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