Category:Definitions/Bounded Above Mappings

This category contains definitions related to Bounded Above Mappings.
Related results can be found in Category:Bounded Above Mappings.

Let $f: S \to T$ be a mapping whose codomain is an ordered set $\struct {T, \preceq}$.

Then $f$ is bounded above on $S$ by the upper bound $H$ if and only if:

$\forall x \in S: \map f x \preceq H$

That is, if and only if $f \sqbrk S = \set {\map f x: x \in S}$ is bounded above by $H$.