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Like $x$, $y$, $z$ are commonly understood to be dimensions and $\theta$ is an angle, $\pi$ is a specific irrational constant, and $\tau$ is two times $\pi$, et cetera.

They must be running out of letters by now. Is that a problem? What's the solution?

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    $\begingroup$ Hebrew, Cyrillic, reusing letters as needed, ..... $\endgroup$ – user296602 Mar 14 '16 at 0:54
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    $\begingroup$ Letters like $\pi$ are used for other things also, with the meaning clear from context. $\endgroup$ – littleO Mar 14 '16 at 0:55
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    $\begingroup$ computer scientists already solved this, just concatenate letters to make words, then the possibilities are endless $\endgroup$ – frogeyedpeas Mar 14 '16 at 0:58
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    $\begingroup$ what about subscripts? You can always use $\alpha_1$,$\beta_3$, etc $\endgroup$ – Aditya Dev Mar 14 '16 at 1:08
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    $\begingroup$ ^ and that is why some differential geometry formulas start looking like centipedes crawling across the page $\endgroup$ – Justin Benfield Mar 14 '16 at 1:09
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This happened a long time ago. Which is why modern mathematics reads the way it does: We declare what our symbols will represent before proceeding with the rest of whatever it is we're doing.

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P. Halmos addressed the problem in his highly recommended paper How to write mathematics. Let me quote his advice (from the end of Section 6).

As history progresses, more and more symbols get frozen. The standard examples are e, i and π, and, of course, 0,1,2,3,... (Who would dare write “Let 6 be a group.”?) A few other letters are almost frozen: many readers would fell offended if “n” were used for a complex number, “ε” for a positive integer, and “z” for a topological space. (A mathematician’s nightmare is a sequence nε that tends to 0 as ε becomes infinite.)

Moral: do not increase the rigid frigidity. Think about the alphabet. It’s a nuisance, but it’s worth it. To save time and trouble later, think about the alphabet for an hour now; then start writing.

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    $\begingroup$ Some things get unfrozen though. I've often seen people use $1_A$ to mean the identity morphism on A. $\endgroup$ – Q the Platypus Mar 14 '16 at 1:03
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    $\begingroup$ @QthePlatypus I thought something similar, in particular because J. H. Conway does use the notation $6$ for a group! But one difference may be that $6$ is always the name of a particular group (in this case, the cyclic one with $6$ elements), so you still won't see "Let $6$ be a group". In your example, you would never write "Let $1_A$ be a morphism," because it always means that one particular morphism! $\endgroup$ – pjs36 Mar 14 '16 at 1:22

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