\begin{definition}[Definition:Bounded Above Mapping/Unbounded]
Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.
Then $f$ is '''unbounded above on $S$''' {{iff}} it is not bounded above on $S$:
:$\neg \exists H \in T: \forall x \in S: \map f x \preceq H$
Category:Definitions/Boundedness
\end{definition}