diff --git "a/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aBB9DzMBL4Y_raw.json" "b/PL9fwy3NUQKwZHPs6l8Fr-st-8cVJxmVek/aBB9DzMBL4Y_raw.json"
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+{"segments": [{"id": 1, "seek": 4973, "start": 21.75, "end": 49.73, "text": "بسم الله الرحمن الرحيم في محاضرة اليوم هنكمل ما بدأنا حاول موضوع ال infinite limits المرة تاعة عرفنا ما معناه ان ال limit ل function and cluster point بالساوية plus او minus infinity وشوفنا نظرية اخر نظرية برهنها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 8978, 3714, 5016, 46958, 25720, 45595, 20498, 8032, 1863, 24793, 1211, 19446, 47525, 10721, 8315, 11331, 995, 12610, 3714, 2407, 11242, 45367, 2423, 13785, 10406, 9673, 25720, 6055, 995, 27884, 6225, 28480, 8315, 19446, 20449, 8315, 3224, 16472, 2423, 4948, 5296, 2445, 293, 13630, 935, 20666, 3794, 995, 2407, 10632, 1804, 1975, 2407, 3175, 13202, 4032, 8592, 38688, 8315, 8717, 19913, 2288, 10632, 1975, 34740, 8717, 19913, 2288, 10632, 4724, 2288, 3224, 1863, 11296], "avg_logprob": -0.15904017644269125, "compression_ratio": 1.6237623762376239, "no_speech_prob": 0.0, "words": [{"start": 21.75, "end": 22.07, "word": "بسم", 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0.84130859375}, {"start": 32.81, "end": 33.19, "word": " infinite", "probability": 0.88330078125}, {"start": 33.19, "end": 33.83, "word": " limits", "probability": 0.943359375}, {"start": 33.83, "end": 35.45, "word": " المرة", "probability": 0.95068359375}, {"start": 35.45, "end": 35.83, "word": " تاعة", "probability": 0.4022623697916667}, {"start": 35.83, "end": 37.11, "word": " عرفنا", "probability": 0.90576171875}, {"start": 37.11, "end": 37.37, "word": " ما", "probability": 0.890625}, {"start": 37.37, "end": 37.89, "word": " معناه", "probability": 0.6995442708333334}, {"start": 37.89, "end": 38.09, "word": " ان", "probability": 0.55517578125}, {"start": 38.09, "end": 38.29, "word": " ال", "probability": 0.54443359375}, {"start": 38.29, "end": 38.71, "word": " limit", "probability": 0.953125}, {"start": 38.71, "end": 38.93, "word": " ل", "probability": 0.6689453125}, {"start": 38.93, "end": 39.57, "word": " function", "probability": 0.7744140625}, {"start": 39.57, "end": 40.69, "word": " and", "probability": 0.9248046875}, {"start": 40.69, "end": 41.21, "word": " cluster", "probability": 0.8134765625}, {"start": 41.21, "end": 41.77, "word": " point", "probability": 0.970703125}, {"start": 41.77, "end": 42.37, "word": " بالساوية", "probability": 0.77509765625}, {"start": 42.37, "end": 42.75, "word": " plus", "probability": 0.91357421875}, {"start": 42.75, "end": 42.95, "word": " او", "probability": 0.7435302734375}, {"start": 42.95, "end": 43.35, "word": " minus", "probability": 0.9921875}, {"start": 43.35, "end": 44.01, "word": " infinity", "probability": 0.91064453125}, {"start": 44.01, "end": 45.89, "word": " وشوفنا", "probability": 0.8934326171875}, {"start": 45.89, "end": 48.03, "word": " نظرية", "probability": 0.9827880859375}, {"start": 48.03, "end": 48.59, "word": " اخر", "probability": 0.800048828125}, {"start": 48.59, "end": 49.05, "word": " نظرية", "probability": 0.9935302734375}, {"start": 49.05, "end": 49.73, "word": " برهنها", "probability": 0.87373046875}], "temperature": 1.0}, {"id": 2, "seek": 7831, "start": 50.96, "end": 78.32, "text": "خاصة بهذا النوع من ال limits كانت النظرية التالية خلينا نكتبها let f و g be functions from a to r و c ال cluster point", "tokens": [9778, 33546, 3660, 39627, 15730, 28239, 45367, 9154, 2423, 10406, 25961, 2655, 28239, 19913, 2288, 10632, 16712, 6027, 10632, 16490, 1211, 9957, 995, 8717, 4117, 2655, 3555, 11296, 718, 283, 4032, 290, 312, 6828, 490, 257, 281, 367, 4032, 269, 2423, 13630, 935], "avg_logprob": -0.13050426170229912, "compression_ratio": 1.282442748091603, "no_speech_prob": 0.0, "words": [{"start": 50.96, "end": 51.64, "word": "خاصة", "probability": 0.9244791666666666}, {"start": 51.64, "end": 52.26, "word": " بهذا", "probability": 0.959716796875}, {"start": 52.26, "end": 52.6, "word": " النوع", "probability": 0.9873046875}, {"start": 52.6, "end": 52.86, "word": " من", "probability": 0.98095703125}, {"start": 52.86, "end": 53.04, "word": " ال", "probability": 0.86376953125}, {"start": 53.04, "end": 53.42, "word": " limits", "probability": 0.88623046875}, {"start": 53.42, "end": 54.02, "word": " كانت", "probability": 0.967529296875}, {"start": 54.02, "end": 54.8, "word": " النظرية", "probability": 0.974365234375}, {"start": 54.8, "end": 55.7, "word": " التالية", "probability": 0.9913736979166666}, {"start": 55.7, "end": 58.3, "word": " خلينا", "probability": 0.748291015625}, {"start": 58.3, "end": 60.02, "word": " نكتبها", "probability": 0.9904296875}, {"start": 60.02, "end": 65.34, "word": " let", "probability": 0.56640625}, {"start": 65.34, "end": 65.82, "word": " f", "probability": 0.763671875}, {"start": 65.82, "end": 66.16, "word": " و", "probability": 0.708984375}, {"start": 66.16, "end": 66.54, "word": " g", "probability": 0.87646484375}, {"start": 66.54, "end": 66.94, "word": " be", "probability": 0.7353515625}, {"start": 66.94, "end": 67.82, "word": " functions", "probability": 0.875}, {"start": 67.82, "end": 68.34, "word": " from", "probability": 0.89013671875}, {"start": 68.34, "end": 69.02, "word": " a", "probability": 0.74560546875}, {"start": 69.02, "end": 69.32, "word": " to", "probability": 0.9716796875}, {"start": 69.32, "end": 70.14, "word": " r", "probability": 0.93896484375}, {"start": 70.14, "end": 72.6, "word": " و", "probability": 0.890625}, {"start": 72.6, "end": 73.36, "word": " c", "probability": 0.7705078125}, {"start": 73.36, "end": 73.9, "word": " ال", "probability": 0.431640625}, {"start": 73.9, "end": 74.42, "word": " cluster", "probability": 0.96728515625}, {"start": 74.42, "end": 78.32, "word": " point", "probability": 0.96826171875}], "temperature": 1.0}, {"id": 3, "seek": 10819, "start": 80.53, "end": 108.19, "text": "of the set A such that f of x less than or equal g of x for every x تمتمي إلى a different from c فشوفنا أنه لو كان ال limit فf of x as x tends", "tokens": [2670, 264, 992, 316, 1270, 300, 283, 295, 2031, 1570, 813, 420, 2681, 290, 295, 2031, 337, 633, 2031, 46811, 39237, 1829, 30731, 257, 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{"start": 89.71, "end": 90.03, "word": " than", "probability": 0.94873046875}, {"start": 90.03, "end": 90.17, "word": " or", "probability": 0.91357421875}, {"start": 90.17, "end": 90.39, "word": " equal", "probability": 0.9111328125}, {"start": 90.39, "end": 90.77, "word": " g", "probability": 0.44677734375}, {"start": 90.77, "end": 91.03, "word": " of", "probability": 0.95751953125}, {"start": 91.03, "end": 91.47, "word": " x", "probability": 0.98388671875}, {"start": 91.47, "end": 93.07, "word": " for", "probability": 0.94970703125}, {"start": 93.07, "end": 93.57, "word": " every", "probability": 0.79541015625}, {"start": 93.57, "end": 93.91, "word": " x", "probability": 0.96435546875}, {"start": 93.91, "end": 94.59, "word": " تمتمي", "probability": 0.6083984375}, {"start": 94.59, "end": 94.85, "word": " إلى", "probability": 0.71484375}, {"start": 94.85, "end": 95.33, "word": " a", "probability": 0.58251953125}, {"start": 95.33, "end": 96.85, "word": " different", "probability": 0.89892578125}, {"start": 96.85, "end": 97.63, "word": " from", "probability": 0.919921875}, {"start": 97.63, "end": 98.15, "word": " c", "probability": 0.76220703125}, {"start": 98.15, "end": 100.95, "word": " فشوفنا", "probability": 0.94287109375}, {"start": 100.95, "end": 101.45, "word": " أنه", "probability": 0.68701171875}, {"start": 101.45, "end": 101.63, "word": " لو", "probability": 0.98486328125}, {"start": 101.63, "end": 102.07, "word": " كان", "probability": 0.9970703125}, {"start": 102.07, "end": 102.25, "word": " ال", "probability": 0.7353515625}, {"start": 102.25, "end": 102.63, "word": " limit", "probability": 0.84814453125}, {"start": 102.63, "end": 105.95, "word": " فf", "probability": 0.39776611328125}, {"start": 105.95, "end": 106.25, "word": " of", "probability": 0.85302734375}, {"start": 106.25, "end": 106.73, "word": " x", "probability": 0.9921875}, {"start": 106.73, "end": 107.29, "word": " as", "probability": 0.87255859375}, {"start": 107.29, "end": 107.75, "word": " x", "probability": 0.71875}, {"start": 107.75, "end": 108.19, "word": " tends", "probability": 0.8779296875}], "temperature": 1.0}, {"id": 4, "seek": 12739, "start": 125.09, "end": 127.39, "text": "وكذلك لو كانت ال limit", "tokens": [2407, 4117, 8848, 23275, 45164, 25961, 2655, 2423, 4948], "avg_logprob": -0.784375011920929, "compression_ratio": 0.875, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 125.09, "end": 125.85, "word": "وكذلك", "probability": 0.505950927734375}, {"start": 125.85, "end": 126.23, "word": " لو", "probability": 0.693359375}, {"start": 126.23, "end": 126.91, "word": " كانت", "probability": 0.92138671875}, {"start": 126.91, "end": 127.03, "word": " ال", "probability": 0.312255859375}, {"start": 127.03, "end": 127.39, "word": " limit", "probability": 0.66552734375}], "temperature": 1.0}, {"id": 5, "seek": 15635, "start": 130.53, "end": 156.35, "text": "لـ u of x as x tends to c بساوي negative infinity فهذا بتضمن ان limit ل f of x as x tends to c بساوي negative infinity طيب ال ..", "tokens": [1211, 39184, 344, 295, 2031, 382, 2031, 12258, 281, 269, 4724, 3794, 995, 45865, 3671, 13202, 6156, 3224, 15730, 39894, 11242, 27842, 16472, 4948, 5296, 283, 295, 2031, 382, 2031, 12258, 281, 269, 4724, 3794, 995, 45865, 3671, 13202, 23032, 1829, 3555, 2423, 4386], "avg_logprob": -0.2690972169240316, "compression_ratio": 1.4272727272727272, "no_speech_prob": 0.0, "words": [{"start": 130.53, "end": 131.53, "word": "لـ", "probability": 0.33795166015625}, {"start": 131.53, "end": 132.53, "word": " u", "probability": 0.12396240234375}, {"start": 132.53, "end": 132.83, "word": " of", "probability": 0.254150390625}, {"start": 132.83, "end": 133.23, "word": " x", "probability": 0.93896484375}, {"start": 133.23, "end": 133.73, "word": " as", "probability": 0.8671875}, {"start": 133.73, "end": 134.19, "word": " x", "probability": 0.9521484375}, {"start": 134.19, "end": 134.51, "word": " tends", "probability": 0.393798828125}, {"start": 134.51, 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"probability": 0.9892578125}, {"start": 143.75, "end": 144.87, "word": " as", "probability": 0.96728515625}, {"start": 144.87, "end": 145.27, "word": " x", "probability": 0.9814453125}, {"start": 145.27, "end": 145.61, "word": " tends", "probability": 0.74267578125}, {"start": 145.61, "end": 145.81, "word": " to", "probability": 0.984375}, {"start": 145.81, "end": 146.11, "word": " c", "probability": 0.95556640625}, {"start": 146.11, "end": 146.81, "word": " بساوي", "probability": 0.9552001953125}, {"start": 146.81, "end": 147.35, "word": " negative", "probability": 0.9716796875}, {"start": 147.35, "end": 148.09, "word": " infinity", "probability": 0.92578125}, {"start": 148.09, "end": 155.73, "word": " طيب", "probability": 0.9679361979166666}, {"start": 155.73, "end": 156.03, "word": " ال", "probability": 0.63525390625}, {"start": 156.03, "end": 156.35, "word": " ..", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 6, "seek": 18621, "start": 161.05, "end": 186.21, "text": "اليوم هنعرف ما معناه ان ال limit and c من اليمين بالساوي infinity او ال limit and c من اليسار بالساوي infinity و كذلك نفس الشيء ال one sided limit and c ما معناه أنها ساوي سالب infinity لأن هذه كانت two sided limit المرة الأخيرة اتعرفنا", "tokens": [6027, 1829, 20498, 8032, 1863, 3615, 28480, 19446, 20449, 8315, 3224, 16472, 2423, 4948, 293, 269, 9154, 45595, 2304, 9957, 20666, 3794, 995, 45865, 13202, 1975, 2407, 2423, 4948, 293, 269, 9154, 45595, 3794, 9640, 20666, 3794, 995, 45865, 13202, 4032, 9122, 8848, 23275, 8717, 36178, 25124, 1829, 38207, 2423, 472, 41651, 4948, 293, 269, 19446, 20449, 8315, 3224, 14739, 11296, 8608, 995, 45865, 8608, 6027, 3555, 13202, 5296, 33456, 29538, 25961, 2655, 732, 41651, 4948, 9673, 25720, 16247, 9778, 48923, 1975, 2655, 3615, 28480, 8315], "avg_logprob": -0.20510057676797624, "compression_ratio": 1.9135135135135135, "no_speech_prob": 0.0, "words": [{"start": 161.05, "end": 161.63, "word": "اليوم", "probability": 0.91796875}, {"start": 161.63, "end": 162.43, "word": " هنعرف", "probability": 0.855712890625}, {"start": 162.43, "end": 162.69, "word": " ما", "probability": 0.78076171875}, {"start": 162.69, "end": 163.19, "word": " معناه", "probability": 0.7765299479166666}, {"start": 163.19, "end": 163.37, "word": " ان", "probability": 0.5517578125}, {"start": 163.37, "end": 163.55, "word": " ال", "probability": 0.488037109375}, {"start": 163.55, "end": 163.95, "word": " limit", "probability": 0.7958984375}, {"start": 163.95, "end": 165.71, "word": " and", "probability": 0.417724609375}, {"start": 165.71, "end": 166.41, "word": " c", "probability": 0.69775390625}, {"start": 166.41, "end": 166.69, "word": " من", "probability": 0.9853515625}, {"start": 166.69, "end": 167.35, "word": " اليمين", "probability": 0.78515625}, {"start": 167.35, "end": 168.31, "word": " بالساوي", "probability": 0.8284912109375}, {"start": 168.31, "end": 168.87, "word": " infinity", "probability": 0.77783203125}, {"start": 168.87, "end": 170.07, "word": " او", "probability": 0.84033203125}, {"start": 170.07, "end": 170.23, "word": " ال", "probability": 0.7421875}, {"start": 170.23, "end": 170.51, "word": " limit", "probability": 0.931640625}, {"start": 170.51, "end": 170.85, "word": " and", "probability": 0.9501953125}, {"start": 170.85, "end": 171.25, "word": " c", "probability": 0.9560546875}, {"start": 171.25, "end": 171.47, "word": " من", "probability": 0.99365234375}, {"start": 171.47, "end": 172.03, "word": " اليسار", "probability": 0.9905598958333334}, {"start": 172.03, "end": 172.49, "word": " بالساوي", "probability": 0.9774169921875}, {"start": 172.49, "end": 172.93, "word": " infinity", "probability": 0.86572265625}, {"start": 172.93, "end": 173.15, "word": " و", "probability": 0.81201171875}, {"start": 173.15, "end": 173.47, "word": " كذلك", "probability": 0.8273111979166666}, {"start": 173.47, "end": 173.79, "word": " نفس", "probability": 0.99365234375}, {"start": 173.79, "end": 174.99, "word": " الشيء", "probability": 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{"start": 430.55, "end": 431.89, "word": " طبعا", "probability": 0.9814453125}, {"start": 431.89, "end": 432.21, "word": " ممكن", "probability": 0.986572265625}, {"start": 432.21, "end": 432.75, "word": " كمان", "probability": 0.9835611979166666}, {"start": 432.75, "end": 434.05, "word": " نعرف", "probability": 0.8048502604166666}, {"start": 434.05, "end": 434.49, "word": " بنفس", "probability": 0.977294921875}, {"start": 434.49, "end": 435.23, "word": " الطريقة", "probability": 0.9890950520833334}, {"start": 435.23, "end": 436.33, "word": " ال", "probability": 0.6103515625}, {"start": 436.33, "end": 437.35, "word": " limit", "probability": 0.81640625}, {"start": 437.35, "end": 437.63, "word": " from", "probability": 0.91357421875}, {"start": 437.63, "end": 437.99, "word": " the", "probability": 0.8896484375}, {"start": 437.99, "end": 438.31, "word": " left", "probability": 0.93896484375}, {"start": 438.31, "end": 438.57, "word": " او", "probability": 0.781982421875}, {"start": 438.57, "end": 438.83, "word": " ال", "probability": 0.67919921875}, {"start": 438.83, "end": 439.19, "word": " left", "probability": 0.931640625}, {"start": 439.19, "end": 439.53, "word": " hand", "probability": 0.80126953125}, {"start": 439.53, "end": 440.01, "word": " limit", "probability": 0.9833984375}, {"start": 440.01, "end": 441.15, "word": " مايعني", "probability": 0.5310872395833334}, {"start": 441.15, "end": 441.41, "word": " ان", "probability": 0.6982421875}, {"start": 441.41, "end": 441.59, "word": " ال", "probability": 0.9169921875}, {"start": 441.59, "end": 441.85, "word": " left", "probability": 0.95166015625}, {"start": 441.85, "end": 442.21, "word": " hand", "probability": 0.91796875}, {"start": 442.21, "end": 442.69, "word": " limit", "probability": 0.9833984375}, {"start": 442.69, "end": 444.41, "word": " تساوي", "probability": 0.8896484375}], "temperature": 1.0}, {"id": 16, "seek": 46793, "start": 445.85, "end": 467.93, "text": "Infinity او سالب Infinity اذا لو انا بدى اعدل اعرف مامعنى ان ال limit ل F عن C من اليسار بالساوية Infinity او مامعنى ان ال limit ل F عن C من اليسار بالساوية سالب Infinity فباخد let F be هكذا", "tokens": [4575, 5194, 507, 1975, 2407, 8608, 6027, 3555, 34762, 1975, 15730, 45164, 1975, 8315, 47525, 7578, 1975, 22488, 1211, 1975, 3615, 28480, 19446, 2304, 3615, 1863, 7578, 16472, 2423, 4948, 5296, 479, 18871, 383, 9154, 45595, 3794, 9640, 20666, 3794, 995, 2407, 10632, 34762, 1975, 2407, 19446, 2304, 3615, 1863, 7578, 16472, 2423, 4948, 5296, 479, 18871, 383, 9154, 45595, 3794, 9640, 20666, 3794, 995, 2407, 10632, 8608, 6027, 3555, 34762, 6156, 3555, 47283, 3215, 718, 479, 312, 8032, 4117, 15730], "avg_logprob": -0.2749619011471911, "compression_ratio": 1.986206896551724, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 445.85, "end": 446.61, "word": "Infinity", "probability": 0.6205851236979166}, {"start": 446.61, "end": 446.93, "word": " او", "probability": 0.64013671875}, {"start": 446.93, "end": 447.47, "word": " 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517.78, "word": " انا", "probability": 0.7215576171875}, {"start": 517.78, "end": 518.18, "word": " عايز", "probability": 0.9552408854166666}, {"start": 518.18, "end": 518.36, "word": " ان", "probability": 0.70556640625}, {"start": 518.36, "end": 518.68, "word": " تكون", "probability": 0.84228515625}, {"start": 518.68, "end": 518.92, "word": " F", "probability": 0.7158203125}, {"start": 518.92, "end": 519.06, "word": " of", "probability": 0.41015625}, {"start": 519.06, "end": 519.26, "word": " X", "probability": 0.99169921875}, {"start": 519.26, "end": 519.66, "word": " أكبر", "probability": 0.9513346354166666}, {"start": 519.66, "end": 519.84, "word": " من", "probability": 0.99365234375}, {"start": 519.84, "end": 520.18, "word": " Alpha", "probability": 0.6484375}, {"start": 520.18, "end": 520.66, "word": " او", "probability": 0.754638671875}, {"start": 520.66, "end": 520.78, "word": " في", "probability": 0.79052734375}, {"start": 520.78, "end": 521.16, "word": " الحالة", "probability": 0.9796549479166666}, {"start": 521.16, "end": 521.56, "word": " هذه", "probability": 0.85791015625}, {"start": 521.56, "end": 522.44, "word": " F", "probability": 0.87744140625}, {"start": 522.44, "end": 522.66, "word": " of", "probability": 0.939453125}, {"start": 522.66, "end": 522.98, "word": " X", "probability": 0.99560546875}, {"start": 522.98, "end": 523.62, "word": " أصغر", "probability": 0.980712890625}, {"start": 523.62, "end": 523.82, "word": " من", "probability": 0.99609375}, {"start": 523.82, "end": 524.4, "word": " Alpha", "probability": 0.97216796875}, {"start": 524.4, "end": 525.14, "word": " هنا", "probability": 0.7958984375}, {"start": 525.14, "end": 525.36, "word": " ذيك", "probability": 0.46630859375}, {"start": 525.36, "end": 525.66, "word": " نكون", "probability": 0.74951171875}, {"start": 525.66, "end": 526.28, "word": " عرفنا", "probability": 0.8313802083333334}], "temperature": 1.0}, {"id": 19, "seek": 55513, "start": 526.99, "end": 555.13, "text": "الـ left limit عن c ما معنى أنها ساوي plus أو minus infinity إذن قلنا إن كل النظريات اللي برهنها for two sided limits هتكون صحيحة لل left limit و لل right limit من ضمنهم النظرية السابقة طيب لو بدي أنا يعني", "tokens": [6027, 39184, 1411, 4948, 18871, 269, 19446, 20449, 1863, 7578, 14739, 11296, 8608, 995, 45865, 1804, 34051, 3175, 13202, 11933, 8848, 1863, 12174, 1211, 8315, 36145, 28242, 28239, 19913, 16572, 9307, 13672, 1829, 4724, 2288, 3224, 1863, 11296, 337, 732, 41651, 10406, 8032, 2655, 30544, 20328, 5016, 1829, 5016, 3660, 24976, 1411, 4948, 4032, 24976, 558, 4948, 9154, 48812, 27842, 16095, 28239, 19913, 2288, 10632, 21136, 16758, 28671, 23032, 1829, 3555, 45164, 4724, 16254, 41850, 37495, 22653], "avg_logprob": -0.26782852029189086, "compression_ratio": 1.5532994923857868, "no_speech_prob": 0.0, "words": [{"start": 526.99, "end": 527.41, "word": "الـ", "probability": 0.52783203125}, {"start": 527.41, "end": 527.63, "word": " left", "probability": 0.55908203125}, {"start": 527.63, "end": 528.11, "word": " limit", "probability": 0.95263671875}, {"start": 528.11, "end": 529.03, "word": " عن", "probability": 0.701171875}, {"start": 529.03, "end": 529.43, "word": " c", "probability": 0.2529296875}, {"start": 529.43, "end": 529.71, "word": " ما", "probability": 0.6103515625}, {"start": 529.71, "end": 530.05, "word": " معنى", "probability": 0.6812337239583334}, {"start": 530.05, "end": 530.27, "word": " أنها", "probability": 0.5989990234375}, {"start": 530.27, "end": 530.63, "word": " ساوي", "probability": 0.7430013020833334}, {"start": 530.63, "end": 531.07, "word": " plus", "probability": 0.73681640625}, {"start": 531.07, "end": 532.03, "word": " أو", "probability": 0.85302734375}, {"start": 532.03, "end": 532.51, "word": " minus", "probability": 0.97216796875}, {"start": 532.51, "end": 533.57, "word": " infinity", "probability": 0.84521484375}, {"start": 533.57, "end": 535.21, "word": " إذن", "probability": 0.5210774739583334}, {"start": 535.21, "end": 535.97, "word": " قلنا", "probability": 0.79638671875}, {"start": 535.97, "end": 536.17, "word": " إن", "probability": 0.544921875}, {"start": 536.17, "end": 536.73, "word": " كل", "probability": 0.80712890625}, {"start": 536.73, "end": 537.49, "word": " النظريات", "probability": 0.84857177734375}, {"start": 537.49, "end": 537.67, "word": " اللي", "probability": 0.734619140625}, {"start": 537.67, "end": 538.21, "word": " برهنها", "probability": 0.83984375}, {"start": 538.21, "end": 538.45, "word": " for", "probability": 0.83837890625}, {"start": 538.45, "end": 538.71, "word": " two", "probability": 0.919921875}, {"start": 538.71, "end": 539.01, "word": " sided", "probability": 0.51123046875}, {"start": 539.01, "end": 539.53, "word": " limits", "probability": 0.9619140625}, {"start": 539.53, "end": 540.31, "word": " هتكون", "probability": 0.8701171875}, {"start": 540.31, "end": 540.81, "word": " صحيحة", "probability": 0.9525390625}, {"start": 540.81, "end": 540.99, "word": " لل", "probability": 0.90625}, {"start": 540.99, "end": 541.23, "word": " left", "probability": 0.46728515625}, {"start": 541.23, "end": 541.71, "word": " limit", "probability": 0.98291015625}, {"start": 541.71, "end": 542.45, "word": " و", "probability": 0.5908203125}, {"start": 542.45, "end": 542.59, "word": " لل", "probability": 0.91650390625}, {"start": 542.59, "end": 542.85, "word": " right", "probability": 0.93896484375}, {"start": 542.85, "end": 545.57, "word": " limit", "probability": 0.98779296875}, {"start": 545.57, "end": 548.27, "word": " من", "probability": 0.96435546875}, {"start": 548.27, "end": 548.73, "word": " ضمنهم", "probability": 0.9912109375}, {"start": 548.73, "end": 549.37, "word": " النظرية", "probability": 0.9693603515625}, {"start": 549.37, "end": 550.23, "word": " السابقة", "probability": 0.7181803385416666}, {"start": 550.23, "end": 554.01, "word": " طيب", "probability": 0.96923828125}, {"start": 554.01, "end": 554.17, "word": " لو", "probability": 0.95654296875}, {"start": 554.17, "end": 554.51, "word": " بدي", "probability": 0.6556396484375}, {"start": 554.51, "end": 554.71, "word": " أنا", "probability": 0.6298828125}, {"start": 554.71, "end": 555.13, "word": " يعني", "probability": 0.97509765625}], "temperature": 1.0}, {"id": 20, "seek": 58516, "start": 558.09, "end": 585.17, "text": "أخد أمثلة كيف نستخدم التعريف هذا فيه إثبات إن ال limits تطلع plus أو minus infinity فناخد أول مثال let f of x بسوي واحد على x حيث x لا يساوي سبق و show", "tokens": [10721, 9778, 3215, 5551, 2304, 12984, 37977, 9122, 33911, 8717, 14851, 9778, 40448, 16712, 3615, 16572, 5172, 23758, 8978, 3224, 11933, 12984, 3555, 9307, 36145, 2423, 10406, 6055, 9566, 1211, 3615, 1804, 34051, 3175, 13202, 6156, 1863, 47283, 3215, 5551, 12610, 50113, 6027, 718, 283, 295, 2031, 4724, 3794, 45865, 36764, 24401, 15844, 2031, 11331, 1829, 12984, 2031, 20193, 7251, 3794, 995, 45865, 8608, 3555, 4587, 4032, 855], "avg_logprob": -0.2744565338328265, "compression_ratio": 1.3952095808383234, "no_speech_prob": 0.0, "words": [{"start": 558.09, "end": 558.65, "word": "أخد", "probability": 0.76904296875}, {"start": 558.65, "end": 559.31, "word": " أمثلة", "probability": 0.8804931640625}, {"start": 559.31, "end": 560.39, "word": " كيف", "probability": 0.903564453125}, {"start": 560.39, "end": 560.97, "word": " نستخدم", "probability": 0.9541015625}, {"start": 560.97, "end": 561.65, "word": " التعريف", "probability": 0.9495849609375}, {"start": 561.65, "end": 562.03, "word": " هذا", "probability": 0.44580078125}, {"start": 562.03, "end": 564.13, "word": " فيه", "probability": 0.4161376953125}, {"start": 564.13, "end": 564.53, "word": " إثبات", "probability": 0.9013671875}, {"start": 564.53, "end": 564.73, "word": " إن", "probability": 0.4921875}, {"start": 564.73, "end": 564.87, "word": " ال", "probability": 0.87255859375}, {"start": 564.87, "end": 565.43, "word": " limits", "probability": 0.78564453125}, {"start": 565.43, "end": 566.33, "word": " تطلع", "probability": 0.8955078125}, {"start": 566.33, "end": 566.85, "word": " plus", "probability": 0.80615234375}, {"start": 566.85, "end": 567.11, "word": " أو", "probability": 0.8037109375}, {"start": 567.11, "end": 567.57, "word": " minus", "probability": 0.98828125}, {"start": 567.57, "end": 569.49, "word": " infinity", "probability": 0.8232421875}, {"start": 569.49, "end": 571.39, "word": " فناخد", "probability": 0.8212890625}, {"start": 571.39, "end": 571.63, "word": " أول", "probability": 0.9482421875}, {"start": 571.63, "end": 572.23, "word": " مثال", "probability": 0.81298828125}, {"start": 572.23, "end": 572.65, "word": " let", "probability": 0.70654296875}, {"start": 572.65, "end": 575.17, "word": " f", "probability": 0.73291015625}, {"start": 575.17, "end": 575.41, "word": " of", "probability": 0.33203125}, {"start": 575.41, "end": 575.85, "word": " x", "probability": 0.83251953125}, {"start": 575.85, "end": 576.89, "word": " بسوي", "probability": 0.6021321614583334}, {"start": 576.89, "end": 580.25, "word": " واحد", "probability": 0.843505859375}, {"start": 580.25, "end": 580.43, "word": " على", "probability": 0.541015625}, {"start": 580.43, "end": 580.81, "word": " x", "probability": 0.5625}, {"start": 580.81, "end": 581.17, "word": " حيث", "probability": 0.5448404947916666}, {"start": 581.17, "end": 581.47, "word": " x", "probability": 0.91455078125}, {"start": 581.47, "end": 581.71, "word": " لا", "probability": 0.830078125}, {"start": 581.71, "end": 582.17, "word": " يساوي", "probability": 0.8507080078125}, {"start": 582.17, "end": 582.69, "word": " سبق", "probability": 0.6231689453125}, {"start": 582.69, "end": 584.57, "word": " و", "probability": 0.9052734375}, {"start": 584.57, "end": 585.17, "word": " show", "probability": 0.5498046875}], "temperature": 1.0}, {"id": 21, "seek": 60996, "start": 589.78, "end": 609.96, "text": "عايزين نفدت واحد ان ال limit لواحد على x او f of x هنا لما x تقول الى ستر من اليمين بساوي ال infinity و 2 limit", "tokens": 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"word": " على", "probability": 0.72607421875}, {"start": 595.72, "end": 596.16, "word": " x", "probability": 0.39599609375}, {"start": 596.16, "end": 597.32, "word": " او", "probability": 0.83544921875}, {"start": 597.32, "end": 597.58, "word": " f", "probability": 0.78662109375}, {"start": 597.58, "end": 597.76, "word": " of", "probability": 0.416259765625}, {"start": 597.76, "end": 598.06, "word": " x", "probability": 0.9619140625}, {"start": 598.06, "end": 598.34, "word": " هنا", "probability": 0.66259765625}, {"start": 598.34, "end": 601.16, "word": " لما", "probability": 0.85546875}, {"start": 601.16, "end": 601.44, "word": " x", "probability": 0.890625}, {"start": 601.44, "end": 601.94, "word": " تقول", "probability": 0.881103515625}, {"start": 601.94, "end": 602.3, "word": " الى", "probability": 0.18939208984375}, {"start": 602.3, "end": 602.88, "word": " ستر", "probability": 0.7814127604166666}, {"start": 602.88, "end": 603.12, "word": " من", "probability": 0.98388671875}, {"start": 603.12, "end": 603.86, "word": " اليمين", "probability": 0.8487955729166666}, {"start": 603.86, "end": 605.24, "word": " بساوي", "probability": 0.65948486328125}, {"start": 605.24, "end": 605.38, "word": " ال", "probability": 0.417724609375}, {"start": 605.38, "end": 605.82, "word": " infinity", "probability": 0.87646484375}, {"start": 605.82, "end": 606.56, "word": " و", "probability": 0.7060546875}, {"start": 606.56, "end": 608.04, "word": " 2", "probability": 0.1600341796875}, {"start": 608.04, "end": 609.96, "word": " limit", "probability": 0.3330078125}], "temperature": 1.0}, {"id": 22, "seek": 62954, "start": 611.3, "end": 629.54, "text": "لف of X لما X تقول ال 0 من اليسار يساوي سالب infinity okay فلو بدنا نبرم الجزء الأول مثلا to show", "tokens": [1211, 5172, 295, 1783, 5296, 15042, 1783, 6055, 39648, 2423, 1958, 9154, 45595, 3794, 9640, 7251, 3794, 995, 45865, 8608, 6027, 3555, 13202, 1392, 6156, 1211, 2407, 47525, 8315, 8717, 26890, 2304, 25724, 11622, 38207, 16247, 12610, 50113, 15040, 281, 855], "avg_logprob": -0.30338541099003385, "compression_ratio": 1.2295081967213115, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 611.3, "end": 611.86, "word": "لف", "probability": 0.3897705078125}, {"start": 611.86, "end": 612.14, "word": " of", "probability": 0.642578125}, {"start": 612.14, "end": 612.52, "word": " X", "probability": 0.50390625}, {"start": 612.52, "end": 613.16, "word": " لما", "probability": 0.718994140625}, {"start": 613.16, "end": 613.48, "word": " X", "probability": 0.95654296875}, {"start": 613.48, "end": 614.12, "word": " تقول", "probability": 0.884521484375}, {"start": 614.12, "end": 615.36, "word": " ال", "probability": 0.338134765625}, {"start": 615.36, "end": 615.98, "word": " 0", "probability": 0.293701171875}, {"start": 615.98, "end": 616.3, "word": " من", "probability": 0.99462890625}, {"start": 616.3, "end": 617.12, "word": " اليسار", "probability": 0.97509765625}, {"start": 617.12, "end": 618.68, "word": " يساوي", "probability": 0.764617919921875}, {"start": 618.68, "end": 619.2, "word": " سالب", "probability": 0.86865234375}, {"start": 619.2, "end": 619.74, "word": " infinity", "probability": 0.456298828125}, {"start": 619.74, "end": 620.52, "word": " okay", "probability": 0.2373046875}, {"start": 620.52, "end": 623.88, "word": " فلو", "probability": 0.88720703125}, {"start": 623.88, "end": 624.16, "word": " بدنا", "probability": 0.961181640625}, {"start": 624.16, "end": 624.72, "word": " نبرم", "probability": 0.734375}, {"start": 624.72, "end": 626.36, "word": " الجزء", "probability": 0.873046875}, {"start": 626.36, "end": 626.76, "word": " الأول", "probability": 0.8603515625}, {"start": 626.76, "end": 627.28, "word": " مثلا", "probability": 0.982177734375}, {"start": 627.28, "end": 629.02, "word": " to", "probability": 0.92333984375}, {"start": 629.02, "end": 629.54, "word": " show", "probability": 0.96875}], "temperature": 1.0}, {"id": 23, "seek": 65921, "start": 632.41, "end": 659.21, "text": "المقاومة لـ f of x as x tends to 0 from the right بساوي infinity فبدي ابدا بـ alpha تنتمي ل R فبقول let alpha belonging to R be given و بدي ارد عليها بDelta", "tokens": [45340, 4587, 995, 20498, 3660, 5296, 39184, 283, 295, 2031, 382, 2031, 12258, 281, 1958, 490, 264, 558, 4724, 3794, 995, 45865, 13202, 6156, 3555, 16254, 48127, 28259, 4724, 39184, 8961, 6055, 29399, 2304, 1829, 5296, 497, 6156, 3555, 39648, 718, 8961, 22957, 281, 497, 312, 2212, 4032, 4724, 16254, 1975, 2288, 3215, 25894, 11296, 4724, 40848, 1328], "avg_logprob": -0.4541843280953876, "compression_ratio": 1.2654320987654322, "no_speech_prob": 0.0, "words": [{"start": 632.4100000000001, "end": 633.33, "word": "المقاومة", "probability": 0.4727783203125}, {"start": 633.33, "end": 634.25, "word": " لـ", "probability": 0.4246826171875}, {"start": 634.25, "end": 634.43, "word": " f", "probability": 0.2445068359375}, {"start": 634.43, "end": 634.67, "word": " of", "probability": 0.227783203125}, {"start": 634.67, "end": 635.09, "word": " x", "probability": 0.83544921875}, {"start": 635.09, "end": 635.61, "word": " as", "probability": 0.141845703125}, {"start": 635.61, "end": 636.07, "word": " x", "probability": 0.892578125}, {"start": 636.07, "end": 636.53, "word": " tends", "probability": 0.76806640625}, {"start": 636.53, "end": 637.63, "word": " to", "probability": 0.9599609375}, {"start": 637.63, "end": 637.95, "word": " 0", "probability": 0.441650390625}, {"start": 637.95, "end": 638.13, "word": " from", "probability": 0.8974609375}, {"start": 638.13, "end": 638.43, "word": " the", "probability": 0.82861328125}, {"start": 638.43, "end": 638.71, "word": " right", "probability": 0.93017578125}, {"start": 638.71, "end": 639.29, "word": " بساوي", "probability": 0.848388671875}, {"start": 639.29, "end": 639.87, "word": " infinity", "probability": 0.44580078125}, {"start": 639.87, "end": 641.89, "word": " فبدي", "probability": 0.4459635416666667}, {"start": 641.89, "end": 642.29, "word": " ابدا", "probability": 0.624755859375}, {"start": 642.29, "end": 642.57, "word": " بـ", "probability": 0.4725341796875}, {"start": 642.57, "end": 642.87, "word": " alpha", "probability": 0.4013671875}, {"start": 642.87, "end": 644.59, "word": " تنتمي", "probability": 0.9407958984375}, {"start": 644.59, "end": 644.67, "word": " ل", "probability": 0.87255859375}, {"start": 644.67, "end": 644.99, "word": " R", "probability": 0.26953125}, {"start": 644.99, "end": 645.67, "word": " فبقول", "probability": 0.9192708333333334}, {"start": 645.67, "end": 646.11, "word": " let", "probability": 0.75830078125}, {"start": 646.11, "end": 648.41, "word": " alpha", "probability": 0.76806640625}, {"start": 648.41, "end": 648.99, "word": " belonging", "probability": 0.69482421875}, {"start": 648.99, "end": 649.33, "word": " to", "probability": 0.98486328125}, {"start": 649.33, "end": 649.87, "word": " R", "probability": 0.98876953125}, {"start": 649.87, "end": 651.55, "word": " be", "probability": 0.79541015625}, {"start": 651.55, "end": 652.17, "word": " given", "probability": 0.84033203125}, {"start": 652.17, "end": 657.49, "word": " و", "probability": 0.7275390625}, {"start": 657.49, "end": 657.89, "word": " بدي", "probability": 0.663818359375}, {"start": 657.89, "end": 658.25, "word": " ارد", "probability": 0.8372395833333334}, {"start": 658.25, "end": 658.63, "word": " عليها", "probability": 0.987548828125}, {"start": 658.63, "end": 659.21, "word": " بDelta", "probability": 0.5944010416666666}], "temperature": 1.0}, {"id": 24, "seek": 68981, "start": 660.67, "end": 689.81, "text": "بدي ارد على ال alpha دي ال delta عدد موجب ويعتمد على ال alpha ف choose delta بتساوي واحد على absolute alpha زاد واحد بالتأكيد هذا عدد موجب لأن absolute ال alpha دي عدد حقيقي القيمة المطلقة له عدد غير سالم ممكن يساوي سفر إذا كانت alpha بالساوية سفر", "tokens": [3555, 16254, 1975, 2288, 3215, 15844, 2423, 8961, 11778, 1829, 2423, 8289, 6225, 3215, 3215, 3714, 29245, 3555, 4032, 1829, 34268, 2304, 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"word": " alpha", "probability": 0.350830078125}, {"start": 662.15, "end": 662.61, "word": " دي", "probability": 0.62255859375}, {"start": 662.61, "end": 662.79, "word": " ال", "probability": 0.313232421875}, {"start": 662.79, "end": 663.25, "word": " delta", "probability": 0.7783203125}, {"start": 663.25, "end": 664.61, "word": " عدد", "probability": 0.9554036458333334}, {"start": 664.61, "end": 665.21, "word": " موجب", "probability": 0.98779296875}, {"start": 665.21, "end": 666.05, "word": " ويعتمد", "probability": 0.817626953125}, {"start": 666.05, "end": 666.25, "word": " على", "probability": 0.84033203125}, {"start": 666.25, "end": 666.43, "word": " ال", "probability": 0.95703125}, {"start": 666.43, "end": 666.85, "word": " alpha", "probability": 0.92822265625}, {"start": 666.85, "end": 667.21, "word": " ف", "probability": 0.625}, {"start": 667.21, "end": 667.93, "word": " choose", "probability": 0.405029296875}, {"start": 667.93, "end": 668.63, "word": " delta", "probability": 0.76318359375}, {"start": 668.63, "end": 670.83, "word": " بتساوي", "probability": 0.808349609375}, {"start": 670.83, "end": 671.49, "word": " واحد", "probability": 0.94970703125}, {"start": 671.49, "end": 671.87, "word": " على", "probability": 0.60986328125}, {"start": 671.87, "end": 672.61, "word": " absolute", "probability": 0.712890625}, {"start": 672.61, "end": 673.37, "word": " alpha", "probability": 0.83984375}, {"start": 673.37, "end": 674.81, "word": " زاد", "probability": 0.68798828125}, {"start": 674.81, "end": 675.21, "word": " واحد", "probability": 0.981201171875}, {"start": 675.21, "end": 675.89, "word": " بالتأكيد", "probability": 0.96923828125}, {"start": 675.89, "end": 676.11, "word": " هذا", "probability": 0.70263671875}, {"start": 676.11, "end": 676.43, "word": " عدد", "probability": 0.9900716145833334}, {"start": 676.43, "end": 676.97, "word": " موجب", "probability": 0.98583984375}, {"start": 676.97, "end": 679.61, "word": " لأن", "probability": 0.756591796875}, {"start": 679.61, "end": 680.35, "word": " absolute", "probability": 0.450439453125}, {"start": 680.35, "end": 680.53, "word": " ال", "probability": 0.7705078125}, {"start": 680.53, "end": 680.79, "word": " alpha", "probability": 0.90966796875}, {"start": 680.79, "end": 681.01, "word": " دي", "probability": 0.96533203125}, {"start": 681.01, "end": 681.29, "word": " عدد", "probability": 0.9943033854166666}, {"start": 681.29, "end": 681.91, "word": " حقيقي", "probability": 0.98486328125}, {"start": 681.91, "end": 682.49, "word": " القيمة", "probability": 0.9560546875}, {"start": 682.49, "end": 682.93, "word": " المطلقة", "probability": 0.9854736328125}, {"start": 682.93, "end": 683.27, "word": " له", "probability": 0.1678466796875}, {"start": 683.27, "end": 684.49, "word": " عدد", "probability": 0.99169921875}, {"start": 684.49, "end": 684.97, "word": " غير", "probability": 0.9970703125}, {"start": 684.97, "end": 685.49, "word": " سالم", "probability": 0.7333984375}, {"start": 685.49, "end": 687.55, "word": " ممكن", "probability": 0.933349609375}, {"start": 687.55, "end": 687.93, "word": " يساوي", "probability": 0.9610595703125}, {"start": 687.93, "end": 688.27, "word": " سفر", "probability": 0.8527018229166666}, {"start": 688.27, "end": 688.45, "word": " إذا", "probability": 0.6920166015625}, {"start": 688.45, "end": 688.81, "word": " كانت", "probability": 0.9228515625}, {"start": 688.81, "end": 688.99, "word": " alpha", "probability": 0.46728515625}, {"start": 688.99, "end": 689.47, "word": " بالساوية", "probability": 0.613330078125}, {"start": 689.47, "end": 689.81, "word": " سفر", "probability": 0.9397786458333334}], "temperature": 1.0}, {"id": 25, "seek": 71164, "start": 690.62, "end": 711.64, "text": "لكن زائد واحد بصير موجب المقام موجب اذا انا بضيف واحد ليه عشان اضمن ان المقام مايسويش سفر لان في احتمال ان ال alpha ساوي سفر فبصير عندى مشكلة عشان اتخلص من المشكلة هذه بجسم على absolute alpha زائد واحد الان هذا عدد موجب", "tokens": [1211, 19452, 30767, 16373, 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0.968994140625}, {"start": 692.0, "end": 692.46, "word": " بصير", "probability": 0.685302734375}, {"start": 692.46, "end": 692.98, "word": " موجب", "probability": 0.9658203125}, {"start": 692.98, "end": 694.32, "word": " المقام", "probability": 0.8468424479166666}, {"start": 694.32, "end": 694.86, "word": " موجب", "probability": 0.9861653645833334}, {"start": 694.86, "end": 695.72, "word": " اذا", "probability": 0.522979736328125}, {"start": 695.72, "end": 695.94, "word": " انا", "probability": 0.763427734375}, {"start": 695.94, "end": 696.34, "word": " بضيف", "probability": 0.88818359375}, {"start": 696.34, "end": 696.74, "word": " واحد", "probability": 0.9833984375}, {"start": 696.74, "end": 696.98, "word": " ليه", "probability": 0.9169921875}, {"start": 696.98, "end": 697.2, "word": " عشان", "probability": 0.782958984375}, {"start": 697.2, "end": 697.58, "word": " اضمن", "probability": 0.8704427083333334}, {"start": 697.58, "end": 697.72, "word": " ان", "probability": 0.888671875}, {"start": 697.72, "end": 698.22, "word": " المقام", "probability": 0.9832356770833334}, {"start": 698.22, "end": 698.82, "word": " مايسويش", "probability": 0.81611328125}, {"start": 698.82, "end": 699.18, "word": " سفر", "probability": 0.9099934895833334}, {"start": 699.18, "end": 700.58, "word": " لان", "probability": 0.86376953125}, {"start": 700.58, "end": 700.74, "word": " في", "probability": 0.8369140625}, {"start": 700.74, "end": 701.16, "word": " احتمال", "probability": 0.9490966796875}, {"start": 701.16, "end": 701.28, "word": " ان", "probability": 0.9462890625}, {"start": 701.28, "end": 701.38, "word": " ال", "probability": 0.599609375}, {"start": 701.38, "end": 701.56, "word": " alpha", "probability": 0.40869140625}, {"start": 701.56, "end": 701.88, "word": " ساوي", "probability": 0.6222330729166666}, {"start": 701.88, "end": 702.36, "word": " سفر", "probability": 0.9698893229166666}, {"start": 702.36, "end": 703.46, "word": " فبصير", "probability": 0.808349609375}, {"start": 703.46, "end": 703.72, "word": " عندى", "probability": 0.72216796875}, {"start": 703.72, "end": 704.1, "word": " مشكلة", "probability": 0.9793294270833334}, {"start": 704.1, "end": 704.3, "word": " عشان", "probability": 0.9765625}, {"start": 704.3, "end": 704.74, "word": " اتخلص", "probability": 0.8982421875}, {"start": 704.74, "end": 704.86, "word": " من", "probability": 0.96826171875}, {"start": 704.86, "end": 705.32, "word": " المشكلة", "probability": 0.9893798828125}, {"start": 705.32, "end": 705.64, "word": " هذه", "probability": 0.363037109375}, {"start": 705.64, "end": 707.1, "word": " بجسم", "probability": 0.8880208333333334}, {"start": 707.1, "end": 707.34, "word": " على", "probability": 0.91015625}, {"start": 707.34, "end": 707.66, "word": " absolute", "probability": 0.6123046875}, {"start": 707.66, "end": 708.06, "word": " alpha", "probability": 0.7509765625}, {"start": 708.06, "end": 708.5, "word": " زائد", "probability": 0.8883463541666666}, {"start": 708.5, "end": 709.62, "word": " واحد", "probability": 0.9736328125}, {"start": 709.62, "end": 710.5, "word": " الان", "probability": 0.6707763671875}, {"start": 710.5, "end": 710.78, "word": " هذا", "probability": 0.7158203125}, {"start": 710.78, "end": 711.14, "word": " عدد", "probability": 0.98681640625}, {"start": 711.14, "end": 711.64, "word": " موجب", "probability": 0.9928385416666666}], "temperature": 1.0}, {"id": 26, "seek": 73133, "start": 713.15, "end": 731.33, "text": "و يعتمد على alpha هي ال delta هي مرتبطة معرفة بدلالة alpha هي معناه أنها تعتمد على alpha إذا لأي alpha ينتمي ل R خد ال delta اللي بتنظرها هي واحد على absolute alpha الذات واحدة", "tokens": [2407, 7251, 34268, 2304, 3215, 15844, 8961, 39896, 2423, 8289, 39896, 3714, 43500, 3555, 9566, 3660, 20449, 28480, 3660, 47525, 1211, 6027, 3660, 8961, 39896, 20449, 8315, 3224, 14739, 11296, 6055, 34268, 2304, 3215, 15844, 8961, 11933, 15730, 5296, 10721, 1829, 8961, 7251, 29399, 2304, 1829, 5296, 497, 16490, 3215, 2423, 8289, 13672, 1829, 39894, 1863, 19913, 2288, 11296, 39896, 36764, 24401, 15844, 8236, 8961, 32545, 9307, 36764, 24401, 3660], "avg_logprob": -0.26408449864723316, "compression_ratio": 1.6646341463414633, "no_speech_prob": 0.0, "words": [{"start": 713.15, "end": 713.39, "word": "و", "probability": 0.63671875}, {"start": 713.39, "end": 713.95, "word": " يعتمد", "probability": 0.789764404296875}, {"start": 713.95, "end": 714.13, "word": " على", "probability": 0.90673828125}, {"start": 714.13, "end": 714.45, "word": " alpha", "probability": 0.375732421875}, {"start": 714.45, "end": 714.75, "word": " هي", "probability": 0.1729736328125}, {"start": 714.75, "end": 714.91, "word": " ال", "probability": 0.350341796875}, {"start": 714.91, "end": 715.29, "word": " delta", "probability": 0.455078125}, {"start": 715.29, "end": 715.53, "word": " هي", "probability": 0.8759765625}, {"start": 715.53, "end": 716.31, "word": " مرتبطة", "probability": 0.938671875}, {"start": 716.31, "end": 717.01, "word": " معرفة", "probability": 0.94140625}, {"start": 717.01, "end": 717.73, "word": " بدلالة", "probability": 0.97607421875}, {"start": 717.73, "end": 718.07, "word": " alpha", "probability": 0.79443359375}, {"start": 718.07, "end": 718.81, "word": " هي", "probability": 0.425048828125}, {"start": 718.81, "end": 719.15, "word": " معناه", "probability": 0.8631184895833334}, {"start": 719.15, "end": 719.33, "word": " أنها", "probability": 0.68994140625}, {"start": 719.33, "end": 720.01, "word": " تعتمد", "probability": 0.97314453125}, {"start": 720.01, "end": 720.61, "word": " على", "probability": 0.9150390625}, {"start": 720.61, "end": 720.95, "word": " alpha", "probability": 0.6865234375}, {"start": 720.95, "end": 721.93, "word": " إذا", "probability": 0.6036376953125}, {"start": 721.93, "end": 722.35, "word": " لأي", "probability": 0.8388671875}, {"start": 722.35, "end": 722.67, "word": " alpha", "probability": 0.88134765625}, {"start": 722.67, "end": 723.17, "word": " ينتمي", "probability": 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0.6435546875}, {"start": 825.18, "end": 825.42, "word": " of", "probability": 0.32177734375}, {"start": 825.42, "end": 825.86, "word": " x", "probability": 0.85107421875}, {"start": 825.86, "end": 827.86, "word": " أكبر", "probability": 0.9563802083333334}, {"start": 827.86, "end": 828.08, "word": " من", "probability": 0.9931640625}, {"start": 828.08, "end": 828.22, "word": " ال", "probability": 0.8505859375}, {"start": 828.22, "end": 828.48, "word": " given", "probability": 0.90087890625}, {"start": 828.48, "end": 828.92, "word": " alpha", "probability": 0.86572265625}], "temperature": 1.0}, {"id": 31, "seek": 86158, "start": 833.52, "end": 861.58, "text": "Okay تمام بما ان ال alpha دي كانت arbitrarily since alpha belong to R was arbitrarily اذا هين اثبتنا اذا معناه هذا الكلام هذا انه لكل alpha فيه delta تعتمد عليها بتخلي f of x اكبر من alpha لكل x قريبة من السفر within مسافة delta", "tokens": [8297, 46811, 10943, 4724, 15042, 16472, 2423, 8961, 11778, 1829, 25961, 2655, 19071, 3289, 1670, 8961, 5784, 281, 497, 390, 19071, 3289, 1975, 15730, 8032, 9957, 1975, 12984, 3555, 2655, 8315, 1975, 15730, 20449, 8315, 3224, 23758, 2423, 28820, 10943, 23758, 16472, 3224, 5296, 28820, 8961, 8978, 3224, 8289, 6055, 34268, 2304, 3215, 25894, 11296, 39894, 9778, 20292, 283, 295, 2031, 1975, 4117, 26890, 9154, 8961, 5296, 28820, 2031, 12174, 16572, 49401, 9154, 21136, 5172, 2288, 1951, 47524, 31845, 3660, 8289], "avg_logprob": -0.291349082821753, "compression_ratio": 1.5951219512195123, "no_speech_prob": 0.0, "words": [{"start": 833.52, "end": 833.98, "word": "Okay", "probability": 0.66796875}, {"start": 833.98, "end": 834.54, "word": " تمام", "probability": 0.9814453125}, {"start": 834.54, "end": 835.54, "word": " بما", "probability": 0.549072265625}, {"start": 835.54, "end": 835.78, "word": " ان", "probability": 0.49072265625}, {"start": 835.78, "end": 836.68, "word": " ال", "probability": 0.65673828125}, {"start": 836.68, "end": 837.04, "word": " alpha", "probability": 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{"start": 846.64, "end": 847.3, "word": " اثبتنا", "probability": 0.91455078125}, {"start": 847.3, "end": 847.5, "word": " اذا", "probability": 0.74462890625}, {"start": 847.5, "end": 847.94, "word": " معناه", "probability": 0.71875}, {"start": 847.94, "end": 848.22, "word": " هذا", "probability": 0.44482421875}, {"start": 848.22, "end": 849.56, "word": " الكلام", "probability": 0.7676595052083334}, {"start": 849.56, "end": 850.08, "word": " هذا", "probability": 0.4404296875}, {"start": 850.08, "end": 851.0, "word": " انه", "probability": 0.642578125}, {"start": 851.0, "end": 851.38, "word": " لكل", "probability": 0.9365234375}, {"start": 851.38, "end": 851.78, "word": " alpha", "probability": 0.7822265625}, {"start": 851.78, "end": 852.18, "word": " فيه", "probability": 0.722412109375}, {"start": 852.18, "end": 852.56, "word": " delta", "probability": 0.61181640625}, {"start": 852.56, "end": 853.48, "word": " تعتمد", "probability": 0.9041748046875}, {"start": 853.48, "end": 854.02, "word": " عليها", "probability": 0.988525390625}, {"start": 854.02, "end": 855.02, "word": " بتخلي", "probability": 0.8694661458333334}, {"start": 855.02, "end": 855.22, "word": " f", "probability": 0.55029296875}, {"start": 855.22, "end": 855.4, "word": " of", "probability": 0.73193359375}, {"start": 855.4, "end": 855.64, "word": " x", "probability": 0.70556640625}, {"start": 855.64, "end": 856.0, "word": " اكبر", "probability": 0.8702799479166666}, {"start": 856.0, "end": 856.14, "word": " من", "probability": 0.44287109375}, {"start": 856.14, "end": 856.38, "word": " alpha", "probability": 0.63134765625}, {"start": 856.38, "end": 856.9, "word": " لكل", "probability": 0.923828125}, {"start": 856.9, "end": 857.28, "word": " x", "probability": 0.8740234375}, {"start": 857.28, "end": 858.38, "word": " قريبة", "probability": 0.9552408854166666}, {"start": 858.38, "end": 858.84, "word": " من", "probability": 0.990234375}, {"start": 858.84, "end": 859.64, "word": " السفر", "probability": 0.8484700520833334}, {"start": 859.64, "end": 860.58, "word": " within", "probability": 0.67529296875}, {"start": 860.58, "end": 861.3, "word": " مسافة", "probability": 0.9879557291666666}, {"start": 861.3, "end": 861.58, "word": " delta", "probability": 0.61865234375}], "temperature": 1.0}, {"id": 32, "seek": 87832, "start": 862.34, "end": 878.32, "text": "إن هذا معناه حسب التعريف إن ال limit ل f of x لما x تقول إلى سفر من اليمين بساوي بورهانش جزء التاني مشابه", "tokens": [28814, 1863, 23758, 20449, 8315, 3224, 11331, 35457, 16712, 3615, 16572, 5172, 36145, 2423, 4948, 5296, 283, 295, 2031, 5296, 15042, 2031, 6055, 39648, 30731, 8608, 5172, 2288, 9154, 2423, 32640, 9957, 4724, 3794, 995, 45865, 4724, 13063, 3224, 7649, 8592, 10874, 11622, 38207, 16712, 7649, 1829, 37893, 16758, 3224], "avg_logprob": -0.3547794094272688, "compression_ratio": 1.3409090909090908, "no_speech_prob": 0.0, "words": [{"start": 862.34, "end": 862.58, "word": "إن", "probability": 0.4678955078125}, {"start": 862.58, "end": 862.8, "word": " هذا", "probability": 0.6748046875}, {"start": 862.8, "end": 863.14, "word": " معناه", "probability": 0.8264973958333334}, {"start": 863.14, "end": 863.44, "word": " حسب", "probability": 0.80859375}, {"start": 863.44, "end": 864.06, "word": " التعريف", "probability": 0.9466552734375}, {"start": 864.06, "end": 864.28, "word": " إن", "probability": 0.14599609375}, {"start": 864.28, "end": 864.5, "word": " ال", "probability": 0.39306640625}, {"start": 864.5, "end": 864.94, "word": " limit", "probability": 0.6943359375}, {"start": 864.94, "end": 866.0, "word": " ل", "probability": 0.7529296875}, {"start": 866.0, "end": 866.26, "word": " f", "probability": 0.3125}, {"start": 866.26, "end": 866.52, "word": " of", "probability": 0.496826171875}, {"start": 866.52, "end": 866.86, "word": " x", "probability": 0.89501953125}, {"start": 866.86, "end": 867.22, "word": " لما", "probability": 0.734619140625}, {"start": 867.22, "end": 867.54, "word": " x", "probability": 0.8798828125}, {"start": 867.54, "end": 868.14, "word": " تقول", "probability": 0.922607421875}, {"start": 868.14, "end": 868.5, "word": " إلى", "probability": 0.84228515625}, {"start": 868.5, "end": 869.06, "word": " سفر", "probability": 0.74853515625}, {"start": 869.06, "end": 869.34, "word": " من", "probability": 0.99072265625}, {"start": 869.34, "end": 870.88, "word": " اليمين", "probability": 0.8517252604166666}, {"start": 870.88, "end": 872.18, "word": " بساوي", "probability": 0.8380126953125}, {"start": 872.18, "end": 876.78, "word": " بورهانش", "probability": 0.675146484375}, {"start": 876.78, "end": 877.1, "word": " جزء", "probability": 0.9716796875}, {"start": 877.1, "end": 877.58, "word": " التاني", "probability": 0.8349609375}, {"start": 877.58, "end": 878.32, "word": " مشابه", "probability": 0.9583333333333334}], "temperature": 1.0}, {"id": 33, "seek": 91488, "start": 887.84, "end": 914.88, "text": "is similar مشابه لل part للجزء الأول يعني فهسيبكم انتوا تكتبوا برهان مشابه مع التعديلات اللازمة و أيه طبعا التعريف تبع ال limit from the left موجود okay تمام اللي هو بالأزرق تمام مثال تاني ممكن برضه", "tokens": [271, 2531, 37893, 16758, 3224, 24976, 644, 24976, 7435, 11622, 38207, 16247, 12610, 37495, 22653, 6156, 3224, 3794, 1829, 3555, 24793, 16472, 2655, 14407, 6055, 4117, 2655, 3555, 14407, 4724, 2288, 3224, 7649, 37893, 16758, 3224, 20449, 16712, 3615, 16254, 1211, 9307, 13672, 31377, 46007, 4032, 36632, 3224, 23032, 3555, 3615, 995, 16712, 3615, 16572, 5172, 6055, 3555, 3615, 2423, 4948, 490, 264, 1411, 3714, 29245, 23328, 1392, 46811, 10943, 13672, 1829, 31439, 20666, 10721, 11622, 2288, 4587, 46811, 10943, 50113, 6027, 6055, 7649, 1829, 3714, 43020, 4724, 43042, 3224], "avg_logprob": -0.16595123397124992, "compression_ratio": 1.5721153846153846, "no_speech_prob": 0.0, "words": [{"start": 887.84, "end": 888.28, "word": "is", "probability": 0.5439453125}, {"start": 888.28, "end": 888.92, "word": " similar", "probability": 0.935546875}, {"start": 888.92, "end": 889.86, "word": " مشابه", "probability": 0.87548828125}, {"start": 889.86, "end": 890.66, "word": " لل", "probability": 0.41650390625}, {"start": 890.66, "end": 891.18, "word": " part", "probability": 0.52197265625}, {"start": 891.18, "end": 892.1, "word": " للجزء", "probability": 0.81396484375}, {"start": 892.1, "end": 892.58, "word": " الأول", "probability": 0.78125}, {"start": 892.58, "end": 893.5, "word": " يعني", "probability": 0.6240234375}, {"start": 893.5, "end": 894.4, "word": " فهسيبكم", "probability": 0.86474609375}, {"start": 894.4, "end": 894.98, "word": " انتوا", "probability": 0.6875}, {"start": 894.98, "end": 896.1, "word": " تكتبوا", "probability": 0.98896484375}, {"start": 896.1, "end": 896.62, "word": " برهان", "probability": 0.9307861328125}, {"start": 896.62, "end": 897.26, "word": " مشابه", "probability": 0.9903971354166666}, {"start": 897.26, "end": 897.58, "word": " مع", "probability": 0.9794921875}, {"start": 897.58, "end": 898.34, "word": " التعديلات", "probability": 0.92568359375}, {"start": 898.34, "end": 899.04, "word": " اللازمة", "probability": 0.99462890625}, {"start": 899.04, "end": 899.86, "word": " و", "probability": 0.736328125}, {"start": 899.86, "end": 900.08, "word": " أيه", "probability": 0.681640625}, {"start": 900.08, "end": 900.4, "word": " طبعا", "probability": 0.9664306640625}, {"start": 900.4, "end": 901.14, "word": " التعريف", "probability": 0.8988037109375}, {"start": 901.14, "end": 901.66, "word": " تبع", "probability": 0.7163899739583334}, {"start": 901.66, "end": 902.76, "word": " ال", "probability": 0.59375}, {"start": 902.76, "end": 903.14, "word": " limit", "probability": 0.92138671875}, {"start": 903.14, "end": 903.82, "word": " from", "probability": 0.90673828125}, {"start": 903.82, "end": 904.08, "word": " the", "probability": 0.90283203125}, {"start": 904.08, "end": 904.48, "word": " left", "probability": 0.96826171875}, {"start": 904.48, "end": 905.66, "word": " موجود", "probability": 0.96337890625}, {"start": 905.66, "end": 906.34, "word": " okay", "probability": 0.5126953125}, {"start": 906.34, "end": 906.78, "word": " تمام", "probability": 0.854736328125}, {"start": 906.78, "end": 906.9, "word": " اللي", "probability": 0.881103515625}, {"start": 906.9, "end": 907.04, "word": " هو", "probability": 0.99609375}, {"start": 907.04, "end": 907.96, "word": " بالأزرق", "probability": 0.8189453125}, {"start": 907.96, "end": 909.68, "word": " تمام", "probability": 0.95654296875}, {"start": 909.68, "end": 913.28, "word": " مثال", "probability": 0.92431640625}, {"start": 913.28, "end": 913.84, "word": " تاني", "probability": 0.94580078125}, {"start": 913.84, "end": 914.36, "word": " ممكن", "probability": 0.987060546875}, {"start": 914.36, "end": 914.88, "word": " برضه", "probability": 0.9905598958333334}], "temperature": 1.0}, {"id": 34, "seek": 94507, "start": 916.89, "end": 945.07, "text": "ناخد مثال تاني show limit for function e to one على x as x tends to zero from the right بساوي infinity", "tokens": [1863, 47283, 3215, 50113, 6027, 6055, 7649, 1829, 855, 4948, 337, 2445, 308, 281, 472, 15844, 2031, 382, 2031, 12258, 281, 4018, 490, 264, 558, 4724, 3794, 995, 45865, 13202], "avg_logprob": -0.3245967818844703, "compression_ratio": 1.0701754385964912, "no_speech_prob": 0.0, "words": [{"start": 916.89, "end": 917.77, "word": "ناخد", "probability": 0.6730143229166666}, {"start": 917.77, "end": 918.65, "word": " مثال", "probability": 0.944091796875}, {"start": 918.65, "end": 933.19, "word": " تاني", "probability": 0.8844401041666666}, {"start": 933.19, "end": 934.71, "word": " show", "probability": 0.15283203125}, {"start": 934.71, "end": 935.37, "word": " limit", "probability": 0.96142578125}, {"start": 935.37, "end": 936.75, "word": " for", "probability": 0.39501953125}, {"start": 936.75, "end": 937.35, "word": " function", "probability": 0.697265625}, {"start": 937.35, "end": 937.67, "word": " e", "probability": 0.404541015625}, {"start": 937.67, "end": 937.89, "word": " to", "probability": 0.73388671875}, {"start": 937.89, "end": 938.17, "word": " one", "probability": 0.4072265625}, {"start": 938.17, "end": 938.49, "word": " على", "probability": 0.60986328125}, {"start": 938.49, "end": 938.87, "word": " x", "probability": 0.8544921875}, {"start": 938.87, "end": 940.21, "word": " as", "probability": 0.92333984375}, {"start": 940.21, "end": 940.65, "word": " x", "probability": 0.96875}, {"start": 940.65, "end": 941.05, "word": " tends", "probability": 0.78564453125}, {"start": 941.05, "end": 941.27, "word": " to", "probability": 0.98583984375}, {"start": 941.27, "end": 941.65, "word": " zero", "probability": 0.875}, {"start": 941.65, "end": 941.95, "word": " from", "probability": 0.89013671875}, {"start": 941.95, "end": 942.21, "word": " the", "probability": 0.87109375}, {"start": 942.21, "end": 942.65, "word": " right", "probability": 0.93603515625}, {"start": 942.65, "end": 944.49, "word": " بساوي", "probability": 0.74365234375}, {"start": 944.49, "end": 945.07, "word": " infinity", "probability": 0.69287109375}], "temperature": 1.0}, {"id": 35, "seek": 98144, "start": 955.92, "end": 981.44, "text": "أنا عندي ال function تبعتي f of x بيسمي E أس واحد على X طبعا ال X هنا ال function مش معرفة عند السفر المجال الدالي هذه كل الأعداد الحقيقية مع ده السفر المثل هذا أخدناه المرة اللي فاتت we have", "tokens": [10721, 8315, 18871, 16254, 2423, 2445, 6055, 3555, 3615, 31371, 283, 295, 2031, 4724, 1829, 38251, 1829, 462, 5551, 3794, 36764, 24401, 15844, 1783, 23032, 3555, 3615, 995, 2423, 1783, 34105, 2423, 2445, 37893, 20449, 28480, 3660, 43242, 21136, 5172, 2288, 9673, 7435, 6027, 32748, 6027, 1829, 29538, 28242, 16247, 22488, 18513, 21542, 38436, 4587, 10632, 20449, 11778, 3224, 21136, 5172, 2288, 9673, 12984, 1211, 23758, 5551, 9778, 3215, 8315, 3224, 9673, 25720, 13672, 1829, 6156, 9307, 2655, 321, 362], "avg_logprob": -0.28838734567901236, "compression_ratio": 1.6302083333333333, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 955.92, "end": 956.4, "word": "أنا", "probability": 0.59698486328125}, {"start": 956.4, "end": 956.84, "word": " عندي", "probability": 0.75927734375}, {"start": 956.84, "end": 957.28, "word": " ال", "probability": 0.92041015625}, {"start": 957.28, "end": 957.9, "word": " function", "probability": 0.61328125}, {"start": 957.9, "end": 958.66, "word": " تبعتي", "probability": 0.8887939453125}, {"start": 958.66, "end": 958.98, "word": " f", "probability": 0.5791015625}, {"start": 958.98, "end": 959.2, "word": " of", "probability": 0.5146484375}, {"start": 959.2, "end": 959.68, "word": " x", "probability": 0.84423828125}, {"start": 959.68, "end": 961.76, "word": " بيسمي", "probability": 0.6204833984375}, {"start": 961.76, "end": 962.02, "word": " E", "probability": 0.10101318359375}, {"start": 962.02, "end": 962.3, "word": " أس", "probability": 0.717041015625}, {"start": 962.3, "end": 962.7, "word": " واحد", "probability": 0.962158203125}, {"start": 962.7, "end": 962.88, "word": " على", "probability": 0.708984375}, {"start": 962.88, "end": 963.18, "word": " X", "probability": 0.677734375}, {"start": 963.18, "end": 963.5, "word": " طبعا", "probability": 0.8570556640625}, {"start": 963.5, "end": 963.72, "word": " ال", "probability": 0.64599609375}, {"start": 963.72, "end": 964.08, "word": " X", "probability": 0.82666015625}, {"start": 964.08, "end": 964.42, "word": " هنا", "probability": 0.93994140625}, {"start": 964.42, "end": 965.76, "word": " ال", "probability": 0.6396484375}, {"start": 965.76, "end": 966.18, "word": " function", "probability": 0.931640625}, {"start": 966.18, "end": 966.48, "word": " مش", "probability": 0.98876953125}, {"start": 966.48, "end": 967.1, "word": " معرفة", "probability": 0.9249674479166666}, {"start": 967.1, "end": 967.32, "word": " عند", "probability": 0.955078125}, {"start": 967.32, "end": 967.84, "word": " السفر", "probability": 0.7864583333333334}, {"start": 967.84, "end": 970.08, "word": " المجال", "probability": 0.8194173177083334}, {"start": 970.08, "end": 970.4, "word": " الدالي", "probability": 0.6315104166666666}, {"start": 970.4, "end": 970.66, "word": " هذه", "probability": 0.104736328125}, {"start": 970.66, "end": 970.92, "word": " كل", "probability": 0.71484375}, {"start": 970.92, "end": 971.32, "word": " الأعداد", "probability": 0.7766927083333334}, {"start": 971.32, "end": 971.98, "word": " الحقيقية", "probability": 0.8773193359375}, {"start": 971.98, "end": 972.2, "word": " مع", "probability": 0.37939453125}, {"start": 972.2, "end": 972.44, "word": " ده", "probability": 0.5760498046875}, {"start": 972.44, "end": 972.9, "word": " السفر", "probability": 0.9825846354166666}, {"start": 972.9, "end": 974.38, "word": " المثل", "probability": 0.8030598958333334}, {"start": 974.38, "end": 974.6, "word": " هذا", "probability": 0.89794921875}, {"start": 974.6, "end": 975.08, "word": " أخدناه", "probability": 0.96240234375}, {"start": 975.08, "end": 975.36, "word": " المرة", "probability": 0.953857421875}, {"start": 975.36, "end": 975.56, "word": " اللي", "probability": 0.93310546875}, {"start": 975.56, "end": 977.14, "word": " فاتت", "probability": 0.9910481770833334}, {"start": 977.14, "end": 980.86, "word": " we", "probability": 0.65185546875}, {"start": 980.86, "end": 981.44, "word": " have", "probability": 0.96484375}], "temperature": 1.0}, {"id": 36, "seek": 101319, "start": 985.65, "end": 1013.19, "text": "from previous example من المثال السابق فانا هادرس سابق انه واحد على اكس اكبر من سفر اصغر من اكس واحد على اكس لكل اكس اكبر من سفر", "tokens": [20579, 3894, 1365, 9154, 9673, 12984, 6027, 21136, 16758, 4587, 6156, 7649, 995, 8032, 18513, 2288, 3794, 8608, 16758, 4587, 16472, 3224, 36764, 24401, 15844, 1975, 4117, 3794, 1975, 4117, 26890, 9154, 8608, 5172, 2288, 1975, 9381, 17082, 2288, 9154, 1975, 4117, 3794, 36764, 24401, 15844, 1975, 4117, 3794, 5296, 28820, 1975, 4117, 3794, 1975, 4117, 26890, 9154, 8608, 5172, 2288], "avg_logprob": -0.275705631702177, "compression_ratio": 1.6484375, "no_speech_prob": 0.0, "words": [{"start": 985.6499999999999, "end": 986.7299999999999, "word": "from", "probability": 0.224365234375}, {"start": 986.7299999999999, "end": 987.81, "word": " previous", "probability": 0.84228515625}, {"start": 987.81, "end": 990.57, "word": " example", "probability": 0.716796875}, {"start": 990.57, "end": 994.41, "word": " من", "probability": 0.76513671875}, {"start": 994.41, "end": 994.95, "word": " المثال", "probability": 0.9075520833333334}, {"start": 994.95, "end": 995.63, "word": " السابق", "probability": 0.7913411458333334}, {"start": 995.63, "end": 996.15, "word": " فانا", "probability": 0.4307861328125}, {"start": 996.15, "end": 997.21, "word": " هادرس", "probability": 0.72222900390625}, {"start": 997.21, "end": 997.65, "word": " سابق", "probability": 0.7853190104166666}, {"start": 997.65, "end": 999.31, "word": " انه", "probability": 0.58203125}, {"start": 999.31, "end": 1004.11, "word": " واحد", "probability": 0.91064453125}, {"start": 1004.11, "end": 1004.35, "word": " على", "probability": 0.6103515625}, {"start": 1004.35, "end": 1004.99, "word": " اكس", "probability": 0.7897135416666666}, {"start": 1004.99, "end": 1006.37, "word": " اكبر", "probability": 0.88427734375}, {"start": 1006.37, "end": 1006.65, "word": " من", "probability": 0.99462890625}, {"start": 1006.65, "end": 1007.11, "word": " سفر", "probability": 0.8640950520833334}, {"start": 1007.11, "end": 1007.67, "word": " اصغر", "probability": 0.9095458984375}, {"start": 1007.67, "end": 1007.89, "word": " من", "probability": 0.99169921875}, {"start": 1007.89, "end": 1008.41, "word": " اكس", "probability": 0.4803466796875}, {"start": 1008.41, "end": 1008.93, "word": " واحد", "probability": 0.959716796875}, {"start": 1008.93, "end": 1009.09, "word": " على", "probability": 0.83154296875}, {"start": 1009.09, "end": 1009.59, "word": " اكس", "probability": 0.9580078125}, {"start": 1009.59, "end": 1011.37, "word": " لكل", "probability": 0.877197265625}, {"start": 1011.37, "end": 1011.95, "word": " اكس", "probability": 0.9275716145833334}, {"start": 1011.95, "end": 1012.49, "word": " اكبر", "probability": 0.9474283854166666}, {"start": 1012.49, "end": 1012.75, "word": " من", "probability": 0.99609375}, {"start": 1012.75, "end": 1013.19, "word": " سفر", "probability": 0.9855143229166666}], "temperature": 1.0}, {"id": 37, "seek": 104433, "start": 1014.98, "end": 1044.34, "text": "لكل x على يمين السفر كان في ندي T أزرق من E of T لكل T عدد مؤجد طيب احنا لسه بتبتيل since ال limit لواحد على x لما x تقول إلى السفر من اليمين", "tokens": [1211, 28820, 2031, 15844, 7251, 2304, 9957, 21136, 5172, 2288, 25961, 8978, 8717, 16254, 314, 5551, 11622, 2288, 4587, 9154, 462, 295, 314, 5296, 28820, 314, 6225, 3215, 3215, 3714, 33604, 7435, 3215, 23032, 1829, 3555, 1975, 5016, 8315, 5296, 3794, 3224, 39894, 3555, 2655, 26895, 1670, 2423, 4948, 5296, 14407, 24401, 15844, 2031, 5296, 15042, 2031, 6055, 39648, 30731, 21136, 5172, 2288, 9154, 45595, 2304, 9957], "avg_logprob": -0.287683825720759, "compression_ratio": 1.4049079754601228, "no_speech_prob": 0.0, "words": [{"start": 1014.98, "end": 1015.52, "word": "لكل", "probability": 0.67626953125}, {"start": 1015.52, "end": 1015.88, "word": " x", "probability": 0.57373046875}, {"start": 1015.88, "end": 1016.08, "word": " على", "probability": 0.8271484375}, {"start": 1016.08, "end": 1016.42, "word": " يمين", "probability": 0.962890625}, {"start": 1016.42, "end": 1017.0, "word": " السفر", "probability": 0.82080078125}, {"start": 1017.0, "end": 1019.44, "word": " كان", "probability": 0.63232421875}, {"start": 1019.44, "end": 1019.68, "word": " في", "probability": 0.7021484375}, {"start": 1019.68, "end": 1020.02, "word": " ندي", "probability": 0.47552490234375}, {"start": 1020.02, "end": 1020.34, "word": " T", "probability": 0.37451171875}, {"start": 1020.34, "end": 1020.9, "word": " أزرق", "probability": 0.74005126953125}, {"start": 1020.9, "end": 1021.08, "word": " من", "probability": 0.9384765625}, {"start": 1021.08, "end": 1021.26, "word": " E", "probability": 0.87060546875}, {"start": 1021.26, "end": 1021.42, "word": " of", "probability": 0.469970703125}, {"start": 1021.42, "end": 1021.62, "word": " T", "probability": 0.88134765625}, {"start": 1021.62, "end": 1021.98, "word": " لكل", "probability": 0.97705078125}, {"start": 1021.98, "end": 1022.2, "word": " T", "probability": 0.94384765625}, {"start": 1022.2, "end": 1022.56, "word": " عدد", "probability": 0.95263671875}, {"start": 1022.56, "end": 1023.1, "word": " مؤجد", "probability": 0.747802734375}, {"start": 1023.1, "end": 1029.98, "word": " طيب", "probability": 0.715576171875}, {"start": 1029.98, "end": 1030.82, "word": " احنا", "probability": 0.8548177083333334}, {"start": 1030.82, "end": 1031.32, "word": " لسه", "probability": 0.9700520833333334}, {"start": 1031.32, "end": 1032.16, "word": " بتبتيل", "probability": 0.62481689453125}, {"start": 1032.16, "end": 1034.68, "word": " since", "probability": 0.70703125}, {"start": 1034.68, "end": 1038.0, "word": " ال", "probability": 0.50146484375}, {"start": 1038.0, "end": 1038.44, "word": " limit", "probability": 0.9375}, {"start": 1038.44, "end": 1040.72, "word": " لواحد", "probability": 0.783203125}, {"start": 1040.72, "end": 1040.92, "word": " على", "probability": 0.826171875}, {"start": 1040.92, "end": 1041.34, "word": " x", "probability": 0.58984375}, {"start": 1041.34, "end": 1041.74, "word": " لما", "probability": 0.86767578125}, {"start": 1041.74, "end": 1042.02, "word": " x", "probability": 0.80078125}, {"start": 1042.02, "end": 1042.56, "word": " تقول", "probability": 0.886962890625}, {"start": 1042.56, "end": 1042.92, "word": " إلى", "probability": 0.5126953125}, {"start": 1042.92, "end": 1043.58, "word": " السفر", "probability": 0.8483072916666666}, {"start": 1043.58, "end": 1043.86, "word": " من", "probability": 0.9912109375}, {"start": 1043.86, "end": 1044.34, "word": " اليمين", "probability": 0.8318684895833334}], "temperature": 1.0}, {"id": 38, "seek": 107580, "start": 1046.54, "end": 1075.8, "text": "بساوي infinity فممكن نطبخ ال comparison test هذا فهي عندي f of x أصغر من g of x يعني خليني أسمي هذه g of x كمشي مع نظري يعني وخلني f of x بساوي واحد على x فهي عندي f of x أصغر من g of x لكل x في R", "tokens": [3555, 3794, 995, 45865, 13202, 6156, 2304, 43020, 8717, 9566, 3555, 9778, 2423, 9660, 1500, 23758, 6156, 3224, 1829, 18871, 16254, 283, 295, 2031, 5551, 9381, 17082, 2288, 9154, 290, 295, 2031, 37495, 22653, 16490, 1211, 9957, 1829, 5551, 38251, 1829, 29538, 290, 295, 2031, 9122, 2304, 8592, 1829, 20449, 8717, 19913, 16572, 37495, 22653, 4032, 9778, 1211, 22653, 283, 295, 2031, 4724, 3794, 995, 45865, 36764, 24401, 15844, 2031, 6156, 3224, 1829, 18871, 16254, 283, 295, 2031, 5551, 9381, 17082, 2288, 9154, 290, 295, 2031, 5296, 28820, 2031, 8978, 497], "avg_logprob": -0.2270720074682132, "compression_ratio": 1.6742857142857144, "no_speech_prob": 0.0, "words": [{"start": 1046.54, "end": 1047.26, "word": "بساوي", "probability": 0.71923828125}, {"start": 1047.26, "end": 1047.98, "word": " infinity", "probability": 0.5751953125}, {"start": 1047.98, "end": 1051.76, "word": " فممكن", "probability": 0.655029296875}, {"start": 1051.76, "end": 1052.32, "word": " نطبخ", "probability": 0.8045654296875}, {"start": 1052.32, "end": 1052.46, "word": " ال", "probability": 0.9150390625}, {"start": 1052.46, "end": 1052.94, "word": " comparison", "probability": 0.81298828125}, {"start": 1052.94, "end": 1053.44, "word": " test", "probability": 0.95703125}, {"start": 1053.44, "end": 1053.82, "word": " هذا", "probability": 0.63525390625}, {"start": 1053.82, "end": 1055.5, "word": " فهي", "probability": 0.560791015625}, {"start": 1055.5, "end": 1055.78, "word": " عندي", "probability": 0.5694580078125}, {"start": 1055.78, "end": 1056.0, "word": " f", "probability": 0.66455078125}, {"start": 1056.0, "end": 1056.22, "word": " of", "probability": 0.4189453125}, {"start": 1056.22, "end": 1056.58, "word": " x", "probability": 0.83154296875}, {"start": 1056.58, "end": 1057.16, "word": " أصغر", "probability": 0.93115234375}, {"start": 1057.16, "end": 1057.34, "word": " من", "probability": 0.986328125}, {"start": 1057.34, "end": 1057.6, "word": " g", "probability": 0.88623046875}, {"start": 1057.6, "end": 1057.82, "word": " of", "probability": 0.94970703125}, {"start": 1057.82, "end": 1058.22, "word": " x", "probability": 0.96484375}, {"start": 1058.22, "end": 1061.22, "word": " يعني", "probability": 0.7098388671875}, {"start": 1061.22, "end": 1061.62, "word": " خليني", "probability": 0.78564453125}, {"start": 1061.62, "end": 1062.18, "word": " أسمي", "probability": 0.888671875}, {"start": 1062.18, "end": 1062.5, "word": " هذه", "probability": 0.60888671875}, {"start": 1062.5, "end": 1062.8, "word": " g", "probability": 0.748046875}, {"start": 1062.8, "end": 1062.98, "word": " of", "probability": 0.94580078125}, {"start": 1062.98, "end": 1063.34, "word": " x", "probability": 0.97802734375}, {"start": 1063.34, "end": 1065.06, "word": " كمشي", "probability": 0.706329345703125}, {"start": 1065.06, "end": 1065.32, "word": " مع", "probability": 0.53515625}, {"start": 1065.32, "end": 1065.8, "word": " نظري", "probability": 0.9256184895833334}, {"start": 1065.8, "end": 1066.28, "word": " يعني", "probability": 0.74267578125}, {"start": 1066.28, "end": 1068.22, "word": " وخلني", "probability": 0.71551513671875}, {"start": 1068.22, "end": 1068.42, "word": " f", "probability": 0.9306640625}, {"start": 1068.42, "end": 1068.6, "word": " of", "probability": 0.97412109375}, {"start": 1068.6, "end": 1068.78, "word": " x", "probability": 0.990234375}, {"start": 1068.78, "end": 1069.26, "word": " بساوي", "probability": 0.8472900390625}, {"start": 1069.26, "end": 1069.54, "word": " واحد", "probability": 0.866943359375}, {"start": 1069.54, "end": 1069.68, "word": " على", "probability": 0.58056640625}, {"start": 1069.68, "end": 1070.06, "word": " x", "probability": 0.880859375}, {"start": 1070.06, "end": 1071.12, "word": " فهي", "probability": 0.9684244791666666}, {"start": 1071.12, "end": 1071.4, "word": " عندي", "probability": 0.94482421875}, {"start": 1071.4, "end": 1071.6, "word": " f", "probability": 0.95703125}, {"start": 1071.6, "end": 1071.8, "word": " of", "probability": 0.98193359375}, {"start": 1071.8, "end": 1072.02, "word": " x", "probability": 0.9912109375}, {"start": 1072.02, "end": 1072.56, "word": " أصغر", "probability": 0.99169921875}, {"start": 1072.56, "end": 1072.82, "word": " من", "probability": 0.9912109375}, {"start": 1072.82, "end": 1073.48, "word": " g", "probability": 0.9404296875}, {"start": 1073.48, "end": 1073.66, "word": " of", "probability": 0.9794921875}, {"start": 1073.66, "end": 1074.0, "word": " x", "probability": 0.98974609375}, {"start": 1074.0, "end": 1074.88, "word": " لكل", "probability": 0.974365234375}, {"start": 1074.88, "end": 1075.22, "word": " x", "probability": 0.95654296875}, {"start": 1075.22, "end": 1075.44, "word": " في", "probability": 0.98779296875}, {"start": 1075.44, "end": 1075.8, "word": " R", "probability": 0.71435546875}], "temperature": 1.0}, {"id": 39, "seek": 110298, "start": 1076.66, "end": 1102.98, "text": "أو لكل X لا يساوي سفر لكل X موجة بقى أو على يمين السفر لكل X في R تقاطع سفر إلى ملا نهاية okay فإذا قلنا النظرية هذه صحيحة لل right limit باستخدام النظرية", "tokens": [10721, 2407, 5296, 28820, 1783, 20193, 7251, 3794, 995, 45865, 8608, 5172, 2288, 5296, 28820, 1783, 3714, 29245, 3660, 4724, 4587, 7578, 34051, 15844, 7251, 2304, 9957, 21136, 5172, 2288, 5296, 28820, 1783, 8978, 497, 6055, 4587, 41193, 3615, 8608, 5172, 2288, 30731, 3714, 15040, 8717, 11296, 10632, 1392, 6156, 28814, 15730, 12174, 1211, 8315, 28239, 19913, 2288, 10632, 29538, 20328, 5016, 1829, 5016, 3660, 24976, 558, 4948, 4724, 995, 14851, 9778, 3215, 10943, 28239, 19913, 2288, 10632], "avg_logprob": -0.16841377072696445, "compression_ratio": 1.5389221556886228, 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0.304443359375}, {"start": 1093.82, "end": 1096.88, "word": " فإذا", "probability": 0.7527669270833334}, {"start": 1096.88, "end": 1098.14, "word": " قلنا", "probability": 0.7734375}, {"start": 1098.14, "end": 1098.62, "word": " النظرية", "probability": 0.8729248046875}, {"start": 1098.62, "end": 1098.86, "word": " هذه", "probability": 0.59912109375}, {"start": 1098.86, "end": 1099.36, "word": " صحيحة", "probability": 0.9865234375}, {"start": 1099.36, "end": 1099.52, "word": " لل", "probability": 0.62841796875}, {"start": 1099.52, "end": 1099.8, "word": " right", "probability": 0.77197265625}, {"start": 1099.8, "end": 1100.3, "word": " limit", "probability": 0.9736328125}, {"start": 1100.3, "end": 1102.32, "word": " باستخدام", "probability": 0.9807942708333334}, {"start": 1102.32, "end": 1102.98, "word": " النظرية", "probability": 0.980712890625}], "temperature": 1.0}, {"id": 40, "seek": 112646, "start": 1103.96, "end": 1126.46, "text": "by above theorem by above theorem for right limits للنهايات من اليمين we have نحصل على انه ال limit", "tokens": [2322, 3673, 20904, 538, 3673, 20904, 337, 558, 10406, 24976, 1863, 11296, 1829, 9307, 9154, 45595, 2304, 9957, 321, 362, 8717, 5016, 36520, 15844, 16472, 3224, 2423, 4948], "avg_logprob": -0.3089978530489165, "compression_ratio": 1.2574257425742574, "no_speech_prob": 0.0, "words": [{"start": 1103.96, "end": 1104.6, "word": "by", "probability": 0.1580810546875}, {"start": 1104.6, "end": 1105.74, "word": " above", "probability": 0.9013671875}, {"start": 1105.74, "end": 1106.36, "word": " theorem", "probability": 0.83251953125}, {"start": 1106.36, "end": 1108.92, "word": " by", "probability": 0.4755859375}, {"start": 1108.92, "end": 1109.5, "word": " above", "probability": 0.96923828125}, {"start": 1109.5, "end": 1111.02, "word": " theorem", "probability": 0.88623046875}, {"start": 1111.02, "end": 1112.88, "word": " for", "probability": 0.7626953125}, {"start": 1112.88, "end": 1113.48, "word": " right", "probability": 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"end": 1143.33, "text": "لقيت واحد على اكس لما اكس تقول إلى سفر من اليمين بساوي plus infinity وهذا اللي بدناه هي مظبوط صح؟ تمام؟", "tokens": [1211, 4587, 36081, 36764, 24401, 15844, 1975, 4117, 3794, 5296, 15042, 1975, 4117, 3794, 6055, 39648, 30731, 8608, 5172, 2288, 9154, 2423, 32640, 9957, 4724, 3794, 995, 45865, 1804, 13202, 37037, 15730, 13672, 1829, 47525, 8315, 3224, 39896, 3714, 19913, 3555, 2407, 9566, 20328, 5016, 22807, 46811, 10943, 22807], "avg_logprob": -0.31421875715255737, "compression_ratio": 1.288888888888889, "no_speech_prob": 0.0, "words": [{"start": 1128.73, "end": 1129.47, "word": "لقيت", "probability": 0.6780598958333334}, {"start": 1129.47, "end": 1129.99, "word": " واحد", "probability": 0.7183837890625}, {"start": 1129.99, "end": 1130.19, "word": " على", "probability": 0.55615234375}, {"start": 1130.19, "end": 1130.59, "word": " اكس", "probability": 0.7411295572916666}, {"start": 1130.59, "end": 1130.87, "word": " لما", "probability": 0.78564453125}, {"start": 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ممكن", "probability": 0.987548828125}, {"start": 1161.65, "end": 1162.13, "word": " أعطي", "probability": 0.9212646484375}, {"start": 1162.13, "end": 1162.57, "word": " برهان", "probability": 0.956298828125}, {"start": 1162.57, "end": 1162.97, "word": " تاني", "probability": 0.97021484375}, {"start": 1162.97, "end": 1163.15, "word": " و", "probability": 0.82958984375}, {"start": 1163.15, "end": 1163.55, "word": " أقول", "probability": 0.88916015625}, {"start": 1163.55, "end": 1165.39, "word": " بما", "probability": 0.596435546875}, {"start": 1165.39, "end": 1165.57, "word": " أن", "probability": 0.783203125}, {"start": 1165.57, "end": 1166.01, "word": " هذه", "probability": 0.8896484375}, {"start": 1166.01, "end": 1167.09, "word": " المتباينة", "probability": 0.9427897135416666}, {"start": 1167.09, "end": 1167.83, "word": " صحيحة", "probability": 0.92841796875}, {"start": 1167.83, "end": 1168.23, "word": " لكل", "probability": 0.97119140625}, {"start": 1168.23, "end": 1168.53, "word": " X", "probability": 0.8798828125}, {"start": 1168.53, "end": 1169.09, "word": " موجبة", "probability": 0.89697265625}], "temperature": 1.0}, {"id": 43, "seek": 118694, "start": 1170.26, "end": 1186.94, "text": "و بما انه ال limit هذه لو احلى ال function واحد على X عن سفر من اليانين بالساوي infinity معناته انا بقدر اخلي واحد ال function واحد على X هذه اكبر من Alpha لأي real number Alpha صح؟", "tokens": [2407, 4724, 15042, 16472, 3224, 2423, 4948, 29538, 45164, 1975, 5016, 23942, 2423, 2445, 36764, 24401, 15844, 1783, 18871, 8608, 5172, 2288, 9154, 45595, 7649, 9957, 20666, 3794, 995, 45865, 13202, 20449, 8315, 47395, 1975, 8315, 4724, 28543, 2288, 1975, 9778, 20292, 36764, 24401, 2423, 2445, 36764, 24401, 15844, 1783, 29538, 1975, 4117, 26890, 9154, 20588, 5296, 10721, 1829, 957, 1230, 20588, 20328, 5016, 22807], "avg_logprob": -0.27509468974489154, "compression_ratio": 1.5480225988700564, "no_speech_prob": 0.0, "words": [{"start": 1170.26, "end": 1170.58, "word": "و", "probability": 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اللي أثبتناها سابقا بس بدل ما X أول ل C بيصير X أول ل infinity ال sequence أول شيء إذا كانت ال limit هذه أو هذه موجودة بسوء عدد L", "tokens": [8297, 23032, 1829, 3555, 1975, 15730, 1975, 8315, 5296, 7649, 8978, 18871, 16254, 37279, 16572, 5172, 9307, 10874, 16254, 41891, 9122, 2304, 7649, 3714, 25720, 28242, 8717, 19913, 16572, 9307, 13672, 1829, 5551, 12984, 3555, 2655, 8315, 11296, 8608, 16758, 4587, 995, 4724, 3794, 47525, 1211, 19446, 1783, 5551, 12610, 5296, 383, 4724, 1829, 9381, 13546, 1783, 5551, 12610, 5296, 13202, 2423, 8310, 5551, 12610, 44049, 38207, 11933, 15730, 25961, 2655, 2423, 4948, 29538, 34051, 29538, 3714, 29245, 23328, 3660, 4724, 3794, 2407, 38207, 6225, 3215, 3215, 441], "avg_logprob": -0.22787921348314608, "compression_ratio": 1.5245098039215685, "no_speech_prob": 0.0, "words": [{"start": 1632.44, "end": 1632.9, "word": "Okay", "probability": 0.6259765625}, {"start": 1632.9, "end": 1634.26, "word": " طيب", "probability": 0.9677734375}, {"start": 1634.26, "end": 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46691], "avg_logprob": -0.324544258415699, "compression_ratio": 1.7083333333333333, "no_speech_prob": 0.0, "words": [{"start": 1722.58, "end": 1722.98, "word": "هي", "probability": 0.584228515625}, {"start": 1722.98, "end": 1723.74, "word": " sequential", "probability": 0.8154296875}, {"start": 1723.74, "end": 1724.66, "word": " theorem", "probability": 0.5908203125}, {"start": 1724.66, "end": 1737.86, "word": " sequential", "probability": 0.83837890625}, {"start": 1737.86, "end": 1738.4, "word": " ..", "probability": 0.46142578125}, {"start": 1738.4, "end": 1743.68, "word": " sequential", "probability": 0.8896484375}, {"start": 1743.68, "end": 1747.5, "word": " criterion", "probability": 0.919921875}, {"start": 1747.5, "end": 1747.9, "word": " ..", "probability": 0.5302734375}, {"start": 1747.9, "end": 1748.7, "word": " sequential", "probability": 0.98681640625}, {"start": 1748.7, "end": 1749.52, "word": " criterion", "probability": 0.9921875}], "temperature": 1.0}, {"id": 63, "seek": 177210, "start": 1751.0, "end": 1772.1, "text": "for limits for limits at infinity the following statements are equivalent are equivalent واحد limit", "tokens": [2994, 10406, 337, 10406, 412, 13202, 264, 3480, 12363, 366, 10344, 366, 10344, 36764, 24401, 4948], "avg_logprob": -0.3485753676470588, "compression_ratio": 1.271604938271605, "no_speech_prob": 0.0, "words": [{"start": 1751.0, "end": 1751.6, "word": "for", "probability": 0.23095703125}, {"start": 1751.6, "end": 1752.8, "word": " limits", "probability": 0.9755859375}, {"start": 1752.8, "end": 1755.28, "word": " for", "probability": 0.4111328125}, {"start": 1755.28, "end": 1756.4, "word": " limits", "probability": 0.97119140625}, {"start": 1756.4, "end": 1758.32, "word": " at", "probability": 0.95849609375}, {"start": 1758.32, "end": 1759.12, "word": " infinity", "probability": 0.8916015625}, {"start": 1759.12, "end": 1763.58, "word": " the", "probability": 0.65478515625}, {"start": 1763.58, "end": 1764.22, "word": " following", "probability": 0.89501953125}, {"start": 1764.22, "end": 1764.92, "word": " statements", "probability": 0.875}, {"start": 1764.92, "end": 1765.84, "word": " are", "probability": 0.96630859375}, {"start": 1765.84, "end": 1766.68, "word": " equivalent", "probability": 0.94677734375}, {"start": 1766.68, "end": 1768.82, "word": " are", "probability": 0.287109375}, {"start": 1768.82, "end": 1769.48, "word": " equivalent", "probability": 0.94921875}, {"start": 1769.48, "end": 1771.6, "word": " واحد", "probability": 0.741943359375}, {"start": 1771.6, "end": 1772.1, "word": " limit", "probability": 0.84619140625}], "temperature": 1.0}, {"id": 64, "seek": 178891, "start": 1773.61, "end": 1788.91, "text": "F of X as X tends to infinity بساوي عدد M اتنين for every sequence", "tokens": [37, 295, 1783, 382, 1783, 12258, 281, 13202, 4724, 3794, 995, 45865, 6225, 3215, 3215, 376, 1975, 2655, 1863, 9957, 337, 633, 8310], "avg_logprob": -0.3139648536841075, "compression_ratio": 0.9080459770114943, "no_speech_prob": 0.0, "words": [{"start": 1773.61, "end": 1774.49, "word": "F", "probability": 0.0618896484375}, {"start": 1774.49, "end": 1774.83, "word": " of", "probability": 0.1864013671875}, {"start": 1774.83, "end": 1775.27, "word": " X", "probability": 0.83740234375}, {"start": 1775.27, "end": 1776.85, "word": " as", "probability": 0.62109375}, {"start": 1776.85, "end": 1777.23, "word": " X", "probability": 0.97265625}, {"start": 1777.23, "end": 1777.71, "word": " tends", "probability": 0.76513671875}, {"start": 1777.71, "end": 1778.31, "word": " to", "probability": 0.96923828125}, {"start": 1778.31, "end": 1779.53, "word": " infinity", "probability": 0.84765625}, {"start": 1779.53, "end": 1780.33, "word": " بساوي", "probability": 0.8116455078125}, {"start": 1780.33, "end": 1780.83, "word": " عدد", "probability": 0.91064453125}, {"start": 1780.83, "end": 1781.13, "word": " M", "probability": 0.6591796875}, {"start": 1781.13, "end": 1782.89, "word": " اتنين", "probability": 0.81414794921875}, {"start": 1782.89, "end": 1784.75, "word": " for", "probability": 0.8330078125}, {"start": 1784.75, "end": 1787.97, "word": " every", "probability": 0.75927734375}, {"start": 1787.97, "end": 1788.91, "word": " sequence", "probability": 0.95947265625}], "temperature": 1.0}, {"id": 65, "seek": 181625, "start": 1791.33, "end": 1816.25, "text": "x in contained in a تقابل فترة مفتوحة من a إلى م للإلهية such that limit x in as n tends to infinity بساوي ال infinity لازم يطلع عندى limit ال image", "tokens": [87, 294, 16212, 294, 257, 6055, 4587, 16758, 1211, 6156, 2655, 25720, 3714, 5172, 2655, 2407, 5016, 3660, 9154, 257, 30731, 3714, 5296, 1211, 28814, 43761, 10632, 1270, 300, 4948, 2031, 294, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 2423, 13202, 5296, 31377, 2304, 7251, 9566, 1211, 3615, 43242, 7578, 4948, 2423, 3256], "avg_logprob": -0.43331474331872805, "compression_ratio": 1.3310810810810811, "no_speech_prob": 0.0, "words": [{"start": 1791.33, "end": 1791.87, "word": "x", "probability": 0.0723876953125}, {"start": 1791.87, "end": 1792.59, "word": " in", "probability": 0.1986083984375}, {"start": 1792.59, "end": 1793.41, "word": " contained", "probability": 0.474365234375}, {"start": 1793.41, "end": 1793.77, "word": " in", "probability": 0.7607421875}, {"start": 1793.77, "end": 1794.17, "word": " a", "probability": 0.68408203125}, {"start": 1794.17, "end": 1795.01, "word": " تقابل", "probability": 0.777099609375}, {"start": 1795.01, "end": 1795.49, "word": " فترة", "probability": 0.9041341145833334}, {"start": 1795.49, "end": 1796.33, "word": " مفتوحة", "probability": 0.9383951822916666}, {"start": 1796.33, "end": 1797.17, "word": " من", "probability": 0.60546875}, {"start": 1797.17, "end": 1797.39, "word": " a", "probability": 0.892578125}, {"start": 1797.39, "end": 1797.57, "word": " إلى", "probability": 0.73388671875}, {"start": 1797.57, "end": 1797.75, "word": " م", "probability": 0.15966796875}, {"start": 1797.75, "end": 1798.59, "word": " للإلهية", "probability": 0.4885986328125}, {"start": 1798.59, "end": 1798.99, "word": " such", "probability": 0.54833984375}, {"start": 1798.99, "end": 1799.55, "word": " that", "probability": 0.93896484375}, {"start": 1799.55, "end": 1801.07, "word": " limit", "probability": 0.87158203125}, {"start": 1801.07, "end": 1803.03, "word": " x", "probability": 0.7822265625}, {"start": 1803.03, "end": 1803.59, "word": " in", "probability": 0.927734375}, {"start": 1803.59, "end": 1804.19, "word": " as", "probability": 0.8271484375}, {"start": 1804.19, "end": 1804.59, "word": " n", "probability": 0.50927734375}, {"start": 1804.59, "end": 1804.89, "word": " tends", "probability": 0.79833984375}, {"start": 1804.89, "end": 1805.03, "word": " to", "probability": 0.9326171875}, {"start": 1805.03, "end": 1805.61, "word": " infinity", "probability": 0.91259765625}, {"start": 1805.61, "end": 1806.47, "word": " بساوي", "probability": 0.571533203125}, {"start": 1806.47, "end": 1806.73, "word": " ال", "probability": 0.6787109375}, {"start": 1806.73, "end": 1807.31, "word": " infinity", "probability": 0.6201171875}, {"start": 1807.31, "end": 1814.41, "word": " لازم", "probability": 0.7443033854166666}, {"start": 1814.41, "end": 1814.73, "word": " يطلع", "probability": 0.940185546875}, {"start": 1814.73, "end": 1815.13, "word": " عندى", "probability": 0.5189208984375}, {"start": 1815.13, "end": 1815.47, "word": " limit", "probability": 0.9228515625}, {"start": 1815.47, "end": 1815.77, "word": " ال", "probability": 0.73681640625}, {"start": 1815.77, "end": 1816.25, "word": " image", "probability": 0.80908203125}], "temperature": 1.0}, {"id": 66, "seek": 184710, "start": 1817.4, "end": 1847.1, "text": "بساوي العدد L لسيكوانس Xn as N times Infinity بساوي العدد L لذا هذه Sequential criterion for limits at infinity وممكن نثبت النظرية هذه زي ما أثبتنا Sequential criterion for finite two-sided limits أو for finite one-sided limits", "tokens": [3555, 3794, 995, 45865, 18863, 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"word": " as", "probability": 0.396728515625}, {"start": 1819.88, "end": 1820.26, "word": " N", "probability": 0.42138671875}, {"start": 1820.26, "end": 1820.6, "word": " times", "probability": 0.63037109375}, {"start": 1820.6, "end": 1821.32, "word": " Infinity", "probability": 0.431396484375}, {"start": 1821.32, "end": 1823.04, "word": " بساوي", "probability": 0.85888671875}, {"start": 1823.04, "end": 1823.6, "word": " العدد", "probability": 0.9759114583333334}, {"start": 1823.6, "end": 1823.98, "word": " L", "probability": 0.951171875}, {"start": 1823.98, "end": 1825.14, "word": " لذا", "probability": 0.3800048828125}, {"start": 1825.14, "end": 1825.38, "word": " هذه", "probability": 0.55126953125}, {"start": 1825.38, "end": 1825.96, "word": " Sequential", "probability": 0.723876953125}, {"start": 1825.96, "end": 1826.54, "word": " criterion", "probability": 0.68359375}, {"start": 1826.54, "end": 1827.08, "word": " for", "probability": 0.63671875}, {"start": 1827.08, "end": 1827.6, "word": " limits", "probability": 0.82275390625}, {"start": 1827.6, "end": 1827.92, "word": " at", "probability": 0.90283203125}, {"start": 1827.92, "end": 1828.5, "word": " infinity", "probability": 0.634765625}, {"start": 1828.5, "end": 1834.58, "word": " وممكن", "probability": 0.86572265625}, {"start": 1834.58, "end": 1835.08, "word": " نثبت", "probability": 0.9876708984375}, {"start": 1835.08, "end": 1835.66, "word": " النظرية", "probability": 0.94921875}, {"start": 1835.66, "end": 1836.14, "word": " هذه", "probability": 0.85009765625}, {"start": 1836.14, "end": 1837.7, "word": " زي", "probability": 0.904541015625}, {"start": 1837.7, "end": 1837.8, "word": " ما", "probability": 0.92333984375}, {"start": 1837.8, "end": 1838.34, "word": " أثبتنا", "probability": 0.95400390625}, {"start": 1838.34, "end": 1839.04, "word": " Sequential", "probability": 0.918701171875}, {"start": 1839.04, "end": 1839.86, "word": " criterion", "probability": 0.96630859375}, {"start": 1839.86, "end": 1841.52, "word": " for", "probability": 0.84912109375}, {"start": 1841.52, "end": 1842.22, "word": " finite", "probability": 0.935546875}, {"start": 1842.22, "end": 1842.62, "word": " two", "probability": 0.88427734375}, {"start": 1842.62, "end": 1842.92, "word": "-sided", "probability": 0.689208984375}, {"start": 1842.92, "end": 1843.48, "word": " limits", "probability": 0.9375}, {"start": 1843.48, "end": 1844.86, "word": " أو", "probability": 0.7255859375}, {"start": 1844.86, "end": 1845.3, "word": " for", "probability": 0.86083984375}, {"start": 1845.3, "end": 1845.92, "word": " finite", "probability": 0.966796875}, {"start": 1845.92, "end": 1846.3, "word": " one", "probability": 0.9599609375}, {"start": 1846.3, "end": 1846.64, "word": "-sided", "probability": 0.947021484375}, {"start": 1846.64, "end": 1847.1, "word": " limits", "probability": 0.740234375}], "temperature": 1.0}, {"id": 67, "seek": 187712, "start": 1848.54, "end": 1877.12, "text": "مثلًا لو أريد أن أثبت واحد implies اتنين فبقول assume أنه one holds هذا معناه أن ال limit لf of x as x tends to infinity بسوى عدد L طيب to prove", "tokens": [2304, 12984, 1211, 14111, 995, 45164, 5551, 16572, 3215, 14739, 5551, 12984, 3555, 2655, 36764, 24401, 18779, 1975, 2655, 1863, 9957, 6156, 3555, 39648, 6552, 14739, 3224, 472, 9190, 23758, 20449, 8315, 3224, 14739, 2423, 4948, 5296, 69, 295, 2031, 382, 2031, 12258, 281, 13202, 4724, 3794, 2407, 7578, 6225, 3215, 3215, 441, 23032, 1829, 3555, 281, 7081], "avg_logprob": -0.37261653350571455, "compression_ratio": 1.2331288343558282, "no_speech_prob": 0.0, "words": [{"start": 1848.54, "end": 1849.28, "word": "مثلًا", "probability": 0.700732421875}, {"start": 1849.28, "end": 1849.4, "word": " لو", "probability": 0.43701171875}, {"start": 1849.4, "end": 1849.72, "word": " أريد", "probability": 0.66943359375}, {"start": 1849.72, "end": 1849.82, "word": " أن", "probability": 0.6357421875}, {"start": 1849.82, "end": 1850.22, "word": " أثبت", "probability": 0.9775390625}, {"start": 1850.22, "end": 1850.82, "word": " واحد", "probability": 0.6011962890625}, {"start": 1850.82, "end": 1851.52, "word": " implies", "probability": 0.08148193359375}, {"start": 1851.52, "end": 1852.34, "word": " اتنين", "probability": 0.908447265625}, {"start": 1852.34, "end": 1855.66, "word": " فبقول", "probability": 0.6022135416666666}, {"start": 1855.66, "end": 1856.44, "word": " assume", "probability": 0.72900390625}, {"start": 1856.44, "end": 1858.9, "word": " أنه", "probability": 0.52099609375}, {"start": 1858.9, "end": 1860.78, "word": " one", "probability": 0.8349609375}, {"start": 1860.78, "end": 1861.66, "word": " holds", "probability": 0.85595703125}, {"start": 1861.66, "end": 1865.08, "word": " هذا", "probability": 0.76025390625}, {"start": 1865.08, "end": 1866.24, "word": " معناه", "probability": 0.89111328125}, {"start": 1866.24, "end": 1867.0, "word": " أن", "probability": 0.701171875}, {"start": 1867.0, "end": 1867.16, "word": " ال", "probability": 0.4033203125}, 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1892.39, "end": 1893.07, "word": " prove", "probability": 0.947265625}, {"start": 1893.07, "end": 1893.49, "word": " two", "probability": 0.89599609375}, {"start": 1893.49, "end": 1894.33, "word": " holes", "probability": 0.449462890625}, {"start": 1894.33, "end": 1898.43, "word": " فابد", "probability": 0.6006673177083334}, {"start": 1898.43, "end": 1898.97, "word": " أثبت", "probability": 0.892578125}, {"start": 1898.97, "end": 1899.39, "word": " لأي", "probability": 0.8943684895833334}, {"start": 1899.39, "end": 1900.09, "word": " sequence", "probability": 0.78125}, {"start": 1900.09, "end": 1902.53, "word": " لأي", "probability": 0.6971435546875}, {"start": 1902.53, "end": 1903.33, "word": " sequence", "probability": 0.94580078125}, {"start": 1903.33, "end": 1905.95, "word": " بالمواصفات", "probability": 0.8948567708333334}, {"start": 1905.95, "end": 1906.43, "word": " هذه", "probability": 0.8486328125}, {"start": 1906.43, "end": 1906.85, "word": " limit", "probability": 0.71533203125}, {"start": 1906.85, "end": 1907.39, "word": " صورتها", "probability": 0.9642333984375}, {"start": 1907.39, "end": 1908.07, "word": " بساوي", "probability": 0.69439697265625}, {"start": 1908.07, "end": 1908.43, "word": " L", "probability": 0.63916015625}, {"start": 1908.43, "end": 1909.43, "word": " فببدأ", "probability": 0.88134765625}, {"start": 1909.43, "end": 1909.79, "word": " بقول", "probability": 0.977294921875}, {"start": 1909.79, "end": 1910.19, "word": " let", "probability": 0.904296875}, {"start": 1910.19, "end": 1912.61, "word": " let", "probability": 0.7958984375}, {"start": 1912.61, "end": 1913.91, "word": " XM", "probability": 0.4266357421875}, {"start": 1913.91, "end": 1917.37, "word": " contain", "probability": 0.73388671875}, {"start": 1917.37, "end": 1918.01, "word": " بالـ", "probability": 0.435302734375}, {"start": 1918.01, "end": 1918.07, "word": " A", "probability": 0.5830078125}, {"start": 1918.07, "end": 1918.81, "word": " قاطع", "probability": 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"تمام هيك إذا هذا ناخده من كوننا ان احنا فرضين ان limit ال sequence xn بالساوية infinity ومن تعريف ال infinite limit لل sequence الان الان في تحول في البرهار now star and double star yield", "tokens": [39237, 10943, 39896, 4117, 11933, 15730, 23758, 8717, 47283, 3215, 3224, 9154, 9122, 11536, 8315, 16472, 1975, 5016, 8315, 6156, 43042, 9957, 16472, 4948, 2423, 8310, 2031, 77, 20666, 3794, 995, 2407, 10632, 13202, 4032, 27842, 37279, 16572, 5172, 2423, 13785, 4948, 24976, 8310, 2423, 7649, 2423, 7649, 8978, 6055, 5016, 12610, 8978, 2423, 26890, 3224, 9640, 586, 3543, 293, 3834, 3543, 11257], "avg_logprob": -0.270019527990371, "compression_ratio": 1.5168539325842696, "no_speech_prob": 0.0, "words": [{"start": 2139.65, "end": 2140.11, "word": "تمام", "probability": 0.599365234375}, {"start": 2140.11, "end": 2140.85, "word": " هيك", "probability": 0.64306640625}, {"start": 2140.85, "end": 2141.41, "word": " إذا", "probability": 0.5709228515625}, {"start": 2141.41, "end": 2141.85, "word": " 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2184.77, "end": 2185.19, "word": " k", "probability": 0.60595703125}, {"start": 2185.19, "end": 2185.73, "word": " هذا", "probability": 0.77783203125}, {"start": 2185.73, "end": 2186.45, "word": " موجود", "probability": 0.9344075520833334}, {"start": 2186.45, "end": 2188.19, "word": " أخدناه", "probability": 0.90107421875}, {"start": 2188.19, "end": 2188.59, "word": " من", "probability": 0.97607421875}, {"start": 2188.59, "end": 2188.97, "word": " double", "probability": 0.74853515625}, {"start": 2188.97, "end": 2189.59, "word": " star", "probability": 0.8662109375}, {"start": 2189.59, "end": 2191.81, "word": " لكل", "probability": 0.821533203125}, {"start": 2191.81, "end": 2192.03, "word": " n", "probability": 0.89404296875}, {"start": 2192.03, "end": 2192.41, "word": " أكبر", "probability": 0.9788411458333334}, {"start": 2192.41, "end": 2192.55, "word": " من", "probability": 0.98876953125}, {"start": 2192.55, "end": 2192.71, "word": " أو", "probability": 0.97900390625}, {"start": 2192.71, "end": 2193.01, "word": " ساوى", "probability": 0.9532470703125}, {"start": 2193.01, "end": 2193.33, "word": " capital", "probability": 0.8017578125}, {"start": 2193.33, "end": 2193.59, "word": " N", "probability": 0.95361328125}, {"start": 2193.59, "end": 2193.93, "word": " بيطلع", "probability": 0.77021484375}, {"start": 2193.93, "end": 2194.33, "word": " xn", "probability": 0.953857421875}, {"start": 2194.33, "end": 2194.69, "word": " أكبر", "probability": 0.9816080729166666}, {"start": 2194.69, "end": 2195.01, "word": " من", "probability": 0.99462890625}, {"start": 2195.01, "end": 2196.35, "word": " k", "probability": 0.80810546875}], "temperature": 1.0}, {"id": 79, "seek": 222184, "start": 2197.78, "end": 2221.84, "text": "طيب و من ال star و هذا بيقدي باستخدام ال star ال star بيقوللي لكل x لو كانت ال x او ال xn أكبر من capital K هذا بيقدي ان صورتها المسافة بينها و بين ال L أصغر من إبسل صح؟", "tokens": [9566, 1829, 3555, 4032, 9154, 2423, 3543, 4032, 23758, 4724, 1829, 4587, 16254, 4724, 995, 14851, 9778, 3215, 10943, 2423, 3543, 2423, 3543, 4724, 1829, 39648, 20292, 5296, 28820, 2031, 45164, 25961, 2655, 2423, 2031, 1975, 2407, 2423, 2031, 77, 5551, 4117, 26890, 9154, 4238, 591, 23758, 4724, 1829, 4587, 16254, 16472, 20328, 13063, 2655, 11296, 9673, 3794, 31845, 3660, 49374, 11296, 4032, 49374, 2423, 441, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 1211, 20328, 5016, 22807], "avg_logprob": -0.18957674276979664, "compression_ratio": 1.6153846153846154, "no_speech_prob": 0.0, "words": [{"start": 2197.78, "end": 2198.2, "word": "طيب", "probability": 0.9295247395833334}, {"start": 2198.2, "end": 2198.32, "word": " و", "probability": 0.95361328125}, {"start": 2198.32, "end": 2198.5, "word": " من", "probability": 0.69287109375}, {"start": 2198.5, "end": 2198.7, "word": " ال", "probability": 0.908203125}, {"start": 2198.7, "end": 2199.02, "word": " star", "probability": 0.53173828125}, {"start": 2199.02, "end": 2199.32, "word": " و", "probability": 0.5849609375}, {"start": 2199.32, "end": 2199.62, "word": " هذا", "probability": 0.91796875}, {"start": 2199.62, "end": 2200.18, "word": " بيقدي", "probability": 0.7171630859375}, {"start": 2200.18, "end": 2200.98, "word": " باستخدام", "probability": 0.9583333333333334}, {"start": 2200.98, "end": 2201.2, "word": " ال", "probability": 0.970703125}, {"start": 2201.2, "end": 2201.54, "word": " star", "probability": 0.93408203125}, {"start": 2201.54, "end": 2202.6, "word": " ال", "probability": 0.8515625}, {"start": 2202.6, "end": 2202.88, "word": " star", "probability": 0.9541015625}, {"start": 2202.88, "end": 2203.44, "word": " بيقوللي", "probability": 0.8251953125}, {"start": 2203.44, "end": 2203.98, "word": " لكل", "probability": 0.81201171875}, {"start": 2203.98, "end": 2204.6, "word": " x", "probability": 0.5947265625}, {"start": 2204.6, "end": 2206.64, "word": " لو", "probability": 0.9375}, {"start": 2206.64, "end": 2207.04, "word": " كانت", "probability": 0.975341796875}, {"start": 2207.04, "end": 2207.16, "word": " ال", "probability": 0.97265625}, {"start": 2207.16, "end": 2207.36, "word": " x", "probability": 0.9130859375}, {"start": 2207.36, "end": 2207.52, "word": " او", "probability": 0.75439453125}, {"start": 2207.52, "end": 2207.64, "word": " ال", "probability": 0.96142578125}, {"start": 2207.64, "end": 2208.1, "word": " xn", "probability": 0.67919921875}, {"start": 2208.1, "end": 2208.6, "word": " أكبر", "probability": 0.7940266927083334}, {"start": 2208.6, "end": 2208.82, "word": " من", "probability": 0.9775390625}, {"start": 2208.82, "end": 2209.26, "word": " capital", "probability": 0.48095703125}, {"start": 2209.26, "end": 2209.72, "word": " K", "probability": 0.75341796875}, {"start": 2209.72, "end": 2210.68, "word": " هذا", "probability": 0.76513671875}, {"start": 2210.68, "end": 2211.26, "word": " بيقدي", "probability": 0.893310546875}, {"start": 2211.26, "end": 2211.5, "word": " ان", "probability": 0.57958984375}, {"start": 2211.5, "end": 2212.26, "word": " صورتها", "probability": 0.9842529296875}, {"start": 2212.26, "end": 2216.86, "word": " المسافة", "probability": 0.9661865234375}, {"start": 2216.86, "end": 2217.24, "word": " بينها", "probability": 0.987548828125}, {"start": 2217.24, "end": 2217.4, "word": " و", "probability": 0.533203125}, {"start": 2217.4, "end": 2217.64, "word": " بين", "probability": 0.95166015625}, {"start": 2217.64, "end": 2217.86, "word": " ال", "probability": 0.9736328125}, {"start": 2217.86, "end": 2218.16, "word": " L", "probability": 0.7978515625}, {"start": 2218.16, "end": 2218.84, "word": " أصغر", "probability": 0.9822998046875}, {"start": 2218.84, "end": 2219.1, "word": " من", "probability": 0.9921875}, {"start": 2219.1, "end": 2219.64, "word": " إبسل", "probability": 0.64105224609375}, {"start": 2219.64, "end": 2221.84, "word": " صح؟", "probability": 0.8937174479166666}], "temperature": 1.0}, {"id": 80, "seek": 225006, "start": 2226.2, "end": 2250.06, "text": "إذا نجي نلخص كمان مرة، إيه اللي عملناها؟ أنا إيش بدأ في بتلقى limited sequence F of X N لما N تقول الـinfinity بالساوي عدد L فهذه البديات بإبسلون أكبر من السفر given أثبتت إن يوجد capital N عدد طبيعي يعتمد على الـK والـK تعتمد على إبسلون، إذا الـN هذه تعتمد على الـgiven إبسلون", "tokens": [28814, 15730, 8717, 7435, 1829, 8717, 1211, 9778, 9381, 9122, 2304, 7649, 3714, 25720, 12399, 11933, 1829, 3224, 13672, 1829, 6225, 42213, 8315, 11296, 22807, 41850, 11933, 1829, 8592, 47525, 10721, 8978, 39894, 1211, 4587, 7578, 5567, 8310, 479, 295, 1783, 426, 5296, 15042, 426, 6055, 39648, 2423, 39184, 259, 5194, 507, 20666, 3794, 995, 45865, 6225, 3215, 3215, 441, 6156, 3224, 24192, 29739, 16254, 9307, 4724, 28814, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 2212, 5551, 12984, 3555, 2655, 2655, 36145, 7251, 29245, 3215, 4238, 426, 6225, 3215, 3215, 23032, 21292, 3615, 1829, 7251, 34268, 2304, 3215, 15844, 2423, 39184, 42, 16070, 39184, 42, 6055, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536, 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0.5830078125}, {"start": 2230.2, "end": 2230.36, "word": " إيش", "probability": 0.8165690104166666}, {"start": 2230.36, "end": 2230.7, "word": " بدأ", "probability": 0.320068359375}, {"start": 2230.7, "end": 2230.78, "word": " في", "probability": 0.38720703125}, {"start": 2230.78, "end": 2231.12, "word": " بتلقى", "probability": 0.57794189453125}, {"start": 2231.12, "end": 2231.42, "word": " limited", "probability": 0.330078125}, {"start": 2231.42, "end": 2232.1, "word": " sequence", "probability": 0.91162109375}, {"start": 2232.1, "end": 2232.46, "word": " F", "probability": 0.246337890625}, {"start": 2232.46, "end": 2232.66, "word": " of", "probability": 0.464599609375}, {"start": 2232.66, "end": 2232.98, "word": " X", "probability": 0.90576171875}, {"start": 2232.98, "end": 2233.3, "word": " N", "probability": 0.28076171875}, {"start": 2233.3, "end": 2234.06, "word": " لما", "probability": 0.87744140625}, {"start": 2234.06, "end": 2234.28, "word": " N", "probability": 0.7041015625}, {"start": 2234.28, "end": 2234.56, "word": " تقول", "probability": 0.93359375}, {"start": 2234.56, "end": 2235.12, "word": " الـinfinity", "probability": 0.6229248046875}, {"start": 2235.12, "end": 2235.58, "word": " بالساوي", "probability": 0.66375732421875}, {"start": 2235.58, "end": 2235.94, "word": " عدد", "probability": 0.9811197916666666}, {"start": 2235.94, "end": 2236.26, "word": " L", "probability": 0.89013671875}, {"start": 2236.26, "end": 2237.34, "word": " فهذه", "probability": 0.7020670572916666}, {"start": 2237.34, "end": 2237.84, "word": " البديات", "probability": 0.7394205729166666}, {"start": 2237.84, "end": 2238.46, "word": " بإبسلون", "probability": 0.7781168619791666}, {"start": 2238.46, "end": 2238.88, "word": " أكبر", "probability": 0.98046875}, {"start": 2238.88, "end": 2239.08, "word": " من", "probability": 0.9921875}, {"start": 2239.08, "end": 2239.54, "word": " السفر", "probability": 0.8863932291666666}, {"start": 2239.54, "end": 2239.94, "word": " given", "probability": 0.71826171875}, {"start": 2239.94, "end": 2241.18, "word": " أثبتت", "probability": 0.98173828125}, {"start": 2241.18, "end": 2241.32, "word": " إن", "probability": 0.67626953125}, {"start": 2241.32, "end": 2241.76, "word": " يوجد", "probability": 0.962890625}, {"start": 2241.76, "end": 2242.24, "word": " capital", "probability": 0.7705078125}, {"start": 2242.24, "end": 2242.54, "word": " N", "probability": 0.96728515625}, {"start": 2242.54, "end": 2242.94, "word": " عدد", "probability": 0.9803059895833334}, {"start": 2242.94, "end": 2243.96, "word": " طبيعي", "probability": 0.9864501953125}, {"start": 2243.96, "end": 2244.6, "word": " يعتمد", "probability": 0.9061279296875}, {"start": 2244.6, "end": 2244.74, "word": " على", "probability": 0.837890625}, {"start": 2244.74, "end": 2245.08, "word": " الـK", "probability": 0.6607259114583334}, {"start": 2245.08, "end": 2245.58, "word": " والـK", "probability": 0.6874186197916666}, {"start": 2245.58, "end": 2246.16, "word": " تعتمد", "probability": 0.9195556640625}, {"start": 2246.16, "end": 2246.32, "word": " على", "probability": 0.92578125}, {"start": 2246.32, "end": 2247.46, "word": " إبسلون،", "probability": 0.9150390625}, {"start": 2247.46, "end": 2247.68, "word": " إذا", "probability": 0.811767578125}, {"start": 2247.68, "end": 2248.14, "word": " الـN", "probability": 0.9104817708333334}, {"start": 2248.14, "end": 2248.42, "word": " هذه", "probability": 0.431640625}, {"start": 2248.42, "end": 2249.0, "word": " تعتمد", "probability": 0.973876953125}, {"start": 2249.0, "end": 2249.14, "word": " على", "probability": 0.91259765625}, {"start": 2249.14, "end": 2249.56, "word": " الـgiven", "probability": 0.7470703125}, {"start": 2249.56, "end": 2250.06, "word": " إبسلون", "probability": 0.9482421875}], "temperature": 1.0}, {"id": 81, "seek": 227127, "start": 2251.55, "end": 2271.27, "text": "و هذه ال N لكل small n أكبر من أو ساوي ال capital N هذه طلع عند المسافة بين الحد النوني لل sequence و L أصغر من Epsilon بما أن Epsilon was arbitrary since Epsilon أكبر من السفر was arbitrary", "tokens": [2407, 29538, 2423, 426, 5296, 28820, 1359, 297, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 2423, 4238, 426, 29538, 23032, 1211, 3615, 43242, 9673, 3794, 31845, 3660, 49374, 21542, 3215, 28239, 11536, 1829, 24976, 8310, 4032, 441, 5551, 9381, 17082, 2288, 9154, 9970, 82, 15754, 4724, 15042, 14739, 9970, 82, 15754, 390, 23211, 1670, 9970, 82, 15754, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 390, 23211], "avg_logprob": -0.2851562561357723, "compression_ratio": 1.5084745762711864, "no_speech_prob": 0.0, "words": [{"start": 2251.55, "end": 2251.87, "word": "و", "probability": 0.82177734375}, {"start": 2251.87, "end": 2252.37, "word": " هذه", "probability": 0.1966552734375}, {"start": 2252.37, "end": 2252.55, "word": " ال", "probability": 0.767578125}, {"start": 2252.55, "end": 2252.83, "word": " N", "probability": 0.401123046875}, {"start": 2252.83, "end": 2253.81, "word": " لكل", "probability": 0.920654296875}, {"start": 2253.81, "end": 2254.21, "word": " small", "probability": 0.64404296875}, {"start": 2254.21, "end": 2254.57, "word": " n", "probability": 0.53173828125}, {"start": 2254.57, "end": 2255.03, "word": " أكبر", "probability": 0.9070638020833334}, {"start": 2255.03, "end": 2255.21, "word": " من", "probability": 0.94091796875}, {"start": 2255.21, "end": 2255.37, "word": " أو", "probability": 0.951171875}, {"start": 2255.37, "end": 2255.77, "word": " ساوي", "probability": 0.8655598958333334}, {"start": 2255.77, "end": 2255.91, "word": " ال", "probability": 0.2578125}, {"start": 2255.91, "end": 2256.21, "word": " capital", "probability": 0.480712890625}, {"start": 2256.21, "end": 2256.53, "word": " N", "probability": 0.849609375}, {"start": 2256.53, "end": 2257.03, "word": " هذه", "probability": 0.505859375}, {"start": 2257.03, "end": 2257.89, "word": " طلع", "probability": 0.6935221354166666}, {"start": 2257.89, "end": 2258.05, "word": " عند", "probability": 0.638671875}, {"start": 2258.05, "end": 2258.63, "word": " المسافة", "probability": 0.9591064453125}, {"start": 2258.63, "end": 2258.87, "word": " بين", "probability": 0.9345703125}, {"start": 2258.87, "end": 2259.31, "word": " الحد", "probability": 0.947998046875}, {"start": 2259.31, "end": 2259.83, "word": " النوني", "probability": 0.7820638020833334}, {"start": 2259.83, "end": 2259.99, "word": " لل", "probability": 0.8544921875}, {"start": 2259.99, "end": 2260.49, "word": " sequence", "probability": 0.8388671875}, {"start": 2260.49, "end": 2260.73, "word": " و", "probability": 0.3193359375}, {"start": 2260.73, "end": 2260.87, "word": " L", "probability": 0.69140625}, {"start": 2260.87, "end": 2261.17, "word": " أصغر", "probability": 0.9696044921875}, {"start": 2261.17, "end": 2261.35, "word": " من", "probability": 0.99462890625}, {"start": 2261.35, "end": 2261.79, "word": " Epsilon", "probability": 0.6659749348958334}, {"start": 2261.79, "end": 2263.11, "word": " بما", "probability": 0.88232421875}, {"start": 2263.11, "end": 2263.27, "word": " أن", "probability": 0.7939453125}, {"start": 2263.27, "end": 2263.71, "word": " Epsilon", "probability": 0.8956705729166666}, {"start": 2263.71, "end": 2263.97, "word": " was", "probability": 0.74169921875}, {"start": 2263.97, "end": 2264.53, "word": " arbitrary", "probability": 0.814453125}, {"start": 2264.53, "end": 2265.35, "word": " since", "probability": 0.7109375}, {"start": 2265.35, "end": 2267.75, "word": " Epsilon", "probability": 0.7762044270833334}, {"start": 2267.75, "end": 2268.25, "word": " أكبر", "probability": 0.9720052083333334}, {"start": 2268.25, "end": 2268.47, "word": " من", "probability": 0.99609375}, {"start": 2268.47, "end": 2269.13, "word": " السفر", "probability": 0.754150390625}, {"start": 2269.13, "end": 2269.99, "word": " was", "probability": 0.890625}, {"start": 2269.99, "end": 2271.27, "word": " arbitrary", "probability": 0.6259765625}], "temperature": 1.0}, {"id": 82, "seek": 230083, "start": 2272.23, "end": 2300.83, "text": "إذا by epsilon capital N definition of limit of sequence بنكون هيك حسب التعريف أثبتنا أنه limit لسيكوينس F of X N as N tends to infinity بالساوي لعدد N وبالتالي هيك بنكون أثبتنا إذا العبارة 2 holds وهيك بنكون أثبتنا أن العبارة statement 1 implies statement 2", "tokens": [28814, 15730, 538, 17889, 4238, 426, 7123, 295, 4948, 295, 8310, 44945, 30544, 39896, 4117, 11331, 35457, 16712, 3615, 16572, 5172, 5551, 12984, 3555, 2655, 8315, 14739, 3224, 4948, 5296, 3794, 1829, 4117, 2407, 9957, 3794, 479, 295, 1783, 426, 382, 426, 12258, 281, 13202, 20666, 3794, 995, 45865, 5296, 22488, 3215, 426, 46599, 6027, 2655, 6027, 1829, 39896, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 11933, 15730, 18863, 3555, 9640, 3660, 568, 9190, 37037, 1829, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 14739, 18863, 3555, 9640, 3660, 5629, 502, 18779, 5629, 568], "avg_logprob": -0.2547200536355376, "compression_ratio": 1.635135135135135, 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"word": " 2", "probability": 0.96337890625}], "temperature": 1.0}, {"id": 83, "seek": 233194, "start": 2302.83, "end": 2331.95, "text": "Okay تمام إذا نحن ممكن نبرهن ال sequential criterion لل infinite limit و لل one sided limit و لكل أنواع ال limit و هاي أثبتنا جزء برهان الجزء التاني مماثل ال proof of 2 implies 1", "tokens": [8297, 46811, 10943, 11933, 15730, 8717, 5016, 1863, 3714, 43020, 8717, 26890, 3224, 1863, 2423, 42881, 46691, 24976, 13785, 4948, 4032, 24976, 472, 41651, 4948, 4032, 5296, 28820, 14739, 14407, 3615, 2423, 4948, 4032, 8032, 47302, 5551, 12984, 3555, 2655, 8315, 10874, 11622, 38207, 4724, 2288, 3224, 7649, 25724, 11622, 38207, 16712, 7649, 1829, 3714, 2304, 5718, 104, 1211, 2423, 8177, 295, 568, 18779, 502], "avg_logprob": -0.2469223511941505, "compression_ratio": 1.4180790960451977, "no_speech_prob": 0.0, "words": [{"start": 2302.83, "end": 2303.23, "word": "Okay", "probability": 0.10931396484375}, {"start": 2303.23, "end": 2303.67, "word": " تمام", 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"probability": 0.9156901041666666}, {"start": 2321.43, "end": 2322.61, "word": " برهان", "probability": 0.9034423828125}, {"start": 2322.61, "end": 2323.07, "word": " الجزء", "probability": 0.9664713541666666}, {"start": 2323.07, "end": 2323.51, "word": " التاني", "probability": 0.9632161458333334}, {"start": 2323.51, "end": 2324.23, "word": " مماثل", "probability": 0.894140625}, {"start": 2324.23, "end": 2327.31, "word": " ال", "probability": 0.3642578125}, {"start": 2327.31, "end": 2327.83, "word": " proof", "probability": 0.9033203125}, {"start": 2327.83, "end": 2328.79, "word": " of", "probability": 0.93359375}, {"start": 2328.79, "end": 2330.73, "word": " 2", "probability": 0.28125}, {"start": 2330.73, "end": 2331.35, "word": " implies", "probability": 0.93017578125}, {"start": 2331.35, "end": 2331.95, "word": " 1", "probability": 0.89453125}], "temperature": 1.0}, {"id": 84, "seek": 236179, "start": 2334.03, "end": 2361.79, "text": "is similar to original proof or proof of original original sequential criterion original sequential criterion مع", "tokens": [271, 2531, 281, 3380, 8177, 420, 8177, 295, 3380, 3380, 42881, 46691, 3380, 42881, 46691, 20449], "avg_logprob": -0.35500919117647056, "compression_ratio": 1.6521739130434783, "no_speech_prob": 0.0, "words": [{"start": 2334.03, "end": 2334.37, "word": "is", "probability": 0.42626953125}, {"start": 2334.37, "end": 2334.95, "word": " similar", "probability": 0.904296875}, {"start": 2334.95, "end": 2338.01, "word": " to", "probability": 0.94921875}, {"start": 2338.01, "end": 2343.41, "word": " original", "probability": 0.80517578125}, {"start": 2343.41, "end": 2344.03, "word": " proof", "probability": 0.91552734375}, {"start": 2344.03, "end": 2344.75, "word": " or", "probability": 0.1600341796875}, {"start": 2344.75, "end": 2345.35, "word": " proof", "probability": 0.63525390625}, {"start": 2345.35, "end": 2348.69, "word": " of", "probability": 0.9541015625}, {"start": 2348.69, "end": 2350.05, "word": " original", "probability": 0.9462890625}, {"start": 2350.05, "end": 2354.81, "word": " original", "probability": 0.255615234375}, {"start": 2354.81, "end": 2357.41, "word": " sequential", "probability": 0.96875}, {"start": 2357.41, "end": 2358.31, "word": " criterion", "probability": 0.935546875}, {"start": 2358.31, "end": 2360.01, "word": " original", "probability": 0.623046875}, {"start": 2360.01, "end": 2360.79, "word": " sequential", "probability": 0.9853515625}, {"start": 2360.79, "end": 2361.47, "word": " criterion", "probability": 0.9833984375}, {"start": 2361.47, "end": 2361.79, "word": " مع", "probability": 0.9580078125}], "temperature": 1.0}, {"id": 85, "seek": 237315, "start": 2362.57, "end": 2373.15, "text": "عمل التعديلات اللازمة فانا بقولكم انكم ترجعوا ل sequential criterion الأساسية تقرأوا البرهان تبعها كيف انا برهان اتنين ده او احد", "tokens": [25957, 1211, 16712, 3615, 16254, 1211, 9307, 13672, 31377, 46007, 6156, 7649, 995, 4724, 39648, 24793, 16472, 24793, 6055, 47341, 3615, 14407, 5296, 42881, 46691, 16247, 3794, 32277, 10632, 6055, 4587, 2288, 10721, 14407, 2423, 26890, 3224, 7649, 6055, 3555, 3615, 11296, 9122, 33911, 1975, 8315, 4724, 2288, 3224, 7649, 1975, 2655, 1863, 9957, 11778, 3224, 1975, 2407, 1975, 24401], "avg_logprob": -0.18609119243309147, "compression_ratio": 1.4276315789473684, "no_speech_prob": 0.0, "words": [{"start": 2362.57, "end": 2363.07, "word": "عمل", "probability": 0.8974609375}, {"start": 2363.07, "end": 2363.85, "word": " التعديلات", "probability": 0.857470703125}, {"start": 2363.85, "end": 2364.49, "word": " اللازمة", "probability": 0.935546875}, {"start": 2364.49, "end": 2365.03, "word": " فانا", "probability": 0.8592122395833334}, {"start": 2365.03, "end": 2365.47, "word": " بقولكم", "probability": 0.6568196614583334}, {"start": 2365.47, "end": 2365.67, "word": " انكم", "probability": 0.7353515625}, {"start": 2365.67, "end": 2366.29, "word": " ترجعوا", "probability": 0.9864501953125}, {"start": 2366.29, "end": 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{"start": 2372.37, "end": 2372.57, "word": " او", "probability": 0.6025390625}, {"start": 2372.57, "end": 2373.15, "word": " احد", "probability": 0.86328125}], "temperature": 1.0}, {"id": 86, "seek": 239801, "start": 2374.01, "end": 2398.01, "text": "و تعملوا التعديلات .. ازاي نبران واحد بدي لاتنين .. okay تمام .. اذا ان هذه تعتبر sequential criterion لل limits at infinity بالمثل ممكن ان احنا نحصل على sequential criterion لل limits at negative infinity يعني ال ..", "tokens": [2407, 6055, 25957, 1211, 14407, 16712, 3615, 16254, 1211, 9307, 4386, 1975, 11622, 47302, 8717, 26890, 7649, 36764, 24401, 4724, 16254, 5296, 9307, 1863, 9957, 4386, 1392, 46811, 10943, 4386, 1975, 15730, 16472, 29538, 6055, 34268, 26890, 42881, 46691, 24976, 10406, 412, 13202, 20666, 2304, 12984, 1211, 3714, 43020, 16472, 1975, 5016, 8315, 8717, 5016, 36520, 15844, 42881, 46691, 24976, 10406, 412, 3671, 13202, 37495, 22653, 2423, 4386], "avg_logprob": -0.36548913389012433, "compression_ratio": 1.6, 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تمام", "probability": 0.927978515625}, {"start": 2380.39, "end": 2380.45, "word": " ..", "probability": 0.382568359375}, {"start": 2380.45, "end": 2380.89, "word": " اذا", "probability": 0.48687744140625}, {"start": 2380.89, "end": 2381.07, "word": " ان", "probability": 0.35107421875}, {"start": 2381.07, "end": 2381.47, "word": " هذه", "probability": 0.65673828125}, {"start": 2381.47, "end": 2382.03, "word": " تعتبر", "probability": 0.9378255208333334}, {"start": 2382.03, "end": 2382.53, "word": " sequential", "probability": 0.82861328125}, {"start": 2382.53, "end": 2383.35, "word": " criterion", "probability": 0.98291015625}, {"start": 2383.35, "end": 2384.31, "word": " لل", "probability": 0.349853515625}, {"start": 2384.31, "end": 2384.65, "word": " limits", "probability": 0.6650390625}, {"start": 2384.65, "end": 2384.91, "word": " at", "probability": 0.9462890625}, {"start": 2384.91, "end": 2385.47, "word": " infinity", "probability": 0.82666015625}, {"start": 2385.47, "end": 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"probability": 0.82421875}, {"start": 2732.29, "end": 2733.19, "word": " okay", "probability": 0.2271728515625}, {"start": 2733.19, "end": 2734.21, "word": " إذن", "probability": 0.7869466145833334}, {"start": 2734.21, "end": 2734.51, "word": " هذا", "probability": 0.8671875}, {"start": 2734.51, "end": 2735.11, "word": " معناه", "probability": 0.990234375}, {"start": 2735.11, "end": 2735.31, "word": " إن", "probability": 0.58349609375}, {"start": 2735.31, "end": 2735.49, "word": " ال", "probability": 0.486328125}, {"start": 2735.49, "end": 2735.85, "word": " limit", "probability": 0.947265625}, {"start": 2735.85, "end": 2737.25, "word": " حسب", "probability": 0.9814453125}, {"start": 2737.25, "end": 2737.97, "word": " التعريف", "probability": 0.992919921875}, {"start": 2737.97, "end": 2738.83, "word": " limit", "probability": 0.9697265625}, {"start": 2738.83, "end": 2739.43, "word": " واحد", "probability": 0.7178955078125}, {"start": 2739.43, "end": 2739.63, "word": " على", "probability": 0.84765625}, {"start": 2739.63, "end": 2740.05, "word": " x", "probability": 0.93310546875}, {"start": 2740.05, "end": 2740.39, "word": " لما", "probability": 0.89990234375}, {"start": 2740.39, "end": 2740.69, "word": " x", "probability": 0.97119140625}, {"start": 2740.69, "end": 2741.23, "word": " تقول", "probability": 0.6727294921875}, {"start": 2741.23, "end": 2742.63, "word": " إلى", "probability": 0.82666015625}, {"start": 2742.63, "end": 2743.41, "word": " infinity", "probability": 0.86181640625}, {"start": 2743.41, "end": 2745.47, "word": " بساوي", "probability": 0.83349609375}, {"start": 2745.47, "end": 2746.03, "word": " سفر", "probability": 0.8912760416666666}], "temperature": 1.0}, {"id": 100, "seek": 277628, "start": 2749.02, "end": 2776.28, "text": "بالمثل ممكن نثبت الجزء التاني نفس البرهان مع التعديل في تعريف limit at سالب infinity ممكن برضه نستخدم sequential criterion لو بدأت استخدم sequential criterion لإثبات limit", "tokens": [3555, 45340, 12984, 1211, 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نستخدم", "probability": 0.9803466796875}, {"start": 2763.38, "end": 2763.98, "word": " sequential", "probability": 0.6953125}, {"start": 2763.98, "end": 2764.66, "word": " criterion", "probability": 0.97021484375}, {"start": 2764.66, "end": 2766.68, "word": " لو", "probability": 0.65478515625}, {"start": 2766.68, "end": 2770.18, "word": " بدأت", "probability": 0.7060546875}, {"start": 2770.18, "end": 2770.72, "word": " استخدم", "probability": 0.8323567708333334}, {"start": 2770.72, "end": 2771.4, "word": " sequential", "probability": 0.91357421875}, {"start": 2771.4, "end": 2772.12, "word": " criterion", "probability": 0.98681640625}, {"start": 2772.12, "end": 2775.9, "word": " لإثبات", "probability": 0.9044921875}, {"start": 2775.9, "end": 2776.28, "word": " limit", "probability": 0.77734375}], "temperature": 1.0}, {"id": 101, "seek": 280587, "start": 2778.67, "end": 2805.87, "text": "بأخد بقول ان هنا let xn be sequence contained in 0 و infinity بحيث انه limit xn تساوي infinity اذا limit f of xn has n times infinity", "tokens": [3555, 10721, 9778, 3215, 4724, 39648, 16472, 34105, 718, 2031, 77, 312, 8310, 16212, 294, 1958, 4032, 13202, 4724, 5016, 1829, 12984, 16472, 3224, 4948, 2031, 77, 6055, 3794, 995, 45865, 13202, 1975, 15730, 4948, 283, 295, 2031, 77, 575, 297, 1413, 13202], "avg_logprob": -0.3469460206952962, "compression_ratio": 1.2366412213740459, "no_speech_prob": 0.0, "words": [{"start": 2778.67, "end": 2779.81, "word": "بأخد", "probability": 0.68646240234375}, {"start": 2779.81, "end": 2781.03, "word": " بقول", "probability": 0.70458984375}, {"start": 2781.03, "end": 2781.67, "word": " ان", "probability": 0.1461181640625}, {"start": 2781.67, "end": 2782.01, "word": " هنا", "probability": 0.9453125}, {"start": 2782.01, "end": 2783.49, "word": " let", "probability": 0.69091796875}, {"start": 2783.49, "end": 2784.31, "word": " xn", "probability": 0.492919921875}, {"start": 2784.31, "end": 2784.93, "word": " be", "probability": 0.3876953125}, {"start": 2784.93, "end": 2785.73, "word": " sequence", "probability": 0.69091796875}, {"start": 2785.73, "end": 2786.47, "word": " contained", "probability": 0.61474609375}, {"start": 2786.47, "end": 2786.89, "word": " in", "probability": 0.95263671875}, {"start": 2786.89, "end": 2787.33, "word": " 0", "probability": 0.51904296875}, {"start": 2787.33, "end": 2787.55, "word": " و", "probability": 0.79638671875}, {"start": 2787.55, "end": 2788.03, "word": " infinity", "probability": 0.43017578125}, {"start": 2788.03, "end": 2790.65, "word": " بحيث", "probability": 0.9306640625}, {"start": 2790.65, "end": 2791.23, "word": " انه", "probability": 0.71630859375}, {"start": 2791.23, "end": 2792.99, "word": " limit", "probability": 0.9716796875}, {"start": 2792.99, "end": 2793.93, "word": " xn", "probability": 0.968017578125}, {"start": 2793.93, "end": 2794.65, "word": " تساوي", "probability": 0.896728515625}, {"start": 2794.65, "end": 2795.25, "word": " infinity", "probability": 0.78271484375}, {"start": 2795.25, "end": 2799.57, "word": " اذا", "probability": 0.54168701171875}, {"start": 2799.57, "end": 2800.15, "word": " limit", "probability": 0.8896484375}, {"start": 2800.15, "end": 2801.91, "word": " f", "probability": 0.82080078125}, {"start": 2801.91, "end": 2802.27, "word": " of", "probability": 0.5205078125}, {"start": 2802.27, "end": 2803.29, "word": " xn", "probability": 0.960693359375}, {"start": 2803.29, "end": 2804.59, "word": " has", "probability": 0.77490234375}, {"start": 2804.59, "end": 2804.93, "word": " n", "probability": 0.76025390625}, {"start": 2804.93, "end": 2805.21, "word": " times", "probability": 0.4267578125}, {"start": 2805.21, "end": 2805.87, "word": " infinity", "probability": 0.91796875}], "temperature": 1.0}, {"id": 102, "seek": 282622, "start": 2807.04, "end": 2826.22, "text": "طبعا هذا بيقدي هذا بيقدي انه limit واحد على xn بساوي سفر exercise أخدناها أخدنا انه limit sequence xn بساوي infinity if and only if limit مقلوب السيكوانس بساوي سفر", "tokens": [9566, 3555, 3615, 995, 23758, 4724, 1829, 4587, 16254, 23758, 4724, 1829, 4587, 16254, 16472, 3224, 4948, 36764, 24401, 15844, 2031, 77, 4724, 3794, 995, 45865, 8608, 5172, 2288, 5380, 5551, 9778, 3215, 8315, 11296, 5551, 9778, 3215, 8315, 16472, 3224, 4948, 8310, 2031, 77, 4724, 3794, 995, 45865, 13202, 498, 293, 787, 498, 4948, 3714, 4587, 1211, 37746, 21136, 1829, 4117, 2407, 7649, 3794, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.25214040442688823, "compression_ratio": 1.577922077922078, "no_speech_prob": 0.0, "words": [{"start": 2807.04, "end": 2807.46, "word": "طبعا", "probability": 0.77020263671875}, {"start": 2807.46, "end": 2807.72, "word": " هذا", "probability": 0.755859375}, {"start": 2807.72, "end": 2808.34, "word": " بيقدي", "probability": 0.71209716796875}, {"start": 2808.34, "end": 2811.5, "word": " هذا", "probability": 0.1551513671875}, {"start": 2811.5, "end": 2811.94, "word": " بيقدي", "probability": 0.9361572265625}, {"start": 2811.94, "end": 2812.2, "word": " انه", "probability": 0.764404296875}, {"start": 2812.2, "end": 2812.62, "word": " limit", "probability": 0.94873046875}, {"start": 2812.62, "end": 2814.38, "word": " واحد", "probability": 0.68017578125}, {"start": 2814.38, "end": 2814.6, "word": " على", "probability": 0.56201171875}, {"start": 2814.6, "end": 2815.46, "word": " xn", "probability": 0.455322265625}, {"start": 2815.46, "end": 2816.24, "word": " بساوي", "probability": 0.8157958984375}, {"start": 2816.24, "end": 2816.84, "word": " سفر", "probability": 0.8741861979166666}, {"start": 2816.84, "end": 2818.32, "word": " exercise", "probability": 0.328125}, {"start": 2818.32, "end": 2819.14, "word": " أخدناها", "probability": 0.815625}, {"start": 2819.14, "end": 2820.4, "word": " أخدنا", "probability": 0.797607421875}, {"start": 2820.4, "end": 2820.64, "word": " انه", "probability": 0.794189453125}, {"start": 2820.64, "end": 2820.82, "word": " limit", "probability": 0.974609375}, {"start": 2820.82, "end": 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{"start": 2834.27, "end": 2835.95, "word": " وهذا", "probability": 0.85986328125}, {"start": 2835.95, "end": 2836.33, "word": " بيساوي", "probability": 0.843115234375}, {"start": 2836.33, "end": 2836.73, "word": " ستة", "probability": 0.44482421875}, {"start": 2836.73, "end": 2841.15, "word": " لأي", "probability": 0.4368896484375}, {"start": 2841.15, "end": 2841.85, "word": " sequence", "probability": 0.92724609375}, {"start": 2841.85, "end": 2842.77, "word": " نهايتها", "probability": 0.869140625}, {"start": 2842.77, "end": 2843.35, "word": " infinity", "probability": 0.8564453125}, {"start": 2843.35, "end": 2844.91, "word": " نهاية", "probability": 0.6475423177083334}, {"start": 2844.91, "end": 2845.59, "word": " سورتها", "probability": 0.845947265625}, {"start": 2845.59, "end": 2846.51, "word": " بيساوي", "probability": 0.9099609375}, {"start": 2846.51, "end": 2846.99, "word": " العدد", "probability": 0.9417317708333334}, {"start": 2846.99, "end": 2847.33, "word": " L", 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" limit", "probability": 0.92333984375}, {"start": 2925.82, "end": 2926.06, "word": " 1", "probability": 0.890625}, {"start": 2926.06, "end": 2926.3, "word": " على", "probability": 0.880859375}, {"start": 2926.3, "end": 2926.84, "word": " xn", "probability": 0.984130859375}, {"start": 2926.84, "end": 2927.46, "word": " تربية", "probability": 0.7720540364583334}, {"start": 2927.46, "end": 2930.16, "word": " يعني", "probability": 0.75341796875}, {"start": 2930.16, "end": 2930.48, "word": " هذا", "probability": 0.96044921875}, {"start": 2930.48, "end": 2931.22, "word": " بيقدر", "probability": 0.6851806640625}, {"start": 2931.22, "end": 2937.5, "word": " وهذا", "probability": 0.7275390625}, {"start": 2937.5, "end": 2938.16, "word": " بيقدر", "probability": 0.8994140625}, {"start": 2938.16, "end": 2938.52, "word": " ان", "probability": 0.712890625}, {"start": 2938.52, "end": 2939.02, "word": " limit", "probability": 0.75146484375}], "temperature": 1.0}, {"id": 107, "seek": 296913, "start": 2940.97, "end": 2969.13, "text": "1 على xn ترجية لما انتقل ل infinity بساوي limit 1 على xn ضرب limit 1 على xn وهذا بساوي 0 ضرب 0 بساوي 0 و limit g ل xn as n tends to infinity بساوي limit", "tokens": [16, 15844, 2031, 77, 6055, 47341, 10632, 5296, 15042, 16472, 2655, 4587, 1211, 5296, 13202, 4724, 3794, 995, 45865, 4948, 502, 15844, 2031, 77, 48812, 25513, 4948, 502, 15844, 2031, 77, 37037, 15730, 4724, 3794, 995, 45865, 1958, 48812, 25513, 1958, 4724, 3794, 995, 45865, 1958, 4032, 4948, 290, 5296, 2031, 77, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 4948], "avg_logprob": -0.22991070766297597, "compression_ratio": 1.6299212598425197, "no_speech_prob": 0.0, "words": [{"start": 2940.97, "end": 2941.49, "word": "1", "probability": 0.1610107421875}, {"start": 2941.49, "end": 2941.87, "word": " على", "probability": 0.30517578125}, {"start": 2941.87, "end": 2942.83, "word": " xn", "probability": 0.61376953125}, {"start": 2942.83, "end": 2943.79, "word": " ترجية", "probability": 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"end": 2997.43, "word": " هذا", "probability": 0.888671875}, {"start": 2997.43, "end": 2997.79, "word": " معناه", "probability": 0.9801432291666666}, {"start": 2997.79, "end": 2997.97, "word": " أن", "probability": 0.65087890625}, {"start": 2997.97, "end": 2998.13, "word": " ال", "probability": 0.64453125}, {"start": 2998.13, "end": 2998.43, "word": " limit", "probability": 0.86376953125}], "temperature": 1.0}, {"id": 109, "seek": 302332, "start": 3000.1, "end": 3023.32, "text": "لـ function g of x لما x تقول انفينيتي بساوي ستة هنا نريد أن نكون أخرجنا الجزء الأول باستخدام sequential criterion بالمثل و كنا نستخدم sequential criterion اللي اتبعت الجزء التالي بس هنا هناخد x الموجودة في الفترة هذه و هكذا", "tokens": [1211, 39184, 2445, 290, 295, 2031, 5296, 15042, 2031, 6055, 39648, 16472, 5172, 9957, 1829, 31371, 4724, 3794, 995, 45865, 8608, 2655, 3660, 34105, 8717, 16572, 3215, 14739, 8717, 30544, 5551, 34740, 7435, 8315, 25724, 11622, 38207, 16247, 12610, 4724, 995, 14851, 9778, 3215, 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{"start": 3005.02, "end": 3005.56, "word": " تقول", "probability": 0.750244140625}, {"start": 3005.56, "end": 3006.54, "word": " انفينيتي", "probability": 0.5547119140625}, {"start": 3006.54, "end": 3007.32, "word": " بساوي", "probability": 0.859375}, {"start": 3007.32, "end": 3007.84, "word": " ستة", "probability": 0.6901041666666666}, {"start": 3007.84, "end": 3009.06, "word": " هنا", "probability": 0.251220703125}, {"start": 3009.06, "end": 3009.3, "word": " نريد", "probability": 0.52923583984375}, {"start": 3009.3, "end": 3009.4, "word": " أن", "probability": 0.5263671875}, {"start": 3009.4, "end": 3009.58, "word": " نكون", "probability": 0.955810546875}, {"start": 3009.58, "end": 3010.18, "word": " أخرجنا", "probability": 0.68475341796875}, {"start": 3010.18, "end": 3010.62, "word": " الجزء", "probability": 0.939453125}, {"start": 3010.62, "end": 3010.98, "word": " الأول", "probability": 0.96875}, {"start": 3010.98, "end": 3011.7, "word": " باستخدام", "probability": 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في القصة السابقة بالكون صحيحة هذا بقى قدر المقلوب ال sequence إذا كانت limit ال sequence infinity فlimit المقلوب سفر وبالتالي limit المقلوب المربع بساوة سفر ممكن كمان نستخدم squeeze theorem ممكن نستخدم squeeze theorem", "tokens": [2407, 8717, 36178, 2423, 1863, 19913, 2288, 10632, 13672, 7578, 16490, 3215, 8315, 11296, 8978, 25062, 9381, 3660, 21136, 16758, 28671, 20666, 30544, 20328, 5016, 1829, 5016, 3660, 23758, 4724, 4587, 7578, 12174, 3215, 2288, 9673, 4587, 1211, 37746, 2423, 8310, 11933, 15730, 25961, 2655, 4948, 2423, 8310, 13202, 6156, 4197, 270, 9673, 4587, 1211, 37746, 8608, 5172, 2288, 46599, 6027, 2655, 6027, 1829, 4948, 9673, 4587, 1211, 37746, 9673, 25513, 3615, 4724, 3794, 995, 2407, 3660, 8608, 5172, 2288, 3714, 43020, 9122, 2304, 7649, 8717, 14851, 9778, 40448, 13578, 20904, 3714, 43020, 8717, 14851, 9778, 40448, 13578, 20904], "avg_logprob": -0.32468749523162843, "compression_ratio": 1.853658536585366, "no_speech_prob": 0.0, "words": [{"start": 3025.06, "end": 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"temperature": 1.0}, {"id": 113, "seek": 312637, "start": 3097.73, "end": 3126.37, "text": "لسه 130 في المثال الأول هذا المثال الثاني في المثال السابق قصدنا ان limit ال function واحد على x لما x تقول infinity تساوي سفر و limit الدالة ثابت سفر لما x تقول infinity تبقى سفر اذا by squeeze theorem by squeeze theorem for limits at infinity", "tokens": [1211, 3794, 3224, 19966, 8978, 9673, 12984, 6027, 16247, 12610, 23758, 9673, 12984, 6027, 6024, 104, 7649, 1829, 8978, 9673, 12984, 6027, 21136, 16758, 4587, 12174, 9381, 3215, 8315, 16472, 4948, 2423, 2445, 36764, 24401, 15844, 2031, 5296, 15042, 2031, 6055, 39648, 13202, 6055, 3794, 995, 45865, 8608, 5172, 2288, 4032, 4948, 2423, 3215, 6027, 3660, 38637, 16758, 2655, 8608, 5172, 2288, 5296, 15042, 2031, 6055, 39648, 13202, 6055, 3555, 4587, 7578, 8608, 5172, 2288, 1975, 15730, 538, 13578, 20904, 538, 13578, 20904, 337, 10406, 412, 13202], "avg_logprob": -0.32404118132862175, "compression_ratio": 1.8186528497409327, "no_speech_prob": 0.0, 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section اربعة تلاتة وبالتالي ننهي ال chapter اللي هو chapter اربعة و بعدين نبدأ في chapter خمسة اللي هو اخر chapter في المخرج هو اهم chapter طبعا في حد عنده اي سؤال او استفسار؟ شكرا لاصغاكم و نشوف ان شاء الله المرة القادمة", "tokens": [2407, 39182, 9957, 8717, 5016, 995, 12610, 8717, 7435, 42213, 3541, 1975, 25513, 27884, 6055, 1211, 9307, 3660, 46599, 6027, 2655, 6027, 1829, 8717, 1863, 3224, 1829, 2423, 7187, 13672, 1829, 31439, 7187, 1975, 25513, 27884, 4032, 39182, 9957, 8717, 44510, 10721, 8978, 7187, 16490, 2304, 3794, 3660, 13672, 1829, 31439, 1975, 34740, 7187, 8978, 9673, 34740, 7435, 31439, 1975, 16095, 7187, 23032, 3555, 3615, 995, 8978, 11331, 3215, 43242, 3224, 1975, 1829, 8608, 33604, 6027, 1975, 2407, 44713, 36178, 9640, 22807, 13412, 4117, 23557, 5296, 33546, 17082, 995, 24793, 4032, 8717, 8592, 38688, 16472, 13412, 16606, 21984, 9673, 25720, 25062, 18513, 46007], "avg_logprob": -0.17518029533899748, "compression_ratio": 1.841121495327103, "no_speech_prob": 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