Definition:Bounded Below Mapping

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

Then $f$ is said to be bounded below (in $T \ $) by the lower bound $L$ iff:
 * $\forall x \in S: L \preceq f \left({x}\right)$

That is, iff $f \left({S}\right) = \left\{{f \left({x}\right): x \in S}\right\}$ is bounded below by $L$.

If there is no such $L \in T$ then $f$ is unbounded below (in $T \ $).

Also see

 * Definition:Lower Bound (Mapping)
 * Definition:Bounded Above Mapping
 * Definition:Upper Bound (Mapping)
 * Definition:Bounded Mapping