Definition:Bounded Below Mapping/Unbounded

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

Then $f$ is unbounded below (in $T \ $) iff there exists no $L \in S$ such that:
 * $\forall x \in S: L \preceq f \left({x}\right)$