I am writing a proof, which uses functions that can handle an arbitrary number of parameters like summing, or averaging. In other words, I'm referring to functions like:
$f(x_1, ... x_n) = \sum_i x_i$, or
$f(x_1, ... x_n) = 1/n \sum_i x_i$, or even
$f(x_1, ... x_n) = \sum_i i \cdot x_i$
Clearly, $n$ can be arbitrary and these definitions would still make sense. I'd like to call these functions a name. Is there an existing name for such functions?
As an example, I'd like to be able to say: "Let $f$ be a ______ function that acts on some (or all) of the elements of $S$" (So here $f$ would be any function that accepts any number of elements from $S$ as arguments". What's the right way to word this?