# Naming arbitrary constants: subscripts, primes, or just more letters?

When choosing names for arbitrary constants either during a lesson or while working with a single student, should one use$$\{n_1,n_2,n_3,\dotsc\}$$ or $$\{n, n', n'', \dotsc\}$$ or $$\{a,b,c,\dotsc\}$$? Is there any evidence that one of these is easier for students to work with than others? Or is less of a barrier to understanding concepts than others?

• Boy, I really think this just depends so much on context. It would be exceedingly interesting to see even modestly 'scientific' research into this, and just as surprising to see that it had been done! In a one-on-one I'd go with making it clear things are different if they have no natural connection (so a,b,c) but could imagine any of these. – kcrisman May 6 '19 at 1:56
• This depends on scope. If you need one or two doohickies that are going to get used once then discarded, prime it up. If you need something slightly more permanent, but only need one or two of them, use distinct variable names ($a,b,c$ for constants, $i,j,k,\ell,m,n$ for integers, $w,x,y,z$ for real numbers, etc). If the number of new symbols needed is large (but countable), use subscripts. Of course, it is always possible to run out of symbols---I found need to use $\omega_{\ell}^{o}$ earlier today, which sucked (that superscript is a little oh, not a zero). – Xander Henderson May 6 '19 at 4:44
• @XanderHenderson I think your comment makes a fine answer, maybe with a couple of examples. I'd encourage you to post it as an answer. – amWhy May 6 '19 at 12:51
• @Namaste In the question, Mike seems to be asking for references. I don't have any peer reviewed research to cite, and have not thought about the issue from a pedagogical perspective (only from the perspective of what is practical for me). As such, I don't think that I can really provide a good answer to the question. – Xander Henderson May 6 '19 at 12:53
• I would put primes aside for derivatives, unless it is geometry, in which case A and A' are prime examples of using prime in cases of, say, similar figures. – Rusty Core May 6 '19 at 16:44

If the context is integral calculus and/or differential equations, I would definitely use $$C_1$$, $$C_2$$, etc. After all the student is used to "$${}+C$$". So keep it as close to what they are used to seeing and thinking about.