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+{"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, 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"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, 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"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": " ��لفرض", "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, 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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, 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"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, 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284.02, "end": 285.04, "word": " إنه", "probability": 0.6064453125}, {"start": 285.04, "end": 285.14, "word": " لو", "probability": 0.429931640625}, {"start": 285.14, "end": 285.48, "word": " كانت", "probability": 0.974853515625}, {"start": 285.48, "end": 285.62, "word": " ال", "probability": 0.9716796875}, {"start": 285.62, "end": 285.92, "word": " series", "probability": 0.9619140625}, {"start": 285.92, "end": 286.34, "word": " yn", "probability": 0.37939453125}, {"start": 286.34, "end": 287.34, "word": " convergent", "probability": 0.83154296875}, {"start": 287.34, "end": 287.94, "word": " فلازم", "probability": 0.9569091796875}, {"start": 287.94, "end": 288.1, "word": " هذا", "probability": 0.34814453125}, {"start": 288.1, "end": 288.3, "word": " يطلع", "probability": 0.83294677734375}, {"start": 288.3, "end": 288.86, "word": " convergent", "probability": 0.890625}, {"start": 288.86, "end": 289.08, "word": " هذا", "probability": 0.67578125}, {"start": 289.08, "end": 289.6, "word": " 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, 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3660, 5296, 426, 6055, 25513, 10632, 4032, 8717, 34268, 26890, 14739, 29538, 2423, 2638, 13412, 21292, 3224, 3660, 34051, 36896, 411, 6055, 2655, 9381, 28480, 30767, 1829, 2423, 2638, 12771, 502, 15844, 426, 6055, 25513, 10632], "avg_logprob": -0.19856771433518994, "compression_ratio": 1.5340909090909092, "no_speech_prob": 0.0, "words": [{"start": 383.11, "end": 383.67, "word": "ممكن", "probability": 0.944091796875}, {"start": 383.67, "end": 384.79, "word": " نقارنها،", "probability": 0.8853759765625}, {"start": 384.79, "end": 385.17, "word": " الحد", "probability": 0.954833984375}, {"start": 385.17, "end": 385.49, "word": " العام", "probability": 0.97216796875}, {"start": 385.49, "end": 386.01, "word": " تبعها", "probability": 0.866943359375}, {"start": 386.01, "end": 387.67, "word": " هذا،", "probability": 0.578857421875}, {"start": 387.67, "end": 388.39, "word": " لما", "probability": 0.91259765625}, {"start": 388.39, "end": 388.61, "word": " N", "probability": 0.46484375}, {"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": " أن", "probability": 0.4404296875}, {"start": 396.41, "end": 396.71, "word": " هذه", "probability": 0.310302734375}, {"start": 396.71, "end": 396.89, "word": " ال", "probability": 0.93603515625}, {"start": 396.89, "end": 397.25, "word": " series", "probability": 0.93603515625}, {"start": 397.25, "end": 398.55, "word": " شبيهة", "probability": 0.8858642578125}, {"start": 398.55, "end": 399.05, "word": " أو", "probability": 0.65185546875}, {"start": 399.05, "end": 399.71, "word": " behaves", "probability": 0.79833984375}, {"start": 399.71, "end": 400.31, "word": " like", "probability": 0.94580078125}, {"start": 400.31, "end": 401.33, "word": " تتصرف", "probability": 0.9771728515625}, {"start": 401.33, "end": 402.55, "word": " زي", "probability": 0.82958984375}, {"start": 402.55, "end": 402.73, "word": " ال", "probability": 0.55517578125}, {"start": 402.73, "end": 403.07, "word": " series", "probability": 0.93212890625}, {"start": 403.07, "end": 403.85, "word": " sigma", "probability": 0.35888671875}, {"start": 403.85, "end": 404.35, "word": " 1", "probability": 0.5048828125}, {"start": 404.35, "end": 404.77, "word": " على", "probability": 0.7373046875}, {"start": 404.77, "end": 405.15, "word": " N", "probability": 0.947265625}, {"start": 405.15, "end": 405.65, "word": " تربية", "probability": 0.97216796875}], "temperature": 1.0}, {"id": 15, "seek": 42695, "start": 410.03, "end": 426.95, "text": "الان بنشوف إذا ممكن نطبق اختبار المقارنة المباشرة ال direct comparison test بنطبقه وإذا ما اقدرناش بنلجأ لاختبار تبع ال limit comparison test", "tokens": [6027, 7649, 44945, 8592, 38688, 11933, 15730, 3714, 43020, 8717, 9566, 3555, 4587, 1975, 46456, 3555, 9640, 9673, 4587, 9640, 1863, 3660, 9673, 3555, 33599, 25720, 2423, 2047, 9660, 1500, 44945, 9566, 3555, 4587, 3224, 4032, 28814, 15730, 19446, 1975, 28543, 2288, 1863, 33599, 44945, 1211, 7435, 10721, 5296, 47283, 2655, 3555, 9640, 6055, 3555, 3615, 2423, 4948, 9660, 1500], "avg_logprob": -0.20120388660274569, "compression_ratio": 1.5241379310344827, "no_speech_prob": 0.0, "words": [{"start": 410.03, "end": 410.41, "word": "الان", "probability": 0.785400390625}, {"start": 410.41, "end": 411.03, "word": " بنشوف", "probability": 0.8966471354166666}, {"start": 411.03, "end": 411.27, "word": " إذا", "probability": 0.7186279296875}, {"start": 411.27, "end": 411.59, "word": " ممكن", "probability": 0.97998046875}, {"start": 411.59, "end": 412.29, "word": " نطبق", "probability": 0.9224853515625}, {"start": 412.29, "end": 413.23, "word": " اختبار", "probability": 0.9224853515625}, {"start": 413.23, "end": 414.05, "word": " المقارنة", "probability": 0.990625}, {"start": 414.05, "end": 414.61, "word": " المباشرة", "probability": 0.8399658203125}, {"start": 414.61, "end": 414.75, "word": " ال", "probability": 0.67529296875}, {"start": 414.75, "end": 415.09, "word": " direct", "probability": 0.33154296875}, {"start": 415.09, "end": 416.31, "word": " comparison", "probability": 0.9150390625}, {"start": 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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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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": 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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 صحي�� 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, 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"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": " 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, 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{"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": " ��وجب", "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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0.8662109375}, {"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 ت��صرف 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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{"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}, 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"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, 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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, 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{"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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"probability": 0.9376953125}, {"start": 1777.3, "end": 1777.76, "word": " بيطلع", "probability": 0.736767578125}, {"start": 1777.76, "end": 1778.12, "word": " عدد", "probability": 0.9931640625}, {"start": 1778.12, "end": 1778.72, "word": " منتهي", "probability": 0.9734700520833334}, {"start": 1778.72, "end": 1780.3, "word": " فما", "probability": 0.851806640625}, {"start": 1780.3, "end": 1780.9, "word": " بأثرش", "probability": 0.806396484375}, {"start": 1780.9, "end": 1781.12, "word": " على", "probability": 0.41650390625}, {"start": 1781.12, "end": 1781.8, "word": " التقارب", "probability": 0.9971923828125}], "temperature": 1.0}, {"id": 66, "seek": 181003, "start": 1784.07, "end": 1810.03, "text": "من series بفرش على التقارب او التباعد او اضافة عدد لان بما ان ال series converges then ال series sigma واحد على n factorial converges من n بالساوية اربعة الى ملامية طبعا هذا بقدر", "tokens": [27842, 2638, 4724, 5172, 2288, 8592, 15844, 16712, 4587, 9640, 3555, 1975, 2407, 16712, 3555, 995, 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" تلاتة", "probability": 0.984619140625}, {"start": 2291.65, "end": 2292.79, "word": " السؤال", "probability": 0.9661458333333334}, {"start": 2292.79, "end": 2293.41, "word": " بيقول", "probability": 0.97802734375}, {"start": 2293.41, "end": 2297.01, "word": " can", "probability": 0.8798828125}, {"start": 2297.01, "end": 2297.45, "word": " you", "probability": 0.9677734375}, {"start": 2297.45, "end": 2298.97, "word": " السؤال", "probability": 0.97509765625}, {"start": 2298.97, "end": 2299.39, "word": " كتير", "probability": 0.9798177083333334}, {"start": 2299.39, "end": 2299.71, "word": " يعني", "probability": 0.96044921875}, {"start": 2299.71, "end": 2300.31, "word": " مهم", "probability": 0.9521484375}, {"start": 2300.31, "end": 2301.11, "word": " و", "probability": 0.99169921875}, {"start": 2301.11, "end": 2301.71, "word": " interesting", "probability": 0.89599609375}, {"start": 2301.71, "end": 2303.27, "word": " can", "probability": 0.92236328125}, {"start": 2303.27, "end": 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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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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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