Definition:Bounded Above Mapping/Real-Valued/Unbounded

This page is about Unbounded Above in the context of Real-Valued Function. For other uses, see Unbounded Above.

Definition

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

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

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