Pointwise Multiplication on Real-Valued Functions is Commutative

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

Let $f \times g: S \to \R$ denote the pointwise product of $f$ and $g$.

Then:
 * $f \times g = g \times f$

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