Talk:Cauchy's Theorem

Should we list Cauchy-Schwarz here? Also, that still needs a merge of some sort I think, but I wasn't sure which notation was right / if the theorems were different (Cauchy–Schwarz Inequality, Cauchy Schwarz Inequality). --Cynic (talk) 17:44, 16 May 2009 (UTC)

Don't think we should, after all it's not known as "Cauchy's Theorem" but "Cauchy's Inequality". Unless we want to add all the theorems with Cauchy's name on them, which is an approach I wouldn't necessarily argue with if you think it's appropriate.

As for the questions about Cauchy–Schwarz Inequality etc, I'm not sure what to do about it because it's such a wide-ranging theorem. The simple one with the summations in it is merely "Cauchy's Inequality". Schwarz and Bunyakovsky extended it to handle integrals whence its current extended name. Then there's the version which uses all the technical language of vector spaces which uses essentially the same proof and (if you translate it out into conventional language) means exactly the same thing.

Unfortunately until someone comes along and makes the definitions rigorous and explains what everything actually means, we can't easily merge the theorems. One mentions vectors in a Euclidean space and the other one doesn't. Either you need the extra stipulation or you don't, or there are unspoken assumptions in the Cauchy–Schwarz Inequality page.

I have some source works which may come in useful, but I need to study them to understand exactly what they're trying to say. In any case, I'm in a different headspace at the moment (although at weekends I try to take time off from the heavy stuff and do a bit of history). --Matt Westwood 18:57, 16 May 2009 (UTC)