Definition:Supremum of Mapping/Real-Valued Function/Definition 1

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This page is about Supremum of Real-Valued Function. For other uses, see Supremum.


Let $f: S \to \R$ be a real-valued function.

Let $f$ be bounded above on $S$.

The supremum of $f$ on $S$ is defined by:

$\ds \sup_{x \mathop \in S} \map f x := \sup f \sqbrk S$


$\sup f \sqbrk S$ is the supremum in $\R$ of the image of $S$ under $f$.

Also see