\begin{definition}[Definition:Pointwise Maximum of Mappings]
Let $X$ be a set.
Let $\struct {S, \preceq}$ be a toset.
Let $f, g: X \to S$ be mappings.
Let $\max$ be the max operation on $\struct {S, \preceq}$.
Then the '''pointwise maximum of $f$ and $g$''', denoted $\map \max {f, g}$, is defined by:
:$\map \max {f, g}: X \to S: \map {\map \max {f, g} } x := \map \max {\map f x, \map g x}$
Hence '''pointwise maximum''' is an instance of a pointwise operation on mappings.
\end{definition}