Category:Definitions/Unbounded Real-Valued Functions

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

Let $S$ be a set.

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

Definition $1$

$f$ is unbounded if and only if it is either unbounded above or unbounded below.

Definition $2$

$f$ is unbounded if and only if:

for every positive real number $M$ there exists $x_M \in \R$ such that:

$\size {\map f {x_M} } > M$