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 $L$ :
 * $\forall x \in S: L \le \map f x$

That is, the set $\set {\map f x: x \in S}$ 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