Talk:Real analysis

Previously someone had written that Dedekind cuts called the concepts of real numbers into question, and that Dedekind cuts relied on the use of the axiom of choice. I've never heard such an insanely wrong description of Dedekind cuts, so I removed the statement. Dedekind cuts most certainly do NOT rely on choice in their description. Moreover, the purpose behind Dedekind cuts is that they allow one to construct the real numbers out of the rationals. So far from calling the existence of the reals into question, Dedekind put the definition of the reals onto solid ground.--Mathoreilly 11:02, 2 July 2008 (EDT)

I agree. Any mathematician who was concerned about Dedekind cuts relying on the axiom of choice was just wrong. They have nothing to do with AC. Nor did they "undercut the assumption of the continuity of the real line". They put the continuity on a firm basis. Nor did they create gaps. They filled them. SamHB 22:30, 20 August 2008 (EDT)

I just changed

<math>\{ N, N+1/N\ |\ N \textrm{\ is\ an\ integer} \ge 2 \}</math>

to

<math>\bigcup_{N \textrm{\ is\ an\ integer\ } \geq 2} (N,N+1/N)</math>

I'm not sure what the notation in the first one is supposed to be. Maybe just add parentheses around (N,N+1/N)? The old version is still in the page as a comment in case I screwed up. P.S.: Anyone know way to get something like \substack{...} in Mediawiki? --MarkGall 23:07, 5 July 2009 (EDT)

You're correct; I was being stupid.

I can't get substack to work either. But stackrel works, as in <math>\stackrel{a}{\widehat{B}}</math> or <math>\stackrel{\textstyle{\rightarrow}}{V}</math> PatrickD 12:22, 6 July 2009 (EDT)