# Definition:Bounded Above Mapping/Unbounded

< Definition:Bounded Above Mapping(Redirected from Definition:Unbounded Above Mapping)

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*This page is about Unbounded Above in the context of Mapping. For other uses, see Unbounded Above.*

## Definition

Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.

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

- $\neg \exists H \in T: \forall x \in S: \map f x \preceq H$

## Also see

- Results about
**unbounded above mappings**can be found**here**.

## Sources

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