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Date: 16-6-2021
1448
Date: 4-7-2017
1111
Date: 10-5-2021
2975
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A metric space which is not complete has a Cauchy sequence which does not converge. The completion of is obtained by adding the limits to the Cauchy sequences.
For example, the rational numbers, with the distance metric, are not complete because there exist Cauchy sequences that do not converge, e.g., 1, 1.4, 1.41, 1.414, ... does not converge because is not rational. The completion of the rationals is the real numbers. Note that the completion depends on the metric. For instance, for any prime , the rationals have a metric given by the p-adic norm, and then the completion of the rationals is the set of p-adic numbers. Another common example of a completion is the space of L2-functions.
Technically speaking, the completion of is the set of Cauchy sequences and is contained in this set, isometrically, as the constant sequences.
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دراسة: عدم ترتيب الغرفة قد يدل على مشاكل نفسية
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علماء: تغير المناخ تسبب في ارتفاع الحرارة خلال موسم الحج
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عمره عام واحد ويعاني من ورم خبيث بوزن (3) كغم وعلى نفقة العتبة الحسينية ... مستشفى خديجة الكبرى (ع) ينجح باستئصال ورم سرطان الكلى لطفل من محافظة الأنبار
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