### Some articles on *convergent, convergent subsequence*:

Cauchy Sequence - Completeness - Other Properties

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**convergent**sequence (with limit s, say) is a Cauchy sequence, since, given any real number ε > 0, beyond some fixed point, every term of sequence is within distance ε/2 of s, so any two ... 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 ... that every bounded sequence of real numbers has a**convergent subsequence**...Main Site Subjects

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