We recently discussed completion in my analysis class and I have a brief question on the subject. The completion X* of the metric space X is defined to be the set of Cauchy sequences of X with a defined equivalence relation ({xn}~{yn} if lim d(xn,yn)=0) and metric (D([xn],[yn])=lim d(xn,yn)). I understand the proof of this being a well-defined metric space, but how is it known that X* itself is complete?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks in advance.

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# Completion of a metric space

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