Question

A Cauchy sequence in (x,d) converges if and only if it has a convergent subsequences

Answer 1

Answer:

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Step-by-step explanation:

Plants are living things that grow on land or in water. ... Plants can be divided into two groups: flowering plants, for example, sunflowers, orchids, and most types of tree. The other group is nonflowering plants, which includes mosses and ferns. All plants make their own food, taking energy from sunlight.

Answer 2

In any metric space, a Cauchy sequence which has a convergent subsequence with limit s is itself convergent (with the same limit), since, given any real number r > 0, beyond some fixed point in the original sequence, every term of the subsequence is within distance r/2 of s, and any two terms of the original sequence ...