# Is there a reference containing standard mathematical notations?

Suppose you are writing a mathematical text (say an article) and you want to call an object (for example, a set) by a letter. It would be cool then to have some reference (optimally available on the internet) where you could find some standard letters and notations of mathematical objects and pick one that you like. Does such a "notation dictionary" exist?

ADDED. Thanks everybody for interesting answers! Maybe it is worth to add that I had in mind rather basic things. The question was trigged by my attempt to find a good letter to denote a subset of the segment $[0,1]$. Finally I decided to call it $T$ (in the course of the proof it turns out that $T$ is equal $[0,1]$ :) ).

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@Dmitri: This is not directly relevant, but you might want to check out mathoverflow.net/questions/18723/… –  Harry Gindi Jul 23 '10 at 23:40
Probably the question should be community wiki. –  Greg Kuperberg Jul 24 '10 at 0:19
Whereas people tend to standardize symbols for particular concerete objects (e.g. the Cantor set is C) there is no need to standardize variables. You can really denote your generic subset of $[0,1]$ by any letter, in lower or capital cases, of the Latin or Greek, or other aplhabets. –  Pietro Majer Jul 26 '10 at 7:16

Really the closest that you can get is Wikipedia or the right kind of search in Google Scholar. The community needs tools to establish or recognize consensus, which of course is an open-ended problem. These tools, while they are certainly far from perfect, are the best tools that exist. If you did embark on a project to document standards, that could be a great thing to do, but it would probably eventually be co-opted by Wikipedia.

When I think about quantum algebra, a topic which is notorious for "notation sprawl", I use Wikipedia and Google Scholar. The more traditional method is follow a few respected papers and textbooks, and this is also still reasonable.

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Greg, since you value Wikipedia so highly, would you like to rewrite the article "Quantum group" so that it contains something besides notation (whether standard or not)? It's one of the weakest advanced math articles I've seen there. By the way, there is no real quality check mechanism on WP: it's all consensus based and depends strongly on the level of expertise of a small set of contributors and degree of voluntary compliance with various policies. –  Victor Protsak Jul 24 '10 at 4:29
Note, however, that notation is not uniformized even across various articles on the same topic on WP! That is the only sensible thing to do, since different people contribute to different articles and editorial coordination involves enormous amount of work and can be difficult to implement on an open wiki. –  Victor Protsak Jul 24 '10 at 4:35
Regardless of my opinion of Wikipedia, it is objectively an extremely useful and influential mathematical reference despite its obvious shortcomings. It would be a great public service for someone to rewrite the article on quantum groups, and various other articles. Unfortunately most people have no professional incentive to do it, and I am no exception. It could be a good issue to discuss with a financial patron. Otherwise, all I can say to people who improve Wikipedia is, "thank you". –  Greg Kuperberg Jul 24 '10 at 5:01
I don't understand the comment about "no professional incentive" to edit Wikipedia. Is there a professional incentive to participate in MathOverflow? –  András Salamon Jul 25 '10 at 16:42
It's true that I don't "need" the visibility. Nonetheless, I enjoy interaction with colleagues, and in this respect MO is more fun than WP. –  Greg Kuperberg Jul 26 '10 at 4:15

I'm not sure this is quite what you have in mind, but there is a "comprehensive" LaTeX symbol list: http://www.ctan.org/tex-archive/info/symbols/comprehensive/symbols-a4.pdf

Unfortunately, it doesn't make suggestions about what kinds of symbols should be used for what kinds of objects, but that's usually a moving target anyway.

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Greg no. 2: +1 for a phantastic sense of humour! –  Wadim Zudilin Jul 24 '10 at 11:14