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 $\left({S, \preceq}\right)$.

Then the pointwise maximum of $f$ and $g$, denoted $\map \max {f, g}$, is defined by:


 * $\map \max {f, g}: X \to S: \map {\map \max {f, g} } x := \map \max {\map f x, \map g x}$

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

Examples

 * Pointwise Maximum of Extended Real-Valued Functions
 * Pointwise Maximum of Real-Valued Functions

Also see

 * Pointwise Minimum of Mappings, an analogous notion tied to the min operation
 * Operation Induced on Set of Mappings