Pointwise Addition on Real-Valued Functions is Commutative

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

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

Then:
 * $f + g = g + f$

That is, pointwise addition of real-valued functions is commutative.