It seems we are now seeing the outcome of the reopening experiment. Our lemonade-maker-in-chief has posted an excellent answer, but much of its merit has been lost on the questioner, who continues to argue banal points. I think with all other things being equal, a universe with this answer is better than a universe without, but the tone of that question still annoys me. It's basically claiming, "Oh, those theorems you thought you proved in analysis? Well, I found a hole in all of them."

For future reference: there is nothing stopping someone posting an answer after the question's been closed (for a short period of time) and that is allowed precisely to avoid this situation.

I voted to close this question and would do so again, were I allowed by the software. I would ask those who voted to reopen it a simple question: what are the merits of the question that led you to vote to reopen it? Joel having a great answer is not sufficient reason to reopen a question. That's a sufficient reason to ask Joel to start a blog, or to edit the Wikipedia page to correct the original mistakes.

I agree with Scott's sentiment but would rephrase it: "A universe with this information is better than a universe without", but (I know that this is a contentious viewpoint), MO is not the universe. Not everything has to be here.

Repeat after me:

A good answer does not a good question make.

@Andrew Stacey: I think the question was interesting and I would have voted to reopen whether or not JDH was going to post an answer. I am trying to adhere to the philosophy of this sentence in Thurston's MO user page: "I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication." The question seemed honest to me even if Anixx is being somewhat obstinate about understanding JDH's answer.

Let's try to keep it civil.

Anixx - I think the accusation of trollery derives from your persistently abrasive and confrontational tone. For instance, as some people observed above, the title of your question came across as argumentative. To be fair, I would guess that a large part of this abrasiveness can be ascribed to the fact (which I presume) that English isn't your first language. Compare

Is the analysis as thought in universities in fact the analysis of definable numbers?

with

Is undergraduate analysis in fact the analysis of definable numbers?

which I think would have been less problematic. The 'taught'/'thought' mistake is unfortunate, and the two questions are the same if you only care about the literal meaning, but the first manages to suggest that 'universities' think about analysis incorrectly or dishonestly.

That said, some of your comments and answers are genuinely rude - I'm thinking of a recently deleted answer to this question. I would suggest that you make a real effort to be less confrontational, and in response I hope some of the others here will cut you more slack.

jbl - I agree with Qiaochu's assessment that many of Anixx's questions have been made in good faith, and as such there's no call to accuse her/him of trollery. Wikipedia defines a troll as

someone who posts inflammatory, extraneous, or off-topic messages in an online community, such as an online discussion forum, chat room, or blog, with the primary intent of provoking other users into a desired emotional response or of otherwise disrupting normal on-topic discussion.

I think it's clear from Anixx's passionate responses that her/his primary goal is usually to engage with the content of the question or answer. Though I agree that that engagement often manifests itself in unfortunate ways.

@wilton, I think you and I rather agree but that you just aren't willing to call someone persistantly confrontational and inflammatory a troll. Note that several users have attempted to communicate to Anixx how s/he could change his or her behavior with exactly 0 effect so far, and that these attempts have either been ignored or met with further complaints. I have no doubt the questions asked are genuine, good-faith questions, but they are mostly inappropriate for MathOverflow (so far 5 of 8 have been closed). There's very little evidence that Anixx has tried to understand anything that has been communicated to him or her about what makes a question appropriate for this site. I am quite comfortable calling this behavior "trolling." If you are not, that's fine, too. :)

Edited: Anixx posted while I was typing. Note that Anixx still hasn't been able to parse my comment about accepting a correct answer. And I think everyone can agree that "confrontational attitude" is an indisputably correct charge. I'll now withdraw from this conversation; if anyone would like to communicate with me, you can find my e-mail by following the link in my MO user page.

Anixx, regardless of who called whom what when, I have provided an explicit example of an instance when you certainly were unambiguously confrontational. Since it has been deleted I can't see it any more, but you and I both know it was there. You need to accept that your behaviour is at least part of what's upsetting people here. If you acknowledge that, and if, as Will Jagy suggests, you make mathematical contributions to MO, then I think you'll find that things will get a lot easier.

Anyway, that's the advice I have, for better or worse.

jbl, I take your point.

Sorry, I see nothing confrontational there, I just wanted to encourage Daniel Geisler by saying that is is quite possible to make a substantial result in his field of activity (rather than in other fields where it is more difficult) even in his age and background.

It came across to me as very dismissive of both the poster and of the field of analysis, and the number of down votes it received suggests that I was not alone in this reading. You said that it was possible to prove new theorems in analysis 'without serious education', or words to that effect, and contrasted this with other fields.