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Complete Metric Space

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A metric space is complete if every Cauchy sequence in it is convergent.

Statement

In the setting of The Real Numbers, with the Natural Numbers, Integers and Rationals Identified with Subsets of the Reals, and Completeness, let (X,d)(X,d) be a metric space.

(X,d)(X,d) is complete if every Cauchy sequence in (X,d)(X,d) is convergent in (X,d)(X,d).

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