User talk:Rybu/archive1

Notation

Please. See Wikipedia:Manual of Style (mathematics).

Wrong: n-1

Right: n − 1

(etc.) Michael Hardy (talk) 12:39, 4 September 2008 (UTC)

Dimension

Hi Rybu, I noticed that in this edit you changed round quite a bit of the lead to Dimension, including removing a source. Can I ask what you disliked about the original content and whether you would object to some of it being reinstated? Thanks Andeggs (talk) 21:01, 28 July 2009 (UTC)

Hi there. Yeah, that was one of many edits around that time. The dimension article was suffering from serious "drift" from lots of edits from various users, it was causing the article to lose focus. Bringing the reference back into the article somewhere would be fine -- IMO that comment on General Relativity would make more sense down in the "In Physics" section, in the "time" part. The thing I objected to about it being in the lead is the distracting nature of comments like "time is the 4th dimension" which combines several potentially confusing issues and providing enough information to clarify that confusion isn't appropriate in the lead. The lead should provide a clear idea of what the dimension concept is. Given the especially confusing nature of dimension for most readers (re: previous edit wars, people repeatedly editing the circle example to say its 2-dimensional, etc), IMO it makes much more sense to push concepts like time-as-an-additional-dimension to further down the article. Rybu (talk) 17:19, 4 August 2009 (UTC)

Kuiper's theorem

Given your comments, you'd better look over what I have done at Kuiper's theorem, and also the claims at weakly contractible. I think the unit sphere is folklore, really, so that documenting it sensibly is a good idea; but you may be correct that the direct proof is not really notable, and certainly fallacious proofs shouldn't be here. Charles Matthews (talk) 11:14, 21 November 2009 (UTC)

I believe the contractibility of the sphere in a seperable countably-infinite dimensional Hilbert space was originally conceived of in terms of explicit homotopies between the identity, right shift and constant maps on $l^{2}$. This argument can be extended to the corresponding Stiefel manifolds of k orthonormal vectors in Hilbert space. So the historical motivation for Kuiper's theorem was that you want to think of these Stiefel spaces as approximations to the group of automorphisms of Hilbert space. But this argument (at least, framed this way) breaks down. Rybu (talk) 19:42, 21 November 2009 (UTC)

MOSMATH

Hello.

You wrote:

the n-1-sphere

I changed it to:

the (n − 1)-sphere

Notice that

• The "1" should not be italicized. Variables in this context are italicized; digits and parentheses, etc., are not.
• A minus sign looks different from a hyphen.
• Spaces precede and follow the minus sign. I made them non-breakable (i.e. no line-break can appear there).

This is codified in WP:MOSMATH. Michael Hardy (talk) 05:14, 22 November 2009 (UTC)