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