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Proof
editI removed this section from the article, because it didn't make any sense. I'm assuming that someone was starting to write it and never finished it.
Proof
editAt first, only as a proper subset of will be studied.
![{\displaystyle \left[a,b\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/f30926fb280a9fdf66fd931e14d4363cb824feaa)
Asmeurer (talk ♬ contribs) 21:46, 7 March 2010 (UTC)
There is a formalized proof here. There's also an informal proof here that resembles the traditional proof of the Bolzano-Weierstrass theorem. But, Cousin's theorem supposedly requires more powerful axioms than B-W (or Heine-Borel),[1] and I haven't spotted the part of the proof where they enter. I believe the article should get a proof of the theorem and a discussion of the metamathematics. User:CBM hasn't been around in a while: can User:CommyMath help? Thanks. 173.228.123.166 (talk) 10:02, 30 December 2018 (UTC)
User:CommyMath here! I will take a stab at said proof in the New Year. This should be easy as a new (Normann-Sanders) proof , based solely on the least upper bound property of bounded subsets of the reals, has in the meantime appeared on the arxiv. —Preceding undated comment added 18:27, 30 December 2018 (UTC)