# How do you choose names for functions/operators/sets?

Maybe the question will be closed since it's quite informal, however I just try it. Last time I started to suffer from the boundness of the latin alphabet: I need to make the name of the function clear and attractive but there are no so many letters.

For sets the solution comes from great letters, for operators - from using math styles like \mathcal or \mathsf.

Greek letters I usually use for measures/other characteristics of sets. The problem comes only about function, for which I usually just staring hopeless at my keyboard.

Any help/advise is appreciated. Maybe you can also refer me to some articles on common notation. If it helps, I am working with stochastic processes.

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You have 26 letters in the latin alphabet, those can be upper or lower case, and you can then use \mathcal or \mathfrak or \mathbf or \mathbb to get variations, plus you have 24 upper and 24 lower case Greek letters (okay, some of them are identical to their latin counterparts) which gives over 300 possible symbols, and I haven't even considered adding an overbar, a caret, a prime or a subscript. How many do you need?! – Chris Taylor Sep 22 '11 at 16:23
Usually \mathfrak for small letter is used for Lie algebras ( big letter I use widely for sets and I don't want to denote functions with big letters, \mathbb does not work with small letters (for \mathcal I don't know) and for big letters - usually denotes spaces. I just want to be consistent, not capricious. – Ilya Sep 22 '11 at 16:26
Anything that looks reasonable. Just don't name a complex number with a capital xi if you plan to divide it by its conjugate... – Arturo Magidin Sep 22 '11 at 16:43
@Gortaur: It's an old story, that Barry Mazur did this during a talk expressly to annoy Serge Lang, who was in the audience. It is even worse when done with sans serif greek letters. – Arturo Magidin Sep 22 '11 at 16:56
Using variations of the same letter for related entities can be helpful sometimes, but should not be overdone. I vaguely recall one lecture where the lecturer used $a$ for a member of the set $A$, which belonged to the collection $\mathbb A$ on which a structure $\mathfrak A$ could be defined. At that point, since I didn't want to keep trying to draw $\mathfrak A$ over and over in my notes, I decided to use $\mathcal A$ instead — only to have the lecturer use that symbol for yet another thing a few minutes later... – Ilmari Karonen Sep 22 '11 at 17:05

Well, if using $\zeta$ and $\xi$ is considered to be OK (which is a nightmare for me, I know instances where authors use for example $\zeta^T\Gamma\xi$ ), I wouldn't mind seeing Cyrillic, Arabic, Persian, Hangul, Hebrew (e.g. cardinal numbers etc.) characters unless they symbolize an unambiguous object.

If you run out of latin characters quickly for, say vectors, matrices etc. I would say there must a better formulation style with less variable names. It usually stems from the insist on using the same type of notation throughout the book, thesis etc. It might be acceptable for some occasions but doing it just for the sake of consistency often does more harm than good.

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Thanks - mostly for the advise to fix the formulation style, though it's not always possible. – Ilya Sep 22 '11 at 16:50