\begin{definition}[Definition:Pointwise Multiplication of Integer-Valued Functions]
Let $S$ be a non-empty set.
Let $f, g: S \to \Z$ be integer-valued functions.
Then the '''pointwise product of $f$ and $g$''' is defined as:
:$f \times g: S \to \Z:$
::$\forall s \in S: \map {\paren {f \times g} } s := \map f s \times \map g s$
where the $\times$ on the {{RHS}} is integer multiplication.
\end{definition}