Talk:Convergent Sequence is Cauchy Sequence

A space in which every Cauchy sequence is convergent is called complete. Hence we should simply remark here that a space where the converse holds is called complete, with a reference to the definnition. And there should be a page "Real Number Line is Complete Metric Space", containing the second part of the proof.

By the way, I have a feeling there's already a result somewhere that a Cauchy sequence is convergent if and only if it has a convergent subsequence. Hence the fact that $$\R$$ is complete follows almost immediately from the Bolzano-Weierstra&szlig; Theorem.

We're moving house on Monday, so just taking a moment off from packing. If I need a break, I'll make these changes. -- lasserempe 12:13, 7 March 2009 (UTC)

The page I mentioned above is called Convergent Subsequences of Cauchy Sequences. lasserempe 12:15, 7 March 2009 (UTC)