Definition:Bounded Below Mapping/Real-Valued/Unbounded

This page is about Unbounded Below Real-Valued Function. For other uses, see Unbounded Below.

Definition

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

Then $f$ is unbounded below on $S$ if and only if it is not bounded below on $S$:

$\neg \exists L \in \R: \forall x \in S: L \le \map f x$