290
+00:36:19,600 --> 00:36:26,080
+الكل 
+
+291
+00:36:26,080 --> 00:36:33,480
+تربيع زائد
+
+292
+00:36:33,480 --> 00:36:44,050
+absolute b الكل تربيع زائد 2 absolute a ضرب bلأن
+
+293
+00:36:44,050 --> 00:36:54,670
+absolute a ضرب absolute b بيطلع absolute a في b و
+
+294
+00:36:54,670 --> 00:36:59,210
+absolute absolute
+
+295
+00:36:59,210 --> 00:37:06,850
+a بساوي الجذر التربيعي ل a تربيع هذا
+
+296
+00:37:06,850 --> 00:37:18,950
+بكافئ أن a أو absolute a الكل تربيع بيساوي a تربيع لو
+
+297
+00:37:18,950 --> 00:37:25,030
+ربعت الطرفين فبطلع absolute a تربيع بيساوي a تربيع
+
+298
+00:37:25,030 --> 00:37:30,490
+وبالتالي ممكن استبدل absolute a تربيع ممكن استبدل
+
+299
+00:37:30,490 --> 00:37:36,530
+absolute a تربيع ب a تربيع و
+
+300
+00:37:36,530 --> 00:37:41,450
+استبدل absolute b تربيع ب b تربيع
+
+301
+00:37:50,020 --> 00:37:57,000
+الآن هذا بيساوي هذا بيساوي a تربيع زائد b تربيع
+
+302
+00:37:57,000 --> 00:38:06,460
+زائد 2 a b if and only if if and only if
+
+303
+00:38:06,460 --> 00:38:10,940
+absolute a b بساوي a في b
+
+304
+00:38:13,940 --> 00:38:17,600
+هذا المقدار اللي فوق متى بيساوي a تربيع زائد b
+
+305
+00:38:17,600 --> 00:38:22,500
+تربيع زائد 2 a ب  اذا absolute a b هو
+
+306
+00:38:22,500 --> 00:38:33,140
+عبارة عن a في b صح؟ وهذا
+
+307
+00:38:33,140 --> 00:38:39,720
+الأخير بيساوي يعني
+
+308
+00:38:39,720 --> 00:38:50,460
+هذا السطر هذا هي تعال نشوف بقد ايه
+
+309
+00:38:50,460 --> 00:39:00,000
+ان absolute a زائد absolute b الكل تربيع بساوي
+
+310
+00:39:03,190 --> 00:39:11,210
+A زائد B الكل تربيع if and only if absolute A B
+
+311
+00:39:11,210 --> 00:39:27,050
+بساوي A B absolute
+
+312
+00:39:27,050 --> 00:39:32,390
+A B بساوي A B ومن claim واحد
+
+313
+00:39:36,690 --> 00:39:43,890
+عمر ال claim واحد هذا بتحقق if and only if a ضرب b
+
+314
+00:39:43,890 --> 00:39:49,610
+أكبر من أو يساوي 0 لأن هذا نتيجة أو بضم ال two
+
+315
+00:39:49,610 --> 00:39:54,070
+claims مع بعض طيب
+
+316
+00:39:54,070 --> 00:39:58,290
+لو أخذنا جذر التربيعي للطرفين فضي جذر التربيعي يعني
+
+317
+00:39:58,290 --> 00:40:02,290
+take square root
+
+318
+00:40:05,210 --> 00:40:14,850
+of both sides فهذا
+
+319
+00:40:14,850 --> 00:40:20,410
+بيؤدي إلى أن absolute a زائد absolute b الجذر
+
+320
+00:40:20,410 --> 00:40:23,030
+التربيعي هنا بعطيني ال absolute value ل a زائد
+
+321
+00:40:23,030 --> 00:40:28,570
+absolute b وهنا بعطيني الجذر التربيعي الجذر
+
+322
+00:40:28,570 --> 00:40:31,370
+التربيعي للعدد التربيعي بعطيني القيمة المطلقة
+
+323
+00:40:31,370 --> 00:40:32,010
+تبعته
+
+324
+00:40:34,820 --> 00:40:41,180
+هذا بتحقق if and only if a ضرب b أكبر من أو يساوي 0
+
+325
+00:40:41,180 --> 00:40:48,200
+وهذا هو المطلوب وهذا هو المطلوب okay تمام فهذا هو
+
+326
+00:40:48,200 --> 00:40:53,140
+المطلوب في
+
+327
+00:40:53,140 --> 00:40:58,220
+أي أسئلة ثانية في
+
+328
+00:40:58,220 --> 00:41:01,700
+عندكم أي سؤال ثاني section 2 أو section 1
+
+329
+00:41:07,070 --> 00:41:12,510
+أن أسئلة كثيرة لو جئت بعدي وأنتم ما بتسألوش ومش
+
+330
+00:41:12,510 --> 00:41:17,650
+هيكون في رجعة بعد هيك لأ أسأل أسئلتنا دي المرة الجاية
+
+331
+00:41:17,650 --> 00:41:21,830
+هنأخذ مناقشة في section اثنين ثلاثة واثنين أربعة
+
+332
+00:41:21,830 --> 00:41:31,370
+في أي أسئلة أفندم في أي section اثنين اثنين
+
+333
+00:41:37,770 --> 00:41:38,370
+حاضر
+
+334
+00:42:02,930 --> 00:42:11,490
+السؤال خمسة عشر سيكشن اثنين نيلو نشوف ايه هو السؤال
+
+335
+00:42:11,490 --> 00:42:25,670
+show
+
+336
+00:42:25,670 --> 00:42:29,790
+if a و b are real numbers
+
+337
+00:42:32,160 --> 00:42:38,560
+و a لا يساوي b then
+
+338
+00:42:38,560 --> 00:42:49,100
+there exist epsilon neighborhoods U
+
+339
+00:42:49,100 --> 00:43:09,390
+of a and V of b such that U تقاطع V بساوي فاي إذن
+
+340
+00:43:09,390 --> 00:43:24,630
+كمان مرة أنا 
+
+341
+00:43:24,630 --> 00:43:25,090
+عندي
+
+342
+00:43:28,550 --> 00:43:35,990
+A وB أعداد حقيقية و A لا يساوي B هذا معناه أن
+
+343
+00:43:35,990 --> 00:43:43,970
+either A less than B ف
+
+344
+00:43:43,970 --> 00:43:52,310
+assume نأخذ الحالة الأولى case one أن
+
+345
+00:43:52,310 --> 00:44:01,330
+A أصغر من B إذا هي خط الأعداد هذا خط الأعداد وهذه a
+
+346
+00:44:01,330 --> 00:44:12,670
+وهذه b و a أصغر من b بدي أثبت أنه في جوار ل a بعمق
+
+347
+00:44:12,670 --> 00:44:22,450
+epsilon اسمه u وفي جوار ل b بعمق epsilon والجوارين
+
+348
+00:44:22,450 --> 00:44:26,170
+هذول المبروهود سقطوهم بسوء في يعني منفصلين عن بعض
+
+349
+00:44:27,430 --> 00:44:35,570
+فبكل بساطة بجيب المسافة من a و b و باخذ نصف المسافة
+
+350
+00:44:35,570 --> 00:44:43,670
+يعني لأن هنا take epsilon
+
+351
+00:44:43,670 --> 00:44:48,770
+بساوي
+
+352
+00:44:48,770 --> 00:44:54,270
+نصف المسافة نصف ال b minus
+
+353
+00:44:57,480 --> 00:45:13,820
+a أو نصف أو نصف المسافة بين A وB فهي
+
+354
+00:45:13,820 --> 00:45:15,920
+نصف المسافة لو كونت فترة
+
+355
+00:45:23,000 --> 00:45:28,520
+فهي منتصف المسافة هذه المسافة
+
+356
+00:45:28,520 --> 00:45:33,260
+هذه منتصف المسافة سميها epsilon فهذه النقطة هتكون
+
+357
+00:45:33,260 --> 00:45:40,960
+a زائد epsilon وهي نفس المسافة a ناقص epsilon وكون
+
+358
+00:45:40,960 --> 00:45:45,660
+فترة مفتوحة وسمي
+
+359
+00:45:45,660 --> 00:45:48,960
+الفترة المفتوحة هذه new
+
+360
+00:46:02,460 --> 00:46:07,900
+فنسمي الفترة المفتوحة هذه U مركزها a و نصف قطرها epsilon
+
+361
+00:46:07,900 --> 00:46:16,200
+و نكوّن فترة ثانية برضه مركزها B و نصف قطرها epsilon
+
+362
+00:46:16,200 --> 00:46:22,080
+يعني هذه النقطة هتصير B زائد epsilon وهذه النقطة هتصير
+
+363
+00:46:25,910 --> 00:46:33,530
+b زائد ابسلون و النقطة هذه ب ناقص ابسلون و نكون فترة
+
+364
+00:46:33,530 --> 00:46:39,970
+مفتوحة تمام
+
+365
+00:46:39,970 --> 00:46:43,310
+إذا
+
+366
+00:46:43,310 --> 00:46:50,890
+أنا في U و نسمي الفترة المفتوحة هذه نسميها
+
+367
+00:46:50,890 --> 00:46:51,030
+ب
+
+368
+00:46:57,180 --> 00:47:01,040
+إذن هذا عبارة عن الـ U الفترة المفتوحة اذا هنا let
+
+369
+00:47:01,040 --> 00:47:14,300
+take
+
+370
+00:47:14,300 --> 00:47:16,480
+u
+
+371
+00:47:18,050 --> 00:47:26,410
+by definition بتساوي a ناقص إبسلون و a زائد إبسلون
+
+372
+00:47:26,410 --> 00:47:40,810
+و V بساوي B ناقص إبسلون B زائد إبسلون فواضح
+
+373
+00:47:40,810 --> 00:47:41,410
+nearly
+
+374
+00:47:46,910 --> 00:47:58,030
+Clearly U is an epsilon neighborhood of A and V is
+
+375
+00:47:58,030 --> 00:48:05,410
+an epsilon neighborhood of B ومش هيكوا بس and ممكن
+
+376
+00:48:05,410 --> 00:48:09,370
+إثبات أن U تقاطع B بساوي فاي
+
+377
+00:48:12,440 --> 00:48:21,120
+يعني لو أخذنا هاي واضح هاي جوار هذا مافيش ولا نقطة
+
+378
+00:48:21,120 --> 00:48:27,940
+فيه موجودة في الجوار الثاني هذه الفترة المفتوحة
+
+379
+00:48:27,940 --> 00:48:35,540
+منفصلة عن الفترة المفتوحة يوم طبعا؟
+
+380
+00:48:39,190 --> 00:48:44,970
+إن هذا الكلام يعني واضح أن هذا عبارة عن epsilon
+
+381
+00:48:44,970 --> 00:48:50,150
+neighborhood ل a فترة مفتوحة مركزها a نصف قطرها
+
+382
+00:48:50,150 --> 00:48:53,590
+epsilon هذا نسميه epsilon neighborhood ل a و V
+
+383
+00:48:53,590 --> 00:48:57,510
+الفترة المفتوحة هذه ب ناقص epsilon و ب زائد
+
+384
+00:48:57,510 --> 00:49:04,310
+epsilon برضه عبارة عن epsilon neighborhood ل B و
+
+385
+00:49:04,310 --> 00:49:09,900
+اثنين حسب الرسم منفصلين و هذا ممكن إثباته باستخدام
+
+386
+00:49:09,900 --> 00:49:14,380
+التناقض يعني افرض أنه في عنصر يعني التقاطع هذا لا
+
+387
+00:49:14,380 --> 00:49:19,900
+يساوي فاي وبالتالي في عنصر موجود في U وموجود في V
+
+388
+00:49:19,900 --> 00:49:25,540
+في أن و واحد واصلي إليه تناقض okay هذا ممكن إثباته
+
+389
+00:49:25,540 --> 00:49:34,280
+بطريقة تحليلية طبعا في السؤال في الحل في حل السؤال
+
+390
+00:49:34,280 --> 00:49:41,370
+هذا يقول مافيش عندنا حالتين الحالة الأولى a أصغر من b
+
+391
+00:49:41,370 --> 00:49:48,110
+والحالة الثانية b أصغر من a وشوفنا هنا أخذنا
+
+392
+00:49:48,110 --> 00:49:51,230
+الحالة اللي فيها a أصغر من b زي اللي هو النضال تحت
+
+393
+00:49:51,230 --> 00:49:57,090
+الاسم هاي a أصغر من b و أثبتنا في الحالة هذه أن u
+
+394
+00:49:57,090 --> 00:50:00,070
+جد epsilon neighborhood ل a
+
+395
+00:50:17,240 --> 00:50:24,820
+باقي الحالة الثانية case 2 نثبت
+
+396
+00:50:24,820 --> 00:50:27,120
+برضه المطلوب
+
+397
+00:50:33,160 --> 00:50:38,320
+البرهان في الحلقة الثانية مماثل للبرهان اللي عملناه
+
+398
+00:50:38,320 --> 00:50:38,880
+في الحلقة
+
+399
+00:50:50,040 --> 00:50:54,040
+و هذا طبعا يكمل البرهان إذا الحالة الثانية اللي 
+
+400
+00:50:54,040 --> 00:50:58,120
+فيها b أصغر من a بس نضع b هنا و a هنا ونفس
+
+401
+00:50:58,120 --> 00:51:05,440
+العادة فتصير هذا الـb و هذا الـa و يعطينا نفس
+
+402
+00:51:05,440 --> 00:51:13,020
+النتيجة إذن كون كملنا البرهان اللي هو التمرين
+
+403
+00:51:14,530 --> 00:51:17,970
+وطبعا بعد ذلك إن شاء الله هنكمل حل التمارين لل
+
+404
+00:51:17,970 --> 00:51:20,870
+سيكشن الخامس في نفس الموضوع 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..fb0195aaf334d8bfe88db38babd45cc1646eb0a1
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Kfhi1a_WpFk_raw.json
@@ -0,0 +1 @@
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يقسم ال B فمعناته في عامل مشترك في common divisor اللي هو P", "tokens": [2407, 430, 23758, 23032, 3555, 3615, 995, 5551, 4117, 26890, 9154, 36764, 24401, 5296, 33456, 2423, 430, 7251, 4587, 38251, 2423, 316, 4032, 430, 7251, 4587, 38251, 2423, 363, 6156, 2304, 3615, 8315, 47395, 8978, 6225, 10943, 1211, 37893, 2655, 31747, 8978, 2689, 25974, 284, 13672, 1829, 31439, 430], "avg_logprob": -0.15468750655651092, "compression_ratio": 1.2878787878787878, "no_speech_prob": 0.0, "words": [{"start": 619.85, "end": 620.17, "word": "و", "probability": 0.91259765625}, {"start": 620.17, "end": 620.35, "word": " P", "probability": 0.64306640625}, {"start": 620.35, "end": 620.61, "word": " هذا", "probability": 0.7548828125}, {"start": 620.61, "end": 621.03, "word": " طبعا", "probability": 0.8934326171875}, {"start": 621.03, "end": 621.59, "word": " أكبر", "probability": 0.8123372395833334}, {"start": 621.59, "end": 621.79, "word": " من", "probability": 0.98681640625}, {"start": 621.79, "end": 622.19, 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"assume star holds المعادلة star صحيحة for m بساوي k أكبر من واحد and n بساوي j أكبر من واحد this means", "tokens": [640, 2540, 3543, 9190, 9673, 3615, 18513, 37977, 3543, 20328, 5016, 1829, 5016, 3660, 337, 275, 4724, 3794, 995, 45865, 350, 5551, 4117, 26890, 9154, 36764, 24401, 293, 297, 4724, 3794, 995, 45865, 361, 5551, 4117, 26890, 9154, 36764, 24401, 341, 1355], "avg_logprob": -0.1392623546511628, "compression_ratio": 1.2946428571428572, "no_speech_prob": 0.0, "words": [{"start": 1083.34, "end": 1084.26, "word": "assume", "probability": 0.650146484375}, {"start": 1084.26, "end": 1085.96, "word": " star", "probability": 0.53271484375}, {"start": 1085.96, "end": 1086.68, "word": " holds", "probability": 0.5810546875}, {"start": 1086.68, "end": 1089.86, "word": " المعادلة", "probability": 0.9544677734375}, {"start": 1089.86, "end": 1090.28, "word": " star", "probability": 0.59814453125}, {"start": 1090.28, "end": 1091.72, "word": " صحيحة", "probability": 0.9712890625}, {"start": 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"probability": 0.880859375}, {"start": 1121.75, "end": 1122.17, "word": " a", "probability": 0.98681640625}, {"start": 1122.17, "end": 1122.43, "word": " to", "probability": 0.98388671875}, {"start": 1122.43, "end": 1122.81, "word": " j", "probability": 0.9931640625}, {"start": 1122.81, "end": 1125.29, "word": " اذا", "probability": 0.47705078125}, {"start": 1125.29, "end": 1125.55, "word": " احنا", "probability": 0.9611002604166666}, {"start": 1125.55, "end": 1125.99, "word": " فرضين", "probability": 0.9661458333333334}, {"start": 1125.99, "end": 1126.47, "word": " صحة", "probability": 0.9508463541666666}, {"start": 1126.47, "end": 1126.99, "word": " المعادلة", "probability": 0.9857177734375}, {"start": 1126.99, "end": 1127.33, "word": " هذه", "probability": 0.53662109375}, {"start": 1127.33, "end": 1127.89, "word": " عندما", "probability": 0.825439453125}, {"start": 1127.89, "end": 1128.15, "word": " m", "probability": 0.64306640625}, {"start": 1128.15, "end": 1128.71, "word": " بساوي", "probability": 0.954345703125}, {"start": 1128.71, "end": 1129.09, "word": " k", "probability": 0.9580078125}, {"start": 1129.09, "end": 1129.73, "word": " و", "probability": 0.64892578125}, {"start": 1129.73, "end": 1130.19, "word": " عندما", "probability": 0.75}, {"start": 1130.19, "end": 1130.41, "word": " n", "probability": 0.95947265625}, {"start": 1130.41, "end": 1130.95, "word": " بساوي", "probability": 0.9730224609375}, {"start": 1130.95, "end": 1131.25, "word": " j", "probability": 0.9873046875}], "temperature": 1.0}, {"id": 40, "seek": 115632, "start": 1132.78, "end": 1156.32, "text": "الان نريد اثبات صحتها عندما M بيساوي K زايد واحد وعندما N بيساوي G زايد واحد تعالى نثبت صحتها في الحالة يعني اذا now A ناخد A to K زايد واحد زايد G زايد واحد", "tokens": [6027, 7649, 8717, 16572, 3215, 1975, 12984, 3555, 9307, 20328, 33753, 11296, 43242, 15042, 376, 4724, 1829, 3794, 995, 45865, 591, 30767, 995, 25708, 36764, 24401, 4032, 3615, 41260, 15042, 426, 4724, 1829, 3794, 995, 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"seek": 142507, "start": 1422.39, "end": 1425.07, "text": "جزء الأول ولا التاني؟ الأول", "tokens": [7435, 11622, 38207, 16247, 12610, 49429, 16712, 7649, 1829, 22807, 16247, 12610], "avg_logprob": -0.24384014423076922, "compression_ratio": 1.1627906976744187, "no_speech_prob": 0.0, "words": [{"start": 1422.39, "end": 1423.31, "word": "جزء", "probability": 0.7421061197916666}, {"start": 1423.31, "end": 1423.53, "word": " الأول", "probability": 0.885009765625}, {"start": 1423.53, "end": 1423.67, "word": " ولا", "probability": 0.7607421875}, {"start": 1423.67, "end": 1424.49, "word": " التاني؟", "probability": 0.7962646484375}, {"start": 1424.49, "end": 1425.07, "word": " الأول", "probability": 0.910400390625}], "temperature": 1.0}, {"id": 51, "seek": 148316, "start": 1456.92, "end": 1483.16, "text": "إذا الجزء الأول مسؤال أربعتاش F zero less than or equal a less than b show أثبتي أنه a تربية أصغر من أو ساوي a في b أصغر من b تربية", "tokens": [28814, 15730, 25724, 11622, 38207, 16247, 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"probability": 0.84619140625}, {"start": 1540.82, "end": 1541.0, "word": " في", "probability": 0.91064453125}, {"start": 1541.0, "end": 1541.38, "word": " الحالة", "probability": 0.97412109375}, {"start": 1541.38, "end": 1541.76, "word": " هذه", "probability": 0.45703125}, {"start": 1541.76, "end": 1542.38, "word": " أكبر", "probability": 0.8933919270833334}, {"start": 1542.38, "end": 1542.62, "word": " من", "probability": 0.9931640625}, {"start": 1542.62, "end": 1542.86, "word": " A", "probability": 0.97216796875}, {"start": 1542.86, "end": 1543.06, "word": " يعني", "probability": 0.9541015625}, {"start": 1543.06, "end": 1543.46, "word": " أكبر", "probability": 0.9611002604166666}, {"start": 1543.46, "end": 1543.64, "word": " من", "probability": 0.9970703125}, {"start": 1543.64, "end": 1544.18, "word": " سفر", "probability": 0.9736328125}, {"start": 1544.18, "end": 1544.88, "word": " لأن", "probability": 0.614501953125}, {"start": 1544.88, "end": 1545.14, "word": " هذا", 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{"start": 1602.05, "end": 1604.13, "word": " in", "probability": 0.91455078125}, {"start": 1604.13, "end": 1604.45, "word": " this", "probability": 0.9697265625}, {"start": 1604.45, "end": 1605.39, "word": " case", "probability": 0.939453125}, {"start": 1605.39, "end": 1608.77, "word": " الحالة", "probability": 0.9778645833333334}, {"start": 1608.77, "end": 1609.27, "word": " التانية", "probability": 0.98193359375}, {"start": 1609.27, "end": 1611.61, "word": " أن", "probability": 0.426513671875}, {"start": 1611.61, "end": 1612.01, "word": " a", "probability": 0.3447265625}, {"start": 1612.01, "end": 1612.61, "word": " أكبر", "probability": 0.9560546875}, {"start": 1612.61, "end": 1612.85, "word": " من", "probability": 0.994140625}, {"start": 1612.85, "end": 1613.19, "word": " 7", "probability": 0.421630859375}], "temperature": 1.0}, {"id": 56, "seek": 163897, "start": 1615.37, "end": 1638.97, "text": "لو كانت a أكبر من صفر by hypothesis من الفرض أنا عندي الآن a أكبر من صفر أصغر من b فنضرب multiply multiply by", "tokens": [1211, 2407, 25961, 2655, 257, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 538, 17291, 9154, 27188, 43042, 41850, 18871, 16254, 6024, 48506, 257, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 272, 6156, 1863, 11242, 25513, 12972, 12972, 538], "avg_logprob": -0.14754970981316132, "compression_ratio": 1.361344537815126, "no_speech_prob": 0.0, "words": [{"start": 1615.37, "end": 1615.75, "word": "لو", "probability": 0.80712890625}, {"start": 1615.75, "end": 1616.19, "word": " كانت", "probability": 0.90478515625}, {"start": 1616.19, "end": 1616.31, "word": " a", "probability": 0.58544921875}, {"start": 1616.31, "end": 1616.73, "word": " أكبر", "probability": 0.9215494791666666}, {"start": 1616.73, "end": 1616.93, "word": " من", "probability": 0.99267578125}, {"start": 1616.93, "end": 1617.33, "word": " صفر", "probability": 0.7861328125}, {"start": 1617.33, "end": 1621.89, "word": " by", "probability": 0.5654296875}, 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0.98046875}, {"start": 2102.89, "end": 2109.37, "word": " طيب", "probability": 0.8717447916666666}, {"start": 2109.37, "end": 2109.87, "word": " الكلام", "probability": 0.7355143229166666}, {"start": 2109.87, "end": 2110.49, "word": " التاني", "probability": 0.9542643229166666}], "temperature": 1.0}, {"id": 73, "seek": 214350, "start": 2116.44, "end": 2143.5, "text": "الكلام التاني absolute a plus absolute b الكل تربية بساوي a زي b الكل تربية if and only if absolute a ضرب b بساوي a في b", "tokens": [6027, 28820, 10943, 16712, 7649, 1829, 8236, 257, 1804, 8236, 272, 2423, 28820, 6055, 25513, 10632, 4724, 3794, 995, 45865, 257, 30767, 1829, 272, 2423, 28820, 6055, 25513, 10632, 498, 293, 787, 498, 8236, 257, 48812, 25513, 272, 4724, 3794, 995, 45865, 257, 8978, 272], "avg_logprob": -0.16032608468895373, "compression_ratio": 1.518181818181818, "no_speech_prob": 0.0, "words": [{"start": 2116.44, "end": 2117.14, "word": "الكلام", "probability": 0.8624674479166666}, {"start": 2117.14, "end": 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في", "probability": 0.91455078125}, {"start": 2143.22, "end": 2143.5, "word": " b", "probability": 0.986328125}], "temperature": 1.0}, {"id": 74, "seek": 217530, "start": 2149.12, "end": 2175.3, "text": "بروف للـ claim هذا هاي لو أخدت absolute a زاد absolute b وربعت فهذا المفروض يساوي absolute a الكتر بيها زاد absolute b الكتر بيها زاد اتنين absolute a في absolute b", "tokens": [3555, 32887, 5172, 24976, 39184, 3932, 23758, 8032, 47302, 45164, 5551, 9778, 3215, 2655, 8236, 257, 30767, 18513, 8236, 272, 4032, 25513, 34268, 6156, 3224, 15730, 9673, 5172, 32887, 11242, 7251, 3794, 995, 45865, 8236, 257, 33251, 2655, 2288, 4724, 1829, 11296, 30767, 18513, 8236, 272, 33251, 2655, 2288, 4724, 1829, 11296, 30767, 18513, 1975, 2655, 1863, 9957, 8236, 257, 8978, 8236, 272], "avg_logprob": -0.2807617331854999, "compression_ratio": 1.7246376811594204, "no_speech_prob": 0.0, "words": [{"start": 2149.1200000000003, "end": 2150.28, "word": "بروف", "probability": 0.3873291015625}, {"start": 2150.28, 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بيساوي", "probability": 0.96669921875}, {"start": 2316.26, "end": 2319.72, "word": " يعني", "probability": 0.87353515625}, {"start": 2319.72, "end": 2319.98, "word": " هذا", "probability": 0.93701171875}, {"start": 2319.98, "end": 2320.4, "word": " السطر", "probability": 0.611328125}, {"start": 2320.4, "end": 2320.78, "word": " هذا", "probability": 0.7333984375}], "temperature": 1.0}, {"id": 80, "seek": 234000, "start": 2322.62, "end": 2340.0, "text": "هي تعالى نشوف بقدّه ان absolute a زاد absolute b الكل تربية بساوي", "tokens": [3224, 1829, 37279, 6027, 7578, 8717, 8592, 38688, 4724, 28543, 11703, 3224, 16472, 8236, 257, 30767, 18513, 8236, 272, 2423, 28820, 6055, 25513, 10632, 4724, 3794, 995, 45865], "avg_logprob": -0.38442888753167515, "compression_ratio": 1.0869565217391304, "no_speech_prob": 0.0, "words": [{"start": 2322.62, "end": 2322.98, "word": "هي", "probability": 0.4742431640625}, {"start": 2322.98, "end": 2323.48, "word": " تعالى", "probability": 0.8370768229166666}, {"start": 2323.48, "end": 2323.92, "word": " نشوف", "probability": 0.9894205729166666}, {"start": 2323.92, "end": 2330.46, "word": " بقدّه", "probability": 0.49383544921875}, {"start": 2330.46, "end": 2330.64, "word": " ان", "probability": 0.401611328125}, {"start": 2330.64, "end": 2331.22, "word": " absolute", "probability": 0.63037109375}, {"start": 2331.22, "end": 2332.24, "word": " a", "probability": 0.51953125}, {"start": 2332.24, "end": 2334.22, "word": " زاد", "probability": 0.585693359375}, {"start": 2334.22, "end": 2334.9, "word": " absolute", "probability": 0.9599609375}, {"start": 2334.9, "end": 2335.82, "word": " b", "probability": 0.677734375}, {"start": 2335.82, "end": 2336.98, "word": " الكل", "probability": 0.653076171875}, {"start": 2336.98, "end": 2337.78, "word": " تربية", "probability": 0.7906901041666666}, {"start": 2337.78, "end": 2340.0, "word": " بساوي", "probability": 0.872802734375}], "temperature": 1.0}, {"id": 81, "seek": 237239, "start": 2343.19, "end": 2372.39, "text": "A زائد B الكل ترمية if and only if absolute A B بساوي A B absolute A B بساوي A B ومن claim واحد", "tokens": [32, 30767, 16373, 3215, 363, 2423, 28820, 6055, 2288, 2304, 10632, 498, 293, 787, 498, 8236, 316, 363, 4724, 3794, 995, 45865, 316, 363, 8236, 316, 363, 4724, 3794, 995, 45865, 316, 363, 4032, 27842, 3932, 36764, 24401], "avg_logprob": -0.3072916559683971, "compression_ratio": 1.2755102040816326, "no_speech_prob": 0.0, "words": [{"start": 2343.19, "end": 2343.65, "word": "A", "probability": 0.33154296875}, {"start": 2343.65, "end": 2344.49, "word": " زائد", "probability": 0.6075846354166666}, {"start": 2344.49, "end": 2344.95, "word": " B", "probability": 0.8603515625}, {"start": 2344.95, "end": 2345.77, "word": " الكل", "probability": 0.71044921875}, {"start": 2345.77, "end": 2346.63, "word": " ترمية", "probability": 0.7186279296875}, {"start": 2346.63, "end": 2347.61, "word": " if", "probability": 0.576171875}, {"start": 2347.61, "end": 2347.99, "word": " and", "probability": 0.94189453125}, {"start": 2347.99, "end": 2348.37, "word": " only", "probability": 0.92822265625}, {"start": 2348.37, "end": 2348.89, "word": " if", "probability": 0.98046875}, {"start": 2348.89, "end": 2350.21, "word": " absolute", "probability": 0.65576171875}, {"start": 2350.21, "end": 2350.77, "word": " A", "probability": 0.385009765625}, {"start": 2350.77, "end": 2351.21, "word": " B", "probability": 0.69970703125}, {"start": 2351.21, "end": 2352.13, "word": " بساوي", "probability": 0.8118896484375}, {"start": 2352.13, "end": 2352.57, "word": " A", "probability": 0.3388671875}, {"start": 2352.57, "end": 2352.89, "word": " B", "probability": 0.9150390625}, {"start": 2352.89, "end": 2367.05, "word": " absolute", "probability": 0.71923828125}, {"start": 2367.05, "end": 2367.67, "word": " A", "probability": 0.8818359375}, {"start": 2367.67, "end": 2367.93, "word": " B", "probability": 0.9833984375}, {"start": 2367.93, "end": 2368.55, "word": " بساوي", 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"word": " أو", "probability": 0.52490234375}, {"start": 2388.53, "end": 2389.11, "word": " بضم", "probability": 0.8111979166666666}, {"start": 2389.11, "end": 2389.29, "word": " ال", "probability": 0.958984375}, {"start": 2389.29, "end": 2389.61, "word": " two", "probability": 0.890625}, {"start": 2389.61, "end": 2390.01, "word": " claims", "probability": 0.9150390625}, {"start": 2390.01, "end": 2390.21, "word": " مع", "probability": 0.9951171875}, {"start": 2390.21, "end": 2390.61, "word": " بعض", "probability": 0.9921875}, {"start": 2390.61, "end": 2394.07, "word": " طيب", "probability": 0.787109375}, {"start": 2394.07, "end": 2394.23, "word": " لو", "probability": 0.98388671875}, {"start": 2394.23, "end": 2394.63, "word": " أخلنا", "probability": 0.87451171875}, {"start": 2394.63, "end": 2394.99, "word": " جدر", "probability": 0.8546549479166666}, {"start": 2394.99, "end": 2395.51, "word": " التربية", "probability": 0.83642578125}, {"start": 2395.51, "end": 2396.45, "word": " 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أثبت أنه في جوار ل a بعمق epsilon اسمه u وفي جوار ل b بعمق epsilon والجوارين هذول المبروهود سقطوهم بسوء في يعني منفصلين عن بعض", "tokens": [3224, 15730, 16490, 9566, 42963, 22488, 18513, 37037, 24192, 257, 37037, 24192, 272, 4032, 257, 5551, 9381, 17082, 2288, 9154, 272, 4724, 16254, 5551, 12984, 3555, 2655, 14739, 3224, 8978, 10874, 2407, 9640, 5296, 257, 4724, 25957, 4587, 17889, 24525, 2304, 3224, 344, 4032, 41185, 10874, 2407, 9640, 5296, 272, 4724, 25957, 4587, 17889, 16070, 7435, 2407, 9640, 9957, 8032, 8848, 12610, 9673, 26890, 2407, 3224, 23328, 8608, 47432, 2407, 16095, 4724, 3794, 2407, 38207, 8978, 37495, 22653, 9154, 5172, 36520, 9957, 18871, 45030, 11242], "avg_logprob": -0.25781251316846804, "compression_ratio": 1.6686046511627908, "no_speech_prob": 0.0, "words": [{"start": 2639.11, "end": 2639.43, "word": "هذا", "probability": 0.869384765625}, {"start": 2639.43, "end": 2639.73, "word": " خط", "probability": 0.980224609375}, {"start": 2639.73, "end": 2640.37, "word": " 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"probability": 0.9169921875}, {"start": 2658.57, "end": 2659.13, "word": " بعمق", "probability": 0.95654296875}, {"start": 2659.13, "end": 2659.71, "word": " epsilon", "probability": 0.955078125}, {"start": 2659.71, "end": 2662.45, "word": " والجوارين", "probability": 0.83984375}, {"start": 2662.45, "end": 2662.89, "word": " هذول", "probability": 0.7783203125}, {"start": 2662.89, "end": 2663.55, "word": " المبروهود", "probability": 0.589306640625}, {"start": 2663.55, "end": 2664.17, "word": " سقطوهم", "probability": 0.7984619140625}, {"start": 2664.17, "end": 2664.57, "word": " بسوء", "probability": 0.6488037109375}, {"start": 2664.57, "end": 2664.79, "word": " في", "probability": 0.48095703125}, {"start": 2664.79, "end": 2665.05, "word": " يعني", "probability": 0.7164306640625}, {"start": 2665.05, "end": 2665.67, "word": " منفصلين", "probability": 0.8602294921875}, {"start": 2665.67, "end": 2665.81, "word": " عن", "probability": 0.884765625}, {"start": 2665.81, "end": 2666.17, "word": " بعض", "probability": 0.981201171875}], "temperature": 1.0}, {"id": 92, "seek": 269427, "start": 2667.43, "end": 2694.27, "text": "فبكل بساطة بجيس المسافة من a و b و باخد نص المسافة يعني لأن هنا take epsilon بساوي نص المسافة نص ال b minus", "tokens": [5172, 3555, 28820, 4724, 3794, 41193, 3660, 4724, 7435, 1829, 3794, 9673, 3794, 31845, 3660, 9154, 257, 4032, 272, 4032, 4724, 47283, 3215, 8717, 9381, 9673, 3794, 31845, 3660, 37495, 22653, 5296, 33456, 34105, 747, 17889, 4724, 3794, 995, 45865, 8717, 9381, 9673, 3794, 31845, 3660, 8717, 9381, 2423, 272, 3175], "avg_logprob": -0.260667065015206, "compression_ratio": 1.421487603305785, "no_speech_prob": 0.0, "words": [{"start": 2667.43, "end": 2668.05, "word": "فبكل", "probability": 0.708251953125}, {"start": 2668.05, "end": 2668.69, "word": " بساطة", "probability": 0.98681640625}, {"start": 2668.69, "end": 2669.95, "word": " بجيس", "probability": 0.84716796875}, {"start": 2669.95, "end": 2670.63, "word": " المسافة", "probability": 0.9818115234375}, {"start": 2670.63, "end": 2670.89, "word": " من", "probability": 0.72802734375}, {"start": 2670.89, "end": 2671.17, "word": " a", "probability": 0.53125}, {"start": 2671.17, "end": 2671.33, "word": " و", "probability": 0.9013671875}, {"start": 2671.33, "end": 2671.63, "word": " b", "probability": 0.412841796875}, {"start": 2671.63, "end": 2674.13, "word": " و", "probability": 0.57666015625}, {"start": 2674.13, "end": 2674.55, "word": " باخد", "probability": 0.9274088541666666}, {"start": 2674.55, "end": 2674.83, "word": " نص", "probability": 0.960693359375}, {"start": 2674.83, "end": 2675.57, "word": " المسافة", "probability": 0.9913330078125}, {"start": 2675.57, "end": 2676.15, "word": " يعني", "probability": 0.509765625}, {"start": 2676.15, "end": 2678.55, "word": " لأن", "probability": 0.37347412109375}, {"start": 2678.55, "end": 2678.85, "word": " هنا", "probability": 0.95166015625}, {"start": 2678.85, "end": 2679.69, "word": " take", "probability": 0.587890625}, {"start": 2679.69, "end": 2683.67, "word": " epsilon", "probability": 0.68310546875}, {"start": 2683.67, "end": 2688.77, "word": " بساوي", "probability": 0.7562255859375}, {"start": 2688.77, "end": 2689.23, "word": " نص", "probability": 0.98974609375}, {"start": 2689.23, "end": 2690.05, "word": " المسافة", "probability": 0.993408203125}, {"start": 2690.05, "end": 2690.63, "word": " نص", "probability": 0.758056640625}, {"start": 2690.63, "end": 2693.45, "word": " ال", "probability": 0.73828125}, {"start": 2693.45, "end": 2693.71, "word": " b", "probability": 0.468994140625}, {"start": 2693.71, "end": 2694.27, "word": " minus", "probability": 0.76806640625}], "temperature": 1.0}, {"id": 93, "seek": 271592, "start": 2697.48, "end": 2715.92, "text": "أو نص او نص المسافة بين A وB فهي نص المسافة لو كونت فترة", "tokens": [10721, 2407, 8717, 9381, 1975, 2407, 8717, 9381, 9673, 3794, 31845, 3660, 49374, 316, 4032, 33, 6156, 3224, 1829, 8717, 9381, 9673, 3794, 31845, 3660, 45164, 9122, 2407, 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E", "probability": 0.91162109375}, {"start": 2779.34, "end": 2780.98, "word": " وهذه", "probability": 0.73388671875}, {"start": 2780.98, "end": 2781.42, "word": " النقطة", "probability": 0.9876302083333334}, {"start": 2781.42, "end": 2782.08, "word": " هتصير", "probability": 0.986328125}], "temperature": 1.0}, {"id": 96, "seek": 281103, "start": 2785.91, "end": 2811.03, "text": "بزائد ابسلون و النقطة هذه بسالب ابسلون و نكون فترة مفتوحة تمام اذا انا في اندي و نسمي الفترة المفتوحة هذه نسميها ب", "tokens": [3555, 11622, 16373, 3215, 1975, 3555, 3794, 1211, 11536, 4032, 28239, 47432, 3660, 29538, 4724, 3794, 6027, 3555, 1975, 3555, 3794, 1211, 11536, 4032, 8717, 30544, 6156, 2655, 25720, 3714, 5172, 2655, 2407, 5016, 3660, 46811, 10943, 1975, 15730, 1975, 8315, 8978, 16472, 16254, 4032, 8717, 38251, 1829, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 29538, 8717, 38251, 1829, 11296, 4724], "avg_logprob": -0.32910156855359674, "compression_ratio": 1.8070175438596492, 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1.0}, {"id": 97, "seek": 283648, "start": 2817.18, "end": 2836.48, "text": "أذن هذا عبارة عن الـ U الفترة المفتوحة اذا هنا led take u", "tokens": [10721, 8848, 1863, 23758, 6225, 3555, 9640, 3660, 18871, 2423, 39184, 624, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 1975, 15730, 34105, 4684, 747, 344], "avg_logprob": -0.4199218824505806, "compression_ratio": 1.1341463414634145, "no_speech_prob": 0.0, "words": [{"start": 2817.18, "end": 2817.58, "word": "أذن", "probability": 0.5462239583333334}, {"start": 2817.58, "end": 2817.86, "word": " هذا", "probability": 0.73095703125}, {"start": 2817.86, "end": 2818.4, "word": " عبارة", "probability": 0.952880859375}, {"start": 2818.4, "end": 2818.64, "word": " عن", "probability": 0.76318359375}, {"start": 2818.64, "end": 2818.72, "word": " الـ", "probability": 0.38189697265625}, {"start": 2818.72, "end": 2818.98, "word": " U", "probability": 0.407958984375}, {"start": 2818.98, "end": 2819.6, "word": " الفترة", "probability": 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U is an epsilon neighborhood of A and V is an epsilon neighborhood of B ومش هيكوا بس and ممكن اثبات ان U تقاطع B بساوي فاي", "tokens": [34, 5797, 356, 624, 307, 364, 17889, 7630, 295, 316, 293, 691, 307, 364, 17889, 7630, 295, 363, 4032, 2304, 8592, 39896, 4117, 14407, 4724, 3794, 293, 3714, 43020, 1975, 12984, 3555, 9307, 16472, 624, 6055, 4587, 41193, 3615, 363, 4724, 3794, 995, 45865, 6156, 47302], "avg_logprob": -0.24102394251113243, "compression_ratio": 1.3225806451612903, "no_speech_prob": 0.0, "words": [{"start": 2866.91, "end": 2867.77, "word": "Clearly", "probability": 0.66912841796875}, {"start": 2867.77, "end": 2869.35, "word": " U", "probability": 0.57958984375}, {"start": 2869.35, "end": 2870.13, "word": " is", "probability": 0.8720703125}, {"start": 2870.13, "end": 2870.93, "word": " an", "probability": 0.86376953125}, {"start": 2870.93, "end": 2871.79, "word": " epsilon", "probability": 0.6767578125}, {"start": 2871.79, "end": 2873.75, "word": " neighborhood", 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الجوار التاني هذه الفترة المفتوحة منفصلة عن الفترة المفتوحة يوم طبعا؟", "tokens": [40228, 22653, 45164, 5551, 9778, 3215, 8315, 8032, 47302, 4032, 46958, 5016, 8032, 47302, 10874, 2407, 9640, 23758, 19446, 41185, 8592, 49429, 8717, 47432, 3660, 8978, 3224, 3714, 29245, 23328, 3660, 8978, 25724, 2407, 9640, 16712, 7649, 1829, 29538, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 5172, 36520, 3660, 18871, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 7251, 20498, 23032, 3555, 3615, 995, 22807], "avg_logprob": -0.13024553954601287, "compression_ratio": 1.7941176470588236, "no_speech_prob": 0.0, "words": [{"start": 2892.44, "end": 2892.8, "word": "يعني", "probability": 0.93408203125}, {"start": 2892.8, "end": 2892.96, "word": " لو", "probability": 0.93896484375}, {"start": 2892.96, "end": 2893.56, "word": " أخدنا", "probability": 0.9425048828125}, {"start": 2893.56, "end": 2896.16, "word": " هاي", "probability": 0.508544921875}, {"start": 2896.16, "end": 2896.9, 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2906.36, "word": " هذه", "probability": 0.48828125}, {"start": 2906.36, "end": 2906.84, "word": " الفترة", "probability": 0.9908854166666666}, {"start": 2906.84, "end": 2907.94, "word": " المفتوحة", "probability": 0.9862467447916666}, {"start": 2907.94, "end": 2910.56, "word": " منفصلة", "probability": 0.967041015625}, {"start": 2910.56, "end": 2910.88, "word": " عن", "probability": 0.98291015625}, {"start": 2910.88, "end": 2911.3, "word": " الفترة", "probability": 0.9871419270833334}, {"start": 2911.3, "end": 2911.96, "word": " المفتوحة", "probability": 0.9930826822916666}, {"start": 2911.96, "end": 2912.3, "word": " يوم", "probability": 0.5582275390625}, {"start": 2912.3, "end": 2915.54, "word": " طبعا؟", "probability": 0.8501953125}], "temperature": 1.0}, {"id": 101, "seek": 294845, "start": 2919.19, "end": 2948.45, "text": "إن هذا الكلام يعني واضح ان هذا عبارة عن epsilon neighborhood ل a فترة مفتوحة مركزها a نصف قطرة epsilon هذا نسميه epsilon neighborhood ل a و V الفترة المفتوحة هذه بي سالب epsilon و V موجب epsilon برضه عبارة عن epsilon neighborhood ل B و اتنين حسب الرسم منفصلين و هذا ممكن اثباته", "tokens": [28814, 1863, 23758, 2423, 28820, 10943, 37495, 22653, 4032, 46958, 5016, 16472, 23758, 6225, 3555, 9640, 3660, 18871, 17889, 7630, 5296, 257, 6156, 2655, 25720, 3714, 5172, 2655, 2407, 5016, 3660, 3714, 31747, 11622, 11296, 257, 8717, 9381, 5172, 12174, 9566, 25720, 17889, 23758, 8717, 38251, 1829, 3224, 17889, 7630, 5296, 257, 4032, 691, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 29538, 4724, 1829, 8608, 6027, 3555, 17889, 4032, 691, 3714, 29245, 3555, 17889, 4724, 43042, 3224, 6225, 3555, 9640, 3660, 18871, 17889, 7630, 5296, 363, 4032, 1975, 2655, 1863, 9957, 11331, 35457, 34892, 38251, 9154, 5172, 36520, 9957, 4032, 23758, 3714, 43020, 1975, 12984, 3555, 9307, 3224], "avg_logprob": -0.23324888031761926, "compression_ratio": 1.9216589861751152, "no_speech_prob": 0.0, "words": [{"start": 2919.19, "end": 2919.51, "word": "إن", "probability": 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"probability": 0.5274658203125}, {"start": 2991.79, "end": 2992.59, "word": " هاي", "probability": 0.4527587890625}, {"start": 2992.59, "end": 2992.77, "word": " a", "probability": 0.900390625}, {"start": 2992.77, "end": 2993.15, "word": " أصغر", "probability": 0.9942626953125}, {"start": 2993.15, "end": 2993.33, "word": " من", "probability": 0.99609375}, {"start": 2993.33, "end": 2993.71, "word": " b", "probability": 0.96923828125}, {"start": 2993.71, "end": 2994.59, "word": " و", "probability": 0.830078125}, {"start": 2994.59, "end": 2995.07, "word": " أثبتنا", "probability": 0.8994140625}, {"start": 2995.07, "end": 2995.19, "word": " في", "probability": 0.88330078125}, {"start": 2995.19, "end": 2995.53, "word": " الحالة", "probability": 0.99169921875}, {"start": 2995.53, "end": 2995.95, "word": " هذه", "probability": 0.8125}, {"start": 2995.95, "end": 2996.73, "word": " أن", "probability": 0.51611328125}, {"start": 2996.73, "end": 2997.09, "word": " u", "probability": 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[{"start": 3017.2400000000002, "end": 3018.42, "word": "باقي", "probability": 0.6471354166666666}, {"start": 3018.42, "end": 3018.94, "word": " الحالة", "probability": 0.9347330729166666}, {"start": 3018.94, "end": 3019.54, "word": " التانية", "probability": 0.9215494791666666}, {"start": 3019.54, "end": 3020.0, "word": " case", "probability": 0.400390625}, {"start": 3020.0, "end": 3020.52, "word": " 2", "probability": 0.488037109375}, {"start": 3020.52, "end": 3024.82, "word": " نثبت", "probability": 0.8289794921875}, {"start": 3024.82, "end": 3025.4, "word": " برضه", "probability": 0.818359375}, {"start": 3025.4, "end": 3027.12, "word": " المطلوب", "probability": 0.9322509765625}], "temperature": 1.0}, {"id": 105, "seek": 303888, "start": 3033.16, "end": 3038.88, "text": "القرآن في الحلقة التانية مماثل للقرآن اللي عملناه في الحلقة", "tokens": [6027, 4587, 2288, 148, 48506, 8978, 21542, 1211, 28671, 16712, 7649, 10632, 3714, 2304, 5718, 104, 1211, 24976, 4587, 2288, 148, 48506, 13672, 1829, 6225, 42213, 8315, 3224, 8978, 21542, 1211, 28671], "avg_logprob": -0.24668560606060605, "compression_ratio": 1.4155844155844155, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3033.16, "end": 3034.06, "word": "القرآن", "probability": 0.592236328125}, {"start": 3034.06, "end": 3034.2, "word": " في", "probability": 0.6826171875}, {"start": 3034.2, "end": 3034.56, "word": " الحلقة", "probability": 0.83642578125}, {"start": 3034.56, "end": 3034.98, "word": " التانية", "probability": 0.9715169270833334}, {"start": 3034.98, "end": 3036.4, "word": " مماثل", "probability": 0.89169921875}, {"start": 3036.4, "end": 3037.68, "word": " للقرآن", "probability": 0.884765625}, {"start": 3037.68, "end": 3037.84, "word": " اللي", "probability": 0.867431640625}, {"start": 3037.84, "end": 3038.32, "word": " عملناه", "probability": 0.9156494140625}, {"start": 3038.32, "end": 3038.38, "word": " في", "probability": 0.8828125}, {"start": 3038.38, "end": 3038.88, "word": " الحلقة", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 106, "seek": 307302, "start": 3050.04, "end": 3073.02, "text": "و هذا طبعا يكمل الفرحة، إذا الحالة التانية اللي فيها P أصفر من A، بس نضع P هنا و A هنا، و نفس العادة، فتصير هذا الـP و هذا الـU، و يعطينا نفس النتيجة، إت من كون كملنا المرهان اللي هو التمريد", "tokens": [2407, 23758, 23032, 3555, 3615, 995, 7251, 24793, 1211, 27188, 2288, 5016, 3660, 12399, 11933, 15730, 21542, 6027, 3660, 16712, 7649, 10632, 13672, 1829, 8978, 11296, 430, 5551, 9381, 5172, 2288, 9154, 316, 12399, 4724, 3794, 8717, 11242, 3615, 430, 34105, 4032, 316, 34105, 12399, 4032, 8717, 36178, 18863, 18513, 3660, 12399, 6156, 2655, 9381, 13546, 23758, 2423, 39184, 47, 4032, 23758, 2423, 39184, 52, 12399, 4032, 7251, 3615, 9566, 1829, 8315, 8717, 36178, 28239, 31371, 7435, 3660, 12399, 11933, 2655, 9154, 9122, 11536, 9122, 42213, 8315, 9673, 2288, 3224, 7649, 13672, 1829, 31439, 16712, 29973, 25708], "avg_logprob": -0.3172831766459407, "compression_ratio": 1.819672131147541, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 3050.04, "end": 3050.28, "word": "و", "probability": 0.42041015625}, {"start": 3050.28, "end": 3050.52, "word": " هذا", "probability": 0.45263671875}, {"start": 3050.52, "end": 3051.0, "word": " طبعا", "probability": 0.78717041015625}, {"start": 3051.0, "end": 3051.64, "word": " يكمل", "probability": 0.8777669270833334}, {"start": 3051.64, "end": 3052.28, "word": " الفرحة،", "probability": 0.651611328125}, {"start": 3052.28, "end": 3052.5, "word": " إذا", "probability": 0.71826171875}, {"start": 3052.5, "end": 3053.5, "word": " الحالة", "probability": 0.8875325520833334}, {"start": 3053.5, "end": 3053.88, "word": " التانية", "probability": 0.96240234375}, {"start": 3053.88, "end": 3054.04, "word": " اللي", "probability": 0.555908203125}, {"start": 3054.04, "end": 3054.38, "word": " فيها", "probability": 0.929443359375}, {"start": 3054.38, "end": 3054.52, "word": " P", "probability": 0.350341796875}, {"start": 3054.52, "end": 3054.96, "word": " أصفر", "probability": 0.73797607421875}, {"start": 3054.96, "end": 3055.14, "word": " من", "probability": 0.9619140625}, {"start": 3055.14, "end": 3055.88, "word": " A،", "probability": 0.775146484375}, {"start": 3055.88, "end": 3056.12, "word": " بس", "probability": 0.97119140625}, {"start": 3056.12, "end": 3056.56, "word": " نضع", "probability": 0.95458984375}, {"start": 3056.56, "end": 3056.82, "word": " P", "probability": 0.9833984375}, {"start": 3056.82, "end": 3057.12, "word": " هنا", "probability": 0.99609375}, {"start": 3057.12, "end": 3057.3, "word": " و", "probability": 0.9541015625}, {"start": 3057.3, "end": 3057.52, "word": " A", "probability": 0.6376953125}, {"start": 3057.52, "end": 3057.82, "word": " هنا،", "probability": 0.7724609375}, {"start": 3057.82, "end": 3057.88, "word": " و", "probability": 0.75927734375}, {"start": 3057.88, "end": 3058.12, "word": " نفس", "probability": 0.84814453125}, {"start": 3058.12, "end": 3060.12, "word": " العادة،", "probability": 0.62518310546875}, {"start": 3060.12, "end": 3060.66, "word": " فتصير", "probability": 0.82568359375}, {"start": 3060.66, "end": 3061.02, "word": " هذا", "probability": 0.8388671875}, {"start": 3061.02, "end": 3061.94, "word": " الـP", "probability": 0.468505859375}, {"start": 3061.94, "end": 3062.12, "word": " و", "probability": 0.77685546875}, {"start": 3062.12, "end": 3062.34, "word": " هذا", "probability": 0.9560546875}, {"start": 3062.34, "end": 3063.82, "word": " الـU،", "probability": 0.8428955078125}, {"start": 3063.82, "end": 3064.16, "word": " و", "probability": 0.96826171875}, {"start": 3064.16, "end": 3065.04, "word": " يعطينا", "probability": 0.85927734375}, {"start": 3065.04, "end": 3065.44, "word": " نفس", "probability": 0.980224609375}, {"start": 3065.44, "end": 3067.0, "word": " النتيجة،", "probability": 0.68935546875}, {"start": 3067.0, "end": 3067.22, "word": " إت", "probability": 0.2977294921875}, {"start": 3067.22, "end": 3067.34, "word": " من", "probability": 0.77587890625}, {"start": 3067.34, "end": 3067.8, "word": " كون", "probability": 0.760009765625}, {"start": 3067.8, "end": 3069.54, "word": " كملنا", "probability": 0.9049479166666666}, {"start": 3069.54, "end": 3071.5, "word": " المرهان", "probability": 0.7618408203125}, {"start": 3071.5, "end": 3072.0, "word": " اللي", "probability": 0.73486328125}, {"start": 3072.0, "end": 3072.3, "word": " هو", "probability": 0.9912109375}, {"start": 3072.3, "end": 3073.02, "word": " التمريد", "probability": 0.77783203125}], "temperature": 1.0}, {"id": 107, "seek": 308087, "start": 3074.53, "end": 3080.87, "text": "وطبعا بعد ذلك ان شاء الله هنكمل حل ال تمارين لل sport الخادم في نفس الموضوع", "tokens": [2407, 9566, 3555, 3615, 995, 39182, 29910, 23275, 16472, 13412, 16606, 21984, 8032, 1863, 24793, 1211, 11331, 1211, 2423, 46811, 9640, 9957, 24976, 7282, 33962, 18513, 2304, 8978, 8717, 36178, 9673, 2407, 11242, 45367], "avg_logprob": -0.3339285714285714, "compression_ratio": 1.2871287128712872, "no_speech_prob": 0.0, "words": [{"start": 3074.53, "end": 3075.09, "word": "وطبعا", "probability": 0.8580078125}, {"start": 3075.09, "end": 3075.39, "word": " بعد", "probability": 0.9033203125}, {"start": 3075.39, "end": 3075.61, "word": " ذلك", "probability": 0.772705078125}, {"start": 3075.61, "end": 3075.73, "word": " ان", "probability": 0.69091796875}, {"start": 3075.73, "end": 3075.99, "word": " شاء", "probability": 0.97509765625}, {"start": 3075.99, "end": 3076.13, "word": " الله", "probability": 0.962890625}, {"start": 3076.13, "end": 3076.81, "word": " هنكمل", "probability": 0.8421630859375}, {"start": 3076.81, "end": 3077.05, "word": " حل", "probability": 0.89990234375}, {"start": 3077.05, "end": 3077.19, "word": " ال", "probability": 0.11358642578125}, {"start": 3077.19, "end": 3077.73, "word": " تمارين", "probability": 0.71142578125}, {"start": 3077.73, "end": 3077.97, "word": " لل", "probability": 0.367431640625}, {"start": 3077.97, "end": 3078.45, "word": " sport", "probability": 0.78369140625}, {"start": 3078.45, "end": 3079.65, "word": " الخادم", "probability": 0.8479817708333334}, {"start": 3079.65, "end": 3079.87, "word": " في", "probability": 0.974609375}, {"start": 3079.87, "end": 3080.29, "word": " نفس", "probability": 0.981689453125}, {"start": 3080.29, "end": 3080.87, "word": " الموضوع", "probability": 0.5843658447265625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 3082.867, "duration_after_vad": 2668.6993749999897}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..61084377a31c7c3ec1d6014a9fab90e717de4238
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_postprocess.srt
@@ -0,0 +1,1780 @@
+1
+00:00:20,750 --> 00:00:26,090
+Okay اذا اليوم ان شاء الله هنكمل موضوع ال limit
+
+2
+00:00:26,090 --> 00:00:32,390
+theorems او نظريات النهايات و من النظريات المهمة
+
+3
+00:00:32,390 --> 00:00:39,710
+هذه هي نظرية 12 بتقول لو في عندي sequence x in و
+
+4
+00:00:39,710 --> 00:00:44,570
+ال sequence هذي convergent ل x فال sequence of
+
+5
+00:00:44,570 --> 00:00:49,350
+absolute valuesبتطلع convergence وال limit تبعتها
+
+6
+00:00:49,350 --> 00:00:55,490
+تطلع absolute .. absolute limit تبعت ال sequence
+
+7
+00:00:55,490 --> 00:01:00,750
+XL فالبرهان
+
+8
+00:01:00,750 --> 00:01:04,470
+بيتمد على ال triangle inequality
+
+9
+00:01:07,360 --> 00:01:13,720
+أحد صور ال triangle inequality كانت المتباينة هذه
+
+10
+00:01:13,720 --> 00:01:20,740
+absolute a minus absolute b وأخد ال absolute value
+
+11
+00:01:20,740 --> 00:01:28,600
+هذا أصغر من أو ساوي absolute a minus bفلو أخدت هنا
+
+12
+00:01:28,600 --> 00:01:36,160
+a بساوي xn و b بساوي x فبطلع الكلام هذا صحيح لكل
+
+13
+00:01:36,160 --> 00:01:43,760
+الأعداد الطبيعية n الآن أنا عندي xn converges to x
+
+14
+00:01:43,760 --> 00:01:51,740
+فلو أخدت أي epsilon أكبر من الصفر given
+
+15
+00:01:55,040 --> 00:02:00,540
+واندي انا x in converge ل x، اذا هذا بيدّي انه
+
+16
+00:02:00,540 --> 00:02:03,580
+يوجد
+
+17
+00:02:03,580 --> 00:02:13,660
+capital N عدد طبيعي يعتمد على epsilon بحيث انه لو
+
+18
+00:02:13,660 --> 00:02:18,260
+كان N أكبر من أو ساوي capital N فهذا بيدّي ان
+
+19
+00:02:18,260 --> 00:02:22,080
+absolute x in minus x أصغر من epsilon
+
+20
+00:02:25,260 --> 00:02:30,300
+وبالتالي من هنا إذا الهدف بيطلع أصغر من epsilon
+
+21
+00:02:30,300 --> 00:02:34,260
+لكل
+
+22
+00:02:34,260 --> 00:02:41,180
+n أكبر من أو ساوي capital N إذا
+
+23
+00:02:41,180 --> 00:02:44,800
+أنا هيك بكون أثبتت إنه لأي epsilon أكبر من سفر
+
+24
+00:02:44,800 --> 00:02:50,760
+يوجد capital N يعتمد على epsilon عدد طبيعي بحيث
+
+25
+00:02:50,760 --> 00:02:57,040
+لكل n أكبر من أو ساوي capital Nالقيمة المطلقة ل
+
+26
+00:02:57,040 --> 00:03:02,480
+absolute xn minus absolute x أصغر من epsilon إذا
+
+27
+00:03:02,480 --> 00:03:07,900
+حسب تعريف epsilon capital N for limits هذا معناه
+
+28
+00:03:07,900 --> 00:03:14,260
+بالظبط أن limit absolute xn as n tends to infinity
+
+29
+00:03:14,260 --> 00:03:21,790
+بساوي absolute x وهو المطلوبOkay تمام اذا هذا
+
+30
+00:03:21,790 --> 00:03:32,890
+بيكمل برهان نظرية اتناش تمام واضح النظرية
+
+31
+00:03:32,890 --> 00:03:39,270
+اللي بعدها نظرية تلاتاش بتقول لو انا فيها اندي
+
+32
+00:03:39,270 --> 00:03:45,490
+sequence حدودها كلها غير سالبة حدود ال sequence xm
+
+33
+00:03:45,490 --> 00:03:50,750
+كلها غير سالبة اعداد غير سالبةوالـ sequence لو
+
+34
+00:03:50,750 --> 00:03:57,730
+كانت الـ sequence Xn convergent to some X فالـ
+
+35
+00:03:57,730 --> 00:04:02,730
+limit للـ sequence of square roots لـ Xn تطلع
+
+36
+00:04:02,730 --> 00:04:08,470
+convergent والـ limit تبعتها بساول square root للـ
+
+37
+00:04:08,470 --> 00:04:09,890
+limit للـ sequence Xn
+
+38
+00:04:13,780 --> 00:04:19,760
+والبرهان تبع النظرية دي سهل انا اول شي عندى احنا
+
+39
+00:04:19,760 --> 00:04:25,060
+فرضين ان ال limit ل Xn بساوي X في نظرية تمانية
+
+40
+00:04:25,060 --> 00:04:28,700
+قلنا ان لو كانت حدود ال sequence Xn كلها غير سالبة
+
+41
+00:04:28,700 --> 00:04:34,360
+ف limit ل sequence Xn اللى هى X ايضا تطلع غير
+
+42
+00:04:34,360 --> 00:04:40,840
+سالبة اذا X اكبر من او ساوى 0الان في عندي حالتين
+
+43
+00:04:40,840 --> 00:04:46,300
+ال X هنا أكبر من أو ساوي سفر ففي عندي احتمالين اما
+
+44
+00:04:46,300 --> 00:04:54,260
+X بساوي سفر او X أكبر من السفر تمام و في كل حالة
+
+45
+00:04:54,920 --> 00:04:59,540
+مطلوب مني ان اثبت ان limit ال square root ل xn
+
+46
+00:04:59,540 --> 00:05:03,960
+بساوي ال square root of x تمام؟ انشوف في الحالة
+
+47
+00:05:03,960 --> 00:05:08,520
+الأولى لو كانت ال x بساوي سفر وانا عندي من الفرض
+
+48
+00:05:08,520 --> 00:05:15,550
+xn converges to x اللي هي سفرأذا لو أخدت أي إبسلون
+
+49
+00:05:15,550 --> 00:05:20,250
+أكبر من السفر من كون ال sequence هذه converge
+
+50
+00:05:20,250 --> 00:05:24,270
+للسفر إذا لأي إبسلون يوجد capital N يعتمد على
+
+51
+00:05:24,270 --> 00:05:30,150
+إبسلون بحيث المسافة بين xn والسفر أصغر من إبسلون
+
+52
+00:05:30,150 --> 00:05:33,470
+تربية لكل N أكبر من أوسعه ال capital N هذا من
+
+53
+00:05:33,470 --> 00:05:36,690
+تعريف ال conversion ممكن أحط هنا إبسلون أو إبسلون
+
+54
+00:05:36,690 --> 00:05:42,940
+تربية مافي مشكلةطيب أنا عندي xn من الفرض الـ xn
+
+55
+00:05:42,940 --> 00:05:48,840
+كلهم أكبر من أو يساوي سفر وبالتالي القيمة المطلقة
+
+56
+00:05:48,840 --> 00:05:53,800
+لـ xn بساوي نفسها ناخد
+
+57
+00:05:53,800 --> 00:05:59,120
+الجدر التربيعي للحدود المتباينة هذه هي ال square
+
+58
+00:05:59,120 --> 00:06:04,790
+root of xnبساوي ال absolute value ل square root ل
+
+59
+00:06:04,790 --> 00:06:10,190
+xn minus صفر وهذا أصغر من إبسلون square root
+
+60
+00:06:10,190 --> 00:06:13,870
+لإبسلون تربية بيطلع إبسلون هذا الكلام صحيح for
+
+61
+00:06:13,870 --> 00:06:18,830
+every n bigger than or equal capital N طب هذا
+
+62
+00:06:18,830 --> 00:06:23,050
+معناه بما أن إبسلون was arbitrarily بما أن احنا
+
+63
+00:06:23,050 --> 00:06:29,850
+أثبتنا هذا الكلام لكل إبسلون عدد موجبهذا من تعريف
+
+64
+00:06:29,850 --> 00:06:34,350
+epsilon capital N for limits للنهايات هذا معناه
+
+65
+00:06:34,350 --> 00:06:40,970
+limit ال square root ل XN بالساوي السفر لما N تولى
+
+66
+00:06:40,970 --> 00:06:47,140
+Nوهذا ايه هذا اللي هو المطلوب طيب السفر هنا احنا
+
+67
+00:06:47,140 --> 00:06:50,780
+ماخدين x بالساوية سفر فالسفر هذا هو square root ل
+
+68
+00:06:50,780 --> 00:06:54,360
+x اذا هين اثبتت ان limit square root ل x in
+
+69
+00:06:54,360 --> 00:06:58,820
+بالساوية square root ل x في حالة لما x بالساوية
+
+70
+00:06:58,820 --> 00:07:07,280
+سفر تمام باقي نثبتالنتيجة نفسها في حالة لما X أكبر
+
+71
+00:07:07,280 --> 00:07:11,740
+من 0 تفضلي قال جيت حكيت أنه ممكن أخد يبسلون مش
+
+72
+00:07:11,740 --> 00:07:15,740
+يبسلون تربيه لما أكمل خطوة بعد تطلع جدر اليبسلون
+
+73
+00:07:15,740 --> 00:07:19,660
+يعني أقل من الجدر يبسلون جدر اليبسلون قولت أن أحنا
+
+74
+00:07:19,660 --> 00:07:23,600
+خلنا يبسلون تربيه عشان لما أخد الجدر يطلع يبسلون
+
+75
+00:07:23,600 --> 00:07:29,520
+مافي مشكلة يعني اعتبر هذه هي اليبسلون مش اليبسلون
+
+76
+00:07:29,520 --> 00:07:34,300
+أكبر عدد أكبر من 0 givenإذا إبسلون تربية برضه عدد
+
+77
+00:07:34,300 --> 00:07:39,880
+موجة بقى تقري هو ال given وبالتالي يوجد أن تعتمد
+
+78
+00:07:39,880 --> 00:07:44,320
+على إبسلون تربية بدل إبسلون طب إبسلون تربية تعتمد
+
+79
+00:07:44,320 --> 00:07:48,420
+على إبسلونإذا ليش ما نقول إذا يوجد N تعتمد على
+
+80
+00:07:48,420 --> 00:07:52,240
+إبسلون وإعتبر الإبسلون تربية بدل إبسلون في ال
+
+81
+00:07:52,240 --> 00:07:55,920
+definition فمافي مشكلة بس خدناها الإبسلون تربية
+
+82
+00:07:55,920 --> 00:07:59,660
+عشان لما ناخد جدر التربية يطلع أندي أصغر من إبسلون
+
+83
+00:07:59,660 --> 00:08:03,760
+وبالتالي نقول حسب التعريف إذا limit جدر X N بساوة
+
+84
+00:08:03,760 --> 00:08:11,840
+ستة تمام اللي هي جدر X في أي سؤال تاني؟طيب، نشوف
+
+85
+00:08:11,840 --> 00:08:16,800
+الحالة التانية، لو كانت ال X هذه أكبر من صفر، إذا
+
+86
+00:08:16,800 --> 00:08:20,640
+جدر ال X بالتأكيد أكبر من الصفر، وبالتالي جدر X in
+
+87
+00:08:20,640 --> 00:08:26,120
+زي جدر X أكبر من أو ساوي جدر ال X، لأن هذا أكبر من
+
+88
+00:08:26,120 --> 00:08:35,430
+أو ساوي صفر، وهذا موجب، لأن ال X موجبةطيب، الآن
+
+89
+00:08:35,430 --> 00:08:40,630
+هذا المقدار أكبر من أو ساوي هذا واتنين موجبين، إذا
+
+90
+00:08:40,630 --> 00:08:47,950
+المقلوب الكبير أصغر من أو ساوي المقلوب الصغير هذه
+
+91
+00:08:47,950 --> 00:08:53,010
+الخاصية أخدناها في chapter one وبناء عليه
+
+92
+00:09:01,430 --> 00:09:06,810
+بنان على ذلك انا ممكن احسب جدر xn minus جدر ال x
+
+93
+00:09:06,810 --> 00:09:12,870
+بضرب المقدار هذا في المرافق تبعه بسطه مقاما، هاي
+
+94
+00:09:12,870 --> 00:09:16,870
+المرافق تبعه بسطه مقام فكأني ضربت المقدار هذا في
+
+95
+00:09:16,870 --> 00:09:23,030
+واحد، اذا هذا بساوي نفسه ضرب مرافقه على مرافقه،
+
+96
+00:09:23,030 --> 00:09:27,870
+تمام؟الان ال bus تحليل الفرق بين المربعين فبطلع
+
+97
+00:09:27,870 --> 00:09:33,170
+مربع هذا سالب مربع هذا اللي هو x in negative x و
+
+98
+00:09:33,170 --> 00:09:38,310
+بيبقى ال end في المقام المقدار هذا الان ناخد
+
+99
+00:09:38,310 --> 00:09:43,370
+القيمة المطلقة للكلام هذا بيساوي القيمة المطلقة
+
+100
+00:09:43,370 --> 00:09:48,230
+للطرف اليمين القيمة المطلقة لل bus على القيمة
+
+101
+00:09:48,230 --> 00:09:53,070
+المطلقة للمقام المقام هذا موجب فالقيمة المطلقة له
+
+102
+00:09:53,070 --> 00:09:58,770
+نفسهأذا الأن أنا في عندي sequence اللي هي الحد
+
+103
+00:09:58,770 --> 00:10:02,810
+العام تبعها square root of xn وفي عندي عدد square
+
+104
+00:10:02,810 --> 00:10:10,390
+root of x المسافة بينهم أصغر من أو يساوي أصغر من
+
+105
+00:10:10,390 --> 00:10:15,610
+أو يساوي هي المسافة هذه بالساوي واحد على square
+
+106
+00:10:15,610 --> 00:10:21,870
+root of xn زي square root of x والكسر هذا من
+
+107
+00:10:21,870 --> 00:10:27,950
+المتباينة تسعةهذا الكثير أصغر من أو يساوي واحد على
+
+108
+00:10:27,950 --> 00:10:32,610
+square root of x ضرب absolute x in سالب x الآن
+
+109
+00:10:32,610 --> 00:10:43,830
+ارجعوا لنظرية اتنين اربعة with
+
+110
+00:10:43,830 --> 00:10:52,060
+c عدد موجب ساوي واحد على جدر ال x هذا عدد موجبو a
+
+111
+00:10:52,060 --> 00:10:59,780
+n بساوي x n minus x إذن
+
+112
+00:10:59,780 --> 00:11:03,940
+هى يوجد c عدد موجب اللى هو واحد على جدر ال X و هى
+
+113
+00:11:03,940 --> 00:11:08,820
+فى عندي sequence a n الحد العام تبعها x n سالد x و
+
+114
+00:11:08,820 --> 00:11:14,680
+ال sequence هذه تقول إلى سفر as n tends to
+
+115
+00:11:14,680 --> 00:11:19,870
+infinityلأن انا من المعطيات عندي xn تقول x أو
+
+116
+00:11:19,870 --> 00:11:24,490
+limit xn بساوي x، لذلك limit الفرق بساوي سفر، لذلك
+
+117
+00:11:24,490 --> 00:11:29,890
+حسب نظرية 2.4، كل شروطة متحققة، وبالتالي، لذلك حسب
+
+118
+00:11:29,890 --> 00:11:34,630
+النظرية هذه، by theorem 2.4، بيطلع عندي limit
+
+119
+00:11:34,630 --> 00:11:41,190
+square root ل xn بساوي square root ل xوهو المطلوب
+
+120
+00:11:41,190 --> 00:11:46,690
+اثباته اذا هاي اثبتنا ان limit ال square root ل X
+
+121
+00:11:46,690 --> 00:11:50,410
+ان بساوي ال square root ل X في حالة لما X تكون
+
+122
+00:11:50,410 --> 00:11:54,750
+موجبة و الحالة الأولى في حالة لما X صفر برضه
+
+123
+00:11:54,750 --> 00:11:58,410
+اثبتنا نفس الحاجة لذلك بنكون كملنا برهان نظرية
+
+124
+00:11:58,410 --> 00:12:02,690
+تمام؟ في حد عنده اي سؤال او استفسار واضح البرهان؟
+
+125
+00:12:05,660 --> 00:12:12,800
+في نظرية هنا ممكن نسميها نعتبرها ratio test اختبار
+
+126
+00:12:12,800 --> 00:12:21,660
+الكسر او النسبة او ايش
+
+127
+00:12:21,660 --> 00:12:27,300
+ال ratio test ماذا هذا ال ratio test بيقول هذا ال
+
+128
+00:12:27,300 --> 00:12:31,120
+ratio test بتعلق بال sequences of positive numbers
+
+129
+00:12:32,030 --> 00:12:35,090
+يعني عشان أنا أطبخ ال ratio test لازم ال sequence
+
+130
+00:12:35,090 --> 00:12:39,170
+تبعتي تكون حدودها كلها موجة بقى فلو في عندي
+
+131
+00:12:39,170 --> 00:12:44,310
+sequence of positive real numbers such that limit
+
+132
+00:12:44,310 --> 00:12:49,050
+ال ratio ل xn زائد واحد على xn exists موجود أو
+
+133
+00:12:49,050 --> 00:12:54,370
+بتساوي عدد حقيقي L و لو كان هذا العدد L أصغر من
+
+134
+00:12:54,370 --> 00:13:01,300
+واحد ف limit ال sequence xn بتساوي سبلهذا هو ال
+
+135
+00:13:01,300 --> 00:13:07,380
+ratio test برهان ال test أو النظرية هذه موجود في
+
+136
+00:13:07,380 --> 00:13:11,680
+الكتاب نظرية تلاتة اتنين احداشر فحاسبكم تقرؤوا
+
+137
+00:13:11,680 --> 00:13:15,780
+البرهان برهان سهل مش صعب بيعتمد على الحاجات اللي
+
+138
+00:13:15,780 --> 00:13:20,340
+أخدناها فعايزينكم
+
+139
+00:13:20,340 --> 00:13:23,660
+تفتحوا الكتاب و تقرؤوا برهان و تفهموا لحالكم بعد
+
+140
+00:13:23,660 --> 00:13:28,800
+ما خدنا كل هالبرهين بدنا ياكم تعتمدوا عن أنفسكم
+
+141
+00:13:28,800 --> 00:13:33,440
+شويةتمام؟ و اللي عنده أي صعوبة في فهم البرهان
+
+142
+00:13:33,440 --> 00:13:38,840
+ترجعليه إذا هسيكم تخرق البرهان من الكتاب طيب نهار
+
+143
+00:13:38,840 --> 00:13:42,540
+.. الآن الكتاب للأسف مش في أمثلة في ال section هذا
+
+144
+00:13:42,540 --> 00:13:49,000
+تلاتة اتنين فهعطيلكم أس .. examples أو أمثلة بحال
+
+145
+00:13:49,000 --> 00:13:52,100
+من التمرين بحال بعض التمرين فأول مثل
+
+146
+00:13:58,060 --> 00:14:02,820
+فأول مثال هو exercise تمانتاش الفرحة c في section
+
+147
+00:14:02,820 --> 00:14:06,700
+تلاتة اتنين أو صفحة تمانية وستين في الكتاب المقرر
+
+148
+00:14:06,700 --> 00:14:10,300
+السؤال هذا بيقول discuss the convergence of the
+
+149
+00:14:10,300 --> 00:14:15,820
+sequence xn اللي لحد العام ال nth term تبعها b to
+
+150
+00:14:15,820 --> 00:14:20,600
+n على n factorial حيث بيه عدد حقيقي أكبر من واحد
+
+151
+00:14:21,470 --> 00:14:24,070
+Discurses ل Convergence يعني بين هل ال sequence
+
+152
+00:14:24,070 --> 00:14:27,850
+هذي Convergent ولا Divergent وده كانت Convergent
+
+153
+00:14:27,850 --> 00:14:35,790
+عايزين نجيب ال limit تبعتها طيب تعالوا أول شي احنا
+
+154
+00:14:35,790 --> 00:14:41,150
+طبعا هنطبق ال ratio test نظرية 2.14 اللي هو الرسم
+
+155
+00:14:41,150 --> 00:14:45,490
+منها ال ratio testلتطبيق ال ratio test بلزمني
+
+156
+00:14:45,490 --> 00:14:50,690
+اتأكد ان ال sequence xn حدودها موجبة وهذا صحيح لان
+
+157
+00:14:50,690 --> 00:14:54,970
+ال bus b اكبر من واحد و b أكبر من واحد و n
+
+158
+00:14:54,970 --> 00:14:57,830
+factorial عدد موجب لان هذه sequence of positive
+
+159
+00:14:57,830 --> 00:15:07,550
+real numbers الآن ال ratio ل xn زياد واحد و xn هي
+
+160
+00:15:07,550 --> 00:15:12,230
+عندي xn زياد واحد عوض عنها بدل n بn زياد واحد
+
+161
+00:15:13,160 --> 00:15:18,740
+وضربها في مقلوب xn هي مقلوب xn وطبعا احنا عارفين
+
+162
+00:15:18,740 --> 00:15:25,460
+ان n plus one factorial بتساوي n plus one في n
+
+163
+00:15:25,460 --> 00:15:31,900
+factorial هذا بنفك حاصل ضرب زي هذا n factorial
+
+164
+00:15:31,900 --> 00:15:37,640
+بتروح مع n factorial وb to n بتروح مع b to n بضل b
+
+165
+00:15:38,750 --> 00:15:43,210
+بعد الاختصارات والتبسيط الكاسر هذا بيطلع بي على n
+
+166
+00:15:43,210 --> 00:15:47,870
+زياد واحد الان لما انت قول ل infinity ان زياد واحد
+
+167
+00:15:47,870 --> 00:15:54,050
+بتقول ل infinity مقلوبة بروح ل سفر ضرب بي عدد موجة
+
+168
+00:15:54,050 --> 00:15:58,990
+بروح ل سفر اذا limit بي على ان زياد واحد بساوي بي
+
+169
+00:15:58,990 --> 00:16:03,290
+في limit واحد على ان زياد واحد اللي هي سفر بي في
+
+170
+00:16:03,290 --> 00:16:10,590
+سفر بساوي سفر تمام؟إذا أنا عندي L اللي هو بمثل
+
+171
+00:16:10,590 --> 00:16:17,570
+limit ال ratio هذا طلع بساوي سفر عدد حقيقي أصغر من
+
+172
+00:16:17,570 --> 00:16:23,910
+واحد إذا حسب ال ratio test limit لل sequence xn
+
+173
+00:16:23,910 --> 00:16:28,030
+بساوي سفر إذا هنا أثبتنا إن ال sequence convergent
+
+174
+00:16:28,030 --> 00:16:34,010
+ونهيتها بتطلع بالساوي سفر تمام؟ واضح؟ إذا تطبيق
+
+175
+00:16:34,010 --> 00:16:35,510
+مباشر على ال ratio test
+
+176
+00:16:38,490 --> 00:16:42,730
+مثال تاني مثال
+
+177
+00:16:42,730 --> 00:16:46,330
+تاني عبارة عن exercise اتنين فرع a section تلاتة
+
+178
+00:16:46,330 --> 00:16:54,610
+اتنين بنشوف ايه ال exercise هذا بيقول give
+
+179
+00:16:54,610 --> 00:17:01,930
+an example of two divergent sequences two
+
+180
+00:17:01,930 --> 00:17:04,090
+divergent sequences
+
+181
+00:17:06,940 --> 00:17:12,840
+such that there are some مجموعهم there
+
+182
+00:17:12,840 --> 00:17:19,020
+are some converges نعطي
+
+183
+00:17:19,020 --> 00:17:24,060
+مثال ل two divergent sequences تنتهي from two
+
+184
+00:17:24,060 --> 00:17:29,140
+divergent لكن مجموعهم convergent فأسهل مثال هو مثل
+
+185
+00:17:29,140 --> 00:17:36,270
+هذا الحلناخد الـ sequence xn للحد العام تبعها سالب
+
+186
+00:17:36,270 --> 00:17:42,430
+واحد to n و n بتبدأ من واحد إلى ملا نهاية طبعا ال
+
+187
+00:17:42,430 --> 00:17:48,210
+sequence هذه لو بيننا انفرفتها فحدودها هتكون هكذا
+
+188
+00:17:48,210 --> 00:17:53,670
+أول حد سالب واحد، تاني واحد، تالت سالب واحد،
+
+189
+00:17:53,670 --> 00:18:00,040
+الرابع واحد، و هكذاوناخد ال sequence yn الحد العام
+
+190
+00:18:00,040 --> 00:18:04,760
+تبعها سالب واحد قص ان زاد واحد وان طبعا تبدأ من
+
+191
+00:18:04,760 --> 00:18:12,080
+واحد فهذه ال sequence حدودها هتكون أول حد واحد،
+
+192
+00:18:12,080 --> 00:18:17,160
+التاني سالب واحد، التالت واحد، الرابع سالب واحد و
+
+193
+00:18:17,160 --> 00:18:17,620
+هكذا
+
+194
+00:18:20,300 --> 00:18:25,720
+تمام احنا اثبتنا بالتفصيل ان ال sequence xn هذي
+
+195
+00:18:25,720 --> 00:18:29,660
+divergent by contradiction فرضنا انها convergent
+
+196
+00:18:29,660 --> 00:18:35,960
+وصلنا الى تناغم صح؟ طب ما هذي هي هذي هي ال
+
+197
+00:18:35,960 --> 00:18:43,750
+sequence ال sequence yn هي سالب ال sequence xnو Xn
+
+198
+00:18:43,750 --> 00:18:47,710
+is divergent و Yn is divergent او بنفس البرهان
+
+199
+00:18:47,710 --> 00:18:51,530
+ممكن نعمل نفس البرهان اذا هي عندي مثال على two
+
+200
+00:18:51,530 --> 00:18:57,670
+sequences كلاهما both are divergent لكن لما نيجي
+
+201
+00:18:57,670 --> 00:19:04,750
+نجمعهم لو أخدت ال sequence جديدة ال inf term تبعها
+
+202
+00:19:04,750 --> 00:19:09,070
+او الحد العام تبعها هو مجموعة ال inf term زي Xn
+
+203
+00:19:09,070 --> 00:19:15,280
+وYn هذه sequence تالتة جديدةما هو الحد العام لهذه
+
+204
+00:19:15,280 --> 00:19:21,360
+الـ sequence؟ اجمع الحد الأول على الأول بيطلع سفر،
+
+205
+00:19:21,360 --> 00:19:25,740
+التاني على التاني سفر، إذا هذه عبارة عن الـ
+
+206
+00:19:25,740 --> 00:19:30,300
+sequence constant zero ثابت سفر أو الـ sequence
+
+207
+00:19:30,300 --> 00:19:35,480
+الحد العام تبعها ثابت سفر وطبعا أي sequence ثابتة
+
+208
+00:19:35,480 --> 00:19:39,880
+بتكون convergent و limit تبعتها هي الحد الثابت
+
+209
+00:19:39,880 --> 00:19:45,000
+نفسه، لذلك limit لهذه الـ sequence ثابت سفرإذا هذا
+
+210
+00:19:45,000 --> 00:19:50,700
+مثال على two divergent sequences their sum is
+
+211
+00:19:50,700 --> 00:19:55,900
+convergent okay تمام؟ في برضه حاجات زي هذه ممكن
+
+212
+00:19:55,900 --> 00:20:00,200
+ينقلب منكم جيبي مثال على two sequences contain
+
+213
+00:20:00,200 --> 00:20:05,820
+مثلا convergent لكن حصل ضربهم divergent يعني حاجات
+
+214
+00:20:05,820 --> 00:20:11,880
+زي هيك و هكذا في الكتاب في تمارينعلى هذا السياق
+
+215
+00:20:11,880 --> 00:20:22,020
+هتشوفوها تمام؟ مفهوم؟ واضح المثال هذا؟ طيب مثال
+
+216
+00:20:22,020 --> 00:20:29,440
+رقم تلاتة هذا
+
+217
+00:20:29,440 --> 00:20:32,900
+عبارة عن exercise أربعة عشر في section تلاتة اتنين
+
+218
+00:20:35,100 --> 00:20:41,360
+بقول خد zn بساوي a to n plus b to n to the power
+
+219
+00:20:41,360 --> 00:20:47,240
+one over n where a و b are positive numbers and a
+
+220
+00:20:47,240 --> 00:20:56,260
+less than b prove أن limit zn بساوي العدد b تمام؟
+
+221
+00:20:56,260 --> 00:21:02,420
+لبرهان ذلك أنا عندي من الفرض a positive إذا a to n
+
+222
+00:21:02,420 --> 00:21:09,520
+positiveوكذلك وبالتالي b to n أصغر من a to n plus
+
+223
+00:21:09,520 --> 00:21:16,460
+b to n الان ناخد ال nth root لطرفي المتبينة هذه
+
+224
+00:21:16,460 --> 00:21:22,700
+فبطلع b أصغر من ال nth root للمجموعة ده اللي احنا
+
+225
+00:21:22,700 --> 00:21:33,440
+سمناه zn اذا الان انا عندي zn بساوي a n زاد b nto
+
+226
+00:21:33,440 --> 00:21:39,580
+the power one over n والان انا عندى بما انه a أصغر
+
+227
+00:21:39,580 --> 00:21:45,740
+من b a أصغر من b من الفرض هى فهذا بالتأكيد بيقدى
+
+228
+00:21:45,740 --> 00:21:52,200
+انه a to n أصغر من b to n اذا
+
+229
+00:21:52,200 --> 00:21:59,680
+هشيل ال a to n هذه و اضع خليها أصغر من b to n زائد
+
+230
+00:21:59,680 --> 00:22:07,730
+b to n الكل to one over nطب هذا بيطلع two ضرب b to
+
+231
+00:22:07,730 --> 00:22:14,450
+n الكل to power one over n وزع ال power فبطلع two
+
+232
+00:22:14,450 --> 00:22:22,290
+to one over n ضرب b صح؟ الآن ال sequence إذا
+
+233
+00:22:22,290 --> 00:22:28,470
+أنا أصبح عندي لو دمجت المتباينتين عشرة و أحداشر مع
+
+234
+00:22:28,470 --> 00:22:35,870
+بعض فبطلع عندي bمن المتباينة عشرة الـ B هدا هي
+
+235
+00:22:35,870 --> 00:22:42,590
+أصغر من ال ZN ومن المتباينة أحداشر ال ZN أصغر من
+
+236
+00:22:42,590 --> 00:22:47,610
+two to one over N times B for every N natural
+
+237
+00:22:47,610 --> 00:22:56,780
+number احنا اتوصلنا لالمتباينة هذه صحيحة لكل Nانا
+
+238
+00:22:56,780 --> 00:23:01,660
+لان عندي الـ sequence ZN هذه اللي انا عايز اثبت ان
+
+239
+00:23:01,660 --> 00:23:07,120
+ال limit تبعتها بالساوي بيه is squeezed between
+
+240
+00:23:07,120 --> 00:23:13,680
+two sequences محصورة من متتاليتين تنتين هاي
+
+241
+00:23:13,680 --> 00:23:20,620
+متتالية وهاي متتالية المتتالية هذه الحد العام
+
+242
+00:23:20,620 --> 00:23:27,340
+تبعها ثابت بيهوبالتالي ال limit تبعت بي لما بي
+
+243
+00:23:27,340 --> 00:23:35,340
+تقول ل infinity بتساوي بي و limit ال sequence هذي
+
+244
+00:23:35,340 --> 00:23:39,380
+two to واحد على n limit two to واحد على n بتساوي
+
+245
+00:23:39,380 --> 00:23:44,760
+واحد اثبتنا احنا قبل هيك ان لو n دي c عدد موجب ف
+
+246
+00:23:44,760 --> 00:23:52,170
+limitc to 1 على n as n tends to infinity بساوة
+
+247
+00:23:52,170 --> 00:23:59,230
+واحد صح فاندي c هنا بساوة اتنين لان ال limit ل two
+
+248
+00:23:59,230 --> 00:24:02,450
+to one over n as n tends to infinity بساوة واحد
+
+249
+00:24:02,450 --> 00:24:07,290
+وبالتالي limit two to one over n times constant b
+
+250
+00:24:07,290 --> 00:24:12,170
+بساوة واحد في b او b في واحد ف limit ال sequence
+
+251
+00:24:12,170 --> 00:24:18,000
+هذه ايضا تطلع bلما انتقل ل infinity، اذا by
+
+252
+00:24:18,000 --> 00:24:23,000
+squeeze theorem بطلع عندي limit ال sequence zm
+
+253
+00:24:23,000 --> 00:24:28,240
+المحصورة في النص بساوي بيه، okay؟ اذا هاي هنا
+
+254
+00:24:28,240 --> 00:24:34,120
+استخدامنا ال sandwich او ال squeeze، تمام؟ واضح؟
+
+255
+00:24:36,340 --> 00:24:40,080
+Okay إذا هذه يعني بعض الأسئلة هي اللي حلناها،
+
+256
+00:24:40,080 --> 00:24:43,480
+حالها مش صعب إما تطبيق على ال sandwich theorem أو
+
+257
+00:24:43,480 --> 00:24:48,680
+على نظرية 2.4 أو الحاجات اللي أخدناها في ال
+
+258
+00:24:48,680 --> 00:24:52,740
+section هذا أو في ال succession السابق أو بالتالي
+
+259
+00:24:52,740 --> 00:24:58,760
+مافيش حاجة يعني غريبة أو تستدى أن احنا نستخدم حاجة
+
+260
+00:24:58,760 --> 00:25:05,270
+مش موجودة في المناجمإذا ما يكون إلا من شطرتكم
+
+261
+00:25:05,270 --> 00:25:10,210
+تحاولوا تحلوا باقي التمرين اللي في ال section هذا
+
+262
+00:25:10,210 --> 00:25:15,550
+طبعا هنا لهنا الامتحان .. الامتحان داخل لحد
+
+263
+00:25:15,550 --> 00:25:21,590
+التمرين هذه الجزء اللي بعد هيك مش داخل في الامتحان
+
+264
+00:25:21,590 --> 00:25:22,310
+النصف الأول
+
+265
+00:25:26,220 --> 00:25:32,640
+تمام فإذا هنا ال section جديد أو أنوان جديد ال
+
+266
+00:25:32,640 --> 00:25:38,160
+monotone sequences المتتاليات اللي بيسموها
+
+267
+00:25:38,160 --> 00:25:42,380
+الواتيرية المتتاليات الواتيرية ال monotone
+
+268
+00:25:42,380 --> 00:25:46,960
+sequence يعني متتالية واتيرية يعني إما متزايدة أو
+
+269
+00:25:46,960 --> 00:25:55,200
+متلاقصة فناخد تعريف let x in be a sequence of real
+
+270
+00:25:55,200 --> 00:26:02,880
+numbersسنقول إن سيكوينس Xn increasing متزايدة إذا
+
+271
+00:26:02,880 --> 00:26:07,400
+كان Xn less
+
+272
+00:26:07,400 --> 00:26:11,800
+than or equal to Xn plus one for every n لو كان كل
+
+273
+00:26:11,800 --> 00:26:17,260
+حد أصغر من أول ساول لبعده فالسيكوينس في الحالة دي
+
+274
+00:26:17,260 --> 00:26:23,860
+بنسميها increasing و بنسميها decreasingإذا كان كل
+
+275
+00:26:23,860 --> 00:26:32,760
+حد أكبر من أو يساوي اللي بعده تمام؟
+
+276
+00:26:32,760 --> 00:26:40,000
+طيب بنسمي ال sequence monotone ال sequence بنسميها
+
+277
+00:26:40,000 --> 00:26:45,460
+monotone أو واتيرية if it is either increasing or
+
+278
+00:26:45,460 --> 00:26:46,040
+decreasing
+
+279
+00:26:48,950 --> 00:26:53,170
+إن المتتالي الوطرية هي متتالية إما increasing أو
+
+280
+00:26:53,170 --> 00:26:58,250
+decreasing معنى
+
+281
+00:26:58,250 --> 00:27:01,490
+آخر كل increasing sequence is monotone sequence
+
+282
+00:27:01,490 --> 00:27:06,090
+and every decreasing sequence is monotone sequence
+
+283
+00:27:06,090 --> 00:27:14,370
+طب هاي أمثلة على monotone sequences فاندي هنا
+
+284
+00:27:14,370 --> 00:27:21,540
+sequence n of natural numbersis increasing واضح ان
+
+285
+00:27:21,540 --> 00:27:26,440
+xn بساوي n أصغر من او ساوي xn plus one اللي هو n
+
+286
+00:27:26,440 --> 00:27:31,440
+زاد واحد لان هذا increasing وهذا increasing ال
+
+287
+00:27:31,440 --> 00:27:36,040
+sequence اللي ال inf term تبعها two to n اللي هي
+
+288
+00:27:36,040 --> 00:27:41,440
+هذه is increasing بينما
+
+289
+00:27:41,440 --> 00:27:46,720
+ال sequence one over n decreasing هي كل حد أكبر من
+
+290
+00:27:46,720 --> 00:27:52,140
+أو ساوي لبعدهو كذلك ال sequence one over two to n
+
+291
+00:27:52,140 --> 00:27:57,580
+طيب، في سؤال هنا بطلح نفسه، هل كل sequence لازم
+
+292
+00:27:57,580 --> 00:28:01,720
+تكون monotone sequence؟ لأ، مو لأ، مش شرط، مش شرط،
+
+293
+00:28:01,720 --> 00:28:03,620
+مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+294
+00:28:03,620 --> 00:28:03,840
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+295
+00:28:03,840 --> 00:28:07,680
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+296
+00:28:07,680 --> 00:28:12,580
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+297
+00:28:12,580 --> 00:28:17,150
+شرط، مش شرط، مش شرطthe following sequence is
+
+298
+00:28:17,150 --> 00:28:20,010
+sequence اللي الحد اللي عام تبعها negative one to
+
+299
+00:28:20,010 --> 00:28:24,830
+n أو n زيادة واحد اللي هي ال alternated sequence
+
+300
+00:28:24,830 --> 00:28:29,750
+ال sequence هذه المتدبدبة alternating يعني
+
+301
+00:28:29,750 --> 00:28:34,930
+المتدبدبة في الإشارة واحد سالب واحد واحد سالب واحد
+
+302
+00:28:34,930 --> 00:28:40,450
+هذه ليست conversion ليست monotone is not
+
+303
+00:28:40,450 --> 00:28:46,980
+increasing and it is not decreasingنفس الشيء ال
+
+304
+00:28:46,980 --> 00:28:51,180
+sequence اللي حد اللي عم تبعها سالب one to n اللي
+
+305
+00:28:51,180 --> 00:28:56,040
+هي سالب واحد موجة بتنين سالب تلاتة و هكذا ال
+
+306
+00:28:56,040 --> 00:29:00,560
+sequence هذه is not monotone لا increasing ولا
+
+307
+00:29:00,560 --> 00:29:05,590
+decreasing تمام واضحإذا ال sequence .. أي .. لو
+
+308
+00:29:05,590 --> 00:29:09,310
+أخدنا أي sequence عشوائية فممكن تكون increasing،
+
+309
+00:29:09,310 --> 00:29:14,070
+ممكن تكون decreasing، ممكن تكون neither، neither
+
+310
+00:29:14,070 --> 00:29:16,810
+increasing nor decreasing زي ال function ممكن تكون
+
+311
+00:29:16,810 --> 00:29:22,950
+odd أو even أو neither، لا odd ولا even، أه؟ تمام؟
+
+312
+00:29:22,950 --> 00:29:26,870
+طيب ال .. في نظرية مهمة هنا في هذا السياق
+
+313
+00:29:29,970 --> 00:29:34,290
+بتخص الـ monotone sequences وبالتالي بنسميها
+
+314
+00:29:34,290 --> 00:29:39,170
+monotone convergence theorem وبنستخدم اختصارات
+
+315
+00:29:39,170 --> 00:29:46,690
+monotone convergence theorem النظرية
+
+316
+00:29:46,690 --> 00:29:52,550
+هذه بتقول خد .. خدي let x and b a monotone
+
+317
+00:29:52,550 --> 00:29:57,650
+sequence خلينا ناخد monotone sequenceالان هذه الـ
+
+318
+00:29:57,650 --> 00:30:01,130
+monotone sequence بتكون convergent if and only if
+
+319
+00:30:01,130 --> 00:30:05,830
+it is bounded تمام؟
+
+320
+00:30:05,830 --> 00:30:10,470
+moreover إضافة إلى ذلك لو كانت ال sequence x in
+
+321
+00:30:10,470 --> 00:30:16,970
+هذه bounded and increasing فأكيد طبعا convergent و
+
+322
+00:30:16,970 --> 00:30:22,370
+ال limit تبعتها بساوي ال supremum إلها ك set كذلك
+
+323
+00:30:22,370 --> 00:30:25,170
+لو كانت ال sequence x in bounded و decreasing
+
+324
+00:30:27,590 --> 00:30:31,190
+فبتكون طبعا convergent و ال limit بتبعتها بساوة ال
+
+325
+00:30:31,190 --> 00:30:36,270
+inform اللي لها ك set طيب
+
+326
+00:30:36,270 --> 00:30:39,430
+احنا عندي انا عندي هنا two statements او تلاتة
+
+327
+00:30:39,430 --> 00:30:47,010
+statements انا عندي العبارة هذه انا
+
+328
+00:30:47,010 --> 00:30:53,490
+عندي بتثبت العبارة هذه و العبارتين هدون فكيف
+
+329
+00:30:53,490 --> 00:31:00,150
+البرهان بتتمأول شي العبارة الأولى اللى فى البرواز
+
+330
+00:31:00,150 --> 00:31:08,610
+هذه if and only if statement صح ففى two parts واحد
+
+331
+00:31:08,610 --> 00:31:15,750
+هذا ال part ال only if part و ال if part نشوف ال
+
+332
+00:31:15,750 --> 00:31:21,260
+only if part يعنىلو كانت x in convergent بينا نثبت
+
+333
+00:31:21,260 --> 00:31:25,680
+إنها it is bounded وهذا أثبتناه في نظرية سابقة
+
+334
+00:31:25,680 --> 00:31:31,120
+أثبتنا إن كل تجارب convergent is bounded اختبار
+
+335
+00:31:31,120 --> 00:31:41,320
+الدم فاكرين؟ إذا هذا was proved proved
+
+336
+00:31:41,320 --> 00:31:49,530
+earlier تم إثباته سابقا في نظرية سابقةلو كانت
+
+337
+00:31:49,530 --> 00:31:54,830
+السيكوانس تبقى convergent ضرورة تكون bounded سواء
+
+338
+00:31:54,830 --> 00:31:58,690
+كانت السيكوانس monotone ولا حتى مش monotone okay؟
+
+339
+00:31:58,690 --> 00:32:02,950
+تمام؟ إن هاي برهان الجزء لهذا موجود في نظرية سابقة
+
+340
+00:32:02,950 --> 00:32:08,970
+باقى نثبت الجزء هذا يعني بنا نثبت أنه لو كانت
+
+341
+00:32:08,970 --> 00:32:17,730
+السيكوانس bounded السيكوانس لو كانت bounded و
+
+342
+00:32:17,730 --> 00:32:18,510
+monotone
+
+343
+00:32:21,420 --> 00:32:25,800
+طبعا احنا فرضين انها monotone اه من البداية x in
+
+344
+00:32:25,800 --> 00:32:32,020
+is monotone فالان عشان نكمل برهان العبارة هذه ال
+
+345
+00:32:32,020 --> 00:32:35,060
+if and only if او ال by conditional statement هذا
+
+346
+00:32:35,060 --> 00:32:40,920
+فبدنا نثبت ان لو كانت ال sequence bounded و
+
+347
+00:32:40,920 --> 00:32:49,520
+monotone فبتطلع convergent طيب
+
+348
+00:32:49,520 --> 00:32:54,920
+monotoneمونوتون لما ال sequence تكون مونوتون
+
+349
+00:32:54,920 --> 00:33:04,060
+معناها اما increasing او decreasing او decreasing
+
+350
+00:33:04,060 --> 00:33:08,260
+اذا
+
+351
+00:33:08,260 --> 00:33:16,500
+عشان اثبت الجزء هذا بده اثبت a و b هذا الجزء هذا
+
+352
+00:33:16,500 --> 00:33:25,750
+لبرهانه بده برهين a و bلأن جزء A بيقول لو كانت ال
+
+353
+00:33:25,750 --> 00:33:29,330
+sequence bounded و increasing فبتثبت أنها
+
+354
+00:33:29,330 --> 00:33:33,510
+convergent صح؟ فهي لو كانت ال sequence bounded و
+
+355
+00:33:33,510 --> 00:33:37,930
+increasing فبتثبت أنها convergent و ال limit
+
+356
+00:33:37,930 --> 00:33:43,530
+تبعتها هي ال suprem من إلها كمجموعة و الجزء B
+
+357
+00:33:43,530 --> 00:33:47,690
+بيثبت أن لو كانت ال sequence bounded و decreasing
+
+358
+00:33:47,690 --> 00:33:54,510
+فبتطلع convergentوإضافة لذلك إن ال limit تبعتها هي
+
+359
+00:33:54,510 --> 00:34:00,390
+ال infront إلى كسب إذا الإكمال برهان الاتجاه هذا و
+
+360
+00:34:00,390 --> 00:34:05,690
+برهان a و b وبالتالي نكمل برهان النظرية يكفي إن
+
+361
+00:34:05,690 --> 00:34:11,290
+أحنا نثبت a و b و أضع يكمل كون أثبتنا إلى عبارة من
+
+362
+00:34:11,290 --> 00:34:16,750
+بروزة هذه و a و b يعني برهاننا النظرية كاملة تمام؟
+
+363
+00:34:17,990 --> 00:34:39,030
+نثبت الآن باقي اثبات a وb نثبت الجزء a فخلّينا
+
+364
+00:34:39,030 --> 00:34:43,130
+نفرض ان ال sequence x in is bounded قلنا bounded
+
+365
+00:34:43,130 --> 00:34:48,700
+زاد increasingطيب من تعريف الـ bounded sequence
+
+366
+00:34:48,700 --> 00:34:54,840
+مدام ال sequence bounded إذا يوجد عدد حقيقي موجب M
+
+367
+00:34:54,840 --> 00:35:03,840
+بحيث أنه absolute Xn أصغر من أو ساوي M لكل N طيب
+
+368
+00:35:03,840 --> 00:35:07,540
+معروف أنه أي عدد حقيقي Xn أصغر من أو ساوي القيمة
+
+369
+00:35:07,540 --> 00:35:14,200
+المطلقة له، مظبوط؟إذا من ال boundedness من فرض ان
+
+370
+00:35:14,200 --> 00:35:18,260
+ال sequence bounded في معدد موجد بحيث ان xn أصغر
+
+371
+00:35:18,260 --> 00:35:23,640
+من أو ساوي M لكل M تمام واضح طيب الآن إذا ال
+
+372
+00:35:23,640 --> 00:35:27,800
+sequence xn bounded above وبالتالي by supremum ال
+
+373
+00:35:27,800 --> 00:35:33,120
+property ال supremum تبعها exist سميه x star
+
+374
+00:35:35,800 --> 00:35:40,000
+الان بيدثبت الادعاء هذا الـ claim الادعاء بيدثبت
+
+375
+00:35:40,000 --> 00:35:45,260
+انه limit ال sequence xn بساوي ال x star اللي هو
+
+376
+00:35:45,260 --> 00:35:51,580
+ال suprem لست xn فلو أثبتت هذا الادعاء معناته
+
+377
+00:35:51,580 --> 00:35:55,600
+أثبتت أنا ان ال sequence xn is convergent و ال
+
+378
+00:35:55,600 --> 00:36:00,650
+limit تبعتها بساوي ال suprem إلها كستتعالى نشوف
+
+379
+00:36:00,650 --> 00:36:04,930
+كيف نثبت ال claim to see this لبرهان ال claim انا
+
+380
+00:36:04,930 --> 00:36:09,430
+ايش بتثبت؟ بتثبت ان ال sequence x in convergent و
+
+381
+00:36:09,430 --> 00:36:13,630
+ال limit تبعتها بساوي العدد x star فهستخدم تعريف
+
+382
+00:36:13,630 --> 00:36:17,830
+epsilon capital N لل limit فلازم ابدأ let epsilon
+
+383
+00:36:17,830 --> 00:36:25,090
+أكبر من الصفر بيه given الان ال x star هذاهو ال
+
+384
+00:36:25,090 --> 00:36:28,430
+supremum لل set هذه لما نطرح من ال supremum عدد
+
+385
+00:36:28,430 --> 00:36:33,830
+موجب بيبطل upper bound بيبطل upper bound لأن ال x
+
+386
+00:36:33,830 --> 00:36:37,690
+star هو أصغر upper bound اطرح منه عدد موجب بيبطل
+
+387
+00:36:37,690 --> 00:36:41,590
+upper bound إذا هذا العدد x star minus y is not an
+
+388
+00:36:41,590 --> 00:36:46,710
+upper bound معناته في أنصر في ال set هذه اللي هو x
+
+389
+00:36:46,710 --> 00:36:51,450
+رقم capital N أكبر من العدد هذا اللي هو ما هوش
+
+390
+00:36:51,450 --> 00:36:55,860
+upper boundوطبعاً العدد هذا المؤشر او ال index
+
+391
+00:36:55,860 --> 00:37:00,040
+capital N ده يعتمد على ال epsilon مرتبط بال
+
+392
+00:37:00,040 --> 00:37:05,500
+epsilon اللي بنيت فيها طبعا انا فرض ان ال sequence
+
+393
+00:37:05,500 --> 00:37:10,860
+xn increasing وبالتالي x capital N أصغر من أو سوى
+
+394
+00:37:10,860 --> 00:37:14,880
+xn لكل N أكبر من أو سوى capital N من تعريف ال
+
+395
+00:37:14,880 --> 00:37:20,500
+increasing sequence اذا انا في عندي هنا هى عندي x
+
+396
+00:37:20,500 --> 00:37:28,280
+capital N هىxN أصغر من أو ساوي xN لكل N أكبر من أو
+
+397
+00:37:28,280 --> 00:37:36,360
+ساوي N طيب و x*) هو ال suprem of ال sequence xN و
+
+398
+00:37:36,360 --> 00:37:42,440
+xN هذا عنصر في ال sequence و x*) upper bound لل
+
+399
+00:37:42,440 --> 00:37:49,540
+sequence إذن xN أصغر من أو ساوي x*) طيب و x*) أصغر
+
+400
+00:37:49,540 --> 00:37:57,820
+من نفسها زاد عدد موجب هذا مافي شكو من هنا .. أيوه
+
+401
+00:37:57,820 --> 00:38:03,460
+.. من المتباينة هذه هي عندي x capital n أكبر من x
+
+402
+00:38:03,460 --> 00:38:11,420
+star سالب y إذا أنا طلع عندي الآن x star أكبر من
+
+403
+00:38:11,420 --> 00:38:13,160
+.. أو x in
+
+404
+00:38:15,810 --> 00:38:25,070
+أكبر من X star minus Y أصغر من X star زاد Y لكل N
+
+405
+00:38:25,070 --> 00:38:30,910
+أكبر من أو ساوي capital N فظبطك صح؟ طيب مهاد
+
+406
+00:38:30,910 --> 00:38:37,890
+المتباينة هي نفسها X N minus X star أصغر من Y أكبر
+
+407
+00:38:37,890 --> 00:38:44,610
+من سالب Y لكل N أكبر من أو ساوي capital Nطب
+
+408
+00:38:44,610 --> 00:38:49,930
+المتباينة هذه هي .. صح؟ أظبط؟ إذن absolute xn
+
+409
+00:38:49,930 --> 00:38:53,210
+minus x star أصغر من إبسلون لكل n أكبر من أوي
+
+410
+00:38:53,210 --> 00:38:58,370
+ساوية كابتن ان الأن since إبسلون was arbitrary هذا
+
+411
+00:38:58,370 --> 00:39:03,810
+بالظبط تعريف إبسلون كابتن ان لل limit أه؟ بأن هذا
+
+412
+00:39:03,810 --> 00:39:08,470
+الكلام صحيح لكل إبسلون أكبر من سفر إذن هذا معناه
+
+413
+00:39:08,470 --> 00:39:13,190
+حسب التعريف إن limit xn بساوي x star
+
+414
+00:39:18,780 --> 00:39:23,660
+إذا هذا بثبت ال claim وبالتالي هكذا نكون أثبتنا
+
+415
+00:39:23,660 --> 00:39:30,560
+الجزء A من النظرية فالجزء
+
+416
+00:39:30,560 --> 00:39:35,300
+التاني B ممكن نستخدم A في برهان ال B
+
+417
+00:39:38,510 --> 00:39:42,310
+ففي الجزء B الان انا عندي ال sequence تبعتي
+
+418
+00:39:42,310 --> 00:39:46,570
+bounded و decreasing اذا ا assume x in is bounded
+
+419
+00:39:46,570 --> 00:39:50,770
+and decreasing فاش
+
+420
+00:39:50,770 --> 00:39:55,690
+عمل هعرف sequence جديدة yn اللي هي negative الحد
+
+421
+00:39:55,690 --> 00:40:01,530
+العام تبعها negative x in تمام؟ الان بما ان x in
+
+422
+00:40:01,530 --> 00:40:05,170
+decreasing اذا ال sequence سالب x in تطلع
+
+423
+00:40:05,170 --> 00:40:10,610
+increasingوطبعا بما أن ال sequence x in bounded
+
+424
+00:40:10,610 --> 00:40:15,670
+إذا ال sequence سالب x in أيضا bounded إذا الأن
+
+425
+00:40:15,670 --> 00:40:18,790
+أنا في عندي sequence جديد اللي هي sequence yn
+
+426
+00:40:18,790 --> 00:40:26,310
+bounded وin crazy إذا حسب الجزء a by part a limit
+
+427
+00:40:26,310 --> 00:40:32,790
+ال sequence yn تطلع existوبتساوي ال supremum لكل
+
+428
+00:40:32,790 --> 00:40:37,870
+ال y in ال supremum لعناصر ال sequence اللي هي y
+
+429
+00:40:37,870 --> 00:40:41,510
+in تمام؟
+
+430
+00:40:41,510 --> 00:40:47,370
+انها ده من ايه؟ من الجزء ايه من النظرية؟طيب ال
+
+431
+00:40:47,370 --> 00:40:51,450
+supremum ل سالب xn هيفقن العدد طبيعي احنا خدنا قبل
+
+432
+00:40:51,450 --> 00:40:56,490
+هيك exercise بيقول supremum او infimum سالب حاجة
+
+433
+00:40:56,490 --> 00:41:02,190
+بساوي سالب ال infimum فهنا بصير هذا سالب ال
+
+434
+00:41:02,190 --> 00:41:07,530
+infimum تمام؟ اذا انا عندي بيطلع عندي limit xn
+
+435
+00:41:07,530 --> 00:41:15,180
+بساوي سالب limit سالب xn تمام؟أضربوا هنا هيندي
+
+436
+00:41:15,180 --> 00:41:18,940
+limit سالب xn أضربوا المعادلة هذه بالسالب واحد
+
+437
+00:41:18,940 --> 00:41:24,700
+فبطلع سالب limit سالب xn بساوي سالب سالب موجب اللي
+
+438
+00:41:24,700 --> 00:41:29,000
+هو ال inform ل xn وهذا اللي بدنا يعني لأن هي
+
+439
+00:41:29,000 --> 00:41:33,280
+أثبتنا أن limit xn موجودة exist يعني ال sequence
+
+440
+00:41:33,280 --> 00:41:37,640
+xn convergent وال limit تبعتها بساوي ال inform
+
+441
+00:41:40,760 --> 00:41:44,680
+بنكمل برهان الـ monotone convergence theorem طبعا
+
+442
+00:41:44,680 --> 00:41:49,280
+الأمثلة هذه اللي هنا كلها أمثلة تطبيق على الـ
+
+443
+00:41:49,280 --> 00:41:53,180
+monotone convergence theorem فارجو أنكم تحاولوا
+
+444
+00:41:53,180 --> 00:41:56,080
+تخرجوا الأمثلة هذه و تشوفوا كيف نستخدم الـ
+
+445
+00:41:56,080 --> 00:41:58,440
+monotone convergence theorem في
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..1c3e9ffcd8c7ce025900060a00269d2b307bad5c
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.json
@@ -0,0 +1 @@
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اللي", "probability": 0.856201171875}, {"start": 213.03, "end": 213.99, "word": " بعدها", "probability": 0.916015625}, {"start": 213.99, "end": 216.21, "word": " نظرية", "probability": 0.952880859375}, {"start": 216.21, "end": 217.03, "word": " تلاتاش", "probability": 0.857666015625}, {"start": 217.03, "end": 218.33, "word": " بتقول", "probability": 0.86328125}, {"start": 218.33, "end": 218.53, "word": " لو", "probability": 0.89794921875}, {"start": 218.53, "end": 218.71, "word": " انا", "probability": 0.837646484375}, {"start": 218.71, "end": 218.97, "word": " فيها", "probability": 0.94384765625}, {"start": 218.97, "end": 219.27, "word": " اندي", "probability": 0.797119140625}, {"start": 219.27, "end": 220.07, "word": " sequence", "probability": 0.87451171875}, {"start": 220.07, "end": 220.79, "word": " حدودها", "probability": 0.9888916015625}, {"start": 220.79, "end": 221.21, "word": " كلها", "probability": 0.9873046875}, {"start": 221.21, "end": 221.57, "word": " غير", "probability": 0.99658203125}, {"start": 221.57, "end": 222.13, "word": " سالبة", "probability": 0.7566731770833334}, {"start": 222.13, "end": 224.49, "word": " حدود", "probability": 0.982421875}, {"start": 224.49, "end": 224.63, "word": " ال", "probability": 0.900390625}, {"start": 224.63, "end": 224.99, "word": " sequence", "probability": 0.98291015625}, {"start": 224.99, "end": 225.49, "word": " xm", "probability": 0.580810546875}, {"start": 225.49, "end": 225.99, "word": " كلها", "probability": 0.990966796875}, {"start": 225.99, "end": 226.47, "word": " غير", "probability": 0.980224609375}, {"start": 226.47, "end": 226.99, "word": " سالبة", "probability": 0.97900390625}, {"start": 226.99, "end": 227.45, "word": " اعداد", "probability": 0.81640625}, {"start": 227.45, "end": 227.73, "word": " غير", "probability": 0.99755859375}, {"start": 227.73, "end": 228.21, "word": " سالبة", "probability": 0.9783528645833334}], "temperature": 1.0}, {"id": 9, "seek": 24989, "start": 229.41, "end": 249.89, "text": "والـ sequence لو كانت الـ sequence Xn convergent to some X فالـ limit للـ sequence of square roots لـ Xn تطلع convergent والـ limit تبعتها بساول square root للـ limit للـ sequence Xn", "tokens": [2407, 6027, 39184, 8310, 45164, 25961, 2655, 2423, 39184, 8310, 1783, 77, 9652, 6930, 281, 512, 1783, 6156, 6027, 39184, 4948, 24976, 39184, 8310, 295, 3732, 10669, 5296, 39184, 1783, 77, 6055, 9566, 1211, 3615, 9652, 6930, 16070, 39184, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 12610, 3732, 5593, 24976, 39184, 4948, 24976, 39184, 8310, 1783, 77], "avg_logprob": -0.2510593230441465, "compression_ratio": 1.7218045112781954, "no_speech_prob": 0.0, "words": [{"start": 229.41, "end": 230.05, "word": "والـ", "probability": 0.599853515625}, {"start": 230.05, "end": 230.53, "word": " sequence", "probability": 0.751953125}, {"start": 230.53, "end": 230.75, "word": " لو", "probability": 0.85302734375}, {"start": 230.75, "end": 231.09, "word": " كانت", "probability": 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{"start": 239.31, "end": 239.85, "word": " square", "probability": 0.63623046875}, {"start": 239.85, "end": 240.49, "word": " roots", "probability": 0.85546875}, {"start": 240.49, "end": 241.05, "word": " لـ", "probability": 0.83447265625}, {"start": 241.05, "end": 241.57, "word": " Xn", "probability": 0.947265625}, {"start": 241.57, "end": 242.73, "word": " تطلع", "probability": 0.9422607421875}, {"start": 242.73, "end": 243.65, "word": " convergent", "probability": 0.915771484375}, {"start": 243.65, "end": 244.69, "word": " والـ", "probability": 0.631591796875}, {"start": 244.69, "end": 244.93, "word": " limit", "probability": 0.98193359375}, {"start": 244.93, "end": 245.63, "word": " تبعتها", "probability": 0.9183349609375}, {"start": 245.63, "end": 246.23, "word": " بساول", "probability": 0.6248779296875}, {"start": 246.23, "end": 246.67, "word": " square", "probability": 0.759765625}, {"start": 246.67, "end": 247.33, "word": " root", "probability": 0.9052734375}, {"start": 247.33, 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{"start": 268.18, "end": 268.7, "word": " سالبة", "probability": 0.80712890625}, {"start": 268.7, "end": 269.64, "word": " ف", "probability": 0.97802734375}, {"start": 269.64, "end": 270.04, "word": " limit", "probability": 0.43994140625}, {"start": 270.04, "end": 270.74, "word": " ل", "probability": 0.6171875}, {"start": 270.74, "end": 271.36, "word": " sequence", "probability": 0.81591796875}, {"start": 271.36, "end": 272.06, "word": " Xn", "probability": 0.972900390625}, {"start": 272.06, "end": 272.66, "word": " اللى", "probability": 0.647216796875}, {"start": 272.66, "end": 272.88, "word": " هى", "probability": 0.85888671875}, {"start": 272.88, "end": 273.12, "word": " X", "probability": 0.97802734375}, {"start": 273.12, "end": 273.56, "word": " ايضا", "probability": 0.8956298828125}, {"start": 273.56, "end": 274.02, "word": " تطلع", "probability": 0.9278564453125}, {"start": 274.02, "end": 274.36, "word": " غير", "probability": 0.996826171875}, {"start": 274.36, "end": 274.84, "word": " سالبة", "probability": 0.9471028645833334}, {"start": 274.84, "end": 275.68, "word": " اذا", "probability": 0.6954345703125}, {"start": 275.68, "end": 276.66, "word": " X", "probability": 0.83203125}, {"start": 276.66, "end": 277.14, "word": " اكبر", "probability": 0.8361002604166666}, {"start": 277.14, "end": 277.32, "word": " من", "probability": 0.97705078125}, {"start": 277.32, "end": 277.5, "word": " او", "probability": 0.6224365234375}, {"start": 277.5, "end": 277.94, "word": " ساوى", "probability": 0.7926025390625}, {"start": 277.94, "end": 278.18, "word": " 0", "probability": 0.51611328125}], "temperature": 1.0}, {"id": 11, "seek": 29426, "start": 279.4, "end": 294.26, "text": "الان في عندي حالتين ال X هنا أكبر من أو ساوي سفر ففي عندي احتمالين اما X بساوي سفر او X أكبر من السفر تمام و في كل حالة", "tokens": [6027, 7649, 8978, 18871, 16254, 11331, 6027, 2655, 9957, 2423, 1783, 34105, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288, 6156, 41185, 18871, 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"word": " من", "probability": 0.8271484375}, {"start": 282.74, "end": 282.88, "word": " أو", "probability": 0.85546875}, {"start": 282.88, "end": 283.22, "word": " ساوي", "probability": 0.6709798177083334}, {"start": 283.22, "end": 283.6, "word": " سفر", "probability": 0.8483072916666666}, {"start": 283.6, "end": 284.68, "word": " ففي", "probability": 0.8203125}, {"start": 284.68, "end": 285.06, "word": " عندي", "probability": 0.976318359375}, {"start": 285.06, "end": 285.98, "word": " احتمالين", "probability": 0.96513671875}, {"start": 285.98, "end": 286.3, "word": " اما", "probability": 0.764892578125}, {"start": 286.3, "end": 286.62, "word": " X", "probability": 0.92724609375}, {"start": 286.62, "end": 287.18, "word": " بساوي", "probability": 0.83642578125}, {"start": 287.18, "end": 287.76, "word": " سفر", "probability": 0.96630859375}, {"start": 287.76, "end": 289.06, "word": " او", "probability": 0.89697265625}, {"start": 289.06, "end": 289.42, "word": " X", "probability": 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16472, 4948, 2423, 3732, 5593, 5296, 2031, 77, 4724, 3794, 995, 45865, 2423, 3732, 5593, 295, 2031, 46811, 10943, 22807, 16472, 8592, 38688, 8978, 21542, 6027, 3660, 16247, 12610, 7578, 45164, 25961, 2655, 2423, 2031, 4724, 3794, 995, 45865, 8608, 5172, 2288, 4032, 7649, 995, 18871, 16254, 9154, 27188, 43042, 2031, 77, 9652, 2880, 281, 2031, 13672, 1829, 39896, 8608, 5172, 2288], "avg_logprob": -0.2358530375200349, "compression_ratio": 1.5562130177514792, "no_speech_prob": 0.0, "words": [{"start": 294.92, "end": 295.64, "word": "مطلوب", "probability": 0.82861328125}, {"start": 295.64, "end": 296.04, "word": " مني", "probability": 0.883056640625}, {"start": 296.04, "end": 296.24, "word": " ان", "probability": 0.2890625}, {"start": 296.24, "end": 296.88, "word": " اثبت", "probability": 0.956298828125}, {"start": 296.88, "end": 297.12, "word": " ان", "probability": 0.90966796875}, {"start": 297.12, "end": 297.58, "word": " limit", "probability": 0.52001953125}, {"start": 297.58, "end": 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{"start": 661.0, "end": 661.42, "word": " موجب", "probability": 0.9451497395833334}, {"start": 661.42, "end": 661.58, "word": " اللى", "probability": 0.78369140625}, {"start": 661.58, "end": 661.7, "word": " هو", "probability": 0.77734375}, {"start": 661.7, "end": 662.0, "word": " واحد", "probability": 0.973876953125}, {"start": 662.0, "end": 662.16, "word": " على", "probability": 0.51123046875}, {"start": 662.16, "end": 662.48, "word": " جدر", "probability": 0.731201171875}, {"start": 662.48, "end": 662.62, "word": " ال", "probability": 0.9091796875}, {"start": 662.62, "end": 662.88, "word": " X", "probability": 0.51611328125}, {"start": 662.88, "end": 663.8, "word": " و", "probability": 0.42333984375}, {"start": 663.8, "end": 663.94, "word": " هى", "probability": 0.767822265625}, {"start": 663.94, "end": 664.08, "word": " فى", "probability": 0.6611328125}, {"start": 664.08, "end": 664.3, "word": " عندي", "probability": 0.63525390625}, {"start": 664.3, "end": 664.86, "word": " sequence", "probability": 0.7490234375}, {"start": 664.86, "end": 665.2, "word": " a", "probability": 0.91259765625}, {"start": 665.2, "end": 665.46, "word": " n", "probability": 0.96533203125}, {"start": 665.46, "end": 665.88, "word": " الحد", "probability": 0.805908203125}, {"start": 665.88, "end": 666.14, "word": " العام", "probability": 0.83544921875}, {"start": 666.14, "end": 666.62, "word": " تبعها", "probability": 0.9281005859375}, {"start": 666.62, "end": 666.88, "word": " x", "probability": 0.60546875}, {"start": 666.88, "end": 667.12, "word": " n", "probability": 0.62255859375}, {"start": 667.12, "end": 667.56, "word": " سالد", "probability": 0.6827799479166666}, {"start": 667.56, "end": 667.86, "word": " x", "probability": 0.6572265625}, {"start": 667.86, "end": 668.82, "word": " و", "probability": 0.391357421875}, {"start": 668.82, "end": 668.94, "word": " ال", "probability": 0.7060546875}, {"start": 668.94, "end": 669.38, "word": " sequence", "probability": 0.9482421875}, {"start": 669.38, "end": 669.86, "word": " هذه", "probability": 0.40966796875}, {"start": 669.86, "end": 670.54, "word": " تقول", "probability": 0.938232421875}, {"start": 670.54, "end": 670.86, "word": " إلى", "probability": 0.7001953125}, {"start": 670.86, "end": 671.32, "word": " سفر", "probability": 0.8546549479166666}, {"start": 671.32, "end": 671.96, "word": " as", "probability": 0.9052734375}, {"start": 671.96, "end": 674.18, "word": " n", "probability": 0.76025390625}, {"start": 674.18, "end": 674.52, "word": " tends", "probability": 0.73681640625}, {"start": 674.52, "end": 674.68, "word": " to", "probability": 0.9716796875}, {"start": 674.68, "end": 675.14, "word": " infinity", "probability": 0.87841796875}], "temperature": 1.0}, {"id": 28, "seek": 69921, "start": 676.57, "end": 699.21, "text": "لأن انا من المعطيات عندي xn تقول x أو limit xn بساوي x، لذلك limit الفرق بساوي سفر، لذلك حسب نظرية 2.4، كل شروطة متحققة، وبالتالي، لذلك حسب النظرية هذه، by theorem 2.4، بيطلع عندي limit square root ل xn بساوي square root ل x", "tokens": [1211, 33456, 1975, 8315, 9154, 9673, 3615, 9566, 1829, 9307, 18871, 16254, 2031, 77, 6055, 39648, 2031, 34051, 4948, 2031, 77, 4724, 3794, 995, 45865, 2031, 12399, 5296, 8848, 23275, 4948, 27188, 2288, 4587, 4724, 3794, 995, 45865, 8608, 5172, 2288, 12399, 5296, 8848, 23275, 11331, 35457, 8717, 19913, 2288, 10632, 568, 13, 19, 12399, 28242, 13412, 32887, 9566, 3660, 44650, 5016, 4587, 28671, 12399, 46599, 6027, 2655, 6027, 1829, 12399, 5296, 8848, 23275, 11331, 35457, 28239, 19913, 2288, 10632, 29538, 12399, 538, 20904, 568, 13, 19, 12399, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 4948, 3732, 5593, 5296, 2031, 77, 4724, 3794, 995, 45865, 3732, 5593, 5296, 2031], "avg_logprob": -0.2430397696115754, "compression_ratio": 1.7164179104477613, "no_speech_prob": 0.0, "words": [{"start": 676.57, "end": 676.97, "word": "لأن", "probability": 0.6119384765625}, {"start": 676.97, "end": 677.13, "word": " انا", "probability": 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86060, "start": 838.06, "end": 860.6, "text": "فأول مثال هو exercise تمانتاش الفرحة c في section تلاتة اتنين أو صفحة تمانية وستين في الكتاب المقرر السؤال هذا بيقول discuss the convergence of the sequence xn اللي لحد العام ال nth term تبعها b to n على n factorial حيث بيه عدد حقيقي أكبر من واحد", "tokens": [5172, 10721, 12610, 50113, 6027, 31439, 5380, 46811, 7649, 2655, 33599, 27188, 2288, 5016, 3660, 269, 8978, 3541, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957, 34051, 20328, 5172, 5016, 3660, 46811, 7649, 10632, 4032, 14851, 9957, 8978, 33251, 2655, 16758, 9673, 4587, 2288, 2288, 21136, 33604, 6027, 23758, 4724, 1829, 39648, 2248, 264, 32181, 295, 264, 8310, 2031, 77, 13672, 1829, 5296, 24401, 18863, 10943, 2423, 297, 392, 1433, 6055, 3555, 3615, 11296, 272, 281, 297, 15844, 297, 36916, 11331, 1829, 12984, 4724, 1829, 3224, 6225, 3215, 3215, 11331, 38436, 38436, 5551, 4117, 26890, 9154, 36764, 24401], "avg_logprob": -0.21922348725675334, "compression_ratio": 1.5308641975308641, 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88223, "start": 861.47, "end": 882.23, "text": "Discurses ل Convergence يعني بين هل ال sequence هذي Convergent ولا Divergent وده كانت Convergent عايزين نجيب ال limit تبعتها طيب تعالوا أول شي احنا طبعا هنطبق ال ratio test نظرية 2.14 اللي هو الرسم منها ال ratio test", "tokens": [35, 5606, 2156, 279, 5296, 2656, 331, 15260, 37495, 22653, 4724, 1829, 1863, 8032, 1211, 2423, 8310, 8032, 8848, 1829, 2656, 331, 6930, 49429, 413, 1837, 6930, 4032, 3215, 3224, 25961, 2655, 2656, 331, 6930, 6225, 47302, 11622, 9957, 8717, 7435, 1829, 3555, 2423, 4948, 6055, 3555, 34268, 11296, 23032, 1829, 3555, 37279, 6027, 14407, 5551, 12610, 44049, 1975, 5016, 8315, 23032, 3555, 3615, 995, 8032, 1863, 9566, 3555, 4587, 2423, 8509, 1500, 8717, 19913, 2288, 10632, 568, 13, 7271, 13672, 1829, 31439, 34892, 38251, 9154, 11296, 2423, 8509, 1500], "avg_logprob": -0.30511674972680897, "compression_ratio": 1.5422885572139304, "no_speech_prob": 0.0, "words": [{"start": 861.47, "end": 862.13, "word": "Discurses", 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{"start": 957.03, "end": 957.17, "word": " على", "probability": 0.71923828125}, {"start": 957.17, "end": 957.37, "word": " ان", "probability": 0.4453125}, {"start": 957.37, "end": 957.69, "word": " زياد", "probability": 0.9173177083333334}, {"start": 957.69, "end": 958.05, "word": " واحد", "probability": 0.9921875}, {"start": 958.05, "end": 958.61, "word": " بساوي", "probability": 0.849365234375}, {"start": 958.61, "end": 958.99, "word": " بي", "probability": 0.927734375}, {"start": 958.99, "end": 959.13, "word": " في", "probability": 0.67529296875}, {"start": 959.13, "end": 959.51, "word": " limit", "probability": 0.986328125}, {"start": 959.51, "end": 960.09, "word": " واحد", "probability": 0.98291015625}, {"start": 960.09, "end": 960.29, "word": " على", "probability": 0.73583984375}, {"start": 960.29, "end": 960.53, "word": " ان", "probability": 0.85107421875}, {"start": 960.53, "end": 960.89, "word": " زياد", "probability": 0.9638671875}, {"start": 960.89, "end": 961.33, "word": " 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1.0}, {"id": 43, "seek": 109761, "start": 1077.38, "end": 1097.62, "text": "وناخد ال sequence yn الحد العام تبعها سالب واحد قص ان زاد واحد وان طبعا تبدأ من واحد فهذه ال sequence حدودها هتكون أول حد واحد، التاني سالب واحد، التالت واحد، الرابع سالب واحد و هكذا", "tokens": [2407, 1863, 47283, 3215, 2423, 8310, 17861, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 36764, 24401, 12174, 9381, 16472, 30767, 18513, 36764, 24401, 4032, 7649, 23032, 3555, 3615, 995, 6055, 44510, 10721, 9154, 36764, 24401, 6156, 3224, 24192, 2423, 8310, 11331, 3215, 23328, 11296, 8032, 2655, 30544, 5551, 12610, 11331, 3215, 36764, 24401, 12399, 16712, 7649, 1829, 8608, 6027, 3555, 36764, 24401, 12399, 16712, 6027, 2655, 36764, 24401, 12399, 34892, 16758, 3615, 8608, 6027, 3555, 36764, 24401, 4032, 8032, 4117, 15730], "avg_logprob": -0.1697856118512708, "compression_ratio": 1.94375, "no_speech_prob": 0.0, "words": [{"start": 1077.38, "end": 1078.0, "word": "وناخد", "probability": 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"probability": 0.9921875}, {"start": 1091.46, "end": 1092.08, "word": " واحد،", "probability": 0.7787272135416666}, {"start": 1092.08, "end": 1092.58, "word": " التاني", "probability": 0.9386393229166666}, {"start": 1092.58, "end": 1093.06, "word": " سالب", "probability": 0.9856770833333334}, {"start": 1093.06, "end": 1093.6, "word": " واحد،", "probability": 0.9812825520833334}, {"start": 1093.6, "end": 1094.1, "word": " التالت", "probability": 0.85107421875}, {"start": 1094.1, "end": 1095.34, "word": " واحد،", "probability": 0.9832356770833334}, {"start": 1095.34, "end": 1095.88, "word": " الرابع", "probability": 0.9850260416666666}, {"start": 1095.88, "end": 1096.44, "word": " سالب", "probability": 0.9879557291666666}, {"start": 1096.44, "end": 1096.98, "word": " واحد", "probability": 0.9921875}, {"start": 1096.98, "end": 1097.16, "word": " و", "probability": 0.6220703125}, {"start": 1097.16, "end": 1097.62, "word": " هكذا", "probability": 0.7611490885416666}], "temperature": 1.0}, {"id": 44, "seek": 112120, "start": 1100.3, "end": 1121.2, "text": "تمام احنا اثبتنا بالتفصيل ان ال sequence xn هذي divergent by contradiction فرضنا انها convergent وصلنا الى تناغم صح؟ طب ما هذي هي هذي هي ال sequence ال sequence yn هي سالب ال sequence xn", "tokens": [2655, 15042, 2304, 1975, 5016, 8315, 1975, 12984, 3555, 2655, 8315, 20666, 2655, 5172, 9381, 26895, 16472, 2423, 8310, 2031, 77, 8032, 8848, 1829, 18558, 6930, 538, 34937, 6156, 43042, 8315, 16472, 11296, 9652, 6930, 4032, 36520, 8315, 2423, 7578, 6055, 1863, 5718, 118, 2304, 20328, 5016, 22807, 23032, 3555, 19446, 8032, 8848, 1829, 39896, 8032, 8848, 1829, 39896, 2423, 8310, 2423, 8310, 17861, 39896, 8608, 6027, 3555, 2423, 8310, 2031, 77], "avg_logprob": -0.24272260273972604, "compression_ratio": 1.6419753086419753, "no_speech_prob": 0.0, "words": [{"start": 1100.3, "end": 1101.18, "word": "تمام", "probability": 0.5717366536458334}, {"start": 1101.18, "end": 1101.88, "word": " احنا", "probability": 0.748291015625}, {"start": 1101.88, "end": 1102.38, "word": " اثبتنا", "probability": 0.92548828125}, {"start": 1102.38, "end": 1103.24, "word": " بالتفصيل", "probability": 0.98359375}, {"start": 1103.24, "end": 1103.84, "word": " ان", "probability": 0.84521484375}, {"start": 1103.84, "end": 1104.04, "word": " ال", "probability": 0.8662109375}, {"start": 1104.04, "end": 1104.46, "word": " sequence", "probability": 0.8271484375}, {"start": 1104.46, "end": 1105.14, "word": " xn", "probability": 0.5482177734375}, {"start": 1105.14, "end": 1105.72, "word": " هذي", "probability": 0.48876953125}, {"start": 1105.72, "end": 1107.16, "word": " divergent", "probability": 0.59002685546875}, {"start": 1107.16, "end": 1107.42, "word": " by", "probability": 0.5771484375}, {"start": 1107.42, "end": 1108.14, "word": " contradiction", "probability": 0.90625}, {"start": 1108.14, "end": 1108.68, "word": " فرضنا", "probability": 0.9148763020833334}, {"start": 1108.68, "end": 1108.9, "word": " انها", "probability": 0.918701171875}, {"start": 1108.9, "end": 1109.66, "word": " convergent", "probability": 0.87939453125}, {"start": 1109.66, "end": 1110.76, "word": " وصلنا", "probability": 0.8919270833333334}, {"start": 1110.76, "end": 1110.98, "word": " الى", "probability": 0.773193359375}, {"start": 1110.98, "end": 1111.44, "word": " تناغم", "probability": 0.917578125}, {"start": 1111.44, "end": 1114.22, "word": " صح؟", "probability": 0.7623697916666666}, {"start": 1114.22, "end": 1114.48, "word": " طب", "probability": 0.961181640625}, {"start": 1114.48, "end": 1114.62, "word": " ما", "probability": 0.53564453125}, {"start": 1114.62, "end": 1115.0, "word": " هذي", "probability": 0.6892903645833334}, {"start": 1115.0, "end": 1115.2, "word": " هي", "probability": 0.57861328125}, {"start": 1115.2, "end": 1115.6, "word": " هذي", "probability": 0.81005859375}, {"start": 1115.6, "end": 1115.78, "word": " هي", "probability": 0.791015625}, {"start": 1115.78, "end": 1115.96, "word": " ال", "probability": 0.8271484375}, {"start": 1115.96, "end": 1116.48, "word": " sequence", "probability": 0.9833984375}, {"start": 1116.48, "end": 1116.86, "word": " ال", "probability": 0.67724609375}, {"start": 1116.86, "end": 1117.36, "word": " sequence", "probability": 0.90771484375}, {"start": 1117.36, "end": 1117.98, "word": " yn", "probability": 0.82666015625}, {"start": 1117.98, "end": 1118.4, "word": " هي", "probability": 0.92041015625}, {"start": 1118.4, "end": 1119.2, "word": " سالب", "probability": 0.9456380208333334}, {"start": 1119.2, "end": 1120.12, "word": " ال", "probability": 0.93994140625}, {"start": 1120.12, "end": 1120.56, "word": " sequence", "probability": 0.99462890625}, {"start": 1120.56, "end": 1121.2, "word": " xn", "probability": 0.9853515625}], "temperature": 1.0}, {"id": 45, "seek": 115213, "start": 1122.93, "end": 1152.13, "text": "و Xn is divergent و Yn is divergent او بنفس البرهان ممكن نعمل نفس البرهان اذا هي عندي مثال على two sequences كلاهما both are divergent لكن لما نيجي نجمعهم لو أخدت ال sequence جديدة ال inf term تبعها او الحد العام تبعها هو مجموعة ال inf term زي Xn وYn هذه sequence تالتة جديدة", "tokens": [2407, 1783, 77, 307, 18558, 6930, 4032, 398, 77, 307, 18558, 6930, 1975, 2407, 44945, 36178, 2423, 26890, 3224, 7649, 3714, 43020, 8717, 25957, 1211, 8717, 36178, 2423, 26890, 3224, 7649, 1975, 15730, 39896, 18871, 16254, 50113, 6027, 15844, 732, 22978, 9122, 15040, 3224, 15042, 1293, 366, 18558, 6930, 44381, 5296, 15042, 8717, 1829, 7435, 1829, 8717, 7435, 2304, 3615, 16095, 45164, 5551, 9778, 3215, 2655, 2423, 8310, 10874, 16254, 41891, 2423, 1536, 1433, 6055, 3555, 3615, 11296, 1975, 2407, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 31439, 3714, 7435, 2304, 2407, 27884, 2423, 1536, 1433, 30767, 1829, 1783, 77, 4032, 56, 77, 29538, 8310, 6055, 6027, 2655, 3660, 10874, 16254, 41891], "avg_logprob": -0.2583607398627097, "compression_ratio": 1.7739130434782608, "no_speech_prob": 0.0, "words": [{"start": 1122.93, "end": 1123.25, "word": 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"word": " are", "probability": 0.95751953125}, {"start": 1135.23, "end": 1136.11, "word": " divergent", "probability": 0.943115234375}, {"start": 1136.11, "end": 1136.53, "word": " لكن", "probability": 0.806640625}, {"start": 1136.53, "end": 1137.35, "word": " لما", "probability": 0.93798828125}, {"start": 1137.35, "end": 1137.67, "word": " نيجي", "probability": 0.85089111328125}, {"start": 1137.67, "end": 1138.37, "word": " نجمعهم", "probability": 0.9869140625}, {"start": 1138.37, "end": 1139.37, "word": " لو", "probability": 0.84619140625}, {"start": 1139.37, "end": 1139.89, "word": " أخدت", "probability": 0.89794921875}, {"start": 1139.89, "end": 1140.05, "word": " ال", "probability": 0.74462890625}, {"start": 1140.05, "end": 1140.63, "word": " sequence", "probability": 0.96337890625}, {"start": 1140.63, "end": 1141.53, "word": " جديدة", "probability": 0.9734700520833334}, {"start": 1141.53, "end": 1142.95, "word": " ال", "probability": 0.82568359375}, {"start": 1142.95, "end": 1143.49, "word": " inf", "probability": 0.1800537109375}, {"start": 1143.49, "end": 1144.09, "word": " term", "probability": 0.89501953125}, {"start": 1144.09, "end": 1144.75, "word": " تبعها", "probability": 0.9078369140625}, {"start": 1144.75, "end": 1144.93, "word": " او", "probability": 0.767822265625}, {"start": 1144.93, "end": 1145.29, "word": " الحد", "probability": 0.9111328125}, {"start": 1145.29, "end": 1145.57, "word": " العام", "probability": 0.972900390625}, {"start": 1145.57, "end": 1146.25, "word": " تبعها", "probability": 0.9705810546875}, {"start": 1146.25, "end": 1147.01, "word": " هو", "probability": 0.83349609375}, {"start": 1147.01, "end": 1147.59, "word": " مجموعة", "probability": 0.92138671875}, {"start": 1147.59, "end": 1147.75, "word": " ال", "probability": 0.9169921875}, {"start": 1147.75, "end": 1148.03, "word": " inf", "probability": 0.2919921875}, {"start": 1148.03, "end": 1148.37, "word": " term", "probability": 0.685546875}, {"start": 1148.37, "end": 1148.61, "word": " زي", "probability": 0.4814453125}, {"start": 1148.61, "end": 1149.07, "word": " Xn", "probability": 0.869384765625}, {"start": 1149.07, "end": 1150.21, "word": " وYn", "probability": 0.83544921875}, {"start": 1150.21, "end": 1150.67, "word": " هذه", "probability": 0.544921875}, {"start": 1150.67, "end": 1151.17, "word": " sequence", "probability": 0.62841796875}, {"start": 1151.17, "end": 1151.67, "word": " تالتة", "probability": 0.85791015625}, {"start": 1151.67, "end": 1152.13, "word": " جديدة", "probability": 0.9778645833333334}], "temperature": 1.0}, {"id": 46, "seek": 118209, "start": 1154.0, "end": 1182.1, "text": "ما هو الحد العام لهذه الـ sequence؟ اجمع الحد الأول على الأول بيطلع سفر، التاني على التاني سفر، إذا هذه عبارة عن الـ sequence constant zero ثابت سفر أو الـ sequence الحد العام تبعها ثابت سفر وطبعا أي sequence ثابتة بتكون convergent و limit تبعتها هي الحد الثابت نفسه، لذلك limit لهذه الـ sequence ثابت سفر", "tokens": [15042, 31439, 21542, 3215, 18863, 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{"start": 1180.42, "end": 1180.62, "word": " لذلك", "probability": 0.56298828125}, {"start": 1180.62, "end": 1180.88, "word": " limit", "probability": 0.6474609375}, {"start": 1180.88, "end": 1181.1, "word": " لهذه", "probability": 0.6376953125}, {"start": 1181.1, "end": 1181.14, "word": " الـ", "probability": 0.820556640625}, {"start": 1181.14, "end": 1181.34, "word": " sequence", "probability": 0.9658203125}, {"start": 1181.34, "end": 1181.78, "word": " ثابت", "probability": 0.859375}, {"start": 1181.78, "end": 1182.1, "word": " سفر", "probability": 0.8818359375}], "temperature": 1.0}, {"id": 47, "seek": 120946, "start": 1184.44, "end": 1209.46, "text": "إذا هذا مثال على two divergent sequences their sum is convergent okay تمام؟ في برضه حاجات زي هذه ممكن ينقلب منكم جيبي مثال على two sequences contain مثلا convergent لكن حصل ضربهم divergent يعني حاجات زي هيك و هكذا في الكتاب في تمارين", "tokens": [28814, 15730, 23758, 50113, 6027, 15844, 732, 18558, 6930, 22978, 641, 2408, 307, 9652, 6930, 1392, 46811, 10943, 22807, 8978, 4724, 43042, 3224, 11331, 26108, 9307, 30767, 1829, 29538, 3714, 43020, 7251, 1863, 4587, 46152, 9154, 24793, 10874, 1829, 21292, 50113, 6027, 15844, 732, 22978, 5304, 50113, 15040, 9652, 6930, 44381, 11331, 36520, 48812, 25513, 16095, 18558, 6930, 37495, 22653, 11331, 26108, 9307, 30767, 1829, 39896, 4117, 4032, 8032, 4117, 15730, 8978, 33251, 2655, 16758, 8978, 46811, 9640, 9957], "avg_logprob": -0.16953125167638064, "compression_ratio": 1.6473429951690821, "no_speech_prob": 0.0, "words": [{"start": 1184.44, "end": 1184.72, "word": "إذا", "probability": 0.66650390625}, {"start": 1184.72, "end": 1185.0, "word": " هذا", "probability": 0.5625}, {"start": 1185.0, "end": 1185.56, "word": " مثال", "probability": 0.97509765625}, {"start": 1185.56, "end": 1185.88, "word": " على", "probability": 0.85986328125}, {"start": 1185.88, "end": 1186.36, "word": " two", "probability": 0.88916015625}, {"start": 1186.36, "end": 1187.64, "word": " divergent", "probability": 0.860107421875}, {"start": 1187.64, "end": 1188.44, "word": " sequences", "probability": 0.95068359375}, {"start": 1188.44, "end": 1189.76, "word": " their", "probability": 0.5625}, {"start": 1189.76, "end": 1190.22, "word": " sum", "probability": 0.9765625}, {"start": 1190.22, "end": 1190.7, "word": " is", "probability": 0.9658203125}, {"start": 1190.7, "end": 1191.52, "word": " convergent", "probability": 0.968505859375}, {"start": 1191.52, "end": 1192.16, "word": " okay", "probability": 0.346923828125}, {"start": 1192.16, "end": 1193.2, "word": " تمام؟", "probability": 0.8001302083333334}, {"start": 1193.2, "end": 1194.34, "word": " في", "probability": 0.76318359375}, {"start": 1194.34, "end": 1194.7, "word": " برضه", "probability": 0.9265950520833334}, {"start": 1194.7, "end": 1195.06, "word": " حاجات", "probability": 0.9969075520833334}, {"start": 1195.06, "end": 1195.32, "word": " زي", "probability": 0.93994140625}, {"start": 1195.32, "end": 1195.58, "word": " هذه", "probability": 0.79541015625}, {"start": 1195.58, "end": 1195.9, "word": " ممكن", "probability": 0.75}, {"start": 1195.9, "end": 1196.58, "word": " ينقلب", "probability": 0.878662109375}, {"start": 1196.58, "end": 1197.04, "word": " منكم", "probability": 0.945068359375}, {"start": 1197.04, "end": 1197.9, "word": " جيبي", "probability": 0.8310546875}, {"start": 1197.9, "end": 1198.36, "word": " مثال", "probability": 0.985107421875}, {"start": 1198.36, "end": 1198.6, "word": " على", "probability": 0.85302734375}, {"start": 1198.6, "end": 1198.82, "word": " two", "probability": 0.9501953125}, {"start": 1198.82, "end": 1199.62, "word": " sequences", "probability": 0.9716796875}, {"start": 1199.62, "end": 1200.2, "word": " contain", "probability": 0.340087890625}, {"start": 1200.2, "end": 1201.52, "word": " مثلا", "probability": 0.82421875}, {"start": 1201.52, "end": 1202.32, "word": " convergent", "probability": 0.89501953125}, {"start": 1202.32, "end": 1202.6, "word": " لكن", 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"probability": 0.93896484375}, {"start": 1208.7, "end": 1209.46, "word": " تمارين", "probability": 0.81005859375}], "temperature": 1.0}, {"id": 48, "seek": 123290, "start": 1210.66, "end": 1232.9, "text": "على هذا السياق هتشوفوها تمام؟ مفهوم؟ واضح المثال هذا؟ طيب مثال رقم تلاتة هذا عبارة عن exercise أربعة عشر في section تلاتة اتنين", "tokens": [3615, 23942, 23758, 21136, 25528, 4587, 8032, 2655, 8592, 38688, 2407, 11296, 46811, 10943, 22807, 3714, 5172, 3224, 20498, 22807, 4032, 46958, 5016, 9673, 12984, 6027, 23758, 22807, 23032, 1829, 3555, 50113, 6027, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 23758, 6225, 3555, 9640, 3660, 18871, 5380, 5551, 25513, 27884, 6225, 46309, 8978, 3541, 6055, 1211, 9307, 3660, 1975, 2655, 1863, 9957], "avg_logprob": -0.13107639220025805, "compression_ratio": 1.4662162162162162, "no_speech_prob": 0.0, "words": [{"start": 1210.66, "end": 1211.0, "word": "على", "probability": 0.923583984375}, {"start": 1211.0, "end": 1211.26, "word": " هذا", "probability": 0.9736328125}, {"start": 1211.26, "end": 1211.88, "word": " السياق", "probability": 0.8697916666666666}, {"start": 1211.88, "end": 1213.48, "word": " هتشوفوها", "probability": 0.8993326822916666}, {"start": 1213.48, "end": 1214.54, "word": " تمام؟", "probability": 0.7250162760416666}, {"start": 1214.54, "end": 1215.34, "word": " مفهوم؟", "probability": 0.908203125}, {"start": 1215.34, "end": 1215.6, "word": " واضح", "probability": 0.974609375}, {"start": 1215.6, "end": 1216.02, "word": " المثال", "probability": 0.9510091145833334}, {"start": 1216.02, "end": 1218.72, "word": " هذا؟", "probability": 0.84130859375}, {"start": 1218.72, "end": 1221.64, "word": " طيب", "probability": 0.9352213541666666}, {"start": 1221.64, "end": 1222.02, "word": " مثال", "probability": 0.894775390625}, {"start": 1222.02, "end": 1222.38, "word": " رقم", "probability": 0.9793294270833334}, {"start": 1222.38, "end": 1224.2, "word": " تلاتة", "probability": 0.925048828125}, {"start": 1224.2, "end": 1229.44, "word": " هذا", "probability": 0.853515625}, {"start": 1229.44, "end": 1229.8, "word": " عبارة", "probability": 0.9962158203125}, {"start": 1229.8, "end": 1229.98, "word": " عن", "probability": 0.99560546875}, {"start": 1229.98, "end": 1230.38, "word": " exercise", "probability": 0.90966796875}, {"start": 1230.38, "end": 1231.08, "word": " أربعة", "probability": 0.6424967447916666}, {"start": 1231.08, "end": 1231.48, "word": " عشر", "probability": 0.658447265625}, {"start": 1231.48, "end": 1231.66, "word": " في", "probability": 0.459716796875}, {"start": 1231.66, "end": 1231.98, "word": " section", "probability": 0.90283203125}, {"start": 1231.98, "end": 1232.46, "word": " تلاتة", "probability": 0.9425048828125}, {"start": 1232.46, "end": 1232.9, "word": " اتنين", "probability": 0.9539794921875}], "temperature": 1.0}, {"id": 49, "seek": 126285, "start": 1235.1, "end": 1262.86, "text": "بقول خد zn بساوي a to n plus b to n to the power one over n where a و b are positive numbers and a less than b prove أن limit zn بساوي العدد b تمام؟ لبرهان ذلك أنا عندي من الفرض a positive إذا a to n positive", "tokens": [3555, 39648, 16490, 3215, 710, 77, 4724, 3794, 995, 45865, 257, 281, 297, 1804, 272, 281, 297, 281, 264, 1347, 472, 670, 297, 689, 257, 4032, 272, 366, 3353, 3547, 293, 257, 1570, 813, 272, 7081, 14739, 4948, 710, 77, 4724, 3794, 995, 45865, 18863, 3215, 3215, 272, 46811, 10943, 22807, 5296, 26890, 3224, 7649, 29910, 23275, 41850, 18871, 16254, 9154, 27188, 43042, 257, 3353, 11933, 15730, 257, 281, 297, 3353], "avg_logprob": -0.21299913856718275, "compression_ratio": 1.4293478260869565, "no_speech_prob": 0.0, "words": [{"start": 1235.1000000000001, "end": 1235.88, "word": "بقول", "probability": 0.64990234375}, {"start": 1235.88, "end": 1236.66, "word": " خد", "probability": 0.694091796875}, {"start": 1236.66, "end": 1237.16, "word": " zn", "probability": 0.388916015625}, {"start": 1237.16, "end": 1237.88, "word": " بساوي", "probability": 0.732177734375}, {"start": 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"probability": 0.94775390625}, {"start": 1242.38, "end": 1243.8, "word": " where", "probability": 0.62158203125}, {"start": 1243.8, "end": 1244.32, "word": " a", "probability": 0.9677734375}, {"start": 1244.32, "end": 1244.56, "word": " و", "probability": 0.7958984375}, {"start": 1244.56, "end": 1244.82, "word": " b", "probability": 0.82421875}, {"start": 1244.82, "end": 1245.26, "word": " are", "probability": 0.91162109375}, {"start": 1245.26, "end": 1245.76, "word": " positive", "probability": 0.9482421875}, {"start": 1245.76, "end": 1246.4, "word": " numbers", "probability": 0.90869140625}, {"start": 1246.4, "end": 1246.88, "word": " and", "probability": 0.90625}, {"start": 1246.88, "end": 1247.24, "word": " a", "probability": 0.98193359375}, {"start": 1247.24, "end": 1247.6, "word": " less", "probability": 0.90478515625}, {"start": 1247.6, "end": 1247.94, "word": " than", "probability": 0.9365234375}, {"start": 1247.94, "end": 1248.3, "word": " b", "probability": 0.98193359375}, {"start": 1248.3, "end": 1250.94, "word": " prove", "probability": 0.7216796875}, {"start": 1250.94, "end": 1251.28, "word": " أن", "probability": 0.3857421875}, {"start": 1251.28, "end": 1251.64, "word": " limit", "probability": 0.53173828125}, {"start": 1251.64, "end": 1252.26, "word": " zn", "probability": 0.905029296875}, {"start": 1252.26, "end": 1252.74, "word": " بساوي", "probability": 0.71478271484375}, {"start": 1252.74, "end": 1253.14, "word": " العدد", "probability": 0.9251302083333334}, {"start": 1253.14, "end": 1253.46, "word": " b", "probability": 0.81298828125}, {"start": 1253.46, "end": 1256.26, "word": " تمام؟", "probability": 0.7141927083333334}, {"start": 1256.26, "end": 1256.86, "word": " لبرهان", "probability": 0.887939453125}, {"start": 1256.86, "end": 1257.34, "word": " ذلك", "probability": 0.9375}, {"start": 1257.34, "end": 1258.4, "word": " أنا", "probability": 0.5361328125}, {"start": 1258.4, "end": 1258.72, "word": " عندي", "probability": 0.95703125}, {"start": 1258.72, "end": 1258.9, "word": " من", "probability": 0.98779296875}, {"start": 1258.9, "end": 1259.36, "word": " الفرض", "probability": 0.958740234375}, {"start": 1259.36, "end": 1259.74, "word": " a", "probability": 0.9462890625}, {"start": 1259.74, "end": 1260.78, "word": " positive", "probability": 0.912109375}, {"start": 1260.78, "end": 1261.58, "word": " إذا", "probability": 0.61376953125}, {"start": 1261.58, "end": 1262.02, "word": " a", "probability": 0.66650390625}, {"start": 1262.02, "end": 1262.18, "word": " to", "probability": 0.97705078125}, {"start": 1262.18, "end": 1262.42, "word": " n", "probability": 0.99072265625}, {"start": 1262.42, "end": 1262.86, "word": " positive", "probability": 0.92724609375}], "temperature": 1.0}, {"id": 50, "seek": 129282, "start": 1264.84, "end": 1292.82, "text": "وكذلك وبالتالي b to n أصغر من a to n plus b to n الان ناخد ال nth root لطرفي المتبينة هذه فبطلع b أصغر من ال nth root للمجموعة ده اللي احنا سمناه zn اذا الان انا عندي zn بساوي a n زاد b n", "tokens": [2407, 4117, 8848, 23275, 46599, 6027, 2655, 6027, 1829, 272, 281, 297, 5551, 9381, 17082, 2288, 9154, 257, 281, 297, 1804, 272, 281, 297, 2423, 7649, 8717, 47283, 3215, 2423, 297, 392, 5593, 5296, 9566, 28480, 1829, 9673, 2655, 3555, 9957, 3660, 29538, 6156, 3555, 9566, 1211, 3615, 272, 5551, 9381, 17082, 2288, 9154, 2423, 297, 392, 5593, 5296, 19528, 7435, 2304, 2407, 27884, 11778, 3224, 13672, 1829, 1975, 5016, 8315, 8608, 2304, 8315, 3224, 710, 77, 1975, 15730, 2423, 7649, 1975, 8315, 18871, 16254, 710, 77, 4724, 3794, 995, 45865, 257, 297, 30767, 18513, 272, 297], "avg_logprob": -0.23070791546179323, "compression_ratio": 1.6201117318435754, "no_speech_prob": 0.0, "words": [{"start": 1264.8400000000001, "end": 1265.68, "word": "وكذلك", "probability": 0.7783203125}, {"start": 1265.68, "end": 1266.52, "word": " وبالتالي", "probability": 0.865625}, {"start": 1266.52, "end": 1266.8, "word": " b", "probability": 0.33642578125}, {"start": 1266.8, "end": 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"end": 1314.88, "word": " اضع", "probability": 0.6710611979166666}, {"start": 1314.88, "end": 1315.92, "word": " خليها", "probability": 0.701416015625}, {"start": 1315.92, "end": 1316.5, "word": " أصغر", "probability": 0.973388671875}, {"start": 1316.5, "end": 1316.84, "word": " من", "probability": 0.9931640625}, {"start": 1316.84, "end": 1317.98, "word": " b", "probability": 0.86328125}, {"start": 1317.98, "end": 1318.3, "word": " to", "probability": 0.96337890625}, {"start": 1318.3, "end": 1318.6, "word": " n", "probability": 0.953125}, {"start": 1318.6, "end": 1319.68, "word": " زائد", "probability": 0.8040364583333334}, {"start": 1319.68, "end": 1320.0, "word": " b", "probability": 0.91455078125}, {"start": 1320.0, "end": 1320.2, "word": " to", "probability": 0.94775390625}, {"start": 1320.2, "end": 1320.44, "word": " n", "probability": 0.9833984375}, {"start": 1320.44, "end": 1321.18, "word": " الكل", "probability": 0.75146484375}, {"start": 1321.18, "end": 1321.48, "word": " to", 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1345.27, "end": 1345.85, "word": " دمجت", "probability": 0.9832763671875}, {"start": 1345.85, "end": 1347.09, "word": " المتباينتين", "probability": 0.9434988839285714}, {"start": 1347.09, "end": 1347.67, "word": " عشرة", "probability": 0.8642578125}, {"start": 1347.67, "end": 1347.79, "word": " و", "probability": 0.8623046875}, {"start": 1347.79, "end": 1348.31, "word": " أحداشر", "probability": 0.737060546875}, {"start": 1348.31, "end": 1348.47, "word": " مع", "probability": 0.9912109375}, {"start": 1348.47, "end": 1348.95, "word": " بعض", "probability": 0.994140625}, {"start": 1348.95, "end": 1350.99, "word": " فبطلع", "probability": 0.9728515625}, {"start": 1350.99, "end": 1351.39, "word": " عندي", "probability": 0.93798828125}, {"start": 1351.39, "end": 1351.71, "word": " b", "probability": 0.732421875}], "temperature": 1.0}, {"id": 53, "seek": 137449, "start": 1352.21, "end": 1374.49, "text": "من المتباينة عشرة الـ B هدا هي أصغر من ال ZN ومن المتباينة أحداشر ال ZN أصغر من two to one over N times B for every N natural number احنا اتوصلنا لالمتباينة هذه صحيحة لكل N", "tokens": [27842, 9673, 2655, 3555, 995, 9957, 3660, 6225, 8592, 25720, 2423, 39184, 363, 8032, 28259, 39896, 5551, 9381, 17082, 2288, 9154, 2423, 1176, 45, 4032, 27842, 9673, 2655, 3555, 995, 9957, 3660, 5551, 24401, 33599, 2288, 2423, 1176, 45, 5551, 9381, 17082, 2288, 9154, 732, 281, 472, 670, 426, 1413, 363, 337, 633, 426, 3303, 1230, 1975, 5016, 8315, 1975, 2655, 2407, 36520, 8315, 5296, 45340, 2655, 3555, 995, 9957, 3660, 29538, 20328, 5016, 1829, 5016, 3660, 5296, 28820, 426], "avg_logprob": -0.22260802763479728, "compression_ratio": 1.535294117647059, "no_speech_prob": 0.0, "words": [{"start": 1352.21, "end": 1352.71, "word": "من", "probability": 0.7861328125}, {"start": 1352.71, "end": 1353.67, "word": " المتباينة", "probability": 0.9475911458333334}, {"start": 1353.67, "end": 1354.09, "word": " عشرة", "probability": 0.8792317708333334}, {"start": 1354.09, "end": 1355.11, "word": " الـ", "probability": 0.5506591796875}, {"start": 1355.11, "end": 1355.29, "word": " B", "probability": 0.326416015625}, {"start": 1355.29, "end": 1355.59, "word": " هدا", "probability": 0.422119140625}, {"start": 1355.59, "end": 1355.87, "word": " هي", "probability": 0.783203125}, {"start": 1355.87, "end": 1356.43, "word": " أصغر", "probability": 0.95751953125}, {"start": 1356.43, "end": 1356.59, "word": " من", "probability": 0.98681640625}, {"start": 1356.59, "end": 1356.71, "word": " ال", "probability": 0.525390625}, {"start": 1356.71, "end": 1357.21, "word": " ZN", "probability": 0.367919921875}, {"start": 1357.21, "end": 1358.49, "word": " ومن", "probability": 0.762451171875}, {"start": 1358.49, "end": 1359.25, "word": " المتباينة", "probability": 0.9853515625}, {"start": 1359.25, "end": 1359.97, "word": " أحداشر", "probability": 0.64337158203125}, {"start": 1359.97, "end": 1360.23, "word": " ال", "probability": 0.79638671875}, {"start": 1360.23, "end": 1360.97, "word": " ZN", "probability": 0.9267578125}, {"start": 1360.97, "end": 1362.25, "word": " أصغر", "probability": 0.984130859375}, {"start": 1362.25, "end": 1362.59, "word": " من", "probability": 0.99462890625}, {"start": 1362.59, "end": 1363.01, "word": " two", "probability": 0.5615234375}, {"start": 1363.01, "end": 1363.27, "word": " to", "probability": 0.71484375}, {"start": 1363.27, "end": 1363.53, "word": " one", "probability": 0.95947265625}, {"start": 1363.53, "end": 1363.91, "word": " over", "probability": 0.90966796875}, {"start": 1363.91, "end": 1364.23, "word": " N", "probability": 0.748046875}, {"start": 1364.23, "end": 1364.85, "word": " times", "probability": 0.759765625}, {"start": 1364.85, "end": 1365.27, "word": " B", "probability": 0.89501953125}, {"start": 1365.27, "end": 1366.27, "word": " for", "probability": 0.8740234375}, {"start": 1366.27, "end": 1366.73, "word": " every", "probability": 0.82177734375}, {"start": 1366.73, "end": 1367.07, "word": " N", "probability": 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بي و limit ال sequence هذي two to واحد على n limit two to واحد على n بتساوي واحد اثبتنا احنا قبل هيك ان لو n دي c عدد موجب ف limit", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 4948, 6055, 3555, 34268, 4724, 1829, 5296, 15042, 4724, 1829, 6055, 4587, 2407, 1211, 5296, 13202, 39894, 3794, 995, 45865, 4724, 1829, 4032, 4948, 2423, 8310, 8032, 8848, 1829, 732, 281, 36764, 24401, 15844, 297, 4948, 732, 281, 36764, 24401, 15844, 297, 39894, 3794, 995, 45865, 36764, 24401, 1975, 12984, 3555, 2655, 8315, 1975, 5016, 8315, 12174, 36150, 39896, 4117, 16472, 45164, 297, 11778, 1829, 269, 6225, 3215, 3215, 3714, 29245, 3555, 6156, 4948], "avg_logprob": -0.3115354938271605, "compression_ratio": 1.6568047337278107, "no_speech_prob": 0.0, "words": [{"start": 1404.16, "end": 1404.96, "word": "وبالتالي", "probability": 0.882470703125}, {"start": 1404.96, "end": 1405.76, "word": " ال", "probability": 0.1939697265625}, {"start": 1405.76, "end": 1406.0, "word": " limit", "probability": 0.7236328125}, 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موجودة في المناجم", "tokens": [8297, 11933, 15730, 29538, 37495, 22653, 45030, 11242, 16247, 3794, 19986, 37977, 39896, 13672, 1829, 11331, 1211, 8315, 11296, 12399, 11331, 6027, 11296, 37893, 20328, 3615, 3555, 11933, 15042, 6055, 9566, 21292, 4587, 15844, 2423, 11141, 20904, 34051, 15844, 8717, 19913, 2288, 10632, 568, 13, 19, 34051, 21542, 26108, 9307, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8978, 2423, 3541, 23758, 34051, 8978, 2423, 36624, 21136, 16758, 4587, 34051, 20666, 2655, 6027, 1829, 19446, 41185, 8592, 11331, 26108, 3660, 37495, 22653, 32771, 16572, 49401, 34051, 6055, 14851, 3215, 7578, 14739, 1975, 5016, 8315, 8717, 14851, 9778, 40448, 11331, 26108, 3660, 37893, 3714, 29245, 23328, 3660, 8978, 9673, 1863, 26108, 2304], "avg_logprob": -0.1725788266809137, "compression_ratio": 1.6653846153846155, "no_speech_prob": 0.0, "words": [{"start": 1476.34, "end": 1476.82, "word": "Okay", "probability": 0.79150390625}, {"start": 1476.82, "end": 1477.14, "word": " إذا", 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{"start": 1532.64, "end": 1533.22, "word": " monotone", "probability": 0.8045247395833334}, {"start": 1533.22, "end": 1534.08, "word": " sequences", "probability": 0.90625}, {"start": 1534.08, "end": 1536.96, "word": " المتتاليات", "probability": 0.9554850260416666}, {"start": 1536.96, "end": 1537.58, "word": " اللي", "probability": 0.706298828125}, {"start": 1537.58, "end": 1538.16, "word": " بيسموها", "probability": 0.96142578125}, {"start": 1538.16, "end": 1539.06, "word": " الواتيرية", "probability": 0.8109375}, {"start": 1539.06, "end": 1541.22, "word": " المتتاليات", "probability": 0.9835611979166666}, {"start": 1541.22, "end": 1541.88, "word": " الواتيرية", "probability": 0.97685546875}, {"start": 1541.88, "end": 1542.02, "word": " ال", "probability": 0.3916015625}, {"start": 1542.02, "end": 1542.38, "word": " monotone", "probability": 0.92626953125}, {"start": 1542.38, "end": 1542.9, "word": " sequence", "probability": 0.7890625}, {"start": 1542.9, "end": 1543.2, "word": " يعني", "probability": 0.936767578125}, {"start": 1543.2, "end": 1544.2, "word": " متتالية", "probability": 0.891357421875}, {"start": 1544.2, "end": 1544.9, "word": " واتيرية", "probability": 0.9852294921875}, {"start": 1544.9, "end": 1545.76, "word": " يعني", "probability": 0.9462890625}, {"start": 1545.76, "end": 1546.0, "word": " إما", "probability": 0.847412109375}, {"start": 1546.0, "end": 1546.82, "word": " متزايدة", "probability": 0.97919921875}, {"start": 1546.82, "end": 1546.96, "word": " أو", "probability": 0.90625}, {"start": 1546.96, "end": 1547.9, "word": " متلاقصة", "probability": 0.777587890625}, {"start": 1547.9, "end": 1549.8, "word": " فناخد", "probability": 0.9512939453125}, {"start": 1549.8, "end": 1550.58, "word": " تعريف", "probability": 0.9786783854166666}, {"start": 1550.58, "end": 1553.4, "word": " let", "probability": 0.87255859375}, {"start": 1553.4, "end": 1553.78, "word": " x", "probability": 0.748046875}, {"start": 1553.78, "end": 1553.98, "word": " in", "probability": 0.5830078125}, {"start": 1553.98, "end": 1554.14, "word": " be", "probability": 0.91259765625}, {"start": 1554.14, "end": 1554.24, "word": " a", "probability": 0.728515625}, {"start": 1554.24, "end": 1554.72, "word": " sequence", "probability": 0.97412109375}, {"start": 1554.72, "end": 1554.98, "word": " of", "probability": 0.98193359375}, {"start": 1554.98, "end": 1555.2, "word": " real", "probability": 0.96435546875}, {"start": 1555.2, "end": 1555.74, "word": " numbers", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 61, "seek": 158056, "start": 1557.04, "end": 1580.56, "text": "سنقول إن سيكوينس Xn increasing متزايدة إذا كان Xn less than or equal to Xn plus one for every n لو كان كل حد أصغر من أول ساول لبعده فالسيكوينس في الحالة دي بنسميها increasing و بنسميها decreasing", "tokens": [3794, 1863, 39648, 36145, 8608, 1829, 4117, 2407, 9957, 3794, 1783, 77, 5662, 44650, 11622, 995, 25708, 3660, 11933, 15730, 25961, 1783, 77, 1570, 813, 420, 2681, 281, 1783, 77, 1804, 472, 337, 633, 297, 45164, 25961, 28242, 11331, 3215, 5551, 9381, 17082, 2288, 9154, 5551, 12610, 8608, 995, 12610, 5296, 3555, 22488, 3224, 6156, 6027, 3794, 1829, 4117, 2407, 9957, 3794, 8978, 21542, 6027, 3660, 11778, 1829, 44945, 38251, 1829, 11296, 5662, 4032, 44945, 38251, 1829, 11296, 23223], "avg_logprob": -0.2900390598922968, "compression_ratio": 1.486910994764398, "no_speech_prob": 0.0, "words": [{"start": 1557.04, "end": 1557.64, "word": "سنقول", "probability": 0.54266357421875}, {"start": 1557.64, "end": 1557.9, "word": " إن", "probability": 0.40673828125}, {"start": 1557.9, "end": 1558.44, "word": " سيكوينس", "probability": 0.6485188802083334}, {"start": 1558.44, "end": 1558.98, "word": " Xn", "probability": 0.4586181640625}, {"start": 1558.98, "end": 1559.64, "word": " increasing", "probability": 0.2132568359375}, {"start": 1559.64, "end": 1561.6, "word": " متزايدة", "probability": 0.90693359375}, {"start": 1561.6, "end": 1562.88, "word": " إذا", "probability": 0.935791015625}, {"start": 1562.88, "end": 1563.36, "word": " كان", "probability": 0.9541015625}, {"start": 1563.36, "end": 1564.36, "word": " Xn", "probability": 0.927734375}, {"start": 1564.36, "end": 1567.4, "word": " less", "probability": 0.1802978515625}, {"start": 1567.4, "end": 1567.66, "word": " than", "probability": 0.96044921875}, {"start": 1567.66, "end": 1567.8, "word": " or", "probability": 0.392333984375}, {"start": 1567.8, "end": 1568.04, "word": " equal", "probability": 0.9326171875}, {"start": 1568.04, "end": 1568.3, "word": " to", "probability": 0.53564453125}, {"start": 1568.3, "end": 1568.82, "word": " Xn", "probability": 0.94287109375}, {"start": 1568.82, "end": 1569.18, "word": " plus", "probability": 0.64697265625}, {"start": 1569.18, "end": 1569.44, "word": " one", "probability": 0.8505859375}, {"start": 1569.44, "end": 1569.7, "word": " for", "probability": 0.927734375}, {"start": 1569.7, "end": 1570.04, "word": " every", "probability": 0.77587890625}, {"start": 1570.04, "end": 1570.36, "word": " n", "probability": 0.71337890625}, {"start": 1570.36, "end": 1571.18, "word": " لو", "probability": 0.280029296875}, {"start": 1571.18, "end": 1571.5, "word": " كان", "probability": 0.97412109375}, {"start": 1571.5, "end": 1571.8, "word": " كل", "probability": 0.94775390625}, {"start": 1571.8, "end": 1572.18, "word": " حد", "probability": 0.9833984375}, {"start": 1572.18, "end": 1572.6, "word": " أصغر", "probability": 0.9866943359375}, {"start": 1572.6, "end": 1572.76, "word": " من", "probability": 0.9833984375}, {"start": 1572.76, "end": 1572.98, "word": " أول", "probability": 0.74853515625}, {"start": 1572.98, "end": 1573.28, "word": " ساول", "probability": 0.7091471354166666}, {"start": 1573.28, "end": 1574.1, "word": " لبعده", "probability": 0.9091796875}, {"start": 1574.1, "end": 1576.84, "word": " فالسيكوينس", "probability": 0.847900390625}, {"start": 1576.84, "end": 1576.92, "word": " في", "probability": 0.68408203125}, {"start": 1576.92, "end": 1577.18, "word": " الحالة", "probability": 0.8186848958333334}, {"start": 1577.18, "end": 1577.26, "word": " دي", "probability": 0.964111328125}, {"start": 1577.26, "end": 1577.76, "word": " بنسميها", "probability": 0.8797607421875}, {"start": 1577.76, "end": 1578.32, "word": " increasing", "probability": 0.955078125}, {"start": 1578.32, "end": 1579.28, "word": " و", "probability": 0.62744140625}, {"start": 1579.28, "end": 1579.96, "word": " بنسميها", "probability": 0.8477783203125}, {"start": 1579.96, "end": 1580.56, "word": " decreasing", "probability": 0.97119140625}], "temperature": 1.0}, {"id": 62, "seek": 160604, "start": 1582.76, "end": 1606.04, "text": "إذا كان كل حد أكبر من أو يساوي اللي بعده تمام؟ طيب بنسمي ال sequence monotone ال sequence بنسميها monotone أو واتيرية if it is either increasing or decreasing", "tokens": [28814, 15730, 25961, 28242, 11331, 3215, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 13672, 1829, 39182, 3224, 46811, 10943, 22807, 23032, 1829, 3555, 44945, 38251, 1829, 2423, 8310, 1108, 310, 546, 2423, 8310, 44945, 38251, 1829, 11296, 1108, 310, 546, 34051, 4032, 9307, 13546, 10632, 498, 309, 307, 2139, 5662, 420, 23223], "avg_logprob": -0.153693180734461, "compression_ratio": 1.4415584415584415, "no_speech_prob": 0.0, "words": [{"start": 1582.76, "end": 1583.1, "word": "إذا", "probability": 0.77392578125}, {"start": 1583.1, "end": 1583.48, "word": " كان", "probability": 0.97265625}, {"start": 1583.48, "end": 1583.86, "word": " كل", "probability": 0.87353515625}, {"start": 1583.86, "end": 1584.48, "word": " حد", "probability": 0.951171875}, {"start": 1584.48, "end": 1585.88, "word": " أكبر", "probability": 0.9288736979166666}, {"start": 1585.88, "end": 1586.14, "word": " من", "probability": 0.95166015625}, {"start": 1586.14, "end": 1586.36, "word": " أو", "probability": 0.95361328125}, {"start": 1586.36, "end": 1586.86, "word": " يساوي", "probability": 0.9451904296875}, {"start": 1586.86, "end": 1587.02, "word": " اللي", "probability": 0.931396484375}, {"start": 1587.02, "end": 1587.56, "word": " بعده", "probability": 0.9111328125}, {"start": 1587.56, "end": 1592.76, "word": " تمام؟", "probability": 0.6607259114583334}, {"start": 1592.76, "end": 1593.74, "word": " طيب", "probability": 0.8580729166666666}, {"start": 1593.74, "end": 1594.4, "word": " بنسمي", "probability": 0.8948567708333334}, {"start": 1594.4, "end": 1594.48, "word": " ال", "probability": 0.86767578125}, {"start": 1594.48, "end": 1594.84, "word": " sequence", "probability": 0.8466796875}, {"start": 1594.84, "end": 1595.84, "word": " monotone", "probability": 0.7692057291666666}, {"start": 1595.84, "end": 1598.48, "word": " ال", "probability": 0.6044921875}, {"start": 1598.48, "end": 1599.36, "word": " sequence", "probability": 0.875}, {"start": 1599.36, "end": 1600.0, "word": " بنسميها", "probability": 0.958251953125}, {"start": 1600.0, "end": 1600.6, "word": " monotone", "probability": 0.9392903645833334}, {"start": 1600.6, "end": 1600.82, "word": " أو", "probability": 0.76611328125}, {"start": 1600.82, "end": 1601.54, "word": " واتيرية", "probability": 0.737548828125}, {"start": 1601.54, "end": 1602.92, "word": " if", "probability": 0.8125}, {"start": 1602.92, "end": 1603.16, "word": " it", "probability": 0.97705078125}, {"start": 1603.16, "end": 1603.44, "word": " is", "probability": 0.91259765625}, {"start": 1603.44, "end": 1604.02, "word": " either", "probability": 0.94091796875}, {"start": 1604.02, "end": 1604.74, "word": " increasing", "probability": 0.96630859375}, {"start": 1604.74, "end": 1605.46, "word": " or", "probability": 0.96826171875}, {"start": 1605.46, "end": 1606.04, "word": " decreasing", "probability": 0.95166015625}], "temperature": 1.0}, {"id": 63, "seek": 163705, "start": 1608.95, "end": 1637.05, "text": "إن المتتالي الوطرية هي متتالية إما increasing أو decreasing معنى آخر كل increasing sequence is monotone sequence and every decreasing sequence is monotone sequence طب هاي أمثلة على monotone sequences فاندي هنا sequence n of natural numbers", "tokens": [28814, 1863, 9673, 2655, 2655, 6027, 1829, 2423, 2407, 9566, 2288, 10632, 39896, 44650, 2655, 6027, 10632, 11933, 15042, 5662, 34051, 23223, 20449, 1863, 7578, 19753, 34740, 28242, 5662, 8310, 307, 1108, 310, 546, 8310, 293, 633, 23223, 8310, 307, 1108, 310, 546, 8310, 23032, 3555, 8032, 47302, 5551, 2304, 12984, 37977, 15844, 1108, 310, 546, 22978, 6156, 7649, 16254, 34105, 8310, 297, 295, 3303, 3547], "avg_logprob": -0.22971081466817145, "compression_ratio": 1.7142857142857142, "no_speech_prob": 0.0, "words": [{"start": 1608.95, "end": 1609.25, "word": "إن", "probability": 0.5556640625}, {"start": 1609.25, "end": 1609.97, "word": " المتتالي", "probability": 0.91982421875}, {"start": 1609.97, "end": 1610.61, "word": " الوطرية", "probability": 0.714453125}, {"start": 1610.61, "end": 1610.97, "word": " هي", "probability": 0.5625}, {"start": 1610.97, "end": 1611.81, "word": " متتالية", "probability": 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"probability": 0.91064453125}, {"start": 1621.49, "end": 1622.33, "word": " and", "probability": 0.67236328125}, {"start": 1622.33, "end": 1622.83, "word": " every", "probability": 0.72412109375}, {"start": 1622.83, "end": 1623.65, "word": " decreasing", "probability": 0.95458984375}, {"start": 1623.65, "end": 1624.39, "word": " sequence", "probability": 0.94775390625}, {"start": 1624.39, "end": 1624.69, "word": " is", "probability": 0.93603515625}, {"start": 1624.69, "end": 1625.35, "word": " monotone", "probability": 0.9803059895833334}, {"start": 1625.35, "end": 1626.09, "word": " sequence", "probability": 0.72900390625}, {"start": 1626.09, "end": 1628.95, "word": " طب", "probability": 0.800537109375}, {"start": 1628.95, "end": 1629.13, "word": " هاي", "probability": 0.6610107421875}, {"start": 1629.13, "end": 1629.67, "word": " أمثلة", "probability": 0.985595703125}, {"start": 1629.67, "end": 1630.07, "word": " على", "probability": 0.75390625}, {"start": 1630.07, "end": 1630.91, "word": " monotone", "probability": 0.9581705729166666}, {"start": 1630.91, "end": 1631.71, "word": " sequences", "probability": 0.87060546875}, {"start": 1631.71, "end": 1634.11, "word": " فاندي", "probability": 0.6166178385416666}, {"start": 1634.11, "end": 1634.37, "word": " هنا", "probability": 0.98876953125}, {"start": 1634.37, "end": 1634.91, "word": " sequence", "probability": 0.76513671875}, {"start": 1634.91, "end": 1635.69, "word": " n", "probability": 0.4658203125}, {"start": 1635.69, "end": 1635.95, "word": " of", "probability": 0.947265625}, {"start": 1635.95, "end": 1636.45, "word": " natural", "probability": 0.8935546875}, {"start": 1636.45, "end": 1637.05, "word": " numbers", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 64, "seek": 166784, "start": 1638.24, "end": 1667.84, "text": "is increasing واضح ان xn بساوي n أصغر من او ساوي xn plus one اللي هو n زاد واحد لان هذا increasing وهذا increasing ال sequence اللي ال inf term تبعها two to n اللي هي هذه is increasing بينما ال sequence one over n decreasing هي كل حد أكبر من أو ساوي لبعده", "tokens": [271, 5662, 4032, 46958, 5016, 16472, 2031, 77, 4724, 3794, 995, 45865, 297, 5551, 9381, 17082, 2288, 9154, 1975, 2407, 8608, 995, 45865, 2031, 77, 1804, 472, 13672, 1829, 31439, 297, 30767, 18513, 36764, 24401, 5296, 7649, 23758, 5662, 37037, 15730, 5662, 2423, 8310, 13672, 1829, 2423, 1536, 1433, 6055, 3555, 3615, 11296, 732, 281, 297, 13672, 1829, 39896, 29538, 307, 5662, 49374, 15042, 2423, 8310, 472, 670, 297, 23223, 39896, 28242, 11331, 3215, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 5296, 3555, 22488, 3224], "avg_logprob": -0.24694683531235004, "compression_ratio": 1.7828282828282829, "no_speech_prob": 0.0, "words": [{"start": 1638.24, "end": 1638.6, "word": "is", "probability": 0.275634765625}, {"start": 1638.6, "end": 1639.22, "word": " increasing", "probability": 0.9423828125}, {"start": 1639.22, "end": 1641.38, "word": " واضح", "probability": 0.94580078125}, {"start": 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0.9886474609375}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98681640625}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.989013671875}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.986328125}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.989013671875}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98583984375}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9888916015625}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.9853515625}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9893798828125}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.984375}, {"start": 1692.58, "end": 1692.58, "word": " شرط،", "probability": 0.9893798828125}, {"start": 1692.58, "end": 1692.58, "word": " مش", "probability": 0.98388671875}, {"start": 1692.58, "end": 1692.6, "word": " شرط،", "probability": 0.9888916015625}, {"start": 1692.6, "end": 1693.66, "word": " مش", "probability": 0.98193359375}, {"start": 1693.66, "end": 1694.54, "word": " شرط", "probability": 0.9952799479166666}], "temperature": 1.0}, {"id": 66, "seek": 172443, "start": 1695.75, "end": 1724.43, "text": "the following sequence is sequence اللي الحد اللي عام تبعها negative one to n أو n زيادة واحد اللي هي ال alternated sequence ال sequence هذه المتدبدبة alternating يعني المتدبدبة في الإشارة واحد سالب واحد واحد سالب واحد هذه ليست conversion ليست monotone is not increasing and it is not decreasing", "tokens": [3322, 3480, 8310, 307, 8310, 13672, 1829, 21542, 3215, 13672, 1829, 6225, 10943, 6055, 3555, 3615, 11296, 3671, 472, 281, 297, 34051, 297, 30767, 1829, 18513, 3660, 36764, 24401, 13672, 1829, 39896, 2423, 5400, 770, 8310, 2423, 8310, 29538, 9673, 2655, 3215, 44510, 49401, 40062, 37495, 22653, 9673, 2655, 3215, 44510, 49401, 8978, 33688, 8592, 9640, 3660, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 36764, 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"probability": 0.956787109375}, {"start": 1712.79, "end": 1713.27, "word": " سالب", "probability": 0.7762044270833334}, {"start": 1713.27, "end": 1713.69, "word": " واحد", "probability": 0.949462890625}, {"start": 1713.69, "end": 1714.11, "word": " واحد", "probability": 0.96875}, {"start": 1714.11, "end": 1714.57, "word": " سالب", "probability": 0.9500325520833334}, {"start": 1714.57, "end": 1714.93, "word": " واحد", "probability": 0.951416015625}, {"start": 1714.93, "end": 1715.35, "word": " هذه", "probability": 0.3779296875}, {"start": 1715.35, "end": 1715.75, "word": " ليست", "probability": 0.9833984375}, {"start": 1715.75, "end": 1716.33, "word": " conversion", "probability": 0.452056884765625}, {"start": 1716.33, "end": 1717.01, "word": " ليست", "probability": 0.8076171875}, {"start": 1717.01, "end": 1717.85, "word": " monotone", "probability": 0.7628580729166666}, {"start": 1717.85, "end": 1720.15, "word": " is", "probability": 0.6572265625}, {"start": 1720.15, "end": 1720.45, "word": " not", "probability": 0.96728515625}, {"start": 1720.45, "end": 1721.07, "word": " increasing", "probability": 0.96240234375}, {"start": 1721.07, "end": 1722.61, "word": " and", "probability": 0.56396484375}, {"start": 1722.61, "end": 1723.07, "word": " it", "probability": 0.97021484375}, {"start": 1723.07, "end": 1723.35, "word": " is", "probability": 0.94384765625}, {"start": 1723.35, "end": 1723.63, "word": " not", "probability": 0.96044921875}, {"start": 1723.63, "end": 1724.43, "word": " decreasing", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 67, "seek": 174308, "start": 1726.04, "end": 1743.08, "text": "نفس الشيء ال sequence اللي حد اللي عم تبعها سالب one to n اللي هي سالب واحد موجة بتنين سالب تلاتة و هكذا ال sequence هذه is not monotone لا increasing ولا decreasing تمام واضح", "tokens": [1863, 36178, 25124, 1829, 38207, 2423, 8310, 13672, 1829, 11331, 3215, 13672, 1829, 6225, 2304, 6055, 3555, 3615, 11296, 8608, 6027, 3555, 472, 281, 297, 13672, 1829, 39896, 8608, 6027, 3555, 36764, 24401, 3714, 29245, 3660, 39894, 1863, 9957, 8608, 6027, 3555, 6055, 1211, 9307, 3660, 4032, 8032, 4117, 15730, 2423, 8310, 29538, 307, 406, 1108, 310, 546, 20193, 5662, 49429, 23223, 46811, 10943, 4032, 46958, 5016], "avg_logprob": -0.26677388916997347, "compression_ratio": 1.5818181818181818, "no_speech_prob": 0.0, "words": [{"start": 1726.04, "end": 1726.5, "word": "نفس", "probability": 0.61328125}, {"start": 1726.5, "end": 1726.84, "word": " الشيء", "probability": 0.9246419270833334}, {"start": 1726.84, "end": 1726.98, "word": " ال", "probability": 0.4033203125}, {"start": 1726.98, "end": 1727.36, "word": " sequence", "probability": 0.58740234375}, {"start": 1727.36, "end": 1727.56, "word": " اللي", "probability": 0.4954833984375}, {"start": 1727.56, "end": 1727.84, "word": " حد", "probability": 0.6461181640625}, {"start": 1727.84, "end": 1727.96, "word": " اللي", "probability": 0.787353515625}, {"start": 1727.96, "end": 1728.06, "word": " عم", "probability": 0.62451171875}, {"start": 1728.06, "end": 1728.46, "word": " تبعها", "probability": 0.811279296875}, {"start": 1728.46, "end": 1728.82, "word": " سالب", "probability": 0.7060546875}, {"start": 1728.82, "end": 1729.04, "word": " one", "probability": 0.8408203125}, {"start": 1729.04, "end": 1729.22, "word": " to", "probability": 0.84033203125}, {"start": 1729.22, "end": 1729.54, "word": " n", "probability": 0.70947265625}, {"start": 1729.54, "end": 1731.18, "word": " اللي", "probability": 0.6280517578125}, {"start": 1731.18, "end": 1731.42, "word": " هي", "probability": 0.88916015625}, {"start": 1731.42, "end": 1731.9, "word": " سالب", "probability": 0.9591471354166666}, {"start": 1731.9, "end": 1732.28, "word": " واحد", "probability": 0.968994140625}, {"start": 1732.28, "end": 1732.68, "word": " موجة", "probability": 0.8719075520833334}, {"start": 1732.68, "end": 1733.18, "word": " بتنين", "probability": 0.78125}, {"start": 1733.18, "end": 1733.62, "word": " سالب", "probability": 0.9417317708333334}, {"start": 1733.62, "end": 1734.08, "word": " تلاتة", "probability": 0.951416015625}, {"start": 1734.08, "end": 1734.2, "word": " و", "probability": 0.580078125}, {"start": 1734.2, "end": 1734.74, "word": " هكذا", "probability": 0.8395182291666666}, {"start": 1734.74, "end": 1736.04, "word": " ال", "probability": 0.8740234375}, {"start": 1736.04, "end": 1736.48, "word": " sequence", "probability": 0.982421875}, {"start": 1736.48, "end": 1736.82, "word": " هذه", "probability": 0.44140625}, {"start": 1736.82, "end": 1737.34, "word": " is", "probability": 0.8447265625}, {"start": 1737.34, "end": 1737.64, "word": " not", "probability": 0.9658203125}, {"start": 1737.64, "end": 1738.52, "word": " monotone", "probability": 0.8024088541666666}, {"start": 1738.52, "end": 1739.54, "word": " لا", "probability": 0.7568359375}, {"start": 1739.54, "end": 1740.02, "word": " increasing", "probability": 0.8720703125}, {"start": 1740.02, "end": 1740.56, "word": " ولا", "probability": 0.94873046875}, {"start": 1740.56, "end": 1741.82, "word": " decreasing", "probability": 0.974609375}, {"start": 1741.82, "end": 1742.62, "word": " تمام", "probability": 0.8642578125}, {"start": 1742.62, "end": 1743.08, "word": " واضح", "probability": 0.8948567708333334}], "temperature": 1.0}, {"id": 68, "seek": 176687, "start": 1743.93, "end": 1766.87, "text": "إذا ال sequence .. أي .. لو أخدنا أي sequence عشوائية فممكن تكون increasing، ممكن تكون decreasing، ممكن تكون neither، neither increasing nor decreasing زي ال function ممكن تكون odd أو even أو neither، لا odd ولا even، أه؟ تمام؟ طيب ال .. في نظرية مهمة هنا في هذا السياق", "tokens": [28814, 15730, 2423, 8310, 4386, 36632, 4386, 45164, 5551, 9778, 3215, 8315, 36632, 8310, 6225, 8592, 2407, 16373, 10632, 6156, 2304, 43020, 6055, 30544, 5662, 12399, 3714, 43020, 6055, 30544, 23223, 12399, 3714, 43020, 6055, 30544, 9662, 12399, 9662, 5662, 6051, 23223, 30767, 1829, 2423, 2445, 3714, 43020, 6055, 30544, 7401, 34051, 754, 34051, 9662, 12399, 20193, 7401, 49429, 754, 12399, 5551, 3224, 22807, 46811, 10943, 22807, 23032, 1829, 3555, 2423, 4386, 8978, 8717, 19913, 2288, 10632, 3714, 16095, 3660, 34105, 8978, 23758, 21136, 25528, 4587], "avg_logprob": -0.1778915212757286, "compression_ratio": 1.8056872037914693, "no_speech_prob": 0.0, "words": [{"start": 1743.93, "end": 1744.31, "word": "إذا", "probability": 0.7958984375}, {"start": 1744.31, "end": 1744.63, "word": " ال", "probability": 0.3447265625}, {"start": 1744.63, "end": 1745.03, "word": " sequence", "probability": 0.7822265625}, {"start": 1745.03, "end": 1745.23, "word": " ..", "probability": 0.529296875}, {"start": 1745.23, "end": 1745.37, "word": " أي", "probability": 0.457763671875}, {"start": 1745.37, "end": 1745.47, "word": " ..", "probability": 0.73681640625}, {"start": 1745.47, "end": 1745.59, "word": " لو", "probability": 0.9296875}, {"start": 1745.59, "end": 1745.89, "word": " أخدنا", "probability": 0.8385009765625}, {"start": 1745.89, "end": 1746.05, "word": " أي", "probability": 0.90576171875}, {"start": 1746.05, "end": 1746.43, "word": " sequence", "probability": 0.98046875}, {"start": 1746.43, "end": 1747.25, "word": " عشوائية", "probability": 0.99365234375}, {"start": 1747.25, "end": 1747.65, "word": " فممكن", "probability": 0.9436848958333334}, {"start": 1747.65, "end": 1748.01, "word": " تكون", "probability": 0.994384765625}, {"start": 1748.01, "end": 1749.31, "word": " increasing،", "probability": 0.541015625}, {"start": 1749.31, "end": 1749.75, "word": " ممكن", "probability": 0.98486328125}, {"start": 1749.75, "end": 1750.25, "word": " تكون", "probability": 0.99462890625}, {"start": 1750.25, "end": 1752.07, "word": " decreasing،", "probability": 0.92041015625}, {"start": 1752.07, "end": 1752.43, "word": " ممكن", "probability": 0.9755859375}, {"start": 1752.43, "end": 1752.91, "word": " تكون", "probability": 0.994140625}, {"start": 1752.91, "end": 1753.75, "word": " neither،", "probability": 0.76904296875}, {"start": 1753.75, "end": 1754.07, "word": " neither", "probability": 0.8447265625}, {"start": 1754.07, "end": 1754.69, "word": " increasing", "probability": 0.96533203125}, {"start": 1754.69, "end": 1754.95, "word": " nor", "probability": 0.77197265625}, {"start": 1754.95, "end": 1755.33, "word": " decreasing", "probability": 0.9541015625}, {"start": 1755.33, "end": 1755.65, "word": " زي", "probability": 0.831787109375}, {"start": 1755.65, "end": 1755.79, "word": " ال", "probability": 0.974609375}, {"start": 1755.79, "end": 1756.15, "word": " function", "probability": 0.92236328125}, {"start": 1756.15, "end": 1756.45, "word": " ممكن", "probability": 0.76806640625}, {"start": 1756.45, "end": 1756.81, "word": " تكون", "probability": 0.99365234375}, {"start": 1756.81, "end": 1757.25, "word": " odd", "probability": 0.93408203125}, {"start": 1757.25, "end": 1758.09, "word": " أو", "probability": 0.8447265625}, {"start": 1758.09, "end": 1758.43, "word": " even", "probability": 0.9287109375}, {"start": 1758.43, "end": 1758.81, "word": " أو", "probability": 0.95654296875}, {"start": 1758.81, "end": 1759.37, "word": " neither،", "probability": 0.797119140625}, {"start": 1759.37, "end": 1759.75, "word": " لا", "probability": 0.91845703125}, {"start": 1759.75, "end": 1760.07, "word": " odd", "probability": 0.8974609375}, {"start": 1760.07, "end": 1760.27, "word": " ولا", "probability": 0.9345703125}, {"start": 1760.27, "end": 1760.79, "word": " even،", "probability": 0.826171875}, {"start": 1760.79, "end": 1761.39, "word": " أه؟", "probability": 0.5234375}, {"start": 1761.39, "end": 1762.95, "word": " تمام؟", "probability": 0.7233072916666666}, {"start": 1762.95, "end": 1763.47, "word": " طيب", "probability": 0.9449869791666666}, {"start": 1763.47, "end": 1763.89, "word": " ال", "probability": 0.64892578125}, {"start": 1763.89, "end": 1764.33, "word": " ..", "probability": 0.982421875}, {"start": 1764.33, "end": 1764.53, "word": " في", "probability": 0.83740234375}, {"start": 1764.53, "end": 1765.07, "word": " نظرية", "probability": 0.984375}, {"start": 1765.07, "end": 1765.59, "word": " مهمة", "probability": 0.99560546875}, {"start": 1765.59, "end": 1765.81, "word": " هنا", "probability": 0.986328125}, {"start": 1765.81, "end": 1766.05, "word": " في", "probability": 0.9794921875}, {"start": 1766.05, "end": 1766.27, "word": " هذا", "probability": 0.984375}, {"start": 1766.27, "end": 1766.87, "word": " السياق", "probability": 0.9542643229166666}], "temperature": 1.0}, {"id": 69, "seek": 179491, "start": 1769.97, "end": 1794.91, "text": "بتخص الـ monotone sequences وبالتالي بنسميها monotone convergence theorem وبنستخدم اختصارات monotone convergence theorem النظرية هذه بتقول خد .. خدي let x and b a monotone sequence خلينا ناخد monotone sequence", "tokens": [3555, 2655, 9778, 9381, 2423, 39184, 1108, 310, 546, 22978, 46599, 6027, 2655, 6027, 1829, 44945, 38251, 1829, 11296, 1108, 310, 546, 32181, 20904, 46599, 1863, 14851, 9778, 40448, 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1775.71, "word": " convergence", "probability": 0.9541015625}, {"start": 1775.71, "end": 1776.29, "word": " theorem", "probability": 0.8837890625}, {"start": 1776.29, "end": 1778.17, "word": " وبنستخدم", "probability": 0.849169921875}, {"start": 1778.17, "end": 1779.17, "word": " اختصارات", "probability": 0.7982421875}, {"start": 1779.17, "end": 1780.07, "word": " monotone", "probability": 0.8590494791666666}, {"start": 1780.07, "end": 1781.03, "word": " convergence", "probability": 0.94580078125}, {"start": 1781.03, "end": 1781.63, "word": " theorem", "probability": 0.81005859375}, {"start": 1781.63, "end": 1786.69, "word": " النظرية", "probability": 0.9239501953125}, {"start": 1786.69, "end": 1786.85, "word": " هذه", "probability": 0.7802734375}, {"start": 1786.85, "end": 1787.35, "word": " بتقول", "probability": 0.97265625}, {"start": 1787.35, "end": 1789.59, "word": " خد", "probability": 0.825439453125}, {"start": 1789.59, "end": 1789.67, "word": " ..", "probability": 0.41650390625}, {"start": 1789.67, "end": 1790.09, "word": " خدي", "probability": 0.8818359375}, {"start": 1790.09, "end": 1791.09, "word": " let", "probability": 0.80615234375}, {"start": 1791.09, "end": 1791.41, "word": " x", "probability": 0.6494140625}, {"start": 1791.41, "end": 1791.63, "word": " and", "probability": 0.42529296875}, {"start": 1791.63, "end": 1791.85, "word": " b", "probability": 0.95361328125}, {"start": 1791.85, "end": 1792.13, "word": " a", "probability": 0.25146484375}, {"start": 1792.13, "end": 1792.55, "word": " monotone", "probability": 0.98681640625}, {"start": 1792.55, "end": 1793.11, "word": " sequence", "probability": 0.97265625}, {"start": 1793.11, "end": 1793.45, "word": " خلينا", "probability": 0.74072265625}, {"start": 1793.45, "end": 1793.91, "word": " ناخد", "probability": 0.9903971354166666}, {"start": 1793.91, "end": 1794.37, "word": " monotone", "probability": 0.9508463541666666}, {"start": 1794.37, "end": 1794.91, "word": " sequence", "probability": 0.97900390625}], "temperature": 1.0}, {"id": 70, "seek": 182517, "start": 1796.49, "end": 1825.17, "text": "الان هذه الـ monotone sequence بتكون convergent if and only if it is bounded تمام؟ moreover إضافة إلى ذلك لو كانت ال sequence x in هذه bounded and increasing فأكيد طبعا convergent و ال limit تبعتها بساوي ال supremum إلها ك set كذلك لو كانت ال sequence x in bounded و decreasing", "tokens": [6027, 7649, 29538, 2423, 39184, 1108, 310, 546, 8310, 39894, 30544, 9652, 6930, 498, 293, 787, 498, 309, 307, 37498, 46811, 10943, 22807, 544, 3570, 11933, 11242, 31845, 3660, 30731, 29910, 23275, 45164, 25961, 2655, 2423, 8310, 2031, 294, 29538, 37498, 293, 5662, 6156, 10721, 4117, 25708, 23032, 3555, 3615, 995, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 2423, 23710, 449, 11933, 1211, 11296, 9122, 992, 9122, 8848, 23275, 45164, 25961, 2655, 2423, 8310, 2031, 294, 37498, 4032, 23223], "avg_logprob": -0.18050508703603302, "compression_ratio": 1.6529680365296804, "no_speech_prob": 0.0, "words": [{"start": 1796.49, "end": 1797.05, "word": "الان", "probability": 0.768798828125}, {"start": 1797.05, "end": 1797.49, "word": " هذه", "probability": 0.77685546875}, {"start": 1797.49, "end": 1797.65, "word": " الـ", "probability": 0.69287109375}, {"start": 1797.65, "end": 1798.03, "word": " monotone", "probability": 0.9046223958333334}, {"start": 1798.03, "end": 1798.63, "word": " sequence", "probability": 0.9501953125}, {"start": 1798.63, "end": 1799.11, "word": " بتكون", "probability": 0.91455078125}, {"start": 1799.11, "end": 1799.89, "word": " convergent", "probability": 0.7919921875}, {"start": 1799.89, "end": 1800.25, "word": " if", "probability": 0.8349609375}, {"start": 1800.25, "end": 1800.51, "word": " and", "probability": 0.85009765625}, {"start": 1800.51, "end": 1800.79, "word": " only", "probability": 0.919921875}, {"start": 1800.79, "end": 1801.13, "word": " if", "probability": 0.97802734375}, {"start": 1801.13, "end": 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in convergent و ال limit تبعتها بساوي العدد x star فهستخدم تعريف epsilon capital N لل limit فلازم ابدأ let epsilon أكبر من الصفر بيه given الان ال x star هذا", "tokens": [2655, 3615, 6027, 7578, 8717, 8592, 38688, 9122, 33911, 8717, 12984, 3555, 2655, 2423, 3932, 281, 536, 341, 5296, 26890, 3224, 7649, 2423, 3932, 1975, 8315, 1975, 1829, 8592, 39894, 12984, 3555, 2655, 22807, 39894, 12984, 3555, 2655, 16472, 2423, 8310, 2031, 294, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 18863, 3215, 3215, 2031, 3543, 6156, 3224, 14851, 9778, 40448, 37279, 16572, 5172, 17889, 4238, 426, 24976, 4948, 6156, 1211, 31377, 2304, 48127, 3215, 10721, 718, 17889, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 4724, 1829, 3224, 2212, 2423, 7649, 2423, 2031, 3543, 23758], "avg_logprob": -0.2337561828075069, "compression_ratio": 1.5895196506550218, "no_speech_prob": 0.0, "words": [{"start": 2159.95, "end": 2160.33, "word": "تعالى", "probability": 0.71441650390625}, {"start": 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"end": 2170.33, "word": " تبعتها", "probability": 0.9251708984375}, {"start": 2170.33, "end": 2170.81, "word": " بساوي", "probability": 0.879150390625}, {"start": 2170.81, "end": 2171.23, "word": " العدد", "probability": 0.9334309895833334}, {"start": 2171.23, "end": 2171.47, "word": " x", "probability": 0.91162109375}, {"start": 2171.47, "end": 2171.87, "word": " star", "probability": 0.06988525390625}, {"start": 2171.87, "end": 2173.09, "word": " فهستخدم", "probability": 0.877099609375}, {"start": 2173.09, "end": 2173.63, "word": " تعريف", "probability": 0.9928385416666666}, {"start": 2173.63, "end": 2174.11, "word": " epsilon", "probability": 0.482177734375}, {"start": 2174.11, "end": 2174.59, "word": " capital", "probability": 0.70703125}, {"start": 2174.59, "end": 2174.87, "word": " N", "probability": 0.63330078125}, {"start": 2174.87, "end": 2175.05, "word": " لل", "probability": 0.53662109375}, {"start": 2175.05, "end": 2175.45, "word": " limit", "probability": 0.9580078125}, {"start": 2175.45, "end": 2176.79, "word": " فلازم", "probability": 0.9649658203125}, {"start": 2176.79, "end": 2177.21, "word": " ابدأ", "probability": 0.6949869791666666}, {"start": 2177.21, "end": 2177.41, "word": " let", "probability": 0.93798828125}, {"start": 2177.41, "end": 2177.83, "word": " epsilon", "probability": 0.91357421875}, {"start": 2177.83, "end": 2178.23, "word": " أكبر", "probability": 0.8566080729166666}, {"start": 2178.23, "end": 2178.39, "word": " من", "probability": 0.99169921875}, {"start": 2178.39, "end": 2178.79, "word": " الصفر", "probability": 0.7105712890625}, {"start": 2178.79, "end": 2179.05, "word": " بيه", "probability": 0.8362630208333334}, {"start": 2179.05, "end": 2179.43, "word": " given", "probability": 0.87841796875}, {"start": 2179.43, "end": 2180.97, "word": " الان", "probability": 0.556640625}, {"start": 2180.97, "end": 2181.27, "word": " ال", "probability": 0.96435546875}, {"start": 2181.27, "end": 2181.91, "word": " x", "probability": 0.7578125}, {"start": 2181.91, "end": 2182.59, "word": " star", "probability": 0.78271484375}, {"start": 2182.59, "end": 2183.11, "word": " هذا", "probability": 0.76220703125}], "temperature": 1.0}, {"id": 84, "seek": 221213, "start": 2184.59, "end": 2212.13, "text": "هو ال supremum لل set هذه لما نطرح من ال supremum عدد موجب بيبطل upper bound بيبطل upper bound لأن ال x star هو أصغر upper bound اطرح منه عدد موجب بيبطل upper bound إذا هذا العدد x star minus y is not an upper bound معناته في أنصر في ال set هذه اللي هو x رقم capital N أكبر من العدد هذا اللي هو ما هوش upper bound", "tokens": [3224, 2407, 2423, 23710, 449, 24976, 992, 29538, 5296, 15042, 8717, 9566, 2288, 5016, 9154, 2423, 23710, 449, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 1829, 3555, 9566, 1211, 6597, 5472, 4724, 1829, 3555, 9566, 1211, 6597, 5472, 5296, 33456, 2423, 2031, 3543, 31439, 5551, 9381, 17082, 2288, 6597, 5472, 1975, 9566, 2288, 5016, 9154, 3224, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 1829, 3555, 9566, 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"probability": 0.99560546875}, {"start": 2197.17, "end": 2197.69, "word": " بيبطل", "probability": 0.984765625}, {"start": 2197.69, "end": 2197.95, "word": " upper", "probability": 0.93359375}, {"start": 2197.95, "end": 2198.25, "word": " bound", "probability": 0.91064453125}, {"start": 2198.25, "end": 2198.45, "word": " إذا", "probability": 0.52490234375}, {"start": 2198.45, "end": 2198.67, "word": " هذا", "probability": 0.828125}, {"start": 2198.67, "end": 2199.51, "word": " العدد", "probability": 0.9695638020833334}, {"start": 2199.51, "end": 2199.83, "word": " x", "probability": 0.7900390625}, {"start": 2199.83, "end": 2200.23, "word": " star", "probability": 0.70947265625}, {"start": 2200.23, "end": 2200.53, "word": " minus", "probability": 0.55224609375}, {"start": 2200.53, "end": 2200.87, "word": " y", "probability": 0.89697265625}, {"start": 2200.87, "end": 2201.17, "word": " is", "probability": 0.771484375}, {"start": 2201.17, "end": 2201.39, "word": " not", "probability": 0.9580078125}, {"start": 2201.39, "end": 2201.59, "word": " an", "probability": 0.55078125}, {"start": 2201.59, "end": 2201.85, "word": " upper", "probability": 0.93115234375}, {"start": 2201.85, "end": 2202.23, "word": " bound", "probability": 0.9169921875}, {"start": 2202.23, "end": 2203.29, "word": " معناته", "probability": 0.9054361979166666}, {"start": 2203.29, "end": 2203.49, "word": " في", "probability": 0.80126953125}, {"start": 2203.49, "end": 2204.03, "word": " أنصر", "probability": 0.8111979166666666}, {"start": 2204.03, "end": 2204.17, "word": " في", "probability": 0.9853515625}, {"start": 2204.17, "end": 2204.33, "word": " ال", "probability": 0.77001953125}, {"start": 2204.33, "end": 2204.61, "word": " set", "probability": 0.97998046875}, {"start": 2204.61, "end": 2205.09, "word": " هذه", "probability": 0.91796875}, {"start": 2205.09, "end": 2206.01, "word": " اللي", "probability": 0.91357421875}, {"start": 2206.01, "end": 2206.29, "word": " هو", "probability": 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0.8046875}, {"start": 2397.99, "end": 2399.93, "word": " تمام؟", "probability": 0.5948893229166666}, {"start": 2399.93, "end": 2400.39, "word": " الان", "probability": 0.817626953125}, {"start": 2400.39, "end": 2400.77, "word": " بما", "probability": 0.979736328125}, {"start": 2400.77, "end": 2400.91, "word": " ان", "probability": 0.85009765625}, {"start": 2400.91, "end": 2401.25, "word": " x", "probability": 0.43701171875}, {"start": 2401.25, "end": 2401.53, "word": " in", "probability": 0.8720703125}, {"start": 2401.53, "end": 2402.11, "word": " decreasing", "probability": 0.859375}, {"start": 2402.11, "end": 2402.97, "word": " اذا", "probability": 0.6639404296875}, {"start": 2402.97, "end": 2403.17, "word": " ال", "probability": 0.91064453125}, {"start": 2403.17, "end": 2403.51, "word": " sequence", "probability": 0.98388671875}, {"start": 2403.51, "end": 2404.15, "word": " سالب", "probability": 0.77392578125}, {"start": 2404.15, "end": 2404.43, "word": " x", "probability": 0.96923828125}, {"start": 2404.43, "end": 2404.65, "word": " in", "probability": 0.90625}, {"start": 2404.65, "end": 2405.17, "word": " تطلع", "probability": 0.95556640625}, {"start": 2405.17, "end": 2406.03, "word": " increasing", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 92, "seek": 242905, "start": 2407.47, "end": 2429.05, "text": "وطبعا بما أن ال sequence x in bounded إذا ال sequence سالب x in أيضا bounded إذا الأن أنا في عندي sequence جديد اللي هي sequence yn bounded وin crazy إذا حسب الجزء a by part a limit ال sequence yn تطلع exist", "tokens": [2407, 9566, 3555, 3615, 995, 4724, 15042, 14739, 2423, 8310, 2031, 294, 37498, 11933, 15730, 2423, 8310, 8608, 6027, 3555, 2031, 294, 36632, 11242, 995, 37498, 11933, 15730, 16247, 1863, 41850, 8978, 18871, 16254, 8310, 10874, 16254, 3215, 13672, 1829, 39896, 8310, 17861, 37498, 4032, 259, 3219, 11933, 15730, 11331, 35457, 25724, 11622, 38207, 257, 538, 644, 257, 4948, 2423, 8310, 17861, 6055, 9566, 1211, 3615, 2514], "avg_logprob": -0.2403492660206907, "compression_ratio": 1.6428571428571428, "no_speech_prob": 0.0, "words": [{"start": 2407.47, "end": 2408.35, "word": "وطبعا", "probability": 0.778076171875}, {"start": 2408.35, "end": 2408.63, "word": " بما", "probability": 0.874267578125}, {"start": 2408.63, "end": 2408.81, "word": " أن", "probability": 0.403076171875}, {"start": 2408.81, "end": 2408.95, "word": " ال", "probability": 0.71630859375}, {"start": 2408.95, "end": 2409.27, "word": " sequence", "probability": 0.75634765625}, {"start": 2409.27, "end": 2409.77, "word": " x", "probability": 0.65966796875}, {"start": 2409.77, "end": 2410.07, "word": " in", "probability": 0.4482421875}, {"start": 2410.07, "end": 2410.61, "word": " bounded", "probability": 0.83154296875}, {"start": 2410.61, "end": 2411.65, "word": " إذا", "probability": 0.67236328125}, {"start": 2411.65, "end": 2411.85, "word": " ال", "probability": 0.52685546875}, {"start": 2411.85, "end": 2412.25, "word": " sequence", "probability": 0.97509765625}, {"start": 2412.25, "end": 2412.77, "word": " سالب", "probability": 0.8133138020833334}, {"start": 2412.77, "end": 2412.99, "word": " x", "probability": 0.951171875}, {"start": 2412.99, "end": 2413.23, "word": " in", "probability": 0.90625}, {"start": 2413.23, "end": 2413.63, "word": " أيضا", "probability": 0.9420572916666666}, {"start": 2413.63, "end": 2414.07, "word": " bounded", "probability": 0.8955078125}, {"start": 2414.07, "end": 2415.29, "word": " إذا", "probability": 0.8505859375}, {"start": 2415.29, "end": 2415.67, "word": " الأن", "probability": 0.59326171875}, {"start": 2415.67, "end": 2415.87, "word": " أنا", "probability": 0.625}, {"start": 2415.87, "end": 2415.97, "word": " في", "probability": 0.7978515625}, {"start": 2415.97, "end": 2416.29, "word": " عندي", "probability": 0.82861328125}, {"start": 2416.29, "end": 2416.79, "word": " sequence", "probability": 0.90478515625}, {"start": 2416.79, "end": 2417.25, "word": " جديد", "probability": 0.8473307291666666}, {"start": 2417.25, "end": 2417.41, "word": " اللي", "probability": 0.920166015625}, {"start": 2417.41, "end": 2417.63, "word": " هي", "probability": 0.9326171875}, {"start": 2417.63, "end": 2418.17, "word": " sequence", "probability": 0.9404296875}, {"start": 2418.17, "end": 2418.79, "word": " yn", "probability": 0.5263671875}, {"start": 2418.79, "end": 2419.99, "word": " bounded", "probability": 0.8173828125}, {"start": 2419.99, "end": 2421.31, "word": " وin", "probability": 0.6473388671875}, {"start": 2421.31, "end": 2421.75, "word": " crazy", "probability": 0.30224609375}, {"start": 2421.75, "end": 2422.75, "word": " إذا", "probability": 0.810546875}, {"start": 2422.75, "end": 2423.17, "word": " حسب", "probability": 0.92822265625}, {"start": 2423.17, "end": 2423.63, "word": " الجزء", "probability": 0.96728515625}, {"start": 2423.63, "end": 2423.91, "word": " a", "probability": 0.71240234375}, {"start": 2423.91, "end": 2424.17, "word": " by", "probability": 0.77978515625}, {"start": 2424.17, "end": 2424.65, "word": " part", "probability": 0.9638671875}, {"start": 2424.65, "end": 2425.01, "word": " a", "probability": 0.87646484375}, {"start": 2425.01, "end": 2426.31, "word": " limit", "probability": 0.88671875}, {"start": 2426.31, "end": 2426.55, "word": " ال", "probability": 0.6259765625}, {"start": 2426.55, "end": 2426.99, "word": " sequence", "probability": 0.9853515625}, {"start": 2426.99, "end": 2427.63, "word": " yn", "probability": 0.96142578125}, {"start": 2427.63, "end": 2428.41, "word": " تطلع", "probability": 0.957763671875}, {"start": 2428.41, "end": 2429.05, "word": " exist", "probability": 0.93017578125}], "temperature": 1.0}, {"id": 93, "seek": 244525, "start": 2429.93, "end": 2445.25, "text": "وبتساوي ال supremum لكل ال y in ال supremum لعناصر ال sequence اللي هي y in تمام؟ انها ده من ايه؟ من الجزء ايه من النظرية؟", "tokens": [2407, 3555, 2655, 3794, 995, 45865, 2423, 23710, 449, 5296, 28820, 2423, 288, 294, 2423, 23710, 449, 5296, 3615, 1863, 33546, 2288, 2423, 8310, 13672, 1829, 39896, 288, 294, 46811, 10943, 22807, 16472, 11296, 11778, 3224, 9154, 1975, 1829, 3224, 22807, 9154, 25724, 11622, 38207, 1975, 1829, 3224, 9154, 28239, 19913, 2288, 10632, 22807], "avg_logprob": -0.3275568268515847, "compression_ratio": 1.4538461538461538, "no_speech_prob": 0.0, "words": [{"start": 2429.93, "end": 2430.67, "word": "وبتساوي", "probability": 0.68695068359375}, {"start": 2430.67, "end": 2430.83, "word": " ال", "probability": 0.623046875}, {"start": 2430.83, "end": 2431.51, "word": " supremum", "probability": 0.6878662109375}, {"start": 2431.51, "end": 2432.79, "word": " لكل", "probability": 0.91162109375}, {"start": 2432.79, "end": 2433.03, "word": " ال", "probability": 0.81884765625}, {"start": 2433.03, "end": 2433.23, "word": " y", "probability": 0.392822265625}, {"start": 2433.23, "end": 2433.63, "word": " in", "probability": 0.2000732421875}, {"start": 2433.63, "end": 2434.05, "word": " ال", "probability": 0.1966552734375}, {"start": 2434.05, "end": 2434.67, "word": " supremum", "probability": 0.842529296875}, {"start": 2434.67, "end": 2436.33, "word": " لعناصر", "probability": 0.87529296875}, {"start": 2436.33, "end": 2436.45, "word": " ال", "probability": 0.92431640625}, {"start": 2436.45, "end": 2436.95, "word": " sequence", "probability": 0.98388671875}, {"start": 2436.95, "end": 2437.15, "word": " اللي", "probability": 0.781005859375}, {"start": 2437.15, "end": 2437.41, "word": " هي", "probability": 0.86181640625}, {"start": 2437.41, "end": 2437.87, "word": " y", "probability": 0.6220703125}, {"start": 2437.87, "end": 2438.37, "word": " in", "probability": 0.8125}, {"start": 2438.37, "end": 2441.51, "word": " تمام؟", "probability": 0.6420084635416666}, {"start": 2441.51, "end": 2442.27, "word": " انها", "probability": 0.236572265625}, {"start": 2442.27, "end": 2442.51, "word": " ده", "probability": 0.821533203125}, {"start": 2442.51, "end": 2442.69, "word": " من", "probability": 0.99072265625}, {"start": 2442.69, "end": 2443.01, "word": " ايه؟", "probability": 0.8309326171875}, {"start": 2443.01, "end": 2443.17, "word": " من", "probability": 0.98095703125}, {"start": 2443.17, "end": 2443.75, "word": " الجزء", "probability": 0.9728190104166666}, {"start": 2443.75, "end": 2444.37, "word": " ايه", "probability": 0.8898111979166666}, {"start": 2444.37, "end": 2444.53, "word": " من", "probability": 0.87939453125}, {"start": 2444.53, "end": 2445.25, "word": " النظرية؟", "probability": 0.94189453125}], "temperature": 1.0}, {"id": 94, "seek": 247215, "start": 2446.49, "end": 2472.15, "text": "طيب ال supremum ل سالب xn هيفقن العدد طبيعي احنا خدنا قبل هيك exercise بيقول supremum او infimum سالب حاجة بساوي سالب ال infimum فهنا بصير هذا سالب ال infimum تمام؟ اذا انا عندي بيطلع عندي limit xn بساوي سالب limit سالب xn تمام؟", "tokens": [9566, 1829, 3555, 2423, 23710, 449, 5296, 8608, 6027, 3555, 2031, 77, 39896, 5172, 4587, 1863, 18863, 3215, 3215, 23032, 21292, 3615, 1829, 1975, 5016, 8315, 16490, 3215, 8315, 12174, 36150, 39896, 4117, 5380, 4724, 1829, 39648, 23710, 449, 1975, 2407, 1536, 332, 449, 8608, 6027, 3555, 11331, 26108, 3660, 4724, 3794, 995, 45865, 8608, 6027, 3555, 2423, 1536, 332, 449, 6156, 3224, 8315, 4724, 9381, 13546, 23758, 8608, 6027, 3555, 2423, 1536, 332, 449, 46811, 10943, 22807, 1975, 15730, 1975, 8315, 18871, 16254, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 4948, 2031, 77, 4724, 3794, 995, 45865, 8608, 6027, 3555, 4948, 8608, 6027, 3555, 2031, 77, 46811, 10943, 22807], "avg_logprob": -0.23155967797244992, "compression_ratio": 1.8624338624338623, "no_speech_prob": 0.0, "words": [{"start": 2446.49, "end": 2446.93, "word": "طيب", "probability": 0.7649739583333334}, {"start": 2446.93, "end": 2447.37, "word": " ال", "probability": 0.75927734375}, {"start": 2447.37, "end": 2448.05, "word": " supremum", "probability": 0.737548828125}, {"start": 2448.05, "end": 2448.23, "word": " ل", "probability": 0.94580078125}, {"start": 2448.23, "end": 2448.73, "word": " سالب", "probability": 0.6598307291666666}, {"start": 2448.73, "end": 2449.27, "word": " xn", "probability": 0.50927734375}, {"start": 2449.27, "end": 2449.75, "word": " هيفقن", "probability": 0.454681396484375}, {"start": 2449.75, "end": 2450.09, "word": " العدد", "probability": 0.8850911458333334}, {"start": 2450.09, "end": 2450.47, "word": " طبيعي", "probability": 0.7552490234375}, {"start": 2450.47, "end": 2450.83, "word": " احنا", "probability": 0.8429361979166666}, {"start": 2450.83, "end": 2451.15, "word": " خدنا", "probability": 0.7738444010416666}, {"start": 2451.15, "end": 2451.45, "word": " قبل", "probability": 0.732177734375}, {"start": 2451.45, "end": 2451.61, "word": " هيك", "probability": 0.63427734375}, {"start": 2451.61, "end": 2452.17, "word": " exercise", "probability": 0.841796875}, {"start": 2452.17, "end": 2452.61, "word": " بيقول", "probability": 0.7451985677083334}, {"start": 2452.61, "end": 2454.07, "word": " supremum", "probability": 0.799072265625}, {"start": 2454.07, "end": 2454.27, "word": " او", "probability": 0.86474609375}, {"start": 2454.27, "end": 2454.83, "word": " infimum", "probability": 0.92626953125}, {"start": 2454.83, "end": 2455.53, "word": " سالب", "probability": 0.9208984375}, {"start": 2455.53, "end": 2456.49, "word": " حاجة", "probability": 0.9884440104166666}, {"start": 2456.49, "end": 2457.77, "word": " بساوي", "probability": 0.820556640625}, {"start": 2457.77, "end": 2458.61, "word": " سالب", "probability": 0.98779296875}, {"start": 2458.61, "end": 2458.81, "word": " ال", "probability": 0.9677734375}, {"start": 2458.81, "end": 2459.41, "word": " infimum", "probability": 0.8972981770833334}, {"start": 2459.41, "end": 2460.95, "word": " فهنا", "probability": 0.7664388020833334}, {"start": 2460.95, "end": 2461.35, "word": " بصير", "probability": 0.6954752604166666}, {"start": 2461.35, "end": 2461.53, "word": " هذا", "probability": 0.83837890625}, {"start": 2461.53, "end": 2462.03, "word": " سالب", "probability": 0.9905598958333334}, {"start": 2462.03, "end": 2462.19, "word": " ال", "probability": 0.966796875}, {"start": 2462.19, "end": 2462.77, "word": " infimum", "probability": 0.96044921875}, {"start": 2462.77, "end": 2464.55, "word": " تمام؟", "probability": 0.6446940104166666}, {"start": 2464.55, "end": 2464.83, "word": " اذا", "probability": 0.884765625}, {"start": 2464.83, "end": 2465.05, "word": " انا", "probability": 0.83056640625}, {"start": 2465.05, "end": 2465.41, "word": " عندي", "probability": 0.84521484375}, {"start": 2465.41, "end": 2466.17, "word": " بيطلع", "probability": 0.79248046875}, {"start": 2466.17, "end": 2466.41, "word": " عندي", "probability": 0.6929931640625}, {"start": 2466.41, "end": 2466.71, "word": " limit", "probability": 0.9619140625}, {"start": 2466.71, "end": 2467.53, "word": " xn", "probability": 0.974853515625}, {"start": 2467.53, "end": 2469.17, "word": " بساوي", "probability": 0.902587890625}, {"start": 2469.17, "end": 2469.85, "word": " سالب", "probability": 0.99072265625}, {"start": 2469.85, "end": 2470.19, "word": " limit", "probability": 0.9873046875}, {"start": 2470.19, "end": 2470.67, "word": " سالب", "probability": 0.9894205729166666}, {"start": 2470.67, "end": 2471.27, "word": " xn", "probability": 0.991943359375}, {"start": 2471.27, "end": 2472.15, "word": " تمام؟", "probability": 0.9676106770833334}], "temperature": 1.0}, {"id": 95, "seek": 249764, "start": 2473.32, "end": 2497.64, "text": "أضربوا هنا هيندي limit سالب xn أضربوا المعادلة هذه بالسالب واحد فبطلع سالب limit سالب xn بساوي سالب سالب موجب اللي هو ال inform ل xn وهذا اللي بدنا يعني لأن هي أثبتنا أن limit xn موجودة exist يعني ال sequence xn convergent وال limit تبعتها بساوي ال inform", "tokens": [10721, 11242, 25513, 14407, 34105, 8032, 9957, 16254, 4948, 8608, 6027, 3555, 2031, 77, 5551, 11242, 25513, 14407, 9673, 3615, 18513, 37977, 29538, 20666, 3794, 6027, 3555, 36764, 24401, 6156, 3555, 9566, 1211, 3615, 8608, 6027, 3555, 4948, 8608, 6027, 3555, 2031, 77, 4724, 3794, 995, 45865, 8608, 6027, 3555, 8608, 6027, 3555, 3714, 29245, 3555, 13672, 1829, 31439, 2423, 1356, 5296, 2031, 77, 37037, 15730, 13672, 1829, 47525, 8315, 37495, 22653, 5296, 33456, 39896, 5551, 12984, 3555, 2655, 8315, 14739, 4948, 2031, 77, 3714, 29245, 23328, 3660, 2514, 37495, 22653, 2423, 8310, 2031, 77, 9652, 6930, 16070, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 2423, 1356], "avg_logprob": -0.25781250894069674, "compression_ratio": 1.863849765258216, "no_speech_prob": 0.0, "words": [{"start": 2473.32, "end": 2474.0, "word": "أضربوا", "probability": 0.450897216796875}, {"start": 2474.0, "end": 2474.22, "word": " هنا", "probability": 0.8935546875}, {"start": 2474.22, "end": 2475.18, "word": " هيندي", "probability": 0.45733642578125}, {"start": 2475.18, "end": 2475.86, "word": " limit", "probability": 0.82177734375}, {"start": 2475.86, "end": 2476.38, "word": " سالب", "probability": 0.6783040364583334}, {"start": 2476.38, "end": 2476.82, "word": " xn", "probability": 0.4163818359375}, {"start": 2476.82, "end": 2477.32, "word": " أضربوا", "probability": 0.82080078125}, {"start": 2477.32, "end": 2477.78, "word": " المعادلة", "probability": 0.966064453125}, {"start": 2477.78, "end": 2478.04, "word": " هذه", "probability": 0.3935546875}, {"start": 2478.04, "end": 2478.54, "word": " بالسالب", "probability": 0.798583984375}, {"start": 2478.54, "end": 2478.94, "word": " واحد", "probability": 0.970947265625}, {"start": 2478.94, "end": 2480.32, "word": " فبطلع", "probability": 0.86025390625}, {"start": 2480.32, "end": 2480.88, "word": " سالب", "probability": 0.8271484375}, {"start": 2480.88, "end": 2481.14, "word": " limit", "probability": 0.96533203125}, {"start": 2481.14, "end": 2481.58, "word": " سالب", "probability": 0.97998046875}, {"start": 2481.58, "end": 2482.08, "word": " xn", "probability": 0.95361328125}, {"start": 2482.08, "end": 2482.68, "word": " بساوي", "probability": 0.9407958984375}, {"start": 2482.68, "end": 2483.14, "word": " سالب", "probability": 0.962890625}, {"start": 2483.14, "end": 2483.52, "word": " سالب", "probability": 0.9806315104166666}, {"start": 2483.52, "end": 2483.98, "word": " موجب", "probability": 0.9627278645833334}, {"start": 2483.98, "end": 2484.7, "word": " اللي", "probability": 0.892333984375}, {"start": 2484.7, "end": 2484.88, "word": " هو", "probability": 0.96875}, {"start": 2484.88, "end": 2485.02, "word": " ال", "probability": 0.90966796875}, {"start": 2485.02, "end": 2485.44, "word": " inform", "probability": 0.185791015625}, {"start": 2485.44, "end": 2485.68, "word": " ل", "probability": 0.9150390625}, {"start": 2485.68, "end": 2486.22, "word": " xn", "probability": 0.715576171875}, {"start": 2486.22, "end": 2487.1, "word": " وهذا", "probability": 0.814208984375}, {"start": 2487.1, "end": 2487.24, "word": " اللي", "probability": 0.9853515625}, {"start": 2487.24, "end": 2487.48, "word": " بدنا", "probability": 0.92724609375}, {"start": 2487.48, "end": 2487.88, "word": " يعني", "probability": 0.50830078125}, {"start": 2487.88, "end": 2488.84, "word": " لأن", "probability": 0.588623046875}, {"start": 2488.84, "end": 2489.0, "word": " هي", "probability": 0.90283203125}, {"start": 2489.0, "end": 2489.52, "word": " أثبتنا", "probability": 0.92705078125}, {"start": 2489.52, "end": 2489.68, "word": " أن", "probability": 0.494384765625}, {"start": 2489.68, "end": 2489.96, "word": " limit", "probability": 0.92578125}, {"start": 2489.96, "end": 2490.5, "word": " xn", "probability": 0.9609375}, {"start": 2490.5, "end": 2491.62, "word": " موجودة", "probability": 0.98193359375}, {"start": 2491.62, "end": 2492.46, "word": " exist", "probability": 0.65673828125}, {"start": 2492.46, "end": 2492.84, "word": " يعني", "probability": 0.900390625}, {"start": 2492.84, "end": 2492.96, "word": " ال", "probability": 0.537109375}, {"start": 2492.96, "end": 2493.28, "word": " sequence", "probability": 0.96435546875}, {"start": 2493.28, "end": 2493.76, "word": " xn", "probability": 0.917236328125}, {"start": 2493.76, "end": 2494.46, "word": " convergent", "probability": 0.6536865234375}, {"start": 2494.46, "end": 2495.36, "word": " وال", "probability": 0.316650390625}, {"start": 2495.36, "end": 2495.62, "word": " limit", "probability": 0.9169921875}, {"start": 2495.62, "end": 2496.26, "word": " تبعتها", "probability": 0.898681640625}, {"start": 2496.26, "end": 2497.08, "word": " بساوي", "probability": 0.9420166015625}, {"start": 2497.08, "end": 2497.36, "word": " ال", "probability": 0.94140625}, {"start": 2497.36, "end": 2497.64, "word": " inform", "probability": 0.7412109375}], "temperature": 1.0}, {"id": 96, "seek": 251844, "start": 2500.76, "end": 2518.44, "text": "بنكمل برهان الـ monotone convergence theorem طبعا الأمثلة هذه اللي هنا كلها أمثلة تطبيق على الـ monotone convergence theorem فارجو أنكم تحاولوا تخرجوا الأمثلة هذه و تشوفوا كيف نستخدم الـ monotone convergence theorem في", "tokens": [3555, 1863, 24793, 1211, 4724, 2288, 3224, 7649, 2423, 39184, 1108, 310, 546, 32181, 20904, 23032, 3555, 3615, 995, 16247, 2304, 12984, 37977, 29538, 13672, 1829, 34105, 28242, 11296, 5551, 2304, 12984, 37977, 6055, 9566, 21292, 4587, 15844, 2423, 39184, 1108, 310, 546, 32181, 20904, 6156, 9640, 7435, 2407, 14739, 24793, 6055, 5016, 995, 12610, 14407, 6055, 34740, 7435, 14407, 16247, 2304, 12984, 37977, 29538, 4032, 6055, 8592, 38688, 14407, 9122, 33911, 8717, 14851, 9778, 40448, 2423, 39184, 1108, 310, 546, 32181, 20904, 8978], "avg_logprob": -0.20036764846128577, "compression_ratio": 1.9230769230769231, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 2500.7599999999998, "end": 2501.6, "word": "بنكمل", "probability": 0.59417724609375}, {"start": 2501.6, "end": 2502.12, "word": " برهان", "probability": 0.844482421875}, {"start": 2502.12, "end": 2502.88, "word": " الـ", "probability": 0.601318359375}, {"start": 2502.88, "end": 2503.26, "word": " monotone", "probability": 0.7140299479166666}, {"start": 2503.26, "end": 2503.86, "word": " convergence", "probability": 0.96044921875}, {"start": 2503.86, "end": 2504.28, "word": " theorem", "probability": 0.89892578125}, {"start": 2504.28, "end": 2504.68, "word": " طبعا", "probability": 0.80340576171875}, {"start": 2504.68, "end": 2505.18, "word": " الأمثلة", "probability": 0.9608154296875}, {"start": 2505.18, "end": 2505.5, "word": " هذه", "probability": 0.399658203125}, {"start": 2505.5, "end": 2505.66, "word": " اللي", "probability": 0.6787109375}, {"start": 2505.66, "end": 2505.92, "word": " هنا", "probability": 0.91650390625}, {"start": 2505.92, "end": 2507.08, "word": " كلها", "probability": 0.93896484375}, {"start": 2507.08, "end": 2508.14, "word": " أمثلة", "probability": 0.937744140625}, {"start": 2508.14, "end": 2508.72, "word": " تطبيق", "probability": 0.9207763671875}, {"start": 2508.72, "end": 2509.0, "word": " على", "probability": 0.8544921875}, {"start": 2509.0, "end": 2509.28, "word": " الـ", "probability": 0.843505859375}, {"start": 2509.28, "end": 2509.62, "word": " monotone", "probability": 0.9482421875}, {"start": 2509.62, "end": 2510.22, "word": " convergence", "probability": 0.95751953125}, {"start": 2510.22, "end": 2510.6, "word": " theorem", "probability": 0.939453125}, {"start": 2510.6, "end": 2511.66, "word": " فارجو", "probability": 0.84228515625}, {"start": 2511.66, "end": 2512.72, "word": " أنكم", "probability": 0.699462890625}, {"start": 2512.72, "end": 2513.18, "word": " تحاولوا", "probability": 0.953515625}, {"start": 2513.18, "end": 2513.56, "word": " تخرجوا", "probability": 0.79803466796875}, {"start": 2513.56, "end": 2513.98, "word": " الأمثلة", "probability": 0.979248046875}, {"start": 2513.98, "end": 2514.3, "word": " هذه", "probability": 0.91064453125}, {"start": 2514.3, "end": 2514.44, "word": " و", "probability": 0.68701171875}, {"start": 2514.44, "end": 2514.84, "word": " تشوفوا", "probability": 0.9801025390625}, {"start": 2514.84, "end": 2515.18, "word": " كيف", "probability": 0.98193359375}, {"start": 2515.18, "end": 2515.84, "word": " نستخدم", "probability": 0.93896484375}, {"start": 2515.84, "end": 2516.08, "word": " الـ", "probability": 0.88525390625}, {"start": 2516.08, "end": 2516.42, "word": " monotone", "probability": 0.9803059895833334}, {"start": 2516.42, "end": 2517.02, "word": " convergence", "probability": 0.95703125}, {"start": 2517.02, "end": 2517.56, "word": " theorem", "probability": 0.90380859375}, {"start": 2517.56, "end": 2518.44, "word": " في", "probability": 0.916015625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2519.133, "duration_after_vad": 2375.1068749999895}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5fe5bfbc7224b0b8a8a3951b7303d10bb1724e75
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Lc2K-uxXK74_raw.srt
@@ -0,0 +1,1784 @@
+1
+00:00:20,750 --> 00:00:26,090
+Okay اذا اليوم ان شاء الله هنكمل موضوع ال limit
+
+2
+00:00:26,090 --> 00:00:32,390
+theorems او نظريات النهايات و من النظريات المهمة
+
+3
+00:00:32,390 --> 00:00:39,710
+هذه هي نظرية 12 بتقول لو في عندي sequence x in و
+
+4
+00:00:39,710 --> 00:00:44,570
+ال sequence هذي convergent ل x فال sequence of
+
+5
+00:00:44,570 --> 00:00:49,350
+absolute valuesبتطلع convergence وال limit تبعتها
+
+6
+00:00:49,350 --> 00:00:55,490
+تطلع absolute .. absolute limit تبعت ال sequence
+
+7
+00:00:55,490 --> 00:01:00,750
+XL فالبرهان
+
+8
+00:01:00,750 --> 00:01:04,470
+بيتمد على ال triangle inequality
+
+9
+00:01:07,360 --> 00:01:13,720
+أحد صور ال triangle inequality كانت المتباينة هذه
+
+10
+00:01:13,720 --> 00:01:20,740
+absolute a minus absolute b وأخد ال absolute value
+
+11
+00:01:20,740 --> 00:01:28,600
+هذا أصغر من أو ساوي absolute a minus bفلو أخدت هنا
+
+12
+00:01:28,600 --> 00:01:36,160
+a بساوي xn و b بساوي x فبطلع الكلام هذا صحيح لكل
+
+13
+00:01:36,160 --> 00:01:43,760
+الأعداد الطبيعية n الآن أنا عندي xn converges to x
+
+14
+00:01:43,760 --> 00:01:51,740
+فلو أخدت أي epsilon أكبر من الصفر given
+
+15
+00:01:55,040 --> 00:02:00,540
+واندي انا x in converge ل x، اذا هذا بيدّي انه
+
+16
+00:02:00,540 --> 00:02:03,580
+يوجد
+
+17
+00:02:03,580 --> 00:02:13,660
+capital N عدد طبيعي يعتمد على epsilon بحيث انه لو
+
+18
+00:02:13,660 --> 00:02:18,260
+كان N أكبر من أو ساوي capital N فهذا بيدّي ان
+
+19
+00:02:18,260 --> 00:02:22,080
+absolute x in minus x أصغر من epsilon
+
+20
+00:02:25,260 --> 00:02:30,300
+وبالتالي من هنا إذا الهدف بيطلع أصغر من epsilon
+
+21
+00:02:30,300 --> 00:02:34,260
+لكل
+
+22
+00:02:34,260 --> 00:02:41,180
+n أكبر من أو ساوي capital N إذا
+
+23
+00:02:41,180 --> 00:02:44,800
+أنا هيك بكون أثبتت إنه لأي epsilon أكبر من سفر
+
+24
+00:02:44,800 --> 00:02:50,760
+يوجد capital N يعتمد على epsilon عدد طبيعي بحيث
+
+25
+00:02:50,760 --> 00:02:57,040
+لكل n أكبر من أو ساوي capital Nالقيمة المطلقة ل
+
+26
+00:02:57,040 --> 00:03:02,480
+absolute xn minus absolute x أصغر من epsilon إذا
+
+27
+00:03:02,480 --> 00:03:07,900
+حسب تعريف epsilon capital N for limits هذا معناه
+
+28
+00:03:07,900 --> 00:03:14,260
+بالظبط أن limit absolute xn as n tends to infinity
+
+29
+00:03:14,260 --> 00:03:21,790
+بساوي absolute x وهو المطلوبOkay تمام اذا هذا
+
+30
+00:03:21,790 --> 00:03:32,890
+بيكمل برهان نظرية اتناش تمام واضح النظرية
+
+31
+00:03:32,890 --> 00:03:39,270
+اللي بعدها نظرية تلاتاش بتقول لو انا فيها اندي
+
+32
+00:03:39,270 --> 00:03:45,490
+sequence حدودها كلها غير سالبة حدود ال sequence xm
+
+33
+00:03:45,490 --> 00:03:50,750
+كلها غير سالبة اعداد غير سالبةوالـ sequence لو
+
+34
+00:03:50,750 --> 00:03:57,730
+كانت الـ sequence Xn convergent to some X فالـ
+
+35
+00:03:57,730 --> 00:04:02,730
+limit للـ sequence of square roots لـ Xn تطلع
+
+36
+00:04:02,730 --> 00:04:08,470
+convergent والـ limit تبعتها بساول square root للـ
+
+37
+00:04:08,470 --> 00:04:09,890
+limit للـ sequence Xn
+
+38
+00:04:13,780 --> 00:04:19,760
+والبرهان تبع النظرية دي سهل انا اول شي عندى احنا
+
+39
+00:04:19,760 --> 00:04:25,060
+فرضين ان ال limit ل Xn بساوي X في نظرية تمانية
+
+40
+00:04:25,060 --> 00:04:28,700
+قلنا ان لو كانت حدود ال sequence Xn كلها غير سالبة
+
+41
+00:04:28,700 --> 00:04:34,360
+ف limit ل sequence Xn اللى هى X ايضا تطلع غير
+
+42
+00:04:34,360 --> 00:04:40,840
+سالبة اذا X اكبر من او ساوى 0الان في عندي حالتين
+
+43
+00:04:40,840 --> 00:04:46,300
+ال X هنا أكبر من أو ساوي سفر ففي عندي احتمالين اما
+
+44
+00:04:46,300 --> 00:04:54,260
+X بساوي سفر او X أكبر من السفر تمام و في كل حالة
+
+45
+00:04:54,920 --> 00:04:59,540
+مطلوب مني ان اثبت ان limit ال square root ل xn
+
+46
+00:04:59,540 --> 00:05:03,960
+بساوي ال square root of x تمام؟ انشوف في الحالة
+
+47
+00:05:03,960 --> 00:05:08,520
+الأولى لو كانت ال x بساوي سفر وانا عندي من الفرض
+
+48
+00:05:08,520 --> 00:05:15,550
+xn converges to x اللي هي سفرأذا لو أخدت أي إبسلون
+
+49
+00:05:15,550 --> 00:05:20,250
+أكبر من السفر من كون ال sequence هذه converge
+
+50
+00:05:20,250 --> 00:05:24,270
+للسفر إذا لأي إبسلون يوجد capital N يعتمد على
+
+51
+00:05:24,270 --> 00:05:30,150
+إبسلون بحيث المسافة بين xn والسفر أصغر من إبسلون
+
+52
+00:05:30,150 --> 00:05:33,470
+تربية لكل N أكبر من أوسعه ال capital N هذا من
+
+53
+00:05:33,470 --> 00:05:36,690
+تعريف ال conversion ممكن أحط هنا إبسلون أو إبسلون
+
+54
+00:05:36,690 --> 00:05:42,940
+تربية مافي مشكلةطيب أنا عندي xn من الفرض الـ xn
+
+55
+00:05:42,940 --> 00:05:48,840
+كلهم أكبر من أو يساوي سفر وبالتالي القيمة المطلقة
+
+56
+00:05:48,840 --> 00:05:53,800
+لـ xn بساوي نفسها ناخد
+
+57
+00:05:53,800 --> 00:05:59,120
+الجدر التربيعي للحدود المتباينة هذه هي ال square
+
+58
+00:05:59,120 --> 00:06:04,790
+root of xnبساوي ال absolute value ل square root ل
+
+59
+00:06:04,790 --> 00:06:10,190
+xn minus صفر وهذا أصغر من إبسلون square root
+
+60
+00:06:10,190 --> 00:06:13,870
+لإبسلون تربية بيطلع إبسلون هذا الكلام صحيح for
+
+61
+00:06:13,870 --> 00:06:18,830
+every n bigger than or equal capital N طب هذا
+
+62
+00:06:18,830 --> 00:06:23,050
+معناه بما أن إبسلون was arbitrarily بما أن احنا
+
+63
+00:06:23,050 --> 00:06:29,850
+أثبتنا هذا الكلام لكل إبسلون عدد موجبهذا من تعريف
+
+64
+00:06:29,850 --> 00:06:34,350
+epsilon capital N for limits للنهايات هذا معناه
+
+65
+00:06:34,350 --> 00:06:40,970
+limit ال square root ل XN بالساوي السفر لما N تولى
+
+66
+00:06:40,970 --> 00:06:47,140
+Nوهذا ايه هذا اللي هو المطلوب طيب السفر هنا احنا
+
+67
+00:06:47,140 --> 00:06:50,780
+ماخدين x بالساوية سفر فالسفر هذا هو square root ل
+
+68
+00:06:50,780 --> 00:06:54,360
+x اذا هين اثبتت ان limit square root ل x in
+
+69
+00:06:54,360 --> 00:06:58,820
+بالساوية square root ل x في حالة لما x بالساوية
+
+70
+00:06:58,820 --> 00:07:07,280
+سفر تمام باقي نثبتالنتيجة نفسها في حالة لما X أكبر
+
+71
+00:07:07,280 --> 00:07:11,740
+من 0 تفضلي قال جيت حكيت أنه ممكن أخد يبسلون مش
+
+72
+00:07:11,740 --> 00:07:15,740
+يبسلون تربيه لما أكمل خطوة بعد تطلع جدر اليبسلون
+
+73
+00:07:15,740 --> 00:07:19,660
+يعني أقل من الجدر يبسلون جدر اليبسلون قولت أن أحنا
+
+74
+00:07:19,660 --> 00:07:23,600
+خلنا يبسلون تربيه عشان لما أخد الجدر يطلع يبسلون
+
+75
+00:07:23,600 --> 00:07:29,520
+مافي مشكلة يعني اعتبر هذه هي اليبسلون مش اليبسلون
+
+76
+00:07:29,520 --> 00:07:34,300
+أكبر عدد أكبر من 0 givenإذا إبسلون تربية برضه عدد
+
+77
+00:07:34,300 --> 00:07:39,880
+موجة بقى تقري هو ال given وبالتالي يوجد أن تعتمد
+
+78
+00:07:39,880 --> 00:07:44,320
+على إبسلون تربية بدل إبسلون طب إبسلون تربية تعتمد
+
+79
+00:07:44,320 --> 00:07:48,420
+على إبسلونإذا ليش ما نقول إذا يوجد N تعتمد على
+
+80
+00:07:48,420 --> 00:07:52,240
+إبسلون وإعتبر الإبسلون تربية بدل إبسلون في ال
+
+81
+00:07:52,240 --> 00:07:55,920
+definition فمافي مشكلة بس خدناها الإبسلون تربية
+
+82
+00:07:55,920 --> 00:07:59,660
+عشان لما ناخد جدر التربية يطلع أندي أصغر من إبسلون
+
+83
+00:07:59,660 --> 00:08:03,760
+وبالتالي نقول حسب التعريف إذا limit جدر X N بساوة
+
+84
+00:08:03,760 --> 00:08:11,840
+ستة تمام اللي هي جدر X في أي سؤال تاني؟طيب، نشوف
+
+85
+00:08:11,840 --> 00:08:16,800
+الحالة التانية، لو كانت ال X هذه أكبر من صفر، إذا
+
+86
+00:08:16,800 --> 00:08:20,640
+جدر ال X بالتأكيد أكبر من الصفر، وبالتالي جدر X in
+
+87
+00:08:20,640 --> 00:08:26,120
+زي جدر X أكبر من أو ساوي جدر ال X، لأن هذا أكبر من
+
+88
+00:08:26,120 --> 00:08:35,430
+أو ساوي صفر، وهذا موجب، لأن ال X موجبةطيب، الآن
+
+89
+00:08:35,430 --> 00:08:40,630
+هذا المقدار أكبر من أو ساوي هذا واتنين موجبين، إذا
+
+90
+00:08:40,630 --> 00:08:47,950
+المقلوب الكبير أصغر من أو ساوي المقلوب الصغير هذه
+
+91
+00:08:47,950 --> 00:08:53,010
+الخاصية أخدناها في chapter one وبناء عليه
+
+92
+00:09:01,430 --> 00:09:06,810
+بنان على ذلك انا ممكن احسب جدر xn minus جدر ال x
+
+93
+00:09:06,810 --> 00:09:12,870
+بضرب المقدار هذا في المرافق تبعه بسطه مقاما، هاي
+
+94
+00:09:12,870 --> 00:09:16,870
+المرافق تبعه بسطه مقام فكأني ضربت المقدار هذا في
+
+95
+00:09:16,870 --> 00:09:23,030
+واحد، اذا هذا بساوي نفسه ضرب مرافقه على مرافقه،
+
+96
+00:09:23,030 --> 00:09:27,870
+تمام؟الان ال bus تحليل الفرق بين المربعين فبطلع
+
+97
+00:09:27,870 --> 00:09:33,170
+مربع هذا سالب مربع هذا اللي هو x in negative x و
+
+98
+00:09:33,170 --> 00:09:38,310
+بيبقى ال end في المقام المقدار هذا الان ناخد
+
+99
+00:09:38,310 --> 00:09:43,370
+القيمة المطلقة للكلام هذا بيساوي القيمة المطلقة
+
+100
+00:09:43,370 --> 00:09:48,230
+للطرف اليمين القيمة المطلقة لل bus على القيمة
+
+101
+00:09:48,230 --> 00:09:53,070
+المطلقة للمقام المقام هذا موجب فالقيمة المطلقة له
+
+102
+00:09:53,070 --> 00:09:58,770
+نفسهأذا الأن أنا في عندي sequence اللي هي الحد
+
+103
+00:09:58,770 --> 00:10:02,810
+العام تبعها square root of xn وفي عندي عدد square
+
+104
+00:10:02,810 --> 00:10:10,390
+root of x المسافة بينهم أصغر من أو يساوي أصغر من
+
+105
+00:10:10,390 --> 00:10:15,610
+أو يساوي هي المسافة هذه بالساوي واحد على square
+
+106
+00:10:15,610 --> 00:10:21,870
+root of xn زي square root of x والكسر هذا من
+
+107
+00:10:21,870 --> 00:10:27,950
+المتباينة تسعةهذا الكثير أصغر من أو يساوي واحد على
+
+108
+00:10:27,950 --> 00:10:32,610
+square root of x ضرب absolute x in سالب x الآن
+
+109
+00:10:32,610 --> 00:10:43,830
+ارجعوا لنظرية اتنين اربعة with
+
+110
+00:10:43,830 --> 00:10:52,060
+c عدد موجب ساوي واحد على جدر ال x هذا عدد موجبو a
+
+111
+00:10:52,060 --> 00:10:59,780
+n بساوي x n minus x إذن
+
+112
+00:10:59,780 --> 00:11:03,940
+هى يوجد c عدد موجب اللى هو واحد على جدر ال X و هى
+
+113
+00:11:03,940 --> 00:11:08,820
+فى عندي sequence a n الحد العام تبعها x n سالد x و
+
+114
+00:11:08,820 --> 00:11:14,680
+ال sequence هذه تقول إلى سفر as n tends to
+
+115
+00:11:14,680 --> 00:11:19,870
+infinityلأن انا من المعطيات عندي xn تقول x أو
+
+116
+00:11:19,870 --> 00:11:24,490
+limit xn بساوي x، لذلك limit الفرق بساوي سفر، لذلك
+
+117
+00:11:24,490 --> 00:11:29,890
+حسب نظرية 2.4، كل شروطة متحققة، وبالتالي، لذلك حسب
+
+118
+00:11:29,890 --> 00:11:34,630
+النظرية هذه، by theorem 2.4، بيطلع عندي limit
+
+119
+00:11:34,630 --> 00:11:41,190
+square root ل xn بساوي square root ل xوهو المطلوب
+
+120
+00:11:41,190 --> 00:11:46,690
+اثباته اذا هاي اثبتنا ان limit ال square root ل X
+
+121
+00:11:46,690 --> 00:11:50,410
+ان بساوي ال square root ل X في حالة لما X تكون
+
+122
+00:11:50,410 --> 00:11:54,750
+موجبة و الحالة الأولى في حالة لما X صفر برضه
+
+123
+00:11:54,750 --> 00:11:58,410
+اثبتنا نفس الحاجة لذلك بنكون كملنا برهان نظرية
+
+124
+00:11:58,410 --> 00:12:02,690
+تمام؟ في حد عنده اي سؤال او استفسار واضح البرهان؟
+
+125
+00:12:05,660 --> 00:12:12,800
+في نظرية هنا ممكن نسميها نعتبرها ratio test اختبار
+
+126
+00:12:12,800 --> 00:12:21,660
+الكسر او النسبة او ايش
+
+127
+00:12:21,660 --> 00:12:27,300
+ال ratio test ماذا هذا ال ratio test بيقول هذا ال
+
+128
+00:12:27,300 --> 00:12:31,120
+ratio test بتعلق بال sequences of positive numbers
+
+129
+00:12:32,030 --> 00:12:35,090
+يعني عشان أنا أطبخ ال ratio test لازم ال sequence
+
+130
+00:12:35,090 --> 00:12:39,170
+تبعتي تكون حدودها كلها موجة بقى فلو في عندي
+
+131
+00:12:39,170 --> 00:12:44,310
+sequence of positive real numbers such that limit
+
+132
+00:12:44,310 --> 00:12:49,050
+ال ratio ل xn زائد واحد على xn exists موجود أو
+
+133
+00:12:49,050 --> 00:12:54,370
+بتساوي عدد حقيقي L و لو كان هذا العدد L أصغر من
+
+134
+00:12:54,370 --> 00:13:01,300
+واحد ف limit ال sequence xn بتساوي سبلهذا هو ال
+
+135
+00:13:01,300 --> 00:13:07,380
+ratio test برهان ال test أو النظرية هذه موجود في
+
+136
+00:13:07,380 --> 00:13:11,680
+الكتاب نظرية تلاتة اتنين احداشر فحاسبكم تقرؤوا
+
+137
+00:13:11,680 --> 00:13:15,780
+البرهان برهان سهل مش صعب بيعتمد على الحاجات اللي
+
+138
+00:13:15,780 --> 00:13:20,340
+أخدناها فعايزينكم
+
+139
+00:13:20,340 --> 00:13:23,660
+تفتحوا الكتاب و تقرؤوا برهان و تفهموا لحالكم بعد
+
+140
+00:13:23,660 --> 00:13:28,800
+ما خدنا كل هالبرهين بدنا ياكم تعتمدوا عن أنفسكم
+
+141
+00:13:28,800 --> 00:13:33,440
+شويةتمام؟ و اللي عنده أي صعوبة في فهم البرهان
+
+142
+00:13:33,440 --> 00:13:38,840
+ترجعليه إذا هسيكم تخرق البرهان من الكتاب طيب نهار
+
+143
+00:13:38,840 --> 00:13:42,540
+.. الآن الكتاب للأسف مش في أمثلة في ال section هذا
+
+144
+00:13:42,540 --> 00:13:49,000
+تلاتة اتنين فهعطيلكم أس .. examples أو أمثلة بحال
+
+145
+00:13:49,000 --> 00:13:52,100
+من التمرين بحال بعض التمرين فأول مثل
+
+146
+00:13:58,060 --> 00:14:02,820
+فأول مثال هو exercise تمانتاش الفرحة c في section
+
+147
+00:14:02,820 --> 00:14:06,700
+تلاتة اتنين أو صفحة تمانية وستين في الكتاب المقرر
+
+148
+00:14:06,700 --> 00:14:10,300
+السؤال هذا بيقول discuss the convergence of the
+
+149
+00:14:10,300 --> 00:14:15,820
+sequence xn اللي لحد العام ال nth term تبعها b to
+
+150
+00:14:15,820 --> 00:14:20,600
+n على n factorial حيث بيه عدد حقيقي أكبر من واحد
+
+151
+00:14:21,470 --> 00:14:24,070
+Discurses ل Convergence يعني بين هل ال sequence
+
+152
+00:14:24,070 --> 00:14:27,850
+هذي Convergent ولا Divergent وده كانت Convergent
+
+153
+00:14:27,850 --> 00:14:35,790
+عايزين نجيب ال limit تبعتها طيب تعالوا أول شي احنا
+
+154
+00:14:35,790 --> 00:14:41,150
+طبعا هنطبق ال ratio test نظرية 2.14 اللي هو الرسم
+
+155
+00:14:41,150 --> 00:14:45,490
+منها ال ratio testلتطبيق ال ratio test بلزمني
+
+156
+00:14:45,490 --> 00:14:50,690
+اتأكد ان ال sequence xn حدودها موجبة وهذا صحيح لان
+
+157
+00:14:50,690 --> 00:14:54,970
+ال bus b اكبر من واحد و b أكبر من واحد و n
+
+158
+00:14:54,970 --> 00:14:57,830
+factorial عدد موجب لان هذه sequence of positive
+
+159
+00:14:57,830 --> 00:15:07,550
+real numbers الآن ال ratio ل xn زياد واحد و xn هي
+
+160
+00:15:07,550 --> 00:15:12,230
+عندي xn زياد واحد عوض عنها بدل n بn زياد واحد
+
+161
+00:15:13,160 --> 00:15:18,740
+وضربها في مقلوب xn هي مقلوب xn وطبعا احنا عارفين
+
+162
+00:15:18,740 --> 00:15:25,460
+ان n plus one factorial بتساوي n plus one في n
+
+163
+00:15:25,460 --> 00:15:31,900
+factorial هذا بنفك حاصل ضرب زي هذا n factorial
+
+164
+00:15:31,900 --> 00:15:37,640
+بتروح مع n factorial وb to n بتروح مع b to n بضل b
+
+165
+00:15:38,750 --> 00:15:43,210
+بعد الاختصارات والتبسيط الكاسر هذا بيطلع بي على n
+
+166
+00:15:43,210 --> 00:15:47,870
+زياد واحد الان لما انت قول ل infinity ان زياد واحد
+
+167
+00:15:47,870 --> 00:15:54,050
+بتقول ل infinity مقلوبة بروح ل سفر ضرب بي عدد موجة
+
+168
+00:15:54,050 --> 00:15:58,990
+بروح ل سفر اذا limit بي على ان زياد واحد بساوي بي
+
+169
+00:15:58,990 --> 00:16:03,290
+في limit واحد على ان زياد واحد اللي هي سفر بي في
+
+170
+00:16:03,290 --> 00:16:10,590
+سفر بساوي سفر تمام؟إذا أنا عندي L اللي هو بمثل
+
+171
+00:16:10,590 --> 00:16:17,570
+limit ال ratio هذا طلع بساوي سفر عدد حقيقي أصغر من
+
+172
+00:16:17,570 --> 00:16:23,910
+واحد إذا حسب ال ratio test limit لل sequence xn
+
+173
+00:16:23,910 --> 00:16:28,030
+بساوي سفر إذا هنا أثبتنا إن ال sequence convergent
+
+174
+00:16:28,030 --> 00:16:34,010
+ونهيتها بتطلع بالساوي سفر تمام؟ واضح؟ إذا تطبيق
+
+175
+00:16:34,010 --> 00:16:35,510
+مباشر على ال ratio test
+
+176
+00:16:38,490 --> 00:16:42,730
+مثال تاني مثال
+
+177
+00:16:42,730 --> 00:16:46,330
+تاني عبارة عن exercise اتنين فرع a section تلاتة
+
+178
+00:16:46,330 --> 00:16:54,610
+اتنين بنشوف ايه ال exercise هذا بيقول give
+
+179
+00:16:54,610 --> 00:17:01,930
+an example of two divergent sequences two
+
+180
+00:17:01,930 --> 00:17:04,090
+divergent sequences
+
+181
+00:17:06,940 --> 00:17:12,840
+such that there are some مجموعهم there
+
+182
+00:17:12,840 --> 00:17:19,020
+are some converges نعطي
+
+183
+00:17:19,020 --> 00:17:24,060
+مثال ل two divergent sequences تنتهي from two
+
+184
+00:17:24,060 --> 00:17:29,140
+divergent لكن مجموعهم convergent فأسهل مثال هو مثل
+
+185
+00:17:29,140 --> 00:17:36,270
+هذا الحلناخد الـ sequence xn للحد العام تبعها سالب
+
+186
+00:17:36,270 --> 00:17:42,430
+واحد to n و n بتبدأ من واحد إلى ملا نهاية طبعا ال
+
+187
+00:17:42,430 --> 00:17:48,210
+sequence هذه لو بيننا انفرفتها فحدودها هتكون هكذا
+
+188
+00:17:48,210 --> 00:17:53,670
+أول حد سالب واحد، تاني واحد، تالت سالب واحد،
+
+189
+00:17:53,670 --> 00:18:00,040
+الرابع واحد، و هكذاوناخد ال sequence yn الحد العام
+
+190
+00:18:00,040 --> 00:18:04,760
+تبعها سالب واحد قص ان زاد واحد وان طبعا تبدأ من
+
+191
+00:18:04,760 --> 00:18:12,080
+واحد فهذه ال sequence حدودها هتكون أول حد واحد،
+
+192
+00:18:12,080 --> 00:18:17,160
+التاني سالب واحد، التالت واحد، الرابع سالب واحد و
+
+193
+00:18:17,160 --> 00:18:17,620
+هكذا
+
+194
+00:18:20,300 --> 00:18:25,720
+تمام احنا اثبتنا بالتفصيل ان ال sequence xn هذي
+
+195
+00:18:25,720 --> 00:18:29,660
+divergent by contradiction فرضنا انها convergent
+
+196
+00:18:29,660 --> 00:18:35,960
+وصلنا الى تناغم صح؟ طب ما هذي هي هذي هي ال
+
+197
+00:18:35,960 --> 00:18:43,750
+sequence ال sequence yn هي سالب ال sequence xnو Xn
+
+198
+00:18:43,750 --> 00:18:47,710
+is divergent و Yn is divergent او بنفس البرهان
+
+199
+00:18:47,710 --> 00:18:51,530
+ممكن نعمل نفس البرهان اذا هي عندي مثال على two
+
+200
+00:18:51,530 --> 00:18:57,670
+sequences كلاهما both are divergent لكن لما نيجي
+
+201
+00:18:57,670 --> 00:19:04,750
+نجمعهم لو أخدت ال sequence جديدة ال inf term تبعها
+
+202
+00:19:04,750 --> 00:19:09,070
+او الحد العام تبعها هو مجموعة ال inf term زي Xn
+
+203
+00:19:09,070 --> 00:19:15,280
+وYn هذه sequence تالتة جديدةما هو الحد العام لهذه
+
+204
+00:19:15,280 --> 00:19:21,360
+الـ sequence؟ اجمع الحد الأول على الأول بيطلع سفر،
+
+205
+00:19:21,360 --> 00:19:25,740
+التاني على التاني سفر، إذا هذه عبارة عن الـ
+
+206
+00:19:25,740 --> 00:19:30,300
+sequence constant zero ثابت سفر أو الـ sequence
+
+207
+00:19:30,300 --> 00:19:35,480
+الحد العام تبعها ثابت سفر وطبعا أي sequence ثابتة
+
+208
+00:19:35,480 --> 00:19:39,880
+بتكون convergent و limit تبعتها هي الحد الثابت
+
+209
+00:19:39,880 --> 00:19:45,000
+نفسه، لذلك limit لهذه الـ sequence ثابت سفرإذا هذا
+
+210
+00:19:45,000 --> 00:19:50,700
+مثال على two divergent sequences their sum is
+
+211
+00:19:50,700 --> 00:19:55,900
+convergent okay تمام؟ في برضه حاجات زي هذه ممكن
+
+212
+00:19:55,900 --> 00:20:00,200
+ينقلب منكم جيبي مثال على two sequences contain
+
+213
+00:20:00,200 --> 00:20:05,820
+مثلا convergent لكن حصل ضربهم divergent يعني حاجات
+
+214
+00:20:05,820 --> 00:20:11,880
+زي هيك و هكذا في الكتاب في تمارينعلى هذا السياق
+
+215
+00:20:11,880 --> 00:20:22,020
+هتشوفوها تمام؟ مفهوم؟ واضح المثال هذا؟ طيب مثال
+
+216
+00:20:22,020 --> 00:20:29,440
+رقم تلاتة هذا
+
+217
+00:20:29,440 --> 00:20:32,900
+عبارة عن exercise أربعة عشر في section تلاتة اتنين
+
+218
+00:20:35,100 --> 00:20:41,360
+بقول خد zn بساوي a to n plus b to n to the power
+
+219
+00:20:41,360 --> 00:20:47,240
+one over n where a و b are positive numbers and a
+
+220
+00:20:47,240 --> 00:20:56,260
+less than b prove أن limit zn بساوي العدد b تمام؟
+
+221
+00:20:56,260 --> 00:21:02,420
+لبرهان ذلك أنا عندي من الفرض a positive إذا a to n
+
+222
+00:21:02,420 --> 00:21:09,520
+positiveوكذلك وبالتالي b to n أصغر من a to n plus
+
+223
+00:21:09,520 --> 00:21:16,460
+b to n الان ناخد ال nth root لطرفي المتبينة هذه
+
+224
+00:21:16,460 --> 00:21:22,700
+فبطلع b أصغر من ال nth root للمجموعة ده اللي احنا
+
+225
+00:21:22,700 --> 00:21:33,440
+سمناه zn اذا الان انا عندي zn بساوي a n زاد b nto
+
+226
+00:21:33,440 --> 00:21:39,580
+the power one over n والان انا عندى بما انه a أصغر
+
+227
+00:21:39,580 --> 00:21:45,740
+من b a أصغر من b من الفرض هى فهذا بالتأكيد بيقدى
+
+228
+00:21:45,740 --> 00:21:52,200
+انه a to n أصغر من b to n اذا
+
+229
+00:21:52,200 --> 00:21:59,680
+هشيل ال a to n هذه و اضع خليها أصغر من b to n زائد
+
+230
+00:21:59,680 --> 00:22:07,730
+b to n الكل to one over nطب هذا بيطلع two ضرب b to
+
+231
+00:22:07,730 --> 00:22:14,450
+n الكل to power one over n وزع ال power فبطلع two
+
+232
+00:22:14,450 --> 00:22:22,290
+to one over n ضرب b صح؟ الآن ال sequence إذا
+
+233
+00:22:22,290 --> 00:22:28,470
+أنا أصبح عندي لو دمجت المتباينتين عشرة و أحداشر مع
+
+234
+00:22:28,470 --> 00:22:35,870
+بعض فبطلع عندي bمن المتباينة عشرة الـ B هدا هي
+
+235
+00:22:35,870 --> 00:22:42,590
+أصغر من ال ZN ومن المتباينة أحداشر ال ZN أصغر من
+
+236
+00:22:42,590 --> 00:22:47,610
+two to one over N times B for every N natural
+
+237
+00:22:47,610 --> 00:22:56,780
+number احنا اتوصلنا لالمتباينة هذه صحيحة لكل Nانا
+
+238
+00:22:56,780 --> 00:23:01,660
+لان عندي الـ sequence ZN هذه اللي انا عايز اثبت ان
+
+239
+00:23:01,660 --> 00:23:07,120
+ال limit تبعتها بالساوي بيه is squeezed between
+
+240
+00:23:07,120 --> 00:23:13,680
+two sequences محصورة من متتاليتين تنتين هاي
+
+241
+00:23:13,680 --> 00:23:20,620
+متتالية وهاي متتالية المتتالية هذه الحد العام
+
+242
+00:23:20,620 --> 00:23:27,340
+تبعها ثابت بيهوبالتالي ال limit تبعت بي لما بي
+
+243
+00:23:27,340 --> 00:23:35,340
+تقول ل infinity بتساوي بي و limit ال sequence هذي
+
+244
+00:23:35,340 --> 00:23:39,380
+two to واحد على n limit two to واحد على n بتساوي
+
+245
+00:23:39,380 --> 00:23:44,760
+واحد اثبتنا احنا قبل هيك ان لو n دي c عدد موجب ف
+
+246
+00:23:44,760 --> 00:23:52,170
+limitc to 1 على n as n tends to infinity بساوة
+
+247
+00:23:52,170 --> 00:23:59,230
+واحد صح فاندي c هنا بساوة اتنين لان ال limit ل two
+
+248
+00:23:59,230 --> 00:24:02,450
+to one over n as n tends to infinity بساوة واحد
+
+249
+00:24:02,450 --> 00:24:07,290
+وبالتالي limit two to one over n times constant b
+
+250
+00:24:07,290 --> 00:24:12,170
+بساوة واحد في b او b في واحد ف limit ال sequence
+
+251
+00:24:12,170 --> 00:24:18,000
+هذه ايضا تطلع bلما انتقل ل infinity، اذا by
+
+252
+00:24:18,000 --> 00:24:23,000
+squeeze theorem بطلع عندي limit ال sequence zm
+
+253
+00:24:23,000 --> 00:24:28,240
+المحصورة في النص بساوي بيه، okay؟ اذا هاي هنا
+
+254
+00:24:28,240 --> 00:24:34,120
+استخدامنا ال sandwich او ال squeeze، تمام؟ واضح؟
+
+255
+00:24:36,340 --> 00:24:40,080
+Okay إذا هذه يعني بعض الأسئلة هي اللي حلناها،
+
+256
+00:24:40,080 --> 00:24:43,480
+حالها مش صعب إما تطبيق على ال sandwich theorem أو
+
+257
+00:24:43,480 --> 00:24:48,680
+على نظرية 2.4 أو الحاجات اللي أخدناها في ال
+
+258
+00:24:48,680 --> 00:24:52,740
+section هذا أو في ال succession السابق أو بالتالي
+
+259
+00:24:52,740 --> 00:24:58,760
+مافيش حاجة يعني غريبة أو تستدى أن احنا نستخدم حاجة
+
+260
+00:24:58,760 --> 00:25:05,270
+مش موجودة في المناجمإذا ما يكون إلا من شطرتكم
+
+261
+00:25:05,270 --> 00:25:10,210
+تحاولوا تحلوا باقي التمرين اللي في ال section هذا
+
+262
+00:25:10,210 --> 00:25:15,550
+طبعا هنا لهنا الامتحان .. الامتحان داخل لحد
+
+263
+00:25:15,550 --> 00:25:21,590
+التمرين هذه الجزء اللي بعد هيك مش داخل في الامتحان
+
+264
+00:25:21,590 --> 00:25:22,310
+النصف الأول
+
+265
+00:25:26,220 --> 00:25:32,640
+تمام فإذا هنا ال section جديد أو أنوان جديد ال
+
+266
+00:25:32,640 --> 00:25:38,160
+monotone sequences المتتاليات اللي بيسموها
+
+267
+00:25:38,160 --> 00:25:42,380
+الواتيرية المتتاليات الواتيرية ال monotone
+
+268
+00:25:42,380 --> 00:25:46,960
+sequence يعني متتالية واتيرية يعني إما متزايدة أو
+
+269
+00:25:46,960 --> 00:25:55,200
+متلاقصة فناخد تعريف let x in be a sequence of real
+
+270
+00:25:55,200 --> 00:26:02,880
+numbersسنقول إن سيكوينس Xn increasing متزايدة إذا
+
+271
+00:26:02,880 --> 00:26:07,400
+كان Xn less
+
+272
+00:26:07,400 --> 00:26:11,800
+than or equal to Xn plus one for every n لو كان كل
+
+273
+00:26:11,800 --> 00:26:17,260
+حد أصغر من أول ساول لبعده فالسيكوينس في الحالة دي
+
+274
+00:26:17,260 --> 00:26:23,860
+بنسميها increasing و بنسميها decreasingإذا كان كل
+
+275
+00:26:23,860 --> 00:26:32,760
+حد أكبر من أو يساوي اللي بعده تمام؟
+
+276
+00:26:32,760 --> 00:26:40,000
+طيب بنسمي ال sequence monotone ال sequence بنسميها
+
+277
+00:26:40,000 --> 00:26:45,460
+monotone أو واتيرية if it is either increasing or
+
+278
+00:26:45,460 --> 00:26:46,040
+decreasing
+
+279
+00:26:48,950 --> 00:26:53,170
+إن المتتالي الوطرية هي متتالية إما increasing أو
+
+280
+00:26:53,170 --> 00:26:58,250
+decreasing معنى
+
+281
+00:26:58,250 --> 00:27:01,490
+آخر كل increasing sequence is monotone sequence
+
+282
+00:27:01,490 --> 00:27:06,090
+and every decreasing sequence is monotone sequence
+
+283
+00:27:06,090 --> 00:27:14,370
+طب هاي أمثلة على monotone sequences فاندي هنا
+
+284
+00:27:14,370 --> 00:27:21,540
+sequence n of natural numbersis increasing واضح ان
+
+285
+00:27:21,540 --> 00:27:26,440
+xn بساوي n أصغر من او ساوي xn plus one اللي هو n
+
+286
+00:27:26,440 --> 00:27:31,440
+زاد واحد لان هذا increasing وهذا increasing ال
+
+287
+00:27:31,440 --> 00:27:36,040
+sequence اللي ال inf term تبعها two to n اللي هي
+
+288
+00:27:36,040 --> 00:27:41,440
+هذه is increasing بينما
+
+289
+00:27:41,440 --> 00:27:46,720
+ال sequence one over n decreasing هي كل حد أكبر من
+
+290
+00:27:46,720 --> 00:27:52,140
+أو ساوي لبعدهو كذلك ال sequence one over two to n
+
+291
+00:27:52,140 --> 00:27:57,580
+طيب، في سؤال هنا بطلح نفسه، هل كل sequence لازم
+
+292
+00:27:57,580 --> 00:28:01,720
+تكون monotone sequence؟ لأ، مو لأ، مش شرط، مش شرط،
+
+293
+00:28:01,720 --> 00:28:03,620
+مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+294
+00:28:03,620 --> 00:28:03,840
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+295
+00:28:03,840 --> 00:28:07,680
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+296
+00:28:07,680 --> 00:28:12,580
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+297
+00:28:12,580 --> 00:28:12,580
+شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش شرط، مش
+
+298
+00:28:12,580 --> 00:28:17,150
+شرط، مش شرط، مش شرطthe following sequence is
+
+299
+00:28:17,150 --> 00:28:20,010
+sequence اللي الحد اللي عام تبعها negative one to
+
+300
+00:28:20,010 --> 00:28:24,830
+n أو n زيادة واحد اللي هي ال alternated sequence
+
+301
+00:28:24,830 --> 00:28:29,750
+ال sequence هذه المتدبدبة alternating يعني
+
+302
+00:28:29,750 --> 00:28:34,930
+المتدبدبة في الإشارة واحد سالب واحد واحد سالب واحد
+
+303
+00:28:34,930 --> 00:28:40,450
+هذه ليست conversion ليست monotone is not
+
+304
+00:28:40,450 --> 00:28:46,980
+increasing and it is not decreasingنفس الشيء ال
+
+305
+00:28:46,980 --> 00:28:51,180
+sequence اللي حد اللي عم تبعها سالب one to n اللي
+
+306
+00:28:51,180 --> 00:28:56,040
+هي سالب واحد موجة بتنين سالب تلاتة و هكذا ال
+
+307
+00:28:56,040 --> 00:29:00,560
+sequence هذه is not monotone لا increasing ولا
+
+308
+00:29:00,560 --> 00:29:05,590
+decreasing تمام واضحإذا ال sequence .. أي .. لو
+
+309
+00:29:05,590 --> 00:29:09,310
+أخدنا أي sequence عشوائية فممكن تكون increasing،
+
+310
+00:29:09,310 --> 00:29:14,070
+ممكن تكون decreasing، ممكن تكون neither، neither
+
+311
+00:29:14,070 --> 00:29:16,810
+increasing nor decreasing زي ال function ممكن تكون
+
+312
+00:29:16,810 --> 00:29:22,950
+odd أو even أو neither، لا odd ولا even، أه؟ تمام؟
+
+313
+00:29:22,950 --> 00:29:26,870
+طيب ال .. في نظرية مهمة هنا في هذا السياق
+
+314
+00:29:29,970 --> 00:29:34,290
+بتخص الـ monotone sequences وبالتالي بنسميها
+
+315
+00:29:34,290 --> 00:29:39,170
+monotone convergence theorem وبنستخدم اختصارات
+
+316
+00:29:39,170 --> 00:29:46,690
+monotone convergence theorem النظرية
+
+317
+00:29:46,690 --> 00:29:52,550
+هذه بتقول خد .. خدي let x and b a monotone
+
+318
+00:29:52,550 --> 00:29:57,650
+sequence خلينا ناخد monotone sequenceالان هذه الـ
+
+319
+00:29:57,650 --> 00:30:01,130
+monotone sequence بتكون convergent if and only if
+
+320
+00:30:01,130 --> 00:30:05,830
+it is bounded تمام؟
+
+321
+00:30:05,830 --> 00:30:10,470
+moreover إضافة إلى ذلك لو كانت ال sequence x in
+
+322
+00:30:10,470 --> 00:30:16,970
+هذه bounded and increasing فأكيد طبعا convergent و
+
+323
+00:30:16,970 --> 00:30:22,370
+ال limit تبعتها بساوي ال supremum إلها ك set كذلك
+
+324
+00:30:22,370 --> 00:30:25,170
+لو كانت ال sequence x in bounded و decreasing
+
+325
+00:30:27,590 --> 00:30:31,190
+فبتكون طبعا convergent و ال limit بتبعتها بساوة ال
+
+326
+00:30:31,190 --> 00:30:36,270
+inform اللي لها ك set طيب
+
+327
+00:30:36,270 --> 00:30:39,430
+احنا عندي انا عندي هنا two statements او تلاتة
+
+328
+00:30:39,430 --> 00:30:47,010
+statements انا عندي العبارة هذه انا
+
+329
+00:30:47,010 --> 00:30:53,490
+عندي بتثبت العبارة هذه و العبارتين هدون فكيف
+
+330
+00:30:53,490 --> 00:31:00,150
+البرهان بتتمأول شي العبارة الأولى اللى فى البرواز
+
+331
+00:31:00,150 --> 00:31:08,610
+هذه if and only if statement صح ففى two parts واحد
+
+332
+00:31:08,610 --> 00:31:15,750
+هذا ال part ال only if part و ال if part نشوف ال
+
+333
+00:31:15,750 --> 00:31:21,260
+only if part يعنىلو كانت x in convergent بينا نثبت
+
+334
+00:31:21,260 --> 00:31:25,680
+إنها it is bounded وهذا أثبتناه في نظرية سابقة
+
+335
+00:31:25,680 --> 00:31:31,120
+أثبتنا إن كل تجارب convergent is bounded اختبار
+
+336
+00:31:31,120 --> 00:31:41,320
+الدم فاكرين؟ إذا هذا was proved proved
+
+337
+00:31:41,320 --> 00:31:49,530
+earlier تم إثباته سابقا في نظرية سابقةلو كانت
+
+338
+00:31:49,530 --> 00:31:54,830
+السيكوانس تبقى convergent ضرورة تكون bounded سواء
+
+339
+00:31:54,830 --> 00:31:58,690
+كانت السيكوانس monotone ولا حتى مش monotone okay؟
+
+340
+00:31:58,690 --> 00:32:02,950
+تمام؟ إن هاي برهان الجزء لهذا موجود في نظرية سابقة
+
+341
+00:32:02,950 --> 00:32:08,970
+باقى نثبت الجزء هذا يعني بنا نثبت أنه لو كانت
+
+342
+00:32:08,970 --> 00:32:17,730
+السيكوانس bounded السيكوانس لو كانت bounded و
+
+343
+00:32:17,730 --> 00:32:18,510
+monotone
+
+344
+00:32:21,420 --> 00:32:25,800
+طبعا احنا فرضين انها monotone اه من البداية x in
+
+345
+00:32:25,800 --> 00:32:32,020
+is monotone فالان عشان نكمل برهان العبارة هذه ال
+
+346
+00:32:32,020 --> 00:32:35,060
+if and only if او ال by conditional statement هذا
+
+347
+00:32:35,060 --> 00:32:40,920
+فبدنا نثبت ان لو كانت ال sequence bounded و
+
+348
+00:32:40,920 --> 00:32:49,520
+monotone فبتطلع convergent طيب
+
+349
+00:32:49,520 --> 00:32:54,920
+monotoneمونوتون لما ال sequence تكون مونوتون
+
+350
+00:32:54,920 --> 00:33:04,060
+معناها اما increasing او decreasing او decreasing
+
+351
+00:33:04,060 --> 00:33:08,260
+اذا
+
+352
+00:33:08,260 --> 00:33:16,500
+عشان اثبت الجزء هذا بده اثبت a و b هذا الجزء هذا
+
+353
+00:33:16,500 --> 00:33:25,750
+لبرهانه بده برهين a و bلأن جزء A بيقول لو كانت ال
+
+354
+00:33:25,750 --> 00:33:29,330
+sequence bounded و increasing فبتثبت أنها
+
+355
+00:33:29,330 --> 00:33:33,510
+convergent صح؟ فهي لو كانت ال sequence bounded و
+
+356
+00:33:33,510 --> 00:33:37,930
+increasing فبتثبت أنها convergent و ال limit
+
+357
+00:33:37,930 --> 00:33:43,530
+تبعتها هي ال suprem من إلها كمجموعة و الجزء B
+
+358
+00:33:43,530 --> 00:33:47,690
+بيثبت أن لو كانت ال sequence bounded و decreasing
+
+359
+00:33:47,690 --> 00:33:54,510
+فبتطلع convergentوإضافة لذلك إن ال limit تبعتها هي
+
+360
+00:33:54,510 --> 00:34:00,390
+ال infront إلى كسب إذا الإكمال برهان الاتجاه هذا و
+
+361
+00:34:00,390 --> 00:34:05,690
+برهان a و b وبالتالي نكمل برهان النظرية يكفي إن
+
+362
+00:34:05,690 --> 00:34:11,290
+أحنا نثبت a و b و أضع يكمل كون أثبتنا إلى عبارة من
+
+363
+00:34:11,290 --> 00:34:16,750
+بروزة هذه و a و b يعني برهاننا النظرية كاملة تمام؟
+
+364
+00:34:17,990 --> 00:34:39,030
+نثبت الآن باقي اثبات a وb نثبت الجزء a فخلّينا
+
+365
+00:34:39,030 --> 00:34:43,130
+نفرض ان ال sequence x in is bounded قلنا bounded
+
+366
+00:34:43,130 --> 00:34:48,700
+زاد increasingطيب من تعريف الـ bounded sequence
+
+367
+00:34:48,700 --> 00:34:54,840
+مدام ال sequence bounded إذا يوجد عدد حقيقي موجب M
+
+368
+00:34:54,840 --> 00:35:03,840
+بحيث أنه absolute Xn أصغر من أو ساوي M لكل N طيب
+
+369
+00:35:03,840 --> 00:35:07,540
+معروف أنه أي عدد حقيقي Xn أصغر من أو ساوي القيمة
+
+370
+00:35:07,540 --> 00:35:14,200
+المطلقة له، مظبوط؟إذا من ال boundedness من فرض ان
+
+371
+00:35:14,200 --> 00:35:18,260
+ال sequence bounded في معدد موجد بحيث ان xn أصغر
+
+372
+00:35:18,260 --> 00:35:23,640
+من أو ساوي M لكل M تمام واضح طيب الآن إذا ال
+
+373
+00:35:23,640 --> 00:35:27,800
+sequence xn bounded above وبالتالي by supremum ال
+
+374
+00:35:27,800 --> 00:35:33,120
+property ال supremum تبعها exist سميه x star
+
+375
+00:35:35,800 --> 00:35:40,000
+الان بيدثبت الادعاء هذا الـ claim الادعاء بيدثبت
+
+376
+00:35:40,000 --> 00:35:45,260
+انه limit ال sequence xn بساوي ال x star اللي هو
+
+377
+00:35:45,260 --> 00:35:51,580
+ال suprem لست xn فلو أثبتت هذا الادعاء معناته
+
+378
+00:35:51,580 --> 00:35:55,600
+أثبتت أنا ان ال sequence xn is convergent و ال
+
+379
+00:35:55,600 --> 00:36:00,650
+limit تبعتها بساوي ال suprem إلها كستتعالى نشوف
+
+380
+00:36:00,650 --> 00:36:04,930
+كيف نثبت ال claim to see this لبرهان ال claim انا
+
+381
+00:36:04,930 --> 00:36:09,430
+ايش بتثبت؟ بتثبت ان ال sequence x in convergent و
+
+382
+00:36:09,430 --> 00:36:13,630
+ال limit تبعتها بساوي العدد x star فهستخدم تعريف
+
+383
+00:36:13,630 --> 00:36:17,830
+epsilon capital N لل limit فلازم ابدأ let epsilon
+
+384
+00:36:17,830 --> 00:36:25,090
+أكبر من الصفر بيه given الان ال x star هذاهو ال
+
+385
+00:36:25,090 --> 00:36:28,430
+supremum لل set هذه لما نطرح من ال supremum عدد
+
+386
+00:36:28,430 --> 00:36:33,830
+موجب بيبطل upper bound بيبطل upper bound لأن ال x
+
+387
+00:36:33,830 --> 00:36:37,690
+star هو أصغر upper bound اطرح منه عدد موجب بيبطل
+
+388
+00:36:37,690 --> 00:36:41,590
+upper bound إذا هذا العدد x star minus y is not an
+
+389
+00:36:41,590 --> 00:36:46,710
+upper bound معناته في أنصر في ال set هذه اللي هو x
+
+390
+00:36:46,710 --> 00:36:51,450
+رقم capital N أكبر من العدد هذا اللي هو ما هوش
+
+391
+00:36:51,450 --> 00:36:55,860
+upper boundوطبعاً العدد هذا المؤشر او ال index
+
+392
+00:36:55,860 --> 00:37:00,040
+capital N ده يعتمد على ال epsilon مرتبط بال
+
+393
+00:37:00,040 --> 00:37:05,500
+epsilon اللي بنيت فيها طبعا انا فرض ان ال sequence
+
+394
+00:37:05,500 --> 00:37:10,860
+xn increasing وبالتالي x capital N أصغر من أو سوى
+
+395
+00:37:10,860 --> 00:37:14,880
+xn لكل N أكبر من أو سوى capital N من تعريف ال
+
+396
+00:37:14,880 --> 00:37:20,500
+increasing sequence اذا انا في عندي هنا هى عندي x
+
+397
+00:37:20,500 --> 00:37:28,280
+capital N هىxN أصغر من أو ساوي xN لكل N أكبر من أو
+
+398
+00:37:28,280 --> 00:37:36,360
+ساوي N طيب و x*) هو ال suprem of ال sequence xN و
+
+399
+00:37:36,360 --> 00:37:42,440
+xN هذا عنصر في ال sequence و x*) upper bound لل
+
+400
+00:37:42,440 --> 00:37:49,540
+sequence إذن xN أصغر من أو ساوي x*) طيب و x*) أصغر
+
+401
+00:37:49,540 --> 00:37:57,820
+من نفسها زاد عدد موجب هذا مافي شكو من هنا .. أيوه
+
+402
+00:37:57,820 --> 00:38:03,460
+.. من المتباينة هذه هي عندي x capital n أكبر من x
+
+403
+00:38:03,460 --> 00:38:11,420
+star سالب y إذا أنا طلع عندي الآن x star أكبر من
+
+404
+00:38:11,420 --> 00:38:13,160
+.. أو x in
+
+405
+00:38:15,810 --> 00:38:25,070
+أكبر من X star minus Y أصغر من X star زاد Y لكل N
+
+406
+00:38:25,070 --> 00:38:30,910
+أكبر من أو ساوي capital N فظبطك صح؟ طيب مهاد
+
+407
+00:38:30,910 --> 00:38:37,890
+المتباينة هي نفسها X N minus X star أصغر من Y أكبر
+
+408
+00:38:37,890 --> 00:38:44,610
+من سالب Y لكل N أكبر من أو ساوي capital Nطب
+
+409
+00:38:44,610 --> 00:38:49,930
+المتباينة هذه هي .. صح؟ أظبط؟ إذن absolute xn
+
+410
+00:38:49,930 --> 00:38:53,210
+minus x star أصغر من إبسلون لكل n أكبر من أوي
+
+411
+00:38:53,210 --> 00:38:58,370
+ساوية كابتن ان الأن since إبسلون was arbitrary هذا
+
+412
+00:38:58,370 --> 00:39:03,810
+بالظبط تعريف إبسلون كابتن ان لل limit أه؟ بأن هذا
+
+413
+00:39:03,810 --> 00:39:08,470
+الكلام صحيح لكل إبسلون أكبر من سفر إذن هذا معناه
+
+414
+00:39:08,470 --> 00:39:13,190
+حسب التعريف إن limit xn بساوي x star
+
+415
+00:39:18,780 --> 00:39:23,660
+إذا هذا بثبت ال claim وبالتالي هكذا نكون أثبتنا
+
+416
+00:39:23,660 --> 00:39:30,560
+الجزء A من النظرية فالجزء
+
+417
+00:39:30,560 --> 00:39:35,300
+التاني B ممكن نستخدم A في برهان ال B
+
+418
+00:39:38,510 --> 00:39:42,310
+ففي الجزء B الان انا عندي ال sequence تبعتي
+
+419
+00:39:42,310 --> 00:39:46,570
+bounded و decreasing اذا ا assume x in is bounded
+
+420
+00:39:46,570 --> 00:39:50,770
+and decreasing فاش
+
+421
+00:39:50,770 --> 00:39:55,690
+عمل هعرف sequence جديدة yn اللي هي negative الحد
+
+422
+00:39:55,690 --> 00:40:01,530
+العام تبعها negative x in تمام؟ الان بما ان x in
+
+423
+00:40:01,530 --> 00:40:05,170
+decreasing اذا ال sequence سالب x in تطلع
+
+424
+00:40:05,170 --> 00:40:10,610
+increasingوطبعا بما أن ال sequence x in bounded
+
+425
+00:40:10,610 --> 00:40:15,670
+إذا ال sequence سالب x in أيضا bounded إذا الأن
+
+426
+00:40:15,670 --> 00:40:18,790
+أنا في عندي sequence جديد اللي هي sequence yn
+
+427
+00:40:18,790 --> 00:40:26,310
+bounded وin crazy إذا حسب الجزء a by part a limit
+
+428
+00:40:26,310 --> 00:40:32,790
+ال sequence yn تطلع existوبتساوي ال supremum لكل
+
+429
+00:40:32,790 --> 00:40:37,870
+ال y in ال supremum لعناصر ال sequence اللي هي y
+
+430
+00:40:37,870 --> 00:40:41,510
+in تمام؟
+
+431
+00:40:41,510 --> 00:40:47,370
+انها ده من ايه؟ من الجزء ايه من النظرية؟طيب ال
+
+432
+00:40:47,370 --> 00:40:51,450
+supremum ل سالب xn هيفقن العدد طبيعي احنا خدنا قبل
+
+433
+00:40:51,450 --> 00:40:56,490
+هيك exercise بيقول supremum او infimum سالب حاجة
+
+434
+00:40:56,490 --> 00:41:02,190
+بساوي سالب ال infimum فهنا بصير هذا سالب ال
+
+435
+00:41:02,190 --> 00:41:07,530
+infimum تمام؟ اذا انا عندي بيطلع عندي limit xn
+
+436
+00:41:07,530 --> 00:41:15,180
+بساوي سالب limit سالب xn تمام؟أضربوا هنا هيندي
+
+437
+00:41:15,180 --> 00:41:18,940
+limit سالب xn أضربوا المعادلة هذه بالسالب واحد
+
+438
+00:41:18,940 --> 00:41:24,700
+فبطلع سالب limit سالب xn بساوي سالب سالب موجب اللي
+
+439
+00:41:24,700 --> 00:41:29,000
+هو ال inform ل xn وهذا اللي بدنا يعني لأن هي
+
+440
+00:41:29,000 --> 00:41:33,280
+أثبتنا أن limit xn موجودة exist يعني ال sequence
+
+441
+00:41:33,280 --> 00:41:37,640
+xn convergent وال limit تبعتها بساوي ال inform
+
+442
+00:41:40,760 --> 00:41:44,680
+بنكمل برهان الـ monotone convergence theorem طبعا
+
+443
+00:41:44,680 --> 00:41:49,280
+الأمثلة هذه اللي هنا كلها أمثلة تطبيق على الـ
+
+444
+00:41:49,280 --> 00:41:53,180
+monotone convergence theorem فارجو أنكم تحاولوا
+
+445
+00:41:53,180 --> 00:41:56,080
+تخرجوا الأمثلة هذه و تشوفوا كيف نستخدم الـ
+
+446
+00:41:56,080 --> 00:41:58,440
+monotone convergence theorem في
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Mk2487qcZF8_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Mk2487qcZF8_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b3dba70e28b6ad2c48e03bfeb13e1b8c446a0275
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Mk2487qcZF8_postprocess.srt
@@ -0,0 +1,1760 @@
+1
+00:00:21,450 --> 00:00:27,950
+Okay إذا احنا في المحاضرة الأخيرة أخدنا الـ
+
+2
+00:00:27,950 --> 00:00:33,670
+monotone convergence theorem وشوفنا
+
+3
+00:00:33,670 --> 00:00:38,970
+أنه في النظرية هذه لو في عندي sequence و ال
+
+4
+00:00:38,970 --> 00:00:42,710
+sequence هذه monotone يعني increasing أو
+
+5
+00:00:42,710 --> 00:00:48,510
+decreasing فعشان فبتكون convergent if and only if
+
+6
+00:00:48,510 --> 00:00:53,060
+it is boundedإذا الـ monotone sequence converges
+
+7
+00:00:53,060 --> 00:01:01,360
+if and only if it is bounded طيب
+
+8
+00:01:01,360 --> 00:01:04,420
+ال monotone sequence نوعين إما increasing أو
+
+9
+00:01:04,420 --> 00:01:07,360
+decreasing فلو كانت ال sequence increasing و طبعا
+
+10
+00:01:07,360 --> 00:01:10,940
+bounded فشوفنا إنها بتكون convergent حسب ال
+
+11
+00:01:10,940 --> 00:01:14,040
+statement الأول و ال limit تبعتها بساوي ال
+
+12
+00:01:14,040 --> 00:01:17,280
+supremum اللي لها ك set و لو كانت ال sequence
+
+13
+00:01:17,280 --> 00:01:22,420
+decreasing و بالطبع boundedفحسب ال statement الأول
+
+14
+00:01:22,420 --> 00:01:28,720
+تطلع convergence ونهايتها هي ال infimum تبعها ك Z
+
+15
+00:01:28,720 --> 00:01:33,040
+وشوفنا
+
+16
+00:01:33,040 --> 00:01:35,560
+برهانة مغرية في المحاضرة السابقة
+
+17
+00:01:38,060 --> 00:01:43,060
+الان بنشوف كيف نطبق النظرية في إثبات إن certain
+
+18
+00:01:43,060 --> 00:01:47,200
+sequences are convergent أو divergent النظرية هذه
+
+19
+00:01:47,200 --> 00:01:51,180
+بالمناسبة ممكن نستخدمها في إثبات إنه monotone
+
+20
+00:01:51,180 --> 00:01:55,960
+sequence معينة إما convergent أو divergent عشان
+
+21
+00:01:55,960 --> 00:01:59,120
+أثبت إن ال monotone sequence إذا عندي أنا monotone
+
+22
+00:01:59,120 --> 00:02:02,760
+sequence عشان أثبت إنها convergent لازم أثبت إنها
+
+23
+00:02:02,760 --> 00:02:08,980
+bounded العكس لو في عنده monotone sequenceوبدي
+
+24
+00:02:08,980 --> 00:02:14,640
+اثبت انها divergent يكفي ان اثبت انها unbounded
+
+25
+00:02:14,640 --> 00:02:21,840
+not bounded فهي ان ال sequence xn بساوي واحد على n
+
+26
+00:02:21,840 --> 00:02:27,240
+هاد ال sequence معروف انه ال limit انها convergent
+
+27
+00:02:27,240 --> 00:02:34,630
+وits limit is zero زيها زي ال sequence واحد على nو
+
+28
+00:02:34,630 --> 00:02:38,270
+ممكن تبرهن أن الـ sequence هذه convergence و
+
+29
+00:02:38,270 --> 00:02:42,030
+نهايتها بالساعة و سفر باستخدام تعريف epsilon
+
+30
+00:02:42,030 --> 00:02:49,070
+capital N لل limit بالظبط زي ما عملنا في برهان ال
+
+31
+00:02:49,070 --> 00:02:52,830
+limit أن ال limit لل sequence واحد علي N بالساعة و
+
+32
+00:02:52,830 --> 00:02:57,810
+سفر باستخدام الarchimedean property فهذا برهان
+
+33
+00:02:57,810 --> 00:03:04,810
+ممكن أي واحدة فيكم تكتبهاللي هو باستخدام تعريف
+
+34
+00:03:04,810 --> 00:03:08,110
+epsilon capital N زائد الـarchimedean property
+
+35
+00:03:08,110 --> 00:03:13,290
+بالظبط زي ما أثبتنا limit 1 على N بساوية 0 اليوم
+
+36
+00:03:13,290 --> 00:03:16,550
+هنشوف برهان تاني باستخدام الـ monotone convergence
+
+37
+00:03:16,550 --> 00:03:16,990
+theorem
+
+38
+00:03:20,740 --> 00:03:25,460
+السيكوانس هي بالحد العام ال n term تبعها xn one
+
+39
+00:03:25,460 --> 00:03:28,960
+over square root of n طبعا square root of n أصغر
+
+40
+00:03:28,960 --> 00:03:32,720
+من square root of z واحد لأي عدد طبيعي وبالتالي
+
+41
+00:03:32,720 --> 00:03:37,680
+مقلوب لكبير أصغر من مقلوب لكبير هذا xn زاد واحد
+
+42
+00:03:37,680 --> 00:03:44,240
+وهذا xn أنا عندي sequence is such that xn زاد واحد
+
+43
+00:03:44,240 --> 00:03:48,560
+أصغر من xn هذا معناه أن ال sequence is increasing
+
+44
+00:03:49,820 --> 00:03:54,740
+كذلك الـ sequence هذه is bounded لأنه هي فيه عدد
+
+45
+00:03:54,740 --> 00:03:59,700
+موجب M بساوي واحد عدد موجب بحيث أنه absolute xn
+
+46
+00:03:59,700 --> 00:04:04,780
+أصغر من أو يساوي M لكل N لأن أنا فيها ال sequence
+
+47
+00:04:04,780 --> 00:04:12,000
+increasingdecreasing و bounded اذا by monotone
+
+48
+00:04:12,000 --> 00:04:16,620
+convergence theorem ال sequence هذه هتكون
+
+49
+00:04:16,620 --> 00:04:23,220
+convergent و ال limit تبعتها بساوي ال infimum طيب
+
+50
+00:04:23,220 --> 00:04:27,740
+ال infimum للمجموعة هذه بتساوي سفر
+
+51
+00:04:30,570 --> 00:04:35,710
+وبرهان ذلك شبيه ببرهان الـ infimum للـ sequence 1
+
+52
+00:04:35,710 --> 00:04:40,310
+على n بالساوي 0 باستخدام الـ Archimedean property
+
+53
+00:04:40,310 --> 00:04:44,350
+راجعوا برهان أن الـ infimum للـ sequence 1 على n
+
+54
+00:04:44,350 --> 00:04:48,610
+وهذا ثمتناه في المحاضرات السابقة راجعوا البرهان
+
+55
+00:04:48,610 --> 00:04:54,800
+وكتبوا برهان مشابه لهبنفس الطريقة نثبت ان الانثرام
+
+56
+00:04:54,800 --> 00:04:58,660
+لسيكوانس هادى او الست هادى سفر اذا حسب الـ
+
+57
+00:04:58,660 --> 00:05:01,400
+monotone convergence theorem ال sequence واحد على
+
+58
+00:05:01,400 --> 00:05:05,700
+جذر M is convergent و ال limit تبعتها بساوي
+
+59
+00:05:05,700 --> 00:05:10,240
+الانثرام تبعها اللى هو سفر اذا هى مثال على تطبيق
+
+60
+00:05:10,240 --> 00:05:15,570
+الـ monotone convergence theoremكذلك ممكن برضه زي
+
+61
+00:05:15,570 --> 00:05:18,810
+ما قلتلكم نستخدم الـ monotone convergence theorem
+
+62
+00:05:18,810 --> 00:05:26,750
+في أثبات أن سيكوانس زي هذه is divergent نشوف
+
+63
+00:05:26,750 --> 00:05:30,870
+مع بعض كيف .. إذا هنا هاي سيكوانس الحد العام تبعها
+
+64
+00:05:30,870 --> 00:05:37,490
+xn هذا الint partial sum بالمناسبة هذا الint
+
+65
+00:05:37,490 --> 00:05:43,330
+partial sum في ال harmonic seriesسيجما من K بساول
+
+66
+00:05:43,330 --> 00:05:50,210
+واحد to infinity لواحد على K وهد
+
+67
+00:05:50,210 --> 00:05:53,110
+ال harmonic series is divergent معروف في calculus
+
+68
+00:05:53,110 --> 00:06:00,190
+بقى ال series هد is divergent وهد الحد العام في ال
+
+69
+00:06:00,190 --> 00:06:04,730
+sequence of partial sums وفي calculus بقى درسنا
+
+70
+00:06:04,730 --> 00:06:10,330
+إذا بتذكروا إذا فاكرين حاجةمن الموضوع هذا انه a
+
+71
+00:06:10,330 --> 00:06:13,970
+series converges if and only if ال sequence of
+
+72
+00:06:13,970 --> 00:06:18,130
+partial sums is convergent فلو ال series is
+
+73
+00:06:18,130 --> 00:06:21,130
+divergent ال sequence of partial sums is divergent
+
+74
+00:06:21,130 --> 00:06:24,830
+هذه هي ال sequence of partial sums حدث بتنها
+
+75
+00:06:24,830 --> 00:06:31,150
+divergent بس مش باستخدام calculus بقى باستخدام ال
+
+76
+00:06:31,150 --> 00:06:37,300
+monotone convergence theoremطيب ال sequence هي
+
+77
+00:06:37,300 --> 00:06:43,920
+الحد العام xn إذا الحد رقم n زياد واحد هي بنضيف
+
+78
+00:06:43,920 --> 00:06:49,400
+زياد واحد على n زياد واحد للمجموع هذا اللي هو xn
+
+79
+00:06:49,400 --> 00:06:54,320
+صح؟ وبالتالي زي ما أنتوا شايفين الحد xn زياد واحد
+
+80
+00:06:54,320 --> 00:07:00,560
+هو الحد xn زائد حد موجب وبالتالي هذا أكبر من xn
+
+81
+00:07:02,310 --> 00:07:06,670
+الكلام هذا صحيح لكل n إذاً هذا معناه إن ال
+
+82
+00:07:06,670 --> 00:07:14,690
+sequence xn is increasing، متزايدة، الآن أنا في
+
+83
+00:07:14,690 --> 00:07:19,410
+ندي sequence xn، هذه الحد الآن تبعها، و ال
+
+84
+00:07:19,410 --> 00:07:25,600
+sequence هذه increasing، monotone يعنيالان الـ
+
+85
+00:07:25,600 --> 00:07:30,700
+monotone convergence بتقول لي عشان أثبت أن ال
+
+86
+00:07:30,700 --> 00:07:34,260
+sequence هذي convergent لازم أثبت أنها bounded
+
+87
+00:07:34,260 --> 00:07:39,860
+وعشان أثبت أنها divergent لازم أثبت أنها unbounded
+
+88
+00:07:39,860 --> 00:07:44,520
+فتعالوا نفحص هل هي bounded ولا لأ إذا طلعت bounded
+
+89
+00:07:44,520 --> 00:07:48,640
+بتكون convergent إذا طلعت unbounded بتكون
+
+90
+00:07:48,640 --> 00:07:49,360
+divergent
+
+91
+00:07:52,580 --> 00:07:57,960
+تعالوا نشوف الحد العام يعني هنا في حاخد ال
+
+92
+00:07:57,960 --> 00:08:04,200
+sequence بدل x in x اللي الحد العام تبعها two to n
+
+93
+00:08:04,200 --> 00:08:09,640
+هذه عبارة عن subsequence فهذه subsequence من ال
+
+94
+00:08:09,640 --> 00:08:10,820
+sequence x in
+
+95
+00:08:16,700 --> 00:08:21,480
+يعني هذه جزء من ال sequence هذه هذه أول حد فيها x
+
+96
+00:08:21,480 --> 00:08:27,400
+رقم مؤشر تبعه اتنين صح؟ يعني هذه حدود ال sequence
+
+97
+00:08:27,400 --> 00:08:32,620
+هذه x اتنين لما n بساوة واحد بعدين اللي بعده x
+
+98
+00:08:32,620 --> 00:08:40,100
+أربع بعدين x تمام يعني و هكذا طبعا هذه الحدود هذه
+
+99
+00:08:40,100 --> 00:08:44,980
+كلها موجودة هنا صح؟ فهذه بنسميها subsequence من ال
+
+100
+00:08:44,980 --> 00:08:49,090
+sequence الأصليالان انا بدي اخد الحد العام لل sub
+
+101
+00:08:49,090 --> 00:08:56,750
+sequence دي اللي المؤشر تبعه 2 أس n بدل n طيب
+
+102
+00:08:56,750 --> 00:09:01,170
+انا عند xn بساوي المجموعة هذا واحد زاد نص زاد تلت
+
+103
+00:09:01,170 --> 00:09:06,290
+اخر حد واحد على n طب لما بدي ال n ب 2 أس n هيطلع
+
+104
+00:09:06,290 --> 00:09:10,650
+عند المجموعة واحد زاد نص زاد تلت الى اخر حد واحد
+
+105
+00:09:10,650 --> 00:09:16,620
+على 2 أس n صح؟ هذا من تعريف ال sequenceالان الحدود
+
+106
+00:09:16,620 --> 00:09:25,340
+هذه تبع المجموع هعملها blocks، بلوكات فواحد لوحده
+
+107
+00:09:25,340 --> 00:09:31,320
+في block، نص لوحده، هاخد التلت والربع مع بعض،
+
+108
+00:09:31,320 --> 00:09:38,080
+بعدين ال block الرابع هتكون خمس و سدس و سبعة و
+
+109
+00:09:38,080 --> 00:09:44,840
+تمان، أربع حدود مع بعض، جمهم مع بعضو هكذا إلى ال
+
+110
+00:09:44,840 --> 00:09:51,220
+block الأخيرة اللي هي 1 على 2 أس N سالب 1 زاد 1
+
+111
+00:09:51,220 --> 00:09:56,660
+إلى 1 على 2 أس N طيب
+
+112
+00:09:56,660 --> 00:10:02,080
+هاي ال 1 نزل النص، الآن التلت هذا، التلت أكبر من
+
+113
+00:10:02,080 --> 00:10:06,820
+ربع إن علامة التساوي هذه صارت أكبر، يعني بدلت
+
+114
+00:10:06,820 --> 00:10:12,650
+التلت بربع، والتلت أكبر من ربعفصار مجموع ربعين
+
+115
+00:10:12,650 --> 00:10:16,090
+الان في ال block اللي بعديها في عندي خمس و سُدس و
+
+116
+00:10:16,090 --> 00:10:22,110
+سبعة تمن كل واحد منهم أكبر من أو يساوي التمن فعشان
+
+117
+00:10:22,110 --> 00:10:27,450
+يصير في عندي هنا تمن زي تمن زي تمن أربع مرات اللي
+
+118
+00:10:27,450 --> 00:10:34,390
+هو بطلع نص أربعة أتمان نص وهنا ربعين نص صح؟ وهنا
+
+119
+00:10:34,390 --> 00:10:39,910
+هذا الحد اللي هنا هذاأكبر من واحد على اتنين أسئن
+
+120
+00:10:39,910 --> 00:10:44,450
+لأنه اتنين أسئن أكبر من اتنين أسئن سالب واحد زائد
+
+121
+00:10:44,450 --> 00:10:49,050
+واحد لكل ان إذاً هذا أكبر من واحد على اتنين أسئن
+
+122
+00:10:49,050 --> 00:10:53,410
+والبعد أكبر من واحد على اتنين أسئن و هكذا إذاً هنا
+
+123
+00:10:53,410 --> 00:10:57,550
+عندي واحد على اتنين أسئن مجموعة على نفسه اتنين
+
+124
+00:10:57,550 --> 00:11:03,890
+أسئن سالب واحد من المراتفمجموهم بيساوي مجموها دول
+
+125
+00:11:03,890 --> 00:11:07,030
+بيساوي اتنين اص ان سالب واحد في واحد على اتنين اص
+
+126
+00:11:07,030 --> 00:11:11,650
+ان بيطلع نص اذا هذا المجموعة نص وهذا نص واللي بعده
+
+127
+00:11:11,650 --> 00:11:16,990
+نص كلهم نصارى ماعدا اول حد اذا واحد وهي نص وهذا نص
+
+128
+00:11:16,990 --> 00:11:23,670
+اللي بعده نص واخر واحد نص طب كام حد في هنا هاي حد
+
+129
+00:11:23,670 --> 00:11:29,950
+ودول عددهم nin من الحدود وهذا وعد هاي in زاد واحد
+
+130
+00:11:29,950 --> 00:11:34,870
+من الحدود طب هدول عددهم in لما أجمع عدد على نفسه
+
+131
+00:11:34,870 --> 00:11:38,810
+in من المرات بيطلع in في نص اللي هو in عتنين زاد
+
+132
+00:11:38,810 --> 00:11:42,770
+واحد طيب لما in تقول ل infinity in عتنين يقول ل
+
+133
+00:11:42,770 --> 00:11:46,570
+infinity وبالتالي واحد زاد in عتنين بيروح ل
+
+134
+00:11:46,570 --> 00:11:50,410
+infinity تمام؟
+
+135
+00:11:50,410 --> 00:11:54,690
+إذا أنا عندي الحد العام لل sequence هذه أو ال
+
+136
+00:11:54,690 --> 00:12:02,730
+subsequenceطولة أكبر من مقدار يقول لـ infinity هو
+
+137
+00:12:02,730 --> 00:12:14,510
+بالتالي إذا
+
+138
+00:12:14,510 --> 00:12:21,510
+أنا عندي x to two to n tends to infinity as n
+
+139
+00:12:21,510 --> 00:12:29,270
+tends to infinityوبالتالي هذا معناه أن X على 2 نص
+
+140
+00:12:29,270 --> 00:12:38,330
+M أكبر من M لكل M عدد موجب ما معناه أن ال limit
+
+141
+00:12:38,330 --> 00:12:42,730
+لحد
+
+142
+00:12:42,730 --> 00:12:47,650
+هذا أو ال sequence X المؤشرات تبقية 2 نص M تقول
+
+143
+00:12:47,650 --> 00:12:52,750
+infinity معناته هذا الحد العام لها أكبر من أي عدد
+
+144
+00:12:52,750 --> 00:12:58,800
+موجبوبالتالي إذا الـ subsequence هذه اللي هي الحد
+
+145
+00:12:58,800 --> 00:13:06,980
+العام تبعها X plus 2N is unbounded وبالتالي
+
+146
+00:13:06,980 --> 00:13:15,560
+فهذا بيقدي إن ال sequence XN نفسها is unbounded
+
+147
+00:13:15,560 --> 00:13:21,300
+لأنه لو كانت ال sequence boundedفأي sub-sequence
+
+148
+00:13:21,300 --> 00:13:25,420
+منها اللي هي جزء منها هتكون bounded صح هذا واضح
+
+149
+00:13:25,420 --> 00:13:30,740
+تمام الان by monotone convergence theorem ال
+
+150
+00:13:30,740 --> 00:13:37,340
+sequence x in unbounded وبالتالي it is divergent
+
+151
+00:13:37,340 --> 00:13:45,000
+لأن لو كانت convergent فلازم تكون bounded okay إذا
+
+152
+00:13:45,000 --> 00:13:49,600
+هاي استخدمنا ال monotone convergence theoremلإثبات
+
+153
+00:13:49,600 --> 00:13:52,140
+أن سيكوانس معينة مُعينة مُعينة مُعينة مُعينة
+
+154
+00:13:52,140 --> 00:13:52,840
+مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة
+
+155
+00:13:52,840 --> 00:13:56,680
+مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة
+
+156
+00:13:56,680 --> 00:13:59,900
+مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة
+
+157
+00:13:59,900 --> 00:14:00,660
+مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة
+
+158
+00:14:00,660 --> 00:14:05,360
+مُعينة مُعينة مُعينة مُعينة مُعينة مُعينة
+
+159
+00:14:05,360 --> 00:14:11,900
+مُعينة مُعينة مُعينة
+
+160
+00:14:11,900 --> 00:14:12,220
+مُعين
+
+161
+00:14:16,610 --> 00:14:21,230
+المثال التالت برضه هنستخدم .. هنطبق عليه اللي هو
+
+162
+00:14:21,230 --> 00:14:23,790
+الـ monotone convergence theorem
+
+163
+00:14:34,440 --> 00:14:40,520
+بس هذا المثال مختلف عن المثالين السابقين الان انا
+
+164
+00:14:40,520 --> 00:14:44,820
+بدي اعرف ال sequence x in inductively بطريقة
+
+165
+00:14:44,820 --> 00:14:52,860
+استقرائية شوفنا
+
+166
+00:14:52,860 --> 00:14:56,460
+احنا لما بدينا ال chapter هذا ان ال sequences can
+
+167
+00:14:56,460 --> 00:15:01,740
+be defined in two waysاما explicitly زي مثلا ال
+
+168
+00:15:01,740 --> 00:15:06,900
+sequence xn بالساوي واحد على n او recursively او
+
+169
+00:15:06,900 --> 00:15:11,520
+inductively بطريقة استقرائية بان انا اخد قيمة للحد
+
+170
+00:15:11,520 --> 00:15:16,440
+الاول او اول حدين اعطيهم قيم محددة و بعدين اعرف
+
+171
+00:15:16,440 --> 00:15:22,510
+الحد العام بدالة الحدود اللي قبلهفهي اندي الحد
+
+172
+00:15:22,510 --> 00:15:28,110
+الاول نفرض انه بساوي واحد الان بنعرف xn زياد واحد
+
+173
+00:15:28,110 --> 00:15:31,870
+على انه square root لاتنين ضرب الحد اللي جابناه
+
+174
+00:15:31,870 --> 00:15:35,970
+وهذا لكل n لان بالطريقة هذه ممكن اعرف ان هذا
+
+175
+00:15:35,970 --> 00:15:39,610
+بيعطينا sequence الان هذه ال sequence عايزين نثبت
+
+176
+00:15:39,610 --> 00:15:44,610
+انها convergent زائد ان ال limit تبقاتها بساوي
+
+177
+00:15:44,610 --> 00:15:45,350
+لعدد اتنين
+
+178
+00:15:48,640 --> 00:15:52,540
+لبرهان ذلك سنستخدم الـ monotone convergence
+
+179
+00:15:52,540 --> 00:15:57,940
+theorem عشان
+
+180
+00:15:57,940 --> 00:16:01,680
+أقدر استخدام الـ monotone convergence theorem ففي
+
+181
+00:16:01,680 --> 00:16:07,300
+عندي ال claim الأول يعني بدي أثبت في الإدعاء الأول
+
+182
+00:16:07,300 --> 00:16:14,260
+هذا ان ال sequence xn is increasing and bounded by
+
+183
+00:16:14,260 --> 00:16:14,640
+2
+
+184
+00:16:18,060 --> 00:16:24,180
+فلبرهان ذلك بنلاحظ
+
+185
+00:16:24,180 --> 00:16:31,920
+أن X1 من التعريف تبع ال sequence X1 بساوي 1 و X2
+
+186
+00:16:31,920 --> 00:16:34,660
+ممكن أجيبها من ال recursive formula أو ال
+
+187
+00:16:34,660 --> 00:16:39,500
+inductive formula إن أنا أاخد n بساوي 1 فبطلع X2
+
+188
+00:16:39,500 --> 00:16:49,840
+بساوي جدر 2 ل X1 و X1 1 إذا X2 بطلع جدر 2وبالتالي
+
+189
+00:16:49,840 --> 00:16:54,160
+من الحسابات هذه بيطلع اندي هاي X واحد X واحد
+
+190
+00:16:54,160 --> 00:16:59,080
+بيساوي واحد وبالتالي اكبر منها بيساوي واحد واسغر
+
+191
+00:16:59,080 --> 00:17:04,420
+من X اتنين لان X اتنين جدر اتنين الواحد اصغر من
+
+192
+00:17:04,420 --> 00:17:08,620
+جدر اتنين و
+
+193
+00:17:08,620 --> 00:17:12,960
+X اتنين اللي هو جدر اتنين اصغر من الاتنين لان كل
+
+194
+00:17:12,960 --> 00:17:13,760
+هذا صحيح
+
+195
+00:17:19,580 --> 00:17:25,920
+تمام؟ لسه ما خلصناهش لسه ما خلصناهش احنا ما فرضنا
+
+196
+00:17:25,920 --> 00:17:30,580
+انه صحيح احنا أثبتناه لسه
+
+197
+00:17:30,580 --> 00:17:35,220
+ما أثبتناش هذا ال claim لسه ما أثبتناه احنا لسه ده
+
+198
+00:17:35,220 --> 00:17:41,110
+بداية البرهانةالبرهان لـ claim بدأنا بما راحظنا ان
+
+199
+00:17:41,110 --> 00:17:47,150
+x1 من التعريف مقطع بساوي واحد و x2 حسبناها منها
+
+200
+00:17:47,150 --> 00:17:51,630
+بساوي جدر اتنين ل x1 اللي هو جدر اتنين وبالتالي
+
+201
+00:17:51,630 --> 00:17:58,270
+بطلع اندي هيك هاي x1 أكبر من أو ساوي واحد و أصغر
+
+202
+00:17:58,270 --> 00:18:03,850
+من جدر اتنين اللي هو x2 و x2 اللي هي جدر اتنين
+
+203
+00:18:03,850 --> 00:18:09,210
+أصغر من اتنينليش احنا عملنا هذا الكلام لان هيبين
+
+204
+00:18:09,210 --> 00:18:16,170
+الان now الان بدي اثبت بدي استخدم ال induction we
+
+205
+00:18:16,170 --> 00:18:28,150
+use induction لاثبات العبارة هذه وهي ان xn اصغر من
+
+206
+00:18:28,150 --> 00:18:32,970
+xn زائد واحد وهذا اصغر من اتنين وهذا اكبر من أوسع
+
+207
+00:18:32,970 --> 00:18:41,020
+الواحد لكلمن البرهن صحة العبارة هذه by induction
+
+208
+00:18:41,020 --> 00:18:47,240
+طيب الحالة اللي فيها خد n بساوية واحد الحالة اللي
+
+209
+00:18:47,240 --> 00:18:53,300
+فيها n بساوية واحد هي هاي x واحد أكبر من أو ساوية
+
+210
+00:18:53,300 --> 00:19:01,340
+واحد هدا هي و أصغر من x اتنين هدا هيو X2 أصغر من 2
+
+211
+00:19:01,340 --> 00:19:05,280
+إذا العبارة هذه صحيحة لما N بساوي 1 لأنه هنا
+
+212
+00:19:05,280 --> 00:19:10,280
+أثبتناها الآن
+
+213
+00:19:10,280 --> 00:19:18,920
+افرضي .. افرضي أن العبارة صحيحة عند N بساوي K يعني
+
+214
+00:19:18,920 --> 00:19:27,820
+عندك هنا XKاكبر من او ساول واحد اصغر من X K زايد
+
+215
+00:19:27,820 --> 00:19:34,100
+واحد اصغر من اتنين هنا فرضنا هذا ال induction high
+
+216
+00:19:34,100 --> 00:19:41,920
+precision وعايزين نثبت ان هذا بيقدي ان القبارة
+
+217
+00:19:41,920 --> 00:19:48,980
+صحيحة and N بيساوي K زايد واحد يعني بدي اثبت هذه
+
+218
+00:19:48,980 --> 00:19:50,660
+المتباينة
+
+219
+00:19:55,390 --> 00:20:02,590
+بدي أثبت المتباينة هذه طبعا فتعالى نشوف كيف نثبت
+
+220
+00:20:02,590 --> 00:20:21,690
+المتباينة هذه طيب
+
+221
+00:20:21,690 --> 00:20:29,980
+أنا عنديهي عندي المتباينة هذه احنا
+
+222
+00:20:29,980 --> 00:20:49,600
+فرضين ان المتباينة هذه صحيحة احنا
+
+223
+00:20:49,600 --> 00:20:52,640
+فرضين من induction hypothesis ان هذه المتباينة
+
+224
+00:20:52,640 --> 00:20:58,910
+صحيحةأضرب المتباينة هذه في اتنين هي اضرب كل
+
+225
+00:20:58,910 --> 00:21:02,710
+الأطراف في اتنين فبصير اتنين اصغر من اتنين XK اصغر
+
+226
+00:21:02,710 --> 00:21:09,290
+من اتنين XK زائد واحد اصغر من اربع وهذا بيقدي ان
+
+227
+00:21:09,290 --> 00:21:11,570
+واحد اصغر من جدر اتنين
+
+228
+00:21:15,730 --> 00:21:21,830
+و اذا انا الان باخد الجذر التربيعى لكل الأطراف هذه
+
+229
+00:21:21,830 --> 00:21:26,750
+اخد الجذر التربيعى فهي جذر اتنين طبعا اكبر من واحد
+
+230
+00:21:26,750 --> 00:21:34,350
+اصغر منه يساوي جذر اتنين XK اللى هو XK زاد واحد
+
+231
+00:21:34,350 --> 00:21:37,770
+هذا طبعا من التعريف تبع ال sequence من ال
+
+232
+00:21:37,770 --> 00:21:43,130
+inductive formula جذر اتنين XK حسب التعريف بساوي
+
+233
+00:21:43,130 --> 00:21:50,440
+XK زاد واحدوهذا أصغر من هنا جدر اتنين xk أصغر من
+
+234
+00:21:50,440 --> 00:21:56,840
+جدر اتنين xk زائد واحد وهذا أصغر من جدر الأربع
+
+235
+00:21:56,840 --> 00:22:01,180
+اللي هو الأتنين إذا هاي بيطلع عندي واحد أصغر من أو
+
+236
+00:22:01,180 --> 00:22:06,580
+يساوي xk زائد واحد وهذا برضه من ال inductive
+
+237
+00:22:06,580 --> 00:22:15,940
+formula الجدر التربيع هذا بيساوي xk زائد اتنينإذا
+
+238
+00:22:15,940 --> 00:22:21,620
+هي 1 أصغر من أو ساوي xk زاد 1 أصغر من xk زاد 2
+
+239
+00:22:21,620 --> 00:22:28,100
+أصغر من 2 وبالتالي إذا أثبتنا إحنا صحة العبارة هذه
+
+240
+00:22:28,100 --> 00:22:34,700
+عن k زاد 1 وبالتالي هيك بنكون كملنا ال induction
+
+241
+00:22:34,700 --> 00:22:43,060
+okay طبعا إذا ال claim تعالوا نشوف الآن ليش ال
+
+242
+00:22:43,060 --> 00:22:48,470
+sequenceأه ليه ال sequence تبعتنا بتطلع bounded
+
+243
+00:22:48,470 --> 00:22:55,530
+وincreasing فاكرين احنا أثبتنا by induction ان x
+
+244
+00:22:55,530 --> 00:23:01,810
+in أصغر من x in زايد واحد أصغر من اتنين أكبر من
+
+245
+00:23:01,810 --> 00:23:10,150
+أوي ساوي واحد لكل in من الجزء هذا نستنتج
+
+246
+00:23:10,150 --> 00:23:14,460
+ان ال sequence is increasing صح؟لأن هى عندى xn
+
+247
+00:23:14,460 --> 00:23:21,640
+أصغر من xn زاد واحد لكل n ومن المتباينة كلها يعني
+
+248
+00:23:21,640 --> 00:23:28,200
+اللى هى xn أصغر من اتنين أكبر من أوسع واحد لكل n
+
+249
+00:23:28,200 --> 00:23:32,080
+هذا معناته ال sequence bounded هى محصورة بين واحد
+
+250
+00:23:32,080 --> 00:23:37,160
+واتنين و bounded above by اتنين لذلك هذا يكمل
+
+251
+00:23:37,160 --> 00:23:42,800
+برهان ال claim الأول يعنيوهو انه sequence x in
+
+252
+00:23:42,800 --> 00:23:47,240
+increasing و bounded الان by monotone convergence
+
+253
+00:23:47,240 --> 00:23:53,140
+theorem ال sequence x in هتكون convergent دعينا
+
+254
+00:23:53,140 --> 00:23:56,840
+نسمي ال limit تبعتها x وطبعا حسب ال monotone
+
+255
+00:23:56,840 --> 00:23:59,480
+convergence theorem بما انه sequence increasing
+
+256
+00:23:59,480 --> 00:24:05,960
+اذا ال limit تبعتها بساوي ال suprem لها ك set اذا
+
+257
+00:24:05,960 --> 00:24:09,600
+انا في عندي الآن ال sequence تبعتي convergent هي
+
+258
+00:24:09,600 --> 00:24:17,620
+عندي limitx in convergent بيساوي x اللي هي طبعا
+
+259
+00:24:17,620 --> 00:24:21,580
+حسب النظرية بيساوي ال supremum الان بدي أجيب قيمة
+
+260
+00:24:21,580 --> 00:24:25,460
+ال x هذا طبعا
+
+261
+00:24:25,460 --> 00:24:30,560
+مش سهل أن أجيب ال supremum ل ال sequence فبجيبها
+
+262
+00:24:30,560 --> 00:24:35,600
+بطريقة تانية إذا
+
+263
+00:24:35,600 --> 00:24:38,560
+ال claim التاني بدي أثبت أن ال x ال limit ل ال
+
+264
+00:24:38,560 --> 00:24:40,720
+sequence اللي هي x بيساوي 2
+
+265
+00:24:43,730 --> 00:24:47,450
+طيب انا عندي من تعريف الـ sequence انا عندي xn زاد
+
+266
+00:24:47,450 --> 00:24:53,070
+واحد بساوي جدر اتنين xn و هذا الكلام صحيح for
+
+267
+00:24:53,070 --> 00:24:57,870
+every m ناخد ال limit لاتطرفين لما n تقول ل
+
+268
+00:24:57,870 --> 00:25:02,050
+infinity بتطلع limit xn زاد واحد بساوي limit جدر
+
+269
+00:25:02,050 --> 00:25:08,390
+اتنين ثابت في limit جدر ال xn مظبوط؟
+
+270
+00:25:09,940 --> 00:25:15,160
+طيب احنا فرضين او احنا استنتجنا احنا لسه مستنتجين
+
+271
+00:25:15,160 --> 00:25:19,340
+من ال monotone convergence ان limit xn بيساوي x
+
+272
+00:25:19,340 --> 00:25:25,400
+وبالتالي limit xn زاد واحد برضه بتساوي x وهي
+
+273
+00:25:25,400 --> 00:25:31,220
+بيساوي جذر اتنين و limit جذر xn بيساوي جذر ال x
+
+274
+00:25:31,220 --> 00:25:36,980
+حسب نظرية سابقة اذا ال limit هذه اذا هي x و جذر
+
+275
+00:25:36,980 --> 00:25:40,820
+اتنين في ال limit هذه بتطلع جذر ال xإذا أصبح أثيان
+
+276
+00:25:40,820 --> 00:25:46,380
+دي معادلة في مجهول واحد x ممكن أحلها و ذلك بتربيع
+
+277
+00:25:46,380 --> 00:25:53,740
+الطرفين فالمعادلة هذه بعد مربعها تصير هيك وهذه في
+
+278
+00:25:53,740 --> 00:25:59,340
+إلها حالين إما x بيطلع بساوي سفر أو x بساوي اتنين
+
+279
+00:25:59,340 --> 00:26:04,940
+احنا عايزين ال x ناخد x بساوي اتنين و نرفض x بساوي
+
+280
+00:26:04,940 --> 00:26:10,700
+سفر طب ليه نرفض x بساوي سفر؟لأن اثبتنا هنا by
+
+281
+00:26:10,700 --> 00:26:20,340
+induction أن xn أكبر من أوسع واحد أصغر من الأتنين
+
+282
+00:26:20,340 --> 00:26:25,960
+و أثبتنا أن ال sequence هذه convergent، إذا حسب
+
+283
+00:26:25,960 --> 00:26:27,200
+نظرية سابقة
+
+284
+00:26:30,490 --> 00:26:38,230
+إذن ال limit لل sequence xn هتطلع محصورة بين 2 و
+
+285
+00:26:38,230 --> 00:26:42,650
+بين 1 خدمة نظرية بتقول لو كانت ال sequence xn
+
+286
+00:26:42,650 --> 00:26:48,610
+convergent و xn أكبر من أو ساوي a أصغر من أو ساوي
+
+287
+00:26:48,610 --> 00:26:53,570
+b لكل n فال limit لل sequence xn بتطلع أيضا محصورة
+
+288
+00:26:53,570 --> 00:26:59,560
+بين a و bيعني طب هدى هى ال X فرضنا ان ال limit هدى
+
+289
+00:26:59,560 --> 00:27:04,060
+X اذا بطلع انا عندي X اكبر من او ساوي واحد اصغر من
+
+290
+00:27:04,060 --> 00:27:07,920
+الاتنين وبالتالي مش ممكن ال X اللى هى محصورة بين
+
+291
+00:27:07,920 --> 00:27:15,420
+واحد واتنين مش ممكن تساوي سفر مش ممكن تساوي سفر
+
+292
+00:27:15,420 --> 00:27:19,820
+اذا لازم الساوي .. وانا عندي سفر او اتنين اذا لازم
+
+293
+00:27:19,820 --> 00:27:25,570
+الساوي اتنينOkay إذا هين هيك استخدمنا الـ monotone
+
+294
+00:27:25,570 --> 00:27:31,030
+convergence بالمثل في أد التمرين زي هذه sequences
+
+295
+00:27:31,030 --> 00:27:36,290
+معرفة inductively و هتثبتوا أنها convergent و
+
+296
+00:27:36,290 --> 00:27:40,750
+تجيبوا قيمة ال limit بنفس الطريقة و بنفس الأسلوب
+
+297
+00:27:40,750 --> 00:27:46,250
+فحاولوا تستفيدوا من حل المثال الأخير هذا في حل مثل
+
+298
+00:27:46,250 --> 00:27:52,770
+هذه التمرين Okay تمام واضحإذن هنا أخدنا تطبيقات
+
+299
+00:27:52,770 --> 00:27:56,230
+متنوعة على الـ monotone convergence theorem وهي
+
+300
+00:27:56,230 --> 00:28:03,570
+التمرين ل section تلاتة تلاتة نبدأ
+
+301
+00:28:03,570 --> 00:28:09,230
+section أربعة أو تلاتة أربعة نعم بيقول إنه ممكن
+
+302
+00:28:09,230 --> 00:28:13,790
+نحل بحر ثاني و نثبت أنه الإثنان يصدرهم للإكسام
+
+303
+00:28:13,790 --> 00:28:17,770
+مظبوط صحيح الإثنان يتحركون على طريق اللملة اللي هي
+
+304
+00:28:17,770 --> 00:28:18,610
+الإكسام
+
+305
+00:28:21,690 --> 00:28:28,990
+والله انت فاكر فيه و بعدين قولي ليه هي
+
+306
+00:28:28,990 --> 00:28:34,050
+عندك sequence حدودها معروفة معرفة ممكن تكتب أول
+
+307
+00:28:34,050 --> 00:28:40,010
+اربع خمس عدود و تحاول تستنتجي ايه هي قيمة ال
+
+308
+00:28:40,010 --> 00:28:44,930
+supreme و تبرهنها طبعا فهذا متروك اليك
+
+309
+00:28:47,810 --> 00:28:52,030
+هذا يعني حل آخر فانا قلت ان ال suprem مش سهل ان
+
+310
+00:28:52,030 --> 00:28:56,070
+احنا نجيبه لمثل هذه ال sequences او ال sets
+
+311
+00:28:56,070 --> 00:28:59,230
+وبالتالي ال monotone convergence في الفيلم كان
+
+312
+00:28:59,230 --> 00:29:03,390
+ممكن يكون أسهل لأن هاي الكلام التاني هذا الأخير
+
+313
+00:29:03,390 --> 00:29:07,270
+مااخدش وجهة يعني أخدنا ال formula ال inductive
+
+314
+00:29:07,270 --> 00:29:11,570
+formula و أخدنا ال limit للطرفين و حلينا معادلة في
+
+315
+00:29:11,570 --> 00:29:16,800
+Xو ادركنا ان ال X ليس لازم تساوي سفر من هنا لان X
+
+316
+00:29:16,800 --> 00:29:20,820
+محصولة بين واحد و اتنين هذا أسهل من ان انا اجيب ال
+
+317
+00:29:20,820 --> 00:29:26,940
+suprem لكن هذا ممنعش ان ممكن حد معين يثبت ان ال
+
+318
+00:29:26,940 --> 00:29:33,060
+suprem هو اتنين اذا كان سهل فكان بيعني نستخدمه مش
+
+319
+00:29:33,060 --> 00:29:35,240
+سهل نستخدم ال monotone convergence
+
+320
+00:29:49,630 --> 00:29:56,070
+الـ sub-sequences and Bolzano-Weierstrass theorem،
+
+321
+00:29:56,070 --> 00:29:59,350
+ال sub-sequences شوفنا قبل شوية sub-sequence
+
+322
+00:30:11,180 --> 00:30:15,400
+شوفنا قبل لحظات في المثال التاني انه في عنده
+
+323
+00:30:15,400 --> 00:30:26,540
+sequence هي عنده sequence xn حدودها x1, x2, x3, x4
+
+324
+00:30:26,540 --> 00:30:34,160
+و هكذا و في كانت sequence تانية لحد الآن تبعها 2
+
+325
+00:30:34,160 --> 00:30:52,420
+أُس nالحدود هذي هتكون X2 X4 X8 و هكذا صح؟ لو سمنا
+
+326
+00:30:52,420 --> 00:31:01,340
+الاتنين هذي R1 والاربعة هذي سمنها R2 والتمانية R3
+
+327
+00:31:04,820 --> 00:31:10,940
+فبنلاحظ أن R1 أكبر من أو ساوء واحد، عدد طبيعي أكبر
+
+328
+00:31:10,940 --> 00:31:19,320
+من أو ساوء واحد وR2 أكبر من R1، اللي هو أربعة أكبر
+
+329
+00:31:19,320 --> 00:31:29,050
+من اتنين وR3 اللي هو تمانية أكبر من R2و هكذا اذا
+
+330
+00:31:29,050 --> 00:31:34,810
+ال sub sequence المؤشرات تبعتها او ال indices انا
+
+331
+00:31:34,810 --> 00:31:40,330
+بسميه index مجموعة index indices ال indices او
+
+332
+00:31:40,330 --> 00:31:44,710
+المؤشرات لل sub sequence هي عداد طبيعية هذا هي
+
+333
+00:31:44,710 --> 00:31:49,890
+اتنين اربعة تمانية هي عداد طبيعية والعداد الطبيعية
+
+334
+00:31:49,890 --> 00:31:55,170
+هذه بتشكل sequence هذه عبارة عن sequence of
+
+335
+00:31:55,170 --> 00:32:01,880
+natural numbersصح؟ و ال sequence هذه is strictly
+
+336
+00:32:01,880 --> 00:32:08,200
+.. strictly increasing
+
+337
+00:32:08,200 --> 00:32:14,580
+.. strictly increasing يعني متزايدة زيادة صحيحة
+
+338
+00:32:14,580 --> 00:32:18,860
+يعني R واحد أصغر منه مش أصغر منه أو يساوي R اتنين
+
+339
+00:32:18,860 --> 00:32:23,280
+و R اتنين أصغر منه و لا تساوي R تلاتة و هكذا
+
+340
+00:32:23,280 --> 00:32:25,780
+مظبوط؟ صح؟
+
+341
+00:32:29,030 --> 00:32:33,430
+إذا السب سيكوانس السب سيكوانس من أي سيكوانس هي
+
+342
+00:32:33,430 --> 00:32:39,350
+مجموعة جزئية منها صح لأن حدودها هي حدود حدود السب
+
+343
+00:32:39,350 --> 00:32:46,130
+سيكوانس هي عناصر أو حدود من السيكوانس العصلية لكن
+
+344
+00:32:46,130 --> 00:32:52,170
+مش أي حدود لازم تكون مرتبة بحيث أن المؤشرات تبعتها
+
+345
+00:32:52,170 --> 00:32:56,890
+اتشكل strictly increasing sequence of natural
+
+346
+00:32:56,890 --> 00:33:03,480
+numbersتمام؟ زي هيك إذاً
+
+347
+00:33:03,480 --> 00:33:06,900
+هذا هو تعريف الـ subsequence إذا لو في أنا عندي
+
+348
+00:33:06,900 --> 00:33:12,060
+sequence XN واخدت strictly increasing sequence of
+
+349
+00:33:12,060 --> 00:33:17,620
+natural numbers فال sequence اللي المؤشرات تبعتها
+
+350
+00:33:17,620 --> 00:33:24,060
+هي ال sequence RN اللي هي هذه عناصرها بنسميها
+
+351
+00:33:24,060 --> 00:33:30,640
+subsequence من ال sequence XNو هاي أمثلة هتابر هذه
+
+352
+00:33:30,640 --> 00:33:33,900
+الـ sequence x in الـ sequence of natural numbers
+
+353
+00:33:33,900 --> 00:33:40,860
+فهذه subsequence منها اتنين in الـ sequence of
+
+354
+00:33:40,860 --> 00:33:44,940
+even numbers او even natural numbers ده هي على
+
+355
+00:33:44,940 --> 00:33:54,800
+سرعة اتنين اربعة ستة و هكذا وهذه عبارة عن sequence
+
+356
+00:33:56,170 --> 00:34:03,930
+of odd national numbers واحد تلاتة خمسة و هكذا
+
+357
+00:34:03,930 --> 00:34:11,550
+وحدود ال sequence هذه هي X R واحد هذا X اتنين هذا
+
+358
+00:34:11,550 --> 00:34:18,430
+رقمه هذا رقم اتنين يعني R واحد بساوة اتنين طيب X R
+
+359
+00:34:18,430 --> 00:34:25,450
+اتنين اربع X R اتنينر2 هذا حد رقم أربعة، ر2 بيساوي
+
+360
+00:34:25,450 --> 00:34:31,610
+أربعة و ر1 بيساوي اتنين، و اتنين أصغر من أربعة، XR
+
+361
+00:34:31,610 --> 00:34:39,130
+تلاتة ستة، ر تلاتة ستة نفس الحاجة، يعني هذه
+
+362
+00:34:39,130 --> 00:34:44,020
+subsequence وهذه subsequence من ال sequence Xلأن
+
+363
+00:34:44,020 --> 00:34:48,280
+مأشراتهم كلهم بشكل strictly increasing sequences
+
+364
+00:34:48,280 --> 00:34:53,000
+of natural numbers بالمثل ال sequence 1 على 2 n
+
+365
+00:34:53,000 --> 00:35:03,540
+سالب 1 و ال sequence 1 على n factorial هدول
+
+366
+00:35:03,540 --> 00:35:07,840
+برضه أيضا sub sequences من ال sequence 1 على n
+
+367
+00:35:11,850 --> 00:35:16,490
+لكن الـ sequence اللي لحد الآن تبقى الحدودها واحد
+
+368
+00:35:16,490 --> 00:35:24,370
+على واحد، سفر، تلت، سفر، خمس، سفر، و هكذا هذه ليست
+
+369
+00:35:24,370 --> 00:35:32,450
+subsequence من الـ sequence واحد على انه لأن السفر
+
+370
+00:35:32,450 --> 00:35:37,150
+هذا هايلها، مش موجودة، ليست ثلاثا تاني لل sequence
+
+371
+00:35:37,150 --> 00:35:43,480
+هذه ومؤشرات الحدوديعني لا تشكل strictly increasing
+
+372
+00:35:43,480 --> 00:35:47,640
+sequence طيب
+
+373
+00:35:47,640 --> 00:35:52,780
+لو أخدت أي tail أي tail M tail حيث M fixed natural
+
+374
+00:35:52,780 --> 00:35:58,740
+number ف X أي tail ده M tail of any sequence X in
+
+375
+00:35:58,740 --> 00:36:03,640
+طبعا ال M tail ده حدوده عبارة عن sequence الحد
+
+376
+00:36:03,640 --> 00:36:10,190
+الأول تبعهاx capital M زاد واحد الحد التاني x
+
+377
+00:36:10,190 --> 00:36:16,870
+capital M زاد اتنين التالت x capital M زاد تلاتة و
+
+378
+00:36:16,870 --> 00:36:21,170
+هكذا فطبعا
+
+379
+00:36:21,170 --> 00:36:26,510
+هذه عبارة عن sub sequence من ال sequence الام لأن
+
+380
+00:36:26,510 --> 00:36:32,430
+كل أنصر في ال sub sequence هذه هي موجودة هنا صح؟
+
+381
+00:36:33,790 --> 00:36:39,710
+والمؤشرات تبعات ال sub-sequence هي M زاد واحد اصغر
+
+382
+00:36:39,710 --> 00:36:45,830
+من R اتنين اللي هو M زاد اتنين وR اتنين اصغر من R
+
+383
+00:36:45,830 --> 00:36:50,130
+تلاتة اللي هو M زاد تلاتة وكده هذا sub-sequence
+
+384
+00:36:50,130 --> 00:36:54,950
+ولا مش sub-sequence؟ لو أخدت أي sequence X in فأي
+
+385
+00:36:54,950 --> 00:37:02,220
+M تل هو sub-sequence منهاكذلك لو أخدت أي sequence
+
+386
+00:37:02,220 --> 00:37:09,400
+xn فالـ sequence x اللي الحد اللي عم تبعها المؤشر
+
+387
+00:37:09,400 --> 00:37:16,020
+تبعه 2 أس n هذي برضه subsequence زي ما شوفنا و x2n
+
+388
+00:37:16,020 --> 00:37:21,340
+الحدود الزوجية لو أخدت الحدود الزوجية فقط فهذا
+
+389
+00:37:21,340 --> 00:37:25,840
+بعطيني subsequence و لو أخدت الحدود الفردية تعطيني
+
+390
+00:37:25,840 --> 00:37:38,470
+subsequence ثانية و لا كدهالان سؤال
+
+391
+00:37:38,470 --> 00:37:42,190
+اللى بهمنا احنا ما هي علاقة ال sequence بال
+
+392
+00:37:42,190 --> 00:37:46,990
+subsequence من حيث ال convergence و ال divergence؟
+
+393
+00:37:54,410 --> 00:37:56,950
+يعني لو كانت ال sequence convergent لو في اندي
+
+394
+00:37:56,950 --> 00:38:01,250
+سيكوانس xn convergent ل x واخدت أي sub sequence
+
+395
+00:38:01,250 --> 00:38:07,490
+منها هل هذه ال sequence لازم تكون convergent زيها
+
+396
+00:38:07,490 --> 00:38:11,890
+ولا divergent لازم تكون convergent و ال limit
+
+397
+00:38:11,890 --> 00:38:22,770
+تبعتها نفس ال limit و لها نفس ال limit ماشي
+
+398
+00:38:22,770 --> 00:38:23,170
+لحظة
+
+399
+00:38:29,060 --> 00:38:29,860
+كثير من الناس
+
+400
+00:38:39,930 --> 00:38:46,370
+إذا كمان مرة بهمني أنا أنه لو في عندي sequence
+
+401
+00:38:46,370 --> 00:38:51,030
+نظرية هذه بتقول لو في عندي sequence xn of real
+
+402
+00:38:51,030 --> 00:38:56,350
+numbers وكانت ال sequence هذه convergent ل x فأي
+
+403
+00:38:56,350 --> 00:39:00,170
+subsequence منها بتكون convergent و ال limit
+
+404
+00:39:00,170 --> 00:39:05,330
+تبعتها هي نفس ال limit لل sequence xn
+
+405
+00:39:08,450 --> 00:39:15,870
+وهذا يعني ممكن ان احنا نثبته بسهولة عشان اثبت ان
+
+406
+00:39:15,870 --> 00:39:22,590
+ال subsequence XRN converge ل X فبستخدم تعريف Y
+
+407
+00:39:22,590 --> 00:39:27,930
+capital N فلو أخدت أي Y أكبر من السفر أنا عندي ال
+
+408
+00:39:27,930 --> 00:39:32,560
+sequence الأصلية هي convergent ل Xوبالتالي من
+
+409
+00:39:32,560 --> 00:39:36,720
+تعريف ال convergence لما أن XM converged ل X إذا
+
+410
+00:39:36,720 --> 00:39:39,940
+يوجد عدد طبيعي يعتمد على إبسلون بحيث أن المسافة
+
+411
+00:39:39,940 --> 00:39:45,700
+بين XM و X أصغر من إبسلون لكل M أكبر من أو يساوي
+
+412
+00:39:45,700 --> 00:39:52,980
+capital M طيب أنا عندي المؤشرات
+
+413
+00:39:52,980 --> 00:39:58,160
+تبع السب سيكوينس بتشكل increasing
+
+414
+00:39:58,160 --> 00:40:03,420
+sequenceوأول واحد .. أول عدد فيها طبعا هذا عدد
+
+415
+00:40:03,420 --> 00:40:09,800
+طبيعي وبالتالي أكبر من أو ساوي الواحد فبالتالي ال
+
+416
+00:40:09,800 --> 00:40:15,160
+Rn هدولة ال Rn ممكن اثبات باستخدام ال induction أن
+
+417
+00:40:15,160 --> 00:40:22,220
+Rn أكبر من أو ساوي N لكل N وبالتالي
+
+418
+00:40:22,220 --> 00:40:28,970
+لو أخدت N أكبر من أو ساوي capital N فعندي أنا Rnمن
+
+419
+00:40:28,970 --> 00:40:34,590
+هنا أكبر من أو ساوي small n و ال n أنا ماخده أكبر
+
+420
+00:40:34,590 --> 00:40:38,750
+من أو ساوي capital N إذا بيطلع عندي RN هاي بيطلع
+
+421
+00:40:38,750 --> 00:40:43,150
+عندي RN أكبر من أو ساوي capital N وبالتالي من ال
+
+422
+00:40:43,150 --> 00:40:48,810
+implication 13 ال implication 13 بتقوللي لأي عدد
+
+423
+00:40:49,980 --> 00:40:55,300
+أكبر من أو ساوية capital N المسافة بين X للعدد هذا
+
+424
+00:40:55,300 --> 00:41:02,090
+للمؤشر هذا سالب X أصغر من Yإذا أنا هيك أثبتت ..
+
+425
+00:41:02,090 --> 00:41:07,550
+أنا هيك أثبتت أنه ال .. لأي epsilon أكبر من السفر
+
+426
+00:41:07,550 --> 00:41:12,190
+في capital N يعتمد على epsilon بحيث لكل N أكبر منه
+
+427
+00:41:12,190 --> 00:41:16,830
+ساوي capital N المسافة بين XRN و X أصغر من epsilon
+
+428
+00:41:16,830 --> 00:41:21,320
+وبالتالي من تعريف epsilon capital N للنهايةأنا هيك
+
+429
+00:41:21,320 --> 00:41:27,640
+بكون أثبتت أنه limit xr n لما n تقول ل infinity
+
+430
+00:41:27,640 --> 00:41:35,720
+بساوي x وهذا هو المطلوب طبعا
+
+431
+00:41:35,720 --> 00:41:40,780
+في هنا أمثلة باقي شوية أمثلةفهذه الأمثلة يعني
+
+432
+00:41:40,780 --> 00:41:46,000
+حاولوا أنكم تقرؤوها في مثلين كيف نطبق النظرية هذه
+
+433
+00:41:46,000 --> 00:41:50,660
+أو نوجد العلاقة بين كيف نثبت ال convergence لل
+
+434
+00:41:50,660 --> 00:41:55,900
+sequence من خلال إثبات
+
+435
+00:41:55,900 --> 00:42:00,290
+ال convergence لل subsequences أو العكسفحاولوا
+
+436
+00:42:00,290 --> 00:42:04,490
+تقرؤوها و هيك نكون يعني تقريبا .. هنكمل ان شاء
+
+437
+00:42:04,490 --> 00:42:10,290
+الله المرة الجاية و .. هن .. هنوقف استخدام ال
+
+438
+00:42:10,290 --> 00:42:14,290
+powerpoint ابتداء من المحاضرة الجاية و هنشره على
+
+439
+00:42:14,290 --> 00:42:19,850
+اللغة okay انتهت المحاضرة نشوفكم ان شاء الله يوم
+
+440
+00:42:19,850 --> 00:42:20,250
+اتنين
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Nztl0T85AIM_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Nztl0T85AIM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..83bb1eec360fa4191f4b569258cbfe0d868d555c
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Nztl0T85AIM_raw.json
@@ -0,0 +1 @@
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"which means that for any real number a exactly one of the three possibilities holds either a belongs to p or a equals zero or negative a belongs to p بناء على هذه الخاصية شفنا أن الأعداد الحقيقية", "tokens": [13690, 1355, 300, 337, 604, 957, 1230, 257, 2293, 472, 295, 264, 1045, 12178, 9190, 2139, 257, 12953, 281, 280, 420, 257, 6915, 4018, 420, 3671, 257, 12953, 281, 280, 44945, 16606, 15844, 29538, 33962, 33546, 10632, 13412, 5172, 8315, 14739, 16247, 22488, 18513, 21542, 38436, 4587, 10632], "avg_logprob": -0.1847895456820118, "compression_ratio": 1.3314285714285714, "no_speech_prob": 0.0, "words": [{"start": 134.24, "end": 134.72, "word": "which", "probability": 0.10272216796875}, {"start": 134.72, "end": 135.28, "word": " means", "probability": 0.93115234375}, {"start": 135.28, "end": 135.68, "word": " that", "probability": 0.9052734375}, {"start": 135.68, "end": 136.0, "word": " for", "probability": 0.91552734375}, {"start": 136.0, "end": 136.32, "word": " any", "probability": 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188.15, "end": 188.65, "word": " عناصر", "probability": 0.9431966145833334}, {"start": 188.65, "end": 188.75, "word": " و", "probability": 0.74658203125}, {"start": 188.75, "end": 188.85, "word": " مش", "probability": 0.705078125}, {"start": 188.85, "end": 189.31, "word": " تلتين", "probability": 0.70758056640625}], "temperature": 1.0}, {"id": 7, "seek": 21521, "start": 190.41, "end": 215.21, "text": "واتحادهم بساوي ال R، لأن هذا بشكل تجزء على ال R، تجزء على ال R أو بنسميها في الرياضيات partition of R ال set P هذه سمنها set of positive real numbers وعرفنا negative P على إنها negative عناصر ال set P", "tokens": [2407, 9307, 5016, 18513, 16095, 4724, 3794, 995, 45865, 2423, 497, 12399, 5296, 33456, 23758, 4724, 8592, 28820, 6055, 7435, 11622, 38207, 15844, 2423, 497, 12399, 6055, 7435, 11622, 38207, 15844, 2423, 497, 34051, 44945, 38251, 1829, 11296, 8978, 2423, 16572, 46958, 1829, 9307, 24808, 295, 497, 2423, 992, 430, 29538, 8608, 27842, 11296, 992, 295, 3353, 957, 3547, 4032, 3615, 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"probability": 0.611328125}, {"start": 346.67, "end": 347.21, "word": " أكبر", "probability": 0.9757486979166666}, {"start": 347.21, "end": 347.45, "word": " من", "probability": 0.99560546875}, {"start": 347.45, "end": 347.73, "word": " A", "probability": 0.97119140625}, {"start": 347.73, "end": 349.51, "word": " and", "probability": 0.69677734375}, {"start": 349.51, "end": 350.43, "word": " C", "probability": 0.97802734375}, {"start": 350.43, "end": 351.51, "word": " أكبر", "probability": 0.9847005208333334}, {"start": 351.51, "end": 352.01, "word": " من", "probability": 0.99755859375}, {"start": 352.01, "end": 352.53, "word": " B", "probability": 0.9921875}, {"start": 352.53, "end": 355.79, "word": " فهذا", "probability": 0.9620768229166666}, {"start": 355.79, "end": 356.39, "word": " بيؤدي", "probability": 0.73486328125}, {"start": 356.39, "end": 356.91, "word": " أنه", "probability": 0.5548095703125}, {"start": 356.91, "end": 357.29, "word": " C", "probability": 0.98095703125}, 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أكبر من b هي a أكبر من b و b أكبر من c فبطلع c أو a بطلع أكبر من c", "tokens": [2304, 16095, 3660, 3714, 29245, 23328, 3660, 34105, 4117, 39896, 257, 5551, 4117, 26890, 9154, 272, 39896, 257, 5551, 4117, 26890, 9154, 272, 4032, 272, 5551, 4117, 26890, 9154, 269, 6156, 3555, 9566, 1211, 3615, 269, 34051, 257, 4724, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 269], "avg_logprob": -0.20279948599636555, "compression_ratio": 1.6904761904761905, "no_speech_prob": 0.0, "words": [{"start": 372.75, "end": 373.25, "word": "مهمة", "probability": 0.6067708333333334}, {"start": 373.25, "end": 373.79, "word": " موجودة", "probability": 0.861572265625}, {"start": 373.79, "end": 374.39, "word": " هناك", "probability": 0.989990234375}, {"start": 374.39, "end": 374.71, "word": " هي", "probability": 0.4970703125}, {"start": 374.71, "end": 375.29, "word": " a", "probability": 0.485595703125}, {"start": 375.29, "end": 376.07, "word": " أكبر", "probability": 0.9348958333333334}, {"start": 376.07, "end": 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0.9812825520833334}, {"start": 402.97, "end": 403.15, "word": " من", "probability": 0.97998046875}, {"start": 403.15, "end": 403.41, "word": " c", "probability": 0.77978515625}, {"start": 403.41, "end": 404.11, "word": " فهذه", "probability": 0.8095703125}, {"start": 404.11, "end": 404.57, "word": " بيسموها", "probability": 0.93994140625}, {"start": 404.57, "end": 404.75, "word": " في", "probability": 0.9384765625}, {"start": 404.75, "end": 405.27, "word": " الرياضيات", "probability": 0.921875}, {"start": 405.27, "end": 406.23, "word": " transitivity", "probability": 0.916748046875}, {"start": 406.23, "end": 407.17, "word": " أو", "probability": 0.740234375}, {"start": 407.17, "end": 407.63, "word": " خاصية", "probability": 0.9847005208333334}, {"start": 407.63, "end": 408.93, "word": " التعدى", "probability": 0.9635416666666666}, {"start": 408.93, "end": 410.73, "word": " الخاصية", "probability": 0.98486328125}, {"start": 410.73, "end": 413.99, "word": " التانية", "probability": 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"probability": 0.9931640625}, {"start": 432.13, "end": 432.49, "word": " b", "probability": 0.9609375}, {"start": 432.49, "end": 433.87, "word": " او", "probability": 0.864013671875}, {"start": 433.87, "end": 434.13, "word": " a", "probability": 0.986328125}, {"start": 434.13, "end": 435.01, "word": " بتساوي", "probability": 0.9217529296875}, {"start": 435.01, "end": 435.59, "word": " b", "probability": 0.9267578125}, {"start": 435.59, "end": 438.23, "word": " او", "probability": 0.958251953125}, {"start": 438.23, "end": 439.19, "word": " a", "probability": 0.98095703125}, {"start": 439.19, "end": 440.59, "word": " اصغر", "probability": 0.9403076171875}, {"start": 440.59, "end": 440.77, "word": " من", "probability": 0.998046875}, {"start": 440.77, "end": 441.15, "word": " b", "probability": 0.935546875}], "temperature": 1.0}, {"id": 17, "seek": 46840, "start": 443.02, "end": 468.4, "text": "لأي عددين حقيقيين A وB واحد فقط من الاحتمالات التلاتة بيكون صحيح وهو اما A أكبر من B أو A بساوي B أو A أصغر من B الـ Antisymmetry property علاقة أكبر من أو ساويها دي بنسميها Antisymmetric يعني ايه؟ بتحقق خاصية تضاد التماثل", "tokens": [1211, 10721, 1829, 6225, 3215, 3215, 9957, 11331, 38436, 38436, 9957, 316, 4032, 33, 36764, 24401, 6156, 47432, 9154, 42963, 33753, 2304, 6027, 9307, 16712, 1211, 9307, 3660, 4724, 1829, 30544, 20328, 5016, 1829, 5016, 37037, 2407, 1975, 15042, 316, 5551, 4117, 26890, 9154, 363, 34051, 316, 4724, 3794, 995, 45865, 363, 34051, 316, 5551, 9381, 17082, 2288, 9154, 363, 2423, 39184, 5130, 14169, 2174, 9889, 4707, 11203, 995, 28671, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 11296, 11778, 1829, 44945, 38251, 1829, 11296, 5130, 14169, 2174, 17475, 37495, 22653, 1975, 1829, 3224, 22807, 39894, 5016, 4587, 4587, 16490, 33546, 10632, 6055, 11242, 18513, 16712, 2304, 5718, 104, 1211], "avg_logprob": -0.15850224876189017, "compression_ratio": 1.651376146788991, "no_speech_prob": 0.0, "words": [{"start": 443.02000000000004, "end": 443.98, "word": "لأي", 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0.82275390625}, {"start": 451.56, "end": 451.86, "word": " اما", "probability": 0.783935546875}, {"start": 451.86, "end": 452.04, "word": " A", "probability": 0.7568359375}, {"start": 452.04, "end": 452.4, "word": " أكبر", "probability": 0.9031575520833334}, {"start": 452.4, "end": 452.6, "word": " من", "probability": 0.95556640625}, {"start": 452.6, "end": 452.8, "word": " B", "probability": 0.9443359375}, {"start": 452.8, "end": 453.08, "word": " أو", "probability": 0.6923828125}, {"start": 453.08, "end": 453.26, "word": " A", "probability": 0.9208984375}, {"start": 453.26, "end": 453.74, "word": " بساوي", "probability": 0.891845703125}, {"start": 453.74, "end": 454.02, "word": " B", "probability": 0.85888671875}, {"start": 454.02, "end": 454.3, "word": " أو", "probability": 0.76611328125}, {"start": 454.3, "end": 454.46, "word": " A", "probability": 0.95654296875}, {"start": 454.46, "end": 454.88, "word": " أصغر", "probability": 0.832275390625}, {"start": 454.88, "end": 455.04, 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Antisymmetric", "probability": 0.8541259765625}, {"start": 464.72, "end": 465.04, "word": " يعني", "probability": 0.941162109375}, {"start": 465.04, "end": 465.7, "word": " ايه؟", "probability": 0.719482421875}, {"start": 465.7, "end": 466.3, "word": " بتحقق", "probability": 0.91064453125}, {"start": 466.3, "end": 466.98, "word": " خاصية", "probability": 0.9786783854166666}, {"start": 466.98, "end": 467.64, "word": " تضاد", "probability": 0.87890625}, {"start": 467.64, "end": 468.4, "word": " التماثل", "probability": 0.95380859375}], "temperature": 1.0}, {"id": 18, "seek": 48824, "start": 469.76, "end": 488.24, "text": "إيه يعني؟ مع أن لو كانت A على علاقة مع B و B على علاقة مع A فلازم يطلع A بساوي B، A أكبر من أو ساوي B و B أكبر من أو ساوي A فلازم A ساوي B، هذي بنسميها Anti-symmetry property", "tokens": [28814, 1829, 3224, 37495, 22653, 22807, 20449, 14739, 45164, 25961, 2655, 316, 15844, 11203, 995, 28671, 20449, 363, 4032, 363, 15844, 11203, 995, 28671, 20449, 316, 6156, 1211, 31377, 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"seek": 50654, "start": 489.92, "end": 506.54, "text": "هنا الخاصية هذه لو كان a أكبر من b وضفت للطرفين أي عدد c فالمتباينة تبقى زي ما هي شريتها زي ما هي طيب لو في عندي متباينة a أكبر من b لان نتحدث عن متباينات inequalities", "tokens": [3224, 8315, 33962, 33546, 10632, 29538, 45164, 25961, 257, 5551, 4117, 26890, 9154, 272, 4032, 11242, 5172, 2655, 24976, 9566, 28480, 9957, 36632, 6225, 3215, 3215, 269, 6156, 45340, 2655, 3555, 995, 9957, 3660, 6055, 3555, 4587, 7578, 30767, 1829, 19446, 39896, 13412, 16572, 2655, 11296, 30767, 1829, 19446, 39896, 23032, 1829, 3555, 45164, 8978, 18871, 16254, 44650, 3555, 995, 9957, 3660, 257, 5551, 4117, 26890, 9154, 272, 5296, 7649, 8717, 2655, 24401, 12984, 18871, 44650, 3555, 995, 9957, 9307, 41874], "avg_logprob": -0.16082317054998585, "compression_ratio": 1.6529411764705881, "no_speech_prob": 0.0, "words": [{"start": 489.92, "end": 490.56, "word": "هنا", "probability": 0.653564453125}, {"start": 490.56, "end": 491.2, "word": " الخاصية", 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المتباينة تبقى كما هي لكن لو ضربت المتباينة في عدد سالب إشارة المتباينة تناكز الخاصية f بتقول أنه لأي عدد حقيقي لا يساوي سفر مربع أي عدد حقيقي لا يساوي سفر دائما بيكون عدد موجب الواحد", "tokens": [1211, 2407, 25961, 257, 5551, 4117, 26890, 9154, 272, 4032, 269, 6225, 3215, 3215, 3714, 29245, 3555, 4032, 11242, 25513, 2655, 41950, 28480, 9957, 8978, 6225, 3215, 3215, 9673, 29245, 3555, 269, 6156, 28814, 8592, 9640, 3660, 9673, 2655, 3555, 995, 9957, 3660, 6055, 3555, 4587, 7578, 9122, 15042, 39896, 44381, 45164, 48812, 25513, 2655, 9673, 2655, 3555, 995, 9957, 3660, 8978, 6225, 3215, 3215, 8608, 6027, 3555, 11933, 8592, 9640, 3660, 9673, 2655, 3555, 995, 9957, 3660, 6055, 8315, 4117, 11622, 33962, 33546, 10632, 283, 39894, 39648, 14739, 3224, 5296, 10721, 1829, 6225, 3215, 3215, 11331, 38436, 38436, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 3714, 25513, 3615, 36632, 6225, 3215, 3215, 11331, 38436, 38436, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 11778, 16373, 15042, 4724, 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المعطيات", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 26, "seek": 69804, "start": 669.24, "end": 698.04, "text": "طيب set P closed under addition مغلقة تحت عملية الجمع إذا مجموعة أنصرين في P بيطلع أنصر تالت في P هذا الأنصر التالت اللي بيقول المجموعة طلع A سالب C هذا معناه مادام الفرخ هذا تملى P معناته الفرخ هذا موجب أو A أكبر من C as required كما هو مطلوب، مظبوط؟ واضح؟ طيب", "tokens": [9566, 1829, 3555, 992, 430, 5395, 833, 4500, 3714, 17082, 1211, 28671, 6055, 33753, 6225, 42213, 10632, 25724, 2304, 3615, 11933, 15730, 3714, 7435, 2304, 2407, 27884, 14739, 9381, 2288, 9957, 8978, 430, 4724, 1829, 9566, 1211, 3615, 14739, 9381, 2288, 6055, 6027, 2655, 8978, 430, 23758, 16247, 1863, 9381, 2288, 16712, 6027, 2655, 13672, 1829, 4724, 1829, 39648, 9673, 7435, 2304, 2407, 27884, 23032, 1211, 3615, 316, 8608, 6027, 3555, 383, 23758, 20449, 8315, 3224, 3714, 18513, 10943, 27188, 2288, 9778, 23758, 46811, 23942, 430, 20449, 8315, 47395, 27188, 2288, 9778, 23758, 3714, 29245, 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{"start": 684.36, "end": 684.82, "word": " الفرخ", "probability": 0.7374674479166666}, {"start": 684.82, "end": 685.08, "word": " هذا", "probability": 0.72900390625}, {"start": 685.08, "end": 685.66, "word": " تملى", "probability": 0.5025634765625}, {"start": 685.66, "end": 686.0, "word": " P", "probability": 0.7607421875}, {"start": 686.0, "end": 687.18, "word": " معناته", "probability": 0.8434244791666666}, {"start": 687.18, "end": 688.32, "word": " الفرخ", "probability": 0.9734700520833334}, {"start": 688.32, "end": 688.56, "word": " هذا", "probability": 0.7529296875}, {"start": 688.56, "end": 689.08, "word": " موجب", "probability": 0.9549153645833334}, {"start": 689.08, "end": 689.44, "word": " أو", "probability": 0.77099609375}, {"start": 689.44, "end": 689.78, "word": " A", "probability": 0.884765625}, {"start": 689.78, "end": 690.22, "word": " أكبر", "probability": 0.9453125}, {"start": 690.22, "end": 690.46, "word": " من", "probability": 0.98388671875}, {"start": 690.46, "end": 690.82, "word": " C", "probability": 0.97607421875}, {"start": 690.82, "end": 692.2, "word": " as", "probability": 0.826171875}, {"start": 692.2, "end": 692.76, "word": " required", "probability": 0.81591796875}, {"start": 692.76, "end": 693.18, "word": " كما", "probability": 0.889404296875}, {"start": 693.18, "end": 693.38, "word": " هو", "probability": 0.99462890625}, {"start": 693.38, "end": 693.9, "word": " مطلوب،", "probability": 0.82578125}, {"start": 693.9, "end": 694.86, "word": " مظبوط؟", "probability": 0.8692220052083334}, {"start": 694.86, "end": 697.42, "word": " واضح؟", "probability": 0.79425048828125}, {"start": 697.42, "end": 698.04, "word": " طيب", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 27, "seek": 72560, "start": 702.86, "end": 725.6, "text": "أي عدد حقيقي له واحد من تلت احتمالات اما موجب او سفر او سالب الان بناء على هذه الخاصية ممكن نثبت الخاصية الثلاثية الخاصية بي", "tokens": [10721, 1829, 6225, 3215, 3215, 11331, 38436, 38436, 46740, 36764, 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"probability": 0.7218424479166666}, {"start": 707.72, "end": 708.42, "word": " احتمالات", "probability": 0.9404296875}, {"start": 708.42, "end": 708.78, "word": " اما", "probability": 0.6053466796875}, {"start": 708.78, "end": 709.7, "word": " موجب", "probability": 0.87841796875}, {"start": 709.7, "end": 709.94, "word": " او", "probability": 0.879150390625}, {"start": 709.94, "end": 710.32, "word": " سفر", "probability": 0.8610026041666666}, {"start": 710.32, "end": 710.52, "word": " او", "probability": 0.959228515625}, {"start": 710.52, "end": 710.98, "word": " سالب", "probability": 0.8543294270833334}, {"start": 710.98, "end": 713.06, "word": " الان", "probability": 0.531036376953125}, {"start": 713.06, "end": 713.8, "word": " بناء", "probability": 0.78466796875}, {"start": 713.8, "end": 714.02, "word": " على", "probability": 0.83642578125}, {"start": 714.02, "end": 714.34, "word": " هذه", "probability": 0.96337890625}, {"start": 714.34, "end": 715.02, "word": " الخاصية", "probability": 0.9381510416666666}, {"start": 715.02, "end": 716.12, "word": " ممكن", "probability": 0.856689453125}, {"start": 716.12, "end": 716.72, "word": " نثبت", "probability": 0.8944091796875}, {"start": 716.72, "end": 717.52, "word": " الخاصية", "probability": 0.9837239583333334}, {"start": 717.52, "end": 718.5, "word": " الثلاثية", "probability": 0.9052734375}, {"start": 718.5, "end": 721.94, "word": " الخاصية", "probability": 0.8248697916666666}, {"start": 721.94, "end": 725.6, "word": " بي", "probability": 0.5260009765625}], "temperature": 1.0}, {"id": 28, "seek": 75387, "start": 729.23, "end": 753.87, "text": "قلنا إن لو كان لأي عددين حقيقيين لأي عددين حقيقيين a و b، a أكبر من b أو a بساوي b أو a أصغر من b فالبرهان ذلك بيعتمد على ال try-cutting property اللي شفناها قبل شوية فأنا عندي", "tokens": [4587, 1211, 8315, 36145, 45164, 25961, 5296, 10721, 1829, 6225, 3215, 3215, 9957, 11331, 38436, 38436, 9957, 5296, 10721, 1829, 6225, 3215, 3215, 9957, 11331, 38436, 38436, 9957, 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"word": " حقيقيين", "probability": 0.8035888671875}, {"start": 732.37, "end": 734.05, "word": " لأي", "probability": 0.7899576822916666}, {"start": 734.05, "end": 734.45, "word": " عددين", "probability": 0.9293212890625}, {"start": 734.45, "end": 735.03, "word": " حقيقيين", "probability": 0.9283447265625}, {"start": 735.03, "end": 735.19, "word": " a", "probability": 0.5009765625}, {"start": 735.19, "end": 735.35, "word": " و", "probability": 0.7568359375}, {"start": 735.35, "end": 735.95, "word": " b،", "probability": 0.33154296875}, {"start": 735.95, "end": 736.11, "word": " a", "probability": 0.80126953125}, {"start": 736.11, "end": 736.57, "word": " أكبر", "probability": 0.9685872395833334}, {"start": 736.57, "end": 736.77, "word": " من", "probability": 0.97705078125}, {"start": 736.77, "end": 736.99, "word": " b", "probability": 0.9658203125}, {"start": 736.99, "end": 737.27, "word": " أو", "probability": 0.9228515625}, {"start": 737.27, "end": 737.47, "word": " a", "probability": 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من B", "tokens": [5016, 35457, 2423, 39184, 504, 480, 310, 8488, 4707, 12399, 45164, 5551, 9778, 3215, 2655, 27188, 2288, 4587, 23758, 12399, 23758, 957, 1230, 6156, 10721, 1829, 957, 1230, 11933, 15042, 3353, 34051, 4724, 3794, 995, 45865, 8608, 5172, 2288, 34051, 3671, 12399, 20328, 5016, 22807, 37037, 15730, 4724, 4117, 31845, 19986, 12399, 2423, 28820, 10943, 23758, 4724, 4117, 31845, 19986, 316, 8608, 6027, 3555, 363, 7251, 29399, 2304, 1829, 5296, 363, 4724, 4117, 31845, 19986, 14739, 3224, 2423, 39184, 316, 5551, 4117, 26890, 9154, 363], "avg_logprob": -0.20530523688987243, "compression_ratio": 1.5, "no_speech_prob": 0.0, "words": [{"start": 757.89, "end": 758.41, "word": "حسب", "probability": 0.865966796875}, {"start": 758.41, "end": 758.69, "word": " الـ", "probability": 0.4697265625}, {"start": 758.69, "end": 759.13, "word": " trichotomy", "probability": 0.6727294921875}, {"start": 759.13, "end": 759.87, "word": " property،", "probability": 0.54052734375}, {"start": 759.87, 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"طب وهذا ينتمي لـ 0 بكافة أن a بساوي b أو الفرق بساوي 0 وبالتالي a بساوي b و الفرق هذا ينتمي ل negative b معناته الفرق هذا سالب يعني معناه أن a أصغر من b وهذا اللي بدنا إياه هذا اللي بدنا إياه طيب الجزء C قلنا اللي هو ال antisymmetry property", "tokens": [9566, 3555, 37037, 15730, 7251, 29399, 2304, 1829, 5296, 39184, 1958, 4724, 4117, 31845, 3660, 14739, 257, 4724, 3794, 995, 45865, 272, 34051, 27188, 2288, 4587, 4724, 3794, 995, 45865, 1958, 46599, 6027, 2655, 6027, 1829, 257, 4724, 3794, 995, 45865, 272, 4032, 27188, 2288, 4587, 23758, 7251, 29399, 2304, 1829, 5296, 3671, 272, 20449, 8315, 47395, 27188, 2288, 4587, 23758, 8608, 6027, 3555, 37495, 22653, 20449, 8315, 3224, 14739, 257, 5551, 9381, 17082, 2288, 9154, 272, 37037, 15730, 13672, 1829, 47525, 8315, 11933, 25528, 3224, 23758, 13672, 1829, 47525, 8315, 11933, 25528, 3224, 23032, 1829, 3555, 25724, 11622, 38207, 383, 12174, 1211, 8315, 13672, 1829, 31439, 2423, 2511, 14169, 2174, 9889, 4707], "avg_logprob": 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797.24, "end": 798.66, "word": " وهذا", "probability": 0.783935546875}, {"start": 798.66, "end": 798.78, "word": " اللي", "probability": 0.918701171875}, {"start": 798.78, "end": 799.08, "word": " بدنا", "probability": 0.942138671875}, {"start": 799.08, "end": 799.4, "word": " إياه", "probability": 0.6841227213541666}, {"start": 799.4, "end": 799.74, "word": " هذا", "probability": 0.282470703125}, {"start": 799.74, "end": 799.94, "word": " اللي", "probability": 0.9912109375}, {"start": 799.94, "end": 800.38, "word": " بدنا", "probability": 0.981201171875}, {"start": 800.38, "end": 801.76, "word": " إياه", "probability": 0.9713541666666666}, {"start": 801.76, "end": 805.62, "word": " طيب", "probability": 0.7953287760416666}, {"start": 805.62, "end": 806.16, "word": " الجزء", "probability": 0.9654947916666666}, {"start": 806.16, "end": 806.58, "word": " C", "probability": 0.62548828125}, {"start": 806.58, "end": 808.34, "word": " قلنا", "probability": 0.796875}, {"start": 808.34, "end": 808.6, "word": " اللي", "probability": 0.92578125}, {"start": 808.6, "end": 808.9, "word": " هو", "probability": 0.990234375}, {"start": 808.9, "end": 809.48, "word": " ال", "probability": 0.7451171875}, {"start": 809.48, "end": 810.48, "word": " antisymmetry", "probability": 0.69891357421875}, {"start": 810.48, "end": 811.08, "word": " property", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 31, "seek": 83221, "start": 812.07, "end": 832.21, "text": "الـ Anti-symmetry property نفكركم فيها بتقول لو كان a أكبر من أو يساوي b and b أكبر من أو يساوي a فهذا بيعدي أن a بساوي b، بظبط؟ طيب", "tokens": [6027, 39184, 27757, 12, 3187, 2174, 9889, 4707, 8717, 5172, 37983, 24793, 8978, 11296, 39894, 39648, 45164, 25961, 257, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 272, 293, 272, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 257, 6156, 3224, 15730, 4724, 1829, 3615, 16254, 14739, 257, 4724, 3794, 995, 45865, 272, 12399, 4724, 19913, 3555, 9566, 22807, 23032, 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{"start": 839.85, "end": 840.39, "word": " هذه", "probability": 0.409912109375}, {"start": 840.39, "end": 841.73, "word": " النتيجة،", "probability": 0.85888671875}, {"start": 841.73, "end": 842.37, "word": " فبدأ", "probability": 0.7018229166666666}, {"start": 842.37, "end": 842.57, "word": " أعمل", "probability": 0.9124348958333334}, {"start": 842.57, "end": 842.93, "word": " برهان", "probability": 0.9278564453125}, {"start": 842.93, "end": 844.47, "word": " بالتناقض،", "probability": 0.9052734375}, {"start": 844.47, "end": 845.11, "word": " فبرهان", "probability": 0.8619384765625}, {"start": 845.11, "end": 845.81, "word": " بالتناقض", "probability": 0.98349609375}, {"start": 845.81, "end": 846.27, "word": " دائما", "probability": 0.85205078125}, {"start": 846.27, "end": 847.31, "word": " نفرض", "probability": 0.7525227864583334}, {"start": 847.31, "end": 847.75, "word": " مافيه", "probability": 0.528564453125}, {"start": 847.75, "end": 848.45, "word": " النتيجة", "probability": 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"probability": 0.84521484375}, {"start": 1661.74, "end": 1662.34, "word": " نتيجة", "probability": 0.8770751953125}, {"start": 1662.34, "end": 1662.48, "word": " اللي", "probability": 0.786376953125}, {"start": 1662.48, "end": 1663.02, "word": " بعدها", "probability": 0.954833984375}], "temperature": 1.0}, {"id": 62, "seek": 169412, "start": 1664.72, "end": 1694.12, "text": "أو أهميتها تظهر في النتيجة اللي بعدها اللي هي corollary 171 corollary 171 بيقول أن أي عدد موجب بيكون أكبر من نصه اللي هو موجب أي عدد حقيقي موجب دايما أكبر من نصه", "tokens": [10721, 2407, 5551, 16095, 36081, 11296, 6055, 19913, 3224, 2288, 8978, 28239, 31371, 7435, 3660, 13672, 1829, 39182, 11296, 13672, 1829, 39896, 1181, 1833, 822, 3282, 16, 1181, 1833, 822, 3282, 16, 4724, 1829, 39648, 14739, 36632, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 1829, 30544, 5551, 4117, 26890, 9154, 8717, 9381, 3224, 13672, 1829, 31439, 3714, 29245, 3555, 36632, 6225, 3215, 3215, 11331, 38436, 38436, 3714, 29245, 3555, 11778, 47302, 15042, 5551, 4117, 26890, 9154, 8717, 9381, 3224], "avg_logprob": -0.15947266332805157, "compression_ratio": 1.7161290322580645, "no_speech_prob": 0.0, "words": [{"start": 1664.72, "end": 1665.08, "word": "أو", "probability": 0.75}, {"start": 1665.08, "end": 1666.34, "word": " أهميتها", "probability": 0.7872314453125}, {"start": 1666.34, "end": 1666.82, "word": " تظهر", "probability": 0.995849609375}, {"start": 1666.82, "end": 1666.96, "word": " في", "probability": 0.94189453125}, {"start": 1666.96, "end": 1667.44, "word": " النتيجة", "probability": 0.9453125}, {"start": 1667.44, "end": 1667.58, "word": " اللي", "probability": 0.828125}, {"start": 1667.58, "end": 1668.16, "word": " بعدها", "probability": 0.916015625}, {"start": 1668.16, "end": 1669.02, "word": " اللي", "probability": 0.807861328125}, {"start": 1669.02, "end": 1669.28, "word": " هي", "probability": 0.90673828125}, {"start": 1669.28, "end": 1669.88, "word": " corollary", "probability": 0.8069661458333334}, {"start": 1669.88, "end": 1671.34, "word": " 171", "probability": 0.4144287109375}, {"start": 1671.34, "end": 1673.58, "word": " corollary", "probability": 0.70947265625}, {"start": 1673.58, "end": 1674.34, "word": " 171", "probability": 0.951904296875}, {"start": 1674.34, "end": 1676.12, "word": " بيقول", "probability": 0.96923828125}, {"start": 1676.12, "end": 1684.62, "word": " أن", "probability": 0.36474609375}, {"start": 1684.62, "end": 1686.4, "word": " أي", "probability": 0.45556640625}, {"start": 1686.4, "end": 1686.88, "word": " عدد", "probability": 0.9850260416666666}, {"start": 1686.88, "end": 1687.48, "word": " موجب", "probability": 0.98486328125}, {"start": 1687.48, "end": 1688.28, "word": " بيكون", "probability": 0.7838541666666666}, {"start": 1688.28, "end": 1688.9, "word": " أكبر", "probability": 0.9679361979166666}, {"start": 1688.9, "end": 1689.16, "word": " من", "probability": 0.99658203125}, {"start": 1689.16, "end": 1689.8, "word": " نصه", "probability": 0.99365234375}, 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1720.0, "text": "وبالتالي هذا معناه في رياضيات أن الأعداد الحقيقية الموجبة مالهاش smallest element مافيش .. لو أخدت الأعداد الحقيقية الموجبة اللي هي set P فهذا ال set ماقدرش أحط أصبعي على أصغر عنصر فيها مالهاش أصغر عنصر", "tokens": [37746, 6027, 2655, 6027, 1829, 23758, 20449, 8315, 3224, 8978, 12602, 1829, 46958, 1829, 9307, 14739, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 9673, 29245, 49401, 19446, 43761, 33599, 16998, 4478, 19446, 41185, 8592, 4386, 45164, 5551, 9778, 3215, 2655, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 9673, 29245, 49401, 13672, 1829, 39896, 992, 430, 6156, 3224, 15730, 2423, 992, 19446, 28543, 2288, 8592, 5551, 5016, 9566, 5551, 9381, 3555, 3615, 1829, 15844, 5551, 9381, 17082, 2288, 18871, 9381, 2288, 8978, 11296, 19446, 43761, 33599, 5551, 9381, 17082, 2288, 18871, 9381, 2288], "avg_logprob": -0.15650201612903225, "compression_ratio": 1.8548387096774193, "no_speech_prob": 0.0, "words": [{"start": 1695.24, "end": 1696.16, "word": "وبالتالي", "probability": 0.9423828125}, {"start": 1696.16, "end": 1696.54, "word": " هذا", "probability": 0.77294921875}, {"start": 1696.54, "end": 1697.26, "word": " معناه", "probability": 0.9249674479166666}, {"start": 1697.26, "end": 1698.52, "word": " في", "probability": 0.83349609375}, {"start": 1698.52, "end": 1699.28, "word": " رياضيات", "probability": 0.8931640625}, {"start": 1699.28, "end": 1700.36, "word": " أن", "probability": 0.51904296875}, {"start": 1700.36, "end": 1701.12, "word": " الأعداد", "probability": 0.9080403645833334}, {"start": 1701.12, "end": 1701.82, "word": " الحقيقية", "probability": 0.9617919921875}, {"start": 1701.82, "end": 1702.42, "word": " الموجبة", "probability": 0.9847005208333334}, {"start": 1702.42, "end": 1703.2, "word": " مالهاش", "probability": 0.6520182291666666}, {"start": 1703.2, "end": 1703.76, "word": " smallest", "probability": 0.98046875}, {"start": 1703.76, "end": 1704.3, "word": " element", "probability": 0.96923828125}, {"start": 1704.3, "end": 1706.18, "word": " مافيش", "probability": 0.9187825520833334}, {"start": 1706.18, "end": 1706.48, "word": " ..", "probability": 0.32958984375}, {"start": 1706.48, "end": 1706.9, "word": " لو", "probability": 0.90283203125}, {"start": 1706.9, "end": 1707.22, "word": " أخدت", "probability": 0.9130859375}, {"start": 1707.22, "end": 1707.52, "word": " الأعداد", "probability": 0.9508463541666666}, {"start": 1707.52, "end": 1707.96, "word": " الحقيقية", "probability": 0.9677734375}, {"start": 1707.96, "end": 1708.62, "word": " الموجبة", "probability": 0.99560546875}, {"start": 1708.62, "end": 1709.96, "word": " اللي", "probability": 0.85888671875}, {"start": 1709.96, "end": 1710.16, "word": " هي", "probability": 0.89306640625}, {"start": 1710.16, "end": 1710.54, "word": " set", "probability": 0.259521484375}, {"start": 1710.54, "end": 1710.96, "word": " P", "probability": 0.7529296875}, {"start": 1710.96, "end": 1713.16, "word": " فهذا", "probability": 0.677978515625}, {"start": 1713.16, "end": 1713.32, "word": " ال", "probability": 0.5791015625}, {"start": 1713.32, "end": 1713.62, "word": " set", "probability": 0.8798828125}, {"start": 1713.62, "end": 1714.28, "word": " ماقدرش", "probability": 0.9022216796875}, {"start": 1714.28, "end": 1714.64, "word": " أحط", "probability": 0.9308268229166666}, {"start": 1714.64, "end": 1715.2, "word": " أصبعي", "probability": 0.819287109375}, {"start": 1715.2, "end": 1715.38, "word": " على", "probability": 0.8759765625}, {"start": 1715.38, "end": 1715.76, "word": " أصغر", "probability": 0.99267578125}, {"start": 1715.76, "end": 1716.14, "word": " عنصر", "probability": 0.8846028645833334}, {"start": 1716.14, "end": 1716.48, "word": " فيها", "probability": 0.856201171875}, {"start": 1716.48, "end": 1717.94, "word": " مالهاش", "probability": 0.7669270833333334}, {"start": 1717.94, "end": 1719.52, "word": " أصغر", "probability": 0.9942626953125}, {"start": 1719.52, "end": 1720.0, "word": " عنصر", "probability": 0.9861653645833334}], "temperature": 1.0}, {"id": 64, "seek": 174562, "start": 1720.96, "end": 1745.62, "text": "has no smallest element لأن لو أخدت أي عنصر موجب و سميته a فبقدر ألاقي عدد موجب أخر أصغر منه اللي هو نصف فبالتالي ال set of positive numbers has no strictly positive element تمام؟ البرهان تبع الكرولري هذا بينتج من نظرية", "tokens": [12438, 572, 16998, 4478, 5296, 33456, 45164, 5551, 9778, 3215, 2655, 36632, 18871, 9381, 2288, 3714, 29245, 3555, 4032, 8608, 2304, 36081, 3224, 257, 6156, 3555, 28543, 2288, 5551, 15040, 38436, 6225, 3215, 3215, 3714, 29245, 3555, 5551, 34740, 5551, 9381, 17082, 2288, 9154, 3224, 13672, 1829, 31439, 8717, 9381, 5172, 6156, 3555, 6027, 2655, 6027, 1829, 2423, 992, 295, 3353, 3547, 575, 572, 20792, 3353, 4478, 46811, 10943, 22807, 29739, 2288, 3224, 7649, 6055, 3555, 3615, 33251, 2288, 12610, 16572, 23758, 4724, 9957, 2655, 7435, 9154, 8717, 19913, 2288, 10632], "avg_logprob": -0.19191576232728752, "compression_ratio": 1.5115207373271888, "no_speech_prob": 0.0, "words": [{"start": 1720.96, "end": 1721.42, "word": "has", "probability": 0.110595703125}, {"start": 1721.42, "end": 1721.78, "word": " no", "probability": 0.951171875}, {"start": 1721.78, "end": 1722.36, "word": " smallest", "probability": 0.99365234375}, {"start": 1722.36, "end": 1722.82, "word": " element", "probability": 0.9140625}, {"start": 1722.82, "end": 1723.18, "word": " لأن", "probability": 0.743896484375}, {"start": 1723.18, "end": 1723.32, "word": " لو", "probability": 0.80517578125}, {"start": 1723.32, "end": 1723.76, "word": " أخدت", "probability": 0.9542236328125}, {"start": 1723.76, "end": 1724.04, "word": " أي", "probability": 0.81787109375}, {"start": 1724.04, "end": 1724.82, "word": " عنصر", "probability": 0.98095703125}, {"start": 1724.82, "end": 1725.88, "word": " موجب", "probability": 0.9737955729166666}, {"start": 1725.88, "end": 1726.2, "word": " و", "probability": 0.7451171875}, {"start": 1726.2, "end": 1726.84, "word": " سميته", "probability": 0.783416748046875}, {"start": 1726.84, "end": 1727.12, "word": " a", "probability": 0.404052734375}, {"start": 1727.12, "end": 1728.58, "word": " فبقدر", "probability": 0.9307861328125}, {"start": 1728.58, "end": 1729.08, "word": " ألاقي", "probability": 0.8517252604166666}, {"start": 1729.08, "end": 1729.7, "word": " عدد", "probability": 0.9453125}, {"start": 1729.7, "end": 1730.18, "word": " موجب", "probability": 0.9954427083333334}, {"start": 1730.18, "end": 1730.7, "word": " أخر", "probability": 0.73828125}, {"start": 1730.7, "end": 1731.22, "word": " أصغر", "probability": 0.9842529296875}, {"start": 1731.22, "end": 1731.6, "word": " منه", "probability": 0.991455078125}, {"start": 1731.6, "end": 1731.8, "word": " اللي", "probability": 0.91455078125}, {"start": 1731.8, "end": 1732.0, "word": " هو", "probability": 0.9853515625}, {"start": 1732.0, "end": 1732.58, "word": " نصف", "probability": 0.8181966145833334}, {"start": 1732.58, "end": 1734.2, "word": " فبالتالي", "probability": 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3660, 39896, 6055, 8592, 38688, 11296, 20449, 45030, 11242, 8717, 19913, 2288, 10632, 36764, 24401, 8608, 2655, 3660, 45164, 5551, 9778, 3215, 2655, 4724, 1829, 4724, 3794, 995, 2407, 3660, 8608, 5172, 2288, 6156, 3555, 9566, 1211, 3615, 1975, 1975, 4117, 26890, 9154, 8717, 9381, 1975, 1975, 4117, 26890, 9154, 8608, 5172, 2288, 1975, 15730, 29538, 8717, 31371, 7435, 3660, 8608, 16572, 27884, 3714, 19913, 3555, 2407, 9566], "avg_logprob": -0.1788366401549613, "compression_ratio": 1.9415584415584415, "no_speech_prob": 0.0, "words": [{"start": 1746.38, "end": 1746.82, "word": "يعني", "probability": 0.673828125}, {"start": 1746.82, "end": 1747.34, "word": " خد", "probability": 0.6273193359375}, {"start": 1747.34, "end": 1747.92, "word": " بي", "probability": 0.703857421875}, {"start": 1747.92, "end": 1748.26, "word": " بساوة", "probability": 0.676123046875}, {"start": 1748.26, "end": 1748.6, "word": " سفر", "probability": 0.9020182291666666}, {"start": 1748.6, "end": 1748.74, "word": " 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1925.61, "end": 1926.67, "word": " صح", "probability": 0.99609375}, {"start": 1926.67, "end": 1927.21, "word": " بناء", "probability": 0.775390625}, {"start": 1927.21, "end": 1927.47, "word": " على", "probability": 0.82080078125}, {"start": 1927.47, "end": 1927.71, "word": " أن", "probability": 0.5546875}, {"start": 1927.71, "end": 1928.25, "word": " الفرض", "probability": 0.888916015625}, {"start": 1928.25, "end": 1928.65, "word": " a", "probability": 0.88134765625}, {"start": 1928.65, "end": 1929.11, "word": " أكبر", "probability": 0.98046875}, {"start": 1929.11, "end": 1929.25, "word": " من", "probability": 0.97509765625}, {"start": 1929.25, "end": 1929.35, "word": " أكبر", "probability": 0.8131510416666666}, {"start": 1929.35, "end": 1929.47, "word": " من", "probability": 0.1610107421875}, {"start": 1929.47, "end": 1929.89, "word": " صفر", "probability": 0.85205078125}, {"start": 1929.89, "end": 1930.13, "word": " وما", "probability": 0.604736328125}, {"start": 1930.13, "end": 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مشكلة تمام؟ إذا العبارة هذه صحيحة عند N بالساوي واحد الآن نفرض أن العبارة صحيحة عند N بالساوي K حيث K أكبر من واحد", "tokens": [6027, 9566, 28480, 25124, 2304, 6027, 36764, 24401, 30767, 16373, 3215, 1783, 16070, 9566, 28480, 2423, 32640, 9957, 4724, 43042, 3224, 36764, 24401, 30767, 16373, 3215, 1783, 6156, 3555, 9566, 1211, 3615, 47524, 995, 14407, 3660, 4032, 9566, 3555, 3615, 995, 9673, 3794, 995, 14407, 3660, 4724, 28543, 2288, 47525, 1211, 11296, 4724, 10721, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 19446, 41185, 37893, 28820, 3660, 46811, 10943, 22807, 11933, 15730, 18863, 3555, 9640, 3660, 29538, 20328, 5016, 1829, 5016, 3660, 43242, 426, 20666, 3794, 995, 45865, 36764, 24401, 6024, 48506, 8717, 5172, 43042, 14739, 18863, 3555, 9640, 3660, 20328, 5016, 1829, 5016, 3660, 43242, 426, 20666, 3794, 995, 45865, 591, 11331, 1829, 12984, 591, 5551, 4117, 26890, 9154, 36764, 24401], "avg_logprob": -0.19480020052096883, "compression_ratio": 2.050251256281407, "no_speech_prob": 0.0, 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"probability": 0.93408203125}, {"start": 2665.94, "end": 2666.5, "word": " تبعتي", "probability": 0.953125}], "temperature": 1.0}, {"id": 100, "seek": 269350, "start": 2667.94, "end": 2693.5, "text": "فبارضه في ال homework هذا موجود ل .. مش ل ال section هذا لكل ال .. المنهج اذا نبدأ نحل المسائل هذه و ان شاء الله لسبوع الجاي بنعمل مناقشة فانا هعمل مناقشة .. انا اللي هكون مناقشة لكم اليوم لأ مافيش مناقشة لأنه لسه احنا يعني ماخدناش material كافية", "tokens": [5172, 3555, 9640, 11242, 3224, 8978, 2423, 14578, 23758, 3714, 29245, 23328, 5296, 4386, 37893, 5296, 2423, 3541, 23758, 5296, 28820, 2423, 4386, 2423, 27842, 3224, 7435, 1975, 15730, 8717, 44510, 10721, 8717, 5016, 1211, 9673, 3794, 16373, 1211, 29538, 4032, 16472, 13412, 16606, 21984, 5296, 35457, 45367, 25724, 47302, 44945, 25957, 1211, 3714, 8315, 4587, 8592, 3660, 6156, 7649, 995, 8032, 25957, 1211, 3714, 8315, 4587, 8592, 3660, 4386, 1975, 8315, 13672, 1829, 8032, 30544, 3714, 8315, 4587, 8592, 3660, 5296, 24793, 45595, 20498, 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"probability": 0.91943359375}, {"start": 2678.4, "end": 2678.84, "word": " هذه", "probability": 0.89697265625}, {"start": 2678.84, "end": 2679.06, "word": " و", "probability": 0.990234375}, {"start": 2679.06, "end": 2679.14, "word": " ان", "probability": 0.73486328125}, {"start": 2679.14, "end": 2679.36, "word": " شاء", "probability": 0.989013671875}, {"start": 2679.36, "end": 2679.48, "word": " الله", "probability": 0.95947265625}, {"start": 2679.48, "end": 2679.92, "word": " لسبوع", "probability": 0.635009765625}, {"start": 2679.92, "end": 2680.6, "word": " الجاي", "probability": 0.70556640625}, {"start": 2680.6, "end": 2681.8, "word": " بنعمل", "probability": 0.9363606770833334}, {"start": 2681.8, "end": 2682.6, "word": " مناقشة", "probability": 0.93984375}, {"start": 2682.6, "end": 2684.18, "word": " فانا", "probability": 0.8115234375}, {"start": 2684.18, "end": 2684.62, "word": " هعمل", "probability": 0.9148763020833334}, {"start": 2684.62, "end": 2685.04, "word": " مناقشة", "probability": 0.86787109375}, {"start": 2685.04, "end": 2685.28, "word": " ..", "probability": 0.7529296875}, {"start": 2685.28, "end": 2685.46, "word": " انا", "probability": 0.93896484375}, {"start": 2685.46, "end": 2685.62, "word": " اللي", "probability": 0.8515625}, {"start": 2685.62, "end": 2685.96, "word": " هكون", "probability": 0.875}, {"start": 2685.96, "end": 2686.6, "word": " مناقشة", "probability": 0.7880859375}, {"start": 2686.6, "end": 2686.94, "word": " لكم", "probability": 0.861328125}, {"start": 2686.94, "end": 2689.04, "word": " اليوم", "probability": 0.87646484375}, {"start": 2689.04, "end": 2689.2, "word": " لأ", "probability": 0.6434326171875}, {"start": 2689.2, "end": 2689.5, "word": " مافيش", "probability": 0.9422200520833334}, {"start": 2689.5, "end": 2690.04, "word": " مناقشة", "probability": 0.96845703125}, {"start": 2690.04, "end": 2690.46, "word": " لأنه", "probability": 0.6646321614583334}, {"start": 2690.46, "end": 2690.72, "word": " لسه", "probability": 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27884, 29538, 21136, 995, 27884, 16247, 9778, 48923, 29538, 9673, 2655, 10721, 34740, 3660, 8717, 25957, 1211, 11296, 3714, 8315, 4587, 8592, 3660], "avg_logprob": -0.13460726452034874, "compression_ratio": 1.6711409395973154, "no_speech_prob": 0.0, "words": [{"start": 2695.29, "end": 2695.71, "word": "او", "probability": 0.69580078125}, {"start": 2695.71, "end": 2696.01, "word": " اللي", "probability": 0.877197265625}, {"start": 2696.01, "end": 2696.39, "word": " لسه", "probability": 0.9737955729166666}, {"start": 2696.39, "end": 2696.69, "word": " يعني", "probability": 0.94287109375}, {"start": 2696.69, "end": 2696.95, "word": " مش", "probability": 0.97119140625}, {"start": 2696.95, "end": 2699.07, "word": " مهيئين", "probability": 0.87529296875}, {"start": 2699.07, "end": 2699.29, "word": " او", "probability": 0.9140625}, {"start": 2699.29, "end": 2699.47, "word": " مش", "probability": 0.9931640625}, {"start": 2699.47, "end": 2700.11, "word": " محضرين", "probability": 0.94375}, {"start": 2700.11, "end": 2702.21, "word": " فهنواصل", "probability": 0.880615234375}, {"start": 2702.21, "end": 2703.03, "word": " ونحاول", "probability": 0.91552734375}, {"start": 2703.03, "end": 2703.19, "word": " ان", "probability": 0.84619140625}, {"start": 2703.19, "end": 2703.47, "word": " شاء", "probability": 0.98876953125}, {"start": 2703.47, "end": 2703.73, "word": " الله", "probability": 0.966796875}, {"start": 2703.73, "end": 2704.91, "word": " أسبوع", "probability": 0.7938639322916666}, {"start": 2704.91, "end": 2705.23, "word": " الجاى", "probability": 0.5010579427083334}, {"start": 2705.23, "end": 2705.69, "word": " ناخد", "probability": 0.9900716145833334}, {"start": 2705.69, "end": 2706.17, "word": " كل", "probability": 0.98681640625}, {"start": 2706.17, "end": 2706.93, "word": " ساعة", "probability": 0.93994140625}, {"start": 2706.93, "end": 2707.39, "word": " هذه", "probability": 0.75439453125}, {"start": 2707.39, "end": 2710.45, "word": " الساعة", "probability": 0.9422200520833334}, {"start": 2710.45, "end": 2710.97, "word": " الأخيرة", "probability": 0.9417317708333334}, {"start": 2710.97, "end": 2711.21, "word": " هذه", "probability": 0.7392578125}, {"start": 2711.21, "end": 2711.91, "word": " المتأخرة", "probability": 0.8720703125}, {"start": 2711.91, "end": 2712.27, "word": " نعملها", "probability": 0.98193359375}, {"start": 2712.27, "end": 2712.93, "word": " مناقشة", "probability": 0.92509765625}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2714.5985, "duration_after_vad": 2517.685624999991}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww.srt
new file mode 100644
index 0000000000000000000000000000000000000000..82abda219b6ce26543a7554afaf79fab562bf3b0
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww.srt
@@ -0,0 +1,1303 @@
+1
+00:00:20,770 --> 00:00:26,750
+السلام عليكم ورحمة الله وبركاته اليوم طبعا
+
+2
+00:00:26,750 --> 00:00:33,950
+فينا لقائن اللقاء الأول هناخد فيه مناقشة زي ما ..
+
+3
+00:00:33,950 --> 00:00:40,390
+زي ما احنا متعودين هنناقش اليوم section ثلاثة
+
+4
+00:00:40,390 --> 00:00:47,170
+أربعة و ثلاثة خمسة فإذا في عندكم أي أسئلة معينة في
+
+5
+00:00:47,170 --> 00:00:53,870
+section ثلاثة أربعة أو ثلاثة خمسة فهذه فرصة عندكم
+
+6
+00:00:53,870 --> 00:01:01,690
+أنكم يعني تسألوا الأسئلة و نحاول نحلها مع بعض فمين
+
+7
+00:01:01,690 --> 00:01:04,470
+في عندك أي سؤال في ال section ثلاثة أربعة الأول
+
+8
+00:01:04,470 --> 00:01:09,010
+السؤال الرابع حصل دار الجامعة التلانية كوشيسي بصرش
+
+9
+00:01:09,010 --> 00:01:13,190
+زيت كادر في ال section ثلاثة أربعة
+
+10
+00:01:16,800 --> 00:01:22,480
+الأول في section ثلاثة أربعة فيها أي أسئلة؟ سؤال
+
+11
+00:01:22,480 --> 00:01:23,020
+ثمانية
+
+12
+00:01:45,600 --> 00:01:57,660
+هذه السؤال ثمانية D section ثلاثة أربعة determine
+
+13
+00:01:57,660 --> 00:02:05,760
+the following limits determine
+
+14
+00:02:05,760 --> 00:02:13,200
+يعني حد دي أو أوج دي ال limit لل sequence اللي
+
+15
+00:02:13,200 --> 00:02:25,120
+الحد العام تبعها واحد زائد اثنين واحد زائد
+
+16
+00:02:25,120 --> 00:02:33,200
+واحد على اثنين N الكل أس ثلاثة N لما
+
+17
+00:02:33,200 --> 00:02:40,640
+N تقول ل Infinity احنا
+
+18
+00:02:40,640 --> 00:02:42,040
+عندنا ال ..
+
+19
+00:02:48,210 --> 00:02:54,670
+We know احنا فيه أن ال limit المعروفة limit واحد
+
+20
+00:02:54,670 --> 00:03:04,010
+زائد X على M الكل أس M as M tends to infinity
+
+21
+00:03:04,010 --> 00:03:10,850
+بساوي E أس X ال limit هذه معروفة موجودة هنا
+
+22
+00:03:14,080 --> 00:03:26,660
+باستخدام ال limit هذه ممكن أن احنا وبالتالي
+
+23
+00:03:26,660 --> 00:03:29,900
+تعالى
+
+24
+00:03:29,900 --> 00:03:36,380
+نشوف واحد زائد واحد على اثنين N الكل أس ثلاثة 
+
+25
+00:03:36,380 --> 00:03:42,060
+N نحاول نكتب هذا على صورة واحد زائد X على M الكل
+
+26
+00:03:42,060 --> 00:03:48,280
+أس M فهذا ممكن كتابته على صورة المقدار هذا على
+
+27
+00:03:48,280 --> 00:03:57,120
+الصورة واحد زائد نصف على M نصف
+
+28
+00:03:57,120 --> 00:04:05,600
+على M الكل أس M الكل
+
+29
+00:04:05,600 --> 00:04:06,160
+تكعيين
+
+30
+00:04:09,900 --> 00:04:19,240
+صحيح وبالتالي therefore limit لما N تنتقل ل Infinity
+
+31
+00:04:19,240 --> 00:04:28,160
+ل ال sequence اللي لحد تبعها هذا بيساوي limit لما
+
+32
+00:04:28,160 --> 00:04:36,570
+N تنتقل ل Infinity ل الكلام هذا للمقدار اللي هنا و هي
+
+33
+00:04:36,570 --> 00:04:43,330
+عندي واحد زي ال X على M أو M الكل أس M ف limit
+
+34
+00:04:43,330 --> 00:04:53,370
+المقدار اللي جوا بيساوي E أس نصف أو E أس X الكل ده
+
+35
+00:04:53,370 --> 00:04:57,150
+كئيب أنا مقدر أدخل ال limit جوا القصير المربعين
+
+36
+00:04:57,150 --> 00:05:02,830
+limit المقدار اللي جوا جوا القصير المربعين نحسب
+
+37
+00:05:02,830 --> 00:05:08,030
+القاعدة أو القانون هذا E أُس X اللي هو نصف وبعدين 2
+
+38
+00:05:08,030 --> 00:05:15,610
+بالكل تكعييب فبيطلع E أُس 3 على 2 إذا هذه هي قيمة ال
+
+39
+00:05:15,610 --> 00:05:19,990
+limit okay تمام في
+
+40
+00:05:19,990 --> 00:05:25,090
+أسئلة ثانية في ال section هذا ثلاثة أربعة
+
+41
+00:05:32,810 --> 00:05:48,550
+PIS love section ثلاثة أربعة طيب
+
+42
+00:05:48,550 --> 00:05:54,230
+section ثلاثة خمسة أنا في السؤال الرابع الشخصي
+
+43
+00:05:54,230 --> 00:05:54,650
+الثاني
+
+44
+00:06:02,810 --> 00:06:07,190
+سيكشن ثلاثة خمسة الرابع ولا الثالث قصدك؟ الرابع
+
+45
+00:06:07,190 --> 00:06:17,710
+سؤال
+
+46
+00:06:17,710 --> 00:06:23,810
+رقم أربعة سيكشن ثلاثة خمسة طيب
+
+47
+00:06:23,810 --> 00:06:27,890
+سؤال
+
+48
+00:06:27,890 --> 00:06:33,710
+أربعة سيكشن ثلاثة خمسة السؤال هذا بتقول show
+
+49
+00:06:33,710 --> 00:06:37,750
+directly from the definition
+
+50
+00:07:01,910 --> 00:07:17,610
+إذا XN و YN هم متتابعات كوشي هم متتابعات
+
+51
+00:07:17,610 --> 00:07:21,070
+كوشي هم
+
+52
+00:07:21,070 --> 00:07:27,550
+متتابعات كوشي هم متتابعات كوشي
+
+53
+00:07:30,650 --> 00:07:34,270
+فبرهان هذه زي البرهان اللي أخدناها قبل هيك في
+
+54
+00:07:34,270 --> 00:07:41,290
+قوانين نهايات proof
+
+55
+00:07:41,290 --> 00:07:50,350
+similar to proof of
+
+56
+00:07:50,350 --> 00:07:53,470
+the fact أن
+
+57
+00:08:18,370 --> 00:08:23,890
+بساوي limit xn ضرب limit yn
+
+58
+00:08:27,620 --> 00:08:31,000
+و أعتقد أن هذا برهنها بالتفصيل using epsilon over two
+
+59
+00:08:31,000 --> 00:08:40,220
+argument تذكره؟ أه فحاولي تكتبي برهان مشابه و إذا
+
+60
+00:08:40,220 --> 00:08:50,280
+كان ماقدرتيش ممكن بعديها أعطيكي برهان تفصيلي okay؟
+
+61
+00:08:50,280 --> 00:08:52,180
+في أي أسئلة ثانية؟
+
+62
+00:08:58,920 --> 00:09:04,620
+section تلقيتها خمسة
+
+63
+00:09:04,620 --> 00:09:15,820
+سؤال
+
+64
+00:09:15,820 --> 00:09:23,200
+عشرة ناس
+
+65
+00:09:23,200 --> 00:09:24,000
+سؤال عشر
+
+66
+00:09:28,420 --> 00:09:38,620
+section ثلاثة خمسة if
+
+67
+00:09:38,620 --> 00:09:46,600
+x one less than x two are
+
+68
+00:09:46,600 --> 00:09:51,660
+arbitrary
+
+69
+00:09:55,690 --> 00:10:09,210
+real numbers and
+
+70
+00:10:09,210 --> 00:10:14,530
+xn
+
+71
+00:10:14,530 --> 00:10:19,470
+بيساوي نصف
+
+72
+00:10:21,890 --> 00:10:37,690
+xn-2 plus xn-1 for n أكبر من 2 show in the
+
+73
+00:10:37,690 --> 00:10:42,470
+sequence xn is convergent
+
+74
+00:10:50,120 --> 00:10:55,760
+what is its limit what is
+
+75
+00:10:55,760 --> 00:11:03,520
+its limit ده هي النهاية تبعتنا بدنا نوجد نهايتها
+
+76
+00:11:03,520 --> 00:11:15,440
+في
+
+77
+00:11:15,440 --> 00:11:25,450
+حد فيكم فكر فيحلل السؤال هذا أي حد يعني حاول
+
+78
+00:11:25,450 --> 00:11:37,510
+ال burn in clever في أي أفكار أي شيء مافيش عندكم
+
+79
+00:11:37,510 --> 00:11:45,650
+أي فكرة عن الحل نحلوا
+
+80
+00:11:45,650 --> 00:11:46,890
+مع بعض نشوف
+
+81
+00:11:49,810 --> 00:11:58,450
+أنا عندي من الفرض x1 أصغر من x2 أعداد حقيقية فهعرف
+
+82
+00:11:58,450 --> 00:12:07,890
+let L بيساوي x2 ناقص x1 هذا بيطلع عدد موجب لأن
+
+83
+00:12:07,890 --> 00:12:16,770
+x2 أكبر من x1 الآن باستخدام ال induction use
+
+84
+00:12:16,770 --> 00:12:17,570
+induction
+
+85
+00:12:21,840 --> 00:12:29,220
+on n بيمكنكم
+
+86
+00:12:29,220 --> 00:12:35,820
+تثبته أن المعادلة
+
+87
+00:12:35,820 --> 00:12:44,080
+التالية absolute xn زائد واحد ناقص xn بيساوي L
+
+88
+00:12:44,080 --> 00:12:49,960
+over two to n ناقص واحد and this is true for
+
+89
+00:12:49,960 --> 00:12:50,820
+every L
+
+90
+00:12:59,660 --> 00:13:08,000
+إذا كان n بيساوي لكل
+
+91
+00:13:08,000 --> 00:13:14,300
+n أكبر من أو يساوي اثنين عشان هنا يكون هذا المعنى
+
+92
+00:13:14,300 --> 00:13:21,290
+فابدى ب n بيساوي اثنين و أثبت أن المعادلة هذه صحيحة
+
+93
+00:13:21,290 --> 00:13:24,910
+بصحيحتها عند n بيساوي k حيث k أكبر من اثنين أعداد
+
+94
+00:13:24,910 --> 00:13:29,410
+طبيعية و أثبت صحيحتها عند n بيساوي k زائد واحد طبعا في
+
+95
+00:13:29,410 --> 00:13:35,070
+الإثباتات بدك تستخدم التعريف تبع xn بدلالة الحدود
+
+96
+00:13:35,070 --> 00:13:35,670
+اللي قبله
+
+97
+00:13:41,020 --> 00:13:45,480
+و التعريف اللي أنا أخذته أن ال هو عبارة عن الفرق
+
+98
+00:13:45,480 --> 00:13:51,340
+بين X2 و X1 إذا هذا سهل ممكن تثبته by induction
+
+99
+00:13:51,340 --> 00:14:01,740
+الآن بعد ما تثبت هذا by induction now use this to
+
+100
+00:14:01,740 --> 00:14:02,540
+show that
+
+101
+00:14:08,470 --> 00:14:20,450
+بنستخدم المعادلة هذه to show that if M أكبر من N
+
+102
+00:14:20,450 --> 00:14:33,250
+أعداد طبيعية then absolute XM ناقص XM ال
+
+103
+00:14:33,250 --> 00:14:40,070
+absolute value لفرق XM و XM طبعا هذا هنخليه أصغر من
+
+104
+00:14:40,070 --> 00:14:48,610
+أو يساوي absolute xn ناقص xn زائد واحد زي absolute
+
+105
+00:14:48,610 --> 00:14:57,510
+xn زائد واحد ناقص xn زائد اثنين و هكذا
+
+106
+00:15:02,520 --> 00:15:09,560
+absolute xm ناقص واحد ناقص xm
+
+107
+00:15:09,560 --> 00:15:13,840
+okay
+
+108
+00:15:13,840 --> 00:15:24,240
+تمام أنا إيش عملت طرحت xn زائد واحد ورجعتها طرحت
+
+109
+00:15:24,240 --> 00:15:29,290
+xn زائد اثنين ورجعتها و بعدين أخذت الأزواج هذه مع
+
+110
+00:15:29,290 --> 00:15:34,530
+بعض و استخدمت ل triangle inequality ال absolute
+
+111
+00:15:34,530 --> 00:15:39,390
+value ل مجموعة كبيرة أصغر من مجموع absolute
+
+112
+00:15:39,390 --> 00:15:47,250
+values فالآن
+
+113
+00:15:47,250 --> 00:15:54,530
+باستخدام لو سمينا المعادلة هاد ال star فباستخدام
+
+114
+00:15:54,530 --> 00:16:04,180
+ال star ال absolute value هذه بيساوي ال over two to
+
+115
+00:16:04,180 --> 00:16:12,840
+n ناقص واحد okay هذه نفسها دي و ال absolute value
+
+116
+00:16:12,840 --> 00:16:24,240
+اللي بعدها بيساوي ال على two to n و هكذا و آخر حد
+
+117
+00:16:24,240 --> 00:16:33,390
+هيكون ال over two to m ناقص اثنين لأن
+
+118
+00:16:33,390 --> 00:16:39,170
+استخدام السارق مظبوط الآن ممكن ناخد عامل مشترك
+
+119
+00:16:39,170 --> 00:16:52,230
+هاخد
+
+120
+00:16:52,230 --> 00:16:54,750
+عامل مشترك L over
+
+121
+00:17:16,500 --> 00:17:17,900
+تمام؟
+
+122
+00:17:20,140 --> 00:17:25,760
+الآن هذا أصغر من واحد على اثنين أس n ناقص واحد
+
+123
+00:17:25,760 --> 00:17:34,980
+و المجموع هذا أصغر من اثنين
+
+124
+00:17:34,980 --> 00:17:41,660
+لأن هذا جزء من الهارمونيك جيومتريكس سيريز اللي هي
+
+125
+00:17:41,660 --> 00:17:46,820
+واحد على اثنين أس n من n equal zero to infinity
+
+126
+00:17:46,820 --> 00:17:51,550
+هذه مجموعتها اثنين فهذا جزء منها وبالتالي المجموعة
+
+127
+00:17:51,550 --> 00:17:55,650
+هذا أصغر من المجموعة ال geometric series هذه
+
+128
+00:17:55,650 --> 00:18:01,490
+المجموعة بيساوي اثنين okay فإذا هذا المجموعة أصغر
+
+129
+00:18:01,490 --> 00:18:06,030
+من اثنين إذا هذا أصغر من واحد على اثنين أس n سالب
+
+130
+00:18:06,030 --> 00:18:14,990
+واحد في اثنين اللي هو عبارة عن واحد على اثنين أس
+
+131
+00:18:14,990 --> 00:18:17,410
+n سالب اثنين
+
+132
+00:18:28,770 --> 00:18:35,790
+الآن هذا بيروح للصفر as n tends to infinity هو
+
+133
+00:18:35,790 --> 00:18:40,770
+بالتالي ده بتطلع عندي أنا ال limit ل absolute xn
+
+134
+00:18:40,770 --> 00:18:49,670
+ناقص xm as m as n tends to infinity و طبعا m
+
+135
+00:18:49,670 --> 00:18:55,410
+تقول infinity تساوي صفر therefore ال sequence xn
+
+136
+00:18:55,410 --> 00:18:57,270
+is Cauchy
+
+137
+00:19:02,500 --> 00:19:09,620
+و بالتالي therefore by Cauchy criterion by Cauchy
+
+138
+00:19:09,620 --> 00:19:17,660
+criterion xn convergence صح؟ say
+
+139
+00:19:26,770 --> 00:19:35,110
+دعينا نسمي ال limit ل xn بيساوي x حيث x is real
+
+140
+00:19:35,110 --> 00:19:41,110
+number الآن مطلوب أن احنا نجد قيمة ال x قيمة ال 
+
+141
+00:19:41,110 --> 00:19:48,470
+limit للـ sequence اللي هي سمنها x فبنرجع للمعادلة
+
+142
+00:19:48,470 --> 00:19:49,730
+هناك
+
+143
+00:20:07,880 --> 00:20:13,020
+to find x
+
+144
+00:20:13,020 --> 00:20:18,980
+take limits
+
+145
+00:20:18,980 --> 00:20:23,960
+of
+
+146
+00:20:23,960 --> 00:20:26,940
+both sides
+
+147
+00:20:32,640 --> 00:20:49,540
+في المعادلة هذه اللي هنا and then
+
+148
+00:20:49,540 --> 00:20:56,480
+take limit of both sides in this equation to get
+
+149
+00:20:56,480 --> 00:21:09,330
+أن limit x in بساوي نص في limit x in negative two
+
+150
+00:21:09,330 --> 00:21:21,850
+زاد limit x in negative one as intensity هذا
+
+151
+00:21:21,850 --> 00:21:28,510
+بيقدّي أن limit x in عبارة عن x بساوي نص هذه
+
+152
+00:21:28,510 --> 00:21:33,460
+subsequence من الـ xn، وبالتالي، الـ limit تبعتها
+
+153
+00:21:33,460 --> 00:21:37,880
+برضه x وهذا الـ subsequence من الـ xn والـ limit
+
+154
+00:21:37,880 --> 00:21:45,400
+تبعتها x لأن كانت الـ sequence convergent لـ x فأي
+
+155
+00:21:45,400 --> 00:21:50,080
+subsequence بتكون convergent لنفس الـ x وهذا بيطلع
+
+156
+00:21:50,080 --> 00:21:51,100
+بساوية
+
+157
+00:22:12,850 --> 00:22:18,570
+فاحنا هيك ما طلعش عندنا إشي جديد طالع X بساوي X
+
+158
+00:22:18,570 --> 00:22:25,950
+فاحنا هيك ما ظبطناش ال limit ما ظبطناش 
+
+159
+00:22:25,950 --> 00:22:26,570
+ال limit
+
+160
+00:22:50,820 --> 00:22:57,180
+فاحنا هيك ما جبناش ال limit وهدي مشكلة أو يعني ال
+
+161
+00:22:57,180 --> 00:22:57,600
+...
+
+162
+00:23:14,130 --> 00:23:21,570
+طب خلينا نرجع للمعادلة اللي أثبتناها أثبتناها
+
+163
+00:23:21,570 --> 00:23:22,410
+by induction
+
+164
+00:24:17,920 --> 00:24:22,600
+طيب خلّي موضوع ال limit هذا لمرة ثانية
+
+165
+00:24:31,270 --> 00:24:33,370
+سي حد عنده أي فكرة؟
+
+166
+00:24:55,010 --> 00:25:03,350
+خلّي ال limit نجيبها المرة الجاية يبدو
+
+167
+00:25:03,350 --> 00:25:09,630
+أن الطريقة تبعتنا ما ... ما زبطت فنحاول نفكر فيها
+
+168
+00:25:09,630 --> 00:25:14,810
+مرة ثانية ونجيبها، مين عنده سؤال ثاني؟ وأنتم
+
+169
+00:25:14,810 --> 00:25:17,830
+كمان طبعا فكروا في إيجاب قيمة ال limit
+
+170
+00:25:25,090 --> 00:25:33,030
+في أي أسئلة ثانية في ال section تلاتة خمسة سؤال
+
+171
+00:25:33,030 --> 00:25:46,130
+ثمانية سؤال ثمانية سؤال
+
+172
+00:25:46,130 --> 00:25:54,030
+ثمانية section تلاتة خمسة show directly
+
+173
+00:25:57,190 --> 00:26:05,590
+مش هو directly that
+
+174
+00:26:05,590 --> 00:26:12,550
+a bounded a
+
+175
+00:26:12,550 --> 00:26:24,370
+bounded a bounded monotone a bounded monotone
+
+176
+00:26:27,280 --> 00:26:36,500
+ماراتون ان كريزم ماراتون
+
+177
+00:26:36,500 --> 00:26:42,560
+ان كريزم الاختصار هو
+
+178
+00:26:42,560 --> 00:26:43,300
+كوشي
+
+179
+00:26:56,170 --> 00:27:01,310
+السيكوينس دي bounded و monotone increasing فاحنا
+
+180
+00:27:01,310 --> 00:27:10,100
+خدنا نظرية بتطلع لازم تكون by monotone convergence
+
+181
+00:27:10,100 --> 00:27:13,100
+theorem it is convergent عسب ال monotone
+
+182
+00:27:13,100 --> 00:27:17,380
+convergence و بالتالي ممكن نقول by Cauchy
+
+183
+00:27:17,380 --> 00:27:20,780
+criterion بما أنها convergent اذا Cauchy هذا برهان
+
+184
+00:27:20,780 --> 00:27:26,180
+وصحيح بس الكتاب مش عايز هذا البرهان عايز برهان
+
+185
+00:27:26,180 --> 00:27:30,500
+مباشر باستخدام ال definition تبع ال Cauchy
+
+186
+00:27:30,500 --> 00:27:38,260
+sequence Okay فالبرهان بسيط وسهل يعني ما هوش صعب
+
+187
+00:27:38,260 --> 00:27:44,060
+proof since
+
+188
+00:27:44,060 --> 00:27:49,820
+طبعا
+
+189
+00:27:49,820 --> 00:27:57,400
+ال sequence خليني أسميها x in since
+
+190
+00:27:57,400 --> 00:28:02,980
+ال sequence تبعتنا x in is bounded بما أن ال
+
+191
+00:28:02,980 --> 00:28:08,980
+sequence is bounded then
+
+192
+00:28:08,980 --> 00:28:25,680
+لو أخدت U بساوي Supremum ل XN-N ينتمي لإن Supremum
+
+193
+00:28:25,680 --> 00:28:28,060
+هذا exists in R
+
+194
+00:28:32,840 --> 00:28:39,620
+by supremum property أو by completeness property
+
+195
+00:28:39,620 --> 00:28:48,520
+أي bounded set has supremum فخلينا نفرض أن ال U هو
+
+196
+00:28:48,520 --> 00:28:54,300
+supremum فهذا بيطلع عدد حقيقي exist يعني عدد حقيقي
+
+197
+00:28:54,300 --> 00:29:01,120
+الآن من ال definition by
+
+198
+00:29:01,120 --> 00:29:08,250
+definition of supremum
+
+199
+00:29:08,250 --> 00:29:16,030
+هو بالأحرى مش من التعريف من ال lemma اللي بتيجي بعد التعريف
+
+200
+00:29:16,030 --> 00:29:19,630
+وال lemma
+
+201
+00:29:19,630 --> 00:29:23,110
+من
+
+202
+00:29:23,110 --> 00:29:29,990
+هنا by Aprilius
+
+203
+00:29:40,440 --> 00:29:44,220
+النظرية هذه خلينا نرجعها أو نجمها أو نجمها أو
+
+204
+00:29:44,220 --> 00:29:48,460
+نجمها أو نجمها U of a set
+
+205
+00:30:02,180 --> 00:30:07,180
+of a set S
+
+206
+00:30:07,180 --> 00:30:11,960
+is
+
+207
+00:30:11,960 --> 00:30:16,440
+the supremum is
+
+208
+00:30:16,440 --> 00:30:17,420
+the supremum
+
+209
+00:30:22,570 --> 00:30:32,010
+S if and only if لكل أبسلون أكبر من الصفر يوجد عنصر
+
+210
+00:30:32,010 --> 00:30:39,950
+S يعتمد على أبسلون في S بحيث أنه لو ضفنا ... لو
+
+211
+00:30:39,950 --> 00:30:45,250
+طرحنا من ال supremum أبسلون فبيبطل أكبر دعوة بيصير
+
+212
+00:30:45,250 --> 00:30:55,520
+أصغر من S باستخدام هذه النظرية السابقة لو أخدت
+
+213
+00:30:55,520 --> 00:31:01,500
+given
+
+214
+00:31:01,500 --> 00:31:04,880
+epsilon
+
+215
+00:31:04,880 --> 00:31:09,620
+أكبر من الصفر لو أخدت epsilon عشوائية أكبر من 
+
+216
+00:31:09,620 --> 00:31:17,320
+الصفر يوجد capital N في N
+
+217
+00:31:22,170 --> 00:31:35,390
+عدد طبيعي بحيث أن ال ... ال ... ال
+
+218
+00:31:35,390 --> 00:31:43,690
+U نيجاتيف XN عرفوا ال U نيجاتيف إبسلون بيطلع أصغر
+
+219
+00:31:43,690 --> 00:31:50,270
+من S Y S Y حقول ده X اللي ال index سبقه capital N
+
+220
+00:31:51,310 --> 00:31:54,710
+إذا هذا العنصر اللي في الـ sequence أو في ال set
+
+221
+00:31:54,710 --> 00:32:01,950
+هذه اللي هو S Y يعتمد على إبسلون ما ال N هذه تعتمد
+
+222
+00:32:01,950 --> 00:32:09,310
+على إبسلون وهي U إترح منه إبسلون بيطلع أصغر من
+
+223
+00:32:09,310 --> 00:32:15,150
+عنصر S Y اللي هو موجود هنا إذا هذا حسب النظرية
+
+224
+00:32:15,150 --> 00:32:20,050
+تمام؟ الآن since
+
+225
+00:32:22,680 --> 00:32:29,060
+لاحظوا أنتم أن ال XIN هذا عنصر في الست وبالتالي و
+
+226
+00:32:29,060 --> 00:32:32,660
+ال U upper bound ال U اللي هو ال supreme دايما
+
+227
+00:32:32,660 --> 00:32:37,180
+بيكون upper bound فهذا بيطلع أصغر من أو يساوي ال U
+
+228
+00:32:37,180 --> 00:32:43,420
+since
+
+229
+00:32:43,420 --> 00:32:50,740
+ال sequence XIN is increasing متزايدة
+
+230
+00:32:55,230 --> 00:32:59,870
+we get نحصل
+
+231
+00:32:59,870 --> 00:33:08,330
+على التالي فنحصل
+
+232
+00:33:08,330 --> 00:33:17,590
+على التالي لو كان M أكبر من أو يساوي N أكبر من أو
+
+233
+00:33:17,590 --> 00:33:26,720
+يساوي capital N فهذا هيقدّي إلى أن u negative
+
+234
+00:33:26,720 --> 00:33:35,200
+epsilon أصغر من x capital N من هنا و x capital N
+
+235
+00:33:35,200 --> 00:33:42,260
+أصغر من أو يساوي x small n لأن ال sequence is
+
+236
+00:33:42,260 --> 00:33:46,730
+increasing و small n أكبر من أو يساوي capital N وهذا
+
+237
+00:33:46,730 --> 00:33:54,070
+أصغر من أو يساوي xm لأن ال sequence increasing و
+
+238
+00:33:54,070 --> 00:33:59,690
+xm أصغر من أو يساوي u لأن ال u upper bound لكل
+
+239
+00:33:59,690 --> 00:34:06,670
+عناصر ال sequence تمام؟ و ال u
+
+240
+00:34:15,980 --> 00:34:22,260
+فهذا هيقدّي ... هذا
+
+241
+00:34:22,260 --> 00:34:30,320
+هيقدّي أن xn minus
+
+242
+00:34:30,320 --> 00:34:37,000
+epsilon أصغر من xn لأن الepsilon عدد موجب فلما
+
+243
+00:34:37,000 --> 00:34:44,570
+يطلع عدد موجب العدد xn بيصغر وعندي xn أصغر من أو
+
+244
+00:34:44,570 --> 00:34:50,490
+يساوي xm لأن ال m أكبر من أو يساوي n و ال sequence
+
+245
+00:34:50,490 --> 00:34:57,110
+تبعتي increasing و xm أصغر من أو يساوي ال u
+
+246
+00:35:11,700 --> 00:35:21,020
+من هنا، من المتباينة هذه واضح أن أنا عندي ال
+
+247
+00:35:21,020 --> 00:35:31,020
+U أصغر من XN زائد إبسلون، صح؟ هل عندي U negative
+
+248
+00:35:31,020 --> 00:35:39,160
+إبسلون أصغر من XN فاضيف إبسلون فبطلع U أصغر من XN
+
+249
+00:35:40,390 --> 00:35:49,470
+زائد ابسلون إذا أنا بطلع عندي xn
+
+250
+00:35:49,470 --> 00:36:02,450
+أو ال ... ال xm تطلع أكبر من xn minus ابسلون أصغر
+
+251
+00:36:02,450 --> 00:36:04,730
+من xn زائد ابسلون
+
+252
+00:36:08,370 --> 00:36:19,010
+وهذا معناه أن absolute xn أو xn minus xm أصغر من
+
+253
+00:36:19,010 --> 00:36:28,730
+epsilon أصبت؟ صح؟ وهذا صحيح لكل M أكبر من أو يساوي
+
+254
+00:36:28,730 --> 00:36:34,030
+M أكبر من أو يساوي capital M تمام؟ إذا بنقول هنا
+
+255
+00:36:34,030 --> 00:36:46,340
+since epsilon أكبر من الصفر was arbitrary it
+
+256
+00:36:46,340 --> 00:36:50,640
+follows بينتج
+
+257
+00:36:50,640 --> 00:36:58,820
+من تعريف الكوشي sequence that sequence xm is
+
+258
+00:36:58,820 --> 00:36:59,620
+cauchy
+
+259
+00:37:03,200 --> 00:37:11,000
+وهنا هيك طبقنا التعريف وهذا برهان مباشر okay تمام
+
+260
+00:37:11,000 --> 00:37:22,940
+واضح في
+
+261
+00:37:22,940 --> 00:37:26,520
+أي سؤال سؤال ثانية واضح البرهان في أي سفصار
+
+262
+00:37:32,980 --> 00:37:38,320
+في أي سؤال ثاني section تلاتة خمسة أو تلاتة ستة
+
+263
+00:37:38,320 --> 00:37:41,600
+لبعده
+
+264
+00:37:41,600 --> 00:37:50,060
+الناس
+
+265
+00:37:50,060 --> 00:37:50,920
+اللي بيدرسوا
+
+266
+00:38:03,440 --> 00:38:10,060
+التلاتة ستة؟ سؤال أربعة في رياضينا.
+
+267
+00:38:23,080 --> 00:38:24,980
+هذا ما حللناه إزاي؟
+
+268
+00:38:44,990 --> 00:38:54,970
+السكتشن تلاتة ستة السؤال الرابع ترى بي establish
+
+269
+00:38:54,970 --> 00:38:58,370
+establish
+
+270
+00:38:58,370 --> 00:39:01,490
+the
+
+271
+00:39:01,490 --> 00:39:05,790
+proper divergence
+
+272
+00:39:05,790 --> 00:39:10,270
+of
+
+273
+00:39:10,270 --> 00:39:12,950
+sequence
+
+274
+00:39:16,730 --> 00:39:25,730
+يجيب الان زي الواحد أن الان اكوار الواحد تنتهي ان
+
+275
+00:39:25,730 --> 00:39:33,910
+أنا أثبت أن أنا أثبت
+
+276
+00:39:33,910 --> 00:39:39,250
+أن أنا أثبت أن أنا أثبت
+
+277
+00:39:39,250 --> 00:39:45,220
+أن أنا أثبت أن أنا أثبت لا ال sequence اللي ال inf
+
+278
+00:39:45,220 --> 00:39:49,820
+term تبعها والحد العام تبعها جدر انزعي الواحد لما
+
+279
+00:39:49,820 --> 00:39:58,300
+M تقوى ل infinity بساوي infinity استاذ ماعرفش طلقة
+
+280
+00:39:58,300 --> 00:40:07,900
+D ماعرفش بيه بيه عرفت حلوة دي طلقة دي 
+
+281
+00:40:07,900 --> 00:40:13,460
+استاذ بدك دي طريقة ديال الفرقة دي
+
+282
+00:40:40,070 --> 00:40:46,330
+يعني هيطلع عندي هنا limit in على جذر in زي الواحد
+
+283
+00:40:46,330 --> 00:40:53,390
+لما in تقول infinity بيساوي infinity ممكن تستخدم
+
+284
+00:40:53,390 --> 00:41:03,190
+limit comparison test أو comparison test اه فال
+
+285
+00:41:07,800 --> 00:41:12,180
+فهل فكرتي أنك تستخدمي comparison test أو limit
+
+286
+00:41:12,180 --> 00:41:16,260
+comparison test؟ فكرت عن نظري يعني برنامج ده يفير
+
+287
+00:41:16,260 --> 00:41:20,140
+لأ و أنت عندك التعريف و عندك في limit comparison
+
+288
+00:41:20,140 --> 00:41:29,620
+test و comparison test لأ
+
+289
+00:41:29,620 --> 00:41:36,110
+هاي موجود في تلاتة ستة في ..مافيش limit comparison
+
+290
+00:41:36,110 --> 00:41:49,030
+test؟ فيك طيب هاي أنا شايف في ..
+
+291
+00:41:49,030 --> 00:41:55,870
+أنت
+
+292
+00:41:55,870 --> 00:42:01,970
+عندك .. ياعمل المقارنة أنت
+
+293
+00:42:01,970 --> 00:42:03,010
+عندك ..
+
+294
+00:42:10,490 --> 00:42:19,450
+يعني قارن ال .. جذر ال N بدك تقارن هذه مع
+
+295
+00:42:19,450 --> 00:42:26,430
+N على جذر ال N لما N تكون كبيرة ابنهم الواحد فهذه
+
+296
+00:42:26,430 --> 00:42:30,090
+بيصير زيها زي ال sequence اللي لحد الآن تبعها N
+
+297
+00:42:30,090 --> 00:42:34,390
+على جذر ال N وهذه بيساوي جذر ال N
+
+298
+00:42:39,240 --> 00:42:43,420
+فبتعمل limit comparison use limit comparison test
+
+299
+00:42:43,420 --> 00:42:51,280
+هاي عندي an ولا إيش مسميهم الكتاب نعم
+
+300
+00:42:51,280 --> 00:42:59,780
+يعني xn وهي yn وتعالى نحسب ال limit
+
+301
+00:43:08,200 --> 00:43:13,480
+تعالى نحسب ال limit ل
+
+302
+00:43:13,480 --> 00:43:21,100
+xn على yn as n tends to infinity بيساوي ال limit ل
+
+303
+00:43:21,100 --> 00:43:31,820
+n على الجذر n زي الواحد تقسيم
+
+304
+00:43:37,120 --> 00:43:43,740
+في واحد على جذر ال N لما N تقول ال infinity بيساوي
+
+305
+00:43:43,740 --> 00:43:47,840
+limit لجذر
+
+306
+00:43:47,840 --> 00:43:55,000
+التربيع A ل N على N زي واحد مظبوط؟
+
+307
+00:43:55,000 --> 00:44:02,380
+بندخل ال limit جوه فبقلع واحد أكبر من صفر الان
+
+308
+00:44:02,380 --> 00:44:09,580
+since احنا اثبتنا أن ال series sigma أو ال sequence
+
+309
+00:44:09,580 --> 00:44:16,700
+since ال sequence أن الحد العام تبعها جذر ال n أو
+
+310
+00:44:16,700 --> 00:44:21,720
+since limit yn
+
+311
+00:44:21,720 --> 00:44:27,480
+as n tends to infinity بيساوي limit جذر ال n as
+
+312
+00:44:27,480 --> 00:44:31,500
+n tends to infinity بيساوي infinity we get
+
+313
+00:44:34,620 --> 00:44:41,340
+from limit comparison test from limit comparison
+
+314
+00:44:41,340 --> 00:44:47,100
+test from limit
+
+315
+00:44:47,100 --> 00:44:48,480
+comparison test from limit comparison test from
+
+316
+00:44:48,480 --> 00:44:48,500
+from limit comparison test from limit comparison
+
+317
+00:44:48,500 --> 00:44:48,600
+from limit comparison test from limit comparison
+
+318
+00:44:48,600 --> 00:44:48,640
+comparison test from limit comparison test from
+
+319
+00:44:48,640 --> 00:44:50,520
+comparison test from limit comparison test from
+
+320
+00:44:50,520 --> 00:44:57,100
+limit comparison test from limit
+
+321
+00:44:57,100 --> 00:45:00,980
+comparison test from limit comparison test
+
+322
+00:45:13,250 --> 00:45:18,150
+تمام؟ okay إذا ممكن نستخدم ال limit comparison
+
+323
+00:45:18,150 --> 00:45:23,290
+test أو ال direct comparison test إذا نفع و نحل باقي
+
+324
+00:45:23,290 --> 00:45:28,010
+التمارين في .. أو الأجزاء الأخرى في exercise أربعة
+
+325
+00:45:28,010 --> 00:45:33,430
+رقم .. section تلاتة ستة okay بنوقف هنا و بنكمل
+
+326
+00:45:33,430 --> 00:45:38,190
+المرة الجاية نكتفي بهذا القدر
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..c2023b613f5d3f440a9fb19691447bffbde806f5
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/QCtISTGMQww_postprocess.srt
@@ -0,0 +1,1304 @@
+1
+00:00:20,770 --> 00:00:26,750
+السلام عليكم بسم الله الرحمن الرحيم اليوم طبعا
+
+2
+00:00:26,750 --> 00:00:33,950
+فينا لقائن اللقاء الأول هناخد فيه مناقشة زي ما ..
+
+3
+00:00:33,950 --> 00:00:40,390
+زي ما احنا متعودين هنناقش اليوم section تلاتة
+
+4
+00:00:40,390 --> 00:00:47,170
+أربعة و تلاتة خمسة فإذا في عندكم أي أسئلة معينة في
+
+5
+00:00:47,170 --> 00:00:53,870
+section تلاتة أربعةأو تلاتة خمسة فهذه فرصة عندكم
+
+6
+00:00:53,870 --> 00:01:01,690
+أنكم يعني تسألوا الأسئلة و نحاول نحلها مع بعض فمين
+
+7
+00:01:01,690 --> 00:01:04,470
+في عندك أي سؤال في ال section تلاتة أربعة الأول
+
+8
+00:01:04,470 --> 00:01:09,010
+السؤال الرابع حصل دار الجامعة التلانية كوشيسي بصرش
+
+9
+00:01:09,010 --> 00:01:13,190
+زيت كادر في ال section تلاتة أربعة
+
+10
+00:01:16,800 --> 00:01:22,480
+الأول في section تلاتة اربعة فيها أي أسئلة؟ سؤال
+
+11
+00:01:22,480 --> 00:01:23,020
+تمانية
+
+12
+00:01:45,600 --> 00:01:57,660
+هذه السؤال تمانية D section تلاتة أربعة determine
+
+13
+00:01:57,660 --> 00:02:05,760
+the following limits determine
+
+14
+00:02:05,760 --> 00:02:13,200
+يعني حد دي أو أوج دي ال limit لل sequence اللي
+
+15
+00:02:13,200 --> 00:02:25,120
+الحد العام تبعهاواحد زائد اتنين واحد زائد
+
+16
+00:02:25,120 --> 00:02:33,200
+واحد على اتنين N الكل أس تلاتة N لما
+
+17
+00:02:33,200 --> 00:02:40,640
+N تقول ل Infinity احنا
+
+18
+00:02:40,640 --> 00:02:42,040
+عندنا ال ..
+
+19
+00:02:48,210 --> 00:02:54,670
+We know احنا فيه ان ال limit المعروفة limit واحد
+
+20
+00:02:54,670 --> 00:03:04,010
+زايد X على M الكل أس M as M tends to infinity
+
+21
+00:03:04,010 --> 00:03:10,850
+بساوي E أس X ال limit هذه معروفة موجودة هنا
+
+22
+00:03:14,080 --> 00:03:26,660
+باستخدام ال limit هذه ممكن ان احنا وبالتالي
+
+23
+00:03:26,660 --> 00:03:29,900
+تعالى
+
+24
+00:03:29,900 --> 00:03:36,380
+نشوف واحد زائد واحد على اتنين in الكل اصلا تلاتة
+
+25
+00:03:36,380 --> 00:03:42,060
+inنحاول نكتب هذا على صورة واحد زائد X على M الكل
+
+26
+00:03:42,060 --> 00:03:48,280
+قص M فهذا ممكن كتابته على صورة المقدار هذا على
+
+27
+00:03:48,280 --> 00:03:57,120
+الصورة واحد زائد نص على M نص
+
+28
+00:03:57,120 --> 00:04:05,600
+على M الكل قص M الكل
+
+29
+00:04:05,600 --> 00:04:06,160
+تكيين
+
+30
+00:04:09,900 --> 00:04:19,240
+صحيح وبالتالي therefore limit لما انتقل ل infinity
+
+31
+00:04:19,240 --> 00:04:28,160
+ل ال sequence اللي لحد تبعها هذا بيساوي limit لما
+
+32
+00:04:28,160 --> 00:04:36,570
+انتقل ل infinity ل الكلام هذا للمفضار اللي هناو هي
+
+33
+00:04:36,570 --> 00:04:43,330
+عندي واحد زي ال X على M او M الكل اص M ف limit
+
+34
+00:04:43,330 --> 00:04:53,370
+المقدار اللي جوا بساوي E اص نص او E اص X الكل ده
+
+35
+00:04:53,370 --> 00:04:57,150
+كئيب انا مقدر ادخل ال limit جوا القصير المربعين
+
+36
+00:04:57,150 --> 00:05:02,830
+limit المقدار اللي جوا جوا القصير المربعينحسب
+
+37
+00:05:02,830 --> 00:05:08,030
+القاعدة او القانون هذا E أُس X اللي هو نص وبعدين 2
+
+38
+00:05:08,030 --> 00:05:15,610
+بالكلتك A فبطلع E أُس 3 على 2 إذا هذه هي قيمة ال
+
+39
+00:05:15,610 --> 00:05:19,990
+limit okay تمام في
+
+40
+00:05:19,990 --> 00:05:25,090
+أسلة تانية في ال section هذا تلاتة أربعة
+
+41
+00:05:32,810 --> 00:05:48,550
+PIS love section تلاتة أربعة طيب
+
+42
+00:05:48,550 --> 00:05:54,230
+section تلاتة خمسة أنا في السؤال الرابع الشخصي
+
+43
+00:05:54,230 --> 00:05:54,650
+التاني
+
+44
+00:06:02,810 --> 00:06:07,190
+سيكشن تلاتة خمسة الرابع ولا التالت قصدك؟ الرابع
+
+45
+00:06:07,190 --> 00:06:17,710
+سؤال
+
+46
+00:06:17,710 --> 00:06:23,810
+رقم أربعة سيكشن تلاتة خمسة طيب
+
+47
+00:06:23,810 --> 00:06:27,890
+سؤال
+
+48
+00:06:27,890 --> 00:06:33,710
+أربعة سيكشن تلاتة خمسةالسؤال هذا بتقول show
+
+49
+00:06:33,710 --> 00:06:37,750
+directly from the definition
+
+50
+00:07:01,910 --> 00:07:17,610
+إذا XIN و YIN هم سيكونات كوشي هم سيكونات
+
+51
+00:07:17,610 --> 00:07:21,070
+كوشي هم
+
+52
+00:07:21,070 --> 00:07:27,550
+سيكونات كوشي هم سيكونات كوشي
+
+53
+00:07:30,650 --> 00:07:34,270
+فبرهان هذه زي البرهان اللي أخدناها قبل هيك في
+
+54
+00:07:34,270 --> 00:07:41,290
+قوانين نهايات proof
+
+55
+00:07:41,290 --> 00:07:50,350
+similar to proof of
+
+56
+00:07:50,350 --> 00:07:53,470
+the fact أنه
+
+57
+00:08:18,370 --> 00:08:23,890
+بساوي limit xn ضرب limit yn
+
+58
+00:08:27,620 --> 00:08:31,000
+و أعتقد هذا برهنها بالتفصيل using epsilon over two
+
+59
+00:08:31,000 --> 00:08:40,220
+argument تذكره؟ أه فحاولي تكتبي برهان مشابه و إذا
+
+60
+00:08:40,220 --> 00:08:50,280
+كان ماقدرتيش ممكن بعديها أعطيكي برهان تفصيلي okay؟
+
+61
+00:08:50,280 --> 00:08:52,180
+في أي أسئلة تانية؟
+
+62
+00:08:58,920 --> 00:09:04,620
+section تلقيتها خمسة
+
+63
+00:09:04,620 --> 00:09:15,820
+سؤال
+
+64
+00:09:15,820 --> 00:09:23,200
+عشرة ناس
+
+65
+00:09:23,200 --> 00:09:24,000
+سؤال عشر
+
+66
+00:09:28,420 --> 00:09:38,620
+section تلاتة خمسة if
+
+67
+00:09:38,620 --> 00:09:46,600
+x one less than x two are
+
+68
+00:09:46,600 --> 00:09:51,660
+arbitrary
+
+69
+00:09:55,690 --> 00:10:09,210
+real numbers and
+
+70
+00:10:09,210 --> 00:10:14,530
+xn
+
+71
+00:10:14,530 --> 00:10:19,470
+بيساوي نص
+
+72
+00:10:21,890 --> 00:10:37,690
+xn-2 plus xn-1 for n أكبر من 2 show in the
+
+73
+00:10:37,690 --> 00:10:42,470
+sequence xn is convergent
+
+74
+00:10:50,120 --> 00:10:55,760
+what is its limit what is
+
+75
+00:10:55,760 --> 00:11:03,520
+its limit ده هي النهاية تبعتنا بدنا نوجد نهايتها
+
+76
+00:11:03,520 --> 00:11:15,440
+في
+
+77
+00:11:15,440 --> 00:11:25,450
+حد فيكم فكر فيحلل السؤال هذاأي حد يعني حاول
+
+78
+00:11:25,450 --> 00:11:37,510
+ال burn in clever في أي أفكار أي شيء مافيش عندكم
+
+79
+00:11:37,510 --> 00:11:45,650
+أي فكرة عن الحل نحلوا
+
+80
+00:11:45,650 --> 00:11:46,890
+مع بعض نشوف
+
+81
+00:11:49,810 --> 00:11:58,450
+أنا عندي من الفرض x1 أصغر من x2 أعداد حقيقية فهعرف
+
+82
+00:11:58,450 --> 00:12:07,890
+let L بساوي x2 negative x1 هذا بيطلع عدد موجب لأن
+
+83
+00:12:07,890 --> 00:12:16,770
+x2 أكبر من x1 الآن باستخدام ال induction use
+
+84
+00:12:16,770 --> 00:12:17,570
+induction
+
+85
+00:12:21,840 --> 00:12:29,220
+on n بيمكنكم
+
+86
+00:12:29,220 --> 00:12:35,820
+تثبته انه المعادلة
+
+87
+00:12:35,820 --> 00:12:44,080
+التالية absolute xn plus one negative xn بساوي L
+
+88
+00:12:44,080 --> 00:12:49,960
+over two to n negative one and this is true for
+
+89
+00:12:49,960 --> 00:12:50,820
+every L
+
+90
+00:12:59,660 --> 00:13:08,000
+إذا كان n بساوي لكل
+
+91
+00:13:08,000 --> 00:13:14,300
+n أكبر من أو يساوي اتنين عشان هنا يكون هذا المعنى
+
+92
+00:13:14,300 --> 00:13:21,290
+فابدى ب n بساوي اتنين و اثبت ان المعادلة هذه صحقفل
+
+93
+00:13:21,290 --> 00:13:24,910
+بصحيته عند n بساوي k حيث k أكبر من اتنين أعداد
+
+94
+00:13:24,910 --> 00:13:29,410
+طبيعي وثبت صحيته عند n بساوي k زاد واحد طبعا في
+
+95
+00:13:29,410 --> 00:13:35,070
+الإثباتات بدك تستخدم التعريف تبع xn بدلالة الحدود
+
+96
+00:13:35,070 --> 00:13:35,670
+اللي جابله
+
+97
+00:13:41,020 --> 00:13:45,480
+و التعريف اللي انا اخدته ان ال هو عبارة عن الفرط
+
+98
+00:13:45,480 --> 00:13:51,340
+بين X2 و X1 اذا هذا سهل ممكن تبعته by induction
+
+99
+00:13:51,340 --> 00:14:01,740
+الان بعد ما تتبت هذا by induction now use this to
+
+100
+00:14:01,740 --> 00:14:02,540
+show that
+
+101
+00:14:08,470 --> 00:14:20,450
+بنستخدم المعادلة هذه to show that if M أكبر من N
+
+102
+00:14:20,450 --> 00:14:33,250
+أعداد طبيعية then absolute XM negative XM ال
+
+103
+00:14:33,250 --> 00:14:40,070
+absolute value لفرق XM و XMطبعا هذا هنخليه اصغر من
+
+104
+00:14:40,070 --> 00:14:48,610
+او ساوي absolute xn minus xn plus one زي absolute
+
+105
+00:14:48,610 --> 00:14:57,510
+xn plus one minus xn plus two و هكذا
+
+106
+00:15:02,520 --> 00:15:09,560
+absolute xm negative one negative xm
+
+107
+00:15:09,560 --> 00:15:13,840
+okay
+
+108
+00:15:13,840 --> 00:15:24,240
+تمام انا ايش عملت طرحت xn زيادة واحد ورجعتها طرحت
+
+109
+00:15:24,240 --> 00:15:29,290
+xn زيادة اتنين ورجعتهاو بعدين أخدت الأزواج هذه مع
+
+110
+00:15:29,290 --> 00:15:34,530
+بعض و استخدمت ل triangle inequality ال absolute
+
+111
+00:15:34,530 --> 00:15:39,390
+value ل مجموعة كبيرة أصغر من أوسع مجموعة absolute
+
+112
+00:15:39,390 --> 00:15:47,250
+values فالان
+
+113
+00:15:47,250 --> 00:15:54,530
+باستخدام لو سمينا المعادلة هاد ال star فباستخدام
+
+114
+00:15:54,530 --> 00:16:04,180
+ال starالـ absolute value هذه بساوي ال over two to
+
+115
+00:16:04,180 --> 00:16:12,840
+n minus واحد okay هذه نفسها دي و ال absolute value
+
+116
+00:16:12,840 --> 00:16:24,240
+اللي بعدها بساوي ال على two to n و هكذا و آخر حد
+
+117
+00:16:24,240 --> 00:16:33,390
+هيكون ال overtwo to m negative two لان
+
+118
+00:16:33,390 --> 00:16:39,170
+استخدام السارق مظبوط الان ممكن ناخد عامل مشترك
+
+119
+00:16:39,170 --> 00:16:52,230
+هاخد
+
+120
+00:16:52,230 --> 00:16:54,750
+عامل مشترك L over
+
+121
+00:17:16,500 --> 00:17:17,900
+تمام؟
+
+122
+00:17:20,140 --> 00:17:25,760
+الان هذا اصغر من واحد على اتنين قص ان نجاتف واحد
+
+123
+00:17:25,760 --> 00:17:34,980
+والمجموع هذا اصغر من اتنين
+
+124
+00:17:34,980 --> 00:17:41,660
+لان هذا جزء من الهارمونيك جيومتريكس سيريز اللي هي
+
+125
+00:17:41,660 --> 00:17:46,820
+واحد على اتنين قص ان من ان equal zero to infinity
+
+126
+00:17:46,820 --> 00:17:51,550
+هذه مجموعة اتنينفهذا جزء منها وبالتالي المجموعة
+
+127
+00:17:51,550 --> 00:17:55,650
+هذا أصغر من المجموعة الـ geometric series هذه
+
+128
+00:17:55,650 --> 00:18:01,490
+المجموعة بساوة اتنين okay فإذا هذا المجموعة أصغر
+
+129
+00:18:01,490 --> 00:18:06,030
+من اتنين إذا هذا أصغر من واحد على اتنين قص ان سالب
+
+130
+00:18:06,030 --> 00:18:14,990
+واحد في اتنين اللي هو عبارة عن واحد على اتنين قص
+
+131
+00:18:14,990 --> 00:18:17,410
+ان سالب اتنين
+
+132
+00:18:28,770 --> 00:18:35,790
+الان هذا بيروح للسفر as n tends to infinityهو
+
+133
+00:18:35,790 --> 00:18:40,770
+بالتالي ده بتطلع عندي أنا ال limit ل absolute xn
+
+134
+00:18:40,770 --> 00:18:49,670
+minus xm as m as n tenths of infinity و طبعاً m
+
+135
+00:18:49,670 --> 00:18:55,410
+تقول infinity تساوي سفر therefore ال sequence xn
+
+136
+00:18:55,410 --> 00:18:57,270
+is Cauchy
+
+137
+00:19:02,500 --> 00:19:09,620
+و بالتالي therefore by cauchy criterion by cauchy
+
+138
+00:19:09,620 --> 00:19:17,660
+criterion x in convergence صح؟ say
+
+139
+00:19:26,770 --> 00:19:35,110
+دعينا نسمي ال limit ل x in بساوي x حيث x is real
+
+140
+00:19:35,110 --> 00:19:41,110
+number الان مطلوب ان احنا نجد قيمة ال x قيمة ال
+
+141
+00:19:41,110 --> 00:19:48,470
+limit لل sequence اللى هى سمنها x فبنرجع للمعادلة
+
+142
+00:19:48,470 --> 00:19:49,730
+هناك
+
+143
+00:20:07,880 --> 00:20:13,020
+to find x
+
+144
+00:20:13,020 --> 00:20:18,980
+take limits
+
+145
+00:20:18,980 --> 00:20:23,960
+of
+
+146
+00:20:23,960 --> 00:20:26,940
+both sides
+
+147
+00:20:32,640 --> 00:20:49,540
+في المعادلة هذه اللي هنا and then
+
+148
+00:20:49,540 --> 00:20:56,480
+take limit of both sides in this equation to get
+
+149
+00:20:56,480 --> 00:21:09,330
+انه limitx in بساوي نص في limit x in negative two
+
+150
+00:21:09,330 --> 00:21:21,850
+زاد limit x in negative one as intensity هذا
+
+151
+00:21:21,850 --> 00:21:28,510
+بيقدي ان limit x in عبارة عن x بساوي نص هذه
+
+152
+00:21:28,510 --> 00:21:33,460
+subsequenceمن الـ xn، وبالتالي، الـ limit تبعتها
+
+153
+00:21:33,460 --> 00:21:37,880
+برضه x وهذا الـ subsequence من الـ xn والـ limit
+
+154
+00:21:37,880 --> 00:21:45,400
+تبعتها x لإن كانت الـ sequence convergent لـ x فأي
+
+155
+00:21:45,400 --> 00:21:50,080
+subsequence بتكون convergent لنفس الـ x وهذا بيطلع
+
+156
+00:21:50,080 --> 00:21:51,100
+بساوية
+
+157
+00:22:12,850 --> 00:22:18,570
+فاحنا هيك ماطلعش عندنا إش جديد طالع X بساوي X
+
+158
+00:22:18,570 --> 00:22:25,950
+فاحنا هيك مازمناش ال limit مازمناش
+
+159
+00:22:25,950 --> 00:22:26,570
+ال limit
+
+160
+00:22:50,820 --> 00:22:57,180
+فاحنا هيك ماجبناش ال limit وهدي مشكلة أو يعني ال
+
+161
+00:22:57,180 --> 00:22:57,600
+..
+
+162
+00:23:14,130 --> 00:23:21,570
+طب خلينا نرجع للمعادلة اللي اثبتناها اثبتناها
+
+163
+00:23:21,570 --> 00:23:22,410
+by induction
+
+164
+00:24:17,920 --> 00:24:22,600
+طيب خلّي موضوع ال limit هذا لمرة تانية
+
+165
+00:24:31,270 --> 00:24:33,370
+سي حد عنده أي فكرة؟
+
+166
+00:24:55,010 --> 00:25:03,350
+خلّي ال limit نجيبها المرة الجاية يبدو
+
+167
+00:25:03,350 --> 00:25:09,630
+أن الطريقة تباعتنا ما .. ما زبطتش فنحاول نفكر فيها
+
+168
+00:25:09,630 --> 00:25:14,810
+مرة تانية و نجيبها، مين عنده سؤال تاني؟ و أنتوا
+
+169
+00:25:14,810 --> 00:25:17,830
+كمان طبعا فكروا في إيجاب قيمة ال limit
+
+170
+00:25:25,090 --> 00:25:33,030
+في أي أسئلة تانية في ال section تلاتة خمسة سؤال
+
+171
+00:25:33,030 --> 00:25:46,130
+تمانية سؤال تمانية سؤال
+
+172
+00:25:46,130 --> 00:25:54,030
+تمانية section تلاتة خمسة show directly
+
+173
+00:25:57,190 --> 00:26:05,590
+مش هو directly that
+
+174
+00:26:05,590 --> 00:26:12,550
+a bounded a
+
+175
+00:26:12,550 --> 00:26:24,370
+bounded a bounded monotone a bounded monotone
+
+176
+00:26:27,280 --> 00:26:36,500
+ماراتون ان كريزم ماراتون
+
+177
+00:26:36,500 --> 00:26:42,560
+ان كريزم الاختصار هو
+
+178
+00:26:42,560 --> 00:26:43,300
+كوشي
+
+179
+00:26:56,170 --> 00:27:01,310
+السيكوينس دي bounded و monotone increasing فاحنا
+
+180
+00:27:01,310 --> 00:27:10,100
+خدنا نظرية بتطلع لازم تكونby monotone convergence
+
+181
+00:27:10,100 --> 00:27:13,100
+theorem it is convergent عسب ال monotone
+
+182
+00:27:13,100 --> 00:27:17,380
+convergence و بالتالي ممكن نقول by Cauchy
+
+183
+00:27:17,380 --> 00:27:20,780
+criterion بما انها convergent اذا Cauchy هذا برهان
+
+184
+00:27:20,780 --> 00:27:26,180
+و صحيح بس الكتاب مش عايز هذا البرهان عايز برهان
+
+185
+00:27:26,180 --> 00:27:30,500
+مباشر باستخدام ال definition تبع ال Cauchy
+
+186
+00:27:30,500 --> 00:27:38,260
+sequenceOkay فالبرهان بسيط وسهل يعني ما هوش صعب
+
+187
+00:27:38,260 --> 00:27:44,060
+proof since
+
+188
+00:27:44,060 --> 00:27:49,820
+طبعا
+
+189
+00:27:49,820 --> 00:27:57,400
+ال sequence خليني أسميها x in since
+
+190
+00:27:57,400 --> 00:28:02,980
+ال sequence تبعتنا x inis bounded بما ان ال
+
+191
+00:28:02,980 --> 00:28:08,980
+sequence is bounded then
+
+192
+00:28:08,980 --> 00:28:25,680
+لو أخدت U بساوي Supremum ل XN-N ينتمي لإن Supremum
+
+193
+00:28:25,680 --> 00:28:28,060
+هذا exists in R
+
+194
+00:28:32,840 --> 00:28:39,620
+by supremum property او by completeness property
+
+195
+00:28:39,620 --> 00:28:48,520
+اي bounded set has supremum فخلينا نفرض ان ال U هو
+
+196
+00:28:48,520 --> 00:28:54,300
+supremum فهذا بيطلع عدد حقيقي exist يعني عدد حقيقي
+
+197
+00:28:54,300 --> 00:29:01,120
+الان من ال definition by
+
+198
+00:29:01,120 --> 00:29:08,250
+definitionof supremum
+
+199
+00:29:08,250 --> 00:29:16,030
+هو بالأحرى مش من التعريف من لمّة تأتي بعد التعريف
+
+200
+00:29:16,030 --> 00:29:19,630
+والمّة
+
+201
+00:29:19,630 --> 00:29:23,110
+من
+
+202
+00:29:23,110 --> 00:29:29,990
+هنا by Aprilius
+
+203
+00:29:40,440 --> 00:29:44,220
+النظرية هذه خلينا نرجعها أو نجمها او نجمها او
+
+204
+00:29:44,220 --> 00:29:48,460
+نجمها او نجمها U of a set
+
+205
+00:30:02,180 --> 00:30:07,180
+of a set S
+
+206
+00:30:07,180 --> 00:30:11,960
+is
+
+207
+00:30:11,960 --> 00:30:16,440
+the supremum is
+
+208
+00:30:16,440 --> 00:30:17,420
+the supremum
+
+209
+00:30:22,570 --> 00:30:32,010
+S F and only F لكل أبسلون أكبر من السفر يوجد عنصر
+
+210
+00:30:32,010 --> 00:30:39,950
+S يعتبد على أبسلون في S بحيث أنه لو ضفنا .. لو
+
+211
+00:30:39,950 --> 00:30:45,250
+طرحنا من ال supremum أبسلون فبيبطل أكبر دعوة بيصير
+
+212
+00:30:45,250 --> 00:30:55,520
+أصغر من Sباستخدام هذه النظرية السابقة لو أخدت
+
+213
+00:30:55,520 --> 00:31:01,500
+given
+
+214
+00:31:01,500 --> 00:31:04,880
+epsilon
+
+215
+00:31:04,880 --> 00:31:09,620
+أكبر من السفر لو أخدت epsilon عشوائية أكبر من
+
+216
+00:31:09,620 --> 00:31:17,320
+السفر يوجد capital N في N
+
+217
+00:31:22,170 --> 00:31:35,390
+عدد طبيعي بحيث ان ال .. ال .. ال
+
+218
+00:31:35,390 --> 00:31:43,690
+U نيجاتيب XN عرفوا ال U نيجاتيب إبسلون بيطلع أصغر
+
+219
+00:31:43,690 --> 00:31:50,270
+من S Y S Y حقول ده X اللي ال index سبقه capital N
+
+220
+00:31:51,310 --> 00:31:54,710
+إذا هذا العنصر اللي في الـ sequence أو في ال set
+
+221
+00:31:54,710 --> 00:32:01,950
+هذه اللي هو S Y يعتمد على إبسلون ما ال N هذه تعتمد
+
+222
+00:32:01,950 --> 00:32:09,310
+على إبسلون وهي U إترح منه إبسلون بيطلع أصغر من
+
+223
+00:32:09,310 --> 00:32:15,150
+عنصر S Y اللي هو موجود هنا إذا هذا حسب النظرية
+
+224
+00:32:15,150 --> 00:32:20,050
+تمام؟ الآن since
+
+225
+00:32:22,680 --> 00:32:29,060
+لاحظوا انتوا ان ال XIN هذا عنصر في الست وبالتالي و
+
+226
+00:32:29,060 --> 00:32:32,660
+ال U upper bound ال U اللي هو ال supreme دايما
+
+227
+00:32:32,660 --> 00:32:37,180
+بيكون upper bound فهذا بيطلع أصغر من أو ساوي ال U
+
+228
+00:32:37,180 --> 00:32:43,420
+since
+
+229
+00:32:43,420 --> 00:32:50,740
+ال sequence XIN is increasing متزايدة
+
+230
+00:32:55,230 --> 00:32:59,870
+we get نحصل
+
+231
+00:32:59,870 --> 00:33:08,330
+على التالي فنحصل
+
+232
+00:33:08,330 --> 00:33:17,590
+على التالي لو كان M أكبر من أو ساوي N أكبر من أو
+
+233
+00:33:17,590 --> 00:33:26,720
+ساوي capital Nفهذا هيقدّي إلى أن u negative
+
+234
+00:33:26,720 --> 00:33:35,200
+epsilon أصغر من x capital N من هنا و x capital N
+
+235
+00:33:35,200 --> 00:33:42,260
+أصغر من أو سوى x small n لأن ال sequence is
+
+236
+00:33:42,260 --> 00:33:46,730
+increasing و small n أكبر من أو سوى capital Nو هذا
+
+237
+00:33:46,730 --> 00:33:54,070
+أصغر من أوي ساوي xm لأن ال sequence increasing و
+
+238
+00:33:54,070 --> 00:33:59,690
+xm أصغر من أوي ساوي u لأن ال u upper bound لكل
+
+239
+00:33:59,690 --> 00:34:06,670
+عناصر ال sequence تمام؟ و ال u
+
+240
+00:34:15,980 --> 00:34:22,260
+فهذا بيقدّي .. هذا
+
+241
+00:34:22,260 --> 00:34:30,320
+بيقدّي ان xn minus
+
+242
+00:34:30,320 --> 00:34:37,000
+epsilon أصغر من xn لأن الepsilon عدد موجب فلما
+
+243
+00:34:37,000 --> 00:34:44,570
+اطلع عدد موجب العدد xn بصغروعندي xn أصغر من أو
+
+244
+00:34:44,570 --> 00:34:50,490
+ساوي xm لأن ال m أكبر من أو ساوي n و ال sequence
+
+245
+00:34:50,490 --> 00:34:57,110
+تبعتي increasing و xm أصغر من أو ساوي ال u
+
+246
+00:35:11,700 --> 00:35:21,020
+من هنا، من المتباينة هذه واضح ان انا عندي ال
+
+247
+00:35:21,020 --> 00:35:31,020
+U أصغر من XN زاد إبسلون، صح؟ هل عندي U negative
+
+248
+00:35:31,020 --> 00:35:39,160
+إبسلون أصغر من XN فاضيف إبسلون فبطلع U أصغر من XN
+
+249
+00:35:40,390 --> 00:35:49,470
+زايد ابسلون اذا انا بطلع عندى xn
+
+250
+00:35:49,470 --> 00:36:02,450
+او ال .. ال xm تطلع اكبر من xn minus ابسلون اصغر
+
+251
+00:36:02,450 --> 00:36:04,730
+من xn زايد ابسلون
+
+252
+00:36:08,370 --> 00:36:19,010
+وهذا معناه ان absolute xn او xn minus xn اصغر من
+
+253
+00:36:19,010 --> 00:36:28,730
+epsilon اصبت؟ صح؟ وهذا صحيح لكل M أكبر من أو ساوي
+
+254
+00:36:28,730 --> 00:36:34,030
+M أكبر من أو ساوي capital M تمام؟ اذا بنقول هنا
+
+255
+00:36:34,030 --> 00:36:46,340
+sinceepsilon أكبر من السفر was arbitrary it
+
+256
+00:36:46,340 --> 00:36:50,640
+follows بينتج
+
+257
+00:36:50,640 --> 00:36:58,820
+من تعريف الكوشي sequence that sequence xm is
+
+258
+00:36:58,820 --> 00:36:59,620
+cauchy
+
+259
+00:37:03,200 --> 00:37:11,000
+وهنا هيك طبقنا التعريف وهذا برهان مباشر okay تمام
+
+260
+00:37:11,000 --> 00:37:22,940
+واضح في
+
+261
+00:37:22,940 --> 00:37:26,520
+أي سؤال سؤال تانية واضح البرهان في أي سفصار
+
+262
+00:37:32,980 --> 00:37:38,320
+في أي سؤال تاني section تلاتة خمسة أو تلاتة ستة
+
+263
+00:37:38,320 --> 00:37:41,600
+لبعده
+
+264
+00:37:41,600 --> 00:37:50,060
+الناس
+
+265
+00:37:50,060 --> 00:37:50,920
+اللي بدرسوا
+
+266
+00:38:03,440 --> 00:38:10,060
+التلاتة ستة؟ سؤال أربعة في رياضينا.
+
+267
+00:38:23,080 --> 00:38:24,980
+هذا ما حللناه إزاي؟
+
+268
+00:38:44,990 --> 00:38:54,970
+السكتشن تلاتة ستة السؤال الرابع ترى بي establish
+
+269
+00:38:54,970 --> 00:38:58,370
+establish
+
+270
+00:38:58,370 --> 00:39:01,490
+the
+
+271
+00:39:01,490 --> 00:39:05,790
+proper divergence
+
+272
+00:39:05,790 --> 00:39:10,270
+of
+
+273
+00:39:10,270 --> 00:39:12,950
+sequence
+
+274
+00:39:16,730 --> 00:39:25,730
+يجيب الان زي الواحد ان الان اكوار الواحد تنتهي ان
+
+275
+00:39:25,730 --> 00:39:33,910
+انا اثبت ان انا اثبت
+
+276
+00:39:33,910 --> 00:39:39,250
+ان انا اثبت ان انا اثبت
+
+277
+00:39:39,250 --> 00:39:45,220
+ان انا اثبت ان انا اثبتلا ال sequence اللي ال inf
+
+278
+00:39:45,220 --> 00:39:49,820
+term تبعها و الحد العام تبعها جدر انزعي الواحد لما
+
+279
+00:39:49,820 --> 00:39:58,300
+M تقوى ل infinity بساوي infinity استاذ ماعرفش طلقة
+
+280
+00:39:58,300 --> 00:40:07,900
+D ماعرفش بيه بيه عرفت حلوة دي طلقة دي
+
+281
+00:40:07,900 --> 00:40:13,460
+استاذ بدك دي طرقة ديالفرقة دي
+
+282
+00:40:40,070 --> 00:40:46,330
+يعني هيطلع عندي هنا limit in على جدر in زي الواحد
+
+283
+00:40:46,330 --> 00:40:53,390
+لما in تقول infinity بساوي infinity ممكن تستخدم
+
+284
+00:40:53,390 --> 00:41:03,190
+limit comparison test او comparison test اه فال
+
+285
+00:41:07,800 --> 00:41:12,180
+فهل فكرتي انك تستخدمي comparison test او limit
+
+286
+00:41:12,180 --> 00:41:16,260
+comparison test؟ فكرت عن نظري يعني برنامج ده يفير
+
+287
+00:41:16,260 --> 00:41:20,140
+لأ و أنت عندك التعريف و عندك في limit comparison
+
+288
+00:41:20,140 --> 00:41:29,620
+test و comparison test لأ
+
+289
+00:41:29,620 --> 00:41:36,110
+هاي موجود في تلاتة ستة في ..مافيش limit comparison
+
+290
+00:41:36,110 --> 00:41:49,030
+test؟ فيك طيب هاي انا شايف في ..
+
+291
+00:41:49,030 --> 00:41:55,870
+انت
+
+292
+00:41:55,870 --> 00:42:01,970
+عندك .. ياعمل المقارنة انت
+
+293
+00:42:01,970 --> 00:42:03,010
+عندك ..
+
+294
+00:42:10,490 --> 00:42:19,450
+يعني قارنة ال .. جدر ال N بدك تقارن هذه مع
+
+295
+00:42:19,450 --> 00:42:26,430
+N على جدر ال N لما N تكون كبيرة ابنهم الواحد فهذه
+
+296
+00:42:26,430 --> 00:42:30,090
+بيصير زيها زي ال sequence اللي لحد الآن تبعها N
+
+297
+00:42:30,090 --> 00:42:34,390
+على جدر ال N وهذه بيساوي جدر ال N
+
+298
+00:42:39,240 --> 00:42:43,420
+فبتعمل limit comparison use limit comparison test
+
+299
+00:42:43,420 --> 00:42:51,280
+هاي عندي an ولا إيش مسميهم الكتاب نعم
+
+300
+00:42:51,280 --> 00:42:59,780
+يعني xn وهي yn وتعالى نحسب ال limit
+
+301
+00:43:08,200 --> 00:43:13,480
+تعالى نحسب ال limit ل
+
+302
+00:43:13,480 --> 00:43:21,100
+xn على yn as n tends to infinity بساوي ال limit ل
+
+303
+00:43:21,100 --> 00:43:31,820
+n على الجذر n زي الواحد تقسيم
+
+304
+00:43:37,120 --> 00:43:43,740
+في واحد على جدر ال N لما N تقول ال infinity بيساوي
+
+305
+00:43:43,740 --> 00:43:47,840
+limit لجدر
+
+306
+00:43:47,840 --> 00:43:55,000
+التربية A ل N على N زي واحد مظبوط؟
+
+307
+00:43:55,000 --> 00:44:02,380
+بندخل ال limit جوه فبقلع واحد اكبر من صفته الان
+
+308
+00:44:02,380 --> 00:44:09,580
+sinceاحنا اثبتنا ان ال series sigma او ال sequence
+
+309
+00:44:09,580 --> 00:44:16,700
+since ال sequence ان الحد العام تبعها جدر ال n او
+
+310
+00:44:16,700 --> 00:44:21,720
+since limit yn
+
+311
+00:44:21,720 --> 00:44:27,480
+as n tends to infinity بالساوية limit جدر ال n as
+
+312
+00:44:27,480 --> 00:44:31,500
+n tends to infinity بالساوية infinity we get
+
+313
+00:44:34,620 --> 00:44:41,340
+from limit comparison test from limit comparison
+
+314
+00:44:41,340 --> 00:44:47,100
+test from limit
+
+315
+00:44:47,100 --> 00:44:48,480
+comparison test from limit comparison test from
+
+316
+00:44:48,480 --> 00:44:48,500
+from limit comparison test from limit comparison
+
+317
+00:44:48,500 --> 00:44:48,600
+from limit comparison test from limit comparison
+
+318
+00:44:48,600 --> 00:44:48,640
+comparison test from limit comparison test from
+
+319
+00:44:48,640 --> 00:44:50,520
+comparison test from limit comparison test from
+
+320
+00:44:50,520 --> 00:44:57,100
+limit comparison test from limit
+
+321
+00:44:57,100 --> 00:45:00,980
+comparison test from limit comparison test
+
+322
+00:45:13,250 --> 00:45:18,150
+تمام؟ okay اذا ممكن نستخدم ال limit comparison
+
+323
+00:45:18,150 --> 00:45:23,290
+test او ال diet comparison test اذا نفع و نحل باج
+
+324
+00:45:23,290 --> 00:45:28,010
+التمارين في .. او الأجزاء الأخرى في exercise أربعة
+
+325
+00:45:28,010 --> 00:45:33,430
+رقم .. section تلاتة ستة okay بنوقف هنا و بنكمل
+
+326
+00:45:33,430 --> 00:45:38,190
+المرة الجاية نكتفي بهذا القدر
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..23f52a821bbbe5eb959e29a5b41374cbfcfc733e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0.srt
@@ -0,0 +1,1611 @@
+1
+00:00:22,080 --> 00:00:28,960
+بسم الله الرحمن الرحيم  .. هنواصل اليوم إن شاء 
+
+2
+00:00:28,960 --> 00:00:39,080
+الله  ..  .. الشيء اللي بدأنا بخصوص المقدمة عن
+
+3
+00:00:39,080 --> 00:00:46,520
+الـ infinite series بعتقد كانت آخر نظرية أخذناها هي
+
+4
+00:00:46,520 --> 00:00:47,700
+Cauchy criterion
+
+5
+00:00:51,790 --> 00:00:56,710
+كوشي كريتيريا for
+
+6
+00:00:56,710 --> 00:01:10,250
+infinite series 
+
+7
+00:01:10,250 --> 00:01:10,810
+series
+
+8
+00:01:22,490 --> 00:01:31,530
+converges if and only if الشرط التالي بيتحقق لكل
+
+9
+00:01:31,530 --> 00:01:38,430
+epsilon أكبر من 0 يوجد  capital N يعتمد على epsilon
+
+10
+00:01:38,430 --> 00:01:46,200
+عدد طبيعي بحيث أنه لو كان M أكبر من N أكبر من أو 
+
+11
+00:01:46,200 --> 00:01:56,560
+ساوي capital M فهذا بيؤدي إلى أن absolute SM minus SN
+
+12
+00:01:56,560 --> 00:02:05,840
+بيساوى absolute XN زائد واحد زائد XN زائد اثنين وهكذا 
+
+13
+00:02:05,840 --> 00:02:07,300
+إلى XM
+
+14
+00:02:11,640 --> 00:02:15,100
+النظرية هذه تبع كوشي أخذناها المرة اللي فاتت و
+
+15
+00:02:15,100 --> 00:02:22,080
+برهناها مظبوط، اليوم هناخد نظرية ثانية ومهمة و
+
+16
+00:02:22,080 --> 00:02:31,660
+النظرية هذه بتقول أنه let x in be sequence of non
+
+17
+00:02:31,660 --> 00:02:39,620
+-negative real numbers then
+
+18
+00:02:39,620 --> 00:02:40,420
+series
+
+19
+00:02:43,080 --> 00:02:49,340
+xn converges if
+
+20
+00:02:49,340 --> 00:02:55,680
+and only if الـ sequence of partial sums its
+
+21
+00:02:55,680 --> 00:03:05,600
+sequence of partial sums اللي 
+
+22
+00:03:05,600 --> 00:03:07,540
+هي sn is bounded
+
+23
+00:03:16,760 --> 00:03:24,080
+proof we have sn
+
+24
+00:03:24,080 --> 00:03:36,020
+بيساوى أو sn زائد واحد بيساوى sn 
+
+25
+00:03:36,020 --> 00:03:42,070
+زائد xn زائد واحد الآن زائد فرص partial sum بيساوى 
+
+26
+00:03:42,070 --> 00:03:46,150
+الـ partial sum وبنضيف عليه لحد رقم n زائد واحد
+
+27
+00:03:58,050 --> 00:04:02,070
+وطبعا الـ Xn زائد واحد هذا احنا فرضين أن حدود الـ
+
+28
+00:04:02,070 --> 00:04:08,530
+sequence Xn كلها غير سالبة فهذا غير سالب وبالتالي
+
+29
+00:04:08,530 --> 00:04:14,790
+المجموع هذا بالتأكيد أكبر من أو يساوى Sn لكل N في N
+
+30
+00:04:14,790 --> 00:04:17,870
+فهذا
+
+31
+00:04:17,870 --> 00:04:24,530
+معناه أن الـ sequence Sn is increasing متزايدة
+
+32
+00:04:26,960 --> 00:04:30,480
+بالتالي، من خلال الوضع الوضع الوضع الوضع الوضع
+
+33
+00:04:30,480 --> 00:04:36,420
+الوضع الوضع
+
+34
+00:04:36,420 --> 00:04:40,960
+الوضع
+
+35
+00:04:40,960 --> 00:04:48,560
+الوضع الوضع
+
+36
+00:05:21,390 --> 00:05:23,410
+وهو المطلوب
+
+37
+00:05:25,890 --> 00:05:29,190
+احنا أخذنا قبل هيك أن أي infinite series بتكون
+
+38
+00:05:29,190 --> 00:05:32,890
+convergent if and only if the sequence of partial
+
+39
+00:05:32,890 --> 00:05:36,810
+sums is convergent، صح؟ طيب، الـ sequence of
+
+40
+00:05:36,810 --> 00:05:42,650
+partial sums بمعنها increasing فهي convergent by
+
+41
+00:05:42,650 --> 00:05:48,050
+monotone convergence theorem بتكون convergent if
+
+42
+00:05:48,050 --> 00:05:52,130
+and only if it is bounded وبالتالي الـ series
+
+43
+00:05:52,130 --> 00:05:54,770
+converges if and only if the sequence of partial
+
+44
+00:05:54,770 --> 00:06:02,210
+sums is bounded وهذا يثبت النظرية تمام؟ إذن هذه
+
+45
+00:06:02,210 --> 00:06:09,410
+النظرية أهميتها في أننا يعني تطبيقها زي ما هنشوف
+
+46
+00:06:09,410 --> 00:06:12,650
+في
+
+47
+00:06:12,650 --> 00:06:14,590
+لما هنا صغيرة لما 
+
+48
+00:06:22,840 --> 00:06:28,020
+إذا .. إذا
+
+49
+00:06:28,020 --> 00:06:35,460
+Sn هي عملية عملية عملية عملية عملية عملية عملية
+
+50
+00:06:35,460 --> 00:06:40,200
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+51
+00:06:40,200 --> 00:06:41,360
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+52
+00:06:41,360 --> 00:06:41,460
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+53
+00:06:41,460 --> 00:06:41,480
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+54
+00:06:41,480 --> 00:06:43,900
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+55
+00:06:43,900 --> 00:06:50,560
+عملية
+
+56
+00:06:50,560 --> 00:07:06,360
+إذا كان هناك تجارب سكن
+
+57
+00:07:06,360 --> 00:07:15,180
+من سن التي مرتبطة
+
+58
+00:07:15,180 --> 00:07:22,480
+فالنتيجة
+
+59
+00:07:25,450 --> 00:07:34,870
+ثم سيكوانس SN نفسها مرتبطة يعني
+
+60
+00:07:34,870 --> 00:07:37,450
+لو كان في عندي سيكوانس of non-negative real
+
+61
+00:07:37,450 --> 00:07:43,790
+numbers والسيكوانس هذه حدودها غير سالبة و
+
+62
+00:07:43,790 --> 00:07:50,030
+increasing متزايدة ولو وجد subsequence من السيكوانس 
+
+63
+00:07:50,030 --> 00:07:57,220
+SN والسيكوانس مرتبطة السيكوانس الأم أو السيكوانس
+
+64
+00:07:57,220 --> 00:08:02,260
+الأصلية بتكون أيضا bounded فالبرهان
+
+65
+00:08:02,260 --> 00:08:05,500
+تبع النظرية اللي هسيبكم هي أن تتبرهنوا كـ exercise
+
+66
+00:08:05,500 --> 00:08:09,980
+for easy
+
+67
+00:08:09,980 --> 00:08:20,880
+exercise إذا أنا هنسيبكم تبرهنوا كتمرين في عندي 
+
+68
+00:08:20,880 --> 00:08:21,580
+الآن
+
+69
+00:08:27,800 --> 00:08:44,940
+the P series test let
+
+70
+00:08:44,940 --> 00:08:51,480
+P عدد موجب أصغر let P
+
+71
+00:08:55,440 --> 00:09:01,680
+هي عدد موجب أي عدد موجب ده
+
+72
+00:09:01,680 --> 00:09:09,640
+P series ده P series اللي هي سيجما from N equals
+
+73
+00:09:09,640 --> 00:09:17,100
+zero to infinity لواحد على N أُس P الـ series هذه 
+
+74
+00:09:17,100 --> 00:09:23,160
+بنسميها P series الـ P series هذه إيش مالها؟ واحد
+
+75
+00:09:25,240 --> 00:09:37,540
+converges if P أكبر من واحد and diverges if
+
+76
+00:09:37,540 --> 00:09:45,620
+P أصغر من أو يساوى واحد prove
+
+77
+00:09:45,620 --> 00:09:52,580
+نثبت الجزء الأول assume
+
+78
+00:09:54,990 --> 00:10:02,570
+إن P أكبر من 1 let
+
+79
+00:10:02,570 --> 00:10:07,510
+R بيساوى
+
+80
+00:10:07,510 --> 00:10:14,490
+واحد على اثنين أُس P سالب واحد الـ P أكبر من واحد
+
+81
+00:10:14,490 --> 00:10:21,330
+فالأس هذا موجب واحد على اثنين أُس موجب طبعا هذا
+
+82
+00:10:21,330 --> 00:10:21,950
+بيطلع
+
+83
+00:10:24,540 --> 00:10:34,800
+عدد موجب وأصغر من واحد then الـ R العدد R هذا أكبر 
+
+84
+00:10:34,800 --> 00:10:44,300
+من صفر أصغر من واحد طيب for K بيساوى اثنين أقصى
+
+85
+00:10:44,300 --> 00:10:52,860
+واحد سالب واحد اللي هو واحد MDS
+
+86
+00:10:58,390 --> 00:11:04,950
+عندي الـ partial sum رقم
+
+87
+00:11:04,950 --> 00:11:10,130
+K اللي
+
+88
+00:11:10,130 --> 00:11:18,970
+هو بيساوى اثنين خليني اسمي هذا K واحد فالـ
+
+89
+00:11:18,970 --> 00:11:26,370
+partial sum S رقم K واحد بيساوى طبعا k1 بيساوى واحد
+
+90
+00:11:26,370 --> 00:11:36,190
+هنا هذا هو s1 بيساوى واحد الـ
+
+91
+00:11:36,190 --> 00:11:39,490
+first partial sum اللي هو مجموع الحد الأول الحد 
+
+92
+00:11:39,490 --> 00:11:47,470
+الأول هنا واحد صح طيب 
+
+93
+00:11:47,470 --> 00:11:49,810
+for لو أخدت k2
+
+94
+00:11:52,090 --> 00:11:57,230
+لو أخدت K2 بيساوى اثنين أقصى اثنين سالب واحد هذا 
+
+95
+00:11:57,230 --> 00:12:01,570
+بيطلع ثلاثة ففي 
+
+96
+00:12:01,570 --> 00:12:09,290
+الحالة هذه بيطلع عندي الـ
+
+97
+00:12:09,290 --> 00:12:14,710
+partial sum رقم K2 هو نفس الـ partial sum رقم ثلاثة 
+
+98
+00:12:14,710 --> 00:12:18,950
+فطبعا هذا هيساوى مجموع أول ثلاثة حدود
+
+99
+00:12:22,250 --> 00:12:33,350
+فعندي هنا هيطلع أول حد واحد، الثاني واحد على اثنين
+
+100
+00:12:33,350 --> 00:12:36,530
+أُس P
+
+101
+00:12:36,530 --> 00:12:42,670
+والحد الثالث واحد على ثلاثة أُس P
+
+102
+00:12:54,470 --> 00:12:58,710
+خلينا هذه الـ N مفروض تكون من واحد لأن n من واحد
+
+103
+00:12:58,710 --> 00:13:05,550
+لأن n فـ S K2 هو S ثلاثة S ثلاثة بيساوى واحد على
+
+104
+00:13:05,550 --> 00:13:10,110
+واحد أُس P اللي هو واحد زائد واحد على اثنين أُس P
+
+105
+00:13:10,110 --> 00:13:17,620
+زائد واحد على ثلاثة أُس P طيب أنا عندي هذا أصغر من 
+
+106
+00:13:17,620 --> 00:13:23,360
+واحد زائد واحد على اثنين أُس P زائد واحد على اثنين
+
+107
+00:13:23,360 --> 00:13:34,820
+أُس P since لأنه اثنين أُس P أصغر من ثلاثة أُس P
+
+108
+00:13:34,820 --> 00:13:42,400
+فبتعني مقلوب ثلاثة أُس P أصغر من مقلوب اثنين أُس P
+
+109
+00:13:42,400 --> 00:13:51,330
+صح؟ وهذا بيساوى واحد زائد واحد على اثنين أُس P زائد
+
+110
+00:13:51,330 --> 00:13:58,850
+اثنين اثنين في واحد على اثنين أُس P هزبوت هدول حدين
+
+111
+00:13:58,850 --> 00:14:03,870
+متشابهين وهذا بيطلع بيساوى واحد زائد واحد على
+
+112
+00:14:03,870 --> 00:14:12,590
+اثنين أُس P سالب واحد وهذا بيساوى واحد زائد أربعة
+
+113
+00:14:14,460 --> 00:14:20,460
+معرف الـ R على إنها 1 على 2 أُس P سالب واحد
+
+114
+00:14:20,460 --> 00:14:24,420
+Similarly
+
+115
+00:14:24,420 --> 00:14:29,820
+بالمثل لو 
+
+116
+00:14:29,820 --> 00:14:39,060
+كانت K ثلاثة بيساوى اثنين أُس ثلاثة سالب واحد يعني
+
+117
+00:14:39,060 --> 00:14:43,140
+سبعة then
+
+118
+00:14:44,850 --> 00:14:53,850
+هيكون SK3 هيطلع بيساوى SK2
+
+119
+00:14:53,850 --> 00:14:58,350
+زائد 
+
+120
+00:14:58,350 --> 00:15:05,210
+واحد على أربعة أُس P زائد واحد على خمسة أُس P زائد 
+
+121
+00:15:05,210 --> 00:15:10,990
+واحد على ستة أُس P زائد واحد على سبعة أُس P مظبوط
+
+122
+00:15:10,990 --> 00:15:11,990
+هيك صح؟
+
+123
+00:15:14,290 --> 00:15:18,410
+لأن S K 2 هو واحد زائد واحد على اثنين أُس P زائد واحد
+
+124
+00:15:18,410 --> 00:15:23,430
+على ثلاثة أُس P وهذا
+
+125
+00:15:23,430 --> 00:15:37,510
+أصغر من .. طبعا S K 2 أصغر من واحد قلنا زائد R
+
+126
+00:15:41,610 --> 00:15:46,750
+وبعدين الحدود هذه .. كل واحد من الحدود هذه أصغر 
+
+127
+00:15:46,750 --> 00:15:52,250
+من أو يساوى واحد على أربعة أُس P واحد على أربعة أُس
+
+128
+00:15:52,250 --> 00:15:57,570
+P .. واحد على أربعة أُس P .. واحد على أربعة أُس P
+
+129
+00:15:57,570 --> 00:16:02,690
+لأن كل واحد من المقامات هذه أكبر من أو يساوى أربعة
+
+130
+00:16:02,690 --> 00:16:09,870
+أُس P طب أقول جدّيش عددهم أربعة هذا بيساوى واحد زائد
+
+131
+00:16:09,870 --> 00:16:17,730
+R زائد أربعة على أربعة أُس P هو بيساوى واحد زائد R
+
+132
+00:16:17,730 --> 00:16:27,810
+زائد واحد على أربعة أُس P سالب واحد إذن بيطلع عندي
+
+133
+00:16:27,810 --> 00:16:38,880
+أنا S K ثلاثة أصغر من واحد زائد R زائد واحد على
+
+134
+00:16:38,880 --> 00:16:43,480
+اثنين اثنين
+
+135
+00:16:43,480 --> 00:16:49,820
+أُس اثنين في P سالب واحد وهذا
+
+136
+00:16:49,820 --> 00:16:58,520
+هو R تربيع هذا بيساوى واحد زائد R زائد R تربيع لو
+
+137
+00:16:58,520 --> 00:17:04,120
+سمرنا في العملية هذه continuing
+
+138
+00:17:07,150 --> 00:17:16,370
+inductively بطريقة استقرائية continuing
+
+139
+00:17:16,370 --> 00:17:22,590
+inductively يعني by induction باستخدام
+
+140
+00:17:22,590 --> 00:17:28,350
+الـ induction we 
+
+141
+00:17:28,350 --> 00:17:32,570
+get we get the following for
+
+142
+00:17:40,680 --> 00:17:50,100
+for K J يساوي 2 I mean J سالب 1 we
+
+143
+00:17:50,100 --> 00:17:55,340
+have S
+
+144
+00:17:55,340 --> 00:18:08,260
+K J هيطلع أصغر من 1 زائد R زائد R تربيع زائد
+
+145
+00:18:10,870 --> 00:18:22,010
+R أس J سالب 1 و
+
+146
+00:18:22,010 --> 00:18:27,830
+هذا صحيح لكل J في N هبوط
+
+147
+00:18:27,830 --> 00:18:36,550
+هيك صح هيتعالى نشوف لما J كانت سالب 1 فطلع
+
+148
+00:18:36,550 --> 00:18:43,660
+عندي S ك 1 يساوي 1 وأصغر من أو يساوي 1
+
+149
+00:18:43,660 --> 00:18:47,600
+لما
+
+150
+00:18:47,600 --> 00:18:54,920
+ك ج يساوي 2 لما 
+
+151
+00:18:54,920 --> 00:19:02,980
+ج يساوي 2 فطلع SK2 أصغر من 1 زائد R 1
+
+152
+00:19:02,980 --> 00:19:09,660
+زائد R أس 2 سالب 1 آسف لما J يساوي 3
+
+153
+00:19:09,660 --> 00:19:15,800
+عندي طلع ال SK 3 أصغر من 1 زائد R زائد R أس
+
+154
+00:19:15,800 --> 00:19:21,280
+3 سالب 1 إذا S sub KJ أصغر من 1 زائد R
+
+155
+00:19:21,280 --> 00:19:30,540
+إلى R أس J ناقص 1 الآن هذا المجموع أصغر من
+
+156
+00:19:30,540 --> 00:19:39,280
+مجموع ال infinite series اللي هي summation من J 
+
+157
+00:19:39,280 --> 00:19:48,980
+يساوي 0 إلى ما لا نهاية ل R أس J صح؟
+
+158
+00:19:50,160 --> 00:19:56,760
+هذا عبارة 
+
+159
+00:19:56,760 --> 00:20:01,440
+عن finite sum أصغر من مجموعة infinite series هذه
+
+160
+00:20:01,440 --> 00:20:10,700
+عبارة عن geometric series with first term 1 وال
+
+161
+00:20:10,700 --> 00:20:18,140
+ratio تبعها R والـ R أكبر من 0 أصغر من 1 إذا
+
+162
+00:20:18,140 --> 00:20:23,080
+الـ geometric series هذه converges ومجموعها يساوي
+
+163
+00:20:23,080 --> 00:20:30,820
+1 على 1 ناقص R الكلام
+
+164
+00:20:30,820 --> 00:20:37,320
+هذا صحيح for all J belong to N وطبعا ال SKJ هذا
+
+165
+00:20:37,320 --> 00:20:42,760
+عبارة عن مجموعة partial sum partial sum لأعداد
+
+166
+00:20:42,760 --> 00:20:44,560
+موجبة وبالتالي موجبة
+
+167
+00:20:47,700 --> 00:20:52,720
+إذا أنا هيك أثبتت إن ال sub
+
+168
+00:20:52,720 --> 00:20:58,700
+sequence SKJ bounded below by 0 و bounded above by
+
+169
+00:20:58,700 --> 00:21:05,420
+العدد الموجب 1 على 1 ناقص R وبالتالي،
+
+170
+00:21:05,420 --> 00:21:10,160
+إذا هيك نستنتج، therefore the subsequence
+
+171
+00:21:13,370 --> 00:21:18,210
+ده sub-sequence اللي هي SKJ هاد ال sub-sequence من
+
+172
+00:21:18,210 --> 00:21:24,370
+مين؟ من ال sequence of partial sums SN شاملها is
+
+173
+00:21:24,370 --> 00:21:31,490
+bounded أثبتنا أنها ايه؟ bounded، مصدقوط؟ طلعنا
+
+174
+00:21:31,490 --> 00:21:35,090
+احنا عملنا construction ل sub-sequence من الـ
+
+175
+00:21:35,090 --> 00:21:37,370
+sequence of partial sums وهي طلعت bounded هي
+
+176
+00:21:37,370 --> 00:21:41,670
+bounded below by 0 bounded above by 1 over 1 minus
+
+177
+00:21:41,670 --> 00:21:53,610
+r لأن حسب اللمّة اللي فاتت so by above lemma ال
+
+178
+00:21:53,610 --> 00:21:56,730
+sequence of partial sums نفسها is bounded
+
+179
+00:22:02,950 --> 00:22:08,570
+وبالتالي إذا by above theorem مدام ال sequence of
+
+180
+00:22:08,570 --> 00:22:11,910
+partial sums is bounded إذا ال series converges
+
+181
+00:22:11,910 --> 00:22:15,710
+okay
+
+182
+00:22:15,710 --> 00:22:23,790
+إذا بعديكم نقول so
+
+183
+00:22:23,790 --> 00:22:29,930
+by above theorem ال
+
+184
+00:22:29,930 --> 00:22:46,080
+series sigma 1 على N أكبر من 1 فهذا
+
+185
+00:22:46,080 --> 00:22:53,300
+يثبت الجزء الأول من النظرية خلّينا
+
+186
+00:22:53,300 --> 00:22:54,640
+نثبت الجزء الثاني
+
+187
+00:23:10,080 --> 00:23:17,200
+using induction you
+
+188
+00:23:17,200 --> 00:23:21,660
+can show أنه
+
+189
+00:23:21,660 --> 00:23:26,800
+for P
+
+190
+00:23:26,800 --> 00:23:29,140
+أكبر من 0 أصغر من 1
+
+191
+00:23:32,370 --> 00:23:37,970
+لو كانت ال P طبعا أكبر من 0 وأصغر من أو ساوي
+
+192
+00:23:37,970 --> 00:23:46,110
+الـ 1 ف N أس P بيطلع أصغر من أو يساوي N لكل N في N
+
+193
+00:23:46,110 --> 00:23:49,670
+صح؟
+
+194
+00:23:49,670 --> 00:23:57,430
+أنا ممكن إثباته by induction So, 1 على n أصغر لو
+
+195
+00:23:57,430 --> 00:24:08,470
+ساوي 1 على n أس P for all n ينتمي إلى N فإن 
+
+196
+00:24:08,470 --> 00:24:12,710
+هذا بيقدي هذا بيقدي
+
+197
+00:24:30,450 --> 00:24:36,590
+this implies أن ال summation from K يساوي 1 to
+
+198
+00:24:36,590 --> 00:24:44,150
+n ل 1 على K أصغر لو ساوي summation من K يساوي
+
+199
+00:24:44,150 --> 00:24:55,850
+1 إلى n ل 1 على n على K أس P طب ما هذا عبارة
+
+200
+00:24:55,850 --> 00:25:02,270
+عن ال partial sum لسمي SN لل harmonic series ..
+
+201
+00:25:02,270 --> 00:25:09,410
+لل .. لل harmonic series و هذا عبارة عن ال partial
+
+202
+00:25:09,410 --> 00:25:17,870
+sum سمي SN star لل P series صح؟ إن أنا أصبح عندي
+
+203
+00:25:17,870 --> 00:25:21,850
+أنا SN أصغر من أو يساوي SN star
+
+204
+00:25:24,550 --> 00:25:29,430
+where لكل n where
+
+205
+00:25:29,430 --> 00:25:36,530
+SN يساوي sigma 1 على K من K يساوي 1 إلى n و
+
+206
+00:25:36,530 --> 00:25:42,230
+SN star يساوي sigma من K يساوي 1 إلى n ل 1
+
+207
+00:25:42,230 --> 00:25:51,630
+على K أس P طيب since أثبتنا احنا قبل هيك انه ال
+
+208
+00:25:51,630 --> 00:25:53,230
+sequence of partial sums
+
+209
+00:25:56,310 --> 00:26:01,790
+السيكوانس SN هذا عبارة عن السيكوانس of partial
+
+210
+00:26:01,790 --> 00:26:02,290
+sums
+
+211
+00:26:12,510 --> 00:26:17,510
+of the harmonic series sigma 1 على n ايش مالهم؟
+
+212
+00:26:17,510 --> 00:26:23,070
+أثبتنا أنهم unbounded ال sequence هذه is unbounded
+
+213
+00:26:23,070 --> 00:26:30,670
+بنالنا ذلك في مثال سابق unbounded
+
+214
+00:26:30,670 --> 00:26:35,070
+فلو سمينا المتباينة
+
+215
+00:26:35,070 --> 00:26:39,530
+هذا star then
+
+216
+00:26:39,530 --> 00:26:40,370
+it follows
+
+217
+00:26:44,900 --> 00:26:50,900
+from star ينتج من المتباينة star إذا كانت ال
+
+218
+00:26:50,900 --> 00:26:55,600
+sequence هذه unbounded
+
+219
+00:26:55,600 --> 00:27:00,620
+لصغيرة unbounded فالحدود أكبر is unbounded ال
+
+220
+00:27:00,620 --> 00:27:11,140
+sequence SN star is unbounded وبالتالي
+
+221
+00:27:11,140 --> 00:27:13,600
+حسب النظرية أعلى so by
+
+222
+00:27:20,890 --> 00:27:26,890
+السيريز هي سيكوينس باشا سمسا بايتالي P Series
+
+223
+00:27:26,890 --> 00:27:32,930
+سيجما من K يساوي 1 وإنفينيتي ل 1 على K أس P
+
+224
+00:27:32,930 --> 00:27:36,290
+is divergent
+
+225
+00:27:41,610 --> 00:27:48,170
+حسب النظرية التي ذكرناها سابقًا، طيب، في عندي هاي
+
+226
+00:27:48,170 --> 00:27:51,750
+series of positive numbers أو non-negative real
+
+227
+00:27:51,750 --> 00:27:55,890
+numbers و ال sequence of partial sums أبعدتها
+
+228
+00:27:55,890 --> 00:28:00,250
+unbounded، إذا حسب النظرية ال series is not
+
+229
+00:28:00,250 --> 00:28:05,260
+convergent أو divergent، صح؟ إذن هذا بتثبت الجزء
+
+230
+00:28:05,260 --> 00:28:09,880
+الثاني وبالتالي هيك بيكون برهاننا اختبار ال P
+
+231
+00:28:09,880 --> 00:28:15,200
+-series test أو ال P-series test إذن
+
+232
+00:28:15,200 --> 00:28:20,960
+أي P-series بتكون convergent إذا ال P أكبر من 1
+
+233
+00:28:20,960 --> 00:28:25,620
+و divergent إذا P أصغر من أو يساوي 1 في أي
+
+234
+00:28:25,620 --> 00:28:26,220
+سؤال؟
+
+235
+00:28:52,320 --> 00:28:55,800
+زي ما أخرنا comparison و limit comparison test
+
+236
+00:28:55,800 --> 00:29:00,920
+لل sequences في comparison test لل series
+
+237
+00:29:00,920 --> 00:29:08,900
+comparison
+
+238
+00:29:08,900 --> 00:29:13,960
+test
+
+239
+00:29:13,960 --> 00:29:17,020
+for series
+
+240
+00:29:33,680 --> 00:29:40,800
+لت XN و YN بـ sequences of non-negative real
+
+241
+00:29:40,800 --> 00:29:41,380
+numbers
+
+242
+00:29:49,780 --> 00:29:58,060
+يكون such that XN أصغر من أو يساوي YN أكبر من أو
+
+243
+00:29:58,060 --> 00:30:06,540
+ساوي 0 for all N أكبر من أو يساوي K for some K
+
+244
+00:30:06,540 --> 00:30:14,660
+ينتمي إلى N أنا
+
+245
+00:30:14,660 --> 00:30:19,950
+لدي two sequences of real numbers التنتين حدودهم غير
+
+246
+00:30:19,950 --> 00:30:26,790
+سالبة من capital .. من capital K و أنت طالع ممكن
+
+247
+00:30:26,790 --> 00:30:30,350
+الحدود اللي قبل .. اللي رقمهم أصغر من K بتكون
+
+248
+00:30:30,350 --> 00:30:36,150
+سالبة مش مشكلة أو ما يكونش XN أصغر .. ممكن يكون XN
+
+249
+00:30:36,150 --> 00:30:41,830
+أكبر من YN مش مشكلة لكن من عند capital K لكل مؤشر
+
+250
+00:30:41,830 --> 00:30:45,810
+لكل index because on and equal K أنا بدي XN أصغر
+
+251
+00:30:45,810 --> 00:30:51,990
+من وسائر YN واتنين يكونوا غير سلبين الآن إذا كانت
+
+252
+00:30:51,990 --> 00:30:58,190
+ال series sigma
+
+253
+00:30:58,190 --> 00:31:06,970
+XN إذا كانت ال series الأولى convergent أو الكبيرة
+
+254
+00:31:09,920 --> 00:31:17,540
+convergent بتقدي ان ال series الأصغر converge and
+
+255
+00:31:17,540 --> 00:31:29,520
+لو كانت ال series الأكبر الأصغر diverge فبتقدي
+
+256
+00:31:29,520 --> 00:31:36,700
+أن ال series الأكبر بالتأكيد diverge وهي
+
+257
+00:31:36,700 --> 00:31:45,380
+البرهان برهن الجزء الأول assume أنه ال series
+
+258
+00:31:45,380 --> 00:31:56,180
+sigma YN converges then
+
+259
+00:31:56,180 --> 00:32:00,000
+by Cauchy
+
+260
+00:32:00,000 --> 00:32:10,000
+criterion for series given
+
+261
+00:32:12,200 --> 00:32:18,900
+epsilon أكبر من الصفر يوجد capital N يعتمد على
+
+262
+00:32:18,900 --> 00:32:26,920
+epsilon عدد طبيعي بحيث أنه لكل M أكبر من small N
+
+263
+00:32:26,920 --> 00:32:31,620
+أكبر من أو يساوي capital N هيطلع عندي absolute
+
+264
+00:32:39,200 --> 00:32:51,200
+YN زائد 1 زائد YN زائد 2 و هكذا إلى YM أصغر من إبسلون هذا من Cauchy
+
+265
+00:32:51,200 --> 00:32:51,760
+criterion
+
+266
+00:33:15,050 --> 00:33:23,830
+طيب أنا عندي let
+
+267
+00:33:23,830 --> 00:33:34,730
+M يساوي ال maximum الأكبر بين N العدد K هذا الطبيعي
+
+268
+00:33:34,730 --> 00:33:40,010
+K والعدد الطبيعي capital N اللي بيعتمد على
+
+269
+00:33:40,010 --> 00:33:40,330
+epsilon
+
+270
+00:33:43,140 --> 00:33:49,360
+فاكيد طبعا هذا عدد طبيعي وهذا عدد طبيعي فإن M
+
+271
+00:33:49,360 --> 00:33:54,200
+هيطلع عدد طبيعي وM يعتمد على إبسلون لأن الـ M
+
+272
+00:33:54,200 --> 00:34:01,500
+يعتمد على capital N وcapital N تعتمد على إبسلون
+
+273
+00:34:01,500 --> 00:34:09,900
+إذا لو أخدت أنا N أكبر من M أو M أكبر من N وN
+
+274
+00:34:09,900 --> 00:34:18,560
+أكبر من أو يساوي capital N فهذا بالتأكيد هيقدي انه
+
+275
+00:34:18,560 --> 00:34:23,480
+ال ..
+
+276
+00:34:23,480 --> 00:34:29,520
+ال .. من هنا من الفرض نسمي الفرض هذا star
+
+277
+00:34:34,930 --> 00:34:45,790
+فمن star هيطلع عندي مفروض XN زائد 1 زائد XN
+
+278
+00:34:45,790 --> 00:34:51,130
+زائد 2 زائد و هكذا إلى XM
+
+279
+00:35:01,640 --> 00:35:06,300
+الـ absolute هذا الآن كله موجب هذه كل حدود موجبة
+
+280
+00:35:06,300 --> 00:35:12,160
+أو غير سالبة لأن ال N أكبر من أو يساوي capital N 
+
+281
+00:35:12,160 --> 00:35:17,380
+وبالتالي هذا بيقدي أن N أكبر من أو يساوي كابتل K
+
+282
+00:35:17,380 --> 00:35:25,520
+صح؟ إذا باستخدام star كابتل 
+
+283
+00:35:25,520 --> 00:35:28,260
+عفواً أن هذه المفروضة تكون M
+
+284
+00:35:31,530 --> 00:35:36,470
+الآن لكل M أكبر من أو يساوي capital M
+
+285
+00:35:36,470 --> 00:35:41,110
+capital M هذه أكبر من أو يساوي K وبالتالي M أكبر من
+
+286
+00:35:41,110 --> 00:35:46,030
+أو يساوي K إذن الحدود هذه كلها موجبة أو غير سالبة
+
+287
+00:35:46,030 --> 00:35:58,830
+صح من star وأصغر من أو يساوي اللي هو YM زائد واحد
+
+288
+00:35:58,830 --> 00:36:10,810
+زائد YM زائد اثنين زائد وهكذا إلى 
+
+289
+00:36:10,810 --> 00:36:19,870
+YM برضه هذه كلها حدود غير سالبة وبالتالي هذه هي
+
+290
+00:36:19,870 --> 00:36:25,370
+نفس ال absolute YN زائد واحد زائد YN زائد اثنين
+
+291
+00:36:25,370 --> 00:36:25,910
+زائد
+
+292
+00:36:29,190 --> 00:36:37,590
+YM ومن هنا لاحظوا أن n أكبر من أو يساوي capital M و
+
+293
+00:36:37,590 --> 00:36:42,870
+الـ M أكبر من أو يساوي capital N فبيطلع عندي كمان هنا
+
+294
+00:36:42,870 --> 00:36:50,630
+أن N أكبر من أو يساوي capital M لأن الـ M أكبر من أو
+
+295
+00:36:50,630 --> 00:36:56,650
+يساوي capital N وبالتالي من ال implication هذه
+
+296
+00:36:56,650 --> 00:37:04,470
+بيطلع أصغر من إبسلم أن أنا طلع عندي absolute xn
+
+297
+00:37:04,470 --> 00:37:11,050
+زائد واحد زائد xn زائد اثنين زائد إلى آخره إلى xn
+
+298
+00:37:11,050 --> 00:37:17,380
+أصغر من إبسلم هذا عدد غير سالب المجموعة دي غير سالب
+
+299
+00:37:17,380 --> 00:37:20,800
+لأن كل الـ X غير سالب وبالتالي ال absolute value هي
+
+300
+00:37:20,800 --> 00:37:24,680
+نفسها هذا هو ال absolute value العدد غير سالب نفسه
+
+301
+00:37:24,680 --> 00:37:31,060
+لأن هنا أثبتنا الكلام هذا صحيح لكل M أكبر من N
+
+302
+00:37:31,060 --> 00:37:36,880
+أكبر من أو يساوي capital M so بنستخدم كوشي
+
+303
+00:37:36,880 --> 00:37:42,780
+criterion كمان مرة by Cauchy criterion
+
+304
+00:37:45,130 --> 00:37:50,250
+for the series الـ
+
+305
+00:37:50,250 --> 00:37:57,310
+series sigma xn converges لأن
+
+306
+00:37:57,310 --> 00:38:02,130
+هذا شرط كوشي متحقق، صح؟
+
+307
+00:38:02,130 --> 00:38:07,390
+هذا لأي إبسلون given إبسلون أكبر من الصفر أثناء أن
+
+308
+00:38:07,390 --> 00:38:13,490
+يوجد capital M يعني يعتمد على إبسلون بحيث لكل M
+
+309
+00:38:13,490 --> 00:38:18,350
+أكبر من N أكبر من أو يساوي كابتل N فلنادي absolute
+
+310
+00:38:18,350 --> 00:38:23,150
+XN زائد واحد زائد إلى XM أصغر من إبسلون إذا حسب
+
+311
+00:38:23,150 --> 00:38:27,050
+Cauchy criterion the series Sigma XN converges هذا
+
+312
+00:38:27,050 --> 00:38:36,790
+بنكمل برهان الجزء الأول الجزء الثاني بينتج
+
+313
+00:38:36,790 --> 00:38:37,890
+من الجزء الأول
+
+314
+00:38:42,270 --> 00:38:52,390
+this is the contrapositive .. the contrapositive
+
+315
+00:38:52,390 --> 00:39:00,330
+أو the contraposition .. this is the
+
+316
+00:39:00,330 --> 00:39:04,930
+contraposition of the statement واحد
+
+317
+00:39:08,170 --> 00:39:12,270
+أنا في عندي قانون في الـ logic بيقول إذا كان P فأدي
+
+318
+00:39:12,270 --> 00:39:19,370
+إلى Q فال statement هذا بكافئ ال counter positive مش 
+
+319
+00:39:19,370 --> 00:39:21,950
+النفي تبعه ال counter positive معناه المعاكس
+
+320
+00:39:21,950 --> 00:39:30,550
+الإيجابي فهذا بكافئ not Q implies not P فإذا
+
+321
+00:39:30,550 --> 00:39:37,130
+أثبتنا أن هذا true فهذا بيكون true طب تعالوا نشوف
+
+322
+00:39:37,130 --> 00:39:39,810
+هذا هذا اللي أنا أثبتنا أنه true اللي هو الجزء أ
+
+323
+00:39:39,810 --> 00:39:43,590
+أو الجزء واحد الجزء الثاني هو ال counter positive
+
+324
+00:39:44,960 --> 00:39:50,320
+هل هذا صحيح تعالوا نقرأ الجزء الثاني أو تعالوا 
+
+325
+00:39:50,320 --> 00:39:55,420
+نجيب ال contrapositive للعبارة في الجزء الأول الـ
+
+326
+00:39:55,420 --> 00:39:59,800
+contrapositive للعبارة في الجزء الأول نفي هذا اللي 
+
+327
+00:39:59,800 --> 00:40:04,160
+هو ال series sigma x in diverges بيقود إلى نفي هذا
+
+328
+00:40:04,160 --> 00:40:08,420
+اللي هو ال series y in diverges وبالتالي هيك بنكون
+
+329
+00:40:08,420 --> 00:40:17,700
+كملنا البرهان تمام؟ واضح؟ في أي سؤال؟ أي استفسار؟
+
+330
+00:40:17,700 --> 00:40:25,180
+أحيانا بيكون صعب أن احنا نعملمقارنة بين حدود الـ
+
+331
+00:40:25,180 --> 00:40:32,500
+series sigma xn وحدود ال series sigma yn بالطريقة
+
+332
+00:40:32,500 --> 00:40:37,480
+المباشرة زي ما في ال star أحيانا مش سهل نعمل
+
+333
+00:40:37,480 --> 00:40:43,020
+مقارنة زي هذه وبالتالي بنلجأ إلى اختبار آخر بنسميه
+
+334
+00:40:43,020 --> 00:40:49,320
+limit comparison test فنكتب ال test هذا دكتور؟ نعم
+
+335
+00:40:49,320 --> 00:40:53,560
+هلأ عبس النظرية برضه خطأ يعني نفس نحو اللي كنا
+
+336
+00:40:53,560 --> 00:40:58,360
+نعمله بال sequence نعمله بال series هي الفترة
+
+337
+00:40:58,360 --> 00:41:01,940
+التالية؟ آه طبعاً يعني أنت لو كان مثلاً هذه صحية 
+
+338
+00:41:01,940 --> 00:41:08,160
+كلامك بالظبط يعني لو كانت ال series ال series مثلاً
+
+339
+00:41:08,160 --> 00:41:14,190
+هذه ال sigma yn diverges هل هذا بيقود أن sigma xn
+
+340
+00:41:14,190 --> 00:41:18,530
+diverges؟ مش بالضرورة ممكن diverge وممكن converge
+
+341
+00:41:18,530 --> 00:41:25,510
+نفس الحاجة لو كانت ال series sigma xn converges هل 
+
+342
+00:41:25,510 --> 00:41:31,030
+sigma yn converges؟ ممكن أو ممكن لأ أكيد وممكن 
+
+343
+00:41:31,030 --> 00:41:34,690
+نجيب counter examples لازم تفكري في إيجاد counter
+
+344
+00:41:34,690 --> 00:41:36,850
+examples وأنت بتدرسيه
+
+345
+00:41:40,810 --> 00:41:53,630
+نشوف ال limit comparison test limit
+
+346
+00:41:53,630 --> 00:42:02,030
+comparison test
+
+347
+00:42:18,300 --> 00:42:27,120
+لت Xn وYn بيكونوا sequence من حدود حقيقية موجبة
+
+348
+00:42:27,120 --> 00:42:36,560
+بيكون حدود حقيقية موجبة بيكون حدود حقيقية موجبة
+
+349
+00:42:36,560 --> 00:42:38,340
+بيكون حدود حقيقية موجبة بيكون حدود حقيقية موجبة
+
+350
+00:42:38,340 --> 00:42:40,480
+بيكون حدود حقيقية موجبة بيكون حدود حقيقية موجبة
+
+351
+00:42:47,730 --> 00:42:56,850
+والـ R هذا يعني عدد حقيقي طبعاً ينتمي إلى R ففي
+
+352
+00:42:56,850 --> 00:43:04,670
+عندي برضه نتيجتين النتيجة الأولى إذا كان الـ R
+
+353
+00:43:04,670 --> 00:43:09,630
+لا يساوي صفر then
+
+354
+00:43:09,630 --> 00:43:15,330
+ال series sigma X M converges if and only if
+
+355
+00:43:24,150 --> 00:43:43,650
+الجزء الثاني من النظرية لو 
+
+356
+00:43:43,650 --> 00:43:52,220
+كان R يساوي صفر بعد ذلك لو الـ R يساوي صفر يعني أن
+
+357
+00:43:52,220 --> 00:44:01,220
+الـ R يساوي صفر then ال series sigma y in diverges
+
+358
+00:44:01,220 --> 00:44:07,840
+بيقود أن ال series sigma x in diverges
+
+359
+00:44:11,380 --> 00:44:19,300
+أو لأ convergence أفضل لو كانت series sigma yn
+
+360
+00:44:19,300 --> 00:44:24,480
+converges بيقود أن series sigma xn converges
+
+361
+00:44:24,480 --> 00:44:27,620
+فقط اتجاه واحد لكن الـ X مش شرط تكون
+
+362
+00:44:27,620 --> 00:44:37,460
+صحيحة okay تمام هو البرهان
+
+363
+00:44:37,460 --> 00:44:38,520
+يعني كثير سهل
+
+364
+00:44:49,520 --> 00:45:02,300
+بنسمي الشرط هذا star الجزء
+
+365
+00:45:02,300 --> 00:45:12,940
+الأول assume أن R لا يساوي صفر طبعاً
+
+366
+00:45:12,940 --> 00:45:21,670
+في الحالة هذه الـ R بيطلع موجب لأن لحظة أنتم أن xn
+
+367
+00:45:21,670 --> 00:45:27,810
+على yn هذه كلها أعداد موجبة وال limit لـ sequence
+
+368
+00:45:27,810 --> 00:45:31,930
+أعداد كل حدودها موجبة بيطلع المفروض يطلع ال limit
+
+369
+00:45:31,930 --> 00:45:37,970
+تبعها موجبة إذا كانت ال limit موجودة واضح؟ إذن
+
+370
+00:45:37,970 --> 00:45:42,090
+هذا من نظرية سابقة لما أن حدود ال sequence xn على
+
+371
+00:45:42,090 --> 00:45:45,930
+yn هذه ال sequence حدودها كلها موجبة إذا نهايتها
+
+372
+00:45:45,930 --> 00:45:58,820
+تطلع أيضاً موجبة طيب وبالتالي take epsilon يساوي R على
+
+373
+00:45:58,820 --> 00:46:09,180
+2 طبعاً هذا بالتأكيد عدد موجب الآن by star since
+
+374
+00:46:09,180 --> 00:46:18,240
+XN على YN converges to R as N tends to infinity
+
+375
+00:46:20,590 --> 00:46:26,850
+بقدر نلاقي capital N يعتمد على إبسلون عدد طبيعي
+
+376
+00:46:26,850 --> 00:46:32,830
+بحيث أنه absolute لكل N أكبر من أو يساوي capital N
+
+377
+00:46:32,830 --> 00:46:39,730
+بيطلع absolute xn على yn ناقص r أصغر من إبسلون
+
+378
+00:46:39,730 --> 00:46:49,430
+اللي هي يساوي R على 2 وهذا بيقود إلى فكينا وعملنا الـ
+
+379
+00:46:49,430 --> 00:46:56,730
+absolute value هيطلع عندي xn 
+
+380
+00:46:56,730 --> 00:47:03,910
+على yn أكبر من أو يساوي R على 2 أصغر من أو يساوي 3R على
+
+381
+00:47:03,910 --> 00:47:11,530
+2 وبما أنه هذا صحيح لكل N أكبر من أو يساوي capital
+
+382
+00:47:11,530 --> 00:47:21,570
+N الآن اضرب في YN YN طبعاً عدد موجب فبيطلع XN أصغر من
+
+383
+00:47:21,570 --> 00:47:27,370
+أو يساوي ثلاثة R على اثنين في YN أكبر من أو يساوي R على
+
+384
+00:47:27,370 --> 00:47:33,510
+اثنين في YN وهذا صحيح لكل N أكبر من أو يساوي
+
+385
+00:47:33,510 --> 00:47:37,330
+capital N تمام الآن now
+
+386
+00:47:45,120 --> 00:47:53,940
+نسمي هذه double star فالآن
+
+387
+00:47:53,940 --> 00:48:03,820
+if sigma x and converge then
+
+388
+00:48:03,820 --> 00:48:12,540
+by double star and comparison test and comparison
+
+389
+00:48:12,540 --> 00:48:22,450
+test واختبار المقارنة إذا كانت هذه convergent فبيطلع
+
+390
+00:48:22,450 --> 00:48:31,810
+هذه ال series convergent صح وبالتالي بيطلع sigma yn
+
+391
+00:48:31,810 --> 00:48:38,370
+converges هذا ثابت موج ممكن نضرب في مقلوب و
+
+392
+00:48:38,370 --> 00:48:42,490
+نتخلص منه إذا كانت هذه convergent فهذه convergent
+
+393
+00:48:46,950 --> 00:48:55,330
+Also إذا كانت ال series sigma y in converges then
+
+394
+00:48:55,330 --> 00:49:00,810
+برضه by المتباينة double star وال comparison
+
+395
+00:49:00,810 --> 00:49:04,890
+test إذا
+
+396
+00:49:04,890 --> 00:49:06,070
+نأخذ الجزء هذا
+
+397
+00:49:09,440 --> 00:49:12,720
+إذا كانت ال series هذي convergent والكبيرة هذي
+
+398
+00:49:12,720 --> 00:49:17,840
+convergent ففي ثابت موجب convergent فهذه تطلع
+
+399
+00:49:19,770 --> 00:49:25,650
+بيطلع sigma xn converges وبالتالي هذا بكمل برهان
+
+400
+00:49:25,650 --> 00:49:30,110
+الجزء الأول طبعاً برهان الجزء الثاني هيكون يعني
+
+401
+00:49:30,110 --> 00:49:36,530
+مشابه فلأن الواجهة انتهت هنوقف وهسيبكم تقرأ برهان
+
+402
+00:49:36,530 --> 00:49:41,890
+الجزء الأول من الكتاب فنكتفي بهذا القدر وإن شاء
+
+403
+00:49:41,890 --> 00:49:43,730
+الله نكمل المحاضرة الجاية
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8000423449d08d0ecce7fc01bf4ffbe40aaf05e0
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.srt
@@ -0,0 +1,1628 @@
+1
+00:00:22,080 --> 00:00:28,960
+بسم الله الرحمن الرحيم ال .. هنواصل اليوم ان شاء
+
+2
+00:00:28,960 --> 00:00:39,080
+الله ال .. ال .. الشئ اللي بدأناه بخصوص المقدمة عن
+
+3
+00:00:39,080 --> 00:00:46,520
+ال infinite series بعتقد كانت أخر نظرية أخدناها هي
+
+4
+00:00:46,520 --> 00:00:47,700
+Cauchy criterion
+
+5
+00:00:51,790 --> 00:00:56,710
+كوشي كريتيريا for
+
+6
+00:00:56,710 --> 00:01:10,250
+infinite series a
+
+7
+00:01:10,250 --> 00:01:10,810
+series
+
+8
+00:01:22,490 --> 00:01:31,530
+converges if and only if الشرط التالي بتحقق لكل
+
+9
+00:01:31,530 --> 00:01:38,430
+epsilon أكبر من 0 يوجد capital N يعتمد على epsilon
+
+10
+00:01:38,430 --> 00:01:46,200
+عدد طبيعي بحيث أنهلو كان M أكبر من N أكبر من أو
+
+11
+00:01:46,200 --> 00:01:56,560
+ساوي capital M فهذا بيقدي أنه absolute SM minus SN
+
+12
+00:01:56,560 --> 00:02:05,840
+بساوي absolute XN زاد واحد زاد XN زاد اتنين و هكذا
+
+13
+00:02:05,840 --> 00:02:07,300
+إلى XM
+
+14
+00:02:11,640 --> 00:02:15,100
+النظرية هذه تبعت كوشي أخدناها المرة اللي فاتت و
+
+15
+00:02:15,100 --> 00:02:22,080
+برهناها مظبوط اليوم هناخد نظرية تانية و مهمة و
+
+16
+00:02:22,080 --> 00:02:31,660
+النظرية هذه بتقول انه let x in be sequence of non
+
+17
+00:02:31,660 --> 00:02:39,620
+-negative real numbers then
+
+18
+00:02:39,620 --> 00:02:40,420
+series
+
+19
+00:02:43,080 --> 00:02:49,340
+xn converges if
+
+20
+00:02:49,340 --> 00:02:55,680
+and only if الsequence of partial sums its
+
+21
+00:02:55,680 --> 00:03:05,600
+sequence of partial sums اللي
+
+22
+00:03:05,600 --> 00:03:07,540
+هي sn is bounded
+
+23
+00:03:16,760 --> 00:03:24,080
+proof we have sn
+
+24
+00:03:24,080 --> 00:03:36,020
+بساوي او sn زايد واحد بساوي sn
+
+25
+00:03:36,020 --> 00:03:42,070
+زايد xn زايد واحدالان زاد فرص partial sum بيساوي
+
+26
+00:03:42,070 --> 00:03:46,150
+الانف partial sum وبنضيف عليه لحد رقم ان زاد واحد
+
+27
+00:03:58,050 --> 00:04:02,070
+و طبعا ال Xn زاد واحد هذا احنا فرضين ان حدود ال
+
+28
+00:04:02,070 --> 00:04:08,530
+sequence Xn كلها غير سالبة فهذا غير سالب وبالتالي
+
+29
+00:04:08,530 --> 00:04:14,790
+المجموع هذا بالتأكيد اكبر من او سوى Sn لكل N في N
+
+30
+00:04:14,790 --> 00:04:17,870
+فهذا
+
+31
+00:04:17,870 --> 00:04:24,530
+معناه ان ال sequence Sn is increasing متزايدة
+
+32
+00:04:26,960 --> 00:04:30,480
+بالتالي، من خلال الوضع الوضع الوضع الوضع الوضع
+
+33
+00:04:30,480 --> 00:04:36,420
+الوضع الوضع
+
+34
+00:04:36,420 --> 00:04:40,960
+الوضع
+
+35
+00:04:40,960 --> 00:04:48,560
+الوضع الوضع
+
+36
+00:05:21,390 --> 00:05:23,410
+وهو المطلوب
+
+37
+00:05:25,890 --> 00:05:29,190
+أحنا أخدنا قبل هيك أن أي infinite series بتكون
+
+38
+00:05:29,190 --> 00:05:32,890
+convergent if and only if the sequence of partial
+
+39
+00:05:32,890 --> 00:05:36,810
+sums is convergent، صح؟ طيب، ال sequence of
+
+40
+00:05:36,810 --> 00:05:42,650
+partial sums بمعنها increasing فهي convergent by
+
+41
+00:05:42,650 --> 00:05:48,050
+monotone convergence theorem بتكون convergent if
+
+42
+00:05:48,050 --> 00:05:52,130
+and only if it is boundedوبالتالي الـ series
+
+43
+00:05:52,130 --> 00:05:54,770
+converges if and only if the sequence of partial
+
+44
+00:05:54,770 --> 00:06:02,210
+sums is bounded وهذا يثبت النظرية تمام؟ إذن هذه
+
+45
+00:06:02,210 --> 00:06:09,410
+النظرية أهميتها في أننا يعني تطبيقها زي ما هنشوف
+
+46
+00:06:09,410 --> 00:06:12,650
+في
+
+47
+00:06:12,650 --> 00:06:14,590
+لما هنا صغيرة لما
+
+48
+00:06:22,840 --> 00:06:28,020
+إذا .. إذا
+
+49
+00:06:28,020 --> 00:06:35,460
+Sn هي عملية عملية عملية عملية عملية عملية عملية
+
+50
+00:06:35,460 --> 00:06:40,200
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+51
+00:06:40,200 --> 00:06:41,360
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+52
+00:06:41,360 --> 00:06:41,460
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+53
+00:06:41,460 --> 00:06:41,460
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+54
+00:06:41,460 --> 00:06:41,460
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+55
+00:06:41,460 --> 00:06:41,480
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+56
+00:06:41,480 --> 00:06:41,480
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+57
+00:06:41,480 --> 00:06:43,900
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+58
+00:06:43,900 --> 00:06:50,560
+عملية
+
+59
+00:06:50,560 --> 00:07:06,360
+عإذا كان هناك تجارب سكن
+
+60
+00:07:06,360 --> 00:07:15,180
+من سن التي مرتبطة
+
+61
+00:07:15,180 --> 00:07:22,480
+فالنتيجة
+
+62
+00:07:25,450 --> 00:07:34,870
+ثم سيكوانس SN نفسها مرتبط يعني
+
+63
+00:07:34,870 --> 00:07:37,450
+لو كان في عندي سيكوانس of non-negative real
+
+64
+00:07:37,450 --> 00:07:43,790
+numbers و السيكوانس هذه حدودها غير سالبة و
+
+65
+00:07:43,790 --> 00:07:50,030
+increase متزايدة و لو وجد subsequence من السيكوانس
+
+66
+00:07:50,030 --> 00:07:57,220
+SN و السيكوانس مرتبطالسيكوانس الأم أو السيكوانس
+
+67
+00:07:57,220 --> 00:08:02,260
+الأصلية بتكون أيضا bounded فالبرهان
+
+68
+00:08:02,260 --> 00:08:05,500
+تبع النظرية اللي هسيبكم هي أن تتبرهنوا ك exercise
+
+69
+00:08:05,500 --> 00:08:09,980
+for easy
+
+70
+00:08:09,980 --> 00:08:20,880
+exercise اذا انا هنسيبكم اتبرهنوا كتمرين في عندي
+
+71
+00:08:20,880 --> 00:08:21,580
+الآن
+
+72
+00:08:27,800 --> 00:08:44,940
+firm ال P series test let
+
+73
+00:08:44,940 --> 00:08:51,480
+P عدد موجب أصغر let P
+
+74
+00:08:55,440 --> 00:09:01,680
+هي عدد موجب اي عدد موجب ده
+
+75
+00:09:01,680 --> 00:09:09,640
+P series ده P series اللي هي سيجما from N equals
+
+76
+00:09:09,640 --> 00:09:17,100
+zero to infinity لواحد على N أُس P ال series هذه
+
+77
+00:09:17,100 --> 00:09:23,160
+بنسميها P series ال P series هذه ايش مالها؟ واحد
+
+78
+00:09:25,240 --> 00:09:37,540
+converges if P أكبر من واحد and name by virges if
+
+79
+00:09:37,540 --> 00:09:45,620
+P أصغر من أو يساوي واحد prove
+
+80
+00:09:45,620 --> 00:09:52,580
+نثبت الجزء الأول assume
+
+81
+00:09:54,990 --> 00:10:02,570
+إن P أكبر من 1 let
+
+82
+00:10:02,570 --> 00:10:07,510
+R بيساوي
+
+83
+00:10:07,510 --> 00:10:14,490
+واحد على اتنين أس P سالب واحد ال P أكبر من واحد
+
+84
+00:10:14,490 --> 00:10:21,330
+فالأس هذا موجب واحد على اتنين أس موجب طبعا هذا
+
+85
+00:10:21,330 --> 00:10:21,950
+بيطلع
+
+86
+00:10:24,540 --> 00:10:34,800
+عدد موجب و أصغر من واحد then ال R العدد R هذا أكبر
+
+87
+00:10:34,800 --> 00:10:44,300
+من سفر أصغر من واحد طيب four K بساوي اتنين اقصى
+
+88
+00:10:44,300 --> 00:10:52,860
+واحد سالب واحد اللي هو واحد MDS
+
+89
+00:10:58,390 --> 00:11:04,950
+عندي ال partial sum رقم
+
+90
+00:11:04,950 --> 00:11:10,130
+K اللي
+
+91
+00:11:10,130 --> 00:11:18,970
+هو بيساوي اتنين خليني اسمي هذا K واحد فال
+
+92
+00:11:18,970 --> 00:11:26,370
+partial sum S رقم K واحدبساوي طبعا k1 بساوي واحد
+
+93
+00:11:26,370 --> 00:11:36,190
+هنا هذا هو s1 بساوي واحد ال
+
+94
+00:11:36,190 --> 00:11:39,490
+first partial sum اللي هو مجموعة الحد الأول الحد
+
+95
+00:11:39,490 --> 00:11:47,470
+الأول هنا واحد صح طيب
+
+96
+00:11:47,470 --> 00:11:49,810
+four لو أخدت k2
+
+97
+00:11:52,090 --> 00:11:57,230
+لو أخدت K2 بيساوي اتنين اقصى اتنين سالب واحد هذا
+
+98
+00:11:57,230 --> 00:12:01,570
+بيطلع تلاتة ففي
+
+99
+00:12:01,570 --> 00:12:09,290
+الحالة هذه بيطلع عندي ال
+
+100
+00:12:09,290 --> 00:12:14,710
+partial sum رقم K2 هو نفس ال partial sum رقم تلاتة
+
+101
+00:12:14,710 --> 00:12:18,950
+فطبعا هذا هيساوي مجموع اول تلاتة حدود
+
+102
+00:12:22,250 --> 00:12:33,350
+فعندي هنا هيطلع أول حد واحد، التاني واحد على اتنين
+
+103
+00:12:33,350 --> 00:12:36,530
+أسقي
+
+104
+00:12:36,530 --> 00:12:42,670
+و الحد التالت واحد على تلاتة أسبيل
+
+105
+00:12:54,470 --> 00:12:58,710
+خلّينا هذه ال N مفروض تكون من واحد لان ات من واحد
+
+106
+00:12:58,710 --> 00:13:05,550
+لان ات ف S K2 هو S تلاتة S تلاتة بساوي واحد على
+
+107
+00:13:05,550 --> 00:13:10,110
+واحد أس P اللي هو واحد زائد واحد على اتنين أس P
+
+108
+00:13:10,110 --> 00:13:17,620
+زائد واحد على تلاتة أس Pطيب أنا عندي هذا أصغر من
+
+109
+00:13:17,620 --> 00:13:23,360
+واحد زايد واحد على اتنين أُس P زايد واحد على اتنين
+
+110
+00:13:23,360 --> 00:13:34,820
+أُس P since لأنه اتنين أُس P أصغر من تلاتة أُس P
+
+111
+00:13:34,820 --> 00:13:42,400
+فبتعني مقلوب تلاتة أُس P أصغر من مقلوب اتنين أُس P
+
+112
+00:13:42,400 --> 00:13:51,330
+صح؟و هذا بيساوي واحد زائد واحد على اتنين اصفى زائد
+
+113
+00:13:51,330 --> 00:13:58,850
+اتنين اتنين في واحد على اتنين اصفى هزبوت هدول حدين
+
+114
+00:13:58,850 --> 00:14:03,870
+متشابهين وهذا بيطلع بيساوي واحد زائد واحد على
+
+115
+00:14:03,870 --> 00:14:12,590
+اتنين اصفى سالب واحد وهذا بيساوي واحد زائد اربع
+
+116
+00:14:14,460 --> 00:14:20,460
+معرف ال R على إنها 1 على 2 أُس P سالب واحد
+
+117
+00:14:20,460 --> 00:14:24,420
+Similarly
+
+118
+00:14:24,420 --> 00:14:29,820
+بالمثل لو
+
+119
+00:14:29,820 --> 00:14:39,060
+كانت K تلاتة بساوي اتنين أس تلاتة سالب واحد يعني
+
+120
+00:14:39,060 --> 00:14:43,140
+سبعة then
+
+121
+00:14:44,850 --> 00:14:53,850
+هيكون SK3 هيطلع بساوي SK2
+
+122
+00:14:53,850 --> 00:14:58,350
+زائد
+
+123
+00:14:58,350 --> 00:15:05,210
+واحد على أربعة أس P زائد واحد على خمسة أس P زائد
+
+124
+00:15:05,210 --> 00:15:10,990
+واحد على ستة أس P زائد واحد على سبعة أس P مظبوط
+
+125
+00:15:10,990 --> 00:15:11,990
+هيك صح؟
+
+126
+00:15:14,290 --> 00:15:18,410
+لأن S K 2 هو واحد زاد واحد على اتنين أسفل زاد واحد
+
+127
+00:15:18,410 --> 00:15:23,430
+على تلاتة أسفل وهذا
+
+128
+00:15:23,430 --> 00:15:37,510
+أصغر من .. طبعا S K 2 أصغر من واحد قلنا زائد R
+
+129
+00:15:41,610 --> 00:15:46,750
+و بعدين الحدود هذه .. كل واحد من الحدود هذه أصغر
+
+130
+00:15:46,750 --> 00:15:52,250
+من أو يساوي واحد على أربعة أس P واحد على أربعة أس
+
+131
+00:15:52,250 --> 00:15:57,570
+P .. واحد على أربعة أس P .. واحد على أربعة أس P
+
+132
+00:15:57,570 --> 00:16:02,690
+لأن كل واحد من المقامات هذه أكبر من أو يساوي أربعة
+
+133
+00:16:02,690 --> 00:16:09,870
+أس Pطب أقول جديش عددهم أربعة هذا بيساوي واحد زايد
+
+134
+00:16:09,870 --> 00:16:17,730
+R زايد أربعة على أربعة أس P هو يساوي واحد زايد R
+
+135
+00:16:17,730 --> 00:16:27,810
+زايد واحد على أربعة أس P سالب واحد إذن بيطلع عندي
+
+136
+00:16:27,810 --> 00:16:38,880
+أنا S K تلاتة أصغر من واحد زايد Rزائد واحد على
+
+137
+00:16:38,880 --> 00:16:43,480
+اتنين اتنين
+
+138
+00:16:43,480 --> 00:16:49,820
+قص اتنين في P سالب واحد وهذا
+
+139
+00:16:49,820 --> 00:16:58,520
+هو R تربية هذا بيساوي واحد زائد R زائد R تربية لو
+
+140
+00:16:58,520 --> 00:17:04,120
+سمرنا في العملية هذه continuing
+
+141
+00:17:07,150 --> 00:17:16,370
+inductively بطريقة استقرائية continuing
+
+142
+00:17:16,370 --> 00:17:22,590
+inductively يعني by induction باستخدام
+
+143
+00:17:22,590 --> 00:17:28,350
+ال induction we
+
+144
+00:17:28,350 --> 00:17:32,570
+get نحصل على التالي for
+
+145
+00:17:40,680 --> 00:17:50,100
+for K J بيساوي اتنين اقصد J سالب واحد we
+
+146
+00:17:50,100 --> 00:17:55,340
+have S
+
+147
+00:17:55,340 --> 00:18:08,260
+K J هيطلع اصغر من واحد زائد R زائد R ترمية زائد
+
+148
+00:18:10,870 --> 00:18:22,010
+R أُس J سالب واحد و
+
+149
+00:18:22,010 --> 00:18:27,830
+هذا صحيح لكل J في N هزبط
+
+150
+00:18:27,830 --> 00:18:36,550
+هيك صح هيتعالى نشوف لما J كانت بالسلب واحد فطلع
+
+151
+00:18:36,550 --> 00:18:43,660
+عندي Sك واحد بيساوي واحد وأصغر من أو يساوي الواحد
+
+152
+00:18:43,660 --> 00:18:47,600
+لما
+
+153
+00:18:47,600 --> 00:18:54,920
+ك ج بيساوي اتنين لما
+
+154
+00:18:54,920 --> 00:19:02,980
+ج بيساوي اتنينفطلع SK2 أصغر من واحد زائد R واحد
+
+155
+00:19:02,980 --> 00:19:09,660
+زائد هاي اتنين سالب واحد الأسف لما J بساوية تلاتة
+
+156
+00:19:09,660 --> 00:19:15,800
+عندي طلع ال SK تلاتة أصغر من واحد زائد R زائد R أس
+
+157
+00:19:15,800 --> 00:19:21,280
+تلاتة سالب واحد إذا S sub KJ أصغر من واحد زائد R
+
+158
+00:19:21,280 --> 00:19:30,540
+إلى R أس J minus واحدالان هذا المجموع أصغر من
+
+159
+00:19:30,540 --> 00:19:39,280
+مجموع ال infinite series اللي هي summation من j
+
+160
+00:19:39,280 --> 00:19:48,980
+بساوي سفر إلى ملا نهاية لR أس J صح؟
+
+161
+00:19:50,160 --> 00:19:56,760
+هذا عبارة
+
+162
+00:19:56,760 --> 00:20:01,440
+عن finite sum أصغر من مجموعة infinite series هذه
+
+163
+00:20:01,440 --> 00:20:10,700
+عبارة عن geometric series with first term واحد وال
+
+164
+00:20:10,700 --> 00:20:18,140
+ratio تبعها R والـ R أكبر من صفر أصغر من واحدإذا
+
+165
+00:20:18,140 --> 00:20:23,080
+الـ geometric series هذه converges ومجموعة بساوي
+
+166
+00:20:23,080 --> 00:20:30,820
+واحد على واحد minus R الكلام
+
+167
+00:20:30,820 --> 00:20:37,320
+هذا صحيح for all j belong to M وطبعا ال SKJ هذا
+
+168
+00:20:37,320 --> 00:20:42,760
+عبارة عن مجموعة partial sum partial sum لأعداد
+
+169
+00:20:42,760 --> 00:20:44,560
+موجبة وبالتالي موجبة
+
+170
+00:20:47,700 --> 00:20:52,720
+إذا أنا هيك أثبتت إن ال sub
+
+171
+00:20:52,720 --> 00:20:58,700
+sequence SKJ bounded below by 0 و bounded above by
+
+172
+00:20:58,700 --> 00:21:05,420
+العدد الموجب 1 على 1 minus R وبالتالي،
+
+173
+00:21:05,420 --> 00:21:10,160
+إذا هيك نستنتج، therefore the subsequence
+
+174
+00:21:13,370 --> 00:21:18,210
+ده sub-sequence اللي هي SKJ هاد ال sub-sequence من
+
+175
+00:21:18,210 --> 00:21:24,370
+مين؟ من ال sequence of partial sums SN اشملها is
+
+176
+00:21:24,370 --> 00:21:31,490
+bounded أثبتنا أنها ايه؟ bounded، مصدقوط؟ طلعنا
+
+177
+00:21:31,490 --> 00:21:35,090
+احنا عملنا construction ل sub-sequenceمن الـ
+
+178
+00:21:35,090 --> 00:21:37,370
+sequence of partial sums وهي طلعت bounded هي
+
+179
+00:21:37,370 --> 00:21:41,670
+bounded below by 0 bounded above by 1 over 1 minus
+
+180
+00:21:41,670 --> 00:21:53,610
+r لأن حسب اللمّة اللي فاتت so by above لمّة ال
+
+181
+00:21:53,610 --> 00:21:56,730
+sequence of partial sums نفسها is bounded
+
+182
+00:22:02,950 --> 00:22:08,570
+وبالتالي إذا by above theorem مدام ال sequence of
+
+183
+00:22:08,570 --> 00:22:11,910
+partial sums is bounded إذا ال series converges
+
+184
+00:22:11,910 --> 00:22:15,710
+okay
+
+185
+00:22:15,710 --> 00:22:23,790
+إذا بعديكم نقول so
+
+186
+00:22:23,790 --> 00:22:29,930
+by above theorem ال
+
+187
+00:22:29,930 --> 00:22:46,080
+series sigma1 على N أكبر من 1 فهذا
+
+188
+00:22:46,080 --> 00:22:53,300
+يثبت الجزء الأول من النظرية خلّينا
+
+189
+00:22:53,300 --> 00:22:54,640
+نثبت الجزء التاني
+
+190
+00:23:10,080 --> 00:23:17,200
+using induction you
+
+191
+00:23:17,200 --> 00:23:21,660
+can show أنه
+
+192
+00:23:21,660 --> 00:23:26,800
+for P
+
+193
+00:23:26,800 --> 00:23:29,140
+أكبر من صفر أصغر من واحد
+
+194
+00:23:32,370 --> 00:23:37,970
+لو كانت ال P طبعا أكبر من صفر وأصغر من أو ساوي
+
+195
+00:23:37,970 --> 00:23:46,110
+الواحد ف N أوس P بطلع أصغر من أو ساوي N لكل N في N
+
+196
+00:23:46,110 --> 00:23:49,670
+صح؟
+
+197
+00:23:49,670 --> 00:23:57,430
+انا ممكن اثباته by inductionSo, 1 على n أصغر لو
+
+198
+00:23:57,430 --> 00:24:08,470
+ساقى 1 على n أُس في for all n ينتمي إلى n فإن
+
+199
+00:24:08,470 --> 00:24:12,710
+هذا بيقدّي هذا بيقدّي
+
+200
+00:24:30,450 --> 00:24:36,590
+this implies أن ال summation from k بساوي واحد to
+
+201
+00:24:36,590 --> 00:24:44,150
+n لواحد على k أصغر لو ساوي summation من k بساوي
+
+202
+00:24:44,150 --> 00:24:55,850
+واحد إلى n لواحد على n على k أوس Pطب ما هذا عبارة
+
+203
+00:24:55,850 --> 00:25:02,270
+عن ال partial sum لسمي S N لل harmonic series ..
+
+204
+00:25:02,270 --> 00:25:09,410
+لل .. لل harmonic series و هذا عبارة عن ال partial
+
+205
+00:25:09,410 --> 00:25:17,870
+sum سمي S N star لل P series صح؟ إن أنا أصبح عندي
+
+206
+00:25:17,870 --> 00:25:21,850
+أنا S N أصغر من أو ساوي S N star
+
+207
+00:25:24,550 --> 00:25:29,430
+where لكل n where
+
+208
+00:25:29,430 --> 00:25:36,530
+sn بساوي sigma واحد على k من k بساوي واحد إلى n و
+
+209
+00:25:36,530 --> 00:25:42,230
+sn star بساوي sigma من k بساوي واحد إلى n لواحد
+
+210
+00:25:42,230 --> 00:25:51,630
+على k أُس P طيب since أثبتنا احنا قبل هيك انه ال
+
+211
+00:25:51,630 --> 00:25:53,230
+sequence of partial sums
+
+212
+00:25:56,310 --> 00:26:01,790
+السيكوانس SN هذا عبارة عن السيكوانس of partial
+
+213
+00:26:01,790 --> 00:26:02,290
+sums
+
+214
+00:26:12,510 --> 00:26:17,510
+of the harmonic series sigma 1 على n ايش مالهم؟
+
+215
+00:26:17,510 --> 00:26:23,070
+اثبتنا انهم unbounded ال sequence هذه is unbounded
+
+216
+00:26:23,070 --> 00:26:30,670
+بنالنا ذلك في مثال سابق unbounded
+
+217
+00:26:30,670 --> 00:26:35,070
+فلو سمينا المتباين
+
+218
+00:26:35,070 --> 00:26:39,530
+هذا star then
+
+219
+00:26:39,530 --> 00:26:40,370
+it follows
+
+220
+00:26:44,900 --> 00:26:50,900
+from star ينتج من المتباينة star إذا كانت ال
+
+221
+00:26:50,900 --> 00:26:55,600
+sequence هذه unbounded
+
+222
+00:26:55,600 --> 00:27:00,620
+لصغيرة unbounded فالحدود أكبر is unbounded ال
+
+223
+00:27:00,620 --> 00:27:11,140
+sequence SM star is unbounded وبالتالي
+
+224
+00:27:11,140 --> 00:27:13,600
+حسب النظرية أعلى so by
+
+225
+00:27:20,890 --> 00:27:26,890
+السيريز هي سيكوينس باشا سمسا بايتالي P Series
+
+226
+00:27:26,890 --> 00:27:32,930
+سيجما من K بساوة واحد وإنفينيتي لواحد على K أوس P
+
+227
+00:27:32,930 --> 00:27:36,290
+is divergent
+
+228
+00:27:41,610 --> 00:27:48,170
+حسب النظرية اللى ذكرناها سابقًا، طيب، في عندي هاي
+
+229
+00:27:48,170 --> 00:27:51,750
+series of positive numbers أو non-negative real
+
+230
+00:27:51,750 --> 00:27:55,890
+numbers و ال sequence of partial sums أبعدتها
+
+231
+00:27:55,890 --> 00:28:00,250
+unbounded، إذا حسب النظرية ال series is not
+
+232
+00:28:00,250 --> 00:28:05,260
+convergent أو divergent، صح؟إذن هذا بتثبت الجزء
+
+233
+00:28:05,260 --> 00:28:09,880
+التاني وبالتاني هيك بيكون بارهاننا اختبار ال P
+
+234
+00:28:09,880 --> 00:28:15,200
+-series test او ال P-series test إذن
+
+235
+00:28:15,200 --> 00:28:20,960
+أي P-series بتكون convergent إذا ال P أكبر من واحد
+
+236
+00:28:20,960 --> 00:28:25,620
+و divergent إذا P أصغر من أول ساول واحد في أي
+
+237
+00:28:25,620 --> 00:28:26,220
+سؤال؟
+
+238
+00:28:52,320 --> 00:28:55,800
+زي ما أخرنا comparison و limit comparison test
+
+239
+00:28:55,800 --> 00:29:00,920
+للsequences في comparison test لل series
+
+240
+00:29:00,920 --> 00:29:08,900
+comparison
+
+241
+00:29:08,900 --> 00:29:13,960
+test
+
+242
+00:29:13,960 --> 00:29:17,020
+for series
+
+243
+00:29:33,680 --> 00:29:40,800
+لت XIN و YIN بـ sequences of non-negative real
+
+244
+00:29:40,800 --> 00:29:41,380
+numbers
+
+245
+00:29:49,780 --> 00:29:58,060
+يكون such that xn أصغر من أو ساوي yn أكبر من أو
+
+246
+00:29:58,060 --> 00:30:06,540
+ساوي سفر for all n أكبر من أو ساوي k for some k
+
+247
+00:30:06,540 --> 00:30:14,660
+ينتمي إلى n أنا
+
+248
+00:30:14,660 --> 00:30:19,950
+لدي two sequences of real numberالتنتين حدودهم غير
+
+249
+00:30:19,950 --> 00:30:26,790
+سالبة من capital .. من capital K و انت طالع ممكن
+
+250
+00:30:26,790 --> 00:30:30,350
+الحدود اللي جابل .. اللي رقمهم أصغر من K بتكون
+
+251
+00:30:30,350 --> 00:30:36,150
+سالبة مش مشكلة أو مايكونش xn أصغر .. ممكن يكون xn
+
+252
+00:30:36,150 --> 00:30:41,830
+أكبر من yn مش مشكلة لكن من عند capital Kلكل مؤشر
+
+253
+00:30:41,830 --> 00:30:45,810
+لكل index because on an equal key أنا بدي xn أصغر
+
+254
+00:30:45,810 --> 00:30:51,990
+من وسائر yn واتنين يكونوا غير سلبين الآن إذا كانت
+
+255
+00:30:51,990 --> 00:30:58,190
+ال series sigma
+
+256
+00:30:58,190 --> 00:31:06,970
+xn إذا كانت ال series الأولى convergent أو الكبيرة
+
+257
+00:31:09,920 --> 00:31:17,540
+convergent بتقدي ان ال series الأصغر converge and
+
+258
+00:31:17,540 --> 00:31:29,520
+لو كانت ال series الأكبر الأصغر diverge فبتقدي
+
+259
+00:31:29,520 --> 00:31:36,700
+أن ال series الأكبر بالتأكيد diverge وهي
+
+260
+00:31:36,700 --> 00:31:45,380
+البرهان البرهن الجزء الأولassume أنه ال series
+
+261
+00:31:45,380 --> 00:31:56,180
+sigma yn converges then
+
+262
+00:31:56,180 --> 00:32:00,000
+by cauchy
+
+263
+00:32:00,000 --> 00:32:10,000
+criterion for series given
+
+264
+00:32:12,200 --> 00:32:18,900
+epsilon أكبر من الصفر يوجد capital N يعتمد على
+
+265
+00:32:18,900 --> 00:32:26,920
+epsilon عدد طبيعي بحيث أنه لكل M أكبر من small n
+
+266
+00:32:26,920 --> 00:32:31,620
+أكبر من أو ساوي capital N هيطلع عندي absolute
+
+267
+00:32:39,200 --> 00:32:51,200
+YNZ1Z YNZ2 و هكذا الى YM أصغر من إبسن هذا من Koshi
+
+268
+00:32:51,200 --> 00:32:51,760
+criterion
+
+269
+00:33:15,050 --> 00:33:23,830
+طيب انا عندي let
+
+270
+00:33:23,830 --> 00:33:34,730
+M بساوي ال maximum الأكبر ب N العدد K هذا الطبيعي
+
+271
+00:33:34,730 --> 00:33:40,010
+K و العدد الطبيعي capital N اللي بيعتمد على
+
+272
+00:33:40,010 --> 00:33:40,330
+epsilon
+
+273
+00:33:43,140 --> 00:33:49,360
+فاكيد طبعا هذا عدد طبيعي وهذا عدد طبيعي فان ام
+
+274
+00:33:49,360 --> 00:33:54,200
+هيطلع عدد طبيعي وام يعتمد على ابسلون لأن الام
+
+275
+00:33:54,200 --> 00:34:01,500
+يعتمد على capital ان وcapital ان تعتمد على ابسلون
+
+276
+00:34:01,500 --> 00:34:09,900
+اذا لو اخدت انا ان اكبر من ام او ام اكبر من ان وان
+
+277
+00:34:09,900 --> 00:34:18,560
+اكبر من او ساوي capital انفهذا بالتأكيد هيقدّي انه
+
+278
+00:34:18,560 --> 00:34:23,480
+ال ..
+
+279
+00:34:23,480 --> 00:34:29,520
+ال .. من هنا من الفرض نسمي الفرض هذا star
+
+280
+00:34:34,930 --> 00:34:45,790
+فمن star هيطلع عندي مفروض xn زائد واحد زائد xn
+
+281
+00:34:45,790 --> 00:34:51,130
+زائد اتنين زائد و هكذا الى xm
+
+282
+00:35:01,640 --> 00:35:06,300
+الـ absolute هذا الان كله موجب هذه كل حدود موجبة
+
+283
+00:35:06,300 --> 00:35:12,160
+أو غير سالبة لأن ال N أكبر من أوي ساوي كابتل N
+
+284
+00:35:12,160 --> 00:35:17,380
+وبالتالي هذا بيقدي ان N أكبر من أوي ساوي كابتل K
+
+285
+00:35:17,380 --> 00:35:25,520
+صح؟ إذا باستخدام star كابتل
+
+286
+00:35:25,520 --> 00:35:28,260
+عفوا ان هذه المفروضة تكون M
+
+287
+00:35:31,530 --> 00:35:36,470
+الان لكل M أكبر من M أكبر من أو ساوي capital M
+
+288
+00:35:36,470 --> 00:35:41,110
+capital M هذه أكبر من أو ساوي K وبالتالي M أكبر من
+
+289
+00:35:41,110 --> 00:35:46,030
+أو ساوي K إذن الحدود هذه كلها موجبة أو غير سالبة
+
+290
+00:35:46,030 --> 00:35:58,830
+صح من star و أصغر من أو ساوي اللي هو YM زاد واحد
+
+291
+00:35:58,830 --> 00:36:10,810
+زاد YMزائد اتنين زائد و هكذا الى الى
+
+292
+00:36:10,810 --> 00:36:19,870
+YM برضه هذه كلها حدود غير سالبة وبالتالي هذه هي
+
+293
+00:36:19,870 --> 00:36:25,370
+نفس ال absolute YN زائد واحد زائد YN زائد اتنين
+
+294
+00:36:25,370 --> 00:36:25,910
+زائد
+
+295
+00:36:29,190 --> 00:36:37,590
+ym ومن هنا لاحظوا ال n أكبر من أو ساوي capital M و
+
+296
+00:36:37,590 --> 00:36:42,870
+ال M أكبر من أو ساوي capital N فبطلع عندي كمان هنا
+
+297
+00:36:42,870 --> 00:36:50,630
+ال N أكبر من أو ساوي capital M لأن ال M أكبر من أو
+
+298
+00:36:50,630 --> 00:36:56,650
+ساوي capital N وبالتالي من ال implication هذههذا
+
+299
+00:36:56,650 --> 00:37:04,470
+بيطلع أصغر من إبسلم إن أنا طلع عندي absolute xn
+
+300
+00:37:04,470 --> 00:37:11,050
+زائد واحد زائد xn زائد اتنين زائد إلى آخرى إلى xn
+
+301
+00:37:11,050 --> 00:37:17,380
+أصغر من إبسلمهذا عدد غير سالب المجموعة ده غير سالب
+
+302
+00:37:17,380 --> 00:37:20,800
+لإن كل ال X غير سالب وبالتالي ال absolute value هي
+
+303
+00:37:20,800 --> 00:37:24,680
+نفسها هذا هو ال absolute value العدد غير سالب نفسه
+
+304
+00:37:24,680 --> 00:37:31,060
+لإن هنا أثبتنا الكلام هذا صحيح لكل M أكبر من N
+
+305
+00:37:31,060 --> 00:37:36,880
+أكبر من أو يساوي capital M so بستخدم كوشي
+
+306
+00:37:36,880 --> 00:37:42,780
+criterion كمان مرة by koshi criterion
+
+307
+00:37:45,130 --> 00:37:50,250
+for series الـ
+
+308
+00:37:50,250 --> 00:37:57,310
+series sigma xn converges لأن
+
+309
+00:37:57,310 --> 00:38:02,130
+هاي شرط كوشي متحقق، صح؟
+
+310
+00:38:02,130 --> 00:38:07,390
+هاي لأي إبسلون given إبسلون أكبر من السفر أثناء أن
+
+311
+00:38:07,390 --> 00:38:13,490
+يوجد capital Mيعني يعتمد على إبسلون بحيث لكل M
+
+312
+00:38:13,490 --> 00:38:18,350
+أكبر من N أكبر من أو ساوي كابتال N فلاندي أبسليوت
+
+313
+00:38:18,350 --> 00:38:23,150
+XN زاد واحد زائد إلى XM أصغر من إبسلون إذا حسب
+
+314
+00:38:23,150 --> 00:38:27,050
+كوشي criterion ال series Sigma XN converges هذا
+
+315
+00:38:27,050 --> 00:38:36,790
+بكمل برهان الجزء الأول الجزء التاني بينتج
+
+316
+00:38:36,790 --> 00:38:37,890
+من الجزء الأول
+
+317
+00:38:42,270 --> 00:38:52,390
+this is the contrapositive .. the contrapositive
+
+318
+00:38:52,390 --> 00:39:00,330
+أو the contraposition .. this is the
+
+319
+00:39:00,330 --> 00:39:04,930
+contraposition of ال statement واحد
+
+320
+00:39:08,170 --> 00:39:12,270
+أنا في عندي قانون في ال logic بيقول إذا كان P فأدي
+
+321
+00:39:12,270 --> 00:39:19,370
+ل Q فال statement هذا بكافئ ال counter positive مش
+
+322
+00:39:19,370 --> 00:39:21,950
+النفي تبعه ال counter positive معناه المعاكس
+
+323
+00:39:21,950 --> 00:39:30,550
+الإيجابي فهذا بكافئ not Q implies not P فذا
+
+324
+00:39:30,550 --> 00:39:37,130
+أثبتنا إن هذا true فهذا بيكون trueطب تعالى نشوف
+
+325
+00:39:37,130 --> 00:39:39,810
+هذا هذا اللى انا اثبتنا انه true اللى هو الجزء ا
+
+326
+00:39:39,810 --> 00:39:43,590
+او الجزء واحد الجزء التانى هو ال counter positive
+
+327
+00:39:44,960 --> 00:39:50,320
+هل هذا صحيح تعالوا نقرأ الجزء التاني او تعالوا
+
+328
+00:39:50,320 --> 00:39:55,420
+نجيب ال contrapositive للعبارة في الجزء الأول ال
+
+329
+00:39:55,420 --> 00:39:59,800
+contrapositive للعبارة في الجزء الأول نفي هذا اللي
+
+330
+00:39:59,800 --> 00:40:04,160
+هو ال series sigma x in by dirge بيقدي الى نفي هذا
+
+331
+00:40:04,160 --> 00:40:08,420
+اللي هو ال series y in by dirgeوبالتالي هيك بنكون
+
+332
+00:40:08,420 --> 00:40:17,700
+كملنا البرران تمام؟ واضح؟ في أي سؤال؟ أي استفسار؟
+
+333
+00:40:17,700 --> 00:40:25,180
+أحيانا بيكون صعب أن احنا نعملمقارنة بين حدود ال
+
+334
+00:40:25,180 --> 00:40:32,500
+series sigma xn و حدود ال series sigma yn بالطريقة
+
+335
+00:40:32,500 --> 00:40:37,480
+المباشرة زي ما في ال star أحيانا مش سهل نعمل
+
+336
+00:40:37,480 --> 00:40:43,020
+مقارنة زي هذه وبالتالي بنلجأ إلى اختبار اخر بنسميه
+
+337
+00:40:43,020 --> 00:40:49,320
+limit comparison testفنكتب ال test هذا دكتور؟ نعم
+
+338
+00:40:49,320 --> 00:40:53,560
+هلأ عبس النظرية برضه خطأ يعني نفس نحو اللي كنا
+
+339
+00:40:53,560 --> 00:40:58,360
+نعمله بال sequence نعمله بال series هى الفترة
+
+340
+00:40:58,360 --> 00:41:01,940
+التالية؟ اه طبعا يعني انت لو كان مثلا هذه الصحية
+
+341
+00:41:01,940 --> 00:41:08,160
+كلامك بالظبط يعني لو كانت ال series ال series مثلا
+
+342
+00:41:08,160 --> 00:41:14,190
+هذه ال sigma yn diverseهل هذا بيقعد ان sigma xn
+
+343
+00:41:14,190 --> 00:41:18,530
+diverge؟ مش بالضرورة ممكن diverge و ممكن converge
+
+344
+00:41:18,530 --> 00:41:25,510
+نفس الحاجة لو كانت ال series sigma xn converge هل
+
+345
+00:41:25,510 --> 00:41:31,030
+sigma yn converge؟ ممكن او ممكن لأ اكيد و ممكن
+
+346
+00:41:31,030 --> 00:41:34,690
+نجيب counter examples لازم تفكري في إيجاد counter
+
+347
+00:41:34,690 --> 00:41:36,850
+examples و انت بتدرسيه
+
+348
+00:41:40,810 --> 00:41:53,630
+نشوف ال limit comparison test limit
+
+349
+00:41:53,630 --> 00:42:02,030
+comparison test
+
+350
+00:42:18,300 --> 00:42:27,120
+لت Xn وYn بيكونوا سيكوانس من حدود حقيقية مفتوحة
+
+351
+00:42:27,120 --> 00:42:36,560
+بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة
+
+352
+00:42:36,560 --> 00:42:38,340
+بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة
+
+353
+00:42:38,340 --> 00:42:40,480
+بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة
+
+354
+00:42:40,480 --> 00:42:40,480
+به
+
+355
+00:42:47,730 --> 00:42:56,850
+و ال R هذا يعني عدد حقيقي طبعا ينتمي إلى R ففي
+
+356
+00:42:56,850 --> 00:43:04,670
+عندي برضه نتيجتين النتيجة الأولى إذا كان ال R
+
+357
+00:43:04,670 --> 00:43:09,630
+بسويش سفر then
+
+358
+00:43:09,630 --> 00:43:15,330
+ال series sigma X M converges if and only if
+
+359
+00:43:24,150 --> 00:43:43,650
+الجزء التاني من النظرية لو
+
+360
+00:43:43,650 --> 00:43:52,220
+كان R بساوي سفربعد ذلك لو الار بيسوي سفر يعني ان
+
+361
+00:43:52,220 --> 00:44:01,220
+الار بيسويش سفر then ال series sigma y in دي درجز
+
+362
+00:44:01,220 --> 00:44:07,840
+بيقدي ان ال series sigma x in دي درجز
+
+363
+00:44:11,380 --> 00:44:19,300
+او لأ convergence افضل لو كانت series sigma yn
+
+364
+00:44:19,300 --> 00:44:24,480
+convergence بيقدي ان series sigma xn ايبان
+
+365
+00:44:24,480 --> 00:44:27,620
+convergence فقط اتجاه واحد لكن الاكس مش شرط تكون
+
+366
+00:44:27,620 --> 00:44:37,460
+صحيح okay تمام هو البرهان
+
+367
+00:44:37,460 --> 00:44:38,520
+يعني كتير سهل
+
+368
+00:44:49,520 --> 00:45:02,300
+بنسمي الشرط هذا star الجزء
+
+369
+00:45:02,300 --> 00:45:12,940
+الأول assume ان R لا يساوي سفر طبعا
+
+370
+00:45:12,940 --> 00:45:21,670
+في الحالة هذه ال R بطلع موجدلأن لحظة انتوا ان xn
+
+371
+00:45:21,670 --> 00:45:27,810
+على yn هذه كلها أعداد موجبة و ال limit ل sequence
+
+372
+00:45:27,810 --> 00:45:31,930
+أعداء كل حدودها موجبة بيطلع المفروض يطلع ال limit
+
+373
+00:45:31,930 --> 00:45:37,970
+تبعتها موجبة إذا كانت ال limit موجودة واضح؟ إذن
+
+374
+00:45:37,970 --> 00:45:42,090
+هذا من نظرية سابقة لما أن حدود ال sequence xn على
+
+375
+00:45:42,090 --> 00:45:45,930
+yn هذه ال sequence حدودها كلها موجبة إذا نهايتها
+
+376
+00:45:45,930 --> 00:45:58,820
+تطلع أيضا موجبةطيب وبالتالي take epsilon بساوي R ع
+
+377
+00:45:58,820 --> 00:46:09,180
+2 طبعا هذا بالتأكيد عدد موجب الان by star since
+
+378
+00:46:09,180 --> 00:46:18,240
+XN على YN converges to R as N tends to infinity
+
+379
+00:46:20,590 --> 00:46:26,850
+بقدر نلاقي capital N يعتمد على إبسلون عدد طبيعي
+
+380
+00:46:26,850 --> 00:46:32,830
+بحيث أنه absolute لكل N أكبر من أو يساوي capital N
+
+381
+00:46:32,830 --> 00:46:39,730
+بيطلع absolute xn على yn minus r أصغر من إبسلون
+
+382
+00:46:39,730 --> 00:46:49,430
+اللي هي بيساوي R ع 2 وهذا بيقديلو فكنا وعملنا ال
+
+383
+00:46:49,430 --> 00:46:56,730
+absolute value هيطلع عندي xn
+
+384
+00:46:56,730 --> 00:47:03,910
+على yn أكبر من أو ساوي R ع 2 أصغر من أو ساوي 3R ع
+
+385
+00:47:03,910 --> 00:47:11,530
+2 وبما أنه هذا صحيح لكل N أكبر من أو ساوي capital
+
+386
+00:47:11,530 --> 00:47:21,570
+Nالان اضرب في YN YN طبعا عدد موجب فبطلع XN أصغر من
+
+387
+00:47:21,570 --> 00:47:27,370
+أو ساوي تلاتة R ع اتنين في YN أكبر من أو ساوي R ع
+
+388
+00:47:27,370 --> 00:47:33,510
+اتنين في YN وهذا صحيح لكل N أكبر من أو ساوي
+
+389
+00:47:33,510 --> 00:47:37,330
+capital N تمام الان now
+
+390
+00:47:45,120 --> 00:47:53,940
+نسمي هذه double star فالان
+
+391
+00:47:53,940 --> 00:48:03,820
+if sigma x and converge then
+
+392
+00:48:03,820 --> 00:48:12,540
+by double star and comparison test and comparison
+
+393
+00:48:12,540 --> 00:48:22,450
+testواختبار المقارنة إذا كانت هذه convergent فبطلع
+
+394
+00:48:22,450 --> 00:48:31,810
+هذه ال series convergent صح وبالتالي بطلع sigma yn
+
+395
+00:48:31,810 --> 00:48:38,370
+convergence هذا ثابت موجة ممكن نضرب في مقلوب و
+
+396
+00:48:38,370 --> 00:48:42,490
+نتخلص منه إذا كانت هذه convergent فهذه convergent
+
+397
+00:48:46,950 --> 00:48:55,330
+Also إذا كانت ال series sigma y in converge then
+
+398
+00:48:55,330 --> 00:49:00,810
+برضه by المتباينة double star and ال comparison
+
+399
+00:49:00,810 --> 00:49:04,890
+test إذا
+
+400
+00:49:04,890 --> 00:49:06,070
+ناخد الجزء هذا
+
+401
+00:49:09,440 --> 00:49:12,720
+إذا كانت ال series هذي convergent و الكبيرة هذي
+
+402
+00:49:12,720 --> 00:49:17,840
+convergent ففي ثابت موجب convergent فهذه تطلع
+
+403
+00:49:19,770 --> 00:49:25,650
+بطلع sigma xn conversion وبالتالي هذا بكمل برهان
+
+404
+00:49:25,650 --> 00:49:30,110
+الجزء الأول طبعا برهان الجزء التاني هيكون يعني
+
+405
+00:49:30,110 --> 00:49:36,530
+مشابه فلأن الواجهة انتهى هنوقف و هسيبكم تقرؤ برهان
+
+406
+00:49:36,530 --> 00:49:41,890
+الجزء الأول من الكتاب فنكتفي بهذا القدر و ان شاء
+
+407
+00:49:41,890 --> 00:49:43,730
+الله نكمل المحاضرة الجاية
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..60a1eb6fbfaa78ccf457aca5662f015d4601cd6e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE.srt
@@ -0,0 +1,1722 @@
+1
+00:00:20,830 --> 00:00:26,410
+بسم الله الرحمن الرحيم احنا في المحاضرة اللي فاتت
+
+2
+00:00:26,410 --> 00:00:32,690
+اتحدثنا عن ال limit comparison test وبرهنّا 
+
+3
+00:00:32,690 --> 00:00:37,470
+الجزء الأول منه فنرجع مع بعض ال limit comparison
+
+4
+00:00:37,470 --> 00:00:43,190
+test for infinite series طبعًا طبعًا في limit
+
+5
+00:00:43,190 --> 00:00:47,450
+comparison test for sequences الآن هذا الاختبار 
+
+6
+00:00:47,450 --> 00:00:52,340
+قصد ال infinite series لو في عندي two sequences of
+
+7
+00:00:52,340 --> 00:00:57,760
+positive real numbers بحيث أن limit ال quotient
+
+8
+00:00:57,760 --> 00:01:05,700
+تبعهم exist بيساوي عدد R ففي عندي نتيجتين، لو كان
+
+9
+00:01:05,700 --> 00:01:12,170
+العدد R أو limit R هذه لا تساوي 0 ففي الحالة هذه
+
+10
+00:01:12,170 --> 00:01:18,130
+sigma x in series sigma x converges if and
+
+11
+00:01:18,130 --> 00:01:21,550
+only if ال series sigma y converges يعني
+
+12
+00:01:21,550 --> 00:01:24,910
+اثنين إما اثنين بيكونوا convergence زي بعض أو
+
+13
+00:01:24,910 --> 00:01:28,630
+اثنين بيكونوا divergence زي بعض الجزء الثاني بيقول
+
+14
+00:01:28,630 --> 00:01:32,010
+لو كانت ال R اللي هي limit لل quotient مساوية صفر
+
+15
+00:01:32,010 --> 00:01:37,110
+وإذا كانت ال series اللي الحد العام تبعها Y converges فال series هذا بيقترب من ال series اللي هي 
+
+16
+00:01:37,110 --> 00:01:41,770
+sigma xn كلها يعني أعتقد أن احنا برهنّا الجزء الأول
+
+17
+00:01:41,770 --> 00:01:48,510
+براهين اللي فاتت بظبط وخلينا نبرهن الجزء الثاني طبعًا
+
+18
+00:01:48,510 --> 00:01:55,750
+since إذا هنا let assume r 
+
+19
+00:01:55,750 --> 00:02:06,370
+بساوي صفر
+20
+00:02:06,370 --> 00:02:07,650
+بساوي صفر
+
+21
+00:02:18,190 --> 00:02:24,490
+أما لو أخدت إبسلون أنا بيساوي العدد واحد فهذا 
+
+22
+00:02:24,490 --> 00:02:29,910
+إبسلون موجبة إحنا 
+
+23
+00:02:29,910 --> 00:02:38,070
+لدينا من الفرض since limit xn over yn as n tends
+
+24
+00:02:38,070 --> 00:02:45,640
+to infinity بيساوي R اللي هو صفر الآن فمن تعريف by
+
+25
+00:02:45,640 --> 00:02:51,260
+definition of limit for epsilon positive زي هذه
+
+26
+00:02:51,260 --> 00:02:57,420
+يوجد capital N يعتمد على epsilon اللي هو الواحد
+
+27
+00:02:57,420 --> 00:03:03,900
+natural number بحيث أنه لكل N أكبر من أو يساوي
+
+28
+00:03:03,900 --> 00:03:11,260
+capital N هذا بيدّي أن ال absolute value ل xn على
+
+29
+00:03:11,260 --> 00:03:18,120
+yn minus zero بيطلع أصغر من ال epsilon اللي احنا
+
+30
+00:03:18,120 --> 00:03:26,660
+ماخدينها واحد طب xn عدد موجب و yn عدد موجب فال
+
+31
+00:03:26,660 --> 00:03:33,760
+quotient هذا كسر هذا موجب سالب صفر فهذا بيقدي ان
+
+32
+00:03:33,760 --> 00:03:42,880
+xn over yn أصغر من واحد لو ضربنا الطرفين بالعدد
+
+33
+00:03:42,880 --> 00:03:58,110
+الموجب yn فهذا هيقدي أن xn أصغر من yn وهذا صحيح لكل
+
+34
+00:03:58,110 --> 00:04:05,550
+N أكبر من أو يسوي capital N now
+
+35
+00:04:05,550 --> 00:04:09,090
+if
+
+36
+00:04:09,090 --> 00:04:20,550
+sigma yn converges then
+
+37
+00:04:21,920 --> 00:04:26,140
+by direct comparison test اللي أخذناها المرة اللي
+
+38
+00:04:26,140 --> 00:04:30,420
+فاتت إذا ال series الحد اللي عام تبعها أكبر 
+
+39
+00:04:30,420 --> 00:04:34,480
+convergent فالاصغر 
+
+40
+00:04:34,480 --> 00:04:42,920
+ال series الاصغر converges وهذا هو المطلوب هذا
+
+41
+00:04:42,920 --> 00:04:46,340
+اللي احنا عايزين نثبتة إنه لو كانت ال series yn 
+
+42
+00:04:46,340 --> 00:04:50,690
+convergent فلازم هذا يطلع convergent هذا صحيح by
+
+43
+00:04:50,690 --> 00:04:55,110
+direct comparison test لذلك هذا يكمل برهان الجزء
+
+44
+00:04:55,110 --> 00:05:02,230
+التالي نرجع الأن ناخد أمثلة على تطبيقات على ال
+
+45
+00:05:02,230 --> 00:05:08,590
+direct comparison test وعلى limit comparison test
+
+46
+00:05:11,980 --> 00:05:15,680
+كيف نستخدم ال comparison tests الاختبارين هدول 
+
+47
+00:05:15,680 --> 00:05:27,780
+في اثبات ان ال series معينة is convergent discuss
+
+48
+00:05:27,780 --> 00:05:38,840
+.. discuss the convergence of
+
+49
+00:05:38,840 --> 00:05:40,360
+the following series
+
+50
+00:06:00,990 --> 00:06:07,110
+فناخد series sigma from n equals one to infinity ل
+
+51
+00:06:07,110 --> 00:06:17,370
+one over n squared plus n بالمناسبة 
+
+52
+00:06:17,370 --> 00:06:18,450
+ال series هذه
+
+53
+00:06:23,110 --> 00:06:29,010
+ممكن نقارنها، الحد العام تبعها هذا، لما N تكون
+
+54
+00:06:29,010 --> 00:06:36,410
+large فممكن نهمل ال N بالنسبة ل N تربيع ونعتبر أن 
+
+55
+00:06:36,410 --> 00:06:42,730
+هذه ال series شبيهة أو behaves like تتصرف زي ال
+
+56
+00:06:42,730 --> 00:06:45,650
+series sigma 1 على N تربيع
+
+57
+00:06:50,030 --> 00:06:54,610
+الآن بنشوف إذا ممكن نطبق اختبار المقارنة المباشرة
+
+58
+00:06:54,610 --> 00:06:58,670
+ال direct comparison test بنطبقه وإذا ما قدرناش 
+
+59
+00:06:58,670 --> 00:07:06,950
+بنلجأ لاختبار تبع ال limit comparison test
+
+60
+00:07:24,400 --> 00:07:37,040
+فهنا ممكن يعني من السهل أن احنا نستخدم ال
+
+61
+00:07:37,040 --> 00:07:43,040
+direct comparison test لأنه أنا عندي ال N تربيع
+
+62
+00:07:43,040 --> 00:07:50,400
+زائد N أكبر من أو يساوي N أكبر من أو يساوي N تربيع 
+
+63
+00:07:50,400 --> 00:08:00,220
+لكل N ينتمي ل N هذا بيقدي أن مقلوب N تربيع زائد N
+
+64
+00:08:00,220 --> 00:08:08,680
+أصغر من أو يساوي مقلوب N تربيع لكل N ك N الآن 
+
+65
+00:08:08,680 --> 00:08:13,020
+ال series
+
+66
+00:08:13,020 --> 00:08:15,360
+sigma واحد على N تربيع
+
+67
+00:08:18,710 --> 00:08:29,730
+a P series is P series صح؟ with P
+
+68
+00:08:29,730 --> 00:08:40,270
+بيساوي اثنين أكبر من واحد so
+
+69
+00:08:40,270 --> 00:08:49,230
+it converges by .. it is convergent by P series
+
+70
+00:08:49,230 --> 00:08:56,550
+test في ال P series test بيقول لي إذا كان أي P
+
+71
+00:08:56,550 --> 00:09:02,890
+series زي هذه بتكون convergent إذا كان P أكبر من
+
+72
+00:09:02,890 --> 00:09:08,530
+واحد و divergent إذا كان P أصغر من أو يساوي واحد وبرهنّا الكلام هذا في المحاضرة السابقة أو الجبلة إذا
+
+73
+00:09:08,530 --> 00:09:14,510
+أنا في عندي two series واحدة الحد العام تبعها واحد
+
+74
+00:09:14,510 --> 00:09:20,250
+على N تربيع وهذا ال convergence وواحدة الحد العام
+
+75
+00:09:20,250 --> 00:09:23,790
+تبعها واحد على N تربيع زائد N وهذا الحد العام
+
+76
+00:09:23,790 --> 00:09:28,090
+أصغر من أو يساوي الحد العام لهذه ال convergence إذا 
+
+77
+00:09:28,090 --> 00:09:31,250
+ممكن أستخدم so
+
+78
+00:09:31,250 --> 00:09:35,630
+by direct comparison test
+
+79
+00:09:35,630 --> 00:09:38,550
+by direct comparison test
+
+80
+00:09:42,520 --> 00:09:46,740
+السيريز اللي هي sigma من n equals one to infinity
+
+81
+00:09:46,740 --> 00:09:56,860
+لواحد على n squared plus n converges
+
+82
+00:09:56,860 --> 00:10:03,340
+إذا السيريز هذه اثبتنا انها convergence by
+
+83
+00:10:03,340 --> 00:10:07,140
+direct comparison استخدمنا ال direct comparison
+
+84
+00:10:07,140 --> 00:10:09,160
+test مفهوم واضح؟
+
+85
+00:10:12,050 --> 00:10:13,950
+ناخد مثال ثاني
+
+86
+00:10:36,080 --> 00:10:39,580
+بتاعة اثنين لو أخذنا series sigma from n equals
+
+87
+00:10:39,580 --> 00:10:47,780
+one to infinity لواحد على n تربيع سالب n زائد
+
+88
+00:10:47,780 --> 00:10:54,180
+واحد بما أن نفحص هل ال series هذي convergent ولا
+
+89
+00:10:54,180 --> 00:10:57,520
+divergent طبعًا 
+
+90
+00:10:59,200 --> 00:11:04,280
+أول شيء بنفكر فيه، بنشوف كيف ال series هذه بتتصرف، 
+
+91
+00:11:04,280 --> 00:11:07,740
+ما هي ال series القريبة منها، واللي احنا عارفين 
+
+92
+00:11:07,740 --> 00:11:12,600
+انها أو ممكن نحكم عليها بسهولة، to be convergent أو
+
+93
+00:11:12,600 --> 00:11:15,980
+divergent، يعني بدي أقارن ال series هذه ب series
+
+94
+00:11:15,980 --> 00:11:20,520
+ثانية من السهل اني احكم عليها هل هي convergent أو 
+
+95
+00:11:20,520 --> 00:11:27,160
+divergent فلما N تكون كبيرة و أن N is sufficiently 
+
+96
+00:11:27,160 --> 00:11:32,900
+large لما N تقول infinity ممكن اهمل N و اهمل 1
+
+97
+00:11:32,900 --> 00:11:41,080
+وبالتالي ال series هذه behaves تتصرف زي ال series
+
+98
+00:11:41,080 --> 00:11:42,880
+1 على N تربيع
+
+99
+00:11:45,470 --> 00:11:55,230
+اللي هي احنا عارفين which is كل بيت واحد طبعًا by P 
+
+100
+00:11:55,230 --> 00:12:01,270
+series test زي ما شرحنا في المثال الأول الآن
+
+101
+00:12:01,270 --> 00:12:10,120
+السؤال اللي بيطرح نفسه is it true هل واحد على إن
+
+102
+00:12:10,120 --> 00:12:15,000
+تربيع سالب إن زائد واحد أصغر من أو يساوي واحد على 
+
+103
+00:12:15,000 --> 00:12:20,640
+إن تربيع عشان نستخدم .. هل هذا الكلام صحيح لكل إن؟
+
+104
+00:12:20,640 --> 00:12:25,920
+لا مش فاكرش أنا فللأسف هذا مش صحيح وبالتالي
+
+105
+00:12:25,920 --> 00:12:29,940
+ما أقدرش أستخدم إن هذا not true
+
+106
+00:12:34,430 --> 00:12:41,410
+for example على سبيل المثال take n بيساوي اثنين
+
+107
+00:12:41,410 --> 00:12:50,310
+هنجد المتباينة هذه مش صح اذا ما أقدرش انا أستخدم ال
+
+108
+00:12:50,310 --> 00:12:54,310
+direct comparison test اذا في الحالة هذه لازم 
+
+109
+00:12:54,310 --> 00:12:59,190
+أستخدم ال limit comparison test أو ابحث عن مقارنة 
+
+110
+00:12:59,190 --> 00:13:01,310
+ثانية however
+
+111
+00:13:06,140 --> 00:13:17,200
+you can show بإمكانكم تَثْبُتُوا أن الواحد على n تربيع
+
+112
+00:13:17,200 --> 00:13:23,500
+negative n زائد واحد هذا أصغر من أو يساوي اثنين على
+
+113
+00:13:23,500 --> 00:13:31,280
+n تربيع وهذا صحيح لكل n في n إذن هذه المتباينة
+
+114
+00:13:31,280 --> 00:13:34,420
+صحيحة وبالتالي ممكن الآن 
+
+115
+00:13:39,990 --> 00:13:46,330
+الآن بإمكانك استخدام 
+
+116
+00:13:46,330 --> 00:13:53,030
+مقارنة مباشرة للتأكيد
+
+117
+00:13:53,030 --> 00:14:02,650
+عشان تستنتجوا ان series sigma واحد على إن تربيع 
+
+118
+00:14:02,650 --> 00:14:08,980
+نيجاتيف n بلس واحد convergent لأنه ال series هذه 
+
+119
+00:14:08,980 --> 00:14:15,920
+لأنه since ال series اللي الحد العام تبعها اثنين
+
+120
+00:14:15,920 --> 00:14:20,740
+على إن تربيع هي نفسها اثنين ضرب ال series sigma
+
+121
+00:14:20,740 --> 00:14:26,600
+واحد على إن تربيع وال series هذه قلنا convergent
+
+122
+00:14:26,600 --> 00:14:29,660
+لأنها في series نضربها في عدد موجب بتضلها
+
+123
+00:14:29,660 --> 00:14:31,700
+convergent
+
+124
+00:14:34,390 --> 00:14:38,990
+لازم نثبت على ذلك الكلام هذا الكلام لازم تثبتيه صح
+
+125
+00:14:38,990 --> 00:14:45,970
+المشكلة في الحل هذا أن أنا أو أنتو كيف بدنا يخطر
+
+126
+00:14:45,970 --> 00:14:53,170
+على بالكم أن المتباينة هذا صح اه it is not easy to 
+
+127
+00:14:53,170 --> 00:14:57,030
+figure out this inequality مش سهل أن يختر على
+
+128
+00:14:57,030 --> 00:15:04,110
+بالنا أو نستنتج ال .. أو يعني .. بنعرف إنه في 
+
+129
+00:15:04,110 --> 00:15:09,870
+متباينة زي هذه صحيحة هذا مش سهل وبالتالي ممكن
+
+130
+00:15:09,870 --> 00:15:14,090
+نستخدم ال limit comparison test ونروح رأسنا ال
+
+131
+00:15:14,090 --> 00:15:16,690
+limit comparison test في الحالة هذه أسهل من إن أنا
+
+132
+00:15:16,690 --> 00:15:21,550
+يعني أخمن 
+
+133
+00:15:21,550 --> 00:15:25,950
+.. أخمن يعني حاجة زي هذه okay فتعالوا نشوف كيف
+
+134
+00:15:25,950 --> 00:15:28,070
+نستخدم ال limit comparison test
+
+135
+00:15:31,920 --> 00:15:40,220
+إذا هنا we use limit 
+
+136
+00:15:40,220 --> 00:15:45,160
+comparison test with
+
+137
+00:15:45,160 --> 00:15:54,640
+an بيساوي واحد على n تربيع minus n زائد واحد أو xn 
+
+138
+00:15:54,640 --> 00:15:55,720
+فالبيسمانيات
+
+139
+00:15:57,840 --> 00:16:07,600
+و Yn بيساوي واحد على n تربيع فإنّي
+
+140
+00:16:07,600 --> 00:16:13,340
+أجي نحسب ال limit ل Xn over Yn as N tends to
+
+141
+00:16:13,340 --> 00:16:21,720
+infinity بساوي الـ limit هاي Xn تقسيم Yn بتطلع M
+
+142
+00:16:21,720 --> 00:16:28,990
+تربيع على M تربيع negative M plus one والـ limit
+
+143
+00:16:28,990 --> 00:16:36,930
+هذا عشان نحسبها بالجسم بس مقام على n تربيع في
+
+144
+00:16:36,930 --> 00:16:41,750
+الـ بس واحد واحد سالب واحد على n موجب واحد على n
+
+145
+00:16:41,750 --> 00:16:47,210
+تربيع لإنها بتقول الـ infinity وهذا بطلع واحد على واحد
+
+146
+00:16:47,210 --> 00:16:54,410
+سالب صفر موجب صفر ويساوي واحد لا يساوي صفر إذن الـ R
+
+147
+00:16:55,770 --> 00:16:59,910
+الـ R في الـ limit comparison test طلعت بالساوي
+
+148
+00:16:59,910 --> 00:17:07,630
+واحد لا يساوي صفر، وأنا عندي إذا since وأنا عندي الـ
+
+149
+00:17:07,630 --> 00:17:13,050
+series sigma yn اللي هي sigma واحد على n تربيع
+
+150
+00:17:13,050 --> 00:17:17,830
+is convergent then
+
+151
+00:17:17,830 --> 00:17:26,700
+by limit comparison test الـ series sigma xnاللي هو
+
+152
+00:17:26,700 --> 00:17:32,960
+الحد اللي عم تبعها واحد على n تربيع minus n زائد 
+
+153
+00:17:32,960 --> 00:17:41,560
+واحد كون بيعجز وهو مطلوب okay إذا هنا استخدمنا الـ
+
+154
+00:17:41,560 --> 00:17:46,020
+limit كون لما يعجز أو يفشل الـ comparison أو الـ
+
+155
+00:17:46,020 --> 00:17:49,920
+direct comparison test بنرجع إلى الـ limit comparison
+
+156
+00:17:49,920 --> 00:17:57,220
+testهنا لازم يجب ملاحظة أنه أي سؤال بنحل بالـ
+
+157
+00:17:57,220 --> 00:18:02,660
+comparison test ممكن حله أو نطبق عليه الـ limit
+
+158
+00:18:02,660 --> 00:18:07,800
+comparison test لكن العكس ليس صحيح وبالتالي الـ
+
+159
+00:18:07,800 --> 00:18:12,240
+limit comparison test أشمّل وأعم من الـ direct
+
+160
+00:18:12,240 --> 00:18:17,460
+comparison test ناخد مثال ثالث واضح الحل في أي
+
+161
+00:18:17,460 --> 00:18:22,470
+سؤال أو استفسار؟إذا دائماً في مخرج يعني إذا أنت مش
+
+162
+00:18:22,470 --> 00:18:26,390
+عارف تعمل direct comparison فاستخدم الـ limit
+
+163
+00:18:26,390 --> 00:18:30,670
+comparison test وهذا مش صعب تشوفي دائماً الـ series
+
+164
+00:18:30,670 --> 00:18:35,730
+اللي قدامك behaves like some familiar series تتصرف
+
+165
+00:18:35,730 --> 00:18:41,130
+زي series معروفة لدينا وإحنا عارفين نقدر من السهل
+
+166
+00:18:41,130 --> 00:18:43,530
+نحكم عليها هل convergent أو divergent
+
+167
+00:18:49,830 --> 00:18:57,370
+فلو أخذنا مثلاً الـ series هذه summation from
+
+168
+00:18:57,370 --> 00:19:03,630
+n equals one to infinity لـ one over square root of
+
+169
+00:19:03,630 --> 00:19:08,530
+n plus one ف
+
+170
+00:19:08,530 --> 00:19:11,910
+الـ series this series behaves طبعاً لما n 
+
+171
+00:19:11,910 --> 00:19:19,330
+when n gets large we neglect الواحد نهمل الواحدوهذه
+
+172
+00:19:19,330 --> 00:19:29,190
+السيريز تتصرف من حيث التقارب والتباعد مثل سيجما
+
+173
+00:19:29,190 --> 00:19:31,210
+واحد على جذر الـ n
+
+174
+00:19:38,390 --> 00:19:46,390
+طيب can we السؤال يتفرج نفسه can we use direct
+
+175
+00:19:46,390 --> 00:19:51,670
+comparison test للإجابة
+
+176
+00:19:51,670 --> 00:19:57,770
+على السؤال هذا بنلاحظ أن n زائد 1 أكبر منها أو يساوي
+
+177
+00:19:57,770 --> 00:20:06,310
+n لكل n هذا بيقدر أن واحد وبالتالي الجذر التربيعي لـ
+
+178
+00:20:06,310 --> 00:20:10,110
+N زائد واحد أكبر من أو يساوي جذر الـ N لكل N
+
+179
+00:20:10,110 --> 00:20:17,910
+وبالتالي هذا بيؤدي أن واحد على الجذر التربيعي لـ N
+
+180
+00:20:17,910 --> 00:20:26,950
+زائد واحد أقل من أو يساوي واحد على جذر الـ N لكل Nو
+
+181
+00:20:26,950 --> 00:20:31,850
+إحنا عارفين أن الـ series هذه divergent لأنها P
+
+182
+00:20:31,850 --> 00:20:36,850
+series والـ P بساوي نص أصغر من واحد وهاد الـ
+
+183
+00:20:36,850 --> 00:20:42,770
+series أصغر منها أو أصغر منها ويساويها فالـ direct
+
+184
+00:20:42,770 --> 00:20:46,970
+comparison test بيعطينيش نتيجة، بيعطينيش نتيجة إذا
+
+185
+00:20:46,970 --> 00:20:50,550
+الكبيرة divergent فالصغيرة ممكن تكون convergent
+
+186
+00:20:50,550 --> 00:20:57,150
+وممكن تكون divergent إذا هنا الـ direct comparison
+
+187
+00:20:57,150 --> 00:21:01,050
+test fails،
+
+188
+00:21:01,050 --> 00:21:09,290
+fails يعني يفشل، يفشل وبالتالي ما فيش أمامنا خيار
+
+189
+00:21:09,290 --> 00:21:13,350
+اللي إحنا اللي اللي حالنا نستعمل أو نستخدم
+
+190
+00:21:13,350 --> 00:21:27,350
+limit comparison test نستخدم
+
+191
+00:21:27,350 --> 00:21:29,970
+limit comparison test
+
+192
+00:21:34,290 --> 00:21:39,970
+with xn بيساوي واحد على الـ square root of n plus
+
+193
+00:21:39,970 --> 00:21:48,230
+one وyn بيساوي one over square root of n نحسم الـ
+
+194
+00:21:48,230 --> 00:21:53,990
+limit لـ xn over yn as n tends to infinity بيساوي
+
+195
+00:21:53,990 --> 00:21:57,770
+الـ limit هاي
+
+196
+00:21:57,770 --> 00:22:06,100
+جسم xn على yn بيطلع الجذر التربيعي لـ n على n plus
+
+197
+00:22:06,100 --> 00:22:11,500
+one لما n تقول الـ infinity دخل الـ limit تحت الجذر
+
+198
+00:22:11,500 --> 00:22:15,740
+لأن الـ square root function is continuous فاندخل
+
+199
+00:22:15,740 --> 00:22:21,660
+الـ limit والـ limit المقدار تحت الجذر بطلع واحد
+
+200
+00:22:21,660 --> 00:22:28,920
+وبالتالي واحد لا يساوي صفر إذا الـ R في الـ limit
+
+201
+00:22:28,920 --> 00:22:34,540
+comparison first طلعت different from zero لا تساوي
+
+202
+00:22:34,540 --> 00:22:44,020
+صفر و since الـ series sigma من n equals one to
+
+203
+00:22:44,020 --> 00:22:52,860
+infinity لواحد على جذر الـ n يعبر عن sigma واحد على
+
+204
+00:22:52,860 --> 00:22:58,160
+n تربيع is a p-series with
+
+205
+00:23:03,240 --> 00:23:11,940
+P بساوي نص أصغر من واحد it diverges
+
+206
+00:23:11,940 --> 00:23:24,780
+يعني بتطلع divergent by P series test الـ series
+
+207
+00:23:24,780 --> 00:23:28,560
+يعني divergent وبالتالي
+
+208
+00:23:31,020 --> 00:23:34,760
+by limit comparison test حسب الـ limit comparison
+
+209
+00:23:34,760 --> 00:23:44,020
+test هيعطيني sigma xn وsigma yn sigma yn ده
+
+210
+00:23:44,020 --> 00:23:51,200
+هي طلعت divergent والـ R limit الرئيسية لا تساوي صفر
+
+211
+00:23:51,200 --> 00:23:56,100
+لأن الثانية زيها divergent ده is sigma xn اللي
+
+212
+00:23:56,100 --> 00:24:02,990
+هو واحد على الجذر التربيعي الـ N زيها by agents
+
+213
+00:24:02,990 --> 00:24:17,470
+حسب الـ limit comparison test okay تمام واضح طيب
+
+214
+00:24:17,470 --> 00:24:18,790
+ناخد كمان مثال
+
+215
+00:24:30,910 --> 00:24:37,470
+مثال رقم أربعة خلّينا نفحص الـ series اللي هي
+
+216
+00:24:37,470 --> 00:24:44,770
+summation from n equals one to infinity لـ one over
+
+217
+00:24:44,770 --> 00:24:52,070
+n factorial طبعاً
+
+218
+00:24:52,070 --> 00:25:00,050
+هذه مش واضحة ممكن تقارنها لأن N factorial N
+
+219
+00:25:00,050 --> 00:25:04,810
+factorial بساوي N نقش واحد N سالب واحد N
+
+220
+00:25:04,810 --> 00:25:11,890
+سالب اثنين إلى ثلاثة في اثنين في واحد فمش
+
+221
+00:25:11,890 --> 00:25:21,350
+عارفين إيش نقارنها آه فهذا مش واضح لكن by trial
+
+222
+00:25:21,350 --> 00:25:31,990
+أنا بتقوله بالتجربة نقدر إحنا نحاول يعني نقرر أو
+
+223
+00:25:31,990 --> 00:25:37,330
+يعني نشوف أن هنا عند عشان n في n سالب واحد في n
+
+224
+00:25:37,330 --> 00:25:43,510
+سالب اثنين فممكن نقارن الـ series هذه بواحد على n
+
+225
+00:25:43,510 --> 00:25:51,750
+تربيع نشوف كيف ممكن نعمل المقارنة إذا هنا في حالتين
+
+226
+00:25:51,750 --> 00:26:01,200
+هنا Solution واحد إحنا نحاول نقارن بالإيه فالـ
+
+227
+00:26:01,200 --> 00:26:08,740
+solution الأول أو الحل الأول بيعتمد use
+
+228
+00:26:08,740 --> 00:26:17,460
+induction to show that ممكن
+
+229
+00:26:17,460 --> 00:26:24,210
+نثبت بالـ induction أنه N تربيع أصغر من N factorial
+
+230
+00:26:24,210 --> 00:26:30,290
+لكل N أكبر من أو يساوي أربعة المتباينة هذه صحيحة
+
+231
+00:26:30,290 --> 00:26:34,050
+لكل الأعداد الطبيعية أكبر من أو يساوي أربعة هذا
+
+232
+00:26:34,050 --> 00:26:38,390
+ممكن نثبته by induction زي ما اتعلمته هذا سؤال في
+
+233
+00:26:38,390 --> 00:26:44,670
+مبادئ رياضيات نشوف مع بعض الهدى صح نشوف أول حالة
+
+234
+00:26:44,670 --> 00:26:48,990
+لحظة الـ N بتبدأ من أربعة مش من واحد فـ N بساوي واحد
+
+235
+00:26:48,990 --> 00:26:52,390
+هنا هتصير N بساوي أربعة والباقي الـ induction زي ما
+
+236
+00:26:52,390 --> 00:26:57,210
+اتعلمنا فلو N بساوي أربعة أربعة تربيع ستة عشر أصغر
+
+237
+00:26:57,210 --> 00:27:01,070
+من أربعة فاكتوريا الأربعة وعشرين ستة عشر أصغر من
+
+238
+00:27:01,070 --> 00:27:05,050
+أربعة وعشرين صحيح إذا العبارة صحيحة عند n بالساوي
+
+239
+00:27:05,050 --> 00:27:09,410
+أربعة افرض صحيتها عند n بالساوي k حيث k أي عدد
+
+240
+00:27:09,410 --> 00:27:13,570
+طبيعي أكبر من أربعة وثبت صحيتها عند n بالساوي k
+
+241
+00:27:13,570 --> 00:27:18,830
+زائد، أعتقد هذه مثل في أخدت زيها في مبادئ رياضية،
+
+242
+00:27:18,830 --> 00:27:23,050
+رح نسيب سيبقى لكم ليه؟ إيه شو بتهارفنا مثلاً
+
+243
+00:27:23,050 --> 00:27:25,610
+نختار الأربعة؟ ليش ما هو مثلاً ثلاثة أو واحد، سيبقى
+
+244
+00:27:25,610 --> 00:27:29,150
+إحنا متعودين في الـ induction؟ آه لأنه أنت الـ 
+
+245
+00:27:29,150 --> 00:27:34,030
+يعني نضل نجرب لحد ما نصر نصر بره صح آه من أربعة و
+
+246
+00:27:34,030 --> 00:27:37,690
+أنت طالع تصير صحيحة أما قبل أربعة بتكون خطأ
+
+247
+00:27:37,690 --> 00:27:42,210
+وبالتالي ما لهاش معنى أما من أربعة وأنت طالع
+
+248
+00:27:42,210 --> 00:27:49,830
+هتكون صحيحة فبنهمل الأول تلت قيم لهم okay إذا و
+
+249
+00:27:49,830 --> 00:27:58,220
+وبالتالي هذا بيؤدي أن واحد على n factorial أصغر من
+
+250
+00:27:58,220 --> 00:28:04,040
+واحد على n تربيع لكل n أكبر من أو يساوي أربعة
+
+251
+00:28:04,040 --> 00:28:11,960
+وبالتالي والـ series طبعاً وبالتالي ممكن نستخدم الـ
+
+252
+00:28:11,960 --> 00:28:15,800
+direct comparison test يعني الحالة هذه
+
+253
+00:28:24,200 --> 00:28:28,020
+ونستخدم الاختصار الوحيد الوحيد الوحيد الوحيد
+
+254
+00:28:28,020 --> 00:28:43,880
+الوحيد الوحيد الوحيد الوحيد
+
+255
+00:28:45,400 --> 00:28:50,520
+هذه الـ series هي الـ key series بس بتبدأ من أربعة
+
+256
+00:28:50,520 --> 00:28:55,240
+فكأني حدث يتأول ثلاث حدود منها فهذا بيأثرش على الـ
+
+257
+00:28:55,240 --> 00:28:59,420
+divergence أو الـ convergence للـ series إذا حدث
+
+258
+00:28:59,420 --> 00:29:04,980
+omitting أو deleting finite number of terms from
+
+259
+00:29:04,980 --> 00:29:09,000
+an infinite series does not affect the convergence
+
+260
+00:29:09,000 --> 00:29:13,240
+or the divergence of the series حدث عدد منتهي من
+
+261
+00:29:13,240 --> 00:29:19,540
+حدود الـ series أو إضافة عدد منتهي كمان إلى حدود الـ
+
+262
+00:29:19,540 --> 00:29:24,180
+series لا يؤثر لا على التقارب ولا على التباعد تبع
+
+263
+00:29:24,180 --> 00:29:34,900
+الـ series هذا حقيقة سهل لو يعني وبدهاش برهان لأن
+
+264
+00:29:34,900 --> 00:29:40,300
+الحدود المنتهية هذه مجموعة بيطلع عدد منتهي فما
+
+265
+00:29:40,300 --> 00:29:47,230
+بيأثرش على التقارب من الـ series بياثرش على التقارب أو
+
+266
+00:29:47,230 --> 00:29:52,310
+التباعد أو إضافة عدد لأن بما أن الـ series
+
+267
+00:29:52,310 --> 00:29:58,110
+converges then الـ series sigma واحد على n
+
+268
+00:29:58,110 --> 00:30:03,990
+factorial converges
+
+269
+00:30:03,990 --> 00:30:11,160
+من n بالساوي أربعة إلى ما لا نهاية طبعاً هذا بيؤدي إن أنا
+
+270
+00:30:11,160 --> 00:30:15,360
+لو ضفت للـ series الحدود المتبقية من n بالساوي واحد
+
+271
+00:30:15,360 --> 00:30:22,160
+إلى ثلاثة وبتصير من infinity هنا لواحد
+
+272
+00:30:22,160 --> 00:30:28,160
+على n factorial تطلع
+
+273
+00:30:28,160 --> 00:30:33,280
+convergent وهذا اللي بدنا يعني إذن هذا أحد
+
+274
+00:30:33,280 --> 00:30:38,100
+الحلول okay؟ زي ما زميلتكم يعني اقترحت بتقول طب
+
+275
+00:30:38,100 --> 00:30:44,050
+وأنا إيش بدي أختار على بالي؟ أن هذا المتباينة
+
+276
+00:30:44,050 --> 00:30:47,890
+الصحيحة اللي اعتمد عليها الحل أو اعتمدت عليها
+
+277
+00:30:47,890 --> 00:30:53,430
+المقارنة فمعكم حاجة ممكن أنك يعني ما حدش يقدر
+
+278
+00:30:53,430 --> 00:30:57,970
+يعني يصل إلى الـ أو الـ percentage المتباينة هذه
+
+279
+00:30:57,970 --> 00:31:03,710
+اللي عليها بيرتكز الحل ففي حل ثاني آخر نشوف الحل
+
+280
+00:31:03,710 --> 00:31:05,930
+الثاني الـ direct limit
+
+281
+00:31:09,330 --> 00:31:14,150
+الحل الثاني solution
+
+282
+00:31:14,150 --> 00:31:18,430
+2 احنا 
+
+283
+00:31:18,430 --> 00:31:26,430
+عارفين أنه لو جسمنا أخذنا
+
+284
+00:31:26,430 --> 00:31:35,130
+xn بسعر واحد على n factorial بساوي واحد على ال
+
+285
+00:31:35,130 --> 00:31:41,770
+تربية كويس؟ زي ما عملناه في الحل الأول و بده يقارن
+
+286
+00:31:41,770 --> 00:31:47,320
+الاثنين هدول بس المقارنة المرة هذه هتكون بطريقة
+
+287
+00:31:47,320 --> 00:31:53,760
+مختلفة فلو أخذت xn و جسمتها على yn فطبعا هذا أكبر 
+
+288
+00:31:53,760 --> 00:32:00,140
+من السبب لأن xn عدد موجب دائما لكل n و yn عدد موجب
+
+289
+00:32:00,140 --> 00:32:06,640
+فقسمت على عددين موجبين بطلع موجب وهذا بساوي n تربيع
+
+290
+00:32:06,640 --> 00:32:13,720
+على yn اللي هو n factorial على n factorial
+
+291
+00:32:18,080 --> 00:32:26,220
+و هذا بساوي n تربيع على n factorial عبارة عن 
+
+292
+00:32:26,220 --> 00:32:34,160
+واحد في اثنين في ثلاثة إلى n سالب اثنين في n سالب
+
+293
+00:32:34,160 --> 00:32:45,700
+واحد في n مظبوط؟ ممكن اختصر n مع n و هيبقى عندي
+
+294
+00:32:54,210 --> 00:33:05,130
+فهيبقى عندي n على واحد في اثنين إلى n سالب اثنين
+
+295
+00:33:05,130 --> 00:33:14,650
+في n سالب واحد الآن ممكن إثبات أن المقام هذا أكبر
+
+296
+00:33:14,650 --> 00:33:17,570
+من اثنين
+
+297
+00:33:20,110 --> 00:33:28,310
+اثنين في N سالب اثنين في N سالب واحد وهذا أكبر من
+
+298
+00:33:28,310 --> 00:33:38,410
+اثنين في N سالب واحد في N وهذا صحيح ليس لكل الـ N
+
+299
+00:33:38,410 --> 00:33:48,270
+مش لكل الأعداد الطبيعية N هذا أكبر من N سالب اثنين
+
+300
+00:33:48,270 --> 00:33:56,730
+في N وهذا صحيح فقط لكل n أكبر من أو يساوي خمسة
+
+301
+00:33:56,730 --> 00:34:01,990
+يعني عند الأربعة مش صح و عند الثلاثة و اثنين و
+
+302
+00:34:01,990 --> 00:34:08,580
+الواحد مش صح Okay؟ إذن N تربيع على N factorial
+
+303
+00:34:08,580 --> 00:34:14,940
+بتطلع .. الآن هذا المقام أكبر من العدد هذا
+
+304
+00:34:14,940 --> 00:34:23,280
+وبالتالي المقلوب بتطلع أصغر من N على N في N سالب 2
+
+305
+00:34:23,280 --> 00:34:32,100
+طبعا N بتروح مع N بيبقى عندي واحد على n سالب اثنين
+
+306
+00:34:32,100 --> 00:34:37,140
+ويقول الكلام هذا صحيح لكل n أكبر من أو يساوي خمسة
+
+307
+00:34:48,530 --> 00:34:55,770
+xn على yn أصغر من واحد على n سالب اثنين طبعا أكبر
+
+308
+00:34:55,770 --> 00:35:01,690
+من صفر أو أكبر من أو يساوي صفر وهذا صحيح لكل n
+
+309
+00:35:01,690 --> 00:35:06,890
+أكبر من أو يساوي خمسة الآن هذا لما ننتقل ل
+
+310
+00:35:06,890 --> 00:35:11,950
+infinity هذا بيروح لصفر لما ننتقل ل infinity هذا
+
+311
+00:35:11,950 --> 00:35:16,610
+بيروح لصفر إذا by sandwich theorem
+
+312
+00:35:23,770 --> 00:35:30,910
+بطلع عند ال limit ل xn over yn as n tends to
+
+313
+00:35:30,910 --> 00:35:36,570
+infinity بساوي صفر هاد هي ال R في ال limit
+
+314
+00:35:36,570 --> 00:35:42,150
+comparison test طيب since
+
+315
+00:35:44,540 --> 00:35:49,640
+سيجما واي ان اللي هي سيجما واحد على ان تربيع
+
+316
+00:35:49,640 --> 00:35:58,740
+converges حسب الجزء الثاني من limit comparison
+
+317
+00:35:58,740 --> 00:36:02,160
+test limit comparison test بيقول إذا كان limit ال
+
+318
+00:36:02,160 --> 00:36:07,600
+ratio بساوي صفر وكانت سيجما واي ان convergent إذا
+
+319
+00:36:07,600 --> 00:36:10,400
+هذا بيقدر
+
+320
+00:36:13,430 --> 00:36:19,310
+سيجما اكس ام اللي هي سيجما وان اوبر ام فاكتوريال
+
+321
+00:36:19,310 --> 00:36:23,490
+convergence رغم المفهوم
+
+322
+00:36:26,800 --> 00:36:29,680
+واحد استخدم ال direct comparison test، الثاني
+
+323
+00:36:29,680 --> 00:36:33,660
+استخدم ال limit comparison test، اثنين كان فيهم
+
+324
+00:36:33,660 --> 00:36:39,940
+شوية شغل مش سهل، لكن هذا هو الموجود، مفيش أسهل من
+
+325
+00:36:39,940 --> 00:36:46,400
+هذا فعلى أي حال يعني ال .. الأسئلة في الكتاب هتكون
+
+326
+00:36:46,400 --> 00:36:50,780
+معظمها سهلة إما في الحل بال limit comparison test
+
+327
+00:36:50,780 --> 00:36:55,520
+أو بال direct comparison test، في أي سؤال أو
+
+328
+00:36:55,520 --> 00:37:00,800
+استفسار؟ الأمور واضحة الحل واضح أنا عارف أنه كيف
+
+329
+00:37:00,800 --> 00:37:05,580
+يخطر على بالنا نعمل المقارنات هذه وهذا كلامكم صحيح
+
+330
+00:37:05,580 --> 00:37:12,980
+هذا يعني شيء مش سهل لكن في بعض المسائل ال .. يعني
+
+331
+00:37:12,980 --> 00:37:21,740
+ال .. مش سهل أن نحنا نعمل المقارنة لكن بنحاول .. 
+
+332
+00:37:21,740 --> 00:37:33,030
+بنحاول اللي بيحاول بيصل إلى حل خليني يعني احنا مش
+
+333
+00:37:33,030 --> 00:37:37,710
+عايزين نبدأ section جديد الصحيح أن هيك يعني ال
+
+334
+00:37:37,710 --> 00:37:42,550
+chapter خلص فعشان مابداش يعني نبدأ المرة الجاية
+
+335
+00:37:42,550 --> 00:37:49,210
+chapter جديد فخليني آخذ أحل سؤال من ال homework
+
+336
+00:37:49,210 --> 00:37:53,590
+problems السؤال هنا question
+
+337
+00:37:57,590 --> 00:38:06,030
+exercise رقم خمسة section ثلاثة سبعة لأن هذا تمرين
+
+338
+00:38:06,030 --> 00:38:10,190
+خمسة في section ثلاثة سبعة اللي هو آخر section في
+
+339
+00:38:10,190 --> 00:38:17,010
+chapter ثلاثة السؤال بيقول can
+
+340
+00:38:17,010 --> 00:38:24,030
+you السؤال كثير يعني مهم و interesting can you
+
+341
+00:38:24,030 --> 00:38:31,770
+give يعني الكتاب بخاطب الطالب بيقول له can you give an
+
+342
+00:38:31,770 --> 00:38:44,810
+example هل بإمكانك تعطي مثال of a convergent of a
+
+343
+00:38:44,810 --> 00:38:53,550
+convergent series sigma xn and a divergent
+
+344
+00:39:03,070 --> 00:39:11,470
+بحيث أن المجموعة تبع ال two series يكون
+
+345
+00:39:11,470 --> 00:39:20,010
+convergent is convergent explain
+
+346
+00:39:20,010 --> 00:39:29,830
+وضحي الإجابة هتكون يا yes يا no و في كل الحالتين بن
+
+347
+00:39:29,830 --> 00:39:37,710
+.. نعطيك تفسر ال yes أو أنه تبعتك فانا بقول أن
+
+348
+00:39:37,710 --> 00:39:44,450
+خلينا نعطيلكم يعني نشوفكم تفكروا نعطيكم دقيقة
+
+349
+00:39:44,450 --> 00:39:53,230
+تفكروا و تحاولوا تجيبوا مثال زي ما هو مطلوب إذا 
+
+350
+00:39:53,230 --> 00:39:53,990
+كده إذا أمكن
+
+351
+00:39:57,650 --> 00:40:04,570
+فمين عندها مثال؟ كمان مرة بنجيب مثال ل two series
+
+352
+00:40:04,570 --> 00:40:10,370
+واحدة convergent اللي هي هذه الأولى والثانية
+
+353
+00:40:10,370 --> 00:40:16,190
+divergent بحيث أن مجموعهم يكون convergent هل هذا
+
+354
+00:40:16,190 --> 00:40:23,190
+ممكن؟ إذا ممكن طيب ممكن تعطيني مثال على ذلك يعني
+
+355
+00:40:23,190 --> 00:40:27,890
+اعطيني مثال يوضح صحة ال .. الكلام هذه ال example
+
+356
+00:40:27,890 --> 00:40:30,930
+مثلا ناخذها هي أسهل إيش الواحد على الأن أو الأول و
+
+357
+00:40:30,930 --> 00:40:36,130
+الرابعين خليني لحظة شوية لو سمحت هاي أخبرتكم 
+
+358
+00:40:36,130 --> 00:40:37,350
+طرح example
+
+359
+00:40:41,280 --> 00:40:47,500
+أيه وقتك؟ ال XN قبل عن الواحد على الان تربيع واحد 
+
+360
+00:40:47,500 --> 00:40:55,520
+على ان تربيع فطبعا هذا بقدر سيجما XN كل ذات يسار
+
+361
+00:40:55,520 --> 00:41:02,740
+سيجما واحد على ان تربيع كل بيرزلأن هذه P series و
+
+362
+00:41:02,740 --> 00:41:07,380
+ال P بيساوي اثنين أكبر من واحد، صح؟ والثانية
+
+363
+00:41:07,380 --> 00:41:13,120
+الواحدة جذر الأن ناخذ YM بيساوي واحد على جذر 
+
+364
+00:41:13,120 --> 00:41:19,860
+الأن بتصير أس نص، طيب، بتصير summation للواحد الأن
+
+365
+00:41:19,860 --> 00:41:25,920
+sigma yn بيساوي sigma 1 على n أس نص  بي سيريز
+
+366
+00:41:25,920 --> 00:41:30,100
+هذه divergent بي بي سيريز هذه بي بي بي بي بي بي
+
+367
+00:41:30,100 --> 00:41:30,400
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+368
+00:41:30,400 --> 00:41:34,760
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+369
+00:41:34,760 --> 00:41:34,800
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+370
+00:41:34,800 --> 00:41:35,040
+بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي بي
+
+371
+00:41:35,040 --> 00:41:44,900
+بي
+
+372
+00:41:44,900 --> 00:41:53,900
+بي هي sigma واحد على N تربيع زائد واحد على N أس نص
+
+373
+00:41:53,900 --> 00:42:02,420
+صح؟ وهذا بيساوي summation ناخذ مقام مشترك N تربيع 
+
+374
+00:42:02,420 --> 00:42:10,140
+فبيطلع واحد زائد N أس .. أس ثلاثة عشان .. أس ثلاثة
+
+375
+00:42:10,140 --> 00:42:14,040
+عشان .. مظبوط؟
+
+376
+00:42:21,390 --> 00:42:30,430
+هل هذه convergent؟ لما n تكون كبيرة .. اه لما n
+
+377
+00:42:30,430 --> 00:42:37,790
+تكون كبيرة هذه بتكون behaves like sigma
+
+378
+00:42:39,040 --> 00:42:45,440
+واحد لأ مش واحد على ان تربيع المهم للواحد وفاضل
+
+379
+00:42:45,440 --> 00:42:50,420
+عندي N أس ثلاثة على اثنين على ان تربيع اللي بيساوي
+
+380
+00:42:50,420 --> 00:42:54,740
+سيجما واحد على N أس نص
+
+381
+00:42:58,550 --> 00:43:03,570
+و ممكن الآن نستخدم ال limit comparison test نثبت 
+
+382
+00:43:03,570 --> 00:43:07,430
+أن هذه divergent لأن هذه divergent باستخدام ال
+
+383
+00:43:07,430 --> 00:43:11,630
+limit comparison test زيادة .. زيادة .. زيادة ..
+
+384
+00:43:11,630 --> 00:43:14,670
+زيادة .. زيادة .. زيادة .. زيادة .. زيادة .. زيادة
+
+385
+00:43:14,670 --> 00:43:19,910
+.. زيادة
+
+386
+00:43:19,910 --> 00:43:30,990
+.. زيادة .. زيادة .. زيادة .. زيادة
+
+387
+00:43:30,990 --> 00:43:31,310
+..
+
+388
+00:43:34,540 --> 00:43:43,240
+another example طيب xn بساوي سالب واحد و سالب n
+
+389
+00:43:43,240 --> 00:43:51,160
+مثلا yn بساوي واحد yn بساوي واحد اه ف ال series
+
+390
+00:43:51,160 --> 00:43:58,520
+sigma x n diverge و sigma y n diverge فتنتهي ال
+
+391
+00:43:58,520 --> 00:44:01,540
+diverge، مانفعش، مانفعش، مانفعش، مانفعش، مانفعش،
+
+392
+00:44:01,540 --> 00:44:01,880
+مانفعش، مانفعش، مانفعش، مانفعش، مانفعش، مانفعش،
+
+393
+00:44:01,880 --> 00:44:02,160
+مانفعش، مانفعش، مانفعش، مانفعش، مانفعش، مانفعش،
+
+394
+00:44:02,160 --> 00:44:03,340
+مانفعش، مانفعش، مانفعش، مانفعش، مانفعش، مانفعش،
+
+395
+00:44:03,340 --> 00:44:08,340
+مانفعش، مانفعش، مانفعش، مانفعش، مانفعش، مانفعش،
+
+396
+00:44:08,340 --> 00:44:14,220
+مانفعش، مانفعش، مانفعش، مانفعش، مانفعش على مدرسة الأرض
+
+397
+00:44:14,220 --> 00:44:18,380
+أن هو من من أنتو ساوي أربعة على مالة نهاية حكينا
+
+398
+00:44:18,380 --> 00:44:20,820
+أن هو من أنتو ساوي أربعة على مالة نهاية هذا converge
+
+399
+00:44:20,820 --> 00:44:25,300
+بس اللي جابله حكينا أن converge أن diverge اللي
+
+400
+00:44:25,300 --> 00:44:28,280
+جابله لنا طيب احنا عشان بسمع أن احنا بنحكي على السؤال
+
+401
+00:44:28,280 --> 00:44:33,860
+هذا خليني احنا في هذا المثال في عندك مثال؟ خلاص 
+
+402
+00:44:33,860 --> 00:44:38,440
+طبعا ال .. ال .. السابق هذا بعدين بنتناقش فيه
+
+403
+00:44:38,440 --> 00:44:43,270
+خليني أجرب عشان أنا مافيش وجهة على السؤال هذا لو 
+
+404
+00:44:43,270 --> 00:44:46,950
+كلّكم حاولتوا .. كل واحدة حاولت تجيب مثال، كل أمثلة
+
+405
+00:44:46,950 --> 00:44:51,370
+أبقتكم هتكون غلط أو هتفشل، ليه؟ لأن مافيش ولا 
+
+406
+00:44:51,370 --> 00:44:56,890
+مثال، لأن مافيش مثال، فأنت قاعدين بتجيبوا .. تعطوا
+
+407
+00:44:56,890 --> 00:45:01,790
+حاجة مستحيلة، مش موجودة، إذا الإجابة على هذا
+
+408
+00:45:01,790 --> 00:45:02,330
+السؤال
+
+409
+00:45:08,820 --> 00:45:19,880
+أن ال answer ال answer is no لا يمكن يعطى مثال على
+
+410
+00:45:19,880 --> 00:45:22,700
+two series واحدة convergent والثانية divergent
+
+411
+00:45:22,700 --> 00:45:26,020
+مجموع بتطلع convergent مستحيل this is impossible
+
+412
+00:45:26,020 --> 00:45:34,660
+لبرهان أو لثبات ذلك if 
+
+413
+00:45:34,660 --> 00:45:47,190
+if this إذا كان هذا صحيح أو إذا كان هذا صحيح يعني
+
+414
+00:45:47,190 --> 00:45:52,230
+لو قدرت أن أجيب series convergent و series
+
+415
+00:45:52,230 --> 00:45:57,710
+divergent و مجموع convergent then
+
+416
+00:45:57,710 --> 00:46:01,610
+we would have
+
+417
+00:46:03,890 --> 00:46:08,590
+أن الـ series sigma yn اللي احنا فرضنا أن ها
+
+418
+00:46:08,590 --> 00:46:15,650
+divergent اللي هي بساوي sigma xn زائد yn ناقص
+
+419
+00:46:15,650 --> 00:46:23,290
+sigma xn احنا قلنا لو هذا كان true معناته ال
+
+420
+00:46:23,290 --> 00:46:27,690
+series هذه convergent معناته هذه convergent ومن 
+
+421
+00:46:27,690 --> 00:46:32,610
+الفرض هذه convergent والفرق بين two convergent
+
+422
+00:46:32,610 --> 00:46:38,330
+series is convergent، إذن هذا هتطلع .. إذن الفرق 
+
+423
+00:46:38,330 --> 00:46:43,830
+هيكون convergent وبالتالي إذن ال series sigma yn
+
+424
+00:46:43,830 --> 00:46:48,930
+is convergent، وهذا contradiction لأن احنا فرضين
+
+425
+00:46:48,930 --> 00:46:56,040
+أنها divergent هذا مش ممكن يكون true عشان هي كانت
+
+426
+00:46:56,040 --> 00:47:01,600
+كتبت if it were true مستحيل ..مستحيل مش if it was
+
+427
+00:47:01,600 --> 00:47:08,280
+true okay طبعا إذا أنا سأستطيع اعطاء مثال يعطيني 
+
+428
+00:47:08,280 --> 00:47:13,800
+المواصفات هذه بالمرة تمام؟ إذا بنوقف هنا وهيك
+
+429
+00:47:13,800 --> 00:47:17,120
+بنكون خلصنا ال chapter تلاتة المرة الجاية إن شاء
+
+430
+00:47:17,120 --> 00:47:22,620
+الله هنبقى في chapter أربعة فشكرا لكم ونشوفكم إن 
+
+431
+00:47:22,620 --> 00:47:23,640
+شاء الله يوم السبت 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4d0b995af9fd927f6fec9e4f8d581499a2000dc3
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/Sym_17KvBqE_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4949, "start": 20.83, "end": 49.49, "text": "بسم الله الرحمن الرحيم احنا في المحاضرة اللى فاتت اتحدثنا عن ال limit comparison test وبرهننا الجزء الاول منه فنرجع مع بعض ال limit comparison test for infinite series طبعا طبعا في limit comparison test for sequences الان هذا الافتبار قصد ال infinite series", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 1975, 5016, 8315, 8978, 9673, 5016, 46958, 25720, 13672, 7578, 6156, 9307, 2655, 1975, 2655, 24401, 12984, 8315, 18871, 2423, 4948, 9660, 1500, 4032, 26890, 3224, 1863, 8315, 25724, 11622, 38207, 42963, 12610, 9154, 3224, 6156, 1863, 47341, 3615, 20449, 45030, 11242, 2423, 4948, 9660, 1500, 337, 13785, 2638, 23032, 3555, 3615, 995, 23032, 3555, 3615, 995, 8978, 4948, 9660, 1500, 337, 22978, 2423, 7649, 23758, 42963, 5172, 2655, 3555, 9640, 12174, 9381, 3215, 2423, 13785, 2638], "avg_logprob": -0.163254303493719, "compression_ratio": 1.8366336633663367, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 20.83, "end": 21.85, "word": "بسم", "probability": 0.880126953125}, {"start": 21.85, "end": 22.03, "word": " الله", "probability": 0.9609375}, {"start": 22.03, "end": 22.49, "word": " الرحمن", "probability": 0.9767252604166666}, {"start": 22.49, "end": 23.03, "word": " الرحيم", "probability": 0.9951171875}, {"start": 23.03, "end": 24.91, "word": " احنا", "probability": 0.9163411458333334}, {"start": 24.91, "end": 25.13, "word": " في", "probability": 0.806640625}, {"start": 25.13, "end": 25.63, "word": " المحاضرة", "probability": 0.96240234375}, {"start": 25.63, "end": 25.83, "word": " اللى", "probability": 0.739013671875}, {"start": 25.83, "end": 26.41, "word": " فاتت", "probability": 0.9920247395833334}, {"start": 26.41, "end": 27.71, "word": " اتحدثنا", "probability": 0.904296875}, {"start": 27.71, "end": 27.95, "word": " عن", "probability": 0.9716796875}, {"start": 27.95, "end": 28.13, "word": " ال", "probability": 0.298583984375}, {"start": 28.13, "end": 28.37, "word": " limit", "probability": 0.94140625}, {"start": 28.37, "end": 29.03, "word": " comparison", "probability": 0.912109375}, {"start": 29.03, "end": 29.59, "word": " test", "probability": 0.9150390625}, {"start": 29.59, "end": 32.69, "word": " وبرهننا", "probability": 0.90009765625}, {"start": 32.69, "end": 33.43, "word": " الجزء", "probability": 0.9357096354166666}, {"start": 33.43, "end": 33.83, "word": " الاول", "probability": 0.94140625}, {"start": 33.83, "end": 34.31, "word": " منه", "probability": 0.9912109375}, {"start": 34.31, "end": 35.15, "word": " فنرجع", "probability": 0.7548828125}, {"start": 35.15, "end": 35.31, "word": " مع", "probability": 0.98046875}, {"start": 35.31, "end": 35.95, "word": " بعض", "probability": 0.992431640625}, {"start": 35.95, "end": 36.71, "word": " ال", "probability": 0.7978515625}, {"start": 36.71, "end": 36.93, "word": " limit", "probability": 0.95751953125}, {"start": 36.93, "end": 37.47, "word": " comparison", "probability": 0.931640625}, {"start": 37.47, "end": 37.95, "word": " test", "probability": 0.9287109375}, {"start": 37.95, "end": 38.41, "word": " for", "probability": 0.951171875}, {"start": 38.41, "end": 39.07, "word": " infinite", "probability": 0.939453125}, {"start": 39.07, "end": 39.59, "word": " series", "probability": 0.9111328125}, {"start": 39.59, "end": 41.77, "word": " طبعا", "probability": 0.99658203125}, {"start": 41.77, "end": 42.83, "word": " طبعا", "probability": 0.9677734375}, {"start": 42.83, "end": 42.97, "word": " في", "probability": 0.556640625}, {"start": 42.97, "end": 43.19, "word": " limit", "probability": 0.9365234375}, {"start": 43.19, "end": 43.77, "word": " comparison", "probability": 0.931640625}, {"start": 43.77, "end": 44.11, "word": " test", "probability": 0.916015625}, {"start": 44.11, "end": 44.35, "word": " for", "probability": 0.97412109375}, {"start": 44.35, "end": 45.03, "word": " sequences", "probability": 0.9345703125}, {"start": 45.03, "end": 46.69, "word": " الان", "probability": 0.546112060546875}, {"start": 46.69, "end": 46.95, "word": " هذا", "probability": 0.9033203125}, {"start": 46.95, "end": 47.45, "word": " الافتبار", "probability": 0.78955078125}, {"start": 47.45, "end": 48.45, "word": " قصد", "probability": 0.4888509114583333}, {"start": 48.45, "end": 48.65, "word": " ال", "probability": 0.537109375}, {"start": 48.65, "end": 48.95, "word": " infinite", "probability": 0.96044921875}, {"start": 48.95, "end": 49.49, "word": " series", "probability": 0.9267578125}], "temperature": 1.0}, {"id": 2, "seek": 6940, "start": 50.18, "end": 69.4, "text": "لو في عندي two sequences of positive real numbers بحيث ان limit ال quotient تبعهم exist بساوي عدد R ففي عندي نتيجتين، لو كان العدد R أو limit R هذه لا تساوي 0", "tokens": [1211, 2407, 8978, 18871, 16254, 732, 22978, 295, 3353, 957, 3547, 4724, 5016, 1829, 12984, 16472, 4948, 2423, 9641, 1196, 6055, 3555, 3615, 16095, 2514, 4724, 3794, 995, 45865, 6225, 3215, 3215, 497, 6156, 41185, 18871, 16254, 8717, 31371, 7435, 2655, 9957, 12399, 45164, 25961, 18863, 3215, 3215, 497, 34051, 4948, 497, 29538, 20193, 6055, 3794, 995, 45865, 1958], "avg_logprob": -0.259635429084301, "compression_ratio": 1.3575757575757577, "no_speech_prob": 0.0, "words": [{"start": 50.18, "end": 50.48, "word": "لو", "probability": 0.6719970703125}, {"start": 50.48, "end": 50.6, "word": " في", "probability": 0.1094970703125}, {"start": 50.6, "end": 50.88, "word": " عندي", "probability": 0.754638671875}, {"start": 50.88, "end": 51.06, "word": " two", "probability": 0.6357421875}, {"start": 51.06, "end": 51.7, "word": " sequences", "probability": 0.923828125}, {"start": 51.7, "end": 52.34, "word": " of", "probability": 0.9677734375}, {"start": 52.34, "end": 52.94, "word": " positive", "probability": 0.86669921875}, {"start": 52.94, "end": 53.3, "word": " real", "probability": 0.9599609375}, {"start": 53.3, "end": 53.94, "word": " numbers", "probability": 0.89111328125}, {"start": 53.94, "end": 56.4, "word": " بحيث", "probability": 0.9287109375}, {"start": 56.4, "end": 56.54, "word": " ان", "probability": 0.55078125}, {"start": 56.54, "end": 56.86, "word": " limit", "probability": 0.78564453125}, {"start": 56.86, "end": 57.12, "word": " ال", "probability": 0.767578125}, {"start": 57.12, "end": 57.76, "word": " quotient", "probability": 0.821533203125}, {"start": 57.76, "end": 58.62, "word": " تبعهم", "probability": 0.871337890625}, {"start": 58.62, "end": 60.48, "word": " exist", "probability": 0.77392578125}, {"start": 60.48, "end": 61.28, "word": " بساوي", "probability": 0.796875}, {"start": 61.28, "end": 61.76, "word": " عدد", "probability": 0.9736328125}, {"start": 61.76, "end": 62.04, "word": " R", "probability": 0.4970703125}, {"start": 62.04, "end": 64.24, "word": " ففي", "probability": 0.85546875}, {"start": 64.24, "end": 64.52, "word": " عندي", "probability": 0.97900390625}, {"start": 64.52, "end": 65.24, "word": " نتيجتين،", "probability": 0.7786458333333334}, {"start": 65.24, "end": 65.42, "word": " لو", "probability": 0.974609375}, {"start": 65.42, "end": 65.7, "word": " كان", "probability": 0.97509765625}, {"start": 65.7, "end": 66.22, "word": " العدد", "probability": 0.90185546875}, {"start": 66.22, "end": 66.46, "word": " R", "probability": 0.94287109375}, {"start": 66.46, "end": 66.64, "word": " أو", "probability": 0.7060546875}, {"start": 66.64, "end": 67.02, "word": " limit", "probability": 0.84814453125}, {"start": 67.02, "end": 67.44, "word": " R", "probability": 0.95947265625}, {"start": 67.44, "end": 68.02, "word": " هذه", "probability": 0.406982421875}, {"start": 68.02, "end": 68.56, "word": " لا", "probability": 0.689453125}, {"start": 68.56, "end": 69.1, "word": " تساوي", "probability": 0.9498291015625}, {"start": 69.1, "end": 69.4, "word": " 0", "probability": 0.18798828125}], "temperature": 1.0}, {"id": 3, "seek": 9765, "start": 70.37, "end": 97.65, "text": "ففي الحالة هذه sigma x in series sigma x in convergence if and only if ال series sigma y in convergence يعني اتنين اما اتنين بيكونوا convergence زي بعض او اتنين بيكونوا divergence زي بعض الجزء التاني بيقول لو كانت ال R اللي هي limit لل quotient مساوة سفر وإذا كانت ال series اللي الحد العام تبع Y in convergence", "tokens": [5172, 41185, 21542, 6027, 3660, 29538, 12771, 2031, 294, 2638, 12771, 2031, 294, 32181, 498, 293, 787, 498, 2423, 2638, 12771, 288, 294, 32181, 37495, 22653, 1975, 2655, 1863, 9957, 1975, 15042, 1975, 2655, 1863, 9957, 4724, 1829, 30544, 14407, 32181, 30767, 1829, 45030, 11242, 1975, 2407, 1975, 2655, 1863, 9957, 4724, 1829, 30544, 14407, 47387, 30767, 1829, 45030, 11242, 25724, 11622, 38207, 16712, 7649, 1829, 4724, 1829, 39648, 45164, 25961, 2655, 2423, 497, 13672, 1829, 39896, 4948, 24976, 9641, 1196, 47524, 995, 2407, 3660, 8608, 5172, 2288, 4032, 28814, 15730, 25961, 2655, 2423, 2638, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 398, 294, 32181], "avg_logprob": -0.26316550925925924, "compression_ratio": 1.9598214285714286, "no_speech_prob": 0.0, "words": [{"start": 70.37, "end": 70.79, "word": "ففي", "probability": 0.5086669921875}, {"start": 70.79, "end": 71.33, "word": " الحالة", "probability": 0.97509765625}, {"start": 71.33, "end": 72.17, "word": " هذه", "probability": 0.52294921875}, {"start": 72.17, "end": 74.97, "word": " sigma", "probability": 0.11724853515625}, {"start": 74.97, "end": 75.37, "word": " x", "probability": 0.61572265625}, {"start": 75.37, "end": 75.65, "word": " in", "probability": 0.79443359375}, {"start": 75.65, "end": 76.11, "word": " series", "probability": 0.7353515625}, {"start": 76.11, "end": 76.49, "word": " sigma", "probability": 0.5361328125}, {"start": 76.49, "end": 76.73, "word": " x", "probability": 0.87353515625}, {"start": 76.73, "end": 76.95, "word": " in", "probability": 0.9443359375}, {"start": 76.95, "end": 77.49, "word": " convergence", "probability": 0.728515625}, {"start": 77.49, "end": 77.89, "word": " if", "probability": 0.7548828125}, {"start": 77.89, "end": 78.13, "word": " and", "probability": 0.94921875}, {"start": 78.13, "end": 78.35, "word": " only", "probability": 0.92578125}, {"start": 78.35, "end": 78.99, "word": " if", "probability": 0.98193359375}, {"start": 78.99, "end": 79.83, "word": " ال", "probability": 0.54833984375}, {"start": 79.83, "end": 79.83, "word": " series", "probability": 0.224365234375}, {"start": 79.83, "end": 80.23, "word": " sigma", "probability": 0.84423828125}, {"start": 80.23, "end": 80.55, "word": " y", "probability": 0.96826171875}, {"start": 80.55, "end": 80.73, "word": " in", "probability": 0.880859375}, {"start": 80.73, "end": 81.23, "word": " convergence", "probability": 0.86865234375}, {"start": 81.23, "end": 81.55, "word": " يعني", "probability": 0.746826171875}, {"start": 81.55, "end": 82.05, "word": " اتنين", "probability": 0.7218017578125}, {"start": 82.05, "end": 82.77, "word": " اما", "probability": 0.683837890625}, {"start": 82.77, "end": 83.11, "word": " اتنين", "probability": 0.902099609375}, {"start": 83.11, "end": 83.49, "word": " بيكونوا", "probability": 0.8648681640625}, {"start": 83.49, "end": 83.99, "word": " convergence", "probability": 0.4794921875}, {"start": 83.99, "end": 84.35, "word": " زي", "probability": 0.955078125}, {"start": 84.35, "end": 84.69, "word": " بعض", "probability": 0.99658203125}, {"start": 84.69, "end": 84.91, "word": " او", "probability": 0.878662109375}, {"start": 84.91, "end": 85.23, "word": " اتنين", "probability": 0.9737548828125}, {"start": 85.23, "end": 85.77, "word": " بيكونوا", "probability": 0.73486328125}, {"start": 85.77, "end": 85.77, "word": " divergence", "probability": 0.595703125}, {"start": 85.77, "end": 86.15, "word": " زي", "probability": 0.982421875}, {"start": 86.15, "end": 86.49, "word": " بعض", "probability": 0.998046875}, {"start": 86.49, "end": 87.95, "word": " الجزء", "probability": 0.9573567708333334}, {"start": 87.95, "end": 88.31, "word": " التاني", "probability": 0.8953450520833334}, {"start": 88.31, "end": 88.63, "word": " بيقول", "probability": 0.9192708333333334}, {"start": 88.63, "end": 88.85, "word": " لو", "probability": 0.861328125}, {"start": 88.85, "end": 89.23, "word": " كانت", "probability": 0.9609375}, {"start": 89.23, "end": 89.35, "word": " ال", "probability": 0.94140625}, {"start": 89.35, "end": 89.67, "word": " R", "probability": 0.470458984375}, {"start": 89.67, "end": 89.87, "word": " اللي", "probability": 0.86474609375}, {"start": 89.87, "end": 90.03, "word": " هي", "probability": 0.94189453125}, {"start": 90.03, "end": 90.37, "word": " limit", "probability": 0.7958984375}, {"start": 90.37, "end": 90.59, "word": " لل", "probability": 0.748046875}, {"start": 90.59, "end": 91.11, "word": " quotient", "probability": 0.92041015625}, {"start": 91.11, "end": 91.59, "word": " مساوة", "probability": 0.596527099609375}, {"start": 91.59, "end": 92.01, "word": " سفر", "probability": 0.8287760416666666}, {"start": 92.01, "end": 93.77, "word": " وإذا", "probability": 0.8523763020833334}, {"start": 93.77, "end": 94.29, "word": " كانت", "probability": 0.994873046875}, {"start": 94.29, "end": 94.57, "word": " ال", "probability": 0.90185546875}, {"start": 94.57, "end": 95.15, "word": " series", "probability": 0.95263671875}, {"start": 95.15, "end": 95.51, "word": " اللي", "probability": 0.9189453125}, {"start": 95.51, "end": 95.87, "word": " الحد", "probability": 0.7025146484375}, {"start": 95.87, "end": 96.15, "word": " العام", "probability": 0.964599609375}, {"start": 96.15, "end": 96.47, "word": " تبع", "probability": 0.8328450520833334}, {"start": 96.47, "end": 96.83, "word": " Y", "probability": 0.406494140625}, {"start": 96.83, "end": 97.11, "word": " in", "probability": 0.77392578125}, {"start": 97.11, "end": 97.65, "word": " convergence", "probability": 0.51904296875}], "temperature": 1.0}, {"id": 4, "seek": 12765, "start": 98.67, "end": 127.65, "text": "فال series هذا بيقدر ال series اللي هي sigma xn كلها يعني اعتقد ان احنا برهن الجزء الأول برا اللي فاتت بظبط و خلينا نبرهن الجزء التاني طبعا since اذا هنا let assume r بساوي سفر", "tokens": [5172, 6027, 2638, 23758, 4724, 1829, 28543, 2288, 2423, 2638, 13672, 1829, 39896, 12771, 2031, 77, 28242, 11296, 37495, 22653, 1975, 34268, 28543, 16472, 1975, 5016, 8315, 4724, 2288, 3224, 1863, 25724, 11622, 38207, 16247, 12610, 4724, 23557, 13672, 1829, 6156, 9307, 2655, 4724, 19913, 3555, 9566, 4032, 16490, 1211, 9957, 995, 8717, 26890, 3224, 1863, 25724, 11622, 38207, 16712, 7649, 1829, 23032, 3555, 3615, 995, 1670, 1975, 15730, 34105, 718, 6552, 367, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.32561728983749577, "compression_ratio": 1.6171428571428572, "no_speech_prob": 0.0, "words": [{"start": 98.67, "end": 99.03, "word": "فال", "probability": 0.3819580078125}, {"start": 99.03, "end": 99.33, "word": " series", "probability": 0.84423828125}, {"start": 99.33, "end": 99.75, "word": " هذا", "probability": 0.4931640625}, {"start": 99.75, "end": 100.25, "word": " بيقدر", "probability": 0.794677734375}, {"start": 100.25, "end": 100.43, "word": " ال", "probability": 0.716796875}, {"start": 100.43, "end": 100.89, "word": " series", "probability": 0.94482421875}, {"start": 100.89, "end": 101.51, "word": " اللي", "probability": 0.685302734375}, {"start": 101.51, "end": 101.77, "word": " هي", "probability": 0.8935546875}, {"start": 101.77, "end": 102.25, "word": " sigma", "probability": 0.705078125}, {"start": 102.25, "end": 102.79, "word": " xn", "probability": 0.56005859375}, {"start": 102.79, "end": 103.35, "word": " كلها", "probability": 0.37835693359375}, {"start": 103.35, "end": 104.19, "word": " يعني", "probability": 0.47955322265625}, {"start": 104.19, "end": 106.93, "word": " اعتقد", "probability": 0.5828450520833334}, {"start": 106.93, "end": 107.03, "word": " ان", "probability": 0.75927734375}, {"start": 107.03, "end": 107.21, "word": " احنا", "probability": 0.9798177083333334}, {"start": 107.21, "end": 107.61, "word": " برهن", "probability": 0.763671875}, {"start": 107.61, "end": 107.97, "word": " الجزء", "probability": 0.6175130208333334}, {"start": 107.97, "end": 108.51, "word": " الأول", "probability": 0.804931640625}, {"start": 108.51, "end": 108.87, "word": " برا", "probability": 0.764404296875}, {"start": 108.87, "end": 109.03, "word": " اللي", "probability": 0.94921875}, {"start": 109.03, "end": 109.55, "word": " فاتت", "probability": 0.8543294270833334}, {"start": 109.55, "end": 110.11, "word": " بظبط", "probability": 0.5819091796875}, {"start": 110.11, "end": 111.39, "word": " و", "probability": 0.943359375}, {"start": 111.39, "end": 111.95, "word": " خلينا", "probability": 0.61566162109375}, {"start": 111.95, "end": 112.39, "word": " نبرهن", "probability": 0.9521484375}, {"start": 112.39, "end": 112.85, "word": " الجزء", "probability": 0.9713541666666666}, {"start": 112.85, "end": 114.05, "word": " التاني", "probability": 0.9402669270833334}, {"start": 114.05, "end": 115.75, "word": " طبعا", "probability": 0.984619140625}, {"start": 115.75, "end": 117.07, "word": " since", "probability": 0.87060546875}, {"start": 117.07, "end": 119.65, "word": " اذا", "probability": 0.57177734375}, {"start": 119.65, "end": 120.01, "word": " هنا", "probability": 0.9814453125}, {"start": 120.01, "end": 120.53, "word": " let", "probability": 0.9111328125}, {"start": 120.53, "end": 122.27, "word": " assume", "probability": 0.87890625}, {"start": 122.27, "end": 126.37, "word": " r", "probability": 0.62646484375}, {"start": 126.37, "end": 127.07, "word": " بساوي", "probability": 0.76239013671875}, {"start": 127.07, "end": 127.65, "word": " سفر", "probability": 0.8837890625}], "temperature": 1.0}, {"id": 5, "seek": 15871, "start": 138.19, "end": 158.71, "text": "أما لو أخدت إبسلون أنا بساوي العدد واحد فهذا إبسلون موجبة إحنا لدينا من الفرض sense limit xn over yn as n tends to infinity", "tokens": [10721, 15042, 45164, 5551, 9778, 3215, 2655, 11933, 3555, 3794, 1211, 11536, 41850, 4724, 3794, 995, 45865, 18863, 3215, 3215, 36764, 24401, 6156, 3224, 15730, 11933, 3555, 3794, 1211, 11536, 3714, 29245, 49401, 11933, 5016, 8315, 5296, 16254, 8315, 9154, 27188, 43042, 2020, 4948, 2031, 77, 670, 17861, 382, 297, 12258, 281, 13202], "avg_logprob": -0.35416666280340264, "compression_ratio": 1.3191489361702127, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 138.19, "end": 139.41, "word": "أما", "probability": 0.186492919921875}, {"start": 139.41, "end": 139.41, "word": " لو", "probability": 0.14501953125}, {"start": 139.41, "end": 140.11, "word": " أخدت", "probability": 0.758544921875}, {"start": 140.11, "end": 141.31, "word": " إبسلون", "probability": 0.7938232421875}, {"start": 141.31, "end": 141.57, "word": " أنا", "probability": 0.334716796875}, {"start": 141.57, "end": 142.47, "word": " بساوي", "probability": 0.7215576171875}, {"start": 142.47, "end": 143.21, "word": " العدد", "probability": 0.8251139322916666}, {"start": 143.21, "end": 143.91, "word": " واحد", "probability": 0.942138671875}, {"start": 143.91, "end": 144.49, "word": " فهذا", "probability": 0.8435872395833334}, {"start": 144.49, "end": 145.05, "word": " إبسلون", "probability": 0.954296875}, {"start": 145.05, "end": 145.67, "word": " موجبة", "probability": 0.7981770833333334}, {"start": 145.67, "end": 149.91, "word": " إحنا", "probability": 0.753662109375}, {"start": 149.91, "end": 150.27, "word": " لدينا", "probability": 0.6735026041666666}, {"start": 150.27, "end": 150.47, "word": " من", "probability": 0.9833984375}, {"start": 150.47, "end": 151.03, "word": " الفرض", "probability": 0.94384765625}, {"start": 151.03, "end": 151.65, "word": " sense", "probability": 0.60595703125}, {"start": 151.65, "end": 152.25, "word": " limit", "probability": 0.951171875}, {"start": 152.25, "end": 154.83, "word": " xn", "probability": 0.590087890625}, {"start": 154.83, "end": 155.33, "word": " over", "probability": 0.52294921875}, {"start": 155.33, "end": 156.27, "word": " yn", "probability": 0.97314453125}, {"start": 156.27, "end": 157.41, "word": " as", "probability": 0.83642578125}, {"start": 157.41, "end": 157.79, "word": " n", "probability": 0.875}, {"start": 157.79, "end": 158.07, "word": " tends", "probability": 0.68798828125}, {"start": 158.07, "end": 158.17, "word": " to", "probability": 0.94091796875}, {"start": 158.17, "end": 158.71, "word": " infinity", "probability": 0.880859375}], "temperature": 1.0}, {"id": 6, "seek": 18470, "start": 159.7, "end": 184.7, "text": "بساوي R اللي هو سفر الآن فمن تعريف by definition of limit for epsilon positive زي هذه يوجد capital N يعتمد على epsilon اللي هو الواحد natural number بحيث انه لكل N أكبر من أو ساوي capital N", "tokens": [3555, 3794, 995, 45865, 497, 13672, 1829, 31439, 8608, 5172, 2288, 6024, 48506, 6156, 27842, 37279, 16572, 5172, 538, 7123, 295, 4948, 337, 17889, 3353, 30767, 1829, 29538, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 17889, 13672, 1829, 31439, 2423, 14407, 24401, 3303, 1230, 4724, 5016, 1829, 12984, 16472, 3224, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426], "avg_logprob": -0.17280783982419257, "compression_ratio": 1.4, "no_speech_prob": 0.0, "words": [{"start": 159.7, "end": 160.46, "word": "بساوي", "probability": 0.80029296875}, {"start": 160.46, "end": 160.92, "word": " R", "probability": 0.6044921875}, {"start": 160.92, "end": 161.12, "word": " اللي", "probability": 0.744873046875}, {"start": 161.12, "end": 161.4, "word": " هو", "probability": 0.98876953125}, {"start": 161.4, "end": 161.9, "word": " سفر", "probability": 0.8839518229166666}, {"start": 161.9, "end": 162.4, "word": " الآن", "probability": 0.56146240234375}, {"start": 162.4, "end": 164.82, "word": " فمن", "probability": 0.848388671875}, {"start": 164.82, "end": 165.38, "word": " تعريف", "probability": 0.9842122395833334}, {"start": 165.38, "end": 165.64, "word": " by", "probability": 0.7353515625}, {"start": 165.64, "end": 166.22, "word": " definition", "probability": 0.8994140625}, {"start": 166.22, "end": 166.62, "word": " of", "probability": 0.97998046875}, {"start": 166.62, "end": 167.1, "word": " limit", "probability": 0.92626953125}, {"start": 167.1, "end": 168.82, "word": " for", "probability": 0.9072265625}, {"start": 168.82, "end": 169.74, "word": " epsilon", "probability": 0.3212890625}, {"start": 169.74, "end": 170.48, "word": " positive", "probability": 0.92724609375}, {"start": 170.48, "end": 170.82, "word": " زي", "probability": 0.966064453125}, {"start": 170.82, "end": 171.26, "word": " هذه", "probability": 0.8525390625}, {"start": 171.26, "end": 173.62, "word": " يوجد", "probability": 0.96337890625}, {"start": 173.62, "end": 174.68, "word": " capital", "probability": 0.74365234375}, {"start": 174.68, "end": 175.0, "word": " N", "probability": 0.869140625}, {"start": 175.0, "end": 175.68, "word": " يعتمد", "probability": 0.9737548828125}, {"start": 175.68, "end": 175.9, "word": " على", "probability": 0.82568359375}, {"start": 175.9, "end": 176.36, "word": " epsilon", "probability": 0.6201171875}, {"start": 176.36, "end": 176.62, "word": " اللي", "probability": 0.981201171875}, {"start": 176.62, "end": 176.8, "word": " هو", "probability": 0.99609375}, {"start": 176.8, "end": 177.42, "word": " الواحد", "probability": 0.9720052083333334}, {"start": 177.42, "end": 178.78, "word": " natural", "probability": 0.765625}, {"start": 178.78, "end": 179.52, "word": " number", "probability": 0.98828125}, {"start": 179.52, "end": 180.12, "word": " بحيث", "probability": 0.7451171875}, {"start": 180.12, "end": 180.64, "word": " انه", "probability": 0.83447265625}, {"start": 180.64, "end": 182.08, "word": " لكل", "probability": 0.981689453125}, {"start": 182.08, "end": 182.42, "word": " N", "probability": 0.54736328125}, {"start": 182.42, "end": 183.0, "word": " أكبر", "probability": 0.9016927083333334}, {"start": 183.0, "end": 183.22, "word": " من", "probability": 0.9423828125}, {"start": 183.22, "end": 183.42, "word": " أو", "probability": 0.82763671875}, {"start": 183.42, "end": 183.9, "word": " ساوي", "probability": 0.9503580729166666}, {"start": 183.9, "end": 184.4, "word": " capital", "probability": 0.697265625}, {"start": 184.4, "end": 184.7, "word": " N", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 7, "seek": 20500, "start": 186.16, "end": 205.0, "text": "هذا بيدّي أن ال absolute value ل xn على yn minus zero بيطلع أصغر من ال epsilon اللي احنا ماخدينها واحد طب xn عدد موجب و yn عدد موجب", "tokens": [3224, 15730, 4724, 25708, 11703, 1829, 14739, 2423, 8236, 2158, 5296, 2031, 77, 15844, 17861, 3175, 4018, 4724, 1829, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 2423, 17889, 13672, 1829, 1975, 5016, 8315, 3714, 47283, 3215, 9957, 11296, 36764, 24401, 23032, 3555, 2031, 77, 6225, 3215, 3215, 3714, 29245, 3555, 4032, 17861, 6225, 3215, 3215, 3714, 29245, 3555], "avg_logprob": -0.2703124910593033, "compression_ratio": 1.3310810810810811, "no_speech_prob": 0.0, "words": [{"start": 186.16, "end": 186.56, "word": "هذا", "probability": 0.61083984375}, {"start": 186.56, "end": 187.18, "word": " بيدّي", "probability": 0.5736083984375}, {"start": 187.18, "end": 187.52, "word": " أن", "probability": 0.50244140625}, {"start": 187.52, "end": 187.7, "word": " ال", "probability": 0.62353515625}, {"start": 187.7, "end": 188.14, "word": " absolute", "probability": 0.48681640625}, {"start": 188.14, "end": 188.96, "word": " value", "probability": 0.986328125}, {"start": 188.96, "end": 190.06, "word": " ل", "probability": 0.833984375}, {"start": 190.06, "end": 190.96, "word": " xn", "probability": 0.3511962890625}, {"start": 190.96, "end": 191.26, "word": " على", "probability": 0.60546875}, {"start": 191.26, "end": 191.96, "word": " yn", "probability": 0.93701171875}, {"start": 191.96, "end": 193.84, "word": " minus", "probability": 0.54150390625}, {"start": 193.84, "end": 194.6, "word": " zero", "probability": 0.5791015625}, {"start": 194.6, "end": 195.26, "word": " بيطلع", "probability": 0.753173828125}, {"start": 195.26, "end": 196.68, "word": " أصغر", "probability": 0.917724609375}, {"start": 196.68, "end": 197.04, "word": " من", "probability": 0.97412109375}, {"start": 197.04, "end": 197.24, "word": " ال", "probability": 0.26171875}, {"start": 197.24, "end": 197.66, "word": " epsilon", "probability": 0.681640625}, {"start": 197.66, "end": 197.9, "word": " اللي", "probability": 0.931884765625}, {"start": 197.9, "end": 198.12, "word": " احنا", "probability": 0.8009440104166666}, {"start": 198.12, "end": 198.68, "word": " ماخدينها", "probability": 0.94052734375}, {"start": 198.68, "end": 199.16, "word": " واحد", "probability": 0.9697265625}, {"start": 199.16, "end": 202.16, "word": " طب", "probability": 0.7451171875}, {"start": 202.16, "end": 202.76, "word": " xn", "probability": 0.81787109375}, {"start": 202.76, "end": 203.1, "word": " عدد", "probability": 0.9781901041666666}, {"start": 203.1, "end": 203.52, "word": " موجب", "probability": 0.99169921875}, {"start": 203.52, "end": 203.68, "word": " و", "probability": 0.9267578125}, {"start": 203.68, "end": 204.0, "word": " yn", "probability": 0.599609375}, {"start": 204.0, "end": 204.42, "word": " عدد", "probability": 0.9913736979166666}, {"start": 204.42, "end": 205.0, "word": " موجب", "probability": 0.9928385416666666}], "temperature": 1.0}, {"id": 8, "seek": 23520, "start": 206.3, "end": 235.2, "text": "فال quotient هذا كسر هذا موجب سالد سفر فهذا بيقدي ان xn over yn أصغر من واحد لو ضربنا الطرفين العدد الموجب yn فهذا هيقدي ان xn أصغر من yn", "tokens": [5172, 6027, 9641, 1196, 23758, 9122, 3794, 2288, 23758, 3714, 29245, 3555, 8608, 6027, 3215, 8608, 5172, 2288, 6156, 3224, 15730, 4724, 1829, 4587, 16254, 16472, 2031, 77, 670, 17861, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 45164, 48812, 25513, 8315, 41950, 28480, 9957, 18863, 3215, 3215, 9673, 29245, 3555, 17861, 6156, 3224, 15730, 39896, 28543, 1829, 16472, 2031, 77, 5551, 9381, 17082, 2288, 9154, 17861], "avg_logprob": -0.1946128673517882, "compression_ratio": 1.5594405594405594, "no_speech_prob": 0.0, "words": [{"start": 206.3, "end": 206.66, "word": "فال", "probability": 0.73974609375}, {"start": 206.66, "end": 207.26, "word": " quotient", "probability": 0.849853515625}, {"start": 207.26, "end": 207.66, "word": " هذا", "probability": 0.865234375}, {"start": 207.66, "end": 208.14, "word": " كسر", "probability": 0.8050130208333334}, {"start": 208.14, "end": 208.38, "word": " هذا", "probability": 0.8994140625}, {"start": 208.38, "end": 208.92, "word": " موجب", "probability": 0.9752604166666666}, {"start": 208.92, "end": 210.06, "word": " سالد", "probability": 0.7591959635416666}, {"start": 210.06, "end": 210.42, "word": " سفر", "probability": 0.8133138020833334}, {"start": 210.42, "end": 212.4, "word": " فهذا", "probability": 0.8751627604166666}, {"start": 212.4, "end": 213.04, "word": " بيقدي", "probability": 0.66680908203125}, {"start": 213.04, "end": 213.76, "word": " ان", "probability": 0.7587890625}, {"start": 213.76, "end": 214.72, "word": " xn", "probability": 0.4710693359375}, {"start": 214.72, "end": 216.3, "word": " over", "probability": 0.74267578125}, {"start": 216.3, "end": 217.28, "word": " yn", "probability": 0.95263671875}, {"start": 217.28, "end": 218.12, "word": " أصغر", "probability": 0.8837890625}, {"start": 218.12, "end": 218.36, "word": " من", "probability": 0.99609375}, {"start": 218.36, "end": 218.78, "word": " واحد", "probability": 0.938232421875}, {"start": 218.78, "end": 220.74, "word": " لو", "probability": 0.814453125}, {"start": 220.74, "end": 221.36, "word": " ضربنا", "probability": 0.9899088541666666}, {"start": 221.36, "end": 222.32, "word": " الطرفين", "probability": 0.9593098958333334}, {"start": 222.32, "end": 222.88, "word": " العدد", "probability": 0.7599283854166666}, {"start": 222.88, "end": 223.46, "word": " الموجب", "probability": 0.9931640625}, {"start": 223.46, "end": 224.2, "word": " yn", "probability": 0.83935546875}, {"start": 224.2, "end": 226.26, "word": " فهذا", "probability": 0.984375}, {"start": 226.26, "end": 227.44, "word": " هيقدي", "probability": 0.6571451822916666}, {"start": 227.44, "end": 229.58, "word": " ان", "probability": 0.5380859375}, {"start": 229.58, "end": 231.68, "word": " xn", "probability": 0.758544921875}, {"start": 231.68, "end": 233.92, "word": " أصغر", "probability": 0.954345703125}, {"start": 233.92, "end": 234.3, "word": " من", "probability": 0.9912109375}, {"start": 234.3, "end": 235.2, "word": " yn", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 9, "seek": 26055, "start": 236.27, "end": 260.55, "text": "وهذا صحيح لكل N أكبر من أو يستوي capital N now if sigma yn converges then", "tokens": [2407, 3224, 15730, 20328, 5016, 1829, 5016, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 7251, 14851, 45865, 4238, 426, 586, 498, 12771, 17861, 9652, 2880, 550], "avg_logprob": -0.34849329612084795, "compression_ratio": 0.9509803921568627, 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" صحيح", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 11, "seek": 30858, "start": 290.27, "end": 308.59, "text": "by direct comparison test لذلك هذا يكمل برهان الجزء التالي نرجع الأن ناخد أمثلة على تطبيقات على ال direct comparison test و على limit comparison test", "tokens": [2322, 2047, 9660, 1500, 5296, 8848, 23275, 23758, 7251, 24793, 1211, 4724, 2288, 3224, 7649, 25724, 11622, 38207, 16712, 6027, 1829, 8717, 47341, 3615, 16247, 1863, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 15844, 6055, 9566, 21292, 4587, 9307, 15844, 2423, 2047, 9660, 1500, 4032, 15844, 4948, 9660, 1500], "avg_logprob": -0.2660937362909317, "compression_ratio": 1.50354609929078, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 290.27, "end": 290.69, "word": "by", "probability": 0.250732421875}, {"start": 290.69, "end": 291.25, "word": " direct", "probability": 0.7763671875}, {"start": 291.25, "end": 291.87, "word": " comparison", "probability": 0.93505859375}, {"start": 291.87, "end": 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"end": 301.47, "word": " تطبيقات", "probability": 0.850439453125}, {"start": 301.47, "end": 301.81, "word": " على", "probability": 0.49462890625}, {"start": 301.81, "end": 302.23, "word": " ال", "probability": 0.52685546875}, {"start": 302.23, "end": 302.59, "word": " direct", "probability": 0.7353515625}, {"start": 302.59, "end": 303.27, "word": " comparison", "probability": 0.931640625}, {"start": 303.27, "end": 303.87, "word": " test", "probability": 0.95361328125}, {"start": 303.87, "end": 304.87, "word": " و", "probability": 0.92333984375}, {"start": 304.87, "end": 305.13, "word": " على", "probability": 0.6162109375}, {"start": 305.13, "end": 305.57, "word": " limit", "probability": 0.751953125}, {"start": 305.57, "end": 307.89, "word": " comparison", "probability": 0.93359375}, {"start": 307.89, "end": 308.59, "word": " test", "probability": 0.947265625}], "temperature": 1.0}, {"id": 12, "seek": 34036, "start": 311.98, "end": 340.36, "text": "كيف نستخدم ال comparison tests الاختبارين هدول فيثبات ان ال series معينة is convergent discuss .. discuss the convergence of the following series", "tokens": [4117, 33911, 8717, 14851, 9778, 40448, 2423, 9660, 6921, 42963, 46456, 3555, 9640, 9957, 8032, 3215, 12610, 8978, 12984, 3555, 9307, 16472, 2423, 2638, 20449, 9957, 3660, 307, 9652, 6930, 2248, 4386, 2248, 264, 32181, 295, 264, 3480, 2638], "avg_logprob": -0.20761719010770321, "compression_ratio": 1.3028169014084507, "no_speech_prob": 0.0, "words": [{"start": 311.98, "end": 312.3, "word": "كيف", "probability": 0.951416015625}, {"start": 312.3, "end": 312.98, "word": " نستخدم", "probability": 0.96923828125}, {"start": 312.98, "end": 313.34, "word": " ال", "probability": 0.97119140625}, {"start": 313.34, "end": 313.86, "word": " comparison", "probability": 0.8544921875}, {"start": 313.86, "end": 314.4, "word": " tests", "probability": 0.461669921875}, {"start": 314.4, "end": 315.24, "word": " الاختبارين", "probability": 0.815576171875}, {"start": 315.24, "end": 315.68, "word": " هدول", "probability": 0.7858072916666666}, {"start": 315.68, "end": 317.32, "word": " فيثبات", "probability": 0.71435546875}, {"start": 317.32, "end": 317.54, "word": " ان", "probability": 0.70361328125}, {"start": 317.54, "end": 317.7, "word": " ال", "probability": 0.70458984375}, {"start": 317.7, "end": 318.08, "word": " series", "probability": 0.9482421875}, {"start": 318.08, "end": 319.16, "word": " معينة", "probability": 0.95361328125}, {"start": 319.16, "end": 319.78, "word": " is", "probability": 0.828125}, {"start": 319.78, "end": 320.68, "word": " convergent", "probability": 0.772216796875}, {"start": 320.68, "end": 327.78, "word": " discuss", "probability": 0.85400390625}, {"start": 327.78, "end": 328.44, "word": " ..", "probability": 0.53466796875}, {"start": 328.44, "end": 331.26, "word": " discuss", "probability": 0.88232421875}, {"start": 331.26, "end": 332.78, "word": " the", "probability": 0.79736328125}, {"start": 332.78, "end": 333.8, "word": " convergence", "probability": 0.9423828125}, {"start": 333.8, "end": 338.84, "word": " of", "probability": 0.9677734375}, {"start": 338.84, "end": 339.14, "word": " the", "probability": 0.939453125}, {"start": 339.14, "end": 339.58, "word": " following", "probability": 0.86767578125}, {"start": 339.58, "end": 340.36, "word": " series", "probability": 0.9345703125}], "temperature": 1.0}, {"id": 13, "seek": 37845, "start": 360.99, "end": 378.45, "text": "فناخد series sigma from n equals one to infinity ل one over n squared plus n بالمناسبة ال series هذه", "tokens": [5172, 1863, 47283, 3215, 2638, 12771, 490, 297, 6915, 472, 281, 13202, 5296, 472, 670, 297, 8889, 1804, 297, 20666, 2304, 8315, 35457, 3660, 2423, 2638, 29538], "avg_logprob": -0.32505579931395395, "compression_ratio": 1.1538461538461537, "no_speech_prob": 0.0, "words": [{"start": 360.99000000000007, "end": 361.95000000000005, "word": "فناخد", "probability": 0.712554931640625}, {"start": 361.95000000000005, "end": 362.91, "word": " series", "probability": 0.132080078125}, {"start": 362.91, "end": 363.39, "word": " sigma", "probability": 0.5859375}, {"start": 363.39, "end": 363.87, "word": " from", "probability": 0.76513671875}, {"start": 363.87, "end": 364.17, "word": " n", "probability": 0.673828125}, {"start": 364.17, "end": 364.65, "word": " equals", "probability": 0.283447265625}, {"start": 364.65, "end": 364.93, "word": " one", "probability": 0.7900390625}, {"start": 364.93, "end": 365.09, "word": " to", "probability": 0.869140625}, {"start": 365.09, "end": 365.63, "word": " infinity", "probability": 0.84814453125}, {"start": 365.63, "end": 367.11, "word": " ل", "probability": 0.5849609375}, {"start": 367.11, "end": 367.53, "word": " one", "probability": 0.4443359375}, {"start": 367.53, "end": 368.15, "word": " over", "probability": 0.9248046875}, {"start": 368.15, "end": 368.59, "word": " n", "probability": 0.86865234375}, {"start": 368.59, "end": 369.25, "word": " squared", "probability": 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{"start": 388.61, "end": 389.01, "word": " تكون", "probability": 0.984375}, {"start": 389.01, "end": 389.57, "word": " large", "probability": 0.78662109375}, {"start": 389.57, "end": 391.17, "word": " فممكن", "probability": 0.84521484375}, {"start": 391.17, "end": 391.71, "word": " نهمل", "probability": 0.9298502604166666}, {"start": 391.71, "end": 391.87, "word": " ال", "probability": 0.8232421875}, {"start": 391.87, "end": 392.09, "word": " N", "probability": 0.875}, {"start": 392.09, "end": 392.67, "word": " بالنسبة", "probability": 0.9678955078125}, {"start": 392.67, "end": 392.77, "word": " ل", "probability": 0.93310546875}, {"start": 392.77, "end": 392.99, "word": " N", "probability": 0.560546875}, {"start": 392.99, "end": 393.45, "word": " تربية", "probability": 0.7799479166666666}, {"start": 393.45, "end": 395.55, "word": " و", "probability": 0.666015625}, {"start": 395.55, "end": 396.15, "word": " نعتبر", "probability": 0.8828125}, {"start": 396.15, "end": 396.41, "word": " 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" المحاضرة", "probability": 0.975341796875}, {"start": 551.39, "end": 551.93, "word": " السابقة", "probability": 0.9842122395833334}, {"start": 551.93, "end": 552.13, "word": " أو", "probability": 0.765625}, {"start": 552.13, "end": 552.67, "word": " الجبلة", "probability": 0.7420247395833334}], "temperature": 1.0}, {"id": 20, "seek": 57854, "start": 554.19, "end": 578.55, "text": "إذا أنا في عندى two series واحدة الحد العام تبعها واحد على انتر بيه وهذا الconversion وواحدة الحد العام تبعها واحد على انتر بيه الزادة وهذا الحد العام أصغر من أو ساوي الحد العام لهذه الconversion إذا ممكن استخدم so by direct comparison test", "tokens": [28814, 15730, 41850, 8978, 43242, 7578, 732, 2638, 36764, 24401, 3660, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 36764, 24401, 15844, 16472, 2655, 2288, 4724, 1829, 3224, 37037, 15730, 2423, 1671, 29153, 4032, 14407, 24401, 3660, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 36764, 24401, 15844, 16472, 2655, 2288, 4724, 1829, 3224, 6024, 110, 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0.8167317708333334}, {"start": 569.09, "end": 569.43, "word": " الحد", "probability": 0.961669921875}, {"start": 569.43, "end": 569.79, "word": " العام", "probability": 0.993408203125}, {"start": 569.79, "end": 570.27, "word": " لهذه", "probability": 0.877197265625}, {"start": 570.27, "end": 570.89, "word": " الconversion", "probability": 0.5321858723958334}, {"start": 570.89, "end": 571.25, "word": " إذا", "probability": 0.72900390625}, {"start": 571.25, "end": 571.61, "word": " ممكن", "probability": 0.7408447265625}, {"start": 571.61, "end": 572.29, "word": " استخدم", "probability": 0.84619140625}, {"start": 572.29, "end": 575.63, "word": " so", "probability": 0.121826171875}, {"start": 575.63, "end": 576.25, "word": " by", "probability": 0.92919921875}, {"start": 576.25, "end": 577.27, "word": " direct", "probability": 0.88623046875}, {"start": 577.27, "end": 577.97, "word": " comparison", "probability": 0.9111328125}, {"start": 577.97, "end": 578.55, "word": " test", "probability": 0.923828125}], "temperature": 1.0}, {"id": 21, "seek": 60916, "start": 582.52, "end": 609.16, "text": "السيريز اللي هي sigma من n equals one to infinity لواحد على n squared plus n converges إذا السيريز هذه أتباعنا هي انها convergence by direct comparison استخدمنا ال direct comparison test مفهوم واضح؟", "tokens": [6027, 3794, 13546, 1829, 11622, 13672, 1829, 39896, 12771, 9154, 297, 6915, 472, 281, 13202, 5296, 14407, 24401, 15844, 297, 8889, 1804, 297, 9652, 2880, 11933, 15730, 21136, 13546, 1829, 11622, 29538, 5551, 2655, 3555, 45761, 8315, 39896, 16472, 11296, 32181, 538, 2047, 9660, 44713, 9778, 40448, 8315, 2423, 2047, 9660, 1500, 3714, 5172, 3224, 20498, 4032, 46958, 5016, 22807], "avg_logprob": -0.35015368070758757, "compression_ratio": 1.427807486631016, "no_speech_prob": 0.0, "words": [{"start": 582.52, "end": 583.24, "word": "السيريز", "probability": 0.69990234375}, {"start": 583.24, "end": 583.44, "word": " اللي", "probability": 0.480224609375}, {"start": 583.44, "end": 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"probability": 0.935546875}, {"start": 589.92, "end": 590.96, "word": " n", "probability": 0.86962890625}, {"start": 590.96, "end": 596.86, "word": " converges", "probability": 0.40338134765625}, {"start": 596.86, "end": 599.76, "word": " إذا", "probability": 0.626220703125}, {"start": 599.76, "end": 600.38, "word": " السيريز", "probability": 0.9124755859375}, {"start": 600.38, "end": 600.66, "word": " هذه", "probability": 0.625}, {"start": 600.66, "end": 601.14, "word": " أتباعنا", "probability": 0.67099609375}, {"start": 601.14, "end": 601.38, "word": " هي", "probability": 0.853515625}, {"start": 601.38, "end": 602.32, "word": " انها", "probability": 0.6427001953125}, {"start": 602.32, "end": 602.84, "word": " convergence", "probability": 0.434326171875}, {"start": 602.84, "end": 603.34, "word": " by", "probability": 0.79638671875}, {"start": 603.34, "end": 603.86, "word": " direct", "probability": 0.89697265625}, {"start": 603.86, "end": 604.62, "word": " comparison", "probability": 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0.7972412109375}, {"start": 637.0, "end": 637.22, "word": " لو", "probability": 0.76025390625}, {"start": 637.22, "end": 637.64, "word": " أخدنا", "probability": 0.852294921875}, {"start": 637.64, "end": 637.98, "word": " series", "probability": 0.388427734375}, {"start": 637.98, "end": 638.44, "word": " sigma", "probability": 0.5517578125}, {"start": 638.44, "end": 638.86, "word": " from", "probability": 0.76708984375}, {"start": 638.86, "end": 639.14, "word": " n", "probability": 0.6552734375}, {"start": 639.14, "end": 639.58, "word": " equals", "probability": 0.418212890625}, {"start": 639.58, "end": 639.9, "word": " one", "probability": 0.8173828125}, {"start": 639.9, "end": 640.06, "word": " to", "probability": 0.93896484375}, {"start": 640.06, "end": 640.58, "word": " infinity", "probability": 0.865234375}, {"start": 640.58, "end": 642.02, "word": " لواحد", "probability": 0.7542317708333334}, {"start": 642.02, "end": 642.3, "word": " على", "probability": 0.63720703125}, {"start": 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"word": " convergent", "probability": 0.6910400390625}, {"start": 653.94, "end": 654.18, "word": " ولا", "probability": 0.78076171875}, {"start": 654.18, "end": 655.08, "word": " divergent", "probability": 0.705810546875}, {"start": 655.08, "end": 657.52, "word": " طبعا", "probability": 0.9532470703125}], "temperature": 1.0}, {"id": 24, "seek": 67648, "start": 659.2, "end": 676.48, "text": "أول شيء بنفكر فيه، بنشوف كيف ال series هذه بتتصرف، ما هي ال series القريبة منها، و اللي احنا عارفين أنها أو ممكن نحكم عليها بسهولة، ن be convergent أو divergent، يعني بدي أقارن ال series هذه ب series تانية", "tokens": [10721, 12610, 44049, 38207, 44945, 5172, 37983, 8978, 3224, 12399, 44945, 8592, 38688, 9122, 33911, 2423, 2638, 29538, 39894, 2655, 9381, 28480, 12399, 19446, 39896, 2423, 2638, 25062, 16572, 49401, 9154, 11296, 12399, 4032, 13672, 1829, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 14739, 11296, 34051, 3714, 43020, 8717, 5016, 24793, 25894, 11296, 4724, 3794, 3224, 12610, 3660, 12399, 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{"start": 668.98, "end": 670.08, "word": " أو", "probability": 0.33251953125}, {"start": 670.08, "end": 670.42, "word": " ممكن", "probability": 0.990478515625}, {"start": 670.42, "end": 670.8, "word": " نحكم", "probability": 0.9845377604166666}, {"start": 670.8, "end": 671.16, "word": " عليها", "probability": 0.991455078125}, {"start": 671.16, "end": 671.7, "word": " بسهولة،", "probability": 0.9308268229166666}, {"start": 671.7, "end": 671.78, "word": " ن", "probability": 0.83740234375}, {"start": 671.78, "end": 671.92, "word": " be", "probability": 0.17578125}, {"start": 671.92, "end": 672.44, "word": " convergent", "probability": 0.940185546875}, {"start": 672.44, "end": 672.6, "word": " أو", "probability": 0.69970703125}, {"start": 672.6, "end": 673.72, "word": " divergent،", "probability": 0.7701822916666666}, {"start": 673.72, "end": 673.92, "word": " يعني", "probability": 0.828857421875}, {"start": 673.92, "end": 674.2, "word": " بدي", "probability": 0.78125}, {"start": 674.2, "end": 674.68, "word": " أقارن", "probability": 0.945556640625}, {"start": 674.68, "end": 674.8, "word": " ال", "probability": 0.9873046875}, {"start": 674.8, "end": 675.14, "word": " series", "probability": 0.9677734375}, {"start": 675.14, "end": 675.48, "word": " هذه", "probability": 0.947265625}, {"start": 675.48, "end": 675.66, "word": " ب", "probability": 0.90869140625}, {"start": 675.66, "end": 675.98, "word": " series", "probability": 0.8994140625}, {"start": 675.98, "end": 676.48, "word": " تانية", "probability": 0.990234375}], "temperature": 1.0}, {"id": 25, "seek": 70288, "start": 677.24, "end": 702.88, "text": "من السهل اني احكم عليها هل هي convergent او divergent فلما N تكون كبيرة و ان N is sufficiently large لما N تقول infinity ممكن اهمل N و اهمل 1 وبالتالي ال series هذه behaves تتصرف زي ال series 1 على N ترمية", "tokens": [27842, 21136, 3224, 1211, 16472, 1829, 1975, 5016, 24793, 25894, 11296, 8032, 1211, 39896, 9652, 6930, 1975, 2407, 18558, 6930, 6156, 1211, 15042, 426, 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"word": " large", "probability": 0.96923828125}, {"start": 687.76, "end": 688.46, "word": " لما", "probability": 0.909912109375}, {"start": 688.46, "end": 688.72, "word": " N", "probability": 0.783203125}, {"start": 688.72, "end": 689.0, "word": " تقول", "probability": 0.914794921875}, {"start": 689.0, "end": 689.58, "word": " infinity", "probability": 0.63232421875}, {"start": 689.58, "end": 691.0, "word": " ممكن", "probability": 0.935302734375}, {"start": 691.0, "end": 691.5, "word": " اهمل", "probability": 0.8121744791666666}, {"start": 691.5, "end": 691.86, "word": " N", "probability": 0.7490234375}, {"start": 691.86, "end": 692.14, "word": " و", "probability": 0.78369140625}, {"start": 692.14, "end": 692.52, "word": " اهمل", "probability": 0.9099934895833334}, {"start": 692.52, "end": 692.9, "word": " 1", "probability": 0.80322265625}, {"start": 692.9, "end": 694.92, "word": " وبالتالي", "probability": 0.910546875}, {"start": 694.92, "end": 695.44, "word": " ال", "probability": 0.88671875}, {"start": 695.44, "end": 695.86, "word": " series", "probability": 0.93115234375}, {"start": 695.86, "end": 696.38, "word": " هذه", "probability": 0.65283203125}, {"start": 696.38, "end": 697.2, "word": " behaves", "probability": 0.81640625}, {"start": 697.2, "end": 698.62, "word": " تتصرف", "probability": 0.91015625}, {"start": 698.62, "end": 700.42, "word": " زي", "probability": 0.885986328125}, {"start": 700.42, "end": 700.62, "word": " ال", "probability": 0.75341796875}, {"start": 700.62, "end": 701.08, "word": " series", "probability": 0.94189453125}, {"start": 701.08, "end": 701.56, "word": " 1", "probability": 0.63525390625}, {"start": 701.56, "end": 701.98, "word": " على", "probability": 0.71533203125}, {"start": 701.98, "end": 702.32, "word": " N", "probability": 0.90673828125}, {"start": 702.32, "end": 702.88, "word": " ترمية", "probability": 0.723876953125}], "temperature": 1.0}, {"id": 26, "seek": 72825, "start": 705.47, "end": 728.25, "text": "اللي هي احنا عارفين which is كل بيت واحد طبعا by P seriousness زي ما شرحنا في المثال الأول الآن السؤال اللي بيطرح نفسه is it true هل واحد على", "tokens": [6027, 20292, 39896, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 597, 307, 28242, 4724, 36081, 36764, 24401, 23032, 3555, 3615, 995, 538, 430, 44880, 30767, 1829, 19446, 13412, 2288, 5016, 8315, 8978, 9673, 12984, 6027, 16247, 12610, 6024, 48506, 21136, 33604, 6027, 13672, 1829, 4724, 1829, 9566, 2288, 5016, 8717, 36178, 3224, 307, 309, 2074, 8032, 1211, 36764, 24401, 15844], "avg_logprob": -0.2622950956469677, "compression_ratio": 1.4088050314465408, "no_speech_prob": 0.0, "words": [{"start": 705.47, "end": 705.83, "word": "اللي", "probability": 0.6126708984375}, {"start": 705.83, "end": 706.23, "word": " هي", "probability": 0.68994140625}, {"start": 706.23, "end": 706.73, "word": " احنا", "probability": 0.9210611979166666}, {"start": 706.73, "end": 707.21, "word": " عارفين", "probability": 0.9866943359375}, {"start": 707.21, "end": 709.23, "word": " which", "probability": 0.66796875}, {"start": 709.23, "end": 711.37, "word": " is", "probability": 0.94482421875}, {"start": 711.37, "end": 711.71, "word": " كل", "probability": 0.1260986328125}, {"start": 711.71, "end": 712.03, "word": " بيت", "probability": 0.372802734375}, {"start": 712.03, "end": 713.63, "word": " واحد", "probability": 0.4591064453125}, {"start": 713.63, "end": 714.73, "word": " طبعا", "probability": 0.94140625}, {"start": 714.73, "end": 714.97, "word": " by", "probability": 0.7021484375}, {"start": 714.97, "end": 715.23, "word": " P", "probability": 0.27392578125}, {"start": 715.23, "end": 715.65, "word": " seriousness", "probability": 0.09600830078125}, {"start": 715.65, "end": 716.05, "word": " زي", "probability": 0.955078125}, {"start": 716.05, "end": 716.15, "word": " ما", "probability": 0.95751953125}, {"start": 716.15, "end": 716.73, "word": " شرحنا", "probability": 0.9591064453125}, {"start": 716.73, "end": 717.35, "word": " في", "probability": 0.70458984375}, {"start": 717.35, "end": 717.77, "word": " المثال", "probability": 0.98291015625}, {"start": 717.77, "end": 718.23, "word": " الأول", "probability": 0.89697265625}, {"start": 718.23, "end": 721.27, "word": " الآن", "probability": 0.782470703125}, {"start": 721.27, "end": 722.41, "word": " السؤال", "probability": 0.9944661458333334}, {"start": 722.41, "end": 722.53, "word": " اللي", "probability": 0.90869140625}, {"start": 722.53, "end": 722.85, "word": " بيطرح", "probability": 0.83359375}, {"start": 722.85, "end": 724.23, "word": " نفسه", "probability": 0.9959309895833334}, {"start": 724.23, "end": 725.63, "word": " is", "probability": 0.8701171875}, {"start": 725.63, "end": 725.85, "word": " it", "probability": 0.96923828125}, {"start": 725.85, "end": 726.27, "word": " true", "probability": 0.9443359375}, {"start": 726.27, "end": 726.75, "word": " هل", "probability": 0.941650390625}, {"start": 726.75, "end": 727.95, "word": " واحد", "probability": 0.982666015625}, {"start": 727.95, "end": 728.25, "word": " على", "probability": 0.78173828125}], "temperature": 1.0}, {"id": 27, "seek": 74994, "start": 729.62, "end": 749.94, "text": "إن تربية سالف إن زاد واحد أصغر من أو يساوي واحد على إن تربية عشان نستخدم .. هل هذا الكلام صحيح لكل إن؟ لأ مش فاكرش أنا فللأسف هذا مش صحيح وبالتالي مابقدرش أستخدم إن هذا not true", "tokens": [28814, 1863, 6055, 25513, 10632, 8608, 6027, 5172, 11933, 1863, 30767, 18513, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 36764, 24401, 15844, 11933, 1863, 6055, 25513, 10632, 6225, 8592, 7649, 8717, 14851, 9778, 40448, 4386, 8032, 1211, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 5296, 28820, 36145, 22807, 5296, 10721, 37893, 6156, 995, 37983, 8592, 41850, 6156, 1211, 1211, 10721, 3794, 5172, 23758, 37893, 20328, 5016, 1829, 5016, 46599, 6027, 2655, 6027, 1829, 3714, 16758, 28543, 2288, 8592, 5551, 14851, 9778, 40448, 36145, 23758, 406, 2074], "avg_logprob": -0.19959676714353664, "compression_ratio": 1.6923076923076923, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 729.62, "end": 730.12, "word": "إن", "probability": 0.6513671875}, {"start": 730.12, "end": 730.6, "word": " تربية", "probability": 0.9046223958333334}, {"start": 730.6, "end": 731.18, "word": " سالف", "probability": 0.60693359375}, {"start": 731.18, "end": 731.38, "word": " إن", "probability": 0.5738525390625}, {"start": 731.38, "end": 731.82, "word": " زاد", "probability": 0.822021484375}, {"start": 731.82, "end": 732.34, "word": " واحد", "probability": 0.985107421875}, {"start": 732.34, "end": 733.14, "word": " أصغر", "probability": 0.97119140625}, {"start": 733.14, "end": 733.4, "word": " من", "probability": 0.9892578125}, {"start": 733.4, "end": 733.68, "word": " أو", "probability": 0.9228515625}, {"start": 733.68, "end": 734.26, "word": " يساوي", "probability": 0.8621826171875}, {"start": 734.26, "end": 734.76, "word": " واحد", "probability": 0.983642578125}, {"start": 734.76, "end": 735.0, "word": " على", "probability": 0.822265625}, {"start": 735.0, "end": 735.3, "word": " إن", "probability": 0.659912109375}, {"start": 735.3, "end": 735.88, "word": " تربية", "probability": 0.97607421875}, {"start": 735.88, "end": 737.36, "word": " عشان", "probability": 0.96826171875}, {"start": 737.36, "end": 738.04, "word": " نستخدم", "probability": 0.9224853515625}, {"start": 738.04, "end": 738.18, "word": " ..", "probability": 0.521484375}, {"start": 738.18, "end": 738.34, "word": " هل", "probability": 0.8515625}, {"start": 738.34, "end": 738.54, "word": " هذا", "probability": 0.97265625}, {"start": 738.54, "end": 738.86, "word": " الكلام", "probability": 0.9215494791666666}, {"start": 738.86, "end": 739.28, "word": " صحيح", "probability": 0.993408203125}, {"start": 739.28, "end": 739.76, "word": " لكل", "probability": 0.905029296875}, {"start": 739.76, "end": 740.64, "word": " إن؟", "probability": 0.5037841796875}, {"start": 740.64, "end": 740.9, "word": " لأ", "probability": 0.697509765625}, {"start": 740.9, "end": 741.16, "word": " مش", "probability": 0.564453125}, {"start": 741.16, "end": 741.62, "word": " فاكرش", "probability": 0.67724609375}, {"start": 741.62, "end": 741.84, "word": " أنا", "probability": 0.271728515625}, {"start": 741.84, "end": 744.48, "word": " فللأسف", "probability": 0.9403483072916666}, {"start": 744.48, "end": 744.74, "word": " هذا", "probability": 0.9287109375}, {"start": 744.74, "end": 744.98, "word": " مش", "probability": 0.98828125}, {"start": 744.98, "end": 745.42, "word": " صحيح", "probability": 0.9984130859375}, {"start": 745.42, "end": 745.92, "word": " وبالتالي", "probability": 0.85625}, {"start": 745.92, "end": 746.42, "word": " مابقدرش", "probability": 0.8283203125}, {"start": 746.42, "end": 747.2, "word": " أستخدم", "probability": 0.9306640625}, {"start": 747.2, "end": 747.76, "word": " إن", "probability": 0.59423828125}, {"start": 747.76, "end": 748.14, "word": " هذا", "probability": 0.962890625}, {"start": 748.14, "end": 749.54, "word": " not", "probability": 0.96240234375}, {"start": 749.54, "end": 749.94, "word": " true", "probability": 0.984375}], "temperature": 1.0}, {"id": 28, "seek": 78131, "start": 754.43, "end": 781.31, "text": "for example على سبيل المثال take m بساوي اتنين هنجد المتباين هذه مش صح اذا مقدرش انا استخدم ال direct comparison test اذا في الحالة هذه لازم استخدم ال limit comparison test او ابحث عن مقارنة تانية however", "tokens": [2994, 1365, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 747, 275, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 8032, 1863, 7435, 3215, 9673, 2655, 3555, 995, 9957, 29538, 37893, 20328, 5016, 1975, 15730, 3714, 28543, 2288, 8592, 1975, 8315, 44713, 9778, 40448, 2423, 2047, 9660, 1500, 1975, 15730, 8978, 21542, 6027, 3660, 29538, 5296, 31377, 2304, 44713, 9778, 40448, 2423, 4948, 9660, 1500, 1975, 2407, 48127, 5016, 12984, 18871, 3714, 4587, 9640, 1863, 3660, 6055, 7649, 10632, 4461], "avg_logprob": -0.20664063189178705, "compression_ratio": 1.5736040609137056, "no_speech_prob": 0.0, "words": [{"start": 754.43, "end": 754.71, "word": "for", "probability": 0.25244140625}, {"start": 754.71, "end": 755.37, "word": " example", "probability": 0.9599609375}, {"start": 755.37, "end": 755.63, "word": " على", "probability": 0.6337890625}, {"start": 755.63, "end": 756.07, "word": " سبيل", "probability": 0.9889322916666666}, {"start": 756.07, "end": 756.59, "word": " المثال", "probability": 0.8976236979166666}, {"start": 756.59, "end": 757.87, "word": " take", "probability": 0.7060546875}, {"start": 757.87, "end": 760.11, "word": " m", "probability": 0.48046875}, {"start": 760.11, "end": 760.81, "word": " بساوي", "probability": 0.58966064453125}, {"start": 760.81, "end": 761.41, "word": " اتنين", "probability": 0.897705078125}, {"start": 761.41, "end": 762.91, "word": " هنجد", "probability": 0.54412841796875}, {"start": 762.91, "end": 763.63, "word": " المتباين", "probability": 0.83984375}, {"start": 763.63, "end": 764.03, "word": " هذه", "probability": 0.368408203125}, {"start": 764.03, "end": 764.77, "word": " مش", "probability": 0.72119140625}, {"start": 764.77, "end": 765.09, "word": " صح", "probability": 0.991943359375}, {"start": 765.09, "end": 768.07, "word": " اذا", "probability": 0.638671875}, {"start": 768.07, "end": 768.71, "word": " مقدرش", "probability": 0.8006591796875}, {"start": 768.71, "end": 769.03, "word": " انا", "probability": 0.91796875}, {"start": 769.03, "end": 770.07, "word": " استخدم", "probability": 0.9134114583333334}, {"start": 770.07, "end": 770.31, "word": " ال", "probability": 0.93505859375}, {"start": 770.31, "end": 770.59, "word": " direct", "probability": 0.72119140625}, {"start": 770.59, "end": 771.23, "word": " comparison", "probability": 0.93212890625}, {"start": 771.23, "end": 771.83, "word": " test", "probability": 0.96728515625}, {"start": 771.83, "end": 773.23, "word": " اذا", "probability": 0.609130859375}, {"start": 773.23, "end": 773.43, "word": " في", "probability": 0.73876953125}, {"start": 773.43, "end": 773.79, "word": " الحالة", "probability": 0.9283854166666666}, {"start": 773.79, "end": 773.97, "word": " هذه", "probability": 0.93017578125}, {"start": 773.97, "end": 774.31, "word": " لازم", "probability": 0.9640299479166666}, {"start": 774.31, "end": 774.89, "word": " استخدم", "probability": 0.9514973958333334}, {"start": 774.89, "end": 775.03, "word": " ال", "probability": 0.7529296875}, {"start": 775.03, "end": 775.29, "word": " limit", "probability": 0.9013671875}, {"start": 775.29, "end": 775.87, "word": " comparison", "probability": 0.9248046875}, {"start": 775.87, "end": 776.27, "word": " test", "probability": 0.9609375}, {"start": 776.27, "end": 776.85, "word": " او", "probability": 0.9560546875}, {"start": 776.85, "end": 777.55, "word": " ابحث", "probability": 0.8888346354166666}, {"start": 777.55, "end": 777.91, "word": " عن", "probability": 0.99560546875}, {"start": 777.91, "end": 779.19, "word": " مقارنة", 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"word": " يعني", "probability": 0.914306640625}, {"start": 900.99, "end": 901.33, "word": " ..", "probability": 0.9296875}], "temperature": 1.0}, {"id": 33, "seek": 92807, "start": 902.79, "end": 928.07, "text": "بنعرف إنه في متباينة زي هذه صحيحة هذا مش سهل وبالتالي ممكن نستخدم ال limit comparison test ونرايح رأسنا ال limit comparison test في الحالة هذه أسهل من إن أنا يعني أخمن .. أخمن يعني حاجة زي هذه okay فتعالوا نشوف كيف نستخدم ال limit comparison test", "tokens": [3555, 1863, 3615, 28480, 36145, 3224, 8978, 44650, 3555, 995, 9957, 3660, 30767, 1829, 29538, 20328, 5016, 1829, 5016, 3660, 23758, 37893, 8608, 3224, 1211, 46599, 6027, 2655, 6027, 1829, 3714, 43020, 8717, 14851, 9778, 40448, 2423, 4948, 9660, 1500, 4032, 1863, 23557, 1829, 5016, 12602, 10721, 3794, 8315, 2423, 4948, 9660, 1500, 8978, 21542, 6027, 3660, 29538, 5551, 3794, 3224, 1211, 9154, 36145, 41850, 37495, 22653, 5551, 9778, 27842, 4386, 5551, 9778, 27842, 37495, 22653, 11331, 26108, 3660, 30767, 1829, 29538, 1392, 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"probability": 0.9967447916666666}, {"start": 907.93, "end": 909.19, "word": " وبالتالي", "probability": 0.90849609375}, {"start": 909.19, "end": 909.87, "word": " ممكن", "probability": 0.9794921875}, {"start": 909.87, "end": 910.45, "word": " نستخدم", "probability": 0.9931640625}, {"start": 910.45, "end": 910.59, "word": " ال", "probability": 0.646484375}, {"start": 910.59, "end": 910.79, "word": " limit", "probability": 0.91357421875}, {"start": 910.79, "end": 911.33, "word": " comparison", "probability": 0.90234375}, {"start": 911.33, "end": 911.69, "word": " test", "probability": 0.9453125}, {"start": 911.69, "end": 912.19, "word": " ونرايح", "probability": 0.803564453125}, {"start": 912.19, "end": 912.73, "word": " رأسنا", "probability": 0.9383544921875}, {"start": 912.73, "end": 914.09, "word": " ال", "probability": 0.828125}, {"start": 914.09, "end": 914.31, "word": " limit", "probability": 0.9619140625}, {"start": 914.31, "end": 914.75, "word": " comparison", "probability": 0.9296875}, {"start": 914.75, "end": 915.11, "word": " test", "probability": 0.95458984375}, {"start": 915.11, "end": 915.21, "word": " في", "probability": 0.86181640625}, {"start": 915.21, "end": 915.49, "word": " الحالة", "probability": 0.9767252604166666}, {"start": 915.49, "end": 915.75, "word": " هذه", "probability": 0.92578125}, {"start": 915.75, "end": 916.15, "word": " أسهل", "probability": 0.9927978515625}, {"start": 916.15, "end": 916.27, "word": " من", "probability": 0.97802734375}, {"start": 916.27, "end": 916.45, "word": " إن", "probability": 0.350341796875}, {"start": 916.45, "end": 916.69, "word": " أنا", "probability": 0.82568359375}, {"start": 916.69, "end": 917.89, "word": " يعني", "probability": 0.7060546875}, {"start": 917.89, "end": 921.55, "word": " أخمن", "probability": 0.9029947916666666}, {"start": 921.55, "end": 921.59, "word": " ..", "probability": 0.417724609375}, {"start": 921.59, "end": 922.49, "word": " أخمن", "probability": 0.7731119791666666}, {"start": 922.49, "end": 922.87, "word": " يعني", "probability": 0.918212890625}, {"start": 922.87, "end": 923.39, "word": " حاجة", "probability": 0.9962565104166666}, {"start": 923.39, "end": 923.61, "word": " زي", "probability": 0.99462890625}, {"start": 923.61, "end": 923.95, "word": " هذه", "probability": 0.9560546875}, {"start": 923.95, "end": 924.45, "word": " okay", "probability": 0.625}, {"start": 924.45, "end": 925.35, "word": " فتعالوا", "probability": 0.93193359375}, {"start": 925.35, "end": 925.69, "word": " نشوف", "probability": 0.998046875}, {"start": 925.69, "end": 925.95, "word": " كيف", "probability": 0.982666015625}, {"start": 925.95, "end": 926.51, "word": " نستخدم", "probability": 0.9947509765625}, {"start": 926.51, "end": 926.69, "word": " ال", "probability": 0.90478515625}, {"start": 926.69, "end": 926.95, "word": " limit", "probability": 0.96142578125}, {"start": 926.95, "end": 927.57, "word": " comparison", "probability": 0.92431640625}, {"start": 927.57, "end": 928.07, "word": " test", "probability": 0.94482421875}], "temperature": 1.0}, {"id": 34, "seek": 95572, "start": 931.92, "end": 955.72, "text": "أذا هنا we use limit comparison test with a n بساوي واحد على n تربيع minus n زايد واحد أو xn فالبسامينات", "tokens": [10721, 15730, 34105, 321, 764, 4948, 9660, 1500, 365, 257, 297, 4724, 3794, 995, 45865, 36764, 24401, 15844, 297, 6055, 2288, 21292, 3615, 3175, 297, 30767, 995, 25708, 36764, 24401, 34051, 2031, 77, 6156, 6027, 3555, 3794, 10943, 1829, 8315, 2655], "avg_logprob": -0.41183035714285715, "compression_ratio": 1.184, "no_speech_prob": 0.0, "words": [{"start": 931.92, "end": 932.26, "word": "أذا", "probability": 0.2160491943359375}, {"start": 932.26, "end": 932.58, "word": " هنا", "probability": 0.96875}, {"start": 932.58, "end": 935.54, "word": " we", "probability": 0.5166015625}, {"start": 935.54, "end": 936.26, "word": " use", "probability": 0.90966796875}, {"start": 936.26, "end": 940.22, "word": " limit", "probability": 0.75}, {"start": 940.22, "end": 940.98, "word": " comparison", "probability": 0.90576171875}, {"start": 940.98, "end": 941.58, "word": " test", "probability": 0.904296875}, {"start": 941.58, "end": 945.16, "word": " with", "probability": 0.85205078125}, {"start": 945.16, "end": 946.92, "word": " a", "probability": 0.51611328125}, {"start": 946.92, "end": 947.32, "word": " n", "probability": 0.38623046875}, {"start": 947.32, "end": 948.06, "word": " بساوي", "probability": 0.708251953125}, {"start": 948.06, "end": 948.74, "word": " واحد", "probability": 0.9814453125}, {"start": 948.74, "end": 949.08, "word": " على", "probability": 0.62255859375}, {"start": 949.08, "end": 950.94, "word": " n", "probability": 0.466064453125}, {"start": 950.94, "end": 951.58, "word": " تربيع", "probability": 0.8095703125}, {"start": 951.58, "end": 952.02, "word": " minus", "probability": 0.72314453125}, {"start": 952.02, "end": 952.58, "word": " n", "probability": 0.87353515625}, {"start": 952.58, "end": 953.18, "word": " زايد", "probability": 0.75390625}, {"start": 953.18, "end": 953.74, "word": " واحد", "probability": 0.992919921875}, {"start": 953.74, "end": 954.0, "word": " أو", "probability": 0.62841796875}, {"start": 954.0, "end": 954.64, "word": " xn", "probability": 0.6126708984375}, {"start": 954.64, "end": 955.72, "word": " فالبسامينات", "probability": 0.5954132080078125}], "temperature": 1.0}, {"id": 35, "seek": 98580, "start": 957.84, "end": 985.8, "text": "و Yn بساوية واحد على M تربية فاني ايجي نحسب ال limit ل Xn over Yn as N tenths of infinity بساوية limit هاي Xn تقسيم Yn بتطلع M تربية على M تربية negative M plus one", "tokens": [2407, 398, 77, 4724, 3794, 995, 2407, 10632, 36764, 24401, 15844, 376, 6055, 2288, 21292, 3660, 6156, 7649, 1829, 1975, 1829, 7435, 1829, 8717, 5016, 35457, 2423, 4948, 5296, 1783, 77, 670, 398, 77, 382, 426, 2064, 32184, 295, 13202, 4724, 3794, 995, 2407, 10632, 4948, 8032, 47302, 1783, 77, 6055, 4587, 3794, 32640, 398, 77, 39894, 9566, 1211, 3615, 376, 6055, 2288, 21292, 3660, 15844, 376, 6055, 2288, 21292, 3660, 3671, 376, 1804, 472], "avg_logprob": -0.34580591477845846, "compression_ratio": 1.464968152866242, "no_speech_prob": 0.0, "words": [{"start": 957.84, "end": 958.28, "word": "و", "probability": 0.3125}, {"start": 958.28, "end": 959.32, "word": " Yn", "probability": 0.19378662109375}, {"start": 959.32, "end": 960.72, "word": " بساوية", "probability": 0.462286376953125}, {"start": 960.72, "end": 962.32, "word": " واحد", "probability": 0.806396484375}, {"start": 962.32, "end": 962.62, "word": " على", "probability": 0.51220703125}, {"start": 962.62, "end": 963.08, "word": " M", "probability": 0.225341796875}, {"start": 963.08, "end": 963.86, "word": " تربية", "probability": 0.805419921875}, {"start": 963.86, "end": 967.6, "word": " فاني", "probability": 0.6031901041666666}, {"start": 967.6, "end": 967.78, "word": " ايجي", "probability": 0.6634521484375}, {"start": 967.78, "end": 968.28, "word": " نحسب", "probability": 0.8763020833333334}, {"start": 968.28, "end": 968.52, "word": " ال", "probability": 0.505859375}, {"start": 968.52, "end": 968.8, "word": " limit", "probability": 0.927734375}, {"start": 968.8, "end": 969.1, "word": " ل", "probability": 0.9443359375}, {"start": 969.1, "end": 969.86, "word": " Xn", "probability": 0.5391845703125}, {"start": 969.86, "end": 970.3, "word": " over", "probability": 0.72607421875}, {"start": 970.3, "end": 971.44, "word": " Yn", "probability": 0.92724609375}, {"start": 971.44, "end": 972.56, "word": " as", "probability": 0.67919921875}, {"start": 972.56, "end": 972.92, "word": " N", "probability": 0.5478515625}, {"start": 972.92, "end": 973.24, "word": " tenths", "probability": 0.4300537109375}, {"start": 973.24, "end": 973.34, "word": " of", "probability": 0.8251953125}, {"start": 973.34, "end": 973.82, "word": " infinity", "probability": 0.88232421875}, {"start": 973.82, "end": 974.52, "word": " بساوية", "probability": 0.92294921875}, {"start": 974.52, "end": 974.96, "word": " limit", "probability": 0.8349609375}, {"start": 974.96, "end": 977.02, "word": " هاي", "probability": 0.7113037109375}, {"start": 977.02, "end": 978.24, "word": " Xn", "probability": 0.8798828125}, {"start": 978.24, "end": 980.26, "word": " تقسيم", "probability": 0.90771484375}, {"start": 980.26, "end": 980.78, "word": " Yn", "probability": 0.962890625}, {"start": 980.78, "end": 981.28, "word": " بتطلع", "probability": 0.7860107421875}, {"start": 981.28, "end": 981.72, "word": " M", "probability": 0.5419921875}, {"start": 981.72, "end": 982.56, "word": " تربية", "probability": 0.9154052734375}, {"start": 982.56, "end": 983.08, "word": " على", "probability": 0.78466796875}, {"start": 983.08, "end": 983.66, "word": " M", "probability": 0.83544921875}, {"start": 983.66, "end": 984.26, "word": " تربية", "probability": 0.9654541015625}, {"start": 984.26, "end": 984.76, "word": " negative", "probability": 0.57470703125}, {"start": 984.76, "end": 985.18, "word": " M", "probability": 0.499755859375}, {"start": 985.18, "end": 985.52, "word": " plus", "probability": 0.92822265625}, {"start": 985.52, "end": 985.8, "word": " one", "probability": 0.78466796875}], "temperature": 1.0}, {"id": 36, "seek": 101441, "start": 988.03, "end": 1014.41, "text": "و ال limit هذا عشان نحسبها بالجسم bust مقام على n تربية ففي ال bust واحد واحد سالب واحد على n موجب واحد على n تربية لإن تقول ال infinity وهذا بطلع واحد على واحد سالب صفر موجب صفر ويساوي واحد لايساوي صفر إذن ال R", "tokens": [2407, 2423, 4948, 23758, 6225, 8592, 7649, 8717, 5016, 35457, 11296, 20666, 7435, 38251, 19432, 3714, 4587, 10943, 15844, 297, 6055, 25513, 10632, 6156, 41185, 2423, 19432, 36764, 24401, 36764, 24401, 8608, 6027, 3555, 36764, 24401, 15844, 297, 3714, 29245, 3555, 36764, 24401, 15844, 297, 6055, 25513, 10632, 5296, 28814, 1863, 6055, 39648, 2423, 13202, 37037, 15730, 4724, 9566, 1211, 3615, 36764, 24401, 15844, 36764, 24401, 8608, 6027, 3555, 20328, 5172, 2288, 3714, 29245, 3555, 20328, 5172, 2288, 4032, 1829, 3794, 995, 45865, 36764, 24401, 20193, 1829, 3794, 995, 45865, 20328, 5172, 2288, 11933, 8848, 1863, 2423, 497], "avg_logprob": -0.2402146425512102, "compression_ratio": 1.9447513812154695, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 988.03, "end": 988.37, "word": "و", "probability": 0.291259765625}, {"start": 988.37, "end": 988.73, "word": " ال", "probability": 0.1845703125}, {"start": 988.73, "end": 988.99, "word": " limit", "probability": 0.7607421875}, {"start": 988.99, "end": 989.31, "word": " هذا", "probability": 0.75048828125}, {"start": 989.31, "end": 989.61, "word": " عشان", "probability": 0.8824869791666666}, {"start": 989.61, "end": 990.19, "word": " نحسبها", "probability": 0.9854736328125}, {"start": 990.19, "end": 990.89, "word": " بالجسم", "probability": 0.9111328125}, {"start": 990.89, "end": 992.59, "word": " bust", "probability": 0.2252197265625}, {"start": 992.59, "end": 993.37, "word": " مقام", "probability": 0.8544921875}, {"start": 993.37, "end": 993.75, "word": " على", "probability": 0.8173828125}, {"start": 993.75, "end": 994.89, "word": " n", "probability": 0.201904296875}, {"start": 994.89, "end": 995.53, "word": " تربية", "probability": 0.8369140625}, {"start": 995.53, "end": 996.93, "word": " ففي", "probability": 0.765625}, {"start": 996.93, "end": 997.05, "word": " ال", "probability": 0.78076171875}, {"start": 997.05, "end": 997.31, "word": " bust", "probability": 0.61083984375}, {"start": 997.31, "end": 997.85, "word": " واحد", "probability": 0.8701171875}, {"start": 997.85, "end": 998.31, "word": " واحد", "probability": 0.89697265625}, {"start": 998.31, "end": 998.81, "word": " سالب", "probability": 0.7596028645833334}, {"start": 998.81, "end": 999.23, "word": " واحد", "probability": 0.98095703125}, {"start": 999.23, "end": 999.39, "word": " على", "probability": 0.70751953125}, {"start": 999.39, "end": 999.71, "word": " n", "probability": 0.6103515625}, {"start": 999.71, "end": 1000.81, "word": " موجب", "probability": 0.9065755208333334}, {"start": 1000.81, "end": 1001.27, "word": " واحد", "probability": 0.994873046875}, {"start": 1001.27, "end": 1001.51, "word": " على", "probability": 0.90087890625}, {"start": 1001.51, "end": 1001.75, "word": " n", "probability": 0.828125}, {"start": 1001.75, "end": 1002.25, "word": " تربية", "probability": 0.9715169270833334}, {"start": 1002.25, "end": 1002.89, "word": " لإن", "probability": 0.5439453125}, {"start": 1002.89, "end": 1003.29, "word": " تقول", "probability": 0.687255859375}, {"start": 1003.29, "end": 1003.47, "word": " ال", "probability": 0.56689453125}, {"start": 1003.47, "end": 1003.95, "word": " infinity", "probability": 0.7431640625}, {"start": 1003.95, "end": 1005.39, "word": " وهذا", "probability": 0.824462890625}, {"start": 1005.39, "end": 1005.85, "word": " بطلع", "probability": 0.78955078125}, {"start": 1005.85, "end": 1006.49, "word": " واحد", "probability": 0.9912109375}, {"start": 1006.49, "end": 1006.69, "word": " على", "probability": 0.80322265625}, {"start": 1006.69, "end": 1007.21, "word": " واحد", "probability": 0.996337890625}, {"start": 1007.21, "end": 1007.69, "word": " سالب", "probability": 0.96630859375}, {"start": 1007.69, "end": 1008.11, "word": " صفر", "probability": 0.8387044270833334}, {"start": 1008.11, "end": 1008.55, "word": " موجب", "probability": 0.9716796875}, {"start": 1008.55, "end": 1009.07, "word": " صفر", "probability": 0.9873046875}, {"start": 1009.07, "end": 1010.49, "word": " ويساوي", "probability": 0.85087890625}, {"start": 1010.49, "end": 1011.03, "word": " واحد", "probability": 0.9892578125}, {"start": 1011.03, "end": 1011.87, "word": " لايساوي", "probability": 0.81767578125}, {"start": 1011.87, "end": 1012.37, "word": " صفر", "probability": 0.9607747395833334}, {"start": 1012.37, "end": 1013.91, "word": " إذن", "probability": 0.6002604166666666}, {"start": 1013.91, "end": 1014.09, "word": " ال", "probability": 0.96533203125}, {"start": 1014.09, "end": 1014.41, "word": " R", "probability": 0.650390625}], "temperature": 1.0}, {"id": 37, "seek": 104458, "start": 1015.77, "end": 1044.59, "text": "الـ R في ال limit comparison test طلعت بالساوي واحد لا يساوي سفر وانا عندى اذا since وانا عندى ال series sigma yn اللى هى sigma واحد على انتر بيان is convergent then by limit comparison test ال series sigma xn", "tokens": [6027, 39184, 497, 8978, 2423, 4948, 9660, 1500, 23032, 1211, 34268, 20666, 3794, 995, 45865, 36764, 24401, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 4032, 7649, 995, 43242, 7578, 1975, 15730, 1670, 4032, 7649, 995, 43242, 7578, 2423, 2638, 12771, 17861, 13672, 7578, 8032, 7578, 12771, 36764, 24401, 15844, 16472, 2655, 2288, 4724, 1829, 7649, 307, 9652, 6930, 550, 538, 4948, 9660, 1500, 2423, 2638, 12771, 2031, 77], "avg_logprob": -0.3020089336803981, "compression_ratio": 1.6569767441860466, "no_speech_prob": 0.0, "words": [{"start": 1015.77, "end": 1016.17, "word": "الـ", "probability": 0.686767578125}, {"start": 1016.17, "end": 1016.41, "word": " R", "probability": 0.43603515625}, {"start": 1016.41, "end": 1016.69, "word": " في", "probability": 0.80322265625}, {"start": 1016.69, "end": 1016.83, "word": " ال", "probability": 0.5283203125}, {"start": 1016.83, "end": 1016.99, "word": " limit", "probability": 0.349609375}, {"start": 1016.99, "end": 1017.65, "word": " comparison", "probability": 0.9248046875}, {"start": 1017.65, "end": 1018.23, "word": " test", "probability": 0.955078125}, {"start": 1018.23, "end": 1019.41, "word": " طلعت", "probability": 0.7334391276041666}, {"start": 1019.41, "end": 1019.91, "word": " بالساوي", "probability": 0.6396484375}, {"start": 1019.91, "end": 1020.31, "word": " واحد", "probability": 0.92333984375}, {"start": 1020.31, "end": 1020.53, "word": " لا", "probability": 0.326416015625}, {"start": 1020.53, "end": 1020.97, "word": " يساوي", "probability": 0.8836669921875}, {"start": 1020.97, "end": 1021.43, "word": " سفر", "probability": 0.9069010416666666}, {"start": 1021.43, "end": 1023.07, "word": " وانا", "probability": 0.602783203125}, {"start": 1023.07, "end": 1023.57, "word": " عندى", "probability": 0.67822265625}, {"start": 1023.57, "end": 1023.99, "word": " اذا", "probability": 0.51092529296875}, {"start": 1023.99, "end": 1024.83, "word": " since", "probability": 0.662109375}, {"start": 1024.83, "end": 1026.93, "word": " وانا", "probability": 0.8932291666666666}, {"start": 1026.93, "end": 1027.37, "word": " عندى", "probability": 0.941162109375}, {"start": 1027.37, "end": 1027.63, "word": " ال", "probability": 0.93896484375}, {"start": 1027.63, "end": 1027.97, "word": " series", "probability": 0.9345703125}, {"start": 1027.97, "end": 1028.49, "word": " sigma", "probability": 0.5927734375}, {"start": 1028.49, "end": 1029.37, "word": " yn", "probability": 0.62451171875}, {"start": 1029.37, "end": 1029.85, "word": " اللى", "probability": 0.890625}, {"start": 1029.85, "end": 1030.09, "word": " هى", "probability": 0.803466796875}, {"start": 1030.09, "end": 1030.53, "word": " sigma", "probability": 0.77099609375}, {"start": 1030.53, "end": 1031.87, "word": " واحد", "probability": 0.9599609375}, {"start": 1031.87, "end": 1032.09, "word": " على", "probability": 0.5849609375}, {"start": 1032.09, "end": 1032.73, "word": " انتر", "probability": 0.6825358072916666}, {"start": 1032.73, "end": 1033.05, "word": " بيان", "probability": 0.672607421875}, {"start": 1033.05, "end": 1033.63, "word": " is", "probability": 0.7705078125}, {"start": 1033.63, "end": 1034.73, "word": " convergent", "probability": 0.975341796875}, {"start": 1034.73, "end": 1037.83, "word": " then", "probability": 0.80859375}, {"start": 1037.83, "end": 1038.37, "word": " by", "probability": 0.93701171875}, {"start": 1038.37, "end": 1038.89, "word": " limit", "probability": 0.96826171875}, {"start": 1038.89, "end": 1039.63, "word": " comparison", "probability": 0.93798828125}, {"start": 1039.63, "end": 1040.29, "word": " test", "probability": 0.935546875}, {"start": 1040.29, "end": 1042.29, "word": " ال", "probability": 0.92626953125}, {"start": 1042.29, "end": 1042.83, "word": " series", "probability": 0.96337890625}, {"start": 1042.83, "end": 1043.61, "word": " sigma", "probability": 0.94384765625}, {"start": 1043.61, "end": 1044.59, "word": " xn", "probability": 0.880615234375}], "temperature": 1.0}, {"id": 38, "seek": 107038, "start": 1045.98, "end": 1070.38, "text": "اللي هو الحد اللي عم تبعها واحد على انتر بيه minus ان زاد واحد كون بيعجز وهو مطلوب okay إذا هنا استخدمنا ال limit كون .. لما يعجز أو يفشل ال comparison أو ال direct comparison test بنرجع إلى limit comparison test", "tokens": [6027, 20292, 31439, 21542, 3215, 13672, 1829, 6225, 2304, 6055, 3555, 3615, 11296, 36764, 24401, 15844, 16472, 2655, 2288, 4724, 1829, 3224, 3175, 16472, 30767, 18513, 36764, 24401, 9122, 11536, 4724, 40228, 7435, 11622, 37037, 2407, 3714, 9566, 1211, 37746, 1392, 11933, 15730, 34105, 44713, 9778, 40448, 8315, 2423, 4948, 9122, 11536, 4386, 5296, 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0.89501953125}, {"start": 1060.66, "end": 1061.42, "word": " استخدمنا", "probability": 0.9111328125}, {"start": 1061.42, "end": 1061.56, "word": " ال", "probability": 0.411865234375}, {"start": 1061.56, "end": 1061.8, "word": " limit", "probability": 0.9482421875}, {"start": 1061.8, "end": 1062.02, "word": " كون", "probability": 0.3798828125}, {"start": 1062.02, "end": 1062.06, "word": " ..", "probability": 0.39306640625}, {"start": 1062.06, "end": 1062.34, "word": " لما", "probability": 0.927734375}, {"start": 1062.34, "end": 1062.9, "word": " يعجز", "probability": 0.9578450520833334}, {"start": 1062.9, "end": 1063.18, "word": " أو", "probability": 0.79443359375}, {"start": 1063.18, "end": 1063.78, "word": " يفشل", "probability": 0.9864501953125}, {"start": 1063.78, "end": 1065.04, "word": " ال", "probability": 0.97314453125}, {"start": 1065.04, "end": 1065.54, "word": " comparison", "probability": 0.94482421875}, {"start": 1065.54, "end": 1065.88, "word": " أو", "probability": 0.8662109375}, {"start": 1065.88, "end": 1066.02, "word": " ال", "probability": 0.92724609375}, {"start": 1066.02, "end": 1066.26, "word": " direct", "probability": 0.892578125}, {"start": 1066.26, "end": 1066.8, "word": " comparison", "probability": 0.91357421875}, {"start": 1066.8, "end": 1067.3, "word": " test", "probability": 0.96044921875}, {"start": 1067.3, "end": 1068.04, "word": " بنرجع", "probability": 0.616455078125}, {"start": 1068.04, "end": 1068.38, "word": " إلى", "probability": 0.8017578125}, {"start": 1068.38, "end": 1069.34, "word": " limit", "probability": 0.47314453125}, {"start": 1069.34, "end": 1069.92, "word": " comparison", "probability": 0.9560546875}, {"start": 1069.92, "end": 1070.38, "word": " test", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 39, "seek": 109872, "start": 1071.9, "end": 1098.72, "text": "هنا لازم يجب ملاحظة انه اي سؤال بنحل بال comparison test ممكن حله او نطبق عليه ال limit comparison test لكن العكس ليس صحيح وبالتالي ال limit comparison test اشمل و اعام من ال direct comparison test ناخد مثال تالت واضح الحل في اي سؤال او استفسار؟", "tokens": [3224, 8315, 5296, 31377, 2304, 7251, 7435, 3555, 3714, 15040, 5016, 19913, 3660, 16472, 3224, 1975, 1829, 8608, 33604, 6027, 44945, 5016, 1211, 20666, 9660, 1500, 3714, 43020, 11331, 43761, 1975, 2407, 8717, 9566, 3555, 4587, 47356, 2423, 4948, 9660, 1500, 44381, 18863, 4117, 3794, 32239, 3794, 20328, 5016, 1829, 5016, 46599, 6027, 2655, 6027, 1829, 2423, 4948, 9660, 1500, 1975, 8592, 42213, 4032, 1975, 3615, 10943, 9154, 2423, 2047, 9660, 1500, 8717, 47283, 3215, 50113, 6027, 6055, 6027, 2655, 4032, 46958, 5016, 21542, 1211, 8978, 1975, 1829, 8608, 33604, 6027, 1975, 2407, 44713, 36178, 9640, 22807], "avg_logprob": -0.13480548028435027, "compression_ratio": 1.832512315270936, "no_speech_prob": 0.0, "words": [{"start": 1071.9, "end": 1072.6, "word": "هنا", "probability": 0.96923828125}, {"start": 1072.6, "end": 1073.02, "word": " لازم", "probability": 0.793212890625}, 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series اللي قدامك behaves like some familiar series تتصرف زي series معروفة لدينا و احنا عارف نقدر من السهل نحكم عليها هل convergent او divergent", "tokens": [28814, 15730, 11778, 16373, 15042, 8978, 3714, 34740, 7435, 37495, 22653, 11933, 15730, 16472, 2655, 37893, 6225, 9640, 5172, 6055, 25957, 1211, 2047, 9660, 6156, 995, 14851, 9778, 40448, 2423, 4948, 9660, 1500, 37037, 15730, 37893, 20328, 3615, 3555, 6055, 8592, 38688, 1829, 11778, 16373, 15042, 2423, 2638, 13672, 1829, 12174, 3215, 10943, 4117, 36896, 411, 512, 4963, 2638, 6055, 2655, 9381, 28480, 30767, 1829, 2638, 20449, 32887, 5172, 3660, 5296, 16254, 8315, 4032, 1975, 5016, 8315, 6225, 9640, 5172, 8717, 28543, 2288, 9154, 21136, 3224, 1211, 8717, 5016, 24793, 25894, 11296, 8032, 1211, 9652, 6930, 1975, 2407, 18558, 6930], "avg_logprob": -0.2388613796470189, "compression_ratio": 1.598360655737705, "no_speech_prob": 0.0, "words": [{"start": 1100.23, "end": 1100.55, "word": "إذا", "probability": 0.58648681640625}, {"start": 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"probability": 0.81103515625}, {"start": 1119.61, "end": 1119.71, "word": " احنا", "probability": 0.7915852864583334}, {"start": 1119.71, "end": 1119.93, "word": " عارف", "probability": 0.7399088541666666}, {"start": 1119.93, "end": 1120.27, "word": " نقدر", "probability": 0.8079427083333334}, {"start": 1120.27, "end": 1120.79, "word": " من", "probability": 0.90478515625}, {"start": 1120.79, "end": 1121.13, "word": " السهل", "probability": 0.9923502604166666}, {"start": 1121.13, "end": 1121.51, "word": " نحكم", "probability": 0.9137369791666666}, {"start": 1121.51, "end": 1121.87, "word": " عليها", "probability": 0.96044921875}, {"start": 1121.87, "end": 1122.09, "word": " هل", "probability": 0.59716796875}, {"start": 1122.09, "end": 1122.73, "word": " convergent", "probability": 0.7587890625}, {"start": 1122.73, "end": 1122.91, "word": " او", "probability": 0.751220703125}, {"start": 1122.91, "end": 1123.53, "word": " divergent", "probability": 0.806640625}], "temperature": 1.0}, {"id": 41, "seek": 115747, "start": 1129.83, "end": 1157.47, "text": "فلو أخدنا مثلا ال series هذه summation from n equals one to infinity ل one over square root of n plus one ف ال series .. this series behaves طبعا لما n .. when n gets large we neglect الواحد نهم الواحد", "tokens": [5172, 1211, 2407, 5551, 9778, 3215, 8315, 50113, 15040, 2423, 2638, 29538, 28811, 490, 297, 6915, 472, 281, 13202, 5296, 472, 670, 3732, 5593, 295, 297, 1804, 472, 6156, 2423, 2638, 4386, 341, 2638, 36896, 23032, 3555, 3615, 995, 5296, 15042, 297, 4386, 562, 297, 2170, 2416, 321, 17745, 2423, 14407, 24401, 8717, 16095, 2423, 14407, 24401], "avg_logprob": -0.2785560262614283, "compression_ratio": 1.3863636363636365, "no_speech_prob": 0.0, "words": [{"start": 1129.83, "end": 1130.57, "word": "فلو", "probability": 0.6029459635416666}, {"start": 1130.57, "end": 1130.99, "word": " أخدنا", "probability": 0.861572265625}, {"start": 1130.99, "end": 1131.35, "word": " مثلا", "probability": 0.939697265625}, {"start": 1131.35, "end": 1131.61, "word": " ال", "probability": 0.72998046875}, {"start": 1131.61, "end": 1131.87, "word": " series", "probability": 0.61669921875}, {"start": 1131.87, "end": 1132.31, "word": " هذه", "probability": 0.5458984375}, {"start": 1132.31, "end": 1132.87, "word": " summation", "probability": 0.1983642578125}, {"start": 1132.87, "end": 1137.37, "word": " from", "probability": 0.64892578125}, {"start": 1137.37, "end": 1137.71, "word": " n", "probability": 0.74072265625}, {"start": 1137.71, "end": 1138.19, "word": " equals", "probability": 0.429931640625}, {"start": 1138.19, "end": 1138.53, "word": " one", "probability": 0.7626953125}, {"start": 1138.53, "end": 1138.71, "word": " to", "probability": 0.88671875}, {"start": 1138.71, "end": 1139.29, "word": " infinity", "probability": 0.84228515625}, {"start": 1139.29, "end": 1139.59, "word": " ل", "probability": 0.69189453125}, {"start": 1139.59, "end": 1140.01, "word": " one", "probability": 0.677734375}, {"start": 1140.01, "end": 1141.75, "word": " over", "probability": 0.90478515625}, {"start": 1141.75, "end": 1142.25, "word": " square", "probability": 0.7802734375}, {"start": 1142.25, "end": 1142.79, "word": " root", "probability": 0.91064453125}, {"start": 1142.79, "end": 1143.63, "word": " of", "probability": 0.96875}, {"start": 1143.63, "end": 1144.53, "word": " n", "probability": 0.771484375}, {"start": 1144.53, "end": 1144.95, "word": " plus", "probability": 0.9482421875}, {"start": 1144.95, "end": 1145.33, "word": " one", "probability": 0.951171875}, {"start": 1145.33, "end": 1148.53, "word": " ف", "probability": 0.91650390625}, {"start": 1148.53, "end": 1148.69, "word": " ال", "probability": 0.41552734375}, {"start": 1148.69, "end": 1149.03, "word": " series", "probability": 0.95751953125}, {"start": 1149.03, "end": 1149.19, "word": " ..", "probability": 0.1943359375}, {"start": 1149.19, "end": 1149.37, "word": " this", "probability": 0.8369140625}, {"start": 1149.37, "end": 1149.77, "word": " series", "probability": 0.93115234375}, {"start": 1149.77, "end": 1150.39, "word": " behaves", "probability": 0.796875}, {"start": 1150.39, "end": 1150.93, "word": " طبعا", "probability": 0.974853515625}, {"start": 1150.93, "end": 1151.25, "word": " لما", "probability": 0.822509765625}, {"start": 1151.25, "end": 1151.55, "word": " n", "probability": 0.63623046875}, {"start": 1151.55, "end": 1151.91, "word": " ..", "probability": 0.77490234375}, {"start": 1151.91, "end": 1151.97, "word": " when", "probability": 0.6416015625}, {"start": 1151.97, "end": 1152.25, "word": " n", "probability": 0.9736328125}, {"start": 1152.25, "end": 1152.59, "word": " gets", "probability": 0.81396484375}, {"start": 1152.59, "end": 1153.13, "word": " large", "probability": 0.970703125}, {"start": 1153.13, "end": 1154.41, "word": " we", "probability": 0.482421875}, {"start": 1154.41, "end": 1155.07, "word": " neglect", "probability": 0.92529296875}, {"start": 1155.07, "end": 1155.95, "word": " الواحد", "probability": 0.93798828125}, {"start": 1155.95, "end": 1156.89, "word": " نهم", "probability": 0.6534423828125}, {"start": 1156.89, "end": 1157.47, "word": " الواحد", "probability": 0.8943684895833334}], "temperature": 1.0}, {"id": 42, "seek": 117121, "start": 1158.15, "end": 1171.21, "text": "وهذه السيريز تتصرف من حيث التقارب والتباعد مثل سيجما واحد على جذر الان", "tokens": [2407, 3224, 24192, 21136, 13546, 1829, 11622, 6055, 2655, 9381, 28480, 9154, 11331, 1829, 12984, 16712, 4587, 9640, 3555, 16070, 2655, 3555, 995, 22488, 50113, 1211, 8608, 1829, 7435, 15042, 36764, 24401, 15844, 10874, 8848, 2288, 2423, 7649], "avg_logprob": -0.28826120725044835, "compression_ratio": 1.3617021276595744, "no_speech_prob": 0.0, "words": [{"start": 1158.15, "end": 1159.33, "word": "وهذه", "probability": 0.3509928385416667}, {"start": 1159.33, "end": 1159.87, "word": " السيريز", "probability": 0.76318359375}, {"start": 1159.87, "end": 1161.39, "word": " تتصرف", "probability": 0.8992919921875}, {"start": 1161.39, "end": 1162.33, "word": " من", "probability": 0.93603515625}, {"start": 1162.33, "end": 1162.75, "word": " حيث", "probability": 0.9191080729166666}, {"start": 1162.75, "end": 1163.39, "word": " التقارب", "probability": 0.9940185546875}, {"start": 1163.39, "end": 1164.31, "word": " والتباعد", "probability": 0.9224609375}, {"start": 1164.31, "end": 1166.25, "word": " مثل", "probability": 0.895263671875}, {"start": 1166.25, "end": 1169.19, "word": " سيجما", "probability": 0.6455078125}, {"start": 1169.19, "end": 1169.83, "word": " واحد", "probability": 0.912841796875}, {"start": 1169.83, "end": 1170.09, "word": " على", "probability": 0.74755859375}, {"start": 1170.09, "end": 1170.75, "word": " جذر", "probability": 0.79736328125}, {"start": 1170.75, "end": 1171.21, "word": " الان", "probability": 0.4931640625}], "temperature": 1.0}, {"id": 43, "seek": 120173, "start": 1178.39, "end": 1201.73, "text": "طيب can we السؤال يتفرج نفسه can we use direct comparison test للإجابة على السؤال هذا بنلاحظ أن n زائد 1 أكبر منها ويساوي n لكل n هذا بيقدر أن واحد", "tokens": [9566, 1829, 3555, 393, 321, 2423, 3794, 33604, 6027, 7251, 2655, 5172, 47341, 8717, 36178, 3224, 393, 321, 764, 2047, 9660, 1500, 24976, 28814, 7435, 16758, 3660, 15844, 21136, 33604, 6027, 23758, 44945, 15040, 5016, 19913, 14739, 297, 30767, 16373, 3215, 502, 5551, 4117, 26890, 9154, 11296, 4032, 1829, 3794, 995, 45865, 297, 5296, 28820, 297, 23758, 4724, 1829, 28543, 2288, 14739, 36764, 24401], "avg_logprob": -0.2879807692307692, "compression_ratio": 1.392638036809816, "no_speech_prob": 0.0, "words": [{"start": 1178.39, "end": 1179.39, "word": "طيب", "probability": 0.791015625}, {"start": 1179.39, "end": 1180.39, "word": " can", "probability": 0.278564453125}, {"start": 1180.39, "end": 1180.83, "word": " we", "probability": 0.97021484375}, {"start": 1180.83, "end": 1182.07, "word": " السؤال", "probability": 0.77801513671875}, {"start": 1182.07, "end": 1182.41, "word": " يتفرج", "probability": 0.40313720703125}, {"start": 1182.41, "end": 1182.87, "word": " نفسه", "probability": 0.9166666666666666}, {"start": 1182.87, "end": 1183.35, "word": " can", "probability": 0.66455078125}, {"start": 1183.35, "end": 1183.75, "word": " we", "probability": 0.9736328125}, {"start": 1183.75, "end": 1185.63, "word": " use", "probability": 0.84375}, {"start": 1185.63, "end": 1186.39, "word": " direct", "probability": 0.8876953125}, {"start": 1186.39, "end": 1187.35, "word": " comparison", "probability": 0.87841796875}, {"start": 1187.35, "end": 1187.95, "word": " test", "probability": 0.9033203125}, {"start": 1187.95, "end": 1191.67, "word": " للإجابة", "probability": 0.9095703125}, {"start": 1191.67, "end": 1191.79, "word": " على", "probability": 0.8193359375}, {"start": 1191.79, "end": 1192.23, "word": " السؤال", "probability": 0.9944661458333334}, {"start": 1192.23, "end": 1192.59, "word": " هذا", "probability": 0.92529296875}, {"start": 1192.59, "end": 1193.27, "word": " بنلاحظ", "probability": 0.81365966796875}, {"start": 1193.27, "end": 1193.45, "word": " أن", "probability": 0.50732421875}, {"start": 1193.45, "end": 1193.93, "word": " n", "probability": 0.1859130859375}, {"start": 1193.93, "end": 1194.85, "word": " زائد", "probability": 0.7708333333333334}, {"start": 1194.85, "end": 1195.39, "word": " 1", "probability": 0.6787109375}, {"start": 1195.39, "end": 1196.67, "word": " أكبر", "probability": 0.9680989583333334}, {"start": 1196.67, "end": 1197.09, "word": " منها", "probability": 0.888671875}, {"start": 1197.09, "end": 1197.77, "word": " ويساوي", "probability": 0.9072265625}, {"start": 1197.77, "end": 1198.07, "word": " n", "probability": 0.6484375}, {"start": 1198.07, "end": 1198.55, "word": " لكل", "probability": 0.97412109375}, {"start": 1198.55, "end": 1198.89, "word": " n", "probability": 0.9072265625}, {"start": 1198.89, "end": 1200.35, "word": " هذا", "probability": 0.83935546875}, {"start": 1200.35, "end": 1200.87, "word": " بيقدر", "probability": 0.797119140625}, {"start": 1200.87, "end": 1201.05, "word": " أن", "probability": 0.52685546875}, {"start": 1201.05, "end": 1201.73, "word": " واحد", "probability": 0.7308349609375}], "temperature": 1.0}, {"id": 44, "seek": 122463, "start": 1203.21, "end": 1224.63, "text": "وبالتالي الجدر التربيعي ل N زائد واحد أكبر من أو ساوي جدر ال N لكل N وبالتالي هذا بيقدي أن واحد على الجدر التربيعي ل N زائد واحد أقل من أو ساوي واحد على جدر ال N لكل N", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 7435, 3215, 2288, 16712, 2288, 21292, 3615, 1829, 5296, 426, 30767, 16373, 3215, 36764, 24401, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 10874, 3215, 2288, 2423, 426, 5296, 28820, 426, 46599, 6027, 2655, 6027, 1829, 23758, 4724, 1829, 4587, 16254, 14739, 36764, 24401, 15844, 25724, 3215, 2288, 16712, 2288, 21292, 3615, 1829, 5296, 426, 30767, 16373, 3215, 36764, 24401, 5551, 4587, 1211, 9154, 34051, 8608, 995, 45865, 36764, 24401, 15844, 10874, 3215, 2288, 2423, 426, 5296, 28820, 426], "avg_logprob": -0.1830486970585446, "compression_ratio": 2.3015873015873014, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1203.2099999999998, "end": 1204.09, "word": "وبالتالي", "probability": 0.89052734375}, {"start": 1204.09, "end": 1204.81, "word": " الجدر", "probability": 0.724365234375}, {"start": 1204.81, "end": 1206.19, "word": " التربيعي", "probability": 0.6420654296875}, {"start": 1206.19, "end": 1206.31, "word": " ل", "probability": 0.94189453125}, {"start": 1206.31, "end": 1206.49, "word": " N", "probability": 0.276123046875}, {"start": 1206.49, "end": 1206.95, "word": " زائد", "probability": 0.7498372395833334}, {"start": 1206.95, "end": 1207.33, "word": " واحد", "probability": 0.923095703125}, {"start": 1207.33, "end": 1207.81, "word": " أكبر", "probability": 0.8728841145833334}, {"start": 1207.81, "end": 1208.01, "word": " من", "probability": 0.9775390625}, {"start": 1208.01, "end": 1208.19, "word": " أو", "probability": 0.90966796875}, {"start": 1208.19, "end": 1208.65, "word": " ساوي", "probability": 0.8621419270833334}, {"start": 1208.65, "end": 1209.13, "word": " جدر", "probability": 0.92919921875}, {"start": 1209.13, "end": 1209.27, "word": " ال", "probability": 0.875}, {"start": 1209.27, "end": 1209.43, "word": " N", "probability": 0.60595703125}, {"start": 1209.43, "end": 1209.87, "word": " لكل", "probability": 0.96923828125}, {"start": 1209.87, "end": 1210.11, "word": " N", "probability": 0.70263671875}, {"start": 1210.11, "end": 1211.77, "word": " وبالتالي", "probability": 0.90234375}, {"start": 1211.77, "end": 1212.05, "word": " هذا", "probability": 0.9111328125}, {"start": 1212.05, "end": 1212.63, "word": " بيقدي", "probability": 0.69512939453125}, {"start": 1212.63, "end": 1212.99, "word": " أن", "probability": 0.391357421875}, {"start": 1212.99, "end": 1214.69, "word": " واحد", "probability": 0.7283935546875}, {"start": 1214.69, "end": 1215.07, "word": " على", "probability": 0.70654296875}, {"start": 1215.07, "end": 1216.59, "word": " الجدر", "probability": 0.9181315104166666}, {"start": 1216.59, "end": 1217.43, "word": " التربيعي", "probability": 0.97802734375}, {"start": 1217.43, "end": 1217.65, "word": " ل", "probability": 0.97021484375}, {"start": 1217.65, "end": 1217.91, "word": " N", "probability": 0.931640625}, {"start": 1217.91, "end": 1218.49, "word": " زائد", "probability": 0.970703125}, {"start": 1218.49, "end": 1219.09, "word": " واحد", "probability": 0.992431640625}, {"start": 1219.09, "end": 1221.27, "word": " أقل", "probability": 0.94287109375}, {"start": 1221.27, "end": 1221.49, "word": " من", "probability": 0.9716796875}, {"start": 1221.49, "end": 1221.73, "word": " أو", "probability": 0.8310546875}, {"start": 1221.73, "end": 1222.23, "word": " ساوي", "probability": 0.94384765625}, {"start": 1222.23, "end": 1222.71, "word": " واحد", "probability": 0.982421875}, {"start": 1222.71, "end": 1222.91, "word": " على", "probability": 0.7783203125}, {"start": 1222.91, "end": 1223.41, "word": " جدر", "probability": 0.96337890625}, {"start": 1223.41, "end": 1223.57, "word": " ال", "probability": 0.939453125}, {"start": 1223.57, "end": 1223.83, "word": " N", "probability": 0.94873046875}, {"start": 1223.83, "end": 1224.35, "word": " لكل", "probability": 0.98876953125}, {"start": 1224.35, "end": 1224.63, "word": " N", "probability": 0.84912109375}], "temperature": 1.0}, {"id": 45, "seek": 124107, "start": 1226.69, "end": 1241.07, "text": "و احنا عارفين ان ال series هذه divergent لأنها P series و ال P بساوي نص أصغر من واحد و هاد ال series أصغر منها أو أصغر منها و يساويها", "tokens": [2407, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 2423, 2638, 29538, 18558, 6930, 5296, 33456, 11296, 430, 2638, 4032, 2423, 430, 4724, 3794, 995, 45865, 8717, 9381, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 4032, 8032, 18513, 2423, 2638, 5551, 9381, 17082, 2288, 9154, 11296, 34051, 5551, 9381, 17082, 2288, 9154, 11296, 4032, 7251, 3794, 995, 45865, 11296], 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{"start": 1946.0, "end": 1946.22, "word": " عن", "probability": 0.99462890625}, {"start": 1946.22, "end": 1946.88, "word": " واحد", "probability": 0.970458984375}, {"start": 1946.88, "end": 1947.34, "word": " في", "probability": 0.73193359375}, {"start": 1947.34, "end": 1947.98, "word": " اتنين", "probability": 0.903076171875}, {"start": 1947.98, "end": 1948.98, "word": " في", "probability": 0.90576171875}, {"start": 1948.98, "end": 1949.74, "word": " تلاتة", "probability": 0.9464111328125}, {"start": 1949.74, "end": 1950.22, "word": " الى", "probability": 0.8212890625}, {"start": 1950.22, "end": 1950.62, "word": " n", "probability": 0.73583984375}, {"start": 1950.62, "end": 1951.52, "word": " سالب", "probability": 0.8981119791666666}, {"start": 1951.52, "end": 1952.24, "word": " اتنين", "probability": 0.972412109375}, {"start": 1952.24, "end": 1953.34, "word": " في", "probability": 0.9150390625}, {"start": 1953.34, "end": 1953.6, "word": " n", "probability": 0.8046875}, {"start": 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of", "probability": 0.83056640625}, {"start": 2319.75, "end": 2321.73, "word": " a", "probability": 0.96337890625}, {"start": 2321.73, "end": 2322.67, "word": " convergent", "probability": 0.915283203125}, {"start": 2322.67, "end": 2324.57, "word": " of", "probability": 0.62060546875}, {"start": 2324.57, "end": 2324.81, "word": " a", "probability": 0.97998046875}, {"start": 2324.81, "end": 2325.63, "word": " convergent", "probability": 0.970947265625}, {"start": 2325.63, "end": 2326.39, "word": " series", "probability": 0.90966796875}, {"start": 2326.39, "end": 2328.81, "word": " sigma", "probability": 0.55126953125}, {"start": 2328.81, "end": 2329.71, "word": " xn", "probability": 0.54150390625}, {"start": 2329.71, "end": 2330.65, "word": " and", "probability": 0.9306640625}, {"start": 2330.65, "end": 2331.29, "word": " a", "probability": 0.9755859375}, {"start": 2331.29, "end": 2333.55, "word": " divergent", "probability": 0.907470703125}], "temperature": 1.0}, {"id": 87, "seek": 236244, "start": 2343.07, "end": 2362.45, "text": "بحيث ان المجموعة تبع ال two series يكون convergent is convergent explain وضحي الإجابة", "tokens": [3555, 5016, 1829, 12984, 16472, 9673, 7435, 2304, 2407, 27884, 6055, 3555, 3615, 2423, 732, 2638, 7251, 30544, 9652, 6930, 307, 9652, 6930, 2903, 4032, 11242, 5016, 1829, 33688, 7435, 16758, 3660], "avg_logprob": -0.34990530303030304, "compression_ratio": 1.1333333333333333, "no_speech_prob": 0.0, "words": [{"start": 2343.0699999999997, "end": 2344.47, "word": "بحيث", "probability": 0.625213623046875}, {"start": 2344.47, "end": 2345.01, "word": " ان", "probability": 0.38232421875}, {"start": 2345.01, "end": 2346.01, "word": " المجموعة", "probability": 0.8548828125}, {"start": 2346.01, "end": 2346.39, "word": " تبع", "probability": 0.8527018229166666}, {"start": 2346.39, "end": 2346.57, "word": " ال", "probability": 0.74169921875}, {"start": 2346.57, "end": 2346.71, "word": " two", "probability": 0.4052734375}, {"start": 2346.71, "end": 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-0.3342014017204444, "compression_ratio": 1.5276073619631902, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2425.4500000000003, "end": 2426.13, "word": "يوضح", "probability": 0.9110107421875}, {"start": 2426.13, "end": 2426.73, "word": " صحة", "probability": 0.9923502604166666}, {"start": 2426.73, "end": 2426.91, "word": " ال", "probability": 0.798828125}, {"start": 2426.91, "end": 2426.99, "word": " ..", "probability": 0.71240234375}, {"start": 2426.99, "end": 2427.57, "word": " الكلام", "probability": 0.87255859375}, {"start": 2427.57, "end": 2427.59, "word": " هذه", "probability": 0.1337890625}, {"start": 2427.59, "end": 2427.59, "word": " ال", "probability": 0.406494140625}, {"start": 2427.59, "end": 2427.89, "word": " example", "probability": 0.322509765625}, {"start": 2427.89, "end": 2428.37, "word": " مثلا", "probability": 0.97509765625}, {"start": 2428.37, "end": 2428.89, "word": " نخدها", "probability": 0.696807861328125}, {"start": 2428.89, "end": 2429.11, 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"probability": 0.9169921875}, {"start": 2453.36, "end": 2454.18, "word": " كل", "probability": 0.556640625}, {"start": 2454.18, "end": 2454.46, "word": " ذات", "probability": 0.373138427734375}, {"start": 2454.46, "end": 2455.52, "word": " يسار", "probability": 0.5599772135416666}, {"start": 2455.52, "end": 2456.0, "word": " سيجما", "probability": 0.8804931640625}, {"start": 2456.0, "end": 2456.52, "word": " واحد", "probability": 0.977294921875}, {"start": 2456.52, "end": 2456.74, "word": " على", "probability": 0.88427734375}, {"start": 2456.74, "end": 2457.14, "word": " ان", "probability": 0.88818359375}, {"start": 2457.14, "end": 2457.74, "word": " تربية", "probability": 0.9757486979166666}, {"start": 2457.74, "end": 2458.14, "word": " كل", "probability": 0.978515625}, {"start": 2458.14, "end": 2458.58, "word": " بيرز", "probability": 0.4945475260416667}], "temperature": 1.0}, {"id": 92, "seek": 247869, "start": 2460.98, "end": 2478.7, "text": "لأن هذه P series و ال P بيساوي اتنين اكبر من واحد، صح؟ والتانية الواحدة الجدر الأن نخدها YM بيساوي واحد على الجدر الأن بتصير أص نص، طيب، بتصير سماشة للواحد", "tokens": [1211, 33456, 29538, 430, 2638, 4032, 2423, 430, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 4117, 26890, 9154, 36764, 24401, 12399, 20328, 5016, 22807, 16070, 2655, 7649, 10632, 2423, 14407, 24401, 3660, 25724, 3215, 2288, 16247, 1863, 8717, 9778, 3215, 11296, 398, 44, 4724, 1829, 3794, 995, 45865, 36764, 24401, 15844, 25724, 3215, 2288, 16247, 1863, 39894, 9381, 13546, 5551, 9381, 8717, 9381, 12399, 23032, 1829, 3555, 12399, 39894, 9381, 13546, 8608, 2304, 33599, 3660, 24976, 14407, 24401], "avg_logprob": -0.24256859465343197, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 2460.98, "end": 2461.4, "word": "لأن", "probability": 0.877197265625}, {"start": 2461.4, "end": 2461.74, "word": " هذه", "probability": 0.389404296875}, {"start": 2461.74, "end": 2462.0, "word": " P", "probability": 0.88427734375}, 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{"start": 2467.94, "end": 2468.76, "word": " الجدر", "probability": 0.8868815104166666}, {"start": 2468.76, "end": 2469.12, "word": " الأن", "probability": 0.77685546875}, {"start": 2469.12, "end": 2469.78, "word": " نخدها", "probability": 0.73455810546875}, {"start": 2469.78, "end": 2470.96, "word": " YM", "probability": 0.2811279296875}, {"start": 2470.96, "end": 2471.76, "word": " بيساوي", "probability": 0.97548828125}, {"start": 2471.76, "end": 2472.5, "word": " واحد", "probability": 0.96484375}, {"start": 2472.5, "end": 2472.7, "word": " على", "probability": 0.79736328125}, {"start": 2472.7, "end": 2473.12, "word": " الجدر", "probability": 0.8963216145833334}, {"start": 2473.12, "end": 2473.46, "word": " الأن", "probability": 0.93798828125}, {"start": 2473.46, "end": 2474.46, "word": " بتصير", "probability": 0.7462565104166666}, {"start": 2474.46, "end": 2474.74, "word": " أص", "probability": 0.5252685546875}, {"start": 2474.74, "end": 2475.78, "word": " نص،", "probability": 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impossible لبرهان أو لثبات ذلك if if this", "tokens": [28814, 1863, 2423, 1867, 2423, 1867, 307, 572, 20193, 7251, 43020, 7251, 3615, 9566, 7578, 50113, 6027, 15844, 732, 2638, 36764, 24401, 3660, 9652, 6930, 16070, 2655, 7649, 10632, 18558, 6930, 3714, 7435, 2304, 2407, 27884, 39894, 9566, 1211, 3615, 9652, 6930, 3714, 14851, 5016, 26895, 341, 307, 6243, 5296, 26890, 3224, 7649, 34051, 5296, 12984, 3555, 9307, 29910, 23275, 498, 498, 341], "avg_logprob": -0.26879882952198386, "compression_ratio": 1.4195402298850575, "no_speech_prob": 0.0, "words": [{"start": 2708.82, "end": 2709.5, "word": "إن", "probability": 0.41064453125}, {"start": 2709.5, "end": 2709.96, "word": " ال", "probability": 0.42138671875}, {"start": 2709.96, "end": 2710.7, "word": " answer", "probability": 0.4892578125}, {"start": 2710.7, "end": 2713.54, "word": " ال", "probability": 0.30029296875}, {"start": 2713.54, "end": 2714.1, "word": " answer", "probability": 0.9814453125}, {"start": 2714.1, "end": 2714.74, 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0.410400390625}, {"start": 2750.91, "end": 2751.73, "word": " convergent", "probability": 0.825927734375}, {"start": 2751.73, "end": 2751.97, "word": " و", "probability": 0.88671875}, {"start": 2751.97, "end": 2752.23, "word": " series", "probability": 0.66455078125}, {"start": 2752.23, "end": 2752.93, "word": " divergent", "probability": 0.86279296875}, {"start": 2752.93, "end": 2753.09, "word": " و", "probability": 0.98388671875}, {"start": 2753.09, "end": 2753.49, "word": " مجموعة", "probability": 0.8060546875}, {"start": 2753.49, "end": 2754.39, "word": " convergent", "probability": 0.84228515625}, {"start": 2754.39, "end": 2757.71, "word": " then", "probability": 0.2137451171875}, {"start": 2757.71, "end": 2759.67, "word": " we", "probability": 0.82080078125}, {"start": 2759.67, "end": 2760.63, "word": " would", "probability": 0.97802734375}, {"start": 2760.63, "end": 2761.61, "word": " have", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 105, "seek": 278943, "start": 2763.89, "end": 2789.43, "text": "إنه الـ series sigma yn اللي احنا فرضين انها divergent اللي هي بساوي sigma xn زائد yn minus sigma xn احنا قلنا لو هذا كان true معناته ال series هذه convergent معناته هذه convergent ومن الفرض هذه convergent", "tokens": [28814, 1863, 3224, 2423, 39184, 2638, 12771, 17861, 13672, 1829, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 11296, 18558, 6930, 13672, 1829, 39896, 4724, 3794, 995, 45865, 12771, 2031, 77, 30767, 16373, 3215, 17861, 3175, 12771, 2031, 77, 1975, 5016, 8315, 12174, 1211, 8315, 45164, 23758, 25961, 2074, 20449, 8315, 47395, 2423, 2638, 29538, 9652, 6930, 20449, 8315, 47395, 29538, 9652, 6930, 4032, 27842, 27188, 43042, 29538, 9652, 6930], "avg_logprob": -0.25982144006661007, "compression_ratio": 1.7575757575757576, "no_speech_prob": 0.0, "words": [{"start": 2763.89, "end": 2764.55, "word": "إنه", "probability": 0.41717529296875}, {"start": 2764.55, "end": 2764.99, "word": " الـ", "probability": 0.66259765625}, {"start": 2764.99, "end": 2765.39, "word": " series", "probability": 0.451416015625}, {"start": 2765.39, "end": 2766.05, "word": " sigma", "probability": 0.54638671875}, {"start": 2766.05, "end": 2766.63, "word": " yn", "probability": 0.73583984375}, {"start": 2766.63, "end": 2767.75, "word": " اللي", "probability": 0.751708984375}, {"start": 2767.75, "end": 2767.95, "word": " احنا", "probability": 0.8580729166666666}, {"start": 2767.95, "end": 2768.39, "word": " فرضين", "probability": 0.98095703125}, {"start": 2768.39, "end": 2768.59, "word": " انها", "probability": 0.6190185546875}, {"start": 2768.59, "end": 2769.39, "word": " divergent", "probability": 0.780517578125}, {"start": 2769.39, "end": 2770.41, "word": " اللي", "probability": 0.8427734375}, {"start": 2770.41, "end": 2770.57, "word": " هي", "probability": 0.64599609375}, {"start": 2770.57, "end": 2771.15, "word": " بساوي", "probability": 0.70220947265625}, {"start": 2771.15, "end": 2771.63, "word": " sigma", "probability": 0.623046875}, {"start": 2771.63, "end": 2772.69, "word": " xn", "probability": 0.87353515625}, {"start": 2772.69, "end": 2773.41, "word": " زائد", "probability": 0.70068359375}, {"start": 2773.41, "end": 2774.01, "word": " yn", "probability": 0.97314453125}, {"start": 2774.01, "end": 2775.65, "word": " minus", "probability": 0.86181640625}, {"start": 2775.65, "end": 2777.99, "word": " sigma", "probability": 0.94482421875}, {"start": 2777.99, "end": 2780.07, "word": " xn", "probability": 0.98193359375}, {"start": 2780.07, "end": 2780.61, "word": " احنا", "probability": 0.93505859375}, {"start": 2780.61, "end": 2780.91, "word": " قلنا", "probability": 0.9122721354166666}, {"start": 2780.91, "end": 2781.13, "word": " لو", "probability": 0.875}, {"start": 2781.13, "end": 2781.45, "word": " هذا", "probability": 0.78271484375}, {"start": 2781.45, "end": 2781.81, "word": " كان", "probability": 0.98486328125}, {"start": 2781.81, "end": 2782.27, "word": " true", "probability": 0.96240234375}, {"start": 2782.27, "end": 2782.99, "word": " معناته", "probability": 0.8218587239583334}, {"start": 2782.99, "end": 2783.29, "word": " ال", "probability": 0.85107421875}, {"start": 2783.29, "end": 2783.65, "word": " series", "probability": 0.8466796875}, {"start": 2783.65, "end": 2783.97, "word": " هذه", "probability": 0.4755859375}, {"start": 2783.97, "end": 2784.75, "word": " convergent", "probability": 0.83837890625}, {"start": 2784.75, "end": 2786.05, "word": " معناته", "probability": 0.93115234375}, {"start": 2786.05, "end": 2786.43, "word": " هذه", "probability": 0.8642578125}, {"start": 2786.43, "end": 2787.33, "word": " convergent", "probability": 0.89013671875}, {"start": 2787.33, "end": 2787.69, "word": " ومن", "probability": 0.734130859375}, {"start": 2787.69, "end": 2788.17, "word": " الفرض", "probability": 0.95849609375}, {"start": 2788.17, "end": 2788.55, "word": " هذه", "probability": 0.86865234375}, {"start": 2788.55, "end": 2789.43, "word": " convergent", "probability": 0.9375}], "temperature": 1.0}, {"id": 106, "seek": 281043, "start": 2790.75, "end": 2810.43, "text": "والفرق بين two convergent series is convergent، إذن هذا هتطلع .. إذن الفرق هيكون convergent وبالتالي إذن ال series sigma yn is convergent، وهذا contradiction لإن احنا فرضين أنها divergent", "tokens": [2407, 6027, 5172, 2288, 4587, 49374, 732, 9652, 6930, 2638, 307, 9652, 6930, 12399, 11933, 8848, 1863, 23758, 8032, 2655, 9566, 1211, 3615, 4386, 11933, 8848, 1863, 27188, 2288, 4587, 39896, 30544, 9652, 6930, 4032, 3555, 6027, 2655, 6027, 1829, 11933, 8848, 1863, 2423, 2638, 12771, 17861, 307, 9652, 6930, 12399, 37037, 15730, 34937, 5296, 28814, 1863, 1975, 5016, 8315, 6156, 43042, 9957, 14739, 11296, 18558, 6930], "avg_logprob": -0.2867647014996585, "compression_ratio": 1.5644171779141105, "no_speech_prob": 0.0, "words": [{"start": 2790.75, "end": 2791.45, "word": "والفرق", "probability": 0.827001953125}, {"start": 2791.45, "end": 2791.73, "word": " بين", "probability": 0.9365234375}, {"start": 2791.73, "end": 2791.95, "word": " two", "probability": 0.75732421875}, {"start": 2791.95, "end": 2792.61, "word": " convergent", "probability": 0.8154296875}, {"start": 2792.61, "end": 2793.19, "word": " series", "probability": 0.89990234375}, {"start": 2793.19, "end": 2794.11, "word": " is", "probability": 0.619140625}, {"start": 2794.11, "end": 2794.99, "word": " convergent،", "probability": 0.76513671875}, {"start": 2794.99, "end": 2795.25, "word": " إذن", "probability": 0.5977376302083334}, {"start": 2795.25, "end": 2795.45, "word": " هذا", "probability": 0.315673828125}, {"start": 2795.45, "end": 2796.79, "word": " هتطلع", "probability": 0.89384765625}, {"start": 2796.79, "end": 2796.83, "word": " ..", "probability": 0.458251953125}, {"start": 2796.83, "end": 2797.43, "word": " إذن", "probability": 0.7718098958333334}, {"start": 2797.43, "end": 2798.33, "word": " الفرق", "probability": 0.9833984375}, {"start": 2798.33, "end": 2798.67, "word": " هيكون", "probability": 0.800048828125}, {"start": 2798.67, "end": 2799.31, "word": " convergent", "probability": 0.842529296875}, {"start": 2799.31, "end": 2801.51, "word": " وبالتالي", "probability": 0.8523356119791666}, {"start": 2801.51, "end": 2801.93, "word": " إذن", "probability": 0.7239583333333334}, {"start": 2801.93, "end": 2802.23, "word": " ال", "probability": 0.9453125}, {"start": 2802.23, "end": 2802.59, "word": " series", "probability": 0.91162109375}, {"start": 2802.59, "end": 2803.15, "word": " sigma", "probability": 0.59228515625}, {"start": 2803.15, "end": 2803.83, "word": " yn", "probability": 0.73486328125}, {"start": 2803.83, "end": 2805.15, "word": " is", "probability": 0.9306640625}, {"start": 2805.15, "end": 2806.83, "word": " convergent،", "probability": 0.7925618489583334}, {"start": 2806.83, "end": 2807.19, "word": " وهذا", "probability": 0.7099609375}, {"start": 2807.19, "end": 2807.91, "word": " contradiction", "probability": 0.6962890625}, {"start": 2807.91, "end": 2808.29, "word": " لإن", "probability": 0.7911783854166666}, {"start": 2808.29, "end": 2808.47, "word": " احنا", "probability": 0.8434244791666666}, {"start": 2808.47, "end": 2808.93, "word": " فرضين", "probability": 0.9837239583333334}, {"start": 2808.93, "end": 2809.19, "word": " أنها", "probability": 0.6798095703125}, {"start": 2809.19, "end": 2810.43, "word": " divergent", "probability": 0.60614013671875}], "temperature": 1.0}, {"id": 107, "seek": 283016, "start": 2811.76, "end": 2830.16, "text": "هذا مش ممكن يكون true عشان هي كانت كتبت if it were true مستحيل ..مستحيل مش if it was true okay طبعا اذا انا ساطيع اعطاء مثال يعطيني المواصفات هذه بالمرة", "tokens": [3224, 15730, 37893, 3714, 43020, 7251, 30544, 2074, 6225, 8592, 7649, 39896, 25961, 2655, 9122, 2655, 3555, 2655, 498, 309, 645, 2074, 3714, 14851, 5016, 26895, 4386, 2304, 14851, 5016, 26895, 37893, 498, 309, 390, 2074, 1392, 23032, 3555, 3615, 995, 1975, 15730, 1975, 8315, 8608, 41193, 40228, 1975, 3615, 9566, 16606, 50113, 6027, 37495, 9566, 1829, 22653, 9673, 2407, 33546, 5172, 9307, 29538, 20666, 2304, 25720], "avg_logprob": -0.18853400143630364, "compression_ratio": 1.4695121951219512, "no_speech_prob": 0.0, "words": [{"start": 2811.76, "end": 2812.34, "word": "هذا", "probability": 0.947998046875}, {"start": 2812.34, "end": 2812.66, "word": " مش", "probability": 0.98681640625}, {"start": 2812.66, "end": 2813.22, "word": " ممكن", "probability": 0.991943359375}, {"start": 2813.22, "end": 2813.78, "word": " يكون", "probability": 0.996337890625}, {"start": 2813.78, "end": 2814.32, "word": " true", "probability": 0.97900390625}, {"start": 2814.32, "end": 2815.7, "word": " عشان", "probability": 0.9267578125}, {"start": 2815.7, "end": 2815.82, "word": " هي", "probability": 0.87451171875}, {"start": 2815.82, "end": 2816.04, "word": " كانت", "probability": 0.947509765625}, {"start": 2816.04, "end": 2816.64, "word": " كتبت", "probability": 0.864990234375}, {"start": 2816.64, "end": 2816.96, "word": " if", "probability": 0.98046875}, {"start": 2816.96, "end": 2817.36, "word": " it", "probability": 0.9716796875}, {"start": 2817.36, "end": 2817.78, "word": " were", "probability": 0.91015625}, {"start": 2817.78, "end": 2818.36, "word": " true", "probability": 0.99365234375}, {"start": 2818.36, "end": 2819.56, "word": " مستحيل", "probability": 0.793060302734375}, {"start": 2819.56, "end": 2820.44, "word": " ..مستحيل", "probability": 0.781591796875}, {"start": 2820.44, "end": 2820.8, "word": " مش", "probability": 0.88330078125}, {"start": 2820.8, "end": 2821.06, "word": " if", "probability": 0.98388671875}, {"start": 2821.06, "end": 2821.28, "word": " it", "probability": 0.98193359375}, {"start": 2821.28, "end": 2821.6, "word": " was", "probability": 0.9765625}, {"start": 2821.6, "end": 2822.02, "word": " true", "probability": 0.99462890625}, {"start": 2822.02, "end": 2823.06, "word": " okay", "probability": 0.443115234375}, {"start": 2823.06, "end": 2823.46, "word": " طبعا", "probability": 0.8287353515625}, {"start": 2823.46, "end": 2823.74, "word": " اذا", "probability": 0.6707763671875}, {"start": 2823.74, "end": 2824.22, "word": " انا", "probability": 0.826416015625}, {"start": 2824.22, "end": 2824.74, "word": " ساطيع", "probability": 0.5398763020833334}, {"start": 2824.74, "end": 2825.72, "word": " اعطاء", "probability": 0.8568115234375}, {"start": 2825.72, "end": 2826.4, "word": " مثال", "probability": 0.8486328125}, {"start": 2826.4, "end": 2828.28, "word": " يعطيني", "probability": 0.73681640625}, {"start": 2828.28, "end": 2829.26, "word": " المواصفات", "probability": 0.95087890625}, {"start": 2829.26, "end": 2829.6, "word": " هذه", "probability": 0.88427734375}, {"start": 2829.6, "end": 2830.16, "word": " بالمرة", "probability": 0.8894856770833334}], "temperature": 1.0}, {"id": 108, "seek": 284364, "start": 2831.26, "end": 2843.64, "text": "تمام؟ إذا بنوقف هنا و هيك بنكون خلصنا ال chapter تلاتة المرة الجاية ان شاء الله هنبقى في chapter أربعة فشكرا لكم و نشوفكم ان شاء الله يوم السبت", "tokens": [39237, 10943, 22807, 11933, 15730, 44945, 30543, 5172, 34105, 4032, 39896, 4117, 44945, 30544, 16490, 1211, 9381, 8315, 2423, 7187, 6055, 1211, 9307, 3660, 9673, 25720, 25724, 995, 10632, 16472, 13412, 16606, 21984, 8032, 1863, 3555, 4587, 7578, 8978, 7187, 5551, 25513, 27884, 6156, 8592, 4117, 23557, 5296, 24793, 4032, 8717, 8592, 38688, 24793, 16472, 13412, 16606, 21984, 7251, 20498, 21136, 3555, 2655], "avg_logprob": -0.13208007300272584, "compression_ratio": 1.5947712418300655, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 2831.26, "end": 2831.86, "word": "تمام؟", "probability": 0.8400065104166666}, {"start": 2831.86, "end": 2832.46, "word": " إذا", "probability": 0.76025390625}, {"start": 2832.46, "end": 2833.12, "word": " بنوقف", "probability": 0.8909505208333334}, {"start": 2833.12, "end": 2833.42, "word": " هنا", "probability": 0.9970703125}, {"start": 2833.42, "end": 2833.6, "word": " و", "probability": 0.8720703125}, {"start": 2833.6, "end": 2833.8, "word": " هيك", "probability": 0.92529296875}, {"start": 2833.8, "end": 2834.06, "word": " بنكون", "probability": 0.917236328125}, {"start": 2834.06, "end": 2834.58, "word": " خلصنا", "probability": 0.9857177734375}, {"start": 2834.58, "end": 2834.68, "word": " ال", "probability": 0.830078125}, {"start": 2834.68, "end": 2834.98, "word": " chapter", "probability": 0.97607421875}, {"start": 2834.98, "end": 2836.22, "word": " تلاتة", "probability": 0.8232421875}, {"start": 2836.22, "end": 2836.54, "word": " المرة", "probability": 0.884765625}, {"start": 2836.54, "end": 2836.88, "word": " الجاية", "probability": 0.7763671875}, {"start": 2836.88, "end": 2836.94, "word": " ان", "probability": 0.78662109375}, {"start": 2836.94, "end": 2837.12, "word": " شاء", "probability": 0.976806640625}, {"start": 2837.12, "end": 2837.2, "word": " الله", "probability": 0.9462890625}, {"start": 2837.2, "end": 2837.66, "word": " هنبقى", "probability": 0.85068359375}, {"start": 2837.66, "end": 2837.8, "word": " في", "probability": 0.8837890625}, {"start": 2837.8, "end": 2838.26, "word": " chapter", "probability": 0.8251953125}, {"start": 2838.26, "end": 2839.58, "word": " أربعة", "probability": 0.7228190104166666}, {"start": 2839.58, "end": 2841.22, "word": " فشكرا", "probability": 0.93017578125}, {"start": 2841.22, "end": 2841.7, "word": " لكم", "probability": 0.78515625}, {"start": 2841.7, "end": 2841.96, "word": " و", "probability": 0.9931640625}, {"start": 2841.96, "end": 2842.44, "word": " نشوفكم", "probability": 0.918701171875}, {"start": 2842.44, "end": 2842.62, "word": " ان", "probability": 0.79931640625}, {"start": 2842.62, "end": 2842.78, "word": " شاء", "probability": 0.99560546875}, {"start": 2842.78, "end": 2842.9, "word": " الله", "probability": 0.97021484375}, {"start": 2842.9, "end": 2843.18, "word": " يوم", "probability": 0.991455078125}, {"start": 2843.18, "end": 2843.64, "word": " السبت", "probability": 0.93408203125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2844.53725, "duration_after_vad": 2599.988124999989}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/VKBf-GBS8EU_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/VKBf-GBS8EU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6620d81cd11549259ab81877a8fef638e4b91a70
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/VKBf-GBS8EU_raw.srt
@@ -0,0 +1,1420 @@
+1
+00:00:21,140 --> 00:00:25,840
+أحنا المرة اللي فات أخدنا موضوع ال sub sequences و
+
+2
+00:00:25,840 --> 00:00:30,840
+أخر نظرية أخدناها في الموضوع هذا كان في نظرية 2.16
+
+3
+00:00:30,840 --> 00:00:36,380
+النظرية هذه بتنص على إنه لو كان في عندي sequence
+
+4
+00:00:36,380 --> 00:00:41,340
+of real numbers و كانت convergent فأي subsequence
+
+5
+00:00:41,340 --> 00:00:47,680
+منها بتكون convergent ويلها نفس ال limit تمام؟
+
+6
+00:00:53,530 --> 00:00:59,850
+الان بدنا نطبق النظرية هذه من خلال الأمثلة التالية
+
+7
+00:00:59,850 --> 00:01:06,250
+فالمثال
+
+8
+00:01:06,250 --> 00:01:13,510
+الأول لو كان واحد أصغر من أو لو كان سفر أصغر من بي
+
+9
+00:01:13,510 --> 00:01:19,410
+أصغر من واحد فبدنا نثبت أن هذا بيقدي أن limit ال
+
+10
+00:01:19,410 --> 00:01:30,240
+sequence bn بساوي سفرفلبورحان ذلك بنعرف
+
+11
+00:01:30,240 --> 00:01:34,680
+الـ sequence Xn اللي الحد العام تبعها بساوي B أُس
+
+12
+00:01:34,680 --> 00:01:42,220
+N تمام؟ الآن من الفرض أنا عندي صفر أصغر من B أصغر
+
+13
+00:01:42,220 --> 00:01:50,360
+من 1 هذا بيقدّي أن Xn اللي هي بساوي B أُس N الـ B
+
+14
+00:01:50,360 --> 00:01:54,360
+هذا عدد موجب أصغر من 1 فكل ما كبرت القوة تبعته كل
+
+15
+00:01:54,360 --> 00:01:59,670
+ما زغريعني هذا أكبر من b أُس n زايد واحد اللي هو
+
+16
+00:01:59,670 --> 00:02:04,410
+xn زايد واحد الكلام هذا صحيح لكل الأعداد الطبيعية
+
+17
+00:02:04,410 --> 00:02:11,350
+n فهذا بيقدي ان ال sequence xn is decreasing
+
+18
+00:02:11,350 --> 00:02:25,510
+متناقصة كذلك احنا في عندنا since بما انهالـ Xn
+
+19
+00:02:25,510 --> 00:02:31,790
+تبعتي اللي احنا عرفناها على عينها B أس N إذا كان B
+
+20
+00:02:31,790 --> 00:02:36,410
+أكبر من 0 أصغر من 1 ف B أس N بيطلع أكبر من أو ساوي
+
+21
+00:02:36,410 --> 00:02:44,210
+0 أصغر من أو ساوي 1 وهذا صحيح لكل N هذا معناه أن
+
+22
+00:02:44,210 --> 00:02:48,690
+السفر حد أدنى لل sequence BN والواحد حد أعلى
+
+23
+00:02:49,370 --> 00:02:53,530
+وبالتالي سيكوانس b in is bounded من أسفل ومن أعلى
+
+24
+00:02:53,530 --> 00:02:59,450
+وبالتالي bounded إذا السيكوانس x in is bounded
+
+25
+00:02:59,450 --> 00:03:03,170
+الآن
+
+26
+00:03:03,170 --> 00:03:06,370
+أنا في اندي سيكوانس x in decreasing وبالتالي
+
+27
+00:03:06,370 --> 00:03:11,670
+monotone وbounded إذا by monotone convergence تطلع
+
+28
+00:03:11,670 --> 00:03:12,170
+conversion
+
+29
+00:03:15,900 --> 00:03:28,260
+by monotone convergence theorem xn converges say
+
+30
+00:03:28,260 --> 00:03:39,320
+دعنا خلّينا نسمي ال limit تبعتها x say limit xn
+
+31
+00:03:39,320 --> 00:03:40,880
+بساوي x
+
+32
+00:03:43,880 --> 00:03:50,460
+الان بدنا نثبت انها هيثبتنا ان ال sequence xn اللي
+
+33
+00:03:50,460 --> 00:03:55,320
+الحد العام تبعها بيوس ن تطلع convergent إلى عدد x
+
+34
+00:03:55,320 --> 00:04:03,660
+الان بدنا نثبت ان ال x هذا هو سفر اكلم ال
+
+35
+00:04:03,660 --> 00:04:17,420
+x بساوي سفر طيب by ال theoremاثنين ستة عشر ال
+
+36
+00:04:17,420 --> 00:04:25,240
+sub sequence لو أخدت ال sub sequence اللي حدودها
+
+37
+00:04:25,240 --> 00:04:31,280
+زوجية لو أخدت الحدود الزوجية من ال sequence xn هذه
+
+38
+00:04:31,280 --> 00:04:38,620
+فهذه sub sequence من xn فهذه أيضا converges ل x
+
+39
+00:04:41,360 --> 00:04:47,460
+حسب نظرية 2.16 الـ sequence x in converge ل x x 2
+
+40
+00:04:47,460 --> 00:04:50,960
+in subsequence من x in وبالتالي convergent by
+
+41
+00:04:50,960 --> 00:05:02,480
+theorem 16 إلى x طيب، الآن so as بما أنه
+
+42
+00:05:06,320 --> 00:05:13,660
+x2n بيساوي بي أس اتنين n x اتنين n بد ان باتنين n
+
+43
+00:05:13,660 --> 00:05:18,700
+بيساوي بي أس اتنين n وهذه ممكن كتبتها على صورة بي
+
+44
+00:05:18,700 --> 00:05:28,700
+أس ان لكل تربية وهذا عبارة عن xn تربية الكلام هذا
+
+45
+00:05:28,700 --> 00:05:33,280
+صحيح لكل n خدوا ال limit للطرفين لما n تقول ل
+
+46
+00:05:33,280 --> 00:05:43,650
+infinityإذا ال limit ل x2n لما n تقول infinity
+
+47
+00:05:43,650 --> 00:05:52,630
+بساوي limit xn تربيع لما n تقول infinity وهذا
+
+48
+00:05:52,630 --> 00:06:00,730
+بساوي limit xn لكل تربيع طيب limit .. أنا عندي
+
+49
+00:06:00,730 --> 00:06:04,270
+limit xn بساوي x إذا هذا x تربيع
+
+50
+00:06:07,550 --> 00:06:13,890
+و limit x2 in بساوي x إن أنا أصبح في عندي معادلة x
+
+51
+00:06:13,890 --> 00:06:19,730
+بساوي x تلبيا حل المعادلة هذه في x فبطلع x بساوي
+
+52
+00:06:19,730 --> 00:06:29,830
+سفر أو x بساوي واحد تمام؟
+
+53
+00:06:36,360 --> 00:06:41,500
+طيب مين أخد السفر و لا الواحد؟
+
+54
+00:06:41,500 --> 00:06:46,620
+أنا عندي ال sequence تبعتي decreasing متناقصة أنا
+
+55
+00:06:46,620 --> 00:06:53,480
+عندي .. أنا عندي ال X since
+
+56
+00:06:53,480 --> 00:07:00,200
+X in is decreasing متناقصة
+
+57
+00:07:04,980 --> 00:07:11,740
+و ال limit تبعتها و x اللي هي بالساوي limit x in
+
+58
+00:07:11,740 --> 00:07:19,660
+من هنا limit x in هتطلع أكبر من أو ساوي سفر أصغر
+
+59
+00:07:19,660 --> 00:07:24,900
+من أو ساوي الواحد و ال x إما بالساوي سفر أو واحد و
+
+60
+00:07:24,900 --> 00:07:32,020
+متناقصة فلازم ال x ال limit تبعتها x ساوي سفر
+
+61
+00:07:35,220 --> 00:07:40,360
+لأنها بتتناقص مش بتزايد okay إذا ال X بساوي سفر
+
+62
+00:07:40,360 --> 00:07:44,120
+برضه
+
+63
+00:07:44,120 --> 00:07:50,740
+ممكن نحن نقول إن ال sequence ال X بساوي ال infimum
+
+64
+00:07:50,740 --> 00:07:58,780
+ل XN حيث N ينتمي ل N حسب ال monotone convergence
+
+65
+00:07:58,780 --> 00:08:03,420
+theorem وهي ال XN bounded below by سفر والسفر هو
+
+66
+00:08:03,420 --> 00:08:12,190
+ال infimum لهاإذاً هذا بيساوي السفر لأن
+
+67
+00:08:12,190 --> 00:08:18,290
+السفر عبارة عن lower bound هو أكبر ممكن إثبات إنه
+
+68
+00:08:18,290 --> 00:08:25,090
+أكبر lower bound طيب واضح المثال هذا؟ كيف طبقنا
+
+69
+00:08:25,090 --> 00:08:31,170
+نظرية 2.16 لإيجاد limit لل-convergent sequence لأن
+
+70
+00:08:31,170 --> 00:08:35,250
+احنا أثبتنا إن ال sequence convergentأخذنا سيكوينس
+
+71
+00:08:35,250 --> 00:08:38,530
+الحد اللي عام تبعها بي أس ان أثبتنا إنها
+
+72
+00:08:38,530 --> 00:08:42,990
+convergence by monotone convergence theorem وجبنا
+
+73
+00:08:42,990 --> 00:08:48,650
+قيمة ال limit باستخدام نظرية 2.16 أو ممكن باستخدام
+
+74
+00:08:48,650 --> 00:08:52,790
+ال monotone convergence theorem تمام؟ ناخد مثال
+
+75
+00:08:52,790 --> 00:08:53,250
+تاني
+
+76
+00:09:04,470 --> 00:09:09,990
+لو كان عندي c عدد حقيقي أكبر من واحد فهذا بيؤدي ان
+
+77
+00:09:09,990 --> 00:09:15,550
+ال limit ل c أس واحد على n لما n تقول infinity
+
+78
+00:09:15,550 --> 00:09:21,030
+بيساوي واحد البرهان
+
+79
+00:09:21,030 --> 00:09:27,430
+بنفس الطريقة اللي برهننا فيها المثال الأول let
+
+80
+00:09:27,430 --> 00:09:33,610
+المرة هذه y in انعرف sequence y inالـ nth term
+
+81
+00:09:33,610 --> 00:09:42,570
+تبقى yn بساوي c أس واحد على n لكل n عدد طبيعي then
+
+82
+00:09:42,570 --> 00:09:49,230
+واضح أن yn زائد واحد بساوي c أس واحد على n زائد
+
+83
+00:09:49,230 --> 00:09:58,530
+واحد و ال c عدد أكبر من واحدوهذا الجذر رقم n زاد
+
+84
+00:09:58,530 --> 00:10:11,230
+واحد له هذا بطلع أكبر من أو أصغر من الجذر رقم n أو
+
+85
+00:10:11,230 --> 00:10:17,690
+الجذر اللوني ل ال c كل ما كبر الجذر كل ما العدد
+
+86
+00:10:17,690 --> 00:10:23,720
+زغر إذا كان العدد أكبر من واحد وهذا بساوي ynو هذا
+
+87
+00:10:23,720 --> 00:10:29,280
+صحيح لكل n هذا معناه yn زياد واحد أصغر من yn
+
+88
+00:10:29,280 --> 00:10:39,160
+معناته ال sequence yn is decreasing متناقصة also
+
+89
+00:10:39,160 --> 00:10:48,180
+أيضا أنا عندي في ال sequence هذه y واحد أكبر من أو
+
+90
+00:10:48,180 --> 00:10:56,200
+ساوي ynلأن الـ sequence متناقصة صح؟
+
+91
+00:10:56,200 --> 00:11:03,900
+و YN من هنا YN بساوي C أس N الـ C أكبر من واحد إذا
+
+92
+00:11:03,900 --> 00:11:07,580
+الجذر النوني لـ C عدد أكبر من واحد بيبقى أكبر من
+
+93
+00:11:07,580 --> 00:11:16,040
+واحد إذا هذا أكبر من أو ساوي واحد تمام؟ وهذا
+
+94
+00:11:16,040 --> 00:11:22,810
+الكلام صحيح لكل N؟إذن هي ال sequence تبعتي y in
+
+95
+00:11:22,810 --> 00:11:28,230
+bounded below by one and bounded above by y one y
+
+96
+00:11:28,230 --> 00:11:36,370
+one عدد حفيفي موجب أكبر من واحد إذن
+
+97
+00:11:36,370 --> 00:11:43,550
+هذا معناه أن ال sequence y inis bounded صح is
+
+98
+00:11:43,550 --> 00:11:52,170
+bounded so by monotone convergence theorem a
+
+99
+00:11:52,170 --> 00:12:04,010
+sequence yn converges converge say ال limit تبعتها
+
+100
+00:12:04,010 --> 00:12:11,970
+بساوي عدد yافترضوا ان ال limit تبعتها بالساعة
+
+101
+00:12:11,970 --> 00:12:21,450
+واحدة الان بنثبت ان ال limit
+
+102
+00:12:21,450 --> 00:12:30,950
+y بالساعة واحدة ال claim ان ال limit y بالساعة
+
+103
+00:12:30,950 --> 00:12:34,550
+واحدة كمان مرة نفس السلسلة اللي بستخدمها برنامج
+
+104
+00:12:34,550 --> 00:12:41,680
+اتنين ستاشر ال subsequence اللي هيمتتالية الحدود
+
+105
+00:12:41,680 --> 00:12:51,880
+الزوجية y2n هذي
+
+106
+00:12:51,880 --> 00:12:56,260
+المفروض تكون convergent لنفس ال limit تبعت ال
+
+107
+00:12:56,260 --> 00:13:02,280
+sequence yn اللي هي y تمام طيب
+
+108
+00:13:02,280 --> 00:13:02,400
+but
+
+109
+00:13:08,660 --> 00:13:17,520
+Y2N شو بيساوي؟ C أس واحد على اتنين N وهذا بيساوي C
+
+110
+00:13:17,520 --> 00:13:24,680
+أس واحد على N الكل أس واحد على اتنين وهذا بيساوي C
+
+111
+00:13:24,680 --> 00:13:32,250
+أس واحد على N عبارة عن YN الكل أس نصالكلام هذا
+
+112
+00:13:32,250 --> 00:13:37,270
+صحيح لكل n إذا لو أخدت ال limit للطرفين لما n تقول
+
+113
+00:13:37,270 --> 00:13:43,950
+infinity فبطلع عندي limit y2n as n times infinity
+
+114
+00:13:43,950 --> 00:13:48,330
+بساوي limit yn
+
+115
+00:13:48,330 --> 00:13:56,210
+لما n تقول infinity أص نص وهذا بساوي limit أص نص
+
+116
+00:14:00,780 --> 00:14:08,440
+طيب limit y in قلنا بتساوي y إذن هذا y أص نص و
+
+117
+00:14:08,440 --> 00:14:14,920
+limit y اتنين in قلنا بتساوي y إذن أنا أصبح في
+
+118
+00:14:14,920 --> 00:14:20,700
+عندي معادلة y بساوي y أص نص لو حلينا المعادلة هذه
+
+119
+00:14:20,700 --> 00:14:28,660
+في y فy تلبية بساوي y ومنها بطلع y بساوي سفر or y
+
+120
+00:14:28,660 --> 00:14:29,940
+بساوي واحدة
+
+121
+00:14:32,490 --> 00:14:38,990
+أحنا عايزين ال y تساوي المثال التاني واحد عايزين
+
+122
+00:14:38,990 --> 00:14:49,090
+ال y تساوي واحد تمام فأنا عندي since limit أنا
+
+123
+00:14:49,090 --> 00:14:49,930
+عندي من هنا
+
+124
+00:14:53,290 --> 00:15:01,650
+أنا عندي yn أكبر من أو ساوي واحد لكل n بيقدي انه
+
+125
+00:15:01,650 --> 00:15:10,350
+limit yn اللي هي y هي خانة نظرية بتقول لو y ال
+
+126
+00:15:10,350 --> 00:15:15,350
+sequence bounded below by a ف limit yn تطلع أكبر
+
+127
+00:15:15,350 --> 00:15:19,350
+من أو ساوي الواحد
+
+128
+00:15:24,190 --> 00:15:29,090
+طيب why أكبر من أو ساوي الواحد و احنا قلنا انه
+
+129
+00:15:29,090 --> 00:15:33,430
+لازم تطلع اما سفر او واحد فمين ال .. ال .. الإجابة
+
+130
+00:15:33,430 --> 00:15:40,090
+المنطقية اذا ال why لازم الساوي واحد وبالتالي هيك
+
+131
+00:15:40,090 --> 00:15:44,130
+ممكن اثبتنا ان ال sequence اللي ال instance تبعها
+
+132
+00:15:44,130 --> 00:15:48,850
+c to one over n is convergent و ال limit تبعتها
+
+133
+00:15:48,850 --> 00:15:51,430
+بالساوي واحد تمام واضح؟
+
+134
+00:15:54,740 --> 00:15:59,300
+في اي سؤال؟ طيب
+
+135
+00:15:59,300 --> 00:16:01,360
+النظرية اللي بعد النظرية هذه
+
+136
+00:16:23,610 --> 00:16:28,650
+نظرية السبعتاش divergence
+
+137
+00:16:28,650 --> 00:16:35,370
+criterion
+
+138
+00:16:51,000 --> 00:16:58,100
+let xn be sequence in R لو
+
+139
+00:16:58,100 --> 00:17:02,200
+كانت xn sequence of real numbers then the
+
+140
+00:17:02,200 --> 00:17:07,700
+following statements are equivalent الأبارات
+
+141
+00:17:07,700 --> 00:17:13,960
+التالية متكافئة xn does not converge ل x ينتمي إلى
+
+142
+00:17:13,960 --> 00:17:14,400
+R
+
+143
+00:17:18,590 --> 00:17:25,790
+تنين يوجد epsilon zero اكبر من سفر بحيث انه such
+
+144
+00:17:25,790 --> 00:17:36,290
+that for any k عدد طبيعي يوجد
+
+145
+00:17:36,290 --> 00:17:44,790
+عدد طبيعي rk ينتمي الى n with
+
+146
+00:17:46,090 --> 00:17:54,350
+rk أكبر من أو يساوي k and and
+
+147
+00:17:54,350 --> 00:18:00,930
+absolute x x
+
+148
+00:18:00,930 --> 00:18:07,550
+رقم rk minus x أكبر من أو يساوي epsilon zero
+
+149
+00:18:07,550 --> 00:18:10,870
+الأبارة التالتة
+
+150
+00:18:14,170 --> 00:18:21,010
+يوجد epsilon zero أكبر من الصفر and a subsequence
+
+151
+00:18:21,010 --> 00:18:34,660
+.. a subsequence xrk أو xrn of ال sequence x in
+
+152
+00:18:34,660 --> 00:18:42,080
+such that absolute xrn
+
+153
+00:18:42,080 --> 00:18:54,540
+minus x أكبر من أو يساوي epsilon zero لكل n تمام؟
+
+154
+00:18:56,650 --> 00:19:05,210
+لبرهان النظرية هذه عشان اثبت تلات عبارات متكافئة
+
+155
+00:19:05,210 --> 00:19:11,790
+حسب ال logic حسب المنطق أو مبادئ الرياضيات لازم
+
+156
+00:19:11,790 --> 00:19:17,490
+نثبت ان واحد بكافئ اتنين و اتنين بكافئ تلاتة وهذا
+
+157
+00:19:17,490 --> 00:19:22,330
+ممكن اثباتهبإن احنا نثبت واحد بيقدي لاتنين و اتنين
+
+158
+00:19:22,330 --> 00:19:26,530
+بيقدي لتلاتة و تلاتة بيقدي لواحد هيك بنغلق الدائرة
+
+159
+00:19:26,530 --> 00:19:32,490
+فهذا اللي هنعمله فنبدأ بالبرهان نثبت الأول ان
+
+160
+00:19:32,490 --> 00:19:41,710
+العبارة الأولى implies التانية بتقدي للتانية ف
+
+161
+00:19:41,710 --> 00:19:42,390
+assume
+
+162
+00:19:45,130 --> 00:19:51,890
+العبارة الأولى صحيحة وهو xm does not converge لx
+
+163
+00:19:54,980 --> 00:20:00,680
+طيب ارجعوا لتعريف epsilon capital N definition of
+
+164
+00:20:00,680 --> 00:20:04,200
+convergence ما معناه ان ال sequence xn converge ل
+
+165
+00:20:04,200 --> 00:20:08,560
+x معناه لكل epsilon أكبر من السفر يوجد capital N
+
+166
+00:20:08,560 --> 00:20:12,280
+يعتمد على epsilon بحيث لكل N أكبر من أو ساوي
+
+167
+00:20:12,280 --> 00:20:17,040
+capital N المسافة بين xn و x أصغر من epsilonطب
+
+168
+00:20:17,040 --> 00:20:20,480
+مايعنى x in لا تتقارب ل x معناه نفي كل الكلام هذا
+
+169
+00:20:20,480 --> 00:20:24,000
+اللي حاكيناه بيحصل بدل لكل epsilon أكبر من الصفر
+
+170
+00:20:24,000 --> 00:20:29,780
+يوجد capital N بصير يوجد epsilon واحدة epsilon
+
+171
+00:20:29,780 --> 00:20:41,960
+zero عدد موجب بحيث such that بحيث انه لكل
+
+172
+00:20:43,760 --> 00:20:50,280
+كبت أو n عدد طبيعي the implication
+
+173
+00:20:57,890 --> 00:21:00,870
+ال implication تبع التعريف epsilon capital n ال
+
+174
+00:21:00,870 --> 00:21:06,070
+implication اللي هي لكل n أكبر من أو ساوي capital
+
+175
+00:21:06,070 --> 00:21:13,970
+K لازم يطلع المسافة بين xn و x أصغر من epsilon
+
+176
+00:21:13,970 --> 00:21:22,830
+zero ال implication هذه is false is false ليست
+
+177
+00:21:22,830 --> 00:21:27,430
+صحيحة طب ما هذا معناه هذا معناه
+
+178
+00:21:31,850 --> 00:21:41,490
+this means هذا يعني this means أنه لكل capital K
+
+179
+00:21:41,490 --> 00:21:48,590
+عدد طبيعي يوجد لكل
+
+180
+00:21:48,590 --> 00:21:54,630
+K عدد طبيعي مايعني أن هذا غلطمعناه يوجد لكل K عدد
+
+181
+00:21:54,630 --> 00:21:59,250
+طبيعي capital K يوجد عدد واحد مش لكل ال N الأكبر
+
+182
+00:21:59,250 --> 00:22:06,030
+منه يوجد عدد طبيعي واحد أكبر من أو ساوي يوجد عدد
+
+183
+00:22:06,030 --> 00:22:13,690
+طبيعي سميه N أو R sub capital K يعتمد على K عدد
+
+184
+00:22:13,690 --> 00:22:17,750
+طبيعي بحيث أنه
+
+185
+00:22:21,710 --> 00:22:27,850
+بحيث أنه طبعا
+
+186
+00:22:27,850 --> 00:22:33,390
+ال RK هذا هيكون
+
+187
+00:22:33,390 --> 00:22:41,190
+أكبر من أو ساوي K and RK
+
+188
+00:22:41,190 --> 00:22:50,050
+أكبر من أو ساوي K and absolute XN أو XRcapital k
+
+189
+00:22:50,050 --> 00:22:55,590
+minus x أكبر من أو يساوي بدل أصغر من epsilon zero
+
+190
+00:22:55,590 --> 00:23:05,410
+النفي تبعها أكبر من أو يساوي epsilon zero now
+
+191
+00:23:05,410 --> 00:23:09,610
+replace
+
+192
+00:23:09,610 --> 00:23:18,450
+badly replace capital k by small k
+
+193
+00:23:22,130 --> 00:23:25,970
+to get الأبارع
+
+194
+00:23:25,970 --> 00:23:32,250
+اتنين holes صح؟
+
+195
+00:23:32,250 --> 00:23:38,950
+هاي بدلي كابتال K بsmall kفهنا أثبتنا أن يوجد يوجد
+
+196
+00:23:38,950 --> 00:23:46,350
+εمسلون زيرو أكبر من سفر بحيث لكل لكل small k يوجد
+
+197
+00:23:46,350 --> 00:23:53,150
+R small k أكبر من أو ساوي small k والمسافة بين X R
+
+198
+00:23:53,150 --> 00:23:56,750
+small k minus X أكبر من أو ساوي امسلون زيرو
+
+199
+00:24:04,730 --> 00:24:14,690
+الأن نثبت اتنين بيقدي لواحد لتلاتة اذا two implies
+
+200
+00:24:14,690 --> 00:24:18,530
+three assume
+
+201
+00:24:18,530 --> 00:24:27,110
+two holds افرضه ان العبارة التانية صحيحة بيبني
+
+202
+00:24:27,110 --> 00:24:30,690
+نثبت ان العبارة التالتة صحيحة طيب؟
+
+203
+00:24:37,940 --> 00:24:48,160
+then for k بساوي واحد يعني تم إلى n الان احنا
+
+204
+00:24:48,160 --> 00:24:53,320
+فرضين اتنين العبارة اتنين صحيحة اذا احنا فرضين ان
+
+205
+00:24:53,320 --> 00:24:58,840
+يوجد epsilon zero بحيث الكلام هذا بتحقق الان لو
+
+206
+00:24:58,840 --> 00:25:04,420
+اخدت k هذه بساوي واحد فيوجد
+
+207
+00:25:06,750 --> 00:25:15,070
+R1 عدد طبيعي وطبعا R1 بالتأكيد أكبر من أو ساوي
+
+208
+00:25:15,070 --> 00:25:24,510
+واحد such that absolute X R1 سالب X أكبر من أو
+
+209
+00:25:24,510 --> 00:25:33,250
+ساوي epsilon zero صح؟ next for
+
+210
+00:25:34,680 --> 00:25:45,900
+ك بساوي R واحد زاد واحد مش
+
+211
+00:25:45,900 --> 00:25:51,380
+هاد عدد طبيعي لو أخدت ك بساوي R واحد زاد واحد R
+
+212
+00:25:51,380 --> 00:25:58,020
+واحد عدد طبيعي زاد واحد عدد طبيعي يوجد R اتنين عدد
+
+213
+00:25:58,020 --> 00:26:08,800
+طبيعيو R اتنين اكبر من او يساوي R
+
+214
+00:26:08,800 --> 00:26:16,480
+واحد زاد واحد such that absolute X R اتنين minus X
+
+215
+00:26:16,480 --> 00:26:24,960
+اكبر من او يساوي epsilon zero صح طيب
+
+216
+00:26:24,960 --> 00:26:30,060
+كمان برضه لو سمرنا في العملية هذه now
+
+217
+00:26:32,620 --> 00:26:40,620
+for R اتنين زائد واحد مش هاد عدد طبيعي لو أخدت K
+
+218
+00:26:40,620 --> 00:26:46,440
+لان بساوي اه لو أخدت K بساوي R اتنين زائد واحد هاد
+
+219
+00:26:46,440 --> 00:26:51,680
+عدد طبيعي هنا اتنين اتنين لو أخدت K بساوي R اتنين
+
+220
+00:26:51,680 --> 00:27:01,160
+زائد واحد اذا حسب اتنين يوجد R تلاتة عدد طبيعيوR
+
+221
+00:27:01,160 --> 00:27:06,280
+تلاتة أكبر من أو ساوي ال K اللي هو R اتنين زائد
+
+222
+00:27:06,280 --> 00:27:13,360
+واحد بحيث انه المسافة بين X R تلاتة minus X أكبر
+
+223
+00:27:13,360 --> 00:27:18,400
+من أو ساوي epsilon zero طب لو استمرنا في العملية
+
+224
+00:27:18,400 --> 00:27:27,040
+هذه شو هنحصل؟ ايه اللي هيحصل؟ continuing this
+
+225
+00:27:27,040 --> 00:27:27,860
+process
+
+226
+00:27:32,720 --> 00:27:35,460
+this process اللي هو سمرنا في العملية دي اللي
+
+227
+00:27:35,460 --> 00:27:49,200
+عملية تطبيق العبارة التانية we obtain هنحصل على we
+
+228
+00:27:49,200 --> 00:27:54,960
+obtain strictly strictly
+
+229
+00:27:54,960 --> 00:28:01,700
+increasing increasing sequence
+
+230
+00:28:06,220 --> 00:28:13,140
+RK من K بساوة واحد لإنفينتي هذه عبارة عن sequence
+
+231
+00:28:13,140 --> 00:28:20,620
+of natural numbers in N such
+
+232
+00:28:20,620 --> 00:28:28,940
+that and hence وبالتالي وبالتالي نحصل على a
+
+233
+00:28:28,940 --> 00:28:33,600
+subsequence XRK
+
+234
+00:28:34,700 --> 00:28:39,240
+من k بساوي واحد في infinity هذه عبارة عن
+
+235
+00:28:39,240 --> 00:28:45,980
+subsequence من ال sequence xn بحيث such that
+
+236
+00:28:45,980 --> 00:28:55,680
+absolute xr k minus x أكبر من أو ساوي epsilon zero
+
+237
+00:28:55,680 --> 00:29:01,160
+والكلام هذا صحيح لكل k ينتمي إلى n
+
+238
+00:29:03,880 --> 00:29:10,500
+هي في الخطوة الأولى حصلنا على R1 وبالتالي على XR1
+
+239
+00:29:10,500 --> 00:29:16,440
+بحيث absolute XR1 minus X أكبر نوى ساوية X نزيلة
+
+240
+00:29:16,440 --> 00:29:23,010
+في الخطوة التانية حصلنا على R2 وبالتالي XR2لاحظوا
+
+241
+00:29:23,010 --> 00:29:30,030
+R2 أكبر من R1 وR3 أكبر من R2، إذن هذه sequence of
+
+242
+00:29:30,030 --> 00:29:33,830
+natural numbers strictly increasing، إذن ال
+
+243
+00:29:33,830 --> 00:29:39,030
+sequence، المؤشرات تبعتها هي الأعداد الطبيعية، هذه
+
+244
+00:29:39,030 --> 00:29:44,110
+subsequence حسب التعريف من sequence Xوبتحقق في
+
+245
+00:29:44,110 --> 00:29:49,510
+الخطوة التانية absolute XR2-X أكبر من أو ساوي Y0
+
+246
+00:29:49,510 --> 00:29:55,590
+خطوة التالتة لما K بساوي تلاتة هي absolute XR3-X
+
+247
+00:29:55,590 --> 00:29:59,510
+أكبر من أو ساوي Y0 وهكذا إذن هنا عملنا
+
+248
+00:29:59,510 --> 00:30:04,470
+construction عملنا بناء بنينا subsequence اللي هي
+
+249
+00:30:04,470 --> 00:30:09,650
+subsequence هذه من ال sequence XN بطريقة استقرائية
+
+250
+00:30:10,920 --> 00:30:15,420
+و هذه الـ subsequence بتحقق المتباينة هذه وهذه
+
+251
+00:30:15,420 --> 00:30:21,800
+بالضبط العبارة تلاتة اذا three العبارة تلاتة whole
+
+252
+00:30:21,800 --> 00:30:24,960
+تمام؟
+
+253
+00:30:24,960 --> 00:30:30,460
+إذا هيك أثبتنا أن اتنين يعدي إلى تلاتة باقي أثبات
+
+254
+00:30:30,460 --> 00:30:36,400
+أن العبارة تلاتة تعني واحدة
+
+255
+00:30:39,780 --> 00:30:48,460
+ف assume .. assume العبارة تلاتة صحيحة يعني يوجد
+
+256
+00:30:48,460 --> 00:30:57,260
+epsilon zero أكبر من صفر and a subsequence xrk
+
+257
+00:30:57,260 --> 00:31:10,090
+of a sequence x in such thatabsolute xrk minus x
+
+258
+00:31:10,090 --> 00:31:18,510
+أكبر من أو ساوي y0 لكل k طيب
+
+259
+00:31:18,510 --> 00:31:29,170
+هذا معناه أو هذا بيقدّي ان xrk
+
+260
+00:31:29,170 --> 00:31:43,760
+او xrn او xrkلا تنتمي لـ X-Y0 X زاد Y0 لا تنتمي
+
+261
+00:31:43,760 --> 00:31:45,220
+للفترة المفتوحة هذه
+
+262
+00:31:49,030 --> 00:31:53,890
+اللي هو هذه الفترة المفتوحة سمناها قبل هيك ابسلون
+
+263
+00:31:53,890 --> 00:31:59,670
+زيرو neighborhood ل X صح؟ هذه فترة مفتوحة مركزها X
+
+264
+00:31:59,670 --> 00:32:04,330
+و نص قطرها ابسلون زيرو المتباينة هذه بتقول إن هذا
+
+265
+00:32:04,330 --> 00:32:10,470
+الكلام لكل K لكل K لو حلت .. لو حلت المتباينة هذه
+
+266
+00:32:10,470 --> 00:32:14,990
+في X بيطلع في X لو حلت المتباينة هذه في XRK بيطلع
+
+267
+00:32:14,990 --> 00:32:23,320
+XRK لا ينتميلأ الفترة مفتوحة وبالتالي
+
+268
+00:32:23,320 --> 00:32:27,460
+hence by
+
+269
+00:32:27,460 --> 00:32:37,860
+definition by ال neighborhood definition of
+
+270
+00:32:37,860 --> 00:32:41,740
+limit
+
+271
+00:32:44,750 --> 00:32:49,850
+فاكرين احنا اخدنا تعريف ال limit لل sequence اول
+
+272
+00:32:49,850 --> 00:32:53,190
+تعريف كان neighborhood definition و بعدين اثبتنا
+
+273
+00:32:53,190 --> 00:32:58,470
+انه بكافئ في نظرية 2.2 اثبتنا انه بكافئ ال epsilon
+
+274
+00:32:58,470 --> 00:33:01,010
+capital N definition لل limit
+
+275
+00:33:10,150 --> 00:33:15,910
+X in converge ل X X in converge ل X معناه لأي
+
+276
+00:33:15,910 --> 00:33:21,390
+neighborhood ل X زي هذا لازم
+
+277
+00:33:21,390 --> 00:33:29,210
+عشان
+
+278
+00:33:29,210 --> 00:33:32,550
+ال subsequence هذه converge ل X لازم أي
+
+279
+00:33:32,550 --> 00:33:37,180
+neighborhood ل X يحتويكل حدود الـ sequence من
+
+280
+00:33:37,180 --> 00:33:41,660
+كابتل N وانت طالع أو من كابتل K وانت طالع لكل
+
+281
+00:33:41,660 --> 00:33:46,920
+small k أكبر من أو ساوي كابتل K هذا لازم يكون صحيح
+
+282
+00:33:46,920 --> 00:33:50,260
+لكل neighborhood طب أنا في .. لأن في عندي there
+
+283
+00:33:50,260 --> 00:33:55,740
+exists epsilon zero neighborhood ل X وكل حدود ال
+
+284
+00:33:55,740 --> 00:34:02,770
+subsequence مش موجودة فيههذا بالظبط نفي تعريف الـ
+
+285
+00:34:02,770 --> 00:34:05,230
+neighborhood definition للـ convergence وبالتالي
+
+286
+00:34:05,230 --> 00:34:09,350
+هذا معناه حسب تعريف الـ neighborhood definition أن
+
+287
+00:34:09,350 --> 00:34:15,550
+الـ subsequence هذه does not converge ل Xطب احنا
+
+288
+00:34:15,550 --> 00:34:19,970
+عايزين نثبت عشان نثبت ان العبارة واحد صحيحة عايزين
+
+289
+00:34:19,970 --> 00:34:23,810
+نثبت ان ال sequence نفسها مش ال subsequence ال
+
+290
+00:34:23,810 --> 00:34:27,650
+sequence نفسها does not converge لأكس اذا انا بدي
+
+291
+00:34:27,650 --> 00:34:38,290
+اكتب هنا claim لبرهان
+
+292
+00:34:38,290 --> 00:34:46,830
+العبارة الأولى باقي اثبات ال claimوهو ان ال
+
+293
+00:34:46,830 --> 00:34:55,150
+sequence x in نفسها does not converge ل x فنشوف
+
+294
+00:34:55,150 --> 00:35:01,370
+مع بعض assume بورهان بالتناقض assume on contrary
+
+295
+00:35:01,370 --> 00:35:05,230
+ان
+
+296
+00:35:05,230 --> 00:35:10,990
+ال sequence x in converge ل x okay بورهان بالتناقض
+
+297
+00:35:10,990 --> 00:35:22,050
+افرض ان ال sequence converge ل xby a theorem اتنين
+
+298
+00:35:22,050 --> 00:35:32,850
+ستاش the subsequence the subsequence اللي هي X R K
+
+299
+00:35:32,850 --> 00:35:37,490
+ال subsequence مش هاد ال subsequence هاد المفروض
+
+300
+00:35:37,490 --> 00:35:44,020
+تطلع convergent ل X وهدا ده ديني contradictionلأن
+
+301
+00:35:44,020 --> 00:35:47,260
+أنا عندي sub sequence هنا استنتجنا أنها does not
+
+302
+00:35:47,260 --> 00:35:53,060
+converge ل X إذا في عندي تناقض التناقض هذا سببه أن
+
+303
+00:35:53,060 --> 00:35:58,680
+احنا فرضنا أن X in converge ل X إذا بطلع عندي X in
+
+304
+00:35:58,680 --> 00:36:04,200
+does not converge ل X وبالتالي إذا one holds إذا
+
+305
+00:36:04,200 --> 00:36:10,120
+one holdsوبالتالي هيك بنكون كملنا برهان النظرية
+
+306
+00:36:10,120 --> 00:36:15,580
+okay تمام اذا هيك اثبتنا ان التلاتة بيعد لواحد
+
+307
+00:36:15,580 --> 00:36:20,560
+وبالتالي العبارات التلاتة هذه متكافئة احنا بهمنا
+
+308
+00:36:20,560 --> 00:36:26,140
+في التطبيق اللي هو الجزء الأخير يعني عشان انا اثبت
+
+309
+00:36:27,620 --> 00:36:32,400
+إنه sequence معينة does not converge to any real
+
+310
+00:36:32,400 --> 00:36:36,360
+number X يكفي
+
+311
+00:36:36,360 --> 00:36:42,920
+اثبات أن يوجد Y0 يوجد subsequence بحيث أن المسافة
+
+312
+00:36:42,920 --> 00:36:47,780
+دي أكبر من أو ساوى Y0 لكل M هنشوف الكلام هذا في
+
+313
+00:36:47,780 --> 00:36:58,230
+أمثلة لاحقة لكن خلينا بس ناخد مثالعلى النظرية هذه
+
+314
+00:36:58,230 --> 00:37:15,210
+إذا
+
+315
+00:37:15,210 --> 00:37:23,470
+ناخد examples هاي
+
+316
+00:37:23,470 --> 00:37:24,410
+مثال واحد
+
+317
+00:37:28,440 --> 00:37:32,300
+الـ sequence اللي الحد العام تبعها سالب واحد plus
+
+318
+00:37:32,300 --> 00:37:40,560
+n is divergent طبعا
+
+319
+00:37:40,560 --> 00:37:43,620
+احنا اثبتنا قبل هيك ان ال sequence هي divergent
+
+320
+00:37:43,620 --> 00:37:47,640
+عملنا proof by contradiction فرضنا ان انا
+
+321
+00:37:47,640 --> 00:37:55,040
+convergent ووصلنا إلى تناقض صح اليوم هناخد برهان
+
+322
+00:37:55,040 --> 00:38:04,780
+تانيباستخدام نظرية 16 أو نظرية التانية يعني نشوف
+
+323
+00:38:04,780 --> 00:38:12,820
+مع بعض prove if
+
+324
+00:38:12,820 --> 00:38:25,060
+it were convergent say
+
+325
+00:38:30,030 --> 00:38:38,350
+-1-N converges to X ينتمي إلى R لو فرضنا إن
+
+326
+00:38:38,350 --> 00:38:44,970
+سيكوانس هذه convergent هنثبت إنها divergent بورحان
+
+327
+00:38:44,970 --> 00:38:51,350
+بالتناقض لو فرضنا إنها convergent to some X إذا
+
+328
+00:38:51,350 --> 00:38:56,570
+كانت convergent إن اسمها لمات then
+
+329
+00:39:00,730 --> 00:39:07,130
+الـ sub sequences اللي
+
+330
+00:39:07,130 --> 00:39:18,390
+هم سالب واحد أس اتنين in and سالب واحد أس اتنين in
+
+331
+00:39:18,390 --> 00:39:25,470
+سالب واحدهذه الـ subsequence هي الحدود الزوجية من
+
+332
+00:39:25,470 --> 00:39:31,150
+هنا و هذه الحدود الفردية إذا كانت ال sequence
+
+333
+00:39:31,150 --> 00:39:36,430
+نفسها converged ل X فالتنتين هذول both converged ل
+
+334
+00:39:36,430 --> 00:39:45,110
+X و
+
+335
+00:39:45,110 --> 00:39:48,670
+بالتالي so X
+
+336
+00:39:51,100 --> 00:40:00,080
+بتساوي limit سالب واحد قص اتنين in صح؟ وهذه بساوي
+
+337
+00:40:00,080 --> 00:40:06,400
+limit سالب واحد قص اتنين in واحد ال sequence هذه
+
+338
+00:40:06,400 --> 00:40:15,620
+ثابت واحد بساوي واحد صح؟ and برضه احنا قلنا ان ال
+
+339
+00:40:15,620 --> 00:40:23,400
+Xبتساوي limit ال subsequence للحدود الفردية اللي
+
+340
+00:40:23,400 --> 00:40:28,580
+هي هذه طيب
+
+341
+00:40:28,580 --> 00:40:36,140
+سالب واحد قص عدد فردي بطلع سالب واحد إذن هذه ال
+
+342
+00:40:36,140 --> 00:40:41,760
+sequence حدودها فردية إذن هي عبارة عن sequence
+
+343
+00:40:41,760 --> 00:40:50,260
+ثابت سالب واحد وبالتالي limit لثابت بطلع ثابتإذا
+
+344
+00:40:50,260 --> 00:40:56,180
+أنا أطلع عندي واحد بساوي x من المعادلة الأولى
+
+345
+00:40:56,180 --> 00:41:01,120
+وكذلك ال x بساوي سالب واحد يعني معناه واحد بساوي
+
+346
+00:41:01,120 --> 00:41:10,130
+سالب واحد وهذا contradictionتمام؟ إذا مستحيل أن ال
+
+347
+00:41:10,130 --> 00:41:13,510
+sequence هذه تكون convergent لأنها لازم تكون
+
+348
+00:41:13,510 --> 00:41:21,050
+divergent okay تمام؟ إذا هنا كلمة where الدلالة
+
+349
+00:41:21,050 --> 00:41:26,470
+على الاستحالة كان ممكن اسمها ال sequence هذه مفرد
+
+350
+00:41:26,470 --> 00:41:32,400
+واحدةمفروض اقول if it was convergent لكن انا عارف
+
+351
+00:41:32,400 --> 00:41:35,400
+انه مستحيل انها تكون convergent فلدلالة على
+
+352
+00:41:35,400 --> 00:41:41,880
+استحالة بستخدم it were زي if I were a king مش if I
+
+353
+00:41:41,880 --> 00:41:47,140
+was a king لكن انا مش king okay تمام؟ اذا بنوقف
+
+354
+00:41:47,140 --> 00:41:50,880
+عند هذا المثال المحاضرة هي انتهت و بنكمل ان شاء
+
+355
+00:41:50,880 --> 00:41:51,720
+الله سبوع جديد
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2faca4e6e4608041c460bc80dabb421d8ad14a5e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_postprocess.srt
@@ -0,0 +1,1052 @@
+1
+00:00:20,670 --> 00:00:27,110
+Okay اليوم هنراجع بس نظرية ال divergence theorem
+
+2
+00:00:27,110 --> 00:00:33,870
+اللي أخدناها أخر مرة بس نسترجعها بسرعة ال
+
+3
+00:00:33,870 --> 00:00:40,370
+divergence theorem
+
+4
+00:00:40,370 --> 00:00:47,370
+عطلناها رقم 2.17 فالنظرية
+
+5
+00:00:47,370 --> 00:00:48,150
+هذه بتقول
+
+6
+00:00:51,110 --> 00:01:04,590
+لت X and contained in R be a sequence then
+
+7
+00:01:04,590 --> 00:01:09,410
+the following statements are equivalent
+
+8
+00:01:11,820 --> 00:01:18,400
+فأول statement sequence x in does not converge ل x
+
+9
+00:01:18,400 --> 00:01:28,200
+ينتمي ل R for any x ينتمي ل R وفي شرط التاني وفي
+
+10
+00:01:28,200 --> 00:01:35,420
+شرط التالت أنا بهمش شرط التالت أو العبارة تالتة
+
+11
+00:01:35,420 --> 00:01:39,840
+there exist إبسلون زيور أكبر من الصفر and a
+
+12
+00:01:39,840 --> 00:01:48,390
+subsequenceأو سبسيكوينس XRN
+
+13
+00:01:48,390 --> 00:01:53,410
+of
+
+14
+00:01:53,410 --> 00:02:05,750
+سيكوينس XN such that absolute XRN minus X أكبر من
+
+15
+00:02:05,750 --> 00:02:08,550
+أو ساوي Y0 لكل M
+
+16
+00:02:13,970 --> 00:02:18,330
+و بدنا ناخد أنثى على النظرية هذه أخدناها المرة
+
+17
+00:02:18,330 --> 00:02:22,290
+الفاتة مثال
+
+18
+00:02:22,290 --> 00:02:29,470
+مثال
+
+19
+00:02:29,470 --> 00:02:39,490
+التانى example consider
+
+20
+00:02:41,810 --> 00:02:49,510
+ناخد ال sequence consider xn where sequence xn لحد
+
+21
+00:02:49,510 --> 00:03:04,610
+العالم تبعها xn معرف على انه بساوي n if n is odd و
+
+22
+00:03:04,610 --> 00:03:06,250
+بتساوي واحد على n
+
+23
+00:03:20,350 --> 00:03:28,690
+مطلوب ان اثبت ان ال sequence xn is divergent
+
+24
+00:03:41,550 --> 00:03:47,630
+سلوشن و لاحظوا ان سيكوانس X انها بيبارى حدودها
+
+25
+00:03:47,630 --> 00:03:53,350
+واحد نص و
+
+26
+00:03:53,350 --> 00:03:59,850
+واحد نص تلاتة رابع و
+
+27
+00:03:59,850 --> 00:04:00,390
+هكذا
+
+28
+00:04:08,080 --> 00:04:12,340
+فالـ sequence هذه بالنسبة لها does not converge
+
+29
+00:04:12,340 --> 00:04:23,040
+لأي x ينتمي لR to show أن x in does not converge ل
+
+30
+00:04:23,040 --> 00:04:29,720
+x for any x
+
+31
+00:04:29,720 --> 00:04:31,440
+ينتمي إلى R
+
+32
+00:04:35,590 --> 00:04:44,030
+fix x ينتمي ل r خلّينا ناخد arbitrary ال
+
+33
+00:04:44,030 --> 00:04:47,470
+real number x ينتمي ل r و نثبت ان x in does not
+
+34
+00:04:47,470 --> 00:04:54,730
+converge enough فعندي then
+
+35
+00:04:54,730 --> 00:04:59,670
+absolute x طبعا أكبر عدد حقيقي أكبر من أوسعه سفر
+
+36
+00:04:59,670 --> 00:05:11,460
+so byArchimedean property يوجد
+
+37
+00:05:11,460 --> 00:05:19,660
+n عدد طبيعي يعتمد على x عدد طبيعي بحيث
+
+38
+00:05:19,660 --> 00:05:38,420
+ان n x هذا is evenand absolute x أصغر من nx هذا
+
+39
+00:05:38,420 --> 00:05:42,990
+ممكن نحصل عليه من الarchimedean propertyالـ
+
+40
+00:05:42,990 --> 00:05:46,990
+argument property بتقول أي عدد حقيقي زي absolute x
+
+41
+00:05:46,990 --> 00:05:53,450
+نقدر نلاقي عدد طبيعي يعتمد على ال x بحيث أنه العدد
+
+42
+00:05:53,450 --> 00:06:02,110
+الطبيعي أكبر من العدد الحقيقي طيب الان لو أخدت
+
+43
+00:06:02,110 --> 00:06:05,150
+epsilon
+
+44
+00:06:05,150 --> 00:06:11,530
+zero عرفت على أنها nx سالب absolute x
+
+45
+00:06:14,250 --> 00:06:24,170
+فهذا بيطلع عدد موجب هذا بيطلع عدد موجب و
+
+46
+00:06:24,170 --> 00:06:30,190
+ال sequence ال
+
+47
+00:06:30,190 --> 00:06:39,390
+sequence الحد العام تبعها N X زائد اتنين M سالد
+
+48
+00:06:39,390 --> 00:06:39,930
+واحد
+
+49
+00:06:43,110 --> 00:06:51,010
+من M بساوي واحد to infinity هذه بالمناسبة الحدود
+
+50
+00:06:51,010 --> 00:07:00,770
+تبعتها هذا عدد فردي عدد طبيعي فردي وهذا
+
+51
+00:07:00,770 --> 00:07:09,190
+NX عدد طبيعي زوجي هذا odd وهذا
+
+52
+00:07:09,190 --> 00:07:09,890
+even
+
+53
+00:07:13,300 --> 00:07:22,960
+ف odd زائد even بطلع odd إذا الحدود
+
+54
+00:07:22,960 --> 00:07:33,340
+العامة لل sequence هذه بتكون odd وبالتالي
+
+55
+00:07:33,340 --> 00:07:39,600
+الحدود هذه كلها حسب التعريف بتطلع بالساوي
+
+56
+00:07:41,460 --> 00:07:48,180
+هي طبعا sub-sequence يعني
+
+57
+00:07:48,180 --> 00:07:54,300
+هدا هتكون لو M بساوة واحد هيطلع NX زائد واحد NX
+
+58
+00:07:54,300 --> 00:08:03,820
+زائد تلاتة و هكذا صح؟ حسب التعريف هدا عبارة عن sub
+
+59
+00:08:03,820 --> 00:08:11,700
+-sequence sub-sequence من ال sequence XMلأن هذه
+
+60
+00:08:11,700 --> 00:08:18,300
+جزء من الحدود الفردية، صح؟ وبالتالي هذه
+
+61
+00:08:18,300 --> 00:08:23,640
+subsequence من xn ومش
+
+62
+00:08:23,640 --> 00:08:35,320
+هيكوا بس and ال absolute value ل nx زائد 2m سالب 1
+
+63
+00:08:35,320 --> 00:08:41,640
+الحد العام لل subsequence هذهالمسافة بينه بين الـ
+
+64
+00:08:41,640 --> 00:08:46,220
+x باستخدام الـ triangle inequality في واحدة من الـ
+
+65
+00:08:46,220 --> 00:08:50,940
+triangle inequalities بتقول absolute a minus b
+
+66
+00:08:50,940 --> 00:08:56,200
+أكبر من أو ساوي absolute a minus absolute b فهذا
+
+67
+00:08:56,200 --> 00:09:02,540
+أكبر من أو ساوي absolute in x زي two m minus واحد
+
+68
+00:09:02,540 --> 00:09:09,720
+minus absolute xهذا عدد موجب هذا عدد طبيعي وهذا
+
+69
+00:09:09,720 --> 00:09:24,860
+عدد طبيعي فردي فممكن نشيل absolute value وهذا
+
+70
+00:09:24,860 --> 00:09:35,880
+العدد هذا العدد أكبر من NX سالب absolute Xهذا
+
+71
+00:09:35,880 --> 00:09:45,580
+العدد هنا أكبر من NX لأن هذا عدد موجب صح فNX زاد
+
+72
+00:09:45,580 --> 00:09:50,440
+عدد موجب أكبر من NX سالب absolute X طب ما هذا
+
+73
+00:09:50,440 --> 00:09:56,000
+بساوي عرفناه على N أبسل زيرو صح؟ الآن الكلام هذا
+
+74
+00:09:56,000 --> 00:09:59,460
+صحيح لكل M ينتمي إلى N
+
+75
+00:10:09,010 --> 00:10:15,890
+أنا اثبتت ان يوجد y0 أكبر من السفر و sub sequence
+
+76
+00:10:15,890 --> 00:10:21,850
+من ال sequence xn و المسافة بين الحد العام لل
+
+77
+00:10:21,850 --> 00:10:28,430
+sequence هذه و ال x أكبر من y0 لكل m في n
+
+78
+00:10:34,110 --> 00:10:44,630
+الـ divergence theorem الجزء التالت هيتحقق شروطه
+
+79
+00:10:44,630 --> 00:10:52,330
+وبالتالي ال sequence x in does not converge to x
+
+80
+00:10:56,670 --> 00:10:59,930
+بما أن x was arbitrary إذا الـ sequence x in does
+
+81
+00:10:59,930 --> 00:11:04,030
+not converge لأي عدد حقيقي x وبالتالي divergent
+
+82
+00:11:04,030 --> 00:11:10,130
+تمام؟ أنا هنا استخدمت ال divergence theorem في
+
+83
+00:11:10,130 --> 00:11:16,150
+أثبات أن ال sequence هذه divergent لاحظوا أن ال
+
+84
+00:11:16,150 --> 00:11:23,710
+sequence 1 على n هذه subsequence من x in وهذه
+
+85
+00:11:23,710 --> 00:11:24,890
+convergent ل0
+
+86
+00:11:28,580 --> 00:11:32,700
+لكن الـ sequence نفسها does not converge هذه برضه
+
+87
+00:11:32,700 --> 00:11:37,220
+subsequence N subsequence .. لما تكون الـ N فردية
+
+88
+00:11:37,220 --> 00:11:42,620
+subsequence من X N وهذه is not convergent هذه ال
+
+89
+00:11:42,620 --> 00:11:49,340
+limit بتاعها infinity طبعا؟ و
+
+90
+00:11:49,340 --> 00:11:50,500
+هذا؟ في عيز سؤال؟
+
+91
+00:12:05,310 --> 00:12:12,050
+monotone subsequence theorem النظرية
+
+92
+00:12:12,050 --> 00:12:23,330
+اتنين تمانتاش أقامها هنا النظرية
+
+93
+00:12:23,330 --> 00:12:32,230
+هذه بتقول every sequence in R has
+
+94
+00:12:36,910 --> 00:12:44,930
+monotone subsequence كل sequence of real numbers
+
+95
+00:12:44,930 --> 00:12:53,770
+ممكن نستخلص منها monotone subsequence البرهان تبع
+
+96
+00:12:53,770 --> 00:12:58,050
+النظرية هذه مش صعب موجود في الكتاب هخليكم تقراه
+
+97
+00:13:00,180 --> 00:13:09,360
+هخليكم تقرا البرهان من الكتاب المقرر C theorem
+
+98
+00:13:09,360 --> 00:13:20,360
+رقم تلاتة اربعة سبعة page تمانية
+
+99
+00:13:20,360 --> 00:13:22,020
+و سبعين in textbook
+
+100
+00:13:27,060 --> 00:13:32,200
+إذن حدؤوكم لقراة البرهان، البرهان سهل مش صعب و
+
+101
+00:13:32,200 --> 00:13:36,380
+حاولوا
+
+102
+00:13:36,380 --> 00:13:40,280
+تقراوه و تفهموه و ده في أي صعوبة تسألوني أو
+
+103
+00:13:40,280 --> 00:13:46,280
+تتناقشوا معي في البرهان okay
+
+104
+00:13:46,280 --> 00:13:49,680
+في
+
+105
+00:13:49,680 --> 00:13:51,320
+نظرية تانية
+
+106
+00:14:00,880 --> 00:14:06,900
+Bolzano-Weierstrass theorem
+
+107
+00:14:06,900 --> 00:14:17,880
+رقم اتنين تسعتاش النظرية
+
+108
+00:14:17,880 --> 00:14:23,980
+هذه بتقول every bounded sequence every
+
+109
+00:14:23,980 --> 00:14:26,540
+bounded
+
+110
+00:14:28,920 --> 00:14:34,800
+سيكوينس of real
+
+111
+00:14:34,800 --> 00:14:41,980
+numbers in R has a
+
+112
+00:14:41,980 --> 00:14:48,500
+convergent subsequence
+
+113
+00:14:53,720 --> 00:14:58,080
+لو فى عندي bounded sequence of real numbers فبقدر
+
+114
+00:14:58,080 --> 00:15:02,820
+أجى جواتها conversion subsequence البرهان تبع
+
+115
+00:15:02,820 --> 00:15:07,720
+نظريها دى سهل باستخدام نظريات السابقة فى لها
+
+116
+00:15:07,720 --> 00:15:14,300
+برهانين واحد short يعني قصير يعتمد على النظريات
+
+117
+00:15:14,300 --> 00:15:17,840
+الكبيرة اللى برهنها سابقا وفى لها برهان
+
+118
+00:15:21,560 --> 00:15:26,680
+طويل نوعا ما وهذا البرهان constructive proof يعني
+
+119
+00:15:26,680 --> 00:15:30,860
+بورجيكم كيف تبنوا ال subsequence اللي هتكون
+
+120
+00:15:30,860 --> 00:15:36,920
+convergent هناخد ال short proof ونخليكم تقرأوا ال
+
+121
+00:15:36,920 --> 00:15:40,980
+long proof رقم
+
+122
+00:15:40,980 --> 00:15:46,700
+واحد let
+
+123
+00:15:46,700 --> 00:15:47,560
+x in
+
+124
+00:15:50,470 --> 00:15:58,910
+contained are bounded sequence
+
+125
+00:15:58,910 --> 00:16:05,110
+of real numbers by
+
+126
+00:16:05,110 --> 00:16:17,490
+حسب النظرية الأخيرة رقم تمانتاش by theorem تمانتاش
+
+127
+00:16:17,490 --> 00:16:19,410
+المونوتون
+
+128
+00:16:22,580 --> 00:16:30,100
+بتقول أي sequence in R سواء bounded أو unbounded
+
+129
+00:16:30,100 --> 00:16:35,540
+every sequence of real numbers has a monotone
+
+130
+00:16:35,540 --> 00:16:44,360
+subsequence إذا ال XN has a monotone
+
+131
+00:16:44,360 --> 00:16:46,980
+subsequence
+
+132
+00:16:51,810 --> 00:17:02,790
+خلّيني أسميها x in k إذاً
+
+133
+00:17:02,790 --> 00:17:12,110
+هذه عبارة عن monotone subsequence طيب since x in
+
+134
+00:17:12,110 --> 00:17:18,150
+is bounded ال
+
+135
+00:17:18,150 --> 00:17:21,090
+subsequence .. the subsequence
+
+136
+00:17:23,040 --> 00:17:32,960
+x in k is also bounded أي
+
+137
+00:17:32,960 --> 00:17:36,540
+sub sequence من bounded sequence is bounded مظبوط
+
+138
+00:17:36,540 --> 00:17:41,520
+صح لأن x
+
+139
+00:17:41,520 --> 00:17:42,880
+in bounded
+
+140
+00:17:46,080 --> 00:17:52,660
+بقدّي ان يوجد M عدد موجب بحيث ان absolute xn أصغر
+
+141
+00:17:52,660 --> 00:18:01,440
+من أو ساوي M لكل N طب ما هذا بقدّي ان absolute xnk
+
+142
+00:18:01,440 --> 00:18:10,380
+أيضا أصغر من أو ساوي M لكل N لأن ال subsequence
+
+143
+00:18:10,380 --> 00:18:13,500
+xnk هي subset من xn
+
+144
+00:18:16,250 --> 00:18:20,130
+مظبوط؟ كل حد في ال subsequence هو حد في ال
+
+145
+00:18:20,130 --> 00:18:26,370
+sequence وبالتالي تحقق نفس الشرط لأن هذا بيقدي ان
+
+146
+00:18:26,370 --> 00:18:34,190
+كل .. هذا صحيح لكل K لأن هاي .. هذا الشرط منه
+
+147
+00:18:34,190 --> 00:18:37,830
+بيطلع X ان K is bounded
+
+148
+00:18:40,520 --> 00:18:44,940
+Okay إذا أنا كتب برهان أنه أي subsequence من
+
+149
+00:18:44,940 --> 00:18:54,900
+bounded sequence is bounded تمام Now ال
+
+150
+00:18:54,900 --> 00:19:01,980
+subsequence x in k is monotone
+
+151
+00:19:01,980 --> 00:19:05,420
+and
+
+152
+00:19:05,420 --> 00:19:05,980
+bounded
+
+153
+00:19:10,700 --> 00:19:15,920
+So by monotone convergence theorem حسب الـ
+
+154
+00:19:15,920 --> 00:19:20,960
+monotone convergence theorem it is convergent
+
+155
+00:19:26,310 --> 00:19:34,310
+ما هو المطلوب؟ لأن هنا أثبتنا أنه أي sequence أي
+
+156
+00:19:34,310 --> 00:19:37,510
+sequence which is bounded أي sequence of real
+
+157
+00:19:37,510 --> 00:19:41,690
+numbers which is bounded has a convergent
+
+158
+00:19:41,690 --> 00:19:50,490
+subsequence تمام؟ لأن هذا برهن النظرية تمام؟ واضح؟
+
+159
+00:19:50,490 --> 00:20:03,750
+في طبعا برهان تانيو هذا البرهان موجود في الكتاب ان
+
+160
+00:20:03,750 --> 00:20:09,610
+البرهان رقم اتنين proof رقم اتنين موجود في الكتاب
+
+161
+00:20:09,610 --> 00:20:16,130
+see page 79
+
+162
+00:20:16,130 --> 00:20:17,630
+in textbook
+
+163
+00:20:23,250 --> 00:20:27,150
+إذا أنا هنسيبكم تقرأوا البرهان التاني من الكتاب
+
+164
+00:20:27,150 --> 00:20:30,190
+طبعا البرهان هذا هيكون constructive proof بيورجيكم
+
+165
+00:20:30,190 --> 00:20:36,090
+كيف بيبني ال subsequence خطوة خطوة و بحيث انها
+
+166
+00:20:36,090 --> 00:20:43,030
+تطلع convergent طيب في كمال نظرية في هذا السياق
+
+167
+00:20:50,570 --> 00:21:03,690
+theorem اتنين عشرين let
+
+168
+00:21:03,690 --> 00:21:07,910
+x in content
+
+169
+00:21:07,910 --> 00:21:23,610
+in R be bounded bounded sequence and letX ينتمي
+
+170
+00:21:23,610 --> 00:21:29,370
+إلى R بـ
+
+171
+00:21:29,370 --> 00:21:36,870
+such that every .. every convergent .. every
+
+172
+00:21:36,870 --> 00:21:41,610
+convergent subsequence
+
+173
+00:21:41,610 --> 00:21:46,310
+.. every convergent subsequence
+
+174
+00:21:50,710 --> 00:21:59,550
+of سمّيها x أو
+
+175
+00:21:59,550 --> 00:22:08,450
+every convergent subsequence of x in converges to
+
+176
+00:22:08,450 --> 00:22:12,430
+x then
+
+177
+00:22:12,430 --> 00:22:16,930
+النتيجة أنه ال sequence x in
+
+178
+00:22:19,750 --> 00:22:27,190
+converges to x إذا
+
+179
+00:22:27,190 --> 00:22:31,730
+أنا في عندي bounded sequence of real numbersو في
+
+180
+00:22:31,730 --> 00:22:36,910
+اندي عدد حقيقي هذا العدد بيحقق الخاصية انه كل
+
+181
+00:22:36,910 --> 00:22:41,070
+convergence subsequence من ال sequence x in بتكون
+
+182
+00:22:41,070 --> 00:22:45,950
+convergent ل x فالحالة هذه ال sequence الأصلية
+
+183
+00:22:45,950 --> 00:22:51,730
+بتكون convergent و ال limit تبعتها هي نفس العدد x
+
+184
+00:22:51,730 --> 00:22:55,430
+برهان نظرية هذه سهل مش صعب
+
+185
+00:22:59,850 --> 00:23:04,850
+هنستخدم البولزانو virus trust theorem اللي هي
+
+186
+00:23:04,850 --> 00:23:22,730
+نظرية تسعتاش في البرهان هنشوف مع بعض prove assume
+
+187
+00:23:29,790 --> 00:23:37,770
+assume on contrary that
+
+188
+00:23:37,770 --> 00:23:42,890
+احنا عايزين نثبت ان ال sequence x in converge ل x
+
+189
+00:23:42,890 --> 00:23:51,550
+فنفرض ان x in does not converge to any x then
+
+190
+00:23:51,550 --> 00:23:55,330
+by divergence
+
+191
+00:23:57,210 --> 00:24:03,170
+by divergence theorem اللى
+
+192
+00:24:03,170 --> 00:24:10,530
+هى اتنين تمانتاش كذبوت
+
+193
+00:24:10,530 --> 00:24:16,390
+او اتنين سبعتاش اعتقد هيك صح اه ال divergence
+
+194
+00:24:16,390 --> 00:24:22,140
+theorem بتقولى x in does not converge ل xمعناته
+
+195
+00:24:22,140 --> 00:24:26,460
+there exist epsilon zero عدد موجب and there exist
+
+196
+00:24:26,460 --> 00:24:32,980
+a subsequence a subsequence
+
+197
+00:24:32,980 --> 00:24:36,180
+xrn
+
+198
+00:24:36,180 --> 00:24:40,200
+of xn
+
+199
+00:24:42,720 --> 00:24:51,320
+such that absolute x are n minus x أكبر من أو ساوي
+
+200
+00:24:51,320 --> 00:25:01,280
+epsilon zero هذا الكلام صحيح لكل n في n نسمي
+
+201
+00:25:01,280 --> 00:25:07,560
+المتباينة هذه star تمام؟ هذا من نظرية ال
+
+202
+00:25:07,560 --> 00:25:11,740
+divergence اتنين سبعتاش ممكن نحصل على كل هذا
+
+203
+00:25:17,200 --> 00:25:22,140
+طيب since xn
+
+204
+00:25:22,140 --> 00:25:36,260
+is bounded لما انه ال sequence xn is bounded then
+
+205
+00:25:36,260 --> 00:25:45,160
+the subsequence the subsequence xrn is bounded
+
+206
+00:25:49,260 --> 00:25:53,140
+أي subsequence من bounded sequence تطلع bounded جب
+
+207
+00:25:53,140 --> 00:25:59,600
+شوية أثبتنا الكلام هذا so
+
+208
+00:25:59,600 --> 00:26:04,780
+by bolzano
+
+209
+00:26:04,780 --> 00:26:11,680
+weierstrass
+
+210
+00:26:11,680 --> 00:26:19,730
+theorem نظرية bolzano weierstrassهنطبقها على الـ
+
+211
+00:26:19,730 --> 00:26:28,190
+sequence XRN اللي هي bounded فبتقول
+
+212
+00:26:28,190 --> 00:26:33,010
+بولزانو فيروس تراثيرم إذا في عندي sequence و
+
+213
+00:26:33,010 --> 00:26:39,970
+bounded ففي إلها convergence subsequence إذن ال
+
+214
+00:26:39,970 --> 00:26:45,070
+sequence ال
+
+215
+00:26:45,070 --> 00:26:47,410
+sequence XRN
+
+216
+00:26:48,810 --> 00:27:01,550
+has a convergent has a convergent subsequence
+
+217
+00:27:01,550 --> 00:27:04,570
+say
+
+218
+00:27:04,570 --> 00:27:13,270
+خلينا نسميها xkxkn
+
+219
+00:27:13,270 --> 00:27:16,170
+تمام؟
+
+220
+00:27:45,490 --> 00:27:50,890
+فاندي ال ..
+
+221
+00:27:50,890 --> 00:27:56,170
+اذا انا في عندي convergent subsequence من ال
+
+222
+00:27:56,170 --> 00:28:03,390
+subsequence هذه و طبعا هذه subsequence من xn وهذه
+
+223
+00:28:03,390 --> 00:28:07,070
+subsequence من هذه، اذا هذه subsequence من xn
+
+224
+00:28:11,210 --> 00:28:15,570
+بما أن XKN
+
+225
+00:28:15,570 --> 00:28:22,950
+هو أيضًا سبسيكوينس لسيكوينس
+
+226
+00:28:22,950 --> 00:28:28,430
+الأصلية XN ثم
+
+227
+00:28:28,430 --> 00:28:32,330
+بي وهو مرتبط
+
+228
+00:28:41,880 --> 00:28:48,020
+وهو مرتبط ثم
+
+229
+00:28:48,020 --> 00:28:54,650
+من حيث الهيبوتاسيزمن الفرض احنا فرضين في النظرية
+
+230
+00:28:54,650 --> 00:28:59,310
+هذه ان every convergent subsequence of xn لازم
+
+231
+00:28:59,310 --> 00:29:04,890
+تكون convergent للعدد x فهي في عندي subsequence من
+
+232
+00:29:04,890 --> 00:29:09,530
+ال sequence xn وconvergent اذا لازم تكون ال limit
+
+233
+00:29:09,530 --> 00:29:13,430
+تبعتها x اذا من الفرض limit
+
+234
+00:29:15,760 --> 00:29:28,480
+لأكس كأن as n tends to infinity بساوي LX تمام طب
+
+235
+00:29:28,480 --> 00:29:37,720
+احنا عايزين نثبت ان ال XN نفسك converge لل X طيب
+
+236
+00:29:37,720 --> 00:29:44,400
+الآن من تعريفأنا في عندي إبسلون زيرو موجود هاي في
+
+237
+00:29:44,400 --> 00:29:48,900
+عندي إبسلون زيرو أنا في عندي إبسلون زيرو هاد عدد
+
+238
+00:29:48,900 --> 00:29:56,460
+موجود من ال divergence في الفيلم hence وعندي ال
+
+239
+00:29:56,460 --> 00:29:59,520
+subsequence هاد ال converge ل X لذا لما انت عارف
+
+240
+00:29:59,520 --> 00:30:06,660
+ال convergence there exist capital N يعتمد على
+
+241
+00:30:06,660 --> 00:30:08,000
+إبسلون زيرو
+
+242
+00:30:11,600 --> 00:30:19,000
+بحيث ان ال absolute value للحد العام لل sequence
+
+243
+00:30:19,000 --> 00:30:27,320
+XKN المسافة بينه بين ال X أصغر من epsilon zero
+
+244
+00:30:27,320 --> 00:30:35,740
+وهذا الكلام صحيح لكل N في N تمام؟
+
+245
+00:30:37,500 --> 00:30:43,940
+بنسمي المتباين هذي double star الان
+
+246
+00:30:43,940 --> 00:30:57,360
+now star and double star بيقدوا انه ال .. هاي عندي
+
+247
+00:30:57,360 --> 00:31:06,910
+absolute x k n minus x هذا أصغر من epsilon zeroهذا
+
+248
+00:31:06,910 --> 00:31:18,330
+من double star من هنا طب و من ال star انا
+
+249
+00:31:18,330 --> 00:31:23,250
+عندي xrm المسافة بين xrm و x أكبر من او ساوي
+
+250
+00:31:23,250 --> 00:31:24,630
+epsilon zero
+
+251
+00:31:27,280 --> 00:31:34,640
+و هذه sub sequence من ال sub sequence هذه يعني كل
+
+252
+00:31:34,640 --> 00:31:39,520
+حد في ال sequence هذه هو حد في هذه و بالتالي ال
+
+253
+00:31:39,520 --> 00:31:47,860
+sub sequence هذه بتحقق المتباينة star إذن هذا صحيح
+
+254
+00:31:47,860 --> 00:31:52,920
+من star ال absolute الفرقة ده بطلع أكبر من أو ساوي
+
+255
+00:31:52,920 --> 00:31:59,240
+epsilon zero الكلام هذا صحيح لكل n في Mإذا أنا
+
+256
+00:31:59,240 --> 00:32:05,280
+عندي طلع هيك epsilon zero أصغر من epsilon zero و
+
+257
+00:32:05,280 --> 00:32:09,960
+هذا بديني تناقض contradiction إذا التناقض هذا
+
+258
+00:32:09,960 --> 00:32:19,040
+السبب تبعه إن إحنا فرضنا إن xn does not converge ل
+
+259
+00:32:19,040 --> 00:32:23,660
+x إذا ال contradiction هذه بتقول إن xn لازم
+
+260
+00:32:23,660 --> 00:32:30,900
+converge ل x و هذا اللي بدنا ياه وهم المطلوبوهو
+
+261
+00:32:30,900 --> 00:32:35,700
+المطلوب okay إذا هيك بنكون برهننا النظرية هذه
+
+262
+00:32:35,700 --> 00:32:43,200
+خلينا ناخد احنا break عشان فينا لقاء تاني لمدة خمس
+
+263
+00:32:43,200 --> 00:32:46,120
+دقايق و بعدين يعني نرجع، ماشي الحال؟
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a39ae25c12e87b0b5992d99a9527da9e8a555cb
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.json
@@ -0,0 +1 @@
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"word": " وفي", "probability": 0.888916015625}, {"start": 88.2, "end": 88.94, "word": " شرط", "probability": 0.96875}, {"start": 88.94, "end": 90.18, "word": " التالت", "probability": 0.9772135416666666}, {"start": 90.18, "end": 93.02, "word": " أنا", "probability": 0.434326171875}, {"start": 93.02, "end": 93.46, "word": " بهمش", "probability": 0.6813151041666666}, {"start": 93.46, "end": 93.78, "word": " شرط", "probability": 0.9554036458333334}, {"start": 93.78, "end": 94.2, "word": " التالت", "probability": 0.9734700520833334}, {"start": 94.2, "end": 94.4, "word": " أو", "probability": 0.7509765625}, {"start": 94.4, "end": 94.84, "word": " العبارة", "probability": 0.968505859375}, {"start": 94.84, "end": 95.42, "word": " تالتة", "probability": 0.75701904296875}, {"start": 95.42, "end": 95.62, "word": " there", "probability": 0.70751953125}, {"start": 95.62, "end": 96.22, "word": " exist", "probability": 0.755859375}, {"start": 96.22, "end": 97.76, "word": " إبسلون", "probability": 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28820, 376], "avg_logprob": -0.4158380553126335, "compression_ratio": 1.1666666666666667, "no_speech_prob": 0.0, "words": [{"start": 102.13, "end": 102.69, "word": "أو", "probability": 0.514801025390625}, {"start": 102.69, "end": 103.95, "word": " سبسيكوينس", "probability": 0.599578857421875}, {"start": 103.95, "end": 108.39, "word": " XRN", "probability": 0.572998046875}, {"start": 108.39, "end": 113.41, "word": " of", "probability": 0.31005859375}, {"start": 113.41, "end": 114.59, "word": " سيكوينس", "probability": 0.8810221354166666}, {"start": 114.59, "end": 115.59, "word": " XN", "probability": 0.783447265625}, {"start": 115.59, "end": 117.49, "word": " such", "probability": 0.51171875}, {"start": 117.49, "end": 118.31, "word": " that", "probability": 0.94921875}, {"start": 118.31, "end": 119.63, "word": " absolute", "probability": 0.49169921875}, {"start": 119.63, "end": 122.41, "word": " XRN", "probability": 0.9324544270833334}, {"start": 122.41, "end": 123.15, "word": " minus", "probability": 0.72705078125}, {"start": 123.15, "end": 123.79, "word": " X", "probability": 0.98828125}, {"start": 123.79, "end": 125.51, "word": " أكبر", "probability": 0.9041341145833334}, {"start": 125.51, "end": 125.75, "word": " من", "probability": 0.9111328125}, {"start": 125.75, "end": 125.95, "word": " أو", "probability": 0.962890625}, {"start": 125.95, "end": 126.57, "word": " ساوي", "probability": 0.8992513020833334}, {"start": 126.57, "end": 127.51, "word": " Y0", "probability": 0.435791015625}, {"start": 127.51, "end": 128.09, "word": " لكل", "probability": 0.9716796875}, {"start": 128.09, "end": 128.55, "word": " M", "probability": 0.318359375}], "temperature": 1.0}, {"id": 5, "seek": 15949, "start": 133.97, "end": 159.49, "text": "و بدنا ناخد أنثى على النظرية هذه أخدناها المرة الفاتة مثال مثال التانى example consider", "tokens": [2407, 47525, 8315, 8717, 47283, 3215, 14739, 12984, 7578, 15844, 28239, 19913, 2288, 10632, 29538, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 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0.7047526041666666}, {"start": 138.95, "end": 142.29, "word": " مثال", "probability": 0.971923828125}, {"start": 142.29, "end": 149.47, "word": " مثال", "probability": 0.7900390625}, {"start": 149.47, "end": 150.05, "word": " التانى", "probability": 0.8792317708333334}, {"start": 150.05, "end": 150.67, "word": " example", "probability": 0.78076171875}, {"start": 150.67, "end": 159.49, "word": " consider", "probability": 0.83154296875}], "temperature": 1.0}, {"id": 6, "seek": 18625, "start": 161.81, "end": 186.25, "text": "ناخد ال sequence consider xn where sequence xn لحد العالم تبعها xn معرف على انه بساوي n if n is odd و بتساوي واحد على n", "tokens": [1863, 47283, 3215, 2423, 8310, 1949, 2031, 77, 689, 8310, 2031, 77, 5296, 24401, 18863, 45340, 6055, 3555, 3615, 11296, 2031, 77, 20449, 28480, 15844, 16472, 3224, 4724, 3794, 995, 45865, 297, 498, 297, 307, 7401, 4032, 39894, 3794, 995, 45865, 36764, 24401, 15844, 297], "avg_logprob": -0.22894021285616833, "compression_ratio": 1.3333333333333333, "no_speech_prob": 0.0, "words": [{"start": 161.81, "end": 162.41, "word": "ناخد", "probability": 0.8004557291666666}, {"start": 162.41, "end": 162.57, "word": " ال", "probability": 0.83251953125}, {"start": 162.57, "end": 162.91, "word": " sequence", "probability": 0.3544921875}, {"start": 162.91, "end": 163.77, "word": " consider", "probability": 0.7021484375}, {"start": 163.77, "end": 164.71, "word": " xn", "probability": 0.695556640625}, {"start": 164.71, "end": 167.69, "word": " where", "probability": 0.712890625}, {"start": 167.69, "end": 168.53, "word": " sequence", "probability": 0.63330078125}, {"start": 168.53, "end": 169.11, "word": " xn", "probability": 0.965087890625}, {"start": 169.11, "end": 169.51, "word": " لحد", "probability": 0.86376953125}, {"start": 169.51, "end": 169.83, "word": " العالم", "probability": 0.961181640625}, {"start": 169.83, "end": 170.49, "word": " تبعها", "probability": 0.909423828125}, {"start": 170.49, "end": 171.97, "word": " xn", "probability": 0.826171875}, {"start": 171.97, "end": 172.69, "word": " معرف", "probability": 0.92236328125}, {"start": 172.69, "end": 172.99, "word": " على", "probability": 0.80322265625}, {"start": 172.99, "end": 173.53, "word": " انه", "probability": 0.71533203125}, {"start": 173.53, "end": 175.85, "word": " بساوي", "probability": 0.8585205078125}, {"start": 175.85, "end": 176.29, "word": " n", "probability": 0.54150390625}, {"start": 176.29, "end": 176.95, "word": " if", "probability": 0.85400390625}, {"start": 176.95, "end": 179.15, "word": " n", "probability": 0.875}, {"start": 179.15, "end": 179.71, "word": " is", "probability": 0.96826171875}, {"start": 179.71, "end": 180.21, "word": " odd", "probability": 0.923828125}, {"start": 180.21, "end": 184.61, "word": " و", "probability": 0.56884765625}, {"start": 184.61, "end": 185.21, "word": " بتساوي", "probability": 0.819091796875}, {"start": 185.21, "end": 185.67, "word": " واحد", "probability": 0.804443359375}, {"start": 185.67, "end": 185.87, "word": " على", "probability": 0.724609375}, {"start": 185.87, "end": 186.25, "word": " n", "probability": 0.67919921875}], "temperature": 1.0}, {"id": 7, "seek": 20869, "start": 200.35, "end": 208.69, "text": "مطلوب ان اثبت ان ال sequence xn is divergent", "tokens": [2304, 9566, 1211, 37746, 16472, 1975, 12984, 3555, 2655, 16472, 2423, 8310, 2031, 77, 307, 18558, 6930], "avg_logprob": -0.5629340509573618, "compression_ratio": 0.9672131147540983, "no_speech_prob": 0.0, "words": [{"start": 200.35000000000002, "end": 201.27, "word": "مطلوب", "probability": 0.60516357421875}, {"start": 201.27, "end": 201.49, "word": " ان", "probability": 0.446044921875}, {"start": 201.49, "end": 202.29, "word": " اثبت", "probability": 0.87744140625}, {"start": 202.29, "end": 202.51, "word": " ان", "probability": 0.93408203125}, {"start": 202.51, "end": 202.67, "word": " ال", "probability": 0.400146484375}, {"start": 202.67, "end": 203.11, "word": " sequence", "probability": 0.37744140625}, {"start": 203.11, "end": 204.01, "word": " xn", "probability": 0.4139404296875}, {"start": 204.01, "end": 204.47, "word": " is", "probability": 0.264892578125}, {"start": 204.47, "end": 208.69, "word": " divergent", "probability": 0.83740234375}], "temperature": 1.0}, {"id": 8, "seek": 24039, "start": 221.55, "end": 240.39, "text": "سلوشن و لاحظوا ان سيكوانس X انها بيبارى حدودها واحد نص و واحد نص تلاتة رابع و هكذا", "tokens": [3794, 1211, 2407, 8592, 1863, 4032, 20193, 5016, 19913, 14407, 16472, 8608, 1829, 4117, 2407, 7649, 3794, 1783, 16472, 11296, 4724, 1829, 3555, 9640, 7578, 11331, 3215, 23328, 11296, 36764, 24401, 8717, 9381, 4032, 36764, 24401, 8717, 9381, 6055, 1211, 9307, 3660, 12602, 16758, 3615, 4032, 8032, 4117, 15730], "avg_logprob": -0.3824999928474426, "compression_ratio": 1.46, "no_speech_prob": 0.0, "words": [{"start": 221.55, "end": 222.55, "word": "سلوشن", "probability": 0.59228515625}, {"start": 222.55, "end": 223.91, "word": " و", "probability": 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0.993408203125}, {"start": 234.35, "end": 236.19, "word": " تلاتة", "probability": 0.8076171875}, {"start": 236.19, "end": 236.65, "word": " رابع", "probability": 0.75732421875}, {"start": 236.65, "end": 239.85, "word": " و", "probability": 0.63623046875}, {"start": 239.85, "end": 240.39, "word": " هكذا", "probability": 0.90185546875}], "temperature": 1.0}, {"id": 9, "seek": 27144, "start": 248.08, "end": 271.44, "text": "فالـ sequence هذه بالنسبة لها does not converge لأي x ينتمي لR to show أن x in does not converge ل x for any x ينتمي إلى R", "tokens": [5172, 6027, 39184, 8310, 29538, 20666, 1863, 35457, 3660, 5296, 11296, 775, 406, 41881, 5296, 10721, 1829, 2031, 7251, 29399, 2304, 1829, 5296, 49, 281, 855, 14739, 2031, 294, 775, 406, 41881, 5296, 2031, 337, 604, 2031, 7251, 29399, 2304, 1829, 30731, 497], "avg_logprob": -0.289595173841173, "compression_ratio": 1.3032786885245902, "no_speech_prob": 0.0, "words": [{"start": 248.08, "end": 248.72, "word": "فالـ", "probability": 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"end": 257.22, "word": " show", "probability": 0.97119140625}, {"start": 257.22, "end": 260.18, "word": " أن", "probability": 0.43994140625}, {"start": 260.18, "end": 260.6, "word": " x", "probability": 0.59765625}, {"start": 260.6, "end": 260.92, "word": " in", "probability": 0.2283935546875}, {"start": 260.92, "end": 261.26, "word": " does", "probability": 0.84814453125}, {"start": 261.26, "end": 261.7, "word": " not", "probability": 0.95556640625}, {"start": 261.7, "end": 262.84, "word": " converge", "probability": 0.9814453125}, {"start": 262.84, "end": 263.04, "word": " ل", "probability": 0.93310546875}, {"start": 263.04, "end": 263.44, "word": " x", "probability": 0.478515625}, {"start": 263.44, "end": 264.6, "word": " for", "probability": 0.9365234375}, {"start": 264.6, "end": 265.14, "word": " any", "probability": 0.8955078125}, {"start": 265.14, "end": 269.72, "word": " x", "probability": 0.46923828125}, {"start": 269.72, "end": 270.62, "word": " ينتمي", "probability": 0.957275390625}, {"start": 270.62, "end": 270.98, "word": " إلى", "probability": 0.7080078125}, {"start": 270.98, "end": 271.44, "word": " R", "probability": 0.96240234375}], "temperature": 1.0}, {"id": 10, "seek": 30219, "start": 275.59, "end": 302.19, "text": "fix x ينتمي ل r خلّينا ناخد arbitrary ال real number x ينتمي ل r و نثبت ان x in does not converge enough فعندي then absolute x طبعا أكبر عدد حقيقي أكبر من أوسعه سفر so by", "tokens": [69, 970, 2031, 7251, 29399, 2304, 1829, 5296, 367, 16490, 1211, 11703, 9957, 995, 8717, 47283, 3215, 23211, 2423, 957, 1230, 2031, 7251, 29399, 2304, 1829, 5296, 367, 4032, 8717, 12984, 3555, 2655, 16472, 2031, 294, 775, 406, 41881, 1547, 6156, 3615, 1863, 16254, 550, 8236, 2031, 23032, 3555, 3615, 995, 5551, 4117, 26890, 6225, 3215, 3215, 11331, 38436, 38436, 5551, 4117, 26890, 9154, 34051, 3794, 3615, 3224, 8608, 5172, 2288, 370, 538], "avg_logprob": -0.301309118802483, "compression_ratio": 1.3563218390804597, "no_speech_prob": 0.0, "words": 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"probability": 0.7752685546875}, {"start": 291.01, "end": 294.73, "word": " then", "probability": 0.72265625}, {"start": 294.73, "end": 295.39, "word": " absolute", "probability": 0.93017578125}, {"start": 295.39, "end": 296.13, "word": " x", "probability": 0.9794921875}, {"start": 296.13, "end": 296.63, "word": " طبعا", "probability": 0.9273681640625}, {"start": 296.63, "end": 297.17, "word": " أكبر", "probability": 0.8836263020833334}, {"start": 297.17, "end": 297.57, "word": " عدد", "probability": 0.93505859375}, {"start": 297.57, "end": 298.09, "word": " حقيقي", "probability": 0.97314453125}, {"start": 298.09, "end": 298.51, "word": " أكبر", "probability": 0.92431640625}, {"start": 298.51, "end": 298.65, "word": " من", "probability": 0.98583984375}, {"start": 298.65, "end": 299.15, "word": " أوسعه", "probability": 0.6783447265625}, {"start": 299.15, "end": 299.67, "word": " سفر", "probability": 0.7576497395833334}, {"start": 299.67, "end": 301.59, "word": " so", "probability": 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"word": " عدد", "probability": 0.96923828125}, {"start": 312.96, "end": 313.5, "word": " طبيعي", "probability": 0.97265625}, {"start": 313.5, "end": 314.1, "word": " يعتمد", "probability": 0.9718017578125}, {"start": 314.1, "end": 314.32, "word": " على", "probability": 0.74267578125}, {"start": 314.32, "end": 314.76, "word": " x", "probability": 0.90185546875}, {"start": 314.76, "end": 315.22, "word": " عدد", "probability": 0.9744466145833334}, {"start": 315.22, "end": 316.18, "word": " طبيعي", "probability": 0.9854736328125}, {"start": 316.18, "end": 319.66, "word": " بحيث", "probability": 0.9473876953125}, {"start": 319.66, "end": 319.96, "word": " ان", "probability": 0.60595703125}, {"start": 319.96, "end": 320.64, "word": " n", "probability": 0.1995849609375}, {"start": 320.64, "end": 321.22, "word": " x", "probability": 0.623046875}, {"start": 321.22, "end": 321.68, "word": " هذا", "probability": 0.66015625}, {"start": 321.68, "end": 322.54, "word": " is", "probability": 0.9033203125}, {"start": 322.54, "end": 323.18, "word": " even", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 12, "seek": 34196, "start": 325.42, "end": 341.96, "text": "and absolute x أصغر من nx هذا ممكن نحصل عليه من الarchimedean property", "tokens": [474, 8236, 2031, 5551, 9381, 17082, 2288, 9154, 297, 87, 23758, 3714, 43020, 8717, 5016, 36520, 47356, 9154, 2423, 1178, 332, 4858, 282, 4707], "avg_logprob": -0.2281249952316284, "compression_ratio": 0.9895833333333334, "no_speech_prob": 0.0, "words": [{"start": 325.42, "end": 326.12, "word": "and", "probability": 0.39404296875}, {"start": 326.12, "end": 327.76, "word": " absolute", "probability": 0.822265625}, {"start": 327.76, "end": 328.72, "word": " x", "probability": 0.76416015625}, {"start": 328.72, "end": 330.2, "word": " أصغر", "probability": 0.9664306640625}, {"start": 330.2, "end": 330.46, "word": " من", "probability": 0.98974609375}, {"start": 330.46, "end": 331.42, "word": " nx", "probability": 0.5673828125}, 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{"start": 379.09, "end": 380.15, "word": " موجب", "probability": 0.9939778645833334}, {"start": 380.15, "end": 384.17, "word": " و", "probability": 0.50048828125}, {"start": 384.17, "end": 385.93, "word": " ال", "probability": 0.8310546875}, {"start": 385.93, "end": 386.55, "word": " sequence", "probability": 0.94384765625}, {"start": 386.55, "end": 390.19, "word": " ال", "probability": 0.75537109375}, {"start": 390.19, "end": 391.07, "word": " sequence", "probability": 0.81982421875}, {"start": 391.07, "end": 391.67, "word": " الحد", "probability": 0.7005615234375}, {"start": 391.67, "end": 391.97, "word": " العام", "probability": 0.90576171875}, {"start": 391.97, "end": 392.65, "word": " تبعها", "probability": 0.9200439453125}, {"start": 392.65, "end": 394.03, "word": " N", "probability": 0.273681640625}, {"start": 394.03, "end": 394.95, "word": " X", "probability": 0.53076171875}, {"start": 394.95, "end": 397.37, "word": " زائد", "probability": 0.70166015625}, {"start": 397.37, "end": 398.09, "word": " اتنين", "probability": 0.88037109375}, {"start": 398.09, "end": 398.63, "word": " M", "probability": 0.916015625}, {"start": 398.63, "end": 399.39, "word": " سالد", "probability": 0.744384765625}, {"start": 399.39, "end": 399.93, "word": " واحد", "probability": 0.981201171875}], "temperature": 1.0}, {"id": 15, "seek": 42989, "start": 403.11, "end": 429.89, "text": "من M بساوي واحد to infinity هذه بالمناسبة الحدود تبعتها هذا عدد فردي عدد طبيعي فردي وهذا NX عدد طبيعي زوجي هذا odd وهذا even", "tokens": [27842, 376, 4724, 3794, 995, 45865, 36764, 24401, 281, 13202, 29538, 20666, 2304, 8315, 35457, 3660, 21542, 3215, 23328, 6055, 3555, 34268, 11296, 23758, 6225, 3215, 3215, 6156, 2288, 16254, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 6156, 2288, 16254, 37037, 15730, 426, 55, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 30767, 29245, 1829, 23758, 7401, 37037, 15730, 754], "avg_logprob": -0.11621094072858493, "compression_ratio": 1.489051094890511, "no_speech_prob": 0.0, "words": [{"start": 403.11, "end": 403.55, "word": "من", "probability": 0.87158203125}, {"start": 403.55, "end": 403.89, "word": " M", "probability": 0.53369140625}, {"start": 403.89, "end": 404.77, "word": " بساوي", "probability": 0.779296875}, {"start": 404.77, "end": 405.51, "word": " واحد", "probability": 0.85791015625}, {"start": 405.51, "end": 405.77, "word": " to", "probability": 0.677734375}, {"start": 405.77, "end": 406.43, "word": " infinity", "probability": 0.73095703125}, {"start": 406.43, "end": 409.41, "word": " هذه", "probability": 0.6279296875}, {"start": 409.41, "end": 410.39, "word": " بالمناسبة", "probability": 0.9779296875}, {"start": 410.39, "end": 411.01, "word": " الحدود", "probability": 0.9065755208333334}, {"start": 411.01, "end": 411.85, "word": " تبعتها", "probability": 0.9276123046875}, {"start": 411.85, "end": 414.09, "word": " هذا", "probability": 0.859375}, {"start": 414.09, "end": 414.53, "word": " عدد", "probability": 0.984375}, {"start": 414.53, "end": 415.05, "word": " فردي", "probability": 0.8186848958333334}, {"start": 415.05, "end": 415.55, "word": " عدد", "probability": 0.92138671875}, {"start": 415.55, "end": 415.99, "word": " طبيعي", "probability": 0.987060546875}, {"start": 415.99, "end": 416.53, "word": " فردي", "probability": 0.9694010416666666}, {"start": 416.53, "end": 420.77, "word": " وهذا", "probability": 0.81298828125}, {"start": 420.77, "end": 421.59, "word": " NX", "probability": 0.673095703125}, {"start": 421.59, "end": 423.07, "word": " عدد", "probability": 0.98583984375}, {"start": 423.07, "end": 423.59, "word": " طبيعي", "probability": 0.9918212890625}, {"start": 423.59, "end": 424.19, "word": " زوجي", "probability": 0.9581705729166666}, {"start": 424.19, "end": 425.15, "word": " هذا", "probability": 0.7421875}, {"start": 425.15, "end": 425.57, "word": " odd", "probability": 0.716796875}, {"start": 425.57, "end": 429.19, "word": " وهذا", "probability": 0.920654296875}, {"start": 429.19, "end": 429.89, "word": " even", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 16, "seek": 45960, "start": 433.3, "end": 459.6, "text": "ف odd زائد even بطلع odd إذا الحدود العامة لل sequence هذه بتكون odd وبالتالي الحدود هذه كلها حسب التعريف بتطلع بالساوي", "tokens": [5172, 7401, 30767, 16373, 3215, 754, 4724, 9566, 1211, 3615, 7401, 11933, 15730, 21542, 3215, 23328, 18863, 10943, 3660, 24976, 8310, 29538, 39894, 30544, 7401, 46599, 6027, 2655, 6027, 1829, 21542, 3215, 23328, 29538, 28242, 11296, 11331, 35457, 16712, 3615, 16572, 5172, 39894, 9566, 1211, 3615, 20666, 3794, 995, 45865], "avg_logprob": -0.22916666725102594, "compression_ratio": 1.462686567164179, "no_speech_prob": 0.0, "words": [{"start": 433.3, "end": 433.72, "word": "ف", "probability": 0.417236328125}, {"start": 433.72, "end": 434.06, "word": " odd", "probability": 0.473876953125}, {"start": 434.06, "end": 434.6, "word": " زائد", "probability": 0.6158040364583334}, {"start": 434.6, "end": 435.08, "word": " even", 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طبيعي فردي فممكن نشيل absolute value وهذا العدد هذا العدد أكبر من NX سالب absolute X", "tokens": [3224, 15730, 6225, 3215, 3215, 3714, 29245, 3555, 23758, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 37037, 15730, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 6156, 2288, 16254, 6156, 2304, 43020, 8717, 8592, 26895, 8236, 2158, 37037, 15730, 18863, 3215, 3215, 23758, 18863, 3215, 3215, 5551, 4117, 26890, 9154, 426, 55, 8608, 6027, 3555, 8236, 1783], "avg_logprob": -0.14610746241452402, "compression_ratio": 1.6355932203389831, "no_speech_prob": 0.0, "words": [{"start": 547.04, "end": 547.4, "word": "هذا", "probability": 0.90771484375}, {"start": 547.4, "end": 547.72, "word": " عدد", "probability": 0.9586588541666666}, {"start": 547.72, "end": 548.26, "word": " موجب", "probability": 0.9537760416666666}, {"start": 548.26, "end": 548.58, "word": " هذا", "probability": 0.34521484375}, {"start": 548.58, "end": 548.86, "word": " عدد", "probability": 0.9908854166666666}, {"start": 548.86, "end": 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"end": 621.59, "word": " العام", "probability": 0.986328125}, {"start": 621.59, "end": 621.85, "word": " لل", "probability": 0.81640625}, {"start": 621.85, "end": 622.29, "word": " sequence", "probability": 0.87109375}, {"start": 622.29, "end": 622.89, "word": " هذه", "probability": 0.4189453125}, {"start": 622.89, "end": 623.95, "word": " و", "probability": 0.8125}, {"start": 623.95, "end": 624.11, "word": " ال", "probability": 0.6318359375}, {"start": 624.11, "end": 624.41, "word": " x", "probability": 0.7099609375}, {"start": 624.41, "end": 625.03, "word": " أكبر", "probability": 0.9664713541666666}, {"start": 625.03, "end": 625.27, "word": " من", "probability": 0.99560546875}, {"start": 625.27, "end": 626.35, "word": " y0", "probability": 0.890625}, {"start": 626.35, "end": 627.57, "word": " لكل", "probability": 0.975830078125}, {"start": 627.57, "end": 627.95, "word": " m", "probability": 0.4814453125}, {"start": 627.95, "end": 628.15, "word": " في", "probability": 0.64892578125}, {"start": 628.15, "end": 628.43, "word": " n", "probability": 0.896484375}], "temperature": 1.0}, {"id": 23, "seek": 65233, "start": 634.11, "end": 652.33, "text": "الـ divergence theorem الجزء التالت هيتحقق شروطه وبالتالي ال sequence x in does not converge to x", "tokens": [6027, 39184, 47387, 20904, 2423, 7435, 11622, 38207, 16712, 6027, 2655, 8032, 36081, 5016, 4587, 4587, 13412, 32887, 9566, 3224, 46599, 6027, 2655, 6027, 1829, 2423, 8310, 2031, 294, 775, 406, 41881, 281, 2031], "avg_logprob": -0.27187499148505073, "compression_ratio": 1.1891891891891893, "no_speech_prob": 0.0, "words": [{"start": 634.11, "end": 634.97, "word": "الـ", "probability": 0.38037109375}, {"start": 634.97, "end": 635.55, "word": " divergence", "probability": 0.818359375}, {"start": 635.55, "end": 638.23, "word": " theorem", "probability": 0.8486328125}, {"start": 638.23, "end": 640.51, "word": " الجزء", "probability": 0.7864990234375}, {"start": 640.51, "end": 641.19, "word": " التالت", "probability": 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"temperature": 1.0}, {"id": 24, "seek": 68489, "start": 656.67, "end": 684.89, "text": "بما أن x was arbitrary إذا الـ sequence x in does not converge لأي عدد حقيقي x وبالتالي divergent تمام؟ أنا هنا استخدمت ال divergence theorem في أثبات أن ال sequence هذه divergent لاحظوا أن ال sequence 1 على n هذه subsequence من x in وهذه convergent ل0", "tokens": [3555, 15042, 14739, 2031, 390, 23211, 11933, 15730, 2423, 39184, 8310, 2031, 294, 775, 406, 41881, 5296, 10721, 1829, 6225, 3215, 3215, 11331, 38436, 38436, 2031, 46599, 6027, 2655, 6027, 1829, 18558, 6930, 46811, 10943, 22807, 41850, 34105, 44713, 9778, 40448, 2655, 2423, 47387, 20904, 8978, 5551, 12984, 3555, 9307, 14739, 2423, 8310, 29538, 18558, 6930, 20193, 5016, 19913, 14407, 14739, 2423, 8310, 502, 15844, 297, 29538, 13924, 655, 9154, 2031, 294, 37037, 24192, 9652, 6930, 5296, 15], "avg_logprob": -0.2994462168669399, "compression_ratio": 1.6066350710900474, "no_speech_prob": 0.0, "words": [{"start": 656.67, "end": 657.11, "word": 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676.67, "end": 677.11, "word": " 1", "probability": 0.451904296875}, {"start": 677.11, "end": 677.41, "word": " على", "probability": 0.640625}, {"start": 677.41, "end": 677.75, "word": " n", "probability": 0.77685546875}, {"start": 677.75, "end": 680.27, "word": " هذه", "probability": 0.64501953125}, {"start": 680.27, "end": 681.17, "word": " subsequence", "probability": 0.891357421875}, {"start": 681.17, "end": 681.39, "word": " من", "probability": 0.97265625}, {"start": 681.39, "end": 681.69, "word": " x", "probability": 0.93212890625}, {"start": 681.69, "end": 681.99, "word": " in", "probability": 0.70703125}, {"start": 681.99, "end": 683.71, "word": " وهذه", "probability": 0.896728515625}, {"start": 683.71, "end": 684.43, "word": " convergent", "probability": 0.7451171875}, {"start": 684.43, "end": 684.89, "word": " ل0", "probability": 0.6121826171875}], "temperature": 1.0}, {"id": 25, "seek": 71050, "start": 688.58, "end": 710.5, "text": "لكن الـ sequence نفسها does not converge هذه برضه subsequence N subsequence .. لما تكون الـ N فردية subsequence من X N وهذه is not convergent هذه ال limit بتاعها infinity طبعا؟ و هذا؟ في عيز سؤال؟", "tokens": [1211, 19452, 2423, 39184, 8310, 8717, 36178, 11296, 775, 406, 41881, 29538, 4724, 43042, 3224, 13924, 655, 426, 13924, 655, 4386, 5296, 15042, 6055, 30544, 2423, 39184, 426, 6156, 2288, 3215, 10632, 13924, 655, 9154, 1783, 426, 37037, 24192, 307, 406, 9652, 6930, 29538, 2423, 4948, 39894, 45761, 11296, 13202, 23032, 3555, 3615, 995, 22807, 4032, 23758, 22807, 8978, 6225, 1829, 11622, 8608, 33604, 6027, 22807], "avg_logprob": -0.3400186700607414, "compression_ratio": 1.502824858757062, "no_speech_prob": 0.0, "words": [{"start": 688.58, "end": 689.06, "word": "لكن", "probability": 0.7435302734375}, {"start": 689.06, "end": 689.2, "word": " الـ", "probability": 0.609130859375}, {"start": 689.2, "end": 689.58, "word": " sequence", "probability": 0.7353515625}, {"start": 689.58, "end": 690.32, "word": " نفسها", 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{"start": 696.54, "end": 696.68, "word": " N", "probability": 0.90869140625}, {"start": 696.68, "end": 697.22, "word": " فردية", "probability": 0.9439697265625}, {"start": 697.22, "end": 698.14, "word": " subsequence", "probability": 0.9609375}, {"start": 698.14, "end": 698.4, "word": " من", "probability": 0.9619140625}, {"start": 698.4, "end": 698.7, "word": " X", "probability": 0.93359375}, {"start": 698.7, "end": 699.0, "word": " N", "probability": 0.498291015625}, {"start": 699.0, "end": 700.76, "word": " وهذه", "probability": 0.794189453125}, {"start": 700.76, "end": 701.04, "word": " is", "probability": 0.267822265625}, {"start": 701.04, "end": 701.3, "word": " not", "probability": 0.95751953125}, {"start": 701.3, "end": 702.0, "word": " convergent", "probability": 0.94189453125}, {"start": 702.0, "end": 702.36, "word": " هذه", "probability": 0.5380859375}, {"start": 702.36, "end": 702.62, "word": " ال", "probability": 0.5322265625}, {"start": 702.62, "end": 702.86, "word": " limit", "probability": 0.66943359375}, {"start": 702.86, "end": 703.24, "word": " بتاعها", "probability": 0.5936686197916666}, {"start": 703.24, "end": 703.8, "word": " infinity", "probability": 0.751953125}, {"start": 703.8, "end": 706.12, "word": " طبعا؟", "probability": 0.78134765625}, {"start": 706.12, "end": 709.34, "word": " و", "probability": 0.66259765625}, {"start": 709.34, "end": 709.66, "word": " هذا؟", "probability": 0.3253173828125}, {"start": 709.66, "end": 709.76, "word": " في", "probability": 0.7900390625}, {"start": 709.76, "end": 709.98, "word": " عيز", "probability": 0.4004720052083333}, {"start": 709.98, "end": 710.5, "word": " سؤال؟", "probability": 0.973876953125}], "temperature": 1.0}, {"id": 26, "seek": 75223, "start": 725.31, "end": 752.23, "text": "monotone subsequence theorem النظرية اتنين تمانتاش أقامها هنا النظرية هذه بتقول every sequence in R has", "tokens": [3317, 310, 546, 13924, 655, 20904, 28239, 19913, 2288, 10632, 1975, 2655, 1863, 9957, 46811, 7649, 2655, 33599, 5551, 4587, 10943, 11296, 34105, 28239, 19913, 2288, 10632, 29538, 39894, 39648, 633, 8310, 294, 497, 575], "avg_logprob": -0.2261284759475125, "compression_ratio": 1.2066115702479339, "no_speech_prob": 0.0, "words": [{"start": 725.3100000000001, "end": 726.71, "word": "monotone", "probability": 0.6883138020833334}, {"start": 726.71, "end": 728.11, "word": " subsequence", "probability": 0.98681640625}, {"start": 728.11, "end": 728.75, "word": " theorem", "probability": 0.884765625}, {"start": 728.75, "end": 732.05, "word": " النظرية", "probability": 0.8603515625}, {"start": 732.05, "end": 732.81, "word": " اتنين", "probability": 0.738372802734375}, {"start": 732.81, "end": 733.79, "word": " تمانتاش", "probability": 0.8101806640625}, {"start": 733.79, "end": 734.39, "word": " أقامها", "probability": 0.81695556640625}, {"start": 734.39, "end": 735.57, "word": " هنا", "probability": 0.71240234375}, {"start": 735.57, "end": 743.33, "word": " النظرية", "probability": 0.9730224609375}, {"start": 743.33, "end": 743.53, "word": " هذه", "probability": 0.443359375}, {"start": 743.53, "end": 743.97, "word": " بتقول", "probability": 0.972412109375}, {"start": 743.97, "end": 744.55, "word": " every", "probability": 0.7314453125}, {"start": 744.55, "end": 746.69, "word": " sequence", "probability": 0.98486328125}, {"start": 746.69, "end": 748.93, "word": " in", "probability": 0.9443359375}, {"start": 748.93, "end": 749.53, "word": " R", "probability": 0.9462890625}, {"start": 749.53, "end": 752.23, "word": " has", "probability": 0.90673828125}], "temperature": 1.0}, {"id": 27, "seek": 77805, "start": 756.91, "end": 778.05, "text": "monotone subsequence كل sequence of real numbers ممكن نستخلص منها monotone subsequence البرهان تبع النظرية هذه مش صعب موجود في الكتاب هخليكم تقراه", "tokens": [3317, 310, 546, 13924, 655, 28242, 8310, 295, 957, 3547, 3714, 43020, 8717, 14851, 9778, 1211, 9381, 9154, 11296, 1108, 310, 546, 13924, 655, 2423, 26890, 3224, 7649, 6055, 3555, 3615, 28239, 19913, 2288, 10632, 29538, 37893, 20328, 3615, 3555, 3714, 29245, 23328, 8978, 33251, 2655, 16758, 8032, 9778, 20292, 24793, 6055, 4587, 23557, 3224], "avg_logprob": -0.137904572433659, "compression_ratio": 1.388157894736842, "no_speech_prob": 0.0, "words": [{"start": 756.9100000000001, "end": 758.19, "word": "monotone", "probability": 0.6192220052083334}, {"start": 758.19, "end": 759.47, "word": " subsequence", "probability": 0.97216796875}, {"start": 759.47, "end": 761.33, "word": " كل", "probability": 0.61083984375}, {"start": 761.33, "end": 763.69, "word": " sequence", "probability": 0.86376953125}, {"start": 763.69, "end": 764.03, "word": " of", "probability": 0.859375}, {"start": 764.03, "end": 764.29, "word": " real", "probability": 0.96435546875}, {"start": 764.29, "end": 764.93, "word": " numbers", "probability": 0.83203125}, {"start": 764.93, "end": 765.95, "word": " ممكن", "probability": 0.969970703125}, {"start": 765.95, "end": 766.63, "word": " نستخلص", "probability": 0.96962890625}, {"start": 766.63, "end": 767.09, "word": " منها", "probability": 0.991455078125}, {"start": 767.09, "end": 768.91, "word": " monotone", "probability": 0.89208984375}, {"start": 768.91, "end": 770.69, "word": " subsequence", "probability": 0.99755859375}, {"start": 770.69, "end": 773.47, "word": " البرهان", "probability": 0.8338623046875}, {"start": 773.47, "end": 773.77, "word": " تبع", "probability": 0.8619791666666666}, {"start": 773.77, "end": 774.29, "word": " النظرية", "probability": 0.9375}, {"start": 774.29, "end": 774.67, "word": " هذه", "probability": 0.78125}, {"start": 774.67, "end": 775.07, "word": " مش", "probability": 0.96533203125}, {"start": 775.07, "end": 775.55, "word": " صعب", "probability": 0.9733072916666666}, {"start": 775.55, "end": 776.11, "word": " موجود", "probability": 0.9306640625}, {"start": 776.11, "end": 776.27, "word": " في", "probability": 0.94189453125}, {"start": 776.27, "end": 776.75, "word": " الكتاب", "probability": 0.98095703125}, {"start": 776.75, "end": 777.39, "word": " هخليكم", "probability": 0.8441162109375}, {"start": 777.39, "end": 778.05, "word": " تقراه", "probability": 0.804931640625}], "temperature": 1.0}, {"id": 28, "seek": 80202, "start": 780.18, "end": 802.02, "text": "هخليكم تقرا البرهان من الكتاب المقرر C theorem رقم تلاتة اربعة سبعة page تمانية و سبعين in textbook", "tokens": [3224, 9778, 20292, 24793, 6055, 4587, 23557, 2423, 26890, 3224, 7649, 9154, 33251, 2655, 16758, 9673, 4587, 2288, 2288, 383, 20904, 12602, 4587, 2304, 6055, 1211, 9307, 3660, 1975, 25513, 27884, 8608, 3555, 27884, 3028, 46811, 7649, 10632, 4032, 8608, 3555, 3615, 9957, 294, 25591], "avg_logprob": -0.15157948855472647, "compression_ratio": 1.2519685039370079, "no_speech_prob": 0.0, "words": [{"start": 780.18, "end": 780.84, "word": "هخليكم", "probability": 0.815185546875}, {"start": 780.84, "end": 781.3, "word": " تقرا", "probability": 0.7545572916666666}, {"start": 781.3, "end": 782.94, "word": " البرهان", "probability": 0.775634765625}, {"start": 782.94, "end": 783.1, "word": " من", "probability": 0.95849609375}, {"start": 783.1, "end": 783.46, "word": " الكتاب", "probability": 0.96826171875}, {"start": 783.46, "end": 784.58, "word": " المقرر", "probability": 0.9952392578125}, {"start": 784.58, "end": 786.32, "word": " C", "probability": 0.38818359375}, {"start": 786.32, "end": 789.36, "word": " theorem", "probability": 0.76806640625}, {"start": 789.36, "end": 790.78, "word": " رقم", "probability": 0.9830729166666666}, {"start": 790.78, "end": 791.84, "word": " تلاتة", "probability": 0.928955078125}, {"start": 791.84, "end": 792.38, "word": " اربعة", "probability": 0.8507486979166666}, {"start": 792.38, "end": 793.16, "word": " سبعة", "probability": 0.9303385416666666}, {"start": 793.16, "end": 795.34, "word": " page", "probability": 0.6162109375}, {"start": 795.34, "end": 800.36, "word": " تمانية", "probability": 0.955078125}, {"start": 800.36, "end": 800.52, "word": " و", "probability": 0.91748046875}, {"start": 800.52, "end": 801.12, "word": " سبعين", "probability": 0.915283203125}, {"start": 801.12, "end": 801.42, "word": " in", "probability": 0.931640625}, {"start": 801.42, "end": 802.02, "word": " textbook", "probability": 0.7626953125}], "temperature": 1.0}, {"id": 29, "seek": 83132, "start": 807.06, "end": 831.32, "text": "إذن حدؤوكم لقراة البرهان، البرهان سهل مش صعب و حاولوا تقراوه و تفهموه و ده في أي صعوبة تسألوني أو تتناقشوا معي في البرهان okay في نظرية تانية", "tokens": [28814, 8848, 1863, 11331, 3215, 33604, 2407, 24793, 5296, 4587, 23557, 3660, 2423, 26890, 3224, 7649, 12399, 2423, 26890, 3224, 7649, 8608, 3224, 1211, 37893, 20328, 3615, 3555, 4032, 11331, 995, 12610, 14407, 6055, 4587, 23557, 2407, 3224, 4032, 6055, 5172, 16095, 2407, 3224, 4032, 11778, 3224, 8978, 36632, 20328, 3615, 37746, 3660, 6055, 3794, 10721, 1211, 11536, 1829, 34051, 6055, 2655, 8315, 4587, 8592, 14407, 20449, 1829, 8978, 2423, 26890, 3224, 7649, 1392, 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816.38, "end": 816.86, "word": " تقراوه", "probability": 0.75478515625}, {"start": 816.86, "end": 816.94, "word": " و", "probability": 0.54345703125}, {"start": 816.94, "end": 817.42, "word": " تفهموه", "probability": 0.97255859375}, {"start": 817.42, "end": 817.5, "word": " و", "probability": 0.333740234375}, {"start": 817.5, "end": 817.56, "word": " ده", "probability": 0.921630859375}, {"start": 817.56, "end": 817.68, "word": " في", "probability": 0.96826171875}, {"start": 817.68, "end": 817.84, "word": " أي", "probability": 0.70849609375}, {"start": 817.84, "end": 818.44, "word": " صعوبة", "probability": 0.9945068359375}, {"start": 818.44, "end": 819.4, "word": " تسألوني", "probability": 0.920166015625}, {"start": 819.4, "end": 820.28, "word": " أو", "probability": 0.8173828125}, {"start": 820.28, "end": 821.04, "word": " تتناقشوا", "probability": 0.989013671875}, {"start": 821.04, "end": 821.32, "word": " معي", "probability": 0.837158203125}, {"start": 821.32, "end": 822.06, "word": " في", "probability": 0.9443359375}, {"start": 822.06, "end": 822.6, "word": " البرهان", "probability": 0.97265625}, {"start": 822.6, "end": 826.28, "word": " okay", "probability": 0.7158203125}, {"start": 826.28, "end": 829.68, "word": " في", "probability": 0.5458984375}, {"start": 829.68, "end": 830.52, "word": " نظرية", "probability": 0.986328125}, {"start": 830.52, "end": 831.32, "word": " تانية", "probability": 0.9939778645833334}], "temperature": 1.0}, {"id": 30, "seek": 86654, "start": 840.88, "end": 866.54, "text": "Bolzano-Weierstrass theorem رقم اتنين تسعتاش النظرية هذه بتقول every bounded sequence every bounded", "tokens": [33, 401, 89, 3730, 12, 4360, 811, 9733, 640, 20904, 12602, 4587, 2304, 1975, 2655, 1863, 9957, 6055, 3794, 34268, 33599, 28239, 19913, 2288, 10632, 29538, 39894, 39648, 633, 37498, 8310, 633, 37498], "avg_logprob": -0.3138786808532827, "compression_ratio": 1.0666666666666667, "no_speech_prob": 0.0, "words": [{"start": 840.88, "end": 842.28, "word": "Bolzano", "probability": 0.68316650390625}, {"start": 842.28, "end": 843.68, "word": "-Weierstrass", "probability": 0.73837890625}, {"start": 843.68, "end": 846.9, "word": " theorem", "probability": 0.6650390625}, {"start": 846.9, "end": 849.78, "word": " رقم", "probability": 0.767578125}, {"start": 849.78, "end": 850.26, "word": " اتنين", "probability": 0.7999267578125}, {"start": 850.26, "end": 851.18, "word": " تسعتاش", "probability": 0.79156494140625}, {"start": 851.18, "end": 857.88, "word": " النظرية", "probability": 0.8485107421875}, {"start": 857.88, "end": 858.1, "word": " هذه", "probability": 0.82275390625}, {"start": 858.1, "end": 858.74, "word": " بتقول", "probability": 0.974609375}, {"start": 858.74, "end": 859.34, "word": " every", "probability": 0.6494140625}, {"start": 859.34, "end": 860.02, "word": " bounded", "probability": 0.94677734375}, {"start": 860.02, "end": 860.84, "word": " sequence", "probability": 0.9873046875}, {"start": 860.84, "end": 863.98, "word": " every", "probability": 0.61181640625}, {"start": 863.98, "end": 866.54, "word": " bounded", "probability": 0.93212890625}], "temperature": 1.0}, {"id": 31, "seek": 88850, "start": 868.92, "end": 888.5, "text": "سيكوينس of real numbers in R has a convergent subsequence", "tokens": [3794, 1829, 4117, 2407, 9957, 3794, 295, 957, 3547, 294, 497, 575, 257, 9652, 6930, 13924, 655], "avg_logprob": -0.4242621527777778, "compression_ratio": 0.9014084507042254, "no_speech_prob": 0.0, "words": [{"start": 868.9200000000001, "end": 870.32, "word": "سيكوينس", "probability": 0.6212056477864584}, {"start": 870.32, "end": 871.72, "word": " of", "probability": 0.1715087890625}, {"start": 871.72, "end": 874.8, "word": " real", "probability": 0.931640625}, {"start": 874.8, "end": 875.46, "word": " numbers", "probability": 0.822265625}, {"start": 875.46, "end": 875.8, "word": " in", "probability": 0.8193359375}, {"start": 875.8, "end": 876.22, "word": " R", "probability": 0.9423828125}, {"start": 876.22, "end": 878.86, "word": " has", "probability": 0.78515625}, {"start": 878.86, "end": 881.98, "word": " a", "probability": 0.4814453125}, {"start": 881.98, "end": 882.96, "word": " convergent", "probability": 0.92138671875}, {"start": 882.96, "end": 888.5, "word": " subsequence", "probability": 0.8486328125}], "temperature": 1.0}, {"id": 32, "seek": 91784, "start": 893.72, "end": 917.84, "text": "لو فى عندي bounded sequence of real numbers فبقدر أجى جواتها conversion subsequence البرهان تبع نظريها دى سهل باستخدام نظريات السابقة فى لها برهانين واحد short يعني قصير يعتمد على النظريات الكبيرة اللى برهنها سابقا وفى لها برهان", "tokens": [1211, 2407, 6156, 7578, 18871, 16254, 37498, 8310, 295, 957, 3547, 6156, 3555, 28543, 2288, 5551, 7435, 7578, 10874, 14407, 2655, 11296, 14298, 13924, 655, 2423, 26890, 3224, 7649, 6055, 3555, 3615, 8717, 19913, 16572, 11296, 11778, 7578, 8608, 3224, 1211, 4724, 995, 14851, 9778, 3215, 10943, 8717, 19913, 16572, 9307, 21136, 16758, 28671, 6156, 7578, 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المونوتون", "tokens": [9000, 3563, 366, 37498, 8310, 295, 957, 3547, 538, 11331, 35457, 28239, 19913, 2288, 10632, 16247, 9778, 48923, 12602, 4587, 2304, 46811, 7649, 2655, 33599, 538, 20904, 46811, 7649, 2655, 33599, 9673, 11536, 35473, 11536], "avg_logprob": -0.2730034622881148, "compression_ratio": 1.2142857142857142, "no_speech_prob": 0.0, "words": [{"start": 950.47, "end": 951.31, "word": "contained", "probability": 0.58984375}, {"start": 951.31, "end": 951.99, "word": " are", "probability": 0.365966796875}, {"start": 951.99, "end": 954.67, "word": " bounded", "probability": 0.17822265625}, {"start": 954.67, "end": 958.91, "word": " sequence", "probability": 0.384033203125}, {"start": 958.91, "end": 960.17, "word": " of", "probability": 0.92041015625}, {"start": 960.17, "end": 960.45, "word": " real", "probability": 0.966796875}, {"start": 960.45, "end": 961.35, "word": " numbers", "probability": 0.8623046875}, {"start": 961.35, "end": 965.11, "word": " by", "probability": 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subsequence", "tokens": [3555, 2655, 39648, 36632, 8310, 294, 497, 8608, 2407, 16606, 37498, 34051, 517, 18767, 292, 633, 8310, 295, 957, 3547, 575, 257, 1108, 310, 546, 13924, 655, 11933, 15730, 2423, 1783, 45, 575, 257, 1108, 310, 546, 13924, 655], "avg_logprob": -0.3169921763241291, "compression_ratio": 1.3416666666666666, "no_speech_prob": 0.0, "words": [{"start": 982.58, "end": 983.74, "word": "بتقول", "probability": 0.6314697265625}, {"start": 983.74, "end": 984.14, "word": " أي", "probability": 0.71142578125}, {"start": 984.14, "end": 985.7, "word": " sequence", "probability": 0.51513671875}, {"start": 985.7, "end": 986.36, "word": " in", "probability": 0.460693359375}, {"start": 986.36, "end": 986.76, "word": " R", "probability": 0.95458984375}, {"start": 986.76, "end": 987.82, "word": " سواء", "probability": 0.8984375}, {"start": 987.82, "end": 988.26, "word": " bounded", "probability": 0.87841796875}, {"start": 988.26, "end": 988.5, "word": " أو", "probability": 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0.9482421875}, {"start": 1117.37, "end": 1117.83, "word": " bounded", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 40, "seek": 114598, "start": 1120.52, "end": 1145.98, "text": "Okay إذا أنا كتب برهان أنه أي subsequence من bounded sequence is bounded تمام Now ال subsequence x in k is monotone and bounded", "tokens": [8297, 11933, 15730, 41850, 9122, 2655, 3555, 4724, 2288, 3224, 7649, 14739, 3224, 36632, 13924, 655, 9154, 37498, 8310, 307, 37498, 46811, 10943, 823, 2423, 13924, 655, 2031, 294, 350, 307, 1108, 310, 546, 293, 37498], "avg_logprob": -0.2958192664223748, "compression_ratio": 1.2941176470588236, "no_speech_prob": 0.0, "words": [{"start": 1120.52, "end": 1120.98, "word": "Okay", "probability": 0.5244140625}, {"start": 1120.98, "end": 1121.34, "word": " إذا", "probability": 0.52276611328125}, {"start": 1121.34, "end": 1121.66, "word": " أنا", "probability": 0.5517578125}, {"start": 1121.66, "end": 1122.34, "word": " كتب", "probability": 0.7584635416666666}, 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في", "probability": 0.9765625}, {"start": 1209.01, "end": 1209.61, "word": " الكتاب", "probability": 0.9892578125}, {"start": 1209.61, "end": 1211.85, "word": " see", "probability": 0.51123046875}, {"start": 1211.85, "end": 1212.65, "word": " page", "probability": 0.95068359375}, {"start": 1212.65, "end": 1216.13, "word": " 79", "probability": 0.32568359375}, {"start": 1216.13, "end": 1216.73, "word": " in", "probability": 0.8818359375}, {"start": 1216.73, "end": 1217.63, "word": " textbook", "probability": 0.787109375}], "temperature": 1.0}, {"id": 44, "seek": 124303, "start": 1223.25, "end": 1243.03, "text": "إذا أنا هنسيبكم تقرأوا البرهان التاني من الكتاب طبعا البرهان هذا هيكون constructive proof بيورجيكم كيف بيبني ال subsequence خطوة خطوة و بحيث انها تطلع convergent طيب في كمال نظرية في هذا السياق", "tokens": [28814, 15730, 41850, 8032, 1863, 3794, 1829, 3555, 24793, 6055, 4587, 2288, 10721, 14407, 2423, 26890, 3224, 7649, 16712, 7649, 1829, 9154, 33251, 2655, 16758, 23032, 3555, 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" ال", "probability": 0.94677734375}, {"start": 1232.17, "end": 1233.07, "word": " subsequence", "probability": 0.77490234375}, {"start": 1233.07, "end": 1233.81, "word": " خطوة", "probability": 0.9884033203125}, {"start": 1233.81, "end": 1234.41, "word": " خطوة", "probability": 0.98583984375}, {"start": 1234.41, "end": 1235.37, "word": " و", "probability": 0.5947265625}, {"start": 1235.37, "end": 1235.93, "word": " بحيث", "probability": 0.93994140625}, {"start": 1235.93, "end": 1236.09, "word": " انها", "probability": 0.5726318359375}, {"start": 1236.09, "end": 1236.53, "word": " تطلع", "probability": 0.987060546875}, {"start": 1236.53, "end": 1237.29, "word": " convergent", "probability": 0.822265625}, {"start": 1237.29, "end": 1240.27, "word": " طيب", "probability": 0.9532877604166666}, {"start": 1240.27, "end": 1240.59, "word": " في", "probability": 0.8662109375}, {"start": 1240.59, "end": 1241.33, "word": " كمال", "probability": 0.857421875}, {"start": 1241.33, "end": 1241.93, "word": " نظرية", "probability": 0.9844970703125}, {"start": 1241.93, "end": 1242.17, "word": " في", "probability": 0.97509765625}, {"start": 1242.17, "end": 1242.39, "word": " هذا", "probability": 0.97998046875}, {"start": 1242.39, "end": 1243.03, "word": " السياق", "probability": 0.9757486979166666}], "temperature": 1.0}, {"id": 45, "seek": 128021, "start": 1250.57, "end": 1280.21, "text": "theorem اتنين عشرين let x in content in R be bounded bounded sequence and let", "tokens": [3322, 37956, 1975, 2655, 1863, 9957, 6225, 46309, 9957, 718, 2031, 294, 2701, 294, 497, 312, 37498, 37498, 8310, 293, 718], "avg_logprob": -0.5344460037621585, "compression_ratio": 1.0740740740740742, "no_speech_prob": 0.0, "words": [{"start": 1250.57, "end": 1251.25, "word": "theorem", "probability": 0.5062408447265625}, {"start": 1251.25, "end": 1252.53, "word": " اتنين", "probability": 0.703216552734375}, {"start": 1252.53, "end": 1253.31, "word": " عشرين", "probability": 0.8577473958333334}, {"start": 1253.31, "end": 1263.69, "word": " let", "probability": 0.6298828125}, {"start": 1263.69, "end": 1264.19, "word": " x", "probability": 0.7001953125}, {"start": 1264.19, "end": 1264.69, "word": " in", "probability": 0.31640625}, {"start": 1264.69, "end": 1267.91, "word": " content", "probability": 0.272216796875}, {"start": 1267.91, "end": 1268.35, "word": " in", "probability": 0.67822265625}, {"start": 1268.35, "end": 1268.85, "word": " R", "probability": 0.85546875}, {"start": 1268.85, "end": 1271.67, "word": " be", "probability": 0.78076171875}, {"start": 1271.67, "end": 1273.07, "word": " bounded", "probability": 0.96435546875}, {"start": 1273.07, "end": 1275.91, "word": " bounded", "probability": 0.368896484375}, {"start": 1275.91, "end": 1277.51, "word": " sequence", "probability": 0.978515625}, {"start": 1277.51, "end": 1279.49, "word": " and", "probability": 0.94140625}, {"start": 1279.49, "end": 1280.21, "word": " let", "probability": 0.9677734375}], "temperature": 1.0}, {"id": 46, "seek": 130631, "start": 1282.25, "end": 1306.31, "text": "X ينتمي إلى R بـ such that every .. every convergent .. every convergent subsequence .. every convergent subsequence", "tokens": [55, 7251, 29399, 2304, 1829, 30731, 497, 4724, 39184, 1270, 300, 633, 4386, 633, 9652, 6930, 4386, 633, 9652, 6930, 13924, 655, 4386, 633, 9652, 6930, 13924, 655], "avg_logprob": -0.27182111246832485, "compression_ratio": 1.575, "no_speech_prob": 0.0, "words": [{"start": 1282.25, "end": 1282.79, "word": "X", "probability": 0.1468505859375}, {"start": 1282.79, "end": 1283.61, "word": " ينتمي", "probability": 0.9039306640625}, {"start": 1283.61, "end": 1283.89, "word": " إلى", "probability": 0.748046875}, {"start": 1283.89, "end": 1284.27, "word": " R", "probability": 0.9384765625}, {"start": 1284.27, "end": 1289.37, "word": " بـ", "probability": 0.369873046875}, {"start": 1289.37, "end": 1290.01, "word": " such", "probability": 0.48583984375}, {"start": 1290.01, "end": 1290.57, "word": " that", "probability": 0.94580078125}, {"start": 1290.57, "end": 1292.63, "word": " every", "probability": 0.7607421875}, {"start": 1292.63, "end": 1292.73, "word": " ..", "probability": 0.59619140625}, {"start": 1292.73, "end": 1294.91, "word": " every", "probability": 0.6982421875}, {"start": 1294.91, "end": 1296.19, "word": " convergent", "probability": 0.967529296875}, {"start": 1296.19, "end": 1296.35, "word": " ..", "probability": 0.90771484375}, {"start": 1296.35, "end": 1296.87, "word": " every", "probability": 0.71044921875}, {"start": 1296.87, "end": 1298.17, "word": " convergent", "probability": 0.982421875}, {"start": 1298.17, "end": 1301.61, "word": " subsequence", "probability": 0.989501953125}, {"start": 1301.61, "end": 1301.85, "word": " ..", "probability": 0.8056640625}, {"start": 1301.85, "end": 1304.45, "word": " every", "probability": 0.7890625}, {"start": 1304.45, "end": 1305.29, "word": " convergent", "probability": 0.978759765625}, {"start": 1305.29, "end": 1306.31, "word": " subsequence", "probability": 0.995361328125}], "temperature": 1.0}, {"id": 47, "seek": 133693, "start": 1310.71, "end": 1336.93, "text": "of سمّيها x أو every convergent subsequence of x in converges to x then النتيجة أنه ال sequence x in", "tokens": [2670, 8608, 2304, 11703, 1829, 11296, 2031, 34051, 633, 9652, 6930, 13924, 655, 295, 2031, 294, 9652, 2880, 281, 2031, 550, 28239, 31371, 7435, 3660, 14739, 3224, 2423, 8310, 2031, 294], "avg_logprob": -0.3295898325741291, "compression_ratio": 1.1428571428571428, "no_speech_prob": 0.0, "words": [{"start": 1310.71, "end": 1311.39, "word": "of", "probability": 0.31787109375}, {"start": 1311.39, "end": 1312.71, "word": " سمّيها", "probability": 0.712939453125}, {"start": 1312.71, "end": 1314.25, "word": " x", "probability": 0.4619140625}, {"start": 1314.25, "end": 1319.55, "word": " أو", "probability": 0.615234375}, {"start": 1319.55, "end": 1319.95, "word": " every", "probability": 0.7060546875}, {"start": 1319.95, "end": 1320.59, "word": " convergent", "probability": 0.719482421875}, {"start": 1320.59, "end": 1321.63, "word": " subsequence", "probability": 0.99072265625}, {"start": 1321.63, "end": 1322.11, "word": " of", "probability": 0.93603515625}, {"start": 1322.11, "end": 1322.57, "word": " x", "probability": 0.92041015625}, {"start": 1322.57, "end": 1323.01, "word": " in", "probability": 0.2254638671875}, {"start": 1323.01, "end": 1325.19, "word": " converges", "probability": 0.782470703125}, {"start": 1325.19, "end": 1328.45, "word": " to", "probability": 0.95068359375}, {"start": 1328.45, "end": 1329.19, "word": " x", "probability": 0.962890625}, {"start": 1329.19, "end": 1332.43, "word": " then", "probability": 0.466552734375}, {"start": 1332.43, "end": 1333.57, "word": " النتيجة", "probability": 0.976806640625}, {"start": 1333.57, "end": 1335.11, "word": " أنه", "probability": 0.549072265625}, {"start": 1335.11, "end": 1335.35, "word": " ال", "probability": 0.705078125}, {"start": 1335.35, "end": 1335.75, "word": " sequence", "probability": 0.74365234375}, {"start": 1335.75, "end": 1336.41, "word": " x", "probability": 0.828125}, {"start": 1336.41, "end": 1336.93, "word": " in", "probability": 0.91748046875}], "temperature": 1.0}, {"id": 48, "seek": 135035, "start": 1339.75, "end": 1350.35, "text": "converges to x إذا أنا في عندي bounded sequence of real numbers", "tokens": [1671, 331, 2880, 281, 2031, 11933, 15730, 41850, 8978, 18871, 16254, 37498, 8310, 295, 957, 3547], "avg_logprob": -0.5160845588235294, "compression_ratio": 0.9375, "no_speech_prob": 0.0, "words": [{"start": 1339.75, "end": 1340.77, "word": "converges", "probability": 0.6420084635416666}, {"start": 1340.77, "end": 1341.73, "word": " to", "probability": 0.78076171875}, {"start": 1341.73, "end": 1342.23, "word": " x", "probability": 0.80419921875}, {"start": 1342.23, "end": 1347.19, "word": " إذا", "probability": 0.62109375}, {"start": 1347.19, "end": 1347.43, "word": " أنا", "probability": 0.7802734375}, 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"seek": 146029, "start": 1437.21, "end": 1460.29, "text": "by divergence theorem اللى هى اتنين تمانتاش كذبوت او اتنين سبعتاش اعتقد هيك صح اه ال divergence theorem بتقولى x in does not converge ل x", "tokens": [2322, 47387, 20904, 13672, 7578, 8032, 7578, 1975, 2655, 1863, 9957, 46811, 7649, 2655, 33599, 9122, 8848, 3555, 35473, 1975, 2407, 1975, 2655, 1863, 9957, 8608, 3555, 34268, 33599, 1975, 34268, 28543, 39896, 4117, 20328, 5016, 1975, 3224, 2423, 47387, 20904, 39894, 39648, 7578, 2031, 294, 775, 406, 41881, 5296, 2031], "avg_logprob": -0.34915864582245165, "compression_ratio": 1.4057971014492754, "no_speech_prob": 0.0, "words": [{"start": 1437.21, "end": 1437.55, "word": "by", "probability": 0.1871337890625}, {"start": 1437.55, "end": 1438.31, "word": " divergence", "probability": 0.93896484375}, {"start": 1438.31, "end": 1439.83, "word": " theorem", "probability": 0.8017578125}, {"start": 1439.83, "end": 1443.17, "word": " اللى", "probability": 0.3975830078125}, {"start": 1443.17, "end": 1443.59, "word": " هى", "probability": 0.83642578125}, {"start": 1443.59, "end": 1444.43, "word": " اتنين", "probability": 0.8404541015625}, {"start": 1444.43, "end": 1447.09, "word": " تمانتاش", "probability": 0.768096923828125}, {"start": 1447.09, "end": 1450.53, "word": " كذبوت", "probability": 0.565673828125}, {"start": 1450.53, "end": 1452.49, "word": " او", "probability": 0.944091796875}, {"start": 1452.49, "end": 1452.81, "word": " اتنين", "probability": 0.9671630859375}, {"start": 1452.81, "end": 1453.51, "word": " سبعتاش", "probability": 0.955322265625}, {"start": 1453.51, "end": 1453.99, "word": " اعتقد", "probability": 0.87255859375}, {"start": 1453.99, "end": 1454.33, "word": " هيك", "probability": 0.60650634765625}, {"start": 1454.33, "end": 1455.53, "word": " صح", "probability": 0.906982421875}, {"start": 1455.53, "end": 1455.87, "word": " اه", "probability": 0.52691650390625}, {"start": 1455.87, "end": 1455.95, "word": " ال", "probability": 0.8759765625}, {"start": 1455.95, "end": 1456.39, "word": " divergence", "probability": 0.9970703125}, {"start": 1456.39, "end": 1456.97, "word": " theorem", "probability": 0.91455078125}, {"start": 1456.97, "end": 1457.87, "word": " بتقولى", "probability": 0.6880289713541666}, {"start": 1457.87, "end": 1458.47, "word": " x", "probability": 0.69921875}, {"start": 1458.47, "end": 1458.69, "word": " in", "probability": 0.477294921875}, {"start": 1458.69, "end": 1458.93, "word": " does", "probability": 0.89990234375}, {"start": 1458.93, "end": 1459.17, "word": " not", "probability": 0.9619140625}, {"start": 1459.17, "end": 1459.71, "word": " converge", "probability": 0.99609375}, {"start": 1459.71, "end": 1459.89, "word": " ل", "probability": 0.92138671875}, {"start": 1459.89, "end": 1460.29, "word": " x", "probability": 0.81494140625}], "temperature": 1.0}, {"id": 53, "seek": 148020, "start": 1461.44, "end": 1480.2, "text": "معناته there exist epsilon zero عدد موجب and there exist a subsequence a subsequence xrn of xn", "tokens": [2304, 3615, 8315, 47395, 456, 2514, 17889, 4018, 6225, 3215, 3215, 3714, 29245, 3555, 293, 456, 2514, 257, 13924, 655, 257, 13924, 655, 2031, 81, 77, 295, 2031, 77], "avg_logprob": -0.22213542014360427, "compression_ratio": 1.1888888888888889, "no_speech_prob": 0.0, "words": [{"start": 1461.44, "end": 1462.14, "word": "معناته", "probability": 0.892578125}, {"start": 1462.14, "end": 1462.4, "word": " there", "probability": 0.6591796875}, {"start": 1462.4, "end": 1462.96, "word": " exist", "probability": 0.5771484375}, {"start": 1462.96, "end": 1463.56, "word": " epsilon", "probability": 0.3623046875}, {"start": 1463.56, "end": 1464.04, "word": " zero", "probability": 0.763671875}, {"start": 1464.04, "end": 1464.4, "word": " عدد", "probability": 0.9541015625}, {"start": 1464.4, "end": 1464.94, "word": " موجب", "probability": 0.9557291666666666}, {"start": 1464.94, "end": 1465.4, "word": " and", "probability": 0.92138671875}, {"start": 1465.4, "end": 1465.84, "word": " there", "probability": 0.90283203125}, {"start": 1465.84, "end": 1466.46, "word": " exist", "probability": 0.90966796875}, {"start": 1466.46, "end": 1467.42, "word": " a", "probability": 0.923828125}, {"start": 1467.42, "end": 1468.66, "word": " subsequence", "probability": 0.963623046875}, {"start": 1468.66, "end": 1468.96, "word": " a", "probability": 0.324951171875}, {"start": 1468.96, "end": 1472.98, "word": " subsequence", "probability": 0.97900390625}, {"start": 1472.98, "end": 1476.18, "word": " xrn", "probability": 0.547607421875}, {"start": 1476.18, "end": 1478.72, "word": " of", "probability": 0.92138671875}, {"start": 1478.72, "end": 1480.2, "word": " xn", "probability": 0.929931640625}], "temperature": 1.0}, {"id": 54, "seek": 151174, "start": 1482.72, "end": 1511.74, "text": "such that absolute x are n minus x أكبر من أو ساوي epsilon zero هذا الكلام صحيح لكل n في n نسمي المتباينة هذه star تمام؟ هذا من نظرية ال divergence اتنين سبعتاش ممكن نحصل على كل هذا", "tokens": [39974, 300, 8236, 2031, 366, 297, 3175, 2031, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 17889, 4018, 23758, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 5296, 28820, 297, 8978, 297, 8717, 38251, 1829, 9673, 2655, 3555, 995, 9957, 3660, 29538, 3543, 46811, 10943, 22807, 23758, 9154, 8717, 19913, 2288, 10632, 2423, 47387, 1975, 2655, 1863, 9957, 8608, 3555, 34268, 33599, 3714, 43020, 8717, 5016, 36520, 15844, 28242, 23758], "avg_logprob": -0.2511160739830562, "compression_ratio": 1.4114583333333333, "no_speech_prob": 0.0, "words": [{"start": 1482.72, "end": 1483.24, "word": "such", "probability": 0.51806640625}, {"start": 1483.24, "end": 1483.86, "word": " that", "probability": 0.9599609375}, {"start": 1483.86, "end": 1485.12, "word": " absolute", "probability": 0.6064453125}, {"start": 1485.12, "end": 1486.0, "word": " x", "probability": 0.76171875}, {"start": 1486.0, "end": 1486.66, "word": " are", "probability": 0.374267578125}, {"start": 1486.66, "end": 1487.14, "word": " n", "probability": 0.841796875}, {"start": 1487.14, "end": 1487.88, "word": " minus", "probability": 0.74853515625}, {"start": 1487.88, "end": 1488.7, "word": " x", "probability": 0.9921875}, {"start": 1488.7, "end": 1490.26, "word": " أكبر", "probability": 0.9052734375}, {"start": 1490.26, "end": 1490.52, "word": " من", "probability": 0.884765625}, {"start": 1490.52, "end": 1490.76, "word": " أو", "probability": 0.96533203125}, {"start": 1490.76, "end": 1491.32, "word": " ساوي", "probability": 0.8435872395833334}, {"start": 1491.32, "end": 1491.76, "word": " epsilon", "probability": 0.2403564453125}, {"start": 1491.76, "end": 1492.34, "word": " zero", "probability": 0.79345703125}, {"start": 1492.34, "end": 1493.36, "word": " هذا", "probability": 0.79833984375}, {"start": 1493.36, "end": 1493.78, "word": " الكلام", "probability": 0.8883463541666666}, {"start": 1493.78, "end": 1494.4, "word": " صحيح", "probability": 0.9888916015625}, {"start": 1494.4, "end": 1495.12, "word": " لكل", "probability": 0.976318359375}, {"start": 1495.12, "end": 1495.66, "word": " n", "probability": 0.7890625}, {"start": 1495.66, "end": 1496.02, "word": " في", "probability": 0.9716796875}, {"start": 1496.02, "end": 1496.52, "word": " n", "probability": 0.89892578125}, {"start": 1496.52, "end": 1501.28, "word": " نسمي", "probability": 0.80126953125}, {"start": 1501.28, "end": 1502.12, "word": " المتباينة", "probability": 0.9232584635416666}, {"start": 1502.12, "end": 1502.56, "word": " هذه", "probability": 0.43115234375}, {"start": 1502.56, "end": 1503.18, "word": " star", "probability": 0.61083984375}, {"start": 1503.18, "end": 1504.94, "word": " تمام؟", "probability": 0.7058512369791666}, {"start": 1504.94, "end": 1505.12, "word": " هذا", "probability": 0.5302734375}, {"start": 1505.12, "end": 1505.26, "word": " من", "probability": 0.96484375}, {"start": 1505.26, "end": 1505.86, "word": " نظرية", "probability": 0.951171875}, {"start": 1505.86, "end": 1507.56, "word": " ال", "probability": 0.8662109375}, {"start": 1507.56, "end": 1508.3, "word": " divergence", "probability": 0.986328125}, {"start": 1508.3, "end": 1509.64, "word": " اتنين", "probability": 0.7296524047851562}, {"start": 1509.64, "end": 1510.32, "word": " سبعتاش", "probability": 0.60382080078125}, {"start": 1510.32, "end": 1510.62, "word": " ممكن", "probability": 0.840087890625}, {"start": 1510.62, "end": 1511.0, "word": " نحصل", "probability": 0.9918619791666666}, {"start": 1511.0, "end": 1511.16, "word": " على", "probability": 0.88134765625}, {"start": 1511.16, "end": 1511.44, "word": " كل", "probability": 0.98486328125}, {"start": 1511.44, "end": 1511.74, "word": " هذا", "probability": 0.92822265625}], "temperature": 1.0}, {"id": 55, "seek": 154516, "start": 1517.2, "end": 1545.16, "text": "طيب since xn is bounded لما انه ال sequence xn is bounded then the subsequence the subsequence xrn is bounded", "tokens": [9566, 1829, 3555, 1670, 2031, 77, 307, 37498, 5296, 15042, 16472, 3224, 2423, 8310, 2031, 77, 307, 37498, 550, 264, 13924, 655, 264, 13924, 655, 2031, 81, 77, 307, 37498], "avg_logprob": -0.21320565092948177, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 1517.2, "end": 1517.78, "word": "طيب", "probability": 0.9425455729166666}, {"start": 1517.78, "end": 1519.08, "word": " since", "probability": 0.60009765625}, {"start": 1519.08, "end": 1522.14, "word": " xn", "probability": 0.516357421875}, {"start": 1522.14, "end": 1523.04, "word": " is", "probability": 0.93603515625}, {"start": 1523.04, "end": 1523.68, "word": " bounded", "probability": 0.9423828125}, {"start": 1523.68, "end": 1525.92, "word": " لما", "probability": 0.7083740234375}, {"start": 1525.92, "end": 1526.22, "word": " انه", "probability": 0.666748046875}, {"start": 1526.22, "end": 1526.28, "word": " ال", "probability": 0.888671875}, {"start": 1526.28, "end": 1526.86, "word": " sequence", "probability": 0.88720703125}, {"start": 1526.86, "end": 1528.9, "word": " xn", "probability": 0.95458984375}, {"start": 1528.9, "end": 1529.26, "word": " is", "probability": 0.9541015625}, {"start": 1529.26, "end": 1529.76, "word": " bounded", "probability": 0.93408203125}, {"start": 1529.76, "end": 1536.26, "word": " then", "probability": 0.7626953125}, {"start": 1536.26, "end": 1536.56, "word": " the", "probability": 0.82666015625}, {"start": 1536.56, "end": 1537.46, "word": " subsequence", "probability": 0.950439453125}, {"start": 1537.46, "end": 1539.94, "word": " the", "probability": 0.33251953125}, {"start": 1539.94, "end": 1541.02, "word": " subsequence", "probability": 0.987548828125}, {"start": 1541.02, "end": 1543.78, "word": " xrn", "probability": 0.85888671875}, {"start": 1543.78, "end": 1544.74, "word": " is", "probability": 0.96435546875}, {"start": 1544.74, "end": 1545.16, "word": " bounded", "probability": 0.93701171875}], "temperature": 1.0}, {"id": 56, "seek": 157716, "start": 1549.26, "end": 1577.16, "text": "أي subsequence من bounded sequence تطلع bounded جب شوية أثبتنا الكلام هذا so by bolzano weierstrass theorem نظرية bolzano weierstrass", "tokens": [10721, 1829, 13924, 655, 9154, 37498, 8310, 6055, 9566, 1211, 3615, 37498, 10874, 3555, 13412, 2407, 10632, 5551, 12984, 3555, 2655, 8315, 2423, 28820, 10943, 23758, 370, 538, 8986, 89, 3730, 321, 811, 9733, 640, 20904, 8717, 19913, 2288, 10632, 8986, 89, 3730, 321, 811, 9733, 640], "avg_logprob": -0.20231119294961294, "compression_ratio": 1.2846153846153847, "no_speech_prob": 0.0, "words": [{"start": 1549.26, "end": 1549.74, "word": "أي", "probability": 0.583984375}, {"start": 1549.74, "end": 1550.8, "word": " subsequence", "probability": 0.750732421875}, {"start": 1550.8, "end": 1551.22, "word": " من", "probability": 0.96484375}, {"start": 1551.22, "end": 1551.7, "word": " bounded", "probability": 0.763671875}, {"start": 1551.7, "end": 1552.22, "word": " sequence", "probability": 0.9501953125}, {"start": 1552.22, "end": 1552.56, "word": " تطلع", "probability": 0.9503173828125}, {"start": 1552.56, "end": 1552.86, "word": " bounded", "probability": 0.60595703125}, {"start": 1552.86, "end": 1553.14, "word": " جب", "probability": 0.592529296875}, {"start": 1553.14, "end": 1553.66, "word": " شوية", "probability": 0.73828125}, {"start": 1553.66, "end": 1554.7, "word": " أثبتنا", "probability": 0.97744140625}, {"start": 1554.7, "end": 1555.1, "word": " الكلام", "probability": 0.9630533854166666}, {"start": 1555.1, "end": 1555.68, "word": " هذا", "probability": 0.849609375}, {"start": 1555.68, "end": 1559.6, "word": " so", "probability": 0.394287109375}, {"start": 1559.6, "end": 1560.24, "word": " by", "probability": 0.96484375}, {"start": 1560.24, "end": 1564.78, "word": " bolzano", "probability": 0.7794596354166666}, {"start": 1564.78, "end": 1571.68, "word": " weierstrass", "probability": 0.81378173828125}, {"start": 1571.68, "end": 1572.72, "word": " theorem", "probability": 0.92529296875}, {"start": 1572.72, "end": 1575.5, "word": " نظرية", "probability": 0.896240234375}, {"start": 1575.5, "end": 1576.24, "word": " bolzano", "probability": 0.8546549479166666}, {"start": 1576.24, "end": 1577.16, "word": " weierstrass", "probability": 0.9228515625}], "temperature": 1.0}, {"id": 57, "seek": 160741, "start": 1578.27, "end": 1607.41, "text": "هنطبقها على الـ sequence XRN اللي هي bounded فبتقول بولزانو فيروس تراثيرم إذا في عندي sequence و bounded ففي إلها convergence subsequence إذن ال sequence ال sequence XRN", "tokens": [3224, 1863, 9566, 3555, 4587, 11296, 15844, 2423, 39184, 8310, 1783, 49, 45, 13672, 1829, 39896, 37498, 6156, 3555, 2655, 39648, 4724, 12610, 11622, 7649, 2407, 8978, 32887, 3794, 6055, 2288, 5718, 104, 13546, 2304, 11933, 15730, 8978, 18871, 16254, 8310, 4032, 37498, 6156, 41185, 11933, 1211, 11296, 32181, 13924, 655, 11933, 8848, 1863, 2423, 8310, 2423, 8310, 1783, 49, 45], "avg_logprob": -0.32333670027794376, "compression_ratio": 1.5192307692307692, "no_speech_prob": 0.0, "words": [{"start": 1578.27, "end": 1579.27, "word": "هنطبقها", "probability": 0.88671875}, {"start": 1579.27, "end": 1579.47, "word": " على", "probability": 0.80712890625}, {"start": 1579.47, "end": 1579.73, "word": " الـ", "probability": 0.60400390625}, {"start": 1579.73, "end": 1580.27, "word": " sequence", "probability": 0.70361328125}, {"start": 1580.27, "end": 1582.05, "word": " XRN", "probability": 0.5916341145833334}, {"start": 1582.05, "end": 1583.79, "word": " اللي", "probability": 0.7265625}, {"start": 1583.79, "end": 1584.11, "word": " هي", "probability": 0.833984375}, {"start": 1584.11, "end": 1584.57, "word": " bounded", "probability": 0.791015625}, {"start": 1584.57, "end": 1588.19, "word": " فبتقول", "probability": 0.96923828125}, {"start": 1588.19, "end": 1589.77, "word": " بولزانو", "probability": 0.739599609375}, {"start": 1589.77, "end": 1590.09, "word": " فيروس", "probability": 0.7671712239583334}, {"start": 1590.09, "end": 1590.73, "word": " تراثيرم", "probability": 0.587646484375}, {"start": 1590.73, "end": 1591.41, "word": " إذا", "probability": 0.7509765625}, {"start": 1591.41, "end": 1591.59, "word": " في", "probability": 0.8173828125}, {"start": 1591.59, "end": 1591.85, "word": " عندي", "probability": 0.5675048828125}, {"start": 1591.85, "end": 1592.51, "word": " sequence", "probability": 0.896484375}, {"start": 1592.51, "end": 1593.01, "word": " و", "probability": 0.6806640625}, {"start": 1593.01, "end": 1593.49, "word": " bounded", "probability": 0.83154296875}, {"start": 1593.49, "end": 1594.99, "word": " ففي", "probability": 0.92529296875}, {"start": 1594.99, "end": 1595.37, "word": " إلها", "probability": 0.7679036458333334}, {"start": 1595.37, "end": 1595.99, "word": " convergence", "probability": 0.83154296875}, {"start": 1595.99, "end": 1597.03, "word": " subsequence", "probability": 0.982177734375}, {"start": 1597.03, "end": 1599.75, "word": " إذن", "probability": 0.65966796875}, {"start": 1599.75, "end": 1599.97, "word": " ال", "probability": 0.92578125}, {"start": 1599.97, "end": 1600.63, "word": " sequence", "probability": 0.90283203125}, {"start": 1600.63, "end": 1605.07, "word": " ال", "probability": 0.244384765625}, {"start": 1605.07, "end": 1605.67, "word": " sequence", "probability": 0.97900390625}, {"start": 1605.67, "end": 1607.41, "word": " XRN", "probability": 0.9454752604166666}], "temperature": 1.0}, {"id": 58, "seek": 163617, "start": 1608.81, "end": 1636.17, "text": "has a convergent has a convergent subsequence say خلينا نسميها xkxkn تمام؟", "tokens": [12438, 257, 9652, 6930, 575, 257, 9652, 6930, 13924, 655, 584, 16490, 20292, 8315, 8717, 38251, 1829, 11296, 2031, 74, 87, 5457, 46811, 10943, 22807], "avg_logprob": -0.2295673036804566, "compression_ratio": 1.125, "no_speech_prob": 0.0, "words": [{"start": 1608.81, "end": 1609.43, "word": "has", "probability": 0.54833984375}, {"start": 1609.43, "end": 1609.99, "word": " a", "probability": 0.978515625}, {"start": 1609.99, "end": 1611.07, "word": " convergent", "probability": 0.951171875}, {"start": 1611.07, "end": 1613.87, "word": " has", "probability": 0.2008056640625}, {"start": 1613.87, "end": 1614.23, "word": " a", "probability": 0.99462890625}, {"start": 1614.23, "end": 1615.23, "word": " convergent", "probability": 0.980712890625}, {"start": 1615.23, "end": 1621.55, "word": " subsequence", "probability": 0.90966796875}, {"start": 1621.55, "end": 1624.57, "word": " say", "probability": 0.8291015625}, {"start": 1624.57, "end": 1626.37, "word": " خلينا", "probability": 0.715576171875}, {"start": 1626.37, "end": 1627.29, "word": " نسميها", "probability": 0.9925537109375}, {"start": 1627.29, "end": 1633.27, "word": " xkxkn", "probability": 0.7103271484375}, {"start": 1633.27, "end": 1636.17, "word": " تمام؟", "probability": 0.9674479166666666}], "temperature": 1.0}, {"id": 59, "seek": 168707, "start": 1665.49, "end": 1687.07, "text": "فاندي ال .. اذا انا في عندي convergent subsequence من ال subsequence هذه و طبعا هذه subsequence من xn وهذه subsequence من هذه، اذا هذه subsequence من xn", "tokens": [5172, 7649, 16254, 2423, 4386, 1975, 15730, 1975, 8315, 8978, 18871, 16254, 9652, 6930, 13924, 655, 9154, 2423, 13924, 655, 29538, 4032, 23032, 3555, 3615, 995, 29538, 13924, 655, 9154, 2031, 77, 37037, 24192, 13924, 655, 9154, 29538, 12399, 1975, 15730, 29538, 13924, 655, 9154, 2031, 77], "avg_logprob": -0.27099610430498916, "compression_ratio": 1.8392857142857142, "no_speech_prob": 0.0, "words": [{"start": 1665.49, "end": 1666.59, "word": "فاندي", "probability": 0.5843098958333334}, {"start": 1666.59, "end": 1667.03, "word": " ال", "probability": 0.6650390625}, {"start": 1667.03, "end": 1670.89, "word": " ..", "probability": 0.5751953125}, {"start": 1670.89, "end": 1671.15, "word": " اذا", "probability": 0.704833984375}, {"start": 1671.15, "end": 1671.43, "word": " انا", "probability": 0.86669921875}, {"start": 1671.43, "end": 1671.59, "word": " في", "probability": 0.91357421875}, {"start": 1671.59, "end": 1672.03, "word": " عندي", "probability": 0.683349609375}, {"start": 1672.03, "end": 1673.25, "word": " convergent", "probability": 0.674072265625}, {"start": 1673.25, "end": 1674.87, "word": " subsequence", "probability": 0.96142578125}, {"start": 1674.87, "end": 1675.97, "word": " من", "probability": 0.98779296875}, {"start": 1675.97, "end": 1676.17, "word": " ال", "probability": 0.60546875}, {"start": 1676.17, "end": 1676.93, "word": " subsequence", "probability": 0.9541015625}, {"start": 1676.93, "end": 1677.35, "word": " هذه", "probability": 0.75244140625}, {"start": 1677.35, "end": 1678.73, "word": " و", "probability": 0.7861328125}, {"start": 1678.73, "end": 1679.21, "word": " طبعا", "probability": 0.9288330078125}, {"start": 1679.21, "end": 1680.33, "word": " هذه", "probability": 0.55029296875}, {"start": 1680.33, "end": 1681.35, "word": " subsequence", "probability": 0.994140625}, {"start": 1681.35, "end": 1681.59, "word": " من", "probability": 0.99462890625}, {"start": 1681.59, "end": 1682.25, "word": " xn", "probability": 0.4947509765625}, {"start": 1682.25, "end": 1683.39, "word": " وهذه", "probability": 0.70458984375}, {"start": 1683.39, "end": 1684.19, "word": " subsequence", "probability": 0.99609375}, {"start": 1684.19, "end": 1684.51, "word": " من", "probability": 0.9931640625}, {"start": 1684.51, "end": 1685.07, "word": " هذه،", "probability": 0.5107421875}, {"start": 1685.07, "end": 1685.27, "word": " اذا", "probability": 0.815673828125}, {"start": 1685.27, "end": 1685.59, "word": " هذه", "probability": 0.751953125}, {"start": 1685.59, "end": 1686.33, "word": " subsequence", "probability": 0.99658203125}, {"start": 1686.33, "end": 1686.53, "word": " من", "probability": 0.9951171875}, {"start": 1686.53, "end": 1687.07, "word": " xn", "probability": 0.958740234375}], "temperature": 1.0}, {"id": 60, "seek": 171233, "start": 1691.21, "end": 1712.33, "text": "بما أن XKN هو أيضًا سبسيكوينس لسيكوينس الأصلية XN ثم بي وهو مرتبط", "tokens": [3555, 15042, 14739, 1783, 42, 45, 31439, 36632, 11242, 14111, 995, 8608, 3555, 3794, 1829, 4117, 2407, 9957, 3794, 5296, 3794, 1829, 4117, 2407, 9957, 3794, 16247, 9381, 20292, 3660, 1783, 45, 38637, 2304, 4724, 1829, 37037, 2407, 3714, 43500, 3555, 9566], "avg_logprob": -0.6079214922217435, "compression_ratio": 1.2696629213483146, "no_speech_prob": 0.0, "words": [{"start": 1691.21, "end": 1692.01, "word": "بما", "probability": 0.4130859375}, {"start": 1692.01, "end": 1692.01, "word": " أن", "probability": 0.54638671875}, {"start": 1692.01, "end": 1695.57, "word": " XKN", "probability": 0.3890787760416667}, {"start": 1695.57, "end": 1696.17, "word": " هو", "probability": 0.422607421875}, {"start": 1696.17, "end": 1697.69, "word": " أيضًا", "probability": 0.7659912109375}, {"start": 1697.69, "end": 1699.87, "word": " سبسيكوينس", "probability": 0.6737594604492188}, {"start": 1699.87, "end": 1702.95, "word": " لسيكوينس", "probability": 0.7531563895089286}, {"start": 1702.95, "end": 1703.67, "word": " الأصلية", "probability": 0.626708984375}, {"start": 1703.67, "end": 1704.45, "word": " XN", "probability": 0.86767578125}, {"start": 1704.45, "end": 1708.43, "word": " ثم", "probability": 0.6883544921875}, {"start": 1708.43, "end": 1709.05, "word": " بي", "probability": 0.5634765625}, {"start": 1709.05, "end": 1711.81, "word": " وهو", "probability": 0.494354248046875}, {"start": 1711.81, "end": 1712.33, "word": " مرتبط", "probability": 0.5533294677734375}], "temperature": 1.0}, {"id": 61, "seek": 172994, "start": 1721.88, "end": 1729.94, "text": "وهو مرتبط ثم من حيث الهيبوتاسيز", "tokens": [2407, 3224, 2407, 3714, 43500, 3555, 9566, 38637, 2304, 9154, 11331, 1829, 12984, 2423, 3224, 1829, 3555, 35473, 32277, 1829, 11622], "avg_logprob": -0.7084517045454546, "compression_ratio": 0.95, "no_speech_prob": 0.0, "words": [{"start": 1721.8799999999999, "end": 1723.28, "word": "وهو", "probability": 0.666015625}, {"start": 1723.28, "end": 1724.68, "word": " مرتبط", "probability": 0.6031494140625}, {"start": 1724.68, "end": 1728.02, "word": " ثم", "probability": 0.529022216796875}, {"start": 1728.02, "end": 1728.64, "word": " من", "probability": 0.240234375}, {"start": 1728.64, "end": 1728.7, "word": " حيث", "probability": 0.6197509765625}, {"start": 1728.7, "end": 1729.94, "word": " الهيبوتاسيز", "probability": 0.6293487548828125}], "temperature": 1.0}, {"id": 62, "seek": 175343, "start": 1731.15, "end": 1753.43, "text": "من الفرض احنا فرضين في النظرية هذه ان every convergent subsequence of xn لازم تكون convergent للعدد x فهي في عندي subsequence من ال sequence xn وconvergent اذا لازم تكون ال limit تبعتها x اذا من الفرض limit", "tokens": [27842, 27188, 43042, 1975, 5016, 8315, 6156, 43042, 9957, 8978, 28239, 19913, 2288, 10632, 29538, 16472, 633, 9652, 6930, 13924, 655, 295, 2031, 77, 5296, 31377, 2304, 6055, 30544, 9652, 6930, 24976, 22488, 3215, 2031, 6156, 3224, 1829, 8978, 18871, 16254, 13924, 655, 9154, 2423, 8310, 2031, 77, 4032, 1671, 331, 6930, 1975, 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"end": 1736.55, "word": " convergent", "probability": 0.905517578125}, {"start": 1736.55, "end": 1737.53, "word": " subsequence", "probability": 0.982421875}, {"start": 1737.53, "end": 1738.15, "word": " of", "probability": 0.916015625}, {"start": 1738.15, "end": 1738.83, "word": " xn", "probability": 0.5040283203125}, {"start": 1738.83, "end": 1739.31, "word": " لازم", "probability": 0.9884440104166666}, {"start": 1739.31, "end": 1739.61, "word": " تكون", "probability": 0.99169921875}, {"start": 1739.61, "end": 1740.41, "word": " convergent", "probability": 0.93017578125}, {"start": 1740.41, "end": 1741.05, "word": " للعدد", "probability": 0.9519856770833334}, {"start": 1741.05, "end": 1741.45, "word": " x", "probability": 0.90576171875}, {"start": 1741.45, "end": 1742.41, "word": " فهي", "probability": 0.84228515625}, {"start": 1742.41, "end": 1742.53, "word": " في", "probability": 0.83837890625}, {"start": 1742.53, "end": 1742.93, "word": " عندي", "probability": 0.943603515625}, {"start": 1742.93, "end": 1744.63, "word": " subsequence", "probability": 0.988525390625}, {"start": 1744.63, "end": 1744.89, "word": " من", "probability": 0.98095703125}, {"start": 1744.89, "end": 1745.03, "word": " ال", "probability": 0.60009765625}, {"start": 1745.03, "end": 1745.43, "word": " sequence", "probability": 0.8349609375}, {"start": 1745.43, "end": 1746.15, "word": " xn", "probability": 0.907470703125}, {"start": 1746.15, "end": 1747.27, "word": " وconvergent", "probability": 0.7677001953125}, {"start": 1747.27, "end": 1748.41, "word": " اذا", "probability": 0.6192626953125}, {"start": 1748.41, "end": 1748.77, "word": " لازم", "probability": 0.9793294270833334}, {"start": 1748.77, "end": 1749.13, "word": " تكون", "probability": 0.984619140625}, {"start": 1749.13, "end": 1749.29, "word": " ال", "probability": 0.806640625}, {"start": 1749.29, "end": 1749.53, "word": " limit", "probability": 0.96484375}, {"start": 1749.53, "end": 1750.11, "word": " تبعتها", "probability": 0.9481201171875}, {"start": 1750.11, "end": 1750.49, "word": " x", "probability": 0.9453125}, {"start": 1750.49, "end": 1751.19, "word": " اذا", "probability": 0.816162109375}, {"start": 1751.19, "end": 1751.43, "word": " من", "probability": 0.9931640625}, {"start": 1751.43, "end": 1751.97, "word": " الفرض", "probability": 0.9794921875}, {"start": 1751.97, "end": 1753.43, "word": " limit", "probability": 0.435791015625}], "temperature": 1.0}, {"id": 63, "seek": 177986, "start": 1755.76, "end": 1779.86, "text": "لأكس كأن as n tends to infinity بساوي LX تمام طب احنا عايزين نثبت ان ال XN نفسك converge لل X طيب الآن من تعريف", "tokens": [1211, 10721, 4117, 3794, 9122, 33456, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 441, 55, 46811, 10943, 23032, 3555, 1975, 5016, 8315, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 16472, 2423, 1783, 45, 8717, 36178, 4117, 41881, 24976, 1783, 23032, 1829, 3555, 6024, 48506, 9154, 37279, 16572, 5172], "avg_logprob": -0.2913161034767444, "compression_ratio": 1.1928571428571428, "no_speech_prob": 0.0, "words": [{"start": 1755.76, "end": 1756.58, "word": "لأكس", "probability": 0.604095458984375}, {"start": 1756.58, "end": 1757.68, "word": " كأن", "probability": 0.544189453125}, {"start": 1757.68, "end": 1758.22, "word": " as", "probability": 0.60009765625}, {"start": 1758.22, "end": 1758.48, "word": " n", "probability": 0.7509765625}, {"start": 1758.48, "end": 1758.82, "word": " tends", "probability": 0.69189453125}, {"start": 1758.82, "end": 1758.96, "word": " to", "probability": 0.927734375}, {"start": 1758.96, "end": 1759.5, "word": " infinity", "probability": 0.8837890625}, {"start": 1759.5, "end": 1760.54, "word": " بساوي", "probability": 0.855712890625}, {"start": 1760.54, "end": 1761.24, "word": " LX", "probability": 0.4625244140625}, {"start": 1761.24, "end": 1763.52, "word": " تمام", "probability": 0.75048828125}, {"start": 1763.52, "end": 1768.48, "word": " طب", "probability": 0.607421875}, {"start": 1768.48, "end": 1768.82, "word": " احنا", "probability": 0.89990234375}, {"start": 1768.82, "end": 1769.44, "word": " عايزين", "probability": 0.9593505859375}, {"start": 1769.44, "end": 1770.36, "word": " نثبت", "probability": 0.9932861328125}, {"start": 1770.36, "end": 1772.48, "word": " ان", "probability": 0.82568359375}, {"start": 1772.48, "end": 1772.7, "word": " ال", "probability": 0.74609375}, {"start": 1772.7, "end": 1773.26, "word": " XN", "probability": 0.5360107421875}, {"start": 1773.26, "end": 1773.96, "word": " نفسك", "probability": 0.978515625}, {"start": 1773.96, "end": 1775.26, "word": " converge", "probability": 0.7861328125}, {"start": 1775.26, "end": 1776.3, "word": " لل", "probability": 0.421630859375}, {"start": 1776.3, "end": 1776.78, "word": " X", "probability": 0.8408203125}, {"start": 1776.78, "end": 1777.72, "word": " طيب", "probability": 0.9697265625}, {"start": 1777.72, "end": 1778.88, "word": " الآن", "probability": 0.631591796875}, {"start": 1778.88, "end": 1779.18, "word": " من", "probability": 0.9853515625}, {"start": 1779.18, "end": 1779.86, "word": " تعريف", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 64, "seek": 180800, "start": 1781.78, "end": 1808.0, "text": "أنا في عندي إبسلون زيرو موجود هاي في عندي إبسلون زيرو أنا في عندي إبسلون زيرو هاد عدد موجود من ال divergence في الفيلم hence وعندي ال subsequence هاد ال converge ل X لذا لما انت عارف ال convergence there exist capital N يعتمد على إبسلون زيرو", "tokens": [10721, 8315, 8978, 18871, 16254, 11933, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 3714, 29245, 23328, 8032, 47302, 8978, 18871, 16254, 11933, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 41850, 8978, 18871, 16254, 11933, 3555, 3794, 1211, 11536, 30767, 13546, 2407, 8032, 18513, 6225, 3215, 3215, 3714, 29245, 23328, 9154, 2423, 47387, 8978, 27188, 1829, 19528, 16678, 4032, 3615, 1863, 16254, 2423, 13924, 655, 8032, 18513, 2423, 41881, 5296, 1783, 5296, 15730, 5296, 15042, 16472, 2655, 6225, 9640, 5172, 2423, 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"word": " إبسلون", "probability": 0.97529296875}, {"start": 1807.5, "end": 1808.0, "word": " زيرو", "probability": 0.9723307291666666}], "temperature": 1.0}, {"id": 65, "seek": 183574, "start": 1811.6, "end": 1835.74, "text": "بحيث ان ال absolute value للحد العام لل sequence XKN المسافة بينه بين ال X أصغر من epsilon zero وهذا الكلام صحيح لكل N في N تمام؟", "tokens": [3555, 5016, 1829, 12984, 16472, 2423, 8236, 2158, 24976, 24401, 18863, 10943, 24976, 8310, 1783, 34559, 9673, 3794, 31845, 3660, 49374, 3224, 49374, 2423, 1783, 5551, 9381, 17082, 2288, 9154, 17889, 4018, 37037, 15730, 2423, 28820, 10943, 20328, 5016, 1829, 5016, 5296, 28820, 426, 8978, 426, 46811, 10943, 22807], "avg_logprob": -0.3546874988079071, "compression_ratio": 1.2763157894736843, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1811.6, "end": 1812.76, "word": "بحيث", "probability": 0.706268310546875}, {"start": 1812.76, "end": 1813.1, "word": " ان", "probability": 0.48876953125}, {"start": 1813.1, "end": 1813.54, "word": " ال", "probability": 0.496337890625}, {"start": 1813.54, "end": 1816.2, "word": " absolute", "probability": 0.56982421875}, {"start": 1816.2, "end": 1817.02, "word": " value", "probability": 0.98828125}, {"start": 1817.02, "end": 1817.6, "word": " للحد", "probability": 0.669921875}, {"start": 1817.6, "end": 1818.18, "word": " العام", "probability": 0.9501953125}, {"start": 1818.18, "end": 1818.5, "word": " لل", "probability": 0.6455078125}, {"start": 1818.5, "end": 1819.0, "word": " sequence", "probability": 0.80810546875}, {"start": 1819.0, "end": 1821.32, "word": " XKN", "probability": 0.25518798828125}, {"start": 1821.32, "end": 1822.38, "word": " المسافة", "probability": 0.86224365234375}, {"start": 1822.38, "end": 1822.72, "word": " بينه", "probability": 0.810546875}, {"start": 1822.72, "end": 1823.0, "word": " بين", "probability": 0.48583984375}, {"start": 1823.0, "end": 1823.16, "word": " ال", "probability": 0.6884765625}, {"start": 1823.16, "end": 1823.54, "word": " X", "probability": 0.79052734375}, {"start": 1823.54, "end": 1825.64, "word": " أصغر", "probability": 0.958740234375}, {"start": 1825.64, "end": 1826.0, "word": " من", "probability": 0.9833984375}, {"start": 1826.0, "end": 1826.58, "word": " epsilon", "probability": 0.15234375}, {"start": 1826.58, "end": 1827.32, "word": " zero", "probability": 0.396484375}, {"start": 1827.32, "end": 1828.42, "word": " وهذا", "probability": 0.779296875}, {"start": 1828.42, "end": 1828.86, "word": " الكلام", "probability": 0.8291829427083334}, {"start": 1828.86, "end": 1829.46, "word": " صحيح", "probability": 0.9945068359375}, {"start": 1829.46, "end": 1830.08, "word": " لكل", "probability": 0.97314453125}, {"start": 1830.08, "end": 1830.52, "word": " N", "probability": 0.39501953125}, {"start": 1830.52, "end": 1830.82, "word": " في", "probability": 0.94287109375}, {"start": 1830.82, "end": 1831.22, "word": " N", "probability": 0.92626953125}, {"start": 1831.22, "end": 1835.74, "word": " تمام؟", "probability": 0.8468424479166666}], "temperature": 1.0}, {"id": 66, "seek": 186430, "start": 1837.5, "end": 1864.3, "text": "بنسمي المتباين هذي double star الان now star and double star بيقدوا انه ال .. هاي عندي absolute x k n minus x هذا أصغر من epsilon zero", "tokens": [3555, 1863, 38251, 1829, 9673, 2655, 3555, 995, 9957, 8032, 8848, 1829, 3834, 3543, 2423, 7649, 586, 3543, 293, 3834, 3543, 4724, 1829, 28543, 14407, 16472, 3224, 2423, 4386, 8032, 47302, 18871, 16254, 8236, 2031, 350, 297, 3175, 2031, 23758, 5551, 9381, 17082, 2288, 9154, 17889, 4018], "avg_logprob": -0.33284505891303223, "compression_ratio": 1.2397260273972603, "no_speech_prob": 0.0, "words": [{"start": 1837.5, "end": 1838.42, "word": "بنسمي", "probability": 0.7591552734375}, {"start": 1838.42, "end": 1839.46, "word": " المتباين", "probability": 0.903125}, {"start": 1839.46, "end": 1839.88, "word": " هذي", "probability": 0.4908040364583333}, {"start": 1839.88, "end": 1840.14, "word": " double", "probability": 0.7294921875}, {"start": 1840.14, "end": 1840.68, "word": " star", "probability": 0.841796875}, {"start": 1840.68, "end": 1843.94, "word": " الان", "probability": 0.6551513671875}, {"start": 1843.94, "end": 1844.64, "word": " now", "probability": 0.60546875}, {"start": 1844.64, "end": 1846.94, "word": " star", "probability": 0.6162109375}, {"start": 1846.94, "end": 1847.62, "word": " and", "probability": 0.9541015625}, {"start": 1847.62, "end": 1848.5, "word": " double", "probability": 0.927734375}, {"start": 1848.5, "end": 1849.1, "word": " star", "probability": 0.9453125}, {"start": 1849.1, "end": 1851.9, "word": " بيقدوا", "probability": 0.67822265625}, {"start": 1851.9, "end": 1854.46, "word": " انه", "probability": 0.718505859375}, {"start": 1854.46, "end": 1854.92, "word": " ال", "probability": 0.58984375}, {"start": 1854.92, "end": 1855.62, "word": " ..", "probability": 0.403564453125}, {"start": 1855.62, "end": 1856.98, "word": " هاي", "probability": 0.656982421875}, {"start": 1856.98, "end": 1857.36, "word": " عندي", "probability": 0.85986328125}, {"start": 1857.36, "end": 1858.0, "word": " absolute", "probability": 0.9169921875}, {"start": 1858.0, "end": 1858.96, "word": " x", "probability": 0.72705078125}, {"start": 1858.96, "end": 1860.42, "word": " k", "probability": 0.215087890625}, {"start": 1860.42, "end": 1860.98, "word": " n", "probability": 0.80078125}, {"start": 1860.98, "end": 1861.7, "word": " minus", "probability": 0.91796875}, {"start": 1861.7, "end": 1862.14, "word": " x", "probability": 0.97216796875}, {"start": 1862.14, "end": 1862.48, "word": " هذا", "probability": 0.6435546875}, {"start": 1862.48, "end": 1863.1, "word": " أصغر", "probability": 0.88134765625}, {"start": 1863.1, "end": 1863.36, "word": " من", "probability": 0.98974609375}, {"start": 1863.36, "end": 1863.82, "word": " epsilon", "probability": 0.56787109375}, {"start": 1863.82, "end": 1864.3, "word": " zero", "probability": 0.79150390625}], "temperature": 1.0}, {"id": 67, "seek": 188463, "start": 1866.49, "end": 1884.63, "text": "هذا من double star من هنا طب و من ال star انا عندي xrm المسافة بين xrm و x أكبر من او ساوي epsilon zero", "tokens": [3224, 15730, 9154, 3834, 3543, 9154, 34105, 23032, 3555, 4032, 9154, 2423, 3543, 1975, 8315, 18871, 16254, 2031, 81, 76, 9673, 3794, 31845, 3660, 49374, 2031, 81, 76, 4032, 2031, 5551, 4117, 26890, 9154, 1975, 2407, 8608, 995, 45865, 17889, 4018], "avg_logprob": -0.29334076316583724, "compression_ratio": 1.25, "no_speech_prob": 0.0, "words": [{"start": 1866.49, "end": 1866.91, "word": "هذا", "probability": 0.80029296875}, {"start": 1866.91, "end": 1867.11, "word": " من", "probability": 0.8447265625}, {"start": 1867.11, "end": 1867.37, "word": " double", "probability": 0.51025390625}, {"start": 1867.37, "end": 1867.91, "word": " star", "probability": 0.92333984375}, {"start": 1867.91, "end": 1869.59, "word": " من", "probability": 0.442138671875}, {"start": 1869.59, "end": 1869.91, "word": " هنا", "probability": 0.96923828125}, {"start": 1869.91, "end": 1872.11, "word": " طب", "probability": 0.859130859375}, {"start": 1872.11, "end": 1872.23, "word": " و", "probability": 0.9609375}, {"start": 1872.23, "end": 1872.39, "word": " من", "probability": 0.958984375}, {"start": 1872.39, "end": 1872.61, "word": " ال", "probability": 0.94140625}, {"start": 1872.61, "end": 1874.93, "word": " star", "probability": 0.845703125}, {"start": 1874.93, "end": 1878.33, "word": " انا", "probability": 0.781494140625}, {"start": 1878.33, "end": 1878.69, "word": " عندي", "probability": 0.786865234375}, {"start": 1878.69, "end": 1879.83, "word": " xrm", "probability": 0.50439453125}, {"start": 1879.83, "end": 1880.61, "word": " المسافة", "probability": 0.872802734375}, {"start": 1880.61, "end": 1880.85, "word": " بين", "probability": 0.9423828125}, {"start": 1880.85, "end": 1881.61, "word": " xrm", "probability": 0.9220377604166666}, {"start": 1881.61, "end": 1881.69, "word": " و", "probability": 0.89697265625}, {"start": 1881.69, "end": 1881.91, "word": " x", "probability": 0.87158203125}, {"start": 1881.91, "end": 1882.35, "word": " أكبر", "probability": 0.9127604166666666}, {"start": 1882.35, "end": 1882.51, "word": " من", "probability": 0.8369140625}, {"start": 1882.51, "end": 1882.65, "word": " او", "probability": 0.478515625}, {"start": 1882.65, "end": 1883.25, "word": " ساوي", "probability": 0.9015299479166666}, {"start": 1883.25, "end": 1884.15, "word": " epsilon", "probability": 0.1973876953125}, {"start": 1884.15, "end": 1884.63, "word": " zero", "probability": 0.76904296875}], "temperature": 1.0}, {"id": 68, "seek": 191680, "start": 1887.28, "end": 1916.8, "text": "و هذه sub sequence من ال sub sequence هذه يعني كل حد في ال sequence هذه هو حد في هذه و بالتالي ال sub sequence هذه بتحقق المتباينة star إذن هذا صحيح من star ال absolute الفرقة ده بطلع أكبر من أو ساوي epsilon zero الكلام هذا صحيح لكل n في M", "tokens": [2407, 29538, 1422, 8310, 9154, 2423, 1422, 8310, 29538, 37495, 22653, 28242, 11331, 3215, 8978, 2423, 8310, 29538, 31439, 11331, 3215, 8978, 29538, 4032, 20666, 2655, 6027, 1829, 2423, 1422, 8310, 29538, 39894, 5016, 4587, 4587, 9673, 2655, 3555, 995, 9957, 3660, 3543, 11933, 8848, 1863, 23758, 20328, 5016, 1829, 5016, 9154, 3543, 2423, 8236, 27188, 2288, 28671, 11778, 3224, 4724, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 17889, 4018, 2423, 28820, 10943, 23758, 20328, 5016, 1829, 5016, 5296, 28820, 297, 8978, 376], "avg_logprob": -0.20543324540961871, "compression_ratio": 1.803030303030303, "no_speech_prob": 0.0, "words": [{"start": 1887.28, "end": 1887.56, "word": "و", "probability": 0.86962890625}, {"start": 1887.56, "end": 1887.98, "word": " هذه", "probability": 0.40087890625}, {"start": 1887.98, "end": 1888.7, "word": " sub", "probability": 0.353515625}, {"start": 1888.7, "end": 1889.36, "word": " sequence", "probability": 0.70263671875}, {"start": 1889.36, "end": 1892.24, "word": " من", "probability": 0.6455078125}, {"start": 1892.24, "end": 1892.78, "word": " ال", "probability": 0.388671875}, {"start": 1892.78, "end": 1893.02, "word": " sub", "probability": 0.615234375}, {"start": 1893.02, "end": 1893.6, "word": " sequence", "probability": 0.9453125}, {"start": 1893.6, "end": 1894.0, "word": " هذه", "probability": 0.697265625}, {"start": 1894.0, "end": 1894.3, "word": " يعني", "probability": 0.9072265625}, {"start": 1894.3, "end": 1894.64, "word": " كل", "probability": 0.93310546875}, {"start": 1894.64, "end": 1895.0, "word": " حد", "probability": 0.9794921875}, {"start": 1895.0, "end": 1895.14, "word": " في", "probability": 0.9521484375}, {"start": 1895.14, "end": 1895.28, "word": " ال", "probability": 0.95458984375}, {"start": 1895.28, "end": 1895.7, "word": " sequence", "probability": 0.9765625}, {"start": 1895.7, "end": 1896.18, "word": " هذه", "probability": 0.74169921875}, {"start": 1896.18, "end": 1897.02, "word": " هو", "probability": 0.9306640625}, {"start": 1897.02, "end": 1897.4, "word": " حد", "probability": 0.993896484375}, {"start": 1897.4, "end": 1897.6, "word": " في", "probability": 0.8681640625}, {"start": 1897.6, "end": 1897.82, "word": " هذه", "probability": 0.8212890625}, {"start": 1897.82, "end": 1897.94, "word": " و", "probability": 0.488525390625}, {"start": 1897.94, "end": 1898.52, "word": " بالتالي", "probability": 0.922607421875}, {"start": 1898.52, "end": 1899.52, "word": " ال", "probability": 0.80078125}, {"start": 1899.52, "end": 1899.76, "word": " sub", "probability": 0.90869140625}, {"start": 1899.76, "end": 1900.16, "word": " sequence", "probability": 0.9638671875}, {"start": 1900.16, "end": 1900.46, "word": " هذه", "probability": 0.8642578125}, {"start": 1900.46, "end": 1901.1, "word": " بتحقق", "probability": 0.962890625}, {"start": 1901.1, "end": 1902.12, "word": " المتباينة", "probability": 0.9530436197916666}, {"start": 1902.12, "end": 1903.28, "word": " star", "probability": 0.55029296875}, {"start": 1903.28, "end": 1905.64, "word": " إذن", "probability": 0.6533203125}, {"start": 1905.64, "end": 1905.98, "word": " هذا", "probability": 0.93017578125}, {"start": 1905.98, "end": 1907.86, "word": " صحيح", "probability": 0.9969482421875}, {"start": 1907.86, "end": 1908.12, "word": " من", "probability": 0.9287109375}, {"start": 1908.12, "end": 1908.66, "word": " star", "probability": 0.611328125}, {"start": 1908.66, "end": 1908.88, "word": " ال", "probability": 0.52294921875}, {"start": 1908.88, "end": 1909.86, "word": " absolute", "probability": 0.8134765625}, {"start": 1909.86, "end": 1910.5, "word": " الفرقة", "probability": 0.7534993489583334}, {"start": 1910.5, "end": 1910.7, "word": " ده", "probability": 0.891845703125}, {"start": 1910.7, "end": 1911.04, "word": " بطلع", "probability": 0.8074951171875}, {"start": 1911.04, "end": 1911.44, "word": " أكبر", "probability": 0.9591471354166666}, {"start": 1911.44, "end": 1911.72, "word": " من", "probability": 0.8408203125}, {"start": 1911.72, "end": 1912.48, "word": " أو", "probability": 0.81298828125}, {"start": 1912.48, "end": 1912.92, "word": " ساوي", "probability": 0.8722330729166666}, {"start": 1912.92, "end": 1913.32, "word": " epsilon", "probability": 0.52392578125}, {"start": 1913.32, "end": 1913.78, "word": " zero", "probability": 0.66064453125}, {"start": 1913.78, "end": 1914.66, "word": " الكلام", "probability": 0.9295247395833334}, {"start": 1914.66, "end": 1914.92, "word": " هذا", "probability": 0.94677734375}, {"start": 1914.92, "end": 1915.48, "word": " صحيح", "probability": 0.9891357421875}, {"start": 1915.48, "end": 1916.02, "word": " لكل", "probability": 0.980712890625}, {"start": 1916.02, "end": 1916.42, "word": " n", "probability": 0.64111328125}, {"start": 1916.42, "end": 1916.62, "word": " في", "probability": 0.53271484375}, {"start": 1916.62, "end": 1916.8, "word": " M", "probability": 0.328369140625}], "temperature": 1.0}, {"id": 69, "seek": 194826, "start": 1918.58, "end": 1948.26, "text": "إذا أنا عندي طلع هيك epsilon zero أصغر من epsilon zero و هذا بديني تناقض contradiction إذا التناقض هذا السبب تبعه إن إحنا فرضنا إن xn does not converge ل x إذا ال contradiction هذه بتقول إن xn لازم converge ل x و هذا اللي بدنا ياه وهم المطلوب", "tokens": [28814, 15730, 41850, 18871, 16254, 23032, 1211, 3615, 39896, 4117, 17889, 4018, 5551, 9381, 17082, 2288, 9154, 17889, 4018, 4032, 23758, 4724, 16254, 22653, 6055, 8315, 4587, 11242, 34937, 11933, 15730, 16712, 8315, 4587, 11242, 23758, 21136, 3555, 3555, 6055, 3555, 3615, 3224, 36145, 11933, 5016, 8315, 6156, 43042, 8315, 36145, 2031, 77, 775, 406, 41881, 5296, 2031, 11933, 15730, 2423, 34937, 29538, 39894, 39648, 36145, 2031, 77, 5296, 31377, 2304, 41881, 5296, 2031, 4032, 23758, 13672, 1829, 47525, 8315, 7251, 40294, 4032, 16095, 9673, 9566, 1211, 37746], "avg_logprob": -0.22120786784739976, "compression_ratio": 1.751219512195122, "no_speech_prob": 0.0, "words": [{"start": 1918.58, "end": 1918.98, "word": "إذا", "probability": 0.64892578125}, {"start": 1918.98, "end": 1919.24, "word": " أنا", "probability": 0.69287109375}, {"start": 1919.24, "end": 1919.72, "word": " عندي", "probability": 0.9091796875}, {"start": 1919.72, "end": 1920.96, "word": " طلع", "probability": 0.9051106770833334}, {"start": 1920.96, "end": 1921.96, "word": " هيك", "probability": 0.944091796875}, {"start": 1921.96, "end": 1923.04, "word": " epsilon", "probability": 0.13134765625}, {"start": 1923.04, "end": 1923.62, "word": " zero", "probability": 0.68310546875}, {"start": 1923.62, "end": 1924.24, "word": " أصغر", "probability": 0.975830078125}, {"start": 1924.24, "end": 1924.4, "word": " من", "probability": 0.98779296875}, {"start": 1924.4, "end": 1924.72, "word": " epsilon", "probability": 0.90234375}, {"start": 1924.72, "end": 1925.14, "word": " zero", "probability": 0.8583984375}, {"start": 1925.14, "end": 1925.28, "word": " و", "probability": 0.291015625}, {"start": 1925.28, "end": 1925.36, "word": " هذا", "probability": 0.72509765625}, {"start": 1925.36, "end": 1925.86, "word": " بديني", "probability": 0.52490234375}, {"start": 1925.86, "end": 1926.42, "word": " تناقض", "probability": 0.9630126953125}, {"start": 1926.42, "end": 1927.08, "word": " contradiction", "probability": 0.84375}, {"start": 1927.08, "end": 1928.78, "word": " إذا", "probability": 0.8720703125}, {"start": 1928.78, "end": 1929.46, "word": " التناقض", "probability": 0.97802734375}, {"start": 1929.46, "end": 1929.96, "word": " هذا", "probability": 0.9189453125}, {"start": 1929.96, "end": 1931.48, "word": " السبب", "probability": 0.9886067708333334}, {"start": 1931.48, "end": 1932.06, "word": " تبعه", "probability": 0.9639892578125}, {"start": 1932.06, "end": 1932.88, "word": " إن", "probability": 0.45068359375}, {"start": 1932.88, "end": 1933.24, "word": " إحنا", "probability": 0.8114420572916666}, {"start": 1933.24, "end": 1935.3, "word": " فرضنا", "probability": 0.9889322916666666}, {"start": 1935.3, "end": 1936.96, "word": " إن", "probability": 0.66748046875}, {"start": 1936.96, "end": 1937.72, "word": " xn", "probability": 0.44580078125}, {"start": 1937.72, "end": 1937.96, "word": " does", "probability": 0.50732421875}, {"start": 1937.96, "end": 1938.28, "word": " not", "probability": 0.9599609375}, {"start": 1938.28, "end": 1938.88, "word": " converge", "probability": 0.98876953125}, {"start": 1938.88, "end": 1939.04, "word": " ل", "probability": 0.95654296875}, {"start": 1939.04, "end": 1939.44, "word": " x", "probability": 0.47705078125}, {"start": 1939.44, "end": 1940.42, "word": " إذا", "probability": 0.727294921875}, {"start": 1940.42, "end": 1940.58, "word": " ال", "probability": 0.9697265625}, {"start": 1940.58, "end": 1941.06, "word": " contradiction", "probability": 0.92919921875}, {"start": 1941.06, "end": 1941.4, "word": " هذه", "probability": 0.5634765625}, {"start": 1941.4, "end": 1941.78, "word": " بتقول", "probability": 0.939453125}, {"start": 1941.78, "end": 1942.0, "word": " إن", "probability": 0.95703125}, {"start": 1942.0, "end": 1942.84, "word": " xn", "probability": 0.98095703125}, {"start": 1942.84, "end": 1943.66, "word": " لازم", "probability": 0.9827473958333334}, {"start": 1943.66, "end": 1944.34, "word": " converge", "probability": 0.9892578125}, {"start": 1944.34, "end": 1944.6, "word": " ل", "probability": 0.97998046875}, {"start": 1944.6, "end": 1945.02, "word": " x", "probability": 0.89501953125}, {"start": 1945.02, "end": 1946.44, "word": " و", "probability": 0.67431640625}, {"start": 1946.44, "end": 1946.64, "word": " هذا", "probability": 0.8740234375}, {"start": 1946.64, "end": 1946.78, "word": " اللي", "probability": 0.7822265625}, {"start": 1946.78, "end": 1947.02, "word": " بدنا", "probability": 0.847900390625}, {"start": 1947.02, "end": 1947.36, "word": " ياه", "probability": 0.4405517578125}, {"start": 1947.36, "end": 1947.68, "word": " وهم", "probability": 0.826416015625}, {"start": 1947.68, "end": 1948.26, "word": " المطلوب", "probability": 0.9935302734375}], "temperature": 1.0}, {"id": 70, "seek": 196612, "start": 1950.26, "end": 1966.12, "text": "وهو المطلوب okay إذا هيك بنكون برهننا النظرية هذه خلينا ناخد احنا break عشان فينا لقاء تاني لمدة خمس دقايق و بعدين يعني نرجع، ماشي الحال؟", "tokens": [2407, 3224, 2407, 9673, 9566, 1211, 37746, 1392, 11933, 15730, 39896, 4117, 44945, 30544, 4724, 2288, 3224, 1863, 8315, 28239, 19913, 2288, 10632, 29538, 16490, 1211, 9957, 995, 8717, 47283, 3215, 1975, 5016, 8315, 1821, 6225, 8592, 7649, 8978, 8315, 5296, 4587, 16606, 6055, 7649, 1829, 32767, 41891, 16490, 2304, 3794, 11778, 4587, 47302, 4587, 4032, 39182, 9957, 37495, 22653, 8717, 47341, 3615, 12399, 3714, 33599, 1829, 21542, 6027, 22807], "avg_logprob": -0.16923414989256522, "compression_ratio": 1.4545454545454546, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1950.26, "end": 1950.9, "word": "وهو", "probability": 0.8849283854166666}, {"start": 1950.9, "end": 1951.72, "word": " المطلوب", "probability": 0.9798583984375}, {"start": 1951.72, "end": 1952.28, "word": " okay", "probability": 0.61328125}, {"start": 1952.28, "end": 1953.2, "word": " إذا", "probability": 0.5819091796875}, {"start": 1953.2, "end": 1953.56, "word": " هيك", "probability": 0.742919921875}, {"start": 1953.56, "end": 1953.9, "word": " بنكون", "probability": 0.88525390625}, {"start": 1953.9, "end": 1954.58, "word": " برهننا", "probability": 0.84609375}, {"start": 1954.58, "end": 1955.3, "word": " النظرية", "probability": 0.9735107421875}, {"start": 1955.3, "end": 1955.7, "word": " هذه", "probability": 0.79638671875}, {"start": 1955.7, "end": 1957.8, "word": " خلينا", "probability": 0.843017578125}, {"start": 1957.8, "end": 1958.22, "word": " ناخد", "probability": 0.9892578125}, {"start": 1958.22, "end": 1958.6, "word": " احنا", "probability": 0.8914388020833334}, {"start": 1958.6, "end": 1959.26, "word": " break", "probability": 0.89599609375}, {"start": 1959.26, "end": 1960.22, "word": " عشان", "probability": 0.98828125}, {"start": 1960.22, "end": 1960.66, "word": " فينا", "probability": 0.65283203125}, {"start": 1960.66, "end": 1961.2, "word": " لقاء", "probability": 0.9583333333333334}, {"start": 1961.2, "end": 1961.7, "word": " تاني", "probability": 0.9708658854166666}, {"start": 1961.7, "end": 1962.86, "word": " لمدة", "probability": 0.8779296875}, {"start": 1962.86, "end": 1963.2, "word": " خمس", "probability": 0.9607747395833334}, {"start": 1963.2, "end": 1963.72, "word": " دقايق", "probability": 0.82415771484375}, {"start": 1963.72, "end": 1963.82, "word": " و", "probability": 0.77392578125}, {"start": 1963.82, "end": 1964.3, "word": " بعدين", "probability": 0.887451171875}, {"start": 1964.3, "end": 1964.6, "word": " يعني", "probability": 0.945068359375}, {"start": 1964.6, "end": 1965.42, "word": " نرجع،", "probability": 0.82257080078125}, {"start": 1965.42, "end": 1965.64, "word": " ماشي", "probability": 0.760986328125}, {"start": 1965.64, "end": 1966.12, "word": " الحال؟", "probability": 0.85693359375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1966.776625, "duration_after_vad": 1727.065624999995}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2faca4e6e4608041c460bc80dabb421d8ad14a5e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/WVOztu-xKaw_raw.srt
@@ -0,0 +1,1052 @@
+1
+00:00:20,670 --> 00:00:27,110
+Okay اليوم هنراجع بس نظرية ال divergence theorem
+
+2
+00:00:27,110 --> 00:00:33,870
+اللي أخدناها أخر مرة بس نسترجعها بسرعة ال
+
+3
+00:00:33,870 --> 00:00:40,370
+divergence theorem
+
+4
+00:00:40,370 --> 00:00:47,370
+عطلناها رقم 2.17 فالنظرية
+
+5
+00:00:47,370 --> 00:00:48,150
+هذه بتقول
+
+6
+00:00:51,110 --> 00:01:04,590
+لت X and contained in R be a sequence then
+
+7
+00:01:04,590 --> 00:01:09,410
+the following statements are equivalent
+
+8
+00:01:11,820 --> 00:01:18,400
+فأول statement sequence x in does not converge ل x
+
+9
+00:01:18,400 --> 00:01:28,200
+ينتمي ل R for any x ينتمي ل R وفي شرط التاني وفي
+
+10
+00:01:28,200 --> 00:01:35,420
+شرط التالت أنا بهمش شرط التالت أو العبارة تالتة
+
+11
+00:01:35,420 --> 00:01:39,840
+there exist إبسلون زيور أكبر من الصفر and a
+
+12
+00:01:39,840 --> 00:01:48,390
+subsequenceأو سبسيكوينس XRN
+
+13
+00:01:48,390 --> 00:01:53,410
+of
+
+14
+00:01:53,410 --> 00:02:05,750
+سيكوينس XN such that absolute XRN minus X أكبر من
+
+15
+00:02:05,750 --> 00:02:08,550
+أو ساوي Y0 لكل M
+
+16
+00:02:13,970 --> 00:02:18,330
+و بدنا ناخد أنثى على النظرية هذه أخدناها المرة
+
+17
+00:02:18,330 --> 00:02:22,290
+الفاتة مثال
+
+18
+00:02:22,290 --> 00:02:29,470
+مثال
+
+19
+00:02:29,470 --> 00:02:39,490
+التانى example consider
+
+20
+00:02:41,810 --> 00:02:49,510
+ناخد ال sequence consider xn where sequence xn لحد
+
+21
+00:02:49,510 --> 00:03:04,610
+العالم تبعها xn معرف على انه بساوي n if n is odd و
+
+22
+00:03:04,610 --> 00:03:06,250
+بتساوي واحد على n
+
+23
+00:03:20,350 --> 00:03:28,690
+مطلوب ان اثبت ان ال sequence xn is divergent
+
+24
+00:03:41,550 --> 00:03:47,630
+سلوشن و لاحظوا ان سيكوانس X انها بيبارى حدودها
+
+25
+00:03:47,630 --> 00:03:53,350
+واحد نص و
+
+26
+00:03:53,350 --> 00:03:59,850
+واحد نص تلاتة رابع و
+
+27
+00:03:59,850 --> 00:04:00,390
+هكذا
+
+28
+00:04:08,080 --> 00:04:12,340
+فالـ sequence هذه بالنسبة لها does not converge
+
+29
+00:04:12,340 --> 00:04:23,040
+لأي x ينتمي لR to show أن x in does not converge ل
+
+30
+00:04:23,040 --> 00:04:29,720
+x for any x
+
+31
+00:04:29,720 --> 00:04:31,440
+ينتمي إلى R
+
+32
+00:04:35,590 --> 00:04:44,030
+fix x ينتمي ل r خلّينا ناخد arbitrary ال
+
+33
+00:04:44,030 --> 00:04:47,470
+real number x ينتمي ل r و نثبت ان x in does not
+
+34
+00:04:47,470 --> 00:04:54,730
+converge enough فعندي then
+
+35
+00:04:54,730 --> 00:04:59,670
+absolute x طبعا أكبر عدد حقيقي أكبر من أوسعه سفر
+
+36
+00:04:59,670 --> 00:05:11,460
+so byArchimedean property يوجد
+
+37
+00:05:11,460 --> 00:05:19,660
+n عدد طبيعي يعتمد على x عدد طبيعي بحيث
+
+38
+00:05:19,660 --> 00:05:38,420
+ان n x هذا is evenand absolute x أصغر من nx هذا
+
+39
+00:05:38,420 --> 00:05:42,990
+ممكن نحصل عليه من الarchimedean propertyالـ
+
+40
+00:05:42,990 --> 00:05:46,990
+argument property بتقول أي عدد حقيقي زي absolute x
+
+41
+00:05:46,990 --> 00:05:53,450
+نقدر نلاقي عدد طبيعي يعتمد على ال x بحيث أنه العدد
+
+42
+00:05:53,450 --> 00:06:02,110
+الطبيعي أكبر من العدد الحقيقي طيب الان لو أخدت
+
+43
+00:06:02,110 --> 00:06:05,150
+epsilon
+
+44
+00:06:05,150 --> 00:06:11,530
+zero عرفت على أنها nx سالب absolute x
+
+45
+00:06:14,250 --> 00:06:24,170
+فهذا بيطلع عدد موجب هذا بيطلع عدد موجب و
+
+46
+00:06:24,170 --> 00:06:30,190
+ال sequence ال
+
+47
+00:06:30,190 --> 00:06:39,390
+sequence الحد العام تبعها N X زائد اتنين M سالد
+
+48
+00:06:39,390 --> 00:06:39,930
+واحد
+
+49
+00:06:43,110 --> 00:06:51,010
+من M بساوي واحد to infinity هذه بالمناسبة الحدود
+
+50
+00:06:51,010 --> 00:07:00,770
+تبعتها هذا عدد فردي عدد طبيعي فردي وهذا
+
+51
+00:07:00,770 --> 00:07:09,190
+NX عدد طبيعي زوجي هذا odd وهذا
+
+52
+00:07:09,190 --> 00:07:09,890
+even
+
+53
+00:07:13,300 --> 00:07:22,960
+ف odd زائد even بطلع odd إذا الحدود
+
+54
+00:07:22,960 --> 00:07:33,340
+العامة لل sequence هذه بتكون odd وبالتالي
+
+55
+00:07:33,340 --> 00:07:39,600
+الحدود هذه كلها حسب التعريف بتطلع بالساوي
+
+56
+00:07:41,460 --> 00:07:48,180
+هي طبعا sub-sequence يعني
+
+57
+00:07:48,180 --> 00:07:54,300
+هدا هتكون لو M بساوة واحد هيطلع NX زائد واحد NX
+
+58
+00:07:54,300 --> 00:08:03,820
+زائد تلاتة و هكذا صح؟ حسب التعريف هدا عبارة عن sub
+
+59
+00:08:03,820 --> 00:08:11,700
+-sequence sub-sequence من ال sequence XMلأن هذه
+
+60
+00:08:11,700 --> 00:08:18,300
+جزء من الحدود الفردية، صح؟ وبالتالي هذه
+
+61
+00:08:18,300 --> 00:08:23,640
+subsequence من xn ومش
+
+62
+00:08:23,640 --> 00:08:35,320
+هيكوا بس and ال absolute value ل nx زائد 2m سالب 1
+
+63
+00:08:35,320 --> 00:08:41,640
+الحد العام لل subsequence هذهالمسافة بينه بين الـ
+
+64
+00:08:41,640 --> 00:08:46,220
+x باستخدام الـ triangle inequality في واحدة من الـ
+
+65
+00:08:46,220 --> 00:08:50,940
+triangle inequalities بتقول absolute a minus b
+
+66
+00:08:50,940 --> 00:08:56,200
+أكبر من أو ساوي absolute a minus absolute b فهذا
+
+67
+00:08:56,200 --> 00:09:02,540
+أكبر من أو ساوي absolute in x زي two m minus واحد
+
+68
+00:09:02,540 --> 00:09:09,720
+minus absolute xهذا عدد موجب هذا عدد طبيعي وهذا
+
+69
+00:09:09,720 --> 00:09:24,860
+عدد طبيعي فردي فممكن نشيل absolute value وهذا
+
+70
+00:09:24,860 --> 00:09:35,880
+العدد هذا العدد أكبر من NX سالب absolute Xهذا
+
+71
+00:09:35,880 --> 00:09:45,580
+العدد هنا أكبر من NX لأن هذا عدد موجب صح فNX زاد
+
+72
+00:09:45,580 --> 00:09:50,440
+عدد موجب أكبر من NX سالب absolute X طب ما هذا
+
+73
+00:09:50,440 --> 00:09:56,000
+بساوي عرفناه على N أبسل زيرو صح؟ الآن الكلام هذا
+
+74
+00:09:56,000 --> 00:09:59,460
+صحيح لكل M ينتمي إلى N
+
+75
+00:10:09,010 --> 00:10:15,890
+أنا اثبتت ان يوجد y0 أكبر من السفر و sub sequence
+
+76
+00:10:15,890 --> 00:10:21,850
+من ال sequence xn و المسافة بين الحد العام لل
+
+77
+00:10:21,850 --> 00:10:28,430
+sequence هذه و ال x أكبر من y0 لكل m في n
+
+78
+00:10:34,110 --> 00:10:44,630
+الـ divergence theorem الجزء التالت هيتحقق شروطه
+
+79
+00:10:44,630 --> 00:10:52,330
+وبالتالي ال sequence x in does not converge to x
+
+80
+00:10:56,670 --> 00:10:59,930
+بما أن x was arbitrary إذا الـ sequence x in does
+
+81
+00:10:59,930 --> 00:11:04,030
+not converge لأي عدد حقيقي x وبالتالي divergent
+
+82
+00:11:04,030 --> 00:11:10,130
+تمام؟ أنا هنا استخدمت ال divergence theorem في
+
+83
+00:11:10,130 --> 00:11:16,150
+أثبات أن ال sequence هذه divergent لاحظوا أن ال
+
+84
+00:11:16,150 --> 00:11:23,710
+sequence 1 على n هذه subsequence من x in وهذه
+
+85
+00:11:23,710 --> 00:11:24,890
+convergent ل0
+
+86
+00:11:28,580 --> 00:11:32,700
+لكن الـ sequence نفسها does not converge هذه برضه
+
+87
+00:11:32,700 --> 00:11:37,220
+subsequence N subsequence .. لما تكون الـ N فردية
+
+88
+00:11:37,220 --> 00:11:42,620
+subsequence من X N وهذه is not convergent هذه ال
+
+89
+00:11:42,620 --> 00:11:49,340
+limit بتاعها infinity طبعا؟ و
+
+90
+00:11:49,340 --> 00:11:50,500
+هذا؟ في عيز سؤال؟
+
+91
+00:12:05,310 --> 00:12:12,050
+monotone subsequence theorem النظرية
+
+92
+00:12:12,050 --> 00:12:23,330
+اتنين تمانتاش أقامها هنا النظرية
+
+93
+00:12:23,330 --> 00:12:32,230
+هذه بتقول every sequence in R has
+
+94
+00:12:36,910 --> 00:12:44,930
+monotone subsequence كل sequence of real numbers
+
+95
+00:12:44,930 --> 00:12:53,770
+ممكن نستخلص منها monotone subsequence البرهان تبع
+
+96
+00:12:53,770 --> 00:12:58,050
+النظرية هذه مش صعب موجود في الكتاب هخليكم تقراه
+
+97
+00:13:00,180 --> 00:13:09,360
+هخليكم تقرا البرهان من الكتاب المقرر C theorem
+
+98
+00:13:09,360 --> 00:13:20,360
+رقم تلاتة اربعة سبعة page تمانية
+
+99
+00:13:20,360 --> 00:13:22,020
+و سبعين in textbook
+
+100
+00:13:27,060 --> 00:13:32,200
+إذن حدؤوكم لقراة البرهان، البرهان سهل مش صعب و
+
+101
+00:13:32,200 --> 00:13:36,380
+حاولوا
+
+102
+00:13:36,380 --> 00:13:40,280
+تقراوه و تفهموه و ده في أي صعوبة تسألوني أو
+
+103
+00:13:40,280 --> 00:13:46,280
+تتناقشوا معي في البرهان okay
+
+104
+00:13:46,280 --> 00:13:49,680
+في
+
+105
+00:13:49,680 --> 00:13:51,320
+نظرية تانية
+
+106
+00:14:00,880 --> 00:14:06,900
+Bolzano-Weierstrass theorem
+
+107
+00:14:06,900 --> 00:14:17,880
+رقم اتنين تسعتاش النظرية
+
+108
+00:14:17,880 --> 00:14:23,980
+هذه بتقول every bounded sequence every
+
+109
+00:14:23,980 --> 00:14:26,540
+bounded
+
+110
+00:14:28,920 --> 00:14:34,800
+سيكوينس of real
+
+111
+00:14:34,800 --> 00:14:41,980
+numbers in R has a
+
+112
+00:14:41,980 --> 00:14:48,500
+convergent subsequence
+
+113
+00:14:53,720 --> 00:14:58,080
+لو فى عندي bounded sequence of real numbers فبقدر
+
+114
+00:14:58,080 --> 00:15:02,820
+أجى جواتها conversion subsequence البرهان تبع
+
+115
+00:15:02,820 --> 00:15:07,720
+نظريها دى سهل باستخدام نظريات السابقة فى لها
+
+116
+00:15:07,720 --> 00:15:14,300
+برهانين واحد short يعني قصير يعتمد على النظريات
+
+117
+00:15:14,300 --> 00:15:17,840
+الكبيرة اللى برهنها سابقا وفى لها برهان
+
+118
+00:15:21,560 --> 00:15:26,680
+طويل نوعا ما وهذا البرهان constructive proof يعني
+
+119
+00:15:26,680 --> 00:15:30,860
+بورجيكم كيف تبنوا ال subsequence اللي هتكون
+
+120
+00:15:30,860 --> 00:15:36,920
+convergent هناخد ال short proof ونخليكم تقرأوا ال
+
+121
+00:15:36,920 --> 00:15:40,980
+long proof رقم
+
+122
+00:15:40,980 --> 00:15:46,700
+واحد let
+
+123
+00:15:46,700 --> 00:15:47,560
+x in
+
+124
+00:15:50,470 --> 00:15:58,910
+contained are bounded sequence
+
+125
+00:15:58,910 --> 00:16:05,110
+of real numbers by
+
+126
+00:16:05,110 --> 00:16:17,490
+حسب النظرية الأخيرة رقم تمانتاش by theorem تمانتاش
+
+127
+00:16:17,490 --> 00:16:19,410
+المونوتون
+
+128
+00:16:22,580 --> 00:16:30,100
+بتقول أي sequence in R سواء bounded أو unbounded
+
+129
+00:16:30,100 --> 00:16:35,540
+every sequence of real numbers has a monotone
+
+130
+00:16:35,540 --> 00:16:44,360
+subsequence إذا ال XN has a monotone
+
+131
+00:16:44,360 --> 00:16:46,980
+subsequence
+
+132
+00:16:51,810 --> 00:17:02,790
+خلّيني أسميها x in k إذاً
+
+133
+00:17:02,790 --> 00:17:12,110
+هذه عبارة عن monotone subsequence طيب since x in
+
+134
+00:17:12,110 --> 00:17:18,150
+is bounded ال
+
+135
+00:17:18,150 --> 00:17:21,090
+subsequence .. the subsequence
+
+136
+00:17:23,040 --> 00:17:32,960
+x in k is also bounded أي
+
+137
+00:17:32,960 --> 00:17:36,540
+sub sequence من bounded sequence is bounded مظبوط
+
+138
+00:17:36,540 --> 00:17:41,520
+صح لأن x
+
+139
+00:17:41,520 --> 00:17:42,880
+in bounded
+
+140
+00:17:46,080 --> 00:17:52,660
+بقدّي ان يوجد M عدد موجب بحيث ان absolute xn أصغر
+
+141
+00:17:52,660 --> 00:18:01,440
+من أو ساوي M لكل N طب ما هذا بقدّي ان absolute xnk
+
+142
+00:18:01,440 --> 00:18:10,380
+أيضا أصغر من أو ساوي M لكل N لأن ال subsequence
+
+143
+00:18:10,380 --> 00:18:13,500
+xnk هي subset من xn
+
+144
+00:18:16,250 --> 00:18:20,130
+مظبوط؟ كل حد في ال subsequence هو حد في ال
+
+145
+00:18:20,130 --> 00:18:26,370
+sequence وبالتالي تحقق نفس الشرط لأن هذا بيقدي ان
+
+146
+00:18:26,370 --> 00:18:34,190
+كل .. هذا صحيح لكل K لأن هاي .. هذا الشرط منه
+
+147
+00:18:34,190 --> 00:18:37,830
+بيطلع X ان K is bounded
+
+148
+00:18:40,520 --> 00:18:44,940
+Okay إذا أنا كتب برهان أنه أي subsequence من
+
+149
+00:18:44,940 --> 00:18:54,900
+bounded sequence is bounded تمام Now ال
+
+150
+00:18:54,900 --> 00:19:01,980
+subsequence x in k is monotone
+
+151
+00:19:01,980 --> 00:19:05,420
+and
+
+152
+00:19:05,420 --> 00:19:05,980
+bounded
+
+153
+00:19:10,700 --> 00:19:15,920
+So by monotone convergence theorem حسب الـ
+
+154
+00:19:15,920 --> 00:19:20,960
+monotone convergence theorem it is convergent
+
+155
+00:19:26,310 --> 00:19:34,310
+ما هو المطلوب؟ لأن هنا أثبتنا أنه أي sequence أي
+
+156
+00:19:34,310 --> 00:19:37,510
+sequence which is bounded أي sequence of real
+
+157
+00:19:37,510 --> 00:19:41,690
+numbers which is bounded has a convergent
+
+158
+00:19:41,690 --> 00:19:50,490
+subsequence تمام؟ لأن هذا برهن النظرية تمام؟ واضح؟
+
+159
+00:19:50,490 --> 00:20:03,750
+في طبعا برهان تانيو هذا البرهان موجود في الكتاب ان
+
+160
+00:20:03,750 --> 00:20:09,610
+البرهان رقم اتنين proof رقم اتنين موجود في الكتاب
+
+161
+00:20:09,610 --> 00:20:16,130
+see page 79
+
+162
+00:20:16,130 --> 00:20:17,630
+in textbook
+
+163
+00:20:23,250 --> 00:20:27,150
+إذا أنا هنسيبكم تقرأوا البرهان التاني من الكتاب
+
+164
+00:20:27,150 --> 00:20:30,190
+طبعا البرهان هذا هيكون constructive proof بيورجيكم
+
+165
+00:20:30,190 --> 00:20:36,090
+كيف بيبني ال subsequence خطوة خطوة و بحيث انها
+
+166
+00:20:36,090 --> 00:20:43,030
+تطلع convergent طيب في كمال نظرية في هذا السياق
+
+167
+00:20:50,570 --> 00:21:03,690
+theorem اتنين عشرين let
+
+168
+00:21:03,690 --> 00:21:07,910
+x in content
+
+169
+00:21:07,910 --> 00:21:23,610
+in R be bounded bounded sequence and letX ينتمي
+
+170
+00:21:23,610 --> 00:21:29,370
+إلى R بـ
+
+171
+00:21:29,370 --> 00:21:36,870
+such that every .. every convergent .. every
+
+172
+00:21:36,870 --> 00:21:41,610
+convergent subsequence
+
+173
+00:21:41,610 --> 00:21:46,310
+.. every convergent subsequence
+
+174
+00:21:50,710 --> 00:21:59,550
+of سمّيها x أو
+
+175
+00:21:59,550 --> 00:22:08,450
+every convergent subsequence of x in converges to
+
+176
+00:22:08,450 --> 00:22:12,430
+x then
+
+177
+00:22:12,430 --> 00:22:16,930
+النتيجة أنه ال sequence x in
+
+178
+00:22:19,750 --> 00:22:27,190
+converges to x إذا
+
+179
+00:22:27,190 --> 00:22:31,730
+أنا في عندي bounded sequence of real numbersو في
+
+180
+00:22:31,730 --> 00:22:36,910
+اندي عدد حقيقي هذا العدد بيحقق الخاصية انه كل
+
+181
+00:22:36,910 --> 00:22:41,070
+convergence subsequence من ال sequence x in بتكون
+
+182
+00:22:41,070 --> 00:22:45,950
+convergent ل x فالحالة هذه ال sequence الأصلية
+
+183
+00:22:45,950 --> 00:22:51,730
+بتكون convergent و ال limit تبعتها هي نفس العدد x
+
+184
+00:22:51,730 --> 00:22:55,430
+برهان نظرية هذه سهل مش صعب
+
+185
+00:22:59,850 --> 00:23:04,850
+هنستخدم البولزانو virus trust theorem اللي هي
+
+186
+00:23:04,850 --> 00:23:22,730
+نظرية تسعتاش في البرهان هنشوف مع بعض prove assume
+
+187
+00:23:29,790 --> 00:23:37,770
+assume on contrary that
+
+188
+00:23:37,770 --> 00:23:42,890
+احنا عايزين نثبت ان ال sequence x in converge ل x
+
+189
+00:23:42,890 --> 00:23:51,550
+فنفرض ان x in does not converge to any x then
+
+190
+00:23:51,550 --> 00:23:55,330
+by divergence
+
+191
+00:23:57,210 --> 00:24:03,170
+by divergence theorem اللى
+
+192
+00:24:03,170 --> 00:24:10,530
+هى اتنين تمانتاش كذبوت
+
+193
+00:24:10,530 --> 00:24:16,390
+او اتنين سبعتاش اعتقد هيك صح اه ال divergence
+
+194
+00:24:16,390 --> 00:24:22,140
+theorem بتقولى x in does not converge ل xمعناته
+
+195
+00:24:22,140 --> 00:24:26,460
+there exist epsilon zero عدد موجب and there exist
+
+196
+00:24:26,460 --> 00:24:32,980
+a subsequence a subsequence
+
+197
+00:24:32,980 --> 00:24:36,180
+xrn
+
+198
+00:24:36,180 --> 00:24:40,200
+of xn
+
+199
+00:24:42,720 --> 00:24:51,320
+such that absolute x are n minus x أكبر من أو ساوي
+
+200
+00:24:51,320 --> 00:25:01,280
+epsilon zero هذا الكلام صحيح لكل n في n نسمي
+
+201
+00:25:01,280 --> 00:25:07,560
+المتباينة هذه star تمام؟ هذا من نظرية ال
+
+202
+00:25:07,560 --> 00:25:11,740
+divergence اتنين سبعتاش ممكن نحصل على كل هذا
+
+203
+00:25:17,200 --> 00:25:22,140
+طيب since xn
+
+204
+00:25:22,140 --> 00:25:36,260
+is bounded لما انه ال sequence xn is bounded then
+
+205
+00:25:36,260 --> 00:25:45,160
+the subsequence the subsequence xrn is bounded
+
+206
+00:25:49,260 --> 00:25:53,140
+أي subsequence من bounded sequence تطلع bounded جب
+
+207
+00:25:53,140 --> 00:25:59,600
+شوية أثبتنا الكلام هذا so
+
+208
+00:25:59,600 --> 00:26:04,780
+by bolzano
+
+209
+00:26:04,780 --> 00:26:11,680
+weierstrass
+
+210
+00:26:11,680 --> 00:26:19,730
+theorem نظرية bolzano weierstrassهنطبقها على الـ
+
+211
+00:26:19,730 --> 00:26:28,190
+sequence XRN اللي هي bounded فبتقول
+
+212
+00:26:28,190 --> 00:26:33,010
+بولزانو فيروس تراثيرم إذا في عندي sequence و
+
+213
+00:26:33,010 --> 00:26:39,970
+bounded ففي إلها convergence subsequence إذن ال
+
+214
+00:26:39,970 --> 00:26:45,070
+sequence ال
+
+215
+00:26:45,070 --> 00:26:47,410
+sequence XRN
+
+216
+00:26:48,810 --> 00:27:01,550
+has a convergent has a convergent subsequence
+
+217
+00:27:01,550 --> 00:27:04,570
+say
+
+218
+00:27:04,570 --> 00:27:13,270
+خلينا نسميها xkxkn
+
+219
+00:27:13,270 --> 00:27:16,170
+تمام؟
+
+220
+00:27:45,490 --> 00:27:50,890
+فاندي ال ..
+
+221
+00:27:50,890 --> 00:27:56,170
+اذا انا في عندي convergent subsequence من ال
+
+222
+00:27:56,170 --> 00:28:03,390
+subsequence هذه و طبعا هذه subsequence من xn وهذه
+
+223
+00:28:03,390 --> 00:28:07,070
+subsequence من هذه، اذا هذه subsequence من xn
+
+224
+00:28:11,210 --> 00:28:15,570
+بما أن XKN
+
+225
+00:28:15,570 --> 00:28:22,950
+هو أيضًا سبسيكوينس لسيكوينس
+
+226
+00:28:22,950 --> 00:28:28,430
+الأصلية XN ثم
+
+227
+00:28:28,430 --> 00:28:32,330
+بي وهو مرتبط
+
+228
+00:28:41,880 --> 00:28:48,020
+وهو مرتبط ثم
+
+229
+00:28:48,020 --> 00:28:54,650
+من حيث الهيبوتاسيزمن الفرض احنا فرضين في النظرية
+
+230
+00:28:54,650 --> 00:28:59,310
+هذه ان every convergent subsequence of xn لازم
+
+231
+00:28:59,310 --> 00:29:04,890
+تكون convergent للعدد x فهي في عندي subsequence من
+
+232
+00:29:04,890 --> 00:29:09,530
+ال sequence xn وconvergent اذا لازم تكون ال limit
+
+233
+00:29:09,530 --> 00:29:13,430
+تبعتها x اذا من الفرض limit
+
+234
+00:29:15,760 --> 00:29:28,480
+لأكس كأن as n tends to infinity بساوي LX تمام طب
+
+235
+00:29:28,480 --> 00:29:37,720
+احنا عايزين نثبت ان ال XN نفسك converge لل X طيب
+
+236
+00:29:37,720 --> 00:29:44,400
+الآن من تعريفأنا في عندي إبسلون زيرو موجود هاي في
+
+237
+00:29:44,400 --> 00:29:48,900
+عندي إبسلون زيرو أنا في عندي إبسلون زيرو هاد عدد
+
+238
+00:29:48,900 --> 00:29:56,460
+موجود من ال divergence في الفيلم hence وعندي ال
+
+239
+00:29:56,460 --> 00:29:59,520
+subsequence هاد ال converge ل X لذا لما انت عارف
+
+240
+00:29:59,520 --> 00:30:06,660
+ال convergence there exist capital N يعتمد على
+
+241
+00:30:06,660 --> 00:30:08,000
+إبسلون زيرو
+
+242
+00:30:11,600 --> 00:30:19,000
+بحيث ان ال absolute value للحد العام لل sequence
+
+243
+00:30:19,000 --> 00:30:27,320
+XKN المسافة بينه بين ال X أصغر من epsilon zero
+
+244
+00:30:27,320 --> 00:30:35,740
+وهذا الكلام صحيح لكل N في N تمام؟
+
+245
+00:30:37,500 --> 00:30:43,940
+بنسمي المتباين هذي double star الان
+
+246
+00:30:43,940 --> 00:30:57,360
+now star and double star بيقدوا انه ال .. هاي عندي
+
+247
+00:30:57,360 --> 00:31:06,910
+absolute x k n minus x هذا أصغر من epsilon zeroهذا
+
+248
+00:31:06,910 --> 00:31:18,330
+من double star من هنا طب و من ال star انا
+
+249
+00:31:18,330 --> 00:31:23,250
+عندي xrm المسافة بين xrm و x أكبر من او ساوي
+
+250
+00:31:23,250 --> 00:31:24,630
+epsilon zero
+
+251
+00:31:27,280 --> 00:31:34,640
+و هذه sub sequence من ال sub sequence هذه يعني كل
+
+252
+00:31:34,640 --> 00:31:39,520
+حد في ال sequence هذه هو حد في هذه و بالتالي ال
+
+253
+00:31:39,520 --> 00:31:47,860
+sub sequence هذه بتحقق المتباينة star إذن هذا صحيح
+
+254
+00:31:47,860 --> 00:31:52,920
+من star ال absolute الفرقة ده بطلع أكبر من أو ساوي
+
+255
+00:31:52,920 --> 00:31:59,240
+epsilon zero الكلام هذا صحيح لكل n في Mإذا أنا
+
+256
+00:31:59,240 --> 00:32:05,280
+عندي طلع هيك epsilon zero أصغر من epsilon zero و
+
+257
+00:32:05,280 --> 00:32:09,960
+هذا بديني تناقض contradiction إذا التناقض هذا
+
+258
+00:32:09,960 --> 00:32:19,040
+السبب تبعه إن إحنا فرضنا إن xn does not converge ل
+
+259
+00:32:19,040 --> 00:32:23,660
+x إذا ال contradiction هذه بتقول إن xn لازم
+
+260
+00:32:23,660 --> 00:32:30,900
+converge ل x و هذا اللي بدنا ياه وهم المطلوبوهو
+
+261
+00:32:30,900 --> 00:32:35,700
+المطلوب okay إذا هيك بنكون برهننا النظرية هذه
+
+262
+00:32:35,700 --> 00:32:43,200
+خلينا ناخد احنا break عشان فينا لقاء تاني لمدة خمس
+
+263
+00:32:43,200 --> 00:32:46,120
+دقايق و بعدين يعني نرجع، ماشي الحال؟
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/YiGM8L9BEY0_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/YiGM8L9BEY0_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7d7882f534f15c01bc820e58b4e175c2408888df
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/YiGM8L9BEY0_raw.srt
@@ -0,0 +1,1352 @@
+1
+00:00:20,920 --> 00:00:26,360
+بسم الله الرحمن الرحيم اليوم هناخد أخر لقاء في ال
+
+2
+00:00:26,360 --> 00:00:31,460
+course وهو تكملة section خمسة أربعة في الكتاب
+
+3
+00:00:31,460 --> 00:00:38,850
+المقرر اللي بتكلم عن ال uniform continuityفي
+
+4
+00:00:38,850 --> 00:00:45,330
+المحاضرة السابقة عرفنا الاتصال المنتظم وشوفنا
+
+5
+00:00:45,330 --> 00:00:49,930
+أثبتنا نظريات
+
+6
+00:00:49,930 --> 00:00:54,170
+مهمة عن الاتصال المنتظم أو عدم الاتصال المنتظم
+
+7
+00:00:54,170 --> 00:00:58,850
+فأخدنا ال non uniform continuity criterion اللي
+
+8
+00:00:58,850 --> 00:01:04,770
+حسبها أو ممكن نستخدمها في اثبات أن دالة محددة ليست
+
+9
+00:01:04,770 --> 00:01:09,750
+uniform ل continuous على مجموعةمحددة جزئية من
+
+10
+00:01:09,750 --> 00:01:13,330
+الأعداد الحقيقية فكان في عندي non uniform
+
+11
+00:01:13,330 --> 00:01:18,270
+continuity criterion و آخر نظرية أثبتنا نظرية مهمة
+
+12
+00:01:18,270 --> 00:01:22,490
+هو هي ال uniform continuity criterion اللي بتقول
+
+13
+00:01:22,490 --> 00:01:27,650
+أنه لو كانت ال function تبعتي متصلة
+
+14
+00:01:28,780 --> 00:01:31,940
+على المجال تبعها والمجال تبعها closed bounded
+
+15
+00:01:31,940 --> 00:01:38,760
+interval فالاتصال يتحول الى اتصال منتظم طبعا احنا
+
+16
+00:01:38,760 --> 00:01:43,120
+شفنا في المحاضرة السابقة انه دايما الاتصال المنتظم
+
+17
+00:01:43,120 --> 00:01:47,200
+اقوى من الاتصال العادى لو كانت الدالة uniform ل
+
+18
+00:01:47,200 --> 00:01:50,960
+continuous فبتكون continuous لكن العكس ليس صحيح
+
+19
+00:01:52,640 --> 00:02:00,080
+فخدنا مثال على دالة function دالة واحد على X شفنا
+
+20
+00:02:00,080 --> 00:02:04,920
+أنها متصلة continuous على الفترة المفتوحة من سفر
+
+21
+00:02:04,920 --> 00:02:09,620
+إلى ملا نهاية but it was not uniformly continuous
+
+22
+00:02:09,620 --> 00:02:15,780
+على نفس الفترة وبالتالي الاتصال العادي لا يؤدي
+
+23
+00:02:15,780 --> 00:02:22,820
+للاتصال المنطماليوم هنتعرف على نوع جديد من ال
+
+24
+00:02:22,820 --> 00:02:27,040
+functions وهو لبسش functions و ال functions هدول
+
+25
+00:02:27,040 --> 00:02:32,200
+هتكونوا دائما كلهم uniformly continuous فنعرف لبسش
+
+26
+00:02:32,200 --> 00:02:38,640
+function definition a
+
+27
+00:02:38,640 --> 00:02:42,680
+function f
+
+28
+00:02:42,680 --> 00:02:44,740
+from a to r
+
+29
+00:02:47,770 --> 00:02:58,050
+إذ لبسش .. بنسميها
+
+30
+00:02:58,050 --> 00:03:03,010
+لبسش on
+
+31
+00:03:03,010 --> 00:03:10,310
+a إذا وجد if there exists k positive number such
+
+32
+00:03:10,310 --> 00:03:13,510
+that absolute f of x
+
+33
+00:03:36,970 --> 00:03:40,090
+وطبعا ممكن اثبات بكل سهولة
+
+34
+00:03:49,120 --> 00:03:55,860
+الأن هنثبت و هنشوف أنه كل لبسش function أو كل
+
+35
+00:03:55,860 --> 00:04:00,320
+function بتحقق لبسش condition اللي هو الشرط هذا
+
+36
+00:04:07,690 --> 00:04:12,250
+كل function بتحقق لبسش condition أو .. أو سمنها
+
+37
+00:04:12,250 --> 00:04:17,910
+لبسش function بتكون uniformly continuous فنشوف
+
+38
+00:04:17,910 --> 00:04:23,390
+المرحلة دالك إذا هنا every أو
+
+39
+00:04:23,390 --> 00:04:33,270
+if .. if from a to r is لبسش is
+
+40
+00:04:33,270 --> 00:04:47,300
+لبشسon a then it is uniformly continuous
+
+41
+00:04:47,300 --> 00:04:56,080
+on a proof
+
+42
+00:04:56,080 --> 00:05:00,840
+assume
+
+43
+00:05:03,530 --> 00:05:10,310
+إذا كان لبسش على
+
+44
+00:05:10,310 --> 00:05:20,250
+a ثم حسب التعريف هناك كمية positive كمية كمية كامة
+
+45
+00:05:20,250 --> 00:05:20,470
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+46
+00:05:20,470 --> 00:05:20,690
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+47
+00:05:20,690 --> 00:05:21,490
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+48
+00:05:21,490 --> 00:05:21,490
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+49
+00:05:21,490 --> 00:05:21,530
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+50
+00:05:21,530 --> 00:05:21,690
+كمية كمية كمية كمية كمية كمية كمية كمية كمية كمية
+
+51
+00:05:21,690 --> 00:05:28,390
+كمية كمية كمية
+
+52
+00:05:28,390 --> 00:05:38,840
+كمk times absolute x minus u for all x where u and
+
+53
+00:05:38,840 --> 00:05:52,180
+a طيب
+
+54
+00:05:52,180 --> 00:05:55,760
+لتسمي ال condition هذا star
+
+55
+00:05:58,650 --> 00:06:02,570
+let epsilon أكبر من السفر بيجبن let epsilon أكبر
+
+56
+00:06:02,570 --> 00:06:05,490
+من السفر بيجبن let epsilon أكبر من السفر بيجبن let
+
+57
+00:06:05,490 --> 00:06:06,290
+epsilon أكبر من السفر بيجبن let epsilon أكبر من
+
+58
+00:06:06,290 --> 00:06:06,550
+السفر بيجبن let epsilon أكبر من السفر بيجبن let
+
+59
+00:06:06,550 --> 00:06:06,570
+epsilon أكبر من السفر بيجبن let epsilon أكبر من
+
+60
+00:06:06,570 --> 00:06:06,570
+السفر بيجبن let epsilon أكبر من السفر بيجبن let
+
+61
+00:06:06,570 --> 00:06:06,570
+epsilon أكبر من السفر بيجبن let epsilon أكبر من
+
+62
+00:06:06,570 --> 00:06:06,570
+السفر بيجبن let epsilon أكبر من السفر بيجبن let
+
+63
+00:06:06,570 --> 00:06:06,570
+epsilon أكبر من السفر بيجبن let epsilon أكبر من
+
+64
+00:06:06,570 --> 00:06:07,810
+السفر بيجبن let epsilon أكبر من السفر بيجبن let
+
+65
+00:06:07,810 --> 00:06:09,990
+epsilon أكبر من السفر بيجبن
+
+66
+00:06:23,960 --> 00:06:29,040
+عدد موجة إبسلون على K بيطلع عدد موجة وبالتالي إذن
+
+67
+00:06:29,040 --> 00:06:35,920
+هنا أثبتت إن user Delta تعتمد على إبسلون فقط فلهذه
+
+68
+00:06:35,920 --> 00:06:42,280
+الإبسلون then لو كانت X و U موجودين في A و
+
+69
+00:06:42,280 --> 00:06:47,840
+Absolute X minus U أصغر من Delta فهذا هيقدّي إن
+
+70
+00:06:47,840 --> 00:07:01,000
+Absolute F of X-f of u باي ستار حسب المتباينة star
+
+71
+00:07:01,000 --> 00:07:06,600
+هذا بيطلع أصغر منه ساوي absolute x minus u
+
+72
+00:07:13,020 --> 00:07:18,320
+وانا عندي absolute x minus u أصغر من دلتا اذا هذا
+
+73
+00:07:18,320 --> 00:07:25,240
+أصغر عفوا by star في عندي هنا k ضرب absolute x
+
+74
+00:07:25,240 --> 00:07:31,780
+minus u الان انا عندي absolute x minus u أصغر من
+
+75
+00:07:31,780 --> 00:07:36,840
+دلتا لأن هذا أصغر من k في دلتا وانا عندي ماخد دلتا
+
+76
+00:07:36,840 --> 00:07:45,940
+بالساوي y على kأصبح هذا أصغر من إبسلون لأي
+
+77
+00:07:45,940 --> 00:07:52,500
+إبسلون أكبر من 0 يوجد delta تعتمد على إبسلون فقط
+
+78
+00:07:52,500 --> 00:07:59,340
+بحيث أنه لكل x و u في a المسافة بينهم أصغر من
+
+79
+00:07:59,340 --> 00:08:02,820
+delta طلع المسافة بين ال images أصغر من إبسلون
+
+80
+00:08:06,120 --> 00:08:11,800
+epsilon أكبر من السفر was arbitrary، إذن هذا صحيح
+
+81
+00:08:11,800 --> 00:08:15,580
+لكل epsilon وبالتالي by definition، إذن ال
+
+82
+00:08:15,580 --> 00:08:20,780
+function f is uniformly continuous
+
+83
+00:08:20,780 --> 00:08:30,340
+on E، وهو المطلوب إذن هناك أثبتنا إن كل لبسش
+
+84
+00:08:30,340 --> 00:08:34,120
+function is uniformly continuous
+
+85
+00:08:36,360 --> 00:08:45,020
+لكن العكس ليس صحيحا .. العكس ليس صحيحا remark ..
+
+86
+00:08:45,020 --> 00:08:55,400
+remark the
+
+87
+00:08:55,400 --> 00:09:00,740
+canvas .. the canvas of above theorem
+
+88
+00:09:05,350 --> 00:09:11,730
+is false for
+
+89
+00:09:11,730 --> 00:09:16,970
+example على سبيل المثال يعني معنى آخر لو كانت ال
+
+90
+00:09:16,970 --> 00:09:24,750
+function uniform ل continuous مش شرط تكون لبسش على
+
+91
+00:09:24,750 --> 00:09:31,370
+نفس ال function على نفس ال .. for example consider
+
+92
+00:09:35,170 --> 00:09:48,950
+Consider الـ function f of x بساوي جدر الـ x هو
+
+93
+00:09:48,950 --> 00:09:54,790
+x ينتمي ل I بساوي closed interval من صفر لاثنين
+
+94
+00:10:07,930 --> 00:10:14,030
+by exercise فى exercise أخدناه اللى هو جبنالكم
+
+95
+00:10:14,030 --> 00:10:23,090
+إياه سؤال فى الامتحان ال exercise هذا كان .. خلينا
+
+96
+00:10:23,090 --> 00:10:23,730
+نشوف
+
+97
+00:10:39,170 --> 00:10:45,750
+أو ممكن اثبات أن الدالة هذه is continuous طيب
+
+98
+00:10:45,750 --> 00:10:52,030
+اه
+
+99
+00:10:52,030 --> 00:10:55,910
+by exercise
+
+100
+00:10:55,910 --> 00:11:04,250
+في chapter اربعة اربعة واحد question تمام اه اربعة
+
+101
+00:11:04,250 --> 00:11:11,540
+واحد مظبوط صحيحby exercise تمامية section اربعة
+
+102
+00:11:11,540 --> 00:11:16,540
+واحد ال
+
+103
+00:11:16,540 --> 00:11:24,940
+function if is continuous على الفترة لأن في هداك
+
+104
+00:11:24,940 --> 00:11:32,480
+ال exercise هتتبتو انه limit جدر ال X لما X تقول ل
+
+105
+00:11:32,480 --> 00:11:42,910
+C بساوي جدر ال Cلكل C أكبر من أو ساوي السفر طبعا
+
+106
+00:11:42,910 --> 00:11:48,030
+في ال exercise ماخد C أكبر من السفر لكن لما C
+
+107
+00:11:48,030 --> 00:11:52,950
+بساوي السفر فهذا trivial وبالتالي هذا معناه أن
+
+108
+00:11:52,950 --> 00:11:59,890
+دالة F هذا
+
+109
+00:11:59,890 --> 00:12:05,330
+معناه شرط الاتصال عن C متحقق فهذا معناه أن F is
+
+110
+00:12:05,330 --> 00:12:12,720
+continuousAt C وده صحيح لكل C أكبر من أوسعها سفر
+
+111
+00:12:12,720 --> 00:12:20,520
+وبالتالي اذا F is continuous على الفترة من سفر إلى
+
+112
+00:12:20,520 --> 00:12:25,140
+ملا نهاية وبالتالي متصلة على الفترة من سفر إلى
+
+113
+00:12:25,140 --> 00:12:33,460
+اتنين اللي هي جزوة منها okay تمام طيب اذا
+
+114
+00:12:40,220 --> 00:12:48,440
+إذا by طيب since I بساو الفترة من الزفر لإتنين
+
+115
+00:12:48,440 --> 00:12:58,140
+الفترة هذه is closed and bounded و
+
+116
+00:12:58,140 --> 00:13:05,080
+if continuous عليها then by
+
+117
+00:13:05,080 --> 00:13:09,520
+uniform continuity theorem
+
+118
+00:13:11,440 --> 00:13:14,900
+نظرية الاتصال المنتظم بتقول إذا كان في عندي
+
+119
+00:13:14,900 --> 00:13:20,060
+function f متصلة على فترة مغلقة أو محدودة فالاتصال
+
+120
+00:13:20,060 --> 00:13:25,320
+هذا بيكون اتصال منتظم uniform continuity ففي عندي
+
+121
+00:13:25,320 --> 00:13:32,800
+by uniform continuity theorem تطلع f is uniformly
+
+122
+00:13:32,800 --> 00:13:39,840
+continuous
+
+123
+00:13:41,540 --> 00:13:48,120
+على الفترة I إذاً هي مثال على function uniform ل
+
+124
+00:13:48,120 --> 00:13:52,880
+continuous على المجال تبعها هنشوف الآن إن هذه ال
+
+125
+00:13:52,880 --> 00:14:07,060
+function ما هياش لبسش على نفس الفترة إذا
+
+126
+00:14:07,060 --> 00:14:07,640
+ال claim
+
+127
+00:14:13,370 --> 00:14:23,650
+if is not .. if is not لبسش على
+
+128
+00:14:23,650 --> 00:14:28,590
+الفترة I فلبرحان
+
+129
+00:14:28,590 --> 00:14:33,990
+ذلك assume
+
+130
+00:14:33,990 --> 00:14:37,950
+on
+
+131
+00:14:37,950 --> 00:14:38,670
+contrary
+
+132
+00:14:43,190 --> 00:14:48,550
+assume on contrary that
+
+133
+00:14:48,550 --> 00:15:01,650
+if is لبسش on
+
+134
+00:15:01,650 --> 00:15:04,090
+I then
+
+135
+00:15:06,570 --> 00:15:14,610
+there exists k أكبر من السفر بحيث أنه absolute f
+
+136
+00:15:14,610 --> 00:15:28,610
+of x minus f of u أصغر منها ساوي k في absolute x
+
+137
+00:15:28,610 --> 00:15:36,950
+minus u لكل xهو you تنتمي للفترة I اللى هى الفترة
+
+138
+00:15:36,950 --> 00:15:39,970
+المغلطة من سفر لاتنين
+
+139
+00:15:59,060 --> 00:16:04,840
+إذا ان هنا فرضنا ال contrary و يطلع ان بيطلع عندى
+
+140
+00:16:04,840 --> 00:16:09,160
+فيه huge العدد موجة بحيث كان أنا ادم اتحقق وهذا
+
+141
+00:16:09,160 --> 00:16:15,340
+بيقدر ان absolute f of x لو خدنا u بساوة سفر minus
+
+142
+00:16:15,340 --> 00:16:24,910
+f of 0 أصغر لو ساوة k فabsolute xوهذا صحيح لكل x
+
+143
+00:16:24,910 --> 00:16:32,150
+تنتمي للفترة I إذا أنا هنا أخدت U بساوي سفر و
+
+144
+00:16:32,150 --> 00:16:39,070
+السفر ينتمي للفترة I طيب أنا عندي F صفر بساوي سفر
+
+145
+00:16:39,070 --> 00:16:44,030
+إذا
+
+146
+00:16:44,030 --> 00:16:47,130
+بطلع عندي absolute
+
+147
+00:16:48,770 --> 00:16:58,510
+f of x أصغر من أو يساوي k في absolute ال X وهذا
+
+148
+00:16:58,510 --> 00:17:04,470
+صحيح لكل X تم تمي لفترة I هي الفترة المغلقة من
+
+149
+00:17:04,470 --> 00:17:09,690
+السفر لفترة بس
+
+150
+00:17:09,690 --> 00:17:14,810
+هذا هيدي لتناقل طيب
+
+151
+00:17:15,530 --> 00:17:28,330
+تاك لو أخدت x بساوي واحد على n تربيها فهذا
+
+152
+00:17:28,330 --> 00:17:33,990
+عبارة عن .. هذا ينتمي للفترة .. للفترة المغلفة من
+
+153
+00:17:33,990 --> 00:17:40,410
+سفر لإتنين اللي هي I لأن هذا عدد موجب لكل n ينتمي
+
+154
+00:17:40,410 --> 00:17:46,820
+ل N لكل عدد طبيعي هذا بطلعينتمي للفترة هذه
+
+155
+00:17:46,820 --> 00:17:54,300
+وبالتالي إذا المفروض يطلع absolute if لواحد على N
+
+156
+00:17:54,300 --> 00:18:02,060
+تربية أصغر من أو يساوي K في absolute واحد على N
+
+157
+00:18:02,060 --> 00:18:10,840
+تربية هذا صحيح لكل N في Nطيب if واحد على ان تربية
+
+158
+00:18:10,840 --> 00:18:16,760
+بيطلع بساوي الجدر التربية إلى واحد على ان تربية
+
+159
+00:18:16,760 --> 00:18:20,200
+اللي
+
+160
+00:18:20,200 --> 00:18:26,600
+هو عبارة عن واحد على ان ف absolute واحد على ان
+
+161
+00:18:26,600 --> 00:18:34,100
+بيطلع واحد على ان أصغر من أو ساوي كفي واحد على ان
+
+162
+00:18:34,100 --> 00:18:43,520
+تربية هذا صحيحلكل N في N اضرب
+
+163
+00:18:43,520 --> 00:18:50,880
+المتدينة هذه في N تربية فبطلع عندي N أصغر من أو
+
+164
+00:18:50,880 --> 00:18:59,320
+ساوي K for all N في N وهذا بتناقض مع ال
+
+165
+00:18:59,320 --> 00:19:06,040
+Archimedean property which contradicts
+
+166
+00:19:07,330 --> 00:19:11,130
+التي تتناقض
+
+167
+00:19:11,130 --> 00:19:19,250
+مع مين؟ التي تتناقض مع الـ Archimedean property
+
+168
+00:19:23,770 --> 00:19:28,110
+خاصية Archimedes لأن خاصية Archimedes بتقوللي لأي
+
+169
+00:19:28,110 --> 00:19:35,690
+عدد K عدد موجب أو أي عدد حقيقي K يوجد N0 عدد طبيعي
+
+170
+00:19:35,690 --> 00:19:45,660
+لحيث أن N0 أكبر من K صح؟و من هنا كل الأعداد
+
+171
+00:19:45,660 --> 00:19:53,360
+الطبيعية من ضمنها N0 أشملها أصغر من أو يساوي ال K
+
+172
+00:19:53,360 --> 00:20:00,740
+فبطلع N0 أكبر من N0 contradiction إذا السبب ال
+
+173
+00:20:00,740 --> 00:20:04,640
+contradiction هذا أنه إيه ال assumption الفرض
+
+174
+00:20:04,640 --> 00:20:12,440
+تبعنا ال assumption تبعنا أن F is لبسش on I okay
+
+175
+00:20:14,100 --> 00:20:19,120
+إذاً هذا بتثبت هذا ال contradiction بتثبت أن ال is
+
+176
+00:20:19,120 --> 00:20:29,820
+عفوًا if is not لبسش on
+
+177
+00:20:29,820 --> 00:20:37,120
+a أو i وهو المطلوب إذاً هذا مثال على function
+
+178
+00:20:37,120 --> 00:20:44,810
+uniformly continuous على set معينةلكنها ليست لبسش
+
+179
+00:20:44,810 --> 00:20:50,450
+لكن أثبتنا قبل ايه ان كل لبسش function is always
+
+180
+00:20:50,450 --> 00:20:57,750
+uniformly continuous ناخد
+
+181
+00:20:57,750 --> 00:20:58,770
+بعض الأمثلة
+
+182
+00:21:26,120 --> 00:21:35,220
+example led f of x بساوي x تربية و x ينتمي
+
+183
+00:21:35,220 --> 00:21:41,800
+للمجموعة a اللي هي الفترة المغلقة من سفر إلى بي
+
+184
+00:21:41,800 --> 00:21:50,410
+حيث بي أي عدد موجب بي أي عدد موجببنأثبت أن الـ
+
+185
+00:21:50,410 --> 00:21:59,950
+function هذه تطلع uniformly continuous show
+
+186
+00:21:59,950 --> 00:22:05,950
+that show
+
+187
+00:22:05,950 --> 00:22:11,670
+أن f is uniformly continuous
+
+188
+00:22:11,670 --> 00:22:23,720
+on a ففيه برهنيناو حالين proof one حال الأول since
+
+189
+00:22:23,720 --> 00:22:28,400
+if
+
+190
+00:22:28,400 --> 00:22:37,400
+is continuous on a being
+
+191
+00:22:37,400 --> 00:22:39,440
+a polynomial
+
+192
+00:22:44,780 --> 00:22:47,300
+لأنها polynomial و احنا قلنا كل polynomial
+
+193
+00:22:47,300 --> 00:22:51,800
+function متصل على R وبالتالي على أي مجموعة جزئية
+
+194
+00:22:51,800 --> 00:22:59,760
+من R زي المجموعة A اللي هي الفترة المغلقة من سفر
+
+195
+00:22:59,760 --> 00:23:05,620
+إلى الـ B ف
+
+196
+00:23:05,620 --> 00:23:10,920
+if is continuous على A كونها polynomial and بما
+
+197
+00:23:10,920 --> 00:23:19,480
+انه and sinceالـ set A هذه اللي هي عبارة عن الفترة
+
+198
+00:23:19,480 --> 00:23:29,320
+المغلقة من سفر لـ B is closed and bounded and
+
+199
+00:23:29,320 --> 00:23:34,500
+bounded interval
+
+200
+00:23:34,500 --> 00:23:44,980
+then by uniform continuity theorem
+
+201
+00:23:47,180 --> 00:23:53,380
+حسب نظرية الاتصال المنتظم اللى بتقول لو كان فيها
+
+202
+00:23:53,380 --> 00:23:57,140
+function مجالها closed bounded interval و ال
+
+203
+00:23:57,140 --> 00:24:03,120
+function متصل عليها فالاتصال بتحول الى اتصال منتظم
+
+204
+00:24:03,120 --> 00:24:08,040
+اذا ال function f is uniformly
+
+205
+00:24:10,270 --> 00:24:16,870
+continuous on a وهذا برهان لأنه ممكن نستخدم ال
+
+206
+00:24:16,870 --> 00:24:20,550
+uniform continuity theorem لإثبات أنه function
+
+207
+00:24:20,550 --> 00:24:24,970
+اللي زي هذه الدالة التربية uniform continuous على
+
+208
+00:24:24,970 --> 00:24:32,550
+أي فترة مغلقة زي الفترة هذه الحل
+
+209
+00:24:32,550 --> 00:24:37,830
+التاني ممكن نثبت أن الدالة هذه لمساش برضه و أستخدم
+
+210
+00:24:37,830 --> 00:24:38,710
+نظرية هذه
+
+211
+00:24:41,510 --> 00:24:48,950
+انشوف مع بعض، هنا البرهان تاني أو برهان رقم اتنين،
+
+212
+00:24:48,950 --> 00:24:58,810
+proof اتنين claim
+
+213
+00:24:58,810 --> 00:25:03,950
+انه F is لبسش
+
+214
+00:25:08,200 --> 00:25:18,740
+on a التي هي الفترة المغلفة من سفر إلى بى
+
+215
+00:25:18,740 --> 00:25:26,260
+فالإثبات هذا الكلام تعالى نشوف هي absolute f of x
+
+216
+00:25:26,260 --> 00:25:35,000
+minus f of u ايش بيساوي absolute x
+
+217
+00:25:35,820 --> 00:25:43,960
+تربية minus U تربية بساوي absolute X زائد U في
+
+218
+00:25:43,960 --> 00:25:51,860
+absolute X minus U وهذا بساوي absolute X زائد U في
+
+219
+00:25:51,860 --> 00:25:58,640
+absolute X negative U و by triangle inequality
+
+220
+00:25:58,640 --> 00:26:04,330
+absolute X زائد U أصغر من أو ساوي absolute Xزاد
+
+221
+00:26:04,330 --> 00:26:13,910
+absolute u كل هذا مضروف absolute x minus u الان
+
+222
+00:26:13,910 --> 00:26:19,970
+ال u و ال x ينتموا للمجال تبع الدولة وبالتالي
+
+223
+00:26:19,970 --> 00:26:29,990
+كلاهما عداد غير سالفة و كلاهما أصغر من أو يساوي ال
+
+224
+00:26:29,990 --> 00:26:37,320
+b صح؟إن هذا أصغر من أوي ساوي بي زائد بي في
+
+225
+00:26:37,320 --> 00:26:45,420
+absolute x minus u for all x و u ينتموا للمجموع
+
+226
+00:26:45,420 --> 00:26:52,520
+اللي هي الفترة المغلفة من سفر إلى بي طبعا هذا
+
+227
+00:26:52,520 --> 00:27:01,660
+بساوياتنين بي في absolute x minus u for all x و u
+
+228
+00:27:01,660 --> 00:27:08,820
+تنتمي الى a اذا هاي شرط لبسيش اتحقق with k بيساو
+
+229
+00:27:08,820 --> 00:27:17,340
+اتنين بيعدد موجب اذا هنا take k
+
+230
+00:27:17,340 --> 00:27:21,800
+بيساو اتنين بيعدد موجب
+
+231
+00:27:36,690 --> 00:27:38,510
+Okay طبعا
+
+232
+00:27:54,180 --> 00:28:09,940
+واضح البران في اي سؤال او استفسار في
+
+233
+00:28:09,940 --> 00:28:17,160
+عندي نظرية تتعلق بال uniform الها علاقة بال
+
+234
+00:28:17,160 --> 00:28:22,180
+uniform continuity وهي النظرية التالية
+
+235
+00:28:38,260 --> 00:28:49,440
+فيرم if if from a to r is uniformly is uniformly
+
+236
+00:28:49,440 --> 00:28:52,540
+continuous
+
+237
+00:28:52,540 --> 00:29:00,780
+on a then
+
+238
+00:29:03,000 --> 00:29:09,640
+For any Cauchy Sequence
+
+239
+00:29:09,640 --> 00:29:18,780
+xn contained in A The
+
+240
+00:29:18,780 --> 00:29:22,700
+sequence f
+
+241
+00:29:22,700 --> 00:29:31,580
+of xn اللي هي ال image لسيقونس xn is Cauchy
+
+242
+00:29:33,110 --> 00:29:40,090
+in R that
+
+243
+00:29:40,090 --> 00:29:45,950
+is that
+
+244
+00:29:45,950 --> 00:29:56,030
+is هذا يعني هذا يعني هذا يعني انه uniformly
+
+245
+00:29:56,030 --> 00:30:01,090
+uniformly continuous
+
+246
+00:30:04,960 --> 00:30:18,040
+functions preserve كوشي
+
+247
+00:30:18,040 --> 00:30:22,460
+sequences
+
+248
+00:30:27,960 --> 00:30:34,420
+يعني الدوال اللي بتكون متصل اتصال منتظم بتحافظ على
+
+249
+00:30:34,420 --> 00:30:39,960
+cushy sequences بمعنى انه لو كانت xn cushy
+
+250
+00:30:39,960 --> 00:30:46,260
+sequence في المجال تبع الدالة A فصورتها هتطلع
+
+251
+00:30:46,260 --> 00:30:52,080
+cushy sequence في المجال المقابل R والبرهان سهل
+
+252
+00:30:53,210 --> 00:30:57,390
+طبعا هذا بس صحيح لل uniform ل continuous functions
+
+253
+00:30:57,390 --> 00:31:02,350
+أما لو كانت ال function بس continuous فمش شرط
+
+254
+00:31:02,350 --> 00:31:07,510
+اتحافظ على كوشي sequences والبرهان
+
+255
+00:31:07,510 --> 00:31:18,670
+سهل بسيط prove let
+
+256
+00:31:18,670 --> 00:31:29,880
+if from A to Rب uniformly continuous on
+
+257
+00:31:29,880 --> 00:31:44,240
+a and let x in contained in a,b كوشي كوشي sequence
+
+258
+00:31:44,240 --> 00:31:50,420
+و بدنا نثبت ان ال image لل sequence x in بتطلع
+
+259
+00:31:50,420 --> 00:31:57,060
+كوشي طيبto show ان
+
+260
+00:31:57,060 --> 00:32:09,340
+ال image لسيكوينس XN is Cauchy لبرهان
+
+261
+00:32:09,340 --> 00:32:15,180
+ان ال sequence هذه ال image لسيكوينس XN is Cauchy
+
+262
+00:32:15,180 --> 00:32:24,130
+نحاول نطبق تعريف Cauchysequence او نحاول نحقق شرط
+
+263
+00:32:24,130 --> 00:32:31,290
+كوشي فكيف نحقق قولت epsilon أكبر من السفر بيه جبن
+
+264
+00:32:31,290 --> 00:32:39,210
+وبينا نرد عليها بcapital N تحققلي شرط كوشي طيب
+
+265
+00:32:39,210 --> 00:32:44,110
+since if
+
+266
+00:32:44,110 --> 00:32:45,390
+is uniformly
+
+267
+00:32:47,670 --> 00:32:55,510
+continuous on a إذا لأي إبسلون موجبة زي هذه يوجد
+
+268
+00:32:55,510 --> 00:33:02,650
+إذا
+
+269
+00:33:02,650 --> 00:33:09,410
+لأي إبسلون زي هذهمع ان if uniform continuous اذا
+
+270
+00:33:09,410 --> 00:33:13,670
+لأي epsilon حسب تعريف ال uniform continuity يوجد
+
+271
+00:33:13,670 --> 00:33:21,510
+delta تعتمد على epsilon عدد موجة بحيث انه لو كان x
+
+272
+00:33:24,390 --> 00:33:30,090
+و U موجودين في A و Absolute X minus U أصغر من
+
+273
+00:33:30,090 --> 00:33:37,570
+Delta فهذا بعدي أن Absolute F of X minus F of U
+
+274
+00:33:37,570 --> 00:33:47,250
+أصغر من Y نسمي ال implication head star الان
+
+275
+00:33:47,250 --> 00:33:53,610
+since ال sequence X in is Cauchy
+
+276
+00:33:58,410 --> 00:34:02,810
+then و delta and
+
+277
+00:34:02,810 --> 00:34:11,090
+delta أكبر من السفر طبعا هذه given is given ال
+
+278
+00:34:11,090 --> 00:34:13,850
+delta هذه قلنا يوجد delta عدد موجة بما أن هذه
+
+279
+00:34:13,850 --> 00:34:20,650
+تعتبر given delta فلل delta هذه اللي هنا عدد موجة
+
+280
+00:34:20,650 --> 00:34:27,960
+بما أن xn is Cauchyإذا there exist يوجد capital N
+
+281
+00:34:27,960 --> 00:34:37,220
+يعتمد على delta عدد طبيعي بحيث انه شرط كوشي يتحقق
+
+282
+00:34:37,220 --> 00:34:43,140
+وهو لكل N و M أكبر من أو ساوي capital N بطل عندي
+
+283
+00:34:43,140 --> 00:34:49,040
+absolute xn minus xm أصغر من delta
+
+284
+00:34:52,280 --> 00:35:01,060
+بنسمي هذه double star now star and double star
+
+285
+00:35:01,060 --> 00:35:14,240
+بيقدّوا أنه يوجد capital N يعتمد على epsilon لأن
+
+286
+00:35:14,240 --> 00:35:18,800
+ال delta بتعتمد على epsilonالـ delta بتعتمد على
+
+287
+00:35:18,800 --> 00:35:26,260
+إبسلون، ملاحظة الحال ف N هذه نفسها N of delta
+
+288
+00:35:26,260 --> 00:35:33,360
+بيساوي N of إبسلون بتتمي ل N بحيث أنه لو كان N و M
+
+289
+00:35:33,360 --> 00:35:40,480
+أكبر من أوي ساوي capital N فهذا بيقدّي أنه by
+
+290
+00:35:40,480 --> 00:35:48,270
+double starهذا بيقدم absolute xn minus xm أصغر من
+
+291
+00:35:48,270 --> 00:35:55,450
+دلتا وحسب ال star by star ال star بتقول لو كان
+
+292
+00:35:55,450 --> 00:36:01,030
+عندي x و u المسافة بينهم أصغر من دلتا فالمسافة بين
+
+293
+00:36:01,030 --> 00:36:08,790
+صورهم اللي هي xn هنا وصورة ال xm تطلع أصغر من إبسم
+
+294
+00:36:10,550 --> 00:36:16,550
+تمام؟ إذا هنا أثبتت لأي إبسلون أكبر من السفر يوجد
+
+295
+00:36:16,550 --> 00:36:20,830
+capital N يعتمد على إبسلون عدد طبيعي بحيث لكل M M
+
+296
+00:36:20,830 --> 00:36:25,510
+أكبر من أو ساوي capital N طلع المسافة بين F of X M
+
+297
+00:36:25,510 --> 00:36:31,650
+و F of X M أصغر من إبسلون إذا بما أنه since إبسلون
+
+298
+00:36:31,650 --> 00:36:39,100
+أكبر من السفر was arbitraryإذا الـ sequence f of x
+
+299
+00:36:39,100 --> 00:36:45,120
+in is Cauchy تطلع الـ sequence هذه Cauchy وهو
+
+300
+00:36:45,120 --> 00:36:54,080
+المطلوب okay تمام ممكن نستخدم النظرية هذه ممكن
+
+301
+00:36:54,080 --> 00:37:01,400
+نستخدم النظرية هذه في ال ..
+
+302
+00:37:01,400 --> 00:37:06,320
+ان نثبت ان function معينة ليستuniform and
+
+303
+00:37:06,320 --> 00:37:16,200
+continuous هاي example use
+
+304
+00:37:16,200 --> 00:37:20,100
+above theorem
+
+305
+00:37:20,100 --> 00:37:31,860
+to show ال function f of x بالسعر واحد على x is
+
+306
+00:37:31,860 --> 00:37:32,280
+not
+
+307
+00:37:35,480 --> 00:37:43,220
+uniformly continuous on a بساوي الفترة المفتوحة من
+
+308
+00:37:43,220 --> 00:37:44,680
+صفر إلى ملا نهار
+
+309
+00:37:57,800 --> 00:38:01,060
+لحظة ان النظرية دي ايش بتقول لو كانت ال function
+
+310
+00:38:01,060 --> 00:38:05,140
+uniform ل continuous فلازم تحافظ على كوشي sequence
+
+311
+00:38:05,140 --> 00:38:09,440
+طب لو محافظتش على كوشي sequence مش ممكن تكون
+
+312
+00:38:09,440 --> 00:38:17,260
+uniform ل continuous صح؟ مظبوط؟ اذا هنا proof
+
+313
+00:38:17,260 --> 00:38:25,680
+by above theorem حسب النظرية على it suffices
+
+314
+00:38:28,360 --> 00:38:36,220
+to show يكفي اثبات ان f is .. if does not .. if
+
+315
+00:38:36,220 --> 00:38:46,960
+does .. does not preserve .. preserve Cauchy
+
+316
+00:38:46,960 --> 00:38:52,860
+sequences ف
+
+317
+00:38:52,860 --> 00:38:53,500
+consider
+
+318
+00:38:56,930 --> 00:39:03,270
+consider ال sequence xn اللي هي بساوي واحد على ن
+
+319
+00:39:03,270 --> 00:39:11,470
+ال sequence هذه converge لصفر وبالتالي
+
+320
+00:39:11,470 --> 00:39:25,130
+اذا xn is Cauchy تمام but صورة ال xn
+
+321
+00:39:28,660 --> 00:39:37,460
+أيش بتطلع؟ صورة الواحد على ان تطلع ال sequence in
+
+322
+00:39:37,460 --> 00:39:43,620
+صح؟ و ال sequence هذه properly divergent to
+
+323
+00:39:43,620 --> 00:39:49,760
+infinity، اذا I'm divergent، اذا I'm not Cauchy
+
+324
+00:39:49,760 --> 00:39:54,220
+تمام؟
+
+325
+00:39:57,130 --> 00:40:01,450
+Okay؟ وبالتالي إذا هاي في عندي .. هاي في عندي ..
+
+326
+00:40:01,450 --> 00:40:08,790
+إذا if لا تحافظ على ال koshi sequences إذا if does
+
+327
+00:40:08,790 --> 00:40:13,210
+not preserve
+
+328
+00:40:13,210 --> 00:40:19,050
+.. preserve koshi
+
+329
+00:40:26,330 --> 00:40:31,610
+sequences وبالتالي حسب النظرية الأخيرة مابتكونش
+
+330
+00:40:31,610 --> 00:40:34,630
+uniformly continuous لأن لو كانت uniformly
+
+331
+00:40:34,630 --> 00:40:38,370
+continuous فالمفروض تاخد كوشي sequence زي هذه
+
+332
+00:40:38,370 --> 00:40:42,730
+تعطينا صورتها كوشي sequence وهذا مستحيل okay تمام
+
+333
+00:40:42,730 --> 00:40:47,970
+واضح في أي سؤال اي استفسار اذا هيك نكتفي بهذا
+
+334
+00:40:47,970 --> 00:40:52,540
+القدر من section خمسة اربعة وزي ما حكينا سابقاهذا
+
+335
+00:40:52,540 --> 00:40:57,260
+كان آخر section هناخده في المقرر و بالتالي هيكون
+
+336
+00:40:57,260 --> 00:41:03,400
+يعني .. يعني ان شاء الله أنهينا ال course كما هو
+
+337
+00:41:03,400 --> 00:41:10,600
+موضح على ال syllabus فشكرا لكم و شكرا لحسن إصداركم
+
+338
+00:41:10,600 --> 00:41:13,580
+و يعطيكم ألف عافية
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_28CmIWMuzY_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_28CmIWMuzY_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ff5626a8ce8ad1ea2e64ecd2bb9391d781b1a90d
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_28CmIWMuzY_postprocess.srt
@@ -0,0 +1,1616 @@
+1
+00:00:21,330 --> 00:00:27,290
+اليوم طبعا هنكمل الشرح
+
+2
+00:00:27,290 --> 00:00:30,650
+أو
+
+3
+00:00:30,650 --> 00:00:35,610
+بعض الملاحظات على النظرية اللي أخدناها في المحاضرة
+
+4
+00:00:35,610 --> 00:00:42,910
+السابقة النظرية هذه بتتحدث عن nested interval
+
+5
+00:00:42,910 --> 00:00:48,620
+property أو خاصية الفترات المتداخلةوشوفنا في
+
+6
+00:00:48,620 --> 00:00:54,720
+النظرية هذه ان لو في عندي sequence of nested
+
+7
+00:00:54,720 --> 00:00:58,660
+intervals الفترات هذه كلهم nested يعني كل واحدة
+
+8
+00:00:58,660 --> 00:01:05,820
+تحتوي اللي بعدها مباشرة زائد ان الفترات هذه كلهم
+
+9
+00:01:05,820 --> 00:01:14,580
+closed كلهم closed و bounded ففي
+
+10
+00:01:14,580 --> 00:01:20,210
+الحالة هذه التقاطةتبع ال sequence of intervals لا
+
+11
+00:01:20,210 --> 00:01:24,310
+يساوي في يعني في على الأقل عنصر واحد بالتقاطة
+
+12
+00:01:24,310 --> 00:01:30,510
+شوفنا برضه لو في الشرط الإضافي هذا اتحقق وهو
+
+13
+00:01:30,510 --> 00:01:35,570
+لاحظوا أن هذه عبارة عن ساو بي ان فهذه sequence من
+
+14
+00:01:35,570 --> 00:01:42,690
+العداد السالمة الغير سالمة و بالمناسبة السفر واضح
+
+15
+00:01:42,690 --> 00:01:48,940
+أنه lower bound للمجموعة هذه صح؟لكن مش شرط أن
+
+16
+00:01:48,940 --> 00:01:54,780
+السفر يكون هو ال infimum للمجموعة هذه فإذا كان ال
+
+17
+00:01:54,780 --> 00:01:57,960
+infimum للمجموعة هذه اللي هو أكبر lower bound هو
+
+18
+00:01:57,960 --> 00:02:06,440
+السفر فالتقاط واحدة في أنصر واحد okay تمام وشوفنا
+
+19
+00:02:06,440 --> 00:02:11,800
+مرين على البرهان المرة اللي فاتت و أعتقد أن
+
+20
+00:02:11,800 --> 00:02:16,860
+البرهان مكتوب بالتفصيلواضح ومرنا عليه جزء جزء
+
+21
+00:02:16,860 --> 00:02:22,000
+فأرجعكم تكونوا قرأتهوا كمان مرة وفهمتهوا في حد
+
+22
+00:02:22,000 --> 00:02:27,860
+عنده استفسار على المرهانة النظرية هذه طيب الآن
+
+23
+00:02:27,860 --> 00:02:35,820
+النظرية هذه نرجع للنظرية كمان مرة الآن
+
+24
+00:02:35,820 --> 00:02:41,480
+في ملاحظة بتقول انه لو انا في النظرية هذه الفترات
+
+25
+00:02:41,480 --> 00:02:49,780
+هذهالفرض ان الفترات in مغلقة closed لو حذفت شيلت
+
+26
+00:02:49,780 --> 00:03:01,600
+الفرض هذا فالنظرية هذه بتبطل تكون صحيحة فالنظرية
+
+27
+00:03:01,600 --> 00:03:05,000
+هذه بتبطل تكون صحيحة وحنشوف counter example يوضح
+
+28
+00:03:05,000 --> 00:03:07,460
+عدم صحتها كذلك
+
+29
+00:03:09,100 --> 00:03:13,220
+طب افرضه ان هذا شرط متحقق في الفترات لكن اللي مش
+
+30
+00:03:13,220 --> 00:03:17,680
+متحقق اللي هو ال boundedness يعني الفترات هذه ليست
+
+31
+00:03:17,680 --> 00:03:21,420
+محدودة ليست bounded برضه في الحالة هذه المظهرية
+
+32
+00:03:21,420 --> 00:03:26,620
+تفشل و في counter example يوضح فشلها okay اذا
+
+33
+00:03:26,620 --> 00:03:30,640
+حنشوف two counter examples خليني نشوفهم مع بعض
+
+34
+00:03:36,610 --> 00:03:39,790
+إذا هدى ال remark اللى انا اتحدث عنها قلت انه it
+
+35
+00:03:39,790 --> 00:03:44,090
+should be noted يجب ملاحظة ان journal بصورة عامة
+
+36
+00:03:44,090 --> 00:03:48,030
+instant sequence of intervals need not have a
+
+37
+00:03:48,030 --> 00:03:51,290
+common point يعني لو فيه ending sequence من
+
+38
+00:03:51,290 --> 00:03:57,010
+الفترات المتداخلة مش شرط تقاطعهم يكون في في يعني
+
+39
+00:03:57,010 --> 00:04:02,650
+اى نقطة او نقطة مشاركة يعني مش شرط ان التقاطع لها
+
+40
+00:04:02,650 --> 00:04:11,000
+يساوي فيهفالأنثى لها دى هدا هى اللى حكينا عنها اول
+
+41
+00:04:11,000 --> 00:04:18,500
+مثال هاى
+
+42
+00:04:18,500 --> 00:04:23,080
+فى المثال الاول الفرض the hypothesis الفرض ان ال
+
+43
+00:04:23,080 --> 00:04:28,940
+intervals I in فى نظرية 22 be closed cannot be
+
+44
+00:04:28,940 --> 00:04:34,800
+dropped يعني لا يمكن حذفهلا يمكن الاستجناء عنه
+
+45
+00:04:34,800 --> 00:04:41,180
+وتبقى النظرية نظرية صحيحة for example على سبيل
+
+46
+00:04:41,180 --> 00:04:49,120
+المثال لو أخدت الفترات I N الفترة I N هي الفترة
+
+47
+00:04:49,120 --> 00:04:55,580
+المفتوحة من 0 ل 1 على N حيث N عدد طبيعي فواضح ان
+
+48
+00:04:55,580 --> 00:05:00,460
+الفترات هدي nested صح؟ لأن الفترة الأولى هتكون
+
+49
+00:05:00,460 --> 00:05:04,820
+الفترة مفتوحة من 0 ل 1الفترة التانية الفترة مفتوحة
+
+50
+00:05:04,820 --> 00:05:12,180
+من سفر لنص وهذه محتوى في I واحد و I تلاتة الفترة
+
+51
+00:05:12,180 --> 00:05:16,540
+مفتوحة من سفر لتلت محتوى داخل I اتنين و هكذا لذلك
+
+52
+00:05:16,540 --> 00:05:21,720
+واضح ان ال sequence of open intervals IN is nested
+
+53
+00:05:21,720 --> 00:05:27,560
+sequence كذلك عناصر ال sequence هذه bounded هذه
+
+54
+00:05:27,560 --> 00:05:33,710
+فترات محصورةلكن الفترات هذه not closed مش closed
+
+55
+00:05:33,710 --> 00:05:38,630
+يعني عبارة عن مجموعات مفتوحة ليست مغلقة، إذن شرط
+
+56
+00:05:38,630 --> 00:05:45,910
+الإغلاق هنا انحذف وبالتالي نتيجة النظرية مش شرط
+
+57
+00:05:45,910 --> 00:05:50,750
+تكون صحيحة، إذن التقاطع هنا لنفس ال sequence هذه
+
+58
+00:05:50,750 --> 00:05:54,410
+بيطلع بساوي fine مافيش common point مافيش نقطة
+
+59
+00:05:54,410 --> 00:05:59,950
+مشتركة في هذه الفترات طبعا هذا مش واضح
+
+60
+00:06:04,230 --> 00:06:08,470
+هذا تقاطع الفترات المفتوحة هذه بساوي في هذا مش
+
+61
+00:06:08,470 --> 00:06:14,310
+واضح يحتاج إلى برهان هي البرهان بين جثين مربعين
+
+62
+00:06:14,310 --> 00:06:21,470
+تعالوا نبره إن تقاطع الفترات هذه بساوي في to see
+
+63
+00:06:21,470 --> 00:06:27,670
+this to see this معناه لبرهان ذلك مش لرأي ذلك هذا
+
+64
+00:06:27,670 --> 00:06:34,040
+تعبير مجازم استخدمه لبرهانالشيء العبارة اللي احنا
+
+65
+00:06:34,040 --> 00:06:38,400
+عايزينها ف to see this suppose in the contrary
+
+66
+00:06:38,400 --> 00:06:43,320
+بنفترض على النقيد انه التقاطع هذا بسويش في يعني في
+
+67
+00:06:43,320 --> 00:06:48,100
+على الأقل عنصر X في التقاطع بنصل لتناقض طيب ال X
+
+68
+00:06:48,100 --> 00:06:53,360
+موجود في التقاطع معناته X موجود في I N لكل N إذن X
+
+69
+00:06:53,360 --> 00:06:58,310
+موجود في كل واحدة من الفترات I Nطيب X موجود في
+
+70
+00:06:58,310 --> 00:07:03,510
+الفترة I N معناته X أكبر من سفر أصغر من واحد على N
+
+71
+00:07:03,510 --> 00:07:09,970
+أصغر من واحد على N أصغر من واحد على N تمام
+
+72
+00:07:09,970 --> 00:07:13,970
+وبالتالي
+
+73
+00:07:13,970 --> 00:07:20,430
+حسب ال Archimedean property هذا عبارة عن أحد صور
+
+74
+00:07:20,430 --> 00:07:25,750
+ال Archimedean property بتقول ليبما ان X هد عدد
+
+75
+00:07:25,750 --> 00:07:33,530
+موجب، الـ X هد عدد موجب، إذا يوجد عدد طبيعي N0
+
+76
+00:07:33,530 --> 00:07:39,150
+مقلوب و أصغر من العدد الموجب وهذا بتديني تناقض،
+
+77
+00:07:39,150 --> 00:07:47,370
+هذا بتديني تناقض، هذا بتناقض مع كون ال X أصغر من 1
+
+78
+00:07:47,370 --> 00:07:53,170
+على N لكل Nيعني ال X هذه أصغر من 1 على N0 وهي في
+
+79
+00:07:53,170 --> 00:07:57,210
+نفس الواجهة أكبر من 1 على N0 لأن هذا بتديني تناقض
+
+80
+00:07:57,210 --> 00:08:04,250
+لأن التناقض هذا سبب ال assumption تبعنا أن يوجد X
+
+81
+00:08:04,250 --> 00:08:09,210
+في التقاطة لأن الصح أن التقاطع هذا مافيش فيه ولا
+
+82
+00:08:09,210 --> 00:08:16,140
+أنصر يعني is the empty setإن هذا مثال بورجي أو
+
+83
+00:08:16,140 --> 00:08:21,900
+بيوضح إنه لو حذفنا شرط إن الفترات في نظرية 22
+
+84
+00:08:21,900 --> 00:08:26,980
+closed فبتطلع الشفرة، النظرية تفشل، بتبطل النظرية
+
+85
+00:08:26,980 --> 00:08:32,720
+و هذا مثال بيوضح فشلها، الآن المثال التاني نفس
+
+86
+00:08:32,720 --> 00:08:38,480
+الحاجة، الفرض إن الفترات في نظرية 22 be bounded
+
+87
+00:08:40,090 --> 00:08:43,690
+بتكون محدودة cannot be dropped لايمكن إسخاطه
+
+88
+00:08:43,690 --> 00:08:48,250
+لايمكن إهماله فعشان
+
+89
+00:08:48,250 --> 00:08:52,750
+نوضح هذا الكلام ب counter example ف for example
+
+90
+00:08:52,750 --> 00:08:56,750
+على سبيل المثال هناخد الفترات المغلقة I N فترة
+
+91
+00:08:56,750 --> 00:09:03,190
+مغلقة من N إلى ملا نهاية حيث N عدد طبيعي هذه
+
+92
+00:09:03,190 --> 00:09:10,150
+الفتراتكل هذه فترة مغلقة كل فترة على الصورة هذه
+
+93
+00:09:10,150 --> 00:09:17,010
+مغلقة إذا شرط الإغلاق متحقق بعدين الفترات هذه نستد
+
+94
+00:09:17,010 --> 00:09:20,430
+لحظة أول فترة هي الفترة المغلقة من واحد لما لا
+
+95
+00:09:20,430 --> 00:09:24,450
+نهاية التانية فترة مغلقة من اتنين لما لا نهاية
+
+96
+00:09:24,450 --> 00:09:30,110
+وهذه محتوى في I واحد الفترة التالتة الفترة المغلقة
+
+97
+00:09:30,110 --> 00:09:33,410
+من تلاتة لما لا نهاية وهذه محتوى في I اتنين وهكذا
+
+98
+00:09:33,410 --> 00:09:38,730
+فالفترات هذه نستدand closed مغلقة لكن ماهياش
+
+99
+00:09:38,730 --> 00:09:42,190
+bounded مش محصورة it's not bounded .. هذه كمجموعة
+
+100
+00:09:42,190 --> 00:09:48,870
+is not bounded above، كمجموعة ليس لها supreme، is
+
+101
+00:09:48,870 --> 00:09:52,390
+not bounded above، اذا شرط ال boundedness اختل
+
+102
+00:09:52,390 --> 00:09:57,970
+وبالتالي نتيجة النظرية هتختلفإذا الفترات هذه
+
+103
+00:09:57,970 --> 00:10:03,410
+closed but unbounded وإذا هنجد إنه تقاطع الفترات
+
+104
+00:10:03,410 --> 00:10:08,930
+هذه مافيش فيه ولا نقطة تقاطع هذا بساوي five كمان
+
+105
+00:10:08,930 --> 00:10:15,350
+مرة المساواة هذه بدها مش واضحة ليست واضحة فبدنا
+
+106
+00:10:15,350 --> 00:10:20,730
+نثبت صحة المساواة هذه كمان مرة نعمل برهان بالتناقض
+
+107
+00:10:20,730 --> 00:10:24,370
+نعمل برهان بالتناقض
+
+108
+00:10:29,770 --> 00:10:34,830
+فافرضي أن التقاطع هذا لا يساوي في I وبالتالي يوجد
+
+109
+00:10:34,830 --> 00:10:40,670
+X في التقاطع إذا X موجود في الفترة I N لكل N هذا
+
+110
+00:10:40,670 --> 00:10:46,950
+من تعريف التقاطع X موجودة في I N معناته X أكبر من
+
+111
+00:10:46,950 --> 00:10:53,870
+أو يساوي N وهذا صحيح لكل Nهذا بتناقض مع الـ
+
+112
+00:10:53,870 --> 00:10:58,510
+Archimedean property نظرية الأساسية نظرية خمستاشر
+
+113
+00:10:58,510 --> 00:11:05,450
+في الشبطرة ده اللي بتقول لأي عدد حقيقي X ينتمي إلى
+
+114
+00:11:05,450 --> 00:11:16,530
+R بتأدي ان يوجد N0 ينتمي إلى N بحيث ان X أصغر من
+
+115
+00:11:16,530 --> 00:11:17,330
+N0
+
+116
+00:11:21,190 --> 00:11:27,210
+هذه هي الـ Archimedean property الأساسية طيب أنا
+
+117
+00:11:27,210 --> 00:11:32,850
+عندي الأن من ال Archimedean property عندي يوجد عدد
+
+118
+00:11:32,850 --> 00:11:42,060
+طبيعي N0 لصد أكبر من X وعندي هناإن X أكبر من أو
+
+119
+00:11:42,060 --> 00:11:47,340
+ساوي N لكل N في N وبالتالي X أكبر من أو ساوي N
+
+120
+00:11:47,340 --> 00:11:51,820
+Zero لأن N Zero ينتمي إلى N فإذا عندي هنا X أكبر
+
+121
+00:11:51,820 --> 00:11:56,180
+من أو ساوي N Zero و X أصغر من N Zero هذا بيديني
+
+122
+00:11:56,180 --> 00:12:02,840
+تناطق إذا في عندي contradiction إذا هذا العنصر غير
+
+123
+00:12:02,840 --> 00:12:07,870
+موجودsuch an x does not exist يعني التقاطة هذا
+
+124
+00:12:07,870 --> 00:12:13,550
+بساوي في كما هو مطلوب، تمام؟ واضح البرهن؟ إذن هذه
+
+125
+00:12:13,550 --> 00:12:17,690
+مثال تاني بوضح أن شرط ال boundedness لا يمكن
+
+126
+00:12:17,690 --> 00:12:25,730
+اسقاطه وتبقى nested intervals theorem صحيحة، okay؟
+
+127
+00:12:25,730 --> 00:12:31,710
+في نظرية تانيةيمكن هذه مرت معاكم في المبادئ لكن
+
+128
+00:12:31,710 --> 00:12:37,170
+اليوم هنعطيلها برهان يعتمد على ال nested intervals
+
+129
+00:12:37,170 --> 00:12:40,610
+theorem او nested intervals property برهان جديد
+
+130
+00:12:40,610 --> 00:12:48,730
+غير اللي أخدته في مبادئ الرياضيات فالنظرية
+
+131
+00:12:48,730 --> 00:12:54,590
+هذه 24 تتحدث عن ال uncountability of the real
+
+132
+00:12:54,590 --> 00:12:59,560
+numbersفبكل بساطة النظرية هذه بتقول أن مجموعة
+
+133
+00:12:59,560 --> 00:13:04,340
+العداد الحقيقية is uncountable the set R of all
+
+134
+00:13:04,340 --> 00:13:09,460
+real numbers is uncountable طيب
+
+135
+00:13:09,460 --> 00:13:15,460
+ما معنى أن ال set تكون countable؟ في حد فيكم
+
+136
+00:13:15,460 --> 00:13:21,380
+بتعرف؟ ال set A أو S definition
+
+137
+00:13:24,240 --> 00:13:31,920
+definition تعريف S is countable if
+
+138
+00:13:31,920 --> 00:13:46,700
+and only if كتوف المبادئ either اما S is finite or
+
+139
+00:13:46,700 --> 00:13:50,040
+او
+
+140
+00:13:50,040 --> 00:13:58,450
+S is denomableأو في بيجيكشن one to one
+
+141
+00:13:58,450 --> 00:14:03,850
+correspondence بينها وبين الأعداد الطبيعية يعني
+
+142
+00:14:03,850 --> 00:14:16,970
+هذا معناه is denumerable قابلة للترقيم طيب
+
+143
+00:14:16,970 --> 00:14:23,330
+إذا كانت ال set ماهياش
+
+144
+00:14:23,330 --> 00:14:29,090
+finiteوماهياش in one to one correspondence with
+
+145
+00:14:29,090 --> 00:14:33,550
+the natural numbers او ماهياش denumerable فبنسميها
+
+146
+00:14:33,550 --> 00:14:38,410
+uncountable غير قابلة للعد countable قابلة للعد
+
+147
+00:14:38,410 --> 00:14:44,750
+uncountable غير قابلة للعد طيب
+
+148
+00:14:44,750 --> 00:14:52,150
+ال
+
+149
+00:14:52,150 --> 00:14:52,390
+..
+
+150
+00:14:55,180 --> 00:15:03,200
+معروف في مبادئ رياضيات درسنا ان ال interval هذي و
+
+151
+00:15:03,200 --> 00:15:08,220
+ال interval هذي كلا هما uncountable الفترة
+
+152
+00:15:08,220 --> 00:15:11,120
+المفتوحة من سفر لواحد infinite set اول حاجة
+
+153
+00:15:11,120 --> 00:15:15,800
+infinite set و
+
+154
+00:15:15,800 --> 00:15:18,900
+طبعا ممكن تثبت انها uncountable
+
+155
+00:15:21,370 --> 00:15:26,370
+و طبعا هذه الفترة المغلقة تحتوي ال six هذه الفترة
+
+156
+00:15:26,370 --> 00:15:29,110
+المفتوحة فإذا كانت هذه uncountable هذه بتكون
+
+157
+00:15:29,110 --> 00:15:35,530
+uncountable وهذا البرهان موجود في نظرية في الكتاب
+
+158
+00:15:35,530 --> 00:15:42,010
+المقرر textbook الكتاب المقرر
+
+159
+00:15:42,010 --> 00:15:47,110
+طبعا
+
+160
+00:15:47,110 --> 00:15:50,410
+طيب
+
+161
+00:15:57,430 --> 00:16:05,570
+الـ احنا عايزين نثبت عشان نثبت ان ال set هذه ال R
+
+162
+00:16:05,570 --> 00:16:14,770
+لاحظوا ان ال R is
+
+163
+00:16:14,770 --> 00:16:18,490
+in one to one correspondence مع الفترة المفتوحة او
+
+164
+00:16:18,490 --> 00:16:22,630
+المغلقة حتى في
+
+165
+00:16:22,630 --> 00:16:28,250
+byjection بينه وبين الفترةالمفتوحة المغلقة 01
+
+166
+00:16:28,250 --> 00:16:36,890
+وبرضه المفتوحة الان لو أثبتنا ان الفترة هذه
+
+167
+00:16:36,890 --> 00:16:44,150
+uncountable فهذه
+
+168
+00:16:44,150 --> 00:16:50,530
+ال 6 in one to one correspondence معها فال 6 هذه R
+
+169
+00:16:50,530 --> 00:16:54,400
+تطلع uncountableهذه نظرية موجودة في مبادئ
+
+170
+00:16:54,400 --> 00:16:58,080
+الرياضيات إذا كانت هناك مجموعتين واثنتين
+
+171
+00:16:58,080 --> 00:17:02,860
+equivalent to each other فهناك بيجيكشن بينهم إذا
+
+172
+00:17:02,860 --> 00:17:06,540
+كانت واحدة countable فالتانية تظهر countable إذا
+
+173
+00:17:06,540 --> 00:17:10,380
+كانت واحدة countable فالتانية تظهر countable إذا
+
+174
+00:17:10,380 --> 00:17:14,140
+كانت هذه finite تظهر هذه finite إذا كانت هذه
+
+175
+00:17:14,140 --> 00:17:19,440
+infinite تظهر هذه infinite كل هذه نظريات موجودة في
+
+176
+00:17:19,440 --> 00:17:24,350
+مبادئ الرياضياتإذا لو أثبتنا إن الفترة هادى
+
+177
+00:17:24,350 --> 00:17:31,010
+uncountable فبطلع R uncountable طيب
+
+178
+00:17:31,010 --> 00:17:42,050
+لإثبات ذلك هنا عايزين نثبت إن الفترة هادى نثبت إن
+
+179
+00:17:42,050 --> 00:17:47,030
+الفترة هادى uncountable لبرهان ذلك نعمل برهان
+
+180
+00:17:47,030 --> 00:17:47,770
+بالتناقض
+
+181
+00:17:57,100 --> 00:18:01,160
+بنثبت ان الفترة المغلقة هذي uncountable نفرض
+
+182
+00:18:01,160 --> 00:18:04,940
+المقيد
+
+183
+00:18:04,940 --> 00:18:08,780
+ان الفترة هذي countable لاحظوا ان الفترة هذي
+
+184
+00:18:08,780 --> 00:18:14,500
+infinite والان countable اذا بتطلع equipotent او
+
+185
+00:18:14,500 --> 00:18:17,640
+in one to one correspondence with natural numbers
+
+186
+00:18:22,850 --> 00:18:26,550
+الأن في الحالة هذه I in one to one correspondence
+
+187
+00:18:26,550 --> 00:18:31,570
+within actual numbers أو بنسميها innumerable صح؟
+
+188
+00:18:33,280 --> 00:18:36,560
+الان ال set I denominable يعني ممكن ترقيمها
+
+189
+00:18:36,560 --> 00:18:41,840
+بالأعداد الطبيعية إذا ممكن نسمي عناصرها xn-n عدد
+
+190
+00:18:41,840 --> 00:18:46,340
+طبيعي اللي هي x1, x2, x3 الاخرى أي set denominable
+
+191
+00:18:46,340 --> 00:18:49,900
+أو in one to one correspondence with natural
+
+192
+00:18:49,900 --> 00:18:55,140
+numbers ممكن ترقيم عناصرها ك list by the natural
+
+193
+00:18:55,140 --> 00:18:59,200
+numbers إذا I هي كل عناصرها رقمناهم بالأعداد
+
+194
+00:18:59,200 --> 00:18:59,800
+الطبيعية
+
+195
+00:19:05,090 --> 00:19:08,350
+لحظة احنا بدنا نصل الى تناقض احنا بدنا القرآن
+
+196
+00:19:08,350 --> 00:19:15,650
+وفرضنا ال contrary هيو Assume ال contrary ان I is
+
+197
+00:19:15,650 --> 00:19:19,870
+countable بدنا نصل الى تناقض طيب هي الفترة I هي
+
+198
+00:19:19,870 --> 00:19:26,890
+الفترة I هي الفترة I هذه
+
+199
+00:19:26,890 --> 00:19:31,550
+Iو في اندس اي هاد الفترة اي هاد يعني عناصرها هي
+
+200
+00:19:31,550 --> 00:19:37,390
+مرقمة اكس واحد اكس اتنين الى ملا نهاية افرض ان اكس
+
+201
+00:19:37,390 --> 00:19:46,510
+واحد موجود هان اول عنصر في الفترة موجود هان فممكن
+
+202
+00:19:46,510 --> 00:19:54,530
+اختار فترة مغلقة اسميها اي واحد ممكن اختار فترة
+
+203
+00:19:54,530 --> 00:20:03,260
+مغلقةأسميها I1 بحيث ان ال X1 هذه لا تنتمي للفترة
+
+204
+00:20:03,260 --> 00:20:07,520
+I1 وممكن
+
+205
+00:20:07,520 --> 00:20:13,100
+اختار فترة مغلقة تانية طب افرضي ان X2 موجودة هنا
+
+206
+00:20:13,100 --> 00:20:19,680
+العنصر التاني في الفترة I ايه رقم X2 موجود هنا او
+
+207
+00:20:19,680 --> 00:20:27,400
+هنا او هنا فبقدر اختار فترة مغلقة تانيةنسميها I2
+
+208
+00:20:27,400 --> 00:20:36,120
+اللي هي الفترة هذه بحيث ان X2 لا تنتمي ل I2 و
+
+209
+00:20:36,120 --> 00:20:42,400
+الفترة I2 هي فترة جزئية من I1 طيب افرض ان X3
+
+210
+00:20:42,400 --> 00:20:50,120
+موجودة هنا او هنا او هنا او اي مكان تاني فبقدر
+
+211
+00:20:50,120 --> 00:20:58,310
+اختار فترة مغلقة تسميها I3اللي هي الفترة هذه بحيث
+
+212
+00:20:58,310 --> 00:21:05,450
+ان X3 لا تنتمي للفترة I3 والفترة I3 جزئية من
+
+213
+00:21:05,450 --> 00:21:12,490
+الفترة I2 ممكن نستمر على هذا النمط هنحصل على
+
+214
+00:21:12,490 --> 00:21:21,110
+sequence of intervals اللي هي I1 تحتوي I2 تحتوي I3
+
+215
+00:21:22,570 --> 00:21:27,550
+و هكذا ممكن نستمر إلى ملا نهاية و كل الفترات هذول
+
+216
+00:21:27,550 --> 00:21:32,570
+محتوى .. كل واحدة منهم محتوى داخل الـ I و كل واحدة
+
+217
+00:21:32,570 --> 00:21:38,710
+من الفترات هذه صممناها بحيث ان XN لا ينتمي إلى IN
+
+218
+00:21:38,710 --> 00:21:47,190
+لكل N بساوي واحد اتنين إلى ملا نهاية صح؟ إذا لو
+
+219
+00:21:47,190 --> 00:21:53,130
+استمرنا في العملية هذههنحصل على sequence of nested
+
+220
+00:21:53,130 --> 00:21:57,170
+intervals و ال intervals هدولة كلهم closed و
+
+221
+00:21:57,170 --> 00:22:01,570
+bounded كلهم closed و bounded و كل الفترات هذه
+
+222
+00:22:01,570 --> 00:22:07,190
+محتوية داخل الفترة I و X in العنصر X in من ال
+
+223
+00:22:07,190 --> 00:22:14,470
+sequence هذه لا ينتمي ل I in لكل N الان ممكن نطبق
+
+224
+00:22:14,470 --> 00:22:18,090
+nested interval property theorem اللي هي theorem
+
+225
+00:22:20,050 --> 00:22:23,550
+بتقول ده في عندي sequence of nested intervals و
+
+226
+00:22:23,550 --> 00:22:29,030
+كلهم closed و bounded فالتقاطع تبعهم لا يساوي في I
+
+227
+00:22:29,030 --> 00:22:34,650
+إذا التقاطع تبعهم موجود في نقطة واحدة دعنا نسميها
+
+228
+00:22:34,650 --> 00:22:43,030
+ساي و الفترات هذه كلها كل الفترات هذه موجودة داخل
+
+229
+00:22:43,030 --> 00:22:47,390
+الفترة I داخل الفترة I
+
+230
+00:22:53,490 --> 00:23:04,810
+ماشي هنا اه
+
+231
+00:23:04,810 --> 00:23:07,630
+ايش صار؟ هي فوق صار
+
+232
+00:23:12,680 --> 00:23:17,360
+إذا حسب نفس ال interval theorem يوجد نقطة psi في
+
+233
+00:23:17,360 --> 00:23:22,080
+تقاطة الفترات الفترات كلهم موجودين داخل I إذا
+
+234
+00:23:22,080 --> 00:23:29,540
+تقاطعهم موجود داخل I وبالتالي النقطة psi هذه
+
+235
+00:23:29,540 --> 00:23:37,060
+موجودة في كل الفترات I in لأن موجودة في تقاطعهم
+
+236
+00:23:37,060 --> 00:23:43,850
+كلهم صح إذا النقطة psi موجودة في I in لكل Nوالفترة
+
+237
+00:23:43,850 --> 00:23:52,690
+I N هذه لا تحتوي من هنا الفترة I N لا تحتوي X N
+
+238
+00:23:52,690 --> 00:23:58,690
+والان تحتوي ساي إذا ساي لا تساوي X N الكلام هذا
+
+239
+00:23:58,690 --> 00:24:04,430
+صحيح لكل N بظبط هذا عنصر في الفترة هذه و X N ليس
+
+240
+00:24:04,430 --> 00:24:07,970
+عنصر فيها إذا مش ممكن يكونوا متساويين صح؟
+
+241
+00:24:10,780 --> 00:24:19,120
+الـ Psi قلنا هي تنتمي إلى I الـ Psi موجودة في I و
+
+242
+00:24:19,120 --> 00:24:27,620
+الفترة I رقمنا عناصرها قبل شوية انا
+
+243
+00:24:27,620 --> 00:24:36,300
+في اندي يوجد عدد حقيقي Psi ينتمي ل I و في نفس
+
+244
+00:24:36,300 --> 00:24:42,430
+الوجهة الفترة I هي كل عناصرهامُرقّمة بالعداد
+
+245
+00:24:42,430 --> 00:24:48,030
+الطبيعي عناصرها X1 و X2 إلى ما لنهائي و الأن في
+
+246
+00:24:48,030 --> 00:24:59,090
+عندي Psi مختلف عن كل عناصر الفترة I فهذا
+
+247
+00:24:59,090 --> 00:25:04,510
+بيدّي أن ال sequence أو ال set هذهis not a
+
+248
+00:25:04,510 --> 00:25:10,330
+complete enumeration of I ليست ترقيم كامل للفترة I
+
+249
+00:25:10,330 --> 00:25:15,750
+وهذا تناقض يعني
+
+250
+00:25:15,750 --> 00:25:20,530
+احنا قلنا الفترة I هذه تطلع countable و infinite
+
+251
+00:25:20,530 --> 00:25:26,830
+اذا ممكن نرقم اذا denumerable يعني ممكن نرقم عن
+
+252
+00:25:26,830 --> 00:25:31,770
+صرها كلها بالاعداد الطبيعي وبالتالي كل عن صرها X
+
+253
+00:25:33,730 --> 00:25:43,170
+تمام؟ الآن في البرهان هذا وجدنا ان في صي أنصر جديد
+
+254
+00:25:43,170 --> 00:25:49,310
+في I مختلف عن كل عناصرها معناته هذه ال list ليست
+
+255
+00:25:49,310 --> 00:25:54,650
+ترقيم كامل ل I في عناصر أخرى زي صي مش مرقمة و هذا
+
+256
+00:25:54,650 --> 00:25:59,950
+تناقضلأن إحنا عندنا ال set I هذي countable و
+
+257
+00:25:59,950 --> 00:26:04,210
+infinite و denomable إذن هي list تبع كل عناصرها
+
+258
+00:26:04,210 --> 00:26:11,230
+فكيف طلع فيه أنصر جديد مختلف عن عناصرها فهذا تناقض
+
+259
+00:26:11,230 --> 00:26:18,140
+إذن هذا التناقض بثبت أن فرضنا أن الفترة Iكانت
+
+260
+00:26:18,140 --> 00:26:22,140
+countable كان فرض خاطر وبالتالي الفترة I تطلع
+
+261
+00:26:22,140 --> 00:26:27,520
+uncountable اذا الان الفترة I uncountable وانا
+
+262
+00:26:27,520 --> 00:26:36,140
+عندي R equivalent لفترة مغلقة 01 ممكن نوجد
+
+263
+00:26:36,140 --> 00:26:40,860
+bijection بينهم اذا ال R تطلع uncountable كما هو
+
+264
+00:26:40,860 --> 00:26:45,080
+مطلوب اذا
+
+265
+00:26:45,080 --> 00:26:50,750
+هذا هو برهانالنظرية اللي فادت هي طبعا برهان بيعتمد
+
+266
+00:26:50,750 --> 00:26:55,430
+على شوفنا ال nested interval theorem وبالتالي هذا
+
+267
+00:26:55,430 --> 00:26:58,510
+برهان مختلف عن البرهان اللي بنعطيه في مبادئ
+
+268
+00:26:58,510 --> 00:27:05,270
+الرياضيات في برهان تاني برضه لنظرية هذه يعطى في
+
+269
+00:27:05,270 --> 00:27:10,710
+مبادئ الرياضيات اللي هو باستخدام counter diagonal
+
+270
+00:27:10,710 --> 00:27:14,690
+argument مشهور
+
+271
+00:27:14,690 --> 00:27:20,990
+يعني البرهانيرجع إلى العالم الرياضي Cantor يسمى
+
+272
+00:27:20,990 --> 00:27:24,750
+Cantor دي اقنع ال argument بثبت ان الفترة المفتوحة
+
+273
+00:27:24,750 --> 00:27:29,330
+من سفر لواحد is uncountable وبالتالي R is
+
+274
+00:27:29,330 --> 00:27:33,310
+uncountable لأن R في byjection بينها وبين ال open
+
+275
+00:27:33,310 --> 00:27:37,670
+interval من سفر لواحد الآن في نتيجة على نظرية
+
+276
+00:27:37,670 --> 00:27:42,490
+الأخيرة هذهالـ set هذه الـ R minus Q اللي هي الـ
+
+277
+00:27:42,490 --> 00:27:46,590
+set of all irrationals أيضًا is uncountable
+
+278
+00:27:46,590 --> 00:27:50,690
+والبرهان هنا نفس البرهان اللي بنعطيه في المبادئ
+
+279
+00:27:50,690 --> 00:27:55,470
+برهان by contradiction assume and contrary إن ال
+
+280
+00:27:55,470 --> 00:28:02,110
+set R minus Q is countable وإحنا عندنا نظرية في
+
+281
+00:28:02,110 --> 00:28:07,640
+المبادئ أخدنا بتقول إن لو في عندي مجموعتين A وBوكل
+
+282
+00:28:07,640 --> 00:28:14,140
+واحدة منهم countable فاتحادهم بيطلع countable الان
+
+283
+00:28:14,140 --> 00:28:17,640
+انا في عند Q countable معروف ان Q is countable
+
+284
+00:28:17,640 --> 00:28:24,160
+والان احنا فرضين ان R-Q is countable اذا اتحاد
+
+285
+00:28:24,160 --> 00:28:28,420
+المجموعتين هدول اللي هو R بيطلع countable وهذا
+
+286
+00:28:28,420 --> 00:28:31,420
+بتناقض مع النتيجة اللي لسه مثبتينها في النظرية
+
+287
+00:28:31,420 --> 00:28:36,240
+السابقةOkay إذا في عندي contradiction إذا الفرض
+
+288
+00:28:36,240 --> 00:28:39,780
+إنه الست هذي countable كان خاطئ إذا الصح إنه الست
+
+289
+00:28:39,780 --> 00:28:45,280
+هذي اللي هي ال irrational number is is uncountable
+
+290
+00:28:45,280 --> 00:28:57,120
+okay تمام إذا ال مع
+
+291
+00:28:57,120 --> 00:29:01,620
+انتهاء النتيجة هذه هيك بنكون غطينا section اتنين
+
+292
+00:29:01,620 --> 00:29:08,660
+خمسةو هاي التمرين المطلوب تهلوها مش عايز ابدأ
+
+293
+00:29:08,660 --> 00:29:14,020
+section جديد عايز ان احنا نستغل الوقت المتبقى من
+
+294
+00:29:14,020 --> 00:29:19,160
+المحاضرة في حل اسئلة discussion يعنيمناقشة فأي
+
+295
+00:29:19,160 --> 00:29:22,360
+واحدة فيكم عندها مناقشة احنا انا عارف ان انتوا
+
+296
+00:29:22,360 --> 00:29:28,100
+هتحضروا حالكم ليوم السبت المناقشة لكن برضه اكيد
+
+297
+00:29:28,100 --> 00:29:32,040
+يعني في بينكم ناس محضرين فلو عندكم أسئلة في
+
+298
+00:29:32,040 --> 00:29:36,680
+section اتنين تلاتة او اتنين اربعة او section
+
+299
+00:29:36,680 --> 00:29:41,160
+اتنين اتنين او اتنين واحد فممكن نحاول نحلها في
+
+300
+00:29:41,160 --> 00:29:47,080
+الوقت المتبقى من المحاضرةماشي الحال فإذا مين عندها
+
+301
+00:29:47,080 --> 00:29:53,540
+أي سؤال في ال .. المحاضرات
+
+302
+00:29:53,540 --> 00:30:03,220
+السابقة أو تمارين المحاضرات السابقة من
+
+303
+00:30:03,220 --> 00:30:08,540
+لديها سؤال؟ في عندنا أسلة كتيرة في المحاضرات
+
+304
+00:30:08,540 --> 00:30:15,470
+السابقة homework كتيرمين لديها سؤال؟ مين عندها
+
+305
+00:30:15,470 --> 00:30:23,170
+سؤال؟ مين بتحلم السؤال؟ ولا
+
+306
+00:30:23,170 --> 00:30:29,690
+واحدة عندها سؤال؟ تفضل طيب
+
+307
+00:30:30,890 --> 00:30:35,570
+طبعا هذه إشارة غير يعني غير إيجابية أو إشارة سلبية
+
+308
+00:30:35,570 --> 00:30:42,530
+يعني لحد تلان أنتوا مش المادة مابتدرسهاش دراسة
+
+309
+00:30:42,530 --> 00:30:49,530
+حقيقية و هذا معناه أن أنتوا مش ماخدينها بجد يعني
+
+310
+00:30:49,530 --> 00:30:59,690
+كما أجب و هذا دليل عليكم تحلوش مسألة فانا
+
+311
+00:30:59,690 --> 00:31:04,600
+هسأل عنكمخليني أحللكم كام سؤال هاي section اتنين
+
+312
+00:31:04,600 --> 00:31:29,640
+تلاتة هنا هاي
+
+313
+00:31:29,640 --> 00:31:31,000
+مثلا سؤال أربعة
+
+314
+00:31:35,030 --> 00:31:43,690
+هي السؤال أربعة سكشن اتنين تلاتة انا
+
+315
+00:31:43,690 --> 00:31:51,850
+عندي set S أربعة بيساوي كل الأعداد واحد سالب سالب
+
+316
+00:31:51,850 --> 00:32:03,910
+واحد رصد N على N حيث N عدد طبيعي والمطلوب
+
+317
+00:32:03,910 --> 00:32:04,490
+find
+
+318
+00:32:07,290 --> 00:32:17,550
+Find الـ Supremum أو الانفمم ل S4 و ايضا ال
+
+319
+00:32:17,550 --> 00:32:29,950
+Supremum ل S4 طيب
+
+320
+00:32:29,950 --> 00:32:34,370
+احنا أخدنا في مثال في ال section هذا
+
+321
+00:32:37,360 --> 00:32:39,940
+خلنا نام هنا ولا لسه؟
+
+322
+00:33:14,820 --> 00:33:21,960
+Solution اخدنا احنا مثال بيقول انه ال .. لو كان في
+
+323
+00:33:21,960 --> 00:33:25,320
+.. في ال section اللي بعد و ممكن الحل باستخدام
+
+324
+00:33:25,320 --> 00:33:32,500
+المثال رقم A يعني by example
+
+325
+00:33:42,050 --> 00:33:52,450
+تنين اربع واحد الجزء A انا عندي ال supremum ل A
+
+326
+00:33:52,450 --> 00:33:58,990
+زاد S A عدد حقيقي S مجموعة جزئية من R اثبتنا ان
+
+327
+00:33:58,990 --> 00:34:09,970
+هذا بساوي A زاد supremum ال S فلو
+
+328
+00:34:09,970 --> 00:34:24,340
+بدى احل الجزء Bف let S بساوي مجموعة ..
+
+329
+00:34:24,340 --> 00:34:29,740
+let
+
+330
+00:34:29,740 --> 00:34:36,560
+S بساوي مجموعة الأعداد سالب
+
+331
+00:34:36,560 --> 00:34:42,140
+واحد أس N على N حيث N عدب طبيعي
+
+332
+00:34:48,030 --> 00:34:54,310
+ممكن نحول السلب لموجة هاد عبارة عن سالب واحد ..
+
+333
+00:34:54,310 --> 00:35:05,610
+سالب واحد و نص و سالب تلت و ربع و كده
+
+334
+00:35:17,860 --> 00:35:29,700
+فممكن اثبات انه ال super mom تبع السيدتها دى
+
+335
+00:35:29,700 --> 00:35:33,820
+أستاذ
+
+336
+00:35:33,820 --> 00:35:40,840
+نعم هنحن لو سالب اللي برا دخلناه يصير سالب واحد
+
+337
+00:35:40,840 --> 00:35:45,980
+plus one plus واحدعلى أنا ممكن اه ممكن ناخد سالب
+
+338
+00:35:45,980 --> 00:35:50,560
+هذا فهذا أكبر أنصر هو الواحد صح هيك بتنحل الصح
+
+339
+00:35:50,560 --> 00:35:56,620
+برضه هذا ممكن فبصير عندى هنا واحد سالب اول أنصر
+
+340
+00:35:56,620 --> 00:36:03,960
+واحد سالب نص فالصبر ممكن يكون واحد بعدين تلت سالب
+
+341
+00:36:03,960 --> 00:36:12,760
+ربع و هكذافال supremum إذاً ال supremum ل S بساوي
+
+342
+00:36:12,760 --> 00:36:17,480
+هاي اللي .. لاحظ ان الأكبر عدد في الست هذه هو
+
+343
+00:36:17,480 --> 00:36:23,840
+الواحد واحد أكبر من أو ساوي كل الأعداد هذه وهو
+
+344
+00:36:23,840 --> 00:36:27,020
+أصغر upper bound إذاً الواحد upper bound للست هذه
+
+345
+00:36:27,020 --> 00:36:32,400
+هي أكبر من أو ساوي كل عناصرها وهو أصغر upper bound
+
+346
+00:36:32,400 --> 00:36:41,930
+إذاً هذا بساوي واحدلأ س .. إيش بس يعني؟
+
+347
+00:36:41,930 --> 00:36:48,850
+ما
+
+348
+00:36:48,850 --> 00:36:54,370
+هو أصغر؟ طلع اتنين اتنين أستاذ ال super اتنين مش
+
+349
+00:36:54,370 --> 00:37:00,770
+هي على حسب القاعدة نحن نحط اي واحد بيصير
+
+350
+00:37:00,770 --> 00:37:04,520
+اتنين؟ لا لااحنا بنحكي عن ال 6 هذه اللي هانا مش
+
+351
+00:37:04,520 --> 00:37:11,020
+اللي هناك هذه S و هذه S4 فبيختلفوا عن بعض ال 6 هذه
+
+352
+00:37:11,020 --> 00:37:15,760
+هدا هي أنصرها فما
+
+353
+00:37:15,760 --> 00:37:21,700
+هو بيناجيب lower bound او اكبر lower bound اكبر
+
+354
+00:37:21,700 --> 00:37:30,120
+lower bound طب نلاحظ سالب نص اصغر من سالب ربع اصغر
+
+355
+00:37:30,120 --> 00:37:47,710
+منبعد هيك سالب سادس اه فاعتقد
+
+356
+00:37:47,710 --> 00:37:52,010
+ان هذا هيطلع سالب نص هذا اكبر lower bound
+
+357
+00:37:58,870 --> 00:38:04,470
+طيب لو طبقنا المضارية هذه أنا أخدت S بساوي الكلام
+
+358
+00:38:04,470 --> 00:38:12,830
+هذا و A بساوي واحد اذا
+
+359
+00:38:12,830 --> 00:38:24,470
+ال supremum ل S أربعة بساوي A زائد ال supremum ل S
+
+360
+00:38:24,470 --> 00:38:34,260
+صح؟و ال a بساوي واحد و ال suprem ل s بساوي واحد
+
+361
+00:38:34,260 --> 00:38:43,460
+فبطلع ال suprem ل s أربعة بساوي اتنين تمام؟ الان
+
+362
+00:38:43,460 --> 00:38:53,660
+بنجيب ال infimum ل s أربعة بنفس الطريقة ممكن
+
+363
+00:38:53,660 --> 00:38:54,340
+اثبات
+
+364
+00:39:00,490 --> 00:39:10,070
+إذا هنا similar
+
+365
+00:39:10,070 --> 00:39:17,590
+example
+
+366
+00:39:17,590 --> 00:39:24,090
+similar
+
+367
+00:39:24,090 --> 00:39:32,030
+example اتنين اربعة واحد ايهممكن من خلاله نثبت ان
+
+368
+00:39:32,030 --> 00:39:38,330
+الانفمام ان
+
+369
+00:39:38,330 --> 00:39:44,490
+الانفمام لست a زياد s بيساوي a زياد الانفمام ل s
+
+370
+00:39:44,490 --> 00:39:49,310
+وبالتالي
+
+371
+00:39:49,310 --> 00:39:53,390
+ان
+
+372
+00:39:53,390 --> 00:40:00,480
+انا لو بدي اجرب على جزء aف ال infimum ل S أربعة
+
+373
+00:40:00,480 --> 00:40:13,780
+بيساوي ال infimum ل A زائد S اللي هو ال infimum ل
+
+374
+00:40:13,780 --> 00:40:22,630
+واحد زائد S و هذا بيساوي واحد زائد infimum ل Sو
+
+375
+00:40:22,630 --> 00:40:28,770
+هذا بيساوي واحد زائد in from ال S سالب نص فبطلع نص
+
+376
+00:40:28,770 --> 00:40:36,210
+okay ان ال in from لست S أربعة بيطلع سالب بيطلع نص
+
+377
+00:40:36,210 --> 00:40:41,910
+هذا حل حل تاني ان انا يعني احاول
+
+378
+00:40:47,360 --> 00:40:54,460
+أه يعني أكتب عناصر المجموعة هذه أفرفتها و أحاول
+
+379
+00:40:54,460 --> 00:40:59,600
+أشوف وين أصغر عنصر و وين أكبر عنصر و وين هيكون في
+
+380
+00:40:59,600 --> 00:41:04,640
+عندي upper bounds و lower bounds و نحاول نثبت أنه
+
+381
+00:41:04,640 --> 00:41:12,060
+ال .. يعني بالطريقة هذه يعني ممكن نحن نحل الاسئلة
+
+382
+00:41:12,060 --> 00:41:20,320
+بطريقة تانيةفهذا حلو يعني
+
+383
+00:41:20,320 --> 00:41:25,900
+هذا ال set ممكن نكتب عناصرها يعني أول عنصر لما n
+
+384
+00:41:25,900 --> 00:41:33,680
+بساوي واحد واحد سالب سالب
+
+385
+00:41:33,680 --> 00:41:44,350
+سالب واحد يعني اتنين الانصر اللي بعدهواحد سالب نص
+
+386
+00:41:44,350 --> 00:41:56,450
+بيطلع نص اللي بعده بيطلع واحد سالب سالب تلت يعني
+
+387
+00:41:56,450 --> 00:42:03,270
+واحد تلت يعني جديش اربعة على تلاتة اللي بعده واحد
+
+388
+00:42:03,270 --> 00:42:07,210
+موجب ربع بيطلع جديش
+
+389
+00:42:09,700 --> 00:42:17,520
+خمس اربع و هكذا فهنلاحظ
+
+390
+00:42:17,520 --> 00:42:24,700
+ان الاتنين اتنين upper bound لان هو هيكون اكبر
+
+391
+00:42:24,700 --> 00:42:31,100
+عنصر و ينتبه للست لو في اي upper bound تاني لو في
+
+392
+00:42:31,100 --> 00:42:33,320
+any upper bound
+
+393
+00:42:37,830 --> 00:42:45,630
+of S4 فهذا بيقدي انه اتنين اصغر من او ساوي ال V
+
+394
+00:42:45,630 --> 00:42:50,890
+لانه اتنين عنصر في الست S4 صح؟ اذا اتنين upper
+
+395
+00:42:50,890 --> 00:42:54,810
+bound واضح انه اتنين اكبر من او ساوي كل عناصر S4
+
+396
+00:42:54,810 --> 00:43:04,320
+صح؟ولو أخدت أي upper bound ل S4 فبما أن V هو upper
+
+397
+00:43:04,320 --> 00:43:09,200
+bound ل S4 واتنين عنصر في S4 إذن اتنين أصغر من أو
+
+398
+00:43:09,200 --> 00:43:14,640
+يساوي V إذن هنا أثبتنا أن اتنين upper bound ل S4
+
+399
+00:43:14,640 --> 00:43:19,500
+واتنين أصغر من أو يساوي أي upper bound ل S4 إذن
+
+400
+00:43:19,500 --> 00:43:23,440
+اتنين هو ال supreme بالمثل ممكن نثبت أن النص هو
+
+401
+00:43:23,440 --> 00:43:28,140
+الانفع إذن هذا برهان تانيانا اتعمد تعطيكم البرهان
+
+402
+00:43:28,140 --> 00:43:32,260
+هذا عشان القوانين هذه نشوف كيف نطبقها برضه هذا
+
+403
+00:43:32,260 --> 00:43:38,520
+برهان صعيب ناجح الحل؟ okay؟
+
+404
+00:43:38,520 --> 00:43:42,080
+في اي سؤال او استفسار؟ اذا احنا هنكتفي بهذا القدر
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_mc9oZHzNxs.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_mc9oZHzNxs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2480bd8dfbdbf09a22aa4a2bce2014e9b341f3c3
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/_mc9oZHzNxs.srt
@@ -0,0 +1,1231 @@
+1
+00:00:20,670 --> 00:00:27,570
+بسم الله الرحمن الرحيم و السلام عليكم هنكمل
+
+2
+00:00:27,570 --> 00:00:33,570
+إن شاء الله اليوم الـ .. المثال رقم اثنين اللي
+
+3
+00:00:33,570 --> 00:00:39,530
+بدأناه في المحاضرة السابقة و ما كملناهوش فنرجعوا مع
+
+4
+00:00:39,530 --> 00:00:48,020
+بعض بسرعة و نحاول نكمل البرهان لهذا المثال وهو أن
+
+5
+00:00:48,020 --> 00:00:53,900
+الـ sequence المعرفة بطريقة استقرائية هنا بنثبت
+
+6
+00:00:53,900 --> 00:00:58,560
+أنها convergent والـ limit تبعتها بيساوي العدد
+
+7
+00:00:58,560 --> 00:01:04,700
+خمسة على ثلاثة تمام فبدأنا البرهان المرة اللي فاتت
+
+8
+00:01:04,700 --> 00:01:11,900
+و أثبتنا claim .. claim واحد و كان في الـ claim هذا
+
+9
+00:01:11,900 --> 00:01:13,680
+أثبتنا أن الـ
+
+10
+00:01:17,150 --> 00:01:22,690
+إن حدود الـ sequence bounded below by one and
+
+11
+00:01:22,690 --> 00:01:29,450
+bounded above by two هذا صحيح لكل n وشوفنا هذا
+
+12
+00:01:29,450 --> 00:01:36,570
+البر هان هذا ممكن يعني ممكن إعطاءه by induction
+
+13
+00:01:36,570 --> 00:01:41,450
+therefore by claim one
+
+14
+00:01:45,770 --> 00:01:52,510
+السيكوانس xn is bounded واضح من الـ claim أن
+
+15
+00:01:52,510 --> 00:01:59,230
+السيكوانس is bounded المرة التي اثبتنا claim رقم 2
+
+16
+00:01:59,230 --> 00:02:03,470
+أثبتنا 
+
+17
+00:02:03,470 --> 00:02:07,470
+أن السيكوانس
+
+18
+00:02:07,470 --> 00:02:15,960
+xn بتحقق المعادلة absolute xn minus xn زائد واحد
+
+19
+00:02:15,960 --> 00:02:22,960
+هذا بيساوي واحد على اثنين أس n negative one for
+
+20
+00:02:22,960 --> 00:02:30,360
+every natural number n وشوفنا برهنة المعادلة
+
+21
+00:02:30,360 --> 00:02:36,020
+هذه أو العبارة هذه لكل عدد طبيعي by induction okay
+
+22
+00:02:38,610 --> 00:02:45,630
+اليوم باستخدام الـ claim 2 and
+
+23
+00:02:45,630 --> 00:02:51,330
+triangle
+
+24
+00:02:51,330 --> 00:03:01,490
+inequality متباينة المثلث نرى
+
+25
+00:03:01,490 --> 00:03:02,070
+أن
+
+26
+00:03:05,510 --> 00:03:16,950
+وإذا m أكبر من n، m و n أعداد طبيعية، و m أكبر من n،
+
+27
+00:03:16,950 --> 00:03:23,190
+فلدينا x m أكبر من x n
+
+28
+00:03:29,470 --> 00:03:35,150
+طبعًا هذا ممكن نكتبه على صورة هي absolute xn هطرح 
+
+29
+00:03:35,150 --> 00:03:43,230
+xn زائد واحد و أرجعها و
+
+30
+00:03:43,230 --> 00:03:55,190
+هطرح xn زائد اثنين و أرجعها و
+
+31
+00:03:55,190 --> 00:03:58,250
+هكذا إلى أن أصل إلى
+
+32
+00:04:03,240 --> 00:04:13,220
+x m negative one سالب x m في الآخر خالص هأطرح x m
+
+33
+00:04:13,220 --> 00:04:19,960
+سالب واحد و أرجعها فكأني أنا يعني ما عملتش ما غيرتش
+
+34
+00:04:19,960 --> 00:04:24,600
+حاجة فالمخضر اللي على اليمين هو نفسه اللي على
+
+35
+00:04:24,600 --> 00:04:30,360
+الشمال لأن طرحت و أضفت طرحت و أضفت كذلك
+
+36
+00:04:30,360 --> 00:04:36,550
+فكأني أضفت صفر الآن نأخذ الحدين هذول مع بعض و هذول
+
+37
+00:04:36,550 --> 00:04:47,810
+مع بعض و هكذا و هذول مع بعض و هذول آخر حدين مع بعض
+
+38
+00:04:47,810 --> 00:04:54,110
+و بنستخدم الـ triangle inequality فـ by triangle
+
+39
+00:04:54,110 --> 00:05:00,330
+inequality الـ absolute value لمجموعة Less than or
+
+40
+00:05:00,330 --> 00:05:06,890
+equal مجموع الـ absolute values فهذا absolute xn
+
+41
+00:05:06,890 --> 00:05:12,850
+minus xn زائد واحد زائد absolute xn زائد واحد minus
+
+42
+00:05:12,850 --> 00:05:21,510
+xn زائد اثنين وهكذا
+
+43
+00:05:21,510 --> 00:05:27,170
+إلى absolute xm negative one minus xm
+
+44
+00:05:30,780 --> 00:05:37,120
+الآن باستخدام claim اثنين الحد الأول هذا عبارة عن
+
+45
+00:05:37,120 --> 00:05:44,100
+واحد على two أس n negative one الحد اللي بعده one
+
+46
+00:05:44,100 --> 00:05:53,000
+over two أس n والحد اللي بعده هكذا و
+
+47
+00:05:53,000 --> 00:06:03,820
+الحد الأخير الحد الأخير هذا هيكون واحد على two أس m
+
+48
+00:06:03,820 --> 00:06:07,580
+ماينص 
+
+49
+00:06:07,580 --> 00:06:14,460
+اثنين إذا 
+
+50
+00:06:14,460 --> 00:06:21,040
+هذا من المعادلة اللي هنا نأخذ
+
+51
+00:06:21,040 --> 00:06:33,760
+عامل مشترك one over two أس n negative one فبيبقى
+
+52
+00:06:33,760 --> 00:06:38,000
+إذا من الحد الأول دي بقى اللي عندي واحد من الحد
+
+53
+00:06:38,000 --> 00:06:46,740
+الثاني بيبقى عندي نصف وهكذا إلى الحد الأخير اللي
+
+54
+00:06:46,740 --> 00:06:56,120
+بيبقى عندي two أس m negative n negative one الآن
+
+55
+00:06:56,120 --> 00:07:01,080
+المجموعة هذا اللي بين قوسين هذا المجموعة أصغر من
+
+56
+00:07:01,080 --> 00:07:06,220
+اثنين لأن هذا المجموع لاحظوا
+
+57
+00:07:06,220 --> 00:07:16,080
+أنتوا واحد زائد نصف زائد إلى one over two to m
+
+58
+00:07:16,080 --> 00:07:23,020
+negative n negative one this is less than one زائد
+
+59
+00:07:23,020 --> 00:07:25,600
+نصف زائد
+
+60
+00:07:29,510 --> 00:07:37,230
+زائد واحد على اثنين أس n زائد إلى ما لا نهاية
+
+61
+00:07:37,230 --> 00:07:44,610
+اللي هو مجموع series sigma from k equals zero to
+
+62
+00:07:44,610 --> 00:07:54,430
+infinity الـ one over two to k هذا
+
+63
+00:07:54,430 --> 00:07:58,010
+جزء من الـ infinite series
+
+64
+00:08:00,560 --> 00:08:07,300
+هذه الـ infinite series هذه أول يعني m سالب n
+
+65
+00:08:07,300 --> 00:08:12,700
+ناقص واحد من حدودها هذه
+
+66
+00:08:12,700 --> 00:08:17,380
+الـ series معروفة هي geometric series geometric
+
+67
+00:08:17,380 --> 00:08:25,320
+series with a الحد الأول واحد والـ ratio r والـ
+
+68
+00:08:25,320 --> 00:08:31,860
+ratio بيساوي نصف في تفاضل بقى تعلمتوا أنه أي
+
+69
+00:08:31,860 --> 00:08:35,200
+geometric series إذا الـ ratio الـ absolute value لـ
+
+70
+00:08:35,200 --> 00:08:40,940
+r أصغر من واحد فالـ series تطلع convergent ومجموع
+
+71
+00:08:40,940 --> 00:08:48,520
+.. مجموع بيساوي a على one minus الأساس وهذا بطلع a
+
+72
+00:08:48,520 --> 00:08:53,720
+اللي هو واحد على واحد ناقص الأساس نصف بطلع بيساوي
+
+73
+00:08:53,720 --> 00:08:57,060
+اثنين okay إذا الـ ..
+
+74
+00:09:00,710 --> 00:09:07,850
+إذا المجموع هذا بيطلع أصغر من اثنين إذا هي حاول
+
+75
+00:09:07,850 --> 00:09:14,690
+أصغر من واحد على اثنين أس n negative واحد ضرب اثنين
+
+76
+00:09:14,690 --> 00:09:25,210
+وهذا بيساوي واحد على اثنين أس n سالب اثنين تمام؟
+
+77
+00:09:36,740 --> 00:09:42,940
+الآن بنا نثبت احنا أن الـ sequence
+
+78
+00:09:42,940 --> 00:09:48,860
+احنا كان بنا نثبت أن الـ sequence xn convergent
+
+79
+00:09:48,860 --> 00:09:52,820
+و قلنا في بداية البرهان المرة اللي فاتت عشان نثبت
+
+80
+00:09:52,820 --> 00:09:57,380
+أنها convergent يكفي أن احنا نثبت أنها Cauchy صح؟
+
+81
+00:09:57,380 --> 00:10:01,400
+لأن إذا كانت Cauchy بتكون convergent by Cauchy's
+
+82
+00:10:01,400 --> 00:10:03,920
+criterion إذا هنا to show
+
+83
+00:10:08,040 --> 00:10:13,900
+إن xn convergent it
+
+84
+00:10:13,900 --> 00:10:18,100
+suffices يعني 
+
+85
+00:10:18,100 --> 00:10:29,100
+يكفي إثبات to show it is Cauchy إذا يكفي إثبات
+
+86
+00:10:29,100 --> 00:10:36,510
+أنها Cauchy طيب هاي عندي .. الآن هأستفيد من المتباينة
+
+87
+00:10:36,510 --> 00:10:45,890
+هذه الأخيرة لإثبات إنها كوشي طيب
+
+88
+00:10:45,890 --> 00:10:54,790
+أنا عندي .. أنا عندي for .. قلنا m أكبر من n
+
+89
+00:10:57,610 --> 00:11:04,270
+أثبتنا أن absolute xn نيجاتيف xm less than one over
+
+90
+00:11:04,270 --> 00:11:16,970
+two to n minus two نسمي الانيقواليتي هذه star الآن
+
+91
+00:11:16,970 --> 00:11:21,010
+let
+
+92
+00:11:21,010 --> 00:11:28,960
+epsilon أكبر من الصفر be given أنا بدأ أُثبت إن الـ
+
+93
+00:11:28,960 --> 00:11:32,980
+sequence تبعتي كوشي فعشان أُثبت إنها كوشي ببدأ
+
+94
+00:11:32,980 --> 00:11:38,840
+بإمسون أكبر من صفر برد عليها بـ capital N بحيث إنه
+
+95
+00:11:38,840 --> 00:11:44,280
+لكل m و n أكبر من أو يساوي capital N لازم المسافة
+
+96
+00:11:44,280 --> 00:11:50,000
+بين xn و xm أصغر من epsilon فـ let epsilon أكبر من الصفر
+
+97
+00:11:50,000 --> 00:11:59,040
+be given by Archimedean property من خاصية
+
+98
+00:11:59,040 --> 00:12:08,700
+Archimedes choose ممكن نختار capital N عدد طبيعي
+
+99
+00:12:08,700 --> 00:12:19,020
+بحيث أنه واحد على n أصغر من epsilon على أربعة وهذا
+
+100
+00:12:19,020 --> 00:12:23,440
+صحيح by the Archimedean property epsilon عدد موجب
+
+101
+00:12:23,440 --> 00:12:26,920
+بتعني epsilon على أربعة عدد موجب لهذا العدد الموجب
+
+102
+00:12:26,920 --> 00:12:31,740
+بقدر ألاقي عدد طبيعي عدد طبيعي مقلوبه وأصغر من العدد
+
+103
+00:12:31,740 --> 00:12:44,060
+الموجب تمام؟ وبالتالي هذا بيقدر أنه الـ .. واحد على 
+
+104
+00:12:44,060 --> 00:12:52,020
+two to n أصغر من epsilon على أربعة لأن
+
+105
+00:12:52,020 --> 00:13:02,640
+since لأن two to n أكبر من n صح؟ وبالتالي مقلوب
+
+106
+00:13:02,640 --> 00:13:07,560
+هذا أصغر من مقلوب الـ n اللي هو أصغر من epsilon على 
+
+107
+00:13:07,560 --> 00:13:10,720
+أربعة okay تمام؟ طيب
+
+108
+00:13:14,350 --> 00:13:25,310
+إذن this .. this and star بيؤدوا إنه لو كان m أكبر 
+
+109
+00:13:25,310 --> 00:13:30,450
+من أو يساوي n أكبر من أو يساوي capital N فهذا
+
+110
+00:13:30,450 --> 00:13:40,050
+بيؤدي إنه absolute xn negative xm أصغر
+
+111
+00:13:40,050 --> 00:13:51,740
+من 1 على 2 to n minus 2 وهذا أصغر من أو يساوي 1 على
+
+112
+00:13:51,740 --> 00:13:58,200
+2 to capital N minus 2 لأن small n أكبر من أو يساوي
+
+113
+00:13:58,200 --> 00:14:04,700
+capital N فـ 2
+
+114
+00:14:04,700 --> 00:14:11,200
+n سالب 2 أصغر يعني مقلوب هذه يعني أنا عندي هنا
+
+115
+00:14:11,200 --> 00:14:16,460
+اثنين أس n سالب اثنين بطلع أكبر من أو يساوي two
+
+116
+00:14:16,460 --> 00:14:21,340
+to capital N سالب اثنين لأن n أكبر من أو يساوي
+
+117
+00:14:21,340 --> 00:14:25,200
+capital N وبالتالي مقلوب الكبير أصغر من أو يساوي
+
+118
+00:14:25,200 --> 00:14:35,420
+مقلوب الكبير أو مقلوب الصغير فهذا صح ومن هنا هذا
+
+119
+00:14:35,420 --> 00:14:39,280
+أصغر هذا من هنا أصغر من epsilon
+
+120
+00:14:42,800 --> 00:14:48,200
+لأن هذا عبارة عن .. هذا بيساوي .. أيوه بيساوي أربعة
+
+121
+00:14:48,200 --> 00:14:53,500
+على اثنين أس n وأربعة على اثنين أس n أصغر من
+
+122
+00:14:53,500 --> 00:15:01,740
+epsilon، صح؟ إذن هذه أثبتت for any given .. for any
+
+123
+00:15:01,740 --> 00:15:06,700
+given epsilon يوجد capital N يعتمد على epsilon، هذا
+
+124
+00:15:06,700 --> 00:15:15,590
+هو يوجد capital N غير مرتبط بـ epsilon بحيث أنه لكل m و n
+
+125
+00:15:15,590 --> 00:15:20,350
+أكبر من أو يساوي capital N فالمسافة بين xn و xm
+
+126
+00:15:20,350 --> 00:15:26,650
+أصغر من epsilon وبالتالي هذا بيثبت أن الـ sequence is
+
+127
+00:15:26,650 --> 00:15:36,270
+Cauchy بس الـ sequence xn is Cauchy
+
+128
+00:15:39,020 --> 00:15:43,660
+and therefore x
+
+129
+00:15:43,660 --> 00:15:50,900
+n converges say
+
+130
+00:15:50,900 --> 00:16:02,740
+الـ limit لـ xn بيساوي some x ينتمي إلى r هنا
+
+131
+00:16:02,740 --> 00:16:08,130
+أثبتنا أن الـ sequence xn convergent by Cauchy
+
+132
+00:16:08,130 --> 00:16:13,790
+criterion وفرضنا أن الـ limit تبعتها بيساوي x عشان
+
+133
+00:16:13,790 --> 00:16:15,870
+كام؟ إذا هنثبت أن الـ sequence تبعتنا
+
+134
+00:16:15,870 --> 00:16:20,070
+convergent الـ limit تبعتها عدد x بقى هنثبت أن الـ
+
+135
+00:16:20,070 --> 00:16:25,790
+x اللي هو limit لـ xn بيساوي خمسة على ثلاثة بيساوي
+
+136
+00:16:25,790 --> 00:16:29,350
+خمسة على ثلاثة okay إذا هنثبت
+
+137
+00:16:34,190 --> 00:16:42,010
+الجزء الأخير هذا وهو نسميه 
+
+138
+00:16:42,010 --> 00:16:50,790
+claim ثلاثة claim three الـ x بيساوي five over three
+
+139
+00:16:50,790 --> 00:17:00,130
+لبرهان ذلك first
+
+140
+00:17:03,450 --> 00:17:08,530
+use induction on 
+
+141
+00:17:08,530 --> 00:17:20,170
+to show الإثبات أن x to n plus one يساوي واحد 
+
+142
+00:17:20,170 --> 00:17:28,610
+زائد نصف زائد واحد على اثنين تكعيب زائد وهكذا one
+
+143
+00:17:28,610 --> 00:17:35,410
+over two to the power of 2n سالب واحد وهذا صحيح لكل natural
+
+144
+00:17:35,410 --> 00:17:42,910
+number n المعادلة هذه ممكن إثباتها by induction on
+
+145
+00:17:42,910 --> 00:17:54,130
+n سهل جدا طبعا ممكن تستخدم .. تحتاج الـ inductive
+
+146
+00:17:54,130 --> 00:17:59,300
+definition في البرهان زي ما شفنا في برهان claim 2
+
+147
+00:17:59,300 --> 00:18:08,440
+طيب الآن افترض أن احنا هذا أثبتناها hence وبالتالي
+
+148
+00:18:08,440 --> 00:18:15,500
+من هنا بيطلع عندي x to the power of 2n plus one يساوي واحد زائد هاخد
+
+149
+00:18:15,500 --> 00:18:21,820
+من المجموع هذا هاخد
+
+150
+00:18:21,820 --> 00:18:28,200
+نصف عامل مشترك فبيبقى عندي واحد زائد واحد على اثنين
+
+151
+00:18:28,200 --> 00:18:36,880
+تربيع زائد واحد على اثنين تربيع لكل تربيع زائد و
+
+152
+00:18:36,880 --> 00:18:44,260
+هكذا زائد واحد على اثنين تربيع to the power of n سالب واحد
+
+153
+00:18:44,260 --> 00:18:52,220
+إذا أنا اخدت من هاي الواحد نزلته واخدت نصف عامل
+
+154
+00:18:52,220 --> 00:18:57,320
+مشترك من باقي الحدود هذه فطلع عندي المجموع هذا هذا
+
+155
+00:18:57,320 --> 00:19:04,120
+مجموع متوالية هندسية geometric progression لأن هذا
+
+156
+00:19:04,120 --> 00:19:08,080
+بشكل geometric
+
+157
+00:19:08,080 --> 00:19:19,740
+.. geometric progression متوالية
+
+158
+00:19:19,740 --> 00:19:20,480
+هندسية
+
+159
+00:19:23,660 --> 00:19:30,740
+with الحد الأول a يساوي واحد والـ ratio يساوي واحد
+
+160
+00:19:30,740 --> 00:19:37,080
+على اثنين تربيع اللي هو ربعها فـ الـ geometric
+
+161
+00:19:37,080 --> 00:19:40,820
+progression فيه قانون لإيجاد مجموع المتوالية
+
+162
+00:19:40,820 --> 00:19:46,080
+الهندسية فيه قانون لإيجاد مجموع فالقانون هذا
+
+163
+00:19:46,080 --> 00:19:54,830
+عبارة عن الحد الأول واحد سالب الحد الأخير مضروب في
+
+164
+00:19:54,830 --> 00:20:02,650
+الأساس اللي هو واحد على اثنين تربيع الكل قسم على
+
+165
+00:20:02,650 --> 00:20:08,150
+واحد minus الأساس على واحد minus الأساس اللي هو
+
+166
+00:20:08,150 --> 00:20:14,270
+واحد على اثنين تربيع وهذا
+
+167
+00:20:14,270 --> 00:20:22,130
+يساوي اي واحد زائد المقام هذا عبارة عن ثلاثة أرباع
+
+168
+00:20:23,720 --> 00:20:32,140
+هذا عبارة عن ثلاثة أرباع فنصف على ثلاثة أرباع بيطلع
+
+169
+00:20:32,140 --> 00:20:37,180
+اثنين على ثلاثة والـ bust هذا هو في الـ bust اللي
+
+170
+00:20:37,180 --> 00:20:45,520
+هو واحد سالب واحد على اثنين اس اثنين in او اربعة
+
+171
+00:20:45,520 --> 00:20:47,440
+اس in
+
+172
+00:20:52,700 --> 00:21:08,740
+الآن نأخذ الـ limit للطرفين إذا
+
+173
+00:21:08,740 --> 00:21:14,380
+نأخذ .. لو أخذنا الـ limit للطرفين فبيطلع limit x to
+
+174
+00:21:14,380 --> 00:21:20,800
+n plus one as n tends to infinity يساوي واحد زائد
+
+175
+00:21:20,800 --> 00:21:28,040
+اثنين على الثلاثة في الـ limit الجوس واحد سالب
+
+176
+00:21:28,040 --> 00:21:34,720
+limit واحد على أربعة اس in as n tends to infinity
+
+177
+00:21:34,720 --> 00:21:41,640
+وهذا يساوي واحد زائد اثنين على ثلاثة في واحد سالب
+
+178
+00:21:41,640 --> 00:21:48,440
+limit واحد على أربعة اس n يساوي صفر فبيطلع يساوي واحد
+
+179
+00:21:50,170 --> 00:21:57,150
+زائد اثنين على ثلاثة يساوي خمسة على ثلاثة طيب
+
+180
+00:21:57,150 --> 00:22:01,070
+هذه عبارة عن sub sequence من الـ sequence xn هذه
+
+181
+00:22:01,070 --> 00:22:05,930
+الحدود الفردية لـ sequence xn طيب و أنا عندي الـ
+
+182
+00:22:05,930 --> 00:22:09,750
+sequence تبعتي convergent هاي أثبتنا أن xn
+
+183
+00:22:09,750 --> 00:22:13,930
+convergent والـ limit تبعتها يساوي العدد x
+
+184
+00:22:20,160 --> 00:22:26,000
+إذا أنا في عندي هنا since x2n
+
+185
+00:22:26,000 --> 00:22:38,600
+plus one is a subsequence of a sequence xn و xn
+
+186
+00:22:38,600 --> 00:22:45,540
+converges to x then by previous theorem حسب نظرية
+
+187
+00:22:45,540 --> 00:22:50,120
+السابقة إذا كانت الـ sequence convergent لـ x فأي
+
+188
+00:22:50,120 --> 00:22:54,960
+subsequence منها بتكون convergent لنفس الـ x إذا
+
+189
+00:22:54,960 --> 00:23:01,460
+limit x اتنين n plus one as n tends to infinity
+
+190
+00:23:01,460 --> 00:23:07,640
+يساوي x وبالتالي إذا x يساوي limit
+
+191
+00:23:12,130 --> 00:23:19,830
+x2n زائد واحد وهذه أثبتنا في السطر الأخير هنا هذه
+
+192
+00:23:19,830 --> 00:23:23,750
+يساوي خمسة على ثلاثة وهذا اللي بدنا يعني إذا هيك
+
+193
+00:23:23,750 --> 00:23:30,770
+بتكون أثبتنا أن الـ sequence x in converges to x و
+
+194
+00:23:30,770 --> 00:23:36,370
+limit x تبعتها هي طلعت يساوي خمسة على ثلاثة كما هو
+
+195
+00:23:36,370 --> 00:23:41,830
+مطلوب Okay إذا هيك بنكون إحنا برهنا إن الـ sequence
+
+196
+00:23:41,830 --> 00:23:46,490
+في المثال هذا اللي معرفة بطريقة استقرائية is
+
+197
+00:23:46,490 --> 00:23:52,870
+convergent ونهايتها خمسة على ثلاثة Okay تمام؟ المفهوم
+
+198
+00:23:52,870 --> 00:23:59,680
+واضح؟ في أي استفسار؟ في أي سؤال؟ طيب نأخذ كمان مثال
+
+199
+00:23:59,680 --> 00:24:02,520
+يمكن يبقى المثال طويل شوية لكن احنا زي ما شفنا
+
+200
+00:24:02,520 --> 00:24:08,660
+احنا جزأناه إلى ثلاثة claims أو three claims وكل
+
+201
+00:24:08,660 --> 00:24:12,340
+claim كان برهانه by induction مش صعب شفنا برهان
+
+202
+00:24:12,340 --> 00:24:18,020
+واحد منهم المرة اللي فاتت التانيين برضه اسأل كمان
+
+203
+00:24:18,020 --> 00:24:23,060
+كل claim بيخطو خطوة إلى الامام بيجرّبني أكثر من
+
+204
+00:24:23,060 --> 00:24:23,540
+البرهان
+
+205
+00:24:27,870 --> 00:24:45,850
+نأخذ مثال آخر، ثالث إذا
+
+206
+00:24:45,850 --> 00:24:54,090
+example three consider
+
+207
+00:24:57,250 --> 00:25:02,550
+الحد العام بحيث الـ sequence xn
+
+208
+00:25:02,550 --> 00:25:09,510
+where حيث الـ term of the sequence الحد العام by
+
+209
+00:25:09,510 --> 00:25:14,070
+definition يساوي one over one plus one over two
+
+210
+00:25:15,270 --> 00:25:22,310
+plus one over three وهكذا and so on until we get
+
+211
+00:25:22,310 --> 00:25:31,730
+one over N حيث N ينتمي إلى N لكل N في N بنعرف XN
+
+212
+00:25:31,730 --> 00:25:36,530
+على أنه المجموع أو مجموعة أول N
+
+213
+00:25:49,690 --> 00:25:57,950
+مجموع أول n من حدود الـ harmonic series فهذا بنسميه
+
+214
+00:25:57,950 --> 00:26:02,210
+الـ nth partial sum هذا عبارة في تفاضل باسم منها الـ
+
+215
+00:26:02,210 --> 00:26:14,410
+nth partial الـ nth partial sum of الـ harmonic الـ
+
+216
+00:26:14,410 --> 00:26:16,110
+harmonic series
+
+217
+00:26:20,920 --> 00:26:26,800
+اللي هي summation from k equals one to infinity لـ
+
+218
+00:26:26,800 --> 00:26:27,880
+one over k
+
+219
+00:26:31,950 --> 00:26:39,910
+المطلوب show أن سيكوينس XN divergence ليست
+
+220
+00:26:39,910 --> 00:26:46,070
+convergent، is not convergent بنثبت أن سيكوينس of
+
+221
+00:26:46,070 --> 00:26:51,090
+partial sums متتالية المجاميع الجزئية للـ harmonic
+
+222
+00:26:51,090 --> 00:26:54,070
+series بتشكل divergence sequence
+
+223
+00:27:00,340 --> 00:27:19,020
+by Cauchy criterion إذا حسب Cauchy criterion by
+
+224
+00:27:19,020 --> 00:27:25,740
+Cauchy criterion it suffices to
+
+225
+00:27:25,740 --> 00:27:32,760
+show يكفي إثبات يكفي إثبات أن الـ sequence عشان نثبت
+
+226
+00:27:32,760 --> 00:27:36,440
+أن الـ sequence is divergent it suffices to show أن
+
+227
+00:27:36,440 --> 00:27:47,920
+الـ sequence xn is not كوشي لأن
+
+228
+00:27:47,920 --> 00:27:52,980
+كوشي criterion بتقول أن الـ sequence is convergent
+
+229
+00:27:52,980 --> 00:27:58,700
+if and only if it is كوشي وبالتالي هذا بكفي أن
+
+230
+00:27:58,700 --> 00:28:02,400
+احنا نقول أن الـ sequence is not convergent if and
+
+231
+00:28:02,400 --> 00:28:06,440
+only if it is not Cauchy عشان نثبت أن الـ sequence
+
+232
+00:28:06,440 --> 00:28:12,780
+is divergent ممكن نثبت أنها is not Cauchy طيب الـ
+
+233
+00:28:12,780 --> 00:28:22,900
+.. الإثبات أنها not Cauchy هنستخدم indeed
+
+234
+00:28:29,180 --> 00:28:41,120
+في حقيقة الأمر لو أخذنا لو كان M أكبر من N فهذا
+
+235
+00:28:41,120 --> 00:28:48,320
+بيقدي أن XM minus
+
+236
+00:28:48,320 --> 00:28:53,660
+XN ايش يساوي؟
+
+237
+00:28:53,660 --> 00:28:55,500
+أنا هي عندي الـ ..
+
+238
+00:29:06,360 --> 00:29:18,240
+هي عندي xn ولو بدك تكتب xm فـ xm هيكون يساوي واحد
+
+239
+00:29:18,240 --> 00:29:25,640
+أول حد زائد نصف زائد
+
+240
+00:29:25,640 --> 00:29:33,140
+ثلت وهكذا زائد
+
+241
+00:29:33,140 --> 00:29:40,460
+واحد على n ولسه كمان هكمل .. هنكمل لأن الـ M أكبر
+
+242
+00:29:40,460 --> 00:29:49,380
+من N هنا الـ M .. الـ M أكبر من N لما تكون M أكبر من
+
+243
+00:29:49,380 --> 00:29:55,640
+N فهيكون الحد اللي بعدها ده واحد على M زائد واحد
+
+244
+00:30:04,780 --> 00:30:10,120
+واحد على الـ n أنا
+
+245
+00:30:10,120 --> 00:30:19,580
+مش نافع one
+
+246
+00:30:19,580 --> 00:30:29,190
+over n plus one وهكذا إلى one over m الآن لما أطرح
+
+247
+00:30:29,190 --> 00:30:37,890
+xn من xm فالحدود المتشابهة هتروح مع بعضها لحد واحد
+
+248
+00:30:37,890 --> 00:30:44,690
+على n بيروح مع واحد على n بيبقى الفرق بين الاثنين
+
+249
+00:30:44,690 --> 00:30:54,930
+الفرق بين الاثنين هيكون عبارة عن واحد
+
+250
+00:30:56,990 --> 00:31:04,630
+على n زائد واحد زائد واحد على n plus two and so on
+
+251
+00:31:04,630 --> 00:31:12,230
+until we get one over m تمام الحدود هدول عددهم كم
+
+252
+00:31:12,230 --> 00:31:23,270
+حد m negative n terms عدد الحدود في المجموع هذا m
+
+253
+00:31:23,270 --> 00:31:37,060
+سالب n هذول حدود عددهم M وهذول عددهم N فالفرق
+
+254
+00:31:37,060 --> 00:31:43,460
+بينهم هيطلع M سالب N الآن
+
+255
+00:31:43,460 --> 00:31:46,700
+هذا المجموع أول حد
+
+256
+00:31:49,570 --> 00:31:57,510
+لاحظوا أن أن الـ M أكبر من N هذا بيقدي أن M أكبر من
+
+257
+00:31:57,510 --> 00:32:04,230
+أو يساوي N زي واحد وهذا بيقدي أن مخلوق واحد على N
+
+258
+00:32:04,230 --> 00:32:10,210
+زي واحد بيطلع أكبر من أو يساوي واحد على N
+
+259
+00:32:13,150 --> 00:32:17,850
+وبالتالي إذا واحد على N زائد واحد أكبر من أو يساوي
+
+260
+00:32:17,850 --> 00:32:22,850
+واحد على M بالمثل واحد على N زائد اثنين لحظة هيكون
+
+261
+00:32:22,850 --> 00:32:29,570
+الـ M الـ M أكبر من أو يساوي N زائد اثنين فمقلوب N زائد
+
+262
+00:32:29,570 --> 00:32:37,230
+اثنين هيطلع أكبر من أو يساوي واحد على M وهكذا إذا
+
+263
+00:32:37,230 --> 00:32:41,670
+كل الحدود هذه كل واحد فيهم أكبر من أو يساوي واحد
+
+264
+00:32:41,670 --> 00:32:46,070
+على M إلى أن نصل لآخر حد واحد على M طبعا أكبر من
+
+265
+00:32:46,070 --> 00:32:51,070
+أو يساوي نفسه عدد الحدود هذه لازال M سالب n
+
+266
+00:32:51,070 --> 00:32:51,810
+terms
+
+267
+00:32:55,640 --> 00:33:00,980
+طيب أنا لما بجمع عدد على نفسه M سالب N من المرات،
+
+268
+00:33:00,980 --> 00:33:06,200
+ايه بيعطيني المجموعة؟ بيطلع يساوي M سالب N في
+
+269
+00:33:06,200 --> 00:33:08,540
+العدد الثابت، صح؟
+
+270
+00:33:14,860 --> 00:33:21,620
+إذن المجموعة الأخيرة هذا هيطلع يساوي M سالب N
+
+271
+00:33:21,620 --> 00:33:30,660
+في واحد على M وهذا يساوي على
+
+272
+00:33:30,660 --> 00:33:40,520
+M هذي آه M وهذا يساوي واحد سالب N على M طيب
+
+273
+00:33:40,520 --> 00:33:48,050
+أنا في التحليل هذا أخدت الـ M أكبر من N يعني هذا
+
+274
+00:33:48,050 --> 00:33:54,670
+الكلام صحيح إذا كان M أكبر من N طيب الآن take M
+
+275
+00:33:54,670 --> 00:34:00,230
+يساوي 2N بالتأكيد 2N أي عدد طبيعي N لأي عدد طبيعي
+
+276
+00:34:00,230 --> 00:34:08,890
+N 2N أكبر من N إذا لو عوضت عن M باثنين N في المتباينة
+
+277
+00:34:08,890 --> 00:34:18,610
+الأخيرة هذه هيطلع عندي XM أو X to N سالب XN
+
+278
+00:34:18,610 --> 00:34:28,670
+بتطلع أكبر من أو يساوي واحد سالب اثنين N على
+
+279
+00:34:28,670 --> 00:34:35,450
+اثنين N صح؟ اللي هو واحد سالب نصف بيطلع one
+
+280
+00:34:35,450 --> 00:34:45,930
+-half نصف الكلام هذا صحيح لكل n ينتمي 
+
+281
+00:34:45,930 --> 00:34:50,470
+إلى n تمام؟
+
+282
+00:34:52,310 --> 00:34:58,910
+إذا أنا أصبح في عندي المتباينة x to the n negative xn
+
+283
+00:34:58,910 --> 00:35:06,750
+أكبر من أو يساوي one half for all n belong to a now
+
+284
+00:35:06,750 --> 00:35:14,710
+you can easily show
+
+285
+00:35:19,500 --> 00:35:28,860
+ممكن بسهولة إثبات أن this implies المتباينة هذه
+
+286
+00:35:28,860 --> 00:35:37,540
+الأخيرة بتقدي this implies that
+
+287
+00:35:37,540 --> 00:35:43,620
+هذا بيقدي أن ال sequence xn is not Cauchy
+
+288
+00:35:46,720 --> 00:36:01,500
+is not Cauchy as desired كما هو مطلوب تمام؟
+
+289
+00:36:01,500 --> 00:36:07,220
+من المتباينة هذه ممكن نثبت أن ال sequence تبعتنا
+
+290
+00:36:07,220 --> 00:36:12,820
+ليست Cauchy، يمكن هذا مش واضح كيف أن هذا بيعدي أن ال
+
+291
+00:36:12,820 --> 00:36:17,520
+sequence not Cauchy، لكن ممكن نعمل برهان بالتناقض
+
+292
+00:36:17,520 --> 00:36:22,680
+افرض أن ال sequence Cauchy واستخدم الشرط هذا أو
+
+293
+00:36:22,680 --> 00:36:26,700
+المتباينة هذه في الوصول إلى تناقض، هسه لكم تكتبوا 
+
+294
+00:36:26,700 --> 00:36:30,580
+البرهان هذا، وكل واحدة بتكتب البرهان في ورقة
+
+295
+00:36:30,580 --> 00:36:35,840
+وبتسلميها في الأيام القادمة، هتاخد علامتين يضافوا
+
+296
+00:36:35,840 --> 00:36:43,000
+لامتحان، علامة امتحان النص فيه الأول، Okay تمام فال
+
+297
+00:36:43,000 --> 00:36:43,360
+..
+
+298
+00:36:55,700 --> 00:37:00,340
+إذن باقي إثبات إن عشان البرهان يكون كامل إنه يثبت
+
+299
+00:37:00,340 --> 00:37:04,460
+إن المتباينة الأخيرة هذه بتأدي إن ال sequence
+
+300
+00:37:04,460 --> 00:37:12,840
+بتاعتنا لا تكون Cauchy، فأنا بقول إذا حابين ممكن إنكم
+
+301
+00:37:12,840 --> 00:37:19,620
+تكتبوا البرهان على ورقة خارجية وتعطوني، إذا برهانكم
+
+302
+00:37:19,620 --> 00:37:23,400
+بيكون صح، بعطيه لكم علامتين يضافوا إلى امتحان النصف
+
+303
+00:37:23,400 --> 00:37:31,150
+الأول، Okay تمام، اتفقنا ولا أعطيكم البرهان و بلاش
+
+304
+00:37:31,150 --> 00:37:42,990
+خلاص؟ Okay إذا بنوقف هنا، نكتفي بالأمثلة هذه، وإن شاء
+
+305
+00:37:42,990 --> 00:37:46,870
+الله المرة الجاية هناخد .. ندخل في الموضوع ال
+
+306
+00:37:46,870 --> 00:37:51,570
+contractive sequences وبعدين نبدأ section جديد إن 
+
+307
+00:37:51,570 --> 00:37:58,010
+شاء الله، فشكرا لكم وال .. نكمل إن شاء الله في
+
+308
+00:37:58,010 --> 00:37:58,830
+اللقاء القادم 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM.srt
new file mode 100644
index 0000000000000000000000000000000000000000..7ca4aa257168b659f7b52717be01bd309a833272
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM.srt
@@ -0,0 +1,1403 @@
+1
+00:00:21,060 --> 00:00:27,740
+اليوم إن شاء الله هنحاول نحل امتحان نصفي سابق
+
+2
+00:00:27,740 --> 00:00:32,680
+كمراجعة للامتحان النصفي الأول اللي هناخده إن شاء 
+
+3
+00:00:32,680 --> 00:00:40,040
+الله غدا أول سؤال في الامتحان هذا عبارة عن سؤال 
+
+4
+00:00:40,040 --> 00:00:45,120
+true or false إذا العبارة صحيحة فبنعلم عليها صح أو 
+
+5
+00:00:45,120 --> 00:00:52,670
+true وإذا خطأ بنعلم عليها خطأ فأول عبارة بتقول لأن 
+
+6
+00:00:52,670 --> 00:00:58,250
+الـ absolute value لـ X سالب Y  بساوي absolute X سالب 
+
+7
+00:00:58,250 --> 00:01:05,030
+absolute Y وحتى 
+
+8
+00:01:05,030 --> 00:01:09,810
+لو كانت تلاقي إشارة موجبة، لو سمحتوا ما تتكلموا 
+
+9
+00:01:09,810 --> 00:01:16,710
+إلا لما ترفع يدك وإذنك هه هل هذا الكلام صحيح 
+
+10
+00:01:16,710 --> 00:01:25,300
+لكل X و Y ينتميان إلى R فالعبارة هذه false ليست صحيحة
+
+11
+00:01:25,300 --> 00:01:32,380
+ممكن نجيب أكثر من counter example صحيحة العبارة
+
+12
+00:01:32,380 --> 00:01:36,300
+الثانية لو كان S subset of the set of all real
+
+13
+00:01:36,300 --> 00:01:42,420
+numbers is finite لو
+
+14
+00:01:42,420 --> 00:01:48,840
+كانت الـ set هذه finite فهذا بيقدّم أن الـ supremum S
+
+15
+00:01:48,840 --> 00:01:59,400
+والـ infimum S ينتميان للـ set S هل هذا true؟ هل لما
+
+16
+00:01:59,400 --> 00:02:03,420
+تكون الـ set finite الـ supremum تبعها والـ infimum 
+
+17
+00:02:03,420 --> 00:02:08,840
+تبعها ينتميان إليها؟ هذا صحيح كان تمرين exercise و
+
+18
+00:02:08,840 --> 00:02:11,380
+برهنة، إذن هذا true
+
+19
+00:02:15,490 --> 00:02:22,250
+ثلاثة لو عرفنا الـ set I of S على أنها the set of
+
+20
+00:02:22,250 --> 00:02:34,870
+all V حيث V بساوي infimum الـ set S فالـ
+
+21
+00:02:34,870 --> 00:02:40,430
+set هذه contains contains 
+
+22
+00:02:40,430 --> 00:02:44,010
+more than one element more than
+
+23
+00:02:46,860 --> 00:02:52,280
+one element المجموعة
+
+24
+00:02:52,280 --> 00:02:58,000
+هذه تحتوي على أكثر من عنصر، هل هذا صحيح؟ هل الـ set 
+
+25
+00:02:58,000 --> 00:03:01,860
+ممكن يكون لها أكثر من infimum؟ لا، لا، لا، لا،
+
+26
+00:03:01,860 --> 00:03:02,560
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+27
+00:03:02,560 --> 00:03:07,020
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+28
+00:03:07,020 --> 00:03:07,100
+لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا، لا،
+
+29
+00:03:07,100 --> 00:03:10,040
+لا، لا، لا، لا، لا، لا، ل
+
+30
+00:03:13,960 --> 00:03:19,580
+العبارة الرابعة every monotone sequence converges
+
+31
+00:03:19,580 --> 00:03:25,980
+if and only if it is bounded هذه 
+
+32
+00:03:25,980 --> 00:03:28,780
+عبارة عن الـ monotone convergence theorem فهذه
+
+33
+00:03:28,780 --> 00:03:34,620
+true ال
+
+34
+00:03:34,620 --> 00:03:40,020
+sequence سالب 
+
+35
+00:03:40,020 --> 00:03:55,840
+واحد أس N على N إن ينتمي لـ N is convergent هل
+
+36
+00:03:55,840 --> 00:03:56,760
+هذا صحيح؟
+
+37
+00:04:06,660 --> 00:04:12,140
+طيب ماشي المشكلة أن الأقلام السوداء اللي عندي كلها 
+
+38
+00:04:12,140 --> 00:04:22,160
+صارت باهتة اه في واحد جبت أنت و
+
+39
+00:04:22,160 --> 00:04:32,480
+الله أنا مش كثير يعني
+
+40
+00:04:32,480 --> 00:04:36,020
+هدم يعني أحسن نشوف يعني
+
+41
+00:04:42,570 --> 00:04:47,330
+فالـ sequence هذه convergent هل هذا صحيح ولا خطأ 
+
+42
+00:04:47,330 --> 00:04:54,790
+هذا true و
+
+43
+00:04:54,790 --> 00:05:00,050
+لو بدنا نبرهن الكلام هذا وبالمناسبة الـ sequence
+
+44
+00:05:00,050 --> 00:05:06,410
+هذه converge لصفر converge والـ limit تبعها صفر 
+
+45
+00:05:07,900 --> 00:05:14,940
+ليه؟ لأنه هي المسافة بين الـ nth term لحد إنه ليه؟
+
+46
+00:05:14,940 --> 00:05:23,620
+سالب واحد أس n على n سالب صفر ايش 
+
+47
+00:05:23,620 --> 00:05:27,520
+هاد بالساوي؟
+
+48
+00:05:27,520 --> 00:05:28,320
+بتساوي
+
+49
+00:05:37,950 --> 00:05:45,590
+بتساوي واحد على n صح؟ نصبوط؟ وهذا أصغر من إذا كان
+
+50
+00:05:45,590 --> 00:05:54,410
+واحد ضرب واحد على n هذا عدد موجب واحد على n تقول
+
+51
+00:05:54,410 --> 00:06:05,090
+للصفر إذن حسب نظرية سابقة رقمها 
+
+52
+00:06:05,090 --> 00:06:11,610
+كان في النقص اثنين أربعة بيطلع limit xn بساوي صفر
+
+53
+00:06:11,610 --> 00:06:15,190
+limit سالب 
+
+54
+00:06:15,190 --> 00:06:20,750
+واحد أس n على n لما n تقوى لـ infinity بساوي صفر 
+
+55
+00:06:20,750 --> 00:06:25,230
+إذا 
+
+56
+00:06:25,230 --> 00:06:28,650
+الـ sequence هذي convergent إذا العبارة هذه true
+
+57
+00:06:28,650 --> 00:06:31,650
+طيب عبارة ثانية
+
+58
+00:06:45,940 --> 00:06:55,320
+product of two divergent sequences
+
+59
+00:06:55,320 --> 00:07:03,700
+is divergent هل 
+
+60
+00:07:03,700 --> 00:07:05,280
+هذا true ولا false؟
+
+61
+00:07:08,090 --> 00:07:10,990
+العبارة هذه false طب لما قلنا لكم جيبوا counter 
+
+62
+00:07:10,990 --> 00:07:17,310
+example ممكن تجيب سالب واحد اثنين وكمان الـ
+
+63
+00:07:17,310 --> 00:07:23,290
+sequence الثانية تكون سالب واحد اثنين أو 
+
+64
+00:07:23,290 --> 00:07:26,830
+ممكن تكون سالب واحد اثنين زائد واحد نفس الشغل
+
+65
+00:07:26,830 --> 00:07:32,390
+بتطلع convergent الـ product هذه الـ divergent وهذه
+
+66
+00:07:32,390 --> 00:07:38,210
+الـ divergent لكن X in في Y in هساوي الـ sequence
+
+67
+00:07:38,210 --> 00:07:44,650
+سالب واحد واست اثنين in لما 
+
+68
+00:07:44,650 --> 00:07:49,370
+نضربهم في بعض فهذا بيعطيني الـ sequence ثابت واحد 
+
+69
+00:07:49,370 --> 00:07:55,730
+وهذه converge لواحد إذا هذه في عندي example of two
+
+70
+00:07:55,730 --> 00:08:01,090
+divergent sequences لكن حصل ضربهم بيطلع convergent
+
+71
+00:08:01,090 --> 00:08:06,230
+وليس divergent طيب 
+
+72
+00:08:06,230 --> 00:08:21,470
+لو كانت S bounded S bounded subset of R و S0
+
+73
+00:08:21,470 --> 00:08:28,510
+subset من S هل هذا بيقدّم إن infimum 
+
+74
+00:08:29,760 --> 00:08:42,480
+S0 subset أصغر من أو يساوي infimum من الـ S هل
+
+75
+00:08:42,480 --> 00:08:51,020
+هذه العبارة صحيحة؟ أي
+
+76
+00:08:51,020 --> 00:08:59,320
+رأيكم؟ العبارة هذه false لما مجموعة تصغر الـ infimum
+
+77
+00:08:59,320 --> 00:09:07,940
+تبعها بيكبر، لكن اللي بيكون صحيح أنه الـ supremum لو 
+
+78
+00:09:07,940 --> 00:09:12,600
+أخذت الـ supremum للمجموعة الجزئية S0 فهذا بيطلع 
+
+79
+00:09:12,600 --> 00:09:17,040
+أصغر من أو يساوي الـ supremum للمجموعة S، هذه العبارة 
+
+80
+00:09:17,040 --> 00:09:17,320
+true
+
+81
+00:09:20,870 --> 00:09:25,710
+الـ supremum لما المجموعة تكبر بيكبر لكن الـ infimum
+
+82
+00:09:25,710 --> 00:09:38,110
+لما المجموعة تكبر بيصغر عكس بعض طيب
+
+83
+00:09:43,200 --> 00:09:50,100
+لو كانت x in sequence of positive real numbers و
+
+84
+00:09:50,100 --> 00:10:02,060
+limit x in زائد واحد over x in بساوي واحد فهذا
+
+85
+00:10:02,060 --> 00:10:08,180
+بيقدّم إن الـ sequence x in diverges 
+
+86
+00:10:08,180 --> 00:10:15,870
+هل هذه العبارة صحيحة ولا خطأ؟ العبارة هذه خطأ لأنه 
+
+87
+00:10:15,870 --> 00:10:22,230
+إحنا فينا في تمرين سابع عشر في section ثلاثة اثنين 
+
+88
+00:10:22,230 --> 00:10:26,230
+بيقول إذا كانت الـ sequence .. إذا كان الـ limit 
+
+89
+00:10:26,230 --> 00:10:29,630
+ratio هذا بساوي واحد فالـ sequence ممكن تكون
+
+90
+00:10:29,630 --> 00:10:33,890
+convergent أو divergent وفي السؤال هذا أعطينا 
+
+91
+00:10:33,890 --> 00:10:41,240
+مثلين واحد لـ sequence convergent الـ ratio limit الـ
+
+92
+00:10:41,240 --> 00:10:45,100
+ratio تبعها بيساوي واحد لكنها convergent ومثال
+
+93
+00:10:45,100 --> 00:10:50,300
+ثاني لـ sequence limit الـ ratio تبعها أيضاً بيساوي 
+
+94
+00:10:50,300 --> 00:10:53,700
+واحد لكنها divergent إذا لو كان limit الـ ratio
+
+95
+00:10:53,700 --> 00:10:57,100
+بيساوي واحد فالـ sequence إما converge أو diverge
+
+96
+00:10:57,100 --> 00:11:01,400
+ما نضايش نجزم إنها convergent أو نجزم إنها
+
+97
+00:11:01,400 --> 00:11:07,020
+divergent okay إذا العبارة هذه خطأ أو false إذا 
+
+98
+00:11:07,020 --> 00:11:13,950
+العبارة هذه false لو بدلت divergent بـ convergent
+
+99
+00:11:13,950 --> 00:11:21,530
+برضه false الصحيح أنها may converge or may diverge
+
+100
+00:11:21,530 --> 00:11:26,810
+طيب
+
+101
+00:11:26,810 --> 00:11:43,910
+العبارة الأخيرة تسعة أي open interval 
+
+102
+00:11:43,910 --> 00:11:47,950
+a و b تحتوي
+
+103
+00:11:47,950 --> 00:11:49,970
+rational number R 
+
+104
+00:11:54,840 --> 00:11:59,220
+في rational number محصور من a و b يعني الـ open
+
+105
+00:11:59,220 --> 00:12:03,920
+interval تحتوي الـ R كذلك في نتيجة الـ density
+
+106
+00:12:03,920 --> 00:12:08,300
+theorem أي open interval زي هذه تحتوي الـ rational
+
+107
+00:12:08,300 --> 00:12:13,780
+إذن هذا الكلام صحيح
+
+108
+00:12:13,780 --> 00:12:18,340
+إذن هذا أول سؤال صح وخطأ السؤال الثاني 
+
+109
+00:12:33,670 --> 00:12:50,070
+Question 2 إذا
+
+110
+00:12:50,070 --> 00:12:55,770
+إحنا
+
+111
+00:12:55,770 --> 00:13:01,210
+بنحل هذا امتحان هذا امتحان Mid
+
+112
+00:13:03,740 --> 00:13:11,660
+term one التاريخ
+
+113
+00:13:11,660 --> 00:13:24,780
+تبعه اثنان وثلاثة ألفيّن وثلاثة عشر السؤال 
+
+114
+00:13:24,780 --> 00:13:32,630
+أو الفرع B من السؤال الأول إذا هذا السؤال الأول
+
+115
+00:13:32,630 --> 00:13:37,290
+الفرق بيه
+
+116
+00:13:37,290 --> 00:13:44,130
+X و Y ينتميان إلى R أعداد حقيقية Such that absolute 
+
+117
+00:13:44,130 --> 00:13:53,190
+X minus Y أصغر من واحد على N لكل N في N لما نثبت 
+
+118
+00:13:53,190 --> 00:13:55,470
+أن هذا بيقدّم X بساوي Y 
+
+119
+00:14:00,570 --> 00:14:09,470
+البرهان هنستخدم الـ Archimedean property assume on
+
+120
+00:14:09,470 --> 00:14:13,930
+contrary على
+
+121
+00:14:13,930 --> 00:14:23,710
+المقيد أن X لا يساوي Y هذا 
+
+122
+00:14:23,710 --> 00:14:24,410
+بيقدّم
+
+123
+00:14:28,910 --> 00:14:44,930
+أكبر من صفر لأي 
+
+124
+00:14:44,930 --> 00:14:53,850
+عدد موجب يوجد in zero عدد طبيعي بحيث إن واحد على n
+
+125
+00:14:53,850 --> 00:15:05,390
+زيرو أصغر من absolute X سالب Y هذا
+
+126
+00:15:05,390 --> 00:15:13,530
+من وين من الـ Archimedean property طيب
+
+127
+00:15:13,530 --> 00:15:16,610
+أنا عندي من الفرض
+
+128
+00:15:19,930 --> 00:15:36,910
+من الفرض by hypothesis هذا أصغر من واحد على n لكل
+
+129
+00:15:36,910 --> 00:15:39,770
+n وبالتالي هذا صحيح لـ n zero
+
+130
+00:15:48,170 --> 00:15:53,370
+إذن بيطلع عندي 1 على N0 أصغر من 1 على N0 إذن هذا
+
+131
+00:15:53,370 --> 00:16:00,590
+بيقدّم إن 1 على N0 أصغر من 1 على N0 وهذا تناقض
+
+132
+00:16:00,590 --> 00:16:07,610
+contradiction تناقض إذن هذا التناقض بيقول إن الـ X 
+
+133
+00:16:07,610 --> 00:16:14,490
+لازم تساوي الـ Y كما هو مطلوب okay تمام إذن هذا 
+
+134
+00:16:14,490 --> 00:16:22,890
+برهان الجزء الثاني من السؤال الأول في عند
+
+135
+00:16:22,890 --> 00:16:35,710
+هنا السؤال الثاني question 
+
+136
+00:16:35,710 --> 00:16:48,690
+2 الفرع a show S&T إن الـ infimum لـ set واحد على
+
+137
+00:16:48,690 --> 00:17:03,630
+الجذر الـ N حيث N عدد طبيعي بساوي صفر نشوف 
+
+138
+00:17:03,630 --> 00:17:08,610
+مع بعض واضح 
+
+139
+00:17:08,610 --> 00:17:14,940
+إن صفر أصغر من أو يساوي واحد على الجذر الـ N لكل n
+
+140
+00:17:14,940 --> 00:17:24,180
+عدد طبيعي صح؟ في حد عنده شك في ذلك؟ وبالتالي 
+
+141
+00:17:24,180 --> 00:17:31,040
+so صفر is zero
+
+142
+00:17:31,040 --> 00:17:41,460
+is a lower bound a lower bound of  المجموعة S  اللي هي
+
+143
+00:17:43,280 --> 00:17:48,720
+بنعرفها لأنها مجموعة العناصر 1 على square root
+
+144
+00:17:48,720 --> 00:17:56,140
+of N حيث N ينتمي إلى N طيب
+
+145
+00:17:56,140 --> 00:18:01,600
+to show أن
+
+146
+00:18:01,600 --> 00:18:07,160
+الصفر هو ال minimum ل S أو هو ال greatest lower
+
+147
+00:18:07,160 --> 00:18:28,050
+bound للمجموعة S فبناخد let W be any lower bound of
+
+148
+00:18:28,050 --> 00:18:37,130
+S فبالنسبة
+
+149
+00:18:37,130 --> 00:18:46,710
+لـ claim بنثبت أن الصفر أصغر من أو يساوي W عفوا W
+
+150
+00:18:46,710 --> 00:18:53,150
+أصغر من أو يساوي 0 وبالتالي هيك يكون الصفر أكبر من
+
+151
+00:18:53,150 --> 00:18:57,150
+أو يساوي أي lower bound يعني الصفر هو ال greatest
+
+152
+00:18:57,150 --> 00:19:04,590
+lower bound صح فلبرهان ذلك assume بنعمل برهان
+
+153
+00:19:04,590 --> 00:19:13,920
+بالتناقض on contrary افرضه على النقيد أن w أكبر من 
+
+154
+00:19:13,920 --> 00:19:18,420
+صفر then
+
+155
+00:19:18,420 --> 00:19:21,540
+by
+
+156
+00:19:21,540 --> 00:19:28,160
+Archimedean property .. by Archimedean property
+
+157
+00:19:28,160 --> 00:19:37,150
+لأي عدد موجب زي هذايوجد عدد طبيعي N0 ينتمي إلى N
+
+158
+00:19:37,150 --> 00:19:43,130
+بحيث أنه مقلوب N0
+
+159
+00:19:43,130 --> 00:19:51,250
+أصغر من العدد الموجب W تربيع طبعا W تربيع إذا W
+
+160
+00:19:51,250 --> 00:19:57,960
+عدد موجب فW تربيع بالتأكيد عدد موجب فأنا بطبق الـ
+
+161
+00:19:57,960 --> 00:20:01,360
+Archimedean property مش على w وعلى w تربيع العدد
+
+162
+00:20:01,360 --> 00:20:06,060
+الموجب w square فبقدر ألاقي by Archimedean
+
+163
+00:20:06,060 --> 00:20:11,140
+property natural number n0 مقلوبه وأصغر من w تربيع
+
+164
+00:20:11,140 --> 00:20:21,940
+طبعا هذا بيقدي أن 1 على جذر n0 أصغر من w ومن
+
+165
+00:20:21,940 --> 00:20:22,240
+ال
+
+166
+00:20:26,300 --> 00:20:34,080
+من الفرض الـ W هذا lower bound للمجموعة S وبالتالي هذا
+
+167
+00:20:34,080 --> 00:20:41,320
+أصغر من أو يساوي 1 على الجذر التربيعي ل N0 لأن
+
+168
+00:20:41,320 --> 00:20:46,440
+هذا ينتمي إلى S، هذا عنصر في S، صح؟ واحنا فرضين أن
+
+169
+00:20:46,440 --> 00:20:53,370
+الـ W أشمى lower bound للمجموعة S وهذا answer في
+
+170
+00:20:53,370 --> 00:20:58,730
+المجموعة S إذا ال W كونه lower bound ل S أصغر من أو
+
+171
+00:20:58,730 --> 00:21:04,310
+يساوي 1 على square root ل N0 فطبعا هذا بيدي ان
+
+172
+00:21:04,310 --> 00:21:09,150
+1 على square root ل N0 أصغر من 1 على square
+
+173
+00:21:09,150 --> 00:21:18,330
+root ل N0 وهذا مدينة تناقض كيف عدد بيطلع أصغر من
+
+174
+00:21:18,330 --> 00:21:21,730
+نفسه هذا تناقض لأن هذا التناقض بيقول لإن ال
+
+175
+00:21:21,730 --> 00:21:26,010
+assumption تبعنا ان ال W أكبر من الصفر خطأ
+
+176
+00:21:26,010 --> 00:21:33,210
+وبالتالي ال W لازم يكون أصغر بدل ما هو أكبر من
+
+177
+00:21:33,210 --> 00:21:37,970
+الصفر يطلع أصغر من أو يساوي صفر وبالتالي ال W
+
+178
+00:21:37,970 --> 00:21:43,830
+الصفر هو أكبر lower bound okay إذا هذا بيكمل
+
+179
+00:21:43,830 --> 00:21:45,750
+البرهان تمام
+
+180
+00:22:04,850 --> 00:22:17,070
+نجاوب على الفرع الثاني بيه من السؤال الثاني show
+
+181
+00:22:17,070 --> 00:22:26,770
+أن ال limit ل 1 على جذر ال N as N times infinity
+
+182
+00:22:26,770 --> 00:22:28,370
+بيساوى صفر
+
+183
+00:22:40,270 --> 00:22:45,910
+Proof بإن إحنا في النهاية بيستخدم تعريف طبعا
+
+184
+00:22:45,910 --> 00:22:51,790
+epsilon capital N للنهايات ففي نهاية الأمر بدنا ال
+
+185
+00:22:51,790 --> 00:22:55,190
+absolute value ل 1 على square root of N ناقص 0
+
+186
+00:22:55,190 --> 00:23:02,270
+بدنا ده يطلع أصغر من أي epsilon صح؟ طب ما هذا
+
+187
+00:23:02,270 --> 00:23:05,070
+بيساوى 1 على square root of N
+
+188
+00:23:09,000 --> 00:23:16,500
+متى هذا بيكون أصغر من epsilon فأنا
+
+189
+00:23:16,500 --> 00:23:24,040
+هاخد هذا
+
+190
+00:23:24,040 --> 00:23:28,080
+لما 1 على n أصغر من epsilon تربيع لو ربعت
+
+191
+00:23:28,080 --> 00:23:33,920
+الطرفين فمتى
+
+192
+00:23:33,920 --> 00:23:35,920
+هذا بيكون أصغر من epsilon تربيع
+
+193
+00:23:38,730 --> 00:23:45,210
+Okay إذا هنا هاخد أنا 1 على capital N أصغر من
+
+194
+00:23:45,210 --> 00:23:54,110
+epsilon تربيع إذا
+
+195
+00:23:54,110 --> 00:23:58,570
+نستخدم ال Archimedean property هذا epsilon تربيع
+
+196
+00:23:58,570 --> 00:24:02,690
+عدد موجب By Archimedean property بقدر ألاقي عدد
+
+197
+00:24:02,690 --> 00:24:07,550
+طبيعي capital N مقلوبه وأصغر من epsilon تربيع ناشي
+
+198
+00:24:08,920 --> 00:24:15,320
+بدا هنا given epsilon
+
+199
+00:24:15,320 --> 00:24:27,320
+أكبر من الصفر use الarchimedean property to choose
+
+200
+00:24:27,320 --> 00:24:36,760
+n عدد طبيعي بحيث أن 1 على n أصغر من epsilon
+
+201
+00:24:39,750 --> 00:24:54,590
+الآن لو خدت small n أكبر من أو يساوي capital N فهذا
+
+202
+00:24:54,590 --> 00:24:59,410
+بيقدي أن 1 على small n أصغر لو يساوي 1 على
+
+203
+00:24:59,410 --> 00:25:00,190
+capital N
+
+204
+00:25:05,570 --> 00:25:09,570
+بيقدي 1 على square root ل N أصغر من لو يساوي
+
+205
+00:25:09,570 --> 00:25:16,450
+1 على square root ل capital N وهذا بيقدي ان ال
+
+206
+00:25:16,450 --> 00:25:23,650
+absolute value ل 1 على square root ل N ناقص صفر
+
+207
+00:25:23,650 --> 00:25:27,790
+بيساوى 1 على square root ل N وهذا أصغر من لو
+
+208
+00:25:27,790 --> 00:25:34,250
+يساوي 1 على square root ل capital N وهذا من هنا
+
+209
+00:25:36,260 --> 00:25:40,760
+لو سمينا الـ inequality هذه الـ star إذا by star
+
+210
+00:25:40,760 --> 00:25:48,620
+1 على square root ل N أصغر من epsilon إذا
+
+211
+00:25:48,620 --> 00:25:53,440
+هاي حققنا تعريف epsilon capital N للنهايات for
+
+212
+00:25:53,440 --> 00:25:58,600
+any given epsilon أثبتنا إنه يوجد capital N عدد
+
+213
+00:25:58,600 --> 00:26:02,760
+طبيعي وهذا العدد الطبيعي يعتمد على epsilon هاي
+
+214
+00:26:02,760 --> 00:26:08,910
+مرتبط بepsilon بحيث لكل n أكبر من أو يساوي capital N
+
+215
+00:26:08,910 --> 00:26:16,010
+طلع المسافة بين xn و x اللي هي صفر أصغر من epsilon
+
+216
+00:26:16,010 --> 00:26:23,530
+إذا by definition by
+
+217
+00:26:23,530 --> 00:26:28,910
+definition بيطلع عندي limit 1 على square root ل
+
+218
+00:26:28,910 --> 00:26:33,290
+n بيساوى صفر وهو المطلوب طبعا
+
+219
+00:26:37,550 --> 00:26:42,930
+طبعا في حال ثانية أو في برهان ثاني باستخدام الـ
+
+220
+00:26:42,930 --> 00:26:48,770
+monotone convergence theorem إذا
+
+221
+00:26:48,770 --> 00:26:54,350
+ال solution to use
+
+222
+00:26:54,350 --> 00:27:01,090
+monotone convergence theorem ال sequence أنا عندي
+
+223
+00:27:01,090 --> 00:27:04,350
+xn بيساوى 1 على square root ل n
+
+224
+00:27:09,010 --> 00:27:14,590
+هذا أكبر من أو يساوي 1 على square root ل n زائد
+
+225
+00:27:14,590 --> 00:27:26,090
+1 اللي هو xn زائد 1 وبالتالي ال sequence is
+
+226
+00:27:26,090 --> 00:27:32,900
+decreasing صح؟ بعدين أنا عندي absolute xn بيساوى
+
+227
+00:27:32,900 --> 00:27:38,300
+absolute 1 على جذر ال n أصغر من أو يساوي 1
+
+228
+00:27:38,300 --> 00:27:47,120
+لكل n لكل
+
+229
+00:27:47,120 --> 00:27:57,520
+n فهذا بيقدي ان ال sequence xn is bounded إذا
+
+230
+00:27:57,520 --> 00:28:02,750
+bounded و decreasing إذا الـ sequence xn by
+
+231
+00:28:02,750 --> 00:28:07,690
+monotone convergence theorem limit xn بيساوى
+
+232
+00:28:07,690 --> 00:28:17,710
+الانفمام ل xn حيث n ينتمي إلى n فأثبتنا أن
+
+233
+00:28:17,710 --> 00:28:24,760
+الانفمام بيساوى صفر بالفرع اللي جابله فهذا برهان
+
+234
+00:28:24,760 --> 00:28:28,540
+ثاني لكن احنا ال .. ال monotone convergence الكلام
+
+235
+00:28:28,540 --> 00:28:34,860
+مش داخلة في الامتحان فممكن انكم يعني ال ..
+
+236
+00:28:34,860 --> 00:28:38,580
+تستخدموا البرهان الأول يعني ممكن تستخدموا البرهان
+
+237
+00:28:38,580 --> 00:28:42,360
+الأول يعني okay
+
+238
+00:28:42,360 --> 00:28:46,400
+تمام طيب نكمل
+
+239
+00:29:09,040 --> 00:29:15,540
+find the supremum الجزء C بإنه نوجد ال supremum
+
+240
+00:29:15,540 --> 00:29:20,800
+ل 1 ناقص 1 على جذر ال N حيث N ينتمي إلى N
+
+241
+00:29:20,800 --> 00:29:32,620
+فهذا حسب exercise أخذنا supremum A زائد 6 بيساوى A
+
+242
+00:29:32,620 --> 00:29:38,640
+زائد supremum المجموعة اللي هي عناصرها سالب 1 على
+
+243
+00:29:38,640 --> 00:29:48,800
+جذر ال N هيف N ينتمي إلى N ويساوى 1 الآن
+
+244
+00:29:48,800 --> 00:29:56,140
+supremum سالب مجموعة بيساوى سالب ال infimum لعناصر
+
+245
+00:29:56,140 --> 00:29:56,640
+المجموعة
+
+246
+00:30:05,050 --> 00:30:09,910
+و احنا لسه مثبتين ان ال infimum هذا بيساوى صفر إذا
+
+247
+00:30:09,910 --> 00:30:15,210
+ال supremum للمجموعة هذه بيطلع 1 طيب
+
+248
+00:30:15,210 --> 00:30:25,970
+فرع ثاني show that اثبتي إنه limit cosine
+
+249
+00:30:25,970 --> 00:30:34,290
+n على n أو على جذر ال N as n tends to infinity
+
+250
+00:30:34,290 --> 00:30:38,650
+بيساوى صفر proof
+
+251
+00:30:38,650 --> 00:30:43,290
+أنا
+
+252
+00:30:43,290 --> 00:30:50,010
+عندي cosine n أكبر من أو أصغر من أو يساوى 1 أكبر
+
+253
+00:30:50,010 --> 00:30:59,630
+من أو يساوى سالب 1 لكل n في N و 1
+
+254
+00:31:01,530 --> 00:31:07,070
+على جذر ال N عدد موجب فلو ضربت المتباينة هذه في
+
+255
+00:31:07,070 --> 00:31:11,550
+1 على جذر ال N فبيطلع سالب 1 على جذر ال N
+
+256
+00:31:11,550 --> 00:31:18,130
+أصغر لو يساوى cosine N على جذر ال N أصغر لو يساوى 1
+
+257
+00:31:18,130 --> 00:31:21,690
+على جذر ال N لكل N في N
+
+258
+00:31:24,530 --> 00:31:28,310
+طيب أنا عند ال sequence لسه مثبتين إحنا هنا في
+
+259
+00:31:28,310 --> 00:31:32,510
+الفرع b إن ال sequence هذه ال limit تبعتها as n
+
+260
+00:31:32,510 --> 00:31:35,970
+tends to infinity بيساوى صفر و ال sequence هذه ال
+
+261
+00:31:35,970 --> 00:31:41,430
+limit تبعتها سالب limit 1 على الجذر ال n و سالب
+
+262
+00:31:41,430 --> 00:31:46,830
+1 بصفر بيطلع صفر as n tends to infinity إذا by
+
+263
+00:31:46,830 --> 00:31:47,910
+squeeze theorem
+
+264
+00:31:51,910 --> 00:31:57,090
+بسكويز ثيورم أو sandwich theorem بيطلع limit ال
+
+265
+00:31:57,090 --> 00:32:02,250
+sequence اللي حدّها محصور في النص اللي هو
+
+266
+00:32:02,250 --> 00:32:06,590
+cosine n على square root ل n as n times infinity
+
+267
+00:32:06,590 --> 00:32:16,070
+بيساوى صفر تمام؟ إذن هذا برهان الجزء d
+
+268
+00:32:23,640 --> 00:32:30,920
+واضحة للحلول question
+
+269
+00:32:30,920 --> 00:32:38,680
+تلاتة الفرع a أنا عندي in بيساوى closed interval
+
+270
+00:32:38,680 --> 00:32:44,480
+من صفر ل 1 على جذر ال n prove
+
+271
+00:32:46,630 --> 00:32:51,890
+إنه ال intersection from n equals one to infinity
+
+272
+00:32:51,890 --> 00:33:02,970
+ل I n بيساوى single twin zipper فممكن
+
+273
+00:33:02,970 --> 00:33:11,570
+نستخدم ال nested interval property proof
+
+274
+00:33:11,570 --> 00:33:23,930
+أول شيء واضح واضح إن صفر ينتمي إلى I N لكل N في N هذا
+
+275
+00:33:23,930 --> 00:33:28,690
+بيقدي إن الصفر ينتمي
+
+276
+00:33:28,690 --> 00:33:35,210
+لتقاطعه صح
+
+277
+00:33:35,210 --> 00:33:40,310
+الفترة المغلقة هذه الصفر دائما ينتمي لها لكل عدد
+
+278
+00:33:40,310 --> 00:33:45,330
+طبيعي الآن أنا في عندي sequence of intervals و
+
+279
+00:33:45,330 --> 00:33:49,970
+الصفر ينتمي لكل عنصر في ال set إذا الصفر ينتمي
+
+280
+00:33:49,970 --> 00:34:00,410
+لتقاطع كل المجموعات طيب الفترة I in is closed صح
+
+281
+00:34:00,410 --> 00:34:06,850
+and bounded لكل
+
+282
+00:34:06,850 --> 00:34:16,080
+و بعدين واضح أن I N contains I N زاد واحد لكل N
+
+283
+00:34:16,080 --> 00:34:23,340
+في N صح؟ يعني ال sequence هذه nested يعني ال
+
+284
+00:34:23,340 --> 00:34:29,200
+sequence I N nested
+
+285
+00:34:29,200 --> 00:34:32,300
+إذا
+
+286
+00:34:32,300 --> 00:34:35,940
+by 
+
+287
+00:34:35,940 --> 00:34:38,000
+nested
+
+288
+00:34:44,870 --> 00:34:50,710
+nested intervals theorem  استقاط
+
+289
+00:34:50,710 --> 00:34:59,510
+و هذا لازم يكون في unique element لأنه أنا عندي طيب
+
+290
+00:34:59,510 --> 00:35:07,490
+قبل ما نطبق نستد أنا عندي ال infimum لواحد على جذر
+
+291
+00:35:07,490 --> 00:35:08,810
+n سالب صفر
+
+292
+00:35:18,070 --> 00:35:26,910
+هذا الآن from أثبتنا أنه بيساوي صفر إذا حسب by
+
+293
+00:35:26,910 --> 00:35:31,470
+nested
+
+294
+00:35:31,470 --> 00:35:36,370
+intervals theorem
+
+295
+00:35:39,780 --> 00:35:47,720
+الـ intersection has a unique element has
+
+296
+00:35:47,720 --> 00:35:52,920
+unique element
+
+297
+00:35:52,920 --> 00:35:57,340
+يعني في التقاطع ما فيش عنصر وحيد طب احنا قلنا أن
+
+298
+00:35:57,340 --> 00:36:03,500
+الصفر ينتمي للتقاطع و التقاطع فيه عنصر واحد لذا لازم
+
+299
+00:36:03,500 --> 00:36:07,960
+يساوي الصفر in
+
+300
+00:36:07,960 --> 00:36:08,780
+a sense
+
+301
+00:36:13,330 --> 00:36:21,210
+بما أن الصفر ينتمي للتقاطع يجب
+
+302
+00:36:21,210 --> 00:36:25,210
+أن
+
+303
+00:36:25,210 --> 00:36:31,070
+يكون التقاطع من N بيساوي واحد إلى infinity ل I N بيساوي
+
+304
+00:36:31,070 --> 00:36:33,610
+بس single tone صفر
+
+305
+00:36:39,670 --> 00:36:44,490
+طبعا ممكن أعطيتكم أنا برهان زي هذا بس كان بدل 1
+
+306
+00:36:44,490 --> 00:36:46,110
+على جدر ال N 1 على N
+
+307
+00:36:50,700 --> 00:36:57,680
+و أثبتنا إن ال set هذه طبعا واضح من هنا إن هذه
+
+308
+00:36:57,680 --> 00:37:04,260
+دايما صحيحة و أثبتنا العكس و قلنا إنه لو أخدت أي x
+
+309
+00:37:04,260 --> 00:37:07,880
+تتقاطع فبنا نثبت إن هذا ال x بيساوي صفر و عملنا
+
+310
+00:37:07,880 --> 00:37:12,800
+برهان بالتناقض افرضي إن ال x ما بيساويش صفر إذا أكبر
+
+311
+00:37:12,800 --> 00:37:16,100
+من صفر و وصلنا إلى تناقض by Archimedean property
+
+312
+00:37:17,080 --> 00:37:21,820
+إذا في برهان ثاني لكن أنا حبيت أعطيكم البرهان هذا
+
+313
+00:37:21,820 --> 00:37:26,840
+الثاني اللي ما خدناش زيه طبعا
+
+314
+00:37:26,840 --> 00:37:30,920
+صح
+
+315
+00:37:30,920 --> 00:37:37,340
+إذا أنا عندكم برهانين طيب
+
+316
+00:37:37,340 --> 00:37:42,700
+هاي كمان الجزء بيه من السؤال هذا أنا في عندي
+
+317
+00:37:42,700 --> 00:37:49,820
+sequence xn sequence mrو عندي xn أصغر من أو يساوي
+
+318
+00:37:49,820 --> 00:38:02,720
+صفر لكل n و بدنا نثبت إنه إذا كان limit xn بيساوي x
+
+319
+00:38:02,720 --> 00:38:10,810
+then ال x بتطلع أيضا أصغر من أو يساوي صفر أنا في
+
+320
+00:38:10,810 --> 00:38:14,610
+عندي sequence of real numbers كل حدودها غير سالبة
+
+321
+00:38:14,610 --> 00:38:18,330
+و ال sequence converge ل X بالدفعة أن ال limit
+
+322
+00:38:18,330 --> 00:38:27,850
+أيضا بتطلع غير سالبة فهي البرهان proof برهان
+
+323
+00:38:27,850 --> 00:38:32,930
+بالتناقض assume on
+
+324
+00:38:32,930 --> 00:38:33,650
+contrary
+
+325
+00:38:36,400 --> 00:38:45,860
+أن X أكبر من صفر و بدنا نصل إلى تناقض افرض
+
+326
+00:38:45,860 --> 00:38:56,620
+أن X أكبر من صفر طيب let epsilon بيساوي X ع 2 هذا
+
+327
+00:38:56,620 --> 00:39:05,960
+بطل عدل موجب بما أنه since .. since xn converges ل
+
+328
+00:39:05,960 --> 00:39:13,010
+x إذا يوجد capital N يعتمد على إبسلون عدد طبيعي
+
+329
+00:39:13,010 --> 00:39:19,190
+بحيث أنه لو كان n أكبر من أو يساوي capital N فهذا
+
+330
+00:39:19,190 --> 00:39:26,110
+بقدر أن absolute xn minus x أصغر من epsilon طيب ال
+
+331
+00:39:26,110 --> 00:39:30,910
+epsilon هذا أخدناها بيساوي x ع 2 إذا أنا عندي هي xn
+
+332
+00:39:30,910 --> 00:39:36,830
+minus x أصغر من x ع 2 أكبر
+
+333
+00:39:36,830 --> 00:39:38,550
+من سالب x ع 2
+
+334
+00:39:42,440 --> 00:39:49,560
+طيب ما هيك بطلع عندي xn ضيفي x لكل الأطراف فبطلع
+
+335
+00:39:49,560 --> 00:40:01,200
+xn أصغر من 3 x ع 2 أكبر من x ع 2 طيب
+
+336
+00:40:01,200 --> 00:40:06,000
+هذا
+
+337
+00:40:06,000 --> 00:40:12,140
+معناه وهذا الكلام صحيح لكل n أكبر من و يساوي
+
+338
+00:40:12,140 --> 00:40:18,740
+capital N فلو أخدت .. إذا بطلع من هنا xn capital N
+
+339
+00:40:18,740 --> 00:40:22,660
+لو أخدت small n هذه بيساوي capital N فبطلع xn
+
+340
+00:40:22,660 --> 00:40:29,740
+capital N أكبر من x ع 2 و أنا عندي x ع 2 عدد موجب
+
+341
+00:40:29,740 --> 00:40:35,100
+أكبر من 0 إذا أنا بطلع عندي xn capital N أكبر من 0
+
+342
+00:40:35,100 --> 00:40:41,550
+و هذا تناقض لأن أنا فرضت أن كل حدود ال sequence كلهم
+
+343
+00:40:41,550 --> 00:40:46,770
+أعداد غير سالبة فكيف طلع الحد رقم capital N موجب
+
+344
+00:40:46,770 --> 00:40:52,090
+هذا بتناقض مع الفرض تمام؟ إذا هذا سبب التناقض هذا
+
+345
+00:40:52,090 --> 00:40:59,550
+هو ال assumption تبعنا أن x أكبر من الصفر okay؟
+
+346
+00:40:59,550 --> 00:41:05,490
+إذا الصح أن x أصغر من أو يساوي صفر وهو المطلوب
+
+347
+00:41:08,070 --> 00:41:16,710
+Okay تمام إذا يعني هذه يعني بعض الأسئلة الأسئلة 
+
+348
+00:41:16,710 --> 00:41:25,630
+الرابعة هذا نظرية أخذناها و اللي بعدي أعتقد حلناها
+
+349
+00:41:25,630 --> 00:41:34,490
+في المحاضرة فهنوقف هنا و هيك بنكون يعني راجعنا
+
+350
+00:41:34,490 --> 00:41:41,290
+تقريبا امتحان للمتحان النصفية و نشوفكم إن شاء الله
+
+351
+00:41:41,290 --> 00:41:41,690
+بقرأ
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d210bf78bc7a533cfe6bd16013a30009b6ba0154
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/a-utq7LmSIM_postprocess.srt
@@ -0,0 +1,1404 @@
+1
+00:00:21,060 --> 00:00:27,740
+اليوم ان شاء الله هنحاول نحل امتحان نصفي سابق
+
+2
+00:00:27,740 --> 00:00:32,680
+كمراجعة للامتحان النصفي الأول اللي هناخده ان شاء
+
+3
+00:00:32,680 --> 00:00:40,040
+الله غدا اول سؤال في الامتحان هذا عبارة عن سؤال
+
+4
+00:00:40,040 --> 00:00:45,120
+true or false اذا العبارة صح فبنعلم عليها صح او
+
+5
+00:00:45,120 --> 00:00:52,670
+true واذا خطأ بنعلم عليها خطأ فأول عبارةبتقول لإن
+
+6
+00:00:52,670 --> 00:00:58,250
+ال absolute value ل X سالب Y بساوي absolute X سالب
+
+7
+00:00:58,250 --> 00:01:05,030
+absolute Y وحتى
+
+8
+00:01:05,030 --> 00:01:09,810
+لو كانت تلاقي إشارة موجبة، لو سمحتوا ما تتكلميش
+
+9
+00:01:09,810 --> 00:01:16,710
+إلا لما ترفع إيدك و إعزالك هه هل هذا الكلام صحيح
+
+10
+00:01:16,710 --> 00:01:25,300
+لكلX وY أنتمي إلى R فالعبارة هذه false ليست صحيحة
+
+11
+00:01:25,300 --> 00:01:32,380
+ممكن نجيب أكتر من counter example صح العبارة
+
+12
+00:01:32,380 --> 00:01:36,300
+التانية لو كان S subset of the set of all real
+
+13
+00:01:36,300 --> 00:01:42,420
+numbers is finite لو
+
+14
+00:01:42,420 --> 00:01:48,840
+كانت ال set هذه finiteفهذا بيقدّي أن ال supremum S
+
+15
+00:01:48,840 --> 00:01:59,400
+و ال infimum S ينتمي لل set S هل هذا true؟ هل لما
+
+16
+00:01:59,400 --> 00:02:03,420
+تكون ال set finite ال supremum تبعها و ال infimum
+
+17
+00:02:03,420 --> 00:02:08,840
+تبعها ينتمي إلها؟ هذا صحيح كان تمرين exercise و
+
+18
+00:02:08,840 --> 00:02:11,380
+برهنة، إذن هذا true
+
+19
+00:02:15,490 --> 00:02:22,250
+تلاتة لو أعرفت ال set I of S على إنها the set of
+
+20
+00:02:22,250 --> 00:02:34,870
+all V حيث V بساوي infimum ال set S فال
+
+21
+00:02:34,870 --> 00:02:40,430
+set هذه contains contains
+
+22
+00:02:40,430 --> 00:02:44,010
+more than one element more than
+
+23
+00:02:46,860 --> 00:02:52,280
+one element المجموعة
+
+24
+00:02:52,280 --> 00:02:58,000
+هذه تحتوي على أكتر من عنصر، هل هذا صحيح؟ هل الست
+
+25
+00:02:58,000 --> 00:03:01,860
+ممكن يكون إلها أكتر من infamous؟ لأ، لأ، لأ، لأ،
+
+26
+00:03:01,860 --> 00:03:02,560
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+27
+00:03:02,560 --> 00:03:07,020
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+28
+00:03:07,020 --> 00:03:07,100
+لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ، لأ،
+
+29
+00:03:07,100 --> 00:03:10,040
+لأ، لأ، لأ، لأ، لأ، لأ، ل
+
+30
+00:03:13,960 --> 00:03:19,580
+العبارة الرابعة every monotone sequence converges
+
+31
+00:03:19,580 --> 00:03:25,980
+if and only if it is bounded هذه
+
+32
+00:03:25,980 --> 00:03:28,780
+عبارة عن الـ monotone convergence theorem فهذه
+
+33
+00:03:28,780 --> 00:03:34,620
+true ال
+
+34
+00:03:34,620 --> 00:03:40,020
+sequence سالب
+
+35
+00:03:40,020 --> 00:03:55,840
+واحد أس N على Nإن ينتمي لإن is convergent هل
+
+36
+00:03:55,840 --> 00:03:56,760
+هذا صحيح؟
+
+37
+00:04:06,660 --> 00:04:12,140
+طيب ماشي المشكلة أن الأقلام السودة اللي عندي كلها
+
+38
+00:04:12,140 --> 00:04:22,160
+صارت فاتعة اه في واحد جبت انت و
+
+39
+00:04:22,160 --> 00:04:32,480
+الله انا مش كتير يعني
+
+40
+00:04:32,480 --> 00:04:36,020
+هدم يعني احسن نشوف يعني
+
+41
+00:04:42,570 --> 00:04:47,330
+فال sequence هذه convergent هل هذا صحيح ولا خطأ
+
+42
+00:04:47,330 --> 00:04:54,790
+هذا true و
+
+43
+00:04:54,790 --> 00:05:00,050
+لو بدنا نبرهن الكلام هذا و بالمناسبة ال sequence
+
+44
+00:05:00,050 --> 00:05:06,410
+هذه converge لصفر converge و ال limit تبعتها صفر
+
+45
+00:05:07,900 --> 00:05:14,940
+ليه؟ لأنه هاي المسافة بين ال inf term لحد انه ليه؟
+
+46
+00:05:14,940 --> 00:05:23,620
+سالب واحد أس ان على n سالب سفر ايش
+
+47
+00:05:23,620 --> 00:05:27,520
+هاد بالساوي؟
+
+48
+00:05:27,520 --> 00:05:28,320
+بتساوي
+
+49
+00:05:37,950 --> 00:05:45,590
+بتساوي واحد على ان صح؟ نصبوت؟ وهذا أصغر من اذا كان
+
+50
+00:05:45,590 --> 00:05:54,410
+واحد ضرب واحد على ان هذا عدد موجب واحد على ان تقول
+
+51
+00:05:54,410 --> 00:06:05,090
+للسفر إذن حسب نظرية سابقة رقمها
+
+52
+00:06:05,090 --> 00:06:11,610
+كان في النقص اتنين اربعةبطلع limit xn بساوي سفر
+
+53
+00:06:11,610 --> 00:06:15,190
+limit سالب
+
+54
+00:06:15,190 --> 00:06:20,750
+واحد بس n على n لما n تقوى ل infinity بساوي سفر
+
+55
+00:06:20,750 --> 00:06:25,230
+إذا
+
+56
+00:06:25,230 --> 00:06:28,650
+ال sequence هذي convergent إذا العبارة هذه true
+
+57
+00:06:28,650 --> 00:06:31,650
+طيب عبارة تانية
+
+58
+00:06:45,940 --> 00:06:55,320
+product of two divergent sequences
+
+59
+00:06:55,320 --> 00:07:03,700
+is divergent هل
+
+60
+00:07:03,700 --> 00:07:05,280
+هذا true ولا false؟
+
+61
+00:07:08,090 --> 00:07:10,990
+العبارة هادف false طب لما قلنا لكوا جيبوا counter
+
+62
+00:07:10,990 --> 00:07:17,310
+example ممكن تجيب سالب واحد اثنان وكمان ال
+
+63
+00:07:17,310 --> 00:07:23,290
+sequence التانية تكون سالب واحد اثنان او
+
+64
+00:07:23,290 --> 00:07:26,830
+ممكن تكون سالب واحد اثنان زائد واحد نفس الشغل
+
+65
+00:07:26,830 --> 00:07:32,390
+بتطلع convergent ال productهذه الـ divergent وهذه
+
+66
+00:07:32,390 --> 00:07:38,210
+الـ divergent لكن X in في Y in هساوي ال sequence
+
+67
+00:07:38,210 --> 00:07:44,650
+سلب واحد واست اتنين in لما
+
+68
+00:07:44,650 --> 00:07:49,370
+نضربهم في بعض فهذا بيعطيني ال sequence ثابت واحد
+
+69
+00:07:49,370 --> 00:07:55,730
+وهذه converge لواحد اذا هذه في عندي example of two
+
+70
+00:07:55,730 --> 00:08:01,090
+divergent sequences لكن حصل ضربهم بيطلعconvergent
+
+71
+00:08:01,090 --> 00:08:06,230
+وليس divergent طيب
+
+72
+00:08:06,230 --> 00:08:21,470
+لو كانت S bounded S bounded subset of R وS0
+
+73
+00:08:21,470 --> 00:08:28,510
+subset من S هل هذا بيقدّي ان انفمم
+
+74
+00:08:29,760 --> 00:08:42,480
+S0 subset أصغر من أو يساوي انفمه من ال S هل
+
+75
+00:08:42,480 --> 00:08:51,020
+هذه العبارة صحيحة؟ أيه
+
+76
+00:08:51,020 --> 00:08:59,320
+رأيكم؟ العبارة هذه falseلما مجموعة تصغر ال inform
+
+77
+00:08:59,320 --> 00:09:07,940
+تباعها بيكبر، لكن اللي بيكون صح أنه ال supremum لو
+
+78
+00:09:07,940 --> 00:09:12,600
+أخدت ال supremum للمجموعة الجزئية S0 فهذا بيطلع
+
+79
+00:09:12,600 --> 00:09:17,040
+أصغر من أو ساوي ال supremum للمجموع S، هذه العبارة
+
+80
+00:09:17,040 --> 00:09:17,320
+true
+
+81
+00:09:20,870 --> 00:09:25,710
+ال supremum لما المجموعه تكبر بيكبر لكن ال infimum
+
+82
+00:09:25,710 --> 00:09:38,110
+لما المجموعه تكبر بيصغر عكس بعض طيب
+
+83
+00:09:43,200 --> 00:09:50,100
+لو كانت x in sequence of positive real numbers و
+
+84
+00:09:50,100 --> 00:10:02,060
+limit x in plus one over x in بساوي واحد فهذا
+
+85
+00:10:02,060 --> 00:10:08,180
+بيقدي ان ال sequence x in diverges
+
+86
+00:10:08,180 --> 00:10:15,870
+هل هذه العبارة صح ولا خطأ؟العبارة هذه خطأ لأنه
+
+87
+00:10:15,870 --> 00:10:22,230
+احنا فينا في تمرين سبتاشر في section تلاتة اتنين
+
+88
+00:10:22,230 --> 00:10:26,230
+بقول اذا كانت ال sequence .. اذا كان ال limit
+
+89
+00:10:26,230 --> 00:10:29,630
+ratio هذا بساوي واحد فال sequence ممكن تكون
+
+90
+00:10:29,630 --> 00:10:33,890
+convergent او divergent وفي السؤال هذا اعطينا
+
+91
+00:10:33,890 --> 00:10:41,240
+مثلين واحد ل sequence convergentال ratio limit ال
+
+92
+00:10:41,240 --> 00:10:45,100
+ratio تبعها بيساوي واحد لكنها convergent ومثال
+
+93
+00:10:45,100 --> 00:10:50,300
+تاني ل sequence limit ال ratio تبعها أيضا بيساوي
+
+94
+00:10:50,300 --> 00:10:53,700
+واحد لكنها divergent إذا لو كان limit ال ratio
+
+95
+00:10:53,700 --> 00:10:57,100
+بيساوي واحد فال sequence إما converge أو divergent
+
+96
+00:10:57,100 --> 00:11:01,400
+مالضايش نجزم إنها convergent أو نجزم إنها
+
+97
+00:11:01,400 --> 00:11:07,020
+divergent okay إذا العبارة هذه خطأ أو false إذا
+
+98
+00:11:07,020 --> 00:11:13,950
+العبارة هذه falseلو بدلت divergent بconvergent
+
+99
+00:11:13,950 --> 00:11:21,530
+برضه false الصح انها may converge or may diverge
+
+100
+00:11:21,530 --> 00:11:26,810
+طيب
+
+101
+00:11:26,810 --> 00:11:43,910
+العبارة الأخيرة تسعةأي open interval
+
+102
+00:11:43,910 --> 00:11:47,950
+a وb تحتوي
+
+103
+00:11:47,950 --> 00:11:49,970
+rational number R
+
+104
+00:11:54,840 --> 00:11:59,220
+في rational number محصور من a وb يعني ال open
+
+105
+00:11:59,220 --> 00:12:03,920
+interval تحتوي ال R كذلك في نتيجة ال density
+
+106
+00:12:03,920 --> 00:12:08,300
+theorem أي open interval زي هذه تحتوي ال rational
+
+107
+00:12:08,300 --> 00:12:13,780
+إذن هذا الكلام صحيح
+
+108
+00:12:13,780 --> 00:12:18,340
+إذن هذا أول سؤال صح وخطأ السؤال التاني
+
+109
+00:12:33,670 --> 00:12:50,070
+Question 2 اذا
+
+110
+00:12:50,070 --> 00:12:55,770
+احنا
+
+111
+00:12:55,770 --> 00:13:01,210
+بنحل هذا امتحان هذا امتحان Med
+
+112
+00:13:03,740 --> 00:13:11,660
+mid term one التاريخ
+
+113
+00:13:11,660 --> 00:13:24,780
+تبعه اتناش تلاتة الفين و تلاتاش السؤال
+
+114
+00:13:24,780 --> 00:13:32,630
+او الفرع B من السؤال الأولإذا هذا السؤال الأول
+
+115
+00:13:32,630 --> 00:13:37,290
+الفرق بيه
+
+116
+00:13:37,290 --> 00:13:44,130
+X و Y ينتموا إلى R أعداد حقيقية Such that absolute
+
+117
+00:13:44,130 --> 00:13:53,190
+X minus Y أصغر من واحد على N لكل N في N لما نثبت
+
+118
+00:13:53,190 --> 00:13:55,470
+أن هذا بقدر X بساوي Y
+
+119
+00:14:00,570 --> 00:14:09,470
+البرهان هنستخدم الـ Archimedean property assume on
+
+120
+00:14:09,470 --> 00:14:13,930
+contrary على
+
+121
+00:14:13,930 --> 00:14:23,710
+المقيد ان X لا يساوي Y هذا
+
+122
+00:14:23,710 --> 00:14:24,410
+بيقدّي
+
+123
+00:14:28,910 --> 00:14:44,930
+أكبر من سفر لأي
+
+124
+00:14:44,930 --> 00:14:53,850
+عدد موجب يوجد in zero عدد طبيعيبحيث ان واحد على ن
+
+125
+00:14:53,850 --> 00:15:05,390
+زيرو أصغر من absolute X سالب Y هذا
+
+126
+00:15:05,390 --> 00:15:13,530
+من وين من ال Archimedean property طيب
+
+127
+00:15:13,530 --> 00:15:16,610
+انا عندي من الفرض
+
+128
+00:15:19,930 --> 00:15:36,910
+من الفرض by hypothesis هذا أصغر من واحد على n لكل
+
+129
+00:15:36,910 --> 00:15:39,770
+n وبالتالي هذا صحيح ل n zero
+
+130
+00:15:48,170 --> 00:15:53,370
+إذن بيطلع عندى 1 على N0 أصغر من 1 على N0 إذن هذا
+
+131
+00:15:53,370 --> 00:16:00,590
+بيقدي إن 1 على N0 أصغر من 1 على N0 وهذا تناقض
+
+132
+00:16:00,590 --> 00:16:07,610
+contradiction تناقض إذن هذا التناقض بيقول إن ال X
+
+133
+00:16:07,610 --> 00:16:14,490
+لازم تساوي ال Y كما هو مطلوب okay تمامإذن هذا
+
+134
+00:16:14,490 --> 00:16:22,890
+برهان الجزء التاني من السؤال الأول في عند
+
+135
+00:16:22,890 --> 00:16:35,710
+هنا السؤال التاني question
+
+136
+00:16:35,710 --> 00:16:48,690
+2 الفرع a show S&Tإن الـ infimum لست واحد على
+
+137
+00:16:48,690 --> 00:17:03,630
+الجذر ال N حيث N عدد طوابيعي بساوي سفر نشوف
+
+138
+00:17:03,630 --> 00:17:08,610
+مع بعض واضح
+
+139
+00:17:08,610 --> 00:17:14,940
+إن سفر أصغر من أو ساوي واحد على الجذر ال Nلكل n
+
+140
+00:17:14,940 --> 00:17:24,180
+عدد طبيعي صح؟ في حد عنده شك في ذلك؟ وبالتالي
+
+141
+00:17:24,180 --> 00:17:31,040
+so سفر is zero
+
+142
+00:17:31,040 --> 00:17:41,460
+is a lower bound a lower bound of ال set S اللي هي
+
+143
+00:17:43,280 --> 00:17:48,720
+بنعرفها لأنها مجموعة العناصر واحد على square root
+
+144
+00:17:48,720 --> 00:17:56,140
+of N حيث N ينتمي ل N طيب
+
+145
+00:17:56,140 --> 00:18:01,600
+to show أن
+
+146
+00:18:01,600 --> 00:18:07,160
+السفر هو ال minimum ل S أو هو ال greatest lower
+
+147
+00:18:07,160 --> 00:18:28,050
+bound لمجموعة S فبناخد let Wbe any lower bound of
+
+148
+00:18:28,050 --> 00:18:37,130
+S فبالنسبة
+
+149
+00:18:37,130 --> 00:18:46,710
+لـ claimبنثبت أن السفر أصغر من أو ساوي W عفوا W
+
+150
+00:18:46,710 --> 00:18:53,150
+أصغر من أو ساوي 0 وبالتالي هيك يكون السفر أكبر من
+
+151
+00:18:53,150 --> 00:18:57,150
+أو ساوي أي lower bound يعني السفر هو ال greatest
+
+152
+00:18:57,150 --> 00:19:04,590
+lower bound صح فلبرهان ذلك assume بنعمل برهان
+
+153
+00:19:04,590 --> 00:19:13,920
+بالتناقض on contraryأفرضه على النقيد أن w أكبر من
+
+154
+00:19:13,920 --> 00:19:18,420
+سفر then
+
+155
+00:19:18,420 --> 00:19:21,540
+by
+
+156
+00:19:21,540 --> 00:19:28,160
+Archimedean property .. by Archimedean property
+
+157
+00:19:28,160 --> 00:19:37,150
+لأي عدد موجب زي هذايوجد عدد طبيعي N0 ينتمي إلى N
+
+158
+00:19:37,150 --> 00:19:43,130
+بحيث انه مقلوب N0
+
+159
+00:19:43,130 --> 00:19:51,250
+أصغر من العدد الموجب W تربية طبعا W تربية إذا W
+
+160
+00:19:51,250 --> 00:19:57,960
+عدد موجب فW تربية بالتأكيد عدد موجبفانا بطبّق الـ
+
+161
+00:19:57,960 --> 00:20:01,360
+Archimedean property مش على w وعلى w تربية العدد
+
+162
+00:20:01,360 --> 00:20:06,060
+الموجب w square فبقدر ألاقي by Archimedean
+
+163
+00:20:06,060 --> 00:20:11,140
+property natural number n0 مقلوب وأصغر من w تربية
+
+164
+00:20:11,140 --> 00:20:21,940
+طبعا هذا بيقدّي أن واحد على جذر n0 أصغر من w ومن
+
+165
+00:20:21,940 --> 00:20:22,240
+ال
+
+166
+00:20:26,300 --> 00:20:34,080
+من الفرض الـ W هذا lower bound للست S وبالتالي هذا
+
+167
+00:20:34,080 --> 00:20:41,320
+أصغر من أو سوى واحد على الجدر التربيهي ل N0 لأن
+
+168
+00:20:41,320 --> 00:20:46,440
+هذا ينتمي ل S، هذا عنصر في S، صح؟ واحنا فرضين أن
+
+169
+00:20:46,440 --> 00:20:53,370
+الـ W أشمل lower boundللمجموع S وهذا answer في
+
+170
+00:20:53,370 --> 00:20:58,730
+المجموع S إذا ال W كونه lower bound ل S أصغر من أو
+
+171
+00:20:58,730 --> 00:21:04,310
+ساوي واحد على square root ل N0 فطبعا هذا بيدي ان
+
+172
+00:21:04,310 --> 00:21:09,150
+واحد على square root ل N0 أصغر من واحد على square
+
+173
+00:21:09,150 --> 00:21:18,330
+root ل N0 وهذا مدينة تناقضكيف عدد بيطلع أصغر من
+
+174
+00:21:18,330 --> 00:21:21,730
+نفسه هذا تناقض لأن هذا التناقض بيقول لإن ال
+
+175
+00:21:21,730 --> 00:21:26,010
+assumption تبعنا ان ال W أكبر من السفر خطأ
+
+176
+00:21:26,010 --> 00:21:33,210
+وبالتالي ال W لازم يكون أصغر بدل ما هو أكبر من
+
+177
+00:21:33,210 --> 00:21:37,970
+السفر يطلع أصغر من أو يساوي سفر وبالتالي ال W
+
+178
+00:21:37,970 --> 00:21:43,830
+السفر هو أكبر lower bound okay إذا هذا بيكمل
+
+179
+00:21:43,830 --> 00:21:45,750
+البرهان تمام
+
+180
+00:22:04,850 --> 00:22:17,070
+انجاب على الفرق بيه من السؤال التاني show
+
+181
+00:22:17,070 --> 00:22:26,770
+ان ال limit لواحد على جذر ال N as N times infinity
+
+182
+00:22:26,770 --> 00:22:28,370
+بساوي سفر
+
+183
+00:22:40,270 --> 00:22:45,910
+Proof بإن احنا في النهاية بيستخدم تعريف طبعا
+
+184
+00:22:45,910 --> 00:22:51,790
+epsilon capital N للنهايات ففي نهاية الأمر بدنا ال
+
+185
+00:22:51,790 --> 00:22:55,190
+absolute value ل 1 على square root of N minus 0
+
+186
+00:22:55,190 --> 00:23:02,270
+بدنا ده يطلع أصغر من أي epsilon صح؟ طب ما هذا
+
+187
+00:23:02,270 --> 00:23:05,070
+بيساوي 1 على square root of N
+
+188
+00:23:09,000 --> 00:23:16,500
+متى هذا بيكون أصغر من epsilon فانا
+
+189
+00:23:16,500 --> 00:23:24,040
+هاخد هذا
+
+190
+00:23:24,040 --> 00:23:28,080
+لما واحد على n أصغر من epsilon تربية لو ربعت
+
+191
+00:23:28,080 --> 00:23:33,920
+الطرفين فمتى
+
+192
+00:23:33,920 --> 00:23:35,920
+هذا بيكون أصغر من epsilon تربية
+
+193
+00:23:38,730 --> 00:23:45,210
+Okay إذا هنا هاخد انا واحد على capital N أصغر من
+
+194
+00:23:45,210 --> 00:23:54,110
+epsilon تربية إذا
+
+195
+00:23:54,110 --> 00:23:58,570
+نستخدم ال Archimedean property هذا epsilon تربية
+
+196
+00:23:58,570 --> 00:24:02,690
+عدد موجب By Archimedean property بقدر ألاقي عدد
+
+197
+00:24:02,690 --> 00:24:07,550
+طبيعي capital N مقلوب وأصغر من epsilon تربية ناشي
+
+198
+00:24:08,920 --> 00:24:15,320
+بدا هنا given epsilon
+
+199
+00:24:15,320 --> 00:24:27,320
+أكبر من السفر use الarchimedean property to choose
+
+200
+00:24:27,320 --> 00:24:36,760
+n عدد طبيعي بحيث أن واحد على n أصغر من epsilon
+
+201
+00:24:39,750 --> 00:24:54,590
+الان لو خدت small n أكبر من أو ساوي capital N فهذا
+
+202
+00:24:54,590 --> 00:24:59,410
+بيقدي أن واحد على small n أصغر لو ساوي واحد على
+
+203
+00:24:59,410 --> 00:25:00,190
+capital N
+
+204
+00:25:05,570 --> 00:25:09,570
+بيقدي واحد على square root ل N أصغر من لو يساوي
+
+205
+00:25:09,570 --> 00:25:16,450
+واحد على square root ل capital N وهذا بيقدي ان ال
+
+206
+00:25:16,450 --> 00:25:23,650
+absolute value لواحد على square root ل N minus صفر
+
+207
+00:25:23,650 --> 00:25:27,790
+بيساوي واحد على square root ل N وهذا أصغر من لو
+
+208
+00:25:27,790 --> 00:25:34,250
+يساوي واحد على square root ل capital N وهذا من هنا
+
+209
+00:25:36,260 --> 00:25:40,760
+لو سمينا الـ inequality هذه الـ star إذا by star
+
+210
+00:25:40,760 --> 00:25:48,620
+واحد على square root ل N أصغر من epsilon إذا
+
+211
+00:25:48,620 --> 00:25:53,440
+هاي نحققنا تعريف epsilon capital N للنهايات for
+
+212
+00:25:53,440 --> 00:25:58,600
+any given epsilon أثبتنا إنه يوجد capital N عدد
+
+213
+00:25:58,600 --> 00:26:02,760
+طبيعي وهذا العدد الطبيعي يعتمد على epsilon هاي
+
+214
+00:26:02,760 --> 00:26:08,910
+مرتبط بepsilonبحيث لكل n أكبر من أو ساوي capital N
+
+215
+00:26:08,910 --> 00:26:16,010
+طلع المسافة بين xn و x اللي هي سفر أصغر من epsilon
+
+216
+00:26:16,010 --> 00:26:23,530
+اذا by definition by
+
+217
+00:26:23,530 --> 00:26:28,910
+definition بطلع عندي limit واحد على square root ل
+
+218
+00:26:28,910 --> 00:26:33,290
+n بساوي سفر وهو المطلوب طبعا
+
+219
+00:26:37,550 --> 00:26:42,930
+طبعاً في حال تاني أو في برهان تاني باستخدام الـ
+
+220
+00:26:42,930 --> 00:26:48,770
+monotone convergence theorem إذا
+
+221
+00:26:48,770 --> 00:26:54,350
+ال solution to use
+
+222
+00:26:54,350 --> 00:27:01,090
+monotone convergence theorem ال sequence أنا عندي
+
+223
+00:27:01,090 --> 00:27:04,350
+xn بساوي واحد على square root ل n
+
+224
+00:27:09,010 --> 00:27:14,590
+هذا أكبر من أو ساوي واحد على square root ل n زايد
+
+225
+00:27:14,590 --> 00:27:26,090
+واحد اللي هو xn زايد واحد وبالتالي ال sequence is
+
+226
+00:27:26,090 --> 00:27:32,900
+decreasing صح؟بعدين انا عندي absolute xn بساوي
+
+227
+00:27:32,900 --> 00:27:38,300
+absolute واحد على جدر ال n أصغر من أو ساوي واحد
+
+228
+00:27:38,300 --> 00:27:47,120
+لكل n لكل
+
+229
+00:27:47,120 --> 00:27:57,520
+n فهذا بيقدي ان ال sequence xn is bounded اذا
+
+230
+00:27:57,520 --> 00:28:02,750
+bounded و decrease inإذا الـ sequence xn by
+
+231
+00:28:02,750 --> 00:28:07,690
+monotone convergence theorem limit xn بساوة
+
+232
+00:28:07,690 --> 00:28:17,710
+الانفمام ل xn حيث n ينتمي إلى n فأثبتنا أن
+
+233
+00:28:17,710 --> 00:28:24,760
+الانفمام بساوة سفر بالفرع اللي جابلهفهذا برهان
+
+234
+00:28:24,760 --> 00:28:28,540
+تاني لكن احنا ال .. ال monotone convergence الكلام
+
+235
+00:28:28,540 --> 00:28:34,860
+مش داخله في الامتحان فممكن انكم يعني ال ..
+
+236
+00:28:34,860 --> 00:28:38,580
+تستخدموا البرهان الأول يعني ممكن تستخدموا البرهان
+
+237
+00:28:38,580 --> 00:28:42,360
+الأول يعني okay
+
+238
+00:28:42,360 --> 00:28:46,400
+تمام طيب نكمل
+
+239
+00:29:09,040 --> 00:29:15,540
+find the supremum الجزء C بإنه نوجد ال supremum
+
+240
+00:29:15,540 --> 00:29:20,800
+لواحد سالب واحد على الجدر ال N حيث N ينتمي ل N
+
+241
+00:29:20,800 --> 00:29:32,620
+فهذا حسب exercise أخدنا supremum A زائد 6 بساوي A
+
+242
+00:29:32,620 --> 00:29:38,640
+زائد supremumالست اللي هي عناصرها سالب واحد على
+
+243
+00:29:38,640 --> 00:29:48,800
+جدر ال N هيف N ينتمي الى N ويساوي واحد الان
+
+244
+00:29:48,800 --> 00:29:56,140
+supremum سالب ست بيساوي سالب ال infimum لعناصر
+
+245
+00:29:56,140 --> 00:29:56,640
+الست
+
+246
+00:30:05,050 --> 00:30:09,910
+و احنا لسه مثبتين ان ال inform هذا بساوي سفر اذا
+
+247
+00:30:09,910 --> 00:30:15,210
+ال suprem للست هذي بطلع واحد طيب
+
+248
+00:30:15,210 --> 00:30:25,970
+فرقة تانية show that اثبتي انه limit cosine
+
+249
+00:30:25,970 --> 00:30:34,290
+n على n او على جدر ال nas n tends to infinity
+
+250
+00:30:34,290 --> 00:30:38,650
+بساوي سفر proof
+
+251
+00:30:38,650 --> 00:30:43,290
+أنا
+
+252
+00:30:43,290 --> 00:30:50,010
+عندي cosine n أكبر من أو أصغر من أو ساوي واحد أكبر
+
+253
+00:30:50,010 --> 00:30:59,630
+من أو ساوي سالب واحد لكل n في n وواحد
+
+254
+00:31:01,530 --> 00:31:07,070
+على جدر ال N عدد موجب فلو ضربت المتباينة هذه في
+
+255
+00:31:07,070 --> 00:31:11,550
+واحد على جدر ال N فبطلع سالب واحد على جدر ال N
+
+256
+00:31:11,550 --> 00:31:18,130
+أصغر لو سوى cosine N على جدر ال N أصغر لو سوى واحد
+
+257
+00:31:18,130 --> 00:31:21,690
+على جدر ال N لكل N في N
+
+258
+00:31:24,530 --> 00:31:28,310
+طيب انا عند ال sequence لسه مثبتين احنا هنا في
+
+259
+00:31:28,310 --> 00:31:32,510
+الفرع b ان ال sequence هذه ال limit تبعتها as n
+
+260
+00:31:32,510 --> 00:31:35,970
+tends to infinity بساوة سفر و ال sequence هذه ال
+
+261
+00:31:35,970 --> 00:31:41,430
+limit تبعتها سالب limit واحد على الجدر ال n و سالب
+
+262
+00:31:41,430 --> 00:31:46,830
+واحد بسفر بطلع سفر as n tends to infinity اذا by
+
+263
+00:31:46,830 --> 00:31:47,910
+squeeze theorem
+
+264
+00:31:51,910 --> 00:31:57,090
+بسكويز تيريم أو sandwich theorem بطلع limit ال
+
+265
+00:31:57,090 --> 00:32:02,250
+sequence اللي لحد تبعها محصور في النص اللي هو
+
+266
+00:32:02,250 --> 00:32:06,590
+cosine n على square root ل n as n times infinity
+
+267
+00:32:06,590 --> 00:32:16,070
+بساوي 7 تمام؟ إذن هذا برهان الجزء دي
+
+268
+00:32:23,640 --> 00:32:30,920
+واضحة للحلول question
+
+269
+00:32:30,920 --> 00:32:38,680
+تلاتة الفرع a انا عندي in بالساوية closed interval
+
+270
+00:32:38,680 --> 00:32:44,480
+من سفر لواحد على جدر ال n prove
+
+271
+00:32:46,630 --> 00:32:51,890
+إنه ال intersection from n equals one to infinity
+
+272
+00:32:51,890 --> 00:33:02,970
+ل I n بساوي single twin zipper فممكن
+
+273
+00:33:02,970 --> 00:33:11,570
+نستخدم ال nested interval property proof
+
+274
+00:33:11,570 --> 00:33:23,930
+أول شي واضحواضح ان سفر ينتمي ل I N لكل N في N هذا
+
+275
+00:33:23,930 --> 00:33:28,690
+بيقدي ان السفر ينتمي
+
+276
+00:33:28,690 --> 00:33:35,210
+لتقاطعه صح
+
+277
+00:33:35,210 --> 00:33:40,310
+الفترة المغلقة هذه السفر دائما ينتمي لها لكل عدد
+
+278
+00:33:40,310 --> 00:33:45,330
+طبيعيالان انا في عندي sequence of intervals و
+
+279
+00:33:45,330 --> 00:33:49,970
+السفر ينتمي لكل عنصر في ال set إذا السفر ينتمي
+
+280
+00:33:49,970 --> 00:34:00,410
+لتقاطه كل المجموعات طيب الفترة I in is closed صح
+
+281
+00:34:00,410 --> 00:34:06,850
+and bounded لكل
+
+282
+00:34:06,850 --> 00:34:16,080
+inو بعدين واضح ان I N contains I N زاد واحد لكل N
+
+283
+00:34:16,080 --> 00:34:23,340
+في N صح؟ يعني ال sequence هذه nested يعني ال
+
+284
+00:34:23,340 --> 00:34:29,200
+sequence I N nested
+
+285
+00:34:29,200 --> 00:34:32,300
+اذا
+
+286
+00:34:32,300 --> 00:34:35,940
+by
+
+287
+00:34:35,940 --> 00:34:38,000
+nested
+
+288
+00:34:44,870 --> 00:34:50,710
+intervals theorem استقاط
+
+289
+00:34:50,710 --> 00:34:59,510
+وهذا لازم يكون في unique element لأنه انا عندي طيب
+
+290
+00:34:59,510 --> 00:35:07,490
+جبل ما نطبق نستد انا عندي ال infimum لواحد على جذر
+
+291
+00:35:07,490 --> 00:35:08,810
+n سالب سفر
+
+292
+00:35:18,070 --> 00:35:26,910
+هذا الان from أثبتنا أنه بساوي سبر إذا حسب by
+
+293
+00:35:26,910 --> 00:35:31,470
+nested
+
+294
+00:35:31,470 --> 00:35:36,370
+intervals theorem
+
+295
+00:35:39,780 --> 00:35:47,720
+الـ intersection has unique element has
+
+296
+00:35:47,720 --> 00:35:52,920
+unique element
+
+297
+00:35:52,920 --> 00:35:57,340
+يعني في التقاطع مافيش أنصر وحيد طب احنا قلنا ان
+
+298
+00:35:57,340 --> 00:36:03,500
+السفر ينتمي لتقاطع وتقاطع في أنصر واحد لذا لازم
+
+299
+00:36:03,500 --> 00:36:07,960
+يساوي السفر in
+
+300
+00:36:07,960 --> 00:36:08,780
+a sense
+
+301
+00:36:13,330 --> 00:36:21,210
+بما أن السفر ينتمي للتقاطع يجب
+
+302
+00:36:21,210 --> 00:36:25,210
+أن
+
+303
+00:36:25,210 --> 00:36:31,070
+يكون التقاطع من N بساوي واحد infinity ل I N بساوي
+
+304
+00:36:31,070 --> 00:36:33,610
+بس single tone سفر
+
+305
+00:36:39,670 --> 00:36:44,490
+طبعا ممكن اعطيتكم انا برهان زي هذا بس كان بدل 1
+
+306
+00:36:44,490 --> 00:36:46,110
+على جدر ال N 1 على N
+
+307
+00:36:50,700 --> 00:36:57,680
+و أثبتنا إن ال set هذى طبعا واضح من هنا إن هذى
+
+308
+00:36:57,680 --> 00:37:04,260
+دايما صحيحة و أثبتنا العكس و قلنا إنه لو أخدت أي x
+
+309
+00:37:04,260 --> 00:37:07,880
+تتقاطع فبنا نثبت إن هذا ال x بساوي سفر و عملنا
+
+310
+00:37:07,880 --> 00:37:12,800
+برهان بالتناقض افرضي إن ال x مابسويش سفر إذا أكبر
+
+311
+00:37:12,800 --> 00:37:16,100
+من سفر و وصلنا إلى تناقض by Archimedean property
+
+312
+00:37:17,080 --> 00:37:21,820
+إذا في برهان تاني لكن أنا حبيت أعطيكم البرهان هذا
+
+313
+00:37:21,820 --> 00:37:26,840
+التاني اللي ما خناش زيه طبعا
+
+314
+00:37:26,840 --> 00:37:30,920
+صح
+
+315
+00:37:30,920 --> 00:37:37,340
+إذا أنا عندكم برهانين طيب
+
+316
+00:37:37,340 --> 00:37:42,700
+هاي كمان الجزء بيه من السؤال هذا أنا في عندي
+
+317
+00:37:42,700 --> 00:37:49,820
+sequence xn sequence mrوعندي xn أصغر من أو ساوي
+
+318
+00:37:49,820 --> 00:38:02,720
+سفر لكل n وبدنا نثبت إنه إذا كان limit xn بساوي x
+
+319
+00:38:02,720 --> 00:38:10,810
+then ال x بتطلع أيضا أصغر من أو ساوي سفرأنا في
+
+320
+00:38:10,810 --> 00:38:14,610
+عندى sequence of real numbers كل حدودها غير ثالثة
+
+321
+00:38:14,610 --> 00:38:18,330
+و ال sequence converge ل X بالدفعة ان ال limit
+
+322
+00:38:18,330 --> 00:38:27,850
+ايضا بتطلع غير ثالثة فهي البرهان proof برهان
+
+323
+00:38:27,850 --> 00:38:32,930
+بالتناقض assume on
+
+324
+00:38:32,930 --> 00:38:33,650
+contrary
+
+325
+00:38:36,400 --> 00:38:45,860
+إن X أكبر من سفر و بدنا نصل إلى تناقض افرض
+
+326
+00:38:45,860 --> 00:38:56,620
+إن X أكبر من سفر طيب let epsilon بساوي X ع 2 هذا
+
+327
+00:38:56,620 --> 00:39:05,960
+بطل عدل موجببما أنه since .. since xn converges ل
+
+328
+00:39:05,960 --> 00:39:13,010
+x إذا يوجد capital N يعتمد على إبسلونعدد طبيعي
+
+329
+00:39:13,010 --> 00:39:19,190
+بحيث أنه لو كان n أكبر من أو ساوي capital N فهذا
+
+330
+00:39:19,190 --> 00:39:26,110
+بقدر أن absolute xn minus x أصغر من epsilon طيب ال
+
+331
+00:39:26,110 --> 00:39:30,910
+epsilon هذا أخدناها بساوي x ع 2 إذا أنا عندي هي xn
+
+332
+00:39:30,910 --> 00:39:36,830
+minus x أصغر من x ع 2 أكبر
+
+333
+00:39:36,830 --> 00:39:38,550
+من سالب x ع 2
+
+334
+00:39:42,440 --> 00:39:49,560
+طيب ما هيك بطلع عندي x in ضيفي x لكل الأطراف فبطلع
+
+335
+00:39:49,560 --> 00:40:01,200
+x in أصغر من تلاتة x عتنين أكبر من x عتنين طيب
+
+336
+00:40:01,200 --> 00:40:06,000
+هذا
+
+337
+00:40:06,000 --> 00:40:12,140
+معناه وهذا الكلام صحيح لكل inأكبر من و ساوي
+
+338
+00:40:12,140 --> 00:40:18,740
+capital N فلو أخدت .. إذا بطلع من هنا X capital N
+
+339
+00:40:18,740 --> 00:40:22,660
+لو أخدت small n هذه بساوي capital N فبطلع X
+
+340
+00:40:22,660 --> 00:40:29,740
+capital N أكبر من X ع 2 و أنا عندي X ع 2 عدد موجب
+
+341
+00:40:29,740 --> 00:40:35,100
+أكبر من 0 إذا أنا بطلع عندي X capital N أكبر من 0
+
+342
+00:40:35,100 --> 00:40:41,550
+وهذا تناقضلأن انا فرض ان كل حدود ال sequence كلهم
+
+343
+00:40:41,550 --> 00:40:46,770
+اعداد غير سالبة فكيف طلع هالحد رقم capital N موجب
+
+344
+00:40:46,770 --> 00:40:52,090
+هذا بتناقض مع الفرض تمام؟ اذا هذا سبب التناقض هذا
+
+345
+00:40:52,090 --> 00:40:59,550
+هو ال assumption تبعنا ان x أكبر من السفر okay؟
+
+346
+00:40:59,550 --> 00:41:05,490
+اذا الصح ان x أصغر من أو ساوي سفر وهو المطلوب
+
+347
+00:41:08,070 --> 00:41:16,710
+Okay تمام اذا يعني هذه يعني بعض الأسئلة الاسئلة
+
+348
+00:41:16,710 --> 00:41:25,630
+الرابعة هذا نظرية أخدناها و اللي بعدي أعتقد حلناها
+
+349
+00:41:25,630 --> 00:41:34,490
+في المحاضرة فهواجف هنا و هيك بنكون يعني راجعنا
+
+350
+00:41:34,490 --> 00:41:41,290
+تقريبا امتحانللمتحانة النصفة ونشوفكم ان شاء الله
+
+351
+00:41:41,290 --> 00:41:41,690
+بقرا
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..268be34dc8187acfb7b65826af5ba650512b9d3f
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_postprocess.srt
@@ -0,0 +1,1884 @@
+1
+00:00:20,960 --> 00:00:27,560
+Okay إذا هنواصل ان شاء الله اللي بدنا في المحاضرة
+
+2
+00:00:27,560 --> 00:00:33,340
+السادقة المرة اللي فاتت خلينا بسرعة بس هيك نمر على
+
+3
+00:00:33,340 --> 00:00:40,220
+الحاجات اللي أخدناها أخدنا اللي هو ال algebraic
+
+4
+00:00:40,220 --> 00:00:43,060
+properties of the real number system اللي هو
+
+5
+00:00:43,060 --> 00:00:48,970
+القواصة الجبريةو أعرفنا اللي هو ال real number
+
+6
+00:00:48,970 --> 00:00:52,930
+system فقلنا إن ال real number system عبارة عن
+
+7
+00:00:52,930 --> 00:00:58,430
+المجموعة R مع عمليتين جبريتين أو ثنائيتين عملية
+
+8
+00:00:58,430 --> 00:01:03,110
+جمع و عملية ضرب و هدول العمليات بحققوا خمس خواص
+
+9
+00:01:03,110 --> 00:01:08,290
+خاصية الإبدال competitive law خاصية الدمج ال
+
+10
+00:01:08,290 --> 00:01:14,180
+associative lawsخواص التوزيع distributive laws
+
+11
+00:01:14,180 --> 00:01:19,120
+خاصية الرابعة وجود ال identity elements الأناصر
+
+12
+00:01:19,120 --> 00:01:25,280
+المحايدة اللي هي سمنها 01 ووجود ال inverse
+
+13
+00:01:25,280 --> 00:01:38,580
+elements أو العناصر النظائر أو المعكسات فلكل عدد
+
+14
+00:01:38,580 --> 00:01:48,850
+حقيقيفيه إله معكوس جمعي اللي هو Salvoو لكل عدد
+
+15
+00:01:48,850 --> 00:01:55,330
+حقيقي غير مختلف عن السفر له نظير ضربي او
+
+16
+00:01:55,330 --> 00:01:59,030
+multiplicative inverse من المظل بالرمز x is
+
+17
+00:01:59,030 --> 00:02:03,050
+negative واحد بحيث لو ضربتم في بعض بيعطوني ال
+
+18
+00:02:03,050 --> 00:02:10,890
+identity element واحد هدول الخمس خواص اللي بتحققهم
+
+19
+00:02:10,890 --> 00:02:15,760
+مجموعة العداد الحقيقية معالعمليات الدرب والجامع
+
+20
+00:02:15,760 --> 00:02:21,600
+اللي عرفناها سابقا في أول خواص أخدناها اللي هي
+
+21
+00:02:21,600 --> 00:02:27,680
+cancellation laws موجودة في نظرية 1 1 فعملية
+
+22
+00:02:27,680 --> 00:02:33,220
+الجامع بتحقق cancellation law يعني انا لو كان عندي
+
+23
+00:02:33,220 --> 00:02:38,940
+x plus z بساوي y plus z فممكن اشطب zمن الطرفين
+
+24
+00:02:38,940 --> 00:02:44,680
+بطلع عندي x بساوي y كذلك عملية الضرب بتحقق ال
+
+25
+00:02:44,680 --> 00:02:51,000
+cancellation law فلو في عندي حصل ضرب زي هذا بساوي
+
+26
+00:02:51,000 --> 00:02:56,140
+حصل الضرب هذا و ال answer w هذا العدد w بسويش سفر
+
+27
+00:02:56,140 --> 00:03:01,470
+فمقدر أجسم الطرفين على wو ascentage X بساوي Y هذه
+
+28
+00:03:01,470 --> 00:03:05,430
+الخواص مهمة و برهنتلكم المرة اللي فاتت الجزء
+
+29
+00:03:05,430 --> 00:03:11,810
+التاني و برهان الجزء الأول مماثل و بالتالي قلنا
+
+30
+00:03:11,810 --> 00:03:17,650
+لكم حاولوا تثبتوا بنفس الطريقة بالمثل كمان أخدنا
+
+31
+00:03:17,650 --> 00:03:22,810
+نظرية تانية اللي هي النظرية هذه ذكرناها المرة اللي
+
+32
+00:03:22,810 --> 00:03:30,050
+فاتت فيها حوالي عشر خواص للأعداد الحقيقيةفاول
+
+33
+00:03:30,050 --> 00:03:35,350
+خاصية لو ضربت أي عدد حقيقي بالصفر سواء من اليمين
+
+34
+00:03:35,350 --> 00:03:39,370
+او اليسار فالنتج العدد الصفري اللي هو ال additive
+
+35
+00:03:39,370 --> 00:03:47,090
+identity صفر فبرهان الجزء هذا هو برهان الجزء الأول
+
+36
+00:03:47,090 --> 00:03:55,210
+يعني باين واحد هنا فكيف بتم البرهان انا عايز اثبت
+
+37
+00:03:55,210 --> 00:04:02,370
+ان x ضرب صفر بساوي صفرطيب انا عندي لو جمعت x ضارب
+
+38
+00:04:02,370 --> 00:04:07,470
+0 زاد x ضارب 0 بقدر باستخدام ال distributive law
+
+39
+00:04:07,470 --> 00:04:13,430
+أخد x عام المشترك كأني ضاربة x في 0 زاد 0 هذا صحيح
+
+40
+00:04:13,430 --> 00:04:17,550
+باستخدام ال distributive law الآن لما أجمع السفر
+
+41
+00:04:17,550 --> 00:04:22,450
+على أي عدد حقيقي حتى لو نفسه الناتج بطلع 0 هذا من
+
+42
+00:04:22,450 --> 00:04:33,170
+خواص المحايد الجامعيو ال X ضرب سفر هو نفسه لو جمعت
+
+43
+00:04:33,170 --> 00:04:37,330
+على العدد هذا سفر فيبقى زي ما هو من خواص السفر
+
+44
+00:04:37,330 --> 00:04:43,950
+الان انا ممكن اشطب باستخدام cancellation law ممكن
+
+45
+00:04:43,950 --> 00:04:49,590
+اشطب هذا و اشطب هذا فبطلع عندي X ضرب سفر بساوي سفر
+
+46
+00:04:49,590 --> 00:04:55,490
+okay تمامالخاصية التانية الخاصية التانية عايزين
+
+47
+00:04:55,490 --> 00:05:01,230
+نثبت أنه لو أخدت أي عدد حقيقي و أخدت سلبه مرتين
+
+48
+00:05:01,230 --> 00:05:06,530
+فهذا هو نفس ال X البرهان برضه بتم كالتالي هاي ال X
+
+49
+00:05:06,530 --> 00:05:12,370
+و بجمع عليه negative X اللي هو المعكوس الجامعي
+
+50
+00:05:12,370 --> 00:05:20,390
+طبعا فهذا بساوة سفر هذا بساوة سفر من خواص المعكوس
+
+51
+00:05:20,390 --> 00:05:26,570
+الجامعيو ممكن ان احنا نبدل هدول مع بعض او لأ، الان
+
+52
+00:05:26,570 --> 00:05:31,610
+برضه لو أخدت هذا، هذا عدد حقيقي، و هذا المعكوس
+
+53
+00:05:31,610 --> 00:05:36,970
+الجمعي تبعه، عدد حقيقي و المعكوس الجمعي تبعه دايما
+
+54
+00:05:36,970 --> 00:05:41,830
+بساوة سفر، الان ممكن نبدل عملية الجمع ابدالية،
+
+55
+00:05:41,830 --> 00:05:46,970
+commutative، فنبدل الحاجات هذه مع بعضالان عملية
+
+56
+00:05:46,970 --> 00:05:50,970
+الجامعة بتحقق قانون الحدث cancellation law إذا
+
+57
+00:05:50,970 --> 00:05:55,390
+ممكن أشطب أنا العنصر هذا مع هذا بيبقى عندي على
+
+58
+00:05:55,390 --> 00:05:59,810
+الشمال X وعلى اليمين بيبقى negative negative X
+
+59
+00:05:59,810 --> 00:06:06,070
+فبالتالي هي كمان أثبتنا صحة الخاصية هذه تمام؟
+
+60
+00:06:07,410 --> 00:06:11,250
+الخاصية التالتة في النظرية اللى شوفناها قبل شوية
+
+61
+00:06:11,250 --> 00:06:17,770
+برهانها مماثل لخاصية تانية وبالتالي هسيبه تمرين،
+
+62
+00:06:17,770 --> 00:06:21,770
+اذا بعض الحاجات اللى برهانها مماثل دايما هنسيبها
+
+63
+00:06:21,770 --> 00:06:26,030
+كتمرين للطالب لإن الفكرة نفسها ورياضيات مجرد أفكار
+
+64
+00:06:26,030 --> 00:06:33,620
+فإذا عرفنا الفكرة انتهى الحل اللغزالخاصية الرابعة،
+
+65
+00:06:33,620 --> 00:06:37,120
+في الخاصية الرابعة عايزين نثبت أنه لو ضربت سالب
+
+66
+00:06:37,120 --> 00:06:42,880
+واحد في x بطلع عندي ال negative x أو المحايد
+
+67
+00:06:42,880 --> 00:06:48,640
+الجمعي ل x فلبرهان ذلك باخد negative واحد في x و
+
+68
+00:06:48,640 --> 00:06:53,820
+بجمعها على x فهذا هو نفسه هي negative واحد في x و
+
+69
+00:06:53,820 --> 00:06:59,970
+ال x هذه عبارة عن واحد في xالان ممكن هنا استخدم
+
+70
+00:06:59,970 --> 00:07:03,070
+الـ distributive law عملية الضرب تتوزع لعملية
+
+71
+00:07:03,070 --> 00:07:07,670
+الجمال فممكن اكتب هذا سالب واحد زاد واحد مضروب من
+
+72
+00:07:07,670 --> 00:07:13,370
+اليمين في X وعملية الضرب ابدالية فهي نفس كما لو
+
+73
+00:07:13,370 --> 00:07:19,040
+ضربت X من اليمين في سالب واحد زاد واحدOkay تمام
+
+74
+00:07:19,040 --> 00:07:24,700
+الان لما اجمع سالب واحد هذا سالب واحد على واحد
+
+75
+00:07:24,700 --> 00:07:31,440
+انصر ونظير الجمع تبعهم مجموعهم سفر و سفر في اي
+
+76
+00:07:31,440 --> 00:07:37,500
+انصر اثبتنا انه بيساوي سفر و السفر هو نفسه سالب x
+
+77
+00:07:37,500 --> 00:07:42,450
+زائد xوبالتالي بقدر استخدم ال cancellation اللي هو
+
+78
+00:07:42,450 --> 00:07:47,250
+عامل cancelling ل X على الطرف الشمال و cancelling
+
+79
+00:07:47,250 --> 00:07:50,990
+ل X على الطرف اليمين يبقى في الشمال سالب واحد في X
+
+80
+00:07:50,990 --> 00:07:55,850
+في اليمين سالب X وبالتالي هيك ممكن أثبتنا الخاصية
+
+81
+00:07:55,850 --> 00:08:01,850
+هذه واضح؟ أي حد عنده أي استفسار؟ خواص سهل و براهين
+
+82
+00:08:01,850 --> 00:08:06,150
+سهلة جدا انت دارسين مبادئ و اللي دارسين مبادئ
+
+83
+00:08:06,150 --> 00:08:11,530
+رياضيات و فاهمينها كويس هذه حاجاتيعني براهين أمثلة
+
+84
+00:08:11,530 --> 00:08:16,170
+كلها على برهان مباشر بسيط باستخدام خواص ذكرناها
+
+85
+00:08:16,170 --> 00:08:22,990
+سابقا فهذا مجرد يعني مبادئ رياضيات الخاصية الخامسة
+
+86
+00:08:22,990 --> 00:08:29,590
+احنا عايزين نثبت لو ضربت x في negative y تطلع ..
+
+87
+00:08:29,590 --> 00:08:34,960
+هي نفسها كم لو ضربت negative x في yو هذه يعني
+
+88
+00:08:34,960 --> 00:08:39,800
+البرهان مش صعب هاي ال X وهي negative Y الخاصية
+
+89
+00:08:39,800 --> 00:08:43,560
+الرابعة أثبتنا فيها إنه negative Y بيساوي negative
+
+90
+00:08:43,560 --> 00:08:48,780
+واحد في Y هذا من الخاصية أربعة ال associative law
+
+91
+00:08:48,780 --> 00:08:52,120
+بيسمح لإن أنا الأقواس هذه أرتبها بالطريقة هذه
+
+92
+00:08:52,120 --> 00:08:56,180
+عملية الضرب associative و كمان عملية الضرب
+
+93
+00:08:56,180 --> 00:09:00,620
+commutative إذا ممكن أبدل ال X مع ال negative واحد
+
+94
+00:09:04,010 --> 00:09:07,470
+الخاصية الرابعة بتقول سالب واحد ضرب X عبارة عن
+
+95
+00:09:07,470 --> 00:09:14,030
+negative X إذاً هذا هو إيه هذا جزء من الجزء الخامس
+
+96
+00:09:14,030 --> 00:09:20,750
+في كمان جزء تاني اللي هو عايزين نثبت إن X ضرب
+
+97
+00:09:20,750 --> 00:09:24,990
+negative Y هو نفس الحاجة كما لو ضربت X في Y الأول
+
+98
+00:09:24,990 --> 00:09:30,950
+وضربت الكل في negativeو لبرهان ذلك هي X في
+
+99
+00:09:30,950 --> 00:09:34,950
+negative Y X في negative Y أثبتنا إنها طلعت بتساوي
+
+100
+00:09:34,950 --> 00:09:41,090
+سالب واحد في X في Y هذا هو نجلتها من هنا الآن
+
+101
+00:09:41,090 --> 00:09:44,470
+باستخدام ال associative law ممكن أيه أبدل الأقواس
+
+102
+00:09:44,470 --> 00:09:50,450
+يعني أخد X وY مع بعض و أضربهم في سالب واحد و طبعا
+
+103
+00:09:50,450 --> 00:09:54,490
+الآن أثبتنا أن سالب واحد لما أضربه في حاجة زي هذه
+
+104
+00:09:54,490 --> 00:09:56,910
+بيطلع سالب X في Y
+
+105
+00:10:01,430 --> 00:10:08,850
+بالنسبة لخاصية رقم 6 ممكن نستخدم الخاصية رقم 4 و
+
+106
+00:10:08,850 --> 00:10:12,510
+ال distributive law في إثباتها فطبعا أنا هنا كاتب
+
+107
+00:10:12,510 --> 00:10:18,030
+لكم use الخاصية أو الجزء الرابع و ال distributive
+
+108
+00:10:18,030 --> 00:10:23,210
+law لبرهان مين؟ الخاصية رقم 6 هذه، هذه أرقام
+
+109
+00:10:23,210 --> 00:10:29,920
+لاتينيةفبتشوفوها انتوا طبعا و بتحاولوا تثبتوها و
+
+110
+00:10:29,920 --> 00:10:35,660
+اذا ماعرفتوش ممكن تتواصلوا معايا نحاول نثبتها لكم
+
+111
+00:10:35,660 --> 00:10:42,780
+بالنسبة لخاصية السابعة ايه هي الخاصية السابعة لو
+
+112
+00:10:42,780 --> 00:10:46,700
+ضربت negative x ف negative y المفروض يطلع نفس
+
+113
+00:10:46,700 --> 00:10:54,530
+الحاجة x ضرب yوهي البرهان بسيط احنا اخدنا ان لو
+
+114
+00:10:54,530 --> 00:10:59,830
+ضربت negative x في انصر negative y هو نفسه كما لو
+
+115
+00:10:59,830 --> 00:11:07,130
+انا ضربت x في الانصر التاني واخدت السالب برا و
+
+116
+00:11:07,130 --> 00:11:07,750
+بعدين
+
+117
+00:11:10,830 --> 00:11:17,230
+نفس الحاجة هنا x في negative y هي
+
+118
+00:11:17,230 --> 00:11:24,890
+نفسها negative x في y بدالت x في negative y ب
+
+119
+00:11:24,890 --> 00:11:30,290
+negative ضرب x y و أثبتنا قبل هيك أن negative ضرب
+
+120
+00:11:30,290 --> 00:11:34,930
+negative negative العنصر بساوي العنصرإذا هذا برضه
+
+121
+00:11:34,930 --> 00:11:45,630
+برهان الجزء هذا الجزء التامن او التاسع are left as
+
+122
+00:11:45,630 --> 00:11:48,410
+exercises برضه أنا سايبلكم اياهم تمرين لان مش
+
+123
+00:11:48,410 --> 00:11:52,310
+ماجون بارهم كل إشي انتوا يعني كبار لان بديتوا
+
+124
+00:11:52,310 --> 00:11:58,050
+تسوابوا بديتوا تفهموا فلازم برضه تشاركوا شويةمش
+
+125
+00:11:58,050 --> 00:12:02,030
+معقول زي اللي .. احنا مش في مدرسة ثانوية، بناشي
+
+126
+00:12:02,030 --> 00:12:06,310
+نقول، عدادية، لازم يشرحلكم كل إشي و لازم يبرهلكم
+
+127
+00:12:06,310 --> 00:12:10,050
+كل إشي، لازم الطالب يشارك شوية، خاصة الحاجات اللي
+
+128
+00:12:10,050 --> 00:12:14,290
+براهينها مشابهةفبتزعلوش و حالكم انتوا تاخدوا
+
+129
+00:12:14,290 --> 00:12:19,430
+الأمور هذه بصدر راحل و كمان مرة بكرر لو اي شيء من
+
+130
+00:12:19,430 --> 00:12:23,570
+الحاجات اللي بنسيبها ماعرفتوش تحلوها او تبرهنوها
+
+131
+00:12:23,570 --> 00:12:28,350
+فانا على استعداد ان اساعدكم في برهنها الجزء الأخر
+
+132
+00:12:28,350 --> 00:12:32,490
+جزء العاشر ايه هو الجزء العاشر الجزء العاشر بيقول
+
+133
+00:12:32,490 --> 00:12:40,530
+دائما بندرسها في مبادئ الرياضياتمثال على برهان غير
+
+134
+00:12:40,530 --> 00:12:44,490
+مباشر في مبادر رياضيات، لو كان X ضرب Y أعداد
+
+135
+00:12:44,490 --> 00:12:50,990
+حقيقية، حصل ضربهم سفر، فإيه بيطلع؟ إما X بساوي سفر
+
+136
+00:12:50,990 --> 00:12:55,650
+أو Y بساوي سفر، بظبط؟
+
+137
+00:13:01,000 --> 00:13:05,060
+فهذا نعطي مثال في المبادئ الرياضية طيب البرهان هو
+
+138
+00:13:05,060 --> 00:13:12,880
+نفسه البرهان هو نفسه عشان اثبت انه x لو كان x ضرب
+
+139
+00:13:12,880 --> 00:13:19,760
+y بساوة 0 فبطلع x بساوة 0 او y بساوة 0 فبأفرض ان x
+
+140
+00:13:19,760 --> 00:13:26,220
+مايسويش 0و بثبت ان y بيساوي 0 او by symmetry
+
+141
+00:13:26,220 --> 00:13:32,080
+بالتماثل ممكن افرض ان y بيساوي 0 و اصل الى ان x
+
+142
+00:13:32,080 --> 00:13:41,640
+بيساوي 0 okay تمام فاللي عملناه هنا هيه لبرهان ان
+
+143
+00:13:41,640 --> 00:13:47,400
+x بيساوي 0 او y بيساوي 0 it suffices يعني يكفي ان
+
+144
+00:13:47,400 --> 00:13:54,070
+افرض to assume ان x لا يساوي 0و أثبت و أثبت أن y
+
+145
+00:13:54,070 --> 00:14:07,690
+بساوي 0 طيب أنا عندي من الفرد x y بساوي 0 ف
+
+146
+00:14:07,690 --> 00:14:14,610
+ال x y بساوي 0 تهيألي
+
+147
+00:14:14,610 --> 00:14:21,110
+فيه إشي هنا مش مبين ده هو خلينا نبينهنعم هاي انا
+
+148
+00:14:21,110 --> 00:14:26,470
+عندي x y من الفرض x y بساوي سفر والسفر هذا ممكن
+
+149
+00:14:26,470 --> 00:14:30,970
+اكتبه على صورة x ضرب سفر برضه هذا بساوي سفر تمام
+
+150
+00:14:30,970 --> 00:14:36,470
+الان انا فارض ان x بساويش سفر فعملية الضرب بتحقق
+
+151
+00:14:36,470 --> 00:14:40,210
+cancellation law اذا من cancellation law تبع عملية
+
+152
+00:14:40,210 --> 00:14:44,470
+الضرب مدام x بساويش سفر فبقدر اجسم عليها فبطلع
+
+153
+00:14:44,470 --> 00:14:50,590
+عندي y بساوي سفر وهذا هو المطلوبOkay تمام إذا هيك
+
+154
+00:14:50,590 --> 00:15:01,290
+بنكون برهننا النظرية التانية كويس
+
+155
+00:15:01,290 --> 00:15:07,770
+تمام هيك طيب
+
+156
+00:15:07,770 --> 00:15:11,690
+ناخد تعريفات أو تعريف مهم
+
+157
+00:15:21,020 --> 00:15:27,480
+في تعريف هنا الخواص
+
+158
+00:15:27,480 --> 00:15:30,660
+الخامسة هذه اللي حكينا عنها ال commutative law ال
+
+159
+00:15:30,660 --> 00:15:37,140
+associative law و ال distributive law existence of
+
+160
+00:15:37,140 --> 00:15:42,780
+identity elements الخاصية الخامسة existence of
+
+161
+00:15:42,780 --> 00:15:47,240
+inverses خمس خواص هذه اللي بتحقيق عمليات الجمع و
+
+162
+00:15:47,240 --> 00:15:52,770
+الدرب على الأعداد الحقيقية هذه الخواصبتشكل تعريف
+
+163
+00:15:52,770 --> 00:15:57,750
+ما يسمى في الجبر في الجبر الحديث في تركيبة جبرية
+
+164
+00:15:57,750 --> 00:16:03,870
+اسمها field او حقل فما
+
+165
+00:16:03,870 --> 00:16:09,130
+هو الحقل لو انتوا هتدرسوا جبر حديث واحد او .. او
+
+166
+00:16:09,130 --> 00:16:14,850
+درستوا فيمكن مار عليكم ال field او الحقل هو عبارة
+
+167
+00:16:14,850 --> 00:16:23,080
+عن set if مع عمليتين ثنائيتينعملية جمع وعملية ضرب
+
+168
+00:16:23,080 --> 00:16:29,300
+معرفين على ال set F بحيث ان العمليتين هدول بيحققوا
+
+169
+00:16:29,300 --> 00:16:33,640
+الخواص الخمسة اللي هي حققتها مجموعة الاعداد
+
+170
+00:16:33,640 --> 00:16:40,250
+الحقيقية، اذا اي مجموعة F مع عمليتين ثنائيتينبحقق
+
+171
+00:16:40,250 --> 00:16:46,630
+الخواص الخمسة بنسميها في الجبر field اذا ال .. ال
+
+172
+00:16:46,630 --> 00:16:51,510
+.. ال R ال R او العداد الحقيقية مع أمليات الجمع
+
+173
+00:16:51,510 --> 00:16:56,650
+والضرب اللي عرفناها سابقا شفنا انها بتحقق الخواص
+
+174
+00:16:56,650 --> 00:17:01,570
+الخمسة وبالتالي بتشكل field فبنسمي it the field of
+
+175
+00:17:01,570 --> 00:17:08,790
+real numbers او المجال ال .. الاعداد الحقيقيةهي
+
+176
+00:17:08,790 --> 00:17:14,430
+مثال فيه أمثلة كتيرة على fields على حقول فهي لو
+
+177
+00:17:14,430 --> 00:17:18,030
+أخدت المجموعة هي أبسط field أصغر و أبسط field
+
+178
+00:17:18,030 --> 00:17:24,190
+موجود في الرياضيات هو ال 6F اللي بتتكون من أنصرين
+
+179
+00:17:24,190 --> 00:17:33,050
+عددين حقيقيين 01الان عشان اكون field على المجموعة
+
+180
+00:17:33,050 --> 00:17:37,590
+F اللي بتكون من عضرين لازم اعرف عملية جمع و ضرب
+
+181
+00:17:37,590 --> 00:17:43,690
+فممكن اعرف عملية جمع و ضرب على F كالتالي ها يعني
+
+182
+00:17:43,690 --> 00:17:50,570
+اعرفت لو ضربت 0 في نفسه او 1 في 0 او 0 في 1 او
+
+183
+00:17:50,570 --> 00:17:57,780
+جمعت 0 على 0 او 1 على 1 هذا باعرفه انه بساوي 0أذا
+
+184
+00:17:57,780 --> 00:18:02,020
+أنا عرفت حاصل الضرب والجمع هذا بالساوية سفر كذلك
+
+185
+00:18:02,020 --> 00:18:05,800
+انا بعرفت انه لو جمعت السفر على الواحد او الواحد
+
+186
+00:18:05,800 --> 00:18:10,000
+على السفر او الواحد على الواحد بطلع واحد الان اذا
+
+187
+00:18:10,000 --> 00:18:16,410
+انا عرفت عمليات جمع وضرب على كل عناصر المجموعةالان
+
+188
+00:18:16,410 --> 00:18:23,610
+من السهل التحقق ان ال خواص الخمسة كلها تتحقق تابعة
+
+189
+00:18:23,610 --> 00:18:28,530
+ال field وبالتالي هذا بيكون field وهذا ال field في
+
+190
+00:18:28,530 --> 00:18:36,770
+الجبر بيرمزوله بالرمز z2 وفي
+
+191
+00:18:36,770 --> 00:18:40,890
+نفس الوجد هو cyclic group of order two إذا في حد
+
+192
+00:18:40,890 --> 00:18:45,120
+فيكم طراز الجبر حديثعلى أي حال احنا هذا مش موضوعنا
+
+193
+00:18:45,120 --> 00:18:49,400
+هذا موضوع جبر فبس يعني هذا مجرد مثال بسيط على
+
+194
+00:18:49,400 --> 00:18:53,600
+field و احنا اهم حاجة انه احنا يعني اللي بدنا احنا
+
+195
+00:18:53,600 --> 00:18:58,420
+نصله انه مجموعة الاعداد الحقيقية تبعتنا مجموعة
+
+196
+00:18:58,420 --> 00:19:04,980
+الاعداد الحقيقية R مع عملية الجامعة و الدرب بتشكل
+
+197
+00:19:04,980 --> 00:19:10,360
+ما يسمى في الجبر بال field تمام؟ هذا اللي احنا
+
+198
+00:19:10,360 --> 00:19:11,980
+عايزين نصله، نعم فضل
+
+199
+00:19:15,080 --> 00:19:18,860
+هذا تعريف احنا .. احنا .. احنا بنعرف انه لو اجمع
+
+200
+00:19:18,860 --> 00:19:23,700
+واحد على واحد يطلع صفر هذا definition تعريف وليس
+
+201
+00:19:23,700 --> 00:19:27,320
+اه يعني هاي مجموعة اه بدي اعرف عليها عملية جمع
+
+202
+00:19:27,320 --> 00:19:31,060
+عملية .. عملية الجمع هانا باعرفها لو جمعت واحد على
+
+203
+00:19:31,060 --> 00:19:39,480
+واحد بطلع صفر لو جمعت واحد اه
+
+204
+00:19:43,240 --> 00:19:52,920
+أه في هنا إشي مش مظبوط هنا هذه المفروض ضرب هذه هذه
+
+205
+00:19:52,920 --> 00:19:58,760
+المفروض ضرب هذه فهذا في خطأ مطبعي صحيح هذا كله
+
+206
+00:19:58,760 --> 00:20:02,200
+تعريف الآن لما هيك أنا بكون عرفت عملية الجمع
+
+207
+00:20:02,200 --> 00:20:07,240
+والضرب هنا في خطأ مطبع دي المفروض تكون ضرب لإن
+
+208
+00:20:07,240 --> 00:20:10,240
+واحد زاد واحد عرفناها تساوي سفر ف
+
+209
+00:20:13,680 --> 00:20:19,300
+حسب التعريف هذا ممكن التحقق ان خمس خواص تبعت ال
+
+210
+00:20:19,300 --> 00:20:22,760
+field بتتحقق فممكن تحققوها اذا بدكم تحققواها اذا
+
+211
+00:20:22,760 --> 00:20:25,700
+بدكم تحققواها اذا بدكم تحققواها اذا بدكم تحققواها
+
+212
+00:20:25,700 --> 00:20:27,620
+اذا بدكم تحققواها اذا بدكم تحققواها اذا بدكم
+
+213
+00:20:27,620 --> 00:20:27,740
+تحققواها اذا بدكم تحققواها اذا بدكم تحققواها اذا
+
+214
+00:20:27,740 --> 00:20:28,060
+بدكم تحققواها اذا بدكم تحققواها اذا بدكم تحققواها
+
+215
+00:20:28,060 --> 00:20:28,700
+اذا بدكم تحققواها اذا بدكم تحققواها اذا بدكم
+
+216
+00:20:28,700 --> 00:20:36,280
+تحققواها اذا بدكم تحققواها اذا بدكم تحققواها اذا
+
+217
+00:20:36,280 --> 00:20:43,660
+بدكم تحققواها اذا بدكم توعملية القسمة هي عملية
+
+218
+00:20:43,660 --> 00:20:47,340
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+219
+00:20:47,340 --> 00:20:49,400
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+220
+00:20:49,400 --> 00:20:53,020
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+221
+00:20:53,020 --> 00:20:54,300
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+222
+00:20:54,300 --> 00:20:56,080
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+223
+00:20:56,080 --> 00:20:56,480
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+224
+00:20:56,480 --> 00:21:01,560
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+225
+00:21:01,560 --> 00:21:06,040
+ضرب،إذن عملية الطرح هي عملية جمعة كذلك عملية
+
+226
+00:21:06,040 --> 00:21:10,320
+القسمة division on R is defined by هاي X على Y
+
+227
+00:21:10,320 --> 00:21:16,740
+بساوي عملية ضرب X في ال multiplicative inverse ل Y
+
+228
+00:21:16,740 --> 00:21:22,320
+أو 1 على Y كذلك بنعرف هذا definition دائما لما
+
+229
+00:21:22,320 --> 00:21:25,660
+يكون فيه نقطتين و وراهم علامة تساوي معناه إن طرف
+
+230
+00:21:25,660 --> 00:21:30,040
+الشمال by definition بساوي الطرف اليمين إذن هذا
+
+231
+00:21:30,040 --> 00:21:36,630
+تعريفلأن أنا بعرف هذا التعريف أن a أس negative one
+
+232
+00:21:36,630 --> 00:21:43,470
+معناها واحد على a a to zero بساوي واحد حسب التعريف
+
+233
+00:21:43,470 --> 00:21:48,970
+a to negative n و n عدد طبيعي هي عبارة عن مقلوب ال
+
+234
+00:21:48,970 --> 00:21:54,630
+a الكل to n فكل هذه تعريفات بناء على التعريفات هذه
+
+235
+00:21:54,630 --> 00:21:58,730
+ممكن أنبرهن خواص كثيرة
+
+236
+00:22:00,150 --> 00:22:03,810
+و هتشوفوا بعضها في التمرين اللي موجودة في نهاية ال
+
+237
+00:22:03,810 --> 00:22:09,970
+section نتطرق
+
+238
+00:22:09,970 --> 00:22:14,330
+لحاجة اسمها rational numbers الاعداد النسبية
+
+239
+00:22:14,330 --> 00:22:20,210
+الاعداد النسبية او rational numbers بنعرفها على
+
+240
+00:22:20,210 --> 00:22:24,130
+انها مجموعة من الاعداد الحقيقية او هي مجموعة جزئية
+
+241
+00:22:24,130 --> 00:22:30,010
+من الاعداد الحقيقيةنموذجها بالرمز boldfaceq هذه
+
+242
+00:22:30,010 --> 00:22:34,370
+الرموز الأحرف هذه أو ال letters هذه نسميها
+
+243
+00:22:34,370 --> 00:22:41,790
+boldface يعني حرف مغمق هذه طبعا بتدل على مجموعات
+
+244
+00:22:43,170 --> 00:22:47,190
+فال rational numbers هي كل الأعداد الحقيقية اللي
+
+245
+00:22:47,190 --> 00:22:52,210
+ممكن كتبتها على صورة rational a على b حيث a و b
+
+246
+00:22:52,210 --> 00:22:56,370
+أعداد صحيحة هذه مجموعة الأعداد الصحيحة bold في ال
+
+247
+00:22:56,370 --> 00:23:00,650
+z و المقام لازم مايسويش سفر لأن القسم على سفر مش
+
+248
+00:23:00,650 --> 00:23:05,840
+معرفةالان لو أخدت الأعداد الحقيقية وشلت منها
+
+249
+00:23:05,840 --> 00:23:09,720
+الأعداد النسبية طرحت منها الأعداد النسبية فالأعداد
+
+250
+00:23:09,720 --> 00:23:13,160
+الحقيقية المتبقية بنسميها irrational numbers
+
+251
+00:23:13,160 --> 00:23:18,480
+irrational numbers الأعداد غير النسبية إذا الأعداد
+
+252
+00:23:18,480 --> 00:23:21,960
+النسبية هي كل الأعداد الحقيقية التي لا يمكن
+
+253
+00:23:21,960 --> 00:23:26,740
+كتابتها على صورة rational a على b حيث a وb أعداد
+
+254
+00:23:26,740 --> 00:23:32,910
+صحيحة والمقان بسويش سفر تمام؟طبعا لو أخدت اتحاد ال
+
+255
+00:23:32,910 --> 00:23:35,590
+rational numbers مع ال irrational numbers بيعطوني
+
+256
+00:23:35,590 --> 00:23:38,770
+كل الأعداد الحقيقية يعني المعنى أخر الأعداد
+
+257
+00:23:38,770 --> 00:23:43,390
+الحقيقية احنا جزقناها إلى مجموعتين irrational
+
+258
+00:23:43,390 --> 00:23:53,270
+numbers اتحاد ال irrational numbers طبعا
+
+259
+00:23:53,270 --> 00:23:57,830
+المجموعتين هدول disjoint يعني منفصلتين مافيش بينهم
+
+260
+00:23:57,830 --> 00:23:58,850
+عناصر مشتركة
+
+261
+00:24:01,750 --> 00:24:08,710
+طيب ال .. النظرية التالية ممكن من السهل ان احنا
+
+262
+00:24:08,710 --> 00:24:14,950
+نثبتها باستخدام خواص الأعداد الصحيحة يعني
+
+263
+00:24:14,950 --> 00:24:25,150
+معروف احنا عندنا ان ال ..
+
+264
+00:24:25,150 --> 00:24:30,090
+معروف ان ال ..
+
+265
+00:24:33,390 --> 00:24:37,450
+لو في عندي عددين صحيحين فمجموعهم بيطلع عدد صحيح
+
+266
+00:24:37,450 --> 00:24:42,570
+وحاصل ضربهم عدد صحيح بمعنى آخر عملية مجموعة
+
+267
+00:24:42,570 --> 00:24:49,220
+الأعداد الصحيحة مغلقة تحت عمليات الجمع والضرببنفس
+
+268
+00:24:49,220 --> 00:24:53,860
+.. باستخدام الحقيقة هذه أو ال fact هذه ممكن اثبات
+
+269
+00:24:53,860 --> 00:24:58,900
+انه مجموعة الاعداد النسبية مغلقة تحت عمليات الضرب
+
+270
+00:24:58,900 --> 00:25:06,270
+والجامعة واخذ ال additive inverseيعني لو كان XY
+
+271
+00:25:06,270 --> 00:25:10,810
+أعداد نسبية فمجموعهم بيطلع عدد نسبي وحاصل ضربهم
+
+272
+00:25:10,810 --> 00:25:15,330
+عدد نسبي و سالب عدد نسبي بيطلع عدد نسبي و لو في
+
+273
+00:25:15,330 --> 00:25:21,330
+عندي عدد نسبي مختلف عن السفر ف ال multiplicative
+
+274
+00:25:21,330 --> 00:25:28,550
+inverse بيطلع عدد نسبيبمعنى آخر، مجموعة الأعداد
+
+275
+00:25:28,550 --> 00:25:33,950
+النسمية مغلقة تحت عملية الجمع والضرب، وأخذ الـ
+
+276
+00:25:33,950 --> 00:25:39,950
+Additive Inverse وأخذ مغلقة تحت الـ Multiplicative
+
+277
+00:25:39,950 --> 00:25:44,470
+Inverse وبالتالي ممكن
+
+278
+00:25:46,690 --> 00:25:51,850
+بنستنتج أن مجموعة الأعداد النسلية بتحقق القواص
+
+279
+00:25:51,850 --> 00:25:56,430
+الخامسة تبع ال field وبالتالي هي بتشكل field بحد
+
+280
+00:25:56,430 --> 00:26:05,690
+ذاتها الان ال Q subset من R وR field وQ subset من
+
+281
+00:26:05,690 --> 00:26:11,830
+R وQ field فبنسمي Q sub field زي لما يكون في عندي
+
+282
+00:26:11,830 --> 00:26:19,160
+set وفي داخلها setفبنقول sub set لو في عندي group
+
+283
+00:26:19,160 --> 00:26:25,240
+و في عندي مجموعة جزئية من ال group فبنسمي المجموعة
+
+284
+00:26:25,240 --> 00:26:31,940
+جزئية نفسها group أيضا فبنسميها sub group اذا ال Q
+
+285
+00:26:31,940 --> 00:26:38,340
+is a sub field of the field R بناء على النظرية هذه
+
+286
+00:26:38,340 --> 00:26:44,770
+اذا هذه كلها حقائق معروفة يعنيو هتركزوا عليها
+
+287
+00:26:44,770 --> 00:26:48,410
+انتوا في الجبر يعني ماحنخوض فيها كتير لإن هذا
+
+288
+00:26:48,410 --> 00:26:53,370
+مواضيع الجبرية احنا هنركز على ال analysis في كمان
+
+289
+00:26:53,370 --> 00:26:57,990
+نظرية هنا مهمة بتخص الأعداد النسبية والغير نسبية
+
+290
+00:26:57,990 --> 00:27:03,570
+وهذه طبعا برضه بنعطيها دائما مثال في مبادئ
+
+291
+00:27:03,570 --> 00:27:04,430
+الرياضيات
+
+292
+00:27:07,090 --> 00:27:14,250
+بورهان على مثال على بورهان غير مباشر النظرية هذه
+
+293
+00:27:14,250 --> 00:27:17,930
+بتقول there does not exist R ينتمي ل Q بحيث R
+
+294
+00:27:17,930 --> 00:27:22,530
+تربية بيساوي اتنين مافيش لا يوجد عدد نسبي مربعه
+
+295
+00:27:22,530 --> 00:27:27,450
+بساوي اتنين يعني بمعنى اخر النظرية هذه باختصار
+
+296
+00:27:27,450 --> 00:27:36,590
+بتقول ان جذر الاتنين ليس عدد نسبي وماليش؟عدد غير
+
+297
+00:27:36,590 --> 00:27:41,830
+نسبي يعني جذر اتنين عدد غير نسبي فهي برهان
+
+298
+00:27:41,830 --> 00:27:45,490
+بالتناقض برهان غير مباشر بالتناقض by contradiction
+
+299
+00:27:45,490 --> 00:27:53,510
+احنا عايزين نثبت انه مافيش عدد او جذر اتنين ليس
+
+300
+00:27:53,510 --> 00:28:01,010
+عدد نسبي فنفرض النقيد نفرض النفي هو الصح يعني نفرض
+
+301
+00:28:01,010 --> 00:28:11,490
+ان جذر الاتنين عدد نسبي يعني بالساويP على Q حيث P
+
+302
+00:28:11,490 --> 00:28:17,310
+و Q أعداد صحيحة و
+
+303
+00:28:17,310 --> 00:28:23,990
+Q لا يساوي سفر تمام؟ و بدنا نصل إلى تناقض إذا
+
+304
+00:28:23,990 --> 00:28:27,870
+وصلنا إلى تناقض معناته فرضنا هذا غلط والصح أن
+
+305
+00:28:27,870 --> 00:28:32,410
+النظرية تكون صحيحة، بصبوت؟ طيب نشوف مع بعض
+
+306
+00:28:36,080 --> 00:28:46,520
+هي فرضنا انه الاتنين عدد هاي اتنين بيساوي هاي
+
+307
+00:28:46,520 --> 00:28:52,320
+فرضنا انه الاتنين بيساوي P على Q او جدر اتنين
+
+308
+00:28:52,320 --> 00:28:57,100
+بيساوي P على Q وبالتالي P على Q ربع فبطلع عند P
+
+309
+00:28:57,100 --> 00:29:02,900
+على Q تربيه بيساوي اتنين صح؟ هايطيب الآن لما يكون
+
+310
+00:29:02,900 --> 00:29:12,820
+في عندي أعداد هذا عدد نسبي فممكن نختصر و نفرض أنه
+
+311
+00:29:12,820 --> 00:29:19,480
+مافيش عامل مشترك بين ال P و ال Q إلا الواحد الصحيح
+
+312
+00:29:19,480 --> 00:29:26,660
+يعني مثلا هي عندي مثلا أربعة على مثلا عشرة هذا عدد
+
+313
+00:29:26,660 --> 00:29:32,130
+نسبيفممكن اكتبه اختصر اجسم على اتنين و اجسم على
+
+314
+00:29:32,130 --> 00:29:36,530
+اتنين بطلع اتنين على خمسة لاحظوا الان مافيش عامل
+
+315
+00:29:36,530 --> 00:29:40,370
+مشترك بين اتنين و الخمسة الا الواحد فهذا في الجبر
+
+316
+00:29:40,370 --> 00:29:44,410
+بيسموه ال greatest common divisor لاتنين و خمسة
+
+317
+00:29:44,410 --> 00:29:53,130
+بساوة واحد هاي مثلا سالب عشرة على تلاتين هاي هذا
+
+318
+00:29:53,130 --> 00:29:59,940
+عدد نسبي فممكن نختصر هذا يصير اتنين علىوالا ايش
+
+319
+00:29:59,940 --> 00:30:06,760
+هذا او سالب واحد على تلاتة فال bus سالب واحد عدد
+
+320
+00:30:06,760 --> 00:30:10,460
+صحيح و المقام تلاتة و ال greatest common divisor
+
+321
+00:30:10,460 --> 00:30:17,420
+لسالب واحد و تلاتة بساوي واحد اذا اي عدد نسبة ممكن
+
+322
+00:30:17,420 --> 00:30:23,260
+اختصره او ابسط و اكتبه بأبسط صورةيعني اخلي ال
+
+323
+00:30:23,260 --> 00:30:29,640
+greatest common divisor ل P و Q هنا بساوي واحد طيب
+
+324
+00:30:29,640 --> 00:30:35,580
+الان تعالوا نربع هنا هذه المعادلة P على Q تربية
+
+325
+00:30:35,580 --> 00:30:40,500
+بساوي اتنين فمنها بنستنتج ان P تربية بساوي اتنين و
+
+326
+00:30:40,500 --> 00:30:47,040
+Q تربيةطيب هي عندي P تربيع بساو 2 في Q تربيع الـ Q
+
+327
+00:30:47,040 --> 00:30:50,820
+هاد عدد صحيح فمربع العدد الصحيح اللي هو Q تربيع
+
+328
+00:30:50,820 --> 00:30:54,720
+بيطلع عدد صحيح عدد صحيح مضروب في 2 بيطلع even
+
+329
+00:30:54,720 --> 00:30:59,400
+number عسب المبادئ صح؟ اذا P تربيع بيطلع even
+
+330
+00:30:59,400 --> 00:31:06,520
+number تمام؟هذا بيؤدي انه ممكن اثبات ان P بيطلع
+
+331
+00:31:06,520 --> 00:31:10,960
+even لو كان مربع عدد صحيح even فممكن اثبات ان
+
+332
+00:31:10,960 --> 00:31:14,860
+العدد الصحيح نفسه لازم يطلع even وهذا ممكن نعمل
+
+333
+00:31:14,860 --> 00:31:21,940
+برهان صغير بالتناقض افرضه ان P مش even يعني odd
+
+334
+00:31:21,940 --> 00:31:28,360
+ربع E فبطلع مربع odd تناقض هاي البرهان اذا هذا ايه
+
+335
+00:31:28,360 --> 00:31:33,220
+الاجابة على ال Yكمان مرة إذا كان عندي P تربية أنا
+
+336
+00:31:33,220 --> 00:31:39,900
+عندي P تربية even هذا بقد أنه P even كيف نبرهن هذا
+
+337
+00:31:39,900 --> 00:31:46,420
+برهان بالتناقض افرض أنه P odd أيه يعني P odd يعني
+
+338
+00:31:46,420 --> 00:31:51,600
+P هاي
+
+339
+00:31:51,600 --> 00:31:58,500
+P بساوي 2K زي 1 هذا معناه oddوطبعا الـ K هي عدد
+
+340
+00:31:58,500 --> 00:32:04,620
+صحيح ربي إذا P تربية بساوي أربعة K تربية زاد أربعة
+
+341
+00:32:04,620 --> 00:32:14,080
+K زاد واحد وهذا بساوي اتنين في اتنين K تربية زاد
+
+342
+00:32:14,080 --> 00:32:19,900
+اتنين K مع بعض زاد واحد وهذا بساوي اتنين في M زاد
+
+343
+00:32:19,900 --> 00:32:26,350
+واحد حيث M عدد صحيحإذاً P تربية طلع بساوة اتنين في
+
+344
+00:32:26,350 --> 00:32:30,410
+عدد صحيح زائد واحد وبالتالي هذا اقض Contradiction
+
+345
+00:32:30,410 --> 00:32:35,590
+تناقض لأن احنا عندنا P تربية P تربية is even okay
+
+346
+00:32:35,590 --> 00:32:42,670
+إذاً هذا برهان ال why طيب إذا احنا وصلنا إلى أن P
+
+347
+00:32:42,670 --> 00:32:48,750
+تربية even بقدر أن P even الآن ال P و ال Q have no
+
+348
+00:32:48,750 --> 00:32:51,410
+common factor other than واحد مافيش بينهم عامل
+
+349
+00:32:51,410 --> 00:32:57,460
+مشترك إلا الواحدو ال P even إذا لازم ال Q يكون odd
+
+350
+00:32:57,460 --> 00:33:03,320
+لأن لو كان ال Q even و ال P even ففيه عامل مشترك
+
+351
+00:33:03,320 --> 00:33:09,560
+بينهم اتنين على الأقل او أربعة وهذا بتناقض مع ايه
+
+352
+00:33:09,560 --> 00:33:13,100
+أنه احنا فرضين أنه مافيش common factor بين ال P و
+
+353
+00:33:13,100 --> 00:33:18,560
+ال Q إلا الواحد تمام إذا أنا عندي هنا سنتجة أن ال
+
+354
+00:33:18,560 --> 00:33:25,030
+Q لازم يكون odd الآنأنا عندي P even يعني المعناته
+
+355
+00:33:25,030 --> 00:33:33,020
+بيساوي 2M for some M عدد صحيح وبالتالي لو ربعتلو
+
+356
+00:33:33,020 --> 00:33:37,780
+نرجع نعوض في المعادلة هذه P تربية بساوة 2Q تربية
+
+357
+00:33:37,780 --> 00:33:43,120
+عوض عن P بساوة 2M فبصير 4M تربية بساوة 2Q تربية
+
+358
+00:33:43,120 --> 00:33:48,760
+فبختصر 2 من الطرفين بطلع 2M تربية بساوة Q تربية
+
+359
+00:33:48,760 --> 00:33:54,620
+إذن Q تربية بساوة 2 ضرب عدد صحيحوبالتالي Q تربية
+
+360
+00:33:54,620 --> 00:34:00,020
+is even وبالتالي منها بنستنتج ان ال Q نفسها is
+
+361
+00:34:00,020 --> 00:34:08,720
+even اذا الان انا عندي ال Q is even وهي نفس ال Q
+
+362
+00:34:08,720 --> 00:34:14,260
+سنتجنا انها odd فهذا
+
+363
+00:34:14,260 --> 00:34:20,680
+تناقض .. هذا تناقض صح؟الـ Q هنا odd وهنا طلعت even
+
+364
+00:34:20,680 --> 00:34:24,240
+فهذا يعطيني contradiction which is a contradiction
+
+365
+00:34:24,240 --> 00:34:30,620
+فهذا التناقض ان احنا هنا وصلنا بدينا بالبرهان احنا
+
+366
+00:34:30,620 --> 00:34:35,860
+عايزين نثبت جدر اتنين لا تنتمي ل Q فرضنا النقيض ال
+
+367
+00:34:35,860 --> 00:34:40,660
+contrary ان جدر اتنين تنتمي ل Q يعني ممكن كتبتها
+
+368
+00:34:40,660 --> 00:34:46,240
+على صورة P على Q P و Q أعداد صحيحةوصلنا لتناقض
+
+369
+00:34:46,240 --> 00:34:50,020
+معناته ان هذا فرضنا غلط الصح ان جدر اتنين لاتن
+
+370
+00:34:50,020 --> 00:34:54,640
+تميلكيه as required كما هو مطلوب okay تمام هذا
+
+371
+00:34:54,640 --> 00:34:59,660
+برهان بالتناقض تمام اذا هنا شوية راجعنا شوية
+
+372
+00:34:59,660 --> 00:35:04,820
+براهين اتعلمتوها في مبادئ رياضيات طبعا الناس اللي
+
+373
+00:35:04,820 --> 00:35:09,180
+اتعلموا مبادئ رياضيات و اخوياء الحاجات هذه
+
+374
+00:35:09,180 --> 00:35:14,870
+بالنسبالهم يعني صارت مجرد تسليةوالناس اللي عندهم
+
+375
+00:35:14,870 --> 00:35:20,790
+مشاكل في المبادئ نجحوا بالعافية فممكن يعني يجد ان
+
+376
+00:35:20,790 --> 00:35:28,670
+هذا مش كتير مستثار طيب هيك بنكون خلصنا ال
+
+377
+00:35:28,670 --> 00:35:33,410
+algebraic properties of R الخواص الجابرية لنظام
+
+378
+00:35:33,410 --> 00:35:37,650
+الأعداد الحقيقية او ال real number system ننتقل ل
+
+379
+00:35:37,650 --> 00:35:40,550
+section تاني داخل ال chapter الأول هيك خلصنا
+
+380
+00:35:40,550 --> 00:35:46,110
+sectionال section التاني عنوانه ال order
+
+381
+00:35:46,110 --> 00:35:52,370
+properties of R خواص الترتيب على Rorder properties
+
+382
+00:35:52,370 --> 00:35:58,470
+خواص الترتيب احنا شفنا او قولنا لما عرفنا نظام
+
+383
+00:35:58,470 --> 00:36:02,070
+الاعداد الحقيقية قولنا ان نظام الاعداد الحقيقية
+
+384
+00:36:02,070 --> 00:36:07,670
+مجرد مجموعة R boldface R مع عمليتين ثنائيتين two
+
+385
+00:36:07,670 --> 00:36:11,710
+binary operations بيحققوا الخمس خواص تبعت ال field
+
+386
+00:36:11,710 --> 00:36:16,730
+اليوم هنفترض ايضا ان نظام الاعداد الحقيقية بيحقق
+
+387
+00:36:17,890 --> 00:36:24,850
+order properties الخاصية رقم ستة هذه الخاصية رقم
+
+388
+00:36:24,850 --> 00:36:30,710
+ستة هذه الخاصية رقم ستة تتجزأ إلى تلات خواص تلات
+
+389
+00:36:30,710 --> 00:36:41,410
+خواص تسميهم order properties او اول خاصية نفترض
+
+390
+00:36:41,410 --> 00:36:48,400
+ماهي order propertyنفترض وجود مجموعة جزئية من R
+
+391
+00:36:48,400 --> 00:36:53,500
+وغير خالية، ليست خالية، non-empty subset of R
+
+392
+00:36:53,500 --> 00:36:58,220
+نفترض أن يوجد مجموعة P subset of R غير خالية
+
+393
+00:36:58,220 --> 00:37:04,620
+وبتحقق التلات خواص هذه ال set P is closed under
+
+394
+00:37:04,620 --> 00:37:09,920
+addition يعني لو خلت أي عنصرين في P فمجموعهم بيطلع
+
+395
+00:37:09,920 --> 00:37:15,040
+عنصر تالتفيها كذلك المجموعة P closed under
+
+396
+00:37:15,040 --> 00:37:20,620
+multiplication يعني لو أخدت أي عنصرين فحصل ضربهم
+
+397
+00:37:20,620 --> 00:37:26,980
+بيطلع عنصر تالت الخاصية التالتة من خاصية الترتيب
+
+398
+00:37:26,980 --> 00:37:32,340
+اللي لها اسم بنسميها trichotomy property الخاصية
+
+399
+00:37:32,340 --> 00:37:37,940
+الثلاثية الخاصية الثلاثية إيه هي؟ لو أخدت أي عدد
+
+400
+00:37:37,940 --> 00:37:39,180
+حقيقي R
+
+401
+00:37:41,750 --> 00:37:51,250
+فواحد من التلت احتمالات هذه لازم يكون صحيح وهو ان
+
+402
+00:37:51,250 --> 00:37:57,290
+اما a تنتمي للمجموعة P هذه او a بالساوء سفر او
+
+403
+00:37:57,290 --> 00:38:01,410
+negative a ينتمي للمجموعة P هذه هي الخاصية
+
+404
+00:38:01,410 --> 00:38:07,670
+التالتية اي عدد حقيقي اما يكون عنصر في P او بساوء
+
+405
+00:38:07,670 --> 00:38:10,630
+سفر او ال negative تبقى انصر في P
+
+406
+00:38:16,020 --> 00:38:21,780
+الان بنعرف المجموعة remark ملاحظة باعرف المجموعة
+
+407
+00:38:21,780 --> 00:38:25,820
+negative P المجموعة negative P هي مجموعة كل
+
+408
+00:38:25,820 --> 00:38:33,050
+العناصر negative A حيث A ينتمي ل Pالان الخاصية C
+
+409
+00:38:33,050 --> 00:38:36,310
+من ال order property اللي هي trichotomy property
+
+410
+00:38:36,310 --> 00:38:43,610
+الخاصية C says تقول أو بتقول ان ال sets المجموعات
+
+411
+00:38:43,610 --> 00:38:52,110
+اللي هي المجموعة الأحدية سفر و المجموعة P و
+
+412
+00:38:52,110 --> 00:38:57,570
+المجموعة negative P التلاتة
+
+413
+00:38:57,570 --> 00:39:02,860
+هدول are pairwise disjointمنفصلة مثنى مثنى
+
+414
+00:39:02,860 --> 00:39:06,840
+pairwise is joint يعني منفصلة مثنى مثنى إيه يعني؟
+
+415
+00:39:06,840 --> 00:39:11,360
+لو أخدت أي تنتين من التلات مجموعات هدول و قاطعتهم
+
+416
+00:39:11,360 --> 00:39:15,200
+مع بعض فاتقعتوا اعتبارهم five مافيش بينهم عناصر
+
+417
+00:39:15,200 --> 00:39:19,060
+مشتركة فبنقول إن المجموعات هذه pairwise is joint
+
+418
+00:39:20,610 --> 00:39:26,410
+ومش هيكوا بس واتحادهم بساوي كل العداد الحقيقية هذا
+
+419
+00:39:26,410 --> 00:39:33,430
+صحيح من الخاصية C لأن C بتقول لأي عدد حقيقي أي A
+
+420
+00:39:33,430 --> 00:39:41,310
+ينتمي إلى R أي A ينتمي إلى R إما ينتمي إلى P أو
+
+421
+00:39:41,310 --> 00:39:45,370
+بساوي 0 وبالتالي ينتمي إلى المجموعة هذه أو ينتمي
+
+422
+00:39:45,370 --> 00:39:52,030
+إلى negative P صح؟وبالتالي كل a هنا موجود في واحدة
+
+423
+00:39:52,030 --> 00:39:54,810
+من هذول التلاتة وبالتالي موجود في اتحادهم مش هيك
+
+424
+00:39:54,810 --> 00:39:59,990
+تعريف اتحاد؟ إذا ال R الأن أصبحت مجموعة جزئية من
+
+425
+00:39:59,990 --> 00:40:06,130
+الاتحاد، مظبوط؟ طب ال P مجموعة جزئية من R و
+
+426
+00:40:06,130 --> 00:40:10,850
+negative P مجموعة جزئية من R و singleton 0 برضه
+
+427
+00:40:10,850 --> 00:40:15,130
+مجموعة جزئية من R إذا اتحادهم بيطلع مجموعة جزئية
+
+428
+00:40:15,130 --> 00:40:20,060
+من Rوبالتالي انا عندي الاحتواء من الناحيتين
+
+429
+00:40:20,060 --> 00:40:24,280
+وبالتالي عندي تساوي اذا هنا برهنتلكم ان الاتحاد
+
+430
+00:40:24,280 --> 00:40:26,740
+هذا بساوي R تمام؟
+
+431
+00:40:33,090 --> 00:40:37,470
+طب ليش هدولة disjoint؟ لأنه لو .. لو فرضت أنه مثلا
+
+432
+00:40:37,470 --> 00:40:42,130
+في عنصر بيقف ينتمي لتقاطه المجموعتين هدول، معناته
+
+433
+00:40:42,130 --> 00:40:45,990
+هذا العنصر بيساوي سفر و في نفس الوجة ينتمي ل P
+
+434
+00:40:45,990 --> 00:40:49,830
+وهذا بتناقض مع الخاصية الثلاثية، الخاصية الثلاثية
+
+435
+00:40:49,830 --> 00:40:53,950
+بتقول لازم و exactly one، واحد من الاحتمالات
+
+436
+00:40:53,950 --> 00:41:00,090
+الثلاثة هذه صح، اما اثنين مش صح، تمام؟ okay
+
+437
+00:41:02,970 --> 00:41:07,390
+العنى المجموعة P هذه اللي عرفناها هنا بنسميها
+
+438
+00:41:07,390 --> 00:41:10,610
+مجموعة الأعداد الحقيقية الموجبة the set of
+
+439
+00:41:10,610 --> 00:41:15,830
+positive real number مجموعة الأعداد الحقيقية
+
+440
+00:41:15,830 --> 00:41:19,750
+الموجبة و ال set negative P هذه بنسميها مجموعة
+
+441
+00:41:19,750 --> 00:41:24,560
+الأعداد الحقيقية السالبةو لما نضيف عليهم السفر هيك
+
+442
+00:41:24,560 --> 00:41:28,980
+بنكون غطينا كل الاعداد الحقيقية صح؟ okay تمام اذا
+
+443
+00:41:28,980 --> 00:41:33,000
+P بنسميها مجموعة الاعداد الحقيقية الموجبة negative
+
+444
+00:41:33,000 --> 00:41:42,440
+P مجموعة الاعداد الحقيقية السالبة و هكذا طيب
+
+445
+00:41:42,440 --> 00:41:47,980
+لحد تلان احنا ماعرفناش علاقة اصغر او اكبر او اصغر
+
+446
+00:41:47,980 --> 00:41:52,380
+من او يساوي او اكبر من او يساوي اللي هو الترتيبففي
+
+447
+00:41:52,380 --> 00:41:56,100
+عندى definition هنا لو أخدت اي عددين حقيقيين a و b
+
+448
+00:41:56,100 --> 00:42:04,620
+فهنكتب او هنعلن ان a أصغر من b او ما يكافئها b
+
+449
+00:42:04,620 --> 00:42:12,640
+أكبر من a هذا معناه نقصد نقصد بذلك ان الفرق بين b
+
+450
+00:42:12,640 --> 00:42:18,920
+و a ينتمي ل p يعني الفرق هذا موجب يعني هذا عدد
+
+451
+00:42:18,920 --> 00:42:26,080
+موجبإذا لو كان الفرق بين b و a عدد موجب فبنكتب a
+
+452
+00:42:26,080 --> 00:42:32,780
+أصغر من b أو b أكبر من a طيب طب
+
+453
+00:42:32,780 --> 00:42:36,840
+متى بكتب a أصغر من أو يساوي b أو b أكبر من أو
+
+454
+00:42:36,840 --> 00:42:45,760
+يساوي a هذا معناه يعني هذا مثلا معناه أن a أصغر من
+
+455
+00:42:45,760 --> 00:42:54,840
+bيعني الفرق بين B و A ينتمي ل P أو A بيساوي B لما
+
+456
+00:42:54,840 --> 00:42:58,860
+يكون A بيساوي B لإحتمال التاني هذا معناه أن الفرق
+
+457
+00:42:58,860 --> 00:43:03,620
+بيساوي سفر يعني ينتمي للمجموعة Singleton Zero okay
+
+458
+00:43:03,620 --> 00:43:07,500
+تمام؟ إذن أصغر من أو سابع أو أكبر من أو سابع
+
+459
+00:43:07,500 --> 00:43:13,410
+معناته الفرق ينتمي ل P اتحاد Singleton Zeroالان في
+
+460
+00:43:13,410 --> 00:43:20,170
+عندي نظرية و النظرية هذه بتعطيني خواص ل .. ال ..
+
+461
+00:43:20,170 --> 00:43:28,450
+ال .. خليني بس نبص عليها بسرعة النظرية
+
+462
+00:43:28,450 --> 00:43:33,410
+هذه بتعطيني خواص لل order properties يعني خواص
+
+463
+00:43:33,410 --> 00:43:40,210
+أخرىنقدر نشتقها من ال order properties و كل هذه
+
+464
+00:43:40,210 --> 00:43:44,990
+خواص معروفة وسهلة وبسيطة و كلها .. كلها عارفين لكن
+
+465
+00:43:44,990 --> 00:43:48,230
+بدها برهان .. بدها برهان ماحدش عمره برهانلنا إياها
+
+466
+00:43:49,460 --> 00:43:54,600
+Okay فحنوقف عند النظرية هذه وإن شاء الله المرة
+
+467
+00:43:54,600 --> 00:44:01,120
+الجاية بنحاول نبرهن النظرية okay حاولوا أنتوا
+
+468
+00:44:01,120 --> 00:44:05,260
+meanwhile في نفس الوقت كتحضير للمحاضرة الجاية
+
+469
+00:44:05,260 --> 00:44:10,140
+حاولوا أنكم تقرأوا البرهان تبع النظرية وشوفوا هل
+
+470
+00:44:10,140 --> 00:44:16,360
+تفهموه ولا لأ okay تمام في أي سؤال okay شكرا لكم
+
+471
+00:44:16,360 --> 00:44:17,540
+ومبارك الله فيكم
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..268be34dc8187acfb7b65826af5ba650512b9d3f
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aQ184E7DSME_raw.srt
@@ -0,0 +1,1884 @@
+1
+00:00:20,960 --> 00:00:27,560
+Okay إذا هنواصل ان شاء الله اللي بدنا في المحاضرة
+
+2
+00:00:27,560 --> 00:00:33,340
+السادقة المرة اللي فاتت خلينا بسرعة بس هيك نمر على
+
+3
+00:00:33,340 --> 00:00:40,220
+الحاجات اللي أخدناها أخدنا اللي هو ال algebraic
+
+4
+00:00:40,220 --> 00:00:43,060
+properties of the real number system اللي هو
+
+5
+00:00:43,060 --> 00:00:48,970
+القواصة الجبريةو أعرفنا اللي هو ال real number
+
+6
+00:00:48,970 --> 00:00:52,930
+system فقلنا إن ال real number system عبارة عن
+
+7
+00:00:52,930 --> 00:00:58,430
+المجموعة R مع عمليتين جبريتين أو ثنائيتين عملية
+
+8
+00:00:58,430 --> 00:01:03,110
+جمع و عملية ضرب و هدول العمليات بحققوا خمس خواص
+
+9
+00:01:03,110 --> 00:01:08,290
+خاصية الإبدال competitive law خاصية الدمج ال
+
+10
+00:01:08,290 --> 00:01:14,180
+associative lawsخواص التوزيع distributive laws
+
+11
+00:01:14,180 --> 00:01:19,120
+خاصية الرابعة وجود ال identity elements الأناصر
+
+12
+00:01:19,120 --> 00:01:25,280
+المحايدة اللي هي سمنها 01 ووجود ال inverse
+
+13
+00:01:25,280 --> 00:01:38,580
+elements أو العناصر النظائر أو المعكسات فلكل عدد
+
+14
+00:01:38,580 --> 00:01:48,850
+حقيقيفيه إله معكوس جمعي اللي هو Salvoو لكل عدد
+
+15
+00:01:48,850 --> 00:01:55,330
+حقيقي غير مختلف عن السفر له نظير ضربي او
+
+16
+00:01:55,330 --> 00:01:59,030
+multiplicative inverse من المظل بالرمز x is
+
+17
+00:01:59,030 --> 00:02:03,050
+negative واحد بحيث لو ضربتم في بعض بيعطوني ال
+
+18
+00:02:03,050 --> 00:02:10,890
+identity element واحد هدول الخمس خواص اللي بتحققهم
+
+19
+00:02:10,890 --> 00:02:15,760
+مجموعة العداد الحقيقية معالعمليات الدرب والجامع
+
+20
+00:02:15,760 --> 00:02:21,600
+اللي عرفناها سابقا في أول خواص أخدناها اللي هي
+
+21
+00:02:21,600 --> 00:02:27,680
+cancellation laws موجودة في نظرية 1 1 فعملية
+
+22
+00:02:27,680 --> 00:02:33,220
+الجامع بتحقق cancellation law يعني انا لو كان عندي
+
+23
+00:02:33,220 --> 00:02:38,940
+x plus z بساوي y plus z فممكن اشطب zمن الطرفين
+
+24
+00:02:38,940 --> 00:02:44,680
+بطلع عندي x بساوي y كذلك عملية الضرب بتحقق ال
+
+25
+00:02:44,680 --> 00:02:51,000
+cancellation law فلو في عندي حصل ضرب زي هذا بساوي
+
+26
+00:02:51,000 --> 00:02:56,140
+حصل الضرب هذا و ال answer w هذا العدد w بسويش سفر
+
+27
+00:02:56,140 --> 00:03:01,470
+فمقدر أجسم الطرفين على wو ascentage X بساوي Y هذه
+
+28
+00:03:01,470 --> 00:03:05,430
+الخواص مهمة و برهنتلكم المرة اللي فاتت الجزء
+
+29
+00:03:05,430 --> 00:03:11,810
+التاني و برهان الجزء الأول مماثل و بالتالي قلنا
+
+30
+00:03:11,810 --> 00:03:17,650
+لكم حاولوا تثبتوا بنفس الطريقة بالمثل كمان أخدنا
+
+31
+00:03:17,650 --> 00:03:22,810
+نظرية تانية اللي هي النظرية هذه ذكرناها المرة اللي
+
+32
+00:03:22,810 --> 00:03:30,050
+فاتت فيها حوالي عشر خواص للأعداد الحقيقيةفاول
+
+33
+00:03:30,050 --> 00:03:35,350
+خاصية لو ضربت أي عدد حقيقي بالصفر سواء من اليمين
+
+34
+00:03:35,350 --> 00:03:39,370
+او اليسار فالنتج العدد الصفري اللي هو ال additive
+
+35
+00:03:39,370 --> 00:03:47,090
+identity صفر فبرهان الجزء هذا هو برهان الجزء الأول
+
+36
+00:03:47,090 --> 00:03:55,210
+يعني باين واحد هنا فكيف بتم البرهان انا عايز اثبت
+
+37
+00:03:55,210 --> 00:04:02,370
+ان x ضرب صفر بساوي صفرطيب انا عندي لو جمعت x ضارب
+
+38
+00:04:02,370 --> 00:04:07,470
+0 زاد x ضارب 0 بقدر باستخدام ال distributive law
+
+39
+00:04:07,470 --> 00:04:13,430
+أخد x عام المشترك كأني ضاربة x في 0 زاد 0 هذا صحيح
+
+40
+00:04:13,430 --> 00:04:17,550
+باستخدام ال distributive law الآن لما أجمع السفر
+
+41
+00:04:17,550 --> 00:04:22,450
+على أي عدد حقيقي حتى لو نفسه الناتج بطلع 0 هذا من
+
+42
+00:04:22,450 --> 00:04:33,170
+خواص المحايد الجامعيو ال X ضرب سفر هو نفسه لو جمعت
+
+43
+00:04:33,170 --> 00:04:37,330
+على العدد هذا سفر فيبقى زي ما هو من خواص السفر
+
+44
+00:04:37,330 --> 00:04:43,950
+الان انا ممكن اشطب باستخدام cancellation law ممكن
+
+45
+00:04:43,950 --> 00:04:49,590
+اشطب هذا و اشطب هذا فبطلع عندي X ضرب سفر بساوي سفر
+
+46
+00:04:49,590 --> 00:04:55,490
+okay تمامالخاصية التانية الخاصية التانية عايزين
+
+47
+00:04:55,490 --> 00:05:01,230
+نثبت أنه لو أخدت أي عدد حقيقي و أخدت سلبه مرتين
+
+48
+00:05:01,230 --> 00:05:06,530
+فهذا هو نفس ال X البرهان برضه بتم كالتالي هاي ال X
+
+49
+00:05:06,530 --> 00:05:12,370
+و بجمع عليه negative X اللي هو المعكوس الجامعي
+
+50
+00:05:12,370 --> 00:05:20,390
+طبعا فهذا بساوة سفر هذا بساوة سفر من خواص المعكوس
+
+51
+00:05:20,390 --> 00:05:26,570
+الجامعيو ممكن ان احنا نبدل هدول مع بعض او لأ، الان
+
+52
+00:05:26,570 --> 00:05:31,610
+برضه لو أخدت هذا، هذا عدد حقيقي، و هذا المعكوس
+
+53
+00:05:31,610 --> 00:05:36,970
+الجمعي تبعه، عدد حقيقي و المعكوس الجمعي تبعه دايما
+
+54
+00:05:36,970 --> 00:05:41,830
+بساوة سفر، الان ممكن نبدل عملية الجمع ابدالية،
+
+55
+00:05:41,830 --> 00:05:46,970
+commutative، فنبدل الحاجات هذه مع بعضالان عملية
+
+56
+00:05:46,970 --> 00:05:50,970
+الجامعة بتحقق قانون الحدث cancellation law إذا
+
+57
+00:05:50,970 --> 00:05:55,390
+ممكن أشطب أنا العنصر هذا مع هذا بيبقى عندي على
+
+58
+00:05:55,390 --> 00:05:59,810
+الشمال X وعلى اليمين بيبقى negative negative X
+
+59
+00:05:59,810 --> 00:06:06,070
+فبالتالي هي كمان أثبتنا صحة الخاصية هذه تمام؟
+
+60
+00:06:07,410 --> 00:06:11,250
+الخاصية التالتة في النظرية اللى شوفناها قبل شوية
+
+61
+00:06:11,250 --> 00:06:17,770
+برهانها مماثل لخاصية تانية وبالتالي هسيبه تمرين،
+
+62
+00:06:17,770 --> 00:06:21,770
+اذا بعض الحاجات اللى برهانها مماثل دايما هنسيبها
+
+63
+00:06:21,770 --> 00:06:26,030
+كتمرين للطالب لإن الفكرة نفسها ورياضيات مجرد أفكار
+
+64
+00:06:26,030 --> 00:06:33,620
+فإذا عرفنا الفكرة انتهى الحل اللغزالخاصية الرابعة،
+
+65
+00:06:33,620 --> 00:06:37,120
+في الخاصية الرابعة عايزين نثبت أنه لو ضربت سالب
+
+66
+00:06:37,120 --> 00:06:42,880
+واحد في x بطلع عندي ال negative x أو المحايد
+
+67
+00:06:42,880 --> 00:06:48,640
+الجمعي ل x فلبرهان ذلك باخد negative واحد في x و
+
+68
+00:06:48,640 --> 00:06:53,820
+بجمعها على x فهذا هو نفسه هي negative واحد في x و
+
+69
+00:06:53,820 --> 00:06:59,970
+ال x هذه عبارة عن واحد في xالان ممكن هنا استخدم
+
+70
+00:06:59,970 --> 00:07:03,070
+الـ distributive law عملية الضرب تتوزع لعملية
+
+71
+00:07:03,070 --> 00:07:07,670
+الجمال فممكن اكتب هذا سالب واحد زاد واحد مضروب من
+
+72
+00:07:07,670 --> 00:07:13,370
+اليمين في X وعملية الضرب ابدالية فهي نفس كما لو
+
+73
+00:07:13,370 --> 00:07:19,040
+ضربت X من اليمين في سالب واحد زاد واحدOkay تمام
+
+74
+00:07:19,040 --> 00:07:24,700
+الان لما اجمع سالب واحد هذا سالب واحد على واحد
+
+75
+00:07:24,700 --> 00:07:31,440
+انصر ونظير الجمع تبعهم مجموعهم سفر و سفر في اي
+
+76
+00:07:31,440 --> 00:07:37,500
+انصر اثبتنا انه بيساوي سفر و السفر هو نفسه سالب x
+
+77
+00:07:37,500 --> 00:07:42,450
+زائد xوبالتالي بقدر استخدم ال cancellation اللي هو
+
+78
+00:07:42,450 --> 00:07:47,250
+عامل cancelling ل X على الطرف الشمال و cancelling
+
+79
+00:07:47,250 --> 00:07:50,990
+ل X على الطرف اليمين يبقى في الشمال سالب واحد في X
+
+80
+00:07:50,990 --> 00:07:55,850
+في اليمين سالب X وبالتالي هيك ممكن أثبتنا الخاصية
+
+81
+00:07:55,850 --> 00:08:01,850
+هذه واضح؟ أي حد عنده أي استفسار؟ خواص سهل و براهين
+
+82
+00:08:01,850 --> 00:08:06,150
+سهلة جدا انت دارسين مبادئ و اللي دارسين مبادئ
+
+83
+00:08:06,150 --> 00:08:11,530
+رياضيات و فاهمينها كويس هذه حاجاتيعني براهين أمثلة
+
+84
+00:08:11,530 --> 00:08:16,170
+كلها على برهان مباشر بسيط باستخدام خواص ذكرناها
+
+85
+00:08:16,170 --> 00:08:22,990
+سابقا فهذا مجرد يعني مبادئ رياضيات الخاصية الخامسة
+
+86
+00:08:22,990 --> 00:08:29,590
+احنا عايزين نثبت لو ضربت x في negative y تطلع ..
+
+87
+00:08:29,590 --> 00:08:34,960
+هي نفسها كم لو ضربت negative x في yو هذه يعني
+
+88
+00:08:34,960 --> 00:08:39,800
+البرهان مش صعب هاي ال X وهي negative Y الخاصية
+
+89
+00:08:39,800 --> 00:08:43,560
+الرابعة أثبتنا فيها إنه negative Y بيساوي negative
+
+90
+00:08:43,560 --> 00:08:48,780
+واحد في Y هذا من الخاصية أربعة ال associative law
+
+91
+00:08:48,780 --> 00:08:52,120
+بيسمح لإن أنا الأقواس هذه أرتبها بالطريقة هذه
+
+92
+00:08:52,120 --> 00:08:56,180
+عملية الضرب associative و كمان عملية الضرب
+
+93
+00:08:56,180 --> 00:09:00,620
+commutative إذا ممكن أبدل ال X مع ال negative واحد
+
+94
+00:09:04,010 --> 00:09:07,470
+الخاصية الرابعة بتقول سالب واحد ضرب X عبارة عن
+
+95
+00:09:07,470 --> 00:09:14,030
+negative X إذاً هذا هو إيه هذا جزء من الجزء الخامس
+
+96
+00:09:14,030 --> 00:09:20,750
+في كمان جزء تاني اللي هو عايزين نثبت إن X ضرب
+
+97
+00:09:20,750 --> 00:09:24,990
+negative Y هو نفس الحاجة كما لو ضربت X في Y الأول
+
+98
+00:09:24,990 --> 00:09:30,950
+وضربت الكل في negativeو لبرهان ذلك هي X في
+
+99
+00:09:30,950 --> 00:09:34,950
+negative Y X في negative Y أثبتنا إنها طلعت بتساوي
+
+100
+00:09:34,950 --> 00:09:41,090
+سالب واحد في X في Y هذا هو نجلتها من هنا الآن
+
+101
+00:09:41,090 --> 00:09:44,470
+باستخدام ال associative law ممكن أيه أبدل الأقواس
+
+102
+00:09:44,470 --> 00:09:50,450
+يعني أخد X وY مع بعض و أضربهم في سالب واحد و طبعا
+
+103
+00:09:50,450 --> 00:09:54,490
+الآن أثبتنا أن سالب واحد لما أضربه في حاجة زي هذه
+
+104
+00:09:54,490 --> 00:09:56,910
+بيطلع سالب X في Y
+
+105
+00:10:01,430 --> 00:10:08,850
+بالنسبة لخاصية رقم 6 ممكن نستخدم الخاصية رقم 4 و
+
+106
+00:10:08,850 --> 00:10:12,510
+ال distributive law في إثباتها فطبعا أنا هنا كاتب
+
+107
+00:10:12,510 --> 00:10:18,030
+لكم use الخاصية أو الجزء الرابع و ال distributive
+
+108
+00:10:18,030 --> 00:10:23,210
+law لبرهان مين؟ الخاصية رقم 6 هذه، هذه أرقام
+
+109
+00:10:23,210 --> 00:10:29,920
+لاتينيةفبتشوفوها انتوا طبعا و بتحاولوا تثبتوها و
+
+110
+00:10:29,920 --> 00:10:35,660
+اذا ماعرفتوش ممكن تتواصلوا معايا نحاول نثبتها لكم
+
+111
+00:10:35,660 --> 00:10:42,780
+بالنسبة لخاصية السابعة ايه هي الخاصية السابعة لو
+
+112
+00:10:42,780 --> 00:10:46,700
+ضربت negative x ف negative y المفروض يطلع نفس
+
+113
+00:10:46,700 --> 00:10:54,530
+الحاجة x ضرب yوهي البرهان بسيط احنا اخدنا ان لو
+
+114
+00:10:54,530 --> 00:10:59,830
+ضربت negative x في انصر negative y هو نفسه كما لو
+
+115
+00:10:59,830 --> 00:11:07,130
+انا ضربت x في الانصر التاني واخدت السالب برا و
+
+116
+00:11:07,130 --> 00:11:07,750
+بعدين
+
+117
+00:11:10,830 --> 00:11:17,230
+نفس الحاجة هنا x في negative y هي
+
+118
+00:11:17,230 --> 00:11:24,890
+نفسها negative x في y بدالت x في negative y ب
+
+119
+00:11:24,890 --> 00:11:30,290
+negative ضرب x y و أثبتنا قبل هيك أن negative ضرب
+
+120
+00:11:30,290 --> 00:11:34,930
+negative negative العنصر بساوي العنصرإذا هذا برضه
+
+121
+00:11:34,930 --> 00:11:45,630
+برهان الجزء هذا الجزء التامن او التاسع are left as
+
+122
+00:11:45,630 --> 00:11:48,410
+exercises برضه أنا سايبلكم اياهم تمرين لان مش
+
+123
+00:11:48,410 --> 00:11:52,310
+ماجون بارهم كل إشي انتوا يعني كبار لان بديتوا
+
+124
+00:11:52,310 --> 00:11:58,050
+تسوابوا بديتوا تفهموا فلازم برضه تشاركوا شويةمش
+
+125
+00:11:58,050 --> 00:12:02,030
+معقول زي اللي .. احنا مش في مدرسة ثانوية، بناشي
+
+126
+00:12:02,030 --> 00:12:06,310
+نقول، عدادية، لازم يشرحلكم كل إشي و لازم يبرهلكم
+
+127
+00:12:06,310 --> 00:12:10,050
+كل إشي، لازم الطالب يشارك شوية، خاصة الحاجات اللي
+
+128
+00:12:10,050 --> 00:12:14,290
+براهينها مشابهةفبتزعلوش و حالكم انتوا تاخدوا
+
+129
+00:12:14,290 --> 00:12:19,430
+الأمور هذه بصدر راحل و كمان مرة بكرر لو اي شيء من
+
+130
+00:12:19,430 --> 00:12:23,570
+الحاجات اللي بنسيبها ماعرفتوش تحلوها او تبرهنوها
+
+131
+00:12:23,570 --> 00:12:28,350
+فانا على استعداد ان اساعدكم في برهنها الجزء الأخر
+
+132
+00:12:28,350 --> 00:12:32,490
+جزء العاشر ايه هو الجزء العاشر الجزء العاشر بيقول
+
+133
+00:12:32,490 --> 00:12:40,530
+دائما بندرسها في مبادئ الرياضياتمثال على برهان غير
+
+134
+00:12:40,530 --> 00:12:44,490
+مباشر في مبادر رياضيات، لو كان X ضرب Y أعداد
+
+135
+00:12:44,490 --> 00:12:50,990
+حقيقية، حصل ضربهم سفر، فإيه بيطلع؟ إما X بساوي سفر
+
+136
+00:12:50,990 --> 00:12:55,650
+أو Y بساوي سفر، بظبط؟
+
+137
+00:13:01,000 --> 00:13:05,060
+فهذا نعطي مثال في المبادئ الرياضية طيب البرهان هو
+
+138
+00:13:05,060 --> 00:13:12,880
+نفسه البرهان هو نفسه عشان اثبت انه x لو كان x ضرب
+
+139
+00:13:12,880 --> 00:13:19,760
+y بساوة 0 فبطلع x بساوة 0 او y بساوة 0 فبأفرض ان x
+
+140
+00:13:19,760 --> 00:13:26,220
+مايسويش 0و بثبت ان y بيساوي 0 او by symmetry
+
+141
+00:13:26,220 --> 00:13:32,080
+بالتماثل ممكن افرض ان y بيساوي 0 و اصل الى ان x
+
+142
+00:13:32,080 --> 00:13:41,640
+بيساوي 0 okay تمام فاللي عملناه هنا هيه لبرهان ان
+
+143
+00:13:41,640 --> 00:13:47,400
+x بيساوي 0 او y بيساوي 0 it suffices يعني يكفي ان
+
+144
+00:13:47,400 --> 00:13:54,070
+افرض to assume ان x لا يساوي 0و أثبت و أثبت أن y
+
+145
+00:13:54,070 --> 00:14:07,690
+بساوي 0 طيب أنا عندي من الفرد x y بساوي 0 ف
+
+146
+00:14:07,690 --> 00:14:14,610
+ال x y بساوي 0 تهيألي
+
+147
+00:14:14,610 --> 00:14:21,110
+فيه إشي هنا مش مبين ده هو خلينا نبينهنعم هاي انا
+
+148
+00:14:21,110 --> 00:14:26,470
+عندي x y من الفرض x y بساوي سفر والسفر هذا ممكن
+
+149
+00:14:26,470 --> 00:14:30,970
+اكتبه على صورة x ضرب سفر برضه هذا بساوي سفر تمام
+
+150
+00:14:30,970 --> 00:14:36,470
+الان انا فارض ان x بساويش سفر فعملية الضرب بتحقق
+
+151
+00:14:36,470 --> 00:14:40,210
+cancellation law اذا من cancellation law تبع عملية
+
+152
+00:14:40,210 --> 00:14:44,470
+الضرب مدام x بساويش سفر فبقدر اجسم عليها فبطلع
+
+153
+00:14:44,470 --> 00:14:50,590
+عندي y بساوي سفر وهذا هو المطلوبOkay تمام إذا هيك
+
+154
+00:14:50,590 --> 00:15:01,290
+بنكون برهننا النظرية التانية كويس
+
+155
+00:15:01,290 --> 00:15:07,770
+تمام هيك طيب
+
+156
+00:15:07,770 --> 00:15:11,690
+ناخد تعريفات أو تعريف مهم
+
+157
+00:15:21,020 --> 00:15:27,480
+في تعريف هنا الخواص
+
+158
+00:15:27,480 --> 00:15:30,660
+الخامسة هذه اللي حكينا عنها ال commutative law ال
+
+159
+00:15:30,660 --> 00:15:37,140
+associative law و ال distributive law existence of
+
+160
+00:15:37,140 --> 00:15:42,780
+identity elements الخاصية الخامسة existence of
+
+161
+00:15:42,780 --> 00:15:47,240
+inverses خمس خواص هذه اللي بتحقيق عمليات الجمع و
+
+162
+00:15:47,240 --> 00:15:52,770
+الدرب على الأعداد الحقيقية هذه الخواصبتشكل تعريف
+
+163
+00:15:52,770 --> 00:15:57,750
+ما يسمى في الجبر في الجبر الحديث في تركيبة جبرية
+
+164
+00:15:57,750 --> 00:16:03,870
+اسمها field او حقل فما
+
+165
+00:16:03,870 --> 00:16:09,130
+هو الحقل لو انتوا هتدرسوا جبر حديث واحد او .. او
+
+166
+00:16:09,130 --> 00:16:14,850
+درستوا فيمكن مار عليكم ال field او الحقل هو عبارة
+
+167
+00:16:14,850 --> 00:16:23,080
+عن set if مع عمليتين ثنائيتينعملية جمع وعملية ضرب
+
+168
+00:16:23,080 --> 00:16:29,300
+معرفين على ال set F بحيث ان العمليتين هدول بيحققوا
+
+169
+00:16:29,300 --> 00:16:33,640
+الخواص الخمسة اللي هي حققتها مجموعة الاعداد
+
+170
+00:16:33,640 --> 00:16:40,250
+الحقيقية، اذا اي مجموعة F مع عمليتين ثنائيتينبحقق
+
+171
+00:16:40,250 --> 00:16:46,630
+الخواص الخمسة بنسميها في الجبر field اذا ال .. ال
+
+172
+00:16:46,630 --> 00:16:51,510
+.. ال R ال R او العداد الحقيقية مع أمليات الجمع
+
+173
+00:16:51,510 --> 00:16:56,650
+والضرب اللي عرفناها سابقا شفنا انها بتحقق الخواص
+
+174
+00:16:56,650 --> 00:17:01,570
+الخمسة وبالتالي بتشكل field فبنسمي it the field of
+
+175
+00:17:01,570 --> 00:17:08,790
+real numbers او المجال ال .. الاعداد الحقيقيةهي
+
+176
+00:17:08,790 --> 00:17:14,430
+مثال فيه أمثلة كتيرة على fields على حقول فهي لو
+
+177
+00:17:14,430 --> 00:17:18,030
+أخدت المجموعة هي أبسط field أصغر و أبسط field
+
+178
+00:17:18,030 --> 00:17:24,190
+موجود في الرياضيات هو ال 6F اللي بتتكون من أنصرين
+
+179
+00:17:24,190 --> 00:17:33,050
+عددين حقيقيين 01الان عشان اكون field على المجموعة
+
+180
+00:17:33,050 --> 00:17:37,590
+F اللي بتكون من عضرين لازم اعرف عملية جمع و ضرب
+
+181
+00:17:37,590 --> 00:17:43,690
+فممكن اعرف عملية جمع و ضرب على F كالتالي ها يعني
+
+182
+00:17:43,690 --> 00:17:50,570
+اعرفت لو ضربت 0 في نفسه او 1 في 0 او 0 في 1 او
+
+183
+00:17:50,570 --> 00:17:57,780
+جمعت 0 على 0 او 1 على 1 هذا باعرفه انه بساوي 0أذا
+
+184
+00:17:57,780 --> 00:18:02,020
+أنا عرفت حاصل الضرب والجمع هذا بالساوية سفر كذلك
+
+185
+00:18:02,020 --> 00:18:05,800
+انا بعرفت انه لو جمعت السفر على الواحد او الواحد
+
+186
+00:18:05,800 --> 00:18:10,000
+على السفر او الواحد على الواحد بطلع واحد الان اذا
+
+187
+00:18:10,000 --> 00:18:16,410
+انا عرفت عمليات جمع وضرب على كل عناصر المجموعةالان
+
+188
+00:18:16,410 --> 00:18:23,610
+من السهل التحقق ان ال خواص الخمسة كلها تتحقق تابعة
+
+189
+00:18:23,610 --> 00:18:28,530
+ال field وبالتالي هذا بيكون field وهذا ال field في
+
+190
+00:18:28,530 --> 00:18:36,770
+الجبر بيرمزوله بالرمز z2 وفي
+
+191
+00:18:36,770 --> 00:18:40,890
+نفس الوجد هو cyclic group of order two إذا في حد
+
+192
+00:18:40,890 --> 00:18:45,120
+فيكم طراز الجبر حديثعلى أي حال احنا هذا مش موضوعنا
+
+193
+00:18:45,120 --> 00:18:49,400
+هذا موضوع جبر فبس يعني هذا مجرد مثال بسيط على
+
+194
+00:18:49,400 --> 00:18:53,600
+field و احنا اهم حاجة انه احنا يعني اللي بدنا احنا
+
+195
+00:18:53,600 --> 00:18:58,420
+نصله انه مجموعة الاعداد الحقيقية تبعتنا مجموعة
+
+196
+00:18:58,420 --> 00:19:04,980
+الاعداد الحقيقية R مع عملية الجامعة و الدرب بتشكل
+
+197
+00:19:04,980 --> 00:19:10,360
+ما يسمى في الجبر بال field تمام؟ هذا اللي احنا
+
+198
+00:19:10,360 --> 00:19:11,980
+عايزين نصله، نعم فضل
+
+199
+00:19:15,080 --> 00:19:18,860
+هذا تعريف احنا .. احنا .. احنا بنعرف انه لو اجمع
+
+200
+00:19:18,860 --> 00:19:23,700
+واحد على واحد يطلع صفر هذا definition تعريف وليس
+
+201
+00:19:23,700 --> 00:19:27,320
+اه يعني هاي مجموعة اه بدي اعرف عليها عملية جمع
+
+202
+00:19:27,320 --> 00:19:31,060
+عملية .. عملية الجمع هانا باعرفها لو جمعت واحد على
+
+203
+00:19:31,060 --> 00:19:39,480
+واحد بطلع صفر لو جمعت واحد اه
+
+204
+00:19:43,240 --> 00:19:52,920
+أه في هنا إشي مش مظبوط هنا هذه المفروض ضرب هذه هذه
+
+205
+00:19:52,920 --> 00:19:58,760
+المفروض ضرب هذه فهذا في خطأ مطبعي صحيح هذا كله
+
+206
+00:19:58,760 --> 00:20:02,200
+تعريف الآن لما هيك أنا بكون عرفت عملية الجمع
+
+207
+00:20:02,200 --> 00:20:07,240
+والضرب هنا في خطأ مطبع دي المفروض تكون ضرب لإن
+
+208
+00:20:07,240 --> 00:20:10,240
+واحد زاد واحد عرفناها تساوي سفر ف
+
+209
+00:20:13,680 --> 00:20:19,300
+حسب التعريف هذا ممكن التحقق ان خمس خواص تبعت ال
+
+210
+00:20:19,300 --> 00:20:22,760
+field بتتحقق فممكن تحققوها اذا بدكم تحققواها اذا
+
+211
+00:20:22,760 --> 00:20:25,700
+بدكم تحققواها اذا بدكم تحققواها اذا بدكم تحققواها
+
+212
+00:20:25,700 --> 00:20:27,620
+اذا بدكم تحققواها اذا بدكم تحققواها اذا بدكم
+
+213
+00:20:27,620 --> 00:20:27,740
+تحققواها اذا بدكم تحققواها اذا بدكم تحققواها اذا
+
+214
+00:20:27,740 --> 00:20:28,060
+بدكم تحققواها اذا بدكم تحققواها اذا بدكم تحققواها
+
+215
+00:20:28,060 --> 00:20:28,700
+اذا بدكم تحققواها اذا بدكم تحققواها اذا بدكم
+
+216
+00:20:28,700 --> 00:20:36,280
+تحققواها اذا بدكم تحققواها اذا بدكم تحققواها اذا
+
+217
+00:20:36,280 --> 00:20:43,660
+بدكم تحققواها اذا بدكم توعملية القسمة هي عملية
+
+218
+00:20:43,660 --> 00:20:47,340
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+219
+00:20:47,340 --> 00:20:49,400
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+220
+00:20:49,400 --> 00:20:53,020
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+221
+00:20:53,020 --> 00:20:54,300
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+222
+00:20:54,300 --> 00:20:56,080
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+223
+00:20:56,080 --> 00:20:56,480
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+224
+00:20:56,480 --> 00:21:01,560
+ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب، ضرب،
+
+225
+00:21:01,560 --> 00:21:06,040
+ضرب،إذن عملية الطرح هي عملية جمعة كذلك عملية
+
+226
+00:21:06,040 --> 00:21:10,320
+القسمة division on R is defined by هاي X على Y
+
+227
+00:21:10,320 --> 00:21:16,740
+بساوي عملية ضرب X في ال multiplicative inverse ل Y
+
+228
+00:21:16,740 --> 00:21:22,320
+أو 1 على Y كذلك بنعرف هذا definition دائما لما
+
+229
+00:21:22,320 --> 00:21:25,660
+يكون فيه نقطتين و وراهم علامة تساوي معناه إن طرف
+
+230
+00:21:25,660 --> 00:21:30,040
+الشمال by definition بساوي الطرف اليمين إذن هذا
+
+231
+00:21:30,040 --> 00:21:36,630
+تعريفلأن أنا بعرف هذا التعريف أن a أس negative one
+
+232
+00:21:36,630 --> 00:21:43,470
+معناها واحد على a a to zero بساوي واحد حسب التعريف
+
+233
+00:21:43,470 --> 00:21:48,970
+a to negative n و n عدد طبيعي هي عبارة عن مقلوب ال
+
+234
+00:21:48,970 --> 00:21:54,630
+a الكل to n فكل هذه تعريفات بناء على التعريفات هذه
+
+235
+00:21:54,630 --> 00:21:58,730
+ممكن أنبرهن خواص كثيرة
+
+236
+00:22:00,150 --> 00:22:03,810
+و هتشوفوا بعضها في التمرين اللي موجودة في نهاية ال
+
+237
+00:22:03,810 --> 00:22:09,970
+section نتطرق
+
+238
+00:22:09,970 --> 00:22:14,330
+لحاجة اسمها rational numbers الاعداد النسبية
+
+239
+00:22:14,330 --> 00:22:20,210
+الاعداد النسبية او rational numbers بنعرفها على
+
+240
+00:22:20,210 --> 00:22:24,130
+انها مجموعة من الاعداد الحقيقية او هي مجموعة جزئية
+
+241
+00:22:24,130 --> 00:22:30,010
+من الاعداد الحقيقيةنموذجها بالرمز boldfaceq هذه
+
+242
+00:22:30,010 --> 00:22:34,370
+الرموز الأحرف هذه أو ال letters هذه نسميها
+
+243
+00:22:34,370 --> 00:22:41,790
+boldface يعني حرف مغمق هذه طبعا بتدل على مجموعات
+
+244
+00:22:43,170 --> 00:22:47,190
+فال rational numbers هي كل الأعداد الحقيقية اللي
+
+245
+00:22:47,190 --> 00:22:52,210
+ممكن كتبتها على صورة rational a على b حيث a و b
+
+246
+00:22:52,210 --> 00:22:56,370
+أعداد صحيحة هذه مجموعة الأعداد الصحيحة bold في ال
+
+247
+00:22:56,370 --> 00:23:00,650
+z و المقام لازم مايسويش سفر لأن القسم على سفر مش
+
+248
+00:23:00,650 --> 00:23:05,840
+معرفةالان لو أخدت الأعداد الحقيقية وشلت منها
+
+249
+00:23:05,840 --> 00:23:09,720
+الأعداد النسبية طرحت منها الأعداد النسبية فالأعداد
+
+250
+00:23:09,720 --> 00:23:13,160
+الحقيقية المتبقية بنسميها irrational numbers
+
+251
+00:23:13,160 --> 00:23:18,480
+irrational numbers الأعداد غير النسبية إذا الأعداد
+
+252
+00:23:18,480 --> 00:23:21,960
+النسبية هي كل الأعداد الحقيقية التي لا يمكن
+
+253
+00:23:21,960 --> 00:23:26,740
+كتابتها على صورة rational a على b حيث a وb أعداد
+
+254
+00:23:26,740 --> 00:23:32,910
+صحيحة والمقان بسويش سفر تمام؟طبعا لو أخدت اتحاد ال
+
+255
+00:23:32,910 --> 00:23:35,590
+rational numbers مع ال irrational numbers بيعطوني
+
+256
+00:23:35,590 --> 00:23:38,770
+كل الأعداد الحقيقية يعني المعنى أخر الأعداد
+
+257
+00:23:38,770 --> 00:23:43,390
+الحقيقية احنا جزقناها إلى مجموعتين irrational
+
+258
+00:23:43,390 --> 00:23:53,270
+numbers اتحاد ال irrational numbers طبعا
+
+259
+00:23:53,270 --> 00:23:57,830
+المجموعتين هدول disjoint يعني منفصلتين مافيش بينهم
+
+260
+00:23:57,830 --> 00:23:58,850
+عناصر مشتركة
+
+261
+00:24:01,750 --> 00:24:08,710
+طيب ال .. النظرية التالية ممكن من السهل ان احنا
+
+262
+00:24:08,710 --> 00:24:14,950
+نثبتها باستخدام خواص الأعداد الصحيحة يعني
+
+263
+00:24:14,950 --> 00:24:25,150
+معروف احنا عندنا ان ال ..
+
+264
+00:24:25,150 --> 00:24:30,090
+معروف ان ال ..
+
+265
+00:24:33,390 --> 00:24:37,450
+لو في عندي عددين صحيحين فمجموعهم بيطلع عدد صحيح
+
+266
+00:24:37,450 --> 00:24:42,570
+وحاصل ضربهم عدد صحيح بمعنى آخر عملية مجموعة
+
+267
+00:24:42,570 --> 00:24:49,220
+الأعداد الصحيحة مغلقة تحت عمليات الجمع والضرببنفس
+
+268
+00:24:49,220 --> 00:24:53,860
+.. باستخدام الحقيقة هذه أو ال fact هذه ممكن اثبات
+
+269
+00:24:53,860 --> 00:24:58,900
+انه مجموعة الاعداد النسبية مغلقة تحت عمليات الضرب
+
+270
+00:24:58,900 --> 00:25:06,270
+والجامعة واخذ ال additive inverseيعني لو كان XY
+
+271
+00:25:06,270 --> 00:25:10,810
+أعداد نسبية فمجموعهم بيطلع عدد نسبي وحاصل ضربهم
+
+272
+00:25:10,810 --> 00:25:15,330
+عدد نسبي و سالب عدد نسبي بيطلع عدد نسبي و لو في
+
+273
+00:25:15,330 --> 00:25:21,330
+عندي عدد نسبي مختلف عن السفر ف ال multiplicative
+
+274
+00:25:21,330 --> 00:25:28,550
+inverse بيطلع عدد نسبيبمعنى آخر، مجموعة الأعداد
+
+275
+00:25:28,550 --> 00:25:33,950
+النسمية مغلقة تحت عملية الجمع والضرب، وأخذ الـ
+
+276
+00:25:33,950 --> 00:25:39,950
+Additive Inverse وأخذ مغلقة تحت الـ Multiplicative
+
+277
+00:25:39,950 --> 00:25:44,470
+Inverse وبالتالي ممكن
+
+278
+00:25:46,690 --> 00:25:51,850
+بنستنتج أن مجموعة الأعداد النسلية بتحقق القواص
+
+279
+00:25:51,850 --> 00:25:56,430
+الخامسة تبع ال field وبالتالي هي بتشكل field بحد
+
+280
+00:25:56,430 --> 00:26:05,690
+ذاتها الان ال Q subset من R وR field وQ subset من
+
+281
+00:26:05,690 --> 00:26:11,830
+R وQ field فبنسمي Q sub field زي لما يكون في عندي
+
+282
+00:26:11,830 --> 00:26:19,160
+set وفي داخلها setفبنقول sub set لو في عندي group
+
+283
+00:26:19,160 --> 00:26:25,240
+و في عندي مجموعة جزئية من ال group فبنسمي المجموعة
+
+284
+00:26:25,240 --> 00:26:31,940
+جزئية نفسها group أيضا فبنسميها sub group اذا ال Q
+
+285
+00:26:31,940 --> 00:26:38,340
+is a sub field of the field R بناء على النظرية هذه
+
+286
+00:26:38,340 --> 00:26:44,770
+اذا هذه كلها حقائق معروفة يعنيو هتركزوا عليها
+
+287
+00:26:44,770 --> 00:26:48,410
+انتوا في الجبر يعني ماحنخوض فيها كتير لإن هذا
+
+288
+00:26:48,410 --> 00:26:53,370
+مواضيع الجبرية احنا هنركز على ال analysis في كمان
+
+289
+00:26:53,370 --> 00:26:57,990
+نظرية هنا مهمة بتخص الأعداد النسبية والغير نسبية
+
+290
+00:26:57,990 --> 00:27:03,570
+وهذه طبعا برضه بنعطيها دائما مثال في مبادئ
+
+291
+00:27:03,570 --> 00:27:04,430
+الرياضيات
+
+292
+00:27:07,090 --> 00:27:14,250
+بورهان على مثال على بورهان غير مباشر النظرية هذه
+
+293
+00:27:14,250 --> 00:27:17,930
+بتقول there does not exist R ينتمي ل Q بحيث R
+
+294
+00:27:17,930 --> 00:27:22,530
+تربية بيساوي اتنين مافيش لا يوجد عدد نسبي مربعه
+
+295
+00:27:22,530 --> 00:27:27,450
+بساوي اتنين يعني بمعنى اخر النظرية هذه باختصار
+
+296
+00:27:27,450 --> 00:27:36,590
+بتقول ان جذر الاتنين ليس عدد نسبي وماليش؟عدد غير
+
+297
+00:27:36,590 --> 00:27:41,830
+نسبي يعني جذر اتنين عدد غير نسبي فهي برهان
+
+298
+00:27:41,830 --> 00:27:45,490
+بالتناقض برهان غير مباشر بالتناقض by contradiction
+
+299
+00:27:45,490 --> 00:27:53,510
+احنا عايزين نثبت انه مافيش عدد او جذر اتنين ليس
+
+300
+00:27:53,510 --> 00:28:01,010
+عدد نسبي فنفرض النقيد نفرض النفي هو الصح يعني نفرض
+
+301
+00:28:01,010 --> 00:28:11,490
+ان جذر الاتنين عدد نسبي يعني بالساويP على Q حيث P
+
+302
+00:28:11,490 --> 00:28:17,310
+و Q أعداد صحيحة و
+
+303
+00:28:17,310 --> 00:28:23,990
+Q لا يساوي سفر تمام؟ و بدنا نصل إلى تناقض إذا
+
+304
+00:28:23,990 --> 00:28:27,870
+وصلنا إلى تناقض معناته فرضنا هذا غلط والصح أن
+
+305
+00:28:27,870 --> 00:28:32,410
+النظرية تكون صحيحة، بصبوت؟ طيب نشوف مع بعض
+
+306
+00:28:36,080 --> 00:28:46,520
+هي فرضنا انه الاتنين عدد هاي اتنين بيساوي هاي
+
+307
+00:28:46,520 --> 00:28:52,320
+فرضنا انه الاتنين بيساوي P على Q او جدر اتنين
+
+308
+00:28:52,320 --> 00:28:57,100
+بيساوي P على Q وبالتالي P على Q ربع فبطلع عند P
+
+309
+00:28:57,100 --> 00:29:02,900
+على Q تربيه بيساوي اتنين صح؟ هايطيب الآن لما يكون
+
+310
+00:29:02,900 --> 00:29:12,820
+في عندي أعداد هذا عدد نسبي فممكن نختصر و نفرض أنه
+
+311
+00:29:12,820 --> 00:29:19,480
+مافيش عامل مشترك بين ال P و ال Q إلا الواحد الصحيح
+
+312
+00:29:19,480 --> 00:29:26,660
+يعني مثلا هي عندي مثلا أربعة على مثلا عشرة هذا عدد
+
+313
+00:29:26,660 --> 00:29:32,130
+نسبيفممكن اكتبه اختصر اجسم على اتنين و اجسم على
+
+314
+00:29:32,130 --> 00:29:36,530
+اتنين بطلع اتنين على خمسة لاحظوا الان مافيش عامل
+
+315
+00:29:36,530 --> 00:29:40,370
+مشترك بين اتنين و الخمسة الا الواحد فهذا في الجبر
+
+316
+00:29:40,370 --> 00:29:44,410
+بيسموه ال greatest common divisor لاتنين و خمسة
+
+317
+00:29:44,410 --> 00:29:53,130
+بساوة واحد هاي مثلا سالب عشرة على تلاتين هاي هذا
+
+318
+00:29:53,130 --> 00:29:59,940
+عدد نسبي فممكن نختصر هذا يصير اتنين علىوالا ايش
+
+319
+00:29:59,940 --> 00:30:06,760
+هذا او سالب واحد على تلاتة فال bus سالب واحد عدد
+
+320
+00:30:06,760 --> 00:30:10,460
+صحيح و المقام تلاتة و ال greatest common divisor
+
+321
+00:30:10,460 --> 00:30:17,420
+لسالب واحد و تلاتة بساوي واحد اذا اي عدد نسبة ممكن
+
+322
+00:30:17,420 --> 00:30:23,260
+اختصره او ابسط و اكتبه بأبسط صورةيعني اخلي ال
+
+323
+00:30:23,260 --> 00:30:29,640
+greatest common divisor ل P و Q هنا بساوي واحد طيب
+
+324
+00:30:29,640 --> 00:30:35,580
+الان تعالوا نربع هنا هذه المعادلة P على Q تربية
+
+325
+00:30:35,580 --> 00:30:40,500
+بساوي اتنين فمنها بنستنتج ان P تربية بساوي اتنين و
+
+326
+00:30:40,500 --> 00:30:47,040
+Q تربيةطيب هي عندي P تربيع بساو 2 في Q تربيع الـ Q
+
+327
+00:30:47,040 --> 00:30:50,820
+هاد عدد صحيح فمربع العدد الصحيح اللي هو Q تربيع
+
+328
+00:30:50,820 --> 00:30:54,720
+بيطلع عدد صحيح عدد صحيح مضروب في 2 بيطلع even
+
+329
+00:30:54,720 --> 00:30:59,400
+number عسب المبادئ صح؟ اذا P تربيع بيطلع even
+
+330
+00:30:59,400 --> 00:31:06,520
+number تمام؟هذا بيؤدي انه ممكن اثبات ان P بيطلع
+
+331
+00:31:06,520 --> 00:31:10,960
+even لو كان مربع عدد صحيح even فممكن اثبات ان
+
+332
+00:31:10,960 --> 00:31:14,860
+العدد الصحيح نفسه لازم يطلع even وهذا ممكن نعمل
+
+333
+00:31:14,860 --> 00:31:21,940
+برهان صغير بالتناقض افرضه ان P مش even يعني odd
+
+334
+00:31:21,940 --> 00:31:28,360
+ربع E فبطلع مربع odd تناقض هاي البرهان اذا هذا ايه
+
+335
+00:31:28,360 --> 00:31:33,220
+الاجابة على ال Yكمان مرة إذا كان عندي P تربية أنا
+
+336
+00:31:33,220 --> 00:31:39,900
+عندي P تربية even هذا بقد أنه P even كيف نبرهن هذا
+
+337
+00:31:39,900 --> 00:31:46,420
+برهان بالتناقض افرض أنه P odd أيه يعني P odd يعني
+
+338
+00:31:46,420 --> 00:31:51,600
+P هاي
+
+339
+00:31:51,600 --> 00:31:58,500
+P بساوي 2K زي 1 هذا معناه oddوطبعا الـ K هي عدد
+
+340
+00:31:58,500 --> 00:32:04,620
+صحيح ربي إذا P تربية بساوي أربعة K تربية زاد أربعة
+
+341
+00:32:04,620 --> 00:32:14,080
+K زاد واحد وهذا بساوي اتنين في اتنين K تربية زاد
+
+342
+00:32:14,080 --> 00:32:19,900
+اتنين K مع بعض زاد واحد وهذا بساوي اتنين في M زاد
+
+343
+00:32:19,900 --> 00:32:26,350
+واحد حيث M عدد صحيحإذاً P تربية طلع بساوة اتنين في
+
+344
+00:32:26,350 --> 00:32:30,410
+عدد صحيح زائد واحد وبالتالي هذا اقض Contradiction
+
+345
+00:32:30,410 --> 00:32:35,590
+تناقض لأن احنا عندنا P تربية P تربية is even okay
+
+346
+00:32:35,590 --> 00:32:42,670
+إذاً هذا برهان ال why طيب إذا احنا وصلنا إلى أن P
+
+347
+00:32:42,670 --> 00:32:48,750
+تربية even بقدر أن P even الآن ال P و ال Q have no
+
+348
+00:32:48,750 --> 00:32:51,410
+common factor other than واحد مافيش بينهم عامل
+
+349
+00:32:51,410 --> 00:32:57,460
+مشترك إلا الواحدو ال P even إذا لازم ال Q يكون odd
+
+350
+00:32:57,460 --> 00:33:03,320
+لأن لو كان ال Q even و ال P even ففيه عامل مشترك
+
+351
+00:33:03,320 --> 00:33:09,560
+بينهم اتنين على الأقل او أربعة وهذا بتناقض مع ايه
+
+352
+00:33:09,560 --> 00:33:13,100
+أنه احنا فرضين أنه مافيش common factor بين ال P و
+
+353
+00:33:13,100 --> 00:33:18,560
+ال Q إلا الواحد تمام إذا أنا عندي هنا سنتجة أن ال
+
+354
+00:33:18,560 --> 00:33:25,030
+Q لازم يكون odd الآنأنا عندي P even يعني المعناته
+
+355
+00:33:25,030 --> 00:33:33,020
+بيساوي 2M for some M عدد صحيح وبالتالي لو ربعتلو
+
+356
+00:33:33,020 --> 00:33:37,780
+نرجع نعوض في المعادلة هذه P تربية بساوة 2Q تربية
+
+357
+00:33:37,780 --> 00:33:43,120
+عوض عن P بساوة 2M فبصير 4M تربية بساوة 2Q تربية
+
+358
+00:33:43,120 --> 00:33:48,760
+فبختصر 2 من الطرفين بطلع 2M تربية بساوة Q تربية
+
+359
+00:33:48,760 --> 00:33:54,620
+إذن Q تربية بساوة 2 ضرب عدد صحيحوبالتالي Q تربية
+
+360
+00:33:54,620 --> 00:34:00,020
+is even وبالتالي منها بنستنتج ان ال Q نفسها is
+
+361
+00:34:00,020 --> 00:34:08,720
+even اذا الان انا عندي ال Q is even وهي نفس ال Q
+
+362
+00:34:08,720 --> 00:34:14,260
+سنتجنا انها odd فهذا
+
+363
+00:34:14,260 --> 00:34:20,680
+تناقض .. هذا تناقض صح؟الـ Q هنا odd وهنا طلعت even
+
+364
+00:34:20,680 --> 00:34:24,240
+فهذا يعطيني contradiction which is a contradiction
+
+365
+00:34:24,240 --> 00:34:30,620
+فهذا التناقض ان احنا هنا وصلنا بدينا بالبرهان احنا
+
+366
+00:34:30,620 --> 00:34:35,860
+عايزين نثبت جدر اتنين لا تنتمي ل Q فرضنا النقيض ال
+
+367
+00:34:35,860 --> 00:34:40,660
+contrary ان جدر اتنين تنتمي ل Q يعني ممكن كتبتها
+
+368
+00:34:40,660 --> 00:34:46,240
+على صورة P على Q P و Q أعداد صحيحةوصلنا لتناقض
+
+369
+00:34:46,240 --> 00:34:50,020
+معناته ان هذا فرضنا غلط الصح ان جدر اتنين لاتن
+
+370
+00:34:50,020 --> 00:34:54,640
+تميلكيه as required كما هو مطلوب okay تمام هذا
+
+371
+00:34:54,640 --> 00:34:59,660
+برهان بالتناقض تمام اذا هنا شوية راجعنا شوية
+
+372
+00:34:59,660 --> 00:35:04,820
+براهين اتعلمتوها في مبادئ رياضيات طبعا الناس اللي
+
+373
+00:35:04,820 --> 00:35:09,180
+اتعلموا مبادئ رياضيات و اخوياء الحاجات هذه
+
+374
+00:35:09,180 --> 00:35:14,870
+بالنسبالهم يعني صارت مجرد تسليةوالناس اللي عندهم
+
+375
+00:35:14,870 --> 00:35:20,790
+مشاكل في المبادئ نجحوا بالعافية فممكن يعني يجد ان
+
+376
+00:35:20,790 --> 00:35:28,670
+هذا مش كتير مستثار طيب هيك بنكون خلصنا ال
+
+377
+00:35:28,670 --> 00:35:33,410
+algebraic properties of R الخواص الجابرية لنظام
+
+378
+00:35:33,410 --> 00:35:37,650
+الأعداد الحقيقية او ال real number system ننتقل ل
+
+379
+00:35:37,650 --> 00:35:40,550
+section تاني داخل ال chapter الأول هيك خلصنا
+
+380
+00:35:40,550 --> 00:35:46,110
+sectionال section التاني عنوانه ال order
+
+381
+00:35:46,110 --> 00:35:52,370
+properties of R خواص الترتيب على Rorder properties
+
+382
+00:35:52,370 --> 00:35:58,470
+خواص الترتيب احنا شفنا او قولنا لما عرفنا نظام
+
+383
+00:35:58,470 --> 00:36:02,070
+الاعداد الحقيقية قولنا ان نظام الاعداد الحقيقية
+
+384
+00:36:02,070 --> 00:36:07,670
+مجرد مجموعة R boldface R مع عمليتين ثنائيتين two
+
+385
+00:36:07,670 --> 00:36:11,710
+binary operations بيحققوا الخمس خواص تبعت ال field
+
+386
+00:36:11,710 --> 00:36:16,730
+اليوم هنفترض ايضا ان نظام الاعداد الحقيقية بيحقق
+
+387
+00:36:17,890 --> 00:36:24,850
+order properties الخاصية رقم ستة هذه الخاصية رقم
+
+388
+00:36:24,850 --> 00:36:30,710
+ستة هذه الخاصية رقم ستة تتجزأ إلى تلات خواص تلات
+
+389
+00:36:30,710 --> 00:36:41,410
+خواص تسميهم order properties او اول خاصية نفترض
+
+390
+00:36:41,410 --> 00:36:48,400
+ماهي order propertyنفترض وجود مجموعة جزئية من R
+
+391
+00:36:48,400 --> 00:36:53,500
+وغير خالية، ليست خالية، non-empty subset of R
+
+392
+00:36:53,500 --> 00:36:58,220
+نفترض أن يوجد مجموعة P subset of R غير خالية
+
+393
+00:36:58,220 --> 00:37:04,620
+وبتحقق التلات خواص هذه ال set P is closed under
+
+394
+00:37:04,620 --> 00:37:09,920
+addition يعني لو خلت أي عنصرين في P فمجموعهم بيطلع
+
+395
+00:37:09,920 --> 00:37:15,040
+عنصر تالتفيها كذلك المجموعة P closed under
+
+396
+00:37:15,040 --> 00:37:20,620
+multiplication يعني لو أخدت أي عنصرين فحصل ضربهم
+
+397
+00:37:20,620 --> 00:37:26,980
+بيطلع عنصر تالت الخاصية التالتة من خاصية الترتيب
+
+398
+00:37:26,980 --> 00:37:32,340
+اللي لها اسم بنسميها trichotomy property الخاصية
+
+399
+00:37:32,340 --> 00:37:37,940
+الثلاثية الخاصية الثلاثية إيه هي؟ لو أخدت أي عدد
+
+400
+00:37:37,940 --> 00:37:39,180
+حقيقي R
+
+401
+00:37:41,750 --> 00:37:51,250
+فواحد من التلت احتمالات هذه لازم يكون صحيح وهو ان
+
+402
+00:37:51,250 --> 00:37:57,290
+اما a تنتمي للمجموعة P هذه او a بالساوء سفر او
+
+403
+00:37:57,290 --> 00:38:01,410
+negative a ينتمي للمجموعة P هذه هي الخاصية
+
+404
+00:38:01,410 --> 00:38:07,670
+التالتية اي عدد حقيقي اما يكون عنصر في P او بساوء
+
+405
+00:38:07,670 --> 00:38:10,630
+سفر او ال negative تبقى انصر في P
+
+406
+00:38:16,020 --> 00:38:21,780
+الان بنعرف المجموعة remark ملاحظة باعرف المجموعة
+
+407
+00:38:21,780 --> 00:38:25,820
+negative P المجموعة negative P هي مجموعة كل
+
+408
+00:38:25,820 --> 00:38:33,050
+العناصر negative A حيث A ينتمي ل Pالان الخاصية C
+
+409
+00:38:33,050 --> 00:38:36,310
+من ال order property اللي هي trichotomy property
+
+410
+00:38:36,310 --> 00:38:43,610
+الخاصية C says تقول أو بتقول ان ال sets المجموعات
+
+411
+00:38:43,610 --> 00:38:52,110
+اللي هي المجموعة الأحدية سفر و المجموعة P و
+
+412
+00:38:52,110 --> 00:38:57,570
+المجموعة negative P التلاتة
+
+413
+00:38:57,570 --> 00:39:02,860
+هدول are pairwise disjointمنفصلة مثنى مثنى
+
+414
+00:39:02,860 --> 00:39:06,840
+pairwise is joint يعني منفصلة مثنى مثنى إيه يعني؟
+
+415
+00:39:06,840 --> 00:39:11,360
+لو أخدت أي تنتين من التلات مجموعات هدول و قاطعتهم
+
+416
+00:39:11,360 --> 00:39:15,200
+مع بعض فاتقعتوا اعتبارهم five مافيش بينهم عناصر
+
+417
+00:39:15,200 --> 00:39:19,060
+مشتركة فبنقول إن المجموعات هذه pairwise is joint
+
+418
+00:39:20,610 --> 00:39:26,410
+ومش هيكوا بس واتحادهم بساوي كل العداد الحقيقية هذا
+
+419
+00:39:26,410 --> 00:39:33,430
+صحيح من الخاصية C لأن C بتقول لأي عدد حقيقي أي A
+
+420
+00:39:33,430 --> 00:39:41,310
+ينتمي إلى R أي A ينتمي إلى R إما ينتمي إلى P أو
+
+421
+00:39:41,310 --> 00:39:45,370
+بساوي 0 وبالتالي ينتمي إلى المجموعة هذه أو ينتمي
+
+422
+00:39:45,370 --> 00:39:52,030
+إلى negative P صح؟وبالتالي كل a هنا موجود في واحدة
+
+423
+00:39:52,030 --> 00:39:54,810
+من هذول التلاتة وبالتالي موجود في اتحادهم مش هيك
+
+424
+00:39:54,810 --> 00:39:59,990
+تعريف اتحاد؟ إذا ال R الأن أصبحت مجموعة جزئية من
+
+425
+00:39:59,990 --> 00:40:06,130
+الاتحاد، مظبوط؟ طب ال P مجموعة جزئية من R و
+
+426
+00:40:06,130 --> 00:40:10,850
+negative P مجموعة جزئية من R و singleton 0 برضه
+
+427
+00:40:10,850 --> 00:40:15,130
+مجموعة جزئية من R إذا اتحادهم بيطلع مجموعة جزئية
+
+428
+00:40:15,130 --> 00:40:20,060
+من Rوبالتالي انا عندي الاحتواء من الناحيتين
+
+429
+00:40:20,060 --> 00:40:24,280
+وبالتالي عندي تساوي اذا هنا برهنتلكم ان الاتحاد
+
+430
+00:40:24,280 --> 00:40:26,740
+هذا بساوي R تمام؟
+
+431
+00:40:33,090 --> 00:40:37,470
+طب ليش هدولة disjoint؟ لأنه لو .. لو فرضت أنه مثلا
+
+432
+00:40:37,470 --> 00:40:42,130
+في عنصر بيقف ينتمي لتقاطه المجموعتين هدول، معناته
+
+433
+00:40:42,130 --> 00:40:45,990
+هذا العنصر بيساوي سفر و في نفس الوجة ينتمي ل P
+
+434
+00:40:45,990 --> 00:40:49,830
+وهذا بتناقض مع الخاصية الثلاثية، الخاصية الثلاثية
+
+435
+00:40:49,830 --> 00:40:53,950
+بتقول لازم و exactly one، واحد من الاحتمالات
+
+436
+00:40:53,950 --> 00:41:00,090
+الثلاثة هذه صح، اما اثنين مش صح، تمام؟ okay
+
+437
+00:41:02,970 --> 00:41:07,390
+العنى المجموعة P هذه اللي عرفناها هنا بنسميها
+
+438
+00:41:07,390 --> 00:41:10,610
+مجموعة الأعداد الحقيقية الموجبة the set of
+
+439
+00:41:10,610 --> 00:41:15,830
+positive real number مجموعة الأعداد الحقيقية
+
+440
+00:41:15,830 --> 00:41:19,750
+الموجبة و ال set negative P هذه بنسميها مجموعة
+
+441
+00:41:19,750 --> 00:41:24,560
+الأعداد الحقيقية السالبةو لما نضيف عليهم السفر هيك
+
+442
+00:41:24,560 --> 00:41:28,980
+بنكون غطينا كل الاعداد الحقيقية صح؟ okay تمام اذا
+
+443
+00:41:28,980 --> 00:41:33,000
+P بنسميها مجموعة الاعداد الحقيقية الموجبة negative
+
+444
+00:41:33,000 --> 00:41:42,440
+P مجموعة الاعداد الحقيقية السالبة و هكذا طيب
+
+445
+00:41:42,440 --> 00:41:47,980
+لحد تلان احنا ماعرفناش علاقة اصغر او اكبر او اصغر
+
+446
+00:41:47,980 --> 00:41:52,380
+من او يساوي او اكبر من او يساوي اللي هو الترتيبففي
+
+447
+00:41:52,380 --> 00:41:56,100
+عندى definition هنا لو أخدت اي عددين حقيقيين a و b
+
+448
+00:41:56,100 --> 00:42:04,620
+فهنكتب او هنعلن ان a أصغر من b او ما يكافئها b
+
+449
+00:42:04,620 --> 00:42:12,640
+أكبر من a هذا معناه نقصد نقصد بذلك ان الفرق بين b
+
+450
+00:42:12,640 --> 00:42:18,920
+و a ينتمي ل p يعني الفرق هذا موجب يعني هذا عدد
+
+451
+00:42:18,920 --> 00:42:26,080
+موجبإذا لو كان الفرق بين b و a عدد موجب فبنكتب a
+
+452
+00:42:26,080 --> 00:42:32,780
+أصغر من b أو b أكبر من a طيب طب
+
+453
+00:42:32,780 --> 00:42:36,840
+متى بكتب a أصغر من أو يساوي b أو b أكبر من أو
+
+454
+00:42:36,840 --> 00:42:45,760
+يساوي a هذا معناه يعني هذا مثلا معناه أن a أصغر من
+
+455
+00:42:45,760 --> 00:42:54,840
+bيعني الفرق بين B و A ينتمي ل P أو A بيساوي B لما
+
+456
+00:42:54,840 --> 00:42:58,860
+يكون A بيساوي B لإحتمال التاني هذا معناه أن الفرق
+
+457
+00:42:58,860 --> 00:43:03,620
+بيساوي سفر يعني ينتمي للمجموعة Singleton Zero okay
+
+458
+00:43:03,620 --> 00:43:07,500
+تمام؟ إذن أصغر من أو سابع أو أكبر من أو سابع
+
+459
+00:43:07,500 --> 00:43:13,410
+معناته الفرق ينتمي ل P اتحاد Singleton Zeroالان في
+
+460
+00:43:13,410 --> 00:43:20,170
+عندي نظرية و النظرية هذه بتعطيني خواص ل .. ال ..
+
+461
+00:43:20,170 --> 00:43:28,450
+ال .. خليني بس نبص عليها بسرعة النظرية
+
+462
+00:43:28,450 --> 00:43:33,410
+هذه بتعطيني خواص لل order properties يعني خواص
+
+463
+00:43:33,410 --> 00:43:40,210
+أخرىنقدر نشتقها من ال order properties و كل هذه
+
+464
+00:43:40,210 --> 00:43:44,990
+خواص معروفة وسهلة وبسيطة و كلها .. كلها عارفين لكن
+
+465
+00:43:44,990 --> 00:43:48,230
+بدها برهان .. بدها برهان ماحدش عمره برهانلنا إياها
+
+466
+00:43:49,460 --> 00:43:54,600
+Okay فحنوقف عند النظرية هذه وإن شاء الله المرة
+
+467
+00:43:54,600 --> 00:44:01,120
+الجاية بنحاول نبرهن النظرية okay حاولوا أنتوا
+
+468
+00:44:01,120 --> 00:44:05,260
+meanwhile في نفس الوقت كتحضير للمحاضرة الجاية
+
+469
+00:44:05,260 --> 00:44:10,140
+حاولوا أنكم تقرأوا البرهان تبع النظرية وشوفوا هل
+
+470
+00:44:10,140 --> 00:44:16,360
+تفهموه ولا لأ okay تمام في أي سؤال okay شكرا لكم
+
+471
+00:44:16,360 --> 00:44:17,540
+ومبارك الله فيكم
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d0a8a047d14dd4941c4a007eb050fec157812b7e
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs.srt
@@ -0,0 +1,1267 @@
+1
+00:00:22,390 --> 00:00:27,410
+إذا ثبتنا أن الـ function أو الـ limit للـ function
+
+2
+00:00:27,410 --> 00:00:33,250
+هذه عن صفر من اليمين does not exist حسب نظرية سابقة
+
+3
+00:00:33,250 --> 00:00:36,410
+و يكفي أن نثبت أن الـ function هذه not
+
+4
+00:00:36,410 --> 00:00:41,790
+bounded عند أي right neighborhood للصفر نعمل برهان
+
+5
+00:00:41,790 --> 00:00:47,490
+بالتناقض assume أن g of x is bounded on some right
+
+6
+00:00:47,490 --> 00:00:50,810
+neighbourhood الـ some right neighbourhood هذا
+
+7
+00:00:50,810 --> 00:00:55,450
+الفترة المفتوحة من الصفر ل delta zero لمن هذا
+
+8
+00:00:55,450 --> 00:01:01,190
+right neighbourhood للصفر هذا معناه
+
+9
+00:01:03,570 --> 00:01:08,150
+there exist m أكبر من الصفر عدد موجب بحيث أن
+
+10
+00:01:08,150 --> 00:01:13,690
+absolute g of x اللي هو بيساوي g of x بالمناسبة
+
+11
+00:01:13,690 --> 00:01:17,790
+لأنه أنا عندي ال function g of x بيساوي إيص واحد
+
+12
+00:01:17,790 --> 00:01:30,370
+على x  هذه قيمها موجبة أصغر من أو يساوي m لكل x في
+
+13
+00:01:30,370 --> 00:01:32,670
+الجوار
+
+14
+00:01:34,580 --> 00:01:40,860
+أو الـ delta الجوار من اليمين للصفر
+
+15
+00:01:40,860 --> 00:01:48,680
+طيب
+
+16
+00:01:48,680 --> 00:02:01,460
+by Archimedean property يوجد أن عدد طبيعي أو أن
+
+17
+00:02:01,460 --> 00:02:12,700
+واحد عدد طبيعي بحيث أن n واحد أكبر
+
+18
+00:02:12,700 --> 00:02:18,220
+من الصفر طيب
+
+19
+00:02:18,220 --> 00:02:22,140
+also by
+
+20
+00:02:22,140 --> 00:02:27,720
+Archimedean property أنا
+
+21
+00:02:27,720 --> 00:02:32,650
+عندي delta zero هذه عدد موجب أنا عندي delta zero
+
+22
+00:02:32,650 --> 00:02:40,270
+عدد موجب بيقدّي أن يوجد عدد طبيعي M2 عدد طبيعي
+
+23
+00:02:40,270 --> 00:02:55,930
+بحيث أنه واحد على M2 أصغر من delta zero left
+
+24
+00:02:55,930 --> 00:02:56,430
+end
+
+25
+00:02:59,360 --> 00:03:07,820
+let n بساوي ال maximum الأكبر بين n واحد و n اتنين
+
+26
+00:03:07,820 --> 00:03:12,740
+واضح
+
+27
+00:03:12,740 --> 00:03:18,520
+لأن n أكبر من أو يساوي n واحد و أكبر من أو يساوي
+
+28
+00:03:18,520 --> 00:03:24,120
+n اتنين وبالتالي x
+
+29
+00:03:31,260 --> 00:03:40,480
+لو أخدت xn بيساوي واحد على n بيساوي
+
+30
+00:03:40,480 --> 00:03:46,080
+واحد على n فهذا
+
+31
+00:03:46,080 --> 00:03:54,800
+ينتمي إلى ال delta zero neighborhood للصفر ال
+
+32
+00:03:54,800 --> 00:04:01,150
+right neighborhood للصفر اللي هو هذاليه؟ لأنه أنا
+
+33
+00:04:01,150 --> 00:04:09,930
+عندي واحد على n since واحد على n أصغر من أو يساوي
+
+34
+00:04:09,930 --> 00:04:16,470
+واحد على n اتنين أصغر من delta zero وأكبر من صفر
+
+35
+00:04:16,470 --> 00:04:21,610
+وبالتالي واحد على n ينتمي للفترة من صفر ل delta
+
+36
+00:04:21,610 --> 00:04:22,670
+zero صح؟
+
+37
+00:04:36,490 --> 00:04:44,450
+So من هال .. من
+
+38
+00:04:44,450 --> 00:04:56,350
+المتباينة هذه بطلع عندي g of x g of xn هذا
+
+39
+00:04:56,350 --> 00:05:06,470
+بيطلع أصغر من أو يساوي M من هذه نسمي هذه double
+
+40
+00:05:06,470 --> 00:05:10,070
+star ونسمي
+
+41
+00:05:10,070 --> 00:05:16,010
+هذه star إذا
+
+42
+00:05:16,010 --> 00:05:25,160
+من double star ال XM هذا اللي هو واحد على n ينتمي
+
+43
+00:05:25,160 --> 00:05:31,520
+للفترة من صفر الى delta zero وبالتالي G ل X N هذا
+
+44
+00:05:31,520 --> 00:05:38,120
+أصغر من أو يساوي M وال M أصغر
+
+45
+00:05:38,120 --> 00:05:39,100
+من n واحد
+
+46
+00:05:51,340 --> 00:05:58,900
+أصغر منها بيساوي M أصغر منها بيساوي M صح؟ أعملها
+
+47
+00:05:58,900 --> 00:06:10,200
+فعلا طيب هنا عندي من ال star G of X M G
+
+48
+00:06:10,200 --> 00:06:17,920
+of X M اللي هي بالساوي من
+
+49
+00:06:17,920 --> 00:06:26,660
+ال star هذا عبارة عن G of n صح؟ لأ G of واحد على n
+
+50
+00:06:26,660 --> 00:06:34,400
+G of G G of واحد على n صح؟
+
+51
+00:06:34,400 --> 00:06:42,780
+ف G of XM بتطلع
+
+52
+00:06:42,780 --> 00:06:44,040
+أكبر من
+
+53
+00:06:52,470 --> 00:06:57,470
+يعني من هنا المفروض يطلع أن الـ g of 1 على n أكبر
+
+54
+00:06:57,470 --> 00:07:06,770
+من n أن الـ g of xn أكبر من 1 على xn صح؟ 1 على xn
+
+55
+00:07:06,770 --> 00:07:10,250
+بيساوي n
+
+56
+00:07:24,110 --> 00:07:29,410
+إذا بيطلع عندي الآن إذا بيطلع عندي n أصغر من n
+
+57
+00:07:29,410 --> 00:07:36,070
+contradiction تمام وبالتالي ال contradiction هذه
+
+58
+00:07:36,070 --> 00:07:41,650
+بتقول إن ال assumption تبعنا إن g of x is bounded
+
+59
+00:07:41,650 --> 00:07:46,370
+on some right neighborhood of zero كان خطأ okay
+
+60
+00:07:46,370 --> 00:07:50,990
+إذا إذا
+
+61
+00:07:55,320 --> 00:08:02,580
+لأن g of x is not bounded on
+
+62
+00:08:02,580 --> 00:08:12,080
+any right neighborhood from zero to delta of zero
+
+63
+00:08:14,120 --> 00:08:20,240
+وبالتالي إذا هذا بثبت زي ما قلنا أن ال limit ل G
+
+64
+00:08:20,240 --> 00:08:25,620
+of X لما X تقول إلى 0 من اليمين does not exist غير
+
+65
+00:08:25,620 --> 00:08:31,460
+موجودة لأن هذا برهان الجزء الأول أن limit E توعد
+
+66
+00:08:31,460 --> 00:08:39,380
+على X لما X تقول إلى 0 مش موجودة برهان
+
+67
+00:08:39,380 --> 00:08:41,140
+الجزء التاني أسهل
+
+68
+00:08:54,110 --> 00:09:01,790
+أنا عندي we have for
+
+69
+00:09:01,790 --> 00:09:10,990
+x أصغر من صفر let T بساوي سالب واحد على X أكبر من
+
+70
+00:09:10,990 --> 00:09:21,440
+صفر in star لو كانت ال X عدد سالب فاخد T بساوي سالب
+
+71
+00:09:21,440 --> 00:09:26,080
+واحد على X طبعا ال X سالبة فسالب واحد على X بطلع
+
+72
+00:09:26,080 --> 00:09:33,380
+موجب وبالتالي لأي T موجبة زي هذه take T بساوي سالب
+
+73
+00:09:33,380 --> 00:09:43,750
+واحد على X to get T هو سالب واحد على X أكبر من صفر
+
+74
+00:09:43,750 --> 00:09:49,810
+أصغر من أو يساوي سالب واحد على X هذا صحيح لكل X أصغر
+
+75
+00:09:49,810 --> 00:09:56,450
+من صفر هذا بيقدّي أو يساوي
+
+76
+00:09:56,450 --> 00:10:06,710
+واحد على X أصغر من سالب X أكبر
+
+77
+00:10:06,710 --> 00:10:16,850
+من صفر لكل x أصغر من صفر الآن سالب x الآن الدالة
+
+78
+00:10:16,850 --> 00:10:21,190
+إيص واحد على x محصورة بين دالتين واحدة سالب x
+
+79
+00:10:21,190 --> 00:10:26,210
+والتانية ثابت صفر وهذا صحيح لكل x على يسار الصفر
+
+80
+00:10:26,210 --> 00:10:33,950
+فالدالة هذه لما x تقول إلى صفر من اليسار ال limit
+
+81
+00:10:33,950 --> 00:10:39,200
+أبقتها صفر الدالة هذه لما X تقول صفر من اليسار
+
+82
+00:10:39,200 --> 00:10:44,540
+أو اليمين ثابت نهايتها صفر إذا by squeeze theorem
+
+83
+00:10:44,540 --> 00:10:51,600
+for left limits مش
+
+84
+00:10:51,600 --> 00:10:56,220
+احنا قلنا ان كل النظريات اللي برهنها ال two sided
+
+85
+00:10:56,220 --> 00:11:00,200
+limits صحيحة ال one sided limit ممضمنها ال squeeze
+
+86
+00:11:00,200 --> 00:11:03,640
+theorem إذا by
+
+87
+00:11:08,280 --> 00:11:15,260
+Squeeze theorem for left
+
+88
+00:11:15,260 --> 00:11:20,980
+-hand limit بطلع
+
+89
+00:11:20,980 --> 00:11:26,740
+عند ال limit ل E أس واحد على X لما X تقول إذا صفر
+
+90
+00:11:26,740 --> 00:11:35,240
+من اليسار بيساوي صفر تمام؟ وهيك بتكون برهنة الجزء
+
+91
+00:11:35,240 --> 00:11:41,100
+التاني إذا هذا مثال على function النهاية تبعتها من
+
+92
+00:11:41,100 --> 00:11:45,380
+اليمين غير موجودة بينما النهاية من اليسار على نفس
+
+93
+00:11:45,380 --> 00:11:51,620
+النقطة موجودة كذلك
+
+94
+00:11:51,620 --> 00:12:01,880
+مثال تالت لو أخدنا let H of X بساوي واحد على واحد
+
+95
+00:12:01,880 --> 00:12:11,550
+زائد E أس واحد على X لو أخدنا الدالة هذه طبعا
+
+96
+00:12:11,550 --> 00:12:19,530
+و X هنا لا يساوي صفر فالممكن
+
+97
+00:12:19,530 --> 00:12:27,270
+إثبات ان ال limit للدالة هذه لما X تقول اللي هي
+
+98
+00:12:27,270 --> 00:12:34,630
+صفر من اليمين موجودة و بتساوي صفر
+
+99
+00:12:38,390 --> 00:12:47,610
+و ال limit لنفس الدالة لما x تقول إلى صفر من
+
+100
+00:12:47,610 --> 00:12:58,570
+اليسار أيضا موجودة لكن بساوي واحد وبالتالي
+
+101
+00:12:58,570 --> 00:13:04,510
+هذا طبعا هذا المثال محلول بالتفصيل في الكتاب
+
+102
+00:13:04,510 --> 00:13:12,670
+وبرهانه أسهل بكثير من المثال اللي فات ويعتمد
+
+103
+00:13:12,670 --> 00:13:17,130
+برضه على المثال السابق اللي هو المثال رقم اتنين
+
+104
+00:13:17,130 --> 00:13:28,330
+see the text انظروا في الكتاب للتفاصيل الكاملة لأن
+
+105
+00:13:28,330 --> 00:13:34,150
+هذا المثال الآخر زي ال signal function الـ one
+
+106
+00:13:34,150 --> 00:13:38,390
+-sided limits both exist لكن مش متساويات وبالتالي
+
+107
+00:13:38,390 --> 00:13:44,430
+ال limit عند الصفر للدالة هذه غير موجودة okay تمام
+
+108
+00:13:44,430 --> 00:13:54,330
+لأن هذه بعض الأمثلة على ال one-sided limits خلينا
+
+109
+00:13:54,330 --> 00:13:58,710
+ننتقل إلى موضوع ال infinite limits
+
+110
+00:14:19,750 --> 00:14:26,410
+فداخل definition let
+
+111
+00:14:26,410 --> 00:14:36,890
+F be function from A to R وC be cluster point
+
+112
+00:14:36,890 --> 00:14:39,550
+of set A
+
+113
+00:14:47,050 --> 00:14:58,250
+نقول إن قيمة f of x كما أن x هو c بساوي plus
+
+114
+00:14:58,250 --> 00:15:02,070
+infinity إذا
+
+115
+00:15:02,070 --> 00:15:11,950
+تحقق الشرط التالي for any alpha
+
+116
+00:15:11,950 --> 00:15:20,870
+real number there exists delta تعتمد على alpha على
+
+117
+00:15:20,870 --> 00:15:29,990
+موجب يعني هذا شبه بتعريف بتعريف
+
+118
+00:15:29,990 --> 00:15:35,690
+أن ال sequence xn ال limit بتاعتها تكون plus
+
+119
+00:15:35,690 --> 00:15:43,610
+infinity فقلنا هذا معناه أن xn أكبر من أي real
+
+120
+00:15:43,610 --> 00:15:51,970
+alpha لكل n أكبر من أو يساوي capital N حيث capital N
+
+121
+00:15:51,970 --> 00:15:56,670
+عدد طبيعي يعتمد على Alpha مش هيك التعريف تقريبا
+
+122
+00:15:56,670 --> 00:16:01,650
+وهذا نفس الحاجة ما معناه ان ال limit لل function
+
+123
+00:16:01,650 --> 00:16:06,590
+نقطة بساوي infinity هذا معناه ان اخلي ال function
+
+124
+00:16:06,590 --> 00:16:12,530
+أكبر من أي given Alpha لكل
+
+125
+00:16:12,530 --> 00:16:15,150
+X قريبة من C
+
+126
+00:16:19,590 --> 00:16:24,390
+أو في جوار Delta لـ C فرقان Alpha يوجد Delta عدد
+
+127
+00:16:24,390 --> 00:16:31,090
+موجب بحيث انه لو كانت X تنتمي إلى A و X هذه في
+
+128
+00:16:31,090 --> 00:16:37,530
+جوار Delta الـ X مختلفة عن الـ C و تقع في جوار
+
+129
+00:16:37,530 --> 00:16:44,270
+Delta لـ C فلازم هذا يقدي ان ال F of X أكبر من ال
+
+130
+00:16:44,270 --> 00:16:53,020
+given Alpha اتنين و Cبالمثل ممكن اتعرف ما معناه
+
+131
+00:16:53,020 --> 00:16:57,340
+انه limit لل function f بساوي سالب infinity limit
+
+132
+00:16:57,340 --> 00:17:04,640
+f of x لما x تقول الى c بساوي negative infinity
+
+133
+00:17:04,640 --> 00:17:16,860
+هذا معناه انه for any beta real number يوجد
+
+134
+00:17:18,350 --> 00:17:27,870
+Delta تعتمد على Beta عدد موجب بحيث انه لكل X ينتمي
+
+135
+00:17:27,870 --> 00:17:35,370
+إلى A و absolute X minus C أصغر من Delta أكبر من 0
+
+136
+00:17:35,370 --> 00:17:43,990
+هذا بتضمن ان F of X أصغر من Beta تمام؟
+
+137
+00:17:43,990 --> 00:17:46,510
+خلّينا ناخد أمثلة
+
+138
+00:17:56,170 --> 00:18:01,870
+لإثبات كيف نستخدم التعريفات لإثبات ان ال limit ل
+
+139
+00:18:01,870 --> 00:18:06,830
+function معينة نقطة معينة بساوي infinity او
+
+140
+00:18:06,830 --> 00:18:17,250
+negative infinity فمثلا show that ان 
+
+141
+00:18:17,250 --> 00:18:22,910
+ال limit لواحد
+
+142
+00:18:25,040 --> 00:18:31,380
+على x تربيع as x tends to zero بساوي plus infinity
+
+143
+00:18:31,380 --> 00:18:42,280
+أنا 
+
+144
+00:18:42,280 --> 00:18:49,520
+عندي let ال function تبعتي f of x بتعرف على أنها
+
+145
+00:18:49,520 --> 00:18:55,470
+مقلوب x تربيع حيث x ده لا تساوي صفر طبعا ده اللي هي دي
+
+146
+00:18:55,470 --> 00:18:59,610
+ال domain تبعها كل الأعداد الحقيقية ما عدا صفر
+
+147
+00:18:59,610 --> 00:19:04,010
+let
+
+148
+00:19:04,010 --> 00:19:13,090
+alpha belong to R be given عشان أنا بدي أثبت أنه
+
+149
+00:19:13,090 --> 00:19:17,510
+limit ال function f of x عند الصفر بساوي
+
+150
+00:19:17,510 --> 00:19:22,460
+infinity بتثبت أنه for any given alpha إذا let
+
+151
+00:19:22,460 --> 00:19:30,040
+alpha belong to R عدد حقيقي بيكون given من
+
+152
+00:19:30,040 --> 00:19:34,080
+أن نرد على ال alpha هذه بـ delta بتخلي ال
+
+153
+00:19:34,080 --> 00:19:39,640
+implication هذه تشتغل صح فنشوف كيف نختار ال delta
+
+154
+00:19:50,090 --> 00:19:53,390
+لو كانت ال alpha هذه عدد موجب لأختارت ال delta
+
+155
+00:19:53,390 --> 00:19:56,970
+بساوي
+
+156
+00:19:56,970 --> 00:20:06,690
+واحد على الجذر التربيعي ل alpha أو
+
+157
+00:20:06,690 --> 00:20:15,890
+ممكن تقول إن أنا بدي f of x أكبر من alpha فهذا
+
+158
+00:20:15,890 --> 00:20:22,330
+عبارة عن واحد على x تربيع أكبر من alpha يعني واحد
+
+159
+00:20:22,330 --> 00:20:28,650
+على ال alpha أصغر من x تربيع يعني x أكبر من واحد
+
+160
+00:20:28,650 --> 00:20:46,830
+على الجذر ال alpha وطبعا 
+
+161
+00:20:46,830 --> 00:20:47,910
+أنا عند ال x هنا
+
+162
+00:20:56,290 --> 00:21:01,330
+لما يكون المسافة بين x والـ 0 أصغر من Delta فالـ
+
+163
+00:21:01,330 --> 00:21:06,430
+Delta يعني هنا هتكون واحد علي جذر ال Alpha المشكلة 
+
+164
+00:21:06,430 --> 00:21:10,370
+هنا إن ال Alpha هذه ممكن ما تكونش موجبة ممكن تساوي
+
+165
+00:21:10,370 --> 00:21:18,690
+صفر فعشان أخرج من هذا الحرج فبأخد ال absolute
+
+166
+00:21:18,690 --> 00:21:23,550
+value ل Alpha عشان أبقى منها غير ثالثة فممكن تكون 
+
+167
+00:21:23,550 --> 00:21:31,380
+زيادة فبضيف واحد ببطلها دقيقة ستة okay تمام إذا لأي
+
+168
+00:21:31,380 --> 00:21:38,760
+alpha belonging to R هنختار delta 
+
+169
+00:21:38,760 --> 00:21:42,400
+choose delta
+
+170
+00:21:42,400 --> 00:21:48,660
+بساوي واحد على الجذر التربيعي ل absolute alpha زي
+
+171
+00:21:48,660 --> 00:21:51,880
+الواحد فبالتأكيد هذا عدد موجب
+
+172
+00:21:54,590 --> 00:22:02,110
+ويعتمد على Alpha دلتا تاني مرتبطة بالـ Alpha 
+
+173
+00:22:02,110 --> 00:22:06,150
+لو كانت x تنتمي لل domain تبع الدالة اللي هو R
+
+174
+00:22:06,150 --> 00:22:13,370
+ما عدا صفر و x لا تساوي صفر يعني x سالب c هنا صفر
+
+175
+00:22:13,370 --> 00:22:19,230
+أكبر من الصفر يعني x لا تساوي صفر وأصغر من الدلتا
+
+176
+00:22:19,230 --> 00:22:21,670
+هذه فهذا
+
+177
+00:22:25,020 --> 00:22:30,320
+بنشوف ايش حياة دينى طيب لما يكون هذا الكلام صح
+
+178
+00:22:30,320 --> 00:22:40,680
+معناه absolute x أصغر من delta وهذا معناه أن x 
+
+179
+00:22:40,680 --> 00:22:48,680
+تربيع أصغر من delta تربيع لأن absolute x بيساوي
+
+180
+00:22:48,680 --> 00:22:49,800
+جذر x تربيع
+
+181
+00:22:52,680 --> 00:23:00,220
+طب و Delta تربيع حسب اختيارنا لـ Delta Delta تربيع
+
+182
+00:23:00,220 --> 00:23:07,060
+بساوي واحد على Absolute Alpha زائد واحد طب ما هذا 
+
+183
+00:23:07,060 --> 00:23:12,640
+بيقودى إن F of X اللي هي مقلوب x تربيع طبعا هذا 
+
+184
+00:23:12,640 --> 00:23:21,820
+موجب على موجب فمقلوب x تربيع هيكون أكبر من مقلوب
+
+185
+00:23:21,820 --> 00:23:27,240
+الكسر هذا اللي هو absolute alpha زائد واحد طب 
+
+186
+00:23:27,240 --> 00:23:31,160
+absolute alpha زائد واحد أكبر من absolute alpha
+
+187
+00:23:31,160 --> 00:23:37,460
+صح؟ طب و absolute alpha أكبر من أو يساوي alpha لأي 
+
+188
+00:23:37,460 --> 00:23:41,800
+real number دا من ال absolute value لل number أكبر 
+
+189
+00:23:41,800 --> 00:23:47,100
+من أو يساوي ال number إذن هي اللي أثبتت أن ال F of
+
+190
+00:23:47,100 --> 00:23:54,230
+X أكبر من ال given alpha وهذا صحيح لكل x بحيث 
+
+191
+00:23:54,230 --> 00:24:00,050
+absolute x ناقص 0 أكبر من 0 أصغر من Delta بما أن 
+
+192
+00:24:00,050 --> 00:24:04,350
+هذا صحيح لكل Alpha أو بما أن ال Alpha دي was
+
+193
+00:24:04,350 --> 00:24:12,900
+arbitrary since Alpha belong to R was arbitrary إذا 
+
+194
+00:24:12,900 --> 00:24:17,240
+أنا أثبتتها إن لكل Alpha فيه Delta تعتمد عليها
+
+195
+00:24:17,240 --> 00:24:22,500
+بتخلي F of X أكبر من Alpha لكل X فيه جوار Delta
+
+196
+00:24:22,500 --> 00:24:29,700
+للصفر إذا by definition هذا معناه إن ال limit لل
+
+197
+00:24:29,700 --> 00:24:35,700
+function F of X لما X تقول صفر بساوي plus infinity
+
+198
+00:24:35,700 --> 00:24:38,880
+تمام؟ وهو المطلوب
+
+199
+00:24:42,370 --> 00:24:55,150
+Okay تمام؟ في 
+
+200
+00:24:55,150 --> 00:25:00,230
+أي سؤال؟ طيب ناخد مثال تاني
+
+201
+00:25:13,670 --> 00:25:18,470
+لأن limit للـ function 1 على x عندما x تساوي إلى 
+
+202
+00:25:18,470 --> 00:25:22,870
+صفر لا تساوي plus أو minus infinity
+
+203
+00:25:45,380 --> 00:25:53,300
+لما أقسط أقول الصفر سواء 
+
+204
+00:25:53,300 --> 00:26:02,360
+من اليمين أو من اليسار هذه two sided limit بقدرش 
+
+205
+00:26:02,360 --> 00:26:05,980
+أقول limit 1 على x لما أقسط أقول الصفر من الجهتين
+
+206
+00:26:05,980 --> 00:26:11,540
+exist وبساوي infinity أو negative infinity لكن 
+
+207
+00:26:11,540 --> 00:26:12,560
+بقدر أقول
+
+208
+00:26:23,530 --> 00:26:28,830
+لكن الصحيح أو الصح إنه limit ال function 1 على x
+
+209
+00:26:28,830 --> 00:26:34,750
+لما x تقول إلى 0 من اليمين هذه بساوي ∞  و
+
+210
+00:26:34,750 --> 00:26:40,510
+limit لـ 1 على x لما x تقول إلى 0 من اليسار بساوي 
+
+211
+00:26:40,510 --> 00:26:48,630
+سالب ∞ ممكن اثبات الـ one sided limits من اليمين 
+
+212
+00:26:48,630 --> 00:26:52,390
+∞ ال one sided limit من اليسار سالب
+
+213
+00:26:52,390 --> 00:26:59,990
+∞ لكن ال limit عند الصفر غير موجودة okay
+
+214
+00:26:59,990 --> 00:27:06,590
+تمام فطيب ليش ال limit عند الصفر مش موجودة لأنه لا 
+
+215
+00:27:06,590 --> 00:27:10,870
+هذا التعريف بالطبق على الدالة الأولى ولا التعريف 
+
+216
+00:27:10,870 --> 00:27:14,230
+الثاني طيب to see
+
+217
+00:27:36,300 --> 00:27:43,100
+لو أخدت أي ألف موجب هذه المرة فطبعا هنا ال alpha 
+
+218
+00:27:43,100 --> 00:27:47,920
+الموجبة هنا المفروض real number يعني هذه ال alpha
+
+219
+00:27:47,920 --> 00:27:52,540
+الموجبة هي برضه real number فالمفروض لل alpha هذه
+
+220
+00:27:52,540 --> 00:27:57,260
+ألاقي delta بحيث أن F of X أكبر من ال alpha
+
+221
+00:28:16,680 --> 00:28:37,280
+أما لو أخدت x سالبة 
+
+222
+00:28:37,280 --> 00:28:46,830
+على x ال function تبعتي واحد على أو F of X
+
+223
+00:28:46,830 --> 00:28:58,190
+بس واحدة لازم تطلع سالبة وهذه
+
+224
+00:28:58,190 --> 00:29:01,870
+أصغر من Alpha صح؟
+
+225
+00:29:07,030 --> 00:29:12,630
+كمان مرة لو أخدت أي alpha موجبة المفروض أنه يطلع
+
+226
+00:29:12,630 --> 00:29:17,010
+عندي ال F of X أقدر أثبت أنها أكبر من ال alpha
+
+227
+00:29:17,010 --> 00:29:23,490
+عشان ال limit تبعتها يكون infinity فبلاقي إنه لكل 
+
+228
+00:29:23,490 --> 00:29:28,990
+X سالبة لكل X سالبة F of X بيساوي واحد على X موجبة
+
+229
+00:29:28,990 --> 00:29:30,150
+لا سالبة
+
+230
+00:29:32,770 --> 00:29:37,730
+مقلوب عدد سالب بيبقى سالب وهذه أصغر من Alpha إذا 
+
+231
+00:29:37,730 --> 00:29:46,270
+طلع F of X تطلع أصغر من Alpha لكل X أصغر من صفر
+
+232
+00:29:46,270 --> 00:29:50,270
+وبالتالي 
+
+233
+00:29:50,270 --> 00:29:55,510
+لكل X فيه جوار لسفر أو جوار من الشمال لسفر
+
+234
+00:29:55,510 --> 00:30:01,290
+وبالتالي هذامش ممكن في الحالة دي أقول إن limit f
+
+235
+00:30:01,290 --> 00:30:08,910
+of x بساوي infinity نفس الحاجة ممكن نقول إن 
+
+236
+00:30:08,910 --> 00:30:17,930
+limit ل f of x بساوي -∞ نفس 
+
+237
+00:30:17,930 --> 00:30:23,930
+الحاجة ممكن نقول إن limit ل 1 على x لا تساوي سالب 
+
+238
+00:30:23,930 --> 00:30:32,320
+∞ لأن for any أو given أو
+
+239
+00:30:32,320 --> 00:30:39,500
+for beta لو أخدت beta عدد موجب we
+
+240
+00:30:39,500 --> 00:30:45,160
+have إن f of x we 
+
+241
+00:30:45,160 --> 00:30:52,940
+have for x أكبر من صفر f of x بيصير واحد على x أكبر 
+
+242
+00:30:52,940 --> 00:30:55,460
+من صفر أكبر من beta
+
+243
+00:31:00,400 --> 00:31:09,060
+لأ لأي beta أصغر من صفر لأي beta سالبة بقدر
+
+244
+00:31:09,060 --> 00:31:16,260
+أنه لكل x أكبر من صفر أجد أن f of x أكبر من ال 
+
+245
+00:31:16,260 --> 00:31:22,380
+beta طبعا عشان تكون ال limit ل f of x بساوي سالب 
+
+246
+00:31:22,380 --> 00:31:27,740
+∞ المفروض إنه لأي beta سواء سالبة أو موجبة أو
+
+247
+00:31:27,740 --> 00:31:34,500
+صغيرة أقدر أخلي f of x أصغر من beta مش أكبر من beta
+
+248
+00:31:34,500 --> 00:31:42,260
+لكل x فيه جوار الصفر وهذا مستحيل okay تمام هذا
+
+249
+00:31:42,260 --> 00:31:46,060
+بورجي لكن 
+
+250
+00:31:47,650 --> 00:31:52,410
+ممكن نثبت زي ما قلت إنه ال limit من اليمين أو من
+
+251
+00:31:52,410 --> 00:31:57,650
+اليسار بساوي اللي بتكون موجودة واحدة بساوي
+
+252
+00:31:57,650 --> 00:32:03,570
+∞ وواحدة سالب ∞ ناخد
+
+253
+00:32:03,570 --> 00:32:07,410
+هنا نظرية زي comparison test
+
+254
+00:32:19,170 --> 00:32:30,030
+العلم يسمح لـ f و g يكونوا دالتين من a إلى r و c
+
+255
+00:32:30,030 --> 00:32:34,930
+يكون مجموعة اتفاقية 
+
+256
+00:32:34,930 --> 00:32:38,690
+من a
+
+257
+00:32:38,690 --> 00:32:50,050
+تجعل f من x أقل أو تساوي g من x for all x تنتمي إلى
+
+258
+00:32:50,050 --> 00:33:02,590
+a و x لا تساوي ال c ففي عندي إذا 
+
+259
+00:33:02,590 --> 00:33:11,910
+كان ال limit لـ f of x لما x تقول إلى c بساوي 
+
+260
+00:33:11,910 --> 00:33:18,190
+∞ فبالتأكيد limit الدالة الأكبر اللي هي g 
+
+261
+00:33:18,190 --> 00:33:26,170
+of x لما x تقول إلى c بساوي ∞ اثنين
+
+262
+00:33:26,170 --> 00:33:29,470
+إذا
+
+263
+00:33:29,470 --> 00:33:35,520
+كانت limit الدالة الكبيرة اللي هي g of x لما x تقول
+
+264
+00:33:35,520 --> 00:33:42,660
+ل c بساوي negative infinity بالتأكيد then limit
+
+265
+00:33:42,660 --> 00:33:51,460
+الدالة الأصغر اللي هي f of x لما x تقول إلى c
+
+266
+00:33:51,460 --> 00:33:53,380
+بساوي negative infinity
+
+267
+00:33:58,330 --> 00:34:05,290
+وبرهان النظرية هذه بسيط وسهل مش بالبرهان النظرية
+
+268
+00:34:05,290 --> 00:34:10,070
+اللي أخدناها ال direct comparison test في حالة ال
+
+269
+00:34:10,070 --> 00:34:16,990
+ال sequences proof
+
+270
+00:34:16,990 --> 00:34:22,390
+برهن الجزء الأول ف
+
+271
+00:34:22,390 --> 00:34:27,210
+assume إنه
+
+272
+00:34:27,210 --> 00:34:35,250
+ال limit لـ f of x as x tends to c بساوي ∞
+
+273
+00:34:35,250 --> 00:34:40,130
+وبدنا نثبت إن ال limit ل g of x لما x تقول ل c
+
+274
+00:34:40,130 --> 00:34:50,150
+بساوي ∞ let alpha belong to R be given
+
+275
+00:34:56,720 --> 00:35:01,200
+طيب حسب التعريف بما أن limit ال function f عن c
+
+276
+00:35:01,200 --> 00:35:07,380
+بساوي ∞ إذا يوجد delta depends on epsilon
+
+277
+00:35:07,380 --> 00:35:12,540
+positive number such that لكل x ينتمي إلى a
+
+278
+00:35:12,540 --> 00:35:18,940
+absolute x ناقص c أصغر من delta أكبر من سفر هذا 
+
+279
+00:35:18,940 --> 00:35:25,240
+بتضمن أن f of x أكبر من الألف
+
+280
+00:35:31,850 --> 00:35:38,290
+بنسمي هذا double star وهذا بفرض star
+
+281
+00:35:38,290 --> 00:35:42,650
+من
+
+282
+00:35:42,650 --> 00:35:47,890
+star
+
+283
+00:35:47,890 --> 00:35:55,890
+and double star بيقدّوا أنه لو كان x ينتمي إلى a و
+
+284
+00:35:55,890 --> 00:36:02,030
+absolute x minus c أكبر من 0 وأصغر من delta فهذا
+
+285
+00:36:02,030 --> 00:36:06,130
+بيقدّي بي
+
+286
+00:36:06,130 --> 00:36:19,990
+ستار D of X أكبر من أو يساوي F of X بي ستار
+
+287
+00:36:25,720 --> 00:36:32,200
+F of X لكل X في جوار Delta لـC بيطلع أكبر من Alpha
+
+288
+00:36:32,200 --> 00:36:40,560
+لأن هاي بيطلع عندي أنه G of X أكبر من Alpha بما أن
+
+289
+00:36:40,560 --> 00:36:45,300
+هذا since Alpha
+
+290
+00:36:45,300 --> 00:36:49,760
+belonged to R was arbitrary
+
+291
+00:36:52,410 --> 00:36:59,570
+بما أن الـ α كانت عشوائية، إذاً هي أثبتت لكل
+
+292
+00:36:59,570 --> 00:37:08,210
+Alpha في R يوجد Delta تعتمد عليها بحيث إن لكل X في
+
+293
+00:37:08,210 --> 00:37:12,390
+جوار Delta لـ C، بيطلع G of X أكبر من Alpha، لذلك
+
+294
+00:37:12,390 --> 00:37:17,450
+by definition هذا معناه إن limit G of X as X tends
+
+295
+00:37:17,450 --> 00:37:20,210
+to C يساوي Infinity
+
+296
+00:37:23,610 --> 00:37:32,470
+برهان الجزء الثاني مشابه ال
+
+297
+00:37:32,470 --> 00:37:39,090
+proof of this part is
+
+298
+00:37:39,090 --> 00:37:43,730
+similar to
+
+299
+00:37:43,730 --> 00:37:49,350
+similar to
+
+300
+00:37:49,350 --> 00:37:50,750
+part one
+
+301
+00:38:03,350 --> 00:38:10,970
+لأن برهان الجزء الثاني مشابه للجزء الأول يعني لو
+
+302
+00:38:10,970 --> 00:38:16,290
+بدي أنا أبرهن لو
+
+303
+00:38:16,290 --> 00:38:24,310
+بدي أبرهن الجزء الثاني لو
+
+304
+00:38:24,310 --> 00:38:31,030
+بدي أبرهن الجزء الثاني فهيكون عندي هنا .. هنفرض ال
+
+305
+00:38:31,030 --> 00:38:41,090
+limit g of x يساوي سالب infinity وهيكون عندي هنا
+
+306
+00:38:41,090 --> 00:38:47,650
+هد هستبدلها ب g of x أصغر من beta وهنا طبعا beta
+
+307
+00:38:54,040 --> 00:39:02,020
+هنا سنستبدل F of X أصغر من أو يساوي G of X أصغر من
+
+308
+00:39:02,020 --> 00:39:02,340
+beta
+
+309
+00:39:08,310 --> 00:39:13,470
+أصغر من beta و بالتالي هذا معناه حسب التعريف انه
+
+310
+00:39:13,470 --> 00:39:19,150
+limit f of x لما x تقول يا c تساوي سالب من beta
+
+311
+00:39:19,150 --> 00:39:22,750
+دكتور بس there is this delta تتمد على alpha مش
+
+312
+00:39:22,750 --> 00:39:30,730
+إيه؟ اه هذا المفروض يكون alpha كانت و الأن في
+
+313
+00:39:30,730 --> 00:39:35,700
+الجزء الثاني هصير beta مظبوط كلامك صحيح إذا هذا
+
+314
+00:39:35,700 --> 00:39:40,780
+بيكون إيه هكذا بيكون برهان الجزء الثاني المرة
+
+315
+00:39:40,780 --> 00:39:47,660
+الجاية هنشوف ناخد تطبيقات على النظرية هذه وناخد
+
+316
+00:39:47,660 --> 00:39:55,320
+مزيد من النظريات على ال infinite limits okay شكرا
+
+317
+00:39:55,320 --> 00:39:58,560
+لسماعكم ونشوفكم إن شاء الله المرة الجاية 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e527ee5421d2983280338a79c92396dff74558ff
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/be-bepplyPs_postprocess.srt
@@ -0,0 +1,1268 @@
+1
+00:00:22,390 --> 00:00:27,410
+إذا نثبت أن الـ function أو الـ limit للـ function
+
+2
+00:00:27,410 --> 00:00:33,250
+هذه عن سفر من يمين does not exist حسب نظرية سابقة
+
+3
+00:00:33,250 --> 00:00:36,410
+و يكفي أن احنا نثبت أن الـ function هذه not
+
+4
+00:00:36,410 --> 00:00:41,790
+bounded عند أي right neighborhood للسفر نعمل برهان
+
+5
+00:00:41,790 --> 00:00:47,490
+بالتناقض assume أن g of x is boundedon some right
+
+6
+00:00:47,490 --> 00:00:50,810
+neighbourhood الـ some right neighbourhood هذا
+
+7
+00:00:50,810 --> 00:00:55,450
+الفترة المفتوحة من السفر ل delta zero لمن هذا
+
+8
+00:00:55,450 --> 00:01:01,190
+right neighbourhood للسفر هذا معناه
+
+9
+00:01:03,570 --> 00:01:08,150
+there exist m أكبر من السفر عدد موجب بحياتي النوبة
+
+10
+00:01:08,150 --> 00:01:13,690
+absolute g of x اللي هو بيساوي g of x بالمناسبة
+
+11
+00:01:13,690 --> 00:01:17,790
+لأنه أنا عندي ال function g of x بيساوي إيص واحد
+
+12
+00:01:17,790 --> 00:01:30,370
+على x ده قيمها موجبة أصغر من أو يساوي m لكل x في
+
+13
+00:01:30,370 --> 00:01:32,670
+الجوار
+
+14
+00:01:34,580 --> 00:01:40,860
+أو الـ delta الجوار من اليمين للصفر
+
+15
+00:01:40,860 --> 00:01:48,680
+طيب
+
+16
+00:01:48,680 --> 00:02:01,460
+by Archimedean property يوجد ان عدد طبيعي او ان
+
+17
+00:02:01,460 --> 00:02:12,700
+واحدعدد طبيعي بحيث ان ان واحد اكبر
+
+18
+00:02:12,700 --> 00:02:18,220
+من ان طيب
+
+19
+00:02:18,220 --> 00:02:22,140
+also by
+
+20
+00:02:22,140 --> 00:02:27,720
+Archimedean property انا
+
+21
+00:02:27,720 --> 00:02:32,650
+عندي delta zero هذه عدد موجةأنا عندي delta zero
+
+22
+00:02:32,650 --> 00:02:40,270
+عدد موجد بيقدّي أن يوجد عدد طبيعي M2 عدد طبيعي
+
+23
+00:02:40,270 --> 00:02:55,930
+بحيث أنه واحد على M2 أصغر من delta zero left
+
+24
+00:02:55,930 --> 00:02:56,430
+end
+
+25
+00:02:59,360 --> 00:03:07,820
+let n بساوي ال maximum الأكبر بين n واحد و n اتنين
+
+26
+00:03:07,820 --> 00:03:12,740
+واضح
+
+27
+00:03:12,740 --> 00:03:18,520
+لأن n أكبر من نهو يساوي n واحد و أكبر من نهو يساوي
+
+28
+00:03:18,520 --> 00:03:24,120
+n اتنين وبالتالي x
+
+29
+00:03:31,260 --> 00:03:40,480
+لو أخدت xn بيساوي واحد على n بيساوي
+
+30
+00:03:40,480 --> 00:03:46,080
+واحد على n فهذا
+
+31
+00:03:46,080 --> 00:03:54,800
+دفلع ينتمي إلى ال delta zero neighborhood للسفر ال
+
+32
+00:03:54,800 --> 00:04:01,150
+right neighborhood للسفر اللي هو هذاليه؟ لأنه انا
+
+33
+00:04:01,150 --> 00:04:09,930
+عندي واحد على n since واحد على n أصغر من أو ساوي
+
+34
+00:04:09,930 --> 00:04:16,470
+واحد على n اتنين أصغر من delta zero وأكبر من سفر
+
+35
+00:04:16,470 --> 00:04:21,610
+وبالتالي واحد على n ينتمي للفترة من سفر ل delta
+
+36
+00:04:21,610 --> 00:04:22,670
+zero صح؟
+
+37
+00:04:36,490 --> 00:04:44,450
+So من هال .. من
+
+38
+00:04:44,450 --> 00:04:56,350
+المتباينة هذه بطلع عندي g of x g of x رقم nهذا
+
+39
+00:04:56,350 --> 00:05:06,470
+بيطلع أصغر من أو يساوي M من هذه نسمي هذه double
+
+40
+00:05:06,470 --> 00:05:10,070
+star ونسمي
+
+41
+00:05:10,070 --> 00:05:16,010
+هذه star إذا
+
+42
+00:05:16,010 --> 00:05:25,160
+من double star ال XM هذا اللي هو واحد على Mينتمي
+
+43
+00:05:25,160 --> 00:05:31,520
+للفترة من صفر الى delta zero وبالتالي G ل X N هذا
+
+44
+00:05:31,520 --> 00:05:38,120
+أصغر من أو ساو M وال M أصغر
+
+45
+00:05:38,120 --> 00:05:39,100
+من N واحد
+
+46
+00:05:51,340 --> 00:05:58,900
+أصغر منها بيساوي M أصغر منها بيساوي M صح؟ أعملها
+
+47
+00:05:58,900 --> 00:06:10,200
+فعلا طيب هنا عندي من ال star G of X M G
+
+48
+00:06:10,200 --> 00:06:17,920
+of X M اللي هي بالساوي من
+
+49
+00:06:17,920 --> 00:06:26,660
+ال star هذا عبارة عنG of T صح؟ لأ G of واحد على T
+
+50
+00:06:26,660 --> 00:06:34,400
+G of G G of واحد على T صح؟
+
+51
+00:06:34,400 --> 00:06:42,780
+ف G of XM بتطلع
+
+52
+00:06:42,780 --> 00:06:44,040
+أكبر من
+
+53
+00:06:52,470 --> 00:06:57,470
+يعني من هنا المفروض يطلع أن الـ g of 1 على t أكبر
+
+54
+00:06:57,470 --> 00:07:06,770
+من t أن الـ g of xn أكبر من 1 على xn صح؟ 1 على xn
+
+55
+00:07:06,770 --> 00:07:10,250
+بيساوي n
+
+56
+00:07:24,110 --> 00:07:29,410
+إذا بيطلع عندي الان إذا بيطلع عندي n أصغر من n
+
+57
+00:07:29,410 --> 00:07:36,070
+contradiction تمام وبالتالي ال contradiction هذه
+
+58
+00:07:36,070 --> 00:07:41,650
+بتقول إن ال assumption تبعنا إن g of x is bounded
+
+59
+00:07:41,650 --> 00:07:46,370
+on some right neighborhood of zero كان خطأ okay
+
+60
+00:07:46,370 --> 00:07:50,990
+إذا إذا
+
+61
+00:07:55,320 --> 00:08:02,580
+لأن g of x is not bounded on
+
+62
+00:08:02,580 --> 00:08:12,080
+any right neighborhood from zero to delta of zero
+
+63
+00:08:14,120 --> 00:08:20,240
+وبالتالي إذا هذا بثبت زي ما قلنا أن ال limit ل G
+
+64
+00:08:20,240 --> 00:08:25,620
+of X لما X تقول إلى 0 من اليمين does not exist غير
+
+65
+00:08:25,620 --> 00:08:31,460
+موجودة لأن هذا برهان الجزء الأول أن limit E توعد
+
+66
+00:08:31,460 --> 00:08:39,380
+على X لما X تقول إلى 0 مش موجودة برهان
+
+67
+00:08:39,380 --> 00:08:41,140
+الجزء التاني أسهل
+
+68
+00:08:54,110 --> 00:09:01,790
+أنا عندي we have for
+
+69
+00:09:01,790 --> 00:09:10,990
+x أصغر من سفر let T بساوي سالب واحد على X أكبر من
+
+70
+00:09:10,990 --> 00:09:21,440
+سفرin star لو كانت ال X عدر سالب فاخد T بساوي سالب
+
+71
+00:09:21,440 --> 00:09:26,080
+واحد على X طبعا ال X سالبة فسالب واحد على X بطلع
+
+72
+00:09:26,080 --> 00:09:33,380
+موجب وبالتالي لأي T موجبة زي هذه take T بساوي سالب
+
+73
+00:09:33,380 --> 00:09:43,750
+واحد على X to getT هو سالب واحد على X أكبر من سفر
+
+74
+00:09:43,750 --> 00:09:49,810
+أصغر من إيقوس سالب واحد على X هذا صحيح لكل X أصغر
+
+75
+00:09:49,810 --> 00:09:56,450
+من سفر هذا بيقدي إيقوس
+
+76
+00:09:56,450 --> 00:10:06,710
+واحد على X أصغر من سالب X أكبر
+
+77
+00:10:06,710 --> 00:10:16,850
+من سفرلكل x أصغر من سفر الآن سالب x الآن الدالة
+
+78
+00:10:16,850 --> 00:10:21,190
+إيص واحد على x محصورة بين دالتين واحدة سالب x
+
+79
+00:10:21,190 --> 00:10:26,210
+والتانية ثابت سفر وهذا صحيح لكل x على يسار السفر
+
+80
+00:10:26,210 --> 00:10:33,950
+فالدالة هذه لما x تقول إلى سفر من اليسار ال limit
+
+81
+00:10:33,950 --> 00:10:39,200
+أبقاتها سفروالدالة هذه لما X أولها سفر من اليسار
+
+82
+00:10:39,200 --> 00:10:44,540
+أو اليمين ثابت نهيتها سفر اذا by squeeze theorem
+
+83
+00:10:44,540 --> 00:10:51,600
+for left limits مش
+
+84
+00:10:51,600 --> 00:10:56,220
+احنا قولنا ان كل النظريات اللي برهنها ال two sided
+
+85
+00:10:56,220 --> 00:11:00,200
+limits صحيحة ال one sided limit ممضمنها ال squeeze
+
+86
+00:11:00,200 --> 00:11:03,640
+theorem اذا by
+
+87
+00:11:08,280 --> 00:11:15,260
+Squeeze theorem for left
+
+88
+00:11:15,260 --> 00:11:20,980
+-hand limit بطلع
+
+89
+00:11:20,980 --> 00:11:26,740
+عند ال limit ل E أس واحد على X لما X تقول إذا سفر
+
+90
+00:11:26,740 --> 00:11:35,240
+من اليسار بيساوي سفر تمام؟ وهيك بتكون فرهنةالجزر
+
+91
+00:11:35,240 --> 00:11:41,100
+التاني إذا هذا مثال على function النهاية تبعتها من
+
+92
+00:11:41,100 --> 00:11:45,380
+اليمين غير موجودة بينما النهاية من اليسار على نفس
+
+93
+00:11:45,380 --> 00:11:51,620
+النقطة موجودة كذلك
+
+94
+00:11:51,620 --> 00:12:01,880
+مثال تالت لو أخدنا let H of X بسوء واحد على واحد
+
+95
+00:12:01,880 --> 00:12:11,550
+زائد E أس واحد على Xلو أخدنا الدالة هذه طبعا
+
+96
+00:12:11,550 --> 00:12:19,530
+و X هنا لا يساوي سفر فالممكن
+
+97
+00:12:19,530 --> 00:12:27,270
+اثبات ان ال limit للدالة هذه لما X تقول اللي هي
+
+98
+00:12:27,270 --> 00:12:34,630
+سفر من اليمين موجودة و بتساوي سفر
+
+99
+00:12:38,390 --> 00:12:47,610
+و ال limit لنفس الدالة لما x تقول إلى سفر من
+
+100
+00:12:47,610 --> 00:12:58,570
+اليسار أيضا موجودة لكن بالساوي واحد وبالتالي
+
+101
+00:12:58,570 --> 00:13:04,510
+هذا طبعا هذا الإمثال محلولبالتفصيل في الكتاب
+
+102
+00:13:04,510 --> 00:13:12,670
+وبرهانه أسهل بكتير من المثال اللي فات ويعتمد
+
+103
+00:13:12,670 --> 00:13:17,130
+برضه على المثال السابق اللي هو المثال رقم اتنين
+
+104
+00:13:17,130 --> 00:13:28,330
+see the text انظروا في الكتاب للتفاصيل الحالية لأن
+
+105
+00:13:28,330 --> 00:13:34,150
+هذا المثال الآخر زي ال signal functionالـ one
+
+106
+00:13:34,150 --> 00:13:38,390
+-sided limits both exist لكن مش متساويات وبالتالي
+
+107
+00:13:38,390 --> 00:13:44,430
+ال limit عند السفر للدالة هذه غير موجودة okay تمام
+
+108
+00:13:44,430 --> 00:13:54,330
+لان هذه بعض الأمثلة على ال one-sided limits خلينا
+
+109
+00:13:54,330 --> 00:13:58,710
+ننتقل إلى موضوع ال infinite limits
+
+110
+00:14:19,750 --> 00:14:26,410
+فداخل definition let
+
+111
+00:14:26,410 --> 00:14:36,890
+F be function from A to R وC be cluster point
+
+112
+00:14:36,890 --> 00:14:39,550
+of set A
+
+113
+00:14:47,050 --> 00:14:58,250
+نقول إن قيمة f of x كما أن x هو c بساوي plus
+
+114
+00:14:58,250 --> 00:15:02,070
+infinity إذا
+
+115
+00:15:02,070 --> 00:15:11,950
+تحقق الشرط التالي for any alpha
+
+116
+00:15:11,950 --> 00:15:20,870
+real numberThere exists delta تعتمد على alpha على
+
+117
+00:15:20,870 --> 00:15:29,990
+موجب يعني هذا شبه بتعريف بتعريف
+
+118
+00:15:29,990 --> 00:15:35,690
+أن ال sequence xn ال limit بتاعتها تكون plus
+
+119
+00:15:35,690 --> 00:15:43,610
+infinity فقلنا هذا معناه أن xn أكبر من أي real
+
+120
+00:15:43,610 --> 00:15:51,970
+alphaلكل n أكبر من أو ساوي capital N حيث capital N
+
+121
+00:15:51,970 --> 00:15:56,670
+عدد طبيعي يعتمد على Alpha مش هيك التعريف تقريبا
+
+122
+00:15:56,670 --> 00:16:01,650
+وهذا نفس الحاجة ما معناه ان ال limit لل function
+
+123
+00:16:01,650 --> 00:16:06,590
+نقطة لساوي infinity هذا معناه ان اخلي ال function
+
+124
+00:16:06,590 --> 00:16:12,530
+أكبر من أي given Alpha لكل
+
+125
+00:16:12,530 --> 00:16:15,150
+X قريبة من C
+
+126
+00:16:19,590 --> 00:16:24,390
+أو في جوار Delta لـ C فرقان Alpha يوجد Delta عدد
+
+127
+00:16:24,390 --> 00:16:31,090
+موجة بحيث انه لو كانت X تنتمي إلى A و X هذه في
+
+128
+00:16:31,090 --> 00:16:37,530
+جوار Delta الـ X مختلفة عن الـ C و تقع في جوار
+
+129
+00:16:37,530 --> 00:16:44,270
+Delta لـ C فلازم هذا يقدي ان ال F of X أكبر من ال
+
+130
+00:16:44,270 --> 00:16:53,020
+given Alpha اتنين و Cبالمثل ممكن اتعرف ما معناه
+
+131
+00:16:53,020 --> 00:16:57,340
+انه limit لل function f بساوي سالب infinity limit
+
+132
+00:16:57,340 --> 00:17:04,640
+f of x لما x تقول الى c بساوي negative infinity
+
+133
+00:17:04,640 --> 00:17:16,860
+هذا معناه انه for any beta real number يوجد
+
+134
+00:17:18,350 --> 00:17:27,870
+Delta تعتمد على Beta عدد موجة بحيث انه لكل X ينتمي
+
+135
+00:17:27,870 --> 00:17:35,370
+إلى A وabsolute X minus C أصغر من Delta أكبر من 0
+
+136
+00:17:35,370 --> 00:17:43,990
+هذا بتضمن ان F of X أصغر من Beta تمام؟
+
+137
+00:17:43,990 --> 00:17:46,510
+خلّينا ناخد أمثلة
+
+138
+00:17:56,170 --> 00:18:01,870
+لإثبات كيف نستخدم التعريفات لإثبات ان ال limit ل
+
+139
+00:18:01,870 --> 00:18:06,830
+function معينة نقطة معينة بالساوي infinity او
+
+140
+00:18:06,830 --> 00:18:17,250
+negative infinity فمثلا show that ان
+
+141
+00:18:17,250 --> 00:18:22,910
+ال limit لواحد
+
+142
+00:18:25,040 --> 00:18:31,380
+على x تربية as x tends to zero بساوي plus infinity
+
+143
+00:18:31,380 --> 00:18:42,280
+أنا
+
+144
+00:18:42,280 --> 00:18:49,520
+عندي let ال function تبعتي f of x بتعرف على أنها
+
+145
+00:18:49,520 --> 00:18:55,470
+مقلوب x تربيةحيث x ده تساوي سفر طبعا ده اللي هي دي
+
+146
+00:18:55,470 --> 00:18:59,610
+ال domain تبعها كل الأعداد الحقيقية مع أعداد السفر
+
+147
+00:18:59,610 --> 00:19:04,010
+let
+
+148
+00:19:04,010 --> 00:19:13,090
+alpha belong to R be given عشان انا بدي اثبت انه
+
+149
+00:19:13,090 --> 00:19:17,510
+limit ال function f of x عند السفر بالساوي
+
+150
+00:19:17,510 --> 00:19:22,460
+infinityبتثبت انه for any given alpha اذا let
+
+151
+00:19:22,460 --> 00:19:30,040
+alpha belong to R عدد حقيقي بيه given من
+
+152
+00:19:30,040 --> 00:19:34,080
+ان نرد على ال alpha هذه ب delta بتخلي ال
+
+153
+00:19:34,080 --> 00:19:39,640
+implication هذه تشتغل صح فنشوف كيف نختار ال delta
+
+154
+00:19:50,090 --> 00:19:53,390
+لو كانت ال alpha هذه عدد موجب لأختارت ال delta
+
+155
+00:19:53,390 --> 00:19:56,970
+بساوي
+
+156
+00:19:56,970 --> 00:20:06,690
+واحد على الجذر التربيهي ل alpha او
+
+157
+00:20:06,690 --> 00:20:15,890
+ممكن تقول ان انا بدي f of x أكبر من alpha فهذا
+
+158
+00:20:15,890 --> 00:20:22,330
+عبارة عن واحد على x تربيه أكبر من alphaيعني واحد
+
+159
+00:20:22,330 --> 00:20:28,650
+على ال alpha أصغر من X تقبية يعني X أكبر من واحد
+
+160
+00:20:28,650 --> 00:20:46,830
+على الجدر ال alpha وطبعا
+
+161
+00:20:46,830 --> 00:20:47,910
+أنا عند ال X هنا
+
+162
+00:20:56,290 --> 00:21:01,330
+لما يكون المسافة بين X والـ 0 أصغر من Delta فالـ
+
+163
+00:21:01,330 --> 00:21:06,430
+Delta يعني هنا هتكون واحد علي جذر ال Alpha المشكلة
+
+164
+00:21:06,430 --> 00:21:10,370
+هنا أن ال Alpha هذه ممكن ما تكونش موجبة ممكن تساوي
+
+165
+00:21:10,370 --> 00:21:18,690
+سفر فعشان أخرج من هذا الحرج فبأخد ال absolute
+
+166
+00:21:18,690 --> 00:21:23,550
+value ل Alpha عشان أبقى منها غير ثالثة فممكن تكون
+
+167
+00:21:23,550 --> 00:21:31,380
+زيادةفبضيف واحد ببطلها دقيقة ستة okay تمام اذا لأي
+
+168
+00:21:31,380 --> 00:21:38,760
+alpha belonging to R هنختار delta ات
+
+169
+00:21:38,760 --> 00:21:42,400
+choose delta
+
+170
+00:21:42,400 --> 00:21:48,660
+بساوي واحد على الجدر التربيعي ل absolute alpha زي
+
+171
+00:21:48,660 --> 00:21:51,880
+الواحد فبالتأكيد هذا عدد موجب
+
+172
+00:21:54,590 --> 00:22:02,110
+و يعتمد على Alpha دلتا تاني مرتبطة بالـ Alpha دل
+
+173
+00:22:02,110 --> 00:22:06,150
+لو كانت X تنتمي لل domain تبع الدالة اللي هو R
+
+174
+00:22:06,150 --> 00:22:13,370
+معدى سفر و X لا يساوي سفر يعني X سالب C هنا سفر
+
+175
+00:22:13,370 --> 00:22:19,230
+أكبر من السفر يعني X لا تساوي سفر وأصغر من الدلتا
+
+176
+00:22:19,230 --> 00:22:21,670
+هذه فهذا
+
+177
+00:22:25,020 --> 00:22:30,320
+بنشوف ايش حياة دينى طيب لما يكون هذا الكلام صح
+
+178
+00:22:30,320 --> 00:22:40,680
+معناه absolute x أصغر من delta و هذا معناه ان x
+
+179
+00:22:40,680 --> 00:22:48,680
+تربية أصغر من delta تربية لأن absolute x بيساوي
+
+180
+00:22:48,680 --> 00:22:49,800
+جدر x تربية
+
+181
+00:22:52,680 --> 00:23:00,220
+طب و Delta تربية حسب اختيارنا لـ Delta Delta تربية
+
+182
+00:23:00,220 --> 00:23:07,060
+بساوي واحد على Absolute Alpha زاد واحد طب ما هذا
+
+183
+00:23:07,060 --> 00:23:12,640
+بيقدي ان F of X اللي هي مقلوب X تربية طبعا هذا
+
+184
+00:23:12,640 --> 00:23:21,820
+موجب على موجب فمقلوب X تربية هيكون اكبر منمقلوب
+
+185
+00:23:21,820 --> 00:23:27,240
+الكسر هذا اللي هو absolute alpha زايد واحد طب
+
+186
+00:23:27,240 --> 00:23:31,160
+absolute alpha زايد واحد أكبر من absolute alpha
+
+187
+00:23:31,160 --> 00:23:37,460
+صح؟ طب و absolute alpha أكبر من أو ساوي alpha لأي
+
+188
+00:23:37,460 --> 00:23:41,800
+real number دا من ال absolute value لل number أكبر
+
+189
+00:23:41,800 --> 00:23:47,100
+من أو ساوي ال number إذن هي اللي أثبتت أن ال F of
+
+190
+00:23:47,100 --> 00:23:54,230
+X أكبر من ال given alphaوهذا صحيح لكل x بحيث
+
+191
+00:23:54,230 --> 00:24:00,050
+absolute x minus 0 أكبر من 0 أصغر من Delta بما أن
+
+192
+00:24:00,050 --> 00:24:04,350
+هذا صحيح لكل Alpha أو بما أن ال Alpha دي was
+
+193
+00:24:04,350 --> 00:24:12,900
+arbitrary since Alpha belong to Rwas arbitrary إذا
+
+194
+00:24:12,900 --> 00:24:17,240
+أنا أثبتتها إن لكل Alpha فيه Delta تعتمد عليها
+
+195
+00:24:17,240 --> 00:24:22,500
+بتخلي F of X أكبر من Alpha لكل X فيه جوار Delta
+
+196
+00:24:22,500 --> 00:24:29,700
+للصفر إذا by definition هذا معناه إن ال limit لل
+
+197
+00:24:29,700 --> 00:24:35,700
+function F of X لما X تقول صفر بكاري plus infinity
+
+198
+00:24:35,700 --> 00:24:38,880
+تمام؟ وهو المطلوب
+
+199
+00:24:42,370 --> 00:24:55,150
+Okay تمام؟ في
+
+200
+00:24:55,150 --> 00:25:00,230
+أي سؤال؟ طيب ناخد مثال تاني
+
+201
+00:25:13,670 --> 00:25:18,470
+لأن limit للـ function 1 على x عندما x تسوى إلى
+
+202
+00:25:18,470 --> 00:25:22,870
+صفر لا تساوي plus أو minus infinity
+
+203
+00:25:45,380 --> 00:25:53,300
+لما أقسط أقول السفر سواء
+
+204
+00:25:53,300 --> 00:26:02,360
+من اليمين أو من اليسار هذه two sided limit بقدرش
+
+205
+00:26:02,360 --> 00:26:05,980
+أقول limit 1 على x لما أقسط أقول السفر من الجهتين
+
+206
+00:26:05,980 --> 00:26:11,540
+exist وبساوي infinity أو negative infinity لكن
+
+207
+00:26:11,540 --> 00:26:12,560
+بقدر أقول
+
+208
+00:26:23,530 --> 00:26:28,830
+لكن الصحيح او الصح انه limit ال function 1 على x
+
+209
+00:26:28,830 --> 00:26:34,750
+لمب اكس تقول الى 0 من اليمين هذي بالساوية 30 و
+
+210
+00:26:34,750 --> 00:26:40,510
+limit ل1 على x لمب اكس تقول الى 0 من اليسار بساوية
+
+211
+00:26:40,510 --> 00:26:48,630
+سالب 30 ممكن اثباتالـ one sided limits من اليمين
+
+212
+00:26:48,630 --> 00:26:52,390
+infinity ال one sided limit من اليسار سارب
+
+213
+00:26:52,390 --> 00:26:59,990
+infinity لكن ال limit عند السفر غير موجودة okay
+
+214
+00:26:59,990 --> 00:27:06,590
+تمام فطيب ليش ال limit عند السفر مش موجودة لأنه لا
+
+215
+00:27:06,590 --> 00:27:10,870
+هذا التعريف بالطبق على الدالة الادى ولا التعريف
+
+216
+00:27:10,870 --> 00:27:14,230
+التاني طيب to see
+
+217
+00:27:36,300 --> 00:27:43,100
+لو أخدت أي ألف موجب هذه المرةفطبعا هنا ال alpha
+
+218
+00:27:43,100 --> 00:27:47,920
+الموجبة هنا المفروض real number يعني هذه ال alpha
+
+219
+00:27:47,920 --> 00:27:52,540
+الموجبة هي برضه real number فالمفروض لل alpha هذه
+
+220
+00:27:52,540 --> 00:27:57,260
+ألاقي delta بحيث أن F of X أكبر من ال alpha
+
+221
+00:28:16,680 --> 00:28:37,280
+أما لو أخدت x سالبة واحد
+
+222
+00:28:37,280 --> 00:28:46,830
+على x ال function تبعتي واحد علىأو F of X
+
+223
+00:28:46,830 --> 00:28:58,190
+بس واحدة لازم تطلع سالق و هذه
+
+224
+00:28:58,190 --> 00:29:01,870
+أصغر من Alpha صح؟
+
+225
+00:29:07,030 --> 00:29:12,630
+كمان مرة لو أخدت أي alpha موجبة المفروض أنه يطلع
+
+226
+00:29:12,630 --> 00:29:17,010
+عندي ال F of X أقدر أثبت أنها أكبر من ال alpha
+
+227
+00:29:17,010 --> 00:29:23,490
+عشان ال limit تبعتها يكون infinity فبلاجي أنه لكل
+
+228
+00:29:23,490 --> 00:29:28,990
+X سالبة لكل X سالبة F of X بيساوي واحد على X موجبة
+
+229
+00:29:28,990 --> 00:29:30,150
+لا سالبة
+
+230
+00:29:32,770 --> 00:29:37,730
+مقلوب عدد سالب بيبقى سالب وهذه أصغر من Alpha إذا
+
+231
+00:29:37,730 --> 00:29:46,270
+طلع F of X تطلع أصغر من Alpha لكل X أصغر من سفر
+
+232
+00:29:46,270 --> 00:29:50,270
+وبالتالي
+
+233
+00:29:50,270 --> 00:29:55,510
+لكل X فيه جوار لسفر أو جوار من الشمال لسفر
+
+234
+00:29:55,510 --> 00:30:01,290
+وبالتالي هذامش ممكن في الحالة دي اقول ان limit f
+
+235
+00:30:01,290 --> 00:30:08,910
+of x بالساوي infinity نفس الحاجة ممكن نقول ان
+
+236
+00:30:08,910 --> 00:30:17,930
+limit ل f of x بالساويش نفس
+
+237
+00:30:17,930 --> 00:30:23,930
+الحاجة ممكن نقول ان limit ل 1 على x لا تساوي سالب
+
+238
+00:30:23,930 --> 00:30:32,320
+infinity لأن for anyأو given او
+
+239
+00:30:32,320 --> 00:30:39,500
+for beta لو أخدت beta عدد موجب we
+
+240
+00:30:39,500 --> 00:30:45,160
+have انه f of x we
+
+241
+00:30:45,160 --> 00:30:52,940
+have for x أكبر من صفر f of x بصير واحد على x أكبر
+
+242
+00:30:52,940 --> 00:30:55,460
+من صفر أكبر من beta
+
+243
+00:31:00,400 --> 00:31:09,060
+لأ لأي beta أصغر من سفر لأي beta سالبة بقدر
+
+244
+00:31:09,060 --> 00:31:16,260
+أنه لكل x أكبر من سفر أجد أن f of x أكبر من ال
+
+245
+00:31:16,260 --> 00:31:22,380
+beta طبعا عشان تكون ال limit ل f of x بساوي سالب
+
+246
+00:31:22,380 --> 00:31:27,740
+infinityمفروض انه لأي beta سواء سالبة او موجبة او
+
+247
+00:31:27,740 --> 00:31:34,500
+صغر اقدر اخلي f of x اصغر من beta مش اكبر من beta
+
+248
+00:31:34,500 --> 00:31:42,260
+لكل x فيه جوار الصفر وهذا مستحيل okay تمام هذا
+
+249
+00:31:42,260 --> 00:31:46,060
+بورجي لكن
+
+250
+00:31:47,650 --> 00:31:52,410
+ممكن نثبت زي ما قولت أنه ال limit من اليمين أو من
+
+251
+00:31:52,410 --> 00:31:57,650
+اليسار بالساوي اللي بتكون موجودة واحدة بالساوي
+
+252
+00:31:57,650 --> 00:32:03,570
+infinity وواحدة سالب infinity ناخد
+
+253
+00:32:03,570 --> 00:32:07,410
+هنا نظرية زي comparison test
+
+254
+00:32:19,170 --> 00:32:30,030
+العلم يسمح لـ f و g يكونوا اتفاقين من a إلى r و c
+
+255
+00:32:30,030 --> 00:32:34,930
+يكون مجموعة اتفاقية
+
+256
+00:32:34,930 --> 00:32:38,690
+من a
+
+257
+00:32:38,690 --> 00:32:50,050
+تجعل f من x اقل او اقل جي من xfor all x تنتمي إلى
+
+258
+00:32:50,050 --> 00:33:02,590
+a و x لا تساوي ال c ففي عندي إذا
+
+259
+00:33:02,590 --> 00:33:11,910
+كانالـ limit لـ f of x لما x تقول إلى c بساوي
+
+260
+00:33:11,910 --> 00:33:18,190
+infinity فبالتأكيد limit الدالة الأكبر اللي هي g
+
+261
+00:33:18,190 --> 00:33:26,170
+of x لما x تقول إلى c بساوي infinity اتنين
+
+262
+00:33:26,170 --> 00:33:29,470
+إذا
+
+263
+00:33:29,470 --> 00:33:35,520
+كانت limitالدالة الكبيرة اللي هي g of x لما x تقول
+
+264
+00:33:35,520 --> 00:33:42,660
+ل c بساوي negative infinity بالتأكيد then limit
+
+265
+00:33:42,660 --> 00:33:51,460
+الدالة الأصغر اللي هي f of x لما x تقول إلى c
+
+266
+00:33:51,460 --> 00:33:53,380
+بساوي negative infinity
+
+267
+00:33:58,330 --> 00:34:05,290
+وبرهان النظرية هذه بسيط وسهل مش بالبرهان النظرية
+
+268
+00:34:05,290 --> 00:34:10,070
+اللي أخدناها ال direct comparison test في حالة ال
+
+269
+00:34:10,070 --> 00:34:16,990
+ال sequences proof
+
+270
+00:34:16,990 --> 00:34:22,390
+برهن الجزء الأول ف
+
+271
+00:34:22,390 --> 00:34:27,210
+assume أنه
+
+272
+00:34:27,210 --> 00:34:35,250
+ال limitلـ f of x as x tends to c بساوي infinity
+
+273
+00:34:35,250 --> 00:34:40,130
+وبدنا نفتح ان ال limit ل g of x لما x تقوى ل c
+
+274
+00:34:40,130 --> 00:34:50,150
+بساوي infinity let alpha belong to R be given
+
+275
+00:34:56,720 --> 00:35:01,200
+طيب حسب التعريف بما أن limit ال function f عن c
+
+276
+00:35:01,200 --> 00:35:07,380
+بساوي infinity إذا يوجد delta depends on epsilon
+
+277
+00:35:07,380 --> 00:35:12,540
+positive number such that لكل x ينتمي إلى a
+
+278
+00:35:12,540 --> 00:35:18,940
+absolute x minus c أصغر من delta أكبر من سفر هذا
+
+279
+00:35:18,940 --> 00:35:25,240
+بتضمن أن f of x أكبر من الألف
+
+280
+00:35:31,850 --> 00:35:38,290
+بنسمي هذا double star و هذا بفرض star
+
+281
+00:35:38,290 --> 00:35:42,650
+من
+
+282
+00:35:42,650 --> 00:35:47,890
+star
+
+283
+00:35:47,890 --> 00:35:55,890
+and double star بيقدّوا أنه لو كان x ينتمي إلى a و
+
+284
+00:35:55,890 --> 00:36:02,030
+absolute x minus c أكبر من 0 أصغر من deltaفهذا
+
+285
+00:36:02,030 --> 00:36:06,130
+بيقدّي بي
+
+286
+00:36:06,130 --> 00:36:19,990
+ستار D of X أكبر من او ساوي F of X بي ستار
+
+287
+00:36:25,720 --> 00:36:32,200
+ف of X لكل X في جوار Delta لـC بيطلع أكبر من Alpha
+
+288
+00:36:32,200 --> 00:36:40,560
+لأن هاي بيطلع عندى انه G of X أكبر من Alpha بما أن
+
+289
+00:36:40,560 --> 00:36:45,300
+هذا since Alpha
+
+290
+00:36:45,300 --> 00:36:49,760
+belonged to R was arbitrary
+
+291
+00:36:52,410 --> 00:36:59,570
+بما أن الـ α كانت أندج عشوية، إذاً هي أثبتت لكل
+
+292
+00:36:59,570 --> 00:37:08,210
+Alpha في R يوجد Delta تعتمد عليها بحيث إن لكل X في
+
+293
+00:37:08,210 --> 00:37:12,390
+جوار Delta لأ سي، بيطلع G of X أكبر من Alpha، لذلك
+
+294
+00:37:12,390 --> 00:37:17,450
+by definition هذا معناه إن limit G of X as X tends
+
+295
+00:37:17,450 --> 00:37:20,210
+to C بساوي Infinity
+
+296
+00:37:23,610 --> 00:37:32,470
+برهان الجزء التاني مشابه ال
+
+297
+00:37:32,470 --> 00:37:39,090
+proof of this part is
+
+298
+00:37:39,090 --> 00:37:43,730
+similar is
+
+299
+00:37:43,730 --> 00:37:49,350
+similar to
+
+300
+00:37:49,350 --> 00:37:50,750
+part one
+
+301
+00:38:03,350 --> 00:38:10,970
+لأن البرهان الجزء التاني مشابه للجزء الأول يعني لو
+
+302
+00:38:10,970 --> 00:38:16,290
+بدي أنا أبرهنه لو
+
+303
+00:38:16,290 --> 00:38:24,310
+بدي أبرهن الجزء التاني لو
+
+304
+00:38:24,310 --> 00:38:31,030
+بدي أبرهن الجزء التانيفهيكون عندي هنا .. هنفرض ال
+
+305
+00:38:31,030 --> 00:38:41,090
+limit g of x بساوي سالب infinity و هيكون عندي هنا
+
+306
+00:38:41,090 --> 00:38:47,650
+هد هستبدلها ب g of x أصغر من beta وهنا طبعا beta
+
+307
+00:38:54,040 --> 00:39:02,020
+هنا سنستبدل F of X أصغر من أو يساوي G of X أصغر من
+
+308
+00:39:02,020 --> 00:39:02,340
+D
+
+309
+00:39:08,310 --> 00:39:13,470
+أصغر من beta و بالتالي هذا معناه حسب التعريف انه
+
+310
+00:39:13,470 --> 00:39:19,150
+limit f of x لما x تقول يا c تساوي ثالث من beta
+
+311
+00:39:19,150 --> 00:39:22,750
+دكتور بس there is this delta تتمد على alpha مش
+
+312
+00:39:22,750 --> 00:39:30,730
+إيه؟ اه هاد المفروض يكون alpha كانت و الأن في
+
+313
+00:39:30,730 --> 00:39:35,700
+الجزء التاني هصير beta مظبوط كرامك صحيحإذا هذا
+
+314
+00:39:35,700 --> 00:39:40,780
+بيكون إيه هكذا بيكون برهان الجزء التاني المرة
+
+315
+00:39:40,780 --> 00:39:47,660
+الجاية هنشوف ناخد تطبيقات على النظرية هذه وناخد
+
+316
+00:39:47,660 --> 00:39:55,320
+مزيد من النظريات على ال infinite limits okay شكرا
+
+317
+00:39:55,320 --> 00:39:58,560
+لصراعكم ونشوفكم ان شاء الله المرة الجاية
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..656f15a0b78cad9bfe18449f1019b9230b7fcd01
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_postprocess.srt
@@ -0,0 +1,1648 @@
+1
+00:00:20,940 --> 00:00:27,720
+بسم الله الرحمن الرحيم ان شاء الله اليوم هناخد في
+
+2
+00:00:27,720 --> 00:00:34,940
+اللقاء الأول مناقشة و المناقشة هذه هتكون على ال
+
+3
+00:00:34,940 --> 00:00:42,360
+section أربعة و section خمسة من ال chapter تلاتة
+
+4
+00:00:42,360 --> 00:00:47,930
+في الكتاباحنا لقشنا قبل هيك section تلاتة واحد و
+
+5
+00:00:47,930 --> 00:00:52,070
+تلاتة اتنين تلاتة تلاتة مظبوط؟ تلاتة تلاتة تلاتة
+
+6
+00:00:52,070 --> 00:00:56,010
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+7
+00:00:56,010 --> 00:00:56,190
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+8
+00:00:56,190 --> 00:01:01,490
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+9
+00:01:01,490 --> 00:01:02,530
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+10
+00:01:02,530 --> 00:01:07,770
+تلاتة تلاتة تلاتة
+
+11
+00:01:14,970 --> 00:01:20,490
+فمين عندها أي سؤال في ال section تلاتة تلاتة تلاتة
+
+12
+00:01:20,490 --> 00:01:28,290
+أربعة أو تلاتة خمسة سيكشن
+
+13
+00:01:28,290 --> 00:01:29,590
+تلاتة تلاتة
+
+14
+00:01:47,340 --> 00:01:54,900
+أي سؤال؟ ستة ستة؟ طب هذا مش مقرر، لأ أنا .. عفوا
+
+15
+00:01:54,900 --> 00:02:02,500
+أنا بتطلع في مكان تاني، تلاتة تلاتة، سؤال ستة،
+
+16
+00:02:02,500 --> 00:02:06,400
+مطلوب هذا السؤال؟ ما كتبتلاش أنت الأسئلة المطلوبة
+
+17
+00:02:06,400 --> 00:02:11,580
+اللي بتتكتب؟موجودة في ال syllabus .. موجودة في ال
+
+18
+00:02:11,580 --> 00:02:15,760
+syllabus فهذا السؤال مش من ضمن الأسئلة اللي ..
+
+19
+00:02:15,760 --> 00:02:17,920
+اللي احنا .. يعني انتوا بتطلعوش على ال syllabus
+
+20
+00:02:17,920 --> 00:02:21,440
+فيه على الصفحه تبعتي ال syllabus و فيه المسائل
+
+21
+00:02:21,440 --> 00:02:25,800
+المطلوبة فبإمكانكم تعرفوا المسائل المطلوبة لكل
+
+22
+00:02:25,800 --> 00:02:30,640
+section من هنا لآخر ال courseفهذا السؤال السادس
+
+23
+00:02:30,640 --> 00:02:33,580
+بالذات مش مطلوب لكن فيها سئلة تانية ممكن أحللك
+
+24
+00:02:33,580 --> 00:02:42,160
+أربعة أو تلاتة زيه فإيه رأيك؟ تلاتة
+
+25
+00:02:42,160 --> 00:02:45,580
+أو أربعة يكونوا نفس الفكرة أه تلاتة أو أربعة شو
+
+26
+00:02:45,580 --> 00:02:52,720
+بدك تلاتة ولا أربعة؟ الحل
+
+27
+00:02:52,720 --> 00:03:00,880
+السؤال أربعة مثلا؟ هاي الحل السؤال الرابعsection
+
+28
+00:03:00,880 --> 00:03:11,920
+تلاتة تلاتة في السؤال هذا let x واحد بساوي واحد
+
+29
+00:03:11,920 --> 00:03:17,920
+and xn
+
+30
+00:03:17,920 --> 00:03:24,660
+plus one بساوي square
+
+31
+00:03:24,660 --> 00:03:28,420
+root لاتنين plus xn
+
+32
+00:03:31,530 --> 00:03:39,530
+for n belong to n show
+
+33
+00:03:39,530 --> 00:03:52,370
+ان ال sequence xn converges and find its limit
+
+34
+00:03:55,460 --> 00:04:00,220
+بنثبت أولا أن الـ sequence هذي convergence ونجيب
+
+35
+00:04:00,220 --> 00:04:10,220
+ال limit تبعتها فمثلة
+
+36
+00:04:10,220 --> 00:04:15,500
+زي هذه بنطبق عليها الـ monotone convergence
+
+37
+00:04:15,500 --> 00:04:23,340
+theorem الـ monotone convergence theoremفلازم نثبت
+
+38
+00:04:23,340 --> 00:04:29,560
+حاجتين ان ال sequence هذه convergent لازم نثبت
+
+39
+00:04:29,560 --> 00:04:33,900
+انها convergent لازم نثبت انها monotone يعني
+
+40
+00:04:33,900 --> 00:04:40,100
+increasing او decreasing و bounded فلحظوا
+
+41
+00:04:40,100 --> 00:04:47,270
+انتوا لو بدى احسب اول يعنيالحل .. لحظة x واحد
+
+42
+00:04:47,270 --> 00:04:52,510
+بساوي واحد طب x اتنين .. خد in بساوي واحد بطلع جدر
+
+43
+00:04:52,510 --> 00:05:00,130
+اتنين زائد .. جدر اتنين زائد x واحد اللي هو جدر
+
+44
+00:05:00,130 --> 00:05:10,400
+التلاتة .. x تلاتة بساوي جدر اتنين زائد x اتنينو
+
+45
+00:05:10,400 --> 00:05:16,740
+يساوي جدر اتنين زاد جدر
+
+46
+00:05:16,740 --> 00:05:24,220
+التلاتة وهكذا
+
+47
+00:05:24,220 --> 00:05:29,640
+اللي
+
+48
+00:05:29,640 --> 00:05:38,120
+بعده X أربعة بساوي جدر اتنين زاد X تلاتة
+
+49
+00:05:56,800 --> 00:06:04,520
+و هذا بيساوي جدر اتنين زائد اللي
+
+50
+00:06:04,520 --> 00:06:10,500
+هو جدر التربية ايه الى اتنين زائد جدر التلاتة
+
+51
+00:06:27,010 --> 00:06:33,310
+فال .. الأدد يعني هذا دايما بيكون أقل من او ساو
+
+52
+00:06:33,310 --> 00:06:42,010
+اتنين أقل من او ساو اتنين صح؟ اه و هذا أصغر من او
+
+53
+00:06:42,010 --> 00:06:45,410
+ساو اتنين يعني جدر التلاتة أصغر من اتنين صح؟ أه
+
+54
+00:06:45,410 --> 00:06:50,750
+فهذا أكيد أصغر من او ساو اتنين و هذا
+
+55
+00:06:53,300 --> 00:06:58,180
+أصغر من أو ساوي اتنين وبالتالي هذا أصغر من أو ساوي
+
+56
+00:06:58,180 --> 00:07:06,560
+جدر الأربعة اللي هو أصغر من أو ساوي اتنيناذا و
+
+57
+00:07:06,560 --> 00:07:11,160
+طبعا و كل واحد من هدول اكبر من او يساوي الواحد اذا
+
+58
+00:07:11,160 --> 00:07:18,040
+ممكن احنا نثبت الان by induction claim ان xn اكبر
+
+59
+00:07:18,040 --> 00:07:24,320
+من او يساوي الواحد اصغر من او يساوي اتنين for
+
+60
+00:07:24,320 --> 00:07:30,590
+every n belong to nاه و هذا ممكن تبرهنه by
+
+61
+00:07:30,590 --> 00:07:34,650
+induction زي ما شوفنا في الأمثلة صح؟ طبعا طبعا
+
+62
+00:07:34,650 --> 00:07:43,730
+طبعا طبعا طبعا
+
+63
+00:07:43,730 --> 00:07:43,970
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+64
+00:07:43,970 --> 00:07:44,150
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+65
+00:07:44,150 --> 00:07:48,410
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+66
+00:07:48,410 --> 00:07:55,130
+طبعا طبعا طبعا طبعا
+
+67
+00:07:55,130 --> 00:07:57,910
+طب
+
+68
+00:08:01,490 --> 00:08:11,110
+الأن من أعلى الاختصارات الموجودة في
+
+69
+00:08:11,110 --> 00:08:17,050
+الوثيقة الاختصار
+
+70
+00:08:17,050 --> 00:08:20,290
+XN مرتبط
+
+71
+00:08:23,380 --> 00:08:27,360
+بعدين بنلاحظ انه قيمة ال sequence بتكبر كل ما اه
+
+72
+00:08:27,360 --> 00:08:34,580
+فممكن اثبات انه claim تاني اذا ال sequence bounded
+
+73
+00:08:34,580 --> 00:08:39,240
+claim x
+
+74
+00:08:39,240 --> 00:08:45,740
+in اصغر
+
+75
+00:08:45,740 --> 00:08:50,460
+منها و ساوي x in زاد واحد for every n
+
+76
+00:08:54,650 --> 00:09:02,290
+IEXN is increasing وهذا ممكن اثباته برضه by
+
+77
+00:09:02,290 --> 00:09:11,410
+induction by induction هنا هنا proof use induction
+
+78
+00:09:11,410 --> 00:09:14,630
+use
+
+79
+00:09:14,630 --> 00:09:20,610
+induction on M فالحالة
+
+80
+00:09:21,890 --> 00:09:30,890
+الحالة n بيساوي واحد انا عندي x واحد بيساوي واحد و
+
+81
+00:09:30,890 --> 00:09:34,810
+x واحد
+
+82
+00:09:34,810 --> 00:09:40,510
+زايد واحد اللي هو x اتنين بيساوي جدر التلاتة جدر
+
+83
+00:09:40,510 --> 00:09:47,810
+التلاتة وهذا بالتأكيد اكبر من واحد اللي هو x واحد
+
+84
+00:09:50,170 --> 00:09:57,350
+إذاً هيطلع عندي X2 أكبر من أو يساوي X1 إذاً
+
+85
+00:09:57,350 --> 00:10:04,170
+العبارة هذه صحيحة عند M بساوي واحد assume
+
+86
+00:10:04,170 --> 00:10:09,970
+induction hypothesis الفرض تبع ال induction assume
+
+87
+00:10:09,970 --> 00:10:13,910
+أنه
+
+88
+00:10:22,570 --> 00:10:24,510
+أصغر من أوي ساوي
+
+89
+00:10:35,580 --> 00:10:40,400
+بنثبت صحة الحق برهد عند n بساوي k زائد واحد اذا ت
+
+90
+00:10:40,400 --> 00:10:46,060
+show xk زائد واحد اصلا لو ساوي xk زائد واحد زائد
+
+91
+00:10:46,060 --> 00:10:55,700
+واحد عن x زائد اتنين we have لدينا لاحظوا
+
+92
+00:10:55,700 --> 00:11:01,180
+xk زائد اتنين من ال definition من ال definition
+
+93
+00:11:01,180 --> 00:11:03,360
+تبع ال sequence
+
+94
+00:11:06,860 --> 00:11:12,440
+من ال inductive formula أو ال recursive formula xk
+
+95
+00:11:12,440 --> 00:11:19,840
+زاد اتنين بسوى جذر التربيعى لاتنين زاد اكس k زاد
+
+96
+00:11:19,840 --> 00:11:28,000
+واحد صح و by induction hypothesis من الفرض تبع ال
+
+97
+00:11:28,000 --> 00:11:35,020
+induction هذا بسوى جذر اتنينو XK زياد واحد هذا
+
+98
+00:11:35,020 --> 00:11:44,080
+ايه؟ هيطلع اصغر من XK زياد واحد اكبر من او ساوي XK
+
+99
+00:11:44,080 --> 00:11:50,380
+انا XK انا نحط شريط اكبر XK زياد اتنين
+
+100
+00:11:55,180 --> 00:12:03,320
+فهذا أكبر من أو ساوي X .. هبدل XK زيادة واحد بأكبر
+
+101
+00:12:03,320 --> 00:12:07,660
+من أو ساوي XK من ال induction hypothesis من الفرب
+
+102
+00:12:07,660 --> 00:12:12,150
+تبع ال inductionوهذا بالـ definition باستخدام الـ
+
+103
+00:12:12,150 --> 00:12:18,310
+definition تبع الـ sequence الجذر هذا بساوي xk زي
+
+104
+00:12:18,310 --> 00:12:24,190
+واحدة إذا هين أثبتنا إن x sub k plus two bigger
+
+105
+00:12:24,190 --> 00:12:30,710
+than or equal to x sub k plus one إذاً this
+
+106
+00:12:30,710 --> 00:12:37,250
+completes this
+
+107
+00:12:37,250 --> 00:12:38,610
+completes the induction
+
+108
+00:12:43,320 --> 00:12:48,000
+وبالتالي إذا هيك بنكون أثبتنا ال claim بتاعي إن
+
+109
+00:12:48,000 --> 00:12:51,780
+أنا في عندي two claims أول شي sequence bounded
+
+110
+00:12:51,780 --> 00:12:57,200
+والتاني بيقول إن ال sequence increasing وبالتالي
+
+111
+00:12:57,200 --> 00:13:05,200
+therefore إذا
+
+112
+00:13:05,200 --> 00:13:09,580
+لو سمينا هذا claim one وهذا claim two
+
+113
+00:13:17,790 --> 00:13:27,210
+فإذا now it claims
+
+114
+00:13:27,210 --> 00:13:32,930
+one and two and الـ monotone convergence theorem
+
+115
+00:13:32,930 --> 00:13:41,530
+بيقدّوا إن sequence x in convergence say
+
+116
+00:13:41,530 --> 00:13:52,080
+دعنا نسمي ال limit تبعتهاlimit x in بساوي x طبعا
+
+117
+00:13:52,080 --> 00:13:56,820
+هذا بيطلع عدد حقيقي الان
+
+118
+00:13:56,820 --> 00:14:07,420
+بنوجد قيمة limit x هذه فبنرجع to find to find x
+
+119
+00:14:07,420 --> 00:14:12,880
+لإيجاد قيمة ال x بناخد
+
+120
+00:14:12,880 --> 00:14:21,340
+ال limittake limit of
+
+121
+00:14:21,340 --> 00:14:28,220
+both sides of
+
+122
+00:14:35,540 --> 00:14:41,820
+بناخد ال limit لطرفين of both sides of المعادلة xn
+
+123
+00:14:41,820 --> 00:14:50,280
+زي الواحد بساوي square root ل two plus xn to
+
+124
+00:14:50,280 --> 00:14:50,800
+get
+
+125
+00:14:53,550 --> 00:14:59,490
+limit xn plus one as n tends to infinity بساوي
+
+126
+00:14:59,490 --> 00:15:02,890
+limit الجدر التربيعي ممكن تدخل ال limit تحت الجدر
+
+127
+00:15:02,890 --> 00:15:08,210
+التربيعي وباستخدام قوانين النهايات limit الاتنين
+
+128
+00:15:08,210 --> 00:15:13,810
+بيطلع اتنين زي limit xn as n tends to infinity طيب
+
+129
+00:15:13,810 --> 00:15:19,170
+انا عندى limit xn زي واحد بساوي x
+
+130
+00:15:26,140 --> 00:15:36,560
+هذه المعادلة بيصير
+
+131
+00:15:36,560 --> 00:15:41,100
+x تربية negative xنجاتف اتنين نجاتف اتنين نجاتف
+
+132
+00:15:41,100 --> 00:15:45,160
+اتنين نجاتف اتنين نجاتف اتنين نجاتف اتنين نجاتف
+
+133
+00:15:45,160 --> 00:15:58,780
+اتنين نجاتف اتنين نجاتف اتنين نجاتف اتنين
+
+134
+00:16:01,690 --> 00:16:08,750
+الـ xn أكبر من أو ساوي واحد أصغر من أو ساوي اتنين
+
+135
+00:16:08,750 --> 00:16:18,250
+لكل n هذا من claim one بيقدي ان ال limit حسب
+
+136
+00:16:18,250 --> 00:16:25,270
+نظرية سابقة هذا بيقدي ان ال limit ل xn أصغر من أو
+
+137
+00:16:25,270 --> 00:16:31,750
+ساوي اتنين أكبر من أو ساوي الواحدو طبعا ال limit
+
+138
+00:16:31,750 --> 00:16:37,110
+قلنا ل xn بساوي x إذا واحد أصغر من او ساوي x أصغر
+
+139
+00:16:37,110 --> 00:16:42,190
+من او ساوي اتنين طب أنا عندي خيارين إما x بساوي
+
+140
+00:16:42,190 --> 00:16:49,450
+اتنين أو x بساوي سالب واحد مش ممكن ال x محصورة بين
+
+141
+00:16:49,450 --> 00:16:54,090
+واحد و اتنين إذا هذه الإجابة غير مقبولة وبالتالي
+
+142
+00:16:54,090 --> 00:16:59,710
+ال x بساوي اتنينو هيك بنكون أثبتنا إن ال sequence
+
+143
+00:16:59,710 --> 00:17:03,650
+is convergent و هي وجدنا ال limit تبعتها بالمثل
+
+144
+00:17:03,650 --> 00:17:09,130
+ممكن نحل باقي الأسئلة زي مثلا سؤال واحد و اتنين و
+
+145
+00:17:09,130 --> 00:17:16,190
+تلاتة و خمسة و ستة و سابعة okay
+
+146
+00:17:16,190 --> 00:17:24,550
+تمام في أي أسئلة تانية في هذا section السؤال تسعة
+
+147
+00:17:37,220 --> 00:18:05,540
+سؤال تسعة هاي
+
+148
+00:18:05,540 --> 00:18:13,770
+السؤال تسعةالسيقشن تلاتة تلاتة السؤال هذا بيقول
+
+149
+00:18:13,770 --> 00:18:22,970
+let a be infinite infinite
+
+150
+00:18:22,970 --> 00:18:32,090
+subset of R و ال set هذه bounded
+
+151
+00:18:34,790 --> 00:18:42,530
+أو bounded above محدودة
+
+152
+00:18:42,530 --> 00:18:50,170
+من أعلى and
+
+153
+00:18:50,170 --> 00:18:53,610
+let ال U
+
+154
+00:18:56,560 --> 00:19:00,740
+بساوي ال supremum لل set A طبعا ال set A bounded
+
+155
+00:19:00,740 --> 00:19:07,480
+above وبالتالي by ال supremum property ال supremum
+
+156
+00:19:07,480 --> 00:19:14,240
+تبعها exist دعنا نسميه U المطلوب
+
+157
+00:19:14,240 --> 00:19:22,340
+show that show
+
+158
+00:19:22,340 --> 00:19:29,900
+there existيوجد an increasing ..an increasing
+
+159
+00:19:29,900 --> 00:19:33,180
+subsequence
+
+160
+00:19:33,180 --> 00:19:40,120
+او sequence there exists an increasing sequence xn
+
+161
+00:19:40,120 --> 00:19:51,480
+contained in A such that ال limit لسيكوينس xn
+
+162
+00:19:51,480 --> 00:19:52,880
+بساوي U
+
+163
+00:20:03,070 --> 00:20:08,150
+I prove من
+
+164
+00:20:08,150 --> 00:20:12,630
+خواص ال supremum
+
+165
+00:20:12,630 --> 00:20:19,850
+احنا
+
+166
+00:20:19,850 --> 00:20:27,650
+فيها انا كان لمبة دخلناها قبل هيك وهذه المبة بتقول
+
+167
+00:20:27,650 --> 00:20:28,230
+انه
+
+168
+00:20:42,440 --> 00:20:51,320
+لما أخدناها في أول chapter بتقول أنه .. أفندم؟
+
+169
+00:20:51,320 --> 00:21:05,800
+بنقول an upper bound an upper bound U of الست A is
+
+170
+00:21:05,800 --> 00:21:09,540
+the supremum
+
+171
+00:21:11,820 --> 00:21:21,120
+the supremum of a, if and only if لكل
+
+172
+00:21:21,120 --> 00:21:29,260
+إبسلون أكبر من السفر يوجد x إبسلون ينتمي إلى a
+
+173
+00:21:29,260 --> 00:21:33,680
+بحيث أنه بحيث
+
+174
+00:21:33,680 --> 00:21:37,920
+أنه u سالب إبسلون أصغر من x إبسلون
+
+175
+00:21:40,930 --> 00:21:46,950
+نظبط صح؟ منطبقها لإن أنا عندي هاي U بساوي ال
+
+176
+00:21:46,950 --> 00:21:52,670
+supremum ل A إذا لو أخدت for epsilon بساوي واحد
+
+177
+00:21:52,670 --> 00:22:04,190
+أكبر من السفر يوجد X واحد ينتمي إلى A such that U
+
+178
+00:22:04,190 --> 00:22:17,500
+سالب واحد أصغر منx واحد next
+
+179
+00:22:17,500 --> 00:22:21,240
+for
+
+180
+00:22:21,240 --> 00:22:27,360
+for
+
+181
+00:22:27,360 --> 00:22:33,400
+epsilon بساوي نص لو
+
+182
+00:22:33,400 --> 00:22:37,200
+أخدت ال epsilon هذه بساوي نص ف choose
+
+183
+00:22:40,760 --> 00:22:51,040
+choose by above لمّا X2
+
+184
+00:22:51,040 --> 00:23:01,180
+تنتمي إلى A وممكن نختار X2 أكبر من أو يساوي X1
+
+185
+00:23:01,180 --> 00:23:08,580
+الأولى هي such that U سالد نص الإبسلون أصغر من X2
+
+186
+00:23:19,440 --> 00:23:29,340
+بعدين now for إبسلون بساوي واحد على تلاتة أكبر من
+
+187
+00:23:29,340 --> 00:23:34,220
+سفر it choose إذا في اللمّة هذه خدوا إبسلون بساوي
+
+188
+00:23:34,220 --> 00:23:39,520
+تلت it choose X تلاتة ينتمي إلى A
+
+189
+00:23:42,410 --> 00:23:48,590
+بحيث انه X تلاتة هذا ممكن اختاره اكبر من او ساوي X
+
+190
+00:23:48,590 --> 00:24:03,090
+اتنين and U اللي هو U سالب تلت اصغر من X تلاتة صح؟
+
+191
+00:24:03,090 --> 00:24:14,810
+continuing in this processلو استمرنا بالعملية الـ
+
+192
+00:24:14,810 --> 00:24:27,910
+continuing in this process we
+
+193
+00:24:27,910 --> 00:24:35,230
+get by induction عملية
+
+194
+00:24:35,230 --> 00:24:36,790
+استقرائية that
+
+195
+00:24:46,820 --> 00:24:52,740
+for epsilon بساوي واحد على ك أكبر من السفر
+
+196
+00:24:56,070 --> 00:25:04,030
+there exists xk أكبر من او ساوي xk زايد واحد such
+
+197
+00:25:04,030 --> 00:25:14,950
+that absolute u سالب واحد على k أصغر من xk وهذا
+
+198
+00:25:14,950 --> 00:25:23,530
+صحيح for every k ينتمي إلى n تمام؟
+
+199
+00:25:32,820 --> 00:25:40,120
+طيب أنا عندي ..
+
+200
+00:25:40,120 --> 00:25:50,560
+خلّيني أمسح اللمّة هذه طيب
+
+201
+00:25:50,560 --> 00:25:56,700
+إذا أنا عندي U نيجاتيب واحد على K طلع أصغر من XK
+
+202
+00:26:00,780 --> 00:26:08,580
+و ال XK هذه أصغر من أو ساوي ال U لأن ال U هو ال
+
+203
+00:26:08,580 --> 00:26:16,240
+supremum ل A و XK عنصر في A و ال U upper bound لل
+
+204
+00:26:16,240 --> 00:26:22,840
+6A ف .. و XK عنصر في A إذا ال XK لازم يكون أصغر من
+
+205
+00:26:22,840 --> 00:26:31,010
+أو ساوي ال U و ال U أصغر من أو ساوي أو أصغر منu
+
+206
+00:26:31,010 --> 00:26:35,790
+زائد واحد على k الكلام هذا صحيح for all k belong
+
+207
+00:26:35,790 --> 00:26:44,830
+to n مظبوط صحيح so احنا اثبتنا هيك ان يوجد
+
+208
+00:26:44,830 --> 00:26:51,810
+sequence يوجد increasing sequence
+
+209
+00:26:51,810 --> 00:27:01,940
+x in او xkمهم XK contained in A such that absolute
+
+210
+00:27:01,940 --> 00:27:10,820
+XK minus U أصغر من واحد على K for all K تنتمي إلى
+
+211
+00:27:10,820 --> 00:27:19,920
+N طيب
+
+212
+00:27:19,920 --> 00:27:23,400
+ما هذا عبارة عن واحد على K في واحد
+
+213
+00:27:26,730 --> 00:27:32,150
+هذا أصغر من أو ساوي واحد في واحد على K لكل K ينتمي
+
+214
+00:27:32,150 --> 00:27:42,410
+ل N اذا hence by previous theorem اللي هي نظرية
+
+215
+00:27:42,410 --> 00:27:47,410
+فاكرينها اتنين اربعة في ال notes نظرية اتنين اربعة
+
+216
+00:27:47,410 --> 00:27:48,810
+في ال notes تبعتنا
+
+217
+00:27:54,490 --> 00:28:02,870
+with c بساوي واحد اكبر من سفر and a n او a k a k
+
+218
+00:28:02,870 --> 00:28:12,410
+بساوي واحد على k tends to zero we get تديني
+
+219
+00:28:22,310 --> 00:28:27,970
+نحصل على ان ال limit ل xk as k tends to infinity
+
+220
+00:28:27,970 --> 00:28:35,470
+بساوي ال U وهذا هو المطلوب مام؟ واضح؟ لأن هذا هو
+
+221
+00:28:35,470 --> 00:28:40,490
+البرهان واضح البرهان؟ في أي استفسار؟ في أي شيء مش
+
+222
+00:28:40,490 --> 00:28:49,730
+واضح؟ طيب ماشي الحال خلينا نشوف هاي سؤال تلاتة
+
+223
+00:29:01,490 --> 00:29:09,710
+سؤال اتنين section تلاتة تلاتة فهنا عندي x واحد
+
+224
+00:29:09,710 --> 00:29:17,070
+انا عندي x واحد عدد اكبر من واحد و x n plus one
+
+225
+00:29:17,070 --> 00:29:22,290
+بيساوي بنعرفه
+
+226
+00:29:22,290 --> 00:29:33,410
+على انه اتنين سالب واحد على x n لكل nعدد طبيعي
+
+227
+00:29:33,410 --> 00:29:45,270
+show اثبتي ان ال sequence x in is
+
+228
+00:29:45,270 --> 00:29:50,150
+bounded and
+
+229
+00:29:50,150 --> 00:29:56,810
+monotone يعني اما increasing او
+
+230
+00:29:56,810 --> 00:29:57,330
+decreasing
+
+231
+00:30:01,980 --> 00:30:09,140
+بعدين find ال limit find its
+
+232
+00:30:09,140 --> 00:30:17,980
+limit إذا إزاي نعملها في سؤال السؤال
+
+233
+00:30:17,980 --> 00:30:24,220
+الرابع إزاي السؤال الرابع okay هنا
+
+234
+00:30:24,220 --> 00:30:25,980
+في بس يعني ال trick
+
+235
+00:30:32,350 --> 00:30:37,550
+لو كتبنا اول تلت اربع خمس حدود نقدر نشوف وين يعني
+
+236
+00:30:37,550 --> 00:30:41,870
+ال sequence محصورة بين اي اعداد ايه هو ال upper
+
+237
+00:30:41,870 --> 00:30:46,950
+bound و ال lower bound لل sequence فمثلا لو بدي
+
+238
+00:30:46,950 --> 00:30:52,390
+احسب الحد رقم اي حد واحد اكبر من واحد طب الحد
+
+239
+00:30:52,390 --> 00:31:00,470
+التاني بساوي اتنين سالب واحد على اكس واحدلأن انا
+
+240
+00:31:00,470 --> 00:31:06,090
+عندى هنا باخد n بالساعة واحد تعطين x اتنين طب انا
+
+241
+00:31:06,090 --> 00:31:12,210
+عندى x واحد اكبر من واحد هذا بيقدى انه مخلوق x
+
+242
+00:31:12,210 --> 00:31:25,390
+واحد اصغر من واحد وبالتالي
+
+243
+00:31:33,910 --> 00:31:44,010
+إذا و هذا طبعا عدد موجب أكيد و أصغر من واحد إذا
+
+244
+00:31:44,010 --> 00:31:48,590
+أنا بطرح .. بطرح من ال .. من ال .. من الاتنين عدد
+
+245
+00:31:48,590 --> 00:31:54,730
+موجب و أصغر من واحد فهذا هيكون يعني أكيد أكبر من
+
+246
+00:31:54,730 --> 00:32:01,540
+واحد أه لأ هذا بدي يكون أصغر من اتنينهذا بالتأكيد
+
+247
+00:32:01,540 --> 00:32:05,980
+أصغر من اتنين لأن هذا عدد موجب هذا عدد موجب في
+
+248
+00:32:05,980 --> 00:32:09,480
+النهاية بغض النظر أكبر من واحد ولا أصغر من واحد
+
+249
+00:32:09,480 --> 00:32:15,440
+لما أطرح أنا عدد موجب من عدد العدد بصغر صح فإذا x
+
+250
+00:32:15,440 --> 00:32:23,900
+اتنين أصغر من اتنين طب و x تلاتة بساوة اتنين سالب
+
+251
+00:32:23,900 --> 00:32:25,540
+واحد على x اتنين
+
+252
+00:32:30,440 --> 00:32:35,840
+برضه هذا عدد موجب فهيكون هذا اصغر من ايه من اتنين
+
+253
+00:32:35,840 --> 00:32:44,960
+و هكذا اذا و طبعا x واحد وهذا
+
+254
+00:32:44,960 --> 00:32:51,740
+العدد اصغر من واحدفهذا اكيد هيطلع اكبر من الواحد
+
+255
+00:32:51,740 --> 00:32:56,460
+اذا هذا هيكون اكبر من واحد و هذا اكبر من واحد اذا
+
+256
+00:32:56,460 --> 00:33:00,880
+واضح ان حدود ال sequence هتكون محصورة بين واحد و
+
+257
+00:33:00,880 --> 00:33:09,880
+اتنين اذا بقدر انا اعمل ادعي بقدر ادعي اقول claim
+
+258
+00:33:09,880 --> 00:33:13,720
+واحد
+
+259
+00:33:13,720 --> 00:33:16,200
+ان ال ..
+
+260
+00:33:21,340 --> 00:33:26,800
+إن Xn أكبر من أو ساوى الواحد أصغر من أو ساوى اتنين
+
+261
+00:33:26,800 --> 00:33:31,840
+لكل N طبعا
+
+262
+00:33:31,840 --> 00:33:41,140
+هذا يعني ممكن برهانه by induction طيب
+
+263
+00:33:41,140 --> 00:33:46,280
+ال .. إذا هنا prove it
+
+264
+00:33:49,440 --> 00:34:00,540
+prove it by induction الكلام
+
+265
+00:34:00,540 --> 00:34:05,860
+التاني ان
+
+266
+00:34:05,860 --> 00:34:14,020
+ال sequence تبعتي بتطلع decreasing x
+
+267
+00:34:14,020 --> 00:34:15,820
+in is decreasing
+
+268
+00:34:21,770 --> 00:34:27,350
+يعني xn أكبر من أو ساوي xn زايد one for every n
+
+269
+00:34:27,350 --> 00:34:33,590
+belonging to n to
+
+270
+00:34:33,590 --> 00:34:41,110
+see this لبرهان ذلك to see this لبرهان ذلك note
+
+271
+00:34:41,110 --> 00:34:47,550
+that note
+
+272
+00:34:47,550 --> 00:34:48,130
+first
+
+273
+00:34:51,100 --> 00:35:05,320
+لاحظى اولا انه x n minus واحد لكل تربية لو اخدت حد
+
+274
+00:35:05,320 --> 00:35:11,120
+رقم n واطرحت منه واحد وربعته هذا مربع كامل فهذا
+
+275
+00:35:11,120 --> 00:35:17,560
+اكيد اكبر من أو يساوي سفر اى مربع كامل اى مربع
+
+276
+00:35:17,560 --> 00:35:23,290
+كامل لأى عدد حقيقي بيطلع غير سالمطبعا هذا لما
+
+277
+00:35:23,290 --> 00:35:30,610
+نربّه بيطلع x x n squared minus اتنين x n plus one
+
+278
+00:35:30,610 --> 00:35:40,470
+وهذا المجموع من
+
+279
+00:35:40,470 --> 00:35:44,690
+المتباينة هذه بنستنتج هذا بيقدّي
+
+280
+00:35:55,680 --> 00:36:10,260
+هذا بيقدي انه اتنين X N زائد واحد او
+
+281
+00:36:10,260 --> 00:36:18,840
+هذا بيقدي انه XXn تربية أكبر من أو ساوي هاي Xn
+
+282
+00:36:18,840 --> 00:36:24,340
+تربية ودي هذا عن ناحية التانية لاحظي هذا كله أكبر
+
+283
+00:36:24,340 --> 00:36:27,820
+من أو ساوي سبر فودي هذا عن ناحية التانية بطلع Xn
+
+284
+00:36:27,820 --> 00:36:33,720
+تربية أكبر من أو ساوي اتنين Xn سالب واحد وهذا
+
+285
+00:36:33,720 --> 00:36:40,660
+الكلام صحيح لكل N وهذا
+
+286
+00:36:40,660 --> 00:36:55,140
+بقدربدوره انه xn xn
+
+287
+00:36:55,140 --> 00:37:06,760
+أكبر من أو يساوي اتنين negative واحد
+
+288
+00:37:06,760 --> 00:37:07,820
+على xn
+
+289
+00:37:18,300 --> 00:37:23,720
+إذا أنا جسمي إضرب في واحد على xn ال xn هنا عدد ال
+
+290
+00:37:23,720 --> 00:37:30,200
+.. ال xn موجة بقى ال xn كلها عداد موجة بقى لاحظي
+
+291
+00:37:30,200 --> 00:37:40,640
+انت هنا .. ان احنا ضربنا في xnعدد موجب او لأ جسمنا
+
+292
+00:37:40,640 --> 00:37:48,360
+او ضربنا في واحد على اكس ان هذا عدد موجب فبطلع
+
+293
+00:37:48,360 --> 00:37:52,100
+عندي اكس ان و شريط المتبانى طبق زي ما هي و اتنين
+
+294
+00:37:52,100 --> 00:37:56,500
+سالب واحد على اكس ان الان هذا by definition of the
+
+295
+00:37:56,500 --> 00:38:00,860
+sequenceمن ال recursive formula هي ال recursive
+
+296
+00:38:00,860 --> 00:38:04,720
+formula او ال inductive formula بتقول ان هذا الفرق
+
+297
+00:38:04,720 --> 00:38:09,900
+بتطلع xn زاد واحد اذا الكلام هذا صحيح لكل n
+
+298
+00:38:09,900 --> 00:38:15,900
+وبالتالي اذا هيطلع اندي xn اكبر من أو ساوي xn زاد
+
+299
+00:38:15,900 --> 00:38:24,140
+واحد لكل n اذا ال sequence xn is decreasing متنقصة
+
+300
+00:38:26,080 --> 00:38:35,420
+الان من ال claims واحد و اتنين تطلع now x
+
+301
+00:38:35,420 --> 00:38:40,700
+in is
+
+302
+00:38:40,700 --> 00:38:44,460
+decreasing and bounded
+
+303
+00:38:48,230 --> 00:38:52,870
+حسب claim واحد و claim اتنين so by monotone
+
+304
+00:38:52,870 --> 00:39:03,610
+convergence theorem xn converges say limit xn
+
+305
+00:39:03,610 --> 00:39:10,670
+بالساوي x for some x ينتمي الى R الان بنجيب قيمة
+
+306
+00:39:10,670 --> 00:39:22,760
+ال limit اللي هي ال Xفنرجع لل inductive formula to
+
+307
+00:39:22,760 --> 00:39:34,360
+find x we have من ال inductive formula أنا عندي ال
+
+308
+00:39:34,360 --> 00:39:44,140
+limit ل x n plus one equals two بالساوية اتنين
+
+309
+00:39:44,140 --> 00:39:50,820
+minusواحد على limit xm هذا لما اخد ال limit
+
+310
+00:39:50,820 --> 00:39:57,140
+للطرفين في ال inductive formula طب هذا طرف الشمال
+
+311
+00:39:57,140 --> 00:40:03,530
+بساوي x و الطرف اليمين واحد على xالان حل المعادلة
+
+312
+00:40:03,530 --> 00:40:08,510
+هاد في X اضرب في X بطلع عندي X تربيع سالب اتنين X
+
+313
+00:40:08,510 --> 00:40:14,770
+موجة بواحد بساوي سفر وانت بتحلل الى X موجة باتنين
+
+314
+00:40:14,770 --> 00:40:25,550
+X سالب واحد الكل تربيع بساوي سفر فبطلع X بساوي
+
+315
+00:40:25,550 --> 00:40:31,630
+واحدو هذا صحيح لأن ال x in لحظوا في claim واحد x
+
+316
+00:40:31,630 --> 00:40:35,150
+in معصورة بين واحد و اتنين اذا ال limit تبقى بتطلع
+
+317
+00:40:35,150 --> 00:40:40,530
+معصورة بين واحد و اتنين فالجواب واحد مقبول اذا هذا
+
+318
+00:40:40,530 --> 00:40:49,890
+هو هاي ال limit طلعت بتساوي واحد تمام في
+
+319
+00:40:49,890 --> 00:40:51,010
+اي أسئلة تانية
+
+320
+00:41:02,130 --> 00:41:06,830
+في معناه وجهة انحال كمان سؤال اذا بتحبه سيكشن
+
+321
+00:41:06,830 --> 00:41:08,210
+البعده تلاتة اربعة
+
+322
+00:41:26,730 --> 00:41:33,870
+سيكشن تلاتة اربعة فش ولا سؤال عندكم
+
+323
+00:41:33,870 --> 00:41:44,030
+فحللكم
+
+324
+00:41:44,030 --> 00:41:49,390
+سؤال يحداش لانه واضح ان انتوا مش دارسين فنحل
+
+325
+00:41:49,390 --> 00:41:52,370
+السؤال هيك انا هحلكم يعني من هندي
+
+326
+00:41:57,800 --> 00:42:07,280
+إذن سؤال 11 سيكشن تلاتة أربعة suppose
+
+327
+00:42:07,280 --> 00:42:10,860
+افترضي
+
+328
+00:42:10,860 --> 00:42:19,320
+ان xn أكبر من أو ساوي سفر for every natural number
+
+329
+00:42:19,320 --> 00:42:30,510
+n and ال limit لل sequenceسارق one to n في xn
+
+330
+00:42:30,510 --> 00:42:34,150
+exists
+
+331
+00:42:34,150 --> 00:42:39,110
+show
+
+332
+00:42:39,110 --> 00:42:48,490
+برهنة انه ال sequence xn convergence
+
+333
+00:43:42,520 --> 00:43:51,900
+Okay خلّينا نشوف ال .. طيب احنا نشوف solution
+
+334
+00:43:55,820 --> 00:44:00,460
+say احنا فرضين ان ال limit لل sequence هذه exist
+
+335
+00:44:00,460 --> 00:44:07,520
+فافترضي ان ال limit لل sequence سالب واحد as n في
+
+336
+00:44:07,520 --> 00:44:14,720
+xn as n tends to infinity ال limit لل sequence هذه
+
+337
+00:44:14,720 --> 00:44:19,620
+بيساوي x for some x ينتمي ال R
+
+338
+00:44:27,140 --> 00:44:39,900
+الان then the subsequences ال subsequences اللي هي
+
+339
+00:44:39,900 --> 00:44:49,780
+لو سالب
+
+340
+00:44:49,780 --> 00:44:57,030
+واحد قصة اتنين in في x اتنين inهذه الـ Converge لـ
+
+341
+00:44:57,030 --> 00:45:02,030
+X هذه الـ subsequence من السيكوانس هذه بس حدودها
+
+342
+00:45:02,030 --> 00:45:09,210
+الزوجية and كمان ال subsequence اللي حدودها
+
+343
+00:45:09,210 --> 00:45:10,050
+الفردية
+
+344
+00:45:18,430 --> 00:45:22,850
+برضه converge ل X لأن في عندي نظرية بتقول إذا كانت
+
+345
+00:45:22,850 --> 00:45:27,070
+ال sequence convergent ل X فأي subsequence منها
+
+346
+00:45:27,070 --> 00:45:31,270
+بتكون convergent لنفس ال X هذه subsequence من ال
+
+347
+00:45:31,270 --> 00:45:37,890
+sequence هذه أخدت الحدود الزوجية وهذه subsequence
+
+348
+00:45:37,890 --> 00:45:41,470
+من ال sequence هذه اللي هي مدة تالية الحدود
+
+349
+00:45:41,470 --> 00:45:49,920
+الفردية طيب من هنالاحظوا سالب واحد الأس تبعها زوجي
+
+350
+00:45:49,920 --> 00:45:54,820
+تطلع واحد وبالتالي ال sequence هذه هي نفس ال
+
+351
+00:45:54,820 --> 00:46:04,500
+sequence اتنين in عفوا x اتنين in و سالب واحد لما
+
+352
+00:46:04,500 --> 00:46:08,220
+يكون الأس تبعها فارد تطلع سالب واحد إذا هذه سالب
+
+353
+00:46:08,220 --> 00:46:14,040
+يعني سالب ال sequence x اتنين in سالب واحد
+
+354
+00:46:16,730 --> 00:46:35,630
+تمام؟ طيب أنا عندي من الفرض by
+
+355
+00:46:35,630 --> 00:46:40,990
+hypothesis من الفرض أنا عندي xn أكبر من أو ساوى
+
+356
+00:46:40,990 --> 00:46:54,340
+سفر لكل n في n فهذا بيدّيإنه X2N و أيضا X2N-1 أكبر
+
+357
+00:46:54,340 --> 00:47:01,940
+من أو يساوي سفر لكل N في ال natural numbers وهذا
+
+358
+00:47:01,940 --> 00:47:11,040
+بيقدي بدوره إلى إنه ال X اللي هي من هنا X بيساوي
+
+359
+00:47:11,040 --> 00:47:14,500
+ليه بيساوي limit X2N
+
+360
+00:47:16,870 --> 00:47:22,690
+هي عندي هذا
+
+361
+00:47:22,690 --> 00:47:32,230
+هو هذا من هان بطلع عندي limit x2n بساوي x و من هان
+
+362
+00:47:32,230 --> 00:47:41,810
+بطلع عندي limit سالب x2n سالب واحد بساوي x او
+
+363
+00:47:45,510 --> 00:47:48,610
+السالب واحد بيطلع برا ال limit فبطلع عندي limit
+
+364
+00:47:48,610 --> 00:47:56,770
+x2n سالب واحد بساوي سالب x مظبوط؟
+
+365
+00:47:56,770 --> 00:48:02,170
+إذا هاي عندي أنا limit x2n سالب واحد هذا بيطلع
+
+366
+00:48:02,170 --> 00:48:10,450
+بساوي سالب x أو لأ في الأول ال x بساوي limit x2n
+
+367
+00:48:10,450 --> 00:48:15,280
+وهذا بيطلع أكبر من أو ساوي سفرلأن أنا عندي x2n
+
+368
+00:48:15,280 --> 00:48:19,900
+أكبر من أوسعها 0 لكل n فلما تكون ال sequence
+
+369
+00:48:19,900 --> 00:48:23,800
+حدودها غير سالبة فال limit تبعتها إذا كانت
+
+370
+00:48:23,800 --> 00:48:27,660
+convergent ال limit تبعتها تطلع غير سالبة و كذلك
+
+371
+00:48:27,660 --> 00:48:36,980
+سالب x اللي هي بتساوي limit x2n سالب واحد برضه أنا
+
+372
+00:48:36,980 --> 00:48:42,850
+عندي x2n سالب واحد كلهمأعداد غير سالبة و ال
+
+373
+00:48:42,850 --> 00:48:46,550
+sequence هذه convergent إذا ال limit تبعتها بتطلع
+
+374
+00:48:46,550 --> 00:48:50,450
+غير سالبة إذا
+
+375
+00:48:50,450 --> 00:48:55,950
+أنا من هنا بطلع عندي حاجتين x أكبر من أو ساوى سفر
+
+376
+00:48:55,950 --> 00:49:04,280
+and negative x and negative x أكبر منأو ساوي سفر
+
+377
+00:49:04,280 --> 00:49:10,060
+هذا بيؤدي ان x أكبر من أو ساوي سفر and اضرب في
+
+378
+00:49:10,060 --> 00:49:15,520
+سالب واحد بيطلع x أصغر من أو ساوي سفر الان انا في
+
+379
+00:49:15,520 --> 00:49:19,740
+عندي عدد حقيقي أكبر من أو ساوي سفر and أصغر من أو
+
+380
+00:49:19,740 --> 00:49:30,300
+ساوي سفر بيؤدي ان x بيساوي سفر تمام اذا طلع عندي
+
+381
+00:49:30,300 --> 00:49:31,020
+هنا ال
+
+382
+00:49:34,250 --> 00:49:40,070
+الـ limit هذه x بالساوية سفر الآن
+
+383
+00:49:40,070 --> 00:49:51,850
+تعالوا نثبت now given إمسلن أكبر من السفر it
+
+384
+00:49:51,850 --> 00:49:59,030
+choose how they exist capital
+
+385
+00:49:59,030 --> 00:50:01,550
+N عدد طبيعي
+
+386
+00:50:04,240 --> 00:50:11,660
+بحيث انه لكل n أكبر من أو ساوي capital N هذا بيقدي
+
+387
+00:50:11,660 --> 00:50:23,140
+ان absolute xn-0 بساوي absolute سالب واحد أُس n في
+
+388
+00:50:23,140 --> 00:50:30,960
+xn-0 لأن
+
+389
+00:50:30,960 --> 00:50:33,340
+هنا المفروض اكتب هنا since
+
+390
+00:50:36,490 --> 00:50:44,610
+مش احنا فرضين انه ال since limit سالب واحد قص ان
+
+391
+00:50:44,610 --> 00:50:54,750
+في x in بساوي x بتساوي سفر احنا
+
+392
+00:50:54,750 --> 00:50:58,910
+من الفرض انا عندي ان ال limit هذه موجودة تمام
+
+393
+00:50:58,910 --> 00:51:04,270
+وفرضناها x و اثبتنا ان ال limit تبعتها طلعت x
+
+394
+00:51:04,270 --> 00:51:10,220
+بساوي سفرالان بما انه limit ال sequence هذه بساوي
+
+395
+00:51:10,220 --> 00:51:14,220
+سفر، اذا من تعريف ال limit for any given epsilon
+
+396
+00:51:14,220 --> 00:51:18,540
+يوجد capital N يعتمد على epsilon بحيث لكل N أكبر
+
+397
+00:51:18,540 --> 00:51:22,960
+من أو ساوي capital N بطلع المسافة بين الحد العام
+
+398
+00:51:22,960 --> 00:51:30,200
+وال limit x اللي هي سفر أصغر من epsilonفهيك أنا
+
+399
+00:51:30,200 --> 00:51:36,540
+بطلع عندي absolute xn minus صفر أصغر من إبسلون إذا
+
+400
+00:51:36,540 --> 00:51:40,120
+هان أثبتت أنه لأي إبسلون أكبر من الصفر يوجد
+
+401
+00:51:40,120 --> 00:51:44,100
+capital N يعتمد على إبسلون بحيث لكل N أكبر منه
+
+402
+00:51:44,100 --> 00:51:48,140
+ساوي capital N المسافة بين xn وصفر أصغر من إبسلون
+
+403
+00:51:48,140 --> 00:51:53,040
+فهذا بيقدي أنه هذا معناه حسب تعريف epsilon capital
+
+404
+00:51:53,040 --> 00:51:58,260
+N أنه ال limit لل sequence xn موجودة و بالساوية
+
+405
+00:51:58,260 --> 00:52:01,890
+صفروبالتالي هيك أثبتنا أن ال sequence x in
+
+406
+00:52:01,890 --> 00:52:06,390
+convergence ومش هيك و بس و نهايتها كمان بالساوى
+
+407
+00:52:06,390 --> 00:52:15,170
+سفر okay تمام إذا هذا حل السؤال 11 و نكتفي بهذا
+
+408
+00:52:15,170 --> 00:52:21,690
+القدر من الحل المسائل و نكمل ان شاء الله حل
+
+409
+00:52:21,690 --> 00:52:26,290
+المسائل في المناقشة القادمة يوم السبت الجاي أو يوم
+
+410
+00:52:26,290 --> 00:52:32,830
+الأربع مع الشعبات تانيةفنوقف هنا ونواصل ان شاء
+
+411
+00:52:32,830 --> 00:52:40,790
+الله يوم السبت الجاي تكمل المناخشة السكاشن اللي هي
+
+412
+00:52:40,790 --> 00:52:43,550
+تلاتة أربعة و تلاتة خمسة و تلاتة ستة
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..aaf172b03082c615e2da86b654b29c7c07820126
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/bwcuptIkF-o_raw.srt
@@ -0,0 +1,1656 @@
+1
+00:00:20,940 --> 00:00:27,720
+بسم الله الرحمن الرحيم ان شاء الله اليوم هناخد في
+
+2
+00:00:27,720 --> 00:00:34,940
+اللقاء الأول مناقشة و المناقشة هذه هتكون على ال
+
+3
+00:00:34,940 --> 00:00:42,360
+section أربعة و section خمسة من ال chapter تلاتة
+
+4
+00:00:42,360 --> 00:00:47,930
+في الكتاباحنا لقشنا قبل هيك section تلاتة واحد و
+
+5
+00:00:47,930 --> 00:00:52,070
+تلاتة اتنين تلاتة تلاتة مظبوط؟ تلاتة تلاتة تلاتة
+
+6
+00:00:52,070 --> 00:00:56,010
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+7
+00:00:56,010 --> 00:00:56,190
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+8
+00:00:56,190 --> 00:01:01,490
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+9
+00:01:01,490 --> 00:01:02,530
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+10
+00:01:02,530 --> 00:01:02,530
+تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة تلاتة
+
+11
+00:01:02,530 --> 00:01:07,770
+تلاتة تلاتة تلاتة
+
+12
+00:01:14,970 --> 00:01:20,490
+فمين عندها أي سؤال في ال section تلاتة تلاتة تلاتة
+
+13
+00:01:20,490 --> 00:01:28,290
+أربعة أو تلاتة خمسة سيكشن
+
+14
+00:01:28,290 --> 00:01:29,590
+تلاتة تلاتة
+
+15
+00:01:47,340 --> 00:01:54,900
+أي سؤال؟ ستة ستة؟ طب هذا مش مقرر، لأ أنا .. عفوا
+
+16
+00:01:54,900 --> 00:02:02,500
+أنا بتطلع في مكان تاني، تلاتة تلاتة، سؤال ستة،
+
+17
+00:02:02,500 --> 00:02:06,400
+مطلوب هذا السؤال؟ ما كتبتلاش أنت الأسئلة المطلوبة
+
+18
+00:02:06,400 --> 00:02:11,580
+اللي بتتكتب؟موجودة في ال syllabus .. موجودة في ال
+
+19
+00:02:11,580 --> 00:02:15,760
+syllabus فهذا السؤال مش من ضمن الأسئلة اللي ..
+
+20
+00:02:15,760 --> 00:02:17,920
+اللي احنا .. يعني انتوا بتطلعوش على ال syllabus
+
+21
+00:02:17,920 --> 00:02:21,440
+فيه على الصفحه تبعتي ال syllabus و فيه المسائل
+
+22
+00:02:21,440 --> 00:02:25,800
+المطلوبة فبإمكانكم تعرفوا المسائل المطلوبة لكل
+
+23
+00:02:25,800 --> 00:02:30,640
+section من هنا لآخر ال courseفهذا السؤال السادس
+
+24
+00:02:30,640 --> 00:02:33,580
+بالذات مش مطلوب لكن فيها سئلة تانية ممكن أحللك
+
+25
+00:02:33,580 --> 00:02:42,160
+أربعة أو تلاتة زيه فإيه رأيك؟ تلاتة
+
+26
+00:02:42,160 --> 00:02:45,580
+أو أربعة يكونوا نفس الفكرة أه تلاتة أو أربعة شو
+
+27
+00:02:45,580 --> 00:02:52,720
+بدك تلاتة ولا أربعة؟ الحل
+
+28
+00:02:52,720 --> 00:03:00,880
+السؤال أربعة مثلا؟ هاي الحل السؤال الرابعsection
+
+29
+00:03:00,880 --> 00:03:11,920
+تلاتة تلاتة في السؤال هذا let x واحد بساوي واحد
+
+30
+00:03:11,920 --> 00:03:17,920
+and xn
+
+31
+00:03:17,920 --> 00:03:24,660
+plus one بساوي square
+
+32
+00:03:24,660 --> 00:03:28,420
+root لاتنين plus xn
+
+33
+00:03:31,530 --> 00:03:39,530
+for n belong to n show
+
+34
+00:03:39,530 --> 00:03:52,370
+ان ال sequence xn converges and find its limit
+
+35
+00:03:55,460 --> 00:04:00,220
+بنثبت أولا أن الـ sequence هذي convergence ونجيب
+
+36
+00:04:00,220 --> 00:04:10,220
+ال limit تبعتها فمثلة
+
+37
+00:04:10,220 --> 00:04:15,500
+زي هذه بنطبق عليها الـ monotone convergence
+
+38
+00:04:15,500 --> 00:04:23,340
+theorem الـ monotone convergence theoremفلازم نثبت
+
+39
+00:04:23,340 --> 00:04:29,560
+حاجتين ان ال sequence هذه convergent لازم نثبت
+
+40
+00:04:29,560 --> 00:04:33,900
+انها convergent لازم نثبت انها monotone يعني
+
+41
+00:04:33,900 --> 00:04:40,100
+increasing او decreasing و bounded فلحظوا
+
+42
+00:04:40,100 --> 00:04:47,270
+انتوا لو بدى احسب اول يعنيالحل .. لحظة x واحد
+
+43
+00:04:47,270 --> 00:04:52,510
+بساوي واحد طب x اتنين .. خد in بساوي واحد بطلع جدر
+
+44
+00:04:52,510 --> 00:05:00,130
+اتنين زائد .. جدر اتنين زائد x واحد اللي هو جدر
+
+45
+00:05:00,130 --> 00:05:10,400
+التلاتة .. x تلاتة بساوي جدر اتنين زائد x اتنينو
+
+46
+00:05:10,400 --> 00:05:16,740
+يساوي جدر اتنين زاد جدر
+
+47
+00:05:16,740 --> 00:05:24,220
+التلاتة وهكذا
+
+48
+00:05:24,220 --> 00:05:29,640
+اللي
+
+49
+00:05:29,640 --> 00:05:38,120
+بعده X أربعة بساوي جدر اتنين زاد X تلاتة
+
+50
+00:05:56,800 --> 00:06:04,520
+و هذا بيساوي جدر اتنين زائد اللي
+
+51
+00:06:04,520 --> 00:06:10,500
+هو جدر التربية ايه الى اتنين زائد جدر التلاتة
+
+52
+00:06:27,010 --> 00:06:33,310
+فال .. الأدد يعني هذا دايما بيكون أقل من او ساو
+
+53
+00:06:33,310 --> 00:06:42,010
+اتنين أقل من او ساو اتنين صح؟ اه و هذا أصغر من او
+
+54
+00:06:42,010 --> 00:06:45,410
+ساو اتنين يعني جدر التلاتة أصغر من اتنين صح؟ أه
+
+55
+00:06:45,410 --> 00:06:50,750
+فهذا أكيد أصغر من او ساو اتنين و هذا
+
+56
+00:06:53,300 --> 00:06:58,180
+أصغر من أو ساوي اتنين وبالتالي هذا أصغر من أو ساوي
+
+57
+00:06:58,180 --> 00:07:06,560
+جدر الأربعة اللي هو أصغر من أو ساوي اتنيناذا و
+
+58
+00:07:06,560 --> 00:07:11,160
+طبعا و كل واحد من هدول اكبر من او يساوي الواحد اذا
+
+59
+00:07:11,160 --> 00:07:18,040
+ممكن احنا نثبت الان by induction claim ان xn اكبر
+
+60
+00:07:18,040 --> 00:07:24,320
+من او يساوي الواحد اصغر من او يساوي اتنين for
+
+61
+00:07:24,320 --> 00:07:30,590
+every n belong to nاه و هذا ممكن تبرهنه by
+
+62
+00:07:30,590 --> 00:07:34,650
+induction زي ما شوفنا في الأمثلة صح؟ طبعا طبعا
+
+63
+00:07:34,650 --> 00:07:43,730
+طبعا طبعا طبعا
+
+64
+00:07:43,730 --> 00:07:43,970
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+65
+00:07:43,970 --> 00:07:44,150
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+66
+00:07:44,150 --> 00:07:44,150
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+67
+00:07:44,150 --> 00:07:48,410
+طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا طبعا
+
+68
+00:07:48,410 --> 00:07:55,130
+طبعا طبعا طبعا طبعا
+
+69
+00:07:55,130 --> 00:07:57,910
+طب
+
+70
+00:08:01,490 --> 00:08:11,110
+الأن من أعلى الاختصارات الموجودة في
+
+71
+00:08:11,110 --> 00:08:17,050
+الوثيقة الاختصار
+
+72
+00:08:17,050 --> 00:08:20,290
+XN مرتبط
+
+73
+00:08:23,380 --> 00:08:27,360
+بعدين بنلاحظ انه قيمة ال sequence بتكبر كل ما اه
+
+74
+00:08:27,360 --> 00:08:34,580
+فممكن اثبات انه claim تاني اذا ال sequence bounded
+
+75
+00:08:34,580 --> 00:08:39,240
+claim x
+
+76
+00:08:39,240 --> 00:08:45,740
+in اصغر
+
+77
+00:08:45,740 --> 00:08:50,460
+منها و ساوي x in زاد واحد for every n
+
+78
+00:08:54,650 --> 00:09:02,290
+IEXN is increasing وهذا ممكن اثباته برضه by
+
+79
+00:09:02,290 --> 00:09:11,410
+induction by induction هنا هنا proof use induction
+
+80
+00:09:11,410 --> 00:09:14,630
+use
+
+81
+00:09:14,630 --> 00:09:20,610
+induction on M فالحالة
+
+82
+00:09:21,890 --> 00:09:30,890
+الحالة n بيساوي واحد انا عندي x واحد بيساوي واحد و
+
+83
+00:09:30,890 --> 00:09:34,810
+x واحد
+
+84
+00:09:34,810 --> 00:09:40,510
+زايد واحد اللي هو x اتنين بيساوي جدر التلاتة جدر
+
+85
+00:09:40,510 --> 00:09:47,810
+التلاتة وهذا بالتأكيد اكبر من واحد اللي هو x واحد
+
+86
+00:09:50,170 --> 00:09:57,350
+إذاً هيطلع عندي X2 أكبر من أو يساوي X1 إذاً
+
+87
+00:09:57,350 --> 00:10:04,170
+العبارة هذه صحيحة عند M بساوي واحد assume
+
+88
+00:10:04,170 --> 00:10:09,970
+induction hypothesis الفرض تبع ال induction assume
+
+89
+00:10:09,970 --> 00:10:13,910
+أنه
+
+90
+00:10:22,570 --> 00:10:24,510
+أصغر من أوي ساوي
+
+91
+00:10:35,580 --> 00:10:40,400
+بنثبت صحة الحق برهد عند n بساوي k زائد واحد اذا ت
+
+92
+00:10:40,400 --> 00:10:46,060
+show xk زائد واحد اصلا لو ساوي xk زائد واحد زائد
+
+93
+00:10:46,060 --> 00:10:55,700
+واحد عن x زائد اتنين we have لدينا لاحظوا
+
+94
+00:10:55,700 --> 00:11:01,180
+xk زائد اتنين من ال definition من ال definition
+
+95
+00:11:01,180 --> 00:11:03,360
+تبع ال sequence
+
+96
+00:11:06,860 --> 00:11:12,440
+من ال inductive formula أو ال recursive formula xk
+
+97
+00:11:12,440 --> 00:11:19,840
+زاد اتنين بسوى جذر التربيعى لاتنين زاد اكس k زاد
+
+98
+00:11:19,840 --> 00:11:28,000
+واحد صح و by induction hypothesis من الفرض تبع ال
+
+99
+00:11:28,000 --> 00:11:35,020
+induction هذا بسوى جذر اتنينو XK زياد واحد هذا
+
+100
+00:11:35,020 --> 00:11:44,080
+ايه؟ هيطلع اصغر من XK زياد واحد اكبر من او ساوي XK
+
+101
+00:11:44,080 --> 00:11:50,380
+انا XK انا نحط شريط اكبر XK زياد اتنين
+
+102
+00:11:55,180 --> 00:12:03,320
+فهذا أكبر من أو ساوي X .. هبدل XK زيادة واحد بأكبر
+
+103
+00:12:03,320 --> 00:12:07,660
+من أو ساوي XK من ال induction hypothesis من الفرب
+
+104
+00:12:07,660 --> 00:12:12,150
+تبع ال inductionوهذا بالـ definition باستخدام الـ
+
+105
+00:12:12,150 --> 00:12:18,310
+definition تبع الـ sequence الجذر هذا بساوي xk زي
+
+106
+00:12:18,310 --> 00:12:24,190
+واحدة إذا هين أثبتنا إن x sub k plus two bigger
+
+107
+00:12:24,190 --> 00:12:30,710
+than or equal to x sub k plus one إذاً this
+
+108
+00:12:30,710 --> 00:12:37,250
+completes this
+
+109
+00:12:37,250 --> 00:12:38,610
+completes the induction
+
+110
+00:12:43,320 --> 00:12:48,000
+وبالتالي إذا هيك بنكون أثبتنا ال claim بتاعي إن
+
+111
+00:12:48,000 --> 00:12:51,780
+أنا في عندي two claims أول شي sequence bounded
+
+112
+00:12:51,780 --> 00:12:57,200
+والتاني بيقول إن ال sequence increasing وبالتالي
+
+113
+00:12:57,200 --> 00:13:05,200
+therefore إذا
+
+114
+00:13:05,200 --> 00:13:09,580
+لو سمينا هذا claim one وهذا claim two
+
+115
+00:13:17,790 --> 00:13:27,210
+فإذا now it claims
+
+116
+00:13:27,210 --> 00:13:32,930
+one and two and الـ monotone convergence theorem
+
+117
+00:13:32,930 --> 00:13:41,530
+بيقدّوا إن sequence x in convergence say
+
+118
+00:13:41,530 --> 00:13:52,080
+دعنا نسمي ال limit تبعتهاlimit x in بساوي x طبعا
+
+119
+00:13:52,080 --> 00:13:56,820
+هذا بيطلع عدد حقيقي الان
+
+120
+00:13:56,820 --> 00:14:07,420
+بنوجد قيمة limit x هذه فبنرجع to find to find x
+
+121
+00:14:07,420 --> 00:14:12,880
+لإيجاد قيمة ال x بناخد
+
+122
+00:14:12,880 --> 00:14:21,340
+ال limittake limit of
+
+123
+00:14:21,340 --> 00:14:28,220
+both sides of
+
+124
+00:14:35,540 --> 00:14:41,820
+بناخد ال limit لطرفين of both sides of المعادلة xn
+
+125
+00:14:41,820 --> 00:14:50,280
+زي الواحد بساوي square root ل two plus xn to
+
+126
+00:14:50,280 --> 00:14:50,800
+get
+
+127
+00:14:53,550 --> 00:14:59,490
+limit xn plus one as n tends to infinity بساوي
+
+128
+00:14:59,490 --> 00:15:02,890
+limit الجدر التربيعي ممكن تدخل ال limit تحت الجدر
+
+129
+00:15:02,890 --> 00:15:08,210
+التربيعي وباستخدام قوانين النهايات limit الاتنين
+
+130
+00:15:08,210 --> 00:15:13,810
+بيطلع اتنين زي limit xn as n tends to infinity طيب
+
+131
+00:15:13,810 --> 00:15:19,170
+انا عندى limit xn زي واحد بساوي x
+
+132
+00:15:26,140 --> 00:15:36,560
+هذه المعادلة بيصير
+
+133
+00:15:36,560 --> 00:15:41,100
+x تربية negative xنجاتف اتنين نجاتف اتنين نجاتف
+
+134
+00:15:41,100 --> 00:15:45,160
+اتنين نجاتف اتنين نجاتف اتنين نجاتف اتنين نجاتف
+
+135
+00:15:45,160 --> 00:15:58,780
+اتنين نجاتف اتنين نجاتف اتنين نجاتف اتنين
+
+136
+00:16:01,690 --> 00:16:08,750
+الـ xn أكبر من أو ساوي واحد أصغر من أو ساوي اتنين
+
+137
+00:16:08,750 --> 00:16:18,250
+لكل n هذا من claim one بيقدي ان ال limit حسب
+
+138
+00:16:18,250 --> 00:16:25,270
+نظرية سابقة هذا بيقدي ان ال limit ل xn أصغر من أو
+
+139
+00:16:25,270 --> 00:16:31,750
+ساوي اتنين أكبر من أو ساوي الواحدو طبعا ال limit
+
+140
+00:16:31,750 --> 00:16:37,110
+قلنا ل xn بساوي x إذا واحد أصغر من او ساوي x أصغر
+
+141
+00:16:37,110 --> 00:16:42,190
+من او ساوي اتنين طب أنا عندي خيارين إما x بساوي
+
+142
+00:16:42,190 --> 00:16:49,450
+اتنين أو x بساوي سالب واحد مش ممكن ال x محصورة بين
+
+143
+00:16:49,450 --> 00:16:54,090
+واحد و اتنين إذا هذه الإجابة غير مقبولة وبالتالي
+
+144
+00:16:54,090 --> 00:16:59,710
+ال x بساوي اتنينو هيك بنكون أثبتنا إن ال sequence
+
+145
+00:16:59,710 --> 00:17:03,650
+is convergent و هي وجدنا ال limit تبعتها بالمثل
+
+146
+00:17:03,650 --> 00:17:09,130
+ممكن نحل باقي الأسئلة زي مثلا سؤال واحد و اتنين و
+
+147
+00:17:09,130 --> 00:17:16,190
+تلاتة و خمسة و ستة و سابعة okay
+
+148
+00:17:16,190 --> 00:17:24,550
+تمام في أي أسئلة تانية في هذا section السؤال تسعة
+
+149
+00:17:37,220 --> 00:18:05,540
+سؤال تسعة هاي
+
+150
+00:18:05,540 --> 00:18:13,770
+السؤال تسعةالسيقشن تلاتة تلاتة السؤال هذا بيقول
+
+151
+00:18:13,770 --> 00:18:22,970
+let a be infinite infinite
+
+152
+00:18:22,970 --> 00:18:32,090
+subset of R و ال set هذه bounded
+
+153
+00:18:34,790 --> 00:18:42,530
+أو bounded above محدودة
+
+154
+00:18:42,530 --> 00:18:50,170
+من أعلى and
+
+155
+00:18:50,170 --> 00:18:53,610
+let ال U
+
+156
+00:18:56,560 --> 00:19:00,740
+بساوي ال supremum لل set A طبعا ال set A bounded
+
+157
+00:19:00,740 --> 00:19:07,480
+above وبالتالي by ال supremum property ال supremum
+
+158
+00:19:07,480 --> 00:19:14,240
+تبعها exist دعنا نسميه U المطلوب
+
+159
+00:19:14,240 --> 00:19:22,340
+show that show
+
+160
+00:19:22,340 --> 00:19:29,900
+there existيوجد an increasing ..an increasing
+
+161
+00:19:29,900 --> 00:19:33,180
+subsequence
+
+162
+00:19:33,180 --> 00:19:40,120
+او sequence there exists an increasing sequence xn
+
+163
+00:19:40,120 --> 00:19:51,480
+contained in A such that ال limit لسيكوينس xn
+
+164
+00:19:51,480 --> 00:19:52,880
+بساوي U
+
+165
+00:20:03,070 --> 00:20:08,150
+I prove من
+
+166
+00:20:08,150 --> 00:20:12,630
+خواص ال supremum
+
+167
+00:20:12,630 --> 00:20:19,850
+احنا
+
+168
+00:20:19,850 --> 00:20:27,650
+فيها انا كان لمبة دخلناها قبل هيك وهذه المبة بتقول
+
+169
+00:20:27,650 --> 00:20:28,230
+انه
+
+170
+00:20:42,440 --> 00:20:51,320
+لما أخدناها في أول chapter بتقول أنه .. أفندم؟
+
+171
+00:20:51,320 --> 00:21:05,800
+بنقول an upper bound an upper bound U of الست A is
+
+172
+00:21:05,800 --> 00:21:09,540
+the supremum
+
+173
+00:21:11,820 --> 00:21:21,120
+the supremum of a, if and only if لكل
+
+174
+00:21:21,120 --> 00:21:29,260
+إبسلون أكبر من السفر يوجد x إبسلون ينتمي إلى a
+
+175
+00:21:29,260 --> 00:21:33,680
+بحيث أنه بحيث
+
+176
+00:21:33,680 --> 00:21:37,920
+أنه u سالب إبسلون أصغر من x إبسلون
+
+177
+00:21:40,930 --> 00:21:46,950
+نظبط صح؟ منطبقها لإن أنا عندي هاي U بساوي ال
+
+178
+00:21:46,950 --> 00:21:52,670
+supremum ل A إذا لو أخدت for epsilon بساوي واحد
+
+179
+00:21:52,670 --> 00:22:04,190
+أكبر من السفر يوجد X واحد ينتمي إلى A such that U
+
+180
+00:22:04,190 --> 00:22:17,500
+سالب واحد أصغر منx واحد next
+
+181
+00:22:17,500 --> 00:22:21,240
+for
+
+182
+00:22:21,240 --> 00:22:27,360
+for
+
+183
+00:22:27,360 --> 00:22:33,400
+epsilon بساوي نص لو
+
+184
+00:22:33,400 --> 00:22:37,200
+أخدت ال epsilon هذه بساوي نص ف choose
+
+185
+00:22:40,760 --> 00:22:51,040
+choose by above لمّا X2
+
+186
+00:22:51,040 --> 00:23:01,180
+تنتمي إلى A وممكن نختار X2 أكبر من أو يساوي X1
+
+187
+00:23:01,180 --> 00:23:08,580
+الأولى هي such that U سالد نص الإبسلون أصغر من X2
+
+188
+00:23:19,440 --> 00:23:29,340
+بعدين now for إبسلون بساوي واحد على تلاتة أكبر من
+
+189
+00:23:29,340 --> 00:23:34,220
+سفر it choose إذا في اللمّة هذه خدوا إبسلون بساوي
+
+190
+00:23:34,220 --> 00:23:39,520
+تلت it choose X تلاتة ينتمي إلى A
+
+191
+00:23:42,410 --> 00:23:48,590
+بحيث انه X تلاتة هذا ممكن اختاره اكبر من او ساوي X
+
+192
+00:23:48,590 --> 00:24:03,090
+اتنين and U اللي هو U سالب تلت اصغر من X تلاتة صح؟
+
+193
+00:24:03,090 --> 00:24:14,810
+continuing in this processلو استمرنا بالعملية الـ
+
+194
+00:24:14,810 --> 00:24:27,910
+continuing in this process we
+
+195
+00:24:27,910 --> 00:24:35,230
+get by induction عملية
+
+196
+00:24:35,230 --> 00:24:36,790
+استقرائية that
+
+197
+00:24:46,820 --> 00:24:52,740
+for epsilon بساوي واحد على ك أكبر من السفر
+
+198
+00:24:56,070 --> 00:25:04,030
+there exists xk أكبر من او ساوي xk زايد واحد such
+
+199
+00:25:04,030 --> 00:25:14,950
+that absolute u سالب واحد على k أصغر من xk وهذا
+
+200
+00:25:14,950 --> 00:25:23,530
+صحيح for every k ينتمي إلى n تمام؟
+
+201
+00:25:32,820 --> 00:25:40,120
+طيب أنا عندي ..
+
+202
+00:25:40,120 --> 00:25:50,560
+خلّيني أمسح اللمّة هذه طيب
+
+203
+00:25:50,560 --> 00:25:56,700
+إذا أنا عندي U نيجاتيب واحد على K طلع أصغر من XK
+
+204
+00:26:00,780 --> 00:26:08,580
+و ال XK هذه أصغر من أو ساوي ال U لأن ال U هو ال
+
+205
+00:26:08,580 --> 00:26:16,240
+supremum ل A و XK عنصر في A و ال U upper bound لل
+
+206
+00:26:16,240 --> 00:26:22,840
+6A ف .. و XK عنصر في A إذا ال XK لازم يكون أصغر من
+
+207
+00:26:22,840 --> 00:26:31,010
+أو ساوي ال U و ال U أصغر من أو ساوي أو أصغر منu
+
+208
+00:26:31,010 --> 00:26:35,790
+زائد واحد على k الكلام هذا صحيح for all k belong
+
+209
+00:26:35,790 --> 00:26:44,830
+to n مظبوط صحيح so احنا اثبتنا هيك ان يوجد
+
+210
+00:26:44,830 --> 00:26:51,810
+sequence يوجد increasing sequence
+
+211
+00:26:51,810 --> 00:27:01,940
+x in او xkمهم XK contained in A such that absolute
+
+212
+00:27:01,940 --> 00:27:10,820
+XK minus U أصغر من واحد على K for all K تنتمي إلى
+
+213
+00:27:10,820 --> 00:27:19,920
+N طيب
+
+214
+00:27:19,920 --> 00:27:23,400
+ما هذا عبارة عن واحد على K في واحد
+
+215
+00:27:26,730 --> 00:27:32,150
+هذا أصغر من أو ساوي واحد في واحد على K لكل K ينتمي
+
+216
+00:27:32,150 --> 00:27:42,410
+ل N اذا hence by previous theorem اللي هي نظرية
+
+217
+00:27:42,410 --> 00:27:47,410
+فاكرينها اتنين اربعة في ال notes نظرية اتنين اربعة
+
+218
+00:27:47,410 --> 00:27:48,810
+في ال notes تبعتنا
+
+219
+00:27:54,490 --> 00:28:02,870
+with c بساوي واحد اكبر من سفر and a n او a k a k
+
+220
+00:28:02,870 --> 00:28:12,410
+بساوي واحد على k tends to zero we get تديني
+
+221
+00:28:22,310 --> 00:28:27,970
+نحصل على ان ال limit ل xk as k tends to infinity
+
+222
+00:28:27,970 --> 00:28:35,470
+بساوي ال U وهذا هو المطلوب مام؟ واضح؟ لأن هذا هو
+
+223
+00:28:35,470 --> 00:28:40,490
+البرهان واضح البرهان؟ في أي استفسار؟ في أي شيء مش
+
+224
+00:28:40,490 --> 00:28:49,730
+واضح؟ طيب ماشي الحال خلينا نشوف هاي سؤال تلاتة
+
+225
+00:29:01,490 --> 00:29:09,710
+سؤال اتنين section تلاتة تلاتة فهنا عندي x واحد
+
+226
+00:29:09,710 --> 00:29:17,070
+انا عندي x واحد عدد اكبر من واحد و x n plus one
+
+227
+00:29:17,070 --> 00:29:22,290
+بيساوي بنعرفه
+
+228
+00:29:22,290 --> 00:29:33,410
+على انه اتنين سالب واحد على x n لكل nعدد طبيعي
+
+229
+00:29:33,410 --> 00:29:45,270
+show اثبتي ان ال sequence x in is
+
+230
+00:29:45,270 --> 00:29:50,150
+bounded and
+
+231
+00:29:50,150 --> 00:29:56,810
+monotone يعني اما increasing او
+
+232
+00:29:56,810 --> 00:29:57,330
+decreasing
+
+233
+00:30:01,980 --> 00:30:09,140
+بعدين find ال limit find its
+
+234
+00:30:09,140 --> 00:30:17,980
+limit إذا إزاي نعملها في سؤال السؤال
+
+235
+00:30:17,980 --> 00:30:24,220
+الرابع إزاي السؤال الرابع okay هنا
+
+236
+00:30:24,220 --> 00:30:25,980
+في بس يعني ال trick
+
+237
+00:30:32,350 --> 00:30:37,550
+لو كتبنا اول تلت اربع خمس حدود نقدر نشوف وين يعني
+
+238
+00:30:37,550 --> 00:30:41,870
+ال sequence محصورة بين اي اعداد ايه هو ال upper
+
+239
+00:30:41,870 --> 00:30:46,950
+bound و ال lower bound لل sequence فمثلا لو بدي
+
+240
+00:30:46,950 --> 00:30:52,390
+احسب الحد رقم اي حد واحد اكبر من واحد طب الحد
+
+241
+00:30:52,390 --> 00:31:00,470
+التاني بساوي اتنين سالب واحد على اكس واحدلأن انا
+
+242
+00:31:00,470 --> 00:31:06,090
+عندى هنا باخد n بالساعة واحد تعطين x اتنين طب انا
+
+243
+00:31:06,090 --> 00:31:12,210
+عندى x واحد اكبر من واحد هذا بيقدى انه مخلوق x
+
+244
+00:31:12,210 --> 00:31:25,390
+واحد اصغر من واحد وبالتالي
+
+245
+00:31:33,910 --> 00:31:44,010
+إذا و هذا طبعا عدد موجب أكيد و أصغر من واحد إذا
+
+246
+00:31:44,010 --> 00:31:48,590
+أنا بطرح .. بطرح من ال .. من ال .. من الاتنين عدد
+
+247
+00:31:48,590 --> 00:31:54,730
+موجب و أصغر من واحد فهذا هيكون يعني أكيد أكبر من
+
+248
+00:31:54,730 --> 00:32:01,540
+واحد أه لأ هذا بدي يكون أصغر من اتنينهذا بالتأكيد
+
+249
+00:32:01,540 --> 00:32:05,980
+أصغر من اتنين لأن هذا عدد موجب هذا عدد موجب في
+
+250
+00:32:05,980 --> 00:32:09,480
+النهاية بغض النظر أكبر من واحد ولا أصغر من واحد
+
+251
+00:32:09,480 --> 00:32:15,440
+لما أطرح أنا عدد موجب من عدد العدد بصغر صح فإذا x
+
+252
+00:32:15,440 --> 00:32:23,900
+اتنين أصغر من اتنين طب و x تلاتة بساوة اتنين سالب
+
+253
+00:32:23,900 --> 00:32:25,540
+واحد على x اتنين
+
+254
+00:32:30,440 --> 00:32:35,840
+برضه هذا عدد موجب فهيكون هذا اصغر من ايه من اتنين
+
+255
+00:32:35,840 --> 00:32:44,960
+و هكذا اذا و طبعا x واحد وهذا
+
+256
+00:32:44,960 --> 00:32:51,740
+العدد اصغر من واحدفهذا اكيد هيطلع اكبر من الواحد
+
+257
+00:32:51,740 --> 00:32:56,460
+اذا هذا هيكون اكبر من واحد و هذا اكبر من واحد اذا
+
+258
+00:32:56,460 --> 00:33:00,880
+واضح ان حدود ال sequence هتكون محصورة بين واحد و
+
+259
+00:33:00,880 --> 00:33:09,880
+اتنين اذا بقدر انا اعمل ادعي بقدر ادعي اقول claim
+
+260
+00:33:09,880 --> 00:33:13,720
+واحد
+
+261
+00:33:13,720 --> 00:33:16,200
+ان ال ..
+
+262
+00:33:21,340 --> 00:33:26,800
+إن Xn أكبر من أو ساوى الواحد أصغر من أو ساوى اتنين
+
+263
+00:33:26,800 --> 00:33:31,840
+لكل N طبعا
+
+264
+00:33:31,840 --> 00:33:41,140
+هذا يعني ممكن برهانه by induction طيب
+
+265
+00:33:41,140 --> 00:33:46,280
+ال .. إذا هنا prove it
+
+266
+00:33:49,440 --> 00:34:00,540
+prove it by induction الكلام
+
+267
+00:34:00,540 --> 00:34:05,860
+التاني ان
+
+268
+00:34:05,860 --> 00:34:14,020
+ال sequence تبعتي بتطلع decreasing x
+
+269
+00:34:14,020 --> 00:34:15,820
+in is decreasing
+
+270
+00:34:21,770 --> 00:34:27,350
+يعني xn أكبر من أو ساوي xn زايد one for every n
+
+271
+00:34:27,350 --> 00:34:33,590
+belonging to n to
+
+272
+00:34:33,590 --> 00:34:41,110
+see this لبرهان ذلك to see this لبرهان ذلك note
+
+273
+00:34:41,110 --> 00:34:47,550
+that note
+
+274
+00:34:47,550 --> 00:34:48,130
+first
+
+275
+00:34:51,100 --> 00:35:05,320
+لاحظى اولا انه x n minus واحد لكل تربية لو اخدت حد
+
+276
+00:35:05,320 --> 00:35:11,120
+رقم n واطرحت منه واحد وربعته هذا مربع كامل فهذا
+
+277
+00:35:11,120 --> 00:35:17,560
+اكيد اكبر من أو يساوي سفر اى مربع كامل اى مربع
+
+278
+00:35:17,560 --> 00:35:23,290
+كامل لأى عدد حقيقي بيطلع غير سالمطبعا هذا لما
+
+279
+00:35:23,290 --> 00:35:30,610
+نربّه بيطلع x x n squared minus اتنين x n plus one
+
+280
+00:35:30,610 --> 00:35:40,470
+وهذا المجموع من
+
+281
+00:35:40,470 --> 00:35:44,690
+المتباينة هذه بنستنتج هذا بيقدّي
+
+282
+00:35:55,680 --> 00:36:10,260
+هذا بيقدي انه اتنين X N زائد واحد او
+
+283
+00:36:10,260 --> 00:36:18,840
+هذا بيقدي انه XXn تربية أكبر من أو ساوي هاي Xn
+
+284
+00:36:18,840 --> 00:36:24,340
+تربية ودي هذا عن ناحية التانية لاحظي هذا كله أكبر
+
+285
+00:36:24,340 --> 00:36:27,820
+من أو ساوي سبر فودي هذا عن ناحية التانية بطلع Xn
+
+286
+00:36:27,820 --> 00:36:33,720
+تربية أكبر من أو ساوي اتنين Xn سالب واحد وهذا
+
+287
+00:36:33,720 --> 00:36:40,660
+الكلام صحيح لكل N وهذا
+
+288
+00:36:40,660 --> 00:36:55,140
+بقدربدوره انه xn xn
+
+289
+00:36:55,140 --> 00:37:06,760
+أكبر من أو يساوي اتنين negative واحد
+
+290
+00:37:06,760 --> 00:37:07,820
+على xn
+
+291
+00:37:18,300 --> 00:37:23,720
+إذا أنا جسمي إضرب في واحد على xn ال xn هنا عدد ال
+
+292
+00:37:23,720 --> 00:37:30,200
+.. ال xn موجة بقى ال xn كلها عداد موجة بقى لاحظي
+
+293
+00:37:30,200 --> 00:37:40,640
+انت هنا .. ان احنا ضربنا في xnعدد موجب او لأ جسمنا
+
+294
+00:37:40,640 --> 00:37:48,360
+او ضربنا في واحد على اكس ان هذا عدد موجب فبطلع
+
+295
+00:37:48,360 --> 00:37:52,100
+عندي اكس ان و شريط المتبانى طبق زي ما هي و اتنين
+
+296
+00:37:52,100 --> 00:37:56,500
+سالب واحد على اكس ان الان هذا by definition of the
+
+297
+00:37:56,500 --> 00:38:00,860
+sequenceمن ال recursive formula هي ال recursive
+
+298
+00:38:00,860 --> 00:38:04,720
+formula او ال inductive formula بتقول ان هذا الفرق
+
+299
+00:38:04,720 --> 00:38:09,900
+بتطلع xn زاد واحد اذا الكلام هذا صحيح لكل n
+
+300
+00:38:09,900 --> 00:38:15,900
+وبالتالي اذا هيطلع اندي xn اكبر من أو ساوي xn زاد
+
+301
+00:38:15,900 --> 00:38:24,140
+واحد لكل n اذا ال sequence xn is decreasing متنقصة
+
+302
+00:38:26,080 --> 00:38:35,420
+الان من ال claims واحد و اتنين تطلع now x
+
+303
+00:38:35,420 --> 00:38:40,700
+in is
+
+304
+00:38:40,700 --> 00:38:44,460
+decreasing and bounded
+
+305
+00:38:48,230 --> 00:38:52,870
+حسب claim واحد و claim اتنين so by monotone
+
+306
+00:38:52,870 --> 00:39:03,610
+convergence theorem xn converges say limit xn
+
+307
+00:39:03,610 --> 00:39:10,670
+بالساوي x for some x ينتمي الى R الان بنجيب قيمة
+
+308
+00:39:10,670 --> 00:39:22,760
+ال limit اللي هي ال Xفنرجع لل inductive formula to
+
+309
+00:39:22,760 --> 00:39:34,360
+find x we have من ال inductive formula أنا عندي ال
+
+310
+00:39:34,360 --> 00:39:44,140
+limit ل x n plus one equals two بالساوية اتنين
+
+311
+00:39:44,140 --> 00:39:50,820
+minusواحد على limit xm هذا لما اخد ال limit
+
+312
+00:39:50,820 --> 00:39:57,140
+للطرفين في ال inductive formula طب هذا طرف الشمال
+
+313
+00:39:57,140 --> 00:40:03,530
+بساوي x و الطرف اليمين واحد على xالان حل المعادلة
+
+314
+00:40:03,530 --> 00:40:08,510
+هاد في X اضرب في X بطلع عندي X تربيع سالب اتنين X
+
+315
+00:40:08,510 --> 00:40:14,770
+موجة بواحد بساوي سفر وانت بتحلل الى X موجة باتنين
+
+316
+00:40:14,770 --> 00:40:25,550
+X سالب واحد الكل تربيع بساوي سفر فبطلع X بساوي
+
+317
+00:40:25,550 --> 00:40:31,630
+واحدو هذا صحيح لأن ال x in لحظوا في claim واحد x
+
+318
+00:40:31,630 --> 00:40:35,150
+in معصورة بين واحد و اتنين اذا ال limit تبقى بتطلع
+
+319
+00:40:35,150 --> 00:40:40,530
+معصورة بين واحد و اتنين فالجواب واحد مقبول اذا هذا
+
+320
+00:40:40,530 --> 00:40:49,890
+هو هاي ال limit طلعت بتساوي واحد تمام في
+
+321
+00:40:49,890 --> 00:40:51,010
+اي أسئلة تانية
+
+322
+00:41:02,130 --> 00:41:06,830
+في معناه وجهة انحال كمان سؤال اذا بتحبه سيكشن
+
+323
+00:41:06,830 --> 00:41:08,210
+البعده تلاتة اربعة
+
+324
+00:41:26,730 --> 00:41:33,870
+سيكشن تلاتة اربعة فش ولا سؤال عندكم
+
+325
+00:41:33,870 --> 00:41:44,030
+فحللكم
+
+326
+00:41:44,030 --> 00:41:49,390
+سؤال يحداش لانه واضح ان انتوا مش دارسين فنحل
+
+327
+00:41:49,390 --> 00:41:52,370
+السؤال هيك انا هحلكم يعني من هندي
+
+328
+00:41:57,800 --> 00:42:07,280
+إذن سؤال 11 سيكشن تلاتة أربعة suppose
+
+329
+00:42:07,280 --> 00:42:10,860
+افترضي
+
+330
+00:42:10,860 --> 00:42:19,320
+ان xn أكبر من أو ساوي سفر for every natural number
+
+331
+00:42:19,320 --> 00:42:30,510
+n and ال limit لل sequenceسارق one to n في xn
+
+332
+00:42:30,510 --> 00:42:34,150
+exists
+
+333
+00:42:34,150 --> 00:42:39,110
+show
+
+334
+00:42:39,110 --> 00:42:48,490
+برهنة انه ال sequence xn convergence
+
+335
+00:43:42,520 --> 00:43:51,900
+Okay خلّينا نشوف ال .. طيب احنا نشوف solution
+
+336
+00:43:55,820 --> 00:44:00,460
+say احنا فرضين ان ال limit لل sequence هذه exist
+
+337
+00:44:00,460 --> 00:44:07,520
+فافترضي ان ال limit لل sequence سالب واحد as n في
+
+338
+00:44:07,520 --> 00:44:14,720
+xn as n tends to infinity ال limit لل sequence هذه
+
+339
+00:44:14,720 --> 00:44:19,620
+بيساوي x for some x ينتمي ال R
+
+340
+00:44:27,140 --> 00:44:39,900
+الان then the subsequences ال subsequences اللي هي
+
+341
+00:44:39,900 --> 00:44:49,780
+لو سالب
+
+342
+00:44:49,780 --> 00:44:57,030
+واحد قصة اتنين in في x اتنين inهذه الـ Converge لـ
+
+343
+00:44:57,030 --> 00:45:02,030
+X هذه الـ subsequence من السيكوانس هذه بس حدودها
+
+344
+00:45:02,030 --> 00:45:09,210
+الزوجية and كمان ال subsequence اللي حدودها
+
+345
+00:45:09,210 --> 00:45:10,050
+الفردية
+
+346
+00:45:18,430 --> 00:45:22,850
+برضه converge ل X لأن في عندي نظرية بتقول إذا كانت
+
+347
+00:45:22,850 --> 00:45:27,070
+ال sequence convergent ل X فأي subsequence منها
+
+348
+00:45:27,070 --> 00:45:31,270
+بتكون convergent لنفس ال X هذه subsequence من ال
+
+349
+00:45:31,270 --> 00:45:37,890
+sequence هذه أخدت الحدود الزوجية وهذه subsequence
+
+350
+00:45:37,890 --> 00:45:41,470
+من ال sequence هذه اللي هي مدة تالية الحدود
+
+351
+00:45:41,470 --> 00:45:49,920
+الفردية طيب من هنالاحظوا سالب واحد الأس تبعها زوجي
+
+352
+00:45:49,920 --> 00:45:54,820
+تطلع واحد وبالتالي ال sequence هذه هي نفس ال
+
+353
+00:45:54,820 --> 00:46:04,500
+sequence اتنين in عفوا x اتنين in و سالب واحد لما
+
+354
+00:46:04,500 --> 00:46:08,220
+يكون الأس تبعها فارد تطلع سالب واحد إذا هذه سالب
+
+355
+00:46:08,220 --> 00:46:14,040
+يعني سالب ال sequence x اتنين in سالب واحد
+
+356
+00:46:16,730 --> 00:46:35,630
+تمام؟ طيب أنا عندي من الفرض by
+
+357
+00:46:35,630 --> 00:46:40,990
+hypothesis من الفرض أنا عندي xn أكبر من أو ساوى
+
+358
+00:46:40,990 --> 00:46:54,340
+سفر لكل n في n فهذا بيدّيإنه X2N و أيضا X2N-1 أكبر
+
+359
+00:46:54,340 --> 00:47:01,940
+من أو يساوي سفر لكل N في ال natural numbers وهذا
+
+360
+00:47:01,940 --> 00:47:11,040
+بيقدي بدوره إلى إنه ال X اللي هي من هنا X بيساوي
+
+361
+00:47:11,040 --> 00:47:14,500
+ليه بيساوي limit X2N
+
+362
+00:47:16,870 --> 00:47:22,690
+هي عندي هذا
+
+363
+00:47:22,690 --> 00:47:32,230
+هو هذا من هان بطلع عندي limit x2n بساوي x و من هان
+
+364
+00:47:32,230 --> 00:47:41,810
+بطلع عندي limit سالب x2n سالب واحد بساوي x او
+
+365
+00:47:45,510 --> 00:47:48,610
+السالب واحد بيطلع برا ال limit فبطلع عندي limit
+
+366
+00:47:48,610 --> 00:47:56,770
+x2n سالب واحد بساوي سالب x مظبوط؟
+
+367
+00:47:56,770 --> 00:48:02,170
+إذا هاي عندي أنا limit x2n سالب واحد هذا بيطلع
+
+368
+00:48:02,170 --> 00:48:10,450
+بساوي سالب x أو لأ في الأول ال x بساوي limit x2n
+
+369
+00:48:10,450 --> 00:48:15,280
+وهذا بيطلع أكبر من أو ساوي سفرلأن أنا عندي x2n
+
+370
+00:48:15,280 --> 00:48:19,900
+أكبر من أوسعها 0 لكل n فلما تكون ال sequence
+
+371
+00:48:19,900 --> 00:48:23,800
+حدودها غير سالبة فال limit تبعتها إذا كانت
+
+372
+00:48:23,800 --> 00:48:27,660
+convergent ال limit تبعتها تطلع غير سالبة و كذلك
+
+373
+00:48:27,660 --> 00:48:36,980
+سالب x اللي هي بتساوي limit x2n سالب واحد برضه أنا
+
+374
+00:48:36,980 --> 00:48:42,850
+عندي x2n سالب واحد كلهمأعداد غير سالبة و ال
+
+375
+00:48:42,850 --> 00:48:46,550
+sequence هذه convergent إذا ال limit تبعتها بتطلع
+
+376
+00:48:46,550 --> 00:48:50,450
+غير سالبة إذا
+
+377
+00:48:50,450 --> 00:48:55,950
+أنا من هنا بطلع عندي حاجتين x أكبر من أو ساوى سفر
+
+378
+00:48:55,950 --> 00:49:04,280
+and negative x and negative x أكبر منأو ساوي سفر
+
+379
+00:49:04,280 --> 00:49:10,060
+هذا بيؤدي ان x أكبر من أو ساوي سفر and اضرب في
+
+380
+00:49:10,060 --> 00:49:15,520
+سالب واحد بيطلع x أصغر من أو ساوي سفر الان انا في
+
+381
+00:49:15,520 --> 00:49:19,740
+عندي عدد حقيقي أكبر من أو ساوي سفر and أصغر من أو
+
+382
+00:49:19,740 --> 00:49:30,300
+ساوي سفر بيؤدي ان x بيساوي سفر تمام اذا طلع عندي
+
+383
+00:49:30,300 --> 00:49:31,020
+هنا ال
+
+384
+00:49:34,250 --> 00:49:40,070
+الـ limit هذه x بالساوية سفر الآن
+
+385
+00:49:40,070 --> 00:49:51,850
+تعالوا نثبت now given إمسلن أكبر من السفر it
+
+386
+00:49:51,850 --> 00:49:59,030
+choose how they exist capital
+
+387
+00:49:59,030 --> 00:50:01,550
+N عدد طبيعي
+
+388
+00:50:04,240 --> 00:50:11,660
+بحيث انه لكل n أكبر من أو ساوي capital N هذا بيقدي
+
+389
+00:50:11,660 --> 00:50:23,140
+ان absolute xn-0 بساوي absolute سالب واحد أُس n في
+
+390
+00:50:23,140 --> 00:50:30,960
+xn-0 لأن
+
+391
+00:50:30,960 --> 00:50:33,340
+هنا المفروض اكتب هنا since
+
+392
+00:50:36,490 --> 00:50:44,610
+مش احنا فرضين انه ال since limit سالب واحد قص ان
+
+393
+00:50:44,610 --> 00:50:54,750
+في x in بساوي x بتساوي سفر احنا
+
+394
+00:50:54,750 --> 00:50:58,910
+من الفرض انا عندي ان ال limit هذه موجودة تمام
+
+395
+00:50:58,910 --> 00:51:04,270
+وفرضناها x و اثبتنا ان ال limit تبعتها طلعت x
+
+396
+00:51:04,270 --> 00:51:10,220
+بساوي سفرالان بما انه limit ال sequence هذه بساوي
+
+397
+00:51:10,220 --> 00:51:14,220
+سفر، اذا من تعريف ال limit for any given epsilon
+
+398
+00:51:14,220 --> 00:51:18,540
+يوجد capital N يعتمد على epsilon بحيث لكل N أكبر
+
+399
+00:51:18,540 --> 00:51:22,960
+من أو ساوي capital N بطلع المسافة بين الحد العام
+
+400
+00:51:22,960 --> 00:51:30,200
+وال limit x اللي هي سفر أصغر من epsilonفهيك أنا
+
+401
+00:51:30,200 --> 00:51:36,540
+بطلع عندي absolute xn minus صفر أصغر من إبسلون إذا
+
+402
+00:51:36,540 --> 00:51:40,120
+هان أثبتت أنه لأي إبسلون أكبر من الصفر يوجد
+
+403
+00:51:40,120 --> 00:51:44,100
+capital N يعتمد على إبسلون بحيث لكل N أكبر منه
+
+404
+00:51:44,100 --> 00:51:48,140
+ساوي capital N المسافة بين xn وصفر أصغر من إبسلون
+
+405
+00:51:48,140 --> 00:51:53,040
+فهذا بيقدي أنه هذا معناه حسب تعريف epsilon capital
+
+406
+00:51:53,040 --> 00:51:58,260
+N أنه ال limit لل sequence xn موجودة و بالساوية
+
+407
+00:51:58,260 --> 00:52:01,890
+صفروبالتالي هيك أثبتنا أن ال sequence x in
+
+408
+00:52:01,890 --> 00:52:06,390
+convergence ومش هيك و بس و نهايتها كمان بالساوى
+
+409
+00:52:06,390 --> 00:52:15,170
+سفر okay تمام إذا هذا حل السؤال 11 و نكتفي بهذا
+
+410
+00:52:15,170 --> 00:52:21,690
+القدر من الحل المسائل و نكمل ان شاء الله حل
+
+411
+00:52:21,690 --> 00:52:26,290
+المسائل في المناقشة القادمة يوم السبت الجاي أو يوم
+
+412
+00:52:26,290 --> 00:52:32,830
+الأربع مع الشعبات تانيةفنوقف هنا ونواصل ان شاء
+
+413
+00:52:32,830 --> 00:52:40,790
+الله يوم السبت الجاي تكمل المناخشة السكاشن اللي هي
+
+414
+00:52:40,790 --> 00:52:43,550
+تلاتة أربعة و تلاتة خمسة و تلاتة ستة
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..da293f04bac99b7d47a730eac04c3c0066196cb7
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.json
@@ -0,0 +1 @@
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sequential criterion كمان بره طبخيها على ال function h بما أن x in sequence نهايتها c إذا نهايت صرتها under h يعني limit h of x in as n tends to infinity بساوي capital H hence", "tokens": [10721, 8315, 18871, 16254, 4948, 2423, 39184, 2445, 276, 295, 2031, 9154, 2031, 6055, 39648, 11296, 269, 4724, 3794, 995, 45865, 276, 538, 42881, 46691, 9122, 2304, 7649, 4724, 2288, 3224, 23032, 3555, 9778, 1829, 11296, 15844, 2423, 2445, 276, 4724, 15042, 14739, 2031, 294, 8310, 8717, 11296, 36081, 11296, 269, 11933, 15730, 8717, 11296, 36081, 20328, 43500, 11296, 833, 276, 37495, 22653, 4948, 276, 295, 2031, 294, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 4238, 389, 16678], "avg_logprob": -0.31983025280045874, "compression_ratio": 1.5196078431372548, "no_speech_prob": 0.0, "words": [{"start": 255.54, "end": 255.88, "word": "أنا", "probability": 0.5667724609375}, {"start": 255.88, "end": 256.22, "word": " عندي", "probability": 0.7408447265625}, {"start": 256.22, "end": 256.48, "word": " 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266.38, "word": " in", "probability": 0.814453125}, {"start": 266.38, "end": 267.12, "word": " sequence", "probability": 0.96923828125}, {"start": 267.12, "end": 268.14, "word": " نهايتها", "probability": 0.8797607421875}, {"start": 268.14, "end": 268.46, "word": " c", "probability": 0.82470703125}, {"start": 268.46, "end": 268.78, "word": " إذا", "probability": 0.581298828125}, {"start": 268.78, "end": 269.26, "word": " نهايت", "probability": 0.7293294270833334}, {"start": 269.26, "end": 269.88, "word": " صرتها", "probability": 0.7880859375}, {"start": 269.88, "end": 270.68, "word": " under", "probability": 0.89404296875}, {"start": 270.68, "end": 271.3, "word": " h", "probability": 0.80322265625}, {"start": 271.3, "end": 272.36, "word": " يعني", "probability": 0.806640625}, {"start": 272.36, "end": 272.8, "word": " limit", "probability": 0.98291015625}, {"start": 272.8, "end": 274.12, "word": " h", "probability": 0.841796875}, {"start": 274.12, "end": 274.46, "word": " of", "probability": 0.89013671875}, {"start": 274.46, "end": 274.92, "word": " x", "probability": 0.98828125}, {"start": 274.92, "end": 275.46, "word": " in", "probability": 0.7646484375}, {"start": 275.46, "end": 276.72, "word": " as", "probability": 0.85546875}, {"start": 276.72, "end": 277.04, "word": " n", "probability": 0.5458984375}, {"start": 277.04, "end": 277.3, "word": " tends", "probability": 0.72705078125}, {"start": 277.3, "end": 277.44, "word": " to", "probability": 0.87890625}, {"start": 277.44, "end": 277.94, "word": " infinity", "probability": 0.8818359375}, {"start": 277.94, "end": 278.88, "word": " بساوي", "probability": 0.9356689453125}, {"start": 278.88, "end": 279.46, "word": " capital", "probability": 0.4599609375}, {"start": 279.46, "end": 279.86, "word": " H", "probability": 0.8994140625}, {"start": 279.86, "end": 283.84, "word": " hence", "probability": 0.728515625}], "temperature": 1.0}, {"id": 10, "seek": 31022, "start": 285.84, "end": 310.22, "text": "وبالتالي ال limit ل f على h of x لما x تقول ل xn لما n تقول ل infinity هذا بساوي limit", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 4948, 5296, 283, 15844, 276, 295, 2031, 5296, 15042, 2031, 6055, 39648, 5296, 2031, 77, 5296, 15042, 297, 6055, 39648, 5296, 13202, 23758, 4724, 3794, 995, 45865, 4948], "avg_logprob": -0.2280133877481733, "compression_ratio": 1.2653061224489797, "no_speech_prob": 0.0, "words": [{"start": 285.84, "end": 286.76, "word": "وبالتالي", "probability": 0.90751953125}, {"start": 286.76, "end": 287.06, "word": " ال", "probability": 0.274658203125}, {"start": 287.06, "end": 287.42, "word": " limit", "probability": 0.7294921875}, {"start": 287.42, "end": 289.06, "word": " ل", "probability": 0.87646484375}, {"start": 289.06, "end": 289.46, "word": " f", "probability": 0.1868896484375}, {"start": 289.46, "end": 289.72, "word": " على", "probability": 0.724609375}, {"start": 289.72, "end": 290.2, "word": " h", "probability": 0.89501953125}, {"start": 290.2, "end": 292.4, 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{"start": 308.64, "end": 309.38, "word": " بساوي", "probability": 0.85595703125}, {"start": 309.38, "end": 310.22, "word": " limit", "probability": 0.7744140625}], "temperature": 1.0}, {"id": 11, "seek": 34114, "start": 312.84, "end": 341.14, "text": "f of x,n على h of x,n لما n تقول infinity ويساوي انا انا اندي limit h of x,n exist وبيستويش سفر وبيستويش سفر فممكن استخدم قوانين النهايات لسيكوانس فlimit sequence على limit sequence بساوي limit البسط", "tokens": [69, 295, 2031, 11, 77, 15844, 276, 295, 2031, 11, 77, 5296, 15042, 297, 6055, 39648, 13202, 4032, 1829, 3794, 995, 45865, 1975, 8315, 1975, 8315, 16472, 16254, 4948, 276, 295, 2031, 11, 77, 2514, 4032, 21292, 14851, 45865, 8592, 8608, 5172, 2288, 4032, 21292, 14851, 45865, 8592, 8608, 5172, 2288, 6156, 2304, 43020, 44713, 9778, 40448, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 5296, 3794, 1829, 4117, 2407, 7649, 3794, 6156, 4197, 270, 8310, 15844, 4948, 8310, 4724, 3794, 995, 45865, 4948, 29739, 3794, 9566], 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0.6511962890625}, {"start": 329.14, "end": 329.56, "word": " سفر", "probability": 0.83154296875}, {"start": 329.56, "end": 331.26, "word": " وبيستويش", "probability": 0.852880859375}, {"start": 331.26, "end": 331.6, "word": " سفر", "probability": 0.99169921875}, {"start": 331.6, "end": 332.02, "word": " فممكن", "probability": 0.93896484375}, {"start": 332.02, "end": 332.52, "word": " استخدم", "probability": 0.94384765625}, {"start": 332.52, "end": 333.02, "word": " قوانين", "probability": 0.9901123046875}, {"start": 333.02, "end": 333.76, "word": " النهايات", "probability": 0.9332275390625}, {"start": 333.76, "end": 335.08, "word": " لسيكوانس", "probability": 0.7633928571428571}, {"start": 335.08, "end": 336.5, "word": " فlimit", "probability": 0.7307942708333334}, {"start": 336.5, "end": 337.02, "word": " sequence", "probability": 0.9736328125}, {"start": 337.02, "end": 337.24, "word": " على", "probability": 0.66455078125}, {"start": 337.24, "end": 337.5, "word": " limit", "probability": 0.95654296875}, {"start": 337.5, "end": 338.26, "word": " sequence", "probability": 0.9833984375}, {"start": 338.26, "end": 340.1, "word": " بساوي", "probability": 0.859619140625}, {"start": 340.1, "end": 340.42, "word": " limit", "probability": 0.974609375}, {"start": 340.42, "end": 341.14, "word": " البسط", "probability": 0.765625}], "temperature": 1.0}, {"id": 12, "seek": 37185, "start": 344.99, "end": 371.85, "text": "limit ال sequence في ال bus على limit ال sequence في المقام و limit ال sequence في المقام بيساوي سفر اذا انا بقدر ايه اقول limit ال quotient بيساوي the quotient of the limits وهذا بيطلع limit ال bus تطلع L limit المقام H وهذا البنية", "tokens": [4197, 270, 2423, 8310, 8978, 2423, 1255, 15844, 4948, 2423, 8310, 8978, 9673, 4587, 10943, 4032, 4948, 2423, 8310, 8978, 9673, 4587, 10943, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 1975, 15730, 1975, 8315, 4724, 28543, 2288, 1975, 1829, 3224, 1975, 39648, 4948, 2423, 9641, 1196, 4724, 1829, 3794, 995, 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{"start": 357.87, "end": 358.01, "word": " انا", "probability": 0.6240234375}, {"start": 358.01, "end": 358.35, "word": " بقدر", "probability": 0.9474283854166666}, {"start": 358.35, "end": 358.79, "word": " ايه", "probability": 0.9733072916666666}, {"start": 358.79, "end": 359.41, "word": " اقول", "probability": 0.83154296875}, {"start": 359.41, "end": 359.73, "word": " limit", "probability": 0.93994140625}, {"start": 359.73, "end": 359.97, "word": " ال", "probability": 0.84130859375}, {"start": 359.97, "end": 360.43, "word": " quotient", "probability": 0.939697265625}, {"start": 360.43, "end": 360.89, "word": " بيساوي", "probability": 0.95390625}, {"start": 360.89, "end": 361.09, "word": " the", "probability": 0.66552734375}, {"start": 361.09, "end": 361.65, "word": " quotient", "probability": 0.989013671875}, {"start": 361.65, "end": 362.25, "word": " of", "probability": 0.9853515625}, {"start": 362.25, "end": 362.41, "word": " the", "probability": 0.814453125}, {"start": 362.41, 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656.08, "end": 657.7, "word": " صح؟", "probability": 0.7952473958333334}, {"start": 657.7, "end": 659.26, "word": " و", "probability": 0.82421875}, {"start": 659.26, "end": 659.82, "word": " لو", "probability": 0.861328125}, {"start": 659.82, "end": 660.06, "word": " أنا", "probability": 0.81884765625}, {"start": 660.06, "end": 660.42, "word": " بدي", "probability": 0.7213134765625}, {"start": 660.42, "end": 660.86, "word": " أكون", "probability": 0.890380859375}, {"start": 660.86, "end": 661.16, "word": " هذا", "probability": 0.96044921875}, {"start": 661.16, "end": 661.96, "word": " خليه", "probability": 0.7898763020833334}], "temperature": 1.0}, {"id": 23, "seek": 69089, "start": 665.31, "end": 690.89, "text": "وبدي في النهاية هذا يكون أصغر من epsilon صح؟ إذا كيف بدي أخد ال delta؟ جدر ال c في epsilon اه okay تمام؟ إذا هنا هذا بيقدي أن ال delta ممكن أخدها أي عدد أصغر من أو ساوي طبعا عدد موجب وأصغر من أو ساوي جدر ال c في epsilon", "tokens": [37746, 16254, 8978, 28239, 11296, 10632, 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"word": " ال", "probability": 0.76416015625}, {"start": 681.83, "end": 682.19, "word": " delta", "probability": 0.95166015625}, {"start": 682.19, "end": 682.51, "word": " ممكن", "probability": 0.977294921875}, {"start": 682.51, "end": 683.07, "word": " أخدها", "probability": 0.9171142578125}, {"start": 683.07, "end": 683.81, "word": " أي", "probability": 0.7734375}, {"start": 683.81, "end": 684.21, "word": " عدد", "probability": 0.9827473958333334}, {"start": 684.21, "end": 684.69, "word": " أصغر", "probability": 0.99072265625}, {"start": 684.69, "end": 684.85, "word": " من", "probability": 0.73388671875}, {"start": 684.85, "end": 684.99, "word": " أو", "probability": 0.85888671875}, {"start": 684.99, "end": 685.63, "word": " ساوي", "probability": 0.9295247395833334}, {"start": 685.63, "end": 686.45, "word": " طبعا", "probability": 0.9052734375}, {"start": 686.45, "end": 686.83, "word": " عدد", "probability": 0.9855143229166666}, {"start": 686.83, "end": 687.31, "word": " موجب", "probability": 0.9713541666666666}, {"start": 687.31, "end": 687.87, "word": " وأصغر", "probability": 0.9095458984375}, {"start": 687.87, "end": 688.09, "word": " من", "probability": 0.99658203125}, {"start": 688.09, "end": 688.31, "word": " أو", "probability": 0.97314453125}, {"start": 688.31, "end": 688.85, "word": " ساوي", "probability": 0.9733072916666666}, {"start": 688.85, "end": 689.27, "word": " جدر", "probability": 0.9951171875}, {"start": 689.27, "end": 689.45, "word": " ال", "probability": 0.93212890625}, {"start": 689.45, "end": 689.81, "word": " c", "probability": 0.92529296875}, {"start": 689.81, "end": 690.51, "word": " في", "probability": 0.98828125}, {"start": 690.51, "end": 690.89, "word": " epsilon", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 24, "seek": 71480, "start": 692.46, "end": 714.8, "text": "عشان يطلع المقدار هذا أصغر من إبسلون بالتالي المقدار هذا أصغر من إبسلون إذا شوفتوا كيف نجيب الـ delta إذا نجيب نقول let epsilon let epsilon أكبر من السفر be given choose delta بتساوي", "tokens": [3615, 8592, 7649, 7251, 9566, 1211, 3615, 9673, 28543, 9640, 23758, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 20666, 2655, 6027, 1829, 9673, 28543, 9640, 23758, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 11933, 15730, 13412, 38688, 2655, 14407, 9122, 33911, 8717, 7435, 1829, 3555, 2423, 39184, 8289, 11933, 15730, 8717, 7435, 1829, 3555, 8717, 39648, 718, 17889, 718, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 312, 2212, 2826, 8289, 39894, 3794, 995, 45865], "avg_logprob": -0.23647103731225178, "compression_ratio": 1.7245508982035929, "no_speech_prob": 0.0, "words": [{"start": 692.46, "end": 692.96, "word": "عشان", "probability": 0.7556966145833334}, {"start": 692.96, "end": 693.32, "word": " يطلع", "probability": 0.8721923828125}, {"start": 693.32, "end": 693.94, "word": " المقدار", "probability": 0.9111328125}, {"start": 693.94, "end": 694.28, "word": " هذا", "probability": 0.875}, 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السفر", "probability": 0.8349609375}, {"start": 707.64, "end": 707.94, "word": " be", "probability": 0.2237548828125}, {"start": 707.94, "end": 708.58, "word": " given", "probability": 0.9013671875}, {"start": 708.58, "end": 711.2, "word": " choose", "probability": 0.3564453125}, {"start": 711.2, "end": 713.84, "word": " delta", "probability": 0.83984375}, {"start": 713.84, "end": 714.8, "word": " بتساوي", "probability": 0.9183349609375}], "temperature": 1.0}, {"id": 25, "seek": 73291, "start": 716.33, "end": 732.91, "text": "الجذر ال C هذا عدد موجب ضرب إمسلن فهذا أكيد بيطلع عدد موجب ويعتمد على إمسلن و هيو بيعتمد على إمسلن then لكل X", "tokens": [6027, 7435, 8848, 2288, 2423, 383, 23758, 6225, 3215, 3215, 3714, 29245, 3555, 48812, 25513, 11933, 2304, 3794, 1211, 1863, 6156, 3224, 15730, 5551, 4117, 25708, 4724, 1829, 9566, 1211, 3615, 6225, 3215, 3215, 3714, 29245, 3555, 4032, 1829, 34268, 2304, 3215, 15844, 11933, 2304, 3794, 1211, 1863, 4032, 39896, 2407, 4724, 1829, 34268, 2304, 3215, 15844, 11933, 2304, 3794, 1211, 1863, 550, 5296, 28820, 1783], "avg_logprob": -0.24207089952568508, "compression_ratio": 1.5365853658536586, "no_speech_prob": 0.0, "words": [{"start": 716.33, "end": 717.01, "word": "الجذر", "probability": 0.69512939453125}, {"start": 717.01, "end": 717.21, "word": " ال", "probability": 0.73193359375}, {"start": 717.21, "end": 717.51, "word": " C", "probability": 0.275634765625}, {"start": 717.51, "end": 717.93, "word": " هذا", "probability": 0.6220703125}, {"start": 717.93, "end": 718.31, "word": " عدد", "probability": 0.9417317708333334}, {"start": 718.31, "end": 718.91, "word": " موجب", "probability": 0.9690755208333334}, {"start": 718.91, "end": 720.29, "word": " ضرب", "probability": 0.862548828125}, {"start": 720.29, "end": 720.87, "word": " إمسلن", "probability": 0.677734375}, {"start": 720.87, "end": 721.41, "word": " فهذا", "probability": 0.7490234375}, {"start": 721.41, "end": 721.79, "word": " أكيد", "probability": 0.951171875}, {"start": 721.79, "end": 722.19, "word": " بيطلع", "probability": 0.832275390625}, {"start": 722.19, "end": 722.49, "word": " عدد", "probability": 0.9793294270833334}, {"start": 722.49, "end": 722.99, "word": " موجب", "probability": 0.99560546875}, {"start": 722.99, "end": 724.33, "word": " ويعتمد", "probability": 0.8439453125}, {"start": 724.33, "end": 724.61, "word": " على", "probability": 0.42236328125}, {"start": 724.61, "end": 725.07, "word": " إمسلن", "probability": 0.944140625}, {"start": 725.07, "end": 725.23, "word": " و", "probability": 0.351806640625}, {"start": 725.23, "end": 725.67, "word": " هيو", "probability": 0.580810546875}, {"start": 725.67, "end": 726.37, "word": " بيعتمد", "probability": 0.843310546875}, {"start": 726.37, "end": 726.57, "word": " على", "probability": 0.8564453125}, {"start": 726.57, "end": 727.55, "word": " إمسلن", "probability": 0.991796875}, {"start": 727.55, "end": 730.87, "word": " then", "probability": 0.673828125}, {"start": 730.87, "end": 732.47, "word": " لكل", "probability": 0.970458984375}, {"start": 732.47, "end": 732.91, "word": " X", "probability": 0.69775390625}], "temperature": 1.0}, {"id": 26, "seek": 75631, "start": 735.01, "end": 756.31, "text": "بحيث absolute x minus c أكبر من سفر أصغر من الـ delta هذه هذا بتضمن أن absolute جذر الـ x minus جذر الـ c قلنا هذا طلع أصغر من أو يساوي", "tokens": [3555, 5016, 1829, 12984, 8236, 2031, 3175, 269, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 2423, 39184, 8289, 29538, 23758, 39894, 11242, 27842, 14739, 8236, 10874, 8848, 2288, 2423, 39184, 2031, 3175, 10874, 8848, 2288, 2423, 39184, 269, 12174, 1211, 8315, 23758, 23032, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865], "avg_logprob": -0.2123463104982845, "compression_ratio": 1.5073529411764706, "no_speech_prob": 0.0, "words": [{"start": 735.01, "end": 735.67, "word": "بحيث", "probability": 0.85113525390625}, {"start": 735.67, "end": 736.19, "word": " absolute", "probability": 0.490966796875}, {"start": 736.19, "end": 736.85, "word": " x", "probability": 0.642578125}, {"start": 736.85, "end": 737.39, "word": " minus", "probability": 0.4697265625}, {"start": 737.39, "end": 737.75, "word": " c", "probability": 0.78515625}, {"start": 737.75, "end": 738.29, "word": " أكبر", "probability": 0.9345703125}, {"start": 738.29, "end": 738.53, "word": " من", "probability": 0.9951171875}, {"start": 738.53, "end": 739.01, "word": " سفر", "probability": 0.77099609375}, {"start": 739.01, "end": 740.57, "word": " أصغر", "probability": 0.9512939453125}, {"start": 740.57, "end": 740.75, "word": " من", "probability": 0.99609375}, {"start": 740.75, "end": 741.03, "word": " الـ", "probability": 0.716064453125}, {"start": 741.03, "end": 741.29, "word": " delta", "probability": 0.48583984375}, {"start": 741.29, "end": 741.79, "word": " هذه", "probability": 0.59814453125}, {"start": 741.79, "end": 743.21, "word": " هذا", "probability": 0.60205078125}, {"start": 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plus f of y", "tokens": [6027, 3794, 33604, 6027, 2272, 1975, 25513, 27884, 1975, 2655, 1863, 9957, 8978, 18871, 16254, 2445, 283, 490, 497, 281, 497, 1270, 300, 283, 295, 2031, 1804, 288, 4724, 3794, 995, 45865, 283, 295, 2031, 1804, 283, 295, 288], "avg_logprob": -0.24316406026482582, "compression_ratio": 1.103448275862069, "no_speech_prob": 0.0, "words": [{"start": 919.79, "end": 920.37, "word": "السؤال", "probability": 0.84521484375}, {"start": 920.37, "end": 920.85, "word": " 12", "probability": 0.2247314453125}, {"start": 920.85, "end": 921.81, "word": " اربعة", "probability": 0.6717122395833334}, {"start": 921.81, "end": 922.49, "word": " اتنين", "probability": 0.8795166015625}, {"start": 922.49, "end": 931.09, "word": " في", "probability": 0.1925048828125}, {"start": 931.09, "end": 931.57, "word": " عندي", "probability": 0.927490234375}, {"start": 931.57, "end": 932.17, "word": " function", "probability": 0.87548828125}, {"start": 932.17, "end": 932.97, "word": " f", "probability": 0.63916015625}, {"start": 932.97, "end": 934.41, "word": " from", "probability": 0.85302734375}, {"start": 934.41, "end": 934.99, "word": " R", "probability": 0.830078125}, {"start": 934.99, "end": 935.23, "word": " to", "probability": 0.95068359375}, {"start": 935.23, "end": 935.83, "word": " R", "probability": 0.99462890625}, {"start": 935.83, "end": 938.85, "word": " such", "probability": 0.86279296875}, {"start": 938.85, "end": 939.43, "word": " that", "probability": 0.95947265625}, {"start": 939.43, "end": 941.05, "word": " f", "probability": 0.6748046875}, {"start": 941.05, "end": 942.65, "word": " of", "probability": 0.5634765625}, {"start": 942.65, "end": 943.09, "word": " x", "probability": 0.59033203125}, {"start": 943.09, "end": 943.53, "word": " plus", "probability": 0.9091796875}, {"start": 943.53, "end": 944.15, "word": " y", "probability": 0.97705078125}, {"start": 944.15, "end": 946.19, "word": " بساوي", "probability": 0.879638671875}, {"start": 946.19, "end": 946.57, "word": " f", "probability": 0.91259765625}, {"start": 946.57, "end": 946.77, "word": " of", "probability": 0.93701171875}, {"start": 946.77, "end": 947.09, "word": " x", "probability": 0.9912109375}, {"start": 947.09, "end": 947.51, "word": " plus", "probability": 0.97216796875}, {"start": 947.51, "end": 947.87, "word": " f", "probability": 0.88525390625}, {"start": 947.87, "end": 948.13, "word": " of", "probability": 0.982421875}, {"start": 948.13, "end": 948.57, "word": " y", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 33, "seek": 97682, "start": 949.84, "end": 976.82, "text": "for every x و y in R assume ان ال limit f of x as x tends to zero بسوى عدد L exists", "tokens": [2994, 633, 2031, 4032, 288, 294, 497, 6552, 16472, 2423, 4948, 283, 295, 2031, 382, 2031, 12258, 281, 4018, 4724, 3794, 2407, 7578, 6225, 3215, 3215, 441, 8198], "avg_logprob": -0.3100754351451479, "compression_ratio": 1.0106382978723405, "no_speech_prob": 0.0, "words": [{"start": 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"probability": 0.18017578125}, {"start": 967.34, "end": 967.74, "word": " x", "probability": 0.97998046875}, {"start": 967.74, "end": 968.3, "word": " as", "probability": 0.93701171875}, {"start": 968.3, "end": 968.76, "word": " x", "probability": 0.97314453125}, {"start": 968.76, "end": 969.22, "word": " tends", "probability": 0.8330078125}, {"start": 969.22, "end": 971.82, "word": " to", "probability": 0.982421875}, {"start": 971.82, "end": 972.5, "word": " zero", "probability": 0.59912109375}, {"start": 972.5, "end": 973.74, "word": " بسوى", "probability": 0.7501220703125}, {"start": 973.74, "end": 974.26, "word": " عدد", "probability": 0.9708658854166666}, {"start": 974.26, "end": 974.62, "word": " L", "probability": 0.7958984375}, {"start": 974.62, "end": 976.82, "word": " exists", "probability": 0.6328125}], "temperature": 1.0}, {"id": 34, "seek": 100495, "start": 979.07, "end": 1004.95, "text": "يعني أدب real number prove حاجتي الواحد ال بساوي سفر لان limit f of x", "tokens": 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function", "probability": 0.806640625}, {"start": 1054.19, "end": 1054.53, "word": " هذه", "probability": 0.401123046875}, {"start": 1054.53, "end": 1055.19, "word": " بتحقق", "probability": 0.8428955078125}, {"start": 1055.19, "end": 1055.73, "word": " الشرط", "probability": 0.9278971354166666}, {"start": 1055.73, "end": 1056.09, "word": " هذا", "probability": 0.88232421875}], "temperature": 1.0}, {"id": 37, "seek": 107478, "start": 1056.86, "end": 1074.78, "text": "بنسميه additivity ال function f بتحافظ على عملية الجمع بتاخد مجموعة حاجتين تعطي صورتها مجموعة صورهم فبنقول f أي function بتحقق خاصية زي هذه بنسميها additive يعني دالة جمعية", "tokens": [3555, 1863, 38251, 1829, 3224, 909, 270, 4253, 2423, 2445, 283, 39894, 5016, 31845, 19913, 15844, 6225, 42213, 10632, 25724, 2304, 3615, 39894, 47283, 3215, 3714, 7435, 2304, 2407, 27884, 11331, 26108, 2655, 9957, 37279, 9566, 1829, 20328, 13063, 2655, 11296, 3714, 7435, 2304, 2407, 27884, 20328, 13063, 16095, 6156, 3555, 1863, 39648, 283, 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فكيف ممكن نثبت الكلام هذا نسمي هذا الفرض star", "tokens": [3555, 2655, 5016, 31845, 19913, 15844, 6225, 42213, 10632, 25724, 2304, 3615, 6055, 3555, 3615, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 6156, 3555, 1863, 16606, 15844, 33962, 33546, 10632, 29538, 45164, 25961, 2655, 2423, 2445, 283, 5296, 11296, 4948, 293, 8608, 5172, 2288, 6156, 6027, 4948, 29538, 5296, 31377, 2304, 6055, 30544, 4724, 3794, 995, 45865, 8608, 5172, 2288, 16490, 2304, 2655, 11296, 8608, 5172, 2288, 6156, 4117, 33911, 3714, 43020, 8717, 12984, 3555, 2655, 2423, 28820, 10943, 23758, 8717, 38251, 1829, 23758, 27188, 43042, 3543], "avg_logprob": -0.19140624525872144, "compression_ratio": 1.626865671641791, "no_speech_prob": 0.0, "words": [{"start": 1075.29, "end": 1076.07, "word": "بتحافظ", "probability": 0.9259765625}, {"start": 1076.07, "end": 1076.27, "word": " على", "probability": 0.734375}, {"start": 1076.27, "end": 1076.71, "word": " عملية", "probability": 0.9889322916666666}, {"start": 1076.71, "end": 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of x زاد x بيساوي f of x زاد f of x صح يعني بيساوي اتنين في f of x تمام طيب take limit of both sides take limit", "tokens": [69, 295, 2031, 30767, 18513, 2031, 4724, 1829, 3794, 995, 45865, 283, 295, 2031, 30767, 18513, 283, 295, 2031, 20328, 5016, 37495, 22653, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 8978, 283, 295, 2031, 46811, 10943, 23032, 1829, 3555, 747, 4948, 295, 1293, 4881, 747, 4948], "avg_logprob": -0.21699616860370247, "compression_ratio": 1.438095238095238, "no_speech_prob": 0.0, "words": [{"start": 1131.23, "end": 1131.63, "word": "f", "probability": 0.3203125}, {"start": 1131.63, "end": 1131.85, "word": " of", "probability": 0.307373046875}, {"start": 1131.85, "end": 1132.13, "word": " x", "probability": 0.96875}, {"start": 1132.13, "end": 1132.57, "word": " زاد", "probability": 0.540283203125}, {"start": 1132.57, "end": 1132.85, "word": " x", "probability": 0.962890625}, {"start": 1132.85, "end": 1133.45, "word": " بيساوي", "probability": 0.7292724609375}, 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119172, "start": 1162.62, "end": 1191.72, "text": "of both sides as x tends to zero we get نحصل على انه ال limit ل f ل 2x لما x تقول ل 0 بساوي 2 في ال limit ل f of x لما x تقول ل 0", "tokens": [2670, 1293, 4881, 382, 2031, 12258, 281, 4018, 321, 483, 8717, 5016, 36520, 15844, 16472, 3224, 2423, 4948, 5296, 283, 5296, 568, 87, 5296, 15042, 2031, 6055, 39648, 5296, 1958, 4724, 3794, 995, 45865, 568, 8978, 2423, 4948, 5296, 283, 295, 2031, 5296, 15042, 2031, 6055, 39648, 5296, 1958], "avg_logprob": -0.2198437437415123, "compression_ratio": 1.352, "no_speech_prob": 0.0, "words": [{"start": 1162.62, "end": 1163.18, "word": "of", "probability": 0.42724609375}, {"start": 1163.18, "end": 1163.62, "word": " both", "probability": 0.91064453125}, {"start": 1163.62, "end": 1164.24, "word": " sides", "probability": 0.91357421875}, {"start": 1164.24, "end": 1169.32, "word": " as", "probability": 0.701171875}, {"start": 1169.32, "end": 1169.76, "word": " x", "probability": 0.83984375}, {"start": 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1305.43, "end": 1333.25, "text": "واضح البرهان هنا تمام نبرهن الجزء التاني طيب نبرهن الجزء التاني برضه الجزء التاني فيه له hint فنستخدم ال hint also", "tokens": [2407, 46958, 5016, 2423, 26890, 3224, 7649, 34105, 46811, 10943, 8717, 26890, 3224, 1863, 25724, 11622, 38207, 16712, 7649, 1829, 23032, 1829, 3555, 8717, 26890, 3224, 1863, 25724, 11622, 38207, 16712, 7649, 1829, 4724, 43042, 3224, 25724, 11622, 38207, 16712, 7649, 1829, 8978, 3224, 46740, 12075, 6156, 1863, 14851, 9778, 40448, 2423, 12075, 611], "avg_logprob": -0.09588068181818182, "compression_ratio": 1.7043478260869565, "no_speech_prob": 0.0, "words": [{"start": 1305.43, "end": 1305.93, "word": "واضح", "probability": 0.9860026041666666}, {"start": 1305.93, "end": 1306.73, "word": " البرهان", "probability": 0.845947265625}, {"start": 1306.73, "end": 1306.99, "word": " هنا", "probability": 0.9521484375}, {"start": 1306.99, "end": 1308.59, "word": " تمام", "probability": 0.818603515625}, {"start": 1308.59, "end": 1310.39, 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1350.19, "end": 1351.63, "word": " f", "probability": 0.66943359375}, {"start": 1351.63, "end": 1351.89, "word": " of", "probability": 0.60888671875}, {"start": 1351.89, "end": 1352.41, "word": " x", "probability": 0.8896484375}, {"start": 1352.41, "end": 1354.55, "word": " هي", "probability": 0.92578125}, {"start": 1354.55, "end": 1355.31, "word": " نفسها", "probability": 0.9016927083333334}, {"start": 1355.31, "end": 1355.69, "word": " f", "probability": 0.91357421875}, {"start": 1355.69, "end": 1357.59, "word": " of", "probability": 0.8837890625}, {"start": 1357.59, "end": 1358.03, "word": " x", "probability": 0.9619140625}, {"start": 1358.03, "end": 1358.51, "word": " ثالث", "probability": 0.7830403645833334}, {"start": 1358.51, "end": 1358.87, "word": " c", "probability": 0.68115234375}, {"start": 1358.87, "end": 1359.35, "word": " زائد", "probability": 0.7999674479166666}, {"start": 1359.35, "end": 1359.75, "word": " c", "probability": 0.87890625}, {"start": 1359.75, "end": 1360.75, "word": " صح؟", "probability": 0.89892578125}], "temperature": 1.0}, {"id": 48, "seek": 139310, "start": 1364.78, "end": 1393.1, "text": "و هذا بيساوي F of X minus C زائد F of C تمام طيب هذا صحيح for all C ينتمي ل R و طبعا for all X و for all X ينتمي ل R", "tokens": [2407, 23758, 4724, 1829, 3794, 995, 45865, 479, 295, 1783, 3175, 383, 30767, 16373, 3215, 479, 295, 383, 46811, 10943, 23032, 1829, 3555, 23758, 20328, 5016, 1829, 5016, 337, 439, 383, 7251, 29399, 2304, 1829, 5296, 497, 4032, 23032, 3555, 3615, 995, 337, 439, 1783, 4032, 337, 439, 1783, 7251, 29399, 2304, 1829, 5296, 497], "avg_logprob": -0.22474888179983413, "compression_ratio": 1.361344537815126, "no_speech_prob": 0.0, "words": [{"start": 1364.78, "end": 1365.1, "word": "و", "probability": 0.9150390625}, {"start": 1365.1, "end": 1365.52, "word": " هذا", "probability": 0.4990234375}, {"start": 1365.52, "end": 1366.3, "word": " بيساوي", "probability": 0.8412109375}, {"start": 1366.3, "end": 1372.2, "word": " F", 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"probability": 0.9892578125}, {"start": 1382.82, "end": 1383.24, "word": " for", "probability": 0.72119140625}, {"start": 1383.24, "end": 1383.9, "word": " all", "probability": 0.9404296875}, {"start": 1383.9, "end": 1384.48, "word": " C", "probability": 0.92431640625}, {"start": 1384.48, "end": 1386.08, "word": " ينتمي", "probability": 0.944091796875}, {"start": 1386.08, "end": 1386.2, "word": " ل", "probability": 0.810546875}, {"start": 1386.2, "end": 1386.52, "word": " R", "probability": 0.5361328125}, {"start": 1386.52, "end": 1387.26, "word": " و", "probability": 0.9072265625}, {"start": 1387.26, "end": 1387.58, "word": " طبعا", "probability": 0.968994140625}, {"start": 1387.58, "end": 1387.8, "word": " for", "probability": 0.908203125}, {"start": 1387.8, "end": 1388.18, "word": " all", "probability": 0.95849609375}, {"start": 1388.18, "end": 1388.58, "word": " X", "probability": 0.98876953125}, {"start": 1388.58, "end": 1390.86, "word": " و", "probability": 0.89453125}, {"start": 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موجودة و limit الحد التاني موجودة وبالتالي limit المجموعة بيساوي مجموعة limits فlimit f of x minus c as x tends to c زائد", "tokens": [6027, 9566, 28480, 45595, 20498, 9957, 3714, 7435, 2304, 2407, 27884, 4948, 3714, 7435, 2304, 2407, 27884, 4724, 1829, 3794, 995, 45865, 3714, 7435, 2304, 45367, 3660, 10406, 5296, 33456, 4948, 21542, 3215, 16247, 12610, 2514, 8032, 1863, 8592, 38688, 16472, 4948, 21542, 3215, 16247, 12610, 3714, 29245, 23328, 3660, 4032, 4948, 21542, 3215, 16712, 7649, 1829, 3714, 29245, 23328, 3660, 46599, 6027, 2655, 6027, 1829, 4948, 9673, 7435, 2304, 2407, 27884, 4724, 1829, 3794, 995, 45865, 3714, 7435, 2304, 2407, 27884, 10406, 6156, 4197, 270, 283, 295, 2031, 3175, 269, 382, 2031, 12258, 281, 269, 30767, 16373, 3215], "avg_logprob": -0.18140625402331353, "compression_ratio": 2.1151515151515152, "no_speech_prob": 0.0, "words": [{"start": 1419.74, "end": 1420.28, "word": "الطرف", "probability": 0.7801106770833334}, {"start": 1420.28, "end": 1420.78, "word": " 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"word": " limit", "probability": 0.984375}, {"start": 1431.58, "end": 1432.32, "word": " المجموعة", "probability": 0.96181640625}, {"start": 1432.32, "end": 1433.34, "word": " بيساوي", "probability": 0.98359375}, {"start": 1433.34, "end": 1433.82, "word": " مجموعة", "probability": 0.91123046875}, {"start": 1433.82, "end": 1434.32, "word": " limits", "probability": 0.84326171875}, {"start": 1434.32, "end": 1435.64, "word": " فlimit", "probability": 0.5302734375}, {"start": 1435.64, "end": 1435.9, "word": " f", "probability": 0.716796875}, {"start": 1435.9, "end": 1436.16, "word": " of", "probability": 0.52734375}, {"start": 1436.16, "end": 1436.48, "word": " x", "probability": 0.8994140625}, {"start": 1436.48, "end": 1437.0, "word": " minus", "probability": 0.89599609375}, {"start": 1437.0, "end": 1437.56, "word": " c", "probability": 0.84423828125}, {"start": 1437.56, "end": 1438.64, "word": " as", "probability": 0.841796875}, {"start": 1438.64, "end": 1439.0, "word": " x", "probability": 0.98046875}, {"start": 1439.0, "end": 1439.4, "word": " tends", "probability": 0.80419921875}, {"start": 1439.4, "end": 1439.68, "word": " to", "probability": 0.9873046875}, {"start": 1439.68, "end": 1440.16, "word": " c", "probability": 0.57861328125}, {"start": 1440.16, "end": 1441.16, "word": " زائد", "probability": 0.83447265625}], "temperature": 1.0}, {"id": 51, "seek": 147396, "start": 1448.36, "end": 1473.96, "text": "limit f of x لمّا x تقول لـ c limit f of x لمّا x تقول لـ c", "tokens": [4197, 270, 283, 295, 2031, 32767, 11703, 995, 2031, 6055, 4587, 12610, 5296, 39184, 269, 4948, 283, 295, 2031, 32767, 11703, 995, 2031, 6055, 4587, 12610, 5296, 39184, 269], "avg_logprob": -0.4236979067325592, "compression_ratio": 1.6122448979591837, "no_speech_prob": 0.0, "words": [{"start": 1448.36, "end": 1449.04, "word": "limit", "probability": 0.6568603515625}, {"start": 1449.04, "end": 1449.6, "word": " f", "probability": 0.751953125}, {"start": 1449.6, "end": 1449.92, 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إياها الكتاب فاحنا ممكن نجيبلكم في الامتحان أسئلة و نعطيلكم hint عليها أساسا كبداية للحل أو البرهان الصحي و الشاطرة اللي تستغلها صحي", "tokens": [28814, 15730, 13412, 5172, 2655, 14407, 34105, 37495, 22653, 9122, 33911, 44713, 17082, 1211, 8315, 27188, 43042, 21136, 9640, 4032, 9122, 33911, 44713, 17082, 1211, 8315, 2423, 12075, 33688, 2288, 8592, 18513, 9307, 13672, 1829, 5551, 3615, 9566, 1829, 8315, 11933, 25528, 11296, 33251, 2655, 16758, 6156, 39319, 8315, 3714, 43020, 8717, 7435, 1829, 3555, 23275, 2304, 8978, 2423, 10943, 2655, 5016, 7649, 5551, 3794, 19986, 37977, 4032, 8717, 3615, 9566, 1829, 23275, 2304, 12075, 25894, 11296, 5551, 3794, 32277, 995, 9122, 3555, 28259, 10632, 24976, 5016, 1211, 34051, 2423, 26890, 3224, 7649, 31767, 5016, 1829, 4032, 25124, 41193, 25720, 13672, 1829, 6055, 14851, 17082, 1211, 11296, 20328, 5016, 1829], "avg_logprob": -0.13689470586476024, "compression_ratio": 1.8666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1638.38, "end": 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" of", "probability": 0.331298828125}, {"start": 1747.94, "end": 1748.54, "word": " x", "probability": 0.9443359375}, {"start": 1748.54, "end": 1749.98, "word": " لما", "probability": 0.851318359375}, {"start": 1749.98, "end": 1750.3, "word": " x", "probability": 0.908203125}, {"start": 1750.3, "end": 1750.74, "word": " تقول", "probability": 0.71337890625}, {"start": 1750.74, "end": 1751.04, "word": " لـ", "probability": 0.603515625}, {"start": 1751.04, "end": 1751.3, "word": " c", "probability": 0.6787109375}, {"start": 1751.3, "end": 1752.42, "word": " exists", "probability": 0.475341796875}, {"start": 1752.42, "end": 1758.36, "word": " prove", "probability": 0.44482421875}, {"start": 1758.36, "end": 1760.68, "word": " أن", "probability": 0.54736328125}, {"start": 1760.68, "end": 1761.12, "word": " ال", "probability": 0.5859375}, {"start": 1761.12, "end": 1761.6, "word": " limit", "probability": 0.5322265625}, {"start": 1761.6, "end": 1763.74, "word": " ل", "probability": 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{"start": 2050.7599999999998, "end": 2051.6, "word": " وهذا", "probability": 0.86962890625}, {"start": 2051.6, "end": 2052.28, "word": " باستخدام", "probability": 0.9706217447916666}, {"start": 2052.28, "end": 2052.44, "word": " ال", "probability": 0.88525390625}, {"start": 2052.44, "end": 2052.88, "word": " triangle", "probability": 0.345458984375}, {"start": 2052.88, "end": 2053.78, "word": " inequality", "probability": 0.9658203125}, {"start": 2053.78, "end": 2056.36, "word": " أصغر", "probability": 0.8548583984375}, {"start": 2056.36, "end": 2056.52, "word": " من", "probability": 0.96337890625}, {"start": 2056.52, "end": 2056.68, "word": " أو", "probability": 0.392822265625}, {"start": 2056.68, "end": 2057.2, "word": " ساوي", "probability": 0.720947265625}, {"start": 2057.2, "end": 2057.72, "word": " absolute", "probability": 0.6484375}, {"start": 2057.72, "end": 2058.32, "word": " f", "probability": 0.302001953125}, {"start": 2058.32, "end": 2058.56, "word": " of", "probability": 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0.6735026041666666}, {"start": 2064.8, "end": 2065.06, "word": " تقول", "probability": 0.850341796875}, {"start": 2065.06, "end": 2065.24, "word": " إن", "probability": 0.6103515625}, {"start": 2065.24, "end": 2065.66, "word": " هذا", "probability": 0.8583984375}, {"start": 2065.66, "end": 2065.82, "word": " ال", "probability": 0.8857421875}, {"start": 2065.82, "end": 2066.14, "word": " absolute", "probability": 0.9306640625}, {"start": 2066.14, "end": 2066.7, "word": " value", "probability": 0.9921875}, {"start": 2066.7, "end": 2067.42, "word": " ل", "probability": 0.560546875}, {"start": 2067.42, "end": 2067.82, "word": " absolute", "probability": 0.70947265625}, {"start": 2067.82, "end": 2068.24, "word": " a", "probability": 0.734375}, {"start": 2068.24, "end": 2068.56, "word": " minus", "probability": 0.953125}, {"start": 2068.56, "end": 2068.98, "word": " absolute", "probability": 0.9248046875}, {"start": 2068.98, "end": 2069.4, "word": " b", "probability": 0.96044921875}, {"start": 2069.4, "end": 2069.94, "word": " أصغر", "probability": 0.9949951171875}, {"start": 2069.94, "end": 2070.14, "word": " من", "probability": 0.99462890625}, {"start": 2070.14, "end": 2070.6, "word": " absolute", "probability": 0.92333984375}, {"start": 2070.6, "end": 2071.08, "word": " a", "probability": 0.97705078125}, {"start": 2071.08, "end": 2071.44, "word": " minus", "probability": 0.98828125}, {"start": 2071.44, "end": 2071.74, "word": " b", "probability": 0.9951171875}], "temperature": 1.0}, {"id": 72, "seek": 209242, "start": 2073.58, "end": 2092.42, "text": "طب انا عندى limit f of x لما x اقولها c بالساوي L فممكن اخلي هذا اصغر من اي given epsilon وبالتالي هذه بتصير اصغر من اي epsilon okay تمام اذا هنا خلينا نشوف", "tokens": [9566, 3555, 1975, 8315, 43242, 7578, 4948, 283, 295, 2031, 5296, 15042, 2031, 1975, 39648, 11296, 269, 20666, 3794, 995, 45865, 441, 6156, 2304, 43020, 1975, 9778, 20292, 23758, 1975, 9381, 17082, 2288, 9154, 1975, 1829, 2212, 17889, 4032, 3555, 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epsilon", "probability": 0.69384765625}, {"start": 2081.84, "end": 2083.42, "word": " وبالتالي", "probability": 0.8133951822916666}, {"start": 2083.42, "end": 2083.68, "word": " هذه", "probability": 0.420166015625}, {"start": 2083.68, "end": 2084.2, "word": " بتصير", "probability": 0.888671875}, {"start": 2084.2, "end": 2084.76, "word": " اصغر", "probability": 0.9818115234375}, {"start": 2084.76, "end": 2085.04, "word": " من", "probability": 0.9931640625}, {"start": 2085.04, "end": 2085.58, "word": " اي", "probability": 0.8896484375}, {"start": 2085.58, "end": 2085.98, "word": " epsilon", "probability": 0.88818359375}, {"start": 2085.98, "end": 2087.54, "word": " okay", "probability": 0.34521484375}, {"start": 2087.54, "end": 2088.16, "word": " تمام", "probability": 0.8740234375}, {"start": 2088.16, "end": 2090.18, "word": " اذا", "probability": 0.586669921875}, {"start": 2090.18, "end": 2090.58, "word": " هنا", "probability": 0.958984375}, {"start": 2090.58, "end": 2091.92, "word": " 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"probability": 0.89990234375}, {"start": 2127.48, "end": 2128.22, "word": " ابسلون", "probability": 0.75469970703125}, {"start": 2128.22, "end": 2128.72, "word": " عدد", "probability": 0.9757486979166666}, {"start": 2128.72, "end": 2129.36, "word": " موجب", "probability": 0.9783528645833334}, {"start": 2129.36, "end": 2130.32, "word": " بحيث", "probability": 0.975341796875}, {"start": 2130.32, "end": 2130.74, "word": " انه", "probability": 0.957763671875}, {"start": 2130.74, "end": 2131.2, "word": " لكل", "probability": 0.9794921875}, {"start": 2131.2, "end": 2131.58, "word": " X", "probability": 0.97802734375}, {"start": 2131.58, "end": 2132.38, "word": " ينتمي", "probability": 0.979736328125}, {"start": 2132.38, "end": 2132.8, "word": " إلى", "probability": 0.63720703125}, {"start": 2132.8, "end": 2133.28, "word": " A", "probability": 0.82421875}, {"start": 2133.28, "end": 2134.12, "word": " و", "probability": 0.77001953125}, {"start": 2134.12, "end": 2134.56, "word": " absolute", "probability": 0.420654296875}, {"start": 2134.56, "end": 2135.18, "word": " X", "probability": 0.92822265625}, {"start": 2135.18, "end": 2135.64, "word": " minus", "probability": 0.87890625}, {"start": 2135.64, "end": 2136.02, "word": " C", "probability": 0.95556640625}, {"start": 2136.02, "end": 2136.5, "word": " اصغر", "probability": 0.8563232421875}, {"start": 2136.5, "end": 2136.7, "word": " من", "probability": 0.99365234375}, {"start": 2136.7, "end": 2137.06, "word": " Delta", "probability": 0.806640625}, {"start": 2137.06, "end": 2137.6, "word": " اكبر", "probability": 0.9332682291666666}, {"start": 2137.6, "end": 2137.84, "word": " من", "probability": 0.99658203125}, {"start": 2137.84, "end": 2138.3, "word": " سفر", "probability": 0.7396647135416666}, {"start": 2138.3, "end": 2139.52, "word": " هذا", "probability": 0.87158203125}, {"start": 2139.52, "end": 2140.28, "word": " بيقدي", "probability": 0.705322265625}], "temperature": 1.0}, {"id": 75, "seek": 216357, "start": 2141.49, "end": 2163.57, "text": "إنه absolute f of x minus L أصغر من إبسلم نسمي هذا star نسمي ال implication هذا star hence", "tokens": [28814, 1863, 3224, 8236, 283, 295, 2031, 3175, 441, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 19528, 8717, 38251, 1829, 23758, 3543, 8717, 38251, 1829, 2423, 37814, 23758, 3543, 16678], "avg_logprob": -0.3300781277939677, "compression_ratio": 1.1111111111111112, "no_speech_prob": 0.0, "words": [{"start": 2141.49, "end": 2142.33, "word": "إنه", "probability": 0.43902587890625}, {"start": 2142.33, "end": 2142.81, "word": " absolute", "probability": 0.6484375}, {"start": 2142.81, "end": 2143.45, "word": " f", "probability": 0.57861328125}, {"start": 2143.45, "end": 2143.73, "word": " of", "probability": 0.51220703125}, {"start": 2143.73, "end": 2144.19, "word": " x", "probability": 0.87939453125}, {"start": 2144.19, "end": 2144.95, "word": " minus", "probability": 0.7275390625}, {"start": 2144.95, "end": 2145.55, "word": " L", "probability": 0.654296875}, {"start": 2145.55, "end": 2147.01, "word": " أصغر", "probability": 0.9708251953125}, {"start": 2147.01, "end": 2147.23, "word": " من", "probability": 0.9921875}, {"start": 2147.23, "end": 2147.79, "word": " إبسلم", "probability": 0.68524169921875}, {"start": 2147.79, "end": 2148.35, "word": " نسمي", "probability": 0.814697265625}, {"start": 2148.35, "end": 2148.67, "word": " هذا", "probability": 0.8603515625}, {"start": 2148.67, "end": 2149.47, "word": " star", "probability": 0.6396484375}, {"start": 2149.47, "end": 2151.33, "word": " نسمي", "probability": 0.9029947916666666}, {"start": 2151.33, "end": 2151.43, "word": " ال", "probability": 0.93505859375}, {"start": 2151.43, "end": 2151.89, "word": " implication", "probability": 0.9482421875}, {"start": 2151.89, "end": 2152.31, "word": " هذا", "probability": 0.435302734375}, {"start": 2152.31, "end": 2152.87, "word": " star", "probability": 0.92041015625}, {"start": 2152.87, "end": 2163.57, "word": " hence", 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0.9697265625}, {"start": 2183.94, "end": 2184.74, "word": " لدينا", "probability": 0.86865234375}, {"start": 2184.74, "end": 2185.9, "word": " لو", "probability": 0.81494140625}, {"start": 2185.9, "end": 2186.26, "word": " كان", "probability": 0.98681640625}, {"start": 2186.26, "end": 2186.64, "word": " x", "probability": 0.95166015625}, {"start": 2186.64, "end": 2187.32, "word": " ينتمي", "probability": 0.97802734375}, {"start": 2187.32, "end": 2187.5, "word": " ل", "probability": 0.8798828125}, {"start": 2187.5, "end": 2187.94, "word": " a", "probability": 0.439697265625}, {"start": 2187.94, "end": 2188.96, "word": " و", "probability": 0.76513671875}, {"start": 2188.96, "end": 2189.38, "word": " absolute", "probability": 0.6279296875}, {"start": 2189.38, "end": 2189.98, "word": " x", "probability": 0.931640625}, {"start": 2189.98, "end": 2190.5, "word": " minus", "probability": 0.771484375}, {"start": 2190.5, "end": 2190.84, "word": " c", "probability": 0.82763671875}, {"start": 2190.84, "end": 2191.32, "word": " أكبر", "probability": 0.9288736979166666}, {"start": 2191.32, "end": 2191.56, "word": " من", "probability": 0.99609375}, {"start": 2191.56, "end": 2191.98, "word": " سفر", "probability": 0.74658203125}, {"start": 2191.98, "end": 2192.68, "word": " أصغر", "probability": 0.9515380859375}, {"start": 2192.68, "end": 2194.66, "word": " من", "probability": 0.9833984375}, {"start": 2194.66, "end": 2195.14, "word": " delta", "probability": 0.466064453125}], "temperature": 1.0}, {"id": 77, "seek": 222606, "start": 2197.04, "end": 2226.06, "text": "فهذا بيقدي انه absolute .. absolute f of x minus absolute ال L هذا بيساوي absolute .. absolute f of x minus absolute L", "tokens": [5172, 3224, 15730, 4724, 1829, 4587, 16254, 16472, 3224, 8236, 4386, 8236, 283, 295, 2031, 3175, 8236, 2423, 441, 23758, 4724, 1829, 3794, 995, 45865, 8236, 4386, 8236, 283, 295, 2031, 3175, 8236, 441], "avg_logprob": -0.2500000068119594, "compression_ratio": 1.7195121951219512, "no_speech_prob": 0.0, "words": [{"start": 2197.04, "end": 2197.92, "word": "فهذا", "probability": 0.8732096354166666}, {"start": 2197.92, "end": 2198.62, "word": " بيقدي", "probability": 0.56817626953125}, {"start": 2198.62, "end": 2200.32, "word": " انه", "probability": 0.448486328125}, {"start": 2200.32, "end": 2200.88, "word": " absolute", "probability": 0.78564453125}, {"start": 2200.88, "end": 2201.68, "word": " ..", "probability": 0.30224609375}, {"start": 2201.68, "end": 2203.68, "word": " absolute", "probability": 0.8955078125}, {"start": 2203.68, "end": 2205.24, "word": " f", "probability": 0.46337890625}, {"start": 2205.24, "end": 2207.52, "word": " of", "probability": 0.6875}, {"start": 2207.52, "end": 2208.24, "word": " x", "probability": 0.92333984375}, {"start": 2208.24, "end": 2209.32, "word": " minus", "probability": 0.9462890625}, {"start": 2209.32, "end": 2211.08, "word": " absolute", "probability": 0.9619140625}, {"start": 2211.08, "end": 2213.02, "word": " ال", "probability": 0.74853515625}, {"start": 2213.02, "end": 2213.5, "word": " L", "probability": 0.56591796875}, {"start": 2213.5, "end": 2215.96, "word": " هذا", "probability": 0.92822265625}, {"start": 2215.96, "end": 2216.98, "word": " بيساوي", "probability": 0.9041015625}, {"start": 2216.98, "end": 2218.16, "word": " absolute", "probability": 0.94189453125}, {"start": 2218.16, "end": 2219.3, "word": " ..", "probability": 0.955078125}, {"start": 2219.3, "end": 2220.44, "word": " absolute", "probability": 0.96875}, {"start": 2220.44, "end": 2221.2, "word": " f", "probability": 0.93798828125}, {"start": 2221.2, "end": 2221.56, "word": " of", "probability": 0.98095703125}, {"start": 2221.56, "end": 2222.08, "word": " x", "probability": 0.9853515625}, {"start": 2222.08, "end": 2224.46, "word": " minus", "probability": 0.99365234375}, {"start": 2224.46, "end": 2225.32, "word": " absolute", "probability": 0.943359375}, {"start": 2225.32, "end": 2226.06, "word": " L", "probability": 0.970703125}], "temperature": 1.0}, {"id": 78, "seek": 226173, "start": 2232.84, "end": 2261.74, "text": "وهذا by ال triangle inequality by ال triangle inequality أصغر من أوي ساوي absolute f of x minus l و by star absolute f of x minus l أصغر من إبسل تمام؟ since إبسلون was arbitrary", "tokens": [2407, 3224, 15730, 538, 2423, 13369, 16970, 538, 2423, 13369, 16970, 5551, 9381, 17082, 2288, 9154, 34051, 1829, 8608, 995, 45865, 8236, 283, 295, 2031, 3175, 287, 4032, 538, 3543, 8236, 283, 295, 2031, 3175, 287, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 46811, 10943, 22807, 1670, 11933, 3555, 3794, 1211, 11536, 390, 23211], "avg_logprob": -0.22299890560016297, "compression_ratio": 1.5492957746478873, "no_speech_prob": 0.0, "words": [{"start": 2232.8399999999997, "end": 2233.7599999999998, "word": "وهذا", "probability": 0.7947591145833334}, {"start": 2233.7599999999998, "end": 2234.68, "word": " by", "probability": 0.59716796875}, {"start": 2234.68, "end": 2234.86, "word": " ال", 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f", "probability": 0.59130859375}, {"start": 2243.56, "end": 2243.78, "word": " of", "probability": 0.732421875}, {"start": 2243.78, "end": 2244.1, "word": " x", "probability": 0.79541015625}, {"start": 2244.1, "end": 2244.52, "word": " minus", "probability": 0.9248046875}, {"start": 2244.52, "end": 2244.92, "word": " l", "probability": 0.466796875}, {"start": 2244.92, "end": 2246.36, "word": " و", "probability": 0.82470703125}, {"start": 2246.36, "end": 2246.68, "word": " by", "probability": 0.84521484375}, {"start": 2246.68, "end": 2247.34, "word": " star", "probability": 0.7763671875}, {"start": 2247.34, "end": 2249.44, "word": " absolute", "probability": 0.90283203125}, {"start": 2249.44, "end": 2249.86, "word": " f", "probability": 0.82666015625}, {"start": 2249.86, "end": 2250.04, "word": " of", "probability": 0.97021484375}, {"start": 2250.04, "end": 2250.24, "word": " x", "probability": 0.99462890625}, {"start": 2250.24, "end": 2250.68, "word": " minus", "probability": 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[{"start": 2267.34, "end": 2267.94, "word": "إذاً", "probability": 0.505615234375}, {"start": 2267.94, "end": 2268.12, "word": " we", "probability": 0.54736328125}, {"start": 2268.12, "end": 2268.64, "word": " have", "probability": 0.9736328125}], "temperature": 1.0}, {"id": 80, "seek": 230019, "start": 2270.83, "end": 2300.19, "text": "هك مكون أسبابنا أنه لأي epsilon أكبر من الصفر يوجد delta تعتمد على epsilon عدد موجب من حيث لكل x ينتمي ل a و المسافة بين x و c أصغر من delta و x لا تساوي c فلل absolute value لf of x minus absolute L أصغر من epsilon، إذن هذا معناه حسب epsilon delta definition of limit", "tokens": [3224, 4117, 3714, 30544, 5551, 35457, 16758, 8315, 14739, 3224, 5296, 10721, 1829, 17889, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 7251, 29245, 3215, 8289, 6055, 34268, 2304, 3215, 15844, 17889, 6225, 3215, 3215, 3714, 29245, 3555, 9154, 11331, 1829, 12984, 5296, 28820, 2031, 7251, 29399, 2304, 1829, 5296, 257, 4032, 9673, 3794, 31845, 3660, 49374, 2031, 4032, 269, 5551, 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2286.69, "word": " delta", "probability": 0.6201171875}, {"start": 2286.69, "end": 2286.93, "word": " و", "probability": 0.85107421875}, {"start": 2286.93, "end": 2287.15, "word": " x", "probability": 0.927734375}, {"start": 2287.15, "end": 2287.35, "word": " لا", "probability": 0.476806640625}, {"start": 2287.35, "end": 2287.91, "word": " تساوي", "probability": 0.872802734375}, {"start": 2287.91, "end": 2288.91, "word": " c", "probability": 0.888671875}, {"start": 2288.91, "end": 2289.39, "word": " فلل", "probability": 0.6160481770833334}, {"start": 2289.39, "end": 2289.83, "word": " absolute", "probability": 0.84033203125}, {"start": 2289.83, "end": 2290.49, "word": " value", "probability": 0.9912109375}, {"start": 2290.49, "end": 2291.11, "word": " لf", "probability": 0.7081298828125}, {"start": 2291.11, "end": 2291.35, "word": " of", "probability": 0.68505859375}, {"start": 2291.35, "end": 2291.63, "word": " x", "probability": 0.97802734375}, {"start": 2291.63, "end": 2291.97, 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2298.59, "word": " definition", "probability": 0.92578125}, {"start": 2298.59, "end": 2299.77, "word": " of", "probability": 0.9697265625}, {"start": 2299.77, "end": 2300.19, "word": " limit", "probability": 0.9619140625}], "temperature": 1.0}, {"id": 81, "seek": 231842, "start": 2300.52, "end": 2318.42, "text": "إن الـ limit ل absolute f of x as x tends to c بساوي absolute ل هو المطلوب وهذا اللي احنا عايزين نثبته هذا هو البرهان", "tokens": [28814, 1863, 2423, 39184, 4948, 5296, 8236, 283, 295, 2031, 382, 2031, 12258, 281, 269, 4724, 3794, 995, 45865, 8236, 5296, 31439, 9673, 9566, 1211, 37746, 37037, 15730, 13672, 1829, 1975, 5016, 8315, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 3224, 23758, 31439, 2423, 26890, 3224, 7649], "avg_logprob": -0.3632015208808743, "compression_ratio": 1.3206106870229009, "no_speech_prob": 0.0, "words": [{"start": 2300.52, "end": 2300.82, "word": "إن", "probability": 0.5079345703125}, {"start": 2300.82, "end": 2301.06, "word": " الـ", "probability": 0.4068603515625}, {"start": 2301.06, "end": 2301.46, "word": " limit", "probability": 0.63134765625}, {"start": 2301.46, "end": 2302.48, "word": " ل", "probability": 0.7431640625}, {"start": 2302.48, "end": 2303.04, "word": " absolute", "probability": 0.36767578125}, {"start": 2303.04, "end": 2303.84, "word": " f", "probability": 0.39013671875}, {"start": 2303.84, "end": 2304.44, "word": " of", "probability": 0.6064453125}, {"start": 2304.44, "end": 2305.0, "word": " x", "probability": 0.87939453125}, {"start": 2305.0, "end": 2306.28, "word": " as", "probability": 0.86962890625}, {"start": 2306.28, "end": 2306.76, "word": " x", "probability": 0.9638671875}, {"start": 2306.76, "end": 2307.18, "word": " tends", "probability": 0.7392578125}, {"start": 2307.18, "end": 2307.38, "word": " to", "probability": 0.98486328125}, {"start": 2307.38, "end": 2307.7, "word": " c", "probability": 0.8994140625}, {"start": 2307.7, "end": 2308.48, "word": " بساوي", "probability": 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2319.94, "end": 2320.3, "word": "إذا", "probability": 0.4813232421875}, {"start": 2320.3, "end": 2320.66, "word": " هنا", "probability": 0.876953125}, {"start": 2320.66, "end": 2321.7, "word": " اللاعب", "probability": 0.7019856770833334}, {"start": 2321.7, "end": 2322.04, "word": " دور", "probability": 0.838134765625}, {"start": 2322.04, "end": 2322.44, "word": " كبير", "probability": 0.9899088541666666}, {"start": 2322.44, "end": 2322.56, "word": " في", "probability": 0.921875}, {"start": 2322.56, "end": 2323.16, "word": " البرهان", "probability": 0.9359130859375}, {"start": 2323.16, "end": 2323.54, "word": " هو", "probability": 0.966796875}, {"start": 2323.54, "end": 2324.62, "word": " ال", "probability": 0.76171875}, {"start": 2324.62, "end": 2325.06, "word": " triangle", "probability": 0.6318359375}, {"start": 2325.06, "end": 2325.82, "word": " inequality", "probability": 0.9619140625}, {"start": 2325.82, "end": 2327.6, "word": " و", "probability": 0.47412109375}, {"start": 2327.6, "end": 2329.28, "word": " الفرض", "probability": 0.835205078125}, {"start": 2329.28, "end": 2329.84, "word": " إنه", "probability": 0.54296875}, {"start": 2329.84, "end": 2330.28, "word": " limit", "probability": 0.8955078125}, {"start": 2330.28, "end": 2330.68, "word": " and", "probability": 0.1474609375}, {"start": 2330.68, "end": 2331.02, "word": " c", "probability": 0.5869140625}, {"start": 2331.02, "end": 2331.8, "word": " موجودة", "probability": 0.9786376953125}, {"start": 2331.8, "end": 2332.42, "word": " بالساوية", "probability": 0.822802734375}, {"start": 2332.42, "end": 2332.68, "word": " L", "probability": 0.1903076171875}, {"start": 2332.68, "end": 2333.7, "word": " okay", "probability": 0.251708984375}, {"start": 2333.7, "end": 2335.04, "word": " تمام؟", "probability": 0.6591796875}, {"start": 2335.04, "end": 2335.6, "word": " إذا", "probability": 0.824462890625}, {"start": 2335.6, "end": 2336.28, "word": " أهمية", "probability": 0.93701171875}, {"start": 2336.28, "end": 2336.48, "word": " ال", "probability": 0.96728515625}, {"start": 2336.48, "end": 2336.88, "word": " exercise", "probability": 0.80615234375}, {"start": 2336.88, "end": 2337.26, "word": " هذا", "probability": 0.69775390625}, {"start": 2337.26, "end": 2337.72, "word": " يعتبر", "probability": 0.9392903645833334}, {"start": 2337.72, "end": 2338.42, "word": " نظرية", "probability": 0.98974609375}, {"start": 2338.42, "end": 2339.5, "word": " و", "probability": 0.51611328125}, {"start": 2339.5, "end": 2339.94, "word": " النظرية", "probability": 0.9385986328125}, {"start": 2339.94, "end": 2340.18, "word": " هذه", "probability": 0.89599609375}, {"start": 2340.18, "end": 2340.64, "word": " بتقول", "probability": 0.972412109375}, {"start": 2340.64, "end": 2340.9, "word": " إذا", "probability": 0.926513671875}, {"start": 2340.9, "end": 2341.16, "word": " كان", "probability": 0.98974609375}, {"start": 2341.16, "end": 2341.32, "word": " في", "probability": 0.9052734375}, {"start": 2341.32, 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1211, 2423, 8236, 2158, 34051, 5551, 44510, 1211, 2423, 4948, 20449, 2423, 8236, 2158, 1392, 46811, 10943, 4032, 46958, 5016, 22807, 8978, 5551, 3794, 19986, 37977, 6055, 7649, 10632, 22807], "avg_logprob": -0.17828824137573812, "compression_ratio": 1.6607142857142858, "no_speech_prob": 0.0, "words": [{"start": 2345.57, "end": 2346.25, "word": "فنهاية", "probability": 0.8892822265625}, {"start": 2346.25, "end": 2346.41, "word": " ال", "probability": 0.45361328125}, {"start": 2346.41, "end": 2346.77, "word": " absolute", "probability": 0.64111328125}, {"start": 2346.77, "end": 2347.39, "word": " value", "probability": 0.98779296875}, {"start": 2347.39, "end": 2347.59, "word": " لل", "probability": 0.65576171875}, {"start": 2347.59, "end": 2348.09, "word": " function", "probability": 0.54052734375}, {"start": 2348.09, "end": 2349.67, "word": " بالساوي", "probability": 0.622314453125}, {"start": 2349.67, "end": 2349.79, "word": " ال", "probability": 0.62451171875}, {"start": 2349.79, "end": 2350.15, "word": " absolute", "probability": 0.93408203125}, {"start": 2350.15, "end": 2350.65, "word": " value", "probability": 0.99072265625}, {"start": 2350.65, "end": 2350.81, "word": " لل", "probability": 0.91748046875}, {"start": 2350.81, "end": 2351.17, "word": " limit", "probability": 0.95751953125}, {"start": 2351.17, "end": 2351.61, "word": " بمعنى", "probability": 0.94091796875}, {"start": 2351.61, "end": 2351.91, "word": " أخر", "probability": 0.7120361328125}, {"start": 2351.91, "end": 2352.09, "word": " أنا", "probability": 0.383056640625}, {"start": 2352.09, "end": 2352.41, "word": " ممكن", "probability": 0.986572265625}, {"start": 2352.41, "end": 2353.01, "word": " أدخل", "probability": 0.9571533203125}, {"start": 2353.01, "end": 2353.15, "word": " ال", "probability": 0.8876953125}, {"start": 2353.15, "end": 2353.55, "word": " limit", "probability": 0.98828125}, {"start": 2353.55, "end": 2354.79, "word": " داخل", "probability": 0.9734700520833334}, {"start": 2354.79, "end": 2354.93, "word": " ال", "probability": 0.96240234375}, {"start": 2354.93, "end": 2355.25, "word": " absolute", "probability": 0.970703125}, {"start": 2355.25, "end": 2355.87, "word": " value", "probability": 0.98974609375}, {"start": 2355.87, "end": 2357.45, "word": " أو", "probability": 0.8681640625}, {"start": 2357.45, "end": 2357.99, "word": " أبدل", "probability": 0.9337565104166666}, {"start": 2357.99, "end": 2358.11, "word": " ال", "probability": 0.95654296875}, {"start": 2358.11, "end": 2358.37, "word": " limit", "probability": 0.990234375}, {"start": 2358.37, "end": 2358.57, "word": " مع", "probability": 0.9873046875}, {"start": 2358.57, "end": 2358.67, "word": " ال", "probability": 0.97998046875}, {"start": 2358.67, "end": 2359.03, "word": " absolute", "probability": 0.9658203125}, {"start": 2359.03, "end": 2359.65, "word": " value", "probability": 0.9892578125}, {"start": 2359.65, "end": 2362.19, "word": " okay", "probability": 0.431396484375}, {"start": 2362.19, "end": 2362.71, "word": " تمام", "probability": 0.916748046875}, {"start": 2362.71, "end": 2365.13, "word": " واضح؟", "probability": 0.788330078125}, {"start": 2365.13, "end": 2365.65, "word": " في", "probability": 0.8388671875}, {"start": 2365.65, "end": 2366.03, "word": " أسئلة", "probability": 0.894775390625}, {"start": 2366.03, "end": 2366.63, "word": " تانية؟", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 84, "seek": 238556, "start": 2375.8, "end": 2385.56, "text": "أي سؤال أي استفسار okay إذا نكتفي بهذا القدر", "tokens": [10721, 1829, 8608, 33604, 6027, 36632, 44713, 36178, 9640, 1392, 11933, 15730, 8717, 4117, 2655, 41185, 39627, 15730, 25062, 3215, 2288], "avg_logprob": -0.2292258454994722, "compression_ratio": 1.0410958904109588, "no_speech_prob": 0.0, "words": [{"start": 2375.8, "end": 2376.14, "word": "أي", "probability": 0.71533203125}, {"start": 2376.14, "end": 2376.66, "word": " سؤال", "probability": 0.9661458333333334}, {"start": 2376.66, "end": 2376.82, "word": " أي", "probability": 0.2310791015625}, {"start": 2376.82, "end": 2377.46, "word": " استفسار", "probability": 0.9759114583333334}, {"start": 2377.46, "end": 2383.26, "word": " okay", "probability": 0.263671875}, {"start": 2383.26, "end": 2383.68, "word": " إذا", "probability": 0.757080078125}, {"start": 2383.68, "end": 2384.6, "word": " نكتفي", "probability": 0.8760986328125}, {"start": 2384.6, "end": 2384.98, "word": " بهذا", "probability": 0.93798828125}, {"start": 2384.98, "end": 2385.56, "word": " القدر", "probability": 0.990234375}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2386.84875, "duration_after_vad": 2053.4187499999907}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..df344fc146566e3feeba9c4f0e118efd09173ce2
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/db6AFymIrl8_raw.srt
@@ -0,0 +1,1228 @@
+1
+00:00:19,490 --> 00:00:23,130
+بسم الله الرحمن الرحيم في المحاضرة هذه هناخد يعني
+
+2
+00:00:23,130 --> 00:00:31,510
+مناقشة أو هنناقش بعض المسائل في section 4-1 و 4-2
+
+3
+00:00:31,510 --> 00:00:41,650
+فإحدى الطالبات سألت في سؤال بقول برهن الجزء B من
+
+4
+00:00:41,650 --> 00:00:52,390
+theorem 4.2.4using sequential criterion لان هنا
+
+5
+00:00:52,390 --> 00:00:56,910
+use sequential
+
+6
+00:00:56,910 --> 00:01:01,370
+.. sequential
+
+7
+00:01:01,370 --> 00:01:06,410
+argument use
+
+8
+00:01:06,410 --> 00:01:15,290
+sequential formulation on
+
+9
+00:01:15,290 --> 00:01:15,750
+limit
+
+10
+00:01:21,840 --> 00:01:27,040
+فالبرهان ذلك let .. هنستخدم الـ sequential
+
+11
+00:01:27,040 --> 00:01:30,380
+criterion
+
+12
+00:01:30,380 --> 00:01:39,860
+let x in بـ sequence contained in A such that
+
+13
+00:01:39,860 --> 00:01:50,000
+limit طبعا الحدود تباعتها مختلفة عن الـ C such
+
+14
+00:01:50,000 --> 00:01:56,610
+that limitx in as n tends to infinity بساوي c
+
+15
+00:01:56,610 --> 00:02:03,050
+خلّينا نختار sequence في المجال المشترك تبع
+
+16
+00:02:03,050 --> 00:02:08,290
+الدالتين FWH وحدودها مختلفة عن ال C ونهايتها بساوي
+
+17
+00:02:08,290 --> 00:02:08,610
+C
+
+18
+00:02:16,250 --> 00:02:21,290
+by sequential criterion حسب sequential criterion
+
+19
+00:02:21,290 --> 00:02:32,430
+for limits to show ان ال limit ل F على H as X
+
+20
+00:02:32,430 --> 00:02:42,590
+tends to C بساوي L على H it
+
+21
+00:02:42,590 --> 00:02:43,570
+suffices
+
+22
+00:02:45,740 --> 00:02:53,260
+it suffices to show يكفي اثبات ان ال limit لل
+
+23
+00:02:53,260 --> 00:03:02,220
+image لسيكوينس xn لما n تقول ل infinity بساوي L
+
+24
+00:03:02,220 --> 00:03:07,020
+على H لو اثبتت الكلام هذا فحسب السيكوينش هي كتير
+
+25
+00:03:07,020 --> 00:03:11,380
+تانيا بطلع limit F على H بساوي capital L على
+
+26
+00:03:11,380 --> 00:03:12,140
+capital H
+
+27
+00:03:17,270 --> 00:03:24,050
+فنشوف to this end to
+
+28
+00:03:24,050 --> 00:03:36,670
+this end و لإثبات ذلك يعني we
+
+29
+00:03:36,670 --> 00:03:40,710
+have from
+
+30
+00:03:40,710 --> 00:03:44,170
+sequential criterion
+
+31
+00:03:47,320 --> 00:03:56,200
+that limit f of x in as n tends to infinity بساوي
+
+32
+00:03:56,200 --> 00:04:01,600
+L أنا عندي فارض ان limit f of x من x أول ل c بساوي
+
+33
+00:04:01,600 --> 00:04:06,720
+L اذا by sequential criterion هذا بكافئ انه لأي
+
+34
+00:04:06,720 --> 00:04:12,680
+sequence x in نهايتها c بطلع نهاية صورتها بساوي L
+
+35
+00:04:12,680 --> 00:04:18,140
+و كذلك andأنا عندي limit الـ function h of x من x
+
+36
+00:04:18,140 --> 00:04:22,320
+تقولها c بساوي h by sequential criterion كمان بره
+
+37
+00:04:22,320 --> 00:04:27,120
+طبخيها على ال function h بما أن x in sequence
+
+38
+00:04:27,120 --> 00:04:34,460
+نهايتها c إذا نهايت صرتها under h يعني limit h of
+
+39
+00:04:34,460 --> 00:04:43,840
+x in as n tends to infinity بساوي capital H hence
+
+40
+00:04:45,840 --> 00:04:57,980
+وبالتالي ال limit ل f على h of x لما x
+
+41
+00:04:57,980 --> 00:05:10,220
+تقول ل xn لما n تقول ل infinity هذا بساوي limit
+
+42
+00:05:12,840 --> 00:05:22,580
+f of x,n على h of x,n لما n تقول infinity ويساوي
+
+43
+00:05:22,580 --> 00:05:29,560
+انا انا اندي limit h of x,n exist وبيستويش سفر
+
+44
+00:05:29,560 --> 00:05:35,080
+وبيستويش سفر فممكن استخدم قوانين النهايات لسيكوانس
+
+45
+00:05:35,080 --> 00:05:40,420
+فlimit sequence على limit sequence بساوي limit
+
+46
+00:05:40,420 --> 00:05:41,140
+البسط
+
+47
+00:05:44,990 --> 00:05:50,170
+limit ال sequence في ال bus على limit ال sequence
+
+48
+00:05:50,170 --> 00:05:55,330
+في المقام و
+
+49
+00:05:55,330 --> 00:05:58,010
+limit ال sequence في المقام بيساوي سفر اذا انا
+
+50
+00:05:58,010 --> 00:06:01,090
+بقدر ايه اقول limit ال quotient بيساوي the
+
+51
+00:06:01,090 --> 00:06:07,330
+quotient of the limits وهذا بيطلع limit ال bus
+
+52
+00:06:07,330 --> 00:06:14,920
+تطلع L limit المقام H وهذا البنيةإن حسب الـ
+
+53
+00:06:14,920 --> 00:06:19,020
+sequential criterion بيطلع limit F على H عندما X
+
+54
+00:06:19,020 --> 00:06:24,020
+تقوى ل C بيساوي L على H هذا هو المقصود الـ
+
+55
+00:06:24,020 --> 00:06:28,740
+sequential formulation واضح؟ طيب، مين عندها أسئلة
+
+56
+00:06:28,740 --> 00:06:35,540
+تانية؟ في section 4, 1 أو 4, 2؟
+
+57
+00:06:35,540 --> 00:06:40,080
+طيب،
+
+58
+00:06:40,080 --> 00:06:41,580
+خليني أمسح اللوحي الأول
+
+59
+00:07:20,820 --> 00:07:28,800
+هذه السؤال تمانية section أربعة واحد show that
+
+60
+00:07:28,800 --> 00:07:38,120
+أثبتي أنه ال limit of the square root of X الـ
+
+61
+00:07:38,120 --> 00:07:44,060
+square root function as X tends to C بساوي ال
+
+62
+00:07:44,060 --> 00:07:48,340
+square root of C for any
+
+63
+00:07:51,920 --> 00:07:59,200
+C أكبر من السفر proof
+
+64
+00:08:02,940 --> 00:08:09,860
+أحنا في النهاية عايزين نثبت أنه الفرق بين f of x
+
+65
+00:08:09,860 --> 00:08:16,700
+absolute الفرق بين f of x و f of c اللي هي جدر ال
+
+66
+00:08:16,700 --> 00:08:21,680
+c بدنا في النهاية هذا يكون أصغر من أي given
+
+67
+00:08:21,680 --> 00:08:22,140
+epsilon
+
+68
+00:08:25,220 --> 00:08:31,760
+حيث x المسافة بينها وبين z ال c أصغر من delta و
+
+69
+00:08:31,760 --> 00:08:36,480
+delta to be determined يعني هيتم تعيينها لاحقا
+
+70
+00:08:36,480 --> 00:08:42,240
+okay طب ما هذا بيساوي absolute
+
+71
+00:08:46,520 --> 00:08:54,060
+must go هاي جدر ال X سالب جدر ال C و بنضرب في
+
+72
+00:08:54,060 --> 00:09:03,660
+المرافق اللي هو جدر ال X زائد جدر ال C في جدر ال X
+
+73
+00:09:03,660 --> 00:09:10,540
+زائد جدر ال C بنضرب
+
+74
+00:09:10,540 --> 00:09:19,050
+بسط مقام في المرافقوهذا بيطلع بيساوي absolute x
+
+75
+00:09:19,050 --> 00:09:32,850
+minus c على جدر x plus جدر sc وهذا
+
+76
+00:09:32,850 --> 00:09:41,810
+بيساوي absolute x minus c على جدر x plus جدر sc
+
+77
+00:09:45,070 --> 00:09:50,090
+طبعا ال X هنا لازم تكون عدد موجب أكبر من أو ساوي
+
+78
+00:09:50,090 --> 00:09:58,470
+سفر إذا هنا عندي .. أنا عندي ال X أكبر من أو ساوي
+
+79
+00:09:58,470 --> 00:10:04,630
+سفر إذا جذر ال X أكبر من أو ساوي سفر وبالتالي جذر
+
+80
+00:10:04,630 --> 00:10:12,230
+ال X plus جذر ال C أكبر من أو ساوي جذر ال C صح؟
+
+81
+00:10:12,230 --> 00:10:14,470
+وبالتالي
+
+82
+00:10:16,780 --> 00:10:23,460
+هذا بيقدر من واحد على جذر ال X زي جذر ال C أصغر من
+
+83
+00:10:23,460 --> 00:10:29,980
+أو ساوي واحد على جذر ال C إذاً هذا بيطلع أصغر من
+
+84
+00:10:29,980 --> 00:10:35,860
+أو ساوي واحد على جذر ال C في absolute X minus C
+
+85
+00:10:35,860 --> 00:10:42,300
+تمام؟ الآن لما يكون هذا أصغر من Delta
+
+86
+00:10:44,960 --> 00:10:48,980
+لما يكون هذا أصغر من دلتا لما يكون هذا أصغر من
+
+87
+00:10:48,980 --> 00:10:56,080
+دلتا فهذا هيكون أصغر من واحد على جدر ال C في دلتا
+
+88
+00:10:56,080 --> 00:11:01,960
+صح؟ و لو أنا بدي أكون هذا خليه
+
+89
+00:11:05,310 --> 00:11:11,610
+وبدي في النهاية هذا يكون أصغر من epsilon صح؟ إذا
+
+90
+00:11:11,610 --> 00:11:17,830
+كيف بدي أخد ال delta؟ جدر ال c في epsilon اه okay
+
+91
+00:11:17,830 --> 00:11:23,810
+تمام؟ إذا هنا هذا بيقدي أن ال delta ممكن أخدها أي
+
+92
+00:11:23,810 --> 00:11:28,850
+عدد أصغر من أو ساوي طبعا عدد موجب وأصغر من أو ساوي
+
+93
+00:11:28,850 --> 00:11:34,840
+جدر ال c في epsilonعشان يطلع المقدار هذا أصغر من
+
+94
+00:11:34,840 --> 00:11:38,400
+إبسلون بالتالي المقدار هذا أصغر من إبسلون إذا
+
+95
+00:11:38,400 --> 00:11:42,340
+شوفتوا كيف نجيب الـ delta إذا نجيب نقول let
+
+96
+00:11:42,340 --> 00:11:51,200
+epsilon let epsilon أكبر من السفر be given choose
+
+97
+00:11:51,200 --> 00:12:01,410
+delta بتساويالجذر ال C هذا عدد موجب ضرب إمسلن فهذا
+
+98
+00:12:01,410 --> 00:12:06,370
+أكيد بيطلع عدد موجب ويعتمد على إمسلن و هيو بيعتمد
+
+99
+00:12:06,370 --> 00:12:10,870
+على إمسلن then
+
+100
+00:12:10,870 --> 00:12:20,750
+لكل Xبحيث absolute x minus c أكبر من سفر أصغر من
+
+101
+00:12:20,750 --> 00:12:27,830
+الـ delta هذه هذا بتضمن أن absolute جذر الـ x
+
+102
+00:12:27,830 --> 00:12:38,260
+minus جذر الـ c قلنا هذا طلع أصغر من أو يساويواحد
+
+103
+00:12:38,260 --> 00:12:46,060
+على جذر C في absolute X minus C وطبعا هذا الأن طلع
+
+104
+00:12:46,060 --> 00:12:57,160
+أصغر من واحد على جذر C في Delta وهذا أصغر من أو
+
+105
+00:12:57,160 --> 00:13:04,100
+يساوي الأبسلون وبالتالي
+
+106
+00:13:04,100 --> 00:13:09,480
+حسب تعريف Epsilon Deltaبطلع عندى اللى .. اللى أنا
+
+107
+00:13:09,480 --> 00:13:22,200
+عايزه since
+
+108
+00:13:22,200 --> 00:13:29,620
+epsilon أكبر من السفر was arbitrary لأن we have
+
+109
+00:13:29,620 --> 00:13:36,510
+أثبتنا حسب التعريفإن ال limit لجدر ال X لما X تقول
+
+110
+00:13:36,510 --> 00:13:47,690
+إلى C بساوي جدر ال C وهو المضمن OK تمام واضح الحل
+
+111
+00:13:47,690 --> 00:13:53,570
+واضح البرهام إذا لكل epsilon أكبر من 0 اختاري ال
+
+112
+00:13:53,570 --> 00:13:58,210
+delta اللي بتشتغل صح هي جدر ال C هذا عدد موجة ثابت
+
+113
+00:13:58,210 --> 00:14:06,940
+ضرب ال epsilon اللي احنا بدينا فيهاتمام؟ okay طيب
+
+114
+00:14:06,940 --> 00:14:12,360
+في أسئلة تانية؟ في أي استفسار؟
+
+115
+00:14:12,360 --> 00:14:22,220
+في أي أسئلة تانية؟ section 4-1 أو 4-2 الناس اللي
+
+116
+00:14:22,220 --> 00:14:28,300
+بتدرس و اللي حاولة تتحل الأسئلة و عندها بعض
+
+117
+00:14:28,300 --> 00:14:34,200
+الصعوبات في حل الأسئلةمين عندها؟ أي استفسار؟
+
+118
+00:14:34,200 --> 00:14:36,520
+السؤال اتناش اربعة اتنين
+
+119
+00:15:19,790 --> 00:15:31,090
+السؤال 12 اربعة اتنين في
+
+120
+00:15:31,090 --> 00:15:38,850
+عندي function f from R to R such
+
+121
+00:15:38,850 --> 00:15:50,420
+that f of x plus y بساوي f of x plus f of yfor
+
+122
+00:15:50,420 --> 00:16:00,780
+every x و y in R assume
+
+123
+00:16:00,780 --> 00:16:03,920
+ان
+
+124
+00:16:03,920 --> 00:16:14,620
+ال limit f of x as x tends to zero بسوى عدد L
+
+125
+00:16:14,620 --> 00:16:16,820
+exists
+
+126
+00:16:19,070 --> 00:16:28,110
+يعني أدب real number prove
+
+127
+00:16:28,110 --> 00:16:40,930
+حاجتي الواحد ال بساوي سفر لان limit
+
+128
+00:16:40,930 --> 00:16:44,290
+f
+
+129
+00:16:44,290 --> 00:16:44,950
+of x
+
+130
+00:16:48,250 --> 00:16:59,370
+كما يظهر X لـ C لجميع الـ C تلتانيه لـ R لما
+
+131
+00:16:59,370 --> 00:17:05,770
+نثبت أن الـ limit لها تساوي سفر ثم الـ function F
+
+132
+00:17:05,770 --> 00:17:12,230
+لها limitالأعداد الحقيقية C والكتاب يعطيك hint
+
+133
+00:17:12,230 --> 00:17:20,490
+يعني إرشاد كيف يعني تبدأ الحل بطريقة صحية proof
+
+134
+00:17:20,490 --> 00:17:24,410
+فخلينا
+
+135
+00:17:24,410 --> 00:17:33,150
+نبرهن الجزء الأول لحظة
+
+136
+00:17:33,150 --> 00:17:37,780
+أن ال function هذه بتحقق الشرط هذابنسميه
+
+137
+00:17:37,780 --> 00:17:42,880
+additivity ال function f بتحافظ على عملية الجمع
+
+138
+00:17:42,880 --> 00:17:48,100
+بتاخد مجموعة حاجتين تعطي صورتها مجموعة صورهم
+
+139
+00:17:48,100 --> 00:17:52,360
+فبنقول f أي function بتحقق خاصية زي هذه بنسميها
+
+140
+00:17:52,360 --> 00:17:57,570
+additive يعني دالة جمعيةبتحافظ على عملية الجمع تبع
+
+141
+00:17:57,570 --> 00:18:03,170
+الأعداد الحقيقية فبناء على الخاصية هذه لو كانت ال
+
+142
+00:18:03,170 --> 00:18:07,450
+function f لها limit and سفر فال limit هذه لازم
+
+143
+00:18:07,450 --> 00:18:13,630
+تكون بساوي سفر خمتها سفر فكيف ممكن نثبت الكلام هذا
+
+144
+00:18:13,630 --> 00:18:19,590
+نسمي
+
+145
+00:18:19,590 --> 00:18:22,190
+هذا الفرض star
+
+146
+00:18:25,940 --> 00:18:34,100
+by hypothesis star من الفرض star انا عندي h او ال
+
+147
+00:18:34,100 --> 00:18:42,500
+function f of two x ايش بتساوي؟ بتساوي f of x زاد
+
+148
+00:18:42,500 --> 00:18:47,260
+x مظبوط و من الفرض star
+
+149
+00:18:51,230 --> 00:18:58,670
+f of x زاد x بيساوي f of x زاد f of x صح يعني
+
+150
+00:18:58,670 --> 00:19:13,710
+بيساوي اتنين في f of x تمام طيب
+
+151
+00:19:13,710 --> 00:19:20,130
+take limit of both sides take limit
+
+152
+00:19:22,620 --> 00:19:29,320
+of both sides as
+
+153
+00:19:29,320 --> 00:19:39,900
+x tends to zero we get نحصل على انه ال limit ل f ل
+
+154
+00:19:39,900 --> 00:19:50,380
+2x لما x تقول ل 0 بساوي 2 في ال limit ل f of x لما
+
+155
+00:19:50,380 --> 00:19:51,720
+x تقول ل 0
+
+156
+00:19:56,790 --> 00:20:01,490
+Limit f of x من اكسا اولا سفر بساوي من الفرض
+
+157
+00:20:01,490 --> 00:20:08,610
+موجودة و بساوي L في اتنين بطلع اتنين L و ال limit
+
+158
+00:20:08,610 --> 00:20:14,230
+هذه هي نفسها limit
+
+159
+00:20:17,140 --> 00:20:27,440
+لـ F of 2X لما 2X تقول لـ 0 صح؟ لما X تقول لـ 0،
+
+160
+00:20:27,440 --> 00:20:38,460
+2X تقول لـ 0 و هذه هي نفسها ال limit ل F of Y لما
+
+161
+00:20:38,460 --> 00:20:48,520
+Y تقول لـ 0 صح؟ خدي Y بساوي 2Xفالمهي هنا limit f
+
+162
+00:20:48,520 --> 00:20:54,400
+of y لما y تقل ل 0 ال independent variable ده سميه
+
+163
+00:20:54,400 --> 00:20:59,760
+x سميه y it doesn't matter مش مهم اه لإن هذا برضه
+
+164
+00:20:59,760 --> 00:21:07,080
+ال limit هذه بساوي L لإن أنا أصبح عندي لإن أنا
+
+165
+00:21:07,080 --> 00:21:14,040
+أصبح عندي أنا معادلة L بساوي two L حل المعادلة هذه
+
+166
+00:21:15,510 --> 00:21:23,150
+في ال فهذا بيقدي ان ال بيساوي سفر صح ان هنا اثبتت
+
+167
+00:21:23,150 --> 00:21:28,350
+ان العدد ال اللي هو limit لل function if and السفر
+
+168
+00:21:28,350 --> 00:21:35,370
+بيطلع بساوي سفر صحيح ولا سهل ان
+
+169
+00:21:35,370 --> 00:21:41,710
+الكتاب بيحط رجلكم قدامكم على بداية الطريق استغلي
+
+170
+00:21:41,710 --> 00:21:42,050
+صح
+
+171
+00:21:45,430 --> 00:21:57,650
+واضح البرهان هنا تمام نبرهن الجزء التاني طيب
+
+172
+00:21:57,650 --> 00:22:03,570
+نبرهن الجزء التاني برضه
+
+173
+00:22:03,570 --> 00:22:13,250
+الجزء التاني فيه له hint فنستخدم ال hint also
+
+174
+00:22:15,670 --> 00:22:24,930
+by hypothesis star حسب
+
+175
+00:22:24,930 --> 00:22:31,630
+الفرض star ال function هذه is additive وبالتالي f
+
+176
+00:22:31,630 --> 00:22:40,750
+of x هي نفسها f of x ثالث c زائد c صح؟
+
+177
+00:22:44,780 --> 00:22:52,200
+و هذا بيساوي F
+
+178
+00:22:52,200 --> 00:23:03,900
+of X minus C زائد F of C تمام طيب هذا صحيح for all
+
+179
+00:23:03,900 --> 00:23:13,100
+C ينتمي ل R و طبعا for all X و for all X ينتمي ل R
+
+180
+00:23:14,280 --> 00:23:19,900
+فى مشكلة طيب الان نفس الحاجة اخد ال limit للطرفين
+
+181
+00:23:19,900 --> 00:23:30,540
+take limit of both sides لما x تقول ل c اذا limit
+
+182
+00:23:30,540 --> 00:23:40,780
+f of x لما x تقول ل c بساوي limitالطرف اليومين
+
+183
+00:23:40,780 --> 00:23:44,240
+مجموعة limit مجموعة بيساوي مجموعة limits لأن limit
+
+184
+00:23:44,240 --> 00:23:48,660
+الحد الأول exist هنشوف ان limit الحد الأول موجودة
+
+185
+00:23:48,660 --> 00:23:52,320
+و limit الحد التاني موجودة وبالتالي limit المجموعة
+
+186
+00:23:52,320 --> 00:23:59,000
+بيساوي مجموعة limits فlimit f of x minus c as x
+
+187
+00:23:59,000 --> 00:24:01,160
+tends to c زائد
+
+188
+00:24:08,360 --> 00:24:25,360
+limit f of x لمّا x تقول لـ c limit
+
+189
+00:24:25,360 --> 00:24:30,140
+f
+
+190
+00:24:30,140 --> 00:24:33,960
+of x لمّا x تقول لـ c
+
+191
+00:24:37,080 --> 00:24:44,860
+ال limit هذه لو أخدت y بساوي x minus c فبطلع x
+
+192
+00:24:44,860 --> 00:24:53,900
+بساوي y زائد c وبالتالي
+
+193
+00:24:53,900 --> 00:25:01,220
+لما x تقول ل c لما x تقول ل c هذا بيقدر ان y تقول
+
+194
+00:25:01,220 --> 00:25:12,090
+ل 0 صح؟ إذن هذه هي نفس limitF of Y لما Y تقول لـ 0
+
+195
+00:25:12,090 --> 00:25:15,550
+وذلك
+
+196
+00:25:15,550 --> 00:25:22,690
+ببتعوض عن X سالب C بساوي Y وهذا عدد ثابت F of C
+
+197
+00:25:22,690 --> 00:25:29,950
+عدد ثابت نهايته نفس العدد الثابت F of C Y ساوي طيب
+
+198
+00:25:29,950 --> 00:25:34,510
+احنا لسه من الفرض فرضين ان limit F of Y لما Y تقول
+
+199
+00:25:34,510 --> 00:25:42,440
+لـ 0 بساوي Lاللي هو سفر إذاً هذا بيساوي العدد L
+
+200
+00:25:42,440 --> 00:25:46,860
+اللي هو سفر زائد
+
+201
+00:25:46,860 --> 00:25:55,600
+F of C اللي هو F of C إذاً
+
+202
+00:25:55,600 --> 00:26:00,160
+هنا أثبتنا إنه limit F of X لما X تقول لـ C exist
+
+203
+00:26:00,160 --> 00:26:01,880
+و بيساوي F of C
+
+204
+00:26:05,410 --> 00:26:09,530
+تمام؟ إذا هين أثبتنا أن ال limit لل function عند
+
+205
+00:26:09,530 --> 00:26:17,170
+أي c exist و بساوي f of c و هذا طبعا الشرط اللي ..
+
+206
+00:26:17,170 --> 00:26:21,090
+لاحظوا أنتوا limit f of x عند أي c بتطلعت بالساوية
+
+207
+00:26:21,090 --> 00:26:25,970
+قيمة الدالة عن ال c هذا حسب chapter 5 هذا معناه أن
+
+208
+00:26:25,970 --> 00:26:31,510
+الدالة هذه تطلع continuous عند أي نقطة في المجال
+
+209
+00:26:31,510 --> 00:26:36,670
+تبعهاOkay إذا النتيجة الخلاصة من ال exercise هذا
+
+210
+00:26:36,670 --> 00:26:43,030
+exercise كتير مهم وهو إنه اللي لو كان في عندى
+
+211
+00:26:43,030 --> 00:26:50,370
+function from R to R و ال function هذه edited و
+
+212
+00:26:50,370 --> 00:26:56,700
+نهايتها عند السفر موجودةفالدال هذا بتطلع متصلة عن
+
+213
+00:26:56,700 --> 00:27:00,100
+كل الأعداد الحقيقية هذا النتيجة النهائية هذا اللي
+
+214
+00:27:00,100 --> 00:27:08,040
+أثبتناه في الجزء التاني okay تمام؟ وهذه نتيجة مهمة
+
+215
+00:27:08,040 --> 00:27:15,020
+ومعروفة في كورسات ال real analysis المتقدمة تمام
+
+216
+00:27:15,020 --> 00:27:20,860
+واضح؟ في أي استفسار؟إذا شفتوا هنا يعني كيف استغلنا
+
+217
+00:27:20,860 --> 00:27:26,080
+الفرض السار و كيف استغلنا ال hint الإرشادات اللي
+
+218
+00:27:26,080 --> 00:27:29,860
+أعطينا إياها الكتاب فاحنا ممكن نجيبلكم في الامتحان
+
+219
+00:27:29,860 --> 00:27:38,320
+أسئلة و نعطيلكم hint عليها أساسا كبداية للحل أو
+
+220
+00:27:38,320 --> 00:27:43,570
+البرهان الصحي و الشاطرة اللي تستغلها صحيOkay تمام
+
+221
+00:27:43,570 --> 00:27:48,130
+في أي أسئلة تانية section اربع واحد او اربع اتنين
+
+222
+00:27:48,130 --> 00:27:50,030
+رقم تلات عشر اربع اتنين
+
+223
+00:28:25,120 --> 00:28:33,640
+أي سؤال تلتاش سيكشن أربعة اتنين في عندي F function
+
+224
+00:28:33,640 --> 00:28:39,020
+from A to R و
+
+225
+00:28:39,020 --> 00:28:49,560
+C belong to R is a cluster point cluster point of
+
+226
+00:28:49,560 --> 00:28:50,220
+A
+
+227
+00:29:03,780 --> 00:29:18,360
+فالـ limit لـ f of x لما x تقول لـ c exists prove
+
+228
+00:29:18,360 --> 00:29:29,240
+أن ال limit ل absolute f of x لما x تقول ل c
+
+229
+00:29:29,240 --> 00:29:31,720
+بيساوي
+
+230
+00:29:34,790 --> 00:29:42,870
+بتساوي absolute limit f of x لما x تقوم بالاسم
+
+231
+00:29:42,870 --> 00:29:48,950
+where
+
+232
+00:29:48,950 --> 00:29:59,690
+حيث و where حيث absolute fالـ absolute value لأي
+
+233
+00:29:59,690 --> 00:30:05,550
+function تطلع function تانية تعريفها عند أي x أو
+
+234
+00:30:05,550 --> 00:30:13,430
+قيمتها عند أي x بساوي absolute f of x لكل x
+
+235
+00:30:27,830 --> 00:30:33,090
+بمعنى اخر اذا كان في عندي function و ال limit لها
+
+236
+00:30:33,090 --> 00:30:38,510
+ان c موجودة ف limit ال absolute value لها بتكون
+
+237
+00:30:38,510 --> 00:30:43,970
+موجودة و تساوي ال absolute value لل limit يعني
+
+238
+00:30:43,970 --> 00:30:48,090
+ممكن ابدل ال limit مع ال absolute value او ادخل ال
+
+239
+00:30:48,090 --> 00:30:53,730
+limit داخل ال absolute value وهذه حقيقة صحيحة لأن
+
+240
+00:30:53,730 --> 00:30:56,550
+ال absolute value function متتصرة
+
+241
+00:31:02,530 --> 00:31:19,850
+Okay تمام ف ..
+
+242
+00:31:19,850 --> 00:31:30,030
+طيب يعني
+
+243
+00:31:30,030 --> 00:31:38,610
+sayدعونا نفترض أن ال limit ل f of x لما x تقول إلى
+
+244
+00:31:38,610 --> 00:31:44,870
+c بساوي عدد L ينتمي ل R مش ال limit had existed
+
+245
+00:31:44,870 --> 00:31:48,830
+سميها L و
+
+246
+00:31:48,830 --> 00:31:52,430
+المطلوب we need to show
+
+247
+00:31:58,250 --> 00:32:08,570
+نحتاج أن نظهر أن الـ limit لـ absolute f of x as x
+
+248
+00:32:08,570 --> 00:32:11,510
+tends to c بساوي absolute L
+
+249
+00:32:35,630 --> 00:32:44,970
+أنا في نهاية
+
+250
+00:32:44,970 --> 00:32:52,570
+الأمر بدي أثبت أن الـ absolute بدي
+
+251
+00:32:52,570 --> 00:32:55,690
+في النهاية يكون هذا أصغر من أي جيبل إبسلون
+
+252
+00:32:58,740 --> 00:33:05,380
+لكل x بحيث ان absolute x minus c أكبر من سفر أصغر
+
+253
+00:33:05,380 --> 00:33:17,660
+من delta where delta to be determined يعني
+
+254
+00:33:17,660 --> 00:33:23,560
+هنحددها لاحقا هذا ايه عشان اثبت ان ال limit ال
+
+255
+00:33:23,560 --> 00:33:29,700
+function هذه يعني x بساوي absolute الفبدأثبت ان
+
+256
+00:33:29,700 --> 00:33:33,300
+absolute الفرخ هذا أصغر من epsilon عندما يكون
+
+257
+00:33:33,300 --> 00:33:39,240
+المسافة بين ال X و ال C أصغر من delta و X لا تساوي
+
+258
+00:33:39,240 --> 00:33:46,580
+ال C for some delta تعتمد على ال given epsilon طب
+
+259
+00:33:46,580 --> 00:33:50,860
+أنا عندي هذا
+
+260
+00:33:50,860 --> 00:33:57,000
+بيساوي absolute absolute F of X minus absolute
+
+261
+00:34:09,920 --> 00:34:16,520
+تمام؟ وهذا باستخدام ال triangle inequality أصغر من
+
+262
+00:34:16,520 --> 00:34:23,440
+أو ساوي absolute f of x minus L صح؟ في صورة من صور
+
+263
+00:34:23,440 --> 00:34:26,140
+ال triangle inequality يجب تقول إن هذا ال absolute
+
+264
+00:34:26,140 --> 00:34:30,140
+value ل absolute a minus absolute b أصغر من
+
+265
+00:34:30,140 --> 00:34:35,880
+absolute a minus bطب انا عندى limit f of x لما x
+
+266
+00:34:35,880 --> 00:34:41,400
+اقولها c بالساوي L فممكن اخلي هذا اصغر من اي given
+
+267
+00:34:41,400 --> 00:34:47,540
+epsilon وبالتالي هذه بتصير اصغر من اي epsilon okay
+
+268
+00:34:47,540 --> 00:34:52,420
+تمام اذا هنا خلينا نشوف
+
+269
+00:35:03,620 --> 00:35:09,800
+let epsilon أكبر
+
+270
+00:35:09,800 --> 00:35:18,820
+من السفر be givenبما انه since ال limit احنا فرضين
+
+271
+00:35:18,820 --> 00:35:25,840
+انه limit ل F of X عند X بساوي C بساوي L اذا يوجد
+
+272
+00:35:25,840 --> 00:35:31,580
+Delta تعتمد على ابسلون عدد موجب بحيث انه لكل X
+
+273
+00:35:31,580 --> 00:35:37,060
+ينتمي إلى A و absolute X minus C اصغر من Delta
+
+274
+00:35:37,060 --> 00:35:45,550
+اكبر من سفر هذا بيقديإنه absolute f of x minus L
+
+275
+00:35:45,550 --> 00:35:51,890
+أصغر من إبسلم نسمي هذا star نسمي ال implication
+
+276
+00:35:51,890 --> 00:36:03,570
+هذا star hence
+
+277
+00:36:08,200 --> 00:36:16,880
+by triangle inequality من متبينة المثلث x ينتمي by
+
+278
+00:36:16,880 --> 00:36:26,260
+triangle inequality and star we have لدينا لو كان
+
+279
+00:36:26,260 --> 00:36:32,680
+x ينتمي ل a و absolute x minus c أكبر من سفر أصغر
+
+280
+00:36:32,680 --> 00:36:48,240
+من deltaفهذا بيقدي انه absolute .. absolute f of x
+
+281
+00:36:48,240 --> 00:36:59,300
+minus absolute ال L هذا بيساوي absolute ..
+
+282
+00:36:59,300 --> 00:37:06,060
+absolute f of x minus absolute L
+
+283
+00:37:12,840 --> 00:37:17,300
+وهذا by ال triangle inequality by ال triangle
+
+284
+00:37:17,300 --> 00:37:24,520
+inequality أصغر من أوي ساوي absolute f of x minus
+
+285
+00:37:24,520 --> 00:37:32,300
+l و by star absolute f of x minus l أصغر من إبسل
+
+286
+00:37:32,300 --> 00:37:41,020
+تمام؟ since إبسلون was
+
+287
+00:37:41,020 --> 00:37:41,740
+arbitrary
+
+288
+00:37:47,340 --> 00:37:53,990
+إذاً we haveهك مكون أسبابنا أنه لأي epsilon أكبر
+
+289
+00:37:53,990 --> 00:37:59,950
+من الصفر يوجد delta تعتمد على epsilon عدد موجب من
+
+290
+00:37:59,950 --> 00:38:06,350
+حيث لكل x ينتمي ل a و المسافة بين x و c أصغر من
+
+291
+00:38:06,350 --> 00:38:11,630
+delta و x لا تساوي c فلل absolute value لf of x
+
+292
+00:38:11,630 --> 00:38:15,930
+minus absolute L أصغر من epsilon، إذن هذا معناه
+
+293
+00:38:15,930 --> 00:38:21,460
+حسب epsilon delta definition of limitإن الـ limit
+
+294
+00:38:21,460 --> 00:38:29,780
+ل absolute f of x as x tends to c بساوي absolute ل
+
+295
+00:38:29,780 --> 00:38:33,140
+هو
+
+296
+00:38:33,140 --> 00:38:38,420
+المطلوب وهذا اللي احنا عايزين نثبته هذا هو البرهان
+
+297
+00:38:39,940 --> 00:38:45,060
+إذا هنا اللاعب دور كبير في البرهان هو ال triangle
+
+298
+00:38:45,060 --> 00:38:52,420
+inequality و الفرض إنه limit and c موجودة بالساوية
+
+299
+00:38:52,420 --> 00:38:58,420
+L okay تمام؟ إذا أهمية ال exercise هذا يعتبر نظرية
+
+300
+00:38:58,420 --> 00:39:02,120
+و النظرية هذه بتقول إذا كان في end function
+
+301
+00:39:02,120 --> 00:39:07,590
+نهايتها and c موجودةفنهاية ال absolute value لل
+
+302
+00:39:07,590 --> 00:39:11,610
+function بالساوي ال absolute value لل limit بمعنى
+
+303
+00:39:11,610 --> 00:39:15,870
+أخر أنا ممكن أدخل ال limit داخل ال absolute value
+
+304
+00:39:15,870 --> 00:39:22,710
+أو أبدل ال limit مع ال absolute value okay تمام
+
+305
+00:39:22,710 --> 00:39:26,630
+واضح؟ في أسئلة تانية؟
+
+306
+00:39:35,800 --> 00:39:43,260
+أي سؤال أي استفسار okay
+
+307
+00:39:43,260 --> 00:39:45,560
+إذا نكتفي بهذا القدر
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..fbc3b3736d01cc7915999b4b9620f12ef3843f3d
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE.srt
@@ -0,0 +1,1235 @@
+1
+00:00:20,910 --> 00:00:26,430
+بسم الله الرحمن الرحيم في المحاضرة اليوم هناخد 
+
+2
+00:00:26,430 --> 00:00:32,890
+انتباه مقدمة بسيطة عن ال infinite series اللي 
+
+3
+00:00:32,890 --> 00:00:37,890
+بدأناها في المحاضرة السابقة، في المحاضرة السابقة
+
+4
+00:00:37,890 --> 00:00:41,610
+عرفنا ما معنى أن infinite series of real numbers
+
+5
+00:00:41,610 --> 00:00:46,050
+converge معناه هذا يكافئ أن ال sequence of partial
+
+6
+00:00:46,050 --> 00:00:51,970
+sums S اللي سميناها Sn حيث أن ال nth partial sum هو
+
+7
+00:00:51,970 --> 00:00:56,170
+مجموع أول n من حدود ال series، إذا كانت ال sequence
+
+8
+00:00:56,170 --> 00:01:00,550
+هذه convergent، إذا ال sequence of partial sums
+
+9
+00:01:00,550 --> 00:01:03,990
+convergent بتكون ال series convergent، إذا ال
+
+10
+00:01:03,990 --> 00:01:06,770
+sequence of partial sums divergent بتكون ال series 
+
+11
+00:01:06,770 --> 00:01:11,760
+divergent، طيب لو كانت ال sequence of partial sums
+
+12
+00:01:11,760 --> 00:01:15,920
+convergent وال limit تبعتها عدد S ففي الحالة هذه 
+
+13
+00:01:15,920 --> 00:01:19,420
+بتقول أن ال series converged طبعا وال sum تبع ال
+
+14
+00:01:19,420 --> 00:01:22,680
+series، مجموع ال series بيساوي ال limit لل sequence 
+
+15
+00:01:22,680 --> 00:01:26,800
+of partial sums اللي هو S، إذا في الحالة هذه S is
+
+16
+00:01:26,800 --> 00:01:32,860
+the sum of the infinite series، الآن في عندي نظرية
+
+17
+00:01:32,860 --> 00:01:38,220
+بتعطيني test for divergence بتسميه ال nth term test
+
+18
+00:01:38,220 --> 00:01:43,360
+زي ما درستها في Calculus B، فالنظرية هذه بتقول لو
+
+19
+00:01:43,360 --> 00:01:46,120
+كان في عندي series وال series كانت convergent
+
+20
+00:01:46,120 --> 00:01:50,440
+فلا بد أن it is necessary that the limit of the nth
+
+21
+00:01:50,440 --> 00:01:57,250
+term بيساوي صفر، البرهان سهل، هاي ال Nth partial sum 
+
+22
+00:01:57,250 --> 00:02:01,830
+مجموع أول N من حدود ال series وهي ال N minus
+
+23
+00:02:01,830 --> 00:02:06,110
+first partial sum اللي هو مجموع N سالب واحد من
+
+24
+00:02:06,110 --> 00:02:12,310
+الحدود الأولانية، لما نيجي نطرح، لما نيجي نطرح فكل 
+
+25
+00:02:12,310 --> 00:02:19,910
+الحدود هذه بتروح مع بعضها يبقى عندي الفرق XN، أنا
+
+26
+00:02:19,910 --> 00:02:23,650
+فارض أن ال series converge، إذا ال limit لل
+
+27
+00:02:23,650 --> 00:02:27,270
+sequence of partial sums exist وبيساوى sum real
+
+28
+00:02:27,270 --> 00:02:32,570
+number S، الآن باخد ال limit للطرفين في ال star هنا 
+
+29
+00:02:33,630 --> 00:02:38,130
+باخد limit of both sides we get أن limit xn
+
+30
+00:02:38,130 --> 00:02:43,590
+بيساوي limit sn  ناقص limit sn ناقص واحد، ال
+
+31
+00:02:43,590 --> 00:02:46,930
+limit ال sequence of partial sums sn وهذه هي نفس ال
+
+32
+00:02:46,930 --> 00:02:51,070
+sequence of partial sums بس حذفنا أو زدنا حد برضه
+
+33
+00:02:51,070 --> 00:02:55,170
+ال limit تبعتها s، إذا ال limit ل xn بيطلع بيساوي
+
+34
+00:02:55,170 --> 00:03:01,710
+صفر كما هو مظلوم، تمام؟ واضح البرهان؟ الآن في عندي 
+
+35
+00:03:01,710 --> 00:03:02,310
+remark
+
+36
+00:03:10,040 --> 00:03:15,900
+the converse of
+
+37
+00:03:15,900 --> 00:03:23,140
+above theorem is
+
+38
+00:03:23,140 --> 00:03:27,860
+false، عكس 
+
+39
+00:03:27,860 --> 00:03:36,120
+النظرية السابقة ليس صحيحا، بمعنى لو كانت xn
+
+40
+00:03:38,350 --> 00:03:45,490
+converge to zero هذا لا يؤدي بالضرورة، لا يؤدي
+
+41
+00:03:45,490 --> 00:03:56,310
+مش شرط يؤدي أن ال series sigma xn converge وهي
+
+42
+00:03:56,310 --> 00:03:58,310
+مثال على ذلك، ناخد مثال
+
+43
+00:04:17,840 --> 00:04:25,520
+example the harmonic series satisfies 
+
+44
+00:04:39,920 --> 00:04:48,080
+أن ال limit ل xn عبارة عن ال limit ل 1 على n يساوي
+
+45
+00:04:48,080 --> 00:04:59,420
+صفر، لكن however، however
+
+46
+00:04:59,420 --> 00:05:04,560
+ال series، ال harmonic series diverges
+
+47
+00:05:09,690 --> 00:05:14,990
+ال harmonic series is divergent مش convergent، ليش؟
+
+48
+00:05:14,990 --> 00:05:22,770
+why؟ 
+
+49
+00:05:22,770 --> 00:05:29,330
+احنا برهنا الكلام هذا في chapter تلاتة بس كش في
+
+50
+00:05:29,330 --> 00:05:31,410
+section تلاتة خمسة 
+
+51
+00:05:36,620 --> 00:05:44,980
+فاكرين أن ال sequence هذه كانت، طيب نجاوب ليه ال
+
+52
+00:05:44,980 --> 00:05:52,720
+harmonic series diverges، في عندي جوابين، answer one
+
+53
+00:05:52,720 --> 00:06:00,660
+الإجابة الأولى، في 
+
+54
+00:06:00,660 --> 00:06:03,740
+عندي مثال أخدنا
+
+55
+00:06:08,530 --> 00:06:14,430
+by example، لسه ماخدينه اللي كان هذا الجزء اللي
+
+56
+00:06:14,430 --> 00:06:18,590
+بتعلق فيه اللي هو ال sequence of partial sums لل
+
+57
+00:06:18,590 --> 00:06:25,470
+series هذه، أثبتنا أنها not cauchy، صح؟ وكان هذا جزء
+
+58
+00:06:25,470 --> 00:06:31,610
+من ايه؟ من تكملة البرهان، صح؟ إذا نشوف الرقم تبعها
+
+59
+00:06:31,610 --> 00:06:34,830
+بالظبط section
+
+60
+00:06:37,490 --> 00:06:50,870
+مثال تلاتة خمسة ستة، الجزء C، by this example the
+
+61
+00:06:50,870 --> 00:07:02,430
+sequence of partial sums Sn
+
+62
+00:07:02,430 --> 00:07:03,370
+where
+
+63
+00:07:05,750 --> 00:07:13,890
+Sn بيساوي سيجما من K بيساوي واحد إلى N لواحد على K
+
+64
+00:07:13,890 --> 00:07:21,150
+اللي هو واحد زائد نص زائد واحد على N، أثبتنا إن ال
+
+65
+00:07:21,150 --> 00:07:30,630
+sequence هذه is not Cauchy، is not Cauchy and
+
+66
+00:07:30,630 --> 00:07:34,850
+therefore not convergent
+
+67
+00:07:40,330 --> 00:07:49,510
+حسب by Cauchy، by Cauchy criterion، Cauchy criterion
+
+68
+00:07:49,510 --> 00:07:52,950
+بتقول أي sequence of real numbers is convergent if
+
+69
+00:07:52,950 --> 00:07:56,190
+and only if it is Cauchy، اللي احنا أثبتنا إن ال
+
+70
+00:07:56,190 --> 00:08:01,180
+sequence هذه في المثال هذا ماهياش كوشي وبالتالي
+
+71
+00:08:01,180 --> 00:08:04,460
+not convergent، طب ما هذه هي ال sequence of partial 
+
+72
+00:08:04,460 --> 00:08:07,680
+... هذه هي ال sequence of partial sums لل harmonic
+
+73
+00:08:07,680 --> 00:08:11,020
+series، إذا by above definition
+
+74
+00:08:15,530 --> 00:08:19,870
+طبعا ال definition المسألة اللي كتبناها أول واحد
+
+75
+00:08:19,870 --> 00:08:23,830
+مادام ال series of partial sums is not convergent
+
+76
+00:08:23,830 --> 00:08:30,150
+إذا ال series نفسها is divergent
+
+77
+00:08:33,300 --> 00:08:38,940
+Okay، إذا هذا كان إحدى الإجابات وليه، ليه ال
+
+78
+00:08:38,940 --> 00:08:42,960
+series هي divergent، هاي الإثبات تبعها هنا جاي من
+
+79
+00:08:42,960 --> 00:08:47,360
+المثال هذا، إن ال sequence of partial sums طلعت not
+
+80
+00:08:47,360 --> 00:08:51,340
+Cauchy وبالتالي not convergent، هذا السبب، في كمان
+
+81
+00:08:51,340 --> 00:09:02,140
+سبب ثاني أو حل ثاني أو إجابة أخرى، answer
+
+82
+00:09:02,140 --> 00:09:13,540
+two، إنه by، في مثال آخر أثبتنا فيه by example
+
+83
+00:09:13,540 --> 00:09:17,900
+تلاتة
+
+84
+00:09:17,900 --> 00:09:24,800
+تلاتة تلاتة بي، إذا في section تلاتة تلاتة 
+
+85
+00:09:24,800 --> 00:09:31,540
+المثال تلاتة بي أثبتنا فيه إن ال sequence و
+
+86
+00:09:31,540 --> 00:09:32,480
+partial sums
+
+87
+00:09:34,910 --> 00:09:40,910
+the sequence of partial sums
+
+88
+00:09:40,910 --> 00:09:44,190
+Sn 
+
+89
+00:09:44,190 --> 00:09:50,370
+is unbounded 
+
+90
+00:09:50,370 --> 00:09:55,910
+أثبتنا بالمثال هذا أن ال sequence Sn of partial
+
+91
+00:09:55,910 --> 00:10:04,760
+sums اللي هي هذه is unbounded and therefore، إذا
+
+92
+00:10:04,760 --> 00:10:08,380
+كانت ال sequence unbounded إذا بتطلع divergent أو
+
+93
+00:10:08,380 --> 00:10:16,060
+not convergent، لأن sn is divergent، لأن لو كانت 
+
+94
+00:10:16,060 --> 00:10:20,800
+convergent بتكون bounded وبالتالي therefore ال
+
+95
+00:10:20,800 --> 00:10:28,090
+series أو ال harmonic series divergent، إذا هذا برضه
+
+96
+00:10:28,090 --> 00:10:33,350
+إجابة ثانية بتخلي ال harmonic series divergent
+
+97
+00:10:33,350 --> 00:10:40,830
+تمام، طيب نرجع ناخد أمثلة أخرى 
+
+98
+00:11:08,590 --> 00:11:18,590
+أول شيء ال geometric series ال
+
+99
+00:11:18,590 --> 00:11:26,210
+geometric series اللي هي summation من k بيساوي صفر
+
+100
+00:11:26,210 --> 00:11:32,090
+to infinity لـ R to the power K، اللي الحد الأول تبعها واحد
+
+101
+00:11:32,090 --> 00:11:37,250
+والأساس تبعها R، اشمالها واحد
+
+102
+00:11:40,350 --> 00:11:49,570
+converges if absolute r أصغر من one and
+
+103
+00:11:49,570 --> 00:12:06,550
+diverges and its sum، its sum بيساوي واحد على واحد 
+
+104
+00:12:06,550 --> 00:12:08,250
+ناقص r
+
+105
+00:12:14,230 --> 00:12:20,410
+and diverges if
+
+106
+00:12:20,410 --> 00:12:27,790
+absolute r أكبر من أو يساوي واحد، أثبتنا
+
+107
+00:12:27,790 --> 00:12:31,250
+هذا الجزء المرة اللي فاتت في الأول ولا ما أثبتناه 
+
+108
+00:12:31,250 --> 00:12:34,350
+مش؟
+
+109
+00:12:34,350 --> 00:12:38,010
+أثبتنا صحيح؟ okay، إذا
+
+110
+00:12:44,740 --> 00:12:52,060
+proof part one was 
+
+111
+00:12:52,060 --> 00:12:55,940
+proved last 
+
+112
+00:12:55,940 --> 00:13:01,400
+time، last time
+
+113
+00:13:01,400 --> 00:13:09,160
+to 
+
+114
+00:13:09,160 --> 00:13:12,760
+prove two, assume
+
+115
+00:13:15,240 --> 00:13:29,520
+absolute r أكبر من أو يساوي الواحد، افترض
+
+116
+00:13:29,520 --> 00:13:36,400
+أن absolute r أكبر من أو يساوي الواحد، طيب then
+
+117
+00:13:44,600 --> 00:13:53,300
+limit xn as n tends to infinity بيساوي limit r to
+
+118
+00:13:53,300 --> 00:13:59,220
+the power n as n tends to infinity، لحظة 
+
+119
+00:13:59,220 --> 00:14:06,940
+n to، absolute r أكبر من واحد بيقدر أن r أكبر من ... 
+
+120
+00:14:06,940 --> 00:14:08,580
+أصغر من واحد
+
+121
+00:14:11,700 --> 00:14:22,700
+or R أكبر من سالب واحد أو 
+
+122
+00:14:22,700 --> 00:14:30,200
+R أكبر من واحد أو R أصغر من سالب 
+
+123
+00:14:30,200 --> 00:14:34,640
+واحد وبالتالي
+
+124
+00:14:34,640 --> 00:14:42,080
+limit R أس N مش ممكن تساوي صفر، limit لـ R أس n شفنا 
+
+125
+00:14:42,080 --> 00:14:50,420
+أن هذه بيساوي صفر فقط لما ال R يكون أصغر من واحد وأكبر 
+
+126
+00:14:50,420 --> 00:14:57,940
+من أو يساوي صفر وبالتالي، إذا by، إذا by 
+
+127
+00:14:57,940 --> 00:15:08,300
+nth، by nth term test، إذا الحد العام، الحد النوني لل
+
+128
+00:15:08,300 --> 00:15:12,700
+series هذه لا يساوي، لا صفر ال limit تبعته ما بيساويش 
+
+129
+00:15:12,700 --> 00:15:20,400
+صفر وبالتالي by the nth term test، المسألة اه إذا كان
+
+130
+00:15:20,400 --> 00:15:25,480
+limit الحد النوني بيساوي صفر فال test بتقول لي أن 
+
+131
+00:15:25,480 --> 00:15:31,500
+ال series is
+
+132
+00:15:31,500 --> 00:15:37,480
+divergent، ال series sigma ل R to the power N من N equal 0 to 
+
+133
+00:15:37,480 --> 00:15:39,000
+infinity diverges
+
+134
+00:15:45,290 --> 00:15:48,990
+لأنه لو كانت convergent فالمفروض limit الحد النوني
+
+135
+00:15:48,990 --> 00:15:55,090
+يساوي صفر وهذا مش موجود، تمام؟ إن أنا شفت هنا كيف
+
+136
+00:15:55,090 --> 00:16:00,710
+أخدنا ال ... أو استخدمنا ال nth term test لإثبات ال
+
+137
+00:16:00,710 --> 00:16:05,150
+divergence، مثال
+
+138
+00:16:05,150 --> 00:16:05,630
+ثاني 
+
+139
+00:16:14,400 --> 00:16:23,600
+show that ال series اللي متولدة من ال sequence
+
+140
+00:16:23,600 --> 00:16:29,840
+سالب واحد to the power n اللي 
+
+141
+00:16:29,840 --> 00:16:37,100
+هي أول حد هيكون واحد بعدين سالب واحد بعدين واحد
+
+142
+00:16:37,100 --> 00:16:43,030
+بعدين سالب واحد وهكذا show that this series
+
+143
+00:16:43,030 --> 00:16:55,610
+diverges تعالوا 
+
+144
+00:16:55,610 --> 00:16:59,510
+نشوف الـ sequence of partial sums ناخد الـ sequence
+
+145
+00:16:59,510 --> 00:17:03,070
+of partial sums والله ده طلعت الـ sequence of
+
+146
+00:17:03,070 --> 00:17:06,810
+partial sums convergent بيكون الـ series convergent
+
+147
+00:17:06,810 --> 00:17:10,730
+والـ sum تبعها بيساوي الـ limit للـ sequence of
+
+148
+00:17:10,730 --> 00:17:14,290
+partial sums مظبوط وإذا طلعت الـ sequence of
+
+149
+00:17:14,290 --> 00:17:19,570
+partial sums divergent فالـ series اللي تابعة إليها
+
+150
+00:17:19,570 --> 00:17:24,650
+بتكون divergent لذا هنا هنفحص هل الـ sequence of
+
+151
+00:17:24,650 --> 00:17:29,410
+partial sums divergent ولا convergent طيب تعالوا 
+
+152
+00:17:29,410 --> 00:17:34,750
+نفحص Sn الـ N في partial sums هذا summation من K 
+
+153
+00:17:34,750 --> 00:17:47,900
+equal 0 to N لـ سالب واحد plus k هذا xk فهذا هيطلع 
+
+154
+00:17:47,900 --> 00:17:57,300
+لقيمتين الـ هيطلع قيمتين
+
+155
+00:17:57,300 --> 00:18:05,300
+لو 
+
+156
+00:18:05,300 --> 00:18:14,590
+كان in even أو n odd لو كانت n even يعني نفرض بأن n
+
+157
+00:18:14,590 --> 00:18:22,470
+بساوي صفر إذن هيطلع واحد، n بساوي اثنين، هيطلع 
+
+158
+00:18:22,470 --> 00:18:29,470
+أندي تلت حدود، مجموعهم برضه واحد، وهكذا، إذن
+
+159
+00:18:29,470 --> 00:18:35,160
+المجموع هذا هيطلع واحد إذا كانت الـ n even أما لو 
+
+160
+00:18:35,160 --> 00:18:40,680
+كانت الـ n odd يعني لو أخدت n بالساوية واحد لو 
+
+161
+00:18:40,680 --> 00:18:46,040
+أخدت n بالساوية واحد فهيطلع عندي حدين مجموعهم صفر
+
+162
+00:18:46,040 --> 00:18:50,960
+لو أخدت n بالساوية ثلاثة هيطلع مجموع أول أربع
+
+163
+00:18:50,960 --> 00:18:56,220
+حدود برضه بيطلع مجموعهم صفر وهكذا إذا صفر الـ n 
+
+164
+00:18:56,220 --> 00:19:00,160
+partial sums بساوية صفر إذا كانت n odd واحد إذا
+
+165
+00:19:00,160 --> 00:19:05,650
+كانت n even وبالتالي therefore therefore a
+
+166
+00:19:05,650 --> 00:19:11,110
+sequence of partial sums is an alternating series
+
+167
+00:19:11,110 --> 00:19:16,170
+يعني حدودها متذبذبة بين صفر وواحد أو أول حد واحد 
+
+168
+00:19:16,170 --> 00:19:23,710
+الثاني صفر واحد صفر وهكذا which
+
+169
+00:19:23,710 --> 00:19:29,710
+is divergent هذه أمرها ما كانت convergent
+
+170
+00:19:33,470 --> 00:19:39,270
+الـ sequence هذه divergent عارفين ليه؟ لأن هي الـ
+
+171
+00:19:39,270 --> 00:19:54,130
+proof الـ subsequence الحدود
+
+172
+00:19:54,130 --> 00:19:58,330
+مثلًا الزوجية S2K
+
+173
+00:20:03,520 --> 00:20:08,760
+هي أول حد وهي الثاني لأن الحدود الزوجية أصفار كلهم
+
+174
+00:20:08,760 --> 00:20:17,120
+صح؟ تكون بترجع صفر and الـ subsequence الثانية اللي 
+
+175
+00:20:17,120 --> 00:20:23,400
+حدودها فردية كلهم
+
+176
+00:20:23,400 --> 00:20:30,960
+واحد، ثابت واحد وهذه تكون بترجع واحد نعم؟
+
+177
+00:20:31,600 --> 00:20:36,180
+وبالتالي إذا ما دام في عندي two subsequences واحدة 
+
+178
+00:20:36,180 --> 00:20:40,120
+converge لصفر وواحدة converge لواحد وصفر لا يساوي 
+
+179
+00:20:40,120 --> 00:20:46,380
+الواحد وصفر لا يساوي الواحد معناته by the
+
+180
+00:20:46,380 --> 00:20:50,400
+divergence criterion الـ sequence هذه is divergent
+
+181
+00:20:51,890 --> 00:20:56,830
+لأن لو كانت الـ sequence هذي convergent فمفروض أي 
+
+182
+00:20:56,830 --> 00:21:00,250
+subsequence تكون convergent لنفس الـ limit يعني 
+
+183
+00:21:00,250 --> 00:21:03,630
+المفروض دول الـ limits تكون متساوية وهذا مستحيل
+
+184
+00:21:03,630 --> 00:21:07,130
+إذا
+
+185
+00:21:07,130 --> 00:21:11,490
+الـ sequence of partial sums هنا divergent وبالتالي
+
+186
+00:21:11,490 --> 00:21:17,130
+نكمل الحل هنا وبالتالي therefore the series
+
+187
+00:21:21,790 --> 00:21:27,290
+المتولد من الـ sequence سالب واحد أس N اللي هي الـ
+
+188
+00:21:27,290 --> 00:21:31,970
+series هذه is
+
+189
+00:21:31,970 --> 00:21:38,510
+divergent okay
+
+190
+00:21:38,510 --> 00:21:43,210
+تمام وبالتالي هيك ممكن أثبتنا هذا مثال على
+
+191
+00:21:43,210 --> 00:21:46,430
+divergence series إذن عشان أثبت الـ series
+
+192
+00:21:46,430 --> 00:21:51,260
+divergent أو convergent بحاول أفحص الـ sequence of
+
+193
+00:21:51,260 --> 00:21:55,120
+partial sums وأفحص هل الـ sequence of partial
+
+194
+00:21:55,120 --> 00:22:01,880
+sums convergent ولا divergent ناخد 
+
+195
+00:22:01,880 --> 00:22:06,760
+كمان مثال مختلف من نوع آخر مثال رقم 3
+
+196
+00:22:21,550 --> 00:22:29,550
+Discuss the convergence of
+
+197
+00:22:29,550 --> 00:22:33,110
+the
+
+198
+00:22:33,110 --> 00:22:43,010
+series sigma from N equals one to infinity لواحد
+
+199
+00:22:43,010 --> 00:22:45,130
+على N في N زائد واحد
+
+200
+00:22:53,320 --> 00:22:59,340
+لما يكون الحد العام للـ series xn عبارة عن كسر زي 
+
+201
+00:22:59,340 --> 00:23:04,260
+هذا والكسر اللي زي هذا ممكن تجزئته إلى كسور جزئية
+
+202
+00:23:04,260 --> 00:23:10,220
+فبنعمل كسور جزئية الأول وبنجزئ الكسر هذا إلى
+
+203
+00:23:10,220 --> 00:23:16,600
+مجموع كسرين جزئيين إذا by partial fractions أو use
+
+204
+00:23:16,600 --> 00:23:22,280
+partial fractions وهذا تعلمته في تفاضل بقى
+
+205
+00:23:25,060 --> 00:23:30,740
+by partial fractions هي
+
+206
+00:23:30,740 --> 00:23:40,560
+عندي واحد على k في k زائد واحد بساوي a على k زائد 
+
+207
+00:23:40,560 --> 00:23:42,920
+b over k plus one
+
+208
+00:23:48,420 --> 00:23:53,360
+الآن لتحديد ثوابت A وB نتخلص من الكسور في المعادلة
+
+209
+00:23:53,360 --> 00:23:58,940
+هذه وذلك بضرب طرفي المعادلة في المقام تبع الطرف
+
+210
+00:23:58,940 --> 00:24:08,530
+اليسار إذا بضرب في K في K زائد واحد يطلع عندي واحد 
+
+211
+00:24:08,530 --> 00:24:16,450
+بساوي a في k plus one زائد b في k الآن خد k بساوي 
+
+212
+00:24:16,450 --> 00:24:22,610
+صفر هذا بيقدر أن a بساوي واحد وخد k بساوي سالب 
+
+213
+00:24:22,610 --> 00:24:29,650
+واحد بيقدر أن السالب b بساوي واحد بيقدر أن b بساوي
+
+214
+00:24:29,650 --> 00:24:38,450
+سالب واحد إذا طلع أنا عندي واحد على ك في ك زائد
+
+215
+00:24:38,450 --> 00:24:45,170
+واحد بساوي واحد على ك سالب واحد على ك زائد واحد
+
+216
+00:24:45,170 --> 00:24:51,550
+الآن now تعالوا نشوف الـ nth partial sum أو نبحث الـ 
+
+217
+00:24:51,550 --> 00:24:55,430
+sequence of partial sums ونبحث هل هي convergent
+
+218
+00:24:55,430 --> 00:25:03,610
+ولا divergent فهي عندي sm بساوي summation من k
+
+219
+00:25:03,610 --> 00:25:13,170
+بساوي واحد إلى n لـ xk اللي
+
+220
+00:25:13,170 --> 00:25:19,670
+هو summation من k بساوي واحد إلى n لواحد على k في
+
+221
+00:25:19,670 --> 00:25:27,210
+k زائد واحد وهذا الآن باستخدام الـ partial fractions
+
+222
+00:25:27,210 --> 00:25:33,810
+summation من k بساوي واحد إلى n إلى واحد على k
+
+223
+00:25:33,810 --> 00:25:42,790
+سالب واحد على k موجب واحد الآن
+
+224
+00:25:42,790 --> 00:25:47,450
+هذا المجموع تعالوا نفرد تعالوا نفرفته let's expand
+
+225
+00:25:47,450 --> 00:25:49,490
+it يعني نفرفته
+
+226
+00:25:53,610 --> 00:25:58,830
+هذا مجموع منتهي في n من الحدود خد k بالساوية واحد 
+
+227
+00:25:58,830 --> 00:26:06,930
+بيطلع أول حد واحد سالب نصف خد k بساوي اثنين بيطلع
+
+228
+00:26:06,930 --> 00:26:16,010
+الحد بعده ونصف سالب ثلث وهكذا إلى الحد الأخير 
+
+229
+00:26:16,010 --> 00:26:23,560
+هيكون واحد على n ناقص واحد على n زائد واحد بنلاحظ 
+
+230
+00:26:23,560 --> 00:26:28,920
+أن المجموع هذا telescoping يعني في حدود فيها ازاي
+
+231
+00:26:28,920 --> 00:26:33,280
+تتلاشى مع الحدود اللي بعديها يعني سالب نصف لاحظوا 
+
+232
+00:26:33,280 --> 00:26:38,640
+بيروح مع موجب نصف وسالب ثلث هيروح مع موجب ثلث في 
+
+233
+00:26:38,640 --> 00:26:43,340
+الحد اللي يليه مباشرة وواحد على n هذا بيروح مع
+
+234
+00:26:43,340 --> 00:26:50,510
+سالب واحد على n في الحد اللي يصدقه مباشرة فيبقى كل
+
+235
+00:26:50,510 --> 00:26:55,650
+شيء بيروح بيظل يبقى عندي واحد negative one over n
+
+236
+00:26:55,650 --> 00:27:01,410
+زائد واحد إذا أنا طلع عيني أثبتت أن sn بساوي واحد 
+
+237
+00:27:01,410 --> 00:27:06,410
+negative واحد على n زائد واحد الكلام هذا صحيح for
+
+238
+00:27:06,410 --> 00:27:10,480
+every natural number n أخذ قيمة كما نسميها limit of
+
+239
+00:27:10,480 --> 00:27:16,580
+both sides as n tends to infinity نحصل على قيمة Sn
+
+240
+00:27:16,580 --> 00:27:17,980
+كما نسميها limit of both sides as n tends to
+
+241
+00:27:17,980 --> 00:27:18,500
+infinity نحصل على قيمة Sn كما نسميها limit of both
+
+242
+00:27:18,500 --> 00:27:19,140
+sides as n tends to infinity نحصل على قيمة Sn كما
+
+243
+00:27:19,140 --> 00:27:20,040
+نحصل على قيمة Sn كما نسميها limit of both sides as
+
+244
+00:27:20,040 --> 00:27:20,180
+n tends to infinity نحصل على قيمة Sn كما نسميها
+
+245
+00:27:20,180 --> 00:27:22,340
+limit of both sides as n tends to infinity نحصل
+
+246
+00:27:22,340 --> 00:27:24,580
+على قيمة Sn كما نسميها limit of both sides as n
+
+247
+00:27:24,580 --> 00:27:29,920
+tends to infinity نحصل على قيمة Sn كما نسميها
+
+248
+00:27:29,920 --> 00:27:36,040
+limit of both sides as
+
+249
+00:27:36,380 --> 00:27:41,720
+is convergent والـ limit تبعها بساوي واحد تمام
+
+250
+00:27:41,720 --> 00:27:46,480
+وبالتالي حسب التعريف تبع الـ convergence للـ
+
+251
+00:27:46,480 --> 00:27:49,680
+infinite series the infinite series اللي احنا
+
+252
+00:27:49,680 --> 00:27:54,320
+عايزين نفحصها اللي هي summation from n equals one
+
+253
+00:27:54,320 --> 00:28:00,200
+to infinity لـ one over n في n plus one إشملها
+
+254
+00:28:00,200 --> 00:28:02,260
+converges
+
+255
+00:28:03,720 --> 00:28:10,920
+and الـ sum تبعها يعني مجموعها بساوي واحد اللي هو 
+
+256
+00:28:10,920 --> 00:28:17,360
+limit للـ sequence of partial sums تمام؟
+
+257
+00:28:17,360 --> 00:28:20,800
+إذا هذا النوع من الـ series بنسميه telescoping ..
+
+258
+00:28:20,800 --> 00:28:28,140
+telescoping .. telescoping series
+
+259
+00:28:31,710 --> 00:28:36,990
+such type of series is called telescoping series
+
+260
+00:28:36,990 --> 00:28:41,110
+okay تمام واضح
+
+261
+00:28:54,430 --> 00:29:00,810
+طيب هناخد بس نظرية سريعة ويعني مش .. البرهان مش 
+
+262
+00:29:00,810 --> 00:29:10,810
+هياخد الا دقيقة واحدة theorem Cauchy
+
+263
+00:29:10,810 --> 00:29:17,930
+.. Cauchy criterion for
+
+264
+00:29:17,930 --> 00:29:20,950
+series
+
+265
+00:29:25,660 --> 00:29:31,060
+احنا أخذنا قبلها كوشي كريتيريا for sequences لأن
+
+266
+00:29:31,060 --> 00:29:37,560
+في كوشي كريتيريا for series فالـ .. الكوشي كريتيريا
+
+267
+00:29:37,560 --> 00:29:45,840
+for series بتنص على أنه الـ series sigma
+
+268
+00:29:45,840 --> 00:29:53,100
+x in converges if
+
+269
+00:29:53,100 --> 00:29:54,500
+and only if
+
+270
+00:29:58,620 --> 00:30:05,760
+لكل ابسلون أكبر من صفر يوجد capital N يعتمد على
+
+271
+00:30:05,760 --> 00:30:13,500
+ابسلون عدد طبيعي بحيث أنه لكل M أكبر من N أكبر من
+
+272
+00:30:13,500 --> 00:30:21,360
+أو يساوي capital N بيطلع absolute SM ناقص SN اللي
+
+273
+00:30:21,360 --> 00:30:28,830
+هو عبارة عن absolute Xm زائد واحد زائد xn زائد
+
+274
+00:30:28,830 --> 00:30:35,030
+اثنين زائد xm أصغر من اكسمن
+
+275
+00:30:49,160 --> 00:30:55,400
+كمان مرة الـ series هذه converges if and only if
+
+276
+00:30:55,400 --> 00:31:00,440
+for every epsilon فيه capital N بحيث لكل M وN
+
+277
+00:31:00,440 --> 00:31:05,140
+أكبر من أو يساوي capital N وM بتكون أكبر من N الـ
+
+278
+00:31:05,140 --> 00:31:10,520
+absolute value للفرق هذا أصغر من epsilon طب هذا هو
+
+279
+00:31:10,520 --> 00:31:11,440
+شرط كوشي
+
+280
+00:31:17,000 --> 00:31:24,920
+that is .. that is .. يعني هذا يعني أنه sigma x in 
+
+281
+00:31:24,920 --> 00:31:30,640
+converges if and only if the sequence of partial
+
+282
+00:31:30,640 --> 00:31:34,860
+sums is Cauchy
+
+283
+00:31:34,860 --> 00:31:39,880
+إذا كانت the sequence of partial sums is Cauchy هذا
+
+284
+00:31:39,880 --> 00:31:45,280
+شرط Cauchy  ينتج من the Cauchy criterion for
+
+285
+00:31:45,280 --> 00:31:51,890
+sequences طيب احنا أخدنا by definition من the 
+
+286
+00:31:51,890 --> 00:31:56,050
+definition تبع the convergence لل series by
+
+287
+00:31:56,050 --> 00:32:00,910
+definition the series sigma
+
+288
+00:32:00,910 --> 00:32:07,510
+xn converges if and only if the sequence of 
+
+289
+00:32:07,510 --> 00:32:13,870
+partial sums اللي 
+
+290
+00:32:13,870 --> 00:32:14,950
+هي Sn
+
+291
+00:32:22,440 --> 00:32:33,300
+converges مظبوط؟ by the Cauchy criterion
+
+292
+00:32:33,300 --> 00:32:41,990
+for sequences .. for the sequences من المتاليات الـ
+
+293
+00:32:41,990 --> 00:32:52,750
+sequence sn converges if and only if sn is Cauchy
+
+294
+00:32:56,430 --> 00:33:02,310
+هو بالتالي the series sigma xn converges if and
+
+295
+00:33:02,310 --> 00:33:06,150
+only if the sequence Sn converges طيب ما هذي
+
+296
+00:33:06,150 --> 00:33:09,690
+converges if and only if it is Cauchy، إذا the
+
+297
+00:33:09,690 --> 00:33:14,870
+series sigma xn converges if and only if the
+
+298
+00:33:14,870 --> 00:33:20,590
+sequence of partial sums is Cauchy، و هذا هو 
+
+299
+00:33:20,590 --> 00:33:21,150
+المطلوب
+
+300
+00:33:24,120 --> 00:33:28,920
+طبعا هذا هو شرط كوشي لحظوا SM  the M هنا أكبر من N
+
+301
+00:33:28,920 --> 00:33:39,020
+فلو اتكتبت الحدود فتبعت SM هيكون X1 إلى XM SN  the N 
+
+302
+00:33:39,020 --> 00:33:45,740
+أصغر من M فالحدود من X1 إلى XN لما أطرح بيضل عندي 
+
+303
+00:33:45,740 --> 00:33:50,260
+كل الحدود المتشابهة بيضل عندي XN زياد واحد XN زياد
+
+304
+00:33:50,260 --> 00:33:51,840
+اتنين إلى XM
+
+305
+00:33:55,430 --> 00:34:02,690
+تمام؟ اذا بنوقف هنا ال .. هذا برهان the Cauchy criterion
+
+306
+00:34:02,690 --> 00:34:07,190
+for series بنوقف عند النظرية هذه و المرة الجاية ان
+
+307
+00:34:07,190 --> 00:34:14,310
+شاء الله بنكمل هناخد the limit comparison test
+
+308
+00:34:21,040 --> 00:34:25,600
+هناك تجارب تجارب تجارب تجارب تجارب تجارب تجارب
+
+309
+00:34:25,600 --> 00:34:27,540
+تجارب تجارب تجارب 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..075da0f4df05e1727c926744a24935b1c13ebd44
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/dw89EvC63CE_raw.json
@@ -0,0 +1 @@
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{"start": 22.45, "end": 22.83, "word": " في", "probability": 0.66259765625}, {"start": 22.83, "end": 23.43, "word": " المحاضرة", "probability": 0.98828125}, {"start": 23.43, "end": 23.99, "word": " اليوم", "probability": 0.96533203125}, {"start": 23.99, "end": 26.43, "word": " هناخد", "probability": 0.9061279296875}, {"start": 26.43, "end": 27.11, "word": " انتباه", "probability": 0.8319091796875}, {"start": 27.11, "end": 29.13, "word": " المقدمة", "probability": 0.8912760416666666}, {"start": 29.13, "end": 30.01, "word": " البسيطة", "probability": 0.96494140625}, {"start": 30.01, "end": 31.01, "word": " عن", "probability": 0.9013671875}, {"start": 31.01, "end": 31.13, "word": " ال", "probability": 0.92236328125}, {"start": 31.13, "end": 31.43, "word": " infinite", "probability": 0.84130859375}, {"start": 31.43, "end": 32.17, "word": " series", "probability": 0.92333984375}, {"start": 32.17, "end": 32.89, "word": " اللي", "probability": 0.780517578125}, {"start": 32.89, "end": 33.47, 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فالنظرية هذه بتقول لو كان في عندي series و ال series كانت convergent فضروري it is necessary that the limit of the inf term بساوي سفر", "tokens": [6027, 1863, 19913, 2288, 10632, 39894, 3615, 9566, 9957, 1829, 1500, 337, 47387, 39894, 38251, 1829, 3224, 2423, 7649, 12984, 1433, 1500, 30767, 1829, 19446, 11778, 2288, 14851, 3224, 8978, 33400, 363, 6156, 6027, 1863, 19913, 2288, 10632, 29538, 39894, 39648, 45164, 25961, 8978, 18871, 16254, 2638, 4032, 2423, 2638, 25961, 2655, 9652, 6930, 6156, 11242, 2288, 13063, 1829, 309, 307, 4818, 300, 264, 4948, 295, 264, 1536, 1433, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.27942370903956426, "compression_ratio": 1.4682926829268292, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 91.98, "end": 92.86, "word": "النظرية", "probability": 0.856298828125}, {"start": 92.86, "end": 93.84, "word": " بتعطيني", "probability": 0.77880859375}, {"start": 93.84, "end": 94.88, "word": " test", "probability": 0.8701171875}, {"start": 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partial sums exist و بالساوية sum real number S الآن باخد ال limit للطرفين في ال star هنا", "tokens": [10721, 8315, 6156, 9640, 11242, 14739, 2423, 2638, 41881, 11933, 15730, 2423, 4948, 24976, 8310, 295, 14641, 34499, 2514, 4032, 20666, 3794, 995, 2407, 10632, 2408, 957, 1230, 318, 6024, 48506, 4724, 47283, 3215, 2423, 4948, 24976, 9566, 28480, 9957, 8978, 2423, 3543, 34105], "avg_logprob": -0.33385415607028535, "compression_ratio": 1.3178807947019868, "no_speech_prob": 0.0, "words": [{"start": 139.15, "end": 139.91, "word": "أنا", "probability": 0.6248779296875}, {"start": 139.91, "end": 140.67, "word": " فارض", "probability": 0.8030598958333334}, {"start": 140.67, "end": 140.83, "word": " أن", "probability": 0.4580078125}, {"start": 140.83, "end": 140.99, "word": " ال", "probability": 0.7861328125}, {"start": 140.99, "end": 141.31, "word": " series", "probability": 0.441162109375}, {"start": 141.31, "end": 142.15, "word": " converge", "probability": 0.7802734375}, {"start": 142.15, 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"end": 178.93, "word": " واضح", "probability": 0.9620768229166666}, {"start": 178.93, "end": 180.57, "word": " البرهان؟", "probability": 0.82421875}, {"start": 180.57, "end": 181.05, "word": " الآن", "probability": 0.6971435546875}, {"start": 181.05, "end": 181.33, "word": " في", "probability": 0.81396484375}, {"start": 181.33, "end": 181.71, "word": " عندي", "probability": 0.9755859375}, {"start": 181.71, "end": 182.31, "word": " remark", "probability": 0.9814453125}], "temperature": 1.0}, {"id": 9, "seek": 21612, "start": 190.04, "end": 216.12, "text": "the converse of above theorem is false عكس النظرية السابقة ليس صحيحا بمعنى لو كانت x in", "tokens": [3322, 416, 4308, 295, 3673, 20904, 307, 7908, 6225, 4117, 3794, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 32239, 3794, 20328, 5016, 1829, 5016, 995, 4724, 2304, 3615, 1863, 7578, 45164, 25961, 2655, 2031, 294], "avg_logprob": -0.14095051628020075, "compression_ratio": 1.0982142857142858, "no_speech_prob": 0.0, "words": [{"start": 190.04, "end": 190.42, "word": "the", "probability": 0.45361328125}, {"start": 190.42, "end": 191.26, "word": " converse", "probability": 0.703369140625}, {"start": 191.26, "end": 195.9, "word": " of", "probability": 0.94970703125}, {"start": 195.9, "end": 196.5, "word": " above", "probability": 0.931640625}, {"start": 196.5, "end": 197.08, "word": " theorem", "probability": 0.87841796875}, {"start": 197.08, "end": 203.14, "word": " is", "probability": 0.9541015625}, {"start": 203.14, "end": 203.84, "word": " false", "probability": 0.900390625}, {"start": 203.84, "end": 207.86, "word": " عكس", "probability": 0.96630859375}, {"start": 207.86, "end": 208.4, "word": " النظرية", "probability": 0.8450927734375}, {"start": 208.4, "end": 209.02, "word": " السابقة", "probability": 0.98681640625}, {"start": 209.02, "end": 209.62, "word": " ليس", "probability": 0.913330078125}, {"start": 209.62, "end": 211.0, "word": " صحيحا", "probability": 0.960546875}, {"start": 211.0, "end": 213.62, "word": " بمعنى", "probability": 0.966796875}, {"start": 213.62, "end": 214.76, "word": " لو", "probability": 0.95947265625}, {"start": 214.76, "end": 215.4, "word": " كانت", "probability": 0.98779296875}, {"start": 215.4, "end": 215.76, "word": " x", "probability": 0.68212890625}, {"start": 215.76, "end": 216.12, "word": " in", "probability": 0.302978515625}], "temperature": 1.0}, {"id": 10, "seek": 23831, "start": 218.35, "end": 238.31, "text": "converge to zero هذا لا يؤدي بالضرورة .. لا يؤدي مش شرط يؤدي ان ال series sigma x in converge وهي مثال على ذلك ناخد مثال", "tokens": [1671, 331, 432, 281, 4018, 23758, 20193, 7251, 33604, 16254, 20666, 11242, 2288, 13063, 3660, 4386, 20193, 7251, 33604, 16254, 37893, 13412, 2288, 9566, 7251, 33604, 16254, 16472, 2423, 2638, 12771, 2031, 294, 41881, 37037, 1829, 50113, 6027, 15844, 29910, 23275, 8717, 47283, 3215, 50113, 6027], "avg_logprob": -0.251662237847105, "compression_ratio": 1.372093023255814, "no_speech_prob": 5.960464477539063e-08, "words": 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"end": 228.97, "word": " يؤدي", "probability": 0.9638671875}, {"start": 228.97, "end": 229.17, "word": " ان", "probability": 0.404541015625}, {"start": 229.17, "end": 229.39, "word": " ال", "probability": 0.7353515625}, {"start": 229.39, "end": 229.73, "word": " series", "probability": 0.78271484375}, {"start": 229.73, "end": 230.93, "word": " sigma", "probability": 0.578125}, {"start": 230.93, "end": 231.29, "word": " x", "probability": 0.78173828125}, {"start": 231.29, "end": 231.71, "word": " in", "probability": 0.779296875}, {"start": 231.71, "end": 234.03, "word": " converge", "probability": 0.38671875}, {"start": 234.03, "end": 236.31, "word": " وهي", "probability": 0.7490234375}, {"start": 236.31, "end": 236.79, "word": " مثال", "probability": 0.98046875}, {"start": 236.79, "end": 236.97, "word": " على", "probability": 0.822265625}, {"start": 236.97, "end": 237.41, "word": " ذلك", "probability": 0.991943359375}, {"start": 237.41, "end": 237.83, "word": " ناخد", "probability": 0.8128255208333334}, {"start": 237.83, "end": 238.31, "word": " مثال", "probability": 0.80712890625}], "temperature": 1.0}, {"id": 11, "seek": 26552, "start": 257.84, "end": 265.52, "text": "example the harmonic series satisfies", "tokens": [3121, 335, 781, 264, 32270, 2638, 44271], "avg_logprob": -0.4367675743997097, "compression_ratio": 0.8604651162790697, "no_speech_prob": 0.0, "words": [{"start": 257.84000000000003, "end": 259.24, "word": "example", "probability": 0.6685994466145834}, {"start": 259.24, "end": 260.64, "word": " the", "probability": 0.58349609375}, {"start": 260.64, "end": 261.24, "word": " harmonic", "probability": 0.83935546875}, {"start": 261.24, "end": 262.04, "word": " series", "probability": 0.89599609375}, {"start": 262.04, "end": 265.52, "word": " satisfies", "probability": 0.7978515625}], "temperature": 1.0}, {"id": 12, "seek": 30456, "start": 279.92, "end": 304.56, "text": "إن ال limit ل xn عبارة عن ال limit ل 1 على n يسوى سفر لكن however .. however ال series ال harmonic series diverges", "tokens": [28814, 1863, 2423, 4948, 5296, 2031, 77, 6225, 3555, 9640, 3660, 18871, 2423, 4948, 5296, 502, 15844, 297, 7251, 3794, 2407, 7578, 8608, 5172, 2288, 44381, 4461, 4386, 4461, 2423, 2638, 2423, 32270, 2638, 18558, 2880], "avg_logprob": -0.3122888416857333, "compression_ratio": 1.3153153153153154, "no_speech_prob": 0.0, "words": [{"start": 279.92, "end": 280.28, "word": "إن", "probability": 0.7127685546875}, {"start": 280.28, "end": 280.46, "word": " ال", "probability": 0.6943359375}, {"start": 280.46, "end": 280.84, "word": " limit", "probability": 0.88330078125}, {"start": 280.84, "end": 282.02, "word": " ل", "probability": 0.91162109375}, {"start": 282.02, "end": 282.98, "word": " xn", "probability": 0.398681640625}, {"start": 282.98, "end": 284.54, "word": " عبارة", "probability": 0.82342529296875}, {"start": 284.54, "end": 284.74, "word": " عن", "probability": 0.99853515625}, {"start": 284.74, "end": 284.88, "word": " ال", "probability": 0.62890625}, {"start": 284.88, "end": 285.28, "word": " limit", "probability": 0.9755859375}, {"start": 285.28, "end": 285.7, "word": " ل", "probability": 0.88916015625}, {"start": 285.7, "end": 286.04, "word": " 1", "probability": 0.53369140625}, {"start": 286.04, "end": 286.42, "word": " على", "probability": 0.619140625}, {"start": 286.42, "end": 286.88, "word": " n", "probability": 0.8193359375}, {"start": 286.88, "end": 288.08, "word": " يسوى", "probability": 0.65740966796875}, {"start": 288.08, "end": 288.6, "word": " سفر", "probability": 0.8740234375}, {"start": 288.6, "end": 291.56, "word": " لكن", "probability": 0.845703125}, {"start": 291.56, "end": 294.1, "word": " however", "probability": 0.88671875}, {"start": 294.1, "end": 294.6, "word": " ..", "probability": 0.2705078125}, {"start": 294.6, "end": 299.42, "word": " however", "probability": 0.900390625}, {"start": 299.42, "end": 300.96, "word": " ال", "probability": 0.7314453125}, {"start": 300.96, "end": 301.4, "word": " series", "probability": 0.95458984375}, {"start": 301.4, "end": 301.62, "word": " ال", "probability": 0.51611328125}, {"start": 301.62, "end": 302.02, "word": " harmonic", "probability": 0.90869140625}, {"start": 302.02, "end": 302.72, "word": " series", "probability": 0.9130859375}, {"start": 302.72, "end": 304.56, "word": " diverges", "probability": 0.715576171875}], "temperature": 1.0}, {"id": 13, "seek": 33141, "start": 309.69, "end": 331.41, "text": "ال harmonic series is divergent مش convergent ليش؟ why؟ احنا برهننا الكلام هذا في chapter تلاتة بس كش في section تلاتة خمسة", "tokens": [6027, 32270, 2638, 307, 18558, 6930, 37893, 9652, 6930, 32239, 8592, 22807, 983, 22807, 1975, 5016, 8315, 4724, 2288, 3224, 1863, 8315, 2423, 28820, 10943, 23758, 8978, 7187, 6055, 1211, 9307, 3660, 4724, 3794, 9122, 8592, 8978, 3541, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660], "avg_logprob": -0.18284574848540286, "compression_ratio": 1.2627737226277371, "no_speech_prob": 0.0, 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{"start": 324.15, "end": 324.61, "word": " هذا", "probability": 0.8662109375}, {"start": 324.61, "end": 325.85, "word": " في", "probability": 0.97802734375}, {"start": 325.85, "end": 327.15, "word": " chapter", "probability": 0.92724609375}, {"start": 327.15, "end": 327.99, "word": " تلاتة", "probability": 0.91748046875}, {"start": 327.99, "end": 328.77, "word": " بس", "probability": 0.57391357421875}, {"start": 328.77, "end": 329.15, "word": " كش", "probability": 0.53564453125}, {"start": 329.15, "end": 329.33, "word": " في", "probability": 0.8466796875}, {"start": 329.33, "end": 330.31, "word": " section", "probability": 0.446533203125}, {"start": 330.31, "end": 330.85, "word": " تلاتة", "probability": 0.960693359375}, {"start": 330.85, "end": 331.41, "word": " خمسة", "probability": 0.9788818359375}], "temperature": 1.0}, {"id": 14, "seek": 36374, "start": 336.62, "end": 363.74, "text": "فاكرين ان ال sequence هذه كانت طيب نجاوب ليه ال harmonic series diverges في عندي جوابين answer one الإجابة الأولى في عندي مثال أخدنا", "tokens": [5172, 995, 37983, 9957, 16472, 2423, 8310, 29538, 25961, 2655, 23032, 1829, 3555, 8717, 7435, 995, 37746, 32239, 3224, 2423, 32270, 2638, 18558, 2880, 8978, 18871, 16254, 10874, 14407, 3555, 9957, 1867, 472, 33688, 7435, 16758, 3660, 16247, 12610, 7578, 8978, 18871, 16254, 50113, 6027, 5551, 9778, 3215, 8315], "avg_logprob": -0.18609374523162842, "compression_ratio": 1.364864864864865, "no_speech_prob": 0.0, "words": [{"start": 336.62, "end": 337.3, "word": "فاكرين", "probability": 0.9510498046875}, {"start": 337.3, "end": 337.52, "word": " ان", "probability": 0.471435546875}, {"start": 337.52, "end": 337.98, "word": " ال", "probability": 0.53857421875}, {"start": 337.98, "end": 338.44, "word": " sequence", "probability": 0.734375}, {"start": 338.44, "end": 339.04, "word": " هذه", "probability": 0.62109375}, {"start": 339.04, "end": 339.82, "word": " كانت", "probability": 0.93017578125}, {"start": 339.82, "end": 342.02, "word": " طيب", "probability": 0.7650553385416666}, {"start": 342.02, "end": 344.32, "word": " نجاوب", "probability": 0.78631591796875}, {"start": 344.32, "end": 344.76, "word": " ليه", "probability": 0.9697265625}, {"start": 344.76, "end": 344.98, "word": " ال", "probability": 0.91162109375}, {"start": 344.98, "end": 345.4, "word": " harmonic", "probability": 0.93701171875}, {"start": 345.4, "end": 345.9, "word": " series", "probability": 0.85107421875}, {"start": 345.9, "end": 346.76, "word": " diverges", "probability": 0.741943359375}, {"start": 346.76, "end": 347.54, "word": " في", "probability": 0.386474609375}, {"start": 347.54, "end": 347.8, "word": " عندي", "probability": 0.876708984375}, {"start": 347.8, "end": 348.42, "word": " جوابين", "probability": 0.948974609375}, {"start": 348.42, "end": 349.78, "word": " answer", "probability": 0.94873046875}, {"start": 349.78, "end": 352.72, "word": " one", "probability": 0.76953125}, {"start": 352.72, "end": 354.1, "word": " الإجابة", "probability": 0.9136962890625}, {"start": 354.1, "end": 356.64, "word": " الأولى", "probability": 0.9886067708333334}, {"start": 356.64, "end": 360.66, "word": " في", "probability": 0.87841796875}, {"start": 360.66, "end": 361.04, "word": " عندي", "probability": 0.989501953125}, {"start": 361.04, "end": 361.72, "word": " مثال", "probability": 0.968994140625}, {"start": 361.72, "end": 363.74, "word": " أخدنا", "probability": 0.9461669921875}], "temperature": 1.0}, {"id": 15, "seek": 39483, "start": 368.53, "end": 394.83, "text": "by example لسه ماخدينه اللي كان هذا الجزء اللي بتعلق فيه اللي هو ال sequence of partial sums لل series هذه اثبتنا انها not cauchy صح؟ وكان هذا جزء من ايه؟ من تكملة البرهان صح؟ اذا نشوف الرقم تبعها بالظبط section", "tokens": [2322, 1365, 5296, 3794, 3224, 3714, 47283, 3215, 9957, 3224, 13672, 1829, 25961, 23758, 25724, 11622, 38207, 13672, 1829, 39894, 30241, 4587, 8978, 3224, 13672, 1829, 31439, 2423, 8310, 295, 14641, 34499, 24976, 2638, 29538, 1975, 12984, 3555, 2655, 8315, 16472, 11296, 406, 1335, 625, 88, 20328, 5016, 22807, 4032, 41361, 23758, 10874, 11622, 38207, 9154, 1975, 1829, 3224, 22807, 9154, 6055, 24793, 37977, 2423, 26890, 3224, 7649, 20328, 5016, 22807, 1975, 15730, 8717, 8592, 38688, 34892, 4587, 2304, 6055, 3555, 3615, 11296, 20666, 19913, 3555, 9566, 3541], "avg_logprob": -0.1501931193169583, "compression_ratio": 1.5942028985507246, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 368.53, "end": 369.05, "word": "by", "probability": 0.638671875}, {"start": 369.05, "end": 370.01, "word": " example", "probability": 0.958984375}, {"start": 370.01, "end": 372.67, "word": " لسه", "probability": 0.9337565104166666}, {"start": 372.67, "end": 373.33, "word": " ماخدينه", "probability": 0.8720703125}, {"start": 373.33, "end": 373.57, "word": " اللي", "probability": 0.76513671875}, {"start": 373.57, "end": 373.81, "word": " كان", "probability": 0.9814453125}, {"start": 373.81, "end": 374.03, "word": " هذا", "probability": 0.88623046875}, {"start": 374.03, "end": 374.31, "word": " الجزء", "probability": 0.9505208333333334}, {"start": 374.31, "end": 374.43, "word": " اللي", "probability": 0.8994140625}, {"start": 374.43, "end": 374.93, "word": " بتعلق", "probability": 0.8746744791666666}, {"start": 374.93, "end": 375.73, "word": " فيه", "probability": 0.97021484375}, {"start": 375.73, "end": 376.49, "word": " اللي", "probability": 0.970947265625}, {"start": 376.49, "end": 376.71, "word": " هو", "probability": 0.9833984375}, {"start": 376.71, "end": 376.85, "word": " ال", "probability": 0.5439453125}, {"start": 376.85, "end": 377.13, "word": " sequence", "probability": 0.93505859375}, {"start": 377.13, "end": 377.51, "word": " of", "probability": 0.95556640625}, {"start": 377.51, "end": 377.93, "word": " partial", "probability": 0.9462890625}, {"start": 377.93, "end": 378.37, "word": " sums", "probability": 0.9677734375}, {"start": 378.37, "end": 378.59, "word": " لل", "probability": 0.60888671875}, {"start": 378.59, "end": 379.01, "word": " series", "probability": 0.8486328125}, {"start": 379.01, "end": 379.47, "word": " هذه", "probability": 0.76953125}, {"start": 379.47, "end": 381.71, "word": " اثبتنا", "probability": 0.8841796875}, {"start": 381.71, "end": 382.15, "word": " انها", "probability": 0.856201171875}, {"start": 382.15, "end": 382.61, "word": " not", "probability": 0.9453125}, {"start": 382.61, "end": 383.11, "word": " cauchy", "probability": 0.649658203125}, {"start": 383.11, "end": 384.53, "word": " صح؟", "probability": 0.80322265625}, {"start": 384.53, "end": 384.89, "word": " وكان", "probability": 0.8076171875}, {"start": 384.89, "end": 385.13, "word": " هذا", "probability": 0.9609375}, {"start": 385.13, "end": 385.47, "word": " جزء", "probability": 0.9964192708333334}, {"start": 385.47, "end": 385.69, "word": " من", "probability": 0.9931640625}, {"start": 385.69, "end": 386.35, "word": " ايه؟", "probability": 0.79248046875}, {"start": 386.35, "end": 386.57, "word": " من", "probability": 0.98779296875}, {"start": 386.57, "end": 387.05, "word": " تكملة", "probability": 0.93896484375}, {"start": 387.05, "end": 387.61, "word": " البرهان", "probability": 0.77996826171875}, {"start": 387.61, "end": 389.17, "word": " صح؟", "probability": 0.94140625}, {"start": 389.17, "end": 389.47, "word": " اذا", "probability": 0.873046875}, {"start": 389.47, "end": 390.67, "word": " نشوف", "probability": 0.9264322916666666}, {"start": 390.67, "end": 391.17, "word": " الرقم", "probability": 0.970703125}, {"start": 391.17, "end": 391.61, "word": " تبعها", "probability": 0.949462890625}, {"start": 391.61, "end": 392.21, "word": " بالظبط", "probability": 0.9927978515625}, {"start": 392.21, "end": 394.83, "word": " section", "probability": 0.580078125}], "temperature": 1.0}, {"id": 16, "seek": 42337, "start": 397.49, "end": 423.37, "text": "مثال تلاتة خمسة ستة الجزء C by this example the sequence of partial sums Sn where", "tokens": [2304, 12984, 6027, 6055, 1211, 9307, 3660, 16490, 2304, 3794, 3660, 8608, 2655, 3660, 25724, 11622, 38207, 383, 538, 341, 1365, 264, 8310, 295, 14641, 34499, 9264, 689], "avg_logprob": -0.16702585795830036, "compression_ratio": 1.02, "no_speech_prob": 0.0, "words": [{"start": 397.49, "end": 398.27, "word": "مثال", "probability": 0.9694010416666666}, {"start": 398.27, "end": 400.21, "word": " تلاتة", "probability": 0.927978515625}, {"start": 400.21, "end": 402.99, "word": " خمسة", "probability": 0.923583984375}, {"start": 402.99, "end": 404.73, "word": " ستة", "probability": 0.9137369791666666}, {"start": 404.73, "end": 405.89, "word": " الجزء", "probability": 0.9412434895833334}, {"start": 405.89, "end": 406.29, "word": " C", "probability": 0.67626953125}, {"start": 406.29, "end": 406.75, "word": " by", "probability": 0.60888671875}, {"start": 406.75, "end": 407.07, "word": " this", "probability": 0.9658203125}, {"start": 407.07, "end": 407.75, "word": " example", "probability": 0.9755859375}, {"start": 407.75, "end": 410.87, "word": " the", "probability": 0.6875}, {"start": 410.87, "end": 411.41, "word": " sequence", "probability": 0.974609375}, {"start": 411.41, "end": 412.01, "word": " of", "probability": 0.9658203125}, {"start": 412.01, "end": 412.73, "word": " partial", "probability": 0.93603515625}, {"start": 412.73, "end": 413.49, "word": " sums", "probability": 0.96875}, {"start": 413.49, "end": 422.43, "word": " Sn", "probability": 0.1976318359375}, {"start": 422.43, "end": 423.37, "word": " where", "probability": 0.78955078125}], "temperature": 1.0}, {"id": 17, "seek": 45485, "start": 425.75, "end": 454.85, "text": "SN بيساوي سيجما من K بيساوي واحد إلى N لواحد على K اللي هو واحد زاد نص زاد واحد على N أثبتنا إن ال sequence هذه is not Cauchy is not Cauchy and therefore not convergent", "tokens": [32481, 4724, 1829, 3794, 995, 45865, 8608, 1829, 7435, 15042, 9154, 591, 4724, 1829, 3794, 995, 45865, 36764, 24401, 30731, 426, 5296, 14407, 24401, 15844, 591, 13672, 1829, 31439, 36764, 24401, 30767, 18513, 8717, 9381, 30767, 18513, 36764, 24401, 15844, 426, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 29538, 307, 406, 7544, 625, 88, 307, 406, 7544, 625, 88, 293, 4412, 406, 9652, 6930], "avg_logprob": -0.19270833468798435, "compression_ratio": 1.509433962264151, "no_speech_prob": 0.0, "words": [{"start": 425.75, "end": 426.51, "word": "SN", "probability": 0.1456298828125}, {"start": 426.51, "end": 427.21, "word": " بيساوي", "probability": 0.623883056640625}, {"start": 427.21, "end": 427.83, "word": " سيجما", "probability": 0.7298583984375}, {"start": 427.83, "end": 428.23, "word": " من", "probability": 0.96240234375}, {"start": 428.23, "end": 428.67, "word": " K", "probability": 0.88623046875}, {"start": 428.67, "end": 429.59, "word": " بيساوي", "probability": 0.968359375}, {"start": 429.59, "end": 430.81, "word": " واحد", "probability": 0.913818359375}, {"start": 430.81, "end": 431.03, "word": " إلى", "probability": 0.58349609375}, {"start": 431.03, "end": 431.51, "word": " N", "probability": 0.93896484375}, {"start": 431.51, "end": 433.15, "word": " لواحد", "probability": 0.7176920572916666}, {"start": 433.15, "end": 433.39, "word": " على", "probability": 0.82177734375}, {"start": 433.39, "end": 433.89, "word": " K", "probability": 0.9697265625}, {"start": 433.89, "end": 434.99, "word": " اللي", "probability": 0.85986328125}, {"start": 434.99, "end": 435.25, "word": " هو", "probability": 0.98486328125}, {"start": 435.25, "end": 435.75, "word": " واحد", "probability": 0.9677734375}, {"start": 435.75, "end": 436.23, "word": " زاد", "probability": 0.84423828125}, {"start": 436.23, "end": 436.71, "word": " نص", "probability": 0.828369140625}, {"start": 436.71, "end": 437.79, "word": " زاد", "probability": 0.975341796875}, {"start": 437.79, "end": 439.63, "word": " واحد", "probability": 0.946533203125}, {"start": 439.63, "end": 439.85, "word": " على", "probability": 0.87158203125}, {"start": 439.85, "end": 440.19, "word": " N", "probability": 0.974609375}, {"start": 440.19, "end": 440.87, "word": " أثبتنا", "probability": 0.97041015625}, {"start": 440.87, "end": 441.03, "word": " إن", "probability": 0.63916015625}, {"start": 441.03, "end": 441.15, "word": " ال", "probability": 0.83203125}, {"start": 441.15, "end": 441.55, "word": " sequence", "probability": 0.58544921875}, {"start": 441.55, "end": 442.09, "word": " هذه", "probability": 0.73974609375}, {"start": 442.09, "end": 444.27, "word": " is", "probability": 0.83056640625}, {"start": 444.27, "end": 444.71, "word": " not", "probability": 0.96044921875}, {"start": 444.71, "end": 445.33, "word": " Cauchy", "probability": 0.8719075520833334}, {"start": 445.33, "end": 446.25, "word": " is", "probability": 0.54833984375}, {"start": 446.25, "end": 446.73, "word": " not", "probability": 0.95947265625}, {"start": 446.73, "end": 449.25, "word": " Cauchy", "probability": 0.9368489583333334}, {"start": 449.25, "end": 450.63, "word": " and", "probability": 0.87060546875}, {"start": 450.63, "end": 451.29, "word": " therefore", "probability": 0.84716796875}, {"start": 451.29, "end": 454.03, "word": " not", "probability": 0.875}, {"start": 454.03, "end": 454.85, "word": " convergent", "probability": 0.958740234375}], "temperature": 1.0}, {"id": 18, "seek": 47787, "start": 460.33, "end": 477.87, "text": "حسب by cushy by cushy criterion cushy criterion بتقول أي sequence of real numbers is convergent if and only if it is cushy اللي إحنا أثبتنا إن ال sequence هذه في المثال هذا", "tokens": [5016, 35457, 538, 18422, 88, 538, 18422, 88, 46691, 18422, 88, 46691, 39894, 39648, 36632, 8310, 295, 957, 3547, 307, 9652, 6930, 498, 293, 787, 498, 309, 307, 18422, 88, 13672, 1829, 11933, 5016, 8315, 5551, 12984, 3555, 2655, 8315, 36145, 2423, 8310, 29538, 8978, 9673, 12984, 6027, 23758], "avg_logprob": -0.2737499862909317, "compression_ratio": 1.436241610738255, "no_speech_prob": 0.0, "words": [{"start": 460.33, "end": 460.93, "word": "حسب", "probability": 0.77978515625}, {"start": 460.93, "end": 461.69, "word": " by", "probability": 0.7021484375}, {"start": 461.69, "end": 463.01, "word": " cushy", "probability": 0.60650634765625}, {"start": 463.01, "end": 464.97, "word": " by", "probability": 0.1129150390625}, {"start": 464.97, "end": 465.69, "word": " cushy", "probability": 0.92138671875}, {"start": 465.69, "end": 466.47, "word": " criterion", "probability": 0.9482421875}, {"start": 466.47, "end": 469.11, "word": " cushy", "probability": 0.547088623046875}, {"start": 469.11, "end": 469.51, "word": " criterion", "probability": 0.97265625}, {"start": 469.51, "end": 469.85, "word": " بتقول", "probability": 0.8955078125}, {"start": 469.85, "end": 470.05, "word": " أي", "probability": 0.7548828125}, {"start": 470.05, "end": 470.45, "word": " sequence", "probability": 0.88818359375}, {"start": 470.45, "end": 470.65, "word": " of", "probability": 0.955078125}, {"start": 470.65, "end": 470.85, "word": " real", "probability": 0.97265625}, {"start": 470.85, "end": 471.33, "word": " numbers", "probability": 0.83935546875}, {"start": 471.33, "end": 471.55, "word": " is", "probability": 0.9482421875}, {"start": 471.55, "end": 472.31, "word": " convergent", "probability": 0.9677734375}, {"start": 472.31, "end": 472.95, "word": " if", "probability": 0.966796875}, {"start": 472.95, "end": 473.15, "word": " and", "probability": 0.94482421875}, {"start": 473.15, "end": 473.35, "word": " only", "probability": 0.93310546875}, {"start": 473.35, "end": 473.55, "word": " if", "probability": 0.9775390625}, {"start": 473.55, "end": 473.73, "word": " it", "probability": 0.97412109375}, {"start": 473.73, "end": 473.91, "word": " is", "probability": 0.9453125}, {"start": 473.91, "end": 474.75, "word": " cushy", "probability": 0.817138671875}, {"start": 474.75, "end": 475.35, "word": " اللي", "probability": 0.57269287109375}, {"start": 475.35, "end": 475.55, "word": " إحنا", "probability": 0.7461751302083334}, {"start": 475.55, "end": 476.01, "word": " أثبتنا", "probability": 0.93466796875}, {"start": 476.01, "end": 476.11, "word": " إن", "probability": 0.71337890625}, {"start": 476.11, "end": 476.19, "word": " ال", "probability": 0.80712890625}, {"start": 476.19, "end": 476.51, "word": " sequence", "probability": 0.95849609375}, {"start": 476.51, "end": 476.93, "word": " هذه", "probability": 0.546875}, {"start": 476.93, "end": 477.07, "word": " في", "probability": 0.9140625}, {"start": 477.07, "end": 477.53, "word": " المثال", "probability": 0.99072265625}, {"start": 477.53, "end": 477.87, "word": " هذا", "probability": 0.958984375}], "temperature": 1.0}, {"id": 19, "seek": 49102, "start": 479.62, "end": 491.02, "text": "ماهياش كوشي و بالتالي not convergent طب ما هذه هي ال sequence of partial .. هذه هي ال sequence of partial sums لل harmonic series اذا by above definition", "tokens": [15042, 3224, 1829, 33599, 9122, 2407, 8592, 1829, 4032, 20666, 2655, 6027, 1829, 406, 9652, 6930, 23032, 3555, 19446, 29538, 39896, 2423, 8310, 295, 14641, 4386, 29538, 39896, 2423, 8310, 295, 14641, 34499, 24976, 32270, 2638, 1975, 15730, 538, 3673, 7123], "avg_logprob": -0.21354166666666666, "compression_ratio": 1.3857142857142857, "no_speech_prob": 0.0, "words": [{"start": 479.62, "end": 480.3, "word": "ماهياش", "probability": 0.8631591796875}, {"start": 480.3, "end": 480.74, "word": " كوشي", "probability": 0.78436279296875}, {"start": 480.74, "end": 480.82, "word": " و", "probability": 0.53857421875}, {"start": 480.82, "end": 481.18, "word": " بالتالي", "probability": 0.8616943359375}, {"start": 481.18, "end": 481.4, "word": " not", "probability": 0.83056640625}, {"start": 481.4, "end": 482.12, "word": " convergent", "probability": 0.91259765625}, {"start": 482.12, "end": 482.78, "word": " طب", "probability": 0.787841796875}, {"start": 482.78, "end": 482.88, "word": " ما", "probability": 0.70166015625}, {"start": 482.88, "end": 483.08, "word": " هذه", "probability": 0.42724609375}, {"start": 483.08, "end": 483.28, "word": " هي", "probability": 0.91357421875}, {"start": 483.28, "end": 483.4, "word": " ال", "probability": 0.76318359375}, {"start": 483.4, "end": 483.7, "word": " sequence", "probability": 0.9609375}, {"start": 483.7, "end": 484.06, "word": " of", "probability": 0.93505859375}, {"start": 484.06, "end": 484.46, "word": " partial", "probability": 0.9384765625}, {"start": 484.46, "end": 484.56, "word": " ..", "probability": 0.47119140625}, {"start": 484.56, "end": 484.84, "word": " هذه", "probability": 0.86572265625}, {"start": 484.84, "end": 485.02, "word": " هي", "probability": 0.978515625}, {"start": 485.02, "end": 485.12, "word": " ال", "probability": 0.921875}, {"start": 485.12, "end": 485.42, "word": " sequence", "probability": 0.99072265625}, {"start": 485.42, "end": 485.68, "word": " of", "probability": 0.9736328125}, {"start": 485.68, "end": 486.04, "word": " partial", "probability": 0.9560546875}, {"start": 486.04, "end": 486.52, "word": " sums", "probability": 0.95458984375}, {"start": 486.52, "end": 487.26, "word": " لل", "probability": 0.8896484375}, {"start": 487.26, "end": 487.68, "word": " harmonic", "probability": 0.88037109375}, {"start": 487.68, "end": 488.26, "word": " series", "probability": 0.93017578125}, {"start": 488.26, "end": 488.94, "word": " اذا", "probability": 0.6334228515625}, {"start": 488.94, "end": 489.98, "word": " by", "probability": 0.95849609375}, {"start": 489.98, "end": 490.44, "word": " above", "probability": 0.9619140625}, {"start": 490.44, "end": 491.02, "word": " definition", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 20, "seek": 51015, "start": 495.53, "end": 510.15, "text": "طبعا ال definition المسعة اللى كتبناها أول واحد مادام ال series of partial sums is not convergent اذا ال series نفسها is divergent", "tokens": [9566, 3555, 3615, 995, 2423, 7123, 9673, 3794, 27884, 13672, 7578, 9122, 2655, 3555, 8315, 11296, 5551, 12610, 36764, 24401, 3714, 18513, 10943, 2423, 2638, 295, 14641, 34499, 307, 406, 9652, 6930, 1975, 15730, 2423, 2638, 8717, 36178, 11296, 307, 18558, 6930], "avg_logprob": -0.1626090171725251, "compression_ratio": 1.2919708029197081, "no_speech_prob": 0.0, "words": [{"start": 495.53, "end": 495.99, "word": "طبعا", "probability": 0.97998046875}, {"start": 495.99, "end": 496.17, "word": " ال", "probability": 0.90966796875}, {"start": 496.17, "end": 496.55, "word": " definition", "probability": 0.93505859375}, {"start": 496.55, "end": 498.01, "word": " المسعة", "probability": 0.5903727213541666}, {"start": 498.01, "end": 498.79, "word": " اللى", "probability": 0.7607421875}, {"start": 498.79, "end": 499.27, "word": " كتبناها", "probability": 0.98115234375}, {"start": 499.27, "end": 499.45, "word": " أول", "probability": 0.782470703125}, {"start": 499.45, "end": 499.87, "word": " واحد", "probability": 0.994140625}, {"start": 499.87, "end": 500.95, "word": " مادام", "probability": 0.6809895833333334}, {"start": 500.95, "end": 501.13, "word": " 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"word": " two", "probability": 0.46923828125}], "temperature": 1.0}, {"id": 22, "seek": 57248, "start": 545.08, "end": 572.48, "text": "إنه by .. في مثال آخر أثبتنا فيه by example تلاتة تلاتة تلاتة بي .. إذا في section تلاتة تلاتة المثال تلاتة بي أثبتنا فيه إن ال sequence و partial sums", "tokens": [28814, 1863, 3224, 538, 4386, 8978, 50113, 6027, 19753, 34740, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 538, 1365, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 4724, 1829, 4386, 11933, 15730, 8978, 3541, 6055, 1211, 9307, 3660, 6055, 1211, 9307, 3660, 9673, 12984, 6027, 6055, 1211, 9307, 3660, 4724, 1829, 5551, 12984, 3555, 2655, 8315, 8978, 3224, 36145, 2423, 8310, 4032, 14641, 34499], "avg_logprob": -0.19202899241792984, "compression_ratio": 1.6985294117647058, "no_speech_prob": 0.0, "words": [{"start": 545.08, "end": 545.78, "word": "إنه", "probability": 0.6820068359375}, {"start": 545.78, "end": 546.68, "word": " by", "probability": 0.74462890625}, {"start": 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"end": 623.36, "text": "إذا كانت الـ sequence unbounded إذا بتطلع divergent أو not convergent لأن sn is divergent لأن لو كانت convergent بتكون bounded وبالتالي therefore ال series أو ال harmonic series", "tokens": [28814, 15730, 25961, 2655, 2423, 39184, 8310, 517, 18767, 292, 11933, 15730, 39894, 9566, 1211, 3615, 18558, 6930, 34051, 406, 9652, 6930, 5296, 33456, 2406, 307, 18558, 6930, 5296, 33456, 45164, 25961, 2655, 9652, 6930, 39894, 30544, 37498, 46599, 6027, 2655, 6027, 1829, 4412, 2423, 2638, 34051, 2423, 32270, 2638], "avg_logprob": -0.2749693744322833, "compression_ratio": 1.509933774834437, "no_speech_prob": 0.0, "words": [{"start": 604.44, "end": 604.76, "word": "إذا", "probability": 0.803466796875}, {"start": 604.76, "end": 605.1, "word": " كانت", "probability": 0.98046875}, {"start": 605.1, "end": 605.16, "word": " الـ", "probability": 0.588134765625}, {"start": 605.16, "end": 605.42, "word": " sequence", "probability": 0.8427734375}, {"start": 605.42, "end": 606.34, 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لو", "probability": 0.78955078125}, {"start": 615.66, "end": 616.06, "word": " كانت", "probability": 0.98876953125}, {"start": 616.06, "end": 616.66, "word": " convergent", "probability": 0.908447265625}, {"start": 616.66, "end": 617.08, "word": " بتكون", "probability": 0.92333984375}, {"start": 617.08, "end": 617.58, "word": " bounded", "probability": 0.8720703125}, {"start": 617.58, "end": 619.4, "word": " وبالتالي", "probability": 0.90546875}, {"start": 619.4, "end": 620.04, "word": " therefore", "probability": 0.370361328125}, {"start": 620.04, "end": 620.8, "word": " ال", "probability": 0.88818359375}, {"start": 620.8, "end": 622.02, "word": " series", "probability": 0.7666015625}, {"start": 622.02, "end": 622.46, "word": " أو", "probability": 0.853515625}, {"start": 622.46, "end": 622.58, "word": " ال", "probability": 0.837890625}, {"start": 622.58, "end": 622.84, "word": " harmonic", "probability": 0.67431640625}, {"start": 622.84, "end": 623.36, "word": " series", 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{"start": 870.64, "end": 874.64, "word": " وبالتالي", "probability": 0.92587890625}, {"start": 874.64, "end": 874.94, "word": " limit", "probability": 0.880859375}, {"start": 874.94, "end": 875.42, "word": " R", "probability": 0.79638671875}, {"start": 875.42, "end": 875.8, "word": " أُس", "probability": 0.672119140625}, {"start": 875.8, "end": 876.18, "word": " N", "probability": 0.60302734375}, {"start": 876.18, "end": 876.56, "word": " مش", "probability": 0.9052734375}, {"start": 876.56, "end": 876.92, "word": " ممكن", "probability": 0.986328125}, {"start": 876.92, "end": 877.4, "word": " تساوي", "probability": 0.8489990234375}, {"start": 877.4, "end": 877.84, "word": " سفر", "probability": 0.8626302083333334}], "temperature": 1.0}, {"id": 33, "seek": 90914, "start": 880.1, "end": 909.14, "text": "limit ل R أسن شفنا أن هذه بساوية سفر فقط لما ال R يكون أصغر من واحد و أكبر من أو بساوية سفر وبالتالي اذا by .. اذا by nth by nth term test اذا الحد العام الحد النوني لل series هذه", 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ال divergence مثال تاني", "tokens": [1211, 33456, 3224, 45164, 25961, 2655, 9652, 6930, 6156, 45340, 5172, 32887, 11242, 4948, 21542, 3215, 13672, 11536, 1829, 7251, 3794, 995, 45865, 8608, 5172, 2288, 37037, 15730, 37893, 3714, 29245, 23328, 46811, 10943, 22807, 16472, 1975, 8315, 13412, 38688, 2655, 34105, 9122, 33911, 5551, 9778, 3215, 8315, 2423, 4386, 1975, 2407, 44713, 9778, 40448, 8315, 2423, 294, 1433, 1500, 5296, 28814, 12984, 3555, 9307, 2423, 47387, 50113, 6027, 6055, 7649, 1829], "avg_logprob": -0.24550513372029345, "compression_ratio": 1.483695652173913, "no_speech_prob": 0.0, "words": [{"start": 945.29, "end": 945.81, "word": "لأنه", "probability": 0.711669921875}, {"start": 945.81, "end": 945.91, "word": " لو", "probability": 0.90771484375}, {"start": 945.91, "end": 946.29, "word": " كانت", "probability": 0.980712890625}, {"start": 946.29, "end": 947.01, "word": " convergent", "probability": 0.655029296875}, {"start": 947.01, "end": 947.65, "word": " فالمفروض", 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"probability": 0.895751953125}, {"start": 1040.83, "end": 1041.57, "word": " لذا", "probability": 0.4581298828125}, {"start": 1041.57, "end": 1041.75, "word": " هنا", "probability": 0.93359375}, {"start": 1041.75, "end": 1042.47, "word": " هنفحص", "probability": 0.84560546875}, {"start": 1042.47, "end": 1043.73, "word": " هل", "probability": 0.9560546875}, {"start": 1043.73, "end": 1044.03, "word": " ال", "probability": 0.94677734375}, {"start": 1044.03, "end": 1044.35, "word": " sequence", "probability": 0.98046875}, {"start": 1044.35, "end": 1044.65, "word": " of", "probability": 0.98046875}, {"start": 1044.65, "end": 1045.03, "word": " partial", "probability": 0.943359375}, {"start": 1045.03, "end": 1045.43, "word": " sums", "probability": 0.9443359375}, {"start": 1045.43, "end": 1046.15, "word": " divergent", "probability": 0.7322998046875}, {"start": 1046.15, "end": 1046.33, "word": " ولا", "probability": 0.74267578125}, {"start": 1046.33, "end": 1048.49, "word": " convergent", 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"probability": 0.97900390625}, {"start": 1054.29, "end": 1054.75, "word": " K", "probability": 0.45654296875}, {"start": 1054.75, "end": 1055.31, "word": " equal", "probability": 0.395751953125}, {"start": 1055.31, "end": 1056.03, "word": " 0", "probability": 0.394775390625}, {"start": 1056.03, "end": 1057.19, "word": " to", "probability": 0.9013671875}, {"start": 1057.19, "end": 1057.49, "word": " N", "probability": 0.96533203125}], "temperature": 1.0}, {"id": 39, "seek": 108676, "start": 1059.24, "end": 1086.76, "text": "لا سالب واحد plus k هذا xk فهذا هيطلع الو قيمتين الو هيطلع قيمتين لو كان in even", "tokens": [15040, 8608, 6027, 3555, 36764, 24401, 1804, 350, 23758, 2031, 74, 6156, 3224, 15730, 39896, 9566, 1211, 3615, 2423, 2407, 12174, 32640, 2655, 9957, 2423, 2407, 39896, 9566, 1211, 3615, 12174, 32640, 2655, 9957, 45164, 25961, 294, 754], "avg_logprob": -0.25781248930173045, "compression_ratio": 1.368421052631579, "no_speech_prob": 0.0, "words": [{"start": 1059.24, "end": 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{"start": 1110.57, "end": 1111.03, "word": " هيطلع", "probability": 0.983642578125}, {"start": 1111.03, "end": 1111.65, "word": " واحد", "probability": 0.994384765625}], "temperature": 1.0}, {"id": 41, "seek": 111930, "start": 1112.6, "end": 1119.3, "text": "إذا كانت ال in even أما لو كانت ال in odd يعني لو أخدت in بالساوية واحد", "tokens": [28814, 15730, 25961, 2655, 2423, 294, 754, 5551, 15042, 45164, 25961, 2655, 2423, 294, 7401, 37495, 22653, 45164, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 36764, 24401], "avg_logprob": -0.21748991743210824, "compression_ratio": 1.2417582417582418, "no_speech_prob": 0.0, "words": [{"start": 1112.6, "end": 1112.94, "word": "إذا", "probability": 0.7069091796875}, {"start": 1112.94, "end": 1113.46, "word": " كانت", "probability": 0.95703125}, {"start": 1113.46, "end": 1113.56, "word": " ال", "probability": 0.93212890625}, {"start": 1113.56, "end": 1113.74, "word": " in", "probability": 0.298583984375}, {"start": 1113.74, "end": 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واحد", "probability": 0.954345703125}], "temperature": 1.0}, {"id": 42, "seek": 114292, "start": 1120.4, "end": 1142.92, "text": "لو أخدت in بالساوية واحد فهيطلع عندي حدين مجموعهم سفر لو أخدت in بالساوية تلاتة هيطلع مجموع أول أربع حدود برضه بيطلع مجموعهم سفر و هكذا اذا سفر ال in partial sums بساوية سفر اذا كانت in odd واحد اذا كانت in even وبالتالي therefore", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 36764, 24401, 6156, 3224, 1829, 9566, 1211, 3615, 18871, 16254, 11331, 3215, 9957, 3714, 7435, 2304, 45367, 16095, 8608, 5172, 2288, 45164, 5551, 9778, 3215, 2655, 294, 20666, 3794, 995, 2407, 10632, 6055, 1211, 9307, 3660, 39896, 9566, 1211, 3615, 3714, 7435, 2304, 45367, 5551, 12610, 5551, 25513, 3615, 11331, 3215, 23328, 4724, 43042, 3224, 4724, 1829, 9566, 1211, 3615, 3714, 7435, 2304, 45367, 16095, 8608, 5172, 2288, 4032, 8032, 4117, 15730, 1975, 15730, 8608, 5172, 2288, 2423, 294, 14641, 34499, 4724, 3794, 995, 2407, 10632, 8608, 5172, 2288, 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0.884765625}], "temperature": 1.0}, {"id": 43, "seek": 116971, "start": 1144.21, "end": 1169.71, "text": "therefore a sequence of partial sums is an alternating series يعني حدودها متدبدة بين صفر و واحد أو أول حد واحد التاني صفر واحد صفر و هكذا which is divergent هذه أمرها ما كانت convergent", "tokens": [15456, 845, 257, 8310, 295, 14641, 34499, 307, 364, 40062, 2638, 37495, 22653, 11331, 3215, 23328, 11296, 44650, 3215, 44510, 3660, 49374, 20328, 5172, 2288, 4032, 36764, 24401, 34051, 5551, 12610, 11331, 3215, 36764, 24401, 16712, 7649, 1829, 20328, 5172, 2288, 36764, 24401, 20328, 5172, 2288, 4032, 8032, 4117, 15730, 597, 307, 18558, 6930, 29538, 5551, 29973, 11296, 19446, 25961, 2655, 9652, 6930], "avg_logprob": -0.27148436615243554, "compression_ratio": 1.449438202247191, "no_speech_prob": 0.0, "words": [{"start": 1144.21, "end": 1145.13, "word": "therefore", "probability": 0.49627685546875}, {"start": 1145.13, "end": 1145.65, "word": " a", "probability": 0.2020263671875}, {"start": 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{"start": 1153.39, "end": 1153.81, "word": " صفر", "probability": 0.8460286458333334}, {"start": 1153.81, "end": 1153.93, "word": " و", "probability": 0.89501953125}, {"start": 1153.93, "end": 1154.29, "word": " واحد", "probability": 0.95947265625}, {"start": 1154.29, "end": 1154.95, "word": " أو", "probability": 0.51806640625}, {"start": 1154.95, "end": 1155.43, "word": " أول", "probability": 0.823974609375}, {"start": 1155.43, "end": 1155.75, "word": " حد", "probability": 0.987548828125}, {"start": 1155.75, "end": 1156.17, "word": " واحد", "probability": 0.94482421875}, {"start": 1156.17, "end": 1156.63, "word": " التاني", "probability": 0.76220703125}, {"start": 1156.63, "end": 1157.15, "word": " صفر", "probability": 0.96630859375}, {"start": 1157.15, "end": 1158.29, "word": " واحد", "probability": 0.904296875}, {"start": 1158.29, "end": 1158.93, "word": " صفر", "probability": 0.927734375}, {"start": 1158.93, "end": 1160.03, "word": " و", "probability": 0.59375}, {"start": 1160.03, 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5172, 9957, 32239, 3224, 22807, 5296, 33456, 39896, 2423, 8177, 2423, 39184, 13924, 655, 2423, 24401, 23328, 50113, 15040, 6024, 110, 29245, 10632, 318, 17, 42], "avg_logprob": -0.27299107483455115, "compression_ratio": 1.1322314049586777, "no_speech_prob": 0.0, "words": [{"start": 1173.47, "end": 1174.11, "word": "الـ", "probability": 0.432373046875}, {"start": 1174.11, "end": 1174.49, "word": " sequence", "probability": 0.84716796875}, {"start": 1174.49, "end": 1174.81, "word": " هذه", "probability": 0.57568359375}, {"start": 1174.81, "end": 1175.59, "word": " divergent", "probability": 0.614990234375}, {"start": 1175.59, "end": 1177.09, "word": " عارفين", "probability": 0.9267578125}, {"start": 1177.09, "end": 1178.33, "word": " ليه؟", "probability": 0.873046875}, {"start": 1178.33, "end": 1178.73, "word": " لأن", "probability": 0.878662109375}, {"start": 1178.73, "end": 1179.03, "word": " هي", "probability": 0.349853515625}, {"start": 1179.03, "end": 1179.27, "word": " ال", "probability": 0.826171875}, {"start": 1179.27, "end": 1179.65, "word": " proof", "probability": 0.935546875}, {"start": 1179.65, "end": 1182.49, "word": " الـ", "probability": 0.4923095703125}, {"start": 1182.49, "end": 1183.43, "word": " subsequence", "probability": 0.932861328125}, {"start": 1183.43, "end": 1194.13, "word": " الحدود", "probability": 0.8248697916666666}, {"start": 1194.13, "end": 1194.59, "word": " مثلا", "probability": 0.97900390625}, {"start": 1194.59, "end": 1195.45, "word": " الزوجية", "probability": 0.91748046875}, {"start": 1195.45, "end": 1198.33, "word": " S2K", "probability": 0.7652994791666666}], "temperature": 1.0}, {"id": 45, "seek": 123096, "start": 1203.52, "end": 1230.96, "text": "هي أول حد وهي التاني لإن الحدود الزوجية أصفار كلهم صح؟ تكون بيرجل سفر and ال subsequence التانية اللي حدودها فردية كلهم واحد، ثابت واحد وهدي تكون بيرجل واحد نعم؟", "tokens": [3224, 1829, 5551, 12610, 11331, 3215, 37037, 1829, 16712, 7649, 1829, 5296, 28814, 1863, 21542, 3215, 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130971, "start": 1281.79, "end": 1309.71, "text": "المتولدة من الـ sequence سالب واحد أس N اللي هي ال series هذه is divergent okay تمام وبالتالي هيك ممكن أثبتنا هذا مثال على divergence series إذن عشان أثبت ال series divergent أو convergent بحاول أفحص", "tokens": [45340, 2655, 12610, 41891, 9154, 2423, 39184, 8310, 8608, 6027, 3555, 36764, 24401, 5551, 3794, 426, 13672, 1829, 39896, 2423, 2638, 29538, 307, 18558, 6930, 1392, 46811, 10943, 46599, 6027, 2655, 6027, 1829, 39896, 4117, 3714, 43020, 5551, 12984, 3555, 2655, 8315, 23758, 50113, 6027, 15844, 47387, 2638, 11933, 8848, 1863, 6225, 8592, 7649, 5551, 12984, 3555, 2655, 2423, 2638, 18558, 6930, 34051, 9652, 6930, 4724, 5016, 995, 12610, 5551, 5172, 5016, 9381], "avg_logprob": -0.2618243251297925, "compression_ratio": 1.553191489361702, "no_speech_prob": 0.0, "words": [{"start": 1281.79, "end": 1282.75, "word": "المتولدة", "probability": 0.9307861328125}, {"start": 1282.75, "end": 1283.05, "word": " من", "probability": 0.98828125}, 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partial sums convergent ولا divergent ناخد كمان مثال مختلف من نوع آخر مثال رقم 3", "tokens": [6027, 39184, 8310, 295, 14641, 34499, 4032, 5551, 5172, 5016, 9381, 8032, 1211, 2423, 39184, 8310, 295, 14641, 34499, 9652, 6930, 49429, 18558, 6930, 8717, 47283, 3215, 9122, 2304, 7649, 50113, 6027, 3714, 46456, 46538, 9154, 8717, 45367, 19753, 34740, 50113, 6027, 12602, 4587, 2304, 805], "avg_logprob": -0.2609707535581386, "compression_ratio": 1.3969465648854962, "no_speech_prob": 0.0, "words": [{"start": 1310.34, "end": 1310.64, "word": "الـ", "probability": 0.27978515625}, {"start": 1310.64, "end": 1310.9, "word": " sequence", "probability": 0.55078125}, {"start": 1310.9, "end": 1311.26, "word": " of", "probability": 0.96044921875}, {"start": 1311.26, "end": 1311.62, "word": " partial", "probability": 0.94677734375}, {"start": 1311.62, "end": 1312.1, "word": " sums", "probability": 0.9736328125}, {"start": 1312.1, "end": 1313.36, "word": " و", "probability": 0.335693359375}, {"start": 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1322.18, "end": 1322.58, "word": " مثال", "probability": 0.9208984375}, {"start": 1322.58, "end": 1323.16, "word": " مختلف", "probability": 0.9899088541666666}, {"start": 1323.16, "end": 1323.36, "word": " من", "probability": 0.9560546875}, {"start": 1323.36, "end": 1323.6, "word": " نوع", "probability": 0.96630859375}, {"start": 1323.6, "end": 1324.16, "word": " آخر", "probability": 0.91943359375}, {"start": 1324.16, "end": 1326.04, "word": " مثال", "probability": 0.92431640625}, {"start": 1326.04, "end": 1326.46, "word": " رقم", "probability": 0.9803059895833334}, {"start": 1326.46, "end": 1326.76, "word": " 3", "probability": 0.50537109375}], "temperature": 1.0}, {"id": 50, "seek": 136513, "start": 1341.55, "end": 1365.13, "text": "Discuss the convergence of the series sigma from N equals one to infinity لواحد على N في N زايد واحد", "tokens": [35, 5606, 2023, 264, 32181, 295, 264, 2638, 12771, 490, 426, 6915, 472, 281, 13202, 5296, 14407, 24401, 15844, 426, 8978, 426, 30767, 995, 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"text": "إذا طلع أنا عندي واحد على ك في ك زائد واحد بساوي واحد على ك سالب واحد على ك زائد واحد الان now تعالوا نشوف ال inf partial sum أو نبحث ال sequence of partial sums ونبحث هل هي convergent ولا divergent", "tokens": [28814, 15730, 23032, 1211, 3615, 41850, 18871, 16254, 36764, 24401, 15844, 9122, 8978, 9122, 30767, 16373, 3215, 36764, 24401, 4724, 3794, 995, 45865, 36764, 24401, 15844, 9122, 8608, 6027, 3555, 36764, 24401, 15844, 9122, 30767, 16373, 3215, 36764, 24401, 2423, 7649, 586, 37279, 6027, 14407, 8717, 8592, 38688, 2423, 1536, 14641, 2408, 34051, 8717, 49628, 12984, 2423, 8310, 295, 14641, 34499, 4032, 1863, 49628, 12984, 8032, 1211, 39896, 9652, 6930, 49429, 18558, 6930], "avg_logprob": -0.24894424789660685, "compression_ratio": 1.7485380116959064, "no_speech_prob": 0.0, "words": [{"start": 1472.41, "end": 1472.77, "word": "إذا", "probability": 0.57861328125}, {"start": 1472.77, "end": 1473.21, "word": " طلع", "probability": 0.8723958333333334}, {"start": 1473.21, "end": 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"word": " ك", "probability": 0.95751953125}, {"start": 1481.45, "end": 1482.01, "word": " سالب", "probability": 0.9588216145833334}, {"start": 1482.01, "end": 1482.63, "word": " واحد", "probability": 0.984375}, {"start": 1482.63, "end": 1483.85, "word": " على", "probability": 0.7607421875}, {"start": 1483.85, "end": 1484.31, "word": " ك", "probability": 0.966796875}, {"start": 1484.31, "end": 1484.77, "word": " زائد", "probability": 0.8600260416666666}, {"start": 1484.77, "end": 1485.17, "word": " واحد", "probability": 0.985595703125}, {"start": 1485.17, "end": 1487.31, "word": " الان", "probability": 0.689208984375}, {"start": 1487.31, "end": 1487.83, "word": " now", "probability": 0.45361328125}, {"start": 1487.83, "end": 1488.73, "word": " تعالوا", "probability": 0.7716471354166666}, {"start": 1488.73, "end": 1489.01, "word": " نشوف", "probability": 0.9625651041666666}, {"start": 1489.01, "end": 1489.19, "word": " ال", "probability": 0.92236328125}, {"start": 1489.19, "end": 1489.41, "word": " inf", "probability": 0.12249755859375}, {"start": 1489.41, "end": 1489.81, "word": " partial", "probability": 0.9638671875}, {"start": 1489.81, "end": 1490.27, "word": " sum", "probability": 0.61474609375}, {"start": 1490.27, "end": 1491.03, "word": " أو", "probability": 0.6201171875}, {"start": 1491.03, "end": 1491.43, "word": " نبحث", "probability": 0.8756510416666666}, {"start": 1491.43, "end": 1491.55, "word": " ال", "probability": 0.93603515625}, {"start": 1491.55, "end": 1491.91, "word": " sequence", "probability": 0.9736328125}, {"start": 1491.91, "end": 1492.13, "word": " of", "probability": 0.3515625}, {"start": 1492.13, "end": 1492.47, "word": " partial", "probability": 0.93896484375}, {"start": 1492.47, "end": 1492.91, "word": " sums", "probability": 0.96044921875}, {"start": 1492.91, "end": 1494.39, "word": " ونبحث", "probability": 0.9268798828125}, {"start": 1494.39, "end": 1494.57, "word": " هل", "probability": 0.966552734375}, {"start": 1494.57, "end": 1494.73, "word": " هي", "probability": 0.8623046875}, {"start": 1494.73, "end": 1495.43, "word": " convergent", "probability": 0.91748046875}, {"start": 1495.43, "end": 1495.65, "word": " ولا", "probability": 0.845703125}, {"start": 1495.65, "end": 1496.35, "word": " divergent", "probability": 0.723388671875}], "temperature": 1.0}, {"id": 56, "seek": 152099, "start": 1497.67, "end": 1520.99, "text": "فهي عندي sm بساوي summation من k بساوي واحد إلى n ل xk اللي هو summation من k بساوي واحد إلى n لواحد على k في k زايد واحد", "tokens": [5172, 3224, 1829, 18871, 16254, 899, 4724, 3794, 995, 45865, 28811, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 30731, 297, 5296, 2031, 74, 13672, 1829, 31439, 28811, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 30731, 297, 5296, 14407, 24401, 15844, 350, 8978, 350, 30767, 995, 25708, 36764, 24401], "avg_logprob": -0.16681985820040984, "compression_ratio": 1.7547169811320755, "no_speech_prob": 0.0, "words": [{"start": 1497.67, "end": 1498.21, "word": "فهي", "probability": 0.83251953125}, {"start": 1498.21, "end": 1498.57, "word": " عندي", "probability": 0.6431884765625}, {"start": 1498.57, "end": 1499.63, "word": " sm", "probability": 0.2120361328125}, {"start": 1499.63, "end": 1500.69, "word": " بساوي", "probability": 0.813720703125}, {"start": 1500.69, "end": 1501.83, "word": " summation", "probability": 0.85791015625}, {"start": 1501.83, "end": 1503.21, "word": " من", "probability": 0.986328125}, {"start": 1503.21, "end": 1503.61, "word": " k", "probability": 0.76611328125}, {"start": 1503.61, "end": 1504.47, "word": " بساوي", "probability": 0.9232177734375}, {"start": 1504.47, "end": 1505.11, "word": " واحد", "probability": 0.92138671875}, {"start": 1505.11, "end": 1505.37, "word": " إلى", "probability": 0.5888671875}, {"start": 1505.37, "end": 1505.91, "word": " n", "probability": 0.8056640625}, {"start": 1505.91, "end": 1507.27, "word": " ل", "probability": 0.82373046875}, {"start": 1507.27, "end": 1509.57, "word": " xk", "probability": 0.810791015625}, {"start": 1509.57, "end": 1513.17, "word": " اللي", "probability": 0.966552734375}, {"start": 1513.17, "end": 1513.49, "word": " هو", "probability": 0.98876953125}, {"start": 1513.49, "end": 1514.19, "word": " summation", "probability": 0.8828125}, {"start": 1514.19, "end": 1515.13, "word": " من", "probability": 0.98486328125}, {"start": 1515.13, "end": 1515.51, "word": " k", "probability": 0.9560546875}, {"start": 1515.51, "end": 1516.13, "word": " بساوي", "probability": 0.9686279296875}, {"start": 1516.13, "end": 1516.63, "word": " واحد", "probability": 0.99169921875}, {"start": 1516.63, "end": 1516.87, "word": " إلى", "probability": 0.970703125}, {"start": 1516.87, "end": 1517.31, "word": " n", "probability": 0.9755859375}, {"start": 1517.31, "end": 1518.67, "word": " لواحد", "probability": 0.8818359375}, {"start": 1518.67, "end": 1518.91, "word": " على", "probability": 0.76318359375}, {"start": 1518.91, "end": 1519.47, "word": " k", "probability": 0.89892578125}, {"start": 1519.47, "end": 1519.67, "word": " في", "probability": 0.8740234375}, {"start": 1519.67, "end": 1520.05, "word": " k", "probability": 0.890625}, {"start": 1520.05, "end": 1520.55, "word": " زايد", "probability": 0.8059895833333334}, {"start": 1520.55, "end": 1520.99, "word": " واحد", "probability": 0.99267578125}], "temperature": 1.0}, {"id": 57, "seek": 154949, "start": 1523.27, "end": 1549.49, "text": "وهذا الان باستخدام ال partial fractions summation من k بساوي واحد الى n الى واحد على k سالب واحد على k موجب واحد الان هذا المجموع تعالوا نفرد تعالوا نفرفته let's expand it يعني نفرفته", "tokens": [2407, 3224, 15730, 2423, 7649, 4724, 995, 14851, 9778, 3215, 10943, 2423, 14641, 36058, 28811, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 2423, 7578, 297, 2423, 7578, 36764, 24401, 15844, 350, 8608, 6027, 3555, 36764, 24401, 15844, 350, 3714, 29245, 3555, 36764, 24401, 2423, 7649, 23758, 9673, 7435, 2304, 45367, 37279, 6027, 14407, 8717, 5172, 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{"start": 1529.51, "end": 1530.09, "word": " بساوي", "probability": 0.62744140625}, {"start": 1530.09, "end": 1530.55, "word": " واحد", "probability": 0.950927734375}, {"start": 1530.55, "end": 1530.85, "word": " الى", "probability": 0.680908203125}, {"start": 1530.85, "end": 1531.23, "word": " n", "probability": 0.61767578125}, {"start": 1531.23, "end": 1532.43, "word": " الى", "probability": 0.734130859375}, {"start": 1532.43, "end": 1532.93, "word": " واحد", "probability": 0.9765625}, {"start": 1532.93, "end": 1533.21, "word": " على", "probability": 0.478759765625}, {"start": 1533.21, "end": 1533.81, "word": " k", "probability": 0.75244140625}, {"start": 1533.81, "end": 1534.59, "word": " سالب", "probability": 0.9189453125}, {"start": 1534.59, "end": 1535.31, "word": " واحد", "probability": 0.986083984375}, {"start": 1535.31, "end": 1535.67, "word": " على", "probability": 0.6708984375}, {"start": 1535.67, "end": 1537.13, "word": " k", "probability": 0.8427734375}, {"start": 1537.13, "end": 1537.69, "word": " موجب", "probability": 0.9189453125}, {"start": 1537.69, "end": 1538.17, "word": " واحد", "probability": 0.9931640625}, {"start": 1538.17, "end": 1542.79, "word": " الان", "probability": 0.798095703125}, {"start": 1542.79, "end": 1543.09, "word": " هذا", "probability": 0.79052734375}, {"start": 1543.09, "end": 1543.69, "word": " المجموع", "probability": 0.9404296875}, {"start": 1543.69, "end": 1544.21, "word": " تعالوا", "probability": 0.9012044270833334}, {"start": 1544.21, "end": 1544.59, "word": " نفرد", "probability": 0.8563232421875}, {"start": 1544.59, "end": 1544.89, "word": " تعالوا", "probability": 0.87158203125}, {"start": 1544.89, "end": 1545.57, "word": " نفرفته", "probability": 0.8853759765625}, {"start": 1545.57, "end": 1546.83, "word": " let's", "probability": 0.788818359375}, {"start": 1546.83, "end": 1547.45, "word": " expand", "probability": 0.91015625}, {"start": 1547.45, "end": 1548.11, "word": " it", "probability": 0.97119140625}, {"start": 1548.11, "end": 1548.79, "word": " يعني", "probability": 0.897216796875}, {"start": 1548.79, "end": 1549.49, "word": " نفرفته", "probability": 0.9705810546875}], "temperature": 1.0}, {"id": 58, "seek": 158135, "start": 1553.61, "end": 1581.35, "text": "هذا مجموع منتهي في n من الحدود خد k بالساوي واحد بطلع أول حد واحد سالب نص خد k بساوي اتنين بطلع الحد البعد و نص سالب تلت و هكذا إلى الحد الأخير هيكون واحد على n minus واحد على n زاد واحد", "tokens": [3224, 15730, 3714, 7435, 2304, 45367, 9154, 47395, 1829, 8978, 297, 9154, 21542, 3215, 23328, 16490, 3215, 350, 20666, 3794, 995, 45865, 36764, 24401, 4724, 9566, 1211, 3615, 5551, 12610, 11331, 3215, 36764, 24401, 8608, 6027, 3555, 8717, 9381, 16490, 3215, 350, 4724, 3794, 995, 45865, 1975, 2655, 1863, 9957, 4724, 9566, 1211, 3615, 21542, 3215, 29739, 22488, 4032, 8717, 9381, 8608, 6027, 3555, 6055, 1211, 2655, 4032, 8032, 4117, 15730, 30731, 21542, 3215, 16247, 9778, 13546, 39896, 30544, 36764, 24401, 15844, 297, 3175, 36764, 24401, 15844, 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1558.83, "word": " واحد", "probability": 0.87548828125}, {"start": 1558.83, "end": 1561.51, "word": " بطلع", "probability": 0.757568359375}, {"start": 1561.51, "end": 1561.87, "word": " أول", "probability": 0.841796875}, {"start": 1561.87, "end": 1562.23, "word": " حد", "probability": 0.994384765625}, {"start": 1562.23, "end": 1562.75, "word": " واحد", "probability": 0.97998046875}, {"start": 1562.75, "end": 1563.21, "word": " سالب", "probability": 0.9034830729166666}, {"start": 1563.21, "end": 1563.61, "word": " نص", "probability": 0.982421875}, {"start": 1563.61, "end": 1565.27, "word": " خد", "probability": 0.947509765625}, {"start": 1565.27, "end": 1565.53, "word": " k", "probability": 0.865234375}, {"start": 1565.53, "end": 1566.05, "word": " بساوي", "probability": 0.94189453125}, {"start": 1566.05, "end": 1566.53, "word": " اتنين", "probability": 0.96337890625}, {"start": 1566.53, "end": 1566.93, "word": " بطلع", "probability": 0.94384765625}, {"start": 1566.93, "end": 1567.27, "word": " الحد", "probability": 0.98779296875}, {"start": 1567.27, "end": 1567.73, "word": " البعد", "probability": 0.63671875}, {"start": 1567.73, "end": 1567.89, "word": " و", "probability": 0.82080078125}, {"start": 1567.89, "end": 1568.29, "word": " نص", "probability": 0.780517578125}, {"start": 1568.29, "end": 1570.01, "word": " سالب", "probability": 0.97314453125}, {"start": 1570.01, "end": 1570.69, "word": " تلت", "probability": 0.9733072916666666}, {"start": 1570.69, "end": 1572.09, "word": " و", "probability": 0.5810546875}, {"start": 1572.09, "end": 1572.77, "word": " هكذا", "probability": 0.9265950520833334}, {"start": 1572.77, "end": 1574.67, "word": " إلى", "probability": 0.76806640625}, {"start": 1574.67, "end": 1575.35, "word": " الحد", "probability": 0.993896484375}, {"start": 1575.35, "end": 1576.01, "word": " الأخير", "probability": 0.9295247395833334}, {"start": 1576.01, "end": 1576.65, "word": " هيكون", "probability": 0.8193359375}, {"start": 1576.65, "end": 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بساوي واحد اللي هو limit لل sequence of partial sums تمام؟ إذا هذا النوع من ال series بنسميه telescoping .. telescoping .. telescoping series", "tokens": [474, 2423, 2408, 6055, 3555, 3615, 11296, 37495, 22653, 3714, 7435, 2304, 45367, 11296, 4724, 3794, 995, 45865, 36764, 24401, 13672, 1829, 31439, 4948, 24976, 8310, 295, 14641, 34499, 46811, 10943, 22807, 11933, 15730, 23758, 28239, 45367, 9154, 2423, 2638, 44945, 38251, 1829, 3224, 37085, 278, 4386, 37085, 278, 4386, 37085, 278, 2638], "avg_logprob": -0.24956596394379935, "compression_ratio": 1.4591194968553458, "no_speech_prob": 0.0, "words": [{"start": 1683.72, "end": 1684.4, "word": "and", "probability": 0.1788330078125}, {"start": 1684.4, "end": 1685.4, "word": " ال", "probability": 0.47998046875}, {"start": 1685.4, "end": 1685.66, "word": " sum", "probability": 0.75537109375}, {"start": 1685.66, "end": 1686.32, "word": " تبعها", "probability": 0.9208984375}, {"start": 1686.32, "end": 1686.8, "word": " يعني", "probability": 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"probability": 0.813232421875}, {"start": 1705.22, "end": 1708.14, "word": " series", "probability": 0.92626953125}], "temperature": 1.0}, {"id": 64, "seek": 172111, "start": 1711.71, "end": 1721.11, "text": "such type of series is called telescoping series okay تمام واضح", "tokens": [39974, 2010, 295, 2638, 307, 1219, 37085, 278, 2638, 1392, 46811, 10943, 4032, 46958, 5016], "avg_logprob": -0.2714843675494194, "compression_ratio": 0.9594594594594594, "no_speech_prob": 0.0, "words": [{"start": 1711.71, "end": 1712.35, "word": "such", "probability": 0.55029296875}, {"start": 1712.35, "end": 1713.41, "word": " type", "probability": 0.96533203125}, {"start": 1713.41, "end": 1713.69, "word": " of", "probability": 0.96826171875}, {"start": 1713.69, "end": 1714.27, "word": " series", "probability": 0.9462890625}, {"start": 1714.27, "end": 1715.11, "word": " is", "probability": 0.9638671875}, {"start": 1715.11, "end": 1715.47, "word": " called", "probability": 0.92041015625}, {"start": 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Cauchy criterion for series", "tokens": [9566, 1829, 3555, 8032, 1863, 47283, 3215, 4724, 3794, 8717, 19913, 2288, 10632, 8608, 16572, 27884, 4032, 37495, 22653, 37893, 4386, 2423, 26890, 3224, 7649, 3660, 37893, 39896, 47283, 3215, 42963, 11778, 38436, 28671, 36764, 24401, 3660, 20904, 7544, 625, 88, 4386, 7544, 625, 88, 46691, 337, 2638], "avg_logprob": -0.16143176020408162, "compression_ratio": 1.2740740740740741, "no_speech_prob": 0.0, "words": [{"start": 1734.43, "end": 1734.99, "word": "طيب", "probability": 0.9845377604166666}, {"start": 1734.99, "end": 1735.75, "word": " هناخد", "probability": 0.851806640625}, {"start": 1735.75, "end": 1736.03, "word": " بس", "probability": 0.95166015625}, {"start": 1736.03, "end": 1736.63, "word": " نظرية", "probability": 0.9605712890625}, {"start": 1736.63, "end": 1737.37, "word": " سريعة", "probability": 0.9523111979166666}, {"start": 1737.37, "end": 1738.85, "word": " و", "probability": 0.72216796875}, {"start": 1738.85, "end": 1739.93, 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diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/nokw77ZubUw_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/nokw77ZubUw_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..54b702a0121ced1f3ed68aced593f9aaa8a049a8
--- /dev/null
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@@ -0,0 +1 @@
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" ساوي", "probability": 0.6736653645833334}, {"start": 206.79, "end": 207.21, "word": " capital", "probability": 0.38818359375}, {"start": 207.21, "end": 207.47, "word": " N", "probability": 0.7119140625}, {"start": 207.47, "end": 209.27, "word": " أصغر", "probability": 0.70947265625}, {"start": 209.27, "end": 209.57, "word": " من", "probability": 0.9755859375}, {"start": 209.57, "end": 211.23, "word": " واحد", "probability": 0.773193359375}, {"start": 211.23, "end": 212.15, "word": " واحد", "probability": 0.860595703125}, {"start": 212.15, "end": 212.75, "word": " زائد", "probability": 0.841796875}, {"start": 212.75, "end": 213.25, "word": " absolute", "probability": 0.82421875}, {"start": 213.25, "end": 214.05, "word": " X", "probability": 0.47705078125}, {"start": 214.05, "end": 216.73, "word": " تمام؟", "probability": 0.65771484375}, {"start": 216.73, "end": 217.25, "word": " الآن", "probability": 0.6104736328125}, {"start": 217.25, "end": 217.51, "word": " لو", "probability": 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{"start": 412.77, "end": 413.55, "word": " وبالتالي", "probability": 0.941015625}, {"start": 413.55, "end": 414.23, "word": " ال", "probability": 0.8916015625}, {"start": 414.23, "end": 414.55, "word": " sequence", "probability": 0.98974609375}, {"start": 414.55, "end": 415.21, "word": " xn", "probability": 0.9609375}, {"start": 415.21, "end": 415.39, "word": " is", "probability": 0.86474609375}, {"start": 415.39, "end": 415.69, "word": " bounded", "probability": 0.94140625}, {"start": 415.69, "end": 416.11, "word": " حسب", "probability": 0.96923828125}, {"start": 416.11, "end": 416.73, "word": " التعريف", "probability": 0.9913330078125}, {"start": 416.73, "end": 417.57, "word": " تمام؟", "probability": 0.8421223958333334}], "temperature": 1.0}, {"id": 17, "seek": 42901, "start": 418.09, "end": 429.01, "text": "إذا هذا يبقى هنا نظرية و هذا طيب في بعض الملاحظات عن نظرية هذه", "tokens": [28814, 15730, 23758, 7251, 3555, 4587, 7578, 34105, 8717, 19913, 2288, 10632, 4032, 23758, 23032, 1829, 3555, 8978, 45030, 11242, 9673, 15040, 5016, 19913, 9307, 18871, 8717, 19913, 2288, 10632, 29538], "avg_logprob": -0.16088867001235485, "compression_ratio": 1.3373493975903614, "no_speech_prob": 0.0, "words": [{"start": 418.09, "end": 418.37, "word": "إذا", "probability": 0.740966796875}, {"start": 418.37, "end": 418.65, "word": " هذا", "probability": 0.43798828125}, {"start": 418.65, "end": 418.93, "word": " يبقى", "probability": 0.8065185546875}, {"start": 418.93, "end": 419.17, "word": " هنا", "probability": 0.87890625}, {"start": 419.17, "end": 419.81, "word": " نظرية", "probability": 0.9443359375}, {"start": 419.81, "end": 422.13, "word": " و", "probability": 0.759765625}, {"start": 422.13, "end": 422.35, "word": " هذا", "probability": 0.89990234375}, {"start": 422.35, "end": 426.35, "word": " طيب", "probability": 0.83544921875}, {"start": 426.35, "end": 426.59, "word": " في", "probability": 0.81103515625}, {"start": 426.59, "end": 427.27, "word": " بعض", "probability": 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9566, 7251, 30544, 20328, 5016, 1829, 5016, 23032, 3555, 19446, 31439, 6225, 4117, 3794, 28239, 19913, 2288, 10632, 28239, 19913, 2288, 10632, 39894, 39648, 28242, 32181, 8310, 307, 37498, 6225, 4117, 3794, 2423, 5629, 23758, 9673, 5172, 32887, 11242, 16472, 7251, 30544, 28242, 37498, 8310, 307, 9652, 6930, 23758, 37893, 20328, 5016], "avg_logprob": -0.13522874202924906, "compression_ratio": 1.7956521739130435, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 440.32, "end": 440.6, "word": "في", "probability": 0.5263671875}, {"start": 440.6, "end": 441.0, "word": " بعض", "probability": 0.917236328125}, {"start": 441.0, "end": 441.72, "word": " الملاحظات", "probability": 0.9263671875}, {"start": 441.72, "end": 442.26, "word": " الملاحظة", "probability": 0.8484375}, {"start": 442.26, "end": 443.02, "word": " الأولى", "probability": 0.93798828125}, {"start": 443.02, "end": 443.7, "word": " بتقول", "probability": 0.94287109375}, {"start": 443.7, "end": 443.98, "word": " ان", "probability": 0.276611328125}, {"start": 443.98, "end": 444.28, "word": " ال", "probability": 0.8359375}, {"start": 444.28, "end": 444.94, "word": " converts", "probability": 0.1512451171875}, {"start": 444.94, "end": 445.3, "word": " of", "probability": 0.94091796875}, {"start": 445.3, "end": 445.72, "word": " theorem", "probability": 0.77001953125}, {"start": 445.72, "end": 446.08, "word": " two", "probability": 0.32568359375}, {"start": 446.08, "end": 446.52, "word": " six", "probability": 0.82666015625}, {"start": 446.52, "end": 447.32, "word": " need", "probability": 0.63916015625}, {"start": 447.32, "end": 447.66, "word": " not", "probability": 0.95947265625}, {"start": 447.66, "end": 447.86, "word": " be", "probability": 0.85546875}, {"start": 447.86, "end": 448.32, "word": " true", "probability": 0.9775390625}, {"start": 448.32, "end": 449.24, "word": " يعني", "probability": 0.939453125}, {"start": 449.24, "end": 449.5, "word": " عكس", "probability": 0.97412109375}, {"start": 449.5, "end": 449.96, "word": " النظرية", "probability": 0.910888671875}, {"start": 449.96, "end": 450.56, "word": " السابقة", "probability": 0.9791666666666666}, {"start": 450.56, "end": 451.4, "word": " مش", "probability": 0.9814453125}, {"start": 451.4, "end": 451.74, "word": " شرط", "probability": 0.9864908854166666}, {"start": 451.74, "end": 451.98, "word": " يكون", "probability": 0.982666015625}, {"start": 451.98, "end": 452.56, "word": " صحيح", "probability": 0.961669921875}, {"start": 452.56, "end": 453.52, "word": " طب", "probability": 0.8671875}, {"start": 453.52, "end": 453.62, "word": " ما", "probability": 0.9150390625}, {"start": 453.62, "end": 453.76, "word": " هو", "probability": 0.728515625}, {"start": 453.76, "end": 454.06, "word": " عكس", "probability": 0.9954427083333334}, {"start": 454.06, "end": 454.6, "word": " النظرية", "probability": 0.981689453125}, {"start": 454.6, "end": 455.1, "word": " النظرية", "probability": 0.91796875}, {"start": 455.1, "end": 455.54, "word": " بتقول", "probability": 0.981689453125}, {"start": 455.54, "end": 455.9, "word": " كل", "probability": 0.95361328125}, {"start": 455.9, "end": 456.5, "word": " convergence", "probability": 0.67529296875}, {"start": 456.5, "end": 457.06, "word": " sequence", "probability": 0.94091796875}, {"start": 457.06, "end": 457.3, "word": " is", "probability": 0.8896484375}, {"start": 457.3, "end": 457.68, "word": " bounded", "probability": 0.90771484375}, {"start": 457.68, "end": 458.74, "word": " عكس", "probability": 0.9949544270833334}, {"start": 458.74, "end": 458.9, "word": " ال", "probability": 0.91552734375}, {"start": 458.9, "end": 459.34, "word": " statement", "probability": 0.94287109375}, {"start": 459.34, "end": 459.88, "word": " هذا", "probability": 0.78955078125}, {"start": 459.88, "end": 461.1, "word": " المفروض", "probability": 0.9736328125}, {"start": 461.1, "end": 461.24, "word": " ان", "probability": 0.56494140625}, {"start": 461.24, "end": 461.62, "word": " يكون", "probability": 0.876953125}, {"start": 461.62, "end": 461.98, "word": " كل", "probability": 0.9541015625}, {"start": 461.98, "end": 462.48, "word": " bounded", "probability": 0.71630859375}, {"start": 462.48, "end": 463.06, "word": " sequence", "probability": 0.96484375}, {"start": 463.06, "end": 463.34, "word": " is", "probability": 0.943359375}, {"start": 463.34, "end": 464.04, "word": " convergent", "probability": 0.9775390625}, {"start": 464.04, "end": 464.76, "word": " هذا", "probability": 0.8623046875}, {"start": 464.76, "end": 465.0, "word": " مش", "probability": 0.9833984375}, {"start": 465.0, "end": 465.26, "word": " صح", "probability": 0.997802734375}], "temperature": 1.0}, {"id": 19, "seek": 47583, "start": 466.49, "end": 475.83, "text": "و هاي في counter example يثبت أو يوضح أن عكس نظرية 2.6 ليس صحيح", "tokens": [2407, 8032, 47302, 8978, 5682, 1365, 7251, 12984, 3555, 2655, 34051, 7251, 2407, 11242, 5016, 14739, 6225, 4117, 3794, 8717, 19913, 2288, 10632, 568, 13, 21, 32239, 3794, 20328, 5016, 1829, 5016], "avg_logprob": -0.2741477272727273, "compression_ratio": 0.96, "no_speech_prob": 0.0, "words": [{"start": 466.49, "end": 466.69, "word": "و", "probability": 0.71630859375}, {"start": 466.69, "end": 466.87, "word": " هاي", "probability": 0.527099609375}, {"start": 466.87, "end": 466.99, "word": " في", "probability": 0.86572265625}, {"start": 466.99, "end": 467.35, "word": " counter", "probability": 0.395263671875}, {"start": 467.35, "end": 469.75, "word": " example", "probability": 0.90380859375}, {"start": 469.75, "end": 471.95, "word": " يثبت", "probability": 0.83941650390625}, {"start": 471.95, "end": 472.27, "word": " أو", "probability": 0.73974609375}, {"start": 472.27, "end": 473.01, "word": " يوضح", "probability": 0.980712890625}, {"start": 473.01, "end": 473.33, "word": " أن", "probability": 0.4970703125}, {"start": 473.33, "end": 473.99, "word": " عكس", "probability": 0.96044921875}, {"start": 473.99, "end": 474.47, "word": " نظرية", "probability": 0.865478515625}, {"start": 474.47, "end": 474.73, "word": " 2", "probability": 0.499755859375}, {"start": 474.73, "end": 475.01, "word": ".6", "probability": 0.6671142578125}, {"start": 475.01, "end": 475.35, "word": " ليس", "probability": 0.7470703125}, {"start": 475.35, "end": 475.83, "word": " صحيح", "probability": 0.8792724609375}], "temperature": 1.0}, {"id": 20, "seek": 50185, "start": 476.75, "end": 501.85, "text": "السيكوانس ان الحد العام تبعها xn بساوي سالب واحد قص ان السيكوانس هذي bounded ليه bounded؟ لأن هاي في عدد موجب capital M بساوي واحد هذا عدد موجب إذا يوجد عدد موجب اللي هو الواحد بحيث ان absolute xn هذا ال absolute value العدد هذا واحد واحد أصغر من اذا بساوي واحد", "tokens": [6027, 3794, 1829, 4117, 2407, 7649, 3794, 16472, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 2031, 77, 4724, 3794, 995, 45865, 8608, 6027, 3555, 36764, 24401, 12174, 9381, 16472, 21136, 1829, 4117, 2407, 7649, 3794, 8032, 8848, 1829, 37498, 32239, 3224, 37498, 22807, 5296, 33456, 8032, 47302, 8978, 6225, 3215, 3215, 3714, 29245, 3555, 4238, 376, 4724, 3794, 995, 45865, 36764, 24401, 23758, 6225, 3215, 3215, 3714, 29245, 3555, 11933, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 3714, 29245, 3555, 13672, 1829, 31439, 2423, 14407, 24401, 4724, 5016, 1829, 12984, 16472, 8236, 2031, 77, 23758, 2423, 8236, 2158, 18863, 3215, 3215, 23758, 36764, 24401, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 1975, 15730, 4724, 3794, 995, 45865, 36764, 24401], "avg_logprob": -0.25994317590697735, "compression_ratio": 1.9906103286384977, "no_speech_prob": 0.0, "words": [{"start": 476.75, "end": 477.61, "word": "السيكوانس", "probability": 0.6936732700892857}, {"start": 477.61, "end": 478.05, "word": " ان", "probability": 0.470458984375}, {"start": 478.05, "end": 478.45, "word": " الحد", "probability": 0.9052734375}, {"start": 478.45, "end": 478.79, "word": " العام", "probability": 0.984619140625}, {"start": 478.79, "end": 479.25, "word": " تبعها", "probability": 0.8673095703125}, {"start": 479.25, "end": 479.89, "word": " xn", "probability": 0.531494140625}, {"start": 479.89, "end": 480.43, "word": " بساوي", "probability": 0.55133056640625}, {"start": 480.43, "end": 480.93, "word": " سالب", "probability": 0.8009440104166666}, {"start": 480.93, "end": 481.29, "word": " واحد", "probability": 0.976806640625}, {"start": 481.29, "end": 481.59, "word": " قص", "probability": 0.76318359375}, {"start": 481.59, "end": 481.91, "word": " ان", "probability": 0.48046875}, {"start": 481.91, "end": 483.37, "word": " السيكوانس", "probability": 0.8628336588541666}, {"start": 483.37, "end": 483.65, "word": " هذي", "probability": 0.4656982421875}, {"start": 483.65, "end": 484.03, "word": " bounded", "probability": 0.8603515625}, {"start": 484.03, "end": 484.47, "word": " ليه", "probability": 0.74560546875}, {"start": 484.47, "end": 486.09, "word": " bounded؟", "probability": 0.6361083984375}, {"start": 486.09, "end": 486.55, "word": " لأن", "probability": 0.879150390625}, {"start": 486.55, "end": 487.15, "word": " هاي", "probability": 0.35369873046875}, {"start": 487.15, "end": 487.37, "word": " في", "probability": 0.8603515625}, {"start": 487.37, "end": 487.81, "word": " عدد", "probability": 0.859375}, {"start": 487.81, "end": 488.27, "word": " موجب", "probability": 0.9851888020833334}, {"start": 488.27, "end": 488.79, "word": " capital", "probability": 0.53857421875}, {"start": 488.79, "end": 489.13, "word": " M", "probability": 0.892578125}, {"start": 489.13, "end": 489.65, "word": " بساوي", "probability": 0.9376220703125}, {"start": 489.65, "end": 490.11, "word": " واحد", "probability": 0.97509765625}, {"start": 490.11, "end": 490.35, "word": " هذا", "probability": 0.391845703125}, {"start": 490.35, "end": 490.65, "word": " عدد", "probability": 0.99365234375}, {"start": 490.65, "end": 491.13, "word": " موجب", "probability": 0.9930013020833334}, {"start": 491.13, "end": 491.53, "word": " إذا", "probability": 0.4884033203125}, {"start": 491.53, "end": 491.89, "word": " يوجد", "probability": 0.95458984375}, {"start": 491.89, "end": 492.19, "word": " عدد", "probability": 0.9925130208333334}, {"start": 492.19, "end": 492.67, "word": " موجب", "probability": 0.9921875}, {"start": 492.67, "end": 493.09, "word": " اللي", "probability": 0.95361328125}, {"start": 493.09, "end": 493.27, "word": " هو", "probability": 0.99560546875}, {"start": 493.27, "end": 493.81, "word": " الواحد", "probability": 0.9788411458333334}, {"start": 493.81, "end": 495.05, "word": " بحيث", "probability": 0.97265625}, {"start": 495.05, "end": 495.21, "word": " ان", "probability": 0.55859375}, {"start": 495.21, "end": 495.67, "word": " absolute", "probability": 0.84765625}, {"start": 495.67, "end": 496.75, "word": " xn", "probability": 0.956298828125}, {"start": 496.75, "end": 497.93, "word": " هذا", "probability": 0.5}, {"start": 497.93, "end": 498.43, "word": " ال", "probability": 0.418701171875}, {"start": 498.43, "end": 498.75, "word": " absolute", "probability": 0.8388671875}, {"start": 498.75, "end": 499.07, "word": " value", "probability": 0.9384765625}, {"start": 499.07, "end": 499.49, "word": " العدد", "probability": 0.88037109375}, {"start": 499.49, "end": 499.67, "word": " هذا", "probability": 0.66552734375}, {"start": 499.67, "end": 500.11, "word": " واحد", "probability": 0.98095703125}, {"start": 500.11, "end": 500.55, "word": " واحد", "probability": 0.70751953125}, {"start": 500.55, "end": 500.95, "word": " أصغر", "probability": 0.9466552734375}, {"start": 500.95, "end": 501.07, "word": " من", "probability": 0.953125}, {"start": 501.07, "end": 501.19, "word": " اذا", "probability": 0.2598876953125}, {"start": 501.19, "end": 501.49, "word": " بساوي", "probability": 0.726318359375}, {"start": 501.49, "end": 501.85, "word": " واحد", "probability": 0.992431640625}], "temperature": 1.0}, {"id": 21, "seek": 52253, "start": 503.09, "end": 522.53, "text": "إن ال absolute xn هي أصغر من أو ساوي عدد موجة بواحد لكل n إذا ال sequence هي bounded واضحة حسب التعريف الآن هذه ال sequence بنثبت إنها ليست convergent إنها divergent فلبرهان ذلك نعمل برهان بالتناقض", "tokens": [28814, 1863, 2423, 8236, 2031, 77, 39896, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 6225, 3215, 3215, 3714, 29245, 3660, 4724, 14407, 24401, 5296, 28820, 297, 11933, 15730, 2423, 8310, 39896, 37498, 4032, 46958, 5016, 3660, 11331, 35457, 16712, 3615, 16572, 5172, 6024, 48506, 29538, 2423, 8310, 44945, 12984, 3555, 2655, 36145, 11296, 32239, 14851, 9652, 6930, 36145, 11296, 18558, 6930, 6156, 46152, 2288, 3224, 7649, 29910, 23275, 8717, 25957, 1211, 4724, 2288, 3224, 7649, 20666, 2655, 8315, 4587, 11242], "avg_logprob": -0.23983434417161598, "compression_ratio": 1.5404040404040404, "no_speech_prob": 0.0, "words": [{"start": 503.09, "end": 503.41, "word": "إن", "probability": 0.44415283203125}, {"start": 503.41, "end": 503.53, "word": " ال", "probability": 0.4345703125}, {"start": 503.53, "end": 503.95, "word": " absolute", "probability": 0.2366943359375}, {"start": 503.95, "end": 504.63, "word": " xn", "probability": 0.523681640625}, {"start": 504.63, "end": 504.81, "word": " هي", "probability": 0.83447265625}, {"start": 504.81, "end": 505.25, "word": " أصغر", "probability": 0.978271484375}, {"start": 505.25, "end": 505.33, "word": " من", "probability": 0.95361328125}, {"start": 505.33, "end": 505.49, "word": " أو", "probability": 0.89013671875}, {"start": 505.49, "end": 505.85, "word": " ساوي", "probability": 0.8899739583333334}, {"start": 505.85, "end": 506.19, "word": " عدد", "probability": 0.9495442708333334}, {"start": 506.19, "end": 506.59, "word": " موجة", "probability": 0.8933919270833334}, {"start": 506.59, "end": 507.03, "word": " بواحد", "probability": 0.9578450520833334}, {"start": 507.03, "end": 507.45, "word": " لكل", "probability": 0.985595703125}, {"start": 507.45, "end": 507.67, "word": " n", "probability": 0.60546875}, {"start": 507.67, "end": 507.87, "word": " إذا", "probability": 0.5257568359375}, {"start": 507.87, "end": 508.03, "word": " ال", "probability": 0.61962890625}, {"start": 508.03, "end": 508.37, "word": " sequence", "probability": 0.92626953125}, {"start": 508.37, "end": 508.59, "word": " هي", "probability": 0.2939453125}, {"start": 508.59, "end": 508.95, "word": " bounded", "probability": 0.669921875}, {"start": 508.95, "end": 509.71, "word": " واضحة", "probability": 0.8402099609375}, {"start": 509.71, "end": 510.51, "word": " حسب", "probability": 0.91455078125}, {"start": 510.51, "end": 511.11, "word": " التعريف", "probability": 0.9857177734375}, {"start": 511.11, "end": 512.23, "word": " الآن", "probability": 0.716796875}, {"start": 512.23, "end": 512.51, "word": " هذه", "probability": 0.75341796875}, {"start": 512.51, "end": 512.63, "word": " ال", "probability": 0.95068359375}, {"start": 512.63, "end": 513.03, "word": " sequence", "probability": 0.9794921875}, {"start": 513.03, "end": 513.73, "word": " بنثبت", "probability": 0.7548065185546875}, {"start": 513.73, "end": 513.97, "word": " إنها", "probability": 0.706298828125}, {"start": 513.97, "end": 514.33, "word": " ليست", "probability": 0.8701171875}, {"start": 514.33, "end": 515.05, "word": " convergent", "probability": 0.781982421875}, {"start": 515.05, "end": 515.33, "word": " إنها", "probability": 0.890869140625}, {"start": 515.33, "end": 516.47, "word": " divergent", "probability": 0.6693115234375}, {"start": 516.47, "end": 519.95, "word": " فلبرهان", "probability": 0.8853515625}, {"start": 519.95, "end": 520.47, "word": " ذلك", "probability": 0.995849609375}, {"start": 520.47, "end": 521.39, "word": " نعمل", "probability": 0.90087890625}, {"start": 521.39, "end": 521.75, "word": " برهان", "probability": 0.9771728515625}, {"start": 521.75, "end": 522.53, "word": " بالتناقض", "probability": 0.96884765625}], "temperature": 1.0}, {"id": 22, "seek": 53807, "start": 523.53, "end": 538.07, "text": "أنا بدأ أثبت أن الـ sequence هذه is not convergent ف assume ال contrary يعني assume أنها convergent to some a belongs to the real numbers افرض أنها convergent وال limit تبعتها عدد a", "tokens": [10721, 8315, 4724, 3215, 10721, 5551, 12984, 3555, 2655, 14739, 2423, 39184, 8310, 29538, 307, 406, 9652, 6930, 6156, 6552, 2423, 19506, 37495, 22653, 6552, 14739, 11296, 9652, 6930, 281, 512, 257, 12953, 281, 264, 957, 3547, 1975, 5172, 43042, 14739, 11296, 9652, 6930, 16070, 4948, 6055, 3555, 34268, 11296, 6225, 3215, 3215, 257], "avg_logprob": -0.36505683010274714, "compression_ratio": 1.4110429447852761, "no_speech_prob": 0.0, "words": [{"start": 523.53, "end": 523.79, "word": "أنا", "probability": 0.5291748046875}, {"start": 523.79, "end": 524.07, "word": " بدأ", "probability": 0.4863077799479167}, {"start": 524.07, "end": 524.27, "word": " أثبت", "probability": 0.8936767578125}, {"start": 524.27, "end": 524.39, "word": " أن", "probability": 0.415771484375}, {"start": 524.39, "end": 524.43, "word": " الـ", "probability": 0.690185546875}, {"start": 524.43, "end": 524.71, "word": " sequence", "probability": 0.546875}, {"start": 524.71, "end": 525.21, "word": " هذه", "probability": 0.505859375}, {"start": 525.21, "end": 525.57, "word": " is", "probability": 0.2958984375}, {"start": 525.57, "end": 526.13, "word": " not", "probability": 0.93359375}, {"start": 526.13, "end": 526.95, "word": " convergent", "probability": 0.957275390625}, {"start": 526.95, "end": 527.43, "word": " ف", "probability": 0.66650390625}, {"start": 527.43, "end": 527.91, "word": " assume", "probability": 0.164794921875}, {"start": 527.91, "end": 528.07, "word": " ال", "probability": 0.8388671875}, {"start": 528.07, "end": 528.63, "word": " contrary", "probability": 0.494140625}, {"start": 528.63, "end": 529.45, "word": " يعني", "probability": 0.842041015625}, {"start": 529.45, "end": 529.91, "word": " assume", "probability": 0.69970703125}, {"start": 529.91, "end": 530.21, "word": " أنها", "probability": 0.80078125}, {"start": 530.21, "end": 531.05, "word": " convergent", "probability": 0.93359375}, {"start": 531.05, "end": 531.65, "word": " to", "probability": 0.94140625}, {"start": 531.65, "end": 532.07, "word": " some", "probability": 0.88671875}, {"start": 532.07, "end": 532.53, "word": " a", "probability": 0.72412109375}, {"start": 532.53, "end": 533.29, "word": " belongs", "probability": 0.377197265625}, {"start": 533.29, "end": 533.57, "word": " to", "probability": 0.9853515625}, {"start": 533.57, "end": 533.67, "word": " the", "probability": 0.8095703125}, {"start": 533.67, "end": 533.85, "word": " real", "probability": 0.96484375}, {"start": 533.85, "end": 534.45, "word": " numbers", "probability": 0.70947265625}, {"start": 534.45, "end": 535.51, "word": " افرض", "probability": 0.6980794270833334}, {"start": 535.51, "end": 535.77, "word": " أنها", "probability": 0.80126953125}, {"start": 535.77, "end": 536.49, "word": " convergent", "probability": 0.91845703125}, {"start": 536.49, "end": 536.67, "word": " وال", "probability": 0.388671875}, {"start": 536.67, "end": 536.95, "word": " limit", "probability": 0.5947265625}, {"start": 536.95, "end": 537.45, "word": " تبعتها", "probability": 0.872314453125}, {"start": 537.45, "end": 537.83, "word": " عدد", "probability": 0.9803059895833334}, {"start": 537.83, "end": 538.07, "word": " a", "probability": 0.84716796875}], "temperature": 1.0}, {"id": 23, "seek": 56794, "start": 539.68, "end": 567.94, "text": "فلو أخدت epsilon بساوي واحد عدد موجب إذا من تعريف ال convergence إذا يوجد capital N يعتمد على ال epsilon اللي أنا مختاره اللي هي الواحد بحيث لكل N أكبر من أو ساوي capital N المسافة بين xn و a أصغر من epsilon الآن ال N هذه اللي هي أكبر من أو ساوي capital N ممكن يكون عدد فردي أو زوجي", "tokens": [5172, 1211, 2407, 5551, 9778, 3215, 2655, 17889, 4724, 3794, 995, 45865, 36764, 24401, 6225, 3215, 3215, 3714, 29245, 3555, 11933, 15730, 9154, 37279, 16572, 5172, 2423, 32181, 11933, 15730, 7251, 29245, 3215, 4238, 426, 7251, 34268, 2304, 3215, 15844, 2423, 17889, 13672, 1829, 41850, 3714, 46456, 9640, 3224, 13672, 1829, 39896, 2423, 14407, 24401, 4724, 5016, 1829, 12984, 5296, 28820, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 9673, 3794, 31845, 3660, 49374, 2031, 77, 4032, 257, 5551, 9381, 17082, 2288, 9154, 17889, 6024, 48506, 2423, 426, 29538, 13672, 1829, 39896, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 3714, 43020, 7251, 30544, 6225, 3215, 3215, 6156, 2288, 16254, 34051, 30767, 29245, 1829], "avg_logprob": -0.14947916145126025, "compression_ratio": 1.838174273858921, "no_speech_prob": 0.0, "words": [{"start": 539.6800000000001, "end": 540.44, "word": "فلو", "probability": 0.7771809895833334}, {"start": 540.44, "end": 540.98, "word": " أخدت", "probability": 0.943359375}, {"start": 540.98, "end": 541.38, "word": " epsilon", "probability": 0.2578125}, {"start": 541.38, "end": 541.92, "word": " بساوي", "probability": 0.71484375}, {"start": 541.92, "end": 542.22, "word": " واحد", "probability": 0.842529296875}, {"start": 542.22, "end": 542.52, "word": " عدد", "probability": 0.9765625}, {"start": 542.52, "end": 543.06, "word": " موجب", "probability": 0.97412109375}, {"start": 543.06, "end": 543.94, "word": " إذا", "probability": 0.44024658203125}, {"start": 543.94, "end": 544.14, "word": " من", "probability": 0.9921875}, {"start": 544.14, "end": 544.56, "word": " تعريف", "probability": 0.99365234375}, {"start": 544.56, "end": 544.68, "word": " ال", "probability": 0.98291015625}, {"start": 544.68, "end": 545.22, "word": " convergence", "probability": 0.888671875}, {"start": 545.22, "end": 545.82, "word": " إذا", "probability": 0.674072265625}, {"start": 545.82, "end": 546.34, "word": " يوجد", "probability": 0.9840494791666666}, {"start": 546.34, "end": 546.78, "word": " capital", "probability": 0.76123046875}, {"start": 546.78, "end": 547.04, "word": " N", "probability": 0.8037109375}, {"start": 547.04, "end": 547.62, "word": " يعتمد", "probability": 0.9664306640625}, {"start": 547.62, "end": 547.74, "word": " على", "probability": 0.6904296875}, {"start": 547.74, "end": 547.84, "word": " ال", "probability": 0.791015625}, {"start": 547.84, "end": 548.22, "word": " epsilon", "probability": 0.87109375}, {"start": 548.22, "end": 548.54, "word": " اللي", "probability": 0.916748046875}, {"start": 548.54, "end": 548.72, "word": " أنا", "probability": 0.68701171875}, {"start": 548.72, "end": 549.22, "word": " مختاره", "probability": 0.8111572265625}, {"start": 549.22, "end": 549.34, "word": " اللي", "probability": 0.949462890625}, {"start": 549.34, "end": 549.46, "word": " هي", "probability": 0.81494140625}, {"start": 549.46, "end": 550.02, "word": " الواحد", "probability": 0.96533203125}, {"start": 550.02, "end": 551.32, "word": " بحيث", "probability": 0.9749755859375}, {"start": 551.32, "end": 551.82, "word": " لكل", "probability": 0.983154296875}, {"start": 551.82, "end": 552.12, "word": " N", "probability": 0.7236328125}, {"start": 552.12, "end": 552.54, "word": " أكبر", "probability": 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"word": " epsilon", "probability": 0.89208984375}, {"start": 557.04, "end": 561.54, "word": " الآن", "probability": 0.6708984375}, {"start": 561.54, "end": 561.72, "word": " ال", "probability": 0.98828125}, {"start": 561.72, "end": 561.98, "word": " N", "probability": 0.65380859375}, {"start": 561.98, "end": 562.46, "word": " هذه", "probability": 0.76708984375}, {"start": 562.46, "end": 562.78, "word": " اللي", "probability": 0.985107421875}, {"start": 562.78, "end": 562.96, "word": " هي", "probability": 0.96875}, {"start": 562.96, "end": 563.3, "word": " أكبر", "probability": 0.9680989583333334}, {"start": 563.3, "end": 563.42, "word": " من", "probability": 0.982421875}, {"start": 563.42, "end": 563.54, "word": " أو", "probability": 0.97900390625}, {"start": 563.54, "end": 563.82, "word": " ساوي", "probability": 0.97265625}, {"start": 563.82, "end": 564.24, "word": " capital", "probability": 0.7705078125}, {"start": 564.24, "end": 564.56, "word": " N", "probability": 0.97216796875}, {"start": 564.56, "end": 565.46, "word": " ممكن", "probability": 0.978759765625}, {"start": 565.46, "end": 565.96, "word": " يكون", "probability": 0.944091796875}, {"start": 565.96, "end": 566.76, "word": " عدد", "probability": 0.8821614583333334}, {"start": 566.76, "end": 567.2, "word": " فردي", "probability": 0.95654296875}, {"start": 567.2, "end": 567.42, "word": " أو", "probability": 0.833984375}, {"start": 567.42, "end": 567.94, "word": " زوجي", "probability": 0.97412109375}], "temperature": 1.0}, {"id": 24, "seek": 59539, "start": 568.77, "end": 595.39, "text": "فلو كانت ال end أكبر من نفسه capital N odd فردي فمن المتباينة خمسة بيصير هذا العدد سالب واحد لأن N فردي فبصير absolute سالب واحد سالب a أصغر من واحد و لو رفعت ال absolute value فبينتج منها أن a أكبر من سالب اتنين أصغر من سفر", "tokens": [5172, 1211, 2407, 25961, 2655, 2423, 917, 5551, 4117, 26890, 9154, 8717, 36178, 3224, 4238, 426, 7401, 6156, 2288, 16254, 6156, 27842, 9673, 2655, 3555, 995, 9957, 3660, 16490, 2304, 3794, 3660, 4724, 1829, 9381, 13546, 23758, 18863, 3215, 3215, 8608, 6027, 3555, 36764, 24401, 5296, 33456, 426, 6156, 2288, 16254, 6156, 3555, 9381, 13546, 8236, 8608, 6027, 3555, 36764, 24401, 8608, 6027, 3555, 257, 5551, 9381, 17082, 2288, 9154, 36764, 24401, 4032, 45164, 12602, 5172, 34268, 2423, 8236, 2158, 6156, 21292, 29399, 7435, 9154, 11296, 14739, 257, 5551, 4117, 26890, 9154, 8608, 6027, 3555, 1975, 2655, 1863, 9957, 5551, 9381, 17082, 2288, 9154, 8608, 5172, 2288], "avg_logprob": -0.21064814193933099, "compression_ratio": 1.7707317073170732, "no_speech_prob": 0.0, "words": [{"start": 568.77, "end": 569.15, "word": "فلو", "probability": 0.64404296875}, {"start": 569.15, "end": 569.57, "word": " كانت", "probability": 0.886962890625}, {"start": 569.57, "end": 569.63, "word": " ال", "probability": 0.7783203125}, {"start": 569.63, "end": 569.83, "word": " end", "probability": 0.47119140625}, {"start": 569.83, "end": 570.27, "word": " أكبر", "probability": 0.8592122395833334}, {"start": 570.27, "end": 570.37, "word": " من", "probability": 0.91162109375}, {"start": 570.37, "end": 570.65, "word": " نفسه", "probability": 0.4664713541666667}, {"start": 570.65, "end": 570.97, "word": " capital", "probability": 0.3955078125}, {"start": 570.97, "end": 571.25, "word": " N", "probability": 0.80126953125}, {"start": 571.25, "end": 571.67, "word": " odd", "probability": 0.11962890625}, {"start": 571.67, "end": 572.21, "word": " فردي", "probability": 0.8966471354166666}, {"start": 572.21, "end": 573.29, "word": " فمن", "probability": 0.92578125}, {"start": 573.29, "end": 574.13, "word": " المتباينة", "probability": 0.957763671875}, {"start": 574.13, "end": 575.11, "word": " خمسة", "probability": 0.905029296875}, {"start": 575.11, "end": 575.91, "word": " بيصير", "probability": 0.7330322265625}, {"start": 575.91, "end": 576.27, "word": " هذا", "probability": 0.65380859375}, {"start": 576.27, "end": 576.97, "word": " العدد", "probability": 0.9415690104166666}, {"start": 576.97, "end": 577.41, "word": " سالب", "probability": 0.8704427083333334}, {"start": 577.41, "end": 577.87, "word": " واحد", "probability": 0.984375}, {"start": 577.87, "end": 578.99, "word": " لأن", "probability": 0.787353515625}, {"start": 578.99, "end": 579.19, "word": " N", "probability": 0.14892578125}, {"start": 579.19, "end": 579.67, "word": " فردي", "probability": 0.95751953125}, {"start": 579.67, "end": 581.27, "word": " فبصير", "probability": 0.8773193359375}, {"start": 581.27, "end": 581.81, "word": " absolute", "probability": 0.88232421875}, {"start": 581.81, "end": 582.55, "word": " سالب", "probability": 0.9410807291666666}, {"start": 582.55, "end": 583.03, "word": " واحد", "probability": 0.990234375}, {"start": 583.03, "end": 583.57, "word": " سالب", "probability": 0.9153645833333334}, {"start": 583.57, "end": 583.75, "word": " a", "probability": 0.55078125}, {"start": 583.75, "end": 584.19, "word": " أصغر", "probability": 0.989990234375}, {"start": 584.19, "end": 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"probability": 0.9749348958333334}, {"start": 593.47, "end": 593.65, "word": " من", "probability": 0.99560546875}, {"start": 593.65, "end": 593.99, "word": " سالب", "probability": 0.9557291666666666}, {"start": 593.99, "end": 594.33, "word": " اتنين", "probability": 0.864013671875}, {"start": 594.33, "end": 594.83, "word": " أصغر", "probability": 0.9720458984375}, {"start": 594.83, "end": 595.01, "word": " من", "probability": 0.99560546875}, {"start": 595.01, "end": 595.39, "word": " سفر", "probability": 0.68994140625}], "temperature": 1.0}, {"id": 25, "seek": 60992, "start": 597.41, "end": 609.93, "text": "لو كرت ال N اللي هي أكبر ما يساوي capital N even فهذا العدد بيصير واحد وبيصير المتباين هذا absolute واحد سالب a أصغر من واحد", "tokens": [1211, 2407, 9122, 43500, 2423, 426, 13672, 1829, 39896, 5551, 4117, 26890, 19446, 7251, 3794, 995, 45865, 4238, 426, 754, 6156, 3224, 15730, 18863, 3215, 3215, 4724, 1829, 9381, 13546, 36764, 24401, 4032, 3555, 1829, 9381, 13546, 9673, 2655, 3555, 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0.9765625}, {"start": 750.34, "end": 750.72, "word": " bounded", "probability": 0.953125}], "temperature": 1.0}, {"id": 31, "seek": 77625, "start": 752.59, "end": 776.25, "text": "not bounded, unbounded، الـ sequence هذه unbounded، okay؟ إذا حسب نظرية 2.6، مدامها unbounded، إذا لازم تكون divergent، لبرهان ذلك، افرضي ال contrary، افرضي إنها convergent، إذا حسب نظرية 2.6، المفروض تطلع bounded، لكنها ليست bounded", "tokens": [2247, 37498, 11, 517, 18767, 292, 12399, 2423, 39184, 8310, 29538, 517, 18767, 292, 12399, 1392, 22807, 11933, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 568, 13, 21, 12399, 3714, 3215, 10943, 11296, 517, 18767, 292, 12399, 11933, 15730, 5296, 31377, 2304, 6055, 30544, 18558, 6930, 12399, 5296, 26890, 3224, 7649, 29910, 23275, 12399, 1975, 5172, 43042, 1829, 2423, 19506, 12399, 1975, 5172, 43042, 1829, 36145, 11296, 9652, 6930, 12399, 11933, 15730, 11331, 35457, 8717, 19913, 2288, 10632, 568, 13, 21, 12399, 9673, 5172, 32887, 11242, 6055, 9566, 1211, 3615, 37498, 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{"start": 773.51, "end": 774.67, "word": " bounded،", "probability": 0.93359375}, {"start": 774.67, "end": 775.39, "word": " لكنها", "probability": 0.984619140625}, {"start": 775.39, "end": 775.87, "word": " ليست", "probability": 0.92822265625}, {"start": 775.87, "end": 776.25, "word": " bounded", "probability": 0.9462890625}], "temperature": 1.0}, {"id": 32, "seek": 80382, "start": 777.9, "end": 803.82, "text": "contradiction إذا ال sequence هذه كونها unbounded حسب نظرية نين سيفتر بتطلع divergent و احنا طبعا عارفين ان ال limit اللي عارفين انها divergent لأن limit n as n tends to infinity بساوي infinity ليس عدد حقيقي ال sequence هذه مالهاش limit okay تمام", "tokens": [9000, 6206, 4105, 11933, 15730, 2423, 8310, 29538, 9122, 11536, 11296, 517, 18767, 292, 11331, 35457, 8717, 19913, 2288, 10632, 8717, 9957, 8608, 1829, 5172, 2655, 2288, 39894, 9566, 1211, 3615, 18558, 6930, 4032, 1975, 5016, 8315, 23032, 3555, 3615, 995, 6225, 9640, 5172, 9957, 16472, 2423, 4948, 13672, 1829, 6225, 9640, 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0.955078125}, {"start": 789.04, "end": 789.76, "word": " اللي", "probability": 0.5538330078125}, {"start": 789.76, "end": 790.26, "word": " عارفين", "probability": 0.991455078125}, {"start": 790.26, "end": 791.08, "word": " انها", "probability": 0.8388671875}, {"start": 791.08, "end": 791.92, "word": " divergent", "probability": 0.857177734375}, {"start": 791.92, "end": 792.26, "word": " لأن", "probability": 0.793701171875}, {"start": 792.26, "end": 792.68, "word": " limit", "probability": 0.515625}, {"start": 792.68, "end": 793.18, "word": " n", "probability": 0.386474609375}, {"start": 793.18, "end": 793.68, "word": " as", "probability": 0.87939453125}, {"start": 793.68, "end": 794.48, "word": " n", "probability": 0.52001953125}, {"start": 794.48, "end": 795.36, "word": " tends", "probability": 0.5888671875}, {"start": 795.36, "end": 795.48, "word": " to", "probability": 0.86376953125}, {"start": 795.48, "end": 795.98, "word": " infinity", "probability": 0.89453125}, {"start": 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"seek": 83354, "start": 810.2, "end": 833.54, "text": "تابع الـ sequence in ليش unbounded؟ ليش الـ sequence هذه unbounded؟ هاي ال proof assume إنها bounded، in is bounded، بدنا نعمل برهان بالتناقل", "tokens": [2655, 16758, 3615, 2423, 39184, 8310, 294, 32239, 8592, 517, 18767, 292, 22807, 32239, 8592, 2423, 39184, 8310, 29538, 517, 18767, 292, 22807, 8032, 47302, 2423, 8177, 6552, 36145, 11296, 37498, 12399, 294, 307, 37498, 12399, 47525, 8315, 8717, 25957, 1211, 4724, 2288, 3224, 7649, 20666, 2655, 8315, 4587, 1211], "avg_logprob": -0.3645833216461481, "compression_ratio": 1.4477611940298507, "no_speech_prob": 0.0, "words": [{"start": 810.2, "end": 810.58, "word": "تابع", "probability": 0.3897298177083333}, {"start": 810.58, "end": 810.7, "word": " الـ", "probability": 0.4864501953125}, {"start": 810.7, "end": 811.14, "word": " sequence", "probability": 0.63916015625}, {"start": 811.14, "end": 811.4, "word": " in", "probability": 0.299072265625}, {"start": 811.4, "end": 811.76, "word": " ليش", "probability": 0.931396484375}, {"start": 811.76, "end": 818.94, "word": " unbounded؟", "probability": 0.813720703125}, {"start": 818.94, "end": 819.7, "word": " ليش", "probability": 0.884765625}, {"start": 819.7, "end": 819.86, "word": " الـ", "probability": 0.7919921875}, {"start": 819.86, "end": 820.16, "word": " sequence", "probability": 0.9716796875}, {"start": 820.16, "end": 820.5, "word": " هذه", "probability": 0.56494140625}, {"start": 820.5, "end": 821.32, "word": " unbounded؟", "probability": 0.95263671875}, {"start": 821.32, "end": 821.5, "word": " هاي", "probability": 0.64697265625}, {"start": 821.5, "end": 821.62, "word": " ال", "probability": 0.97509765625}, {"start": 821.62, "end": 822.08, "word": " proof", "probability": 0.86767578125}, {"start": 822.08, "end": 824.28, "word": " assume", "probability": 0.48876953125}, {"start": 824.28, "end": 827.06, "word": " إنها", "probability": 0.6090087890625}, {"start": 827.06, "end": 828.04, "word": " bounded،", "probability": 0.6566162109375}, {"start": 828.04, "end": 828.38, "word": " in", "probability": 0.3388671875}, {"start": 828.38, "end": 829.02, "word": " is", "probability": 0.9541015625}, {"start": 829.02, "end": 829.72, "word": " bounded،", "probability": 0.621826171875}, {"start": 829.72, "end": 832.02, "word": " بدنا", "probability": 0.6282958984375}, {"start": 832.02, "end": 832.28, "word": " نعمل", "probability": 0.9934895833333334}, {"start": 832.28, "end": 832.74, "word": " برهان", "probability": 0.931396484375}, {"start": 832.74, "end": 833.54, "word": " بالتناقل", "probability": 0.8017578125}], "temperature": 1.0}, {"id": 34, "seek": 85828, "start": 834.64, "end": 858.28, "text": "إذا يوجد عدد مجد M أكبر من سفر بحيث أنه absolute xn اللي هي M أصغر من M لكل M belonging to N طيب by Archimedean property", "tokens": [28814, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 3714, 7435, 3215, 376, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 4724, 5016, 1829, 12984, 14739, 3224, 8236, 2031, 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0.91650390625}, {"start": 839.46, "end": 839.8, "word": " أنه", "probability": 0.5694580078125}, {"start": 839.8, "end": 840.62, "word": " absolute", "probability": 0.69580078125}, {"start": 840.62, "end": 842.02, "word": " xn", "probability": 0.361083984375}, {"start": 842.02, "end": 842.2, "word": " اللي", "probability": 0.79345703125}, {"start": 842.2, "end": 842.48, "word": " هي", "probability": 0.84765625}, {"start": 842.48, "end": 842.84, "word": " M", "probability": 0.9130859375}, {"start": 842.84, "end": 843.5, "word": " أصغر", "probability": 0.9853515625}, {"start": 843.5, "end": 843.8, "word": " من", "probability": 0.986328125}, {"start": 843.8, "end": 844.34, "word": " M", "probability": 0.96630859375}, {"start": 844.34, "end": 845.86, "word": " لكل", "probability": 0.978515625}, {"start": 845.86, "end": 847.28, "word": " M", "probability": 0.76806640625}, {"start": 847.28, "end": 847.78, "word": " belonging", "probability": 0.40576171875}, {"start": 847.78, "end": 848.04, "word": " to", "probability": 0.9677734375}, {"start": 848.04, "end": 848.36, "word": " N", "probability": 0.65625}, {"start": 848.36, "end": 856.38, "word": " طيب", "probability": 0.7849934895833334}, {"start": 856.38, "end": 856.68, "word": " by", "probability": 0.4306640625}, {"start": 856.68, "end": 857.6, "word": " Archimedean", "probability": 0.937255859375}, {"start": 857.6, "end": 858.28, "word": " property", "probability": 0.89208984375}], "temperature": 1.0}, {"id": 35, "seek": 89566, "start": 865.94, "end": 895.66, "text": "م أكبر من السفر بتأدي لأي عدد موجب يوجد عدد طبيعي n0 ينتمي إلى n بحيث انه n0 أكبر من m طبعا هذا بساوي n لأن لو سميت هذه واحد و هذه اتنين فمن واحد و اتنين from واحد", "tokens": [2304, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 39894, 10721, 16254, 5296, 10721, 1829, 6225, 3215, 3215, 3714, 29245, 3555, 7251, 29245, 3215, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 297, 15, 7251, 29399, 2304, 1829, 30731, 297, 4724, 5016, 1829, 12984, 16472, 3224, 297, 15, 5551, 4117, 26890, 9154, 275, 23032, 3555, 3615, 995, 23758, 4724, 3794, 995, 45865, 297, 5296, 33456, 45164, 8608, 2304, 36081, 29538, 36764, 24401, 4032, 29538, 1975, 2655, 1863, 9957, 6156, 27842, 36764, 24401, 4032, 1975, 2655, 1863, 9957, 490, 36764, 24401], "avg_logprob": -0.22507022739796156, "compression_ratio": 1.6993865030674846, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 865.94, "end": 866.4, "word": "م", "probability": 0.36962890625}, {"start": 866.4, "end": 867.04, "word": " أكبر", "probability": 0.89892578125}, {"start": 867.04, "end": 867.26, "word": " من", "probability": 0.9765625}, {"start": 867.26, "end": 867.88, "word": " السفر", "probability": 0.7538248697916666}, {"start": 867.88, "end": 868.68, "word": " بتأدي", "probability": 0.4343668619791667}, {"start": 868.68, "end": 869.26, "word": " لأي", "probability": 0.84423828125}, {"start": 869.26, "end": 869.6, "word": " عدد", "probability": 0.9759114583333334}, {"start": 869.6, "end": 870.14, "word": " موجب", "probability": 0.9571940104166666}, {"start": 870.14, "end": 870.8, "word": " يوجد", "probability": 0.9210611979166666}, {"start": 870.8, "end": 872.48, "word": " عدد", "probability": 0.9918619791666666}, {"start": 872.48, "end": 873.22, "word": " طبيعي", "probability": 0.953125}, {"start": 873.22, "end": 873.94, "word": " n0", "probability": 0.3673095703125}, {"start": 873.94, "end": 874.68, "word": " ينتمي", "probability": 0.958740234375}, {"start": 874.68, "end": 874.98, "word": " إلى", "probability": 0.65234375}, {"start": 874.98, "end": 875.42, "word": " n", "probability": 0.6962890625}, {"start": 875.42, "end": 876.1, "word": " بحيث", "probability": 0.97705078125}, {"start": 876.1, "end": 877.04, "word": " انه", "probability": 0.50048828125}, {"start": 877.04, "end": 877.86, "word": " n0", "probability": 0.82275390625}, {"start": 877.86, "end": 878.56, "word": " أكبر", "probability": 0.9329427083333334}, {"start": 878.56, "end": 878.86, "word": " من", "probability": 0.99267578125}, {"start": 878.86, "end": 879.2, "word": " m", "probability": 0.388671875}, {"start": 879.2, "end": 882.3, "word": " طبعا", "probability": 0.9344482421875}, {"start": 882.3, "end": 882.6, "word": " هذا", "probability": 0.7314453125}, {"start": 882.6, "end": 883.18, "word": " بساوي", "probability": 0.78955078125}, {"start": 883.18, "end": 884.12, "word": " n", "probability": 0.58935546875}, {"start": 884.12, "end": 887.04, "word": " لأن", "probability": 0.4293212890625}, {"start": 887.04, "end": 887.24, "word": " لو", "probability": 0.947265625}, {"start": 887.24, "end": 887.78, "word": " سميت", "probability": 0.9775390625}, {"start": 887.78, "end": 888.08, "word": " هذه", "probability": 0.8076171875}, {"start": 888.08, "end": 888.54, "word": " واحد", "probability": 0.94287109375}, {"start": 888.54, "end": 888.72, "word": " و", "probability": 0.3037109375}, {"start": 888.72, "end": 888.98, "word": " هذه", "probability": 0.6474609375}, {"start": 888.98, "end": 889.48, "word": " اتنين", "probability": 0.974609375}, {"start": 889.48, "end": 893.4, "word": " فمن", "probability": 0.91015625}, {"start": 893.4, "end": 893.86, "word": " واحد", "probability": 0.987548828125}, {"start": 893.86, "end": 894.04, "word": " و", "probability": 0.93310546875}, {"start": 894.04, "end": 894.54, "word": " اتنين", "probability": 0.915771484375}, {"start": 894.54, "end": 894.92, "word": " from", "probability": 0.669921875}, {"start": 894.92, "end": 895.66, "word": " واحد", "probability": 0.952880859375}], "temperature": 1.0}, {"id": 36, "seek": 92474, "start": 896.72, "end": 924.74, "text": "and اتنين بيطلع عندي N0 أكبر من M و M أكبر من N0 يعني N0 أكبر من N0 هذا تناقض فى عدد أكبر من نفسه مافيش لأن التناقض هذا بيقول ان ال sequence هذه مش ممكن تكون bounded تمام استخدمنا هنا ال Archimedean property", "tokens": [474, 1975, 2655, 1863, 9957, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 426, 15, 5551, 4117, 26890, 9154, 376, 4032, 376, 5551, 4117, 26890, 9154, 426, 15, 37495, 22653, 426, 15, 5551, 4117, 26890, 9154, 426, 15, 23758, 6055, 8315, 4587, 11242, 6156, 7578, 6225, 3215, 3215, 5551, 4117, 26890, 9154, 8717, 36178, 3224, 19446, 41185, 8592, 5296, 33456, 16712, 8315, 4587, 11242, 23758, 4724, 1829, 39648, 16472, 2423, 8310, 29538, 37893, 3714, 43020, 6055, 30544, 37498, 46811, 10943, 44713, 9778, 40448, 8315, 34105, 2423, 10984, 332, 4858, 282, 4707], "avg_logprob": -0.25566621796115413, "compression_ratio": 1.5804878048780489, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 896.72, "end": 897.32, "word": "and", "probability": 0.19970703125}, {"start": 897.32, "end": 897.94, "word": " اتنين", "probability": 0.753997802734375}, {"start": 897.94, "end": 898.62, "word": " بيطلع", "probability": 0.698779296875}, {"start": 898.62, "end": 899.08, "word": " عندي", "probability": 0.66552734375}, {"start": 899.08, "end": 899.96, "word": " N0", "probability": 0.2906494140625}, {"start": 899.96, "end": 902.44, "word": " أكبر", 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limit تبعتها بساوي مجموعة النهايات كذلك نفس الشيء بالنسبة للفرق الآن ال sequence اللي لحد الآن تبعها حاصل ضرب", "tokens": [6027, 39184, 8310, 13672, 1829, 5296, 24401, 6024, 48506, 6055, 3555, 3615, 11296, 3714, 7435, 2304, 2407, 27884, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 2423, 8310, 2031, 77, 4032, 2423, 8310, 17861, 2423, 8310, 23758, 9652, 6930, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 4724, 3794, 995, 45865, 3714, 7435, 2304, 2407, 27884, 28239, 11296, 1829, 9307, 9122, 8848, 23275, 8717, 36178, 25124, 1829, 38207, 20666, 1863, 35457, 3660, 24976, 5172, 2288, 4587, 6024, 48506, 2423, 8310, 13672, 1829, 5296, 24401, 6024, 48506, 6055, 3555, 3615, 11296, 11331, 33546, 1211, 48812, 25513], "avg_logprob": -0.2372007927996047, "compression_ratio": 1.9453551912568305, "no_speech_prob": 0.0, "words": [{"start": 956.61, "end": 956.95, "word": "الـ", "probability": 0.5985107421875}, {"start": 956.95, "end": 957.35, "word": " sequence", "probability": 0.62841796875}, {"start": 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"probability": 0.9383138020833334}, {"start": 1247.81, "end": 1248.21, "word": " capital", "probability": 0.55810546875}, {"start": 1248.21, "end": 1248.43, "word": " N", "probability": 0.95751953125}, {"start": 1248.43, "end": 1248.89, "word": " واحد", "probability": 0.96435546875}, {"start": 1248.89, "end": 1249.71, "word": " بيطلع", "probability": 0.77158203125}, {"start": 1249.71, "end": 1250.23, "word": " المسافة", "probability": 0.98291015625}, {"start": 1250.23, "end": 1250.45, "word": " بين", "probability": 0.93701171875}, {"start": 1250.45, "end": 1250.91, "word": " XM", "probability": 0.89599609375}, {"start": 1250.91, "end": 1251.19, "word": " X", "probability": 0.84033203125}, {"start": 1251.19, "end": 1251.71, "word": " أصغر", "probability": 0.9857177734375}, {"start": 1251.71, "end": 1251.89, "word": " من", "probability": 0.99267578125}, {"start": 1251.89, "end": 1252.51, "word": " إبسلون", "probability": 0.95693359375}, {"start": 1252.51, "end": 1253.15, "word": " أو", "probability": 0.9189453125}, {"start": 1253.15, "end": 1253.65, "word": " إبسلون", "probability": 0.90478515625}, {"start": 1253.65, "end": 1253.81, "word": " على", "probability": 0.265380859375}, {"start": 1253.81, "end": 1254.39, "word": " 2M", "probability": 0.687255859375}, {"start": 1254.39, "end": 1254.83, "word": " يعتبر", "probability": 0.8268229166666666}, {"start": 1254.83, "end": 1255.07, "word": " هذا", "probability": 0.89453125}, {"start": 1255.07, "end": 1255.29, "word": " هو", "probability": 0.99169921875}, {"start": 1255.29, "end": 1255.79, "word": " الإبسلون", "probability": 0.93857421875}, {"start": 1255.79, "end": 1255.93, "word": " في", "probability": 0.7197265625}, {"start": 1255.93, "end": 1256.57, "word": " التعريف", "probability": 0.9949951171875}, {"start": 1256.57, "end": 1257.89, "word": " لأنها", "probability": 0.70263671875}, {"start": 1257.89, "end": 1258.01, "word": " دا", "probability": 0.669189453125}, {"start": 1258.01, "end": 1258.19, "word": " عدد", "probability": 0.6442057291666666}, {"start": 1258.19, "end": 1258.57, "word": " موجة", "probability": 0.90771484375}, {"start": 1258.57, "end": 1259.09, "word": " وبيعتمد", "probability": 0.77783203125}, {"start": 1259.09, "end": 1259.23, "word": " على", "probability": 0.91064453125}, {"start": 1259.23, "end": 1259.63, "word": " إبسلون", "probability": 0.9837890625}], "temperature": 1.0}, {"id": 51, "seek": 128067, "start": 1260.73, "end": 1280.67, "text": "ليش حطينا 2M لحاجة في نفس يعقوب، عشان في النهاية أخلي ال absolute value هذه أصغر من إبسلون، هنشوفها هنا، بقطوة هذه طيب، إذا قلنا بما إن it's unconventional ل X، فلأي إبسلون فيه capital N واحد، بحيث ال implication هذه تتحقق", "tokens": [20292, 8592, 11331, 9566, 1829, 8315, 568, 44, 5296, 5016, 26108, 3660, 8978, 8717, 36178, 37495, 4587, 37746, 12399, 6225, 8592, 7649, 8978, 28239, 11296, 10632, 5551, 9778, 20292, 2423, 8236, 2158, 29538, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536, 12399, 8032, 1863, 8592, 38688, 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{"start": 1625.38, "end": 1625.6, "word": " من", "probability": 0.998046875}, {"start": 1625.6, "end": 1626.0, "word": " صفر", "probability": 0.7108561197916666}, {"start": 1626.0, "end": 1626.36, "word": " وهذا", "probability": 0.931884765625}, {"start": 1626.36, "end": 1626.96, "word": " جدّيني", "probability": 0.752978515625}, {"start": 1626.96, "end": 1627.7, "word": " contradiction", "probability": 0.87939453125}, {"start": 1627.7, "end": 1630.4, "word": " ليه؟", "probability": 0.6840413411458334}, {"start": 1630.4, "end": 1631.08, "word": " لأنه", "probability": 0.9425455729166666}, {"start": 1631.08, "end": 1631.28, "word": " أنا", "probability": 0.76416015625}, {"start": 1631.28, "end": 1631.72, "word": " فارق", "probability": 0.8024088541666666}, {"start": 1631.72, "end": 1631.86, "word": " في", "probability": 0.95751953125}, {"start": 1631.86, "end": 1632.48, "word": " النظرية", "probability": 0.9739990234375}, {"start": 1632.48, "end": 1632.8, "word": " أن", "probability": 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"word": " غير", "probability": 0.996826171875}, {"start": 1660.41, "end": 1660.85, "word": " سالبة", "probability": 0.9733072916666666}], "temperature": 1.0}, {"id": 69, "seek": 169165, "start": 1666.25, "end": 1691.65, "text": "طب لو كانت ال sequence convergent و حدودها غير موجبة كل حدودها غير موجبة فنهايتها ايضا هتكون غير موجبة و البرهان مشابه لبرهان نظرية السابقة النظرية اللي بعدها لو في عندي two sequences و التنتين convergent", "tokens": [9566, 3555, 45164, 25961, 2655, 2423, 8310, 9652, 6930, 4032, 11331, 3215, 23328, 11296, 32771, 13546, 3714, 29245, 49401, 28242, 11331, 3215, 23328, 11296, 32771, 13546, 3714, 29245, 49401, 6156, 1863, 11296, 36081, 11296, 1975, 1829, 11242, 995, 8032, 2655, 30544, 32771, 13546, 3714, 29245, 49401, 4032, 2423, 26890, 3224, 7649, 37893, 16758, 3224, 5296, 26890, 3224, 7649, 8717, 19913, 2288, 10632, 21136, 16758, 28671, 28239, 19913, 2288, 10632, 13672, 1829, 39182, 11296, 45164, 8978, 18871, 16254, 732, 22978, 4032, 16712, 29399, 9957, 9652, 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1677.75, "word": " لبرهان", "probability": 0.941162109375}, {"start": 1677.75, "end": 1678.17, "word": " نظرية", "probability": 0.865234375}, {"start": 1678.17, "end": 1678.75, "word": " السابقة", "probability": 0.9407552083333334}, {"start": 1678.75, "end": 1682.43, "word": " النظرية", "probability": 0.8948974609375}, {"start": 1682.43, "end": 1682.57, "word": " اللي", "probability": 0.767333984375}, {"start": 1682.57, "end": 1683.71, "word": " بعدها", "probability": 0.9443359375}, {"start": 1683.71, "end": 1688.73, "word": " لو", "probability": 0.85302734375}, {"start": 1688.73, "end": 1688.95, "word": " في", "probability": 0.56494140625}, {"start": 1688.95, "end": 1689.19, "word": " عندي", "probability": 0.687255859375}, {"start": 1689.19, "end": 1689.37, "word": " two", "probability": 0.80712890625}, {"start": 1689.37, "end": 1690.15, "word": " sequences", "probability": 0.966796875}, {"start": 1690.15, "end": 1690.33, "word": " و", "probability": 0.84375}, {"start": 1690.33, "end": 1690.79, "word": " التنتين", "probability": 0.7047526041666666}, {"start": 1690.79, "end": 1691.65, "word": " convergent", "probability": 0.846923828125}], "temperature": 1.0}, {"id": 70, "seek": 170937, "start": 1692.81, "end": 1709.37, "text": "والحد العاملة الأولى أصغر من أو ساوي الحد العاملة التانية فنهاية الأولى أصغر من أو ساوي نهاية التانية والبرهان تطبيق مباشر على نظرية اللى فاتت", "tokens": [2407, 6027, 24401, 18863, 10943, 37977, 16247, 12610, 7578, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 21542, 3215, 18863, 10943, 37977, 16712, 7649, 10632, 6156, 1863, 11296, 10632, 16247, 12610, 7578, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8717, 11296, 10632, 16712, 7649, 10632, 16070, 26890, 3224, 7649, 6055, 9566, 21292, 4587, 3714, 3555, 33599, 2288, 15844, 8717, 19913, 2288, 10632, 13672, 7578, 6156, 9307, 2655], "avg_logprob": -0.10233274542949569, "compression_ratio": 2.08, "no_speech_prob": 0.0, "words": [{"start": 1692.81, "end": 1693.39, "word": "والحد", "probability": 0.7233072916666666}, {"start": 1693.39, "end": 1693.97, "word": " العاملة", "probability": 0.9620768229166666}, {"start": 1693.97, "end": 1694.51, "word": " الأولى", "probability": 0.97119140625}, {"start": 1694.51, "end": 1694.95, "word": " أصغر", "probability": 0.9140625}, {"start": 1694.95, "end": 1695.01, "word": " من", "probability": 0.587890625}, {"start": 1695.01, "end": 1695.15, "word": " أو", "probability": 0.406005859375}, {"start": 1695.15, "end": 1695.39, "word": " ساوي", "probability": 0.8863932291666666}, {"start": 1695.39, "end": 1695.71, "word": " الحد", "probability": 0.933349609375}, {"start": 1695.71, "end": 1696.13, "word": " العاملة", "probability": 0.9851888020833334}, {"start": 1696.13, "end": 1696.67, "word": " التانية", "probability": 0.962890625}, {"start": 1696.67, "end": 1698.03, "word": " فنهاية", "probability": 0.885009765625}, {"start": 1698.03, "end": 1699.31, "word": " الأولى", "probability": 0.9646809895833334}, {"start": 1699.31, "end": 1699.71, "word": " أصغر", "probability": 0.9837646484375}, {"start": 1699.71, "end": 1699.81, "word": " من", "probability": 0.966796875}, {"start": 1699.81, "end": 1699.97, "word": " أو", "probability": 0.984375}, {"start": 1699.97, "end": 1700.49, "word": " ساوي", "probability": 0.9493815104166666}, {"start": 1700.49, "end": 1702.11, "word": " نهاية", "probability": 0.96435546875}, {"start": 1702.11, "end": 1703.07, "word": " التانية", "probability": 0.9788411458333334}, {"start": 1703.07, "end": 1704.81, "word": " والبرهان", "probability": 0.8270263671875}, {"start": 1704.81, "end": 1707.07, "word": " تطبيق", "probability": 0.9794921875}, {"start": 1707.07, "end": 1707.83, "word": " مباشر", "probability": 0.9932861328125}, {"start": 1707.83, "end": 1708.25, "word": " على", "probability": 0.8203125}, {"start": 1708.25, "end": 1708.71, "word": " نظرية", "probability": 0.8734130859375}, {"start": 1708.71, "end": 1708.89, "word": " اللى", "probability": 0.79638671875}, {"start": 1708.89, "end": 1709.37, "word": " فاتت", "probability": 0.9879557291666666}], "temperature": 1.0}, {"id": 71, "seek": 172970, "start": 1711.16, "end": 1729.7, "text": "لو اخدت انا عندي احنا فرضين ان xn أصغر من أو يساوي yn لكل n هذا معناه ان yn minus xn أكبر من أو يساوي سفر لكل n", "tokens": [1211, 2407, 1975, 9778, 3215, 2655, 1975, 8315, 18871, 16254, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 17861, 5296, 28820, 297, 23758, 20449, 8315, 3224, 16472, 288, 77, 3175, 2031, 77, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 28820, 297], "avg_logprob": -0.22325212167481245, "compression_ratio": 1.4634146341463414, "no_speech_prob": 0.0, "words": [{"start": 1711.16, "end": 1711.52, "word": "لو", "probability": 0.64208984375}, {"start": 1711.52, "end": 1712.04, "word": " اخدت", "probability": 0.75433349609375}, {"start": 1712.04, "end": 1712.38, "word": " انا", "probability": 0.5986328125}, {"start": 1712.38, "end": 1713.16, "word": " عندي", "probability": 0.75927734375}, {"start": 1713.16, "end": 1713.96, "word": " احنا", "probability": 0.8994140625}, {"start": 1713.96, "end": 1714.46, "word": " فرضين", "probability": 0.984375}, {"start": 1714.46, "end": 1714.62, "word": " ان", "probability": 0.9033203125}, {"start": 1714.62, "end": 1715.42, "word": " xn", "probability": 0.2938232421875}, {"start": 1715.42, "end": 1717.34, "word": " أصغر", "probability": 0.85009765625}, {"start": 1717.34, "end": 1717.56, "word": " من", "probability": 0.98974609375}, {"start": 1717.56, "end": 1717.78, "word": " أو", "probability": 0.900390625}, {"start": 1717.78, "end": 1718.48, "word": " يساوي", "probability": 0.92626953125}, {"start": 1718.48, "end": 1719.0, "word": " yn", "probability": 0.76025390625}, {"start": 1719.0, "end": 1719.8, "word": " لكل", "probability": 0.981689453125}, {"start": 1719.8, "end": 1720.18, "word": " n", "probability": 0.87841796875}, {"start": 1720.18, "end": 1721.02, "word": " هذا", "probability": 0.578125}, {"start": 1721.02, "end": 1721.7, "word": " معناه", "probability": 0.9820963541666666}, {"start": 1721.7, "end": 1721.98, "word": " ان", "probability": 0.82421875}, {"start": 1721.98, "end": 1724.36, "word": " yn", "probability": 0.624755859375}, {"start": 1724.36, "end": 1724.98, "word": " minus", "probability": 0.361328125}, {"start": 1724.98, "end": 1725.82, "word": " xn", "probability": 0.991943359375}, {"start": 1725.82, "end": 1726.42, "word": " أكبر", "probability": 0.9016927083333334}, {"start": 1726.42, "end": 1726.68, "word": " من", "probability": 0.97998046875}, {"start": 1726.68, "end": 1726.94, "word": " أو", "probability": 0.95263671875}, {"start": 1726.94, "end": 1727.38, "word": " يساوي", "probability": 0.95361328125}, {"start": 1727.38, "end": 1727.9, "word": " سفر", "probability": 0.7823893229166666}, {"start": 1727.9, "end": 1729.42, "word": " لكل", "probability": 0.986572265625}, {"start": 1729.42, "end": 1729.7, "word": " n", "probability": 0.923828125}], "temperature": 1.0}, {"id": 72, "seek": 175040, "start": 1733.62, "end": 1750.4, "text": "فلو أخدت zn عرفت zn على أنه الفرق بين yn و xn فقلنا الفرق هذا غير سالب لكل n إذن هذه ال sequence جديدة حد العام تبعها zn وهذا الحد العام غير سالب لكل n", "tokens": [5172, 1211, 2407, 5551, 9778, 3215, 2655, 710, 77, 6225, 28480, 2655, 710, 77, 15844, 14739, 3224, 27188, 2288, 4587, 49374, 17861, 4032, 2031, 77, 6156, 4587, 1211, 8315, 27188, 2288, 4587, 23758, 32771, 13546, 8608, 6027, 3555, 5296, 28820, 297, 11933, 8848, 1863, 29538, 2423, 8310, 10874, 16254, 41891, 11331, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 710, 77, 37037, 15730, 21542, 3215, 18863, 10943, 32771, 13546, 8608, 6027, 3555, 5296, 28820, 297], "avg_logprob": -0.20104166905085247, "compression_ratio": 1.6423841059602649, "no_speech_prob": 0.0, "words": [{"start": 1733.62, "end": 1734.24, "word": "فلو", "probability": 0.5553385416666666}, {"start": 1734.24, "end": 1734.86, "word": " أخدت", "probability": 0.8643798828125}, {"start": 1734.86, "end": 1735.54, "word": " zn", "probability": 0.3443603515625}, {"start": 1735.54, "end": 1736.08, "word": " عرفت", "probability": 0.7821451822916666}, {"start": 1736.08, "end": 1736.64, "word": " zn", "probability": 0.86962890625}, {"start": 1736.64, "end": 1736.82, "word": " على", "probability": 0.599609375}, {"start": 1736.82, "end": 1737.26, "word": " أنه", "probability": 0.764892578125}, {"start": 1737.26, "end": 1738.22, "word": " الفرق", "probability": 0.9646809895833334}, {"start": 1738.22, "end": 1738.48, "word": " بين", "probability": 0.92529296875}, {"start": 1738.48, "end": 1738.8, "word": " yn", "probability": 0.7353515625}, {"start": 1738.8, "end": 1739.12, "word": " و", "probability": 0.9599609375}, {"start": 1739.12, "end": 1739.62, "word": " xn", "probability": 0.861328125}, {"start": 1739.62, "end": 1740.08, "word": " فقلنا", "probability": 0.81597900390625}, {"start": 1740.08, "end": 1740.5, "word": " الفرق", "probability": 0.9742838541666666}, {"start": 1740.5, "end": 1740.8, "word": " هذا", "probability": 0.8955078125}, {"start": 1740.8, "end": 1741.2, "word": " غير", "probability": 0.970703125}, {"start": 1741.2, "end": 1742.14, "word": " سالب", "probability": 0.87890625}, {"start": 1742.14, "end": 1742.62, "word": " لكل", "probability": 0.98583984375}, {"start": 1742.62, "end": 1742.78, "word": " n", "probability": 0.515625}, {"start": 1742.78, "end": 1743.0, "word": " إذن", "probability": 0.5371907552083334}, {"start": 1743.0, "end": 1743.2, "word": " هذه", "probability": 0.81201171875}, {"start": 1743.2, "end": 1743.3, "word": " ال", "probability": 0.91455078125}, {"start": 1743.3, "end": 1743.58, "word": " sequence", "probability": 0.6552734375}, {"start": 1743.58, "end": 1744.56, "word": " جديدة", "probability": 0.9669596354166666}, {"start": 1744.56, "end": 1745.46, "word": " حد", "probability": 0.962158203125}, {"start": 1745.46, "end": 1745.74, "word": " العام", "probability": 0.969970703125}, {"start": 1745.74, "end": 1746.22, "word": " تبعها", "probability": 0.9122314453125}, {"start": 1746.22, "end": 1746.82, "word": " zn", "probability": 0.855224609375}, {"start": 1746.82, "end": 1747.76, "word": " وهذا", "probability": 0.904296875}, {"start": 1747.76, "end": 1748.26, "word": " الحد", "probability": 0.95654296875}, {"start": 1748.26, "end": 1748.76, "word": " العام", "probability": 0.993896484375}, {"start": 1748.76, "end": 1749.24, "word": " غير", "probability": 0.976318359375}, {"start": 1749.24, "end": 1749.7, "word": " سالب", "probability": 0.99072265625}, {"start": 1749.7, "end": 1750.08, "word": " لكل", "probability": 0.98681640625}, {"start": 1750.08, "end": 1750.4, "word": " n", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 73, "seek": 177753, "start": 1751.71, "end": 1777.53, "text": "والـ sequence xn convergent وyn convergent حسب قوانين النهايات limit الفرق هذا موجود أو بساوي فرق النهايات إذا ال sequence zn حدودها كلها غير سالبة وconvergent لأنها الفرق بين two convergent sequences", "tokens": [2407, 6027, 39184, 8310, 2031, 77, 9652, 6930, 4032, 2534, 9652, 6930, 11331, 35457, 12174, 2407, 7649, 9957, 28239, 11296, 1829, 9307, 4948, 27188, 2288, 4587, 23758, 3714, 29245, 23328, 34051, 4724, 3794, 995, 45865, 6156, 2288, 4587, 28239, 11296, 1829, 9307, 11933, 15730, 2423, 8310, 710, 77, 11331, 3215, 23328, 11296, 28242, 11296, 32771, 13546, 8608, 6027, 49401, 4032, 1671, 331, 6930, 5296, 33456, 11296, 27188, 2288, 4587, 49374, 732, 9652, 6930, 22978], "avg_logprob": -0.240000003973643, "compression_ratio": 1.6666666666666667, "no_speech_prob": 0.0, "words": [{"start": 1751.71, "end": 1752.33, "word": "والـ", "probability": 0.5057779947916666}, {"start": 1752.33, "end": 1752.65, "word": " sequence", "probability": 0.70947265625}, {"start": 1752.65, "end": 1753.25, "word": " xn", "probability": 0.4512939453125}, {"start": 1753.25, "end": 1754.01, "word": " convergent", "probability": 0.692138671875}, {"start": 1754.01, "end": 1754.53, "word": " وyn", "probability": 0.6864013671875}, {"start": 1754.53, "end": 1755.53, "word": " convergent", "probability": 0.95068359375}, {"start": 1755.53, "end": 1756.77, "word": " حسب", "probability": 0.696533203125}, {"start": 1756.77, "end": 1760.51, "word": " قوانين", "probability": 0.9337158203125}, {"start": 1760.51, "end": 1761.13, "word": " النهايات", "probability": 0.8931884765625}, {"start": 1761.13, "end": 1763.03, "word": " limit", "probability": 0.1484375}, {"start": 1763.03, "end": 1764.47, "word": " الفرق", "probability": 0.9430338541666666}, {"start": 1764.47, "end": 1765.01, "word": " هذا", "probability": 0.56884765625}, {"start": 1765.01, "end": 1766.77, "word": " موجود", "probability": 0.9147135416666666}, {"start": 1766.77, "end": 1766.97, "word": " أو", "probability": 0.80517578125}, {"start": 1766.97, "end": 1767.43, "word": " بساوي", "probability": 0.7276611328125}, {"start": 1767.43, "end": 1767.79, "word": " فرق", "probability": 0.98583984375}, {"start": 1767.79, "end": 1768.45, "word": " النهايات", "probability": 0.9752197265625}, {"start": 1768.45, "end": 1770.63, "word": " إذا", "probability": 0.4444580078125}, {"start": 1770.63, "end": 1770.81, "word": " ال", "probability": 0.87744140625}, {"start": 1770.81, "end": 1771.11, "word": " sequence", "probability": 0.56494140625}, {"start": 1771.11, "end": 1771.77, "word": " zn", "probability": 0.710693359375}, {"start": 1771.77, "end": 1772.31, "word": " حدودها", "probability": 0.981201171875}, {"start": 1772.31, "end": 1772.61, "word": " كلها", "probability": 0.885986328125}, {"start": 1772.61, "end": 1772.91, "word": " غير", "probability": 0.996337890625}, {"start": 1772.91, "end": 1773.43, "word": " سالبة", "probability": 0.8992513020833334}, {"start": 1773.43, "end": 1774.73, "word": " وconvergent", "probability": 0.92333984375}, {"start": 1774.73, "end": 1775.23, "word": " لأنها", "probability": 0.91455078125}, {"start": 1775.23, "end": 1775.71, "word": " الفرق", "probability": 0.93505859375}, {"start": 1775.71, "end": 1776.07, "word": " بين", "probability": 0.94189453125}, {"start": 1776.07, "end": 1776.25, "word": " two", "probability": 0.8583984375}, {"start": 1776.25, "end": 1776.95, "word": " convergent", "probability": 0.8720703125}, {"start": 1776.95, "end": 1777.53, "word": " sequences", "probability": 0.92333984375}], "temperature": 1.0}, {"id": 74, "seek": 180673, "start": 1780.87, "end": 1806.73, "text": "وبالتالي حسب النظرية السابقة إذا ال limit ال sequence zn هذه بتطلع غير سالبة طب limit ال zn عسب قوانين النهيات بيساوي limit yn سالب limit xn و ادى هذه عن ناحية التانية فبيطلع limit yn أكبر من لو ساوي limit xn وهذا هو المظلومة okay تمام؟ راضى؟ دى اي سؤال؟", "tokens": [37746, 6027, 2655, 6027, 1829, 11331, 35457, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 11933, 15730, 2423, 4948, 2423, 8310, 710, 77, 29538, 39894, 9566, 1211, 3615, 32771, 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النظرية", "probability": 0.9437255859375}, {"start": 1854.45, "end": 1854.81, "word": " هذه", "probability": 0.861328125}, {"start": 1854.81, "end": 1855.75, "word": " بنطبق", "probability": 0.9371337890625}, {"start": 1855.75, "end": 1858.37, "word": " نظرية", "probability": 0.9659423828125}, {"start": 1858.37, "end": 1858.69, "word": " 2", "probability": 0.54296875}, {"start": 1858.69, "end": 1859.13, "word": ".9", "probability": 0.60198974609375}, {"start": 1859.13, "end": 1860.23, "word": " مرتين", "probability": 0.9931640625}, {"start": 1860.23, "end": 1863.85, "word": " مرة", "probability": 0.9716796875}], "temperature": 1.0}, {"id": 77, "seek": 189209, "start": 1864.75, "end": 1892.09, "text": "على الـ sequence الثابتة a اللي الحدود تبعتها أصغر من حدود ال sequence xn هذه convergence نهايتها a وهذه convergence نهايتها a إذا limit limit ال sequence الثابتة a بساوي a أصغر من أو ساوي limit ال sequence xn", "tokens": [3615, 23942, 2423, 39184, 8310, 6024, 104, 16758, 2655, 3660, 257, 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"probability": 0.90625}, {"start": 1875.31, "end": 1876.47, "word": " وهذه", "probability": 0.838134765625}, {"start": 1876.47, "end": 1877.13, "word": " convergence", "probability": 0.6875}, {"start": 1877.13, "end": 1878.07, "word": " نهايتها", "probability": 0.9671630859375}, {"start": 1878.07, "end": 1879.09, "word": " a", "probability": 0.75732421875}, {"start": 1879.09, "end": 1880.97, "word": " إذا", "probability": 0.5087890625}, {"start": 1880.97, "end": 1881.53, "word": " limit", "probability": 0.83203125}, {"start": 1881.53, "end": 1884.25, "word": " limit", "probability": 0.6513671875}, {"start": 1884.25, "end": 1884.47, "word": " ال", "probability": 0.90283203125}, {"start": 1884.47, "end": 1885.17, "word": " sequence", "probability": 0.85107421875}, {"start": 1885.17, "end": 1885.95, "word": " الثابتة", "probability": 0.9599609375}, {"start": 1885.95, "end": 1886.27, "word": " a", "probability": 0.94921875}, {"start": 1886.27, "end": 1886.91, "word": " بساوي", "probability": 0.848388671875}, {"start": 1886.91, "end": 1887.31, "word": " a", "probability": 0.9267578125}, {"start": 1887.31, "end": 1888.45, "word": " أصغر", "probability": 0.9896240234375}, {"start": 1888.45, "end": 1888.59, "word": " من", "probability": 0.98779296875}, {"start": 1888.59, "end": 1888.73, "word": " أو", "probability": 0.93505859375}, {"start": 1888.73, "end": 1889.27, "word": " ساوي", "probability": 0.94580078125}, {"start": 1889.27, "end": 1889.71, "word": " limit", "probability": 0.98193359375}, {"start": 1889.71, "end": 1890.99, "word": " ال", "probability": 0.63037109375}, {"start": 1890.99, "end": 1891.45, "word": " sequence", "probability": 0.99169921875}, {"start": 1891.45, "end": 1892.09, "word": " xn", "probability": 0.98486328125}], "temperature": 1.0}, {"id": 78, "seek": 191753, "start": 1894.93, "end": 1917.53, "text": "كذلك أنا عندي الـ sequence xn من الفرض أنا عندي الـ sequence xn أصغر من أو ساوي الـ sequence اللي الحد العام تبعها ثابت بيه إذا ال limit حسب النظرية 8 إذا ال limit xn أصغر من أو ساوي limit ال sequence اللي الحد العام تبعها ثابت اللي هو بيه", "tokens": [4117, 8848, 23275, 41850, 18871, 16254, 2423, 39184, 8310, 2031, 77, 9154, 27188, 43042, 41850, 18871, 16254, 2423, 39184, 8310, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 39184, 8310, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 38637, 16758, 2655, 4724, 1829, 3224, 11933, 15730, 2423, 4948, 11331, 35457, 28239, 19913, 2288, 10632, 1649, 11933, 15730, 2423, 4948, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 4948, 2423, 8310, 13672, 1829, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 38637, 16758, 2655, 13672, 1829, 31439, 4724, 1829, 3224], "avg_logprob": -0.17976641323831347, "compression_ratio": 2.245508982035928, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1894.93, "end": 1895.53, "word": "كذلك", "probability": 0.8094889322916666}, {"start": 1895.53, "end": 1895.71, 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"probability": 0.8323567708333334}], "temperature": 1.0}, {"id": 79, "seek": 194932, "start": 1919.56, "end": 1949.32, "text": "من هنا بطلع الـ delimit xn هي أكبر من أو ساوي a أصغر من أو ساوي b و هو المفروض في ال squeeze theorem أو نظرية الـ sandwich في ناس يسموها squeeze theorem في ناس يسموها sandwich theorem هذه في التفاضل والتكامل", "tokens": [27842, 34105, 4724, 9566, 1211, 3615, 2423, 39184, 1103, 332, 270, 2031, 77, 39896, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 257, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 272, 4032, 31439, 9673, 5172, 32887, 11242, 8978, 2423, 13578, 20904, 34051, 8717, 19913, 2288, 10632, 2423, 39184, 11141, 8978, 8717, 32277, 7251, 38251, 2407, 11296, 13578, 20904, 8978, 8717, 32277, 7251, 38251, 2407, 11296, 11141, 20904, 29538, 8978, 16712, 5172, 46958, 1211, 16070, 2655, 4117, 10943, 1211], "avg_logprob": -0.26851851263164, "compression_ratio": 1.7374301675977655, "no_speech_prob": 0.0, "words": [{"start": 1919.56, "end": 1920.52, "word": "من", "probability": 0.55712890625}, {"start": 1920.52, "end": 1920.88, "word": " هنا", "probability": 0.9599609375}, {"start": 1920.88, "end": 1921.28, "word": " بطلع", "probability": 0.68768310546875}, {"start": 1921.28, "end": 1921.44, "word": " الـ", "probability": 0.269317626953125}, {"start": 1921.44, "end": 1921.82, "word": " delimit", "probability": 0.7926432291666666}, {"start": 1921.82, "end": 1922.5, "word": " xn", "probability": 0.315673828125}, {"start": 1922.5, "end": 1923.3, "word": " هي", "probability": 0.78662109375}, {"start": 1923.3, "end": 1923.86, "word": " أكبر", "probability": 0.9127604166666666}, {"start": 1923.86, "end": 1924.04, "word": " من", "probability": 0.96923828125}, {"start": 1924.04, "end": 1924.2, "word": " أو", "probability": 0.9521484375}, {"start": 1924.2, "end": 1924.7, "word": " ساوي", "probability": 0.9256184895833334}, {"start": 1924.7, "end": 1925.04, "word": " a", "probability": 0.81005859375}, {"start": 1925.04, "end": 1925.62, "word": " أصغر", "probability": 0.9649658203125}, {"start": 1925.62, "end": 1925.82, "word": " من", "probability": 0.994140625}, {"start": 1925.82, "end": 1926.04, "word": " أو", "probability": 0.9716796875}, {"start": 1926.04, "end": 1926.58, "word": " ساوي", "probability": 0.9619140625}, {"start": 1926.58, "end": 1927.26, "word": " b", "probability": 0.9423828125}, {"start": 1927.26, "end": 1927.9, "word": " و", "probability": 0.47265625}, {"start": 1927.9, "end": 1928.08, "word": " هو", "probability": 0.72509765625}, {"start": 1928.08, "end": 1929.02, "word": " المفروض", "probability": 0.78564453125}, {"start": 1929.02, "end": 1934.28, "word": " في", "probability": 0.791015625}, {"start": 1934.28, "end": 1934.66, "word": " ال", "probability": 0.63671875}, {"start": 1934.66, "end": 1935.1, "word": " squeeze", "probability": 0.55908203125}, {"start": 1935.1, "end": 1935.66, "word": " theorem", "probability": 0.92529296875}, {"start": 1935.66, "end": 1937.3, "word": " أو", "probability": 0.72607421875}, {"start": 1937.3, "end": 1937.76, "word": " نظرية", "probability": 0.945068359375}, {"start": 1937.76, "end": 1938.08, "word": " الـ", "probability": 0.6988525390625}, {"start": 1938.08, "end": 1938.58, "word": " sandwich", "probability": 0.5498046875}, {"start": 1938.58, "end": 1942.18, "word": " في", "probability": 0.489501953125}, {"start": 1942.18, "end": 1942.4, "word": " ناس", "probability": 0.9697265625}, {"start": 1942.4, "end": 1942.9, "word": " يسموها", "probability": 0.821533203125}, {"start": 1942.9, "end": 1943.36, "word": " squeeze", "probability": 0.89453125}, {"start": 1943.36, "end": 1943.8, "word": " theorem", "probability": 0.8876953125}, {"start": 1943.8, "end": 1943.96, "word": " في", "probability": 0.42431640625}, {"start": 1943.96, "end": 1944.14, "word": " ناس", "probability": 0.977294921875}, {"start": 1944.14, "end": 1944.6, "word": " يسموها", "probability": 0.9539794921875}, {"start": 1944.6, "end": 1945.16, "word": " sandwich", "probability": 0.94482421875}, {"start": 1945.16, "end": 1945.74, "word": " theorem", "probability": 0.8564453125}, {"start": 1945.74, "end": 1947.32, "word": " هذه", "probability": 0.209228515625}, {"start": 1947.32, "end": 1947.52, "word": " في", "probability": 0.7021484375}, {"start": 1947.52, "end": 1948.56, "word": " التفاضل", "probability": 0.9290771484375}, {"start": 1948.56, "end": 1949.32, "word": " والتكامل", "probability": 0.93427734375}], "temperature": 1.0}, {"id": 80, "seek": 197743, "start": 1949.97, "end": 1977.43, "text": "بسموها sandwich sandwich firm أو squeeze firm فالنظرية هذه بتقول لو في عندي three sequences XN, YN و ZN و العلاقة بينهم هكذا YN محصورة بين XN و ZN", "tokens": [3555, 38251, 2407, 11296, 11141, 11141, 6174, 34051, 13578, 6174, 6156, 6027, 1863, 19913, 2288, 10632, 29538, 39894, 39648, 45164, 8978, 18871, 16254, 1045, 22978, 1783, 45, 11, 398, 45, 4032, 1176, 45, 4032, 18863, 15040, 28671, 49374, 16095, 8032, 4117, 15730, 398, 45, 3714, 5016, 9381, 13063, 3660, 49374, 1783, 45, 4032, 1176, 45], "avg_logprob": -0.23632811914597238, "compression_ratio": 1.2875, "no_speech_prob": 0.0, "words": [{"start": 1949.97, "end": 1950.81, "word": "بسموها", "probability": 0.7960205078125}, {"start": 1950.81, "end": 1951.45, "word": " sandwich", "probability": 0.78955078125}, {"start": 1951.45, "end": 1959.07, "word": " sandwich", "probability": 0.81005859375}, {"start": 1959.07, "end": 1959.67, "word": " firm", "probability": 0.10528564453125}, {"start": 1959.67, "end": 1962.75, "word": " أو", "probability": 0.638671875}, {"start": 1962.75, "end": 1963.23, "word": " squeeze", "probability": 0.73291015625}, {"start": 1963.23, "end": 1963.73, "word": " firm", "probability": 0.912109375}, {"start": 1963.73, "end": 1965.69, "word": " فالنظرية", "probability": 0.9244791666666666}, {"start": 1965.69, "end": 1965.87, "word": " هذه", "probability": 0.160400390625}, {"start": 1965.87, "end": 1966.15, "word": " بتقول", "probability": 0.975341796875}, {"start": 1966.15, "end": 1966.25, "word": " لو", "probability": 0.740234375}, {"start": 1966.25, "end": 1966.43, "word": " في", "probability": 0.521484375}, {"start": 1966.43, "end": 1966.73, "word": " عندي", "probability": 0.947509765625}, {"start": 1966.73, "end": 1966.99, "word": " three", "probability": 0.8359375}, {"start": 1966.99, "end": 1967.79, "word": " sequences", "probability": 0.9130859375}, {"start": 1967.79, "end": 1968.59, "word": " XN,", "probability": 0.3729248046875}, {"start": 1968.77, "end": 1969.25, "word": " YN", "probability": 0.8818359375}, {"start": 1969.25, "end": 1969.41, "word": " و", "probability": 0.8994140625}, {"start": 1969.41, "end": 1969.89, "word": " ZN", "probability": 0.89501953125}, {"start": 1969.89, "end": 1971.29, "word": " و", "probability": 0.6865234375}, {"start": 1971.29, "end": 1971.99, "word": " العلاقة", "probability": 0.9583333333333334}, {"start": 1971.99, "end": 1972.51, "word": " بينهم", "probability": 0.976806640625}, {"start": 1972.51, "end": 1973.15, "word": " هكذا", "probability": 0.95458984375}, {"start": 1973.15, "end": 1974.71, "word": " YN", "probability": 0.768798828125}, {"start": 1974.71, "end": 1975.49, "word": " محصورة", "probability": 0.95224609375}, {"start": 1975.49, "end": 1975.75, "word": " بين", "probability": 0.94677734375}, {"start": 1975.75, "end": 1976.41, "word": " XN", "probability": 0.9736328125}, {"start": 1976.41, "end": 1976.67, "word": " و", "probability": 0.9912109375}, {"start": 1976.67, "end": 1977.43, "word": " ZN", "probability": 0.9443359375}], "temperature": 1.0}, {"id": 81, "seek": 199415, "start": 1979.59, "end": 1994.15, "text": "و لو كانت الـ sequences الحدود العامة تبعتها على الأطراف convergent يعني ال sequence x in convergent و ال sequence z in convergent و التنتين ال limit تبعتهم متساوية", "tokens": [2407, 45164, 25961, 2655, 2423, 39184, 22978, 21542, 3215, 23328, 18863, 10943, 3660, 6055, 3555, 34268, 11296, 15844, 16247, 9566, 23557, 5172, 9652, 6930, 37495, 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"word": " على", "probability": 0.88671875}, {"start": 1983.21, "end": 1984.01, "word": " الأطراف", "probability": 0.951171875}, {"start": 1984.01, "end": 1985.47, "word": " convergent", "probability": 0.6771240234375}, {"start": 1985.47, "end": 1986.67, "word": " يعني", "probability": 0.765625}, {"start": 1986.67, "end": 1986.79, "word": " ال", "probability": 0.81396484375}, {"start": 1986.79, "end": 1987.05, "word": " sequence", "probability": 0.63671875}, {"start": 1987.05, "end": 1987.41, "word": " x", "probability": 0.52294921875}, {"start": 1987.41, "end": 1987.59, "word": " in", "probability": 0.432861328125}, {"start": 1987.59, "end": 1988.39, "word": " convergent", "probability": 0.8720703125}, {"start": 1988.39, "end": 1989.43, "word": " و", "probability": 0.630859375}, {"start": 1989.43, "end": 1989.55, "word": " ال", "probability": 0.8681640625}, {"start": 1989.55, "end": 1989.97, "word": " sequence", "probability": 0.97998046875}, {"start": 1989.97, "end": 1990.29, "word": " z", "probability": 0.95849609375}, {"start": 1990.29, "end": 1990.53, "word": " in", "probability": 0.93017578125}, {"start": 1990.53, "end": 1991.21, "word": " convergent", "probability": 0.964111328125}, {"start": 1991.21, "end": 1991.35, "word": " و", "probability": 0.68212890625}, {"start": 1991.35, "end": 1991.99, "word": " التنتين", "probability": 0.8336588541666666}, {"start": 1991.99, "end": 1992.23, "word": " ال", "probability": 0.69873046875}, {"start": 1992.23, "end": 1992.51, "word": " limit", "probability": 0.8857421875}, {"start": 1992.51, "end": 1993.25, "word": " تبعتهم", "probability": 0.956787109375}, {"start": 1993.25, "end": 1994.15, "word": " متساوية", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 82, "seek": 202109, "start": 1996.99, "end": 2021.09, "text": "فلابد أو لازم أن الـ sequence المحصورة بينهم بتكون أيضًا convergent ونهايتها بتساوي القيمة المشتركة لنهايات للنهايات limit yn بتكون موجودة ونهايتها بتساوي نهاية xn ونهاية zn البرهان برضه مش صعب", "tokens": [5172, 15040, 44510, 34051, 5296, 31377, 2304, 14739, 2423, 39184, 8310, 9673, 5016, 9381, 13063, 3660, 49374, 16095, 39894, 30544, 36632, 11242, 14111, 995, 9652, 6930, 4032, 1863, 11296, 36081, 11296, 39894, 3794, 995, 45865, 25062, 32640, 3660, 9673, 8592, 2655, 31747, 3660, 5296, 1863, 11296, 1829, 9307, 24976, 1863, 11296, 1829, 9307, 4948, 17861, 39894, 30544, 3714, 29245, 23328, 3660, 4032, 1863, 11296, 36081, 11296, 39894, 3794, 995, 45865, 8717, 11296, 10632, 2031, 77, 4032, 1863, 11296, 10632, 710, 77, 2423, 26890, 3224, 7649, 4724, 43042, 3224, 37893, 20328, 3615, 3555], "avg_logprob": -0.16666667115303777, "compression_ratio": 1.7301587301587302, "no_speech_prob": 0.0, "words": [{"start": 1996.99, "end": 1998.39, "word": "فلابد", "probability": 0.5844319661458334}, {"start": 1998.39, "end": 1998.67, "word": " أو", "probability": 0.66064453125}, {"start": 1998.67, "end": 1999.21, "word": " لازم", "probability": 0.9807942708333334}, {"start": 1999.21, "end": 1999.41, "word": " أن", "probability": 0.51708984375}, {"start": 1999.41, "end": 1999.57, "word": " الـ", "probability": 0.751953125}, {"start": 1999.57, "end": 2000.01, "word": " sequence", "probability": 0.5791015625}, {"start": 2000.01, "end": 2000.77, "word": " المحصورة", "probability": 0.9708984375}, {"start": 2000.77, "end": 2001.35, "word": " بينهم", "probability": 0.967041015625}, {"start": 2001.35, "end": 2002.39, "word": " بتكون", "probability": 0.65869140625}, {"start": 2002.39, "end": 2002.73, "word": " أيضًا", "probability": 0.7894287109375}, {"start": 2002.73, "end": 2003.53, "word": " convergent", "probability": 0.78125}, {"start": 2003.53, "end": 2004.45, "word": " ونهايتها", "probability": 0.85693359375}, {"start": 2004.45, "end": 2005.75, "word": " بتساوي", "probability": 0.83251953125}, {"start": 2005.75, "end": 2006.51, "word": " القيمة", "probability": 0.9651692708333334}, {"start": 2006.51, "end": 2007.13, "word": " المشتركة", "probability": 0.99326171875}, {"start": 2007.13, "end": 2007.87, "word": " لنهايات", "probability": 0.91455078125}, {"start": 2007.87, "end": 2009.31, "word": " للنهايات", "probability": 0.879443359375}, {"start": 2009.31, "end": 2010.47, "word": " limit", "probability": 0.59326171875}, {"start": 2010.47, "end": 2010.91, "word": " yn", "probability": 0.3974609375}, {"start": 2010.91, "end": 2011.39, "word": " بتكون", "probability": 0.95703125}, {"start": 2011.39, "end": 2012.17, "word": " موجودة", "probability": 0.982177734375}, {"start": 2012.17, "end": 2013.07, "word": " ونهايتها", "probability": 0.88544921875}, {"start": 2013.07, "end": 2013.43, "word": " بتساوي", "probability": 0.919677734375}, {"start": 2013.43, "end": 2013.83, "word": " نهاية", "probability": 0.921875}, {"start": 2013.83, "end": 2014.57, "word": " xn", "probability": 0.86083984375}, {"start": 2014.57, "end": 2015.89, "word": " ونهاية", "probability": 0.925048828125}, {"start": 2015.89, "end": 2016.81, "word": " zn", "probability": 0.717529296875}, {"start": 2016.81, "end": 2019.91, "word": " البرهان", "probability": 0.85748291015625}, {"start": 2019.91, "end": 2020.29, "word": " برضه", "probability": 0.9768880208333334}, {"start": 2020.29, "end": 2020.53, "word": " مش", "probability": 0.9814453125}, {"start": 2020.53, "end": 2021.09, "word": " صعب", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 83, "seek": 204639, "start": 2026.21, "end": 2046.39, "text": "أحنا فرضين أن limit sequence x in موجودة و limit sequence z in موجودة وتنتين متساويات فدعونا نسمي ال limit هذه مشتركة a عدد a الأن ناخد let epsilon أكبر من صفر b", "tokens": [10721, 5016, 8315, 6156, 43042, 9957, 14739, 4948, 8310, 2031, 294, 3714, 29245, 23328, 3660, 4032, 4948, 8310, 710, 294, 3714, 29245, 23328, 3660, 34683, 29399, 9957, 44650, 3794, 995, 45865, 9307, 6156, 3215, 3615, 2407, 8315, 8717, 38251, 1829, 2423, 4948, 29538, 37893, 2655, 31747, 3660, 257, 6225, 3215, 3215, 257, 16247, 1863, 8717, 47283, 3215, 718, 17889, 5551, 4117, 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"text": "بما أن ال sequence xn converge ل a، إذا يوجد عدد طبيعي capital N يعتمد على إبسلون، بحيث لكل N أكبر من وسوء capital N، المسافة بين xn و a أصغر من إبسلون", "tokens": [3555, 15042, 14739, 2423, 8310, 2031, 77, 41881, 5296, 257, 12399, 11933, 15730, 7251, 29245, 3215, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 4238, 426, 7251, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536, 12399, 4724, 5016, 1829, 12984, 5296, 28820, 426, 5551, 4117, 26890, 9154, 46952, 2407, 38207, 4238, 426, 12399, 9673, 3794, 31845, 3660, 49374, 2031, 77, 4032, 257, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.23994007175915863, "compression_ratio": 1.3832335329341316, "no_speech_prob": 0.0, "words": [{"start": 2048.61, "end": 2049.05, "word": "بما", "probability": 0.9736328125}, {"start": 2049.05, "end": 2049.23, "word": " أن", "probability": 0.630859375}, {"start": 2049.23, "end": 2049.31, "word": " ال", "probability": 0.55810546875}, {"start": 2049.31, "end": 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capital", "probability": 0.82568359375}, {"start": 2084.61, "end": 2084.83, "word": " N", "probability": 0.95068359375}, {"start": 2084.83, "end": 2085.07, "word": " هذا", "probability": 0.75439453125}, {"start": 2085.07, "end": 2085.23, "word": " ال", "probability": 0.455810546875}, {"start": 2085.23, "end": 2085.71, "word": " maximum", "probability": 0.96875}, {"start": 2085.71, "end": 2086.53, "word": " لل", "probability": 0.71240234375}, {"start": 2086.53, "end": 2086.83, "word": " N", "probability": 0.63330078125}, {"start": 2086.83, "end": 2087.31, "word": " الأولى", "probability": 0.9918619791666666}, {"start": 2087.31, "end": 2087.41, "word": " و", "probability": 0.499267578125}, {"start": 2087.41, "end": 2087.85, "word": " التانية", "probability": 0.9205729166666666}, {"start": 2087.85, "end": 2088.03, "word": " زي", "probability": 0.872802734375}, {"start": 2088.03, "end": 2088.15, "word": " ما", "probability": 0.8876953125}, {"start": 2088.15, "end": 2088.49, "word": " شوفنا", "probability": 0.8492838541666666}, {"start": 2088.49, "end": 2088.61, "word": " في", "probability": 0.88330078125}, {"start": 2088.61, "end": 2088.97, "word": " القرآن", "probability": 0.6673583984375}, {"start": 2088.97, "end": 2089.49, "word": " السابق", "probability": 0.9283854166666666}], "temperature": 1.0}, {"id": 86, "seek": 211103, "start": 2090.87, "end": 2111.03, "text": "وبالتالي لكل n أكبر من مسافة capital N بقدر أخلي المسافة هذه أصغر من epsilon الآن من الفرض و من ال implication تمانية نحصل على ال implication الجديدة هذه", "tokens": [37746, 6027, 2655, 6027, 1829, 5296, 28820, 297, 5551, 4117, 26890, 9154, 47524, 31845, 3660, 4238, 426, 4724, 28543, 2288, 5551, 9778, 20292, 9673, 3794, 31845, 3660, 29538, 5551, 9381, 17082, 2288, 9154, 17889, 6024, 48506, 9154, 27188, 43042, 4032, 9154, 2423, 37814, 46811, 7649, 10632, 8717, 5016, 36520, 15844, 2423, 37814, 25724, 16254, 41891, 29538], "avg_logprob": -0.29002192145899724, "compression_ratio": 1.5384615384615385, "no_speech_prob": 0.0, "words": [{"start": 2090.8700000000003, "end": 2091.59, "word": "وبالتالي", "probability": 0.9240234375}, {"start": 2091.59, "end": 2091.99, "word": " لكل", "probability": 0.5806884765625}, {"start": 2091.99, "end": 2092.25, "word": " n", "probability": 0.375244140625}, {"start": 2092.25, "end": 2092.59, "word": " أكبر", "probability": 0.91845703125}, {"start": 2092.59, "end": 2092.71, "word": " من", "probability": 0.9716796875}, {"start": 2092.71, "end": 2092.99, "word": " مسافة", "probability": 0.6583251953125}, {"start": 2092.99, "end": 2093.31, "word": " capital", "probability": 0.439453125}, {"start": 2093.31, "end": 2093.53, "word": " N", "probability": 0.8544921875}, {"start": 2093.53, "end": 2093.89, "word": " بقدر", "probability": 0.6984049479166666}, {"start": 2093.89, "end": 2094.17, "word": " أخلي", "probability": 0.5863850911458334}, {"start": 2094.17, "end": 2094.71, "word": " المسافة", "probability": 0.9317626953125}, {"start": 2094.71, "end": 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"word": " نحصل", "probability": 0.9256184895833334}, {"start": 2108.19, "end": 2108.69, "word": " على", "probability": 0.91455078125}, {"start": 2108.69, "end": 2109.43, "word": " ال", "probability": 0.8896484375}, {"start": 2109.43, "end": 2110.03, "word": " implication", "probability": 0.9765625}, {"start": 2110.03, "end": 2110.69, "word": " الجديدة", "probability": 0.8486328125}, {"start": 2110.69, "end": 2111.03, "word": " هذه", "probability": 0.833984375}], "temperature": 1.0}, {"id": 87, "seek": 213677, "start": 2118.35, "end": 2136.77, "text": "يعني من هنا انا عندي xn minus a أصغر من ي وطبعا أكبر من سالب ي ومن هنا انا عندي zn minus a أصغر من ي أكبر من سالب ي", "tokens": [40228, 22653, 9154, 34105, 1975, 8315, 18871, 16254, 2031, 77, 3175, 257, 5551, 9381, 17082, 2288, 9154, 7251, 4032, 9566, 3555, 3615, 995, 5551, 4117, 26890, 9154, 8608, 6027, 3555, 7251, 4032, 27842, 34105, 1975, 8315, 18871, 16254, 710, 77, 3175, 257, 5551, 9381, 17082, 2288, 9154, 7251, 5551, 4117, 26890, 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يساوي Yn إذا لو طرحت A من هنا وطرحت A من هنا فبيطلع عندي Xn-A أصغر من يساوي Yn-A", "tokens": [12, 36, 16592, 5551, 9381, 17082, 2288, 9154, 1783, 77, 12, 32, 36725, 8315, 18871, 16254, 1783, 77, 5551, 9381, 17082, 2288, 9154, 7251, 3794, 995, 45865, 398, 77, 11933, 15730, 45164, 23032, 2288, 33753, 316, 9154, 34105, 4032, 9566, 2288, 33753, 316, 9154, 34105, 6156, 21292, 9566, 1211, 3615, 18871, 16254, 1783, 77, 12, 32, 5551, 9381, 17082, 2288, 9154, 7251, 3794, 995, 45865, 398, 77, 12, 32], "avg_logprob": -0.23705356631960187, "compression_ratio": 1.5819672131147542, "no_speech_prob": 0.0, "words": [{"start": 2164.86, "end": 2165.9, "word": "-Epsilon", "probability": 0.4396158854166667}, {"start": 2165.9, "end": 2166.78, "word": " أصغر", "probability": 0.90576171875}, {"start": 2166.78, "end": 2166.96, "word": " من", "probability": 0.98828125}, {"start": 2166.96, "end": 2167.52, "word": " Xn", "probability": 0.660888671875}, {"start": 2167.52, "end": 2168.34, "word": "-A", 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"word": " بيساوي", "probability": 0.7416015625}, {"start": 2521.27, "end": 2522.69, "word": " السفر", "probability": 0.8377278645833334}, {"start": 2522.69, "end": 2523.39, "word": " okay", "probability": 0.55859375}, {"start": 2523.39, "end": 2523.95, "word": " تمام", "probability": 0.767333984375}, {"start": 2523.95, "end": 2525.79, "word": " طب", "probability": 0.8388671875}, {"start": 2525.79, "end": 2525.95, "word": " لو", "probability": 0.98974609375}, {"start": 2525.95, "end": 2526.35, "word": " كانت", "probability": 0.975341796875}, {"start": 2526.35, "end": 2526.47, "word": " ال", "probability": 0.93359375}, {"start": 2526.47, "end": 2526.73, "word": " limit", "probability": 0.97607421875}, {"start": 2526.73, "end": 2527.13, "word": " هذه", "probability": 0.6337890625}, {"start": 2527.13, "end": 2527.79, "word": " بيساوي", "probability": 0.886328125}, {"start": 2527.79, "end": 2528.23, "word": " سفر", "probability": 0.9734700520833334}, {"start": 2528.23, "end": 2528.55, "word": " وهذه", "probability": 0.799072265625}, {"start": 2528.55, "end": 2529.15, "word": " بيساوي", "probability": 0.96025390625}, {"start": 2529.15, "end": 2529.73, "word": " واحد", "probability": 0.98193359375}, {"start": 2529.73, "end": 2530.95, "word": " ماقدرش", "probability": 0.834228515625}, {"start": 2530.95, "end": 2531.51, "word": " أطبق", "probability": 0.8297119140625}, {"start": 2531.51, "end": 2531.73, "word": " ال", "probability": 0.7236328125}, {"start": 2531.73, "end": 2532.09, "word": " squeeze", "probability": 0.85498046875}, {"start": 2532.09, "end": 2532.49, "word": " theorem", "probability": 0.87890625}, {"start": 2532.49, "end": 2533.41, "word": " لازم", "probability": 0.982421875}, {"start": 2533.41, "end": 2533.67, "word": " ال", "probability": 0.98193359375}, {"start": 2533.67, "end": 2534.21, "word": " sequences", "probability": 0.92724609375}, {"start": 2534.21, "end": 2534.53, "word": " اللي", "probability": 0.9736328125}, {"start": 2534.53, "end": 2534.71, "word": " على", "probability": 0.904296875}, {"start": 2534.71, "end": 2535.31, "word": " أطراف", "probability": 0.9371337890625}], "temperature": 1.0}, {"id": 103, "seek": 256233, "start": 2535.91, "end": 2562.33, "text": "مش بس يكونوا convergent ويلهم نفس ال limit تكون نفس القيمة okay تمام؟ اذا يعني هذا .. هذا بعض الأمثلة المرة الجاية طبعا هنكمل .. اذا المرة الجاية هنكمل نشوف بعض نظريات النهايات و ..", "tokens": [2304, 8592, 4724, 3794, 7251, 30544, 14407, 9652, 6930, 4032, 26895, 16095, 8717, 36178, 2423, 4948, 6055, 30544, 8717, 36178, 25062, 32640, 3660, 1392, 46811, 10943, 22807, 1975, 15730, 37495, 22653, 23758, 4386, 23758, 45030, 11242, 16247, 2304, 12984, 37977, 9673, 25720, 25724, 995, 10632, 23032, 3555, 3615, 995, 8032, 1863, 24793, 1211, 4386, 1975, 15730, 9673, 25720, 25724, 995, 10632, 8032, 1863, 24793, 1211, 8717, 8592, 38688, 45030, 11242, 8717, 19913, 16572, 9307, 28239, 11296, 1829, 9307, 4032, 4386], "avg_logprob": -0.17650462962962962, "compression_ratio": 1.664835164835165, "no_speech_prob": 0.0, "words": [{"start": 2535.91, "end": 2536.27, "word": "مش", "probability": 0.913330078125}, {"start": 2536.27, "end": 2536.53, "word": " بس", "probability": 0.979736328125}, {"start": 2536.53, "end": 2536.91, "word": " يكونوا", "probability": 0.9560546875}, {"start": 2536.91, "end": 2537.63, "word": " convergent", "probability": 0.759033203125}, {"start": 2537.63, "end": 2538.09, "word": " ويلهم", "probability": 0.6411946614583334}, {"start": 2538.09, "end": 2538.49, "word": " نفس", "probability": 0.987548828125}, {"start": 2538.49, "end": 2538.69, "word": " ال", "probability": 0.58544921875}, {"start": 2538.69, "end": 2538.91, "word": " limit", "probability": 0.6826171875}, {"start": 2538.91, "end": 2539.83, "word": " تكون", "probability": 0.711181640625}, {"start": 2539.83, "end": 2540.35, "word": " نفس", "probability": 0.929931640625}, {"start": 2540.35, "end": 2541.37, "word": " القيمة", "probability": 0.9736328125}, {"start": 2541.37, "end": 2541.77, "word": " okay", "probability": 0.61181640625}, {"start": 2541.77, "end": 2542.79, "word": " تمام؟", "probability": 0.6275227864583334}, {"start": 2542.79, "end": 2543.39, "word": " اذا", "probability": 0.7117919921875}, {"start": 2543.39, "end": 2544.49, "word": " يعني", "probability": 0.91845703125}, {"start": 2544.49, "end": 2545.03, "word": " هذا", "probability": 0.7294921875}, {"start": 2545.03, "end": 2545.51, "word": " ..", "probability": 0.69287109375}, {"start": 2545.51, "end": 2546.29, "word": " هذا", "probability": 0.76123046875}, {"start": 2546.29, "end": 2546.69, "word": " بعض", "probability": 0.978271484375}, {"start": 2546.69, "end": 2548.33, "word": " الأمثلة", "probability": 0.8321533203125}, {"start": 2548.33, "end": 2549.99, "word": " المرة", "probability": 0.85546875}, {"start": 2549.99, "end": 2550.31, "word": " الجاية", "probability": 0.9396158854166666}, {"start": 2550.31, "end": 2550.69, "word": " طبعا", "probability": 0.9942626953125}, {"start": 2550.69, "end": 2551.87, "word": " هنكمل", "probability": 0.9210205078125}, {"start": 2551.87, "end": 2551.89, "word": " ..", "probability": 0.7587890625}, {"start": 2551.89, "end": 2557.35, "word": " اذا", "probability": 0.840087890625}, {"start": 2557.35, "end": 2557.73, "word": " المرة", "probability": 0.9873046875}, {"start": 2557.73, "end": 2558.03, "word": " الجاية", "probability": 0.9847005208333334}, {"start": 2558.03, "end": 2558.67, "word": " هنكمل", "probability": 0.99560546875}, {"start": 2558.67, "end": 2558.91, "word": " نشوف", "probability": 0.8356119791666666}, {"start": 2558.91, "end": 2559.21, "word": " بعض", "probability": 0.984375}, {"start": 2559.21, "end": 2559.81, "word": " نظريات", "probability": 0.835205078125}, {"start": 2559.81, "end": 2560.51, "word": " النهايات", "probability": 0.939453125}, {"start": 2560.51, "end": 2561.85, "word": " و", "probability": 0.8837890625}, {"start": 2561.85, "end": 2562.33, "word": " ..", "probability": 0.9658203125}], "temperature": 1.0}, {"id": 104, "seek": 259071, "start": 2563.75, "end": 2590.71, "text": "هنخلص اللي هو section اتنين اتنين مش يعني ضايل كتير و هحللكم بعض التمرين و ناخد ال homework ل section تلات اتنين okay تمام فحاولوا تحضروا هذا الكلام للمحاضرة الجاية و نشوف مع بعض الحاجات هذه", "tokens": [3224, 1863, 9778, 1211, 9381, 13672, 1829, 31439, 3541, 1975, 2655, 1863, 9957, 1975, 2655, 1863, 9957, 37893, 37495, 22653, 48812, 995, 26895, 9122, 2655, 13546, 4032, 8032, 5016, 1211, 23275, 2304, 45030, 11242, 16712, 29973, 9957, 4032, 8717, 47283, 3215, 2423, 14578, 5296, 3541, 6055, 1211, 9307, 1975, 2655, 1863, 9957, 1392, 46811, 10943, 6156, 5016, 995, 12610, 14407, 6055, 5016, 11242, 2288, 14407, 23758, 2423, 28820, 10943, 5296, 19528, 5016, 46958, 25720, 25724, 995, 10632, 4032, 8717, 8592, 38688, 20449, 45030, 11242, 21542, 26108, 9307, 29538], "avg_logprob": -0.11938201912333456, "compression_ratio": 1.696808510638298, "no_speech_prob": 0.0, "words": [{"start": 2563.75, "end": 2564.61, "word": "هنخلص", "probability": 0.97841796875}, {"start": 2564.61, "end": 2564.77, "word": " اللي", "probability": 0.674560546875}, {"start": 2564.77, "end": 2564.99, "word": " هو", "probability": 0.96826171875}, {"start": 2564.99, "end": 2565.49, "word": " section", "probability": 0.85400390625}, {"start": 2565.49, "end": 2567.43, "word": " اتنين", "probability": 0.74420166015625}, {"start": 2567.43, "end": 2567.95, "word": " اتنين", "probability": 0.98681640625}, {"start": 2567.95, "end": 2569.17, "word": " مش", "probability": 0.88525390625}, {"start": 2569.17, "end": 2569.47, "word": " يعني", "probability": 0.8876953125}, {"start": 2569.47, "end": 2570.31, "word": " ضايل", "probability": 0.65966796875}, {"start": 2570.31, "end": 2570.81, "word": " كتير", "probability": 0.9864908854166666}, {"start": 2570.81, "end": 2573.49, "word": " و", "probability": 0.8134765625}, {"start": 2573.49, "end": 2574.15, "word": " هحللكم", "probability": 0.837109375}, {"start": 2574.15, "end": 2574.45, "word": " بعض", "probability": 0.9794921875}, {"start": 2574.45, "end": 2575.17, "word": " التمرين", "probability": 0.85107421875}, {"start": 2575.17, "end": 2576.37, "word": " و", "probability": 0.9873046875}, {"start": 2576.37, "end": 2576.87, "word": " ناخد", "probability": 0.9913736979166666}, {"start": 2576.87, "end": 2577.03, "word": " ال", "probability": 0.9892578125}, {"start": 2577.03, "end": 2577.63, "word": " homework", "probability": 0.58251953125}, {"start": 2577.63, "end": 2578.47, "word": " ل", "probability": 0.93359375}, {"start": 2578.47, "end": 2578.89, "word": " section", "probability": 0.84423828125}, {"start": 2578.89, "end": 2579.27, "word": " تلات", "probability": 0.8759765625}, {"start": 2579.27, "end": 2579.75, "word": " اتنين", "probability": 0.86724853515625}, {"start": 2579.75, "end": 2580.69, "word": " okay", "probability": 0.72998046875}, {"start": 2580.69, "end": 2581.45, "word": " تمام", "probability": 0.85791015625}, {"start": 2581.45, "end": 2582.37, "word": " فحاولوا", "probability": 0.94560546875}, {"start": 2582.37, "end": 2582.87, "word": " تحضروا", "probability": 0.9669921875}, {"start": 2582.87, "end": 2583.07, "word": " هذا", "probability": 0.93603515625}, {"start": 2583.07, "end": 2583.51, "word": " الكلام", "probability": 0.9397786458333334}, {"start": 2583.51, "end": 2584.31, "word": " للمحاضرة", "probability": 0.94921875}, {"start": 2584.31, "end": 2584.95, "word": " الجاية", "probability": 0.8780924479166666}, {"start": 2584.95, "end": 2586.15, "word": " و", "probability": 0.97705078125}, {"start": 2586.15, "end": 2588.03, "word": " نشوف", "probability": 0.9759114583333334}, {"start": 2588.03, "end": 2588.25, "word": " مع", "probability": 0.9970703125}, {"start": 2588.25, "end": 2588.63, "word": " بعض", "probability": 0.9951171875}, {"start": 2588.63, "end": 2590.29, "word": " الحاجات", "probability": 0.9943033854166666}, {"start": 2590.29, "end": 2590.71, "word": " هذه", "probability": 0.8447265625}], "temperature": 1.0}, {"id": 105, "seek": 259944, "start": 2591.73, "end": 2599.45, "text": "و نشرحها okay إذا انتهت المحاضرة نكمل ان شاء الله المرة الجاية", "tokens": [2407, 8717, 46309, 5016, 11296, 1392, 11933, 15730, 16472, 47395, 2655, 9673, 5016, 46958, 25720, 8717, 24793, 1211, 16472, 13412, 16606, 21984, 9673, 25720, 25724, 995, 10632], "avg_logprob": -0.13065010894622123, "compression_ratio": 1.1978021978021978, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 2591.73, "end": 2592.05, "word": "و", "probability": 0.84716796875}, {"start": 2592.05, "end": 2592.79, "word": " نشرحها", "probability": 0.9508056640625}, {"start": 2592.79, "end": 2594.21, "word": " okay", "probability": 0.4326171875}, {"start": 2594.21, "end": 2594.63, "word": " إذا", "probability": 0.72021484375}, {"start": 2594.63, "end": 2596.01, "word": " انتهت", "probability": 0.8683268229166666}, {"start": 2596.01, "end": 2597.31, "word": " المحاضرة", "probability": 0.9920654296875}, {"start": 2597.31, "end": 2598.11, "word": " نكمل", "probability": 0.92724609375}, {"start": 2598.11, "end": 2598.23, "word": " ان", "probability": 0.650390625}, {"start": 2598.23, "end": 2598.45, "word": " شاء", "probability": 0.988037109375}, {"start": 2598.45, "end": 2598.55, "word": " الله", "probability": 0.9599609375}, {"start": 2598.55, "end": 2598.93, "word": " المرة", "probability": 0.885986328125}, {"start": 2598.93, "end": 2599.45, "word": " الجاية", "probability": 0.92236328125}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 2601.0065, "duration_after_vad": 2371.6624999999904}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/r7wN576DqQ0.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/r7wN576DqQ0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f6a719d1bad5bd7c00d4ab71fe1c516262778c68
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/r7wN576DqQ0.srt
@@ -0,0 +1,1367 @@
+1
+00:00:21,190 --> 00:00:26,170
+السلام عليكم في المحاضرة هذه إن شاء الله هناخد
+
+2
+00:00:26,170 --> 00:00:32,530
+section رقم اثنين وشبطر أربعة اللي هو section أربعة
+
+3
+00:00:32,530 --> 00:00:39,250
+عنوانه limit theorems أو قوانين النهايات للدوال
+
+4
+00:00:39,250 --> 00:00:45,070
+functions أو الدالة قبل ما نتعرض ل limit theorems
+
+5
+00:00:45,070 --> 00:00:53,310
+أو قوانين النهايات للدوال بناخد تعريفها معنى أن 
+
+6
+00:00:53,310 --> 00:00:59,410
+الـ function معرفة على subset of R A ما معنى أنَّها
+
+7
+00:00:59,410 --> 00:01:06,230
+تكون bounded على جوار لنقطة C وهي في C cluster
+
+8
+00:01:06,230 --> 00:01:10,610
+point للمجال تبع الدالة ما معنى أن الدالة تكون 
+
+9
+00:01:10,610 --> 00:01:19,650
+bounded محصورة على جوار لنقطة C هذا معناه أن يوجد
+
+10
+00:01:19,650 --> 00:01:29,150
+Delta neighborhood جوار Delta لنقطة C بعمق Delta ويوجد
+
+11
+00:01:29,150 --> 00:01:34,570
+عدد موجب M بحيث أن الـ absolute value لقيم الدالة
+
+12
+00:01:34,570 --> 00:01:39,950
+أصغر من أو يساوي العدد الموجب لكل X في مجال الدالة
+
+13
+00:01:39,950 --> 00:01:47,010
+واللي موجود في الـ Delta neighborhood للـ C إذا قدرت ألاقي
+
+14
+00:01:47,010 --> 00:01:51,210
+delta neighborhood للنقطة C بحيث وعدد موجب بحيث
+
+15
+00:01:51,210 --> 00:01:55,490
+المتباينة هذه تتحقق لكل X في الـ delta neighborhood
+
+16
+00:01:55,490 --> 00:02:00,710
+وطبعًا هو موجود في الـ A فبقول أنَّ الدالة is bounded on
+
+17
+00:02:00,710 --> 00:02:03,190
+a neighborhood of C
+
+18
+00:02:05,840 --> 00:02:11,200
+النظرية هذه بتقول إنه لو أنا فيه أي فانكشن زي
+
+19
+00:02:11,200 --> 00:02:16,740
+هذه والـ limit تبعتها عند الـ cluster point C exist
+
+20
+00:02:16,740 --> 00:02:22,340
+فلابد ضروري جدًا أن من الضروري أن تكون الدالة
+
+21
+00:02:22,340 --> 00:02:30,000
+bounded على جوار لنقطة C okay فتعالوا نلخص الكلام
+
+22
+00:02:30,000 --> 00:02:35,410
+هذا let epsilon يساوي واحد عدد موجب بما أنه من
+
+23
+00:02:35,410 --> 00:02:40,050
+الفرض بما أنه limit f of x as x tends to z يساوي
+
+24
+00:02:40,050 --> 00:02:44,870
+عدد L إذا حسب تعريف الـ epsilon دلتا للـ limit of
+
+25
+00:02:44,870 --> 00:02:47,690
+function there exists delta that depends on
+
+26
+00:02:47,690 --> 00:02:51,410
+epsilon اللي هو واحد عدد موجب بحيث الـ implication
+
+27
+00:02:51,410 --> 00:02:56,230
+هي تتحقق اللي أنا باستخدام الـ triangle inequality
+
+28
+00:02:56,230 --> 00:03:01,330
+absolute f of x يساوي absolute F of X minus L
+
+29
+00:03:01,330 --> 00:03:06,850
+لأن طرحت L ورجعتها بعدين باخد اثنين هدول مع بعض By
+
+30
+00:03:06,850 --> 00:03:10,030
+the triangle equality هذا أصغر من F of X minus L
+
+31
+00:03:10,030 --> 00:03:14,510
+زائد absolute L وهذا من فوق أصغر من واحد زائد
+
+32
+00:03:14,510 --> 00:03:22,930
+absolute هذا الكلام صحيح لكل X لكل X ينتمي ل A لكل
+
+33
+00:03:22,930 --> 00:03:27,590
+X ينتمي ل A وأيضًا 
+
+34
+00:03:29,110 --> 00:03:39,530
+لكل X مختلفة عن الـ C إذا الـ X هنا لا تساوي C وأيضًا
+
+35
+00:03:39,530 --> 00:03:45,170
+هذا من هنا X لا تساوي C ومن هنا هذا معناه absolute
+
+36
+00:03:45,170 --> 00:03:50,870
+X ناقص C أصغر من Delta معناه الـ X تنتمي للـ Delta
+
+37
+00:03:50,870 --> 00:03:58,950
+neighborhood للـ C تمام أن هذا الكلام صحيح لكل x في a مختلف
+
+38
+00:03:58,950 --> 00:04:05,090
+عن ال c و لكل و في نفس الوقت موجود ال x في ال
+
+39
+00:04:05,090 --> 00:04:12,010
+delta neighborhood ل c طيب
+
+40
+00:04:12,010 --> 00:04:20,600
+احنا بما نثبت أنه بما نثبت أن الـ absolute value أو
+
+41
+00:04:20,600 --> 00:04:35,240
+وجدنا delta neighborhood لـ C نحن
+
+42
+00:04:35,240 --> 00:04:43,120
+عايزين نثبت أن absolute F of X أصغر من أو يساوي M أو
+
+43
+00:04:43,120 --> 00:04:47,860
+there exists M أكبر من الصفر بحيث أن absolute F of
+
+44
+00:04:47,860 --> 00:04:55,540
+X أصغر من أو يساوي M لكل X ينتمي إلى A تقاطع Delta
+
+45
+00:04:55,540 --> 00:05:03,240
+of C مش هيك تعريف اللي هو المتباينة هذه طيب we
+
+46
+00:05:03,240 --> 00:05:04,300
+have two cases
+
+47
+00:05:11,240 --> 00:05:17,160
+case واحد إذا كانت الـ C تنتمي إلى A الـ cluster
+
+48
+00:05:17,160 --> 00:05:22,200
+point C هي الـ cluster point الـ C is a cluster
+
+49
+00:05:22,200 --> 00:05:29,680
+point لست A فممكن الـ C تنتمي لـ A وممكن ما تنتميش
+
+50
+00:05:29,680 --> 00:05:36,000
+إذا في اثنين حالات لو كانت الـ C تنتمي لـ A in this
+
+51
+00:05:36,000 --> 00:05:47,190
+case in this case choose M يساوي
+
+52
+00:05:47,190 --> 00:05:59,230
+الـ maximum لـ absolute F of C و 1 زائد absolute L
+
+53
+00:05:59,230 --> 00:06:03,790
+then
+
+54
+00:06:03,790 --> 00:06:08,630
+الحالة هذه absolute F of X
+
+55
+00:06:11,500 --> 00:06:16,520
+إذا كانت الـ X هذه هي الـ C فـ absolute F of X
+
+56
+00:06:16,520 --> 00:06:21,800
+يساوي absolute F of C وبالتالي أصغر من أو يساوي
+
+57
+00:06:21,800 --> 00:06:28,400
+absolute F of C اللي هي أصغر من أو يساوي M وإذا
+
+58
+00:06:28,400 --> 00:06:34,660
+كانت الـ X هذه مختلفة عن الـ C
+
+59
+00:06:40,340 --> 00:06:45,700
+ففي الحالة هذه بيطلع absolute F of X أصغر من واحد
+
+60
+00:06:45,700 --> 00:06:51,980
+زائد absolute L وهذا العدد أصغر من أو يساوي M ففي
+
+61
+00:06:51,980 --> 00:06:57,560
+كل الأحوال هذا الكلام صحيح لكل X تنتمي إلى A تقاطع
+
+62
+00:06:57,560 --> 00:07:05,800
+Delta of C وهو المطلوب طبعًا نشوف الحالة الثانية
+
+63
+00:07:05,800 --> 00:07:13,770
+Case 2 إنَّ الـ X لا تنتمي إلى A in
+
+64
+00:07:13,770 --> 00:07:20,810
+this case we
+
+65
+00:07:20,810 --> 00:07:32,390
+have absolute F in this case we take M
+
+66
+00:07:32,390 --> 00:07:37,310
+يساوي واحد زائد absolute L
+
+67
+00:07:40,850 --> 00:07:45,550
+في الحالة هذه هنأخد M يساوي واحد زائد absolute L
+
+68
+00:07:45,550 --> 00:07:49,670
+باستخدام
+
+69
+00:07:49,670 --> 00:07:54,030
+المتباينة هذه الأخيرة اللي هي سميها star
+
+70
+00:08:03,260 --> 00:08:10,660
+بيطلع عندي absolute f of x إذا كانت الـ
+
+71
+00:08:10,660 --> 00:08:17,860
+c لا تنتمي إلى a فبيصير هذه a وطرح منها c هي a
+
+72
+00:08:17,860 --> 00:08:23,760
+صح؟ وبالتالي الكلام هذا بيصير أصغر من 1 زائد
+
+73
+00:08:23,760 --> 00:08:29,700
+absolute L اللي هو أصغر من أو يساوي M وهذا صحيح لكل
+
+74
+00:08:29,700 --> 00:08:36,000
+x ينتمي إلى a تقاطع Delta of c وبسيط لأن الـ C مش
+
+75
+00:08:36,000 --> 00:08:42,320
+موجودة في إيه فاطرحها أو ماطرحاش ما بتفرقش لأن هنا
+
+76
+00:08:42,320 --> 00:08:48,700
+استخدمنا star وهنا برضه استخدمنا star then by
+
+77
+00:08:48,700 --> 00:08:56,580
+star الـ absolute value هنا طلعنا بيساوي absolute
+
+78
+00:08:56,580 --> 00:09:01,340
+of f of c إذا كانت x يساوي c وإذا كانت x مختلفة
+
+79
+00:09:01,340 --> 00:09:06,080
+عن c فمن الـ star absolute of f of x تطلع أصغر من
+
+80
+00:09:06,080 --> 00:09:10,000
+واحد زائد absolute ل وهادي أصغر من أو يساوي M في
+
+81
+00:09:10,000 --> 00:09:14,620
+الحالتين هين أثبتنا أن يوجد عدد موجب M هي العدد
+
+82
+00:09:14,620 --> 00:09:18,680
+الموجب في الحالة الأولى هو maximum هذا العدد الموجب
+
+83
+00:09:20,790 --> 00:09:25,610
+أو في الحالة الثانية M هو واحد زائد absolute L و
+
+84
+00:09:25,610 --> 00:09:30,790
+هذا عدد موجب وفي الحالتين absolute F of X أصغر من
+
+85
+00:09:30,790 --> 00:09:41,090
+M لكل X في A تقاطع Delta إذن F is bounded on
+
+86
+00:09:41,090 --> 00:09:47,950
+a neighborhood on a neighborhood bounded on a
+
+87
+00:09:47,950 --> 00:09:53,630
+neighborhood of c وهو المطلوب إذن النظرية بتقول أي
+
+88
+00:09:53,630 --> 00:09:57,730
+function لها limit على نقطة محددة لازم تكون
+
+89
+00:09:57,730 --> 00:10:05,970
+bounded على جوار لهذه النقطة واضح المطلوب؟ في أي
+
+90
+00:10:05,970 --> 00:10:16,380
+استفسار؟ مش واضح؟ لأن هذه النظرية ممكن نستخدمها في
+
+91
+00:10:16,380 --> 00:10:22,200
+إثبات أن الـ limits لـ functions معينة لنقاط معينة
+
+92
+00:10:22,200 --> 00:10:31,220
+غير موجودة فمثلًا على سبيل المثال example
+
+93
+00:10:31,220 --> 00:10:34,780
+show أن الـ limit
+
+94
+00:10:37,670 --> 00:10:43,190
+هنا الـ function 1 على x لما x تؤول لصفر does not
+
+95
+00:10:43,190 --> 00:10:55,490
+exist in R إذن
+
+96
+00:10:55,490 --> 00:11:01,550
+هنا الـ function تبعتي f of x بتساوي 1 على x حيث x
+
+97
+00:11:01,550 --> 00:11:02,690
+طبعًا لا يساوي صفر
+
+98
+00:11:09,460 --> 00:11:13,900
+ومن هنا اثبت أن الـ limit لـ f of x عند الصفر مش
+
+99
+00:11:13,900 --> 00:11:27,400
+موجودة فالبرهان ذلك by above theorem it
+
+100
+00:11:27,400 --> 00:11:33,100
+suffices it suffices to show
+
+101
+00:11:36,350 --> 00:11:44,610
+أنَّ الـ function تبعتنا الـ 
+
+102
+00:11:44,610 --> 00:11:49,750
+function
+
+103
+00:11:49,750 --> 00:11:59,130
+f هذه اللي عرضناها that الـ function f is not is
+
+104
+00:11:59,130 --> 00:12:04,590
+not bounded on
+
+105
+00:12:06,370 --> 00:12:19,450
+any delta neighborhood of zero
+
+106
+00:12:39,000 --> 00:12:44,700
+عشان أثبت أن الدالة ليست bounded ليست ... ماليهاش 
+
+107
+00:12:44,700 --> 00:12:49,620
+limit عند الصفر حسب النظرية يكفي إثبات أن الدالة
+
+108
+00:12:49,620 --> 00:12:58,800
+هذه is not bounded على أي جوار للصفر لأن 
+
+109
+00:12:58,800 --> 00:13:05,760
+لو كانت bounded على جوار واحد للصفر لو كانت الـ 
+
+110
+00:13:05,760 --> 00:13:11,480
+limit ... لأن لو كانت الـ limit تبعتها موجودة فلازم
+
+111
+00:13:11,480 --> 00:13:17,820
+تكون bounded على جوار معين للصفر فعشان أستنتج أن
+
+112
+00:13:17,820 --> 00:13:23,000
+الـ limit مش موجودة بحيث أثبت أن الـ function
+
+113
+00:13:23,000 --> 00:13:28,960
+ما هيش bounded على كل الجوارات للصفر أو على أي
+
+114
+00:13:28,960 --> 00:13:30,080
+جوار للصفر
+
+115
+00:13:37,200 --> 00:13:45,620
+فال ... إذا ال ... البرهان هنا now
+
+116
+00:13:45,620 --> 00:13:51,240
+is proved by contradiction
+
+117
+00:13:58,300 --> 00:14:04,240
+يعني حاسبكم أن تكملوا البرهان بالتناقض افرضي أنه
+
+118
+00:14:04,240 --> 00:14:11,660
+يوجد جوار يوجد
+
+119
+00:14:11,660 --> 00:14:18,860
+جوار أو function bounded عليه يوجد جوار Delta معين
+
+120
+00:14:18,860 --> 00:14:24,060
+والـ function هذه bounded عليه وحاول يوصلني إلى
+
+121
+00:14:24,060 --> 00:14:24,580
+تناقض
+
+122
+00:14:27,970 --> 00:14:33,810
+هذا بيعطي برهان ثاني إذا نجحت طبعًا في بيعطيه برهان 
+
+123
+00:14:33,810 --> 00:14:37,130
+Contradiction فهيبقى بيصير عندك برهان ثاني إنه
+
+124
+00:14:37,130 --> 00:14:41,510
+limit الـ function واحد على x لأن x تؤول لـ 0 غير 
+
+125
+00:14:41,510 --> 00:14:45,650
+موجودة طبعًا احنا أخذنا المرة اللي فاتت باستخدام الـ 
+
+126
+00:14:45,650 --> 00:14:50,650
+sequential criterion أثبتنا إنه الـ limit للـ
+
+127
+00:14:50,650 --> 00:14:54,540
+function هذه عند الصفر مش موجودة اللي فيه برهان
+
+128
+00:14:54,540 --> 00:14:57,640
+باستخدام الـ sequential criterion واليوم هيفيه 
+
+129
+00:14:57,640 --> 00:15:04,960
+برهان ثاني باستخدام النظرية اللي هيحاولوا
+
+130
+00:15:04,960 --> 00:15:09,680
+تبرهنوها هذا أو إذا ما عرفتوها احكولي أو تعالولي على
+
+131
+00:15:09,680 --> 00:15:15,880
+المكتب خلال ساعات المكتب دي طيب
+
+132
+00:15:15,880 --> 00:15:17,880
+نرجع لللي هي نظريات النهايات
+
+133
+00:15:50,720 --> 00:16:00,200
+دع F و G يكونا عاملين من A to R يكونا عاملين
+
+134
+00:16:12,190 --> 00:16:21,810
+بـClusterPoint و C ينتمي لـ R عدد حقيقي and limit
+
+135
+00:16:23,250 --> 00:16:32,030
+f of x as x tends to c يساوي n ينتمي إلى r و limit
+
+136
+00:16:32,030 --> 00:16:43,910
+g of x as x tends to c يساوي m عدد حقيقي أيضًا then
+
+137
+00:16:43,910 --> 00:16:48,750
+النتيجة واحد
+
+138
+00:16:48,750 --> 00:17:01,570
+limit أو الـ limit لـ f زائد g of x and x tends to c
+
+139
+00:17:01,570 --> 00:17:10,510
+يساوي n زائد m ولو أخدت الفرق بين الدالتين فـ limit
+
+140
+00:17:10,510 --> 00:17:13,350
+الفرق يساوي فرق الـ limits 
+
+141
+00:17:16,580 --> 00:17:27,340
+الـ limit لحاصل ضرب F في G as X tends to C بساوية لضرب
+
+142
+00:17:27,340 --> 00:17:34,200
+L في M
+
+143
+00:17:34,200 --> 00:17:38,960
+limit لثابت B في F
+
+144
+00:17:49,320 --> 00:17:51,640
+والجزء الأخير
+
+145
+00:18:06,970 --> 00:18:16,090
+لـ F over G of X as X tends to C يساوي L over M
+
+146
+00:18:16,090 --> 00:18:22,470
+طبعا بشرط وراية لإن M لا يساوي
+
+147
+00:18:30,390 --> 00:18:33,910
+الآن هذه قواعد أو قوانين النهايات نفس قوانين
+
+148
+00:18:33,910 --> 00:18:38,810
+النهايات اللي أخذناها بخصوص ال sequences والـ
+
+149
+00:18:38,810 --> 00:18:43,790
+functions وبالمناسبة إحنا قلنا أن ال sequence هي
+
+150
+00:18:43,790 --> 00:18:51,690
+الـ function  الـ function  بنوع خاص طيب في
+
+151
+00:18:51,690 --> 00:18:55,950
+طريقتين لبرهان النظرية هذه  proof one
+
+152
+00:19:03,810 --> 00:19:15,070
+باستخدام epsilon delta definition زي
+
+153
+00:19:15,070 --> 00:19:21,750
+اللي شفنا في حالة النهايات ال limits لل
+
+154
+00:19:21,750 --> 00:19:25,310
+sequences هنا استخدمنا epsilon capital N 
+
+155
+00:19:25,310 --> 00:19:29,510
+definition هنا هنستخدم epsilon delta definition
+
+156
+00:19:29,510 --> 00:19:36,260
+فمثلاً يعني لو بالبداية to show لو بدأت بالجزء الأول
+
+157
+00:19:36,260 --> 00:19:45,020
+مثلاً بي show limit لـ f plus g of x as x tends to c
+
+158
+00:19:45,020 --> 00:19:53,300
+بساوي L plus M let epsilon أكبر من الصفر be given
+
+159
+00:19:53,300 --> 00:19:57,000
+since
+
+160
+00:20:01,260 --> 00:20:08,660
+لما يكون f of x as x tends to c يساوي L هنا هناك
+
+161
+00:20:08,660 --> 00:20:15,540
+delta one تعتمد على epsilon عدد موجب لكل x ينتمي
+
+162
+00:20:15,540 --> 00:20:20,530
+إلى a و absolute x minus c أصغر من الـ delta و أكبر من 0
+
+163
+00:20:20,530 --> 00:20:27,610
+هذا بتضمن أن absolute f of x minus l 
+
+164
+00:20:27,610 --> 00:20:35,430
+أصغر من epsilon على اتنين هذا
+
+165
+00:20:35,430 --> 00:20:43,750
+من تعريف epsilon delta definition also أيضاً since
+
+166
+00:20:46,390 --> 00:20:52,030
+أنا عندي أن limit لل function g of x as x
+
+167
+00:20:52,030 --> 00:20:59,530
+tends to c exists ويساوي عدد حقيقي M فليه for the
+
+168
+00:20:59,530 --> 00:21:04,750
+same epsilon for the same given epsilon من تعريف
+
+169
+00:21:04,750 --> 00:21:11,570
+ال limit يوجد Delta 2 عدد موجب يعتمد على epsilon
+
+170
+00:21:11,570 --> 00:21:19,290
+بحيث أنه لكل x ينتمي إلى a بحيث absolute x minus c 
+
+171
+00:21:19,290 --> 00:21:24,490
+أصغر من delta 2 أكبر من الصفر هذا بتضمن أن
+
+172
+00:21:24,490 --> 00:21:33,210
+absolute g of x minus m أصغر من epsilon على
+
+173
+00:21:33,210 --> 00:21:49,020
+اتنين the Sample Implication Double Star Now
+
+174
+00:21:49,020 --> 00:21:53,960
+لـ
+
+175
+00:21:53,960 --> 00:22:01,060
+Delta دلينا نقرّح Delta على أنها الـ minimum الأصغر
+
+176
+00:22:03,020 --> 00:22:09,000
+الأصغر بين Delta 1 و Delta 2 طبعاً Delta 1
+
+177
+00:22:09,000 --> 00:22:13,780
+و Delta 2 عدد موجب إذا الـ delta هذه عدد موجب بعدين
+
+178
+00:22:13,780 --> 00:22:18,080
+Delta 1 و Delta 2 depend on epsilon إذا الـ delta 
+
+179
+00:22:18,080 --> 00:22:22,320
+هذه depend on epsilon لأن هي أثبتنا أن يوجد Delta
+
+180
+00:22:22,320 --> 00:22:25,080
+عدد موجب بحيث أنه
+
+181
+00:22:29,490 --> 00:22:38,050
+لكل x ينتمي إلى a إذا حدث أن absolute x minus c
+
+182
+00:22:38,050 --> 00:22:45,450
+أكبر من الصفر يعني x تساوي c وأصغر من delta هذا
+
+183
+00:22:45,450 --> 00:22:49,570
+هيضمن أن
+
+184
+00:22:49,570 --> 00:23:02,710
+absolute f plus g of x minus L زي ما الـ
+
+185
+00:23:02,710 --> 00:23:08,190
+absolute value هذي بما أنها تطلع أصغر من epsilon طيب
+
+186
+00:23:08,190 --> 00:23:18,780
+f plus g of x هذي عبارة عن f of x plus g of x وباستخدام
+
+187
+00:23:18,780 --> 00:23:22,060
+الـ triangle inequality هذا أصغر من أو يساوي
+
+188
+00:23:22,060 --> 00:23:32,360
+absolute f of x minus L زائد absolute g 
+
+189
+00:23:32,360 --> 00:23:39,520
+of x minus M مظبوطة الآن
+
+190
+00:23:39,520 --> 00:23:41,080
+باستخدام الـ star
+
+191
+00:23:43,690 --> 00:23:49,910
+أنا عندي x موجودة في A والمسافة بين x و c أصغر من
+
+192
+00:23:49,910 --> 00:23:55,760
+delta والـ delta هذه أصغر من أو يساوي delta 1 فهي
+
+193
+00:23:55,760 --> 00:23:58,200
+delta الـ minimum الأصغر من delta 1 يعني الـ
+
+194
+00:23:58,200 --> 00:24:02,260
+delta هنا من تعريف الـ delta delta أصغر من أو يساوي
+
+195
+00:24:02,260 --> 00:24:05,520
+delta 1 وأصغر من أو يساوي delta minimum طيب لما
+
+196
+00:24:05,520 --> 00:24:08,820
+يكون الـ absolute value لـ x minus c أصغر من delta
+
+197
+00:24:08,820 --> 00:24:14,320
+1 أصغر من delta 1 إذا by star بيطلع absolute
+
+198
+00:24:14,320 --> 00:24:20,290
+f of x minus L أصغر من epsilon على 2 وكذلك الـ delta
+
+199
+00:24:20,290 --> 00:24:26,730
+اللي قلنا أصغر من أو يساوي delta 2 من تعريفها طب
+
+200
+00:24:26,730 --> 00:24:30,290
+لما يكون absolute x minus c أكبر من الصفر وأصغر من
+
+201
+00:24:30,290 --> 00:24:38,970
+delta 2 إذا by double star by
+
+202
+00:24:38,970 --> 00:24:44,550
+double star بيطلع absolute g of x minus m أصغر من
+
+203
+00:24:44,550 --> 00:24:51,340
+epsilon على اتنين مجموعهم بيطلع epsilon نلخص إيش
+
+204
+00:24:51,340 --> 00:24:57,560
+أثبتنا هنا اللي أثبتناه هو ما نريده for any epsilon
+
+205
+00:24:57,560 --> 00:25:01,240
+for any given epsilon أكبر من الصفر there exists
+
+206
+00:25:01,240 --> 00:25:06,040
+delta positive number ويعتمد على epsilon لأن delta
+
+207
+00:25:06,040 --> 00:25:10,500
+1 و delta 2 يعتمدوا على epsilon بحيث لكل x هي
+
+208
+00:25:10,500 --> 00:25:15,460
+أيّ و absolute x minus c أكبر من الصفر أصغر من الـ delta
+
+209
+00:25:15,460 --> 00:25:17,700
+هذه طلع absolute
+
+210
+00:25:21,470 --> 00:25:25,930
+الـ function تبعتي اللي هي مجموع f و g ناقص الـ
+
+211
+00:25:25,930 --> 00:25:32,150
+limit المقترحة أصغر من epsilon طبعاً؟
+
+212
+00:25:32,150 --> 00:25:39,970
+إذا حسب التعريف بما أن هذا صحيح since epsilon أكبر
+
+213
+00:25:39,970 --> 00:25:46,070
+من الصفر was arbitrary معناته إحنا أثبتنا أن هذا
+
+214
+00:25:46,070 --> 00:25:51,360
+الكلام لكل epsilon موجبة في delta تعطيني الـ
+
+215
+00:25:51,360 --> 00:25:56,980
+implication تبقى تعريف الـ limit وبالتالي by
+
+216
+00:25:56,980 --> 00:26:02,740
+definition by definition أو epsilon delta
+
+217
+00:26:02,740 --> 00:26:06,800
+definition of limit بتطلع عندي الـ limit للـ
+
+218
+00:26:06,800 --> 00:26:14,700
+function f plus g as x tends to c بتطلع بساوية
+
+219
+00:26:14,700 --> 00:26:21,270
+لعدد L زائد M يعني وهو المطلوب تمام؟ لأن هنا
+
+220
+00:26:21,270 --> 00:26:26,150
+استخدمنا تعريف epsilon delta لإثبات أن limit مجموع
+
+221
+00:26:26,150 --> 00:26:30,070
+two functions بيساوي مجموع limits لـ two functions
+
+222
+00:26:30,070 --> 00:26:36,350
+the limit of a sum is the sum of limits بالمثل
+
+223
+00:26:36,350 --> 00:26:43,630
+ممكن البرهان باقي أجزاء النظرية similarly or the
+
+224
+00:26:43,630 --> 00:26:47,410
+proof of
+
+225
+00:26:47,410 --> 00:26:48,390
+the other
+
+226
+00:26:52,480 --> 00:27:02,220
+parts is similar .. is similar لبرهان
+
+227
+00:27:02,220 --> 00:27:07,060
+اللي إحنا أخذناه وبالتالي هسيبكم أنتم تكتبوا 
+
+228
+00:27:14,260 --> 00:27:20,000
+ارجعوا لبرهان الـ limit لحاصل ضرب two sequences
+
+229
+00:27:20,000 --> 00:27:24,180
+بساوي لحاصل ضرب الـ limits وحاولوا تجلدوا البرهان
+
+230
+00:27:24,180 --> 00:27:28,220
+نفس الحاجة برضه هذا .. هذا طبعاً corollary على
+
+231
+00:27:28,220 --> 00:27:32,460
+الجزء اللي قبله والثاني هناك limit خارج قسم الـ two
+
+232
+00:27:32,460 --> 00:27:38,840
+sequences يساوي خارج قسم الـ limits فممكن برضه نُعمّم
+
+233
+00:27:38,840 --> 00:27:42,910
+البرهان تبع الـ sequence لـ الـ functions فحاولوا
+
+234
+00:27:42,910 --> 00:27:47,470
+تكتبوا البراهين هذه لأنه ممكن كل بساطة انتحار نصف
+
+235
+00:27:47,470 --> 00:27:52,830
+الثاني أو النهائي هأقول لك مثلاً برهن لك أن الـ limit
+
+236
+00:27:52,830 --> 00:27:55,890
+حاصل ضرب two functions بسبب حاصل ضرب الـ limit
+
+237
+00:27:55,890 --> 00:28:03,850
+using epsilon delta definition حدد لك الطريقة يجب
+
+238
+00:28:03,850 --> 00:28:08,750
+أنكم تكتبوا براهين باقي الأجزاء تمام؟
+
+239
+00:28:10,180 --> 00:28:14,320
+طيب هذا برهان الأول باستخدام epsilon delta
+
+240
+00:28:14,320 --> 00:28:19,160
+definition لكن في برهان ثاني باستخدام الـ
+
+241
+00:28:19,160 --> 00:28:22,700
+sequential criterion اللي أخذناه المرة اللي فاتت
+
+242
+00:28:22,700 --> 00:28:28,880
+فنشوف البرهان الثاني
+
+243
+00:28:28,880 --> 00:28:36,940
+إذا
+
+244
+00:28:36,940 --> 00:28:38,400
+proof 2
+
+245
+00:29:03,440 --> 00:29:09,520
+فمثلاً to show البرهان
+
+246
+00:29:09,520 --> 00:29:16,180
+جزء طبعاً باقي الأعزاء برهناها بالمثل المرة هذه مثلاً
+
+247
+00:29:16,180 --> 00:29:26,880
+لتبعت مثلاً يزر بي to show limit لـ f ضرب g of x as
+
+248
+00:29:26,880 --> 00:29:35,200
+x tends to c يساوي L times M هنستخدم الـ
+
+249
+00:29:35,200 --> 00:29:43,200
+sequential criterion فـ let xn be sequence in A
+
+250
+00:29:45,300 --> 00:29:55,540
+وحدودها مختلفة عن الـ C such that limit xn as n 
+
+251
+00:29:55,540 --> 00:30:04,580
+tends to infinity is C We must show
+
+252
+00:30:04,580 --> 00:30:09,620
+عشان أُثبت limit حاصل ضرب دالتين هنا الـ C موجودة
+
+253
+00:30:10,370 --> 00:30:14,950
+بيساوي L في M حسب الـ sequential criterion لازم
+
+254
+00:30:14,950 --> 00:30:18,370
+أثبت أنه لأي sequence حدودها مختلفة عن النقطة C
+
+255
+00:30:18,370 --> 00:30:26,450
+ونهايتها C لازم نهاية صورتها لازم نثبت نهاية
+
+256
+00:30:26,450 --> 00:30:35,130
+صورتها limit الـ f ضرب g للـ sequence xn as n tends to
+
+257
+00:30:35,130 --> 00:30:42,140
+infinity يساوي L ضرب M فلتكن أن الـ limit صورة الـ
+
+258
+00:30:42,140 --> 00:30:47,260
+sequence xn under the function f ضرب g بساوية L
+
+259
+00:30:47,260 --> 00:30:51,740
+M لأن حسب الـ sequential criterion تطلع الدالة تبعت
+
+260
+00:30:51,740 --> 00:30:56,260
+الـ limit لعنصر موجودة و بساوية العدد L في M
+
+261
+00:30:56,260 --> 00:31:02,580
+تمام؟ لأن باقي نثبت أن الـ limit لل image of this
+
+262
+00:31:02,580 --> 00:31:06,760
+sequence أبقى عن العدد LM طيب
+
+263
+00:31:09,150 --> 00:31:17,010
+لبرهان ذلك .. Now .. تعالوا نثبت الكلام هذا Now الـ
+
+264
+00:31:17,010 --> 00:31:26,770
+limit لـ f ضرب g of xn as n tends to infinity يساوي
+
+265
+00:31:26,770 --> 00:31:29,810
+الـ
+
+266
+00:31:29,810 --> 00:31:36,280
+limit حاصل ضرب two functions عند أي x أو xn هذا
+
+267
+00:31:36,280 --> 00:31:44,720
+عبارة عن f of xn ضرب g of xn لأن هذا من تعريف حاصل
+
+268
+00:31:44,720 --> 00:31:50,120
+ضرب two functions الآن هذه عبارة عن sequence وهذه
+
+269
+00:31:50,120 --> 00:31:54,900
+عبارة عن sequence و limit الـ sequence الأولى exist
+
+270
+00:31:54,900 --> 00:31:59,340
+و limit الـ sequence الثانية exist إذا by limit
+
+271
+00:31:59,340 --> 00:32:03,460
+theorems لsequences إن الـ limit حاصل الضرب يساوي
+
+272
+00:32:03,460 --> 00:32:11,300
+حاصل ضرب الـ limits فهذا يساوي limit f of xn ضرب
+
+273
+00:32:12,730 --> 00:32:21,230
+limit g of xn as n tends to infinity as n tends to
+
+274
+00:32:21,230 --> 00:32:29,850
+infinity طب إيش اللي ضمن لي ماذا يضمن إن الـ limit لـ
+
+275
+00:32:29,850 --> 00:32:36,270
+f of xn موجودة و limit لـ g of xn موجودة لأنه أنا
+
+276
+00:32:36,270 --> 00:32:48,500
+فارد since limit f of x as x tends to c exists لأن
+
+277
+00:32:48,500 --> 00:32:57,200
+هذا exists يساوي L exists and equals L and الـ limit
+
+278
+00:32:57,200 --> 00:33:03,700
+لل function g of x as x tends to c exists and يساوي
+
+279
+00:33:03,700 --> 00:33:08,300
+العدد M وعندي
+
+280
+00:33:08,300 --> 00:33:19,540
+xn و limit xn يساوي c فـ by sequential criterion إذا 
+
+281
+00:33:19,540 --> 00:33:26,330
+limit صورة ال xn under f موجودة صح؟  أهو limit صورة
+
+282
+00:33:26,330 --> 00:33:32,150
+ال sequence xn under g موجودة okay إذا هذا مضمون
+
+283
+00:33:32,150 --> 00:33:37,630
+وجود ال limit هذه وجود ال limit هذه مضمون لأن
+
+284
+00:33:37,630 --> 00:33:40,930
+limit ال f عن c موجودة وبالتالي و limit ال
+
+285
+00:33:40,930 --> 00:33:45,610
+sequence xn بالساوى c إذا هذه موجودة من ال
+
+286
+00:33:45,610 --> 00:33:48,790
+sequential criterion و كذلك هذه من ال sequential
+
+287
+00:33:48,790 --> 00:33:49,330
+criterion
+
+288
+00:33:52,710 --> 00:33:59,930
+طيب ما هدى ال limit الأخيرة هدى بالساوي L by 
+
+289
+00:33:59,930 --> 00:34:05,050
+sequential criterion إذا كانت limit f of x اما x
+
+290
+00:34:05,050 --> 00:34:08,890
+أو لا c موجودة وبالساوي L وإن دي فيه sequence
+
+291
+00:34:08,890 --> 00:34:13,850
+نهايتها C فنهاية صورة ال sequence under F بالساوي
+
+292
+00:34:13,850 --> 00:34:20,550
+L وكذلك نفس الحاجة بما أن limit g and c موجودة و
+
+293
+00:34:20,550 --> 00:34:25,250
+بيساوي m و xn نهايتها c إذا by sequential
+
+294
+00:34:25,250 --> 00:34:32,550
+criterion limit g صورة ال xn under g بيساوي m إذا
+
+295
+00:34:32,550 --> 00:34:42,410
+هذا by sequential criterion وهذا 
+
+296
+00:34:42,410 --> 00:34:43,650
+اللي احنا عايزين نثبته
+
+297
+00:34:48,110 --> 00:34:53,630
+عايزين نثبت أن limit f ضارب g أو ال image لسيكوينس
+
+298
+00:34:53,630 --> 00:34:57,890
+x in under ال function f ضارب g بالساوي ال M هاي
+
+299
+00:34:57,890 --> 00:35:02,050
+بدينا ب limit ال image لسيكوينس x in under f g
+
+300
+00:35:02,050 --> 00:35:09,110
+وطلعت هي بالساوي ال M إذا by sequential
+
+301
+00:35:26,030 --> 00:35:34,050
+البرهين الأجزاء الأخرى مماثلة ال proof of the
+
+302
+00:35:34,050 --> 00:35:37,510
+other parts
+
+303
+00:35:40,000 --> 00:35:50,560
+is similar مشابه exercise it
+
+304
+00:35:50,560 --> 00:35:59,140
+اتمرن عليهم اتمرن على كتابة البرهيم اكتبوهم okay
+
+305
+00:35:59,140 --> 00:36:03,340
+تمام إذا ما في عندي نهائي من القرآن لlimits
+
+306
+00:36:05,580 --> 00:36:10,940
+ناخد لنا بس مثال أو اتنين أو خلينا ناخد corollary
+
+307
+00:36:10,940 --> 00:36:19,420
+خليني 
+
+308
+00:36:19,420 --> 00:36:23,600
+بس يعني اخدلي corollary سريع على النظرية هذه
+
+309
+00:36:39,870 --> 00:36:45,390
+Corollary 1 F
+
+310
+00:36:48,310 --> 00:36:58,610
+f1,f2 إلى fm are functions from a to r و c a 
+
+311
+00:36:58,610 --> 00:37:02,190
+cluster point
+
+312
+00:37:02,190 --> 00:37:14,130
+of a and limit fk of x as x tends to c بالساوي ال
+
+313
+00:37:14,130 --> 00:37:17,750
+then
+
+314
+00:37:19,410 --> 00:37:29,030
+وطبعا هنا for all k بيساوي واحد اتنين إلى M then
+
+315
+00:37:29,030 --> 00:37:42,870
+واحد limit ل F1 زي F2 زي وهاكذا زي Fn of X بيساوي
+
+316
+00:37:42,870 --> 00:38:02,630
+لما X تقول ل C هذا بيساوي N1 زي NL2 زائد زائد
+
+317
+00:38:02,630 --> 00:38:08,790
+LL اتنين limit لحاصل
+
+318
+00:38:08,790 --> 00:38:21,970
+ضرب F1 ضرب F2 ضرب FNF of X as X tends to C بيساوي
+
+319
+00:38:21,970 --> 00:38:30,190
+L1 ضرب L2 ضرب و هكذا ضرب LL تلاتة
+
+320
+00:38:30,190 --> 00:38:34,130
+F
+
+321
+00:38:34,130 --> 00:38:41,090
+limit F of X as X tends to C بيساوي L
+
+322
+00:38:45,730 --> 00:38:55,510
+ل F of X الكل أُس N as X tends to C بيساوي L أُس N
+
+323
+00:38:55,510 --> 00:39:08,870
+لبرهان
+
+324
+00:39:08,870 --> 00:39:15,920
+ال Corollary هذا هذا الجزء الأول هو نتيجة على
+
+325
+00:39:15,920 --> 00:39:27,940
+الجزء A من النظرية زائد induction on M إذاً
+
+326
+00:39:27,940 --> 00:39:38,580
+to prove one and two use above theorem and
+
+327
+00:39:38,580 --> 00:39:39,280
+induction
+
+328
+00:39:42,280 --> 00:39:49,140
+invection on edge هنا 
+
+329
+00:39:49,140 --> 00:39:56,840
+في اثبات الجزء التالت to prove تلاتة 
+
+330
+00:40:00,320 --> 00:40:17,960
+أخذ F1 بساوي F2 بساوي Fn بساوي F in part اتنين to
+
+331
+00:40:17,960 --> 00:40:22,960
+get the
+
+332
+00:40:22,960 --> 00:40:23,420
+result
+
+333
+00:40:30,710 --> 00:40:35,510
+يعني لدرهان الكلام هذا إذا كانت limit F عن C بيساوي
+
+334
+00:40:35,510 --> 00:40:42,330
+L فعوضي أو خدي F واحد هي F و F اتنين F و كلهم
+
+335
+00:40:42,330 --> 00:40:50,570
+بساوي F فكأن إذا هنا limit F to the power N and X
+
+336
+00:40:50,570 --> 00:40:55,630
+هيطلع بيساوي L مضروبة في نفس M المرات اللي هو إذا 
+
+337
+00:40:55,630 --> 00:41:00,960
+هذا الجزء التالت corollary على الجزء التاني Okay
+
+338
+00:41:00,960 --> 00:41:04,040
+تمام؟
+
+339
+00:41:04,040 --> 00:41:08,220
+Okay إذا بنوقف هنا وإن شاء الله المرة الجاية هنأكل
+
+340
+00:41:08,220 --> 00:41:14,340
+أمثلة على المظريات هذه ونحاول 
+
+341
+00:41:14,340 --> 00:41:19,260
+ناخد قصارى أخرى لل limits of functions إذا نكتفي
+
+342
+00:41:19,260 --> 00:41:23,600
+بهذا القدر ونشوفكم إن شاء الله يوم الأثنين
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY.srt
new file mode 100644
index 0000000000000000000000000000000000000000..351390abfc8b9ba35622bace12b8ebf68082625f
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY.srt
@@ -0,0 +1,1559 @@
+1
+00:00:21,400 --> 00:00:26,440
+المرة اللي فاتت إحنا يعني أخذنا ال Archimedean 
+
+2
+00:00:26,440 --> 00:00:33,820
+property وشوفنا فيه صور متعددة لها أو صور مختلفة
+
+3
+00:00:33,820 --> 00:00:39,140
+اللي هي الصور الثلاث هذه فكل 
+
+4
+00:00:39,140 --> 00:00:43,160
+واحدة من الخواص دي تعتبر Archimedean property أو
+
+5
+00:00:43,160 --> 00:00:48,670
+مكافئة لخاصية Archimedes أو Archimedes وأهم واحدة
+
+6
+00:00:48,670 --> 00:00:55,930
+في الصور الثلاث اللي هي الخاصية دي D اللي بتقول
+
+7
+00:00:55,930 --> 00:01:01,490
+أو بتنص على أنه لأي عدد حقيقي موجب أيًّا بقدر ألاقي 
+
+8
+00:01:01,490 --> 00:01:06,650
+عدد طبيعي مقلوبه أصغر من العدد الموجب أيًّا 
+
+9
+00:01:10,990 --> 00:01:15,490
+وشفنا المرة اللي فاتت البرهان بتاع الأجزاء الثلاث
+
+10
+00:01:15,490 --> 00:01:21,530
+هذه وهذا مثال قلنا هذا مثال على set والـ set هذه
+
+11
+00:01:21,530 --> 00:01:26,950
+bounded وأثبتنا.. شفنا كيف نثبت أن الـ infimum 
+
+12
+00:01:26,950 --> 00:01:34,090
+بتاعها بيساوي 7 إذن هذا كان مجرد مثال على كيف نثبت 
+
+13
+00:01:34,090 --> 00:01:36,170
+أو كيف نوجد الـ infimum للـ set
+
+14
+00:01:40,130 --> 00:01:53,370
+الآن في عندي نظرية كتير مهمة إحنا أخذنا في الـ
+
+15
+00:01:53,370 --> 00:01:59,570
+citation السابقة أثبتنا كان في عندي example أعتقد 
+
+16
+00:01:59,570 --> 00:02:05,850
+أو fact أنه 
+
+17
+00:02:05,850 --> 00:02:18,320
+الـ.. لا يوجد.. لا يوجد T ينتمي لـ Q بحيث أنّه T
+
+18
+00:02:18,320 --> 00:02:28,060
+تربيعه بيساوي 2 ما فيش عدد نسبي تربيعه بيساوي 2 
+
+19
+00:02:28,060 --> 00:02:36,220
+أو بمعنى آخر.. أو بمعنى آخر جذر الـ 2 ليس عدد
+
+20
+00:02:36,220 --> 00:02:43,960
+نسبي وهذا أثبتناه في مثال سابق أثبتنا؟ في هذا المثال
+
+21
+00:02:43,960 --> 00:02:52,580
+افترضنا ضمنيًّا أن جذر 2 هذا هو عدد حقيقي لأن هذا
+
+22
+00:02:52,580 --> 00:02:58,260
+عبارة عن عدد حقيقي اليوم
+
+23
+00:02:58,260 --> 00:03:06,400
+هنرجع ونثبت في نظرية 1.17 أن جذر 2 هذا فعلاً هو عدد 
+
+24
+00:03:06,400 --> 00:03:13,130
+حقيقي بنثبت أنه يوجد عدد حقيقي اللي هو اسمه جذر
+
+25
+00:03:13,130 --> 00:03:21,050
+2 هذا العدد موجود ممكن يعني إثبات أنه موجود 
+
+26
+00:03:21,050 --> 00:03:30,290
+إذا النظرية هذه بتقول يوجد عدد حقيقي موجب تربيعه 
+
+27
+00:03:30,290 --> 00:03:35,510
+بيساو 2 بمعنى آخر جذر 2 هو عدد حقيقي
+
+28
+00:03:38,190 --> 00:03:43,250
+فالبرهان ذلك ده ما.. هذا ما نسميه يعني هنا 
+
+29
+00:03:43,250 --> 00:03:48,910
+البرهان constructive proof أو يعني برهان بناء أو
+
+30
+00:03:48,910 --> 00:03:54,670
+بالبناء لأنه بنا نثبت الـ existence بتاع شغلة فلازم
+
+31
+00:03:54,670 --> 00:03:57,790
+هذه الشغلة اللي بنا نثبت وجودها بنا نبنيها بنا 
+
+32
+00:03:57,790 --> 00:04:05,160
+نكونها ففي عملية بناء هنا في البراهين اللي زي هذه
+
+33
+00:04:05,160 --> 00:04:09,740
+بنعرف set وبنعرف شغلات بنثبت أنها هي الحاجات
+
+34
+00:04:09,740 --> 00:04:16,360
+المطلوبة فـ let S نعرف مجموعة S على أنها كل العناصر 
+
+35
+00:04:16,360 --> 00:04:23,500
+S في R كل الأعداد الحقيقية S اللي بتكون غير سالبة 
+
+36
+00:04:23,500 --> 00:04:29,860
+ومربعها أصغر من الـ 2 الآن
+
+37
+00:04:29,860 --> 00:04:36,210
+المجموعة هذه غير خالية ليه؟ لأن الـ 1.. الـ 1 
+
+38
+00:04:36,210 --> 00:04:41,650
+ينتمي ليها تعالوا نتأكد ليه الـ 1 ينتمي للـ set هذه؟
+
+39
+00:04:41,650 --> 00:04:46,890
+لأن الـ 1 بيحقق الشرطين بتاعا الـ set أول شيء 1
+
+40
+00:04:46,890 --> 00:04:51,870
+أكبر من أو يساوي صفر هذا صحيح 1 تربيع بيساوي
+
+41
+00:04:51,870 --> 00:04:55,390
+1 أصغر من الـ 2 لأن هذه المجموعة فيها على 
+
+42
+00:04:55,390 --> 00:05:01,490
+الأقل الـ 1 وبالتالي هذه مجموعة غير خالية non
+
+43
+00:05:01,490 --> 00:05:02,070
+-empty
+
+44
+00:05:05,790 --> 00:05:16,350
+كذلك المجموعة هذه bounded above by 2 لو
+
+45
+00:05:16,350 --> 00:05:26,350
+كان بنثبت أن T أصغر من أو يساوي 2 لكل T في S
+
+46
+00:05:34,900 --> 00:05:38,820
+T أصغر من أو يساوي 2 لكل T في S يعني 2 upper
+
+47
+00:05:38,820 --> 00:05:43,480
+bound للـ set S فالبرهان
+
+48
+00:05:43,480 --> 00:05:47,700
+ذلك بالتناقض برهنها 
+
+49
+00:05:47,700 --> 00:05:53,160
+بالتناقض assume أنه 
+
+50
+00:05:53,160 --> 00:06:01,430
+يوجد T0 كيف بتعدّل في الجملة هذه؟ بدل لكل T في S يوجد 
+
+51
+00:06:01,430 --> 00:06:08,330
+T0 في S such that T0 بدل أصغر من أو يساوي بيصير
+
+52
+00:06:08,330 --> 00:06:15,030
+أكبر من الـ 2 هذا بيقود إلى أن T0 تربيع أكبر من
+
+53
+00:06:15,030 --> 00:06:25,110
+4 صح؟ و4 أكبر من الـ 2 طب T0 هذا ينتمي
+
+54
+00:06:25,110 --> 00:06:35,900
+لـ S معناته T0 تربيع هذا أصغر من الـ 2 صح؟ أظبط؟
+
+55
+00:06:35,900 --> 00:06:39,660
+إذا بيطلع عندي 2 أكبر من الـ 2 2 أكبر من
+
+56
+00:06:39,660 --> 00:06:44,720
+الـ 2 contradiction تناقض تمام؟ إذا هذا التناقض
+
+57
+00:06:44,720 --> 00:06:45,920
+بيثبت لك ليه؟
+
+58
+00:06:51,390 --> 00:06:55,630
+إذا أنا هقدر أقول إنّه بيقول لي أن الـ S is bounded 
+
+59
+00:06:55,630 --> 00:07:05,110
+above by 2 الـ S محدودة من أعلى by 2 طيب 
+
+60
+00:07:05,110 --> 00:07:11,830
+لإن أنا عندي S non-empty و bounded above إذا
+
+61
+00:07:11,830 --> 00:07:17,190
+by completeness property الـ S هذه لازم يكون فيه
+
+62
+00:07:17,190 --> 00:07:23,290
+لها supremum it has a supremum in R say دعنا نسميه 
+
+63
+00:07:23,290 --> 00:07:28,870
+X إذا الـ X اللي هو الـ supremum لـ S هذا exist in R
+
+64
+00:07:28,870 --> 00:07:34,390
+by completeness property هذا الـ X اللي هو الـ 
+
+65
+00:07:34,390 --> 00:07:42,060
+supremum لـ S برضه بيطلع أكبر من 1 ليه؟ لأن 5 
+
+66
+00:07:42,060 --> 00:07:47,780
+على 4 ينتمي لـ S عنصر في S لهذا صح تعالوا نتأكد
+
+67
+00:07:47,780 --> 00:07:53,080
+الـ 5 على 4 أكبر من أو يساوي صفر و5 على
+
+68
+00:07:53,080 --> 00:07:57,040
+4 تربيع اللي هو 25 على 16 أصغر من
+
+69
+00:07:57,040 --> 00:08:03,030
+الـ 2 إذن هذا العدد ينتمي لـ S والـ X هذا supremum
+
+70
+00:08:03,030 --> 00:08:08,870
+لـ S وبالتالي X upper bound لـ S الـ X upper bound لـ
+
+71
+00:08:08,870 --> 00:08:14,410
+S إذن أكبر من أو يساوي كل عناصرها إذن الـ X أكبر من 
+
+72
+00:08:14,410 --> 00:08:19,070
+أو يساوي 5 على 4 و5 على 4 أكبر من 
+
+73
+00:08:19,070 --> 00:08:25,470
+1 إذن X أكبر من 1 تمام؟ إذن هنا أثبتنا إن الـ 
+
+74
+00:08:25,470 --> 00:08:31,610
+S يوجد عدد حقيقي x اللي هو الـ supremum لـ S وهذا الـ
+
+75
+00:08:31,610 --> 00:08:39,910
+x أكبر من 1 الآن هذا الـ x هو.. بنثبت هو الجذر
+
+76
+00:08:39,910 --> 00:08:42,690
+التربيعي للـ 2
+
+77
+00:08:49,400 --> 00:08:53,760
+الآن هذا الـ X اللي هو طلع موجود by completeness of
+
+78
+00:08:53,760 --> 00:08:58,600
+property وعدد أكبر من 1 بنثبت أنه تربيعه بيساوي 
+
+79
+00:08:58,600 --> 00:09:05,180
+2 يعني هو العدد المطلوب أن الـ X هو جذر 2 
+
+80
+00:09:11,980 --> 00:09:15,800
+فإذا أثبتنا الـ claim هذا بتكون كملنا برهان نظرية
+
+81
+00:09:15,800 --> 00:09:19,760
+طيب هذا الـ claim برضه متبرهّن بالتناقض assume الـ 
+
+82
+00:09:19,760 --> 00:09:25,060
+contrary إن x تربيع بيساويش 2 if by tricotomy 
+
+83
+00:09:25,060 --> 00:09:30,020
+property إما x تربيع أصغر من 2 أو أكبر من
+
+84
+00:09:30,020 --> 00:09:34,160
+2 إذا أنا في عندي حالتين هنا لازم أخدهم في
+
+85
+00:09:34,160 --> 00:09:40,610
+الاعتبار عشان أكمل برهان الـ claim الحالة الأولى
+
+86
+00:09:40,610 --> 00:09:47,190
+فيها x تربيع أصغر من الـ 2 و بتؤدي في الحالة 
+
+87
+00:09:47,190 --> 00:09:51,790
+هذه لتناقض عشان أثبت الـ claim لإن الـ claim بدينا
+
+88
+00:09:51,790 --> 00:09:56,810
+برهانه بالتناقض assume the contrary فرضنا النقيض
+
+89
+00:09:58,620 --> 00:10:02,360
+تعالوا نشوف كيف نصل لتناقض في الحالة هذه أنا عندي n 
+
+90
+00:10:02,360 --> 00:10:07,640
+لكل n عدد طبيعي n تربيع أكبر من أو يساوي n و
+
+91
+00:10:07,640 --> 00:10:10,700
+بالتالي مقلوب n تربيع دائمًا أصغر من أو يساوي مقلوب
+
+92
+00:10:10,700 --> 00:10:18,500
+الـ n هذا صحيح الآن x زائد 1 على n الكل تربيع ربع
+
+93
+00:10:18,500 --> 00:10:23,820
+بيطلع x تربيع زائد 2 زائد ضعف الأول في الثاني زائد 
+
+94
+00:10:23,820 --> 00:10:31,370
+مربع الثاني الآن بدي أشيل 1 على n تربيع هدّي أشيلها 
+
+95
+00:10:31,370 --> 00:10:37,250
+وأستبدلها بحاجة أكبر من.. أكبر من أو يساوي اللي 
+
+96
+00:10:37,250 --> 00:10:42,030
+هو 1 على n لأن هنا لما أستبدل هذه بـ 1 على n بيصير 
+
+97
+00:10:42,030 --> 00:10:47,250
+هذا أصغر من أو يساوي x تربيع زائد 2x على n زائد 1 
+
+98
+00:10:47,250 --> 00:10:51,410
+على n ولما أخذ من الحدين هدول 1 على n عامل مشترك
+
+99
+00:10:51,410 --> 00:10:53,610
+بيضل 2x زائد 1
+
+100
+00:11:02,350 --> 00:11:07,870
+تمام؟ إذا أنا عندي أصبح الـ x زائد 1 على n الكل
+
+101
+00:11:07,870 --> 00:11:15,110
+تربيع أصغر من أو يساوي المقدار هذا طيب إحنا من الـ
+
+102
+00:11:15,110 --> 00:11:20,150
+.. إحنا فرضنا x تربيع أصغر من 2 إذا 2 سالب x تربيع
+
+103
+00:11:20,150 --> 00:11:25,410
+بيطلع عدد موجب والـ x عدد أكبر من 1، إذا 2x
+
+104
+00:11:25,410 --> 00:11:30,050
+زائد 1 عدد موجب، إذا كسر بسطه موجب ومقامه موجب،
+
+105
+00:11:30,050 --> 00:11:34,330
+بيطلع عدد موجب، إذا حسب الـ property اللي أنا
+
+106
+00:11:34,330 --> 00:11:38,670
+علمتها بالـ star لأيّ
+
+107
+00:11:38,670 --> 00:11:43,530
+عدد موجب، قلنا يوجد عدد طبيعي N0 مقلوبه أصغر من
+
+108
+00:11:43,530 --> 00:11:49,810
+العدد الموجب أضرب الطرفين في العدد الموجود 2x زائد 1 
+
+109
+00:11:49,810 --> 00:11:56,990
+بيصير المتباينة هذه شكلها هكذا الآن 
+
+110
+00:11:56,990 --> 00:12:01,710
+من المتباينة 3 هاي المتباينة 3 هاي عندي x
+
+111
+00:12:01,710 --> 00:12:05,590
+أنا
+
+112
+00:12:05,590 --> 00:12:11,000
+عندي يوجد in zero ينتمي لـ N طبعًا هذا الكلام 
+
+113
+00:12:11,000 --> 00:12:15,160
+المتباينة 3 هذه صحيحة لكل الأعداد الطبيعية N 
+
+114
+00:12:15,160 --> 00:12:21,240
+وبالتالي صحيحة للعدد الطبيعي N0 إذا تعالوا نقرأ 
+
+115
+00:12:21,240 --> 00:12:26,380
+المتباينة 3 ونبدّل N بـ N0 فبيصير x زائد 1 على 
+
+116
+00:12:26,380 --> 00:12:29,840
+N0 تربيع أصغر من
+
+117
+00:12:34,400 --> 00:12:39,760
+مفروض أصغر منها يساوي x تربيع زيادة 1 على N Zero 
+
+118
+00:12:39,760 --> 00:12:47,860
+في 2x زيادة 1 و1
+
+119
+00:12:47,860 --> 00:12:53,640
+على N Zero في 2x زيادة 1 أصغر من 2 سالب
+
+120
+00:12:53,640 --> 00:13:00,200
+x تربيع إذن هذا هيصير أصغر من 2 سالب x تربيع y
+
+121
+00:13:00,200 --> 00:13:02,880
+x تربيع اللي هو بيطلع 2
+
+122
+00:13:08,840 --> 00:13:14,640
+إذا أنا في عندي الآن عدد العدد اللي هو x زيادة 1
+
+123
+00:13:14,640 --> 00:13:21,600
+على N Zero مربعه أصغر من الـ 2 إذا هذا العدد
+
+124
+00:13:21,600 --> 00:13:25,320
+اللي هو x زيادة 1 على N Zero هو عدد غير سالب
+
+125
+00:13:25,320 --> 00:13:29,320
+ومربعه أصغر من الـ 2 إذا هذا ينتمي للمجموعة S 
+
+126
+00:13:29,320 --> 00:13:33,880
+اللي عرفتها في بداية البرهان إذا هذا العدد ينتمي 
+
+127
+00:13:33,880 --> 00:13:34,920
+للمجموعة S 
+
+128
+00:13:37,690 --> 00:13:44,950
+و هذا بي.. بيقود إلى أنّه الـ.. العدد هذا مش ممكن 
+
+129
+00:13:44,950 --> 00:13:53,790
+يكون upper bound للـ set S هذا
+
+130
+00:13:53,790 --> 00:13:58,650
+مش ممكن يكون upper bound للـ set S لأن الـ X هو upper 
+
+131
+00:13:58,650 --> 00:14:04,390
+bound هو الـ supremum و
+
+132
+00:14:04,390 --> 00:14:05,850
+بالتالي 
+
+133
+00:14:14,060 --> 00:14:18,100
+إحنا أثبتنا إنّ X هي الـ upper bound لكن لجينا X زيادة 
+
+134
+00:14:18,100 --> 00:14:22,100
+1 على N not هي ثانوية لـ S فبالتالي في عنصر أكبر
+
+135
+00:14:22,100 --> 00:14:31,140
+من X فهذا الـ contradiction مظبوط لأن هذا
+
+136
+00:14:31,140 --> 00:14:38,730
+عنصر في S وبالتالي هذا بيقود هذا بيقود إلى أنّ X 
+
+137
+00:14:38,730 --> 00:14:47,890
+ماهوش upper bound لأنه الـ X أصغر من 1 من X
+
+138
+00:14:47,890 --> 00:14:54,650
+زيادة 1 على N زيرو وهذا
+
+139
+00:14:54,650 --> 00:14:55,590
+ينتمي لـ S
+
+140
+00:15:01,160 --> 00:15:06,760
+فهذا عنصر في S وأكبر من X هذا معناه أنّ الـ X هذا 
+
+141
+00:15:06,760 --> 00:15:12,420
+مش ممكن يكون upper bound لـ S وهذا بتناقض مع كون X 
+
+142
+00:15:12,420 --> 00:15:18,160
+هو upper bound لأنه supreme لـ S احنا قلنا أن الـ X
+
+143
+00:15:18,160 --> 00:15:22,840
+هذا اللي في الـ claim أيه الـ X هذا هو supreme لـ S
+
+144
+00:15:22,840 --> 00:15:27,180
+وبالتالي upper bound لـ S وهنا وصلنا لأن الـ X مش
+
+145
+00:15:27,180 --> 00:15:31,160
+ممكن يكون upper bound لـ S لأنه أصغر من عنصر ما
+
+146
+00:15:31,160 --> 00:15:34,720
+ينتمي لـ S إذا فيه تناقض لأن هنا وصلنا إلى
+
+147
+00:15:34,720 --> 00:15:41,480
+contradiction إذا فرضنا X بيه أصغر من 2 وصلتنا لـ
+
+148
+00:15:41,480 --> 00:15:46,760
+contradiction بالمثل بالمثل
+
+149
+00:15:46,760 --> 00:15:51,480
+في الحالة الثانية في
+
+150
+00:15:51,480 --> 00:15:56,980
+الحالة الثانية لو فرضنا أن x تربيع المرة دي أكبر من 
+
+151
+00:15:56,980 --> 00:16:03,100
+الاثنين فبرضه ممكن نصل بنفس الطريقة و بنفس الأسلوب
+
+152
+00:16:03,100 --> 00:16:09,220
+في النهاية إلى contradiction نصل إلى contradiction
+
+153
+00:16:09,220 --> 00:16:15,100
+وبالتالي إذا احنا فرضنا أنه احنا كنا كان الـ claim
+
+154
+00:16:15,100 --> 00:16:20,520
+تبعنا الذكرى في البرنامج احنا كنا عايزين نثبت أن x
+
+155
+00:16:20,520 --> 00:16:26,060
+تربيع بساوي 2 ففرضنا أن x تربيع لا يساوي 2
+
+156
+00:16:26,060 --> 00:16:33,520
+وبالتالي هذا بيقدر أن x تربيع أصغر من 2 أو x
+
+157
+00:16:33,520 --> 00:16:38,200
+تربيع أكبر من 2 وفي كل حالة من الحالات هذه
+
+158
+00:16:38,200 --> 00:16:43,520
+وصلنا إلى تناقض إذا التناقض هذا سببه أنه إذا احنا
+
+159
+00:16:43,520 --> 00:16:49,620
+فرضنا هو فرضنا أن x تربيع لا يساوي 2 هذا بيثبت 
+
+160
+00:16:49,620 --> 00:16:54,980
+الـ claim اللي هو x تربيع بساوي 2 و بكمل البرهان
+
+161
+00:16:54,980 --> 00:17:03,440
+okay تمام إذا هذا هو برهان الـ .. النظرية هذه إذا
+
+162
+00:17:03,440 --> 00:17:09,440
+الآن أصبح عندي في نظريتين واحدة بتقول أنه جذر 2
+
+163
+00:17:09,440 --> 00:17:14,660
+هو عدد حقيقي ونظرية
+
+164
+00:17:14,660 --> 00:17:19,300
+ثانية أو حقيقة ثانية أن جذر 2 ليس عدد نسبي
+
+165
+00:17:36,150 --> 00:17:44,930
+طيب في كمان نتيجة مهمة على النتائج هذه أو نظرية
+
+166
+00:17:44,930 --> 00:17:49,490
+مهمة اللي هي density theorem نظرية الكثافة الـ
+
+167
+00:17:49,490 --> 00:17:55,530
+density theorem الـ density theorem بتقول بين أي
+
+168
+00:17:55,530 --> 00:18:01,230
+عددين حقيقيين يوجد عدد نسبي يعني لو أنا في عندي
+
+169
+00:18:02,110 --> 00:18:11,650
+عددين حقيقيين X أصغر من Y هاي X وهاي Y يوجد عدد
+
+170
+00:18:11,650 --> 00:18:20,390
+نسبي R ينتمي لـ Q بحيث أن R أكبر من X أصغر من Y أو
+
+171
+00:18:20,390 --> 00:18:27,320
+بمعنى آخر، لو في عندي فترة مفتوحة X وY فلازم هذه
+
+172
+00:18:27,320 --> 00:18:34,100
+الفترة وفي هذه الفترة غير خالية فلازم نلاقي R
+
+173
+00:18:34,100 --> 00:18:41,700
+ينتمي للفترة المفتوحة و R هذا عدد نسبي إذا الـ
+
+174
+00:18:41,700 --> 00:18:45,520
+density theorem بكل بساطة بتقول between any two
+
+175
+00:18:45,520 --> 00:18:50,990
+real numbers there exists a rational number أو Any
+
+176
+00:18:50,990 --> 00:18:55,030
+non-empty open interval contains a rational number
+
+177
+00:18:55,030 --> 00:19:02,170
+نفس الشيء أو نفس الـ statement البرهان مش صعب
+
+178
+00:19:02,170 --> 00:19:05,210
+تعالوا 
+
+179
+00:19:05,210 --> 00:19:10,410
+نشوف البرهان أنا عندي فرض أن X أصغر من Y فرض X
+
+180
+00:19:10,410 --> 00:19:16,790
+أصغر من Y وبالتالي Y سالب X عدد موجب إذا by the
+
+181
+00:19:16,790 --> 00:19:20,330
+Archimedean property بقدر ألاقي عدد هنا المفروض
+
+182
+00:19:20,330 --> 00:19:28,050
+يكون جزء B فـ by
+
+183
+00:19:28,050 --> 00:19:31,590
+Archimedean property واحد ستاشر بيه اللي أعطيناها
+
+184
+00:19:31,590 --> 00:19:37,930
+إشارة نجمة لأي عدد موجب زي هذا يوجد عدد طبيعي n
+
+185
+00:19:37,930 --> 00:19:45,930
+مقلوب وأصغر من عدد الموجب الآن بدي أعرف أن أكبر عدد
+
+186
+00:19:45,930 --> 00:19:50,190
+صحيح أصغر من أو يساوي n X هذه دالة أكبر عدد صحيح
+
+187
+00:19:50,190 --> 00:19:55,290
+وأضيف عليها واحد طبعًا هذا عدد صحيح زائد واحد
+
+188
+00:19:55,290 --> 00:19:59,930
+الواحد عدد صحيح فمجموعهم بيطلع عدد صحيح إذا أنا
+
+189
+00:19:59,930 --> 00:20:04,250
+عرفت عدد صحيح m ينتمي إلى z على أنه the greatest
+
+190
+00:20:04,250 --> 00:20:09,110
+integer less than or equal to n X plus one الآن
+
+191
+00:20:09,110 --> 00:20:16,650
+بتثبت أنه في عندي claim بتثبت أن هذا العدد m بيحقق
+
+192
+00:20:16,650 --> 00:20:22,110
+المتباينة هذه إذا
+
+193
+00:20:22,110 --> 00:20:31,330
+أنا عايز أثبت أنه الـ claim تبعي one أنه m negative
+
+194
+00:20:31,330 --> 00:20:35,850
+one less than or equal n X less than m
+
+195
+00:20:39,470 --> 00:20:46,730
+طيب من تعريف دالة أكبر عدد صحيح by definition of
+
+196
+00:20:46,730 --> 00:20:52,970
+the greatest integer function هذا العدد دائمًا أكبر
+
+197
+00:20:52,970 --> 00:20:58,150
+من نفسه العدد اللي جوا سالب واحد وأصغر من أو ساوي
+
+198
+00:20:58,150 --> 00:21:05,870
+نفسه صح؟ هذا العدد أكبر عدد صحيح أصغر من أو ساوي NX
+
+199
+00:21:05,870 --> 00:21:11,970
+يعني نفسر نفسه إذا هذا العدد أصغر من أو ساوي NX و
+
+200
+00:21:11,970 --> 00:21:18,250
+أكبر من NX للمطرح منها واحد طيب ننقل الواحد عن
+
+201
+00:21:18,250 --> 00:21:22,970
+ناحية الثانية فبصراحة اندي NX أصغر من أكبر عدد صحيح
+
+202
+00:21:22,970 --> 00:21:28,690
+أصغر من أو ساوي NX زائد واحد وهذا من هنا أصغر من أو
+
+203
+00:21:28,690 --> 00:21:39,010
+يساوي NX زائد واحد الآن هذا سمينا احنا هذا M فبيطلع
+
+204
+00:21:39,010 --> 00:21:45,930
+عندي M أكبر من NX أصغر من أو يساوي NX زائد واحد
+
+205
+00:21:45,930 --> 00:21:54,340
+نطرح واحد من كل الأطراف فبيطلع عندي M سالب واحد M
+
+206
+00:21:54,340 --> 00:22:02,180
+سالب واحد أصغر من أو ساوي NX و NX من هنا NX
+
+207
+00:22:02,180 --> 00:22:09,160
+أصغر من M وهذا اللي بدنا نقنعه لأن هنا برهن الـ
+
+208
+00:22:09,160 --> 00:22:13,200
+claim لأن
+
+209
+00:22:13,200 --> 00:22:18,960
+من هذا الـ claim من
+
+210
+00:22:18,960 --> 00:22:21,800
+هذا الـ claim نستنتج
+
+211
+00:22:24,560 --> 00:22:33,840
+هذه الكلام اللي برهناه لو أنا ضربت ..
+
+212
+00:22:33,840 --> 00:22:37,100
+لو
+
+213
+00:22:37,100 --> 00:22:43,940
+أضفت واحد لكل الأطراف فبصير عندي M أصغر من أو يساوي
+
+214
+00:22:43,940 --> 00:22:50,160
+NX زائد واحد أصغر من M زائد واحد
+
+215
+00:22:56,000 --> 00:23:05,300
+و لو قسمت على N أو ضربت في N نضرب في 1 على N فهذا
+
+216
+00:23:05,300 --> 00:23:15,400
+بيقدر أن M على N أصغر من أو يساوي X زائد 1 على N
+
+217
+00:23:26,950 --> 00:23:31,950
+طيب أنا عندي .. أنا 
+
+218
+00:23:31,950 --> 00:23:34,110
+عندي من نفس المتباينة هذه
+
+219
+00:24:07,700 --> 00:24:15,700
+أنا عندي 1 على n أصغر من y ناقص x أنا
+
+220
+00:24:15,700 --> 00:24:23,580
+عندي 1 على n 1 على n أصغر من y سالب x هذا بيقدي
+
+221
+00:24:23,580 --> 00:24:33,260
+أنه x زائد 1 على n أصغر من y لأن هذا أصغر من y تمام
+
+222
+00:24:39,380 --> 00:24:45,180
+هو أكبر من X نعم؟ هو أكبر من X لأن X هيت واحدة
+
+223
+00:24:45,180 --> 00:24:55,720
+عنها اه و بدي هذا يكون أكبر من X اه
+
+224
+00:24:55,720 --> 00:25:02,780
+M على N أكبر اه من هنا من
+
+225
+00:25:02,780 --> 00:25:10,740
+هنا قسمت على M لما أضرب في 1 على N فبصير عندي M
+
+226
+00:25:10,740 --> 00:25:17,860
+على N أكبر من X نظمت هيك صح؟ إذا أصبح عندي أنا
+
+227
+00:25:17,860 --> 00:25:25,220
+بأحصل على X أصغر من M على N أصغر من Y الآن هذا
+
+228
+00:25:25,220 --> 00:25:33,060
+عبارة عن عدد نسبي هذا هو هذا العدد هو الـ R هذا عدد
+
+229
+00:25:33,060 --> 00:25:38,000
+نسبي لأن عدد النسبي عبارة عن عدد صحيح على عدد صحيح
+
+230
+00:25:38,000 --> 00:25:44,470
+لا يساوي صفر إذن هذه أثبتت إن يوجد عدد نسبي أكبر من
+
+231
+00:25:44,470 --> 00:25:49,790
+X وأصغر من Y أو يوجد عدد نسبي بين X وY إذن هذا
+
+232
+00:25:49,790 --> 00:26:02,470
+بيكمل البرهان تبع الـ density theorem في
+
+233
+00:26:02,470 --> 00:26:07,870
+كمان نتيجة ثانية برضه بنسميها density theorem أو
+
+234
+00:26:07,870 --> 00:26:11,800
+نتيجة على الـ density theorem وفي بعض الناس برضه
+
+235
+00:26:11,800 --> 00:26:15,620
+نفسها بيسموها density theorem فـ الـ density theorem
+
+236
+00:26:15,620 --> 00:26:19,100
+هذه الثانية أو النتيجة عليها بتقول أن بين أي
+
+237
+00:26:19,100 --> 00:26:24,440
+between any two real numbers x and y there exists
+
+238
+00:26:24,440 --> 00:26:29,860
+an irrational number يوجد عدد Z بين x و y وهذا Z
+
+239
+00:26:29,860 --> 00:26:36,100
+irrational number إذا
+
+240
+00:26:36,100 --> 00:26:47,170
+كمان مرة لو في عندي أي عددين حقيقيين x و y هو
+
+241
+00:26:47,170 --> 00:26:56,830
+x أصغر من y فبنقدر نلاقي r أو p وهذا ينتمي لـ r
+
+242
+00:26:56,830 --> 00:27:06,170
+ناقص q عدد غير نسبي بين أكبر من x و أصغر من y
+
+243
+00:27:07,390 --> 00:27:12,950
+البرهان تبع النتيجة هذه أول
+
+244
+00:27:12,950 --> 00:27:18,050
+شيء احنا لسه مثبتين قبل شوية أن جدر 2 is a real
+
+245
+00:27:18,050 --> 00:27:22,730
+number جدر 2 كان هو supremum لـ S وبالتالي
+
+246
+00:27:22,730 --> 00:27:27,690
+exist in R وأثبتنا أن جدر 2 هذا أكبر من صفر
+
+247
+00:27:27,690 --> 00:27:31,910
+حتى أثبتنا أنه أكبر من واحد كان الـ X أكبر من واحد
+
+248
+00:27:31,910 --> 00:27:37,900
+وبالتالي موجبة إن جدر 2 عدد موجب وبالتالي مقلوبه
+
+249
+00:27:37,900 --> 00:27:46,480
+عدد موجب لأن أنا لما يكون عندي x أصغر من y وأضرب
+
+250
+00:27:46,480 --> 00:27:50,440
+المتباينة هذه في 1 على جدر 2 اللي هو عدد
+
+251
+00:27:50,440 --> 00:27:55,040
+موجب فتصير المتباينة هذه x على جدر 2 أصغر من y
+
+252
+00:27:55,040 --> 00:28:01,030
+على جدر 2 تمام الآن إذا هذا real number وهذا
+
+253
+00:28:01,030 --> 00:28:05,630
+real number by density theorem between any two
+
+254
+00:28:05,630 --> 00:28:09,270
+real numbers there exist irrational number عدد
+
+255
+00:28:09,270 --> 00:28:13,750
+نسبي سمي R طبعًا هذا العدد النسبي لا يساوي صفر لأن
+
+256
+00:28:13,750 --> 00:28:20,170
+دي عدد موجب جذر 2 إذا أنا في عندي عدد نسبي R بين
+
+257
+00:28:20,170 --> 00:28:25,310
+العددين الحقيقيين حسب الـ density theorem الآن لو
+
+258
+00:28:25,310 --> 00:28:32,530
+أخذت لو عرفت لو عرفت العدد Z على أنه R ضرب جذر
+
+259
+00:28:32,530 --> 00:28:38,110
+2 فهذا بيطلع عدد غير نسبي تعالوا نبرهن ذلك
+
+260
+00:28:38,110 --> 00:28:42,950
+لإثبات أن العدد Z اللي هو R في جذر 2 عدد غير
+
+261
+00:28:42,950 --> 00:28:49,210
+نسبي افرض otherwise يعني خلاف ذلك افرض خلاف ذلك
+
+262
+00:28:49,210 --> 00:28:56,250
+يعني افرض أن العدد هذا نسبي افرض
+
+263
+00:28:56,250 --> 00:29:02,030
+أن هذا نسبي إذا لما قسمه هذا هو R في جدر 2 عدد
+
+264
+00:29:02,030 --> 00:29:08,130
+نسبي و R احنا فرضنا و R طبعًا هذا عدد نسبي إذا عدد
+
+265
+00:29:08,130 --> 00:29:11,770
+نسبي على عدد نسبي بيطلع عدد نسبي إذا هذا هيطلع عدد
+
+266
+00:29:11,770 --> 00:29:15,810
+نسبي اللي هو بيساوي جدر 2 وهذا تناقض مع
+
+267
+00:29:15,810 --> 00:29:21,490
+الحقيقة اللي أثبتناها سابقًا إذا .. إذا هذا العدد
+
+268
+00:29:21,490 --> 00:29:28,090
+لازم .. مش ممكن يكون نسبي لازم يكون غير نسبي طيب
+
+269
+00:29:31,920 --> 00:29:37,240
+أضرب المتباينة هذه في
+
+270
+00:29:37,240 --> 00:29:42,500
+جدر 2 لو ضربنا المتباينة هذه في جدر 2
+
+271
+00:29:42,500 --> 00:29:45,620
+فبصير
+
+272
+00:29:45,620 --> 00:29:52,440
+عندي X أصغر من R في جدر 2 اللي سميناها Z أصغر
+
+273
+00:29:52,440 --> 00:29:53,340
+من Y
+
+274
+00:29:55,970 --> 00:30:00,250
+وبالتالي هنا أثبتنا أن يوجد عدد غير نسبي وهذا
+
+275
+00:30:00,250 --> 00:30:05,710
+العدد الغير نسبي between X and Y وهو المطلوب هذا
+
+276
+00:30:05,710 --> 00:30:10,870
+هو المطلوب تمام؟
+
+277
+00:30:10,870 --> 00:30:14,250
+في
+
+278
+00:30:14,250 --> 00:30:22,590
+أي سؤال أو استفسار؟ إن شاء الله يكون احنا خلصنا أربع
+
+279
+00:30:22,590 --> 00:30:29,150
+سكاشن من الشتر واحد وهي في تمارين على الـ section
+
+280
+00:30:29,150 --> 00:30:40,510
+هذا ونبدأ section جديد الـ 
+
+281
+00:30:40,510 --> 00:30:43,950
+هذا السيكشن الجديد بيتحدث عن الـ intervals الفترات
+
+282
+00:30:43,950 --> 00:30:50,710
+طبعًا كلكم درستم تفاضل وتكامل ومرت عليكم أنواع
+
+283
+00:30:50,710 --> 00:30:59,210
+الفترات في كورس تفاضل وتكامل، لو أخذت أي عددين 
+
+284
+00:30:59,210 --> 00:31:08,710
+حقيقيين a و b، و a أصغر من أو يساوي b، فممكن نعرف الـ
+
+285
+00:31:08,710 --> 00:31:13,730
+open interval على أنها كل الأعداد الحقيقية x اللي بين 
+
+286
+00:31:13,730 --> 00:31:20,010
+a و b، فهذا الـ open interval from a to b، وفيه ممكن 
+
+287
+00:31:20,010 --> 00:31:24,580
+نعرف closed interval from a to b على أنها كل الـ
+
+288
+00:31:24,580 --> 00:31:27,820
+real numbers اللي أكبر من أو يساوي a، وأصغر من أو 
+
+289
+00:31:27,820 --> 00:31:34,880
+يساوي b، الـ half open فيه برضه نوع من الفترات بنسميه
+
+290
+00:31:34,880 --> 00:31:42,700
+half open أو half closed على الصورة هذه، هذه 
+
+291
+00:31:42,700 --> 00:31:47,890
+بنسميها half open أو half closed يعني مفتوحة من جهة 
+
+292
+00:31:47,890 --> 00:31:53,010
+ومغلقة من جهة أخرى، فهذه طبعًا واضح تعريفها كل الـ X 
+
+293
+00:31:53,010 --> 00:31:59,250
+اللي أكبر من a،  أصغر من أو يساوي b، وهذه زيها، في كمان 
+
+294
+00:31:59,250 --> 00:32:05,650
+نوع آخر من الـ intervals، زي الـ interval هذه بنسميها
+
+295
+00:32:05,650 --> 00:32:14,430
+open left ray شعاع أيسر مفتوح، يعني على خط الأعداد
+
+296
+00:32:14,430 --> 00:32:18,970
+ليه بيسموها left ray لأن فعلًا هي قايمة زي الشعاع كده
+
+297
+00:32:18,970 --> 00:32:26,830
+هذا خط الأعداد، وهنا في b عدد حقيقي، فالفترة المفتوحة
+
+298
+00:32:26,830 --> 00:32:32,370
+من سالب ما لا نهاية إلى b هي الفترة هذه، هي مصدر
+
+299
+00:32:32,370 --> 00:32:36,350
+الضوء، إن هنا في مصدر ضوء، وهذا الضوء بيشع إلى 
+
+300
+00:32:36,350 --> 00:32:43,140
+اليسار، فهذه الفترة هي من سالب ما لا نهاية إلى b
+
+301
+00:32:43,140 --> 00:32:48,580
+open interval صح؟
+
+302
+00:32:48,580 --> 00:32:53,400
+كل الأعداد الحقيقية اللي أصغر من b، إذن هذه تعريفها
+
+303
+00:32:53,400 --> 00:32:57,460
+كل الأعداد الحقيقية اللي أصغر من b، بالمثل ممكن أن
+
+304
+00:32:57,460 --> 00:33:06,040
+أعرف right ray، right ray زي ذلك، يعني d، وما لا 
+
+305
+00:33:06,040 --> 00:33:11,230
+نهاية أو a، وما إلى نهاية، كل الأعداد الحقيقية اللي
+
+306
+00:33:11,230 --> 00:33:13,190
+أكبر من أو على يمين الـ a
+
+307
+00:33:16,510 --> 00:33:21,690
+طبعًا ممكن نعرف closed left ray، لأن لو أخذت النقطة
+
+308
+00:33:21,690 --> 00:33:28,090
+هذه موجودة ضمن الفترة، يعني أغلقت الفترة زي كده، فهذه
+
+309
+00:33:28,090 --> 00:33:32,890
+بنسميها closed left ray، وكذلك لو أخذت الـ beam
+
+310
+00:33:32,890 --> 00:33:37,730
+أضفتها على الفترة فهذه بنسميها closed right ray
+
+311
+00:33:37,730 --> 00:33:45,660
+وفي طبعًا هذه الـ ... الـ two-sided ray، أي ده، صح؟
+
+312
+00:33:45,660 --> 00:33:51,000
+التعبير اللي هو خط الأعداد كله، كل الأعداد، بحثوا في
+
+313
+00:33:51,000 --> 00:33:54,060
+ملاحظة
+
+314
+00:33:54,060 --> 00:34:01,860
+هنا إن الأول ثلاثة أنواع من الـ intervals هدول بنسميهم
+
+315
+00:34:01,860 --> 00:34:05,580
+bounded هم 
+
+316
+00:34:05,580 --> 00:34:11,460
+فعلًا bounded، الفترات هذه محصورة، محدودة، ممكن نحصرها
+
+317
+00:34:13,670 --> 00:34:19,010
+أما الأنواع... الأنواع ال... ال... الأخرى، الخامسة
+
+318
+00:34:19,010 --> 00:34:25,350
+الأخرى هذه unbounded، unbounded
+
+319
+00:34:25,350 --> 00:34:29,030
+غير
+
+320
+00:34:29,030 --> 00:34:33,230
+محصورة، وغير محدودة، الفترات هذه غير محدودة، هذا 
+
+321
+00:34:33,230 --> 00:34:37,810
+شعاع أيسر، لاحظ الشعاع هذا مقدرش أحصر عليه
+
+322
+00:34:39,020 --> 00:34:44,220
+يعني بيمتد إلى سالب ما لا نهاية، أو بيمتد إلى ما
+
+323
+00:34:44,220 --> 00:34:49,580
+لا نهاية، إذن الفترات هذه unbounded، النوع هذا من
+
+324
+00:34:49,580 --> 00:34:53,580
+الفترات bounded، وبالتالي الفترات متقسمة إلى two
+
+325
+00:34:53,580 --> 00:34:58,260
+types، bounded intervals و unbounded intervals
+
+326
+00:35:13,980 --> 00:35:26,320
+طيب، في ملاحظة هنا على الفترات، لو
+
+327
+00:35:26,320 --> 00:35:29,740
+أخذت أي interval بغض النظر هل هي bounded ولا 
+
+328
+00:35:29,740 --> 00:35:35,200
+unbounded، open, closed, half-open, half-closed، بغض
+
+329
+00:35:35,200 --> 00:35:39,280
+النظر أي واحدة من الأنواع الثمانية اللي شفناهم، لو
+
+330
+00:35:39,280 --> 00:35:48,350
+I كانت أي interval، فالـ interval I بتحقق الخاصية هذه
+
+331
+00:35:48,350 --> 00:35:54,130
+أي interval بتحقق الخاصية هذه، إن أنا لو أخذت أي
+
+332
+00:35:54,130 --> 00:36:00,070
+عنصرين في الفترة، وواحد أصغر من الثاني، فالعناصر
+
+333
+00:36:00,070 --> 00:36:05,770
+اللي بينهم بتكون موجودة في الفترة، يعني هي إن عندي
+
+334
+00:36:05,770 --> 00:36:11,730
+فترة مفتوحة، مغلقة، أو 
+
+335
+00:36:13,570 --> 00:36:20,230
+left ray مثلًا، و
+
+336
+00:36:20,230 --> 00:36:29,330
+الـ symbol فترة هذه مثلًا a,b أو مثلًا [a,b]، فلو
+
+337
+00:36:29,330 --> 00:36:34,790
+أخذت سواء هذه الفترة أو هذه أو أي واحدة من أنواع
+
+338
+00:36:34,790 --> 00:36:44,960
+الثمانية وجئت أخذت عنصرين x و y، وx أصغر من y،
+
+339
+00:36:44,960 --> 00:36:50,660
+موجودين في الفترة هذه، فالفترة هذه بتتمتع بالخاصية
+
+340
+00:36:50,660 --> 00:36:58,480
+إن أي عنصر في الفترة هذه المغلقة من x و y لو أخذت
+
+341
+00:36:58,480 --> 00:37:05,200
+أي t، يعني كل عناصر الفترة المغلقة هذه كلها بتطلع
+
+342
+00:37:05,200 --> 00:37:11,840
+موجودة في الفترة الكبيرة، نفس الحاجة هنا، هات أخذ x
+
+343
+00:37:13,020 --> 00:37:24,020
+هو y، فكل العناصر t في الفترة المغلقة موجودة
+
+344
+00:37:24,020 --> 00:37:33,590
+في الـ left-ray، إذن أي فترة i لو أخذت داخلها أي عنصرين
+
+345
+00:37:33,590 --> 00:37:37,910
+x أصغر من y، فكل العناصر في الفترة المغلقة من x لـ y
+
+346
+00:37:37,910 --> 00:37:42,050
+أو الفترة المغلقة من x لـ y، تطلع مجموعة جزئية من
+
+347
+00:37:42,050 --> 00:37:48,710
+الفترة اللي أنا واخدها، okay؟ الآن نظرية أخرى من
+
+348
+00:37:48,710 --> 00:37:57,000
+عشرين بتقول لي إن العكس صحيح، العكس صحيح، يعني لو أنا
+
+349
+00:37:57,000 --> 00:38:02,320
+فيه عندي مجموعة جزئية s، مجموعة جزئية من r، الـ
+
+350
+00:38:02,320 --> 00:38:07,140
+cardinal number تبع s أكبر من أو يساوي 2، الـ
+
+351
+00:38:07,140 --> 00:38:10,780
+cardinal number هنا يعني معناه عدد عناصر الـ set
+
+352
+00:38:10,780 --> 00:38:15,740
+المجموعة
+
+353
+00:38:15,740 --> 00:38:21,720
+يعني roughly speaking يعني معناه إنه يعني إذا كانت
+
+354
+00:38:21,720 --> 00:38:25,460
+الـ set finite فهذا عدد عناصرها، is infinite طبعًا
+
+355
+00:38:26,560 --> 00:38:37,180
+بيكون يعني له تعريف عام من عدد العناصر، فده كانت s
+
+356
+00:38:37,180 --> 00:38:41,200
+مجموعة جزئية و cardinalها أكبر من أو يساوي 2
+
+357
+00:38:41,200 --> 00:38:48,380
+يعني المجموعة فيها على الأقل عنصرين أو أكثر، وكانت 
+
+358
+00:38:48,380 --> 00:38:52,980
+المجموعة s هذه بتحقق الخاصية 4
+
+359
+00:38:55,110 --> 00:39:01,230
+فلازم الـ s هذه تطلع interval كمان مرة، احنا قلنا في
+
+360
+00:39:01,230 --> 00:39:08,050
+الملاحظة هذه، أي interval بتحقق الخاصية 4 اللي
+
+361
+00:39:08,050 --> 00:39:13,310
+شرحناها هنا، الآن العكس، لو في عندي مجموعة جزئية s
+
+362
+00:39:13,310 --> 00:39:17,530
+من r، أنا مش عارف إنها فترة ولا لا، مجرد مجموعة
+
+363
+00:39:17,530 --> 00:39:22,510
+جزئية من r، وفيها على الأقل عنصرين، تحتوي على الأقل
+
+364
+00:39:22,510 --> 00:39:23,650
+عنصرين أو أكثر
+
+365
+00:39:26,310 --> 00:39:31,210
+وإذا كانت المجموعة الجزئية s هذه بتحقق الخاصية 4
+
+366
+00:39:31,210 --> 00:39:38,390
+فلازم هذه الـ s تطلع فترة واحدة من الفترات
+
+367
+00:39:38,390 --> 00:39:43,970
+الثمانية، وبرهان
+
+368
+00:39:43,970 --> 00:39:54,130
+النظرية هذه برضه برهان طويل شوية، لكن بيعتمد 
+
+369
+00:39:54,130 --> 00:40:01,730
+على أربع أربع حالات، فمن 
+
+370
+00:40:01,730 --> 00:40:08,250
+جسم البرهان إلى أربع حالات، الحالة الأولى إن الـ set
+
+371
+00:40:08,250 --> 00:40:14,070
+s بتكون bounded، محصورة، الـ set بتكون bounded، إذا
+
+372
+00:40:14,070 --> 00:40:19,030
+كانت bounded above and bounded below، أو s is
+
+373
+00:40:19,030 --> 00:40:24,090
+bounded above but not below، يعني محدود من أعلى
+
+374
+00:40:24,090 --> 00:40:29,760
+وليست محدود من أسفل، وهذا وارد، أو s is bounded
+
+375
+00:40:29,760 --> 00:40:33,280
+below but not above، يعني محدود من أسفل وليست
+
+376
+00:40:33,280 --> 00:40:37,520
+محدودة من الأعلى، الحالة الرابعة إن s تكون neither
+
+377
+00:40:37,520 --> 00:40:41,180
+bounded above nor below، يعني لا محدودة من أسفل ولا
+
+378
+00:40:41,180 --> 00:40:45,200
+محدودة من الأعلى زي r، زي مجموعة الأعداد الحقيقية
+
+379
+00:40:45,200 --> 00:40:52,670
+تمام؟ وفي كل حالة بنا نثبت إن s تطلع فترة، في كل 
+
+380
+00:40:52,670 --> 00:40:58,750
+حالة بنا نثبت إن s تطلع فترة، يعني ها أنا 
+
+381
+00:40:58,750 --> 00:41:04,130
+مثبت لكم الحالة الأولى والثانية، والحالتين الثالثة
+
+382
+00:41:04,130 --> 00:41:11,330
+والرابعة، ممكن يعني برهانهم بالمثل، فحدد لكم تقرأوا
+
+383
+00:41:11,330 --> 00:41:16,450
+البرهان، لأن هذا البرهان مجرد تفاصيل، حدد لكم إنكم 
+
+384
+00:41:16,450 --> 00:41:18,870
+تقراؤوا البرهان، تفهموه، لأنه مش هشرحه
+
+385
+00:41:21,750 --> 00:41:25,570
+فحاولوا تقرأوه، تفهموه، وأنا متأكد إنكم هتفهموه
+
+386
+00:41:25,570 --> 00:41:28,910
+فنتوقف
+
+387
+00:41:28,910 --> 00:41:33,130
+عند هذا... نكتفي بهذا القدر وإن شاء الله المرة 
+
+388
+00:41:33,130 --> 00:41:36,850
+الجاية هنتحدث
+
+389
+00:41:36,850 --> 00:41:43,510
+عن موضوع nested intervals، okay؟ في حد عنده أي سؤال
+
+390
+00:41:43,510 --> 00:41:44,330
+أو سؤال؟ 
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a76a12d40fcdf22b14469b0182d80c8db1afc9cf
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/t35SQVeADNY_raw.srt
@@ -0,0 +1,1560 @@
+1
+00:00:21,400 --> 00:00:26,440
+المرة اللى فاتت احنا يعني اخدنا ال Archimedean
+
+2
+00:00:26,440 --> 00:00:33,820
+property وشوفنا فيه صور متعددة لها او صور مختلفة
+
+3
+00:00:33,820 --> 00:00:39,140
+اللى هي الصور التلاتة هذه فكل
+
+4
+00:00:39,140 --> 00:00:43,160
+واحدة من الخواصة دى تعتبر Archimedean property او
+
+5
+00:00:43,160 --> 00:00:48,670
+مكافئة لخاصية Archimedes او Archimedesو أهم واحدة
+
+6
+00:00:48,670 --> 00:00:55,930
+في الصور التلاتة اللي هي الخاصية دي D اللي بتقول
+
+7
+00:00:55,930 --> 00:01:01,490
+أو بتنص على أنه لأي عدد حقيقي موج ابواي بقدر ألاقي
+
+8
+00:01:01,490 --> 00:01:06,650
+عدد طبيعي مقلوبه أصغر من العدد الموج ابواي
+
+9
+00:01:10,990 --> 00:01:15,490
+وشوفت المرة اللي فتحت البرهين تبعت الأجزاء التلاتة
+
+10
+00:01:15,490 --> 00:01:21,530
+هذه و هذا مثال قولنا هذا مثال على set و ال set هذه
+
+11
+00:01:21,530 --> 00:01:26,950
+bounded و أثبتنا .. شوفنا كيف نثبت أن ال infimum
+
+12
+00:01:26,950 --> 00:01:34,090
+تبعها بساوى 7 إذن هذا كان مجرد مثال على كيف نثبت
+
+13
+00:01:34,090 --> 00:01:36,170
+أو كيف نوجد ال infimum لل set
+
+14
+00:01:40,130 --> 00:01:53,370
+الان في أنا نظرية كتير مهمة احنا أخدنا في ال
+
+15
+00:01:53,370 --> 00:01:59,570
+citation السابقة أثبتنا كان في عندي example اعتقد
+
+16
+00:01:59,570 --> 00:02:05,850
+او fact انه
+
+17
+00:02:05,850 --> 00:02:18,320
+ال ..لا يوجد .. لا يوجد T ينتبه لل Q بحيث انه T
+
+18
+00:02:18,320 --> 00:02:28,060
+تربية بساوي اتنين مافيش عدد نسبي مربع بساوي اتنين
+
+19
+00:02:28,060 --> 00:02:36,220
+او بمعنى اخر .. او بمعنى اخر جذر الاتنين ليس عدد
+
+20
+00:02:36,220 --> 00:02:43,960
+نسبيوهذا أثبتناه في مثال سابق أثبوت؟ في هذا المثال
+
+21
+00:02:43,960 --> 00:02:52,580
+افترضنا ضمنيا أن جذر 2 هذا هو عدد حقيقي لأن هذا
+
+22
+00:02:52,580 --> 00:02:58,260
+عبارة عن عدد حقيقي اليوم
+
+23
+00:02:58,260 --> 00:03:06,400
+هنرجع ونثبت في نظرية 1.17 أن جذر 2 هذا فعلا هو عدد
+
+24
+00:03:06,400 --> 00:03:13,130
+حقيقيبنثبت انه يوجد عدد حقيقي اللي هو اسمه جدر
+
+25
+00:03:13,130 --> 00:03:21,050
+اتنين هذا العدد موجود ممكن يعني اثبات انه موجود
+
+26
+00:03:21,050 --> 00:03:30,290
+اذا النظرية هذه بتقول يوجد عدد حقيقي موجب مربع
+
+27
+00:03:30,290 --> 00:03:35,510
+بساوة اتنين بمعنى اخر جدر اتنين هو عدد حقيقي
+
+28
+00:03:38,190 --> 00:03:43,250
+فالبرهان ذلك ده ما .. هذا ما نسميه يعني هنا
+
+29
+00:03:43,250 --> 00:03:48,910
+البرهان constructive proof أو يعني برهان بناء أو
+
+30
+00:03:48,910 --> 00:03:54,670
+بالبناء لأنه بنا نثبت ال existence تبع شغلة فلازم
+
+31
+00:03:54,670 --> 00:03:57,790
+هذا الشغلة اللي بنا نثبت وجودها بنا نبنيها بنا
+
+32
+00:03:57,790 --> 00:04:05,160
+نكونها ففي عملية بناء هناففي البراهين اللي زي هذه
+
+33
+00:04:05,160 --> 00:04:09,740
+بنعرف set وبنعرف شغلات بنثبت أنها هي الحاجات
+
+34
+00:04:09,740 --> 00:04:16,360
+المطلوبة ف let S نعرف مجموعة S على أنها كل العناصر
+
+35
+00:04:16,360 --> 00:04:23,500
+S في R كل الأعداد الحقيقية S اللي بتكون غير سالبة
+
+36
+00:04:23,500 --> 00:04:29,860
+ومربعها أصغر من الإتنين الآن
+
+37
+00:04:29,860 --> 00:04:36,210
+المجموعة هذه غير خاليةليه؟ لأن الواحد .. الواحد
+
+38
+00:04:36,210 --> 00:04:41,650
+ينتمي إلها تعالى نتأكد ليه الواحد ينتمي للست هذه؟
+
+39
+00:04:41,650 --> 00:04:46,890
+لأن الواحد بيحقق الشرقين تبعات الست أول شيء واحد
+
+40
+00:04:46,890 --> 00:04:51,870
+أكبر من أو ساوي سفر هذا صحيح واحد تربية بيساوي
+
+41
+00:04:51,870 --> 00:04:55,390
+واحد أصغر من الأتنين لأن هذه المجموعة فيها على
+
+42
+00:04:55,390 --> 00:05:01,490
+الأقل الواحد وبالتالي هذه مجموعة غير خالية non
+
+43
+00:05:01,490 --> 00:05:02,070
+-empty
+
+44
+00:05:05,790 --> 00:05:16,350
+كذلك المجموعة هذه bounded above by two لو
+
+45
+00:05:16,350 --> 00:05:26,350
+كان بنثبت أن T أصغر من أو يساوي اتنين لكل T في S
+
+46
+00:05:34,900 --> 00:05:38,820
+T أصغر من او سوى اتنين لكل T في S يعني اتنين upper
+
+47
+00:05:38,820 --> 00:05:43,480
+bound لست S فالبرهان
+
+48
+00:05:43,480 --> 00:05:47,700
+ذلك بالتناقض برهنها
+
+49
+00:05:47,700 --> 00:05:53,160
+بالتناقض assume أنه
+
+50
+00:05:53,160 --> 00:06:01,430
+يوجد T0 كيف بتدن في الجملة هذه؟بدل لكل T في S يوجد
+
+51
+00:06:01,430 --> 00:06:08,330
+T0 في S such that T0 بدل أصغر من أو يساوي بيصير
+
+52
+00:06:08,330 --> 00:06:15,030
+أكبر من الأتنين هذا بيقدي أن T0 تربية أكبر من
+
+53
+00:06:15,030 --> 00:06:25,110
+أربعة صح؟ و أربعة أكبر من الأتنين طب T0 هذا ينتمي
+
+54
+00:06:25,110 --> 00:06:35,900
+ل Sمعناته T0 تربيع هذا أصغر من الأتنين صح؟ أظبط؟
+
+55
+00:06:35,900 --> 00:06:39,660
+إذا بيطلع عندى اتنين أكبر من الأتنين اتنين أكبر من
+
+56
+00:06:39,660 --> 00:06:44,720
+الأتنين contradiction تناخد تمام؟ إذا هذا التناخد
+
+57
+00:06:44,720 --> 00:06:45,920
+بيثبت لك ليه؟
+
+58
+00:06:51,390 --> 00:06:55,630
+إذا انا هقدر اقلين بيقوللي ان ال 6S is bounded
+
+59
+00:06:55,630 --> 00:07:05,110
+above by 2 ال 6S محدودة من أعلى by 2 طيب
+
+60
+00:07:05,110 --> 00:07:11,830
+لإن أنا فيه اندي 6S non-empty و bounded aboveإذا
+
+61
+00:07:11,830 --> 00:07:17,190
+by completeness property ال 6S هذه لازم يكون فيه
+
+62
+00:07:17,190 --> 00:07:23,290
+لها supremum it has a supremum in R say دعنا نسميه
+
+63
+00:07:23,290 --> 00:07:28,870
+X إذا ال X اللي هو ال supremum ل S هذا exist in R
+
+64
+00:07:28,870 --> 00:07:34,390
+by completeness property هذا ال X اللي هو ال
+
+65
+00:07:34,390 --> 00:07:42,060
+supremum ل S برضه بطلع أكبر من واحد ليه؟لأن خمسة
+
+66
+00:07:42,060 --> 00:07:47,780
+على أربعة ينتمي ل S عنصر في S لهذا صح تعالى نتأكد
+
+67
+00:07:47,780 --> 00:07:53,080
+الخمسة على أربعة أكبر من أو ساوى سفر وخمسة على
+
+68
+00:07:53,080 --> 00:07:57,040
+أربعة تربيع اللي هو خمسة عشرين على ستاشر أصغر من
+
+69
+00:07:57,040 --> 00:08:03,030
+الإتنينإذن هذا العدد ينتمي ل S وال X هذا supremum
+
+70
+00:08:03,030 --> 00:08:08,870
+ل S وبالتالي X upper bound ل S ال X upper bound ل
+
+71
+00:08:08,870 --> 00:08:14,410
+6S إذن أكبر من أو ساوي كل عناصرها إذن ال X أكبر من
+
+72
+00:08:14,410 --> 00:08:19,070
+أو ساوي خمسة على أربعة وخمسة على أربعة أكبر من
+
+73
+00:08:19,070 --> 00:08:25,470
+واحد إذن X أكبر من واحد تمام؟ إذن هين أثبتنا إن ال
+
+74
+00:08:25,470 --> 00:08:31,610
+6 يوجدعدد حقيقي x اللي هو الـ suprem ل S وهذا الـ
+
+75
+00:08:31,610 --> 00:08:39,910
+x أكبر من واحد الآن هذا الـ x هو .. بنثبت هو الجذر
+
+76
+00:08:39,910 --> 00:08:42,690
+التربيعي للإتنين
+
+77
+00:08:49,400 --> 00:08:53,760
+الان هذا ال X اللي هو طلع موجود by completeness of
+
+78
+00:08:53,760 --> 00:08:58,600
+property وعدد اكبر من واحد بنثبت انه مربع و بساوي
+
+79
+00:08:58,600 --> 00:09:05,180
+اتنين يعني هو العدد المطلوب ان ال X هو جدر اتنين
+
+80
+00:09:11,980 --> 00:09:15,800
+فإذا أثبتنا ال claim هذا بتكون كملنا برهانة نظرية
+
+81
+00:09:15,800 --> 00:09:19,760
+طيب هذا ال claim برضه متبرهن بالتناقض assume ال
+
+82
+00:09:19,760 --> 00:09:25,060
+contrary إن x تربية بسويش اتنين if by tricotomy
+
+83
+00:09:25,060 --> 00:09:30,020
+property إما x تربية أصغر من اتنين أو أكبر من
+
+84
+00:09:30,020 --> 00:09:34,160
+اتنين إذا أنا في عندي حالتين هنا لازم أخدهم في
+
+85
+00:09:34,160 --> 00:09:40,610
+الاعتبارعشان أكمل برهان ال claim الحالة الأولى
+
+86
+00:09:40,610 --> 00:09:47,190
+فيها extra بيها أصغر من الإتنين و بتدصل في الحالة
+
+87
+00:09:47,190 --> 00:09:51,790
+هذه لتناقض عشان أثبت ال claim لإن ال claim بدينا
+
+88
+00:09:51,790 --> 00:09:56,810
+برهانه بالتناقض assume the contrary فرضنا النقيد
+
+89
+00:09:58,620 --> 00:10:02,360
+تعالى نشوف كيف نصل لتناقض في الحالة هذه انا عندي n
+
+90
+00:10:02,360 --> 00:10:07,640
+لكل n عدد طبيعى n تربيع اكبر من او ساوى n و
+
+91
+00:10:07,640 --> 00:10:10,700
+بالتاني مقلوب n تربيع دايما اصغر من او ساوى مقلوب
+
+92
+00:10:10,700 --> 00:10:18,500
+ال n هذا صحيح الان x زائد واحد على n لكل تربيع ربع
+
+93
+00:10:18,500 --> 00:10:23,820
+بطلع x تربيع زاد اتنين زاد ضعف الاول في التانى زاد
+
+94
+00:10:23,820 --> 00:10:31,370
+مربع التانىالان بدي أشيل 1 على n تربية هدي أشيلها
+
+95
+00:10:31,370 --> 00:10:37,250
+و أستبدلها بحاجة أكبر من .. أكبر من او ساوية اللي
+
+96
+00:10:37,250 --> 00:10:42,030
+هو 1 على n لأن هنا لما أستبدل هذه ب1 على n بصير
+
+97
+00:10:42,030 --> 00:10:47,250
+هذا أصغر من او ساوية x تربية زاد 2x على n زاد 1
+
+98
+00:10:47,250 --> 00:10:51,410
+على n و لما أخد من الحدين هدول 1 على n عامل مشترك
+
+99
+00:10:51,410 --> 00:10:53,610
+بيضل 2x زاد 1
+
+100
+00:11:02,350 --> 00:11:07,870
+تمام؟ اذا انا عندي أصبح ال X زاد واحد على M لكل
+
+101
+00:11:07,870 --> 00:11:15,110
+تربية أصغر من أو ساوي المقدار هذا طيب احنا من ال
+
+102
+00:11:15,110 --> 00:11:20,150
+.. احنا فرضين X تربية أصغر من 2 اذا 2 سالب X تربية
+
+103
+00:11:20,150 --> 00:11:25,410
+بيطلع عدد موجبو ال X عدد اكبر من واحد، اذا اتنين X
+
+104
+00:11:25,410 --> 00:11:30,050
+زاد واحد عدد موجب، اذا كسر بسطه موجب و مقامه موجب،
+
+105
+00:11:30,050 --> 00:11:34,330
+بيطلع عدد موجب، اذا حسب ال property اللي انا
+
+106
+00:11:34,330 --> 00:11:38,670
+علمتها بال star لأي
+
+107
+00:11:38,670 --> 00:11:43,530
+عدد موجب، قولنا يوجد عدد طبيعي N0 مقلوب و أصغر من
+
+108
+00:11:43,530 --> 00:11:49,810
+العدد الموجبأدرج الطرفين في العدد الموجود 2x زاد 1
+
+109
+00:11:49,810 --> 00:11:56,990
+بصير المتباينة هذه شكلها هكذا الان
+
+110
+00:11:56,990 --> 00:12:01,710
+من المتباينة تلاتة هاي المتباينة تلاتة هاي عندي x
+
+111
+00:12:01,710 --> 00:12:05,590
+انا
+
+112
+00:12:05,590 --> 00:12:11,000
+عندي يوجد in zero ينتمي ل inطبعا هذا الكلام
+
+113
+00:12:11,000 --> 00:12:15,160
+المتباينة تلاتة هذه صحيحة لكل العداد الطبيعي N
+
+114
+00:12:15,160 --> 00:12:21,240
+وبالتالي صحيحة للعدد الطبيعي N0 إذا نتعالوا نقرأ
+
+115
+00:12:21,240 --> 00:12:26,380
+المتباينة تلاتة ونبدل N ب N0 فبصير X زاد واحد على
+
+116
+00:12:26,380 --> 00:12:29,840
+N0 ترديد أصغر من
+
+117
+00:12:34,400 --> 00:12:39,760
+مفروض أصغر منها يساوي X تربية زياد واحد على N Zero
+
+118
+00:12:39,760 --> 00:12:47,860
+في اتنين X زياد واحد وواحد
+
+119
+00:12:47,860 --> 00:12:53,640
+على N Zero في اتنين X زياد واحد أصغر من اتنين سالب
+
+120
+00:12:53,640 --> 00:13:00,200
+X تربية إذن هذا هيصير أصغر من اتنين سالب X تربية Y
+
+121
+00:13:00,200 --> 00:13:02,880
+X تربية اللي هو بيطلع اتنين
+
+122
+00:13:08,840 --> 00:13:14,640
+إذا أنا في عندي الآن عدد العدد اللي هو X زياد واحد
+
+123
+00:13:14,640 --> 00:13:21,600
+على N Zero مربعه أصغر من الإتنين إذا هذا العدد
+
+124
+00:13:21,600 --> 00:13:25,320
+اللي هو X زياد واحد على N Zero هو عدد غير سالب
+
+125
+00:13:25,320 --> 00:13:29,320
+ومربعه أصغر من الإتنين إذا هذا ينتمي للمجموع S
+
+126
+00:13:29,320 --> 00:13:33,880
+اللي عرفته في بداية البرهان إذا هذا العدد ينتمي
+
+127
+00:13:33,880 --> 00:13:34,920
+للمجموع S
+
+128
+00:13:37,690 --> 00:13:44,950
+و هذا بي .. بيقدّي انه ال .. العدد هذا مش ممكن
+
+129
+00:13:44,950 --> 00:13:53,790
+يكون upper bound للست S هذا
+
+130
+00:13:53,790 --> 00:13:58,650
+مش ممكن يكون upper bound للست S لأن ال X هو upper
+
+131
+00:13:58,650 --> 00:14:04,390
+bound هو ال supreme و
+
+132
+00:14:04,390 --> 00:14:05,850
+بالتالي
+
+133
+00:14:14,060 --> 00:14:18,100
+إحنا أثبتنا إن X هي ال upper bound لكن لجينا X زاد
+
+134
+00:14:18,100 --> 00:14:22,100
+واحد على N not هي ثانوية ل S فبالتالي في عنصر أكبر
+
+135
+00:14:22,100 --> 00:14:31,140
+من X فهذا ال contradiction مظبوط لأن هذا
+
+136
+00:14:31,140 --> 00:14:38,730
+عنصر في S وبالتالي هذا بيقدّي هذا بيقدّيإن X
+
+137
+00:14:38,730 --> 00:14:47,890
+ماهواش upper bound لأنه ال X أصغر من واحد من X
+
+138
+00:14:47,890 --> 00:14:54,650
+زائد واحد على N زيرو وهذا
+
+139
+00:14:54,650 --> 00:14:55,590
+ينتمي ل S
+
+140
+00:15:01,160 --> 00:15:06,760
+فهذا عنصر في S و أكبر من X هذا معناه ان ال X هذا
+
+141
+00:15:06,760 --> 00:15:12,420
+مش ممكن يكون upper bound ل S وهذا بتناقض مع كون X
+
+142
+00:15:12,420 --> 00:15:18,160
+هو upper bound لأنه supreme ل S احنا قلنا ان ال X
+
+143
+00:15:18,160 --> 00:15:22,840
+هذا اللي في ال claim ايه ال X هذا هو supreme ل S
+
+144
+00:15:22,840 --> 00:15:27,180
+وبالتالي upper bound ل Sو هنا وصلنا لأن ال X مش
+
+145
+00:15:27,180 --> 00:15:31,160
+ممكن يكون upper bound ل S لأنه أصغر من عنصر ما
+
+146
+00:15:31,160 --> 00:15:34,720
+ينتمي ل S إذا فيه تناقض لأن هنا وصلنا إلى
+
+147
+00:15:34,720 --> 00:15:41,480
+contradiction إذا فرضنا X بيه أصغر من 2 وصلتنا ل
+
+148
+00:15:41,480 --> 00:15:46,760
+contradiction بالمثل بالمثل
+
+149
+00:15:46,760 --> 00:15:51,480
+في الحالة التانية في
+
+150
+00:15:51,480 --> 00:15:56,980
+الحالة التانيةلو فرضنا ان x ثربيه المرة دي اكبر من
+
+151
+00:15:56,980 --> 00:16:03,100
+الاتنين فبرضه ممكن نصل بنفس الطريقة و بنفس الاسلوب
+
+152
+00:16:03,100 --> 00:16:09,220
+في النهاية الى contradiction نصل الى contradiction
+
+153
+00:16:09,220 --> 00:16:15,100
+وبالتالي اذا احنا فرضنا انه احنا كنا كان ال claim
+
+154
+00:16:15,100 --> 00:16:20,520
+تبعناالذكروا في البرنامج احنا كنا عايزين نثبت ان x
+
+155
+00:16:20,520 --> 00:16:26,060
+تربية بساوة اتنين ففرضنا ان x تربية لات ساوة اتنين
+
+156
+00:16:26,060 --> 00:16:33,520
+وبالتالي هذا بيقدر ان x تربية اصغر من اتنين او x
+
+157
+00:16:33,520 --> 00:16:38,200
+تربية اكبر من اتنين وفي كل حالة من الحالات هذه
+
+158
+00:16:38,200 --> 00:16:43,520
+وصلنا الى تناقضإذا التناقض هذا سببه انه اذا احنا
+
+159
+00:16:43,520 --> 00:16:49,620
+فرضنا هو فرضنا ان extra b لايه ساو اتنين هذا بثبت
+
+160
+00:16:49,620 --> 00:16:54,980
+ال claim اللي هو extra b بساو اتنين و بكمل البرهان
+
+161
+00:16:54,980 --> 00:17:03,440
+okay تمام إذا هذا هو برهان ال .. النظرية هذه إذا
+
+162
+00:17:03,440 --> 00:17:09,440
+الأن أصبح عندي في نظريتين واحدة بتقول انهجذر اتنين
+
+163
+00:17:09,440 --> 00:17:14,660
+هو عدد حقيقي ونظرية
+
+164
+00:17:14,660 --> 00:17:19,300
+تانية او حقيقة تانية ان جذر اتنين ليس عدد نصي
+
+165
+00:17:36,150 --> 00:17:44,930
+طيب في كمان نتيجة مهمة على النتائج هذه او نظرية
+
+166
+00:17:44,930 --> 00:17:49,490
+مهمة اللي هي density theorem نظرية الكثافة ال
+
+167
+00:17:49,490 --> 00:17:55,530
+density theorem ال density theorem بتقول بين اي
+
+168
+00:17:55,530 --> 00:18:01,230
+عددين حقيقيين يوجد عدد مثل يعني لو انا في عندى
+
+169
+00:18:02,110 --> 00:18:11,650
+عددين حقيقيين X أصغر من Y هاي X وهاي Y فيوجد عدد
+
+170
+00:18:11,650 --> 00:18:20,390
+نسبي R ينتمي لـ Q بحيث أن R أكبر من X أصغر من Y أو
+
+171
+00:18:20,390 --> 00:18:27,320
+بمعنى آخر، لو في عندي فترة مفتوحة X وYفلازم هذه
+
+172
+00:18:27,320 --> 00:18:34,100
+الفترة وفي هذه الفترة غير خالية فلازم نلاقي R
+
+173
+00:18:34,100 --> 00:18:41,700
+ينتمي للفترة المفتوحة و R هذا عدد نسمة اذا ال
+
+174
+00:18:41,700 --> 00:18:45,520
+density theorem بكل بساطة بتقول between any two
+
+175
+00:18:45,520 --> 00:18:50,990
+real numbers there exists a rational number اوAny
+
+176
+00:18:50,990 --> 00:18:55,030
+non-empty open interval contains a rational number
+
+177
+00:18:55,030 --> 00:19:02,170
+نفس الصيرة أو نفس ال statement البرهان مش صعب
+
+178
+00:19:02,170 --> 00:19:05,210
+تعالى
+
+179
+00:19:05,210 --> 00:19:10,410
+نشوف البرهان أنا عندي فرض ان X أصغر من Y فرض X
+
+180
+00:19:10,410 --> 00:19:16,790
+أصغر من Yو بالتالي y سالب x عدد موجب اذا by the
+
+181
+00:19:16,790 --> 00:19:20,330
+Archimedean property بقدر الاقي عدد هنا المفروض
+
+182
+00:19:20,330 --> 00:19:28,050
+يكون جزء b فby
+
+183
+00:19:28,050 --> 00:19:31,590
+Archimedean property واحد ستاشر بيه اللي اعطيناها
+
+184
+00:19:31,590 --> 00:19:37,930
+إشارة نجمة لأي عدد موجب زي هذا يوجد عدد طبيعي n
+
+185
+00:19:37,930 --> 00:19:45,930
+مقلوب وأصغر من عدد الموجبالان بدي اعرف ان اكبر عدد
+
+186
+00:19:45,930 --> 00:19:50,190
+صحيح اصغر من او يساوي n x هذه دالة اكبر عدد صحيح
+
+187
+00:19:50,190 --> 00:19:55,290
+واضيف عليها واحد طبعا هذا عدد صحيح زائد واحد
+
+188
+00:19:55,290 --> 00:19:59,930
+الواحد عدد صحيح فمجموعهم بطلع عدد صحيح اذا انا
+
+189
+00:19:59,930 --> 00:20:04,250
+عرفت عدد صحيح m ينتمي الى z على انه the greatest
+
+190
+00:20:04,250 --> 00:20:09,110
+integer less than or equal to n x plus oneالان
+
+191
+00:20:09,110 --> 00:20:16,650
+بتثبت انه في عندى claim بتثبت ان هذا العدد m بيحقق
+
+192
+00:20:16,650 --> 00:20:22,110
+المتباينة هذه اذا
+
+193
+00:20:22,110 --> 00:20:31,330
+انا عايز اثبت انه ال claim تبعى one انه m negative
+
+194
+00:20:31,330 --> 00:20:35,850
+one less than or equal n x less than m
+
+195
+00:20:39,470 --> 00:20:46,730
+طيب من تعريف دالة أكبر عدد صحيح by definition of
+
+196
+00:20:46,730 --> 00:20:52,970
+the greatest integer function هذا العدد دايما أكبر
+
+197
+00:20:52,970 --> 00:20:58,150
+من نفسه الأدد اللي جوا سالب واحد وأصغر من أو ساوي
+
+198
+00:20:58,150 --> 00:21:05,870
+نفسه صح؟هذا العدد أكبر عدد صحيح أصغر من أو ساوي NX
+
+199
+00:21:05,870 --> 00:21:11,970
+يعني نفسر نفسه إذا هذا العدد أصغر من أو ساوي NX و
+
+200
+00:21:11,970 --> 00:21:18,250
+أكبر من NX للمطرح منها واحد طيب ننجل الواحد عن
+
+201
+00:21:18,250 --> 00:21:22,970
+ناحية التانية فبصرا اندي NX أصغر من أكبر عدد صحيح
+
+202
+00:21:22,970 --> 00:21:28,690
+أصغر من أو ساوي NX زاد واحدوهذا من هنا أصغر من أو
+
+203
+00:21:28,690 --> 00:21:39,010
+يساوي NX زايد واحد الان هذا سمينا احنا هذا M فبطلع
+
+204
+00:21:39,010 --> 00:21:45,930
+عندي M أكبر من NX أصغر من أو يساوي NX زايد واحد
+
+205
+00:21:45,930 --> 00:21:54,340
+نطرح واحد من كل الأطراف فبطلع عندي M سالب واحدم
+
+206
+00:21:54,340 --> 00:22:02,180
+سالب واحد اصغر من او ساوي نكس و نكس من هنا نكس
+
+207
+00:22:02,180 --> 00:22:09,160
+اصغر من م وهذا اللي بدنا يقنعه لان هنا برهن ال
+
+208
+00:22:09,160 --> 00:22:13,200
+claim لان
+
+209
+00:22:13,200 --> 00:22:18,960
+من هذا ال claim من
+
+210
+00:22:18,960 --> 00:22:21,800
+هذا ال claim نستنتج
+
+211
+00:22:24,560 --> 00:22:33,840
+هذه الكلام اللي برهناه لو أنا ضربت ..
+
+212
+00:22:33,840 --> 00:22:37,100
+لو
+
+213
+00:22:37,100 --> 00:22:43,940
+ضفت واحد لكل الأطراف فبصير عندي M أصغر من أو يساوي
+
+214
+00:22:43,940 --> 00:22:50,160
+NX زايد واحد أصغر من M زايد واحد
+
+215
+00:22:56,000 --> 00:23:05,300
+و لو جسمت على N أو ضربت في N نضرب في 1 على N فهذا
+
+216
+00:23:05,300 --> 00:23:15,400
+بيقدر ان M على N أصغر من أو يساوي X زائد 1 على N
+
+217
+00:23:26,950 --> 00:23:31,950
+طيب انا عندي .. انا
+
+218
+00:23:31,950 --> 00:23:34,110
+عندي من نفس المتباينة هذه
+
+219
+00:24:07,700 --> 00:24:15,700
+أنا عندي 1 على n أصغر من y minus x أنا
+
+220
+00:24:15,700 --> 00:24:23,580
+عندي 1 على n 1 على n أصغر من y سالب x هذا بيقدي
+
+221
+00:24:23,580 --> 00:24:33,260
+أنه x زاد 1 على n أصغر من y لأن هذا أصغر من y تمام
+
+222
+00:24:39,380 --> 00:24:45,180
+هو أكبر من X نعم؟ هو أكبر من X لأن X هيت واحدة
+
+223
+00:24:45,180 --> 00:24:55,720
+عنها اه و بدي هذا يكون أكبر من X اه
+
+224
+00:24:55,720 --> 00:25:02,780
+M على N أكبر اه من هنا من
+
+225
+00:25:02,780 --> 00:25:10,740
+هنا اجسم على M لما أضرب في واحد على Nفبصير عندي M
+
+226
+00:25:10,740 --> 00:25:17,860
+على N أكبر من X نظمت هيك صح؟ إذا أصبح عندي أنا
+
+227
+00:25:17,860 --> 00:25:25,220
+بحصل على X أصغر من M على N أصغر من Y الآن هذا
+
+228
+00:25:25,220 --> 00:25:33,060
+عبارة عن عدد نسبي هذا هو هذا العدد هو ال R هذا عدد
+
+229
+00:25:33,060 --> 00:25:38,000
+نسبي لأن عدد النسبي عبارة عن عدد صحيح على عدد صحيح
+
+230
+00:25:38,000 --> 00:25:44,470
+لا يساوي سفرإذن هذه أثبتت إن يوجد عدد نسبي أكبر من
+
+231
+00:25:44,470 --> 00:25:49,790
+X وأصغر من Y أو يوجد عدد نسبي بين X وY إذن هذا
+
+232
+00:25:49,790 --> 00:26:02,470
+بيكمل البرهان تبع ال density theorem في
+
+233
+00:26:02,470 --> 00:26:07,870
+كمان نتيجة تانية برضه بنسميها density theorem أو
+
+234
+00:26:07,870 --> 00:26:11,800
+نتيجة على ال density theoremو في بعض الناس برضه
+
+235
+00:26:11,800 --> 00:26:15,620
+نفسها بيسموها density theorem ف ال density theorem
+
+236
+00:26:15,620 --> 00:26:19,100
+هذه التانية أو النتيجة عليها بتقول ان بين اي
+
+237
+00:26:19,100 --> 00:26:24,440
+between any two real numbers x and y there exists
+
+238
+00:26:24,440 --> 00:26:29,860
+an irrational number يوجد عدد z بين x و y وهذا z
+
+239
+00:26:29,860 --> 00:26:36,100
+irrational number اذا
+
+240
+00:26:36,100 --> 00:26:47,170
+كمان مرةلو في عندى اي عددين حقيقيين x و y هو
+
+241
+00:26:47,170 --> 00:26:56,830
+x أصغر من y فبنقدر نلاقي r أو p وهذا ينتمي ل r
+
+242
+00:26:56,830 --> 00:27:06,170
+minus q عدد غير نسبي بين أكبر من x و أصغر من y
+
+243
+00:27:07,390 --> 00:27:12,950
+البرهان تبع النتيجة هذه اول
+
+244
+00:27:12,950 --> 00:27:18,050
+شي احنا لسه مثبتين قبل شوية ان جدر اتنين is a real
+
+245
+00:27:18,050 --> 00:27:22,730
+number جدر اتنين كان هو supremum ل 6 وبالتالي
+
+246
+00:27:22,730 --> 00:27:27,690
+exist in R واثبتنا ان جدر اتنين هذا اكبر من صفر
+
+247
+00:27:27,690 --> 00:27:31,910
+حتى اثبتنا انه اكبر من واحد كان ال X اكبر من واحد
+
+248
+00:27:31,910 --> 00:27:37,900
+وبالتالي موجةإن جدر اتنين عدد موجب وبالتالي مقلوبه
+
+249
+00:27:37,900 --> 00:27:46,480
+عدر موجب لإن أنا لما يكون عندي x أصغر من y و أضرب
+
+250
+00:27:46,480 --> 00:27:50,440
+المتباينة هذه في واحد على جدر اتنين اللي هو عدد
+
+251
+00:27:50,440 --> 00:27:55,040
+موجب فتصير المتباينة هذه x على جدر اتنين أصغر من y
+
+252
+00:27:55,040 --> 00:28:01,030
+على جدر اتنينتمام الان اذا هذا real number وهذا
+
+253
+00:28:01,030 --> 00:28:05,630
+real number by density theorem between any two
+
+254
+00:28:05,630 --> 00:28:09,270
+real numbers there exist irrational number عدد
+
+255
+00:28:09,270 --> 00:28:13,750
+نسبي سمي R طبعا هذا العدد النسبي لا يساوي سفر لان
+
+256
+00:28:13,750 --> 00:28:20,170
+دي عداد موجة باتنين اذا انا في عندي عدد نسبي R بين
+
+257
+00:28:20,170 --> 00:28:25,310
+العددين الحقيقين حسب ال density theorem الان لو
+
+258
+00:28:25,310 --> 00:28:32,530
+اخدت لو عرفتلو عرفت العدد z على انه r ضرب جذر
+
+259
+00:28:32,530 --> 00:28:38,110
+اتنين فهذا بيطلع عدد غير نسبي تعالوا نبرهم ذلك
+
+260
+00:28:38,110 --> 00:28:42,950
+لإثبات ان العدد z اللي هو r في جذر اتنين عدد غير
+
+261
+00:28:42,950 --> 00:28:49,210
+نسبي افرض otherwise يعني خلاف ذلك افرض خلاف ذلك
+
+262
+00:28:49,210 --> 00:28:56,250
+يعني افرض ان العدد هذا نسبي افرض
+
+263
+00:28:56,250 --> 00:29:02,030
+ان هذا نسبيإذا لما جسمه هذا هو R في جدر اتنين عدد
+
+264
+00:29:02,030 --> 00:29:08,130
+نسبي و R احنا فرضيه و R طبعا هذا عدد نسبي إذا عدد
+
+265
+00:29:08,130 --> 00:29:11,770
+نسبي على عدد نسبي بيطلع عدد نسبي إذا هذا هيطلع عدد
+
+266
+00:29:11,770 --> 00:29:15,810
+نسبي اللي هو بيساوي جدر اتنين وهذا تناقض مع
+
+267
+00:29:15,810 --> 00:29:21,490
+الحقيقة اللي أثبتناها سابقا إذا .. إذا هذا العدد
+
+268
+00:29:21,490 --> 00:29:28,090
+لازم .. مش ممكن يكون نسبي لازم يكون غير نسبي طيب
+
+269
+00:29:31,920 --> 00:29:37,240
+أضرب المتباينة هذه في
+
+270
+00:29:37,240 --> 00:29:42,500
+جدر اتنين لو ضربنا المتباينة هذه في جدر اتنين
+
+271
+00:29:42,500 --> 00:29:45,620
+فبصير
+
+272
+00:29:45,620 --> 00:29:52,440
+عندي X أصغر من R في جدر اتنين اللي سمناها Z أصغر
+
+273
+00:29:52,440 --> 00:29:53,340
+من Y
+
+274
+00:29:55,970 --> 00:30:00,250
+وبالتالي هنا أثبتنا أن يوجد عدد غير نسبي وهذا
+
+275
+00:30:00,250 --> 00:30:05,710
+العدد الغير نسبي between X and Y وهو المطلوب هذا
+
+276
+00:30:05,710 --> 00:30:10,870
+هو المطلوب تمام؟
+
+277
+00:30:10,870 --> 00:30:14,250
+في
+
+278
+00:30:14,250 --> 00:30:22,590
+أي سؤال أو استفسار؟ إن ذلك يكون احنا خلصنا أربع
+
+279
+00:30:22,590 --> 00:30:29,150
+سكاش م الشتر واحدو هاي في تمارين على ال section
+
+280
+00:30:29,150 --> 00:30:40,510
+هذا و نبدأ section جديد ال
+
+281
+00:30:40,510 --> 00:30:43,950
+section الجديد هذا بتحدث عن ال intervals الفترات
+
+282
+00:30:43,950 --> 00:30:50,710
+طبعا كلكم درستوا تفاضل و تكامل و مرت عليكم أنواع
+
+283
+00:30:50,710 --> 00:30:59,210
+الفترات في course تفاضل و تكامللو أخذت اي عددين
+
+284
+00:30:59,210 --> 00:31:08,710
+حقيقياً a و b و a أصغر من أو ساول b فممكن نعرف ال
+
+285
+00:31:08,710 --> 00:31:13,730
+open interval على أن كل العداد الحقيقية x اللي بين
+
+286
+00:31:13,730 --> 00:31:20,010
+a و b فهذا ال open interval from a to b و فيه ممكن
+
+287
+00:31:20,010 --> 00:31:24,580
+نعرف closed interval from a to bعلى انها كل ال
+
+288
+00:31:24,580 --> 00:31:27,820
+real numbers اللي أكبر من أو ساوي a أصغر من أو
+
+289
+00:31:27,820 --> 00:31:34,880
+ساوي b ال half open فيه برضه نوع من الفترات بنسميه
+
+290
+00:31:34,880 --> 00:31:42,700
+half open أو half closed على الصورة هذه .. هذه
+
+291
+00:31:42,700 --> 00:31:47,890
+بنسميها half openأو half closed يعني مفتوحة من جهة
+
+292
+00:31:47,890 --> 00:31:53,010
+ومغلقة من جهة أخرى فهذه طبعا واضح تعريفة كل ال X
+
+293
+00:31:53,010 --> 00:31:59,250
+اللي أكبر من A أثر من أو ساوى B وهذه زيها في كمان
+
+294
+00:31:59,250 --> 00:32:05,650
+نوع أخر من ال intervals زي ال interval هذه بسميها
+
+295
+00:32:05,650 --> 00:32:14,430
+open left ray شعاع أيصر مفتوح يعني هايخط الأعداد
+
+296
+00:32:14,430 --> 00:32:18,970
+ليه بيسموها left ray لأن فعلا قاملة زي الشعار هاي
+
+297
+00:32:18,970 --> 00:32:26,830
+هذا خط الأعداد وهي بي عدد حقيقي فالفترة المفتوحة
+
+298
+00:32:26,830 --> 00:32:32,370
+من سالب من النهاية إلى بي هي الفترة هذه هي مصدر
+
+299
+00:32:32,370 --> 00:32:36,350
+الصورة أن هنا في مصدر ضوء وهذا الضوء بيشع إلى
+
+300
+00:32:36,350 --> 00:32:43,140
+اليسارفهذه الفترة هي من سالب مقالة نهاية إلى B
+
+301
+00:32:43,140 --> 00:32:48,580
+open interval صح؟
+
+302
+00:32:48,580 --> 00:32:53,400
+كل الأعداد الحقيقية اللي أصغر من B إذن هذه تعريفها
+
+303
+00:32:53,400 --> 00:32:57,460
+كل الأعداد الحقيقية اللي أصغر من B بالمثل ممكن أن
+
+304
+00:32:57,460 --> 00:33:06,040
+أعرف right ray right ray زي ذلك يعني D ومقالة
+
+305
+00:33:06,040 --> 00:33:11,230
+نهايةأو A وما إلى نهاية كل الإعداد الحقيقي اللي
+
+306
+00:33:11,230 --> 00:33:13,190
+أكبر أو على يمين ال A
+
+307
+00:33:16,510 --> 00:33:21,690
+طبعا ممكن نعرف closed left tray لأن لو أخلت النقطة
+
+308
+00:33:21,690 --> 00:33:28,090
+هذه موجودة ضمن الفترة يعني أغلقت الفترة زيك فهذه
+
+309
+00:33:28,090 --> 00:33:32,890
+بسميها closed left tray و كذلك لو أخدت ال beam
+
+310
+00:33:32,890 --> 00:33:37,730
+أضفتها على الفترة فهذه بسميها closed right tray
+
+311
+00:33:37,730 --> 00:33:45,660
+وفي طبعا هذه ال ..الـ two-sided ray إي ده صح
+
+312
+00:33:45,660 --> 00:33:51,000
+التعبير اللي هو خط الأعداد كله كل الأعداد بحثوا في
+
+313
+00:33:51,000 --> 00:33:54,060
+ملاحظة
+
+314
+00:33:54,060 --> 00:34:01,860
+هنا أن الأول تلت أنواع من ال intervals هدول نسميهم
+
+315
+00:34:01,860 --> 00:34:05,580
+bounded هم
+
+316
+00:34:05,580 --> 00:34:11,460
+فعلا bounded الفترات هذه محصورة محدودة ممكن نحصرها
+
+317
+00:34:13,670 --> 00:34:19,010
+أما الأنواع .. الأنواع ال .. ال .. الأخرى الخامسة
+
+318
+00:34:19,010 --> 00:34:25,350
+الأخرى هذه unbounded .. unbounded
+
+319
+00:34:25,350 --> 00:34:29,030
+غير
+
+320
+00:34:29,030 --> 00:34:33,230
+محصورة و غير محدودة الفترات هذه غير محدودة هذا
+
+321
+00:34:33,230 --> 00:34:37,810
+شعاع أيصر، لاحظ الشعاع هذا مقدرش ايه أcipher عليه
+
+322
+00:34:39,020 --> 00:34:44,220
+يعني بيمتد إلى سالب من النهاية أو بيمتد إلى من
+
+323
+00:34:44,220 --> 00:34:49,580
+النهاية، إذا الفترات هذه unbounded، النوح هذا من
+
+324
+00:34:49,580 --> 00:34:53,580
+الفترات bounded وبالتالي الفترات متجسمة إلى two
+
+325
+00:34:53,580 --> 00:34:58,260
+types bounded intervals وunbounded intervals
+
+326
+00:35:13,980 --> 00:35:26,320
+طيب في ملاحظة هنا على الفترات لو
+
+327
+00:35:26,320 --> 00:35:29,740
+أخدت أي interval بغض النظر هل هي bounded ولا
+
+328
+00:35:29,740 --> 00:35:35,200
+unbounded open, closed, half-open, half-closed بغض
+
+329
+00:35:35,200 --> 00:35:39,280
+النظر أي واحدة من الأنواع التمانية اللي شفناهم لو
+
+330
+00:35:39,280 --> 00:35:48,350
+I كانت أي intervalف ال interval I بتحقق الخصية هذه
+
+331
+00:35:48,350 --> 00:35:54,130
+اي interval بتحقق الخصية هذه ان انا لو اخدت اي
+
+332
+00:35:54,130 --> 00:36:00,070
+انصرين في الفترة و واحد اصغر من التاني فالعناصر
+
+333
+00:36:00,070 --> 00:36:05,770
+اللي بينهم بتكون موجودة في الفترة يعني هي ان عندي
+
+334
+00:36:05,770 --> 00:36:11,730
+فترة مفتوحة مغلقة او
+
+335
+00:36:13,570 --> 00:36:20,230
+left ray مثلا و
+
+336
+00:36:20,230 --> 00:36:29,330
+ال symbol فترة هذه مثلا a,b او مثلا high b فلو
+
+337
+00:36:29,330 --> 00:36:34,790
+أخدت سواء هذه الفترة او هذه او اي واحدة من انواع
+
+338
+00:36:34,790 --> 00:36:44,960
+التمنية و جيت أخدت عنصرين x و yو X أصغر من Y
+
+339
+00:36:44,960 --> 00:36:50,660
+موجودين في الفترة هذه فالفترة هذه بتتمتع بالخاصية
+
+340
+00:36:50,660 --> 00:36:58,480
+أن أي عنصر في الفترة هذه المغلقة من X و Y لو أخدت
+
+341
+00:36:58,480 --> 00:37:05,200
+أي تي يعني كل عناصر الفترة المغلقة هذه كلها بتطلع
+
+342
+00:37:05,200 --> 00:37:11,840
+موجودة في الفترة الكبيرة نفس الحاجة هنا هاي أخدي X
+
+343
+00:37:13,020 --> 00:37:24,020
+هو Y فكل العناصر T في الفترة المغلقة موجودة
+
+344
+00:37:24,020 --> 00:37:33,590
+في lift-ray اذا اي فترة Iلو أخدت داخلها أي عنصرين
+
+345
+00:37:33,590 --> 00:37:37,910
+X أزرع من Y فكل العناصر في الفترة المغلقة من X ل Y
+
+346
+00:37:37,910 --> 00:37:42,050
+أو الفترة المغلقة من X ل Y تطلع مجموعة جزئية من
+
+347
+00:37:42,050 --> 00:37:48,710
+الفترة اللي أنا ماخدها okay؟ الآن نظرية أشر أخر من
+
+348
+00:37:48,710 --> 00:37:57,000
+عشرين بتقوللي أنه العكس صحيح العكس صحيح يعنيلو أنا
+
+349
+00:37:57,000 --> 00:38:02,320
+فيه عندي مجموعة جزئية S مجموعة جزئية من R ال
+
+350
+00:38:02,320 --> 00:38:07,140
+cardinal number تبع S أكبر من أوي ساوى اتنين ال
+
+351
+00:38:07,140 --> 00:38:10,780
+cardinal number هنا يعني معناته عدد عناصر ال set
+
+352
+00:38:10,780 --> 00:38:15,740
+تجربة
+
+353
+00:38:15,740 --> 00:38:21,720
+يعني roughly speaking يعني معناه انه يعني اذا كانت
+
+354
+00:38:21,720 --> 00:38:25,460
+ال set finite فهذا عدد عناصرها is infinite طبعا
+
+355
+00:38:26,560 --> 00:38:37,180
+بيكون يعني له تعريف عام من عدد العناصر فده كانت S
+
+356
+00:38:37,180 --> 00:38:41,200
+مجموعة جزئية و cardinalها أكبر من أو ساو اتنين
+
+357
+00:38:41,200 --> 00:38:48,380
+يعني المجموعة فيها على الأقل عنصرين أو أكتر وكانت
+
+358
+00:38:48,380 --> 00:38:52,980
+المجموعة S هذه بتحقق الخاصية أربعة
+
+359
+00:38:55,110 --> 00:39:01,230
+فلازم ال 6 هذه تطلع interval كمان مرة احنا قلنا في
+
+360
+00:39:01,230 --> 00:39:08,050
+الملاحظة هذه اي interval بتحقق خاصية 4 اللي
+
+361
+00:39:08,050 --> 00:39:13,310
+شرحناها هنا الان العكس لو في عندي مجموعة جزئية S
+
+362
+00:39:13,310 --> 00:39:17,530
+من R انا مش عارف انها فترة ولا لا مجرد مجموعة
+
+363
+00:39:17,530 --> 00:39:22,510
+جزئية من R وفيها على الأقل عنصرين تحتوي على الأقل
+
+364
+00:39:22,510 --> 00:39:23,650
+عنصرين او اكتر
+
+365
+00:39:26,310 --> 00:39:31,210
+وإذا كانت المجموعة الجزئية S هذه بتحقق خاصية أربعة
+
+366
+00:39:31,210 --> 00:39:38,390
+فلازم هذه الست S تطلع فترة واحدة من الفترات
+
+367
+00:39:38,390 --> 00:39:43,970
+التمانية وبرهان
+
+368
+00:39:43,970 --> 00:39:54,130
+النظرية هذه برضه برهان طويل شوية لكن بعتمد
+
+369
+00:39:54,130 --> 00:40:01,730
+على أربعةأربع حالات فمن
+
+370
+00:40:01,730 --> 00:40:08,250
+جسم البرهان إلى أربع حالات الحالة الأولى ان ال set
+
+371
+00:40:08,250 --> 00:40:14,070
+S بتكون bounded محصورة ال set بتكون bounded إذا
+
+372
+00:40:14,070 --> 00:40:19,030
+كانت bounded above and bounded below أو S is
+
+373
+00:40:19,030 --> 00:40:24,090
+bounded above but not below يعني محدودا من أعلى
+
+374
+00:40:24,090 --> 00:40:29,760
+وليست محدودا من أسفلوهذا وارد أو S is bounded
+
+375
+00:40:29,760 --> 00:40:33,280
+below but not above يعني محدودا من أسفل وليست
+
+376
+00:40:33,280 --> 00:40:37,520
+محدودا من الأعلى الحالة الرابعة أن S تكون neither
+
+377
+00:40:37,520 --> 00:40:41,180
+bounded above nor below يعني لا محدودا من أسفل ولا
+
+378
+00:40:41,180 --> 00:40:45,200
+محدودا من الأعلى زي R زي مجموعة الأداء من حفظين
+
+379
+00:40:45,200 --> 00:40:52,670
+تمام؟ وفي كل حالة بنا نثبت أن S تطلع فترةفي كل
+
+380
+00:40:52,670 --> 00:40:58,750
+حالة بنا نثبت المقاس تطلع فترة فيعني هاي انا
+
+381
+00:40:58,750 --> 00:41:04,130
+مثبتلكم الحالة الأولى و التانية و الحالتين التالتة
+
+382
+00:41:04,130 --> 00:41:11,330
+و الرابعة ممكن يعني برهانهم بالمثل فحدؤوكم تقرؤوا
+
+383
+00:41:11,330 --> 00:41:16,450
+البرهان لأن هذا البرهان مجرد تفاصيلات حدؤوكم انكم
+
+384
+00:41:16,450 --> 00:41:18,870
+تقرؤوا البرهان تفهموه لأنه مش هشلحهم
+
+385
+00:41:21,750 --> 00:41:25,570
+فحاولوا تقرؤوه تفهموه و انا متأكد انكم هتفهموه
+
+386
+00:41:25,570 --> 00:41:28,910
+فنتوقف
+
+387
+00:41:28,910 --> 00:41:33,130
+عند هذا .. نكتفي بهذا القدر و ان شاء الله المرة
+
+388
+00:41:33,130 --> 00:41:36,850
+الجاية هنتحدث
+
+389
+00:41:36,850 --> 00:41:43,510
+عن موضوع nested intervals okay؟ في حد عنده اي سؤال
+
+390
+00:41:43,510 --> 00:41:44,330
+او صف سؤال؟
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tKghhKfPOf0.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tKghhKfPOf0.srt
new file mode 100644
index 0000000000000000000000000000000000000000..8aa8c205cbd9fddf26a9a0c1e8f7a582d308a665
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tKghhKfPOf0.srt
@@ -0,0 +1,1399 @@
+1
+00:00:21,680 --> 00:00:30,360
+بسم الله الرحمن الرحيم في اللقاء هذا هنحاول نكمل
+
+2
+00:00:30,360 --> 00:00:35,700
+ما بدأناه في section خمسة اثنين آخر نظرية أخذناها
+
+3
+00:00:35,700 --> 00:00:39,700
+في المحاضرة السابقة كانت الـ boundedness theorem
+
+4
+00:00:39,700 --> 00:00:45,160
+بتقول لو كان في أي  f function continuous على ال
+
+5
+00:00:45,160 --> 00:00:50,080
+interval I و الـ interval I is closed and bounded
+
+6
+00:00:50,080 --> 00:00:56,000
+فالـ function بتطلع bounded على الفترة I مبرهنة
+
+7
+00:00:56,000 --> 00:01:04,100
+نظرية في اللقاء السابق الآن في شوية ملاحظات في ال
+
+8
+00:01:04,100 --> 00:01:08,260
+boundedness theorem في النظرية هذه أي شرط من
+
+9
+00:01:08,260 --> 00:01:13,330
+الشروط الـ boundedness و الـ closed و الاتصال تبعد
+
+10
+00:01:13,330 --> 00:01:18,590
+الدالة على الفترة I أي شرط لو أي شرط من الشروط هذه
+
+11
+00:01:18,590 --> 00:01:24,890
+نجد أو اختلف فالنظرية تفشل ما تبقى نظرية بصير
+
+12
+00:01:24,890 --> 00:01:33,790
+ما لهاش معنى فعلى سبيل المثال لو كانت الفترة ما هيش 
+
+13
+00:01:33,790 --> 00:01:35,710
+bounded الفترة I ما كانتش bounded
+
+14
+00:01:38,580 --> 00:01:45,820
+فالنظرية بتفشل و هذا مثال يوضح ذلك نأخذ الـ
+
+15
+00:01:45,820 --> 00:01:53,160
+identity function f و نأخذ الـ I هي الفترة المغلقة
+
+16
+00:01:53,160 --> 00:01:59,100
+من صفر إلى مالانهاية واضح أن الفترة I هذه ما هيش
+
+17
+00:01:59,100 --> 00:01:59,480
+bounded
+
+18
+00:02:05,080 --> 00:02:10,740
+و واضح أن الـ identity function F continuous على
+
+19
+00:02:10,740 --> 00:02:17,160
+الفترة I لأنها continuous على كل الـ R لكن الـ
+
+20
+00:02:17,160 --> 00:02:24,070
+function F ما هيش bounded على الفترة I ليست bounded
+
+21
+00:02:24,070 --> 00:02:32,490
+على I و البرهان لأي عدد موجب أقدر أختار XM X عنصر
+
+22
+00:02:32,490 --> 00:02:42,170
+يعتمد على M هذا ينتمي للفترة I و
+
+23
+00:02:42,170 --> 00:02:46,750
+الـ absolute value لـ F of XM تطلع absolute M زائد
+
+24
+00:02:46,750 --> 00:02:51,230
+واحد اللي هي M زائد واحد لأن هذا عدد موجب أكبر من
+
+25
+00:02:51,230 --> 00:02:57,750
+M حسب الـ remark اللي هي بتكافئ تعريف الـ bounded
+
+26
+00:02:57,750 --> 00:03:03,430
+تعريف الـ unboundedness الـ function بتحقق شرط ال
+
+27
+00:03:03,430 --> 00:03:07,370
+unboundedness و بالتالي الـ function unbounded on I
+
+28
+00:03:07,370 --> 00:03:15,630
+لأن هنا عشان الفترة ليست bounded النظرية فشلت في
+
+29
+00:03:15,630 --> 00:03:18,890
+الملاحظة الثانية لو الـ boundedness theorem is
+
+30
+00:03:18,890 --> 00:03:25,230
+false تفشل إذا كانت الـ interval ما هيش مغلقة فع
+
+31
+00:03:25,230 --> 00:03:29,730
+سبيل المثال consider الـ function واحد على X حيث X
+
+32
+00:03:29,730 --> 00:03:36,850
+أكبر من صفر و أصغر من أو يساوي واحد فواضح
+
+33
+00:03:36,850 --> 00:03:43,490
+إن الفترة I هذه not closed ليست مغلقة و الدالة G
+
+34
+00:03:43,490 --> 00:03:48,650
+of X متصلة عليها لأنها لا تحتوي الصفر لأن هذه عندي
+
+35
+00:03:48,650 --> 00:03:55,080
+function G continuous على الفترة I الفترة I ما هيش
+
+36
+00:03:55,080 --> 00:04:00,460
+closed و بالتالي
+
+37
+00:04:00,460 --> 00:04:05,520
+وفي نفس الوجهة الـ function هذه ليست bounded على
+
+38
+00:04:05,520 --> 00:04:10,040
+الفترة I إحنا شفنا أن الـ function 1 على X في بداية
+
+39
+00:04:10,040 --> 00:04:16,600
+اللقاء اللي فات ليست bounded على الفترة من صفر إلى
+
+40
+00:04:16,600 --> 00:04:23,910
+مالانهاية و بالمثل ليست bounded على الفترة من صفر
+
+41
+00:04:23,910 --> 00:04:30,070
+إلى واحد ممكن إعطاء برهان مشابه، إذا هذا مثال على
+
+42
+00:04:30,070 --> 00:04:35,850
+function متصلة على فترة ولكنها ليست bounded على
+
+43
+00:04:35,850 --> 00:04:39,930
+نفس الفترة لأن الفترة هذه السبب أن الفترة هذه ليست
+
+44
+00:04:39,930 --> 00:04:44,130
+closed، تمام؟
+
+45
+00:04:44,130 --> 00:04:48,700
+إذا الفترة هذه لو ما كانتش closed، النظرية بتفشل طب
+
+46
+00:04:48,700 --> 00:04:54,060
+لو كانت closed و لا bounded، برضه بتفشل، لأن هذا
+
+47
+00:04:54,060 --> 00:05:01,060
+الشرط ضروري و هذا الشرط ضروري كذلك الـ function
+
+48
+00:05:01,060 --> 00:05:04,760
+لازم تكون continuous على الفترة هذه، يعني لو كانت
+
+49
+00:05:04,760 --> 00:05:07,820
+الفترة هذه closed و bounded، فالـ function مش
+
+50
+00:05:07,820 --> 00:05:12,140
+continuous، فالنظرية تفشل، لأن هنا the boundedness
+
+51
+00:05:12,140 --> 00:05:12,640
+theorem
+
+52
+00:05:19,930 --> 00:05:31,430
+is false if الـ function لو كانت الدالة F is not
+
+53
+00:05:31,430 --> 00:05:34,690
+continuous
+
+54
+00:05:34,690 --> 00:05:39,910
+on الفترة I فعلى سبيل المثال
+
+55
+00:05:51,070 --> 00:05:58,870
+for example ممكن نعرف define H
+
+56
+00:05:58,870 --> 00:06:06,710
+من الفترة المغلقة من
+
+57
+00:06:06,710 --> 00:06:17,470
+صفر إلى واحد إلى R by H of X بالساوي
+
+58
+00:06:24,650 --> 00:06:34,070
+1 على x إذا كان x أكبر من 0 أصغر من أو يساوي 1
+
+59
+00:06:34,070 --> 00:06:46,730
+و خليني آخذها بالساوي 1 إذا كان x بالساوي 0 ال
+
+60
+00:06:46,730 --> 00:06:50,510
+function h of x 1 على x إذا كان x أكبر من 0 أصغر
+
+61
+00:06:50,510 --> 00:06:56,950
+من أو يساوي 1 وعند الصفر خليها يساوي 1 فطبعا ال
+
+62
+00:06:56,950 --> 00:07:10,430
+function h is not continuous at x يساوي صفر ليست
+
+63
+00:07:10,430 --> 00:07:18,070
+متصلة عند الصفر لأن الـ limit للـ function h of x
+
+64
+00:07:18,070 --> 00:07:22,490
+لما x تؤول إلى الصفر
+
+65
+00:07:25,030 --> 00:07:33,670
+من اليمين يساوي infinity لا تساوي
+
+66
+00:07:33,670 --> 00:07:41,690
+h عند الواحد عند الصفر اللي هو يساوي واحد أو كون
+
+67
+00:07:41,690 --> 00:07:46,690
+الـ limit يساوي infinity إذا does not exist in R
+
+68
+00:07:46,690 --> 00:07:50,690
+و بالتالي هذا يكفي أن إحنا نقول أن الـ function
+
+69
+00:07:50,690 --> 00:08:00,080
+ما هيش continuous عند الصفر في نفس الوجهة Note
+
+70
+00:08:00,080 --> 00:08:04,360
+that الفترة
+
+71
+00:08:04,360 --> 00:08:15,740
+I يساوي صفر و واحد is closed and bounded يعني أنا
+
+72
+00:08:15,740 --> 00:08:22,180
+ما فيش عند الاتصال عند الصفر الـ function هذه H طبعا
+
+73
+00:08:22,180 --> 00:08:29,870
+زي ما الـ function هذيك Note also that
+
+74
+00:08:29,870 --> 00:08:35,890
+the function H is unbounded
+
+75
+00:08:35,890 --> 00:08:43,830
+على الفترة من صفر لواحد لأنها
+
+76
+00:08:43,830 --> 00:08:48,210
+unbounded على الفترة المفتوحة H يساوي واحد على X
+
+77
+00:08:48,210 --> 00:08:52,590
+على الفترة نصف المفتوحة هذه و يقول لنا أن الـ
+
+78
+00:08:52,590 --> 00:08:57,050
+function 1 على x ليست bounded 1 على x ما هيش
+
+79
+00:08:57,050 --> 00:09:03,570
+bounded على الفترة من 0 إلى 1 إذا
+
+80
+00:09:03,570 --> 00:09:07,850
+النظرية تفشل لأن الـ function تبعت هنا ليست
+
+81
+00:09:07,850 --> 00:09:12,750
+continuous عند الصفر و بالتالي ليست continuous على
+
+82
+00:09:12,750 --> 00:09:19,150
+كل الفترة الواحد هنا H is not continuous على كل
+
+83
+00:09:19,150 --> 00:09:24,200
+الفترة I لأنها مش continuous عند الصفر اللي هي
+
+84
+00:09:24,200 --> 00:09:28,020
+answer في أي عشان تكون الـ function continuous على
+
+85
+00:09:28,020 --> 00:09:31,840
+كل الفترة لازم تكون continuous عند كل نقطة في
+
+86
+00:09:31,840 --> 00:09:34,220
+الفترة لو كانت مش continuous عند نقطة واحدة في
+
+87
+00:09:34,220 --> 00:09:43,760
+الفترة فما يقدرش أقول continuous على الفترة تمام
+
+88
+00:09:43,760 --> 00:09:47,600
+إذا نأخذ
+
+89
+00:09:54,630 --> 00:10:04,450
+تعريف definition a
+
+90
+00:10:04,450 --> 00:10:13,030
+function f from A to R has
+
+91
+00:10:13,030 --> 00:10:18,090
+an absolute
+
+92
+00:10:18,090 --> 00:10:19,110
+maximum
+
+93
+00:10:27,530 --> 00:10:39,550
+respectively على التوالي absolute minimum at
+
+94
+00:10:39,550 --> 00:10:47,110
+on
+
+95
+00:10:47,110 --> 00:10:56,610
+الفأس set A if الشرط التالي بيتحقق there exist x
+
+96
+00:10:56,610 --> 00:11:01,370
+super star respectively
+
+97
+00:11:01,370 --> 00:11:08,530
+x lower star تنتمي
+
+98
+00:11:08,530 --> 00:11:13,190
+إلى a بحيث
+
+99
+00:11:13,190 --> 00:11:22,650
+أن f of x أصغر من أو يساوي f of x super star
+
+100
+00:11:25,650 --> 00:11:33,030
+respectively على التوالي f of x lower star أصغر من
+
+101
+00:11:33,030 --> 00:11:42,630
+أو يساوي f of x لكل x تنتمي إلى a كمان
+
+102
+00:11:42,630 --> 00:11:48,030
+براء الـ function f بيكون لها absolute maximum value
+
+103
+00:11:48,030 --> 00:11:54,170
+على المجموعة a إذا قدرنا نلاقي x super star ينتمي
+
+104
+00:11:54,170 --> 00:12:01,280
+لـ a و قيمة الدالة أصغر من أو يساوي قيمة الدالة عن الـ X
+
+105
+00:12:01,280 --> 00:12:06,160
+Superstar لكل X في A فهذا ما نسميها Absolute
+
+106
+00:12:06,160 --> 00:12:11,100
+Maximum Value أكبر قيمة عظمة مطلقة و كذلك نستطيع
+
+107
+00:12:11,100 --> 00:12:13,900
+أن نعرف أن الـ function لها Absolute Minimum Value
+
+108
+00:12:13,900 --> 00:12:21,640
+على المجموعة A إذا نجد X Lower Star عنصر في A بحيث
+
+109
+00:12:21,640 --> 00:12:26,290
+أن قيمة الـ f of x lower star أصغر من أو يساوي
+
+110
+00:12:26,290 --> 00:12:36,250
+كل قيمها على المجموعة a in this case يا دي الحلقة
+
+111
+00:12:36,250 --> 00:12:46,950
+x super star respectively على التوالي x lower star
+
+112
+00:12:46,950 --> 00:12:50,710
+is called
+
+113
+00:12:57,680 --> 00:13:06,760
+an absolute maximum and absolute maximum point
+
+114
+00:13:06,760 --> 00:13:15,880
+maximum respectively على التوالي absolute minimum
+
+115
+00:13:15,880 --> 00:13:20,700
+point
+
+116
+00:13:20,700 --> 00:13:24,480
+of
+
+117
+00:13:25,260 --> 00:13:31,720
+الـ function f on a إذا
+
+118
+00:13:31,720 --> 00:13:34,800
+النقطة x super star اللي دالها عندها absolute
+
+119
+00:13:34,800 --> 00:13:41,210
+maximum بنسميها نقطة نهاية عظمة للدالة على المجموعة و
+
+120
+00:13:41,210 --> 00:13:44,970
+X lower star اللي عندها الدالة اللي لها absolute
+
+121
+00:13:44,970 --> 00:13:50,970
+minimum value بنسميها نقطة absolute minimum point
+
+122
+00:13:50,970 --> 00:13:57,330
+of F على A نقطة نهاية صغيرة okay كلها مجرد تعريفات
+
+123
+00:13:57,330 --> 00:14:04,490
+الآن في عندي الـ maximum minimum theorem أو الـ
+
+124
+00:14:04,490 --> 00:14:07,770
+extreme value theorem مدرية دخلتها في Calculus A
+
+125
+00:14:09,520 --> 00:14:17,420
+لكن أمرنا بقلبنا منكم برهان فهو theorem max
+
+126
+00:14:17,420 --> 00:14:29,760
+minimum theorem نظرية
+
+127
+00:14:29,760 --> 00:14:33,420
+القيام القصوى أو القيام العظمى أو الصغرى
+
+128
+00:14:37,040 --> 00:14:48,300
+لت I يساوي closed ب .. ب closed and bounded
+
+129
+00:14:48,300 --> 00:14:56,120
+interval if
+
+130
+00:14:56,120 --> 00:15:04,400
+الـ function F from I to R is continuous
+
+131
+00:15:06,950 --> 00:15:17,350
+on I then if attains its
+
+132
+00:15:17,350 --> 00:15:29,490
+maximum أو its absolute maximum and absolute
+
+133
+00:15:29,490 --> 00:15:33,810
+minimum on I
+
+134
+00:15:37,830 --> 00:15:45,050
+that is هذا يعني there exist x upper star و x
+
+135
+00:15:45,050 --> 00:15:54,610
+lower star في I such that f of x أصغر أو يساوي f of
+
+136
+00:15:54,610 --> 00:16:06,090
+x super star لكل x في I and F of X lower star أصغر
+
+137
+00:16:06,090 --> 00:16:13,130
+من أو يساوي F of X لكل X في I تمام؟ لأن هذه هي
+
+138
+00:16:13,130 --> 00:16:17,210
+نظرية القيامة القصوى لو كانت الدالة متصلة على
+
+139
+00:16:17,210 --> 00:16:20,590
+المجال تبعها و المجال تبعها closed bounded interval
+
+140
+00:16:20,590 --> 00:16:25,010
+فلابد أن كل الدالة قيمة عظمة مطلقة و قيمة صغيرة 
+
+141
+00:16:25,010 --> 00:16:37,600
+مطلقة على هذه الفترة تمام؟ okay البرهان البرهان سهل
+
+142
+00:16:37,600 --> 00:16:44,660
+proof
+
+143
+00:16:44,660 --> 00:16:50,760
+note
+
+144
+00:16:50,760 --> 00:16:55,740
+first that
+
+145
+00:17:01,890 --> 00:17:08,190
+the non-empty set
+
+146
+00:17:08,190 --> 00:17:20,130
+اللي 
+
+147
+00:17:20,130 --> 00:17:28,490
+هي F of I اللي هي كل الـ F of X هي في X ينتمي لـ I
+
+148
+00:17:29,720 --> 00:17:35,420
+الـ set is non-empty لأن الفترة I هنا طبعا ليست
+
+149
+00:17:35,420 --> 00:17:48,620
+فترة خالية، فيها على الأقل عنصرين 
+
+150
+00:17:48,620 --> 00:17:54,740
+الفترة هذه is bounded
+
+151
+00:17:58,460 --> 00:18:09,140
+by boundedness theorem احنا
+
+152
+00:18:09,140 --> 00:18:13,080
+أخدنا نظرية اللي جابت هذه كانت في اللقاء الأول
+
+153
+00:18:13,080 --> 00:18:19,500
+بتقول لو كانت if function from I to R وكانت الدالة
+
+154
+00:18:19,500 --> 00:18:23,790
+هذه continuous و I closed bounded interval فالـ
+
+155
+00:18:23,790 --> 00:18:28,550
+function f بتطلع bounded على الفترة I الـ function
+
+156
+00:18:28,550 --> 00:18:32,250
+bounded على الفترة I المعنية هو الـ range تبع الـ
+
+157
+00:18:32,250 --> 00:18:36,190
+function اللي هي الـ set هذه is a bounded set okay
+
+158
+00:18:36,190 --> 00:18:40,630
+تمام هذا بنحصل عليه من الـ boundedness theorem
+
+159
+00:18:40,630 --> 00:18:44,210
+طيب
+
+160
+00:18:44,210 --> 00:18:46,230
+وبالتالي
+
+161
+00:18:50,070 --> 00:18:53,570
+احنا عايزين الأن نثبت الـ claim .. بنا نثبت الـ
+
+162
+00:18:53,570 --> 00:19:01,370
+claim التالي الـ claim هذا بتكون من جزئين أنه يوجد
+
+163
+00:19:01,370 --> 00:19:09,350
+.. أه طيب كام الـ claim hence مادام
+
+164
+00:19:09,350 --> 00:19:12,270
+الست هذي bounded .. إذا bounded above و bounded
+
+165
+00:19:12,270 --> 00:19:15,230
+below و بالتالي في إليها supremum و في إليها
+
+166
+00:19:15,230 --> 00:19:21,810
+infimum by supremum and infimum properties إذاً S
+
+167
+00:19:21,810 --> 00:19:27,910
+Superstar اللي هو بساوي الـ supremum لـ set F of I
+
+168
+00:19:27,910 --> 00:19:36,310
+exist in R and S Lower Star اللي هو حاخده الـ
+
+169
+00:19:36,310 --> 00:19:45,450
+infimum لـ set F of I برضه exist in R هذا by supremum
+
+170
+00:19:45,450 --> 00:20:09,180
+property وهذا by infimum property Okay تمام الأن
+
+171
+00:20:09,180 --> 00:20:14,900
+بدي اثبت الـ claim التالي الـ claim هذا بتكون من 
+
+172
+00:20:14,900 --> 00:20:24,610
+جزءين الجزء الأول انه there exist x superstar ينتمي
+
+173
+00:20:24,610 --> 00:20:33,510
+للفترة I بحيث انه F of X Superstar بساوي S
+
+174
+00:20:33,510 --> 00:20:34,490
+Superstar
+
+175
+00:20:37,010 --> 00:20:44,930
+and الجزء الثاني ان يوجد x lower star عنصر ما في
+
+176
+00:20:44,930 --> 00:20:50,890
+الفترة i بحيث ان f ل x lower star بساوي s lower
+
+177
+00:20:50,890 --> 00:20:55,110
+star فلو
+
+178
+00:20:55,110 --> 00:21:01,710
+أثبتنا الجزء الأول معناته ال x star هذه نقطة
+
+179
+00:21:01,710 --> 00:21:06,530
+الدالة بتاخد قيمتها العظمى المطلقة عندها وهذا معناه
+
+180
+00:21:06,530 --> 00:21:11,790
+ان x lower star هي نقطة قيمة صغرى المطلقة لل
+
+181
+00:21:11,790 --> 00:21:17,710
+function f لأن هذه قيمة الصغرى المطلقة لل function
+
+182
+00:21:17,710 --> 00:21:18,330
+f على i
+
+183
+00:21:32,020 --> 00:21:36,920
+فلو أثبتنا واحد و اثنين يكون أثبتنا النظرية حنثبت
+
+184
+00:21:36,920 --> 00:21:41,260
+واحد و برهان الثاني بالمثل مشابه فحاسبكم أنتم 
+
+185
+00:21:41,260 --> 00:21:47,740
+تكتبوا هنا we prove one
+
+186
+00:21:47,740 --> 00:22:02,280
+and leave the proof of two for you زي ما قلنا
+
+187
+00:22:02,280 --> 00:22:10,500
+البرهان هذا تبع الجزء الثاني مشابه للأول طيب
+
+188
+00:22:10,500 --> 00:22:25,160
+since S star بساوي الـ supremum لـ F of I then
+
+189
+00:22:25,160 --> 00:22:29,700
+for each N عدد طبيعي
+
+190
+00:22:32,660 --> 00:22:45,420
+S star minus one upon n is not upper bound of
+
+191
+00:22:45,420 --> 00:22:52,280
+set F of I لأن
+
+192
+00:22:52,280 --> 00:22:54,240
+هذا عبارة عن least upper bound
+
+193
+00:23:00,430 --> 00:23:07,710
+So وبالتالي there exists xn ينتمي للفترة I بحيث
+
+194
+00:23:07,710 --> 00:23:21,290
+أنه F of xn ده أكبر من S star minus واحد على M هذا
+
+195
+00:23:21,290 --> 00:23:26,050
+العدد ليس upper bound لل set هذه طب ما إذا يوجد
+
+196
+00:23:26,050 --> 00:23:31,430
+عنصر في الـ set هذه اللي هو صورة لعنصر في I وهذا
+
+197
+00:23:31,430 --> 00:23:37,640
+العنصر أكبر من S star ناقص واحد الان (S*) هذا عبارة عن
+
+198
+00:23:37,640 --> 00:23:42,420
+upper bound للـ set F of I وهذا العنصر ينتمي لـ F of
+
+199
+00:23:42,420 --> 00:23:46,180
+I، إذن هذا أصغر من أو يساوي الـ upper bound لكل
+
+200
+00:23:46,180 --> 00:23:50,400
+المجموعة اللي بتحتوي العناصر اللي زي هذا، إذن هذا
+
+201
+00:23:50,400 --> 00:23:59,240
+أصغر من أو يساوي S*)، okay؟ وهذا طبعا صحيح لكل N في 
+
+202
+00:23:59,240 --> 00:24:09,550
+N، كل N في N تمام إذا إن أنا في عندي المتباينة هذه
+
+203
+00:24:09,550 --> 00:24:13,010
+بما
+
+204
+00:24:13,010 --> 00:24:25,010
+أنه الـ .. الـ set since
+
+205
+00:24:25,010 --> 00:24:30,710
+الفترة I is closed and bounded is bounded
+
+206
+00:24:34,570 --> 00:24:41,410
+و X in .. لاحظوا X in الـ sequence هذه contained in
+
+207
+00:24:41,410 --> 00:24:53,230
+I then الـ sequence X in is bounded so
+
+208
+00:24:53,230 --> 00:25:00,530
+by Bolzano Weierstrass theorem
+
+209
+00:25:03,780 --> 00:25:07,160
+النظرية بولزانو فايرستراسي بتقول لكل bounded
+
+210
+00:25:07,160 --> 00:25:11,940
+sequence في لها convergent subsequence إذا there
+
+211
+00:25:11,940 --> 00:25:23,980
+exist a subsequence x in k of sequence x in which
+
+212
+00:25:23,980 --> 00:25:33,710
+converges بتكون convergent say يعني اننا دعينا نسمي
+
+213
+00:25:33,710 --> 00:25:37,950
+الـ limit تبع الـ subsequence اللي احنا قلنا انها
+
+214
+00:25:37,950 --> 00:25:45,050
+convergent دعينا نسمي الـ limit تبعتها x وهذا ينتمي
+
+215
+00:25:45,050 --> 00:25:55,620
+الى R تمام؟ كمان مرة since الـ subsequence X, N, K
+
+216
+00:25:55,620 --> 00:26:03,260
+كل عناصرها موجودة في I اللي هي الفترة المغلقة A و
+
+217
+00:26:03,260 --> 00:26:08,980
+B و الـ subsequence هي convergent إذا حسب نظرية في
+
+218
+00:26:08,980 --> 00:26:13,280
+chapter 3 إذا كانت الـ sequence عناصرها محصورة بين
+
+219
+00:26:13,280 --> 00:26:17,380
+A و B و convergent فنهايتها هتكون محصورة بين A و B
+
+220
+00:26:17,380 --> 00:26:27,050
+إذا ال X تنتمي للفترة A و B اللي هي ال I طيب بما
+
+221
+00:26:27,050 --> 00:26:34,070
+أنه الـ F continuous الـ function F continuous على
+
+222
+00:26:34,070 --> 00:26:39,590
+الفترة I و
+
+223
+00:26:39,590 --> 00:26:47,110
+X خلينا نسمي الـ X هذا X star عشان بس يكون ايه
+
+224
+00:26:47,110 --> 00:26:51,350
+نتمشي مع ايه مع النص خلينا نسمي الـ X هذا X
+
+225
+00:26:51,350 --> 00:26:59,970
+Superstar إذا by hypothesis احنا فرضنا ان الـ
+
+226
+00:26:59,970 --> 00:27:04,270
+function F متصل على الفترة I و X Superstar عنصر في
+
+227
+00:27:04,270 --> 00:27:14,470
+I إذا F is continuous at X Superstar اللي هو عنصر
+
+228
+00:27:14,470 --> 00:27:19,610
+في I تمام؟ و في عندي الـ sequence او الـ subsequence
+
+229
+00:27:19,610 --> 00:27:23,850
+هي دي convergent ل x star و if continuous at
+
+230
+00:27:23,850 --> 00:27:28,490
+continuous at x star إذا by sequential criterion
+
+231
+00:27:28,490 --> 00:27:35,190
+for continuous function hence by sequential
+
+232
+00:27:35,190 --> 00:27:41,610
+criterion for continuous functions بطلع الـ limit
+
+233
+00:27:43,100 --> 00:27:48,160
+للـ image للـ convergence sequence اللي هي X in K
+
+234
+00:27:48,160 --> 00:27:59,560
+K تقوى لإنفينتي بتساوي الـ image ل X Superstar تمام
+
+235
+00:27:59,560 --> 00:28:05,320
+إذا أنا في عندي الـ image للـ sequence أو لل
+
+236
+00:28:05,320 --> 00:28:09,240
+subsequence X in K تطلع convergent
+
+237
+00:28:13,340 --> 00:28:24,480
+و الـ ..
+
+238
+00:28:24,480 --> 00:28:29,460
+و متحقق طبعا ..
+
+239
+00:28:29,460 --> 00:28:33,020
+نعم
+
+240
+00:28:33,020 --> 00:28:36,940
+من
+
+241
+00:28:36,940 --> 00:28:41,520
+هنا .. من هنا نسمي هذه قصة
+
+242
+00:28:46,300 --> 00:29:03,200
+by star we have f بدل x in ب x in k فهذا أصغر من
+
+243
+00:29:03,200 --> 00:29:09,900
+أو يساوي s star و أكبر من أو يساوي s super star
+
+244
+00:29:09,900 --> 00:29:13,340
+ناقص واحد على nk
+
+245
+00:29:19,300 --> 00:29:27,860
+وهذا صحيح لكل K ينتمي إلى N، بظبط؟ الآن خلّي الـ K
+
+246
+00:29:27,860 --> 00:29:34,760
+تقوى لـ Infinity فإذا 1 على NK لما K تقوى لـ
+
+247
+00:29:34,760 --> 00:29:40,720
+Infinity بطلع صفر وبالتالي هذا بيروح لـ S*) وهذا
+
+248
+00:29:40,720 --> 00:29:47,070
+ثابت لما K تقوى لـ Infinity هذه sequence الحد اللي
+
+249
+00:29:47,070 --> 00:29:52,870
+عام تبعها ثابت بتروح لـ S Star So
+
+250
+00:29:52,870 --> 00:29:57,890
+by Squeeze Theorem
+
+251
+00:29:57,890 --> 00:30:08,670
+بتطلع عند الـ limit لـ F of X in K as K till
+
+252
+00:30:08,670 --> 00:30:15,050
+infinity بساوي S Super Star Hence
+
+253
+00:30:17,550 --> 00:30:23,450
+بنسمي هذه double star this
+
+254
+00:30:23,450 --> 00:30:30,170
+and double star المعادلة
+
+255
+00:30:30,170 --> 00:30:39,030
+الأخيرة هو double star yield بيعطوني التالي ان f
+
+256
+00:30:39,030 --> 00:30:53,120
+of x super star بساوي الـ limit لـ f of x in k لما k
+
+257
+00:30:53,120 --> 00:31:02,260
+تقول لإنفينيتي و limit من هنا limit f of x in k
+
+258
+00:31:02,260 --> 00:31:07,520
+بساوي الـ super star وهذا اللي بدنا إياه هو المطلوب
+
+259
+00:31:09,430 --> 00:31:17,250
+البرهان هذا اثبتنا ان يوجد X Superstar في R و X
+
+260
+00:31:17,250 --> 00:31:23,880
+Superstar هذا طلع في الفترة I موجود في I بحيث أن
+
+261
+00:31:23,880 --> 00:31:29,360
+صورة الـ F عند X Superstar بساوي S Superstar، اللي
+
+262
+00:31:29,360 --> 00:31:32,540
+هو الـ Supremum لـ Range الـ Function F، اللي هي
+
+263
+00:31:32,540 --> 00:31:37,400
+القيمة العظمى المطلقة، إذن هنا هيوجد نقطة X
+
+264
+00:31:37,400 --> 00:31:40,920
+Superstar في I عندها الـ Function تأخذ قيمتها
+
+265
+00:31:40,920 --> 00:31:45,560
+العظمى المطلقة، بالمثل ممكن نبرهن الجزء الثاني،
+
+266
+00:31:45,560 --> 00:31:51,320
+وهذا يكمل برهان النظرية تمام؟ إذا البرهان مش صعب
+
+267
+00:31:51,320 --> 00:31:56,860
+يمكن صحيح طويل شوية لكن يعني ممكن أي واحد يعني
+
+268
+00:31:56,860 --> 00:32:09,040
+يبرهنه لو فهمه الفهم الصحيح النظرية هذه طبعا
+
+269
+00:32:09,040 --> 00:32:14,600
+في يعني ملاحظات أنه يعني المفروض نتطرق لهم
+
+270
+00:32:20,990 --> 00:32:24,830
+أنه لازم عشان النظرية تكون صحيحة لازم الفترة I
+
+271
+00:32:24,830 --> 00:32:30,750
+تكون closed و bounded يعني لو كانت closed ماهيّاش
+
+272
+00:32:30,750 --> 00:32:35,330
+bounded مش ممكن الـ function تكون النظرية صحيحة و لو
+
+273
+00:32:35,330 --> 00:32:39,190
+كانت bounded و مش closed مش ممكن تكون النظرية صحيحة
+
+274
+00:32:39,190 --> 00:32:44,070
+لو كان مجال الدالة هذه الفترة I closed و bounded
+
+275
+00:32:44,070 --> 00:32:49,470
+زي ما هو مطلوب لكن الدالة مش متصلة فممكن تكون لها
+
+276
+00:32:49,470 --> 00:32:51,990
+absolute maximum او absolute minimum على الأقل
+
+277
+00:32:51,990 --> 00:33:03,430
+واحدة منهم بتكون مش موجودة okay فمثلا
+
+278
+00:33:03,430 --> 00:33:11,190
+marks
+
+279
+00:33:11,190 --> 00:33:15,810
+واحد
+
+280
+00:33:15,810 --> 00:33:21,330
+a function أو a continuous function .. a continuous 
+
+281
+00:33:21,330 --> 00:33:35,230
+a function on a set .. on a set A may
+
+282
+00:33:35,230 --> 00:33:39,070
+not have 
+
+283
+00:33:39,070 --> 00:33:46,870
+an absolute maximum or absolute
+
+284
+00:33:51,480 --> 00:34:01,680
+minimum on a  فعلى سبيل المثال consider خد ال
+
+285
+00:34:01,680 --> 00:34:12,240
+function f of x بساوي واحد على x و x ينتمي للفترة
+
+286
+00:34:12,240 --> 00:34:14,020
+المفتوحة من صفر إلى مالانهاية
+
+287
+00:34:17,550 --> 00:34:25,970
+هذه the function  if has neither
+
+288
+00:34:25,970 --> 00:34:39,150
+absolute maximum nor absolute minimum on the اللي هي
+
+289
+00:34:39,150 --> 00:34:41,950
+الفترة المفتوحة من صفر إلى مالانهاية
+
+290
+00:34:44,130 --> 00:34:50,190
+رغم أن الدالة متصلة رغم أن الدالة متصلة السبب أن
+
+291
+00:34:50,190 --> 00:34:57,370
+الفترة هذه ليست مغلقة وليست  محدودة وبالتالي ماقدرش
+
+292
+00:34:57,370 --> 00:35:04,990
+أستنتج نتيجة النظرية، النظرية هذه ماتتطبقش وهذا
+
+293
+00:35:04,990 --> 00:35:11,510
+واضح من الرسم، هذه ال function تبعتي هي واحد على X
+
+294
+00:35:12,820 --> 00:35:18,600
+F of X بيساوي واحد على X و X أكبر من الصفر هذه هي
+
+295
+00:35:18,600 --> 00:35:25,520
+فال function هذه مالهاش قيمة صغيرة مافيش X lower
+
+296
+00:35:25,520 --> 00:35:32,320
+bound لاحظوا أنتم أن ال infimum ل F of A هنا
+
+297
+00:35:32,320 --> 00:35:35,260
+بيساوي صفر
+
+298
+00:35:40,900 --> 00:35:47,580
+القيمة الـ infimum تبعها بساوي صفر لكن الدالة
+
+299
+00:35:47,580 --> 00:35:52,880
+مالهاش الصفر ليس absolute minimum لل function هذه
+
+300
+00:35:52,880 --> 00:36:01,460
+لأن مافيش x lower bound عنده
+
+301
+00:36:01,460 --> 00:36:06,240
+قيمة ال function بساوي صفر مافيش في
+
+302
+00:36:07,510 --> 00:36:14,370
+أي x lower bound ينتمي لـ A للفترة هذه وعنده الدالة بساوي
+
+303
+00:36:14,370 --> 00:36:20,270
+صفر مافيش كذلك الدالة هذه مالهاش قيمة عظمى الدالة
+
+304
+00:36:20,270 --> 00:36:26,190
+هذه unbounded from above يعني مافيش
+
+305
+00:36:26,190 --> 00:36:34,550
+أي x upper bound عنده الدالة بتساوي أكبر قيمة okay
+
+306
+00:36:36,570 --> 00:36:40,170
+إذًا الدالة ممكن مايكونش لها قيمة صغيرة مطلقة
+
+307
+00:36:40,170 --> 00:36:51,250
+ولا قيمة عظمى مطلقة كذلك ال ..
+
+308
+00:36:51,250 --> 00:36:57,970
+ملاحظة ثانية ال continuous function
+
+309
+00:37:08,760 --> 00:37:15,340
+إذا كانت الـ function لديه
+
+310
+00:37:15,340 --> 00:37:25,960
+نقطة  أكبر  maximum point maximum point 
+
+311
+00:37:25,960 --> 00:37:31,640
+maximum point maximum point maximum point maximum point maximum point maximum point maximum point 
+
+312
+00:37:31,640 --> 00:37:37,020
+maximum point maximum point maximum point maximum point this point is not
+
+313
+00:37:37,020 --> 00:37:40,440
+necessarily
+
+314
+00:37:40,440 --> 00:37:52,180
+مش من الضروري not necessarily uniquely determined
+
+315
+00:38:03,370 --> 00:38:06,750
+يعني لو كانت دالة لها absolute maximum أو لها
+
+316
+00:38:06,750 --> 00:38:13,450
+absolute minimum فالقيمة هذه الأكبر أو الصغرى مش
+
+317
+00:38:13,450 --> 00:38:18,950
+شرط تكون يعني مش شرط ان احنا نحصل عليها عند نقطة
+
+318
+00:38:18,950 --> 00:38:23,150
+واحدة ممكن دالة يكون لها absolute maximum أو 
+
+319
+00:38:23,150 --> 00:38:26,850
+absolute minimum عند أكثر من نقطة في المدى تبعها
+
+320
+00:38:26,850 --> 00:38:32,110
+for example على سبيل المثال consider
+
+321
+00:38:33,800 --> 00:38:43,480
+اعتبري the function f of x بساوي x تربيع وطبعا هنا
+
+322
+00:38:43,480 --> 00:38:48,480
+x ينتمي إلى R ده للتربيعية المجال تبعها كل العداد
+
+323
+00:38:48,480 --> 00:38:55,000
+الحقيقية خلينا ناخد الـ x بس في الفترة المغلقة
+
+324
+00:38:55,000 --> 00:39:02,420
+و المحدودة من سالب واحد إلى واحد تمام؟
+
+325
+00:39:03,700 --> 00:39:08,380
+فال function f is
+
+326
+00:39:08,380 --> 00:39:16,480
+continuous on I and بنلاحظ 
+
+327
+00:39:16,480 --> 00:39:24,740
+أن f عن سالب واحد بساوي f عن واحد بساوي واحد is an 
+
+328
+00:39:24,740 --> 00:39:28,260
+absolute maximum
+
+329
+00:39:33,020 --> 00:39:42,000
+at x بساوي سالب واحد وواحد إذًا سالب واحد وواحد عبارة
+
+330
+00:39:42,000 --> 00:39:45,260
+عن absolute maximum points مظبوط هاي الدالة
+
+331
+00:39:45,260 --> 00:39:50,840
+التربيعية أنا بس ماخد المجال تبعها اللي هو الفترة 
+
+332
+00:39:50,840 --> 00:39:54,900
+المغلقة والمحدودة من سالب واحد إلى واحد فطبعًا
+
+333
+00:39:54,900 --> 00:39:56,120
+رسمتها زي هيك
+
+334
+00:40:00,870 --> 00:40:05,170
+هذه الدالة التربيعية  إن المجال تبعها الفترة المغلقة
+
+335
+00:40:05,170 --> 00:40:10,230
+هذه فواضح أنها لها absolute maximum اللي هي
+
+336
+00:40:10,230 --> 00:40:15,630
+الواحد وال absolute maximum هذا حصلنا عليه عند نقطتين
+
+337
+00:40:15,630 --> 00:40:24,870
+تالي سالب واحد وواحد نعم مظبوط صحيح وطبعًا هنا
+
+338
+00:40:24,870 --> 00:40:29,980
+فيها absolute minimum واحدة اللي هي الصفر واضح
+
+339
+00:40:29,980 --> 00:40:34,940
+هنا أن الدالة هنا المجال تبعها فترة مغلقة ومحدودة
+
+340
+00:40:34,940 --> 00:40:38,900
+إذا by maximum minimum theorem اكيد فيه اللي هي
+
+341
+00:40:38,900 --> 00:40:41,980
+absolute maximum وفيه اللي هي absolute minimum ال
+
+342
+00:40:41,980 --> 00:40:45,640
+absolute minimum point هي الصفر الـ absolute
+
+343
+00:40:45,640 --> 00:40:50,380
+maximum point هنا في نقطتين النظرية مجرد يعني مجرد
+
+344
+00:40:50,380 --> 00:40:53,820
+يوجد على الأقل نقطة واحدة  في end absolute maximum
+
+345
+00:40:53,820 --> 00:41:03,500
+فلو كانوا اثنتين لا ضرر لا بأس تمام okay إذن يعني
+
+346
+00:41:03,500 --> 00:41:11,440
+هذه بعض الملاحظات على ال maximum theorem ال
+
+347
+00:41:11,440 --> 00:41:11,820
+..
+
+348
+00:41:22,530 --> 00:41:29,810
+أعتقد أننا سنكتفي بهذا القدر وإن شاء الله
+
+349
+00:41:29,810 --> 00:41:36,850
+سنكمل ال section هذا في المحاضرة القادمة فشكراً لكم
+
+350
+00:41:36,850 --> 00:41:44,390
+لحسن استماعكم وإن شاء الله نلتقي يوم الاثنين
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5992d06fe3a8ac5561592e8e0fe85aa48437d42c
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_postprocess.srt
@@ -0,0 +1,960 @@
+1
+00:00:23,300 --> 00:00:28,680
+الـ completeness property of R عشان نعرف أيه ال
+
+2
+00:00:28,680 --> 00:00:33,540
+completeness property of R فبنحتاج لبعض التعريفات
+
+3
+00:00:33,540 --> 00:00:39,380
+فأول تعريف ما معناه أن عدد حقيقي يكون upper bound
+
+4
+00:00:39,380 --> 00:00:44,460
+للمجموعة S معناه أن ال U أكبر من أو ساوي كل عناصر
+
+5
+00:00:44,460 --> 00:00:50,800
+ال 6Sما معناه ان عدد حقيقي w يكون lower bound ل S
+
+6
+00:00:50,800 --> 00:00:58,580
+معناه ان ال w أصغر من أو يساوي كل عناصر ال set S و
+
+7
+00:00:58,580 --> 00:01:06,600
+من السهل ان احنا من التعريف
+
+8
+00:01:06,600 --> 00:01:12,760
+هذا ممكن نلاحظ الملاحظات التالية ان اي set ممكن
+
+9
+00:01:13,520 --> 00:01:16,740
+يكونيلها upper bound وممكن مايكونيلهاش upper bound
+
+10
+00:01:16,740 --> 00:01:23,380
+فع سبيل المثال مجموعة الأعداد الحقيقية هذه ليس لها
+
+11
+00:01:23,380 --> 00:01:29,740
+upper bound أو أي lower bound في المقابل الفترة
+
+12
+00:01:29,740 --> 00:01:38,520
+المغلقة S من صفر لواحدأو الفترة المغلقة المفتوحة
+
+13
+00:01:38,520 --> 00:01:44,480
+من سفر لواحد هذه إلها lower bounds السفر أو أي عدد
+
+14
+00:01:44,480 --> 00:01:50,540
+أصلا أو ساوى سفر و كذلك إلها upper bounds الواحد
+
+15
+00:01:50,540 --> 00:01:55,540
+أو أي عدد أكبر من أو ساوى الواحد بالمثل للمجموعة
+
+16
+00:01:55,540 --> 00:02:00,920
+اللي تحت كذلك لو المجموعة
+
+17
+00:02:02,480 --> 00:02:08,060
+الها upper bound U فبكون لها infinitely many upper
+
+18
+00:02:08,060 --> 00:02:12,700
+bounds إذا كان U upper bound لمجموعة زي هذه فكل
+
+19
+00:02:12,700 --> 00:02:16,200
+عدد أكبر من ال upper bound هو upper bound آخر
+
+20
+00:02:16,200 --> 00:02:20,600
+بالمثل بالنسبة لل lower bounds إذا المجموعة لها
+
+21
+00:02:20,600 --> 00:02:24,660
+lower bound واحد فممكن نجد عدد لانهاء من ال lower
+
+22
+00:02:24,660 --> 00:02:30,770
+boundsلو أخدنا المجموعة S بالساوية فاي فأي عدد
+
+23
+00:02:30,770 --> 00:02:35,170
+حقيقي بيكون upper bound وفي نفس الوقت بيكون lower
+
+24
+00:02:35,170 --> 00:02:40,330
+bound للمجموعة هذه و البرهان by contradiction نفرض
+
+25
+00:02:40,330 --> 00:02:46,470
+على النقيض أن يوجد R0 عدد حقيقي و هذا العدد
+
+26
+00:02:46,470 --> 00:02:52,200
+الحقيقي ما هوش upper boundمعناته إذا كان R0 ليس
+
+27
+00:02:52,200 --> 00:02:55,940
+upper bound لـ S معناته بقدر ألاقي عنصر S في
+
+28
+00:02:55,940 --> 00:03:02,820
+المجموعة capital S أكبر من الـ R0 وهذا بتديني
+
+29
+00:03:02,820 --> 00:03:08,960
+التناقض لأن المجموعة S لا يوجد بيها عناصر فرض أنه
+
+30
+00:03:08,960 --> 00:03:17,960
+يوجد فرض
+
+31
+00:03:17,960 --> 00:03:24,460
+أنه يوجدعدد حقيقي وما هواش upper bound هذا خطأ هذا
+
+32
+00:03:24,460 --> 00:03:29,360
+معناه ان every real number is upper bound بالمثل
+
+33
+00:03:29,360 --> 00:03:33,160
+ممكن اثبات ان every real number is lower bound
+
+34
+00:03:33,160 --> 00:03:35,840
+للمجموعة الخالية five
+
+35
+00:03:56,010 --> 00:04:01,510
+بنقول إن المجموعة أي مجموعة من R bounded above إذا
+
+36
+00:04:01,510 --> 00:04:06,770
+كان إلها upper bound وبنقول إنها bounded below إذا
+
+37
+00:04:06,770 --> 00:04:15,310
+كانت إذا كان إلها lower bound إذا كانت المجموعة
+
+38
+00:04:15,310 --> 00:04:20,810
+بنسميها bounded إذا كانت bounded above and bounded
+
+39
+00:04:20,810 --> 00:04:26,720
+below في نفس الوجد وبنسميها unboundedإذا كان
+
+40
+00:04:26,720 --> 00:04:32,220
+ينقصها إنها تكون bounded above أو بينقصها إنها
+
+41
+00:04:32,220 --> 00:04:36,780
+تكون bounded below مثال على unbounded set اللي هو
+
+42
+00:04:36,780 --> 00:04:41,100
+الأعداد الحقيقية، هذه ال set unbounded غير محدودة،
+
+43
+00:04:41,100 --> 00:04:47,180
+غير محصورة، لأنه ليس لها upper bounds أو lower
+
+44
+00:04:47,180 --> 00:04:51,620
+boundsمثال على bounded sets ال set هذه وال set هذه
+
+45
+00:04:51,620 --> 00:04:57,740
+ال sets هذول كل منهم bounded above and bounded
+
+46
+00:04:57,740 --> 00:05:07,080
+below وبالتالي bounded المجموعة
+
+47
+00:05:07,080 --> 00:05:11,940
+أي subset من S، ده التعريف definition أي subset S
+
+48
+00:05:11,940 --> 00:05:14,260
+من R، بنسميه bounded above
+
+49
+00:05:22,060 --> 00:05:26,400
+بنسميها bounded below إذا كان في إلها upper bound
+
+50
+00:05:26,400 --> 00:05:27,860
+إذا كان في إلها lower bound
+
+51
+00:05:36,000 --> 00:05:41,960
+المجموعة bounded if كانت كان لها upper bound و
+
+52
+00:05:41,960 --> 00:05:46,140
+lower bound او كانت bounded above و bounded below
+
+53
+00:05:46,140 --> 00:05:52,720
+اذا ال set بنسميها bounded if كانت bounded above و
+
+54
+00:05:52,720 --> 00:05:57,520
+bounded below المجموعة بتكون محدودة او محصورة اذا
+
+55
+00:05:57,520 --> 00:06:02,740
+كانت محصورة من الاعلى و من اسفل في نفس الوجد اما
+
+56
+00:06:04,210 --> 00:06:08,550
+if S lacks either an upper bound or lower bound
+
+57
+00:06:08,550 --> 00:06:15,810
+فبنسميها unbounded S بنسميها unbounded إذا
+
+58
+00:06:15,810 --> 00:06:19,750
+المجموعة لو كانت بنخصها upper bound يعني مالهاش أي
+
+59
+00:06:19,750 --> 00:06:26,250
+upper bound وإلها lower bounds بتكون unbounded أو
+
+60
+00:06:26,250 --> 00:06:32,250
+لو كانت المجموعةbounded below مالهاش upper bounds
+
+61
+00:06:32,250 --> 00:06:38,670
+او not bounded above برضه بنسميها unbounded اذا ال
+
+62
+00:06:38,670 --> 00:06:41,890
+bounded معناته bounded above و below في نفس الوجه
+
+63
+00:06:41,890 --> 00:06:48,710
+اذا واحد مش متحقق بنسميها unbounded اعسى بيه
+
+64
+00:06:48,710 --> 00:06:53,690
+المثال مجموعة الاعداد الحقيقية are and is
+
+65
+00:06:53,690 --> 00:06:58,350
+unbounded لأنه ليست bounded above ولا bounded
+
+66
+00:06:58,350 --> 00:06:58,710
+below
+
+67
+00:07:01,720 --> 00:07:08,900
+كذلك المجموعة هذه لو
+
+68
+00:07:08,900 --> 00:07:14,260
+أخدنا مجموعة الأعداد الحقيقية الغير سالبة
+
+69
+00:07:14,260 --> 00:07:17,660
+فالمجموعة
+
+70
+00:07:17,660 --> 00:07:20,920
+هذه is bounded below، لها lower bound، سفر أو أي
+
+71
+00:07:20,920 --> 00:07:26,060
+عدد أصغر من أسابع سفر لكن it is not bounded above،
+
+72
+00:07:26,060 --> 00:07:28,240
+إذا المجموعة هذه unbounded
+
+73
+00:07:32,210 --> 00:07:40,410
+it is unbounded المجموعة هذي هذي bounded لأنها
+
+74
+00:07:40,410 --> 00:07:45,450
+bounded above and bounded below طبعا إذا فهمنا شو
+
+75
+00:07:45,450 --> 00:07:54,890
+معناه bounded و unbounded ناخد تعريف تاني لو
+
+76
+00:07:54,890 --> 00:08:01,410
+كانت S bounded aboveفبنعرف ال supremum أو ال least
+
+77
+00:08:01,410 --> 00:08:07,730
+upper bound للست S على أنه العدد الحقيقي U اللي
+
+78
+00:08:07,730 --> 00:08:12,910
+بيحقق الشرطين هدول الشرط الأول أنه العدد U is an
+
+79
+00:08:12,910 --> 00:08:18,610
+upper bound of S U أكبر من أو ساوي كل عناصر S يعني
+
+80
+00:08:18,610 --> 00:08:24,450
+U upper bound ل S اتنين لو أخدت أي upper bound V
+
+81
+00:08:26,010 --> 00:08:35,150
+فلازم ال U يطلع أصغر من أو ساوي تمام؟
+
+82
+00:08:35,150 --> 00:08:43,250
+فإذا ال .. ال .. ال supremum هو أصغر upper bound
+
+83
+00:08:43,250 --> 00:08:48,490
+للمجموعة هو أصغر upper bound ال supremum هو least
+
+84
+00:08:48,490 --> 00:08:54,640
+.. ال least upper bound أصغر حد أعلىإذا إيش هو
+
+85
+00:08:54,640 --> 00:08:59,960
+أصغر حد أعلى؟ متى بيكون U هو أصغر حد أعلى للمجموعة
+
+86
+00:08:59,960 --> 00:09:08,500
+إذا كان أول شي upper bound للمجموعة اتنين U أصغر
+
+87
+00:09:08,500 --> 00:09:14,580
+من أو يساوي أي upper bound أخر ال
+
+88
+00:09:14,580 --> 00:09:20,360
+supremum أو أصغر حد أعلى نرمزله بالرمز supremum S
+
+89
+00:09:20,360 --> 00:09:22,800
+أو least upper bound ل S
+
+90
+00:09:25,630 --> 00:09:32,390
+بالمثل ممكن انعرف ال minimum او اكبر حد ادنى اكبر
+
+91
+00:09:32,390 --> 00:09:35,330
+حد ادنى للمجموعة
+
+92
+00:09:40,350 --> 00:09:45,970
+لازم تكون ال set bounded below عشان اقدر اعرف ال
+
+93
+00:09:45,970 --> 00:09:49,990
+minimum او اكبر حد ادنى لازم تكون ال set bounded
+
+94
+00:09:49,990 --> 00:09:55,230
+below فلو كانت ال set bounded below فأي عدد حقيقي
+
+95
+00:09:55,230 --> 00:10:02,110
+w بيكون ال minimum لل set او بنسميه greatest lower
+
+96
+00:10:02,110 --> 00:10:08,180
+bound لل setإذا حقق شرطين الشرط الأول أن ال W
+
+97
+00:10:08,180 --> 00:10:14,120
+أبارعا lower bound ل 6S الشرط التاني أن ال W أكبر
+
+98
+00:10:14,120 --> 00:10:20,940
+من أو يساوي أي upper bound Z أي lower bound Z ل 6S
+
+99
+00:10:22,820 --> 00:10:27,200
+وبالتالي من الشرطين هدول .. الشرطين هدول معناهم مع
+
+100
+00:10:27,200 --> 00:10:33,320
+بعض أنه ال minimum أو greatest lower bound لل 6 هو
+
+101
+00:10:33,320 --> 00:10:38,240
+أكبر حد أدنى .. أكبر حد أدنى أو greatest lower
+
+102
+00:10:38,240 --> 00:10:45,280
+bound لل 6S نرمز لل infimum أو greatest lower
+
+103
+00:10:45,280 --> 00:10:52,560
+bound بالرمز هذا inf Sأو GLP ل S هذا اختصار
+
+104
+00:10:52,560 --> 00:10:59,400
+greatest lower bound of S تمام ففي
+
+105
+00:10:59,400 --> 00:11:07,080
+المثال هذا اللي هنا في
+
+106
+00:11:07,080 --> 00:11:11,900
+المثال اللي فوق هذا بنلاحظ
+
+107
+00:11:11,900 --> 00:11:19,080
+أنه Zero بساوي ال infimumلـ S اللي هي الفترة
+
+108
+00:11:19,080 --> 00:11:24,180
+المغلقة من سفر ل واحد لأن
+
+109
+00:11:24,180 --> 00:11:28,620
+السفر عبارة
+
+110
+00:11:28,620 --> 00:11:34,160
+عن lower bound أصغر من أو ساوي كل عناصر الست S
+
+111
+00:11:34,160 --> 00:11:40,340
+كمان لو أخدت أي lower bound للست S لازم هذا ال
+
+112
+00:11:40,340 --> 00:11:43,560
+lower bound يكون أصغر من أو ساوي السفر
+
+113
+00:11:46,660 --> 00:11:50,360
+وبالتالي السفر أكبر من أو يساوي أي lower bound هذا
+
+114
+00:11:50,360 --> 00:12:01,280
+واضح طيب كذلك الواحد بيساوي ال supremum لل 6S اللي
+
+115
+00:12:01,280 --> 00:12:08,170
+هي الفترة المغلقة من سفر لواحدليه؟ لأن الواحد
+
+116
+00:12:08,170 --> 00:12:12,470
+أبارعا upper bound للست هذه أكبر من أو ساوي كل
+
+117
+00:12:12,470 --> 00:12:20,650
+عناصر الفترة و لو أخدت أي V أكبر من أو ساوي كل
+
+118
+00:12:20,650 --> 00:12:24,950
+عناصر الفترة لكل
+
+119
+00:12:24,950 --> 00:12:28,630
+S في الفترة من 0 ل1
+
+120
+00:12:32,170 --> 00:12:37,050
+فبطلع عندى V أكبر من أو ساوي الواحد لأن الواحد
+
+121
+00:12:37,050 --> 00:12:43,130
+عنصر في الست و V أكبر من أو ساوي كل عناصر الست ف V
+
+122
+00:12:43,130 --> 00:12:49,130
+أكبر من أو ساوي الواحد وبالتالي V أو الواحد أصغر
+
+123
+00:12:49,130 --> 00:12:52,610
+من أو ساوي أي حد أعلى آخر
+
+124
+00:12:56,370 --> 00:13:02,410
+إذا الواحد هو عبارة عن ال supremum للست سفر و واحد
+
+125
+00:13:02,410 --> 00:13:08,190
+ال
+
+126
+00:13:08,190 --> 00:13:16,650
+.. عندي شوية ملاحظات هنا نشوفهم
+
+127
+00:13:16,650 --> 00:13:17,190
+مع بعض
+
+128
+00:13:30,420 --> 00:13:36,600
+لو الـ supremum تبع ال 6 موجود لو
+
+129
+00:13:36,600 --> 00:13:41,240
+ال 6 S ال supremum تبعها exists يعني إلها supremum
+
+130
+00:13:41,240 --> 00:13:47,180
+زي ال 6 هذه فلازم ال supremum هذا يكون unique وحيد
+
+131
+00:13:47,180 --> 00:13:52,540
+يعني مافيش أكتر من supremum فلبرهان
+
+132
+00:13:52,540 --> 00:13:53,060
+ذلك
+
+133
+00:13:59,930 --> 00:14:08,490
+اللي برهان ذلك افرضه ان ال 6S لها اكتر
+
+134
+00:14:08,490 --> 00:14:20,750
+من Supremum U1 Supremum and U2 Supremum تاني بدنا
+
+135
+00:14:20,750 --> 00:14:29,710
+نثبت ان U1 بدنا نثبتأن U1 بساوي U2 وبالتالي ال two
+
+136
+00:14:29,710 --> 00:14:32,990
+supremums بنطبقوا على بعض يعني ال supremum واحد
+
+137
+00:14:32,990 --> 00:14:41,590
+طيب أنا فيه أندي U1 upper bound
+
+138
+00:14:46,410 --> 00:14:52,110
+لست S ليه لأن U واحد عبارة عن supermom و ال
+
+139
+00:14:52,110 --> 00:14:55,990
+supermom بيكون upper كل supermom هو upper bound من
+
+140
+00:14:55,990 --> 00:15:03,510
+تعريفه صح الشرط الأول و U اتنين بساوي ال supermom
+
+141
+00:15:03,510 --> 00:15:13,770
+اللي هو least upper bound ل S هو أصغر حد أعلى
+
+142
+00:15:16,780 --> 00:15:25,220
+و هذا حد أعلى إذا .. إذا بيطلع عندي هذا أصغر حد
+
+143
+00:15:25,220 --> 00:15:30,360
+أعلى ل S وهذا حد أعلى فمن تعريف ال supremum أو
+
+144
+00:15:30,360 --> 00:15:36,720
+أصغر حد أعلى إذا U2 بيطلع أصغر من أو ساوي U1
+
+145
+00:15:36,720 --> 00:15:43,640
+نستنتج أن U2 أصغر من أو ساوي 1 نسمي المتباينة هذه
+
+146
+00:15:43,640 --> 00:15:53,050
+1كذلك انا عندي U1 او U2 المرة هاد هاخد U2 هاد
+
+147
+00:15:53,050 --> 00:16:03,770
+عبارة عن upper upper bound ل S ليه؟ لأنه ال
+
+148
+00:16:03,770 --> 00:16:09,530
+supremum ل S وكل supremum هو upper bound وعندي
+
+149
+00:16:09,530 --> 00:16:13,930
+كمان U1 عبارة عن
+
+150
+00:16:16,610 --> 00:16:24,390
+الـ least upper bound ل S يعني U1 هو أكبر upper
+
+151
+00:16:24,390 --> 00:16:30,170
+bound ل S و U2 upper bound فمن تعريف ال least
+
+152
+00:16:30,170 --> 00:16:37,030
+upper bound بطلع عندي أن ال U1 لازم يكون أصغر من
+
+153
+00:16:37,030 --> 00:16:45,010
+أو يساوي U2 فبنسمي المتباينة هذه اتنين الآن من
+
+154
+00:16:45,010 --> 00:16:46,050
+واحد و اتنين
+
+155
+00:16:49,530 --> 00:16:57,290
+أذا from واحد and اتنين نستنتج
+
+156
+00:16:57,290 --> 00:17:02,250
+أن يو اتنين أصغر من لو يساوي يو واحد و يو واحد
+
+157
+00:17:02,250 --> 00:17:03,850
+أصغر من لو يساوي يو اتنين
+
+158
+00:17:09,610 --> 00:17:15,170
+وبالتالي إذا هيك لو سمحت ما تتكلميش معي هنا بشرح
+
+159
+00:17:15,170 --> 00:17:16,910
+اللي بتتكلم ماتتكلمش
+
+160
+00:17:20,750 --> 00:17:25,170
+هين أثبتنا أنه لو الست إلها أكتر من supremum فال
+
+161
+00:17:25,170 --> 00:17:28,410
+supremums بيساويوا بعض وبالتالي في عندي ال
+
+162
+00:17:28,410 --> 00:17:34,050
+supremum is unique بالمثل ممكن أثبت أنه لو كانت
+
+163
+00:17:34,050 --> 00:17:37,730
+الست S إلها infimum يعني ال infimum تبعها exist
+
+164
+00:17:37,730 --> 00:17:44,990
+فأيضا بيطلع unique هو البرهانالمثل لبرهان ان ال
+
+165
+00:17:44,990 --> 00:17:49,490
+supreme م unique تمام؟ فحاسبكم الجزء التاني هذا
+
+166
+00:17:49,490 --> 00:17:55,530
+تكتب البرهان تبعه كتمرين او ك exercise في اي سؤال
+
+167
+00:17:55,530 --> 00:18:02,030
+واضح بالبرهان؟ في اي استفسار على البرهان؟
+
+168
+00:18:02,030 --> 00:18:08,430
+طيب ال .. في عندي لمة واحد
+
+169
+00:18:08,430 --> 00:18:23,560
+اتناش لمة كتير مهمةواللمة هذه تعتبر
+
+170
+00:18:23,560 --> 00:18:28,080
+يعني بتكافئ بتعريف ال supremum يعني ما معنى لو
+
+171
+00:18:28,080 --> 00:18:31,900
+أخدت مجموعة غير خالية مجموعة جزية من الأعداد
+
+172
+00:18:31,900 --> 00:18:38,680
+الحقيقية غير خالية وفرضت أن U is upper bound لها
+
+173
+00:18:40,090 --> 00:18:44,790
+فالسؤال متى ال upper bound U لست هذه S بيكون هو ال
+
+174
+00:18:44,790 --> 00:18:48,890
+super bound الجواب
+
+175
+00:18:48,890 --> 00:18:54,430
+في اللملة ان if and only if اذا كانت ال U بتحقق
+
+176
+00:18:54,430 --> 00:19:01,330
+الشرط هذا طب نشوف الشرط هذا نحاول نشوف الشرط هذا
+
+177
+00:19:01,330 --> 00:19:04,810
+نوضحه على رسمة
+
+178
+00:19:11,720 --> 00:19:19,300
+هذه مجموعة الأعداد الحقيقية وهذه
+
+179
+00:19:19,300 --> 00:19:30,040
+مجموعة S وهذه مجموعة جزئية من R وغير خالية تمام؟
+
+180
+00:19:30,040 --> 00:19:39,120
+وهذه U upper bound لل 6Sاللي لما بتقول عشان ال
+
+181
+00:19:39,120 --> 00:19:44,180
+upper bound هذا يكون هو ال supreme لازم يتحقق انه
+
+182
+00:19:44,180 --> 00:19:50,200
+لأي epsilon أكبر من السفر لازم ألاقي .. لازم ألاقي
+
+183
+00:19:50,200 --> 00:20:00,960
+هنا في عنصر نسميه S epsilon ينتمي ل S بحيث انه لو
+
+184
+00:20:00,960 --> 00:20:02,280
+طرحت من ال U
+
+185
+00:20:05,140 --> 00:20:12,320
+لو طرحت من ال U إبسلون فلازم ألاقي أنصر S إبسلون
+
+186
+00:20:12,320 --> 00:20:17,820
+يعتمد على إبسلون في S وهذا الأنصر أكبر من U سالب
+
+187
+00:20:17,820 --> 00:20:23,840
+إبسلون زي ما هو في الرسم مرة
+
+188
+00:20:23,840 --> 00:20:29,380
+تانية عشان ال upper bound هذا يكونSupremum ل S هو
+
+189
+00:20:29,380 --> 00:20:35,240
+أصغر حد أعلى لازم لأي أبسلون أكبر من السفر لو طرحت
+
+190
+00:20:35,240 --> 00:20:39,840
+من ال U الأبسلون العدد الموجب فلازم ألاقي عنصر في
+
+191
+00:20:39,840 --> 00:20:46,300
+ال set أكبر من U سالب أبسلون نشوف البرهان طبعا هذا
+
+192
+00:20:46,300 --> 00:20:50,670
+by conditional statementففي ال logic أو في
+
+193
+00:20:50,670 --> 00:20:56,250
+البراهين في ال only if part و ال if part من جزء
+
+194
+00:20:56,250 --> 00:21:00,690
+البرهان إلى جزعين هذا بيسميه ال if part و هذا ال
+
+195
+00:21:00,690 --> 00:21:06,870
+only if part نثبت الاتجاه هذا الآن هفرض أن الشرط
+
+196
+00:21:06,870 --> 00:21:14,550
+هذا متحقق و أثبت أن u هو ال supreme هو نعم مش s
+
+197
+00:21:14,550 --> 00:21:19,630
+epsilon هي عبارة عن ماذا بتقول؟neighborhood لأ لأ
+
+198
+00:21:19,630 --> 00:21:24,050
+ماحدش حاكى حاجة عن neighborhood لأ لأ دا ك U
+
+199
+00:21:24,050 --> 00:21:31,090
+capital U و بيكون يعني موضح في السياقه مافيش هنا
+
+200
+00:21:31,090 --> 00:21:35,730
+اي حاجة تتعلق بال neighborhood U عدد حقيقي اذا U
+
+201
+00:21:35,730 --> 00:21:41,000
+هنا بس عبارة عن upper bound ل Sعشان يكون هو الـ
+
+202
+00:21:41,000 --> 00:21:44,140
+supremum هو أصغر upper bound لازم يتحقق الشرط هذا
+
+203
+00:21:44,140 --> 00:21:52,200
+فنشوف افرض ان الشرط هذا يتحقق و بينا نثبت الـ U هو
+
+204
+00:21:52,200 --> 00:21:59,340
+ال supremum فلإثبات ال U هو ال supremumأحنا فرضين
+
+205
+00:21:59,340 --> 00:22:03,560
+أن ال U upper bound ارجع لتعريف ال supremum ال U
+
+206
+00:22:03,560 --> 00:22:07,980
+بيكون supremum إذا كان واحد upper bound وهذا ما
+
+207
+00:22:07,980 --> 00:22:11,780
+اتحقق من الفرض فرضينه upper bound الشرط التاني لو
+
+208
+00:22:11,780 --> 00:22:16,520
+أخدنا أي upper bound بيه فلازم نثبت أن ال U أصغر
+
+209
+00:22:16,520 --> 00:22:20,880
+من أو يساوي فتعالوا نثبت الشرط التاني من شروط ال
+
+210
+00:22:20,880 --> 00:22:28,570
+supremum let V be any upper bound ل Sلو كان ال U
+
+211
+00:22:28,570 --> 00:22:33,670
+بيساوي ال D فبطلع U أصغر من أو ساوي V وهو المطلوب،
+
+212
+00:22:33,670 --> 00:22:40,610
+إذا بفرض أن V لا يساوي ال U، إذا بدي أثبت أن U
+
+213
+00:22:40,610 --> 00:22:47,850
+أصغر من Vفإذا كان الان v و u أعداد حقيقية مختلفة
+
+214
+00:22:47,850 --> 00:22:51,350
+إذا الخاصية الثلاثية retricut من property بتقول
+
+215
+00:22:51,350 --> 00:22:56,550
+إما u أصغر من .. إما v أصغر من u أو u أصغر من v
+
+216
+00:22:56,550 --> 00:23:01,370
+أنا بدي u أثبت u أصغر من v تعالوا ناخد الاحتمال
+
+217
+00:23:01,370 --> 00:23:07,410
+الأول و نشوف إن هذا مستحيل ف assume
+
+218
+00:23:10,700 --> 00:23:15,960
+إذا هنا أخذنا الاحتمال الأول وفرضنا أنه هو الصح
+
+219
+00:23:15,960 --> 00:23:23,560
+الآن الفرق بين U وV بيطلع عدد موجب لأن U أكبر من V
+
+220
+00:23:24,640 --> 00:23:29,820
+الان سمى هذا الفرق ابسلون اذا الان ابسلون اللى هو
+
+221
+00:23:29,820 --> 00:23:35,660
+الفرق هذا عدد موجب طب من الفرض من الفرض هذا هذا هو
+
+222
+00:23:35,660 --> 00:23:41,320
+لأى ابسلون زى هذه لأى عدد موجب ابسلون هو ليكن هذا
+
+223
+00:23:41,320 --> 00:23:50,840
+احنا فرضين انه يوجد يوجد S ابسلون في Sوهذا ال S Y
+
+224
+00:23:50,840 --> 00:23:57,820
+أكبر من U سالب Y مصدود؟ هذا من الفرض الآن من هنا
+
+225
+00:23:57,820 --> 00:24:06,140
+من تعريف ال Y ال U سالب Y بساوي D إذا هنا عندي
+
+226
+00:24:06,140 --> 00:24:13,980
+أصبح D أصغر من S Y وهذا بتناقض مع كون V upper
+
+227
+00:24:13,980 --> 00:24:19,460
+boundأحنا فرضين أن V upper bound ل S فكيف V upper
+
+228
+00:24:19,460 --> 00:24:25,260
+bound و في نفس الوقت V أصغر من عنصر M في المجموعة
+
+229
+00:24:25,260 --> 00:24:31,080
+S هذا بتناقض مع تعريف ال upper bound إذا هذا
+
+230
+00:24:31,080 --> 00:24:37,920
+التناقض بيقول لي إن الاحتمال هذا غلط أو مستحيل طيب
+
+231
+00:24:37,920 --> 00:24:44,550
+أنا عندياحنا استنتجنا من ال hypothesis ان الاحتمال
+
+232
+00:24:44,550 --> 00:24:50,790
+هذا او هذا صح الان هذا مش صح اذا يبقى ان هذا صح
+
+233
+00:24:50,790 --> 00:24:56,730
+اذا we are left يعني الان احنا طريقنا بان you أصغر
+
+234
+00:24:56,730 --> 00:25:01,050
+من me وبالتالي هذا بيكمل برهان الشرط التاني من ال
+
+235
+00:25:01,050 --> 00:25:05,750
+supremem يعني you هو ال suprememإذن هنا أثبتنا إنه
+
+236
+00:25:05,750 --> 00:25:10,470
+لو الشرط هذا اتحقق فال upper bound U هذا بيطلع هو
+
+237
+00:25:10,470 --> 00:25:15,090
+ال supreme هو أصغر upper bound اللي يعني بدنا نثبت
+
+238
+00:25:15,090 --> 00:25:23,110
+العكس .. نثبت العكس .. نثبت العكس لو كان .. لو ..
+
+239
+00:25:23,110 --> 00:25:27,450
+لو كان U هو ال supreme لو فرضنا U هو ال supreme
+
+240
+00:25:27,450 --> 00:25:31,550
+بدنا نثبت إن ال U بيحقق الشرط اللي على اليمين
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..372e8b2061acb1dafa4feb71b068e7c0193bf943
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4518, "start": 23.3, "end": 45.18, "text": "الـ completeness property of R عشان نعرف أيه ال completeness property of R فبنحتاج لبعض التعريفات فأول تعريف ما معناه أن عدد حقيقي يكون upper bound للمجموعة S معناه أن ال U أكبر من أو ساوي كل عناصر ال 6S", "tokens": [6027, 39184, 1557, 15264, 4707, 295, 497, 6225, 8592, 7649, 8717, 3615, 28480, 36632, 3224, 2423, 1557, 15264, 4707, 295, 497, 6156, 3555, 1863, 33753, 26108, 5296, 3555, 3615, 11242, 16712, 3615, 16572, 5172, 9307, 6156, 10721, 12610, 37279, 16572, 5172, 19446, 20449, 8315, 3224, 14739, 6225, 3215, 3215, 11331, 38436, 38436, 7251, 30544, 6597, 5472, 5296, 19528, 7435, 2304, 2407, 27884, 318, 20449, 8315, 3224, 14739, 2423, 624, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 28242, 18871, 33546, 2288, 2423, 1386, 50], "avg_logprob": -0.168474262602189, "compression_ratio": 1.5824742268041236, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 23.3, "end": 24.08, "word": "الـ", 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0.8573404947916666}, {"start": 131.5, "end": 131.78, "word": " زي", "probability": 0.952880859375}, {"start": 131.78, "end": 132.14, "word": " هذه", "probability": 0.92236328125}, {"start": 132.14, "end": 132.7, "word": " فكل", "probability": 0.974609375}, {"start": 132.7, "end": 133.06, "word": " عدد", "probability": 0.9873046875}, {"start": 133.06, "end": 133.48, "word": " أكبر", "probability": 0.9630533854166666}, {"start": 133.48, "end": 133.68, "word": " من", "probability": 0.9951171875}, {"start": 133.68, "end": 133.78, "word": " ال", "probability": 0.72900390625}, {"start": 133.78, "end": 134.04, "word": " upper", "probability": 0.8134765625}, {"start": 134.04, "end": 134.42, "word": " bound", "probability": 0.923828125}, {"start": 134.42, "end": 134.6, "word": " هو", "probability": 0.978515625}, {"start": 134.6, "end": 134.9, "word": " upper", "probability": 0.9150390625}, {"start": 134.9, "end": 135.32, "word": " bound", "probability": 0.91455078125}, {"start": 135.32, "end": 136.2, "word": " آخر", "probability": 0.78271484375}, {"start": 136.2, "end": 137.54, "word": " بالمثل", "probability": 0.923583984375}, {"start": 137.54, "end": 138.2, "word": " بالنسبة", "probability": 0.992431640625}, {"start": 138.2, "end": 138.56, "word": " لل", "probability": 0.9267578125}, {"start": 138.56, "end": 139.24, "word": " lower", "probability": 0.65185546875}, {"start": 139.24, "end": 139.7, "word": " bounds", "probability": 0.75537109375}, {"start": 139.7, "end": 139.9, "word": " إذا", "probability": 0.86572265625}, {"start": 139.9, "end": 140.36, "word": " المجموعة", "probability": 0.91806640625}, {"start": 140.36, "end": 140.6, "word": " لها", "probability": 0.934326171875}, {"start": 140.6, "end": 140.86, "word": " lower", "probability": 0.92236328125}, {"start": 140.86, "end": 141.22, "word": " bound", "probability": 0.90087890625}, {"start": 141.22, "end": 141.68, "word": " واحد", "probability": 0.94384765625}, {"start": 141.68, "end": 142.6, "word": " فممكن", "probability": 0.9469401041666666}, {"start": 142.6, "end": 143.06, "word": " نجد", "probability": 0.99267578125}, {"start": 143.06, "end": 143.68, "word": " عدد", "probability": 0.9884440104166666}, {"start": 143.68, "end": 144.14, "word": " لانهاء", "probability": 0.8101806640625}, {"start": 144.14, "end": 144.3, "word": " من", "probability": 0.982421875}, {"start": 144.3, "end": 144.44, "word": " ال", "probability": 0.79833984375}, {"start": 144.44, "end": 144.66, "word": " lower", "probability": 0.78173828125}, {"start": 144.66, "end": 145.12, "word": " bounds", "probability": 0.82861328125}], "temperature": 1.0}, {"id": 6, "seek": 16861, "start": 146.09, "end": 168.61, "text": "لو أخدنا المجموعة S بالساوية فاي فأي عدد حقيقي بيكون upper bound وفي نفس الوقت بيكون lower bound للمجموعة هذه و البرهان by contradiction نفرض على النقيض أن يوجد R0 عدد حقيقي و هذا العدد الحقيقي ما هوش upper bound", "tokens": [1211, 2407, 5551, 9778, 3215, 8315, 9673, 7435, 2304, 2407, 27884, 318, 20666, 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0.7154296875}, {"start": 149.13, "end": 149.51, "word": " فاي", "probability": 0.4605712890625}, {"start": 149.51, "end": 150.43, "word": " فأي", "probability": 0.88671875}, {"start": 150.43, "end": 150.77, "word": " عدد", "probability": 0.986328125}, {"start": 150.77, "end": 151.41, "word": " حقيقي", "probability": 0.9851888020833334}, {"start": 151.41, "end": 151.97, "word": " بيكون", "probability": 0.83251953125}, {"start": 151.97, "end": 152.29, "word": " upper", "probability": 0.8515625}, {"start": 152.29, "end": 152.71, "word": " bound", "probability": 0.892578125}, {"start": 152.71, "end": 152.93, "word": " وفي", "probability": 0.671142578125}, {"start": 152.93, "end": 153.13, "word": " نفس", "probability": 0.997314453125}, {"start": 153.13, "end": 153.53, "word": " الوقت", "probability": 0.84521484375}, {"start": 153.53, "end": 154.01, "word": " بيكون", "probability": 0.837890625}, {"start": 154.01, "end": 155.17, "word": " lower", "probability": 0.87255859375}, {"start": 155.17, "end": 155.57, "word": " bound", "probability": 0.91845703125}, {"start": 155.57, "end": 156.31, "word": " للمجموعة", "probability": 0.904296875}, {"start": 156.31, "end": 156.71, "word": " هذه", "probability": 0.7548828125}, {"start": 156.71, "end": 156.95, "word": " و", "probability": 0.548828125}, {"start": 156.95, "end": 157.93, "word": " البرهان", "probability": 0.761505126953125}, {"start": 157.93, "end": 158.13, "word": " by", "probability": 0.79833984375}, {"start": 158.13, "end": 158.89, "word": " contradiction", "probability": 0.92919921875}, {"start": 158.89, "end": 160.33, "word": " نفرض", "probability": 0.7914225260416666}, {"start": 160.33, "end": 161.35, "word": " على", "probability": 0.8994140625}, {"start": 161.35, "end": 161.99, "word": " النقيض", "probability": 0.8663736979166666}, {"start": 161.99, "end": 162.23, "word": " أن", "probability": 0.5693359375}, {"start": 162.23, "end": 162.85, "word": " يوجد", "probability": 0.912109375}, {"start": 162.85, "end": 163.57, "word": " R0", "probability": 0.614013671875}, {"start": 163.57, "end": 163.91, "word": " عدد", "probability": 0.9853515625}, {"start": 163.91, "end": 164.49, "word": " حقيقي", "probability": 0.9847005208333334}, {"start": 164.49, "end": 165.63, "word": " و", "probability": 0.5498046875}, {"start": 165.63, "end": 166.01, "word": " هذا", "probability": 0.8330078125}, {"start": 166.01, "end": 166.47, "word": " العدد", "probability": 0.9744466145833334}, {"start": 166.47, "end": 167.03, "word": " الحقيقي", "probability": 0.9641927083333334}, {"start": 167.03, "end": 167.25, "word": " ما", "probability": 0.90869140625}, {"start": 167.25, "end": 167.81, "word": " هوش", "probability": 0.554443359375}, {"start": 167.81, "end": 168.19, "word": " upper", "probability": 0.88037109375}, {"start": 168.19, "end": 168.61, "word": " bound", "probability": 0.92578125}], "temperature": 1.0}, {"id": 7, "seek": 19884, "start": 169.96, "end": 198.84, "text": "معناته إذا كان R0 ليس upper bound لـ S معناته بقدر ألاقي عنصر S في المجموعة capital S أكبر من الـ R0 وهذا بتديني التناقض لأن المجموعة S لا يوجد بيها عناصر فرض أنه يوجد فرض أنه يوجد", "tokens": [2304, 3615, 8315, 47395, 11933, 15730, 25961, 497, 15, 32239, 3794, 6597, 5472, 5296, 39184, 318, 20449, 8315, 47395, 4724, 28543, 2288, 5551, 15040, 38436, 18871, 9381, 2288, 318, 8978, 9673, 7435, 2304, 2407, 27884, 4238, 318, 5551, 4117, 26890, 9154, 2423, 39184, 497, 15, 37037, 15730, 39894, 3215, 9957, 1829, 16712, 8315, 4587, 11242, 5296, 33456, 9673, 7435, 2304, 2407, 27884, 318, 20193, 7251, 29245, 3215, 4724, 1829, 11296, 18871, 33546, 2288, 6156, 43042, 14739, 3224, 7251, 29245, 3215, 6156, 43042, 14739, 3224, 7251, 29245, 3215], "avg_logprob": -0.22531959516080943, "compression_ratio": 1.664804469273743, "no_speech_prob": 0.0, "words": [{"start": 169.96, "end": 170.78, "word": "معناته", "probability": 0.8876953125}, {"start": 170.78, "end": 171.06, "word": " إذا", "probability": 0.7222900390625}, {"start": 171.06, "end": 171.38, "word": " كان", "probability": 0.9560546875}, {"start": 171.38, "end": 171.84, "word": " R0", "probability": 0.5150146484375}, {"start": 171.84, "end": 172.2, "word": " ليس", "probability": 0.93212890625}, {"start": 172.2, "end": 172.44, "word": " upper", "probability": 0.79248046875}, {"start": 172.44, "end": 172.74, "word": " bound", "probability": 0.873046875}, {"start": 172.74, "end": 172.94, "word": " لـ", "probability": 0.5682373046875}, {"start": 172.94, "end": 173.06, "word": " S", "probability": 0.70947265625}, {"start": 173.06, "end": 173.46, "word": " معناته", "probability": 0.7334391276041666}, {"start": 173.46, "end": 173.82, "word": " بقدر", "probability": 0.9396158854166666}, {"start": 173.82, "end": 174.32, "word": " ألاقي", "probability": 0.7430013020833334}, {"start": 174.32, "end": 175.38, "word": " عنصر", "probability": 0.8818359375}, {"start": 175.38, "end": 175.66, "word": " S", "probability": 0.94921875}, {"start": 175.66, "end": 175.94, "word": " في", "probability": 0.951171875}, {"start": 175.94, "end": 176.54, "word": " المجموعة", "probability": 0.9421875}, {"start": 176.54, "end": 176.96, "word": " capital", "probability": 0.64794921875}, {"start": 176.96, "end": 177.36, "word": " S", "probability": 0.97412109375}, {"start": 177.36, "end": 177.86, "word": " أكبر", "probability": 0.9611002604166666}, {"start": 177.86, "end": 179.0, "word": " من", "probability": 0.990234375}, {"start": 179.0, "end": 179.16, "word": " الـ", "probability": 0.712646484375}, {"start": 179.16, "end": 179.76, "word": " R0", "probability": 0.88818359375}, {"start": 179.76, "end": 182.4, "word": " وهذا", "probability": 0.90771484375}, {"start": 182.4, "end": 182.82, "word": " بتديني", "probability": 0.693756103515625}, {"start": 182.82, "end": 183.28, "word": " التناقض", "probability": 0.8126220703125}, {"start": 183.28, "end": 183.48, "word": " لأن", "probability": 0.802978515625}, {"start": 183.48, "end": 184.06, "word": " المجموعة", "probability": 0.9337890625}, {"start": 184.06, "end": 184.38, "word": " S", "probability": 0.96630859375}, {"start": 184.38, "end": 184.64, "word": " لا", "probability": 0.72705078125}, {"start": 184.64, "end": 185.0, "word": " يوجد", "probability": 0.9036458333333334}, {"start": 185.0, "end": 185.26, "word": " بيها", "probability": 0.9152018229166666}, {"start": 185.26, "end": 185.82, "word": " عناصر", "probability": 0.9562174479166666}, {"start": 185.82, "end": 188.46, "word": " فرض", "probability": 0.5928955078125}, {"start": 188.46, "end": 188.96, "word": " أنه", "probability": 0.662841796875}, {"start": 188.96, "end": 189.88, "word": " يوجد", "probability": 0.97900390625}, {"start": 189.88, "end": 197.96, "word": " فرض", "probability": 0.6422119140625}, {"start": 197.96, "end": 198.32, "word": " أنه", "probability": 0.824462890625}, {"start": 198.32, "end": 198.84, "word": " يوجد", "probability": 0.9851888020833334}], "temperature": 1.0}, {"id": 8, "seek": 21584, "start": 199.58, "end": 215.84, "text": "عدد حقيقي وما هواش upper bound هذا خطأ هذا معناه ان every real number is upper bound بالمثل ممكن اثبات ان every real number is lower bound للمجموعة الخالية five", "tokens": [22488, 3215, 11331, 38436, 38436, 4032, 15042, 31439, 33599, 6597, 5472, 23758, 16490, 9566, 10721, 23758, 20449, 8315, 3224, 16472, 633, 957, 1230, 307, 6597, 5472, 20666, 2304, 12984, 1211, 3714, 43020, 1975, 12984, 3555, 9307, 16472, 633, 957, 1230, 307, 3126, 5472, 5296, 19528, 7435, 2304, 2407, 27884, 33962, 6027, 10632, 1732], "avg_logprob": -0.1457609937146858, "compression_ratio": 1.4768211920529801, "no_speech_prob": 0.0, "words": [{"start": 199.58, "end": 200.0, "word": "عدد", "probability": 0.900634765625}, {"start": 200.0, "end": 200.68, "word": " حقيقي", "probability": 0.9860026041666666}, {"start": 200.68, "end": 201.98, "word": " وما", "probability": 0.939697265625}, {"start": 201.98, "end": 202.42, "word": " هواش", "probability": 0.796630859375}, {"start": 202.42, "end": 202.68, "word": " upper", "probability": 0.86572265625}, {"start": 202.68, "end": 203.08, "word": " bound", "probability": 0.8984375}, {"start": 203.08, "end": 203.32, "word": " هذا", "probability": 0.42724609375}, {"start": 203.32, "end": 203.82, "word": " خطأ", "probability": 0.9908854166666666}, {"start": 203.82, "end": 204.46, "word": " هذا", "probability": 0.366455078125}, {"start": 204.46, "end": 204.9, "word": " معناه", "probability": 0.9754231770833334}, {"start": 204.9, "end": 205.1, "word": " ان", "probability": 0.68994140625}, {"start": 205.1, "end": 206.04, "word": " every", "probability": 0.671875}, {"start": 206.04, "end": 206.6, "word": " real", "probability": 0.9375}, {"start": 206.6, "end": 206.98, "word": " number", "probability": 0.97998046875}, {"start": 206.98, "end": 207.26, "word": " is", "probability": 0.94921875}, {"start": 207.26, "end": 207.62, "word": " upper", "probability": 0.89111328125}, {"start": 207.62, "end": 208.36, "word": " bound", "probability": 0.91552734375}, {"start": 208.36, "end": 209.36, "word": " بالمثل", "probability": 0.9462890625}, {"start": 209.36, "end": 209.7, "word": " ممكن", "probability": 0.980224609375}, {"start": 209.7, "end": 210.1, "word": " اثبات", "probability": 0.9285888671875}, {"start": 210.1, "end": 210.28, "word": " ان", "probability": 0.92529296875}, {"start": 210.28, "end": 210.58, "word": " every", "probability": 0.796875}, {"start": 210.58, "end": 210.92, "word": " real", "probability": 0.9443359375}, {"start": 210.92, "end": 211.42, "word": " number", "probability": 0.96826171875}, {"start": 211.42, "end": 212.26, "word": " is", "probability": 0.9443359375}, {"start": 212.26, "end": 212.66, "word": " lower", "probability": 0.75341796875}, {"start": 212.66, "end": 213.16, "word": " bound", "probability": 0.91796875}, {"start": 213.16, "end": 214.3, "word": " للمجموعة", "probability": 0.866455078125}, {"start": 214.3, "end": 215.0, "word": " الخالية", "probability": 0.9889322916666666}, {"start": 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ساوي الواحد لأن الواحد عنصر في الست و V أكبر من أو ساوي كل عناصر الست ف V أكبر من أو ساوي الواحد وبالتالي V أو الواحد أصغر من أو ساوي أي حد أعلى آخر", "tokens": [5172, 3555, 9566, 1211, 3615, 43242, 7578, 691, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 14407, 24401, 5296, 33456, 2423, 14407, 24401, 18871, 9381, 2288, 8978, 21136, 2655, 4032, 691, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 28242, 18871, 33546, 2288, 21136, 2655, 6156, 691, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 14407, 24401, 46599, 6027, 2655, 6027, 1829, 691, 34051, 2423, 14407, 24401, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 36632, 11331, 3215, 5551, 3615, 23942, 19753, 34740], "avg_logprob": -0.11745689364000299, "compression_ratio": 2.255639097744361, "no_speech_prob": 0.0, "words": [{"start": 752.1700000000001, "end": 752.97, "word": "فبطلع", "probability": 0.71630859375}, {"start": 752.97, "end": 753.37, "word": " عندى", "probability": 0.6611328125}, {"start": 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" bound", "probability": 0.8955078125}], "temperature": 1.0}, {"id": 34, "seek": 91377, "start": 886.41, "end": 913.77, "text": "لست S ليه لأن U واحد عبارة عن supermom و ال supermom بيكون upper كل supermom هو upper bound من تعريفه صح الشرط الأول و U اتنين بساوي ال supermom اللي هو least upper bound ل S هو أصغر حد أعلى", "tokens": [1211, 14851, 318, 32239, 3224, 5296, 33456, 624, 36764, 24401, 6225, 3555, 9640, 3660, 18871, 1687, 42544, 4032, 2423, 1687, 42544, 4724, 1829, 30544, 6597, 28242, 1687, 42544, 31439, 6597, 5472, 9154, 37279, 16572, 5172, 3224, 20328, 5016, 25124, 2288, 9566, 16247, 12610, 4032, 624, 1975, 2655, 1863, 9957, 4724, 3794, 995, 45865, 2423, 1687, 42544, 13672, 1829, 31439, 1935, 6597, 5472, 5296, 318, 31439, 5551, 9381, 17082, 2288, 11331, 3215, 5551, 3615, 23942], "avg_logprob": -0.23291667302449545, "compression_ratio": 1.5747126436781609, "no_speech_prob": 0.0, "words": [{"start": 886.41, "end": 887.15, "word": "لست", "probability": 0.6650390625}, {"start": 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upper", "probability": 0.3876953125}, {"start": 893.23, "end": 893.53, "word": " كل", "probability": 0.370849609375}, {"start": 893.53, "end": 894.47, "word": " supermom", "probability": 0.962890625}, {"start": 894.47, "end": 894.95, "word": " هو", "probability": 0.9599609375}, {"start": 894.95, "end": 895.27, "word": " upper", "probability": 0.90380859375}, {"start": 895.27, "end": 895.65, "word": " bound", "probability": 0.8896484375}, {"start": 895.65, "end": 895.99, "word": " من", "probability": 0.90869140625}, {"start": 895.99, "end": 896.55, "word": " تعريفه", "probability": 0.98876953125}, {"start": 896.55, "end": 896.87, "word": " صح", "probability": 0.87158203125}, {"start": 896.87, "end": 897.71, "word": " الشرط", "probability": 0.8279622395833334}, {"start": 897.71, "end": 898.11, "word": " الأول", "probability": 0.928955078125}, {"start": 898.11, "end": 900.15, "word": " و", "probability": 0.86865234375}, {"start": 900.15, "end": 900.43, "word": " U", "probability": 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"probability": 0.9871826171875}, {"start": 996.85, "end": 997.03, "word": " من", "probability": 0.9755859375}, {"start": 997.03, "end": 997.25, "word": " أو", "probability": 0.93896484375}, {"start": 997.25, "end": 997.97, "word": " يساوي", "probability": 0.9405517578125}, {"start": 997.97, "end": 998.83, "word": " U2", "probability": 0.983154296875}, {"start": 998.83, "end": 1001.33, "word": " فبنسمي", "probability": 0.96015625}, {"start": 1001.33, "end": 1002.13, "word": " المتباينة", "probability": 0.94384765625}, {"start": 1002.13, "end": 1002.67, "word": " هذه", "probability": 0.67431640625}, {"start": 1002.67, "end": 1003.19, "word": " اتنين", "probability": 0.813232421875}, {"start": 1003.19, "end": 1004.75, "word": " الآن", "probability": 0.701904296875}, {"start": 1004.75, "end": 1005.01, "word": " من", "probability": 0.99072265625}, {"start": 1005.01, "end": 1005.43, "word": " واحد", "probability": 0.963134765625}, {"start": 1005.43, "end": 1005.59, "word": " و", 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1034.63, "end": 1034.75, "word": " هنا", "probability": 0.93408203125}, {"start": 1034.75, "end": 1035.17, "word": " بشرح", "probability": 0.8878580729166666}, {"start": 1035.17, "end": 1035.77, "word": " اللي", "probability": 0.777099609375}, {"start": 1035.77, "end": 1036.21, "word": " بتتكلم", "probability": 0.945556640625}, {"start": 1036.21, "end": 1036.91, "word": " ماتتكلمش", "probability": 0.8687337239583334}], "temperature": 1.0}, {"id": 40, "seek": 106147, "start": 1040.75, "end": 1061.47, "text": "هين أثبتنا أنه لو الست إلها أكتر من supremum فال supremums بيساويوا بعض وبالتالي في عندي ال supremum is unique بالمثل ممكن أثبت أنه لو كانت الست S إلها infimum يعني ال infimum تبعها exist فأيضا بيطلع unique هو البرهان", "tokens": [3224, 9957, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 45164, 2423, 14851, 11933, 1211, 11296, 5551, 4117, 2655, 2288, 9154, 23710, 449, 6156, 6027, 23710, 8099, 4724, 1829, 3794, 995, 45865, 14407, 45030, 11242, 46599, 6027, 2655, 6027, 1829, 8978, 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كتمرين او ك exercise في اي سؤال واضح بالبرهان؟ في اي استفسار على البرهان؟ طيب ال .. في عندي لمة واحد اتناش لمة كتير مهمة", "tokens": [45340, 12984, 1211, 5296, 26890, 3224, 7649, 16472, 2423, 27756, 3714, 3845, 46811, 10943, 22807, 6156, 5016, 32277, 3555, 24793, 25724, 11622, 38207, 16712, 7649, 1829, 23758, 6055, 4117, 2655, 3555, 2423, 26890, 3224, 7649, 6055, 3555, 3615, 3224, 9122, 39237, 2288, 9957, 1975, 2407, 9122, 5380, 8978, 1975, 1829, 8608, 33604, 6027, 4032, 46958, 5016, 20666, 26890, 3224, 7649, 22807, 8978, 1975, 1829, 44713, 36178, 9640, 15844, 2423, 26890, 3224, 7649, 22807, 23032, 1829, 3555, 2423, 4386, 8978, 18871, 16254, 32767, 3660, 36764, 24401, 1975, 2655, 1863, 33599, 32767, 3660, 9122, 2655, 13546, 3714, 16095, 3660], "avg_logprob": -0.20232779882392105, "compression_ratio": 1.6650717703349283, "no_speech_prob": 0.0, "words": [{"start": 1062.13, "end": 1063.11, "word": "المثل", "probability": 0.656982421875}, {"start": 1063.11, "end": 1063.85, "word": " 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"word": " نشوف", "probability": 0.9645182291666666}, {"start": 1138.33, "end": 1138.83, "word": " الشرط", "probability": 0.9767252604166666}, {"start": 1138.83, "end": 1139.25, "word": " هذا", "probability": 0.9072265625}, {"start": 1139.25, "end": 1140.21, "word": " نحاول", "probability": 0.8858642578125}, {"start": 1140.21, "end": 1140.53, "word": " نشوف", "probability": 0.9305013020833334}, {"start": 1140.53, "end": 1140.99, "word": " الشرط", "probability": 0.9791666666666666}, {"start": 1140.99, "end": 1141.33, "word": " هذا", "probability": 0.9462890625}, {"start": 1141.33, "end": 1143.05, "word": " نوضحه", "probability": 0.85341796875}, {"start": 1143.05, "end": 1144.17, "word": " على", "probability": 0.90771484375}, {"start": 1144.17, "end": 1144.81, "word": " رسمة", "probability": 0.8670247395833334}], "temperature": 1.0}, {"id": 44, "seek": 117598, "start": 1151.72, "end": 1175.98, "text": "هذه مجموعة الأعداد الحقيقية وهذه مجموعة S وهذه مجموعة جزئية من R وغير خالية تمام؟ وهذه U upper bound لل 6S", "tokens": [3224, 24192, 3714, 7435, 2304, 2407, 27884, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 37037, 24192, 3714, 7435, 2304, 2407, 27884, 318, 37037, 24192, 3714, 7435, 2304, 2407, 27884, 10874, 11622, 19986, 10632, 9154, 497, 4032, 17082, 13546, 16490, 6027, 10632, 46811, 10943, 22807, 37037, 24192, 624, 6597, 5472, 24976, 1386, 50], "avg_logprob": -0.24012382300394886, "compression_ratio": 1.462809917355372, "no_speech_prob": 0.0, "words": [{"start": 1151.72, "end": 1152.2, "word": "هذه", "probability": 0.763427734375}, {"start": 1152.2, "end": 1153.42, "word": " مجموعة", "probability": 0.87099609375}, {"start": 1153.42, "end": 1153.94, "word": " الأعداد", "probability": 0.7832845052083334}, {"start": 1153.94, "end": 1154.84, "word": " الحقيقية", "probability": 0.9254150390625}, {"start": 1154.84, "end": 1159.3, "word": " وهذه", "probability": 0.812744140625}, {"start": 1159.3, "end": 1160.08, "word": " مجموعة", "probability": 0.83642578125}, {"start": 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0.98828125}, {"start": 1280.89, "end": 1281.27, "word": " neighborhood", "probability": 0.69677734375}, {"start": 1281.27, "end": 1283.21, "word": " لأ", "probability": 0.593017578125}, {"start": 1283.21, "end": 1283.37, "word": " لأ", "probability": 0.978759765625}, {"start": 1283.37, "end": 1283.67, "word": " دا", "probability": 0.699951171875}, {"start": 1283.67, "end": 1283.81, "word": " ك", "probability": 0.7421875}, {"start": 1283.81, "end": 1284.05, "word": " U", "probability": 0.83447265625}, {"start": 1284.05, "end": 1284.51, "word": " capital", "probability": 0.5986328125}, {"start": 1284.51, "end": 1284.91, "word": " U", "probability": 0.8642578125}, {"start": 1284.91, "end": 1285.23, "word": " و", "probability": 0.70751953125}, {"start": 1285.23, "end": 1286.33, "word": " بيكون", "probability": 0.736572265625}, {"start": 1286.33, "end": 1286.65, "word": " يعني", "probability": 0.9697265625}, {"start": 1286.65, "end": 1288.05, "word": " موضح", "probability": 0.969970703125}, {"start": 1288.05, "end": 1288.69, "word": " في", "probability": 0.92822265625}, {"start": 1288.69, "end": 1289.49, "word": " السياقه", "probability": 0.8106689453125}, {"start": 1289.49, "end": 1290.87, "word": " مافيش", "probability": 0.9464518229166666}, {"start": 1290.87, "end": 1291.09, "word": " هنا", "probability": 0.974609375}, {"start": 1291.09, "end": 1291.33, "word": " اي", "probability": 0.7139892578125}, {"start": 1291.33, "end": 1291.73, "word": " حاجة", "probability": 0.9913736979166666}, {"start": 1291.73, "end": 1292.21, "word": " تتعلق", "probability": 0.8782958984375}, {"start": 1292.21, "end": 1292.35, "word": " بال", "probability": 0.9638671875}, {"start": 1292.35, "end": 1292.67, "word": " neighborhood", "probability": 0.68798828125}, {"start": 1292.67, "end": 1293.59, "word": " U", "probability": 0.568359375}, {"start": 1293.59, "end": 1293.95, "word": " عدد", "probability": 0.97021484375}, {"start": 1293.95, "end": 1294.43, "word": " حقيقي", "probability": 0.9775390625}, {"start": 1294.43, "end": 1295.43, "word": " اذا", "probability": 0.6356201171875}, {"start": 1295.43, "end": 1295.73, "word": " U", "probability": 0.796875}, {"start": 1295.73, "end": 1296.11, "word": " هنا", "probability": 0.98681640625}, {"start": 1296.11, "end": 1296.73, "word": " بس", "probability": 0.977783203125}, {"start": 1296.73, "end": 1297.29, "word": " عبارة", "probability": 0.9501953125}, {"start": 1297.29, "end": 1297.45, "word": " عن", "probability": 0.9853515625}, {"start": 1297.45, "end": 1297.75, "word": " upper", "probability": 0.8671875}, {"start": 1297.75, "end": 1298.13, "word": " bound", "probability": 0.87841796875}, {"start": 1298.13, "end": 1298.31, "word": " ل", "probability": 0.97119140625}, {"start": 1298.31, "end": 1298.63, "word": " S", "probability": 0.81689453125}], "temperature": 1.0}, {"id": 50, "seek": 131626, "start": 1299.76, "end": 1316.26, "text": "عشان يكون هو الـ supremum هو أصغر upper bound لازم يتحقق الشرط هذا فنشوف افرض ان الشرط هذا يتحقق و بينا نثبت الـ U هو ال supremum فلإثبات ال U هو ال supremum", "tokens": [3615, 8592, 7649, 7251, 30544, 31439, 2423, 39184, 23710, 449, 31439, 5551, 9381, 17082, 2288, 6597, 5472, 5296, 31377, 2304, 7251, 2655, 5016, 4587, 4587, 25124, 2288, 9566, 23758, 6156, 1863, 8592, 38688, 1975, 5172, 43042, 16472, 25124, 2288, 9566, 23758, 7251, 2655, 5016, 4587, 4587, 4032, 4724, 1829, 8315, 8717, 12984, 3555, 2655, 2423, 39184, 624, 31439, 2423, 23710, 449, 6156, 1211, 28814, 12984, 3555, 9307, 2423, 624, 31439, 2423, 23710, 449], "avg_logprob": -0.24070945261298, "compression_ratio": 1.662162162162162, "no_speech_prob": 0.0, "words": [{"start": 1299.76, "end": 1300.24, "word": "عشان", "probability": 0.8821614583333334}, {"start": 1300.24, "end": 1300.56, "word": " يكون", "probability": 0.970947265625}, {"start": 1300.56, "end": 1300.8, "word": " هو", "probability": 0.8671875}, {"start": 1300.8, "end": 1301.0, "word": " الـ", "probability": 0.643310546875}, {"start": 1301.0, 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"probability": 0.9658203125}, {"start": 1336.08, "end": 1336.52, "word": " أصغر", "probability": 0.9915771484375}, {"start": 1336.52, "end": 1336.72, "word": " من", "probability": 0.97021484375}, {"start": 1336.72, "end": 1336.84, "word": " أو", "probability": 0.81005859375}, {"start": 1336.84, "end": 1337.34, "word": " يساوي", "probability": 0.802490234375}, {"start": 1337.34, "end": 1339.08, "word": " فتعالوا", "probability": 0.816162109375}, {"start": 1339.08, "end": 1339.4, "word": " نثبت", "probability": 0.9910888671875}, {"start": 1339.4, "end": 1339.76, "word": " الشرط", "probability": 0.9820963541666666}, {"start": 1339.76, "end": 1340.16, "word": " التاني", "probability": 0.9871419270833334}, {"start": 1340.16, "end": 1340.38, "word": " من", "probability": 0.94189453125}, {"start": 1340.38, "end": 1340.74, "word": " شروط", "probability": 0.9786783854166666}, {"start": 1340.74, "end": 1340.88, "word": " ال", "probability": 0.8759765625}, {"start": 1340.88, "end": 1341.38, "word": " supremum", "probability": 0.90087890625}, {"start": 1341.38, "end": 1342.84, "word": " let", "probability": 0.259033203125}, {"start": 1342.84, "end": 1343.24, "word": " V", "probability": 0.74365234375}, {"start": 1343.24, "end": 1343.56, "word": " be", "probability": 0.87060546875}, {"start": 1343.56, "end": 1343.96, "word": " any", "probability": 0.9306640625}, {"start": 1343.96, "end": 1344.34, "word": " upper", "probability": 0.86181640625}, {"start": 1344.34, "end": 1344.7, "word": " bound", "probability": 0.90478515625}, {"start": 1344.7, "end": 1344.86, "word": " ل", "probability": 0.9482421875}, {"start": 1344.86, "end": 1345.2, "word": " S", "probability": 0.828125}], "temperature": 1.0}, {"id": 52, "seek": 136153, "start": 1347.11, "end": 1361.53, "text": "لو كان ال U بيساوي ال D فبطلع U أصغر من أو ساوي V وهو المطلوب، إذا بفرض أن V لا يساوي ال U، إذا بدي أثبت أن U أصغر من V", "tokens": [1211, 2407, 25961, 2423, 624, 4724, 1829, 3794, 995, 45865, 2423, 413, 6156, 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1526.09, "end": 1526.57, "word": " فرضنا", "probability": 0.9959309895833334}, {"start": 1526.57, "end": 1526.73, "word": " U", "probability": 0.96826171875}, {"start": 1526.73, "end": 1526.95, "word": " هو", "probability": 0.998046875}, {"start": 1526.95, "end": 1527.09, "word": " ال", "probability": 0.9560546875}, {"start": 1527.09, "end": 1527.45, "word": " supreme", "probability": 0.88916015625}, {"start": 1527.45, "end": 1528.53, "word": " بدنا", "probability": 0.962890625}, {"start": 1528.53, "end": 1528.89, "word": " نثبت", "probability": 0.998046875}, {"start": 1528.89, "end": 1529.05, "word": " إن", "probability": 0.5498046875}, {"start": 1529.05, "end": 1529.23, "word": " ال", "probability": 0.669921875}, {"start": 1529.23, "end": 1529.47, "word": " U", "probability": 0.900390625}, {"start": 1529.47, "end": 1530.21, "word": " بيحقق", "probability": 0.98251953125}, {"start": 1530.21, "end": 1530.73, "word": " الشرط", "probability": 0.9812825520833334}, {"start": 1530.73, "end": 1530.89, "word": " اللي", "probability": 0.978759765625}, {"start": 1530.89, "end": 1531.03, "word": " على", "probability": 0.89892578125}, {"start": 1531.03, "end": 1531.55, "word": " اليمين", "probability": 0.9200846354166666}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1532.191875, "duration_after_vad": 1393.9362499999972}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..5992d06fe3a8ac5561592e8e0fe85aa48437d42c
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/tY_G9XVDP9s_raw.srt
@@ -0,0 +1,960 @@
+1
+00:00:23,300 --> 00:00:28,680
+الـ completeness property of R عشان نعرف أيه ال
+
+2
+00:00:28,680 --> 00:00:33,540
+completeness property of R فبنحتاج لبعض التعريفات
+
+3
+00:00:33,540 --> 00:00:39,380
+فأول تعريف ما معناه أن عدد حقيقي يكون upper bound
+
+4
+00:00:39,380 --> 00:00:44,460
+للمجموعة S معناه أن ال U أكبر من أو ساوي كل عناصر
+
+5
+00:00:44,460 --> 00:00:50,800
+ال 6Sما معناه ان عدد حقيقي w يكون lower bound ل S
+
+6
+00:00:50,800 --> 00:00:58,580
+معناه ان ال w أصغر من أو يساوي كل عناصر ال set S و
+
+7
+00:00:58,580 --> 00:01:06,600
+من السهل ان احنا من التعريف
+
+8
+00:01:06,600 --> 00:01:12,760
+هذا ممكن نلاحظ الملاحظات التالية ان اي set ممكن
+
+9
+00:01:13,520 --> 00:01:16,740
+يكونيلها upper bound وممكن مايكونيلهاش upper bound
+
+10
+00:01:16,740 --> 00:01:23,380
+فع سبيل المثال مجموعة الأعداد الحقيقية هذه ليس لها
+
+11
+00:01:23,380 --> 00:01:29,740
+upper bound أو أي lower bound في المقابل الفترة
+
+12
+00:01:29,740 --> 00:01:38,520
+المغلقة S من صفر لواحدأو الفترة المغلقة المفتوحة
+
+13
+00:01:38,520 --> 00:01:44,480
+من سفر لواحد هذه إلها lower bounds السفر أو أي عدد
+
+14
+00:01:44,480 --> 00:01:50,540
+أصلا أو ساوى سفر و كذلك إلها upper bounds الواحد
+
+15
+00:01:50,540 --> 00:01:55,540
+أو أي عدد أكبر من أو ساوى الواحد بالمثل للمجموعة
+
+16
+00:01:55,540 --> 00:02:00,920
+اللي تحت كذلك لو المجموعة
+
+17
+00:02:02,480 --> 00:02:08,060
+الها upper bound U فبكون لها infinitely many upper
+
+18
+00:02:08,060 --> 00:02:12,700
+bounds إذا كان U upper bound لمجموعة زي هذه فكل
+
+19
+00:02:12,700 --> 00:02:16,200
+عدد أكبر من ال upper bound هو upper bound آخر
+
+20
+00:02:16,200 --> 00:02:20,600
+بالمثل بالنسبة لل lower bounds إذا المجموعة لها
+
+21
+00:02:20,600 --> 00:02:24,660
+lower bound واحد فممكن نجد عدد لانهاء من ال lower
+
+22
+00:02:24,660 --> 00:02:30,770
+boundsلو أخدنا المجموعة S بالساوية فاي فأي عدد
+
+23
+00:02:30,770 --> 00:02:35,170
+حقيقي بيكون upper bound وفي نفس الوقت بيكون lower
+
+24
+00:02:35,170 --> 00:02:40,330
+bound للمجموعة هذه و البرهان by contradiction نفرض
+
+25
+00:02:40,330 --> 00:02:46,470
+على النقيض أن يوجد R0 عدد حقيقي و هذا العدد
+
+26
+00:02:46,470 --> 00:02:52,200
+الحقيقي ما هوش upper boundمعناته إذا كان R0 ليس
+
+27
+00:02:52,200 --> 00:02:55,940
+upper bound لـ S معناته بقدر ألاقي عنصر S في
+
+28
+00:02:55,940 --> 00:03:02,820
+المجموعة capital S أكبر من الـ R0 وهذا بتديني
+
+29
+00:03:02,820 --> 00:03:08,960
+التناقض لأن المجموعة S لا يوجد بيها عناصر فرض أنه
+
+30
+00:03:08,960 --> 00:03:17,960
+يوجد فرض
+
+31
+00:03:17,960 --> 00:03:24,460
+أنه يوجدعدد حقيقي وما هواش upper bound هذا خطأ هذا
+
+32
+00:03:24,460 --> 00:03:29,360
+معناه ان every real number is upper bound بالمثل
+
+33
+00:03:29,360 --> 00:03:33,160
+ممكن اثبات ان every real number is lower bound
+
+34
+00:03:33,160 --> 00:03:35,840
+للمجموعة الخالية five
+
+35
+00:03:56,010 --> 00:04:01,510
+بنقول إن المجموعة أي مجموعة من R bounded above إذا
+
+36
+00:04:01,510 --> 00:04:06,770
+كان إلها upper bound وبنقول إنها bounded below إذا
+
+37
+00:04:06,770 --> 00:04:15,310
+كانت إذا كان إلها lower bound إذا كانت المجموعة
+
+38
+00:04:15,310 --> 00:04:20,810
+بنسميها bounded إذا كانت bounded above and bounded
+
+39
+00:04:20,810 --> 00:04:26,720
+below في نفس الوجد وبنسميها unboundedإذا كان
+
+40
+00:04:26,720 --> 00:04:32,220
+ينقصها إنها تكون bounded above أو بينقصها إنها
+
+41
+00:04:32,220 --> 00:04:36,780
+تكون bounded below مثال على unbounded set اللي هو
+
+42
+00:04:36,780 --> 00:04:41,100
+الأعداد الحقيقية، هذه ال set unbounded غير محدودة،
+
+43
+00:04:41,100 --> 00:04:47,180
+غير محصورة، لأنه ليس لها upper bounds أو lower
+
+44
+00:04:47,180 --> 00:04:51,620
+boundsمثال على bounded sets ال set هذه وال set هذه
+
+45
+00:04:51,620 --> 00:04:57,740
+ال sets هذول كل منهم bounded above and bounded
+
+46
+00:04:57,740 --> 00:05:07,080
+below وبالتالي bounded المجموعة
+
+47
+00:05:07,080 --> 00:05:11,940
+أي subset من S، ده التعريف definition أي subset S
+
+48
+00:05:11,940 --> 00:05:14,260
+من R، بنسميه bounded above
+
+49
+00:05:22,060 --> 00:05:26,400
+بنسميها bounded below إذا كان في إلها upper bound
+
+50
+00:05:26,400 --> 00:05:27,860
+إذا كان في إلها lower bound
+
+51
+00:05:36,000 --> 00:05:41,960
+المجموعة bounded if كانت كان لها upper bound و
+
+52
+00:05:41,960 --> 00:05:46,140
+lower bound او كانت bounded above و bounded below
+
+53
+00:05:46,140 --> 00:05:52,720
+اذا ال set بنسميها bounded if كانت bounded above و
+
+54
+00:05:52,720 --> 00:05:57,520
+bounded below المجموعة بتكون محدودة او محصورة اذا
+
+55
+00:05:57,520 --> 00:06:02,740
+كانت محصورة من الاعلى و من اسفل في نفس الوجد اما
+
+56
+00:06:04,210 --> 00:06:08,550
+if S lacks either an upper bound or lower bound
+
+57
+00:06:08,550 --> 00:06:15,810
+فبنسميها unbounded S بنسميها unbounded إذا
+
+58
+00:06:15,810 --> 00:06:19,750
+المجموعة لو كانت بنخصها upper bound يعني مالهاش أي
+
+59
+00:06:19,750 --> 00:06:26,250
+upper bound وإلها lower bounds بتكون unbounded أو
+
+60
+00:06:26,250 --> 00:06:32,250
+لو كانت المجموعةbounded below مالهاش upper bounds
+
+61
+00:06:32,250 --> 00:06:38,670
+او not bounded above برضه بنسميها unbounded اذا ال
+
+62
+00:06:38,670 --> 00:06:41,890
+bounded معناته bounded above و below في نفس الوجه
+
+63
+00:06:41,890 --> 00:06:48,710
+اذا واحد مش متحقق بنسميها unbounded اعسى بيه
+
+64
+00:06:48,710 --> 00:06:53,690
+المثال مجموعة الاعداد الحقيقية are and is
+
+65
+00:06:53,690 --> 00:06:58,350
+unbounded لأنه ليست bounded above ولا bounded
+
+66
+00:06:58,350 --> 00:06:58,710
+below
+
+67
+00:07:01,720 --> 00:07:08,900
+كذلك المجموعة هذه لو
+
+68
+00:07:08,900 --> 00:07:14,260
+أخدنا مجموعة الأعداد الحقيقية الغير سالبة
+
+69
+00:07:14,260 --> 00:07:17,660
+فالمجموعة
+
+70
+00:07:17,660 --> 00:07:20,920
+هذه is bounded below، لها lower bound، سفر أو أي
+
+71
+00:07:20,920 --> 00:07:26,060
+عدد أصغر من أسابع سفر لكن it is not bounded above،
+
+72
+00:07:26,060 --> 00:07:28,240
+إذا المجموعة هذه unbounded
+
+73
+00:07:32,210 --> 00:07:40,410
+it is unbounded المجموعة هذي هذي bounded لأنها
+
+74
+00:07:40,410 --> 00:07:45,450
+bounded above and bounded below طبعا إذا فهمنا شو
+
+75
+00:07:45,450 --> 00:07:54,890
+معناه bounded و unbounded ناخد تعريف تاني لو
+
+76
+00:07:54,890 --> 00:08:01,410
+كانت S bounded aboveفبنعرف ال supremum أو ال least
+
+77
+00:08:01,410 --> 00:08:07,730
+upper bound للست S على أنه العدد الحقيقي U اللي
+
+78
+00:08:07,730 --> 00:08:12,910
+بيحقق الشرطين هدول الشرط الأول أنه العدد U is an
+
+79
+00:08:12,910 --> 00:08:18,610
+upper bound of S U أكبر من أو ساوي كل عناصر S يعني
+
+80
+00:08:18,610 --> 00:08:24,450
+U upper bound ل S اتنين لو أخدت أي upper bound V
+
+81
+00:08:26,010 --> 00:08:35,150
+فلازم ال U يطلع أصغر من أو ساوي تمام؟
+
+82
+00:08:35,150 --> 00:08:43,250
+فإذا ال .. ال .. ال supremum هو أصغر upper bound
+
+83
+00:08:43,250 --> 00:08:48,490
+للمجموعة هو أصغر upper bound ال supremum هو least
+
+84
+00:08:48,490 --> 00:08:54,640
+.. ال least upper bound أصغر حد أعلىإذا إيش هو
+
+85
+00:08:54,640 --> 00:08:59,960
+أصغر حد أعلى؟ متى بيكون U هو أصغر حد أعلى للمجموعة
+
+86
+00:08:59,960 --> 00:09:08,500
+إذا كان أول شي upper bound للمجموعة اتنين U أصغر
+
+87
+00:09:08,500 --> 00:09:14,580
+من أو يساوي أي upper bound أخر ال
+
+88
+00:09:14,580 --> 00:09:20,360
+supremum أو أصغر حد أعلى نرمزله بالرمز supremum S
+
+89
+00:09:20,360 --> 00:09:22,800
+أو least upper bound ل S
+
+90
+00:09:25,630 --> 00:09:32,390
+بالمثل ممكن انعرف ال minimum او اكبر حد ادنى اكبر
+
+91
+00:09:32,390 --> 00:09:35,330
+حد ادنى للمجموعة
+
+92
+00:09:40,350 --> 00:09:45,970
+لازم تكون ال set bounded below عشان اقدر اعرف ال
+
+93
+00:09:45,970 --> 00:09:49,990
+minimum او اكبر حد ادنى لازم تكون ال set bounded
+
+94
+00:09:49,990 --> 00:09:55,230
+below فلو كانت ال set bounded below فأي عدد حقيقي
+
+95
+00:09:55,230 --> 00:10:02,110
+w بيكون ال minimum لل set او بنسميه greatest lower
+
+96
+00:10:02,110 --> 00:10:08,180
+bound لل setإذا حقق شرطين الشرط الأول أن ال W
+
+97
+00:10:08,180 --> 00:10:14,120
+أبارعا lower bound ل 6S الشرط التاني أن ال W أكبر
+
+98
+00:10:14,120 --> 00:10:20,940
+من أو يساوي أي upper bound Z أي lower bound Z ل 6S
+
+99
+00:10:22,820 --> 00:10:27,200
+وبالتالي من الشرطين هدول .. الشرطين هدول معناهم مع
+
+100
+00:10:27,200 --> 00:10:33,320
+بعض أنه ال minimum أو greatest lower bound لل 6 هو
+
+101
+00:10:33,320 --> 00:10:38,240
+أكبر حد أدنى .. أكبر حد أدنى أو greatest lower
+
+102
+00:10:38,240 --> 00:10:45,280
+bound لل 6S نرمز لل infimum أو greatest lower
+
+103
+00:10:45,280 --> 00:10:52,560
+bound بالرمز هذا inf Sأو GLP ل S هذا اختصار
+
+104
+00:10:52,560 --> 00:10:59,400
+greatest lower bound of S تمام ففي
+
+105
+00:10:59,400 --> 00:11:07,080
+المثال هذا اللي هنا في
+
+106
+00:11:07,080 --> 00:11:11,900
+المثال اللي فوق هذا بنلاحظ
+
+107
+00:11:11,900 --> 00:11:19,080
+أنه Zero بساوي ال infimumلـ S اللي هي الفترة
+
+108
+00:11:19,080 --> 00:11:24,180
+المغلقة من سفر ل واحد لأن
+
+109
+00:11:24,180 --> 00:11:28,620
+السفر عبارة
+
+110
+00:11:28,620 --> 00:11:34,160
+عن lower bound أصغر من أو ساوي كل عناصر الست S
+
+111
+00:11:34,160 --> 00:11:40,340
+كمان لو أخدت أي lower bound للست S لازم هذا ال
+
+112
+00:11:40,340 --> 00:11:43,560
+lower bound يكون أصغر من أو ساوي السفر
+
+113
+00:11:46,660 --> 00:11:50,360
+وبالتالي السفر أكبر من أو يساوي أي lower bound هذا
+
+114
+00:11:50,360 --> 00:12:01,280
+واضح طيب كذلك الواحد بيساوي ال supremum لل 6S اللي
+
+115
+00:12:01,280 --> 00:12:08,170
+هي الفترة المغلقة من سفر لواحدليه؟ لأن الواحد
+
+116
+00:12:08,170 --> 00:12:12,470
+أبارعا upper bound للست هذه أكبر من أو ساوي كل
+
+117
+00:12:12,470 --> 00:12:20,650
+عناصر الفترة و لو أخدت أي V أكبر من أو ساوي كل
+
+118
+00:12:20,650 --> 00:12:24,950
+عناصر الفترة لكل
+
+119
+00:12:24,950 --> 00:12:28,630
+S في الفترة من 0 ل1
+
+120
+00:12:32,170 --> 00:12:37,050
+فبطلع عندى V أكبر من أو ساوي الواحد لأن الواحد
+
+121
+00:12:37,050 --> 00:12:43,130
+عنصر في الست و V أكبر من أو ساوي كل عناصر الست ف V
+
+122
+00:12:43,130 --> 00:12:49,130
+أكبر من أو ساوي الواحد وبالتالي V أو الواحد أصغر
+
+123
+00:12:49,130 --> 00:12:52,610
+من أو ساوي أي حد أعلى آخر
+
+124
+00:12:56,370 --> 00:13:02,410
+إذا الواحد هو عبارة عن ال supremum للست سفر و واحد
+
+125
+00:13:02,410 --> 00:13:08,190
+ال
+
+126
+00:13:08,190 --> 00:13:16,650
+.. عندي شوية ملاحظات هنا نشوفهم
+
+127
+00:13:16,650 --> 00:13:17,190
+مع بعض
+
+128
+00:13:30,420 --> 00:13:36,600
+لو الـ supremum تبع ال 6 موجود لو
+
+129
+00:13:36,600 --> 00:13:41,240
+ال 6 S ال supremum تبعها exists يعني إلها supremum
+
+130
+00:13:41,240 --> 00:13:47,180
+زي ال 6 هذه فلازم ال supremum هذا يكون unique وحيد
+
+131
+00:13:47,180 --> 00:13:52,540
+يعني مافيش أكتر من supremum فلبرهان
+
+132
+00:13:52,540 --> 00:13:53,060
+ذلك
+
+133
+00:13:59,930 --> 00:14:08,490
+اللي برهان ذلك افرضه ان ال 6S لها اكتر
+
+134
+00:14:08,490 --> 00:14:20,750
+من Supremum U1 Supremum and U2 Supremum تاني بدنا
+
+135
+00:14:20,750 --> 00:14:29,710
+نثبت ان U1 بدنا نثبتأن U1 بساوي U2 وبالتالي ال two
+
+136
+00:14:29,710 --> 00:14:32,990
+supremums بنطبقوا على بعض يعني ال supremum واحد
+
+137
+00:14:32,990 --> 00:14:41,590
+طيب أنا فيه أندي U1 upper bound
+
+138
+00:14:46,410 --> 00:14:52,110
+لست S ليه لأن U واحد عبارة عن supermom و ال
+
+139
+00:14:52,110 --> 00:14:55,990
+supermom بيكون upper كل supermom هو upper bound من
+
+140
+00:14:55,990 --> 00:15:03,510
+تعريفه صح الشرط الأول و U اتنين بساوي ال supermom
+
+141
+00:15:03,510 --> 00:15:13,770
+اللي هو least upper bound ل S هو أصغر حد أعلى
+
+142
+00:15:16,780 --> 00:15:25,220
+و هذا حد أعلى إذا .. إذا بيطلع عندي هذا أصغر حد
+
+143
+00:15:25,220 --> 00:15:30,360
+أعلى ل S وهذا حد أعلى فمن تعريف ال supremum أو
+
+144
+00:15:30,360 --> 00:15:36,720
+أصغر حد أعلى إذا U2 بيطلع أصغر من أو ساوي U1
+
+145
+00:15:36,720 --> 00:15:43,640
+نستنتج أن U2 أصغر من أو ساوي 1 نسمي المتباينة هذه
+
+146
+00:15:43,640 --> 00:15:53,050
+1كذلك انا عندي U1 او U2 المرة هاد هاخد U2 هاد
+
+147
+00:15:53,050 --> 00:16:03,770
+عبارة عن upper upper bound ل S ليه؟ لأنه ال
+
+148
+00:16:03,770 --> 00:16:09,530
+supremum ل S وكل supremum هو upper bound وعندي
+
+149
+00:16:09,530 --> 00:16:13,930
+كمان U1 عبارة عن
+
+150
+00:16:16,610 --> 00:16:24,390
+الـ least upper bound ل S يعني U1 هو أكبر upper
+
+151
+00:16:24,390 --> 00:16:30,170
+bound ل S و U2 upper bound فمن تعريف ال least
+
+152
+00:16:30,170 --> 00:16:37,030
+upper bound بطلع عندي أن ال U1 لازم يكون أصغر من
+
+153
+00:16:37,030 --> 00:16:45,010
+أو يساوي U2 فبنسمي المتباينة هذه اتنين الآن من
+
+154
+00:16:45,010 --> 00:16:46,050
+واحد و اتنين
+
+155
+00:16:49,530 --> 00:16:57,290
+أذا from واحد and اتنين نستنتج
+
+156
+00:16:57,290 --> 00:17:02,250
+أن يو اتنين أصغر من لو يساوي يو واحد و يو واحد
+
+157
+00:17:02,250 --> 00:17:03,850
+أصغر من لو يساوي يو اتنين
+
+158
+00:17:09,610 --> 00:17:15,170
+وبالتالي إذا هيك لو سمحت ما تتكلميش معي هنا بشرح
+
+159
+00:17:15,170 --> 00:17:16,910
+اللي بتتكلم ماتتكلمش
+
+160
+00:17:20,750 --> 00:17:25,170
+هين أثبتنا أنه لو الست إلها أكتر من supremum فال
+
+161
+00:17:25,170 --> 00:17:28,410
+supremums بيساويوا بعض وبالتالي في عندي ال
+
+162
+00:17:28,410 --> 00:17:34,050
+supremum is unique بالمثل ممكن أثبت أنه لو كانت
+
+163
+00:17:34,050 --> 00:17:37,730
+الست S إلها infimum يعني ال infimum تبعها exist
+
+164
+00:17:37,730 --> 00:17:44,990
+فأيضا بيطلع unique هو البرهانالمثل لبرهان ان ال
+
+165
+00:17:44,990 --> 00:17:49,490
+supreme م unique تمام؟ فحاسبكم الجزء التاني هذا
+
+166
+00:17:49,490 --> 00:17:55,530
+تكتب البرهان تبعه كتمرين او ك exercise في اي سؤال
+
+167
+00:17:55,530 --> 00:18:02,030
+واضح بالبرهان؟ في اي استفسار على البرهان؟
+
+168
+00:18:02,030 --> 00:18:08,430
+طيب ال .. في عندي لمة واحد
+
+169
+00:18:08,430 --> 00:18:23,560
+اتناش لمة كتير مهمةواللمة هذه تعتبر
+
+170
+00:18:23,560 --> 00:18:28,080
+يعني بتكافئ بتعريف ال supremum يعني ما معنى لو
+
+171
+00:18:28,080 --> 00:18:31,900
+أخدت مجموعة غير خالية مجموعة جزية من الأعداد
+
+172
+00:18:31,900 --> 00:18:38,680
+الحقيقية غير خالية وفرضت أن U is upper bound لها
+
+173
+00:18:40,090 --> 00:18:44,790
+فالسؤال متى ال upper bound U لست هذه S بيكون هو ال
+
+174
+00:18:44,790 --> 00:18:48,890
+super bound الجواب
+
+175
+00:18:48,890 --> 00:18:54,430
+في اللملة ان if and only if اذا كانت ال U بتحقق
+
+176
+00:18:54,430 --> 00:19:01,330
+الشرط هذا طب نشوف الشرط هذا نحاول نشوف الشرط هذا
+
+177
+00:19:01,330 --> 00:19:04,810
+نوضحه على رسمة
+
+178
+00:19:11,720 --> 00:19:19,300
+هذه مجموعة الأعداد الحقيقية وهذه
+
+179
+00:19:19,300 --> 00:19:30,040
+مجموعة S وهذه مجموعة جزئية من R وغير خالية تمام؟
+
+180
+00:19:30,040 --> 00:19:39,120
+وهذه U upper bound لل 6Sاللي لما بتقول عشان ال
+
+181
+00:19:39,120 --> 00:19:44,180
+upper bound هذا يكون هو ال supreme لازم يتحقق انه
+
+182
+00:19:44,180 --> 00:19:50,200
+لأي epsilon أكبر من السفر لازم ألاقي .. لازم ألاقي
+
+183
+00:19:50,200 --> 00:20:00,960
+هنا في عنصر نسميه S epsilon ينتمي ل S بحيث انه لو
+
+184
+00:20:00,960 --> 00:20:02,280
+طرحت من ال U
+
+185
+00:20:05,140 --> 00:20:12,320
+لو طرحت من ال U إبسلون فلازم ألاقي أنصر S إبسلون
+
+186
+00:20:12,320 --> 00:20:17,820
+يعتمد على إبسلون في S وهذا الأنصر أكبر من U سالب
+
+187
+00:20:17,820 --> 00:20:23,840
+إبسلون زي ما هو في الرسم مرة
+
+188
+00:20:23,840 --> 00:20:29,380
+تانية عشان ال upper bound هذا يكونSupremum ل S هو
+
+189
+00:20:29,380 --> 00:20:35,240
+أصغر حد أعلى لازم لأي أبسلون أكبر من السفر لو طرحت
+
+190
+00:20:35,240 --> 00:20:39,840
+من ال U الأبسلون العدد الموجب فلازم ألاقي عنصر في
+
+191
+00:20:39,840 --> 00:20:46,300
+ال set أكبر من U سالب أبسلون نشوف البرهان طبعا هذا
+
+192
+00:20:46,300 --> 00:20:50,670
+by conditional statementففي ال logic أو في
+
+193
+00:20:50,670 --> 00:20:56,250
+البراهين في ال only if part و ال if part من جزء
+
+194
+00:20:56,250 --> 00:21:00,690
+البرهان إلى جزعين هذا بيسميه ال if part و هذا ال
+
+195
+00:21:00,690 --> 00:21:06,870
+only if part نثبت الاتجاه هذا الآن هفرض أن الشرط
+
+196
+00:21:06,870 --> 00:21:14,550
+هذا متحقق و أثبت أن u هو ال supreme هو نعم مش s
+
+197
+00:21:14,550 --> 00:21:19,630
+epsilon هي عبارة عن ماذا بتقول؟neighborhood لأ لأ
+
+198
+00:21:19,630 --> 00:21:24,050
+ماحدش حاكى حاجة عن neighborhood لأ لأ دا ك U
+
+199
+00:21:24,050 --> 00:21:31,090
+capital U و بيكون يعني موضح في السياقه مافيش هنا
+
+200
+00:21:31,090 --> 00:21:35,730
+اي حاجة تتعلق بال neighborhood U عدد حقيقي اذا U
+
+201
+00:21:35,730 --> 00:21:41,000
+هنا بس عبارة عن upper bound ل Sعشان يكون هو الـ
+
+202
+00:21:41,000 --> 00:21:44,140
+supremum هو أصغر upper bound لازم يتحقق الشرط هذا
+
+203
+00:21:44,140 --> 00:21:52,200
+فنشوف افرض ان الشرط هذا يتحقق و بينا نثبت الـ U هو
+
+204
+00:21:52,200 --> 00:21:59,340
+ال supremum فلإثبات ال U هو ال supremumأحنا فرضين
+
+205
+00:21:59,340 --> 00:22:03,560
+أن ال U upper bound ارجع لتعريف ال supremum ال U
+
+206
+00:22:03,560 --> 00:22:07,980
+بيكون supremum إذا كان واحد upper bound وهذا ما
+
+207
+00:22:07,980 --> 00:22:11,780
+اتحقق من الفرض فرضينه upper bound الشرط التاني لو
+
+208
+00:22:11,780 --> 00:22:16,520
+أخدنا أي upper bound بيه فلازم نثبت أن ال U أصغر
+
+209
+00:22:16,520 --> 00:22:20,880
+من أو يساوي فتعالوا نثبت الشرط التاني من شروط ال
+
+210
+00:22:20,880 --> 00:22:28,570
+supremum let V be any upper bound ل Sلو كان ال U
+
+211
+00:22:28,570 --> 00:22:33,670
+بيساوي ال D فبطلع U أصغر من أو ساوي V وهو المطلوب،
+
+212
+00:22:33,670 --> 00:22:40,610
+إذا بفرض أن V لا يساوي ال U، إذا بدي أثبت أن U
+
+213
+00:22:40,610 --> 00:22:47,850
+أصغر من Vفإذا كان الان v و u أعداد حقيقية مختلفة
+
+214
+00:22:47,850 --> 00:22:51,350
+إذا الخاصية الثلاثية retricut من property بتقول
+
+215
+00:22:51,350 --> 00:22:56,550
+إما u أصغر من .. إما v أصغر من u أو u أصغر من v
+
+216
+00:22:56,550 --> 00:23:01,370
+أنا بدي u أثبت u أصغر من v تعالوا ناخد الاحتمال
+
+217
+00:23:01,370 --> 00:23:07,410
+الأول و نشوف إن هذا مستحيل ف assume
+
+218
+00:23:10,700 --> 00:23:15,960
+إذا هنا أخذنا الاحتمال الأول وفرضنا أنه هو الصح
+
+219
+00:23:15,960 --> 00:23:23,560
+الآن الفرق بين U وV بيطلع عدد موجب لأن U أكبر من V
+
+220
+00:23:24,640 --> 00:23:29,820
+الان سمى هذا الفرق ابسلون اذا الان ابسلون اللى هو
+
+221
+00:23:29,820 --> 00:23:35,660
+الفرق هذا عدد موجب طب من الفرض من الفرض هذا هذا هو
+
+222
+00:23:35,660 --> 00:23:41,320
+لأى ابسلون زى هذه لأى عدد موجب ابسلون هو ليكن هذا
+
+223
+00:23:41,320 --> 00:23:50,840
+احنا فرضين انه يوجد يوجد S ابسلون في Sوهذا ال S Y
+
+224
+00:23:50,840 --> 00:23:57,820
+أكبر من U سالب Y مصدود؟ هذا من الفرض الآن من هنا
+
+225
+00:23:57,820 --> 00:24:06,140
+من تعريف ال Y ال U سالب Y بساوي D إذا هنا عندي
+
+226
+00:24:06,140 --> 00:24:13,980
+أصبح D أصغر من S Y وهذا بتناقض مع كون V upper
+
+227
+00:24:13,980 --> 00:24:19,460
+boundأحنا فرضين أن V upper bound ل S فكيف V upper
+
+228
+00:24:19,460 --> 00:24:25,260
+bound و في نفس الوقت V أصغر من عنصر M في المجموعة
+
+229
+00:24:25,260 --> 00:24:31,080
+S هذا بتناقض مع تعريف ال upper bound إذا هذا
+
+230
+00:24:31,080 --> 00:24:37,920
+التناقض بيقول لي إن الاحتمال هذا غلط أو مستحيل طيب
+
+231
+00:24:37,920 --> 00:24:44,550
+أنا عندياحنا استنتجنا من ال hypothesis ان الاحتمال
+
+232
+00:24:44,550 --> 00:24:50,790
+هذا او هذا صح الان هذا مش صح اذا يبقى ان هذا صح
+
+233
+00:24:50,790 --> 00:24:56,730
+اذا we are left يعني الان احنا طريقنا بان you أصغر
+
+234
+00:24:56,730 --> 00:25:01,050
+من me وبالتالي هذا بيكمل برهان الشرط التاني من ال
+
+235
+00:25:01,050 --> 00:25:05,750
+supremem يعني you هو ال suprememإذن هنا أثبتنا إنه
+
+236
+00:25:05,750 --> 00:25:10,470
+لو الشرط هذا اتحقق فال upper bound U هذا بيطلع هو
+
+237
+00:25:10,470 --> 00:25:15,090
+ال supreme هو أصغر upper bound اللي يعني بدنا نثبت
+
+238
+00:25:15,090 --> 00:25:23,110
+العكس .. نثبت العكس .. نثبت العكس لو كان .. لو ..
+
+239
+00:25:23,110 --> 00:25:27,450
+لو كان U هو ال supreme لو فرضنا U هو ال supreme
+
+240
+00:25:27,450 --> 00:25:31,550
+بدنا نثبت إن ال U بيحقق الشرط اللي على اليمين
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/u5C7kmY6Ltw_postprocess.srt b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/u5C7kmY6Ltw_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..2757e1f9cef4bbf4f135526b6a7d8af28e916510
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/u5C7kmY6Ltw_postprocess.srt
@@ -0,0 +1,1516 @@
+1
+00:00:20,100 --> 00:00:29,020
+بسم الله الرحمن الرحيم ناخد اليومالجزء المتعلق بال
+
+2
+00:00:29,020 --> 00:00:33,400
+composition of continuous functions لو كان في عندي
+
+3
+00:00:33,400 --> 00:00:38,960
+اقترانين متصلين فهنشوف ان ال composition تبعهم
+
+4
+00:00:38,960 --> 00:00:47,360
+بيطلع ايضا متصل على المجال الدالة الاولى وبعد هيك
+
+5
+00:00:47,360 --> 00:00:54,360
+بعد ما نقلص هنبدأ ب section خمسة تلاتةاللي بتحدث
+
+6
+00:00:54,360 --> 00:00:58,100
+عن ال continuous functions على ال intervals أو على
+
+7
+00:00:58,100 --> 00:01:06,420
+الفترات الأول بناخد النظرية اللي خاصة بال
+
+8
+00:01:06,420 --> 00:01:18,240
+composition of continuous functions النظرية
+
+9
+00:01:18,240 --> 00:01:19,360
+هذه بتقول
+
+10
+00:01:22,140 --> 00:01:34,600
+Let a و b be subsets of R و if from a to b is
+
+11
+00:01:34,600 --> 00:01:38,960
+continuous is
+
+12
+00:01:38,960 --> 00:01:47,700
+continuous at c تنتمي إلى a and g function
+
+13
+00:01:51,030 --> 00:01:59,250
+from a to r هنا و g function from b to r إذا مجال
+
+14
+00:01:59,250 --> 00:02:05,010
+ال function g هو ال set b مجال ال function f هو ال
+
+15
+00:02:05,010 --> 00:02:10,370
+set a be
+
+16
+00:02:10,370 --> 00:02:14,070
+continuous at
+
+17
+00:02:17,610 --> 00:02:27,310
+B بساوي F of C تنتمي الى
+
+18
+00:02:27,310 --> 00:02:32,530
+الـ B where
+
+19
+00:02:32,530 --> 00:02:41,410
+طبعا ال range لل function F is contained in Bعشان
+
+20
+00:02:41,410 --> 00:02:45,990
+يكون ال composition لل two functions f و g يكون
+
+21
+00:02:45,990 --> 00:02:50,590
+معرف لازم range ال f يكون subset من domain ال g
+
+22
+00:02:50,590 --> 00:03:00,410
+then في الحالة هذه the composite function the
+
+23
+00:03:00,410 --> 00:03:10,680
+composite function f circle g او g circle fG
+
+24
+00:03:10,680 --> 00:03:15,660
+Circle F from
+
+25
+00:03:15,660 --> 00:03:26,360
+A to R is continuous تطلع continuous at C
+
+26
+00:03:39,140 --> 00:03:45,580
+أنا في عندي function يعني المجال تبعها A و
+
+27
+00:03:45,580 --> 00:03:57,140
+F function من A ل R و كنتيل يوسع عند النقطة C و في
+
+28
+00:03:57,140 --> 00:04:05,180
+عندي function تانية يعني عندي ال 6 هذه F of A
+
+29
+00:04:09,920 --> 00:04:17,400
+F of A subset من الـ B المجموعة هذه نسميها B وهي F
+
+30
+00:04:17,400 --> 00:04:24,140
+of A subset فالان وفي function G continuous
+
+31
+00:04:24,140 --> 00:04:28,840
+function G
+
+32
+00:04:28,840 --> 00:04:31,140
+is continuous عند النقطة
+
+33
+00:04:36,550 --> 00:04:43,070
+النقطة f of c بيبساوي f of c اذا ال function g
+
+34
+00:04:43,070 --> 00:04:48,450
+فاندي f continuous عند c تنتمي ل a و g continuous
+
+35
+00:04:48,450 --> 00:04:57,110
+عند b اللي هي صورة ال f and c اذا في المحصلة تطلع
+
+36
+00:04:57,110 --> 00:05:04,420
+عندي ال function طبعا هي المفروض تطلع g of bففي
+
+37
+00:05:04,420 --> 00:05:07,220
+المحصلة بيطلع عند الـ function G circle F
+
+38
+00:05:07,220 --> 00:05:13,620
+continuous تطلع continuous عند النقطة C طبعا عشان
+
+39
+00:05:13,620 --> 00:05:17,400
+ال composition هذا يكون معرف لازم range ال F اللي
+
+40
+00:05:17,400 --> 00:05:22,020
+هو ده هو F of A يكون subset من ال B اللي هو domain
+
+41
+00:05:22,020 --> 00:05:29,160
+ال function G وهذا طبعا احنا فرضينهلبرهان ذلك
+
+42
+00:05:29,160 --> 00:05:33,380
+هنستخدم الـ neighborhood definition of continuity
+
+43
+00:05:33,380 --> 00:05:48,380
+at a point ف let W be an epsilon neighborhood of G
+
+44
+00:05:48,380 --> 00:06:02,050
+circle F ل C اللي هي G ل F of Cاللي هي جي او بي
+
+45
+00:06:02,050 --> 00:06:10,710
+صح؟ وبنثبت أنه يوجد Delta neighborhood للـC اللي
+
+46
+00:06:10,710 --> 00:06:15,210
+هي تنتمي لـA بحيث أنه صورة ال neighborhood هذا
+
+47
+00:06:15,210 --> 00:06:19,110
+subset من الـW neighborhood هنا تعريف ال
+
+48
+00:06:19,110 --> 00:06:22,730
+neighborhood definition للاتصال عن النقطة طيب
+
+49
+00:06:22,730 --> 00:06:25,650
+since
+
+50
+00:06:28,450 --> 00:06:40,530
+الفنشن الـ g is continuous at b اللي هي بالساوي f
+
+51
+00:06:40,530 --> 00:06:47,430
+of c تنتمي ل b وهي في عندي w neighborhood w is
+
+52
+00:06:47,430 --> 00:06:52,810
+epsilon neighborhood ل g of b إذا من تعريف الاتصال
+
+53
+00:06:52,810 --> 00:07:04,400
+عن النقطة يوجدdelta neighborhood نسميه V of ال
+
+54
+00:07:04,400 --> 00:07:12,120
+B بحيث انه لكل
+
+55
+00:07:12,120 --> 00:07:24,000
+Y ينتمي إلى B تقاطع ال V لازم يطلع عندى صورة ال YG
+
+56
+00:07:24,000 --> 00:07:35,680
+of Y تنتمي لـ W الـ
+
+57
+00:07:35,680 --> 00:07:39,460
+function
+
+58
+00:07:39,460 --> 00:07:45,700
+G continuous عند B في مجالها وبالتالي حسب الاتصال
+
+59
+00:07:45,700 --> 00:07:53,520
+لأي epsilon neighborhood لصورة Bيوجد delta
+
+60
+00:07:53,520 --> 00:07:59,820
+neighborhood V للـ B بحيث انه لكل Y في ال
+
+61
+00:07:59,820 --> 00:08:04,520
+neighborhood و في مجال الدالة صورته تطلع موجودة في
+
+62
+00:08:04,520 --> 00:08:08,720
+ال epsilon neighborhood نسمي هذه ال implication
+
+63
+00:08:08,720 --> 00:08:19,400
+star طيب since انا
+
+64
+00:08:19,400 --> 00:08:20,620
+عندي ال function
+
+65
+00:08:25,730 --> 00:08:34,370
+Since الـ function F is continuous at
+
+66
+00:08:34,370 --> 00:08:43,550
+C و هي NDV عبارة عن delta neighborhood للـ B اللي
+
+67
+00:08:43,550 --> 00:08:47,810
+هي F of C إذا
+
+68
+00:08:47,810 --> 00:08:57,710
+يوجد Gammaneighborhood نسميه U of
+
+69
+00:08:57,710 --> 00:09:01,570
+..
+
+70
+00:09:01,570 --> 00:09:14,250
+of C بحيث أنه لكل X ينتمي إلى A تقاطع ال U بطلع
+
+71
+00:09:14,250 --> 00:09:20,410
+عندي صورة ال X تنتمي ل ال U
+
+72
+00:09:24,690 --> 00:09:43,130
+بنسمي هذه double star اذا
+
+73
+00:09:43,130 --> 00:09:59,970
+now from star and double starأثبتنا إنه يوجد Gamma
+
+74
+00:09:59,970 --> 00:10:08,110
+neighborhood اللي هو U of C تنتمي إلى A بحيث إنه
+
+75
+00:10:08,110 --> 00:10:20,830
+كل X ينتمي إلى A تخاطى U هذا بيؤدي إنه F
+
+76
+00:10:20,830 --> 00:10:21,510
+of X
+
+77
+00:10:26,740 --> 00:10:42,500
+تنتمي الى لأ
+
+78
+00:10:42,500 --> 00:10:47,120
+هذا المفروض يطلع تنتمي
+
+79
+00:10:47,120 --> 00:10:52,100
+يعني
+
+80
+00:10:52,100 --> 00:10:53,980
+المفروض تنتمي الى D
+
+81
+00:10:58,230 --> 00:11:05,750
+الـ F continuous and الـ C و V neighborhood ل B
+
+82
+00:11:05,750 --> 00:11:07,110
+اللي هي صورة الـ C
+
+83
+00:11:10,240 --> 00:11:14,920
+Gamma neighbourhood U للـC بحيث لكل X مجال الدالة
+
+84
+00:11:14,920 --> 00:11:19,740
+وفي الـGamma neighbourhood صورة الـX هتطلع موجودة
+
+85
+00:11:19,740 --> 00:11:24,560
+في الـV neighbourhood الـneighbourhood لF of C V
+
+86
+00:11:24,560 --> 00:11:29,140
+اللي هو neighbourhood لمين of B اللي هي بالساوي F
+
+87
+00:11:29,140 --> 00:11:32,380
+of C إذن هذا الكلام صحيح
+
+88
+00:11:39,160 --> 00:11:49,360
+الان من star هذا بيقدي ان f of x ينتمي الى f of a
+
+89
+00:11:49,360 --> 00:11:57,340
+تقاطع .. تقاطع
+
+90
+00:11:57,340 --> 00:11:58,860
+f of u
+
+91
+00:12:06,740 --> 00:12:13,500
+وعندي هذا ال F of A من الفرض subset من B و ال F of
+
+92
+00:12:13,500 --> 00:12:17,120
+U او
+
+93
+00:12:17,120 --> 00:12:23,120
+لكل X ينتمي ل U F of X ينتمي ل V هذا موجود في V
+
+94
+00:12:23,120 --> 00:12:25,640
+وبالتالي التقاطع هذا
+
+95
+00:12:32,220 --> 00:12:41,340
+أذا هذا بيقدي أن f of x تنتمي إلى b تقاطع ال v هذا
+
+96
+00:12:41,340 --> 00:12:51,520
+باستخدام double star انه
+
+97
+00:12:51,520 --> 00:12:59,560
+لكل x في a تقاطع u f of x تنتمي لf of u اللي هي
+
+98
+00:12:59,560 --> 00:13:01,120
+subset من b
+
+99
+00:13:10,220 --> 00:13:17,340
+أو ممكن حتى كمان هنا بلاش هذه ممكن نحط هنا V لأن
+
+100
+00:13:17,340 --> 00:13:23,840
+هي لكل X في A تقاطة U F of X ينتمي ل B و لكل X
+
+101
+00:13:23,840 --> 00:13:29,620
+ينتمي إلى A تقاطة U ما ده subset من A فبطلع F of X
+
+102
+00:13:29,620 --> 00:13:37,660
+ينتمي ل F of A إذا F of X ينتمي ل F of A و ينتمي ل
+
+103
+00:13:37,660 --> 00:13:46,030
+ال Bطيب الآن من star لما
+
+104
+00:13:46,030 --> 00:13:53,010
+اكون عندي لو سمي هذه y لما اكون عندي y تنتمي ل b
+
+105
+00:13:53,010 --> 00:13:59,830
+تقاطع بيه فبطلع عندي g of y اللي هي g ل f of x
+
+106
+00:13:59,830 --> 00:14:07,730
+تنتمي ل w طب ما هذه عبارة عن g circle f ل x
+
+107
+00:14:12,350 --> 00:14:24,070
+الان since w was an arbitrary epsilon neighborhood
+
+108
+00:14:24,070 --> 00:14:29,110
+of g
+
+109
+00:14:29,110 --> 00:14:37,270
+circle f of c we
+
+110
+00:14:37,270 --> 00:14:49,290
+getfrom the neighborhood definition of
+
+111
+00:14:49,290 --> 00:14:57,770
+continuity that G
+
+112
+00:14:57,770 --> 00:15:03,650
+circle F is continuous at
+
+113
+00:15:03,650 --> 00:15:12,870
+C وهو المصممكمان مرة مامعنى ان الـ function هذه
+
+114
+00:15:12,870 --> 00:15:16,590
+مامعنى ان الـ composite function اللى هى G circle
+
+115
+00:15:16,590 --> 00:15:21,530
+if it's continuous in C هذا حسب التعريف التعريف
+
+116
+00:15:21,530 --> 00:15:27,370
+الجوار للاتصال and نقطة هذا معناه لأى W نبرهود
+
+117
+00:15:27,370 --> 00:15:30,810
+لصورة الـ C يوجد
+
+118
+00:15:32,310 --> 00:15:40,450
+Gamma neighborhood U لـ C بحيث لكل X في مجال A
+
+119
+00:15:40,450 --> 00:15:48,430
+تقاطع Gamma neighborhood تطلع صورة X هذه تنتمي لـ
+
+120
+00:15:48,430 --> 00:15:52,830
+Y neighborhood اللي بدأنا فيه وبالتالي حسب التعريف
+
+121
+00:15:52,830 --> 00:15:57,550
+أن الـ function هي continuous and اسي okay إذا هذا
+
+122
+00:15:57,550 --> 00:16:04,270
+برهن النظرية تمامفي اي سؤال في اي صفارة على
+
+123
+00:16:04,270 --> 00:16:08,350
+البرهان ناخد
+
+124
+00:16:08,350 --> 00:16:14,830
+امثلة او تطبقات على نظرية هذه نظرية هذه كتير قوية
+
+125
+00:16:14,830 --> 00:16:19,210
+لان هنشوف الجهتنا بتبرهن انها نظريات سابقة برهنها
+
+126
+00:16:19,210 --> 00:16:28,330
+سابقا فمثلا
+
+127
+00:16:28,330 --> 00:16:30,070
+عندي ال function
+
+128
+00:16:38,720 --> 00:16:47,700
+بالمناسبة النظرية دي ممكن طبعا انعممها و بدل
+
+129
+00:16:47,700 --> 00:16:52,720
+ما تكون صحيحة على الاتصال عند نقطة بصي صحيح على
+
+130
+00:16:52,720 --> 00:16:57,420
+الاتصال على مجموعة يعني لو كانت if continuous على
+
+131
+00:16:57,420 --> 00:17:02,680
+كل مجموعة a on
+
+132
+00:17:02,680 --> 00:17:04,700
+a and g is continuous
+
+133
+00:17:06,910 --> 00:17:13,690
+على كل المجال تبعها on b then the composite
+
+134
+00:17:13,690 --> 00:17:21,690
+function is continuous على كل ال a وهو نتيجة عن
+
+135
+00:17:21,690 --> 00:17:27,890
+نظرية السابقة الان
+
+136
+00:17:27,890 --> 00:17:37,550
+لو أخدنا letجي وان او اكس بساوي اكسل يوت اكس و اكس
+
+137
+00:17:37,550 --> 00:17:42,950
+ينتمي الار claim
+
+138
+00:17:42,950 --> 00:17:46,910
+جي
+
+139
+00:17:46,910 --> 00:17:54,750
+is continuous on R let
+
+140
+00:17:54,750 --> 00:18:00,710
+ابسلون اكبر من السفر be given choose
+
+141
+00:18:06,010 --> 00:18:11,910
+دلتا بساوي إبسلون، عدد موجة بيعتمد على إبسلون،
+
+142
+00:18:11,910 --> 00:18:20,410
+then لو كان X ينتمي إلى مجال الدالة اللي هو R و
+
+143
+00:18:20,410 --> 00:18:24,930
+absolute X minus C
+
+144
+00:18:36,770 --> 00:18:42,650
+خلّيني أقول هنا fix C
+
+145
+00:18:42,650 --> 00:18:52,290
+ينتمي إلى R and let epsilon
+
+146
+00:18:52,290 --> 00:18:56,770
+أكبر من السفر be given أنا بدأ أثبت أن الـ
+
+147
+00:18:56,770 --> 00:19:01,990
+function G continuous على الـ R فبأثبت الـ C ينتمي
+
+148
+00:19:01,990 --> 00:19:05,450
+إلى R و أثبت أن الـ function continuous عند النقطة
+
+149
+00:19:05,450 --> 00:19:10,720
+Cالأول بعدين بقول بما أنه C was arbitrary إذا ال
+
+150
+00:19:10,720 --> 00:19:15,600
+function continuous على كل ال R فلأي إبسلون أكبر
+
+151
+00:19:15,600 --> 00:19:20,580
+من السفر ت choose دلتا بساوي إبسلون then لكل X في
+
+152
+00:19:20,580 --> 00:19:25,580
+R و absolute X minus C أصغر من دلتا هذا بيقدر أنه
+
+153
+00:19:25,580 --> 00:19:34,900
+absolute G1 of Xg1 of x minus g1 of c اللي هو
+
+154
+00:19:34,900 --> 00:19:41,700
+بيساوي absolute absolute x minus absolute c طبعا
+
+155
+00:19:41,700 --> 00:19:44,800
+هذا by triangle inequality أصغر من أو ساوي
+
+156
+00:19:44,800 --> 00:19:54,440
+absolute x minus c ومن الفرض ومن
+
+157
+00:19:54,440 --> 00:19:58,960
+الفرض أنا ماخد ال x لحياتي اللي مسافة بينها وبين
+
+158
+00:19:58,960 --> 00:20:02,660
+ال c أصغر من دلتاعشان هيك انا اختارت الـ delta
+
+159
+00:20:02,660 --> 00:20:07,080
+بالساوية epsilon عشان يطلع absolute g1 ل x minus
+
+160
+00:20:07,080 --> 00:20:14,520
+g1 ل c أصغر من epsilon و بما انه since epsilon
+
+161
+00:20:14,520 --> 00:20:23,160
+أكبر من سفر was arbitrary اذا g1 is continuous
+
+162
+00:20:27,330 --> 00:20:29,730
+بما أن الـ C ينتبه إلى الـ R كان عبارة عن الـ
+
+163
+00:20:29,730 --> 00:20:50,630
+Arbitrary فالفنشن G1 مستمر على كل الـ R تمام فهو
+
+164
+00:20:50,630 --> 00:21:03,110
+فنشن من A إلى Ris continuous is continuous on
+
+165
+00:21:03,110 --> 00:21:18,650
+a then by composition theorem بيطلع
+
+166
+00:21:18,650 --> 00:21:31,550
+عندي g و g onecircle F absolute F is continuous on
+
+167
+00:21:31,550 --> 00:21:37,770
+A هاي ال composition theorem او النتيجة تبعتها انا
+
+168
+00:21:37,770 --> 00:21:46,190
+لسه اثبات ان ال G1 function from R to R is
+
+169
+00:21:46,190 --> 00:21:50,730
+continuous وفي
+
+170
+00:21:50,730 --> 00:21:51,830
+عندى ال
+
+171
+00:21:54,980 --> 00:22:06,640
+عندي f function from a to r f
+
+172
+00:22:06,640 --> 00:22:10,500
+function from a to r continuous انا فرض ان f is
+
+173
+00:22:10,500 --> 00:22:20,000
+continuous على a و ال function التاني g1 g1
+
+174
+00:22:20,000 --> 00:22:24,680
+function from r to rأيضا أثبتنا أنها continuous
+
+175
+00:22:24,680 --> 00:22:28,980
+فلو كانت هذه continuous من A ل B فال composition
+
+176
+00:22:28,980 --> 00:22:33,960
+تبعهم G1 circle F اللي بيطلع absolute F تطلع
+
+177
+00:22:33,960 --> 00:22:37,080
+continuous على A وهذه نظرية أثبتناها المرة اللي
+
+178
+00:22:37,080 --> 00:22:45,400
+فاتت فهي برهان أخر لهذه النظرية تمام مثال
+
+179
+00:22:45,400 --> 00:22:50,560
+تاني let G2
+
+180
+00:22:57,490 --> 00:23:04,270
+let let مثال تاني let g2 of x function بيساوي
+
+181
+00:23:04,270 --> 00:23:08,810
+square root of x و x أكبر من أو بيساوي سفر طبعا ده
+
+182
+00:23:08,810 --> 00:23:11,910
+اللي تجد التربيه بس معرفة للأعداد الحقيقية غير
+
+183
+00:23:11,910 --> 00:23:19,510
+السالبة claim g2 أثبتنا احنا ملاش claim by
+
+184
+00:23:19,510 --> 00:23:24,800
+previous exerciseأجيبنالكم في الامتحان حتى مثال في
+
+185
+00:23:24,800 --> 00:23:37,120
+الامتحان by a previous exercise g2
+
+186
+00:23:37,120 --> 00:23:43,020
+is continuous تطلع continuous على كل فترة من السفر
+
+187
+00:23:43,020 --> 00:23:47,140
+إلى ما نهيها هذا السؤال في الامتحان المناسب أخر
+
+188
+00:23:47,140 --> 00:23:51,300
+سؤال في الامتحان now
+
+189
+00:23:53,630 --> 00:24:02,570
+إذا .. إذا من a إلى r هو
+
+190
+00:24:02,570 --> 00:24:08,890
+مثلًا إن f من
+
+191
+00:24:08,890 --> 00:24:19,050
+x أكبر من أو ساقو سفر لكل x تنتمي إلى a و f
+
+192
+00:24:19,050 --> 00:24:20,130
+مستمر
+
+193
+00:24:23,230 --> 00:24:29,110
+on A then
+
+194
+00:24:29,110 --> 00:24:33,810
+by composition composition
+
+195
+00:24:33,810 --> 00:24:40,130
+theorem بطلع
+
+196
+00:24:40,130 --> 00:24:48,210
+G to circle F اللي هي بسوى جذر ال F is continuous
+
+197
+00:24:48,210 --> 00:24:57,810
+على المجموعة Aوهذا بيعطي برهان آخر لنظرية أخدناها
+
+198
+00:24:57,810 --> 00:25:02,570
+في آخر محاضرة بتقول لو كانت F دل غير سالب على
+
+199
+00:25:02,570 --> 00:25:07,630
+المجال تبعها ومتصلة على مجالها ف ال square root لل
+
+200
+00:25:07,630 --> 00:25:12,010
+function بتطلع أيضا متصلة على مجالها صح؟ وهذا
+
+201
+00:25:12,010 --> 00:25:17,170
+بيعتبر برهان آخر غير عن البرهان اللي أخدناه في
+
+202
+00:25:17,170 --> 00:25:19,210
+المحاضرة السابقة okay تمام؟
+
+203
+00:25:29,990 --> 00:25:35,230
+بثال تلاتة we
+
+204
+00:25:35,230 --> 00:25:41,310
+know ان ال function f
+
+205
+00:25:41,310 --> 00:25:49,690
+of x بساوي sin x is continuous اثبتنا ان الدالي
+
+206
+00:25:49,690 --> 00:25:53,490
+هاد continuous on R صح؟
+
+207
+00:25:58,290 --> 00:26:04,870
+خلّيني أسميها g of x وفي
+
+208
+00:26:04,870 --> 00:26:18,670
+عندي f of x بساوي واحد على x و
+
+209
+00:26:18,670 --> 00:26:23,050
+x لا يساوي سفر is continuous
+
+210
+00:26:29,880 --> 00:26:34,600
+for all x لا يساوي السفر ده لما اتصل معدى عند
+
+211
+00:26:34,600 --> 00:26:41,940
+السفر صح is continuous on a اللي هي بساوي r معدى
+
+212
+00:26:41,940 --> 00:26:46,520
+السفر
+
+213
+00:26:46,520 --> 00:26:55,960
+hence by composition theorem
+
+214
+00:26:55,960 --> 00:27:04,070
+اللي هو النتيجة هذهبطلع عندي g circle f of x اللي
+
+215
+00:27:04,070 --> 00:27:14,350
+هو g ل f of x اللي هي بتطلع بالساوي sin واحد على x
+
+216
+00:27:14,350 --> 00:27:21,390
+is continuous على
+
+217
+00:27:21,390 --> 00:27:29,730
+كل الأعداد الحقيقية مع عدد السفرOkay فالـ function
+
+218
+00:27:29,730 --> 00:27:37,410
+هذه متصلة مع ذا عند السفر وهي البرهان تبعها ان هذه
+
+219
+00:27:37,410 --> 00:27:43,230
+كلها تطبيقات على ال composition theorem فهذا
+
+220
+00:27:43,230 --> 00:27:49,390
+بورجيكم قوة ال composition theorem تمام؟ هيك ممكن
+
+221
+00:27:49,390 --> 00:27:54,610
+خلصنا section اتنين خمسة اتنين خلينا نبدأ في
+
+222
+00:27:54,610 --> 00:27:56,350
+section خمسة تلاتة
+
+223
+00:28:15,560 --> 00:28:30,180
+continuous functions on
+
+224
+00:28:30,180 --> 00:28:40,780
+intervals الدول
+
+225
+00:28:40,780 --> 00:28:47,270
+المتصلة على الفتراتقبل ان نبدأ في هذا الموضوع
+
+226
+00:28:47,270 --> 00:28:58,450
+نحتاج التعريف التالي a function f from A to R is
+
+227
+00:28:58,450 --> 00:29:04,630
+bounded on
+
+228
+00:29:04,630 --> 00:29:14,650
+المجموعة A إذا تحققالشرط التالي يوجد M عدد موجب
+
+229
+00:29:14,650 --> 00:29:22,090
+بحيث أنه absolute F of X أصغر بيكون أصغر من أو
+
+230
+00:29:22,090 --> 00:29:31,670
+ساوي M لكل X ينتمي إلى A that
+
+231
+00:29:31,670 --> 00:29:39,030
+is هذا معناه أنه the range
+
+232
+00:29:42,830 --> 00:29:52,470
+The range of F which is the set F of A which is
+
+233
+00:29:52,470 --> 00:29:57,950
+the whole F of X حيث X ينتبه إلى A
+
+234
+00:30:12,380 --> 00:30:18,740
+is a bounded subset
+
+235
+00:30:18,740 --> 00:30:23,320
+of
+
+236
+00:30:23,320 --> 00:30:28,240
+R الـ
+
+237
+00:30:28,240 --> 00:30:31,400
+function بتكون bounded function إذا كان ال range
+
+238
+00:30:31,400 --> 00:30:35,520
+تبعها كمجموعة بتطلع bounded set إيه يعني bounded
+
+239
+00:30:35,520 --> 00:30:40,080
+set يعني يوجد عدد موجة بحيث القيمة المطلقة لكل
+
+240
+00:30:40,080 --> 00:30:55,220
+عناصر ال set هذهأصغر من أو يساوي الـ M طيب
+
+241
+00:30:55,220 --> 00:30:59,660
+لو بدى أقول ما معنى أن تكون الدالة unbounded على
+
+242
+00:30:59,660 --> 00:31:09,660
+المجموعة A لأن هنا F from A to R is unbounded
+
+243
+00:31:13,140 --> 00:31:18,900
+is unbounded on
+
+244
+00:31:18,900 --> 00:31:26,580
+a if الشرط
+
+245
+00:31:26,580 --> 00:31:36,020
+التالي اتحقق خلّينا
+
+246
+00:31:36,020 --> 00:31:37,220
+ننفي الشرط هذا
+
+247
+00:31:41,360 --> 00:31:47,660
+ننفي الشرق بقى الـ bounded فيوجد M عدد موجب لكل
+
+248
+00:31:47,660 --> 00:31:57,700
+بيصير لكل M عدد موجب يوجد X يوجد X يعتمد على M في
+
+249
+00:31:57,700 --> 00:32:03,600
+مجال الدولة بحيث انه نفي المتبين هذا يتحقق اللي هو
+
+250
+00:32:03,600 --> 00:32:17,160
+absolute F of Xبطلع أكبر من أو ساوي أكبر
+
+251
+00:32:17,160 --> 00:32:22,500
+من أو ساوي ال M أكبر من أو ساوي ال M هذا معناه أن
+
+252
+00:32:22,500 --> 00:32:27,700
+الدالة ما تكونش bounded على المجال تبعها معناه أنه
+
+253
+00:32:27,700 --> 00:32:31,920
+لأي عدد موجب بقدر ألاقي عنصر يعتمد على عدد الموجب
+
+254
+00:32:31,920 --> 00:32:35,520
+هذا في مجال الدالة والقيمة المطلقة
+
+255
+00:32:38,330 --> 00:32:44,270
+قيمة الدالة عند العنصر أكبر من أو يساوي ال M فمثال
+
+256
+00:32:44,270 --> 00:32:51,010
+على ذلك هاي
+
+257
+00:32:51,010 --> 00:33:00,450
+مثال example لو
+
+258
+00:33:00,450 --> 00:33:14,520
+أخدت ال function f of xshow that f of x بيساوي
+
+259
+00:33:14,520 --> 00:33:22,240
+واحد على x و x أكبر من سفر is unbounded
+
+260
+00:33:22,240 --> 00:33:26,500
+على
+
+261
+00:33:26,500 --> 00:33:31,680
+المجموعة a اللي هي الفترة المفتوحة من سفر إلى مانا
+
+262
+00:33:31,680 --> 00:33:32,320
+نهائي
+
+263
+00:33:49,080 --> 00:33:57,820
+proof حسب تعريف ال unboundedness بدي اخد ابدأ let
+
+264
+00:33:57,820 --> 00:34:06,960
+m be an arbitrarily positive number بيه given بدي
+
+265
+00:34:06,960 --> 00:34:14,440
+ارد عليه باكس اعتمد xm بحيث ان المتباين هذا تتحقق
+
+266
+00:34:14,440 --> 00:34:24,160
+ف chooseإذاً لهذا العدد الموجب هختار XM X يعتمد
+
+267
+00:34:24,160 --> 00:34:31,920
+على M على إنه واحد على M زائد واحد فهذا بالتأكيد
+
+268
+00:34:31,920 --> 00:34:39,440
+عدد موجب لأن M عدد موجب صح؟ فبالتالي هذا ينتبه
+
+269
+00:34:39,440 --> 00:34:44,180
+للفترة المفتوحة من صفر إلى ملد يعني اللي هي ال A
+
+270
+00:34:47,860 --> 00:34:53,380
+يعني هاي لأي عدد موجب يعني وجدت there exist xm
+
+271
+00:34:53,380 --> 00:34:59,800
+ينتمي للمجال تبع الدالة وهذا يثبت أنه بحقق
+
+272
+00:34:59,800 --> 00:35:04,340
+المتباين هذا then
+
+273
+00:35:04,340 --> 00:35:15,540
+absolute f of xm بساوي absolute مقلوب
+
+274
+00:35:17,150 --> 00:35:26,330
+الـ Xm هو absolute واحد على Xm وهذا بيساوي M زياد
+
+275
+00:35:26,330 --> 00:35:32,290
+واحد هو مفروض اكتب absolute M زياد واحد اللي هو M
+
+276
+00:35:32,290 --> 00:35:39,450
+زياد واحد لأن M عدد موجة وهذا أكبر من M لأن هذه
+
+277
+00:35:39,450 --> 00:35:47,910
+المتباينة اتحققت أكبر من Mلأن نفي أصغر من أوي
+
+278
+00:35:47,910 --> 00:35:53,330
+الساوي مفروض يكون أكبر وهي أثبتت لأي عدد موجة
+
+279
+00:35:53,330 --> 00:35:58,570
+بيوجد XM في مجال الدالة وAbsolute صورة ال XM أكبر
+
+280
+00:35:58,570 --> 00:36:05,470
+من أمي okay تمام حسب التعريف أو ال remark بنطلع ال
+
+281
+00:36:05,470 --> 00:36:09,830
+function تبعتي unbounded على الفترة المفتوحة من
+
+282
+00:36:09,830 --> 00:36:12,630
+صفر إلى ملا نهائي تمام
+
+283
+00:36:15,080 --> 00:36:28,840
+الان في عندي boundedness theorem في
+
+284
+00:36:28,840 --> 00:36:41,220
+نظرية مهمة اسمها boundedness theorem boundedness
+
+285
+00:36:47,400 --> 00:36:54,560
+bound this theorem let
+
+286
+00:36:54,560 --> 00:37:04,580
+خلينا ناخد I let I be closed and bounded interval
+
+287
+00:37:04,580 --> 00:37:10,740
+be closed and
+
+288
+00:37:10,740 --> 00:37:16,500
+bounded interval
+
+289
+00:37:18,720 --> 00:37:27,740
+لو كانت F F from I to R is continuous is
+
+290
+00:37:27,740 --> 00:37:41,980
+continuous on I then F is bounded on
+
+291
+00:37:41,980 --> 00:37:49,110
+I لإن لو كان مجلة ده close bounded intervalوكانت
+
+292
+00:37:49,110 --> 00:37:53,950
+ال function continuous على I فلابد انها تطلع
+
+293
+00:37:53,950 --> 00:38:05,750
+bounded على الفترة I ولبرهان ذلك البرهان سهل proof
+
+294
+00:38:05,750 --> 00:38:13,590
+برهان بالتناقض assume on
+
+295
+00:38:13,590 --> 00:38:14,330
+contrary
+
+296
+00:38:18,360 --> 00:38:23,540
+إذا كان الـ F
+
+297
+00:38:23,540 --> 00:38:29,060
+غير مجموعة على
+
+298
+00:38:29,060 --> 00:38:34,620
+I فبعد
+
+299
+00:38:34,620 --> 00:38:35,780
+ذلك بمعالجة أعلى
+
+300
+00:38:43,910 --> 00:38:46,770
+by above remark اللي هي ال remark اللي مسحناها
+
+301
+00:38:46,770 --> 00:38:55,790
+اللي هي تعطيني تعريف ال unboundedness لكل n for
+
+302
+00:38:55,790 --> 00:39:10,890
+every n عدد طبيعي يوجد x يعتمد على n في الفترة I
+
+303
+00:39:10,890 --> 00:39:12,250
+في مجال الدالة
+
+304
+00:39:15,350 --> 00:39:24,050
+بحيث أنه بحيث
+
+305
+00:39:24,050 --> 00:39:35,750
+أنه صورة ال XN أكبر من .. أوي أكبر من LN
+
+306
+00:39:35,750 --> 00:39:45,140
+أثبت ال function F is unbounded on Iهذا معناه لكل
+
+307
+00:39:45,140 --> 00:39:50,140
+n عدد موجب وبالتالي لكل n عدد طبيعي لإن العداد
+
+308
+00:39:50,140 --> 00:39:56,180
+الطبيعي كلها موجبة يوجد x يعتمد على n في مجال الدل
+
+309
+00:39:56,180 --> 00:40:02,240
+بحيث f of x n يكون أكبر من n
+
+310
+00:40:11,940 --> 00:40:17,960
+طيب ما هذا بتديني طبعا
+
+311
+00:40:17,960 --> 00:40:22,340
+هنا في absolute value احنا نسين ال absolute value
+
+312
+00:40:22,340 --> 00:40:29,060
+اذا يوجد هيك بنكون كوّننا so there exist a
+
+313
+00:40:29,060 --> 00:40:38,180
+sequence x in contained in I such
+
+314
+00:40:38,180 --> 00:40:38,740
+that
+
+315
+00:40:42,110 --> 00:40:48,930
+absolute f of x in أكبر من n for all n belong to n
+
+316
+00:40:48,930 --> 00:40:55,690
+خليني أسميها دستار طيب
+
+317
+00:40:55,690 --> 00:41:03,770
+since ال sequence x in contained
+
+318
+00:41:03,770 --> 00:41:07,990
+in
+
+319
+00:41:07,990 --> 00:41:08,530
+I
+
+320
+00:41:11,610 --> 00:41:18,170
+والـ I عبارة عن الفترة المغلقة من A ل B إذا X in
+
+321
+00:41:18,170 --> 00:41:26,690
+is bounded لأن كل حدود ال sequence محصورة X in
+
+322
+00:41:26,690 --> 00:41:32,070
+أكبر من أو ساوي A أصفر من أو ساوي B لكل M هذه ال
+
+323
+00:41:32,070 --> 00:41:35,350
+sequence محدودة من أسفل ومحدودة من أعلى كل حدودها
+
+324
+00:41:35,350 --> 00:41:39,630
+محصورة بين A وB إذا ال sequence هذه bounded صح؟
+
+325
+00:41:40,270 --> 00:41:44,810
+وبالتالي So
+
+326
+00:41:44,810 --> 00:41:52,470
+by Bolzano-Weierstrass theorem نظرية Bolzano
+
+327
+00:41:52,470 --> 00:41:55,410
+-Weierstrass بتقول كل bounded sequence has a
+
+328
+00:41:55,410 --> 00:41:59,790
+convergent subsequence لإن هنا there exists a
+
+329
+00:41:59,790 --> 00:42:08,950
+subsequence سمية X in R of a sequence X in
+
+330
+00:42:12,270 --> 00:42:19,590
+which converges وهذه الـ subsequence converges say
+
+331
+00:42:19,590 --> 00:42:27,550
+خلّينا نفترض إنه limit لـ subsequence x in R as R
+
+332
+00:42:27,550 --> 00:42:36,790
+tends to infinity بساوي x تمام؟ since
+
+333
+00:42:38,330 --> 00:42:45,570
+الـ X in R أكبر من أو ساوي A أصغر من أو ساوي B لكل
+
+334
+00:42:45,570 --> 00:42:51,190
+R في N الـ sequence X in contained in I وهذه
+
+335
+00:42:51,190 --> 00:42:55,090
+subsequence منها لأن علاصتها موجودة في I بالتالي
+
+336
+00:42:55,090 --> 00:43:01,610
+محصورة بين A وB والsequence هذه converge ل Xإذا
+
+337
+00:43:01,610 --> 00:43:06,010
+حسب نظرية سابقة لما تكون ال sequence محصورة بين a
+
+338
+00:43:06,010 --> 00:43:13,670
+و b وconvergent فنهايتها أيضا we get from previous
+
+339
+00:43:13,670 --> 00:43:22,850
+theorem أن x تنتمي إلى I أو
+
+340
+00:43:22,850 --> 00:43:28,310
+تنتمي للفترة المغلقة من a إلى b اللي هي I تمام
+
+341
+00:43:32,130 --> 00:43:39,430
+طيب بما أن F continuous على I hence F is
+
+342
+00:43:39,430 --> 00:43:46,710
+continuous at X لأن F continuous على كل الفترة I و
+
+343
+00:43:46,710 --> 00:43:55,890
+X تنتمي ل I لأن F continuous at X طيب so by
+
+344
+00:43:55,890 --> 00:43:57,910
+sequential criterion
+
+345
+00:43:59,960 --> 00:44:04,080
+بسيطة لشركات مستمرين هيفي عند سيكوينس كونتينيوس ل
+
+346
+00:44:04,080 --> 00:44:12,200
+X و F continuous عند ال X إذا بسيطة لشركات مستمرين
+
+347
+00:44:12,200 --> 00:44:19,640
+نحصل على انه limit ال image لل subsequence X in R
+
+348
+00:44:19,640 --> 00:44:25,380
+as R tends to infinity بساوي F of X
+
+349
+00:44:30,470 --> 00:44:36,850
+طبما هذا معناه ان ال sequence هذه او ال image لل
+
+350
+00:44:36,850 --> 00:44:40,330
+subsequence اللي هي sequence اخرى convergent
+
+351
+00:44:40,330 --> 00:44:53,750
+وبالتالي فهي bounded okay تمام اذا it follows thus
+
+352
+00:44:53,750 --> 00:44:57,210
+the sequence
+
+353
+00:45:00,200 --> 00:45:08,660
+اللي هي f of x in R من R بالساوية واحدة لإنفينيتي
+
+354
+00:45:08,660 --> 00:45:15,980
+is bounded لإن أنا convergence كل convergence
+
+355
+00:45:15,980 --> 00:45:22,380
+sequence is bounded حسب نظرية السابقة وبالتالي so
+
+356
+00:45:22,380 --> 00:45:31,870
+there existSo there exist m عدد موجب بحيث انه
+
+357
+00:45:31,870 --> 00:45:44,450
+absolute
+
+358
+00:45:44,450 --> 00:45:52,730
+f of x in R تطلع اصغر من او ساوي m لكل
+
+359
+00:46:07,550 --> 00:46:19,170
+by our chameleon by our
+
+360
+00:46:19,170 --> 00:46:30,390
+chameleon propertyيوجد R ينتمي إلى N أو خلّيني
+
+361
+00:46:30,390 --> 00:46:41,390
+أسميه R0 ينتمي إلى N بحيث أنه R0 أكبر من M صح؟
+
+362
+00:46:41,390 --> 00:46:45,690
+لأي عدد حقيقي سواء موجب أو سالب فيه دائما عدد
+
+363
+00:46:45,690 --> 00:46:58,760
+طبيعي أكبر منه now by starand double star we have
+
+364
+00:46:58,760 --> 00:47:10,740
+لدينا انه ال M أكبر من أو يساوي absolute F of X in
+
+365
+00:47:10,740 --> 00:47:18,320
+R0 صح؟ هاي من هنا خدي R بساوي R0 فهذا الكلام صحيح
+
+366
+00:47:18,320 --> 00:47:21,500
+هذا من double star
+
+367
+00:47:24,010 --> 00:47:32,970
+و من star هذا أكبر من .. إذا من star f of x in R0
+
+368
+00:47:32,970 --> 00:47:41,450
+أكبر من in R0 هذا صحيح لكل عناصر ال sequence x in
+
+369
+00:47:41,450 --> 00:47:50,330
+وبالتالي صحيح لكل عناصر ال subsequence x in Rو in
+
+370
+00:47:50,330 --> 00:47:54,410
+R0 من تعريف الـ subsequence دائما أكبر من أو ساوي
+
+371
+00:47:54,410 --> 00:48:01,570
+R0 و من هنا R0 أكبر من M فنحن
+
+372
+00:48:01,570 --> 00:48:10,210
+نحصل على M أكبر من M Contradiction فالتناقض هذا
+
+373
+00:48:10,210 --> 00:48:14,610
+يقول لي أن ال assumption تبعي ال assumption تبعنا
+
+374
+00:48:16,810 --> 00:48:22,790
+إن ال function if is unbounded on I كان assumption
+
+375
+00:48:22,790 --> 00:48:26,870
+خاطئ، إذا ليس صح إن ال function تطلع bounded على I
+
+376
+00:48:26,870 --> 00:48:32,850
+وهذا بيكمل برهان أنبضرية، okay تمام؟ واضح؟
+
+377
+00:48:47,090 --> 00:48:53,650
+طيب ناخد احنا شوية break نكتفي
+
+378
+00:48:53,650 --> 00:49:00,710
+بهذا القدر و هناخد ان شاء الله break و نواصل في
+
+379
+00:49:00,710 --> 00:49:01,650
+اللقاء القادم
+
diff --git a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/xZkuM2ApdRM_raw.json b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/xZkuM2ApdRM_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..f85bdaacef9fc3cfe4d24ab739ea09b9ed7d9224
--- /dev/null
+++ b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/xZkuM2ApdRM_raw.json
@@ -0,0 +1 @@
+{"segments": [{"id": 1, "seek": 4379, "start": 21.19, "end": 43.79, "text": "في المحاضرة السابقة تعرفنا على أنواع الفترات أو ال intervals وشوفنا أن أول تلت أنواع من الفترات اللي هي ال open و ال closed و ال half open أو half closed intervals كل الفترات هذه كانت bounded intervals أو فترات محدودة", "tokens": [41185, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 37279, 28480, 8315, 15844, 14739, 14407, 3615, 27188, 2655, 2288, 9307, 34051, 2423, 26651, 4032, 8592, 38688, 8315, 14739, 5551, 12610, 6055, 1211, 2655, 14739, 14407, 3615, 9154, 27188, 2655, 2288, 9307, 13672, 1829, 39896, 2423, 1269, 4032, 2423, 5395, 4032, 2423, 1922, 1269, 34051, 1922, 5395, 26651, 28242, 27188, 2655, 2288, 9307, 29538, 25961, 2655, 37498, 26651, 34051, 6156, 2655, 2288, 9307, 3714, 24401, 23328, 3660], "avg_logprob": -0.10783305930856027, "compression_ratio": 1.8342541436464088, "no_speech_prob": 0.0, "words": [{"start": 21.19, "end": 21.45, "word": "في", "probability": 0.955078125}, {"start": 21.45, 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كلها", "probability": 0.974853515625}, {"start": 53.05, "end": 53.69, "word": " فترات", "probability": 0.980712890625}, {"start": 53.69, "end": 54.13, "word": " غير", "probability": 0.99609375}, {"start": 54.13, "end": 54.71, "word": " محدودة", "probability": 0.98779296875}, {"start": 54.71, "end": 54.91, "word": " أو", "probability": 0.7783203125}, {"start": 54.91, "end": 55.75, "word": " unbounded", "probability": 0.861328125}, {"start": 55.75, "end": 56.41, "word": " intervals", "probability": 0.93310546875}, {"start": 56.41, "end": 58.13, "word": " و", "probability": 0.43798828125}, {"start": 58.13, "end": 59.37, "word": " الفترات", "probability": 0.929931640625}, {"start": 59.37, "end": 59.61, "word": " هذه", "probability": 0.45166015625}, {"start": 59.61, "end": 60.03, "word": " عبارة", "probability": 0.9906005859375}, {"start": 60.03, "end": 61.23, "word": " عن", "probability": 0.998046875}, {"start": 61.23, "end": 61.71, "word": " النوع", "probability": 0.924072265625}, {"start": 61.71, "end": 62.23, "word": " الرابع", "probability": 0.9874674479166666}, {"start": 62.23, "end": 62.71, "word": " open", "probability": 0.927734375}, {"start": 62.71, "end": 63.11, "word": " left", "probability": 0.787109375}, {"start": 63.11, "end": 63.43, "word": " tray", "probability": 0.54541015625}, {"start": 63.43, "end": 64.15, "word": " شعاع", "probability": 0.8597005208333334}, {"start": 64.15, "end": 65.51, "word": " أيصر", "probability": 0.7958984375}, {"start": 65.51, "end": 66.19, "word": " مفتوح", "probability": 0.99560546875}, {"start": 66.19, "end": 67.73, "word": " أو", "probability": 0.79736328125}, {"start": 67.73, "end": 68.39, "word": " open", "probability": 0.9560546875}, {"start": 68.39, "end": 68.83, "word": " right", "probability": 0.9453125}, {"start": 68.83, "end": 69.27, "word": " tray", "probability": 0.921875}, {"start": 69.27, "end": 70.41, "word": " شعاع", "probability": 0.9835611979166666}, {"start": 70.41, "end": 70.81, "word": " أيمن", "probability": 0.836181640625}, {"start": 70.81, "end": 71.45, "word": " مفتوح", "probability": 0.99775390625}, {"start": 71.45, "end": 72.63, "word": " أو", "probability": 0.8369140625}, {"start": 72.63, "end": 73.11, "word": " closed", "probability": 0.74951171875}, {"start": 73.11, "end": 73.41, "word": " left", "probability": 0.93359375}, {"start": 73.41, "end": 73.75, "word": " tray", "probability": 0.9228515625}, {"start": 73.75, "end": 74.31, "word": " شعاع", "probability": 0.974609375}, {"start": 74.31, "end": 74.75, "word": " أيمن", "probability": 0.9541015625}], "temperature": 1.0}, {"id": 3, "seek": 8409, "start": 75.65, "end": 84.09, "text": "مغلق closed writer شعاع أيمن مغلق أو شعاع الجبلة شعاع أيصر مغلق", "tokens": [2304, 17082, 1211, 4587, 5395, 9936, 13412, 3615, 45761, 36632, 27842, 3714, 17082, 1211, 4587, 34051, 13412, 3615, 45761, 25724, 36150, 3660, 13412, 3615, 45761, 36632, 9381, 2288, 3714, 17082, 1211, 4587], "avg_logprob": -0.2547348484848485, "compression_ratio": 1.3205128205128205, "no_speech_prob": 0.0, "words": [{"start": 75.65, "end": 76.65, "word": "مغلق", "probability": 0.9622802734375}, {"start": 76.65, "end": 77.59, "word": " closed", "probability": 0.60400390625}, {"start": 77.59, "end": 79.13, "word": " writer", "probability": 0.265869140625}, {"start": 79.13, "end": 79.89, "word": " شعاع", "probability": 0.7067057291666666}, {"start": 79.89, "end": 80.27, "word": " أيمن", "probability": 0.667236328125}, {"start": 80.27, "end": 80.71, "word": " مغلق", "probability": 0.9775390625}, {"start": 80.71, "end": 80.93, "word": " أو", "probability": 0.425048828125}, {"start": 80.93, "end": 81.39, "word": " شعاع", "probability": 0.96484375}, {"start": 81.39, "end": 82.45, "word": " الجبلة", "probability": 0.585205078125}, {"start": 82.45, "end": 82.89, "word": " شعاع", "probability": 0.87841796875}, {"start": 82.89, "end": 83.49, "word": " أيصر", "probability": 0.7864583333333334}, {"start": 83.49, "end": 84.09, "word": " مغلق", "probability": 0.9942626953125}], "temperature": 1.0}, {"id": 4, "seek": 11236, "start": 84.74, "end": 112.36, "text": "و طبعا هذه عبارة عن فترات زي ما احنا شايفين النوع الأخير اللي هو مجموعة كل الأعداد اللي حصلت فيها the set of all real numbers اللي هي الفترة من ثالث من النهاية للملا نهاية وهذه طبعا أيضا unbounded interval فترة غير محصورة أو غير محدودة لو بصينا لأي نوع من أنواع التمانية هذه", "tokens": [2407, 23032, 3555, 3615, 995, 29538, 6225, 3555, 9640, 3660, 18871, 6156, 2655, 2288, 9307, 30767, 1829, 19446, 1975, 5016, 8315, 13412, 995, 33911, 9957, 28239, 45367, 16247, 9778, 13546, 13672, 1829, 31439, 3714, 7435, 2304, 2407, 27884, 28242, 16247, 22488, 18513, 13672, 1829, 11331, 36520, 2655, 8978, 11296, 264, 992, 295, 439, 957, 3547, 13672, 1829, 39896, 27188, 2655, 25720, 9154, 38637, 6027, 12984, 9154, 28239, 11296, 10632, 5296, 19528, 15040, 8717, 11296, 10632, 37037, 24192, 23032, 3555, 3615, 995, 36632, 11242, 995, 517, 18767, 292, 15035, 6156, 2655, 25720, 32771, 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{"start": 97.28, "end": 97.78, "word": " نهاية", "probability": 0.9108072916666666}, {"start": 97.78, "end": 98.76, "word": " وهذه", "probability": 0.81396484375}, {"start": 98.76, "end": 99.16, "word": " طبعا", "probability": 0.9783935546875}, {"start": 99.16, "end": 100.46, "word": " أيضا", "probability": 0.9264322916666666}, {"start": 100.46, "end": 102.58, "word": " unbounded", "probability": 0.84130859375}, {"start": 102.58, "end": 102.98, "word": " interval", "probability": 0.98828125}, {"start": 102.98, "end": 103.44, "word": " فترة", "probability": 0.92431640625}, {"start": 103.44, "end": 103.72, "word": " غير", "probability": 0.99462890625}, {"start": 103.72, "end": 104.8, "word": " محصورة", "probability": 0.9455078125}, {"start": 104.8, "end": 105.22, "word": " أو", "probability": 0.6025390625}, {"start": 105.22, "end": 105.56, "word": " غير", "probability": 0.9951171875}, {"start": 105.56, "end": 106.4, "word": " محدودة", "probability": 0.9403076171875}, {"start": 106.4, "end": 109.64, "word": " لو", "probability": 0.94873046875}, {"start": 109.64, "end": 110.28, "word": " بصينا", "probability": 0.95166015625}, {"start": 110.28, "end": 110.6, "word": " لأي", "probability": 0.9296875}, {"start": 110.6, "end": 110.84, "word": " نوع", "probability": 0.99072265625}, {"start": 110.84, "end": 111.06, "word": " من", "probability": 0.99365234375}, {"start": 111.06, "end": 111.44, "word": " أنواع", "probability": 0.8736979166666666}, {"start": 111.44, "end": 112.0, "word": " التمانية", "probability": 0.8555908203125}, {"start": 112.0, "end": 112.36, "word": " هذه", "probability": 0.91259765625}], "temperature": 1.0}, {"id": 5, "seek": 14255, "start": 113.77, "end": 142.55, "text": "من الفترات لو أخذنا أي نوع من الأنواع التمانية فبنلاحظ وسمينا الفترة هذه I لأن لو أخذنا one of the eight types of interval سمناها I فبنلاحظ أن الفترة I هذه بتحقق الخاصية اللي هي أمامنا هذه", "tokens": [27842, 27188, 2655, 2288, 9307, 45164, 5551, 9778, 8848, 8315, 36632, 8717, 45367, 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أربع احتمالات اما بتكون bounded يعني محدودة من الجهتين", "tokens": [2407, 4587, 1211, 8315, 14739, 39237, 4724, 2304, 41361, 24793, 6055, 4587, 2288, 33604, 2407, 3224, 6055, 5172, 16095, 2407, 3224, 2423, 26890, 3224, 7649, 44945, 7435, 11622, 3224, 5296, 10721, 25513, 3615, 11331, 6027, 9307, 9673, 7435, 2304, 2407, 27884, 318, 29538, 13672, 1829, 1975, 5016, 8315, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 16472, 11296, 15035, 8978, 11296, 5551, 25513, 3615, 1975, 33753, 2304, 6027, 9307, 1975, 15042, 39894, 30544, 37498, 37495, 22653, 3714, 24401, 23328, 3660, 9154, 25724, 3224, 2655, 9957], "avg_logprob": -0.19004360621058664, "compression_ratio": 1.544502617801047, "no_speech_prob": 0.0, "words": [{"start": 318.79, "end": 319.93, "word": "وقلنا", "probability": 0.65093994140625}, {"start": 319.93, "end": 320.33, "word": " أنتم", "probability": 0.4595947265625}, {"start": 320.33, "end": 321.03, "word": " بمكانكم", "probability": 0.887451171875}, {"start": 321.03, "end": 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sequence على سرها فترات I N فال sequence هذه بنسميها nested ال sequence of intervals هذه بنسميها nested", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 8310, 295, 26651, 286, 426, 29538, 6225, 3555, 9640, 3660, 18871, 6156, 2655, 25720, 2423, 7649, 29538, 6225, 3555, 9640, 3660, 18871, 8310, 15844, 8608, 2288, 11296, 6156, 2655, 2288, 9307, 286, 426, 6156, 6027, 8310, 29538, 44945, 38251, 1829, 11296, 15646, 292, 2423, 8310, 295, 26651, 29538, 44945, 38251, 1829, 11296, 15646, 292], "avg_logprob": -0.22643443013800948, "compression_ratio": 1.7553956834532374, "no_speech_prob": 0.0, "words": [{"start": 583.0, "end": 583.38, "word": "لو", "probability": 0.74560546875}, {"start": 583.38, "end": 583.88, "word": " أخدت", "probability": 0.887451171875}, {"start": 583.88, "end": 584.26, "word": " sequence", "probability": 0.68896484375}, {"start": 584.26, "end": 584.7, "word": " of", "probability": 0.96826171875}, {"start": 584.7, "end": 585.42, "word": " intervals", "probability": 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المغلقة من سفر لواحد على N حيث N أي عدد طبيعي فالفترات هذه", "tokens": [6780, 44271, 341, 4707, 44945, 38251, 1829, 11296, 15646, 292, 309, 311, 1219, 15646, 292, 8310, 295, 26651, 29538, 50113, 6027, 50113, 6027, 15844, 8310, 295, 15646, 292, 26651, 45164, 5551, 9778, 3215, 2655, 27188, 2655, 25720, 286, 426, 39896, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 8608, 5172, 2288, 5296, 14407, 24401, 15844, 426, 11331, 1829, 12984, 426, 36632, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 6156, 6027, 5172, 2655, 2288, 9307, 29538], "avg_logprob": -0.19500410968535825, "compression_ratio": 1.5124378109452736, "no_speech_prob": 0.0, "words": [{"start": 624.24, "end": 624.42, "word": "that", "probability": 0.07598876953125}, {"start": 624.42, "end": 625.18, "word": " satisfies", "probability": 0.82080078125}, {"start": 625.18, "end": 625.54, "word": " this", "probability": 0.91943359375}, {"start": 625.54, "end": 626.36, "word": " property", "probability": 0.955078125}, {"start": 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"word": " sequence", "probability": 0.84423828125}, {"start": 637.08, "end": 637.76, "word": " of", "probability": 0.95263671875}, {"start": 637.76, "end": 638.22, "word": " nested", "probability": 0.984619140625}, {"start": 638.22, "end": 638.78, "word": " intervals", "probability": 0.916015625}, {"start": 638.78, "end": 639.8, "word": " لو", "probability": 0.875}, {"start": 639.8, "end": 640.24, "word": " أخدت", "probability": 0.9713134765625}, {"start": 640.24, "end": 640.82, "word": " الفترة", "probability": 0.9933268229166666}, {"start": 640.82, "end": 642.04, "word": " I", "probability": 0.486572265625}, {"start": 642.04, "end": 642.34, "word": " N", "probability": 0.2626953125}, {"start": 642.34, "end": 642.5, "word": " هي", "probability": 0.916015625}, {"start": 642.5, "end": 642.94, "word": " الفترة", "probability": 0.9871419270833334}, {"start": 642.94, "end": 643.54, "word": " المغلقة", "probability": 0.9527587890625}, {"start": 643.54, "end": 643.86, "word": " من", 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"text": "واضح جدا انها nested هاي خط العداد هاي خط العداد هاي سفر واحد هاي فترة هادي I واحد خد ان بس I واحد I واحد فترة مغلقة من سفر ل واحد", "tokens": [2407, 46958, 5016, 10874, 28259, 16472, 11296, 15646, 292, 8032, 47302, 16490, 9566, 18863, 3215, 18513, 8032, 47302, 16490, 9566, 18863, 3215, 18513, 8032, 47302, 8608, 5172, 2288, 36764, 24401, 8032, 47302, 6156, 2655, 25720, 8032, 995, 16254, 286, 36764, 24401, 16490, 3215, 16472, 4724, 3794, 286, 36764, 24401, 286, 36764, 24401, 6156, 2655, 25720, 3714, 17082, 1211, 28671, 9154, 8608, 5172, 2288, 5296, 36764, 24401], "avg_logprob": -0.2653917874862899, "compression_ratio": 1.8571428571428572, "no_speech_prob": 0.0, "words": [{"start": 650.56, "end": 651.54, "word": "واضح", "probability": 0.9529622395833334}, {"start": 651.54, "end": 652.0, "word": " جدا", "probability": 0.974365234375}, {"start": 652.0, "end": 652.82, "word": " انها", "probability": 0.689453125}, {"start": 652.82, "end": 654.48, "word": " nested", "probability": 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703.18, "word": " هذه", "probability": 0.8876953125}], "temperature": 1.0}, {"id": 26, "seek": 73399, "start": 705.73, "end": 733.99, "text": "هذه الفترة I ثلاثة و I ثلاثة واضح هنا contained I اتنين و هكذا اذا واضح هنا ان I one contains I two contains I three and so on و هكذا وبالتالي ال sequence of intervals هذه تطلع nested تمام؟ طيب", "tokens": [3224, 24192, 27188, 2655, 25720, 286, 38637, 1211, 5718, 104, 3660, 4032, 286, 38637, 1211, 5718, 104, 3660, 4032, 46958, 5016, 34105, 16212, 286, 1975, 2655, 1863, 9957, 4032, 8032, 4117, 15730, 1975, 15730, 4032, 46958, 5016, 34105, 16472, 286, 472, 8306, 286, 732, 8306, 286, 1045, 293, 370, 322, 4032, 8032, 4117, 15730, 46599, 6027, 2655, 6027, 1829, 2423, 8310, 295, 26651, 29538, 6055, 9566, 1211, 3615, 15646, 292, 46811, 10943, 22807, 23032, 1829, 3555], "avg_logprob": -0.2256493576161273, "compression_ratio": 1.5542857142857143, "no_speech_prob": 0.0, "words": [{"start": 705.73, "end": 706.15, "word": "هذه", "probability": 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{"start": 745.35, "end": 746.95, "word": " فهنجد", "probability": 0.93828125}, {"start": 746.95, "end": 747.43, "word": " أنه", "probability": 0.414794921875}, {"start": 747.43, "end": 747.97, "word": " التقاطع", "probability": 0.9556884765625}, {"start": 747.97, "end": 748.35, "word": " تبعها", "probability": 0.9544677734375}, {"start": 748.35, "end": 748.49, "word": " لا", "probability": 0.8916015625}, {"start": 748.49, "end": 748.93, "word": " يساوي", "probability": 0.9525146484375}, {"start": 748.93, "end": 749.15, "word": " في", "probability": 0.9697265625}, {"start": 749.15, "end": 749.41, "word": " يعني", "probability": 0.95361328125}, {"start": 749.41, "end": 749.73, "word": " ممكن", "probability": 0.985107421875}, {"start": 749.73, "end": 750.29, "word": " ألاقي", "probability": 0.8030598958333334}, {"start": 750.29, "end": 751.23, "word": " على", "probability": 0.9306640625}, {"start": 751.23, "end": 751.63, "word": " الأقل", "probability": 0.95068359375}, {"start": 751.63, 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1095.63, "end": 1096.07, "word": " هذه", "probability": 0.85595703125}, {"start": 1096.07, "end": 1096.83, "word": " بتعمم", "probability": 0.9371744791666666}, {"start": 1096.83, "end": 1097.65, "word": " المعلومات", "probability": 0.9903564453125}, {"start": 1097.65, "end": 1097.83, "word": " اللي", "probability": 0.875732421875}, {"start": 1097.83, "end": 1098.05, "word": " هنا", "probability": 0.9619140625}, {"start": 1098.05, "end": 1099.37, "word": " او", "probability": 0.75830078125}, {"start": 1099.37, "end": 1099.89, "word": " النتيجة", "probability": 0.9373779296875}, {"start": 1099.89, "end": 1100.03, "word": " اللي", "probability": 0.95654296875}, {"start": 1100.03, "end": 1100.29, "word": " هنا", "probability": 0.2369384765625}, {"start": 1100.29, "end": 1100.81, "word": " اللي", "probability": 0.936279296875}, {"start": 1100.81, "end": 1101.51, "word": " شفناها", "probability": 0.8759765625}, {"start": 1101.51, "end": 1101.57, "word": " في", "probability": 0.84228515625}, 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" سفر", "probability": 0.830078125}], "temperature": 1.0}, {"id": 42, "seek": 119031, "start": 1161.93, "end": 1190.31, "text": "فالعدد ساي هذا بيكون وحيد يعني التقاطع هذا مافيش فيه إلا عنصر واحد بالضبط زي ما شوفنا هنا إذا إن الجزء التاني الجزء التاني من النظرية لو فرضنا إن ال infimum للعداد غير الساري بهذا بالساوي سفر فال ساي بتكون هي نقطة الوحيدة الموجودة في التقاطع تبع الفترات زي ما في المثال بالظبط السفر هي النقطة الوحيدة", "tokens": [5172, 6027, 22488, 3215, 8608, 47302, 23758, 4724, 1829, 30544, 4032, 5016, 25708, 37495, 22653, 16712, 4587, 41193, 3615, 23758, 19446, 41185, 8592, 8978, 3224, 11933, 15040, 18871, 9381, 2288, 36764, 24401, 20666, 11242, 3555, 9566, 30767, 1829, 19446, 13412, 38688, 8315, 34105, 11933, 15730, 36145, 25724, 11622, 38207, 16712, 7649, 1829, 25724, 11622, 38207, 16712, 7649, 1829, 9154, 28239, 19913, 2288, 10632, 45164, 6156, 43042, 8315, 36145, 2423, 1536, 332, 449, 24976, 22488, 18513, 32771, 13546, 21136, 9640, 1829, 39627, 15730, 20666, 3794, 995, 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"start": 1465.32, "end": 1484.12, "text": "ان التقاط على كل آي ان بساوي ساي لأ او يحتوي ساي تنتمي للتقاط على كل آي ان وهذا بيكون برهان هذا بيكمل برهان الجزء الأول", "tokens": [7649, 16712, 4587, 41193, 15844, 28242, 19753, 1829, 16472, 4724, 3794, 995, 45865, 8608, 47302, 5296, 10721, 1975, 2407, 7251, 33753, 45865, 8608, 47302, 6055, 29399, 2304, 1829, 24976, 2655, 4587, 41193, 15844, 28242, 19753, 1829, 16472, 37037, 15730, 4724, 1829, 30544, 4724, 2288, 3224, 7649, 23758, 4724, 1829, 24793, 1211, 4724, 2288, 3224, 7649, 25724, 11622, 38207, 16247, 12610], "avg_logprob": -0.23552766100305025, "compression_ratio": 1.8362068965517242, "no_speech_prob": 0.0, "words": [{"start": 1465.32, "end": 1465.62, "word": "ان", "probability": 0.462890625}, {"start": 1465.62, "end": 1466.24, "word": " التقاط", "probability": 0.9410807291666666}, {"start": 1466.24, "end": 1466.46, "word": " على", "probability": 0.908203125}, {"start": 1466.46, "end": 1466.84, "word": " كل", "probability": 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باق نثبت المتباينة هذه ستة فالإثبات المتباينة الستة هذه يكفي لإثبات المتباينة ستة هذه", "tokens": [28814, 15730, 1975, 5016, 8315, 6225, 47302, 11622, 9957, 8717, 12984, 3555, 2655, 9673, 2655, 3555, 995, 9957, 3660, 8608, 2655, 3660, 29538, 23032, 1211, 34268, 16490, 2304, 3794, 3660, 37037, 24192, 23032, 1211, 34268, 45164, 24401, 11296, 4724, 995, 4587, 8717, 12984, 3555, 2655, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8608, 2655, 3660, 6156, 6027, 28814, 12984, 3555, 9307, 9673, 2655, 3555, 995, 9957, 3660, 21136, 2655, 3660, 29538, 7251, 4117, 41185, 5296, 28814, 12984, 3555, 9307, 9673, 2655, 3555, 995, 9957, 3660, 8608, 2655, 3660, 29538], "avg_logprob": -0.15486111839612324, "compression_ratio": 2.2338709677419355, "no_speech_prob": 0.0, "words": [{"start": 1485.45, "end": 1485.77, "word": "إذا", "probability": 0.5999755859375}, {"start": 1485.77, "end": 1486.03, "word": " احنا", "probability": 0.777099609375}, {"start": 1486.03, "end": 1486.43, "word": " عايزين", 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احنا قبل شوية قلنا ان ال supremum للمجموعة هذه هو psi انا عندي psi بساوي ال supremum ال supremum للمجموعة هذه بساوي psi فلو اثبتت ان b in upper bound للمجموعة هذه", "tokens": [9566, 3555, 1975, 5016, 8315, 12174, 36150, 13412, 2407, 10632, 12174, 1211, 8315, 16472, 2423, 23710, 449, 5296, 19528, 7435, 2304, 2407, 27884, 29538, 31439, 20304, 1975, 8315, 18871, 16254, 20304, 4724, 3794, 995, 45865, 2423, 23710, 449, 2423, 23710, 449, 5296, 19528, 7435, 2304, 2407, 27884, 29538, 4724, 3794, 995, 45865, 20304, 6156, 1211, 2407, 1975, 12984, 3555, 2655, 2655, 16472, 272, 294, 6597, 5472, 5296, 19528, 7435, 2304, 2407, 27884, 29538], "avg_logprob": -0.2493665435829678, "compression_ratio": 1.7622377622377623, "no_speech_prob": 0.0, "words": [{"start": 1542.63, "end": 1542.89, "word": "طب", "probability": 0.7144775390625}, {"start": 1542.89, "end": 1543.09, "word": " احنا", "probability": 0.9366861979166666}, {"start": 1543.09, "end": 1543.39, "word": " قبل", "probability": 0.89990234375}, 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"text": "طبعا اذا باقى نثبت a المتباينة اللى هنا لثبات المتباينة هذه بنثبت n و بناخد اي arbitrary national number k فبنلاحظ ان ال n اما هتكون اصغر من أو يساوي k او n اكبر من k by trichotomy property ان ك عداد طبيعى اذا اما n اصغر من أو يساوي k او n اكبر من k", "tokens": [9566, 3555, 3615, 995, 1975, 15730, 4724, 995, 4587, 7578, 8717, 12984, 3555, 2655, 257, 9673, 2655, 3555, 995, 9957, 3660, 13672, 7578, 34105, 5296, 12984, 3555, 9307, 9673, 2655, 3555, 995, 9957, 3660, 29538, 44945, 12984, 3555, 2655, 297, 4032, 44945, 47283, 3215, 1975, 1829, 23211, 4048, 1230, 350, 6156, 3555, 1863, 15040, 5016, 19913, 16472, 2423, 297, 1975, 15042, 8032, 2655, 30544, 1975, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 350, 1975, 2407, 297, 1975, 4117, 26890, 9154, 350, 538, 504, 480, 310, 8488, 4707, 16472, 9122, 6225, 3215, 18513, 23032, 21292, 3615, 7578, 1975, 15730, 1975, 15042, 297, 1975, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 350, 1975, 2407, 297, 1975, 4117, 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هي الأصغر تمام؟ إذا أنا بطلع عندي I K subset من I N", "tokens": [9566, 1829, 3555, 8978, 21542, 6027, 3660, 16247, 12610, 7578, 45164, 25961, 2655, 2423, 426, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 591, 1975, 5016, 8315, 6225, 9640, 5172, 9957, 16472, 27188, 2655, 2288, 9307, 29538, 8717, 14851, 3215, 46599, 6027, 2655, 6027, 1829, 27188, 2655, 25720, 13672, 1829, 2423, 8186, 6055, 3555, 3615, 11296, 5551, 4117, 26890, 6055, 9566, 1211, 3615, 39896, 16247, 9381, 17082, 2288, 46811, 10943, 22807, 11933, 15730, 41850, 4724, 9566, 1211, 3615, 18871, 16254, 286, 591, 25993, 9154, 286, 426], "avg_logprob": -0.18767555777946215, "compression_ratio": 1.5958549222797926, "no_speech_prob": 0.0, "words": [{"start": 1628.82, "end": 1629.26, "word": "طيب", "probability": 0.7654622395833334}, {"start": 1629.26, "end": 1629.7, "word": " في", "probability": 0.57470703125}, {"start": 1629.7, "end": 1630.16, "word": " الحالة", "probability": 0.95361328125}, {"start": 1630.16, 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"end": 1642.52, "word": " هي", "probability": 0.84423828125}, {"start": 1642.52, "end": 1643.24, "word": " الأصغر", "probability": 0.9853515625}, {"start": 1643.24, "end": 1646.38, "word": " تمام؟", "probability": 0.5015869140625}, {"start": 1646.38, "end": 1646.76, "word": " إذا", "probability": 0.6346435546875}, {"start": 1646.76, "end": 1646.92, "word": " أنا", "probability": 0.57861328125}, {"start": 1646.92, "end": 1647.28, "word": " بطلع", "probability": 0.8487548828125}, {"start": 1647.28, "end": 1647.6, "word": " عندي", "probability": 0.796142578125}, {"start": 1647.6, "end": 1648.04, "word": " I", "probability": 0.8330078125}, {"start": 1648.04, "end": 1648.56, "word": " K", "probability": 0.67041015625}, {"start": 1648.56, "end": 1649.16, "word": " subset", "probability": 0.97021484375}, {"start": 1649.16, "end": 1649.48, "word": " من", "probability": 0.99560546875}, {"start": 1649.48, "end": 1649.8, "word": " I", "probability": 0.8486328125}, {"start": 1649.8, "end": 1650.18, "word": " N", "probability": 0.98095703125}], "temperature": 1.0}, {"id": 60, "seek": 168073, "start": 1652.77, "end": 1680.73, "text": "وبالتالي هاي نرسم هاي IK هاي الفترة IK نقاط أطرافها AK BK وهاي الفترة وهذه محتوى داخل الفترة IN هاي الفترة IN كبّر شوية", "tokens": [37746, 6027, 2655, 6027, 1829, 8032, 47302, 8717, 2288, 38251, 8032, 47302, 286, 42, 8032, 47302, 27188, 2655, 25720, 286, 42, 8717, 4587, 41193, 5551, 9566, 23557, 5172, 11296, 24789, 363, 42, 37037, 47302, 27188, 2655, 25720, 37037, 24192, 3714, 33753, 2407, 7578, 11778, 47283, 1211, 27188, 2655, 25720, 6892, 8032, 47302, 27188, 2655, 25720, 6892, 9122, 3555, 11703, 2288, 13412, 2407, 10632], "avg_logprob": -0.21142578148283064, "compression_ratio": 1.7058823529411764, "no_speech_prob": 0.0, "words": [{"start": 1652.77, "end": 1653.79, "word": "وبالتالي", "probability": 0.922265625}, {"start": 1653.79, "end": 1654.69, "word": " هاي", "probability": 0.5716552734375}, {"start": 1654.69, "end": 1655.67, "word": " نرسم", "probability": 0.92041015625}, {"start": 1655.67, "end": 1656.07, "word": " هاي", "probability": 0.677734375}, {"start": 1656.07, "end": 1657.09, "word": " IK", "probability": 0.58154296875}, {"start": 1657.09, "end": 1658.11, "word": " هاي", "probability": 0.792724609375}, {"start": 1658.11, "end": 1658.77, "word": " الفترة", "probability": 0.9781901041666666}, {"start": 1658.77, "end": 1660.41, "word": " IK", "probability": 0.921630859375}, {"start": 1660.41, "end": 1665.03, "word": " نقاط", "probability": 0.8743489583333334}, {"start": 1665.03, "end": 1665.71, "word": " أطرافها", "probability": 0.92001953125}, {"start": 1665.71, "end": 1666.09, "word": " AK", "probability": 0.87255859375}, {"start": 1666.09, "end": 1666.99, "word": " BK", "probability": 0.58349609375}, {"start": 1666.99, "end": 1668.37, "word": " وهاي", "probability": 0.6224365234375}, {"start": 1668.37, "end": 1669.03, "word": " الفترة", "probability": 0.9920247395833334}, {"start": 1669.03, "end": 1672.77, "word": " وهذه", "probability": 0.6552734375}, {"start": 1672.77, "end": 1673.47, "word": " محتوى", "probability": 0.912353515625}, {"start": 1673.47, "end": 1674.01, "word": " داخل", "probability": 0.9482421875}, {"start": 1674.01, "end": 1674.51, "word": " الفترة", "probability": 0.9083658854166666}, {"start": 1674.51, "end": 1675.03, "word": " IN", "probability": 0.83935546875}, {"start": 1675.03, "end": 1675.35, "word": " هاي", "probability": 0.782470703125}, {"start": 1675.35, "end": 1675.85, "word": " الفترة", "probability": 0.9899088541666666}, {"start": 1675.85, "end": 1676.43, "word": " IN", "probability": 0.904296875}, {"start": 1676.43, "end": 1680.33, "word": " كبّر", "probability": 0.68524169921875}, {"start": 1680.33, "end": 1680.73, "word": " شوية", "probability": 0.90966796875}], "temperature": 1.0}, {"id": 61, "seek": 169795, "start": 1682.33, "end": 1697.95, "text": "هذه الفترة IN هذه نقاط أطرافها فبما أن الفترة IK subset من الفترة IN", "tokens": [3224, 24192, 27188, 2655, 25720, 6892, 29538, 8717, 4587, 41193, 5551, 9566, 23557, 5172, 11296, 6156, 3555, 15042, 14739, 27188, 2655, 25720, 286, 42, 25993, 9154, 27188, 2655, 25720, 6892], "avg_logprob": -0.22353831318116957, "compression_ratio": 1.2906976744186047, "no_speech_prob": 0.0, "words": [{"start": 1682.33, "end": 1682.77, "word": "هذه", "probability": 0.789794921875}, {"start": 1682.77, "end": 1683.35, "word": " الفترة", "probability": 0.8644205729166666}, {"start": 1683.35, "end": 1685.99, "word": " IN", "probability": 0.11907958984375}, {"start": 1685.99, "end": 1687.65, "word": " هذه", "probability": 0.5244140625}, {"start": 1687.65, "end": 1688.19, "word": " نقاط", "probability": 0.8414713541666666}, {"start": 1688.19, "end": 1690.29, "word": " أطرافها", "probability": 0.9166015625}, {"start": 1690.29, "end": 1694.95, "word": " فبما", "probability": 0.876953125}, {"start": 1694.95, "end": 1695.15, "word": " أن", "probability": 0.71728515625}, {"start": 1695.15, "end": 1695.63, "word": " الفترة", "probability": 0.9705403645833334}, {"start": 1695.63, "end": 1696.19, "word": " IK", "probability": 0.73974609375}, {"start": 1696.19, "end": 1696.67, "word": " subset", "probability": 0.63037109375}, {"start": 1696.67, "end": 1696.91, "word": " من", "probability": 0.93310546875}, {"start": 1696.91, "end": 1697.35, "word": " الفترة", "probability": 0.9488932291666666}, {"start": 1697.35, "end": 1697.95, "word": " IN", "probability": 0.88916015625}], "temperature": 1.0}, {"id": 62, "seek": 172160, "start": 1699.36, "end": 1721.6, "text": "إذا اللي بطلع عندى aK أصغر من أو يساوي bK و bK أصغر من أو يساوي bN وبالتالي هيني أثبتت أن aK أصغر من أو يساوي bN كما هو مطلوب طيب في الحالة التانية افرض أن N هي اللي أكبر من K", "tokens": [28814, 15730, 13672, 1829, 4724, 9566, 1211, 3615, 43242, 7578, 257, 42, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 272, 42, 4032, 272, 42, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 272, 45, 46599, 6027, 2655, 6027, 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0.62158203125}, {"start": 1708.82, "end": 1709.44, "word": " أثبتت", "probability": 0.98173828125}, {"start": 1709.44, "end": 1709.62, "word": " أن", "probability": 0.58740234375}, {"start": 1709.62, "end": 1710.5, "word": " aK", "probability": 0.72802734375}, {"start": 1710.5, "end": 1711.1, "word": " أصغر", "probability": 0.9921875}, {"start": 1711.1, "end": 1711.26, "word": " من", "probability": 0.9951171875}, {"start": 1711.26, "end": 1711.44, "word": " أو", "probability": 0.98486328125}, {"start": 1711.44, "end": 1712.18, "word": " يساوي", "probability": 0.980224609375}, {"start": 1712.18, "end": 1713.0, "word": " bN", "probability": 0.959228515625}, {"start": 1713.0, "end": 1714.06, "word": " كما", "probability": 0.953369140625}, {"start": 1714.06, "end": 1714.28, "word": " هو", "probability": 0.990234375}, {"start": 1714.28, "end": 1714.8, "word": " مطلوب", "probability": 0.9478759765625}, {"start": 1714.8, "end": 1716.54, "word": " طيب", "probability": 0.9627278645833334}, {"start": 1716.54, "end": 1716.68, "word": " في", "probability": 0.71923828125}, {"start": 1716.68, "end": 1717.08, "word": " الحالة", "probability": 0.9583333333333334}, {"start": 1717.08, "end": 1718.32, "word": " التانية", "probability": 0.9765625}, {"start": 1718.32, "end": 1718.94, "word": " افرض", "probability": 0.8836263020833334}, {"start": 1718.94, "end": 1719.22, "word": " أن", "probability": 0.347412109375}, {"start": 1719.22, "end": 1719.68, "word": " N", "probability": 0.482421875}, {"start": 1719.68, "end": 1720.3, "word": " هي", "probability": 0.96337890625}, {"start": 1720.3, "end": 1720.54, "word": " اللي", "probability": 0.93408203125}, {"start": 1720.54, "end": 1721.04, "word": " أكبر", "probability": 0.9601236979166666}, {"start": 1721.04, "end": 1721.28, "word": " من", "probability": 0.990234375}, {"start": 1721.28, "end": 1721.6, "word": " K", "probability": 0.92529296875}], "temperature": 1.0}, {"id": 63, "seek": 174615, "start": 1723.05, "end": 1746.15, "text": "ففي الحالة هذه بما ان ال sequence in nested إذا in محتوى داخل ik إذا هاي عندي in", "tokens": [5172, 41185, 21542, 6027, 3660, 29538, 4724, 15042, 16472, 2423, 8310, 294, 15646, 292, 11933, 15730, 294, 3714, 33753, 2407, 7578, 11778, 47283, 1211, 4320, 11933, 15730, 8032, 47302, 18871, 16254, 294], "avg_logprob": -0.4131155303030303, "compression_ratio": 1.174757281553398, "no_speech_prob": 0.0, "words": [{"start": 1723.05, "end": 1723.51, "word": "ففي", "probability": 0.358642578125}, {"start": 1723.51, "end": 1723.81, "word": " الحالة", "probability": 0.93310546875}, {"start": 1723.81, "end": 1724.05, "word": " هذه", "probability": 0.51025390625}, {"start": 1724.05, "end": 1724.29, "word": " بما", "probability": 0.7159423828125}, {"start": 1724.29, "end": 1724.53, "word": " ان", "probability": 0.498291015625}, {"start": 1724.53, "end": 1724.95, "word": " ال", "probability": 0.5068359375}, {"start": 1724.95, "end": 1725.45, "word": " sequence", "probability": 0.71923828125}, {"start": 1725.45, "end": 1726.11, "word": " in", "probability": 0.445556640625}, {"start": 1726.11, "end": 1727.23, "word": " nested", "probability": 0.557525634765625}, {"start": 1727.23, "end": 1727.91, "word": " إذا", "probability": 0.5611572265625}, {"start": 1727.91, "end": 1728.87, "word": " in", "probability": 0.5380859375}, {"start": 1728.87, "end": 1730.41, "word": " محتوى", "probability": 0.93408203125}, {"start": 1730.41, "end": 1731.01, "word": " داخل", "probability": 0.9191080729166666}, {"start": 1731.01, "end": 1731.67, "word": " ik", "probability": 0.533203125}, {"start": 1731.67, "end": 1742.27, "word": " إذا", "probability": 0.781494140625}, {"start": 1742.27, "end": 1742.53, "word": " هاي", "probability": 0.550048828125}, {"start": 1742.53, "end": 1743.03, "word": " عندي", "probability": 0.865478515625}, {"start": 1743.03, "end": 1746.15, "word": " in", "probability": 0.798828125}], "temperature": 1.0}, {"id": 64, "seek": 177342, "start": 1751.08, "end": 1773.42, "text": "الفترة IN هذا هي محتوى داخل الفترة IK يعني نقاط أطرافها AK BK وبالتالي في الحالة هذه بيطلع AK أصغر من أو ساوي AN أصغر من أو ساوي BN", "tokens": [6027, 5172, 2655, 25720, 6892, 23758, 39896, 3714, 33753, 2407, 7578, 11778, 47283, 1211, 27188, 2655, 25720, 286, 42, 37495, 22653, 8717, 4587, 41193, 5551, 9566, 23557, 5172, 11296, 24789, 363, 42, 46599, 6027, 2655, 6027, 1829, 8978, 21542, 6027, 3660, 29538, 4724, 1829, 9566, 1211, 3615, 24789, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 5252, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 363, 45], "avg_logprob": -0.1882812546832221, "compression_ratio": 1.5602836879432624, "no_speech_prob": 0.0, "words": [{"start": 1751.08, "end": 1751.76, "word": "الفترة", "probability": 0.866455078125}, {"start": 1751.76, "end": 1752.4, "word": " IN", "probability": 0.37646484375}, {"start": 1752.4, "end": 1752.68, "word": " هذا", "probability": 0.145751953125}, {"start": 1752.68, "end": 1753.12, "word": " هي", "probability": 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أثبتناها فباستخدام برهان شبيه ببرهان المتباينة sex ممكن نصل إلى", "tokens": [6027, 7649, 538, 364, 6770, 538, 364, 6770, 2531, 281, 264, 8177, 295, 3260, 1975, 5016, 8315, 13412, 38688, 8315, 12174, 36150, 13412, 2407, 10632, 44650, 3555, 995, 9957, 3660, 3260, 5551, 12984, 3555, 2655, 8315, 11296, 6156, 3555, 995, 14851, 9778, 3215, 10943, 4724, 2288, 3224, 7649, 13412, 21292, 3224, 4724, 26890, 3224, 7649, 9673, 2655, 3555, 995, 9957, 3660, 3260, 3714, 43020, 8717, 36520, 30731], "avg_logprob": -0.11259190957335864, "compression_ratio": 1.4936708860759493, "no_speech_prob": 0.0, "words": [{"start": 2025.47, "end": 2026.13, "word": "الان", "probability": 0.7587890625}, {"start": 2026.13, "end": 2027.71, "word": " by", "probability": 0.74658203125}, {"start": 2027.71, "end": 2028.11, "word": " an", "probability": 0.9345703125}, {"start": 2028.11, "end": 2028.89, "word": " argument", "probability": 0.88134765625}, {"start": 2028.89, "end": 2029.83, "word": " by", "probability": 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بيطلع عندي هنا Psi بيطلع أصغر من أو يساوي Eta إذا طلع عندي أنا هنا Psi أصغر من أو يساوي Eta", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 23710, 449, 5296, 19528, 7435, 2304, 45367, 3660, 29538, 4724, 1829, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 2423, 6597, 5472, 23758, 13672, 1829, 31439, 430, 7691, 11933, 15730, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 34105, 430, 7691, 4724, 1829, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 462, 1328, 11933, 15730, 23032, 1211, 3615, 18871, 16254, 41850, 34105, 430, 7691, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 462, 1328], "avg_logprob": -0.19259510642808417, "compression_ratio": 1.9281045751633987, "no_speech_prob": 0.0, "words": [{"start": 2100.43, "end": 2101.13, "word": "وبالتالي", "probability": 0.882470703125}, {"start": 2101.13, "end": 2101.31, "word": " ال", "probability": 0.389892578125}, {"start": 2101.31, "end": 2101.77, "word": " 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{"start": 2444.13, "end": 2444.55, "word": " إبسلون", "probability": 0.97666015625}, {"start": 2444.55, "end": 2445.31, "word": " وبالتالي", "probability": 0.931640625}, {"start": 2445.31, "end": 2445.89, "word": " فيه", "probability": 0.560546875}, {"start": 2445.89, "end": 2446.49, "word": " يوجد", "probability": 0.9822591145833334}, {"start": 2446.49, "end": 2447.53, "word": " عنصر", "probability": 0.9822591145833334}, {"start": 2447.53, "end": 2447.69, "word": " في", "probability": 0.9296875}, {"start": 2447.69, "end": 2447.87, "word": " ال", "probability": 0.931640625}, {"start": 2447.87, "end": 2448.13, "word": " set", "probability": 0.8603515625}, {"start": 2448.13, "end": 2448.65, "word": " هذه", "probability": 0.4658203125}, {"start": 2448.65, "end": 2450.01, "word": " أصغر", "probability": 0.9810791015625}, {"start": 2450.01, "end": 2450.93, "word": " من", "probability": 0.9931640625}, {"start": 2450.93, "end": 2451.11, "word": " ال", "probability": 0.90771484375}, {"start": 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"text": "بن إبسلون أكبر من أو ساوي إتا وان إبسلون أصغر من أو ساوي ساي فالفرق بين هدول أصغر من أو ساوي الفرق بين هدول وانا عندي ساي أصغر من أو ساوي إتا فالفرق بين ساي و إتا أكبر من أو ساوي سفر", "tokens": [3555, 1863, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 11933, 2655, 995, 4032, 7649, 11933, 3555, 3794, 1211, 11536, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8608, 47302, 6156, 6027, 5172, 2288, 4587, 49374, 8032, 3215, 12610, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 27188, 2288, 4587, 49374, 8032, 3215, 12610, 4032, 7649, 995, 18871, 16254, 8608, 47302, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 11933, 2655, 995, 6156, 6027, 5172, 2288, 4587, 49374, 8608, 47302, 4032, 11933, 2655, 995, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.18810096755623817, "compression_ratio": 2.7142857142857144, "no_speech_prob": 0.0, "words": [{"start": 2460.35, "end": 2461.13, 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ساوي", "probability": 0.9759114583333334}, {"start": 2468.45, "end": 2468.89, "word": " ساي", "probability": 0.3895263671875}, {"start": 2468.89, "end": 2470.25, "word": " فالفرق", "probability": 0.8009765625}, {"start": 2470.25, "end": 2470.45, "word": " بين", "probability": 0.9326171875}, {"start": 2470.45, "end": 2470.77, "word": " هدول", "probability": 0.676025390625}, {"start": 2470.77, "end": 2471.15, "word": " أصغر", "probability": 0.9818115234375}, {"start": 2471.15, "end": 2471.23, "word": " من", "probability": 0.98974609375}, {"start": 2471.23, "end": 2471.37, "word": " أو", "probability": 0.95166015625}, {"start": 2471.37, "end": 2471.51, "word": " ساوي", "probability": 0.9814453125}, {"start": 2471.51, "end": 2471.93, "word": " الفرق", "probability": 0.89013671875}, {"start": 2471.93, "end": 2472.13, "word": " بين", "probability": 0.955078125}, {"start": 2472.13, "end": 2472.85, "word": " هدول", "probability": 0.7152506510416666}, {"start": 2472.85, "end": 2475.31, "word": " وانا", "probability": 0.6832682291666666}, {"start": 2475.31, "end": 2475.77, "word": " عندي", "probability": 0.83935546875}, {"start": 2475.77, "end": 2477.13, "word": " ساي", "probability": 0.720947265625}, {"start": 2477.13, "end": 2479.53, "word": " أصغر", "probability": 0.98828125}, {"start": 2479.53, "end": 2479.75, "word": " من", "probability": 0.99560546875}, {"start": 2479.75, "end": 2479.97, "word": " أو", "probability": 0.994140625}, {"start": 2479.97, "end": 2480.43, "word": " ساوي", "probability": 0.9716796875}, {"start": 2480.43, "end": 2480.99, "word": " إتا", "probability": 0.9651692708333334}, {"start": 2480.99, "end": 2482.45, "word": " فالفرق", "probability": 0.8912109375}, {"start": 2482.45, "end": 2482.81, "word": " بين", "probability": 0.93505859375}, {"start": 2482.81, "end": 2484.11, "word": " ساي", "probability": 0.746337890625}, {"start": 2484.11, "end": 2484.23, "word": " و", "probability": 0.921875}, {"start": 2484.23, "end": 2484.61, "word": " إتا", "probability": 0.86474609375}, {"start": 2484.61, "end": 2484.97, "word": " أكبر", "probability": 0.9777018229166666}, {"start": 2484.97, "end": 2485.11, "word": " من", "probability": 0.99267578125}, {"start": 2485.11, "end": 2485.29, "word": " أو", "probability": 0.9931640625}, {"start": 2485.29, "end": 2485.57, "word": " ساوي", "probability": 0.97705078125}, {"start": 2485.57, "end": 2485.99, "word": " سفر", "probability": 0.880859375}], "temperature": 1.0}, {"id": 93, "seek": 250828, "start": 2486.92, "end": 2508.28, "text": "تمام؟ إذا المتباين الأخيرة هذه بحصل منها على إيه؟ المتباين الأخير منها هذه بحصل على إنه صفر أصغر من أوي ساوي eta minus epsilon أصغر من epsilon لأ عفوا هذه eta minus psi", "tokens": [39237, 10943, 22807, 11933, 15730, 9673, 2655, 3555, 995, 9957, 16247, 9778, 13546, 3660, 29538, 4724, 5016, 36520, 9154, 11296, 15844, 11933, 1829, 3224, 22807, 9673, 2655, 3555, 995, 9957, 16247, 9778, 13546, 9154, 11296, 29538, 4724, 5016, 36520, 15844, 36145, 3224, 20328, 5172, 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2497.86, "end": 2498.28, "word": " ساوي", "probability": 0.89794921875}, {"start": 2498.28, "end": 2498.72, "word": " eta", "probability": 0.263916015625}, {"start": 2498.72, "end": 2499.28, "word": " minus", "probability": 0.9423828125}, {"start": 2499.28, "end": 2500.04, "word": " epsilon", "probability": 0.79052734375}, {"start": 2500.04, "end": 2501.86, "word": " أصغر", "probability": 0.990478515625}, {"start": 2501.86, "end": 2502.26, "word": " من", "probability": 0.99560546875}, {"start": 2502.26, "end": 2503.88, "word": " epsilon", "probability": 0.80810546875}, {"start": 2503.88, "end": 2505.26, "word": " لأ", "probability": 0.6468505859375}, {"start": 2505.26, "end": 2505.56, "word": " عفوا", "probability": 0.9052734375}, {"start": 2505.56, "end": 2505.84, "word": " هذه", "probability": 0.5654296875}, {"start": 2505.84, "end": 2506.3, "word": " eta", "probability": 0.78662109375}, {"start": 2506.3, "end": 2507.7, "word": " minus", "probability": 0.99267578125}, {"start": 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/0MG_WyJdBaA_raw.json b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/0MG_WyJdBaA_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..6a5ba5e27c09995e0c3c51b42ec892d65c3645be
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/0MG_WyJdBaA_raw.json
@@ -0,0 +1 @@
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"text": "تنزل إمكانية إنها تحدث عند المريض طبع الضغط لو عالجته بطريقة سليمة من 20% لـ 25% رقم رهائن وطبعا هذه الأرقام تتحسن مع الوجد يا جماعة يعني بمعنى كل ما تطور الطب وكل ما العيان أو المريض أو الإنسان الإجبالي", "tokens": [2655, 1863, 11622, 1211, 11933, 2304, 41361, 10632, 36145, 11296, 6055, 24401, 12984, 43242, 9673, 16572, 11242, 23032, 3555, 3615, 6024, 114, 17082, 9566, 45164, 6225, 6027, 7435, 47395, 4724, 9566, 16572, 28671, 8608, 20292, 46007, 9154, 945, 4, 5296, 39184, 3552, 4, 12602, 4587, 2304, 12602, 3224, 16373, 1863, 4032, 9566, 3555, 3615, 995, 29538, 16247, 2288, 4587, 10943, 6055, 2655, 5016, 3794, 1863, 20449, 2423, 29245, 3215, 35186, 10874, 15042, 27884, 37495, 22653, 4724, 2304, 3615, 1863, 7578, 28242, 19446, 6055, 9566, 13063, 41950, 3555, 4032, 28820, 19446, 18863, 1829, 7649, 34051, 9673, 16572, 11242, 34051, 33688, 1863, 3794, 7649, 33688, 7435, 3555, 6027, 1829], "avg_logprob": -0.15176505057348144, "compression_ratio": 1.7355769230769231, 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"probability": 0.9890625}, {"start": 1860.58, "end": 1860.94, "word": " ممكن", "probability": 0.96044921875}, {"start": 1860.94, "end": 1861.94, "word": " ملاحظة", "probability": 0.98955078125}, {"start": 1861.94, "end": 1862.38, "word": " إيجابية", "probability": 0.990234375}, {"start": 1862.38, "end": 1863.2, "word": " طبعاً", "probability": 0.869384765625}, {"start": 1863.2, "end": 1863.58, "word": " إنه", "probability": 0.85791015625}, {"start": 1863.58, "end": 1863.92, "word": " أقدر", "probability": 0.9954427083333334}, {"start": 1863.92, "end": 1864.86, "word": " أحسن", "probability": 0.99072265625}, {"start": 1864.86, "end": 1865.42, "word": " في", "probability": 0.97216796875}, {"start": 1865.42, "end": 1865.76, "word": " وصول", "probability": 0.994140625}, {"start": 1865.76, "end": 1866.28, "word": " المعلومة", "probability": 0.994384765625}, {"start": 1866.28, "end": 1866.68, "word": " إلكوا", "probability": 0.7509765625}, {"start": 1866.68, "end": 1867.34, "word": " بأي", "probability": 0.9744466145833334}, {"start": 1867.34, "end": 1868.34, "word": " صورة", "probability": 0.9944661458333334}, {"start": 1868.34, "end": 1870.14, "word": " لأن", "probability": 0.939697265625}, {"start": 1870.14, "end": 1871.62, "word": " الفرصة", "probability": 0.925537109375}, {"start": 1871.62, "end": 1871.8, "word": " هذه", "probability": 0.67919921875}, {"start": 1871.8, "end": 1872.02, "word": " مش", "probability": 0.98583984375}, {"start": 1872.02, "end": 1873.12, "word": " موجودة", "probability": 0.992431640625}, {"start": 1873.12, "end": 1874.14, "word": " في", "probability": 0.9453125}, {"start": 1874.14, "end": 1874.52, "word": " تعليم", "probability": 0.9606119791666666}, {"start": 1874.52, "end": 1874.98, "word": " الـ", "probability": 0.923583984375}], "temperature": 1.0}, {"id": 78, "seek": 190587, "start": 1876.63, "end": 1905.87, "text": "الإلكتروني لكن لو كان وجاهي بقدر واحد يشرح ويزيد ويعيد وكذا لكن الآن حقيقة محصور لأ أي حد بده أي حاجة على الرقم اللي عندكم على الواتس أب يرسلني مباشرة ماعندي مشكلة حتى يعني بدون .. بدون ما اتبايلوا على فريزة ابعتولي لو في أي حاجة إيش بقدر أعمل حاول .. حاول نخفف بدنا نعدي هذه الفترة على خير ونشوف وشكوا على خير إن شاء الله السلام عليكم", "tokens": [6027, 28814, 23275, 2655, 2288, 11536, 1829, 44381, 45164, 25961, 49610, 40294, 1829, 4724, 28543, 2288, 36764, 24401, 7251, 46309, 5016, 4032, 1829, 11622, 25708, 4032, 40228, 25708, 4032, 4117, 15730, 44381, 6024, 48506, 11331, 38436, 28671, 3714, 5016, 9381, 13063, 5296, 10721, 36632, 11331, 3215, 47525, 3224, 36632, 11331, 26108, 3660, 15844, 34892, 4587, 2304, 13672, 1829, 43242, 24793, 15844, 2423, 2407, 9307, 3794, 5551, 3555, 7251, 2288, 3794, 1211, 22653, 3714, 3555, 33599, 25720, 19446, 3615, 1863, 16254, 37893, 28820, 3660, 11331, 49975, 37495, 22653, 47525, 11536, 4386, 47525, 11536, 19446, 1975, 2655, 3555, 995, 26895, 14407, 15844, 6156, 16572, 11622, 3660, 48127, 34268, 12610, 1829, 45164, 8978, 36632, 11331, 26108, 3660, 11933, 1829, 8592, 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"end": 1905.57, "word": " السلام", "probability": 0.869140625}, {"start": 1905.57, "end": 1905.87, "word": " عليكم", "probability": 0.842529296875}], "temperature": 1.0}], "language": "ar", "language_probability": 1.0, "duration": 1910.46825, "duration_after_vad": 1851.654999999996}
\ No newline at end of file
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/1Du05IN_hTA.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/1Du05IN_hTA.srt
new file mode 100644
index 0000000000000000000000000000000000000000..b1f12c267830b36c0d99390355062d89dc79f076
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/1Du05IN_hTA.srt
@@ -0,0 +1,1597 @@
+1
+00:00:00,960 --> 00:00:03,520
+بسم الله الرحمن الرحيم اليوم إن شاء الله محاضرة
+
+2
+00:00:03,520 --> 00:00:07,960
+جديدة اليوم طبعا تسجيل من البيت ادعوا ربنا الكرات
+
+3
+00:00:07,960 --> 00:00:12,700
+والهيك ما يكونوش كتيرة ع كل حال هيكوا عارفين لو
+
+4
+00:00:12,700 --> 00:00:18,760
+سمعتولكوا صوت حطب بيقوسة جزر جزاز مكسر أي حاجة ع
+
+5
+00:00:18,760 --> 00:00:21,800
+كل حال اليوم هنتحدث إن شاء الله برضه في الجهاز
+
+6
+00:00:21,800 --> 00:00:26,970
+الهضمي كنا بدأنا وحكينا إذا فاكرين عن الـ
+
+7
+00:00:26,970 --> 00:00:30,090
+gastroesophageal reflux والبيبتكالثر والدودنالالثر
+
+8
+00:00:30,090 --> 00:00:33,730
+الآن بنروح للـ gallbladder إيش عن ال gallbladder
+
+9
+00:00:33,730 --> 00:00:39,210
+المرارة gallbladder disorders أمراض المرارة
+
+10
+00:00:39,210 --> 00:00:44,410
+المرارة يعني احنا زي ما كلنا عارفين هي عبارة عن
+
+11
+00:00:44,410 --> 00:00:49,990
+عضو 
+
+12
+00:00:50,930 --> 00:00:53,670
+موجود في الـ right upper quadrant of the abdomen
+
+13
+00:00:53,670 --> 00:00:58,710
+right below the liver تحت ال liver على الطولة يعني
+
+14
+00:00:58,710 --> 00:01:03,610
+ال liver منه تحت ال gallbladder هي عبارة عن a part
+
+15
+00:01:03,610 --> 00:01:10,530
+of the biliary system نقول عنه الجهاز البابي biliary
+
+16
+00:01:10,530 --> 00:01:16,010
+system اللي هو اللي بيصدر ال fluids من ال liver
+
+17
+00:01:16,010 --> 00:01:22,730
+للجهاز الهضمي والـ Gall Bladder يا جماعة لازم نكون
+
+18
+00:01:22,730 --> 00:01:30,130
+كلنا عارفين إن هي بتصنعش حاجة هي بس storage
+
+19
+00:01:30,130 --> 00:01:36,670
+reservoir for the bile بس لإنها بتجمع ال bile
+
+20
+00:01:36,670 --> 00:01:42,130
+المادة الأساسية الصفراوية فيها بس إذا كمان مرة ال
+
+21
+00:01:42,130 --> 00:01:47,070
+main function is to store bile not produce which
+
+22
+00:01:47,070 --> 00:01:52,410
+helps the body digest fats طبعا ال digest fats
+
+23
+00:01:52,410 --> 00:01:57,930
+اللي هو زي ما قلنا اللي هو ال ال ال ال ال ال fluid
+
+24
+00:01:57,930 --> 00:02:05,670
+ال bile نفسه مش ال ال ال ال gold bladderالكبد 
+
+25
+00:02:05,670 --> 00:02:16,210
+بيكوّن الـ bile وعن
+
+26
+00:02:16,210 --> 00:02:20,210
+طريق الممرات بيروح على الـ gallbladder لما نأكل أو
+
+27
+00:02:20,210 --> 00:02:25,410
+نشرب خاصة الحاجات اللي فيها fat ال bile released
+
+28
+00:02:25,410 --> 00:02:30,350
+بس بيخرج from the gallbladder into the upper small
+
+29
+00:02:30,350 --> 00:02:34,890
+intestine في منطق دي الدودينم بتلاقوا to help
+
+30
+00:02:34,890 --> 00:02:37,950
+break down fats زي ما احنا شايفين هان اللي هو
+
+31
+00:02:37,950 --> 00:02:42,210
+الكبد ال gallbladder اللي هي الجطع الخضر هاي الممر
+
+32
+00:02:42,210 --> 00:02:48,230
+اللي طالع من ال gallbladder ورايح من خلال ال head
+
+33
+00:02:48,230 --> 00:02:54,170
+of pancreas ودخل في ال sphincter of Oddi دخل في
+
+34
+00:02:54,170 --> 00:02:58,920
+وين؟ في الدودينم الدودينم اللي هو ال 12 الـ
+
+35
+00:02:58,920 --> 00:03:04,480
+Duodenum اللي هو الـ 12 طبعاً بيلتجي وانا طبعاً
+
+36
+00:03:04,480 --> 00:03:09,540
+مهم الملاحظات هاي بيلتجي الـ Sphincter المخرج تبع
+
+37
+00:03:09,540 --> 00:03:14,780
+ال Common Bile Duct اللي هو اللي طالع من الـ Gall
+
+38
+00:03:14,780 --> 00:03:19,200
+Bladder بيلتجي في نفس المنطقة أو نفس الفتحة اللي
+
+39
+00:03:19,200 --> 00:03:23,460
+بيصب فيها كمان من الـ Pancreas الـ Pancreatic Duct
+
+40
+00:03:23,460 --> 00:03:28,020
+يعني الـ Pancreatic Ductبيشتمع مع الـ Common Bile
+
+41
+00:03:28,020 --> 00:03:31,900
+Duct وبيصب وين في الـ Duodenum ليش هذا الموضوع
+
+42
+00:03:31,900 --> 00:03:36,620
+مهم بالنسبة لنا؟ لأن أي مشكلة في المنطقة هذه، يعني
+
+43
+00:03:36,620 --> 00:03:40,300
+عند الفتحة هذه، ممكن تعملي كمان مشاكل في وين، في
+
+44
+00:03:40,300 --> 00:03:48,040
+الـPancreas yes ممكن يكون المشكلة هي stone يعني
+
+45
+00:03:48,040 --> 00:03:56,740
+حصوة ممكن يكون tumor كمان ومسكر ليه طبعاً بيحجز
+
+46
+00:03:56,740 --> 00:04:02,900
+المادة الصفراء من دخول الدودينام لكن في نفس الوقت
+
+47
+00:04:02,900 --> 00:04:06,680
+المادة الصفراء بتنتشر في الجسم وبصير عندنا الصفار
+
+48
+00:04:06,680 --> 00:04:10,200
+الصفار اللي هو نتيجة المادة الصفراء يفجأ كمان مرة
+
+49
+00:04:11,300 --> 00:04:15,180
+في عيننا اللي هو اللي بيطلع من الـ Common bile
+
+50
+00:04:15,180 --> 00:04:18,740
+duct اللي هو الـ Common bile duct وهو نتيجة الـ
+
+51
+00:04:18,740 --> 00:04:21,320
+Common bile duct اجتماع الـ Common hepatic duct
+
+52
+00:04:21,320 --> 00:04:23,960
+والـ Cystic duct بيجتمعوا مع بعض الـ Common
+
+53
+00:04:23,960 --> 00:04:29,000
+hepatic duct جاي من اللفر والـ
+
+54
+00:04:29,000 --> 00:04:34,920
+Cystic duct جاي من الـ Gallbladder الـ Common
+
+55
+00:04:34,920 --> 00:04:39,770
+bile ductبيصب في الدودينام من نفس المكان اللي هو
+
+56
+00:04:39,770 --> 00:04:43,950
+«سفينكتر أوف أودي» Oddi هذا اسم شخص اللي هو فتحة
+
+57
+00:04:43,950 --> 00:04:50,750
+Oddi مع الـ pancreatic duct بيصب في الدودينام الـ
+
+58
+00:04:50,750 --> 00:04:57,550
+gallbladder diseases بس كشوية هيك معلومات و
+
+59
+00:04:57,550 --> 00:05:02,910
+تعريفات في عندنا الـ gallbladder stones والتهاب للـ
+
+60
+00:05:02,910 --> 00:05:06,880
+gallbladder هدول أهم اتنين الـ Gallbladder Stones
+
+61
+00:05:06,880 --> 00:05:13,720
+حصوات المرارة وفيه التهاب المرارة الـ Chole
+
+62
+00:05:13,720 --> 00:05:17,640
+Lithiasis اللي هو الـ Chole اللي هي الـ Cyst هي
+
+63
+00:05:17,640 --> 00:05:20,880
+نفسها اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+64
+00:05:20,880 --> 00:05:21,220
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+65
+00:05:21,220 --> 00:05:21,680
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+66
+00:05:21,680 --> 00:05:21,700
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+67
+00:05:21,700 --> 00:05:21,760
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+68
+00:05:21,760 --> 00:05:21,940
+اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+69
+00:05:21,940 --> 00:05:30,320
+اللي اللي اللي اللي اللي اللي اللي
+
+70
+00:05:30,320 --> 00:05:34,540
+اللي اللي within the gallbladder أو في الـBiliary
+
+71
+00:05:34,540 --> 00:05:39,040
+Duct System يعني هذا بقول عنه Cholelithiasis أي
+
+72
+00:05:39,040 --> 00:05:42,540
+تكوين حصوات جوا الـ Gallbladder أو في الممرات
+
+73
+00:05:42,540 --> 00:05:47,540
+البابية اللي هي في الـBiliary Duct System بسميها
+
+74
+00:05:47,540 --> 00:05:51,640
+Cholelithiasis حصوات المرارة أو Gallbladder Stones
+
+75
+00:05:53,190 --> 00:05:56,570
+الآن كل الـ Cholecystitis اللي كمان مرة اللي هي الـ
+
+76
+00:05:56,570 --> 00:06:01,590
+Gallbladder أو الصفاء الصفراء الـ Cyst اللي هي الكيس
+
+77
+00:06:01,590 --> 00:06:05,710
+كيس الصفراء it is the inflammation of جوا ال
+
+78
+00:06:05,710 --> 00:06:10,770
+Gallbladder كل الـ Cholecystitis طيب وكل الـ Cholangitis
+
+79
+00:06:10,770 --> 00:06:14,630
+inflammation of biliary duct لحالة طبعا نادرة لكن
+
+80
+00:06:14,630 --> 00:06:19,300
+لازم نذكرها إن inflammation of the biliary duct الـ
+
+81
+00:06:19,300 --> 00:06:20,760
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+82
+00:06:20,760 --> 00:06:20,880
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+83
+00:06:20,880 --> 00:06:21,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+84
+00:06:21,480 --> 00:06:22,960
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+85
+00:06:22,960 --> 00:06:26,460
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+86
+00:06:26,460 --> 00:06:31,200
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+87
+00:06:31,200 --> 00:06:33,840
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+88
+00:06:33,840 --> 00:06:34,320
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+89
+00:06:34,320 --> 00:06:45,060
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+90
+00:06:45,060 --> 00:06:47,960
+الـ الـ الـBiliary
+
+91
+00:06:47,960 --> 00:07:12,780
+Stasis of the biliary’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’’
+
+92
+00:07:15,740 --> 00:07:20,700
+أي حد بدي يحكي عن المرارة بنسمع في غالبية الأحيان
+
+93
+00:07:20,700 --> 00:07:26,140
+غالبية الأحيان بنسمع Gall stones اللي هي حصوات
+
+94
+00:07:26,140 --> 00:07:29,360
+مرارية عنده حصوات مرارية عنده ماعندش بسمع والله
+
+95
+00:07:29,360 --> 00:07:34,060
+عنده التهابات فيها أو عنده كذا لأ هو by far Gall
+
+96
+00:07:34,060 --> 00:07:38,920
+bladder stones by far the most common problemفي
+
+97
+00:07:38,920 --> 00:07:43,380
+منطقة اللي هي الـ gallbladder وهي زي ما قلنا الـ
+
+98
+00:07:43,380 --> 00:07:47,700
+stones tiny stones that form from hardening bile
+
+99
+00:07:47,700 --> 00:07:52,800
+and cholesterol متكونة من عصارة صفروية متجمدة مع
+
+100
+00:07:52,800 --> 00:07:59,540
+cholesterol علشان هيك الحاجات الدهنية بتساعد على تكوين
+
+101
+00:07:59,540 --> 00:08:03,780
+الـ gallstones الكلسترول هي في حد ذاتها مافيش فيها
+
+102
+00:08:03,780 --> 00:08:05,960
+مشكلة كبيرة لكن هي لو عملت block
+
+103
+00:08:13,230 --> 00:08:19,250
+الرسم الأولاني لو أجى أي stone في أي مكان هي الرسم
+
+104
+00:08:19,250 --> 00:08:25,110
+الأولى اللي هي في العنوان هنلاحظ الـ Gall Stones
+
+105
+00:08:28,390 --> 00:08:32,770
+الـ Gall Stones لما وقفلي عند الـ Common Bile Duct
+
+106
+00:08:32,770 --> 00:08:36,270
+والبنكريات الدكت فعملي حجز ال Gall Stones لما
+
+107
+00:08:36,270 --> 00:08:40,610
+عمللي Blocking لل Common Bile Duct فعملي حجز ال
+
+108
+00:08:40,610 --> 00:08:45,730
+Gall Stones وهي في جلب ال Gall Bladder عمليا مش
+
+109
+00:08:45,730 --> 00:08:50,170
+عاملالي مشاكل عمليا مش عاملالي مشاكل يبقى أنا هنا
+
+110
+00:08:50,170 --> 00:08:56,790
+مشكلتي أنجل على الرسمة برضه اللي فوقGallstones في
+
+111
+00:08:56,790 --> 00:09:03,210
+الجول بلادر Gallstones في الـ cystic duct Gallstones
+
+112
+00:09:03,210 --> 00:09:07,670
+في ال common bile duct وزي ما قلنا Gallstones عند
+
+113
+00:09:07,670 --> 00:09:11,930
+اللي هي الممر المشترك بين الـ pancreatic duct و
+
+114
+00:09:11,930 --> 00:09:18,210
+بين ال common bile duct تعود نرجع يبقى أنا مشكلتي
+
+115
+00:09:18,210 --> 00:09:25,840
+في ال Gallstones blockage وهذا ما
+
+116
+00:09:25,840 --> 00:09:32,820
+يعمل أيه؟ طبعاً أي حاجة لأن الـ«bile
+
+117
+00:09:32,820 --> 00:09:39,540
+duct» هي عبارة عن ممرات الممرات هي فيها نوع من
+
+118
+00:09:39,540 --> 00:09:45,520
+الـ«peristalsis» فهي ممكن لما يكون في حصوى ينحجز جوا
+
+119
+00:09:45,520 --> 00:09:50,670
+الـ«duct» الحصوى فتعمل لـSevere Pain طبعا غير أنه
+
+120
+00:09:50,670 --> 00:09:54,550
+الـ bile كمان بينحجز في ال .. في الـ gallbladder
+
+121
+00:09:54,550 --> 00:09:58,010
+فممكن يعملي كمان pain، severe pain particularly
+
+122
+00:09:58,010 --> 00:10:02,150
+after eating fatty أو greasy زيتي foods، joints
+
+123
+00:10:02,150 --> 00:10:05,630
+اسمه يعملي صفار طبعا yellowing of the skin and
+
+124
+00:10:05,630 --> 00:10:11,220
+eyes ليش؟ لأن الصفار بطل يروح الجهاز الهضمي فإيش
+
+125
+00:10:11,220 --> 00:10:15,840
+بيعمل ليه؟ بيطلع، بيمتص في الدم وبعد هيك بيبين
+
+126
+00:10:15,840 --> 00:10:19,920
+كصفار في الجلد، وإيش كمان؟ طبعا وجود حصوة في
+
+127
+00:10:19,920 --> 00:10:22,980
+الممرات هاي أو في الـgallbladder ممكن يديني كل
+
+128
+00:10:22,980 --> 00:10:25,600
+الـcholecystitis التهيابات و irritation و inflammation
+
+129
+00:10:25,600 --> 00:10:32,180
+للإلهام كمان ممكن إيش يصير؟ نتيجة الاحتقان اللي صار
+
+130
+00:10:32,180 --> 00:10:37,720
+عند مدخل الـpancreas للـgallbladder للـduodenum ممكن يصير
+
+131
+00:10:37,720 --> 00:10:43,370
+عندي pancreatitis زي ما حكينا في لما يعملوا
+
+132
+00:10:43,370 --> 00:10:47,150
+blockage للـ pancreatic ducts ممكن يصير عندي bowel
+
+133
+00:10:47,150 --> 00:10:50,950
+obstruction caused by gall stone passing into the
+
+134
+00:10:50,950 --> 00:10:54,190
+intestine and then blocking the intestine الآن
+
+135
+00:10:54,190 --> 00:10:59,210
+فرضا دخلت الحصوة على الأمعاء وفي الأمعاء ممكن تجمع
+
+136
+00:10:59,210 --> 00:11:03,170
+الحصوة حواليها كمان حاجة ممكن تعملي obstruction لل
+
+137
+00:11:03,170 --> 00:11:09,010
+bowel للأمعاءproblem like Gall stones may never
+
+138
+00:11:09,010 --> 00:11:13,930
+cause any pain at all but that doesn't mean they
+
+139
+00:11:13,930 --> 00:11:16,470
+will resolve themselves هو طبعا ممكن تكون
+
+140
+00:11:16,470 --> 00:11:19,510
+asymptomatic stones يا جماعة خاصة لما تكون ال Gall
+
+
+
+141
+00:11:19,510 --> 00:11:22,290
+stone موجودة في الـ cyst في الـ gold bladder itself
+
+142
+00:11:22,290 --> 00:11:26,670
+في المرارة نفسها ممكن ما تعملليش ولا مشكلة لكن هذا
+
+143
+00:11:26,670 --> 00:11:31,230
+لا يعني أنها هتدوب لحالها هذا مهم،أنا مافيش حاجة
+
+144
+00:11:31,230 --> 00:11:33,910
+إنه أنا شوفت والله gold platter و .. و .. و خلاص
+
+145
+00:11:33,910 --> 00:11:37,210
+بتروح لوحدها okay مش عاملة مشاكل ممكن لكن لا يعني
+
+146
+00:11:37,210 --> 00:11:42,050
+إنها بتروح لوحدها الـ gold stones قلنا اسمها
+
+147
+00:11:42,050 --> 00:11:43,230
+polylithiasis
+
+148
+00:11:46,570 --> 00:11:52,530
+وهو مشكلة عامة وعامة بين الناس الأكبر من عمرها
+
+149
+00:11:52,530 --> 00:11:57,310
+أربعين بعد المشروع، الـ gallbladder تتعامل بالعادة
+
+150
+00:11:57,310 --> 00:12:03,590
+تتعامل بالعادة وبتعمل إخراج للجزء إلى الانتستان
+
+151
+00:12:03,590 --> 00:12:08,470
+لإيقاف الانتجاش وزي ما قلنا، الجزء يستفيد منه في
+
+152
+00:12:08,470 --> 00:12:09,670
+انتجاش الزبدة
+
+153
+00:12:15,130 --> 00:12:18,490
+وهي حاجة من الحاجات اللي عملت أن الـPile اللي بصنع
+
+154
+00:12:18,490 --> 00:12:22,650
+الـPile زي الـWaste Product الـBelarubin أو
+
+155
+00:12:22,650 --> 00:12:23,330
+الكوليسترول
+
+156
+00:12:31,340 --> 00:12:34,300
+الـ «جولسترون» يجلس فقط في الـ «جول بلدر» و لا
+
+157
+00:12:34,300 --> 00:12:40,140
+يسبب مشاكل في العادة لكن بعض الأحيان يحفظون الخروج
+
+158
+00:12:40,140 --> 00:12:45,240
+من الـ «جول بلدر» باسم «دكت سيستيك» حكينا عنه زي
+
+159
+00:12:45,240 --> 00:12:48,640
+ما هو مبين في الصورة فعندما يحدث هذا الـ «جول
+
+160
+00:12:48,640 --> 00:12:56,510
+بلدر» يدفع إلىويصبح مصابًا ويصبح عندي كوليسيستايتس
+
+161
+00:12:56,510 --> 00:13:05,650
+ويمكن أن يتحسن لوحده أو يتحسن إلى حالة أكتر صعبة
+
+162
+00:13:05,650 --> 00:13:12,070
+مثل بكتيريا انفكشن من جول بلدة المصابة ليبقى أنا
+
+163
+00:13:12,070 --> 00:13:15,910
+مش مشكلتي بس لما يصبح عندى blockage لأي مكان في ال
+
+164
+00:13:15,910 --> 00:13:20,240
+goal system إنه يكون عندى بس blockage إنما ممكن
+
+165
+00:13:20,240 --> 00:13:23,460
+برضه يعملى احتقان في الـ gallbladder و بعد هيك
+
+166
+00:13:23,460 --> 00:13:26,720
+يعملى inflammation و بعد هيك طبعا هذه ال
+
+167
+00:13:26,720 --> 00:13:31,500
+complications كبيرة لها طب هم مين المجموعات
+
+168
+00:13:31,500 --> 00:13:37,880
+اللى ممكن يصير عندها gallbladder خاصة
+
+169
+00:13:37,880 --> 00:13:42,500
+إنه احنا زى ما احنا عارفين إنه الناس الرسكى هي ال
+
+170
+00:13:42,500 --> 00:13:45,080
+family history of gall الناس الرسكى هم الناس اللى
+
+171
+00:13:45,080 --> 00:13:48,560
+عندهم family history of gallstones Taking
+
+172
+00:13:48,560 --> 00:13:53,100
+medication to lower cholesterol levels طبعاً
+
+173
+00:13:53,100 --> 00:13:57,480
+Having الناس اللي عندها diabetes a rapid large
+
+174
+00:13:57,480 --> 00:14:01,240
+loss of weight ليش؟ لأنه بيصير عندنا فيه كوليسترول
+
+175
+00:14:01,240 --> 00:14:05,880
+كتير Taking birth control pills or hormone
+
+176
+00:14:05,880 --> 00:14:11,140
+replacement therapy الناس اللي بتاخد حبوب من الحمل
+
+177
+00:14:11,140 --> 00:14:12,000
+عن طريق الفم
+
+178
+00:14:15,070 --> 00:14:19,270
+بينج بريجنانت، ليش؟ لأنه ضغط أو حتى الـ overweight
+
+179
+00:14:19,270 --> 00:14:26,770
+بتغطينا على الـ gall bladder من تحت، فبصير الترسيب
+
+180
+00:14:26,770 --> 00:14:32,190
+أكبر في الممرات بتتضغط،
+
+181
+00:14:32,190 --> 00:14:36,310
+الممرات اللي هو الـ barrier system فبصير الترسيب
+
+182
+00:14:36,310 --> 00:14:41,490
+أكتر، eating a diet rich in fat وكلسترول طبيعي and
+
+183
+00:14:41,490 --> 00:14:43,510
+without enough fiber
+
+184
+00:14:46,980 --> 00:14:53,320
+جولستونز سيمتومز عادة زي ما قلنا ممكن مايكونش فيه
+
+185
+00:14:53,320 --> 00:14:56,960
+asymptomatic تكون و عادي رايحين نعمل فحص للبطن
+
+186
+00:14:56,960 --> 00:15:00,720
+عشان سبب من الأسباب لاجوا جولستونز okay فش إشي
+
+187
+00:15:00,720 --> 00:15:06,560
+كبير نسكت عنها و بنراجبها بس لكن في ناس جولستونز
+
+188
+00:15:06,560 --> 00:15:11,320
+can cause symptoms زي مثلا symptoms of
+
+189
+00:15:11,320 --> 00:15:16,270
+cholestastitis ممكن الدينبلياريكوليككليك يعني ياخد
+
+190
+00:15:16,270 --> 00:15:22,330
+نص ساعة ساعة وجع شديد في الـ right upper part of
+
+191
+00:15:22,330 --> 00:15:30,070
+the abdomen وحتى ممكن يسمع في الظهر بين اللي هو
+
+192
+00:15:30,070 --> 00:15:36,350
+الكتفينو بسوق fever ممكن يصير wind kill يعني حرارة
+
+193
+00:15:36,350 --> 00:15:40,350
+ماقش عريرة وممكن يعملني vomiting and nausea ممكن
+
+194
+00:15:40,350 --> 00:15:44,350
+زي ما قلنا يعملنا صفار طبيعي طبعا بما أنه الآن
+
+195
+00:15:44,350 --> 00:15:48,870
+الصفار أو المادة الصفرة بطلت تروح الجهاز الهضمي
+
+196
+00:15:48,870 --> 00:15:54,640
+وعادة البراز بياخد لونه الغامج منمن المادة الصفراء
+
+197
+00:15:54,640 --> 00:16:00,040
+الان لو ما اخدش مارحش مادة صفراء او الـ pile مارحش
+
+198
+00:16:00,040 --> 00:16:05,160
+فالبراز بيصير فاتح زي الـ clay بيقول عنه clay color
+
+199
+00:16:05,160 --> 00:16:09,880
+فاتح لونه فاتح البراز لونه فاتح كتير كتير زي
+
+200
+00:16:09,880 --> 00:16:15,700
+الطحينية البيضة عمليا pain that strikes after
+
+201
+00:16:15,700 --> 00:16:19,880
+eating a fatty meal و بيصير عندنا غزات و bloating
+
+202
+00:16:21,650 --> 00:16:25,890
+كيف بشخصه؟ زي ما قلنا تشخيصه سهل حقيقة من أسهل
+
+203
+00:16:25,890 --> 00:16:29,550
+التشخيصات بالـ ultrasound which uses sound waves
+
+204
+00:16:29,550 --> 00:16:33,410
+to visualize the area كيف بيبين الحصوة بتبقى عمالة
+
+205
+00:16:33,410 --> 00:16:36,830
+عملالي حاجة زي shadow زي ما احنا شايفين في الصورة
+
+206
+00:16:36,830 --> 00:16:41,640
+والسهم هذه الحصوة وشايفين الـ shadow هذا مثل الضل
+
+207
+00:16:41,640 --> 00:16:45,340
+بيشوفها الدكتور فبيعرف إنه في حصوات نفس الكلام
+
+208
+00:16:45,340 --> 00:16:49,440
+بينطبق على حصوات تبع الكلة في التشغيل وفي ناس ممكن
+
+209
+00:16:49,440 --> 00:16:53,620
+تدّي oral كل Instagram بس هذا لاحقا ماحدش بيعمله
+
+210
+00:16:53,620 --> 00:16:57,780
+عمليا to show the gallbladder after the patients
+
+211
+00:16:57,780 --> 00:17:03,020
+swallow pills containing dye وهذا بتبين الموضوع ال
+
+212
+00:17:03,020 --> 00:17:04,380
+gallstone therapy
+
+213
+00:17:07,200 --> 00:17:10,820
+في أكتر من option حسب الـ symptoms وحسب الـ severity
+
+214
+00:17:10,820 --> 00:17:17,000
+طبعا انا لو بحكي جاعد والله واحد في عنده عنده كل
+
+215
+00:17:17,000 --> 00:17:23,040
+يعني حاجة تدعي الـ surgery لابد انه surgically او
+
+216
+00:17:23,040 --> 00:17:28,900
+laparoscope اعمل removal لل goalie bladder باللي
+
+217
+00:17:28,900 --> 00:17:29,180
+فيها
+
+218
+00:17:32,560 --> 00:17:36,160
+هذا طبعا في الـ severe symptoms عادة ذلك بنحاول
+
+219
+00:17:36,160 --> 00:17:39,680
+جدر الإمكان إذا مش عاملالي مشاكل low-fat diet to
+
+220
+00:17:39,680 --> 00:17:43,160
+help relieve the gall stones symptoms ممكن ندي
+
+221
+00:17:43,160 --> 00:17:47,220
+medications في بعض الـ medications ممكن تساعد salts
+
+222
+00:17:47,220 --> 00:17:52,360
+تساعد to break down small gall stones to reduce
+
+223
+00:17:52,360 --> 00:17:53,420
+pain and symptoms
+
+224
+00:17:56,370 --> 00:18:02,610
+مش كل واحد ممكن تديله الـ medications هاي اللي فيه
+
+225
+00:18:02,610 --> 00:18:06,890
+طبعا الـ forceful sound اللي هو lithotripsy litho
+
+226
+00:18:06,890 --> 00:18:10,650
+زي ما قلنا litho هي حصوات tripsy تفتيت تفتيت
+
+227
+00:18:10,650 --> 00:18:15,130
+الحصوات are aimed directly at the gall stones to
+
+228
+00:18:15,130 --> 00:18:20,510
+break them into tiny أو tiny fragments usually
+
+229
+00:18:20,510 --> 00:18:24,210
+followed by medication to dissolve the pieces وهذه
+
+230
+00:18:24,210 --> 00:18:27,870
+تقريبا من الحاجات اللي بيستخدموها إلى جانب ال
+
+231
+00:18:27,870 --> 00:18:34,190
+surgery أنه بموجات فوق صوتية بأدى forceful sounds
+
+232
+00:18:34,190 --> 00:18:37,550
+بحاول
+
+233
+00:18:37,550 --> 00:18:42,770
+أكسر الحصوات هاي بأملح معينة أو أدوية معينة ممكن
+
+234
+00:18:42,770 --> 00:18:46,130
+تنزل وطبعا في حال لما يكون فينا pain بندى pain
+
+235
+00:18:46,130 --> 00:18:53,830
+killer وهذا بدخلنا على الحاجة التانية اللي هي what
+
+236
+00:18:53,830 --> 00:19:01,830
+is cholecystitis is a big word for the simple but
+
+237
+00:19:01,830 --> 00:19:04,550
+potentially painful problem gallbladder
+
+238
+00:19:04,550 --> 00:19:05,630
+inflammation
+
+239
+00:19:11,620 --> 00:19:15,680
+طبعاً بنجسمها الـ acute cholecystitis لـ two
+
+240
+00:19:15,680 --> 00:19:21,720
+divisions الـ acute cholecystitis مع calculus يعني
+
+241
+00:19:21,720 --> 00:19:25,940
+بحصوة يعني cholecystitis يا بيصير بحصوات يا بدون
+
+242
+00:19:25,940 --> 00:19:31,800
+حصوات الغالبية العظمة 85% بتكون بحصوات عادة 85% ل
+
+243
+00:19:31,800 --> 00:19:36,190
+90% of cases بتبقى acute الخاصة المعروفة هي الـ
+
+244
+00:19:36,190 --> 00:19:44,010
+Calculus Cholecystitis أكيد
+
+245
+00:19:44,010 --> 00:19:49,150
+أكل كولاس اللي هو حوالي يعني بدون كالكولاس يعني
+
+246
+00:19:49,150 --> 00:19:51,270
+عشر إلى خمس عشر فرمية of cases
+
+247
+00:19:54,920 --> 00:19:57,440
+طبعاً نفس الكلام، mild fever، anorexia،
+
+248
+00:19:57,440 --> 00:20:00,900
+تاكيكارديا، sweating، nausea، vomiting وممكن برضه
+
+249
+00:20:00,900 --> 00:20:04,660
+hyperpleropenemia حسب اللي هو زيادة الصفار،
+
+250
+00:20:04,660 --> 00:20:09,040
+التهيابات، leucocytosis، زيادة في عدد القرايات
+
+251
+00:20:09,040 --> 00:20:14,420
+البيضة طبعاً
+
+252
+00:20:14,420 --> 00:20:15,740
+المنطقة
+
+253
+00:20:17,450 --> 00:20:21,990
+المنطقة الـ Colitis Cystitis المنطقة اللي فيها الـ
+
+254
+00:20:21,990 --> 00:20:26,310
+Gall Bladder بصورة عامة هي منطقة تخضع لكثير من
+
+255
+00:20:26,310 --> 00:20:28,790
+الـDifferential Diagnosis يعني أنا مش من حد ميجين
+
+256
+00:20:28,790 --> 00:20:31,910
+الأيام بعرف إنه في عنده Acute Colitis Cystitis أو
+
+257
+00:20:31,910 --> 00:20:35,450
+إنه عنده Gall Bladder، خدوا بقى الـCollage لأنه في
+
+258
+00:20:35,450 --> 00:20:38,670
+عندنا أمراض الكبد، في عندنا الـChest لفوق منه، في
+
+259
+00:20:38,670 --> 00:20:43,310
+عندنا اللي تحت منه، في عندنا الـDaudenum، في عندنا
+
+260
+00:20:43,310 --> 00:20:48,470
+الـGastric عنا الـ heart فإحنا هذه كلها المنطقة
+
+261
+00:20:48,470 --> 00:20:52,690
+أصلا بتساقب التشخيص Untreated cholecystitis can
+
+262
+00:20:52,690 --> 00:20:57,130
+lead to complications So don't brush off these
+
+263
+00:20:57,130 --> 00:21:01,710
+symptoms as just a little indigestion or stomach
+
+264
+00:21:01,710 --> 00:21:05,730
+bug يعني كمان الغلطة اللي بيعملوها كتير من الطباء
+
+265
+00:21:05,730 --> 00:21:10,150
+مثلا أو حتى من الناس حوالين المريض أنه شوية برد،
+
+266
+00:21:10,150 --> 00:21:13,370
+شوية flu، شوية ماعرفش إيش وهو بيبقى في عنده
+
+267
+00:21:13,370 --> 00:21:16,990
+cholecystitis وزي ما قلنا الـcholestrostitis ممكن
+
+268
+00:21:16,990 --> 00:21:20,510
+يكون كرونيك كمان بـresistant long standing أو long
+
+269
+00:21:20,510 --> 00:21:24,330
+lasting swelling and damage to the gallbladder و
+
+270
+00:21:24,330 --> 00:21:27,410
+acute sudden attack that cause swelling and
+
+271
+00:21:27,410 --> 00:21:30,930
+irritation of the gallbladder الأسباب تاعتها طبعا
+
+272
+00:21:30,930 --> 00:21:35,190
+على القمة الهرماللي هو الـ Gold Stones الحصوات
+
+273
+00:21:35,190 --> 00:21:40,750
+وقلنا 85، 90% من الـ Cholestastitis من التهاب
+
+274
+00:21:40,750 --> 00:21:45,770
+المرارة بيصير عن طريق الـ Gold Stones Complication
+
+275
+00:21:45,770 --> 00:21:54,050
+ممكن يكون نتيجة سكري، نتيجة HIV ممكن يكون كمان
+
+276
+00:21:54,050 --> 00:21:58,350
+نتيجة بكتيريا infection نتيجة tumor in the liver
+
+277
+00:21:58,350 --> 00:22:02,470
+أو بنكرياس الـ blood flow to the bladder بيبقى
+
+278
+00:22:02,470 --> 00:22:05,290
+reduced كل bladder في حاجة اسمها كل bladder
+
+279
+00:22:05,290 --> 00:22:08,610
+sludge، sludge هو زي ما بتشوفوا لما بيشتروا الزيت
+
+280
+00:22:08,610 --> 00:22:12,960
+لجديد في الآخر الزيت الجديد بتخليه أسبوعين تلاتة
+
+281
+00:22:12,960 --> 00:22:18,460
+عشان يصفي تحت اللي هي بقايا
+
+282
+00:22:18,460 --> 00:22:22,900
+عملية التعصير في جدار المرارة وهذا اللي بيصير في
+
+283
+00:22:22,900 --> 00:22:28,630
+الـ Gall Bladder أنه بيصير عندي substanceثخين
+
+284
+00:22:28,630 --> 00:22:38,370
+سبستانس بيبقى في السائل المراري وعامله زي وكأنه 
+
+285
+00:22:38,370 --> 00:22:43,330
+وكأنه مش نظيف وهذا بترسب لا يمطس بترسب وبيعمل
+
+286
+00:22:43,330 --> 00:22:49,170
+ليه اللي هي الطبقة اللي بيقول عنها sludge وفي
+
+287
+00:22:49,170 --> 00:22:52,910
+الأخر بتعمل ليه زي مش حصوات زي التكونات الفيلياري
+
+288
+00:22:52,910 --> 00:22:57,470
+sludge هو viscous pileالـ Precursor هو المقدمة
+
+289
+00:22:57,470 --> 00:23:00,870
+للحصوات الطبيعي المقدمة للحصوات
+
+290
+00:23:05,820 --> 00:23:10,960
+مشاركة بـ Prolonged TPN TPN هو Total Parental
+
+291
+00:23:10,960 --> 00:23:14,020
+Nutrition الناس اللي بيديهم تغذية وريدية and
+
+292
+00:23:14,020 --> 00:23:16,820
+fasting الناس اللي بتصوم عادة تجدها في تجارب
+
+293
+00:23:16,820 --> 00:23:19,960
+التجارب التجاربية الإحصائية عادة زي ما احنا
+
+294
+00:23:19,960 --> 00:23:24,100
+شايفين في الصورة هو هذا الـ sludge عبارة عن ترسبات
+
+295
+00:23:24,100 --> 00:23:29,860
+زيتية دهنية في المرارة وهذا بتبقى مقدمة لإيش للـ
+
+296
+00:23:29,860 --> 00:23:31,800
+gall stones formation
+
+297
+00:23:35,110 --> 00:23:38,850
+بالفحص، medical history، ultrasound، وممكن بعض
+
+298
+00:23:38,850 --> 00:23:41,930
+الأحيان نعمل X-ray Complication of cholecystitis
+
+299
+00:23:41,930 --> 00:23:46,110
+وهنا طبعا احنا بيصير للواحد شوية مشاكل ليش؟ لأنه
+
+300
+00:23:46,110 --> 00:23:49,370
+بطلت بتصير المشكلة مش restricted على جدار الـ
+
+301
+00:23:49,370 --> 00:23:54,530
+bladder itself إنما ممكن توصلي تعملي sepsis يعني
+
+302
+00:23:54,530 --> 00:24:00,140
+bacterial super infection with cholangitisأو
+
+303
+00:24:00,140 --> 00:24:03,420
+يدّيني سبسيس Gall Bladder Perforation ممكن الـ
+
+304
+00:24:03,420 --> 00:24:06,980
+Gall Bladder هي ملتهبة، إيش تعملي؟ حواليها تعملي
+
+305
+00:24:06,980 --> 00:24:16,190
+زي أبسس مدة وتعملي زي .. وترتبط ترتبط مع الأمعاء
+
+306
+00:24:16,190 --> 00:24:18,570
+أو حاجة وممكن تعملي peritonitis الاتهاب اللي في
+
+307
+00:24:18,570 --> 00:24:20,830
+الـ Gall Bladder لو بنقول زي ما بنقول احنا في
+
+308
+00:24:20,830 --> 00:24:25,430
+لغتنا لو فجعت أو أو الاتهاب تبعها انتشر ممكن تديني
+
+309
+00:24:25,430 --> 00:24:29,550
+peritonitis التهاب جدار البطن من الداخل وهذه طبعا
+
+310
+00:24:29,550 --> 00:24:34,480
+Life-threatening conditions ممكن يصير عنديبيلياري
+
+311
+00:24:34,480 --> 00:24:39,480
+انتريك فستولة زي ما قلنا تتواصل يصير فيه ممر بين
+
+312
+00:24:39,480 --> 00:24:42,220
+الـGall Bladder وبين الأمعاء وهذه مشكلة عايزة
+
+313
+00:24:42,220 --> 00:24:46,320
+طبعا حقيقة وممكن طبعا لو واحد عنده cardiac أو
+
+314
+00:24:46,320 --> 00:24:50,960
+pulmonary أو renal decompensation decompensation
+
+315
+00:24:50,960 --> 00:24:55,300
+هذه تعمل aggravating لإلها يعني كل الـCholecystitis مع
+
+316
+00:24:55,300 --> 00:25:02,000
+واحد عنده جلب الأمر بيبقى أكبر وطبعا الـ «Gall Bladder»
+
+317
+00:25:02,000 --> 00:25:09,040
+ممكن تديني حاجة اسمها «Porcelain Gall Bladder» يصير
+
+318
+00:25:09,040 --> 00:25:15,160
+نتيجة الحصوات والالتهابات المتكررة زي الحجر الكبير
+
+319
+00:25:15,160 --> 00:25:19,320
+جوا الـ «Gall Bladder» وهذا تعمل
+
+320
+00:25:19,320 --> 00:25:24,140
+«increased risk of cancer» أو «of cancer» كيف
+
+321
+00:25:24,140 --> 00:25:28,480
+بنعالج الكوليستيتس؟وهو الـ Most Common Treatment
+
+322
+00:25:28,480 --> 00:25:36,060
+«خلص السيستيتسمي» الباب اللي بيجيك
+
+323
+00:25:36,060 --> 00:25:39,720
+منه الريح سده واستريح طبعا إلى جانب الـSwitching
+
+324
+00:25:39,720 --> 00:25:44,140
+to a Low-Fat Diet Medication to Manage Pain
+
+325
+00:25:44,140 --> 00:25:52,520
+Medication to Dissolve the Gall Stones ممكن نديها
+
+326
+00:25:52,520 --> 00:25:58,020
+عشان ما يكونش الواحد Gall Stonesولكن فعليتها تبقى
+
+327
+00:25:58,020 --> 00:26:02,240
+أضعف، في حالات الـMild كل الـCholecystitis بطيبه شوية
+
+328
+00:26:02,240 --> 00:26:06,420
+مضادات حيوية ونعمله Diet وسوائل كتير وبتمشي
+
+329
+00:26:06,420 --> 00:26:10,460
+الدنيا، لكن الـSerious كل الـCholecystitis طبعا بيصير
+
+330
+00:26:10,460 --> 00:26:14,880
+زي ما حكينا، بده أعالجه الـComplication تبعته،
+
+331
+00:26:14,880 --> 00:26:21,240
+Pancreatitis، الـJoints عصب المثال، أعالجها، وطبعا
+
+332
+00:26:21,240 --> 00:26:25,370
+Surgery Intervention كمانطب إيش الـ Surgery اللي
+
+333
+00:26:25,370 --> 00:26:29,170
+بنعمله عادة الـ Cholecystectomy؟ بنعمل الـ Open
+
+334
+00:26:29,170 --> 00:26:33,470
+اللي هي الصورة اللي على الشمال اللي هم الفاتحين
+
+335
+00:26:33,470 --> 00:26:41,820
+فيها البطن Open Cholecystectomy Open فمفتوحكل الـ
+
+336
+00:26:41,820 --> 00:26:44,680
+Gall Bladder زي ما اتعرفنا عليها اللي هي الصفروية ال- cyst
+
+337
+00:26:44,680 --> 00:26:52,080
+معناته الكيس أو المرارة نفسها اكتومي الباب اللي
+
+338
+00:26:52,080 --> 00:26:57,330
+بيجيك منه سد واستريح بنشيل المرارةبطريقة ال open
+
+339
+00:26:57,330 --> 00:27:01,350
+هذه طبعا كانت زمان هي المنتشرة الآن أقل من هيك
+
+340
+00:27:01,350 --> 00:27:05,610
+الغالبة بيعمل حاجة اسمها laparoscopic Cholecystectomy
+
+341
+00:27:05,610 --> 00:27:09,890
+بدخلوا على البطن بأربع بمنظار عمليا بالمنظر و
+
+342
+00:27:09,890 --> 00:27:14,290
+بشيلوها بدون أي مشاكل بأنصح مش غلط تشوفوا
+
+343
+00:27:14,290 --> 00:27:18,410
+العمليتين فرصة الواحد تشوفوا العمليتين على
+
+344
+00:27:18,410 --> 00:27:24,020
+اليوتيوب حلوين صحيح لو اتفرج عليهم الواحد ولو حد
+
+345
+00:27:24,020 --> 00:27:30,240
+بدي يتبرع يحط على الـ group سواء الشباب أو البنات
+
+346
+00:27:30,240 --> 00:27:38,760
+يحط الفيديوهات بيبقى كتير كويسة في حاجة بنقول عنها
+
+347
+00:27:38,760 --> 00:27:42,880
+وهذه يمكن تسمعوها كمان في المستشفيات لابد أن أحكيها
+
+348
+00:27:42,880 --> 00:27:47,500
+حاجة اسمها الـ ERCP الـ ERCP هو عبارة عن
+
+349
+00:27:47,500 --> 00:27:52,820
+Endoscopic برضه بالمنظار Retrograde لكن خلفييعني
+
+350
+00:27:52,820 --> 00:27:59,160
+أنا بدخل للممرات المرارية مش للمرارة للممرات المرارية
+
+351
+00:27:59,160 --> 00:28:04,280
+بطريقة عن طريق المعدة خلفي قدنا بنشوف كيف بنقول
+
+352
+00:28:04,280 --> 00:28:10,780
+endoscopic منظري retrograde رجوعا هيك معناته
+
+353
+00:28:13,400 --> 00:28:17,820
+Cholangio اللي هو زي ما قلنا عنه القلي اللي هي المرارية
+
+354
+00:28:17,820 --> 00:28:22,800
+Angiography الممرات المرارية البنكرياس الممرات المرارية
+
+355
+00:28:22,800 --> 00:28:29,620
+والبنكرياسية إيجرافي عملية إيش اللي هي رسم يعني
+
+356
+00:28:29,620 --> 00:28:34,230
+Cholangiopancreatography Endoscopic Retrograde
+
+357
+00:28:34,230 --> 00:28:39,150
+Cholangiopancreatography اللي هو ERCP باختصار ERCP
+
+358
+00:28:39,150 --> 00:28:42,430
+مشهورة في المستشفيات بيسمعها عمره ما واحد بيقول
+
+359
+00:28:42,430 --> 00:28:46,130
+الاسم اللي فوق كلهم بيقولوا عنها ERCP وقت إيش
+
+360
+00:28:46,130 --> 00:28:51,070
+بعملها one or more gallstones have migrated out of
+
+361
+00:28:51,070 --> 00:28:53,270
+the Gall Bladder يعني أحلاها لما كانت في ال
+
+362
+00:28:53,270 --> 00:28:56,010
+Gall Bladder بنشيل ال Gall Bladder لكن بعض الأحيان
+
+363
+00:28:57,580 --> 00:29:01,100
+تبقاش في الـ Gall Bladder migrated out of the
+
+364
+00:29:01,100 --> 00:29:04,960
+Gall Bladder into the common bile duct which
+
+365
+00:29:04,960 --> 00:29:07,720
+carries bile to the small intestine to aid
+
+366
+00:29:07,720 --> 00:29:12,440
+digestion الـ ERCP، the endoscope، is guided down
+
+367
+00:29:12,440 --> 00:29:16,840
+عن طريق الـ throat into the stomach، على المعدة، و
+
+368
+00:29:16,840 --> 00:29:19,900
+بعدين بروح into the common bile duct عن طريق
+
+369
+00:29:19,900 --> 00:29:23,940
+الدودنم، الممر اللي فكرينه اللي كنا بلتجيه ال
+
+370
+00:29:23,940 --> 00:29:26,800
+common bile duct مع الpancreatic duct في النقطة
+
+371
+00:29:26,800 --> 00:29:30,460
+هذهكبدخل عن طريقها زي ما احنا شايفين في الصورة
+
+372
+00:29:30,460 --> 00:29:35,400
+المنظر وبروح بدخل في المدخل الصغير هذا وبدخل على
+
+373
+00:29:35,400 --> 00:29:40,600
+الـ Bile Duct الآن if gall stones are present an
+
+374
+00:29:40,600 --> 00:29:44,840
+instrument can be insertedإلى الـ Endoscope
+
+375
+00:29:44,840 --> 00:29:48,580
+ويقومون بإزالتهم المريض بشكل عام يستيقظ عامًا في
+
+376
+00:29:48,580 --> 00:29:53,360
+وقت ERCP ولكن يتم إعطاءه Sedatives لترهيئه ERCP
+
+377
+00:29:53,360 --> 00:29:58,200
+يتعامل عامًا في الاتصال مع إزالة الـ Gall Bladder
+
+378
+00:29:58,200 --> 00:30:05,240
+يعني مش بس بشوف بظبط الممرات كمان بحاول أشيل اللام
+
+379
+00:30:05,240 --> 00:30:08,200
+في كمان حاجة ممكن نعملها بعض الأحيان اللي هي في
+
+380
+00:30:08,200 --> 00:30:11,790
+الـ Gall Bladder Surgery اللي هي Drainingهذه لما
+
+381
+00:30:11,790 --> 00:30:16,210
+يكون في عنا احتقان
+
+382
+00:30:16,210 --> 00:30:19,210
+لكن أنا مش قادر أعمله عملية لنتيجة وضع العام على
+
+383
+00:30:19,210 --> 00:30:23,710
+سبيل المثال بعملها draining cholecystectomy
+
+384
+00:30:23,710 --> 00:30:28,250
+يعني بس فتحة وبطلع الصفار اللي محتقن عاملي احتقان
+
+385
+00:30:28,250 --> 00:30:31,570
+في الـ Gall Bladder وبعد هيك بشوف أيش بده أعمل مع
+
+386
+00:30:31,570 --> 00:30:36,350
+الـ Gall Bladder هيك احنا بجهات حدتنا عن ال .. ال
+
+387
+00:30:36,350 --> 00:30:39,370
+.. ال .. ال .. ان شاء الله ماكنش طويلة هو تلاتين
+
+388
+00:30:39,370 --> 00:30:42,970
+دقيقة يعني دقيقة واحدة وتلاتينلكن المواضيع هي ممتعة
+
+389
+00:30:42,970 --> 00:30:48,530
+يا جماعة حاولوا زي ما قلتلكوا تشوفوا أربع فيديوهات
+
+390
+00:30:48,530 --> 00:30:52,350
+ولو حد اتبرع وجهنا وحطهم على الشيطان بيبقى كتير
+
+391
+00:30:52,350 --> 00:31:00,520
+كتير كويساللي هو ال video الأول اللي هو ال surgery
+
+392
+00:31:00,520 --> 00:31:06,520
+سواء open cholecystectomy أو لا Laparoscopic كمان هي
+
+393
+00:31:06,520 --> 00:31:09,740
+ال video الثاني ال video الثالث ERCP حلو لو شفناه
+
+394
+00:31:09,740 --> 00:31:13,500
+كيف بنعمل وطبعا أنا عارف أسألكوا أنا الكلام وفيه
+
+395
+00:31:13,500 --> 00:31:18,510
+كمان ال cholecystectomy أو Gall Bladder draining لو
+
+396
+00:31:18,510 --> 00:31:22,230
+حطينا كمان فيديو بيبقى رائع كتير كتير حتى نشوف إيش
+
+397
+00:31:22,230 --> 00:31:25,990
+اللي بيصير في الدنيا بصورة عامة مواضيع زي ما كنا
+
+398
+00:31:25,990 --> 00:31:31,190
+حلوة مواضيع مفيدة إن شاء الله تعالى وأتمنى لكوا
+
+399
+00:31:31,190 --> 00:31:32,170
+نهار سعيد 
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3JwIJvxqtYE_raw.json b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3JwIJvxqtYE_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..866a6b4353b244486a150807b838fcc5f1f8c69a
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3JwIJvxqtYE_raw.json
@@ -0,0 +1 @@
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function can delay emptying of the stomach وهذا بيخلي الحامض back up into the esophagus الأزمة ليش؟ لأنه في عندنا some asthma medications that widen أو dilate airways", "tokens": [10721, 2407, 2423, 39184, 20352, 1776, 34051, 32847, 16355, 34051, 8679, 2445, 393, 8577, 6113, 1840, 295, 264, 9665, 37037, 15730, 4724, 1829, 9778, 20292, 21542, 10943, 11242, 646, 493, 666, 264, 785, 5317, 32813, 16247, 11622, 46007, 32239, 8592, 22807, 5296, 33456, 3224, 8978, 43242, 8315, 512, 33409, 17504, 300, 32552, 34051, 11504, 473, 1988, 942], "avg_logprob": -0.3009159426236975, "compression_ratio": 1.2828282828282829, "no_speech_prob": 0.0, "words": [{"start": 829.03, "end": 829.29, "word": "أو", "probability": 0.77880859375}, {"start": 829.29, "end": 829.41, "word": " الـ", "probability": 0.755859375}, {"start": 829.41, "end": 829.97, "word": " ulcer", "probability": 0.53094482421875}, {"start": 829.97, "end": 830.35, "word": " أو", "probability": 0.82470703125}, {"start": 830.35, "end": 830.73, 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pH monitoring بدخل واحد زي حاجة هيك sensor عند ثم المعدة وبيجيس حموضة الحموضة في المنطقة حوالين بين المعدة و بين", "tokens": [2304, 43020, 9122, 2304, 7649, 4724, 15042, 14739, 3224, 1975, 5016, 8315, 12174, 995, 22488, 9957, 8717, 39648, 18871, 8258, 5191, 8978, 9673, 1863, 9566, 28671, 29538, 3714, 43020, 8717, 25957, 43761, 307, 2670, 271, 831, 21677, 11028, 47525, 9778, 1211, 36764, 24401, 30767, 1829, 11331, 26108, 3660, 39896, 4117, 10200, 43242, 38637, 2304, 9673, 22488, 3660, 4032, 21292, 7435, 1829, 3794, 11331, 2304, 2407, 11242, 3660, 21542, 2304, 2407, 11242, 3660, 8978, 9673, 1863, 9566, 28671, 11331, 2407, 6027, 9957, 49374, 9673, 22488, 3660, 4032, 49374], "avg_logprob": -0.25142044946551323, "compression_ratio": 1.608910891089109, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 910.93, "end": 911.37, "word": "ممكن", "probability": 0.7000732421875}, {"start": 911.37, "end": 912.39, "word": " كمان", "probability": 0.8722330729166666}, {"start": 912.39, 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Ranidine كتير منكم بيعرفوا عنه يقولوا سنة تقريبا موقف الـ Ranidine لأنه هذا إيش بعملنا؟ بعملنا reduction of the production of acid reduction بس ال PPI عملنا blockage لل production هذا عملنا بس reduction لل production they don't act as quickly as antacid", "tokens": [11622, 1829, 2423, 39184, 27948, 327, 533, 9122, 2655, 13546, 9154, 24793, 4724, 40228, 28480, 14407, 18871, 3224, 7251, 39648, 14407, 8608, 1863, 3660, 6055, 4587, 16572, 3555, 995, 3714, 30543, 5172, 2423, 39184, 27948, 327, 533, 5296, 33456, 3224, 23758, 11933, 1829, 8592, 4724, 25957, 1211, 8315, 22807, 4724, 25957, 1211, 8315, 11004, 295, 264, 4265, 295, 8258, 11004, 4724, 3794, 2423, 430, 31701, 6225, 42213, 8315, 3461, 609, 24976, 4265, 23758, 6225, 42213, 8315, 4724, 3794, 11004, 24976, 4265, 436, 500, 380, 605, 382, 2661, 382, 2511, 326, 327], "avg_logprob": -0.2781929347826087, "compression_ratio": 1.6875, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1341.41, "end": 1341.75, "word": "زي", 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2007.99, "word": " antacid", "probability": 0.6487630208333334}, {"start": 2007.99, "end": 2008.23, "word": " أو", "probability": 0.90185546875}, {"start": 2008.23, "end": 2008.55, "word": " acid", "probability": 0.96533203125}, {"start": 2008.55, "end": 2009.27, "word": " reducing", "probability": 0.7158203125}, {"start": 2009.27, "end": 2010.37, "word": " medication", "probability": 0.9599609375}, {"start": 2010.37, "end": 2010.71, "word": " زي", "probability": 0.951171875}, {"start": 2010.71, "end": 2010.87, "word": " ال", "probability": 0.9189453125}, {"start": 2010.87, "end": 2011.39, "word": " PPI", "probability": 0.794677734375}, {"start": 2011.39, "end": 2011.95, "word": " معاهم", "probability": 0.9755859375}], "temperature": 1.0}, {"id": 87, "seek": 203897, "start": 2013.07, "end": 2038.97, "text": "لما يكون عندنا Peripheric Ulcer «العوامل التي تؤدي» أو «التجارب» لـ Gastric Ulcer اللي هو Reduction of Drug Intake حاول أنتبه للـ Helicobacter، الـ «دايت»", "tokens": [1211, 15042, 7251, 30544, 43242, 8315, 3026, 21240, 299, 24853, 1776, 4657, 6027, 3615, 2407, 10943, 1211, 38392, 6055, 33604, 16254, 5933, 34051, 4657, 6027, 2655, 7435, 9640, 3555, 5933, 5296, 39184, 31988, 1341, 24853, 1776, 13672, 1829, 31439, 4477, 27549, 295, 35806, 5681, 619, 11331, 995, 12610, 14739, 2655, 3555, 3224, 24976, 39184, 6128, 299, 996, 14125, 12399, 2423, 39184, 4657, 28259, 36081, 5933], "avg_logprob": -0.5639204337741389, "compression_ratio": 1.2584269662921348, "no_speech_prob": 0.0, "words": [{"start": 2013.07, "end": 2013.33, "word": "لما", "probability": 0.58770751953125}, {"start": 2013.33, "end": 2013.53, "word": " يكون", "probability": 0.952880859375}, {"start": 2013.53, "end": 2014.17, "word": " عندنا", "probability": 0.549468994140625}, {"start": 2014.17, "end": 2014.65, "word": " Peripheric", "probability": 0.4722493489583333}, {"start": 2014.65, "end": 2015.01, "word": " Ulcer", "probability": 0.721435546875}, {"start": 2015.01, "end": 2023.79, "word": " «العوامل", 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"word": " Drug", "probability": 0.91015625}, {"start": 2033.31, "end": 2034.57, "word": " Intake", "probability": 0.8955078125}, {"start": 2034.57, "end": 2035.87, "word": " حاول", "probability": 0.7970377604166666}, {"start": 2035.87, "end": 2036.37, "word": " أنتبه", "probability": 0.9033203125}, {"start": 2036.37, "end": 2036.73, "word": " للـ", "probability": 0.753662109375}, {"start": 2036.73, "end": 2038.09, "word": " Helicobacter،", "probability": 0.6424072265625}, {"start": 2038.09, "end": 2038.47, "word": " الـ", "probability": 0.742919921875}, {"start": 2038.47, "end": 2038.97, "word": " «دايت»", "probability": 0.6070556640625}], "temperature": 1.0}, {"id": 88, "seek": 205909, "start": 2039.63, "end": 2059.09, "text": "stress smoking and alcohol اللي هي تحت اسم lifestyle risk factors دايما إذا إذا اتغلبت على المسببات بتغلب على المرض بإذن الله تعالى وربنا هو الشافعي و بتمنالكوا يوم سعيد", "tokens": [372, 735, 14055, 293, 7658, 13672, 1829, 39896, 6055, 33753, 24525, 2304, 11716, 3148, 6771, 11778, 47302, 15042, 11933, 15730, 11933, 15730, 1975, 2655, 17082, 46152, 2655, 15844, 9673, 35457, 3555, 9307, 39894, 17082, 46152, 15844, 9673, 43042, 4724, 28814, 8848, 1863, 21984, 37279, 6027, 7578, 4032, 25513, 8315, 31439, 25124, 31845, 3615, 1829, 4032, 39894, 27842, 6027, 4117, 14407, 7251, 20498, 8608, 3615, 25708], "avg_logprob": -0.1750710155024673, "compression_ratio": 1.4696132596685083, "no_speech_prob": 4.172325134277344e-07, "words": [{"start": 2039.63, "end": 2040.29, "word": "stress", "probability": 0.5173797607421875}, {"start": 2040.29, "end": 2041.19, "word": " smoking", "probability": 0.66796875}, {"start": 2041.19, "end": 2041.49, "word": " and", "probability": 0.9033203125}, {"start": 2041.49, "end": 2042.05, "word": " alcohol", "probability": 0.8994140625}, {"start": 2042.05, "end": 2042.47, "word": " اللي", "probability": 0.822265625}, {"start": 2042.47, "end": 2042.73, "word": " هي", "probability": 0.814453125}, {"start": 2042.73, "end": 2043.09, "word": " تحت", "probability": 0.991943359375}, {"start": 2043.09, "end": 2043.51, "word": " اسم", "probability": 0.967041015625}, {"start": 2043.51, "end": 2044.51, "word": " lifestyle", "probability": 0.64697265625}, {"start": 2044.51, "end": 2045.17, "word": " risk", "probability": 0.94970703125}, {"start": 2045.17, "end": 2045.71, "word": " factors", "probability": 0.96337890625}, {"start": 2045.71, "end": 2046.35, "word": " دايما", "probability": 0.86767578125}, {"start": 2046.35, "end": 2046.73, "word": " إذا", "probability": 0.874267578125}, {"start": 2046.73, "end": 2047.55, "word": " إذا", "probability": 0.85791015625}, {"start": 2047.55, "end": 2048.53, "word": " اتغلبت", "probability": 0.92587890625}, {"start": 2048.53, "end": 2048.73, "word": " على", "probability": 0.900390625}, {"start": 2048.73, "end": 2050.09, "word": " المسببات", "probability": 0.9853515625}, {"start": 2050.09, "end": 2052.29, "word": " بتغلب", "probability": 0.9236653645833334}, {"start": 2052.29, "end": 2052.67, "word": " على", "probability": 0.8759765625}, {"start": 2052.67, "end": 2053.13, "word": " المرض", "probability": 0.991943359375}, {"start": 2053.13, "end": 2053.55, "word": " بإذن", "probability": 0.9678955078125}, {"start": 2053.55, "end": 2053.75, "word": " الله", "probability": 0.919921875}, {"start": 2053.75, "end": 2054.31, "word": " تعالى", "probability": 0.9293619791666666}, {"start": 2054.31, "end": 2055.09, "word": " وربنا", "probability": 0.9148763020833334}, {"start": 2055.09, "end": 2055.35, "word": " هو", "probability": 0.994140625}, {"start": 2055.35, "end": 2056.53, "word": " الشافعي", "probability": 0.799560546875}, {"start": 2056.53, "end": 2056.71, "word": " و", "probability": 0.63330078125}, {"start": 2056.71, "end": 2057.65, "word": " بتمنالكوا", "probability": 0.7171875}, {"start": 2057.65, "end": 2058.33, "word": " يوم", "probability": 0.98828125}, {"start": 2058.33, "end": 2059.09, "word": " سعيد", "probability": 0.96435546875}], 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3Wq-KibOkfU.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3Wq-KibOkfU.srt
new file mode 100644
index 0000000000000000000000000000000000000000..f6282af624318cec6c855b7e742f18095da6f08c
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/3Wq-KibOkfU.srt
@@ -0,0 +1,1835 @@
+1
+00:00:01,850 --> 00:00:04,970
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,970 --> 00:00:07,790
+والصلاة والسلام علي سيدنا محمد وسيد المرسلين
+
+3
+00:00:07,790 --> 00:00:12,430
+أجمعين يعني إحنا اليوم إن شاء الله تعالى الصوت إن
+
+4
+00:00:12,430 --> 00:00:15,470
+شاء الله واضح يا جماعة معكم الدكتور محمد أبو ندا
+
+5
+00:00:15,470 --> 00:00:21,310
+إن شاء الله تعالى هنتحدث عن الـ 
+
+6
+00:00:21,310 --> 00:00:26,320
+hypertension الـ Hypertension يا جماعة يعني بمجرد 
+
+7
+00:00:26,320 --> 00:00:30,760
+أنه أنا أقول Hypertension معناته أنا بحكي عن الـ
+
+8
+00:00:30,760 --> 00:00:34,160
+arterial Hypertension ليش هو في حاجات تانية
+
+9
+00:00:34,160 --> 00:00:39,840
+بنسميها برضه Hypertension؟ آه طبعًا في عندنا على
+
+10
+00:00:39,840 --> 00:00:47,600
+سبيل المثال اللي هو الـ
+
+11
+00:00:47,600 --> 00:00:50,520
+intracranial Hypertension increased intracranial
+
+12
+00:00:50,520 --> 00:00:54,110
+Hypertension في عندنا كمان الـ Pulmonary
+
+13
+00:00:54,110 --> 00:00:59,050
+Hypertension في عندنا كمان الـ Portal Hypertension
+
+14
+00:00:59,050 --> 00:01:04,650
+في عندنا كمان الـ .. طبعًا أنا موضحتش إيش كل واحدة
+
+15
+00:01:04,650 --> 00:01:07,950
+معناتها يعني هو مطلوب أن تحاولوا قدر الإمكان
+
+16
+00:01:07,950 --> 00:01:13,170
+تعرفوا إيش كل واحدة في عندنا Hypertension of the
+
+17
+00:01:13,170 --> 00:01:18,330
+Pressure Intraocular اللي بيقول عنه Glaucoma عشان
+
+18
+00:01:18,330 --> 00:01:24,440
+المثال، هذه كلها صور لـ Increased Hypertension في أماكن
+
+19
+00:01:24,440 --> 00:01:27,480
+مختلفة في الجسم لكن يوم إذا ما بقول Hypertension
+
+20
+00:01:27,480 --> 00:01:32,760
+هيك اللي هي في اللسان العامة عند الناس كلها بقصد
+
+21
+00:01:32,760 --> 00:01:37,140
+فيها arterial Hypertension طيب يعني هو دكتور محمد
+
+22
+00:01:37,140 --> 00:01:42,670
+أنت بدأت بموضوع يعني خلّيني نقول الـ Hypertension
+
+23
+00:01:42,670 --> 00:01:46,770
+إيش أهميته؟ تبدأ بيه في مادة الباطنة، مع أن في 
+
+24
+00:01:46,770 --> 00:01:49,370
+عندنا قلب و عندنا صدرية و عندنا أمراض تانية، إيش
+
+25
+00:01:49,370 --> 00:01:52,250
+معنى الـ Hypertension؟ آه، لأن الـ Hypertension
+
+26
+00:01:52,250 --> 00:01:58,970
+حقيقة هو عبارة عن، زي ما بقولوها، مرض شعبي، مرض
+
+27
+00:01:58,970 --> 00:02:03,630
+شعبي National هو الـ Diabetes Mellitus الـ
+
+28
+00:02:03,630 --> 00:02:07,530
+Hypertension most common primary diagnosis in
+
+29
+00:02:07,530 --> 00:02:10,670
+America طبعًا مش بس in America إحنا دايمًا زي ما 
+
+30
+00:02:10,670 --> 00:02:14,330
+بعيدها دايمًا و بزيد Hypertension اللي اللي اللي
+
+31
+00:02:14,330 --> 00:02:15,150
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+32
+00:02:15,150 --> 00:02:15,250
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+33
+00:02:15,250 --> 00:02:15,710
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+34
+00:02:15,710 --> 00:02:16,510
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+35
+00:02:16,510 --> 00:02:16,550
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+36
+00:02:16,550 --> 00:02:17,690
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+37
+00:02:17,690 --> 00:02:20,390
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+38
+00:02:20,390 --> 00:02:20,750
+اللي اللي اللي اللي اللي اللي اللي اللي اللي اللي
+
+39
+00:02:20,750 --> 00:02:36,430
+اللي
+
+40
+00:02:36,430 --> 00:02:46,330
+اللي الخمسة و تلاتين مليون وفيزيات خمسين
+
+41
+00:02:46,330 --> 00:02:50,630
+مليون أو أكثر عندهم high blood pressure أو
+
+42
+00:02:50,630 --> 00:02:56,510
+Hypertension worldwide prevalence estimates for
+
+43
+00:02:56,510 --> 00:03:00,130
+Hypertension أنه تقريبًا حوالي واحد Billion يعني
+
+44
+00:03:00,130 --> 00:03:09,190
+السبع البشرية عندها عندها ضغط مش بس، سبعة أو واحد
+
+45
+00:03:09,190 --> 00:03:15,370
+مليون بموتوا مباشرة بسبب الـ Hypertension وهذا رقم
+
+46
+00:03:15,370 --> 00:03:20,310
+مهول يا جماعة، هذا رقم مهول لو طلعنا على القاعدة
+
+47
+00:03:20,310 --> 00:03:24,530
+التلت أو واحد من تلاتة اللي هي على طول في الـ Slide
+
+48
+00:03:24,530 --> 00:03:32,110
+على الـ Jump بنلاقي أن واحد من كل تلاتة بالغين بـ
+
+49
+00:03:34,950 --> 00:03:43,490
+واحد من كل تلاتة بالغين يعاني
+
+50
+00:03:43,490 --> 00:03:44,470
+من الـ Hypertension
+
+51
+00:03:56,620 --> 00:04:01,720
+عفوًا للقطع اللي أنا عملت وضع الطيار نعود نستمر
+
+52
+00:04:01,720 --> 00:04:07,860
+لأن واحد من كل تلاتة بالغين في العالم أو حتى في في
+
+53
+00:04:07,860 --> 00:04:11,960
+أمريكا بيصير عنده Hypertension هلجيت واحد من كل
+
+54
+00:04:11,960 --> 00:04:18,180
+تلاتة من البالغين اللي عندهم ضغط بيعرفوش أنه عندهم
+
+55
+00:04:18,180 --> 00:04:22,760
+ضغط واحد من كل تلاتة بالغين
+
+56
+00:04:26,080 --> 00:04:30,960
+و عندهم ضغط و بيتعالجوا للضغط بيقدرش الواحد يتحكم
+
+57
+00:04:30,960 --> 00:04:34,700
+و هناك أسباب كثيرة بالضغط اللي هي مشاكل عدم التحكم
+
+58
+00:04:34,700 --> 00:04:38,580
+في الضغط يبقى أنا قاعد بحكي عن موضوع غاية في
+
+59
+00:04:38,580 --> 00:04:42,100
+الأهمية طب و أنا يعني كعلاج طبيعي أنتو جيت مخطروا
+
+60
+00:04:42,100 --> 00:04:46,480
+على بالكم و إيش دخلنا في الضغط؟ هو أنا بدأ أعمله
+
+61
+00:04:46,480 --> 00:04:49,880
+علاج طبيعي و أنا بدأ أشوف الضغط تبعه؟ لأ هو
+
+62
+00:04:49,880 --> 00:04:56,000
+كأخصائي علاج طبيعي لابد أن يكون فيه عند واحد محصلة
+
+63
+00:04:56,000 --> 00:05:01,260
+كاملة عن ارتفاع ضغط الدم عن السكري عن بعض الأمراض
+
+64
+00:05:01,260 --> 00:05:06,240
+الباطنة بل بالعكس في الـ Assessment بتتاخد الأمور
+
+65
+00:05:06,240 --> 00:05:12,500
+هاي في الاعتبار لاجوا أن الـ Hypertension بما أن
+
+66
+00:05:12,500 --> 00:05:20,130
+كثير من الزباين في العلاج الطبيعي old age طولتين
+
+67
+00:05:20,130 --> 00:05:24,930
+طولتين الناس اللي فوق الـ 65 عندهم Hypertension
+
+68
+00:05:24,930 --> 00:05:32,110
+طولتين يعني لو عندي 101 على سبيل المثال الـ 100 هدول
+
+69
+00:05:32,110 --> 00:05:40,410
+فوق الـ 65 66 واحد عنده ضغط جدًّا اه معناته على
+
+70
+00:05:40,410 --> 00:05:45,580
+الضمان أنا أي واحد كبير تقريبًا على الضمان بقدر وفوق
+
+71
+00:05:45,580 --> 00:05:48,620
+الـ 65 أقوله والله بالشباب والأبو الخيرية في 
+
+72
+00:05:48,620 --> 00:05:52,620
+الحالة هاي أنه شكله أنه أنت عندك Hypertension
+
+73
+00:05:52,620 --> 00:05:57,700
+بعمله فحص ضغط بلقي عالي عنده فبيبقى أنا إيش زبطت 
+
+74
+00:05:57,700 --> 00:06:03,300
+معايا الناس هدول أكثر ناس صعب التحكم في الضغط
+
+75
+00:06:03,300 --> 00:06:06,200
+عندهم وهنعرف ليش
+
+76
+00:06:09,270 --> 00:06:13,850
+هو علاج ارتفاع ضغط الدم حقيقة في كل واحد في
+
+77
+00:06:13,850 --> 00:06:19,970
+العالم كل واحد لكن حقيقة من المشاكل اللي بتواجه 
+
+78
+00:06:19,970 --> 00:06:25,590
+بعض المجموعات من الناس في التحكم في الضغط هو الـ
+
+79
+00:06:25,590 --> 00:06:30,330
+Lifestyle و الـ Socioeconomic factors هذه من
+
+80
+00:06:30,330 --> 00:06:35,890
+الحاجات اللي بتعمل Limitation للعلاج في حالات الـ
+
+81
+00:06:35,890 --> 00:06:41,230
+Hypertension طيب هو أنا من الصبح Hypertension
+
+82
+00:06:41,230 --> 00:06:43,890
+Hypertension إيش بنقصده Hypertension؟ إيش الـ
+
+83
+00:06:43,890 --> 00:06:49,590
+Definition؟ طبعًا هذا موضوع غاية في الأهمية و طبعًا
+
+84
+00:06:49,590 --> 00:06:52,990
+هتلاقي الأرقام هيك شوية هتقولوا طيب وإيش علي لو
+
+85
+00:06:52,990 --> 00:06:55,910
+زدنا واحد ولا نقصنا واحد ولا إيش لو زدنا خمسة
+
+86
+00:06:55,910 --> 00:07:01,390
+ونقصنا خمسة؟ إحنا بنحكي هنا عن مرضى بالبلايين
+
+87
+00:07:01,390 --> 00:07:05,920
+بالبليون إحنا بنحكي عن One Billion Patient في 
+
+88
+00:07:05,920 --> 00:07:10,600
+العالم عشان أنا أحرك الأرقام هذه في لحظة من 
+
+89
+00:07:10,600 --> 00:07:15,860
+اللحظات الأعداد يا بتقل يا بتزيد، إيش يعني؟ طب
+
+90
+00:07:15,860 --> 00:07:20,600
+بتقل وتزيد، لأ لأ، في سياسات اقتصادية عالمية
+
+91
+00:07:20,600 --> 00:07:25,340
+متعلقة بالموضوع، حياة ناس متعلقة بالموضوع بلاد 
+
+92
+00:07:25,340 --> 00:07:29,960
+كاملة متعلقة بالموضوع فالموضوع ليس التأمينات 
+
+93
+00:07:29,960 --> 00:07:34,240
+والمعامل التأمينات والمعاشات متعلقة بالموضوع فيبقى
+
+94
+00:07:34,240 --> 00:07:39,440
+الموضوع مدروس كويس وانحطت هذه الـ Definition بناء
+
+95
+00:07:39,440 --> 00:07:43,840
+على Statistics عالمية متعرف عليها بمعنى الـ
+
+96
+00:07:43,840 --> 00:07:46,360
+Definition اللي هحكيه الآن ما هتلاقوا أنه مثلًا في
+
+97
+00:07:46,360 --> 00:07:50,520
+الصين مختلف أو في اليابان مختلف أو عند العرب مختلف 
+
+98
+00:07:50,520 --> 00:07:53,850
+لأ هي نفس الـ Definition الـ Definition هو
+
+99
+00:07:53,850 --> 00:07:58,150
+«Sustained»، إيش يعني «Sustained»؟ «Sustained»
+
+100
+00:07:58,150 --> 00:08:04,910
+يعني طول الوقت، يعني مش إنه والله فلان خاف، ارتفع
+
+101
+00:08:04,910 --> 00:08:07,050
+ضغطه، جينا له الضغط، جينا عليه، قلنا له عندك
+
+102
+00:08:07,050 --> 00:08:11,690
+ارتفاع ضغط الدم، لأ ما ينفعش الطريقة هاي، ها كيف،
+
+103
+00:08:11,690 --> 00:08:17,610
+أنا يعني بأقيس له عدة مرات، هنحكي عن الطريقة عدة 
+
+104
+00:08:17,610 --> 00:08:22,430
+مرات، في أوقات مختلفة وفي ظروف مختلفة وفي أماكن 
+
+105
+00:08:22,430 --> 00:08:28,450
+مختلفة ولقيّنا إنه دايمًا عنده الضغط مرتفع طب هو
+
+106
+00:08:28,450 --> 00:08:35,750
+أنه من ضمن الـ systolic blood pressure أكثر من 139 و
+
+107
+00:08:35,750 --> 00:08:42,110
+الـ diastolic أكثر من 89 هيك أنا و أنا مرتاح بقول
+
+108
+00:08:42,110 --> 00:08:43,590
+is Hypertension
+
+109
+00:08:50,330 --> 00:08:54,330
+وطبعًا زي ما قلنا مش من أول رقم بروح بقول للناس أنت
+
+110
+00:08:54,330 --> 00:08:57,590
+عندك Hypertension لابد يكون عنده أكثر من Sitting
+
+111
+00:08:57,590 --> 00:09:03,070
+أو أكثر من Visit عشان أقول الموضوع هذا لأن عشان 
+
+112
+00:09:03,070 --> 00:09:08,830
+أقيس الضغط للناس لابد أنه أقيس صحّ الـ Equipment
+
+113
+00:09:08,830 --> 00:09:16,290
+اللي بأقيس فيها تكون معايرة وصحيحة اللي بيقيس لازم
+
+114
+00:09:16,290 --> 00:09:22,170
+يكون Trained و Retrained الـ Patient must be properly 
+
+115
+00:09:22,170 --> 00:09:27,490
+prepared and positioned and seated quietly for at
+
+116
+00:09:27,490 --> 00:09:30,530
+least خمسة minutes in a chair بمعنى أنا روحت على
+
+117
+00:09:30,530 --> 00:09:33,730
+الصيدلية بدي أقيس المفروض أنه الجهاز كويس اللي 
+
+118
+00:09:33,730 --> 00:09:37,110
+عنده المفروض أنه اللي بدي أقيس له الصيدلاني يعرف يقيس
+
+119
+00:09:37,110 --> 00:09:40,870
+كويس ومتدرب ومش من حد ما أجف عنده على طول يقيس لي
+
+120
+00:09:40,870 --> 00:09:44,550
+و أنا واقف المفروض يجاعدني يجاعدني خمس لعشر دقائق
+
+121
+00:09:44,550 --> 00:09:52,990
+عبيّن مرتاح وبعدين بهدوء يقيس لي وطبعًا مهم يسألني
+
+122
+00:09:52,990 --> 00:09:59,890
+شربت في آخر نص ساعة قهوة، شاي، Coca Cola؟ هل عملت
+
+123
+00:09:59,890 --> 00:10:04,550
+Exercise؟ مش معقول جاي والله من .. عارفمش من الجندة
+
+124
+00:10:04,550 --> 00:10:08,450
+ورايح على الزيتون وبعدها بدأ أجلس؟ طبعًا حاجة ضغط 
+
+125
+00:10:08,450 --> 00:10:14,490
+عالي المفروض ما يكونش كمان Smoking avoided for at
+
+126
+00:10:14,490 --> 00:10:17,790
+least 30 minutes before blood pressure
+
+127
+00:10:17,790 --> 00:10:21,700
+measurements مهم جدًا جدًا أن الكف اللي أنا
+
+128
+00:10:21,700 --> 00:10:28,640
+بستعملها لقياس الضغط تكون كمان مناسبة للإيد وحجم 
+
+129
+00:10:28,640 --> 00:10:34,660
+الإيد لازم أقيس زي ما قلنا مرتين على الأقل وطبعًا 
+
+130
+00:10:34,660 --> 00:10:37,800
+لابد أنّه أنا أقول للمريض أفهمه أن الرقم الأولاني
+
+131
+00:10:37,800 --> 00:10:41,600
+هو العالي هو الـ systolic والتاني اللي هو الواط
+
+132
+00:10:41,600 --> 00:10:45,060
+اللي هو الـ diastolic أفهم الموضوع هذا ضروري يعرف
+
+133
+00:10:45,060 --> 00:10:49,110
+الموضوع هذا طب الآن في عملولها Classification Blood
+
+134
+00:10:49,110 --> 00:10:55,550
+Pressure الـ Classification تبعها Systolic and 
+
+135
+00:10:55,550 --> 00:11:00,430
+Diastolic الـ Normal هو أقل من 120 و أقل من 80 في 
+
+136
+00:11:00,430 --> 00:11:05,570
+الدايستوليك الـ Prehypertension وهنعرف إيش يعني
+
+137
+00:11:05,570 --> 00:11:10,590
+الـ Prehypertension من 120 لـ 139 في الـ Systolic و
+
+138
+00:11:10,590 --> 00:11:15,900
+من 80 لـ 89 في الدياستوليك و Stage One Hypertension وبعدين
+
+139
+00:11:15,900 --> 00:11:23,480
+سنعرف إيش يعني Stage One 140 لـ 159 و 90 لـ 99 في
+
+140
+00:11:23,480 --> 00:11:29,180
+الدايستوليك و Stage Two Hypertension أكثر من 160 أو 160
+
+141
+00:11:29,180 --> 00:11:39,980
+وأكثر في الـ Systolic أو أكثر من 100 أو يساوي 100 في
+
+142
+00:11:39,980 --> 00:11:40,720
+الـ Diastolic
+
+143
+00:11:43,160 --> 00:11:47,000
+طبعاً ممكن الـ Prehypertension والـ Stage 1 والـ
+
+144
+00:11:47,000 --> 00:11:50,420
+Stage 2 يكون واحد من الاثنين عالي يعني الـ
+
+145
+00:11:50,420 --> 00:11:53,780
+Systolic لحاله ممكن والـ Diastolic لحاله ممكن و
+
+146
+00:11:53,780 --> 00:11:57,760
+ممكن يكونوا الاثنين لكن ممكن أقول والله الـ
+
+147
+00:11:57,760 --> 00:12:01,700
+Prehypertension بالرغم من أنه.. أسمي المثال الـ
+
+148
+00:12:01,700 --> 00:12:06,680
+Prehypertension الـ Systolic 130 لكن الـ Diastolic 
+
+149
+00:12:06,680 --> 00:12:13,480
+79 بِفعْلِ يعني هو رقم من الرقمين بكفي عشان أنا أقول
+
+150
+00:12:13,480 --> 00:12:21,020
+عنه أنه Hypertension طب ايش الـ Pre-hypertension؟
+
+151
+00:12:21,020 --> 00:12:27,060
+الـ Pre-hypertension زي ما قلنا قبل شوية فوق الـ
+
+152
+00:12:27,060 --> 00:12:30,800
+120 ميلي 
+
+153
+00:12:30,800 --> 00:12:41,460
+متر quicksilva وأقل من 139 في الـ Systolic الـ
+
+154
+00:12:41,460 --> 00:12:47,420
+Diastolic من 80 وأقل من 89 الـ Pre hypertension
+
+155
+00:12:47,420 --> 00:12:51,440
+كمان مرة يا جماعة is not a disease يعني بتقدرش
+
+156
+00:12:51,440 --> 00:12:54,120
+تقول لو واحد أنت Hypertension أنت عندك ضغط دم
+
+157
+00:12:54,120 --> 00:13:04,390
+بتقدرش هو مش Disease هو عبارة عن إشارة تلميح للمريض
+
+158
+00:13:04,390 --> 00:13:09,910
+أنه خذ بالك أنك في حالة عالية لتطور الـ
+
+159
+00:13:09,910 --> 00:13:13,470
+Hypertension هذه
+
+160
+00:13:13,470 --> 00:13:17,450
+النقطة الأولى أن أنت احتمال كبير يحصل عندك الضغط
+
+161
+00:13:17,450 --> 00:13:23,130
+خذ بالك ومش بس و I'm not a candidate for drug 
+
+162
+00:13:23,130 --> 00:13:26,680
+therapy ولكن مش هتديله علاج، Pre hypertension مش
+
+163
+00:13:26,680 --> 00:13:31,080
+هتديله علاج، لكن هذا عبارة عن تلميح، عن إشارة، عن
+
+164
+00:13:31,080 --> 00:13:35,640
+أنه خذ بالك يا هذا، أنت احتمال كبير يصير عندك 
+
+165
+00:13:35,640 --> 00:13:42,100
+Hypertension لو ما أخدتش بالك لازم لازم لازم تغير
+
+166
+00:13:42,100 --> 00:13:46,320
+نفسك كيف أغير نفسي Lifestyle هتسمعوا كلمة
+
+167
+00:13:46,320 --> 00:13:50,480
+practicing lifestyle modification كثير في
+
+168
+00:13:50,480 --> 00:13:54,900
+محاضراتنا لأن هذا جزء كبير من الـ Education للعيان
+
+169
+00:13:54,900 --> 00:14:00,520
+how to change lifestyle أنا طول النهار قاعد على ال
+
+170
+00:14:00,520 --> 00:14:04,540
+Laptop ولا على الـ Computer وأكل مع أكل مع أكل و
+
+171
+00:14:04,540 --> 00:14:11,480
+تدخين و Pizza وما أعرفش إيش طبعاً وباتحركش من
+
+172
+00:14:11,480 --> 00:14:16,220
+الكنباية للطبخ ومن الطبخ للكنباية طبيعي جداً جداً
+
+173
+00:14:16,220 --> 00:14:21,380
+أن هذا bad lifestyle وأنه لو صار عندي ضغط لو صار
+
+174
+00:14:21,380 --> 00:14:24,240
+عندي ضغط لابد أنه أو Pre hypertension لابد أنه
+
+175
+00:14:24,240 --> 00:14:28,360
+أغير الـ Lifestyle لحتى أتغلب على Pre hypertension
+
+176
+00:14:29,650 --> 00:14:32,890
+يبقى الـ Pre-hypertension عبارة عن تلميح للمريض
+
+177
+00:14:32,890 --> 00:14:37,750
+تلميح إنه إشارة، خذ بالك، نين، not a candidate for
+
+178
+00:14:37,750 --> 00:14:44,510
+drug therapy لكن لازم نعمله advising to practice 
+
+179
+00:14:44,510 --> 00:14:46,410
+lifestyle modification
+
+180
+00:14:51,410 --> 00:14:54,410
+يُستثنى من الناس دول الـ Pre-hypertension الناس
+
+181
+00:14:54,410 --> 00:14:57,390
+اللي عندها Diabetes، عندها سكري أو عندها مرض كِلى
+
+182
+00:14:57,390 --> 00:15:04,010
+ممكن، ممكن، ممكن يُعطى دواء if a trial of lifestyle 
+
+183
+00:15:04,010 --> 00:15:08,690
+modification fails إذا ما زبطتش معنا في قضية إن
+
+184
+00:15:08,690 --> 00:15:11,690
+الـ Lifestyle وقال لك أنا مش قادر، أنا مش كذا
+
+185
+00:15:11,690 --> 00:15:16,930
+فممكن إنه fails to reduce blood pressure لـ 130،
+
+186
+00:15:16,930 --> 00:15:20,030
+لـ 80 أو أقل، يعني إذا جئنا إن الـ Blood pressure
+
+187
+00:15:21,540 --> 00:15:25,300
+مش راضي يظبط معنا بالـ Lifestyle أدِه دواء أدِه
+
+188
+00:15:25,300 --> 00:15:32,460
+علاج عشان أخفض الضغط تبعه من 130 من أجل من 130 ل
+
+189
+00:15:32,460 --> 00:15:38,800
+80 أو أجل احنا قلنا قبل شوية أنه مش لازم عشان أقول 
+
+190
+00:15:38,800 --> 00:15:43,960
+Hypertension مش لازم يكون الاثنين الرقمين الـ Systolic
+
+191
+00:15:43,960 --> 00:15:46,200
+والـ Diastolic لازم يكونوا عاليين مش لازم
+
+192
+00:15:49,840 --> 00:15:53,820
+واحد منهم لو كان عالي بكفي فوق الحدود فأنا أقول
+
+193
+00:15:53,820 --> 00:15:57,800
+عنه Isolated systolic hypertension أو Isolated
+
+194
+00:15:57,800 --> 00:16:03,920
+Diastolic hypertension طبعاً هو ما يختلفش في العلاج
+
+195
+00:16:03,920 --> 00:16:07,760
+كثير لكن لابد أنه ننتبه للقضية هي Systolic blood
+
+196
+00:16:07,760 --> 00:16:10,300
+pressure should be primarily considered during
+
+197
+00:16:10,300 --> 00:16:14,740
+treatment and not just diagnostic blood pressure،
+
+198
+00:16:14,740 --> 00:16:15,740
+Diastolic blood pressure
+
+199
+00:16:18,480 --> 00:16:22,420
+الـ Systolic طبعاً هو يُعتبر الأخطر برضه عشان ما نديش
+
+200
+00:16:22,420 --> 00:16:25,300
+الثانية نفس القيمة Systolic ليش؟ لأن الـ Systolic
+
+201
+00:16:25,300 --> 00:16:29,560
+يمثل الـ Systemic Blood Pressure في كل الجسم
+
+202
+00:16:29,560 --> 00:16:33,480
+الـ Diastolic له علاقة أكثر بالـ Diastole وبالـ
+
+203
+00:16:33,480 --> 00:16:38,080
+Pulmonary Crisis Diastolic Blood Pressure is 
+
+204
+00:16:38,080 --> 00:16:42,160
+more important قبل عمر خمسين يبقى بعد عمر خمسين
+
+205
+00:16:42,160 --> 00:16:52,390
+الـ Diastolic أهم قبل عمر خمسين طيب هو أجاني عيان و
+
+206
+00:16:52,390 --> 00:16:57,030
+قست له ضغطه مرة مرتين وجدت ضغطه طبيعي، ايش أقول له؟
+
+207
+00:16:57,030 --> 00:17:01,650
+أقول له الله سهّل عليك ضغطك طبيعي، دير بالك على حالك،
+
+208
+00:17:01,650 --> 00:17:06,550
+وبعد سنتين ابقى قيس كم مرة، هذا ري تشيك، تشيك
+
+209
+00:17:06,550 --> 00:17:11,250
+كل سنتين، كل ثلاث، هذا وضع طبيعي لأي بني آدم أنه
+
+210
+00:17:11,250 --> 00:17:17,010
+يعمله فحص ضغط الدم الـ Prehypertension، آه أقول له
+
+211
+00:17:17,010 --> 00:17:23,060
+بدك تغير حياتك Lifestyle modification تجلل الملح
+
+212
+00:17:23,060 --> 00:17:31,180
+تزيد الحركة بتاعتك تأكل فواكه وخضار أكثر.. و
+
+213
+00:17:31,180 --> 00:17:34,920
+بلاش قعدات ال..ال..الـ Laptop والـ Computer و
+
+214
+00:17:34,920 --> 00:17:39,300
+ال..الـ Pizza و.. والحاجات هي اتحرك أكثر لما
+
+215
+00:17:39,300 --> 00:17:42,840
+تروح على الجامع حاول خذ طريق طويل وأنت راجع 
+
+216
+00:17:42,840 --> 00:17:48,300
+برضه بلاش بالسيارة وحاول سطل الزبالة في مكتبك بدل
+
+217
+00:17:48,300 --> 00:17:52,000
+ما يكون تحت رجلك حاول حطه بعيد عشان كل شوية تقوم
+
+218
+00:17:52,000 --> 00:17:55,620
+لسطل الزبالة وتتحرك ولو ما جرى Lifestyle
+
+219
+00:17:55,620 --> 00:18:00,880
+modification لازم أغير حياتي أغير حياتي بالطريقة
+
+220
+00:18:00,880 --> 00:18:04,840
+هذه ممكن أتغلب على الـ Pre hypertension لكن بدي
+
+221
+00:18:04,840 --> 00:18:09,880
+أقيس بعد شهر بعد سنة عفواً ثاني ممكن قبل بس يعني
+
+222
+00:18:09,880 --> 00:18:15,960
+احنا بنحكي عن زي ما بقولوها Guidelines Stage one
+
+223
+00:18:15,960 --> 00:18:20,020
+Hypertension إذا جئنا عنده والله شوية ريحة
+
+224
+00:18:20,020 --> 00:18:23,400
+Hypertension بدي أشوفه بعد شهرين أقيس للضغط ثاني
+
+225
+00:18:24,060 --> 00:18:28,400
+Stage 2 Hypertension طبعاً
+
+226
+00:18:28,400 --> 00:18:32,360
+حسب لكن في الأصل أنه ما أطوّلش وعود أدِيس له لأن هذه
+
+227
+00:18:32,360 --> 00:18:36,860
+بنعتبرها من أنواع هنحكي عنهم Emergency أو 
+
+228
+00:18:36,860 --> 00:18:43,720
+Emergency Hypertension فيه
+
+229
+00:18:43,720 --> 00:18:49,680
+إننا طبعاً احنا Risk Factors للـ Risk Factors هذه
+
+230
+00:18:49,680 --> 00:18:54,100
+لـ Cardiovascular Risk Factors على رأسها يعني أنا
+
+231
+00:18:54,100 --> 00:18:58,320
+عشان أقول والله فلان عنده أمراض قلب وأوعية دموية
+
+232
+00:18:58,320 --> 00:19:03,520
+في Risk Factor مهم جداً جداً بأهتم به اللي هو قضية
+
+233
+00:19:03,520 --> 00:19:07,240
+الضغط واللي هو رقم 1 يعني طبعاً بالإضافة للتدخين و
+
+234
+00:19:07,240 --> 00:19:09,400
+الـ Obesity والـ Physical inactivity والـ
+
+235
+00:19:09,400 --> 00:19:13,000
+Dyslipidemia والـ Diabetes mellitus ومشاكل الكلى
+
+236
+00:19:13,730 --> 00:19:16,950
+العمر Family history هذه كلها Risk factors للـ
+
+237
+00:19:16,950 --> 00:19:21,630
+Cardiovascular diseases يعني أي واحد بأجي اكتشف
+
+238
+00:19:21,630 --> 00:19:24,690
+عنده مشكلة في القلب أول حاجة بتخطر على بالي خذ
+
+239
+00:19:24,690 --> 00:19:30,730
+بالك ضغطه احتمال ضغطه يكون عالي طب واحنا بنحكي
+
+240
+00:19:30,730 --> 00:19:38,270
+قلنا والله في حاجة اسمها Crisis ايش يعني Crisis ايش
+
+241
+00:19:38,270 --> 00:19:42,850
+يعني Crisis Crisis أنه هي أزمة معناتها Crisis يعني
+
+242
+00:19:42,850 --> 00:19:49,040
+أزمة هذه اللي بتصير إنها Crisis عندما يرتفع ضغط
+
+243
+00:19:49,040 --> 00:19:56,680
+الدم فوق أرقام معينة ويظهر إليها تأثير سنحكي عن
+
+244
+00:19:56,680 --> 00:20:00,440
+الموضوع هذا تأثير بطريقة أو بأخرى على باقي الأعضاء
+
+245
+00:20:00,440 --> 00:20:07,560
+يبقى Crisis is a severe abruptly elevation in 
+
+246
+00:20:07,560 --> 00:20:13,540
+blood pressure ارتفاع شديد مفاجئ في ضغط الدم
+
+247
+00:20:17,350 --> 00:20:20,910
+ومهم جداً هو لو واحد يقول لك أنا والله عايش ضغط عالي
+
+248
+00:20:20,910 --> 00:20:26,130
+طول عمري ضغط 170 على 110 أو هيني زي الـ Full صحيح، 
+
+249
+00:20:26,130 --> 00:20:29,210
+احنا بنحكي عن “appropriately” حاجة سريعة، حاجة
+
+250
+00:20:29,210 --> 00:20:32,730
+فجائية بتصير الـ “rate of increase of blood
+
+251
+00:20:32,730 --> 00:20:35,930
+pressure” بلعب دور عنها إنه الارتفاع خلال ربع
+
+252
+00:20:35,930 --> 00:20:39,950
+ساعة، خلال نصف ساعة ولا ارتفاع خلال أيام أو شهور
+
+253
+00:20:39,950 --> 00:20:43,250
+فهذا مهم بالنسبة لنا في تعريف الـ Crisis
+
+254
+00:20:43,250 --> 00:20:47,370
+الـ Hypertensive Crisis وهذه اللي بنسمعها ولا فلان
+
+255
+00:20:47,370 --> 00:20:52,650
+عنده ضغط الصحي الصبح عنده شلل نصفي أو عنده ذبحة
+
+256
+00:20:52,650 --> 00:20:56,910
+صدرية أو عنده كذا نتيجة ارتفاع مفاجئ في ضغط الدم
+
+257
+00:20:56,910 --> 00:21:03,810
+لسبب أو لآخر الـ Patient with a history of 
+
+258
+00:21:03,810 --> 00:21:07,630
+hypertension who have failed to comply with 
+
+259
+00:21:07,630 --> 00:21:11,450
+medication or who have been under-medicated الناس
+
+260
+00:21:11,450 --> 00:21:15,630
+هدول غالباً يا إما بطل ياخذ الدواء صاوي عن
+
+261
+00:21:15,630 --> 00:21:21,310
+الموضوع أو إن الدواء اللي بياخده يُعتبر جليل عملياً
+
+262
+00:21:21,310 --> 00:21:26,930
+مش كفاية فهدول بيميلوا عند أي Stress بغض النظر
+
+263
+00:21:26,930 --> 00:21:31,670
+Organic ولا Psychic إنه يرتفع ضغط الدم عندهم بدنا
+
+264
+00:21:31,670 --> 00:21:35,570
+نفرّق هنا بين حاجتين الحاجة الأولى Hypertensive
+
+265
+00:21:37,740 --> 00:21:43,000
+طبعاً كله تحت Crisis الـ Emergency أجواء وأشد ولا الـ 
+
+266
+00:21:43,000 --> 00:21:45,400
+Emergency أجواء وأشد؟ هنقول الآن
+
+267
+00:21:48,540 --> 00:21:52,800
+الـ Hypertensive Emergency No Progressive Target 
+
+268
+00:21:52,800 --> 00:21:55,980
+Organ Dysfunction بنقول عنه Accelerated
+
+269
+00:21:55,980 --> 00:22:00,520
+Hypertension يعني هو بِيرتفع ضغط الدم لكن لا بيصير
+
+270
+00:22:00,520 --> 00:22:05,040
+مع الواحد وجع رأس ولا طنة في الأذن ولا دُوخة ولا
+
+271
+00:22:05,040 --> 00:22:10,180
+ولا ولا ولا لكن الـ Emergency بيصير عنده End Organ 
+
+272
+00:22:10,180 --> 00:22:13,740
+Dysfunction بنقول عنه Malignant Hypertension يبدأ
+
+273
+00:22:13,740 --> 00:22:18,540
+مين الأخطر الـ Emergency ولا الـ Emergency؟ الـ
+
+274
+00:22:18,540 --> 00:22:24,400
+Emergency هي الأخطر وهي اللي بتعملنا مشاكل تمام
+
+275
+00:22:24,400 --> 00:22:30,000
+مرة نرجع الـ Hypertensive Emergency Severe 
+
+276
+00:22:30,000 --> 00:22:33,500
+elevated blood pressure in the upper range of 
+
+277
+00:22:33,500 --> 00:22:38,740
+stage 2 hypertension without progressive end organ
+
+278
+00:22:38,740 --> 00:22:39,460
+dysfunction
+
+279
+00:22:42,590 --> 00:22:45,210
+زي ما قلنا highly elevated blood pressure without 
+
+280
+00:22:45,210 --> 00:22:50,130
+severe headache shortness of breath or chest pain
+
+281
+00:22:50,130 --> 00:22:54,930
+usually في الغالب usually إيش يعني usually لما 
+
+282
+00:22:54,930 --> 00:22:59,390
+نقولها 100% النسبة بتاعة usually ولا always 100%
+
+283
+00:22:59,390 --> 00:23:04,790
+always 100% usually غالبا ناتج عن under controlled 
+
+284
+00:23:04,790 --> 00:23:05,990
+hypertension
+
+285
+00:23:07,930 --> 00:23:12,170
+إنه لأ غير متحكم في الضغط طيب الـ Hypertensive
+
+286
+00:23:12,170 --> 00:23:17,390
+Emergency هي Severely Elevated Blood Pressure فوق
+
+287
+00:23:17,390 --> 00:23:21,790
+الـ 180 للمائة وعشرين With Progressive Target 
+
+288
+00:23:21,790 --> 00:23:27,670
+Organ Dysfunction وRequire Emergent Lowering Of
+
+289
+00:23:27,670 --> 00:23:31,250
+Blood Pressure ماقدرش أسكت عنه هداك الـ Emergency
+
+290
+00:23:31,250 --> 00:23:33,690
+أحنا سكتنا عنه لكن هذا ماقدرش نسكت عنه
+
+291
+00:23:36,760 --> 00:23:40,340
+مش ممكن يبينلي؟ ممكن يجيني الواحد بـHypertensive
+
+292
+00:23:40,340 --> 00:23:43,320
+Encephalopathy إيش يعني Encephalopathy؟
+
+293
+00:23:43,320 --> 00:23:47,320
+Encephalopathy، Encephalopathy،
+
+294
+00:23:47,320 --> 00:23:48,220
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+295
+00:23:48,220 --> 00:23:48,260
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+296
+00:23:48,260 --> 00:23:48,660
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+297
+00:23:48,660 --> 00:23:48,840
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+298
+00:23:48,840 --> 00:23:48,860
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+299
+00:23:48,860 --> 00:23:49,940
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+300
+00:23:49,940 --> 00:23:55,440
+Encephalopathy، Encephalopathy، Encephalopathy،
+
+301
+00:23:55,440 --> 00:24:00,160
+Encephalopathy، Encephalopathy،
+
+302
+00:24:00,160 --> 00:24:03,600
+Encephalopathy،
+
+303
+00:24:03,600 --> 00:24:08,870
+Enللقلب اليسرى لأن الـ left ventricle هو اللي بدخ
+
+304
+00:24:08,870 --> 00:24:14,630
+دم لمين؟ لباقي الجسم وباقي الجسم ضغطه عالي فلما 
+
+305
+00:24:14,630 --> 00:24:19,310
+ييجي الـ left heart يدخ دم فبيصير عنده failure
+
+306
+00:24:19,310 --> 00:24:24,050
+بيقدرش ليش؟ لأنه بدخ على ضغط عالي with pulmonary
+
+307
+00:24:24,050 --> 00:24:29,840
+edema وبيصير عنده تحفيز للسوائل في الرئتينممكن
+
+308
+00:24:29,840 --> 00:24:34,260
+يصير عنا Acute MI أو Unstable Angina Vector الذبحة 
+
+309
+00:24:34,260 --> 00:24:39,480
+صدرية وحنتحدث بعدين في يوم الأيام وممكن يصير عنا
+
+310
+00:24:39,480 --> 00:24:43,240
+Dissecting Aortic Aneurysm إيش يا دي Dissecting
+
+311
+00:24:43,240 --> 00:24:47,520
+Aortic Aneurysm؟
+
+312
+00:24:47,520 --> 00:24:55,280
+طبعا لأ أنا يعني لأ كله لحتى الآن اللي بتقولوه
+
+313
+00:24:55,280 --> 00:24:59,640
+بدكوا تقولوهمن خلال ايش الـ «dissecting aortic
+
+314
+00:24:59,640 --> 00:25:04,200
+aneurysm»؟ من خلال هذه رقم واحد في الـassignment
+
+315
+00:25:04,200 --> 00:25:10,100
+تبع اليوم What is dissecting aortic aneurysm؟ وهل
+
+316
+00:25:10,100 --> 00:25:14,200
+في عندنا أنواع من الـaortic aneurysm؟ طب في
+
+317
+00:25:14,200 --> 00:25:19,960
+aneurysms بتصير في أماكن تانية غير الأورطة؟ هذا 
+
+318
+00:25:19,960 --> 00:25:25,150
+الجزء الأول من الـassignment تبع اليومواللي
+
+319
+00:25:25,150 --> 00:25:32,830
+هتبعتوليها على ال model كيف 
+
+320
+00:25:32,830 --> 00:25:36,170
+أنا الأن كيف بدأ أعرف أي واحد عنده hypertensive 
+
+321
+00:25:36,170 --> 00:25:42,170
+crisis طبعا أنا بجيسله ضغط صح كلامكم بس لكن بيبين
+
+322
+00:25:42,170 --> 00:25:48,830
+عليه المريض اللي ضغته برتفع بصورة emergency بيصير
+
+323
+00:25:48,830 --> 00:25:51,710
+عنده hypertensive encephalopathy بيصير عنده renal
+
+324
+00:25:51,710 --> 00:25:55,570
+insufficiency بيصير عنده heart failureالموناري
+
+325
+00:25:55,570 --> 00:26:00,750
+قديمة الـ Diaphoreses وهذا الجزء التاني من الـ
+
+326
+00:26:00,750 --> 00:26:06,050
+assignment إيش يعني Diaphoreses؟ وإيش في كلمات 
+
+327
+00:26:06,050 --> 00:26:12,070
+بتشبهها؟ Diaphoreses وفي كلمات بتشبهها بتدي شبيه
+
+328
+00:26:12,070 --> 00:26:17,540
+المعنى تبعهابرضه هدى الجزء التانى من ال assignment
+
+329
+00:26:17,540 --> 00:26:22,600
+طب أنا كيف ال hypertensive crisis واحد الآن ضغطه 
+
+330
+00:26:22,600 --> 00:26:28,060
+190 ع 120 زلمة عمره 65 ومعصب متقاتل مع ولاده مش
+
+331
+00:26:28,060 --> 00:26:32,820
+راضين يدوله مصروف او مش راضين يخلوه متجوز ولا اي
+
+332
+00:26:32,820 --> 00:26:38,700
+عاجة المهم عصب صار عنده hypertensive crisis كيف
+
+333
+00:26:38,700 --> 00:26:44,560
+بدى علاجها؟ طبعا هذا لابد من مستشفى رقم واحدالـ IV 
+
+334
+00:26:44,560 --> 00:26:49,460
+Drug Therapy بيعطوه أدوية بالـ IV لازم توا حكينا
+
+335
+00:26:49,460 --> 00:26:54,200
+إذا فاكرين مع الـ hypertensive crisis بيصير عندنا
+
+336
+00:26:54,200 --> 00:26:58,280
+heart failure يعني بدي أعمله monitor لل cardiac
+
+337
+00:26:58,280 --> 00:27:03,380
+and renal function بدي أعمله عشان ال hypertensive 
+
+338
+00:27:03,380 --> 00:27:08,580
+encephalopathy بدي أعمله neurologic check و بدي 
+
+339
+00:27:08,580 --> 00:27:13,180
+أدور على السببالسبب ليه صار معه هيك؟ طب ليش أنا
+
+340
+00:27:13,180 --> 00:27:16,600
+بدي السبب؟ عشان مايتكررش، أنا صراحة مش هرجع لورا،
+
+341
+00:27:16,600 --> 00:27:18,060
+لكن عشان مايتكررش
+
+342
+00:27:20,150 --> 00:27:24,330
+لازم نقعد مع الناس Communication مع الناس عشان
+
+343
+00:27:24,330 --> 00:27:28,450
+أمنع to avoid future crisis لأن ال crisis زي ما
+
+344
+00:27:28,450 --> 00:27:31,690
+انتوا شايفينه يا جماعة ممكن تعمللي مشاكل كتير على 
+
+345
+00:27:31,690 --> 00:27:35,350
+جميع أعضاء الجسم فموضوع الضغط ما هواش موضوع بس
+
+346
+00:27:35,350 --> 00:27:38,170
+بيعمللي شوية وجع راس وطنة في الدهن، لأ فهو ممكن
+
+347
+00:27:38,170 --> 00:27:41,750
+يأثرلي ويعملي coma ممكن يعملي encephalopathy ممكن
+
+348
+00:27:41,750 --> 00:27:46,030
+يعملي MI ممكن يعملي renal failure ممكن يعملي أمور
+
+349
+00:27:46,030 --> 00:27:51,480
+كتير زي ما حكينا قبل شويةالمهم أن ننتبه لهذا
+
+350
+00:27:51,480 --> 00:27:56,600
+الموضوع حكينا
+
+351
+00:27:56,600 --> 00:27:59,100
+عن الـ Classification قبل قليل لأننا نحكي عن الـ
+
+352
+00:27:59,100 --> 00:28:01,220
+Types of Hypertension في فرق بين الـ
+
+353
+00:28:01,220 --> 00:28:05,320
+Classification و بين الـ Types إيش الـ Types؟
+
+354
+00:28:05,320 --> 00:28:11,480
+الأنواع، في Hypertension هيك منه و فيه مالك يا
+
+355
+00:28:11,480 --> 00:28:16,000
+فلان والله قالولي عندك ضغط، من إيش؟ إيش من إيش؟ من
+
+356
+00:28:16,000 --> 00:28:19,900
+ولا إشي، هو الضغط هو المرض نفسههذا بيقول عنه
+
+357
+00:28:19,900 --> 00:28:24,700
+primary hypertension يعني مش جاي نتيجة حاجة بيقول
+
+358
+00:28:24,700 --> 00:28:30,760
+عنه essential hypertension وهذا يا جماعة بيمثل 95%
+
+359
+00:28:30,760 --> 00:28:35,080
+of cases of hypertension يعني بمعنى زي كمان مرة
+
+360
+00:28:35,080 --> 00:28:39,440
+السيناريو مالك يا فلان والله قالولي عندك ضغط من
+
+361
+00:28:39,440 --> 00:28:44,440
+إيش؟ مافيش من إيش هو هيك هو ضغط هو هو المرض اسمه
+
+362
+00:28:44,440 --> 00:28:44,800
+hypertension
+
+363
+00:28:48,310 --> 00:28:51,490
+وبنلاقيش إله سبب يا جماعة عادة مش إنه مالوش سبب
+
+364
+00:28:51,490 --> 00:28:56,330
+بنلاقيش إله سبب وإيش النوع التاني اسمه secondary
+
+365
+00:28:56,330 --> 00:28:58,650
+hypertension إيش يعني secondary هدا ال primary
+
+366
+00:28:58,650 --> 00:29:04,050
+يعني يعني هو البداية بداية رقم واحد ال secondary
+
+367
+00:29:04,050 --> 00:29:08,650
+هو ناشق عن وجود برض معين عملّي حاجة اسمها
+
+368
+00:29:08,650 --> 00:29:12,020
+secondary hypertensionطبعا انتوا لحد تلقاه
+
+369
+00:29:12,020 --> 00:29:17,400
+ماسمعتوش حد نادى بندورة ولا با نادى قخ ولا غاز ولا
+
+370
+00:29:17,400 --> 00:29:20,980
+حاجة ملاحظين؟ اه لإن أنا في منطقة معزولة عمليا في
+
+371
+00:29:20,980 --> 00:29:25,260
+المستشفى قاعد بسجل فمافيش حد يقول حاجة زيك مستقبلا
+
+372
+00:29:25,260 --> 00:29:28,840
+طبعا تتوقعوا تسمعوا حاجة زي هي لما أكون في البيت
+
+373
+00:29:28,840 --> 00:29:32,280
+هيني قلتلكوا سر وقت إيش أنا بسجل في البيت و وقت
+
+374
+00:29:32,280 --> 00:29:37,720
+إيش بسجل في المستشفىكمان مرة نعود نرجع secondary
+
+375
+00:29:37,720 --> 00:29:41,600
+hypertension less common cause of hypertension
+
+376
+00:29:41,600 --> 00:29:45,800
+خمسة في المية و هي زي ما قلنا بيبقى في عندي سبب 
+
+377
+00:29:45,800 --> 00:29:49,920
+عندي مرض في الكلة فعمللي hypertension بقول عنه 
+
+378
+00:29:49,920 --> 00:29:55,120
+secondary طيب إيش الأسباب اللي ممكن تعملي
+
+379
+00:29:55,120 --> 00:30:02,640
+secondary hypertension؟ و هذا
+
+380
+00:30:02,640 --> 00:30:13,860
+هو هحكيهموهذا هو السبب أو الجزء التالت من الـ
+
+381
+00:30:13,860 --> 00:30:19,440
+assignment تبعنا اللي هو الـ causes of secondary
+
+382
+00:30:19,440 --> 00:30:23,460
+hypertension أنا هحكيهم أشرح عنهم بعض الحاجات لكن
+
+383
+00:30:23,460 --> 00:30:29,570
+بدي منكم على كل واحدة ينكتبمن ثلاث لأربع أسطور
+
+384
+00:30:29,570 --> 00:30:36,730
+كتابة و برضه تبعتولياهم على
+
+385
+00:30:36,730 --> 00:30:40,230
+ال
+
+386
+00:30:40,230 --> 00:30:45,510
+model و هذا الكلام ما يطولش عن من تاريخ ما تشوفوا
+
+387
+00:30:45,510 --> 00:30:52,290
+المحاضرة من تاريخ ما أنزلها Maximum تلات أيام وبعد
+
+388
+00:30:52,290 --> 00:30:57,840
+هيك ما هتلجح حاجةلأنه لازم خلاص نتنشط، بدي أحاول
+
+389
+00:30:57,840 --> 00:31:01,380
+ألزم معاكوا وأنتوا تلتزموا معايا عشان مايتحوشش
+
+390
+00:31:01,380 --> 00:31:04,740
+عليكم المحاضرات وفي الآخر ما تلاحظوش لا أهدأ ولا
+
+391
+00:31:04,740 --> 00:31:08,080
+أهدأ ولا أهدأ، بحاول إن شاء الله أنا مع فريزة إن
+
+392
+00:31:08,080 --> 00:31:11,640
+شاء الله تعالى نحدد مواعيد وأحاول أحافظ عليها جدر
+
+393
+00:31:11,640 --> 00:31:14,580
+الإمكان، إن شاء الله تعالى، طيب إيش ال causes of
+
+394
+00:31:14,580 --> 00:31:19,620
+secondary hypertension؟ واحد sleep أبنية، إيش
+
+395
+00:31:19,620 --> 00:31:25,020
+يعني؟السليب أبنية يعني by sleep بيصير الواحد عنده
+
+396
+00:31:25,020 --> 00:31:29,180
+أبنية، إيش يعني أبنية؟ cessation of breathing،
+
+397
+00:31:29,180 --> 00:31:33,040
+يعني توقف عن النفس لمدة تزيد عن عشر ثواني، هذه
+
+398
+00:31:33,040 --> 00:31:35,700
+بقول عنها sleep أبنية، إليها أسباب كتير، في الغالب
+
+399
+00:31:35,700 --> 00:31:40,340
+obstructive، هذه بتعمل ليه؟ hypertension، drug
+
+400
+00:31:40,340 --> 00:31:44,900
+-induced، وهذه فرصة للكم عشان إيش؟ تقولوا ليه؟ بعض
+
+401
+00:31:44,900 --> 00:31:50,610
+ال drugs اللي بتعمل hypertensionChronic kidney
+
+402
+00:31:50,610 --> 00:31:56,310
+disease كرونيك
+
+403
+00:31:56,310 --> 00:31:58,530
+كيدني ديسيز كرونيك كيدني ديسيز كرونيك كيدني ديسيز
+
+404
+00:31:58,530 --> 00:31:58,610
+كرونيك كيدني ديسيز كرونيك كيدني ديسيز كرونيك كيدني
+
+405
+00:31:58,610 --> 00:32:00,670
+ديسيز كرونيك كيدني ديسيز كرونيك كيدني ديسيز كرونيك
+
+406
+00:32:00,670 --> 00:32:02,670
+كيدني ديسيز كرونيك كيدني ديسيز كرونيك كيدني ديسيز
+
+407
+00:32:02,670 --> 00:32:06,810
+كرونيك كيدني ديسيز كرونيك كيدني ديسيز كرونيك كيدني
+
+408
+00:32:06,810 --> 00:32:13,050
+ديسيز كرونيك كيدني ديسيز كرونيك كيدني ديسيز كرونيك
+
+409
+00:32:13,050 --> 00:32:19,150
+كيدني ديسيChronic Steroid Therapy and Caching
+
+410
+00:32:19,150 --> 00:32:23,110
+Syndrome فينا
+
+411
+00:32:23,110 --> 00:32:34,430
+حاجة اسمها Pheochromocytoma Pheochromocytoma
+
+412
+00:32:34,430 --> 00:32:39,870
+Pheochromocytoma Pheochromocytoma Pheochromocytoma
+
+413
+00:32:39,870 --> 00:32:43,650
+Pheochromocytoma Pheochromocytoma Pheochromocytoma
+
+414
+00:32:44,230 --> 00:32:48,710
+النوع من أنواع الورم في بعض الخلايا مش هقولكوا وين
+
+415
+00:32:48,710 --> 00:32:53,750
+لأن انتوا تجروا عنها الآن و تبعتولي وهذه بتزيد
+
+416
+00:32:53,750 --> 00:32:58,550
+إفراز هرمون معين برضه مش هقولكوا إيش الهرمون و
+
+417
+00:32:58,550 --> 00:33:04,090
+الهرمون هذا إيش بعمل؟ صح برفع ضغط الدم بصورة كبيرة
+
+418
+00:33:04,090 --> 00:33:11,530
+طب إيش العلاج تبعه؟ انتوا هتقولولي الـHyper and
+
+419
+00:33:11,530 --> 00:33:17,280
+Hypothyroidismكمان بيعملنا hypertension اتصوروا
+
+420
+00:33:17,280 --> 00:33:21,480
+أنا لسه ما قلتش كل الأسباب هذه بعض الأسباب إذا أي
+
+421
+00:33:21,480 --> 00:33:25,420
+حد بيقدر يضيف كمان أسباب secondary hypertension 
+
+422
+00:33:25,420 --> 00:33:32,820
+بيبقى كتير كويس في الجواب تبعه بيبقى كتير كويس 
+
+423
+00:33:32,820 --> 00:33:35,880
+كمان مرة Causes of secondary hypertension Sleep 
+
+424
+00:33:35,880 --> 00:33:40,240
+apnea Drug-induced and/or related causes Chronic
+
+425
+00:33:40,240 --> 00:33:44,100
+kidney disease Renovascular disease Chronic
+
+426
+00:33:44,100 --> 00:33:47,280
+steroid therapy and Cushing syndrome فيه
+
+427
+00:33:47,280 --> 00:33:52,560
+Pheochromocytoma Coarctation of the aorta Hyper- and
+
+428
+00:33:52,560 --> 00:33:58,660
+hypothyroidism or hyperthyroidism هنا في مشروع بعض 
+
+429
+00:33:58,660 --> 00:33:59,220
+الحاجات
+
+430
+00:34:04,100 --> 00:34:07,080
+وهتوقف أنا هأقف على أساس أن أنا بس في المحاضرة الأولى
+
+431
+00:34:07,080 --> 00:34:10,340
+ومش حابب أطيل عليكم كتير أنه في عندنا
+
+432
+00:34:10,340 --> 00:34:13,340
+complications للـ uncontrolled hypertension يعني 
+
+433
+00:34:13,340 --> 00:34:17,240
+مجموعة الناس هذه اللي بتقولك لأ أنا ما عنديش ضغط 
+
+434
+00:34:17,240 --> 00:34:21,160
+وأنا ما بديش أدوية ضغط أو ما بديش ألتزم في
+
+435
+00:34:21,160 --> 00:34:25,800
+الـ complications بتصير، الـ complications هي حقيقة على
+
+436
+00:34:25,800 --> 00:34:31,020
+المدى الطويل فيها مشكلة كبيرة نتحدث عنها في المرات
+
+437
+00:34:31,020 --> 00:34:33,620
+القادمة. الـ Complication تبدأ على الـ Heart، على 
+
+438
+00:33:33,620 --> 00:34:37,440
+الـ Brain، على الـ Kidney، على الـ Arteries، على
+
+439
+00:34:37,440 --> 00:34:43,300
+الـ Retina، وكما قلنا عن الـ Nervous System، على
+
+440
+00:34:43,300 --> 00:34:49,380
+العيون، ممكن تعملنا مشاكل. وهنتحدث المرة الجاية عن
+
+441
+00:34:49,380 --> 00:34:53,060
+الـ Patient Evaluation Objectives إيش اللي بديها
+
+442
+00:34:53,060 --> 00:34:56,100
+في العلاج؟ لو وين بدأ أوصل في العلاج؟ إيش فايدة
+
+443
+00:34:56,100 --> 00:35:00,380
+العلاج؟ إيش ممكن يحسنلي في وضع البني آدم؟ هنتحدث
+
+444
+00:35:00,380 --> 00:35:05,980
+عن الـ Lifestyle Modification How to do it؟ هنتحدث
+
+445
+00:35:05,980 --> 00:35:13,980
+كمان عن الأدوية، مش هندخل عليها لكن بالصورة هاي تقريبا
+
+446
+00:35:13,980 --> 00:35:20,860
+بنبقى للمرة الجاية إن شاء الله تعالى. خلصنا محاضرة
+
+447
+00:35:20,860 --> 00:35:24,180
+الـ Hypertension واللي هي محاضرة مش طويلة لكن زي
+
+448
+00:35:24,180 --> 00:35:29,060
+ما قلنا يعني ممتدة بين مواضيع كتير من الموضوعات
+
+449
+00:35:29,340 --> 00:35:33,720
+يعني أرجو أنه أكون سهلت عليكم الموضوع قدر الإمكان
+
+450
+00:35:33,720 --> 00:35:38,140
+هحاول أبعتلكوا المادة إن شاء الله تعالى على أساس
+
+451
+00:35:38,140 --> 00:35:41,400
+اللي بده يبدأ يدرس احنا عندنا المادة موجودة على
+
+452
+00:35:41,400 --> 00:35:44,520
+اللي هي الـ PowerPoint هبعتلكوا إياها. لكن المادة 
+
+453
+00:35:44,520 --> 00:35:48,700
+التانية اللي هي في بعض المواضيع أنا هبعتلكوا فيها 
+
+454
+00:35:48,700 --> 00:35:57,140
+ملف Word على أساس إنه تركزوا في الدراسة لهذا 
+
+455
+00:35:57,140 --> 00:36:01,810
+الموضوع من ملف الـ Word كمان. توقعنا على الله إن شاء
+
+456
+00:36:01,810 --> 00:36:06,030
+الله. نهاركوا سعيد وربنا يسر الأمور إن شاء الله
+
+457
+00:36:06,030 --> 00:36:11,250
+وتنسوش فريزة تنسيش تبعتولي بس القائمة بالـ ..
+
+458
+00:36:11,250 --> 00:36:15,650
+بالمجموعات عشان نبدأ نشوف إيش بدنا نسوي. السلام
+
+459
+00:36:15,650 --> 00:36:15,970
+عليكم 
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/EDmMWZTraVE.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/EDmMWZTraVE.srt
new file mode 100644
index 0000000000000000000000000000000000000000..6d3ed04ecb52c556fd3c74164c89f35d9487156e
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/EDmMWZTraVE.srt
@@ -0,0 +1,1683 @@
+1
+00:00:01,500 --> 00:00:03,900
+بسم الله الرحمن الرحيم الحمد لله ورحمة الله وسلام
+
+2
+00:00:03,900 --> 00:00:07,940
+علي سيدنا محمد وسيد المسيحين اليوم هنحدث إن شاء 
+
+3
+00:00:07,940 --> 00:00:11,720
+الله في عضو آخر من أعضاء الجهاز التنفسي اللي هو
+
+4
+00:00:11,720 --> 00:00:16,080
+the liver و هنحكي عن الـ hepatic disorders بقصد هنا
+
+5
+00:00:16,080 --> 00:00:20,020
+طبعا أنا الـ hepatitis طبعا في liver cirrhosis اللي
+
+6
+00:00:20,020 --> 00:00:28,120
+هو عملية التشمع بتاعة الكبد مش هنحكي عنها لكن كثير
+
+7
+00:00:28,120 --> 00:00:31,280
+من الحاجات اللي هنحكيها بتروح على liver cirrhosis
+
+8
+00:00:32,050 --> 00:00:34,930
+الـ Hepatic Disorders اللي هنحكي عنه الآن اللي هو
+
+9
+00:00:34,930 --> 00:00:39,210
+الـ Hepatitis بناخد بالنا جماعة لما نحكي
+
+10
+00:00:39,210 --> 00:00:43,590
+Hepatitis Hepat اللي هو كبد its معناته
+
+11
+00:00:43,590 --> 00:00:47,730
+inflammation و الـ Hepatitis إيه له أسباب كثير
+
+12
+00:00:48,530 --> 00:00:53,890
+أكثرها أو خليني أقول أشهرها في البلاد غير أوروبا
+
+13
+00:00:53,890 --> 00:00:57,890
+وأمريكا اللي هو الـ infection لكن في أوروبا وأمريكا
+
+14
+00:00:57,890 --> 00:01:04,330
+الأسباب أكثرها الـ alcohol هو السبب الأساسي يبقى كمان
+
+15
+00:01:04,330 --> 00:01:07,310
+مرة الـ hepatic disorders hepatitis هنحكي عن
+
+16
+00:01:07,310 --> 00:01:13,130
+hepatitis liver صورة عامة بس هنكي نتحدث حاجة خفيفة 
+
+17
+00:01:14,150 --> 00:01:17,590
+The liver is located in the upper right quadrant of the
+
+18
+00:01:17,590 --> 00:01:20,730
+abdomen وطبعا هذا المكان اتعرفنا عليه قبل هيك
+
+19
+00:01:20,730 --> 00:01:25,510
+وقتاش لما حكينا عن الـ gall bladder صح؟ في الـ right
+
+20
+00:01:25,510 --> 00:01:30,050
+في الـ upper right quadrant أو الـ right upper
+
+21
+00:01:30,050 --> 00:01:34,890
+quadrant الكبد شغلته إيش؟ الكبد خدوا بالكم من أهم
+
+22
+00:01:34,890 --> 00:01:41,940
+الأعضاء في الجسم هو بيعملنا cleaning للـ blood،
+
+23
+00:01:41,940 --> 00:01:45,640
+regulate hormones، helps with blood clotting، اللي
+
+24
+00:01:45,640 --> 00:01:49,640
+عملية التخفة والتجلط، من عنده بتبدأ، هو اللي بيفرز
+
+25
+00:01:49,640 --> 00:01:57,000
+الـ bile، هو اللي بيصنع الـ bile، وهو طبعا أهم
+
+26
+00:01:57,000 --> 00:02:02,200
+صانع لبروتينز، maintaining blood sugar level،
+
+27
+00:02:02,200 --> 00:02:07,860
+وكثير حاجات تانية، مافيش داعي لأذكرها الآن،الـ
+
+28
+00:02:07,860 --> 00:02:12,300
+liver is essential for life بدون liver ما بنقدر
+
+29
+00:02:12,300 --> 00:02:18,660
+نعيش الـ anatomy بتاعة الـ liver زي ما قلنا هو في الـ
+
+30
+00:02:18,660 --> 00:02:23,840
+right upper quadrant في الاتجاه الآخر للمعدة يعني
+
+31
+00:02:23,840 --> 00:02:27,020
+المعدة على جهة هو على جهة وفي تحت منه الـ
+
+32
+00:02:27,020 --> 00:02:31,940
+gallbladder بيطلع من الـ liver
+
+33
+00:02:31,940 --> 00:02:36,580
+زي ما قلنا الـ common bile duct وبيخش لإله الـ
+
+34
+00:02:36,580 --> 00:02:43,520
+portal vein و الـ hepatic artery what is
+
+35
+00:02:43,520 --> 00:02:48,100
+hepatitis؟ hepatitis means inflammation محدش
+
+36
+00:02:48,100 --> 00:02:52,160
+يقوللي infection الـ infection معناته في عندي micro
+
+37
+00:02:52,160 --> 00:02:56,640
+organism هو العملية عمللي inflammation لكن الـ
+
+38
+00:02:56,640 --> 00:02:58,920
+inflammation ممكن يكون هو
+
+39
+00:03:02,320 --> 00:03:06,700
+Inflammation بشيء ثاني غير الفيروس أو البكتيريا أو
+
+40
+00:03:06,700 --> 00:03:10,740
+الـ micro organism ممكن يكون زي ما قلنا نتيجة مشاكل
+
+41
+00:03:10,740 --> 00:03:15,980
+مشاكل هنحكي عن الـ causes بعد شوية زي الـ alcohol عسب
+
+42
+00:03:15,980 --> 00:03:21,430
+المثال يبقى viral hepatitis means there is a
+
+43
+00:03:21,430 --> 00:03:24,390
+specific virus that is causing the liver to
+
+44
+00:03:24,390 --> 00:03:27,950
+inflame طبعا inflammation بياخد كل صفات الـ
+
+45
+00:03:27,950 --> 00:03:33,150
+inflammation swelling or become larger than normal
+
+46
+00:03:33,150 --> 00:03:40,530
+الـ causes of hepatitis reactions
+
+47
+00:03:40,530 --> 00:03:47,760
+to chemical agents drugs and toxins حلو لو أنا في
+
+48
+00:03:47,760 --> 00:03:54,080
+الواحد إيش chemicals agent أو chemical agents إيش
+
+49
+00:03:54,080 --> 00:03:58,380
+drugs إيش toxins ممكن تديني تعملي hepatitis أو
+
+50
+00:03:58,380 --> 00:04:04,480
+autoimmune disease و viruses هذه هي الأسباب الـ
+
+51
+00:04:04,480 --> 00:04:11,350
+viruses Viral Hepatitis دينا Hepatitis A وB وC وD
+
+52
+00:04:11,350 --> 00:04:15,890
+وE على أيامنا بالمناسبة لما أنا درست كان عندنا A
+
+53
+00:04:15,890 --> 00:04:21,970
+وB وفي الآخر في واحد اللي جوا واكتشفوا اللي هو C
+
+54
+00:04:21,970 --> 00:04:26,750
+بس مسموهوش C كانوا يقولوا non A non B لا A ولا B
+
+55
+00:04:26,750 --> 00:04:31,890
+يعني حاجة تانية C ولكن هي مع الوجه الآن صار إنها C
+
+56
+00:04:31,890 --> 00:04:36,870
+وD وE واحتمال في السنوات الجاية يكون في اكتشاف لا
+
+57
+00:04:36,870 --> 00:04:43,610
+في فيروسات تانية الـ Hepatitis A and E الـ A and E
+
+58
+00:04:43,610 --> 00:04:46,590
+بدأ نبدأ يا جماعة من الآن نفرج بين الخمس أنواع
+
+59
+00:04:46,590 --> 00:04:49,610
+لأنه 
+
+60
+00:04:49,610 --> 00:04:55,650
+فعلا بيختلفوا عن بعض الـ A and E الذين يتسببون
+
+61
+00:04:55,650 --> 00:04:59,690
+بالإصابة من الطعام الملوث أو الماء
+
+62
+00:05:02,840 --> 00:05:08,400
+الطريقة تبقى الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+63
+00:05:08,400 --> 00:05:08,860
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+64
+00:05:08,860 --> 00:05:09,500
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+65
+00:05:09,500 --> 00:05:09,700
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+66
+00:05:09,700 --> 00:05:11,040
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+67
+00:05:11,040 --> 00:05:12,900
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+68
+00:05:12,900 --> 00:05:17,220
+الـ الـ الـ الـ الـ الـ
+
+69
+00:05:17,220 --> 00:05:20,480
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+70
+00:05:20,480 --> 00:05:20,940
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+71
+00:05:20,940 --> 00:05:32,780
+الـ الـ الـ الـ الـ الـ الـ الـ الـ 
+
+72
+00:05:32,910 --> 00:05:39,350
+الـ B والـ C والـ D عادةً
+
+73
+00:05:39,350 --> 00:05:42,970
+caused أو typically caused by contact with
+
+74
+00:05:42,970 --> 00:05:48,390
+contaminated blood or blood fluids blood or blood
+
+75
+00:05:48,390 --> 00:05:51,770
+fluids نقصد فيها طبعا أي fluid بيبقى فيها الـ
+
+76
+00:05:51,770 --> 00:05:54,190
+semen أسباب مثال بيبقى فيها الـ blood
+
+77
+00:06:01,840 --> 00:06:05,420
+يبقى هذه عملية الانتقال تبعتهم A وB وC وD وE
+
+78
+00:06:05,420 --> 00:06:08,700
+بالخصوص
+
+79
+00:06:08,700 --> 00:06:14,180
+الـ Hepatitis type B وC بيوصلوني إلى chronic
+
+80
+00:06:14,180 --> 00:06:21,060
+disease في مئات الملايين من الناس وهم the most
+
+81
+00:06:21,060 --> 00:06:24,840
+common cause of liver cirrhosis and cancer مع بعض
+
+82
+00:06:24,840 --> 00:06:26,160
+التانين مع بعض الـB وC
+
+83
+00:06:36,270 --> 00:06:40,410
+يبقى الـ POC كمان مرة، lead to chronic disease in
+
+84
+00:06:40,410 --> 00:06:44,910
+hundreds of millions of people and together are
+
+85
+00:06:44,910 --> 00:06:48,250
+the most common cause of liver cirrhosis and
+
+86
+00:06:48,250 --> 00:06:54,670
+cancer واحد مليون die each year from causes
+
+87
+00:06:54,670 --> 00:07:00,430
+related to viral hepatitis الآن كمان مرة الـ type
+
+88
+00:07:00,430 --> 00:07:05,310
+of hepatitis A و B و C و D الآن الـ source of virus
+
+89
+00:07:05,310 --> 00:07:10,510
+الـ A قلنا و الـ E الـ faces البراز فيكو oral بينتقل من
+
+90
+00:07:10,510 --> 00:07:15,350
+الـ faces البراز إلى الـ oral و B و C و D عن طريق
+
+91
+00:07:15,350 --> 00:07:22,540
+الـ blood و الـ blood derived و الـ body fluids الـ
+
+92
+00:07:22,540 --> 00:07:27,640
+Root of Transmission A فيكو أورال مش Orophical
+
+93
+00:07:27,640 --> 00:07:32,620
+فيكو أورال والـ A فيكو أورال لكن الـ B و الـ C و
+
+94
+00:07:32,620 --> 00:07:38,700
+الـ D عادة عن طريق الـ Mucosa Percutaneous ميوكوزا
+
+95
+00:07:43,720 --> 00:07:48,180
+chronic infection الـ E والـ E الـ A والـ E مفيش
+
+96
+00:07:48,180 --> 00:07:52,060
+chronic infection لكن الـ B والـ C والـ D نعم الـ
+
+97
+00:07:52,060 --> 00:07:55,200
+prevention وهذا طبعا مهم بالنسبة لنا الـ prevention
+
+98
+00:07:55,200 --> 00:08:00,620
+أنه الـ A حاجة منقول عنها pre and post exposure
+
+99
+00:08:00,620 --> 00:08:08,140
+immunization فيه لقاحات طيب الـ B برضه فيه لقاحات
+
+100
+00:08:08,140 --> 00:08:11,560
+طيب C
+
+101
+00:08:12,980 --> 00:08:18,280
+مافيش له تطعيم الـD له قصة تانية، هنحكيها بعد
+
+102
+00:08:18,280 --> 00:08:23,520
+شوية هو له تطعيم بس من خلال تطعيم الـB والـE
+
+103
+00:08:23,520 --> 00:08:26,360
+مالوش تطعيم، يبقى اللي ما لهم مش أكيد تطعيم الـC
+
+104
+00:08:26,360 --> 00:08:33,490
+والـE الـA والـB والـD اللي هم تطعيملكن الـ D مش
+
+105
+00:08:33,490 --> 00:08:37,450
+تطعيم خصوصي بيه، إنما أنا من خلال تطعيمي للـ B
+
+106
+00:08:37,450 --> 00:08:43,110
+بأثر على الـ D بالصورة هذه، هنحكي الآن عن كل واحد،
+
+107
+00:08:43,110 --> 00:08:46,270
+إيش 
+
+108
+00:08:46,270 --> 00:08:48,330
+الـ signs و الـ symptoms اللي بنشوفها في الناس اللي
+
+109
+00:08:48,330 --> 00:08:56,490
+عندهم Hepatitis، بيبقوا tired، nausea، muscle or
+
+110
+00:08:56,490 --> 00:08:59,810
+joint pain، ملاحظين أن هذه الحاجات اللي بنسمعها في
+
+111
+00:08:59,810 --> 00:09:03,910
+كثير من الـ viral infection Trouble sleeping Loss of
+
+112
+00:09:03,910 --> 00:09:10,990
+appetite Light stools Weight loss Abdominal pain
+
+113
+00:09:10,990 --> 00:09:16,530
+Itchiness من الصفار بيصير في حكة Depression Dark
+
+114
+00:09:16,530 --> 00:09:22,250
+urine والبول بيبقى غامق والبراز بيبقى فاتح 
+
+115
+00:09:26,760 --> 00:09:31,340
+من أهم الـ symptoms اللي احنا بنشوفها اللي هو
+
+116
+00:09:31,340 --> 00:09:35,600
+jaundice الـ jaundice يعني اصفرار yellowing of skin
+
+117
+00:09:35,600 --> 00:09:43,370
+or eyes طبعا or and eyes ممكن Skin or Eyes
+
+118
+00:09:43,370 --> 00:09:50,270
+Yellowing بيسمي إيش jaundice وإيش كمعاملة الـ
+
+119
+00:09:50,270 --> 00:09:52,730
+Symptoms؟ بتلاقي في عنده Pale Stool اللي قلنا قبل
+
+120
+00:09:52,730 --> 00:09:56,390
+شوية عنه Light Stool بتلاقي إنه البراز إذا فاكرين
+
+121
+00:09:56,390 --> 00:09:59,910
+المرة اللي فات تحدتنا بيبقى شكله زي طحينة بيضة
+
+122
+00:09:59,910 --> 00:10:07,420
+Pale Pale الـ Hepatitis A من أهم الأنواع الـ
+
+123
+00:10:07,420 --> 00:10:12,080
+Hepatitis واللي هو معظمنا عملها، أخدها، وإحنا
+
+124
+00:10:12,080 --> 00:10:15,560
+صغار، لأنه هو الـ Hepatitis اللي بنقول عنه اللي هو
+
+125
+00:10:15,560 --> 00:10:20,740
+التهاب الكبد الوبائي، الـA بالذات، التهاب الكبد
+
+126
+00:10:20,740 --> 00:10:24,740
+الوبائي هو طبعا الكلمة كبيرة، لكن هو الأمر أسهل
+
+127
+00:10:24,740 --> 00:10:27,460
+وكافي، بيصير في الأطفال الـ Hepatitis A، ممكن يكون
+
+128
+00:10:27,460 --> 00:10:32,040
+في الأكبر، لكن هو is a pediatric is a child
+
+129
+00:10:32,040 --> 00:10:38,610
+disease معظمنا أخدوا وعدّى عليه يوم أو يومين وكأنه
+
+130
+00:10:38,610 --> 00:10:42,590
+انفلونزا وكأنه رشح وكأنه كذا شوية صفار وانتهت
+
+131
+00:10:42,590 --> 00:10:48,790
+الأمور هنحكي في الفيروسات الآن أنه لكل فيروس فيه
+
+132
+00:10:48,790 --> 00:10:49,770
+إيقاع
+
+133
+00:10:52,300 --> 00:10:57,680
+الـ Incubation Period بنتفق أنه أنه أنا هحكي مش
+
+134
+00:10:57,680 --> 00:11:01,800
+Range هحكي Average عشان أسهل لإلكوا وانتوا خدوا 
+
+135
+00:11:01,800 --> 00:11:06,160
+بالكم الـ Average الـ Incubation اللي هو الفترة
+
+136
+00:11:06,160 --> 00:11:11,740
+التي تمر بينما أنه الطفل ياخد العدوى وبينما تظهر
+
+137
+00:11:11,740 --> 00:11:20,790
+الأعراض حوالي 30 يوم الـ Age Group اللي أقل من 6
+
+138
+00:11:20,790 --> 00:11:28,490
+سنين بتصير معاهم أقل من 10% 6 إلى 14 سنة ربعها لـ
+
+139
+00:11:28,490 --> 00:11:33,370
+50% أكثر من 14 سنة بيصير عندهم Jaundice يعني الآن
+
+140
+00:11:33,370 --> 00:11:41,430
+هنلاقي أنه اللي أقل من 6 سنين يعني عملياً أقل من 
+
+141
+00:11:41,430 --> 00:11:44,690
+10% من الأطفال أقل من 6 سنين بيصير معاهم Jaundice
+
+142
+00:11:44,690 --> 00:11:49,580
+يعني كتير منهم بمر عليه بياخد الفيروس بدون ما يصير
+
+143
+00:11:49,580 --> 00:11:55,540
+عنده Jaundice كل ما كبر الواحد كل ما الصفار بيّن
+
+144
+00:11:55,540 --> 00:11:58,600
+عنده يعني الناس اللي بين ست سنين و أربع عشرة سنة في
+
+145
+00:11:58,600 --> 00:12:02,160
+العمر لأربعين لخمسين في المية منهم يعني من كل
+
+146
+00:12:02,160 --> 00:12:05,700
+اثنين واحد بيبين عنده صفار قولنا الأقل من ست سنين
+
+147
+00:12:05,700 --> 00:12:08,580
+تقريبا معظمهم بيبينش يعني أقل من عشر في المية
+
+148
+00:12:08,580 --> 00:12:11,980
+بيبين عندهم صفار لأن فوق أربع عشرة في المية
+
+149
+00:12:11,980 --> 00:12:19,030
+أربع عشرة سنة الأكبار لو صار عنده Hepatitis A 70 لـ
+
+150
+00:12:19,030 --> 00:12:26,450
+80% بيبين عنده صفار أمراض الأطفال يا جماعة اللي هي
+
+151
+00:12:26,450 --> 00:12:30,590
+specific للأطفال لو صارت عند الكبار تتعبهم جدا في
+
+152
+00:12:30,590 --> 00:12:35,130
+حين أن الطفل ما بتعبش منها كتير لكن الكبار بتعبوا
+
+153
+00:12:35,130 --> 00:12:37,510
+منها جدا وهذا اللي بنلاحظه الآن على سبيل المثال في
+
+154
+00:12:37,510 --> 00:12:41,230
+الكورونا أن الأطفال ما بتعب من فيروس الكورونا كتير
+
+155
+00:12:41,230 --> 00:12:45,900
+Okay في مجموعة لكن الغالب Hepatitis نفس الكلام
+
+156
+00:12:45,900 --> 00:12:49,740
+فيها لـ Chickenpox اللي هو الجدري الماء برضه إذا 
+
+157
+00:12:49,740 --> 00:12:53,840
+أخذوها طفولة الواحد وهو طفل ولا في مشاكل لكن إذا 
+
+158
+00:12:53,840 --> 00:12:57,520
+هو كبير أخذه بيتعب ممكن يحتاج مستشفيات كمان، نوع 
+
+159
+00:12:57,520 --> 00:13:02,380
+مستشفي أهم Complication للـ Hepatitis A اللي هو
+
+160
+00:13:02,380 --> 00:13:05,400
+الـ Fulminating Hepatitis إيش يعني Fulminating؟ ده
+
+161
+00:13:05,400 --> 00:13:10,840
+اللي يصير إن التهاب حاد شديد للكبد وطبعا ممكن
+
+162
+00:13:10,840 --> 00:13:17,490
+يروح فيها الواحد ولكن هذا Complication أو Relapsing
+
+163
+00:13:17,490 --> 00:13:22,670
+Hepatitis يعني ممكن اللي أجاله Hepatitis A يجيله
+
+164
+00:13:22,670 --> 00:13:28,890
+كمان مرة نعم لكن بالنسبة قليلة بالنسبة قليلة والـ
+
+165
+00:13:28,890 --> 00:13:32,370
+Hepatitis A عمره ما بيصير Chronic عمره ما بيصير Chronic
+
+166
+00:13:32,370 --> 00:13:36,550
+يبقى احنا الآن حكينا مجموعة حقائق عن الـ Hepatitis
+
+167
+00:13:36,550 --> 00:13:44,220
+A بداية من طريقة العدوى قلنا فيكوا Oral قلنا إن الـ
+
+168
+00:13:44,220 --> 00:13:48,240
+Incubation تبعه حوالي ثلاثين يوم الناس كل ما كبر
+
+169
+00:13:48,240 --> 00:13:51,660
+الواحد الـ Jaundice بيبين عنده أكثر وقلنا النسب الـ
+
+170
+00:13:51,660 --> 00:13:54,960
+Complications of Fulminant Hepatitis و Relapsing
+
+171
+00:13:54,960 --> 00:13:58,180
+Hepatitis الـ Relapsing يعني برضه بيجي و الـ No
+
+172
+00:13:58,180 --> 00:14:05,960
+Chronic Sequelae طيب
+
+173
+00:14:05,960 --> 00:14:09,770
+هو ممكن ينتقل عن طريق الدم؟ نعم لكن نادر كتير كتير
+
+174
+00:14:09,770 --> 00:14:14,700
+كتير كتير هو بينتقل عادة Close Personal Contact زي
+
+175
+00:14:14,700 --> 00:14:20,640
+الروضات والحضانات وقلنا كمان أنه بينتقل عن طريق الـ
+
+176
+00:14:20,640 --> 00:14:24,860
+Contaminated Food و الـ Water الناس البائعين
+
+177
+00:14:24,860 --> 00:14:29,240
+الجوالين الناس اللي بتبيع وبتحافظش بتحافظش على 
+
+178
+00:14:29,240 --> 00:14:32,880
+الناس اللي بيأكلوا السمك نهي الناس البائعين
+
+179
+00:14:32,880 --> 00:14:40,360
+الجوالين اللي على الكارات اللي يعني عمليا نسبة
+
+180
+00:14:40,360 --> 00:14:45,660
+النظافة بتبقى عندهم Zero طبعا هدول واحد بيخاف منهم
+
+181
+00:14:45,660 --> 00:14:48,480
+أنهم يعملوا و Blood Exposure in Very Rare
+
+182
+00:14:48,480 --> 00:14:52,680
+Transmission
+
+183
+00:14:52,680 --> 00:14:59,060
+الـ Hepatitis B هو طبعا مختلف لأنه احنا قلنا الـ
+
+184
+00:14:59,060 --> 00:15:02,940
+Hepatitis B بينتقل عن طريق Blood و Blood Products و
+
+185
+00:15:02,940 --> 00:15:07,340
+عن طريق Fluids of the Body الـ Incubation تبعه
+
+186
+00:15:07,340 --> 00:15:12,980
+حوالي من شهر لثلاثة شهر الـ Average نحكي عن الـ
+
+187
+00:15:12,980 --> 00:15:19,440
+Average الـ Clinical Illness بالنسبة
+
+188
+00:15:19,440 --> 00:15:25,180
+للصفار أقل من 5 سنين أقل من 10% لكن 5 سنين وفوق من
+
+189
+00:15:25,180 --> 00:15:30,960
+30 لـ 50% يعني النص يبين عندهم صفار يعني ممكن واحد
+
+190
+00:15:30,960 --> 00:15:35,520
+ياخد عدوى Hepatitis وما يبينش عنده أه ممكن طبعا
+
+191
+00:15:36,190 --> 00:15:39,870
+الخطر هو أن يجاله من خمس سنين ثلاثين لتسعين في
+
+192
+00:15:39,870 --> 00:15:44,830
+المائة بيصير عندهم Chronicity لكن خمس سنين وفوق
+
+193
+00:15:44,830 --> 00:15:47,970
+من اثنين لعشرة في المائة بيصير عندهم Chronicity
+
+194
+00:15:47,970 --> 00:15:52,130
+وممكن طبعا الواحد لأنه احنا قلنا بيصير Chronic
+
+195
+00:15:52,130 --> 00:15:55,790
+Disease من خمسة عشر لخمسة وعشرين في المائة ممكن
+
+196
+00:15:55,790 --> 00:15:59,010
+يموتوا Premature Mortality من Chronic Liver
+
+197
+00:15:59,010 --> 00:16:05,770
+Disease الـ Hepatitis B إيه بعض الحاجات اللي لازم 
+
+198
+00:16:05,770 --> 00:16:09,250
+ننتبه عليها اللي هو الـ Transmission Mode of
+
+199
+00:16:09,250 --> 00:16:18,910
+Hepatitis B أول حاجة اللي هو الـ Perinatal لأن
+
+200
+00:16:18,910 --> 00:16:23,410
+في عندنا الـ Perinatal Transmission بينتقل الـ
+
+201
+00:16:23,410 --> 00:16:30,870
+«فيروس» من الأم الحامل للطفل 90% من الأطفال 
+
+202
+00:16:30,870 --> 00:16:34,870
+المصابين بيصبحوا مصابين بشكل كرونيكي
+
+203
+00:16:34,870 --> 00:16:37,890
+والأُمّ
+
+204
+00:16:37,890 --> 00:16:41,790
+اللي مصابة بشكل كرونيكي هي أكثر ممكن تتعامل مع
+
+205
+00:16:41,790 --> 00:16:47,870
+أطفالها للطفل ليش؟ لأن هو بياخد الدم يعني عن طريق
+
+206
+00:16:47,870 --> 00:16:48,210
+الـ 
+
+207
+00:16:50,900 --> 00:16:54,580
+بياخد الدم، بياخد عن طريق الدم، طبيعي، وفيه طبعا
+
+208
+00:16:54,580 --> 00:16:59,880
+الـ Sexual كمان غير طبعا عن طريق الدم، هذه طريقة
+
+209
+00:16:59,880 --> 00:17:02,940
+Modes of Transmission of Hepatitis B الـ Sex
+
+210
+00:17:02,940 --> 00:17:07,900
+Worker and Homosexuals are Particular at Risk زي
+
+211
+00:17:07,900 --> 00:17:14,840
+الـ HIV نفس الكلام بينتقل اللي هو الـ Hepatitis
+
+212
+00:17:14,840 --> 00:17:16,000
+عن طريق
+
+213
+00:17:20,010 --> 00:17:26,370
+عن طريق اللي هو الـ Sexual Contacts طبعا سواء كانت
+
+214
+00:17:26,370 --> 00:17:30,150
+في إطار القانون أو في إطار خارج القانون الـ Health
+
+215
+00:17:30,150 --> 00:17:32,810
+Care Worker ممكن ينتقل لهم Child to Child ممكن
+
+216
+00:17:32,810 --> 00:17:36,710
+ينتقل لهم زي ما قلنا الـ Contaminated Needles الناس 
+
+217
+00:17:36,710 --> 00:17:42,070
+اللي بتاخد مخدرات وبياخدوا Needles من بعض هدول 
+
+218
+00:17:42,070 --> 00:17:46,130
+كمان ممكن ينتقل لهم الـ Blood Transfusion عشان هيك هذا 
+
+219
+00:17:46,130 --> 00:17:48,650
+بنقول عنه «Horizontal Transmission» اللي هو الـ
+
+220
+00:17:48,650 --> 00:17:52,370
+«Host to Other» «Recipient» لكن من الـ «Mother»
+
+221
+00:17:52,370 --> 00:17:57,170
+للـ «Infant» بنقول عنه «Perinatal» أو «Vertical»
+
+222
+00:17:57,170 --> 00:18:01,730
+Transmission عشان أشخص أنا الـ Hepatitis B في
+
+223
+00:18:01,730 --> 00:18:06,610
+مجموعة من الـ «Serological Tests» بتنعمل مش لعيلة
+
+224
+00:18:06,610 --> 00:18:11,550
+ذكرى أو متابعتها لأن هذه حاجة تقصصية للـ «Acute»
+
+225
+00:18:11,550 --> 00:18:14,070
+والـ «Chronic» Hepatitis B طب كيف بنعالج الـ
+
+226
+00:18:14,070 --> 00:18:14,750
+Hepatitis؟
+
+227
+00:18:18,540 --> 00:18:22,720
+بالـ Interferon من 30 لـ 40% الـ Response Rate يعني
+
+228
+00:18:22,720 --> 00:18:25,720
+ضعيف عمليا مش كتير Successful Response to
+
+229
+00:18:25,720 --> 00:18:29,280
+Treatment و Result in the Disappearance of 
+
+230
+00:18:29,280 --> 00:18:34,200
+Hepatitis B Antigen المهم حقيقة في موضوعنا في الـ
+
+231
+00:18:34,200 --> 00:18:37,400
+Hepatitis B هو الـ Prevention وركزوا في موضوع الـ
+
+232
+00:18:37,400 --> 00:18:39,920
+Hepatitis مش على الـ Treatment على الـ Prevention
+
+233
+00:18:39,920 --> 00:18:47,340
+Vaccination وطبعا هذا الكل بياخده في برنامج
+
+234
+00:18:47,340 --> 00:18:51,800
+التطعيمات العالمي ودي موجود عندنا في القطاع من
+
+235
+00:18:51,800 --> 00:18:56,340
+واحد وهو طفل بياخده Highly Effective Recombinant 
+
+236
+00:18:56,340 --> 00:19:00,780
+Vaccine are Now Available Vaccine can be Given to
+
+237
+00:19:00,780 --> 00:19:04,100
+Those who are at Increased Risk of Hepatitis B 
+
+238
+00:19:04,100 --> 00:19:07,460
+Virus Infection زي الـ Health Care Worker يعني لو
+
+239
+00:19:07,460 --> 00:19:11,030
+واحد بده يروح يتوظف في الحكومة بيعملوله بيشوف الـ
+
+240
+00:19:11,030 --> 00:19:13,110
+Antibody عنده لو لقوا عنده عنده مشكلة في الـ
+
+241
+00:19:13,110 --> 00:19:16,450
+Antibodies بيطعموه كمان بيعملوله Vaccination It is
+
+242
+00:19:16,450 --> 00:19:20,270
+Also Given Routinely to Neonates as a Universal
+
+243
+00:19:20,270 --> 00:19:24,710
+Vaccination in Many Countries Hepatitis B طيب واحد
+
+244
+00:19:24,710 --> 00:19:28,710
+الآن ولد وأمه عنده Hepatitis B بينعطى
+
+245
+00:19:32,690 --> 00:19:39,090
+اللي هو Hemoglobin بـ Hepatitis B Immunoglobulin
+
+246
+00:19:39,480 --> 00:19:42,760
+ممكن يتم استخدامها لحماية الأشخاص اللي اتعرضوا لـ
+
+247
+00:19:42,760 --> 00:19:50,360
+Hepatitis B وزي ما قلنا أنها تحدث في 48
+
+248
+00:19:50,360 --> 00:19:54,280
+ساعة من الحادثة هنا طبعا بنحكي احنا الفرق بين
+
+249
+00:19:54,280 --> 00:19:58,080
+اللقاح والـ Muscle الـ Vaccination هو اللقاح الـ
+
+250
+00:19:58,080 --> 00:20:01,500
+Muscle اللي هو الـ Immunoglobulin اللي بنعطيه الآن 
+
+251
+00:20:01,500 --> 00:20:05,300
+على أساس أنه يدينا Effect الـ Vaccination بياخد وقت 
+
+252
+00:20:05,300 --> 00:20:09,950
+عبارة عن ما بيجيبولكن الـ Muscle بيساعد على طول في
+
+253
+00:20:09,950 --> 00:20:16,170
+أنه يدينا يكون Efficient It may Also be Given to
+
+254
+00:20:16,170 --> 00:20:20,650
+Neonate who are at Increased Risk of Contracting
+
+255
+00:20:20,650 --> 00:20:24,970
+Hepatitis B ممكن يكون آخر إجراءات أخرى Screening of
+
+256
+00:20:24,970 --> 00:20:29,490
+Blood Donors Blood and Blood Fluid Precautions 
+
+257
+00:20:29,490 --> 00:20:30,850
+طبعا
+
+258
+00:20:33,380 --> 00:20:37,940
+في العلاقات على سبيل المثال سواء الزوجية أو غير 
+
+259
+00:20:37,940 --> 00:20:40,620
+الزوجية على أساس أنه بينتقل كمان Sexual من واحد
+
+260
+00:20:40,620 --> 00:20:46,240
+Positive لواحد مش Positive أو للطرف الآخر مش لابد 
+
+261
+00:20:46,240 --> 00:20:51,320
+من أخذ سبل الوقاية في هذا الموضوع نقل الدم في
+
+262
+00:20:51,320 --> 00:20:54,640
+المستشفيات يتم الانتباه لهذا الموضوع بنفحص الدم
+
+263
+00:20:54,640 --> 00:21:01,320
+المتبرع على Hepatitis B مش بس على Hepatitis C كمان
+
+264
+00:21:01,320 --> 00:21:07,450
+و بنفحص على الـ HIV اللي هو الـ AIDS وهذا بنجيلنا
+
+265
+00:21:07,450 --> 00:21:11,490
+لموضوع الـ Hepatitis C هو طبعا الـ Hepatitis C بدأ
+
+266
+00:21:11,490 --> 00:21:15,250
+ينتشر بصورة مهولة خاصة في دول زي جيراننا في مصر
+
+267
+00:21:15,250 --> 00:21:19,030
+الـ Incubation Period الـ Average ستة لسبع أسابيع
+
+268
+00:21:20,360 --> 00:21:24,080
+احفظوا الـ Average يا جماعة الـ Jaundice 30% لـ 40
+
+269
+00:21:24,080 --> 00:21:28,160
+% ممكن تشوفوا عند الناس اللي بيصير معهم يعني مش كل 
+
+270
+00:21:28,160 --> 00:21:30,660
+واحد بيصير عنده Hepatitis بيصير عنده Jaundice
+
+271
+00:21:30,660 --> 00:21:35,600
+Chronicity كبيرة 70% Persistent Infection بيظل
+
+272
+00:21:35,600 --> 00:21:40,760
+الفيروس موجود في الكبد والـ Immunity ما فيش أنه 
+
+273
+00:21:40,760 --> 00:21:46,420
+Protective Antibody Response Identified لحد ما تلقاه
+
+274
+00:21:46,420 --> 00:21:51,480
+ما فيش حد يطيب لإله الـ Hepatitis C تأثير على كل شخص 
+
+275
+00:21:51,480 --> 00:21:54,920
+بشكل مختلف في الآخر ما صار المرض عند كل واحد مختلف
+
+276
+00:21:54,920 --> 00:21:57,620
+لا يوجد مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+277
+00:21:57,620 --> 00:21:57,680
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+278
+00:21:57,680 --> 00:22:00,440
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+279
+00:22:00,440 --> 00:22:02,340
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+280
+00:22:02,340 --> 00:22:03,900
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر مصادر 
+
+281
+00:22:03,900 --> 00:22:18,080
+مصادر مصادر مصادر مصادر مصادر مصادر مصادر
+
+282
+00:22:19,720 --> 00:22:23,440
+إنه لما يصير عندي acute infection بالـ Hepatitis
+
+283
+00:22:23,440 --> 00:22:26,720
+C، only 20% will show symptoms initially، زي ما 
+
+284
+00:22:26,720 --> 00:22:30,740
+اتفرجنا، يعني مش بالضرورة كله يبين لي أي symptoms،
+
+285
+00:22:30,740 --> 00:22:33,860
+وبدخل في إيش؟ في chronicity، شايفين احنا الـ curve؟
+
+286
+00:22:33,860 --> 00:22:37,060
+بدخل في chronic infection، بعد الـ chronic الجسم 
+
+287
+00:22:37,060 --> 00:22:42,880
+بتغلب في 20% على الفيروس، لكن في عندنا 80% بيظلوا 
+
+288
+00:22:42,880 --> 00:22:47,990
+موجودين، في الكبد وبيعملوا لنا liver damage وبعدين
+
+289
+00:22:47,990 --> 00:22:51,950
+بدخلوا في chronicity زي ما حكينا chronic hepatitis
+
+290
+00:22:51,950 --> 00:22:56,430
+وبعدين 20% لـ 30% منهم بدخلوا على liver cirrhosis
+
+291
+00:22:56,430 --> 00:23:02,830
+وفي منهم بيصير عنده liver cancer من 1% لـ 4% لكل سنة
+
+292
+00:23:02,830 --> 00:23:05,750
+most symptoms begin to show only when the liver is
+
+293
+00:23:05,750 --> 00:23:08,850
+more severely damaged يعني لما تبدأ تبين الـ
+
+294
+00:23:08,850 --> 00:23:14,180
+symptoms عادة بيبقى في عندنا مشكلة كبيرة فيه، هنا مشكلة 
+
+295
+00:23:14,180 --> 00:23:21,280
+كبيرة في الكبد، Risk
+
+296
+00:23:21,280 --> 00:23:24,720
+factors associated with transmission of hepatitis
+
+297
+00:23:24,720 --> 00:23:31,270
+C virus زي ما قلنا، Transfusion أو transplant من 
+
+298
+00:23:31,270 --> 00:23:36,010
+واحد infected donor أو استخدام نفس الـ lineات نفس
+
+299
+00:23:36,010 --> 00:23:40,350
+الـ canulas من واحد معدي عنده hepatitis C لواحد ما 
+
+300
+00:23:40,350 --> 00:23:44,230
+عندهوش، injecting drug use الناس اللي بيعملوا
+
+301
+00:23:44,230 --> 00:23:49,160
+غسيل كده، accidental injury with needle or sharps
+
+302
+00:23:49,160 --> 00:23:53,540
+الإبار وكذا في المستشفيات، sexual أو household
+
+303
+00:23:53,540 --> 00:23:57,360
+exposure to antihepatitis C virus positive
+
+304
+00:23:57,360 --> 00:24:03,860
+contacts، multiple sexual partners فاهمين، birth to
+
+305
+00:24:03,860 --> 00:24:08,480
+hepatitis C virus infected mothers كمان، وطبعا
+
+306
+00:24:08,480 --> 00:24:13,760
+التشخيص بيحصل من خلال surgical tests، treatment
+
+307
+00:24:16,820 --> 00:24:24,580
+الـ interferon و الـ ribavirin، يعني ممكن لوحدها الـ «انترفيرون»
+
+308
+00:24:24,580 --> 00:24:30,760
+تدينا نسبة 50% response مع الـ«ريبافيرين» تتحسن
+
+309
+00:24:30,760 --> 00:24:34,880
+النسبة، المهم كمان مرة مش العلاج، okay بنعرف إن
+
+310
+00:24:34,880 --> 00:24:40,840
+الـ«ريبافيرين» و«انترفيرون» كويسين لكن أهم حاجة 
+
+311
+00:24:40,840 --> 00:24:44,620
+لـ prevention، screening of blood، organ and tissue
+
+312
+00:24:44,620 --> 00:24:48,340
+donors، high risk behavior modification، blood and
+
+313
+00:24:48,340 --> 00:24:52,060
+body fluid precautions، طبعا لازم نبقى فاهمين بعض 
+
+314
+00:24:52,060 --> 00:24:55,700
+الحاجات إن الـ Hepatitis C لا تتم تفريغها 
+
+315
+00:24:55,700 --> 00:25:02,580
+بـ hugging، kissing اللي هو الـ Casual Contacts،
+
+316
+00:25:02,580 --> 00:25:07,020
+الـ hugging، يعني الحضن، sharing, eating, utensils،
+
+317
+00:25:07,580 --> 00:25:13,520
+drinking, glasses، العطس، scuffing، shaking hands،
+
+318
+00:25:13,520 --> 00:25:17,140
+sitting on a toilet seat، يعني هذه ما بتعمل عملية
+
+319
+00:25:17,140 --> 00:25:24,080
+نقل للفيروس، الآن زي ما عرفنا الـ Current Vaccine
+
+320
+00:25:24,080 --> 00:25:27,440
+حكيناها احنا قبل شوي، قولنا الـ Hepatitis A والـ B
+
+321
+00:25:27,440 --> 00:25:35,540
+والـ C في اللهم تطعيم عفواً الـ A والـ B والـ D
+
+322
+00:25:35,540 --> 00:25:38,780
+اللهم تطعيم الـ D، indirect حنحكي بعد شوي، والـ C
+
+323
+00:25:38,780 --> 00:25:43,720
+مالوش طبعا للأسف، الـ Hepatitis D بنقول عنه Delta
+
+324
+00:25:43,720 --> 00:25:49,780
+Virus هو عبارة عن بيجي إما كـ Co-infection، severe 
+
+325
+00:25:49,780 --> 00:25:53,560
+acute disease، low risk of chronic infection أو 
+
+326
+00:25:53,560 --> 00:25:58,120
+super infection، يعني إما بيجي مع الـ B مع بعض أو 
+
+327
+00:25:58,990 --> 00:26:02,370
+بيجي، usually develop chronic hepatitis D virus
+
+328
+00:26:02,370 --> 00:26:05,690
+infection، high risk to severe chronic liver
+
+329
+00:26:05,690 --> 00:26:09,870
+disease may present as an acute hepatitis، بيجي بعد
+
+330
+00:26:09,870 --> 00:26:13,750
+الـ B ما ييجي يعني مش بيجي مع الـ B بيجي بعد الـ B
+
+331
+00:26:17,420 --> 00:26:21,460
+وطبعاً ممكن ييجي عن طريق الـ Percutaneous Exposure
+
+332
+00:26:21,460 --> 00:26:24,880
+زي الـ Injecting Drug Use أو عن طريق الـ Per
+
+333
+00:26:24,880 --> 00:26:29,380
+-Mucosal Exposure اللي هو الـ Sexual Contacts
+
+334
+00:26:29,380 --> 00:26:36,910
+Prevention الـ Hepatitis B Virus مع الـ Hepatitis D
+
+335
+00:26:36,910 --> 00:26:40,650
+Virus Co-infection لما يجوا مع بعض بينفعنا مين لـ 
+
+336
+00:26:40,650 --> 00:26:44,730
+Pre- أو Post-Exposure Prophylaxis لتمنع الـ
+
+337
+00:26:44,730 --> 00:26:53,230
+Hepatitis B Virus، لكن لما يكون Super Infection
+
+338
+00:26:53,230 --> 00:27:01,240
+بصراحة بفتش كتير التطعيم، ليش؟ لأنه هو بيجي بعد الـ B،
+
+339
+00:27:01,240 --> 00:27:05,080
+يعني صار في عندنا التهاب B فبينفجر الـ Education to
+
+340
+00:27:05,080 --> 00:27:08,500
+reduce risk behavior among persons with chronic
+
+341
+00:27:08,500 --> 00:27:12,980
+hepatitis B virus، ما هيفيد التطعيم في الأحوال 
+
+342
+00:27:12,980 --> 00:27:16,880
+زي كده، بقى التطعيم بيجي في الـ Hepatitis D لما
+
+343
+00:27:16,880 --> 00:27:20,840
+بيستفيد منه مريض الـ Hepatitis D لما يكون Co
+
+344
+00:27:20,840 --> 00:27:25,640
+-infection، يعني Co معاه جاي، مش Super، Super يعني 
+
+345
+00:27:25,640 --> 00:27:30,170
+موجود الـ Hepatitis B وأجعله الـ D فوق منه
+
+346
+00:27:30,170 --> 00:27:33,710
+الـ Hepatitis E قولنا هو عبارة عن الـ Average تبعه 
+
+347
+00:27:33,710 --> 00:27:37,870
+حوالي 40 Day والـ Case
+
+348
+00:27:37,870 --> 00:27:42,250
+Fatality Rate حوالي 1% لـ 3%، طبعا pregnant woman
+
+349
+00:27:42,250 --> 00:27:47,710
+بالذات إن السيفيريتي increased with age وإنّه ما فيش 
+
+350
+00:27:47,710 --> 00:27:53,310
+Chronic Sequel في العادة، وهذا بنلاقي عادة في
+
+351
+00:27:53,310 --> 00:27:57,940
+الـ Fecally Contaminated Drinking Water المجاري 
+
+352
+00:27:57,940 --> 00:28:03,960
+بتطف على المية العادية، Prevention تبع الـ E هو زي 
+
+353
+00:28:03,960 --> 00:28:09,280
+ما قلنا، Avoid drinking water، uncooked
+
+354
+00:28:09,280 --> 00:28:12,720
+shell-filled fish، uncooked fruits and vegetables
+
+355
+00:28:12,720 --> 00:28:19,760
+not peeled or prepared by travelers، وممكن ياخد
+
+356
+00:28:19,760 --> 00:28:25,260
+الواحد immunoglobulin بس 
+
+357
+00:28:25,260 --> 00:28:31,030
+يعني في الآخر ما يفيدش كتير للتطبيق، الـ Diagnostic
+
+358
+00:28:31,030 --> 00:28:33,950
+طبعا كل الـ Hepatitis أنا بعمل حاجة اسمها
+
+359
+00:28:33,950 --> 00:28:40,310
+بالفحوصات «Liver Function Test»، «Alkaline 
+
+360
+00:28:40,310 --> 00:28:43,430
+Phosphatase»، «Serum Bilirubin»، «Liver Biopsy»
+
+361
+00:28:43,430 --> 00:28:47,210
+«Antigen Specific»، «Specific»، حقيقة يعني ما ملزمكوش
+
+362
+00:28:47,210 --> 00:28:50,590
+كتير الموضوع هذا، لكن اللي ملزمنا أكثر الـ
+
+363
+00:28:50,590 --> 00:28:55,410
+Prevention و Treatment، الـ «Treatment Diet»، «High
+
+364
+00:28:55,410 --> 00:28:58,590
+Calories Protein Low Fat» على أساس أريح الكبد
+
+365
+00:29:00,270 --> 00:29:06,530
+الفيتامين زي الـ B و الـ K، الـ Stop Alcohol، Drugs 
+
+366
+00:29:06,530 --> 00:29:11,770
+الفيتامين B و K يا جماعة هما بنقول عنهم الـ Fat Soluble
+
+367
+00:29:11,770 --> 00:29:16,810
+الـ E و الـ D و الـ K و الـ A هدول الفيتامينات
+
+368
+00:29:16,810 --> 00:29:22,470
+اللي هي بنقول عنها تذوب في الدهون تذوب في الدهون و
+
+369
+00:29:22,470 --> 00:29:26,150
+طبعاً احنا هنا بيبقى إنه أنا عندي مشكلة في الكبد
+
+370
+00:29:26,150 --> 00:29:31,390
+فهذول الذوبان تبعهم بيبقى قليل فأنا بديهم خارجي 
+
+371
+00:29:31,390 --> 00:29:35,330
+في العادة ليش؟ لأن الكبد لا يستطيع إنه يتعامل
+
+372
+00:29:35,330 --> 00:29:38,310
+معاهم، stop alcohol and drugs، fluid management، bed
+
+373
+00:29:38,310 --> 00:29:41,350
+rest وطبعاً drug therapy زي الـ interferon
+
+374
+00:29:41,350 --> 00:29:44,930
+و الـ mepivodine و الـ ribavirin والحاجات هاي، و prevention
+
+375
+00:29:44,930 --> 00:29:51,390
+للهيباتيتس A والهيباتيتس B، الآن في الـ prevention
+
+376
+00:29:53,710 --> 00:29:59,310
+Never Share Drug Equipment، ممنوع الـ needles، السرنجات، 
+
+377
+00:29:59,310 --> 00:30:02,450
+الـ water، الـ filter، الـ cooker، الـ pipes، هذا كله
+
+378
+00:30:02,450 --> 00:30:05,230
+الـ straws، الـ pills، كله ممنوع نستخدمه مع بعض
+
+379
+00:30:05,230 --> 00:30:10,030
+Never Share Toothbrushes، فراش الأسنان، الماكينات 
+
+380
+00:30:10,030 --> 00:30:13,630
+الإحلاقية اللي هي الشفرات، ليش؟ لأن هذا ممكن في
+
+381
+00:30:13,630 --> 00:30:18,590
+لحظة من لحظة تنتقل عدوات، Prevention بصورة عامة، 
+
+382
+00:30:18,590 --> 00:30:23,310
+خدوا بالكم يا جماعة، always make sure a new and 
+
+383
+00:30:23,310 --> 00:30:27,210
+sterilized equipment is being used for tattooing 
+
+384
+00:30:27,210 --> 00:30:29,850
+and piercing، يمكن ما عندناش احنا كتير هيك لكن
+
+385
+00:30:29,850 --> 00:30:32,830
+tattooing اللي هو الوشم، و الـ piercing لما بيحطوا
+
+386
+00:30:32,830 --> 00:30:36,450
+قطع في المناخير، و في الأذن هيك الحلوج و كذا، فهذه
+
+387
+00:30:36,450 --> 00:30:42,210
+طبعاً بتنتقل عدوات، مش بس حتى الحبر اللي بيعمله منه
+
+388
+00:30:42,210 --> 00:30:48,250
+الـ tattooing اللي هو عملية الوشم كمان ممكن يكون فيه 
+
+389
+00:30:48,250 --> 00:30:53,190
+Hepatitis نوع من الأنواع اللي بتنتقل عن طريق الجلد
+
+390
+00:30:53,190 --> 00:30:56,750
+«Don't touch dirty needles»، الإبر في المستشفيات
+
+391
+00:30:56,750 --> 00:30:59,630
+«without proper equipment» أو «following proper
+
+392
+00:30:59,630 --> 00:31:02,830
+procedures»، «Main prevention measures for 
+
+393
+00:31:02,830 --> 00:31:05,730
+Hepatitis B and C»، وهذا من المناطق المهمة جداً 
+
+394
+00:31:05,730 --> 00:31:08,930
+عندنا في الامتحانات، «Promote vaccination against
+
+395
+00:31:08,930 --> 00:31:12,490
+Hepatitis B»، «Ensure needles and syringe program
+
+396
+00:31:12,490 --> 00:31:17,580
+to avoid sharing injecting، التجارب التجاربية تحفظ
+
+397
+00:31:17,580 --> 00:31:21,100
+الهواتف تحفظ الـ Safe Sex، تحفظ التجارب التجاربية 
+
+398
+00:31:21,100 --> 00:31:23,940
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+399
+00:31:23,940 --> 00:31:24,460
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+400
+00:31:24,460 --> 00:31:24,940
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+401
+00:31:24,940 --> 00:31:26,600
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+402
+00:31:26,600 --> 00:31:26,760
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+403
+00:31:26,760 --> 00:31:29,940
+التحفظ الهواتف التحفظ الهواتف التحفظ الهواتف
+
+404
+00:31:29,940 --> 00:31:34,630
+التحفظ الهواتف التحفظ الهواتف التحفظ كـ population.
+
+405
+00:31:34,930 --> 00:31:38,830
+Dirty needles، إيش عامل فيها؟ Handle only if you 
+
+406
+00:31:38,830 --> 00:31:42,930
+have proper equipment. Place needles in puncture
+
+407
+00:31:42,930 --> 00:31:46,630
+proof containers. في containers بنحط فيه الـ 
+
+408
+00:31:46,630 --> 00:31:52,710
+needles هاي. Can dispose containers in garbage but
+
+409
+00:31:52,710 --> 00:31:57,010
+better if it is taken to health clinic or needle
+
+410
+00:31:57,010 --> 00:32:01,510
+exchange زي المحارق وكذا. إذا إذا إذا أصلاً عندك
+
+411
+00:32:01,510 --> 00:32:02,150
+needle break
+
+412
+00:32:05,460 --> 00:32:08,980
+انغزيت بإبرة، بغض النظر فيها أو ما فيها، don't
+
+413
+00:32:08,980 --> 00:32:13,140
+milk the prick site، ما تقعدش تعصص عليها عشان بدك تطلع 
+
+414
+00:32:13,140 --> 00:32:16,680
+دم منها، wash the area with soap and water، go to
+
+415
+00:32:16,680 --> 00:32:19,600
+the nearest emergency department for assessment and
+
+416
+00:32:19,830 --> 00:32:23,930
+Treatment، بهيك احنا بنبقى عملنا محاضرة الـ
+
+417
+00:32:23,930 --> 00:32:27,090
+Hepatitis، أنا كنت أتوقع حقيقة تاخد وقت أكثر من
+
+418
+00:32:27,090 --> 00:32:31,390
+هيك، بس ربنا يسر ومشيته الأمور، بتمنى لكوا إنّها أيام
+
+419
+00:32:31,390 --> 00:32:35,830
+سعيد، واهتموا في موضوع الـ Hepatitis، مهم كتير
+
+420
+00:32:35,830 --> 00:32:39,590
+بالنسبة لنا، خاصة في الامتحانات، مكان مهم للأسئلة 
+
+421
+00:32:39,590 --> 00:32:40,490
+لكثير 
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/Pm6glBUJbFE_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/Pm6glBUJbFE_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ac11acd7603388ed5177690af96fe648c49fac2a
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/Pm6glBUJbFE_raw.srt
@@ -0,0 +1,1724 @@
+1
+00:00:00,000 --> 00:00:03,320
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:03,320 --> 00:00:05,900
+الصلاة و السلام علي سيدنا محمد و سيد الباسلين
+
+3
+00:00:05,900 --> 00:00:12,860
+اجمعين اليوم حقيقة هنحكي في موضوع غاية في العملية
+
+4
+00:00:12,860 --> 00:00:19,100
+كتير منتشر عند بعضكم كمان، عند أهليكم، عند الكل
+
+5
+00:00:19,100 --> 00:00:26,260
+عملي جدا الموضوع هذا، مين عمره ماجهوش أو مين عمره
+
+6
+00:00:26,260 --> 00:00:32,680
+أجاه اللي بنقول عنها الحزاز أو الحمودةيعني حاجة
+
+7
+00:00:32,680 --> 00:00:36,400
+حراجة هيت أو قوله في ناس شعاع عنه عن تم المعدة
+
+8
+00:00:36,400 --> 00:00:42,700
+لفوق زي ما احنا شايفين في الصورة نار مشعللة في
+
+9
+00:00:42,700 --> 00:00:46,540
+منطقة تم المعدة وطبعا تم المعدة موجودة في منطقة
+
+10
+00:00:46,540 --> 00:00:50,700
+الصدر يعني جريب من الجلب جريب من الرقتين جريب من
+
+11
+00:00:50,700 --> 00:00:57,030
+حاجات كتير هذا ايش بيقول عنه؟Gastro-Oesophageal
+
+12
+00:00:57,030 --> 00:01:03,130
+Reflex، مش Reflex، Reflex Disease الكل ممكن يكون
+
+13
+00:01:03,130 --> 00:01:09,630
+معاه نتيجة
+
+14
+00:01:09,630 --> 00:01:14,610
+أكل معين، طريقة معينة في الأكل، يصير عنده Gastro
+
+15
+00:01:14,610 --> 00:01:15,310
+يعني معدى،
+
+16
+00:01:19,830 --> 00:01:25,230
+الحامض أو الأكل من المعدة إلى المريء وهو عبارة عن
+
+17
+00:01:25,230 --> 00:01:29,030
+disease عامليا gastroesophageal reflux disease
+
+18
+00:01:29,030 --> 00:01:34,910
+اللي بنقول عنه ايش؟ GERD زي GERD يعني GERD اختصار
+
+19
+00:01:34,910 --> 00:01:39,250
+ل gastroesophageal reflux disease زي ما قلنا كتير
+
+20
+00:01:39,250 --> 00:01:43,170
+من الناس بيصير معاهم مين بيصير معاها او بيصير
+
+21
+00:01:43,170 --> 00:01:48,840
+معاها زي هيك؟حمودة أو شعاع أو حزاز زي ما نقول عنها
+
+22
+00:01:48,840 --> 00:01:53,980
+أو ارتجاع حتى في بعض الناس في نص الليل لما بتعشى
+
+23
+00:01:53,980 --> 00:01:57,920
+متأخر ممكن يكون زي المخنوق ليش؟ لإنه صار عنده
+
+24
+00:01:57,920 --> 00:02:03,940
+ارتجاع للمادة الحامضة هاي وين طلعت من المعدة
+
+25
+00:02:03,940 --> 00:02:08,240
+للمريق ومش بس وراحت دخلت على التركيا راحت دخلت على
+
+26
+00:02:08,240 --> 00:02:11,320
+ال larynx على الحندرة وعلى التركيا وهذه من الحاجات
+
+27
+00:02:11,320 --> 00:02:16,690
+الصعبة اللي بحس الواحد بعض الاحيان بالليللتحدّث
+
+28
+00:02:16,690 --> 00:02:20,290
+الآن عن Gehrig's gastroesophageal reflux disease
+
+29
+00:02:20,290 --> 00:02:26,520
+وبنقول عنه كمان acid refluxهو عبارة عن a chronic
+
+30
+00:02:26,520 --> 00:02:30,380
+illness that affects خمسة لسبعة في المية of the
+
+31
+00:02:30,380 --> 00:02:35,320
+world population وانا بأكد هذا خمسة لسبعة لكل ال
+
+32
+00:02:35,320 --> 00:02:39,320
+world لكن في منطقة البحر الأبيض المتوسط في بلادنا
+
+33
+00:02:39,320 --> 00:02:42,700
+الناس اللي بتستخدم الشطة والفلفل في المكسيك وكذا
+
+34
+00:02:42,700 --> 00:02:46,020
+هتلاقيها أعلى بكثير and it's associated with a
+
+35
+00:02:46,020 --> 00:02:49,880
+serious medical complication if untreated قضية
+
+36
+00:02:49,880 --> 00:02:55,190
+الآن أنا مش بس بحكي عن بس حموظة ويلاوبأخد أحاجة
+
+37
+00:02:55,190 --> 00:02:58,270
+وبمشي لحالة يعني بعض الأحيان تعملي مشاكل هنتعرف
+
+38
+00:02:58,270 --> 00:03:01,090
+على الموضوع هذا من خلال المحاضرة it's a condition
+
+39
+00:03:01,090 --> 00:03:05,570
+in which the liquid content السائل الموجود في
+
+40
+00:03:05,570 --> 00:03:10,310
+المعدة of the stomach regurgitates بيصير له عملية
+
+41
+00:03:10,310 --> 00:03:16,830
+إيش ارتجاع back up or reflux into the esophagus
+
+42
+00:03:16,830 --> 00:03:21,370
+the liquid can inflame هذا طبعا ال liquid عبارة
+
+43
+00:03:21,370 --> 00:03:30,350
+عمليا عن ميه نارحامض شديد الحمودة حامض
+
+44
+00:03:30,350 --> 00:03:41,530
+الـ HCL وهذا الحامض المفروض أنه لا يهضم المعدة لأن
+
+45
+00:03:41,530 --> 00:03:46,470
+المعدة مهيئة بجدار يحميها من الحامض لكن إذا الحامض
+
+46
+00:03:46,470 --> 00:03:51,410
+هذا راح على منطقة مافيش فيها هذا الجدار زي المريء
+
+47
+00:03:51,410 --> 00:03:56,400
+الاسوفيقاThis occurs in a minority of patients
+
+48
+00:03:56,400 --> 00:04:01,920
+ساعتها بيصير عندي مشكلة محترمة شايفين الصورة
+
+49
+00:04:01,920 --> 00:04:06,500
+الصغيرة هان اللي فيها حمار هذه احتقان وحمرار
+
+50
+00:04:06,500 --> 00:04:12,320
+والتهاب تم المعدة الصورة هاي شكلها تصورواالواحد
+
+51
+00:04:12,320 --> 00:04:15,640
+لما بيكون على جلده في حاجة محمرة وكذا بيعرفش يقعد
+
+52
+00:04:15,640 --> 00:04:19,900
+منها فبانا لما تكون على تُم المعدة مش بس بتعملي زي
+
+53
+00:04:19,900 --> 00:04:23,100
+ما قلنا حموضة وارتجاع لكن هتعملي حاجات تانية بعد
+
+54
+00:04:23,100 --> 00:04:30,300
+شوية The regurgated liquid usually contains حامض
+
+55
+00:04:30,300 --> 00:04:36,610
+ومبسينالبيبسين بتفرزه مين؟ بتفرزه المعدة بيبسين is
+
+56
+00:04:36,610 --> 00:04:41,230
+an enzyme that begins the digestion of protein in
+
+57
+00:04:41,230 --> 00:04:45,560
+the stomach هتجد الـ Reflex liquidممكن زي ما قلنا
+
+58
+00:04:45,560 --> 00:04:48,780
+يكون فيه أيضًا إيش بايل إيش بايل العصارة الصفروية
+
+59
+00:04:48,780 --> 00:04:52,860
+هذه اللي بتبقى جاية من وين من الدودنام الـ12 جاية
+
+60
+00:04:52,860 --> 00:04:57,960
+على المعدد لكن حقيقة هذا المحتوى تبع الحامض أو تبع
+
+61
+00:04:57,960 --> 00:05:01,880
+الـFluid اللي بيسير في عملية ارتجاع عبارة عن حامض
+
+62
+00:05:01,880 --> 00:05:07,420
+بيبسين وكمان في بايل اللي هو المادة الصفرة اللي
+
+63
+00:05:07,420 --> 00:05:13,660
+بترجع من من الدودنام تيجي علىبتيجي على المعدة لكن
+
+64
+00:05:13,660 --> 00:05:18,440
+أسوأهم أو أكترهم serious هو اللي بيعمللي المشكلة
+
+65
+00:05:18,440 --> 00:05:22,240
+كلها هو الحامض عشان يكونوا برضه واضحينالـPepsin
+
+66
+00:05:22,240 --> 00:05:28,060
+والـPile قد يؤذي الـEsophagus ولكن رقمهم في بناء
+
+67
+00:05:28,060 --> 00:05:34,880
+Esophagus إنفلامش ودمج ليس واضحًا كرم أسد يعني
+
+68
+00:05:34,880 --> 00:05:39,500
+صريح بلعبه دور لكن مش بالوضوح اللي بيعملوا الحامل
+
+69
+00:05:39,500 --> 00:05:42,640
+طب إيش الـSymptoms اللي بتختلف عن اللي تابوت حدثنا
+
+70
+00:05:42,640 --> 00:05:49,120
+عنه؟ طبعًا الـDisease اللي هو الـGerd ممكن يكون
+
+71
+00:05:49,120 --> 00:05:54,660
+موجودبدون symptoms asymptomatic وممكن يكون
+
+72
+00:05:54,660 --> 00:06:00,500
+symptomatic إذا ال acid only backs up إذا الحامض
+
+73
+00:06:00,500 --> 00:06:05,680
+هذا بيرجع لحد مسافة بس ال maria ال esophagus ال
+
+74
+00:06:05,680 --> 00:06:09,460
+geared symptoms بتلاقيها دايما بس heart burn heart
+
+75
+00:06:09,460 --> 00:06:16,280
+burn يعني حموضة heart قلب burnحرجان الحراجان القلب
+
+76
+00:06:16,280 --> 00:06:20,200
+هم زمان لما سموها heartburn كانوا يفكروا إنه حاجة
+
+77
+00:06:20,200 --> 00:06:24,980
+إلها علاقة بالقلب وقريبة من القلب فجال يقولوا عنه
+
+78
+00:06:24,980 --> 00:06:29,140
+heartburn ما زال واحد بيقول عنه heartburn حتى الآن
+
+79
+00:06:29,140 --> 00:06:34,940
+لكنها ما لهاش علاقة بالقلب if the acid إذا الحامض
+
+80
+00:06:34,940 --> 00:06:40,340
+رجع لحد ال larynx يعني رجع في ال esophagus لفوق
+
+81
+00:06:40,340 --> 00:06:47,100
+لفوق لفوق ونزللحد منطقة الارنز أن هما هناك فيه
+
+82
+00:06:47,100 --> 00:06:50,280
+نقطة التقاء الـSleeper النائم و الـwake up
+
+83
+00:06:50,280 --> 00:06:54,220
+coughing and choking زي ما حكينا coughing and
+
+84
+00:06:54,220 --> 00:07:01,220
+choking sometimes GERD can cause serious
+
+85
+00:07:01,220 --> 00:07:04,000
+complications including inflammation of the
+
+86
+00:07:04,000 --> 00:07:08,300
+esophagus from stomach acid that causes bleeding
+
+87
+00:07:08,300 --> 00:07:09,520
+or ulcer
+
+88
+00:07:16,470 --> 00:07:21,170
+طيب بيبقى كمان مرة انه sometimes GERD can cause
+
+89
+00:07:21,170 --> 00:07:25,290
+serious complications including inflammation بما
+
+90
+00:07:25,290 --> 00:07:30,810
+فيها التهيابات للمريء لكن ممكن بعض الأحيان توصل
+
+91
+00:07:30,810 --> 00:07:37,800
+لإن الاتهابات هاي يحصل فيهاbleeding أو ulcers يعني
+
+92
+00:07:37,800 --> 00:07:41,320
+جروح نتيجة الموضوع هذا وهذا اللي بنقول عنه احنا
+
+93
+00:07:41,320 --> 00:07:45,580
+بعد شوية اللي هو apoptic ulcer مش بس في بعض
+
+94
+00:07:45,580 --> 00:07:50,840
+الحالات في بعض الحالات بينشأ ان حاجة اسمها بارت
+
+95
+00:07:50,840 --> 00:07:54,420
+إيزوفيقيا إيزوفيقيا إيزوفيقيا إيزوفيقيا إيزوفيقيا
+
+96
+00:07:56,330 --> 00:08:00,270
+هذا عبارة عن تغيير في الخلايا للحمض طول الوقت نازل
+
+97
+00:08:00,270 --> 00:08:05,470
+يغيرها بيصير عملية تغيير داخلي للخلايا تاعت الـ
+
+98
+00:08:05,470 --> 00:08:09,750
+Esophagus نتيجة زي ما قلنا ضغط الحامض عليها طول
+
+99
+00:08:09,750 --> 00:08:13,490
+الوقت وهذا ممكن يكون brain cancer أو ممكن lead to
+
+100
+00:08:13,490 --> 00:08:17,430
+brain cancer يبقى أو to cancer برت Esophagus هو
+
+101
+00:08:17,430 --> 00:08:21,250
+عبارة عن brain cancer condition ناتجة عن طريق عن
+
+102
+00:08:21,250 --> 00:08:25,550
+موضوع الـ GERD Most patients with GERD experience
+
+103
+00:08:32,810 --> 00:08:35,850
+أو محاولة النوم أو أول النوم، يعني بتلاقي أنهم
+
+104
+00:08:35,850 --> 00:08:40,870
+بتعبوا منها أكتر و الـ severity بتزيد أكتر، خاصة
+
+105
+00:08:40,870 --> 00:08:47,030
+لو كانوا من النوع اللي بتعشى متأخر باستمراريبقى
+
+106
+00:08:47,030 --> 00:08:50,390
+الـ Symptoms persistent heartburn يعني مش من مرة
+
+107
+00:08:50,390 --> 00:08:53,530
+واحدة حموضة بقدر أقول أنا Geared أو مرتين، لأ،
+
+108
+00:08:53,530 --> 00:08:57,130
+احنا بنحكي عن Chronic Condition اسمها Geared اللي
+
+109
+00:08:57,130 --> 00:09:01,310
+هو Gastro-Oesophageal Reflex الـCs وهذه persistent
+
+110
+00:09:01,310 --> 00:09:08,170
+heartburn حموضة مستمرة وبتيجي كمان مع حاجات تانية
+
+111
+00:09:08,170 --> 00:09:11,770
+زي الـ Nausea بيصير نفسه زي المايع، Coughing،
+
+112
+00:09:11,770 --> 00:09:16,410
+بيصير يكح، يعني الحامض بتقول لاالريقتين فبيعمللي
+
+113
+00:09:16,410 --> 00:09:21,570
+coughing sore taste in the mouth طبعاً لإن هو
+
+114
+00:09:21,570 --> 00:09:24,470
+هيكيت بصل حامض كمان بعض الأحيان للطم ال
+
+115
+00:09:24,470 --> 00:09:27,590
+respiratory conditions زي الأسباب pneumonia و
+
+116
+00:09:27,590 --> 00:09:30,930
+chronic bronchitis كتير من الأحيان يا جماعة خليني
+
+117
+00:09:30,930 --> 00:09:36,870
+أدخل على طب الأطفال شوي أطفال بيجينا ب recurrent
+
+118
+00:09:36,870 --> 00:09:42,230
+chest infection التهابات السدر المتكررة من أهم
+
+119
+00:09:42,230 --> 00:09:46,170
+الأسبابأو الـ differential diagnosis تبعها الأسباب
+
+120
+00:09:46,170 --> 00:09:49,670
+اللي بتعملي chest infection متكرر اللي هي
+
+121
+00:09:49,670 --> 00:09:55,330
+gastroesophageal reflux disease إلى جانب أمراض
+
+122
+00:09:55,330 --> 00:10:00,830
+القلب على سبيل المثال إلى جانب ضعف ال immunity إلى
+
+123
+00:10:00,830 --> 00:10:06,820
+جانب وجود جسم غريب بلق جسم غريب على سبيل المثالهذه
+
+124
+00:10:06,820 --> 00:10:10,080
+أربعة conditions حكيتها الآن أنا مش موجودة في
+
+125
+00:10:10,080 --> 00:10:14,020
+السلايدات أربعة conditions بتعملي إيش recurrent
+
+126
+00:10:14,020 --> 00:10:20,220
+chest infection منها كمان الخامس cystic fibrosis
+
+127
+00:10:20,220 --> 00:10:26,600
+يبقى خمس حاجات المفروض أنه أنا لما أشوف حالة دايما
+
+128
+00:10:26,600 --> 00:10:31,020
+بيصير عندها chronic أو بيشوف حالة بيصير عندها
+
+129
+00:10:31,020 --> 00:10:35,750
+pneumoniaRecurrent Pneumonia أو Recurrent Chest
+
+130
+00:10:35,750 --> 00:10:40,250
+Infection المفروض أنه بفكر فيهم heart disease
+
+131
+00:10:40,250 --> 00:10:45,790
+كنجينة ال heart disease phone body inhalation ال
+
+132
+00:10:45,790 --> 00:10:51,910
+immunity system defect اللي بنحكي عنه
+
+133
+00:10:51,910 --> 00:10:56,930
+gastroesophageal reflux واتحدتنا
+
+134
+00:10:56,930 --> 00:11:01,290
+عن اللي هو ال phone cystic fibrosis أو phone body
+
+135
+00:11:02,570 --> 00:11:10,960
+الـ Causes تبعت الـ Geared طبعاً حسبالها أسباب وهي
+
+136
+00:11:10,960 --> 00:11:14,660
+نفسها محفزات الـ Age كل ما كبر الواحد كل ما صارت
+
+137
+00:11:14,660 --> 00:11:19,620
+أكتر نوعية الأكل الناس اللي بتاكل Spicy دايما اللي
+
+138
+00:11:19,620 --> 00:11:23,860
+دايما أكلها خدنا نقول بندورة معجدة على سبيل المثال
+
+139
+00:11:23,860 --> 00:11:29,140
+اللي بيأكلوا دايما البيتزا الناس اللي بتاكل فلفل
+
+140
+00:11:29,140 --> 00:11:32,860
+كتير على سبيل المثال وأملاح كتير الناس اللي بتاكل
+
+141
+00:11:32,860 --> 00:11:37,910
+متأخرو بتاكل متأخر و أكل كتير يعني بتدب المعدة
+
+142
+00:11:37,910 --> 00:11:42,130
+الناس اللي بتاخد alcohol الناس اللي بتدخل ال
+
+143
+00:11:42,130 --> 00:11:46,760
+pregnancy ليش ال pregnancy؟والـ Obesity لأنه
+
+144
+00:11:46,760 --> 00:11:51,500
+بنتيجة الـ Pregnancy المقدة مضغوطة لفوق فالحامض
+
+145
+00:11:51,500 --> 00:11:54,960
+بتجمع بصورة أكبر و بيصل للـ Esophagias بصورة أكبر
+
+146
+00:11:54,960 --> 00:11:59,040
+و الـ Obesity نفس الكلام في هناك certain foods
+
+147
+00:11:59,040 --> 00:12:03,680
+associated with reflux events طبعا مش معناته بس هم
+
+148
+00:12:03,680 --> 00:12:06,580
+هدولة جماعة كل واحد فيه إلو حاجة بتعمله
+
+149
+00:12:06,580 --> 00:12:12,360
+Destroesophageal refluxاللي ممكن يعمل لي ممكن
+
+150
+00:12:12,360 --> 00:12:17,600
+مايعملش للآخر و هيك لكن فينا تجارب عصابي مثال يمكن
+
+151
+00:12:17,600 --> 00:12:21,820
+كلكم بتستحضروا اللي بيأكلوا الجرشلة بالشاي عصابي
+
+152
+00:12:21,820 --> 00:12:25,600
+مثال عصابي مثال اللي بيأكلوا الفلافل بالشاي بيصير
+
+153
+00:12:25,600 --> 00:12:32,360
+معاهم حموضة عصابي مثال فالـ Spicy Foods الـ Garlic
+
+154
+00:12:32,360 --> 00:12:39,920
+and Onion الشدول التومة والبصلCitrus fruits طبعاً
+
+155
+00:12:39,920 --> 00:12:43,900
+لأنه احنا قاعدين نحكي عن حمضيات حوامض من اسمها
+
+156
+00:12:43,900 --> 00:12:49,120
+طبعا ممكن ما بتتعاملش عند كتير ناس لكن لو الواحد
+
+157
+00:12:49,120 --> 00:12:52,340
+liable وهو معرض أو في عنده مشاكل لو أكلها ممكن
+
+158
+00:12:52,340 --> 00:12:55,670
+تتعامل معاه مشاكلكل المشروبات أو المشروبات اللي
+
+159
+00:12:55,670 --> 00:12:59,650
+فيها كفائين نقصدش بس الجهوة هان ولا بنقصد بس
+
+160
+00:12:59,650 --> 00:13:03,390
+الكوكاكولا السوداء لكن أي مشروب فيه كفائين ممكن
+
+161
+00:13:03,390 --> 00:13:08,510
+يعملنا هيك شوكليت شوكولاتة فاتي and فريد فودز mint
+
+162
+00:13:08,510 --> 00:13:14,850
+flavorings اللي هي الحاجات اللي عليها الحلو اللي
+
+163
+00:13:14,850 --> 00:13:20,430
+عليه نعنع نعنع بصورة عامة وفي حاجات ال tomatoباست
+
+164
+00:13:20,430 --> 00:13:23,590
+فودز زي الـ Spaghetti والشيلي والبيتزا والحاجات
+
+165
+00:13:23,590 --> 00:13:26,810
+هذه ال risk factors اتحدتنا قبل شويه وقولنا ال
+
+166
+00:13:26,810 --> 00:13:31,530
+obesity pregnancy, hepatic ulcer الناس اللي في
+
+167
+00:13:31,530 --> 00:13:36,350
+عندها delaying of stomach emptying طبعا ليش؟ لأنه
+
+168
+00:13:36,350 --> 00:13:40,290
+ال stomach بتصير تحبس والحمض بزيد فهذا كله يتوقش
+
+169
+00:13:40,290 --> 00:13:47,010
+بعمل ليه؟ بعمل ليه ارتفاع الحمض في المريض إلى جانب
+
+170
+00:13:47,010 --> 00:13:51,190
+زي مثلا ال diabetesأو الـ ulcer أو abnormal nerve
+
+171
+00:13:51,190 --> 00:13:54,690
+أو muscle function can delay emptying of the
+
+172
+00:13:54,690 --> 00:13:58,370
+stomach وهذا بيخلي الحامض back up into the
+
+173
+00:13:58,370 --> 00:14:05,150
+esophagus الأزمة ليش؟ لأنه في عندنا some asthma
+
+174
+00:14:05,150 --> 00:14:12,540
+medications that widen أو dilate airwaysممكن أيضًا
+
+175
+00:14:12,540 --> 00:14:20,400
+أن يتراجع مخرج الإيزوفيجيا السفينكتر اللي مع
+
+176
+00:14:20,400 --> 00:14:30,320
+المعدة ويجعل الحامض يرجع إلى الإيزوفيجيا السكريلأن
+
+177
+00:14:30,320 --> 00:14:33,740
+one of the many complications of diabetes is
+
+178
+00:14:33,740 --> 00:14:38,340
+gastroparesis يعني زي ما بيقولوها ضعف حركة المعدة
+
+179
+00:14:38,340 --> 00:14:42,900
+وهذا الموضوع يجعل الأكل و الحامض يظل فترة طويلة في
+
+180
+00:14:42,900 --> 00:14:46,920
+المعدة، لماذا؟ لأن الـemptying بطيء، فهذا بدي فرصة
+
+181
+00:14:46,920 --> 00:14:51,440
+للحامض أنه
+
+182
+00:14:51,440 --> 00:14:55,620
+يرجع على المريض طب كيف بنشخص الـGERD،
+
+183
+00:14:55,620 --> 00:15:00,860
+gastroesophageal reflux؟تشخيصه طبعاً فيه different
+
+184
+00:15:00,860 --> 00:15:05,460
+modalities بما فيها upper gastrointestinal
+
+185
+00:15:05,460 --> 00:15:11,370
+endoscopy من ظهر لمنطقة المعدة والمريق من فوقممكن
+
+186
+00:15:11,370 --> 00:15:16,130
+كمان بما أنه احنا قاعدين نقول عن acid activity في
+
+187
+00:15:16,130 --> 00:15:19,430
+المنطقة هذه ممكن نعمله isofisial pH monitoring
+
+188
+00:15:19,430 --> 00:15:25,190
+بدخل واحد زي حاجة هيك sensor عند ثم المعدة وبيجيس
+
+189
+00:15:25,190 --> 00:15:30,250
+حموضة الحموضة
+
+190
+00:15:30,250 --> 00:15:35,920
+في المنطقة حوالين بين المعدة و بينوهذا على مدى
+
+191
+00:15:35,920 --> 00:15:41,080
+ساعات معينة 24 ساعة وفيه software على الكمبيوتر
+
+192
+00:15:41,080 --> 00:15:46,040
+السنسور بتفرج على الكمبيوتر وبنشوف جداش النسب
+
+193
+00:15:46,040 --> 00:15:47,900
+وجداش الحمورة
+
+194
+00:15:59,550 --> 00:16:04,590
+ولا طريقة منهم تدّيك مية في المية الحل وكل واحدة
+
+195
+00:16:04,590 --> 00:16:15,270
+لها مشاكل كل واحدة لها مشاكل من الطروج الاندوسكوبي
+
+196
+00:16:15,270 --> 00:16:19,670
+فقط لا يحتاج لشعور بشكل كام الـ pH Monitoring ليس
+
+197
+00:16:19,670 --> 00:16:20,630
+دائما متوفر
+
+198
+00:16:23,320 --> 00:16:27,960
+ولكن بقولكوا إيش اللي بيصير الآن، فيش حد من حد ما
+
+199
+00:16:27,960 --> 00:16:30,480
+بيشكي من Gastro-Oesophageal Reflex Disease بروح
+
+200
+00:16:30,480 --> 00:16:33,960
+بعمل فحوصات بالصورة اللي مكتوبة هنا، اللي هي قضية
+
+201
+00:16:33,960 --> 00:16:37,820
+إنه منظار أو pH Monitoring أو Radiological
+
+202
+00:16:37,820 --> 00:16:42,800
+Studies، ها إيش بنعمل؟ بنعمل حاجة اسمها Gared
+
+203
+00:16:42,800 --> 00:16:46,000
+Treatment-Based Approach، يعني على الـ Clinical
+
+204
+00:16:46,000 --> 00:16:50,060
+اللي شكّيها المريض، وبما إنه منتشر كتير، فبندّي
+
+205
+00:16:50,060 --> 00:16:51,740
+علاج لهذا الموضوع
+
+206
+00:16:55,460 --> 00:17:00,180
+وبندى أدوية وزى ما قلنا بنخفف عنه اللى هو الفحوصات
+
+207
+00:17:00,180 --> 00:17:05,460
+هاى وبترايه الآن فرضا ماتحسنش مع العلاج طبعا مع
+
+208
+00:17:05,460 --> 00:17:08,340
+الـ diet يعنى هو فيه قوله diet ونقوله إيش يعمل في
+
+209
+00:17:08,340 --> 00:17:10,900
+قضية الأكل لإنه مابنفعش أنا أقول والله عندي
+
+210
+00:17:10,900 --> 00:17:16,730
+gastroesophageal reflux diseaseوبدأ أظل أشرب
+
+211
+00:17:16,730 --> 00:17:21,070
+Alcohol أو بدأ أظل أدخل أو بدأ أظل مع ال pregnancy
+
+212
+00:17:21,070 --> 00:17:25,130
+بنتهي الموضوع أو بدأ أظل أكل حاجات Spicy أو Tomato
+
+213
+00:17:25,130 --> 00:17:29,610
+أو Mint أو كذا، ماينفعش المفروض أنه أنا مع العلاج
+
+214
+00:17:29,610 --> 00:17:34,580
+بأعمل تحمية اللي هو lifestyle modificationوإذا
+
+215
+00:17:34,580 --> 00:17:38,300
+ضال، طبعاً ساعتها بدك، بده الواحد يضطر يروح يعمل
+
+216
+00:17:38,300 --> 00:17:43,540
+فحوصات ليشوف differential diagnoses لأنه ممكن يكون
+
+217
+00:17:43,540 --> 00:17:49,060
+عنده بيبتكالثر، ممكن يكون عندنا cancer على سبيل
+
+218
+00:17:49,060 --> 00:17:52,220
+المثال و ال presentation تبعه بالصورة هذه،
+
+219
+00:17:52,220 --> 00:17:55,440
+فالمفروض أنه الواحد بياخد باله من الموضوع هذا لو
+
+220
+00:17:55,440 --> 00:17:59,880
+ما اتحسنش ال treatment method to effectively treat
+
+221
+00:17:59,880 --> 00:18:04,940
+guard range from lifestyle measuresto the use of
+
+222
+00:18:04,940 --> 00:18:09,640
+geared medication أو إذا في الأخر في الأخر في
+
+223
+00:18:09,640 --> 00:18:14,740
+الأخر في مشاكل بنعمل surgical procedures لهد درجة
+
+224
+00:18:14,740 --> 00:18:16,900
+أه ما هو في ناس عندها مشكلة في الموضوع
+
+225
+00:18:27,770 --> 00:18:31,890
+زي ما قلنا كمان مرة مهم جدا جدا للناس اللي عندهم
+
+226
+00:18:31,890 --> 00:18:35,050
+persistent heartburn او other chronic and
+
+227
+00:18:35,050 --> 00:18:38,190
+recurrent symptoms of gout to seek an accurate
+
+228
+00:18:38,190 --> 00:18:41,930
+diagnosis ماكان فيش انه انا اظن ابلبع في حاجة في
+
+229
+00:18:41,930 --> 00:18:45,930
+السوق موجودة اسمها الرينيه الرينيه عبارة حبوب
+
+230
+00:18:45,930 --> 00:18:49,690
+بيقولوا عنها جرش وهذه بتخفف الحموظة لأن الرينيه
+
+231
+00:18:49,690 --> 00:18:53,710
+هذه عبارة عن حاجة بتعمل neutralization تتفاعل مع
+
+232
+00:18:53,710 --> 00:18:59,400
+الحمض بتعمل neutralizationللحمض وخلاص وبرتحصل واحد
+
+233
+00:18:59,400 --> 00:19:02,660
+أو في ناس بتاخد مالوكس أو في ناس بتاكل عدس أو في
+
+234
+00:19:02,660 --> 00:19:06,020
+ناس بتشرب حليب طبعا الحليب يلو موضوع تاني لإن هو
+
+235
+00:19:06,020 --> 00:19:09,540
+يعتبر غلط لإن هو ساعتها بيعمل ال release ساعتها
+
+236
+00:19:09,540 --> 00:19:13,360
+ساعتها لكن بعد شوية الحموضة بتزيد أو في ناس بتاكل
+
+237
+00:19:13,360 --> 00:19:18,020
+موز أو في ناس تشرب ميه المهم إنه كل واحد يلو
+
+238
+00:19:18,020 --> 00:19:20,480
+طريقته في إنه يعمل release لل heart pain بس مش هي
+
+239
+00:19:20,480 --> 00:19:25,180
+هذه الجضية الجضية إنه إنهمايصيرش هذا chronic، مش
+
+240
+00:19:25,180 --> 00:19:28,060
+كل ما أكل، كل ما أفطر، كل ما أتغدى، كل ما أتعشى،
+
+241
+00:19:28,060 --> 00:19:31,120
+بيصير معايا، هذا الموضوع بيصير كبير في الأحوال
+
+242
+00:19:31,120 --> 00:19:34,060
+اللي زي هي ال medications اللي إحنا بنديها في
+
+243
+00:19:34,060 --> 00:19:36,680
+الحقيقة للـ gastroesophageal reflux disease، تو
+
+244
+00:19:36,680 --> 00:19:40,880
+حكيت أنا عن واحد منهم الـ Anti-acid، إيش يعني Anti
+
+245
+00:19:40,880 --> 00:19:46,250
+-acid؟ إشي مضاد للحمودةزي الـ Malox أو زي ما يكون
+
+246
+00:19:46,250 --> 00:19:51,490
+فيه تمس في عصابي المثال الـ RNA عصابي المثال وهذا
+
+247
+00:19:51,490 --> 00:19:58,350
+ايش بيعمل ليه؟ Neutralize stomach acidand can
+
+248
+00:19:58,350 --> 00:20:03,210
+provide quick relief بتحسن على السريع الحامض خلاص
+
+249
+00:20:03,210 --> 00:20:08,190
+متعدل راحة المشكلة antacid alone won't heal an
+
+250
+00:20:08,190 --> 00:20:12,450
+inflamed esophagus damaged by stomach acid يعني ما
+
+251
+00:20:12,450 --> 00:20:15,070
+تتصورش أنه لو في أنا في عندي inflammation أنه
+
+252
+00:20:15,070 --> 00:20:20,580
+هتروح بالحالة هو بس الحامض خف لكنالـ الـ الـ الـ
+
+253
+00:20:20,580 --> 00:20:21,060
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+254
+00:20:21,060 --> 00:20:21,060
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+255
+00:20:21,060 --> 00:20:21,060
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+256
+00:20:21,060 --> 00:20:22,940
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+257
+00:20:22,940 --> 00:20:29,340
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+258
+00:20:29,340 --> 00:20:33,020
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+259
+00:20:33,020 --> 00:20:34,880
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+260
+00:20:34,880 --> 00:20:34,880
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+261
+00:20:34,880 --> 00:20:37,280
+الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ الـ
+
+262
+00:20:37,280 --> 00:20:40,340
+الـ الـ
+
+263
+00:20:41,610 --> 00:20:44,950
+اللي هي شغالة على طريقة الباب اللي بيجيك منه الريح
+
+264
+00:20:44,950 --> 00:20:50,010
+سده و استريح اللي هي ال PPI بيقولوا عنها PPI أو
+
+265
+00:20:50,010 --> 00:20:56,150
+Proton Bump Inhibitors زي الومي برازول مشهور ال ..
+
+266
+00:20:56,150 --> 00:20:59,190
+ال .. these guard medications إيش بتعملوا؟ بتعملوا
+
+267
+00:20:59,190 --> 00:21:04,830
+Blockage of Acid Production تماما، بيبطل يطلع حامض
+
+268
+00:21:04,830 --> 00:21:12,130
+وهذه طبعا بتدي وقتفرصة لإن الـ Damaged أو Inflamed
+
+269
+00:21:12,130 --> 00:21:17,810
+Esophageal Tissue تهيل زمان
+
+270
+00:21:17,810 --> 00:21:22,810
+كانت لازم تنكتب روشتة، الآن صارت تنكتب صارت عادة
+
+271
+00:21:22,810 --> 00:21:26,790
+تشتريها من الصيدلية، بنقول عنها OTC، إيش يعني OTC؟
+
+272
+00:21:26,790 --> 00:21:28,890
+Over The Count، يعني بتقدر تروح الصيدلية تقولي
+
+273
+00:21:28,890 --> 00:21:31,190
+والله ديلي أم برازول، بتديك أم برازول، طبعا مش في
+
+274
+00:21:31,190 --> 00:21:34,310
+بلاد أنا بحكي عن برا، هنا برا بتشتري الصيدلية و
+
+275
+00:21:34,310 --> 00:21:37,350
+الصيدلي و العيلة و كل البلد، مافيش مشكلة، إيش اللي
+
+276
+00:21:37,350 --> 00:21:37,910
+بدكيها؟
+
+277
+00:21:41,130 --> 00:21:44,890
+الآن يعني خلاص صار مش لازم ينكتب بروشيطة ممكن
+
+278
+00:21:44,890 --> 00:21:47,730
+الواحد يجيبه لحاله طبعا بس هذا خدوا بالكوا بيغش
+
+279
+00:21:47,730 --> 00:21:52,190
+الموضوع هذا لأنه لأنه لأنه القضية ممكن مايكونش
+
+280
+00:21:52,190 --> 00:21:53,570
+موضوع موضوع بس
+
+281
+00:21:56,130 --> 00:21:59,890
+ممكن يكون بيبتيكازر، ممكن يكون كانسر، ممكن يكون
+
+282
+00:21:59,890 --> 00:22:02,990
+بارت إيزوفيجيا، ممكن يكون حاجات كتير، فيبقى ياخد
+
+283
+00:22:02,990 --> 00:22:06,550
+باله الواحد إذا دل كرونيك الموضوع، لابد من التوجه
+
+284
+00:22:06,550 --> 00:22:10,190
+للطبيب لمعرفة السبب اللي عملنا الموضوع هذا الـH2
+
+285
+00:22:10,190 --> 00:22:14,290
+-Receptors اللي هو الهستامين Two Receptors
+
+286
+00:22:14,290 --> 00:22:21,870
+Blockers، هذه نوعية أخرى من الـMedicationزي الـ
+
+287
+00:22:21,870 --> 00:22:24,550
+Ranidine كتير منكم بيعرفوا عنه يقولوا سنة تقريبا
+
+288
+00:22:24,550 --> 00:22:29,370
+موقف الـ Ranidine لأنه هذا إيش بعملنا؟ بعملنا
+
+289
+00:22:29,370 --> 00:22:33,770
+reduction of the production of acid reduction بس
+
+290
+00:22:33,770 --> 00:22:42,170
+ال PPI عملنا blockage لل production هذا عملنا بس
+
+291
+00:22:42,170 --> 00:22:46,230
+reduction لل production they don't act as quickly
+
+292
+00:22:46,230 --> 00:22:50,250
+as antacidولكنها تقدر تقدر تقدر تقدر تقدر تقدر
+
+293
+00:22:50,250 --> 00:22:57,670
+تقدر تقدر تقدر تقدر تقدر تقدر تقدر
+
+294
+00:22:57,830 --> 00:23:02,550
+مين اللي بيريحنا بسرعة؟ اللي هو الـ Antacid لكن
+
+295
+00:23:02,550 --> 00:23:07,150
+هاي الـ Proton Bomb Inhibitor أو الـ PPI والـ H2
+
+296
+00:23:07,150 --> 00:23:11,470
+Receptor Blockers هذه بتديناش Release سريع لكن
+
+297
+00:23:11,470 --> 00:23:17,530
+مفقولها أكبر، ليش؟ لأنها عمليا بتخفف أو بتوقف
+
+298
+00:23:17,530 --> 00:23:21,510
+إفراز الحامض اللي أهم من هيك يا جماعة وهذا لاحظناه
+
+299
+00:23:21,510 --> 00:23:27,790
+عند ناس كتير اللي هي الـ Garde Dietالـ Gear Diet
+
+300
+00:23:27,790 --> 00:23:34,390
+إنه أنا أحاول أمتنع عن الباكلات أو الأدوية اللي
+
+301
+00:23:34,390 --> 00:23:41,470
+بتسبب للموضوع هذا Avoid foods such as citrus،
+
+302
+00:23:41,470 --> 00:23:47,130
+tomato، coffee، هذي بتعملي directly irritation
+
+303
+00:23:47,130 --> 00:23:52,270
+للـmucosa، onion، شوكليت، peppermint، طبعا الكمية
+
+304
+00:23:52,270 --> 00:23:55,530
+كمان بتلعب دوري يا بابا، إحنا الآن في عصر المجات
+
+305
+00:23:55,530 --> 00:23:59,110
+للأسفكيف يعني عصر المجات؟ صارت الناس لما بدأت تشرب
+
+306
+00:23:59,110 --> 00:24:02,150
+زمان كنا نشرب الجهوة السادة والمرة في فنجان صغير
+
+307
+00:24:02,150 --> 00:24:05,730
+نصه هيك أو فنجان على أجال الفنجان الجهوة التركي
+
+308
+00:24:05,730 --> 00:24:09,710
+العادي، هذا الآن صار كله بيشرب في مجات والكمية
+
+309
+00:24:09,710 --> 00:24:13,750
+الكبيرة هيك كمان بتأثرنا على الموضوعاللي
+
+310
+00:24:13,750 --> 00:24:17,410
+الـpeppermint and any food with high fat content
+
+311
+00:24:17,410 --> 00:24:21,830
+that affects pressure in the stomach Limit or cut
+
+312
+00:24:21,830 --> 00:24:24,910
+the use of non-steroidal ناس اللي بتاخد دايكلوفين
+
+313
+00:24:24,910 --> 00:24:29,850
+و Ibuprofen that may irritate the esophagus and
+
+314
+00:24:29,850 --> 00:24:34,110
+stomach lining Individuals with GERD should avoid
+
+315
+00:24:34,110 --> 00:24:40,770
+whole milkTry to maintain a low-fat diet by
+
+316
+00:24:40,770 --> 00:24:44,670
+staying away from fatty meats and processed meats
+
+317
+00:24:44,670 --> 00:24:48,030
+called cuts اللي هي المرتدلة والحاجات هذه If you
+
+318
+00:24:48,030 --> 00:24:52,450
+must have coffee أو tea حاول تشوف الكافي اللي بدون
+
+319
+00:24:52,450 --> 00:24:55,350
+كفائين أو herbal tea، شاي، عشاب
+
+320
+00:25:00,960 --> 00:25:06,320
+Eat smaller meals Control your weight Don't smoke
+
+321
+00:25:06,320 --> 00:25:10,740
+Eliminate hot pain trigger Don't lie down after a
+
+322
+00:25:10,740 --> 00:25:16,900
+meal Raise the head of the bed وهذا بتدخلنا بعد
+
+323
+00:25:16,900 --> 00:25:21,640
+شوية في موضوع الـBaptic Ulcer
+
+324
+00:25:23,880 --> 00:25:31,020
+والـ Peptic Ulcer Disease بيو دي بيو دي فيه منه
+
+325
+00:25:31,020 --> 00:25:33,240
+gastric ulcer زي ما احنا شايفين في الصورة وفيه
+
+326
+00:25:33,240 --> 00:25:38,340
+دودنال ulcer يعني ulcer اللي هو المعدة و ulcer أو
+
+327
+00:25:38,340 --> 00:25:42,420
+قروحة المعدة و قروحة الأثنى عشر الـ Peptic Ulcer
+
+328
+00:25:42,420 --> 00:25:46,640
+Disease known as Peptic Ulcer or Stomach Ulcer is
+
+329
+00:25:46,640 --> 00:25:50,770
+a prickأو breakage in the lining of the stomach،
+
+330
+00:25:50,770 --> 00:25:55,410
+first part of the small intestine أو الدودنوم زي
+
+331
+00:25:55,410 --> 00:26:00,750
+ما بنقول و occasionally the lower esophagus الـ
+
+332
+00:26:00,750 --> 00:26:04,790
+ulcer in the stomach is known as a gastric ulcer
+
+333
+00:26:04,790 --> 00:26:08,670
+في حين اللي هو في ال small أو first part of the
+
+334
+00:26:08,670 --> 00:26:15,050
+intestine بنقول عنه دودنال ulcerالخطر العمري
+
+335
+00:26:15,050 --> 00:26:20,530
+للتطور من الـ Apoptic Ulcer هو حوالي 10% تقريبًا،
+
+336
+00:26:20,530 --> 00:26:24,450
+طبعًا أنا أعتقد أن الموضوع أكبر من هيك و أكتر من
+
+337
+00:26:24,450 --> 00:26:28,170
+هيك، لكن ليش؟ لأن كتير من الناس بتعالج نفسها
+
+338
+00:26:28,170 --> 00:26:32,230
+بالطرق الـ Herbal العادية بدون متوجه للإحصائيات،
+
+339
+00:26:32,230 --> 00:26:36,670
+في البلدان الغربية الـ Bad scent of people with
+
+340
+00:26:36,670 --> 00:26:40,410
+helicobacter pylori، الـ helicobacter pylori هي
+
+341
+00:26:40,410 --> 00:26:47,020
+عبارة عنعبارة عن اللي هو البكتيريا اللي الآن اتهمت
+
+342
+00:26:47,020 --> 00:26:51,080
+اتهام مباشر بإنها سبب الـ Peptic وDowdenal Ulcer
+
+343
+00:26:51,080 --> 00:26:55,160
+اللي هي البكتيريا
+
+344
+00:26:55,160 --> 00:27:00,060
+العصوية أو حاجة زي هي Helicobacter Pylori
+
+345
+00:27:00,060 --> 00:27:04,900
+Infection Roughly Match Age 20% من الناس العمرهم
+
+346
+00:27:04,900 --> 00:27:10,460
+عشرين سنة عندهم Helicobacterثلاثين في المية من
+
+347
+00:27:10,460 --> 00:27:12,720
+عمرهم ثلاثين تمانين في المية من عمرهم تمانين عندهم
+
+348
+00:27:12,720 --> 00:27:14,900
+helicopter infection
+
+349
+00:27:17,650 --> 00:27:20,410
+وزي ما قلنا الـ ECO-FACTOR من أهم الأسباب اللي
+
+350
+00:27:20,410 --> 00:27:23,950
+بتعملنا Gastroesophageal، عفوا، Peptic Ulcer
+
+351
+00:27:23,950 --> 00:27:28,910
+Transmission is by food contaminated groundwater و
+
+352
+00:27:28,910 --> 00:27:33,190
+through human saliva زي kissing مثلا أو sharing
+
+353
+00:27:33,190 --> 00:27:38,830
+food utensils استعمال الأدوات والمعالج والشوك ورا
+
+354
+00:27:38,830 --> 00:27:42,870
+بعض من الـ Symptoms والـ Sign تبقى الـ Peptic
+
+355
+00:27:42,870 --> 00:27:47,680
+Ulcer الـ Abdominal Painبالذات Epigastric المنطقة
+
+356
+00:27:47,680 --> 00:27:53,640
+اللي هي تحت الجلب زي ما احنا شايفين في الصورةفي
+
+357
+00:27:53,640 --> 00:27:59,280
+حالة دودنالألسر، الشعور يظهر خلال ثلاث ساعات بعد
+
+358
+00:27:59,280 --> 00:28:03,260
+أخذ طعام، يعني في الـGastric Ulcers، ع السريع
+
+359
+00:28:03,260 --> 00:28:06,840
+الوجع، بتاكل و بتتوجع، الدودنالألسر بعد ثلاث
+
+360
+00:28:06,840 --> 00:28:10,260
+ساعات، من ساعته لثلاث ساعات بعد الميل، Bloating،
+
+361
+00:28:10,260 --> 00:28:13,600
+بيصير إنه نفخة، أبدوم للـFullness، حاسس بطن ملان،
+
+362
+00:28:13,600 --> 00:28:17,760
+Nausea and vomiting، ممكن يكون كمان، من الـSigns
+
+363
+00:28:17,760 --> 00:28:23,050
+and Symptoms، Loss of Appetite،Weight Loss،
+
+364
+00:28:23,050 --> 00:28:30,690
+Hematemesis، Hematemesis
+
+365
+00:28:30,690 --> 00:28:34,730
+ملينا، ملينا
+
+366
+00:28:34,730 --> 00:28:38,570
+هو الدم اللي بنزل من المعدة لكن بدخل على الجهاز
+
+367
+00:28:38,570 --> 00:28:43,950
+الهضمي وبتفاعل مع الحامضبالـ DNA بيصيروا عملية
+
+368
+00:28:43,950 --> 00:28:48,110
+Oxidation للـ Iron اللي فيه من اللي في الـ
+
+369
+00:28:48,110 --> 00:28:53,810
+Hemoglobin وهذا عبارة عن دم بس بشكله زي الزفتة
+
+370
+00:28:53,810 --> 00:29:01,190
+الطريقة فاول Smelling Faces بوراز زي الزفتة هيك
+
+371
+00:29:01,190 --> 00:29:05,650
+ريحته سيئة و بنلاقيها نزلت مع البوراز هذا عبارة عن
+
+372
+00:29:05,650 --> 00:29:15,030
+دم لكن صار له عملية Oxidationالأسباب هي أهم متهم
+
+373
+00:29:15,030 --> 00:29:18,290
+major causative factor is chronic inflammation
+
+374
+00:29:18,290 --> 00:29:23,810
+بالـ Helicobacter pylori that colonize the mucosa
+
+375
+00:29:23,810 --> 00:29:30,250
+60% of gastric ulcer هي السبب 50 إلى 75% of Dowden
+
+376
+00:29:30,250 --> 00:29:31,410
+ulcer
+
+377
+00:29:33,500 --> 00:29:37,420
+المتهم التاني اللي هي الـ Non-steroidal أدوية Non
+
+378
+00:29:37,420 --> 00:29:41,740
+-steroidal Anti-inflammatory drugs وزي ما قلنا هي
+
+379
+00:29:41,740 --> 00:29:47,220
+المتهم الآخر، المتهم التاني يعني
+
+380
+00:29:47,220 --> 00:29:54,820
+معلومة مشهورة عند الكل ونتيجة كتر وانتشار استعمال
+
+381
+00:29:56,270 --> 00:29:58,790
+اللي هو الـ Non-Steroidal Anti-Inflammatory Drugs
+
+382
+00:29:58,790 --> 00:30:04,530
+الـ ميكانيزم هي موجودة عندكم مكتوبة أدت إلى إنه
+
+383
+00:30:04,530 --> 00:30:07,570
+يصير عندنا Peptic Ulcer أو Dowden Ulcer والحاجة
+
+384
+00:30:07,570 --> 00:30:10,670
+التالتة واللي برضه مشهورة بصورة كبيرة لـ Stress
+
+385
+00:30:10,670 --> 00:30:14,890
+due to serious health problems واحنا بنقول غالبا
+
+386
+00:30:14,890 --> 00:30:20,830
+الناس اللي بت dampفي العناية المركزة لسبب آخر
+
+387
+00:30:20,830 --> 00:30:23,730
+نتيجة الـ stress اللي صار معهم لازم تكون حاجة
+
+388
+00:30:23,730 --> 00:30:27,410
+كبيرة تعملنا الموضوع والحاجة الرابعة من ال causes
+
+389
+00:30:27,410 --> 00:30:29,890
+اللي هو ال dietالشيء الوحيد هو الواقعيات البيوترية
+
+390
+00:30:29,890 --> 00:30:35,290
+مثل المشروع والتناول الكفاين والكوفي والألكوهول
+
+391
+00:30:35,290 --> 00:30:40,330
+أيضًا مفهومًا لإسباب أو إكسسيربات ألثار وطبعًا
+
+392
+00:30:40,330 --> 00:30:46,450
+النار كمان لاجوا يعني بعض الـ studies لاجت فيه
+
+393
+00:30:46,450 --> 00:30:50,530
+علاقة بالموضوع الـ diagnosis how to diagnose
+
+394
+00:30:50,530 --> 00:30:56,830
+mainly based on the characteristic symptoms
+
+395
+00:31:02,120 --> 00:31:15,880
+وهنا بيصير عندنا
+
+396
+00:31:15,880 --> 00:31:22,180
+في assignment how to diagnose غير اللي أنا كاتبه
+
+397
+00:31:22,180 --> 00:31:22,380
+هنا
+
+398
+00:31:26,110 --> 00:31:31,270
+الـ Helicobacter Infestation
+
+399
+00:31:31,270 --> 00:31:37,510
+عند المريض كيف الـ diagnosis تبع الـ Helicobacter؟
+
+400
+00:31:37,510 --> 00:31:40,470
+ايش الفحوصات اللي بتنعمل؟ في تلت اربع فحوصات، اشي
+
+401
+00:31:40,470 --> 00:31:47,070
+من الدم، اشي من الاستول، اشي من الـ antibody، اشي
+
+402
+00:31:47,070 --> 00:31:54,290
+من النفس، بدي الطرقوإيش أفضلها ممكن نعمل
+
+403
+00:31:54,290 --> 00:31:59,190
+comparison بين الطرق بس جدول هيك الطرق اللي بعمل
+
+404
+00:31:59,190 --> 00:32:03,230
+فيها فحص وإيش أفضلها هذا ال assignment التبعنا
+
+405
+00:32:05,270 --> 00:32:07,450
+Gastrointestinal bleeding طبعاً بدل ما أنا عندي
+
+406
+00:32:07,450 --> 00:32:10,210
+جرح ممكن يصير عندي نزيف The most common
+
+407
+00:32:10,210 --> 00:32:13,050
+complication لهذا الدرجة أه طبعا sudden large
+
+408
+00:32:13,050 --> 00:32:15,790
+bleeding can be life threatening وطبعا ال bleeding
+
+409
+00:32:15,790 --> 00:32:21,330
+ممكن يدخلنا بhypovolemic الشك زي ما الكل عارف إيش
+
+410
+00:32:21,330 --> 00:32:25,310
+كمان perforation أه ممكن يصير عندي مش بس bleeding
+
+411
+00:32:25,310 --> 00:32:28,730
+تفتح المعدة لبرا وهذه طبعا catastrophic
+
+412
+00:32:28,730 --> 00:32:35,360
+complication ممكن نتيجة أنه بعد فترةلو كان عندي
+
+413
+00:32:35,360 --> 00:32:37,840
+على الـ gastric outlet على مخرج المعدة فيه عندي
+
+414
+00:32:37,840 --> 00:32:47,140
+هناك قرحة وصارت طابت أو راجت عملت الـ Scarring و
+
+415
+00:32:47,140 --> 00:32:51,600
+بعد الـ Scarring عملت له obstruction of the outlet
+
+416
+00:32:51,600 --> 00:32:55,860
+وطبعا اللي حكينا عنه في الـ differential يعني لازم
+
+417
+00:32:55,860 --> 00:32:57,900
+أحطه في الـ differential diagnosis ما هوش بس
+
+418
+00:32:57,900 --> 00:33:03,360
+complication هو الـ cancer وطبعا لابد من عينة
+
+419
+00:33:04,010 --> 00:33:12,070
+العلاج الحقيقة بيتمثل في أكتر من حاجة الحاجة
+
+420
+00:33:12,070 --> 00:33:15,790
+الأولى acid reducing medication الحاجة التانية لل
+
+421
+00:33:15,790 --> 00:33:19,390
+infection لازم أدي علاج two antibiotics يبقى بدي
+
+422
+00:33:19,390 --> 00:33:23,030
+إشي مضاد للحاجة اسمها triple therapy triple يعني
+
+423
+00:33:23,030 --> 00:33:28,230
+ثلاثي therapy نين مضادات حيوية واحد antacid أو
+
+424
+00:33:28,230 --> 00:33:33,530
+acid reducing medication زي ال PPI معاهملما يكون
+
+425
+00:33:33,530 --> 00:33:43,790
+عندنا Peripheric Ulcer «العوامل
+
+426
+00:33:43,790 --> 00:33:51,710
+التي تؤدي» أو «التجارب» لـ Gastric Ulcer اللي هو
+
+427
+00:33:51,710 --> 00:33:56,730
+Reduction of Drug Intake حاول أنتبه للـ
+
+428
+00:33:56,730 --> 00:34:02,050
+Helicobacter، الـ «دايت»stress smoking and alcohol
+
+429
+00:34:02,050 --> 00:34:06,730
+اللي هي تحت اسم lifestyle risk factors دايما إذا
+
+430
+00:34:06,730 --> 00:34:13,750
+إذا اتغلبت على المسببات بتغلب على المرض بإذن الله
+
+431
+00:34:13,750 --> 00:34:19,090
+تعالى وربنا هو الشافعي و بتمنالكوا يوم سعيد
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.json b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.json
new file mode 100644
index 0000000000000000000000000000000000000000..4f92ac8f29315f831197c045be988870d6f8c4e2
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.json
@@ -0,0 +1 @@
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"probability": 0.8134765625}, {"start": 1046.02, "end": 1046.6, "word": " الـ", "probability": 0.70068359375}, {"start": 1046.6, "end": 1046.82, "word": " Whole", "probability": 0.43017578125}, {"start": 1046.82, "end": 1047.16, "word": " Body", "probability": 0.6279296875}, {"start": 1047.16, "end": 1048.0, "word": " Circulation", "probability": 0.93408203125}, {"start": 1048.0, "end": 1048.54, "word": " فينا", "probability": 0.45770263671875}, {"start": 1048.54, "end": 1048.84, "word": " حاجة", "probability": 0.9962565104166666}, {"start": 1048.84, "end": 1049.24, "word": " اسمها", "probability": 0.8634440104166666}, {"start": 1049.24, "end": 1049.96, "word": " Coronary", "probability": 0.826171875}, {"start": 1049.96, "end": 1051.36, "word": " Circulation", "probability": 0.93798828125}, {"start": 1051.36, "end": 1053.24, "word": " الـ", "probability": 0.776611328125}, {"start": 1053.24, "end": 1053.6, "word": " Coronary", "probability": 0.87451171875}, {"start": 1053.6, "end": 1054.3, "word": " Circulation", "probability": 0.93798828125}, {"start": 1054.3, "end": 1054.62, "word": " هاي", "probability": 0.714599609375}, {"start": 1054.62, "end": 1056.16, "word": " شغلتها", "probability": 0.908984375}, {"start": 1056.16, "end": 1056.96, "word": " إيش؟", "probability": 0.9656982421875}], "temperature": 1.0}, {"id": 45, "seek": 106884, "start": 1057.35, "end": 1068.85, "text": "طبيعي هو صحيح القلب بدعم كل الجسم لكن هو نفسه كمان بده الـ circulation خاص بيه لتغذية to supply blood to the heart muscle", "tokens": [9566, 21292, 3615, 1829, 31439, 20328, 5016, 1829, 5016, 25062, 46152, 47525, 25957, 28242, 25724, 38251, 44381, 31439, 8717, 36178, 3224, 9122, 2304, 7649, 47525, 3224, 2423, 39184, 23168, 16490, 33546, 4724, 1829, 3224, 5296, 2655, 17082, 8848, 10632, 281, 5847, 3390, 281, 264, 1917, 8679], "avg_logprob": -0.2004654306046506, "compression_ratio": 1.2430555555555556, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1057.35, "end": 1057.89, 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"text": "يبقى الـ Atrium Ventricular Valves موجودة بين الـ Atrium والـ Ventricle وشغلتها تمنع الـ Backflow، الدم مايرجعش لما يصير عندي الـ Diastolicum مايرجعش الدم من الـ Atrium to the Ventricle لأنه لو رجع، بعملي Overload عوين على الـ Ventricles لأنه عبّى فيه دم بزيادة، دم مش لازم يتعبّى هناك", "tokens": [1829, 3555, 4587, 7578, 2423, 39184, 1711, 13015, 28290, 42750, 7188, 977, 3714, 29245, 23328, 3660, 49374, 2423, 39184, 1711, 13015, 16070, 39184, 28290, 1341, 306, 4032, 8592, 17082, 1211, 2655, 11296, 46811, 1863, 3615, 2423, 39184, 5833, 10565, 12399, 32748, 2304, 19446, 13546, 7435, 3615, 8592, 5296, 15042, 7251, 9381, 13546, 18871, 16254, 2423, 39184, 8789, 525, 7940, 449, 19446, 13546, 7435, 3615, 8592, 32748, 2304, 9154, 2423, 39184, 1711, 13015, 281, 264, 28290, 1341, 306, 5296, 33456, 3224, 45164, 12602, 7435, 3615, 12399, 4724, 25957, 20292, 4886, 2907, 6225, 2407, 9957, 15844, 2423, 39184, 28290, 1341, 904, 5296, 33456, 3224, 6225, 3555, 11703, 7578, 8978, 3224, 11778, 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1381.82, "end": 1406.46, "text": "في عندنا أو الـ pericardium في عندنا الـ myocardium و بعدين ال endocardium ال myocardium بيمثل ال cardiac muscle layer forming bulk وقولنا ال heart من برا بنشوف فيه ال mainly ال right ventricle و left ventricle مع ال coronary arteries و ال auricles و بنشوف ال pulmonary artery", "tokens": [41185, 43242, 8315, 34051, 2423, 39184, 680, 299, 515, 2197, 8978, 43242, 8315, 2423, 39184, 452, 905, 515, 2197, 4032, 39182, 9957, 2423, 917, 905, 515, 2197, 2423, 452, 905, 515, 2197, 4724, 32640, 12984, 1211, 2423, 32129, 8679, 4583, 15745, 16139, 4032, 39648, 8315, 2423, 1917, 9154, 4724, 23557, 44945, 8592, 38688, 8978, 3224, 2423, 8704, 2423, 558, 6931, 1341, 306, 4032, 1411, 6931, 1341, 306, 20449, 2423, 10451, 822, 44801, 4032, 2423, 19145, 5350, 4032, 44945, 8592, 38688, 2423, 8331, 46386, 38520], "avg_logprob": -0.21341911343967213, "compression_ratio": 1.7365853658536585, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 1381.82, "end": 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1401.46, "word": " ventricle", "probability": 0.9710286458333334}, {"start": 1401.46, "end": 1401.86, "word": " مع", "probability": 0.96728515625}, {"start": 1401.86, "end": 1402.04, "word": " ال", "probability": 0.86865234375}, {"start": 1402.04, "end": 1402.5, "word": " coronary", "probability": 0.936767578125}, {"start": 1402.5, "end": 1403.04, "word": " arteries", "probability": 0.98876953125}, {"start": 1403.04, "end": 1403.92, "word": " و", "probability": 0.8291015625}, {"start": 1403.92, "end": 1404.22, "word": " ال", "probability": 0.9287109375}, {"start": 1404.22, "end": 1404.9, "word": " auricles", "probability": 0.926513671875}, {"start": 1404.9, "end": 1405.12, "word": " و", "probability": 0.94580078125}, {"start": 1405.12, "end": 1405.4, "word": " بنشوف", "probability": 0.9794921875}, {"start": 1405.4, "end": 1405.52, "word": " ال", "probability": 0.69140625}, {"start": 1405.52, "end": 1405.88, "word": " pulmonary", "probability": 0.941162109375}, {"start": 1405.88, "end": 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" حاجات", "probability": 0.9851888020833334}, {"start": 1412.96, "end": 1413.3, "word": " كتير", "probability": 0.9275716145833334}, {"start": 1413.3, "end": 1413.82, "word": " تانية", "probability": 0.974609375}, {"start": 1413.82, "end": 1414.52, "word": " زي", "probability": 0.790283203125}, {"start": 1414.52, "end": 1414.86, "word": " اللي", "probability": 0.78955078125}, {"start": 1414.86, "end": 1415.12, "word": " هي", "probability": 0.84716796875}, {"start": 1415.12, "end": 1415.26, "word": " الـ", "probability": 0.60546875}, {"start": 1415.26, "end": 1415.58, "word": " Pulmonary", "probability": 0.921875}, {"start": 1415.58, "end": 1416.14, "word": " Veins", "probability": 0.895751953125}, {"start": 1416.14, "end": 1416.82, "word": " و", "probability": 0.8759765625}, {"start": 1416.82, "end": 1417.78, "word": " الـ", "probability": 0.69189453125}, {"start": 1417.78, "end": 1417.92, "word": " Vena", "probability": 0.623779296875}, {"start": 1417.92, "end": 1418.18, "word": " 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\ No newline at end of file
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..e25332dc6450b269b756fc220491010f5f2ba985
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/TvX3vXGCsd4_raw.srt
@@ -0,0 +1,1412 @@
+1
+00:00:01,400 --> 00:00:03,420
+بسم الله الرحمن الرحيم والحمد للرحمن الرحيم الصلاة
+
+2
+00:00:03,420 --> 00:00:06,980
+والسلام علي سيدنا محمد وسيد المرسلين اجمعين طبعا
+
+3
+00:00:06,980 --> 00:00:13,100
+ريحناكم اول انبارح السبت وننطلق مرة تانية ان شاء
+
+4
+00:00:13,100 --> 00:00:19,240
+الله تعالى في بداية ال cardiovascular systemالان
+
+5
+00:00:19,240 --> 00:00:23,920
+هنتحدث عن ال heart هنحكي شوية anatomy و شوية
+
+6
+00:00:23,920 --> 00:00:26,820
+physiology بس عشان أسهل عليكم الموضوع بعد هيك بس
+
+7
+00:00:26,820 --> 00:00:31,120
+يعني انما هو يعني ال heart عشان أحكي في ال anatomy
+
+8
+00:00:31,120 --> 00:00:34,500
+تبعه و ال physiology يعني ممكن يحتاج الواحد فصول
+
+9
+00:00:34,500 --> 00:00:38,040
+أو فصل للموضوع عادة لكن احنا بنحاول نتعرف على ال
+
+10
+00:00:38,040 --> 00:00:42,690
+heart بصورة كبيرةحتى نفهم الـ Diseases اللي بتنشأ
+
+11
+00:00:42,690 --> 00:00:49,150
+نتيجة مشكلة الـ Heart الـ Heart Anatomy حقيقة يعني
+
+12
+00:00:49,150 --> 00:00:54,290
+هو عبارة عن بقدر القبضة، قبضة الإيد، يعني Size of
+
+13
+00:00:54,290 --> 00:00:58,970
+your fist تقريبا، وبيحد الـ Heart
+
+14
+00:01:05,400 --> 00:01:11,240
+وهو خلف الـsternum،
+
+15
+00:01:11,240 --> 00:01:16,110
+أمام الـvertebral columnبشويه شمال من الـ midline
+
+16
+00:01:16,110 --> 00:01:21,030
+وهو يعلو الـ diaphragm هاي المقصود في الموضوع يبقى
+
+17
+00:01:21,030 --> 00:01:27,690
+مهم نعرف مكان القلب طيب هو احنا قلنا left to the
+
+18
+00:01:27,690 --> 00:01:36,230
+midline هو فيه right to the midline يعني left to
+
+19
+00:01:36,230 --> 00:01:39,350
+the midline الوضع الطبيعي بيقول عنه «sense through
+
+20
+00:01:39,350 --> 00:01:43,270
+cardiac»طيب write to the midline هذا إذا في إيش
+
+21
+00:01:43,270 --> 00:01:49,990
+بقول عنه دكسترا cardiac دكسترا يمين cardiac قلب
+
+22
+00:01:49,990 --> 00:01:52,870
+قلب عاليمين في منه الكلام هذا وبيجي في إطار
+
+23
+00:01:52,870 --> 00:01:57,730
+abnormality و و syndromes يعني متلازمة في الغالب و
+
+24
+00:01:57,730 --> 00:02:02,090
+بيبقى كل أعضاء الجسم بالطريقة هذه لافة اللي ع
+
+25
+00:02:02,090 --> 00:02:04,250
+الشمال موجود ع اليمين و اللي ع اليمين موجود ع
+
+26
+00:02:04,250 --> 00:02:09,060
+الشمالطيب، إيش الـ Coverings of the Heart؟ إيش
+
+27
+00:02:09,060 --> 00:02:15,260
+الحاجات اللي هي محيطة بالقلب؟ رقم واحد، بدنا نحكي
+
+28
+00:02:15,260 --> 00:02:19,860
+عن البريكارديوم البريكارديوم هو حاجة برنية، دعوني
+
+29
+00:02:19,860 --> 00:02:23,840
+أشوف الصورة اللي بعدها البريكارديوم هو إشي من برا
+
+30
+00:02:23,840 --> 00:02:29,040
+البريكارديوم هذا بتكون من Double
+
+31
+00:02:29,040 --> 00:02:33,680
+-Walled sack around the heartوهو الـ Double-walled
+
+32
+00:02:33,680 --> 00:02:39,400
+sack كيس حوالين دبل وولد اللي له جدارين حنعرف إن
+
+33
+00:02:39,400 --> 00:02:44,600
+هما الجدارين sack around a heart وبيتكون من حاجة
+
+34
+00:02:44,600 --> 00:02:47,950
+superficial وحاجة deepفى الـ Subficial بيبقى
+
+35
+00:02:47,950 --> 00:02:50,710
+Fibrous Pericardium بنقول عنه زى ما احنا شايفينه
+
+36
+00:02:50,710 --> 00:02:53,770
+فى الرسمة Fibrous Pericardium وفى عندنا الـ Deep
+
+37
+00:02:53,770 --> 00:02:57,510
+اللى هو الـ Two Layer Serous Pericardium بيبقى
+
+38
+00:02:57,510 --> 00:03:00,610
+عندنا Fibrous Pericardium وSerous Pericardium
+
+39
+00:03:00,610 --> 00:03:03,810
+Serous Pericardium لجوا من الجلب أو على الجلب
+
+40
+00:03:03,810 --> 00:03:07,470
+وبيبقى بتكون من Two Layers الـ Two Layers واحدة
+
+41
+00:03:07,470 --> 00:03:13,850
+اسمها Parietal Layer وهدى Lines The Internal
+
+42
+00:03:13,850 --> 00:03:18,400
+Surface Of The Fibrousبريكارديوم وفيه الـ visceral
+
+43
+00:03:18,400 --> 00:03:25,840
+layer or ابيكارديوم بنسمي الـ visceral layer للسرس
+
+44
+00:03:25,840 --> 00:03:29,420
+بريكارديوم بنقول عنه ابيكارديوم lines the surface
+
+45
+00:03:29,420 --> 00:03:36,160
+of the heart وبيبقى بينهم هدول ال two layers اللي
+
+46
+00:03:36,160 --> 00:03:40,160
+هو ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+47
+00:03:40,160 --> 00:03:40,520
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+48
+00:03:40,520 --> 00:03:41,360
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+49
+00:03:41,360 --> 00:03:42,100
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+50
+00:03:42,100 --> 00:03:42,140
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+51
+00:03:42,140 --> 00:03:42,140
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+52
+00:03:42,140 --> 00:03:42,140
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+53
+00:03:42,140 --> 00:03:42,140
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+54
+00:03:42,140 --> 00:03:44,840
+ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال ال
+
+55
+00:03:44,840 --> 00:03:49,460
+البين الـ two layers يبقى أحدى الآن كمان مرة الـ
+
+56
+00:03:49,460 --> 00:03:53,360
+pericardium يتكون من two أو double walled sack
+
+57
+00:03:53,360 --> 00:03:57,180
+around the heart اللي من برا superficial fibrous
+
+58
+00:03:57,180 --> 00:04:00,160
+pericardium من جوا أديب two layer cerous
+
+59
+00:04:00,160 --> 00:04:05,140
+pericardium اللي على طول على حدود ال superficial
+
+60
+00:04:05,140 --> 00:04:10,120
+fibrous pericardium اسمه parietal layer واللي جوا
+
+61
+00:04:10,120 --> 00:04:12,800
+بنسميه visceral layer طلعوا على الرسمة عشان
+
+62
+00:04:12,800 --> 00:04:18,500
+تساعدكمفي التصور الـ visceral layer أو الـ
+
+63
+00:04:18,500 --> 00:04:21,740
+Epicardium لعنوان الـ service of the heart وبين
+
+64
+00:04:21,740 --> 00:04:24,700
+الـ two layers اللي هي البريطال و الvisceral في
+
+65
+00:04:24,700 --> 00:04:28,120
+عندنا fluid-filled cavity بيقولوا هنا pericardial
+
+66
+00:04:28,120 --> 00:04:35,030
+cavity هي الصورةاللي هو الـ Fibrous Pericardium
+
+67
+00:04:35,030 --> 00:04:38,230
+وبعدين بندخل على الـ Two Layers اللي هي الـ
+
+68
+00:04:38,230 --> 00:04:41,110
+Visceral Layer و البريطال Layer بينهم Pericardial
+
+69
+00:04:41,110 --> 00:04:44,870
+Cavity و الـ Visceral Layer اللي قولنا عنها
+
+70
+00:04:44,870 --> 00:04:48,330
+Epicardium على طول بيجي على مين؟ على الـ
+
+71
+00:04:48,330 --> 00:04:53,110
+Myocardium ماحنشوف بعد شوية طيب هي إيش شغلة
+
+72
+00:04:53,110 --> 00:04:58,440
+البريكارديوم؟ واضح إن هيمربطة الجلب عمليًا protect
+
+73
+00:04:58,440 --> 00:05:01,960
+وتحمي القلب and anchor the heart prevent over
+
+74
+00:05:01,960 --> 00:05:05,800
+filling لو الجلب بده يتعب بزيادة هذه بتيجي ال wall
+
+75
+00:05:05,800 --> 00:05:13,360
+ال elastic wall هاي بتمنعه من أنه يتمدد و allows
+
+76
+00:05:13,360 --> 00:05:17,460
+the heart to work in a relatively friction-free
+
+77
+00:05:17,460 --> 00:05:21,380
+environment مايخلوش يحق يظل يحق في الأعضاء ما حوله
+
+78
+00:05:21,920 --> 00:05:26,680
+يبقى احنا حكينا قبل شوية عن مين، كمان مرة، ايوة
+
+79
+00:05:26,680 --> 00:05:30,700
+صحيح عن البريكارديوم، وقولنا البريكارديوم في عنده
+
+80
+00:05:30,700 --> 00:05:39,000
+double wall ال wall براني، اش اسمه؟ fibrous
+
+81
+00:05:39,000 --> 00:05:44,880
+pericardium، و الجواني، ايوة, cerous pericardium،
+
+82
+00:05:44,880 --> 00:05:50,240
+الcerous pericardium في منه البرايتلوفيه منه الـ
+
+83
+00:05:50,240 --> 00:05:53,420
+Vesceral الـ Vesceral بيقول عنه Epicardium و بينهم
+
+84
+00:05:53,420 --> 00:05:57,720
+فيه اللي هو Cavity و ال Cavity هي Fluid Filled
+
+85
+00:05:57,720 --> 00:06:07,820
+Pericardial Fluid و بيقول عنه Pericardial
+
+86
+00:06:07,820 --> 00:06:13,280
+Cavity بعدين بيجي لتحت من ال Epicardium مين؟
+
+87
+00:06:13,280 --> 00:06:16,820
+شايفين انتوا العضل هذا العضلة العضلة؟ هذه ال
+
+88
+00:06:16,820 --> 00:06:21,990
+Myocardiumوهذا هو عبارة عن muscle layer forming
+
+89
+00:06:21,990 --> 00:06:27,070
+the bulk of the heart هذه العضلة القلبية الـ
+
+90
+00:06:27,070 --> 00:06:32,750
+myocardium هي المادة الـ bulk تبع القلب وبعدين
+
+91
+00:06:32,750 --> 00:06:35,510
+بيجي عنا حاجة زي fibrous skeleton
+
+92
+00:06:39,120 --> 00:06:43,420
+وهي كما بيقولوها layer زي connective tissue وبعدين
+
+93
+00:06:43,420 --> 00:06:45,960
+بيجي عنا الـ endocardium و اللي بنسمع عنه كتير و
+
+94
+00:06:45,960 --> 00:06:49,040
+اللي بيصير فيه كتير endocarditis التهابات اللي هو
+
+95
+00:06:49,040 --> 00:06:53,020
+الـ endocardium من جوا على الدم عدل يعني الدم هو
+
+96
+00:06:53,020 --> 00:06:55,840
+على طول في جلب الجلب مضرب في مين؟ في ال
+
+97
+00:06:55,840 --> 00:06:59,820
+endocardium يبقى Epicardium, Myocardium andوهنا
+
+98
+00:06:59,820 --> 00:07:01,820
+يوجد أيضًا Endocardium، Epicardium، Myocardium
+
+99
+00:07:01,820 --> 00:07:05,260
+وEndocardium وفي بينهم Fibrous Skeleton أو
+
+100
+00:07:05,260 --> 00:07:10,680
+Connective Tissue هذا بالنسبة للـ Wall of the
+
+101
+00:07:10,680 --> 00:07:15,040
+Heart كيف اتكون، الآن نتحدث أيش المحتويات تاعة
+
+102
+00:07:15,040 --> 00:07:19,600
+القلب لو أنا طلعتله من قدامي، يعني فتحت صدر حد
+
+103
+00:07:20,450 --> 00:07:24,370
+وفتحت الـ sternum و طلعت على القلب هشوف المنظر
+
+104
+00:07:24,370 --> 00:07:26,750
+اللي أنا شايفه الآن اللي هو الـ External heart
+
+105
+00:07:26,750 --> 00:07:31,150
+vessels that supply أو drain their heart زي ما
+
+106
+00:07:31,150 --> 00:07:34,610
+احنا شايفين شايفين احنا الـ left ventricle طبعا
+
+107
+00:07:34,610 --> 00:07:37,690
+للأسف مش قادر أشيرلكوا لأن حتى البرنامج مش بسمحش
+
+108
+00:07:37,690 --> 00:07:40,510
+بهيك لكن تبعوا معايا أنا مش هحك كتير في الموضوع
+
+109
+00:07:40,510 --> 00:07:44,730
+هذا انتوا حاولوا تشوفوا إيش الحاجات وإن الـ left
+
+110
+00:07:44,730 --> 00:07:47,590
+ventricle أو ال right ventricle و ال left
+
+111
+00:07:47,590 --> 00:07:52,480
+ventricleعلى جهة هاي و بعدين في عندنا الأورطة اللي
+
+112
+00:07:52,480 --> 00:07:57,120
+بالأحمر طالع و في عندنا طبعا ال apex اللي تحت تحت
+
+113
+00:07:57,120 --> 00:08:02,980
+على الآخر قمة القلب و بعدين في عندنا من ال right
+
+114
+00:08:02,980 --> 00:08:06,260
+ventricle طالع اللي هو pulmonary artery أو
+
+115
+00:08:06,260 --> 00:08:11,980
+pulmonary trunk و هذا جنب على طول ال .. في حاجة
+
+116
+00:08:11,980 --> 00:08:15,700
+اسمها ligamentum arteriosum موجودة بين pulmonary
+
+117
+00:08:15,700 --> 00:08:19,700
+artery و بين الأورطةوفي الـVenacava Superior
+
+118
+00:08:19,700 --> 00:08:22,580
+وVenacava Inferior هدول دخلين على وين؟ على
+
+119
+00:08:22,580 --> 00:08:29,600
+الـRight Atrium لكن
+
+120
+00:08:29,600 --> 00:08:35,100
+لما أتيت أطلع على الـHeart من الخلف بيختلف المنظر
+
+121
+00:08:35,100 --> 00:08:39,940
+هلاقي أنه أنا بحكي الـPulmonary Veins الأربعة هدول
+
+122
+00:08:39,940 --> 00:08:44,620
+جايين دخلين على الـLeft Atrium
+
+123
+00:08:47,460 --> 00:08:51,760
+وحشوف إن الـ Left Ventricle كتير بشوف منه جزء و
+
+124
+00:08:51,760 --> 00:08:55,140
+الـ Right Ventricle كمان وفيه طبعا أكتر حاجة
+
+125
+00:08:55,140 --> 00:08:58,740
+شايفها اللون الأزرق هدول اللي هما Left Pulmonary
+
+126
+00:08:58,740 --> 00:09:02,220
+Artery وRight Pulmonary Artery لكن برضه ما ننساش
+
+127
+00:09:02,220 --> 00:09:05,120
+إن الـVena Cava Superior وVena Cava Inferior من
+
+128
+00:09:05,120 --> 00:09:09,760
+الخلف بيانين كتير وفي إن الـCoronary Sinus كمان في
+
+129
+00:09:09,760 --> 00:09:15,700
+نص الـHeart بياخد دم من القلب وبيصب على الـHeart
+
+130
+00:09:17,850 --> 00:09:20,630
+طيب لو جينا تطلعنا على ال gross anatomy of the
+
+131
+00:09:20,630 --> 00:09:29,670
+heart هنلاقي إنه عندنا هذا قطع طولي من ال heart
+
+132
+00:09:29,670 --> 00:09:34,590
+هنلاقي خلينا نمشي vena cava inferior and superior
+
+133
+00:09:34,590 --> 00:09:38,290
+وين بيدخل بيجي الدم بدخل منهم ال vena cava
+
+134
+00:09:38,290 --> 00:09:43,840
+inferiorبجيبلي دم من ال lower limbs و ال superior
+
+135
+00:09:43,840 --> 00:09:50,680
+بجيبلي من ال upper trunk و ال head و بدخل الدم
+
+136
+00:09:50,680 --> 00:09:56,460
+لوين بروح على ال right atrium من ال right atrium
+
+137
+00:09:56,460 --> 00:10:00,440
+بدخل الدم على ال right ventricle و زي ما نشايفين
+
+138
+00:10:00,440 --> 00:10:04,340
+ال right ventricle الجدار دبعه ضعيف كتير كتير
+
+139
+00:10:08,130 --> 00:10:14,130
+بعد ما يدخل الدم على الـ right ventricle نتيجة الـ
+
+140
+00:10:14,130 --> 00:10:17,470
+contraction أو الـ «سوستوليكوم» اللي بيصير بيدخلنا
+
+141
+00:10:17,470 --> 00:10:23,230
+الدم على الـ pulmonary artery والـ pulmonary
+
+142
+00:10:23,230 --> 00:10:31,800
+arteries بتودي على ال lungs في نفس الوجدوببقى برضه
+
+143
+00:10:31,800 --> 00:10:36,540
+على الجهة التانية شغال أنه دخل عنا دم من الـ
+
+144
+00:10:36,540 --> 00:10:41,120
+Pulmonary Veins على الـ Left Atrium ومن الـ Left
+
+145
+00:10:41,120 --> 00:10:45,360
+Atrium على الـ Left Ventricle وعند ما يصير نفس
+
+146
+00:10:45,360 --> 00:10:48,020
+الستوليكم اللي صار قبل شوية هو نفس الستوليكم
+
+147
+00:10:48,020 --> 00:10:53,690
+بيدخلي في الأورطة والأورطة بيودي على الـوبعد ذلك
+
+148
+00:10:53,690 --> 00:10:57,790
+يدفع على الـ brain ويدفع على الأبدوميل الأورطة
+
+149
+00:10:57,790 --> 00:11:06,910
+ويدفع دم على whole the body يبقى طب في زي اللي
+
+150
+00:11:06,910 --> 00:11:09,390
+إحنا شايفينهم حاجة زي اللي هي
+
+151
+00:11:12,130 --> 00:11:17,770
+الـ valves موجودة بين الـ right atrium و الـ right
+
+152
+00:11:17,770 --> 00:11:24,190
+ventricle في عندنا الـ tricuspid valve و
+
+153
+00:11:24,190 --> 00:11:28,250
+بين الـ left atrium و ال left ventricle في عندنا
+
+154
+00:11:28,250 --> 00:11:31,830
+الـ bicuspid valve اللي يسمونها الـ neutral valve
+
+155
+00:11:32,970 --> 00:11:35,930
+ولكن في نفس الوقت في عندى لو أنا شايف من الأورطة
+
+156
+00:11:35,930 --> 00:11:40,310
+مش مبين من الأورطة لكن البولمونري البولمونري
+
+157
+00:11:40,310 --> 00:11:45,070
+artery في عندنا اللى هى اللى احنا شايفينها حاجة
+
+158
+00:11:45,070 --> 00:11:52,690
+اسمها semilunar valve زى الهلال هيك valve طالع من
+
+159
+00:11:52,690 --> 00:11:56,750
+ال right ventricle
+
+160
+00:11:56,750 --> 00:11:57,870
+to the lungs
+
+161
+00:12:00,540 --> 00:12:03,920
+طبعا مافيش شيء أصعب من أنه تحكي عن الـ anatomy
+
+162
+00:12:03,920 --> 00:12:09,800
+وانت بس يعني مش .. مش قادر توضح أكتر بالرسم أو
+
+163
+00:12:09,800 --> 00:12:12,460
+بالكذا أو بالألوان أو بالحاجات هذه لكن anyway
+
+164
+00:12:12,460 --> 00:12:17,920
+الموضوع سهل ممكن تفتحه يا جماعة على أي حد على
+
+165
+00:12:17,920 --> 00:12:23,900
+اليوتيوب بيشرح .. بيشرح اللي هو ال .. ال anatomy
+
+166
+00:12:23,900 --> 00:12:29,620
+of the heartالـ Anatomy of the heart والفيسيولوجيا
+
+167
+00:12:29,620 --> 00:12:33,700
+of the heart قصيرة يكون بس ويحاول يشوفوه ويشرح
+
+168
+00:12:33,700 --> 00:12:39,320
+بطريقة ممكن الرسم أو كذا ممكن يساعدكم كتير اشي
+
+169
+00:12:39,320 --> 00:12:44,730
+كتير ان شاء اللهالأن الـ Atrium حقيقة هي receiving
+
+170
+00:12:44,730 --> 00:12:47,910
+chambers of the heart هي يعني الـ left atrium و ال
+
+171
+00:12:47,910 --> 00:12:51,970
+right atrium هم اللي بيستلموا الدم و كل atrium في
+
+172
+00:12:51,970 --> 00:12:54,390
+عنده حاجة اللي بنقول أنا protruding auricle زي
+
+173
+00:12:54,390 --> 00:12:59,430
+أذين صغير معها ال blood بدخل ال right atria from
+
+174
+00:12:59,430 --> 00:13:03,670
+superior and inferior vena cava و coronary sinus
+
+175
+00:13:03,670 --> 00:13:08,790
+برضه بيودّي فيها blood enters the left atria from
+
+176
+00:13:08,790 --> 00:13:12,260
+pulmonary veinsVentricles are the discharging
+
+177
+00:13:12,260 --> 00:13:15,520
+chambers of the heart يعني هم بيستلموا الدم من الـ
+
+178
+00:13:15,520 --> 00:13:19,520
+atrium، both atrium و بعدين هم اللي بيطلعوا الدم ل
+
+179
+00:13:19,520 --> 00:13:23,060
+further
+
+180
+00:13:23,060 --> 00:13:27,320
+parts of the body Right ventricle bumps blood into
+
+181
+00:13:27,320 --> 00:13:30,500
+the pulmonary trunk Left ventricle bumps blood
+
+182
+00:13:30,500 --> 00:13:36,890
+into the aortaطيب، الآن بس نوضح بعض الحقائق أنه
+
+183
+00:13:36,890 --> 00:13:40,170
+احنا الـmyocardial thickness بيختلف في القلب، مش
+
+184
+00:13:40,170 --> 00:13:43,070
+كل القلب واحد، يعني عندنا الـleft ventricle زي ما
+
+185
+00:13:43,070 --> 00:13:49,310
+احنا شايفين ونلأسهم، لكن الـleft ventricle wall is
+
+186
+00:13:49,310 --> 00:13:53,150
+the thickest to supply systemic circulation، ليش؟
+
+187
+00:13:53,150 --> 00:13:55,670
+الـleft ventricle، لأن الـleft ventricle بمب،
+
+188
+00:13:55,670 --> 00:13:59,830
+blood،to the whole body يعني هو جاعت بيحارب ضد الـ
+
+189
+00:13:59,830 --> 00:14:02,930
+high blood pressure أو الـ systemic blood pressure
+
+190
+00:14:02,930 --> 00:14:06,750
+of the body كل الجسم فحين أنه ال left ventricle ال
+
+191
+00:14:06,750 --> 00:14:12,150
+right ventricle بس بودع ال pulmonary وطبعا هذا ال
+
+192
+00:14:12,150 --> 00:14:17,680
+flow resistance جليل عندهيبقى هذه السبب ليش عندنا
+
+193
+00:14:17,680 --> 00:14:26,020
+الـ «Left ventricle thicker than the
+
+194
+00:14:26,020 --> 00:14:28,940
+right ventricle» طلعوا الرسمة هنا، هذه عبارة عن
+
+195
+00:14:28,940 --> 00:14:33,140
+قطع في القلب، قطع عرضي، بنلاقي أن الـ «Left
+
+196
+00:14:33,140 --> 00:14:37,960
+ventricle» فعلا الـ «wall» very thick في حين أن
+
+197
+00:14:37,960 --> 00:14:46,330
+الـ «right ventricle» very thinأو thinner ال
+
+198
+00:14:46,330 --> 00:14:48,930
+pathway of the blood through the heart and lungs
+
+199
+00:14:48,930 --> 00:14:55,270
+الأمر سهل وبسيط ال right atrium عن طريق ال
+
+200
+00:14:55,270 --> 00:14:58,570
+tricuspidal valve بودع ال right ventricle ال right
+
+201
+00:14:58,570 --> 00:15:01,570
+ventricle عن طريق ال pulmonary semilunar valve في
+
+202
+00:15:01,570 --> 00:15:04,750
+ال systolic في ال systolicum بودع ال pulmonary
+
+203
+00:15:04,750 --> 00:15:09,050
+artery وهذا بودع على ال lungs ال lungs بترجع الدم
+
+204
+00:15:09,050 --> 00:15:12,180
+pulmonary veins بتوديها على ال left ventricleالـ
+
+205
+00:15:12,180 --> 00:15:16,400
+Left Atrium بودّينا على الـ Bicuspid عن طريق الـ
+
+206
+00:15:16,400 --> 00:15:18,720
+Bicuspid Valve بودّينا على الـ Left Ventricle
+
+207
+00:15:18,720 --> 00:15:21,440
+وLeft Ventricle عن طريق الـ Aortic Semilunar Valve
+
+208
+00:15:21,440 --> 00:15:23,360
+بودّينا على الأورطة والأورطة على الـ Systemic
+
+209
+00:15:23,360 --> 00:15:26,880
+Circulation يا جماعة، لما احنا بنحكي مش إنه هذه
+
+210
+00:15:26,880 --> 00:15:31,800
+دائرة وقعدة بتدور هي بتدور في نفس الوقت، بمعنى أنا
+
+211
+00:15:31,800 --> 00:15:35,400
+لما يكون عندي سيستوليكوم الـ Right Ventricle بدوخ
+
+212
+00:15:35,400 --> 00:15:40,490
+والـ Left Ventricle بدوخالـ right ventricle يدخل
+
+213
+00:15:40,490 --> 00:15:44,910
+الـ pulmonary والـ left ventricle يدخل الـ body في
+
+214
+00:15:44,910 --> 00:15:49,290
+نفس اللحظة عندما يصير عنده diastolicumبنفس القدر
+
+215
+00:15:49,290 --> 00:15:54,790
+بدخل دم على الـ Atrium و الـ Atrium في نفس اللحظة
+
+216
+00:15:54,790 --> 00:16:00,730
+بدخل دم على الـ Ventricles فهي كلها مش إن والله
+
+217
+00:16:00,730 --> 00:16:04,050
+هذا بفضي و هذا بملق و هذا بفضي و هذا بملق لأ كله
+
+218
+00:16:04,050 --> 00:16:06,830
+في نفس اللحظة بيصير و الـ Heart هذا اللي احنا
+
+219
+00:16:06,830 --> 00:16:11,090
+مستجلين فيه و مش هذا بخدم سبعين و تمانين و تسعين
+
+220
+00:16:11,090 --> 00:16:18,250
+سنة جاعد بدون ما يقول أخصحك و احنا بنظل نقاش بس
+
+221
+00:16:18,250 --> 00:16:22,450
+نعكس عليه حياته بالـ stress و بالأكل و بالزيوت و
+
+222
+00:16:22,450 --> 00:16:30,210
+بالسكر و بالمشاكل هذه لكن لو مرة جال أخ تبدأ
+
+223
+00:16:30,210 --> 00:16:36,090
+مشاكلنا في الغالب طيب pathway of blood through the
+
+224
+00:16:36,090 --> 00:16:40,190
+heart and lung حكينا عنها في نفس الصورة هذه طبعا
+
+225
+00:16:40,190 --> 00:16:44,130
+بنبقى عارفين أن الدماللي طالع من القلب بيبقى
+
+226
+00:16:44,130 --> 00:16:48,210
+oxygenated لو طالع من left ventricle وطالع لل body
+
+227
+00:16:48,210 --> 00:16:51,370
+بيبقى oxygenated لو طالع من ال right ventricle
+
+228
+00:16:51,370 --> 00:16:58,970
+بيبقى مش oxygenated ورايح لل oxygenation يارب أكون
+
+229
+00:16:58,970 --> 00:17:02,170
+قولتها صح كمان مرة لو طالع من ال left ventricle
+
+230
+00:17:02,170 --> 00:17:05,490
+بيبقى oxygenated ورايح لل body و لو طالع من ال
+
+231
+00:17:05,490 --> 00:17:09,640
+right ventricle بيبقىدي أكسجينيتش، مافي أكسجين
+
+232
+00:17:09,640 --> 00:17:13,040
+بيوديه على الـ lung عشان يصير له عملية إيش؟
+
+233
+00:17:13,040 --> 00:17:17,760
+Oxygenation عشان يفرج الـ CO2 اللي معاه ويعبي
+
+234
+00:17:17,760 --> 00:17:24,320
+أكسجين ويرجع للجلب عشان يضخه على الجسم في حاجة
+
+235
+00:17:24,320 --> 00:17:28,540
+اسمها غير اللي هي الـ Whole Body Circulation فينا
+
+236
+00:17:28,540 --> 00:17:33,600
+حاجة اسمها Coronary Circulation الـ Coronary
+
+237
+00:17:33,600 --> 00:17:38,910
+Circulation هاي شغلتها إيش؟طبيعي هو صحيح القلب
+
+238
+00:17:38,910 --> 00:17:42,090
+بدعم كل الجسم لكن هو نفسه كمان بده الـ circulation
+
+239
+00:17:42,090 --> 00:17:48,850
+خاص بيه لتغذية to supply blood to the heart muscle
+
+240
+00:17:50,380 --> 00:17:53,200
+وطبعاً زي ما بنقول دايماً coronavirus circulation
+
+241
+00:17:53,200 --> 00:17:56,000
+هو الأساس لكن برضه في عندنا حاجة اسمها collateral
+
+242
+00:17:56,000 --> 00:17:59,940
+roots اللي هو الشوارع الفرعية للشوارع الأساسية
+
+243
+00:17:59,940 --> 00:18:02,260
+يعني أنا عند الشارع الأساسي شارع عمرو مقتار
+
+244
+00:18:02,260 --> 00:18:06,140
+والتلاتيني والوحدة بكفيش للبلد لحالهم بدي شوارع
+
+245
+00:18:06,140 --> 00:18:10,890
+جانبية عشان تخفف من الضغطاللي بيصير هذه اسمها
+
+246
+00:18:10,890 --> 00:18:16,650
+collateral roots وطبعا بنفس القدر لكن بأقل أهمية
+
+247
+00:18:16,650 --> 00:18:19,970
+يمكن الـVenous supply of the heart وبرضه بيقول
+
+248
+00:18:19,970 --> 00:18:25,590
+عنها coronary venous supplyمن الأجزاء الأساسية
+
+249
+00:18:25,590 --> 00:18:29,170
+واللي إحنا هنحكيها بعد ذلك في محاضرة اللي هي الـ
+
+250
+00:18:29,170 --> 00:18:32,470
+Heart Valves الـ Heart Valves هذه طبعاً بتعملنا
+
+251
+00:18:32,470 --> 00:18:36,970
+مشاكل كتير زي أي Valve في الجسم الـ Valves تبعت
+
+252
+00:18:36,970 --> 00:18:42,410
+الـ Heart بتبقى شغلتها شغلتها
+
+253
+00:18:42,410 --> 00:18:49,860
+هي Unidirectional Blood FlowThrough the heart يعني
+
+254
+00:18:49,860 --> 00:18:56,120
+هذا الأساس تبع الـ heart valves دايما تحافظ على دم
+
+255
+00:18:56,120 --> 00:19:02,180
+في اتجاه واحد داخل القلب وطبعا تمنع ال «backflow
+
+256
+00:19:02,180 --> 00:19:05,100
+into the atrium when ventricle contracts» يعني
+
+257
+00:19:05,100 --> 00:19:08,780
+احنا زي ما بيقولوها الـ atrioventricular كل valve
+
+258
+00:19:08,780 --> 00:19:11,240
+بين الـ atrium و الـ valve بيقول atrioventricular
+
+259
+00:19:11,240 --> 00:19:14,940
+عنها وقولنا هدول اللي هم مين الـ tricusp و الـ
+
+260
+00:19:14,940 --> 00:19:19,190
+mitralولكن في عندنا حاجة اسمها غير الـ
+
+261
+00:19:19,190 --> 00:19:25,150
+atrioventricular أنها الـ semilunar valves وهذه
+
+262
+00:19:25,150 --> 00:19:29,390
+عبارة عن الـ valves اللي عند الأورطة وعند
+
+263
+00:19:29,390 --> 00:19:33,440
+البلمونيري موجودةيبقى الـ Atrium Ventricular
+
+264
+00:19:33,440 --> 00:19:36,400
+Valves موجودة بين الـ Atrium والـ Ventricle
+
+265
+00:19:36,400 --> 00:19:41,780
+وشغلتها تمنع الـ Backflow، الدم مايرجعش لما يصير
+
+266
+00:19:41,780 --> 00:19:45,620
+عندي الـ Diastolicum مايرجعش الدم من الـ Atrium to
+
+267
+00:19:45,620 --> 00:19:50,200
+the Ventricle لأنه لو رجع، بعملي Overload عوين على
+
+268
+00:19:50,200 --> 00:19:54,160
+الـ Ventricles لأنه عبّى فيه دم بزيادة، دم مش لازم
+
+269
+00:19:54,160 --> 00:19:58,440
+يتعبّى هناكفي عندنا حاجة اسمها كردة تندنى وهذه
+
+270
+00:19:58,440 --> 00:20:02,240
+تبقى زي ال .. زي ما بقولوا شفتوا الخيبة و ببقى زي
+
+271
+00:20:02,240 --> 00:20:06,020
+خطان مسكاها من هنا و من هنا هذه الكردة تندنى تبقى
+
+272
+00:20:06,020 --> 00:20:11,240
+زي .. زي ال .. ال .. الجام تبع الإحصان بحرك رأس
+
+273
+00:20:11,240 --> 00:20:14,560
+الإحصان وين بروح وهذه رابطة على وين على حاجة اسمها
+
+274
+00:20:14,560 --> 00:20:18,300
+popularity muscles ويلها علاقة في عملية الفتح
+
+275
+00:20:18,300 --> 00:20:19,560
+والتسكير للـ valves
+
+276
+00:20:22,650 --> 00:20:26,810
+زي ما قلنا الـ Heart valves اللي هي الـ
+
+277
+00:20:26,810 --> 00:20:30,770
+Atrioventricular valves بتمنع الـ Backflow of
+
+278
+00:20:30,770 --> 00:20:34,810
+blood to the ventricles الآن الـ Seminolar اللي
+
+279
+00:20:34,810 --> 00:20:40,230
+هما الموجودات عند الـ Pulmonary وعند الأورتك
+
+280
+00:20:40,230 --> 00:20:44,650
+بيمنعوا الـ Backflow of blood into the ventricles
+
+281
+00:20:47,010 --> 00:20:49,370
+هذه الفكرة تاعت الموضوع يعني جماعة طول ما احنا
+
+282
+00:20:49,370 --> 00:20:52,750
+بنحكي في المحاضرة أو elsewhere حاولوا جدر الإمكان
+
+283
+00:20:52,750 --> 00:20:57,330
+تتصوروا ميكانية ميكانيكية وقالية عمل القلب عشان
+
+284
+00:20:57,330 --> 00:21:00,210
+تتصوروا ال text هذا اللي مكتوب كيف بيصير ماعنديش
+
+285
+00:21:00,210 --> 00:21:04,510
+نحفظ الموضوع، موضوع القلب، موضوع بينفهم مش بنحفظ
+
+286
+00:21:07,020 --> 00:21:09,800
+طب الأوردكسميونر وين موجود؟ موجود بين الـ left
+
+287
+00:21:09,800 --> 00:21:12,940
+ventricle and أورطة والبلمونري موجود بين الـ right
+
+288
+00:21:12,940 --> 00:21:16,700
+ventricle و الـ pulmonary trunk طبعا التصور يا
+
+289
+00:21:16,700 --> 00:21:20,160
+جماعة اللي بدي يكون مش أنه كل valve موجود في level
+
+290
+00:21:20,160 --> 00:21:24,340
+لوحده هم موجودين في القلب هو كل القلب جد الإيد فهم
+
+291
+00:21:24,340 --> 00:21:26,880
+موجودين كل هيتهم في level واحد تقريبا زي ما أحنا
+
+292
+00:21:26,880 --> 00:21:31,080
+شايفينهم في القطع اللي موجود في الصورة A أو B مثلا
+
+293
+00:21:31,080 --> 00:21:34,840
+كلهم في نفس الـ level موجودين
+
+294
+00:21:44,350 --> 00:21:51,420
+كمان مرة وبسرعة الـ Anatomy of the heartعلى أساس
+
+295
+00:21:51,420 --> 00:21:57,600
+أنه فعلا يعني ركز معانا أنه عبارة قلنا تقريبا
+
+296
+00:21:57,600 --> 00:22:03,880
+about your fist في منه superior surface of the
+
+297
+00:22:03,880 --> 00:22:07,140
+ديافرام القلب left to the midline anterior to the
+
+298
+00:22:07,140 --> 00:22:11,780
+vertebral column و posterior to the sternum وقلنا
+
+299
+00:22:11,780 --> 00:22:15,620
+coverings of the heart البريكارديوم البريكارديوم
+
+300
+00:22:15,620 --> 00:22:20,340
+بتكون من double wall sackوالـ Subficial Fibrous
+
+301
+00:22:20,340 --> 00:22:23,280
+Pericardium وفيه Deep Two-Layer Serrous
+
+302
+00:22:23,280 --> 00:22:26,080
+Pericardium وهذا بتكون من Two-Layer, Parietal
+
+303
+00:22:26,080 --> 00:22:30,040
+Layer وInternal Surface of the Fibrous Pericardium
+
+304
+00:22:30,040 --> 00:22:35,170
+وVisceral Layer أو بيقول عنه Epicardiumهو عبارة
+
+305
+00:22:35,170 --> 00:22:40,830
+«داخل لجوا القلب» يعني «lines the surface of the
+
+306
+00:22:40,830 --> 00:22:45,870
+heart» و «separated» هدول بـ «fluid filled
+
+307
+00:22:45,870 --> 00:22:49,670
+pericardium» وقلنا إن شغلة البريكارديوم «protect
+
+308
+00:22:49,670 --> 00:22:53,210
+and anchor the heart» «prevent the overfilling»
+
+309
+00:22:53,210 --> 00:22:59,290
+وبيسمح للقلب يشتغل في «friction-free environment»
+
+310
+00:22:59,290 --> 00:23:03,880
+وقلنا بعد الـ «epicardium»في عندنا أو الـ
+
+311
+00:23:03,880 --> 00:23:07,420
+pericardium في عندنا الـ myocardium و بعدين ال
+
+312
+00:23:07,420 --> 00:23:10,800
+endocardium ال myocardium بيمثل ال cardiac muscle
+
+313
+00:23:10,800 --> 00:23:16,540
+layer forming bulk وقولنا ال heart من برا بنشوف
+
+314
+00:23:16,540 --> 00:23:21,460
+فيه ال mainly ال right ventricle و left ventricle
+
+315
+00:23:21,460 --> 00:23:25,520
+مع ال coronary arteries و ال auricles و بنشوف ال
+
+316
+00:23:25,520 --> 00:23:29,400
+pulmonary arteryوالـ Pulmonary Trunk وبنشوف
+
+317
+00:23:29,400 --> 00:23:33,300
+الأورطة من الخلف لكن من خلف القلب بنشوف حاجات كتير
+
+318
+00:23:33,300 --> 00:23:37,920
+تانية زي اللي هي الـ Pulmonary Veins و الـ Vena
+
+319
+00:23:37,920 --> 00:23:41,040
+Cava Superior و Vena Cava Inferior و mainly الـ
+
+320
+00:23:41,040 --> 00:23:48,740
+Left Ventricleولو فتحنا الجلب بقطع طولي هنشوف إنه
+
+321
+00:23:48,740 --> 00:23:56,380
+فيه هنا Right ventricle فاتح على .. عفوا Right
+
+322
+00:23:56,380 --> 00:24:01,630
+atrium فاتح عن طريق الـ Tricusp ده الـ Valveعلى
+
+323
+00:24:01,630 --> 00:24:06,030
+الـ right ventricle والـ right ventricle بضخ الدم
+
+324
+00:24:06,030 --> 00:24:09,610
+في الـ systolicum عن طريق البلمونary trunk عن طريق
+
+325
+00:24:09,610 --> 00:24:15,250
+البلمونary semilunar valve to the lungs وبالعكس في
+
+326
+00:24:15,250 --> 00:24:21,590
+استرجاع الدم عن طريق الـ liftمن الـ left atrium
+
+327
+00:24:21,590 --> 00:24:24,350
+إلى الـ right إلى الـ left ventricle والـ left
+
+328
+00:24:24,350 --> 00:24:31,150
+ventricle عن طريق الأورطة بدخ على الجسم كمرة قلنا
+
+329
+00:24:31,150 --> 00:24:34,110
+إن الـ left ventricle wall is the thickest to
+
+330
+00:24:34,110 --> 00:24:40,120
+supply systemic circulationثم الـ Right Myocardium
+
+331
+00:24:40,120 --> 00:24:44,580
+وقلنا إن مصار الدم و الـ Flow هذا مهم كلنا نعرفه
+
+332
+00:24:44,580 --> 00:24:47,680
+Right Atrium عن طريق الـ Tricuspidal Valve على الـ
+
+333
+00:24:47,680 --> 00:24:49,480
+Right Ventricle الـ Right Ventricle عن طريق الـ
+
+334
+00:24:49,480 --> 00:24:52,240
+Pulmonary Semilunar Valve بروح على الـ Pulmonary
+
+335
+00:24:52,240 --> 00:24:54,700
+Arteries وهذا على الـ Lung بيعملوا Blood Exchange
+
+336
+00:24:54,700 --> 00:24:58,400
+أو Gas Exchangeبرجع للدم عن طريق الـ Pulmonary
+
+337
+00:24:58,400 --> 00:25:01,000
+veins to the left atrium من الـ left atrium to
+
+338
+00:25:01,000 --> 00:25:05,600
+bicusp valve و بعدين to left ventricle و الـ left
+
+339
+00:25:05,600 --> 00:25:08,340
+ventricle بيبقوا بباقي الشغل عن طريق الأورطة
+
+340
+00:25:08,340 --> 00:25:11,740
+بودّيلي على الـ systemic circulation في عندنا طبعا
+
+341
+00:25:11,740 --> 00:25:15,900
+زي ما قلنا الـ coronary circulation و هنحكي في الـ
+
+342
+00:25:15,900 --> 00:25:19,460
+MI أو الـ ischemic heart disease عن الـ coronary
+
+343
+00:25:19,460 --> 00:25:23,700
+arteries و في طبعا collateral roots و كذلك في
+
+344
+00:25:23,700 --> 00:25:29,410
+عندنا ال veinsأقل أهمية في الموضوع تبعنا لكن بصورة
+
+345
+00:25:29,410 --> 00:25:35,090
+عامة الـ Heart valves غاية في الأهمية أتريا و الـ
+
+346
+00:25:35,090 --> 00:25:37,830
+ventricular valves بتربط بين الأتريا و الـ
+
+347
+00:25:37,830 --> 00:25:42,650
+ventricle وفي عندنا الـ semilunar valves بتربط بين
+
+348
+00:25:42,650 --> 00:25:47,190
+الـ ventricles and the aorta and pulmonary trunk
+
+349
+00:25:50,020 --> 00:25:53,560
+of the blood into the ventricles وإن شاء الله
+
+350
+00:25:53,560 --> 00:25:58,580
+تعالى في محاضرة قريبة أنا مش حابب أطول كتير بس
+
+351
+00:25:58,580 --> 00:26:01,680
+عشان تستوعبوا الموضوع هذا وبنحكي كمان عشرة slides
+
+352
+00:26:01,680 --> 00:26:06,060
+عن ال physiology إن شاء الله تعالى ويعطيكوا ألف
+
+353
+00:26:06,060 --> 00:26:06,760
+عافية
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_postprocess.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..ce9cd5adf21436987c1d4d1f3d1fbab793f276c4
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_postprocess.srt
@@ -0,0 +1,1560 @@
+1
+00:00:02,160 --> 00:00:04,400
+بسم الله الرحمن الرحيم الحمد لله رب العالمين و
+
+2
+00:00:04,400 --> 00:00:08,200
+الصلاة والسلام عزيزينا المحمد سيد الوصلين أجمعين
+
+3
+00:00:08,200 --> 00:00:13,580
+ان شاء الله تعالى اليوم هنكمل محاضراتنا و هنتحدث
+
+4
+00:00:13,580 --> 00:00:17,880
+بإذن الله تعالى عن ال valvular heart disease إيش
+
+5
+00:00:17,880 --> 00:00:24,870
+يعني؟ يعني الأمراض الناتجة عن مشاكل في ال valvesو
+
+6
+00:00:24,870 --> 00:00:31,110
+احنا كنا اتحدثنا المرة اللي فاتت و قولنا انه اذا
+
+7
+00:00:31,110 --> 00:00:38,670
+فاكرين احنا نوعين من ال valves جوا ال heart النوع
+
+8
+00:00:38,670 --> 00:00:45,830
+الأول اللي هو بيربط ال ventricles بالأتريا والنوع
+
+9
+00:00:45,830 --> 00:00:50,150
+التاني اللي هو بيربط ال ventricles بال pulmonary
+
+10
+00:00:50,150 --> 00:00:52,870
+artery و بالأبورتا
+
+11
+00:00:54,200 --> 00:01:00,440
+وتحدثنا عن الفرق بينهم لما تحدثنا في محاضرة اللي
+
+12
+00:01:00,440 --> 00:01:09,000
+هو الـ Heart Anatomy وقلنا إن بين الـRight Atrium
+
+13
+00:01:09,000 --> 00:01:13,180
+وRight Ventricle موجود عندنا Atrioventricular
+
+14
+00:01:13,180 --> 00:01:20,250
+Valveأو بنقول عنها Tricuspidal Valve، Tricuspidal
+
+15
+00:01:20,250 --> 00:01:24,610
+يعني إلها زي .. زي الخيمة، إلها تلت أجنحة و بين
+
+16
+00:01:24,610 --> 00:01:29,550
+الـ Left Atrium و الـ Left Ventricle فينا Valve
+
+17
+00:01:29,550 --> 00:01:37,130
+اسمه Mitral Valve، Mitral Valve و بين الـ Left ..
+
+18
+00:01:37,130 --> 00:01:42,210
+بين الـ Right Ventricle و بين الـ Pulmonary Artery
+
+19
+00:01:42,210 --> 00:01:47,920
+فينا Semilunar Pulmonary Valveوبين طبعا الـ lift
+
+20
+00:01:47,920 --> 00:01:54,420
+ventricle و الـ aorta ان الـ aortic valve و برضه
+
+21
+00:01:54,420 --> 00:01:59,100
+semi lunar زي ما احنا شايفين في المقطع اللي في
+
+22
+00:01:59,100 --> 00:02:04,340
+الصورة في هذا الصورة المقطع اللي على اليمين تحت
+
+23
+00:02:04,340 --> 00:02:09,780
+بنلاقي ان الـ tricusp تلت جطع تلت خيام تلت
+
+24
+00:02:09,780 --> 00:02:18,060
+والميترال تنتين في حين ان ال aortic valveوالـ
+
+25
+00:02:18,060 --> 00:02:23,800
+Pulmonary Valve بيربطوا بين ال Ventricles و
+
+26
+00:02:23,800 --> 00:02:29,220
+Pulmonary و الAortic Pulmonary
+
+27
+00:02:29,220 --> 00:02:32,880
+و الAortic والشغلتهم
+
+28
+00:02:32,880 --> 00:02:36,060
+ال Valve زي ما اتحدتنا قبل هيك يقولنا Maintain
+
+29
+00:02:36,060 --> 00:02:41,000
+Forward Flow and Prevent Reversal of Flow يعني هم
+
+30
+00:02:41,000 --> 00:02:46,650
+بيخلوا الدنيا تمشي في اتجاه واحدتجاه واحد مش
+
+31
+00:02:46,650 --> 00:02:50,170
+اتجاهين هي شغلة الـ Valve حتى في ال veins في ال
+
+32
+00:02:50,170 --> 00:02:54,470
+legs حتى في ال arteries في ال legs دايما ال Valve
+
+33
+00:02:54,470 --> 00:03:00,250
+ليسمح بالتوجه ل fluids في اتجاه واحد وعدم السماح
+
+34
+00:03:00,250 --> 00:03:04,310
+له بالرجوع الآن لو سمح له بالرجوع بنقول عنه
+
+35
+00:03:04,310 --> 00:03:08,770
+insufficient انه مش شغال زي الناس لو سمح له
+
+36
+00:03:08,770 --> 00:03:12,910
+بالرجوع ممنوع يسمح له بالرجوع طب وقتاش بيصير عندنا
+
+37
+00:03:12,910 --> 00:03:18,490
+سمح له بالرجوعلما يكون في عينة weakness وما تسكرش
+
+38
+00:03:18,490 --> 00:03:22,470
+الـ valves زي الناس فبتلاقي ان ال fluid بعود برجع
+
+39
+00:03:25,540 --> 00:03:29,560
+Open and close in response to pressure difference
+
+40
+00:03:29,560 --> 00:03:33,200
+هذه جملة أساسية مهمة جدا جدا أن الـ valves هاي
+
+41
+00:03:33,200 --> 00:03:37,840
+بتفتح و بتسكر نتيجة اختلاف الضغوط الـ gradients
+
+42
+00:03:37,840 --> 00:03:41,000
+اللي هو اختلاف الضغوط between cardiac chambers
+
+43
+00:03:41,000 --> 00:03:46,880
+يعني بدخل الدم من جهة لجهة لحد ما يوصل من يعني
+
+44
+00:03:46,880 --> 00:03:51,580
+خليني أقول خليني أقول الآن من ال right atrium to
+
+45
+00:03:51,580 --> 00:03:57,270
+the right ventricleفي الـ Diastolic لحد ما يصير
+
+46
+00:03:57,270 --> 00:04:04,490
+الضغط جوا الـ Ventric الأعلى بيسكر الـ Valve طيب،
+
+47
+00:04:04,490 --> 00:04:09,830
+إيش الحاجات اللي ممكن تصير في أي Valve عندنا؟ إيش
+
+48
+00:04:09,830 --> 00:04:12,850
+المشاكل اللي ممكن تصير؟ هي يعني أحد المشاكل
+
+49
+00:04:12,850 --> 00:04:16,770
+الأساسية مشكلتين كبيرتين المشكلة الأولى إنه يصير
+
+50
+00:04:16,770 --> 00:04:21,570
+فيه Obstruction اللي احنا بيقول عنه Stenosis تضيق
+
+51
+00:04:22,390 --> 00:04:25,310
+المشكلة التانية عكسها إنه يصير في عنده
+
+52
+00:04:25,310 --> 00:04:33,350
+insufficient أو regurgitation ارتخاء فيصير عنده
+
+53
+00:04:33,350 --> 00:04:40,370
+ارتجاع للدم من مكان إلى مكان ارتجاع للدم يبقى
+
+54
+00:04:40,370 --> 00:04:46,970
+stenosis أو insufficient طبعا مش كل ال valves
+
+55
+00:04:46,970 --> 00:04:51,410
+بيصير عندها بنفس القدر stenosis
+
+56
+00:04:52,760 --> 00:04:58,620
+وزي ما بنقول دايما اللي بيشتغل أكتر بيتعب أكتر هنا
+
+57
+00:04:58,620 --> 00:05:04,780
+بالنسبة لنا فاحنا بنلاقي أن الـ Mitral Valve و
+
+58
+00:05:04,780 --> 00:05:08,780
+الAortic Valve هما أكتر ال valves اللي affected
+
+59
+00:05:08,780 --> 00:05:14,360
+ليش؟ لأنهم بيشتغلوا أكتر ناس طب ليش بيشتغلوا أكتر
+
+60
+00:05:14,360 --> 00:05:21,980
+ناس؟ لأن هم اللي بيودوا الدم لأقل
+
+61
+00:05:22,230 --> 00:05:28,230
+the body أو whole the body فهم عندهم ال most work
+
+62
+00:05:28,230 --> 00:05:32,230
+تقريباً في ال heart عشان هيك بنلاقي المشاكل معظمها
+
+63
+00:05:32,230 --> 00:05:36,670
+بتتركز في اللي هي ال .. ال .. ال .. ال mitral
+
+64
+00:05:36,670 --> 00:05:42,510
+valve و ال aortic valve valvular stenosis when a
+
+65
+00:05:42,510 --> 00:05:49,810
+valve opening is smaller than normal في إلى أسباب
+
+66
+00:05:52,080 --> 00:05:55,100
+ولكن الـ valvular insufficiency أو الـ
+
+67
+00:05:55,100 --> 00:06:02,660
+regurgitation بيسكر
+
+68
+00:06:02,660 --> 00:06:05,080
+الحفة على الحفة على الآخر
+
+69
+00:06:08,080 --> 00:06:12,240
+بيخلّي فيه زي الرخاوة في الـ «فولف» و «ذاف» وهذا
+
+70
+00:06:12,240 --> 00:06:17,880
+يسمح بإدخال الدم من الخلف يتسحول
+
+71
+00:06:17,880 --> 00:06:21,860
+ويدخل داخل الـ «فولف» وداخل الـ «فنترك» لنتيجة
+
+72
+00:06:21,860 --> 00:06:25,440
+الضعف اللي في الـ «فولف» زي ما قلنا، الـ
+
+73
+00:06:25,440 --> 00:06:31,380
+«فولفولار» يمكن أن يتعامل مع كل 4 «فولف» لكن بنسبة
+
+74
+00:06:31,380 --> 00:06:36,410
+مختلفة أو أكتر من ذلكمن الحاجات اللي احنا ممكن
+
+75
+00:06:36,410 --> 00:06:41,150
+نبدأ نتحدث فيها الـ Mitral Stenosis Mitral
+
+76
+00:06:41,150 --> 00:06:47,110
+Regurgitation ارتجاع الميترال وتضيق الميترال أو
+
+77
+00:06:47,110 --> 00:06:54,370
+أورتيكستينوزس أو أورتيكرجورغيتيشن لأن الـ Tricusp
+
+78
+00:06:54,370 --> 00:06:57,730
+Valve اللي هو الـ Atrioventricular Valve is
+
+79
+00:06:57,730 --> 00:07:03,530
+affected infrequentlyTricusp Stenosis بيعملنا
+
+80
+00:07:03,530 --> 00:07:08,210
+Right Heart Failure وTricusp Regurgitation الـ
+
+81
+00:07:08,210 --> 00:07:10,810
+causes of valvular diseases ليش طيب بيصير عندنا
+
+82
+00:07:10,810 --> 00:07:17,610
+valvular diseases؟ أول حاجة يكون congenital، مخلوق
+
+83
+00:07:17,610 --> 00:07:21,830
+فيه، فيه عنده abnormality في الvalves زي أي مكان
+
+84
+00:07:21,830 --> 00:07:28,610
+في الجسم، congenital mostly affect the aortic or
+
+85
+00:07:28,610 --> 00:07:36,680
+pulmonicValve هذا الـ congenital الـ acquired يعني
+
+86
+00:07:36,680 --> 00:07:42,180
+حاجة صارت over the time عملتلي
+
+87
+00:07:42,180 --> 00:07:45,980
+Valvular disease زي مين؟ زي ال rheumatic fever ايش
+
+88
+00:07:45,980 --> 00:07:51,060
+ال rheumatic fever؟ مين فاكر حاجة عن ال rheumatic
+
+89
+00:07:51,060 --> 00:07:53,320
+fever؟ طب ايش سببها بالعربي؟
+
+90
+00:07:56,080 --> 00:08:01,660
+الحمة الروماتيزمية، هذه كانت زمان مشهورة ومنتشرة،
+
+91
+00:08:01,660 --> 00:08:06,560
+إيش الحمة الروماتيزمية؟ هنحكيها في الـ slide اللي
+
+92
+00:08:06,560 --> 00:08:11,460
+بعده، إيش كمان بعملي Valvular Disease؟ Infective
+
+93
+00:08:11,460 --> 00:08:15,560
+Endocarditis، إحنا عارفين إن الـ valves إمتداد
+
+94
+00:08:15,560 --> 00:08:21,620
+لمين؟ إمتداد للـ endocardiumلأن لما بيصير عندي
+
+95
+00:08:21,620 --> 00:08:24,220
+infection في الـ endocardium انفكت في الـ
+
+96
+00:08:24,220 --> 00:08:29,040
+endocarditis فالـ valves برضه بتلتهب طيب الآن
+
+97
+00:08:29,040 --> 00:08:33,000
+تصوروا قدامك و هيك أي إشي الحاجات اللي بتلتهب خاصة
+
+98
+00:08:33,000 --> 00:08:38,900
+لما تكون حاجات هيك نعمة زي الـ valves لما بتلتهب
+
+99
+00:08:38,900 --> 00:08:44,540
+إيش بيصير؟ يا إما يضيق الـ valve يا إما الـ valve
+
+100
+00:08:44,540 --> 00:08:51,980
+بيصير فيه رخاوة و بيصير عندناالـ coronary artery
+
+101
+00:08:51,980 --> 00:08:55,460
+disease لماذا؟ لأنه لا يصل إلى الـ valves تخدية
+
+102
+00:08:55,460 --> 00:09:01,660
+كيف هي؟ آه، الـ cardiomyopathy إنه يكون الـ heart
+
+103
+00:09:01,660 --> 00:09:07,460
+muscle صار فيه عنده disease وهذا إيش بيعملنا
+
+104
+00:09:07,460 --> 00:09:12,160
+cardiomyopathy؟ بيعملنا cardiomegaly اتصوروا إنه
+
+105
+00:09:12,160 --> 00:09:18,280
+القلب بالـ valves تبعته كما هي كويس لكن لما يكبر
+
+106
+00:09:18,280 --> 00:09:26,980
+قلبه يتوسعفبتتوسع الـ Valve فبتبعد الـ Caps اللي
+
+107
+00:09:26,980 --> 00:09:30,860
+هي تبعت ال Valves عن بعض فبيصير عنا Re-Orgitation
+
+108
+00:09:30,860 --> 00:09:34,920
+الـ Hypertension، الـ Aortic Aneurysm، الـ
+
+109
+00:09:34,920 --> 00:09:37,940
+Connective Tissue Disease هذه كلها من الأسباب اللي
+
+110
+00:09:37,940 --> 00:09:45,500
+بتعملنا Valvular Diseases طب نعرج على بعض الـالـ
+
+111
+00:09:45,500 --> 00:09:49,080
+Diseases بس من باب الشرح الـ Rheumatic Heart
+
+112
+00:09:49,080 --> 00:09:54,980
+Disease إيش بنقصد فيه؟ هو عبارة عن باختصار جدا الـ
+
+113
+00:09:54,980 --> 00:09:59,100
+Rheumatic Heart Disease هو عبارة عن post
+
+114
+00:09:59,100 --> 00:10:02,760
+-infectious disease كيف يعني post-infectious؟ يعني
+
+115
+00:10:02,760 --> 00:10:06,540
+بيصير infectious بعد بأسبوع أو أسبوعين بيصير في
+
+116
+00:10:06,540 --> 00:10:12,300
+عندنا ردة فعل autoimmune ضد
+
+117
+00:10:12,300 --> 00:10:17,120
+خلايا الـ valves أو القلبوهذا هنشوفه في عدة أمراض
+
+118
+00:10:17,120 --> 00:10:21,940
+مثل «جولين باري سندروم» مثلًا مثلًا مثلًا مثلًا
+
+119
+00:10:21,940 --> 00:10:26,240
+مثلًا
+
+120
+00:10:26,240 --> 00:10:29,260
+مثلًا
+
+121
+00:10:29,260 --> 00:10:29,920
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+122
+00:10:29,920 --> 00:10:31,640
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+123
+00:10:31,640 --> 00:10:35,260
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+124
+00:10:35,260 --> 00:10:35,780
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+125
+00:10:35,780 --> 00:10:35,800
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+126
+00:10:35,800 --> 00:10:39,280
+مثلًا مثلًا مثلًا
+
+127
+00:10:43,020 --> 00:10:48,540
+زي الصواريخ ضد المفروض ضد البكتيريا اللي عملت
+
+128
+00:10:48,540 --> 00:10:53,920
+الاتحام وبما أن البروتين تبع البكتيريا بيشبه لبعض
+
+129
+00:10:53,920 --> 00:10:58,280
+خلاياالجسم فبتخربط الجهاز المناعي بدل ما يضرب
+
+130
+00:10:58,280 --> 00:11:03,720
+البكتيريا بروح بدرب ايش بدرب نفسه بدرب اللي هو
+
+131
+00:11:03,720 --> 00:11:07,160
+خلايا الجسم وهذا اللي بيصير في القلب أو في الـ
+
+132
+00:11:07,160 --> 00:11:12,880
+valves انه انه تهاجم الـ valves من الجهاز المناعي
+
+133
+00:11:12,880 --> 00:11:17,200
+تبع البني آدم نفسه ليش؟ لأنه ماعرفش يفرج الجهاز
+
+134
+00:11:17,200 --> 00:11:22,410
+المناعي بين البكتيريا اللي عملاله التهاب وبيناللي
+
+135
+00:11:22,410 --> 00:11:27,310
+هي خلايا الـ valves فبيهاجمها بصورة واضحة فبيصير
+
+136
+00:11:27,310 --> 00:11:31,170
+عندنا ما نسميه بـ heart أو rheumatic heart disease
+
+137
+00:11:31,170 --> 00:11:34,010
+inflammatory process that may affect the
+
+138
+00:11:34,010 --> 00:11:38,910
+myocardium pericardium and or endocardium وهذا
+
+139
+00:11:38,910 --> 00:11:43,090
+بيصير بيعمل ليه ايش؟ distortion و scarring of the
+
+140
+00:11:43,090 --> 00:11:46,150
+valve أي التهاب في أي valve بيعمل scarring و
+
+141
+00:11:46,150 --> 00:11:51,260
+distortion لإلهوهذا بيصير نتيجة «Type II
+
+142
+00:11:51,260 --> 00:11:55,260
+Inflammatory Reaction»of inflammatory reaction هذا
+
+143
+00:11:55,260 --> 00:11:59,560
+type 2 secondary to sore throat نتيجة التهاب
+
+144
+00:11:59,560 --> 00:12:03,120
+اللواز عشان هي انا بنركز يا جماعة لما بيصير التهاب
+
+145
+00:12:03,120 --> 00:12:05,820
+لواز بكتيري عن طريق اللي هو الـ streptococcus
+
+146
+00:12:05,820 --> 00:12:12,100
+biogenes أو كوكاي streptococci beta-haemolytic
+
+147
+00:12:12,100 --> 00:12:15,400
+streptococci بنقول للناس لابد إنه نعالج ببنسلين
+
+148
+00:12:15,400 --> 00:12:19,160
+لأنه لو تركنا موضوعه ممكن هذا الأمر يترك لي أثر
+
+149
+00:12:19,160 --> 00:12:24,890
+على القلب ويعمل لي rheumatic heartعلى الـ kidney
+
+150
+00:12:24,890 --> 00:12:33,570
+ويعملّي glomerulonephritis على الـ joints ويعملّي
+
+151
+00:12:33,570 --> 00:12:39,970
+arthritis، rheumatic arthritis يبقى أنا لما بعالج
+
+152
+00:12:39,970 --> 00:12:45,070
+اللوز، التهاب اللوز البكتيري لما بعالجه، بعالجه مش
+
+153
+00:12:45,070 --> 00:12:48,730
+عشان التهاب اللوز itself ولو إنه مهم، لكن بعالجه
+
+154
+00:12:48,730 --> 00:12:56,620
+حتى إنه ما يعجب، ما يترك أثرعدم العلاج على vital
+
+155
+00:12:56,620 --> 00:13:02,060
+organs زي القلب زي الـ Heart زي الـ Kidneys زي الـ
+
+156
+00:13:02,060 --> 00:13:06,620
+Joints هد هو إيش الـ Rheumatic Heart Disease زي ما
+
+157
+00:13:06,620 --> 00:13:10,260
+بيقول دايما هو عبارة عن Autoimmune Disease
+
+158
+00:13:10,260 --> 00:13:14,300
+Autoimmune Disease يعني نيران صديقة الجسم بيهاجم
+
+159
+00:13:14,300 --> 00:13:17,600
+نفسه بيفكر حاله بيهاجم عدو
+
+160
+00:13:19,960 --> 00:13:24,100
+الـ Infective Endocarditis أي Infection زي القلب
+
+161
+00:13:24,100 --> 00:13:31,050
+زيه زي أي مكان بالعكس هومن أكثر الأعضاء لأنهم
+
+162
+00:13:31,050 --> 00:13:35,250
+يمروا عليها كل الدم عمليًا في الجسم فأي بكتيريا
+
+163
+00:13:35,250 --> 00:13:38,950
+مضرة ممكن في الآخر تعملي طبعًا في أنواع ما نحكي
+
+164
+00:13:38,950 --> 00:13:45,250
+أحنا عن الـinfective heart diseases بعد هيك ممكن
+
+165
+00:13:45,250 --> 00:13:48,350
+يعملي infection على heart valve commonly بكتيريا
+
+166
+00:13:48,350 --> 00:13:52,470
+result in damage to valve structure giving rise to
+
+167
+00:13:52,470 --> 00:13:53,670
+stenosis أو regurgitation
+
+168
+00:13:57,290 --> 00:14:02,390
+هذه من بعض الأسباب اللي
+
+169
+00:14:02,390 --> 00:14:12,730
+ممكن تعملنا الـ Valve Disease يعني احنا من باب
+
+170
+00:14:12,730 --> 00:14:18,310
+الآن الذكر طيب هو صار عندى الـ Stenosis في الـ
+
+171
+00:14:18,310 --> 00:14:23,550
+Mitral عسم المثال هو إيش يعني هيصير؟بتفكروا يا
+
+172
+00:14:23,550 --> 00:14:27,030
+جماعة و تتصوروا الـ «circulation» اللي اتحدثنا
+
+173
+00:14:27,030 --> 00:14:31,370
+عليه في الأول تبع الدم «mitral stenosis» يعني وين
+
+174
+00:14:31,370 --> 00:14:35,230
+بتكون المشكلة؟ بتكون في الـ «mitral valve»
+
+175
+00:14:35,230 --> 00:14:38,290
+والمشكلة في الغالب في الـ «stenosis» في الـ
+
+176
+00:14:38,290 --> 00:14:45,430
+«systolicum» لما يضخ الجلب لما
+
+177
+00:14:45,430 --> 00:14:48,470
+في الـ «diastolicum» لما ينبسط القلب، وين المشكلة
+
+178
+00:14:48,470 --> 00:14:49,030
+بتصير؟
+
+179
+00:14:51,960 --> 00:14:57,040
+الميترال شغله في الـ diastolicum لما الـ left
+
+180
+00:14:57,040 --> 00:15:03,060
+atrium بده يدخل الدم على الـ left ventricle كمان
+
+181
+00:15:03,060 --> 00:15:08,480
+مرة، diastolicum بده يدخل الدم من الـ left atrium
+
+182
+00:15:08,480 --> 00:15:13,580
+to the left ventricle الاستينوزز هنا بتلعب دور،
+
+183
+00:15:13,580 --> 00:15:18,290
+ليش؟لأنه بيصير الـ Left Atrium مش جادر يدخل كل
+
+184
+00:15:18,290 --> 00:15:21,770
+الدم اللي وصله من الـ Lung للـ Left Ventricle
+
+185
+00:15:21,770 --> 00:15:27,110
+وبالتالي الـ Left Ventricle مقدرش يدقق دم كتير على
+
+186
+00:15:27,110 --> 00:15:35,270
+الجسم يبقى الاستينوزز بيتركلي أثر زيادة تحميل على
+
+187
+00:15:35,270 --> 00:15:43,830
+الـ Left Atrium ونقص تحميل على الـ Left Ventricle
+
+188
+00:15:47,260 --> 00:15:50,000
+طيب، وإذا أنا في عندي زيادة التحميل على الـ left
+
+189
+00:15:50,000 --> 00:15:54,420
+atrium، إيش بيصير؟ لأنه مش قادر يدخل كل الدم نتيجة
+
+190
+00:15:54,420 --> 00:15:58,520
+الـ stenosis، نتيجة الدضايق، مش قادر يدخل كل الدم
+
+191
+00:15:58,520 --> 00:16:02,960
+على الـ left ventricles، إيش بيصير؟ آه، بيجي الـ
+
+192
+00:16:02,960 --> 00:16:11,730
+left ventricle بيقول للـ pulmonary veinsاللي جايبة
+
+193
+00:16:11,730 --> 00:16:16,770
+دم من الـ lungs لأ بيكفي انا مش جادر اخد دم منك يا
+
+194
+00:16:16,770 --> 00:16:21,130
+lung كفاية كتير ليش؟ لأنه انا مش جادر اديه للـ
+
+195
+00:16:21,130 --> 00:16:25,570
+left ventricle فبيصير عندي إيش احتقان في ال lungs
+
+196
+00:16:25,570 --> 00:16:30,110
+إذا صار في عندي احتقان في ال lungs بيجي ال right
+
+197
+00:16:30,110 --> 00:16:33,210
+ventricle الآن مش عن ال left الجدا بيجي ال right
+
+198
+00:16:33,210 --> 00:16:38,350
+ventricle مش جادر يضخ دم في ال lungs ليش؟ لأن ال
+
+199
+00:16:38,350 --> 00:16:46,120
+lungs ملانة دمطيب فبصير في عندنا حاجة اسمها Right
+
+200
+00:16:46,120 --> 00:16:52,100
+-sided heart failure symptoms إذا الـ Right heart
+
+201
+00:16:52,100 --> 00:16:57,340
+أو الـ Right ventricle و الـ Right heart صار في
+
+202
+00:16:57,340 --> 00:17:05,130
+عنده ملان دم و محتقن لن يأخذ دم من وينمن الجسم من
+
+203
+00:17:05,130 --> 00:17:10,050
+الـVenacava Superior والـVenacava Inferior فبيصير
+
+204
+00:17:10,050 --> 00:17:21,090
+عندنا Symptoms في الجسم ناتجة عن احتقان أعضاء
+
+205
+00:17:21,090 --> 00:17:25,890
+الجسملأنها مش قادرة على طريق الـ Venacava Superior
+
+206
+00:17:25,890 --> 00:17:29,410
+و Inferior تدّي الـ Right Atrium و الـ Right
+
+207
+00:17:29,410 --> 00:17:32,930
+Atrium مش قادر يدّي الـ Right Ventricle ليش؟ لأن
+
+208
+00:17:32,930 --> 00:17:35,810
+الـ Right Ventricle مش قادر ياخد من الـ Lung لأن
+
+209
+00:17:35,810 --> 00:17:39,450
+الـ Lung مش قادرة تدّي الـ Left Atrium ليش؟ نتيجة
+
+210
+00:17:39,450 --> 00:17:46,430
+التضيقفي الـ «ميترال فالف»، كل هذا ما هي المشكلة
+
+211
+00:17:46,430 --> 00:17:50,530
+وإحنا ليش بنبكي لما يكون في عندنا Stenosis في الـ
+
+212
+00:17:50,530 --> 00:17:54,350
+«ميترال فالف»؟ ليش؟ لأنه تأثيره تأثير غير مباشر
+
+213
+00:17:54,350 --> 00:17:57,070
+على معظم أعضاء الجسم، ولو أنه تضيق بس في الـ
+
+214
+00:17:57,070 --> 00:18:02,450
+«ميترال فالف»، عرفتوا؟ كل إشي هيك بده يتفسر يا
+
+215
+00:18:02,450 --> 00:18:04,990
+جماعة، كل إشي هيك بده يتفسر، ليش الـ «فالفولار
+
+216
+00:18:04,990 --> 00:18:09,940
+ديزيزيز» اللي هي التأثير الكبيرطيب، هل هناك حلول؟
+
+217
+00:18:09,940 --> 00:18:14,400
+نعم، هذه القضية أني لدي حلول للمواضيع هذه طب
+
+218
+00:18:14,400 --> 00:18:19,220
+الميترالفالف، من أيش بيصير في العادة؟ طبعا، يمكن
+
+219
+00:18:19,220 --> 00:18:23,600
+أني فرضت الآن الشرح للـmitral valve لأهميته ولأنه
+
+220
+00:18:23,600 --> 00:18:28,620
+بس obvious وواضح ويعني الواحد بيقدر يتصور الموضوع
+
+221
+00:18:28,620 --> 00:18:33,040
+usually result from rheumatic carditisوإيش اللي
+
+222
+00:18:33,040 --> 00:18:35,760
+بيصير؟ بيصير عندي thickening by fibrosis
+
+223
+00:18:35,760 --> 00:18:39,340
+وcalcification نتيجة الـ Rheumatic Carditis
+
+224
+00:18:39,340 --> 00:18:44,260
+thickening by fibrosis and calcification طبعاً
+
+225
+00:18:44,260 --> 00:18:47,600
+ممكن يكون نتيجة tumor أو thrombus لكن الأساس إنه
+
+226
+00:18:47,600 --> 00:18:52,300
+Rheumatic Carditis إيش اللي بيصير؟ نتيجة الاتهابات
+
+227
+00:18:52,300 --> 00:18:55,480
+الـ leaflets of the valves اللي هي الفروع بتاعة
+
+228
+00:18:55,480 --> 00:19:02,140
+الـ valves fuse تتلتحم مع بعضوبصير عندى narrowing
+
+229
+00:19:02,140 --> 00:19:08,320
+of the opening وهذا بمنع normal blood flow from
+
+230
+00:19:08,320 --> 00:19:12,320
+left atrium to the left ventricle left atrium
+
+231
+00:19:12,320 --> 00:19:20,260
+pressure بزيد ال left atrium dilates البلمونة
+
+232
+00:19:20,260 --> 00:19:26,800
+الارتريه pressure بزيد فإيش بيصير عندى بالتالي
+
+233
+00:19:26,800 --> 00:19:31,400
+right ventricle hypertrophyزي ما قلنا الـ
+
+234
+00:19:31,400 --> 00:19:34,620
+Pulmonary congestion احتقان القلب الـ Pulmonary
+
+235
+00:19:34,620 --> 00:19:39,120
+الاريعتين بيعملولي Right-sided heart failures
+
+236
+00:19:39,120 --> 00:19:45,200
+وطبعاً بعكرلي كل الموضوع الـ Mitral Stenosis في
+
+237
+00:19:45,200 --> 00:19:48,140
+منها طبعاً مش كل الـ Mitral Stenosis مش كل تضيق هو
+
+238
+00:19:48,140 --> 00:19:52,680
+يعتبر تضيق مهم في كتير ناس عندها تضيق لكن الأمور
+
+239
+00:19:52,680 --> 00:19:57,240
+compensated في حالات الـ mild و بتبقى asymptomatic
+
+240
+00:19:58,760 --> 00:20:02,120
+لكن بعض الأحيان بنلاقي انه with progression بتزيد
+
+241
+00:20:02,120 --> 00:20:04,860
+مع الوقت بتزيد وإحنا مابنحكيش عن acute هنا يا
+
+242
+00:20:04,860 --> 00:20:08,900
+جماعة لإن السبب مش .. مش .. مش thrombus مثلا أو ..
+
+243
+00:20:08,900 --> 00:20:12,140
+أو حاجة إنما إحنا بنحكي عن حاجة chronic over the
+
+244
+00:20:12,140 --> 00:20:19,880
+time بتصير with progression بصير dyspnea، أرتبنية،
+
+245
+00:20:19,880 --> 00:20:23,640
+dry cough، hemoptysis، إيش عن hemoptysis؟
+
+246
+00:20:27,540 --> 00:20:34,720
+وإيش معناة hematemesis طب
+
+247
+00:20:34,720 --> 00:20:41,700
+hematuria طب التلت كلمات هدول بدي عن كل واحدة سطرة
+
+248
+00:20:41,700 --> 00:20:47,180
+تكتبولي إيش يعني hemoptysis إيش يعني hematuria إيش
+
+249
+00:20:47,180 --> 00:20:52,560
+يعني hematemesis and pulmonary edema may appear
+
+250
+00:20:52,560 --> 00:20:58,700
+يبدأ ال assignmentالجزء تبعه الأولاني بدنا الفرق
+
+251
+00:20:58,700 --> 00:21:03,000
+بين الـ hemoptysis الـ hematuria and الـ
+
+252
+00:21:03,000 --> 00:21:07,860
+hematemesis right-sided heart failure symptoms
+
+253
+00:21:07,860 --> 00:21:11,360
+occur later وبعدين بيصير عندي atrial fibrillation
+
+254
+00:21:11,360 --> 00:21:15,260
+وممكن يصير عندي ميرمر كمان في القلب مش مهم جدا
+
+255
+00:21:15,260 --> 00:21:23,820
+بالنسبة لك هل الـ aortic stenosisاللي بيصير بيصير
+
+256
+00:21:23,820 --> 00:21:29,400
+تضيق الأورطة بيصير بنفس الصورة وبيعمللي مشاكل نعم
+
+257
+00:21:29,400 --> 00:21:34,660
+هو بنفس الفكرة بالمناسبة إنه ال right ال left
+
+258
+00:21:34,660 --> 00:21:39,080
+ventricle اللي هو عن طريق الأورتك بيبعد دم للجسم
+
+259
+00:21:39,080 --> 00:21:45,560
+مقدرش يبعد كل الدم لأنه عنده stenosis هلجيت الجسم
+
+260
+00:21:45,560 --> 00:21:50,000
+بيصلوش دم كفاية وهذا بيعمللي مشاكل تصوروا الدماغ
+
+261
+00:21:50,000 --> 00:21:59,190
+مايصلوش دمبيصير عندى Psycho خاصة لما فيه exertion،
+
+262
+00:21:59,190 --> 00:22:07,170
+فيه تعب، فيه حركة، لما القلب وشرين القلب مايصلهاش
+
+263
+00:22:07,170 --> 00:22:12,930
+دم كفاية، بيصير عندنا Angina، ليش؟ لأن ال supply
+
+264
+00:22:12,930 --> 00:22:22,650
+جال تبع الدم لل heart muscles، بيصير عندنا dyspnea
+
+265
+00:22:24,590 --> 00:22:29,670
+بسبب نفسي الـ Heart Failure بسبب
+
+266
+00:22:29,670 --> 00:22:32,230
+نفسي الـ Heart Failure بسبب نفسي الـ Heart Failure
+
+267
+00:22:32,230 --> 00:22:36,170
+بسبب نفسي الـ Heart Failure بسبب نفسي الـ Heart
+
+268
+00:22:36,170 --> 00:22:37,890
+Failure بسبب نفسي الـ Heart Failure بسبب نفسي الـ
+
+269
+00:22:37,890 --> 00:22:38,070
+Failure بسبب نفسي الـ Heart Failure بسبب نفسي الـ
+
+270
+00:22:38,070 --> 00:22:40,650
+نفسي الـ Heart Failure بسبب نفسي الـ Heart Failure
+
+271
+00:22:40,650 --> 00:22:45,630
+بسبب نفسي الـ Heart Failure بسبب نفسي الـ Heart
+
+272
+00:22:45,630 --> 00:22:52,400
+Failure بسبب نفسي الـ Heart Failure بسبب نالان
+
+273
+00:22:52,400 --> 00:22:55,760
+بعيدا عن ايش بتصير في الـ heart باقي الجسم مش
+
+274
+00:22:55,760 --> 00:23:00,300
+هيصله دم فبصير ان المشاكل هذه الأعضاء الـ vital
+
+275
+00:23:00,300 --> 00:23:04,160
+organs بيصير فيها مشاكل ليش؟ لأنه ماوصلهاش
+
+276
+00:23:04,160 --> 00:23:07,800
+perfusion كفاية طيب من ايش بيصير الـ aortic
+
+277
+00:23:07,800 --> 00:23:15,980
+stenosis؟ commonly نتيجة age related progressive
+
+278
+00:23:15,980 --> 00:23:21,790
+calcification وبرضه rheumatic aortic stenosisالـ
+
+279
+00:23:21,790 --> 00:23:24,570
+Rheumatic-Aortic Stenosis Clinical Representation
+
+280
+00:23:24,570 --> 00:23:30,070
+مهم نعرفه «سينكوب» في الـ Exertional Stage خاصة
+
+281
+00:23:30,070 --> 00:23:37,810
+عند الـ Angina، Dyspnea، and Sudden Death الـ
+
+282
+00:23:37,810 --> 00:23:42,730
+Aortic Regurgitation أو الـ Insufficiency هو عبارة
+
+283
+00:23:42,730 --> 00:23:48,500
+عنleaking of aortic valve of the heart that causes
+
+284
+00:23:48,500 --> 00:23:52,160
+blood to flow in the reverse direction during
+
+285
+00:23:52,160 --> 00:23:57,260
+ventricular diastole بيجي القلب ع سلامته بيعمل
+
+286
+00:23:57,260 --> 00:24:01,640
+diastolicum المفروض أن الدم بيجي كل هيته من وين؟
+
+287
+00:24:01,640 --> 00:24:06,240
+من الـ mitral valve و من الtricuspidal valve فإذا
+
+288
+00:24:06,240 --> 00:24:09,600
+به بيجيله دم كمان من ال aortic valve و من
+
+289
+00:24:09,600 --> 00:24:13,320
+البلبونary valve إيش بيصير هيك؟ بيصير عنا overload
+
+290
+00:24:14,440 --> 00:24:20,520
+الـ Lymph ventricle بيدخله كمان دم من الـ aortic
+
+291
+00:24:20,520 --> 00:24:25,620
+غير اللي دخله من في
+
+292
+00:24:25,620 --> 00:24:28,560
+الـ diastolic غير اللي دخله من اللي هو الـ left
+
+293
+00:24:28,560 --> 00:24:34,560
+atrium أسباب
+
+294
+00:24:34,560 --> 00:24:38,300
+الـ regurgitation ممكن يكون Infective endocarditis
+
+295
+00:24:38,300 --> 00:24:45,900
+رويماتيك، disease ممكن، traumaفي عندنا بعض الأمراض
+
+296
+00:24:45,900 --> 00:24:50,160
+زي الـ Marfan و الـ Syndrome و الـ Syphilis هذه
+
+297
+00:24:50,160 --> 00:24:53,820
+بتديني Aortic Dilatation يبقى أنا بحكي عنها كمان
+
+298
+00:24:53,820 --> 00:24:57,440
+وهذا الـ Assignment التاني عفوا الجزء التاني من
+
+299
+00:24:57,440 --> 00:25:01,260
+الـ Assignment اللي هو بدي تلت تسطر عن الـ Marfan
+
+300
+00:25:01,260 --> 00:25:05,540
+Syndrome و تلت تسطر عن الـ Syphilis تلت تسطر بس
+
+301
+00:25:05,540 --> 00:25:09,860
+تلتة تلتة واتفجنا في الجبل شوية عن
+
+302
+00:25:16,660 --> 00:25:20,380
+في الجزء الأول من الـ Assignment نكتب الفرق بين
+
+303
+00:25:20,380 --> 00:25:26,060
+الهيماتوريا والـ hematemesis والـ hemoptysis هدول
+
+304
+00:25:26,060 --> 00:25:29,980
+الـ Assignment اللي هو جزءين ومايزدش أي حاجة
+
+305
+00:25:29,980 --> 00:25:33,060
+بتنكتب عن تلت تستر عن أي حاجة في الموضوع هذا
+
+306
+00:25:33,060 --> 00:25:37,200
+بالذات اليوم في حين الـ mitral regurgitation بنفس
+
+307
+00:25:37,200 --> 00:25:40,640
+الصورة occurs when the mitral valve does not close
+
+308
+00:25:40,640 --> 00:25:48,250
+properly في حين heart bumps out bloodنفس الفكرة
+
+309
+00:25:48,250 --> 00:25:53,690
+ممكن تترك لي أثار كبيرة الـ diagnosis كيف أنا بشخص
+
+310
+00:25:53,690 --> 00:25:59,610
+الـ valvular diseases رقم واحد الـ
+
+311
+00:25:59,610 --> 00:26:02,930
+echocardiography و احنا اتحدثنا أيامها الفرق بين
+
+312
+00:26:02,930 --> 00:26:06,930
+ال ECG و ال echo إذا فاكرين و ال catheter و قلنا
+
+313
+00:26:06,930 --> 00:26:12,930
+إن ال echocardiography هو اللي يكشف لي مشاكل ال
+
+314
+00:26:12,930 --> 00:26:16,640
+musclesومشاكل الـ Valves
+
+315
+00:26:19,150 --> 00:26:22,550
+وممكن طبعا بعض الأحيان تبقى الـ Echocardiography
+
+316
+00:26:22,550 --> 00:26:32,450
+لأنها Trans-toracal من خلال الصدر من برا نعملها
+
+317
+00:26:32,450 --> 00:26:35,990
+Echocardiography بيبين ليش بعض الحاجات فبنضطر ندخل
+
+318
+00:26:35,990 --> 00:26:40,110
+بجهاز الـ Echo لكن عن طريق الـ Esophagus عن طريق
+
+319
+00:26:40,110 --> 00:26:44,490
+المرية نقول عنها Transesophageal Echocardiography
+
+320
+00:26:44,490 --> 00:26:50,390
+إذا عرفنا إنه في حاجةوبدها تشخيص أكتر وأكتر بتحتاج
+
+321
+00:26:50,390 --> 00:26:53,750
+خاصة لو بدها intervention بنحتاج إليها cardiac
+
+322
+00:26:53,750 --> 00:26:59,310
+catheter بنقول عنه أنجيوغرام بدها أنجيوغرام طبعا
+
+323
+00:26:59,310 --> 00:27:03,030
+في الصورة واضح عندنا اللي هو حاجة بنقول عنها ال
+
+324
+00:27:03,030 --> 00:27:09,220
+four valve أو four chamber viewطبعاً هذه بدها
+
+325
+00:27:09,220 --> 00:27:12,440
+أخصائي القلب هو اللي بيقوم بيها الشغل هاي و بيشوف
+
+326
+00:27:12,440 --> 00:27:17,260
+مدى كيف ال .. ال .. ال .. ال valves وضعها و كيف
+
+327
+00:27:17,260 --> 00:27:21,980
+مرور الدم من خلالها بمجسات معينة بيجيسوها على
+
+328
+00:27:21,980 --> 00:27:24,620
+الجهاز فبيعرفوا أنه في مشكلة أو لأ و طبعا ممكن
+
+329
+00:27:24,620 --> 00:27:31,180
+نضطر نروح على ال MRI هذا طبعا اللي هو ال .. ال ..
+
+330
+00:27:31,180 --> 00:27:37,810
+ال .. الـ Angiogram هنحكي في ساعتهطب كيف أتعالج
+
+331
+00:27:37,810 --> 00:27:42,990
+الـ «valvular diseases»؟ هو لو الـ «valvular
+
+332
+00:27:42,990 --> 00:27:47,130
+diseases» عملتلي مشاكل في الـ «myocardium» وفي
+
+333
+00:27:47,130 --> 00:27:54,070
+القلب ممكن أحتاج drugs حتى أخفف الضغط عنها لكن
+
+334
+00:27:54,070 --> 00:27:58,090
+الأصل أنه أنا بعمل للـ «valves» هاي إما repair أو
+
+335
+00:27:58,090 --> 00:28:04,550
+replacement إما repair أو replacementوالتحقيق
+
+336
+00:28:04,550 --> 00:28:09,890
+بإصلاحها بإستخدام مجهزة ممكنة للتحقيق بإستخدام
+
+337
+00:28:09,890 --> 00:28:16,290
+مجهزة ممكنة للتحقيق بإستخدام
+
+338
+00:28:16,290 --> 00:28:16,810
+مجهزة
+
+339
+00:28:19,550 --> 00:28:23,490
+ممكن أدى Diuretics، ممكن أدى Beta Blockers، بغض
+
+340
+00:28:23,490 --> 00:28:27,650
+النظر عن وظيفة كل واحد، مع حالة كبيرة طريقتنا من
+
+341
+00:28:27,650 --> 00:28:31,050
+الأول، زي ما اتفقنا، Diuretics، هذه كلها بتخفف
+
+342
+00:28:31,050 --> 00:28:35,710
+الوضع أو الضغط عن القلب، Beta Blockers، Dioxin،
+
+343
+00:28:35,710 --> 00:28:39,070
+O2، Oxygen، Vasodilators، Prophylactic Antibiotic،
+
+344
+00:28:39,070 --> 00:28:45,150
+ممكن أدىوإذا كان هناك إتريال أو فايروليشن، يمكن أن
+
+345
+00:28:45,150 --> 00:28:48,650
+أعمله إتريال أو فايروليشن إذا كان ممكن أو يمكن أن
+
+346
+00:28:48,650 --> 00:28:55,750
+نعمل استخدام لـ Anticoagulation الـ Surgical
+
+347
+00:28:55,750 --> 00:29:00,740
+Management يحدث كما قلناكل Valve إله طريقة معينة
+
+348
+00:29:00,740 --> 00:29:05,340
+بتنعمل فيه، مش كله زي بعض و هذه إلها ناس أخصائيين
+
+349
+00:29:05,340 --> 00:29:08,480
+فيها لكن إحنا بنحكي عن الأساسيات تبع الموضوع
+
+350
+00:29:08,480 --> 00:29:12,080
+«ميترال فالف» ممكن أعمله replacement أو «فالفولو
+
+351
+00:29:12,080 --> 00:29:15,680
+بلاستي» بلون «فالفولو بلاستي» عمل التوزيع بالبالون
+
+352
+00:29:15,680 --> 00:29:20,600
+أو «أورتيك فالف» replacement في حالات لما يكون
+
+353
+00:29:20,600 --> 00:29:29,190
+عندي problemهذه صور من الموضوع الـ «Valves» وموضوع
+
+354
+00:29:29,190 --> 00:29:36,070
+كبير، موضوع مهم أخد على مدى التاريخ كتير تجارب
+
+355
+00:29:36,070 --> 00:29:43,500
+لحتى وصلوا لموضوع الـ «Valves»سواء الـ Repair أو
+
+356
+00:29:43,500 --> 00:29:48,300
+الـ Replacement بنحس إنه عبر التاريخ كان في عندنا
+
+357
+00:29:48,300 --> 00:29:53,820
+أنواع من الـ Valves سواء mechanical أو حتى tissue
+
+358
+00:29:53,820 --> 00:30:02,700
+valves مخودة من مكان آخر، biological valves بنقول
+
+359
+00:30:02,700 --> 00:30:11,590
+عنها ال advantages of surgical repair طبعاًبتخفف
+
+360
+00:30:11,590 --> 00:30:15,290
+ليه موضوع أن الـ heart failure فشل القلب لأنه
+
+361
+00:30:15,290 --> 00:30:19,230
+القلب بعد فترة بقدرش يكمل و بيصير عنا better
+
+362
+00:30:19,230 --> 00:30:23,710
+functional outcome ال disadvantages طبعا ال valve
+
+363
+00:30:23,710 --> 00:30:28,230
+برضه في الآخر خاصة لما أحطه لطفل حضر بعد هيك لو
+
+364
+00:30:28,230 --> 00:30:31,570
+ربنا أداه العمر أعود أحطله valve تاني لأنه ماحي
+
+365
+00:30:31,570 --> 00:30:34,750
+يقعد معاه سبعين تمانين سنة أكيد فيصير عندي valve
+
+366
+00:30:34,750 --> 00:30:40,490
+failure وطبعا في بعض ال valvesأنواع منها بتحتاج
+
+367
+00:30:40,490 --> 00:30:43,610
+Life-Long Anticoagulation لأنها أجسام غريبة فممكن
+
+368
+00:30:43,610 --> 00:30:46,530
+تعمل الـ Coagulation تعمل الـ Thrombus Building
+
+369
+00:30:46,530 --> 00:30:51,750
+فبدها Anticoagulation الحقيقة
+
+370
+00:30:51,750 --> 00:30:56,710
+يعني حكينا في الـ Valvular Diseases بصورة عملية
+
+371
+00:30:56,710 --> 00:31:01,650
+مختصرة جداً جداً يعني بس عرفنا تعريف عنها في حوالي
+
+372
+00:31:01,650 --> 00:31:06,050
+22 slide في نص ساعة أو أكتر من نص ساعة لكن زي ما
+
+373
+00:31:06,050 --> 00:31:11,740
+قلنا الموضوع أكبر من هيكهو أنا بالمناسبة خلال
+
+374
+00:31:11,740 --> 00:31:15,220
+اليومين اللي جايين هابعت لكل مجموعة من المجموعات
+
+375
+00:31:15,220 --> 00:31:19,600
+اللي اتكونناها موضوع بدا تبدأ تحضره الموضوع هذا
+
+376
+00:31:19,600 --> 00:31:27,000
+وتعمل فيه زي بحث البحث هذا طبعاً
+
+377
+00:31:27,000 --> 00:31:30,220
+إله علاقة بالمنهج لكن مش من مواد المنهج لكن إله
+
+378
+00:31:30,220 --> 00:31:34,340
+علاقة بالمنهج تبعنا البحث هذا هتنعمله في عشر صفحات
+
+379
+00:31:34,340 --> 00:31:40,580
+Word مع الـ Referencesسأبدأ بالكتابة عليه وبعد ذلك
+
+380
+00:31:40,580 --> 00:31:48,220
+ينعمل على شكل PowerPointوتلقوه كل مجموعة تلقي بإذا
+
+381
+00:31:48,220 --> 00:31:52,540
+صار في تعليم وجاهي بنعمله في الجامعة إذا ما صارش
+
+382
+00:31:52,540 --> 00:31:57,520
+بحدد النقطة النقطة للبدأ إن شاء الله تعالى على
+
+383
+00:31:57,520 --> 00:32:00,580
+أساس تعملوه بنفس الطريقة اللي أنا قاعد بعمل فيها
+
+384
+00:32:00,580 --> 00:32:06,200
+المحاضرة وتبعتوليها وممكن المحاضرة الأفضل أو أفضل
+
+385
+00:32:06,200 --> 00:32:12,890
+محاضرتين أن نحطهم على صفحة الجامعة أو علىللجميع
+
+386
+00:32:12,890 --> 00:32:16,610
+حتى يشوفوها إن شاء الله تعالى طبعا غير إنه إنه هذه
+
+387
+00:32:16,610 --> 00:32:21,570
+جزء من النشاط اللي ممكن يجيب للواحد علامات
+
+388
+00:32:21,570 --> 00:32:23,790
+للمهتمين بالموضوع هذا إن شاء الله لكن هو طبعا
+
+389
+00:32:23,790 --> 00:32:27,210
+هيكون واجب مهم بالنسبالنا يعطيكوا العافية
+
+390
+00:32:27,210 --> 00:32:30,050
+وانهاركوا سعيد إن شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..1c5560aff2e5aed684270bd87dff04504f710eeb
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/ajehxymKNRU_raw.srt
@@ -0,0 +1,1576 @@
+1
+00:00:02,160 --> 00:00:04,400
+بسم الله الرحمن الرحيم الحمد لله رب العالمين و
+
+2
+00:00:04,400 --> 00:00:08,200
+الصلاة والسلام عزيزينا المحمد سيد الوصلين أجمعين
+
+3
+00:00:08,200 --> 00:00:13,580
+ان شاء الله تعالى اليوم هنكمل محاضراتنا و هنتحدث
+
+4
+00:00:13,580 --> 00:00:17,880
+بإذن الله تعالى عن ال valvular heart disease إيش
+
+5
+00:00:17,880 --> 00:00:24,870
+يعني؟ يعني الأمراض الناتجة عن مشاكل في ال valvesو
+
+6
+00:00:24,870 --> 00:00:31,110
+احنا كنا اتحدثنا المرة اللي فاتت و قولنا انه اذا
+
+7
+00:00:31,110 --> 00:00:38,670
+فاكرين احنا نوعين من ال valves جوا ال heart النوع
+
+8
+00:00:38,670 --> 00:00:45,830
+الأول اللي هو بيربط ال ventricles بالأتريا والنوع
+
+9
+00:00:45,830 --> 00:00:50,150
+التاني اللي هو بيربط ال ventricles بال pulmonary
+
+10
+00:00:50,150 --> 00:00:52,870
+artery و بالأبورتا
+
+11
+00:00:54,200 --> 00:01:00,440
+وتحدثنا عن الفرق بينهم لما تحدثنا في محاضرة اللي
+
+12
+00:01:00,440 --> 00:01:09,000
+هو الـ Heart Anatomy وقلنا إن بين الـRight Atrium
+
+13
+00:01:09,000 --> 00:01:13,180
+وRight Ventricle موجود عندنا Atrioventricular
+
+14
+00:01:13,180 --> 00:01:20,250
+Valveأو بنقول عنها Tricuspidal Valve، Tricuspidal
+
+15
+00:01:20,250 --> 00:01:24,610
+يعني إلها زي .. زي الخيمة، إلها تلت أجنحة و بين
+
+16
+00:01:24,610 --> 00:01:29,550
+الـ Left Atrium و الـ Left Ventricle فينا Valve
+
+17
+00:01:29,550 --> 00:01:37,130
+اسمه Mitral Valve، Mitral Valve و بين الـ Left ..
+
+18
+00:01:37,130 --> 00:01:42,210
+بين الـ Right Ventricle و بين الـ Pulmonary Artery
+
+19
+00:01:42,210 --> 00:01:47,920
+فينا Semilunar Pulmonary Valveوبين طبعا الـ lift
+
+20
+00:01:47,920 --> 00:01:54,420
+ventricle و الـ aorta ان الـ aortic valve و برضه
+
+21
+00:01:54,420 --> 00:01:59,100
+semi lunar زي ما احنا شايفين في المقطع اللي في
+
+22
+00:01:59,100 --> 00:02:04,340
+الصورة في هذا الصورة المقطع اللي على اليمين تحت
+
+23
+00:02:04,340 --> 00:02:09,780
+بنلاقي ان الـ tricusp تلت جطع تلت خيام تلت
+
+24
+00:02:09,780 --> 00:02:18,060
+والميترال تنتين في حين ان ال aortic valveوالـ
+
+25
+00:02:18,060 --> 00:02:23,800
+Pulmonary Valve بيربطوا بين ال Ventricles و
+
+26
+00:02:23,800 --> 00:02:29,220
+Pulmonary و الAortic Pulmonary
+
+27
+00:02:29,220 --> 00:02:32,880
+و الAortic والشغلتهم
+
+28
+00:02:32,880 --> 00:02:36,060
+ال Valve زي ما اتحدتنا قبل هيك يقولنا Maintain
+
+29
+00:02:36,060 --> 00:02:41,000
+Forward Flow and Prevent Reversal of Flow يعني هم
+
+30
+00:02:41,000 --> 00:02:46,650
+بيخلوا الدنيا تمشي في اتجاه واحدتجاه واحد مش
+
+31
+00:02:46,650 --> 00:02:50,170
+اتجاهين هي شغلة الـ Valve حتى في ال veins في ال
+
+32
+00:02:50,170 --> 00:02:54,470
+legs حتى في ال arteries في ال legs دايما ال Valve
+
+33
+00:02:54,470 --> 00:03:00,250
+ليسمح بالتوجه ل fluids في اتجاه واحد وعدم السماح
+
+34
+00:03:00,250 --> 00:03:04,310
+له بالرجوع الآن لو سمح له بالرجوع بنقول عنه
+
+35
+00:03:04,310 --> 00:03:08,770
+insufficient انه مش شغال زي الناس لو سمح له
+
+36
+00:03:08,770 --> 00:03:12,910
+بالرجوع ممنوع يسمح له بالرجوع طب وقتاش بيصير عندنا
+
+37
+00:03:12,910 --> 00:03:18,490
+سمح له بالرجوعلما يكون في عينة weakness وما تسكرش
+
+38
+00:03:18,490 --> 00:03:22,470
+الـ valves زي الناس فبتلاقي ان ال fluid بعود برجع
+
+39
+00:03:25,540 --> 00:03:29,560
+Open and close in response to pressure difference
+
+40
+00:03:29,560 --> 00:03:33,200
+هذه جملة أساسية مهمة جدا جدا أن الـ valves هاي
+
+41
+00:03:33,200 --> 00:03:37,840
+بتفتح و بتسكر نتيجة اختلاف الضغوط الـ gradients
+
+42
+00:03:37,840 --> 00:03:41,000
+اللي هو اختلاف الضغوط between cardiac chambers
+
+43
+00:03:41,000 --> 00:03:46,880
+يعني بدخل الدم من جهة لجهة لحد ما يوصل من يعني
+
+44
+00:03:46,880 --> 00:03:51,580
+خليني أقول خليني أقول الآن من ال right atrium to
+
+45
+00:03:51,580 --> 00:03:57,270
+the right ventricleفي الـ Diastolic لحد ما يصير
+
+46
+00:03:57,270 --> 00:04:04,490
+الضغط جوا الـ Ventric الأعلى بيسكر الـ Valve طيب،
+
+47
+00:04:04,490 --> 00:04:09,830
+إيش الحاجات اللي ممكن تصير في أي Valve عندنا؟ إيش
+
+48
+00:04:09,830 --> 00:04:12,850
+المشاكل اللي ممكن تصير؟ هي يعني أحد المشاكل
+
+49
+00:04:12,850 --> 00:04:16,770
+الأساسية مشكلتين كبيرتين المشكلة الأولى إنه يصير
+
+50
+00:04:16,770 --> 00:04:21,570
+فيه Obstruction اللي احنا بيقول عنه Stenosis تضيق
+
+51
+00:04:22,390 --> 00:04:25,310
+المشكلة التانية عكسها إنه يصير في عنده
+
+52
+00:04:25,310 --> 00:04:33,350
+insufficient أو regurgitation ارتخاء فيصير عنده
+
+53
+00:04:33,350 --> 00:04:40,370
+ارتجاع للدم من مكان إلى مكان ارتجاع للدم يبقى
+
+54
+00:04:40,370 --> 00:04:46,970
+stenosis أو insufficient طبعا مش كل ال valves
+
+55
+00:04:46,970 --> 00:04:51,410
+بيصير عندها بنفس القدر stenosis
+
+56
+00:04:52,760 --> 00:04:58,620
+وزي ما بنقول دايما اللي بيشتغل أكتر بيتعب أكتر هنا
+
+57
+00:04:58,620 --> 00:05:04,780
+بالنسبة لنا فاحنا بنلاقي أن الـ Mitral Valve و
+
+58
+00:05:04,780 --> 00:05:08,780
+الAortic Valve هما أكتر ال valves اللي affected
+
+59
+00:05:08,780 --> 00:05:14,360
+ليش؟ لأنهم بيشتغلوا أكتر ناس طب ليش بيشتغلوا أكتر
+
+60
+00:05:14,360 --> 00:05:21,980
+ناس؟ لأن هم اللي بيودوا الدم لأقل
+
+61
+00:05:22,230 --> 00:05:28,230
+the body أو whole the body فهم عندهم ال most work
+
+62
+00:05:28,230 --> 00:05:32,230
+تقريباً في ال heart عشان هيك بنلاقي المشاكل معظمها
+
+63
+00:05:32,230 --> 00:05:36,670
+بتتركز في اللي هي ال .. ال .. ال .. ال mitral
+
+64
+00:05:36,670 --> 00:05:42,510
+valve و ال aortic valve valvular stenosis when a
+
+65
+00:05:42,510 --> 00:05:49,810
+valve opening is smaller than normal في إلى أسباب
+
+66
+00:05:52,080 --> 00:05:55,100
+ولكن الـ valvular insufficiency أو الـ
+
+67
+00:05:55,100 --> 00:06:02,660
+regurgitation بيسكر
+
+68
+00:06:02,660 --> 00:06:05,080
+الحفة على الحفة على الآخر
+
+69
+00:06:08,080 --> 00:06:12,240
+بيخلّي فيه زي الرخاوة في الـ «فولف» و «ذاف» وهذا
+
+70
+00:06:12,240 --> 00:06:17,880
+يسمح بإدخال الدم من الخلف يتسحول
+
+71
+00:06:17,880 --> 00:06:21,860
+ويدخل داخل الـ «فولف» وداخل الـ «فنترك» لنتيجة
+
+72
+00:06:21,860 --> 00:06:25,440
+الضعف اللي في الـ «فولف» زي ما قلنا، الـ
+
+73
+00:06:25,440 --> 00:06:31,380
+«فولفولار» يمكن أن يتعامل مع كل 4 «فولف» لكن بنسبة
+
+74
+00:06:31,380 --> 00:06:36,410
+مختلفة أو أكتر من ذلكمن الحاجات اللي احنا ممكن
+
+75
+00:06:36,410 --> 00:06:41,150
+نبدأ نتحدث فيها الـ Mitral Stenosis Mitral
+
+76
+00:06:41,150 --> 00:06:47,110
+Regurgitation ارتجاع الميترال وتضيق الميترال أو
+
+77
+00:06:47,110 --> 00:06:54,370
+أورتيكستينوزس أو أورتيكرجورغيتيشن لأن الـ Tricusp
+
+78
+00:06:54,370 --> 00:06:57,730
+Valve اللي هو الـ Atrioventricular Valve is
+
+79
+00:06:57,730 --> 00:07:03,530
+affected infrequentlyTricusp Stenosis بيعملنا
+
+80
+00:07:03,530 --> 00:07:08,210
+Right Heart Failure وTricusp Regurgitation الـ
+
+81
+00:07:08,210 --> 00:07:10,810
+causes of valvular diseases ليش طيب بيصير عندنا
+
+82
+00:07:10,810 --> 00:07:17,610
+valvular diseases؟ أول حاجة يكون congenital، مخلوق
+
+83
+00:07:17,610 --> 00:07:21,830
+فيه، فيه عنده abnormality في الvalves زي أي مكان
+
+84
+00:07:21,830 --> 00:07:28,610
+في الجسم، congenital mostly affect the aortic or
+
+85
+00:07:28,610 --> 00:07:36,680
+pulmonicValve هذا الـ congenital الـ acquired يعني
+
+86
+00:07:36,680 --> 00:07:42,180
+حاجة صارت over the time عملتلي
+
+87
+00:07:42,180 --> 00:07:45,980
+Valvular disease زي مين؟ زي ال rheumatic fever ايش
+
+88
+00:07:45,980 --> 00:07:51,060
+ال rheumatic fever؟ مين فاكر حاجة عن ال rheumatic
+
+89
+00:07:51,060 --> 00:07:53,320
+fever؟ طب ايش سببها بالعربي؟
+
+90
+00:07:56,080 --> 00:08:01,660
+الحمة الروماتيزمية، هذه كانت زمان مشهورة ومنتشرة،
+
+91
+00:08:01,660 --> 00:08:06,560
+إيش الحمة الروماتيزمية؟ هنحكيها في الـ slide اللي
+
+92
+00:08:06,560 --> 00:08:11,460
+بعده، إيش كمان بعملي Valvular Disease؟ Infective
+
+93
+00:08:11,460 --> 00:08:15,560
+Endocarditis، إحنا عارفين إن الـ valves إمتداد
+
+94
+00:08:15,560 --> 00:08:21,620
+لمين؟ إمتداد للـ endocardiumلأن لما بيصير عندي
+
+95
+00:08:21,620 --> 00:08:24,220
+infection في الـ endocardium انفكت في الـ
+
+96
+00:08:24,220 --> 00:08:29,040
+endocarditis فالـ valves برضه بتلتهب طيب الآن
+
+97
+00:08:29,040 --> 00:08:33,000
+تصوروا قدامك و هيك أي إشي الحاجات اللي بتلتهب خاصة
+
+98
+00:08:33,000 --> 00:08:38,900
+لما تكون حاجات هيك نعمة زي الـ valves لما بتلتهب
+
+99
+00:08:38,900 --> 00:08:44,540
+إيش بيصير؟ يا إما يضيق الـ valve يا إما الـ valve
+
+100
+00:08:44,540 --> 00:08:51,980
+بيصير فيه رخاوة و بيصير عندناالـ coronary artery
+
+101
+00:08:51,980 --> 00:08:55,460
+disease لماذا؟ لأنه لا يصل إلى الـ valves تخدية
+
+102
+00:08:55,460 --> 00:09:01,660
+كيف هي؟ آه، الـ cardiomyopathy إنه يكون الـ heart
+
+103
+00:09:01,660 --> 00:09:07,460
+muscle صار فيه عنده disease وهذا إيش بيعملنا
+
+104
+00:09:07,460 --> 00:09:12,160
+cardiomyopathy؟ بيعملنا cardiomegaly اتصوروا إنه
+
+105
+00:09:12,160 --> 00:09:18,280
+القلب بالـ valves تبعته كما هي كويس لكن لما يكبر
+
+106
+00:09:18,280 --> 00:09:26,980
+قلبه يتوسعفبتتوسع الـ Valve فبتبعد الـ Caps اللي
+
+107
+00:09:26,980 --> 00:09:30,860
+هي تبعت ال Valves عن بعض فبيصير عنا Re-Orgitation
+
+108
+00:09:30,860 --> 00:09:34,920
+الـ Hypertension، الـ Aortic Aneurysm، الـ
+
+109
+00:09:34,920 --> 00:09:37,940
+Connective Tissue Disease هذه كلها من الأسباب اللي
+
+110
+00:09:37,940 --> 00:09:45,500
+بتعملنا Valvular Diseases طب نعرج على بعض الـالـ
+
+111
+00:09:45,500 --> 00:09:49,080
+Diseases بس من باب الشرح الـ Rheumatic Heart
+
+112
+00:09:49,080 --> 00:09:54,980
+Disease إيش بنقصد فيه؟ هو عبارة عن باختصار جدا الـ
+
+113
+00:09:54,980 --> 00:09:59,100
+Rheumatic Heart Disease هو عبارة عن post
+
+114
+00:09:59,100 --> 00:10:02,760
+-infectious disease كيف يعني post-infectious؟ يعني
+
+115
+00:10:02,760 --> 00:10:06,540
+بيصير infectious بعد بأسبوع أو أسبوعين بيصير في
+
+116
+00:10:06,540 --> 00:10:12,300
+عندنا ردة فعل autoimmune ضد
+
+117
+00:10:12,300 --> 00:10:17,120
+خلايا الـ valves أو القلبوهذا هنشوفه في عدة أمراض
+
+118
+00:10:17,120 --> 00:10:21,940
+مثل «جولين باري سندروم» مثلًا مثلًا مثلًا مثلًا
+
+119
+00:10:21,940 --> 00:10:26,240
+مثلًا
+
+120
+00:10:26,240 --> 00:10:29,260
+مثلًا
+
+121
+00:10:29,260 --> 00:10:29,920
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+122
+00:10:29,920 --> 00:10:31,640
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+123
+00:10:31,640 --> 00:10:35,260
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+124
+00:10:35,260 --> 00:10:35,780
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+125
+00:10:35,780 --> 00:10:35,800
+مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا مثلًا
+
+126
+00:10:35,800 --> 00:10:39,280
+مثلًا مثلًا مثلًا
+
+127
+00:10:43,020 --> 00:10:48,540
+زي الصواريخ ضد المفروض ضد البكتيريا اللي عملت
+
+128
+00:10:48,540 --> 00:10:53,920
+الاتحام وبما أن البروتين تبع البكتيريا بيشبه لبعض
+
+129
+00:10:53,920 --> 00:10:58,280
+خلاياالجسم فبتخربط الجهاز المناعي بدل ما يضرب
+
+130
+00:10:58,280 --> 00:11:03,720
+البكتيريا بروح بدرب ايش بدرب نفسه بدرب اللي هو
+
+131
+00:11:03,720 --> 00:11:07,160
+خلايا الجسم وهذا اللي بيصير في القلب أو في الـ
+
+132
+00:11:07,160 --> 00:11:12,880
+valves انه انه تهاجم الـ valves من الجهاز المناعي
+
+133
+00:11:12,880 --> 00:11:17,200
+تبع البني آدم نفسه ليش؟ لأنه ماعرفش يفرج الجهاز
+
+134
+00:11:17,200 --> 00:11:22,410
+المناعي بين البكتيريا اللي عملاله التهاب وبيناللي
+
+135
+00:11:22,410 --> 00:11:27,310
+هي خلايا الـ valves فبيهاجمها بصورة واضحة فبيصير
+
+136
+00:11:27,310 --> 00:11:31,170
+عندنا ما نسميه بـ heart أو rheumatic heart disease
+
+137
+00:11:31,170 --> 00:11:34,010
+inflammatory process that may affect the
+
+138
+00:11:34,010 --> 00:11:38,910
+myocardium pericardium and or endocardium وهذا
+
+139
+00:11:38,910 --> 00:11:43,090
+بيصير بيعمل ليه ايش؟ distortion و scarring of the
+
+140
+00:11:43,090 --> 00:11:46,150
+valve أي التهاب في أي valve بيعمل scarring و
+
+141
+00:11:46,150 --> 00:11:51,260
+distortion لإلهوهذا بيصير نتيجة «Type II
+
+142
+00:11:51,260 --> 00:11:55,260
+Inflammatory Reaction»of inflammatory reaction هذا
+
+143
+00:11:55,260 --> 00:11:59,560
+type 2 secondary to sore throat نتيجة التهاب
+
+144
+00:11:59,560 --> 00:12:03,120
+اللواز عشان هي انا بنركز يا جماعة لما بيصير التهاب
+
+145
+00:12:03,120 --> 00:12:05,820
+لواز بكتيري عن طريق اللي هو الـ streptococcus
+
+146
+00:12:05,820 --> 00:12:12,100
+biogenes أو كوكاي streptococci beta-haemolytic
+
+147
+00:12:12,100 --> 00:12:15,400
+streptococci بنقول للناس لابد إنه نعالج ببنسلين
+
+148
+00:12:15,400 --> 00:12:19,160
+لأنه لو تركنا موضوعه ممكن هذا الأمر يترك لي أثر
+
+149
+00:12:19,160 --> 00:12:24,890
+على القلب ويعمل لي rheumatic heartعلى الـ kidney
+
+150
+00:12:24,890 --> 00:12:33,570
+ويعملّي glomerulonephritis على الـ joints ويعملّي
+
+151
+00:12:33,570 --> 00:12:39,970
+arthritis، rheumatic arthritis يبقى أنا لما بعالج
+
+152
+00:12:39,970 --> 00:12:45,070
+اللوز، التهاب اللوز البكتيري لما بعالجه، بعالجه مش
+
+153
+00:12:45,070 --> 00:12:48,730
+عشان التهاب اللوز itself ولو إنه مهم، لكن بعالجه
+
+154
+00:12:48,730 --> 00:12:56,620
+حتى إنه ما يعجب، ما يترك أثرعدم العلاج على vital
+
+155
+00:12:56,620 --> 00:13:02,060
+organs زي القلب زي الـ Heart زي الـ Kidneys زي الـ
+
+156
+00:13:02,060 --> 00:13:06,620
+Joints هد هو إيش الـ Rheumatic Heart Disease زي ما
+
+157
+00:13:06,620 --> 00:13:10,260
+بيقول دايما هو عبارة عن Autoimmune Disease
+
+158
+00:13:10,260 --> 00:13:14,300
+Autoimmune Disease يعني نيران صديقة الجسم بيهاجم
+
+159
+00:13:14,300 --> 00:13:17,600
+نفسه بيفكر حاله بيهاجم عدو
+
+160
+00:13:19,960 --> 00:13:24,100
+الـ Infective Endocarditis أي Infection زي القلب
+
+161
+00:13:24,100 --> 00:13:31,050
+زيه زي أي مكان بالعكس هومن أكثر الأعضاء لأنهم
+
+162
+00:13:31,050 --> 00:13:35,250
+يمروا عليها كل الدم عمليًا في الجسم فأي بكتيريا
+
+163
+00:13:35,250 --> 00:13:38,950
+مضرة ممكن في الآخر تعملي طبعًا في أنواع ما نحكي
+
+164
+00:13:38,950 --> 00:13:45,250
+أحنا عن الـinfective heart diseases بعد هيك ممكن
+
+165
+00:13:45,250 --> 00:13:48,350
+يعملي infection على heart valve commonly بكتيريا
+
+166
+00:13:48,350 --> 00:13:52,470
+result in damage to valve structure giving rise to
+
+167
+00:13:52,470 --> 00:13:53,670
+stenosis أو regurgitation
+
+168
+00:13:57,290 --> 00:14:02,390
+هذه من بعض الأسباب اللي
+
+169
+00:14:02,390 --> 00:14:12,730
+ممكن تعملنا الـ Valve Disease يعني احنا من باب
+
+170
+00:14:12,730 --> 00:14:18,310
+الآن الذكر طيب هو صار عندى الـ Stenosis في الـ
+
+171
+00:14:18,310 --> 00:14:23,550
+Mitral عسم المثال هو إيش يعني هيصير؟بتفكروا يا
+
+172
+00:14:23,550 --> 00:14:27,030
+جماعة و تتصوروا الـ «circulation» اللي اتحدثنا
+
+173
+00:14:27,030 --> 00:14:31,370
+عليه في الأول تبع الدم «mitral stenosis» يعني وين
+
+174
+00:14:31,370 --> 00:14:35,230
+بتكون المشكلة؟ بتكون في الـ «mitral valve»
+
+175
+00:14:35,230 --> 00:14:38,290
+والمشكلة في الغالب في الـ «stenosis» في الـ
+
+176
+00:14:38,290 --> 00:14:45,430
+«systolicum» لما يضخ الجلب لما
+
+177
+00:14:45,430 --> 00:14:48,470
+في الـ «diastolicum» لما ينبسط القلب، وين المشكلة
+
+178
+00:14:48,470 --> 00:14:49,030
+بتصير؟
+
+179
+00:14:51,960 --> 00:14:57,040
+الميترال شغله في الـ diastolicum لما الـ left
+
+180
+00:14:57,040 --> 00:15:03,060
+atrium بده يدخل الدم على الـ left ventricle كمان
+
+181
+00:15:03,060 --> 00:15:08,480
+مرة، diastolicum بده يدخل الدم من الـ left atrium
+
+182
+00:15:08,480 --> 00:15:13,580
+to the left ventricle الاستينوزز هنا بتلعب دور،
+
+183
+00:15:13,580 --> 00:15:18,290
+ليش؟لأنه بيصير الـ Left Atrium مش جادر يدخل كل
+
+184
+00:15:18,290 --> 00:15:21,770
+الدم اللي وصله من الـ Lung للـ Left Ventricle
+
+185
+00:15:21,770 --> 00:15:27,110
+وبالتالي الـ Left Ventricle مقدرش يدقق دم كتير على
+
+186
+00:15:27,110 --> 00:15:35,270
+الجسم يبقى الاستينوزز بيتركلي أثر زيادة تحميل على
+
+187
+00:15:35,270 --> 00:15:43,830
+الـ Left Atrium ونقص تحميل على الـ Left Ventricle
+
+188
+00:15:47,260 --> 00:15:50,000
+طيب، وإذا أنا في عندي زيادة التحميل على الـ left
+
+189
+00:15:50,000 --> 00:15:54,420
+atrium، إيش بيصير؟ لأنه مش قادر يدخل كل الدم نتيجة
+
+190
+00:15:54,420 --> 00:15:58,520
+الـ stenosis، نتيجة الدضايق، مش قادر يدخل كل الدم
+
+191
+00:15:58,520 --> 00:16:02,960
+على الـ left ventricles، إيش بيصير؟ آه، بيجي الـ
+
+192
+00:16:02,960 --> 00:16:11,730
+left ventricle بيقول للـ pulmonary veinsاللي جايبة
+
+193
+00:16:11,730 --> 00:16:16,770
+دم من الـ lungs لأ بيكفي انا مش جادر اخد دم منك يا
+
+194
+00:16:16,770 --> 00:16:21,130
+lung كفاية كتير ليش؟ لأنه انا مش جادر اديه للـ
+
+195
+00:16:21,130 --> 00:16:25,570
+left ventricle فبيصير عندي إيش احتقان في ال lungs
+
+196
+00:16:25,570 --> 00:16:30,110
+إذا صار في عندي احتقان في ال lungs بيجي ال right
+
+197
+00:16:30,110 --> 00:16:33,210
+ventricle الآن مش عن ال left الجدا بيجي ال right
+
+198
+00:16:33,210 --> 00:16:38,350
+ventricle مش جادر يضخ دم في ال lungs ليش؟ لأن ال
+
+199
+00:16:38,350 --> 00:16:46,120
+lungs ملانة دمطيب فبصير في عندنا حاجة اسمها Right
+
+200
+00:16:46,120 --> 00:16:52,100
+-sided heart failure symptoms إذا الـ Right heart
+
+201
+00:16:52,100 --> 00:16:57,340
+أو الـ Right ventricle و الـ Right heart صار في
+
+202
+00:16:57,340 --> 00:17:05,130
+عنده ملان دم و محتقن لن يأخذ دم من وينمن الجسم من
+
+203
+00:17:05,130 --> 00:17:10,050
+الـVenacava Superior والـVenacava Inferior فبيصير
+
+204
+00:17:10,050 --> 00:17:21,090
+عندنا Symptoms في الجسم ناتجة عن احتقان أعضاء
+
+205
+00:17:21,090 --> 00:17:25,890
+الجسملأنها مش قادرة على طريق الـ Venacava Superior
+
+206
+00:17:25,890 --> 00:17:29,410
+و Inferior تدّي الـ Right Atrium و الـ Right
+
+207
+00:17:29,410 --> 00:17:32,930
+Atrium مش قادر يدّي الـ Right Ventricle ليش؟ لأن
+
+208
+00:17:32,930 --> 00:17:35,810
+الـ Right Ventricle مش قادر ياخد من الـ Lung لأن
+
+209
+00:17:35,810 --> 00:17:39,450
+الـ Lung مش قادرة تدّي الـ Left Atrium ليش؟ نتيجة
+
+210
+00:17:39,450 --> 00:17:46,430
+التضيقفي الـ «ميترال فالف»، كل هذا ما هي المشكلة
+
+211
+00:17:46,430 --> 00:17:50,530
+وإحنا ليش بنبكي لما يكون في عندنا Stenosis في الـ
+
+212
+00:17:50,530 --> 00:17:54,350
+«ميترال فالف»؟ ليش؟ لأنه تأثيره تأثير غير مباشر
+
+213
+00:17:54,350 --> 00:17:57,070
+على معظم أعضاء الجسم، ولو أنه تضيق بس في الـ
+
+214
+00:17:57,070 --> 00:18:02,450
+«ميترال فالف»، عرفتوا؟ كل إشي هيك بده يتفسر يا
+
+215
+00:18:02,450 --> 00:18:04,990
+جماعة، كل إشي هيك بده يتفسر، ليش الـ «فالفولار
+
+216
+00:18:04,990 --> 00:18:09,940
+ديزيزيز» اللي هي التأثير الكبيرطيب، هل هناك حلول؟
+
+217
+00:18:09,940 --> 00:18:14,400
+نعم، هذه القضية أني لدي حلول للمواضيع هذه طب
+
+218
+00:18:14,400 --> 00:18:19,220
+الميترالفالف، من أيش بيصير في العادة؟ طبعا، يمكن
+
+219
+00:18:19,220 --> 00:18:23,600
+أني فرضت الآن الشرح للـmitral valve لأهميته ولأنه
+
+220
+00:18:23,600 --> 00:18:28,620
+بس obvious وواضح ويعني الواحد بيقدر يتصور الموضوع
+
+221
+00:18:28,620 --> 00:18:33,040
+usually result from rheumatic carditisوإيش اللي
+
+222
+00:18:33,040 --> 00:18:35,760
+بيصير؟ بيصير عندي thickening by fibrosis
+
+223
+00:18:35,760 --> 00:18:39,340
+وcalcification نتيجة الـ Rheumatic Carditis
+
+224
+00:18:39,340 --> 00:18:44,260
+thickening by fibrosis and calcification طبعاً
+
+225
+00:18:44,260 --> 00:18:47,600
+ممكن يكون نتيجة tumor أو thrombus لكن الأساس إنه
+
+226
+00:18:47,600 --> 00:18:52,300
+Rheumatic Carditis إيش اللي بيصير؟ نتيجة الاتهابات
+
+227
+00:18:52,300 --> 00:18:55,480
+الـ leaflets of the valves اللي هي الفروع بتاعة
+
+228
+00:18:55,480 --> 00:19:02,140
+الـ valves fuse تتلتحم مع بعضوبصير عندى narrowing
+
+229
+00:19:02,140 --> 00:19:08,320
+of the opening وهذا بمنع normal blood flow from
+
+230
+00:19:08,320 --> 00:19:12,320
+left atrium to the left ventricle left atrium
+
+231
+00:19:12,320 --> 00:19:20,260
+pressure بزيد ال left atrium dilates البلمونة
+
+232
+00:19:20,260 --> 00:19:26,800
+الارتريه pressure بزيد فإيش بيصير عندى بالتالي
+
+233
+00:19:26,800 --> 00:19:31,400
+right ventricle hypertrophyزي ما قلنا الـ
+
+234
+00:19:31,400 --> 00:19:34,620
+Pulmonary congestion احتقان القلب الـ Pulmonary
+
+235
+00:19:34,620 --> 00:19:39,120
+الاريعتين بيعملولي Right-sided heart failures
+
+236
+00:19:39,120 --> 00:19:45,200
+وطبعاً بعكرلي كل الموضوع الـ Mitral Stenosis في
+
+237
+00:19:45,200 --> 00:19:48,140
+منها طبعاً مش كل الـ Mitral Stenosis مش كل تضيق هو
+
+238
+00:19:48,140 --> 00:19:52,680
+يعتبر تضيق مهم في كتير ناس عندها تضيق لكن الأمور
+
+239
+00:19:52,680 --> 00:19:57,240
+compensated في حالات الـ mild و بتبقى asymptomatic
+
+240
+00:19:58,760 --> 00:20:02,120
+لكن بعض الأحيان بنلاقي انه with progression بتزيد
+
+241
+00:20:02,120 --> 00:20:04,860
+مع الوقت بتزيد وإحنا مابنحكيش عن acute هنا يا
+
+242
+00:20:04,860 --> 00:20:08,900
+جماعة لإن السبب مش .. مش .. مش thrombus مثلا أو ..
+
+243
+00:20:08,900 --> 00:20:12,140
+أو حاجة إنما إحنا بنحكي عن حاجة chronic over the
+
+244
+00:20:12,140 --> 00:20:19,880
+time بتصير with progression بصير dyspnea، أرتبنية،
+
+245
+00:20:19,880 --> 00:20:23,640
+dry cough، hemoptysis، إيش عن hemoptysis؟
+
+246
+00:20:27,540 --> 00:20:34,720
+وإيش معناة hematemesis طب
+
+247
+00:20:34,720 --> 00:20:41,700
+hematuria طب التلت كلمات هدول بدي عن كل واحدة سطرة
+
+248
+00:20:41,700 --> 00:20:47,180
+تكتبولي إيش يعني hemoptysis إيش يعني hematuria إيش
+
+249
+00:20:47,180 --> 00:20:52,560
+يعني hematemesis and pulmonary edema may appear
+
+250
+00:20:52,560 --> 00:20:58,700
+يبدأ ال assignmentالجزء تبعه الأولاني بدنا الفرق
+
+251
+00:20:58,700 --> 00:21:03,000
+بين الـ hemoptysis الـ hematuria and الـ
+
+252
+00:21:03,000 --> 00:21:07,860
+hematemesis right-sided heart failure symptoms
+
+253
+00:21:07,860 --> 00:21:11,360
+occur later وبعدين بيصير عندي atrial fibrillation
+
+254
+00:21:11,360 --> 00:21:15,260
+وممكن يصير عندي ميرمر كمان في القلب مش مهم جدا
+
+255
+00:21:15,260 --> 00:21:23,820
+بالنسبة لك هل الـ aortic stenosisاللي بيصير بيصير
+
+256
+00:21:23,820 --> 00:21:29,400
+تضيق الأورطة بيصير بنفس الصورة وبيعمللي مشاكل نعم
+
+257
+00:21:29,400 --> 00:21:34,660
+هو بنفس الفكرة بالمناسبة إنه ال right ال left
+
+258
+00:21:34,660 --> 00:21:39,080
+ventricle اللي هو عن طريق الأورتك بيبعد دم للجسم
+
+259
+00:21:39,080 --> 00:21:45,560
+مقدرش يبعد كل الدم لأنه عنده stenosis هلجيت الجسم
+
+260
+00:21:45,560 --> 00:21:50,000
+بيصلوش دم كفاية وهذا بيعمللي مشاكل تصوروا الدماغ
+
+261
+00:21:50,000 --> 00:21:59,190
+مايصلوش دمبيصير عندى Psycho خاصة لما فيه exertion،
+
+262
+00:21:59,190 --> 00:22:07,170
+فيه تعب، فيه حركة، لما القلب وشرين القلب مايصلهاش
+
+263
+00:22:07,170 --> 00:22:12,930
+دم كفاية، بيصير عندنا Angina، ليش؟ لأن ال supply
+
+264
+00:22:12,930 --> 00:22:22,650
+جال تبع الدم لل heart muscles، بيصير عندنا dyspnea
+
+265
+00:22:24,590 --> 00:22:29,670
+بسبب نفسي الـ Heart Failure بسبب
+
+266
+00:22:29,670 --> 00:22:32,230
+نفسي الـ Heart Failure بسبب نفسي الـ Heart Failure
+
+267
+00:22:32,230 --> 00:22:36,170
+بسبب نفسي الـ Heart Failure بسبب نفسي الـ Heart
+
+268
+00:22:36,170 --> 00:22:37,890
+Failure بسبب نفسي الـ Heart Failure بسبب نفسي الـ
+
+269
+00:22:37,890 --> 00:22:37,890
+Heart Failure بسبب نفسي الـ Heart Failure بسبب
+
+270
+00:22:37,890 --> 00:22:37,890
+نفسي الـ Heart Failure بسبب نفسي الـ Heart Failure
+
+271
+00:22:37,890 --> 00:22:37,890
+بسبب نفسي الـ Heart Failure بسبب نفسي الـ Heart
+
+272
+00:22:37,890 --> 00:22:38,070
+Failure بسبب نفسي الـ Heart Failure بسبب نفسي الـ
+
+273
+00:22:38,070 --> 00:22:38,070
+Heart Failure بسبب نفسي الـ Heart Failure بسبب
+
+274
+00:22:38,070 --> 00:22:40,650
+نفسي الـ Heart Failure بسبب نفسي الـ Heart Failure
+
+275
+00:22:40,650 --> 00:22:45,630
+بسبب نفسي الـ Heart Failure بسبب نفسي الـ Heart
+
+276
+00:22:45,630 --> 00:22:52,400
+Failure بسبب نفسي الـ Heart Failure بسبب نالان
+
+277
+00:22:52,400 --> 00:22:55,760
+بعيدا عن ايش بتصير في الـ heart باقي الجسم مش
+
+278
+00:22:55,760 --> 00:23:00,300
+هيصله دم فبصير ان المشاكل هذه الأعضاء الـ vital
+
+279
+00:23:00,300 --> 00:23:04,160
+organs بيصير فيها مشاكل ليش؟ لأنه ماوصلهاش
+
+280
+00:23:04,160 --> 00:23:07,800
+perfusion كفاية طيب من ايش بيصير الـ aortic
+
+281
+00:23:07,800 --> 00:23:15,980
+stenosis؟ commonly نتيجة age related progressive
+
+282
+00:23:15,980 --> 00:23:21,790
+calcification وبرضه rheumatic aortic stenosisالـ
+
+283
+00:23:21,790 --> 00:23:24,570
+Rheumatic-Aortic Stenosis Clinical Representation
+
+284
+00:23:24,570 --> 00:23:30,070
+مهم نعرفه «سينكوب» في الـ Exertional Stage خاصة
+
+285
+00:23:30,070 --> 00:23:37,810
+عند الـ Angina، Dyspnea، and Sudden Death الـ
+
+286
+00:23:37,810 --> 00:23:42,730
+Aortic Regurgitation أو الـ Insufficiency هو عبارة
+
+287
+00:23:42,730 --> 00:23:48,500
+عنleaking of aortic valve of the heart that causes
+
+288
+00:23:48,500 --> 00:23:52,160
+blood to flow in the reverse direction during
+
+289
+00:23:52,160 --> 00:23:57,260
+ventricular diastole بيجي القلب ع سلامته بيعمل
+
+290
+00:23:57,260 --> 00:24:01,640
+diastolicum المفروض أن الدم بيجي كل هيته من وين؟
+
+291
+00:24:01,640 --> 00:24:06,240
+من الـ mitral valve و من الtricuspidal valve فإذا
+
+292
+00:24:06,240 --> 00:24:09,600
+به بيجيله دم كمان من ال aortic valve و من
+
+293
+00:24:09,600 --> 00:24:13,320
+البلبونary valve إيش بيصير هيك؟ بيصير عنا overload
+
+294
+00:24:14,440 --> 00:24:20,520
+الـ Lymph ventricle بيدخله كمان دم من الـ aortic
+
+295
+00:24:20,520 --> 00:24:25,620
+غير اللي دخله من في
+
+296
+00:24:25,620 --> 00:24:28,560
+الـ diastolic غير اللي دخله من اللي هو الـ left
+
+297
+00:24:28,560 --> 00:24:34,560
+atrium أسباب
+
+298
+00:24:34,560 --> 00:24:38,300
+الـ regurgitation ممكن يكون Infective endocarditis
+
+299
+00:24:38,300 --> 00:24:45,900
+رويماتيك، disease ممكن، traumaفي عندنا بعض الأمراض
+
+300
+00:24:45,900 --> 00:24:50,160
+زي الـ Marfan و الـ Syndrome و الـ Syphilis هذه
+
+301
+00:24:50,160 --> 00:24:53,820
+بتديني Aortic Dilatation يبقى أنا بحكي عنها كمان
+
+302
+00:24:53,820 --> 00:24:57,440
+وهذا الـ Assignment التاني عفوا الجزء التاني من
+
+303
+00:24:57,440 --> 00:25:01,260
+الـ Assignment اللي هو بدي تلت تسطر عن الـ Marfan
+
+304
+00:25:01,260 --> 00:25:05,540
+Syndrome و تلت تسطر عن الـ Syphilis تلت تسطر بس
+
+305
+00:25:05,540 --> 00:25:09,860
+تلتة تلتة واتفجنا في الجبل شوية عن
+
+306
+00:25:16,660 --> 00:25:20,380
+في الجزء الأول من الـ Assignment نكتب الفرق بين
+
+307
+00:25:20,380 --> 00:25:26,060
+الهيماتوريا والـ hematemesis والـ hemoptysis هدول
+
+308
+00:25:26,060 --> 00:25:29,980
+الـ Assignment اللي هو جزءين ومايزدش أي حاجة
+
+309
+00:25:29,980 --> 00:25:33,060
+بتنكتب عن تلت تستر عن أي حاجة في الموضوع هذا
+
+310
+00:25:33,060 --> 00:25:37,200
+بالذات اليوم في حين الـ mitral regurgitation بنفس
+
+311
+00:25:37,200 --> 00:25:40,640
+الصورة occurs when the mitral valve does not close
+
+312
+00:25:40,640 --> 00:25:48,250
+properly في حين heart bumps out bloodنفس الفكرة
+
+313
+00:25:48,250 --> 00:25:53,690
+ممكن تترك لي أثار كبيرة الـ diagnosis كيف أنا بشخص
+
+314
+00:25:53,690 --> 00:25:59,610
+الـ valvular diseases رقم واحد الـ
+
+315
+00:25:59,610 --> 00:26:02,930
+echocardiography و احنا اتحدثنا أيامها الفرق بين
+
+316
+00:26:02,930 --> 00:26:06,930
+ال ECG و ال echo إذا فاكرين و ال catheter و قلنا
+
+317
+00:26:06,930 --> 00:26:12,930
+إن ال echocardiography هو اللي يكشف لي مشاكل ال
+
+318
+00:26:12,930 --> 00:26:16,640
+musclesومشاكل الـ Valves
+
+319
+00:26:19,150 --> 00:26:22,550
+وممكن طبعا بعض الأحيان تبقى الـ Echocardiography
+
+320
+00:26:22,550 --> 00:26:32,450
+لأنها Trans-toracal من خلال الصدر من برا نعملها
+
+321
+00:26:32,450 --> 00:26:35,990
+Echocardiography بيبين ليش بعض الحاجات فبنضطر ندخل
+
+322
+00:26:35,990 --> 00:26:40,110
+بجهاز الـ Echo لكن عن طريق الـ Esophagus عن طريق
+
+323
+00:26:40,110 --> 00:26:44,490
+المرية نقول عنها Transesophageal Echocardiography
+
+324
+00:26:44,490 --> 00:26:50,390
+إذا عرفنا إنه في حاجةوبدها تشخيص أكتر وأكتر بتحتاج
+
+325
+00:26:50,390 --> 00:26:53,750
+خاصة لو بدها intervention بنحتاج إليها cardiac
+
+326
+00:26:53,750 --> 00:26:59,310
+catheter بنقول عنه أنجيوغرام بدها أنجيوغرام طبعا
+
+327
+00:26:59,310 --> 00:27:03,030
+في الصورة واضح عندنا اللي هو حاجة بنقول عنها ال
+
+328
+00:27:03,030 --> 00:27:09,220
+four valve أو four chamber viewطبعاً هذه بدها
+
+329
+00:27:09,220 --> 00:27:12,440
+أخصائي القلب هو اللي بيقوم بيها الشغل هاي و بيشوف
+
+330
+00:27:12,440 --> 00:27:17,260
+مدى كيف ال .. ال .. ال .. ال valves وضعها و كيف
+
+331
+00:27:17,260 --> 00:27:21,980
+مرور الدم من خلالها بمجسات معينة بيجيسوها على
+
+332
+00:27:21,980 --> 00:27:24,620
+الجهاز فبيعرفوا أنه في مشكلة أو لأ و طبعا ممكن
+
+333
+00:27:24,620 --> 00:27:31,180
+نضطر نروح على ال MRI هذا طبعا اللي هو ال .. ال ..
+
+334
+00:27:31,180 --> 00:27:37,810
+ال .. الـ Angiogram هنحكي في ساعتهطب كيف أتعالج
+
+335
+00:27:37,810 --> 00:27:42,990
+الـ «valvular diseases»؟ هو لو الـ «valvular
+
+336
+00:27:42,990 --> 00:27:47,130
+diseases» عملتلي مشاكل في الـ «myocardium» وفي
+
+337
+00:27:47,130 --> 00:27:54,070
+القلب ممكن أحتاج drugs حتى أخفف الضغط عنها لكن
+
+338
+00:27:54,070 --> 00:27:58,090
+الأصل أنه أنا بعمل للـ «valves» هاي إما repair أو
+
+339
+00:27:58,090 --> 00:28:04,550
+replacement إما repair أو replacementوالتحقيق
+
+340
+00:28:04,550 --> 00:28:09,890
+بإصلاحها بإستخدام مجهزة ممكنة للتحقيق بإستخدام
+
+341
+00:28:09,890 --> 00:28:16,290
+مجهزة ممكنة للتحقيق بإستخدام
+
+342
+00:28:16,290 --> 00:28:16,810
+مجهزة
+
+343
+00:28:19,550 --> 00:28:23,490
+ممكن أدى Diuretics، ممكن أدى Beta Blockers، بغض
+
+344
+00:28:23,490 --> 00:28:27,650
+النظر عن وظيفة كل واحد، مع حالة كبيرة طريقتنا من
+
+345
+00:28:27,650 --> 00:28:31,050
+الأول، زي ما اتفقنا، Diuretics، هذه كلها بتخفف
+
+346
+00:28:31,050 --> 00:28:35,710
+الوضع أو الضغط عن القلب، Beta Blockers، Dioxin،
+
+347
+00:28:35,710 --> 00:28:39,070
+O2، Oxygen، Vasodilators، Prophylactic Antibiotic،
+
+348
+00:28:39,070 --> 00:28:45,150
+ممكن أدىوإذا كان هناك إتريال أو فايروليشن، يمكن أن
+
+349
+00:28:45,150 --> 00:28:48,650
+أعمله إتريال أو فايروليشن إذا كان ممكن أو يمكن أن
+
+350
+00:28:48,650 --> 00:28:55,750
+نعمل استخدام لـ Anticoagulation الـ Surgical
+
+351
+00:28:55,750 --> 00:29:00,740
+Management يحدث كما قلناكل Valve إله طريقة معينة
+
+352
+00:29:00,740 --> 00:29:05,340
+بتنعمل فيه، مش كله زي بعض و هذه إلها ناس أخصائيين
+
+353
+00:29:05,340 --> 00:29:08,480
+فيها لكن إحنا بنحكي عن الأساسيات تبع الموضوع
+
+354
+00:29:08,480 --> 00:29:12,080
+«ميترال فالف» ممكن أعمله replacement أو «فالفولو
+
+355
+00:29:12,080 --> 00:29:15,680
+بلاستي» بلون «فالفولو بلاستي» عمل التوزيع بالبالون
+
+356
+00:29:15,680 --> 00:29:20,600
+أو «أورتيك فالف» replacement في حالات لما يكون
+
+357
+00:29:20,600 --> 00:29:29,190
+عندي problemهذه صور من الموضوع الـ «Valves» وموضوع
+
+358
+00:29:29,190 --> 00:29:36,070
+كبير، موضوع مهم أخد على مدى التاريخ كتير تجارب
+
+359
+00:29:36,070 --> 00:29:43,500
+لحتى وصلوا لموضوع الـ «Valves»سواء الـ Repair أو
+
+360
+00:29:43,500 --> 00:29:48,300
+الـ Replacement بنحس إنه عبر التاريخ كان في عندنا
+
+361
+00:29:48,300 --> 00:29:53,820
+أنواع من الـ Valves سواء mechanical أو حتى tissue
+
+362
+00:29:53,820 --> 00:30:02,700
+valves مخودة من مكان آخر، biological valves بنقول
+
+363
+00:30:02,700 --> 00:30:11,590
+عنها ال advantages of surgical repair طبعاًبتخفف
+
+364
+00:30:11,590 --> 00:30:15,290
+ليه موضوع أن الـ heart failure فشل القلب لأنه
+
+365
+00:30:15,290 --> 00:30:19,230
+القلب بعد فترة بقدرش يكمل و بيصير عنا better
+
+366
+00:30:19,230 --> 00:30:23,710
+functional outcome ال disadvantages طبعا ال valve
+
+367
+00:30:23,710 --> 00:30:28,230
+برضه في الآخر خاصة لما أحطه لطفل حضر بعد هيك لو
+
+368
+00:30:28,230 --> 00:30:31,570
+ربنا أداه العمر أعود أحطله valve تاني لأنه ماحي
+
+369
+00:30:31,570 --> 00:30:34,750
+يقعد معاه سبعين تمانين سنة أكيد فيصير عندي valve
+
+370
+00:30:34,750 --> 00:30:40,490
+failure وطبعا في بعض ال valvesأنواع منها بتحتاج
+
+371
+00:30:40,490 --> 00:30:43,610
+Life-Long Anticoagulation لأنها أجسام غريبة فممكن
+
+372
+00:30:43,610 --> 00:30:46,530
+تعمل الـ Coagulation تعمل الـ Thrombus Building
+
+373
+00:30:46,530 --> 00:30:51,750
+فبدها Anticoagulation الحقيقة
+
+374
+00:30:51,750 --> 00:30:56,710
+يعني حكينا في الـ Valvular Diseases بصورة عملية
+
+375
+00:30:56,710 --> 00:31:01,650
+مختصرة جداً جداً يعني بس عرفنا تعريف عنها في حوالي
+
+376
+00:31:01,650 --> 00:31:06,050
+22 slide في نص ساعة أو أكتر من نص ساعة لكن زي ما
+
+377
+00:31:06,050 --> 00:31:11,740
+قلنا الموضوع أكبر من هيكهو أنا بالمناسبة خلال
+
+378
+00:31:11,740 --> 00:31:15,220
+اليومين اللي جايين هابعت لكل مجموعة من المجموعات
+
+379
+00:31:15,220 --> 00:31:19,600
+اللي اتكونناها موضوع بدا تبدأ تحضره الموضوع هذا
+
+380
+00:31:19,600 --> 00:31:27,000
+وتعمل فيه زي بحث البحث هذا طبعاً
+
+381
+00:31:27,000 --> 00:31:30,220
+إله علاقة بالمنهج لكن مش من مواد المنهج لكن إله
+
+382
+00:31:30,220 --> 00:31:34,340
+علاقة بالمنهج تبعنا البحث هذا هتنعمله في عشر صفحات
+
+383
+00:31:34,340 --> 00:31:40,580
+Word مع الـ Referencesسأبدأ بالكتابة عليه وبعد ذلك
+
+384
+00:31:40,580 --> 00:31:48,220
+ينعمل على شكل PowerPointوتلقوه كل مجموعة تلقي بإذا
+
+385
+00:31:48,220 --> 00:31:52,540
+صار في تعليم وجاهي بنعمله في الجامعة إذا ما صارش
+
+386
+00:31:52,540 --> 00:31:57,520
+بحدد النقطة النقطة للبدأ إن شاء الله تعالى على
+
+387
+00:31:57,520 --> 00:32:00,580
+أساس تعملوه بنفس الطريقة اللي أنا قاعد بعمل فيها
+
+388
+00:32:00,580 --> 00:32:06,200
+المحاضرة وتبعتوليها وممكن المحاضرة الأفضل أو أفضل
+
+389
+00:32:06,200 --> 00:32:12,890
+محاضرتين أن نحطهم على صفحة الجامعة أو علىللجميع
+
+390
+00:32:12,890 --> 00:32:16,610
+حتى يشوفوها إن شاء الله تعالى طبعا غير إنه إنه هذه
+
+391
+00:32:16,610 --> 00:32:21,570
+جزء من النشاط اللي ممكن يجيب للواحد علامات
+
+392
+00:32:21,570 --> 00:32:23,790
+للمهتمين بالموضوع هذا إن شاء الله لكن هو طبعا
+
+393
+00:32:23,790 --> 00:32:27,210
+هيكون واجب مهم بالنسبالنا يعطيكوا العافية
+
+394
+00:32:27,210 --> 00:32:30,050
+وانهاركوا سعيد إن شاء الله تعالى
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bBU74brkUFs.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bBU74brkUFs.srt
new file mode 100644
index 0000000000000000000000000000000000000000..d1a2354f75b9854745db648b4aedebfaea9e24d8
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bBU74brkUFs.srt
@@ -0,0 +1,1527 @@
+1
+00:00:02,160 --> 00:00:04,300
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:04,300 --> 00:00:06,700
+والصلاة والسلام علي سيدنا محمد وسيد المرسلين
+
+3
+00:00:06,700 --> 00:00:10,980
+الأجمعين يعني اليوم إن شاء الله تعالى بنكمل  لكن
+
+4
+00:00:10,980 --> 00:00:16,720
+بنكمل محاضرات البطن والقلب والصدرية لكن هنبدأ 
+
+5
+00:00:16,720 --> 00:00:21,520
+بأولى خليني أقول chapter محاضرات chapter اللي هو
+
+6
+00:00:21,520 --> 00:00:26,760
+respiratory system هنحاول زي ما عملنا في القلب حتى
+
+7
+00:00:26,760 --> 00:00:29,820
+في الـ Anatomy والـ Physiology نحاول ناخد من كل
+
+8
+00:00:29,820 --> 00:00:33,900
+بستان زهرة يعني ما هنقول والله منهج متكامل لأنه مش 
+
+9
+00:00:33,900 --> 00:00:38,080
+حقيقي في الموضوع لكن هنحكي الأمور المهمة التي قد 
+
+10
+00:00:38,080 --> 00:00:42,280
+في لحظة من اللحظات تساعدنا في فهم طبيعة الأمراض
+
+11
+00:00:42,280 --> 00:00:47,700
+للـ Respiratory System والـ Respiratory System زي
+
+12
+00:00:47,700 --> 00:00:53,600
+ما احنا عارفين يعني واضح أنه أهم حاجة عنده العملية 
+
+13
+00:00:53,600 --> 00:01:01,100
+الرئيسية هي الهواء أو الهواء وطبعا معروف أن عملية
+
+14
+00:01:01,100 --> 00:01:06,680
+الهواء أو الهواء بتتم على أساس أنه تمنح أكسجين
+
+15
+00:01:06,680 --> 00:01:12,940
+للجسم وأنه يزيل كربون ديوكسيد CO2 من الجسم عن 
+
+16
+00:01:12,940 --> 00:01:18,800
+طريق طبعا اللغة External Respiration Exchange of
+
+17
+00:01:18,800 --> 00:01:22,240
+Oxygen and Carbon Dioxide هذا الـ External
+
+18
+00:01:22,240 --> 00:01:25,860
+Respiration إذا في External Respiration معناته في
+
+19
+00:01:25,860 --> 00:01:31,260
+Internal Respiration وهذه فرصة لوحدكوا لإلكوا 
+
+20
+00:01:31,260 --> 00:01:35,120
+تتطلعوا ما هو ال Internal Respiration بما أن ال
+
+21
+00:01:35,120 --> 00:01:38,740
+External Respiration هو عبارة عن Exchange of 
+
+22
+00:01:38,740 --> 00:01:41,680
+Oxygen and Carbon Dioxide ما هو ال Internal
+
+23
+00:01:41,680 --> 00:01:47,640
+Respiration أقضاء اللي طبعا اللي حكينا بالنسبة
+
+24
+00:01:47,640 --> 00:01:51,860
+للـinternal respiration مش assignment لكل واحد 
+
+25
+00:01:51,860 --> 00:01:57,460
+الحرية يكشف كما يريد الـ organs of the respiratory
+
+26
+00:01:57,460 --> 00:02:01,240
+system زي ما احنا عارفين بتبدأ بالـ nose، بالـ
+
+27
+00:02:01,240 --> 00:02:03,240
+pharynx، الـ pharynx اللي هو البلعوم، الـ larynx 
+
+28
+00:02:03,240 --> 00:02:06,520
+الحنجرة، تراكية القصبة الهوائية، bronchial tree
+
+29
+00:02:06,520 --> 00:02:13,140
+شجرة القصبة الهوائية، و الرئتين ال lungs ال organs
+
+30
+00:02:13,140 --> 00:02:17,580
+هي بس باختصار جدا إيه وظيفة كل عضو 
+
+31
+00:02:20,360 --> 00:02:26,940
+النازل كافيتى في الأول نبدأ من الناس من الناس نازل
+
+32
+00:02:26,940 --> 00:02:31,560
+سبتم دفع النازل كافيتى إلى الجزء اليسار والجزء
+
+33
+00:02:31,560 --> 00:02:39,620
+اليسار نازل كونشي يستمع النازل نازل كافيتى العملية
+
+34
+00:02:39,620 --> 00:02:43,920
+الـ moistening والـ warmness of the air بصورة أحسن
+
+35
+00:02:43,920 --> 00:02:49,100
+ميوكاس منبرين warms and moistens the air and سيليا
+
+36
+00:02:49,100 --> 00:02:51,740
+helps eliminate particles في أن الـ Paranasal
+
+37
+00:02:51,740 --> 00:02:56,340
+sinus واللي احنا بنسمع دايما عنها افلان في عنده 
+
+38
+00:02:56,340 --> 00:03:01,140
+جيوب هي ال Paranasal sinuses هي الجيوب اللي احنا
+
+39
+00:03:01,140 --> 00:03:08,600
+بنقصدها دايما وهذه عبارة عن أماكن أو spaces within
+
+40
+00:03:08,600 --> 00:03:14,620
+the skull bone في جلب الـ bone «أيرفيلد» فيها هوا
+
+41
+00:03:14,620 --> 00:03:22,300
+وهي طبعاً الـ «أسكال» لو نتصورها عضم صبة جامد كان 
+
+42
+00:03:22,300 --> 00:03:25,600
+على جهها أدقل من هي كتير وهذا تقل على أيش؟ على
+
+43
+00:03:25,600 --> 00:03:31,920
+الجسم وحتى لما ينخبط الواحد في رأسه أو يجعب لو 
+
+44
+00:03:31,920 --> 00:03:37,000
+كانت عضم بحت ممكن تأثر تأثيرات كبيرة لكن لما تكون 
+
+45
+00:03:37,000 --> 00:03:38,180
+«أيرفيلد»
+
+46
+00:03:40,370 --> 00:03:47,510
+بتخلّي حجم أو وزن الـ skull لجل وبتدّي كمان مش بس 
+
+47
+00:03:47,510 --> 00:03:52,010
+بما أن في عندنا غرف هوائية بتخلّي الـ voice له حدة
+
+48
+00:03:52,010 --> 00:03:59,270
+معينة أيضًا طول معين الـ skull bones with الصينيات
+
+49
+00:03:59,270 --> 00:04:01,570
+تحتوي على الصينيات الصحيحة الصحيحة الصحيحة الصحيحة
+
+50
+00:04:01,570 --> 00:04:02,070
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+51
+00:04:02,070 --> 00:04:04,910
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+52
+00:04:04,910 --> 00:04:07,910
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+53
+00:04:07,910 --> 00:04:09,030
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+54
+00:04:09,030 --> 00:04:13,750
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+55
+00:04:13,750 --> 00:04:18,610
+الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة الصحيحة
+
+56
+00:04:18,610 --> 00:04:24,510
+الصحيحة الصحيحة
+
+57
+00:04:24,510 --> 00:04:31,970
+الصعنا طبعا مدخل الأنف بالـInferior Turbinate
+
+58
+00:04:31,970 --> 00:04:38,150
+والـMiddle وSuperior Turbinate والأن بنشوفه في
+
+59
+00:04:38,150 --> 00:04:41,330
+صورة تانية الـSinus Cavities أحنا قولنا كام كام
+
+60
+00:04:41,330 --> 00:04:47,330
+Sinus فيه عندنا Frontal Sinus أثمويدل Sinus
+
+61
+00:04:47,330 --> 00:04:51,510
+frontal فوق العين على طول فوق الحاجب أثمويدل بين
+
+62
+00:04:51,510 --> 00:04:56,890
+الأنفين منطقة بين الأنفين في عندنا الـ maxillary
+
+63
+00:04:56,890 --> 00:05:01,590
+sinus وفي الـ maxillary sinus طبعا جنب الأنف وفي 
+
+64
+00:05:01,590 --> 00:05:05,110
+الـ sphenoidal اللي هو من الصورة من الأمام بنشوفوش 
+
+65
+00:05:05,110 --> 00:05:09,010
+لكن ممكن من ال to the sides sphenoidal sinus نشوف
+
+66
+00:05:09,010 --> 00:05:16,950
+هذه صورة X-ray للـ sinuses دي اللي ماببعت انا اي حد 
+
+67
+00:05:16,950 --> 00:05:20,530
+يعمل صورة sinus بيعمله الصورة هاي زي ما احنا
+
+68
+00:05:20,530 --> 00:05:24,210
+شايفين رقم واحد ال nasal septum رقم اتنين frontal
+
+69
+00:05:24,210 --> 00:05:29,830
+sinus فوق رقم تلاتة ال maxillary sinus ethmoidal
+
+70
+00:05:29,830 --> 00:05:35,170
+sinus رقم اربعة اللي هو بين ال ال ال two eyes
+
+71
+00:05:36,590 --> 00:05:40,970
+الـ Nose وفي عندنا خمسة اللي هو الـ Inferior
+
+72
+00:05:40,970 --> 00:05:45,750
+Turbinate اللي بيبين أنها لفوق منه في اللي اللي هو
+
+73
+00:05:45,750 --> 00:05:51,790
+ال middle وستة في عندنا ال Odontoid Process اللي
+
+74
+00:05:51,790 --> 00:05:57,110
+هو منطقة الأسنان هنا صورة جديدة الصورة هذه بتقولي
+
+75
+00:05:57,110 --> 00:06:01,110
+على الجهة الخضراء على الجهة اليمين Healthy Sinuses
+
+76
+00:06:01,110 --> 00:06:05,510
+شايفين أن الـ Sinuses Free عاملياً برضه كمان مرة
+
+77
+00:06:05,510 --> 00:06:11,270
+frontal Sphenoidal, ethmoidal and maxillary sinus
+
+78
+00:06:11,270 --> 00:06:16,450
+لكن على الجهة التانية Inflamed sinus lining وسبب
+
+79
+00:06:16,450 --> 00:06:19,070
+ال inflammation في الغالب في الغالب بيبقى
+
+80
+00:06:19,070 --> 00:06:22,350
+infection لكن برضه بعض الأحيان ممكن يكون allergy
+
+81
+00:06:22,350 --> 00:06:29,990
+أو fluid filled أو ميوكس يبقى موجود وهذه بتعملنا 
+
+82
+00:06:29,990 --> 00:06:34,110
+التجول والتهابات في الجيوب الأنفية خاصة بعد
+
+83
+00:06:34,110 --> 00:06:38,430
+الإصابة بال influenza من الـ organs of the
+
+84
+00:06:38,430 --> 00:06:41,390
+respiratory system اللي هو الـ pharynx البلعوم 
+
+85
+00:06:41,390 --> 00:06:47,290
+وطبعا البلعوم هو منطقة مشتركة بين ال digestive
+
+86
+00:06:47,290 --> 00:06:54,480
+system and respiratory system Larynx Voice Box هو
+
+87
+00:06:54,480 --> 00:06:59,240
+صندوق الصوت زي ما بيقولوها حبة الصوت زي ما بيقول
+
+88
+00:06:59,240 --> 00:07:04,520
+في الحاجات التانية Larynx Voice Box moves air in
+
+89
+00:07:04,520 --> 00:07:11,160
+and out of the trachea هو المدخل و المخرج نتيجة
+
+90
+00:07:11,160 --> 00:07:16,500
+دخول و خروج الهواء بيصير عينها voice وبتكون ال
+
+91
+00:07:16,500 --> 00:07:21,760
+larynx من تلت أمور من تلت cartilage اللي هي ال
+
+92
+00:07:21,760 --> 00:07:26,660
+cartilage الغضروف من تلت غضاريف thyroid cartilage
+
+93
+00:07:26,660 --> 00:07:33,120
+ال epiglottic cartilage وال cricoid cartilage زي
+
+94
+00:07:33,120 --> 00:07:35,820
+ما احنا شايفين في الصورة
+
+95
+00:07:38,020 --> 00:07:43,180
+من مساوية هذا التعليم إن الواحد ما بيقدرش يأشر على
+
+96
+00:07:43,180 --> 00:07:48,280
+الحاجات لكن أجروا و أتبعوا بالظبط ال vocal cord
+
+97
+00:07:48,280 --> 00:07:52,160
+ننزل على الأحبال الصوتية هي عبارة عن cords من
+
+98
+00:07:52,160 --> 00:07:57,380
+اسمها أحبال stretched between ممدودة بين thyroid
+
+99
+00:07:57,380 --> 00:08:01,960
+cartilage and the cracoid cartilage بين الثيرويد
+
+100
+00:08:01,960 --> 00:08:06,940
+والكريكويد الـ Upper vocal cords are false cords 
+
+101
+00:08:06,940 --> 00:08:10,520
+and lower are true vocal cords اللي هي الأصلية
+
+102
+00:08:10,520 --> 00:08:11,880
+اللي احنا شايفينها في الصورة
+
+103
+00:08:15,200 --> 00:08:18,820
+الـ Glottis is the opening between the vocal cords 
+
+104
+00:08:18,820 --> 00:08:22,140
+لما يفتح ال vocal cords عن بعض، بيبين قدامنا أش
+
+105
+00:08:22,140 --> 00:08:26,160
+للـ Glottis The major vocal cords are stretched
+
+106
+00:08:26,160 --> 00:08:32,920
+the more عفواً كل ما شدت ال cords كل ما كان الصوت
+
+107
+00:08:32,920 --> 00:08:40,990
+high pitched أو higher the voice pitch بيصير حاد
+
+108
+00:08:40,990 --> 00:08:47,390
+بالصوت هذا بيصير بعدين 
+
+109
+00:08:47,390 --> 00:08:50,690
+بيجينا لتركيا و لبرونكاي و لبرونكيولز زي ما احنا
+
+110
+00:08:50,690 --> 00:08:53,470
+شايفين الترتيب تركيا هو القصبة الهوائية
+
+111
+00:08:53,470 --> 00:08:57,670
+البرونكيولز هي عبارة عن القصايبات والبرونكيولز 
+
+112
+00:08:57,670 --> 00:09:01,350
+البرونكاي هي عبارة عن القصايب والبرونكيولز
+
+113
+00:09:01,350 --> 00:09:06,100
+عبارة عن الشعيبات الهوائية والتركية زي ما احنا
+
+114
+00:09:06,100 --> 00:09:13,920
+بنعرفه إله اسم باللغة الإنجليزية اسمه windpipe وهو
+
+115
+00:09:13,920 --> 00:09:18,320
+عبارة عن tubular organ made of rings عبارة عن
+
+116
+00:09:18,320 --> 00:09:24,380
+حلقات من الـ cartilage و smooth muscles عبارة عن
+
+117
+00:09:24,380 --> 00:09:29,040
+عضلات و cartilage وجواته في حاجة جوة التركية
+
+118
+00:09:29,040 --> 00:09:38,960
+السيلية اللي هي الهديبات التنفسية و التركية
+
+119
+00:09:38,960 --> 00:09:43,700
+بيمتد من الـ larynx حتى الـ bronchi السيلية أو
+
+120
+00:09:43,700 --> 00:09:49,780
+الهديبات هاي بتحركنا البلغم تطلعوا من عن طريق
+
+121
+00:09:49,780 --> 00:09:55,360
+الحلق وطبعا هذا اللي بعد هيك احنا أما بيصير يعني
+
+122
+00:09:55,360 --> 00:10:00,680
+بيكحوا الواحد أو بتفو أو كذا ما هان أول مشاكل 
+
+123
+00:10:00,680 --> 00:10:06,650
+الأولى مشاكل الـ Smoking اللي هو Destroy السيليا
+
+124
+00:10:06,650 --> 00:10:11,730
+عشان هيك بنلاقي إن المدخنين الصبح دايما بيطلعوا
+
+125
+00:10:11,730 --> 00:10:15,870
+كميات مهولة من البلغم اللي اتجمعت نتيجة التدخين
+
+126
+00:10:15,870 --> 00:10:19,830
+ونتيجة ال environment ونتيجة ولم تخرج في ساعتها
+
+127
+00:10:19,830 --> 00:10:23,610
+يعني ما قامتش السيلياس بإخراجها تتجمع في الصدر
+
+128
+00:10:23,610 --> 00:10:28,830
+وتاني يوم الصبح بيحاول يطلعها اللي هو المدخن
+
+129
+00:10:30,550 --> 00:10:33,090
+الـ lungs طبعا زي ما احنا كلنا عارفين هي عبارة عن 
+
+130
+00:10:33,090 --> 00:10:36,670
+cone-shaped organs right lung has three lobes
+
+131
+00:10:36,670 --> 00:10:42,530
+loops and left lung has two loops ال left عنده 
+
+132
+00:10:42,530 --> 00:10:45,470
+فصين و ال right عنده تلاتة the membrane
+
+133
+00:10:45,470 --> 00:10:53,170
+surrounding the lungs is called pleura ال
+
+134
+00:10:53,170 --> 00:10:56,070
+lung contains connective tissue, bronchial tree,
+
+135
+00:10:56,250 --> 00:10:59,430
+nerves, lymphatic vessels and blood vessels
+
+136
+00:10:59,430 --> 00:11:03,680
+باختصار طيب هو إيش اللي بيصير بالظبط الـ mechanism
+
+137
+00:11:03,680 --> 00:11:07,080
+of breathing؟ بيصير عندنا inspiration and
+
+138
+00:11:07,080 --> 00:11:14,360
+expiration inspiration هو عبارة عن عملية الشهيق
+
+139
+00:11:14,360 --> 00:11:22,740
+and auto rich air هو محمل بالأكسجين يدخل الجسم من 
+
+140
+00:11:22,740 --> 00:11:26,700
+الجو الديافرام إيش بيصير في الديافرام اللي هو 
+
+141
+00:11:26,700 --> 00:11:36,350
+الحجاب الحاجز؟ contracts or flattens يعني هو يتسطح
+
+142
+00:11:36,350 --> 00:11:42,410
+هو contracts ويتسطح the intercostal muscles raise
+
+143
+00:11:42,410 --> 00:11:50,150
+the ribs اللي هو القفص الصدري بالعضلات يكبر ويرتفع
+
+144
+00:11:50,980 --> 00:11:54,060
+الـ Breathing أو الـ Pulmonary Ventilation
+
+145
+00:11:54,060 --> 00:11:57,220
+Consists of Inspiration, Inhalation and Expiration
+
+146
+00:11:57,220 --> 00:12:01,140
+اللي هو الـ Exhalation و اللي بتحكم فيه زي ما قلنا
+
+147
+00:12:01,140 --> 00:12:07,580
+طبعا الـ Expiration هو عبارة عن خروج CO2
+
+148
+00:12:07,580 --> 00:12:12,680
+Rich Air من الـ Lungs الديافرام بالعكس طبعا زي ال
+
+149
+00:12:12,680 --> 00:12:15,640
+Inspiration بيصيروا عملية Relaxation والـ
+
+150
+00:12:15,640 --> 00:12:20,030
+Intercostal طبعا Relaxation معناته هيرتفعوالـ
+
+151
+00:12:20,030 --> 00:12:27,890
+Intercostal muscles lower the ribs اللي بتحكم في
+
+152
+00:12:27,890 --> 00:12:31,690
+عملية الـ Ventilation الـ Breathing هو الميدولا
+
+153
+00:12:31,690 --> 00:12:35,290
+Oblongata هنحكي عنها بزيادة شوي بعد شوي Control
+
+154
+00:12:35,290 --> 00:12:39,730
+the rhythm and depth of the breathing الـ Pons
+
+155
+00:12:39,730 --> 00:12:46,500
+اللي هو تحته للميدولا Oblongata الجزء من الدماغ
+
+156
+00:12:46,500 --> 00:12:52,060
+يتحكم عفوا فوقه للميدولا أبلونجيتا يتحكم على رتب
+
+157
+00:12:52,060 --> 00:12:57,400
+الهواء يبقى الـ Depth وRhythm يتحكم عليها الميدولا
+
+158
+00:12:57,400 --> 00:13:01,380
+أبلونجيتا والـ Pons يتحكم عليها رتب الهواء، سنشوف 
+
+159
+00:13:01,380 --> 00:13:01,720
+كيف
+
+160
+00:13:10,630 --> 00:13:16,570
+واضح إنه لابد أن يرتبط الأكسجين بالدم ويدّينا
+
+161
+00:13:16,570 --> 00:13:22,510
+أكسو-هيموغلوبين في حين أن الـCarbon Dioxide بيدخل
+
+162
+00:13:22,510 --> 00:13:28,250
+Bloodstream كـBicarbonate وبعد
+
+163
+00:13:28,250 --> 00:13:29,570
+ما يدخل بالصورة هذه
+
+164
+00:13:32,380 --> 00:13:38,140
+بيتحلل مرة ثانية وجزء منه اللي هو ثاني أكسيد
+
+165
+00:13:38,140 --> 00:13:42,260
+الكربون بيرتبط على الـ hemoglobin وجزء منه بيتحلل
+
+166
+00:13:42,260 --> 00:13:45,380
+إلى carbon dioxide and water بيصير له عملية
+
+167
+00:13:45,380 --> 00:13:51,330
+expiration أو exhalation والwater كبخار ماء
+
+168
+00:13:51,330 --> 00:13:55,230
+حاجة اسمها كيف أنا أقيّم اللي هو الـ Pulmonary
+
+169
+00:13:55,230 --> 00:13:58,490
+Function Test يعني احنا فحوصات الـ Lungs مش كتيرة
+
+170
+00:13:58,490 --> 00:14:03,810
+حقيقة، اللي هي بعض الفحوصات، لكن أهمها ومشهور عنها
+
+171
+00:14:03,810 --> 00:14:10,790
+اللي هو Pulmonary Function Test، Lung Function
+
+172
+00:14:10,790 --> 00:14:15,990
+Test اللي هو بنقول عنه باسم آخر Spirometer، جهاز
+
+173
+00:14:15,990 --> 00:14:20,680
+Spirometer زي هيك هدف الجهاز هذا بيحاول أن الـ
+
+174
+00:14:20,680 --> 00:14:25,000
+Instrument consisting of a hollow inverted over
+
+175
+00:14:25,000 --> 00:14:29,860
+water used to evaluate respiratory function للـ
+
+176
+00:14:29,860 --> 00:14:34,120
+functions، Spirometer إيش بيعمل؟ بيفرّق بين، هل
+
+177
+00:14:34,120 --> 00:14:36,440
+اللي أنا بحكي عنه، المرض اللي بحكي عنه
+
+178
+00:14:36,440 --> 00:14:43,290
+obstructive، و سنعرف الفرق، pulmonary disease كلما
+
+179
+00:14:43,290 --> 00:14:46,030
+كان فيه عنوان Obstruction كلما كان الـ Resistance
+
+180
+00:14:46,030 --> 00:14:52,770
+أعلى تبع الـ Airway و لا Restrictive الـ
+
+181
+00:14:52,770 --> 00:14:56,830
+Restrictive بيعمل Restriction للـ Lung Volume الـ
+
+182
+00:14:56,830 --> 00:15:01,290
+Capacity of the lung بتقل نتيجة مشاكل في الـ
+
+183
+00:15:01,290 --> 00:15:06,040
+Structure أو الـ Functional Lung Changes هذا شغلت
+
+184
+00:15:06,040 --> 00:15:08,360
+الـ Spirometer اللي يبقى Spirometer أو الـ
+
+185
+00:15:08,360 --> 00:15:12,460
+Pulmonary lung function أو test function test lung
+
+186
+00:15:12,460 --> 00:15:18,900
+test بيفرّق لي بين الـ Obstructive Pulmonary Disease
+
+187
+00:15:18,900 --> 00:15:23,160
+والـ Restrictive Pulmonary Disease وقلنا الفرق بين
+
+188
+00:15:23,160 --> 00:15:25,620
+الأثنين الـ Obstructive Pulmonary Disease بيبقى
+
+189
+00:15:25,620 --> 00:15:28,580
+عندنا increased airway resistance يعني الهواء
+
+190
+00:15:28,580 --> 00:15:32,290
+نتيجة الـ Obstruction ما بتخلّش بالصورة اللي بدنا
+
+191
+00:15:32,290 --> 00:15:35,270
+إيها restrictive معناته فيها reduction في الـ
+
+192
+00:15:35,270 --> 00:15:40,710
+total lung capacity نتيجة مشكلة في الـ structure
+
+193
+00:15:40,710 --> 00:15:47,390
+أو الـ function of the lung ال
+
+194
+00:15:47,390 --> 00:15:51,810
+respiratory volumes اللي أنا بشوفها مسجلة عندي أو
+
+195
+00:15:51,810 --> 00:15:58,400
+عن طريق رسمة في الصورة هايبتديني بعض الـ hints
+
+196
+00:15:58,400 --> 00:16:03,500
+يمكن نتعرف عليها من باب اللي بيروح lung
+
+197
+00:16:03,500 --> 00:16:07,300
+rehabilitation على سبيل المثال أو حاجة أو
+
+198
+00:16:07,300 --> 00:16:10,300
+respiratory rehabilitation مستقبلاً لابد أن يكون
+
+199
+00:16:10,300 --> 00:16:11,400
+سامع بالموضوع
+
+200
+00:16:14,330 --> 00:16:17,610
+أن يكون الواحد عارف عن الموضوع Respiratory volumes
+
+201
+00:16:17,610 --> 00:16:23,810
+اللي بيقيّسها الجهاز حاجة اسمها tidal volume وإيش هذا
+
+202
+00:16:23,810 --> 00:16:28,390
+tidal volume؟ هذا عبارة عن amount of air كمية
+
+203
+00:16:28,390 --> 00:16:34,410
+الهواء that moves in or out the lungs during a
+
+204
+00:16:34,410 --> 00:16:38,870
+normal breath حوالي 500 ملي يعني أنا و أنا بتنفس
+
+205
+00:16:38,870 --> 00:16:42,310
+عادي، نفس عادي، بطلع و بنزل هذا بقول عنه tidal
+
+206
+00:16:42,310 --> 00:16:47,020
+volume حوالي 500 ملي reflects the amount of air
+
+207
+00:16:47,020 --> 00:16:51,300
+that moves in or out of the lungs during a normal
+
+208
+00:16:51,300 --> 00:16:56,200
+breath في عندنا بعد ذلك حاجة ثانية اللي هي الـ
+
+209
+00:16:56,200 --> 00:17:00,400
+inspiratory reserve volume والـ expiratory reserve
+
+210
+00:17:00,400 --> 00:17:04,760
+volume من اسمها reserve، reserve معناته احتياطي هو
+
+211
+00:17:04,760 --> 00:17:10,020
+عبارة عن كمية الهواء اللي can be forcefully
+
+212
+00:17:10,020 --> 00:17:13,500
+inhaled بعد normal inhalation يعني صار واحد عنده
+
+213
+00:17:13,500 --> 00:17:22,540
+normal inhalation عادي جداً جداً جداً لكن وأطلع
+
+214
+00:17:22,540 --> 00:17:27,540
+كمية الهواء جد ما يستطيع أكثر حاجة مقدر يطلعها هذه
+
+215
+00:17:27,540 --> 00:17:32,400
+بقول أنا inspiratory reserve volume هي حوالي 2 لتر
+
+216
+00:17:32,400 --> 00:17:38,360
+لـ 3 لتر، 2100 لـ 3200 ملي، كمية كبيرة طب الـ
+
+217
+00:17:38,360 --> 00:17:42,340
+expiratory reserve volume هي عبارة عن كمية الـ air
+
+218
+00:17:42,340 --> 00:17:46,180
+that can be forcefully exhaled following a normal
+
+219
+00:17:46,180 --> 00:17:51,340
+exhalation يعني أنا عملت normal exhalation، تنفس،
+
+220
+00:17:51,340 --> 00:17:59,110
+زفير طبيعي وروحت طلعت كم هوا كمان بالقوة فوق اللي
+
+221
+00:17:59,110 --> 00:18:05,470
+أخرجته طبيعي بأطلع حوالي ألف لألف ومئتين مليون دول
+
+222
+00:18:05,470 --> 00:18:08,170
+بتلاقيهم في ال curve اللي موجودة تحت بالمناسبة
+
+223
+00:18:08,170 --> 00:18:13,790
+بتقدر تطلع على lung function test على اليوتيوب في
+
+224
+00:18:13,790 --> 00:18:17,830
+ناس بتشرحها بالفصحى أو العامية بصورة رائعة وأنصح
+
+225
+00:18:17,830 --> 00:18:21,510
+بالموضوع الـ Reserve Volume هي عبارة عن كمية الـ
+
+226
+00:18:21,510 --> 00:18:24,690
+Volume of Air That Always Remains اللي بيضل دائماً
+
+227
+00:18:24,690 --> 00:18:30,050
+في الـ Lungs حتى بعد ما أطلق كمية الهواء الكاملة
+
+228
+00:18:30,050 --> 00:18:34,810
+بيضل كمية صغيرة 1200 يعني ما في Lung بيصير لها Zero
+
+229
+00:18:34,810 --> 00:18:38,870
+يعني ما في Lung بتطلع كل الهواء اللي فيها وخلاص
+
+230
+00:18:38,870 --> 00:18:41,870
+وتصير Zero فالكمية اللي بتضل في ال Lungs بعد
+
+231
+00:18:41,870 --> 00:18:48,980
+Forcefully Exhalation يعني إذا فير بآخر ما أستطيع
+
+232
+00:18:48,980 --> 00:18:53,060
+اللي بيضل في ال lungs بقول عنه residual volume فيه
+
+233
+00:18:53,060 --> 00:18:57,220
+أن ال vital capacity وهو عبارة عن حساب هي كمية
+
+234
+00:18:57,220 --> 00:19:01,720
+الهواء اللي can be forcefully exhaled after
+
+235
+00:19:01,720 --> 00:19:08,360
+the deepest inhalation يعني أنا بعد ما أخد نفس
+
+236
+00:19:08,360 --> 00:19:14,320
+Deep على الآخر كمية الهواء اللي بطلع بطلعها اللي
+
+237
+00:19:14,320 --> 00:19:19,960
+هي عبارة عن total volume عبارة عن Inspiratory
+
+238
+00:19:19,960 --> 00:19:23,320
+Reserve Volume وExpiratory Reserve Volume هي عبارة
+
+239
+00:19:23,320 --> 00:19:26,480
+عن الـ Vital Capacity وفيه عندنا الـ Total Lung
+
+240
+00:19:26,480 --> 00:19:33,100
+Capacity وهو عبارة عن حساب
+
+241
+00:19:33,100 --> 00:19:38,700
+الـ Total Amount Of Air Of The Lungs Can Be Hold هو
+
+242
+00:19:38,700 --> 00:19:42,740
+أكثر كمية من الهواء ممكن تدخل الـ Lungs بأي صورة
+
+243
+00:19:42,740 --> 00:19:46,740
+من الصور وهي عبارة عن 6 لتر الـ Pulmonary Function
+
+244
+00:19:46,740 --> 00:19:51,640
+Test في له حسابات ثانية حقيقية غير هدول اللي احنا
+
+245
+00:19:51,640 --> 00:19:56,060
+بنعتبرهم وفي بعض الأمراض بيعتبروهم تشخيصيين يعني هم
+
+246
+00:19:56,060 --> 00:20:00,680
+بيشخصهم عملياً زي الـ Total Ventilation وهي حساب
+
+247
+00:20:00,680 --> 00:20:04,940
+عبارة عن Total Amount of Gas Flow in to or out of
+
+248
+00:20:04,940 --> 00:20:08,260
+the respiratory tract in one minute يعني كمية
+
+249
+00:20:08,260 --> 00:20:14,200
+الهواء بتروح وبتيجي في ال respiratory tract في one
+
+250
+00:20:14,200 --> 00:20:19,670
+minute أو في أن الـ Forced Vital Capacity عبارة عن
+
+251
+00:20:19,670 --> 00:20:24,550
+جاز Forcibly expelled after taking a deep
+
+252
+00:20:24,550 --> 00:20:30,310
+breathing وهذا اللي قلنا عنه قبل شوية هو الـ Vital
+
+253
+00:20:30,310 --> 00:20:33,930
+Capacity أو في أن الـForced Expiratory Volume هو
+
+254
+00:20:33,930 --> 00:20:37,430
+عبارة عن كمية الجاز expelled during specific time
+
+255
+00:20:37,430 --> 00:20:45,270
+intervals of the Forced Vital Capacity خلال الرسم
+
+256
+00:20:45,270 --> 00:20:50,810
+عندنا موجودة؟ بنلاحظ أن الـ Tidal Volume، بعدين غير
+
+257
+00:20:50,810 --> 00:20:53,650
+الـTidal Volume، في عندنا الـInspiratory Reserve
+
+258
+00:20:53,650 --> 00:20:56,590
+Volume، عندنا الـExpiratory Reserve Volume، وفي عندنا
+
+259
+00:20:56,590 --> 00:20:58,690
+الـResidual، لأن لما نجمع الـInspiratory Reserve
+
+260
+00:20:58,690 --> 00:21:01,230
+Volume والـTidal Volume والـExpiratory Reserve
+
+261
+00:21:01,230 --> 00:21:04,730
+Volume والـResidual Volume، إيش بدنا؟ صحيح، بدنا
+
+262
+00:21:04,730 --> 00:21:09,800
+Total Lung Capacity الـ Vital Capacity بتجمع بين
+
+263
+00:21:09,800 --> 00:21:12,320
+الـ Inspiratory Reserve Volume مع الـ Tidal Volume
+
+264
+00:21:12,320 --> 00:21:16,200
+والـ Expiratory Reserve Volume والـ Total Lung
+
+265
+00:21:16,200 --> 00:21:21,260
+Capacity هي عبارة عن كل 6 لتر كل الهواء اللي
+
+266
+00:21:21,260 --> 00:21:25,860
+يستطيع أن تحتويه الـ Lungs كمان مرة بنصح بأن على
+
+267
+00:21:25,860 --> 00:21:30,490
+اليوتيوب وهي حاجة بيشرحها بالإيد، بالرسم، بيبقى
+
+268
+00:21:30,490 --> 00:21:36,130
+كثير رائع، وبيفهمها الواحد بصورة أكبر، وهي simple،
+
+269
+00:21:36,130 --> 00:21:40,090
+ما فيش فيها، بس يفهم إيش الواحد الـ background تبعه
+
+270
+00:21:43,270 --> 00:21:45,970
+respiratory air moves احنا كنا نحكي Inspiration و
+
+271
+00:21:45,970 --> 00:21:50,510
+Expiration لكن ال movements للهواء فيه حاجة non
+
+272
+00:21:50,510 --> 00:21:53,950
+-respiratory حاجات أنا بدخل هوا وبطلع هوا لكن مش
+
+273
+00:21:53,950 --> 00:21:58,870
+عشان التنفس هي عبارة عن reflex action زي على سبيل
+
+274
+00:21:58,870 --> 00:22:03,480
+المثال الكحة لما بكح بطلع هوا وبأخد هوا،
+
+275
+00:22:03,480 --> 00:22:07,340
+sneezing، العطس، crying، laughing، hiccuping، and
+
+276
+00:22:07,340 --> 00:22:14,360
+yawning هذه الحاجات كلها
+
+277
+00:22:14,360 --> 00:22:19,930
+non-respiratory air movement في أن حاجة برضه زي ما
+
+278
+00:22:19,930 --> 00:22:23,810
+قلنا كمان مرة احنا بنحاول قدر الإمكان نلقي نظرة
+
+279
+00:22:23,810 --> 00:22:28,150
+على كل حاجة ممكن تفيدنا في المحاضرات بعد هيك
+
+280
+00:22:28,150 --> 00:22:31,350
+نشرحها في الأول وممكن بعد هيك نسيب فيها في 
+
+281
+00:22:31,350 --> 00:22:35,210
+المحاضرات زي الـ Ventilation-Perfusion Coupling
+
+282
+00:22:35,210 --> 00:22:40,650
+الـ Ventilation is the amount of gas reaching the
+
+283
+00:22:40,650 --> 00:22:43,270
+alveoli والـ Perfusion is the blood flow reaching
+
+284
+00:22:43,270 --> 00:22:46,230
+the alveoli، بس للتعريف الـ Ventilation هو كمية
+
+285
+00:22:46,230 --> 00:22:50,790
+الهواء اللي بدخل على الـ Alveoli الـ Perfusion 
+
+286
+00:22:50,790 --> 00:22:55,610
+كمية الدم اللي بتروح على الـ Alveoli لازم يكون فيه
+
+287
+00:22:55,610 --> 00:23:01,390
+تناغم بين الـ Ventilation مع الـ Perfusion لأن لو
+
+288
+00:23:01,390 --> 00:23:05,210
+أنا عندي تسكير في الشرايين والـ Veins يعني الـ
+
+289
+00:23:05,210 --> 00:23:11,350
+Perfusion حيصير عندي مشكلة فيه، صح؟ طيب لما يكون
+
+290
+00:23:11,350 --> 00:23:14,430
+عنده الـ Perfusion فيه مشكلة لكن الهواء رايح جاي
+
+291
+00:23:14,430 --> 00:23:18,330
+بفيد؟ مفيدش كتير فهو لازم يكون فيه تناغم 
+
+292
+00:23:18,330 --> 00:23:21,730
+ventilation and perfusion must be tightly
+
+293
+00:23:21,730 --> 00:23:26,550
+regulated for efficient gas exchange مش عشان
+
+294
+00:23:26,550 --> 00:23:32,030
+براعوا خواطر بعض لأ لأنه واحد بدون التاني ال
+
+295
+00:23:32,030 --> 00:23:33,930
+ventilation بدون ال perfusion بقدرش يشتغل ال
+
+296
+00:23:33,930 --> 00:23:36,130
+perfusion بدون ال ventilation بقدرش يشتغل حتى لو
+
+297
+00:23:36,130 --> 00:23:38,770
+كان في عندي perfusion كويس لكن مافيش ventilation
+
+298
+00:23:38,770 --> 00:23:43,540
+واتجبتفهم يكونوا التانيين ventilation and
+
+299
+00:23:43,540 --> 00:23:50,280
+perfusion coupled أو متزامنين مين بتحكم أكتر واحد
+
+300
+00:23:50,280 --> 00:23:55,500
+في الموضوع هذا؟ الـCO2، changes in PCO2 اللي هو
+
+301
+00:23:55,500 --> 00:23:58,500
+الـpartial pressure P، هذه الـpartial pressure 
+
+302
+00:23:58,500 --> 00:24:03,100
+عبارة عن الضغط، ضغط الـCO2 in the alveolicus،
+
+303
+00:24:03,100 --> 00:24:08,890
+changes in the diameter of bronchioles وبنلاقي الـ
+
+304
+00:24:08,890 --> 00:24:13,970
+Passageways Serving Areas Where Alveolar Carbon
+
+305
+00:24:13,970 --> 00:24:18,330
+Dioxide Is High Dilate يعني كل ما زاد كمية ثاني
+
+306
+00:24:18,330 --> 00:24:21,490
+أكسيد الكربون في مكان بيصير عندى dilatation في وين
+
+307
+00:24:21,490 --> 00:24:26,590
+في الـ alveolar في ال .. في ال .. كل ما زاد ثاني
+
+308
+00:24:26,590 --> 00:24:29,930
+أكسيد الكربون كل ما زاد اللي هو في الارتريويل ال
+
+309
+00:24:29,930 --> 00:24:35,010
+dilatation وكل ما جال ال carbon dioxide في ال
+
+310
+00:24:35,010 --> 00:24:43,280
+alveols كلما جال، بيصير عندي تضيق في الـ… في الـ…
+
+311
+00:24:43,280 --> 00:24:45,560
+في الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+312
+00:24:45,560 --> 00:24:47,420
+الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+313
+00:24:47,420 --> 00:24:47,560
+الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+314
+00:24:47,560 --> 00:24:52,200
+الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+315
+00:24:52,200 --> 00:24:52,860
+الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+316
+00:24:52,860 --> 00:24:55,560
+الـ… في الـ… في الـ… في الـ… في الـ… في الـ… في
+
+317
+00:24:55,560 --> 00:25:02,580
+الـ… في الـ… في
+
+318
+00:25:04,730 --> 00:25:09,490
+لما كان عندى reduce alveolar ventilation فاش هوا
+
+319
+00:25:09,490 --> 00:25:14,210
+كتير شايفين انتوا الفقاعة اللى هى الصفرة الفقاعة
+
+320
+00:25:14,210 --> 00:25:18,770
+جال ال alveolar ventilation طبعا لما يجي ال
+
+321
+00:25:18,770 --> 00:25:21,710
+alveolar ventilation ايش بيصير؟ بيزيد ال CO2 طبعا
+
+322
+00:25:21,710 --> 00:25:24,530
+لأنه مافيش عملية تبادل oxygen و ثانو oxygen
+
+323
+00:25:24,530 --> 00:25:27,130
+الكربون فبيزيد ثانو oxygen الكربون و بيبقى فيه
+
+324
+00:25:27,130 --> 00:25:30,190
+عندنا excessive perfusion ايش بروح بيصير؟ لما يزيد
+
+325
+00:25:30,190 --> 00:25:33,290
+ثانو oxygen الكربون على طول بتضيق البولبنري
+
+326
+00:25:33,290 --> 00:25:40,190
+artules أرتيويل بيصيروا تضيق والأرتيويل اللي بروح
+
+327
+00:25:40,190 --> 00:25:43,010
+على الالفيول هاي بيصيروا تضيق ولمّا يصيروا تضيق
+
+328
+00:25:43,010 --> 00:25:48,730
+على طول بيصير عندنا reduced perfusion بمعنى أنا
+
+329
+00:25:48,730 --> 00:25:52,230
+لما جيت لما يزيد سانو اكسيد الكربون في الالفيول
+
+330
+00:25:52,230 --> 00:25:59,080
+والبرفيوجين لسه شغال زي الناس بيأخد Action الجسم
+
+331
+00:25:59,080 --> 00:26:05,120
+وبيخلّي الـ «أرتيويل» يـ Constrict نتيجة ارتفاع
+
+332
+00:26:05,120 --> 00:26:08,820
+ثاني أكسيد الكربون فبيجيل كمية الدم اللي بتروح
+
+333
+00:26:08,820 --> 00:26:14,240
+هناك بالصورة هاي يعني مش عملية عكسية عملية بيرتبوا
+
+334
+00:26:14,240 --> 00:26:19,000
+وشغلوا مع بعض والله جال الهواء اللي بيروح وبيجي
+
+335
+00:26:19,000 --> 00:26:22,700
+فبيزيد ثاني أكسيد الكربون وبيضيق الـ «أرتيويل»
+
+336
+00:26:22,700 --> 00:26:29,740
+الآن بالعكس زاد الـ Alveolar Ventilation فجال الـ
+
+337
+00:26:29,740 --> 00:26:32,180
+Alveolar Ventilation زاد معناته سينيوكسيد الكربون
+
+338
+00:26:32,180 --> 00:26:35,180
+بيصير ينطرد كتير لما ينطرد كتير معناته بيجيل في
+
+339
+00:26:35,180 --> 00:26:41,820
+الـ Alveolar Ventilation فأنا إيش بعمل؟ لما يجيل
+
+340
+00:26:41,820 --> 00:26:45,260
+سينيوكسيد الكربون بيتوسع الارتريول لما يتوسع
+
+341
+00:26:45,260 --> 00:26:52,230
+الارتريول بيزيد اللي هو الـ Perfusion بشتغل مع
+
+342
+00:26:52,230 --> 00:26:55,990
+التاني هذه اسمها ventilation-perfusion coupling
+
+343
+00:26:55,990 --> 00:27:01,090
+ممكن نسمعها في المحاضرات بعدها ال service area and
+
+344
+00:27:01,090 --> 00:27:04,410
+thickness برضه وردة جديدة يعني زي ما قلنا مواضيع
+
+345
+00:27:04,410 --> 00:27:08,310
+مختلفة بندخل من حاجة بندخل في حاجة لكن أنا للتوضيح
+
+346
+00:27:08,310 --> 00:27:15,480
+يعني وهذه آخر slide للمحاضرة اليوم اللي هو سبحانك
+
+347
+00:27:15,480 --> 00:27:19,900
+ربي يعني عملية الـ Gas Exchange اللي بتسير في الـ
+
+348
+00:27:19,900 --> 00:27:29,120
+Lungs بتسير فيه جدر جدر كتير fine فبنلاقي إنه الـ
+
+349
+00:27:29,120 --> 00:27:33,780
+Respiratory Membranes حوالي نص لواحد Micro-Thick
+
+350
+00:27:33,780 --> 00:27:37,160
+Allowing for Efficient Gas Exchange عشان يصير
+
+351
+00:27:37,160 --> 00:27:42,140
+عملية يعني إيش أكتر حاجة بتتصوروا إنها أرجيجة
+
+352
+00:27:42,140 --> 00:27:46,780
+ونعمة هادي أجل منها يدوب مبينة عمليًا يدوب مبينة
+
+353
+00:27:46,780 --> 00:27:52,280
+عمليًا من 0.5 نص لواحد Micro-Meter Thick Allowing
+
+354
+00:27:52,280 --> 00:27:55,720
+Efficient Gas Exchange لو تيجي تجمع في الـLungs
+
+355
+00:27:55,720 --> 00:27:58,620
+عند الرجال ع سبيل المثال بتلاقي إنه حوالي 60 متر
+
+356
+00:27:58,620 --> 00:28:05,640
+مربع هذه جد أربعين مرة That one's skin جد الجلد لما
+
+357
+00:28:05,640 --> 00:28:09,360
+تجمع Total Surface Area في الـMills ويقال إنها
+
+358
+00:28:09,360 --> 00:28:19,340
+تساوي مساحة ملعب كرة التنس لأن لو صار في عندي
+
+359
+00:28:19,340 --> 00:28:25,170
+أديمة بالموناري إديمة إيش بيصير في الـ .. في الـ
+
+360
+00:28:25,170 --> 00:28:30,370
+membranes هاي بيصير thick أكتر وأكتر طبعاً لما كل
+
+361
+00:28:30,370 --> 00:28:34,270
+ما زاد ال thickness تبعها بيصير ال gas exchange
+
+362
+00:28:34,270 --> 00:28:38,230
+inadequate و بيصير عندنا نقص أكسجين بيصير عندنا
+
+363
+00:28:38,230 --> 00:28:42,470
+gas deprivation ليش؟ لأن ال lung هذه اللي فيها
+
+364
+00:28:42,470 --> 00:28:47,200
+edematous walls جواتها مش قادرة تعمل gas exchange
+
+365
+00:28:47,200 --> 00:28:51,400
+زي الناس فبصير عندى hypo ventilation أو بيصير عندى
+
+366
+00:28:51,400 --> 00:28:56,080
+oxygen أو asphyxia معنى آخر لأن كل ما جل ال
+
+367
+00:28:56,080 --> 00:29:02,890
+surface زي في الـ Enphysema ‏when walls of alveoli
+
+368
+00:29:02,890 --> 00:29:07,350
+break through يعني بتقل الـ service وبرضه بتقل
+
+369
+00:29:07,350 --> 00:29:13,450
+عملية الـ oxygen exchange نتيجة وجود Enphysema،
+
+370
+00:29:13,450 --> 00:29:18,390
+ليش؟ لأن الـ service أصلا اتدهور فبالصورة هذه بيصير
+
+371
+00:29:18,390 --> 00:29:23,910
+عندنا نفس الـ Effect إنه بدخل عند العيّان في
+
+372
+00:29:23,910 --> 00:29:28,990
+أسفكسيا بطريقة أو بأخرى وهاكذا معظم الـ Mechanisms
+
+373
+00:29:28,990 --> 00:29:35,890
+يعني أنا عارف إنه الممكن فيه شويه ناشفة المعلومات
+
+374
+00:29:35,890 --> 00:29:40,550
+لأنه مش practical كتير لكن هي زي ما قلنا عبارة عن
+
+375
+00:29:40,550 --> 00:29:43,410
+بعض الإضاءات
+
+376
+00:29:44,020 --> 00:29:47,120
+في الـ Anatomy and Physiology of Respiratory
+
+377
+00:29:47,120 --> 00:29:52,780
+System وبنحاول في المحاضرات الأمراض أنه نرجع لل
+
+378
+00:29:52,780 --> 00:29:56,720
+basics هاي هي مهمة كتير حقيقة وحتى يعني احنا
+
+379
+00:29:56,720 --> 00:29:59,840
+بنستهدفها في الامتحانات كتير على أساس أنه ال
+
+380
+00:29:59,840 --> 00:30:03,320
+basics لازم الواحد يكون فاهمه قدر الممكن أنا
+
+381
+00:30:03,320 --> 00:30:09,920
+بشكرلكم حسن الاستماع ويعطيكم الف عافية السلام
+
+382
+00:30:09,920 --> 00:30:10,300
+عليكم
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bWJL4CfrdXk_postprocess.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bWJL4CfrdXk_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..a6141d317e14234881223696f0dd324f1b7a9c26
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/bWJL4CfrdXk_postprocess.srt
@@ -0,0 +1,1488 @@
+1
+00:00:01,670 --> 00:00:04,930
+بسم الله الرحمن الرحيم الحمد لله رب العالمين بدنا
+
+2
+00:00:04,930 --> 00:00:09,450
+يا جماعة نقترب من النهاية اليوم هنتحدث .. ممكن
+
+3
+00:00:09,450 --> 00:00:13,550
+ماحدش حتى الآن خلال دراستكوا تحدث عن ال cancer
+
+4
+00:00:13,550 --> 00:00:18,150
+طبعا احنا مش هروح بتوسع لكن بدنا نكون عارفين بعض
+
+5
+00:00:18,150 --> 00:00:22,810
+ال terminology بعض المبادئ الأساسية في ال cancer
+
+6
+00:00:22,810 --> 00:00:26,710
+هو ان انتوا في يوم من الأيام في لحظة من اللحظات
+
+7
+00:00:26,710 --> 00:00:34,740
+هتكون عندكواشغل مع مرضى الـ Cancer من خلال فرق الـ
+
+8
+00:00:34,740 --> 00:00:36,940
+Palliative أو من خلال الناس اللي بتحتاج إيداش
+
+9
+00:00:36,940 --> 00:00:39,820
+طبيعي أو الناس اللي عندها breast cancer و اللي
+
+10
+00:00:39,820 --> 00:00:48,020
+بنعملها طبعاً lymph drainage فـ what is cancer؟
+
+11
+00:00:48,020 --> 00:00:52,280
+cancer begins when cells in a part of the body
+
+12
+00:00:52,280 --> 00:00:57,140
+become abnormal لما تتحول خلايا لخلايا غير طبيعية
+
+13
+00:00:59,430 --> 00:01:02,710
+مش اللي بيصير more abnormal cells forming a mass
+
+14
+00:01:02,710 --> 00:01:11,090
+of tissue called growth or cancerous tumor يعني ال
+
+15
+00:01:11,090 --> 00:01:15,390
+tumor هو عبارة عن ورم، مش شرط يكون ورم، ورم خبير،
+
+16
+00:01:15,390 --> 00:01:19,150
+ورم ممكن يكون الدم اللي بعمل ورم، فهذا ما نقول عنه
+
+17
+00:01:19,150 --> 00:01:22,150
+space-occupying lesion
+
+18
+00:01:29,250 --> 00:01:34,210
+ليجن مش شرط يكون ماليجنان ممكن يكون tumor أبسس
+
+19
+00:01:34,210 --> 00:01:40,550
+نسيج نسيج lipoma ممكن يكون أكتر من حاجة لكن هو
+
+20
+00:01:40,550 --> 00:01:46,350
+بيظل ورم فالورم مش اللي احنا هنقص ضهان مش اللي
+
+21
+00:01:46,350 --> 00:01:50,230
+دارج على الإسان العام الناس اللي بتحكي ان ورم
+
+22
+00:01:50,230 --> 00:01:57,560
+معناته خلاص cancer و هيموت وكذا لأ ورمهو عبارة عن
+
+23
+00:01:57,560 --> 00:02:03,360
+mass of tissue بنقول عنها growth أو tumor وهذا
+
+24
+00:02:03,360 --> 00:02:07,860
+ممكن يكون cancerous يعني حاجة سرطانية malignant
+
+25
+00:02:07,860 --> 00:02:15,060
+cancer cells can break away and spread وهذه
+
+26
+00:02:15,060 --> 00:02:21,010
+خطورتها أن بعض ال cancersبتعمل «Mets» أو
+
+27
+00:02:21,010 --> 00:02:24,810
+«Metastases» «Mets» المختصر تبعها «Metastatic
+
+28
+00:02:24,810 --> 00:02:30,410
+Cancer» بتنتجل من مكان إلى مكان في الجسم مش كل
+
+29
+00:02:30,410 --> 00:02:34,730
+خدوا بالكم الجملة هاي «Tumors are cancerous» مش كل
+
+30
+00:02:34,730 --> 00:02:42,070
+ورم معناته cancer «Benign tumors don't spread to
+
+31
+00:02:42,070 --> 00:02:44,990
+other parts of the body» وهذه القاعدة وهذه من
+
+32
+00:02:44,990 --> 00:02:49,500
+الحاجات اللي بتفرج بين الـ «Benign»وبين الـ
+
+33
+00:02:49,500 --> 00:02:57,100
+Malignant عكس Benign حميد Malignant خبيث Cancer
+
+34
+00:02:57,100 --> 00:03:01,080
+usually start in one part of the bodyولكن إذا أصبح
+
+35
+00:03:01,080 --> 00:03:04,740
+عضو الحرارة أكبر، فهو يمكن أن يؤذي، وليس فقط
+
+36
+00:03:04,740 --> 00:03:07,800
+بندقل، لكن هو ممكن يضغط على حاجات حواليه زي
+
+37
+00:03:07,800 --> 00:03:11,140
+الـcancer of brain عسم المثال، ممكن يسكرلي أي
+
+38
+00:03:11,140 --> 00:03:15,560
+فرامن ويعمللي hydrocephalus مثلا أو يخرّبني
+
+39
+00:03:15,560 --> 00:03:18,960
+النسيجي لجنبه، وإذا وجدت عضو الحرارة قريبًا،
+
+40
+00:03:18,960 --> 00:03:23,650
+فالتعامل هو أكثر ممكن أن يعملاللي هو بيعتمد عليه
+
+41
+00:03:23,650 --> 00:03:28,750
+الموضوع الـ Screening إنه كل ما اكتشفت الـ Cancer
+
+42
+00:03:28,750 --> 00:03:36,330
+بدري كل ما كانت إمكانية أنه أعالجه كل ما كانت أفضل
+
+43
+00:03:36,330 --> 00:03:39,690
+وهذا طبعاً بتمش إلا بالـ Screening اللي هي عملية
+
+44
+00:03:39,690 --> 00:03:42,970
+الافتشاف
+
+45
+00:03:42,970 --> 00:03:48,870
+مبكر Early Treatmentوكل ما علجناه بدري، هذا can
+
+46
+00:03:48,870 --> 00:03:52,510
+shrink or destroy the cancer tumor and stop it
+
+47
+00:03:52,510 --> 00:03:56,310
+from growing and spreading كل ما علجناه بدري، كل
+
+48
+00:03:56,310 --> 00:03:59,770
+ما سيطرنا عليه بدري، كل ما جدرش الـ cancer هذا إيش
+
+49
+00:03:59,770 --> 00:04:01,670
+ينجل إلى أماكن أخرى
+
+50
+00:04:04,090 --> 00:04:11,590
+عندما تحصل على شكب عادى وكيفية معرفة شكب عادى وشكب
+
+51
+00:04:11,590 --> 00:04:14,630
+عادى
+
+52
+00:04:14,630 --> 00:04:16,390
+وشكب عادى وشكب عادى وشكب عادى وشكب عادى وشكب عادى
+
+53
+00:04:16,390 --> 00:04:17,750
+وشكب عادى وشكب عادى وشكب عادى وشكب عادى وشكب عادى
+
+54
+00:04:17,750 --> 00:04:19,310
+وشكب عادى وشكب عادى وشكب عادى وشكب عادى وشكب عادى
+
+55
+00:04:19,310 --> 00:04:19,350
+وشكب عادى وشكب عادى وشكب عادى وشكب عادى وشكب عادى
+
+56
+00:04:19,350 --> 00:04:23,050
+وشكب عادى وشكب عادى وشكب عادى وشكب عادى وشكب عادى
+
+57
+00:04:23,050 --> 00:04:32,960
+وشكب عادى وشكب عادى وشاللي فوق الخمسين سنة على
+
+58
+00:04:32,960 --> 00:04:36,980
+سبيل المثال اللي هي في موضوع الـ Prostate هذه أمور
+
+59
+00:04:36,980 --> 00:04:41,640
+يعني بيقدر الواحد من بدري يكتشفها لو دار باله
+
+60
+00:04:41,640 --> 00:04:46,660
+أحاله مجموعة من مئات مخلوقات مختلفة موجودة يعني
+
+61
+00:04:46,660 --> 00:04:53,220
+حواليها Cancer are a large family of diseases that
+
+62
+00:04:53,220 --> 00:04:56,960
+involve abnormal cell growth with the potential to
+
+63
+00:04:56,960 --> 00:05:02,410
+invade or spread to other parts of the bodyوهي
+
+64
+00:05:02,410 --> 00:05:06,230
+بتمثل نوع من أنواع الـ Neoplasm نفس القضية هي
+
+65
+00:05:06,230 --> 00:05:10,050
+نفسها نيوبلازم ممكن تكون cancer a neoplasm or
+
+66
+00:05:10,050 --> 00:05:13,230
+tumor is a group of cells that have undergone
+
+67
+00:05:13,230 --> 00:05:19,610
+unregulated growth and will often form a mass or
+
+68
+00:05:19,610 --> 00:05:23,710
+lump بيعمل زي كتلة أو lump برضه كتلة but maybe
+
+69
+00:05:23,710 --> 00:05:28,530
+distributed diffusely وهذه مشكلة الـ Neoplasm
+
+70
+00:05:28,530 --> 00:05:33,030
+بصورة عامةالـ Classification وهذا يمكن المهم اللي
+
+71
+00:05:33,030 --> 00:05:38,410
+بدنا يهيأه الآن أنه Classified by the type of
+
+72
+00:05:38,410 --> 00:05:43,150
+cells that the tumor cells resemble and is
+
+73
+00:05:43,150 --> 00:05:47,910
+therefore presumed to be the origin of the tumor
+
+74
+00:05:47,910 --> 00:05:53,950
+الـ Type هاي Carcinoma رقم واحد، ما بنقول هوكتشف
+
+75
+00:05:53,950 --> 00:05:55,850
+وما بنقول Carcinoma
+
+76
+00:05:58,040 --> 00:06:01,960
+طبعاً لما أقول Carcinoma معناته أنا بحكي عن Benign
+
+77
+00:06:01,960 --> 00:06:07,080
+ولا Malignant؟ Malignant هي عبارة عن الـCancers
+
+78
+00:06:07,080 --> 00:06:11,200
+اللي بتيجي من الـepithelial cells يعني المصدر
+
+79
+00:06:11,200 --> 00:06:14,420
+تبعها، المخرج تبعها الـepithelial cells
+
+80
+00:06:22,660 --> 00:06:26,060
+وهذه بتمثّر many of the most common cancers
+
+81
+00:06:26,060 --> 00:06:30,300
+particularly in the aged and include nearly all
+
+82
+00:06:30,300 --> 00:06:34,300
+those developing in the breast, prostate, lung,
+
+83
+00:06:34,760 --> 00:06:40,080
+pancreas and colon نقول عنها Carcinoma وزي ما قلنا
+
+84
+00:06:40,080 --> 00:06:42,500
+بتطلع من وين خدوا بالكوا من هالكلمات هاي
+
+85
+00:06:42,500 --> 00:06:48,840
+Epithelial cells وفي أن الساركومة هذه cancers
+
+86
+00:06:48,840 --> 00:06:51,860
+بتطلع من ال connective tissues إيش يعني connective
+
+87
+00:06:51,860 --> 00:06:58,700
+tissue؟الـ bone cartilage الـ fat الـ nerves وهذه
+
+88
+00:06:58,700 --> 00:07:03,400
+طبعا تطلع من الـ organating in the mesenchymal
+
+89
+00:07:03,400 --> 00:07:06,240
+cells outside the bone marrow، مش من الـ bone
+
+90
+00:07:06,240 --> 00:07:10,060
+marrow، من فرع من الـ mesenchymal itself، نقول
+
+91
+00:07:10,060 --> 00:07:16,380
+عنها Sarcoma، من أسوأ أنواع الـ cancer كمل، في
+
+92
+00:07:16,380 --> 00:07:21,310
+عندنا الـ lymphoma and leukemiaأو في الـ cancers
+
+93
+00:07:21,310 --> 00:07:24,710
+هنحكي عن اللوكيميا بعد شوية أو في المحاضرة اللي
+
+94
+00:07:24,710 --> 00:07:27,250
+جاي these two classes of cancer arise from
+
+95
+00:07:27,250 --> 00:07:31,410
+hematopoietic blood-forming cells يعني هما بيطلعوا
+
+96
+00:07:31,410 --> 00:07:37,210
+من الأماكن اللي بتصليعلي اللي هي خلايا الدم الأسس
+
+97
+00:07:37,210 --> 00:07:42,330
+تبع خلاية الدم blood-forming cells that leave the
+
+98
+00:07:42,330 --> 00:07:45,130
+marrow من ال bone marrow يعني and tend to mature
+
+99
+00:07:45,130 --> 00:07:49,250
+in the lymph node and bloodالليوكيميا هي الـmost
+
+100
+00:07:49,250 --> 00:07:53,530
+common type of cancer في الأطفال تعتمد على حوالي
+
+101
+00:07:53,530 --> 00:07:58,150
+30% في الأطفال، الليوكيميا، بس طبعا الإشارة الحلوة
+
+102
+00:07:58,150 --> 00:08:03,090
+فيها إنه كتير منهم بيصير له healing لكن في بعضهم
+
+103
+00:08:03,090 --> 00:08:06,410
+ما بيصيروش، يمكن اللينفومة الليوكيميا هي عبارة عن
+
+104
+00:08:06,410 --> 00:08:10,830
+cancer بيطلع من الـhematopoietic، hematoderm
+
+105
+00:08:10,830 --> 00:08:17,820
+poietic معناته يصنع، blood formingأو مكوّن cells
+
+106
+00:08:17,820 --> 00:08:22,100
+that leave the marrow وبتروح على الدم أو على الـ
+
+107
+00:08:22,100 --> 00:08:27,310
+lymph node وهناك بيصير لها عملية cancerفيه جرم
+
+108
+00:08:27,310 --> 00:08:31,250
+cell tumor هي عبارة عن cancers derived من
+
+109
+00:08:31,250 --> 00:08:36,810
+pluripotent cells عبارة بتتخرج يعني بتطلعلي من
+
+110
+00:08:36,810 --> 00:08:41,270
+المناطق اللي مخلوطة الخلايا زي عنا على سبيل المثال
+
+111
+00:08:41,270 --> 00:08:45,970
+اللي موجودة في ال testicles أو ال ovary testicles
+
+112
+00:08:45,970 --> 00:08:52,590
+اللي هي الخصيتين ال ovary المبيضين بنقول عنها
+
+113
+00:08:52,590 --> 00:08:55,350
+seminoma أو dysgerminoma
+
+114
+00:08:57,050 --> 00:09:01,030
+وفينا الـ Plastoma هي عبارة عن Cancer بتطلع من الـ
+
+115
+00:09:01,030 --> 00:09:07,190
+Immature precursor cells أو الـ Embryonic tissue
+
+116
+00:09:07,190 --> 00:09:10,930
+لسه الخلايا ما كبرتش، بيقول عنها إيش؟ Plastoma
+
+117
+00:09:10,930 --> 00:09:18,850
+وهدي common في الأطفال أكتر منه في الـ Adult الـ
+
+118
+00:09:18,850 --> 00:09:21,830
+Cancer عادة ماحدش بيجي ويقول مثلا و الله عنده
+
+119
+00:09:21,830 --> 00:09:25,750
+liver، carcinoma، لأ، فيه إلها اسموهذا بتتكون
+
+120
+00:09:25,750 --> 00:09:29,850
+عادةً، فهذه تكميلة الـ classification تتكون من
+
+121
+00:09:29,850 --> 00:09:33,410
+كلمة مثلاً كارسينوما، ساركوما، بلاستوما، اللي
+
+122
+00:09:33,410 --> 00:09:38,750
+قررناه متى وبنحط في الأول اسم العضو أو اسم الـ
+
+123
+00:09:38,750 --> 00:09:46,330
+tissue اللي طالع منه الـ cancer كيف يعني؟ هجيت
+
+124
+00:09:46,330 --> 00:09:49,510
+عندنا cancer of the liver parenchyma ال liver
+
+125
+00:09:49,510 --> 00:09:54,360
+parenchyma بنقول عنهاوهي طالعة من الـ Epithelial
+
+126
+00:09:54,360 --> 00:10:00,340
+cells وكبد
+
+127
+00:10:00,340 --> 00:10:01,760
+Hepato
+
+128
+00:10:09,740 --> 00:10:13,800
+طيب لو نفس الكلام هو طالع من الكبد لكن طالع من
+
+129
+00:10:13,800 --> 00:10:18,040
+الـPrimitive Liver Precursor Cells وهي
+
+130
+00:10:18,040 --> 00:10:21,360
+Hepatoplastoma إحنا قولنا اللي Plastoma هي عبارة
+
+131
+00:10:21,360 --> 00:10:24,940
+عن الـImmature Precursor Cells أو الـEmbryonic
+
+132
+00:10:24,940 --> 00:10:31,840
+Cells A cancer arising from fat cells، بيقول عنه
+
+133
+00:10:31,840 --> 00:10:38,200
+برضه fatالفات قبل قليل صار كومة رقم اتنين صار كومة
+
+134
+00:10:38,200 --> 00:10:42,820
+من الفات لأنه connective tissue صار كومة وهي fat
+
+135
+00:10:42,820 --> 00:10:47,220
+cells بيقول عنها Lipo Lipo-Sarcoma فيه طبعا الـ
+
+136
+00:10:47,220 --> 00:10:51,240
+Benign tumors وهذه ليس كانسر
+
+137
+00:10:57,760 --> 00:11:05,900
+بنفس الكلام عادةً لما يكون بنائي مثلًا لو في شيء
+
+138
+00:11:05,900 --> 00:11:11,920
+طالع من خلايا العضلات العادية نقول عنها Lymyoma
+
+139
+00:11:12,430 --> 00:11:18,570
+أوما اللي هي أنه بيناين ليما يوما معناته الاسم
+
+140
+00:11:18,570 --> 00:11:21,830
+العام للأشخاص اللي يحدث بشكل عام بيناين تمور في
+
+141
+00:11:21,830 --> 00:11:26,050
+الجلد هي الفيبرويد هذه مشهورة عند الفميل خاصة
+
+142
+00:11:26,050 --> 00:11:29,670
+الأصغار في العمر بيصير عندهم فيبرويد يوتراس وهذا
+
+143
+00:11:29,670 --> 00:11:34,790
+بنقول عنه ليما يوما هذه مش كانسر لكن بيناين تمور
+
+144
+00:11:34,790 --> 00:11:41,280
+بعض الأحيان من الكانسر يسمونمرة تانية for the size
+
+145
+00:11:41,280 --> 00:11:45,540
+and shape of that cells حسب ما هي مبينة في ال
+
+146
+00:11:45,540 --> 00:11:48,860
+microscope زي اللي بنقولها giant cell carcinoma أو
+
+147
+00:11:48,860 --> 00:11:52,360
+spindle cell carcinoma أو small cell carcinoma هذه
+
+148
+00:11:52,360 --> 00:11:56,560
+الأسماء برضه واردة إنها تكون موجودة كمان مرة
+
+149
+00:11:56,560 --> 00:12:02,280
+namingاللي هو الـ prefix اللي هو المقدمة تبعته لو
+
+150
+00:12:02,280 --> 00:12:05,640
+كان أنا بحكي عن gland طلع الصورة يا جماعة لو بحكي
+
+151
+00:12:05,640 --> 00:12:10,280
+عن gland بقول adeno cartilage chondro red blood
+
+152
+00:12:10,280 --> 00:12:16,920
+cells erythro blood vessels hemangio liver hepato
+
+153
+00:12:16,920 --> 00:12:22,570
+fat lipo lymphocyte lymphoBig Men Cells Milano
+
+154
+00:12:22,570 --> 00:12:29,730
+Bone Marrow Myelo Muscle Myoc Bone Osteo حسب فبقول
+
+155
+00:12:29,730 --> 00:12:36,030
+Osteo Sarcoma Myo Myoma هيك طب أيش أسباب الـ
+
+156
+00:12:36,030 --> 00:12:45,710
+Cancer حقيقة أنه في أسباب كتيرة في
+
+157
+00:12:45,710 --> 00:12:52,410
+جزئية منها تتعلق بالـ Geneticوهذا يتمثل 5 إلى 10%
+
+158
+00:12:52,410 --> 00:12:57,030
+من الحالات وإن الواحد يكون لاياب اللي يصير عنده
+
+159
+00:12:57,030 --> 00:13:03,190
+وال environment تمثل 90 إلى 95% يعني هذا ما صنعناه
+
+160
+00:13:03,190 --> 00:13:09,410
+أنفسنا إحنا اللي جيبناه لنفسنا ال environment
+
+161
+00:13:09,410 --> 00:13:15,070
+الجزء الكبير تمثل ال tobacco التدخين وال diet
+
+162
+00:13:15,070 --> 00:13:21,630
+والأكل اللي بناكلهالناس اللي بتاخد الكحول الناس
+
+163
+00:13:21,630 --> 00:13:24,250
+الـ obesity ليبل يكون أكتر من غيرها ال infections
+
+164
+00:13:24,250 --> 00:13:28,690
+وحنا حكينا مثلا على سبيل المثال الهيباطيتس C صحيح؟
+
+165
+00:13:28,690 --> 00:13:31,270
+كنا بيصير cancer، الهيباطيتس B بيصير cancer،
+
+166
+00:13:31,270 --> 00:13:35,930
+tobacco، الدخان حكينا عنه، هذه اللي هي ال
+
+167
+00:13:35,930 --> 00:13:38,630
+environmental causes of cancer
+
+168
+00:13:48,850 --> 00:13:52,750
+Tobacco use is the cause of about 22% of cancer
+
+169
+00:13:52,750 --> 00:13:58,350
+deaths رقم كتير مهم 22% من حالات الوفيات بتاعة ال
+
+170
+00:13:58,350 --> 00:14:03,290
+cancer بمثلها التدخين The incidence of lung cancer
+
+171
+00:14:03,290 --> 00:14:06,970
+is highly correlated with smoking كتير من الأحيان
+
+172
+00:14:06,970 --> 00:14:11,130
+حتى لو كان الناس اللي حضرت عن smoking and cancer
+
+173
+00:14:11,130 --> 00:14:16,150
+حتى لو كان passive smoker اش يعني passive smoker؟
+
+174
+00:14:17,600 --> 00:14:21,960
+يعني هو مش هو اللي بدخن نفسه اللي بدخن .. اللي
+
+175
+00:14:21,960 --> 00:14:28,240
+بدخن حد تاني بس هو بشمعه عشرة في المية ناتج عن
+
+176
+00:14:28,240 --> 00:14:32,020
+طريق الـ obesity بوردية طريقة الأكل المستسلمة lack
+
+177
+00:14:32,020 --> 00:14:36,380
+of physical activity consumption of alcohol other
+
+178
+00:14:36,380 --> 00:14:40,620
+factors include certain infections ionizing
+
+179
+00:14:40,620 --> 00:14:43,940
+radiation environmental pollutants
+
+180
+00:14:46,270 --> 00:14:53,030
+التي هي الحاجات للبيئة
+
+181
+00:14:53,030 --> 00:14:56,090
+في التطور
+
+182
+00:15:01,910 --> 00:15:07,710
+والعالم التالت 20% نتيجة انفكشن على رأسها
+
+183
+00:15:07,710 --> 00:15:13,810
+الهيباطايتس بي وهيباطايتس سي وهيومان بابيلوما
+
+184
+00:15:13,810 --> 00:15:14,570
+فيروس
+
+185
+00:15:18,640 --> 00:15:25,820
+تعمل لـ Cancer في العالم التالت وممكن أكتر من الـ
+
+186
+00:15:25,820 --> 00:15:29,400
+Smoking لكن بدأنا نلحقهم وهنا بدنا نفوتهم
+
+187
+00:15:29,400 --> 00:15:33,560
+للأوروبيين These factors act at least partly by
+
+188
+00:15:33,560 --> 00:15:36,960
+changing the genes of cells يعني ممكن مايكونش هو
+
+189
+00:15:36,960 --> 00:15:41,480
+السبب الأساسي لكن على الأقل بيلعب دور Genetic
+
+190
+00:15:41,480 --> 00:15:46,430
+changes are acquired before cancer developsخمسة
+
+191
+00:15:46,430 --> 00:15:48,790
+لعشرة في المية of cancers are due to genetic
+
+192
+00:15:48,790 --> 00:15:54,850
+defects inherited from a person's parents وهذه
+
+193
+00:15:54,850 --> 00:15:59,310
+كلها بنعرف جثة الممثلة اللي شالت لبريست نتيجة أن
+
+194
+00:15:59,310 --> 00:16:03,430
+أمها وستها واختها كان عندهم عاملة فحص جيني لاجت أن
+
+195
+00:16:03,430 --> 00:16:07,440
+هي liable يصير عندهايصير عندها breast cancer فقبل
+
+196
+00:16:07,440 --> 00:16:10,820
+ما يصير عندها breast cancer راحت شالت ال breast
+
+197
+00:16:10,820 --> 00:16:13,660
+طبعا أنا مش بدأ أقول إن هذا صح أو غلط، لأ إنما
+
+198
+00:16:13,660 --> 00:16:18,860
+الموضوع هذا بلعب دور ويبدو إنه في المستقبل هياخد
+
+199
+00:16:18,860 --> 00:16:27,500
+دور أكبر، طيب إيه ال incidence of cancer؟ طبعا عند
+
+200
+00:16:27,500 --> 00:16:31,340
+رجالالعدد تقريبًا مشابه إحنا بنحكي عن أمريكا في
+
+201
+00:16:31,340 --> 00:16:36,500
+2015 أمريكا في 2015 تقريبًا 848 مليون صار عندهم
+
+202
+00:16:36,500 --> 00:16:42,680
+cancer ال woman الرجال 848 و ال woman 810 يعني
+
+203
+00:16:42,680 --> 00:16:47,720
+جريمين من بعض مش بعاد لكن مثلت لبروستيت 26% عند ال
+
+204
+00:16:47,720 --> 00:16:52,550
+men ل breast 29% عند ال woman ال lungبالصلاة وعن
+
+205
+00:16:52,550 --> 00:16:56,930
+النبي عند الرجال 14% وعند الستات بدوا يلحقونا
+
+206
+00:16:56,930 --> 00:17:02,710
+ويقعدهم ويوصلونا 13% ليش؟ لأن بدوا الستات برضه
+
+207
+00:17:02,710 --> 00:17:07,470
+يكونوا مدخنين وشيشة وهيك ال colon عند الرجال
+
+208
+00:17:07,470 --> 00:17:13,030
+والستات 8 8 وبعد هيك بيصير فيه خصوصية لموضوع ال
+
+209
+00:17:13,030 --> 00:17:16,880
+cancerأو بيبطل فيه خصوصية عفوًا لموضوع الـ Cancer
+
+210
+00:17:16,880 --> 00:17:19,760
+بيصير جاربين من بعض لكن هي المشكلة كلها الـ
+
+211
+00:17:19,760 --> 00:17:23,480
+Prostate والـ Breast اللي فيهم الخلاف والباقي كله
+
+212
+00:17:23,480 --> 00:17:25,180
+جاريب من بعض
+
+213
+00:17:35,720 --> 00:17:40,800
+وهو مجموع الارجال والستات اللي شوفناهم في الـ
+
+214
+00:17:40,800 --> 00:17:48,240
+«سلايد» هذا 800 و 800 تقريباً مليون و ستمية new
+
+215
+00:17:48,240 --> 00:17:52,700
+casesكانت برستيتكالة أكتر قصر عامة بين الرجال، 26
+
+216
+00:17:52,700 --> 00:17:56,860
+%، ثم أجابعاء الـLung، ثم الـColon and Rectum، في
+
+217
+00:17:56,860 --> 00:18:00,240
+الفتاة 29% برستكالة، ثم الـLung، ثم الـColon and
+
+218
+00:18:00,240 --> 00:18:05,560
+Rectum، كانت أكتر قصر عامة بين الرجال، الـColon
+
+219
+00:18:05,560 --> 00:18:08,500
+and Rectum كانت أكتر قصر عامة بين الرجال، الـColon
+
+220
+00:18:08,500 --> 00:18:09,440
+and Rectum كانت أكتر قصر عامة بين الرجال، الـColon
+
+221
+00:18:09,440 --> 00:18:09,680
+and Rectum كانت أكتر قصر عامة بين الرجال، الـColon
+
+222
+00:18:09,680 --> 00:18:09,880
+and Rectum كانت أكتر قصر عامة بين الرجال، الـColon
+
+223
+00:18:09,880 --> 00:18:10,220
+and Rectum كانت أكتر قصر عامة بين الرجال،
+
+224
+00:18:17,910 --> 00:18:22,150
+بتحسن الامور كل مانكشف الـ cancer بدري، بتعالج
+
+225
+00:18:22,150 --> 00:18:26,610
+بدري، بينحطله حد بدري، for example due to
+
+226
+00:18:26,610 --> 00:18:29,890
+improvement of treatment the five year relative
+
+227
+00:18:29,890 --> 00:18:35,390
+survival rate for leukemia has increased من 34% في
+
+228
+00:18:35,390 --> 00:18:40,190
+السبعيناتلـ 60% لتاريخ كتابة هذه المحاضرة والآن
+
+229
+00:18:40,190 --> 00:18:43,150
+يمكن يوصل لـ 70% أو 80% بالنسبة للـ Leukemia في
+
+230
+00:18:43,150 --> 00:18:46,410
+الأطفال، إيش يعني الـ Five Year Relative Survivor
+
+231
+00:18:46,410 --> 00:18:52,730
+Rate؟ في الأورام لا نقول إنه سيعيش عمر طويل، دائما
+
+232
+00:18:52,730 --> 00:18:56,950
+نحكم على خمس سنين، حسبوها حسبة جداش نسبة من الناس
+
+233
+00:18:56,950 --> 00:19:01,550
+بتصمت خمس سنين، تصوروا؟ هيك بتنحسب، اللي هي Five
+
+234
+00:19:01,550 --> 00:19:03,530
+Year Survivor Rate
+
+235
+00:19:06,890 --> 00:19:10,470
+الـ 2012 كان فيه 14 مليون new case of cancer
+
+236
+00:19:10,470 --> 00:19:14,110
+occurred globally بدون طبعا ال skin cancer اللي هي
+
+237
+00:19:14,110 --> 00:19:19,150
+بدون ال skin cancers العادية ما عدا ال melanoma it
+
+238
+00:19:19,150 --> 00:19:26,810
+caused about 8.2 مليون death or 14.6% of all human
+
+239
+00:19:26,810 --> 00:19:33,060
+death ال symptoms اللي بنشوفها حسبعشان هيك مقدرش
+
+240
+00:19:33,060 --> 00:19:38,200
+الواحد الآن يقول والله حسب العضو يعني أنت ممكن أي
+
+241
+00:19:38,200 --> 00:19:42,400
+symptom يصير صحيح يكون simple لكن ممكن يكون وراه
+
+242
+00:19:42,400 --> 00:19:48,060
+حاجة كبيرة زي مثلا أجا
+
+243
+00:19:48,060 --> 00:19:51,680
+واحد شاف كتلة في ال breast ست شافت كتلة في ال
+
+244
+00:19:51,680 --> 00:19:55,360
+breast maybe a sign of breast cancer ممكن مايكونش
+
+245
+00:19:55,360 --> 00:20:01,820
+ممكن دمل ممكن lipoma لكن وجود a thickening أو lump
+
+246
+00:20:02,110 --> 00:20:06,710
+في جسم، في أي مكان، وخاصة لما يكون في الـ breast
+
+247
+00:20:06,710 --> 00:20:12,970
+بتفكر في أنه يكون tumor واحد بدون سبب نزل وزنه من
+
+248
+00:20:12,970 --> 00:20:18,510
+تسعين كيلو صار ستين، لا عنده سكري ولا بلعب رياضة
+
+249
+00:20:18,510 --> 00:20:23,590
+ولا عنده اكتئاب وعادي، unexplained weight loss
+
+250
+00:20:23,590 --> 00:20:27,870
+feeling weak or very tired، دائما تعبان، دائما
+
+251
+00:20:27,870 --> 00:20:33,420
+هلكان، unusual bleeding or dischargeالستات، بنزل
+
+252
+00:20:33,420 --> 00:20:37,040
+دايما عندها، وفي الأخر بتقول استحاضة مثلا، لأ،
+
+253
+00:20:37,040 --> 00:20:40,500
+بدها تاخد بالها، بدها تفحص، خاصة كل أو discharge
+
+254
+00:20:40,500 --> 00:20:45,980
+أو سوائل، خاصة كل ما كبرت في العمر، a sore that
+
+255
+00:20:45,980 --> 00:20:49,380
+does not heal، جرح ومش راضي يطيب، ممكن يكون سكري،
+
+256
+00:20:49,380 --> 00:20:54,460
+أه، بس ممكن يكون برضه حاجة تانية، hoarseness، بحة
+
+257
+00:20:54,460 --> 00:20:58,060
+أو cough that does not go away، مش راضي تحسن الكحة
+
+258
+00:21:00,460 --> 00:21:02,000
+التغييرات في الـ bowel أو العبادات الدمية
+
+259
+00:21:05,300 --> 00:21:09,020
+discomfort after eating دائما بعد الأكل تعبان ومش
+
+260
+00:21:09,020 --> 00:21:11,800
+مرتاح a hard time swallowing يا جماعة هذه الـ
+
+261
+00:21:11,800 --> 00:21:13,880
+symptoms ممكن تكون symptoms لحاجة تانية زي بيبتك
+
+262
+00:21:13,880 --> 00:21:17,960
+ألصر زي كذا لكن مش شرط أنه يكون cancer لكن لازم
+
+263
+00:21:17,960 --> 00:21:21,360
+أحط الموضوع في بالي most often these symptoms are
+
+264
+00:21:21,360 --> 00:21:24,380
+not due to cancer they may be caused by non
+
+265
+00:21:24,380 --> 00:21:27,660
+cancers or benign tumors or other problems بس بدنا
+
+266
+00:21:27,660 --> 00:21:32,820
+ناخد بالنا منهم ال cancer يا جماعة أو ال massإله
+
+267
+00:21:32,820 --> 00:21:37,520
+أكتر من تأثير يعني هو مش بس ع جد مشبوك في حاله
+
+268
+00:21:37,520 --> 00:21:44,370
+إنما هوبعملي مشاكل Locally بعملي Mass Effect زي
+
+269
+00:21:44,370 --> 00:21:47,150
+الـ Lung Cancer بيعملي Blockage of the Bronchus
+
+270
+00:21:47,150 --> 00:21:51,110
+Resulting in Cough أو Pneumonia يعني هو بتغطلي على
+
+271
+00:21:51,110 --> 00:21:54,550
+أماكن تانية Esophageal Cancer can cause Narrowing
+
+272
+00:21:54,550 --> 00:21:58,390
+of the Esophagus Making difficult or painful to
+
+273
+00:21:58,390 --> 00:22:01,650
+swallow هذا المشكلة Correctal Cancer ممكن يعملي
+
+274
+00:22:01,650 --> 00:22:09,240
+Narrowing أو Blockage of the bowelمثلما يبين على
+
+275
+00:22:09,240 --> 00:22:13,880
+طول فيه جروح و نزيق دم عشان هيك لو ما بنلاقي دم
+
+276
+00:22:13,880 --> 00:22:18,380
+لازم ناخد بانا if the lung will lead to a coughing
+
+277
+00:22:18,380 --> 00:22:23,280
+of blood الـ hemoptysis in the bowel بيصير
+
+278
+00:22:23,280 --> 00:22:26,160
+اندوانيميا و rectal bleeding in the bladder blood
+
+279
+00:22:26,160 --> 00:22:29,580
+in the urine hematuria in the uterus بديني vaginal
+
+280
+00:22:29,580 --> 00:22:42,150
+bleeding و في الأخر بطلع ورا حاجة كبيرةأي ورم
+
+281
+00:22:42,150 --> 00:22:53,750
+بيجعش بيخوف أكتر من اللي بيجعقريب من قاعدة بعض
+
+282
+00:22:53,750 --> 00:22:57,230
+الأنواع الـ cancers بتعمل إيه؟ اللي هو زي ascites
+
+283
+00:22:57,230 --> 00:22:59,990
+اللي هو fluid in the abdomen أو pleural effusion
+
+284
+00:22:59,990 --> 00:23:05,500
+زي in the pleural cavity يكون فيه عنده fluidطبعاً
+
+285
+00:23:05,500 --> 00:23:08,720
+إلو إلو الـ Cancer إحنا بنحكي حاجات قاعدين
+
+286
+00:23:08,720 --> 00:23:11,600
+generalize يا جماعة general، معلومات عامة اللي
+
+287
+00:23:11,600 --> 00:23:14,880
+بنحكيها general symptoms occur due to distant
+
+288
+00:23:14,880 --> 00:23:18,140
+effects of the cancer that are not related to
+
+289
+00:23:18,140 --> 00:23:23,180
+direct or metastatic sprintيعني الـ General
+
+290
+00:23:23,180 --> 00:23:26,480
+Systemic Symptoms اللي هو أنا يكون عندي Weakness
+
+291
+00:23:26,480 --> 00:23:31,000
+على سبيل المثال أو Headache أو زي ما قلنا ينزل
+
+292
+00:23:31,000 --> 00:23:35,120
+وزني أو عندي Fever بدون ما يكون فيه Metastasis هذه
+
+293
+00:23:35,120 --> 00:23:40,800
+ما بيقولها أنا Systemic Symptoms بجمبها وبدنا
+
+294
+00:23:40,800 --> 00:23:44,620
+ناخد بالنا لو أجاني حد بـPersistent Unknown Cause
+
+295
+00:23:44,620 --> 00:23:50,780
+of Fever ممكن يكون وراهايكون وراها لويكيميا أو
+
+296
+00:23:50,780 --> 00:23:53,880
+cancer of the liver أو kidney ده ناخد بالنا من قبل
+
+297
+00:23:53,880 --> 00:24:03,240
+يعنى الـ metastases أو الـ mets هي عبارة can
+
+298
+00:24:03,240 --> 00:24:08,370
+spread its original sideبالـ Local Spread يعني هي
+
+299
+00:24:08,370 --> 00:24:12,870
+بتعمل الـ Mets أو الـ Metastases أو البنات أو
+
+300
+00:24:12,870 --> 00:24:16,410
+الأخوات هدول اللي بنتشروا من الـ Cancer لباقية
+
+301
+00:24:16,410 --> 00:24:20,050
+الجسم بعدة طرق إما Local Spread بتغطي على اللي
+
+302
+00:24:20,050 --> 00:24:23,470
+جنبه أو Lymphatic Spread عن طريق الـ Lymph Nodes
+
+303
+00:24:23,470 --> 00:24:31,530
+أو Hematogenous Spread اللي هو عن طريق الدم وبروحه
+
+304
+00:24:31,530 --> 00:24:36,760
+على two distant sites أماكن بعيدةيعني بلاقي عصب
+
+305
+00:24:36,760 --> 00:24:40,380
+المثال من الكبد بروح أدماغ أو من الـ lung بروح
+
+306
+00:24:40,380 --> 00:24:45,480
+أدماغ وهذه بنقول عنها metastases أو metes the new
+
+307
+00:24:45,480 --> 00:24:50,420
+tumor are called metastatic tumors اللي بيصير جديد
+
+308
+00:24:50,420 --> 00:24:55,260
+لكن ال original is called a primary tumor يعني ال
+
+309
+00:24:55,260 --> 00:25:00,860
+primary tumor هو الأصل واللي راحله بنقول عنه
+
+310
+00:25:00,860 --> 00:25:03,900
+metastatic tumor almost all cancers can
+
+311
+00:25:03,900 --> 00:25:08,080
+metastasizemost cancer deaths are due to cancer
+
+312
+00:25:08,080 --> 00:25:11,340
+that has spread from its primary site to other
+
+313
+00:25:11,340 --> 00:25:14,560
+organs يعني معظم الحالات اللي بتتوفى وبيصير عندها
+
+314
+00:25:14,560 --> 00:25:17,960
+مشاكل نتيجة الـ metastases الـ mets different
+
+315
+00:25:17,960 --> 00:25:22,060
+types of cancer tend to metastase to particular
+
+316
+00:25:22,060 --> 00:25:25,560
+organs طبعا معروف عند الأطباء والله إذا كان عندى
+
+317
+00:25:25,560 --> 00:25:29,140
+tumor في المكان اللي فلاني الأماكن المحببة اللي
+
+318
+00:25:29,140 --> 00:25:34,060
+بيبعت عليها mets هي كذا وكذا وكذا وكذا most common
+
+319
+00:25:34,060 --> 00:25:38,580
+placesوهذه الأماكن اللي بيروحلها لـLung,
+
+320
+00:25:38,680 --> 00:25:48,600
+Liver, Brain and Bone عندما
+
+321
+00:25:48,600 --> 00:25:52,540
+يتفرق الحرارة بطريقة هيموتوجينية، يتفرق بشكل عام
+
+322
+00:25:52,540 --> 00:25:59,560
+للجميع على جسمممكن يصير عندى إنلاج love node، ممكن
+
+323
+00:25:59,560 --> 00:26:02,200
+يكون عندى إنلاج liver، ممكن يكون عندى إنلاج
+
+324
+00:26:02,200 --> 00:26:07,440
+spleen، ممكن يصير عندى نتيجة متس هاي pain أو
+
+325
+00:26:07,440 --> 00:26:10,500
+fracture في ال bone، ممكن يكون عندى لو راق على ال
+
+326
+00:26:10,500 --> 00:26:15,360
+brain يعملني neurological symptoms كيف بشخص؟ chest
+
+327
+00:26:15,360 --> 00:26:18,420
+x-ray، showing lung cancer
+
+328
+00:26:20,980 --> 00:26:24,080
+عشان المثال، أكثر المصابين بالنسبة لي هم المصابين
+
+329
+00:26:24,080 --> 00:26:29,540
+بسبب وجود إشارات أو إشارات أو من خلال الـ
+
+330
+00:26:29,540 --> 00:26:34,800
+Screening طبعاً بدنا ندّي دايما، ندّي دايما نعمل
+
+331
+00:26:34,800 --> 00:26:38,860
+صور حسب وين الشكوى، يعني واحد بيشكي من severe
+
+332
+00:26:38,860 --> 00:26:42,020
+headache وrecurrent و projectile vomiting، بده يشك
+
+333
+00:26:42,020 --> 00:26:44,720
+في brain tumor، بده يعمله CT مثلا
+
+334
+00:26:52,010 --> 00:26:56,790
+إذا أي واحد من هؤلاء لم يصبح لديه نتيجة تقريبًا
+
+335
+00:26:56,790 --> 00:26:57,890
+لديه نتيجة تقريبًا لديه نتيجة تقريبًا لديه نتيجة
+
+336
+00:26:57,890 --> 00:27:00,130
+تقريبًا لديه نتيجة تقريبًا لديه نتيجة تقريبًا لديه
+
+337
+00:27:00,130 --> 00:27:00,530
+نتيجة تقريبًا لديه نتيجة تقريبًا لديه نتيجة
+
+338
+00:27:00,530 --> 00:27:00,710
+تقريبًا لديه نتيجة تقريبًا لديه نتيجة تقريبًا لديه
+
+339
+00:27:00,710 --> 00:27:01,350
+نتيجة تقريبًا لديه نتيجة تقريبًا لديه نتيجة
+
+340
+00:27:01,350 --> 00:27:04,650
+تقريبًا لديه نتيجة تقريبًا لديه نتيجة تقريبًا لدي
+
+341
+00:27:07,380 --> 00:27:11,460
+والذين يشبهوا القنصر يتم تحقيقهم بمجال مجال مجال
+
+342
+00:27:11,460 --> 00:27:12,420
+مجال مجال مجال مجال مجال مجال مجال مجال مجال مجال
+
+343
+00:27:12,420 --> 00:27:16,840
+مجال مجال مجال مجال مجال مجال مجال مجال مجال مجال
+
+344
+00:27:16,840 --> 00:27:17,260
+مجال مجال مجال مجال مجال مجال مجال مجال مجال مجال
+
+345
+00:27:17,260 --> 00:27:17,540
+مجال مجال مجال مجال مجال مجال مجال مجال مجال مجال
+
+346
+00:27:17,540 --> 00:27:18,180
+مجال مجال مجال مجال مجال مجال مجال مجال مجال مجال
+
+347
+00:27:18,180 --> 00:27:33,680
+مجال مجال مجال مجال مج
+
+348
+00:27:35,000 --> 00:27:38,350
+لو فيه symptoms مش screening بيصير diagnosisيعني
+
+349
+00:27:38,350 --> 00:27:41,590
+واحد ماعندهوش ولي حاجة صار عمره مثلا ست صار عمرها
+
+350
+00:27:41,590 --> 00:27:45,090
+خمسة وعشرين أو تلاتين الـ Screening تبعها إنها
+
+351
+00:27:45,090 --> 00:27:48,930
+تعمل التحسيس لحالها أو الدكتورة تشوفيها تحت القفات
+
+352
+00:27:48,930 --> 00:27:52,410
+وكذا وهيك هذا بقول عنه Screening لكن والله أجد
+
+353
+00:27:52,410 --> 00:27:54,890
+الست تقول والله يا دكتورة أنا حاسة زي كتلة اندي في
+
+354
+00:27:54,890 --> 00:27:57,930
+سدري وفحصة الدكتورة هذا ما اسمهش Screening هذا
+
+355
+00:27:57,930 --> 00:28:01,130
+اسمه Diagnosis بيصير خلاص Screening may involve
+
+356
+00:28:01,130 --> 00:28:05,050
+physical examination lab test or test to look at
+
+357
+00:28:05,050 --> 00:28:12,730
+internal organsHow is cancer treated؟ في كتير
+
+358
+00:28:12,730 --> 00:28:16,690
+علاجات، Surgery, Radiation therapy, Chemotherapy،
+
+359
+00:28:16,690 --> 00:28:21,710
+Anticancer drugs and Palliative for some cancers
+
+360
+00:28:29,990 --> 00:28:34,290
+Okay يعني أنا هوقف عند الـ slide هاي وإن شاء الله
+
+361
+00:28:34,290 --> 00:28:38,370
+تعالى آخر محاضرة هنعملها على ال weekend هبعتلكوا
+
+362
+00:28:38,370 --> 00:28:40,870
+إياها إن شاء الله تعالى اللي هي هنحكي عن ال
+
+363
+00:28:40,870 --> 00:28:46,950
+leukemia خمس تاشر slide يمكن بالنسبة للمحاضرة هي
+
+364
+00:28:46,950 --> 00:28:49,110
+يا جماعة إحنا لما أديتكوا إياها أديتكوا إياها
+
+365
+00:28:49,110 --> 00:28:52,770
+كاملة بس إحنا هنضلنا بس ماشيين لحد slide تلاتة
+
+366
+00:28:52,770 --> 00:29:00,620
+وتلاتين بس ل slide تلاتة وتلاتينومش هدخل على
+
+367
+00:29:00,620 --> 00:29:06,100
+التفاصيل بس هنوقف لحد slide تلاتة و تلاتين في هذه
+
+368
+00:29:06,100 --> 00:29:11,400
+وبيفهم بدي أكمل على الـ Leukemia برضه عشر، خمسة
+
+369
+00:29:11,400 --> 00:29:14,660
+أشهر slide وبعدين هيك بيبجنتها إن شاء الله تعالى
+
+370
+00:29:14,660 --> 00:29:20,680
+المنهج بإذن الله تعالى يعني أشكركم على حسن
+
+371
+00:29:20,680 --> 00:29:24,900
+الاستماع في الفترة الجاي هديكوا شوية تفاصيل كيف
+
+372
+00:29:24,900 --> 00:29:30,980
+الامتحانومن وين هيكون و هيك ان شاء الله انتظرونا
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/e2BPn_M30ww.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/e2BPn_M30ww.srt
new file mode 100644
index 0000000000000000000000000000000000000000..843d44b301685d8fb4579108ba163bb4aca4403a
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/e2BPn_M30ww.srt
@@ -0,0 +1,1671 @@
+1
+00:00:00,000 --> 00:00:03,660
+بسم الله الرحمن الرحيم والحمد لله الرحمن الرحيم والصلاة 
+
+2
+00:00:03,660 --> 00:00:07,480
+والسلام على سيدنا محمد يوم جديد وسعيد إن شاء الله
+
+3
+00:00:07,480 --> 00:00:11,840
+أتمنى إليكم اليوم هنتحدث إن شاء الله عن الـ urinary 
+
+4
+00:00:11,840 --> 00:00:18,960
+tract system طبعًا إحنا في خمسين سلايد الآن أو في
+
+5
+00:00:18,960 --> 00:00:25,680
+ساعة من المحاضرة،  سيب المثالمش هنلم بكل الموضوع زي
+
+6
+00:00:25,680 --> 00:00:29,240
+ما أنتم عارفين موضوع طويل لكن إحنا حبينا زي ما
+
+7
+00:00:29,240 --> 00:00:33,200
+قلنا في الـ gastrointestinal tract  عصب المثل أو في 
+
+8
+00:00:33,200 --> 00:00:37,880
+الـ pulmonary أو في الـ cancer أو في الـ urinary 
+
+9
+00:00:37,880 --> 00:00:42,180
+tract أنه نلقي بعض الضوء على بعض الأمراض بحيث أن 
+
+10
+00:00:42,180 --> 00:00:46,400
+أخصائي العلاج الطبيعي يكون عنده فكرة عن كل حاجة
+
+11
+00:00:46,400 --> 00:00:50,660
+وفكرة مش قليلة يعني فكرة كويسة عن كل حاجة لكن طبعًا
+
+12
+00:00:50,660 --> 00:00:55,840
+هو بيظل له التخصص تبعه الأساس هو العلاج الطبيعي
+
+13
+00:00:55,840 --> 00:00:59,760
+بالعلاقة مع الأمراض البطنية الجراحية والعصبية على
+
+14
+00:00:59,760 --> 00:01:03,500
+سبيل المثال، فإحنا هنلقي بعض الضوء هنحكي في الأول 
+
+15
+00:01:03,500 --> 00:01:09,400
+عن الـ Urinary Tract Anatomy
+
+16
+00:01:09,400 --> 00:01:12,780
+بمعنى فيسيولوجيا حاجة خفيفة جدًا جدًا كمان سلايد 
+
+17
+00:01:12,780 --> 00:01:16,640
+بتوضح بعض الأمور وبعد هيك ندخل على بعض الـ
+
+18
+00:01:16,640 --> 00:01:21,840
+Diseases الـ Renal Stones أو الـ Urinary Tract
+
+19
+00:01:21,840 --> 00:01:25,760
+Infection  ونحكي عن الـ Acute Renal Failure وعن
+
+20
+00:01:25,760 --> 00:01:30,980
+الـ Chronic Renal Failure وهيك بنبقى تقريبًا غطينا
+
+21
+00:01:30,980 --> 00:01:39,980
+جزء محترم من الـ Urinary Tract Infection الـ
+
+22
+00:01:39,980 --> 00:01:43,780
+Urinary System هو عبارة عن زي ما إحنا شايفين في
+
+23
+00:01:43,780 --> 00:01:49,660
+الصورة قدامنا الـ Kidneys رقم واحد وهدول موجودات
+
+24
+00:01:49,660 --> 00:01:54,640
+في الـ posterior wall of the abdominal cavity يعني
+
+25
+00:01:54,640 --> 00:01:58,800
+مش في الأمام، أنا لما أجي أفحص الكلى ما أفحصهم من
+
+26
+00:01:58,800 --> 00:02:03,340
+الظهر من ورا مش من قدام لأن قدام موجود عندي زي ما
+
+27
+00:02:03,340 --> 00:02:07,680
+إحنا عارفين الـ .. الـ .. الـ .. الكبد مع المرارة
+
+28
+00:02:07,680 --> 00:02:12,900
+وعالجهة التانية موجود عند المعدة مع الـ .. مع الطحال
+
+29
+00:02:12,900 --> 00:02:16,760
+فهما وراهم في الـ cavity مش وراهم لزجين فيهم في
+
+30
+00:02:16,760 --> 00:02:21,420
+بينهم طبعًا هدول في الـ anterior abdomen و الـ
+
+31
+00:02:21,420 --> 00:02:26,660
+kidneys في الـ posterior abdomen في منطقة بيقول
+
+32
+00:02:26,660 --> 00:02:31,860
+عنها retro-peritoneal يعني الـ peritoneal space
+
+33
+00:02:31,860 --> 00:02:37,020
+اللي هو محطوط فيه كل الأعضاء زي الـ intestine  والكبد
+
+34
+00:02:37,020 --> 00:02:42,180
+و الكذا لكن الـ kidneys في الـ retro peritoneum
+
+35
+00:02:42,180 --> 00:02:48,140
+retro يعني خلف خلف الـ peritoneum طبعًا محاط بـ
+
+36
+00:02:48,140 --> 00:02:53,770
+connective tissue وهذه اللي بتمسك الـ kidneys in
+
+37
+00:02:53,770 --> 00:03:01,610
+place وطبعًا في أيضًا adipose tissue  كاشن الـ kidneys فهذه
+
+38
+00:03:01,610 --> 00:03:09,650
+الـ capsule ماسكة الكلتين الـ connective tissue وفي
+
+39
+00:03:09,650 --> 00:03:14,800
+طبعًا لو هنشوف ادنا بعد شوي صورة إن الـ lower rib الـ
+
+40
+00:03:14,800 --> 00:03:19,560
+Cage partially includes the kidneys and protect
+
+41
+00:03:19,560 --> 00:03:23,380
+them يعني حماية سبحان الله العظيم الدهون و الـ
+
+42
+00:03:23,380 --> 00:03:27,480
+capsule وبعدين الـ lower ribs هدول كلهم بيحموا
+
+43
+00:03:27,480 --> 00:03:34,900
+الكلاب kidneys هما طبعًا اثنين ممكن يكون أكثر اه
+
+44
+00:03:34,900 --> 00:03:37,740
+طبعًا ممكن يكون أكثر وممكن يكون بس أقل واحدة كمان
+
+45
+00:03:38,060 --> 00:03:43,740
+ممكن يكون أكثر أكثر أنه طبعًا بتبقى واحدة منهم
+
+46
+00:03:43,740 --> 00:03:47,280
+دخيلة
+
+47
+00:03:47,280 --> 00:03:51,040
+على الموضوع فيه اثنين Ureter إيش الـ Ureter؟ الـ
+
+48
+00:03:51,040 --> 00:03:55,220
+Ureter اللي هو الحالب اللي هو البرفيش اللي زي ما
+
+49
+00:03:55,220 --> 00:04:00,000
+نشاهدناه نازل من حوض الكلة نازل عوين على المثانة
+
+50
+00:04:00,000 --> 00:04:05,920
+بعدين لدينا bladder المثانة وفي الـ Urethra الوريثرة 
+
+51
+00:04:05,920 --> 00:04:13,440
+اللي هو حسب إذا كان male ولا female في الـ
+
+52
+00:04:13,440 --> 00:04:16,660
+female اللي هو الـ vagina وفي الـ male بيبقى الـ
+
+53
+00:04:16,660 --> 00:04:22,280
+penis وبعدين في عندنا الـ Nephron من ضمن الآن هذه
+
+54
+00:04:22,280 --> 00:04:26,460
+الجهاز الـ Urinary System بصورة عامة، الآن في
+
+55
+00:04:26,460 --> 00:04:29,440
+عندنا حاجة اسمها الـ Nephron Unit، الـ Nephron الـ
+
+56
+00:04:29,440 --> 00:04:34,200
+Nephron هو عبارة عن وحدات، Unit، وحدات، هذه الوحدة 
+
+57
+00:04:34,200 --> 00:04:38,420
+موجودة، الوحدات هي موجودة جوا الكلة، وفي من كل كلة
+
+58
+00:04:38,420 --> 00:04:42,260
+في عندها حوالي مليون Nephron، مليون Nephron، حاجات 
+
+59
+00:04:42,260 --> 00:04:47,020
+هنشوف تركيبة الـ Nephron، مليون Nephron كل كل كلة 
+
+60
+00:04:48,620 --> 00:04:54,780
+وشغلتها أن هي اللي بتكوننا الـ ball وطبعًا متكونة من
+
+61
+00:04:54,780 --> 00:04:59,680
+أنابيب وشرايين وأوردة هذا الـ nephron اللي فيه منه 
+
+62
+00:04:59,680 --> 00:05:03,660
+مليون طبعًا وهي زي ما بنقول عنها الـ functional unit
+
+63
+00:05:03,660 --> 00:05:06,800
+of the kidneys كمان مرة صورة هنا
+
+64
+00:05:12,250 --> 00:05:16,290
+الـ Kidneys اللي شايفينه مكتوب كِدْني وبعدين الـ
+
+65
+00:05:16,290 --> 00:05:23,040
+Ureter بالأصفر وبعد ذلك يوجد الـ Urinary Bladder
+
+66
+00:05:23,040 --> 00:05:29,260
+داخل الحالب وبعد ذلك يوجد الـ Urethra في ميل هان
+
+67
+00:05:29,260 --> 00:05:37,940
+الخارجة من البلدر تقريبًا هو هكذا في الموضوع يدخل
+
+68
+00:05:37,940 --> 00:05:41,740
+الموضوع اللي عندنا هنا اللي هو الرحم والـ ovaries 
+
+69
+00:05:41,740 --> 00:05:45,640
+وفي عندنا طبعًا فوق الـ kidneys حاجة اسمها adrenal
+
+70
+00:05:45,640 --> 00:05:52,120
+glands وكل هيتو زي ما قلنا retro-peritoneal موجودة
+
+71
+00:05:52,120 --> 00:05:57,400
+هذا
+
+72
+00:05:57,400 --> 00:06:02,180
+من الخلف الآن قطعة 
+
+73
+00:06:02,180 --> 00:06:08,040
+من الخلف طبعًا ما يبينش بالصورة هي لكن للتصور وين 
+
+74
+00:06:08,040 --> 00:06:12,920
+بتبجي الكيلتين عمليًا في حدود الكيلتين بتبجي في
+
+75
+00:06:12,920 --> 00:06:21,490
+حدود الـ .. الـ .. الـ 11th و الـ 12th ribs هما هدول
+
+76
+00:06:21,490 --> 00:06:26,970
+مغطيين على الكلة بحيث يحموها بحيث يحموها الـ left
+
+77
+00:06:26,970 --> 00:06:33,870
+kidney و الـ right kidney و
+
+78
+00:06:33,870 --> 00:06:38,250
+طبعًا هما موجودين في حدود علي تقريبًا الكلتين في علي
+
+79
+00:06:38,250 --> 00:06:40,330
+الـ one الـ one 
+
+80
+00:06:45,000 --> 00:06:53,940
+الـ Kidney Structure لو قطعناها قطع طولي مثل حبة 
+
+81
+00:06:53,940 --> 00:07:00,140
+الفصوليا مثلًا، لو قطعناها قطع طولي، فمن جوا الـ
+
+82
+00:07:00,140 --> 00:07:01,480
+Kidney Reddish Brown
+
+83
+00:07:04,470 --> 00:07:10,370
+بني مائل على أحمر زي البين وحوالي عشرة سم في خمسة 
+
+84
+00:07:10,370 --> 00:07:14,450
+سم، خمسة سم عرض في عشرة سم، مش إيش مش كبير، لما 
+
+85
+00:07:14,450 --> 00:07:17,850
+نقارن الناس اللي بتروح بتغسل كِلة بدها ماكينة ومي
+
+86
+00:07:17,850 --> 00:07:24,240
+وموظفين وكذا، بتيجي قطعة بتدخل كِلية خمسة في عشرة 
+
+87
+00:07:24,240 --> 00:07:28,900
+سم  وبتقول له بالشغل هذا طبعًا سبحان الله العظيم
+
+88
+00:07:28,900 --> 00:07:33,240
+وبعدين فيها الـ hilus الـ hilus اللي هو المخرج من الكِلية
+
+89
+00:07:33,240 --> 00:07:37,300
+where blood vessels and structures enter or exit
+
+90
+00:07:37,300 --> 00:07:44,700
+the kidneys كل حاجة بتدخل الكِلية وبتطلع من هناك من
+
+91
+00:07:44,700 --> 00:07:51,130
+الـ hilus اسمها الـ hilus الآن الـ kidney مكونة
+
+92
+00:07:51,130 --> 00:07:56,390
+لو قطعناها قطع طولي من ثلاث regions
+
+93
+00:07:56,390 --> 00:08:01,930
+الـ region الأولاني اللي هو الـ cortex مكبر شوية الـ
+
+94
+00:08:01,930 --> 00:08:06,810
+renal cortex طبعًا فيه في الأول fibrous capsule هو
+
+95
+00:08:06,810 --> 00:08:08,890
+اللي يمسك أو الـ renal capsule هو اللي يمسك
+
+96
+00:08:08,890 --> 00:08:12,170
+الكلاب بعدين عندنا الـ renal cortex بعدين بيجي 
+
+97
+00:08:12,170 --> 00:08:18,620
+عندنا لتحت منه الـ renal medulla وبعدين في عندنا الـ
+
+98
+00:08:18,620 --> 00:08:24,160
+Renal Pelvis اللي هو الحوض تبع الكلاب، حوض الكِلاب، 
+
+99
+00:08:24,160 --> 00:08:28,780
+هي تقريبًا الثلاث regions اللي موجودة Renal Cortex،
+
+100
+00:08:28,780 --> 00:08:34,210
+Renal Medulla، and Renal Pelvis طبعًا في عندنا بعض 
+
+101
+00:08:34,210 --> 00:08:38,730
+الحاجات كمان هذا يقولنا coronal section coronal
+
+102
+00:08:38,730 --> 00:08:42,090
+section بنشوف في الموضوع ده طبعًا في عندنا بعض
+
+103
+00:08:42,090 --> 00:08:45,490
+الحاجات التانية اللي ممكن نشوفها في الصورة لكن زي
+
+104
+00:08:45,490 --> 00:08:49,270
+ما قلت لكم أنا ما بدنا الآن ندخل deep في طبعًا و
+
+105
+00:08:49,270 --> 00:08:52,870
+هاي زي ما إحنا شايفينه renal pelvis بيطلع في الـ
+
+106
+00:08:52,870 --> 00:08:56,890
+Ureter بيطلع عن طريق الـ Ureter بدناش ندخل deep 
+
+107
+00:08:56,890 --> 00:09:00,390
+في الـ Anatomy و الـ Physiology إحنا بنحاول قدر 
+
+108
+00:09:00,390 --> 00:09:00,790
+الممكن
+
+109
+00:09:03,470 --> 00:09:08,690
+نتعرف على القطع
+
+110
+00:09:08,690 --> 00:09:14,610
+الأساسية تبع الكِلية وبها تقريبًا ممكن يكفينا وخلال 
+
+111
+00:09:14,610 --> 00:09:17,790
+المحاضرة ممكن نلقي الضوء على بعض الحاجات التالية 
+
+112
+00:09:17,790 --> 00:09:21,650
+زي ما قلنا fibrous capsule renal cortex renal
+
+113
+00:09:21,650 --> 00:09:26,670
+medulla renal pelvis وطالع من الـ renal pelvis
+
+114
+00:09:26,670 --> 00:09:29,730
+بيطلع بعد ما بتجمع الـ بول في الحوض تبع الكِلية 
+
+115
+00:09:30,140 --> 00:09:37,080
+بيطلع عن طريق اللي هو الـ ureter للمثانة 
+
+116
+00:09:37,080 --> 00:09:41,180
+الآن
+
+117
+00:09:41,180 --> 00:09:45,200
+اللي إحنا شايفينها في الصورة الصغيرة هاي خليني 
+
+118
+00:09:45,200 --> 00:09:56,240
+أجربها عن وحدة النفرون وحدة النفرون اللي هي 
+
+119
+00:09:59,690 --> 00:10:08,210
+الـ functional unit of the kidney هلجيت 
+
+120
+00:10:08,210 --> 00:10:11,470
+الـ nephron هاي فيه منها في كل كِلية زي ما قلنا
+
+121
+00:10:11,470 --> 00:10:19,610
+مليون بتتكون من الـ 
+
+122
+00:10:19,610 --> 00:10:23,650
+glomerulus 
+
+123
+00:10:23,650 --> 00:10:27,470
+اللي هو إحنا شايفينه الدوائر الحمراء هاي في الصورة
+
+124
+00:10:27,470 --> 00:10:36,590
+هاي الدوائر الحمراء Glomerulus هو عبارة عن شريان صغير 
+
+125
+00:10:36,590 --> 00:10:44,570
+داخل وشريان وريد خارج وطبعًا الدم يدخل ويتصفى ثم 
+
+126
+00:10:44,570 --> 00:10:49,710
+يطلع عن طريق الوريد والبول اللي يتصفى يدخل على
+
+127
+00:10:49,710 --> 00:10:57,340
+اللي هو على الـ Tubules والـ Tubules بتعمل للبول
+
+128
+00:10:57,340 --> 00:11:01,040
+هذا Collecting طبعًا مش كل اللي بتصفيه بتاخده
+
+129
+00:11:01,040 --> 00:11:06,460
+الكِلية لسه في عندنا Process بيصير بحيث أن ترجع
+
+130
+00:11:06,460 --> 00:11:10,640
+كثير من المواد اللي بتصفيه ترجعها للجسم وبصف 
+
+131
+00:11:10,640 --> 00:11:15,700
+البول على اللي إحنا بنعرفه 2 لتر في النهار فعمليه
+
+132
+00:11:15,700 --> 00:11:20,540
+مش بس تصفية إنما كمان عملية تركيز عملية التركيز 
+
+133
+00:11:24,600 --> 00:11:27,700
+مش هندخل على إيش اللي بيصير بالظبط، إنما .. و هذه 
+
+134
+00:11:27,700 --> 00:11:31,180
+فكرة الـ .. الـ .. الـ .. الـ .. الـ Nephron و كيف 
+
+135
+00:11:31,180 --> 00:11:38,920
+بيشتغل طيب، كيف تشتغل الـ kidney؟ نحتاج لـ blood
+
+136
+00:11:38,920 --> 00:11:41,740
+supply طبيعي، brought to the kidney، via renal
+
+137
+00:11:41,740 --> 00:11:45,600
+artery، بدخل عن طريق الـ .. الـ .. الـ .. الـ renal 
+
+138
+00:11:45,600 --> 00:11:49,020
+artery، الـ renal artery stems from the abdominal
+
+139
+00:11:49,020 --> 00:11:52,280
+aorta، زي ما شفنا الـ abdominal aorta، الـ renal
+
+140
+00:11:52,280 --> 00:11:52,980
+artery، 
+
+141
+00:11:55,520 --> 00:11:58,580
+الـrenal artery زي ما احنا شايفينه هان جايينها من
+
+142
+00:11:58,580 --> 00:12:04,580
+وين؟ جايينها من الأبورتا من الأورطة، بعدين 20 ل 25%
+
+143
+00:12:04,580 --> 00:12:09,500
+of cardiac output goes to the kidneys، بروح على
+
+144
+00:12:09,500 --> 00:12:13,460
+الكلية Smaller arteries supply blood to the
+
+145
+00:12:13,460 --> 00:12:17,040
+nephron unit Blood leaves the kidney via renal
+
+146
+00:12:17,040 --> 00:12:21,440
+veins والرينالفينز بتروح، بتصب وين؟ في الـVena
+
+147
+00:12:21,440 --> 00:12:26,780
+Cava، في الـVena Cava، inferior طب الـ kidney إيش 
+
+148
+00:12:26,780 --> 00:12:34,880
+بتساوي؟ الـ kidney هي طبعا أهم حاجة عندها اللي هو
+
+149
+00:12:34,880 --> 00:12:39,200
+السموم بتاعة الجسم السموم مايقصدش السم اللي هو
+
+150
+00:12:39,200 --> 00:12:43,340
+الخارج إنما السموم الناتجة حتى عن التغذية كمان زي
+
+151
+00:12:43,340 --> 00:12:46,780
+ال ammonia و ال creatinine و الurea أو ال waste
+
+152
+00:12:46,780 --> 00:12:51,000
+nitrogenous waste بتعملها excretion بتخرجها من
+
+153
+00:12:51,000 --> 00:12:56,940
+الجسم هذا واحد، تاني regulate blood volume طبعا هي
+
+154
+00:12:56,940 --> 00:13:02,840
+نتيجة أننا نشرب سوائل و نأكل في الآخر في عيننا الـ
+
+155
+00:13:02,840 --> 00:13:06,880
+blood volume بزيد هي بتعود بترجع لوضعه الطبيعي كما
+
+156
+00:13:06,880 --> 00:13:11,700
+يجب و ينبغي مش بس حتى الأملاح حتى الأحماض تحت
+
+157
+00:13:11,700 --> 00:13:16,620
+الجسم هي regulation ال acid base balance ومش بس
+
+158
+00:13:16,620 --> 00:13:19,800
+حتى في ال blood pressure لها دور و كمان في ال red
+
+159
+00:13:19,800 --> 00:13:21,740
+cells production هنشوف كيف
+
+160
+00:13:33,660 --> 00:13:37,320
+يبقى الـ Formation of urine وهي أهم وظيفة من وظائف
+
+161
+00:13:37,320 --> 00:13:40,560
+الكلى Formation of urine of each kidney Contains
+
+162
+00:13:40,560 --> 00:13:44,280
+about one million nephron unit The number does not
+
+163
+00:13:44,280 --> 00:13:48,520
+increase after birth يعني باختصار بمعنى آخر
+
+164
+00:13:48,520 --> 00:13:55,240
+النفرون اللي بيخرب سلامة سلمك وتعيش بيزيدش يعني لو
+
+165
+00:13:55,240 --> 00:13:59,160
+واحد ولدانولد عنده مليون هان و مليون مليون في
+
+166
+00:13:59,160 --> 00:14:02,760
+الكلاوي و مليون في الكلاوي الآن و صار ياخد من عارف
+
+167
+00:14:02,760 --> 00:14:06,120
+أدوية و مسكنات و ماعرفش ايش و هذه كلها بتعمل
+
+168
+00:14:06,120 --> 00:14:11,260
+damage للنفرون صار عنده 200 ألف هان و 150 ألف هان
+
+169
+00:14:11,260 --> 00:14:16,410
+مثلا وهدول يدول بيكفوا لأن كأرقام ما تدقوش عليها بس
+
+170
+00:14:16,410 --> 00:14:20,630
+أنا بقصد كمثل مش بتجددوا أو بيأكل أنواع أكل بتحسن
+
+171
+00:14:20,630 --> 00:14:24,610
+لعدد الـ Nephrons لأ لأ سلامة سلمك وتعيش فيش
+
+172
+00:14:24,610 --> 00:14:28,570
+نفرون جديدة بتنبنى زي مشكلة الأعصاب الخلية اللي
+
+173
+00:14:28,570 --> 00:14:34,390
+بتموت مافيش حاجة تسد عنها ها إيش صحيح الكلية بتشتغل
+
+174
+00:14:34,390 --> 00:14:37,670
+أكتر لكن في يوم من الأيام بتعود و بتهلك فعشان هيك
+
+175
+00:14:37,670 --> 00:14:41,350
+لازم الواحد يدير باله على الكليتين من ناحية
+
+176
+00:14:41,350 --> 00:14:46,870
+المأكلات، السموم، الأدوية، الـdrugs، الـinfections
+
+177
+00:14:46,870 --> 00:14:52,730
+على سبيل المثال They cannot be replaced if damaged
+
+178
+00:14:52,730 --> 00:15:00,310
+الكلام واضح وسهل الجتنفرون هذا بتكون من two parts
+
+179
+00:15:00,310 --> 00:15:05,530
+أو components الأولى رينال تبيول والثانية vascular
+
+180
+00:15:05,530 --> 00:15:08,570
+تبيول زي ما احنا شايفين هنا الرسم اللي فوق
+
+181
+00:15:13,680 --> 00:15:18,980
+ودخل الشريان الشريان طبعاً الصغيرة دخلت على الـ
+
+182
+00:15:18,980 --> 00:15:21,360
+Glomerulus الـ Glomerulus هي الوحدة اللي فيها
+
+183
+00:15:21,360 --> 00:15:26,540
+عملية تجميع على الشريان و الأوردة و بتصير عملية
+
+184
+00:15:26,540 --> 00:15:33,000
+الـ Bowman Capsule فيها و الـ Glomerulus و بتبدأ
+
+185
+00:15:33,000 --> 00:15:39,710
+عملية التصفية خلال اللي هو الـ Tubular System يعني
+
+186
+00:15:39,710 --> 00:15:43,130
+في الأول الـ Vascular و بعدين الـ Tubular System
+
+187
+00:15:43,130 --> 00:15:48,970
+في الـ Tubular System بتجمع الـ Ball بعد ما يتصفى
+
+188
+00:15:48,970 --> 00:15:52,390
+في حاجة اسمها Collecting Duct و الـ Collecting
+
+189
+00:15:52,390 --> 00:15:56,210
+Duct بتجمع بتجمع في الآخر بتروح عندنا على الـ
+
+190
+00:15:56,210 --> 00:16:01,570
+Renal Pelvis و بيصير عملية تخرج للـ Ball من هناك
+
+191
+00:16:06,820 --> 00:16:13,740
+الـUrine يصبح في نفرون و يبقى استرال، مايعني استرال؟
+
+192
+00:16:13,740 --> 00:16:17,700
+يعني نظيف، معقم، ولا ورن، لكن هو معقم، معقم،
+
+193
+00:16:17,700 --> 00:16:22,480
+مايعني معقم؟ مايعني ليس فيه بكتيريا، 95% منه ماء
+
+194
+00:16:22,480 --> 00:16:26,630
+والباقي وست والباقي يوريا أمونيا كرياتينين اللي هي
+
+195
+00:16:26,630 --> 00:16:31,170
+نتروجيناس containing waste نتيجة هضم البروتين وهضم
+
+196
+00:16:31,170 --> 00:16:35,750
+الدهن و هضم الأكل والسموم وكذا كلها بتبقى موجودة في
+
+197
+00:16:35,750 --> 00:16:38,650
+الـBall وبرضه الـBall فيه electrolytes فيه أملاح
+
+198
+00:16:38,650 --> 00:16:43,790
+اللي بيصير يا جماعة برضه باختصار جدا جدا في تلاتة
+
+199
+00:16:43,790 --> 00:16:46,810
+process في عملية تكوين الـBall تلت حاجات بتصير
+
+200
+00:16:46,810 --> 00:16:51,560
+الأولى اللي هو الـ Glomerular Filtration اللي عملية
+
+201
+00:16:51,560 --> 00:16:55,000
+التصفية اللي بتصير في الـ Glomerulus اللي هي
+
+202
+00:16:55,000 --> 00:16:59,280
+الجزئية الحمرة اللي هي الـ Glomerulus الجزئية
+
+203
+00:16:59,280 --> 00:17:03,490
+الحمرة هذه اللي احنا شايفينها زي الشبكة جوا هذه
+
+204
+00:17:03,490 --> 00:17:07,430
+اسمها Glomerular Filtration عملية تصفية تصفية
+
+205
+00:17:07,430 --> 00:17:11,150
+filtration حاجة تانية اللي بتصير Tubular
+
+206
+00:17:11,150 --> 00:17:15,730
+Reabsorption راح البول طبعا كمية كبيرة بيصيرها
+
+207
+00:17:15,730 --> 00:17:20,890
+عملية تصفية بتروح على الـ Tubular وبيصير عملية
+
+208
+00:17:20,890 --> 00:17:25,710
+إعادة امتصاص لبعض الحاجات اللي صفاها اللي هو
+
+209
+00:17:25,710 --> 00:17:29,530
+Glomerulus وبعد هيك اللي بيصير أنه بيصير عندنا
+
+210
+00:17:31,600 --> 00:17:34,840
+Secretion لبعض الحاجات اللي اكتشف الجسم انه بدوش
+
+211
+00:17:34,840 --> 00:17:38,780
+هيها بعملها عملية Secretion يبقى تلاتة مراحل بتسير
+
+212
+00:17:38,780 --> 00:17:44,220
+في عملية تبوين الـBall تلاتة Glomerular Filtration,
+
+213
+00:17:44,640 --> 00:17:49,400
+Tubular Reabsorption و Tubular Secretion احنا طبعا
+
+214
+00:17:49,400 --> 00:17:53,640
+كما تشايفين بنحكي من كل جستان زهرة عمليا يعني
+
+215
+00:17:53,640 --> 00:17:56,520
+بندخل من حاجة بنطلع في حاجة بس عشان ألقى الضوء
+
+216
+00:17:56,520 --> 00:17:59,080
+عشان لما نحكي بعد هيك بتبقى أنتوا إيش في الأمراض
+
+217
+00:17:59,080 --> 00:18:01,620
+بتبقى عندكوا فكرة عن إيش بنحكي الـUrine testing
+
+218
+00:18:01,620 --> 00:18:04,900
+الفحص تبع الـBall كتير من الناس بييجي ويقولك والله
+
+219
+00:18:04,900 --> 00:18:07,640
+أنا عندي حرجان في الـBall بتقوله روح اعمل فحص الـBall
+
+220
+00:18:08,180 --> 00:18:11,720
+في فحص الـBall بتلاقي ورقة الـBall فيها جزءين
+
+221
+00:18:11,720 --> 00:18:15,800
+جزء مكتوب عليه Microscopic Examination وجزء مكتوب
+
+222
+00:18:15,800 --> 00:18:22,260
+عليه اللي هو الـUrine dipstick اللي هو بفحص الـ
+
+223
+00:18:22,260 --> 00:18:27,580
+Ball بشريط شريط عليه ست، سبعة، تمان، تسعة حاجات
+
+224
+00:18:27,580 --> 00:18:33,480
+حسب قداش ايش الشريط هذا عندهم وبشوف الـ .. الـ ..
+
+225
+00:18:34,790 --> 00:18:42,030
+الالتهابات مبدئيا مبدئيا بتدي مفتاح السكر حموضة
+
+226
+00:18:42,030 --> 00:18:49,880
+قاعدية بشوف كل الحاجات هذه لكن الأصل أنه هو ممكن
+
+227
+00:18:49,880 --> 00:18:53,200
+يطلع كمان تحت الـmicroscope Microscopic
+
+228
+00:18:53,200 --> 00:18:56,960
+examination هو فحص بول و بحطه تحت الـmicroscope و
+
+229
+00:18:56,960 --> 00:19:02,480
+بشوف إذا في أي حاجات دم كمان بشوفها طبعا ممكن
+
+230
+00:19:02,480 --> 00:19:05,460
+أعمله Culture and Sensitivity بنزرع الـUrine في
+
+231
+00:19:05,460 --> 00:19:09,100
+Culture في مزرعة و بعدين Culture and Sensitivity
+
+232
+00:19:09,100 --> 00:19:12,880
+بنشوف بالـSensitivity إذا طلع في عندي بكتيريا أنه
+
+233
+00:19:12,880 --> 00:19:17,140
+أحسن الـAntibiotic أو الـAntibiotics واستجابته
+
+234
+00:19:17,140 --> 00:19:20,360
+أو استجابة البكتيريا هذه للـAntibiotics وممكن بعض
+
+235
+00:19:20,360 --> 00:19:24,500
+الأحيان أعمل 24 hours Urine testing على
+
+236
+00:19:24,500 --> 00:19:27,820
+أساس أشوف بعد تجميع 24 ساعة بعض الحاجات
+
+237
+00:19:27,820 --> 00:19:32,680
+زي البروتين والكالسيوم والحاجات هذه بعدين بعد ال
+
+238
+00:19:32,680 --> 00:19:32,960
+kidney
+
+239
+00:19:36,250 --> 00:19:38,910
+الـUreters و الـUrinary Bladder و الـUrethra
+
+240
+00:19:38,910 --> 00:19:44,730
+الـUreters شغلتها بس Transport urine هي عبارة عن
+
+241
+00:19:44,730 --> 00:19:48,670
+حاجة عضلية لأن الأنابيب هذه الـUreters عبارة عن
+
+242
+00:19:48,670 --> 00:19:55,190
+حاجة عضلية يعني عشان هيك لما حصوة بتجي في جلب
+
+243
+00:19:55,190 --> 00:20:02,750
+الـUreters بتعملنا وجع فظيع عادة والبول بتحرك فيها
+
+244
+00:20:03,290 --> 00:20:12,010
+كانت نتيجة لـGravity لأنه من فوق لتحت وهذا
+
+245
+00:20:12,010 --> 00:20:15,310
+الجزئية الأولى والجزئية الثانية نتيجة أنه فيها
+
+246
+00:20:15,310 --> 00:20:17,670
+Muscles والـMuscles أنتو عارفين بيصير عملية
+
+247
+00:20:17,670 --> 00:20:23,910
+Peristaltic في الـUreters وزي ما قلنا عشان هيك لما
+
+248
+00:20:23,910 --> 00:20:28,830
+يكون في حصوى عادة والـUreter يصير يعمل
+
+249
+00:20:28,830 --> 00:20:33,190
+Peristaltic أو Contraction على الحصوة هيبدينا وجع
+
+250
+00:20:33,190 --> 00:20:37,710
+مهول متعدد وفي بعد هيك بنزل وين؟ في الـBladder الـ
+
+251
+00:20:37,710 --> 00:20:42,370
+Bladder إيه شغلتها؟ Stores urine temporarily until
+
+252
+00:20:42,370 --> 00:20:46,550
+Elimination لحد ما يصير عملية التبول هي بس بتعمل
+
+253
+00:20:46,550 --> 00:20:52,610
+Storing للـUrine ويم موجودة في اللي هي Located
+
+254
+00:20:52,610 --> 00:20:57,550
+behind the symphysis pubis و a distended bladder
+
+255
+00:20:57,550 --> 00:21:00,730
+أو full bladder can be palpated above the
+
+256
+00:21:00,730 --> 00:21:03,090
+symphysis in the abdominal cavity اللي الواحد لو
+
+257
+00:21:03,090 --> 00:21:06,350
+عنده المثانة ملانة ممكن تحسها عند أي طفل أو عند أي
+
+258
+00:21:06,350 --> 00:21:09,370
+واحد كبير فوق منطقة اللي هي العانة
+
+259
+00:21:14,040 --> 00:21:18,880
+فيقول عنها عملية التبول ميكتوريشن أو Urination
+
+260
+00:21:18,880 --> 00:21:24,740
+ميكتوريشن أو Urination وهي عبارة عن Expelling
+
+261
+00:21:24,740 --> 00:21:29,500
+Urine from the bladder عملية إخراج البول من اسمها
+
+262
+00:21:29,500 --> 00:21:34,840
+Urination واكتشاف يبدأ الواحد يحس إنه بده يروح
+
+263
+00:21:34,840 --> 00:21:39,360
+الحمام عند ما يصير فيه في الـBladder 200 ملي كده 
+
+264
+00:21:39,360 --> 00:21:42,540
+أنا الـ200 ملي؟ شوفت علبة الكولا على سبيل المثال؟
+
+265
+00:21:43,240 --> 00:21:46,720
+ثلثين علبة الكولا، علبة الكولا اللي هي 333
+
+266
+00:21:46,720 --> 00:21:52,160
+طولتينها تقريبا، هذه عبارة عن 200 ملي، لو صار في
+
+267
+00:21:52,160 --> 00:21:55,960
+إنه جد علبة الكولا لي 300 ملي في الـBladder، بيصير
+
+268
+00:21:55,960 --> 00:21:59,200
+الواحد مش مرتاح، بيصير خلاص، يعني أنا لازم أروح
+
+269
+00:21:59,200 --> 00:22:07,540
+الحمام، مش مرتاح، الآن وقتش بقول والله المثانة
+
+270
+00:22:07,540 --> 00:22:14,380
+تقريبا ملانة لما يكون عندي نص لتر، 500 ملي، وOver
+
+271
+00:22:14,380 --> 00:22:19,300
+-extended تبقى لما تكون ملي ألف ملي يعني لتر
+
+272
+00:22:19,300 --> 00:22:23,200
+تصوروا لتر في جلب المثانة وهي بتعمل وجع فظيع ليش؟
+
+273
+00:22:23,200 --> 00:22:27,580
+لأن المثانة هي زي البلون في الآخر البلون بفتح معاك
+
+274
+00:22:27,580 --> 00:22:32,540
+البلون لما تنفخه بتديه بتديه لكن إلى حد معين بعدين
+
+275
+00:22:32,540 --> 00:22:37,730
+بنبطل لكن المثانة هي عبارة عن أرجاني عضو وفيه أعصاب
+
+276
+00:22:37,730 --> 00:22:42,590
+فانت كل ما عملتله Extension أكتر بيصير له
+
+277
+00:22:42,590 --> 00:22:45,330
+Distention أكتر و الـDistention بيعملنا Pain
+
+278
+00:22:45,330 --> 00:22:51,210
+Pain واحنا بنعبي في المثانة و Pain كمان عند منفض
+
+279
+00:22:51,210 --> 00:22:55,810
+المثانة كتير مننا بعد ما يكون فعلا كان لازم يروح
+
+280
+00:22:55,810 --> 00:23:00,720
+الحمام كتير الـUrine بنلاقي إنه بعد ما بيروح الحمام 
+
+281
+00:23:00,720 --> 00:23:03,720
+برضه بيظل فيه وجع، ليش؟ لأن المثانة بدأت ترجع
+
+282
+00:23:03,720 --> 00:23:07,380
+لوضعها الطبيعي، وعشان ترجع لوضعها الطبيعي بتعمللي 
+
+283
+00:23:07,380 --> 00:23:08,300
+pain بعض الأحيان
+
+284
+00:23:12,290 --> 00:23:15,790
+باكتيريا في دماغك مرتفعة كل أربع ساعات عشان هيك
+
+285
+00:23:15,790 --> 00:23:19,150
+احنا بنقول واحد مش لازم يحبس البول ليش؟ لأنه كل ما
+
+286
+00:23:19,150 --> 00:23:22,090
+حبسنا البول وهو مشكلة الأولاد والبنات في المدارس
+
+287
+00:23:22,090 --> 00:23:26,430
+اللي بيجرفوا يروحوا على الحمامات أنه بيحبس البول
+
+288
+00:23:26,430 --> 00:23:29,530
+أربع، خمس، ست ساعات طبعا هذا بيخلي عند الطفل
+
+289
+00:23:29,530 --> 00:23:34,310
+liable أنه يصير فيه عنده urinary tract infection
+
+290
+00:23:34,310 --> 00:23:38,450
+التهيبات في البولزي ما قلنا الـ Stimulated اللي هو
+
+291
+00:23:38,450 --> 00:23:41,910
+عملية الـ Urination By Stretch Receptors يعني كل
+
+292
+00:23:41,910 --> 00:23:48,550
+ما الحجم كمية الـ Bladder اللي موجودة هي اللي بتديني
+
+293
+00:23:48,550 --> 00:23:52,070
+Reflex 
+
+294
+00:23:52,070 --> 00:23:59,090
+بتعمل Stimulation للـ Stretch Receptors بتعمل
+
+295
+00:23:59,090 --> 00:24:04,130
+Stimulation وبتدى إشارة للمخ والمخ يطلب عملية الـ
+
+296
+00:24:04,130 --> 00:24:09,080
+Micturition أو التفريرفي حاجتين لازم نعرفهم الـ
+
+297
+00:24:09,080 --> 00:24:12,740
+Retention هو عبارة عن inability to void عدم
+
+298
+00:24:12,740 --> 00:24:20,220
+القدرة على التبول وهذا مختلف يا جماعة عن ال
+
+299
+00:24:20,220 --> 00:24:23,760
+suppression ال retention موجود بول لكن مش قادر
+
+300
+00:24:23,760 --> 00:24:29,120
+أطلعه في ال suppression مابيصيرش عملية تكوين بول
+
+301
+00:24:29,120 --> 00:24:33,710
+من الأصل كدا بالكدا الفرق بين الأتنينوهذه تصبح
+
+302
+00:24:33,710 --> 00:24:36,550
+الـ suppression نتيجة Kidney dysfunction كدني مش
+
+303
+00:24:36,550 --> 00:24:41,250
+شغالة بتفلترش بول لكن ال retention أنا فيه بول لكن
+
+304
+00:24:41,250 --> 00:24:44,310
+مش قادر أطلعه وهذه نتيجة بعض الأحيان الانستيزيا
+
+305
+00:24:44,310 --> 00:24:47,130
+post-operative أو مشكلة في البلد
+
+306
+00:24:54,110 --> 00:24:58,210
+أز وي أيش كل ما نكبر بإيش تمانين تمانين في المية
+
+307
+00:24:58,210 --> 00:25:01,890
+reduction of the nephron units لعمره تمانين سنة
+
+308
+00:25:01,890 --> 00:25:06,210
+بتلاقي عدد ال nephrons إذا مافيش أمراض وفيش كذا
+
+309
+00:25:06,210 --> 00:25:11,010
+بالوضع الطبيعي بتجيل نتيجة الأمر وطبعا decreased
+
+310
+00:25:11,010 --> 00:25:15,730
+ability to concentrate urine مش بس حتى الـ urine
+
+311
+00:25:15,730 --> 00:25:18,930
+bladder شرنج عشان هيك بتلاقي الاختيارية والكبار في
+
+312
+00:25:18,930 --> 00:25:22,090
+العمر كل شويه بيروح الحمام غير بالنسبة للرجال عشان
+
+313
+00:25:22,090 --> 00:25:28,750
+موضوع البرستاتا لكن في موضوع ال urine bladder تصغر
+
+314
+00:25:28,750 --> 00:25:37,250
+عند كل ما كبر الواحد لست قادرة على التفكير وتتسكّر
+
+315
+00:25:37,250 --> 00:25:43,190
+البلدر مثل الناس الصغيرة، لذلك يجب أن يتجاوز الناس
+
+316
+00:25:43,190 --> 00:25:46,050
+الأكبر بشكل عام في الحمام بشكل عام وفي الليلة اللي
+
+317
+00:25:46,050 --> 00:25:47,470
+بيصحى بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام
+
+318
+00:25:47,470 --> 00:25:51,710
+بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل
+
+319
+00:25:51,710 --> 00:25:52,230
+عام بشكل عام بشكل عام بشكل عام بشكل عام بشكل عام
+
+320
+00:25:52,230 --> 00:25:57,490
+بشكل عام بشكل عام بشكل عوطبعاً نتيجة الـ weakening
+
+321
+00:25:57,490 --> 00:26:01,590
+الـ weakened muscles ممكن يصير increase in urinary
+
+322
+00:26:01,590 --> 00:26:07,820
+incontinence اللي هو التبول عند الكباربالنسبة للـ
+
+323
+00:26:07,820 --> 00:26:13,100
+Disorders of the Urinary System الآن هنحكي عن حاجة
+
+324
+00:26:13,100 --> 00:26:17,660
+واحدة في المحاضرة هذه وبكرا أو خلال الأسبوع أو
+
+325
+00:26:17,660 --> 00:26:21,660
+بداية الأسبوع هنحكي عن باقي الأمراض هحكي الآن عن
+
+326
+00:26:21,660 --> 00:26:24,840
+الـ Kidney Stones احنا كنا الـ Stones اتعرفنا
+
+327
+00:26:24,840 --> 00:26:32,980
+عليها في وين؟ صحيح، اللي هو في الـ Gallbladder 
+
+328
+00:26:32,980 --> 00:26:33,520
+Stones
+
+329
+00:26:36,180 --> 00:26:40,740
+الأن نحن نقول الـ kidney stones نفرو ليثيازز
+
+330
+00:26:40,740 --> 00:26:44,140
+kidney stones اللي بيقولون عن كالكولاي برضه are
+
+331
+00:26:44,140 --> 00:26:48,140
+hardening mineral deposits that form in the
+
+332
+00:26:48,140 --> 00:26:56,140
+kidneys هي عبارة عن حاجات ملحية بتتجمع
+
+333
+00:26:56,140 --> 00:27:04,640
+و بتتيبس وبتكون نفسها في ال kidneys وطبعاً معروف
+
+334
+00:27:04,640 --> 00:27:09,960
+إنه كل إنه هذي بتترسب ترسب when waste materials in
+
+335
+00:27:09,960 --> 00:27:13,900
+the urine don't dissolve completely crystals and
+
+336
+00:27:13,900 --> 00:27:17,680
+kidney stones are a likely to form small stones
+
+337
+00:27:17,680 --> 00:27:24,760
+can cause some disconformوهي تنتقل من جسمها كل ما
+
+338
+00:27:24,760 --> 00:27:28,820
+زغرت ممكن تطلع لواحدة الحصوة لكن في بعض الأحيان ما
+
+339
+00:27:28,820 --> 00:27:31,280
+تطلع لواحدة الحصوة يعني زي ما احنا شايفين في
+
+340
+00:27:31,280 --> 00:27:36,080
+الصورة هاي اللي في الحوض تبع الحوض الكيلة وعبارة
+
+341
+00:27:36,080 --> 00:27:41,100
+عن stone ماخد كل الحوض
+
+342
+00:27:41,100 --> 00:27:44,560
+تبع الكيلة زي ما احنا شايفينها تحت في الصورة
+
+343
+00:27:49,120 --> 00:27:58,020
+بغض النظر عن حجم الـ stone الـ stones may pass out
+
+344
+00:27:58,020 --> 00:28:00,540
+of the kidneys and become lodged in the ureter هذه
+
+345
+00:28:00,540 --> 00:28:04,140
+المصيبة الكبيرة أن الحصوة الصغيرة كما نرى في
+
+346
+00:28:04,140 --> 00:28:09,220
+الصورة هنا تكونت في الحوض ولسبب الأسباب راحت وعملت
+
+347
+00:28:09,220 --> 00:28:14,970
+ليه lodging أو حجزت ليه الـ ureter لما تحجز
+
+348
+00:28:14,970 --> 00:28:19,170
+الـUreter، ما يحصل؟ الـUrine يتكوّن في الكلة ويجب
+
+349
+00:28:19,170 --> 00:28:24,130
+أن يطلع و لا يجد ممر فأين نحجز الـUrine كله؟ في حوض
+
+350
+00:28:24,130 --> 00:28:29,130
+الكلة وبتصير الكلة تكبر تكبر تكبر بما نقول عنه
+
+351
+00:28:29,130 --> 00:28:35,570
+بعمل لي نفرو الـUreter
+
+352
+00:28:35,570 --> 00:28:38,650
+to the bladder and cause severe pain مش بس
+
+353
+00:29:03,250 --> 00:29:04,650
+بالدينة اللي هو
+
+354
+00:29:11,370 --> 00:29:16,590
+بتدينا Hydronephrosis زي Hydrocephalus لما الراس
+
+355
+00:29:16,590 --> 00:29:20,010
+صار فيها ميه كتير نتيجة تضيق هذه بيصير عنها
+
+356
+00:29:20,010 --> 00:29:23,070
+Hydronephrosis
+
+357
+00:29:23,070 --> 00:29:28,090
+الأنواع تبعت الـ Stones زي ما أحنا شايفين الـ
+
+358
+00:29:28,090 --> 00:29:32,870
+Types تبعها الـ Calcium Stones وهذا الـ Most
+
+359
+00:29:32,870 --> 00:29:36,070
+Common Calcium Stones الـ Uric Acid الناس اللي
+
+360
+00:29:36,070 --> 00:29:43,260
+بتاكل لحمة كتير Cystine Stones وStruvite Stones،
+
+361
+00:29:43,260 --> 00:29:47,720
+أجل، أنواعها لكن هو الـMost Common اللي هي
+
+362
+00:29:47,720 --> 00:29:51,480
+الـCalcium
+
+363
+00:29:51,480 --> 00:29:54,600
+Stones According to the، هذه بس الإحصائيات عشان
+
+364
+00:29:54,600 --> 00:29:58,520
+تعرف كيف الدنيا، كيف الموضوع، لكن هي غير مهمة
+
+365
+00:29:58,520 --> 00:30:02,440
+كأرقام، لكن عشان تعرفوا أنه كثير بتيجي قضية
+
+366
+00:30:02,440 --> 00:30:05,220
+الـStones According to the U.S. National
+
+367
+00:30:05,220 --> 00:30:09,430
+Institutes of Health، one in ten people في عشرةمن كل
+
+368
+00:30:09,430 --> 00:30:14,830
+عشرة، واحد تطور كدنيا صغيرة خلال زمان حياته والـ
+
+369
+00:30:14,830 --> 00:30:20,390
+«renal stones» تعتبر حوالي سبعة لعشرة من كل
+
+370
+00:30:20,390 --> 00:30:25,730
+ألف مدرسات المستشفى، تصوروا؟ يعني مش سهل الموضوع،
+
+371
+00:30:25,730 --> 00:30:28,990
+الـ kidney stones are most prevalent in patients
+
+372
+00:30:28,990 --> 00:30:33,370
+between ages 30 and 45 وبعد اللي هو
+
+373
+00:30:33,370 --> 00:30:40,330
+العمر الخمسين، بيصير له declineالـ Causes and Risk
+
+374
+00:30:40,330 --> 00:30:45,610
+Factors، عدم
+
+375
+00:30:45,610 --> 00:30:47,830
+أخذ سوائل كثير، الناس اللي بتشربش، الـ
+
+376
+00:30:47,830 --> 00:30:50,750
+dehydration، الجفاف اللي بيصير، reduce urinary
+
+377
+00:30:50,750 --> 00:30:55,430
+flow and volume، بعض ال .. ال .. ال .. ال ..
+
+378
+00:30:55,430 --> 00:30:58,230
+certain chemical levels in the urine that are too
+
+379
+00:30:58,230 --> 00:31:00,690
+high زي الـ Calcium و الـ Oxalate و الـ Uric Acid
+
+380
+00:31:00,690 --> 00:31:06,060
+أو too low زي الـ Citrate أو أي شيء يقوم بتحطيم أو
+
+381
+00:31:06,060 --> 00:31:09,340
+تقوم بتحطيم مستوى الـ Salt أو الـ Salt تقوم
+
+382
+00:31:09,340 --> 00:31:13,280
+بتحطيم الـ Salt أو الـ Salt تقوم بتحطيم
+
+383
+00:31:13,280 --> 00:31:16,560
+الـ Salt أو الـ Salt ما هي الـ Symptoms and
+
+384
+00:31:16,560 --> 00:31:19,600
+Signs؟ بيلاقي Hematuria إيش قولنا احنا يومها
+
+385
+00:31:19,600 --> 00:31:22,880
+Hematuria؟ قولنا Blood in Urine و Hematuria لإيش؟
+
+386
+00:31:22,880 --> 00:31:27,060
+لأنه هذه حصوة حصوة إلا حفاف ممكن تجرح تجرح يعني
+
+387
+00:31:27,060 --> 00:31:30,580
+سيية للدم دم يعني نزل في البول وهذه Hematuria
+
+388
+00:31:30,580 --> 00:31:34,860
+Nausea Vomiting ردة فعل Pain during urination
+
+389
+00:31:34,860 --> 00:31:39,360
+Burning بيصير عملية Burning أو Dysuria Tenderness
+
+390
+00:31:43,670 --> 00:31:47,630
+هي حوالين الحصوات هي هذا الجسم غريب ممكن يتكون
+
+391
+00:31:47,630 --> 00:31:51,350
+بكتيريا والبكتيريا هي التي تعملنا infection
+
+392
+00:31:53,990 --> 00:31:58,530
+Kidney function tests زي blood urea and creatinine فحص
+
+393
+00:31:58,530 --> 00:32:02,670
+بول وممكن نعمل ultrasound للأبضمن أو للكدنى زي ما
+
+394
+00:32:02,670 --> 00:32:06,650
+نشاهد في الـ ultrasound الفكرة اللي هي الحصوة الـ
+
+395
+00:32:06,650 --> 00:32:10,790
+calculus والشدوينج اللي هو الضل تبعها اللي بنشوفه
+
+396
+00:32:10,790 --> 00:32:11,310
+في الـ ultrasound
+
+397
+00:32:16,630 --> 00:32:22,990
+بنعمل صورة أشياء في الـ kidney stones مثلًا في
+
+398
+00:32:22,990 --> 00:32:27,670
+الدوائر بتبين في الـ X-ray
+
+399
+00:32:30,560 --> 00:32:33,880
+العلاج حقيقية Acute Treatment of Urinary Calculi
+
+400
+00:32:33,880 --> 00:32:36,480
+Consists of Hydration سوائل كثير كثير كثير and
+
+401
+00:32:36,480 --> 00:32:39,740
+Analgesia هذا ساعة ما تصبح المشكلة ساعة ما ايش
+
+402
+00:32:39,740 --> 00:32:43,940
+بتصبح المشكلة يعني هذي acute The treatment that
+
+403
+00:32:43,940 --> 00:32:47,120
+applies to all metabolic stones conditions دي
+
+404
+00:32:47,120 --> 00:32:49,780
+Obstructive abnormalities that require repair الآن
+
+405
+00:32:49,780 --> 00:32:53,880
+إذا والله واحد عنده مشكلة في الحالب أصلا هذا طبعا
+
+406
+00:32:53,880 --> 00:32:58,380
+بده بده حل مشكلة الحالب بصورة عامةوهو ممكن طبعاً
+
+407
+00:32:58,380 --> 00:33:03,180
+دايما قلنا نعمل lithotripsy عملية تروح
+
+408
+00:33:03,180 --> 00:33:08,040
+اليورولوجيست على طبيب مثالك وممكن نعمل lithotripsy
+
+409
+00:33:08,040 --> 00:33:12,460
+قلنا هو عبارة عن عملية تفتيت وطبعا accordingly حسب
+
+410
+00:33:12,460 --> 00:33:15,720
+إذا في عندي obstruction، عندي مشاكل، ممكن ينعمل
+
+411
+00:33:15,720 --> 00:33:22,230
+surgical repair وهيك بنبقى أتحدثنا كمان عن الـ
+
+412
+00:33:22,230 --> 00:33:26,090
+Prolithiasis إن شاء الله تعالى الجزء التاني هنتحدث
+
+413
+00:33:26,090 --> 00:33:32,110
+عن الـ Urinary Tract Infection وهنتحدث عن Acute
+
+414
+00:33:32,110 --> 00:33:39,930
+Renal Failure هنتحدث عن Chronic Renal Failure
+
+415
+00:33:41,300 --> 00:33:47,120
+وبعد هيك هنتحدث عن بعض الـ Hemodialysis كيف بالعمل
+
+416
+00:33:47,120 --> 00:33:49,760
+و بنبقى المرة اللي جاية ان شاء الله بنخلص الجزء
+
+417
+00:33:49,760 --> 00:33:52,820
+التالي بإذن الله تعالى اتمنى لكوا يوم سعيد ان شاء
+
+418
+00:33:52,820 --> 00:33:53,300
+الله تعالى
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bf33ea6262602f9498be5c0b5edb5012f1a3ea1f
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w.srt
@@ -0,0 +1,1703 @@
+1
+00:00:01,920 --> 00:00:04,040
+بسم الله الرحمن الرحيم الحمد لله رب العالمين والصلاة 
+
+2
+00:00:04,040 --> 00:00:06,820
+والسلام على سيدنا محمد وعلى آله وصحبه أجمعين، لأن 
+
+3
+00:00:06,820 --> 00:00:09,100
+كمان مرة اليوم إن شاء الله تعالى طول محمد أبو ندا 
+
+4
+00:00:09,100 --> 00:00:14,140
+معكم في محاضرة جديدة الآن، بنبدأ ندخل في أمراض 
+
+5
+00:00:14,140 --> 00:00:17,480
+القلب، الـ Coronary Artery Disease أو الـ Ischemic 
+
+6
+00:00:17,480 --> 00:00:22,780
+Heart Disease نفس الاسم، لأن الإصابة بتبقى في الـ
+
+7
+00:00:22,780 --> 00:00:25,860
+Coronaries، أيش الـ Coronaries يعني الشرايين التاجية
+
+8
+00:00:26,760 --> 00:00:29,840
+ماذا يعني شريان تاجي؟ شريان تاجي يعني هو زي ما 
+
+9
+00:00:29,840 --> 00:00:35,320
+أقولها ضرورة ثمّامة، أو يعني هو أفضل شيء تقريباً في
+
+10
+00:00:35,320 --> 00:00:39,780
+القلب، ليش؟ لأن عشان أشغل القلب لابد أنه يغذي
+
+11
+00:00:39,780 --> 00:00:46,020
+القلب، أغذيه بإيش؟ أغذيه بـ Nutrients، بالـ Oxygen،
+
+12
+00:00:46,020 --> 00:00:49,120
+بالـ Vitamins، بالحاجات هذه، وكيف هاتصلوا؟ 
+
+13
+00:00:49,120 --> 00:00:52,690
+يصلوا زي وزي أي بالرغم من أنه هو القلب اللي بيبعت
+
+14
+00:00:52,690 --> 00:00:59,110
+دم للجسم كله إلا أنه نفسه يحتاج إلى الدم عن طريق 
+
+15
+00:00:59,110 --> 00:01:03,050
+كيف؟ عن طريق الـ Coronaries اللي هو الـ Coronary Artery
+
+16
+00:01:03,050 --> 00:01:10,510
+Disease الآن، أي مشكلة بتصير جوات الـ Coronaries في 
+
+17
+00:01:10,510 --> 00:01:16,470
+الغالب سببها Ischemic، يعني الـ Obstruction 
+
+18
+00:01:16,470 --> 00:01:22,830
+الـ Obstruction ممكن يكون نتيجة تضيق في الشريان نفسه 
+
+19
+00:01:22,830 --> 00:01:29,010
+وممكن نتيجة Thrombus building على سبيل المثال، يبقى What
+
+20
+00:01:29,010 --> 00:01:33,390
+is Coronary Artery Disease is a narrowing of the 
+
+21
+00:01:33,390 --> 00:01:38,610
+Coronary Arteries that prevents adequate blood 
+
+22
+00:01:38,610 --> 00:01:43,050
+supply to the heart muscles، كمان مرة عبارة عن 
+
+23
+00:01:43,050 --> 00:01:46,570
+Narrowing بغض النظر الـ Ischemic أو الـ Coronary
+
+24
+00:01:46,570 --> 00:01:49,770
+Heart Disease أو Coronary Artery Disease، Narrowing
+
+25
+00:01:49,770 --> 00:01:55,390
+of the Coronary Arteries اللي هذه بتوصل لي الدم
+
+26
+00:01:55,390 --> 00:01:59,830
+لعضلات القلب، وفي الغالب في الغالب في الغالب
+
+27
+00:01:59,830 --> 00:02:03,710
+usually caused by Atherosclerosis، أيش الـ
+
+28
+00:02:03,710 --> 00:02:09,850
+Atherosclerosis اللي هو بنقول عنه أيش؟ تكلس الشرايين
+
+29
+00:02:10,810 --> 00:02:14,070
+it may progress to the point where the heart 
+
+30
+00:02:14,070 --> 00:02:17,190
+muscle is damaged due to the lack of blood supply
+
+31
+00:02:17,190 --> 00:02:22,670
+طبيعي، أنا مكان قاعد مش قادر أوصله دم نتيجة الـ
+
+32
+00:02:22,670 --> 00:02:26,610
+Obstruction اللي صار، فالـ Muscle Cells بيصير لها
+
+33
+00:02:26,610 --> 00:02:30,150
+Damaging وبعد هيك بيصير عندنا ما يسمى بالإيش؟ بالـ 
+
+34
+00:02:30,150 --> 00:02:35,330
+Infraction، طبعاً لما يصير عندك Infraction والعضلة
+
+35
+00:02:35,330 --> 00:02:43,020
+هذه ما وصلهاش دم بيصير حتى الـ Electric Activity 
+
+36
+00:02:43,020 --> 00:02:49,280
+تبعها بتصير مش سليمة، طبيعي، وبعدين حتى الخلية تحت
+
+37
+00:02:49,280 --> 00:02:53,300
+القلب تفشل، ولما يكون عندي عدد من الخلايا فشلت 
+
+38
+00:02:53,300 --> 00:02:56,460
+بيصير عندي حاجة اسمها Heart Failure، يبقى Such
+
+39
+00:02:56,460 --> 00:03:01,480
+Damage May Result in Infection Arrhythmia يعني
+
+40
+00:03:01,480 --> 00:03:06,720
+مشاكل في اللي هو نبض القلب، and Heart Failure، هذا
+
+41
+00:03:06,720 --> 00:03:07,280
+مبدئياً 
+
+42
+00:03:10,060 --> 00:03:14,760
+الـ Coronary Artery Disease هو The Largest Killer
+
+43
+00:03:14,760 --> 00:03:21,180
+Of American Males And Females، هو أكثر المشكلة الآن
+
+44
+00:03:21,180 --> 00:03:25,420
+بتواجههم Female و Males طبعاً كله نتيجة إيش؟ هنيجي 
+
+45
+00:03:25,420 --> 00:03:33,330
+الآن نتيجة Life Style اللي متبهدلين به، المهول من الـ
+
+46
+00:03:33,330 --> 00:03:38,350
+Calories اللي بياخدوها، قلة الحركة، الـ Alcohol عند
+
+47
+00:03:38,350 --> 00:03:44,790
+بعض الفئات، 13 مليون أمريكي have coronary heart
+
+48
+00:03:44,790 --> 00:03:51,570
+disease، الآن كل 26 ثانية أمريكي بيصير عنده
+
+49
+00:03:51,570 --> 00:03:59,950
+Coronary Event، كل 60 ثانية يعني دقيقة أمريكي 
+
+50
+00:04:01,820 --> 00:04:05,000
+والذين يموتون من أسباب الـ Coronavirus نحن نتكلم
+
+51
+00:04:05,000 --> 00:04:10,560
+عن الإحصائيات الآن، 84% من الذين يموتون من أسباب
+
+52
+00:04:10,560 --> 00:04:14,840
+الـ Coronavirus فوق الـ 65% طبعاً هذا بيتماشى مع
+
+53
+00:04:14,840 --> 00:04:18,200
+الفكرة أن الـ Coronavirus مع الوقت بيصير
+
+54
+00:04:18,200 --> 00:04:24,340
+Progressive أو الـ Process يعني ما بيجيش بيسكر الـ 
+
+55
+00:04:24,340 --> 00:04:27,300
+Coronary، بيصير فيه Obstruction للـ Coronary Artery
+
+56
+00:04:27,300 --> 00:04:31,460
+Disease إلا لو كان فيه Thrombus وهيك مرة واحدة، دب 
+
+57
+00:04:31,460 --> 00:04:34,460
+اللي هو مسكر، مش هو هذا اللي بيصير، اللي بيصير أنه
+
+58
+00:04:34,460 --> 00:04:39,940
+هذا الـ Process بتصير Building of Sclerotic Plaques
+
+59
+00:04:39,940 --> 00:04:44,180
+في الـ Artery أو في الـ Intima of the Coronary Artery
+
+60
+00:04:44,340 --> 00:04:48,600
+وهذا بيعمل لنا Obstruction Over the Time، بتكون على 
+
+61
+00:04:48,600 --> 00:04:55,880
+الـ Obstruction هذا، Black's التجمعات كلسية من 
+
+62
+00:04:55,880 --> 00:04:59,640
+كريات الدم الحمراء، من الدهون، من الـ Calcium، من
+
+63
+00:04:59,640 --> 00:05:02,860
+الـ Neutrophils، هذه التجمعات في الآخر بتعمل لي
+
+64
+00:05:02,860 --> 00:05:08,240
+تسكير فوق تسكير، هذه اللي بيصير، طيب الـ Average of 
+
+65
+00:05:08,240 --> 00:05:17,450
+أي واحد بيصير عنده MI حياته بتنقص 11 سنة ونصف، الـ 
+
+66
+00:05:17,450 --> 00:05:20,070
+Average بتبقى تنقص، طبعاً زي ما قلنا Statistically
+
+67
+00:05:20,070 --> 00:05:23,290
+يعني لا يعني أن كل واحد بيجيله Heart Attack
+
+68
+00:05:23,290 --> 00:05:26,630
+معناته خلاص حيموت 11 سنة ونصف، مش هو هذا الموضوع
+
+69
+00:05:26,630 --> 00:05:29,690
+الموضوع أنه لاجوا أنه نسبة الأعمار أو Life
+
+70
+00:05:29,690 --> 00:05:32,790
+Expectancy عند الناس اللي بيصير عندها Coronary
+
+71
+00:05:32,790 --> 00:05:37,530
+Disease أو MI Myocardial Infection، بتبقى الـ Life
+
+72
+00:05:37,530 --> 00:05:42,700
+Expectancy تبعهم أقل بـ 11 سنة ونصف عن الثانية، مهم 
+
+73
+00:05:42,700 --> 00:05:47,680
+أن نعرف أن 50% من الرجال و64% من النساء اللي قد 
+
+74
+00:05:47,680 --> 00:05:57,420
+ماتت بسبب كورونا لا كان عندهم أي 
+
+75
+00:05:57,420 --> 00:06:01,080
+مشاكل 
+
+76
+00:06:01,080 --> 00:06:07,340
+قبلها، الذين لديهم قصة مؤلفة من الـMI لديهم خمس إلى
+
+77
+00:06:07,340 --> 00:06:11,460
+ست مرات أكثر، مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+78
+00:06:11,460 --> 00:06:12,360
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+79
+00:06:12,360 --> 00:06:12,380
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+80
+00:06:12,380 --> 00:06:13,120
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+81
+00:06:13,120 --> 00:06:13,340
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+82
+00:06:13,340 --> 00:06:17,560
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+83
+00:06:17,560 --> 00:06:28,680
+مؤلفة مؤلف
+
+84
+00:06:30,110 --> 00:06:33,490
+فاهمين إيش بقصد؟ فهو هذه الفكرة في قضية Previous 
+
+85
+00:06:33,490 --> 00:06:38,230
+History of MI في خمسة لستة times Sudden Death Rate
+
+86
+00:06:38,230 --> 00:06:41,910
+Compared to the General Population، طب إيش الـ 
+
+87
+00:06:41,910 --> 00:06:45,070
+Statistics هاي الآن اللي احنا شايفينها؟ هاي اللي
+
+88
+00:06:45,070 --> 00:06:48,930
+باللون الأزرق Male وباللون التوتي والله ما أعرف إيش 
+
+89
+00:06:48,930 --> 00:06:53,710
+أزرق، المهم، ليلكي وتوتي أو حاجة زي هيك Female
+
+90
+00:06:53,710 --> 00:06:59,530
+باللغة إنه معظم اللي بيموتوا في بين عمره عشرين لتسعة
+
+91
+00:06:59,530 --> 00:07:04,430
+وعشرين هم Men الآن
+
+92
+00:07:04,430 --> 00:07:08,790
+من ثلاثين لتسعة وثلاثين شوية Women، والباقي Men 
+
+93
+00:07:08,790 --> 00:07:16,210
+من اللي بيموتوا، وأربعين لتسعة وأربعين معظمهم برضه
+
+94
+00:07:16,210 --> 00:07:21,750
+رجال، والـ Women أجل بمعنى
+
+95
+00:07:24,870 --> 00:07:29,370
+أنه يبدو إن اللي بالـ "توتي" هدول هم اللي بيخلصوا 
+
+96
+00:07:29,370 --> 00:07:34,650
+على اللي بالأزرق أو بالليلكي كده، ملاحظين؟ يعني في 
+
+97
+00:07:34,650 --> 00:07:41,930
+الأول كلهم بيموتوا أو معظم رجال، ولحد عمر سبعين 
+
+98
+00:07:41,930 --> 00:07:46,710
+لتسعة وسبعين هو الغالبية رجال بيموتوا، لكن الستات
+
+99
+00:07:46,710 --> 00:07:49,150
+مش هم الغالبين، وبعد هيك بيصيروا الستات الغالبية 
+
+100
+00:07:49,150 --> 00:07:51,510
+بين ثمانين وتسعين، ما هو أصلاً بيبقوا خلصوا الرجال 
+
+101
+00:07:51,510 --> 00:07:56,130
+وخلصوا عليهم، طبعاً هذه مزحة لشك، لكن هو طبعاً
+
+102
+00:07:56,130 --> 00:08:03,650
+الـMI أو المشاكل القلبية هي أكثر منها في الرجال من 
+
+103
+00:08:03,650 --> 00:08:11,410
+الستات، والسبب غالباً له علاقة بالـ Estrogen على سبيل 
+
+104
+00:08:11,410 --> 00:08:17,960
+المثال وتكون الـ Building والحركة وكذا، طيب، إيش الـ 
+
+105
+00:08:17,960 --> 00:08:22,560
+Risk Factors؟ إحنا قلنا المشاكل هذه طبعاً ما
+
+106
+00:08:22,560 --> 00:08:25,700
+لهاش علاقة بس في أمريكا، إن شاء الله الـ Risk 
+
+107
+00:08:25,700 --> 00:08:29,000
+Factors هي تعملها وما تعملها، أو تعمليها وما
+
+108
+00:08:29,000 --> 00:08:33,580
+تعمليها، وتمارسها وما تمارسها، في الآخر هتعمل ليه؟
+
+109
+00:08:33,580 --> 00:08:37,770
+مشاكل Coronary Heart Disease، الـ Coronary Heart
+
+110
+00:08:37,770 --> 00:08:39,690
+Disease لديها الكثير من العوامل الخطرة بالنسبة
+
+111
+00:08:39,690 --> 00:08:43,330
+لها، وخاصة فيها أشياء غير قابلة للتحكم، وليس بيدي
+
+112
+00:08:43,330 --> 00:08:47,470
+ولا بيدك، مثل الـ Age، الـ Race، الـ Hereditary،
+
+113
+00:08:47,470 --> 00:08:51,110
+الجنس الانساني، هذا ما أقدرش أتحكم فيه، لأننا كنا 
+
+114
+00:08:51,110 --> 00:08:53,910
+رجال بنصاب أكثر من الستات، فإيش ذنب الرجل وإيش 
+
+115
+00:08:53,910 --> 00:08:56,930
+ذنب المرأة؟ ما فيش، ما فيش، هذه غير قابلة للتحكم، لا
+
+116
+00:08:56,930 --> 00:09:01,650
+بيدي ولا بيدك، لكن في حاجات ما جيناه على أنفسنا، 
+
+117
+00:09:01,650 --> 00:09:06,520
+احنا دخان وارتي وارتيك، الـ Hypertension وقلنا
+
+118
+00:09:06,520 --> 00:09:10,680
+ليش بنشغل الـ Hypertension، إرادتي وإرادتك، الـ 
+
+119
+00:09:10,680 --> 00:09:12,840
+Diabetes إرادتي وإرادتك، أو خلّيني أقول
+
+120
+00:09:12,840 --> 00:09:16,760
+Controllable، بلاش نقول إرادات، إنما في إمكانية 
+
+121
+00:09:16,760 --> 00:09:19,860
+أتحكم في Hyperlipidemia، Radiotherapy of the 
+
+122
+00:09:19,860 --> 00:09:23,900
+chest، هذه كلها زي ما بقولها Controllable، Risk
+
+123
+00:09:23,900 --> 00:09:29,000
+Factors وبتؤدي لموضوع الـ MI. طب هو إيش اللي 
+
+124
+00:09:29,000 --> 00:09:32,180
+بيحصل؟ إيش الـ Pathophysiology؟ قلنا هي بتتكون 
+
+125
+00:09:32,180 --> 00:09:38,560
+عندنا الـ Atherosclerotic Blocks، تجمعات الـ
+
+126
+00:09:38,560 --> 00:09:41,820
+Atherosclerotic وهذه بتعمل لنا تضيق 
+
+127
+00:09:44,240 --> 00:09:48,720
+وهذه في الأكثر بتيجي في منطقة اسمها الـ Intima، أنه 
+
+128
+00:09:48,720 --> 00:09:53,480
+خلّيني أقول كل نفايات الجسم اللي هو المكتوب عنها 
+
+129
+00:09:53,480 --> 00:09:58,300
+Grung هنا زي الـ Calcium Deposits، Fatty Deposits،
+
+130
+00:09:58,300 --> 00:10:04,520
+Abnormal Inflammatory Cells بتتكون في مناطق خلّيني
+
+131
+00:10:04,520 --> 00:10:09,160
+أقول بدأت تتضيق أو مناطق مجروحة لسبب أو من الأسباب
+
+132
+00:10:09,160 --> 00:10:14,770
+Legion بيتكلس هناك Blocks تجمعات أو تكونات، وبعد
+
+133
+00:10:14,770 --> 00:10:19,990
+وقت التكونات هذه بتزيد، وبتزيد، وفي الآخر بتسكر
+
+134
+00:10:19,990 --> 00:10:22,930
+الشارع، يعني بتتصوروا أنا بقى الشارع نظيف وبدوا 
+
+135
+00:10:22,930 --> 00:10:27,850
+الناس على جنب الشارع يكبوا زبالة وكل الناس صارت 
+
+136
+00:10:27,850 --> 00:10:30,750
+كل حرطيجة كوب زبالة، في الآخر الزبالة هي في الشارع
+
+137
+00:10:30,750 --> 00:10:35,270
+عشان بتعمل كوب بتضيق المواصلات، بيصير السيارات بدل 
+
+138
+00:10:35,270 --> 00:10:40,310
+ما هي رايحة وجاية، بيصير تستنى اللي رايح عشان اللي 
+
+139
+00:10:40,310 --> 00:10:42,910
+جاي ما يدخل عشان هو يعود يدخل، ليش؟ لأنه كملة 
+
+140
+00:10:42,910 --> 00:10:47,410
+زبالة مسكر عليه ومرة على مرة، مرة على مرة، في 
+
+141
+00:10:47,410 --> 00:10:51,730
+الآخر بيصير عندنا تسكير للشارع من الزبالة هذه اللي
+
+142
+00:10:51,730 --> 00:10:54,050
+احنا بنقول عنها «grung» أو بنقول عنها زي ما قلنا
+
+143
+00:10:57,690 --> 00:11:02,630
+النفايات الجسم اللي بتتكون طبعاً الدم في الآخر
+
+144
+00:11:02,630 --> 00:11:07,630
+بيصير ما يلاقيش مسار جوا الشريان و بيصير طبعاً يصير 
+
+145
+00:11:07,630 --> 00:11:14,760
+turbulence حاجة اسمها turbulence و بيصير يبطق، يبطق،
+
+146
+00:11:14,760 --> 00:11:20,840
+بيصير يبطق، يعني مش بس على جد أنه تسكر الشارع أو
+
+147
+00:11:20,840 --> 00:11:23,840
+تضيق الشارع، إنما بيصير يبطق، وبيصير إنه
+
+148
+00:11:23,840 --> 00:11:28,140
+turbulence، وهذا الموضوع بيؤدي في لحظة من اللحظات
+
+149
+00:11:29,800 --> 00:11:35,640
+لأنه بيقلل كمية الأكسجين اللي بتصل للقلب كمية
+
+150
+00:11:35,640 --> 00:11:39,120
+الـperfusion اللي بتصل للقلب بتقل وطبعاً بالتالي
+
+151
+00:11:39,120 --> 00:11:42,720
+كمية الـNutrients، الـVitamins، كمية الأكسجين
+
+152
+00:11:42,720 --> 00:11:47,280
+طبعاً احنا هنا بيهمننا الـO2 supply the heart is not
+
+153
+00:11:47,280 --> 00:11:53,420
+in danger of hypoxia لحد 50% of the vessel is 
+
+154
+00:11:53,420 --> 00:12:00,360
+occluded إذا سكر الشريان لـ50% أو أكثر من 50% بيبدأ
+
+155
+00:12:00,360 --> 00:12:06,220
+لحد ساعتها ما بتأثرش القلب لسه ما فيش عندنا danger
+
+156
+00:12:06,220 --> 00:12:11,300
+مافيش خطر و بتأثر بس مافيش خطر until 50% of the
+
+157
+00:12:11,300 --> 00:12:16,720
+vessel is occluded at the heart since a decrease
+
+158
+00:12:16,720 --> 00:12:20,080
+إذا حس القلب إنه فيه نقص في ال oxygen بيحاول إيش
+
+159
+00:12:20,080 --> 00:12:23,940
+يعمل compensation لأنه خف عليه فإيش بيروح و بيعمل
+
+160
+00:12:23,940 --> 00:12:28,990
+بيزيد ال heart rate هذه هي ميكانيزمات التعامل بالقلب
+
+161
+00:12:28,990 --> 00:12:37,050
+في تجارب الـ O2 بتزيد حرارة القلب تزيد حرارة
+
+162
+00:12:37,050 --> 00:12:41,830
+الدم وأيش كمان؟ وبتزيد الأترومة اللي صارت الـ
+
+163
+00:12:41,830 --> 00:12:44,710
+Plaques اللي موجودة نتيجة الهيبوكسيا برضه بتزيد
+
+164
+00:12:44,710 --> 00:12:49,540
+الآن إذا وصلنا لـ 70% of the artery is occluded بيبدأ
+
+165
+00:12:49,540 --> 00:12:53,940
+يبين عندنا أعراض أعراض بصورة Angina Pectoris إيش
+
+166
+00:12:53,940 --> 00:12:57,800
+يعني Angina Pectoris؟ معناها ذبحة صدرية Angina
+
+167
+00:12:57,800 --> 00:13:00,920
+Pectoris تبدأ بعد ما يوصل لـ 70% of the artery is
+
+168
+00:13:00,920 --> 00:13:07,490
+occluded هذه صورة اللي زي الجبل هنا وفيه خلايا
+
+169
+00:13:07,490 --> 00:13:11,330
+عندنا جواتها monocytes و macrophages و endothelial
+
+170
+00:13:11,330 --> 00:13:15,730
+و smooth cells و fatty و necrotic tissue هذا قلنا
+
+171
+00:13:15,730 --> 00:13:18,230
+كم النفايات أو الزبالة اللي سكّرنا الشارع اللي هو
+
+172
+00:13:18,230 --> 00:13:21,570
+اللي أطلّعنا الصورة اللي جنبها بنلاقي كيف ال plaques
+
+173
+00:13:21,570 --> 00:13:27,210
+بدأت تسكر الشريان وفي مقطع عرضي للشريان بنشوف إنه
+
+174
+00:13:27,210 --> 00:13:32,130
+الشريان تضيق نتيجة process اسمه atherosclerosis
+
+175
+00:13:32,130 --> 00:13:36,350
+طيب إيش ال symptoms اللي بنشوفها؟ في ال coronary
+
+176
+00:13:36,350 --> 00:13:38,490
+heart disease ممكن ما يكونش في symptoms
+
+177
+00:13:42,880 --> 00:13:49,140
+ممكن يكون asymptomatic لكن ممكن أشوف chest
+
+178
+00:13:49,140 --> 00:13:53,400
+heaviness كيف يعني تقل على الصدر تحس أنه كأنه
+
+179
+00:13:53,400 --> 00:13:56,740
+بلاطة على منطقة القلب موجودة أو على الصدر ضغط
+
+180
+00:13:56,740 --> 00:14:03,720
+نفسه بيصير مش طبيعي، fatigue،  تحس بتعب، هل كان، chest
+
+181
+00:14:03,720 --> 00:14:08,200
+pain طبيعي، chest pain وهذا cardinal symptom of
+
+182
+00:14:08,200 --> 00:14:12,320
+myocardial ischemia أنجينا طبعاً حكينا و MI اللي هي
+
+183
+00:14:12,320 --> 00:14:14,460
+النتائج اللي هنشوفها ischemic heart disease
+
+184
+00:14:14,460 --> 00:14:18,060
+classification  احنا اخترنا أنا بس حاجات بسيطة
+
+185
+00:14:18,060 --> 00:14:22,480
+أنجاين بيكتورس العادية وفي unstable أنجينا بيكتورس
+
+186
+00:14:22,480 --> 00:14:26,580
+هنشوف الفرق بينهم وفي عندنا ال MI أو myocardial
+
+187
+00:14:26,580 --> 00:14:29,980
+infection وفي عندنا ال chronic ischemic heart
+
+188
+00:14:29,980 --> 00:14:34,980
+disease with heart failure طب الـ Angina Pectoris
+
+189
+00:14:34,980 --> 00:14:41,140
+قلنا هي إيش؟ ذبحة صدرية؟ 75% of coronary artery
+
+190
+00:14:41,140 --> 00:14:45,280
+resulting in pain إيش نوع ال pain هذا؟ لازم نقدر
+
+191
+00:14:45,280 --> 00:14:49,140
+نوصل في ال pain مش أي pain على الصدر يا جماعة مش
+
+192
+00:14:49,140 --> 00:14:54,660
+أي pain على الصدر على ال chest يعني من Angina
+
+193
+00:14:54,660 --> 00:15:02,130
+Pectoris أو MI  هإيش؟ آه هذه هي الـ Next Assignment
+
+194
+00:15:02,130 --> 00:15:08,010
+اللي هتكتبوليها بالإيد وتكتبولي الـ Differential
+
+195
+00:15:08,010 --> 00:15:13,770
+Diagnosis of Chest Pain بالنسبة 
+
+196
+00:15:13,770 --> 00:15:19,770
+طبعا، مين حسب مين أكثر من مين خلينا نقول Maximum
+
+197
+00:15:19,770 --> 00:15:23,640
+10 أسطور بديش موضوع just pain differential
+
+198
+00:15:23,640 --> 00:15:29,380
+diagnosis والنسبة تبعتهم مين أكثر بنشوفه وطبعا لو
+
+199
+00:15:29,380 --> 00:15:32,640
+في كلمات غريبة في ال differential diagnosis اكتبوا
+
+200
+00:15:32,640 --> 00:15:37,120
+قبلها إيش بتقصدوها يعني مش يعني حاولوا قدر الإمكان
+
+201
+00:15:37,120 --> 00:15:41,520
+اللي بتكتبوه تكونوا فاهمينه مهم جدا الموضوع هذا
+
+202
+00:15:43,170 --> 00:15:46,310
+وهذا أجى عدة مرات سؤال في الامتحانات
+
+203
+00:15:46,310 --> 00:15:50,030
+classification of chest pain مش كل بني آدم مش كل
+
+204
+00:15:50,030 --> 00:15:54,470
+واحد بيقول و الله صدري واجعني معناته عنده MI أو
+
+205
+00:15:54,470 --> 00:15:57,810
+عنده .. طب إيش نوع ال pain اللي بنحكي عنه يبقى
+
+206
+00:15:57,810 --> 00:16:02,390
+قلنا عن ال assignment اللي هو هنعمله اليوم؟Chest
+
+207
+00:16:02,390 --> 00:16:07,050
+pain – radiating pain to left shoulder, jaw – left
+
+208
+00:16:07,050 --> 00:16:11,110
+or to right arm يعني فيه إشعاع يمتد،
+
+209
+00:16:11,110 --> 00:16:14,070
+بتلاقي المريض بيقولك أه والله كتفي شمال، إيدي
+
+210
+00:16:14,070 --> 00:16:20,020
+شمال، فكي، هذه كلها هتلاحظها أحيانًا يتم إجراءها من
+
+211
+00:16:20,020 --> 00:16:23,640
+خلال الـ Physical Exertion في الغالب، في الغالب،
+
+212
+00:16:23,640 --> 00:16:25,980
+لما الواحد بيبقى بيعمل عملية عملية عملية عملية
+
+213
+00:16:25,980 --> 00:16:27,640
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+214
+00:16:27,640 --> 00:16:28,280
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+215
+00:16:28,280 --> 00:16:28,500
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+216
+00:16:28,500 --> 00:16:30,600
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+217
+00:16:30,600 --> 00:16:35,190
+عملية عملية عملية عملية عملية عملية يعني ننظف الشارع،
+
+218
+00:16:35,190 --> 00:16:40,450
+أجري شوية، أطلع على الشجرة، أجد الزتونات، أي
+
+219
+00:16:40,450 --> 00:16:43,690
+حاجة بلاقي أنه صار عنده chest pain، ليش؟ لأن القلب
+
+220
+00:16:43,690 --> 00:16:47,070
+صار مطلوب منه أكثر، لكن الـ coronary artery مش
+
+221
+00:16:47,070 --> 00:16:53,970
+قادرة تدخل أكثر، فإيش بيصير؟ أن القلب بيزيد نشاطه،
+
+222
+00:16:53,970 --> 00:16:59,160
+وهذا لما يزيد نشاطه بيحاول يدخل دم أكثر، بيقدرش
+
+223
+00:16:59,160 --> 00:17:05,000
+يدخل دم أكثر، فبيصير عندنا الـ pain  إفس وهذا في
+
+224
+00:17:05,000 --> 00:17:09,980
+الغالب إذا وقفت الشغل اللي بشتغله، بيروح الوجع في
+
+225
+00:17:09,980 --> 00:17:12,420
+العادة، طبعا لازم أروح للدكتور، ده شك، بس أنا
+
+226
+00:17:12,420 --> 00:17:15,180
+بحكيلكوا إيش يعني الـ angina pectoris إذا وقفت ال
+
+227
+00:17:15,180 --> 00:17:19,270
+exertion، بيخف ال pain الأنجينابيكترون يمكن أن
+
+228
+00:17:19,270 --> 00:17:21,550
+يكونوا مستقلة أو غير مستقلة، وهنا الفرق بين مستقلة
+
+229
+00:17:21,550 --> 00:17:25,390
+وغير مستقلة، المستقلة هو الحرارة والبطن من الأحداث
+
+230
+00:17:25,390 --> 00:17:31,390
+غير متغيرة، دائما نفس الوجع، الطريقة والوجع هو
+
+231
+00:17:31,390 --> 00:17:35,230
+نفسه، خلال مرحلة من الوقت، أكثر من ذلك بسبب الضغط
+
+232
+00:17:35,230 --> 00:17:39,390
+أو التجارب، جاية من التجارب، طيب والغير مستقلة،
+
+233
+00:17:39,390 --> 00:17:45,750
+الحرارة والبطن بتتغير، الأمر الثاني بما يكون في مدة
+
+234
+00:17:45,750 --> 00:17:50,550
+كمان شدة لفرقوانسي وبتيجي mostly in rest مش زي
+
+235
+00:17:50,550 --> 00:17:54,450
+هديك لما أنا تعبت unstable لما أنا تعبت صار عندي
+
+236
+00:17:54,450 --> 00:18:00,330
+chest pain ال unstable بدون تعب في rest الموضوع ال
+
+237
+00:18:00,330 --> 00:18:07,730
+myocardial infection عند ما يصير عندنا partial or
+
+238
+00:18:07,730 --> 00:18:11,150
+total occlusion of one or more of the coronaries
+
+239
+00:18:11,150 --> 00:18:15,660
+واحنا عارفين ال coronaries أكثر من واحد arteries due
+
+240
+00:18:15,660 --> 00:18:20,260
+to atheroma, thrombus أو emboli resulting in cell
+
+241
+00:18:20,260 --> 00:18:25,540
+death بيصير عندي infarction يعني مجرد التذكير بدون
+
+242
+00:18:25,540 --> 00:18:29,040
+ما يأثر على ال heart muscle بنقول عنه angina لكن
+
+243
+00:18:29,040 --> 00:18:33,400
+إذا صار مأثرلي ومديني علامات MI هذه بنقول عنها
+
+244
+00:18:33,400 --> 00:18:41,030
+إيش؟ بنقول عنها MI عندما يحدث الـMI، يكون هناك عملية
+
+245
+00:18:41,030 --> 00:18:45,250
+ثلاثة إلى أربعة ملايين ملايين ملايين ملايين
+
+246
+00:18:45,250 --> 00:18:46,770
+ملايين ملايين ملايين ملايين ملايين ملايين
+
+247
+00:18:46,770 --> 00:18:54,330
+ملايين ملايين ملايين ملايين ملايين
+
+248
+00:18:55,880 --> 00:18:59,800
+حوالي في أمريكا طبعاً ربع مليون death per year
+
+249
+00:18:59,800 --> 00:19:02,700
+ثلاثين في المائة mortality within the first two
+
+250
+00:19:02,700 --> 00:19:05,740
+hours يعني لو واحد صار عنده MI ثلاثين في المائة
+
+251
+00:19:05,740 --> 00:19:08,840
+بيموتوا من أول ساعة في أمريكا في الصين في غزة في
+
+252
+00:19:08,840 --> 00:19:11,720
+مصر في غزة ممكن يكون أكثر لكن بيموتوا في أول
+
+253
+00:19:11,720 --> 00:19:15,620
+ساعتين عشان هيك بتقولك والله على طول صار عنده جلطة
+
+254
+00:19:15,620 --> 00:19:21,600
+قلبية بنشتغل التذكير وتوفى بعد ساعة أو بعد نص ساعة أو
+
+255
+00:19:21,600 --> 00:19:25,300
+لسه ما وصلوش فيه المستشفى لو كان متوفي ليش؟ لأن هذا
+
+256
+00:19:25,300 --> 00:19:30,980
+الوضع الطبيعي في 30% من الحالات أنه بيموت خلال
+
+257
+00:19:30,980 --> 00:19:36,240
+ساعتين 45% minutes of ischemia بتديني a cardiac
+
+258
+00:19:36,240 --> 00:19:39,440
+muscle death أو cancer كيف بنعمل ال diagnosis of
+
+259
+00:19:39,440 --> 00:19:45,550
+MI؟ طبعا بنعمله ECG بالـ Electrocardiographic
+
+260
+00:19:45,550 --> 00:19:50,150
+Changes بنلاقي في حاجة اسمها ST elevation احنا بنفكر
+
+261
+00:19:50,150 --> 00:19:55,630
+إن جونا PQRST، الـ ST بنلاقيها عالية Myocardial
+
+262
+00:19:55,630 --> 00:19:59,010
+enzyme elevation زي الـCK و التروبونين
+
+263
+00:19:59,010 --> 00:20:08,390
+و السيرياكتيبروتين طبعا
+
+264
+00:20:08,390 --> 00:20:12,590
+أنتوا عارفين إيش .. إيش .. إيش الفرق بين ال thrombus
+
+265
+00:20:12,590 --> 00:20:19,920
+و الـEmboli ولا مش عارفين؟ أكيد عارفين ال
+
+266
+00:20:19,920 --> 00:20:22,260
+Complication of Myocardial Infection طبعاً عندنا
+
+267
+00:20:22,260 --> 00:20:26,900
+مشكلة، يعني الجذية مش جذية أنه صار عندي muscle tissue
+
+268
+00:20:26,900 --> 00:20:33,460
+death وخلص وخلصناها، لأ المشكلة أن الـ Infection
+
+269
+00:20:33,460 --> 00:20:40,120
+بتخلي القلب غير قادر أنه يعمل، هو إيش شغلة القلب؟
+
+270
+00:20:40,120 --> 00:20:44,620
+إنه يضخ دم لكل الجسم، طيب إذا والله الـ motor في
+
+271
+00:20:44,620 --> 00:20:49,110
+قطعة منه صارت تعبانة، ما راح يقدر يضخ appropriate
+
+272
+00:20:49,110 --> 00:20:52,750
+بيصير يعني يدوب على الجد مش قادر يشتغل فبيصير
+
+273
+00:20:52,750 --> 00:20:56,070
+leading to heart failure رقم واحد الـMI ممكن تعملي
+
+274
+00:20:56,070 --> 00:20:59,410
+heart failure ممكن تدينا pain دائما pain دائما
+
+275
+00:20:59,410 --> 00:21:04,010
+pain ممكن تعملنا shock ممكن المنطقة اللي ماتت في
+
+276
+00:21:04,010 --> 00:21:09,770
+خلايا القلب بيصير إيش فيها؟ Aneurysm يعني إيش يعني
+
+277
+00:21:09,770 --> 00:21:15,470
+Aneurysm؟ أنه بتنبعج يعني المنطقة الضعيفة اللي
+
+278
+00:21:15,470 --> 00:21:20,490
+ماتت في جدار القلب سواء في الـ left ventricle أو
+
+279
+00:21:20,490 --> 00:21:24,130
+في ال right ventricle نتيجة إنها ماتت بتعملي زي
+
+280
+00:21:24,130 --> 00:21:26,950
+انبعاج والانبعاج هي ده اللي بنقول عليه aneurysm ممكن 
+
+281
+00:21:26,950 --> 00:21:30,690
+يصير فيه في أي لحظة كمان rupture طبعاً هذا الانبعاج
+
+282
+00:21:31,830 --> 00:21:34,750
+كمان إيش ممكن يعملي؟ ممكن يعملي Embolism تكوين
+
+283
+00:21:34,750 --> 00:21:38,730
+لجلطات في جلبه وممكن يعملي طبعاً نتيجة موت خلايا
+
+284
+00:21:38,730 --> 00:21:43,510
+في خلايا القلب يعملي Arrhythmias من الحاجات المهمة
+
+285
+00:21:43,510 --> 00:21:46,750
+الـ Complications اللي هي زي ما قلنا الـ sudden
+
+286
+00:21:46,750 --> 00:21:52,550
+death قلنا ربع مليون حالة بتموت في أمريكا due to
+
+287
+00:21:52,550 --> 00:21:58,350
+sudden cardiac death مرة واحدة بيجي في القلب و
+
+288
+00:21:58,350 --> 00:22:02,010
+بموت المريض والـ Sudden Death بنقول عنه Massive
+
+289
+00:22:02,010 --> 00:22:09,030
+Heart Attack Massive Heart Attack وهذا 
+
+290
+00:22:09,030 --> 00:22:18,510
+طبعاً نتيجة Shock صار لنا تكبّن شخص جون غير الموضوع
+
+291
+00:22:18,510 --> 00:22:26,870
+الآن الموضوع اللي كنا حكينا قبل شوي عن التشخيص
+
+292
+00:22:28,400 --> 00:22:33,680
+بتاع الـ Enzymes الـ Enzymes و ECG تحدثنا عنه فيه
+
+293
+00:22:33,680 --> 00:22:36,520
+كمان بنعمله Eco-cardiography في الـ Diagnosis 
+
+294
+00:22:36,520 --> 00:22:41,520
+وممكن للـ Angina نعمل Stress Test لأنه إحنا قلنا
+
+295
+00:22:41,520 --> 00:22:48,400
+الـ Angina Pectoris العادية تنكشفش إلا بالـخلينا 
+
+296
+00:22:48,400 --> 00:22:50,740
+أقول في الـ Definition تبعها إنه صار في عندي 
+
+297
+00:22:50,740 --> 00:22:55,280
+stress أو exercise فأنا عشان أشوف changes في ال
+
+298
+00:22:55,280 --> 00:22:58,860
+ECG بروح بعمل حاجة اسمها stress test هنحكي عنه
+
+299
+00:22:58,860 --> 00:23:04,340
+وبعد فترة أنا في عندي طبعاً تغليقات أو إغلاقات جوا
+
+300
+00:23:04,340 --> 00:23:09,290
+الشريان الـ Coronary فبتعمله حاجة اسمها تصوير 
+
+301
+00:23:09,290 --> 00:23:13,690
+للشريان بنعمل عن طريق القسطرة اسمه Angiography عشان 
+
+302
+00:23:13,690 --> 00:23:18,550
+أعرف قداش التسكير ونسبة التسكير ال ECG إيش بيعمل
+
+303
+00:23:18,550 --> 00:23:21,130
+ليه؟ خدوا بالكم يا جماعة الفحوصات هي كل فحص له
+
+304
+00:23:21,130 --> 00:23:25,230
+فايدة معينة مش يعني يلا أطلب كل فحوصاته مع
+
+305
+00:23:25,230 --> 00:23:29,010
+السلامة ال ECG أو Electrocardiogram أو ال ECG
+
+306
+00:23:29,010 --> 00:23:32,950
+provides a record of the heart electrical activity
+
+307
+00:23:32,950 --> 00:23:34,770
+يعني هو بي
+
+308
+00:23:37,850 --> 00:23:44,610
+بيصورلي أو بيخططلي كهرباء القلب خذوا بالكم أنتو
+
+309
+00:23:44,610 --> 00:23:49,310
+كيف؟ كهرباء القلب بس الـ electrical activity وهو
+
+310
+00:23:49,310 --> 00:23:53,090
+simple test records any abnormal findings in the
+
+311
+00:23:53,090 --> 00:23:56,210
+heart electrical impulse وبيصير عن طريق electrodes
+
+312
+00:23:56,210 --> 00:23:58,250
+زي ما إحنا شايفين في الصورة ويمكن شفتوها في
+
+313
+00:23:58,250 --> 00:24:02,810
+المستشفيات عن طريق electrodes بتتحط على الصدر
+
+314
+00:24:02,810 --> 00:24:07,630
+وعلى اليدين والرجلين ال echo مختلف ال echo it may
+
+315
+00:24:07,630 --> 00:24:10,650
+be ordered if your doctor suspects a problem in
+
+316
+00:24:10,650 --> 00:24:14,270
+the heart muscle إذا في عندي مشكلة في ال muscle أو 
+
+317
+00:24:14,270 --> 00:24:20,690
+في ال valves هذه الفرق بين الـ ECG و الـ Echo
+
+318
+00:24:20,690 --> 00:24:25,370
+Stress Test هذا عن طريق الـ treadmill أو الـ
+
+319
+00:24:25,370 --> 00:24:31,990
+exercise أنه أنا بعمله ECG أثناء بشوف وضع القلب
+
+320
+00:24:31,990 --> 00:24:37,070
+أثناء الـ physical exertion أثناء الجهد Stress
+
+321
+00:24:37,070 --> 00:24:42,050
+Test أثناء الجهد ECG أثناء الجهد يعني لو بيبينش
+
+322
+00:24:43,970 --> 00:24:48,470
+التغييرات في الـ ECG في الوضع الطبيعي المفروض أنه
+
+323
+00:24:48,470 --> 00:24:53,130
+أثناء الجهد يبين المشكلة الـ Angiogram أو الـ
+
+324
+00:24:53,130 --> 00:24:57,430
+Angiography The most accurate means by which to
+
+325
+00:24:57,430 --> 00:25:01,970
+examine the coronary arteries عشان أعمل فحص للـ
+
+326
+00:25:01,970 --> 00:25:04,650
+coronary arteries أنا بروح بعمله Angiography الـ 
+
+327
+00:25:04,650 --> 00:25:09,710
+Angiography is requires a surgical procedure نقول
+
+328
+00:25:09,710 --> 00:25:13,790
+عنه cardiac catheter أو catheterization بنعمل
+
+329
+00:25:13,790 --> 00:25:19,170
+cardiac catheter اللي هو during
+
+330
+00:25:19,170 --> 00:25:24,810
+the procedure catheters small thin plastic tubes
+
+331
+00:25:24,810 --> 00:25:28,290
+are placed in the artery of the legs or the arm
+
+332
+00:25:28,290 --> 00:25:32,930
+where directed using an x-ray machine to the
+
+333
+00:25:32,930 --> 00:25:39,530
+opening of each of the coronary arteries يعني بندخل
+
+334
+00:25:39,530 --> 00:25:43,370
+عن طريق شريان من الرجل أو من اليد وبنروح مع الـ X
+
+335
+00:25:43,370 --> 00:25:47,810
+-ray وبنروح على الشرايين التاجية وبنفحصها وبنحط
+
+336
+00:25:47,810 --> 00:25:51,430
+Contrast فيها مادة بتنحقن شايفين الصورة السوداء
+
+337
+00:25:51,430 --> 00:25:54,810
+عندنا في الـ slide هذا بتنحقن بيبينلي كيف الشرايين
+
+338
+00:25:54,810 --> 00:26:00,970
+وهل الشريان متضيق في منطقة معينة أو مش موجود
+
+339
+00:26:00,970 --> 00:26:08,100
+بالمرة أو مسكر أو كذا بيبين بنصح طبعاً على اليوتيوب
+
+340
+00:26:08,100 --> 00:26:13,680
+تطلعوا How is angiography made؟ How is ECG made؟
+
+341
+00:26:13,680 --> 00:26:19,620
+How is Echo made؟ هتلاقوا فيديوهات كتير فرجوا 
+
+342
+00:26:19,620 --> 00:26:23,120
+تشوفوا ال process كيف بيصير يا جماعة لما تروح
+
+343
+00:26:23,120 --> 00:26:27,100
+المستشفيات في حاجات كتير مش لازم تحس حالك غريب
+
+344
+00:26:27,100 --> 00:26:29,700
+بالنسبة للـ procedures بتنعمل هناك، لازم تبقى 
+
+345
+00:26:29,700 --> 00:26:33,820
+familiar قدر الإمكان مع الـ procedures، ما بديش
+
+346
+00:26:33,820 --> 00:26:37,180
+أقول بتعرف تعملها، بس على الأقل، على الأقل، تبقى
+
+347
+00:26:37,180 --> 00:26:40,380
+عارف أن هذا ECG وهذا Echo، هذا بيجيز كذا، وهذا
+
+348
+00:26:40,380 --> 00:26:43,800
+بيعمل كذا، وهذا Angiogram، طلبوله Angiogram، آه
+
+349
+00:26:43,800 --> 00:26:47,760
+والله الـ Angiogram، عشان أشوف الشرايين التاجية من 
+
+350
+00:26:47,760 --> 00:26:51,420
+جوا، وأشوف إذا فيها تضيق، وقد إيش نسبة التضيق، وهل
+
+351
+00:26:51,420 --> 00:26:54,400
+بدها ballooning، هل بدها حطوطها بلون، هل بدها
+
+352
+00:26:54,400 --> 00:26:57,400
+dilatation، هذه الحاجات المفروض إنه في لحظة في 
+
+353
+00:26:57,400 --> 00:27:00,300
+لحظات بعد ما نخلص الـcourse تبعنا، المساق تبعنا،
+
+354
+00:27:00,300 --> 00:27:03,800
+تكونوا familiar معاها، يعني تروحوا على المستشفيات،
+
+355
+00:27:03,800 --> 00:27:06,800
+عارفين حاجات كتير بتصير في المستشفيات، هذا مش
+
+356
+00:27:06,800 --> 00:27:10,720
+لصالحهم، مش ل .. مش ل .. يمكن للعلاج الطبيعي فقط، 
+
+357
+00:27:10,720 --> 00:27:15,220
+إنما كمان للمعرفة العامة والسلوك العام، treatment،
+
+358
+00:27:15,220 --> 00:27:17,780
+many people are able to manage coronary artery
+
+359
+00:27:17,780 --> 00:27:22,130
+disease with lifestyle changes and medication يعني
+
+360
+00:27:22,130 --> 00:27:26,050
+مش كل إشي بده على طول جراحات و كمية Other people
+
+361
+00:27:26,050 --> 00:27:29,210
+with severe coronary artery disease may need
+
+362
+00:27:29,210 --> 00:27:35,650
+angioplasty or surgery نحكي لغاية كيف ال lifestyle
+
+363
+00:27:35,650 --> 00:27:39,790
+changes؟ عن طريق ال weight control، smoking
+
+364
+00:27:39,790 --> 00:27:45,930
+cessation، exercise، healthy diet أربع كلمات سهلات 
+
+365
+00:27:45,930 --> 00:27:49,550
+بسيطات بس في التطبيق هيكونوا صعبين لكن بيدها إرادة 
+
+366
+00:27:49,550 --> 00:27:53,550
+اللي بده حاجة بعملها ال medications بندي أدوية 
+
+367
+00:27:53,550 --> 00:27:59,670
+الأدوية هي to treat coronary disease cholesterol
+
+368
+00:27:59,670 --> 00:28:05,090
+lowering medications الستاتينز وهذا بجللي كمية ال
+
+369
+00:28:05,090 --> 00:28:12,420
+bad cholesterol أو ال LDL وبندي كمان Vasodilatation
+
+370
+00:28:12,420 --> 00:28:16,960
+نتروغلُسِرين بيحطه المريض تحت اللسان على أساس تعمل
+
+371
+00:28:16,960 --> 00:28:22,790
+Vasculature Vasodilatation بندي دوا لـ Anti
+
+372
+00:28:22,790 --> 00:28:27,150
+-hypertension drugs على أساس أنه أخفف الضغط فأخفف
+
+373
+00:28:27,150 --> 00:28:34,930
+اللي هو تقول عن القلب أنه يضخ ضد ضغط كبير جداً جداً 
+
+374
+00:28:34,930 --> 00:28:39,250
+في الجسم وبندي كمان أسبرين عشان يمنع الـ
+
+375
+00:28:39,250 --> 00:28:44,720
+aggregation طبعاً لحد فترة مش زمان كان كل واحد فوق
+
+376
+00:28:44,720 --> 00:28:48,360
+الأربعين ينصحه ياخد 81 ملي جرام أسبيرين
+
+377
+00:28:48,360 --> 00:28:52,600
+بيبي أسبيرين يومياً لكن ما ثبتتش صحة هذا الموضوع 
+
+378
+00:28:52,600 --> 00:28:56,000
+إلا إنه لسه ما زال بعض المجتمعات بتدي 81 
+
+379
+00:28:56,000 --> 00:29:03,160
+ملي جرام أسبيرين لكل إنسان لكل
+
+380
+00:29:03,160 --> 00:29:07,320
+إنسان فوق الأربعين سنة الـ Aspirin هو أصلاً pain
+
+381
+00:29:07,320 --> 00:29:10,140
+killer وإحنا ما ندوّش لل pain killer هو لمنع ال
+
+382
+00:29:10,140 --> 00:29:14,260
+aggregation of platelets الـ Surgical Intervention 
+
+383
+00:29:14,260 --> 00:29:19,820
+حسب إما بنعمل بالون، بالون يعني توسيع أو بنحط
+
+384
+00:29:19,820 --> 00:29:24,000
+Stent أو بنعمل حاجة اسمها Coronary Artery Bypass
+
+385
+00:29:24,000 --> 00:29:28,020
+Grafting كابج، كابج اسمها بيقولونها في المستشفيات 
+
+386
+00:29:28,020 --> 00:29:31,940
+الـ Stent اللي بنعمله زي ما إحنا شايفين في الصور 
+
+387
+00:29:31,940 --> 00:29:36,900
+أنه أنا بدخل بالقسطرة القلبية وباجي بدخل بـ Tubes
+
+388
+00:29:36,900 --> 00:29:43,360
+و Tubes هاي إما بعملها لو عندي الـ Coronary
+
+389
+00:29:43,360 --> 00:29:48,000
+Obstruction بالـ Dilatation ممكن أوسع وخلاص أخرج
+
+390
+00:29:48,000 --> 00:29:51,520
+ولكن في بعض الأحيان بحتاج أحط دعمات هذه اللي بنسعى
+
+391
+00:29:51,520 --> 00:29:55,040
+عنها حطوله دعامة وحطوله نتين وحطوله تلاتة بنحط 
+
+392
+00:29:55,040 --> 00:29:59,660
+دعمات جوا القلب طبعاً ما فيش إشي بدون complications
+
+393
+00:29:59,660 --> 00:30:03,400
+و الـ Angioplasty زي ما قلنا بندخل البالون و
+
+394
+00:30:03,400 --> 00:30:09,420
+بنحاول زي ما إحنا شايفين أنه نوسع و .. و .. عم ..
+
+395
+00:30:09,420 --> 00:30:11,580
+عن طريق حاجة زي هيك زي الـ rotation
+
+396
+00:30:14,560 --> 00:30:19,080
+وهذه بتوسع الشريان نوعاً ما يعني هو عملياً زي
+
+397
+00:30:19,080 --> 00:30:23,120
+حياتنا العملية لما أدخل في أي مكان مثلًا مجاري على
+
+398
+00:30:23,120 --> 00:30:26,500
+سبيل المثال بدي أدخل في المواسير عشان أسلك هي
+
+399
+00:30:26,500 --> 00:30:29,780
+عبارة عن عملية تسليك طبعاً لكن بطريقة طبية سليمة
+
+400
+00:30:29,780 --> 00:30:33,240
+مئة في المئة وفي طبعاً بقى أدهيك إذا والله لجينا 
+
+401
+00:30:33,240 --> 00:30:38,740
+تسكيرات في عدة شرايين بنعمله حاجة اسمها coronary
+
+402
+00:30:38,740 --> 00:30:42,560
+artery bypass grafting الـ CABG و is advised
+
+403
+00:30:42,560 --> 00:30:46,820
+for selected groups of patients with significant
+
+404
+00:30:46,820 --> 00:30:50,480
+narrowing and blockage of the heart arteries
+
+405
+00:30:50,480 --> 00:30:53,880
+coronary artery disease الـ CABG creates new
+
+406
+00:30:53,880 --> 00:30:59,500
+roots إيش بنعمل إحنا؟ والله بنجيب قطعة من وريد
+
+407
+00:31:00,760 --> 00:31:05,000
+وبنعمل تحويدة حوالين التسكير في منطقة تانية هو هذا
+
+408
+00:31:05,000 --> 00:31:08,520
+اللي بيشتغلوا CABG surgery creates new roots
+
+409
+00:31:08,520 --> 00:31:12,120
+around narrowed and blocked arteries allowing
+
+410
+00:31:12,120 --> 00:31:15,600
+sufficient blood flow to deliver oxygen and
+
+411
+00:31:15,600 --> 00:31:20,660
+nutrients to the heart muscle يعني حقيقة هذه من
+
+412
+00:31:20,660 --> 00:31:24,160
+المحاضرات اللي المفروض أنه فعلاً بتنشرح وجاهي لأن
+
+413
+00:31:24,160 --> 00:31:28,730
+كتير حاجات بتنجل و بتتوضح لكن هذه الوضع يعني أتمنى
+
+414
+00:31:28,730 --> 00:31:31,550
+مع الأخبار الجديدة إن شاء الله تعالى في الفترات 
+
+415
+00:31:31,550 --> 00:31:34,630
+الجاية يتحول التعليم للتعليم وجاهي يبقى في فرصة
+
+416
+00:31:34,630 --> 00:31:38,590
+أكبر أن الواحد يشرح أكثر يعني أتمنى أن تكونوا 
+
+417
+00:31:38,590 --> 00:31:41,230
+الفكرة وصلتكم في قضية الـ Coronary Heart Disease أو
+
+418
+00:31:41,230 --> 00:31:43,490
+الـ Coronary Artery Disease نصيختي الحاجات اللي 
+
+419
+00:31:43,490 --> 00:31:48,210
+حكينا عنها الـCABG الـ Angioplasty مع الـ
+
+420
+00:31:48,210 --> 00:31:54,690
+Ballooning مع وضع الـ Stent مع كيف بنعمل الـ ECG 
+
+421
+00:31:54,690 --> 00:32:01,410
+كيف بنعمل الـ ECO؟ كيف بنعمل الـ Stress Test؟ حاولوا 
+
+422
+00:32:01,410 --> 00:32:06,550
+على فيديوهات على اليوتيوب، وهذا سهل وموجودة، تحاولوا 
+
+423
+00:32:06,550 --> 00:32:09,890
+تشوفوا كيف بنعمل، وهذا كتير مهم بالنسبة لنا الـ 
+
+424
+00:32:09,890 --> 00:32:14,070
+assignment تبعنا فاكرينه ولا أفكركوا فيه؟ أكيد
+
+425
+00:32:14,070 --> 00:32:17,050
+فاكرينه، يطيكوا العافية للمحاضرة اللي جاي إن شاء 
+
+426
+00:32:17,050 --> 00:32:19,510
+الله تعالى، وأن شاء الله نهاركم سعيد 
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w_postprocess.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..0331614ba273a057eded596c7dc43cbb566649ce
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/kYZ19Phl55w_postprocess.srt
@@ -0,0 +1,1704 @@
+1
+00:00:01,920 --> 00:00:04,040
+بسم الله الرحمن الرحيم الحمد لله و ربنا و الصلاة
+
+2
+00:00:04,040 --> 00:00:06,820
+والسلام علي سيدنا محمد وسيد الموثيقين الأجمعين لإن
+
+3
+00:00:06,820 --> 00:00:09,100
+كمان مرة اليوم ان شاء الله تعالى طول محمد أبو ندا
+
+4
+00:00:09,100 --> 00:00:14,140
+معكوا في محاضرة جديدة الآن بنبدأ ندخل في أمراض
+
+5
+00:00:14,140 --> 00:00:17,480
+القلب ال coronary artery disease أو ال ischemic
+
+6
+00:00:17,480 --> 00:00:22,780
+heart disease نفس الإسم لأن الإصابة بتبقى في ال
+
+7
+00:00:22,780 --> 00:00:25,860
+coronaries أيش ال coronaries يعني الشرايين التاجية
+
+8
+00:00:26,760 --> 00:00:29,840
+ماذا يعني شريان التاجي؟ شريان التاجي يعني هو زي ما
+
+9
+00:00:29,840 --> 00:00:35,320
+أقولها ضروة ثنام أو يعني هو أفضل شي تقريبا في
+
+10
+00:00:35,320 --> 00:00:39,780
+القلب، ليش؟ لأن عشان أشغل القلب لابد أنه أغذ
+
+11
+00:00:39,780 --> 00:00:46,020
+القلب، أغذيه بإيش؟ أغذيه بـNutrients، بالـOxygen،
+
+12
+00:00:46,020 --> 00:00:49,120
+بالـVitamins، بالحاجات هذه، وكيف هاتبتصلوا؟
+
+13
+00:00:49,120 --> 00:00:52,690
+ابتصلوا زي وزي أيبالرغم من أنه هو القلب اللي بيبعت
+
+14
+00:00:52,690 --> 00:00:59,110
+دم لجسم كله إلا أنه نفسه يحتاج إلى الدم عن طريق
+
+15
+00:00:59,110 --> 00:01:03,050
+كيف؟ عن طريق coronaries اللي هو coronary artery
+
+16
+00:01:03,050 --> 00:01:10,510
+disease الآن أي مشكلة بتصير جوات ال coronaries في
+
+17
+00:01:10,510 --> 00:01:16,470
+الغالب سببها ischemic يعني obstructionالـ
+
+18
+00:01:16,470 --> 00:01:22,830
+Obstruction ممكن يكون نتيجة تضيق في الشريان نفسه
+
+19
+00:01:22,830 --> 00:01:29,010
+وممكن نتيجة ترمبز بيلدنج على سبيل المثال يبقى what
+
+20
+00:01:29,010 --> 00:01:33,390
+is coronary artery disease is a narrowing of the
+
+21
+00:01:33,390 --> 00:01:38,610
+coronary arteries that prevents adequate blood
+
+22
+00:01:38,610 --> 00:01:43,050
+supply to the heart musclesكمان مرة عبارة عن
+
+23
+00:01:43,050 --> 00:01:46,570
+narrowing بغض النظر الـ ischemic أو الـ coronary
+
+24
+00:01:46,570 --> 00:01:49,770
+heart disease أو coronary artery disease narrowing
+
+25
+00:01:49,770 --> 00:01:55,390
+of the coronary arteries اللي هذي بتوصلي الدم
+
+26
+00:01:55,390 --> 00:01:59,830
+لعضلات القلب وفي الغالب في الغالب في الغالب
+
+27
+00:01:59,830 --> 00:02:03,710
+usually caused by atherosclerosis ايش ال
+
+28
+00:02:03,710 --> 00:02:09,850
+atherosclerosis اللي هو بنقول عنه ايش تكلس الشراين
+
+29
+00:02:10,810 --> 00:02:14,070
+it may progress to the point where the heart
+
+30
+00:02:14,070 --> 00:02:17,190
+muscle is damaged due to the lack of blood supply
+
+31
+00:02:17,190 --> 00:02:22,670
+طبيعي أنا مكان قاعد مش جادر أوصله دم نتيجة الـ
+
+32
+00:02:22,670 --> 00:02:26,610
+Obstruction اللي صار فالـ muscle cells بيصير لها
+
+33
+00:02:26,610 --> 00:02:30,150
+damaging و بعد هيك بيصير عندنا ما يسمى بالإيش بالـ
+
+34
+00:02:30,150 --> 00:02:35,330
+infraction طبعاً لما يصير عندك infraction و العضلة
+
+35
+00:02:35,330 --> 00:02:43,020
+هذه ماصلهاش دم بيصير حتىالـ Electric Activity
+
+36
+00:02:43,020 --> 00:02:49,280
+تبعتها بتصير مش سليمة طبيعي و بعدين حتى الخلية تحت
+
+37
+00:02:49,280 --> 00:02:53,300
+القلب تفشل و لما يكون عندي عدد من الخلايا فشلت
+
+38
+00:02:53,300 --> 00:02:56,460
+بيصير عندي حاجة اسمها Heart Failure يبقى Such
+
+39
+00:02:56,460 --> 00:03:01,480
+Damage May Result in Infection Arrhythmia يعني
+
+40
+00:03:01,480 --> 00:03:06,720
+مشاكل في اللي هو نبض القلب and Heart Failure هذا
+
+41
+00:03:06,720 --> 00:03:07,280
+مبدأيا
+
+42
+00:03:10,060 --> 00:03:14,760
+الـ Coronary Artery Disease هو The Largest Killer
+
+43
+00:03:14,760 --> 00:03:21,180
+Of American Males And Females هو أكتر المشكلة الآن
+
+44
+00:03:21,180 --> 00:03:25,420
+بتوجيههم Female و Males طبعا كله نتيجة إيش؟ هنيجي
+
+45
+00:03:25,420 --> 00:03:33,330
+الآن نتيجة Life Style اللي متبهالكم المهول من الـ
+
+46
+00:03:33,330 --> 00:03:38,350
+Calories اللي بياخدوها قلة الحركة الـ Alcohol عند
+
+47
+00:03:38,350 --> 00:03:44,790
+بعض الفئات 13 مليون أمريكي ‏have coronary heart
+
+48
+00:03:44,790 --> 00:03:51,570
+disease ‏الآن كل 26 ثانية أمريكي بيصير عنده
+
+49
+00:03:51,570 --> 00:03:59,950
+coronary event ‏كل 60 ثانية يعني دقيقة أمريكي
+
+50
+00:04:01,820 --> 00:04:05,000
+والذين يموتون من أسباب الـ Coronavirus نحن نتكلم
+
+51
+00:04:05,000 --> 00:04:10,560
+عن الاستاتيكز الآن 84% من الذين يموتون من أسباب
+
+52
+00:04:10,560 --> 00:04:14,840
+الـ Coronavirus فوق الـ 65% طبعاً هذا بيتماشى مع
+
+53
+00:04:14,840 --> 00:04:18,200
+الفكرة أن الـ Coronavirus مع الوجد بيصير
+
+54
+00:04:18,200 --> 00:04:24,340
+progressiveأو الـ process يعني ما بيجيش بيسكر الـ
+
+55
+00:04:24,340 --> 00:04:27,300
+coronary بيصيرش فيه obstruction لـ coronary artery
+
+56
+00:04:27,300 --> 00:04:31,460
+disease إلا لو كان فيه thrombus و هيك مرة واحدة دب
+
+57
+00:04:31,460 --> 00:04:34,460
+اللي هو مسكر مش هو هذا اللي بيصير اللي بيصير أنه
+
+58
+00:04:34,460 --> 00:04:39,940
+هذا ال process بتصير building of sclerotic plaques
+
+59
+00:04:39,940 --> 00:04:44,180
+في الارتري أو في الانتما of the coronary artery
+
+60
+00:04:44,340 --> 00:04:48,600
+وهذا بيعملنا Obstruction over the time بتكون على
+
+61
+00:04:48,600 --> 00:04:55,880
+الـ Obstruction هذا Blacks التجمعات كالسية من
+
+62
+00:04:55,880 --> 00:04:59,640
+كوريات الدم الحمراء من الدهون من الـ Calcium من
+
+63
+00:04:59,640 --> 00:05:02,860
+الـ Neutrophils هذه التجمعات في الآخر بتعمللي
+
+64
+00:05:02,860 --> 00:05:08,240
+تسكير فوق تسكير هذه اللي بيصير طيب الـ Average of
+
+65
+00:05:08,240 --> 00:05:17,450
+أي واحد بيصير عنده MIحياته بتكسر 11 سنة و نص الـ
+
+66
+00:05:17,450 --> 00:05:20,070
+Average تبقى بتكسر طبعاً زي ما قلنا Statistically
+
+67
+00:05:20,070 --> 00:05:23,290
+يعني لا يعني أنه كل واحد بيجيله Heart Attack
+
+68
+00:05:23,290 --> 00:05:26,630
+معناته خلاص حيموت 11 سنة و نص مش هو هذا الموضوع
+
+69
+00:05:26,630 --> 00:05:29,690
+الموضوع أنه لاجوا أنه نسبة الأعمار أو Life
+
+70
+00:05:29,690 --> 00:05:32,790
+Expectancy عند الناس اللي بيصير عندها Coronavirus
+
+71
+00:05:32,790 --> 00:05:37,530
+Disease أو MI Myocardial Infection بتبقى الـ Life
+
+72
+00:05:37,530 --> 00:05:42,700
+Expectancy تبعهم أجل بـ 11 سنة و نص عن التانيةمهم
+
+73
+00:05:42,700 --> 00:05:47,680
+أن نعرف أن 50% من الرجال و 64% من المرأة اللي قد
+
+74
+00:05:47,680 --> 00:05:57,420
+ماتت بسبب كورونا لا كانوش عندهم أي
+
+75
+00:05:57,420 --> 00:06:01,080
+مشاكل
+
+76
+00:06:01,080 --> 00:06:07,340
+قبلهاالذين لديهم قصة مؤلفة من الـMI لديهم خمس إلى
+
+77
+00:06:07,340 --> 00:06:11,460
+ست مرات مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+78
+00:06:11,460 --> 00:06:12,360
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+79
+00:06:12,360 --> 00:06:12,380
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+80
+00:06:12,380 --> 00:06:13,120
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+81
+00:06:13,120 --> 00:06:13,340
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+82
+00:06:13,340 --> 00:06:17,560
+مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة مؤلفة
+
+83
+00:06:17,560 --> 00:06:28,680
+مؤلفة مؤلف
+
+84
+00:06:30,110 --> 00:06:33,490
+فاهمين إيش بقصود فهو هذه الفكرة في قضية previous
+
+85
+00:06:33,490 --> 00:06:38,230
+history of MI في خمسة لستة times sudden death rate
+
+86
+00:06:38,230 --> 00:06:41,910
+compared to the general population طب إيش ال
+
+87
+00:06:41,910 --> 00:06:45,070
+statistics هاي الآن اللي إحنا شايفينها؟ هاي اللي
+
+88
+00:06:45,070 --> 00:06:48,930
+باللون الأزرق male و باللون التوتي والله ماعرف إيش
+
+89
+00:06:48,930 --> 00:06:53,710
+أزرق المهم ليلكي وتوتي أو حاجة زي هيك female
+
+90
+00:06:53,710 --> 00:06:59,530
+باللغة إنه معظم اللي بموتهفي بين عمره عشرين لتسعة
+
+91
+00:06:59,530 --> 00:07:04,430
+و عشرين هما Men الآن
+
+92
+00:07:04,430 --> 00:07:08,790
+من تلاتين لتسعة و تلاتين شوية Women و الباقي Men
+
+93
+00:07:08,790 --> 00:07:16,210
+من البموته و أربعين لتسعة و أربعين معظمهم برضه
+
+94
+00:07:16,210 --> 00:07:21,750
+رجال و ال Women أجل بمعنى
+
+95
+00:07:24,870 --> 00:07:29,370
+إنه يبدو إن اللي بالـ «توتي» هدول هم اللي بيخلصوا
+
+96
+00:07:29,370 --> 00:07:34,650
+على اللي بالأزرق أو بالليلة كده، ملاحظين؟ يعني في
+
+97
+00:07:34,650 --> 00:07:41,930
+الأول كلهم بيموتوا أو المعظم رجال و لحد عمر سبعين
+
+98
+00:07:41,930 --> 00:07:46,710
+لتسعة وسبعين هو الغالبية رجال بيموتوا، لكن الستات
+
+99
+00:07:46,710 --> 00:07:49,150
+مش هم الغالبين، وبعد هيك بيصيروا الستات الغالبية
+
+100
+00:07:49,150 --> 00:07:51,510
+بين تمانين وتسعين، ما هو أصلا بيبقوا خلصوا الرجال
+
+101
+00:07:51,510 --> 00:07:56,130
+وخلصوا عليهم،طبعاً هذه مزحة لشك، لكن هو طبعاً
+
+102
+00:07:56,130 --> 00:08:03,650
+الـMI أو المشاكل القلب هي أكتر منها في الرجال من
+
+103
+00:08:03,650 --> 00:08:11,410
+الستات والسبب غالباً له علاقة بالأستروجين على سبيل
+
+104
+00:08:11,410 --> 00:08:17,960
+المثال وتكون ال building والحركة وكذاطيب، إيش الـ
+
+105
+00:08:17,960 --> 00:08:22,560
+Risk Factors؟ إحنا تقولنا المشاكل هذه طبعاً ما
+
+106
+00:08:22,560 --> 00:08:25,700
+لهاش علاقة بس في أمريكا، إن شاء الله الـ Risk
+
+107
+00:08:25,700 --> 00:08:29,000
+Factors هي تعملها وما تعملها أو تعمليها وما
+
+108
+00:08:29,000 --> 00:08:33,580
+تعمليها، وتمارسها وما تمارسها، في الآخر هتعمل ليه؟
+
+109
+00:08:33,580 --> 00:08:37,770
+مشاكل Coronary Heart Diseaseالـ Coronary Heart
+
+110
+00:08:37,770 --> 00:08:39,690
+Disease لديها الكثير من الوضعات الخطرية بالنسبة
+
+111
+00:08:39,690 --> 00:08:43,330
+لها، وخاصة فيها أشياء غير قابلة للتحكم، وليس بيدي
+
+112
+00:08:43,330 --> 00:08:47,470
+ولا بيدك، مثل الـ Age، الـ Race، الـ Hereditary،
+
+113
+00:08:47,470 --> 00:08:51,110
+الجنس الإنسان، هذا ماقدرش أتحكم فيه، لأننا كنا
+
+114
+00:08:51,110 --> 00:08:53,910
+رجال بنصابوا أكتر من الستات، فإيش ذنب الراجل وإيش
+
+115
+00:08:53,910 --> 00:08:56,930
+ذنب السنت؟ مافيش، مافيش، هذه غير قابلة للتحكم، لا
+
+116
+00:08:56,930 --> 00:09:01,650
+بيدي ولا بيدي، لكن في حاجات ما جنيناه على أنفسنا،
+
+117
+00:09:01,650 --> 00:09:06,520
+إحنا دخان إيراتي وإيراتيك،الـ Hypertension وقلنا
+
+118
+00:09:06,520 --> 00:09:10,680
+ليش بنشغل الـ Hypertension إيرادتي وإيرادتك، الـ
+
+119
+00:09:10,680 --> 00:09:12,840
+Diabetes إيرادتي وإيرادتك أو خلّيني أقول
+
+120
+00:09:12,840 --> 00:09:16,760
+Controllable، بلاش نقول إيرادات، إنما في إمكانية
+
+121
+00:09:16,760 --> 00:09:19,860
+أتحكم في Hyperlipidemia، Radiotherapy of the
+
+122
+00:09:19,860 --> 00:09:23,900
+chest، هذه كلها زي ما بقولها Controllable، Risk
+
+123
+00:09:23,900 --> 00:09:29,000
+Factors وبتأدى لموضوع الـ MI. طب هو إيش اللي
+
+124
+00:09:29,000 --> 00:09:32,180
+بيحصل؟ إيش ال Pathophysiology؟ قلنا هي بتتكون
+
+125
+00:09:32,180 --> 00:09:38,560
+عندناالـ Pterosclerotic blocks تجمعات الـ
+
+126
+00:09:38,560 --> 00:09:41,820
+Pterosclerotic وهذه بتعملنا تضيق
+
+127
+00:09:44,240 --> 00:09:48,720
+وهذه في الأكتر بتيجي في منطقة اسمها الـ Intima إنه
+
+128
+00:09:48,720 --> 00:09:53,480
+خلّيني أقول كل نفايات الجسم اللي هو المكتوب عنها
+
+129
+00:09:53,480 --> 00:09:58,300
+Grung هنا زي الـ Calcium Deposits، Fatty Deposits،
+
+130
+00:09:58,300 --> 00:10:04,520
+Abnormal Inflammatory Cells بتتكون في مناطق خلّيني
+
+131
+00:10:04,520 --> 00:10:09,160
+أقول بدأت تتضيق أو مناطق مجروحة لسبب أو من الأسباب
+
+132
+00:10:09,160 --> 00:10:14,770
+Legionبيتكوّل هناك Blacks تجمعات أو تكونات وبعد
+
+133
+00:10:14,770 --> 00:10:19,990
+وقت التكونات هذه بتزيد و بتزيد و في الآخر بتسكر
+
+134
+00:10:19,990 --> 00:10:22,930
+الشارع يعني بتتصوروا أنا بقى الشارع نظيف و بدوا
+
+135
+00:10:22,930 --> 00:10:27,850
+الناس على جنب الشارع يكبوا زبالة و كل الناس صارت
+
+136
+00:10:27,850 --> 00:10:30,750
+كل حرطيجة كوب زبالة في الآخر الزبالة هي في الشارع
+
+137
+00:10:30,750 --> 00:10:35,270
+عشان بتعمل كوب بتضيق المواصلات بيصير السيارات بدل
+
+138
+00:10:35,270 --> 00:10:40,310
+ما هي رايحة و جاية بيصير يستنى اللي رايحع بين اللي
+
+139
+00:10:40,310 --> 00:10:42,910
+جاي ما يدخل عشان هو يعود يدخل، ليش؟ لأنه كملة
+
+140
+00:10:42,910 --> 00:10:47,410
+زبالة مسكر عليه ومرة على مرة، مرة على مرة، في
+
+141
+00:10:47,410 --> 00:10:51,730
+الآخر بيصير عندنا تسكير للشارع من الزبالة هذه اللي
+
+142
+00:10:51,730 --> 00:10:54,050
+احنا بيقول عنها «grung» أو بيقول عنها زي ما قلنا
+
+143
+00:10:57,690 --> 00:11:02,630
+النفايات الجسم اللي بتتكون طبعاً الدم في الآخر
+
+144
+00:11:02,630 --> 00:11:07,630
+بيصير مايلاجيش مسار جوا الشريان و بيصير طبعاً يصير
+
+145
+00:11:07,630 --> 00:11:14,760
+turbulence حاجة اسمها turbulence و بيصيرتبطق، بطق،
+
+146
+00:11:14,760 --> 00:11:20,840
+بيصير بطق، يعني مش بس على جد أنه تسكر الشارع أو
+
+147
+00:11:20,840 --> 00:11:23,840
+تضيق الشارع، إنما بيصير بطق، وبيصير إنه
+
+148
+00:11:23,840 --> 00:11:28,140
+turbulence، وهذا الموضوع بيقدّي في لحظة من اللحظات
+
+149
+00:11:29,800 --> 00:11:35,640
+لأنه يجل كمية الأكسجين اللي بتصل للقلب كمية
+
+150
+00:11:35,640 --> 00:11:39,120
+الـperfusion اللي بتصل للقلب بتجل وطبعاً بالتالي
+
+151
+00:11:39,120 --> 00:11:42,720
+كمية الـNutrients، الـVitamins، كمية الأكسجين
+
+152
+00:11:42,720 --> 00:11:47,280
+طبعاً احنا هنا بهمنا الـO2 supply The heart is not
+
+153
+00:11:47,280 --> 00:11:53,420
+in danger of hypoxia لحد 50% of the vessel is
+
+154
+00:11:53,420 --> 00:12:00,360
+occluded إذا سكر الشريان لـ50%أو أكتر من 50% بيبدأ
+
+155
+00:12:00,360 --> 00:12:06,220
+لحد ساعتها ما بتأثرش القلب لسه مافيش عنا danger
+
+156
+00:12:06,220 --> 00:12:11,300
+مافيش خطر و بتأثر بس مافيش خطر until 50% of the
+
+157
+00:12:11,300 --> 00:12:16,720
+vessel is occluded at the heart since a decrease
+
+158
+00:12:16,720 --> 00:12:20,080
+إذا حس الجلب إنه فيه نقص في ال oxygen بيحاول إيش
+
+159
+00:12:20,080 --> 00:12:23,940
+يعمل compensation لأنه خف عليه فإيش بيروح و بيعمل
+
+160
+00:12:23,940 --> 00:12:28,990
+بيزيد ال heart rateهذه هي ميكانيزات التعامل بالقلب
+
+161
+00:12:28,990 --> 00:12:37,050
+في تجارب الـ O2 تفتثت تزيد حرارة القلب تزيد حرارة
+
+162
+00:12:37,050 --> 00:12:41,830
+الدم وأيش كمان؟ وبتسوق الأترومة اللي صارت الـ
+
+163
+00:12:41,830 --> 00:12:44,710
+Blacks اللي موجودة نتيجة الهيبوكسيا برضه بتزيد
+
+164
+00:12:44,710 --> 00:12:49,540
+الآن إذا وين 70% of the artery is occludedببدأ
+
+165
+00:12:49,540 --> 00:12:53,940
+يبين عنا أعراض أعراض بصورة Angina Pectoris إيش
+
+166
+00:12:53,940 --> 00:12:57,800
+يعني Angina Pectoris؟ ميناتها ذبحة صدرية Angina
+
+167
+00:12:57,800 --> 00:13:00,920
+Pectoris تبدأ بعد وين 70% of the artery is
+
+168
+00:13:00,920 --> 00:13:07,490
+occluded هذه صورةاللي زي الجبل هنا وفيه خلايا
+
+169
+00:13:07,490 --> 00:13:11,330
+عندنا جواتها monocytes و macrophages و endothelial
+
+170
+00:13:11,330 --> 00:13:15,730
+و smooth cells و fatty و necrotic tissue هذا قلنا
+
+171
+00:13:15,730 --> 00:13:18,230
+كم النفايات أو الزبالة اللي سكّرنا الشارع اللي هو
+
+172
+00:13:18,230 --> 00:13:21,570
+الأطلقطالع الصورة اللي جنبها بنلاقي كيف ال blacks
+
+173
+00:13:21,570 --> 00:13:27,210
+بدأت تسكر الشريان وفي مقطع عرضي للشريان بنشوف إنه
+
+174
+00:13:27,210 --> 00:13:32,130
+الشريان تضيق نتيجة process اسمه atherosclerosis
+
+175
+00:13:32,130 --> 00:13:36,350
+طيب إيش ال symptoms اللي بشوفها؟ في ال coronary
+
+176
+00:13:36,350 --> 00:13:38,490
+heart disease ممكن ولا symptoms
+
+177
+00:13:42,880 --> 00:13:49,140
+ممكن يكون asymptomatic لكن ممكن أشوف chest
+
+178
+00:13:49,140 --> 00:13:53,400
+heaviness كيف يعني تقل على السدر تحس أنه كأنه
+
+179
+00:13:53,400 --> 00:13:56,740
+بلاطة على منطقة الجلب موجودة أو على السدر دسنية
+
+180
+00:13:56,740 --> 00:14:03,720
+نفسه بيصير مش طبيعي، fatigue، تحبان، هل كان، chest
+
+181
+00:14:03,720 --> 00:14:08,200
+pain طبيعي، chest pain وهذا cardinal symptom of
+
+182
+00:14:08,200 --> 00:14:12,320
+myocardial ischemiaأنجاينة طبعاً حكينا وMI اللي هي
+
+183
+00:14:12,320 --> 00:14:14,460
+النتائج اللي هنشوفها ischemic heart disease
+
+184
+00:14:14,460 --> 00:14:18,060
+classification احنا اختارت أنا بس حاجات بسيطة
+
+185
+00:14:18,060 --> 00:14:22,480
+أنجاين بيكتورس العادية وفي unstable أنجاين بيكتورس
+
+186
+00:14:22,480 --> 00:14:26,580
+هنشوف الفرق بينهم وفي عندنا ال MI او myocardial
+
+187
+00:14:26,580 --> 00:14:29,980
+infection وفي عندنا ال chronic ischemic heart
+
+188
+00:14:29,980 --> 00:14:34,980
+disease with heart failureطب الـ Angina Victoris
+
+189
+00:14:34,980 --> 00:14:41,140
+قلنا هي إيش؟ زبحة صدرية؟ 75% of coronary artery
+
+190
+00:14:41,140 --> 00:14:45,280
+resulting in pain إيش نوع ال pain هذا؟ لازم نقدر
+
+191
+00:14:45,280 --> 00:14:49,140
+نوصل في ال pain مش أي pain على الصدر يا جماعة مش
+
+192
+00:14:49,140 --> 00:14:54,660
+أي pain على الصدر على ال chest يعني من Angina
+
+193
+00:14:54,660 --> 00:15:02,130
+Victoris أو MI هإيش؟ آه هذه هيالـ Next Assignment
+
+194
+00:15:02,130 --> 00:15:08,010
+اللي هتكتبوليها بالإيد وتكتبولي الـ Differential
+
+195
+00:15:08,010 --> 00:15:13,770
+Diagnosis of Chest Pain بالنسبة
+
+196
+00:15:13,770 --> 00:15:19,770
+طبعا، مين حسب مين أكتر من مين خلينا نقول Maximum
+
+197
+00:15:19,770 --> 00:15:23,640
+10 أسطوربديش موضوع just pain differential
+
+198
+00:15:23,640 --> 00:15:29,380
+diagnosis والنسبة تبعتهم مين أكتر بنشوفه و طبعا لو
+
+199
+00:15:29,380 --> 00:15:32,640
+في كلمات غريبة في ال differential diagnosis اكتبوا
+
+200
+00:15:32,640 --> 00:15:37,120
+قبلها إيش بتقصدوها يعني مش يعني حاولوا جدر الإمكان
+
+201
+00:15:37,120 --> 00:15:41,520
+اللي بتكتبوه تكونوا فاهمينه مهم جدا الموضوع هذا
+
+202
+00:15:43,170 --> 00:15:46,310
+وهذا أجى عدة مرات سؤال في الامتحانات
+
+203
+00:15:46,310 --> 00:15:50,030
+classification of chest pain مش كل بني آدم مش كل
+
+204
+00:15:50,030 --> 00:15:54,470
+واحد بيقول و الله صدري واجعني معناته عنده MI أو
+
+205
+00:15:54,470 --> 00:15:57,810
+عنده .. طب إيش نوع ال pain اللي بنحكي عنه يبقى
+
+206
+00:15:57,810 --> 00:16:02,390
+قولنا عن ال assignment اللي هو هنعمله اليوم؟Chest
+
+207
+00:16:02,390 --> 00:16:07,050
+pain – radiating pain to left shoulder, jaw – left
+
+208
+00:16:07,050 --> 00:16:11,110
+or to right arm يعني فيه إله radiation يمتد،
+
+209
+00:16:11,110 --> 00:16:14,070
+بتلاقي المريض بيقولك أه والله كتفي شمال، إيدي
+
+210
+00:16:14,070 --> 00:16:20,020
+شمال، دجني، هذه كلها هيتهاأحيانًا يتم إجراءها من
+
+211
+00:16:20,020 --> 00:16:23,640
+خلال الـ Physical Exertion في الغالب، في الغالب،
+
+212
+00:16:23,640 --> 00:16:25,980
+لما الواحد بيبقى بيعمل عملية عملية عملية عملية
+
+213
+00:16:25,980 --> 00:16:27,640
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+214
+00:16:27,640 --> 00:16:28,280
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+215
+00:16:28,280 --> 00:16:28,500
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+216
+00:16:28,500 --> 00:16:30,600
+عملية عملية عملية عملية عملية عملية عملية عملية
+
+217
+00:16:30,600 --> 00:16:35,190
+عملية عملية عملية عملية عملية عملية عأناضف الشارع،
+
+218
+00:16:35,190 --> 00:16:40,450
+أجري لي شوي، أطلع على الشجرة، أجد الزتونات، أي
+
+219
+00:16:40,450 --> 00:16:43,690
+حاجة بلاقي أنه صار عنده chest pain، ليش؟ لأن القلب
+
+220
+00:16:43,690 --> 00:16:47,070
+صار مطلوب منه أكتر، لكن الـ coronary artery مش
+
+221
+00:16:47,070 --> 00:16:53,970
+قادر يدخل أكتر، فإيش بيصير؟ أن القلب بيزيد نشاطه،
+
+222
+00:16:53,970 --> 00:16:59,160
+وهذا لما يزيد نشاطهو بيحاول يدخل دم أكتر، بيقدرش
+
+223
+00:16:59,160 --> 00:17:05,000
+يدخل دم أكتر، فبيصير عندنا الـ pain إفس وهذا في
+
+224
+00:17:05,000 --> 00:17:09,980
+الغالب إذا وقفت الشغل اللي بشتغله، بروح الوجع في
+
+225
+00:17:09,980 --> 00:17:12,420
+العادة، طبعا لازم أروح الدكتور، ده شك، بس أنا
+
+226
+00:17:12,420 --> 00:17:15,180
+بحكيلكوا إيش يعني الـ angina pectoris إذا وقفت ال
+
+227
+00:17:15,180 --> 00:17:19,270
+exertion، بخف ال painالأنجينابيكترون يمكن أن
+
+228
+00:17:19,270 --> 00:17:21,550
+يكونوا مستقل أو غير مستقل، وهنا الفرق بين مستقل
+
+229
+00:17:21,550 --> 00:17:25,390
+وغير مستقل، المستقل هو الحرارة والبطن من الأحداث
+
+230
+00:17:25,390 --> 00:17:31,390
+غير تغيّر، دائما نفس الوجع، الطريقة والوجع هو
+
+231
+00:17:31,390 --> 00:17:35,230
+نفسه، خلال مرحلة من الوقت، أكثر من ذلك بسبب الضغط
+
+232
+00:17:35,230 --> 00:17:39,390
+أو التجارب، جنة من التجارب، طيب والغير مستقل،
+
+233
+00:17:39,390 --> 00:17:45,750
+الحرارة والبطن تغير، الأمر التانيبما يكون في مدت
+
+234
+00:17:45,750 --> 00:17:50,550
+كمان شدة لفرقوانسي وبتيجي mostly in rest مش زي
+
+235
+00:17:50,550 --> 00:17:54,450
+هديك لما انا تعبت unstable لما انا تعبت صار عندى
+
+236
+00:17:54,450 --> 00:18:00,330
+chest pain ال unstable بدون تعب في rest الموضوع ال
+
+237
+00:18:00,330 --> 00:18:07,730
+myocardial infection عند ما يصير عندنا partial or
+
+238
+00:18:07,730 --> 00:18:11,150
+total occlusion of one or more of the coronaries
+
+239
+00:18:11,150 --> 00:18:15,660
+واحنا عارفين ال coronaries أكتر من واحدأرتريز due
+
+240
+00:18:15,660 --> 00:18:20,260
+to atheroma, thrombus او emboli resulting in cell
+
+241
+00:18:20,260 --> 00:18:25,540
+death بيصير عندي infarction يعني مجرد التذكير بدون
+
+242
+00:18:25,540 --> 00:18:29,040
+ما يأثر على ال heart muscle بقول عنه angina لكن
+
+243
+00:18:29,040 --> 00:18:33,400
+إذا صار مأثرلي و مديني علامات MI هذه بقول عنها
+
+244
+00:18:33,400 --> 00:18:41,030
+إيش؟ بقول عنها MIعندما يحدث الـMI، يكون هناك عملية
+
+245
+00:18:41,030 --> 00:18:45,250
+تلاتة إلى أربعة مخلوقات مخلوقات مخلوقات مخلوقات
+
+246
+00:18:45,250 --> 00:18:46,770
+مخلوقات مخلوقات مخلوقات مخلوقات مخلوقات مخلوقات
+
+247
+00:18:46,770 --> 00:18:54,330
+مخلوقات مخلوقات مخلوقات مخلوقات مخلوقات
+
+248
+00:18:55,880 --> 00:18:59,800
+حوالي في أمريكا طبعاً ربع مليون death per year
+
+249
+00:18:59,800 --> 00:19:02,700
+تلاتين في المية mortality within the first two
+
+250
+00:19:02,700 --> 00:19:05,740
+hours يعني لو واحد صار عنده MI تلاتين في المية
+
+251
+00:19:05,740 --> 00:19:08,840
+بيموتوا من أول ساعة في أمريكا في الصين في غزة في
+
+252
+00:19:08,840 --> 00:19:11,720
+مصر في غزة ممكن يكون أكتر لكن بيموتوا في أول
+
+253
+00:19:11,720 --> 00:19:15,620
+ساعتين عشان هيك بتقولك والله على طول صار عنده جلطة
+
+254
+00:19:15,620 --> 00:19:21,600
+قلبيةبتشت التذكير وتوفى بعد ساعة أو بعد نص ساعة أو
+
+255
+00:19:21,600 --> 00:19:25,300
+لسه ماوصلوا فيه المستشفى لو كان متوفي ليش؟ لأن هذا
+
+256
+00:19:25,300 --> 00:19:30,980
+الوضع الطبيعي في 30% من الحالات أنه تموت خلال
+
+257
+00:19:30,980 --> 00:19:36,240
+ساعتين 45% minutes of ischemia تديني a cardiac
+
+258
+00:19:36,240 --> 00:19:39,440
+muscle death or cancer كيف بعمل ال diagnosis of
+
+259
+00:19:39,440 --> 00:19:45,550
+MI؟ طبعاً بعمله ECGبالـ Electrocardiographic
+
+260
+00:19:45,550 --> 00:19:50,150
+Changes بلاقي في حاجة اسمها ST elevation احنا نفكر
+
+261
+00:19:50,150 --> 00:19:55,630
+إن جونا PQRST، الـ ST بلاقيها عالية Myocardial
+
+262
+00:19:55,630 --> 00:19:59,010
+enzyme elevation زي الـCK والتروبونين
+
+263
+00:19:59,010 --> 00:20:08,390
+والسيرياكتيبروتين طبعا
+
+264
+00:20:08,390 --> 00:20:12,590
+أنتوا عارفين إيش .. إيش .. إيش الفرق بين الترمبس
+
+265
+00:20:12,590 --> 00:20:19,920
+والـEmboli ولا مش عارفين؟ أكيد عارفينالـ
+
+266
+00:20:19,920 --> 00:20:22,260
+Complication of Biocardial Infection طبعاً عندنا
+
+267
+00:20:22,260 --> 00:20:26,900
+مشكلة، يعني الجذية مش جذية أنه صار عندي muscle تسل
+
+268
+00:20:26,900 --> 00:20:33,460
+death وخلص وخلصناها، لأ المشكلة أن الـ Infection
+
+269
+00:20:33,460 --> 00:20:40,120
+بتخلي القلب غير قادر أنه يعمل، هو إيش شغلة القلب؟
+
+270
+00:20:40,120 --> 00:20:44,620
+إنه يضخ دم لكل الجسم، طيب إذا والله الـ motor في
+
+271
+00:20:44,620 --> 00:20:49,110
+قطعة منه صارت تعبانة،مامش هيقدر يضخ appropriate
+
+272
+00:20:49,110 --> 00:20:52,750
+بيصير يعني يدوب على الجد مش جادر يشتغل فبصير
+
+273
+00:20:52,750 --> 00:20:56,070
+leading to heart failure رقم واحد الـMI ممكن تعملي
+
+274
+00:20:56,070 --> 00:20:59,410
+heart failure ممكن تدينا pain دايما pain دايما
+
+275
+00:20:59,410 --> 00:21:04,010
+pain ممكن تعملنا shock ممكن المنطقة اللي ماتت في
+
+276
+00:21:04,010 --> 00:21:09,770
+خلايا القلبيصير إيش فيها؟ Aneurysma يعني إيش يعني
+
+277
+00:21:09,770 --> 00:21:15,470
+Aneurysma؟ أنه تتنبعج يعني المنطقة الضعيفة اللي
+
+278
+00:21:15,470 --> 00:21:20,490
+ماتت في جدار القلب سواء في الـ left ventricle أو
+
+279
+00:21:20,490 --> 00:21:24,130
+في ال right ventricle نتيجة إنها ماتت بتعملي زي
+
+280
+00:21:24,130 --> 00:21:26,950
+انبعاج والانبعاج هي ده اللي بيقول aneurysm ممكن
+
+281
+00:21:26,950 --> 00:21:30,690
+يصيره في أي لحظة كمان rupture طبعاً هذا الانبعاج
+
+282
+00:21:31,830 --> 00:21:34,750
+كمان إيش ممكن يعملي؟ ممكن يعملي Embolism تكوين
+
+283
+00:21:34,750 --> 00:21:38,730
+لتجلطات في جلبه وممكن يعملي طبعا نتيجة موت خلايا
+
+284
+00:21:38,730 --> 00:21:43,510
+في خلايا القلب يعملي Arrhythmias من الحاجات المهمة
+
+285
+00:21:43,510 --> 00:21:46,750
+الـ Complication اللي هي زي ما قلنا الـ sudden
+
+286
+00:21:46,750 --> 00:21:52,550
+death قلنا ربع مليون حالة بتموت في أمريكا due to
+
+287
+00:21:52,550 --> 00:21:58,350
+sudden cardiac death مرة واحدة بيجي في الجلب و
+
+288
+00:21:58,350 --> 00:22:02,010
+بموت العيانوالـ Sudden Death بنقول عنه Massive
+
+289
+00:22:02,010 --> 00:22:09,030
+Heart Attack Massive Heart Attack وهذا
+
+290
+00:22:09,030 --> 00:22:18,510
+طبعا نتيجة Shock صار لنا تكبّن شخص جون غير الموضوع
+
+291
+00:22:18,510 --> 00:22:26,870
+الآن الموضوع اللي كنا حكينا قبل شوي عن التشخيص
+
+292
+00:22:28,400 --> 00:22:33,680
+بتاع الـ Enzyme الـ Enzyme و ECG تحدثنا عنه فيه
+
+293
+00:22:33,680 --> 00:22:36,520
+كمان بنعمله Eco-cardiography في الـ Diagnosis
+
+294
+00:22:36,520 --> 00:22:41,520
+وممكن للـ Angina نعمل Stress Test لأنه احنا قلنا
+
+295
+00:22:41,520 --> 00:22:48,400
+الـ Angina Victors العادية تنكشفش إلا بالـخلّيني
+
+296
+00:22:48,400 --> 00:22:50,740
+أقول في الـ Definition تبعها إنه صار في عندي
+
+297
+00:22:50,740 --> 00:22:55,280
+stress أو exercise فأنا عشان أشوف changes في ال
+
+298
+00:22:55,280 --> 00:22:58,860
+ECG بروح بعمل حاجة اسمها stress test حنحكي عنه
+
+299
+00:22:58,860 --> 00:23:04,340
+وبعد فترة أنا في عندي طبعا تغليقات أو إغلاقات جوا
+
+300
+00:23:04,340 --> 00:23:09,290
+الشريانالـ Coronary فبتعمله حاجة اسمها تصوير
+
+301
+00:23:09,290 --> 00:23:13,690
+للشريان نعمل عن طريق القسطرة اسمه Angiography عشان
+
+302
+00:23:13,690 --> 00:23:18,550
+أعرف جداش التسكير و نسبة التسكير ال ECG ايش بيعمل
+
+303
+00:23:18,550 --> 00:23:21,130
+ليه؟ خدوا بالكوا يا جماعة الفحوصات هي كل فحص له
+
+304
+00:23:21,130 --> 00:23:25,230
+فايدة معينة مش يعني يلّا أطلب كل فحوصاته مع
+
+305
+00:23:25,230 --> 00:23:29,010
+السلامة ال ECG أو Electrocardiogram أو ال ECG
+
+306
+00:23:29,010 --> 00:23:32,950
+provide a record of the heart electrical activity
+
+307
+00:23:32,950 --> 00:23:34,770
+يعني هو بي
+
+308
+00:23:37,850 --> 00:23:44,610
+بيصورلي أو بيخططلي كهربت القلب ماحتيين بالك انتوا
+
+309
+00:23:44,610 --> 00:23:49,310
+كيف؟ كهربت القلب بس الـ electrical activityوهو
+
+310
+00:23:49,310 --> 00:23:53,090
+simple test records any abnormal findings in the
+
+311
+00:23:53,090 --> 00:23:56,210
+heart electrical impulse وبيصير عن طريق electrodes
+
+312
+00:23:56,210 --> 00:23:58,250
+زي ما احنا شايفين في الصورة ويمكن شفتوها في
+
+313
+00:23:58,250 --> 00:24:02,810
+المستشفيات عن طريق electrodes بتبتحط على السدر
+
+314
+00:24:02,810 --> 00:24:07,630
+وعلى الإدلين والرجلين ال echo مختلف ال echo it may
+
+315
+00:24:07,630 --> 00:24:10,650
+be ordered if your doctor suspects a problem in
+
+316
+00:24:10,650 --> 00:24:14,270
+the heart muscle إذا في عندي مشكلة في ال muscle أو
+
+317
+00:24:14,270 --> 00:24:20,690
+في ال valvesهذه الفرق بين الـ ECG و الـ Echo
+
+318
+00:24:20,690 --> 00:24:25,370
+Stress Test هذا عن طريق الـ treadmill أو الـ
+
+319
+00:24:25,370 --> 00:24:31,990
+exercise أنه أنا بعمله ECG أثناء بشوف وضع القلب
+
+320
+00:24:31,990 --> 00:24:37,070
+أثناء الـ physical exertion أثناء الجهد Stress
+
+321
+00:24:37,070 --> 00:24:42,050
+Test أثناء الجهد ECG أثناء الجهد يعني لو ببينش
+
+322
+00:24:43,970 --> 00:24:48,470
+التغييرات في الـ ECG في الوضع الطبيعي المفروض أنه
+
+323
+00:24:48,470 --> 00:24:53,130
+أثناء الجهد يبين المشكلة الـ Angiogram أو الـ
+
+324
+00:24:53,130 --> 00:24:57,430
+Angiography The most accurate means by which to
+
+325
+00:24:57,430 --> 00:25:01,970
+examine the coronary arteries عشان أعمل فحص للـ
+
+326
+00:25:01,970 --> 00:25:04,650
+coronary arteries أنا بروح بعمله Angiography الـ
+
+327
+00:25:04,650 --> 00:25:09,710
+Angiography is requires a surgical procedure نقول
+
+328
+00:25:09,710 --> 00:25:13,790
+عنه cardiac catheter أو catheterizationبعمل
+
+329
+00:25:13,790 --> 00:25:19,170
+cardiac catheter اللي هو during
+
+330
+00:25:19,170 --> 00:25:24,810
+the procedure catheters small thin plastic tubes
+
+331
+00:25:24,810 --> 00:25:28,290
+are placed in the artery of the legs or the arm
+
+332
+00:25:28,290 --> 00:25:32,930
+where directed using an x-ray machine to the
+
+333
+00:25:32,930 --> 00:25:39,530
+opening of each of the coronary arteries يعنيبندخل
+
+334
+00:25:39,530 --> 00:25:43,370
+عن طريق شريان من الرجل أو من الإيد وبنروح مع الـ X
+
+335
+00:25:43,370 --> 00:25:47,810
+-ray وبنروح على الشرايين التاجية وبنفحصها وبنحط
+
+336
+00:25:47,810 --> 00:25:51,430
+Contrast فيها مادة بتنحقن شايفين الصورة السوداء
+
+337
+00:25:51,430 --> 00:25:54,810
+عندنا في الـ slide هذا بتنحقن بيبينلي كيف الشرايين
+
+338
+00:25:54,810 --> 00:26:00,970
+وهل الشريان متضيق في منطقة معينة أو مش موجود
+
+339
+00:26:00,970 --> 00:26:08,100
+بالمرة أو مسكر أو كذا بيبينوبنصح طبعا على اليوتيوب
+
+340
+00:26:08,100 --> 00:26:13,680
+تطلعوا How is angiography made؟ How is ECG made؟
+
+341
+00:26:13,680 --> 00:26:19,620
+How is Eco made؟ هتلاقوا فيديوهات كتير فرجوا
+
+342
+00:26:19,620 --> 00:26:23,120
+تشوفوا ال process كيف بيصيريا جماعة لما تروح
+
+343
+00:26:23,120 --> 00:26:27,100
+المستشفيات في حاجات كتير مش لازم تحس حالك غريب
+
+344
+00:26:27,100 --> 00:26:29,700
+بالنسبة للـ procedures بتنعمل هناك، لازم تبقى
+
+345
+00:26:29,700 --> 00:26:33,820
+familiar جدر الإمكان مع الـ procedures، مابديش
+
+346
+00:26:33,820 --> 00:26:37,180
+أقول بتعرف تعملها، بس على الأقل، على الأقل، تبقى
+
+347
+00:26:37,180 --> 00:26:40,380
+عارف أن هذا ECG وهذا Echo، هذا بيجيز كذا، وهذا
+
+348
+00:26:40,380 --> 00:26:43,800
+بيعمل كذا، وهذا Angiogram، طلبوله Angiogram، آه
+
+349
+00:26:43,800 --> 00:26:47,760
+والله الـ Angiogram، عشان أشوف الشرايين التاجية من
+
+350
+00:26:47,760 --> 00:26:51,420
+جوا، وأشوف إذا فيها تضيق، وقدش نسبة التضيق،وهل
+
+351
+00:26:51,420 --> 00:26:54,400
+بدها ballooning، هل بدها حطوتها بلون، هل بدها
+
+352
+00:26:54,400 --> 00:26:57,400
+dilatation، هذه الحاجات المفروض إنه في لحظة في
+
+353
+00:26:57,400 --> 00:27:00,300
+لحظات بعد ما نخلص الcourse تبعنا، المساق تبعنا،
+
+354
+00:27:00,300 --> 00:27:03,800
+تكونوا familiar معاها، يعني تروحوا على المستشفيات،
+
+355
+00:27:03,800 --> 00:27:06,800
+عارفين حاجات كتير بتصير في المستشفيات، هذا مش
+
+356
+00:27:06,800 --> 00:27:10,720
+لصالحهم، مش ل .. مش ل .. يمكن للعلاج الطبيعي فقط،
+
+357
+00:27:10,720 --> 00:27:15,220
+إنما كمان للمعرفة العامة والسلوك العام، treatment،
+
+358
+00:27:15,220 --> 00:27:17,780
+many people are able to manage coronary artery
+
+359
+00:27:17,780 --> 00:27:22,130
+disease with lifestyle changes and medicationيعني
+
+360
+00:27:22,130 --> 00:27:26,050
+مش كل إشي بده على طول جراحات و كمية Other people
+
+361
+00:27:26,050 --> 00:27:29,210
+with severe coronary artery disease may need
+
+362
+00:27:29,210 --> 00:27:35,650
+angioplasty or surgery نحكي لغاية كيف ال lifestyle
+
+363
+00:27:35,650 --> 00:27:39,790
+changes؟ عن طريق ال weight control، smoking
+
+364
+00:27:39,790 --> 00:27:45,930
+cessation، exercise، healthy dietأربع كلمات سهلات
+
+365
+00:27:45,930 --> 00:27:49,550
+بسيطات بس في التطبيق هيكونوا صعبين لكن بيدها إرادة
+
+366
+00:27:49,550 --> 00:27:53,550
+اللي بده حاجة بعملها ال medications بندي أدوية
+
+367
+00:27:53,550 --> 00:27:59,670
+الأدوية هي to treat coronary disease cholesterol
+
+368
+00:27:59,670 --> 00:28:05,090
+lowering medications الستاتينز وهذا بجللي كمية ال
+
+369
+00:28:05,090 --> 00:28:12,420
+bad cholesterol أو ال LDLوبندى كمان Vasodilatation
+
+370
+00:28:12,420 --> 00:28:16,960
+نتروغلוצيرين بيحطه المريض تحت اللسان على أساس تعمل
+
+371
+00:28:16,960 --> 00:28:22,790
+Vasculature Vasodilatationبندى دوة لـ Anti
+
+372
+00:28:22,790 --> 00:28:27,150
+-hypertension drugs على أساس أنه أخفف الضغط فأخفف
+
+373
+00:28:27,150 --> 00:28:34,930
+اللي هو تقول عن الجلب أنه يضخ ضد ضغط كبير جدا جدا
+
+374
+00:28:34,930 --> 00:28:39,250
+في الجسم وبدى كمان أسبرين عشان يمنع الـ
+
+375
+00:28:39,250 --> 00:28:44,720
+aggregationطبعاً لحد فترة مش زمان كان كل واحد فوق
+
+376
+00:28:44,720 --> 00:28:48,360
+الأربعين ينصحه ياخد تسعة وتمانين ميلي جرام أسبيرين
+
+377
+00:28:48,360 --> 00:28:52,600
+بيبي أسبيرين يومياً لكن ما أثبتتش صحة هذا الموضوع
+
+378
+00:28:52,600 --> 00:28:56,000
+إلا إنه لسه ما زال بعض المجتمعات بتدي تسعة وتمانين
+
+379
+00:28:56,000 --> 00:29:03,160
+ميلي جرام أسبيرين لكلإنسان لكل
+
+380
+00:29:03,160 --> 00:29:07,320
+إنسان فوق الأربعين سنة الـ Aspirin هو أصلاً pain
+
+381
+00:29:07,320 --> 00:29:10,140
+killer وأحنا ما ندوش لل pain killer هو لمنع ال
+
+382
+00:29:10,140 --> 00:29:14,260
+aggregation of plateletsالـ Surgical Intervention
+
+383
+00:29:14,260 --> 00:29:19,820
+حسب إما بنعمل بالون، بالون يعني توسيع أو بنحط
+
+384
+00:29:19,820 --> 00:29:24,000
+Stent أو بنعمل حاجة اسمها Coronary Artery Bypass
+
+385
+00:29:24,000 --> 00:29:28,020
+Grafting كابج، كابج اسمها بيقولونها في المستشفيات
+
+386
+00:29:28,020 --> 00:29:31,940
+الـ Stent اللي بنعمله زي ما أحنا شايفين في الصور
+
+387
+00:29:31,940 --> 00:29:36,900
+أنه أنا بدخل بالقسطرة القلبية وباجي بدخل بـ Tubes
+
+388
+00:29:36,900 --> 00:29:43,360
+وTubes هاي إما بعملها لو عنديالـ Coronary
+
+389
+00:29:43,360 --> 00:29:48,000
+Obstruction بالـ Dilatation ممكن أوسع وخلاص أخرج
+
+390
+00:29:48,000 --> 00:29:51,520
+ولكن في بعض الأحيان بحتاج أحط دعمات هذه اللي بنسعى
+
+391
+00:29:51,520 --> 00:29:55,040
+عنها حطوله دعامة وحطوله تنتين وحطوله تلاتة بنحط
+
+392
+00:29:55,040 --> 00:29:59,660
+دعمات جوا القلبطبعاً مافيش إشي بدون complications
+
+393
+00:29:59,660 --> 00:30:03,400
+و الـ Angioplasty زي ما قلنا بندخل البالون و
+
+394
+00:30:03,400 --> 00:30:09,420
+بنحاول زي ما أحنا شايفين أنه نوسع و .. و .. عم ..
+
+395
+00:30:09,420 --> 00:30:11,580
+عن طريق حاجة زي هيك زي الـ rotation
+
+396
+00:30:14,560 --> 00:30:19,080
+وهذه بتوسع الشريان نوعًا ما يعني هو عمليًا زي
+
+397
+00:30:19,080 --> 00:30:23,120
+حياتنا العملية لما أدخل في أي مكان مثلًا مجاري على
+
+398
+00:30:23,120 --> 00:30:26,500
+سبيل المثال بدي أدخل في المواسير عشان أسلك هي
+
+399
+00:30:26,500 --> 00:30:29,780
+عبارة عن عملية تسليك طبعًا لكن بطريقة طبية سليمة
+
+400
+00:30:29,780 --> 00:30:33,240
+مية في المية وفي طبعًا بقى أدهيك إذا والله لجينا
+
+401
+00:30:33,240 --> 00:30:38,740
+تسكيرات في عدة شراينبنعمله حاجة اسمها coronary
+
+402
+00:30:38,740 --> 00:30:42,560
+artery bypass grafting الـ Cabbage و is advised
+
+403
+00:30:42,560 --> 00:30:46,820
+for selected groups of patients with significant
+
+404
+00:30:46,820 --> 00:30:50,480
+narrowing and blockage of the heart arteries
+
+405
+00:30:50,480 --> 00:30:53,880
+coronary artery disease الـ Cabbage creates new
+
+406
+00:30:53,880 --> 00:30:59,500
+roots إيش بنعمل إحنا؟ والله بنجيب قطعة من وريد
+
+407
+00:31:00,760 --> 00:31:05,000
+وبنعمل تحويدة حوالين التسكير في منطقة تانية هو هذا
+
+408
+00:31:05,000 --> 00:31:08,520
+اللي بيشتغلوا Cabbage surgery creates new roots
+
+409
+00:31:08,520 --> 00:31:12,120
+around narrowed and blocked arteries allowing
+
+410
+00:31:12,120 --> 00:31:15,600
+sufficient blood flow to deliver oxygen and
+
+411
+00:31:15,600 --> 00:31:20,660
+nutrients to the heart muscle يعني حقيقة هذه من
+
+412
+00:31:20,660 --> 00:31:24,160
+المحاضرات اللي المفروض أنه فعلا بتنشرح وجاهي لأن
+
+413
+00:31:24,160 --> 00:31:28,730
+كتير حاجات بتنجل و بتتوضحلكن هذه الوضع يعني أتمنى
+
+414
+00:31:28,730 --> 00:31:31,550
+مع الأخبار الجديدة ان شاء الله تعالى في الفترات
+
+415
+00:31:31,550 --> 00:31:34,630
+الجاية يتحول التعليم للتعليم وجاهي يبقى في فرصة
+
+416
+00:31:34,630 --> 00:31:38,590
+أكبر أن الواحد يشرح أكتر يعني أتمنى أن تكونوا
+
+417
+00:31:38,590 --> 00:31:41,230
+الفكرة وصلتكم في قضية الـCoronary Heart Disease أو
+
+418
+00:31:41,230 --> 00:31:43,490
+الـChemical Heart Disease نصيختي الحاجات اللي
+
+419
+00:31:43,490 --> 00:31:48,210
+حكينا عنها الـCabbageالـ Angioplasty مع الـ
+
+420
+00:31:48,210 --> 00:31:54,690
+Ballooning مع وضع الـ Stent مع كيف بنعمل الـ ECG
+
+421
+00:31:54,690 --> 00:32:01,410
+كيف بنعمل الـ ECO كيف بنعمل الـ Stress Test حاولوا
+
+422
+00:32:01,410 --> 00:32:06,550
+على فيديوهات على اليوتيوب وهذا سهل وموجودة تحاولوا
+
+423
+00:32:06,550 --> 00:32:09,890
+تشوفوا كيف بنعمل وهذا كتير مهم بالنسبة لنا ال
+
+424
+00:32:09,890 --> 00:32:14,070
+assignment تبعنا فاكرينه ولا أفكركوا فيه؟أكيد
+
+425
+00:32:14,070 --> 00:32:17,050
+فاكرينه يطيكوا العافية للمحاضرة اللي جاي ان شاء
+
+426
+00:32:17,050 --> 00:32:19,510
+الله تعالى وانهاركوا سعيد
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/wIJdyXlauDk_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/wIJdyXlauDk_raw.srt
new file mode 100644
index 0000000000000000000000000000000000000000..bbcf71d171cabb2fc5a983792d6e8681e005664e
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/wIJdyXlauDk_raw.srt
@@ -0,0 +1,1408 @@
+1
+00:00:00,960 --> 00:00:03,660
+بسم الله الرحمن الرحيم الحمد لله رب العالمين إحنا
+
+2
+00:00:03,660 --> 00:00:07,040
+الآن إن شاء الله تعالى هنشرح .. خلّيني أقول جزء من
+
+3
+00:00:07,040 --> 00:00:10,720
+ال physiology وزي ما قلنا المرات اللي فاتت إنه
+
+4
+00:00:10,720 --> 00:00:13,680
+يعني إحنا بنشرح أشياء دي رتوش بس من ال Anatomy و
+
+5
+00:00:13,680 --> 00:00:16,820
+ال physiology و ممكن بعض الأمور تعود تمر معانا في
+
+6
+00:00:16,820 --> 00:00:21,500
+خلال محاضرات و الحديث عن ال diseases اللي بتصيب ال
+
+7
+00:00:21,500 --> 00:00:26,330
+cardiovascular diseaseالـ .. كنا نتحدث عن الـ
+
+8
+00:00:26,330 --> 00:00:29,710
+anatomy of the heart، اليوم هنتحدث short،
+
+9
+00:00:29,710 --> 00:00:33,410
+وأبعتلكوا كمان فيديو، ممكن أحاول أحطه على البرنامج
+
+10
+00:00:33,410 --> 00:00:36,910
+هان، مش عارف يظبط ولا لأ، لكن خلّينا نجرب، أو
+
+11
+00:00:36,910 --> 00:00:41,090
+ببعتلكوا إياه على الـWhatsApp، فيديو animation،
+
+12
+00:00:41,090 --> 00:00:47,360
+لكيف بيصير ال cardiac functionالـ Cardiac Muscle
+
+13
+00:00:47,360 --> 00:00:51,520
+Contraction زي ما أحنا عارفين أن الـ «هارد» الـ
+
+14
+00:00:51,520 --> 00:00:53,660
+«هارد» الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد»
+
+15
+00:00:53,660 --> 00:00:55,400
+الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد» الـ
+
+16
+00:00:55,400 --> 00:00:57,320
+«هارد» الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد»
+
+17
+00:00:57,320 --> 00:01:00,400
+الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد» الـ
+
+18
+00:01:00,400 --> 00:01:02,160
+«هارد» الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد»
+
+19
+00:01:02,160 --> 00:01:09,680
+الـ «هارد» الـ «هارد» الـ «هارد» الـ «هارد»
+
+20
+00:01:09,680 --> 00:01:12,280
+الـ «هارد» الـ
+
+21
+00:01:15,780 --> 00:01:19,040
+الذي يسمّى Contract as a Unit Cardiac muscle
+
+22
+00:01:19,040 --> 00:01:21,540
+contraction is similar to skeletal muscle
+
+23
+00:01:21,540 --> 00:01:27,000
+contraction طبعاً
+
+24
+00:01:27,000 --> 00:01:30,900
+الـ Heart physiology sequence of excitation بيبدأ
+
+25
+00:01:30,900 --> 00:01:35,570
+عندنا الموضوع اللي هوالـ «self-automatically» أو
+
+26
+00:01:35,570 --> 00:01:38,990
+«automatism» بتبدأ من حاجة اسمها اللي هي النقطة
+
+27
+00:01:38,990 --> 00:01:42,170
+البيضاء النقطة الصفراء اللي موجودة في الـ «right
+
+28
+00:01:42,170 --> 00:01:47,370
+atrium» اللي هي «SA node» أو «sino-atrial node»
+
+29
+00:01:47,370 --> 00:01:50,250
+وهذه بنقول عنها الـ «pace maker» هي اللي بتدي الـ
+
+30
+00:01:50,250 --> 00:01:54,850
+«pace» هي اللي بتدي البداية وبعد هيك بيبدأ يتحرك
+
+31
+00:01:54,850 --> 00:02:00,470
+الـ «discharge»أو الـ Excitation زي ما هنشوف عندنا
+
+32
+00:02:00,470 --> 00:02:05,950
+في الرسمات في اتجاه الـ muscles اللي هي الـ
+
+33
+00:02:05,950 --> 00:02:09,750
+muscles of the right atrium to the left atrium
+
+34
+00:02:09,750 --> 00:02:13,830
+وبعدين بدخل كمان على من خلال حاجة اسمها الـ
+
+35
+00:02:13,830 --> 00:02:18,210
+internodal pathway بدخل للـ atrioventricular node
+
+36
+00:02:18,210 --> 00:02:24,230
+اللي هي رقم 2 بعد الـ sinoatrial sinusSinus أو
+
+37
+00:02:24,230 --> 00:02:25,690
+Sino-Atrial Node
+
+38
+00:02:30,970 --> 00:02:36,130
+هذا ما رأيناه في الـ SA نود بدأ ينتشر الـ
+
+39
+00:02:36,130 --> 00:02:39,450
+Discharge، ينشر الـ Impulses، يبدأ الـ Atrial
+
+40
+00:02:39,450 --> 00:02:45,010
+Excitation، وينتشر إلى أين يذهب الـ Impulse إلى
+
+41
+00:02:45,010 --> 00:02:49,090
+الـ AV نود، الـ Atrioventricular نود، ويذهب إلى
+
+42
+00:02:49,090 --> 00:02:53,410
+الـ Atrium في نفسه، وهذا طبعا في مدة مهولة، مدة
+
+43
+00:02:53,410 --> 00:02:57,870
+كبيرة بيصير الموضوعالآن لو بدنا نمثل اللي صار في
+
+44
+00:02:57,870 --> 00:03:02,490
+ECG الـ ECG اللي هو Electrocardiogram هنلاقي إنه
+
+45
+00:03:02,490 --> 00:03:06,090
+هذا بيمثل الجزئية اللي هي الـ P wave اللي هي اللي
+
+46
+00:03:06,090 --> 00:03:11,450
+أحنا شايفينها بدت في الصورة الـ heart التانية أخدت
+
+47
+00:03:11,450 --> 00:03:16,210
+الـ 2 أتريام وعملت ليه الـ P wave كاملة يبقى الـ P
+
+48
+00:03:16,210 --> 00:03:24,550
+wave بيمثل الـ Atrial Excitation أو Depolarization
+
+49
+00:03:26,770 --> 00:03:34,150
+ببدأ من الـ Sinus Atrium Node بينتشر في الـ Right
+
+50
+00:03:34,150 --> 00:03:38,370
+Atrium والـ Left Atrium وبعدين بدّي اللي هو الـ
+
+51
+00:03:38,370 --> 00:03:41,690
+Discharge عالمياً للـ AV Node الـ Atrioventricular
+
+52
+00:03:41,690 --> 00:03:46,180
+Node من الـ Atrioventricular Nodeبيطلع من عنا حاجة
+
+53
+00:03:46,180 --> 00:03:49,420
+اسمها «Atrioventricular Bundle» «AV Bundle» أو
+
+54
+00:03:49,420 --> 00:03:52,960
+بنقول «His Bundle» أو «Bundle of His» وين بيروح
+
+55
+00:03:52,960 --> 00:03:57,200
+هذا؟ هذا بيروح، بدخل على اللي هي الـ
+
+56
+00:03:57,200 --> 00:04:01,960
+«Interventricular
+
+57
+00:04:01,960 --> 00:04:05,200
+Septum» اللي هو الـ «Septum» اللي بين الـ «Right
+
+58
+00:04:05,200 --> 00:04:08,760
+Ventricle» والـ «Right Ventricle» والـ «Left
+
+59
+00:04:08,760 --> 00:04:12,350
+Ventricle»بعد ما يشير عيني الأطرا في الـ
+
+60
+00:04:12,350 --> 00:04:17,930
+ventricular node بيتفرع إلى الـ bundle branches
+
+61
+00:04:17,930 --> 00:04:23,010
+والـ bundle branches بتظل ماشية في الـ septum
+
+62
+00:04:23,010 --> 00:04:28,030
+وبعدين عند الـ apex في نهاية القلب تحت بتتفرع إلى
+
+63
+00:04:28,030 --> 00:04:29,730
+البركنجي fibers
+
+64
+00:04:33,610 --> 00:04:41,010
+وهذه الـ «بركنجي فايبرز» بتروح للـ «ventricle
+
+65
+00:04:41,010 --> 00:04:45,470
+wall» في الـ «لفت» وفي الـ «رايت» طيب كيف هي
+
+66
+00:04:45,470 --> 00:04:50,270
+related to ECG بتصير؟قلنا قبل شوية إن الـ
+
+67
+00:04:50,270 --> 00:04:54,290
+Excitation بدأ بالـ Sinus أتريام نوت و بدأ ينتشر
+
+68
+00:04:54,290 --> 00:04:59,210
+في الـ Right و Left أتريام و بعدين أدى كهربط لمن؟
+
+69
+00:04:59,210 --> 00:05:03,290
+للـ AV نوت هذه بيمثلها قلنا من الـ P Wave هذه اللي
+
+70
+00:05:03,290 --> 00:05:08,690
+شفناها الصغيرة أول الـ ECGبعد هيك بيبدأ يدخل الـ
+
+71
+00:05:08,690 --> 00:05:14,930
+Excitation في الـ Atrioventricular node وبعد هيك
+
+72
+00:05:14,930 --> 00:05:18,990
+بدخل على الـ Atrioventricular bundle أو bundle of
+
+73
+00:05:18,990 --> 00:05:22,950
+his وبعدين هذا نفسه بنزل في ال bundle of branches
+
+74
+00:05:22,950 --> 00:05:28,990
+وهذا بيدينا لسه لحد الآن بيدينا الـ Q الـ Q اللي
+
+75
+00:05:28,990 --> 00:05:35,130
+هي هيك اللي لتحت هي زي الدنبل الصغيرة لتحت Q يبقى
+
+76
+00:05:36,110 --> 00:05:40,630
+الـ Q بتمثلها الـ Excitation في الـ AV وفي الـ
+
+77
+00:05:40,630 --> 00:05:44,650
+Interventricular أو الـ bundle of branches لحد ما
+
+78
+00:05:44,650 --> 00:05:49,810
+توصل البركنجي branches بعد هيك ال Excitation بتدخل
+
+79
+00:05:49,810 --> 00:05:54,390
+على ال muscles ال right و ال left ventricle فبدينا
+
+80
+00:05:55,500 --> 00:05:59,000
+الـ R اللي احنا شايفينها اللي هي زي الشوكة عاملة
+
+81
+00:05:59,000 --> 00:06:04,080
+لفوق هيك Q R و بعد هيك بيبدأ ينسحب الكهرب مرة
+
+82
+00:06:04,080 --> 00:06:10,860
+تانية بالديني بعد هيك اللي هي الـ T Wave يبقى الـ
+
+83
+00:06:10,860 --> 00:06:14,960
+Excitation of Atrial Atrial Excitation في الـ P
+
+84
+00:06:14,960 --> 00:06:22,440
+الـ Q بيديني الـ Excitation في الـ AV Bundle مع
+
+85
+00:06:22,440 --> 00:06:29,470
+الـ Bundle of Branchesبتدينا الـ Q و الـ R تدينا
+
+86
+00:06:29,470 --> 00:06:36,030
+البركنجي fiber مع الـ right and left ventricle و
+
+87
+00:06:36,030 --> 00:06:41,110
+الـ T بعدين بتيجي هذه عمارة عن اللي هو التفريغ
+
+88
+00:06:41,110 --> 00:06:44,830
+الكهربي تبع ال ventricles اللي هو بنقول عنه الـ T
+
+89
+00:06:44,830 --> 00:06:48,310
+أو الـ repolarization اللي بيصير في مين؟ في ال
+
+90
+00:06:48,310 --> 00:06:52,010
+right and left ventricle كمان مرة
+
+91
+00:06:56,430 --> 00:07:02,150
+الآن يا جماعة وأنا هأديكوا اللي هو الـ Cardiac
+
+92
+00:07:02,150 --> 00:07:09,630
+Circle نفهم إنه كل اللي بيصير هذا سواء الـ
+
+93
+00:07:09,630 --> 00:07:15,050
+Excitation مع الـ Repolarization مع عملية الـ
+
+94
+00:07:15,050 --> 00:07:19,310
+Systolic و الـ Diastolic لا تحصل كلها كل واحدة
+
+95
+00:07:19,310 --> 00:07:24,430
+بمعزل عن الآخرلا تحصل كل واحدة بمعزل عن الآخر
+
+96
+00:07:24,430 --> 00:07:29,490
+بمعنى كلها بتتم في نفس الوقت بطريقة regular دون
+
+97
+00:07:29,490 --> 00:07:38,090
+حدوث أي مشاكل وأوريكم الفيديو بعد شوية يبقىهذا
+
+98
+00:07:38,090 --> 00:07:41,310
+بالنسبة للـ «Internal Innovation of the Heart» لكن
+
+99
+00:07:41,310 --> 00:07:46,130
+برضه احنا فيها حاجات تانية بتأثر على الـ «Heart»
+
+100
+00:07:46,130 --> 00:07:52,190
+زي الـ «Extrinsic Innovation» وهو عبارة عن أنه
+
+101
+00:07:52,190 --> 00:07:58,190
+يتحكمفي القلب كمان بعض الأمور، سواء الـStimulation
+
+102
+00:07:58,190 --> 00:08:00,590
+أو الـInhibition اللي هو الـSympathetic
+
+103
+00:08:00,590 --> 00:08:06,330
+والـParasympathetic والـParasympathetic أو
+
+104
+00:08:06,330 --> 00:08:09,670
+الـSympathetic بيبقى موجود في اللي هو الـSpinal
+
+105
+00:08:09,670 --> 00:08:13,400
+Cord، الـToracic Spinal Cordفي الـ Sympathetic
+
+106
+00:08:13,400 --> 00:08:18,160
+Trunk وهذا بيمثل Stimulation أما الـ Cardio
+
+107
+00:08:18,160 --> 00:08:21,800
+-Inhibitory
+
+108
+00:08:21,800 --> 00:08:27,620
+Center موجود، الـ Parasympathetic موجود في الـ
+
+109
+00:08:27,620 --> 00:08:31,720
+Vegas أو بوصل الكهربا عن طريق الـ Vegas nerves للـ
+
+110
+00:08:31,720 --> 00:08:37,480
+Sinus Atrial Node
+
+111
+00:08:37,480 --> 00:08:39,080
+و للـ AV Node
+
+112
+00:08:41,760 --> 00:08:46,580
+يبقى كمان مرة الـ electrical activity recorded
+
+113
+00:08:46,580 --> 00:08:50,880
+بالـ ECG الـ P wave correspond اللي هو الـ
+
+114
+00:08:50,880 --> 00:08:54,860
+excitation أو الـ depolarization of SE node الـ
+
+115
+00:08:54,860 --> 00:08:59,740
+QRS complex أي ما أحنا شايفينها في الرسمها بتمثل
+
+116
+00:08:59,740 --> 00:09:04,180
+أو correspond to ventricular depolarization والـ T
+
+117
+00:09:04,180 --> 00:09:07,420
+waveوالتفريغ هو عملية تفريغ الـ Ventricular
+
+118
+00:09:07,420 --> 00:09:13,860
+Repolarization طيب و ليش ما صارش للـ Atrium تفريغ؟
+
+119
+00:09:13,860 --> 00:09:19,480
+لأ، هو صار تفريغ ولكن كبر الـ QRS غطالي على
+
+120
+00:09:19,480 --> 00:09:29,620
+الكهربا البسيطة اللي طالعة من الـ Atrium وطبعا
+
+121
+00:09:29,620 --> 00:09:34,750
+الـ EC هي جماعة بيشخصنا الـ Electricityمش بس الـ
+
+122
+00:09:34,750 --> 00:09:40,770
+Discharge أو الـ Excitation أو الـ Rhythm of the
+
+123
+00:09:40,770 --> 00:09:45,930
+Heart إنما كمان ممكن يشخصلي الـ Thickness of the
+
+124
+00:09:45,930 --> 00:09:48,170
+Muscles كمان، ممكن يديني إشارة
+
+125
+00:09:51,300 --> 00:09:57,080
+فالـ ECG الشغلته زي الـ EEG في الدماغ لما أنا بدأ
+
+126
+00:09:57,080 --> 00:10:00,520
+أشوف الـ Epilepsy بنفس الصورة، في أننا طبعا حاجة
+
+127
+00:10:00,520 --> 00:10:04,340
+تانية بنشوف ونسمعها زي ما قلنا بناخد من كل بستان
+
+128
+00:10:04,340 --> 00:10:09,800
+زهرة تقريبا اللي هي الـ hard soundالـ heart sounds
+
+129
+00:10:09,800 --> 00:10:14,000
+اللي هي لب دب are associated with closing of the
+
+130
+00:10:14,000 --> 00:10:18,520
+heart valves يعني لما تيجي ال valves اتسكر بسمع
+
+131
+00:10:18,520 --> 00:10:22,180
+اللي هو اللب دب اللي بسمعها ال heart sound في
+
+132
+00:10:22,180 --> 00:10:29,160
+القلب و ال first sound occurs as AV valve close
+
+133
+00:10:30,480 --> 00:10:35,040
+وبتدلني الـ Fast Sound لما بسمعها بتقوللي أن الـ
+
+134
+00:10:35,040 --> 00:10:39,000
+atrioventricular valve سكر لكن برضه بتقوللي خد
+
+135
+00:10:39,000 --> 00:10:42,080
+بالك هينا بدينا ال beginning of the systolicum
+
+136
+00:10:42,080 --> 00:10:46,400
+اللي هو ال contraction second sound لما ال
+
+137
+00:10:46,400 --> 00:10:51,840
+simulator valves اللي هو ال pulmonaryالـ aortic
+
+138
+00:10:51,840 --> 00:10:57,140
+valve بيسكروا نفس الكلام وبتقول لي خد بالك الآن
+
+139
+00:10:57,140 --> 00:11:01,120
+هيو بدأ إيش beginning of the ventricular diastole
+
+140
+00:11:01,120 --> 00:11:09,460
+ال regulation of the heart rate بيقوم بيها ال
+
+141
+00:11:09,460 --> 00:11:10,700
+sympathetic والبرا sympathetic
+
+142
+00:11:13,770 --> 00:11:17,070
+والـ Parasympathetic دمونيز الـ Autonomic
+
+143
+00:11:17,070 --> 00:11:21,170
+Stimulation وبيعملي slowing heart rate and caused
+
+144
+00:11:21,170 --> 00:11:25,930
+vagal tone لكن الـ Sympathetic stimulation is
+
+145
+00:11:25,930 --> 00:11:28,850
+activated by stress and anxiety excitement،
+
+146
+00:11:28,850 --> 00:11:31,450
+exercise، هذه الحاجات كلها بتسريعلي فهي بتعمل
+
+147
+00:11:31,450 --> 00:11:34,310
+excitement، بتعمل activation اللي هو الـ
+
+148
+00:11:34,310 --> 00:11:37,230
+Sympathetic وفيه طبعا عندنا بعض الهرمونات كمان
+
+149
+00:11:37,530 --> 00:11:41,710
+بتأثر وبتدّينا، بتعملنا، بتأثرني عن الـregulation
+
+150
+00:11:41,710 --> 00:11:47,230
+of the heart زي الـHormones، الـAdrenaline
+
+151
+00:11:47,230 --> 00:11:50,450
+والتيروكسين وممكن طبعاً نفس الكلام الـIntra and
+
+152
+00:11:50,450 --> 00:11:56,010
+Extracellular Ion Concentration زي البوتاسيوم على
+
+153
+00:11:56,010 --> 00:12:01,970
+سبيل المثال، بيأثرلي وبيعملي مشاكل في الـheart
+
+154
+00:12:01,970 --> 00:12:19,890
+rateسنعود الآن ببطء للفيديو
+
+155
+00:12:19,890 --> 00:12:20,230
+الأول
+
+156
+00:12:24,030 --> 00:12:27,330
+النظام التجاري أيضًا يحتوي على نظام الليمفاتيكي
+
+157
+00:12:27,330 --> 00:12:30,810
+اللي يتجارب الليمف، ولكن كلمات نظام التجاري
+
+158
+00:12:30,810 --> 00:12:34,630
+والنظام الكارديوفاسكي مستخدمة عامًا تتعامل مع
+
+159
+00:12:34,630 --> 00:12:38,950
+بعضها لتعامل مع تجارة الدم.نظام الكارديوفاسكي
+
+160
+00:12:38,950 --> 00:12:43,490
+يحتوي على قلب، دم، ومخدرات الدم. القلب هو أساسًا
+
+161
+00:12:43,490 --> 00:12:45,730
+محطة تتحرك دم من خلال المخدرات.
+
+162
+00:12:50,380 --> 00:12:54,760
+العمل الأفضل المعروف من نظام التجارب هو ربما تحميل
+
+163
+00:12:54,760 --> 00:13:01,020
+الهواء الهوائي من الجلد إلى عضلات الجسم وإزالة
+
+164
+00:13:01,020 --> 00:13:04,460
+الهواء الكربونيكسي في الاتجاه التعريفي لإنهاء
+
+165
+00:13:04,460 --> 00:13:15,580
+الهواء بسيطًا، بسيطًا، بسيطًا، بسيطًا، بسيطًا،
+
+166
+00:13:15,580 --> 00:13:16,120
+بسيطًا، بسيطًا، بسيطًا، بسيطًا، بسيطًا، بسيطًا،
+
+167
+00:13:16,120 --> 00:13:17,040
+بسيطًا، بسيطًا، بسيطًا، بسيطًا، بسيطًا، بسيطًا،
+
+168
+00:13:17,040 --> 00:13:18,910
+بسيطًا، بسيطًا، بسيطًا، بسيالدم الكثير من الحمض
+
+169
+00:13:18,910 --> 00:13:22,850
+يرجع إلى الجانب اليساري من القلب هذا الجزء من
+
+170
+00:13:22,850 --> 00:13:26,730
+النظام يدعى الـ Pulmonary Circuit الجانب اليساري
+
+171
+00:13:26,730 --> 00:13:30,770
+من القلب يدفع الدم الكثير من الحمض لجسام الجسم حيث
+
+172
+00:13:30,770 --> 00:13:32,010
+يدفع الدم الكثير من الحمض يدفع الدم الكثير من
+
+173
+00:13:32,010 --> 00:13:33,870
+الحمض يدفع الدم الكثير من الحمض يدفع الدم الكثير
+
+174
+00:13:33,870 --> 00:13:36,690
+من الحمض يدفع الدم الكثير من الحمض يدفع الدم
+
+175
+00:13:36,690 --> 00:13:39,230
+الكثير من الحمض يدفع الدم الكثير من الحمض يدفع
+
+176
+00:13:39,230 --> 00:13:39,310
+الدم الكثير من الحمض يدفع الدم الكثير من الحمض
+
+177
+00:13:39,310 --> 00:13:40,350
+يدفع الدم الكثير من الحمض يدفع الدم الكثير من
+
+178
+00:13:40,350 --> 00:13:46,000
+الحمض يدفع الدم الكثيربسبب أن جسد الجسد اليسار يجب
+
+179
+00:13:46,000 --> 00:13:48,880
+أن يدفع الدم إلى جسمه تمامًا، فهو يحتوي على عضو
+
+180
+00:13:48,880 --> 00:13:53,520
+أكبر من الجسد اليسار. يوجد أربع عضوات التي تساعد
+
+181
+00:13:53,520 --> 00:13:56,140
+في تأكيد نطاقة الدم من طريق واحدة من خلال الجسد.
+
+182
+00:13:57,000 --> 00:13:59,480
+الدم المدخن السليموني يدفع من أعضاء الأعضاء
+
+183
+00:13:59,480 --> 00:14:01,620
+الأيمين إلى أعضاء الفترة الأيمين إلى أعضاء
+
+184
+00:14:01,620 --> 00:14:03,840
+الحلوانات الحلوانية، بينما الدم المدخن السليموني
+
+185
+00:14:03,840 --> 00:14:07,900
+يدفع من أعضاء الأيمين إلى أعضاء الفترة الأيمين إلى
+
+186
+00:14:07,900 --> 00:14:11,740
+أعضاء الفترة الأيور.القلب مغلق في مصدر مدفع مدفع
+
+187
+00:14:11,740 --> 00:14:12,680
+مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع
+
+188
+00:14:12,680 --> 00:14:19,500
+مدفع
+
+189
+00:14:19,500 --> 00:14:24,760
+مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع
+
+190
+00:14:24,760 --> 00:14:24,880
+مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع مدفع
+
+191
+00:14:35,300 --> 00:14:39,300
+وهي مرتبطة بالخزانات والخزانات والخزانات والخزانات
+
+192
+00:14:39,300 --> 00:14:45,000
+والخزانات والخزانات
+
+193
+00:14:45,000 --> 00:14:57,680
+والخزانات والخزانات
+
+194
+00:14:57,680 --> 00:15:00,520
+والخزانات والخزانات والخزانات والخزانات والخزانات
+
+195
+00:15:00,520 --> 00:15:00,520
+والخزانات والخزانات والخزانات والخزانات والخزانات
+
+196
+00:15:00,520 --> 00:15:00,520
+والخزانات والخزانات والخزانات والخزانات والخزانات
+
+197
+00:15:00,520 --> 00:15:00,520
+والخزانات والخزانات والخزانات والخزانات والخزانات
+
+198
+00:15:00,520 --> 00:15:05,980
+والخزانات والخزانات والخزاناتالإنفعارات تبدأ من
+
+199
+00:15:05,980 --> 00:15:08,420
+قطعة صغيرة من الجلدات تدعى جلدات الـ Pacemaker
+
+200
+00:15:08,420 --> 00:15:13,300
+التي تكون جزء من نظام التدخل الكاردياكي التدخل
+
+201
+00:15:13,300 --> 00:15:17,000
+الرئيسي لـ Pacemaker هو الـSA نود إنه يؤدي إلى
+
+202
+00:15:17,000 --> 00:15:21,660
+جميع الحربيات ويحكم حرية القلوب خارقة من تحميل
+
+203
+00:15:21,660 --> 00:15:25,040
+غيزات، الدم أيضًا يدفع جسد الجسد إلى جزء من
+
+204
+00:15:25,040 --> 00:15:29,380
+الحيوانات مع ميزات ويقوم بإزالة غيزات متابعيةتحصل
+
+205
+00:15:29,380 --> 00:15:30,960
+على نتائج من نظام الانتاج اللي يسمى الـ Digestive
+
+206
+00:15:30,960 --> 00:15:33,640
+System اللي يسمى الـ Digestive System اللي يسمى
+
+207
+00:15:33,640 --> 00:15:36,560
+الانتاج اللي يسمى الانتاج اللي يسمى الانتاج اللي
+
+208
+00:15:36,560 --> 00:15:37,660
+يسمى الانتاج اللي يسمى الانتاج اللي يسمى الانتاج
+
+209
+00:15:37,660 --> 00:15:38,280
+اللي يسمى الانتاج اللي يسمى الانتاج اللي يسمى
+
+210
+00:15:38,280 --> 00:15:38,280
+الانتاج اللي يسمى الانتاج اللي يسمى الانتاج اللي
+
+211
+00:15:38,280 --> 00:15:38,280
+يسمى الانتاج اللي يسمى الانتاج اللي يسمى الانتاج
+
+212
+00:15:38,280 --> 00:15:38,280
+اللي يسمى الانتاج اللي يسمى الانتاج اللي يسمى
+
+213
+00:15:38,280 --> 00:15:40,960
+الانتاج اللي يسمى الانتاج اللي يسمى الانتاج اللي
+
+214
+00:15:40,960 --> 00:15:48,500
+يسمى الانتاج
+
+215
+00:15:48,500 --> 00:15:53,220
+اللي
+
+216
+00:15:53,220 --> 00:15:57,620
+يسمى الالدم أيضًا يتحمل حرمونات من جذعين
+
+217
+00:15:57,620 --> 00:16:01,500
+الاندوكرين لجهات عضوية ويمكنها أن تلعب رولة مهمة
+
+218
+00:16:01,500 --> 00:16:04,980
+في حفرة حفرة الحيوانات الجسمية الدم يحتوي على
+
+219
+00:16:04,980 --> 00:16:09,580
+اتجارات أساسية أساسية أساسية أساسية مسمى Plasma
+
+220
+00:16:09,580 --> 00:16:15,220
+ومجموعة أساسية أساسية أساسية أساسية أساسية أساسية
+
+221
+00:16:15,220 --> 00:16:15,220
+أساسية أساسية أساسية أساسية أساسية أساسية أساسية
+
+222
+00:16:15,220 --> 00:16:15,260
+أساسية أساسية أساسية أساسية أساسية أساسية أساسية
+
+223
+00:16:15,260 --> 00:16:15,360
+أساسية أساسية أساسية أساسية أساسية أساسية أساسية
+
+224
+00:16:15,360 --> 00:16:19,300
+أساسية أساسية
+
+225
+00:16:19,300 --> 00:16:24,380
+أساسمخلوقات الدم البيضاء تتعمل في ميزات محافظة
+
+226
+00:16:24,380 --> 00:16:27,900
+مختلفة ضد أنشطة تهيأم العضلات، بينما الـ Platelets
+
+227
+00:16:27,900 --> 00:16:31,960
+هم المسؤولين عن مخلوق الدم لتقديم مخاطر الدم خلال
+
+228
+00:16:31,960 --> 00:16:36,380
+مصابة مصابة مصابة مصابة مصابة مصابة مصابة مصابة
+
+229
+00:16:36,380 --> 00:16:39,160
+مصابة مصابة مصابة مصابة مصابة مصابة مصابة مصابة
+
+230
+00:16:39,160 --> 00:16:39,420
+مصابة مصابة مصابة مصابة مصابة مصابة مصابة مصابة
+
+231
+00:16:39,420 --> 00:16:39,420
+مصابة مصابة مصابة مصابة مصابة مصابة مصابة مصابة
+
+232
+00:16:39,420 --> 00:16:47,120
+مصابة مصابة مصابة مصابة
+
+233
+00:16:47,120 --> 00:16:51,220
+مأشجار تتحرك الدم بعيدًا من القلب يسمونها أشجار
+
+234
+00:16:51,220 --> 00:16:54,500
+بينما أشجار تتحرك الدم بعيدًا من القلب يسمونها
+
+235
+00:16:54,500 --> 00:16:58,360
+أشجار أشجار تتحرك الدم بعيدًا من القلب تتحرك الدم
+
+236
+00:16:58,360 --> 00:16:59,720
+بعيدًا من القلب تتحرك الدم بعيدًا من القلب تتحرك
+
+237
+00:16:59,720 --> 00:17:00,920
+الدم بعيدًا من القلب تتحرك الدم بعيدًا من القلب
+
+238
+00:17:00,920 --> 00:17:01,700
+تتحرك الدم بعيدًا من القلب تتحرك الدم بعيدًا من
+
+239
+00:17:01,700 --> 00:17:01,700
+القلب تتحرك الدم بعيدًا من القلب تتحرك الدم بعيدًا
+
+240
+00:17:01,700 --> 00:17:03,860
+من القلب تتحرك الدم بعيدًا من القلب تتحرك الدم
+
+241
+00:17:03,860 --> 00:17:10,320
+بعيدًا من القلب تتحرك الدم بعيدًا من القلب تتحرك
+
+242
+00:17:10,320 --> 00:17:14,100
+الدم بعيدًا من الق
+
+243
+00:17:17,370 --> 00:17:21,370
+ثم أصغر جسد الدم يسمونه الـ Capillaries حيث يحدث
+
+244
+00:17:21,370 --> 00:17:26,530
+تغيير المادة الدم ثم يجمع الدم إلى صفرين صغيرين
+
+245
+00:17:26,530 --> 00:17:31,510
+يسمونه الـ Venules ثم إلى صفرين أكبر وعن طريق قلبي
+
+246
+00:17:31,510 --> 00:17:35,850
+عضلات وصفرين أساسيا يساعدون في تجارب الدم مجتمعها
+
+247
+00:17:35,850 --> 00:17:38,630
+مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها
+
+248
+00:17:38,630 --> 00:17:38,630
+مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها
+
+249
+00:17:38,630 --> 00:17:38,810
+مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها
+
+250
+00:17:38,810 --> 00:17:44,170
+مجتمعها مجتمعها مجتمعها مجتمعها مجتمعها
+
+251
+00:17:45,000 --> 00:17:49,540
+مجزرة أساسية عضوية ومتسلسلة تسمح للجسم بإستجابة أو
+
+252
+00:17:49,540 --> 00:17:54,740
+تدخل تحرير نمو الدم ومجزرة أساسية عضوية ومتسلسلة
+
+253
+00:17:54,740 --> 00:17:56,820
+تسمح للجسم بإستجابة أو تدخل تحرير نمو الدم
+
+254
+00:17:56,820 --> 00:18:00,520
+ومتسلسلة تسمح للجسم بإستجابة أو تدخل تحرير نمو
+
+255
+00:18:00,520 --> 00:18:04,760
+الدم ومتسلسلة تسمح للجسم بإستجابة أو تدخل تحرير
+
+256
+00:18:04,760 --> 00:18:06,540
+نمو الدم ومتسلسلة تسمح للجسم بإستجابة أو تدخل
+
+257
+00:18:06,540 --> 00:18:08,980
+تحرير نمو الدم ومتسلسلة تسمح للجسم بإستجابة أو
+
+258
+00:18:08,980 --> 00:18:14,680
+تدخل تحرير نمو الدم وويجب أن يتحمل أضغطات أعلى
+
+259
+00:18:14,680 --> 00:18:20,600
+التي تم إجراءها من حرق القلوب. عبارة عن عبارة عن
+
+260
+00:18:20,600 --> 00:18:22,320
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+261
+00:18:22,320 --> 00:18:22,660
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+262
+00:18:22,660 --> 00:18:22,680
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+263
+00:18:22,680 --> 00:18:22,980
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+264
+00:18:22,980 --> 00:18:23,640
+عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة
+
+265
+00:18:23,640 --> 00:18:24,080
+عن عبارة عن عبارة عن عبارة عن عبارة عن عبارة عن
+
+266
+00:18:24,080 --> 00:18:33,280
+عبارة عن عبارة عن عبارة
+
+267
+00:18:33,280 --> 00:18:33,500
+عن عب
+
+268
+00:18:51,320 --> 00:18:54,680
+السيكول الكاردياكي يتعلق بالتجارة من الأحداث التي
+
+269
+00:18:54,680 --> 00:18:59,280
+تحدث و تتكرر مع كل حربي يمكن أن يكون مقاطعا إلى
+
+270
+00:18:59,280 --> 00:19:03,860
+أتصالين مهمة سيستالي و ديستالي كل واحدة منها
+
+271
+00:19:03,860 --> 00:19:09,020
+تتقاطع إلى أتصالين أصغر و أصغر سيستالي و ديستالي
+
+272
+00:19:09,020 --> 00:19:12,120
+عندما لا يتم تصميمها بشكل غير محدد يتعلق بالتدخل
+
+273
+00:19:12,120 --> 00:19:14,360
+والتدخل والتدخل والتدخل والتدخل والتدخل والتدخل
+
+274
+00:19:14,360 --> 00:19:15,200
+والتدخل والتدخل والتدخل والتدخل والتدخل والتدخل
+
+275
+00:19:15,200 --> 00:19:16,920
+والتدخل والتدخل والتدخل والتدخل والتدخل والتدخل
+
+276
+00:19:16,920 --> 00:19:20,880
+وال
+
+277
+00:19:21,590 --> 00:19:27,090
+التسلق يزيد الضرر في مصالحها بينما تتسلق تسلق
+
+278
+00:19:27,090 --> 00:19:30,470
+الضرر في مصالحها تفتح مصالح الـ AV عندما تسلق
+
+279
+00:19:30,470 --> 00:19:34,830
+الضرر في مصالحها أعلى من مصالحها التسلق والتغير
+
+280
+00:19:34,830 --> 00:19:39,710
+عندما تغير مصالحها تسلق تفتح مصالح الـ semilunar
+
+281
+00:19:39,710 --> 00:19:44,470
+عندما تسلق مصالحها التسلق أعلى من مصالحها التسلق
+
+282
+00:19:44,470 --> 00:19:52,100
+والتغير عندما تغيرالسيكلة تبدأ مع إطلاق الـSA نوت
+
+283
+00:19:52,100 --> 00:19:57,280
+الذي يشغّل الـatria لتنقل هذا موضوع موضوع الـP
+
+284
+00:19:57,280 --> 00:20:01,800
+-wave على الـECG التنقل الهوائي يبدأ قليلًا بعد أن
+
+285
+00:20:01,800 --> 00:20:06,720
+تبدأ الـP-wave وتسبب الضغط داخل الهوائي لتنقل،
+
+286
+00:20:06,720 --> 00:20:11,490
+ويجعل الدم يدخل إلى الجلدمع ذلك، فإن عبارة عن
+
+287
+00:20:11,490 --> 00:20:16,330
+مجزرة من المدخل المدخلي تدخل عبارة عن مجزرة من
+
+288
+00:20:16,330 --> 00:20:16,390
+المدخل المدخلي تدخل عبارة عن مجزرة من المدخل
+
+289
+00:20:16,390 --> 00:20:18,070
+المدخلي تدخل عبارة عن مجزرة من المدخل المدخلي تدخل
+
+290
+00:20:18,070 --> 00:20:19,770
+عبارة عن مجزرة من المدخل المدخلي تدخل عبارة عن
+
+291
+00:20:19,770 --> 00:20:20,410
+مجزرة من المدخل المدخلي تدخل عبارة عن مجزرة من
+
+292
+00:20:20,410 --> 00:20:22,430
+المدخل المدخلي تدخل عبارة عن مجزرة من المدخل
+
+293
+00:20:22,430 --> 00:20:29,330
+المدخلي تدخل عبارة
+
+294
+00:20:29,330 --> 00:20:34,470
+عن مجزرة من المدخل المدخلي تدخل عبارة عن مجزرة
+
+295
+00:20:38,620 --> 00:20:43,140
+وهي البداية لـSystole في هذا النقطة، الانتجار
+
+296
+00:20:43,140 --> 00:20:45,880
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+297
+00:20:45,880 --> 00:20:46,800
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+298
+00:20:46,800 --> 00:20:49,940
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+299
+00:20:49,940 --> 00:20:51,320
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+300
+00:20:51,320 --> 00:20:51,320
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+301
+00:20:51,320 --> 00:20:51,500
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+302
+00:20:51,500 --> 00:20:55,280
+الانتجار الانتجار الانتجار الانتجار الانتجار
+
+303
+00:20:55,280 --> 00:21:07,600
+الانتجار الانتجار الانتجار الانتجار الانتجار الان
+
+304
+00:21:07,720 --> 00:21:11,180
+because no blood is ejected and ventricular volume
+
+305
+00:21:11,180 --> 00:21:15,700
+is unchangedventricular ejection starts when
+
+306
+00:21:15,700 --> 00:21:18,800
+ventricular pressures exceed the pressures within
+
+307
+00:21:18,800 --> 00:21:22,280
+the aorta and pulmonary artery the aortic and
+
+308
+00:21:22,280 --> 00:21:26,220
+pulmonic valves open and blood is ejected out of
+
+309
+00:21:26,220 --> 00:21:30,630
+the ventricles this is the rapid ejection phaseعند
+
+310
+00:21:30,630 --> 00:21:34,070
+إعادة الانتقال الفلسفية المشهودة من تجارب الـ T
+
+311
+00:21:34,070 --> 00:21:38,850
+-Wave تبدأ الضغط الفلسفي يبدأ بالتسلق وفرصة
+
+312
+00:21:38,850 --> 00:21:43,710
+الانتقال تتخلص عندما تسلق الضغط الفلسفي تتسلق تحت
+
+313
+00:21:43,710 --> 00:21:46,390
+الضغط الأيورتيكي والبومانيريي، تغلق الشبكات
+
+314
+00:21:46,390 --> 00:21:51,470
+الميولوناريةماركة نهاية السيستالي وبداية
+
+315
+00:21:51,470 --> 00:21:55,510
+الدياستالي إغلاق المحطات السيولونية تنتج صوت قلب
+
+316
+00:21:55,510 --> 00:22:01,130
+الثاني S2 الجزء الأول من الدياستالي هو مرة أخرى
+
+317
+00:22:01,130 --> 00:22:05,030
+ايسو-وليومتريكي بسبب تهيأة المحطات بإغلاق جميع
+
+318
+00:22:05,030 --> 00:22:09,690
+المحطات مفتوحة الضغط الفلسفية تتسلق بسرعة ولكن
+
+319
+00:22:09,690 --> 00:22:15,570
+مقاومتها لا تتغيرمع ذلك، الـ atria يتم ملحقه
+
+320
+00:22:15,570 --> 00:22:20,530
+بطموح، وحرارة الحرارة تنزل بسرعة، ومباركة الحرارة
+
+321
+00:22:20,530 --> 00:22:23,830
+تبدأ عندما تنزل حرارة الحرارة تنزل تحت حرارة
+
+322
+00:22:23,830 --> 00:22:24,830
+الحرارة تنزل تحت حرارة الحرارة تنزل تحت حرارة
+
+323
+00:22:24,830 --> 00:22:25,790
+الحرارة تنزل تحت حرارة الحرارة تنزل تحت حرارة
+
+324
+00:22:25,790 --> 00:22:27,050
+الحرارة تنزل تحت حرارة الحرارة تنزل تحت حرارة
+
+325
+00:22:27,050 --> 00:22:29,550
+الحرارة تنزل تحت حرارة الحرارة تنزل تحت حرارة
+
+326
+00:22:29,550 --> 00:22:37,710
+الحرارة تنزل تحت حرارة الحرارة تنزل تحت
+
+327
+00:22:37,710 --> 00:22:37,710
+حرارة الحرارة تنز
+
+328
+00:22:45,560 --> 00:22:48,360
+Thank you for watching. Please feel free to
+
+329
+00:22:48,360 --> 00:22:51,260
+suggest a topic you want us to cover by leaving a
+
+330
+00:22:51,260 --> 00:22:56,290
+comment belowوبعد ما تشوفنا الفيديو هنا احنا الآن
+
+331
+00:22:56,290 --> 00:23:01,470
+هنبدأ في اللي هي الأمراض الأمراض القلب و هنبدأ
+
+332
+00:23:01,470 --> 00:23:04,070
+بحاجة اسمها ال coronary artery disease أو ال
+
+333
+00:23:04,070 --> 00:23:09,110
+ischemic heart disease ال ischemic اختصارها I S I
+
+334
+00:23:09,110 --> 00:23:16,870
+H D او coronary artery disease بنفس الصورةوهنتحدث
+
+335
+00:23:16,870 --> 00:23:19,790
+إيش يعني الـ Coronary Artery Disease إن هو عبارة
+
+336
+00:23:19,790 --> 00:23:23,330
+عن narrowing of the coronary arteries وحنحكي عن ال
+
+337
+00:23:23,330 --> 00:23:27,970
+statistics وقداش منتشر هذا المرض بصورة عامة ال
+
+338
+00:23:27,970 --> 00:23:33,410
+risk factors اللي هنسمعها باستمرار و ال
+
+339
+00:23:33,410 --> 00:23:38,170
+pathophysiology هتستغرب وقداش أنه إحنا البشر السبب
+
+340
+00:23:38,170 --> 00:23:43,150
+في هذا الموضوع وزي ما بنقول دايماالـ Ischemic
+
+341
+00:23:43,150 --> 00:23:46,070
+Heart Disease ممكن نصيب أي حد فينا، لصغير و لكبير
+
+342
+00:23:46,070 --> 00:23:52,450
+ممكن نصيب أهالينا، ميتنا، أبواتنا وإنه فينا طبعا
+
+343
+00:23:52,450 --> 00:23:55,950
+أنواع من الـ Ischemic Heart Disease هنتحدث عنه في
+
+344
+00:23:55,950 --> 00:24:01,570
+وقته وكيف الـ Symptoms بتبعتها وإيش الفرق بين
+
+345
+00:24:01,570 --> 00:24:06,230
+الـMI و بين الـAngina Bacteris و بين الـStable
+
+346
+00:24:06,230 --> 00:24:13,010
+Angina Bacteris و الـUnstable Angina Bacterisهدف
+
+347
+00:24:13,010 --> 00:24:15,530
+المحاضرة اللي جاية إن شاء الله تعالى يعني حاولوا
+
+348
+00:24:15,530 --> 00:24:18,550
+تركزوا شويه في موضوع اللي .. اللي اتحدثنا عنه
+
+349
+00:24:18,550 --> 00:24:22,850
+لموضوع ال .. الموضوع ال anatomy و ال .. واستعينوا
+
+350
+00:24:22,850 --> 00:24:25,750
+طبعا و ال physiology استعينوا بطلق بعض الفيديوهات
+
+351
+00:24:25,750 --> 00:24:30,510
+اللي هي بتعمل animation و ممكن تسهل عليكم إشي كتير
+
+352
+00:24:30,510 --> 00:24:33,530
+إن شاء الله تعالى، نهاركوا سعيدة
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/wKbEPHOGwtg_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/wKbEPHOGwtg_raw.srt
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@@ -0,0 +1,1916 @@
+1
+00:00:01,250 --> 00:00:03,270
+بسم الله الرحمن الرحيم والحمد لله رب العالمين
+
+2
+00:00:03,270 --> 00:00:06,770
+والصلاة والسلام علي سيدنا محمد وسيدنا أجمعين اليوم
+
+3
+00:00:06,770 --> 00:00:09,530
+ان شاء الله تعالى هنتحدث عن ال disorders of
+
+4
+00:00:09,530 --> 00:00:17,010
+respiratory system لكن قبل ما نبدأ هنحاول هذه
+
+5
+00:00:17,010 --> 00:00:23,830
+المحاضرة هتكون على two partsهنحكي في الأول عن شوية
+
+6
+00:00:23,830 --> 00:00:29,290
+general symptoms of respiratory disease زي على
+
+7
+00:00:29,290 --> 00:00:32,750
+سبيل المثال، إيش الـhypoxia؟ تعريف الـhypoxia
+
+8
+00:00:32,750 --> 00:00:39,050
+تعريف الـhypoxia هي decrease level of oxygen in
+
+9
+00:00:39,050 --> 00:00:44,510
+the tissue، مش في blood الـhypoxemia هو decrease
+
+10
+00:00:44,510 --> 00:00:49,560
+level of oxygen in arterial bloodالـ hypercapnia
+
+11
+00:00:49,560 --> 00:00:53,560
+increased level of CO2 in the blood والتسنية
+
+12
+00:00:53,560 --> 00:00:59,140
+difficult breathingالتكيبنية rapid rate of
+
+13
+00:00:59,140 --> 00:01:03,740
+breathing سيانوزز حكينا عنها قبل هيك بلوش
+
+14
+00:01:03,740 --> 00:01:07,860
+discoloration of the skin and mucous membranes due
+
+15
+00:01:07,860 --> 00:01:11,860
+to poor oxygenation of the blood و hemoptysis كنا
+
+16
+00:01:11,860 --> 00:01:17,900
+حكينا الفرق بين hemoptysis و ash و hematemesis و
+
+17
+00:01:17,900 --> 00:01:21,200
+hematuria hemoptysis هو إبانة عن blood in the
+
+18
+00:01:21,200 --> 00:01:24,990
+sputumهذه التعريفات بسيطة، يجب أن نكون عارفينها
+
+19
+00:01:24,990 --> 00:01:28,910
+ونحكي عن الـ Disorders أو Diseases of the
+
+20
+00:01:28,910 --> 00:01:32,890
+Respiratory System هنتحدث في الأول عن تجسيمة
+
+21
+00:01:32,890 --> 00:01:37,880
+Respiratory Infectionالإنفكشن في الـ Respiratory
+
+22
+00:01:37,880 --> 00:01:41,020
+Tract يمكن أن يحدث في الـ Upper Respiratory Tract
+
+23
+00:01:41,020 --> 00:01:48,020
+Infection اختصارها URT
+
+24
+00:01:48,020 --> 00:01:51,080
+أو Upper Respiratory Tract Infection وفيه Lower
+
+25
+00:01:51,080 --> 00:01:54,200
+Respiratory Tract Infection وممكن يكونوا مخصصين مع
+
+26
+00:01:54,200 --> 00:02:01,340
+بعضالـ الـ الـ organisms اللي بتعملنا infections
+
+27
+00:02:01,340 --> 00:02:06,480
+في ال respiratory system طبعا ال ال ال ال ال
+
+28
+00:02:06,480 --> 00:02:11,540
+bacteria ال viruses و ال fungi لابد من الانتباه أن
+
+29
+00:02:11,540 --> 00:02:14,820
+the majority of upper respiratory tract infections
+
+30
+00:02:14,820 --> 00:02:16,380
+are caused by virus
+
+31
+00:02:18,980 --> 00:02:21,840
+الرينوفيروس والبرانفلونزافيروس والبرانفلونزافيروس
+
+32
+00:02:21,840 --> 00:02:24,860
+علشان هيك بتسمعونا كتير بنقول in the upper
+
+33
+00:02:24,860 --> 00:02:29,560
+respiratory tract infection there is no need for
+
+34
+00:02:29,560 --> 00:02:33,500
+antibioticلأيش؟ لأن الـ Antibiotic للبكتيريا بما
+
+35
+00:02:33,500 --> 00:02:37,880
+أن الـ Upper Respiratory Tract Infection معظم سبب
+
+36
+00:02:37,880 --> 00:02:46,140
+الانفكشن فيروس فإنه No Need وحسب الأورجانيزم و ال
+
+37
+00:02:46,140 --> 00:02:49,320
+extent of infection the manifestation can range
+
+38
+00:02:49,320 --> 00:02:53,800
+from mild to severe and even life threatening حسب
+
+39
+00:02:53,800 --> 00:02:58,190
+الأورجانيزم و حسب ال extent of infectionبدنا نبدأ
+
+40
+00:02:58,190 --> 00:03:00,590
+في الأول في الـ Common Cold اللي احنا بنقول عنه
+
+41
+00:03:00,590 --> 00:03:03,810
+بلغتنا العامية الرشح الـ Most Common Viral
+
+42
+00:03:03,810 --> 00:03:07,230
+Pathogen للـ Common Cold are Rhinovirus,
+
+43
+00:03:07,390 --> 00:03:10,990
+Parainfluenza Virus Respiratory Sinitial Virus,
+
+44
+00:03:11,110 --> 00:03:15,810
+Adenovirus and Coronavirus طبعاً هذه المحاضرة
+
+45
+00:03:15,810 --> 00:03:20,790
+معمولة قبل ما يحصل الكورونا يعني هذه من أربع أو
+
+46
+00:03:20,790 --> 00:03:23,870
+خمس سنين المحاضرة وكنا ذاكرين فيها الـ Coronavirus
+
+47
+00:03:25,470 --> 00:03:41,750
+وهذه الفيروسات تتراوح في أوقات السنة وبتدخل
+
+48
+00:03:41,750 --> 00:03:48,110
+عن طريق الـ nasal mucosa
+
+49
+00:03:48,110 --> 00:03:52,940
+وsurfaces of the eyesوهذا اللي طول النهار بيحكي
+
+50
+00:03:52,940 --> 00:03:56,600
+فيه يا جماعة تحكيش في وجهك اللي بديه يعتص أو بديه
+
+51
+00:03:56,600 --> 00:04:00,520
+يكح ميكحش في وجه التانين و دايما غسل اليدين عشان
+
+52
+00:04:00,520 --> 00:04:03,820
+لو ايدك أخدت شوية فيروسات و جيت حكيت في منخيرك أو
+
+53
+00:04:03,820 --> 00:04:08,880
+في عينك أو في كذا ممكن ينتجل فيروس they are
+
+54
+00:04:08,880 --> 00:04:12,260
+readily spread from person to person via
+
+55
+00:04:12,260 --> 00:04:17,180
+respiratory secretionsmanifestations of the common
+
+56
+00:04:17,180 --> 00:04:20,760
+cold ممكن يكون rhinitis inflammation of the nasal
+
+57
+00:04:20,760 --> 00:04:25,620
+mucosa rhinitis inflammation of the nasal mucosa
+
+58
+00:04:25,620 --> 00:04:29,840
+sinusitis inflammation of the sinus mucosa و احنا
+
+59
+00:04:29,840 --> 00:04:34,800
+اتعرفنا على ال sinuses و قلنا انه في عندنا كام نوع
+
+60
+00:04:34,800 --> 00:04:40,380
+من ال sinuses في الوجه صح ايش و ايش و ايش ايوة
+
+61
+00:04:40,380 --> 00:04:43,020
+صحيح
+
+62
+00:04:44,800 --> 00:04:51,340
+مكسيري صحيح اثمويدل صحيح سفينويدل صحيح frontal
+
+63
+00:04:51,340 --> 00:04:55,860
+صحيح نعم فى اننا كمان الـ pharyngitis اللى هو
+
+64
+00:04:55,860 --> 00:05:00,020
+التهاب الحلق pharynx and throat ممكن يعملنا
+
+65
+00:05:00,020 --> 00:05:03,400
+headache كمان و nasal discharge and congestion
+
+66
+00:05:03,400 --> 00:05:10,600
+احتقال هذا بالنسبة لل common cold وهذا أسهل أنواع
+
+67
+00:05:10,600 --> 00:05:11,980
+التهابات
+
+68
+00:05:13,840 --> 00:05:17,420
+التنفسية العليا اللي هو الـ Common Cold الرشح أو
+
+69
+00:05:17,420 --> 00:05:23,400
+بما نقول عنه الزكاة طيب ال Influenza و اللي هي
+
+70
+00:05:23,400 --> 00:05:27,600
+برضه بتيجي بصورة كبيرة كمان Influenza و اللي هي
+
+71
+00:05:27,600 --> 00:05:32,860
+الآن منتشرة و بتعملنا بتخربطنا في موضوع هل اللي
+
+72
+00:05:32,860 --> 00:05:38,390
+جبالي أنا مفلوز ولا عنده كورونا ولا مكرونلأن
+
+73
+00:05:38,390 --> 00:05:44,390
+الانفلوانزا الموسينية مشهورة أنه بداية الخريف دخول
+
+74
+00:05:44,390 --> 00:05:48,950
+الشتاء تنتشر بصورة كبيرة انفلوانزا is a viral
+
+75
+00:05:48,950 --> 00:05:52,030
+infection كمان مرة اه viral infection انفلوانزا
+
+76
+00:05:52,030 --> 00:05:56,370
+هذا اللي بنبلبع و بند الأطفال مضادات حيوية عشانها
+
+77
+00:05:56,370 --> 00:05:59,570
+انها هي viral infection ت affect upper respiratory
+
+78
+00:05:59,570 --> 00:06:03,290
+tract infection upper respiratory tract and or
+
+79
+00:06:03,290 --> 00:06:10,220
+lower respiratory tractفي عنده تلت أنواع من الـ
+
+80
+00:06:10,220 --> 00:06:13,440
+forms of influenza virus أو strains بتقول عنها
+
+81
+00:06:21,620 --> 00:06:25,920
+أشهر واحد في التلاتة لو الـType-A هو الـMost
+
+82
+00:06:25,920 --> 00:06:30,520
+Common ويسبب فيه الموضوع أكتر من المرضين الـType-A
+
+83
+00:06:30,520 --> 00:06:38,980
+الـInfluenza Virus هو بينتقل
+
+84
+00:06:38,980 --> 00:06:50,390
+بسهولة جدًا جدًابسبب وجود تتعييم
+
+85
+00:06:50,390 --> 00:06:54,130
+انفلوازية مختلف عن السنة السابقة لأنهم بيحطوا
+
+86
+00:06:54,130 --> 00:06:58,810
+قطعين تلاتة أو أربعة قطعان داخل التطعيم هذا ولكن
+
+87
+00:06:58,810 --> 00:07:02,390
+بضطرين لأن نفس الفيروس تبقى السنة اللي فاتت مش هو
+
+88
+00:07:02,390 --> 00:07:05,290
+اللي بيبقى المرة هاي ليش؟ لأنه بيغير المادة
+
+89
+00:07:05,290 --> 00:07:08,990
+الوراثية تبعته وهذا الكلام اللي بيقعدين بنقول أنه
+
+90
+00:07:08,990 --> 00:07:13,940
+عنده تتعييم مختلفGenetic mutation يعني بيغير مادته
+
+91
+00:07:13,940 --> 00:07:20,400
+الوراثية وبعملي نسخة جديدة من هذا الفيروس وبتصيب
+
+92
+00:07:20,400 --> 00:07:30,060
+بطريقة أخرى وطبعا حسب الأماكن اللي بيصيب فيها عشان
+
+93
+00:07:30,060 --> 00:07:32,940
+هيك بيصير عندنا متذكرين أنتوا انفلونزة الطيور
+
+94
+00:07:32,940 --> 00:07:38,310
+وانفلونزة الخنازير وهي الآن بدأنا ندخلفي أنواع
+
+95
+00:07:38,310 --> 00:07:41,650
+تانية غير الـ Influenza في الـ Corona في حاجة
+
+96
+00:07:41,650 --> 00:07:45,110
+اسمها Pandemics الـ Pandemics هو Spreading of
+
+97
+00:07:45,110 --> 00:07:48,250
+Infection Across a Large Region يعني في منطقة
+
+98
+00:07:48,250 --> 00:07:53,050
+كبيرة Of Influenza أرسين كل تمام لعشر سنين بيصير
+
+99
+00:07:53,050 --> 00:07:58,200
+عندنابنديميا أو بنقول عنها endemic أو pandemic
+
+100
+00:07:58,200 --> 00:08:03,600
+وبتبقى serious وهذه نتيجة أنه بيغير هذا ال virus
+
+101
+00:08:03,600 --> 00:08:07,220
+اللي هو ال influenza virus بيغير المادة الجينية
+
+102
+00:08:07,220 --> 00:08:12,260
+تبعته فيعجز الجسم عن محاربته وبتنتشر هذا الفيروس
+
+103
+00:08:12,260 --> 00:08:19,200
+بنتشر بصورة كبيرة بين الناس وهنا شايفين أخوه لل
+
+104
+00:08:19,200 --> 00:08:22,520
+influenza virus اللي هو ال coronavirus إيش عامل في
+
+105
+00:08:22,520 --> 00:08:25,790
+العالمإيش عامل في العالم؟ symptoms of influenza
+
+106
+00:08:25,790 --> 00:08:29,430
+infection headache طبعا احنا شوفنا تو في ال common
+
+107
+00:08:29,430 --> 00:08:33,350
+cold ماكانش فيه headache يعني احنا بنحس إن إن ال
+
+108
+00:08:33,350 --> 00:08:37,110
+influenza تأثير تبعها systemic أكتر يعني على الجسم
+
+109
+00:08:37,110 --> 00:08:41,190
+أكتر مع ال upper respiratory لكن كمان بيأثرلي على
+
+110
+00:08:41,190 --> 00:08:43,770
+الجسم إن حنشوف في ال symptoms لكن ال common cold
+
+111
+00:08:43,770 --> 00:08:48,870
+أو الذكام يعني زي ما بقولها restricted الالتهاب في
+
+112
+00:08:48,870 --> 00:08:52,930
+منطقة المناخية ومنطقة الحلق و هيك يعنيالـ Symptoms
+
+113
+00:08:52,930 --> 00:08:56,370
+of Influenza Infection Headache, Fever, Chills،
+
+114
+00:08:56,370 --> 00:09:00,350
+إيش يعني Chills؟ بيصير عنده نتيجة الحرارة اللي هي
+
+115
+00:09:00,350 --> 00:09:04,630
+ال .. إيش بيقولوها؟ جشعريرة، بيصير عنده muscle
+
+116
+00:09:04,630 --> 00:09:08,310
+aches، بيصير عنده وجع في العضلات، nasal discharge,
+
+117
+00:09:08,470 --> 00:09:11,790
+unproductive cough, un-thor, un-sore throat
+
+118
+00:09:14,450 --> 00:09:17,610
+الإنفلوانزا الانفكار يمكن أن يسبب انفلام الهوائي
+
+119
+00:09:17,610 --> 00:09:18,470
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+120
+00:09:18,470 --> 00:09:18,730
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+121
+00:09:18,730 --> 00:09:22,170
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+122
+00:09:22,170 --> 00:09:22,650
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+123
+00:09:22,650 --> 00:09:23,970
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+124
+00:09:23,970 --> 00:09:27,850
+الهوائي الهوائي الهوائي الهوائي الهوائي الهوائي
+
+125
+00:09:27,850 --> 00:09:32,280
+الهوائي الهوائي الهوائيInfection may lead to co
+
+126
+00:09:32,280 --> 00:09:35,440
+-infection of the respiratory passages with
+
+127
+00:09:35,440 --> 00:09:38,500
+bacteria هذا أحنا مشكلتنا وعشان هي كتير بتلاقي
+
+128
+00:09:38,500 --> 00:09:41,020
+بتحججوا ناس في ال Influenza أنا بدي مضاد حيوي
+
+129
+00:09:41,020 --> 00:09:44,440
+لحمايته من أنه يصير عنده co-infection أو التهاب
+
+130
+00:09:44,440 --> 00:09:48,400
+بكتيري super infection أو co-infection طبعا يا
+
+131
+00:09:48,400 --> 00:09:53,520
+جماعة يعني في مغلطة كبيرة هنا ما لازم أحنا أدي أنا
+
+132
+00:09:53,520 --> 00:09:58,340
+مضاد حيوي مقدما الآن لو حصل أنه شوفت أنه في إشارات
+
+133
+00:09:58,340 --> 00:10:04,510
+ل bacterial infectionطبعاً Co-infection مع
+
+134
+00:10:04,510 --> 00:10:08,290
+الـViral ساعتها بأدى Antibiotic لكن أن أدى
+
+135
+00:10:08,290 --> 00:10:11,570
+الـViral انفكشن Antibiotic هذه غلطة كبيرة It's
+
+136
+00:10:11,570 --> 00:10:14,830
+also possible for influenza virus to infect the
+
+137
+00:10:14,830 --> 00:10:19,330
+tissues of the lung itself and cause viral
+
+138
+00:10:19,330 --> 00:10:23,820
+infectionنمونيا يعني ممكن تنزل فعلا التهاب
+
+139
+00:10:23,820 --> 00:10:26,980
+الفيروسي ينزل وينزل ع الرئتين ويعمل إيه التهاب
+
+140
+00:10:26,980 --> 00:10:33,320
+الفيروسي ال treatment of influenza طبعا بدرس تراحة
+
+141
+00:10:33,320 --> 00:10:38,260
+fluids سوائل دفع and إذا في يعني زي مثلا في
+
+142
+00:10:38,260 --> 00:10:43,670
+الكورونا الآن في محاولات ال antiviral drugsوطبعاً
+
+143
+00:10:43,670 --> 00:10:48,430
+إحنا بندّي حقيقة اللي هو الـ Influenza Vaccine
+
+144
+00:10:48,430 --> 00:10:51,210
+سنوي في شهر 10 وشهر 11
+
+145
+00:10:53,950 --> 00:11:00,570
+مقارنة بـA وB مخلوقات الفلوانزا التي تتوقع أن تكون
+
+146
+00:11:00,570 --> 00:11:05,090
+مميزة في عام محدد الفلوانزا يجب أن يتم تحرير
+
+147
+00:11:05,090 --> 00:11:08,490
+وإدارة الفلوانزا في عام محدد الفلوانزا لكي تكون
+
+148
+00:11:08,490 --> 00:11:09,170
+مفيدا
+
+149
+00:11:17,530 --> 00:11:22,070
+ولكنه لا يعطي حماية كاملة من الـ Influenza فيه
+
+150
+00:11:22,070 --> 00:11:25,890
+strains في الـ Influenza مش محتوطة في التطعيم هذه
+
+151
+00:11:25,890 --> 00:11:28,150
+طبعا تقدر تصيب الواحد بالـ Influenza وفي منها
+
+152
+00:11:28,150 --> 00:11:32,510
+عشرات دون الالتفات للـ Vaccine اللي صار يعني الـ
+
+153
+00:11:32,510 --> 00:11:38,370
+Vaccine بس بيحمي من الفيروسات اللي موجودة في الـ
+
+154
+00:11:38,370 --> 00:11:42,560
+Strains اللي موجودة في التطعيمالفاكسينة
+
+155
+00:11:42,560 --> 00:11:48,920
+الانفلوانزا تشير بشكل خاص للناس الأكبر من 6 أشهر
+
+156
+00:11:48,920 --> 00:11:50,900
+من العمر للناس الأكبر من 6 أشهر من العمر للناس
+
+157
+00:11:50,900 --> 00:11:52,560
+الأكبر من 6 أشهر من العمر للناس الأكبر من 6 أشهر
+
+158
+00:11:52,560 --> 00:11:54,520
+من العمر للناس الأكبر من 6 أشهر من العمر للناس
+
+159
+00:11:54,520 --> 00:11:55,160
+الأكبر من 6 أشهر من العمر للناس الأكبر من 6 أشهر
+
+160
+00:11:55,160 --> 00:11:55,300
+من العمر للناس الأكبر من 6 أشهر من العمر للناس
+
+161
+00:11:55,300 --> 00:11:55,300
+الأكبر من 6 أشهر من العمر للناس الأكبر من 6 أشهر
+
+162
+00:11:55,300 --> 00:11:55,300
+من العمر للناس الأكبر من 6 أشهر من العمر للناس
+
+163
+00:11:55,300 --> 00:11:57,340
+الأكبر من 6 أشهر من العمر للناس الأكبر من 6 أشهر
+
+164
+00:11:57,340 --> 00:12:00,660
+من
+
+165
+00:12:00,660 --> 00:12:02,480
+العمر للناس الأكبر
+
+166
+00:12:12,950 --> 00:12:20,210
+وحقيقة أن الـ Respiratory Tract عادة مش بسهولة أن
+
+167
+00:12:20,210 --> 00:12:24,750
+الواحد ممكن ينصاب بالـ Lower Respiratory Tract
+
+168
+00:12:24,750 --> 00:12:27,450
+Infection يعني نصير عنده اتهاب في الرقى لابد أن
+
+169
+00:12:27,450 --> 00:12:32,640
+يكون فيه هناك عواملأضعفت الجسم، أضعفت الجسم اللي
+
+170
+00:12:32,640 --> 00:12:39,500
+هو الوضع المناعي تبع البني آدم وهي أثرت أنه انصاب
+
+171
+00:12:39,500 --> 00:12:44,800
+بالتهاب بكتيري أو التهاب فيروسي للـ Lower
+
+172
+00:12:44,800 --> 00:12:50,820
+Respiratory Tract Infection طيب، ليش؟ لأنه أصلاً
+
+173
+00:12:50,820 --> 00:12:57,040
+هناك آليات Defense Mechanisms آليات حماية للجسم
+
+174
+00:12:58,900 --> 00:13:04,760
+وخماية من؟ الـ Lungs بالذات، عشان البكتيريا هذه أو
+
+175
+00:13:04,760 --> 00:13:07,220
+الفيروس هذه ما تصل الرئتين
+
+176
+00:13:12,720 --> 00:13:17,180
+طبعاً هناك عوام الأخرى مدى شدة البكتيريا نفس
+
+177
+00:13:17,180 --> 00:13:22,080
+البكتيريا تكون virulent تكون هي نفسها متعبة كمان
+
+178
+00:13:22,080 --> 00:13:26,740
+بالعضو يبقى من الـ Host Defense Barriers بس بي ..
+
+179
+00:13:26,740 --> 00:13:33,160
+بنحكي عنها اللي بتضعفها اللي هي cigarette smoking
+
+180
+00:13:33,160 --> 00:13:40,340
+التدخين من الحاجات اللي بتضعفنا الجهاز المناعي و
+
+181
+00:13:40,340 --> 00:13:46,980
+بتعمل weakeningللـ Respiratory Defence Barriers زي
+
+182
+00:13:46,980 --> 00:13:51,900
+ما قلنا ليش؟ لأنها بتعمل Paralysing للـCilia
+
+183
+00:13:51,900 --> 00:13:55,780
+فاكرين الأهداف اللي حكينا عنها؟ بتعملها Paralysing
+
+184
+00:13:55,780 --> 00:14:00,160
+و بتعملها Damaging وهذه الـCilias هي كانت المسؤولة
+
+185
+00:14:00,160 --> 00:14:04,200
+في لحظة من اللحظات إن نتيجة حركتها إلى فوق
+
+186
+00:14:04,200 --> 00:14:11,650
+الشعيرات هذه أو الأهداف هذه إنها تخرج كلما يسبب
+
+187
+00:14:11,650 --> 00:14:17,570
+بلغم أو يسبب secretions أو يسبب particles أو micro
+
+188
+00:14:17,570 --> 00:14:21,490
+organism هي بترضه فلمّا أجت سيجارة smoking على
+
+189
+00:14:21,490 --> 00:14:25,950
+المدى الطويل عملت damaging للـcelias هاي بطلت
+
+190
+00:14:25,950 --> 00:14:29,650
+تشتغل بتصير ال particles زي البكتيريا و الحاجات
+
+191
+00:14:29,650 --> 00:14:36,430
+هاي تنزل دون حماية لمين للريقتينطبعاً لابد أنه كما
+
+192
+00:14:36,430 --> 00:14:43,230
+قلنا الـ virulence اللي هي شدة الـ شدة البكتيريا
+
+193
+00:14:43,230 --> 00:14:47,890
+هاي و قوتها بتلعب دور و مش بس الأجواء المحيطة
+
+194
+00:14:47,890 --> 00:14:52,270
+بتلعب دور زي الـ cold weather عسب اللي تعرف من
+
+195
+00:14:52,270 --> 00:14:57,010
+برضه الـ defence mechanisms اللي هو
+
+196
+00:15:00,630 --> 00:15:05,590
+السيرفيس كلها بدأت من الأنف والحلق كلها مويست و
+
+197
+00:15:05,590 --> 00:15:12,450
+عليها زي نوع من الـ mucous وهذه تتلقط الأورجانيزم
+
+198
+00:15:12,450 --> 00:15:15,970
+و الـ particles فيه إن الـ isosomes و الـ cell
+
+199
+00:15:15,970 --> 00:15:19,750
+service IGA فيه إن زي ما حكينا قبل شوية الـ
+
+200
+00:15:19,750 --> 00:15:23,210
+ciliated epithelium عنا كمان حاجة ربنا أدانا إياها
+
+201
+00:15:23,210 --> 00:15:28,040
+هي الكحةاليّة أو ميكانيكية الكحّة أو ردّة فعل
+
+202
+00:15:28,040 --> 00:15:30,500
+الكحّة كل ما ييجي يدخل إشي يعني زي الواحد اللي
+
+203
+00:15:30,500 --> 00:15:34,020
+ميجي تشردق يدخل إشي على الرئتين على طول واحد بكح
+
+204
+00:15:34,020 --> 00:15:37,980
+فبطلعها هذه نعمة من ربنا الكحّة نعمة من ربنا
+
+205
+00:15:37,980 --> 00:15:43,400
+الدنياها to prevent aspiration شردقة of particles
+
+206
+00:15:43,400 --> 00:15:48,700
+and irritants into the lower airways وفيه طبعا أن
+
+207
+00:15:48,700 --> 00:15:54,290
+أنواع زي اللي هو الـ Pulmonary Macrophageالـ
+
+208
+00:15:54,290 --> 00:16:00,710
+Microfage الكبير اللي بتحاول تعمل فجوط صيتز الـ
+
+209
+00:16:00,710 --> 00:16:06,210
+foreign particles أو الـ organisms طبعاً
+
+210
+00:16:06,210 --> 00:16:09,470
+لما أنا بقول lung tissue infection بقصد فيها
+
+211
+00:16:09,470 --> 00:16:15,250
+pneumonia pneumonia ال P ممكن أنه ما ألفزهاش لفظ
+
+212
+00:16:15,250 --> 00:16:18,410
+كامل pneumonia في ناس بتقول عن ابنومونيا لكن هي
+
+213
+00:16:18,410 --> 00:16:23,160
+pneumonia pneumonia is a condition thatالتي تتعلق
+
+214
+00:16:23,160 --> 00:16:27,340
+بالإنفلام من الـ Lower Lung Structures مثل الـ
+
+215
+00:16:27,340 --> 00:16:32,700
+Alveoli و الـ Interstitial Spaces يعني كل ال .. ال
+
+216
+00:16:32,700 --> 00:16:35,060
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+217
+00:16:35,060 --> 00:16:35,760
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+218
+00:16:35,760 --> 00:16:35,860
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+219
+00:16:35,860 --> 00:16:36,220
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+220
+00:16:36,220 --> 00:16:36,380
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+221
+00:16:36,380 --> 00:16:36,480
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+222
+00:16:36,480 --> 00:16:37,160
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+223
+00:16:37,160 --> 00:16:37,200
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+224
+00:16:37,200 --> 00:16:37,440
+.. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال ..
+
+225
+00:16:37,440 --> 00:16:37,440
+ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال .. ال
+
+226
+00:16:37,440 --> 00:16:43,140
+.. ال .. ال .. ال .. ال .. ال ..
+
+227
+00:16:43,140 --> 00:16:44,360
+ال
+
+228
+00:16:53,800 --> 00:16:56,560
+طبعاً الـ Pneumonia الـ prevalence تبعها و الـ
+
+229
+00:16:56,560 --> 00:16:59,660
+severity of pneumonia have been heightened in
+
+230
+00:16:59,660 --> 00:17:05,220
+recent years due to the emergence of HIV فاكرين
+
+231
+00:17:05,220 --> 00:17:09,940
+إيش الـ HIV؟ صحيح الـ AIDS as well as antibiotic
+
+232
+00:17:09,940 --> 00:17:17,000
+resistance نتيجة إنه صار فيه كتير HIV وهذا اسمه
+
+233
+00:17:17,000 --> 00:17:24,410
+ضعف المناع المكتسبونتيجة إنه صار في عنا تكون
+
+234
+00:17:24,410 --> 00:17:29,750
+مقاومة للمضادات الحيوية نتيجة استعمال غير الرشيد
+
+235
+00:17:29,750 --> 00:17:34,650
+للمضادات الحيوية فزادت الـ severity و ال
+
+236
+00:17:34,650 --> 00:17:39,210
+prevalence of pneumonia و ال classification تبع
+
+237
+00:17:39,210 --> 00:17:42,170
+الـ pneumonia حسب ممكن نقولها حسب الـ pathogen حسب
+
+238
+00:17:42,170 --> 00:17:45,430
+المادة اللي عملت التهاب يعني viral pneumonia أو
+
+239
+00:17:45,430 --> 00:17:51,210
+bacterial pneumoniaوممكن لكن نقول عنها كمان
+
+240
+00:17:51,210 --> 00:17:56,570
+التفريق التاني أقول عنها hospital أو community
+
+241
+00:17:56,570 --> 00:18:02,670
+pneumonia أو hospital nosocomial pneumonia ال
+
+242
+00:18:02,670 --> 00:18:07,330
+individuals most at risk of pneumonia الالدرلي
+
+243
+00:18:07,330 --> 00:18:11,870
+الناس اللي عندها viral infection ال chronic ill ال
+
+244
+00:18:11,870 --> 00:18:15,690
+HIV أو ال AIDS والimmune suppressant patient
+
+245
+00:18:15,690 --> 00:18:21,330
+smokersبشيء مثل الـ Bronchial Asthma بشيء ممكن
+
+246
+00:18:21,330 --> 00:18:26,330
+كمان مرة في عنا نمونيا اسمها community acquired
+
+247
+00:18:26,330 --> 00:18:30,250
+community acquired يعني من المجتمع وفي عنا
+
+248
+00:18:30,250 --> 00:18:34,410
+aspiration pneumonia الشردقة ينزل حاجة على الرئتين
+
+249
+00:18:34,410 --> 00:18:38,730
+وفي عنا ال hospital acquired فرجوها قالوا في
+
+250
+00:18:38,730 --> 00:18:42,620
+hospital acquired pneumonia وفي ventilatorبنتليتر
+
+251
+00:18:42,620 --> 00:18:46,180
+جوز جهزتنا في الصناعي associated pneumonia وفيه
+
+252
+00:18:46,180 --> 00:18:49,320
+health care associated pneumonia زي ما هنحكي بعد
+
+253
+00:18:49,320 --> 00:18:55,040
+شوية ال
+
+254
+00:18:55,040 --> 00:18:59,680
+potential pathogens اللي احنا بنعرفه يعني خلنا
+
+255
+00:18:59,680 --> 00:19:05,230
+نقول ممكن نتعرف على اتنين تلاتة من كل واحدوهي الـ
+
+256
+00:19:05,230 --> 00:19:06,850
+atypical pneumonia الـ atypical pneumonia هي
+
+257
+00:19:06,850 --> 00:19:10,310
+النمونيا العادية المتوقعة زي الـ Streptococcus
+
+258
+00:19:10,310 --> 00:19:13,770
+pneumonia و الـ Hemophilus influenza و الـ
+
+259
+00:19:13,770 --> 00:19:15,790
+Klebsiella pneumonia و الـ Mycobacterium
+
+260
+00:19:15,790 --> 00:19:18,350
+catarrhalis و الـ atypical زي الـ Chlamydia
+
+261
+00:19:18,350 --> 00:19:22,670
+pneumonia و Legionella pneumonia و Mycoplasma
+
+262
+00:19:22,670 --> 00:19:30,190
+pneumonia هذه الصورة بتوضح لنا أن بعض الأنواع
+
+263
+00:19:32,690 --> 00:19:39,850
+والـ classification للـ pneumonia هنرجعلها
+
+264
+00:19:39,850 --> 00:19:47,710
+بنحكي الآن عن ال typical و ال atypical إيش بنقصد
+
+265
+00:19:47,710 --> 00:19:54,090
+فيهم؟ كال pneumonia حسب
+
+266
+00:19:56,930 --> 00:20:01,990
+حسب اللي هو قلنا فيه typical و atypical حسب
+
+267
+00:20:01,990 --> 00:20:06,090
+specific structure لأصيبة في الـ lung الـ typical
+
+268
+00:20:06,090 --> 00:20:12,470
+عادة بتبقى بكتيريا in origin و organisms replicate
+
+269
+00:20:12,470 --> 00:20:17,090
+يعني عملية توالد أو تجدد ال organisms بتصير كلها
+
+270
+00:20:17,090 --> 00:20:21,210
+في ال alveoli ال manifestation تبعها يبقى
+
+271
+00:20:21,210 --> 00:20:25,410
+inflammation of and fluid accumulation are seen in
+
+272
+00:20:25,410 --> 00:20:29,680
+the alveoliبالتالي White Cell Infiltration and
+
+273
+00:20:29,680 --> 00:20:33,380
+Exudation Can Be Seen On Chest Radiograph لو عملنا
+
+274
+00:20:33,380 --> 00:20:39,700
+X-Ray بنلاقي إنه في عندنا Infiltration بنلاقي High
+
+275
+00:20:39,700 --> 00:20:43,940
+Fever، Chest Pain، Chills، Malaise، تعب ماليز
+
+276
+00:20:44,680 --> 00:20:55,180
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+277
+00:20:55,180 --> 00:20:55,180
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+278
+00:20:55,180 --> 00:20:55,180
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+279
+00:20:55,180 --> 00:20:56,100
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+280
+00:20:56,100 --> 00:20:57,340
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+281
+00:20:57,340 --> 00:21:03,360
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+282
+00:21:03,360 --> 00:21:03,360
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+283
+00:21:03,360 --> 00:21:03,380
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+284
+00:21:03,380 --> 00:21:04,200
+بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت بيرولنت
+
+285
+00:21:04,200 --> 00:21:07,380
+بيرولنت
+
+286
+00:21:07,380 --> 00:21:13,520
+بيرولنتوالعضلات تتعادل في المقاطع حول الـ alveoli
+
+287
+00:21:13,520 --> 00:21:18,240
+قبل قليل كانت في المقاطع حول الـ alveoli جوة الـ
+
+288
+00:21:18,240 --> 00:21:22,520
+alveoli لكن هنا حوالين الـ alveoli بنلاقي إن الـ
+
+289
+00:21:22,520 --> 00:21:25,520
+atypical أو الـ viral هي mild
+
+290
+00:21:29,250 --> 00:21:32,570
+وبنلاقيش في الـ alveoli infiltration زي ما احنا
+
+291
+00:21:32,570 --> 00:21:36,550
+بنشوفها و lack of fluid accumulation in the
+
+292
+00:21:36,550 --> 00:21:40,730
+alveoli not usually evident on radiographs ممكن
+
+293
+00:21:40,730 --> 00:21:44,650
+أعمل X-ray وما لاجيهاش، ماشوفهاش و may make the
+
+294
+00:21:44,650 --> 00:21:48,390
+patient susceptible to bacterial pneumonia نبقى
+
+295
+00:21:48,390 --> 00:21:51,270
+هنا احنا حكينا عن واحد من أنواع ال classification
+
+296
+00:21:51,270 --> 00:21:56,500
+الـtypical و الـatypical pneumoniaفي عندنا كمان
+
+297
+00:21:56,500 --> 00:21:59,720
+حاجة احنا بنعرفها اللي هي الـ opportunistic
+
+298
+00:21:59,720 --> 00:22:05,080
+organisms يعني احنا كنا bacterial و viral لأننا
+
+299
+00:22:05,080 --> 00:22:08,920
+ندخل على opportunistic organisms وهي عبارة عن
+
+300
+00:22:08,920 --> 00:22:11,460
+number of organisms not commonly associated with
+
+301
+00:22:11,460 --> 00:22:15,460
+respiratory illness in otherwise healthy
+
+302
+00:22:15,460 --> 00:22:18,540
+individuals can cause severeالـ Respiratory
+
+303
+00:22:18,540 --> 00:22:23,540
+Infection باختصار هدولة نوع من أنواع الـ Organism
+
+304
+00:22:23,540 --> 00:22:27,800
+زي الـ Histoplasma و الـ Pneumocystis carinae يعني
+
+305
+00:22:27,800 --> 00:22:30,760
+الـ Fungal Infection مع الـ Protozoa اللي هو
+
+306
+00:22:30,760 --> 00:22:34,280
+Pneumocystis carinae و الـ Mycobacteria في الوضع
+
+307
+00:22:34,280 --> 00:22:39,220
+الطبيعي في الـ Healthy Body بيعملوش حاجة ها بتجد
+
+308
+00:22:39,220 --> 00:22:44,640
+عنهم لما بدعف الجسم عشان هيك بنقول عنهم المستنفعين
+
+309
+00:22:44,640 --> 00:22:49,290
+opportunistic organismمستنفعين، these organisms
+
+310
+00:22:49,290 --> 00:22:53,750
+include زي ما قلنا Mycobacteria أو fungus زي
+
+311
+00:22:53,750 --> 00:22:57,090
+الهيستو بلازما أو Protisuga زي الـ Gnemosis carini
+
+312
+00:22:57,090 --> 00:23:00,590
+treatment of these organisms require specific drug
+
+313
+00:23:00,590 --> 00:23:06,510
+therapy and in case of Protisuga بنحتاجه طبعاً
+
+314
+00:23:06,510 --> 00:23:10,470
+بتبقى صعبة علاجها لأن هي بتبقى توحشت نتيجة إن
+
+315
+00:23:10,470 --> 00:23:14,670
+الimmune نتيجة إن الimmune system ضعيف عند ال
+
+316
+00:23:14,670 --> 00:23:18,560
+patientهذه ما بيقولها opportunistic organisms
+
+317
+00:23:18,560 --> 00:23:22,620
+حكينا
+
+318
+00:23:22,620 --> 00:23:24,960
+عن infection، هندخل على الـ Obstructive
+
+319
+00:23:24,960 --> 00:23:28,080
+Respiratory Disorders إيش يعني Obstructive؟ فيه
+
+320
+00:23:28,080 --> 00:23:31,900
+تضيق Respiratory Disorders الأمراض المرتبطة
+
+321
+00:23:31,900 --> 00:23:37,580
+بالتضيق طبعا
+
+322
+00:23:37,580 --> 00:23:44,110
+أهمها لـ Bronchial Asthmaاللي بنقول عنها احنا اللي
+
+323
+00:23:44,110 --> 00:23:47,310
+هي حساسية السدر في ناس بتقول عنها النهجة في ناس
+
+324
+00:23:47,310 --> 00:23:52,070
+بتقول عنها الأزمة في ناس بتقول عنها الربو أزمة is
+
+325
+00:23:52,070 --> 00:23:54,650
+a condition characterized by reversible
+
+326
+00:23:54,650 --> 00:23:58,310
+bronchospasm reversible يعني بيروحوا بي .. ممكن
+
+327
+00:23:58,310 --> 00:24:03,350
+يروحوا ييجي bronchospasm تضيق في البرونكيولز and
+
+328
+00:24:03,350 --> 00:24:07,290
+chronic inflammation of airway passages وكمان مش
+
+329
+00:24:07,290 --> 00:24:13,120
+بسبتدينا inflammation مش infection inflammation of
+
+330
+00:24:13,120 --> 00:24:16,980
+airway passages the incidence of asthma has been
+
+331
+00:24:16,980 --> 00:24:20,400
+steadily increasing in the recent years فعلا بتزيد
+
+332
+00:24:20,400 --> 00:24:27,320
+نتيجة ال environmental pollution although the
+
+333
+00:24:27,320 --> 00:24:31,800
+extent the exact etiology is still uncertain there
+
+334
+00:24:31,800 --> 00:24:36,440
+appears to be a definite genetic predisposition to
+
+335
+00:24:36,440 --> 00:24:38,020
+the development of asthma
+
+336
+00:24:41,660 --> 00:24:45,520
+لكن كمان في عندنا الـ Genetic Predisposition
+
+337
+00:24:49,030 --> 00:24:53,330
+وورثياً جينياً إنها يصير عندها اكي كومبوننط of
+
+338
+00:24:53,330 --> 00:24:57,770
+أزمة appears to be airway hyper reactivity اللي هي
+
+339
+00:24:57,770 --> 00:25:02,530
+زيادة حساسية اللي هو ال .. ال .. ال .. ال airway
+
+340
+00:25:02,530 --> 00:25:06,890
+اللي هي المسالك التنفسية in affected individuals
+
+341
+00:25:06,890 --> 00:25:11,110
+exposure to certain triggers can include marked
+
+342
+00:25:11,110 --> 00:25:15,670
+bronchospasm and airway inflammationفي مستخدم
+
+343
+00:25:15,670 --> 00:25:15,870
+مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم
+
+344
+00:25:15,870 --> 00:25:18,210
+مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم
+
+345
+00:25:18,210 --> 00:25:18,470
+مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم
+
+346
+00:25:18,470 --> 00:25:21,930
+مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم
+
+347
+00:25:21,930 --> 00:25:27,570
+مستخدم مستخدم مستخدم مستخدم مستخدم مستخدم
+
+348
+00:25:27,570 --> 00:25:30,310
+مستخدم
+
+349
+00:25:38,690 --> 00:25:41,310
+فبصير عندنا صورة اللي هي الـ bronchial asthma
+
+350
+00:25:41,310 --> 00:25:45,110
+Individuals with asthma appear to produce large
+
+351
+00:25:45,110 --> 00:25:51,970
+amounts of antibody IGE that attach to the mast
+
+352
+00:25:51,970 --> 00:25:57,790
+cells present in many tissues هلجيت ال exposure to
+
+353
+00:25:57,790 --> 00:26:02,210
+a trigger such as pollen اللي هي الحاجات اللي
+
+354
+00:26:02,210 --> 00:26:05,880
+بتطلع من الشجروالرزولت في الـ Allergy-Binding
+
+355
+00:26:05,880 --> 00:26:10,740
+Muscles-Pound IgE اللي يسبب في إطلاق إطلاق مدينة
+
+356
+00:26:10,740 --> 00:26:14,200
+انفلامات مثل الهستامين والليكوترين
+
+357
+00:26:14,200 --> 00:26:19,100
+والأيزوفينيكيكيموتاكتك فاكتور الاتجاه للطبيعي مع
+
+358
+00:26:19,100 --> 00:26:23,620
+الأزمة لتلك التغييرات ممكن أقول عنه في منه early
+
+359
+00:26:23,620 --> 00:26:28,570
+phase و في late phaseمن الـ triggers اللي لازم
+
+360
+00:26:28,570 --> 00:26:36,110
+طبعا ابحثوا عن بعضهم ممكن تبحثوا تجروا الألراجين
+
+361
+00:26:36,110 --> 00:26:40,810
+زي الـ pollen، الpit، الdander، الفنجاي، ال dust
+
+362
+00:26:40,810 --> 00:26:46,250
+bites، cold air، pollutants، cigarette smoking،
+
+363
+00:26:46,250 --> 00:26:49,490
+strong emotion، exercise، respiratory tract
+
+364
+00:26:49,490 --> 00:26:53,520
+infection، كل هاي برنكا الأزمةأو potential trigger
+
+365
+00:26:53,520 --> 00:26:56,220
+طبعاً لا يعني أنه ما فيش اللي هي ممكن كل واحد إله
+
+366
+00:26:56,220 --> 00:27:00,660
+ال triggers تبعته اللي ممكن تعمله الموضوع هذا why
+
+367
+00:27:00,660 --> 00:27:04,680
+asthma makes it hard to breathe طبعاً زي ما احنا
+
+368
+00:27:04,680 --> 00:27:11,640
+شايفين هي ال two bronchial tube الجهة اللي فيها
+
+369
+00:27:11,640 --> 00:27:17,920
+صار عندنا affection نتيجة ألرجي معين عملتنا
+
+370
+00:27:17,920 --> 00:27:22,800
+inflamed bronchial tubeوالـ Obstruction مع
+
+371
+00:27:22,800 --> 00:27:25,400
+Inflammation في الجهة التانية Normal Bronchial
+
+372
+00:27:25,400 --> 00:27:31,200
+Tube واسع وبقدر واحد يتنفس زي الناس فيه طبعا عندنا
+
+373
+00:27:31,200 --> 00:27:37,500
+حكينا عن الـ Early Phase و الـ Late Phase خلّيني
+
+374
+00:27:37,500 --> 00:27:39,360
+أحكيه ما وجهته وبعدين نرجع لـ Clinical
+
+375
+00:27:39,360 --> 00:27:44,060
+Classification Early Phase of Asthma characterized
+
+376
+00:27:44,060 --> 00:27:46,820
+by mild
+
+377
+00:27:49,530 --> 00:27:53,950
+أو marked construction of bronchial airways بيصير
+
+378
+00:27:53,950 --> 00:28:00,090
+إديمة in the airway وفي عندنا production of excess
+
+379
+00:28:00,090 --> 00:28:03,630
+mucus يبقى marked construction of bronchial
+
+380
+00:28:03,630 --> 00:28:06,530
+airways bronchospasm إديمة in the airway
+
+381
+00:28:06,530 --> 00:28:11,890
+وproduction of excess mucus
+
+382
+00:28:13,910 --> 00:28:17,950
+وطبعاً الـ Bronchospasm جاء نتيجة أول حاجة Direct
+
+383
+00:28:17,950 --> 00:28:23,050
+نتيجة الـ inflammation لكن كمان نتيجة اللي هو الـ
+
+384
+00:28:23,050 --> 00:28:28,210
+الـ الـ الـ الـ mucous building الـ Late phase
+
+385
+00:28:28,210 --> 00:28:32,990
+طبعا
+
+386
+00:28:32,990 --> 00:28:35,230
+الـ Mediators الأساسية كانت في الـ Early phase
+
+387
+00:28:35,230 --> 00:28:40,470
+اللي هي Histamine, Prostaglandin and Predicanin في
+
+388
+00:28:40,470 --> 00:28:45,620
+الـ Early في ال Late phaseهذا بيجي طبعا بعد بضع
+
+389
+00:28:45,620 --> 00:28:49,240
+ساعات after the initial onset of symptoms and
+
+390
+00:28:49,240 --> 00:28:53,440
+manifests mainly as inflammatory response خدوا
+
+391
+00:28:53,440 --> 00:28:57,380
+بالكم الأولاني كان Bronchospasm ما inflammation،
+
+392
+00:28:57,380 --> 00:29:01,680
+الآن بس inflammatory response وهذا الفكرة بتفيدنا
+
+393
+00:29:01,680 --> 00:29:06,080
+في قضية العلاج بصورة عامة The primary mediators of
+
+394
+00:29:06,080 --> 00:29:10,440
+inflammation during the asthmatic response are the
+
+395
+00:29:10,440 --> 00:29:15,140
+white blood cells اللي هي الـAzonophilsيبقى في الـ
+
+396
+00:29:15,140 --> 00:29:19,260
+Late Phase of Asthma الـ eosinophils لعبت دور كبير
+
+397
+00:29:19,260 --> 00:29:23,400
+في الموضوع وsubsequent infiltration of the airway
+
+398
+00:29:23,400 --> 00:29:27,260
+tissue with white blood cells such as neutrophils
+
+399
+00:29:27,260 --> 00:29:29,800
+و الـ lymphocytes also contribute to the overall
+
+400
+00:29:29,800 --> 00:29:34,020
+inflammatory response of the Late Phase of Asthma
+
+401
+00:29:34,020 --> 00:29:37,220
+يبقى بدنا نفرج بين إيش بيصير في الـ Early Phase
+
+402
+00:29:37,220 --> 00:29:46,150
+وإيش بيصير في ال Late Phaseفي عنا طبعاً symptoms،
+
+403
+00:29:46,150 --> 00:29:49,110
+manifestation الـ symptoms اللي بتصير عنا في الـ
+
+404
+00:29:49,110 --> 00:29:52,630
+bronchial asthma اللي هي coughing، wheezing، إيش
+
+405
+00:29:52,630 --> 00:29:55,670
+يعني wheezing؟ بيصير يسفر السدر، يزمر، difficulty
+
+406
+00:29:55,670 --> 00:29:59,810
+breathing, rapid and shallow breathing, increased
+
+407
+00:29:59,810 --> 00:30:02,470
+respiratory rate, excess mucus production and
+
+408
+00:30:02,470 --> 00:30:05,430
+significant anxiety، مافيش حرارة، خدوا بالكم، هاد
+
+409
+00:30:05,430 --> 00:30:11,510
+هو ال manifestation of bronchial asthmaفي عنا طبعا
+
+410
+00:30:11,510 --> 00:30:17,090
+حاجة اسمها staging of
+
+411
+00:30:17,090 --> 00:30:23,100
+acute asthma attackأو حد على المستشفى مجرد ما
+
+412
+00:30:23,100 --> 00:30:26,200
+شوفته أنا عرفت أن البرونكيل أزمة بدأ أقيمه هو
+
+413
+00:30:26,200 --> 00:30:30,200
+stage one ولا two ولا three ولا four طب إيش one؟
+
+414
+00:30:30,200 --> 00:30:35,300
+one mild، two moderate، three severe، and four
+
+415
+00:30:35,300 --> 00:30:38,420
+respiratory failure يعني بده عناية مركزة عمليًا هو
+
+416
+00:30:38,420 --> 00:30:41,900
+والتلاتة ممكن يحتاجوا عناية مركزة stage تلاتة وال
+
+417
+00:30:41,900 --> 00:30:45,650
+respiratory failure stage أربعةطب إيش بيصير في الـ
+
+418
+00:30:45,650 --> 00:30:49,310
+Mild بيصير ديسنيا خفيفة diffuse wheezing يعني في
+
+419
+00:30:49,310 --> 00:30:56,390
+تسفيرة عنده ولكن نفسه كويس لو حطيته على جهاز ال
+
+420
+00:30:56,390 --> 00:31:00,310
+monitor بلاقي ال oxygen كويس stage two moderate
+
+421
+00:31:01,460 --> 00:31:05,280
+متوسط يعني Respiratory distress وهو جاعد لأ نفسه
+
+422
+00:31:05,280 --> 00:31:12,980
+تعبان وصورة واضحة صورة الصوت التسفير في جسمه في
+
+423
+00:31:12,980 --> 00:31:17,100
+صدره واضح Stage 3 Severe Marked Respiratory
+
+424
+00:31:17,100 --> 00:31:21,130
+distressأه بدأ يصير أزرق الآن يعني مش بس صار عنده
+
+425
+00:31:21,130 --> 00:31:27,150
+ضيوف في النفس أزرق وحتى بدون يعني بشوف إنه فيه
+
+426
+00:31:27,150 --> 00:31:31,910
+تسفير واضح أو إنه كتم صدره من الكترب وهم سكر صدره،
+
+427
+00:31:31,910 --> 00:31:35,690
+سكر صدره بالظبط absence of breath sounds يعني أنا
+
+428
+00:31:35,690 --> 00:31:39,110
+ماحط السماعة بسمعش ولا حاجة، ليش؟ لأنه اتسكرت
+
+429
+00:31:39,110 --> 00:31:42,070
+الطرق obstructed لإن احنا برنكيل الأزمة قلنا إيش
+
+430
+00:31:42,070 --> 00:31:44,370
+اللي بيصير؟ بيصير يعني obstruction of bronchioles
+
+431
+00:31:44,370 --> 00:31:48,210
+فهو سكرالـ Stage IV الـ Respiratory Failure هو
+
+432
+00:31:48,210 --> 00:31:51,450
+عبارة عن Severe Respiratory Stress، Lethargy، بدأ
+
+433
+00:31:51,450 --> 00:31:54,650
+يتأثر، Confusion، بطل يصل الدم للدماج، فصار يصير
+
+434
+00:31:54,650 --> 00:31:58,270
+عنده Confusion، Prominent Pulses Paradoxical، هذه
+
+435
+00:31:58,270 --> 00:32:02,750
+اللي هي لما يجيني واحد كده أقيمه في الـ Acute
+
+436
+00:32:02,750 --> 00:32:07,070
+Attack، ساعة ما بيجيني الـ Severe، الـ Severity،
+
+437
+00:32:07,070 --> 00:32:09,550
+Staging of the Severity، خدوا بالكم من العنوان،
+
+438
+00:32:09,550 --> 00:32:13,050
+Staging of the Severity of the Acute Asthma
+
+439
+00:32:13,050 --> 00:32:17,940
+Attack،لكن في عنا حاجة تانية احنا كنا فطناها قبل
+
+440
+00:32:17,940 --> 00:32:21,640
+شويه اللي هي Classification من الأزمة هذا بصورة
+
+441
+00:32:21,640 --> 00:32:25,980
+عامة مش الـ Acute أي واحد عنده أزمة وبيجيني هو
+
+442
+00:32:25,980 --> 00:32:30,660
+هيكون واحد من أربع Classification Clinical
+
+443
+00:32:30,660 --> 00:32:35,360
+Classification الـMild Intermittent وMild
+
+444
+00:32:35,360 --> 00:32:38,540
+Persistent، Moderate Persistent وSevere Persistent
+
+445
+00:32:40,550 --> 00:32:44,610
+الـ Mild Intermittent أنه بتجيله نوبات مرتين في
+
+446
+00:32:44,610 --> 00:32:49,990
+الأسبوع أو أقل النوبة اللي حكينا عنها قبل شوية الـ
+
+447
+00:32:49,990 --> 00:32:53,050
+Mild Persistent attacks occur more than two times
+
+448
+00:32:53,050 --> 00:32:57,330
+per week هذا Mild Persistent أكتر من تنتين الـ
+
+449
+00:32:57,330 --> 00:33:02,350
+Moderate Persistent هو attacks occur daily or
+
+450
+00:33:02,350 --> 00:33:08,110
+almost daily يوميا أو تقريبا يومياand are severe
+
+451
+00:33:08,110 --> 00:33:13,210
+enough to affect activity مجعدا، رميا، تعبا، يوميا
+
+452
+00:33:13,210 --> 00:33:17,110
+و الـ severe persistent attacks are very frequent
+
+453
+00:33:17,110 --> 00:33:20,750
+and persistent for a long period of time attacks
+
+454
+00:33:20,750 --> 00:33:24,570
+severely limit activity يبقى هذه اسمها clinical
+
+455
+00:33:24,570 --> 00:33:28,770
+classification of asthma كم نوبة بتيجي عنده خلال
+
+456
+00:33:28,770 --> 00:33:34,690
+الأسبوع أو بصورة عامة اللي حكيناه قبلها اللي هوالـ
+
+457
+00:33:34,690 --> 00:33:38,350
+Staging هذه للـ Acute Attack كيف بقى أقيم كل Acute
+
+458
+00:33:38,350 --> 00:33:41,450
+Attack؟
+
+459
+00:33:41,450 --> 00:33:46,210
+نكمل
+
+460
+00:33:46,210 --> 00:33:48,430
+بس لأنه ضايق سلايدين بس في الـ Bronchial Asthma
+
+461
+00:33:48,430 --> 00:33:53,690
+possible complications of asthma can includeطبعاً
+
+462
+00:33:53,690 --> 00:33:56,790
+status asthmaticus اللي بيقول severe acute أزمة
+
+463
+00:33:56,790 --> 00:33:59,910
+وهذا is a life-threatening condition زي status
+
+464
+00:33:59,910 --> 00:34:06,190
+epilepticus النوبة الصراع الكبرى هذه نوبة الأزمة
+
+465
+00:34:06,190 --> 00:34:11,000
+الكبرى واللي بيحتاج prolongedالبرونكوسبازم هو
+
+466
+00:34:11,000 --> 00:34:14,920
+البرونكوسبازم اللي عادةً لا يتراجع للدواء الترابي
+
+467
+00:34:14,920 --> 00:34:18,500
+كمان بتدي دوة مفيدش كتير، في الآخر بده ايش؟ بده
+
+468
+00:34:18,500 --> 00:34:22,440
+تنفس صناعي، ايش كمان ممكن يحصل؟ بنوعي Motorax،
+
+469
+00:34:22,440 --> 00:34:25,700
+هنحكي عن بنوعي Motorax هي عبارة عن possible
+
+470
+00:34:25,700 --> 00:34:32,800
+consequence of lung pressure increasesيمكن أن
+
+471
+00:34:32,800 --> 00:34:36,300
+ينتهي من الصعوبة الكهربائية المرتبطة في الانتصاف
+
+472
+00:34:36,300 --> 00:34:41,380
+خلال اتكاب أزمة مستمر، فإن فشل الهيبوكسيميا
+
+473
+00:34:41,380 --> 00:34:49,100
+والأسدوزية قد يحدث تعامل
+
+474
+00:34:49,100 --> 00:34:54,170
+الأزمةحقيقة يعني احنا زي ما قلنا برضه مش لازمنا
+
+475
+00:34:54,170 --> 00:34:59,510
+كتير الأدوية لكن لابد انه نتعرف على الحاجات
+
+476
+00:34:59,510 --> 00:35:04,330
+الأساسية تبع ال treatment of asthma وهذا بنتركه لل
+
+477
+00:35:04,330 --> 00:35:07,570
+slide اللي جاي عشان مايصيرش كتير عليكم، يعطيكوا
+
+478
+00:35:07,570 --> 00:35:11,170
+العافية وإيقاع القطاع، ان شاء الله هنكمل ال
+
+479
+00:35:11,170 --> 00:35:17,790
+obstructive respiratory tract disorders
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/xJGkNKjINVE_postprocess.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/xJGkNKjINVE_postprocess.srt
new file mode 100644
index 0000000000000000000000000000000000000000..af64c1ece2ef78194d3f84a3fbd268cfa208b597
--- /dev/null
+++ b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/xJGkNKjINVE_postprocess.srt
@@ -0,0 +1,1768 @@
+1
+00:00:00,000 --> 00:00:02,800
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:02,800 --> 00:00:06,280
+والصلاة والسلام علي سيدنا محمد سيد المرسلين أجمعين
+
+3
+00:00:06,280 --> 00:00:10,020
+يعني اليوم ان شاء الله تعالى هندخل على موضوع تاني
+
+4
+00:00:10,020 --> 00:00:17,320
+موضوع طويل موضوع مهم موضوع عمليا في كل بيت موجود
+
+5
+00:00:17,320 --> 00:00:21,200
+إن ماكانش في كل بيت في البيت اللي جنبه أوي يعني
+
+6
+00:00:21,200 --> 00:00:24,560
+يعني ببعنى إنه من كل بيتين هتلاجوا في بيت حد عنده
+
+7
+00:00:24,560 --> 00:00:30,240
+سكري كانوا زمان يقولوا عنه سكر البوللكن الأن هو
+
+8
+00:00:30,240 --> 00:00:34,520
+السكري السكر لبول لإنه كانوا زمان أول ما يكتشفوه
+
+9
+00:00:34,520 --> 00:00:39,020
+يكتشفوه من كتر التبول وإنه كان فيه سكر في البول
+
+10
+00:00:39,020 --> 00:00:44,260
+نتيجة تهريب الكيلة للسكر لزيادة على أي حال الـ
+
+11
+00:00:44,260 --> 00:00:50,640
+diabetes mellitus الديابتس ميليتس طيب هو أنا لما
+
+12
+00:00:50,640 --> 00:00:54,760
+أقول والله فلان عنده الديابتس هل بقصد فيه بس ال
+
+13
+00:00:54,760 --> 00:00:59,300
+diabetes mellitus السكري العادي تبعنا؟أه لكن في
+
+14
+00:00:59,300 --> 00:01:05,660
+ديابتس انسبدس نوع تاني ديابتس انسبدس حاجة تانية هي
+
+15
+00:01:05,660 --> 00:01:11,740
+صحيح مرتبطة بكتر البول برضه لكن اشي تاني يختلف عن
+
+16
+00:01:11,740 --> 00:01:18,020
+الـ diabetes mellitus صح كلامكوا مية في المية ال
+
+17
+00:01:18,020 --> 00:01:24,140
+assignment تبعنا مجسوم من حاجتين اليوم أول حاجةفي
+
+18
+00:01:24,140 --> 00:01:28,860
+نص صفحة مصورة تصوير مكتوبة بالإيد ومصورة تصوير
+
+19
+00:01:28,860 --> 00:01:35,000
+تحكولي عن الـDiabetes Encephalitis ما هو أنواعه
+
+20
+00:01:35,000 --> 00:01:39,180
+وطرق علاجه كلمات يا جماعة بديش شرح شرح ملزمنيش
+
+21
+00:01:39,180 --> 00:01:44,500
+موجودش الكتب الشرح اجروا انتوا كثير واطلعولي بملخص
+
+22
+00:01:44,500 --> 00:01:47,220
+صغير عن الـDiabetes Encephalitis بالحاجات اللي انا
+
+23
+00:01:47,220 --> 00:01:50,320
+ذكرتها عن الـEncephalitis الـDiabetes Melitus انا
+
+24
+00:01:50,320 --> 00:01:53,780
+هحكي عنه اللي هو السكريهذا الجزء الأول من الـ
+
+25
+00:01:53,780 --> 00:01:57,660
+Assignment هنحكي عن الجزء التاني بعد شوية من الـ
+
+26
+00:01:57,660 --> 00:02:02,280
+Assignment الـ Diabetes Militas الاختصار تبعه DM
+
+27
+00:02:02,280 --> 00:02:08,880
+Diabetes DM Militas وهو عبارة عن Metabolic Disease
+
+28
+00:02:08,880 --> 00:02:14,320
+إيش يعني Metabolic؟ Metabolic المقصود فيه إنه يختص
+
+29
+00:02:14,320 --> 00:02:21,050
+بموضوع الاستقلاب الخليةمش حاجة من بعيد ورم ولا إيد
+
+30
+00:02:21,050 --> 00:02:26,750
+مقصورة ولا دهر ولا desk لأ إنما حاجة جوا الخلية
+
+31
+00:02:26,750 --> 00:02:33,570
+بتسير هذا مقصود في metabolic واللي أهم معلم بنشوفه
+
+32
+00:02:33,570 --> 00:02:38,970
+فيها وبدونه ماينفعش أقول diabetes high blood sugar
+
+33
+00:02:38,970 --> 00:02:44,250
+level في الدم over خدوا بالكم الجمعة الجملة هاي
+
+34
+00:02:44,250 --> 00:02:48,200
+prolonged periodنفس الكلام اللي حكيناه عن مين عن
+
+35
+00:02:48,200 --> 00:02:50,720
+الـ hypertension مش مابقول أنا أجيس لواحد مرة ضغط
+
+36
+00:02:50,720 --> 00:02:53,340
+علاجية عالية أقول له يا أبو الشباب والله شكلك عندك
+
+37
+00:02:53,340 --> 00:02:57,660
+ضغط أو والله عملتله فحص سكر اللي جاته مرة عالي لأ،
+
+38
+00:02:57,660 --> 00:03:00,500
+لها شروط هذه الجذيع وهذا هنحكي عنه في المحاضرة
+
+39
+00:03:00,500 --> 00:03:06,660
+يبقى prolonged period لازم عدة مجسات في عدة أوقات
+
+40
+00:03:06,660 --> 00:03:11,720
+مختلفة وعدت للسكر طبعا ساعتها بقول عنه diabetes
+
+41
+00:03:11,720 --> 00:03:15,730
+and diabetes هنحكي عن الموضوع هذا خلالخلال
+
+42
+00:03:15,730 --> 00:03:23,770
+المحاضرة الـ diabetes مشكلته multi system بمعنى
+
+43
+00:03:23,770 --> 00:03:29,490
+مافيش مكان في الجسم إلا بيغزوه هذه خطورته أنه هو
+
+44
+00:03:29,490 --> 00:03:39,750
+بيأثرلي تأثيرات مباشرة أنه
+
+45
+00:03:39,750 --> 00:03:44,710
+هو بيأثرلي تأثيرات مباشرة على العين
+
+46
+00:03:46,660 --> 00:03:50,720
+بأثرلي تأثيرات مباشرة على الدورة الدموية، على
+
+47
+00:03:50,720 --> 00:03:54,960
+القلب، على الكلا، على الشراين الترافية، على
+
+48
+00:03:54,960 --> 00:03:58,080
+الأعصاب الترافية، طب وإيش ضال في البني آدم؟ أه ما
+
+49
+00:03:58,080 --> 00:04:03,240
+هي مشكلة السكر، السكر دمار، السكري دمار، طيب هو
+
+50
+00:04:04,600 --> 00:04:08,680
+شوّقتنا يعني السكري يعني هو بيصيب كل واحد ولا كيف
+
+51
+00:04:08,680 --> 00:04:11,820
+الموضوع ولا إيش اللي بيصير هذا اللي هنحكي عنه وهذا
+
+52
+00:04:11,820 --> 00:04:15,380
+اللي لازم أنتوا تكونوا جزء من الموضوع أنا بحكي في
+
+53
+00:04:15,380 --> 00:04:19,920
+تاني أهم موضوع في الباطنة اللي هو الـ Diabetes
+
+54
+00:04:19,920 --> 00:04:23,740
+Mellitus كمان مرة طيب اللي هو إيش اللي بيصير
+
+55
+00:04:23,740 --> 00:04:27,760
+بالظبط حاجة من حاجتين هنحكي بعد هيك إحنا كيف الـ
+
+56
+00:04:27,760 --> 00:04:31,600
+Type 1 و Type 2 لكن من الأول إنه بيكون عند
+
+57
+00:04:31,600 --> 00:04:37,740
+الإنسولينالانسولين عبارة عن هرمون هذا شغله ينظم
+
+58
+00:04:37,740 --> 00:04:47,200
+دخول السكر للخلية للخلية الجسدية ينظم دخول السكر
+
+59
+00:04:47,200 --> 00:04:52,460
+للخلية الان ممكن يكون عنده الانسولين production
+
+60
+00:04:52,460 --> 00:04:56,420
+abnormal جليل
+
+61
+00:04:56,420 --> 00:05:01,780
+كتير او مافيش فمين ينظم دخول السكر للخلية؟يبقى
+
+62
+00:05:01,780 --> 00:05:06,200
+السكر وين بيضل؟ بيضل في الدم فاهمين عليه كيف؟ يعني
+
+63
+00:05:06,200 --> 00:05:12,740
+وكأنه الخلية غرفة ويلها باب وفي مفتاح المفتاح عشان
+
+64
+00:05:12,740 --> 00:05:16,860
+يدخل السكر الغرفة هو الـ Insulin طب وإذا المفتاح
+
+65
+00:05:16,860 --> 00:05:20,280
+ضاع ومافيش مفتاح كيف بدي يدخل الغرفة السكر؟ مش
+
+66
+00:05:20,280 --> 00:05:24,000
+هيدخل الغرفة، هيضل وين؟ هيضل برا، وين برا؟ في
+
+67
+00:05:24,000 --> 00:05:27,540
+الشراين يعني وعشان هيك لما نعمل فحص السكر بيقول لك
+
+68
+00:05:27,540 --> 00:05:35,180
+السكر عالي لأنه الجسم ماأخدشما أخدش السكر الحاجة
+
+69
+00:05:35,180 --> 00:05:38,320
+التانية اللي ممكن تحصل الـ Impaired احنا بنحكي عن
+
+70
+00:05:38,320 --> 00:05:41,820
+Abnormal Insulin Production أو Impaired Insulin
+
+71
+00:05:41,820 --> 00:05:48,600
+Utilization يعني عملية إنه كيف يدبر نفسه السكر مع
+
+72
+00:05:48,600 --> 00:05:51,920
+الخلية في فشل أو التنين أو الموضوعين الموجودين
+
+73
+00:05:51,920 --> 00:05:56,240
+يعني نقص في السكر وإنه مش قادر يدخل نتيجة مشكلة
+
+74
+00:05:56,240 --> 00:05:59,020
+الـ Receptor مثلا على سبيل المثال هنحكي عن الموضوع
+
+75
+00:05:59,020 --> 00:06:05,560
+يا جماعة موضوع السكرما هواش بس إنه والله فلان دمه
+
+76
+00:06:05,560 --> 00:06:11,000
+حلو وخفيف وعنده سكر، لأ، لأ، لأ المشكلة إن هو
+
+77
+00:06:11,000 --> 00:06:14,700
+الـleading cause of heart disease اتصوروا إنه
+
+78
+00:06:14,700 --> 00:06:18,500
+مشاكل الجلب، تلاحظين الآن واحنا بنحكي blood
+
+79
+00:06:18,500 --> 00:06:20,840
+pressure ال hypertension المرة اللي فاتت، المرة
+
+80
+00:06:20,840 --> 00:06:24,060
+اللي هي السكر وبنربطها في heart disease وبنربطها
+
+81
+00:06:24,060 --> 00:06:30,080
+في ال stroke، حتى الضغط ربطنا بال strokeالآن
+
+82
+00:06:30,080 --> 00:06:33,380
+بدخلني على الـ Adult Blindness العمى تبع الناس
+
+83
+00:06:33,380 --> 00:06:36,860
+الكبار، من أيش انعمى؟ كان زمان العمى يصير نتيجة
+
+84
+00:06:36,860 --> 00:06:40,760
+التهابات وكذا، الآن لأ، نتيجة سكري، ليش؟ لأنه
+
+85
+00:06:40,760 --> 00:06:44,300
+بيصير عندنا Retinal Detachment، هذا شفناه وين؟ قبل
+
+86
+00:06:44,300 --> 00:06:46,980
+أكمل المحاضرة اللي فات أو اللي قبلها، برضه في
+
+87
+00:06:46,980 --> 00:06:51,360
+الضغط، وفيه كمان حاجة جديدة، Non-traumaticLower
+
+88
+00:06:51,360 --> 00:06:55,500
+limb amputation طول عمرنا بنسمع و الله مسيرات
+
+89
+00:06:55,500 --> 00:06:58,940
+العودة جسوله رجله، لأ، الآن احنا بنقول انه non
+
+90
+00:06:58,940 --> 00:07:02,440
+-traumatic، لا حادث سيارة، ولا مسيرات عودة، ولا
+
+91
+00:07:02,440 --> 00:07:07,040
+وجع من فوق و انقطعت رجله، ولا حاجة، لأ، هذه نتيجة
+
+92
+00:07:07,040 --> 00:07:10,540
+لما لاجد راجل كبير انقطعت جديد رجله، بقول هذا في
+
+93
+00:07:10,540 --> 00:07:13,840
+الغالب في الغالب يبدو ان عندك سكر، بيبقى عنده سكر
+
+94
+00:07:14,650 --> 00:07:18,790
+إذا السُكر طب يعني هو كل الدنيا كل واحد عنده سُكر
+
+95
+00:07:18,790 --> 00:07:22,090
+يبتعالج هو المفروض إنه يتعالج لأنه if left
+
+96
+00:07:22,090 --> 00:07:25,710
+untreated إذا انتركت، diabetes can cause many
+
+97
+00:07:25,710 --> 00:07:28,790
+complicationsالآن طبعًا أنا يا جماعة قاعد بحكي
+
+98
+00:07:28,790 --> 00:07:33,090
+عموميات، هدخل على الخصوصيات بعد شوية من الـ Acute
+
+99
+00:07:33,090 --> 00:07:35,530
+Complication هذه الـ Chronic Complication اللي
+
+100
+00:07:35,530 --> 00:07:38,090
+حكيناها قبل شوية اللي هو الـ Heart Disease و الـ
+
+101
+00:07:38,090 --> 00:07:40,210
+Stroke و الـ Blindness و الـ Non-Traumatic Lower
+
+102
+00:07:40,210 --> 00:07:45,590
+Limb Amputation وهذه كلها Complication طويلة
+
+103
+00:07:45,590 --> 00:07:48,890
+الأمد، لكن فيه Complications قصيرة الأمد، بيقول
+
+104
+00:07:48,890 --> 00:07:52,290
+عنها Acute Complicationيعني انا اذا سكر صار 500
+
+105
+00:07:52,290 --> 00:07:56,750
+ولا 600 بدخل في حاجة اسمها diabetic ketoacidosis
+
+106
+00:07:56,750 --> 00:08:02,330
+بيصير عنده حموضة في الدم نتيجة ارتفاع كمية السكر
+
+107
+00:08:02,330 --> 00:08:05,590
+أو بيقول أنا DKA كمية السكر في الدم، هنحكي عنها
+
+108
+00:08:05,590 --> 00:08:09,310
+بعد شوية، بس خلوها في بالكم acute complication
+
+109
+00:08:09,310 --> 00:08:14,350
+diabetic ketoacidosisالـ Serious Long Term
+
+110
+00:08:14,350 --> 00:08:16,970
+Complications تحدثنا عنها قبل شويه مشاكل الـ
+
+111
+00:08:16,970 --> 00:08:22,110
+cardiovascular stroke chronic kidney failure foot
+
+112
+00:08:22,110 --> 00:08:28,130
+ulcer damage to the eyesالوضع الطبيعي إنه أنا باجي
+
+113
+00:08:28,130 --> 00:08:32,170
+بفطر وبتغدى وبتعشى breakfast lunch and dinner في
+
+114
+00:08:32,170 --> 00:08:35,250
+الفترة هذه بيطلع الانسولين بيزيد الانسولين في الدم
+
+115
+00:08:35,250 --> 00:08:39,210
+ليش؟ عشان الأكل اللي أكلته اللي قاعد بنهضم احنا
+
+116
+00:08:39,210 --> 00:08:43,090
+عارفين يا جماعة أنه أي أكل أنا باكله بتكون من تلت
+
+117
+00:08:43,090 --> 00:08:50,330
+أنواع من الأكل ال carbohydrate والبروتينات
+
+118
+00:08:50,330 --> 00:08:57,660
+والدهنياتالدهنيات تتحول لـ Fatty Acids البروتينات
+
+119
+00:08:57,660 --> 00:09:02,120
+تتحول لـ Amino Acids لكن الـ Carbohydrate تتحول
+
+120
+00:09:02,120 --> 00:09:12,970
+لإيش؟ لسكر لجلوكوز الجلوكوز هذا الآن بدهمفاتيح
+
+121
+00:09:12,970 --> 00:09:16,510
+تدخلوا على الخلايا بعد ما اتحلل الأكل للآخر في
+
+122
+00:09:16,510 --> 00:09:20,390
+الجهاز الهضمى تم امتصاصه في الدم الدم بتودي للـ
+
+123
+00:09:20,390 --> 00:09:26,130
+cells الآن بدوا مفاتيح مين المفاتيح الانسولين
+
+124
+00:09:26,130 --> 00:09:30,750
+بيسير بطريقة أو باخره بيطلع الانسولين في الجسم و
+
+125
+00:09:30,750 --> 00:09:37,500
+بفتح الخلايا عشانالسكر يدخل أو الجلوكوز يدخل على
+
+126
+00:09:37,500 --> 00:09:41,580
+الخلايا، لو مافيش انسولين بيضل السكر وين؟ مرة
+
+127
+00:09:41,580 --> 00:09:45,820
+تانية بيضل في الشرايين، يبقى في عندي انا
+
+128
+00:09:45,820 --> 00:09:51,700
+breakfast، lunch، dinner وهذه بيصير فيها ازيادة او
+
+129
+00:09:51,700 --> 00:09:58,680
+افراز لهرمون الانسولين واللي بيحاول يحافظلي على
+
+130
+00:09:58,680 --> 00:10:05,700
+كمياتعلى مستوى سكر طبيعي في الدم يتراوح بين تلاتة
+
+131
+00:10:05,700 --> 00:10:10,400
+وتسعة من عشرة لستة وسبعة من عشرة ميلي مول في
+
+132
+00:10:10,400 --> 00:10:14,960
+الليتر ايه الشاي ميلي مول طول عمرنا بنقول والله
+
+133
+00:10:14,960 --> 00:10:23,970
+فلان السكر تبعه مية تسعين تمانين105 سكر طبيعي يطلع
+
+134
+00:10:23,970 --> 00:10:29,310
+من وين بـ 3.9 و 6.7 ملي مول بالليتر هذه الحسبة
+
+135
+00:10:29,310 --> 00:10:33,630
+الأمريكية في الحسبة التي تبعتنا فيها طريقة للحسبة
+
+136
+00:10:33,630 --> 00:10:39,810
+كيفية تحويل الملي مول بالليتر لملي جرام
+
+137
+00:10:39,810 --> 00:10:44,030
+بالديتسليتر اللي احنا بنحسب فيها نضربها في 17 مش
+
+138
+00:10:44,030 --> 00:10:48,950
+حتى اعبكوا كتير نضربها في 17 بيطلع الحسبة تبعتنا
+
+139
+00:10:52,350 --> 00:10:59,390
+الـ Normal Insulin Metabolism يدخل
+
+140
+00:10:59,390 --> 00:11:04,970
+للجلوكوز يسهّل للجلوكوز يتبع من مصادر الدم من خلال
+
+141
+00:11:04,970 --> 00:11:08,710
+مصادر الجلوكز إلى مصادر الجلوكز من خلال مصادر
+
+142
+00:11:08,710 --> 00:11:09,390
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+143
+00:11:09,390 --> 00:11:13,390
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+144
+00:11:13,390 --> 00:11:16,370
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+145
+00:11:16,370 --> 00:11:16,470
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+146
+00:11:16,470 --> 00:11:16,710
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+147
+00:11:16,710 --> 00:11:18,600
+الجلوكز من خلال مصادر الجلوكز من خلالآن بعد ما
+
+148
+00:11:18,600 --> 00:11:22,160
+أكل، بزيد الإنسولين، إيش بيعمل الإنسولين؟ شغلته
+
+149
+00:11:22,160 --> 00:11:27,660
+الطبيعية، stimulate storage of glucose as glycogen
+
+150
+00:11:27,660 --> 00:11:33,900
+طبعاً الخلية بتستهلك ما تحتاج، قولي بزيد، بتروح،
+
+151
+00:11:33,900 --> 00:11:40,520
+بتخزنه في الكبد، جا ك glycogen، هذا شغلته يعني
+
+152
+00:11:40,520 --> 00:11:45,790
+يعني العكس تمام لو مافيش إنسولينإيش بيعمل كمان؟
+
+153
+00:11:45,790 --> 00:11:50,510
+Inhibits glyconeogenesis إيش يعني glyconeogenesis؟
+
+154
+00:11:50,510 --> 00:11:57,410
+glyconeogenesis هو عبارة عن تحويل لبروتين لسكر هو
+
+155
+00:11:57,410 --> 00:12:01,130
+بيوقف الموضوع هذا لإن عندنا سكر كفاية فهو بيوقفها
+
+156
+00:12:01,130 --> 00:12:07,110
+الأمر التاني بيزيد fat deposition in a deposed
+
+157
+00:12:07,110 --> 00:12:13,110
+tissueبزيد لي اللي هي تخزين الدهنيات في مناطق
+
+158
+00:12:13,110 --> 00:12:17,210
+الدهنية هذا شغل الإنسولين increase protein
+
+159
+00:12:17,210 --> 00:12:21,870
+synthesis اللي بيزيد يعني هو من الشغلات تبعته أنه
+
+160
+00:12:21,870 --> 00:12:30,370
+بيبني لبروتين طيب هو أنا كيف بدي أعرف أن فلان عنده
+
+161
+00:12:30,370 --> 00:12:35,690
+سكري؟ كيف بدي أعرف؟في حاجات نعرفها في اللسان تبعنا
+
+162
+00:12:35,690 --> 00:12:41,450
+اللسان العادى كثير من الناس بتيجي شايفة زميلتك او
+
+163
+00:12:41,450 --> 00:12:48,430
+صاحبتك او اي حد بتعرفيه او بتعرفه شفته قبل فترة و
+
+164
+00:12:48,430 --> 00:12:51,830
+اليوم شفته ايه ما الوزنك نازل هيك مرة واحدة ايش
+
+165
+00:12:51,830 --> 00:12:57,370
+اول حاجة بتفكر فيها على طول اه ايوة احكوا ايش لأ
+
+166
+00:12:57,370 --> 00:13:02,390
+غلط مش ديابتسأي واحد بشوفه نازل وزنه بطريقة
+
+167
+00:13:02,390 --> 00:13:06,490
+unexpected وانا مش عارف من إيش بفكر بالوضع الطبيعي
+
+168
+00:13:06,490 --> 00:13:09,690
+يا جماعة common is common فاكروش بعيد فاكروش حتى
+
+169
+00:13:09,690 --> 00:13:16,610
+في السكري في إيش بدنا نفكر؟ في إيش بدنا نفكر؟
+
+170
+00:13:16,610 --> 00:13:20,190
+أتبرونا وكأنه الآن تعليم وجاهي حاولوا تجاوبوني صوت
+
+171
+00:13:20,190 --> 00:13:28,260
+عالي علوا أه أيوة لأ مش صحلأ مش صح ايوة صح احتمال
+
+172
+00:13:28,260 --> 00:13:34,480
+بروح الجيم و بعمل diet اه عشان هيك نزل وزنه في
+
+173
+00:13:34,480 --> 00:13:41,040
+أسباب تانية اه للـ Unexpected وبسرعة
+
+174
+00:13:41,040 --> 00:13:46,080
+ينزل وزن لازم افكر في الـ Diabetes إلى جانب الجيم
+
+175
+00:13:46,080 --> 00:13:49,050
+و الحاجات التاليةلازم أفكر في مشاكل في الـ Thyroid
+
+176
+00:13:49,050 --> 00:13:53,610
+لازم أفكر في مشاكل في Cancer على سبيل المثال لازم
+
+177
+00:13:53,610 --> 00:13:57,690
+أفكر في مشاكل Tuberculosis إيش يعني Tuberculosis؟
+
+178
+00:13:57,690 --> 00:14:01,190
+Cell، مرض الـ Cell آه، مجموعة كبيرة من الأمراض
+
+179
+00:14:01,190 --> 00:14:04,990
+بتنزلي وزن البني آدم بدون ما يكون جاصد، unexpected
+
+180
+00:14:04,990 --> 00:14:09,650
+لكن إحنا هنا في إطار الـ Diabetes Mellitus من أهم
+
+181
+00:14:09,650 --> 00:14:12,590
+الحاجات اللي بنلاقيها الـ Classic Symptoms اللي
+
+182
+00:14:12,590 --> 00:14:19,550
+بنقول عنها is Weight Lossفقدان الوزن و ايش كمان
+
+183
+00:14:19,550 --> 00:14:25,290
+التلاتة P ايش التلاتة P هاي اول P و تاني P و تالت
+
+184
+00:14:25,290 --> 00:14:31,030
+P ال polyuria ايش يعني polyuria يعني urine كتير
+
+185
+00:14:31,030 --> 00:14:36,690
+increase urination كل شويه رايح جاي على حمام طب هو
+
+186
+00:14:36,690 --> 00:14:39,750
+كل واحد بشوفه رايح جاي على حمام اول حاجة بفكر فيها
+
+187
+00:14:39,750 --> 00:14:49,180
+سكري لأ هإيش اتهابات البولحسب إذا أنا بحكي عن راجل
+
+188
+00:14:49,180 --> 00:14:55,940
+كبير بفكر كمان فيه بروستاتا نتفرع
+
+189
+00:14:55,940 --> 00:15:00,480
+بس هيك أنا أفكار أنا قلتلكوا موضوع الباطنةالموضوع
+
+190
+00:15:00,480 --> 00:15:05,100
+ممتع، مش قضية إنه بس علم، مش بس بس بدي أحفظ منهج،
+
+191
+00:15:05,100 --> 00:15:09,980
+الموضوع مش موضوع منهج، الموضوع موضوع علم، موضوع
+
+192
+00:15:09,980 --> 00:15:14,180
+أعرف في الطب، مضلش restricted على حركات العلاج
+
+193
+00:15:14,180 --> 00:15:17,280
+الطبيعي والعضلات وكذا، لأ، أنا بدي أعرف البني آدم
+
+194
+00:15:17,280 --> 00:15:22,220
+أكتر من جهازه الحركي، بدي أعرف البني آدم أجزاءه من
+
+195
+00:15:22,220 --> 00:15:22,980
+جوا كمان
+
+196
+00:15:27,740 --> 00:15:31,300
+وأفهم في الأمراض هذه لأن كلها هيك هيك لها
+
+197
+00:15:31,300 --> 00:15:36,560
+relationship to my subject كعلاج طبيعي إيش كمان ال
+
+198
+00:15:36,560 --> 00:15:39,160
+P التاني بولي ديبسيا إيش يعني بولي ديبسيا
+
+199
+00:15:39,160 --> 00:15:44,920
+increased thirst بشرب كتير دائما عتشان وإيش كمان
+
+200
+00:15:44,920 --> 00:15:51,780
+بوليفاجيا بياكل كتير increased hungerهناك حاجات
+
+201
+00:15:51,780 --> 00:15:55,000
+تانية يا جماعة بس هي هذه الأساسيات Weight Loss،
+
+202
+00:15:55,000 --> 00:15:58,080
+Polyuria، Polydipsia و Polyphasia زي إيش عندنا
+
+203
+00:15:58,080 --> 00:16:00,980
+حاجات بيصير يشوف blurry vision، إيش يعني blurry
+
+204
+00:16:00,980 --> 00:16:06,080
+vision؟ blurry vision يعني مش بيشوف وهتز الصورة،
+
+205
+00:16:06,080 --> 00:16:11,670
+double visionهدق باجع راس فتيق دايما تعبان slow
+
+206
+00:16:11,670 --> 00:16:16,030
+healing of cuts الجروح عنده بتطول لما بتطيب ايش
+
+207
+00:16:16,030 --> 00:16:19,490
+كمان itchy skin vision changes ليش ال vision بيصير
+
+208
+00:16:19,490 --> 00:16:23,300
+في مشاكل اكتر من حاجة ممكن يكون نتيجةاللي هو
+
+209
+00:16:23,300 --> 00:16:25,700
+المشاكل اللي بتصير في الـ Retina لكن ممكن تكون
+
+210
+00:16:25,700 --> 00:16:29,620
+نتيجة الـ Hyperglycemia بتعمل ليه؟ Can cause
+
+211
+00:16:29,620 --> 00:16:33,120
+glucose absorption in the lens في العدسات وهذه
+
+212
+00:16:33,120 --> 00:16:37,060
+بتؤدي لـ Changes in its shape resulting in vision
+
+213
+00:16:37,060 --> 00:16:42,240
+changes يعني تأثيرها على عدسات العين كمان مرة الـ
+
+214
+00:16:42,240 --> 00:16:48,020
+Symptoms باللسان العادي اللسان الناس العادية
+
+215
+00:16:48,020 --> 00:16:53,920
+دايماً tiredرايح جاي على الحمام بنزل وزن وصدن
+
+216
+00:16:53,920 --> 00:16:59,980
+wound that once healed فيه طبعا sexual problems
+
+217
+00:16:59,980 --> 00:17:07,540
+بتصير بالذات من جهة الراجل always hungry دايما
+
+218
+00:17:07,540 --> 00:17:15,480
+جعان blurry vision numbness خدلان و .. و .. و .. و
+
+219
+00:17:15,480 --> 00:17:15,740
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+220
+00:17:15,740 --> 00:17:16,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+221
+00:17:16,060 --> 00:17:16,900
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+222
+00:17:16,900 --> 00:17:17,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+223
+00:17:17,060 --> 00:17:17,180
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+224
+00:17:17,180 --> 00:17:17,540
+.. و .. و .. و .. و .. و .. و .. و .. و ..
+
+225
+00:17:23,310 --> 00:17:28,590
+اللي هي في اللسان العادى ال symptoms اللي بنلاقيها
+
+226
+00:17:28,590 --> 00:17:31,730
+مش لازم كلها تكون موجودة يا جماعة بعضها موجودة أو
+
+227
+00:17:31,730 --> 00:17:34,250
+واحدة منهم موجودة لازم أفكر في ال diabetes
+
+228
+00:17:37,690 --> 00:17:40,730
+اللي فيها إنها طبعاً للـDiabetes Emergencies مش
+
+229
+00:17:40,730 --> 00:17:44,550
+هحكي عنها الآن، ذكروني فيها بس، هحكي معها بعد هيك،
+
+230
+00:17:44,550 --> 00:17:46,830
+في الآخر لما أحكي عن الـDKA، هحكي عن
+
+231
+00:17:46,830 --> 00:17:50,750
+الـHypoglycemia فبدأ أروح على الـClassification of
+
+232
+00:17:50,750 --> 00:17:55,470
+Diabetes حقيقة إنه في أكتر من الـClassification،
+
+233
+00:17:55,470 --> 00:17:59,360
+لكن إحنا اللي اعتمدناهاDiabetes mellitus عنده
+
+234
+00:17:59,360 --> 00:18:04,600
+أربعة broad categories اللي هو diabetes type 1 و
+
+235
+00:18:04,600 --> 00:18:09,900
+type 2 و في gestational diabetes اللي مرتبط بالحمل
+
+236
+00:18:09,900 --> 00:18:16,580
+أو سكر الحمل و في specific types يعني عدد منها
+
+237
+00:18:16,580 --> 00:18:20,900
+هنتحدث عنها في حينها مش كلها لكن هذكر بعضها حسب
+
+238
+00:18:20,900 --> 00:18:26,200
+الواجهة اللي معناها طيب إيش الفرق بين type 1 و
+
+239
+00:18:26,200 --> 00:18:36,900
+type 2؟ومن أكتر بيجي الـ
+
+240
+00:18:36,900 --> 00:18:40,760
+Type يعني الآن أنا هدي هحكي بعد شوية إيش الـ Type
+
+241
+00:18:40,760 --> 00:18:43,640
+I و Type II لكن خدوا بالكوا من ال curve اللي موجود
+
+242
+00:18:43,640 --> 00:18:51,110
+الدائرة هاي إنه الأحمر هو Type IIوهو غالبية يعني
+
+243
+00:18:51,110 --> 00:18:53,750
+هنا في أمريكا على سبيل المثال وقولنا أحنا مرة مرة
+
+244
+00:18:53,750 --> 00:18:56,570
+تانية يا جماعة عشان ما تاخدوش .. ما أخدلش ده
+
+245
+00:18:56,570 --> 00:18:58,930
+مابجيب إحصائيات هم الأمريكان عندهم إحصائيات باقى
+
+246
+00:18:58,930 --> 00:19:03,090
+الدول معظمها ماعندهاش إحصائيات عشان هيك بنعتمد
+
+247
+00:19:03,090 --> 00:19:11,370
+الإحصائيات المنشورة طبعة أمريكا في أمريكا في سنة
+
+248
+00:19:11,370 --> 00:19:16,890
+من السنوات سنة الألفين من قد النظر عن الأرقام لكن
+
+249
+00:19:17,340 --> 00:19:23,260
+كان عدد سكان أمريكا حدود 300 مليون يعني وانتوا
+
+250
+00:19:23,260 --> 00:19:27,940
+بتحسبوا احسبوا 300 مليون عدد الناس اللي الـ type 2
+
+251
+00:19:27,940 --> 00:19:33,600
+كان عشرة مليون واحد عنده سكري type 2 type 1 لأ نص
+
+252
+00:19:33,600 --> 00:19:39,600
+مليون لمليون أجل يعني تقريبا أجل أجل وفيه طبعا
+
+253
+00:19:39,600 --> 00:19:44,260
+نسبة كبيرة شايفين الأخضر هذا الرقم الأسئ هذا الرقم
+
+254
+00:19:45,200 --> 00:19:49,020
+خمسة مليون عندهم سكري بس مش مشخصين لا هم رايحين
+
+255
+00:19:49,020 --> 00:19:52,460
+على الدكاترة ولا الدكاترة باكتشفينهم و هم هذا
+
+256
+00:19:52,460 --> 00:19:56,220
+الرقم أسود يعني أنا بحكي عاقعد عن ستة عشر مليون أو
+
+257
+00:19:56,220 --> 00:20:01,020
+سبعتاشر مليون أمريكي في سنة الألفين كان عندهم سكري
+
+258
+00:20:01,020 --> 00:20:07,000
+type 2 هو الماسكون خمسة وتسعين في المية من السكري
+
+259
+00:20:07,000 --> 00:20:11,020
+اللي موجود خمسة وتسعين type 2 طب واش الفرق بين
+
+260
+00:20:11,020 --> 00:20:15,740
+type 1 وtype 2؟هو فيه فروق كبيرة بينهم type one
+
+261
+00:20:15,740 --> 00:20:19,360
+مافيش
+
+262
+00:20:19,360 --> 00:20:21,900
+insulin بالمرة بالمناسبة الإنسولين هو من وين بيجي؟
+
+263
+00:20:21,900 --> 00:20:27,100
+من وين بيطلع؟ الغدا النخامية في الدماغ بيجي؟ ولا
+
+264
+00:20:27,100 --> 00:20:31,600
+من خلايا Beta تاعة الـ Langerhans Islet Cells
+
+265
+00:20:31,600 --> 00:20:37,040
+الموجودة في البنكرياز؟ ولا من وين بيطلع؟ آه من الـ
+
+266
+00:20:37,040 --> 00:20:42,320
+Islet Cellsاللي هو الـ Langerhans جزر Langerhans
+
+267
+00:20:42,320 --> 00:20:47,460
+في البنكرياز من خلايا Beta بيطلع الان هذي لو
+
+268
+00:20:47,460 --> 00:20:53,720
+اتدمرت المصنع هذا لو اتدمر مش هيطلع انسولين طب هو
+
+269
+00:20:53,720 --> 00:20:58,080
+أيش بدي دمره؟ أه في عنا أكتر من سبب لتدبيره ممكن
+
+270
+00:20:58,080 --> 00:21:03,920
+يكون autoimmune بمعنى دمر نفسه بنفسه أو يكون نتيجة
+
+271
+00:21:03,920 --> 00:21:09,670
+التهيابات المهمإنها بتطلعش Insulin No Insulin هذا
+
+272
+00:21:09,670 --> 00:21:14,130
+الـ Type I في الـ Islet Cells فإذا مافيش Insulin
+
+273
+00:21:14,130 --> 00:21:18,070
+يبقى على الدنيا السلام يبقى مافيش مفاتيح للغرف
+
+274
+00:21:18,070 --> 00:21:23,230
+يبقى السكر هيظل برا والخلايا مش هيروحلها سكر طيب
+
+275
+00:21:23,230 --> 00:21:27,150
+وبدأ تعيش بدون سكر ماهي المشكلة هو ليش بيصير عندنا
+
+276
+00:21:27,150 --> 00:21:30,590
+كل ال symptoms طب و ال diabetes type 2 إيش اللي
+
+277
+00:21:30,590 --> 00:21:40,330
+بيصير؟ هو في Insulinلكن المفتاح ماتجيع الجفل أو
+
+278
+00:21:40,330 --> 00:21:46,250
+بتحط المفتاح في الباب وبتحاول تفتح بعصلج الباب
+
+279
+00:21:46,250 --> 00:21:51,450
+برضهاش يفتح بنقول عنه Insulin Resistance Insulin
+
+280
+00:21:51,450 --> 00:21:58,070
+Resistance في عدم قدرة لدخول السكر إلى داخل الخلية
+
+281
+00:21:58,070 --> 00:22:05,420
+نتيجة إنه Insulin Resistanceالـ Gestational هو تبع
+
+282
+00:22:05,420 --> 00:22:09,640
+الحمل مثل الـ Type 2 تقريباً بس هو بيجي .. هنحكي
+
+283
+00:22:09,640 --> 00:22:13,500
+عنه بيجي في فترة الحمل .. فترات معينة في الحمل
+
+284
+00:22:24,370 --> 00:22:32,610
+النقص حقيقي أو نقص عدم وجود إنسولين حقيقي موجود في
+
+285
+00:22:32,610 --> 00:22:32,930
+الجسم
+
+286
+00:22:38,370 --> 00:22:40,450
+وهذا بنقول عنه Relatively، يعني أنا في عندى
+
+287
+00:22:40,450 --> 00:22:44,290
+Insulin لكن مش قادر يشتغل الشغل اللي بدناياه وهذا
+
+288
+00:22:44,290 --> 00:22:50,610
+بيقدّي لبعد فترة، نتيجة إنه ال Insulin بحاول يفتح،
+
+289
+00:22:50,610 --> 00:22:56,670
+بيرضاش، بيدّي إشارة للجسم،
+
+290
+00:22:56,670 --> 00:23:00,830
+نتيجة زيادة السُكّة، إشارة للبنكرياس، افرز أكتر،
+
+291
+00:23:00,830 --> 00:23:05,480
+بيظل يفرز أكتر البنكرياسونتيجة الإفراز الأكتر الـ
+
+292
+00:23:05,480 --> 00:23:09,140
+beta cells برضه في الآخر بتضعف وبتقولك خلاص أنا
+
+293
+00:23:09,140 --> 00:23:12,420
+أطلعت كل الانسولين اللي عندي فبيصير عندي انسولين
+
+294
+00:23:12,420 --> 00:23:17,460
+beta cells failure وطبعاً في عندنا ال gestational
+
+295
+00:23:17,460 --> 00:23:25,870
+diabetes اللي هو عبارة عن subtype لtype 2الـType-2
+
+296
+00:23:25,870 --> 00:23:28,790
+هي الـSecondary Form لـType-2 اللي قلنا بنقول عنها
+
+297
+00:23:28,790 --> 00:23:34,510
+بعد شوية الـModi وExocrine Pancreas Disease
+
+298
+00:23:34,510 --> 00:23:38,310
+والـSteroids هذه عبارة عن حاجات بتعمل زي Type-2،
+
+299
+00:23:38,310 --> 00:23:41,730
+هنحكي عنها بعد شوية طيب، ندخل الآن على تفاصيل
+
+300
+00:23:41,730 --> 00:23:46,470
+الـType-1، أيه أسماء تانية الـType-1؟بنقوله
+
+301
+00:23:46,470 --> 00:23:50,130
+juvenile onset or insulin dependent diabetes
+
+302
+00:23:50,130 --> 00:23:56,110
+جوفينايل لأنه لاحظوا أنه الغالبية خدوا باركم كلمة
+
+303
+00:23:56,110 --> 00:24:03,550
+الغالبية بتصير عند الأطفال مفهوم
+
+304
+00:24:03,550 --> 00:24:07,150
+باركم تقول الغالبية لكن مش مية في المية عند
+
+305
+00:24:07,150 --> 00:24:11,770
+الأطفال ممكن type one يجي عند ناس غير الأطفال عشان
+
+306
+00:24:11,770 --> 00:24:17,010
+هيك قالوا زمان juvenileفيه اسم تاني Insulin
+
+307
+00:24:17,010 --> 00:24:24,030
+Dependent لأن علاجه لا يتم الا بالانسولين بدون هيك
+
+308
+00:24:24,030 --> 00:24:27,530
+يبقى ممنفعش الانسولين type one يا جماعة عفوا ان ال
+
+309
+00:24:27,530 --> 00:24:31,890
+diabetes type one لا يعالج الا بالانسولين الابار
+
+310
+00:24:31,890 --> 00:24:34,930
+ماينفعش يعالجه بحبوب عشان هيك جاله dependent
+
+311
+00:24:34,930 --> 00:24:40,210
+dependent يعني أنك متعلق بيهوهذا بيجي عند الناس
+
+312
+00:24:40,210 --> 00:24:43,170
+الأقل من تلاتين سنة عشان هيك ربطه بالأطفال كانت مش
+
+313
+00:24:43,170 --> 00:24:48,890
+صح لأنه هيوا بيصير لحتى تلاتين سنة يعني جوفينية
+
+314
+00:24:50,330 --> 00:24:54,470
+لكن العمر المشهور لإله اللي بيبين فيه سكري بين 11
+
+315
+00:24:54,470 --> 00:25:00,730
+و 13 سنة و بيصير عندنا طب ليش؟ طب ما هيوا تسع عشر
+
+316
+00:25:00,730 --> 00:25:05,110
+سنين مسلك؟ آه، مسلك و ماعندوش سكر الطفل، شو يعني
+
+317
+00:25:05,110 --> 00:25:07,670
+أنا الآن اتدمر؟ بمجرد صراحة عندي progressive
+
+318
+00:25:07,670 --> 00:25:12,410
+destruction للـBeta cells؟لحد ما وصل مرحلة على عمر
+
+319
+00:25:12,410 --> 00:25:16,990
+11، 12، 13، 14، ماعرفش وابتش لحد ما اتدمرت كامل
+
+320
+00:25:16,990 --> 00:25:22,550
+الخلايا وصار عندنا الـ Destruction للـ Pancreatic
+
+321
+00:25:22,550 --> 00:25:26,480
+Beta Cellsوهذه زي ما قلنا في الغالب Auto
+
+322
+00:25:26,480 --> 00:25:31,380
+Antibodies عبارة عن نيران صديقة هي بتعملي
+
+323
+00:25:31,380 --> 00:25:34,740
+reduction لـ8 لـ90% of normal beta cells function
+
+324
+00:25:34,740 --> 00:25:37,740
+قبل manifestation it occurs يعني يوم بصير عندي
+
+325
+00:25:37,740 --> 00:25:41,700
+manifestation ببجي عارف أنه على ال beta cells اللي
+
+326
+00:25:41,700 --> 00:25:47,320
+بتفرز الإنسلين السلامالأسباب لحد الآن تتفسر
+
+327
+00:25:47,320 --> 00:25:51,860
+بـGenetic Predisposition وفي قال لك لأ ممكن يكون
+
+328
+00:25:51,860 --> 00:25:57,280
+نتيجة Exposure to a virus الـ Onset مش مختلف كتير
+
+329
+00:25:57,280 --> 00:26:01,940
+الـ Symptoms في الـ Type 1 Manifestation developed
+
+330
+00:26:01,940 --> 00:26:05,380
+when the pancreas can no longer produce insulin
+
+331
+00:26:05,380 --> 00:26:10,120
+Rapid onset of symptoms presentفي الغالب في الغالب
+
+332
+00:26:10,120 --> 00:26:14,340
+هدولة أول ما بيبين عنده بيبين بالصورة الصعبة يعني
+
+333
+00:26:14,340 --> 00:26:18,200
+بيجيني الطفل بحاجة اسمها diabetic ketoacidosis
+
+334
+00:26:18,200 --> 00:26:25,050
+يعني عمليا أو بندوسيروعمليا في حالة صعبة بيجيونا
+
+335
+00:26:25,050 --> 00:26:28,430
+الأطفال في العادة زي ما بيجيونا في الديابتس 1 ليش؟
+
+336
+00:26:28,430 --> 00:26:33,610
+لأنه مرة واحدة بينتقل من سكر معجول لـ Ketoacidos
+
+337
+00:26:33,610 --> 00:26:38,690
+حموضة في الدم نتيجة ارتفاع حاد في السكر وطبعا هذا
+
+338
+00:26:38,690 --> 00:26:43,070
+بيأثرلي على باق الجسم ممكن يجيني بـ Weight Loss
+
+339
+00:26:43,070 --> 00:26:46,270
+وكمان مرة ممكن يجيني بـWeakness، Fatigue،
+
+340
+00:26:46,270 --> 00:26:49,950
+Polyphagia، Polydipsia و Polyuria
+
+341
+00:26:52,810 --> 00:26:57,530
+زي ما حكينا قبل شوية زي
+
+342
+00:26:57,530 --> 00:27:01,890
+ما حكينا قبل شوية is characterized by insulin
+
+343
+00:27:01,890 --> 00:27:06,350
+resistance which may be combined with relatively
+
+344
+00:27:06,350 --> 00:27:10,890
+reduced insulin secretion characterized by insulin
+
+345
+00:27:10,890 --> 00:27:15,910
+resistance أنه مش قادر الإنسلين يغزو هذه الغرفة
+
+346
+00:27:15,910 --> 00:27:20,940
+لسبب من الأسبابوهذا which may be combined with
+
+347
+00:27:20,940 --> 00:27:24,060
+relatively reduced insulin secretion بعد شويه
+
+348
+00:27:24,060 --> 00:27:26,600
+بتصير repeated cells مش قادرة تطلع انسلين ليش؟
+
+349
+00:27:26,600 --> 00:27:29,400
+لأنه طلعت كتير نتيجة أنه مش داخل الانسلين داخل
+
+350
+00:27:29,400 --> 00:27:36,340
+الخلايا فبقل كمية الانسلين The defective
+
+351
+00:27:36,340 --> 00:27:45,240
+responsiveness استجابة خلايا الجسمللإنسولين is
+
+352
+00:27:45,240 --> 00:27:49,200
+believed to involve the insulin receptors وقال إن
+
+353
+00:27:49,200 --> 00:27:54,380
+الـ Receptors هي السبب تبع الموضوع ديابتس ميليتاس
+
+354
+00:27:54,380 --> 00:27:58,200
+is the second .. is the most common type تسعين في
+
+355
+00:27:58,200 --> 00:28:01,100
+المية of patient تسعين أو خمسة أو تسعين في المية
+
+356
+00:28:01,100 --> 00:28:05,280
+usually تيجي بعد في الناس اللي usually وإيش معنى
+
+357
+00:28:05,280 --> 00:28:10,620
+usually مش always usually يعني غالبا occur in
+
+358
+00:28:10,620 --> 00:28:19,090
+people over 40الـ 98% of patients are overweight
+
+359
+00:28:19,090 --> 00:28:25,290
+لكن ممكن واحد مش overweight برضه يصير عنده type 2
+
+360
+00:28:25,290 --> 00:28:30,190
+لكن لاحظوا ان type 2 diabetes is due to primarily
+
+361
+00:28:30,190 --> 00:28:35,910
+two lifestyle factors and genetics احنا في لغتنا
+
+362
+00:28:35,910 --> 00:28:40,130
+بنقول عنه multifactorial ايش يعني multifactorial؟
+
+363
+00:28:40,540 --> 00:28:43,660
+يعني بتحكم فيه أكتر من حاجة هو ممكن يكون الواحد
+
+364
+00:28:43,660 --> 00:28:50,600
+genetic predisposition لكن الممارسة السيئة بتظهر
+
+365
+00:28:50,600 --> 00:28:55,860
+المرض ممكن كتير ناس تكون عندها حاجات لكن الممارسة
+
+366
+00:28:55,860 --> 00:29:02,820
+السيئة هي اللي اتبينهاللي من الحاجات اللي .. اللي
+
+367
+00:29:02,820 --> 00:29:05,460
+من ال .. اللي لها علاقة بالـ lifestyle مرة تانية،
+
+368
+00:29:05,460 --> 00:29:08,980
+هين بدينا نيجي للـ lifestyle وطريقة الحياة اللي مش
+
+369
+00:29:08,980 --> 00:29:12,520
+كويسة، مابديش أقولها الكلمة، اللي إحنا عايشينها هي
+
+370
+00:29:12,520 --> 00:29:15,060
+اللي عاملانا المشكلة، اللي هو الـ obesity
+
+371
+00:29:18,240 --> 00:29:21,300
+وكنا حكينا عن الـ Body Mass Index of Greater Than
+
+372
+00:29:21,300 --> 00:29:25,680
+30 لأن أنا لما أقول Body Mass Index أكتر من تلاتين
+
+373
+00:29:25,680 --> 00:29:29,480
+في الـ Obesity كلكم فاهمين لأن احنا في الـ
+
+374
+00:29:29,480 --> 00:29:35,780
+Assignment اللي فاتت شرحنا إيش الـ PMI وقلنا إيش
+
+375
+00:29:35,780 --> 00:29:40,020
+يعني PMI ال Body Mass Index وكيف نحسب وقلنا
+
+376
+00:29:40,020 --> 00:29:43,430
+الدرجات تبعته فاكرين ولا مش فاكرين؟ديروي بالكوا
+
+377
+00:29:43,430 --> 00:29:45,570
+أنا دايما بركز عليه الموضوع هذا الـ Body Mass
+
+378
+00:29:45,570 --> 00:29:48,650
+Index لأنه من الحاجات الأساسية اللي ما اتعلمناها
+
+379
+00:29:48,650 --> 00:29:52,250
+في المدارس لكن الآن it's time نكون عارفين إيش
+
+380
+00:29:52,250 --> 00:29:55,990
+الموضوع هذا اللي أقل من 30 اللي أكتر من 30 الـ
+
+381
+00:29:55,990 --> 00:29:59,730
+Body Mass Index تبعه opposite أو opposite هذا من
+
+382
+00:29:59,730 --> 00:30:04,210
+اللي هو ال factors اللي بتساعد أنه يكون عند الواحد
+
+383
+00:30:04,210 --> 00:30:08,110
+diabetes type 2 lack of physical activity يا سلام
+
+384
+00:30:08,110 --> 00:30:12,900
+نفس الكلام عن الضغط الجعدة وجلة الحركةالـ Poor
+
+385
+00:30:12,900 --> 00:30:20,140
+Diet، الطيح رايح، إيش بيجي، بيتاكل، شبسي كل يوم،
+
+386
+00:30:20,140 --> 00:30:24,120
+كوكاكولا كل يوم، جنان كبيرة و جنان صغيرة رايح جاي،
+
+387
+00:30:24,120 --> 00:30:28,540
+حاجات فيها بيتزا عالفاض و عالملان، ماكرونة عالفاض
+
+388
+00:30:28,540 --> 00:30:33,140
+و عالملان، حاجات فاضية، طيب كله سلطات؟ لأ، بدناش
+
+389
+00:30:33,140 --> 00:30:38,520
+سلطات، حاجة خضرة؟ لأ، بدناش حاجة خضرة، زيوت طبيعية
+
+390
+00:30:38,520 --> 00:30:41,540
+زي الزتون و حاجات؟ لأ، لازم يكون حاجات مهدرجة و
+
+391
+00:30:41,540 --> 00:30:49,890
+حاجاتيعني poor diet أكل مالوش لازم نهائي بالإضافة
+
+392
+00:30:49,890 --> 00:30:53,170
+للـ stress اللي احنا عايشين و لا فيه شغل ولا ولا
+
+393
+00:30:53,170 --> 00:30:57,610
+ولا ولا هذا أمر طبعاً هذه الأمور كلها لما تتجمع في
+
+394
+00:30:57,610 --> 00:31:02,270
+وجود الواحد يكون predisposition يعني هو مؤهل أمه و
+
+395
+00:31:02,270 --> 00:31:04,990
+أبوه و كل عيلته عندها سكري في الآخر هيصير عنده
+
+396
+00:31:04,990 --> 00:31:05,470
+سكري
+
+397
+00:31:08,780 --> 00:31:12,680
+من الـ .. زي ما قلنا الحاجات اللي بنشوفها في الـ
+
+398
+00:31:12,680 --> 00:31:17,900
+Dietary Factors المأكلات اللي بناكلها و اللي بتأهل
+
+399
+00:31:17,900 --> 00:31:21,380
+إنه يصير عند الواحد Type 2 Consumption of Sugar
+
+400
+00:31:21,380 --> 00:31:25,360
+-Sweetened Drinks In Excess، خدوا بالك In Excess،
+
+401
+00:31:25,360 --> 00:31:28,820
+إحنا مابنقولش ممنوع يا جماعة، خير الأمور الوسط،
+
+402
+00:31:28,820 --> 00:31:31,140
+طول عُرّى بنحكي خير الأمور الوسط، تمنعش حالك ولا
+
+403
+00:31:31,140 --> 00:31:35,840
+عن حاجة، لكن مش معقول كل يوم حلويات، مش معقول كل
+
+404
+00:31:35,840 --> 00:31:38,460
+يوم شوكولاتة، كل شوكولاتة حلوة، شوكولاتة منيحة
+
+405
+00:31:38,690 --> 00:31:43,530
+كويسة للمزاج وكويسة لـ .. كويسة ماشي بس مش كل يوم
+
+406
+00:31:43,530 --> 00:31:47,150
+لوح يعني شو هذا الموضوع؟ يا ريت شوكراتة من نوع
+
+407
+00:31:47,150 --> 00:31:51,010
+اللي كويس من نوع اللي تافه وهذا مشكلة consumption
+
+408
+00:31:51,010 --> 00:31:55,410
+of sugar-sweetened drinks in excess is associated
+
+409
+00:31:55,410 --> 00:32:00,370
+with increased risk type of fats نوع الدهنيات اللي
+
+410
+00:32:00,370 --> 00:32:04,990
+بنستخدمها اللي هي saturated fats and trans fatty
+
+411
+00:32:04,990 --> 00:32:11,010
+acids increasing the risk ofوانواع الـ unsaturated
+
+412
+00:32:11,010 --> 00:32:15,870
+وانواع الـ monounsaturated fat تقليز الخطر خدوا
+
+413
+00:32:15,870 --> 00:32:18,810
+بالك أنواع الـ fat وهذا الجزء التاني من الـ
+
+414
+00:32:18,810 --> 00:32:23,950
+assignment إيش أنواع الـ fat اللي هو saturated و
+
+415
+00:32:23,950 --> 00:32:27,890
+unsaturated و أنواع الـ unsaturated و الفرق بينهم
+
+416
+00:32:27,890 --> 00:32:37,050
+بدي جدول مقارنة بينهم saturated و unsaturated و ال
+
+417
+00:32:37,050 --> 00:32:42,440
+trans fatمش الفرق بينهم في جدول مش أكتر من جدول
+
+418
+00:32:42,440 --> 00:32:47,300
+وينكتب بالإيد ويتصور وينبعتليه لأن هذا غاية في
+
+419
+00:32:47,300 --> 00:32:51,080
+الأهمية وإما هنروح في القلب في ال lung في الباطنة
+
+420
+00:32:51,080 --> 00:32:58,240
+دايما هنتحدث عن أنواع ال fats eating lots of white
+
+421
+00:32:58,240 --> 00:33:04,660
+rice مقارنة ورز كتيرالـ Lack of Exercise ممكن في 7
+
+422
+00:33:04,660 --> 00:33:09,840
+% من الـ cases يكون سببها Lack of Exercise جلة
+
+423
+00:33:09,840 --> 00:33:16,500
+حركة تكون هي السبب في الموضوع يا جماعة موضوع
+
+424
+00:33:16,500 --> 00:33:21,080
+السكري موضوع غاية في الأهمية اللي أنا حكيته الآن
+
+425
+00:33:21,080 --> 00:33:25,240
+حكيت عن الـ Type 2 و لسه مادخلناش في التفاصيل
+
+426
+00:33:25,240 --> 00:33:30,590
+تبعهاأنا بتهيألي المحاضرة هذه احتمال تكون تلاتة
+
+427
+00:33:30,590 --> 00:33:38,090
+parts هحاول نسرع لأن المنهج عن جد طويل هجوموني على
+
+428
+00:33:38,090 --> 00:33:42,350
+ال assignment اللي حكيناهم يا جماعة ال assignment
+
+429
+00:33:42,350 --> 00:33:46,450
+مش انتجام منكم ال assignment حتى تجروا المادة و
+
+430
+00:33:46,450 --> 00:33:51,290
+تتبعوا معايا يعني يكفينا اللي احنا في جضية المنهج
+
+431
+00:33:51,290 --> 00:33:56,650
+وزي ما قلتلكوا انا حذر جدا ان كل فكرةفي الباطنة،
+
+432
+00:33:56,650 --> 00:33:59,730
+بغض النظر عن الامتحانات وبغض النظر عن العلامات،
+
+433
+00:33:59,730 --> 00:34:03,530
+وهي مهمة حقيقة، مش بتجلل من أهميتها، لكن بدي
+
+434
+00:34:03,530 --> 00:34:07,510
+المادة تهضمها، وهذا من خلال متابعتكم وراجعتكم
+
+435
+00:34:07,510 --> 00:34:10,970
+معايا أول بأول، ومش نترك المنهج لحد جاب الامتحان
+
+436
+00:34:10,970 --> 00:34:14,370
+بيوم، وبعدين نقعد نحكي، لأ هيك، بتتابعوا معايا جدر
+
+437
+00:34:14,370 --> 00:34:20,330
+الإمكانأنا بقدر ما انا حريص منكوا تاخدوا علامات و
+
+438
+00:34:20,330 --> 00:34:28,390
+تتوفجوا لكن حريص جدا انكوا تهضموا المادة طبعا مش
+
+439
+00:34:28,390 --> 00:34:32,730
+هقولكوا انه شئتم او أبيتم بدكوا تعرفوا باطنة و
+
+440
+00:34:32,730 --> 00:34:36,970
+بدكوا تعرفوا أطفال يعني هذا مافيش مجال لإلكوا
+
+441
+00:34:36,970 --> 00:34:39,630
+للحياة و هتتذكروني في يوم من الأيام يعطيكوا
+
+442
+00:34:39,630 --> 00:34:41,030
+العافية وسلامات
+
diff --git a/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/xJGkNKjINVE_raw.srt b/PL9fwy3NUQKwaf4aPlmtIQXiASpDxVLEnO/xJGkNKjINVE_raw.srt
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index 0000000000000000000000000000000000000000..d0298085d3321f7919b8a362ca312bfce680e97b
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@@ -0,0 +1,1776 @@
+1
+00:00:00,000 --> 00:00:02,800
+بسم الله الرحمن الرحيم الحمد لله رب العالمين
+
+2
+00:00:02,800 --> 00:00:06,280
+والصلاة والسلام علي سيدنا محمد سيد المرسلين أجمعين
+
+3
+00:00:06,280 --> 00:00:10,020
+يعني اليوم ان شاء الله تعالى هندخل على موضوع تاني
+
+4
+00:00:10,020 --> 00:00:17,320
+موضوع طويل موضوع مهم موضوع عمليا في كل بيت موجود
+
+5
+00:00:17,320 --> 00:00:21,200
+إن ماكانش في كل بيت في البيت اللي جنبه أوي يعني
+
+6
+00:00:21,200 --> 00:00:24,560
+يعني ببعنى إنه من كل بيتين هتلاجوا في بيت حد عنده
+
+7
+00:00:24,560 --> 00:00:30,240
+سكري كانوا زمان يقولوا عنه سكر البوللكن الأن هو
+
+8
+00:00:30,240 --> 00:00:34,520
+السكري السكر لبول لإنه كانوا زمان أول ما يكتشفوه
+
+9
+00:00:34,520 --> 00:00:39,020
+يكتشفوه من كتر التبول وإنه كان فيه سكر في البول
+
+10
+00:00:39,020 --> 00:00:44,260
+نتيجة تهريب الكيلة للسكر لزيادة على أي حال الـ
+
+11
+00:00:44,260 --> 00:00:50,640
+diabetes mellitus الديابتس ميليتس طيب هو أنا لما
+
+12
+00:00:50,640 --> 00:00:54,760
+أقول والله فلان عنده الديابتس هل بقصد فيه بس ال
+
+13
+00:00:54,760 --> 00:00:59,300
+diabetes mellitus السكري العادي تبعنا؟أه لكن في
+
+14
+00:00:59,300 --> 00:01:05,660
+ديابتس انسبدس نوع تاني ديابتس انسبدس حاجة تانية هي
+
+15
+00:01:05,660 --> 00:01:11,740
+صحيح مرتبطة بكتر البول برضه لكن اشي تاني يختلف عن
+
+16
+00:01:11,740 --> 00:01:18,020
+الـ diabetes mellitus صح كلامكوا مية في المية ال
+
+17
+00:01:18,020 --> 00:01:24,140
+assignment تبعنا مجسوم من حاجتين اليوم أول حاجةفي
+
+18
+00:01:24,140 --> 00:01:28,860
+نص صفحة مصورة تصوير مكتوبة بالإيد ومصورة تصوير
+
+19
+00:01:28,860 --> 00:01:35,000
+تحكولي عن الـDiabetes Encephalitis ما هو أنواعه
+
+20
+00:01:35,000 --> 00:01:39,180
+وطرق علاجه كلمات يا جماعة بديش شرح شرح ملزمنيش
+
+21
+00:01:39,180 --> 00:01:44,500
+موجودش الكتب الشرح اجروا انتوا كثير واطلعولي بملخص
+
+22
+00:01:44,500 --> 00:01:47,220
+صغير عن الـDiabetes Encephalitis بالحاجات اللي انا
+
+23
+00:01:47,220 --> 00:01:50,320
+ذكرتها عن الـEncephalitis الـDiabetes Melitus انا
+
+24
+00:01:50,320 --> 00:01:53,780
+هحكي عنه اللي هو السكريهذا الجزء الأول من الـ
+
+25
+00:01:53,780 --> 00:01:57,660
+Assignment هنحكي عن الجزء التاني بعد شوية من الـ
+
+26
+00:01:57,660 --> 00:02:02,280
+Assignment الـ Diabetes Militas الاختصار تبعه DM
+
+27
+00:02:02,280 --> 00:02:08,880
+Diabetes DM Militas وهو عبارة عن Metabolic Disease
+
+28
+00:02:08,880 --> 00:02:14,320
+إيش يعني Metabolic؟ Metabolic المقصود فيه إنه يختص
+
+29
+00:02:14,320 --> 00:02:21,050
+بموضوع الاستقلاب الخليةمش حاجة من بعيد ورم ولا إيد
+
+30
+00:02:21,050 --> 00:02:26,750
+مقصورة ولا دهر ولا desk لأ إنما حاجة جوا الخلية
+
+31
+00:02:26,750 --> 00:02:33,570
+بتسير هذا مقصود في metabolic واللي أهم معلم بنشوفه
+
+32
+00:02:33,570 --> 00:02:38,970
+فيها وبدونه ماينفعش أقول diabetes high blood sugar
+
+33
+00:02:38,970 --> 00:02:44,250
+level في الدم over خدوا بالكم الجمعة الجملة هاي
+
+34
+00:02:44,250 --> 00:02:48,200
+prolonged periodنفس الكلام اللي حكيناه عن مين عن
+
+35
+00:02:48,200 --> 00:02:50,720
+الـ hypertension مش مابقول أنا أجيس لواحد مرة ضغط
+
+36
+00:02:50,720 --> 00:02:53,340
+علاجية عالية أقول له يا أبو الشباب والله شكلك عندك
+
+37
+00:02:53,340 --> 00:02:57,660
+ضغط أو والله عملتله فحص سكر اللي جاته مرة عالي لأ،
+
+38
+00:02:57,660 --> 00:03:00,500
+لها شروط هذه الجذيع وهذا هنحكي عنه في المحاضرة
+
+39
+00:03:00,500 --> 00:03:06,660
+يبقى prolonged period لازم عدة مجسات في عدة أوقات
+
+40
+00:03:06,660 --> 00:03:11,720
+مختلفة وعدت للسكر طبعا ساعتها بقول عنه diabetes
+
+41
+00:03:11,720 --> 00:03:15,730
+and diabetes هنحكي عن الموضوع هذا خلالخلال
+
+42
+00:03:15,730 --> 00:03:23,770
+المحاضرة الـ diabetes مشكلته multi system بمعنى
+
+43
+00:03:23,770 --> 00:03:29,490
+مافيش مكان في الجسم إلا بيغزوه هذه خطورته أنه هو
+
+44
+00:03:29,490 --> 00:03:39,750
+بيأثرلي تأثيرات مباشرة أنه
+
+45
+00:03:39,750 --> 00:03:44,710
+هو بيأثرلي تأثيرات مباشرة على العين
+
+46
+00:03:46,660 --> 00:03:50,720
+بأثرلي تأثيرات مباشرة على الدورة الدموية، على
+
+47
+00:03:50,720 --> 00:03:54,960
+القلب، على الكلا، على الشراين الترافية، على
+
+48
+00:03:54,960 --> 00:03:58,080
+الأعصاب الترافية، طب وإيش ضال في البني آدم؟ أه ما
+
+49
+00:03:58,080 --> 00:04:03,240
+هي مشكلة السكر، السكر دمار، السكري دمار، طيب هو
+
+50
+00:04:04,600 --> 00:04:08,680
+شوّقتنا يعني السكري يعني هو بيصيب كل واحد ولا كيف
+
+51
+00:04:08,680 --> 00:04:11,820
+الموضوع ولا إيش اللي بيصير هذا اللي هنحكي عنه وهذا
+
+52
+00:04:11,820 --> 00:04:15,380
+اللي لازم أنتوا تكونوا جزء من الموضوع أنا بحكي في
+
+53
+00:04:15,380 --> 00:04:19,920
+تاني أهم موضوع في الباطنة اللي هو الـ Diabetes
+
+54
+00:04:19,920 --> 00:04:23,740
+Mellitus كمان مرة طيب اللي هو إيش اللي بيصير
+
+55
+00:04:23,740 --> 00:04:27,760
+بالظبط حاجة من حاجتين هنحكي بعد هيك إحنا كيف الـ
+
+56
+00:04:27,760 --> 00:04:31,600
+Type 1 و Type 2 لكن من الأول إنه بيكون عند
+
+57
+00:04:31,600 --> 00:04:37,740
+الإنسولينالانسولين عبارة عن هرمون هذا شغله ينظم
+
+58
+00:04:37,740 --> 00:04:47,200
+دخول السكر للخلية للخلية الجسدية ينظم دخول السكر
+
+59
+00:04:47,200 --> 00:04:52,460
+للخلية الان ممكن يكون عنده الانسولين production
+
+60
+00:04:52,460 --> 00:04:56,420
+abnormal جليل
+
+61
+00:04:56,420 --> 00:05:01,780
+كتير او مافيش فمين ينظم دخول السكر للخلية؟يبقى
+
+62
+00:05:01,780 --> 00:05:06,200
+السكر وين بيضل؟ بيضل في الدم فاهمين عليه كيف؟ يعني
+
+63
+00:05:06,200 --> 00:05:12,740
+وكأنه الخلية غرفة ويلها باب وفي مفتاح المفتاح عشان
+
+64
+00:05:12,740 --> 00:05:16,860
+يدخل السكر الغرفة هو الـ Insulin طب وإذا المفتاح
+
+65
+00:05:16,860 --> 00:05:20,280
+ضاع ومافيش مفتاح كيف بدي يدخل الغرفة السكر؟ مش
+
+66
+00:05:20,280 --> 00:05:24,000
+هيدخل الغرفة، هيضل وين؟ هيضل برا، وين برا؟ في
+
+67
+00:05:24,000 --> 00:05:27,540
+الشراين يعني وعشان هيك لما نعمل فحص السكر بيقول لك
+
+68
+00:05:27,540 --> 00:05:35,180
+السكر عالي لأنه الجسم ماأخدشما أخدش السكر الحاجة
+
+69
+00:05:35,180 --> 00:05:38,320
+التانية اللي ممكن تحصل الـ Impaired احنا بنحكي عن
+
+70
+00:05:38,320 --> 00:05:41,820
+Abnormal Insulin Production أو Impaired Insulin
+
+71
+00:05:41,820 --> 00:05:48,600
+Utilization يعني عملية إنه كيف يدبر نفسه السكر مع
+
+72
+00:05:48,600 --> 00:05:51,920
+الخلية في فشل أو التنين أو الموضوعين الموجودين
+
+73
+00:05:51,920 --> 00:05:56,240
+يعني نقص في السكر وإنه مش قادر يدخل نتيجة مشكلة
+
+74
+00:05:56,240 --> 00:05:59,020
+الـ Receptor مثلا على سبيل المثال هنحكي عن الموضوع
+
+75
+00:05:59,020 --> 00:06:05,560
+يا جماعة موضوع السكرما هواش بس إنه والله فلان دمه
+
+76
+00:06:05,560 --> 00:06:11,000
+حلو وخفيف وعنده سكر، لأ، لأ، لأ المشكلة إن هو
+
+77
+00:06:11,000 --> 00:06:14,700
+الـleading cause of heart disease اتصوروا إنه
+
+78
+00:06:14,700 --> 00:06:18,500
+مشاكل الجلب، تلاحظين الآن واحنا بنحكي blood
+
+79
+00:06:18,500 --> 00:06:20,840
+pressure ال hypertension المرة اللي فاتت، المرة
+
+80
+00:06:20,840 --> 00:06:24,060
+اللي هي السكر وبنربطها في heart disease وبنربطها
+
+81
+00:06:24,060 --> 00:06:30,080
+في ال stroke، حتى الضغط ربطنا بال strokeالآن
+
+82
+00:06:30,080 --> 00:06:33,380
+بدخلني على الـ Adult Blindness العمى تبع الناس
+
+83
+00:06:33,380 --> 00:06:36,860
+الكبار، من أيش انعمى؟ كان زمان العمى يصير نتيجة
+
+84
+00:06:36,860 --> 00:06:40,760
+التهابات وكذا، الآن لأ، نتيجة سكري، ليش؟ لأنه
+
+85
+00:06:40,760 --> 00:06:44,300
+بيصير عندنا Retinal Detachment، هذا شفناه وين؟ قبل
+
+86
+00:06:44,300 --> 00:06:46,980
+أكمل المحاضرة اللي فات أو اللي قبلها، برضه في
+
+87
+00:06:46,980 --> 00:06:51,360
+الضغط، وفيه كمان حاجة جديدة، Non-traumaticLower
+
+88
+00:06:51,360 --> 00:06:55,500
+limb amputation طول عمرنا بنسمع و الله مسيرات
+
+89
+00:06:55,500 --> 00:06:58,940
+العودة جسوله رجله، لأ، الآن احنا بنقول انه non
+
+90
+00:06:58,940 --> 00:07:02,440
+-traumatic، لا حادث سيارة، ولا مسيرات عودة، ولا
+
+91
+00:07:02,440 --> 00:07:07,040
+وجع من فوق و انقطعت رجله، ولا حاجة، لأ، هذه نتيجة
+
+92
+00:07:07,040 --> 00:07:10,540
+لما لاجد راجل كبير انقطعت جديد رجله، بقول هذا في
+
+93
+00:07:10,540 --> 00:07:13,840
+الغالب في الغالب يبدو ان عندك سكر، بيبقى عنده سكر
+
+94
+00:07:14,650 --> 00:07:18,790
+إذا السُكر طب يعني هو كل الدنيا كل واحد عنده سُكر
+
+95
+00:07:18,790 --> 00:07:22,090
+يبتعالج هو المفروض إنه يتعالج لأنه if left
+
+96
+00:07:22,090 --> 00:07:25,710
+untreated إذا انتركت، diabetes can cause many
+
+97
+00:07:25,710 --> 00:07:28,790
+complicationsالآن طبعًا أنا يا جماعة قاعد بحكي
+
+98
+00:07:28,790 --> 00:07:33,090
+عموميات، هدخل على الخصوصيات بعد شوية من الـ Acute
+
+99
+00:07:33,090 --> 00:07:35,530
+Complication هذه الـ Chronic Complication اللي
+
+100
+00:07:35,530 --> 00:07:38,090
+حكيناها قبل شوية اللي هو الـ Heart Disease و الـ
+
+101
+00:07:38,090 --> 00:07:40,210
+Stroke و الـ Blindness و الـ Non-Traumatic Lower
+
+102
+00:07:40,210 --> 00:07:45,590
+Limb Amputation وهذه كلها Complication طويلة
+
+103
+00:07:45,590 --> 00:07:48,890
+الأمد، لكن فيه Complications قصيرة الأمد، بيقول
+
+104
+00:07:48,890 --> 00:07:52,290
+عنها Acute Complicationيعني انا اذا سكر صار 500
+
+105
+00:07:52,290 --> 00:07:56,750
+ولا 600 بدخل في حاجة اسمها diabetic ketoacidosis
+
+106
+00:07:56,750 --> 00:08:02,330
+بيصير عنده حموضة في الدم نتيجة ارتفاع كمية السكر
+
+107
+00:08:02,330 --> 00:08:05,590
+أو بيقول أنا DKA كمية السكر في الدم، هنحكي عنها
+
+108
+00:08:05,590 --> 00:08:09,310
+بعد شوية، بس خلوها في بالكم acute complication
+
+109
+00:08:09,310 --> 00:08:14,350
+diabetic ketoacidosisالـ Serious Long Term
+
+110
+00:08:14,350 --> 00:08:16,970
+Complications تحدثنا عنها قبل شويه مشاكل الـ
+
+111
+00:08:16,970 --> 00:08:22,110
+cardiovascular stroke chronic kidney failure foot
+
+112
+00:08:22,110 --> 00:08:28,130
+ulcer damage to the eyesالوضع الطبيعي إنه أنا باجي
+
+113
+00:08:28,130 --> 00:08:32,170
+بفطر وبتغدى وبتعشى breakfast lunch and dinner في
+
+114
+00:08:32,170 --> 00:08:35,250
+الفترة هذه بيطلع الانسولين بيزيد الانسولين في الدم
+
+115
+00:08:35,250 --> 00:08:39,210
+ليش؟ عشان الأكل اللي أكلته اللي قاعد بنهضم احنا
+
+116
+00:08:39,210 --> 00:08:43,090
+عارفين يا جماعة أنه أي أكل أنا باكله بتكون من تلت
+
+117
+00:08:43,090 --> 00:08:50,330
+أنواع من الأكل ال carbohydrate والبروتينات
+
+118
+00:08:50,330 --> 00:08:57,660
+والدهنياتالدهنيات تتحول لـ Fatty Acids البروتينات
+
+119
+00:08:57,660 --> 00:09:02,120
+تتحول لـ Amino Acids لكن الـ Carbohydrate تتحول
+
+120
+00:09:02,120 --> 00:09:12,970
+لإيش؟ لسكر لجلوكوز الجلوكوز هذا الآن بدهمفاتيح
+
+121
+00:09:12,970 --> 00:09:16,510
+تدخلوا على الخلايا بعد ما اتحلل الأكل للآخر في
+
+122
+00:09:16,510 --> 00:09:20,390
+الجهاز الهضمى تم امتصاصه في الدم الدم بتودي للـ
+
+123
+00:09:20,390 --> 00:09:26,130
+cells الآن بدوا مفاتيح مين المفاتيح الانسولين
+
+124
+00:09:26,130 --> 00:09:30,750
+بيسير بطريقة أو باخره بيطلع الانسولين في الجسم و
+
+125
+00:09:30,750 --> 00:09:37,500
+بفتح الخلايا عشانالسكر يدخل أو الجلوكوز يدخل على
+
+126
+00:09:37,500 --> 00:09:41,580
+الخلايا، لو مافيش انسولين بيضل السكر وين؟ مرة
+
+127
+00:09:41,580 --> 00:09:45,820
+تانية بيضل في الشرايين، يبقى في عندي انا
+
+128
+00:09:45,820 --> 00:09:51,700
+breakfast، lunch، dinner وهذه بيصير فيها ازيادة او
+
+129
+00:09:51,700 --> 00:09:58,680
+افراز لهرمون الانسولين واللي بيحاول يحافظلي على
+
+130
+00:09:58,680 --> 00:10:05,700
+كمياتعلى مستوى سكر طبيعي في الدم يتراوح بين تلاتة
+
+131
+00:10:05,700 --> 00:10:10,400
+وتسعة من عشرة لستة وسبعة من عشرة ميلي مول في
+
+132
+00:10:10,400 --> 00:10:14,960
+الليتر ايه الشاي ميلي مول طول عمرنا بنقول والله
+
+133
+00:10:14,960 --> 00:10:23,970
+فلان السكر تبعه مية تسعين تمانين105 سكر طبيعي يطلع
+
+134
+00:10:23,970 --> 00:10:29,310
+من وين بـ 3.9 و 6.7 ملي مول بالليتر هذه الحسبة
+
+135
+00:10:29,310 --> 00:10:33,630
+الأمريكية في الحسبة التي تبعتنا فيها طريقة للحسبة
+
+136
+00:10:33,630 --> 00:10:39,810
+كيفية تحويل الملي مول بالليتر لملي جرام
+
+137
+00:10:39,810 --> 00:10:44,030
+بالديتسليتر اللي احنا بنحسب فيها نضربها في 17 مش
+
+138
+00:10:44,030 --> 00:10:48,950
+حتى اعبكوا كتير نضربها في 17 بيطلع الحسبة تبعتنا
+
+139
+00:10:52,350 --> 00:10:59,390
+الـ Normal Insulin Metabolism يدخل
+
+140
+00:10:59,390 --> 00:11:04,970
+للجلوكوز يسهّل للجلوكوز يتبع من مصادر الدم من خلال
+
+141
+00:11:04,970 --> 00:11:08,710
+مصادر الجلوكز إلى مصادر الجلوكز من خلال مصادر
+
+142
+00:11:08,710 --> 00:11:09,390
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+143
+00:11:09,390 --> 00:11:13,390
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+144
+00:11:13,390 --> 00:11:16,370
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+145
+00:11:16,370 --> 00:11:16,470
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+146
+00:11:16,470 --> 00:11:16,710
+الجلوكز من خلال مصادر الجلوكز من خلال مصادر
+
+147
+00:11:16,710 --> 00:11:18,600
+الجلوكز من خلال مصادر الجلوكز من خلالآن بعد ما
+
+148
+00:11:18,600 --> 00:11:22,160
+أكل، بزيد الإنسولين، إيش بيعمل الإنسولين؟ شغلته
+
+149
+00:11:22,160 --> 00:11:27,660
+الطبيعية، stimulate storage of glucose as glycogen
+
+150
+00:11:27,660 --> 00:11:33,900
+طبعاً الخلية بتستهلك ما تحتاج، قولي بزيد، بتروح،
+
+151
+00:11:33,900 --> 00:11:40,520
+بتخزنه في الكبد، جا ك glycogen، هذا شغلته يعني
+
+152
+00:11:40,520 --> 00:11:45,790
+يعني العكس تمام لو مافيش إنسولينإيش بيعمل كمان؟
+
+153
+00:11:45,790 --> 00:11:50,510
+Inhibits glyconeogenesis إيش يعني glyconeogenesis؟
+
+154
+00:11:50,510 --> 00:11:57,410
+glyconeogenesis هو عبارة عن تحويل لبروتين لسكر هو
+
+155
+00:11:57,410 --> 00:12:01,130
+بيوقف الموضوع هذا لإن عندنا سكر كفاية فهو بيوقفها
+
+156
+00:12:01,130 --> 00:12:07,110
+الأمر التاني بيزيد fat deposition in a deposed
+
+157
+00:12:07,110 --> 00:12:13,110
+tissueبزيد لي اللي هي تخزين الدهنيات في مناطق
+
+158
+00:12:13,110 --> 00:12:17,210
+الدهنية هذا شغل الإنسولين increase protein
+
+159
+00:12:17,210 --> 00:12:21,870
+synthesis اللي بيزيد يعني هو من الشغلات تبعته أنه
+
+160
+00:12:21,870 --> 00:12:30,370
+بيبني لبروتين طيب هو أنا كيف بدي أعرف أن فلان عنده
+
+161
+00:12:30,370 --> 00:12:35,690
+سكري؟ كيف بدي أعرف؟في حاجات نعرفها في اللسان تبعنا
+
+162
+00:12:35,690 --> 00:12:41,450
+اللسان العادى كثير من الناس بتيجي شايفة زميلتك او
+
+163
+00:12:41,450 --> 00:12:48,430
+صاحبتك او اي حد بتعرفيه او بتعرفه شفته قبل فترة و
+
+164
+00:12:48,430 --> 00:12:51,830
+اليوم شفته ايه ما الوزنك نازل هيك مرة واحدة ايش
+
+165
+00:12:51,830 --> 00:12:57,370
+اول حاجة بتفكر فيها على طول اه ايوة احكوا ايش لأ
+
+166
+00:12:57,370 --> 00:13:02,390
+غلط مش ديابتسأي واحد بشوفه نازل وزنه بطريقة
+
+167
+00:13:02,390 --> 00:13:06,490
+unexpected وانا مش عارف من إيش بفكر بالوضع الطبيعي
+
+168
+00:13:06,490 --> 00:13:09,690
+يا جماعة common is common فاكروش بعيد فاكروش حتى
+
+169
+00:13:09,690 --> 00:13:16,610
+في السكري في إيش بدنا نفكر؟ في إيش بدنا نفكر؟
+
+170
+00:13:16,610 --> 00:13:20,190
+أتبرونا وكأنه الآن تعليم وجاهي حاولوا تجاوبوني صوت
+
+171
+00:13:20,190 --> 00:13:28,260
+عالي علوا أه أيوة لأ مش صحلأ مش صح ايوة صح احتمال
+
+172
+00:13:28,260 --> 00:13:34,480
+بروح الجيم و بعمل diet اه عشان هيك نزل وزنه في
+
+173
+00:13:34,480 --> 00:13:41,040
+أسباب تانية اه للـ Unexpected وبسرعة
+
+174
+00:13:41,040 --> 00:13:46,080
+ينزل وزن لازم افكر في الـ Diabetes إلى جانب الجيم
+
+175
+00:13:46,080 --> 00:13:49,050
+و الحاجات التاليةلازم أفكر في مشاكل في الـ Thyroid
+
+176
+00:13:49,050 --> 00:13:53,610
+لازم أفكر في مشاكل في Cancer على سبيل المثال لازم
+
+177
+00:13:53,610 --> 00:13:57,690
+أفكر في مشاكل Tuberculosis إيش يعني Tuberculosis؟
+
+178
+00:13:57,690 --> 00:14:01,190
+Cell، مرض الـ Cell آه، مجموعة كبيرة من الأمراض
+
+179
+00:14:01,190 --> 00:14:04,990
+بتنزلي وزن البني آدم بدون ما يكون جاصد، unexpected
+
+180
+00:14:04,990 --> 00:14:09,650
+لكن إحنا هنا في إطار الـ Diabetes Mellitus من أهم
+
+181
+00:14:09,650 --> 00:14:12,590
+الحاجات اللي بنلاقيها الـ Classic Symptoms اللي
+
+182
+00:14:12,590 --> 00:14:19,550
+بنقول عنها is Weight Lossفقدان الوزن و ايش كمان
+
+183
+00:14:19,550 --> 00:14:25,290
+التلاتة P ايش التلاتة P هاي اول P و تاني P و تالت
+
+184
+00:14:25,290 --> 00:14:31,030
+P ال polyuria ايش يعني polyuria يعني urine كتير
+
+185
+00:14:31,030 --> 00:14:36,690
+increase urination كل شويه رايح جاي على حمام طب هو
+
+186
+00:14:36,690 --> 00:14:39,750
+كل واحد بشوفه رايح جاي على حمام اول حاجة بفكر فيها
+
+187
+00:14:39,750 --> 00:14:49,180
+سكري لأ هإيش اتهابات البولحسب إذا أنا بحكي عن راجل
+
+188
+00:14:49,180 --> 00:14:55,940
+كبير بفكر كمان فيه بروستاتا نتفرع
+
+189
+00:14:55,940 --> 00:15:00,480
+بس هيك أنا أفكار أنا قلتلكوا موضوع الباطنةالموضوع
+
+190
+00:15:00,480 --> 00:15:05,100
+ممتع، مش قضية إنه بس علم، مش بس بس بدي أحفظ منهج،
+
+191
+00:15:05,100 --> 00:15:09,980
+الموضوع مش موضوع منهج، الموضوع موضوع علم، موضوع
+
+192
+00:15:09,980 --> 00:15:14,180
+أعرف في الطب، مضلش restricted على حركات العلاج
+
+193
+00:15:14,180 --> 00:15:17,280
+الطبيعي والعضلات وكذا، لأ، أنا بدي أعرف البني آدم
+
+194
+00:15:17,280 --> 00:15:22,220
+أكتر من جهازه الحركي، بدي أعرف البني آدم أجزاءه من
+
+195
+00:15:22,220 --> 00:15:22,980
+جوا كمان
+
+196
+00:15:27,740 --> 00:15:31,300
+وأفهم في الأمراض هذه لأن كلها هيك هيك لها
+
+197
+00:15:31,300 --> 00:15:36,560
+relationship to my subject كعلاج طبيعي إيش كمان ال
+
+198
+00:15:36,560 --> 00:15:39,160
+P التاني بولي ديبسيا إيش يعني بولي ديبسيا
+
+199
+00:15:39,160 --> 00:15:44,920
+increased thirst بشرب كتير دائما عتشان وإيش كمان
+
+200
+00:15:44,920 --> 00:15:51,780
+بوليفاجيا بياكل كتير increased hungerهناك حاجات
+
+201
+00:15:51,780 --> 00:15:55,000
+تانية يا جماعة بس هي هذه الأساسيات Weight Loss،
+
+202
+00:15:55,000 --> 00:15:58,080
+Polyuria، Polydipsia و Polyphasia زي إيش عندنا
+
+203
+00:15:58,080 --> 00:16:00,980
+حاجات بيصير يشوف blurry vision، إيش يعني blurry
+
+204
+00:16:00,980 --> 00:16:06,080
+vision؟ blurry vision يعني مش بيشوف وهتز الصورة،
+
+205
+00:16:06,080 --> 00:16:11,670
+double visionهدق باجع راس فتيق دايما تعبان slow
+
+206
+00:16:11,670 --> 00:16:16,030
+healing of cuts الجروح عنده بتطول لما بتطيب ايش
+
+207
+00:16:16,030 --> 00:16:19,490
+كمان itchy skin vision changes ليش ال vision بيصير
+
+208
+00:16:19,490 --> 00:16:23,300
+في مشاكل اكتر من حاجة ممكن يكون نتيجةاللي هو
+
+209
+00:16:23,300 --> 00:16:25,700
+المشاكل اللي بتصير في الـ Retina لكن ممكن تكون
+
+210
+00:16:25,700 --> 00:16:29,620
+نتيجة الـ Hyperglycemia بتعمل ليه؟ Can cause
+
+211
+00:16:29,620 --> 00:16:33,120
+glucose absorption in the lens في العدسات وهذه
+
+212
+00:16:33,120 --> 00:16:37,060
+بتؤدي لـ Changes in its shape resulting in vision
+
+213
+00:16:37,060 --> 00:16:42,240
+changes يعني تأثيرها على عدسات العين كمان مرة الـ
+
+214
+00:16:42,240 --> 00:16:48,020
+Symptoms باللسان العادي اللسان الناس العادية
+
+215
+00:16:48,020 --> 00:16:53,920
+دايماً tiredرايح جاي على الحمام بنزل وزن وصدن
+
+216
+00:16:53,920 --> 00:16:59,980
+wound that once healed فيه طبعا sexual problems
+
+217
+00:16:59,980 --> 00:17:07,540
+بتصير بالذات من جهة الراجل always hungry دايما
+
+218
+00:17:07,540 --> 00:17:15,480
+جعان blurry vision numbness خدلان و .. و .. و .. و
+
+219
+00:17:15,480 --> 00:17:15,740
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+220
+00:17:15,740 --> 00:17:16,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+221
+00:17:16,060 --> 00:17:16,900
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+222
+00:17:16,900 --> 00:17:17,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+223
+00:17:17,060 --> 00:17:17,060
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+224
+00:17:17,060 --> 00:17:17,180
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+225
+00:17:17,180 --> 00:17:17,180
+.. و .. و .. و .. و .. و .. و .. و .. و .. و .. و
+
+226
+00:17:17,180 --> 00:17:17,540
+.. و .. و .. و .. و .. و .. و .. و .. و ..
+
+227
+00:17:23,310 --> 00:17:28,590
+اللي هي في اللسان العادى ال symptoms اللي بنلاقيها
+
+228
+00:17:28,590 --> 00:17:31,730
+مش لازم كلها تكون موجودة يا جماعة بعضها موجودة أو
+
+229
+00:17:31,730 --> 00:17:34,250
+واحدة منهم موجودة لازم أفكر في ال diabetes
+
+230
+00:17:37,690 --> 00:17:40,730
+اللي فيها إنها طبعاً للـDiabetes Emergencies مش
+
+231
+00:17:40,730 --> 00:17:44,550
+هحكي عنها الآن، ذكروني فيها بس، هحكي معها بعد هيك،
+
+232
+00:17:44,550 --> 00:17:46,830
+في الآخر لما أحكي عن الـDKA، هحكي عن
+
+233
+00:17:46,830 --> 00:17:50,750
+الـHypoglycemia فبدأ أروح على الـClassification of
+
+234
+00:17:50,750 --> 00:17:55,470
+Diabetes حقيقة إنه في أكتر من الـClassification،
+
+235
+00:17:55,470 --> 00:17:59,360
+لكن إحنا اللي اعتمدناهاDiabetes mellitus عنده
+
+236
+00:17:59,360 --> 00:18:04,600
+أربعة broad categories اللي هو diabetes type 1 و
+
+237
+00:18:04,600 --> 00:18:09,900
+type 2 و في gestational diabetes اللي مرتبط بالحمل
+
+238
+00:18:09,900 --> 00:18:16,580
+أو سكر الحمل و في specific types يعني عدد منها
+
+239
+00:18:16,580 --> 00:18:20,900
+هنتحدث عنها في حينها مش كلها لكن هذكر بعضها حسب
+
+240
+00:18:20,900 --> 00:18:26,200
+الواجهة اللي معناها طيب إيش الفرق بين type 1 و
+
+241
+00:18:26,200 --> 00:18:36,900
+type 2؟ومن أكتر بيجي الـ
+
+242
+00:18:36,900 --> 00:18:40,760
+Type يعني الآن أنا هدي هحكي بعد شوية إيش الـ Type
+
+243
+00:18:40,760 --> 00:18:43,640
+I و Type II لكن خدوا بالكوا من ال curve اللي موجود
+
+244
+00:18:43,640 --> 00:18:51,110
+الدائرة هاي إنه الأحمر هو Type IIوهو غالبية يعني
+
+245
+00:18:51,110 --> 00:18:53,750
+هنا في أمريكا على سبيل المثال وقولنا أحنا مرة مرة
+
+246
+00:18:53,750 --> 00:18:56,570
+تانية يا جماعة عشان ما تاخدوش .. ما أخدلش ده
+
+247
+00:18:56,570 --> 00:18:58,930
+مابجيب إحصائيات هم الأمريكان عندهم إحصائيات باقى
+
+248
+00:18:58,930 --> 00:19:03,090
+الدول معظمها ماعندهاش إحصائيات عشان هيك بنعتمد
+
+249
+00:19:03,090 --> 00:19:11,370
+الإحصائيات المنشورة طبعة أمريكا في أمريكا في سنة
+
+250
+00:19:11,370 --> 00:19:16,890
+من السنوات سنة الألفين من قد النظر عن الأرقام لكن
+
+251
+00:19:17,340 --> 00:19:23,260
+كان عدد سكان أمريكا حدود 300 مليون يعني وانتوا
+
+252
+00:19:23,260 --> 00:19:27,940
+بتحسبوا احسبوا 300 مليون عدد الناس اللي الـ type 2
+
+253
+00:19:27,940 --> 00:19:33,600
+كان عشرة مليون واحد عنده سكري type 2 type 1 لأ نص
+
+254
+00:19:33,600 --> 00:19:39,600
+مليون لمليون أجل يعني تقريبا أجل أجل وفيه طبعا
+
+255
+00:19:39,600 --> 00:19:44,260
+نسبة كبيرة شايفين الأخضر هذا الرقم الأسئ هذا الرقم
+
+256
+00:19:45,200 --> 00:19:49,020
+خمسة مليون عندهم سكري بس مش مشخصين لا هم رايحين
+
+257
+00:19:49,020 --> 00:19:52,460
+على الدكاترة ولا الدكاترة باكتشفينهم و هم هذا
+
+258
+00:19:52,460 --> 00:19:56,220
+الرقم أسود يعني أنا بحكي عاقعد عن ستة عشر مليون أو
+
+259
+00:19:56,220 --> 00:20:01,020
+سبعتاشر مليون أمريكي في سنة الألفين كان عندهم سكري
+
+260
+00:20:01,020 --> 00:20:07,000
+type 2 هو الماسكون خمسة وتسعين في المية من السكري
+
+261
+00:20:07,000 --> 00:20:11,020
+اللي موجود خمسة وتسعين type 2 طب واش الفرق بين
+
+262
+00:20:11,020 --> 00:20:15,740
+type 1 وtype 2؟هو فيه فروق كبيرة بينهم type one
+
+263
+00:20:15,740 --> 00:20:19,360
+مافيش
+
+264
+00:20:19,360 --> 00:20:21,900
+insulin بالمرة بالمناسبة الإنسولين هو من وين بيجي؟
+
+265
+00:20:21,900 --> 00:20:27,100
+من وين بيطلع؟ الغدا النخامية في الدماغ بيجي؟ ولا
+
+266
+00:20:27,100 --> 00:20:31,600
+من خلايا Beta تاعة الـ Langerhans Islet Cells
+
+267
+00:20:31,600 --> 00:20:37,040
+الموجودة في البنكرياز؟ ولا من وين بيطلع؟ آه من الـ
+
+268
+00:20:37,040 --> 00:20:42,320
+Islet Cellsاللي هو الـ Langerhans جزر Langerhans
+
+269
+00:20:42,320 --> 00:20:47,460
+في البنكرياز من خلايا Beta بيطلع الان هذي لو
+
+270
+00:20:47,460 --> 00:20:53,720
+اتدمرت المصنع هذا لو اتدمر مش هيطلع انسولين طب هو
+
+271
+00:20:53,720 --> 00:20:58,080
+أيش بدي دمره؟ أه في عنا أكتر من سبب لتدبيره ممكن
+
+272
+00:20:58,080 --> 00:21:03,920
+يكون autoimmune بمعنى دمر نفسه بنفسه أو يكون نتيجة
+
+273
+00:21:03,920 --> 00:21:09,670
+التهيابات المهمإنها بتطلعش Insulin No Insulin هذا
+
+274
+00:21:09,670 --> 00:21:14,130
+الـ Type I في الـ Islet Cells فإذا مافيش Insulin
+
+275
+00:21:14,130 --> 00:21:18,070
+يبقى على الدنيا السلام يبقى مافيش مفاتيح للغرف
+
+276
+00:21:18,070 --> 00:21:23,230
+يبقى السكر هيظل برا والخلايا مش هيروحلها سكر طيب
+
+277
+00:21:23,230 --> 00:21:27,150
+وبدأ تعيش بدون سكر ماهي المشكلة هو ليش بيصير عندنا
+
+278
+00:21:27,150 --> 00:21:30,590
+كل ال symptoms طب و ال diabetes type 2 إيش اللي
+
+279
+00:21:30,590 --> 00:21:40,330
+بيصير؟ هو في Insulinلكن المفتاح ماتجيع الجفل أو
+
+280
+00:21:40,330 --> 00:21:46,250
+بتحط المفتاح في الباب وبتحاول تفتح بعصلج الباب
+
+281
+00:21:46,250 --> 00:21:51,450
+برضهاش يفتح بنقول عنه Insulin Resistance Insulin
+
+282
+00:21:51,450 --> 00:21:58,070
+Resistance في عدم قدرة لدخول السكر إلى داخل الخلية
+
+283
+00:21:58,070 --> 00:22:05,420
+نتيجة إنه Insulin Resistanceالـ Gestational هو تبع
+
+284
+00:22:05,420 --> 00:22:09,640
+الحمل مثل الـ Type 2 تقريباً بس هو بيجي .. هنحكي
+
+285
+00:22:09,640 --> 00:22:13,500
+عنه بيجي في فترة الحمل .. فترات معينة في الحمل
+
+286
+00:22:24,370 --> 00:22:32,610
+النقص حقيقي أو نقص عدم وجود إنسولين حقيقي موجود في
+
+287
+00:22:32,610 --> 00:22:32,930
+الجسم
+
+288
+00:22:38,370 --> 00:22:40,450
+وهذا بنقول عنه Relatively، يعني أنا في عندى
+
+289
+00:22:40,450 --> 00:22:44,290
+Insulin لكن مش قادر يشتغل الشغل اللي بدناياه وهذا
+
+290
+00:22:44,290 --> 00:22:50,610
+بيقدّي لبعد فترة، نتيجة إنه ال Insulin بحاول يفتح،
+
+291
+00:22:50,610 --> 00:22:56,670
+بيرضاش، بيدّي إشارة للجسم،
+
+292
+00:22:56,670 --> 00:23:00,830
+نتيجة زيادة السُكّة، إشارة للبنكرياس، افرز أكتر،
+
+293
+00:23:00,830 --> 00:23:05,480
+بيظل يفرز أكتر البنكرياسونتيجة الإفراز الأكتر الـ
+
+294
+00:23:05,480 --> 00:23:09,140
+beta cells برضه في الآخر بتضعف وبتقولك خلاص أنا
+
+295
+00:23:09,140 --> 00:23:12,420
+أطلعت كل الانسولين اللي عندي فبيصير عندي انسولين
+
+296
+00:23:12,420 --> 00:23:17,460
+beta cells failure وطبعاً في عندنا ال gestational
+
+297
+00:23:17,460 --> 00:23:25,870
+diabetes اللي هو عبارة عن subtype لtype 2الـType-2
+
+298
+00:23:25,870 --> 00:23:28,790
+هي الـSecondary Form لـType-2 اللي قلنا بنقول عنها
+
+299
+00:23:28,790 --> 00:23:34,510
+بعد شوية الـModi وExocrine Pancreas Disease
+
+300
+00:23:34,510 --> 00:23:38,310
+والـSteroids هذه عبارة عن حاجات بتعمل زي Type-2،
+
+301
+00:23:38,310 --> 00:23:41,730
+هنحكي عنها بعد شوية طيب، ندخل الآن على تفاصيل
+
+302
+00:23:41,730 --> 00:23:46,470
+الـType-1، أيه أسماء تانية الـType-1؟بنقوله
+
+303
+00:23:46,470 --> 00:23:50,130
+juvenile onset or insulin dependent diabetes
+
+304
+00:23:50,130 --> 00:23:56,110
+جوفينايل لأنه لاحظوا أنه الغالبية خدوا باركم كلمة
+
+305
+00:23:56,110 --> 00:24:03,550
+الغالبية بتصير عند الأطفال مفهوم
+
+306
+00:24:03,550 --> 00:24:07,150
+باركم تقول الغالبية لكن مش مية في المية عند
+
+307
+00:24:07,150 --> 00:24:11,770
+الأطفال ممكن type one يجي عند ناس غير الأطفال عشان
+
+308
+00:24:11,770 --> 00:24:17,010
+هيك قالوا زمان juvenileفيه اسم تاني Insulin
+
+309
+00:24:17,010 --> 00:24:24,030
+Dependent لأن علاجه لا يتم الا بالانسولين بدون هيك
+
+310
+00:24:24,030 --> 00:24:27,530
+يبقى ممنفعش الانسولين type one يا جماعة عفوا ان ال
+
+311
+00:24:27,530 --> 00:24:31,890
+diabetes type one لا يعالج الا بالانسولين الابار
+
+312
+00:24:31,890 --> 00:24:34,930
+ماينفعش يعالجه بحبوب عشان هيك جاله dependent
+
+313
+00:24:34,930 --> 00:24:40,210
+dependent يعني أنك متعلق بيهوهذا بيجي عند الناس
+
+314
+00:24:40,210 --> 00:24:43,170
+الأقل من تلاتين سنة عشان هيك ربطه بالأطفال كانت مش
+
+315
+00:24:43,170 --> 00:24:48,890
+صح لأنه هيوا بيصير لحتى تلاتين سنة يعني جوفينية
+
+316
+00:24:50,330 --> 00:24:54,470
+لكن العمر المشهور لإله اللي بيبين فيه سكري بين 11
+
+317
+00:24:54,470 --> 00:25:00,730
+و 13 سنة و بيصير عندنا طب ليش؟ طب ما هيوا تسع عشر
+
+318
+00:25:00,730 --> 00:25:05,110
+سنين مسلك؟ آه، مسلك و ماعندوش سكر الطفل، شو يعني
+
+319
+00:25:05,110 --> 00:25:07,670
+أنا الآن اتدمر؟ بمجرد صراحة عندي progressive
+
+320
+00:25:07,670 --> 00:25:12,410
+destruction للـBeta cells؟لحد ما وصل مرحلة على عمر
+
+321
+00:25:12,410 --> 00:25:16,990
+11، 12، 13، 14، ماعرفش وابتش لحد ما اتدمرت كامل
+
+322
+00:25:16,990 --> 00:25:22,550
+الخلايا وصار عندنا الـ Destruction للـ Pancreatic
+
+323
+00:25:22,550 --> 00:25:26,480
+Beta Cellsوهذه زي ما قلنا في الغالب Auto
+
+324
+00:25:26,480 --> 00:25:31,380
+Antibodies عبارة عن نيران صديقة هي بتعملي
+
+325
+00:25:31,380 --> 00:25:34,740
+reduction لـ8 لـ90% of normal beta cells function
+
+326
+00:25:34,740 --> 00:25:37,740
+قبل manifestation it occurs يعني يوم بصير عندي
+
+327
+00:25:37,740 --> 00:25:41,700
+manifestation ببجي عارف أنه على ال beta cells اللي
+
+328
+00:25:41,700 --> 00:25:47,320
+بتفرز الإنسلين السلامالأسباب لحد الآن تتفسر
+
+329
+00:25:47,320 --> 00:25:51,860
+بـGenetic Predisposition وفي قال لك لأ ممكن يكون
+
+330
+00:25:51,860 --> 00:25:57,280
+نتيجة Exposure to a virus الـ Onset مش مختلف كتير
+
+331
+00:25:57,280 --> 00:26:01,940
+الـ Symptoms في الـ Type 1 Manifestation developed
+
+332
+00:26:01,940 --> 00:26:05,380
+when the pancreas can no longer produce insulin
+
+333
+00:26:05,380 --> 00:26:10,120
+Rapid onset of symptoms presentفي الغالب في الغالب
+
+334
+00:26:10,120 --> 00:26:14,340
+هدولة أول ما بيبين عنده بيبين بالصورة الصعبة يعني
+
+335
+00:26:14,340 --> 00:26:18,200
+بيجيني الطفل بحاجة اسمها diabetic ketoacidosis
+
+336
+00:26:18,200 --> 00:26:25,050
+يعني عمليا أو بندوسيروعمليا في حالة صعبة بيجيونا
+
+337
+00:26:25,050 --> 00:26:28,430
+الأطفال في العادة زي ما بيجيونا في الديابتس 1 ليش؟
+
+338
+00:26:28,430 --> 00:26:33,610
+لأنه مرة واحدة بينتقل من سكر معجول لـ Ketoacidos
+
+339
+00:26:33,610 --> 00:26:38,690
+حموضة في الدم نتيجة ارتفاع حاد في السكر وطبعا هذا
+
+340
+00:26:38,690 --> 00:26:43,070
+بيأثرلي على باق الجسم ممكن يجيني بـ Weight Loss
+
+341
+00:26:43,070 --> 00:26:46,270
+وكمان مرة ممكن يجيني بـWeakness، Fatigue،
+
+342
+00:26:46,270 --> 00:26:49,950
+Polyphagia، Polydipsia و Polyuria
+
+343
+00:26:52,810 --> 00:26:57,530
+زي ما حكينا قبل شوية زي
+
+344
+00:26:57,530 --> 00:27:01,890
+ما حكينا قبل شوية is characterized by insulin
+
+345
+00:27:01,890 --> 00:27:06,350
+resistance which may be combined with relatively
+
+346
+00:27:06,350 --> 00:27:10,890
+reduced insulin secretion characterized by insulin
+
+347
+00:27:10,890 --> 00:27:15,910
+resistance أنه مش قادر الإنسلين يغزو هذه الغرفة
+
+348
+00:27:15,910 --> 00:27:20,940
+لسبب من الأسبابوهذا which may be combined with
+
+349
+00:27:20,940 --> 00:27:24,060
+relatively reduced insulin secretion بعد شويه
+
+350
+00:27:24,060 --> 00:27:26,600
+بتصير repeated cells مش قادرة تطلع انسلين ليش؟
+
+351
+00:27:26,600 --> 00:27:29,400
+لأنه طلعت كتير نتيجة أنه مش داخل الانسلين داخل
+
+352
+00:27:29,400 --> 00:27:36,340
+الخلايا فبقل كمية الانسلين The defective
+
+353
+00:27:36,340 --> 00:27:45,240
+responsiveness استجابة خلايا الجسمللإنسولين is
+
+354
+00:27:45,240 --> 00:27:49,200
+believed to involve the insulin receptors وقال إن
+
+355
+00:27:49,200 --> 00:27:54,380
+الـ Receptors هي السبب تبع الموضوع ديابتس ميليتاس
+
+356
+00:27:54,380 --> 00:27:58,200
+is the second .. is the most common type تسعين في
+
+357
+00:27:58,200 --> 00:28:01,100
+المية of patient تسعين أو خمسة أو تسعين في المية
+
+358
+00:28:01,100 --> 00:28:05,280
+usually تيجي بعد في الناس اللي usually وإيش معنى
+
+359
+00:28:05,280 --> 00:28:10,620
+usually مش always usually يعني غالبا occur in
+
+360
+00:28:10,620 --> 00:28:19,090
+people over 40الـ 98% of patients are overweight
+
+361
+00:28:19,090 --> 00:28:25,290
+لكن ممكن واحد مش overweight برضه يصير عنده type 2
+
+362
+00:28:25,290 --> 00:28:30,190
+لكن لاحظوا ان type 2 diabetes is due to primarily
+
+363
+00:28:30,190 --> 00:28:35,910
+two lifestyle factors and genetics احنا في لغتنا
+
+364
+00:28:35,910 --> 00:28:40,130
+بنقول عنه multifactorial ايش يعني multifactorial؟
+
+365
+00:28:40,540 --> 00:28:43,660
+يعني بتحكم فيه أكتر من حاجة هو ممكن يكون الواحد
+
+366
+00:28:43,660 --> 00:28:50,600
+genetic predisposition لكن الممارسة السيئة بتظهر
+
+367
+00:28:50,600 --> 00:28:55,860
+المرض ممكن كتير ناس تكون عندها حاجات لكن الممارسة
+
+368
+00:28:55,860 --> 00:29:02,820
+السيئة هي اللي اتبينهاللي من الحاجات اللي .. اللي
+
+369
+00:29:02,820 --> 00:29:05,460
+من ال .. اللي لها علاقة بالـ lifestyle مرة تانية،
+
+370
+00:29:05,460 --> 00:29:08,980
+هين بدينا نيجي للـ lifestyle وطريقة الحياة اللي مش
+
+371
+00:29:08,980 --> 00:29:12,520
+كويسة، مابديش أقولها الكلمة، اللي إحنا عايشينها هي
+
+372
+00:29:12,520 --> 00:29:15,060
+اللي عاملانا المشكلة، اللي هو الـ obesity
+
+373
+00:29:18,240 --> 00:29:21,300
+وكنا حكينا عن الـ Body Mass Index of Greater Than
+
+374
+00:29:21,300 --> 00:29:25,680
+30 لأن أنا لما أقول Body Mass Index أكتر من تلاتين
+
+375
+00:29:25,680 --> 00:29:29,480
+في الـ Obesity كلكم فاهمين لأن احنا في الـ
+
+376
+00:29:29,480 --> 00:29:35,780
+Assignment اللي فاتت شرحنا إيش الـ PMI وقلنا إيش
+
+377
+00:29:35,780 --> 00:29:40,020
+يعني PMI ال Body Mass Index وكيف نحسب وقلنا
+
+378
+00:29:40,020 --> 00:29:43,430
+الدرجات تبعته فاكرين ولا مش فاكرين؟ديروي بالكوا
+
+379
+00:29:43,430 --> 00:29:45,570
+أنا دايما بركز عليه الموضوع هذا الـ Body Mass
+
+380
+00:29:45,570 --> 00:29:48,650
+Index لأنه من الحاجات الأساسية اللي ما اتعلمناها
+
+381
+00:29:48,650 --> 00:29:52,250
+في المدارس لكن الآن it's time نكون عارفين إيش
+
+382
+00:29:52,250 --> 00:29:55,990
+الموضوع هذا اللي أقل من 30 اللي أكتر من 30 الـ
+
+383
+00:29:55,990 --> 00:29:59,730
+Body Mass Index تبعه opposite أو opposite هذا من
+
+384
+00:29:59,730 --> 00:30:04,210
+اللي هو ال factors اللي بتساعد أنه يكون عند الواحد
+
+385
+00:30:04,210 --> 00:30:08,110
+diabetes type 2 lack of physical activity يا سلام
+
+386
+00:30:08,110 --> 00:30:12,900
+نفس الكلام عن الضغط الجعدة وجلة الحركةالـ Poor
+
+387
+00:30:12,900 --> 00:30:20,140
+Diet، الطيح رايح، إيش بيجي، بيتاكل، شبسي كل يوم،
+
+388
+00:30:20,140 --> 00:30:24,120
+كوكاكولا كل يوم، جنان كبيرة و جنان صغيرة رايح جاي،
+
+389
+00:30:24,120 --> 00:30:28,540
+حاجات فيها بيتزا عالفاض و عالملان، ماكرونة عالفاض
+
+390
+00:30:28,540 --> 00:30:33,140
+و عالملان، حاجات فاضية، طيب كله سلطات؟ لأ، بدناش
+
+391
+00:30:33,140 --> 00:30:38,520
+سلطات، حاجة خضرة؟ لأ، بدناش حاجة خضرة، زيوت طبيعية
+
+392
+00:30:38,520 --> 00:30:41,540
+زي الزتون و حاجات؟ لأ، لازم يكون حاجات مهدرجة و
+
+393
+00:30:41,540 --> 00:30:49,890
+حاجاتيعني poor diet أكل مالوش لازم نهائي بالإضافة
+
+394
+00:30:49,890 --> 00:30:53,170
+للـ stress اللي احنا عايشين و لا فيه شغل ولا ولا
+
+395
+00:30:53,170 --> 00:30:57,610
+ولا ولا هذا أمر طبعاً هذه الأمور كلها لما تتجمع في
+
+396
+00:30:57,610 --> 00:31:02,270
+وجود الواحد يكون predisposition يعني هو مؤهل أمه و
+
+397
+00:31:02,270 --> 00:31:04,990
+أبوه و كل عيلته عندها سكري في الآخر هيصير عنده
+
+398
+00:31:04,990 --> 00:31:05,470
+سكري
+
+399
+00:31:08,780 --> 00:31:12,680
+من الـ .. زي ما قلنا الحاجات اللي بنشوفها في الـ
+
+400
+00:31:12,680 --> 00:31:17,900
+Dietary Factors المأكلات اللي بناكلها و اللي بتأهل
+
+401
+00:31:17,900 --> 00:31:21,380
+إنه يصير عند الواحد Type 2 Consumption of Sugar
+
+402
+00:31:21,380 --> 00:31:25,360
+-Sweetened Drinks In Excess، خدوا بالك In Excess،
+
+403
+00:31:25,360 --> 00:31:28,820
+إحنا مابنقولش ممنوع يا جماعة، خير الأمور الوسط،
+
+404
+00:31:28,820 --> 00:31:31,140
+طول عُرّى بنحكي خير الأمور الوسط، تمنعش حالك ولا
+
+405
+00:31:31,140 --> 00:31:35,840
+عن حاجة، لكن مش معقول كل يوم حلويات، مش معقول كل
+
+406
+00:31:35,840 --> 00:31:38,460
+يوم شوكولاتة، كل شوكولاتة حلوة، شوكولاتة منيحة
+
+407
+00:31:38,690 --> 00:31:43,530
+كويسة للمزاج وكويسة لـ .. كويسة ماشي بس مش كل يوم
+
+408
+00:31:43,530 --> 00:31:47,150
+لوح يعني شو هذا الموضوع؟ يا ريت شوكراتة من نوع
+
+409
+00:31:47,150 --> 00:31:51,010
+اللي كويس من نوع اللي تافه وهذا مشكلة consumption
+
+410
+00:31:51,010 --> 00:31:55,410
+of sugar-sweetened drinks in excess is associated
+
+411
+00:31:55,410 --> 00:32:00,370
+with increased risk type of fats نوع الدهنيات اللي
+
+412
+00:32:00,370 --> 00:32:04,990
+بنستخدمها اللي هي saturated fats and trans fatty
+
+413
+00:32:04,990 --> 00:32:11,010
+acids increasing the risk ofوانواع الـ unsaturated
+
+414
+00:32:11,010 --> 00:32:15,870
+وانواع الـ monounsaturated fat تقليز الخطر خدوا
+
+415
+00:32:15,870 --> 00:32:18,810
+بالك أنواع الـ fat وهذا الجزء التاني من الـ
+
+416
+00:32:18,810 --> 00:32:23,950
+assignment إيش أنواع الـ fat اللي هو saturated و
+
+417
+00:32:23,950 --> 00:32:27,890
+unsaturated و أنواع الـ unsaturated و الفرق بينهم
+
+418
+00:32:27,890 --> 00:32:37,050
+بدي جدول مقارنة بينهم saturated و unsaturated و ال
+
+419
+00:32:37,050 --> 00:32:42,440
+trans fatمش الفرق بينهم في جدول مش أكتر من جدول
+
+420
+00:32:42,440 --> 00:32:47,300
+وينكتب بالإيد ويتصور وينبعتليه لأن هذا غاية في
+
+421
+00:32:47,300 --> 00:32:51,080
+الأهمية وإما هنروح في القلب في ال lung في الباطنة
+
+422
+00:32:51,080 --> 00:32:58,240
+دايما هنتحدث عن أنواع ال fats eating lots of white
+
+423
+00:32:58,240 --> 00:33:04,660
+rice مقارنة ورز كتيرالـ Lack of Exercise ممكن في 7
+
+424
+00:33:04,660 --> 00:33:09,840
+% من الـ cases يكون سببها Lack of Exercise جلة
+
+425
+00:33:09,840 --> 00:33:16,500
+حركة تكون هي السبب في الموضوع يا جماعة موضوع
+
+426
+00:33:16,500 --> 00:33:21,080
+السكري موضوع غاية في الأهمية اللي أنا حكيته الآن
+
+427
+00:33:21,080 --> 00:33:25,240
+حكيت عن الـ Type 2 و لسه مادخلناش في التفاصيل
+
+428
+00:33:25,240 --> 00:33:30,590
+تبعهاأنا بتهيألي المحاضرة هذه احتمال تكون تلاتة
+
+429
+00:33:30,590 --> 00:33:38,090
+parts هحاول نسرع لأن المنهج عن جد طويل هجوموني على
+
+430
+00:33:38,090 --> 00:33:42,350
+ال assignment اللي حكيناهم يا جماعة ال assignment
+
+431
+00:33:42,350 --> 00:33:46,450
+مش انتجام منكم ال assignment حتى تجروا المادة و
+
+432
+00:33:46,450 --> 00:33:51,290
+تتبعوا معايا يعني يكفينا اللي احنا في جضية المنهج
+
+433
+00:33:51,290 --> 00:33:56,650
+وزي ما قلتلكوا انا حذر جدا ان كل فكرةفي الباطنة،
+
+434
+00:33:56,650 --> 00:33:59,730
+بغض النظر عن الامتحانات وبغض النظر عن العلامات،
+
+435
+00:33:59,730 --> 00:34:03,530
+وهي مهمة حقيقة، مش بتجلل من أهميتها، لكن بدي
+
+436
+00:34:03,530 --> 00:34:07,510
+المادة تهضمها، وهذا من خلال متابعتكم وراجعتكم
+
+437
+00:34:07,510 --> 00:34:10,970
+معايا أول بأول، ومش نترك المنهج لحد جاب الامتحان
+
+438
+00:34:10,970 --> 00:34:14,370
+بيوم، وبعدين نقعد نحكي، لأ هيك، بتتابعوا معايا جدر
+
+439
+00:34:14,370 --> 00:34:20,330
+الإمكانأنا بقدر ما انا حريص منكوا تاخدوا علامات و
+
+440
+00:34:20,330 --> 00:34:28,390
+تتوفجوا لكن حريص جدا انكوا تهضموا المادة طبعا مش
+
+441
+00:34:28,390 --> 00:34:32,730
+هقولكوا انه شئتم او أبيتم بدكوا تعرفوا باطنة و
+
+442
+00:34:32,730 --> 00:34:36,970
+بدكوا تعرفوا أطفال يعني هذا مافيش مجال لإلكوا
+
+443
+00:34:36,970 --> 00:34:39,630
+للحياة و هتتذكروني في يوم من الأيام يعطيكوا
+
+444
+00:34:39,630 --> 00:34:41,030
+العافية وسلامات
+