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+{"segments": [{"id": 1, "seek": 4285, "start": 20.89, "end": 42.85, "text": "أحنا هنكمل الموضوع لـ Properly Divergent Sequences اللي بدأناه المحاضرة السابقة فشوفنا في المحاضرة السابقة تعريف ما معنى أنه limit ل sequence xn بساوي infinity وما معنى أنه limit ل sequence xn بساوي negative infinity", "tokens": [10721, 5016, 8315, 8032, 1863, 24793, 1211, 9673, 2407, 11242, 45367, 5296, 39184, 27627, 356, 413, 1837, 6930, 46859, 2667, 13672, 1829, 47525, 10721, 8315, 3224, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 6156, 8592, 38688, 8315, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 37279, 16572, 5172, 19446, 20449, 1863, 7578, 14739, 3224, 4948, 5296, 8310, 2031, 77, 4724, 3794, 995, 45865, 13202, 4032, 15042, 20449, 1863, 7578, 14739, 3224, 4948, 5296, 8310, 2031, 77, 4724, 3794, 995, 45865, 3671, 13202], "avg_logprob": -0.17752259036144577, "compression_ratio": 1.7282608695652173, "no_speech_prob": 0.0, "words": [{"start": 20.89, "end": 21.89, "word": "أحنا", "probability": 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تبعتي هذه أكبر من أو ساوي M وبالتالي XN أصغر من أو ساوي YN وكذلك ال N لما تكون ال N أكبر من أو ساوي N", "tokens": [10721, 4117, 26890, 9154, 34051, 8608, 995, 45865, 376, 4032, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 426, 295, 9861, 46599, 6027, 2655, 6027, 1829, 5296, 15042, 5551, 7435, 1829, 5551, 9778, 3215, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 4238, 426, 4724, 10721, 11242, 27842, 14739, 2423, 426, 6055, 3555, 3615, 31371, 29538, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 376, 46599, 6027, 2655, 6027, 1829, 1783, 45, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 398, 45, 4032, 4117, 8848, 23275, 2423, 426, 5296, 15042, 6055, 30544, 2423, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 45865, 426], "avg_logprob": -0.1594929242471479, "compression_ratio": 2.2, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 417.0, "end": 417.56, "word": "أكبر", "probability": 0.7646484375}, {"start": 417.56, "end": 417.78, "word": " من", 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{"start": 436.34, "end": 436.52, "word": " أو", "probability": 0.99169921875}, {"start": 436.52, "end": 436.8, "word": " ساوي", "probability": 0.9794921875}, {"start": 436.8, "end": 437.82, "word": " YN", "probability": 0.92626953125}, {"start": 437.82, "end": 442.94, "word": " وكذلك", "probability": 0.9195556640625}, {"start": 442.94, "end": 443.22, "word": " ال", "probability": 0.720703125}, {"start": 443.22, "end": 443.48, "word": " N", "probability": 0.92431640625}, {"start": 443.48, "end": 443.74, "word": " لما", "probability": 0.947021484375}, {"start": 443.74, "end": 444.06, "word": " تكون", "probability": 0.99072265625}, {"start": 444.06, "end": 444.24, "word": " ال", "probability": 0.7626953125}, {"start": 444.24, "end": 444.54, "word": " N", "probability": 0.9423828125}, {"start": 444.54, "end": 445.14, "word": " أكبر", "probability": 0.98193359375}, {"start": 445.14, "end": 445.32, "word": " من", "probability": 0.9970703125}, {"start": 445.32, "end": 445.5, "word": " أو", 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464.96, "word": " طبعا", "probability": 0.993896484375}, {"start": 464.96, "end": 465.4, "word": " ممكن", "probability": 0.9794921875}, {"start": 465.4, "end": 466.46, "word": " نعطيه", "probability": 0.8708984375}, {"start": 466.46, "end": 466.74, "word": " في", "probability": 0.77587890625}, {"start": 466.74, "end": 467.08, "word": " حالة", "probability": 0.99267578125}, {"start": 467.08, "end": 467.34, "word": " لما", "probability": 0.8974609375}, {"start": 467.34, "end": 467.72, "word": " يكون", "probability": 0.7470703125}, {"start": 467.72, "end": 468.0, "word": " بدي", "probability": 0.64990234375}, {"start": 468.0, "end": 468.3, "word": " أبرهن", "probability": 0.88525390625}, {"start": 468.3, "end": 468.68, "word": " الجزء", "probability": 0.9736328125}, {"start": 468.68, "end": 468.96, "word": " A", "probability": 0.9580078125}, {"start": 468.96, "end": 469.62, "word": " فباخد", "probability": 0.947021484375}, {"start": 469.62, "end": 469.76, "word": " ال", "probability": 0.97265625}, {"start": 469.76, "end": 469.96, "word": " N", "probability": 0.63232421875}, {"start": 469.96, "end": 470.9, "word": " المطلوبة", "probability": 0.98486328125}, {"start": 470.9, "end": 471.44, "word": " هي", "probability": 0.875}, {"start": 471.44, "end": 471.6, "word": " ال", "probability": 0.422119140625}, {"start": 471.6, "end": 472.0, "word": " maximum", "probability": 0.97900390625}, {"start": 472.0, "end": 472.3, "word": " ل", "probability": 0.98046875}, {"start": 472.3, "end": 472.56, "word": " M", "probability": 0.79248046875}, {"start": 472.56, "end": 472.96, "word": " وN", "probability": 0.782958984375}, {"start": 472.96, "end": 473.12, "word": " of", "probability": 0.96630859375}, {"start": 473.12, "end": 473.54, "word": " alpha", "probability": 0.430419921875}, {"start": 473.54, "end": 474.26, "word": " في", "probability": 0.7490234375}, {"start": 474.26, "end": 474.82, "word": " برهان", "probability": 0.959716796875}, {"start": 474.82, "end": 475.24, "word": " A", "probability": 0.91064453125}, {"start": 475.24, "end": 475.82, "word": " تحت", "probability": 0.986572265625}, {"start": 475.82, "end": 476.28, "word": " شرط", "probability": 0.9010416666666666}, {"start": 476.28, "end": 476.66, "word": " star", "probability": 0.60205078125}], "temperature": 1.0}, {"id": 17, "seek": 50766, "start": 478.34, "end": 507.66, "text": "هذه أول ملاحظة الملاحظة التانية الملاحظة التانية if condition star holds إذا كان الشرط star holds then", "tokens": [3224, 24192, 5551, 12610, 3714, 15040, 5016, 19913, 3660, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632, 9673, 15040, 5016, 19913, 3660, 16712, 7649, 10632, 498, 4188, 3543, 9190, 11933, 15730, 25961, 25124, 2288, 9566, 3543, 9190, 550], "avg_logprob": -0.1271033669129396, "compression_ratio": 1.5196078431372548, "no_speech_prob": 0.0, "words": [{"start": 478.34, "end": 478.68, "word": "هذه", "probability": 0.814208984375}, {"start": 478.68, "end": 478.92, "word": " أول", "probability": 0.8212890625}, {"start": 478.92, "end": 479.7, "word": " ملاحظة", "probability": 0.98134765625}, {"start": 479.7, "end": 480.68, "word": " الملاحظة", "probability": 0.95732421875}, {"start": 480.68, "end": 481.6, "word": " التانية", "probability": 0.9773763020833334}, {"start": 481.6, "end": 495.36, "word": " الملاحظة", "probability": 0.9798828125}, {"start": 495.36, "end": 496.46, "word": " التانية", "probability": 0.9928385416666666}, {"start": 496.46, "end": 498.28, "word": " if", "probability": 0.7685546875}, {"start": 498.28, "end": 499.18, "word": " condition", "probability": 0.921875}, {"start": 499.18, "end": 501.5, "word": " star", "probability": 0.748046875}, {"start": 501.5, "end": 502.18, "word": " holds", "probability": 0.74951171875}, {"start": 502.18, "end": 504.44, "word": " إذا", "probability": 0.669189453125}, {"start": 504.44, "end": 504.66, "word": " كان", "probability": 0.79296875}, {"start": 504.66, "end": 505.06, "word": " الشرط", "probability": 0.8548177083333334}, {"start": 505.06, "end": 505.48, "word": " star", "probability": 0.8271484375}, {"start": 505.48, "end": 505.98, "word": " holds", "probability": 0.775390625}, {"start": 505.98, "end": 507.66, "word": " then", "probability": 0.79833984375}], "temperature": 1.0}, {"id": 18, "seek": 52665, "start": 517.13, "end": 526.65, "text": "النتيجة ان y in tends to infinity does not necessarily implies ان x in tends to infinity", "tokens": [6027, 29399, 1829, 7435, 3660, 16472, 288, 294, 12258, 281, 13202, 775, 406, 4725, 18779, 16472, 2031, 294, 12258, 281, 13202], "avg_logprob": -0.4055397618900646, "compression_ratio": 1.1927710843373494, "no_speech_prob": 0.0, "words": [{"start": 517.13, "end": 518.05, "word": "النتيجة", "probability": 0.8849609375}, {"start": 518.05, "end": 518.27, "word": " ان", "probability": 0.48388671875}, {"start": 518.27, "end": 518.61, "word": " y", "probability": 0.16796875}, {"start": 518.61, "end": 519.05, "word": " in", "probability": 0.232177734375}, {"start": 519.05, "end": 519.63, "word": " tends", "probability": 0.50927734375}, {"start": 519.63, "end": 519.79, "word": " to", "probability": 0.89599609375}, {"start": 519.79, "end": 520.35, "word": " infinity", "probability": 0.87109375}, {"start": 520.35, "end": 521.75, "word": " does", "probability": 0.396240234375}, {"start": 521.75, "end": 522.07, "word": " not", "probability": 0.958984375}, {"start": 522.07, "end": 522.79, "word": " necessarily", "probability": 0.7431640625}, {"start": 522.79, "end": 523.79, "word": " implies", "probability": 0.8857421875}, {"start": 523.79, "end": 524.69, "word": " ان", "probability": 0.76171875}, {"start": 524.69, "end": 525.11, "word": " x", "probability": 0.90380859375}, {"start": 525.11, "end": 525.51, "word": " in", "probability": 0.9521484375}, {"start": 525.51, "end": 525.97, "word": " tends", "probability": 0.387939453125}, {"start": 525.97, "end": 526.11, "word": " to", "probability": 0.9091796875}, {"start": 526.11, "end": 526.65, "word": " infinity", "probability": 0.8916015625}], "temperature": 1.0}, {"id": 19, "seek": 56023, "start": 533.43, "end": 560.23, "text": "وكان limit ال yn بساوي infinity فليس من الضروري ان يكون limit xn بساوي infinity وهي مثال يوضح ذلك for example على سبيل المثال consider consider ال sequence 1 على n أصغر من أو بساوي n لكل n في n", "tokens": [2407, 41361, 4948, 2423, 288, 77, 4724, 3794, 995, 45865, 13202, 6156, 20292, 3794, 9154, 6024, 114, 2288, 13063, 1829, 16472, 7251, 30544, 4948, 2031, 77, 4724, 3794, 995, 45865, 13202, 37037, 1829, 50113, 6027, 7251, 2407, 11242, 5016, 29910, 23275, 337, 1365, 15844, 8608, 21292, 1211, 9673, 12984, 6027, 1949, 1949, 2423, 8310, 502, 15844, 297, 5551, 9381, 17082, 2288, 9154, 34051, 4724, 3794, 995, 45865, 297, 5296, 28820, 297, 8978, 297], "avg_logprob": -0.16986908662963557, "compression_ratio": 1.5706214689265536, "no_speech_prob": 0.0, "words": [{"start": 533.43, "end": 534.01, "word": "وكان", "probability": 0.79638671875}, {"start": 534.01, "end": 534.49, "word": " limit", "probability": 0.82958984375}, {"start": 534.49, "end": 535.41, "word": " ال", "probability": 0.336669921875}, {"start": 535.41, "end": 535.87, "word": " yn", "probability": 0.220245361328125}, {"start": 535.87, "end": 536.41, "word": " بساوي", "probability": 0.70458984375}, {"start": 536.41, "end": 536.97, "word": " infinity", "probability": 0.7685546875}, {"start": 536.97, "end": 538.37, "word": " فليس", "probability": 0.88427734375}, {"start": 538.37, "end": 538.57, "word": " من", "probability": 0.9912109375}, {"start": 538.57, "end": 539.55, "word": " الضروري", "probability": 0.9466796875}, {"start": 539.55, "end": 540.27, "word": " ان", "probability": 0.5302734375}, {"start": 540.27, "end": 540.79, "word": " يكون", "probability": 0.94775390625}, {"start": 540.79, "end": 541.25, "word": " limit", "probability": 0.96826171875}, {"start": 541.25, "end": 541.79, "word": " xn", "probability": 0.955078125}, {"start": 541.79, "end": 542.35, "word": " بساوي", "probability": 0.9522705078125}, {"start": 542.35, "end": 542.89, "word": " infinity", "probability": 0.82958984375}, {"start": 542.89, "end": 543.69, "word": " وهي", "probability": 0.5765380859375}, {"start": 543.69, "end": 544.17, "word": " مثال", "probability": 0.967041015625}, {"start": 544.17, "end": 544.67, "word": " يوضح", "probability": 0.9853515625}, {"start": 544.67, "end": 545.19, "word": " ذلك", "probability": 0.994873046875}, {"start": 545.19, "end": 546.09, "word": " for", "probability": 0.69189453125}, {"start": 546.09, "end": 546.67, "word": " example", "probability": 0.9599609375}, {"start": 546.67, "end": 546.91, "word": " على", "probability": 0.83544921875}, {"start": 546.91, "end": 547.35, "word": " سبيل", "probability": 0.9851888020833334}, {"start": 547.35, "end": 548.03, "word": " المثال", "probability": 0.9866536458333334}, {"start": 548.03, "end": 550.49, "word": " consider", "probability": 0.9150390625}, {"start": 550.49, "end": 553.55, "word": " consider", "probability": 0.72802734375}, {"start": 553.55, "end": 553.71, "word": " ال", "probability": 0.48486328125}, {"start": 553.71, "end": 554.05, "word": " sequence", "probability": 0.97412109375}, {"start": 554.05, "end": 554.59, "word": " 1", "probability": 0.55029296875}, {"start": 554.59, "end": 554.97, "word": " على", "probability": 0.62744140625}, {"start": 554.97, "end": 555.39, "word": " n", "probability": 0.86328125}, {"start": 555.39, "end": 556.05, "word": " أصغر", "probability": 0.9461669921875}, {"start": 556.05, "end": 556.25, "word": " من", "probability": 0.9677734375}, {"start": 556.25, "end": 556.43, "word": " أو", "probability": 0.75439453125}, {"start": 556.43, "end": 556.99, "word": " بساوي", "probability": 0.895263671875}, {"start": 556.99, "end": 557.33, "word": " n", "probability": 0.744140625}, {"start": 557.33, "end": 558.99, "word": " لكل", "probability": 0.962890625}, {"start": 558.99, "end": 559.49, "word": " n", "probability": 0.87646484375}, {"start": 559.49, "end": 559.81, "word": " في", "probability": 0.98095703125}, {"start": 559.81, "end": 560.23, "word": " n", "probability": 0.80908203125}], "temperature": 1.0}, {"id": 20, "seek": 58961, "start": 561.99, "end": 589.61, "text": "إذن هى انا عندي xn وهى عندي yn وهى xn أصغر من يساوي yn الشرط الصغير متحقق لكن أنا عندي ال limit ل sequence yn اللى الحد العام تبعها n هدى بساوي infinity but ال limit ل xn اللى هى واحد على n", "tokens": [28814, 8848, 1863, 8032, 7578, 1975, 8315, 18871, 16254, 2031, 77, 37037, 7578, 18871, 16254, 17861, 37037, 7578, 2031, 77, 5551, 9381, 17082, 2288, 9154, 7251, 3794, 995, 45865, 17861, 25124, 2288, 9566, 2423, 9381, 17082, 13546, 44650, 5016, 4587, 4587, 44381, 41850, 18871, 16254, 2423, 4948, 5296, 8310, 17861, 13672, 7578, 21542, 3215, 18863, 10943, 6055, 3555, 3615, 11296, 297, 8032, 3215, 7578, 4724, 3794, 995, 45865, 13202, 457, 2423, 4948, 5296, 2031, 77, 13672, 7578, 8032, 7578, 36764, 24401, 15844, 297], "avg_logprob": -0.30189731397799086, "compression_ratio": 1.69364161849711, "no_speech_prob": 0.0, "words": [{"start": 561.99, "end": 562.37, "word": "إذن", "probability": 0.5745442708333334}, {"start": 562.37, "end": 562.61, "word": " هى", "probability": 0.353515625}, {"start": 562.61, "end": 562.79, "word": " انا", "probability": 0.760986328125}, {"start": 562.79, "end": 563.15, "word": " عندي", "probability": 0.784912109375}, {"start": 563.15, "end": 563.83, "word": " xn", "probability": 0.493408203125}, {"start": 563.83, "end": 564.59, "word": " وهى", "probability": 0.677490234375}, {"start": 564.59, "end": 564.89, "word": " عندي", "probability": 0.958251953125}, {"start": 564.89, "end": 565.45, "word": " yn", "probability": 0.91259765625}, {"start": 565.45, "end": 566.69, "word": " وهى", "probability": 0.89453125}, {"start": 566.69, "end": 567.27, "word": " xn", "probability": 0.974365234375}, {"start": 567.27, "end": 567.73, "word": " أصغر", "probability": 0.9178466796875}, {"start": 567.73, "end": 567.89, "word": " من", "probability": 0.96533203125}, {"start": 567.89, "end": 568.41, "word": " يساوي", "probability": 0.5680389404296875}, {"start": 568.41, "end": 568.95, "word": " yn", "probability": 0.74267578125}, {"start": 568.95, "end": 569.99, "word": " الشرط", "probability": 0.9580078125}, {"start": 569.99, "end": 570.31, "word": " الصغير", "probability": 0.53790283203125}, {"start": 570.31, "end": 571.01, "word": " متحقق", "probability": 0.938720703125}, {"start": 571.01, "end": 572.89, "word": " لكن", "probability": 0.86767578125}, {"start": 572.89, "end": 573.13, "word": " أنا", "probability": 0.572265625}, {"start": 573.13, "end": 573.51, "word": " عندي", "probability": 0.95751953125}, {"start": 573.51, "end": 573.75, "word": " ال", "probability": 0.80810546875}, {"start": 573.75, "end": 574.09, "word": " limit", "probability": 0.93212890625}, {"start": 574.09, "end": 575.45, "word": " ل", "probability": 0.6201171875}, {"start": 575.45, "end": 576.07, "word": " sequence", "probability": 0.383544921875}, {"start": 576.07, "end": 576.83, "word": " yn", "probability": 0.84716796875}, {"start": 576.83, "end": 577.09, "word": " اللى", "probability": 0.869873046875}, {"start": 577.09, "end": 577.47, "word": " الحد", "probability": 0.889892578125}, {"start": 577.47, "end": 577.73, "word": " العام", "probability": 0.86669921875}, {"start": 577.73, "end": 578.21, "word": " تبعها", "probability": 0.81396484375}, {"start": 578.21, "end": 578.47, "word": " n", "probability": 0.7412109375}, {"start": 578.47, "end": 578.91, "word": " هدى", "probability": 0.6095377604166666}, {"start": 578.91, "end": 579.33, "word": " بساوي", "probability": 0.73388671875}, {"start": 579.33, "end": 579.87, "word": " infinity", "probability": 0.8828125}, {"start": 579.87, "end": 582.55, "word": " but", "probability": 0.7275390625}, {"start": 582.55, "end": 585.43, "word": " ال", "probability": 0.73291015625}, {"start": 585.43, "end": 585.81, "word": " limit", "probability": 0.97314453125}, {"start": 585.81, "end": 587.19, "word": " ل", "probability": 0.9658203125}, {"start": 587.19, "end": 587.95, "word": " xn", "probability": 0.833251953125}, {"start": 587.95, "end": 588.29, "word": " اللى", "probability": 0.985107421875}, {"start": 588.29, "end": 588.55, "word": " هى", "probability": 0.849609375}, {"start": 588.55, "end": 589.05, "word": " واحد", "probability": 0.88623046875}, {"start": 589.05, "end": 589.27, "word": " على", "probability": 0.6064453125}, {"start": 589.27, "end": 589.61, "word": " n", "probability": 0.845703125}], "temperature": 1.0}, {"id": 21, "seek": 61660, "start": 590.84, "end": 616.6, "text": "بساوي سفر لا تساوي infinity السفر لا يساوي infinity okay تمام إذا الشرط star ما بيخلنيش أستنتج أنه limit x in بالساوية infinity عندما limit y in بالساوية infinity بالمثل if condition star holds", "tokens": [3555, 3794, 995, 45865, 8608, 5172, 2288, 20193, 6055, 3794, 995, 45865, 13202, 21136, 5172, 2288, 20193, 7251, 3794, 995, 45865, 13202, 1392, 46811, 10943, 11933, 15730, 25124, 2288, 9566, 3543, 19446, 4724, 1829, 9778, 1211, 22653, 8592, 5551, 14851, 29399, 7435, 14739, 3224, 4948, 2031, 294, 20666, 3794, 995, 2407, 10632, 13202, 43242, 15042, 4948, 288, 294, 20666, 3794, 995, 2407, 10632, 13202, 20666, 2304, 12984, 1211, 498, 4188, 3543, 9190], "avg_logprob": -0.2564212394087282, "compression_ratio": 1.6890243902439024, "no_speech_prob": 0.0, "words": [{"start": 590.84, "end": 591.44, "word": "بساوي", "probability": 0.63128662109375}, {"start": 591.44, "end": 591.84, "word": " سفر", "probability": 0.7852376302083334}, {"start": 591.84, "end": 593.8, "word": " لا", "probability": 0.47216796875}, {"start": 593.8, "end": 594.44, "word": " تساوي", "probability": 0.9468994140625}, {"start": 594.44, "end": 594.92, "word": " infinity", "probability": 0.56494140625}, {"start": 594.92, "end": 596.52, "word": " السفر", "probability": 0.90869140625}, {"start": 596.52, "end": 596.68, "word": " لا", "probability": 0.95068359375}, {"start": 596.68, "end": 597.22, "word": " يساوي", "probability": 0.978271484375}, {"start": 597.22, "end": 597.64, "word": " infinity", "probability": 0.75927734375}, {"start": 597.64, "end": 599.86, "word": " okay", "probability": 0.347900390625}, {"start": 599.86, "end": 600.4, "word": " تمام", "probability": 0.738525390625}, {"start": 600.4, "end": 601.64, "word": " إذا", "probability": 0.42596435546875}, {"start": 601.64, "end": 602.94, "word": " الشرط", "probability": 0.8727213541666666}, {"start": 602.94, "end": 603.34, "word": " star", "probability": 0.6142578125}, {"start": 603.34, "end": 603.54, "word": " ما", "probability": 0.623046875}, {"start": 603.54, "end": 604.32, "word": " بيخلنيش", "probability": 0.7002766927083334}, {"start": 604.32, "end": 605.06, "word": " أستنتج", "probability": 0.842041015625}, {"start": 605.06, "end": 605.9, "word": " أنه", "probability": 0.590576171875}, {"start": 605.9, "end": 606.12, "word": " limit", "probability": 0.97021484375}, {"start": 606.12, "end": 606.44, "word": " x", "probability": 0.8662109375}, {"start": 606.44, "end": 606.62, "word": " in", "probability": 0.431396484375}, {"start": 606.62, "end": 607.06, "word": " بالساوية", "probability": 0.7646484375}, {"start": 607.06, "end": 607.44, "word": " infinity", "probability": 0.8017578125}, {"start": 607.44, "end": 607.98, "word": " عندما", "probability": 0.91650390625}, {"start": 607.98, "end": 608.3, "word": " limit", "probability": 0.96240234375}, {"start": 608.3, "end": 608.6, "word": " y", "probability": 0.95947265625}, {"start": 608.6, "end": 608.8, "word": " in", "probability": 0.95263671875}, {"start": 608.8, "end": 609.2, "word": " بالساوية", "probability": 0.9783203125}, {"start": 609.2, "end": 609.64, "word": " infinity", "probability": 0.8291015625}, {"start": 609.64, "end": 611.46, "word": " بالمثل", "probability": 0.9527587890625}, {"start": 611.46, "end": 613.42, "word": " if", "probability": 0.89794921875}, {"start": 613.42, "end": 614.16, "word": " condition", 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643.82, "end": 644.36, "word": " ذلك", "probability": 0.993896484375}, {"start": 644.36, "end": 646.78, "word": " ممكن", "probability": 0.967529296875}, {"start": 646.78, "end": 647.1, "word": " نفس", "probability": 0.99609375}, {"start": 647.1, "end": 647.6, "word": " المثال", "probability": 0.9659830729166666}, {"start": 647.6, "end": 648.02, "word": " بس", "probability": 0.948486328125}], "temperature": 1.0}, {"id": 23, "seek": 66277, "start": 651.51, "end": 662.77, "text": "for example بس نضرب في سالب هي عندي negative n أصغر من أو ساوي negative واحد على n لكل n في n", "tokens": [2994, 1365, 4724, 3794, 8717, 11242, 25513, 8978, 8608, 6027, 3555, 39896, 18871, 16254, 3671, 297, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 3671, 36764, 24401, 15844, 297, 5296, 28820, 297, 8978, 297], "avg_logprob": -0.22504339615503946, "compression_ratio": 1.1637931034482758, "no_speech_prob": 0.0, "words": [{"start": 651.51, "end": 651.79, "word": "for", "probability": 0.286865234375}, {"start": 651.79, "end": 652.45, "word": " example", "probability": 0.970703125}, {"start": 652.45, "end": 653.87, "word": " بس", "probability": 0.782958984375}, {"start": 653.87, "end": 654.19, "word": " نضرب", "probability": 0.9703776041666666}, {"start": 654.19, "end": 654.35, "word": " في", "probability": 0.84716796875}, {"start": 654.35, "end": 655.17, "word": " سالب", "probability": 0.8681640625}, {"start": 655.17, "end": 655.91, "word": " هي", "probability": 0.199951171875}, {"start": 655.91, "end": 656.29, "word": " عندي", "probability": 0.764892578125}, {"start": 656.29, "end": 656.85, "word": " negative", "probability": 0.923828125}, {"start": 656.85, "end": 657.37, "word": " n", "probability": 0.609375}, {"start": 657.37, "end": 658.03, "word": " أصغر", "probability": 0.95166015625}, {"start": 658.03, "end": 658.17, "word": " من", "probability": 0.8955078125}, {"start": 658.17, "end": 658.33, "word": " أو", "probability": 0.389892578125}, {"start": 658.33, "end": 658.79, "word": " ساوي", "probability": 0.9054361979166666}, {"start": 658.79, "end": 659.17, "word": " negative", "probability": 0.8505859375}, {"start": 659.17, "end": 659.79, "word": " واحد", "probability": 0.942138671875}, {"start": 659.79, "end": 660.03, "word": " على", "probability": 0.73046875}, {"start": 660.03, "end": 660.41, "word": " n", "probability": 0.78466796875}, {"start": 660.41, "end": 661.67, "word": " لكل", "probability": 0.98486328125}, {"start": 661.67, "end": 662.11, "word": " n", "probability": 0.859375}, {"start": 662.11, "end": 662.39, "word": " في", "probability": 0.984375}, {"start": 662.39, "end": 662.77, "word": " n", "probability": 0.78466796875}], "temperature": 1.0}, {"id": 24, "seek": 68140, "start": 664.6, "end": 681.4, "text": "هل هذا كلام صح؟ انا عندي واحد على n أصغر من أو ساوي n لكل n هذا صح اضرب في سالب واحد تناقص هاه؟ هاي عندك xn بساوي سالب n وهي عندنا yn", "tokens": [3224, 1211, 23758, 28242, 10943, 20328, 5016, 22807, 1975, 8315, 18871, 16254, 36764, 24401, 15844, 297, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 297, 5296, 28820, 297, 23758, 20328, 5016, 1975, 11242, 25513, 8978, 8608, 6027, 3555, 36764, 24401, 6055, 8315, 4587, 9381, 8032, 40294, 22807, 8032, 47302, 43242, 4117, 2031, 77, 4724, 3794, 995, 45865, 8608, 6027, 3555, 297, 37037, 1829, 43242, 8315, 17861], "avg_logprob": -0.23851103226051612, "compression_ratio": 1.591549295774648, "no_speech_prob": 0.0, "words": [{"start": 664.6, "end": 664.9, "word": "هل", "probability": 0.9482421875}, {"start": 664.9, "end": 665.08, "word": " هذا", "probability": 0.837890625}, {"start": 665.08, "end": 665.44, "word": " كلام", "probability": 0.858642578125}, {"start": 665.44, "end": 666.86, "word": " صح؟", "probability": 0.9124348958333334}, {"start": 666.86, "end": 667.0, "word": " انا", "probability": 0.653076171875}, {"start": 667.0, "end": 667.36, "word": " عندي", "probability": 0.864990234375}, {"start": 667.36, "end": 667.82, "word": " واحد", "probability": 0.8779296875}, {"start": 667.82, "end": 668.02, "word": " على", "probability": 0.7138671875}, {"start": 668.02, "end": 668.34, "word": " n", "probability": 0.368896484375}, {"start": 668.34, "end": 668.88, "word": " أصغر", "probability": 0.7625732421875}, {"start": 668.88, "end": 668.98, "word": " من", "probability": 0.97802734375}, {"start": 668.98, "end": 669.14, "word": " أو", "probability": 0.55810546875}, {"start": 669.14, "end": 669.52, "word": " ساوي", "probability": 0.5887858072916666}, {"start": 669.52, "end": 669.78, "word": " n", "probability": 0.81982421875}, {"start": 669.78, "end": 670.2, "word": " لكل", "probability": 0.9697265625}, {"start": 670.2, "end": 670.48, "word": " n", "probability": 0.87451171875}, {"start": 670.48, "end": 670.5, "word": " هذا", "probability": 0.454345703125}, {"start": 670.5, "end": 672.42, "word": " صح", "probability": 0.991943359375}, {"start": 672.42, "end": 672.96, "word": " اضرب", "probability": 0.8811848958333334}, {"start": 672.96, "end": 673.12, "word": " في", "probability": 0.5927734375}, {"start": 673.12, "end": 673.46, "word": " سالب", "probability": 0.89453125}, {"start": 673.46, "end": 673.94, "word": " واحد", "probability": 0.985595703125}, {"start": 673.94, "end": 674.9, "word": " تناقص", "probability": 0.802490234375}, {"start": 674.9, "end": 675.72, "word": " هاه؟", "probability": 0.4392903645833333}, {"start": 675.72, "end": 676.62, "word": " هاي", "probability": 0.644287109375}, {"start": 676.62, "end": 677.04, "word": " عندك", "probability": 0.96728515625}, {"start": 677.04, "end": 677.7, "word": " xn", "probability": 0.73193359375}, {"start": 677.7, "end": 678.92, "word": " بساوي", "probability": 0.9259033203125}, {"start": 678.92, "end": 679.32, "word": " سالب", "probability": 0.9793294270833334}, {"start": 679.32, "end": 679.66, "word": " n", "probability": 0.90283203125}, {"start": 679.66, "end": 680.64, "word": " وهي", "probability": 0.812744140625}, {"start": 680.64, "end": 681.0, "word": " عندنا", "probability": 0.880615234375}, {"start": 681.0, "end": 681.4, "word": " yn", "probability": 0.90283203125}], "temperature": 1.0}, {"id": 25, "seek": 71131, "start": 683.69, "end": 711.31, "text": "بساوي negative واحد على n الان انا عندي limit xn اللي هو سالب n لما طبعا n تقول infinity بساوي negative infinity but لكن limit ا�� yn اللي هو واحد على n ايش بتساوي؟ ساوي سفر سالب واحد عفوا سالب واحد على n limit سالب واحد على n بساوي سفر", "tokens": [3555, 3794, 995, 45865, 3671, 36764, 24401, 15844, 297, 2423, 7649, 1975, 8315, 18871, 16254, 4948, 2031, 77, 13672, 1829, 31439, 8608, 6027, 3555, 297, 5296, 15042, 23032, 3555, 3615, 995, 297, 6055, 39648, 13202, 4724, 3794, 995, 45865, 3671, 13202, 457, 44381, 4948, 2423, 288, 77, 13672, 1829, 31439, 36764, 24401, 15844, 297, 1975, 1829, 8592, 39894, 3794, 995, 45865, 22807, 8608, 995, 45865, 8608, 5172, 2288, 8608, 6027, 3555, 36764, 24401, 6225, 5172, 14407, 8608, 6027, 3555, 36764, 24401, 15844, 297, 4948, 8608, 6027, 3555, 36764, 24401, 15844, 297, 4724, 3794, 995, 45865, 8608, 5172, 2288], "avg_logprob": -0.15072600829480876, "compression_ratio": 2.086705202312139, "no_speech_prob": 0.0, "words": [{"start": 683.69, "end": 684.19, "word": "بساوي", "probability": 0.852294921875}, {"start": 684.19, "end": 684.55, "word": " negative", "probability": 0.783203125}, {"start": 684.55, "end": 684.99, "word": " واحد", "probability": 0.9453125}, {"start": 684.99, "end": 685.17, "word": " على", "probability": 0.6142578125}, {"start": 685.17, "end": 685.39, "word": " n", "probability": 0.426025390625}, {"start": 685.39, "end": 686.39, "word": " الان", "probability": 0.6614990234375}, {"start": 686.39, "end": 686.61, "word": " انا", "probability": 0.84521484375}, {"start": 686.61, "end": 687.07, "word": " عندي", "probability": 0.89697265625}, {"start": 687.07, "end": 687.81, "word": " limit", "probability": 0.9873046875}, {"start": 687.81, "end": 689.35, "word": " xn", "probability": 0.778564453125}, {"start": 689.35, "end": 689.53, "word": " اللي", "probability": 0.87060546875}, {"start": 689.53, "end": 689.75, "word": " هو", "probability": 0.98974609375}, {"start": 689.75, "end": 690.25, "word": " سالب", "probability": 0.9620768229166666}, {"start": 690.25, "end": 690.53, "word": " n", "probability": 0.8212890625}, {"start": 690.53, "end": 691.59, "word": " لما", "probability": 0.940673828125}, {"start": 691.59, "end": 691.97, "word": " طبعا", "probability": 0.8994140625}, {"start": 691.97, "end": 692.25, "word": " n", "probability": 0.58251953125}, {"start": 692.25, "end": 692.65, "word": " تقول", "probability": 0.928466796875}, {"start": 692.65, "end": 693.31, "word": " infinity", "probability": 0.669921875}, {"start": 693.31, "end": 694.09, "word": " بساوي", "probability": 0.95458984375}, {"start": 694.09, "end": 694.51, "word": " negative", "probability": 0.97216796875}, {"start": 694.51, "end": 695.21, "word": " infinity", "probability": 0.91064453125}, {"start": 695.21, "end": 697.17, "word": " but", "probability": 0.7578125}, {"start": 697.17, "end": 697.93, "word": " لكن", "probability": 0.8076171875}, {"start": 697.93, "end": 698.49, "word": " limit", "probability": 0.98583984375}, {"start": 698.49, "end": 700.21, "word": " ال", "probability": 0.828125}, {"start": 700.21, "end": 700.93, "word": " yn", "probability": 0.683837890625}, {"start": 700.93, "end": 701.25, "word": " اللي", "probability": 0.9892578125}, {"start": 701.25, "end": 701.53, "word": " هو", "probability": 0.99169921875}, {"start": 701.53, "end": 702.09, "word": " واحد", "probability": 0.99072265625}, {"start": 702.09, "end": 702.27, "word": " على", "probability": 0.8779296875}, {"start": 702.27, "end": 702.65, "word": " n", "probability": 0.9296875}, {"start": 702.65, "end": 703.99, "word": " ايش", "probability": 0.85693359375}, {"start": 703.99, "end": 704.91, "word": " بتساوي؟", "probability": 0.89306640625}, {"start": 704.91, "end": 705.55, "word": " ساوي", "probability": 0.7461751302083334}, {"start": 705.55, "end": 705.99, "word": " سفر", "probability": 0.82958984375}, {"start": 705.99, "end": 706.87, "word": " سالب", "probability": 0.722900390625}, {"start": 706.87, "end": 707.05, "word": " واحد", "probability": 0.91162109375}, {"start": 707.05, "end": 707.33, "word": " عفوا", "probability": 0.8990885416666666}, {"start": 707.33, "end": 707.77, "word": " سالب", "probability": 0.8894856770833334}, {"start": 707.77, "end": 708.07, "word": " واحد", "probability": 0.99462890625}, {"start": 708.07, "end": 708.21, "word": " على", "probability": 0.79541015625}, {"start": 708.21, "end": 708.41, "word": " n", "probability": 0.89013671875}, {"start": 708.41, "end": 709.51, "word": " limit", "probability": 0.94482421875}, {"start": 709.51, "end": 709.95, "word": " سالب", "probability": 0.9601236979166666}, {"start": 709.95, "end": 710.27, "word": " واحد", "probability": 0.992431640625}, {"start": 710.27, "end": 710.41, "word": " على", "probability": 0.89453125}, {"start": 710.41, "end": 710.55, "word": " n", "probability": 0.9296875}, {"start": 710.55, "end": 710.93, "word": " بساوي", "probability": 0.9237060546875}, {"start": 710.93, "end": 711.31, "word": " سفر", "probability": 0.9894205729166666}], "temperature": 1.0}, {"id": 26, "seek": 73061, "start": 712.95, "end": 730.61, "text": "و ليست سالب infinity okay تمام؟ إذا النظرية ال comparison test لا يقبل .. لا يقبل التأويل زي ما بيقولوا بس النتائج تبعتها كما هي في a و b أي شيء آخر مش مظبوط", "tokens": [2407, 32239, 14851, 8608, 6027, 3555, 13202, 1392, 46811, 10943, 22807, 11933, 15730, 28239, 19913, 2288, 10632, 2423, 9660, 1500, 20193, 7251, 4587, 36150, 4386, 20193, 7251, 4587, 36150, 16712, 10721, 2407, 26895, 30767, 1829, 19446, 4724, 1829, 39648, 14407, 4724, 3794, 28239, 2655, 16373, 7435, 6055, 3555, 34268, 11296, 9122, 15042, 39896, 8978, 257, 4032, 272, 36632, 44049, 38207, 19753, 34740, 37893, 3714, 19913, 3555, 2407, 9566], "avg_logprob": -0.2250905814378158, "compression_ratio": 1.4180790960451977, "no_speech_prob": 0.0, "words": [{"start": 712.95, "end": 713.19, "word": "و", "probability": 0.74951171875}, {"start": 713.19, "end": 713.79, "word": " ليست", "probability": 0.711669921875}, {"start": 713.79, "end": 714.97, "word": " سالب", "probability": 0.6280924479166666}, {"start": 714.97, "end": 715.47, "word": " infinity", "probability": 0.7041015625}, {"start": 715.47, "end": 716.63, "word": " okay", "probability": 0.273193359375}, {"start": 716.63, "end": 717.43, "word": " تمام؟", "probability": 0.6568603515625}, {"start": 717.43, "end": 718.03, "word": " إذا", "probability": 0.64892578125}, {"start": 718.03, "end": 718.89, "word": " النظرية", "probability": 0.84075927734375}, {"start": 718.89, "end": 719.25, "word": " ال", "probability": 0.802734375}, {"start": 719.25, "end": 719.65, "word": " comparison", "probability": 0.8984375}, {"start": 719.65, "end": 720.19, "word": " test", "probability": 0.95458984375}, {"start": 720.19, "end": 721.13, "word": " لا", "probability": 0.81787109375}, {"start": 721.13, "end": 721.71, "word": " يقبل", "probability": 0.9778645833333334}, {"start": 721.71, "end": 722.17, "word": " ..", "probability": 0.60498046875}, {"start": 722.17, "end": 722.43, "word": " لا", "probability": 0.8212890625}, {"start": 722.43, "end": 722.81, "word": " يقبل", "probability": 0.9900716145833334}, {"start": 722.81, "end": 723.41, "word": " التأويل", "probability": 0.96142578125}, {"start": 723.41, "end": 723.65, "word": " زي", "probability": 0.944091796875}, {"start": 723.65, "end": 723.73, "word": " ما", "probability": 0.97607421875}, {"start": 723.73, "end": 724.47, "word": " بيقولوا", "probability": 0.853515625}, {"start": 724.47, "end": 725.43, "word": " بس", "probability": 0.9140625}, {"start": 725.43, "end": 726.21, "word": " النتائج", "probability": 0.887451171875}, {"start": 726.21, "end": 726.71, "word": " تبعتها", "probability": 0.76715087890625}, {"start": 726.71, "end": 727.01, "word": " كما", "probability": 0.928955078125}, {"start": 727.01, "end": 727.23, "word": " هي", "probability": 0.94384765625}, {"start": 727.23, "end": 727.43, "word": " في", "probability": 0.97412109375}, {"start": 727.43, "end": 727.59, "word": " a", "probability": 0.61865234375}, {"start": 727.59, "end": 727.71, "word": " و", "probability": 0.9521484375}, {"start": 727.71, "end": 727.89, "word": " b", "probability": 0.53271484375}, {"start": 727.89, "end": 728.15, "word": " أي", "probability": 0.37646484375}, {"start": 728.15, "end": 728.51, "word": " شيء", "probability": 0.86572265625}, {"start": 728.51, "end": 728.89, "word": " آخر", "probability": 0.770263671875}, {"start": 728.89, "end": 729.99, "word": " مش", "probability": 0.98828125}, {"start": 729.99, "end": 730.61, "word": " مظبوط", "probability": 0.97197265625}], "temperature": 1.0}, {"id": 27, "seek": 75535, "start": 732.05, "end": 755.35, "text": "هو أمثلة بتوضح الأشياء الأخرى تمام؟ في كمان اختبار أخر زي هذا بنسميه limit comparison test فال .. نمسح", "tokens": [3224, 2407, 5551, 2304, 12984, 37977, 39894, 2407, 11242, 5016, 16247, 8592, 1829, 16606, 16247, 34740, 7578, 46811, 10943, 22807, 8978, 9122, 2304, 7649, 1975, 46456, 3555, 9640, 5551, 34740, 30767, 1829, 23758, 44945, 38251, 1829, 3224, 4948, 9660, 1500, 6156, 6027, 4386, 8717, 2304, 3794, 5016], "avg_logprob": -0.1875000068296989, "compression_ratio": 1.2313432835820894, "no_speech_prob": 0.0, "words": [{"start": 732.05, "end": 732.35, "word": "هو", "probability": 0.9208984375}, {"start": 732.35, "end": 732.77, "word": " أمثلة", "probability": 0.8070068359375}, {"start": 732.77, "end": 733.31, "word": " بتوضح", "probability": 0.9044189453125}, {"start": 733.31, "end": 733.83, "word": " الأشياء", "probability": 0.9884033203125}, {"start": 733.83, "end": 735.19, "word": " الأخرى", "probability": 0.8258463541666666}, {"start": 735.19, "end": 736.81, "word": " تمام؟", "probability": 0.76513671875}, {"start": 736.81, "end": 738.27, "word": " في", "probability": 0.72021484375}, 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{"id": 28, "seek": 80103, "start": 776.53, "end": 801.03, "text": "limit comparison test خلّيني أاخد two sequences x in و y in بsequences of positive real numbers", "tokens": [4197, 270, 9660, 1500, 16490, 1211, 11703, 9957, 1829, 5551, 47283, 3215, 732, 22978, 2031, 294, 4032, 288, 294, 4724, 11834, 2667, 295, 3353, 957, 3547], "avg_logprob": -0.29195602734883624, "compression_ratio": 1.0594059405940595, "no_speech_prob": 0.0, "words": [{"start": 776.53, "end": 777.77, "word": "limit", "probability": 0.6502685546875}, {"start": 777.77, "end": 779.01, "word": " comparison", "probability": 0.88525390625}, {"start": 779.01, "end": 779.65, "word": " test", "probability": 0.90380859375}, {"start": 779.65, "end": 791.09, "word": " خلّيني", "probability": 0.82080078125}, {"start": 791.09, "end": 791.59, "word": " أاخد", "probability": 0.644287109375}, {"start": 791.59, "end": 791.87, "word": " two", "probability": 0.75}, {"start": 791.87, "end": 792.55, "word": " sequences", "probability": 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ل xn over yn as n tends to infinity بساوي L عدد موجبة", "tokens": [3555, 6027, 2655, 6027, 1829, 8608, 1829, 30544, 21542, 3215, 23328, 9673, 29245, 49401, 5296, 4117, 1829, 7251, 30544, 14407, 8608, 6027, 49401, 46599, 3615, 11242, 16095, 8608, 6027, 49401, 46599, 3615, 11242, 16095, 3714, 29245, 49401, 4724, 1829, 1270, 300, 4948, 5296, 2031, 77, 670, 17861, 382, 297, 12258, 281, 13202, 4724, 3794, 995, 45865, 441, 6225, 3215, 3215, 3714, 29245, 3555, 3660], "avg_logprob": -0.48125, "compression_ratio": 1.4932432432432432, "no_speech_prob": 0.0, "words": [{"start": 804.56, "end": 804.88, "word": "بالتالي", "probability": 0.5478515625}, {"start": 804.88, "end": 805.34, "word": " سيكون", "probability": 0.5824381510416666}, {"start": 805.34, "end": 808.76, "word": " الحدود", "probability": 0.7108968098958334}, {"start": 808.76, "end": 809.26, "word": " الموجبة", "probability": 0.7732747395833334}, {"start": 809.26, "end": 809.78, "word": " لكي", "probability": 0.4790445963541667}, 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3215, 3215, 11331, 38436, 38436, 2423], "avg_logprob": -0.22983870679332363, "compression_ratio": 1.16, "no_speech_prob": 0.0, "words": [{"start": 899.92, "end": 901.12, "word": "let", "probability": 0.62451171875}, {"start": 901.12, "end": 902.32, "word": " assume", "probability": 0.9033203125}, {"start": 902.32, "end": 905.26, "word": " ال", "probability": 0.62841796875}, {"start": 905.26, "end": 905.88, "word": " أكبر", "probability": 0.9226888020833334}, {"start": 905.88, "end": 906.12, "word": " من", "probability": 0.9951171875}, {"start": 906.12, "end": 906.72, "word": " السفر", "probability": 0.8116861979166666}, {"start": 906.72, "end": 910.86, "word": " satisfies", "probability": 0.677734375}, {"start": 910.86, "end": 915.3, "word": " المعادلة", "probability": 0.9676513671875}, {"start": 915.3, "end": 915.68, "word": " لسه", "probability": 0.6349283854166666}, {"start": 915.68, "end": 916.1, "word": " نفرض", "probability": 0.777587890625}, {"start": 916.1, "end": 916.24, "word": " ان", "probability": 0.283935546875}, {"start": 916.24, "end": 916.42, "word": " في", "probability": 0.78466796875}, {"start": 916.42, "end": 916.86, "word": " عدد", "probability": 0.93505859375}, {"start": 916.86, "end": 917.48, "word": " حقيقي", "probability": 0.9549153645833334}, {"start": 917.48, "end": 917.74, "word": " ال", "probability": 0.8408203125}], "temperature": 1.0}, {"id": 33, "seek": 94079, "start": 918.69, "end": 940.79, "text": "وهو بحقق star يعني هو limit ل ratio ل xn على yn تمام؟ take epsilon بساوي L على 2", "tokens": [2407, 3224, 2407, 4724, 5016, 4587, 4587, 3543, 37495, 22653, 31439, 4948, 5296, 8509, 5296, 2031, 77, 15844, 17861, 46811, 10943, 22807, 747, 17889, 4724, 3794, 995, 45865, 441, 15844, 568], "avg_logprob": -0.3100586012005806, "compression_ratio": 1.088235294117647, "no_speech_prob": 0.0, "words": [{"start": 918.69, "end": 919.45, "word": "وهو", "probability": 0.8693033854166666}, {"start": 919.45, "end": 920.49, "word": " بحقق", "probability": 0.8270263671875}, {"start": 920.49, "end": 920.91, "word": " star", "probability": 0.431884765625}, {"start": 920.91, "end": 921.17, "word": " يعني", "probability": 0.75048828125}, {"start": 921.17, "end": 921.39, "word": " هو", "probability": 0.9638671875}, {"start": 921.39, "end": 921.91, "word": " limit", "probability": 0.87451171875}, {"start": 921.91, "end": 923.21, "word": " ل", "probability": 0.5380859375}, {"start": 923.21, "end": 924.71, "word": " ratio", "probability": 0.78857421875}, {"start": 924.71, "end": 925.01, "word": " ل", "probability": 0.69677734375}, {"start": 925.01, "end": 925.53, "word": " xn", "probability": 0.54052734375}, {"start": 925.53, "end": 925.71, "word": " على", "probability": 0.736328125}, {"start": 925.71, "end": 926.13, "word": " yn", "probability": 0.9619140625}, {"start": 926.13, "end": 930.89, "word": " تمام؟", "probability": 0.6334635416666666}, {"start": 930.89, "end": 931.39, "word": " take", "probability": 0.7431640625}, {"start": 931.39, "end": 934.65, "word": " epsilon", "probability": 0.65576171875}, {"start": 934.65, "end": 938.93, "word": " بساوي", "probability": 0.9063720703125}, {"start": 938.93, "end": 940.35, "word": " L", "probability": 0.5205078125}, {"start": 940.35, "end": 940.57, "word": " على", "probability": 0.35791015625}, {"start": 940.57, "end": 940.79, "word": " 2", "probability": 0.81103515625}], "temperature": 1.0}, {"id": 34, "seek": 96586, "start": 943.48, "end": 965.86, "text": "Since L is positive L over 2 is positive لأن أنا جبت إبسلون which is positive طيب since من الفرض since by star XN over YN converges to L", "tokens": [50, 259, 384, 441, 307, 3353, 441, 670, 568, 307, 3353, 5296, 33456, 41850, 10874, 3555, 2655, 11933, 3555, 3794, 1211, 11536, 597, 307, 3353, 23032, 1829, 3555, 1670, 9154, 27188, 43042, 1670, 538, 3543, 1783, 45, 670, 398, 45, 9652, 2880, 281, 441], "avg_logprob": -0.3840277830759684, "compression_ratio": 1.2677165354330708, "no_speech_prob": 0.0, "words": [{"start": 943.48, "end": 944.12, "word": "Since", "probability": 0.545166015625}, {"start": 944.12, "end": 944.42, "word": " L", "probability": 0.74853515625}, {"start": 944.42, "end": 944.66, "word": " is", "probability": 0.78271484375}, {"start": 944.66, "end": 945.22, "word": " positive", "probability": 0.89208984375}, {"start": 945.22, "end": 945.68, "word": " L", "probability": 0.40478515625}, {"start": 945.68, "end": 946.0, "word": " over", "probability": 0.81005859375}, {"start": 946.0, "end": 946.28, "word": " 2", "probability": 0.70703125}, {"start": 946.28, "end": 946.46, "word": " is", "probability": 0.89892578125}, {"start": 946.46, "end": 946.92, "word": " positive", "probability": 0.94921875}, {"start": 946.92, "end": 947.12, "word": " لأن", "probability": 0.412353515625}, {"start": 947.12, "end": 947.42, "word": " أنا", "probability": 0.19921875}, {"start": 947.42, "end": 949.04, "word": " جبت", "probability": 0.845703125}, {"start": 949.04, "end": 949.62, "word": " إبسلون", "probability": 0.8116943359375}, {"start": 949.62, "end": 951.42, "word": " which", "probability": 0.485107421875}, {"start": 951.42, "end": 951.88, "word": " is", "probability": 0.966796875}, {"start": 951.88, "end": 953.62, "word": " positive", "probability": 0.94384765625}, {"start": 953.62, "end": 954.56, "word": " طيب", "probability": 0.7571614583333334}, {"start": 954.56, "end": 955.1, "word": " since", "probability": 0.327392578125}, {"start": 955.1, "end": 957.36, "word": " من", "probability": 0.927734375}, {"start": 957.36, "end": 957.9, "word": " الفرض", "probability": 0.9482421875}, {"start": 957.9, "end": 958.5, "word": " since", "probability": 0.58837890625}, {"start": 958.5, "end": 960.44, "word": " by", "probability": 0.64306640625}, {"start": 960.44, "end": 961.02, "word": " star", "probability": 0.83203125}, {"start": 961.02, "end": 961.94, "word": " XN", "probability": 0.51220703125}, {"start": 961.94, "end": 962.48, "word": " over", "probability": 0.916015625}, {"start": 962.48, "end": 963.62, "word": " YN", "probability": 0.875}, {"start": 963.62, "end": 964.98, "word": " converges", "probability": 0.964111328125}, {"start": 964.98, "end": 965.38, "word": " to", "probability": 0.98193359375}, {"start": 965.38, "end": 965.86, "word": " L", "probability": 0.9892578125}], "temperature": 1.0}, {"id": 35, "seek": 98030, "start": 967.88, "end": 980.3, "text": "وهي عندي إبسلون أكبر من الصفر is given إذا by definition of convergence by epsilon capital N definition لإبسلون هذه for this إبسلون", "tokens": [2407, 3224, 1829, 18871, 16254, 11933, 3555, 3794, 1211, 11536, 5551, 4117, 26890, 9154, 31767, 5172, 2288, 307, 2212, 11933, 15730, 538, 7123, 295, 32181, 538, 17889, 4238, 426, 7123, 5296, 28814, 3555, 3794, 1211, 11536, 29538, 337, 341, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.2965277645323012, "compression_ratio": 1.2985074626865671, "no_speech_prob": 0.0, "words": [{"start": 967.88, "end": 968.3, "word": "وهي", "probability": 0.609375}, {"start": 968.3, "end": 968.62, "word": " عندي", "probability": 0.80908203125}, {"start": 968.62, "end": 969.1, "word": " إبسلون", "probability": 0.809423828125}, {"start": 969.1, "end": 969.48, "word": " أكبر", "probability": 0.9656575520833334}, {"start": 969.48, "end": 969.62, "word": " من", "probability": 0.9873046875}, {"start": 969.62, "end": 970.06, "word": " الصفر", "probability": 0.8333333333333334}, {"start": 970.06, "end": 970.18, "word": " is", "probability": 0.74755859375}, {"start": 970.18, "end": 970.46, "word": " given", "probability": 0.92236328125}, {"start": 970.46, "end": 970.74, "word": " إذا", "probability": 0.5506591796875}, {"start": 970.74, "end": 970.98, "word": " by", "probability": 0.87841796875}, {"start": 970.98, "end": 971.46, "word": " definition", "probability": 0.86181640625}, {"start": 971.46, "end": 971.96, "word": " of", "probability": 0.96826171875}, {"start": 971.96, "end": 973.58, "word": " convergence", "probability": 0.9765625}, {"start": 973.58, "end": 974.26, "word": " by", "probability": 0.5009765625}, {"start": 974.26, "end": 974.7, "word": " epsilon", "probability": 0.3623046875}, {"start": 974.7, "end": 975.08, "word": " capital", "probability": 0.7587890625}, {"start": 975.08, "end": 975.4, "word": " N", "probability": 0.8037109375}, {"start": 975.4, "end": 976.26, "word": " definition", "probability": 0.90380859375}, {"start": 976.26, "end": 978.32, "word": " لإبسلون", "probability": 0.9055989583333334}, {"start": 978.32, "end": 978.76, "word": " هذه", "probability": 0.404052734375}, {"start": 978.76, "end": 979.1, "word": " for", "probability": 0.78857421875}, {"start": 979.1, "end": 979.56, "word": " this", "probability": 0.96630859375}, {"start": 979.56, "end": 980.3, "word": " إبسلون", "probability": 0.827880859375}], "temperature": 1.0}, {"id": 36, "seek": 100886, "start": 981.5, "end": 1008.86, "text": "there exist capital N يعتمد على إبسلون يعتمد على الإبسلون اللي هي بتعتمد على العدد L natural number بحيث أنه لكل N أكبر منه سوى capital N بيطلع عندي absolute xn over yn negative L less than إبسلون", "tokens": [15456, 2514, 4238, 426, 7251, 34268, 2304, 3215, 15844, 11933, 3555, 3794, 1211, 11536, 7251, 34268, 2304, 3215, 15844, 33688, 3555, 3794, 1211, 11536, 13672, 1829, 39896, 39894, 34268, 2304, 3215, 15844, 18863, 3215, 3215, 441, 3303, 1230, 4724, 5016, 1829, 12984, 14739, 3224, 5296, 28820, 426, 5551, 4117, 26890, 9154, 3224, 8608, 2407, 7578, 4238, 426, 4724, 1829, 9566, 1211, 3615, 18871, 16254, 8236, 2031, 77, 670, 17861, 3671, 441, 1570, 813, 11933, 3555, 3794, 1211, 11536], "avg_logprob": -0.24327531758742996, "compression_ratio": 1.5524861878453038, "no_speech_prob": 0.0, "words": [{"start": 981.5, "end": 981.86, "word": "there", "probability": 0.285888671875}, {"start": 981.86, "end": 982.4, "word": " exist", "probability": 0.55224609375}, {"start": 982.4, "end": 982.94, "word": " capital", "probability": 0.64990234375}, {"start": 982.94, "end": 983.24, 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"probability": 0.638671875}, {"start": 993.22, "end": 994.78, "word": " natural", "probability": 0.62255859375}, {"start": 994.78, "end": 995.58, "word": " number", "probability": 0.982421875}, {"start": 995.58, "end": 996.24, "word": " بحيث", "probability": 0.9691162109375}, {"start": 996.24, "end": 996.6, "word": " أنه", "probability": 0.728515625}, {"start": 996.6, "end": 997.16, "word": " لكل", "probability": 0.9873046875}, {"start": 997.16, "end": 997.58, "word": " N", "probability": 0.87646484375}, {"start": 997.58, "end": 998.74, "word": " أكبر", "probability": 0.9728190104166666}, {"start": 998.74, "end": 999.1, "word": " منه", "probability": 0.748291015625}, {"start": 999.1, "end": 999.6, "word": " سوى", "probability": 0.7266438802083334}, {"start": 999.6, "end": 1000.08, "word": " capital", "probability": 0.626953125}, {"start": 1000.08, "end": 1000.48, "word": " N", "probability": 0.9384765625}, {"start": 1000.48, "end": 1001.62, "word": " بيطلع", "probability": 0.77314453125}, {"start": 1001.62, "end": 1001.88, "word": " عندي", "probability": 0.781005859375}, {"start": 1001.88, "end": 1002.56, "word": " absolute", "probability": 0.779296875}, {"start": 1002.56, "end": 1003.58, "word": " xn", "probability": 0.46826171875}, {"start": 1003.58, "end": 1004.1, "word": " over", "probability": 0.83203125}, {"start": 1004.1, "end": 1005.02, "word": " yn", "probability": 0.9482421875}, {"start": 1005.02, "end": 1006.38, "word": " negative", "probability": 0.76171875}, {"start": 1006.38, "end": 1007.04, "word": " L", "probability": 0.7353515625}, {"start": 1007.04, "end": 1007.7, "word": " less", "probability": 0.89892578125}, {"start": 1007.7, "end": 1008.22, "word": " than", "probability": 0.947265625}, {"start": 1008.22, "end": 1008.86, "word": " إبسلون", "probability": 0.9212890625}], "temperature": 1.0}, {"id": 37, "seek": 103792, "start": 1010.22, "end": 1037.92, "text": "هزبوت هيك؟ طيب الـ Y بسوي L over 2 خلّينا نشيل ال absolute value فبصير اندي Xn over Yn minus L less than L two bigger than negative L ع اتنين و هذا صحيح لكل N bigger than or equal N اجمع L على كل الأطراف", "tokens": [3224, 11622, 3555, 35473, 39896, 4117, 22807, 23032, 1829, 3555, 2423, 39184, 398, 4724, 3794, 45865, 441, 670, 568, 16490, 1211, 11703, 9957, 995, 8717, 8592, 26895, 2423, 8236, 2158, 6156, 3555, 9381, 13546, 16472, 16254, 1783, 77, 670, 398, 77, 3175, 441, 1570, 813, 441, 732, 3801, 813, 3671, 441, 6225, 1975, 2655, 1863, 9957, 4032, 23758, 20328, 5016, 1829, 5016, 5296, 28820, 426, 3801, 813, 420, 2681, 426, 1975, 7435, 2304, 3615, 441, 15844, 28242, 16247, 9566, 23557, 5172], "avg_logprob": -0.27667683362960815, "compression_ratio": 1.3142857142857143, "no_speech_prob": 0.0, "words": [{"start": 1010.22, "end": 1010.74, "word": "هزبوت", "probability": 0.669189453125}, {"start": 1010.74, "end": 1011.96, "word": " هيك؟", "probability": 0.79296875}, {"start": 1011.96, "end": 1012.66, "word": " طيب", "probability": 0.8235677083333334}, {"start": 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1019.72, "word": " اندي", "probability": 0.557861328125}, {"start": 1019.72, "end": 1020.28, "word": " Xn", "probability": 0.5662841796875}, {"start": 1020.28, "end": 1020.62, "word": " over", "probability": 0.90625}, {"start": 1020.62, "end": 1021.38, "word": " Yn", "probability": 0.6453857421875}, {"start": 1021.38, "end": 1022.56, "word": " minus", "probability": 0.74072265625}, {"start": 1022.56, "end": 1022.9, "word": " L", "probability": 0.8701171875}, {"start": 1022.9, "end": 1023.2, "word": " less", "probability": 0.84619140625}, {"start": 1023.2, "end": 1023.56, "word": " than", "probability": 0.95166015625}, {"start": 1023.56, "end": 1023.9, "word": " L", "probability": 0.9287109375}, {"start": 1023.9, "end": 1024.38, "word": " two", "probability": 0.416748046875}, {"start": 1024.38, "end": 1024.76, "word": " bigger", "probability": 0.9501953125}, {"start": 1024.76, "end": 1025.34, "word": " than", "probability": 0.94580078125}, {"start": 1025.34, "end": 1026.98, "word": " negative", "probability": 0.7451171875}, {"start": 1026.98, "end": 1027.74, "word": " L", "probability": 0.9560546875}, {"start": 1027.74, "end": 1027.92, "word": " ع", "probability": 0.48388671875}, {"start": 1027.92, "end": 1028.36, "word": " اتنين", "probability": 0.8043212890625}, {"start": 1028.36, "end": 1030.96, "word": " و", "probability": 0.454833984375}, {"start": 1030.96, "end": 1031.16, "word": " هذا", "probability": 0.74462890625}, {"start": 1031.16, "end": 1031.72, "word": " صحيح", "probability": 0.998046875}, {"start": 1031.72, "end": 1032.3, "word": " لكل", "probability": 0.979248046875}, {"start": 1032.3, "end": 1032.74, "word": " N", "probability": 0.437744140625}, {"start": 1032.74, "end": 1033.72, "word": " bigger", "probability": 0.9541015625}, {"start": 1033.72, "end": 1034.06, "word": " than", "probability": 0.96044921875}, {"start": 1034.06, "end": 1034.18, "word": " or", "probability": 0.8701171875}, {"start": 1034.18, "end": 1034.42, "word": " equal", "probability": 0.9111328125}, {"start": 1034.42, "end": 1034.86, "word": " N", "probability": 0.50439453125}, {"start": 1034.86, "end": 1036.4, "word": " اجمع", "probability": 0.90576171875}, {"start": 1036.4, "end": 1036.72, "word": " L", "probability": 0.724609375}, {"start": 1036.72, "end": 1036.9, "word": " على", "probability": 0.83203125}, {"start": 1036.9, "end": 1037.2, "word": " كل", "probability": 0.9912109375}, {"start": 1037.2, "end": 1037.92, "word": " الأطراف", "probability": 0.96484375}], "temperature": 1.0}, {"id": 38, "seek": 106668, "start": 1039.08, "end": 1066.68, "text": "إن أنا بطلع عندي xn over yn less than three over two L bigger than L over two and this is true for every n bigger than or equal n نسمي المتباينة هذه double star now", "tokens": [28814, 1863, 41850, 4724, 9566, 1211, 3615, 18871, 16254, 2031, 77, 670, 17861, 1570, 813, 1045, 670, 732, 441, 3801, 813, 441, 670, 732, 293, 341, 307, 2074, 337, 633, 297, 3801, 813, 420, 2681, 297, 8717, 38251, 1829, 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1073.84, "end": 1074.38, "word": " star", "probability": 0.91162109375}, {"start": 1074.38, "end": 1077.04, "word": " انا", "probability": 0.6728515625}, {"start": 1077.04, "end": 1077.48, "word": " عندي", "probability": 0.799072265625}, {"start": 1077.48, "end": 1078.48, "word": " xn", "probability": 0.640869140625}, {"start": 1078.48, "end": 1080.04, "word": " على", "probability": 0.775390625}, {"start": 1080.04, "end": 1080.56, "word": " yn", "probability": 0.90771484375}, {"start": 1080.56, "end": 1081.42, "word": " اصغر", "probability": 0.885498046875}, {"start": 1081.42, "end": 1081.74, "word": " من", "probability": 0.99072265625}, {"start": 1081.74, "end": 1082.28, "word": " تلاتة", "probability": 0.8896484375}, {"start": 1082.28, "end": 1082.4, "word": " ع", "probability": 0.7021484375}, {"start": 1082.4, "end": 1082.8, "word": " اتنين", "probability": 0.832763671875}, {"start": 1082.8, "end": 1083.1, "word": " ال", "probability": 0.392333984375}, {"start": 1083.1, "end": 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لكل", "probability": 0.969482421875}, {"start": 1114.68, "end": 1114.98, "word": " N", "probability": 0.86083984375}, {"start": 1114.98, "end": 1115.28, "word": " bigger", "probability": 0.93701171875}, {"start": 1115.28, "end": 1115.66, "word": " than", "probability": 0.96337890625}, {"start": 1115.66, "end": 1115.82, "word": " or", "probability": 0.78857421875}, {"start": 1115.82, "end": 1116.12, "word": " equal", "probability": 0.92333984375}, {"start": 1116.12, "end": 1118.86, "word": " N", "probability": 0.52685546875}, {"start": 1118.86, "end": 1120.6, "word": " تصبوت", "probability": 0.539306640625}, {"start": 1120.6, "end": 1120.88, "word": " هيك", "probability": 0.8212890625}, {"start": 1120.88, "end": 1121.84, "word": " صح؟", "probability": 0.7111002604166666}, {"start": 1121.84, "end": 1125.26, "word": " هذه", "probability": 0.23583984375}, {"start": 1125.26, "end": 1125.98, "word": " المتباينة", "probability": 0.8841145833333334}, {"start": 1125.98, "end": 1126.4, "word": " بتقدر", "probability": 0.71337890625}, {"start": 1126.4, "end": 1126.78, "word": " هذه", "probability": 0.68408203125}, {"start": 1126.78, "end": 1129.08, "word": " هي", "probability": 0.7509765625}, {"start": 1129.08, "end": 1129.36, "word": " نفس", "probability": 0.9990234375}, {"start": 1129.36, "end": 1129.72, "word": " هذه", "probability": 0.86767578125}], "temperature": 1.0}, {"id": 41, "seek": 115069, "start": 1133.61, "end": 1150.69, "text": "so as limit احنا فرض .. now now او .. او so if", "tokens": [539, 382, 4948, 1975, 5016, 8315, 6156, 43042, 4386, 586, 586, 1975, 2407, 4386, 1975, 2407, 370, 498], "avg_logprob": -0.31517268795716136, "compression_ratio": 1.0, "no_speech_prob": 0.0, "words": [{"start": 1133.61, "end": 1134.21, "word": "so", "probability": 0.501953125}, {"start": 1134.21, "end": 1135.57, "word": " as", "probability": 0.9345703125}, {"start": 1135.57, "end": 1138.01, "word": " limit", "probability": 0.92236328125}, {"start": 1138.01, "end": 1139.05, "word": " احنا", "probability": 0.83837890625}, {"start": 1139.05, "end": 1139.37, "word": " فرض", "probability": 0.87841796875}, {"start": 1139.37, "end": 1139.53, "word": " ..", "probability": 0.138671875}, {"start": 1139.53, "end": 1140.43, "word": " now", "probability": 0.861328125}, {"start": 1140.43, "end": 1145.29, "word": " now", "probability": 0.71142578125}, {"start": 1145.29, "end": 1147.17, "word": " او", "probability": 0.811767578125}, {"start": 1147.17, "end": 1147.25, "word": " ..", "probability": 0.432861328125}, {"start": 1147.25, "end": 1148.61, "word": " او", "probability": 0.937255859375}, {"start": 1148.61, "end": 1149.05, "word": " so", "probability": 0.8642578125}, {"start": 1149.05, "end": 1150.69, "word": " if", "probability": 0.94580078125}], "temperature": 1.0}, {"id": 42, "seek": 118017, "start": 1152.93, "end": 1180.17, "text": "limit xn بساوي infinity إذا كان limit xn بساوي infinity و هذا ثابت موجب this is positive constant ف limit كل هذا برضه بساوي plus infinity و بالتالي by comparison test then by comparison by comparison", "tokens": [4197, 270, 2031, 77, 4724, 3794, 995, 45865, 13202, 11933, 15730, 25961, 4948, 2031, 77, 4724, 3794, 995, 45865, 13202, 4032, 23758, 38637, 16758, 2655, 3714, 29245, 3555, 341, 307, 3353, 5754, 6156, 4948, 28242, 23758, 4724, 43042, 3224, 4724, 3794, 995, 45865, 1804, 13202, 4032, 20666, 2655, 6027, 1829, 538, 9660, 1500, 550, 538, 9660, 538, 9660], "avg_logprob": -0.1557203364574303, "compression_ratio": 1.6556291390728477, "no_speech_prob": 0.0, "words": [{"start": 1152.93, "end": 1153.99, "word": "limit", "probability": 0.84912109375}, {"start": 1153.99, "end": 1155.05, "word": " xn", "probability": 0.58935546875}, {"start": 1155.05, "end": 1156.07, "word": " بساوي", "probability": 0.6398162841796875}, {"start": 1156.07, "end": 1156.61, "word": " infinity", "probability": 0.76123046875}, {"start": 1156.61, "end": 1157.87, "word": " إذا", "probability": 0.687744140625}, {"start": 1157.87, "end": 1158.13, 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1163.49, "word": " constant", "probability": 0.96728515625}, {"start": 1163.49, "end": 1164.65, "word": " ف", "probability": 0.953125}, {"start": 1164.65, "end": 1165.01, "word": " limit", "probability": 0.7158203125}, {"start": 1165.01, "end": 1165.37, "word": " كل", "probability": 0.9716796875}, {"start": 1165.37, "end": 1165.79, "word": " هذا", "probability": 0.96484375}, {"start": 1165.79, "end": 1166.29, "word": " برضه", "probability": 0.97802734375}, {"start": 1166.29, "end": 1166.77, "word": " بساوي", "probability": 0.975341796875}, {"start": 1166.77, "end": 1167.13, "word": " plus", "probability": 0.943359375}, {"start": 1167.13, "end": 1167.69, "word": " infinity", "probability": 0.90771484375}, {"start": 1167.69, "end": 1171.65, "word": " و", "probability": 0.52734375}, {"start": 1171.65, "end": 1172.53, "word": " بالتالي", "probability": 0.8995361328125}, {"start": 1172.53, "end": 1172.73, "word": " by", "probability": 0.9375}, {"start": 1172.73, "end": 1173.33, "word": " comparison", "probability": 0.9365234375}, {"start": 1173.33, "end": 1173.71, "word": " test", "probability": 0.95703125}, {"start": 1173.71, "end": 1174.09, "word": " then", "probability": 0.646484375}, {"start": 1174.09, "end": 1175.55, "word": " by", "probability": 0.939453125}, {"start": 1175.55, "end": 1176.51, "word": " comparison", "probability": 0.908203125}, {"start": 1176.51, "end": 1179.45, "word": " by", "probability": 0.81201171875}, {"start": 1179.45, "end": 1180.17, "word": " comparison", "probability": 0.9169921875}], "temperature": 1.0}, {"id": 43, "seek": 120472, "start": 1182.94, "end": 1204.72, "text": "by comparison test النظرية اللى فاتت مع الشرط المخفف مع الشرط المخفف لأن فى النظرية اللى فاتت كان عندي xn أصغر من أو يسوى yn لكل n بعدين قلنا أن هذا الشرط لو خففناه لكل n أكبر من أو سوى عدد طبيعى ما وليكن capital N هنا برضه بتظل صحيحة", "tokens": [2322, 9660, 1500, 28239, 19913, 2288, 10632, 13672, 7578, 6156, 9307, 2655, 20449, 25124, 2288, 9566, 9673, 9778, 5172, 5172, 20449, 25124, 2288, 9566, 9673, 9778, 5172, 5172, 5296, 33456, 6156, 7578, 28239, 19913, 2288, 10632, 13672, 7578, 6156, 9307, 2655, 25961, 18871, 16254, 2031, 77, 5551, 9381, 17082, 2288, 9154, 34051, 7251, 3794, 2407, 7578, 17861, 5296, 28820, 297, 39182, 9957, 12174, 1211, 8315, 14739, 23758, 25124, 2288, 9566, 45164, 16490, 5172, 5172, 8315, 3224, 5296, 28820, 297, 5551, 4117, 26890, 9154, 34051, 8608, 2407, 7578, 6225, 3215, 3215, 23032, 21292, 3615, 7578, 19446, 4032, 20292, 19452, 4238, 426, 34105, 4724, 43042, 3224, 39894, 19913, 1211, 20328, 5016, 1829, 5016, 3660], "avg_logprob": -0.16703539612018956, "compression_ratio": 1.8177570093457944, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 1182.94, "end": 1183.28, "word": "by", "probability": 0.4345703125}, {"start": 1183.28, "end": 1183.94, "word": " comparison", "probability": 0.935546875}, {"start": 1183.94, "end": 1184.46, "word": " test", "probability": 0.91259765625}, {"start": 1184.46, "end": 1185.0, "word": " النظرية", "probability": 0.84747314453125}, {"start": 1185.0, "end": 1185.18, "word": " اللى", "probability": 0.745849609375}, {"start": 1185.18, "end": 1185.76, "word": " فاتت", "probability": 0.99267578125}, {"start": 1185.76, "end": 1186.98, "word": " مع", "probability": 0.9794921875}, {"start": 1186.98, "end": 1187.48, "word": " الشرط", "probability": 0.98095703125}, {"start": 1187.48, "end": 1188.2, "word": " المخفف", "probability": 0.987060546875}, {"start": 1188.2, "end": 1189.52, "word": " مع", "probability": 0.4990234375}, {"start": 1189.52, "end": 1189.96, "word": " الشرط", "probability": 0.9884440104166666}, {"start": 1189.96, "end": 1190.5, "word": " المخفف", "probability": 0.9930419921875}, {"start": 1190.5, "end": 1190.68, "word": " لأن", "probability": 0.71826171875}, {"start": 1190.68, "end": 1190.82, "word": " فى", "probability": 0.76513671875}, {"start": 1190.82, "end": 1191.16, "word": " النظرية", "probability": 0.8929443359375}, {"start": 1191.16, "end": 1191.28, "word": " اللى", "probability": 0.9921875}, {"start": 1191.28, "end": 1191.64, "word": " فاتت", "probability": 0.99365234375}, {"start": 1191.64, "end": 1191.82, "word": " كان", "probability": 0.97607421875}, {"start": 1191.82, "end": 1192.16, "word": " عندي", "probability": 0.829345703125}, {"start": 1192.16, "end": 1193.24, "word": " xn", "probability": 0.4627685546875}, {"start": 1193.24, "end": 1193.7, "word": " أصغر", "probability": 0.89599609375}, {"start": 1193.7, "end": 1193.86, "word": " من", "probability": 0.986328125}, {"start": 1193.86, "end": 1194.02, "word": " أو", "probability": 0.85595703125}, {"start": 1194.02, "end": 1194.42, "word": " يسوى", "probability": 0.7418212890625}, {"start": 1194.42, "end": 1194.8, "word": " yn", "probability": 0.6787109375}, {"start": 1194.8, "end": 1195.36, "word": " لكل", "probability": 0.9892578125}, {"start": 1195.36, "end": 1195.68, "word": " n", "probability": 0.82568359375}, {"start": 1195.68, "end": 1196.54, "word": " بعدين", "probability": 0.6494140625}, {"start": 1196.54, "end": 1196.8, "word": " قلنا", "probability": 0.735107421875}, {"start": 1196.8, "end": 1196.94, "word": " أن", "probability": 0.28955078125}, {"start": 1196.94, "end": 1197.22, "word": " هذا", "probability": 0.85546875}, {"start": 1197.22, "end": 1197.66, "word": " الشرط", "probability": 0.9820963541666666}, {"start": 1197.66, "end": 1197.78, "word": " لو", "probability": 0.96826171875}, {"start": 1197.78, "end": 1198.44, "word": " خففناه", "probability": 0.96650390625}, {"start": 1198.44, "end": 1198.82, "word": " لكل", "probability": 0.99169921875}, {"start": 1198.82, "end": 1199.1, "word": " n", "probability": 0.7919921875}, {"start": 1199.1, "end": 1199.88, "word": " أكبر", "probability": 0.9615885416666666}, {"start": 1199.88, "end": 1200.02, "word": " من", "probability": 0.9619140625}, {"start": 1200.02, "end": 1200.1, "word": " أو", "probability": 0.8876953125}, {"start": 1200.1, "end": 1200.44, "word": " سوى", "probability": 0.908203125}, {"start": 1200.44, "end": 1200.7, "word": " عدد", "probability": 0.9801432291666666}, {"start": 1200.7, "end": 1201.2, "word": " طبيعى", "probability": 0.9547119140625}, {"start": 1201.2, "end": 1201.46, "word": " ما", "probability": 0.681640625}, {"start": 1201.46, "end": 1202.6, "word": " وليكن", "probability": 0.7347005208333334}, {"start": 1202.6, "end": 1203.0, "word": " capital", "probability": 0.60400390625}, {"start": 1203.0, "end": 1203.26, "word": " N", "probability": 0.76171875}, {"start": 1203.26, "end": 1203.46, "word": " هنا", "probability": 0.9736328125}, {"start": 1203.46, "end": 1203.86, "word": " برضه", "probability": 0.94091796875}, {"start": 1203.86, "end": 1204.2, "word": " بتظل", "probability": 0.6466471354166666}, {"start": 1204.2, "end": 1204.72, "word": " صحيحة", "probability": 0.92314453125}], "temperature": 1.0}, {"id": 44, "seek": 123238, "start": 1205.72, "end": 1232.38, "text": "ف by comparison test and limit ال sequence هذه بساوي infinity إذا limit الأكبر limit yn بساوي infinity تمام؟ الآن بنثبت العكس نثبت الآن العكس طيب conversely", "tokens": [5172, 538, 9660, 1500, 293, 4948, 2423, 8310, 29538, 4724, 3794, 995, 45865, 13202, 11933, 15730, 4948, 16247, 4117, 26890, 4948, 17861, 4724, 3794, 995, 45865, 13202, 46811, 10943, 22807, 6024, 48506, 44945, 12984, 3555, 2655, 18863, 4117, 3794, 8717, 12984, 3555, 2655, 6024, 48506, 18863, 4117, 3794, 23032, 1829, 3555, 2615, 736], "avg_logprob": -0.263599529310509, "compression_ratio": 1.469387755102041, "no_speech_prob": 0.0, "words": [{"start": 1205.72, "end": 1206.0, "word": "ف", "probability": 0.5556640625}, {"start": 1206.0, "end": 1206.44, "word": " by", "probability": 0.40869140625}, {"start": 1206.44, "end": 1207.06, "word": " comparison", "probability": 0.900390625}, {"start": 1207.06, "end": 1208.4, "word": " test", "probability": 0.92333984375}, {"start": 1208.4, "end": 1209.82, "word": " and", "probability": 0.2266845703125}, {"start": 1209.82, "end": 1210.3, "word": " limit", "probability": 0.95947265625}, {"start": 1210.3, "end": 1211.4, "word": " ال", "probability": 0.63818359375}, {"start": 1211.4, "end": 1211.84, "word": " sequence", "probability": 0.810546875}, {"start": 1211.84, "end": 1212.2, "word": " هذه", "probability": 0.4912109375}, {"start": 1212.2, "end": 1212.62, "word": " بساوي", "probability": 0.8248291015625}, {"start": 1212.62, "end": 1213.16, "word": " infinity", "probability": 0.818359375}, {"start": 1213.16, "end": 1213.84, "word": " إذا", "probability": 0.52996826171875}, {"start": 1213.84, "end": 1214.18, "word": " limit", "probability": 0.64013671875}, {"start": 1214.18, "end": 1214.88, "word": " الأكبر", "probability": 0.97705078125}, {"start": 1214.88, "end": 1217.18, "word": " limit", "probability": 0.73486328125}, {"start": 1217.18, "end": 1219.14, "word": " yn", "probability": 0.495849609375}, {"start": 1219.14, "end": 1220.06, "word": " بساوي", "probability": 0.929931640625}, {"start": 1220.06, "end": 1220.7, "word": " infinity", "probability": 0.84716796875}, {"start": 1220.7, "end": 1223.26, "word": " تمام؟", "probability": 0.7381998697916666}, {"start": 1223.26, "end": 1223.76, "word": " الآن", "probability": 0.625244140625}, {"start": 1223.76, "end": 1224.34, "word": " بنثبت", "probability": 0.830078125}, {"start": 1224.34, "end": 1225.52, "word": " العكس", "probability": 0.9923502604166666}, {"start": 1225.52, "end": 1227.92, "word": " نثبت", "probability": 0.887939453125}, {"start": 1227.92, "end": 1228.3, "word": " الآن", "probability": 0.85498046875}, {"start": 1228.3, "end": 1229.22, "word": " العكس", "probability": 0.9978841145833334}, {"start": 1229.22, "end": 1231.22, "word": " طيب", "probability": 0.90087890625}, {"start": 1231.22, "end": 1232.38, "word": " conversely", "probability": 0.8935546875}], "temperature": 1.0}, {"id": 45, "seek": 126402, "start": 1240.74, "end": 1264.02, "text": "Conversely Assume Assume المرهد أنه limit yn بساوي infinity من double star من double star لو أخدت النص .. النص هذا من المتباينة النص الآخر", "tokens": [9838, 4308, 356, 6281, 2540, 6281, 2540, 9673, 2288, 3224, 3215, 14739, 3224, 4948, 17861, 4724, 3794, 995, 45865, 13202, 9154, 3834, 3543, 9154, 3834, 3543, 45164, 5551, 9778, 3215, 2655, 28239, 9381, 4386, 28239, 9381, 23758, 9154, 9673, 2655, 3555, 995, 9957, 3660, 28239, 9381, 6024, 95, 34740], "avg_logprob": -0.2425000011920929, "compression_ratio": 1.3402777777777777, "no_speech_prob": 0.0, "words": [{"start": 1240.7399999999998, "end": 1242.1399999999999, "word": "Conversely", "probability": 0.5782063802083334}, {"start": 1242.1399999999999, "end": 1243.54, "word": " Assume", "probability": 0.707763671875}, {"start": 1243.54, "end": 1245.98, "word": " Assume", "probability": 0.6297607421875}, {"start": 1245.98, "end": 1247.12, "word": " المرهد", "probability": 0.9090576171875}, {"start": 1247.12, "end": 1247.48, "word": " أنه", "probability": 0.593017578125}, {"start": 1247.48, "end": 1247.84, "word": " limit", "probability": 0.7548828125}, {"start": 1247.84, "end": 1250.16, "word": " yn", "probability": 0.251953125}, {"start": 1250.16, "end": 1251.08, "word": " بساوي", "probability": 0.845947265625}, {"start": 1251.08, "end": 1251.8, "word": " infinity", "probability": 0.77294921875}, {"start": 1251.8, "end": 1254.26, "word": " من", "probability": 0.962890625}, {"start": 1254.26, "end": 1255.62, "word": " double", "probability": 0.6435546875}, {"start": 1255.62, "end": 1256.26, "word": " star", "probability": 0.8720703125}, {"start": 1256.26, "end": 1257.12, "word": " من", "probability": 0.83056640625}, {"start": 1257.12, "end": 1257.5, "word": " double", "probability": 0.92138671875}, {"start": 1257.5, "end": 1258.04, "word": " star", "probability": 0.966796875}, {"start": 1258.04, "end": 1259.28, "word": " لو", "probability": 0.916015625}, {"start": 1259.28, "end": 1259.7, "word": " أخدت", "probability": 0.9742431640625}, {"start": 1259.7, "end": 1260.46, "word": " النص", "probability": 0.798828125}, {"start": 1260.46, "end": 1260.58, "word": " ..", "probability": 0.420654296875}, {"start": 1260.58, "end": 1261.04, "word": " النص", "probability": 0.934326171875}, {"start": 1261.04, "end": 1261.38, "word": " هذا", "probability": 0.3486328125}, {"start": 1261.38, "end": 1261.58, "word": " من", "probability": 0.98193359375}, {"start": 1261.58, "end": 1262.58, "word": " المتباينة", "probability": 0.9525553385416666}, {"start": 1262.58, "end": 1263.52, "word": " النص", "probability": 0.905517578125}, {"start": 1263.52, "end": 1264.02, "word": " الآخر", "probability": 0.9274088541666666}], "temperature": 1.0}, {"id": 46, "seek": 129490, "start": 1265.44, "end": 1294.9, "text": "فعندي انا L على 2 أصغر من XN على YN هذا صحيح for every N أكبر من أو ساوية capital N طيب هذا بيقدي ان ال L over 2 في YN أصغر من XN لكل N bigger than or equal to capital N طيب since", "tokens": [5172, 3615, 1863, 16254, 1975, 8315, 441, 15844, 568, 5551, 9381, 17082, 2288, 9154, 1783, 45, 15844, 398, 45, 23758, 20328, 5016, 1829, 5016, 337, 633, 426, 5551, 4117, 26890, 9154, 34051, 8608, 995, 2407, 10632, 4238, 426, 23032, 1829, 3555, 23758, 4724, 1829, 4587, 16254, 16472, 2423, 441, 670, 568, 8978, 398, 45, 5551, 9381, 17082, 2288, 9154, 1783, 45, 5296, 28820, 426, 3801, 813, 420, 2681, 281, 4238, 426, 23032, 1829, 3555, 1670], "avg_logprob": -0.26583058857604075, "compression_ratio": 1.4588235294117646, "no_speech_prob": 0.0, "words": [{"start": 1265.44, "end": 1266.2, "word": "فعندي", "probability": 0.70074462890625}, {"start": 1266.2, "end": 1266.52, "word": " انا", "probability": 0.6436767578125}, {"start": 1266.52, "end": 1266.92, "word": " L", "probability": 0.326904296875}, {"start": 1266.92, "end": 1267.78, "word": " على", "probability": 0.27978515625}, {"start": 1267.78, "end": 1268.12, "word": " 2", "probability": 0.54736328125}, {"start": 1268.12, "end": 1268.76, "word": " أصغر", "probability": 0.8753662109375}, {"start": 1268.76, "end": 1268.98, "word": " من", "probability": 0.99169921875}, {"start": 1268.98, "end": 1269.74, "word": " XN", "probability": 0.50927734375}, {"start": 1269.74, "end": 1270.08, "word": " على", "probability": 0.82275390625}, {"start": 1270.08, "end": 1271.04, "word": " YN", "probability": 0.903564453125}, {"start": 1271.04, "end": 1271.72, "word": " هذا", "probability": 0.83642578125}, {"start": 1271.72, "end": 1272.18, "word": " صحيح", "probability": 0.990234375}, {"start": 1272.18, "end": 1272.5, "word": " for", "probability": 0.75}, {"start": 1272.5, "end": 1272.84, "word": " every", "probability": 0.828125}, {"start": 1272.84, "end": 1273.12, "word": " N", "probability": 0.63720703125}, {"start": 1273.12, "end": 1273.6, "word": " أكبر", "probability": 0.9573567708333334}, {"start": 1273.6, "end": 1273.78, "word": " من", "probability": 0.9755859375}, {"start": 1273.78, "end": 1273.94, "word": " أو", "probability": 0.8447265625}, {"start": 1273.94, "end": 1274.26, "word": " ساوية", "probability": 0.71771240234375}, {"start": 1274.26, "end": 1274.58, "word": " capital", "probability": 0.4990234375}, {"start": 1274.58, "end": 1274.94, "word": " N", "probability": 0.9501953125}, {"start": 1274.94, "end": 1276.32, "word": " طيب", "probability": 0.7024739583333334}, {"start": 1276.32, "end": 1276.72, "word": " هذا", "probability": 0.6767578125}, {"start": 1276.72, "end": 1277.42, "word": " بيقدي", "probability": 0.7025146484375}, {"start": 1277.42, "end": 1278.82, "word": " ان", "probability": 0.6767578125}, {"start": 1278.82, "end": 1279.4, "word": " ال", "probability": 0.85205078125}, {"start": 1279.4, "end": 1282.12, "word": " L", "probability": 0.49462890625}, {"start": 1282.12, "end": 1282.72, "word": " over", "probability": 0.8779296875}, {"start": 1282.72, "end": 1283.38, "word": " 2", "probability": 0.84716796875}, {"start": 1283.38, "end": 1285.0, "word": " في", "probability": 0.8056640625}, {"start": 1285.0, "end": 1285.8, "word": " YN", "probability": 0.891845703125}, 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chapter", "probability": 0.90576171875}, {"start": 1383.28, "end": 1385.22, "word": " تلاتة", "probability": 0.909423828125}], "temperature": 1.0}, {"id": 51, "seek": 143292, "start": 1412.72, "end": 1432.92, "text": "السيكشن الأخير سيكشن تلاتة سبعة في شبكر 3 هذا هيكون أبراعا مقدمة introduction to infinite series", "tokens": [6027, 3794, 1829, 4117, 8592, 1863, 16247, 9778, 13546, 8608, 1829, 4117, 8592, 1863, 6055, 1211, 9307, 3660, 8608, 3555, 27884, 8978, 13412, 3555, 4117, 2288, 805, 23758, 8032, 1829, 30544, 5551, 3555, 23557, 3615, 995, 3714, 28543, 46007, 9339, 281, 13785, 2638], "avg_logprob": -0.3433948972008445, "compression_ratio": 1.2131147540983607, "no_speech_prob": 0.0, "words": [{"start": 1412.72, "end": 1413.64, "word": "السيكشن", "probability": 0.6215413411458334}, {"start": 1413.64, "end": 1414.22, "word": " الأخير", "probability": 0.8566080729166666}, {"start": 1414.22, "end": 1417.66, "word": " سيكشن", "probability": 0.859765625}, {"start": 1417.66, "end": 1418.16, "word": " تلاتة", "probability": 0.888916015625}, {"start": 1418.16, "end": 1418.66, "word": " سبعة", "probability": 0.91650390625}, {"start": 1418.66, "end": 1419.06, "word": " في", "probability": 0.65185546875}, {"start": 1419.06, "end": 1419.74, "word": " شبكر", "probability": 0.52008056640625}, {"start": 1419.74, "end": 1420.08, "word": " 3", "probability": 0.411865234375}, {"start": 1420.08, "end": 1421.34, "word": " هذا", "probability": 0.5087890625}, {"start": 1421.34, "end": 1422.34, "word": " هيكون", "probability": 0.6173502604166666}, {"start": 1422.34, "end": 1423.12, "word": " أبراعا", "probability": 0.7595703125}, {"start": 1423.12, "end": 1423.82, "word": " مقدمة", "probability": 0.9622395833333334}, {"start": 1423.82, "end": 1424.7, "word": " introduction", "probability": 0.83740234375}, {"start": 1424.7, "end": 1427.86, "word": " to", "probability": 0.93212890625}, {"start": 1427.86, "end": 1428.6, "word": " infinite", "probability": 0.86376953125}, {"start": 1428.6, 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1440.36, "word": " series", "probability": 0.90185546875}, {"start": 1440.36, "end": 1441.96, "word": " مقدمة", "probability": 0.8011881510416666}, {"start": 1441.96, "end": 1442.38, "word": " في", "probability": 0.82568359375}, {"start": 1442.38, "end": 1443.86, "word": " المتسلسلات", "probability": 0.9664481026785714}, {"start": 1443.86, "end": 1446.94, "word": " اللانهائية", "probability": 0.891796875}, {"start": 1446.94, "end": 1449.42, "word": " نعرف", "probability": 0.8484700520833334}, {"start": 1449.42, "end": 1449.66, "word": " شو", "probability": 0.822021484375}, {"start": 1449.66, "end": 1450.96, "word": " معناه", "probability": 0.8357747395833334}, {"start": 1450.96, "end": 1451.94, "word": " متسلسلة", "probability": 0.91171875}, {"start": 1451.94, "end": 1452.86, "word": " لانهائية", "probability": 0.93310546875}, {"start": 1452.86, "end": 1455.26, "word": " let", "probability": 0.290771484375}, {"start": 1455.26, "end": 1459.46, "word": " xn", "probability": 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"end": 1586.89, "word": " S2", "probability": 0.926513671875}, {"start": 1586.89, "end": 1587.17, "word": " على", "probability": 0.94970703125}, {"start": 1587.17, "end": 1588.51, "word": " أنه", "probability": 0.954345703125}, {"start": 1588.51, "end": 1590.29, "word": " S1", "probability": 0.977294921875}, {"start": 1590.29, "end": 1590.81, "word": " زاد", "probability": 0.62451171875}, {"start": 1590.81, "end": 1591.69, "word": " X2", "probability": 0.995361328125}, {"start": 1591.69, "end": 1592.63, "word": " بساوي", "probability": 0.8148193359375}, {"start": 1592.63, "end": 1593.35, "word": " X1", "probability": 0.966552734375}, {"start": 1593.35, "end": 1593.99, "word": " زاد", "probability": 0.943115234375}, {"start": 1593.99, "end": 1595.53, "word": " X2", "probability": 0.9970703125}, {"start": 1595.53, "end": 1597.95, "word": " S3", "probability": 0.958251953125}, {"start": 1597.95, "end": 1598.65, "word": " بساوي", "probability": 0.9365234375}, {"start": 1598.65, "end": 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"word": " one", "probability": 0.810546875}, {"start": 1642.84, "end": 1644.64, "word": " بنضيف", "probability": 0.8284505208333334}, {"start": 1644.64, "end": 1644.96, "word": " لها", "probability": 0.7423095703125}, {"start": 1644.96, "end": 1645.62, "word": " xn", "probability": 0.94580078125}, {"start": 1645.62, "end": 1647.96, "word": " فهذا", "probability": 0.9658203125}, {"start": 1647.96, "end": 1648.4, "word": " بيطلع", "probability": 0.860546875}, {"start": 1648.4, "end": 1649.26, "word": " بيساوي", "probability": 0.857421875}, {"start": 1649.26, "end": 1650.24, "word": " summation", "probability": 0.80517578125}, {"start": 1650.24, "end": 1652.12, "word": " من", "probability": 0.9619140625}, {"start": 1652.12, "end": 1652.58, "word": " k", "probability": 0.78759765625}, {"start": 1652.58, "end": 1653.38, "word": " equals", "probability": 0.64453125}, {"start": 1653.38, "end": 1653.72, "word": " one", "probability": 0.82666015625}, {"start": 1653.72, "end": 1653.98, "word": " to", "probability": 0.9423828125}, {"start": 1653.98, "end": 1654.34, "word": " n", "probability": 0.90966796875}], "temperature": 1.0}, {"id": 60, "seek": 168394, "start": 1658.08, "end": 1683.94, "text": "to for xk اذا sn هو مجموع الحدود من اول حد الى حد رقم n وهكذا ممكن نستمر الى ملا نهاية and so on الان انا كوّنت sequence لاحظوا s1, s2, s3, sn هذا عبارة عن sequence ال sequence الجديدة هذه لها اسم", "tokens": [1353, 337, 2031, 74, 1975, 15730, 2406, 31439, 3714, 7435, 2304, 45367, 21542, 3215, 23328, 9154, 1975, 12610, 11331, 3215, 2423, 7578, 11331, 3215, 12602, 4587, 2304, 297, 37037, 4117, 15730, 3714, 43020, 8717, 14851, 29973, 2423, 7578, 3714, 15040, 8717, 11296, 10632, 293, 370, 322, 2423, 7649, 1975, 8315, 9122, 2407, 11703, 29399, 8310, 20193, 5016, 19913, 14407, 262, 16, 11, 262, 17, 11, 262, 18, 11, 2406, 23758, 6225, 3555, 9640, 3660, 18871, 8310, 2423, 8310, 25724, 16254, 41891, 29538, 5296, 11296, 24525, 2304], "avg_logprob": -0.26867817119620313, "compression_ratio": 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الى", "probability": 0.715576171875}, {"start": 1667.28, "end": 1667.62, "word": " حد", "probability": 0.87646484375}, {"start": 1667.62, "end": 1668.02, "word": " رقم", "probability": 0.98291015625}, {"start": 1668.02, "end": 1668.32, "word": " n", "probability": 0.744140625}, {"start": 1668.32, "end": 1669.84, "word": " وهكذا", "probability": 0.82568359375}, {"start": 1669.84, "end": 1670.12, "word": " ممكن", "probability": 0.83447265625}, {"start": 1670.12, "end": 1670.68, "word": " نستمر", "probability": 0.9845377604166666}, {"start": 1670.68, "end": 1671.0, "word": " الى", "probability": 0.94775390625}, {"start": 1671.0, "end": 1671.32, "word": " ملا", "probability": 0.6982421875}, {"start": 1671.32, "end": 1671.7, "word": " نهاية", "probability": 0.83349609375}, {"start": 1671.7, "end": 1671.92, "word": " and", "probability": 0.81689453125}, {"start": 1671.92, "end": 1672.12, "word": " so", "probability": 0.8974609375}, {"start": 1672.12, "end": 1672.64, "word": " on", 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عن", "probability": 0.98828125}, {"start": 1680.36, "end": 1680.92, "word": " sequence", "probability": 0.9619140625}, {"start": 1680.92, "end": 1682.16, "word": " ال", "probability": 0.53369140625}, {"start": 1682.16, "end": 1682.58, "word": " sequence", "probability": 0.93408203125}, {"start": 1682.58, "end": 1683.08, "word": " الجديدة", "probability": 0.9148763020833334}, {"start": 1683.08, "end": 1683.32, "word": " هذه", "probability": 0.463623046875}, {"start": 1683.32, "end": 1683.54, "word": " لها", "probability": 0.60302734375}, {"start": 1683.54, "end": 1683.94, "word": " اسم", "probability": 0.904541015625}], "temperature": 1.0}, {"id": 61, "seek": 170921, "start": 1685.15, "end": 1709.21, "text": "و sequence مهمة of partial sums مظبوط قعدت نسميها اذا طرست تفاضل الف وفهمته الموضوع هذا هناك الموضوع ال series قعدت نسميها the sequence of partial sums اذا the sequence", "tokens": [2407, 8310, 3714, 16095, 3660, 295, 14641, 34499, 3714, 19913, 3555, 2407, 9566, 12174, 22488, 2655, 8717, 38251, 1829, 11296, 1975, 15730, 23032, 2288, 14851, 6055, 5172, 46958, 1211, 27188, 4032, 5172, 16095, 47395, 9673, 2407, 11242, 45367, 23758, 34105, 4117, 9673, 2407, 11242, 45367, 2423, 2638, 12174, 22488, 2655, 8717, 38251, 1829, 11296, 264, 8310, 295, 14641, 34499, 1975, 15730, 264, 8310], "avg_logprob": -0.2805175641551614, "compression_ratio": 1.6333333333333333, "no_speech_prob": 0.0, "words": [{"start": 1685.15, "end": 1685.55, "word": "و", "probability": 0.46484375}, {"start": 1685.55, "end": 1686.97, "word": " sequence", "probability": 0.740234375}, {"start": 1686.97, "end": 1687.99, "word": " مهمة", "probability": 0.9708658854166666}, {"start": 1687.99, "end": 1688.19, "word": " of", "probability": 0.517578125}, {"start": 1688.19, "end": 1688.59, "word": " partial", "probability": 0.93017578125}, {"start": 1688.59, "end": 1688.99, "word": " sums", "probability": 0.951171875}, {"start": 1688.99, "end": 1690.69, "word": " مظبوط", "probability": 0.8494140625}, {"start": 1690.69, "end": 1691.01, "word": " قعدت", "probability": 0.4569498697916667}, {"start": 1691.01, "end": 1691.63, "word": " نسميها", "probability": 0.84539794921875}, {"start": 1691.63, "end": 1691.79, "word": " اذا", "probability": 0.66064453125}, {"start": 1691.79, "end": 1692.21, "word": " طرست", "probability": 0.74755859375}, {"start": 1692.21, "end": 1692.71, "word": " تفاضل", "probability": 0.54840087890625}, {"start": 1692.71, "end": 1693.01, "word": " الف", "probability": 0.457763671875}, {"start": 1693.01, "end": 1694.57, "word": " وفهمته", "probability": 0.771240234375}, {"start": 1694.57, "end": 1696.51, "word": " الموضوع", "probability": 0.9974365234375}, {"start": 1696.51, "end": 1696.89, "word": " هذا", "probability": 0.76611328125}, {"start": 1696.89, "end": 1697.55, "word": " هناك", "probability": 0.996337890625}, {"start": 1697.55, "end": 1698.61, "word": " الموضوع", "probability": 0.907958984375}, {"start": 1698.61, "end": 1698.79, "word": " ال", "probability": 0.90869140625}, {"start": 1698.79, "end": 1699.25, "word": " series", "probability": 0.931640625}, {"start": 1699.25, "end": 1700.33, "word": " قعدت", "probability": 0.7369791666666666}, {"start": 1700.33, "end": 1700.95, "word": " نسميها", "probability": 0.9932861328125}, {"start": 1700.95, "end": 1701.13, "word": " the", "probability": 0.71044921875}, {"start": 1701.13, "end": 1701.85, "word": " sequence", "probability": 0.97900390625}, {"start": 1701.85, "end": 1702.15, "word": " of", "probability": 0.9833984375}, {"start": 1702.15, "end": 1702.59, "word": " partial", "probability": 0.96044921875}, {"start": 1702.59, "end": 1703.11, "word": " sums", "probability": 0.9462890625}, {"start": 1703.11, "end": 1705.83, "word": " اذا", "probability": 0.83251953125}, {"start": 1705.83, "end": 1706.57, "word": " the", "probability": 0.54541015625}, {"start": 1706.57, "end": 1709.21, "word": " sequence", "probability": 0.99169921875}], "temperature": 1.0}, {"id": 62, "seek": 174030, "start": 1710.94, "end": 1740.3, "text": "SN from N equals one to infinity is called بنسميها the sequence the sequence of partial sums sequence of partial sums of the series", "tokens": [32481, 490, 426, 6915, 472, 281, 13202, 307, 1219, 44945, 38251, 1829, 11296, 264, 8310, 264, 8310, 295, 14641, 34499, 8310, 295, 14641, 34499, 295, 264, 2638], "avg_logprob": -0.33816964605024885, "compression_ratio": 1.3529411764705883, "no_speech_prob": 0.0, "words": [{"start": 1710.94, "end": 1711.94, "word": "SN", "probability": 0.09149169921875}, {"start": 1711.94, "end": 1712.46, "word": " from", "probability": 0.2919921875}, {"start": 1712.46, "end": 1712.82, "word": " N", "probability": 0.7470703125}, {"start": 1712.82, "end": 1713.3, "word": " equals", "probability": 0.378662109375}, {"start": 1713.3, "end": 1713.56, "word": " one", "probability": 0.6474609375}, {"start": 1713.56, "end": 1713.76, "word": " to", "probability": 0.9267578125}, {"start": 1713.76, "end": 1714.26, "word": " infinity", "probability": 0.86083984375}, {"start": 1714.26, "end": 1715.58, "word": " is", "probability": 0.5}, {"start": 1715.58, "end": 1716.3, "word": " called", "probability": 0.91748046875}, {"start": 1716.3, "end": 1717.98, "word": " بنسميها", "probability": 0.82666015625}, {"start": 1717.98, "end": 1719.86, "word": " the", "probability": 0.32470703125}, {"start": 1719.86, "end": 1720.8, "word": " sequence", "probability": 0.97216796875}, {"start": 1720.8, "end": 1723.72, "word": " the", "probability": 0.25732421875}, {"start": 1723.72, "end": 1724.68, "word": " sequence", "probability": 0.9716796875}, {"start": 1724.68, "end": 1726.14, "word": " of", "probability": 0.974609375}, {"start": 1726.14, "end": 1727.66, "word": " partial", "probability": 0.9345703125}, {"start": 1727.66, "end": 1731.18, "word": " sums", "probability": 0.927734375}, {"start": 1731.18, "end": 1733.24, "word": " sequence", "probability": 0.94287109375}, {"start": 1733.24, "end": 1734.02, "word": " of", "probability": 0.978515625}, {"start": 1734.02, "end": 1734.64, "word": " partial", "probability": 0.94677734375}, {"start": 1734.64, "end": 1735.3, "word": " sums", "probability": 0.93896484375}, {"start": 1735.3, "end": 1736.88, "word": " of", "probability": 0.96728515625}, {"start": 1736.88, "end": 1739.5, "word": " the", "probability": 0.9130859375}, {"start": 1739.5, "end": 1740.3, "word": " series", "probability": 0.9130859375}], "temperature": 1.0}, {"id": 63, "seek": 176928, "start": 1742.34, "end": 1769.28, "text": "اللي هي sigma xn او sigma من n بساعة واحد لانفينيتي okay الان now if ال sequence sn converges say", "tokens": [6027, 20292, 39896, 12771, 2031, 77, 1975, 2407, 12771, 9154, 297, 4724, 3794, 995, 27884, 36764, 24401, 5296, 7649, 5172, 9957, 1829, 31371, 1392, 2423, 7649, 586, 498, 2423, 8310, 2406, 9652, 2880, 584], "avg_logprob": -0.3506696479661124, "compression_ratio": 1.1293103448275863, "no_speech_prob": 0.0, "words": [{"start": 1742.34, "end": 1742.78, "word": "اللي", "probability": 0.73388671875}, {"start": 1742.78, "end": 1743.04, "word": " هي", "probability": 0.90478515625}, {"start": 1743.04, "end": 1743.52, "word": " sigma", "probability": 0.465087890625}, {"start": 1743.52, "end": 1744.52, "word": " xn", "probability": 0.574951171875}, {"start": 1744.52, "end": 1746.34, "word": " او", "probability": 0.712646484375}, {"start": 1746.34, "end": 1746.7, "word": " sigma", "probability": 0.7626953125}, {"start": 1746.7, "end": 1747.44, "word": " من", "probability": 0.94921875}, {"start": 1747.44, "end": 1747.78, "word": " n", "probability": 0.69775390625}, {"start": 1747.78, "end": 1748.2, "word": " بساعة", "probability": 0.756103515625}, {"start": 1748.2, "end": 1748.7, "word": " واحد", "probability": 0.941650390625}, {"start": 1748.7, "end": 1750.08, "word": " لانفينيتي", "probability": 0.7154134114583334}, {"start": 1750.08, "end": 1751.08, "word": " okay", "probability": 0.4248046875}, {"start": 1751.08, "end": 1753.2, "word": " الان", "probability": 0.67578125}, {"start": 1753.2, "end": 1754.32, "word": " now", "probability": 0.403564453125}, {"start": 1754.32, "end": 1758.66, "word": " if", "probability": 0.83837890625}, {"start": 1758.66, "end": 1761.22, "word": " ال", "probability": 0.638671875}, {"start": 1761.22, "end": 1761.84, "word": " sequence", "probability": 0.95361328125}, {"start": 1761.84, "end": 1762.94, "word": " sn", "probability": 0.448486328125}, {"start": 1762.94, "end": 1765.42, "word": " converges", "probability": 0.863525390625}, {"start": 1765.42, "end": 1769.28, "word": " say", "probability": 0.84375}], "temperature": 1.0}, {"id": 64, "seek": 180027, "start": 1771.11, "end": 1800.27, "text": "limit sn بالساوي عدد s ينتمي إلى r طبعا then we say في الحالة هذه بنقول أنه the series اللي هي summation xn from n equals one to infinity converges", "tokens": [4197, 270, 2406, 20666, 3794, 995, 45865, 6225, 3215, 3215, 262, 7251, 29399, 2304, 1829, 30731, 367, 23032, 3555, 3615, 995, 550, 321, 584, 8978, 21542, 6027, 3660, 29538, 44945, 39648, 14739, 3224, 264, 2638, 13672, 1829, 39896, 28811, 2031, 77, 490, 297, 6915, 472, 281, 13202, 9652, 2880], "avg_logprob": -0.24187500149011612, "compression_ratio": 1.2435897435897436, "no_speech_prob": 0.0, "words": [{"start": 1771.1100000000001, "end": 1772.23, "word": "limit", "probability": 0.757080078125}, {"start": 1772.23, "end": 1773.35, "word": " sn", "probability": 0.2998046875}, {"start": 1773.35, "end": 1774.13, "word": " بالساوي", "probability": 0.5901718139648438}, {"start": 1774.13, "end": 1774.61, "word": " عدد", "probability": 0.9500325520833334}, {"start": 1774.61, "end": 1775.09, "word": " s", "probability": 0.5751953125}, {"start": 1775.09, "end": 1776.39, "word": " ينتمي", "probability": 0.83624267578125}, {"start": 1776.39, "end": 1776.53, "word": " إلى", "probability": 0.5888671875}, {"start": 1776.53, "end": 1776.79, "word": " r", "probability": 0.424072265625}, {"start": 1776.79, "end": 1777.31, "word": " طبعا", "probability": 0.9744873046875}, {"start": 1777.31, "end": 1782.09, "word": " then", "probability": 0.55859375}, {"start": 1782.09, "end": 1782.65, "word": " we", "probability": 0.91748046875}, {"start": 1782.65, "end": 1783.39, "word": " say", "probability": 0.9677734375}, {"start": 1783.39, "end": 1784.47, "word": " في", "probability": 0.7353515625}, {"start": 1784.47, "end": 1784.81, "word": " الحالة", "probability": 0.9498697916666666}, {"start": 1784.81, "end": 1784.99, "word": " هذه", "probability": 0.7080078125}, {"start": 1784.99, "end": 1785.45, "word": " بنقول", "probability": 0.8203125}, {"start": 1785.45, "end": 1786.75, "word": " أنه", "probability": 0.5953369140625}, {"start": 1786.75, "end": 1787.05, "word": " the", "probability": 0.64453125}, {"start": 1787.05, "end": 1787.81, "word": " series", "probability": 0.923828125}, {"start": 1787.81, "end": 1791.39, "word": " اللي", "probability": 0.760498046875}, {"start": 1791.39, "end": 1791.83, "word": " هي", "probability": 0.94921875}, {"start": 1791.83, "end": 1793.85, "word": " summation", "probability": 0.86572265625}, {"start": 1793.85, "end": 1795.67, "word": " xn", "probability": 0.77685546875}, {"start": 1795.67, "end": 1795.99, "word": " from", "probability": 0.76416015625}, {"start": 1795.99, "end": 1796.37, "word": " n", "probability": 0.916015625}, {"start": 1796.37, "end": 1797.61, "word": " equals", "probability": 0.82373046875}, {"start": 1797.61, "end": 1797.89, "word": " one", "probability": 0.8466796875}, {"start": 1797.89, "end": 1798.07, "word": " to", "probability": 0.95654296875}, {"start": 1798.07, "end": 1798.63, "word": " infinity", "probability": 0.90380859375}, {"start": 1798.63, "end": 1800.27, "word": " converges", "probability": 0.892578125}], "temperature": 1.0}, {"id": 65, "seek": 183273, "start": 1809.07, "end": 1832.73, "text": "and its sum is summation from n equals one to infinity ل x in ال summation تبعها أو المجموعة تبعها عبارة عن limit لل sequence of partial sums اللي هو العدد S", "tokens": [474, 1080, 2408, 307, 28811, 490, 297, 6915, 472, 281, 13202, 5296, 2031, 294, 2423, 28811, 6055, 3555, 3615, 11296, 34051, 9673, 7435, 2304, 2407, 27884, 6055, 3555, 3615, 11296, 6225, 3555, 9640, 3660, 18871, 4948, 24976, 8310, 295, 14641, 34499, 13672, 1829, 31439, 18863, 3215, 3215, 318], "avg_logprob": -0.22863520408163265, "compression_ratio": 1.342281879194631, "no_speech_prob": 0.0, "words": [{"start": 1809.0700000000002, "end": 1810.1100000000001, "word": "and", "probability": 0.10943603515625}, {"start": 1810.1100000000001, "end": 1811.15, "word": " its", "probability": 0.59228515625}, {"start": 1811.15, "end": 1812.53, "word": " sum", "probability": 0.92041015625}, {"start": 1812.53, "end": 1814.49, "word": " is", "probability": 0.93310546875}, {"start": 1814.49, "end": 1816.35, "word": " summation", "probability": 0.77392578125}, {"start": 1816.35, "end": 1817.01, "word": " from", "probability": 0.8642578125}, {"start": 1817.01, "end": 1817.35, "word": " n", "probability": 0.763671875}, {"start": 1817.35, "end": 1817.85, "word": " equals", "probability": 0.488037109375}, {"start": 1817.85, "end": 1818.11, "word": " one", "probability": 0.8271484375}, {"start": 1818.11, "end": 1818.29, "word": " to", "probability": 0.9453125}, {"start": 1818.29, "end": 1818.81, "word": " infinity", "probability": 0.87109375}, {"start": 1818.81, "end": 1819.99, "word": " ل", "probability": 0.74609375}, {"start": 1819.99, "end": 1820.37, "word": " x", "probability": 0.272216796875}, {"start": 1820.37, "end": 1820.77, "word": " in", "probability": 0.27587890625}, {"start": 1820.77, "end": 1821.29, "word": " ال", "probability": 0.381103515625}, {"start": 1821.29, "end": 1821.73, "word": " summation", "probability": 0.74072265625}, {"start": 1821.73, "end": 1822.41, "word": " تبعها", "probability": 0.9278564453125}, {"start": 1822.41, "end": 1822.95, "word": " أو", "probability": 0.7236328125}, {"start": 1822.95, "end": 1823.53, "word": " المجموعة", "probability": 0.97568359375}, {"start": 1823.53, "end": 1824.03, "word": " تبعها", "probability": 0.9754638671875}, {"start": 1824.03, "end": 1824.49, "word": " عبارة", "probability": 0.9476318359375}, {"start": 1824.49, "end": 1824.77, "word": " عن", "probability": 0.998046875}, {"start": 1824.77, "end": 1825.31, "word": " limit", "probability": 0.646484375}, {"start": 1825.31, "end": 1826.51, "word": " لل", "probability": 0.453857421875}, {"start": 1826.51, "end": 1826.95, "word": " sequence", "probability": 0.94140625}, {"start": 1826.95, "end": 1827.35, "word": " of", "probability": 0.97412109375}, {"start": 1827.35, "end": 1827.87, "word": " partial", "probability": 0.94091796875}, {"start": 1827.87, "end": 1828.45, "word": " sums", "probability": 0.95751953125}, {"start": 1828.45, "end": 1830.89, "word": " اللي", "probability": 0.95849609375}, {"start": 1830.89, "end": 1831.95, "word": " هو", "probability": 0.921875}, {"start": 1831.95, "end": 1832.45, "word": " العدد", "probability": 0.9583333333333334}, {"start": 1832.45, "end": 1832.73, "word": " S", "probability": 0.5}], "temperature": 1.0}, {"id": 66, "seek": 186588, "start": 1837.16, "end": 1865.88, "text": "لو كانت الـ sequence divergent if الـ sequence is in diverges we say أنه الـ series sigma x in diverges", "tokens": [1211, 2407, 25961, 2655, 2423, 39184, 8310, 18558, 6930, 498, 2423, 39184, 8310, 307, 294, 18558, 2880, 321, 584, 14739, 3224, 2423, 39184, 2638, 12771, 2031, 294, 18558, 2880], "avg_logprob": -0.3981770714124044, "compression_ratio": 1.3595505617977528, "no_speech_prob": 0.0, "words": [{"start": 1837.16, "end": 1837.54, "word": "لو", "probability": 0.85498046875}, {"start": 1837.54, "end": 1837.98, "word": " كانت", "probability": 0.990234375}, {"start": 1837.98, "end": 1838.08, "word": " الـ", "probability": 0.795166015625}, {"start": 1838.08, "end": 1838.66, "word": " sequence", "probability": 0.76806640625}, {"start": 1838.66, "end": 1843.18, "word": " divergent", "probability": 0.6280517578125}, {"start": 1843.18, "end": 1844.94, "word": " if", "probability": 0.354736328125}, {"start": 1844.94, "end": 1845.62, "word": " الـ", "probability": 0.64111328125}, {"start": 1845.62, "end": 1846.06, "word": " sequence", "probability": 0.9208984375}, {"start": 1846.06, "end": 1846.36, "word": " is", "probability": 0.349365234375}, {"start": 1846.36, "end": 1846.7, "word": " in", "probability": 0.88916015625}, {"start": 1846.7, "end": 1847.62, "word": " diverges", "probability": 0.6141357421875}, {"start": 1847.62, "end": 1850.74, "word": " we", "probability": 0.58154296875}, {"start": 1850.74, "end": 1851.32, "word": " say", "probability": 0.9609375}, {"start": 1851.32, "end": 1854.02, "word": " أنه", "probability": 0.4552001953125}, {"start": 1854.02, "end": 1854.2, "word": " الـ", "probability": 0.666748046875}, {"start": 1854.2, "end": 1854.66, "word": " series", "probability": 0.861328125}, {"start": 1854.66, "end": 1860.12, "word": " sigma", "probability": 0.255859375}, {"start": 1860.12, "end": 1862.74, "word": " x", "probability": 0.7236328125}, {"start": 1862.74, "end": 1863.24, "word": " in", "probability": 0.84912109375}, {"start": 1863.24, "end": 1865.88, "word": " diverges", "probability": 0.822021484375}], "temperature": 1.0}, {"id": 67, "seek": 189511, "start": 1869.09, "end": 1895.11, "text": "إذا ال convergence و ال divergence depends on the divergence أو convergence of the infinite series depends on the convergence or divergence of the sequence of partial sums مرتبط بيها ال sequence of partial sums convergent السيريز اللي تابع إليها convergent", "tokens": [28814, 15730, 2423, 32181, 4032, 2423, 47387, 5946, 322, 264, 47387, 34051, 32181, 295, 264, 13785, 2638, 5946, 322, 264, 32181, 420, 47387, 295, 264, 8310, 295, 14641, 34499, 3714, 43500, 3555, 9566, 4724, 1829, 11296, 2423, 8310, 295, 14641, 34499, 9652, 6930, 21136, 13546, 1829, 11622, 13672, 1829, 6055, 16758, 3615, 11933, 20292, 11296, 9652, 6930], "avg_logprob": -0.23612608477987093, "compression_ratio": 1.879746835443038, "no_speech_prob": 0.0, "words": [{"start": 1869.09, "end": 1869.43, "word": "إذا", "probability": 0.615478515625}, {"start": 1869.43, "end": 1869.61, "word": " ال", "probability": 0.93798828125}, {"start": 1869.61, "end": 1870.17, "word": " convergence", "probability": 0.6689453125}, {"start": 1870.17, "end": 1870.53, "word": " و", "probability": 0.71923828125}, {"start": 1870.53, "end": 1870.61, "word": " ال", "probability": 0.7294921875}, {"start": 1870.61, "end": 1871.15, "word": " divergence", "probability": 0.9951171875}, {"start": 1871.15, "end": 1872.75, "word": " depends", "probability": 0.446533203125}, {"start": 1872.75, "end": 1873.23, "word": " on", "probability": 0.92578125}, {"start": 1873.23, "end": 1873.41, "word": " the", "probability": 0.525390625}, {"start": 1873.41, "end": 1875.63, "word": " divergence", "probability": 0.17041015625}, {"start": 1875.63, "end": 1876.11, "word": " أو", "probability": 0.4208984375}, {"start": 1876.11, "end": 1876.67, "word": " convergence", "probability": 0.93994140625}, {"start": 1876.67, "end": 1877.63, "word": " of", "probability": 0.908203125}, {"start": 1877.63, "end": 1877.83, "word": " the", "probability": 0.87109375}, {"start": 1877.83, "end": 1878.11, "word": " infinite", "probability": 0.85693359375}, {"start": 1878.11, "end": 1878.63, "word": " series", "probability": 0.8984375}, {"start": 1878.63, "end": 1879.51, "word": " depends", "probability": 0.70849609375}, {"start": 1879.51, "end": 1880.09, "word": " on", "probability": 0.95556640625}, {"start": 1880.09, "end": 1880.31, "word": " the", "probability": 0.8583984375}, {"start": 1880.31, "end": 1880.83, "word": " convergence", "probability": 0.94482421875}, {"start": 1880.83, "end": 1881.27, "word": " or", "probability": 0.77197265625}, {"start": 1881.27, "end": 1881.79, "word": " divergence", "probability": 0.95361328125}, {"start": 1881.79, "end": 1883.03, "word": " of", "probability": 0.97314453125}, {"start": 1883.03, "end": 1883.91, "word": " the", "probability": 0.83935546875}, {"start": 1883.91, "end": 1885.65, "word": " sequence", "probability": 0.95263671875}, {"start": 1885.65, "end": 1885.83, "word": " of", "probability": 0.7626953125}, {"start": 1885.83, "end": 1886.25, "word": " partial", "probability": 0.93359375}, {"start": 1886.25, "end": 1886.73, "word": " sums", "probability": 0.96875}, {"start": 1886.73, "end": 1888.99, "word": " مرتبط", "probability": 0.8701171875}, {"start": 1888.99, "end": 1889.31, "word": " بيها", "probability": 0.95263671875}, {"start": 1889.31, "end": 1890.11, "word": " ال", "probability": 0.6572265625}, {"start": 1890.11, "end": 1890.39, "word": " sequence", "probability": 0.94775390625}, {"start": 1890.39, "end": 1890.69, "word": " of", "probability": 0.94921875}, {"start": 1890.69, "end": 1890.99, "word": " partial", "probability": 0.92041015625}, {"start": 1890.99, "end": 1891.31, "word": " sums", "probability": 0.95849609375}, {"start": 1891.31, "end": 1891.93, "word": " convergent", "probability": 0.766357421875}, {"start": 1891.93, "end": 1892.59, "word": " السيريز", "probability": 0.78045654296875}, {"start": 1892.59, "end": 1893.67, "word": " اللي", "probability": 0.8466796875}, {"start": 1893.67, "end": 1894.01, "word": " تابع", "probability": 0.9716796875}, {"start": 1894.01, "end": 1894.35, "word": " إليها", "probability": 0.7615559895833334}, {"start": 1894.35, "end": 1895.11, "word": " convergent", "probability": 0.793212890625}], "temperature": 1.0}, {"id": 68, "seek": 192172, "start": 1896.34, "end": 1921.72, "text": "و العكس إذا كانت ال sequence of partial sums divergent ال series ال infinite series التابعة إلى divergent طيب ناخد بعض الأمثلة طبعا ال Sn هذا ال Sn", "tokens": [2407, 18863, 4117, 3794, 11933, 15730, 25961, 2655, 2423, 8310, 295, 14641, 34499, 18558, 6930, 2423, 2638, 2423, 13785, 2638, 16712, 16758, 27884, 30731, 18558, 6930, 23032, 1829, 3555, 8717, 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"word": " divergent", "probability": 0.6175537109375}, {"start": 1899.4, "end": 1899.62, "word": " ال", "probability": 0.42138671875}, {"start": 1899.62, "end": 1899.98, "word": " series", "probability": 0.7890625}, {"start": 1899.98, "end": 1900.16, "word": " ال", "probability": 0.86962890625}, {"start": 1900.16, "end": 1900.38, "word": " infinite", "probability": 0.6513671875}, {"start": 1900.38, "end": 1900.78, "word": " series", "probability": 0.8720703125}, {"start": 1900.78, "end": 1901.26, "word": " التابعة", "probability": 0.904296875}, {"start": 1901.26, "end": 1901.52, "word": " إلى", "probability": 0.3076171875}, {"start": 1901.52, "end": 1903.14, "word": " divergent", "probability": 0.786865234375}, {"start": 1903.14, "end": 1911.84, "word": " طيب", "probability": 0.6883138020833334}, {"start": 1911.84, "end": 1912.92, "word": " ناخد", "probability": 0.9602864583333334}, {"start": 1912.92, "end": 1913.24, "word": " بعض", "probability": 0.975830078125}, {"start": 1913.24, "end": 1913.88, "word": " الأمثلة", "probability": 0.9820556640625}, {"start": 1913.88, "end": 1918.18, "word": " طبعا", "probability": 0.85845947265625}, {"start": 1918.18, "end": 1918.38, "word": " ال", "probability": 0.9599609375}, {"start": 1918.38, "end": 1918.98, "word": " Sn", "probability": 0.29443359375}, {"start": 1918.98, "end": 1919.44, "word": " هذا", "probability": 0.7236328125}, {"start": 1919.44, "end": 1921.08, "word": " ال", "probability": 0.89453125}, {"start": 1921.08, "end": 1921.72, "word": " Sn", "probability": 0.802734375}], "temperature": 1.0}, {"id": 69, "seek": 194829, "start": 1924.61, "end": 1948.29, "text": "هذا بنسميه الانث partial sum الانث partial sum انث partial sum المجموع الجزئي أنوني okay هو الحد العام لل sequence و partial sums", "tokens": [3224, 15730, 44945, 38251, 1829, 3224, 2423, 7649, 12984, 14641, 2408, 2423, 7649, 12984, 14641, 2408, 16472, 12984, 14641, 2408, 9673, 7435, 2304, 45367, 25724, 11622, 19986, 1829, 14739, 11536, 1829, 1392, 31439, 21542, 3215, 18863, 10943, 24976, 8310, 4032, 14641, 34499], "avg_logprob": -0.26507993492969245, "compression_ratio": 1.525, "no_speech_prob": 0.0, "words": [{"start": 1924.61, "end": 1924.97, "word": "هذا", "probability": 0.823486328125}, {"start": 1924.97, "end": 1925.83, "word": " بنسميه", "probability": 0.7672119140625}, {"start": 1925.83, "end": 1926.39, "word": " الانث", "probability": 0.6005452473958334}, {"start": 1926.39, "end": 1926.89, "word": " partial", "probability": 0.80712890625}, {"start": 1926.89, "end": 1927.43, "word": " sum", "probability": 0.9453125}, {"start": 1927.43, "end": 1929.37, "word": " الانث", "probability": 0.8601888020833334}, {"start": 1929.37, "end": 1930.61, "word": " partial", "probability": 0.8828125}, {"start": 1930.61, "end": 1935.81, "word": " sum", "probability": 0.7392578125}, {"start": 1935.81, "end": 1936.53, "word": " انث", "probability": 0.591796875}, {"start": 1936.53, "end": 1937.05, "word": " partial", "probability": 0.88525390625}, {"start": 1937.05, "end": 1937.71, "word": " sum", "probability": 0.95068359375}, {"start": 1937.71, "end": 1939.19, "word": " المجموع", "probability": 0.900146484375}, {"start": 1939.19, "end": 1939.89, "word": " الجزئي", "probability": 0.763671875}, {"start": 1939.89, "end": 1940.75, "word": " أنوني", "probability": 0.81591796875}, {"start": 1940.75, "end": 1942.41, "word": " okay", "probability": 0.496337890625}, {"start": 1942.41, "end": 1945.69, "word": " هو", "probability": 0.62255859375}, {"start": 1945.69, "end": 1946.13, "word": " الحد", "probability": 0.99072265625}, {"start": 1946.13, "end": 1946.55, "word": " العام", "probability": 0.986083984375}, {"start": 1946.55, "end": 1946.75, "word": " لل", "probability": 0.8515625}, {"start": 1946.75, "end": 1947.15, "word": " sequence", "probability": 0.9072265625}, {"start": 1947.15, "end": 1947.53, "word": " و", "probability": 0.6943359375}, {"start": 1947.53, "end": 1947.85, "word": " partial", "probability": 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"probability": 0.44976806640625}, {"start": 1950.24, "end": 1950.44, "word": " لما", "probability": 0.7091064453125}, {"start": 1950.44, "end": 1950.76, "word": " بدى", "probability": 0.3966064453125}, {"start": 1950.76, "end": 1951.32, "word": " نخبر", "probability": 0.7205403645833334}, {"start": 1951.32, "end": 1951.78, "word": " هل", "probability": 0.92236328125}, {"start": 1951.78, "end": 1951.88, "word": " ال", "probability": 0.9306640625}, {"start": 1951.88, "end": 1952.1, "word": " series", "probability": 0.70361328125}, {"start": 1952.1, "end": 1952.64, "word": " convergent", "probability": 0.6898193359375}, {"start": 1952.64, "end": 1952.8, "word": " ولا", "probability": 0.55517578125}, {"start": 1952.8, "end": 1953.52, "word": " divergent", "probability": 0.6627197265625}, {"start": 1953.52, "end": 1954.62, "word": " بجيب", "probability": 0.92529296875}, {"start": 1954.62, "end": 1954.76, "word": " ال", "probability": 0.8544921875}, {"start": 1954.76, "end": 1955.06, "word": " sequence", "probability": 0.888671875}, {"start": 1955.06, "end": 1955.3, "word": " of", "probability": 0.87255859375}, {"start": 1955.3, "end": 1955.68, "word": " partial", "probability": 0.947265625}, {"start": 1955.68, "end": 1956.04, "word": " sums", "probability": 0.96484375}, {"start": 1956.04, "end": 1956.48, "word": " وبجيب", "probability": 0.8253173828125}, {"start": 1956.48, "end": 1956.86, "word": " الحد", "probability": 0.98193359375}, {"start": 1956.86, "end": 1957.28, "word": " العام", "probability": 0.988037109375}, {"start": 1957.28, "end": 1958.38, "word": " لل", "probability": 0.8134765625}, {"start": 1958.38, "end": 1958.82, "word": " sequence", "probability": 0.93408203125}, {"start": 1958.82, "end": 1959.02, "word": " of", "probability": 0.93310546875}, {"start": 1959.02, "end": 1959.36, "word": " partial", "probability": 0.94873046875}, {"start": 1959.36, "end": 1959.7, "word": " sums", "probability": 0.90673828125}, {"start": 1959.7, "end": 1960.42, "word": " وبأفحص", "probability": 0.77119140625}, {"start": 1960.42, "end": 1960.64, "word": " هل", "probability": 0.966796875}, {"start": 1960.64, "end": 1960.76, "word": " ال", "probability": 0.9189453125}, {"start": 1960.76, "end": 1961.16, "word": " sequence", "probability": 0.98779296875}, {"start": 1961.16, "end": 1961.78, "word": " هذي", "probability": 0.564697265625}, {"start": 1961.78, "end": 1962.82, "word": " convergent", "probability": 0.891845703125}, {"start": 1962.82, "end": 1963.06, "word": " ولا", "probability": 0.89599609375}, {"start": 1963.06, "end": 1963.8, "word": " divergent", "probability": 0.898681640625}, {"start": 1963.8, "end": 1967.68, "word": " ناخد", "probability": 0.672119140625}, {"start": 1967.68, "end": 1967.96, "word": " بعض", "probability": 0.964111328125}, {"start": 1967.96, "end": 1968.62, "word": " الأمثلة", "probability": 0.98828125}], "temperature": 1.0}, {"id": 71, "seek": 200702, "start": 1982.76, "end": 2007.02, "text": "المثال الأول consider sequence R to N from N equals 0 to infinity طبعا هذه sequence of real numbers", "tokens": [45340, 12984, 6027, 16247, 12610, 1949, 8310, 497, 281, 426, 490, 426, 6915, 1958, 281, 13202, 23032, 3555, 3615, 995, 29538, 8310, 295, 957, 3547], "avg_logprob": -0.27073317995438206, "compression_ratio": 1.0636363636363637, "no_speech_prob": 0.0, "words": [{"start": 1982.76, "end": 1983.4, "word": "المثال", "probability": 0.9402669270833334}, {"start": 1983.4, "end": 1983.98, "word": " الأول", "probability": 0.94287109375}, {"start": 1983.98, "end": 1994.56, "word": " consider", "probability": 0.448974609375}, {"start": 1994.56, "end": 1997.78, "word": " sequence", "probability": 0.51123046875}, {"start": 1997.78, "end": 2000.06, "word": " R", "probability": 0.278076171875}, {"start": 2000.06, "end": 2000.34, "word": " to", "probability": 0.611328125}, {"start": 2000.34, "end": 2000.7, "word": " N", "probability": 0.97802734375}, {"start": 2000.7, "end": 2001.16, "word": " from", "probability": 0.826171875}, {"start": 2001.16, "end": 2001.58, "word": " N", "probability": 0.94287109375}, {"start": 2001.58, "end": 2002.06, "word": " equals", "probability": 0.266845703125}, {"start": 2002.06, "end": 2002.5, "word": " 0", "probability": 0.5029296875}, {"start": 2002.5, "end": 2002.7, "word": " to", "probability": 0.9765625}, {"start": 2002.7, "end": 2003.32, "word": " infinity", "probability": 0.7880859375}, {"start": 2003.32, "end": 2005.28, "word": " طبعا", "probability": 0.9146728515625}, {"start": 2005.28, "end": 2005.48, "word": " هذه", "probability": 0.47998046875}, {"start": 2005.48, "end": 2005.88, "word": " sequence", "probability": 0.74609375}, {"start": 2005.88, "end": 2006.2, "word": " of", "probability": 0.88525390625}, {"start": 2006.2, "end": 2006.46, "word": " real", "probability": 0.92822265625}, {"start": 2006.46, "end": 2007.02, "word": " numbers", "probability": 0.837890625}], "temperature": 1.0}, {"id": 72, "seek": 203433, "start": 2009.15, "end": 2034.33, "text": "Where R is a real number which generates الsequence هذه generates the geometric .. the so-called geometric series .. geometric series", "tokens": [14436, 497, 307, 257, 957, 1230, 597, 23815, 2423, 11834, 655, 29538, 23815, 264, 33246, 4386, 264, 370, 12, 11880, 33246, 2638, 4386, 33246, 2638], "avg_logprob": -0.5054086446762085, "compression_ratio": 1.3663366336633664, "no_speech_prob": 0.0, "words": [{"start": 2009.15, "end": 2009.69, "word": "Where", "probability": 0.08111572265625}, {"start": 2009.69, "end": 2010.67, "word": " R", "probability": 0.60205078125}, {"start": 2010.67, "end": 2012.07, "word": " is", "probability": 0.78466796875}, {"start": 2012.07, "end": 2012.85, "word": " a", "probability": 0.95654296875}, {"start": 2012.85, "end": 2013.15, "word": " real", "probability": 0.93896484375}, {"start": 2013.15, "end": 2013.65, "word": " number", "probability": 0.970703125}, {"start": 2013.65, "end": 2018.21, "word": " which", "probability": 0.470703125}, {"start": 2018.21, "end": 2020.77, "word": " generates", "probability": 0.93359375}, {"start": 2020.77, "end": 2023.13, "word": " الsequence", "probability": 0.5599365234375}, {"start": 2023.13, "end": 2023.45, "word": " هذه", "probability": 0.61865234375}, {"start": 2023.45, "end": 2025.03, "word": " generates", "probability": 0.182861328125}, {"start": 2025.03, "end": 2026.87, "word": " the", "probability": 0.70849609375}, {"start": 2026.87, "end": 2029.15, "word": " geometric", "probability": 0.8427734375}, {"start": 2029.15, "end": 2029.63, "word": " ..", "probability": 0.321044921875}, {"start": 2029.63, "end": 2029.79, "word": " the", "probability": 0.56298828125}, {"start": 2029.79, "end": 2030.01, "word": " so", "probability": 0.94189453125}, {"start": 2030.01, "end": 2030.45, "word": "-called", "probability": 0.6717529296875}, {"start": 2030.45, "end": 2031.01, "word": " geometric", "probability": 0.939453125}, {"start": 2031.01, "end": 2031.77, "word": " series", "probability": 0.9169921875}, {"start": 2031.77, "end": 2032.61, "word": " ..", "probability": 0.5556640625}, {"start": 2032.61, "end": 2033.01, "word": " geometric", "probability": 0.85791015625}, {"start": 2033.01, "end": 2034.33, "word": " series", "probability": 0.91357421875}], "temperature": 1.0}, {"id": 73, "seek": 206527, "start": 2037.05, "end": 2065.27, "text": "اللي هي summation from n equals zero to infinity from r to n okay اذا هي ال sequence هذه of real numbers بتولد infinite series او generates this infinite series اللي هي حدودها اول حد لما n بساوي سفر واحد بعدين r بعدين r تربيه", "tokens": [6027, 20292, 39896, 28811, 490, 297, 6915, 4018, 281, 13202, 490, 367, 281, 297, 1392, 1975, 15730, 39896, 2423, 8310, 29538, 295, 957, 3547, 39894, 12610, 3215, 13785, 2638, 1975, 2407, 23815, 341, 13785, 2638, 13672, 1829, 39896, 11331, 3215, 23328, 11296, 1975, 12610, 11331, 3215, 5296, 15042, 297, 4724, 3794, 995, 45865, 8608, 5172, 2288, 36764, 24401, 39182, 9957, 367, 39182, 9957, 367, 6055, 2288, 21292, 3224], "avg_logprob": -0.3211050776467807, "compression_ratio": 1.544502617801047, "no_speech_prob": 0.0, "words": [{"start": 2037.05, "end": 2037.47, "word": "اللي", "probability": 0.569091796875}, {"start": 2037.47, "end": 2037.85, "word": " هي", "probability": 0.89453125}, {"start": 2037.85, "end": 2038.71, "word": " summation", "probability": 0.6640625}, {"start": 2038.71, "end": 2040.77, "word": " from", "probability": 0.70263671875}, {"start": 2040.77, "end": 2041.09, "word": " n", "probability": 0.62451171875}, {"start": 2041.09, "end": 2041.47, "word": " equals", "probability": 0.370361328125}, {"start": 2041.47, "end": 2041.83, "word": " zero", "probability": 0.478759765625}, {"start": 2041.83, "end": 2042.03, "word": " to", "probability": 0.9658203125}, {"start": 2042.03, "end": 2042.61, "word": " infinity", "probability": 0.8779296875}, {"start": 2042.61, "end": 2043.87, "word": " from", "probability": 0.302734375}, {"start": 2043.87, "end": 2044.25, "word": " r", "probability": 0.3994140625}, {"start": 2044.25, "end": 2044.49, "word": " to", "probability": 0.85693359375}, {"start": 2044.49, "end": 2044.79, "word": " n", "probability": 0.92578125}, {"start": 2044.79, "end": 2045.55, "word": " okay", "probability": 0.1973876953125}, {"start": 2045.55, "end": 2048.15, "word": " اذا", "probability": 0.5694580078125}, {"start": 2048.15, "end": 2048.49, "word": " هي", "probability": 0.58056640625}, {"start": 2048.49, "end": 2048.73, "word": " ال", "probability": 0.83837890625}, {"start": 2048.73, "end": 2049.17, "word": " sequence", "probability": 0.78662109375}, {"start": 2049.17, "end": 2049.63, "word": " هذه", "probability": 0.469970703125}, {"start": 2049.63, "end": 2049.97, "word": " of", "probability": 0.505859375}, {"start": 2049.97, "end": 2050.21, "word": " real", "probability": 0.9619140625}, {"start": 2050.21, "end": 2050.73, "word": " numbers", "probability": 0.8212890625}, {"start": 2050.73, "end": 2052.71, "word": " بتولد", "probability": 0.95947265625}, {"start": 2052.71, "end": 2053.31, "word": " infinite", "probability": 0.94970703125}, {"start": 2053.31, "end": 2053.77, "word": " series", "probability": 0.92041015625}, {"start": 2053.77, "end": 2054.03, "word": " او", "probability": 0.812744140625}, {"start": 2054.03, "end": 2054.61, "word": " generates", "probability": 0.7509765625}, {"start": 2054.61, "end": 2055.65, "word": " this", "probability": 0.87744140625}, {"start": 2055.65, "end": 2056.05, "word": " infinite", "probability": 0.9501953125}, {"start": 2056.05, "end": 2056.75, "word": " series", "probability": 0.8974609375}, {"start": 2056.75, "end": 2059.11, "word": " اللي", "probability": 0.9326171875}, {"start": 2059.11, "end": 2059.35, "word": " هي", "probability": 0.9091796875}, {"start": 2059.35, "end": 2059.87, "word": " حدودها", "probability": 0.950927734375}, {"start": 2059.87, "end": 2060.11, "word": " اول", "probability": 0.833984375}, {"start": 2060.11, "end": 2060.37, "word": " حد", "probability": 0.970703125}, {"start": 2060.37, "end": 2060.63, "word": " لما", "probability": 0.6826171875}, {"start": 2060.63, "end": 2060.81, "word": " n", "probability": 0.55224609375}, {"start": 2060.81, "end": 2061.21, "word": " بساوي", "probability": 0.649658203125}, {"start": 2061.21, "end": 2061.61, "word": " سفر", "probability": 0.8170572916666666}, {"start": 2061.61, "end": 2062.11, "word": " واحد", "probability": 0.9833984375}, {"start": 2062.11, "end": 2063.35, "word": " بعدين", "probability": 0.807861328125}, {"start": 2063.35, "end": 2063.79, "word": " r", "probability": 0.6767578125}, {"start": 2063.79, "end": 2064.35, "word": " بعدين", "probability": 0.81640625}, {"start": 2064.35, "end": 2064.65, "word": " r", "probability": 0.67333984375}, {"start": 2064.65, "end": 2065.27, "word": " تربيه", "probability": 0.59765625}], "temperature": 1.0}, {"id": 74, "seek": 208982, "start": 2066.58, "end": 2089.82, "text": "و R أس N و هكذا ف such series is called geometric series هذه ال series اللي على الصورة هذه بنسميها geometric series الآن ال series هذه", "tokens": [2407, 497, 5551, 3794, 426, 4032, 8032, 4117, 15730, 6156, 1270, 2638, 307, 1219, 33246, 2638, 29538, 2423, 2638, 13672, 1829, 15844, 31767, 13063, 3660, 29538, 44945, 38251, 1829, 11296, 33246, 2638, 6024, 48506, 2423, 2638, 29538], "avg_logprob": -0.3595805999479796, "compression_ratio": 1.40625, "no_speech_prob": 0.0, "words": [{"start": 2066.58, "end": 2066.92, "word": "و", "probability": 0.489990234375}, {"start": 2066.92, "end": 2067.5, "word": " R", "probability": 0.29541015625}, {"start": 2067.5, "end": 2068.12, "word": " أس", "probability": 0.4912109375}, {"start": 2068.12, "end": 2069.92, "word": " N", "probability": 0.174560546875}, {"start": 2069.92, "end": 2073.62, "word": " و", "probability": 0.64208984375}, {"start": 2073.62, "end": 2074.86, "word": " هكذا", "probability": 0.90087890625}, {"start": 2074.86, "end": 2075.8, "word": " ف", "probability": 0.8671875}, {"start": 2075.8, "end": 2076.52, "word": " such", "probability": 0.38134765625}, {"start": 2076.52, "end": 2078.5, "word": " series", "probability": 0.60302734375}, {"start": 2078.5, "end": 2079.7, "word": " is", "probability": 0.90625}, {"start": 2079.7, "end": 2080.06, "word": " called", "probability": 0.8876953125}, {"start": 2080.06, "end": 2080.52, "word": " geometric", "probability": 0.84716796875}, {"start": 2080.52, "end": 2080.94, "word": " series", "probability": 0.91357421875}, {"start": 2080.94, "end": 2081.12, "word": " هذه", "probability": 0.34228515625}, {"start": 2081.12, "end": 2081.54, "word": " ال", "probability": 0.80517578125}, {"start": 2081.54, "end": 2081.82, "word": " series", "probability": 0.88671875}, {"start": 2081.82, "end": 2082.02, "word": " اللي", "probability": 0.630615234375}, {"start": 2082.02, "end": 2082.12, "word": " على", "probability": 0.6796875}, {"start": 2082.12, "end": 2082.48, "word": " الصورة", "probability": 0.97900390625}, {"start": 2082.48, "end": 2082.88, "word": " هذه", "probability": 0.52294921875}, {"start": 2082.88, "end": 2083.88, "word": " بنسميها", "probability": 0.867919921875}, {"start": 2083.88, "end": 2084.3, "word": " geometric", "probability": 0.841796875}, {"start": 2084.3, "end": 2085.06, "word": " series", "probability": 0.92529296875}, {"start": 2085.06, "end": 2086.62, "word": " الآن", "probability": 0.680419921875}, {"start": 2086.62, "end": 2088.56, "word": " ال", "probability": 0.9423828125}, {"start": 2088.56, "end": 2089.26, "word": " series", "probability": 0.9658203125}, {"start": 2089.26, "end": 2089.82, "word": " هذه", "probability": 0.8681640625}], "temperature": 1.0}, {"id": 75, "seek": 212609, "start": 2098.17, "end": 2126.09, "text": "this series واحد converges and its sum اللي هو sigma from n equals zero to infinity لRn بساوي واحد على واحد minus R إذا كان absolute R أصغر من واحد", "tokens": [11176, 2638, 36764, 24401, 9652, 2880, 293, 1080, 2408, 13672, 1829, 31439, 12771, 490, 297, 6915, 4018, 281, 13202, 5296, 49, 77, 4724, 3794, 995, 45865, 36764, 24401, 15844, 36764, 24401, 3175, 497, 11933, 15730, 25961, 8236, 497, 5551, 9381, 17082, 2288, 9154, 36764, 24401], "avg_logprob": -0.2666440249785133, "compression_ratio": 1.2418300653594772, "no_speech_prob": 0.0, "words": [{"start": 2098.17, "end": 2098.61, "word": "this", "probability": 0.158935546875}, {"start": 2098.61, "end": 2099.27, "word": " series", "probability": 0.90771484375}, {"start": 2099.27, "end": 2102.19, "word": " واحد", "probability": 0.6583251953125}, {"start": 2102.19, "end": 2103.45, "word": " converges", "probability": 0.711181640625}, {"start": 2103.45, "end": 2108.53, "word": " and", "probability": 0.31591796875}, {"start": 2108.53, "end": 2110.27, "word": " its", "probability": 0.744140625}, {"start": 2110.27, "end": 2111.51, "word": " sum", "probability": 0.9677734375}, {"start": 2111.51, "end": 2113.59, "word": " اللي", "probability": 0.620849609375}, {"start": 2113.59, "end": 2113.81, 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2655, 1863, 9957, 18558, 2880, 498, 8236, 366, 5551, 4117, 26890, 9154, 34051, 7251, 3794, 995, 45865, 36764, 24401, 16490, 1211, 11703, 9957, 995, 8717, 12984, 3555, 2655, 25724, 11622, 38207, 16247, 12610], "avg_logprob": -0.2169471153846154, "compression_ratio": 1.1538461538461537, "no_speech_prob": 0.0, "words": [{"start": 2128.09, "end": 2128.65, "word": "and", "probability": 0.350341796875}, {"start": 2128.65, "end": 2129.65, "word": " diverges", "probability": 0.787841796875}, {"start": 2129.65, "end": 2135.21, "word": " and", "probability": 0.49560546875}, {"start": 2135.21, "end": 2135.89, "word": " اتنين", "probability": 0.86590576171875}, {"start": 2135.89, "end": 2137.31, "word": " diverges", "probability": 0.813232421875}, {"start": 2137.31, "end": 2141.35, "word": " if", "probability": 0.93212890625}, {"start": 2141.35, "end": 2142.03, "word": " absolute", "probability": 0.66357421875}, {"start": 2142.03, "end": 2142.87, "word": " are", "probability": 0.91064453125}, 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K", "probability": 0.92578125}, {"start": 2176.35, "end": 2179.27, "word": " اللي", "probability": 0.947509765625}, {"start": 2179.27, "end": 2179.53, "word": " هو", "probability": 0.9921875}, {"start": 2179.53, "end": 2180.01, "word": " واحد", "probability": 0.935791015625}, {"start": 2180.01, "end": 2180.57, "word": " زائد", "probability": 0.9098307291666666}, {"start": 2180.57, "end": 2181.05, "word": " R", "probability": 0.96630859375}, {"start": 2181.05, "end": 2181.57, "word": " زائد", "probability": 0.9431966145833334}, {"start": 2181.57, "end": 2181.95, "word": " R", "probability": 0.984375}, {"start": 2181.95, "end": 2182.57, "word": " تلبية", "probability": 0.64093017578125}, {"start": 2182.57, "end": 2183.25, "word": " زائد", "probability": 0.97705078125}], "temperature": 1.0}, {"id": 78, "seek": 220098, "start": 2185.34, "end": 2200.98, "text": "R Sn وفي عندي .. في عندي .. لو ضربت Sn في R", "tokens": [49, 9264, 4032, 41185, 18871, 16254, 4386, 8978, 18871, 16254, 4386, 45164, 48812, 25513, 2655, 9264, 8978, 497], "avg_logprob": -0.44490131265238714, "compression_ratio": 1.2307692307692308, "no_speech_prob": 0.0, "words": [{"start": 2185.34, "end": 2185.92, "word": "R", "probability": 0.368408203125}, {"start": 2185.92, "end": 2186.52, "word": " Sn", "probability": 0.125732421875}, {"start": 2186.52, "end": 2187.36, "word": " وفي", "probability": 0.4676513671875}, {"start": 2187.36, "end": 2188.5, "word": " عندي", "probability": 0.758056640625}, {"start": 2188.5, "end": 2188.5, "word": " ..", "probability": 0.420654296875}, {"start": 2188.5, "end": 2190.64, "word": " في", "probability": 0.6162109375}, {"start": 2190.64, "end": 2191.32, "word": " عندي", "probability": 0.97802734375}, {"start": 2191.32, "end": 2194.64, "word": " ..", "probability": 0.46923828125}, {"start": 2194.64, "end": 2197.78, "word": " لو", "probability": 0.96142578125}, {"start": 2197.78, "end": 2198.42, "word": " ضربت", "probability": 0.970703125}, {"start": 2198.42, "end": 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هكذا", "probability": 0.8541666666666666}, {"start": 2210.6, "end": 2212.04, "word": " زاد", "probability": 0.7685546875}, {"start": 2212.04, "end": 2212.48, "word": " R", "probability": 0.91015625}, {"start": 2212.48, "end": 2212.82, "word": " أس", "probability": 0.663330078125}, {"start": 2212.82, "end": 2213.1, "word": " N", "probability": 0.85986328125}, {"start": 2213.1, "end": 2213.3, "word": " و", "probability": 0.76708984375}, {"start": 2213.3, "end": 2213.62, "word": " آخر", "probability": 0.83349609375}, {"start": 2213.62, "end": 2213.92, "word": " حد", "probability": 0.967041015625}, {"start": 2213.92, "end": 2214.5, "word": " هيكون", "probability": 0.844482421875}, {"start": 2214.5, "end": 2215.06, "word": " R", "probability": 0.9541015625}, {"start": 2215.06, "end": 2216.16, "word": " أس", "probability": 0.956298828125}, {"start": 2216.16, "end": 2216.38, "word": " N", "probability": 0.9619140625}, {"start": 2216.38, "end": 2216.78, "word": " زاد", "probability": 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"probability": 0.8564453125}, {"start": 2264.67, "end": 2266.25, "word": " واحد", "probability": 0.987548828125}, {"start": 2266.25, "end": 2266.79, "word": " سالب", "probability": 0.9842122395833334}, {"start": 2266.79, "end": 2267.17, "word": " R", "probability": 0.9677734375}, {"start": 2267.17, "end": 2272.99, "word": " ممكن", "probability": 0.965087890625}, {"start": 2272.99, "end": 2273.27, "word": " هذا", "probability": 0.7431640625}, {"start": 2273.27, "end": 2273.77, "word": " نوديه", "probability": 0.79144287109375}, {"start": 2273.77, "end": 2273.87, "word": " على", "probability": 0.5029296875}, {"start": 2273.87, "end": 2274.25, "word": " ناحية", "probability": 0.7843424479166666}, {"start": 2274.25, "end": 2274.83, "word": " التانية", "probability": 0.9736328125}, {"start": 2274.83, "end": 2276.97, "word": " فبصير", "probability": 0.92919921875}, {"start": 2276.97, "end": 2277.97, "word": " عندى", "probability": 0.66015625}, {"start": 2277.97, "end": 2278.51, "word": " هذا", "probability": 0.96630859375}, {"start": 2278.51, "end": 2279.07, "word": " سالب", "probability": 0.9791666666666666}, {"start": 2279.07, "end": 2279.53, "word": " هذا", "probability": 0.9716796875}, {"start": 2279.53, "end": 2281.35, "word": " بساوي", "probability": 0.93310546875}], "temperature": 1.0}, {"id": 82, "seek": 231087, "start": 2283.07, "end": 2310.87, "text": "سالب R to N زياد واحد على واحد سالب R الآن إذا ناخد ال absolute value للطرفين Sn سالب واحد على واحد سالب R بيطلع بيساوي الكلام هذا وهذا أصغر من أو ساوي absolute R أسن زياد واحد على absolute واحد minus R تمام؟", "tokens": [3794, 6027, 3555, 497, 281, 426, 30767, 1829, 18513, 36764, 24401, 15844, 36764, 24401, 8608, 6027, 3555, 497, 6024, 48506, 11933, 15730, 8717, 47283, 3215, 2423, 8236, 2158, 24976, 9566, 28480, 9957, 9264, 8608, 6027, 3555, 36764, 24401, 15844, 36764, 24401, 8608, 6027, 3555, 497, 4724, 1829, 9566, 1211, 3615, 4724, 1829, 3794, 995, 45865, 2423, 28820, 10943, 23758, 37037, 15730, 5551, 9381, 17082, 2288, 9154, 34051, 8608, 995, 45865, 8236, 497, 5551, 3794, 1863, 30767, 1829, 18513, 36764, 24401, 15844, 8236, 36764, 24401, 3175, 497, 46811, 10943, 22807], "avg_logprob": -0.21805556250943078, "compression_ratio": 1.8587570621468927, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 2283.07, "end": 2283.81, "word": "سالب", "probability": 0.6210479736328125}, {"start": 2283.81, "end": 2284.11, "word": " R", "probability": 0.517578125}, {"start": 2284.11, "end": 2284.29, "word": " to", "probability": 0.27197265625}, {"start": 2284.29, "end": 2284.49, "word": " N", "probability": 0.8935546875}, {"start": 2284.49, "end": 2284.95, "word": " زياد", "probability": 0.5927734375}, {"start": 2284.95, "end": 2285.43, "word": " واحد", "probability": 0.88232421875}, {"start": 2285.43, "end": 2285.71, "word": " على", "probability": 0.5703125}, {"start": 2285.71, "end": 2286.87, "word": " واحد", "probability": 0.970703125}, {"start": 2286.87, "end": 2287.33, "word": " سالب", 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"probability": 0.9347330729166666}, {"start": 2301.73, "end": 2302.73, "word": " absolute", "probability": 0.72998046875}, {"start": 2302.73, "end": 2303.63, "word": " R", "probability": 0.9619140625}, {"start": 2303.63, "end": 2304.65, "word": " أسن", "probability": 0.638671875}, {"start": 2304.65, "end": 2305.13, "word": " زياد", "probability": 0.84765625}, {"start": 2305.13, "end": 2305.55, "word": " واحد", "probability": 0.9892578125}, {"start": 2305.55, "end": 2305.83, "word": " على", "probability": 0.78466796875}, {"start": 2305.83, "end": 2306.93, "word": " absolute", "probability": 0.90087890625}, {"start": 2306.93, "end": 2307.83, "word": " واحد", "probability": 0.988037109375}, {"start": 2307.83, "end": 2308.21, "word": " minus", "probability": 0.8896484375}, {"start": 2308.21, "end": 2308.71, "word": " R", "probability": 0.982421875}, {"start": 2308.71, "end": 2310.87, "word": " تمام؟", "probability": 0.93896484375}], "temperature": 1.0}, {"id": 83, "seek": 233202, "start": 2314.94, "end": 2332.02, "text": "أذا عندي أنا هاي واحد على absolute واحد سالب R ضرب absolute R أسن زائد واحد الان if absolute R أصغر من واحد", "tokens": [10721, 15730, 18871, 16254, 41850, 8032, 47302, 36764, 24401, 15844, 8236, 36764, 24401, 8608, 6027, 3555, 497, 48812, 25513, 8236, 497, 5551, 3794, 1863, 30767, 16373, 3215, 36764, 24401, 2423, 7649, 498, 8236, 497, 5551, 9381, 17082, 2288, 9154, 36764, 24401], "avg_logprob": -0.2775297590664455, "compression_ratio": 1.4298245614035088, "no_speech_prob": 0.0, "words": [{"start": 2314.94, "end": 2316.06, "word": "أذا", "probability": 0.459228515625}, {"start": 2316.06, "end": 2316.48, "word": " عندي", "probability": 0.6251220703125}, {"start": 2316.48, "end": 2316.66, "word": " أنا", "probability": 0.367431640625}, {"start": 2316.66, "end": 2316.98, "word": " هاي", "probability": 0.654296875}, {"start": 2316.98, "end": 2317.54, "word": " واحد", "probability": 0.76708984375}, {"start": 2317.54, "end": 2317.8, "word": " على", 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0.67529296875}, {"start": 2327.36, "end": 2330.1, "word": " absolute", "probability": 0.8935546875}, {"start": 2330.1, "end": 2330.8, "word": " R", "probability": 0.9091796875}, {"start": 2330.8, "end": 2331.36, "word": " أصغر", "probability": 0.9803466796875}, {"start": 2331.36, "end": 2331.54, "word": " من", "probability": 0.99462890625}, {"start": 2331.54, "end": 2332.02, "word": " واحد", "probability": 0.971435546875}], "temperature": 1.0}, {"id": 84, "seek": 236291, "start": 2334.25, "end": 2362.91, "text": "فهذا بيؤدي ان ال limit ل absolute R to N زي 1 لما N تقول ل infinity هذا بيساوي سفر أخدناها قبل هيك وبالتالي اذا ال .. اذا انا عند ال absolute value هذه أكبر من أو ساوي سفر و أصغر من أو ساوي ثابت موجب في sequence", "tokens": [5172, 3224, 15730, 4724, 1829, 33604, 16254, 16472, 2423, 4948, 5296, 8236, 497, 281, 426, 30767, 1829, 502, 5296, 15042, 426, 6055, 39648, 5296, 13202, 23758, 4724, 1829, 3794, 995, 45865, 8608, 5172, 2288, 5551, 9778, 3215, 8315, 11296, 12174, 36150, 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"probability": 0.9788411458333334}, {"start": 2360.33, "end": 2360.85, "word": " ثابت", "probability": 0.9830729166666666}, {"start": 2360.85, "end": 2361.45, "word": " موجب", "probability": 0.9812825520833334}, {"start": 2361.45, "end": 2362.27, "word": " في", "probability": 0.96923828125}, {"start": 2362.27, "end": 2362.91, "word": " sequence", "probability": 0.9501953125}], "temperature": 1.0}, {"id": 85, "seek": 237233, "start": 2363.95, "end": 2372.33, "text": "الـ sequence هذه تقول لـ 0 وهذه الـ sequence ثابتة تقول لـ 0 اذا by sandwich theorem", "tokens": [6027, 39184, 8310, 29538, 6055, 39648, 5296, 39184, 1958, 37037, 24192, 2423, 39184, 8310, 38637, 16758, 2655, 3660, 6055, 39648, 5296, 39184, 1958, 1975, 15730, 538, 11141, 20904], "avg_logprob": -0.297144392441059, "compression_ratio": 1.3, "no_speech_prob": 0.0, "words": [{"start": 2363.95, "end": 2364.27, "word": "الـ", "probability": 0.5257568359375}, {"start": 2364.27, "end": 2364.65, "word": " sequence", "probability": 0.6474609375}, {"start": 2364.65, "end": 2364.97, "word": " هذه", "probability": 0.71142578125}, {"start": 2364.97, "end": 2365.45, "word": " تقول", "probability": 0.927001953125}, {"start": 2365.45, "end": 2365.73, "word": " لـ", "probability": 0.666015625}, {"start": 2365.73, "end": 2365.97, "word": " 0", "probability": 0.60498046875}, {"start": 2365.97, "end": 2367.51, "word": " وهذه", "probability": 0.5626220703125}, {"start": 2367.51, "end": 2367.63, "word": " الـ", "probability": 0.735595703125}, {"start": 2367.63, "end": 2368.01, "word": " sequence", "probability": 0.97900390625}, {"start": 2368.01, "end": 2368.61, "word": " ثابتة", "probability": 0.947265625}, {"start": 2368.61, "end": 2369.05, "word": " تقول", "probability": 0.978271484375}, {"start": 2369.05, "end": 2369.35, "word": " لـ", "probability": 0.9619140625}, {"start": 2369.35, "end": 2369.69, "word": " 0", "probability": 0.89697265625}, {"start": 2369.69, "end": 2370.91, "word": " اذا", "probability": 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limit", "probability": 0.90087890625}, {"start": 2399.8, "end": 2400.58, "word": " sn", "probability": 0.857421875}, {"start": 2400.58, "end": 2401.96, "word": " لما", "probability": 0.963623046875}, {"start": 2401.96, "end": 2402.22, "word": " n", "probability": 0.96044921875}, {"start": 2402.22, "end": 2402.6, "word": " تقول", "probability": 0.9039713541666666}, {"start": 2402.6, "end": 2402.72, "word": " ل", "probability": 0.966796875}, {"start": 2402.72, "end": 2403.24, "word": " infinity", "probability": 0.8720703125}, {"start": 2403.24, "end": 2403.96, "word": " بساوي", "probability": 0.9664306640625}, {"start": 2403.96, "end": 2404.34, "word": " 1", "probability": 0.900390625}, {"start": 2404.34, "end": 2404.66, "word": " على", "probability": 0.84033203125}, {"start": 2404.66, "end": 2405.04, "word": " 1", "probability": 0.9345703125}, {"start": 2405.04, "end": 2405.56, "word": " سالب", "probability": 0.7744140625}, {"start": 2405.56, "end": 2405.82, "word": " r", "probability": 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