\begin{definition}[Definition:Bounded Above Mapping/Real-Valued/Unbounded]
Let $f: S \to \R$ be a real-valued function.
Then $f$ is '''unbounded above on $S$''' {{iff}} it is not bounded above on $S$:
:$\neg \exists H \in \R: \forall x \in S: \map f x \le H$
Category:Definitions/Boundedness
\end{definition}