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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?

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    $\begingroup$ I'd say whatever is more convenient for you. $\endgroup$
    – Nathaniel
    Commented Jan 21, 2023 at 18:02
  • $\begingroup$ 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. $\endgroup$
    – user16034
    Commented Jan 21, 2023 at 19:14

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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).

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