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Often, certain symbols in mathematics denote different things in different fields. Is there any sort of ordered list that will tell you what a certain symbol means in alphabetical order by the symbol's alias in LaTeX, perhaps with the way to pronounce it out loud?

I'm thinking of something like this Wikipedia page but more comprehensive and usefully ordered by LaTeX alias (The one on wikipedia has very few symbols, and I am familiar with all of them already). The problem is that when you want to find the meaning of a symbol, there is no way to search on google (because google has no support at all for searching for symbols). Oftentimes, I'm forced to ask someone around the department what it means or how to say it out loud.

For example, I'm trying to find the meaning of the symbol $\uplus$, but I have no way of finding out what it means. Also, for the longest time, I couldn't figure out what to call $f_!$ or $f^!$. How should I know that they're called "f lower shriek" or "f upper shriek".

So for the question: Does any such list exist for either pronunciation, meaning, or both (aside from the one on Wikipedia that I just noted)?

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On a closely related note, I have often found myself wanting to use some symbol for my own purposes, but I am often held back by a worry that in so doing, I am trampling all over some established use for that symbol, thus confusing the heck out of my readers. (For example, I have no idea what symbols like $\sqcap$, $\sqcup$, $\sqsubset$, $\sqsupset$ are typically used for.) Apart from the usefulness of a comprehensive list, what do people think about co-opting symbols whose normal use is unknown to the author? –  Harald Hanche-Olsen Mar 19 '10 at 12:06
@Harald: unless you are branching into another field of mathematics, I'm sure just asking a few colleagues in your field whether they know of any alternative meanings will suffice. Then you can just be upfront about it and define those symbols (preferably all at the beginning/end of the introduction, or in an appendix). I feel that co-opting symbols is one of those things where if someone points it out to you, you buy him/her a beer and have a good laugh. It is much more important to be self-consistent and make sure the readers understand what each symbol mean when you use it. –  Willie Wong Mar 19 '10 at 12:29
Of course there is no such list. Mathematics is far too diverse. In fact, we are lucky if a book contains a list of symbols showing how they are used in just that book. –  Gerald Edgar Mar 19 '10 at 12:30
If you're so confused you don't even know how to TeX the symbol in question: detexify.kirelabs.org/classify.html –  Qiaochu Yuan Mar 19 '10 at 13:44

3 Answers 3

up vote 4 down vote accepted

Comments suggest this ...
However, a designation like "rightwards arrow above reverse tilde operator" doesn't really answer the question here, does it?

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It gives the name of the symbol, which is a partial answer. –  Harry Gindi Mar 19 '10 at 13:44
This is actually a really good answer now that I look, and it's very likely to be accepted, since you can infer a lot of the information just from the name. For example, this answers both my and Harald's questions. –  Harry Gindi Mar 19 '10 at 14:28
It doesn't look like any other answers are going to be given, so I'm accepting this one. –  Harry Gindi Mar 19 '10 at 19:05

Relatedly, the Detexify utility can help you find the LaTeX name for a symbol you can draw.

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Not a complete answer to your question, but as far as your problem is drawing symbols in LaTeX, you'll hardly find anything more complete than the Comprehensive LaTeX symbols list

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Yes, I know about this. I'm looking for something like that that also names the symbol. –  Harry Gindi Mar 19 '10 at 13:43

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