Talk:Real analysis
Pre-July-2009 comments
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)
Post-July-2009 comments
- The article was completely rewritten in July 2009, and the comments above are no longer relevant.
I just changed
to
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. In fact, looking at my initial draft, I did have parens to indicate open intervals, and must have thought, at the last minute, that it looked wrong. In any case, the union operation is the right thing.
- I can't get substack to work either. But stackrel works, as in
or 
I'll add this to the other page. That stuff should be moved into a separate page of "tips for writing math articles". PatrickD 12:22, 6 July 2009 (EDT)
- Next, I have to do neighborhoods. This will be somewhat more daunting than watching Mr. Rogers. PatrickD 12:28, 6 July 2009 (EDT)
- Looking good so far. If there's anything you want to delegate, I'm happy to help. Not sure where you're headed, but I can write up a few examples or something if you give me a topic. --MarkGall 12:33, 6 July 2009 (EDT)
