Talk:Heine–Cantor theorem

Delete "See also" section[edit]

"See also" section does not introduce any new information. I suggest to delete it.

I agree, and have deleted it now. Akvilas (talk) 16:20, 14 February 2009 (UTC)[reply]

Non-constructive[edit]

As the proof is by contradiction (rather than by passing to the contrapositive), it is not constructive. It may be worth pointing this out in the article itself. Katzmik (talk) 11:31, 26 October 2008 (UTC)[reply]

Actually, it is possible to give a proof that is not a proof by contradiction. See [1]. I thought this one is more standard. (In fact, it appears in Rudin, if I remember correctly.) -- Taku (talk) 13:14, 26 October 2008 (UTC)[reply]

The proof of the existence of a finite subcover used here is surely non-constructive. I would be surprised if there exists a constructive proof for this theorem. There may be deep reasons for this. Katzmik (talk) 14:12, 26 October 2008 (UTC)[reply]

The theorem is most definitely nonconstructive. I don't recall the exact argument, but it implies something which is considered false in the constructive setting. This is also the reason why Bishop in his constructive analysis defines continuous real functions by what would normally be read as "continuous, and uniformly continuous on each bounded interval". — Emil J. 14:13, 25 March 2009 (UTC)[reply]

Choosing the subsequences[edit]

One should be careful selecting the subsequences guaranteed by the compactess. In order to make them both converging to the same point one should first choose a subsequence of the x_n's and then a subsequence of the y_{n_k} with the same indices so one can use that d(x_n,y_n)<1/n. Maybe this should be pointed out in the proof. — Preceding unsigned comment added by 200.49.224.88 (talk) 13:48, 4 August 2011 (UTC)[reply]