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+{"segments": [{"id": 1, "seek": 3092, "start": 5.62, "end": 30.92, "text": "بسم الله الرحمن الرحيم المحاضرة الثالثة في مساق تحليل رياضي 2 أو تحليل حقيقي 2 كلية العلوم قسم الرياضيات بالجامعة الإسلامية مراجعة سريعة لما تم في المحاضرة السابقة والتي قبلها", "tokens": [3555, 38251, 21984, 34892, 5016, 27842, 34892, 5016, 32640, 9673, 5016, 46958, 25720, 6024, 104, 6027, 12984, 3660, 8978, 47524, 995, 4587, 6055, 5016, 20292, 1211, 12602, 1829, 46958, 1829, 568, 34051, 6055, 5016, 20292, 1211, 11331, 38436, 38436, 568, 28242, 10632, 18863, 1211, 20498, 12174, 38251, 2423, 16572, 46958, 1829, 9307, 20666, 7435, 10943, 27884, 33688, 3794, 37440, 10632, 3714, 2288, 26108, 27884, 8608, 16572, 27884, 32767, 995, 46811, 8978, 9673, 5016, 46958, 25720, 21136, 16758, 28671, 16070, 31371, 12174, 36150, 11296], "avg_logprob": -0.07468378002799693, "compression_ratio": 1.9451219512195121, "no_speech_prob": 4.76837158203125e-07, "words": [{"start": 5.62, "end": 5.98, "word": "بسم", "probability": 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404.61, "end": 404.81, "word": " مين؟", "probability": 0.9248046875}, {"start": 404.81, "end": 404.97, "word": " هي", "probability": 0.7421875}, {"start": 404.97, "end": 405.13, "word": " ال", "probability": 0.94775390625}, {"start": 405.13, "end": 405.43, "word": " F", "probability": 0.96533203125}, {"start": 405.43, "end": 406.21, "word": " inverse", "probability": 0.84130859375}], "temperature": 1.0}, {"id": 17, "seek": 43566, "start": 407.18, "end": 435.66, "text": "الآن الشرط أنه if F is differentiable at C at C then اللي هي G اللي هي الـ F inverse دي في الواقع F inverse اللي سمناها مين؟ F inverse لازم تكون differentiable at F of C and", "tokens": [6027, 148, 48506, 25124, 2288, 9566, 14739, 3224, 498, 479, 307, 819, 9364, 412, 383, 412, 383, 550, 13672, 1829, 39896, 460, 13672, 1829, 39896, 2423, 39184, 479, 17340, 11778, 1829, 8978, 2423, 14407, 4587, 3615, 479, 17340, 13672, 1829, 8608, 2304, 8315, 11296, 3714, 9957, 22807, 479, 17340, 5296, 31377, 2304, 6055, 30544, 819, 9364, 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local أو relative maximum when اللي هو there exists", "tokens": [3615, 1863, 16254, 2445, 283, 9154, 512, 15035, 286, 5296, 3615, 41260, 497, 8032, 47302, 2423, 39184, 2445, 13672, 1829, 18871, 16254, 34105, 9154, 34105, 5296, 3224, 8315, 44945, 39648, 383, 4478, 294, 286, 412, 383, 4478, 294, 286, 321, 362, 257, 2654, 34051, 4972, 6674, 562, 13672, 1829, 31439, 456, 8198], "avg_logprob": -0.2713738252531807, "compression_ratio": 1.4625, "no_speech_prob": 0.0, "words": [{"start": 1050.87, "end": 1051.27, "word": "عندي", "probability": 0.6962076822916666}, {"start": 1051.27, "end": 1051.63, "word": " function", "probability": 0.693359375}, {"start": 1051.63, "end": 1052.13, "word": " f", "probability": 0.68017578125}, {"start": 1052.13, "end": 1052.51, "word": " من", "probability": 0.869140625}, {"start": 1052.51, "end": 1052.77, "word": " some", "probability": 0.57666015625}, {"start": 1052.77, "end": 1053.25, "word": " interval", "probability": 0.9716796875}, {"start": 1053.25, "end": 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للدالة F of C أكبر أو سوى F of X لكل X في هذا الجوار", "tokens": [53, 18183, 295, 383, 37495, 22653, 44945, 15040, 38436, 10874, 2407, 9640, 11331, 2407, 6027, 9957, 2423, 39184, 383, 44945, 9381, 5172, 12174, 9566, 2288, 18183, 383, 8717, 4587, 9381, 18183, 295, 383, 30767, 16373, 3215, 18183, 8978, 23758, 25724, 2407, 9640, 1270, 300, 39894, 30544, 479, 295, 383, 39896, 5551, 4117, 26890, 12174, 32640, 3660, 24976, 3215, 6027, 3660, 479, 295, 383, 5551, 4117, 26890, 34051, 8608, 2407, 7578, 479, 295, 1783, 5296, 28820, 1783, 8978, 23758, 25724, 2407, 9640], "avg_logprob": -0.14300686375397006, "compression_ratio": 1.6184971098265897, "no_speech_prob": 7.212162017822266e-06, "words": [{"start": 1078.6, "end": 1079.24, "word": "V", "probability": 0.42529296875}, {"start": 1079.24, "end": 1079.82, "word": " Delta", "probability": 0.2064208984375}, {"start": 1079.82, "end": 1080.18, "word": " of", "probability": 0.74853515625}, {"start": 1080.18, "end": 1080.46, "word": " C", 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{"id": 46, "seek": 116555, "start": 1148.27, "end": 1165.55, "text": "there exist أي جوار آخر بتكون تسموه V Delta Prime أو V Delta of D such that يعني بنلاقي .. بنقول هذه النقطة في عندها relative minimum إذا كان لقينا جوار حواليها", "tokens": [15456, 2514, 36632, 10874, 2407, 9640, 19753, 34740, 39894, 30544, 6055, 38251, 2407, 3224, 691, 18183, 9655, 34051, 691, 18183, 295, 413, 1270, 300, 37495, 22653, 44945, 15040, 38436, 4386, 44945, 39648, 29538, 28239, 47432, 3660, 8978, 43242, 11296, 4972, 7285, 11933, 15730, 25961, 5296, 4587, 9957, 995, 10874, 2407, 9640, 11331, 2407, 6027, 1829, 11296], "avg_logprob": -0.23985745614035087, "compression_ratio": 1.3072625698324023, "no_speech_prob": 1.8477439880371094e-06, "words": [{"start": 1148.27, "end": 1148.71, "word": "there", "probability": 0.2462158203125}, {"start": 1148.71, "end": 1149.57, "word": " exist", "probability": 0.6259765625}, {"start": 1149.57, "end": 1150.69, "word": " أي", "probability": 0.81103515625}, {"start": 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{"start": 1213.62, "end": 1214.44, "word": " بنقصد", "probability": 0.898193359375}, {"start": 1214.44, "end": 1214.58, "word": " و", "probability": 0.4111328125}, {"start": 1214.58, "end": 1215.12, "word": " بنقول", "probability": 0.94384765625}, {"start": 1215.12, "end": 1216.26, "word": " local", "probability": 0.796875}, {"start": 1216.26, "end": 1217.58, "word": " extremum", "probability": 0.84521484375}, {"start": 1217.58, "end": 1218.6, "word": " معناته", "probability": 0.93701171875}, {"start": 1218.6, "end": 1219.12, "word": " يا", "probability": 0.80517578125}, {"start": 1219.12, "end": 1219.54, "word": " local", "probability": 0.89794921875}, {"start": 1219.54, "end": 1220.24, "word": " maximum", "probability": 0.9658203125}, {"start": 1220.24, "end": 1220.88, "word": " أو", "probability": 0.59423828125}, {"start": 1220.88, "end": 1221.38, "word": " local", "probability": 0.87744140625}, {"start": 1221.38, "end": 1222.12, "word": " minimum", "probability": 0.98046875}, 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12610, 7578, 1975, 5016, 8315, 9122, 8315, 8978, 2423, 33400, 11933, 15730, 39894, 2655, 8848, 37983, 4032, 8717, 3794, 10721, 1211, 8608, 33604, 6027], "avg_logprob": -0.2358530469842859, "compression_ratio": 1.198019801980198, "no_speech_prob": 5.960464477539063e-08, "words": [{"start": 1227.42, "end": 1227.9, "word": "نجي", "probability": 0.57861328125}, {"start": 1227.9, "end": 1228.26, "word": " الآن", "probability": 0.6734619140625}, {"start": 1228.26, "end": 1230.12, "word": " لنظريتنا", "probability": 0.9013671875}, {"start": 1230.12, "end": 1230.92, "word": " الأولى", "probability": 0.9889322916666666}, {"start": 1230.92, "end": 1231.58, "word": " احنا", "probability": 0.80908203125}, {"start": 1231.58, "end": 1231.84, "word": " كنا", "probability": 0.99072265625}, {"start": 1231.84, "end": 1231.98, "word": " في", "probability": 0.90478515625}, {"start": 1231.98, "end": 1232.08, "word": " ال", "probability": 0.95263671875}, {"start": 1232.08, "end": 1232.38, "word": " calculus", "probability": 0.36376953125}, {"start": 1232.38, "end": 1232.7, "word": " إذا", "probability": 0.6474609375}, {"start": 1232.7, "end": 1233.24, "word": " بتتذكر", "probability": 0.930908203125}, {"start": 1233.24, "end": 1233.36, "word": " و", "probability": 0.701171875}, {"start": 1233.36, "end": 1233.72, "word": " نسأل", "probability": 0.80352783203125}, {"start": 1233.72, "end": 1234.18, "word": " سؤال", "probability": 0.97314453125}], "temperature": 1.0}, {"id": 51, "seek": 126181, "start": 1235.77, "end": 1261.81, "text": "لما بدنا نبحث في مسألة اللي هو الـ maximum و الـ minimum سواء local maximum و local minimum أو absolute maximum و absolute minimum كنا نسأل حالنا سؤال طبعا مش معجول أنا بدي آجي كل نقاط ال domain أفحص فيه عند maximum ولا minimum لأن نقاط ال domain عدد لا نهائي uncountable number of points في غالبها", "tokens": [1211, 15042, 47525, 8315, 8717, 49628, 12984, 8978, 47524, 10721, 37977, 13672, 1829, 31439, 2423, 39184, 6674, 4032, 2423, 39184, 7285, 8608, 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طبعا", "probability": 0.9033203125}, {"start": 1251.29, "end": 1251.43, "word": " مش", "probability": 0.8369140625}, {"start": 1251.43, "end": 1251.89, "word": " معجول", "probability": 0.6904296875}, {"start": 1251.89, "end": 1252.13, "word": " أنا", "probability": 0.6875}, {"start": 1252.13, "end": 1252.47, "word": " بدي", "probability": 0.7099609375}, {"start": 1252.47, "end": 1252.91, "word": " آجي", "probability": 0.715087890625}, {"start": 1252.91, "end": 1253.47, "word": " كل", "probability": 0.9775390625}, {"start": 1253.47, "end": 1253.93, "word": " نقاط", "probability": 0.9392903645833334}, {"start": 1253.93, "end": 1254.09, "word": " ال", "probability": 0.84326171875}, {"start": 1254.09, "end": 1254.39, "word": " domain", "probability": 0.57666015625}, {"start": 1254.39, "end": 1254.95, "word": " أفحص", "probability": 0.91259765625}, {"start": 1254.95, "end": 1255.17, "word": " فيه", "probability": 0.98779296875}, {"start": 1255.17, "end": 1255.35, "word": " عند", "probability": 0.951171875}, {"start": 1255.35, "end": 1255.85, "word": " maximum", "probability": 0.6552734375}, {"start": 1255.85, "end": 1256.17, "word": " ولا", "probability": 0.493896484375}, {"start": 1256.17, "end": 1256.59, "word": " minimum", "probability": 0.93701171875}, {"start": 1256.59, "end": 1257.37, "word": " لأن", "probability": 0.758544921875}, {"start": 1257.37, "end": 1257.83, "word": " نقاط", "probability": 0.95849609375}, {"start": 1257.83, "end": 1257.99, "word": " ال", "probability": 0.943359375}, {"start": 1257.99, "end": 1258.35, "word": " domain", "probability": 0.9716796875}, {"start": 1258.35, "end": 1258.81, "word": " عدد", "probability": 0.9768880208333334}, {"start": 1258.81, "end": 1259.01, "word": " لا", "probability": 0.71923828125}, {"start": 1259.01, "end": 1259.49, "word": " نهائي", "probability": 0.884765625}, {"start": 1259.49, "end": 1260.23, "word": " uncountable", "probability": 0.7154947916666666}, {"start": 1260.23, "end": 1260.59, "word": " number", "probability": 0.97607421875}, {"start": 1260.59, "end": 1260.79, "word": " of", "probability": 0.9794921875}, {"start": 1260.79, "end": 1261.17, "word": " points", "probability": 0.93505859375}, {"start": 1261.17, "end": 1261.31, "word": " في", "probability": 0.80615234375}, {"start": 1261.31, "end": 1261.81, "word": " غالبها", "probability": 0.808349609375}], "temperature": 1.0}, {"id": 52, "seek": 128794, "start": 1262.26, "end": 1287.94, "text": "فإيش كنت حصرها؟ كنا نقول أين يمكن إيجاد الـlocal maximum أو الـlocal minimum بعد ما نحدد النقاط هذه بنقول يأتي الآن الفحص إنه هل هي local maximum ولا local minimum إذن مسألة اللي هو إيجاد ال maximum و ال minimum تبرع عبر خطوتين الخطوة الأولى وين ممكن نلاقيها", "tokens": [5172, 28814, 1829, 8592, 9122, 29399, 11331, 9381, 2288, 11296, 22807, 9122, 8315, 8717, 39648, 5551, 9957, 7251, 43020, 11933, 1829, 7435, 18513, 2423, 39184, 5842, 304, 6674, 34051, 2423, 39184, 5842, 304, 7285, 39182, 19446, 8717, 24401, 3215, 28239, 4587, 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"probability": 0.98193359375}, {"start": 1278.7, "end": 1279.58, "word": " إذن", "probability": 0.6885579427083334}, {"start": 1279.58, "end": 1280.06, "word": " مسألة", "probability": 0.9763997395833334}, {"start": 1280.06, "end": 1280.24, "word": " اللي", "probability": 0.9287109375}, {"start": 1280.24, "end": 1280.58, "word": " هو", "probability": 0.9033203125}, {"start": 1280.58, "end": 1281.66, "word": " إيجاد", "probability": 0.844970703125}, {"start": 1281.66, "end": 1281.78, "word": " ال", "probability": 0.921875}, {"start": 1281.78, "end": 1282.12, "word": " maximum", "probability": 0.5322265625}, {"start": 1282.12, "end": 1282.34, "word": " و", "probability": 0.69287109375}, {"start": 1282.34, "end": 1282.38, "word": " ال", "probability": 0.5703125}, {"start": 1282.38, "end": 1282.64, "word": " minimum", "probability": 0.9013671875}, {"start": 1282.64, "end": 1283.1, "word": " تبرع", "probability": 0.8805338541666666}, {"start": 1283.1, "end": 1283.34, "word": " عبر", "probability": 0.889892578125}, {"start": 1283.34, "end": 1284.74, "word": " خطوتين", "probability": 0.84320068359375}, {"start": 1284.74, "end": 1285.18, "word": " الخطوة", "probability": 0.9658203125}, {"start": 1285.18, "end": 1285.76, "word": " الأولى", "probability": 0.99609375}, {"start": 1285.76, "end": 1286.56, "word": " وين", "probability": 0.887451171875}, {"start": 1286.56, "end": 1287.2, "word": " ممكن", "probability": 0.9931640625}, {"start": 1287.2, "end": 1287.94, "word": " نلاقيها", "probability": 0.866943359375}], "temperature": 1.0}, {"id": 53, "seek": 130300, "start": 1288.3, "end": 1303.0, "text": "والخطوة الثانية اللي هي هل هي فعلا local maximum ولا local minimum ولا لا local maximum ولا local minimum اللي بده يشرعلنا الإجابة الأولى هي النظرية هذه", "tokens": [2407, 6027, 9778, 9566, 2407, 3660, 6024, 104, 7649, 10632, 13672, 1829, 39896, 8032, 1211, 39896, 6156, 3615, 15040, 2654, 6674, 49429, 2654, 7285, 49429, 20193, 2654, 6674, 49429, 2654, 7285, 13672, 1829, 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{"start": 1293.12, "end": 1293.72, "word": " ولا", "probability": 0.76513671875}, {"start": 1293.72, "end": 1294.08, "word": " local", "probability": 0.9169921875}, {"start": 1294.08, "end": 1294.62, "word": " minimum", "probability": 0.98388671875}, {"start": 1294.62, "end": 1295.5, "word": " ولا", "probability": 0.82763671875}, {"start": 1295.5, "end": 1296.22, "word": " لا", "probability": 0.6904296875}, {"start": 1296.22, "end": 1296.66, "word": " local", "probability": 0.91845703125}, {"start": 1296.66, "end": 1297.26, "word": " maximum", "probability": 0.95263671875}, {"start": 1297.26, "end": 1297.7, "word": " ولا", "probability": 0.958984375}, {"start": 1297.7, "end": 1298.08, "word": " local", "probability": 0.90478515625}, {"start": 1298.08, "end": 1298.58, "word": " minimum", "probability": 0.9755859375}, {"start": 1298.58, "end": 1299.3, "word": " اللي", "probability": 0.960205078125}, {"start": 1299.3, "end": 1299.64, "word": " بده", "probability": 0.728271484375}, {"start": 1299.64, "end": 1300.5, "word": " يشرعلنا", "probability": 0.8372802734375}, {"start": 1300.5, "end": 1301.52, "word": " الإجابة", "probability": 0.967041015625}, {"start": 1301.52, "end": 1301.98, "word": " الأولى", "probability": 0.9845377604166666}, {"start": 1301.98, "end": 1302.1, "word": " هي", "probability": 0.9638671875}, {"start": 1302.1, "end": 1302.7, "word": " النظرية", "probability": 0.834716796875}, {"start": 1302.7, "end": 1303.0, "word": " هذه", "probability": 0.91943359375}], "temperature": 1.0}, {"id": 54, "seek": 133237, "start": 1303.61, "end": 1332.37, "text": "النظرية هذه كنا كمان نجاوب نقول الإجابة توجد الـlocal maximum أو الـlocal minimum في أحد ثلاث مناطق إما F prime بساوي سفر أو F prime does not exist كنقات داخلية أو عند الـendpoints فكنا نحصرها في تلت أنهي مناطق فبصير عدد النقاط اللي بدنا نفحص الـlocal max أو الـlocal minimum عددها محدود وقليل بصير السؤال مقدور عليه", "tokens": [6027, 1863, 19913, 2288, 10632, 29538, 9122, 8315, 9122, 2304, 7649, 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1367.9, "text": "حتى اسمها اللي هي interior extremum theorem interior extremum theorem يعني هنحكي عن ال interior point بتقولي نفترض إن C عبارة عن نقطة داخلية لمين ل some interval I C اللي هو إشمالة نقطة داخلية ل I ال interval اللي عندي", "tokens": [33753, 7578, 24525, 2304, 11296, 13672, 1829, 39896, 10636, 4040, 449, 20904, 10636, 4040, 449, 20904, 37495, 22653, 8032, 1863, 5016, 4117, 1829, 18871, 2423, 10636, 935, 39894, 39648, 1829, 8717, 5172, 2655, 43042, 36145, 383, 6225, 3555, 9640, 3660, 18871, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 32767, 9957, 5296, 512, 15035, 286, 383, 13672, 1829, 31439, 11933, 8592, 2304, 6027, 3660, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 5296, 286, 2423, 15035, 13672, 1829, 18871, 16254], "avg_logprob": -0.19363132722770113, "compression_ratio": 1.7486033519553073, "no_speech_prob": 3.5762786865234375e-07, "words": [{"start": 1345.56, "end": 1346.12, "word": "حتى", "probability": 0.945556640625}, {"start": 1346.12, "end": 1346.58, "word": 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146270, "start": 1441.82, "end": 1462.7, "text": "وكانت عندها relative maximum أو relative minimum قطعاً هتكون الـ F prime إليها إيش بتساوي .. بتساوي سفر يعني عند .. عند النقاط الداخلية اللي الـ F prime إليها موجودة و بتشاويش سفر انساها و ماتبحثش فيها قطعا فيش فيها لا relative maximum ولا relative إيش .. minimum", "tokens": [2407, 41361, 2655, 43242, 11296, 4972, 6674, 34051, 4972, 7285, 12174, 9566, 3615, 995, 14111, 8032, 2655, 30544, 2423, 39184, 479, 5835, 11933, 20292, 11296, 11933, 1829, 8592, 39894, 3794, 995, 45865, 4386, 39894, 3794, 995, 45865, 8608, 5172, 2288, 37495, 22653, 43242, 4386, 43242, 28239, 4587, 41193, 32748, 47283, 1211, 10632, 13672, 1829, 2423, 39184, 479, 5835, 11933, 20292, 11296, 3714, 29245, 23328, 3660, 4032, 39894, 8592, 995, 45865, 8592, 8608, 5172, 2288, 16472, 3794, 995, 11296, 4032, 3714, 9307, 49628, 12984, 8592, 8978, 11296, 12174, 9566, 3615, 995, 8978, 8592, 8978, 11296, 20193, 4972, 6674, 49429, 4972, 11933, 1829, 8592, 4386, 7285], 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{"start": 1502.85, "end": 1503.29, "word": " هنا", "probability": 0.97314453125}, {"start": 1503.29, "end": 1504.47, "word": " بنجاوب", "probability": 0.9381103515625}, {"start": 1504.47, "end": 1504.63, "word": " على", "probability": 0.76904296875}, {"start": 1504.63, "end": 1505.23, "word": " سؤالنا،", "probability": 0.8673828125}, {"start": 1505.23, "end": 1505.49, "word": " هذه", "probability": 0.431396484375}, {"start": 1505.49, "end": 1505.61, "word": " اللي", "probability": 0.988525390625}, {"start": 1505.61, "end": 1506.11, "word": " بتجاوبنا", "probability": 0.97900390625}, {"start": 1506.11, "end": 1506.23, "word": " على", "probability": 0.875}, {"start": 1506.23, "end": 1506.55, "word": " سؤالنا", "probability": 0.9429931640625}, {"start": 1506.55, "end": 1506.97, "word": " بتقول", "probability": 0.901611328125}], "temperature": 1.0}, {"id": 63, "seek": 153038, "start": 1507.24, "end": 1530.38, "text": "اللي هو الـ relative maximum أو الـ relative minimum هتكون في أحد ثلاث مناطق يا F prime does not exist يا F prime بالساوية سفر يا end point واضح؟ أي سؤال؟ واضح أه؟ طيب، دي يجي تبرهن النظرية", "tokens": [6027, 20292, 31439, 2423, 39184, 4972, 6674, 34051, 2423, 39184, 4972, 7285, 8032, 2655, 30544, 8978, 5551, 24401, 38637, 1211, 5718, 104, 9154, 41193, 4587, 35186, 479, 5835, 775, 406, 2514, 35186, 479, 5835, 20666, 3794, 995, 2407, 10632, 8608, 5172, 2288, 35186, 917, 935, 4032, 46958, 5016, 22807, 36632, 8608, 33604, 6027, 22807, 4032, 46958, 5016, 5551, 3224, 22807, 23032, 1829, 3555, 12399, 11778, 1829, 7251, 7435, 1829, 6055, 26890, 3224, 1863, 28239, 19913, 2288, 10632], "avg_logprob": -0.20773236701885858, "compression_ratio": 1.4607329842931938, "no_speech_prob": 1.9073486328125e-06, "words": [{"start": 1507.24, "end": 1507.82, "word": "اللي", "probability": 0.704833984375}, {"start": 1507.82, "end": 1508.06, "word": " هو", "probability": 0.97607421875}, {"start": 1508.06, "end": 1508.66, "word": " الـ", "probability": 0.742919921875}, {"start": 1508.66, "end": 1508.98, "word": " relative", "probability": 0.80810546875}, {"start": 1508.98, "end": 1509.58, "word": " maximum", "probability": 0.953125}, {"start": 1509.58, "end": 1509.86, "word": " أو", "probability": 0.84521484375}, {"start": 1509.86, "end": 1509.98, "word": " الـ", "probability": 0.76904296875}, {"start": 1509.98, "end": 1510.2, "word": " relative", "probability": 0.9775390625}, {"start": 1510.2, "end": 1510.56, "word": " minimum", "probability": 0.9833984375}, {"start": 1510.56, "end": 1511.1, "word": " هتكون", "probability": 0.7933756510416666}, {"start": 1511.1, "end": 1511.28, "word": " في", "probability": 0.96826171875}, {"start": 1511.28, "end": 1511.48, "word": " أحد", "probability": 0.927978515625}, {"start": 1511.48, "end": 1511.8, "word": " ثلاث", "probability": 0.9642333984375}, {"start": 1511.8, "end": 1512.34, "word": " مناطق", "probability": 0.96826171875}, {"start": 1512.34, "end": 1513.16, "word": " يا", "probability": 0.6171875}, {"start": 1513.16, "end": 1513.88, "word": " F", "probability": 0.529296875}, {"start": 1513.88, "end": 1514.28, "word": " prime", "probability": 0.2744140625}, {"start": 1514.28, "end": 1514.5, "word": " does", "probability": 0.72314453125}, {"start": 1514.5, "end": 1514.7, "word": " not", "probability": 0.966796875}, {"start": 1514.7, "end": 1515.24, "word": " exist", "probability": 0.9501953125}, {"start": 1515.24, "end": 1516.0, "word": " يا", "probability": 0.75927734375}, {"start": 1516.0, "end": 1516.24, "word": " F", "probability": 0.98876953125}, {"start": 1516.24, "end": 1516.54, "word": " prime", "probability": 0.81201171875}, {"start": 1516.54, "end": 1516.94, "word": " بالساوية", "probability": 0.7162109375}, {"start": 1516.94, "end": 1517.36, "word": " سفر", "probability": 0.8170572916666666}, {"start": 1517.36, "end": 1518.06, "word": " يا", "probability": 0.57861328125}, {"start": 1518.06, "end": 1518.56, "word": " end", "probability": 0.7275390625}, {"start": 1518.56, "end": 1519.3, "word": " point", "probability": 0.634765625}, {"start": 1519.3, "end": 1522.0, "word": " واضح؟", "probability": 0.876953125}, {"start": 1522.0, "end": 1522.72, "word": " أي", "probability": 0.80224609375}, {"start": 1522.72, "end": 1524.96, "word": " سؤال؟", "probability": 0.9730224609375}, {"start": 1524.96, "end": 1526.04, "word": " واضح", "probability": 0.9871419270833334}, {"start": 1526.04, "end": 1527.18, "word": " أه؟", "probability": 0.6534016927083334}, {"start": 1527.18, "end": 1527.64, "word": " طيب،", "probability": 0.76947021484375}, {"start": 1527.64, "end": 1527.78, "word": " دي", "probability": 0.9208984375}, {"start": 1527.78, "end": 1527.96, "word": " يجي", "probability": 0.7312825520833334}, {"start": 1527.96, "end": 1528.4, "word": " تبرهن", "probability": 0.8951416015625}, {"start": 1528.4, "end": 1530.38, "word": " النظرية", "probability": 0.9403076171875}], "temperature": 1.0}, {"id": 64, "seek": 155839, "start": 1530.93, "end": 1558.39, "text": "الآن هو البروحان اللي مكتوب هنا we prove for the case that F has relative maximum at C هيه مكتوب أنا مابديش أبرهن ال maximum بتبرهنكم مين ال minimum إذا الآن بدنا نفترض نفترض ال proof خليني أكتب هنا ال proof بدي أفترض", "tokens": [6027, 148, 48506, 31439, 2423, 26890, 2407, 5016, 7649, 13672, 1829, 3714, 4117, 2655, 37746, 34105, 321, 7081, 337, 264, 1389, 300, 479, 575, 4972, 6674, 412, 383, 39896, 3224, 3714, 4117, 2655, 37746, 41850, 3714, 16758, 16254, 8592, 5551, 26890, 3224, 1863, 2423, 6674, 39894, 26890, 3224, 1863, 24793, 3714, 9957, 2423, 7285, 11933, 15730, 6024, 48506, 47525, 8315, 8717, 5172, 2655, 43042, 8717, 5172, 2655, 43042, 2423, 8177, 16490, 1211, 9957, 1829, 5551, 4117, 2655, 3555, 34105, 2423, 8177, 4724, 16254, 5551, 5172, 2655, 43042], "avg_logprob": -0.2745028402317654, "compression_ratio": 1.6927083333333333, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1530.93, "end": 1531.55, "word": "الآن", "probability": 0.71728515625}, {"start": 1531.55, "end": 1533.91, "word": " هو", "probability": 0.876953125}, {"start": 1533.91, "end": 1535.05, "word": " البروحان", "probability": 0.86904296875}, {"start": 1535.05, "end": 1535.19, "word": " اللي", "probability": 0.707763671875}, {"start": 1535.19, "end": 1535.55, "word": " مكتوب", "probability": 0.9898681640625}, {"start": 1535.55, "end": 1535.97, "word": " هنا", "probability": 0.97900390625}, {"start": 1535.97, "end": 1536.55, "word": " we", "probability": 0.390625}, {"start": 1536.55, "end": 1537.01, "word": " prove", "probability": 0.8935546875}, {"start": 1537.01, "end": 1538.53, "word": " for", "probability": 0.720703125}, {"start": 1538.53, "end": 1538.77, "word": " the", "probability": 0.88330078125}, {"start": 1538.77, "end": 1539.11, "word": " case", "probability": 0.94677734375}, {"start": 1539.11, "end": 1539.45, "word": " that", "probability": 0.92919921875}, {"start": 1539.45, "end": 1539.65, "word": " F", "probability": 0.5712890625}, {"start": 1539.65, "end": 1539.89, "word": " has", "probability": 0.90869140625}, {"start": 1539.89, "end": 1540.29, "word": " relative", "probability": 0.90185546875}, {"start": 1540.29, "end": 1540.91, "word": " maximum", "probability": 0.94677734375}, {"start": 1540.91, "end": 1541.17, "word": " at", "probability": 0.50439453125}, {"start": 1541.17, "end": 1541.37, "word": " C", "probability": 0.61083984375}, {"start": 1541.37, "end": 1541.91, "word": " هيه", "probability": 0.3560791015625}, {"start": 1541.91, "end": 1542.41, "word": " مكتوب", "probability": 0.9825439453125}, {"start": 1542.41, "end": 1543.09, "word": " أنا", "probability": 0.767578125}, {"start": 1543.09, "end": 1543.51, "word": " مابديش", "probability": 0.70440673828125}, {"start": 1543.51, "end": 1543.95, "word": " أبرهن", "probability": 0.85986328125}, {"start": 1543.95, "end": 1544.05, "word": " ال", "probability": 0.84716796875}, {"start": 1544.05, "end": 1544.37, "word": " maximum", "probability": 0.939453125}, {"start": 1544.37, "end": 1545.15, "word": " بتبرهنكم", "probability": 0.7531494140625}, {"start": 1545.15, "end": 1545.49, "word": " مين", "probability": 0.5552978515625}, {"start": 1545.49, "end": 1546.03, "word": " ال", "probability": 0.8935546875}, {"start": 1546.03, "end": 1546.39, "word": " minimum", "probability": 0.97119140625}, {"start": 1546.39, "end": 1546.85, "word": " إذا", "probability": 0.7685546875}, {"start": 1546.85, "end": 1547.41, "word": " الآن", "probability": 0.761474609375}, {"start": 1547.41, "end": 1548.43, "word": " بدنا", "probability": 0.942138671875}, {"start": 1548.43, "end": 1549.81, "word": " نفترض", "probability": 0.9906005859375}, {"start": 1549.81, "end": 1551.73, "word": " نفترض", "probability": 0.9288330078125}, {"start": 1551.73, "end": 1551.89, "word": " ال", "probability": 0.182373046875}, {"start": 1551.89, "end": 1552.29, "word": " proof", "probability": 0.8857421875}, {"start": 1552.29, "end": 1552.69, "word": " خليني", "probability": 0.7745361328125}, {"start": 1552.69, "end": 1552.93, "word": " أكتب", "probability": 0.874267578125}, {"start": 1552.93, "end": 1553.29, "word": " هنا", "probability": 0.97705078125}, {"start": 1553.29, "end": 1554.23, "word": " ال", "probability": 0.72265625}, {"start": 1554.23, "end": 1554.79, "word": " proof", "probability": 0.98828125}, {"start": 1554.79, "end": 1557.87, "word": " بدي", "probability": 0.4412841796875}, {"start": 1557.87, "end": 1558.39, "word": " أفترض", "probability": 0.8985595703125}], "temperature": 1.0}, {"id": 65, "seek": 158812, "start": 1559.3, "end": 1588.12, "text": "C نقطة داخلية ونفترض إن F أشبهلها have a relative minimum relative maximum محلولة لأن suppose that F has a relative maximum at C element in I0 ماشي؟", "tokens": [34, 8717, 47432, 3660, 11778, 47283, 1211, 10632, 4032, 1863, 5172, 2655, 43042, 36145, 479, 5551, 8592, 3555, 3224, 1211, 11296, 362, 257, 4972, 7285, 4972, 6674, 3714, 5016, 1211, 12610, 3660, 5296, 33456, 7297, 300, 479, 575, 257, 4972, 6674, 412, 383, 4478, 294, 286, 15, 3714, 33599, 1829, 22807], "avg_logprob": -0.30618990843112653, "compression_ratio": 1.230263157894737, "no_speech_prob": 1.1920928955078125e-07, "words": [{"start": 1559.3, "end": 1559.76, "word": "C", "probability": 0.625}, {"start": 1559.76, "end": 1560.5, "word": " نقطة", "probability": 0.89697265625}, {"start": 1560.5, "end": 1561.18, "word": " داخلية", "probability": 0.9940185546875}, {"start": 1561.18, "end": 1562.6, "word": " ونفترض", "probability": 0.95107421875}, {"start": 1562.6, "end": 1562.76, "word": " إن", "probability": 0.2734375}, {"start": 1562.76, "end": 1563.0, "word": " F", "probability": 0.6982421875}, {"start": 1563.0, "end": 1563.84, "word": " أشبهلها", "probability": 0.7257080078125}, {"start": 1563.84, "end": 1564.56, "word": " have", "probability": 0.251708984375}, {"start": 1564.56, "end": 1564.82, "word": " a", "probability": 0.8427734375}, {"start": 1564.82, "end": 1565.14, "word": " relative", "probability": 0.9736328125}, {"start": 1565.14, "end": 1565.56, "word": " minimum", "probability": 0.7353515625}, {"start": 1565.56, "end": 1566.04, "word": " relative", "probability": 0.71826171875}, {"start": 1566.04, "end": 1566.42, "word": " maximum", "probability": 0.97802734375}, {"start": 1566.42, "end": 1568.02, "word": " محلولة", "probability": 0.8470703125}, {"start": 1568.02, "end": 1568.56, "word": " لأن", "probability": 0.3917236328125}, {"start": 1568.56, "end": 1569.46, "word": " suppose", "probability": 0.79736328125}, {"start": 1569.46, "end": 1572.64, "word": " that", "probability": 0.8896484375}, {"start": 1572.64, "end": 1574.32, "word": " F", "probability": 0.8720703125}, {"start": 1574.32, "end": 1576.08, "word": " has", "probability": 0.93798828125}, {"start": 1576.08, "end": 1577.2, "word": " a", "probability": 0.8193359375}, {"start": 1577.2, "end": 1578.0, "word": " relative", "probability": 0.9599609375}, {"start": 1578.0, "end": 1581.02, "word": " maximum", "probability": 0.9677734375}, {"start": 1581.02, "end": 1582.6, "word": " at", "probability": 0.9638671875}, {"start": 1582.6, "end": 1583.38, "word": " C", "probability": 0.8583984375}, {"start": 1583.38, "end": 1584.0, "word": " element", "probability": 0.83935546875}, {"start": 1584.0, "end": 1584.4, "word": " in", "probability": 0.59814453125}, {"start": 1584.4, "end": 1586.46, "word": " I0", "probability": 0.3023681640625}, {"start": 1586.46, "end": 1588.12, "word": " ماشي؟", "probability": 0.88427734375}], "temperature": 1.0}, {"id": 66, "seek": 160188, "start": 1597.0, "end": 1601.88, "text": "نعم نفترض إنها minimum لأن ال case تبعت ال maximum محلولة", "tokens": [1863, 25957, 8717, 5172, 2655, 43042, 36145, 11296, 7285, 5296, 33456, 2423, 1389, 6055, 3555, 34268, 2423, 6674, 3714, 5016, 1211, 12610, 3660], "avg_logprob": -0.359375, "compression_ratio": 1.011764705882353, "no_speech_prob": 2.3245811462402344e-06, "words": [{"start": 1596.9999999999998, "end": 1597.6799999999998, "word": "نعم", "probability": 0.78125}, {"start": 1597.6799999999998, "end": 1598.36, "word": " نفترض", "probability": 0.6769866943359375}, {"start": 1598.36, "end": 1598.62, "word": " إنها", "probability": 0.639404296875}, {"start": 1598.62, "end": 1599.02, "word": " minimum", "probability": 0.85498046875}, {"start": 1599.02, "end": 1599.84, "word": " لأن", "probability": 0.671630859375}, {"start": 1599.84, "end": 1599.98, "word": " ال", "probability": 0.306396484375}, {"start": 1599.98, "end": 1600.28, "word": " case", "probability": 0.810546875}, {"start": 1600.28, "end": 1600.62, "word": " تبعت", "probability": 0.76904296875}, {"start": 1600.62, "end": 1600.74, "word": " ال", "probability": 0.4853515625}, {"start": 1600.74, "end": 1601.08, "word": " maximum", "probability": 0.95703125}, {"start": 1601.08, "end": 1601.88, "word": " محلولة", "probability": 0.97841796875}], "temperature": 1.0}, {"id": 67, "seek": 162266, "start": 1602.38, "end": 1622.66, "text": "واضح؟ الان لو كان F as relative extremum بدنا نصل الان extreme يابتكون maximum يابتكون minimum case ال maximum هي مكتوبة بتجروها لحالكوا نفس الفكرة ده أكتف بت mean F as a relative H minimum", "tokens": [2407, 46958, 5016, 22807, 2423, 7649, 45164, 25961, 479, 382, 4972, 4040, 449, 47525, 8315, 8717, 36520, 2423, 7649, 8084, 7251, 16758, 2655, 30544, 6674, 7251, 16758, 2655, 30544, 7285, 1389, 2423, 6674, 39896, 3714, 4117, 2655, 37746, 3660, 39894, 7435, 32887, 11296, 5296, 5016, 6027, 4117, 14407, 8717, 36178, 27188, 4117, 25720, 11778, 3224, 5551, 4117, 2655, 5172, 39894, 914, 479, 382, 257, 4972, 389, 7285], "avg_logprob": -0.3384650792269146, "compression_ratio": 1.5549132947976878, "no_speech_prob": 2.980232238769531e-07, "words": [{"start": 1602.38, "end": 1603.62, "word": "واضح؟", "probability": 0.926513671875}, {"start": 1603.62, "end": 1604.12, "word": " الان", "probability": 0.53082275390625}, {"start": 1604.12, "end": 1605.72, "word": " لو", "probability": 0.68505859375}, {"start": 1605.72, "end": 1606.02, "word": " كان", "probability": 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minus c as x بتروح لل c برضه ايش ماله أصغر من 0 إذا في جوار there exist v delta of x و باخد ال delta اللي هي delta prime بقدر أخدها و أصغر يساوي ال delta prime by such that", "tokens": [1211, 9566, 15040, 4587, 9566, 3714, 33599, 1829, 21542, 6027, 2423, 7649, 1975, 1829, 8592, 20449, 8315, 3224, 283, 5835, 295, 269, 5551, 4117, 26890, 9154, 1958, 44945, 36178, 16247, 3794, 1211, 37746, 4948, 283, 295, 2031, 8717, 995, 4587, 9381, 283, 295, 269, 15844, 2031, 3175, 269, 382, 2031, 39894, 32887, 5016, 24976, 269, 4724, 43042, 3224, 1975, 1829, 8592, 3714, 6027, 3224, 5551, 9381, 17082, 2288, 9154, 1958, 11933, 15730, 8978, 10874, 2407, 9640, 456, 2514, 371, 8289, 295, 2031, 4032, 4724, 47283, 3215, 2423, 8289, 13672, 1829, 39896, 8289, 5835, 4724, 28543, 2288, 5551, 9778, 3215, 11296, 4032, 5551, 9381, 17082, 2288, 7251, 3794, 995, 45865, 2423, 8289, 5835, 538, 1270, 300], "avg_logprob": -0.2591594771064561, "compression_ratio": 1.598360655737705, "no_speech_prob": 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{"start": 2043.38, "end": 2043.54, "word": " من", "probability": 0.99755859375}, {"start": 2043.54, "end": 2043.86, "word": " 0", "probability": 0.876953125}, {"start": 2043.86, "end": 2044.8, "word": " إذا", "probability": 0.595703125}, {"start": 2044.8, "end": 2045.06, "word": " في", "probability": 0.86328125}, {"start": 2045.06, "end": 2045.76, "word": " جوار", "probability": 0.9202473958333334}, {"start": 2045.76, "end": 2046.58, "word": " there", "probability": 0.75439453125}, {"start": 2046.58, "end": 2047.12, "word": " exist", "probability": 0.53515625}, {"start": 2047.12, "end": 2048.22, "word": " v", "probability": 0.53564453125}, {"start": 2048.22, "end": 2048.62, "word": " delta", "probability": 0.65478515625}, {"start": 2048.62, "end": 2048.9, "word": " of", "probability": 0.9775390625}, {"start": 2048.9, "end": 2049.28, "word": " x", "probability": 0.98095703125}, {"start": 2049.28, "end": 2049.4, "word": " و", "probability": 0.55908203125}, {"start": 2049.4, "end": 2049.68, "word": " باخد", "probability": 0.9405924479166666}, {"start": 2049.68, "end": 2049.82, "word": " ال", "probability": 0.74951171875}, {"start": 2049.82, "end": 2050.08, "word": " delta", "probability": 0.529296875}, {"start": 2050.08, "end": 2050.32, "word": " اللي", "probability": 0.90673828125}, {"start": 2050.32, "end": 2050.66, "word": " هي", "probability": 0.9072265625}, {"start": 2050.66, "end": 2051.4, "word": " delta", "probability": 0.7802734375}, {"start": 2051.4, "end": 2051.94, "word": " prime", "probability": 0.8740234375}, {"start": 2051.94, "end": 2052.4, "word": " بقدر", "probability": 0.8896484375}, {"start": 2052.4, "end": 2052.82, "word": " أخدها", "probability": 0.9259033203125}, {"start": 2052.82, "end": 2053.02, "word": " و", "probability": 0.328125}, {"start": 2053.02, "end": 2053.26, "word": " أصغر", "probability": 0.9803466796875}, {"start": 2053.26, "end": 2053.5, "word": " يساوي", "probability": 0.821533203125}, {"start": 2053.5, "end": 2053.6, "word": " ال", "probability": 0.73095703125}, {"start": 2053.6, "end": 2053.74, "word": " delta", "probability": 0.86474609375}, {"start": 2053.74, "end": 2054.18, "word": " prime", "probability": 0.87158203125}, {"start": 2054.18, "end": 2055.12, "word": " by", "probability": 0.236083984375}, {"start": 2055.12, "end": 2055.56, "word": " such", "probability": 0.9716796875}, {"start": 2055.56, "end": 2055.98, "word": " that", "probability": 0.94873046875}], "temperature": 1.0}, {"id": 84, "seek": 208357, "start": 2057.23, "end": 2083.57, "text": "اللي هو f of x ناقص f of c على x minus c أصغر من مين؟ من 0 الآن اللي بيوصلني لتناقض هتلاقيها مش choosing x هنا و انا هاختارها في الجهة التانية في الجهة بتشوف كيف لأن بيقول choose x element in c و c زائد delta then", "tokens": [6027, 20292, 31439, 283, 295, 2031, 8717, 995, 4587, 9381, 283, 295, 269, 15844, 2031, 3175, 269, 5551, 9381, 17082, 2288, 9154, 3714, 9957, 22807, 9154, 1958, 6024, 48506, 13672, 1829, 4724, 1829, 2407, 36520, 22653, 5296, 2655, 8315, 4587, 11242, 8032, 2655, 15040, 38436, 11296, 37893, 10875, 2031, 34105, 4032, 1975, 8315, 8032, 47283, 2655, 9640, 11296, 8978, 25724, 3224, 3660, 16712, 7649, 10632, 8978, 25724, 3224, 3660, 39894, 8592, 38688, 9122, 33911, 5296, 33456, 4724, 1829, 39648, 2826, 2031, 4478, 294, 269, 4032, 269, 30767, 16373, 3215, 8289, 550], "avg_logprob": -0.255264942412791, "compression_ratio": 1.5233644859813085, "no_speech_prob": 1.6570091247558594e-05, "words": [{"start": 2057.23, "end": 2057.51, "word": "اللي", "probability": 0.726318359375}, {"start": 2057.51, "end": 2057.73, "word": " هو", "probability": 0.96630859375}, {"start": 2057.73, "end": 2058.01, "word": " f", "probability": 0.354248046875}, {"start": 2058.01, "end": 2058.19, "word": " of", "probability": 0.46240234375}, {"start": 2058.19, "end": 2058.65, "word": " x", "probability": 0.763671875}, {"start": 2058.65, "end": 2060.71, "word": " ناقص", "probability": 0.80755615234375}, {"start": 2060.71, "end": 2060.95, 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"probability": 0.6885986328125}, {"start": 2067.17, "end": 2067.31, "word": " اللي", "probability": 0.94287109375}, {"start": 2067.31, "end": 2067.93, "word": " بيوصلني", "probability": 0.759814453125}, {"start": 2067.93, "end": 2068.59, "word": " لتناقض", "probability": 0.9298828125}, {"start": 2068.59, "end": 2069.23, "word": " هتلاقيها", "probability": 0.87958984375}, {"start": 2069.23, "end": 2069.49, "word": " مش", "probability": 0.884765625}, {"start": 2069.49, "end": 2069.99, "word": " choosing", "probability": 0.828125}, {"start": 2069.99, "end": 2070.39, "word": " x", "probability": 0.88720703125}, {"start": 2070.39, "end": 2070.77, "word": " هنا", "probability": 0.8916015625}, {"start": 2070.77, "end": 2071.33, "word": " و", "probability": 0.94384765625}, {"start": 2071.33, "end": 2071.43, "word": " انا", "probability": 0.39508056640625}, {"start": 2071.43, "end": 2072.27, "word": " هاختارها", "probability": 0.832958984375}, {"start": 2072.27, "end": 2072.87, "word": " في", "probability": 0.9541015625}, {"start": 2072.87, "end": 2073.19, "word": " الجهة", "probability": 0.9845377604166666}, {"start": 2073.19, "end": 2073.47, "word": " التانية", "probability": 0.9500325520833334}, {"start": 2073.47, "end": 2073.59, "word": " في", "probability": 0.1221923828125}, {"start": 2073.59, "end": 2073.85, "word": " الجهة", "probability": 0.8935546875}, {"start": 2073.85, "end": 2074.47, "word": " بتشوف", "probability": 0.7584635416666666}, {"start": 2074.47, "end": 2074.79, "word": " كيف", "probability": 0.9765625}, {"start": 2074.79, "end": 2075.45, "word": " لأن", "probability": 0.6796875}, {"start": 2075.45, "end": 2075.79, "word": " بيقول", "probability": 0.8924153645833334}, {"start": 2075.79, "end": 2077.17, "word": " choose", "probability": 0.87939453125}, {"start": 2077.17, "end": 2078.69, "word": " x", "probability": 0.85302734375}, {"start": 2078.69, "end": 2079.39, "word": " element", "probability": 0.84423828125}, {"start": 2079.39, "end": 2079.77, "word": " in", "probability": 0.89208984375}, {"start": 2079.77, "end": 2080.13, "word": " c", "probability": 0.63916015625}, {"start": 2080.13, "end": 2080.37, "word": " و", "probability": 0.9326171875}, {"start": 2080.37, "end": 2080.75, "word": " c", "probability": 0.75732421875}, {"start": 2080.75, "end": 2081.41, "word": " زائد", "probability": 0.79931640625}, {"start": 2081.41, "end": 2081.83, "word": " delta", "probability": 0.3720703125}, {"start": 2081.83, "end": 2083.57, "word": " then", "probability": 0.292724609375}], "temperature": 1.0}, {"id": 85, "seek": 209719, "start": 2087.03, "end": 2097.19, "text": "هيكون عندى الآن الـ X minus C إيش ماله أكبر من 0 واضح أه؟", "tokens": [3224, 1829, 30544, 43242, 7578, 6024, 48506, 2423, 39184, 1783, 3175, 383, 11933, 1829, 8592, 3714, 6027, 3224, 5551, 4117, 26890, 9154, 1958, 4032, 46958, 5016, 5551, 3224, 22807], "avg_logprob": -0.29244790474573773, "compression_ratio": 1.0108695652173914, "no_speech_prob": 1.7881393432617188e-07, "words": [{"start": 2087.03, "end": 2087.53, "word": "هيكون", "probability": 0.7618001302083334}, {"start": 2087.53, "end": 2087.93, "word": " عندى", "probability": 0.8251953125}, {"start": 2087.93, "end": 2088.31, "word": " الآن", "probability": 0.6416015625}, {"start": 2088.31, "end": 2088.71, "word": " الـ", "probability": 0.89306640625}, {"start": 2088.71, "end": 2088.97, "word": " X", "probability": 0.488037109375}, {"start": 2088.97, "end": 2089.41, "word": " minus", "probability": 0.33203125}, {"start": 2089.41, "end": 2089.99, "word": " C", "probability": 0.95556640625}, {"start": 2089.99, "end": 2091.25, "word": " إيش", "probability": 0.6885579427083334}, {"start": 2091.25, "end": 2091.79, "word": " ماله", "probability": 0.8185221354166666}, {"start": 2091.79, "end": 2093.71, "word": " أكبر", "probability": 0.8929036458333334}, {"start": 2093.71, "end": 2093.87, "word": " من", "probability": 0.9970703125}, {"start": 2093.87, "end": 2094.13, "word": " 0", "probability": 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"end": 2562.53, "text": "طبعا حسب .. حسب الدالة اللي هو أكيد بتلاقي إذا تحققت الشروط الأقل في نقطة عندها اللي هو المماس بوازي محور السينات أي سؤال؟ ال proof ال proof برضه احنا كنا أحيانا نبرهنه في ال calculus خلينا نبرهنوها، أكيد هندرهنوها عندي", "tokens": [9566, 3555, 3615, 995, 11331, 35457, 4386, 11331, 35457, 32748, 6027, 3660, 13672, 1829, 31439, 5551, 4117, 25708, 39894, 15040, 38436, 11933, 15730, 6055, 5016, 4587, 38149, 25124, 32887, 9566, 16247, 4587, 1211, 8978, 8717, 47432, 3660, 43242, 11296, 13672, 1829, 31439, 9673, 15042, 3794, 4724, 2407, 31377, 1829, 3714, 5016, 13063, 21136, 1829, 8315, 2655, 36632, 8608, 33604, 6027, 22807, 2423, 8177, 2423, 8177, 4724, 43042, 3224, 1975, 5016, 8315, 9122, 8315, 5551, 5016, 1829, 7649, 995, 8717, 26890, 3224, 1863, 3224, 8978, 2423, 33400, 16490, 20292, 8315, 8717, 26890, 3224, 1863, 2407, 11296, 12399, 5551, 4117, 25708, 8032, 41260, 2288, 3224, 1863, 2407, 11296, 18871, 16254], "avg_logprob": -0.14936927207019352, 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"probability": 0.76904296875}, {"start": 2850.88, "end": 2851.8, "word": " برهان", "probability": 0.8477783203125}, {"start": 2851.8, "end": 2851.94, "word": " ال", "probability": 0.90087890625}, {"start": 2851.94, "end": 2852.38, "word": " roles", "probability": 0.25537109375}, {"start": 2852.38, "end": 2853.14, "word": " theory", "probability": 0.49462890625}], "temperature": 1.0}, {"id": 116, "seek": 287751, "start": 2854.07, "end": 2877.51, "text": "أي سؤال اللي بعده الآن أوصلنا لإن نقدر الآن نحكي عن اللي هو نظرية القيمة المتوسطة أو الـ Mean Value Theorem نظرية القيمة المتوسطة أو الـ Mean Value Theorem برضه", "tokens": [10721, 1829, 8608, 33604, 6027, 13672, 1829, 39182, 3224, 6024, 48506, 34051, 36520, 8315, 5296, 28814, 1863, 8717, 28543, 2288, 6024, 48506, 8717, 5016, 4117, 1829, 18871, 13672, 1829, 31439, 8717, 19913, 2288, 10632, 25062, 32640, 3660, 9673, 2655, 41779, 9566, 3660, 34051, 2423, 39184, 12302, 39352, 440, 37956, 8717, 19913, 2288, 10632, 25062, 32640, 3660, 9673, 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3257.15, "end": 3257.49, "word": " طريق", "probability": 0.9949544270833334}, {"start": 3257.49, "end": 3257.89, "word": " الـ", "probability": 0.48779296875}, {"start": 3257.89, "end": 3257.89, "word": " Mean", "probability": 0.454345703125}, {"start": 3257.89, "end": 3259.81, "word": " Value", "probability": 0.95458984375}, {"start": 3259.81, "end": 3260.63, "word": " Theorem", "probability": 0.84033203125}, {"start": 3260.63, "end": 3262.73, "word": " النظرية", "probability": 0.95751953125}, {"start": 3262.73, "end": 3262.83, "word": " اللي", "probability": 0.98486328125}, {"start": 3262.83, "end": 3263.21, "word": " بتقول", "probability": 0.980224609375}, {"start": 3263.21, "end": 3263.57, "word": " ليه", "probability": 0.794189453125}], "temperature": 1.0}, {"id": 132, "seek": 328954, "start": 3264.16, "end": 3289.54, "text": "اللي هي اللي باختصار بنقول أنه لو كانت المشتقة الأولى لدالة بتساوي سفر إذن هي اللي هتكون مين هي المشتقة الثابتة طيب نشوف بالظبط أيش اللي بقوله بقولوا .. نفترض أن F continuous F عبارة عن دالة من A و B", "tokens": [6027, 20292, 39896, 13672, 1829, 4724, 47283, 2655, 9381, 9640, 44945, 39648, 14739, 3224, 45164, 25961, 2655, 9673, 8592, 2655, 28671, 16247, 12610, 7578, 5296, 3215, 6027, 3660, 39894, 3794, 995, 45865, 8608, 5172, 2288, 11933, 8848, 1863, 39896, 13672, 1829, 8032, 2655, 30544, 3714, 9957, 39896, 9673, 8592, 2655, 28671, 6024, 104, 16758, 2655, 3660, 23032, 1829, 3555, 8717, 8592, 38688, 20666, 19913, 3555, 9566, 36632, 8592, 13672, 1829, 4724, 39648, 3224, 4724, 39648, 14407, 4386, 8717, 5172, 2655, 43042, 14739, 479, 10957, 479, 6225, 3555, 9640, 3660, 18871, 11778, 6027, 3660, 9154, 316, 4032, 363], "avg_logprob": -0.18016581784705726, "compression_ratio": 1.71, "no_speech_prob": 1.6689300537109375e-06, "words": [{"start": 3264.16, "end": 3264.48, "word": "اللي", "probability": 0.880615234375}, {"start": 3264.48, "end": 3264.62, "word": " هي", "probability": 0.5859375}, {"start": 3264.62, "end": 3264.82, "word": " اللي", 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0.91552734375}, {"start": 3532.65, "end": 3532.99, "word": " I,", "probability": 0.9775390625}, {"start": 3533.07, "end": 3533.19, "word": " A", "probability": 0.82568359375}, {"start": 3533.19, "end": 3533.51, "word": " وB", "probability": 0.6767578125}, {"start": 3533.51, "end": 3534.53, "word": " then", "probability": 0.73046875}, {"start": 3534.53, "end": 3536.53, "word": " that", "probability": 0.82861328125}, {"start": 3536.53, "end": 3536.97, "word": " they", "probability": 0.9404296875}, {"start": 3536.97, "end": 3537.27, "word": " are", "probability": 0.92333984375}, {"start": 3537.27, "end": 3537.95, "word": " differentiable", "probability": 0.9404296875}, {"start": 3537.95, "end": 3538.19, "word": " on", "probability": 0.82666015625}, {"start": 3538.19, "end": 3538.41, "word": " A", "probability": 0.9755859375}, {"start": 3538.41, "end": 3538.59, "word": " وB", "probability": 0.939208984375}, {"start": 3538.59, "end": 3538.81, "word": " يعني", "probability": 0.82861328125}, {"start": 3538.81, "end": 3539.43, "word": " نفترض", "probability": 0.9796142578125}, {"start": 3539.43, "end": 3540.19, "word": " أن", "probability": 0.5673828125}, {"start": 3540.19, "end": 3541.19, "word": " الدالتين", "probability": 0.724578857421875}, {"start": 3541.19, "end": 3541.39, "word": " F", "probability": 0.9296875}, {"start": 3541.39, "end": 3541.79, "word": " وG", "probability": 0.854248046875}, {"start": 3541.79, "end": 3542.99, "word": " continuous", "probability": 0.92333984375}, {"start": 3542.99, "end": 3543.23, "word": " على", "probability": 0.60791015625}, {"start": 3543.23, "end": 3543.33, "word": " ال", "probability": 0.783203125}, {"start": 3543.33, "end": 3543.69, "word": " closed", "probability": 0.380615234375}, {"start": 3543.69, "end": 3543.97, "word": " اللي", "probability": 0.89501953125}, {"start": 3543.97, "end": 3544.15, "word": " هي", "probability": 0.78759765625}, {"start": 3544.15, "end": 3545.23, "word": " bounded", "probability": 0.525390625}, {"start": 3545.23, "end": 3545.69, "word": " interval", "probability": 0.984375}, {"start": 3545.69, "end": 3545.97, "word": " A", "probability": 0.90576171875}, {"start": 3545.97, "end": 3546.29, "word": " وB", "probability": 0.96044921875}, {"start": 3546.29, "end": 3547.99, "word": " وdifferentiable", "probability": 0.86572265625}, {"start": 3547.99, "end": 3548.15, "word": " على", "probability": 0.8857421875}, {"start": 3548.15, "end": 3548.27, "word": " ال", "probability": 0.7626953125}, {"start": 3548.27, "end": 3548.43, "word": " open", "probability": 0.78662109375}, {"start": 3548.43, "end": 3548.91, "word": " interval", "probability": 0.97802734375}, {"start": 3548.91, "end": 3549.19, "word": " A", "probability": 0.9853515625}, {"start": 3549.19, "end": 3549.43, "word": " وB", "probability": 0.992431640625}], "temperature": 1.0}, {"id": 142, "seek": 357533, "start": 3550.11, "end": 3575.33, "text": "والـ derivative للأولى بساوي ال derivative للثانية عند كل نقطة من النقاط الـ A و الـ B إذا there exists a constant C such that F بتساوي G زائد H زائد C طبعا البرهان سهل و أكيد يمكن بعضكم برهنه في راسه let H بتساوي F ناقص G مظبوط؟ الآن then", "tokens": [2407, 6027, 39184, 13760, 24976, 10721, 12610, 7578, 4724, 3794, 995, 45865, 2423, 13760, 24976, 12984, 7649, 10632, 43242, 28242, 8717, 47432, 3660, 9154, 28239, 4587, 41193, 2423, 39184, 316, 4032, 2423, 39184, 363, 11933, 15730, 456, 8198, 257, 5754, 383, 1270, 300, 479, 4724, 2655, 3794, 995, 45865, 460, 30767, 16373, 3215, 389, 30767, 16373, 3215, 383, 23032, 3555, 3615, 995, 2423, 26890, 3224, 7649, 8608, 3224, 1211, 4032, 5551, 4117, 25708, 7251, 43020, 45030, 11242, 24793, 4724, 2288, 3224, 1863, 3224, 8978, 12602, 32277, 3224, 718, 389, 4724, 2655, 3794, 995, 45865, 479, 8717, 995, 4587, 9381, 460, 3714, 19913, 3555, 2407, 9566, 22807, 6024, 48506, 550], "avg_logprob": -0.2410511404275894, "compression_ratio": 1.5381355932203389, "no_speech_prob": 5.364418029785156e-07, "words": [{"start": 3550.11, "end": 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3554.03, "end": 3554.25, "word": " الـ", "probability": 0.701171875}, {"start": 3554.25, "end": 3554.35, "word": " A", "probability": 0.33251953125}, {"start": 3554.35, "end": 3554.49, "word": " و", "probability": 0.66357421875}, {"start": 3554.49, "end": 3554.61, "word": " الـ", "probability": 0.69921875}, {"start": 3554.61, "end": 3554.87, "word": " B", "probability": 0.78369140625}, {"start": 3554.87, "end": 3555.69, "word": " إذا", "probability": 0.719970703125}, {"start": 3555.69, "end": 3556.25, "word": " there", "probability": 0.5966796875}, {"start": 3556.25, "end": 3556.77, "word": " exists", "probability": 0.5546875}, {"start": 3556.77, "end": 3556.95, "word": " a", "probability": 0.98974609375}, {"start": 3556.95, "end": 3557.37, "word": " constant", "probability": 0.96533203125}, {"start": 3557.37, "end": 3557.65, "word": " C", "probability": 0.8232421875}, {"start": 3557.65, "end": 3557.91, "word": " such", "probability": 0.84375}, {"start": 3557.91, "end": 3558.19, "word": " that", "probability": 0.9580078125}, {"start": 3558.19, "end": 3558.37, "word": " F", "probability": 0.7548828125}, {"start": 3558.37, "end": 3558.73, "word": " بتساوي", "probability": 0.7263671875}, {"start": 3558.73, "end": 3558.91, "word": " G", "probability": 0.7119140625}, {"start": 3558.91, "end": 3559.29, "word": " زائد", "probability": 0.7783203125}, {"start": 3559.29, "end": 3559.73, "word": " H", "probability": 0.26220703125}, {"start": 3559.73, "end": 3560.61, "word": " زائد", "probability": 0.9192708333333334}, {"start": 3560.61, "end": 3560.85, "word": " C", "probability": 0.9384765625}, {"start": 3560.85, "end": 3561.73, "word": " طبعا", "probability": 0.969482421875}, {"start": 3561.73, "end": 3562.77, "word": " البرهان", "probability": 0.8865966796875}, {"start": 3562.77, "end": 3563.47, "word": " سهل", "probability": 0.9977213541666666}, {"start": 3563.47, "end": 3564.27, "word": " و", "probability": 0.5087890625}, {"start": 3564.27, "end": 3564.59, "word": " أكيد", "probability": 0.8751627604166666}, {"start": 3564.59, "end": 3564.89, "word": " يمكن", "probability": 0.940673828125}, {"start": 3564.89, "end": 3565.35, "word": " بعضكم", "probability": 0.9734700520833334}, {"start": 3565.35, "end": 3565.79, "word": " برهنه", "probability": 0.777685546875}, {"start": 3565.79, "end": 3565.89, "word": " في", "probability": 0.7919921875}, {"start": 3565.89, "end": 3566.33, "word": " راسه", "probability": 0.87353515625}, {"start": 3566.33, "end": 3567.47, "word": " let", "probability": 0.67529296875}, {"start": 3567.47, "end": 3568.93, "word": " H", "probability": 0.8330078125}, {"start": 3568.93, "end": 3569.55, "word": " بتساوي", "probability": 0.847021484375}, {"start": 3569.55, "end": 3570.07, "word": " F", "probability": 0.98974609375}, {"start": 3570.07, "end": 3571.47, "word": " ناقص", "probability": 0.9217529296875}, {"start": 3571.47, "end": 3571.73, "word": " G", "probability": 0.9853515625}, {"start": 3571.73, "end": 3573.71, "word": " مظبوط؟", "probability": 0.7209879557291666}, {"start": 3573.71, "end": 3574.39, "word": " الآن", "probability": 0.6629638671875}, {"start": 3574.39, "end": 3575.33, "word": " then", "probability": 0.6259765625}], "temperature": 1.0}, {"id": 143, "seek": 359521, "start": 3576.67, "end": 3595.21, "text": "F و G continuous إذن H is continuous on A و B و أيضًا F و G differentiable على A و B and H is differentiable on A و B moreover", "tokens": [37, 4032, 460, 10957, 11933, 8848, 1863, 389, 307, 10957, 322, 316, 4032, 363, 4032, 36632, 11242, 14111, 995, 479, 4032, 460, 819, 9364, 15844, 316, 4032, 363, 293, 389, 307, 819, 9364, 322, 316, 4032, 363, 544, 3570], "avg_logprob": -0.2289062563329935, "compression_ratio": 1.3883495145631068, "no_speech_prob": 2.384185791015625e-07, "words": [{"start": 3576.67, "end": 3577.07, "word": "F", "probability": 0.459228515625}, {"start": 3577.07, "end": 3577.27, "word": " و", "probability": 0.79638671875}, {"start": 3577.27, "end": 3577.37, "word": " G", "probability": 0.62841796875}, {"start": 3577.37, "end": 3578.11, "word": " continuous", "probability": 0.6259765625}, {"start": 3578.11, "end": 3578.57, "word": " إذن", "probability": 0.5338541666666666}, {"start": 3578.57, "end": 3578.97, "word": " H", "probability": 0.87353515625}, {"start": 3578.97, "end": 3579.53, "word": " is", "probability": 0.7978515625}, {"start": 3579.53, "end": 3581.11, "word": " continuous", "probability": 0.9150390625}, {"start": 3581.11, "end": 3582.35, "word": " on", "probability": 0.91162109375}, {"start": 3582.35, "end": 3582.89, "word": " A", "probability": 0.91357421875}, {"start": 3582.89, "end": 3583.27, "word": " و", "probability": 0.95556640625}, {"start": 3583.27, "end": 3583.53, "word": " B", "probability": 0.517578125}, {"start": 3583.53, "end": 3584.47, "word": " و", "probability": 0.69091796875}, {"start": 3584.47, "end": 3585.05, "word": " أيضًا", "probability": 0.8682861328125}, {"start": 3585.05, "end": 3585.65, "word": " F", "probability": 0.88916015625}, {"start": 3585.65, "end": 3585.83, "word": " و", "probability": 0.98095703125}, {"start": 3585.83, "end": 3585.93, "word": " G", "probability": 0.95654296875}, {"start": 3585.93, "end": 3586.83, "word": " differentiable", "probability": 0.859375}, {"start": 3586.83, "end": 3587.23, "word": " على", "probability": 0.73388671875}, {"start": 3587.23, "end": 3587.43, "word": " A", "probability": 0.8828125}, {"start": 3587.43, "end": 3587.51, "word": " و", "probability": 0.98583984375}, {"start": 3587.51, "end": 3587.83, "word": " B", "probability": 0.814453125}, {"start": 3587.83, "end": 3588.93, "word": " and", "probability": 0.57373046875}, {"start": 3588.93, "end": 3590.17, "word": " H", "probability": 0.9560546875}, {"start": 3590.17, "end": 3591.21, "word": " is", "probability": 0.96533203125}, {"start": 3591.21, "end": 3592.23, "word": " differentiable", "probability": 0.973388671875}, {"start": 3592.23, "end": 3593.41, "word": " on", "probability": 0.94873046875}, {"start": 3593.41, "end": 3593.91, "word": " A", "probability": 0.99169921875}, {"start": 3593.91, "end": 3594.07, "word": " و", "probability": 0.99072265625}, {"start": 3594.07, "end": 3594.27, "word": " B", "probability": 0.87158203125}, {"start": 3594.27, "end": 3595.21, "word": " moreover", "probability": 0.827392578125}], "temperature": 1.0}, {"id": 144, "seek": 362386, "start": 3597.7, "end": 3623.86, "text": "عندي H برايم اللي هو بساوي F برايم نقص G برايم طبعا عند ال X عند ال X of X of X of X بساوي صفر لكل X موجودة في ال A و ال B then by the above theorem اللي بنحكي عنها اللي هي theorem by theorem 625 H", "tokens": [3615, 1863, 16254, 389, 4724, 23557, 32640, 13672, 1829, 31439, 4724, 3794, 995, 45865, 479, 4724, 23557, 32640, 8717, 4587, 9381, 460, 4724, 23557, 32640, 23032, 3555, 3615, 995, 43242, 2423, 1783, 43242, 2423, 1783, 295, 1783, 295, 1783, 295, 1783, 4724, 3794, 995, 45865, 20328, 5172, 2288, 5296, 28820, 1783, 3714, 29245, 23328, 3660, 8978, 2423, 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