# When to use subscript and when to make it a function?

Let's say, I have a set of cats $$C = \{ a, b, c, ... \}$$. Each cat has a tail. I can say, that the lengths of the tails of cats are denoted as $$t_a$$, $$t_b$$, etc. Otherwise, I can say that they are denoted as $$t(a)$$, $$t(b)$$, etc. Which option is preferable and when?

• I'd say whatever is more convenient for you. Commented Jan 21, 2023 at 18:02
• In the case of discrete, non-numeric data, subscripts are fine. The functional notation would be appropriate in discourse explicitly related to set theory, IMO. But the nuance is thin.
– user16034
Commented Jan 21, 2023 at 19:14

Both are valid, and the choice is based on personal preference and taste. One benefit of the notation $$t(a),\dots$$ is that it allows you to refer to the function $$t$$ that maps from $$C$$ to lengths, which may be useful in some contexts. One benefit of the notation $$t_a,\dots$$ is that if $$C$$ is finite and small, in some settings it might be intuitive to think of $$t_a,t_b,\dots$$ as separate variables (though of course the two are still equivalent).