# Definition:Pointwise Maximum of Mappings

## Definition

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.