# Definition:Pointwise Maximum of Mappings

## Definition

Let $X$ be a set, and let $\left({S, \preceq}\right)$ be a toset.

Let $f, g: X \to S$ be mappings.

Let $\max$ be the max operation on $\left({S, \preceq}\right)$.

Then the pointwise maximum of $f$ and $g$, denoted $\max \left({f, g}\right)$, is defined by:

$\max \left({f, g}\right): X \to S: \max \left({f, g}\right) \, \left({x}\right) := \max \left({f \left({x}\right), g \left({x}\right)}\right)$

Pointwise maximum thence is an instance of a pointwise operation on mappings.