Definition:Pointwise Maximum of Mappings
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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.
Examples
- Definition:Pointwise Maximum of Extended Real-Valued Functions
- Definition:Pointwise Maximum of Real-Valued Functions
Also see
- Definition:Pointwise Minimum of Mappings, an analogous notion tied to the min operation
- Definition:Pointwise Operation