Pointwise Addition on Real-Valued Functions is Associative

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

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

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

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