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0.9046875}, {"start": 344.61, "end": 344.83, "word": " احكي", "probability": 0.9586181640625}, {"start": 344.83, "end": 344.97, "word": " عن", "probability": 0.86279296875}, {"start": 344.97, "end": 345.47, "word": " مجموع", "probability": 0.9571533203125}, {"start": 345.47, "end": 345.89, "word": " عناصر", "probability": 0.9903971354166666}, {"start": 345.89, "end": 346.33, "word": " بينها", "probability": 0.9736328125}, {"start": 346.33, "end": 346.79, "word": " او", "probability": 0.92578125}, {"start": 346.79, "end": 347.15, "word": " scale", "probability": 0.213134765625}, {"start": 347.15, "end": 347.33, "word": " and", "probability": 0.87548828125}, {"start": 347.33, "end": 347.71, "word": " multiplication", "probability": 0.89453125}, {"start": 347.71, "end": 348.41, "word": " لالا", "probability": 0.5484212239583334}, {"start": 348.41, "end": 348.67, "word": " لالا", "probability": 0.9046223958333334}, {"start": 348.67, "end": 348.77, "word": " لالا", "probability": 0.8468424479166666}, {"start": 348.77, "end": 349.49, "word": " الان", "probability": 0.6552734375}, {"start": 349.49, "end": 349.85, "word": " صار", "probability": 0.828125}, {"start": 349.85, "end": 350.35, "word": " عندنا", "probability": 0.91357421875}, {"start": 350.35, "end": 350.59, "word": " اللي", "probability": 0.944580078125}, {"start": 350.59, "end": 350.99, "word": " هو", "probability": 0.99365234375}], "temperature": 1.0}, {"id": 14, "seek": 37376, "start": 351.28, "end": 373.76, "text": "عبارة عن norm وهذا عبارة عن norm فهذا عبارة عن vector space مشرّع إلى الحديث عن الجمع وعن الـ scalar multiplication بناء عليه بنفع أقول الآن على مجموع عناصر يعني بنفع أروح باتجاه اللي هو series نشوف كيف let xn be a sequence in a normed space X", "tokens": [3615, 3555, 9640, 3660, 18871, 2026, 37037, 15730, 6225, 3555, 9640, 3660, 18871, 2026, 6156, 3224, 15730, 6225, 3555, 9640, 3660, 18871, 8062, 1901, 37893, 2288, 11703, 3615, 30731, 21542, 16254, 12984, 18871, 25724, 2304, 3615, 4032, 3615, 1863, 2423, 39184, 39684, 27290, 44945, 16606, 47356, 44945, 5172, 3615, 5551, 39648, 6024, 48506, 15844, 3714, 7435, 2304, 45367, 18871, 33546, 2288, 37495, 22653, 44945, 5172, 3615, 5551, 32887, 5016, 4724, 9307, 7435, 40294, 13672, 1829, 31439, 2638, 8717, 8592, 38688, 9122, 33911, 718, 2031, 77, 312, 257, 8310, 294, 257, 2026, 292, 1901, 1783], "avg_logprob": -0.22039474374369572, "compression_ratio": 1.5714285714285714, "no_speech_prob": 5.960464477539062e-07, "words": [{"start": 351.28, "end": 352.02, "word": "عبارة", "probability": 0.9415283203125}, {"start": 352.02, "end": 352.22, "word": " عن", "probability": 0.9912109375}, {"start": 352.22, "end": 352.66, "word": " norm", "probability": 0.460205078125}, {"start": 352.66, "end": 353.08, "word": " وهذا", "probability": 0.721435546875}, {"start": 353.08, "end": 353.38, "word": " عبارة", "probability": 0.99609375}, {"start": 353.38, "end": 353.52, "word": " عن", "probability": 0.97021484375}, {"start": 353.52, "end": 353.86, "word": " norm", "probability": 0.1651611328125}, {"start": 353.86, "end": 354.44, "word": " فهذا", "probability": 0.5516764322916666}, {"start": 354.44, "end": 354.74, "word": " عبارة", "probability": 0.9935302734375}, {"start": 354.74, "end": 354.82, "word": " عن", "probability": 0.98779296875}, {"start": 354.82, "end": 355.04, "word": " vector", "probability": 0.87890625}, {"start": 355.04, "end": 355.62, "word": " space", "probability": 0.94287109375}, {"start": 355.62, "end": 357.04, "word": " مشرّع", "probability": 0.7738037109375}, {"start": 357.04, "end": 357.32, "word": " إلى", "probability": 0.38818359375}, {"start": 357.32, "end": 358.0, "word": " الحديث", "probability": 0.9842122395833334}, {"start": 358.0, "end": 358.24, "word": " عن", "probability": 0.98876953125}, {"start": 358.24, "end": 358.74, "word": " الجمع", "probability": 0.8193359375}, {"start": 358.74, "end": 359.32, "word": " وعن", "probability": 0.8741861979166666}, {"start": 359.32, "end": 359.6, "word": " الـ", "probability": 0.5462646484375}, {"start": 359.6, "end": 359.94, "word": " scalar", "probability": 0.7451171875}, {"start": 359.94, "end": 360.62, "word": " multiplication", "probability": 0.80517578125}, {"start": 360.62, "end": 361.56, "word": " بناء", "probability": 0.922607421875}, {"start": 361.56, "end": 362.16, "word": " عليه", "probability": 0.63916015625}, {"start": 362.16, "end": 363.1, "word": " بنفع", "probability": 0.83984375}, {"start": 363.1, "end": 363.5, "word": " أقول", "probability": 0.841796875}, {"start": 363.5, "end": 364.1, "word": " الآن", "probability": 0.775390625}, {"start": 364.1, "end": 364.54, "word": " على", "probability": 0.85009765625}, {"start": 364.54, "end": 365.02, "word": " مجموع", "probability": 0.947265625}, {"start": 365.02, "end": 365.6, "word": " عناصر", "probability": 0.9915364583333334}, {"start": 365.6, "end": 365.9, "word": " يعني", "probability": 0.862548828125}, {"start": 365.9, "end": 366.44, "word": " بنفع", "probability": 0.8942057291666666}, {"start": 366.44, "end": 366.82, "word": " أروح", "probability": 0.9554036458333334}, {"start": 366.82, "end": 367.46, "word": " باتجاه", "probability": 0.9190673828125}, {"start": 367.46, "end": 367.66, "word": " اللي", "probability": 0.703369140625}, {"start": 367.66, "end": 367.8, "word": " هو", "probability": 0.984375}, {"start": 367.8, "end": 368.3, "word": " series", "probability": 0.8388671875}, {"start": 368.3, "end": 369.0, "word": " نشوف", "probability": 0.8585611979166666}, {"start": 369.0, "end": 369.68, "word": " كيف", "probability": 0.9814453125}, {"start": 369.68, "end": 370.96, "word": " let", "probability": 0.39306640625}, {"start": 370.96, "end": 371.44, "word": " xn", "probability": 0.3624267578125}, {"start": 371.44, "end": 371.6, "word": " be", "probability": 0.890625}, {"start": 371.6, "end": 371.8, "word": " a", "probability": 0.94580078125}, {"start": 371.8, "end": 372.28, "word": " sequence", "probability": 0.97705078125}, {"start": 372.28, "end": 372.56, "word": " in", "probability": 0.953125}, {"start": 372.56, "end": 372.74, "word": " a", "probability": 0.953125}, {"start": 372.74, "end": 373.12, "word": " normed", "probability": 0.9130859375}, {"start": 373.12, "end": 373.4, "word": " space", "probability": 0.783203125}, {"start": 373.4, "end": 373.76, "word": " X", "probability": 0.712890625}], "temperature": 1.0}, {"id": 15, "seek": 39923, "start": 374.47, "end": 399.23, "text": "and let S1 be a sequence of partial sums يعني S1 بيساوي X1 S2 بيساوي X1 زي X2 S3 بيساوي X1 زي X2 زي X3 S1 in general X1 زي X2 زي XN صارت هذه الـ S1 عبارة عن sequence of partial sums زي اللي أخدناها في الكالكولاست العادى بس كنا احنا اللي عارية نشتغل", "tokens": [474, 718, 318, 16, 312, 257, 8310, 295, 14641, 34499, 37495, 22653, 318, 16, 4724, 1829, 3794, 995, 45865, 1783, 16, 318, 17, 4724, 1829, 3794, 995, 45865, 1783, 16, 30767, 1829, 1783, 17, 318, 18, 4724, 1829, 3794, 995, 45865, 1783, 16, 30767, 1829, 1783, 17, 30767, 1829, 1783, 18, 318, 16, 294, 2674, 1783, 16, 30767, 1829, 1783, 17, 30767, 1829, 1783, 45, 20328, 9640, 2655, 29538, 2423, 39184, 318, 16, 6225, 3555, 9640, 3660, 18871, 8310, 295, 14641, 34499, 30767, 1829, 13672, 1829, 5551, 9778, 3215, 8315, 11296, 8978, 33251, 6027, 4117, 12610, 995, 14851, 18863, 18513, 7578, 4724, 3794, 9122, 8315, 1975, 5016, 8315, 13672, 1829, 6225, 9640, 10632, 8717, 8592, 2655, 17082, 1211], "avg_logprob": -0.19012605643072047, "compression_ratio": 1.76, "no_speech_prob": 0.181640625, "words": [{"start": 374.47, "end": 374.89, "word": "and", "probability": 0.4765625}, {"start": 374.89, "end": 375.29, "word": " let", "probability": 0.931640625}, {"start": 375.29, "end": 375.83, "word": " S1", "probability": 0.40081787109375}, {"start": 375.83, "end": 376.25, "word": " be", "probability": 0.8193359375}, {"start": 376.25, "end": 377.37, "word": " a", "probability": 0.93310546875}, {"start": 377.37, "end": 377.89, "word": " sequence", "probability": 0.96435546875}, {"start": 377.89, "end": 378.15, "word": " of", "probability": 0.9794921875}, {"start": 378.15, "end": 378.55, "word": " partial", "probability": 0.92431640625}, {"start": 378.55, "end": 379.03, "word": " sums", "probability": 0.9384765625}, {"start": 379.03, "end": 379.49, "word": " يعني", "probability": 0.7049560546875}, {"start": 379.49, "end": 380.11, "word": " S1", "probability": 0.94580078125}, {"start": 380.11, "end": 380.47, "word": " بيساوي", "probability": 0.475390625}, {"start": 380.47, "end": 381.05, "word": " X1", "probability": 0.94091796875}, {"start": 381.05, "end": 382.03, "word": " S2", "probability": 0.899169921875}, {"start": 382.03, "end": 382.47, "word": " بيساوي", "probability": 0.97666015625}, {"start": 382.47, "end": 382.93, "word": " X1", "probability": 0.9853515625}, {"start": 382.93, "end": 383.11, "word": " زي", "probability": 0.810791015625}, {"start": 383.11, "end": 383.73, "word": " X2", "probability": 0.9560546875}, {"start": 383.73, "end": 384.63, "word": " S3", "probability": 0.93310546875}, {"start": 384.63, "end": 384.99, "word": " بيساوي", "probability": 0.97080078125}, {"start": 384.99, "end": 385.45, "word": " X1", "probability": 0.99267578125}, {"start": 385.45, "end": 385.67, "word": " زي", "probability": 0.93603515625}, {"start": 385.67, "end": 386.11, "word": " X2", "probability": 0.9912109375}, {"start": 386.11, "end": 386.31, "word": " زي", "probability": 0.9931640625}, {"start": 386.31, "end": 386.91, "word": " X3", "probability": 0.997314453125}, {"start": 386.91, "end": 387.79, "word": " S1", "probability": 0.7529296875}, {"start": 387.79, "end": 388.03, "word": " in", "probability": 0.95751953125}, {"start": 388.03, "end": 388.53, "word": " general", "probability": 0.90869140625}, {"start": 388.53, "end": 389.41, "word": " X1", "probability": 0.908203125}, {"start": 389.41, "end": 389.63, "word": " زي", "probability": 0.96337890625}, {"start": 389.63, "end": 390.09, "word": " X2", "probability": 0.971435546875}, {"start": 390.09, "end": 390.31, "word": " زي", "probability": 0.99462890625}, {"start": 390.31, "end": 390.61, "word": " XN", "probability": 0.798583984375}, {"start": 390.61, "end": 390.99, "word": " صارت", "probability": 0.9264322916666666}, {"start": 390.99, "end": 391.25, "word": " هذه", "probability": 0.80126953125}, {"start": 391.25, "end": 391.37, "word": " الـ", "probability": 0.7177734375}, {"start": 391.37, "end": 391.69, "word": " S1", "probability": 0.877197265625}, {"start": 391.69, "end": 392.11, "word": " عبارة", "probability": 0.99560546875}, {"start": 392.11, "end": 392.37, "word": " عن", "probability": 0.99658203125}, {"start": 392.37, "end": 393.21, "word": " sequence", "probability": 0.93994140625}, {"start": 393.21, "end": 393.77, "word": " of", "probability": 0.9765625}, {"start": 393.77, "end": 394.21, "word": " partial", "probability": 0.92578125}, {"start": 394.21, "end": 394.79, "word": " sums", "probability": 0.921875}, {"start": 394.79, "end": 395.47, "word": " زي", "probability": 0.98681640625}, {"start": 395.47, "end": 395.59, "word": " اللي", "probability": 0.974609375}, {"start": 395.59, "end": 395.97, "word": " أخدناها", "probability": 0.89990234375}, {"start": 395.97, "end": 396.07, "word": " في", "probability": 0.93408203125}, {"start": 396.07, "end": 396.57, "word": " الكالكولاست", "probability": 0.6195271809895834}, {"start": 396.57, "end": 396.97, "word": " العادى", "probability": 0.82666015625}, {"start": 396.97, "end": 397.15, "word": " بس", "probability": 0.906494140625}, {"start": 397.15, "end": 397.43, "word": " كنا", "probability": 0.98193359375}, {"start": 397.43, "end": 397.81, "word": " احنا", "probability": 0.8958333333333334}, {"start": 397.81, "end": 398.23, "word": " اللي", "probability": 0.6571044921875}, {"start": 398.23, "end": 398.65, "word": " عارية", "probability": 0.3901774088541667}, {"start": 398.65, "end": 399.23, "word": " نشتغل", "probability": 0.98818359375}], "temperature": 1.0}, {"id": 16, "seek": 42434, "start": 404.56, "end": 424.34, "text": "إذا كان الـ S مرتبط بـ S فإن الـ Infinite Series Summation XI قد يكون مرتبط بـ S وS يسمى بالنسبة للعدة من السلسلين وقال S بالسلمانية XI يعني اللي بيقوله لو عندي أن أعرف شو معنات السلسلين مرتبط", "tokens": [28814, 15730, 25961, 2423, 39184, 318, 3714, 43500, 3555, 9566, 4724, 39184, 318, 6156, 28814, 1863, 2423, 39184, 43368, 13934, 318, 40879, 399, 1783, 40, 12174, 3215, 7251, 30544, 3714, 43500, 3555, 9566, 4724, 39184, 318, 4032, 50, 7251, 38251, 7578, 20666, 1863, 35457, 3660, 24976, 3615, 41891, 9154, 21136, 1211, 3794, 1211, 9957, 4032, 4587, 6027, 318, 20666, 3794, 19528, 7649, 10632, 1783, 40, 37495, 22653, 13672, 1829, 4724, 1829, 39648, 3224, 45164, 18871, 16254, 14739, 5551, 3615, 28480, 13412, 2407, 20449, 8315, 2655, 21136, 1211, 3794, 1211, 9957, 3714, 43500, 3555, 9566], "avg_logprob": -0.6687499774129767, "compression_ratio": 1.6526315789473685, "no_speech_prob": 1.7881393432617188e-06, "words": [{"start": 404.56, "end": 405.28, "word": "إذا", "probability": 0.5960693359375}, {"start": 405.28, "end": 405.94, "word": " كان", "probability": 0.28076171875}, {"start": 405.94, "end": 405.94, "word": " الـ", "probability": 0.5015869140625}, {"start": 405.94, "end": 406.12, "word": " S", "probability": 0.71630859375}, {"start": 406.12, "end": 406.7, "word": " مرتبط", "probability": 0.517486572265625}, {"start": 406.7, "end": 407.12, "word": " بـ", "probability": 0.5814208984375}, {"start": 407.12, "end": 407.5, "word": " S", "probability": 0.51611328125}, {"start": 407.5, "end": 408.08, "word": " فإن", "probability": 0.4815673828125}, {"start": 408.08, "end": 408.08, "word": " الـ", "probability": 0.279815673828125}, {"start": 408.08, "end": 408.48, "word": " Infinite", "probability": 0.324951171875}, {"start": 408.48, "end": 408.9, "word": " Series", "probability": 0.73583984375}, {"start": 408.9, "end": 409.46, "word": " Summation", "probability": 0.5919596354166666}, {"start": 409.46, "end": 410.12, "word": " XI", "probability": 0.484619140625}, {"start": 410.12, "end": 410.94, "word": " قد", "probability": 0.26531982421875}, {"start": 410.94, "end": 411.58, "word": " يكون", "probability": 0.5560302734375}, {"start": 411.58, "end": 412.1, "word": " مرتبط", "probability": 0.8731689453125}, {"start": 412.1, "end": 412.48, "word": " بـ", "probability": 0.6773681640625}, {"start": 412.48, "end": 412.48, "word": " S", "probability": 0.7939453125}, {"start": 412.48, "end": 412.8, "word": " وS", "probability": 0.4351806640625}, {"start": 412.8, "end": 413.18, "word": " يسمى", "probability": 0.5802815755208334}, {"start": 413.18, "end": 413.86, "word": " بالنسبة", "probability": 0.59393310546875}, {"start": 413.86, "end": 414.18, "word": " للعدة", "probability": 0.2454833984375}, {"start": 414.18, "end": 414.48, "word": " من", "probability": 0.5087890625}, {"start": 414.48, "end": 415.06, "word": " السلسلين", "probability": 0.517578125}, {"start": 415.06, "end": 415.56, "word": " وقال", "probability": 0.30340576171875}, {"start": 415.56, "end": 415.76, "word": " S", "probability": 0.36474609375}, {"start": 415.76, "end": 416.64, "word": " بالسلمانية", "probability": 0.37314453125}, {"start": 416.64, "end": 417.14, "word": " XI", "probability": 0.79931640625}, {"start": 417.14, "end": 417.36, "word": " يعني", "probability": 0.817626953125}, {"start": 417.36, "end": 417.52, "word": " اللي", "probability": 0.958984375}, {"start": 417.52, "end": 418.4, "word": " بيقوله", "probability": 0.880615234375}, {"start": 418.4, "end": 419.34, "word": " لو", "probability": 0.625}, {"start": 419.34, "end": 420.62, "word": " عندي", "probability": 0.764404296875}, {"start": 420.62, "end": 421.64, "word": " أن", "probability": 0.1494140625}, {"start": 421.64, "end": 422.04, "word": " أعرف", "probability": 0.7994791666666666}, {"start": 422.04, "end": 422.32, "word": " شو", "probability": 0.678955078125}, {"start": 422.32, "end": 422.86, "word": " معنات", "probability": 0.758544921875}, {"start": 422.86, "end": 423.68, "word": " السلسلين", "probability": 0.82177734375}, {"start": 423.68, "end": 424.34, "word": " مرتبط", "probability": 0.8905029296875}], "temperature": 1.0}, {"id": 17, "seek": 44178, "start": 426.64, "end": 441.78, "text": "الان عند الـ sequence of partial sums S N اللي هي الـ S N بتساوي X 1 زائد X N هذا كله اللي موجود في الـ normed space طيب بنقول ان S N بتروح ل S", "tokens": [6027, 7649, 43242, 2423, 39184, 8310, 295, 14641, 34499, 318, 426, 13672, 1829, 39896, 2423, 39184, 318, 426, 39894, 3794, 995, 45865, 1783, 502, 30767, 16373, 3215, 1783, 426, 23758, 28242, 3224, 13672, 1829, 3714, 29245, 23328, 8978, 2423, 39184, 2026, 292, 1901, 23032, 1829, 3555, 44945, 39648, 16472, 318, 426, 39894, 32887, 5016, 5296, 318], "avg_logprob": -0.30975877611260666, "compression_ratio": 1.3164556962025316, "no_speech_prob": 8.344650268554688e-07, "words": [{"start": 426.64, "end": 427.3, "word": "الان", "probability": 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0.8411865234375}, {"start": 464.12, "end": 464.9, "word": " بساوي", "probability": 0.8648681640625}, {"start": 464.9, "end": 465.2, "word": " S", "probability": 0.884765625}, {"start": 465.2, "end": 465.3, "word": " و", "probability": 0.7021484375}, {"start": 465.3, "end": 465.58, "word": " بنقول", "probability": 0.917236328125}, {"start": 465.58, "end": 466.04, "word": " عنه", "probability": 0.968994140625}, {"start": 466.04, "end": 466.38, "word": " ال", "probability": 0.452880859375}, {"start": 466.38, "end": 466.96, "word": " sequence", "probability": 0.791015625}], "temperature": 1.0}, {"id": 19, "seek": 49296, "start": 467.2, "end": 492.96, "text": "الـ series في هذه الحالة converts to sum اللي هو element S هذا اللي هو sum of the series طيب إذا كان ال norm لـ X1 زاد norm لـ X2 زاد norm لـ X3 إلى ما لا نهاية بدل ما أجمع ال X1 و X2 و X3 بأجمع مين ال normات اللي هين و أسارتي اللي هى جمع عداد حقيقية موجبة إذا كان مجموح إن هدولة exist", "tokens": [6027, 39184, 2638, 8978, 29538, 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"end": 1097.04, "text": "Now assume that there is a sequence تانية αI of scalars such that X- α1 E1 زائد α2 E2 زائد αN EN بتروح لـ 0 أزن جثمين تنفيذ لان افترض انها اشمالها في واحدة تانية بتحقق نفس الشروط الأولى و بعدين اثبتلك انه هتطلع حد ال sequence αI هي نفسها مين لـ Xi I فبتكون خلاص is unique", "tokens": [13267, 6552, 300, 456, 307, 257, 8310, 6055, 7649, 10632, 5691, 40, 295, 15664, 685, 1270, 300, 1783, 12, 5691, 16, 462, 16, 30767, 16373, 3215, 5691, 17, 462, 17, 30767, 16373, 3215, 5691, 45, 462, 45, 39894, 32887, 5016, 5296, 39184, 1958, 5551, 11622, 1863, 10874, 12984, 2304, 9957, 6055, 1863, 41185, 8848, 5296, 7649, 1975, 5172, 2655, 43042, 16472, 11296, 1975, 8592, 2304, 6027, 11296, 8978, 36764, 24401, 3660, 6055, 7649, 10632, 39894, 5016, 4587, 4587, 8717, 36178, 25124, 32887, 9566, 16247, 12610, 7578, 4032, 39182, 9957, 1975, 12984, 3555, 2655, 23275, 16472, 3224, 8032, 2655, 9566, 1211, 3615, 11331, 3215, 2423, 8310, 5691, 40, 39896, 8717, 36178, 11296, 3714, 9957, 5296, 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صارت واضحة في ال X hat في ال X hat عملية الجمع كده باجي باجمع باخد X hat arbitrary هات و Y hat arbitrary هات", "tokens": [6027, 39184, 9052, 655, 1508, 6055, 3555, 3615, 1829, 6055, 47283, 3215, 11296, 4032, 38251, 1829, 11296, 11933, 1829, 8592, 3714, 6027, 11296, 1176, 2385, 11933, 15730, 6225, 42213, 10632, 25724, 2304, 3615, 20328, 9640, 2655, 4032, 46958, 5016, 3660, 8978, 2423, 1783, 2385, 8978, 2423, 1783, 2385, 6225, 42213, 10632, 25724, 2304, 3615, 9122, 3215, 3224, 4724, 26108, 1829, 4724, 26108, 2304, 3615, 4724, 47283, 3215, 1783, 2385, 23211, 8032, 9307, 4032, 398, 2385, 23211, 8032, 9307], "avg_logprob": -0.23219936520238466, "compression_ratio": 1.6728395061728396, "no_speech_prob": 1.6093254089355469e-06, "words": [{"start": 1756.36, "end": 1756.68, "word": "الـ", "probability": 0.628173828125}, {"start": 1756.68, "end": 1757.3, "word": " equivalence", "probability": 0.6583251953125}, {"start": 1757.3, "end": 1757.74, "word": " class", "probability": 0.96142578125}, 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1840.43, "word": " نشوف", "probability": 0.8257649739583334}, {"start": 1840.43, "end": 1841.09, "word": " كده", "probability": 0.9036458333333334}, {"start": 1841.09, "end": 1841.51, "word": " in", "probability": 0.61669921875}, {"start": 1841.51, "end": 1842.03, "word": " fact", "probability": 0.93603515625}, {"start": 1842.03, "end": 1842.69, "word": " لو", "probability": 0.9384765625}, {"start": 1842.69, "end": 1843.09, "word": " انت", "probability": 0.713134765625}, {"start": 1843.09, "end": 1843.57, "word": " اخترت", "probability": 0.9567057291666666}, {"start": 1843.57, "end": 1843.99, "word": " عشان", "probability": 0.9684244791666666}, {"start": 1843.99, "end": 1844.39, "word": " الجامع", "probability": 0.8468424479166666}, {"start": 1844.39, "end": 1844.53, "word": " اللي", "probability": 0.767822265625}, {"start": 1844.53, "end": 1844.81, "word": " قولنا", "probability": 0.8460286458333334}, {"start": 1844.81, "end": 1844.99, "word": " عنه", "probability": 0.987548828125}, {"start": 1844.99, "end": 1845.21, "word": " قبل", "probability": 0.964599609375}, {"start": 1845.21, "end": 1845.69, "word": " شوية", "probability": 0.92333984375}, {"start": 1845.69, "end": 1846.55, "word": " XN", "probability": 0.4400634765625}, {"start": 1846.55, "end": 1847.85, "word": " واخترت", "probability": 0.7430419921875}, {"start": 1847.85, "end": 1848.49, "word": " WN", "probability": 0.9072265625}, {"start": 1848.49, "end": 1848.93, "word": " معناته", "probability": 0.962890625}, {"start": 1848.93, "end": 1849.33, "word": " التنتين", "probability": 0.8048502604166666}, {"start": 1849.33, "end": 1849.47, "word": " في", "probability": 0.91064453125}, {"start": 1849.47, "end": 1849.59, "word": " نفس", "probability": 0.99267578125}, {"start": 1849.59, "end": 1849.69, "word": " ال", "probability": 0.88818359375}, {"start": 1849.69, "end": 1850.07, "word": " equivalence", "probability": 0.86083984375}, {"start": 1850.07, "end": 1850.53, "word": " class", "probability": 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"word": " عرفنا", "probability": 0.9718424479166666}, {"start": 1878.2, "end": 1878.28, "word": " ال", "probability": 0.93603515625}, {"start": 1878.28, "end": 1878.54, "word": " relation", "probability": 0.99462890625}, {"start": 1878.54, "end": 1878.88, "word": " المرة", "probability": 0.968994140625}, {"start": 1878.88, "end": 1879.36, "word": " الماضية", "probability": 0.99560546875}, {"start": 1879.36, "end": 1880.58, "word": " related", "probability": 0.97607421875}, {"start": 1880.58, "end": 1880.82, "word": " to", "probability": 0.97802734375}, {"start": 1880.82, "end": 1881.5, "word": " WN", "probability": 0.973388671875}], "temperature": 1.0}, {"id": 80, "seek": 190456, "start": 1882.18, "end": 1904.56, "text": "في حال كانت ال limit لل distance بين ال Xn و ال Wn إيش هتساوي؟ هتساوي سفر طب ما هي ال distance الآن إحنا بنحكي عن اللي هو norm ال metric هذا اللي الآن induced by the norm يعني بمعنى آخر norm ال Xn نقص Wn إيش هيساوي؟ limitه هيساوي سفر إذا لما Xn", "tokens": [41185, 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"probability": 0.9111328125}, {"start": 1906.04, "end": 1906.58, "word": " wn", "probability": 0.76708984375}, {"start": 1906.58, "end": 1907.06, "word": " معناته", "probability": 0.56787109375}, {"start": 1907.06, "end": 1907.3, "word": " اصبح", "probability": 0.4447021484375}, {"start": 1907.3, "end": 1907.58, "word": " limit", "probability": 0.61181640625}, {"start": 1907.58, "end": 1908.12, "word": " xn", "probability": 0.45294189453125}, {"start": 1908.12, "end": 1909.84, "word": " نقص", "probability": 0.8006184895833334}, {"start": 1909.84, "end": 1910.14, "word": " wn", "probability": 0.359375}, {"start": 1910.14, "end": 1911.08, "word": " بساوي", "probability": 0.58795166015625}, {"start": 1911.08, "end": 1911.46, "word": " سفر", "probability": 0.7688802083333334}, {"start": 1911.46, "end": 1911.8, "word": " و", "probability": 0.4921875}, {"start": 1911.8, "end": 1912.18, "word": " limit", "probability": 0.806640625}, {"start": 1912.18, "end": 1913.28, "word": " yn", 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1972.71, "end": 1973.19, "word": " الحالة", "probability": 0.9842122395833334}, {"start": 1973.19, "end": 1973.55, "word": " إنه", "probability": 0.5245361328125}, {"start": 1973.55, "end": 1974.15, "word": " فعلا", "probability": 0.875}, {"start": 1974.15, "end": 1974.37, "word": " ال", "probability": 0.92333984375}, {"start": 1974.37, "end": 1974.57, "word": " Z", "probability": 0.93115234375}, {"start": 1974.57, "end": 1974.83, "word": " hat", "probability": 0.9892578125}, {"start": 1974.83, "end": 1975.13, "word": " بيساوي", "probability": 0.53182373046875}, {"start": 1975.13, "end": 1975.35, "word": " X", "probability": 0.85498046875}, {"start": 1975.35, "end": 1975.45, "word": " hat", "probability": 0.9619140625}, {"start": 1975.45, "end": 1975.63, "word": " زي", "probability": 0.796142578125}, {"start": 1975.63, "end": 1975.89, "word": " Y", "probability": 0.7080078125}, {"start": 1975.89, "end": 1976.33, "word": " hat", "probability": 0.97900390625}, {"start": 1976.33, "end": 1976.93, "word": " is", "probability": 0.814453125}, {"start": 1976.93, "end": 1977.41, "word": " well", "probability": 0.95947265625}, {"start": 1977.41, "end": 1978.01, "word": " defined", "probability": 0.7587890625}, {"start": 1978.01, "end": 1978.47, "word": " اطلع", "probability": 0.9508056640625}, {"start": 1978.47, "end": 1978.75, "word": " لفوق", "probability": 0.8123372395833334}, {"start": 1978.75, "end": 1979.15, "word": " شوية", "probability": 0.92822265625}], "temperature": 1.0}, {"id": 85, "seek": 200594, "start": 1979.86, "end": 2005.94, "text": "إذا نخلصنا من عملية الجمع اللي مبنية على اللي عندنا Similarly بالنسبة لمين we define the product Alpha X hat اللي هيكون element من X hat of a scalar Alpha and X hat to be the equivalence class for which Alpha X hat is representative إيش يعني؟ يعني بنفس الطريقة", "tokens": [28814, 15730, 8717, 9778, 1211, 9381, 8315, 9154, 6225, 42213, 10632, 2423, 7435, 2304, 3615, 13672, 1829, 3714, 3555, 1863, 10632, 15844, 13672, 1829, 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1983.8, "end": 1984.44, "word": " مبنية", "probability": 0.874267578125}, {"start": 1984.44, "end": 1984.72, "word": " على", "probability": 0.7607421875}, {"start": 1984.72, "end": 1985.8, "word": " اللي", "probability": 0.7607421875}, {"start": 1985.8, "end": 1986.24, "word": " عندنا", "probability": 0.80029296875}, {"start": 1986.24, "end": 1987.56, "word": " Similarly", "probability": 0.3818359375}, {"start": 1987.56, "end": 1989.26, "word": " بالنسبة", "probability": 0.915283203125}, {"start": 1989.26, "end": 1989.74, "word": " لمين", "probability": 0.7685546875}, {"start": 1989.74, "end": 1990.02, "word": " we", "probability": 0.1593017578125}, {"start": 1990.02, "end": 1990.7, "word": " define", "probability": 0.9560546875}, {"start": 1990.7, "end": 1990.9, "word": " the", "probability": 0.83251953125}, {"start": 1990.9, "end": 1991.46, "word": " product", "probability": 0.95068359375}, {"start": 1991.46, "end": 1991.94, "word": " Alpha", "probability": 0.270751953125}, {"start": 1991.94, "end": 1992.42, "word": " X", "probability": 0.853515625}, {"start": 1992.42, "end": 1992.86, "word": " hat", "probability": 0.5673828125}, {"start": 1992.86, "end": 1994.0, "word": " اللي", "probability": 0.7861328125}, {"start": 1994.0, "end": 1994.66, "word": " هيكون", "probability": 0.910888671875}, {"start": 1994.66, "end": 1995.04, "word": " element", "probability": 0.87548828125}, {"start": 1995.04, "end": 1995.28, "word": " من", "probability": 0.521484375}, {"start": 1995.28, "end": 1995.82, "word": " X", "probability": 0.481201171875}, {"start": 1995.82, "end": 1996.18, "word": " hat", "probability": 0.892578125}, {"start": 1996.18, "end": 1996.5, "word": " of", "probability": 0.75732421875}, {"start": 1996.5, "end": 1997.26, "word": " a", "probability": 0.8330078125}, {"start": 1997.26, "end": 1997.68, "word": " scalar", "probability": 0.85888671875}, {"start": 1997.68, "end": 1998.1, "word": " Alpha", "probability": 0.85888671875}, {"start": 1998.1, "end": 1998.4, "word": " and", "probability": 0.81005859375}, {"start": 1998.4, "end": 1998.64, "word": " X", "probability": 0.98828125}, {"start": 1998.64, "end": 1999.0, "word": " hat", "probability": 0.91064453125}, {"start": 1999.0, "end": 1999.46, "word": " to", "probability": 0.83837890625}, {"start": 1999.46, "end": 1999.66, "word": " be", "probability": 0.95361328125}, {"start": 1999.66, "end": 1999.8, "word": " the", "probability": 0.6826171875}, {"start": 1999.8, "end": 2000.34, "word": " equivalence", "probability": 0.877197265625}, {"start": 2000.34, "end": 2000.82, "word": " class", "probability": 0.9609375}, {"start": 2000.82, "end": 2001.08, "word": " for", "probability": 0.93603515625}, {"start": 2001.08, "end": 2001.36, "word": " which", "probability": 0.9130859375}, {"start": 2001.36, "end": 2001.7, "word": " Alpha", "probability": 0.94091796875}, {"start": 2001.7, "end": 2001.88, "word": " X", "probability": 0.96044921875}, {"start": 2001.88, "end": 2002.08, "word": " hat", "probability": 0.822265625}, {"start": 2002.08, "end": 2002.3, "word": " is", "probability": 0.9453125}, {"start": 2002.3, "end": 2003.04, "word": " representative", "probability": 0.751953125}, {"start": 2003.04, "end": 2003.8, "word": " إيش", "probability": 0.74853515625}, {"start": 2003.8, "end": 2004.6, "word": " يعني؟", "probability": 0.9161783854166666}, {"start": 2004.6, "end": 2005.1, "word": " يعني", "probability": 0.91064453125}, {"start": 2005.1, "end": 2005.42, "word": " بنفس", "probability": 0.9833984375}, {"start": 2005.42, "end": 2005.94, "word": " الطريقة", "probability": 0.9871419270833334}], "temperature": 1.0}, {"id": 86, "seek": 202166, "start": 2006.62, "end": 2021.66, "text": "عشان اعرف اللي هو شو معناته اخد x hat element in x hat واخد alpha scalar بده اعرف الآن عملية ال scalar multiplication في داخل ال x hat", "tokens": [3615, 8592, 7649, 1975, 3615, 28480, 13672, 1829, 31439, 13412, 2407, 20449, 8315, 47395, 1975, 9778, 3215, 2031, 2385, 4478, 294, 2031, 2385, 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product and vector addition اللي حكينا عنه قبل شوية in excel we have نحسب الآن احسبلي الآن alpha في ax زائد a من ay الان عندي بساوي ال a من وين جاية يا جماعة ال a اللي هي هذه", "tokens": [6027, 20292, 4077, 281, 2031, 293, 2423, 39184, 288, 2385, 39896, 6225, 3555, 9640, 3660, 18871, 28242, 2423, 39184, 22978, 4077, 24976, 39184, 17861, 538, 1228, 264, 7123, 295, 39684, 1674, 293, 8062, 4500, 13672, 1829, 11331, 4117, 1829, 8315, 18871, 3224, 12174, 36150, 13412, 2407, 10632, 294, 454, 4933, 321, 362, 8717, 5016, 35457, 6024, 48506, 1975, 5016, 35457, 20292, 6024, 48506, 8961, 8978, 6360, 30767, 16373, 3215, 257, 9154, 7494, 2423, 7649, 18871, 16254, 4724, 3794, 995, 45865, 2423, 257, 9154, 4032, 9957, 10874, 995, 10632, 35186, 10874, 15042, 27884, 2423, 257, 13672, 1829, 39896, 29538], "avg_logprob": -0.26420454485247835, "compression_ratio": 1.58, "no_speech_prob": 1.0788440704345703e-05, "words": [{"start": 2342.7, "end": 2343.12, "word": "اللي", "probability": 0.727783203125}, 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"end": 2356.4, "word": " الآن", "probability": 0.7015380859375}, {"start": 2356.4, "end": 2357.44, "word": " احسبلي", "probability": 0.66973876953125}, {"start": 2357.44, "end": 2357.66, "word": " الآن", "probability": 0.749267578125}, {"start": 2357.66, "end": 2358.04, "word": " alpha", "probability": 0.2880859375}, {"start": 2358.04, "end": 2358.28, "word": " في", "probability": 0.88427734375}, {"start": 2358.28, "end": 2358.58, "word": " ax", "probability": 0.7265625}, {"start": 2358.58, "end": 2359.0, "word": " زائد", "probability": 0.8282877604166666}, {"start": 2359.0, "end": 2359.26, "word": " a", "probability": 0.88427734375}, {"start": 2359.26, "end": 2359.42, "word": " من", "probability": 0.7119140625}, {"start": 2359.42, "end": 2360.28, "word": " ay", "probability": 0.82666015625}, {"start": 2360.28, "end": 2361.5, "word": " الان", "probability": 0.802001953125}, {"start": 2361.5, "end": 2362.74, "word": " عندي", "probability": 0.782958984375}, {"start": 2362.74, "end": 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2391.16, "end": 2391.52, "word": " ال", "probability": 0.94580078125}, {"start": 2391.52, "end": 2391.92, "word": " AX", "probability": 0.848876953125}, {"start": 2391.92, "end": 2392.2, "word": " وين", "probability": 0.5565185546875}, {"start": 2392.2, "end": 2392.3, "word": " هي", "probability": 0.53173828125}, {"start": 2392.3, "end": 2393.12, "word": " تروح؟", "probability": 0.8306884765625}], "temperature": 1.0}, {"id": 103, "seek": 241717, "start": 2393.45, "end": 2417.17, "text": "لـ Element في داخل الـ Main الـ W و الـ W لما كنا أخدنا الـ Element أخدناها الـ Main كل ال equivalency classes X و X و X و X و X ده بتتذكروا يعني بمعنى أخر اللي هي ال A X هي نفسها مين ال X hat هي عرفناها زائد A of Y مين هي ال Y hat", "tokens": [1211, 39184, 20900, 8978, 11778, 47283, 1211, 2423, 39184, 12383, 2423, 39184, 343, 4032, 2423, 39184, 343, 5296, 15042, 9122, 8315, 5551, 9778, 3215, 8315, 2423, 39184, 20900, 5551, 9778, 3215, 8315, 11296, 2423, 39184, 12383, 28242, 2423, 9052, 3020, 5359, 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"probability": 0.1702880859375}, {"start": 2514.05, "end": 2514.37, "word": " المرة", "probability": 0.939208984375}, {"start": 2514.37, "end": 2514.87, "word": " الماضية", "probability": 0.98876953125}, {"start": 2514.87, "end": 2514.99, "word": " بقى", "probability": 0.8074544270833334}, {"start": 2514.99, "end": 2515.87, "word": " ايضا", "probability": 0.804931640625}, {"start": 2515.87, "end": 2516.47, "word": " عندي", "probability": 0.7509765625}, {"start": 2516.47, "end": 2516.69, "word": " لان", "probability": 0.5947265625}, {"start": 2516.69, "end": 2517.07, "word": " خلينا", "probability": 0.7802734375}, {"start": 2517.07, "end": 2517.43, "word": " ناخد", "probability": 0.9781901041666666}, {"start": 2517.43, "end": 2517.65, "word": " بس", "probability": 0.6015625}, {"start": 2517.65, "end": 2518.23, "word": " هالشغل", "probability": 0.616796875}, {"start": 2518.23, "end": 2518.61, "word": " قبل", "probability": 0.758544921875}, {"start": 2518.61, "end": 2519.35, "word": " for", "probability": 0.697265625}, {"start": 2519.35, "end": 2519.69, "word": " y", "probability": 0.5}, {"start": 2519.69, "end": 2520.01, "word": " hat", "probability": 0.71728515625}, {"start": 2520.01, "end": 2520.51, "word": " بتساوي", "probability": 0.76007080078125}, {"start": 2520.51, "end": 2520.99, "word": " ay", "probability": 0.359130859375}, {"start": 2520.99, "end": 2521.51, "word": " ال", "probability": 0.802734375}, {"start": 2521.51, "end": 2521.79, "word": " ay", "probability": 0.445556640625}, {"start": 2521.79, "end": 2521.97, "word": " ايش", "probability": 0.7923990885416666}, {"start": 2521.97, "end": 2522.55, "word": " بنسميها", "probability": 0.8509521484375}, {"start": 2522.55, "end": 2523.31, "word": " احنا؟", "probability": 0.82952880859375}, {"start": 2523.31, "end": 2523.57, "word": " y", "probability": 0.666015625}, {"start": 2523.57, "end": 2524.01, "word": " hat", "probability": 0.95849609375}, {"start": 2524.01, "end": 2524.65, "word": " y", 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اللي من من؟ اللي من X ماشي هذا حكيناه المرة الماضية فالآن Y hat بيساوي A Y we have بدنا نعرف النورم 1 هالمين على W", "tokens": [28814, 15730, 39894, 2655, 8848, 37983, 14407, 5296, 15042, 12602, 4117, 11703, 3555, 8315, 11296, 2423, 39184, 398, 2385, 6225, 3555, 9640, 3660, 18871, 2423, 9052, 3020, 1508, 5296, 318, 398, 4032, 398, 4032, 398, 4032, 398, 13672, 1829, 41881, 5296, 9154, 22807, 5296, 2423, 39184, 17182, 5296, 2423, 39184, 398, 9307, 13672, 1829, 9154, 9154, 22807, 13672, 1829, 9154, 1783, 3714, 33599, 1829, 23758, 11331, 4117, 1829, 8315, 3224, 9673, 25720, 9673, 46958, 10632, 6156, 6027, 148, 48506, 398, 2385, 4724, 1829, 3794, 995, 45865, 316, 398, 321, 362, 47525, 8315, 8717, 3615, 28480, 28239, 13063, 2304, 502, 8032, 45340, 9957, 15844, 343], "avg_logprob": -0.32797620182945614, "compression_ratio": 1.611353711790393, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 2529.27, "end": 2529.53, "word": "إذا", "probability": 0.844482421875}, {"start": 2529.53, 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