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