\begin{definition}[Definition:Bounded Below Mapping]
Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.
Then $f$ is said to be '''bounded below (in $T$)''' by the lower bound $L$ {{iff}}:
:$\forall x \in S: L \preceq \map f x$
That is, iff $f \sqbrk S = \set {\map f x: x \in S}$ is bounded below by $L$.
\end{definition}