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