diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/8Xs3EWM1_9g_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/8Xs3EWM1_9g_raw.json"
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+{"segments": [{"id": 1, "seek": 4476, "start": 21.62, "end": 44.76, "text": "طيب ناخد أمثلة كيف نجيب ال supremum و ال infimum لمجموعات جزئية من مجموعة الأعداد الحقيقية فلو أخدت الفترة المغلقة من سفر لواحد فعايز أفبت claim هنا ادعي ان ال supremum لست اسم سار واحد", "tokens": [9566, 1829, 3555, 8717, 47283, 3215, 5551, 2304, 12984, 37977, 9122, 33911, 8717, 7435, 1829, 3555, 2423, 23710, 449, 4032, 2423, 1536, 332, 449, 5296, 2304, 7435, 2304, 45367, 9307, 10874, 11622, 19986, 10632, 9154, 3714, 7435, 2304, 2407, 27884, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 6156, 1211, 2407, 5551, 9778, 3215, 2655, 27188, 2655, 25720, 9673, 17082, 1211, 28671, 9154, 8608, 5172, 2288, 5296, 14407, 24401, 6156, 3615, 47302, 11622, 5551, 5172, 3555, 2655, 3932, 34105, 1975, 3215, 3615, 1829, 16472, 2423, 23710, 449, 5296, 14851, 24525, 2304, 8608, 9640, 36764, 24401], "avg_logprob": -0.2215460529452876, "compression_ratio": 1.612565445026178, "no_speech_prob": 0.0, "words": [{"start": 21.62, 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supremum لتين مثال تالت احنا شفنا قبل شوية في بداية المحاضرة ان كل عدد حقيقي هو upper bound و كذلك lower bound ��لمجموع الخالي Phi و بناء على ذلك Phi does not have a supremum ولا infimum", "tokens": [2304, 2655, 5016, 4587, 4587, 46599, 6027, 2655, 6027, 1829, 36764, 24401, 31439, 2423, 23710, 449, 5296, 2655, 9957, 50113, 6027, 6055, 6027, 2655, 1975, 5016, 8315, 13412, 5172, 8315, 12174, 36150, 13412, 2407, 10632, 8978, 4724, 28259, 10632, 9673, 5016, 46958, 25720, 16472, 28242, 6225, 3215, 3215, 11331, 38436, 38436, 31439, 6597, 5472, 4032, 9122, 8848, 23275, 3126, 5472, 5296, 19528, 7435, 2304, 45367, 33962, 6027, 1829, 41435, 4032, 44945, 16606, 15844, 29910, 23275, 41435, 775, 406, 362, 257, 23710, 449, 49429, 1536, 332, 449], "avg_logprob": -0.15939295291900635, "compression_ratio": 1.5311004784688995, "no_speech_prob": 0.0, "words": [{"start": 332.69, "end": 333.49, "word": "متحقق", "probability": 0.96572265625}, {"start": 333.49, "end": 334.21, "word": " وبالتالي", 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423.53, "word": " five", "probability": 0.52294921875}], "temperature": 1.0}, {"id": 16, "seek": 44315, "start": 425.99, "end": 443.15, "text": "كمان مرة نفرض ان U جد U نفرض ان U جد U جد U بالنمط R و هو Supremum ل Phi طيب U سالب واحد أصغر من U", "tokens": [24793, 7649, 3714, 25720, 8717, 5172, 43042, 16472, 624, 10874, 3215, 624, 8717, 5172, 43042, 16472, 624, 10874, 3215, 624, 10874, 3215, 624, 20666, 1863, 2304, 9566, 497, 4032, 31439, 9141, 2579, 449, 5296, 41435, 23032, 1829, 3555, 624, 8608, 6027, 3555, 36764, 24401, 5551, 9381, 17082, 2288, 9154, 624], "avg_logprob": -0.3844975548632005, "compression_ratio": 1.3043478260869565, "no_speech_prob": 0.0, "words": [{"start": 425.99, "end": 426.43, "word": "كمان", "probability": 0.792724609375}, {"start": 426.43, "end": 426.83, "word": " مرة", "probability": 0.95263671875}, {"start": 426.83, "end": 427.43, "word": " نفرض", "probability": 0.8693033854166666}, {"start": 427.43, "end": 427.65, "word": " ان", "probability": 0.50244140625}, 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472.34, "text": "و قبل شوية كنا ملاحظة ان اي عدد حقيقي زي هذا عبارة عن upper bound لفائي ف K في ال U .. 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supremum أو ال completeness property خاصية التمام للأعداد الحقيقية الآن زي ما قلتلكم قبل هيك في توقع ما بين ال upper bounds و ال lower bounds ال supremums و ال infimums", "tokens": [28814, 1829, 8592, 31439, 22807, 6225, 8592, 7649, 8717, 7435, 1829, 3555, 3224, 5296, 31377, 2304, 8717, 25957, 1211, 4724, 2288, 3224, 7649, 30767, 1829, 19446, 13412, 38688, 8315, 8978, 16247, 2304, 12984, 37977, 21136, 16758, 28671, 8032, 3215, 39896, 2423, 23710, 449, 34051, 2423, 1557, 15264, 4707, 16490, 33546, 10632, 16712, 2304, 10943, 24976, 10721, 22488, 18513, 21542, 38436, 4587, 10632, 6024, 48506, 30767, 1829, 19446, 12174, 1211, 2655, 23275, 2304, 12174, 36150, 39896, 4117, 8978, 33427, 4587, 3615, 19446, 49374, 2423, 6597, 29905, 4032, 2423, 3126, 29905, 2423, 23710, 8099, 4032, 2423, 1536, 332, 8099], "avg_logprob": -0.18000637998386304, "compression_ratio": 1.6359649122807018, "no_speech_prob": 0.0, "words": [{"start": 561.51, "end": 561.89, "word": "إيش", "probability": 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"probability": 0.8765869140625}, {"start": 574.49, "end": 575.73, "word": " الآن", "probability": 0.74560546875}, {"start": 575.73, "end": 575.97, "word": " زي", "probability": 0.9814453125}, {"start": 575.97, "end": 576.03, "word": " ما", "probability": 0.986328125}, {"start": 576.03, "end": 576.53, "word": " قلتلكم", "probability": 0.94873046875}, {"start": 576.53, "end": 576.83, "word": " قبل", "probability": 0.888671875}, {"start": 576.83, "end": 577.25, "word": " هيك", "probability": 0.97314453125}, {"start": 577.25, "end": 577.49, "word": " في", "probability": 0.7939453125}, {"start": 577.49, "end": 578.01, "word": " توقع", "probability": 0.68798828125}, {"start": 578.01, "end": 578.17, "word": " ما", "probability": 0.91650390625}, {"start": 578.17, "end": 578.51, "word": " بين", "probability": 0.9833984375}, {"start": 578.51, "end": 579.35, "word": " ال", "probability": 0.92431640625}, {"start": 579.35, "end": 579.61, "word": " upper", "probability": 0.82666015625}, {"start": 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completeness property corollary", "tokens": [5172, 6027, 4386, 2423, 4386, 1975, 1829, 16490, 33546, 10632, 20328, 5016, 1829, 5016, 3660, 24976, 27756, 39894, 30544, 8978, 4724, 4587, 16758, 1211, 11296, 16490, 33546, 10632, 20328, 5016, 1829, 5016, 3660, 24976, 1536, 332, 449, 6156, 41185, 8717, 31371, 7435, 3660, 34105, 15844, 1557, 15264, 4707, 1181, 1833, 822], "avg_logprob": -0.16466346268470472, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 585.11, "end": 585.97, "word": "فال", "probability": 0.69482421875}, {"start": 585.97, "end": 586.11, "word": " ..", "probability": 0.7919921875}, {"start": 586.11, "end": 587.67, "word": " ال", "probability": 0.90185546875}, {"start": 587.67, "end": 588.23, "word": " ..", "probability": 0.97802734375}, {"start": 588.23, "end": 589.35, "word": " اي", "probability": 0.648681640625}, {"start": 589.35, "end": 590.11, "word": " خاصية", "probability": 0.96728515625}, {"start": 590.11, "end": 591.95, "word": " صحيحة", 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"probability": 0.9921875}, {"start": 1117.83, "end": 1118.55, "word": " وبالتالي", "probability": 0.90107421875}, {"start": 1118.55, "end": 1119.23, "word": " هذا", "probability": 0.9482421875}, {"start": 1119.23, "end": 1119.79, "word": " التناقض", "probability": 0.9921875}, {"start": 1119.79, "end": 1120.13, "word": " بيقول", "probability": 0.9191080729166666}, {"start": 1120.13, "end": 1120.27, "word": " لي", "probability": 0.5966796875}, {"start": 1120.27, "end": 1120.41, "word": " أن", "probability": 0.5966796875}, {"start": 1120.41, "end": 1120.97, "word": " الفرض", "probability": 0.77294921875}, {"start": 1120.97, "end": 1122.05, "word": " الفرض", "probability": 0.820556640625}, {"start": 1122.05, "end": 1122.55, "word": " تبعنا", "probability": 0.9375}, {"start": 1122.55, "end": 1122.99, "word": " هذا", "probability": 0.96923828125}], "temperature": 1.0}, {"id": 42, "seek": 114950, "start": 1125.58, "end": 1149.5, "text": "إن small s is not lower bound كان فرض خطأ إذا لازم يكون s lower bound وهذا بيكمل برهان ال claim تمام؟ في ال section القادم", "tokens": [28814, 1863, 1359, 262, 307, 406, 3126, 5472, 25961, 6156, 43042, 16490, 9566, 10721, 11933, 15730, 5296, 31377, 2304, 7251, 30544, 262, 3126, 5472, 37037, 15730, 4724, 1829, 24793, 1211, 4724, 2288, 3224, 7649, 2423, 3932, 46811, 10943, 22807, 8978, 2423, 3541, 25062, 18513, 2304], "avg_logprob": -0.23963995277881622, "compression_ratio": 1.2681159420289856, "no_speech_prob": 0.0, "words": [{"start": 1125.58, "end": 1125.94, "word": "إن", "probability": 0.6231689453125}, {"start": 1125.94, "end": 1126.48, "word": " small", "probability": 0.6396484375}, {"start": 1126.48, "end": 1127.04, "word": " s", "probability": 0.6513671875}, {"start": 1127.04, "end": 1128.26, "word": " is", "probability": 0.85302734375}, {"start": 1128.26, "end": 1128.6, "word": " not", "probability": 0.958984375}, {"start": 1128.6, "end": 1128.94, "word": " lower", "probability": 0.88623046875}, {"start": 1128.94, "end": 1129.28, 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0.27301025390625}, {"start": 1158.53, "end": 1159.19, "word": " property", "probability": 0.9677734375}, {"start": 1159.19, "end": 1164.41, "word": " فالتطبيقات", "probability": 0.8894391741071429}, {"start": 1164.41, "end": 1164.63, "word": " هذه", "probability": 0.5791015625}, {"start": 1164.63, "end": 1165.05, "word": " هتكون", "probability": 0.9402669270833334}, {"start": 1165.05, "end": 1165.25, "word": " على", "probability": 0.95556640625}, {"start": 1165.25, "end": 1165.67, "word": " شكل", "probability": 0.98583984375}, {"start": 1165.67, "end": 1166.71, "word": " أمثلة", "probability": 0.9542236328125}, {"start": 1166.71, "end": 1175.23, "word": " فمثلا", "probability": 0.913330078125}, {"start": 1175.23, "end": 1175.59, "word": " أول", "probability": 0.84375}, {"start": 1175.59, "end": 1176.27, "word": " تطبيق", "probability": 0.9854736328125}], "temperature": 1.0}, {"id": 44, "seek": 120486, "start": 1177.33, "end": 1204.87, "text": "لو أخدت أي subset من R و bounded above و A أي عدد حقيقي فمنعرف A زائد capital S على أنه مجموعة كل العناصر على الصورة A plus X حيث X ينتمي لS الآن ممكن أثبت أن ال supremum للمجموعة هذه هو عبارة عن A زائد ال supremum لS", "tokens": [1211, 2407, 5551, 9778, 3215, 2655, 36632, 25993, 9154, 497, 4032, 37498, 3673, 4032, 316, 36632, 6225, 3215, 3215, 11331, 38436, 38436, 6156, 27842, 3615, 28480, 316, 30767, 16373, 3215, 4238, 318, 15844, 14739, 3224, 3714, 7435, 2304, 2407, 27884, 28242, 18863, 8315, 9381, 2288, 15844, 31767, 13063, 3660, 316, 1804, 1783, 11331, 1829, 12984, 1783, 7251, 29399, 2304, 1829, 5296, 50, 6024, 48506, 3714, 43020, 5551, 12984, 3555, 2655, 14739, 2423, 23710, 449, 5296, 19528, 7435, 2304, 2407, 27884, 29538, 31439, 6225, 3555, 9640, 3660, 18871, 316, 30767, 16373, 3215, 2423, 23710, 449, 5296, 50], "avg_logprob": -0.17992912862718718, "compression_ratio": 1.5395348837209302, "no_speech_prob": 0.0, "words": [{"start": 1177.33, "end": 1177.67, "word": "لو", "probability": 0.81640625}, {"start": 1177.67, 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"word": " حقيقي", "probability": 0.9873046875}, {"start": 1184.97, "end": 1185.85, "word": " فمنعرف", "probability": 0.8419189453125}, {"start": 1185.85, "end": 1186.33, "word": " A", "probability": 0.66015625}, {"start": 1186.33, "end": 1186.99, "word": " زائد", "probability": 0.546875}, {"start": 1186.99, "end": 1187.61, "word": " capital", "probability": 0.64501953125}, {"start": 1187.61, "end": 1188.07, "word": " S", "probability": 0.9736328125}, {"start": 1188.07, "end": 1189.01, "word": " على", "probability": 0.79248046875}, {"start": 1189.01, "end": 1189.51, "word": " أنه", "probability": 0.656005859375}, {"start": 1189.51, "end": 1190.77, "word": " مجموعة", "probability": 0.97841796875}, {"start": 1190.77, "end": 1191.07, "word": " كل", "probability": 0.970703125}, {"start": 1191.07, "end": 1191.63, "word": " العناصر", "probability": 0.8228759765625}, {"start": 1191.63, "end": 1191.83, "word": " على", "probability": 0.58935546875}, {"start": 1191.83, "end": 1192.29, "word": " 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"start": 1207.46, "end": 1229.62, "text": "و هذا يعني البرهان مش صعب أيه بسيط وسهل نشوف مع بعض نفرض ان U هو ال suprem ل S ال set S is bounded above، إذن إلها suprem هذا مضمون حسب ال suprem property", "tokens": [2407, 23758, 37495, 22653, 2423, 26890, 3224, 7649, 37893, 20328, 3615, 3555, 36632, 3224, 4724, 3794, 1829, 9566, 46952, 3224, 1211, 8717, 8592, 38688, 20449, 45030, 11242, 8717, 5172, 43042, 16472, 624, 31439, 2423, 23710, 5296, 318, 2423, 992, 318, 307, 37498, 3673, 12399, 11933, 8848, 1863, 11933, 1211, 11296, 23710, 23758, 3714, 11242, 2304, 11536, 11331, 35457, 2423, 23710, 4707], "avg_logprob": -0.2797379142815067, "compression_ratio": 1.3987730061349692, "no_speech_prob": 0.0, "words": [{"start": 1207.46, "end": 1207.8, "word": "و", "probability": 0.90869140625}, {"start": 1207.8, "end": 1208.36, "word": " هذا", "probability": 0.425537109375}, {"start": 1208.36, "end": 1208.78, "word": " يعني", "probability": 0.94873046875}, {"start": 1208.78, "end": 1211.06, "word": " 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