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

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*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:

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

where

## Also see

## Sources

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