In which cases the subscript is a "0" (zero) and an "o" (letter o)?

Question

As stated in the title, the question is simple, about formatting. Reading through physics papers, I have seen $\varepsilon_o$, $\rho_o$, $\mu_o$, to denote some physical constants. Note that all of them use the "$_o$" subscript (lower case o), but other autors use a "$_0$" subscript (number zero), for example, in $\aleph_0$.

Is there a consensus about this notation? Which one should be used? Are they both preferred depending on the field?

P.D.: I am spanish, so maybe I am not using the exact or correct terms to ask this question. I hope it is understandable.

Answer 1

There isn't a system to it. There are some heuristics, but ultimately the correct answer is "Whatever the author thinks conveys their thoughts the best", and what's already established tradition for the particular symbol they are using is a big part of that.

The most important heuristics (with examples) are:

• The numeral $0$ is used when whatever your using it on is the initial something: $\aleph_0$ is the initial infinite cardinal, $a_0$ is a very common generic name for the initial term of a sequence, and so on (also if it's not initial, but the number $0$ is still relevant to the specific object, either through construction or through meaning)
• The letter o signifies a word that begins with o, or an already established object denoted by $o$: given a set $X$ of integers, if you want to split it into subsets according to parity, it is common to let $X_o$ signify the odd subset

Generally, I would say the numeral $0$ is a lot more common.