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

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

Definition

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

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

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

$\ds \inf_{x \mathop \in S} \map f x = \inf f \sqbrk S$

where

$\inf f \sqbrk S$ is the infimum in $\R$ of the image of $S$ under $f$.

Also see

• Equivalence of Definitions of Infimum of Real-Valued Function

Sources

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