# User talk:Shreyas patankar

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To comment on the talk part of an article, you can click on the "discussion" tab at the top of the article in question, and then add your comment there, like I am doing right now (be sure to sign by adding ~~~~ to the end of your message!). Have fun editing, Azjps (talk) 10:39, 26 January 2008 (EST)

Hi, please be careful that what you add to the wiki is absolutely correct. I refer specifically to the additions you made to the page on the natural numbers. In constructing the natural numbers, you assumed the existance of a set $\mathcal{F}$ of successor sets, as defined on the wiki. This is problematic, because in the wiki article, you defined a successor set to be a subset of $\mathbb{R}$. After defining $\mathbb{R}$, you may perfectly well construct a set of all successor sets as a set of certain subsets of $\mathbb{R}$. But in the standard progression of things, $\mathbb{R}$ is constructed from $\mathbb{N}$, so you are essentially using the natural numbers to construct themselves. You see the problem? Thanks. Cheers, Boy Soprano II 11:13, 26 January 2008 (EST)

Re: your reply. You're not at all at fault for not realizing that sets cannot be arbitrarily defined. It took mathematicians many years to realize this, I think. Anyhow, the problem is that if you go around saying that you can make a set of all sets with any given property, you run into various contradictions. The most famous of these is Russell's Paradox, which essentially asks: What about the set of sets that do not contain themselves? Is this set a member of itself?
Mathematicians proposed several solutions to this problem; the most widely accepted was the Zermelo-Fraenkel system of rigorous axioms of sets. As far as I know, no contradictions have been found with these axioms, and pretty much all the rest of mathematics can be derived from them. The critics of the axioms say that they are too restrictive, and that few branches of mathematics require all the axioms of the theory.
Anyhow, don't think that you're "not qualified" enough to add to an article. You were quite right that the article needs a rigorous construction of the natural numbers. Just check your work carefully, and consult a reference when possible. —Boy Soprano II 13:01, 27 January 2008 (EST)

## Captialization

The wiki is case-sensitive (except for the first letter of each article title, e.g. square and Square are automatically the same). Articles Cartesian product and ordered pair exist; Cartesian Product and Ordered Pair do not. If you're creating dead links, one thing to do is use the search function on the wiki to see if the article you're trying to link to exists but with different capitalization.--JBL 16:30, 28 January 2008 (EST)

Also, please note conventions for article titles -- we treat theorems as proper nouns, so "Intermediate Value Theorem" rather than "Intermediate value theorem." (It's also not a bad idea to simultaneously create improperly-capitalized pages as redirects.) --JBL 16:52, 15 February 2008 (EST)

## Integral

Personally, I thin the best way to do such a thing is to divide the page integral into several sections (see Help:Text formatting for how to use sections), some of them introductory, some advanced. I'm glad that you're helping out on the AoPSWiki. Temperalxy 15:56, 15 February 2008 (EST)

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