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

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*This page is about Unbounded Above in the context of Real-Valued Function. For other uses, see Unbounded Above.*

## Definition

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

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

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

## Also see

- Results about
**unbounded above real-valued functions**can be found**here**.

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