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"probability": 0.88134765625}, {"start": 123.7, "end": 123.92, "word": " و", "probability": 0.9375}, {"start": 123.92, "end": 124.4, "word": " سالبة", "probability": 0.796875}, {"start": 124.4, "end": 125.66, "word": " فلازم", "probability": 0.9329833984375}, {"start": 125.66, "end": 126.06, "word": " حدود", "probability": 0.9908854166666666}, {"start": 126.06, "end": 126.22, "word": " ال", "probability": 0.97412109375}, {"start": 126.22, "end": 126.64, "word": " sequence", "probability": 0.99560546875}, {"start": 126.64, "end": 126.88, "word": " من", "probability": 0.98828125}, {"start": 126.88, "end": 127.18, "word": " capital", "probability": 0.86962890625}, {"start": 127.18, "end": 127.42, "word": " N", "probability": 0.93310546875}, {"start": 127.42, "end": 127.72, "word": " وانت", "probability": 0.9256184895833334}, {"start": 127.72, "end": 128.14, "word": " طالع", "probability": 0.9275716145833334}, {"start": 128.14, "end": 129.0, "word": " كلها", "probability": 0.98779296875}, {"start": 129.0, "end": 129.32, "word": " تكون", "probability": 0.98095703125}, {"start": 129.32, "end": 129.88, "word": " سالبة", "probability": 0.9791666666666666}, {"start": 129.88, "end": 130.44, "word": " فهذه", "probability": 0.7352701822916666}, {"start": 130.44, "end": 130.9, "word": " شبيهة", "probability": 0.874267578125}, {"start": 130.9, "end": 131.2, "word": " فيها", "probability": 0.976806640625}], "temperature": 1.0}, {"id": 5, "seek": 16006, "start": 131.78, "end": 160.06, "text": "والبرهان سهل وشبيه بالبرهان تبع النظرية المشابهة في حالة ال sequences فناخد الحالة assume ناخد الحالة اللي فيها ال limit ل f of x at c exists and equals عدد l موجب", "tokens": [2407, 6027, 26890, 3224, 7649, 8608, 3224, 1211, 4032, 8592, 21292, 3224, 20666, 26890, 3224, 7649, 6055, 3555, 3615, 28239, 19913, 2288, 10632, 9673, 8592, 16758, 3224, 3660, 8978, 11331, 6027, 3660, 2423, 22978, 6156, 1863, 47283, 3215, 21542, 6027, 3660, 6552, 8717, 47283, 3215, 21542, 6027, 3660, 13672, 1829, 8978, 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140.0, "word": " ال", "probability": 0.88916015625}, {"start": 140.0, "end": 140.52, "word": " sequences", "probability": 0.40380859375}, {"start": 140.52, "end": 142.94, "word": " فناخد", "probability": 0.9122314453125}, {"start": 142.94, "end": 143.52, "word": " الحالة", "probability": 0.9910481770833334}, {"start": 143.52, "end": 144.32, "word": " assume", "probability": 0.58251953125}, {"start": 144.32, "end": 147.36, "word": " ناخد", "probability": 0.8531901041666666}, {"start": 147.36, "end": 147.96, "word": " الحالة", "probability": 0.9949544270833334}, {"start": 147.96, "end": 148.26, "word": " اللي", "probability": 0.8193359375}, {"start": 148.26, "end": 148.7, "word": " فيها", "probability": 0.983154296875}, {"start": 148.7, "end": 148.96, "word": " ال", "probability": 0.669921875}, {"start": 148.96, "end": 149.36, "word": " limit", "probability": 0.966796875}, {"start": 149.36, "end": 152.4, "word": " ل", "probability": 0.7607421875}, {"start": 152.4, "end": 152.68, "word": " f", "probability": 0.365478515625}, {"start": 152.68, "end": 152.92, "word": " of", "probability": 0.455810546875}, {"start": 152.92, "end": 153.36, "word": " x", "probability": 0.9033203125}, {"start": 153.36, "end": 154.78, "word": " at", "probability": 0.86083984375}, {"start": 154.78, "end": 155.12, "word": " c", "probability": 0.7890625}, {"start": 155.12, "end": 155.82, "word": " exists", "probability": 0.71484375}, {"start": 155.82, "end": 157.52, "word": " and", "probability": 0.94873046875}, {"start": 157.52, "end": 158.16, "word": " equals", "probability": 0.95703125}, {"start": 158.16, "end": 158.74, "word": " عدد", "probability": 0.9814453125}, {"start": 158.74, "end": 159.14, "word": " l", "probability": 0.245849609375}, {"start": 159.14, "end": 160.06, "word": " موجب", "probability": 0.9319661458333334}], "temperature": 1.0}, {"id": 6, "seek": 20080, "start": 173.88, "end": 200.8, "text": "فإذا كانت ال limit موجبة بنا أثبت أن يوجد delta neverhood إلى آخر A فخلّينا ناخد let epsilon في الحالة دي let epsilon بساوي L على 2 فهذا عدد موجب", "tokens": [5172, 28814, 15730, 25961, 2655, 2423, 4948, 3714, 29245, 49401, 4724, 8315, 5551, 12984, 3555, 2655, 14739, 7251, 29245, 3215, 8289, 1128, 3809, 30731, 19753, 34740, 316, 6156, 9778, 1211, 11703, 9957, 995, 8717, 47283, 3215, 718, 17889, 8978, 21542, 6027, 3660, 11778, 1829, 718, 17889, 4724, 3794, 995, 45865, 441, 15844, 568, 6156, 3224, 15730, 6225, 3215, 3215, 3714, 29245, 3555], "avg_logprob": -0.3554067517083789, "compression_ratio": 1.3272727272727274, "no_speech_prob": 0.0, "words": [{"start": 173.88, "end": 174.48, "word": "فإذا", "probability": 0.6401774088541666}, {"start": 174.48, "end": 174.92, "word": " كانت", "probability": 0.93017578125}, {"start": 174.92, "end": 175.02, "word": " ال", "probability": 0.51025390625}, {"start": 175.02, "end": 175.38, "word": " limit", "probability": 0.71337890625}, {"start": 175.38, "end": 176.48, "word": " موجبة", "probability": 0.9217122395833334}, {"start": 176.48, "end": 178.86, "word": " بنا", "probability": 0.196044921875}, {"start": 178.86, "end": 179.28, "word": " أثبت", "probability": 0.84033203125}, {"start": 179.28, "end": 179.4, "word": " أن", "probability": 0.370849609375}, {"start": 179.4, "end": 179.9, "word": " يوجد", "probability": 0.8671875}, {"start": 179.9, "end": 180.2, "word": " delta", "probability": 0.473876953125}, {"start": 180.2, "end": 181.04, "word": " neverhood", "probability": 0.3687744140625}, {"start": 181.04, "end": 181.32, "word": " إلى", "probability": 0.75927734375}, {"start": 181.32, "end": 181.8, "word": " آخر", "probability": 0.83447265625}, {"start": 181.8, "end": 182.16, "word": " A", "probability": 0.2412109375}, {"start": 182.16, "end": 187.24, "word": " فخلّينا", "probability": 0.7157796223958334}, {"start": 187.24, "end": 187.8, "word": " ناخد", "probability": 0.9251302083333334}, {"start": 187.8, "end": 188.12, "word": " let", "probability": 0.9384765625}, {"start": 188.12, "end": 188.66, "word": " epsilon", "probability": 0.841796875}, {"start": 188.66, "end": 188.9, "word": " في", "probability": 0.75537109375}, {"start": 188.9, "end": 189.36, "word": " الحالة", "probability": 0.9645182291666666}, {"start": 189.36, "end": 189.72, "word": " دي", "probability": 0.9892578125}, {"start": 189.72, "end": 190.08, "word": " let", "probability": 0.82080078125}, {"start": 190.08, "end": 192.04, "word": " epsilon", "probability": 0.966796875}, {"start": 192.04, "end": 197.74, "word": " بساوي", "probability": 0.801513671875}, {"start": 197.74, "end": 198.24, "word": " L", "probability": 0.78271484375}, {"start": 198.24, "end": 198.42, "word": " على", "probability": 0.350830078125}, {"start": 198.42, "end": 198.88, "word": " 2", "probability": 0.90869140625}, {"start": 198.88, "end": 199.94, "word": " فهذا", "probability": 0.570556640625}, {"start": 199.94, "end": 200.24, "word": " عدد", "probability": 0.6901041666666666}, {"start": 200.24, "end": 200.8, "word": " موجب", "probability": 0.9192708333333334}], "temperature": 1.0}, {"id": 7, "seek": 22328, "start": 203.14, "end": 223.28, "text": "الان by definition of limit of function by epsilon delta definition لأي epsilon موجبة زي هذه يوجد delta تعتمد على L على 2 اللي هي ال epsilon عدد موجب بحيث انه لو كان X", "tokens": [6027, 7649, 538, 7123, 295, 4948, 295, 2445, 538, 17889, 8289, 7123, 5296, 10721, 1829, 17889, 3714, 29245, 49401, 30767, 1829, 29538, 7251, 29245, 3215, 8289, 6055, 34268, 2304, 3215, 15844, 441, 15844, 568, 13672, 1829, 39896, 2423, 17889, 6225, 3215, 3215, 3714, 29245, 3555, 4724, 5016, 1829, 12984, 16472, 3224, 45164, 25961, 1783], "avg_logprob": -0.19247158819978888, "compression_ratio": 1.421383647798742, "no_speech_prob": 0.0, "words": [{"start": 203.14, "end": 203.6, "word": "الان", "probability": 0.572998046875}, {"start": 203.6, "end": 203.92, "word": " by", "probability": 0.775390625}, {"start": 203.92, "end": 204.56, "word": " definition", "probability": 0.8974609375}, {"start": 204.56, "end": 206.18, "word": " of", "probability": 0.8828125}, {"start": 206.18, "end": 206.6, "word": " limit", "probability": 0.73876953125}, {"start": 206.6, "end": 206.78, "word": " of", "probability": 0.955078125}, {"start": 206.78, "end": 207.44, "word": " function", "probability": 0.9453125}, {"start": 207.44, "end": 208.06, "word": " by", "probability": 0.6708984375}, {"start": 208.06, "end": 208.46, "word": " epsilon", "probability": 0.73046875}, {"start": 208.46, "end": 208.8, "word": " delta", "probability": 0.73193359375}, {"start": 208.8, "end": 209.52, "word": " definition", "probability": 0.91650390625}, {"start": 209.52, "end": 212.64, "word": " لأي", "probability": 0.8128255208333334}, {"start": 212.64, "end": 213.02, "word": " epsilon", "probability": 0.81787109375}, {"start": 213.02, "end": 213.48, "word": " موجبة", "probability": 0.8260091145833334}, {"start": 213.48, "end": 213.78, "word": " زي", "probability": 0.876708984375}, {"start": 213.78, "end": 214.08, "word": " هذه", "probability": 0.88916015625}, {"start": 214.08, "end": 214.7, "word": " يوجد", "probability": 0.9720052083333334}, {"start": 214.7, "end": 215.2, "word": " delta", "probability": 0.62451171875}, {"start": 215.2, "end": 216.8, "word": " تعتمد", "probability": 0.96728515625}, {"start": 216.8, "end": 217.12, "word": " على", "probability": 0.86865234375}, {"start": 217.12, "end": 217.56, "word": " L", "probability": 0.5986328125}, {"start": 217.56, "end": 217.78, "word": " على", "probability": 0.286376953125}, {"start": 217.78, "end": 218.14, "word": " 2", "probability": 0.86181640625}, {"start": 218.14, "end": 218.34, "word": " اللي", "probability": 0.7998046875}, {"start": 218.34, "end": 218.54, "word": " هي", "probability": 0.93505859375}, {"start": 218.54, "end": 218.68, "word": " ال", "probability": 0.87939453125}, {"start": 218.68, "end": 219.12, "word": " epsilon", "probability": 0.5341796875}, {"start": 219.12, "end": 219.76, "word": " عدد", "probability": 0.947265625}, {"start": 219.76, "end": 220.42, "word": " موجب", "probability": 0.9638671875}, {"start": 220.42, "end": 221.74, "word": " بحيث", "probability": 0.960205078125}, {"start": 221.74, "end": 222.04, "word": " انه", "probability": 0.70751953125}, {"start": 222.04, "end": 222.22, "word": " لو", "probability": 0.98779296875}, {"start": 222.22, "end": 222.68, "word": " كان", "probability": 0.99658203125}, {"start": 222.68, "end": 223.28, "word": " X", "probability": 0.6181640625}], "temperature": 1.0}, {"id": 8, "seek": 24451, "start": 225.89, "end": 244.51, "text": "ينتمي إلى a و absolute x minus c أصغر من delta أكبر من 0 فهذا بتضمن أن absolute f of x minus L أصغر من إبسلم اللي هي عبارة عن L ع 2", "tokens": [1829, 29399, 2304, 1829, 30731, 257, 4032, 8236, 2031, 3175, 269, 5551, 9381, 17082, 2288, 9154, 8289, 5551, 4117, 26890, 9154, 1958, 6156, 3224, 15730, 39894, 11242, 27842, 14739, 8236, 283, 295, 2031, 3175, 441, 5551, 9381, 17082, 2288, 9154, 11933, 3555, 3794, 19528, 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230.65, "end": 231.09, "word": " delta", "probability": 0.544921875}, {"start": 231.09, "end": 232.67, "word": " أكبر", "probability": 0.95556640625}, {"start": 232.67, "end": 232.91, "word": " من", "probability": 0.99609375}, {"start": 232.91, "end": 233.27, "word": " 0", "probability": 0.359619140625}, {"start": 233.27, "end": 233.87, "word": " فهذا", "probability": 0.94482421875}, {"start": 233.87, "end": 234.53, "word": " بتضمن", "probability": 0.9306640625}, {"start": 234.53, "end": 235.65, "word": " أن", "probability": 0.71435546875}, {"start": 235.65, "end": 236.21, "word": " absolute", "probability": 0.88525390625}, {"start": 236.21, "end": 236.91, "word": " f", "probability": 0.77880859375}, {"start": 236.91, "end": 237.21, "word": " of", "probability": 0.544921875}, {"start": 237.21, "end": 237.69, "word": " x", "probability": 0.970703125}, {"start": 237.69, "end": 239.29, "word": " minus", "probability": 0.953125}, {"start": 239.29, "end": 239.79, "word": " L", "probability": 0.537109375}, {"start": 239.79, "end": 240.45, "word": " أصغر", "probability": 0.9930419921875}, {"start": 240.45, "end": 240.79, "word": " من", "probability": 0.9951171875}, {"start": 240.79, "end": 241.37, "word": " إبسلم", "probability": 0.70343017578125}, {"start": 241.37, "end": 242.77, "word": " اللي", "probability": 0.911865234375}, {"start": 242.77, "end": 242.97, "word": " هي", "probability": 0.66748046875}, {"start": 242.97, "end": 243.45, "word": " عبارة", "probability": 0.99462890625}, {"start": 243.45, "end": 243.75, "word": " عن", "probability": 0.98828125}, {"start": 243.75, "end": 244.09, "word": " L", "probability": 0.9384765625}, {"start": 244.09, "end": 244.33, "word": " ع", "probability": 0.490966796875}, {"start": 244.33, "end": 244.51, "word": " 2", "probability": 0.40185546875}], "temperature": 1.0}, {"id": 9, "seek": 27035, "start": 248.17, "end": 270.35, "text": "فحل المتباينة هذه في f of x فتصير f of x minus L أصغر من L على 2 أكبر من سالب L على 2 وهذا بيقدي أن f of x", "tokens": [5172, 5016, 1211, 9673, 2655, 3555, 995, 9957, 3660, 29538, 8978, 283, 295, 2031, 6156, 2655, 9381, 13546, 283, 295, 2031, 3175, 441, 5551, 9381, 17082, 2288, 9154, 441, 15844, 568, 5551, 4117, 26890, 9154, 8608, 6027, 3555, 441, 15844, 568, 37037, 15730, 4724, 1829, 4587, 16254, 14739, 283, 295, 2031], "avg_logprob": -0.2137920641555236, "compression_ratio": 1.288, "no_speech_prob": 0.0, "words": [{"start": 248.17000000000002, "end": 249.03, "word": "فحل", "probability": 0.760009765625}, {"start": 249.03, "end": 249.85, "word": " المتباينة", "probability": 0.85400390625}, {"start": 249.85, "end": 250.19, "word": " هذه", "probability": 0.5166015625}, {"start": 250.19, "end": 250.59, "word": " في", "probability": 0.869140625}, {"start": 250.59, "end": 251.05, "word": " f", "probability": 0.51220703125}, {"start": 251.05, "end": 251.25, "word": " of", "probability": 0.50439453125}, {"start": 251.25, "end": 251.67, "word": " x", "probability": 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ناحية التانية فتصير F of X أكبر من L سالب L على 2 تطلع L على 2 و ال L موجبة إذا L على 2 موجبة إذا هيك بنكون أثبتنا", "tokens": [27842, 34105, 479, 295, 1783, 6055, 9566, 1211, 3615, 5551, 4117, 26890, 9154, 441, 15844, 568, 5296, 33456, 3224, 5296, 15042, 5551, 9778, 3215, 8608, 6027, 3555, 441, 14739, 7435, 1211, 11296, 18871, 8717, 39319, 10632, 16712, 7649, 10632, 6156, 2655, 9381, 13546, 479, 295, 1783, 5551, 4117, 26890, 9154, 441, 8608, 6027, 3555, 441, 15844, 568, 6055, 9566, 1211, 3615, 441, 15844, 568, 4032, 2423, 441, 3714, 29245, 49401, 11933, 15730, 441, 15844, 568, 3714, 29245, 49401, 11933, 15730, 39896, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315], "avg_logprob": -0.17673610581292046, "compression_ratio": 1.7380952380952381, "no_speech_prob": 0.0, "words": [{"start": 274.74, "end": 275.42, "word": "من", "probability": 0.66015625}, {"start": 275.42, "end": 275.8, "word": " هنا", "probability": 0.9814453125}, {"start": 275.8, "end": 276.1, "word": " F", 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"word": " و", "probability": 0.91796875}, {"start": 333.48, "end": 333.64, "word": " مش", "probability": 0.6806640625}, {"start": 333.64, "end": 334.3, "word": " موجودة", "probability": 0.9879150390625}, {"start": 334.3, "end": 334.48, "word": " في", "probability": 0.83349609375}, {"start": 334.48, "end": 335.8, "word": " singleton", "probability": 0.548095703125}, {"start": 335.8, "end": 336.22, "word": " set", "probability": 0.8427734375}, {"start": 336.22, "end": 336.66, "word": " C", "probability": 0.916015625}, {"start": 336.66, "end": 337.68, "word": " و", "probability": 0.6142578125}, {"start": 337.68, "end": 338.66, "word": " المتباينة", "probability": 0.9331868489583334}, {"start": 338.66, "end": 339.2, "word": " هذه", "probability": 0.73974609375}, {"start": 339.2, "end": 341.64, "word": " هذي", "probability": 0.5790608723958334}, {"start": 341.64, "end": 342.36, "word": " معناها", "probability": 0.9674479166666666}, {"start": 342.36, "end": 342.72, "word": " إن", 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0.40966796875}, {"start": 862.86, "end": 863.3, "word": " لكل", "probability": 0.935546875}, {"start": 863.3, "end": 863.5, "word": " ال", "probability": 0.76953125}, {"start": 863.5, "end": 863.92, "word": " X", "probability": 0.9345703125}, {"start": 863.92, "end": 864.8, "word": " موجود", "probability": 0.9803059895833334}, {"start": 864.8, "end": 865.0, "word": " في", "probability": 0.951171875}, {"start": 865.0, "end": 865.22, "word": " A", "probability": 0.97509765625}, {"start": 865.22, "end": 865.34, "word": " و", "probability": 0.63623046875}, {"start": 865.34, "end": 865.7, "word": " أكبر", "probability": 0.95556640625}, {"start": 865.7, "end": 865.9, "word": " من", "probability": 0.9873046875}, {"start": 865.9, "end": 866.18, "word": " C", "probability": 0.9775390625}], "temperature": 1.0}, {"id": 32, "seek": 90151, "start": 872.71, "end": 901.51, "text": "فبنقول إن ال limit عند x بالساوية c أو ال function في إلها right-hand limit و ال right-hand limit هي العدد L إذا كان لأي إبسلون أكبر من السفر بتقدر نلاقي delta عدد موجة بيعتمد على إبسلون بحيث لكل x في المجموعة A إذا كانت ال X هذه على يمين ال C", "tokens": [5172, 3555, 1863, 39648, 36145, 2423, 4948, 43242, 2031, 20666, 3794, 995, 2407, 10632, 269, 34051, 2423, 2445, 8978, 11933, 1211, 11296, 558, 12, 5543, 4948, 4032, 2423, 558, 12, 5543, 4948, 39896, 18863, 3215, 3215, 441, 11933, 15730, 25961, 5296, 10721, 1829, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 39894, 28543, 2288, 8717, 15040, 38436, 8289, 6225, 3215, 3215, 3714, 29245, 3660, 4724, 1829, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536, 4724, 5016, 1829, 12984, 5296, 28820, 2031, 8978, 9673, 7435, 2304, 2407, 27884, 316, 11933, 15730, 25961, 2655, 2423, 1783, 29538, 15844, 7251, 2304, 9957, 2423, 383], "avg_logprob": -0.21509930630710639, "compression_ratio": 1.6309012875536482, "no_speech_prob": 0.0, "words": [{"start": 872.71, "end": 873.43, "word": "فبنقول", "probability": 0.8428955078125}, {"start": 873.43, "end": 873.65, "word": " إن", "probability": 0.269287109375}, {"start": 873.65, "end": 873.81, "word": " ال", "probability": 0.74560546875}, {"start": 873.81, "end": 874.19, "word": " limit", "probability": 0.68603515625}, {"start": 874.19, "end": 874.75, "word": " عند", "probability": 0.85205078125}, {"start": 874.75, "end": 875.05, "word": " x", "probability": 0.63916015625}, {"start": 875.05, "end": 875.51, "word": " بالساوية", "probability": 0.70673828125}, {"start": 875.51, "end": 875.97, "word": " c", "probability": 0.481201171875}, {"start": 875.97, "end": 877.07, "word": " أو", "probability": 0.79833984375}, {"start": 877.07, "end": 877.21, "word": " ال", "probability": 0.96337890625}, {"start": 877.21, "end": 877.65, "word": " function", "probability": 0.7314453125}, {"start": 877.65, "end": 878.01, "word": " في", "probability": 0.54443359375}, {"start": 878.01, "end": 878.35, "word": " إلها", "probability": 0.662109375}, {"start": 878.35, "end": 878.77, "word": " right", "probability": 0.9267578125}, {"start": 878.77, "end": 879.07, "word": "-hand", "probability": 0.6082763671875}, {"start": 879.07, "end": 879.51, "word": " limit", "probability": 0.95849609375}, {"start": 879.51, "end": 881.01, "word": " و", "probability": 0.361572265625}, {"start": 881.01, "end": 881.15, "word": " ال", "probability": 0.6240234375}, {"start": 881.15, "end": 881.37, "word": " right", "probability": 0.908203125}, {"start": 881.37, "end": 881.65, "word": "-hand", "probability": 0.911865234375}, {"start": 881.65, "end": 881.95, "word": " limit", "probability": 0.984375}, {"start": 881.95, "end": 882.15, "word": " هي", "probability": 0.94873046875}, {"start": 882.15, "end": 882.63, "word": " العدد", "probability": 0.97314453125}, {"start": 882.63, "end": 882.97, "word": " L", "probability": 0.744140625}, {"start": 882.97, "end": 885.51, "word": " إذا", "probability": 0.9521484375}, {"start": 885.51, "end": 885.85, "word": " كان", "probability": 0.99462890625}, {"start": 885.85, "end": 886.29, "word": " لأي", "probability": 0.9534505208333334}, {"start": 886.29, "end": 886.87, "word": " إبسلون", "probability": 0.7806396484375}, {"start": 886.87, "end": 887.27, "word": " أكبر", "probability": 0.9791666666666666}, {"start": 887.27, "end": 887.45, "word": " من", "probability": 0.99365234375}, {"start": 887.45, "end": 887.95, "word": " السفر", "probability": 0.761962890625}, {"start": 887.95, "end": 888.41, "word": " بتقدر", "probability": 0.70263671875}, {"start": 888.41, "end": 888.69, "word": " نلاقي", "probability": 0.9075520833333334}, {"start": 888.69, "end": 889.15, "word": " delta", "probability": 0.404541015625}, {"start": 889.15, "end": 889.53, "word": " عدد", "probability": 0.92529296875}, {"start": 889.53, "end": 889.87, "word": " موجة", "probability": 0.7867838541666666}, {"start": 889.87, "end": 890.45, "word": " بيعتمد", "probability": 0.8775390625}, {"start": 890.45, "end": 890.63, "word": " على", "probability": 0.89306640625}, {"start": 890.63, "end": 891.77, "word": " إبسلون", "probability": 0.97646484375}, {"start": 891.77, "end": 892.59, "word": " بحيث", "probability": 0.9622802734375}, {"start": 892.59, "end": 893.09, "word": " لكل", "probability": 0.985107421875}, {"start": 893.09, "end": 893.39, "word": " x", "probability": 0.68212890625}, {"start": 893.39, "end": 893.55, "word": " في", "probability": 0.978515625}, {"start": 893.55, "end": 894.19, "word": " المجموعة", "probability": 0.93251953125}, {"start": 894.19, "end": 894.59, "word": " A", "probability": 0.845703125}, {"start": 894.59, "end": 897.43, "word": " إذا", "probability": 0.982177734375}, {"start": 897.43, "end": 897.85, "word": " كانت", "probability": 0.982666015625}, {"start": 897.85, "end": 897.99, "word": " ال", "probability": 0.95361328125}, {"start": 897.99, "end": 898.35, "word": " X", "probability": 0.51025390625}, {"start": 898.35, "end": 899.01, "word": " هذه", "probability": 0.7626953125}, {"start": 899.01, "end": 900.53, "word": " على", "probability": 0.91796875}, {"start": 900.53, "end": 900.99, "word": " يمين", "probability": 0.9860026041666666}, {"start": 900.99, "end": 901.23, "word": " ال", "probability": 0.9482421875}, {"start": 901.23, "end": 901.51, "word": " C", "probability": 0.79736328125}], "temperature": 1.0}, {"id": 33, "seek": 92822, "start": 905.14, "end": 928.22, "text": "والمسافة بينها وبين الـ C أصغر من Delta فبتطلع المسافة بين F و XL أصغر من Y بالمثل ممكن نعرف ال limit from the right يعني أنا بدي أعرف ال limit from the right أو ال right hand limit", "tokens": [2407, 45340, 3794, 31845, 3660, 49374, 11296, 46599, 9957, 2423, 39184, 383, 5551, 9381, 17082, 2288, 9154, 18183, 6156, 3555, 2655, 9566, 1211, 3615, 9673, 3794, 31845, 3660, 49374, 479, 4032, 37210, 5551, 9381, 17082, 2288, 9154, 398, 20666, 2304, 12984, 1211, 3714, 43020, 8717, 3615, 28480, 2423, 4948, 490, 264, 558, 37495, 22653, 41850, 4724, 16254, 5551, 3615, 28480, 2423, 4948, 490, 264, 558, 34051, 2423, 558, 1011, 4948], "avg_logprob": -0.2137984167522108, "compression_ratio": 1.6729559748427674, "no_speech_prob": 0.0, "words": [{"start": 905.14, "end": 905.78, "word": "والمسافة", "probability": 0.88837890625}, {"start": 905.78, "end": 906.34, "word": " بينها", "probability": 0.974609375}, {"start": 906.34, "end": 908.1, "word": " وبين", "probability": 0.7152099609375}, {"start": 908.1, "end": 908.32, "word": " الـ", "probability": 0.688232421875}, {"start": 908.32, "end": 908.54, "word": " C", "probability": 0.341552734375}, {"start": 908.54, "end": 909.12, "word": " أصغر", "probability": 0.9842529296875}, {"start": 909.12, "end": 909.32, "word": " من", "probability": 0.99267578125}, {"start": 909.32, "end": 909.72, "word": " Delta", "probability": 0.4609375}, {"start": 909.72, "end": 912.46, "word": " فبتطلع", "probability": 0.9071451822916666}, {"start": 912.46, "end": 913.1, "word": " المسافة", "probability": 0.9873046875}, {"start": 913.1, "end": 913.34, "word": " بين", "probability": 0.865234375}, {"start": 913.34, "end": 913.6, "word": " F", "probability": 0.873046875}, {"start": 913.6, "end": 913.76, "word": " و", "probability": 0.74609375}, {"start": 913.76, "end": 914.24, "word": " XL", "probability": 0.393310546875}, {"start": 914.24, "end": 914.84, "word": " أصغر", "probability": 0.99365234375}, {"start": 914.84, "end": 915.02, "word": " من", "probability": 0.98828125}, {"start": 915.02, "end": 915.32, "word": " Y", "probability": 0.3984375}, {"start": 915.32, "end": 919.86, "word": " بالمثل", "probability": 0.807373046875}, {"start": 919.86, "end": 920.2, "word": " ممكن", "probability": 0.9267578125}, {"start": 920.2, "end": 920.7, "word": " نعرف", "probability": 0.7039388020833334}, {"start": 920.7, "end": 920.98, "word": " ال", "probability": 0.68212890625}, {"start": 920.98, "end": 921.26, "word": " limit", "probability": 0.70068359375}, {"start": 921.26, "end": 921.56, "word": " from", "probability": 0.91357421875}, {"start": 921.56, "end": 921.86, "word": " the", "probability": 0.9013671875}, {"start": 921.86, "end": 922.2, "word": " right", "probability": 0.90869140625}, {"start": 922.2, "end": 923.78, "word": " يعني", "probability": 0.81396484375}, {"start": 923.78, "end": 923.88, "word": " أنا", "probability": 0.479736328125}, {"start": 923.88, "end": 924.1, "word": " بدي", "probability": 0.6339111328125}, {"start": 924.1, "end": 925.12, "word": " أعرف", "probability": 0.93212890625}, {"start": 925.12, "end": 925.34, "word": " ال", "probability": 0.8603515625}, {"start": 925.34, "end": 925.7, "word": " limit", "probability": 0.95751953125}, {"start": 925.7, "end": 926.12, "word": " from", "probability": 0.9208984375}, {"start": 926.12, "end": 926.38, "word": " the", "probability": 0.91748046875}, {"start": 926.38, "end": 926.7, "word": " right", "probability": 0.9267578125}, {"start": 926.7, "end": 926.96, "word": " أو", "probability": 0.8671875}, {"start": 926.96, "end": 927.12, "word": " ال", "probability": 0.837890625}, {"start": 927.12, "end": 927.4, "word": " right", "probability": 0.88232421875}, {"start": 927.4, "end": 927.8, "word": " hand", "probability": 0.59765625}, {"start": 927.8, "end": 928.22, "word": " limit", "probability": 0.9833984375}], "temperature": 1.0}, {"id": 34, "seek": 95563, "start": 929.39, "end": 955.63, "text": "هي نفس let f be function from A to R و C cluster point للمجموعة A تقاطع الفترة المفتوحة من سالب مالة نهاية إلى C اللي هي كل ال X في A حيث X هتكون أصغر من مرة هذه أصغر من C", "tokens": [3224, 1829, 8717, 36178, 718, 283, 312, 2445, 490, 316, 281, 497, 4032, 383, 13630, 935, 5296, 19528, 7435, 2304, 2407, 27884, 316, 6055, 4587, 41193, 3615, 27188, 2655, 25720, 9673, 5172, 2655, 2407, 5016, 3660, 9154, 8608, 6027, 3555, 3714, 6027, 3660, 8717, 11296, 10632, 30731, 383, 13672, 1829, 39896, 28242, 2423, 1783, 8978, 316, 11331, 1829, 12984, 1783, 8032, 2655, 30544, 5551, 9381, 17082, 2288, 9154, 3714, 25720, 29538, 5551, 9381, 17082, 2288, 9154, 383], "avg_logprob": -0.19340946085942098, "compression_ratio": 1.4207650273224044, "no_speech_prob": 0.0, "words": [{"start": 929.39, "end": 930.19, "word": "هي", "probability": 0.37255859375}, {"start": 930.19, "end": 930.59, "word": " نفس", "probability": 0.927490234375}, {"start": 930.59, "end": 931.25, "word": " let", "probability": 0.53564453125}, {"start": 931.25, "end": 931.55, "word": " f", "probability": 0.62060546875}, {"start": 931.55, "end": 931.73, "word": " be", "probability": 0.84033203125}, {"start": 931.73, "end": 932.27, "word": " function", "probability": 0.5634765625}, {"start": 932.27, "end": 932.81, "word": " from", "probability": 0.8447265625}, {"start": 932.81, "end": 933.13, "word": " A", "probability": 0.46826171875}, {"start": 933.13, "end": 933.29, "word": " to", "probability": 0.962890625}, {"start": 933.29, "end": 933.71, "word": " R", "probability": 0.9853515625}, {"start": 933.71, "end": 934.55, "word": " و", "probability": 0.654296875}, {"start": 934.55, "end": 934.75, "word": " C", "probability": 0.56396484375}, {"start": 934.75, "end": 935.25, "word": " cluster", "probability": 0.755859375}, {"start": 935.25, "end": 935.95, "word": " point", "probability": 0.96484375}, {"start": 935.95, "end": 937.15, "word": " للمجموعة", "probability": 0.88037109375}, {"start": 937.15, "end": 937.45, "word": " A", "probability": 0.92041015625}, {"start": 937.45, "end": 938.47, "word": " تقاطع", "probability": 0.971923828125}, {"start": 938.47, "end": 939.93, "word": " الفترة", "probability": 0.984375}, {"start": 939.93, "end": 940.75, "word": " المفتوحة", "probability": 0.9901529947916666}, {"start": 940.75, "end": 941.01, "word": " من", "probability": 0.98779296875}, {"start": 941.01, "end": 941.61, "word": " سالب", "probability": 0.7491861979166666}, {"start": 941.61, "end": 942.01, "word": " مالة", "probability": 0.5889078776041666}, {"start": 942.01, "end": 942.69, "word": " نهاية", "probability": 0.9583333333333334}, {"start": 942.69, "end": 944.15, "word": " إلى", "probability": 0.8681640625}, {"start": 944.15, "end": 944.87, "word": " C", "probability": 0.8876953125}, {"start": 944.87, "end": 947.39, "word": " اللي", "probability": 0.715087890625}, {"start": 947.39, "end": 947.59, "word": " هي", "probability": 0.857421875}, {"start": 947.59, "end": 947.89, "word": " كل", "probability": 0.96630859375}, {"start": 947.89, "end": 948.07, "word": " ال", "probability": 0.64404296875}, {"start": 948.07, "end": 948.25, "word": " X", "probability": 0.87353515625}, {"start": 948.25, "end": 948.49, "word": " في", "probability": 0.98388671875}, {"start": 948.49, "end": 948.67, "word": " A", "probability": 0.96826171875}, {"start": 948.67, "end": 949.27, "word": " حيث", "probability": 0.97998046875}, {"start": 949.27, "end": 950.85, "word": " X", "probability": 0.8515625}, {"start": 950.85, "end": 952.01, "word": " هتكون", "probability": 0.87158203125}, {"start": 952.01, "end": 952.81, "word": " أصغر", "probability": 0.960693359375}, 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تعريف ال lift hand limit او ال limit from the lift okay تعديل بسيط بس طيب ال limits هذه هنشوف يعني بعد شوية ان ال one sided limits ده functional نقطة", "tokens": [3555, 3794, 297, 4724, 3794, 995, 45865, 441, 43, 1392, 16472, 11296, 37279, 16572, 5172, 2423, 5533, 1011, 4948, 1975, 2407, 2423, 4948, 490, 264, 5533, 1392, 37279, 16254, 1211, 4724, 3794, 1829, 9566, 4724, 3794, 23032, 1829, 3555, 2423, 10406, 29538, 8032, 1863, 8592, 38688, 37495, 22653, 39182, 13412, 2407, 10632, 16472, 2423, 472, 41651, 10406, 11778, 3224, 11745, 8717, 47432, 3660], "avg_logprob": -0.3525390671566129, "compression_ratio": 1.4545454545454546, "no_speech_prob": 0.0, "words": [{"start": 1054.23, "end": 1054.69, "word": "بس", "probability": 0.679931640625}, {"start": 1054.69, "end": 1055.03, "word": " n", "probability": 0.06793212890625}, {"start": 1055.03, "end": 1055.99, "word": " بساوي", "probability": 0.717529296875}, {"start": 1055.99, "end": 1056.53, "word": " LL", "probability": 0.4373779296875}, 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{"start": 1060.83, "end": 1061.17, "word": " lift", "probability": 0.71923828125}, {"start": 1061.17, "end": 1061.83, "word": " okay", "probability": 0.66748046875}, {"start": 1061.83, "end": 1064.89, "word": " تعديل", "probability": 0.6944986979166666}, {"start": 1064.89, "end": 1065.37, "word": " بسيط", "probability": 0.99072265625}, {"start": 1065.37, "end": 1065.89, "word": " بس", "probability": 0.91796875}, {"start": 1065.89, "end": 1070.77, "word": " طيب", "probability": 0.8956705729166666}, {"start": 1070.77, "end": 1071.13, "word": " ال", "probability": 0.97509765625}, {"start": 1071.13, "end": 1072.51, "word": " limits", "probability": 0.845703125}, {"start": 1072.51, "end": 1072.97, "word": " هذه", "probability": 0.47607421875}, {"start": 1072.97, "end": 1073.69, "word": " هنشوف", "probability": 0.961669921875}, {"start": 1073.69, "end": 1074.01, "word": " يعني", "probability": 0.933349609375}, {"start": 1074.01, "end": 1074.31, "word": " بعد", "probability": 0.89990234375}, {"start": 1074.31, "end": 1074.91, "word": " شوية", "probability": 0.9396158854166666}, {"start": 1074.91, "end": 1076.25, "word": " ان", "probability": 0.8330078125}, {"start": 1076.25, "end": 1076.77, "word": " ال", "probability": 0.6640625}, {"start": 1076.77, "end": 1077.73, "word": " one", "probability": 0.52392578125}, {"start": 1077.73, "end": 1078.17, "word": " sided", "probability": 0.564453125}, {"start": 1078.17, "end": 1078.73, "word": " limits", "probability": 0.91845703125}, {"start": 1078.73, "end": 1078.99, "word": " ده", "probability": 0.6942138671875}, {"start": 1078.99, "end": 1079.43, "word": " functional", "probability": 0.5947265625}, {"start": 1079.43, "end": 1080.05, "word": " نقطة", "probability": 0.87744140625}], "temperature": 1.0}, {"id": 40, "seek": 110407, "start": 1081.13, "end": 1104.07, "text": "ممكن يعني التنتين يكونوا موجودين عند النقطة ويلهم نفس القيمة أو ممكن التنتين يكونوا موجودين عند نقطة لكن قيمهم مختلفة زي الـ Signum function عند الصفر شوفنا أن ال limit تبعتها من اليمين واحد و ال limit تبعتها من اليسار ثالث واحد", "tokens": [2304, 43020, 37495, 22653, 16712, 29399, 9957, 7251, 30544, 14407, 3714, 29245, 23328, 9957, 43242, 28239, 47432, 3660, 4032, 26895, 16095, 8717, 36178, 25062, 32640, 3660, 34051, 3714, 43020, 16712, 29399, 9957, 7251, 30544, 14407, 3714, 29245, 23328, 9957, 43242, 8717, 47432, 3660, 44381, 12174, 32640, 16095, 3714, 46456, 46538, 3660, 30767, 1829, 2423, 39184, 13515, 449, 2445, 43242, 31767, 5172, 2288, 13412, 38688, 8315, 14739, 2423, 4948, 6055, 3555, 34268, 11296, 9154, 2423, 32640, 9957, 36764, 24401, 4032, 2423, 4948, 6055, 3555, 34268, 11296, 9154, 45595, 3794, 9640, 38637, 6027, 12984, 36764, 24401], "avg_logprob": -0.15789473276389274, "compression_ratio": 2.0364583333333335, "no_speech_prob": 0.0, "words": [{"start": 1081.13, "end": 1081.73, "word": "ممكن", "probability": 0.800537109375}, {"start": 1081.73, "end": 1082.05, "word": " يعني", "probability": 0.607177734375}, {"start": 1082.05, 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تبعتها", "probability": 0.9366455078125}, {"start": 1102.81, "end": 1102.93, "word": " من", "probability": 0.98388671875}, {"start": 1102.93, "end": 1103.35, "word": " اليسار", "probability": 0.9915364583333334}, {"start": 1103.35, "end": 1103.77, "word": " ثالث", "probability": 0.7211100260416666}, {"start": 1103.77, "end": 1104.07, "word": " واحد", "probability": 0.974609375}], "temperature": 1.0}, {"id": 41, "seek": 112208, "start": 1105.63, "end": 1122.09, "text": "إذا ممكن ال two sided limits يكونوا موجودات لكن they are different مختلفات، ممكن برضه one sided limit تكون موجودة and the other may not exist، ممكن ما تكونش موجودة من أساسه", "tokens": [28814, 15730, 3714, 43020, 2423, 732, 41651, 10406, 7251, 30544, 14407, 3714, 29245, 23328, 9307, 44381, 436, 366, 819, 3714, 46456, 46538, 9307, 12399, 3714, 43020, 4724, 43042, 3224, 472, 41651, 4948, 6055, 30544, 3714, 29245, 23328, 3660, 293, 264, 661, 815, 406, 2514, 12399, 3714, 43020, 19446, 6055, 30544, 8592, 3714, 29245, 23328, 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الأول خلّينا نبرهن النظرية التالية", "tokens": [2304, 43020, 2423, 472, 41651, 10406, 49429, 36764, 24401, 3660, 8978, 16095, 6055, 30544, 3714, 29245, 23328, 3660, 6156, 28820, 21542, 1211, 4587, 9307, 29538, 8032, 1863, 8592, 38688, 11296, 8978, 5551, 2304, 12984, 37977, 20193, 5016, 28671, 44381, 16247, 12610, 16490, 1211, 11703, 9957, 995, 8717, 26890, 3224, 1863, 28239, 19913, 2288, 10632, 16712, 6027, 10632], "avg_logprob": -0.180226293874198, "compression_ratio": 1.4509803921568627, "no_speech_prob": 0.0, "words": [{"start": 1124.8099999999997, "end": 1126.2099999999998, "word": "ممكن", "probability": 0.7734375}, {"start": 1126.2099999999998, "end": 1127.61, "word": " ال", "probability": 0.53173828125}, {"start": 1127.61, "end": 1129.59, "word": " one", "probability": 0.335693359375}, {"start": 1129.59, "end": 1129.95, "word": " sided", "probability": 0.5126953125}, {"start": 1129.95, "end": 1130.45, "word": " limits", "probability": 0.9248046875}, {"start": 1130.45, "end": 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"probability": 0.98759765625}, {"start": 1175.57, "end": 1176.27, "word": " بخصوص", "probability": 0.996484375}, {"start": 1176.27, "end": 1177.33, "word": " ال", "probability": 0.88720703125}, {"start": 1177.33, "end": 1177.63, "word": " left", "probability": 0.9677734375}, {"start": 1177.63, "end": 1178.03, "word": " hand", "probability": 0.82421875}, {"start": 1178.03, "end": 1178.43, "word": " limit", "probability": 0.98291015625}], "temperature": 1.0}, {"id": 44, "seek": 121009, "start": 1181.1, "end": 1210.1, "text": "فعلى سبيل المثال وليس الحصر احنا أخدنا sequential criterion sequential criterion for two sided limit الآن هنكتب برضه sequential criterion for right limit sequential criterion for right hand", "tokens": [5172, 3615, 23942, 8608, 21292, 1211, 9673, 12984, 6027, 4032, 20292, 3794, 21542, 9381, 2288, 1975, 5016, 8315, 5551, 9778, 3215, 8315, 42881, 46691, 42881, 46691, 337, 732, 41651, 4948, 6024, 48506, 8032, 1863, 4117, 2655, 3555, 4724, 43042, 3224, 42881, 46691, 337, 558, 4948, 42881, 46691, 337, 558, 1011], "avg_logprob": -0.1660539239060645, "compression_ratio": 1.6595744680851063, "no_speech_prob": 0.0, "words": [{"start": 1181.1, "end": 1181.54, "word": "فعلى", "probability": 0.8782552083333334}, {"start": 1181.54, "end": 1181.94, "word": " سبيل", "probability": 0.9768880208333334}, {"start": 1181.94, "end": 1182.48, "word": " المثال", "probability": 0.95654296875}, {"start": 1182.48, "end": 1182.98, "word": " وليس", "probability": 0.9020182291666666}, {"start": 1182.98, "end": 1183.58, "word": " الحصر", "probability": 0.97119140625}, {"start": 1183.58, "end": 1185.26, "word": " احنا", "probability": 0.8898111979166666}, {"start": 1185.26, "end": 1185.74, "word": " أخدنا", "probability": 0.9031982421875}, {"start": 1185.74, "end": 1186.24, "word": " sequential", "probability": 0.9140625}, {"start": 1186.24, "end": 1187.14, "word": " criterion", "probability": 0.9658203125}, {"start": 1187.14, "end": 1188.98, "word": " sequential", "probability": 0.5595703125}, {"start": 1188.98, "end": 1189.68, "word": " criterion", "probability": 0.9833984375}, {"start": 1189.68, "end": 1190.2, "word": " for", "probability": 0.96826171875}, {"start": 1190.2, "end": 1190.5, "word": " two", "probability": 0.90283203125}, {"start": 1190.5, "end": 1190.8, "word": " sided", "probability": 0.62109375}, {"start": 1190.8, "end": 1191.24, "word": " limit", "probability": 0.71875}, {"start": 1191.24, "end": 1192.64, "word": " الآن", "probability": 0.58233642578125}, {"start": 1192.64, "end": 1193.42, "word": " هنكتب", "probability": 0.95458984375}, {"start": 1193.42, "end": 1194.1, "word": " برضه", "probability": 0.9765625}, {"start": 1194.1, "end": 1195.22, "word": " sequential", "probability": 0.935546875}, {"start": 1195.22, "end": 1195.9, "word": " criterion", "probability": 0.95556640625}, {"start": 1195.9, "end": 1196.3, "word": " for", "probability": 0.97412109375}, {"start": 1196.3, "end": 1196.58, "word": " right", "probability": 0.445556640625}, {"start": 1196.58, "end": 1196.96, "word": " limit", "probability": 0.90185546875}, {"start": 1196.96, "end": 1199.4, "word": " sequential", "probability": 0.1988525390625}, {"start": 1199.4, "end": 1202.14, "word": " criterion", "probability": 0.98974609375}, {"start": 1202.14, "end": 1204.22, "word": " for", "probability": 0.94091796875}, {"start": 1204.22, "end": 1209.42, "word": " right", "probability": 0.896484375}, {"start": 1209.42, "end": 1210.1, "word": " hand", "probability": 0.771484375}], "temperature": 1.0}, {"id": 45, "seek": 123733, "start": 1225.97, "end": 1237.33, "text": "limits let f from a to r be function and c be cluster", "tokens": [4197, 1208, 718, 283, 490, 257, 281, 367, 312, 2445, 293, 269, 312, 13630], "avg_logprob": -0.3088541706403097, "compression_ratio": 0.9814814814814815, "no_speech_prob": 0.0, "words": [{"start": 1225.9699999999998, "end": 1227.37, "word": "limits", "probability": 0.5631103515625}, {"start": 1227.37, "end": 1228.77, "word": " let", "probability": 0.24267578125}, {"start": 1228.77, "end": 1229.63, "word": " f", "probability": 0.72998046875}, {"start": 1229.63, "end": 1231.09, "word": " from", "probability": 0.87255859375}, {"start": 1231.09, "end": 1231.55, "word": " a", "probability": 0.7373046875}, {"start": 1231.55, "end": 1231.71, "word": " to", "probability": 0.96044921875}, {"start": 1231.71, "end": 1232.25, "word": " r", "probability": 0.9326171875}, {"start": 1232.25, "end": 1233.31, "word": " be", "probability": 0.8544921875}, {"start": 1233.31, "end": 1233.87, "word": " function", "probability": 0.84033203125}, {"start": 1233.87, "end": 1234.61, "word": " and", "probability": 0.94091796875}, {"start": 1234.61, "end": 1235.15, "word": " c", "probability": 0.9609375}, {"start": 1235.15, "end": 1235.67, "word": " be", "probability": 0.912109375}, {"start": 1235.67, "end": 1237.33, "word": " cluster", "probability": 0.75}], "temperature": 1.0}, {"id": 46, "seek": 126603, "start": 1239.23, "end": 1266.03, "text": "point of A then the following statements are equivalent الأبارات التالية متكافئة واحد ال limit ل F of X as X tends to C from the right exist وبساوي عدد L اتنين", "tokens": [6053, 295, 316, 550, 264, 3480, 12363, 366, 10344, 16247, 3555, 9640, 9307, 16712, 6027, 10632, 44650, 4117, 31845, 19986, 3660, 36764, 24401, 2423, 4948, 5296, 479, 295, 1783, 382, 1783, 12258, 281, 383, 490, 264, 558, 2514, 4032, 3555, 3794, 995, 45865, 6225, 3215, 3215, 441, 1975, 2655, 1863, 9957], "avg_logprob": -0.2328725941479206, "compression_ratio": 1.216867469879518, "no_speech_prob": 0.0, "words": [{"start": 1239.23, "end": 1239.85, "word": "point", "probability": 0.7861328125}, {"start": 1239.85, "end": 1241.53, "word": " of", "probability": 0.94091796875}, {"start": 1241.53, "end": 1242.11, "word": " A", "probability": 0.435791015625}, {"start": 1242.11, "end": 1242.57, "word": " then", "probability": 0.5244140625}, {"start": 1242.57, "end": 1245.09, "word": " the", "probability": 0.7216796875}, {"start": 1245.09, "end": 1246.23, "word": " following", "probability": 0.8330078125}, {"start": 1246.23, "end": 1247.39, "word": " statements", "probability": 0.89306640625}, {"start": 1247.39, "end": 1247.91, "word": " are", "probability": 0.958984375}, {"start": 1247.91, "end": 1248.69, "word": " equivalent", "probability": 0.94140625}, {"start": 1248.69, "end": 1250.69, "word": " الأبارات", "probability": 0.64068603515625}, {"start": 1250.69, "end": 1251.23, "word": " التالية", "probability": 0.99365234375}, {"start": 1251.23, "end": 1252.07, "word": " متكافئة", "probability": 0.9380859375}, {"start": 1252.07, "end": 1252.73, "word": " واحد", "probability": 0.750244140625}, {"start": 1252.73, "end": 1253.75, "word": " ال", "probability": 0.43408203125}, {"start": 1253.75, "end": 1254.19, "word": " limit", "probability": 0.87353515625}, {"start": 1254.19, "end": 1255.65, "word": " ل", "probability": 0.76416015625}, {"start": 1255.65, "end": 1256.01, "word": " F", "probability": 0.406005859375}, {"start": 1256.01, "end": 1256.25, "word": " of", "probability": 0.78466796875}, {"start": 1256.25, "end": 1256.61, "word": " X", "probability": 0.97314453125}, {"start": 1256.61, "end": 1257.11, "word": " as", "probability": 0.92236328125}, {"start": 1257.11, "end": 1257.63, "word": " X", "probability": 0.98828125}, {"start": 1257.63, "end": 1258.89, "word": " tends", "probability": 0.86083984375}, {"start": 1258.89, "end": 1259.15, "word": " to", "probability": 0.97802734375}, {"start": 1259.15, "end": 1259.43, "word": " C", "probability": 0.78564453125}, {"start": 1259.43, "end": 1259.75, "word": " from", "probability": 0.9208984375}, {"start": 1259.75, "end": 1259.99, "word": " the", "probability": 0.9169921875}, {"start": 1259.99, "end": 1260.37, "word": " right", "probability": 0.9384765625}, {"start": 1260.37, "end": 1261.81, "word": " exist", "probability": 0.450927734375}, {"start": 1261.81, "end": 1262.67, "word": " وبساوي", "probability": 0.758349609375}, {"start": 1262.67, "end": 1263.25, "word": " عدد", "probability": 0.9822591145833334}, {"start": 1263.25, "end": 1263.63, "word": " L", "probability": 0.7978515625}, {"start": 1263.63, "end": 1266.03, "word": " اتنين", "probability": 0.81939697265625}], "temperature": 1.0}, {"id": 47, "seek": 129653, "start": 1273.83, "end": 1296.53, "text": "for for every sequence x in contained in a تقاطع c و infinity such that", "tokens": [2994, 337, 633, 8310, 2031, 294, 16212, 294, 257, 6055, 4587, 41193, 3615, 269, 4032, 13202, 1270, 300], "avg_logprob": -0.23766447054712395, "compression_ratio": 0.9625, "no_speech_prob": 0.0, "words": [{"start": 1273.83, "end": 1275.23, "word": "for", "probability": 0.493408203125}, {"start": 1275.23, "end": 1276.63, "word": " for", "probability": 0.75}, {"start": 1276.63, "end": 1277.25, "word": " every", "probability": 0.8134765625}, {"start": 1277.25, "end": 1280.37, "word": " sequence", "probability": 0.974609375}, {"start": 1280.37, "end": 1282.85, "word": " x", "probability": 0.84765625}, {"start": 1282.85, "end": 1283.39, "word": " in", "probability": 0.448974609375}, {"start": 1283.39, "end": 1286.17, "word": " contained", "probability": 0.54150390625}, {"start": 1286.17, "end": 1288.67, "word": " in", "probability": 0.95751953125}, {"start": 1288.67, "end": 1289.87, "word": " a", "probability": 0.5927734375}, {"start": 1289.87, "end": 1291.19, "word": " تقاطع", "probability": 0.92236328125}, {"start": 1291.19, "end": 1292.27, "word": " c", "probability": 0.71826171875}, {"start": 1292.27, "end": 1292.53, "word": " و", "probability": 0.9443359375}, {"start": 1292.53, "end": 1293.03, "word": " infinity", "probability": 0.45556640625}, {"start": 1293.03, "end": 1295.99, "word": " such", "probability": 0.9619140625}, {"start": 1295.99, "end": 1296.53, "word": " that", "probability": 0.95849609375}], "temperature": 1.0}, {"id": 48, "seek": 131917, "start": 1298.21, "end": 1319.17, "text": "limit x in as n tends to infinity بيساوي c we have limit لل image of the sequence x in بيساوي العدد L", "tokens": [4197, 270, 2031, 294, 382, 297, 12258, 281, 13202, 4724, 1829, 3794, 995, 45865, 269, 321, 362, 4948, 24976, 3256, 295, 264, 8310, 2031, 294, 4724, 1829, 3794, 995, 45865, 18863, 3215, 3215, 441], "avg_logprob": -0.2609375136239188, "compression_ratio": 1.1214953271028036, "no_speech_prob": 0.0, "words": [{"start": 1298.21, "end": 1298.81, "word": "limit", "probability": 0.63525390625}, {"start": 1298.81, "end": 1299.21, "word": " x", "probability": 0.78759765625}, {"start": 1299.21, "end": 1299.65, "word": " in", "probability": 0.3193359375}, {"start": 1299.65, "end": 1300.13, "word": " as", "probability": 0.9130859375}, {"start": 1300.13, "end": 1300.49, "word": " n", "probability": 0.7275390625}, {"start": 1300.49, "end": 1300.77, "word": " tends", "probability": 0.81103515625}, {"start": 1300.77, "end": 1300.89, "word": " to", "probability": 0.93701171875}, {"start": 1300.89, "end": 1301.45, "word": " infinity", "probability": 0.89697265625}, {"start": 1301.45, "end": 1302.47, "word": " بيساوي", "probability": 0.755517578125}, {"start": 1302.47, "end": 1303.01, "word": " c", "probability": 0.51171875}, {"start": 1303.01, "end": 1304.53, "word": " we", "probability": 0.408447265625}, {"start": 1304.53, "end": 1307.29, "word": " have", "probability": 0.974609375}, {"start": 1307.29, "end": 1311.09, "word": " limit", "probability": 0.728515625}, {"start": 1311.09, "end": 1312.75, "word": " لل", "probability": 0.7109375}, {"start": 1312.75, "end": 1313.25, "word": " image", "probability": 0.499267578125}, {"start": 1313.25, "end": 1313.61, "word": " of", "probability": 0.97412109375}, {"start": 1313.61, "end": 1313.85, "word": " the", "probability": 0.8310546875}, {"start": 1313.85, "end": 1314.45, "word": " sequence", "probability": 0.9814453125}, {"start": 1314.45, "end": 1314.87, "word": " x", "probability": 0.98193359375}, {"start": 1314.87, "end": 1315.45, "word": " in", "probability": 0.84033203125}, {"start": 1315.45, "end": 1318.17, "word": " بيساوي", "probability": 0.9353515625}, {"start": 1318.17, "end": 1318.85, "word": " العدد", "probability": 0.9772135416666666}, {"start": 1318.85, "end": 1319.17, "word": " L", "probability": 0.64599609375}], "temperature": 1.0}, {"id": 49, "seek": 135510, "start": 1330.34, "end": 1355.1, "text": "البرهان شبيه بالبرهان الخاص بالـ two-sided limit فمثلا لو بدنا نبرهن proof لو بدى برهن الأبعار الأولى بتأدي للتانية فبنقول assume .. نبدأ ب assume أن ال limit ال right limit", "tokens": [6027, 26890, 3224, 7649, 13412, 21292, 3224, 20666, 26890, 3224, 7649, 33962, 33546, 20666, 39184, 732, 12, 30941, 4948, 6156, 2304, 12984, 15040, 45164, 47525, 8315, 8717, 26890, 3224, 1863, 8177, 45164, 47525, 7578, 4724, 2288, 3224, 1863, 16247, 3555, 3615, 9640, 16247, 12610, 7578, 39894, 10721, 16254, 24976, 2655, 7649, 10632, 6156, 3555, 1863, 39648, 6552, 4386, 8717, 44510, 10721, 4724, 6552, 14739, 2423, 4948, 2423, 558, 4948], "avg_logprob": -0.2316964247397014, "compression_ratio": 1.5952380952380953, "no_speech_prob": 0.0, "words": [{"start": 1330.34, "end": 1331.26, "word": "البرهان", "probability": 0.96484375}, {"start": 1331.26, "end": 1332.42, "word": " شبيه", "probability": 0.8653971354166666}, {"start": 1332.42, "end": 1335.06, "word": " بالبرهان", "probability": 0.9346923828125}, {"start": 1335.06, "end": 1335.72, "word": " الخاص", "probability": 0.973876953125}, {"start": 1335.72, "end": 1336.02, "word": " بالـ", "probability": 0.6444091796875}, {"start": 1336.02, "end": 1336.24, "word": " two", "probability": 0.72314453125}, {"start": 1336.24, "end": 1336.62, "word": "-sided", "probability": 0.7685546875}, {"start": 1336.62, "end": 1337.06, "word": " limit", "probability": 0.91259765625}, {"start": 1337.06, "end": 1339.08, "word": " فمثلا", "probability": 0.93115234375}, {"start": 1339.08, "end": 1339.82, "word": " لو", "probability": 0.673828125}, {"start": 1339.82, "end": 1340.18, "word": " بدنا", "probability": 0.962890625}, {"start": 1340.18, "end": 1340.9, "word": " نبرهن", "probability": 0.71844482421875}, {"start": 1340.9, "end": 1341.62, "word": " proof", "probability": 0.5625}, {"start": 1341.62, "end": 1342.86, "word": " لو", "probability": 0.818359375}, {"start": 1342.86, "end": 1343.2, "word": " بدى", "probability": 0.544189453125}, {"start": 1343.2, "end": 1343.64, "word": " برهن", "probability": 0.8782958984375}, {"start": 1343.64, "end": 1344.1, "word": " الأبعار", "probability": 0.58392333984375}, {"start": 1344.1, "end": 1344.58, "word": " الأولى", "probability": 0.9833984375}, {"start": 1344.58, "end": 1345.4, "word": " بتأدي", "probability": 0.7711588541666666}, {"start": 1345.4, "end": 1346.48, "word": " للتانية", "probability": 0.934326171875}, {"start": 1346.48, "end": 1349.18, "word": " فبنقول", "probability": 0.9326171875}, {"start": 1349.18, "end": 1350.0, "word": " assume", "probability": 0.84912109375}, {"start": 1350.0, "end": 1350.16, "word": " ..", "probability": 0.444580078125}, {"start": 1350.16, "end": 1350.62, "word": " نبدأ", "probability": 0.9462890625}, {"start": 1350.62, "end": 1350.72, "word": " ب", "probability": 0.916015625}, {"start": 1350.72, "end": 1351.46, "word": " assume", "probability": 0.473388671875}, {"start": 1351.46, "end": 1352.62, "word": " أن", "probability": 0.541015625}, {"start": 1352.62, "end": 1353.02, "word": " ال", "probability": 0.66748046875}, {"start": 1353.02, "end": 1353.46, "word": " limit", "probability": 0.9248046875}, {"start": 1353.46, "end": 1354.28, "word": " ال", "probability": 0.32763671875}, {"start": 1354.28, "end": 1354.64, "word": " right", "probability": 0.90869140625}, {"start": 1354.64, "end": 1355.1, "word": " limit", "probability": 0.98193359375}], "temperature": 1.0}, {"id": 50, "seek": 137626, "start": 1356.36, "end": 1376.26, "text": "الـ F عند الـ C exist بساوي L وبدنا نثبت أن الـ two بيطلع العبارة تنين بتطلع صحيحة لبرهان العبارة to prove two holds", "tokens": [6027, 39184, 479, 43242, 2423, 39184, 383, 2514, 4724, 3794, 995, 45865, 441, 4032, 44510, 8315, 8717, 12984, 3555, 2655, 14739, 2423, 39184, 732, 4724, 1829, 9566, 1211, 3615, 18863, 3555, 9640, 3660, 6055, 1863, 9957, 39894, 9566, 1211, 3615, 20328, 5016, 1829, 5016, 3660, 5296, 26890, 3224, 7649, 18863, 3555, 9640, 3660, 281, 7081, 732, 9190], "avg_logprob": -0.31761852369226257, "compression_ratio": 1.3455882352941178, "no_speech_prob": 0.0, "words": [{"start": 1356.36, "end": 1356.74, "word": "الـ", "probability": 0.586669921875}, {"start": 1356.74, "end": 1357.04, "word": " F", "probability": 0.49658203125}, {"start": 1357.04, "end": 1357.52, "word": " عند", "probability": 0.9228515625}, {"start": 1357.52, "end": 1357.88, "word": " الـ", "probability": 0.7705078125}, {"start": 1357.88, "end": 1358.24, "word": " C", "probability": 0.77587890625}, {"start": 1358.24, "end": 1359.76, "word": " exist", "probability": 0.3125}, {"start": 1359.76, "end": 1360.7, "word": " بساوي", "probability": 0.7476806640625}, {"start": 1360.7, "end": 1361.16, "word": " L", "probability": 0.79541015625}, {"start": 1361.16, "end": 1364.24, "word": " وبدنا", "probability": 0.53826904296875}, {"start": 1364.24, "end": 1364.6, "word": " نثبت", "probability": 0.9918212890625}, {"start": 1364.6, "end": 1364.76, "word": " أن", "probability": 0.436279296875}, {"start": 1364.76, "end": 1364.92, "word": " الـ", "probability": 0.571533203125}, {"start": 1364.92, "end": 1365.1, "word": " two", "probability": 0.58642578125}, {"start": 1365.1, "end": 1365.6, "word": " بيطلع", "probability": 0.824169921875}, {"start": 1365.6, "end": 1366.28, "word": " العبارة", "probability": 0.773468017578125}, {"start": 1366.28, "end": 1367.38, "word": " تنين", "probability": 0.54638671875}, {"start": 1367.38, "end": 1367.8, "word": " بتطلع", "probability": 0.842041015625}, {"start": 1367.8, "end": 1368.68, "word": " صحيحة", "probability": 0.98076171875}, {"start": 1368.68, "end": 1369.6, "word": " لبرهان", "probability": 0.9019775390625}, {"start": 1369.6, "end": 1370.8, "word": " العبارة", "probability": 0.9952392578125}, {"start": 1370.8, "end": 1371.26, "word": " to", "probability": 0.8251953125}, {"start": 1371.26, "end": 1371.84, "word": " prove", "probability": 0.9541015625}, {"start": 1371.84, "end": 1375.4, "word": " two", "probability": 0.919921875}, {"start": 1375.4, "end": 1376.26, "word": " holds", "probability": 0.7060546875}], "temperature": 1.0}, {"id": 51, "seek": 140684, "start": 1379.5, "end": 1406.84, "text": "لت نبدأ لت xn contained in a تقاطع c إلى infinity بsequence such that ال limit تبعتها as n tends to infinity بساوي c إذا أنا باخد sequence في المجموعة a وحدودها كلهم أكبر من c", "tokens": [1211, 2655, 8717, 44510, 10721, 5296, 2655, 2031, 77, 16212, 294, 257, 6055, 4587, 41193, 3615, 269, 30731, 13202, 4724, 11834, 655, 1270, 300, 2423, 4948, 6055, 3555, 34268, 11296, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 269, 11933, 15730, 41850, 4724, 47283, 3215, 8310, 8978, 9673, 7435, 2304, 2407, 27884, 257, 4032, 24401, 23328, 11296, 28242, 16095, 5551, 4117, 26890, 9154, 269], "avg_logprob": -0.27509468974489154, "compression_ratio": 1.3519553072625698, "no_speech_prob": 0.0, "words": [{"start": 1379.5, "end": 1380.0, "word": "لت", "probability": 0.30706787109375}, {"start": 1380.0, "end": 1380.66, "word": " نبدأ", "probability": 0.9557291666666666}, {"start": 1380.66, "end": 1381.38, "word": " لت", "probability": 0.6356201171875}, {"start": 1381.38, "end": 1382.96, "word": " xn", "probability": 0.2958984375}, {"start": 1382.96, "end": 1384.74, "word": " contained", "probability": 0.52978515625}, {"start": 1384.74, "end": 1385.2, "word": " in", "probability": 0.93017578125}, {"start": 1385.2, "end": 1385.52, "word": " a", "probability": 0.37890625}, {"start": 1385.52, "end": 1386.74, "word": " تقاطع", "probability": 0.93701171875}, {"start": 1386.74, "end": 1387.3, "word": " c", "probability": 0.76806640625}, {"start": 1387.3, "end": 1387.68, "word": " إلى", "probability": 0.755859375}, {"start": 1387.68, "end": 1388.32, "word": " infinity", "probability": 0.7333984375}, {"start": 1388.32, "end": 1392.36, "word": " بsequence", "probability": 0.7347819010416666}, {"start": 1392.36, "end": 1393.62, "word": " such", "probability": 0.80126953125}, {"start": 1393.62, "end": 1394.18, "word": " that", "probability": 0.955078125}, {"start": 1394.18, "end": 1395.7, "word": " ال", "probability": 0.55029296875}, {"start": 1395.7, "end": 1396.02, "word": " limit", "probability": 0.8037109375}, {"start": 1396.02, "end": 1396.84, "word": " تبعتها", "probability": 0.90966796875}, {"start": 1396.84, "end": 1397.7, "word": " as", "probability": 0.90478515625}, {"start": 1397.7, "end": 1398.04, "word": " n", "probability": 0.6103515625}, {"start": 1398.04, "end": 1398.3, "word": " tends", "probability": 0.33251953125}, {"start": 1398.3, "end": 1398.42, "word": " to", "probability": 0.9189453125}, {"start": 1398.42, "end": 1399.04, "word": " infinity", "probability": 0.90185546875}, {"start": 1399.04, "end": 1400.5, "word": " بساوي", "probability": 0.82568359375}, {"start": 1400.5, "end": 1400.82, "word": " c", "probability": 0.86474609375}, {"start": 1400.82, "end": 1401.5, "word": " إذا", "probability": 0.42047119140625}, {"start": 1401.5, "end": 1401.7, "word": " أنا", "probability": 0.904296875}, {"start": 1401.7, "end": 1402.08, "word": " باخد", "probability": 0.9541015625}, {"start": 1402.08, "end": 1402.7, "word": " sequence", "probability": 0.95703125}, {"start": 1402.7, "end": 1403.56, "word": " في", "probability": 0.9375}, {"start": 1403.56, "end": 1404.24, "word": " المجموعة", "probability": 0.891748046875}, {"start": 1404.24, "end": 1404.44, "word": " a", "probability": 0.75146484375}, {"start": 1404.44, "end": 1405.12, "word": " وحدودها", "probability": 0.923583984375}, {"start": 1405.12, "end": 1405.72, "word": " كلهم", "probability": 0.93408203125}, {"start": 1405.72, "end": 1406.3, "word": " أكبر", "probability": 0.962890625}, {"start": 1406.3, "end": 1406.5, "word": " من", "probability": 0.99462890625}, {"start": 1406.5, "end": 1406.84, "word": " c", "probability": 0.9453125}], "temperature": 1.0}, {"id": 52, "seek": 143587, "start": 1408.17, "end": 1435.87, "text": "و بفرض أن ال limit لل sequence يادي بيساوي العدد c نحتاج أن نظهر عشان نثبت اتنين باقي نثبت أن ال limit نحتاج أن نظهر أن ال limit لل image of the sequence xn as n tends to infinity بساوي L", "tokens": [2407, 4724, 5172, 43042, 14739, 2423, 4948, 24976, 8310, 7251, 18513, 1829, 4724, 1829, 3794, 995, 45865, 18863, 3215, 3215, 269, 8717, 33753, 26108, 14739, 8717, 19913, 3224, 2288, 6225, 8592, 7649, 8717, 12984, 3555, 2655, 1975, 2655, 1863, 9957, 4724, 995, 38436, 8717, 12984, 3555, 2655, 14739, 2423, 4948, 8717, 33753, 26108, 14739, 8717, 19913, 3224, 2288, 14739, 2423, 4948, 24976, 3256, 295, 264, 8310, 2031, 77, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 441], "avg_logprob": -0.36293511828289754, "compression_ratio": 1.622754491017964, "no_speech_prob": 0.0, "words": [{"start": 1408.17, "end": 1408.51, "word": "و", "probability": 0.396240234375}, {"start": 1408.51, "end": 1409.25, "word": " بفرض", "probability": 0.7413736979166666}, {"start": 1409.25, "end": 1409.43, "word": " أن", "probability": 0.48876953125}, {"start": 1409.43, "end": 1409.59, "word": " ال", "probability": 0.494873046875}, {"start": 1409.59, "end": 1409.91, "word": " limit", "probability": 0.51123046875}, {"start": 1409.91, "end": 1410.41, "word": " لل", "probability": 0.5771484375}, {"start": 1410.41, "end": 1410.79, "word": " sequence", "probability": 0.66064453125}, {"start": 1410.79, "end": 1411.17, "word": " يادي", "probability": 0.3896891276041667}, {"start": 1411.17, "end": 1411.55, "word": " بيساوي", "probability": 0.714794921875}, {"start": 1411.55, "end": 1411.91, "word": " العدد", "probability": 0.7992350260416666}, {"start": 1411.91, "end": 1412.25, "word": " c", "probability": 0.3583984375}, {"start": 1412.25, "end": 1414.95, "word": " نحتاج", "probability": 0.5382486979166666}, {"start": 1414.95, "end": 1415.01, "word": " أن", "probability": 0.38818359375}, {"start": 1415.01, "end": 1415.43, "word": " نظهر", "probability": 0.78326416015625}, {"start": 1415.43, "end": 1418.87, "word": " عشان", "probability": 0.7102864583333334}, {"start": 1418.87, "end": 1420.13, "word": " نثبت", "probability": 0.9912109375}, {"start": 1420.13, "end": 1420.69, "word": " اتنين", "probability": 0.82568359375}, {"start": 1420.69, "end": 1421.97, "word": " باقي", "probability": 0.7742513020833334}, {"start": 1421.97, "end": 1422.59, "word": " نثبت", "probability": 0.9727783203125}, {"start": 1422.59, "end": 1422.89, "word": " أن", "probability": 0.5732421875}, {"start": 1422.89, "end": 1423.29, "word": " ال", "probability": 0.5849609375}, {"start": 1423.29, "end": 1423.75, "word": " limit", "probability": 0.92431640625}, {"start": 1423.75, "end": 1424.61, "word": " نحتاج", "probability": 0.7305501302083334}, {"start": 1424.61, "end": 1424.73, "word": " أن", "probability": 0.58642578125}, {"start": 1424.73, "end": 1425.91, "word": " نظهر", "probability": 0.9835205078125}, {"start": 1425.91, "end": 1426.25, "word": " أن", "probability": 0.4892578125}, {"start": 1426.25, "end": 1426.63, "word": " ال", "probability": 0.65185546875}, {"start": 1426.63, "end": 1427.05, "word": " limit", "probability": 0.92236328125}, {"start": 1427.05, "end": 1429.73, "word": " لل", "probability": 0.82177734375}, {"start": 1429.73, "end": 1430.23, "word": " image", "probability": 0.7939453125}, {"start": 1430.23, "end": 1430.57, "word": " of", "probability": 0.90625}, {"start": 1430.57, "end": 1430.81, "word": " the", "probability": 0.5859375}, {"start": 1430.81, "end": 1431.41, "word": " sequence", "probability": 0.98095703125}, {"start": 1431.41, "end": 1432.23, "word": " xn", "probability": 0.489013671875}, {"start": 1432.23, "end": 1432.73, "word": " as", "probability": 0.85302734375}, {"start": 1432.73, "end": 1433.09, "word": " n", "probability": 0.8173828125}, {"start": 1433.09, "end": 1433.37, "word": " tends", "probability": 0.7490234375}, {"start": 1433.37, "end": 1433.53, "word": " to", "probability": 0.9326171875}, {"start": 1433.53, "end": 1434.09, "word": " infinity", "probability": 0.89794921875}, {"start": 1434.09, "end": 1435.57, "word": " بساوي", "probability": 0.86279296875}, {"start": 1435.57, "end": 1435.87, "word": " L", "probability": 0.8291015625}], "temperature": 1.0}, {"id": 53, "seek": 145113, "start": 1438.29, "end": 1451.13, "text": "هيك بنكون أثبتنا أن العبارة 2 صحيحة، مصبوط، صح؟ طيب لبرهان ذلك to see this", "tokens": [3224, 1829, 4117, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 14739, 18863, 3555, 9640, 3660, 568, 20328, 5016, 1829, 5016, 3660, 12399, 3714, 9381, 3555, 2407, 9566, 12399, 20328, 5016, 22807, 23032, 1829, 3555, 5296, 26890, 3224, 7649, 29910, 23275, 281, 536, 341], "avg_logprob": -0.2244318232617595, "compression_ratio": 1.1272727272727272, "no_speech_prob": 0.0, "words": [{"start": 1438.29, "end": 1438.63, "word": "هيك", "probability": 0.7257486979166666}, {"start": 1438.63, "end": 1438.93, "word": " بنكون", "probability": 0.722900390625}, {"start": 1438.93, "end": 1439.59, "word": " أثبتنا", "probability": 0.97119140625}, {"start": 1439.59, "end": 1440.41, "word": " أن", "probability": 0.55322265625}, {"start": 1440.41, "end": 1441.39, "word": " العبارة", "probability": 0.9561767578125}, {"start": 1441.39, "end": 1441.63, "word": " 2", "probability": 0.459228515625}, {"start": 1441.63, "end": 1442.37, "word": " صحيحة،", "probability": 0.8743896484375}, {"start": 1442.37, "end": 1442.95, "word": " مصبوط،", "probability": 0.6713460286458334}, {"start": 1442.95, "end": 1444.99, "word": " صح؟", "probability": 0.9607747395833334}, {"start": 1444.99, "end": 1445.45, "word": " طيب", "probability": 0.9700520833333334}, {"start": 1445.45, "end": 1446.01, "word": " لبرهان", "probability": 0.8330078125}, {"start": 1446.01, "end": 1447.03, "word": " ذلك", "probability": 0.99560546875}, {"start": 1447.03, "end": 1450.15, "word": " to", "probability": 0.340087890625}, {"start": 1450.15, "end": 1450.71, "word": " see", "probability": 0.9462890625}, {"start": 1450.71, "end": 1451.13, "word": " this", "probability": 0.96875}], "temperature": 1.0}, {"id": 54, "seek": 147241, "start": 1456.09, "end": 1472.41, "text": "بدأ اثبت ان ال limit لل sequence هذه بساوي عدد L فبستخدم تعريف epsilon capital N لل limit فلازم نبدأ with epsilon أكبر من السفر ب given طيب مش احنا فرضين", "tokens": [3555, 3215, 10721, 1975, 12984, 3555, 2655, 16472, 2423, 4948, 24976, 8310, 29538, 4724, 3794, 995, 45865, 6225, 3215, 3215, 441, 6156, 3555, 14851, 9778, 40448, 37279, 16572, 5172, 17889, 4238, 426, 24976, 4948, 6156, 1211, 31377, 2304, 8717, 44510, 10721, 365, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 4724, 2212, 23032, 1829, 3555, 37893, 1975, 5016, 8315, 6156, 43042, 9957], "avg_logprob": -0.28695437737873625, "compression_ratio": 1.3452380952380953, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1456.09, "end": 1456.59, "word": "بدأ", "probability": 0.3612467447916667}, {"start": 1456.59, "end": 1456.83, "word": " اثبت", "probability": 0.837646484375}, {"start": 1456.83, "end": 1456.95, "word": " ان", "probability": 0.78515625}, {"start": 1456.95, "end": 1457.09, "word": " ال", "probability": 0.64013671875}, {"start": 1457.09, "end": 1457.35, "word": " limit", "probability": 0.5595703125}, {"start": 1457.35, "end": 1457.57, "word": " لل", "probability": 0.6591796875}, {"start": 1457.57, "end": 1457.99, "word": " sequence", "probability": 0.77587890625}, {"start": 1457.99, "end": 1458.33, "word": " هذه", "probability": 0.494140625}, {"start": 1458.33, "end": 1458.75, "word": " بساوي", "probability": 0.61834716796875}, {"start": 1458.75, "end": 1459.11, "word": " عدد", "probability": 0.9580078125}, {"start": 1459.11, "end": 1459.39, "word": " L", "probability": 0.447998046875}, {"start": 1459.39, "end": 1460.51, "word": " فبستخدم", "probability": 0.90498046875}, {"start": 1460.51, "end": 1460.97, "word": " تعريف", "probability": 0.9934895833333334}, {"start": 1460.97, "end": 1461.41, "word": " epsilon", "probability": 0.6533203125}, {"start": 1461.41, "end": 1461.83, "word": " capital", "probability": 0.626953125}, {"start": 1461.83, "end": 1462.19, "word": " N", "probability": 0.90576171875}, {"start": 1462.19, "end": 1462.41, "word": " لل", "probability": 0.728515625}, {"start": 1462.41, "end": 1462.81, "word": " limit", "probability": 0.9033203125}, {"start": 1462.81, "end": 1463.89, "word": " فلازم", "probability": 0.9132080078125}, {"start": 1463.89, "end": 1464.31, "word": " نبدأ", "probability": 0.98388671875}, {"start": 1464.31, "end": 1464.53, "word": " with", "probability": 0.2376708984375}, {"start": 1464.53, "end": 1465.33, "word": " epsilon", "probability": 0.91357421875}, 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1617.38, "text": "hence و بالتالي star and double star imply بيؤدوا إلى ما يلي انه لو كانت ال N أكبر من أو ساوي capital N فمن double star", "tokens": [2932, 384, 4032, 20666, 2655, 6027, 1829, 3543, 293, 3834, 3543, 33616, 4724, 1829, 33604, 3215, 14407, 30731, 19446, 7251, 20292, 16472, 3224, 45164, 25961, 2655, 2423, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 6156, 27842, 3834, 3543], "avg_logprob": -0.2436409904513248, "compression_ratio": 1.2748091603053435, "no_speech_prob": 0.0, "words": [{"start": 1590.4800000000002, "end": 1591.8400000000001, "word": "hence", "probability": 0.547576904296875}, {"start": 1591.8400000000001, "end": 1593.2, "word": " و", "probability": 0.294677734375}, {"start": 1593.2, "end": 1594.18, "word": " بالتالي", "probability": 0.85107421875}, {"start": 1594.18, "end": 1596.16, "word": " star", "probability": 0.53173828125}, {"start": 1596.16, "end": 1596.84, "word": " and", "probability": 0.91455078125}, {"start": 1596.84, "end": 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"probability": 0.338623046875}, {"start": 1641.34, "end": 1642.1, "word": " بيقدّي", "probability": 0.677978515625}, {"start": 1642.1, "end": 1643.08, "word": " أن", "probability": 0.397216796875}, {"start": 1643.08, "end": 1644.8, "word": " xn", "probability": 0.849365234375}], "temperature": 1.0}, {"id": 61, "seek": 166936, "start": 1646.36, "end": 1669.36, "text": "minus C أكبر من سفر أصغر من Delta ليه؟ لأن ال XM موجودة تنتمي لإيه؟ هو أكبر من C، لذلك هذا لأن XM أكبر من C", "tokens": [2367, 301, 383, 5551, 4117, 26890, 9154, 8608, 5172, 2288, 5551, 9381, 17082, 2288, 9154, 18183, 32239, 3224, 22807, 5296, 33456, 2423, 1783, 44, 3714, 29245, 23328, 3660, 6055, 29399, 2304, 1829, 5296, 28814, 1829, 3224, 22807, 31439, 5551, 4117, 26890, 9154, 383, 12399, 5296, 8848, 23275, 23758, 5296, 33456, 1783, 44, 5551, 4117, 26890, 9154, 383], "avg_logprob": -0.2727640224941846, "compression_ratio": 1.376, "no_speech_prob": 0.0, "words": [{"start": 1646.36, "end": 1647.04, "word": "minus", "probability": 0.6212158203125}, {"start": 1647.04, "end": 1647.32, "word": " C", "probability": 0.505859375}, {"start": 1647.32, "end": 1647.9, "word": " أكبر", "probability": 0.93603515625}, {"start": 1647.9, "end": 1648.16, "word": " من", "probability": 0.9951171875}, {"start": 1648.16, "end": 1648.68, "word": " سفر", "probability": 0.752685546875}, {"start": 1648.68, "end": 1650.36, "word": " أصغر", "probability": 0.9476318359375}, {"start": 1650.36, "end": 1650.56, "word": " من", "probability": 0.998046875}, {"start": 1650.56, "end": 1650.96, "word": " Delta", "probability": 0.494140625}, {"start": 1650.96, "end": 1653.86, "word": " ليه؟", "probability": 0.728515625}, {"start": 1653.86, "end": 1654.32, "word": " لأن", "probability": 0.96240234375}, {"start": 1654.32, "end": 1654.52, "word": " ال", "probability": 0.64306640625}, {"start": 1654.52, "end": 1655.4, "word": " XM", "probability": 0.49957275390625}, {"start": 1655.4, "end": 1658.12, "word": " موجودة", "probability": 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exercises يعني اتمرنوا عليها", "tokens": [3322, 42881, 46691, 337, 732, 12, 30941, 4948, 11900, 37495, 22653, 1975, 2655, 29973, 1863, 14407, 25894, 11296], "avg_logprob": -0.32915295425214264, "compression_ratio": 0.967391304347826, "no_speech_prob": 0.0, "words": [{"start": 1884.13, "end": 1884.51, "word": "the", "probability": 0.1903076171875}, {"start": 1884.51, "end": 1885.31, "word": " sequential", "probability": 0.96630859375}, {"start": 1885.31, "end": 1886.45, "word": " criterion", "probability": 0.962890625}, {"start": 1886.45, "end": 1889.19, "word": " for", "probability": 0.951171875}, {"start": 1889.19, "end": 1890.37, "word": " two", "probability": 0.90234375}, {"start": 1890.37, "end": 1891.25, "word": "-sided", "probability": 0.70361328125}, {"start": 1891.25, "end": 1894.57, "word": " limit", "probability": 0.6982421875}, {"start": 1894.57, "end": 1905.85, "word": " exercises", "probability": 0.1864013671875}, {"start": 1905.85, "end": 1906.93, "word": " يعني", 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"text": "Okay فيعني احنا مش هنكتب طبعا نظرية دي هنعتبرها نظرية قائمة و صحيحة و مش بدون برهان okay تمام؟", "tokens": [8297, 6156, 40228, 22653, 1975, 5016, 8315, 37893, 8032, 1863, 4117, 2655, 3555, 23032, 3555, 3615, 995, 8717, 19913, 2288, 10632, 11778, 1829, 8032, 1863, 34268, 26890, 11296, 8717, 19913, 2288, 10632, 12174, 16373, 46007, 4032, 20328, 5016, 1829, 5016, 3660, 4032, 37893, 47525, 11536, 4724, 2288, 3224, 7649, 1392, 46811, 10943, 22807], "avg_logprob": -0.13953992503660698, "compression_ratio": 1.35, "no_speech_prob": 0.0, "words": [{"start": 1961.04, "end": 1961.48, "word": "Okay", "probability": 0.9130859375}, {"start": 1961.48, "end": 1962.62, "word": " فيعني", "probability": 0.7688802083333334}, {"start": 1962.62, "end": 1962.82, "word": " احنا", "probability": 0.95849609375}, {"start": 1962.82, "end": 1963.0, "word": " مش", "probability": 0.9931640625}, {"start": 1963.0, "end": 1963.42, "word": " هنكتب", "probability": 0.97265625}, {"start": 1963.42, "end": 1963.72, 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2152.02, "end": 2177.78, "text": "بالبرهان البرهان يعني كتير سهل ينتج من التعريفات proof ف .. هحاول أبرهنلكم ال F part هذا مسمى ال F part يعني هفرض أنه assume أنه ال one sided limits", "tokens": [3555, 6027, 26890, 3224, 7649, 2423, 26890, 3224, 7649, 37495, 22653, 9122, 2655, 13546, 8608, 3224, 1211, 7251, 29399, 7435, 9154, 16712, 3615, 16572, 5172, 9307, 8177, 6156, 4386, 8032, 5016, 995, 12610, 5551, 26890, 3224, 1863, 23275, 2304, 2423, 479, 644, 23758, 3714, 38251, 7578, 2423, 479, 644, 37495, 22653, 8032, 5172, 43042, 14739, 3224, 6552, 14739, 3224, 2423, 472, 41651, 10406], "avg_logprob": -0.19604492210783064, "compression_ratio": 1.4556962025316456, "no_speech_prob": 0.0, "words": [{"start": 2152.02, "end": 2152.84, "word": "بالبرهان", "probability": 0.8900390625}, {"start": 2152.84, "end": 2154.56, "word": " البرهان", "probability": 0.8814697265625}, {"start": 2154.56, "end": 2154.98, "word": " يعني", "probability": 0.9365234375}, {"start": 2154.98, "end": 2155.48, "word": " 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"seek": 265587, "start": 2642.17, "end": 2655.87, "text": "طب ما هذا هو تعريف epsilon delta لل limit of function صح؟ إذا نيجي بنقول هنا since epsilon أكبر من السفر was arbitrary", "tokens": [9566, 3555, 19446, 23758, 31439, 37279, 16572, 5172, 17889, 8289, 24976, 4948, 295, 2445, 20328, 5016, 22807, 11933, 15730, 8717, 1829, 7435, 1829, 44945, 39648, 34105, 1670, 17889, 5551, 4117, 26890, 9154, 21136, 5172, 2288, 390, 23211], "avg_logprob": -0.24979440318910698, "compression_ratio": 1.1726618705035972, "no_speech_prob": 0.0, "words": [{"start": 2642.17, "end": 2642.49, "word": "طب", "probability": 0.76513671875}, {"start": 2642.49, "end": 2642.63, "word": " ما", "probability": 0.26171875}, {"start": 2642.63, "end": 2642.83, "word": " هذا", "probability": 0.80322265625}, {"start": 2642.83, "end": 2643.11, "word": " هو", "probability": 0.98095703125}, {"start": 2643.11, "end": 2643.77, "word": " تعريف", "probability": 0.99267578125}, {"start": 2643.77, "end": 2644.25, "word": " epsilon", 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"probability": 0.798828125}, {"start": 2651.81, "end": 2652.27, "word": " أكبر", "probability": 0.9485677083333334}, {"start": 2652.27, "end": 2652.47, "word": " من", "probability": 0.99462890625}, {"start": 2652.47, "end": 2653.05, "word": " السفر", "probability": 0.7809244791666666}, {"start": 2653.05, "end": 2653.73, "word": " was", "probability": 0.95068359375}, {"start": 2653.73, "end": 2655.87, "word": " arbitrary", "probability": 0.85546875}], "temperature": 1.0}, {"id": 99, "seek": 268493, "start": 2657.41, "end": 2684.93, "text": "إذا احنا بنكون أثبتنا لكل إبسلون أكبر من سفر يوجد Delta تعتمد على إبسلون عدد موجب بحيث لكل X تنتمي ل A و Absolute X minus C أكبر من سفر أصغر من Delta طلع عندي Absolute F of X في الحالتين minus L أصغر من إبسلون وبالتالي إذا هذا صحيح لكل إبسلون وبالتالي by إبسلون Delta definition of limit", "tokens": [28814, 15730, 1975, 5016, 8315, 44945, 30544, 5551, 12984, 3555, 2655, 8315, 5296, 28820, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 8608, 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موجودين متساويتين، لأ لو كان ال one sided limits", "tokens": [10721, 2407, 2445, 321, 362, 5551, 12984, 3555, 2655, 8315, 14739, 2423, 4948, 5296, 283, 295, 2031, 382, 2031, 12258, 281, 269, 4724, 3794, 995, 45865, 18863, 3215, 3215, 441, 1392, 46811, 10943, 12399, 11933, 15730, 23758, 4724, 12984, 3555, 2655, 13672, 1829, 31439, 45164, 25961, 2423, 732, 41651, 10406, 3714, 29245, 23328, 9957, 44650, 3794, 995, 45865, 2655, 9957, 12399, 5296, 10721, 45164, 25961, 2423, 472, 41651, 10406], "avg_logprob": -0.2899553430931909, "compression_ratio": 1.5057471264367817, "no_speech_prob": 0.0, "words": [{"start": 2685.38, "end": 2685.62, "word": "أو", "probability": 0.4063720703125}, {"start": 2685.62, "end": 2686.1, "word": " function", "probability": 0.2259521484375}, {"start": 2686.1, "end": 2687.0, "word": " we", "probability": 0.278076171875}, {"start": 2687.0, "end": 2687.7, "word": " have", "probability": 0.9560546875}, {"start": 2687.7, "end": 2689.5, "word": " أثبتنا", "probability": 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