Definition:Bounded Below Mapping/Real-Valued

Definition
Let $f: S \to \R$ be a real-valued function.

Then $f$ is bounded below on $S$ by the lower bound $L$ iff:
 * $\forall x \in S: L \le f \left({x}\right)$

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

Also see

 * Definition:Lower Bound of Real-Valued Function


 * Definition:Bounded Above Real-Valued Function
 * Definition:Upper Bound of Real-Valued Function


 * Definition:Bounded Real-Valued Function