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

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

Definition

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:

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

where

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

Also see

• Equivalence of Definitions of Supremum of Real-Valued Function

Sources

• 1977: K.G. Binmore: Mathematical Analysis: A Straightforward Approach ... (previous) ... (next): $\S 7.13$