# Definition:Bounded Below Mapping/Real-Valued/Unbounded

< Definition:Bounded Below Mapping | Real-Valued(Redirected from Definition:Unbounded Below Real-Valued Function)

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*This page is about Unbounded Below Real-Valued Function. For other uses, see Unbounded Below.*

## Definition

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

Then $f$ is **unbounded below on $S$** if and only if it is not bounded below on $S$:

- $\neg \exists L \in \R: \forall x \in S: L \le \map f x$