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What does one do when one needs a lot of symbols and one has exhausted the useful symbols of the latin and greek alphabets? (I say useful symbols because letters like iota (ι) and upsilon (υ) seem too close to "i" and "u" or nu (ν) to be useful.)

What is the next most common list of symbols used in mathematics? Or, does one resort to referring entities in equations using longer words?

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Go Cantor: $\aleph,\beth,\gimel,\ldots$! :-) –  Asaf Karagila Apr 21 '12 at 22:39
@AsafKaragila: I remembered seeing someone use Hebrew letters — they definitely have a good contrast against Latin and Greek letters. –  Neil G Apr 21 '12 at 22:40
Although remember that $\aleph,\beth,\gimel$ are already taken with a very strict context in set theory; I also heard Cantor used $\tav$ (ת) but I have never seen this in modern texts. –  Asaf Karagila Apr 21 '12 at 22:41
Use more than one letter, like in computer science. I bet you know examples like $\sin$, $\gcd$, $\max$ or $\det$ ;-) Often this is even more readable than single letters, note that the potential readers will have to remember all of them to understand what you write. It will be much more helpful to use mnemonics or even full names instead of $a$, $\beta$ and $\gimel$ in a long text. –  dtldarek Apr 21 '12 at 23:03
And of course there are different fonts: $A, \mathcal{A}, \mathbf{A}, \mathtt{A}, \mathfrak{A}, \mathbb{A}$, etc. –  dtldarek Apr 21 '12 at 23:17
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3 Answers

up vote 4 down vote accepted

Aside of the comment to use the Hebrew alphabet, I should add a short story and a remark on notational nightmares:

One of my friends decided that he is annoyed with the usual $x$ and $t$ variables. He submitted a homework assignment in ODE where all the variables were replaced by full words or drawings of flowers and buttons. The objects were chosen to fit several Hebrew based jokes.

The homework were graded and returned a week or two later, his grade was good but whoever graded it left a message on the last page:

"PLEASE Don't do that again!"

The lesson here is that if you have too many variables it might be a good time to re-evaluate your approach to the problem and see if you can write it with less letters. If it ends up incredibly difficult to follow, people will not follow it.

Also, whatever you choose to use make sure it is not something which has a very concrete meaning. Write $f\colon\mathbb R^3\to\mathbb R$ as: $$f(\aleph_1,\aleph_2,\aleph_3)=\aleph_1+\frac{\aleph_2}{\aleph_3}$$ Will probably cause people which are not set theorist to be confused as well.

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I am not sure whether or not I should mark this answer CW. I feel that it is really just a long comment, but at the same time... it's not. –  Asaf Karagila Apr 21 '12 at 22:54
:-| I would like to upvote and downvote at once :-P First, I definitely agree with "might be a good time to re-evaluate your approach", on the other hand there are times when you just do need more variables. After all, if you have a finite set of symbols, then you can introduce only finite number of entities without reusing them. I don't think that using drawings of flowers and buttons is a good technique, but I saw proofs using full words (along with letters of course) which wouldn't be as clear without those names. Used appropriately, long names are great (e.g. $\det$, $\max$, $\sin$)! –  dtldarek Apr 21 '12 at 23:14
to my defense, it wasn't that I got bored of the usual $t$ an $x$ notation, it's that our lecturer made ODE a notational nightmare using a minimum of $\aleph$ variables in each proof, usually interchanging between them freely without informing us :-). –  kneidell Apr 22 '12 at 11:17
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May this be of inspiration: LaTeX symbols

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Careful and appropriate use of subscripts and superscripts is often the best approach. If you truly need to distinguish between 40+ variables, parameters, etc., your readers are going to have a hard time following you without being distracted by unusual symbols. In the case that sub/superscripts won't work, I would use double-character variables and put spaces in where necessary, e.g., $aa\,bb+ab/ij=cc$. The little space between $aa$ and $bb$ is from \,, maybe an explicit $aa\cdot bb$ is clearer.

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