# Indexing notation after $i$, $j$ and $k$ have been used?

If I have already used $i,j,k$ as indices, and need two more, where should I look? $l,m$?, $m$? I know from my previous questions that I can use anything I want as long as I define it, but I use $n$ quite a bit, and it seems that using $m$ as an index could be confusing.

I have thought of using $s$ and $t$, or $s_i$ and $t_i$ which are the initials of the categorical variables over which I am indexing? I don't think that there would be a confusion between the use of $s$ in $\beta{_\text{style}}_s$ and the standard use of $s$ for standard deviation... but perhaps there is a more standard convention that will be more clear / intuitive?

-
What would you use $m$ for, except for indexes and natural numbers? $s$ and $t$ tend to be used for continuous variables. If there are multiple indexes (and they form a reasonable sequence), you would usually use double index, like so: $x_{i_1},x_{i_2}\ldots,x_{i_n}$. I've seen as many as four indexes one on top over another (they were Greek characters, before you ask) in some way. At that point it does get quite confusing, but... What is intuitive really depends on the context, and how the various indexes relate to one another. – tomasz Jul 11 '12 at 21:25
$a_l$ sometimes looks dangerously similar to $a_1$, so $a_\ell$ is preferable (as in the answer by @AsafKaraglia). (Of course, MSE/MathJax typesetting is another story altogether...) – user31373 Jul 11 '12 at 21:33
I agree with Leonid. Please, never use $l$ in mathematical texts. Only use $\ell$. – TMM Jul 11 '12 at 21:59
If your indices all serve related purposes, maybe just $i_1, ... i_5$? – Qiaochu Yuan Dec 31 '12 at 21:31

It really depends on the context.

If you are indexing with ordinals, $\xi$ is a common index, so is $\alpha$.

On the other hand if you are using natural numbers to index, then $\ell$ and $s$ might be used in case you wish to avoid $n,m$ for as long as possible.

-

If you have so many indices, why not start at the beginning of the alphabet and use $a,b,c,d,e,f,g$?

Some of those letters are considered "taken" but it might be clear from the context. $A,B,C,D,E,F,G$ and $\mathfrak{a,b,c,d,e,f,g}$ are also available.

It's probably clearer to use simpler letters rather than resorting to subscripts.

-
I disagree. There are writing conventions, and much like how you use the conventional names the choice of letters is also important. Mathematicians, in particular, love single-letter variables so when I see $\alpha_i$ in the context of set theory I will immediately suspect that $\alpha$ is an ordinal and $i$ is an index set; whereas $\alpha_n$ will immediately be guessed as a countable sequence of ordinals indexed by $\omega$. Much like the name "ordinal" is conventional, so are the choice letters. – Asaf Karagila Dec 31 '12 at 21:21
@AsafKaragila Yes, conventions exist. But how much lower is the proportion of humans who enjoy mathematics due to our usage of symbols like $\hat{X}_{\xi_1} {}^{\tilde{\xi}_2}$? – isomorphismes Dec 31 '12 at 21:26
Do you find the Japanese grammar something to enjoy from? How about the English one? The German one? The Hebrew grammar? What about the one in your native tongue? It's easier to talk to people in their native tongue, and when discussing with a layman one should avoid confusing and obfuscating notation. But when you are talking to a mathematician, there's no harm in the conventional notation, in fact there is harm deviating from it. – Asaf Karagila Dec 31 '12 at 21:38
AsafKaragila I guess in answer to @Abe's question we could say it depends on the intended audience. – isomorphismes Dec 31 '12 at 21:45