Pointwise Addition on Integer-Valued Functions is Associative

Theorem
Let $S$ be a set. Let $f, g, h: S \to \Z$ be integer-valued functions.

Let $f + g: S \to \Z$ denote the pointwise sum of $f$ and $g$.

Then:
 * $\paren {f + g} + h = f + \paren {g + h}$

That is, pointwise addition on integer-valued functions is associative.