Category:Definitions/Unbounded Above Real-Valued Functions

This category contains definitions related to Unbounded Above Real-Valued Functions.
Related results can be found in Category:Unbounded Above Real-Valued Functions.

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 $S$:

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