diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.json"
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+++ "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/SrQnjpF43P0_raw.json"
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+{"segments": [{"id": 1, "seek": 4770, "start": 22.08, "end": 47.7, "text": "بسم الله الرحمن الرحيم ال .. هنواصل اليوم ان شاء الله ال .. ال .. الشئ اللي بدأناه بخصوص المقدمة عن ال infinite series بعتقد كانت أخر نظرية أخدناها هي Cauchy criterion", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 2423, 4386, 8032, 1863, 2407, 33546, 1211, 45595, 20498, 16472, 13412, 16606, 21984, 2423, 4386, 2423, 4386, 25124, 19986, 13672, 1829, 47525, 10721, 8315, 3224, 4724, 9778, 9381, 2407, 9381, 9673, 28543, 46007, 18871, 2423, 13785, 2638, 4724, 34268, 28543, 25961, 2655, 5551, 34740, 8717, 19913, 2288, 10632, 5551, 9778, 3215, 8315, 11296, 39896, 7544, 625, 88, 46691], "avg_logprob": -0.11351102645344593, "compression_ratio": 1.5227272727272727, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 22.080000000000002, "end": 23.32, "word": "بسم", "probability": 0.91748046875}, {"start": 23.32, "end": 23.46, "word": " الله", "probability": 0.96484375}, {"start": 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"word": " يوجد", "probability": 0.9724934895833334}, {"start": 93.79, "end": 94.75, "word": " capital", "probability": 0.77880859375}, {"start": 94.75, "end": 95.45, "word": " N", "probability": 0.7421875}, {"start": 95.45, "end": 97.35, "word": " يعتمد", "probability": 0.9371337890625}, {"start": 97.35, "end": 97.65, "word": " على", "probability": 0.88134765625}, {"start": 97.65, "end": 98.43, "word": " epsilon", "probability": 0.65185546875}, {"start": 98.43, "end": 100.19, "word": " عدد", "probability": 0.923828125}, {"start": 100.19, "end": 100.83, "word": " طبيعي", "probability": 0.968994140625}, {"start": 100.83, "end": 101.47, "word": " بحيث", "probability": 0.9090576171875}, {"start": 101.47, "end": 102.07, "word": " أنه", "probability": 0.744140625}], "temperature": 1.0}, {"id": 4, "seek": 12730, "start": 102.58, "end": 127.3, "text": "لو كان M أكبر من N أكبر من أو ساوي capital M فهذا بيقدي أنه absolute SM minus SN بساوي absolute XN زاد واحد زاد XN زاد اتنين و هكذا إلى XM", 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"end": 127.3, "word": " XM", "probability": 0.94140625}], "temperature": 1.0}, {"id": 5, "seek": 16041, "start": 131.64, "end": 160.42, "text": "النظرية هذه تبعت كوشي أخدناها المرة اللي فاتت و برهناها مظبوط اليوم هناخد نظرية تانية و مهمة و النظرية هذه بتقول انه let x in be sequence of non-negative real numbers then series", "tokens": [6027, 1863, 19913, 2288, 10632, 29538, 6055, 3555, 34268, 9122, 2407, 8592, 1829, 5551, 9778, 3215, 8315, 11296, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 4032, 4724, 2288, 3224, 8315, 11296, 3714, 19913, 3555, 2407, 9566, 45595, 20498, 8032, 1863, 47283, 3215, 8717, 19913, 2288, 10632, 6055, 7649, 10632, 4032, 3714, 16095, 3660, 4032, 28239, 19913, 2288, 10632, 29538, 39894, 39648, 16472, 3224, 718, 2031, 294, 312, 8310, 295, 2107, 12, 28561, 1166, 957, 3547, 550, 2638], "avg_logprob": -0.21814904476587588, "compression_ratio": 1.5251396648044693, "no_speech_prob": 0.0, "words": [{"start": 131.64, "end": 132.46, "word": "النظرية", "probability": 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149.12, "word": " be", "probability": 0.8056640625}, {"start": 149.12, "end": 149.96, "word": " sequence", "probability": 0.6181640625}, {"start": 149.96, "end": 151.36, "word": " of", "probability": 0.97998046875}, {"start": 151.36, "end": 151.66, "word": " non", "probability": 0.9306640625}, {"start": 151.66, "end": 152.1, "word": "-negative", "probability": 0.7692057291666666}, {"start": 152.1, "end": 152.38, "word": " real", "probability": 0.970703125}, {"start": 152.38, "end": 153.0, "word": " numbers", "probability": 0.89208984375}, {"start": 153.0, "end": 159.62, "word": " then", "probability": 0.69921875}, {"start": 159.62, "end": 160.42, "word": " series", "probability": 0.72216796875}], "temperature": 1.0}, {"id": 6, "seek": 18754, "start": 163.08, "end": 187.54, "text": "xn converges if and only if الsequence of partial sums its sequence of partial sums اللي هي sn is bounded", "tokens": [87, 77, 9652, 2880, 498, 293, 787, 498, 2423, 11834, 655, 295, 14641, 34499, 1080, 8310, 295, 14641, 34499, 13672, 1829, 39896, 2406, 307, 37498], "avg_logprob": -0.4134615453389975, "compression_ratio": 1.2696629213483146, "no_speech_prob": 0.0, "words": [{"start": 163.08, "end": 164.08, "word": "xn", "probability": 0.23931884765625}, {"start": 164.08, "end": 165.16, "word": " converges", "probability": 0.5767822265625}, {"start": 165.16, "end": 169.34, "word": " if", "probability": 0.87451171875}, {"start": 169.34, "end": 169.6, "word": " and", "probability": 0.92529296875}, {"start": 169.6, "end": 169.9, "word": " only", "probability": 0.908203125}, {"start": 169.9, "end": 170.32, "word": " if", "probability": 0.98486328125}, {"start": 170.32, "end": 172.26, "word": " الsequence", "probability": 0.6436360677083334}, {"start": 172.26, "end": 172.48, "word": " of", "probability": 0.96533203125}, {"start": 172.48, "end": 172.98, "word": " partial", "probability": 0.92333984375}, {"start": 172.98, "end": 173.5, "word": " sums", "probability": 0.9697265625}, {"start": 173.5, "end": 175.68, "word": " its", "probability": 0.2734375}, {"start": 175.68, "end": 176.46, "word": " sequence", "probability": 0.94921875}, {"start": 176.46, "end": 177.0, "word": " of", "probability": 0.9267578125}, {"start": 177.0, "end": 177.76, "word": " partial", "probability": 0.93701171875}, {"start": 177.76, "end": 179.0, "word": " sums", "probability": 0.958984375}, {"start": 179.0, "end": 185.6, "word": " اللي", "probability": 0.617431640625}, {"start": 185.6, "end": 185.88, "word": " هي", "probability": 0.681640625}, {"start": 185.88, "end": 186.6, "word": " sn", "probability": 0.5146484375}, {"start": 186.6, "end": 187.06, "word": " is", "probability": 0.912109375}, {"start": 187.06, "end": 187.54, "word": " bounded", "probability": 0.97998046875}], "temperature": 1.0}, {"id": 7, "seek": 21840, "start": 196.76, "end": 218.4, "text": "proof we have sn بساوي او sn زايد واحد بساوي sn زايد xn زايد واحد", "tokens": [15690, 321, 362, 2406, 4724, 3794, 995, 45865, 1975, 2407, 2406, 30767, 995, 25708, 36764, 24401, 4724, 3794, 995, 45865, 2406, 30767, 995, 25708, 2031, 77, 30767, 995, 25708, 36764, 24401], "avg_logprob": -0.16076660342514515, "compression_ratio": 1.5396825396825398, "no_speech_prob": 0.0, "words": [{"start": 196.76, "end": 198.16, "word": "proof", "probability": 0.455078125}, {"start": 198.16, "end": 199.56, "word": " we", "probability": 0.63037109375}, {"start": 199.56, "end": 201.04, "word": " have", "probability": 0.97900390625}, {"start": 201.04, "end": 204.08, "word": " sn", "probability": 0.662109375}, {"start": 204.08, "end": 205.26, "word": " بساوي", "probability": 0.7723388671875}, {"start": 205.26, "end": 206.14, "word": " او", "probability": 0.845947265625}, {"start": 206.14, "end": 206.86, "word": " sn", "probability": 0.9052734375}, {"start": 206.86, "end": 209.74, "word": " زايد", "probability": 0.7132975260416666}, {"start": 209.74, "end": 210.24, "word": " واحد", "probability": 0.963623046875}, {"start": 210.24, "end": 211.02, "word": " بساوي", "probability": 0.962890625}, {"start": 211.02, "end": 216.02, "word": " sn", "probability": 0.880859375}, {"start": 216.02, "end": 216.76, "word": " زايد", "probability": 0.93359375}, {"start": 216.76, "end": 217.54, "word": " xn", "probability": 0.87353515625}, {"start": 217.54, "end": 217.96, "word": " زايد", "probability": 0.98046875}, {"start": 217.96, "end": 218.4, "word": " واحد", "probability": 0.982177734375}], "temperature": 1.0}, {"id": 8, "seek": 22615, "start": 219.59, "end": 226.15, "text": "الان زاد فرص partial sum بيساوي الانف partial sum وبنضيف عليه لحد رقم ان زاد واحد", "tokens": [6027, 7649, 30767, 18513, 6156, 2288, 9381, 14641, 2408, 4724, 1829, 3794, 995, 45865, 2423, 7649, 5172, 14641, 2408, 46599, 1863, 11242, 33911, 47356, 5296, 24401, 12602, 4587, 2304, 16472, 30767, 18513, 36764, 24401], "avg_logprob": -0.4140624931880406, "compression_ratio": 1.2959183673469388, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 219.59, "end": 220.11, "word": "الان", "probability": 0.32806396484375}, {"start": 220.11, "end": 220.45, "word": " زاد", "probability": 0.56884765625}, {"start": 220.45, "end": 220.85, "word": " فرص", "probability": 0.4414876302083333}, {"start": 220.85, "end": 221.29, "word": " partial", "probability": 0.5634765625}, {"start": 221.29, "end": 221.61, "word": " sum", "probability": 0.81787109375}, {"start": 221.61, "end": 222.07, "word": " بيساوي", "probability": 0.6555419921875}, {"start": 222.07, "end": 222.47, "word": " الانف", "probability": 0.5662434895833334}, {"start": 222.47, "end": 222.79, "word": " partial", "probability": 0.76318359375}, {"start": 222.79, "end": 223.33, "word": " sum", "probability": 0.97119140625}, {"start": 223.33, "end": 224.37, "word": " وبنضيف", "probability": 0.81787109375}, {"start": 224.37, "end": 224.63, "word": " عليه", "probability": 0.9765625}, {"start": 224.63, "end": 224.95, "word": " لحد", "probability": 0.75244140625}, {"start": 224.95, "end": 225.37, "word": " رقم", "probability": 0.9801432291666666}, {"start": 225.37, "end": 225.57, "word": " ان", "probability": 0.5810546875}, {"start": 225.57, "end": 225.85, "word": " زاد", "probability": 0.888671875}, {"start": 225.85, "end": 226.15, "word": " واحد", "probability": 0.981201171875}], "temperature": 1.0}, {"id": 9, "seek": 26452, "start": 238.05, "end": 264.53, "text": "و طبعا ال Xn زاد واحد هذا احنا فرضين ان حدود ال sequence Xn كلها غير سالبة فهذا غير سالب وبالتالي المجموع هذا بالتأكيد اكبر من او سوى Sn لكل N في N فهذا معناه ان ال sequence Sn is increasing متزايدة", "tokens": [2407, 23032, 3555, 3615, 995, 2423, 1783, 77, 30767, 18513, 36764, 24401, 23758, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 11331, 3215, 23328, 2423, 8310, 1783, 77, 28242, 11296, 32771, 13546, 8608, 6027, 49401, 6156, 3224, 15730, 32771, 13546, 8608, 6027, 3555, 46599, 6027, 2655, 6027, 1829, 9673, 7435, 2304, 45367, 23758, 20666, 2655, 10721, 4117, 25708, 1975, 4117, 26890, 9154, 1975, 2407, 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0.9708658854166666}, {"start": 241.37, "end": 241.51, "word": " ان", "probability": 0.7060546875}, {"start": 241.51, "end": 241.89, "word": " حدود", "probability": 0.98779296875}, {"start": 241.89, "end": 242.07, "word": " ال", "probability": 0.93603515625}, {"start": 242.07, "end": 242.63, "word": " sequence", "probability": 0.923828125}, {"start": 242.63, "end": 243.87, "word": " Xn", "probability": 0.755859375}, {"start": 243.87, "end": 244.27, "word": " كلها", "probability": 0.9560546875}, {"start": 244.27, "end": 244.55, "word": " غير", "probability": 0.9970703125}, {"start": 244.55, "end": 245.05, "word": " سالبة", "probability": 0.8736979166666666}, {"start": 245.05, "end": 245.55, "word": " فهذا", "probability": 0.9274088541666666}, {"start": 245.55, "end": 245.85, "word": " غير", "probability": 0.994873046875}, {"start": 245.85, "end": 246.51, "word": " سالب", "probability": 0.9697265625}, {"start": 246.51, "end": 248.53, "word": " وبالتالي", "probability": 0.89951171875}, {"start": 248.53, "end": 249.07, "word": " المجموع", "probability": 0.9173583984375}, {"start": 249.07, "end": 249.41, "word": " هذا", "probability": 0.9287109375}, {"start": 249.41, "end": 250.31, "word": " بالتأكيد", "probability": 0.96845703125}, {"start": 250.31, "end": 250.85, "word": " اكبر", "probability": 0.83154296875}, {"start": 250.85, "end": 251.05, "word": " من", "probability": 0.931640625}, {"start": 251.05, "end": 251.25, "word": " او", "probability": 0.739990234375}, {"start": 251.25, "end": 251.69, "word": " سوى", "probability": 0.8484700520833334}, {"start": 251.69, "end": 252.23, "word": " Sn", "probability": 0.83447265625}, {"start": 252.23, "end": 254.11, "word": " لكل", "probability": 0.97998046875}, {"start": 254.11, "end": 254.39, "word": " N", "probability": 0.397705078125}, {"start": 254.39, "end": 254.59, "word": " في", "probability": 0.890625}, {"start": 254.59, "end": 254.79, "word": " N", "probability": 0.8193359375}, {"start": 254.79, "end": 257.87, "word": " فهذا", "probability": 0.9786783854166666}, {"start": 257.87, "end": 258.47, "word": " معناه", "probability": 0.9742838541666666}, {"start": 258.47, "end": 258.77, "word": " ان", "probability": 0.875}, {"start": 258.77, "end": 258.99, "word": " ال", "probability": 0.83056640625}, {"start": 258.99, "end": 259.37, "word": " sequence", "probability": 0.9833984375}, {"start": 259.37, "end": 260.35, "word": " Sn", "probability": 0.89208984375}, {"start": 260.35, "end": 261.91, "word": " is", "probability": 0.8525390625}, {"start": 261.91, "end": 262.79, "word": " increasing", "probability": 0.96875}, {"start": 262.79, "end": 264.53, "word": " متزايدة", "probability": 0.89111328125}], "temperature": 1.0}, {"id": 10, "seek": 28856, "start": 266.96, "end": 288.56, "text": "بالتالي، من خلال الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع الوضع", "tokens": [3555, 6027, 2655, 6027, 1829, 12399, 9154, 16490, 1211, 6027, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615, 2423, 2407, 11242, 3615], "avg_logprob": -0.5698529528636559, "compression_ratio": 3.111111111111111, "no_speech_prob": 0.0, "words": [{"start": 266.96000000000004, "end": 268.36, "word": "بالتالي،", "probability": 0.4211629231770833}, {"start": 268.36, "end": 268.44, "word": " من", "probability": 0.429931640625}, {"start": 268.44, "end": 268.78, "word": " خلال", "probability": 0.7412109375}, {"start": 268.78, "end": 268.78, "word": " الوضع", "probability": 0.441680908203125}, {"start": 268.78, "end": 269.36, "word": " الوضع", "probability": 0.428741455078125}, {"start": 269.36, "end": 269.76, "word": " الوضع", "probability": 0.58868408203125}, {"start": 269.76, "end": 269.8, "word": " الوضع", "probability": 0.7760009765625}, {"start": 269.8, "end": 270.48, "word": " الوضع", "probability": 0.82391357421875}, {"start": 270.48, "end": 271.44, "word": " الوضع", "probability": 0.865966796875}, {"start": 271.44, "end": 276.42, "word": " الوضع", "probability": 0.9134521484375}, {"start": 276.42, "end": 280.96, "word": " الوضع", "probability": 0.94677734375}, {"start": 280.96, "end": 283.34, "word": " الوضع", "probability": 0.9639892578125}, {"start": 283.34, "end": 288.56, "word": " الوضع", "probability": 0.9727783203125}], "temperature": 1.0}, {"id": 11, "seek": 32341, "start": 321.39, "end": 323.41, "text": "وهو المطلوب", "tokens": [2407, 3224, 2407, 9673, 9566, 1211, 37746], "avg_logprob": -0.3278808668255806, "compression_ratio": 0.7241379310344828, "no_speech_prob": 0.0, "words": [{"start": 321.39000000000004, "end": 322.79, "word": "وهو", "probability": 0.5489095052083334}, {"start": 322.79, "end": 323.41, "word": " المطلوب", "probability": 0.9825439453125}], "temperature": 1.0}, {"id": 12, "seek": 34951, "start": 325.89, "end": 349.51, "text": "أحنا أخدنا قبل هيك أن أي infinite series بتكون convergent if and only if the sequence of partial sums is convergent، صح؟ طيب، ال sequence of partial sums بمعنها increasing فهي convergent by monotone convergence theorem بتكون convergent if and only if it is bounded", "tokens": [10721, 5016, 8315, 5551, 9778, 3215, 8315, 12174, 36150, 39896, 4117, 14739, 36632, 13785, 2638, 39894, 30544, 9652, 6930, 498, 293, 787, 498, 264, 8310, 295, 14641, 34499, 307, 9652, 6930, 12399, 20328, 5016, 22807, 23032, 1829, 3555, 12399, 2423, 8310, 295, 14641, 34499, 4724, 2304, 3615, 1863, 11296, 5662, 6156, 3224, 1829, 9652, 6930, 538, 1108, 310, 546, 32181, 20904, 39894, 30544, 9652, 6930, 498, 293, 787, 498, 309, 307, 37498], "avg_logprob": -0.1565710632768396, "compression_ratio": 1.6421052631578947, "no_speech_prob": 0.0, "words": [{"start": 325.89, "end": 326.29, "word": "أحنا", "probability": 0.7166341145833334}, {"start": 326.29, "end": 326.67, "word": " أخدنا", "probability": 0.77520751953125}, {"start": 326.67, "end": 326.99, "word": " قبل", "probability": 0.903564453125}, {"start": 326.99, "end": 327.35, "word": " هيك", "probability": 0.705078125}, {"start": 327.35, "end": 327.55, "word": " أن", "probability": 0.7373046875}, {"start": 327.55, "end": 327.93, "word": " أي", "probability": 0.67138671875}, {"start": 327.93, "end": 328.31, "word": " infinite", "probability": 0.73486328125}, {"start": 328.31, "end": 328.77, "word": " series", "probability": 0.90087890625}, {"start": 328.77, "end": 329.19, "word": " بتكون", "probability": 0.929931640625}, {"start": 329.19, "end": 329.93, "word": " convergent", "probability": 0.86279296875}, {"start": 329.93, "end": 330.21, "word": " if", "probability": 0.78369140625}, {"start": 330.21, "end": 330.47, "word": " and", "probability": 0.8486328125}, {"start": 330.47, "end": 330.69, "word": " only", "probability": 0.9150390625}, {"start": 330.69, "end": 331.01, "word": " if", "probability": 0.982421875}, {"start": 331.01, "end": 331.79, "word": " the", "probability": 0.426025390625}, {"start": 331.79, "end": 332.23, "word": " sequence", "probability": 0.96044921875}, {"start": 332.23, "end": 332.51, "word": " of", "probability": 0.9765625}, {"start": 332.51, "end": 332.89, "word": " partial", "probability": 0.931640625}, {"start": 332.89, "end": 333.25, "word": " sums", "probability": 0.9501953125}, {"start": 333.25, "end": 333.49, "word": " is", "probability": 0.9404296875}, {"start": 333.49, "end": 334.13, "word": " convergent،", "probability": 0.8312174479166666}, {"start": 334.13, "end": 335.57, "word": " صح؟", "probability": 0.96240234375}, {"start": 335.57, "end": 336.07, "word": " طيب،", "probability": 0.896728515625}, {"start": 336.07, "end": 336.19, "word": " ال", "probability": 0.89306640625}, {"start": 336.19, "end": 336.45, "word": " sequence", "probability": 0.74951171875}, {"start": 336.45, "end": 336.81, "word": " of", "probability": 0.9833984375}, {"start": 336.81, "end": 337.19, "word": " partial", "probability": 0.9404296875}, {"start": 337.19, "end": 337.67, "word": " sums", "probability": 0.92529296875}, {"start": 337.67, "end": 338.21, "word": " بمعنها", "probability": 0.7478515625}, {"start": 338.21, "end": 338.91, "word": " increasing", "probability": 0.87353515625}, {"start": 338.91, "end": 341.37, "word": " فهي", "probability": 0.9402669270833334}, {"start": 341.37, "end": 342.33, "word": " convergent", "probability": 0.941162109375}, {"start": 342.33, "end": 342.65, "word": " by", "probability": 0.91650390625}, {"start": 342.65, "end": 343.17, "word": " monotone", "probability": 0.9327799479166666}, {"start": 343.17, "end": 343.77, "word": " convergence", "probability": 0.912109375}, {"start": 343.77, "end": 344.39, "word": " theorem", "probability": 0.84326171875}, {"start": 344.39, "end": 346.97, "word": " بتكون", "probability": 0.92236328125}, {"start": 346.97, "end": 347.75, "word": " convergent", "probability": 0.959228515625}, {"start": 347.75, "end": 348.05, "word": " if", "probability": 0.9794921875}, {"start": 348.05, "end": 348.29, "word": " and", "probability": 0.962890625}, {"start": 348.29, "end": 348.53, "word": " only", "probability": 0.9296875}, {"start": 348.53, "end": 348.79, "word": " if", "probability": 0.97509765625}, {"start": 348.79, "end": 348.97, "word": " it", "probability": 0.97314453125}, {"start": 348.97, "end": 349.17, "word": " is", "probability": 0.9580078125}, {"start": 349.17, "end": 349.51, "word": " bounded", "probability": 0.94970703125}], "temperature": 1.0}, {"id": 13, "seek": 37459, "start": 350.71, "end": 374.59, "text": "وبالتالي الـ series converges if and only if the sequence of partial sums is bounded وهذا يثبت النظرية تمام؟ إذن هذه النظرية أهميتها في أننا يعني تطبيقها زي ما هنشوف في لما هنا صغيرة لما", "tokens": [37746, 6027, 2655, 6027, 1829, 2423, 39184, 2638, 9652, 2880, 498, 293, 787, 498, 264, 8310, 295, 14641, 34499, 307, 37498, 37037, 15730, 7251, 12984, 3555, 2655, 28239, 19913, 2288, 10632, 46811, 10943, 22807, 11933, 8848, 1863, 29538, 28239, 19913, 2288, 10632, 5551, 16095, 36081, 11296, 8978, 14739, 8315, 37495, 22653, 6055, 9566, 21292, 4587, 11296, 30767, 1829, 19446, 8032, 1863, 8592, 38688, 8978, 5296, 15042, 34105, 20328, 17082, 48923, 5296, 15042], "avg_logprob": -0.24935787344632082, "compression_ratio": 1.4455958549222798, "no_speech_prob": 0.0, "words": [{"start": 350.71, "end": 351.61, "word": "وبالتالي", "probability": 0.89765625}, {"start": 351.61, "end": 351.87, "word": " الـ", "probability": 0.594970703125}, {"start": 351.87, "end": 352.13, "word": " series", "probability": 0.6220703125}, {"start": 352.13, "end": 352.81, "word": " converges", "probability": 0.894287109375}, {"start": 352.81, "end": 353.05, "word": " if", "probability": 0.9189453125}, {"start": 353.05, "end": 353.25, "word": " and", "probability": 0.845703125}, {"start": 353.25, "end": 353.49, "word": " only", "probability": 0.9287109375}, {"start": 353.49, "end": 353.71, "word": " if", "probability": 0.96484375}, {"start": 353.71, "end": 353.89, "word": " the", "probability": 0.724609375}, {"start": 353.89, "end": 354.25, "word": " sequence", "probability": 0.94921875}, {"start": 354.25, "end": 354.47, "word": " of", "probability": 0.94921875}, {"start": 354.47, "end": 354.77, "word": " partial", "probability": 0.923828125}, {"start": 354.77, "end": 355.21, "word": " sums", "probability": 0.86865234375}, {"start": 355.21, "end": 356.03, "word": " is", "probability": 0.94287109375}, {"start": 356.03, "end": 356.49, "word": " bounded", "probability": 0.92626953125}, {"start": 356.49, "end": 357.19, "word": " وهذا", "probability": 0.777099609375}, {"start": 357.19, "end": 358.37, "word": " يثبت", "probability": 0.8712158203125}, {"start": 358.37, "end": 359.35, "word": " النظرية", "probability": 0.925537109375}, {"start": 359.35, "end": 360.99, "word": " تمام؟", "probability": 0.5804341634114584}, {"start": 360.99, "end": 362.01, "word": " إذن", "probability": 0.5928548177083334}, {"start": 362.01, "end": 362.21, "word": 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for", "probability": 0.93505859375}], "temperature": 1.0}, {"id": 37, "seek": 108826, "start": 1060.68, "end": 1088.26, "text": "for K J بيساوي اتنين اقصد J سالب واحد we have S K J هيطلع اصغر من واحد زائد R زائد R ترمية زائد", "tokens": [2994, 591, 508, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 1975, 4587, 9381, 3215, 508, 8608, 6027, 3555, 36764, 24401, 321, 362, 318, 591, 508, 39896, 9566, 1211, 3615, 1975, 9381, 17082, 2288, 9154, 36764, 24401, 30767, 16373, 3215, 497, 30767, 16373, 3215, 497, 6055, 2288, 2304, 10632, 30767, 16373, 3215], "avg_logprob": -0.2290219846698973, "compression_ratio": 1.2820512820512822, "no_speech_prob": 0.0, "words": [{"start": 1060.68, "end": 1061.12, "word": "for", "probability": 0.57275390625}, {"start": 1061.12, "end": 1061.54, "word": " K", "probability": 0.50634765625}, {"start": 1061.54, "end": 1062.14, "word": " J", "probability": 0.2423095703125}, {"start": 1062.14, "end": 1063.74, "word": " بيساوي", "probability": 0.643408203125}, 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"probability": 0.6165771484375}, {"start": 1113.21, "end": 1113.75, "word": " واحد", "probability": 0.986328125}, {"start": 1113.75, "end": 1116.55, "word": " فطلع", "probability": 0.9593505859375}, {"start": 1116.55, "end": 1116.95, "word": " عندي", "probability": 0.84423828125}, {"start": 1116.95, "end": 1117.55, "word": " S", "probability": 0.96728515625}], "temperature": 1.0}, {"id": 39, "seek": 113616, "start": 1118.84, "end": 1136.16, "text": "ك واحد بيساوي واحد وأصغر من أو يساوي الواحد لما ك ج بيساوي اتنين لما ج بيساوي اتنين", "tokens": [4117, 36764, 24401, 4724, 1829, 3794, 995, 45865, 36764, 24401, 36725, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 995, 45865, 2423, 14407, 24401, 5296, 15042, 9122, 10874, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957, 5296, 15042, 10874, 4724, 1829, 3794, 995, 45865, 1975, 2655, 1863, 9957], "avg_logprob": -0.17044005588609346, "compression_ratio": 1.7738095238095237, "no_speech_prob": 0.0, "words": [{"start": 1118.84, "end": 1119.1, 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اللي", "probability": 0.5458984375}, {"start": 1175.12, "end": 1175.34, "word": " هي", "probability": 0.89892578125}, {"start": 1175.34, "end": 1175.98, "word": " summation", "probability": 0.8818359375}, {"start": 1175.98, "end": 1176.68, "word": " من", "probability": 0.95263671875}, {"start": 1176.68, "end": 1179.28, "word": " j", "probability": 0.5693359375}, {"start": 1179.28, "end": 1180.24, "word": " بساوي", "probability": 0.7890625}, {"start": 1180.24, "end": 1180.86, "word": " سفر", "probability": 0.8042805989583334}, {"start": 1180.86, "end": 1181.08, "word": " إلى", "probability": 0.92041015625}, {"start": 1181.08, "end": 1181.42, "word": " ملا", "probability": 0.6483154296875}, {"start": 1181.42, "end": 1182.12, "word": " نهاية", "probability": 0.9375}, {"start": 1182.12, "end": 1184.56, "word": " لR", "probability": 0.5948486328125}, {"start": 1184.56, "end": 1184.86, "word": " أس", "probability": 0.5025634765625}, {"start": 1184.86, "end": 1185.22, "word": " J", "probability": 0.595703125}, {"start": 1185.22, "end": 1188.98, "word": " صح؟", "probability": 0.8551432291666666}], "temperature": 1.0}, {"id": 42, "seek": 121682, "start": 1190.16, "end": 1216.82, "text": "هذا عبارة عن finite sum أصغر من مجموعة infinite series هذه عبارة عن geometric series with first term واحد وال ratio تبعها R والـ R أكبر من صفر أصغر من واحد", "tokens": [3224, 15730, 6225, 3555, 9640, 3660, 18871, 19362, 2408, 5551, 9381, 17082, 2288, 9154, 3714, 7435, 2304, 2407, 27884, 13785, 2638, 29538, 6225, 3555, 9640, 3660, 18871, 33246, 2638, 365, 700, 1433, 36764, 24401, 16070, 8509, 6055, 3555, 3615, 11296, 497, 16070, 39184, 497, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 36764, 24401], "avg_logprob": -0.3027012600737103, "compression_ratio": 1.4899328859060403, "no_speech_prob": 0.0, "words": [{"start": 1190.16, "end": 1190.62, "word": "هذا", "probability": 0.3240966796875}, {"start": 1190.62, "end": 1196.76, "word": " عبارة", "probability": 0.764556884765625}, {"start": 1196.76, "end": 1196.86, "word": " عن", "probability": 0.99462890625}, {"start": 1196.86, "end": 1197.16, "word": " finite", "probability": 0.427978515625}, {"start": 1197.16, "end": 1197.76, "word": " sum", "probability": 0.955078125}, {"start": 1197.76, "end": 1198.54, "word": " أصغر", "probability": 0.9439697265625}, {"start": 1198.54, "end": 1198.68, "word": " من", "probability": 0.9833984375}, {"start": 1198.68, "end": 1199.18, "word": " مجموعة", "probability": 0.869970703125}, {"start": 1199.18, "end": 1199.46, "word": " infinite", "probability": 0.266845703125}, {"start": 1199.46, "end": 1200.72, "word": " series", "probability": 0.8203125}, {"start": 1200.72, "end": 1201.44, "word": " هذه", "probability": 0.137939453125}, {"start": 1201.44, "end": 1201.8, "word": " عبارة", "probability": 0.9827880859375}, {"start": 1201.8, "end": 1201.98, "word": " عن", "probability": 0.99267578125}, {"start": 1201.98, "end": 1202.4, "word": " geometric", "probability": 0.39453125}, {"start": 1202.4, "end": 1203.18, "word": " series", "probability": 0.919921875}, {"start": 1203.18, "end": 1205.66, "word": " with", "probability": 0.7099609375}, {"start": 1205.66, "end": 1206.88, "word": " first", "probability": 0.74853515625}, {"start": 1206.88, "end": 1207.3, "word": " term", "probability": 0.97998046875}, {"start": 1207.3, "end": 1207.92, "word": " واحد", "probability": 0.780517578125}, {"start": 1207.92, "end": 1210.7, "word": " وال", "probability": 0.291259765625}, {"start": 1210.7, "end": 1211.84, "word": " ratio", "probability": 0.90673828125}, {"start": 1211.84, "end": 1212.48, "word": " تبعها", "probability": 0.798583984375}, {"start": 1212.48, "end": 1212.92, "word": " R", "probability": 0.52294921875}, {"start": 1212.92, "end": 1214.18, "word": " والـ", "probability": 0.4989013671875}, {"start": 1214.18, "end": 1214.5, "word": " R", "probability": 0.53564453125}, {"start": 1214.5, "end": 1214.98, "word": " أكبر", "probability": 0.97265625}, {"start": 1214.98, "end": 1215.22, "word": " من", "probability": 0.9951171875}, {"start": 1215.22, "end": 1215.62, "word": " صفر", "probability": 0.753173828125}, {"start": 1215.62, "end": 1216.08, "word": " أصغر", "probability": 0.958251953125}, {"start": 1216.08, "end": 1216.28, "word": " من", "probability": 0.9951171875}, {"start": 1216.28, "end": 1216.82, "word": " واحد", "probability": 0.984375}], "temperature": 1.0}, {"id": 43, "seek": 124456, "start": 1217.8, "end": 1244.56, "text": "إذا الـ geometric series هذه converges ومجموعة بساوي واحد على واحد minus R الكلام هذا صحيح for all j belong to M وطبعا ال SKJ هذا عبارة عن مجموعة partial sum partial sum لأعداد موجبة وبالتالي موجبة", "tokens": [28814, 15730, 2423, 39184, 33246, 2638, 29538, 9652, 2880, 4032, 2304, 7435, 2304, 2407, 27884, 4724, 3794, 995, 45865, 36764, 24401, 15844, 36764, 24401, 3175, 497, 2423, 28820, 10943, 23758, 20328, 5016, 1829, 5016, 337, 439, 361, 5784, 281, 376, 4032, 9566, 3555, 3615, 995, 2423, 21483, 41, 23758, 6225, 3555, 9640, 3660, 18871, 3714, 7435, 2304, 2407, 27884, 14641, 2408, 14641, 2408, 5296, 10721, 22488, 18513, 3714, 29245, 49401, 46599, 6027, 2655, 6027, 1829, 3714, 29245, 49401], "avg_logprob": -0.18601661731925193, "compression_ratio": 1.4522613065326633, "no_speech_prob": 0.0, "words": [{"start": 1217.8, "end": 1218.14, "word": "إذا", "probability": 0.468505859375}, {"start": 1218.14, "end": 1218.32, "word": " الـ", "probability": 0.7841796875}, {"start": 1218.32, "end": 1218.6, "word": " geometric", "probability": 0.60498046875}, {"start": 1218.6, "end": 1219.12, "word": " series", "probability": 0.89892578125}, {"start": 1219.12, "end": 1219.52, "word": " هذه", "probability": 0.453857421875}, {"start": 1219.52, "end": 1221.1, "word": " converges", "probability": 0.640869140625}, {"start": 1221.1, "end": 1222.52, "word": " ومجموعة", "probability": 0.9151204427083334}, {"start": 1222.52, "end": 1223.08, "word": " بساوي", "probability": 0.8055419921875}, {"start": 1223.08, "end": 1223.72, "word": " واحد", "probability": 0.7763671875}, {"start": 1223.72, "end": 1225.72, "word": " على", "probability": 0.732421875}, {"start": 1225.72, "end": 1226.32, "word": " واحد", "probability": 0.983154296875}, {"start": 1226.32, "end": 1226.94, "word": " minus", "probability": 0.91064453125}, {"start": 1226.94, "end": 1227.5, "word": " R", "probability": 0.716796875}, {"start": 1227.5, "end": 1230.82, "word": " الكلام", "probability": 0.9049479166666666}, {"start": 1230.82, "end": 1231.1, "word": " هذا", "probability": 0.9345703125}, {"start": 1231.1, "end": 1231.66, "word": " صحيح", "probability": 0.9974365234375}, {"start": 1231.66, "end": 1231.98, "word": " for", "probability": 0.76953125}, {"start": 1231.98, "end": 1232.44, "word": " all", "probability": 0.951171875}, {"start": 1232.44, "end": 1232.8, "word": " j", "probability": 0.72021484375}, {"start": 1232.8, "end": 1233.32, "word": " belong", "probability": 0.462158203125}, {"start": 1233.32, "end": 1233.6, "word": " to", "probability": 0.97900390625}, {"start": 1233.6, "end": 1233.9, "word": " M", "probability": 0.52001953125}, {"start": 1233.9, "end": 1235.96, "word": " وطبعا", "probability": 0.941015625}, {"start": 1235.96, "end": 1236.12, "word": " ال", "probability": 0.9599609375}, {"start": 1236.12, "end": 1236.92, "word": " SKJ", "probability": 0.42626953125}, {"start": 1236.92, "end": 1237.32, "word": " هذا", "probability": 0.7333984375}, {"start": 1237.32, "end": 1237.68, "word": " عبارة", "probability": 0.985107421875}, {"start": 1237.68, "end": 1237.9, "word": " عن", "probability": 0.9921875}, {"start": 1237.9, "end": 1238.4, "word": " مجموعة", "probability": 0.98154296875}, {"start": 1238.4, "end": 1238.76, "word": " partial", "probability": 0.94287109375}, {"start": 1238.76, "end": 1239.22, "word": " sum", "probability": 0.94873046875}, {"start": 1239.22, "end": 1240.32, "word": " partial", "probability": 0.83349609375}, {"start": 1240.32, "end": 1240.92, "word": " sum", "probability": 0.97119140625}, {"start": 1240.92, "end": 1242.76, "word": " لأعداد", "probability": 0.905517578125}, {"start": 1242.76, "end": 1243.32, "word": " موجبة", "probability": 0.9677734375}, {"start": 1243.32, "end": 1244.02, "word": " وبالتالي", "probability": 0.86787109375}, {"start": 1244.02, "end": 1244.56, "word": " موجبة", "probability": 0.93603515625}], "temperature": 1.0}, {"id": 44, "seek": 127016, "start": 1247.7, "end": 1270.16, "text": "إذا أنا هيك أثبتت إن ال sub sequence SKJ bounded below by 0 و bounded above by العدد الموجب 1 على 1 minus R وبالتالي، إذا هيك نستنتج، therefore the subsequence", "tokens": [28814, 15730, 41850, 39896, 4117, 5551, 12984, 3555, 2655, 2655, 36145, 2423, 1422, 8310, 21483, 41, 37498, 2507, 538, 1958, 4032, 37498, 3673, 538, 2423, 22488, 3215, 9673, 29245, 3555, 502, 15844, 502, 3175, 497, 46599, 6027, 2655, 6027, 1829, 12399, 11933, 15730, 39896, 4117, 8717, 14851, 29399, 7435, 12399, 4412, 264, 13924, 655], "avg_logprob": -0.3531249989162792, "compression_ratio": 1.2891566265060241, "no_speech_prob": 0.0, "words": [{"start": 1247.7, "end": 1248.1, "word": "إذا", "probability": 0.46453857421875}, {"start": 1248.1, "end": 1248.44, "word": " أنا", "probability": 0.55322265625}, {"start": 1248.44, "end": 1248.68, "word": " هيك", "probability": 0.710205078125}, {"start": 1248.68, "end": 1249.22, "word": " أثبتت", "probability": 0.98251953125}, {"start": 1249.22, "end": 1249.44, "word": " إن", "probability": 0.385986328125}, {"start": 1249.44, "end": 1249.66, "word": " ال", "probability": 0.4716796875}, {"start": 1249.66, "end": 1252.72, "word": " sub", "probability": 0.2113037109375}, {"start": 1252.72, "end": 1253.36, "word": " sequence", "probability": 0.58203125}, {"start": 1253.36, "end": 1254.26, "word": " SKJ", "probability": 0.605712890625}, {"start": 1254.26, "end": 1254.68, "word": " bounded", "probability": 0.68896484375}, {"start": 1254.68, "end": 1255.16, "word": " below", "probability": 0.78466796875}, {"start": 1255.16, "end": 1255.48, "word": " by", "probability": 0.837890625}, {"start": 1255.48, "end": 1255.9, "word": " 0", "probability": 0.69384765625}, {"start": 1255.9, "end": 1256.94, "word": " و", "probability": 0.76904296875}, {"start": 1256.94, "end": 1257.38, "word": " bounded", "probability": 0.859375}, {"start": 1257.38, "end": 1258.06, "word": " above", "probability": 0.95068359375}, {"start": 1258.06, "end": 1258.7, "word": " by", "probability": 0.87646484375}, {"start": 1258.7, "end": 1259.26, "word": " العدد", "probability": 0.813720703125}, {"start": 1259.26, "end": 1259.82, "word": " الموجب", "probability": 0.8727213541666666}, {"start": 1259.82, "end": 1260.18, "word": " 1", "probability": 0.82470703125}, {"start": 1260.18, "end": 1260.52, "word": " على", "probability": 0.56298828125}, {"start": 1260.52, "end": 1260.86, "word": " 1", "probability": 0.8837890625}, {"start": 1260.86, "end": 1261.34, "word": " minus", "probability": 0.748046875}, {"start": 1261.34, "end": 1261.72, "word": " R", "probability": 0.6943359375}, {"start": 1261.72, "end": 1265.42, "word": " وبالتالي،", "probability": 0.7632649739583334}, {"start": 1265.42, "end": 1265.92, "word": " إذا", "probability": 0.774169921875}, {"start": 1265.92, "end": 1266.26, "word": " هيك", "probability": 0.948486328125}, {"start": 1266.26, "end": 1267.08, "word": " نستنتج،", "probability": 0.7013427734375}, {"start": 1267.08, "end": 1267.48, "word": " therefore", "probability": 0.7001953125}, {"start": 1267.48, "end": 1269.04, "word": " the", "probability": 0.5390625}, {"start": 1269.04, "end": 1270.16, "word": " subsequence", "probability": 0.793701171875}], "temperature": 1.0}, {"id": 45, "seek": 129369, "start": 1273.37, "end": 1293.69, "text": "ده sub-sequence اللي هي SKJ هاد ال sub-sequence من مين؟ من ال sequence of partial sums SN اشملها is bounded أثبتنا أنها ايه؟ bounded، مصدقوط؟ طلعنا احنا عملنا construction ل sub-sequence", "tokens": [3215, 3224, 1422, 12, 11834, 655, 13672, 1829, 39896, 21483, 41, 8032, 18513, 2423, 1422, 12, 11834, 655, 9154, 3714, 9957, 22807, 9154, 2423, 8310, 295, 14641, 34499, 13955, 1975, 8592, 2304, 1211, 11296, 307, 37498, 5551, 12984, 3555, 2655, 8315, 14739, 11296, 1975, 1829, 3224, 22807, 37498, 12399, 3714, 9381, 3215, 4587, 2407, 9566, 22807, 23032, 1211, 3615, 8315, 1975, 5016, 8315, 6225, 42213, 8315, 6435, 5296, 1422, 12, 11834, 655], "avg_logprob": -0.38570206785855227, "compression_ratio": 1.44, "no_speech_prob": 0.0, "words": [{"start": 1273.37, "end": 1273.71, "word": "ده", "probability": 0.483123779296875}, {"start": 1273.71, "end": 1273.93, "word": " sub", "probability": 0.250732421875}, {"start": 1273.93, "end": 1274.47, "word": "-sequence", "probability": 0.75390625}, {"start": 1274.47, "end": 1274.61, "word": " اللي", "probability": 0.56494140625}, {"start": 1274.61, "end": 1274.87, "word": " هي", "probability": 0.83154296875}, {"start": 1274.87, "end": 1276.49, "word": " SKJ", "probability": 0.72802734375}, {"start": 1276.49, "end": 1277.31, "word": " هاد", "probability": 0.3509521484375}, {"start": 1277.31, "end": 1277.41, "word": " ال", "probability": 0.7763671875}, {"start": 1277.41, "end": 1277.57, "word": " sub", "probability": 0.466796875}, {"start": 1277.57, "end": 1277.99, "word": "-sequence", "probability": 0.9461263020833334}, {"start": 1277.99, "end": 1278.21, "word": " من", "probability": 0.98681640625}, {"start": 1278.21, "end": 1279.63, "word": " مين؟", "probability": 0.8304036458333334}, {"start": 1279.63, "end": 1280.01, "word": " من", "probability": 0.92236328125}, {"start": 1280.01, "end": 1280.23, "word": " ال", "probability": 0.78759765625}, {"start": 1280.23, "end": 1280.73, "word": " sequence", "probability": 0.93115234375}, {"start": 1280.73, "end": 1280.99, "word": " of", "probability": 0.828125}, {"start": 1280.99, "end": 1281.35, "word": " partial", "probability": 0.9013671875}, {"start": 1281.35, "end": 1281.65, "word": " sums", "probability": 0.9482421875}, {"start": 1281.65, "end": 1282.29, "word": " SN", "probability": 0.48388671875}, {"start": 1282.29, "end": 1283.07, "word": " اشملها", "probability": 0.742578125}, {"start": 1283.07, "end": 1284.37, "word": " is", "probability": 0.58349609375}, {"start": 1284.37, "end": 1284.99, "word": " bounded", "probability": 0.9267578125}, {"start": 1284.99, "end": 1286.19, "word": " أثبتنا", "probability": 0.9390625}, {"start": 1286.19, "end": 1286.93, "word": " أنها", "probability": 0.705322265625}, {"start": 1286.93, "end": 1287.35, "word": " ايه؟", "probability": 0.63299560546875}, {"start": 1287.35, "end": 1288.07, "word": " bounded،", "probability": 0.3812255859375}, {"start": 1288.07, "end": 1290.41, "word": " مصدقوط؟", "probability": 0.6548549107142857}, {"start": 1290.41, "end": 1291.49, "word": " طلعنا", "probability": 0.75616455078125}, {"start": 1291.49, "end": 1291.69, "word": " احنا", "probability": 0.7977701822916666}, {"start": 1291.69, "end": 1292.03, "word": " عملنا", "probability": 0.9708658854166666}, {"start": 1292.03, "end": 1292.69, "word": " construction", "probability": 0.92041015625}, {"start": 1292.69, "end": 1292.91, "word": " ل", "probability": 0.94970703125}, {"start": 1292.91, "end": 1293.15, "word": " sub", "probability": 0.72900390625}, {"start": 1293.15, "end": 1293.69, "word": "-sequence", "probability": 0.9558919270833334}], "temperature": 1.0}, {"id": 46, "seek": 131673, "start": 1294.67, "end": 1316.73, "text": "من الـ sequence of partial sums وهي طلعت bounded هي bounded below by 0 bounded above by 1 over 1 minus r لأن حسب اللمّة اللي فاتت so by above لمّة ال sequence of partial sums نفسها is bounded", "tokens": [27842, 2423, 39184, 8310, 295, 14641, 34499, 37037, 1829, 23032, 1211, 34268, 37498, 39896, 37498, 2507, 538, 1958, 37498, 3673, 538, 502, 670, 502, 3175, 367, 5296, 33456, 11331, 35457, 13672, 2304, 11703, 3660, 13672, 1829, 6156, 9307, 2655, 370, 538, 3673, 32767, 11703, 3660, 2423, 8310, 295, 14641, 34499, 8717, 36178, 11296, 307, 37498], "avg_logprob": -0.24818638871823037, "compression_ratio": 1.4842767295597483, "no_speech_prob": 0.0, "words": [{"start": 1294.67, "end": 1294.93, "word": "من", "probability": 0.494140625}, {"start": 1294.93, "end": 1295.09, "word": " الـ", "probability": 0.51806640625}, {"start": 1295.09, "end": 1295.35, "word": " sequence", "probability": 0.67236328125}, {"start": 1295.35, "end": 1295.65, "word": " of", "probability": 0.95654296875}, {"start": 1295.65, "end": 1296.01, "word": " partial", "probability": 0.94677734375}, {"start": 1296.01, "end": 1296.35, "word": " sums", "probability": 0.9599609375}, {"start": 1296.35, "end": 1296.57, "word": " وهي", "probability": 0.697021484375}, {"start": 1296.57, "end": 1296.91, "word": " طلعت", "probability": 0.9353841145833334}, {"start": 1296.91, "end": 1297.19, "word": " bounded", "probability": 0.447021484375}, {"start": 1297.19, "end": 1297.37, "word": " هي", "probability": 0.2115478515625}, {"start": 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"word": " لأن", "probability": 0.65771484375}, {"start": 1302.97, "end": 1303.33, "word": " حسب", "probability": 0.983154296875}, {"start": 1303.33, "end": 1303.75, "word": " اللمّة", "probability": 0.7086181640625}, {"start": 1303.75, "end": 1303.91, "word": " اللي", "probability": 0.9169921875}, {"start": 1303.91, "end": 1304.57, "word": " فاتت", "probability": 0.994140625}, {"start": 1304.57, "end": 1306.39, "word": " so", "probability": 0.287841796875}, {"start": 1306.39, "end": 1306.93, "word": " by", "probability": 0.96484375}, {"start": 1306.93, "end": 1307.91, "word": " above", "probability": 0.8837890625}, {"start": 1307.91, "end": 1308.53, "word": " لمّة", "probability": 0.7906901041666666}, {"start": 1308.53, "end": 1313.61, "word": " ال", "probability": 0.92236328125}, {"start": 1313.61, "end": 1314.19, "word": " sequence", "probability": 0.95361328125}, {"start": 1314.19, "end": 1314.57, "word": " of", "probability": 0.9775390625}, {"start": 1314.57, "end": 1314.97, "word": " partial", "probability": 0.947265625}, {"start": 1314.97, "end": 1315.35, "word": " sums", "probability": 0.95263671875}, {"start": 1315.35, "end": 1315.95, "word": " نفسها", "probability": 0.974609375}, {"start": 1315.95, "end": 1316.27, "word": " is", "probability": 0.95654296875}, {"start": 1316.27, "end": 1316.73, "word": " bounded", "probability": 0.95458984375}], "temperature": 1.0}, {"id": 47, "seek": 135091, "start": 1322.95, "end": 1350.91, "text": "وبالتالي إذا by above theorem مدام ال sequence of partial sums is bounded إذا ال series converges okay إذا بعديكم نقول so by above theorem ال series sigma", "tokens": [37746, 6027, 2655, 6027, 1829, 11933, 15730, 538, 3673, 20904, 3714, 3215, 10943, 2423, 8310, 295, 14641, 34499, 307, 37498, 11933, 15730, 2423, 2638, 9652, 2880, 1392, 11933, 15730, 45030, 16254, 24793, 8717, 39648, 370, 538, 3673, 20904, 2423, 2638, 12771], "avg_logprob": -0.3158482185431889, "compression_ratio": 1.3741007194244603, "no_speech_prob": 0.0, "words": [{"start": 1322.95, "end": 1323.95, "word": "وبالتالي", "probability": 0.92822265625}, {"start": 1323.95, "end": 1324.57, "word": " إذا", "probability": 0.51885986328125}, {"start": 1324.57, "end": 1325.03, "word": " by", "probability": 0.58935546875}, {"start": 1325.03, "end": 1325.61, "word": " above", "probability": 0.9365234375}, {"start": 1325.61, "end": 1326.17, "word": " theorem", "probability": 0.580078125}, {"start": 1326.17, "end": 1327.77, "word": " مدام", "probability": 0.602294921875}, {"start": 1327.77, "end": 1327.93, "word": " ال", "probability": 0.78466796875}, {"start": 1327.93, "end": 1328.21, "word": " sequence", "probability": 0.87353515625}, {"start": 1328.21, "end": 1328.57, "word": " of", "probability": 0.83837890625}, {"start": 1328.57, "end": 1328.93, "word": " partial", "probability": 0.93701171875}, {"start": 1328.93, "end": 1329.29, "word": " sums", "probability": 0.97265625}, {"start": 1329.29, "end": 1329.51, "word": " is", "probability": 0.92236328125}, {"start": 1329.51, "end": 1329.95, "word": " bounded", "probability": 0.93994140625}, {"start": 1329.95, "end": 1330.67, "word": " إذا", "probability": 0.7294921875}, {"start": 1330.67, "end": 1330.89, "word": " ال", "probability": 0.80078125}, {"start": 1330.89, "end": 1331.09, "word": " series", "probability": 0.82275390625}, {"start": 1331.09, "end": 1331.91, "word": " converges", "probability": 0.852783203125}, {"start": 1331.91, "end": 1335.71, "word": " okay", "probability": 0.52587890625}, {"start": 1335.71, "end": 1336.23, "word": " إذا", "probability": 0.879638671875}, {"start": 1336.23, "end": 1338.61, "word": " بعديكم", "probability": 0.6291910807291666}, {"start": 1338.61, "end": 1339.07, "word": " نقول", "probability": 0.97509765625}, {"start": 1339.07, "end": 1343.79, "word": " so", "probability": 0.55810546875}, {"start": 1343.79, "end": 1344.39, "word": " by", "probability": 0.98046875}, {"start": 1344.39, "end": 1344.91, "word": " above", "probability": 0.97216796875}, {"start": 1344.91, "end": 1345.55, "word": " theorem", "probability": 0.7861328125}, {"start": 1345.55, "end": 1349.93, "word": " ال", "probability": 0.65380859375}, {"start": 1349.93, "end": 1350.27, "word": " series", "probability": 0.953125}, {"start": 1350.27, "end": 1350.91, "word": " sigma", "probability": 0.48388671875}], "temperature": 1.0}, {"id": 48, "seek": 137464, "start": 1351.94, "end": 1374.64, "text": "1 على N أكبر من 1 فهذا يثبت الجزء الأول من النظرية خلّينا نثبت الجزء التاني", "tokens": [16, 15844, 426, 5551, 4117, 26890, 9154, 502, 6156, 3224, 15730, 7251, 12984, 3555, 2655, 25724, 11622, 38207, 16247, 12610, 9154, 28239, 19913, 2288, 10632, 16490, 1211, 11703, 9957, 995, 8717, 12984, 3555, 2655, 25724, 11622, 38207, 16712, 7649, 1829], "avg_logprob": -0.39977134727850194, "compression_ratio": 1.375, "no_speech_prob": 0.0, "words": [{"start": 1351.94, "end": 1352.44, "word": "1", "probability": 0.1978759765625}, {"start": 1352.44, "end": 1352.84, "word": " على", "probability": 0.263427734375}, {"start": 1352.84, "end": 1354.02, "word": " N", "probability": 0.110595703125}, {"start": 1354.02, "end": 1354.34, "word": " أكبر", "probability": 0.5881754557291666}, {"start": 1354.34, "end": 1354.76, "word": " من", "probability": 0.96240234375}, {"start": 1354.76, "end": 1354.76, "word": " 1", "probability": 0.81103515625}, {"start": 1354.76, "end": 1366.08, "word": " فهذا", "probability": 0.4403483072916667}, {"start": 1366.08, "end": 1366.78, "word": " يثبت", "probability": 0.78546142578125}, {"start": 1366.78, "end": 1367.22, "word": " الجزء", "probability": 0.9425455729166666}, {"start": 1367.22, "end": 1367.76, "word": " الأول", "probability": 0.9765625}, {"start": 1367.76, "end": 1368.76, "word": " من", "probability": 0.86962890625}, {"start": 1368.76, "end": 1369.54, "word": " النظرية", "probability": 0.83013916015625}, {"start": 1369.54, "end": 1373.3, "word": " خلّينا", "probability": 0.6406494140625}, {"start": 1373.3, "end": 1373.7, "word": " نثبت", "probability": 0.97900390625}, {"start": 1373.7, "end": 1374.08, "word": " الجزء", "probability": 0.9903971354166666}, {"start": 1374.08, "end": 1374.64, "word": " التاني", "probability": 0.8937174479166666}], "temperature": 1.0}, {"id": 49, "seek": 140914, "start": 1390.08, "end": 1409.14, "text": "using induction you can show أنه for P أكبر من صفر أصغر من واحد", "tokens": [7981, 33371, 291, 393, 855, 14739, 3224, 337, 430, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 36764, 24401], "avg_logprob": -0.24755858381589255, "compression_ratio": 0.9883720930232558, "no_speech_prob": 0.0, "words": [{"start": 1390.08, "end": 1391.26, "word": "using", "probability": 0.268310546875}, {"start": 1391.26, "end": 1392.32, "word": " induction", "probability": 0.96533203125}, {"start": 1392.32, "end": 1397.2, "word": " you", "probability": 0.7138671875}, {"start": 1397.2, "end": 1397.78, "word": " can", "probability": 0.9638671875}, {"start": 1397.78, "end": 1398.42, "word": " show", "probability": 0.96142578125}, {"start": 1398.42, "end": 1401.66, "word": " أنه", "probability": 0.572509765625}, {"start": 1401.66, "end": 1402.26, "word": " for", "probability": 0.47119140625}, {"start": 1402.26, "end": 1406.8, "word": " P", "probability": 0.359619140625}, {"start": 1406.8, "end": 1407.3, "word": " أكبر", "probability": 0.9405924479166666}, {"start": 1407.3, "end": 1407.54, "word": " من", "probability": 0.98828125}, {"start": 1407.54, "end": 1407.92, "word": " صفر", "probability": 0.7914225260416666}, {"start": 1407.92, "end": 1408.4, "word": " أصغر", "probability": 0.962890625}, {"start": 1408.4, "end": 1408.58, "word": " من", "probability": 0.99462890625}, {"start": 1408.58, "end": 1409.14, "word": " واحد", "probability": 0.905029296875}], "temperature": 1.0}, {"id": 50, "seek": 143123, "start": 1412.37, "end": 1431.23, "text": "لو كانت ال P طبعا أكبر من صفر وأصغر من أو ساوي الواحد ف N أوس P بطلع أصغر من أو ساوي N لكل N في N صح؟ انا ممكن اثباته by induction", "tokens": [1211, 2407, 25961, 2655, 2423, 430, 23032, 3555, 3615, 995, 5551, 4117, 26890, 9154, 20328, 5172, 2288, 36725, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 2423, 14407, 24401, 6156, 426, 34051, 3794, 430, 4724, 9566, 1211, 3615, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 426, 5296, 28820, 426, 8978, 426, 20328, 5016, 22807, 1975, 8315, 3714, 43020, 1975, 12984, 3555, 9307, 3224, 538, 33371], "avg_logprob": -0.2101332738119013, "compression_ratio": 1.4452054794520548, "no_speech_prob": 0.0, "words": [{"start": 1412.37, "end": 1412.77, "word": "لو", "probability": 0.7763671875}, {"start": 1412.77, "end": 1413.17, "word": " كانت", "probability": 0.939208984375}, {"start": 1413.17, "end": 1413.31, "word": " ال", "probability": 0.88134765625}, {"start": 1413.31, "end": 1413.63, "word": " P", "probability": 0.59765625}, {"start": 1413.63, "end": 1415.73, "word": " طبعا", "probability": 0.915283203125}, {"start": 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"end": 1430.15, "word": " ممكن", "probability": 0.939697265625}, {"start": 1430.15, "end": 1430.61, "word": " اثباته", "probability": 0.7634765625}, {"start": 1430.61, "end": 1430.79, "word": " by", "probability": 0.880859375}, {"start": 1430.79, "end": 1431.23, "word": " induction", "probability": 0.98583984375}], "temperature": 1.0}, {"id": 51, "seek": 145271, "start": 1432.53, "end": 1452.71, "text": "So, 1 على n أصغر لو ساقى 1 على n أُس في for all n ينتمي إلى n فإن هذا بيقدّي هذا بيقدّي", "tokens": [6455, 11, 502, 15844, 297, 5551, 9381, 17082, 2288, 45164, 8608, 995, 4587, 7578, 502, 15844, 297, 5551, 10859, 3794, 8978, 337, 439, 297, 7251, 29399, 2304, 1829, 30731, 297, 6156, 28814, 1863, 23758, 4724, 1829, 28543, 11703, 1829, 23758, 4724, 1829, 28543, 11703, 1829], "avg_logprob": -0.4194972858480785, "compression_ratio": 1.3173076923076923, "no_speech_prob": 0.0, "words": [{"start": 1432.53, "end": 1433.05, "word": "So,", "probability": 0.066650390625}, {"start": 1434.39, "end": 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"word": " all", "probability": 0.95361328125}, {"start": 1441.09, "end": 1441.47, "word": " n", "probability": 0.8623046875}, {"start": 1441.47, "end": 1442.25, "word": " ينتمي", "probability": 0.953125}, {"start": 1442.25, "end": 1442.53, "word": " إلى", "probability": 0.96826171875}, {"start": 1442.53, "end": 1442.87, "word": " n", "probability": 0.38818359375}, {"start": 1442.87, "end": 1448.47, "word": " فإن", "probability": 0.7810872395833334}, {"start": 1448.47, "end": 1448.79, "word": " هذا", "probability": 0.72216796875}, {"start": 1448.79, "end": 1449.43, "word": " بيقدّي", "probability": 0.67021484375}, {"start": 1449.43, "end": 1452.03, "word": " هذا", "probability": 0.75146484375}, {"start": 1452.03, "end": 1452.71, "word": " بيقدّي", "probability": 0.9640625}], "temperature": 1.0}, {"id": 52, "seek": 149263, "start": 1470.45, "end": 1492.63, "text": "this implies أن ال summation from k بساوي واحد to n لواحد على k أصغر لو ساوي summation من k بساوي واحد إلى n لواحد على n على k أوس P", "tokens": [11176, 18779, 14739, 2423, 28811, 490, 350, 4724, 3794, 995, 45865, 36764, 24401, 281, 297, 5296, 14407, 24401, 15844, 350, 5551, 9381, 17082, 2288, 45164, 8608, 995, 45865, 28811, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 30731, 297, 5296, 14407, 24401, 15844, 297, 15844, 350, 34051, 3794, 430], "avg_logprob": -0.2499999976158142, "compression_ratio": 1.578512396694215, "no_speech_prob": 0.0, "words": [{"start": 1470.45, "end": 1470.89, "word": "this", "probability": 0.29736328125}, {"start": 1470.89, "end": 1471.59, "word": " implies", "probability": 0.9541015625}, {"start": 1471.59, "end": 1471.89, "word": " أن", "probability": 0.568359375}, {"start": 1471.89, "end": 1472.11, "word": " ال", "probability": 0.5810546875}, {"start": 1472.11, "end": 1472.73, "word": " summation", "probability": 0.70361328125}, {"start": 1472.73, "end": 1473.53, "word": " from", "probability": 0.66552734375}, {"start": 1473.53, "end": 1474.23, "word": " k", "probability": 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0.56396484375}, {"start": 1483.33, "end": 1483.59, "word": " k", "probability": 0.779296875}, {"start": 1483.59, "end": 1484.15, "word": " بساوي", "probability": 0.97509765625}, {"start": 1484.15, "end": 1484.69, "word": " واحد", "probability": 0.98876953125}, {"start": 1484.69, "end": 1484.97, "word": " إلى", "probability": 0.9306640625}, {"start": 1484.97, "end": 1485.51, "word": " n", "probability": 0.87255859375}, {"start": 1485.51, "end": 1487.97, "word": " لواحد", "probability": 0.8922526041666666}, {"start": 1487.97, "end": 1488.23, "word": " على", "probability": 0.92626953125}, {"start": 1488.23, "end": 1488.73, "word": " n", "probability": 0.84716796875}, {"start": 1488.73, "end": 1489.13, "word": " على", "probability": 0.82275390625}, {"start": 1489.13, "end": 1489.77, "word": " k", "probability": 0.9697265625}, {"start": 1489.77, "end": 1492.41, "word": " أوس", "probability": 0.3448486328125}, {"start": 1492.41, "end": 1492.63, "word": " P", "probability": 0.794921875}], "temperature": 1.0}, {"id": 53, "seek": 152185, "start": 1494.65, "end": 1521.85, "text": "طب ما هذا عبارة عن ال partial sum لسمي S N لل harmonic series .. لل .. لل harmonic series و هذا عبارة عن ال partial sum سمي S N star لل P series صح؟ إن أنا أصبح عندي أنا S N أصغر من أو ساوي S N star", "tokens": [9566, 3555, 19446, 23758, 6225, 3555, 9640, 3660, 18871, 2423, 14641, 2408, 5296, 38251, 1829, 318, 426, 24976, 32270, 2638, 4386, 24976, 4386, 24976, 32270, 2638, 4032, 23758, 6225, 3555, 9640, 3660, 18871, 2423, 14641, 2408, 8608, 2304, 1829, 318, 426, 3543, 24976, 430, 2638, 20328, 5016, 22807, 36145, 41850, 5551, 9381, 49628, 18871, 16254, 41850, 318, 426, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 318, 426, 3543], "avg_logprob": -0.23041373197461518, "compression_ratio": 1.70625, "no_speech_prob": 0.0, "words": [{"start": 1494.65, "end": 1494.97, "word": "طب", "probability": 0.865966796875}, {"start": 1494.97, "end": 1495.11, "word": " ما", "probability": 0.46826171875}, {"start": 1495.11, "end": 1495.41, "word": " هذا", "probability": 0.54638671875}, {"start": 1495.41, "end": 1495.85, "word": " عبارة", "probability": 0.9945068359375}, {"start": 1495.85, "end": 1496.05, "word": " عن", "probability": 0.998046875}, {"start": 1496.05, "end": 1496.21, "word": " ال", "probability": 0.91796875}, {"start": 1496.21, "end": 1496.65, "word": " partial", "probability": 0.87451171875}, {"start": 1496.65, "end": 1497.27, "word": " sum", "probability": 0.96484375}, {"start": 1497.27, "end": 1497.95, "word": " لسمي", "probability": 0.7083333333333334}, {"start": 1497.95, "end": 1498.39, "word": " S", "probability": 0.2342529296875}, {"start": 1498.39, "end": 1499.79, "word": " N", "probability": 0.6337890625}, {"start": 1499.79, "end": 1501.21, "word": " لل", "probability": 0.45068359375}, {"start": 1501.21, "end": 1501.69, "word": " harmonic", "probability": 0.82958984375}, {"start": 1501.69, "end": 1502.25, "word": " series", "probability": 0.76708984375}, {"start": 1502.25, "end": 1502.27, "word": " ..", "probability": 0.419189453125}, {"start": 1502.27, "end": 1502.59, "word": " لل", "probability": 0.88037109375}, {"start": 1502.59, "end": 1503.99, "word": " ..", "probability": 0.90576171875}, {"start": 1503.99, "end": 1505.93, "word": " لل", "probability": 0.95751953125}, {"start": 1505.93, "end": 1506.31, "word": " harmonic", "probability": 0.974609375}, {"start": 1506.31, "end": 1506.95, "word": " series", "probability": 0.94677734375}, {"start": 1506.95, "end": 1508.03, "word": " و", "probability": 0.56640625}, {"start": 1508.03, "end": 1508.27, "word": " هذا", "probability": 0.85888671875}, {"start": 1508.27, "end": 1508.69, "word": " عبارة", "probability": 0.9986572265625}, {"start": 1508.69, "end": 1508.85, "word": " عن", "probability": 0.99755859375}, {"start": 1508.85, "end": 1509.03, "word": " ال", "probability": 0.94482421875}, {"start": 1509.03, "end": 1509.41, "word": " partial", "probability": 0.97314453125}, {"start": 1509.41, "end": 1509.93, "word": " sum", "probability": 0.98193359375}, {"start": 1509.93, "end": 1510.45, "word": " سمي", "probability": 0.8631184895833334}, {"start": 1510.45, "end": 1510.77, "word": " S", "probability": 0.8525390625}, {"start": 1510.77, "end": 1511.07, "word": " N", "probability": 0.8984375}, {"start": 1511.07, "end": 1511.61, "word": " star", "probability": 0.15625}, {"start": 1511.61, "end": 1513.19, "word": " لل", "probability": 0.6796875}, {"start": 1513.19, "end": 1513.43, "word": " P", "probability": 0.95849609375}, {"start": 1513.43, "end": 1513.89, "word": " series", "probability": 0.70654296875}, {"start": 1513.89, "end": 1516.81, "word": " صح؟", "probability": 0.86669921875}, {"start": 1516.81, "end": 1516.97, "word": " إن", "probability": 0.183837890625}, {"start": 1516.97, "end": 1517.11, "word": " أنا", "probability": 0.62744140625}, {"start": 1517.11, "end": 1517.51, "word": " أصبح", "probability": 0.8504231770833334}, {"start": 1517.51, "end": 1517.87, "word": " عندي", "probability": 0.777099609375}, {"start": 1517.87, "end": 1518.19, "word": " أنا", "probability": 0.70947265625}, {"start": 1518.19, "end": 1518.61, "word": " S", "probability": 0.9208984375}, {"start": 1518.61, "end": 1519.11, "word": " N", "probability": 0.96923828125}, {"start": 1519.11, "end": 1519.73, "word": " أصغر", "probability": 0.9942626953125}, {"start": 1519.73, "end": 1519.89, "word": " من", "probability": 0.98193359375}, {"start": 1519.89, "end": 1520.05, "word": " أو", "probability": 0.943359375}, {"start": 1520.05, "end": 1520.57, "word": " ساوي", "probability": 0.8898111979166666}, {"start": 1520.57, "end": 1520.93, "word": " S", "probability": 0.364013671875}, {"start": 1520.93, "end": 1521.31, "word": " N", "probability": 0.978515625}, {"start": 1521.31, "end": 1521.85, "word": " star", "probability": 0.755859375}], "temperature": 1.0}, {"id": 54, "seek": 155323, "start": 1524.55, "end": 1553.23, "text": "where لكل n where sn بساوي sigma واحد على k من k بساوي واحد إلى n و sn star بساوي sigma من k بساوي واحد إلى n لواحد على k أُس P طيب since أثبتنا احنا قبل هيك انه ال sequence of partial sums", "tokens": [1992, 5296, 28820, 297, 689, 2406, 4724, 3794, 995, 45865, 12771, 36764, 24401, 15844, 350, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 30731, 297, 4032, 2406, 3543, 4724, 3794, 995, 45865, 12771, 9154, 350, 4724, 3794, 995, 45865, 36764, 24401, 30731, 297, 5296, 14407, 24401, 15844, 350, 5551, 10859, 3794, 430, 23032, 1829, 3555, 1670, 5551, 12984, 3555, 2655, 8315, 1975, 5016, 8315, 12174, 36150, 39896, 4117, 16472, 3224, 2423, 8310, 295, 14641, 34499], "avg_logprob": -0.22923519932910016, "compression_ratio": 1.6646341463414633, "no_speech_prob": 0.0, "words": [{"start": 1524.55, "end": 1525.07, "word": "where", "probability": 0.308837890625}, {"start": 1525.07, "end": 1525.95, "word": " لكل", "probability": 0.928466796875}, {"start": 1525.95, "end": 1526.41, "word": " n", "probability": 0.6806640625}, {"start": 1526.41, "end": 1529.43, "word": " where", "probability": 0.61865234375}, {"start": 1529.43, "end": 1530.05, "word": " sn", "probability": 0.377197265625}, {"start": 1530.05, "end": 1530.79, "word": " بساوي", "probability": 0.53076171875}, {"start": 1530.79, "end": 1531.33, "word": " sigma", "probability": 0.40869140625}, {"start": 1531.33, "end": 1532.15, "word": " واحد", "probability": 0.791748046875}, {"start": 1532.15, "end": 1532.37, "word": " على", "probability": 0.54638671875}, {"start": 1532.37, "end": 1532.79, "word": " k", "probability": 0.69482421875}, {"start": 1532.79, "end": 1532.91, "word": " من", "probability": 0.9443359375}, {"start": 1532.91, "end": 1533.21, "word": " k", "probability": 0.8046875}, {"start": 1533.21, "end": 1533.69, "word": " بساوي", "probability": 0.936279296875}, {"start": 1533.69, "end": 1534.17, "word": " واحد", "probability": 0.980712890625}, {"start": 1534.17, "end": 1535.81, "word": " إلى", "probability": 0.65625}, {"start": 1535.81, "end": 1536.29, "word": " n", "probability": 0.83544921875}, {"start": 1536.29, "end": 1536.53, "word": " و", "probability": 0.904296875}, {"start": 1536.53, "end": 1537.11, "word": " sn", "probability": 0.6943359375}, {"start": 1537.11, "end": 1537.93, "word": " star", "probability": 0.149169921875}, {"start": 1537.93, "end": 1539.57, "word": " بساوي", "probability": 0.9462890625}, {"start": 1539.57, "end": 1539.91, "word": " sigma", "probability": 0.81494140625}, {"start": 1539.91, "end": 1540.15, "word": " من", "probability": 0.98779296875}, {"start": 1540.15, "end": 1540.41, "word": " k", "probability": 0.94482421875}, {"start": 1540.41, "end": 1540.87, "word": " بساوي", "probability": 0.9727783203125}, {"start": 1540.87, "end": 1541.27, "word": " واحد", "probability": 0.989990234375}, {"start": 1541.27, "end": 1541.45, "word": " إلى", "probability": 0.85595703125}, {"start": 1541.45, "end": 1541.67, "word": " n", "probability": 0.9541015625}, {"start": 1541.67, "end": 1542.23, "word": " لواحد", "probability": 0.7486165364583334}, {"start": 1542.23, "end": 1542.51, "word": " على", "probability": 0.90087890625}, {"start": 1542.51, "end": 1543.11, "word": " k", "probability": 0.9560546875}, {"start": 1543.11, "end": 1543.61, "word": " أُس", "probability": 0.6221516927083334}, {"start": 1543.61, "end": 1543.91, "word": " P", "probability": 0.490478515625}, {"start": 1543.91, "end": 1546.89, "word": " طيب", "probability": 0.9303385416666666}, {"start": 1546.89, "end": 1547.43, "word": " since", "probability": 0.7392578125}, {"start": 1547.43, "end": 1549.23, "word": " أثبتنا", "probability": 0.98671875}, {"start": 1549.23, "end": 1549.39, "word": " احنا", "probability": 0.82373046875}, {"start": 1549.39, "end": 1549.69, "word": " قبل", "probability": 0.66259765625}, {"start": 1549.69, "end": 1550.17, "word": " هيك", "probability": 0.938232421875}, {"start": 1550.17, "end": 1551.35, "word": " انه", "probability": 0.525634765625}, {"start": 1551.35, "end": 1551.63, "word": " ال", "probability": 0.92333984375}, {"start": 1551.63, "end": 1552.01, "word": " sequence", "probability": 0.95849609375}, {"start": 1552.01, "end": 1552.35, "word": " of", "probability": 0.7509765625}, {"start": 1552.35, "end": 1552.77, "word": " partial", "probability": 0.951171875}, {"start": 1552.77, "end": 1553.23, "word": " sums", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 55, "seek": 156229, "start": 1556.31, "end": 1562.29, "text": "السيكوانس SN هذا عبارة عن السيكوانس of partial sums", "tokens": [6027, 3794, 1829, 4117, 2407, 7649, 3794, 13955, 23758, 6225, 3555, 9640, 3660, 18871, 21136, 1829, 4117, 2407, 7649, 3794, 295, 14641, 34499], "avg_logprob": -0.358398428807656, "compression_ratio": 1.082191780821918, "no_speech_prob": 0.0, "words": [{"start": 1556.31, "end": 1557.27, "word": "السيكوانس", "probability": 0.703125}, {"start": 1557.27, "end": 1558.01, "word": " SN", "probability": 0.329833984375}, {"start": 1558.01, "end": 1560.27, "word": " هذا", "probability": 0.17529296875}, {"start": 1560.27, "end": 1560.61, "word": " عبارة", "probability": 0.978271484375}, {"start": 1560.61, "end": 1560.73, "word": " عن", "probability": 0.99658203125}, {"start": 1560.73, "end": 1561.29, "word": " السيكوانس", "probability": 0.8376668294270834}, {"start": 1561.29, "end": 1561.41, "word": " of", "probability": 0.69677734375}, {"start": 1561.41, "end": 1561.79, "word": " partial", "probability": 0.95751953125}, {"start": 1561.79, "end": 1562.29, "word": " sums", "probability": 0.81591796875}], "temperature": 1.0}, {"id": 56, "seek": 160037, "start": 1572.51, "end": 1600.37, "text": "of the harmonic series sigma 1 على n ايش مالهم؟ اثبتنا انهم unbounded ال sequence هذه is unbounded بنالنا ذلك في مثال سابق unbounded فلو سمينا المتباين هذا star then it follows", "tokens": [2670, 264, 32270, 2638, 12771, 502, 15844, 297, 1975, 1829, 8592, 3714, 6027, 16095, 22807, 1975, 12984, 3555, 2655, 8315, 16472, 16095, 517, 18767, 292, 2423, 8310, 29538, 307, 517, 18767, 292, 44945, 6027, 8315, 29910, 23275, 8978, 50113, 6027, 8608, 16758, 4587, 517, 18767, 292, 6156, 1211, 2407, 8608, 2304, 1829, 8315, 9673, 2655, 3555, 995, 9957, 23758, 3543, 550, 309, 10002], "avg_logprob": -0.3371582077816129, "compression_ratio": 1.393063583815029, "no_speech_prob": 0.0, "words": [{"start": 1572.51, "end": 1573.03, "word": "of", "probability": 0.057220458984375}, {"start": 1573.03, "end": 1573.41, "word": " the", "probability": 0.259033203125}, {"start": 1573.41, "end": 1573.91, "word": " harmonic", "probability": 0.8720703125}, {"start": 1573.91, "end": 1574.45, "word": " series", "probability": 0.8916015625}, {"start": 1574.45, "end": 1574.77, "word": " sigma", "probability": 0.3330078125}, {"start": 1574.77, "end": 1575.13, "word": " 1", "probability": 0.487548828125}, {"start": 1575.13, "end": 1575.47, "word": " على", "probability": 0.466552734375}, {"start": 1575.47, "end": 1575.85, "word": " n", "probability": 0.51123046875}, {"start": 1575.85, "end": 1576.71, "word": " ايش", "probability": 0.5757649739583334}, {"start": 1576.71, "end": 1577.51, "word": " مالهم؟", "probability": 0.80859375}, {"start": 1577.51, "end": 1578.33, "word": " اثبتنا", "probability": 0.87099609375}, {"start": 1578.33, "end": 1578.71, "word": " انهم", "probability": 0.830078125}, {"start": 1578.71, "end": 1579.53, "word": " unbounded", "probability": 0.8230794270833334}, {"start": 1579.53, "end": 1579.75, "word": " ال", "probability": 0.6611328125}, {"start": 1579.75, "end": 1580.05, "word": " sequence", "probability": 0.456787109375}, {"start": 1580.05, "end": 1580.57, "word": " هذه", "probability": 0.4912109375}, {"start": 1580.57, "end": 1580.83, "word": " is", "probability": 0.59619140625}, {"start": 1580.83, "end": 1583.07, "word": " unbounded", "probability": 0.8782552083333334}, {"start": 1583.07, "end": 1583.57, "word": " بنالنا", "probability": 0.68212890625}, {"start": 1583.57, "end": 1583.89, "word": " ذلك", "probability": 0.978759765625}, {"start": 1583.89, "end": 1584.07, "word": " في", "probability": 0.87060546875}, {"start": 1584.07, "end": 1584.41, "word": " مثال", "probability": 0.894287109375}, {"start": 1584.41, "end": 1584.93, "word": " سابق", "probability": 0.8478190104166666}, {"start": 1584.93, "end": 1590.67, "word": " unbounded", "probability": 0.7858072916666666}, {"start": 1590.67, "end": 1591.33, "word": " فلو", "probability": 0.9723307291666666}, {"start": 1591.33, "end": 1591.99, "word": " سمينا", "probability": 0.955078125}, {"start": 1591.99, "end": 1595.07, "word": " المتباين", "probability": 0.8876953125}, {"start": 1595.07, "end": 1595.39, "word": " هذا", "probability": 0.25439453125}, {"start": 1595.39, "end": 1595.99, "word": " star", "probability": 0.56689453125}, {"start": 1595.99, "end": 1599.53, "word": " then", "probability": 0.64404296875}, {"start": 1599.53, "end": 1599.89, "word": " it", "probability": 0.96337890625}, {"start": 1599.89, "end": 1600.37, "word": " follows", "probability": 0.9091796875}], "temperature": 1.0}, {"id": 57, "seek": 163360, "start": 1604.9, "end": 1633.6, "text": "from star ينتج من المتباينة star إذا كانت ال sequence هذه unbounded لصغيرة unbounded فالحدود أكبر is unbounded ال sequence SM star is unbounded وبالتالي حسب النظرية أعلى so by", "tokens": [20579, 3543, 7251, 29399, 7435, 9154, 9673, 2655, 3555, 995, 9957, 3660, 3543, 11933, 15730, 25961, 2655, 2423, 8310, 29538, 517, 18767, 292, 5296, 9381, 17082, 48923, 517, 18767, 292, 6156, 6027, 24401, 23328, 5551, 4117, 26890, 307, 517, 18767, 292, 2423, 8310, 13115, 3543, 307, 517, 18767, 292, 46599, 6027, 2655, 6027, 1829, 11331, 35457, 28239, 19913, 2288, 10632, 5551, 3615, 23942, 370, 538], "avg_logprob": -0.23615057382619742, "compression_ratio": 1.4727272727272727, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1604.9, "end": 1605.3, "word": "from", "probability": 0.1429443359375}, {"start": 1605.3, "end": 1605.9, "word": " star", "probability": 0.53857421875}, {"start": 1605.9, "end": 1606.82, "word": " ينتج", "probability": 0.9285481770833334}, {"start": 1606.82, "end": 1607.06, "word": " من", "probability": 0.9755859375}, {"start": 1607.06, "end": 1608.02, "word": " المتباينة", "probability": 0.7827555338541666}, {"start": 1608.02, "end": 1608.4, "word": " star", "probability": 0.64599609375}, {"start": 1608.4, "end": 1610.38, "word": " إذا", "probability": 0.83203125}, {"start": 1610.38, "end": 1610.76, "word": " كانت", "probability": 0.9794921875}, {"start": 1610.76, "end": 1610.9, "word": " ال", "probability": 0.88916015625}, {"start": 1610.9, "end": 1611.26, "word": " sequence", "probability": 0.80615234375}, {"start": 1611.26, "end": 1612.02, "word": " هذه", "probability": 0.451416015625}, {"start": 1612.02, "end": 1615.6, "word": " unbounded", "probability": 0.8818359375}, {"start": 1615.6, "end": 1616.2, "word": " لصغيرة", "probability": 0.6812744140625}, {"start": 1616.2, "end": 1617.06, "word": " unbounded", "probability": 0.91650390625}, {"start": 1617.06, "end": 1617.84, "word": " فالحدود", "probability": 0.931396484375}, {"start": 1617.84, "end": 1618.46, "word": " أكبر", "probability": 0.9013671875}, {"start": 1618.46, "end": 1619.7, "word": " is", "probability": 0.71923828125}, {"start": 1619.7, "end": 1620.4, "word": " unbounded", "probability": 0.9611002604166666}, {"start": 1620.4, "end": 1620.62, "word": " ال", "probability": 0.29248046875}, {"start": 1620.62, "end": 1621.24, "word": " sequence", "probability": 0.95361328125}, {"start": 1621.24, "end": 1622.0, "word": " SM", "probability": 0.29052734375}, {"start": 1622.0, "end": 1622.62, "word": " star", "probability": 0.176025390625}, {"start": 1622.62, "end": 1624.36, "word": " is", "probability": 0.85205078125}, {"start": 1624.36, "end": 1627.24, "word": " unbounded", "probability": 0.9669596354166666}, {"start": 1627.24, "end": 1631.14, "word": " وبالتالي", "probability": 0.9517578125}, {"start": 1631.14, "end": 1631.56, "word": " حسب", "probability": 0.933349609375}, {"start": 1631.56, "end": 1632.18, "word": " النظرية", "probability": 0.93896484375}, {"start": 1632.18, "end": 1632.6, "word": " أعلى", "probability": 0.7900390625}, {"start": 1632.6, "end": 1633.1, "word": " so", "probability": 0.68896484375}, {"start": 1633.1, "end": 1633.6, "word": " by", "probability": 0.919921875}], "temperature": 1.0}, {"id": 58, "seek": 165629, "start": 1640.89, "end": 1656.29, "text": "السيريز هي سيكوينس باشا سمسا بايتالي P Series سيجما من K بساوة واحد وإنفينيتي لواحد على K أوس P is divergent", "tokens": [6027, 3794, 1829, 16572, 11622, 39896, 8608, 1829, 4117, 2407, 9957, 3794, 4724, 33599, 995, 8608, 2304, 3794, 995, 4724, 995, 36081, 6027, 1829, 430, 13934, 8608, 1829, 7435, 15042, 9154, 591, 4724, 3794, 995, 2407, 3660, 36764, 24401, 4032, 28814, 1863, 5172, 9957, 1829, 31371, 5296, 14407, 24401, 15844, 591, 34051, 3794, 430, 307, 18558, 6930], "avg_logprob": -0.6212284215565386, "compression_ratio": 1.2962962962962963, "no_speech_prob": 0.0, "words": [{"start": 1640.89, "end": 1641.93, "word": "السيريز", "probability": 0.4827880859375}, {"start": 1641.93, "end": 1642.97, "word": " هي", "probability": 0.2044677734375}, {"start": 1642.97, "end": 1644.49, "word": " سيكوينس", "probability": 0.680908203125}, {"start": 1644.49, "end": 1644.95, "word": " باشا", "probability": 0.5549723307291666}, {"start": 1644.95, "end": 1645.41, "word": " سمسا", "probability": 0.462646484375}, {"start": 1645.41, "end": 1645.91, "word": " بايتالي", "probability": 0.4662109375}, {"start": 1645.91, "end": 1646.23, "word": " P", "probability": 0.3916015625}, {"start": 1646.23, "end": 1646.89, "word": " Series", "probability": 0.337646484375}, {"start": 1646.89, "end": 1647.85, "word": " سيجما", "probability": 0.6285400390625}, {"start": 1647.85, "end": 1648.07, "word": " من", "probability": 0.9677734375}, {"start": 1648.07, "end": 1648.31, "word": " K", "probability": 0.51123046875}, {"start": 1648.31, "end": 1648.85, "word": " بساوة", "probability": 0.484130859375}, {"start": 1648.85, "end": 1649.37, "word": " واحد", "probability": 0.911865234375}, {"start": 1649.37, "end": 1650.09, "word": " وإنفينيتي", "probability": 0.7238595145089286}, {"start": 1650.09, "end": 1651.55, "word": " لواحد", "probability": 0.7743326822916666}, {"start": 1651.55, "end": 1651.79, "word": " على", "probability": 0.595703125}, {"start": 1651.79, "end": 1652.23, "word": " K", "probability": 0.82470703125}, {"start": 1652.23, "end": 1652.61, "word": " أوس", "probability": 0.50933837890625}, {"start": 1652.61, "end": 1652.93, "word": " P", "probability": 0.8251953125}, {"start": 1652.93, "end": 1655.39, "word": " is", "probability": 0.318359375}, {"start": 1655.39, "end": 1656.29, "word": " divergent", "probability": 0.739990234375}], "temperature": 1.0}, {"id": 59, "seek": 168229, "start": 1661.61, "end": 1682.29, "text": "حسب النظرية اللى ذكرناها سابقًا، طيب، في عندي هاي series of positive numbers أو non-negative real numbers و ال sequence of partial sums أبعدتها unbounded، إذا حسب النظرية ال series is not convergent أو divergent، صح؟", "tokens": [5016, 35457, 28239, 19913, 2288, 10632, 13672, 7578, 29910, 37983, 8315, 11296, 8608, 16758, 4587, 14111, 995, 12399, 23032, 1829, 3555, 12399, 8978, 18871, 16254, 8032, 47302, 2638, 295, 3353, 3547, 34051, 2107, 12, 28561, 1166, 957, 3547, 4032, 2423, 8310, 295, 14641, 34499, 5551, 3555, 22488, 2655, 11296, 517, 18767, 292, 12399, 11933, 15730, 11331, 35457, 28239, 19913, 2288, 10632, 2423, 2638, 307, 406, 9652, 6930, 34051, 18558, 6930, 12399, 20328, 5016, 22807], "avg_logprob": -0.2945833396911621, "compression_ratio": 1.4846938775510203, "no_speech_prob": 0.0, "words": [{"start": 1661.61, "end": 1662.09, "word": "حسب", "probability": 0.7376708984375}, {"start": 1662.09, "end": 1662.85, "word": " النظرية", "probability": 0.944580078125}, {"start": 1662.85, "end": 1664.41, "word": " اللى", "probability": 0.444091796875}, {"start": 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0.73291015625}, {"start": 1671.15, "end": 1671.53, "word": "-negative", "probability": 0.8626302083333334}, {"start": 1671.53, "end": 1671.75, "word": " real", "probability": 0.85009765625}, {"start": 1671.75, "end": 1672.25, "word": " numbers", "probability": 0.8681640625}, {"start": 1672.25, "end": 1673.83, "word": " و", "probability": 0.428466796875}, {"start": 1673.83, "end": 1674.09, "word": " ال", "probability": 0.55419921875}, {"start": 1674.09, "end": 1674.39, "word": " sequence", "probability": 0.88427734375}, {"start": 1674.39, "end": 1674.73, "word": " of", "probability": 0.966796875}, {"start": 1674.73, "end": 1675.03, "word": " partial", "probability": 0.96044921875}, {"start": 1675.03, "end": 1675.39, "word": " sums", "probability": 0.865234375}, {"start": 1675.39, "end": 1675.89, "word": " أبعدتها", "probability": 0.6732177734375}, {"start": 1675.89, "end": 1676.81, "word": " unbounded،", "probability": 0.8951416015625}, {"start": 1676.81, "end": 1676.97, "word": " إذا", "probability": 0.64111328125}, {"start": 1676.97, "end": 1677.31, "word": " حسب", "probability": 0.9345703125}, {"start": 1677.31, "end": 1677.95, "word": " النظرية", "probability": 0.992431640625}, {"start": 1677.95, "end": 1679.09, "word": " ال", "probability": 0.6923828125}, {"start": 1679.09, "end": 1679.49, "word": " series", "probability": 0.92919921875}, {"start": 1679.49, "end": 1679.91, "word": " is", "probability": 0.92724609375}, {"start": 1679.91, "end": 1680.25, "word": " not", "probability": 0.96533203125}, {"start": 1680.25, "end": 1680.97, "word": " convergent", "probability": 0.959228515625}, {"start": 1680.97, "end": 1681.19, "word": " أو", "probability": 0.8916015625}, {"start": 1681.19, "end": 1681.91, "word": " divergent،", "probability": 0.8289388020833334}, {"start": 1681.91, "end": 1682.29, "word": " صح؟", "probability": 0.98681640625}], "temperature": 1.0}, {"id": 60, "seek": 170622, "start": 1683.92, "end": 1706.22, "text": "إذن هذا بتثبت الجزء التاني وبالتاني هيك بيكون بارهاننا اختبار ال P-series test او ال P-series test إذن أي P-series بتكون convergent إذا ال P أكبر من واحد و divergent إذا P أصغر من أول ساول واحد في أي سؤال؟", "tokens": [28814, 8848, 1863, 23758, 39894, 12984, 3555, 2655, 25724, 11622, 38207, 16712, 7649, 1829, 46599, 6027, 2655, 7649, 1829, 39896, 4117, 4724, 1829, 30544, 4724, 9640, 3224, 7649, 8315, 1975, 46456, 3555, 9640, 2423, 430, 12, 12484, 530, 1500, 1975, 2407, 2423, 430, 12, 12484, 530, 1500, 11933, 8848, 1863, 36632, 430, 12, 12484, 530, 39894, 30544, 9652, 6930, 11933, 15730, 2423, 430, 5551, 4117, 26890, 9154, 36764, 24401, 4032, 18558, 6930, 11933, 15730, 430, 5551, 9381, 17082, 2288, 9154, 5551, 12610, 8608, 995, 12610, 36764, 24401, 8978, 36632, 8608, 33604, 6027, 22807], "avg_logprob": -0.23454122086788745, "compression_ratio": 1.7472527472527473, "no_speech_prob": 0.0, "words": [{"start": 1683.92, "end": 1684.24, "word": "إذن", "probability": 0.4517415364583333}, {"start": 1684.24, "end": 1684.46, "word": " هذا", "probability": 0.85009765625}, {"start": 1684.46, "end": 1684.92, "word": " بتثبت", "probability": 0.8214111328125}, {"start": 1684.92, "end": 1685.26, "word": " الجزء", "probability": 0.9632161458333334}, {"start": 1685.26, "end": 1685.62, "word": " التاني", "probability": 0.9075520833333334}, {"start": 1685.62, "end": 1686.0, "word": " وبالتاني", "probability": 0.73955078125}, {"start": 1686.0, "end": 1686.18, "word": " هيك", "probability": 0.77685546875}, {"start": 1686.18, "end": 1686.52, "word": " بيكون", "probability": 0.7430826822916666}, {"start": 1686.52, "end": 1687.64, "word": " بارهاننا", "probability": 0.7322265625}, {"start": 1687.64, "end": 1689.54, "word": " اختبار", "probability": 0.920166015625}, {"start": 1689.54, "end": 1689.74, "word": " ال", "probability": 0.8505859375}, {"start": 1689.74, "end": 1689.88, "word": " P", "probability": 0.6640625}, {"start": 1689.88, "end": 1690.38, "word": "-series", "probability": 0.6171875}, {"start": 1690.38, "end": 1690.74, "word": " test", "probability": 0.91455078125}, {"start": 1690.74, "end": 1690.9, "word": " او", "probability": 0.782958984375}, {"start": 1690.9, "end": 1691.04, "word": " ال", "probability": 0.7021484375}, {"start": 1691.04, "end": 1691.18, "word": " P", "probability": 0.90478515625}, {"start": 1691.18, "end": 1691.58, "word": "-series", "probability": 0.85791015625}, {"start": 1691.58, "end": 1692.1, "word": " test", "probability": 0.94873046875}, {"start": 1692.1, "end": 1695.2, "word": " إذن", "probability": 0.6724446614583334}, {"start": 1695.2, "end": 1695.42, "word": " أي", "probability": 0.6064453125}, {"start": 1695.42, "end": 1696.16, "word": " P", "probability": 0.56298828125}, {"start": 1696.16, "end": 1696.78, "word": "-series", "probability": 0.9095052083333334}, {"start": 1696.78, "end": 1698.84, "word": " بتكون", "probability": 0.9169921875}, {"start": 1698.84, "end": 1699.6, "word": " convergent", "probability": 0.8056640625}, {"start": 1699.6, "end": 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"probability": 0.82666015625}, {"start": 1703.12, "end": 1703.52, "word": " ساول", "probability": 0.7589518229166666}, {"start": 1703.52, "end": 1703.94, "word": " واحد", "probability": 0.96923828125}, {"start": 1703.94, "end": 1705.5, "word": " في", "probability": 0.5576171875}, {"start": 1705.5, "end": 1705.62, "word": " أي", "probability": 0.70556640625}, {"start": 1705.62, "end": 1706.22, "word": " سؤال؟", "probability": 0.9661865234375}], "temperature": 1.0}, {"id": 61, "seek": 175702, "start": 1732.32, "end": 1757.02, "text": "زي ما أخرنا comparison و limit comparison test للsequences في comparison test لل series comparison test for series", "tokens": [11622, 1829, 19446, 5551, 34740, 8315, 9660, 4032, 4948, 9660, 1500, 24976, 11834, 2667, 8978, 9660, 1500, 24976, 2638, 9660, 1500, 337, 2638], "avg_logprob": -0.2830403658250968, "compression_ratio": 1.4444444444444444, "no_speech_prob": 0.0, "words": [{"start": 1732.32, "end": 1732.74, "word": "زي", "probability": 0.819580078125}, {"start": 1732.74, "end": 1732.86, "word": " ما", "probability": 0.93798828125}, {"start": 1732.86, "end": 1733.4, "word": " أخرنا", "probability": 0.7200520833333334}, {"start": 1733.4, "end": 1734.18, "word": " comparison", "probability": 0.377197265625}, {"start": 1734.18, "end": 1734.48, "word": " و", "probability": 0.82568359375}, {"start": 1734.48, "end": 1734.72, "word": " limit", "probability": 0.921875}, {"start": 1734.72, "end": 1735.28, "word": " comparison", "probability": 0.93701171875}, {"start": 1735.28, "end": 1735.8, "word": " test", "probability": 0.8994140625}, {"start": 1735.8, "end": 1737.2, "word": " للsequences", "probability": 0.5744222005208334}, {"start": 1737.2, "end": 1738.24, "word": " في", "probability": 0.53857421875}, {"start": 1738.24, "end": 1739.6, "word": " comparison", "probability": 0.7578125}, {"start": 1739.6, "end": 1740.14, "word": " test", "probability": 0.87353515625}, {"start": 1740.14, "end": 1740.4, "word": " لل", "probability": 0.78173828125}, {"start": 1740.4, "end": 1740.92, "word": " series", "probability": 0.88232421875}, {"start": 1740.92, "end": 1748.9, "word": " comparison", "probability": 0.8408203125}, {"start": 1748.9, "end": 1753.96, "word": " test", "probability": 0.9365234375}, {"start": 1753.96, "end": 1756.34, "word": " for", "probability": 0.91845703125}, {"start": 1756.34, "end": 1757.02, "word": " series", "probability": 0.92138671875}], "temperature": 1.0}, {"id": 62, "seek": 178138, "start": 1773.68, "end": 1781.38, "text": "لت XIN و YIN بـ sequences of non-negative real numbers", "tokens": [1211, 2655, 1783, 1464, 4032, 398, 1464, 4724, 39184, 22978, 295, 2107, 12, 28561, 1166, 957, 3547], "avg_logprob": -0.5377604299121432, "compression_ratio": 0.8939393939393939, "no_speech_prob": 0.0, "words": [{"start": 1773.68, "end": 1774.24, "word": "لت", "probability": 0.398284912109375}, {"start": 1774.24, "end": 1775.2, "word": " XIN", "probability": 0.38916015625}, {"start": 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series الأكبر بالتأكيد diverge وهي البرهان البرهن الجزء الأول", "tokens": [1671, 331, 6930, 39894, 4587, 16254, 16472, 2423, 2638, 16247, 9381, 17082, 2288, 41881, 293, 45164, 25961, 2655, 2423, 2638, 16247, 4117, 26890, 16247, 9381, 17082, 2288, 18558, 432, 6156, 3555, 2655, 4587, 16254, 14739, 2423, 2638, 16247, 4117, 26890, 20666, 2655, 10721, 4117, 25708, 18558, 432, 37037, 1829, 2423, 26890, 3224, 7649, 2423, 26890, 3224, 1863, 25724, 11622, 38207, 16247, 12610], "avg_logprob": -0.21775793414267283, "compression_ratio": 1.8043478260869565, "no_speech_prob": 0.0, "words": [{"start": 1869.92, "end": 1870.8, "word": "convergent", "probability": 0.8185221354166666}, {"start": 1870.8, "end": 1871.42, "word": " بتقدي", "probability": 0.6357421875}, {"start": 1871.42, "end": 1871.64, "word": " ان", "probability": 0.378173828125}, {"start": 1871.64, "end": 1871.82, "word": " ال", "probability": 0.5556640625}, {"start": 1871.82, "end": 1872.14, "word": " series", "probability": 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cauchy criterion for series given", "tokens": [640, 2540, 14739, 3224, 2423, 2638, 12771, 17861, 9652, 2880, 550, 538, 1335, 625, 88, 46691, 337, 2638, 2212], "avg_logprob": -0.2908203214406967, "compression_ratio": 1.036144578313253, "no_speech_prob": 0.0, "words": [{"start": 1901.02, "end": 1901.88, "word": "assume", "probability": 0.798828125}, {"start": 1901.88, "end": 1904.76, "word": " أنه", "probability": 0.5260009765625}, {"start": 1904.76, "end": 1905.02, "word": " ال", "probability": 0.8671875}, {"start": 1905.02, "end": 1905.38, "word": " series", "probability": 0.61669921875}, {"start": 1905.38, "end": 1905.9, "word": " sigma", "probability": 0.67724609375}, {"start": 1905.9, "end": 1906.5, "word": " yn", "probability": 0.59033203125}, {"start": 1906.5, "end": 1908.96, "word": " converges", "probability": 0.776611328125}, {"start": 1908.96, "end": 1916.18, "word": " then", "probability": 0.7568359375}, {"start": 1916.18, "end": 1916.78, "word": " by", "probability": 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0.982421875}, {"start": 2250.74, "end": 2251.06, "word": " N", "probability": 0.90771484375}, {"start": 2251.06, "end": 2251.64, "word": " أكبر", "probability": 0.9480794270833334}, {"start": 2251.64, "end": 2251.82, "word": " من", "probability": 0.98876953125}, {"start": 2251.82, "end": 2252.0, "word": " أو", "probability": 0.1729736328125}, {"start": 2252.0, "end": 2252.44, "word": " يساوي", "probability": 0.8399658203125}, {"start": 2252.44, "end": 2252.86, "word": " capital", "probability": 0.34765625}, {"start": 2252.86, "end": 2253.28, "word": " M", "probability": 0.98828125}, {"start": 2253.28, "end": 2254.52, "word": " so", "probability": 0.36376953125}, {"start": 2254.52, "end": 2256.48, "word": " بستخدم", "probability": 0.886474609375}, {"start": 2256.48, "end": 2256.88, "word": " كوشي", "probability": 0.774566650390625}, {"start": 2256.88, "end": 2257.38, "word": " criterion", "probability": 0.9423828125}, {"start": 2257.38, "end": 2258.02, "word": " كمان", "probability": 0.9500325520833334}, {"start": 2258.02, "end": 2258.62, "word": " مرة", "probability": 0.984375}, {"start": 2258.62, "end": 2259.1, "word": " by", "probability": 0.638671875}, {"start": 2259.1, "end": 2259.78, "word": " koshi", "probability": 0.49755859375}, {"start": 2259.78, "end": 2262.78, "word": " criterion", "probability": 0.94775390625}], "temperature": 1.0}, {"id": 80, "seek": 228887, "start": 2265.13, "end": 2288.87, "text": "for series الـ series sigma xn converges لأن هاي شرط كوشي متحقق، صح؟ هاي لأي إبسلون given إبسلون أكبر من السفر أثناء أن يوجد capital M", "tokens": [2994, 2638, 2423, 39184, 2638, 12771, 2031, 77, 9652, 2880, 5296, 33456, 8032, 47302, 13412, 2288, 9566, 9122, 2407, 8592, 1829, 44650, 5016, 4587, 4587, 12399, 20328, 5016, 22807, 8032, 47302, 5296, 10721, 1829, 11933, 3555, 3794, 1211, 11536, 2212, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 5551, 12984, 1863, 16606, 14739, 7251, 29245, 3215, 4238, 376], "avg_logprob": 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{"start": 2322.77, "end": 2323.29, "word": " is", "probability": 0.9755859375}, {"start": 2323.29, "end": 2323.97, "word": " the", "probability": 0.91162109375}, {"start": 2323.97, "end": 2325.05, "word": " contrapositive", "probability": 0.8956298828125}, {"start": 2325.05, "end": 2325.15, "word": " ..", "probability": 0.53515625}, {"start": 2325.15, "end": 2327.39, "word": " the", "probability": 0.469970703125}, {"start": 2327.39, "end": 2332.39, "word": " contrapositive", "probability": 0.9356689453125}, {"start": 2332.39, "end": 2334.91, "word": " أو", "probability": 0.5244140625}, {"start": 2334.91, "end": 2335.13, "word": " the", "probability": 0.78955078125}, {"start": 2335.13, "end": 2336.17, "word": " contraposition", "probability": 0.9578450520833334}, {"start": 2336.17, "end": 2337.07, "word": " ..", "probability": 0.546875}, {"start": 2337.07, "end": 2339.99, "word": " this", "probability": 0.93310546875}, {"start": 2339.99, "end": 2340.15, "word": " is", "probability": 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contrapositive للعبارة في الجزء الأول نفي هذا اللي هو ال series sigma x in by dirge بيقدي الى نفي هذا اللي هو ال series y in by dirge", "tokens": [3224, 1211, 23758, 20328, 5016, 1829, 5016, 37279, 6027, 14407, 8717, 4587, 2288, 10721, 25724, 11622, 38207, 16712, 7649, 1829, 1975, 2407, 37279, 6027, 14407, 8717, 7435, 1829, 3555, 2423, 660, 4007, 329, 2187, 24976, 3615, 3555, 9640, 3660, 8978, 25724, 11622, 38207, 16247, 12610, 2423, 660, 4007, 329, 2187, 24976, 3615, 3555, 9640, 3660, 8978, 25724, 11622, 38207, 16247, 12610, 8717, 41185, 23758, 13672, 1829, 31439, 2423, 2638, 12771, 2031, 294, 538, 4746, 432, 4724, 1829, 4587, 16254, 2423, 7578, 8717, 41185, 23758, 13672, 1829, 31439, 2423, 2638, 288, 294, 538, 4746, 432], "avg_logprob": -0.23240131296609579, "compression_ratio": 2.0290697674418605, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2384.96, "end": 2385.24, "word": "هل", "probability": 0.9716796875}, {"start": 2385.24, "end": 2385.44, "word": " هذا", 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2414.08, "word": " أي", "probability": 0.53857421875}, {"start": 2414.08, "end": 2414.92, "word": " سؤال؟", "probability": 0.9287109375}, {"start": 2414.92, "end": 2415.04, "word": " أي", "probability": 0.7841796875}, {"start": 2415.04, "end": 2417.7, "word": " استفسار؟", "probability": 0.9481201171875}, {"start": 2417.7, "end": 2418.48, "word": " أحيانا", "probability": 0.95244140625}, {"start": 2418.48, "end": 2420.7, "word": " بيكون", "probability": 0.9423828125}, {"start": 2420.7, "end": 2421.16, "word": " صعب", "probability": 0.998046875}, {"start": 2421.16, "end": 2421.3, "word": " أن", "probability": 0.55078125}, {"start": 2421.3, "end": 2421.52, "word": " احنا", "probability": 0.8829752604166666}, {"start": 2421.52, "end": 2422.04, "word": " نعمل", "probability": 0.9967447916666666}], "temperature": 1.0}, {"id": 87, "seek": 244454, "start": 2423.08, "end": 2444.54, "text": "مقارنة بين حدود ال series sigma xn و حدود ال series sigma yn بالطريقة المباشرة زي ما في ال star أحيانا مش سهل نعمل مقارنة زي هذه وبالتالي بنلجأ إلى اختبار اخر بنسميه limit comparison test", "tokens": [2304, 4587, 9640, 1863, 3660, 49374, 11331, 3215, 23328, 2423, 2638, 12771, 2031, 77, 4032, 11331, 3215, 23328, 2423, 2638, 12771, 17861, 20666, 9566, 16572, 28671, 9673, 3555, 33599, 25720, 30767, 1829, 19446, 8978, 2423, 3543, 5551, 5016, 1829, 7649, 995, 37893, 8608, 3224, 1211, 8717, 25957, 1211, 3714, 4587, 9640, 1863, 3660, 30767, 1829, 29538, 46599, 6027, 2655, 6027, 1829, 44945, 1211, 7435, 10721, 30731, 1975, 46456, 3555, 9640, 1975, 34740, 44945, 38251, 1829, 3224, 4948, 9660, 1500], "avg_logprob": -0.13496094159781932, "compression_ratio": 1.5675675675675675, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 2423.08, "end": 2424.0, "word": "مقارنة", "probability": 0.93310546875}, {"start": 2424.0, "end": 2424.46, "word": " بين", "probability": 0.89892578125}, {"start": 2424.46, "end": 2424.96, "word": " حدود", "probability": 0.98828125}, {"start": 2424.96, "end": 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2434.12, "word": " زي", "probability": 0.676025390625}, {"start": 2434.12, "end": 2434.24, "word": " ما", "probability": 0.93896484375}, {"start": 2434.24, "end": 2434.38, "word": " في", "probability": 0.8701171875}, {"start": 2434.38, "end": 2434.48, "word": " ال", "probability": 0.89453125}, {"start": 2434.48, "end": 2434.78, "word": " star", "probability": 0.33935546875}, {"start": 2434.78, "end": 2436.44, "word": " أحيانا", "probability": 0.94775390625}, {"start": 2436.44, "end": 2436.66, "word": " مش", "probability": 0.9052734375}, {"start": 2436.66, "end": 2436.96, "word": " سهل", "probability": 0.9957682291666666}, {"start": 2436.96, "end": 2437.48, "word": " نعمل", "probability": 0.8971354166666666}, {"start": 2437.48, "end": 2438.1, "word": " مقارنة", "probability": 0.99169921875}, {"start": 2438.1, "end": 2438.34, "word": " زي", "probability": 0.966552734375}, {"start": 2438.34, "end": 2438.68, "word": " هذه", "probability": 0.75927734375}, {"start": 2438.68, "end": 2440.52, "word": " وبالتالي", "probability": 0.92333984375}, {"start": 2440.52, "end": 2441.06, "word": " بنلجأ", "probability": 0.95703125}, {"start": 2441.06, "end": 2441.36, "word": " إلى", "probability": 0.46240234375}, {"start": 2441.36, "end": 2442.02, "word": " اختبار", "probability": 0.926025390625}, {"start": 2442.02, "end": 2442.38, "word": " اخر", "probability": 0.7064208984375}, {"start": 2442.38, "end": 2443.02, "word": " بنسميه", "probability": 0.919677734375}, {"start": 2443.02, "end": 2443.26, "word": " limit", "probability": 0.92626953125}, {"start": 2443.26, "end": 2443.98, "word": " comparison", "probability": 0.890625}, {"start": 2443.98, "end": 2444.54, "word": " test", "probability": 0.93408203125}], "temperature": 1.0}, {"id": 88, "seek": 247092, "start": 2445.54, "end": 2470.92, "text": "فنكتب ال test هذا دكتور؟ نعم هلأ عبس النظرية برضه خطأ يعني نفس نحو اللي كنا نعمله بال sequence نعمله بال series هى الفترة التالية؟ اه طبعا يعني انت لو كان مثلا هذه الصحية كلامك بالظبط يعني لو كانت ال series ال series مثلا هذه ال sigma yn diverse", "tokens": [5172, 1863, 4117, 2655, 3555, 2423, 1500, 23758, 11778, 4117, 2655, 13063, 22807, 8717, 25957, 8032, 1211, 10721, 6225, 3555, 3794, 28239, 19913, 2288, 10632, 4724, 43042, 3224, 16490, 9566, 10721, 37495, 22653, 8717, 36178, 8717, 5016, 2407, 13672, 1829, 9122, 8315, 8717, 25957, 43761, 20666, 8310, 8717, 25957, 43761, 20666, 2638, 8032, 7578, 27188, 2655, 25720, 16712, 6027, 10632, 22807, 1975, 3224, 23032, 3555, 3615, 995, 37495, 22653, 16472, 2655, 45164, 25961, 50113, 15040, 29538, 31767, 5016, 10632, 28242, 10943, 4117, 20666, 19913, 3555, 9566, 37495, 22653, 45164, 25961, 2655, 2423, 2638, 2423, 2638, 50113, 15040, 29538, 2423, 12771, 17861, 9521], "avg_logprob": -0.266535199961616, "compression_ratio": 1.817351598173516, "no_speech_prob": 0.0, "words": [{"start": 2445.54, "end": 2446.32, "word": "فنكتب", "probability": 0.9609375}, {"start": 2446.32, "end": 2446.46, "word": " ال", "probability": 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0.4803059895833333}, {"start": 2452.96, "end": 2453.2, "word": " اللي", "probability": 0.639892578125}, {"start": 2453.2, "end": 2453.56, "word": " كنا", "probability": 0.61248779296875}, {"start": 2453.56, "end": 2453.86, "word": " نعمله", "probability": 0.8854166666666666}, {"start": 2453.86, "end": 2454.02, "word": " بال", "probability": 0.740234375}, {"start": 2454.02, "end": 2454.3, "word": " sequence", "probability": 0.96728515625}, {"start": 2454.3, "end": 2454.82, "word": " نعمله", "probability": 0.9430338541666666}, {"start": 2454.82, "end": 2455.02, "word": " بال", "probability": 0.96484375}, {"start": 2455.02, "end": 2455.46, "word": " series", "probability": 0.96337890625}, {"start": 2455.46, "end": 2456.86, "word": " هى", "probability": 0.4014892578125}, {"start": 2456.86, "end": 2458.36, "word": " الفترة", "probability": 0.9619140625}, {"start": 2458.36, "end": 2458.68, "word": " التالية؟", "probability": 0.77337646484375}, {"start": 2458.68, "end": 2458.88, "word": " اه", "probability": 0.753662109375}, {"start": 2458.88, "end": 2459.32, "word": " طبعا", "probability": 0.997314453125}, {"start": 2459.32, "end": 2459.58, "word": " يعني", "probability": 0.849609375}, {"start": 2459.58, "end": 2459.86, "word": " انت", "probability": 0.809326171875}, {"start": 2459.86, "end": 2460.02, "word": " لو", "probability": 0.98095703125}, {"start": 2460.02, "end": 2460.26, "word": " كان", "probability": 0.9931640625}, {"start": 2460.26, "end": 2460.6, "word": " مثلا", "probability": 0.98681640625}, {"start": 2460.6, "end": 2461.08, "word": " هذه", "probability": 0.51171875}, {"start": 2461.08, "end": 2461.94, "word": " الصحية", "probability": 0.8810221354166666}, {"start": 2461.94, "end": 2462.48, "word": " كلامك", "probability": 0.9856770833333334}, {"start": 2462.48, "end": 2463.88, "word": " بالظبط", "probability": 0.978271484375}, {"start": 2463.88, "end": 2464.2, "word": " يعني", "probability": 0.919921875}, {"start": 2464.2, "end": 2464.4, "word": " لو", "probability": 0.99169921875}, {"start": 2464.4, "end": 2464.72, "word": " كانت", "probability": 0.99462890625}, {"start": 2464.72, "end": 2464.88, "word": " ال", "probability": 0.96826171875}, {"start": 2464.88, "end": 2465.34, "word": " series", "probability": 0.97509765625}, {"start": 2465.34, "end": 2467.34, "word": " ال", "probability": 0.58544921875}, {"start": 2467.34, "end": 2467.74, "word": " series", "probability": 0.9658203125}, {"start": 2467.74, "end": 2468.16, "word": " مثلا", "probability": 0.997802734375}, {"start": 2468.16, "end": 2468.76, "word": " هذه", "probability": 0.763671875}, {"start": 2468.76, "end": 2469.52, "word": " ال", "probability": 0.41552734375}, {"start": 2469.52, "end": 2469.86, "word": " sigma", "probability": 0.93310546875}, {"start": 2469.86, "end": 2470.42, "word": " yn", "probability": 0.52587890625}, {"start": 2470.42, "end": 2470.92, "word": " diverse", "probability": 0.268798828125}], "temperature": 1.0}, {"id": 89, "seek": 249685, "start": 2472.07, "end": 2496.85, "text": "هل هذا بيقعد ان sigma xn diverge؟ مش بالضرورة ممكن diverge و ممكن converge نفس الحاجة لو كانت ال series sigma xn converge هل sigma yn converge؟ ممكن او ممكن لأ اكيد و ممكن نجيب counter examples لازم تفكري في إيجاد counter examples و انت بتدرسيه", "tokens": [3224, 1211, 23758, 4724, 1829, 4587, 22488, 16472, 12771, 2031, 77, 18558, 432, 22807, 37893, 20666, 11242, 2288, 13063, 3660, 3714, 43020, 18558, 432, 4032, 3714, 43020, 41881, 8717, 36178, 21542, 26108, 3660, 45164, 25961, 2655, 2423, 2638, 12771, 2031, 77, 41881, 8032, 1211, 12771, 17861, 41881, 22807, 3714, 43020, 1975, 2407, 3714, 43020, 5296, 10721, 1975, 4117, 25708, 4032, 3714, 43020, 8717, 7435, 1829, 3555, 5682, 5110, 5296, 31377, 2304, 6055, 5172, 4117, 16572, 8978, 11933, 1829, 7435, 18513, 5682, 5110, 4032, 16472, 2655, 39894, 3215, 2288, 3794, 1829, 3224], "avg_logprob": -0.1946331534696662, "compression_ratio": 1.7058823529411764, "no_speech_prob": 0.0, "words": [{"start": 2472.07, 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2477.71, "end": 2477.97, "word": " ممكن", "probability": 0.879638671875}, {"start": 2477.97, "end": 2478.53, "word": " converge", "probability": 0.99169921875}, {"start": 2478.53, "end": 2478.89, "word": " نفس", "probability": 0.890625}, {"start": 2478.89, "end": 2479.65, "word": " الحاجة", "probability": 0.98486328125}, {"start": 2479.65, "end": 2480.35, "word": " لو", "probability": 0.861328125}, {"start": 2480.35, "end": 2480.81, "word": " كانت", "probability": 0.990966796875}, {"start": 2480.81, "end": 2480.99, "word": " ال", "probability": 0.85205078125}, {"start": 2480.99, "end": 2481.81, "word": " series", "probability": 0.91943359375}, {"start": 2481.81, "end": 2482.33, "word": " sigma", "probability": 0.93994140625}, {"start": 2482.33, "end": 2483.27, "word": " xn", "probability": 0.990478515625}, {"start": 2483.27, "end": 2484.05, "word": " converge", "probability": 0.9462890625}, {"start": 2484.05, "end": 2485.51, "word": " هل", "probability": 0.951904296875}, {"start": 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2491.81, "end": 2492.43, "word": " examples", "probability": 0.853515625}, {"start": 2492.43, "end": 2493.25, "word": " لازم", "probability": 0.8301595052083334}, {"start": 2493.25, "end": 2493.75, "word": " تفكري", "probability": 0.81756591796875}, {"start": 2493.75, "end": 2493.91, "word": " في", "probability": 0.97265625}, {"start": 2493.91, "end": 2494.33, "word": " إيجاد", "probability": 0.9393310546875}, {"start": 2494.33, "end": 2494.69, "word": " counter", "probability": 0.79150390625}, {"start": 2494.69, "end": 2495.27, "word": " examples", "probability": 0.88427734375}, {"start": 2495.27, "end": 2495.89, "word": " و", "probability": 0.9697265625}, {"start": 2495.89, "end": 2496.07, "word": " انت", "probability": 0.76123046875}, {"start": 2496.07, "end": 2496.85, "word": " بتدرسيه", "probability": 0.9192708333333334}], "temperature": 1.0}, {"id": 90, "seek": 252203, "start": 2500.81, "end": 2522.03, "text": "نشوف ال limit comparison test limit comparison test", "tokens": [1863, 8592, 38688, 2423, 4948, 9660, 1500, 4948, 9660, 1500], "avg_logprob": -0.297762778672305, "compression_ratio": 1.2391304347826086, "no_speech_prob": 0.0, "words": [{"start": 2500.81, "end": 2501.31, "word": "نشوف", "probability": 0.7620442708333334}, {"start": 2501.31, "end": 2501.47, "word": " ال", "probability": 0.352294921875}, {"start": 2501.47, "end": 2501.65, "word": " limit", "probability": 0.65576171875}, {"start": 2501.65, "end": 2502.23, "word": " comparison", "probability": 0.92626953125}, {"start": 2502.23, "end": 2503.15, "word": " test", "probability": 0.93115234375}, {"start": 2503.15, "end": 2513.63, "word": " limit", "probability": 0.818359375}, {"start": 2513.63, "end": 2515.09, "word": " comparison", "probability": 0.94482421875}, {"start": 2515.09, "end": 2522.03, "word": " test", "probability": 0.9296875}], "temperature": 1.0}, {"id": 91, "seek": 256048, "start": 2538.3, "end": 2560.48, "text": "لت Xn وYn بيكونوا سيكوانس من حدود حق��قية مفتوحة بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة بيكون حدود حقيقية مفتوحة به", "tokens": [1211, 2655, 1783, 77, 4032, 56, 77, 4724, 1829, 30544, 14407, 8608, 1829, 4117, 2407, 7649, 3794, 9154, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 4724, 1829, 30544, 11331, 3215, 23328, 11331, 38436, 4587, 10632, 3714, 5172, 2655, 2407, 5016, 3660, 39627], "avg_logprob": -0.35901162790697677, "compression_ratio": 4.22093023255814, "no_speech_prob": 0.0, "words": [{"start": 2538.2999999999997, "end": 2539.7, "word": "لت", "probability": 0.52850341796875}, {"start": 2539.7, "end": 2541.1, "word": " Xn", "probability": 0.2882080078125}, {"start": 2541.1, "end": 2543.14, "word": " وYn", "probability": 0.8056640625}, {"start": 2543.14, "end": 2543.8, "word": " بيكونوا", "probability": 0.65423583984375}, {"start": 2543.8, "end": 2544.62, "word": " سيكوانس", "probability": 0.634033203125}, {"start": 2544.62, "end": 2545.82, "word": " من", "probability": 0.212158203125}, {"start": 2545.82, "end": 2546.42, "word": " حدود", "probability": 0.2880452473958333}, {"start": 2546.42, "end": 2547.12, "word": " حقيقية", "probability": 0.8104248046875}, {"start": 2547.12, "end": 2547.12, "word": " مفتوحة", "probability": 0.4933675130208333}, {"start": 2547.12, "end": 2550.12, "word": " بيكون", "probability": 0.7083333333333334}, {"start": 2550.12, "end": 2550.42, "word": " حدود", "probability": 0.34197998046875}, {"start": 2550.42, "end": 2550.42, "word": " حقيقية", "probability": 0.617431640625}, {"start": 2550.42, "end": 2550.42, "word": " مفتوحة", "probability": 0.8872477213541666}, {"start": 2550.42, "end": 2553.22, "word": " بيكون", "probability": 0.5984700520833334}, {"start": 2553.22, "end": 2553.44, "word": " حدود", "probability": 0.828125}, {"start": 2553.44, "end": 2555.3, "word": " حقيقية", "probability": 0.9539794921875}, {"start": 2555.3, "end": 2556.56, "word": " مفتوحة", "probability": 0.9469401041666666}, {"start": 2556.56, "end": 2556.96, "word": " بيكون", "probability": 0.7079264322916666}, {"start": 2556.96, "end": 2557.02, "word": " حدود", "probability": 0.8787434895833334}, {"start": 2557.02, "end": 2558.02, "word": " حقيقية", "probability": 0.9732666015625}, {"start": 2558.02, "end": 2558.02, "word": " مفتوحة", "probability": 0.96533203125}, {"start": 2558.02, "end": 2558.34, "word": " بيكون", "probability": 0.80908203125}, {"start": 2558.34, "end": 2558.34, "word": " حدود", "probability": 0.9016927083333334}, {"start": 2558.34, "end": 2558.34, "word": " حقيقية", "probability": 0.9791259765625}, {"start": 2558.34, "end": 2558.34, "word": " مفتوحة", "probability": 0.974853515625}, {"start": 2558.34, "end": 2558.46, "word": " بيكون", "probability": 0.9065755208333334}, {"start": 2558.46, "end": 2558.46, "word": " حدود", "probability": 0.9314778645833334}, {"start": 2558.46, "end": 2558.52, "word": " حقيقية", "probability": 0.982177734375}, {"start": 2558.52, "end": 2558.52, "word": " مفتوحة", "probability": 0.981201171875}, {"start": 2558.52, "end": 2558.52, "word": " بيكون", "probability": 0.953125}, {"start": 2558.52, "end": 2558.52, "word": " حدود", "probability": 0.9482421875}, {"start": 2558.52, "end": 2560.48, "word": " حقيقية", "probability": 0.9822998046875}, {"start": 2560.48, "end": 2560.48, "word": " مفتوحة", "probability": 0.9853515625}, {"start": 2560.48, "end": 2560.48, "word": " به", "probability": 0.007335662841796875}], "temperature": 1.0}, {"id": 92, "seek": 259533, "start": 2567.73, "end": 2595.33, "text": "و ال R هذا يعني عدد حقيقي طبعا ينتمي إلى R ففي عندي برضه نتيجتين النتيجة الأولى إذا كان ال R بسويش سفر then ال series sigma X M converges if and only if", "tokens": [2407, 2423, 497, 23758, 37495, 22653, 6225, 3215, 3215, 11331, 38436, 38436, 23032, 3555, 3615, 995, 7251, 29399, 2304, 1829, 30731, 497, 6156, 41185, 18871, 16254, 4724, 43042, 3224, 8717, 31371, 7435, 2655, 9957, 28239, 31371, 7435, 3660, 16247, 12610, 7578, 11933, 15730, 25961, 2423, 497, 4724, 3794, 45865, 8592, 8608, 5172, 2288, 550, 2423, 2638, 12771, 1783, 376, 9652, 2880, 498, 293, 787, 498], "avg_logprob": -0.21425188942389053, "compression_ratio": 1.3668639053254439, "no_speech_prob": 0.0, "words": [{"start": 2567.73, "end": 2568.01, "word": "و", "probability": 0.77294921875}, {"start": 2568.01, "end": 2568.17, "word": " ال", "probability": 0.65234375}, {"start": 2568.17, "end": 2568.45, "word": " R", "probability": 0.51611328125}, {"start": 2568.45, "end": 2569.03, "word": " هذا", "probability": 0.6962890625}, {"start": 2569.03, "end": 2569.47, "word": " يعني", "probability": 0.93359375}, {"start": 2569.47, "end": 2569.85, "word": " عدد", "probability": 0.9833984375}, {"start": 2569.85, "end": 2570.33, "word": " حقيقي", "probability": 0.9856770833333334}, {"start": 2570.33, "end": 2570.81, "word": " طبعا", "probability": 0.986328125}, {"start": 2570.81, "end": 2572.11, "word": " ينتمي", "probability": 0.75250244140625}, {"start": 2572.11, "end": 2572.33, "word": " إلى", "probability": 0.446044921875}, {"start": 2572.33, "end": 2572.81, "word": " R", "probability": 0.82421875}, {"start": 2572.81, "end": 2576.85, "word": " ففي", "probability": 0.85888671875}, {"start": 2576.85, "end": 2577.39, "word": " عندي", "probability": 0.91650390625}, {"start": 2577.39, "end": 2579.01, "word": " برضه", "probability": 0.9423828125}, {"start": 2579.01, "end": 2580.05, "word": " نتيجتين", "probability": 0.95703125}, {"start": 2580.05, "end": 2581.51, "word": " النتيجة", "probability": 0.9342041015625}, {"start": 2581.51, "end": 2581.93, "word": " الأولى", "probability": 0.8997395833333334}, {"start": 2581.93, "end": 2582.17, "word": " إذا", "probability": 0.796875}, {"start": 2582.17, "end": 2582.71, "word": " كان", "probability": 0.98681640625}, {"start": 2582.71, "end": 2584.35, "word": " ال", "probability": 0.89404296875}, {"start": 2584.35, "end": 2584.67, "word": " R", "probability": 0.96142578125}, {"start": 2584.67, "end": 2585.29, "word": " بسويش", "probability": 0.747314453125}, {"start": 2585.29, "end": 2585.79, "word": " سفر", "probability": 0.7730305989583334}, {"start": 2585.79, "end": 2589.63, "word": " then", "probability": 0.5302734375}, {"start": 2589.63, "end": 2589.97, "word": " ال", "probability": 0.37890625}, {"start": 2589.97, "end": 2590.37, "word": " series", "probability": 0.9150390625}, {"start": 2590.37, "end": 2590.83, "word": " sigma", "probability": 0.52392578125}, {"start": 2590.83, "end": 2591.15, "word": " X", "probability": 0.52783203125}, {"start": 2591.15, "end": 2591.47, "word": " M", "probability": 0.40673828125}, {"start": 2591.47, "end": 2592.45, "word": " converges", "probability": 0.8447265625}, {"start": 2592.45, "end": 2594.45, "word": " if", "probability": 0.814453125}, {"start": 2594.45, "end": 2594.67, "word": " and", "probability": 0.89501953125}, {"start": 2594.67, "end": 2594.95, "word": " only", "probability": 0.68017578125}, {"start": 2594.95, "end": 2595.33, "word": " if", "probability": 0.978515625}], "temperature": 1.0}, {"id": 93, "seek": 262583, "start": 2604.15, "end": 2625.83, "text": "الجزء التاني من النظرية لو كان R بساوي سفر", "tokens": [6027, 7435, 11622, 38207, 16712, 7649, 1829, 9154, 28239, 19913, 2288, 10632, 45164, 25961, 497, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.26307743528614874, "compression_ratio": 1.056338028169014, "no_speech_prob": 0.0, "words": [{"start": 2604.15, "end": 2605.35, "word": "الجزء", "probability": 0.7430419921875}, {"start": 2605.35, "end": 2605.95, "word": " التاني", "probability": 0.8592122395833334}, {"start": 2605.95, "end": 2606.29, "word": " من", "probability": 0.9365234375}, {"start": 2606.29, "end": 2607.53, "word": " النظرية", "probability": 0.96630859375}, {"start": 2607.53, "end": 2623.65, "word": " لو", "probability": 0.387451171875}, {"start": 2623.65, "end": 2624.15, "word": " كان", "probability": 0.97021484375}, {"start": 2624.15, "end": 2624.67, "word": " R", "probability": 0.37255859375}, {"start": 2624.67, "end": 2625.29, "word": " بساوي", "probability": 0.5796051025390625}, {"start": 2625.29, "end": 2625.83, "word": " سفر", "probability": 0.82763671875}], "temperature": 1.0}, {"id": 94, "seek": 264784, "start": 2628.2, "end": 2647.84, "text": "بعد ذلك لو الار بيسوي سفر يعني ان الار بيسويش سفر then ال series sigma y in دي درجز بيقدي ان ال series sigma x in دي درجز", "tokens": [3555, 22488, 29910, 23275, 45164, 2423, 9640, 4724, 1829, 3794, 45865, 8608, 5172, 2288, 37495, 22653, 16472, 2423, 9640, 4724, 1829, 3794, 45865, 8592, 8608, 5172, 2288, 550, 2423, 2638, 12771, 288, 294, 11778, 1829, 11778, 47341, 11622, 4724, 1829, 4587, 16254, 16472, 2423, 2638, 12771, 2031, 294, 11778, 1829, 11778, 47341, 11622], "avg_logprob": -0.527199058621018, "compression_ratio": 1.564102564102564, "no_speech_prob": 0.0, "words": [{"start": 2628.2, "end": 2628.78, "word": "بعد", "probability": 0.37554931640625}, {"start": 2628.78, "end": 2628.86, "word": " ذلك", "probability": 0.75341796875}, {"start": 2628.86, "end": 2630.38, "word": " لو", "probability": 0.1248779296875}, {"start": 2630.38, "end": 2630.94, "word": " الار", "probability": 0.36572265625}, {"start": 2630.94, "end": 2631.4, "word": " بيسوي", "probability": 0.5701904296875}, {"start": 2631.4, "end": 2631.88, "word": " سفر", "probability": 0.7125651041666666}, {"start": 2631.88, "end": 2632.06, "word": " يعني", "probability": 0.6029052734375}, {"start": 2632.06, "end": 2632.22, "word": " ان", "probability": 0.1578369140625}, {"start": 2632.22, "end": 2632.54, "word": " الار", "probability": 0.8720703125}, {"start": 2632.54, "end": 2633.18, "word": " بيسويش", "probability": 0.80361328125}, {"start": 2633.18, "end": 2633.66, "word": " سفر", "probability": 0.970703125}, {"start": 2633.66, "end": 2636.66, "word": " then", "probability": 0.1434326171875}, {"start": 2636.66, "end": 2638.12, "word": " ال", "probability": 0.359375}, {"start": 2638.12, "end": 2638.5, "word": " series", "probability": 0.583984375}, {"start": 2638.5, "end": 2639.08, "word": " sigma", "probability": 0.57958984375}, {"start": 2639.08, "end": 2639.56, "word": " y", "probability": 0.71875}, {"start": 2639.56, "end": 2639.94, "word": " in", "probability": 0.5966796875}, {"start": 2639.94, "end": 2640.4, "word": " دي", "probability": 0.279052734375}, {"start": 2640.4, "end": 2641.22, "word": " درجز", "probability": 0.64794921875}, {"start": 2641.22, "end": 2643.16, "word": " بيقدي", "probability": 0.713134765625}, {"start": 2643.16, "end": 2643.38, "word": " ان", "probability": 0.77978515625}, {"start": 2643.38, "end": 2643.58, "word": " ال", "probability": 0.89453125}, {"start": 2643.58, "end": 2643.86, "word": " series", "probability": 0.8876953125}, {"start": 2643.86, "end": 2644.34, "word": " sigma", "probability": 0.91064453125}, {"start": 2644.34, "end": 2644.7, "word": " x", "probability": 0.93798828125}, {"start": 2644.7, "end": 2645.36, "word": " in", "probability": 0.91845703125}, {"start": 2645.36, "end": 2647.18, "word": " دي", "probability": 0.750244140625}, {"start": 2647.18, "end": 2647.84, "word": " درجز", "probability": 0.9884440104166666}], "temperature": 1.0}, {"id": 95, "seek": 267852, "start": 2651.38, "end": 2678.52, "text": "او لأ convergence افضل لو كانت series sigma yn convergence بيقدي ان series sigma xn ايبان convergence فقط اتجاه واحد لكن الاكس مش شرط تكون صحيح okay تمام هو البرهان يعني كتير سهل", "tokens": [995, 2407, 5296, 10721, 32181, 1975, 5172, 11242, 1211, 45164, 25961, 2655, 2638, 12771, 17861, 32181, 4724, 1829, 4587, 16254, 16472, 2638, 12771, 2031, 77, 1975, 1829, 3555, 7649, 32181, 6156, 47432, 1975, 2655, 7435, 40294, 36764, 24401, 44381, 42963, 4117, 3794, 37893, 13412, 2288, 9566, 6055, 30544, 20328, 5016, 1829, 5016, 1392, 46811, 10943, 31439, 2423, 26890, 3224, 7649, 37495, 22653, 9122, 2655, 13546, 8608, 3224, 1211], "avg_logprob": -0.3034420393515324, "compression_ratio": 1.5086705202312138, "no_speech_prob": 0.0, "words": [{"start": 2651.38, "end": 2651.8, "word": "او", "probability": 0.5211944580078125}, {"start": 2651.8, "end": 2652.04, "word": " لأ", "probability": 0.6624755859375}, {"start": 2652.04, "end": 2652.58, "word": " convergence", "probability": 0.210205078125}, {"start": 2652.58, "end": 2653.22, "word": " افضل", "probability": 0.7657470703125}, {"start": 2653.22, "end": 2654.66, "word": " لو", "probability": 0.7451171875}, {"start": 2654.66, "end": 2655.2, "word": " كانت", "probability": 0.955810546875}, {"start": 2655.2, "end": 2657.06, "word": " series", "probability": 0.59228515625}, {"start": 2657.06, "end": 2657.74, "word": " sigma", "probability": 0.6318359375}, {"start": 2657.74, "end": 2659.3, "word": " yn", "probability": 0.67431640625}, {"start": 2659.3, "end": 2660.12, "word": " convergence", "probability": 0.83544921875}, {"start": 2660.12, "end": 2660.66, "word": " بيقدي", "probability": 0.6197509765625}, {"start": 2660.66, "end": 2660.84, "word": " ان", "probability": 0.75}, {"start": 2660.84, "end": 2661.74, "word": " series", "probability": 0.46240234375}, {"start": 2661.74, "end": 2662.32, "word": " sigma", "probability": 0.880859375}, {"start": 2662.32, "end": 2663.24, "word": " xn", "probability": 0.953369140625}, {"start": 2663.24, "end": 2664.48, "word": " ايبان", "probability": 0.639984130859375}, {"start": 2664.48, "end": 2665.16, "word": " convergence", "probability": 0.7158203125}, 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0.83544921875}, {"start": 2850.59, "end": 2851.33, "word": " صحيح", "probability": 0.9951171875}, {"start": 2851.33, "end": 2851.89, "word": " لكل", "probability": 0.981201171875}, {"start": 2851.89, "end": 2852.27, "word": " N", "probability": 0.8818359375}, {"start": 2852.27, "end": 2852.79, "word": " أكبر", "probability": 0.9554036458333334}, {"start": 2852.79, "end": 2853.01, "word": " من", "probability": 0.99462890625}, {"start": 2853.01, "end": 2853.19, "word": " أو", "probability": 0.9638671875}, {"start": 2853.19, "end": 2853.51, "word": " ساوي", "probability": 0.9742838541666666}, {"start": 2853.51, "end": 2853.91, "word": " capital", "probability": 0.52734375}, {"start": 2853.91, "end": 2854.49, "word": " N", "probability": 0.66064453125}, {"start": 2854.49, "end": 2855.11, "word": " تمام", "probability": 0.677734375}, {"start": 2855.11, "end": 2857.13, "word": " الان", "probability": 0.6884765625}, {"start": 2857.13, "end": 2857.33, "word": " now", "probability": 0.476318359375}], "temperature": 1.0}, {"id": 102, "seek": 289318, "start": 2865.12, "end": 2893.18, "text": "نسمي هذه double star فالان if sigma x and converge then by double star and comparison test and comparison test", "tokens": [1863, 38251, 1829, 29538, 3834, 3543, 6156, 6027, 7649, 498, 12771, 2031, 293, 41881, 550, 538, 3834, 3543, 293, 9660, 1500, 293, 9660, 1500], "avg_logprob": -0.2326562547683716, "compression_ratio": 1.2708333333333333, "no_speech_prob": 0.0, "words": [{"start": 2865.12, "end": 2865.82, "word": "نسمي", "probability": 0.7162272135416666}, {"start": 2865.82, "end": 2866.2, "word": " هذه", "probability": 0.8173828125}, {"start": 2866.2, "end": 2866.56, "word": " double", "probability": 0.75341796875}, {"start": 2866.56, "end": 2867.08, "word": " star", "probability": 0.89990234375}, {"start": 2867.08, "end": 2873.94, "word": " فالان", "probability": 0.8653971354166666}, {"start": 2873.94, "end": 2874.66, "word": " if", "probability": 0.58447265625}, {"start": 2874.66, "end": 2877.16, "word": " sigma", "probability": 0.734375}, {"start": 2877.16, "end": 2878.86, "word": " x", "probability": 0.83740234375}, {"start": 2878.86, "end": 2879.28, "word": " and", "probability": 0.491943359375}, {"start": 2879.28, "end": 2880.22, "word": " converge", "probability": 0.8359375}, {"start": 2880.22, "end": 2883.82, "word": " then", "probability": 0.77587890625}, {"start": 2883.82, "end": 2886.2, "word": " by", "probability": 0.94677734375}, {"start": 2886.2, "end": 2886.58, "word": " double", "probability": 0.93798828125}, {"start": 2886.58, "end": 2887.16, "word": " star", "probability": 0.94970703125}, {"start": 2887.16, "end": 2889.52, "word": " and", "probability": 0.9296875}, {"start": 2889.52, "end": 2890.2, "word": " comparison", "probability": 0.93896484375}, {"start": 2890.2, "end": 2890.78, "word": " test", "probability": 0.93359375}, {"start": 2890.78, "end": 2891.72, "word": " and", "probability": 0.73828125}, {"start": 2891.72, "end": 2892.54, "word": " comparison", "probability": 0.912109375}, {"start": 2892.54, "end": 2893.18, "word": " test", "probability": 0.9072265625}], "temperature": 1.0}, {"id": 103, "seek": 292249, "start": 2895.01, "end": 2922.49, "text": "واختبار المقارنة إذا كانت هذه convergent فبطلع هذه ال series convergent صح وبالتالي بطلع sigma yn convergence هذا ثابت موجة ممكن نضرب في مقلوب و نتخلص منه إذا كانت هذه convergent فهذه convergent", "tokens": [2407, 47283, 2655, 3555, 9640, 9673, 4587, 9640, 1863, 3660, 11933, 15730, 25961, 2655, 29538, 9652, 6930, 6156, 3555, 9566, 1211, 3615, 29538, 2423, 2638, 9652, 6930, 20328, 5016, 46599, 6027, 2655, 6027, 1829, 4724, 9566, 1211, 3615, 12771, 17861, 32181, 23758, 38637, 16758, 2655, 3714, 29245, 3660, 3714, 43020, 8717, 11242, 25513, 8978, 3714, 4587, 1211, 37746, 4032, 8717, 2655, 9778, 1211, 9381, 9154, 3224, 11933, 15730, 25961, 2655, 29538, 9652, 6930, 6156, 3224, 24192, 9652, 6930], "avg_logprob": -0.15822785338269005, "compression_ratio": 1.697674418604651, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 2895.01, "end": 2895.69, "word": "واختبار", "probability": 0.8736328125}, {"start": 2895.69, "end": 2896.47, "word": " المقارنة", "probability": 0.990234375}, {"start": 2896.47, "end": 2897.07, "word": " إذا", "probability": 0.7047119140625}, {"start": 2897.07, "end": 2897.53, "word": " كانت", "probability": 0.92822265625}, {"start": 2897.53, "end": 2897.81, "word": " هذه", "probability": 0.69921875}, {"start": 2897.81, "end": 2898.77, "word": " convergent", "probability": 0.66064453125}, {"start": 2898.77, "end": 2902.45, "word": " فبطلع", "probability": 0.84521484375}, {"start": 2902.45, "end": 2902.95, "word": " هذه", "probability": 0.87548828125}, {"start": 2902.95, "end": 2903.19, "word": " ال", "probability": 0.77685546875}, {"start": 2903.19, "end": 2903.67, "word": " series", "probability": 0.80615234375}, {"start": 2903.67, "end": 2905.11, "word": " convergent", "probability": 0.900390625}, {"start": 2905.11, "end": 2906.01, "word": " صح", "probability": 0.792236328125}, {"start": 2906.01, "end": 2908.01, "word": " وبالتالي", "probability": 0.851318359375}, {"start": 2908.01, "end": 2909.95, "word": " بطلع", "probability": 0.9327392578125}, {"start": 2909.95, "end": 2911.29, "word": " sigma", "probability": 0.6416015625}, {"start": 2911.29, "end": 2911.81, "word": " yn", "probability": 0.59375}, {"start": 2911.81, "end": 2913.05, "word": " convergence", "probability": 0.56640625}, {"start": 2913.05, "end": 2915.79, "word": " هذا", "probability": 0.411865234375}, {"start": 2915.79, "end": 2916.19, "word": " ثابت", "probability": 0.9812825520833334}, {"start": 2916.19, "end": 2916.57, "word": " موجة", "probability": 0.96044921875}, {"start": 2916.57, "end": 2916.81, "word": " ممكن", "probability": 0.89208984375}, {"start": 2916.81, "end": 2917.29, "word": " نضرب", "probability": 0.9783528645833334}, {"start": 2917.29, "end": 2917.83, "word": " في", "probability": 0.7724609375}, {"start": 2917.83, "end": 2918.27, "word": " مقلوب", "probability": 0.9317626953125}, {"start": 2918.27, "end": 2918.37, "word": " و", "probability": 0.70654296875}, {"start": 2918.37, "end": 2918.87, "word": " نتخلص", "probability": 0.8955078125}, {"start": 2918.87, "end": 2919.27, "word": " منه", "probability": 0.984619140625}, {"start": 2919.27, "end": 2920.13, "word": " إذا", "probability": 0.939697265625}, {"start": 2920.13, "end": 2920.49, "word": " كانت", "probability": 0.9794921875}, {"start": 2920.49, "end": 2920.65, "word": " هذه", "probability": 0.8701171875}, {"start": 2920.65, "end": 2921.37, "word": " convergent", "probability": 0.951904296875}, {"start": 2921.37, "end": 2921.79, "word": " فهذه", "probability": 0.9554036458333334}, {"start": 2921.79, "end": 2922.49, "word": " convergent", "probability": 0.881103515625}], "temperature": 1.0}, {"id": 104, "seek": 294607, "start": 2926.95, "end": 2946.07, "text": "Also إذا كانت ال series sigma y in converge then برضه by المتباينة double star and ال comparison test إذا ناخد الجزء هذا", "tokens": [9171, 539, 11933, 15730, 25961, 2655, 2423, 2638, 12771, 288, 294, 41881, 550, 4724, 43042, 3224, 538, 9673, 2655, 3555, 995, 9957, 3660, 3834, 3543, 293, 2423, 9660, 1500, 11933, 15730, 8717, 47283, 3215, 25724, 11622, 38207, 23758], "avg_logprob": -0.26161857904532015, "compression_ratio": 1.1691176470588236, "no_speech_prob": 0.0, "words": [{"start": 2926.9500000000003, "end": 2927.9900000000002, "word": "Also", "probability": 0.6490478515625}, {"start": 2927.9900000000002, "end": 2929.03, "word": " إذا", "probability": 0.7064208984375}, {"start": 2929.03, "end": 2929.75, "word": " كانت", "probability": 0.97314453125}, {"start": 2929.75, "end": 2930.81, "word": " ال", "probability": 0.68798828125}, {"start": 2930.81, "end": 2931.09, "word": " series", "probability": 0.62451171875}, {"start": 2931.09, "end": 2931.53, "word": " sigma", "probability": 0.54833984375}, {"start": 2931.53, "end": 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