# Definition:Bounded Above Mapping/Unbounded

This page is about mappings which are unbounded above. For other uses, see Definition:Unbounded Above.

## Definition

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

Then $f$ is unbounded above on $S$ iff it is not bounded above on $S$:

$\neg \exists H \in T: \forall x \in S: f \left({x}\right) \preceq H$