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