Category:Bounded Mappings

This category contains results about Bounded Mappings.
Definitions specific to this category can be found in Definitions/Bounded Mappings.

Let $S$ be a set.

Let $\struct {T, \preceq}$ be an ordered set.

Let $f: S \to T$ be a mapping.

Let the image of $f$ be bounded.

Then $f$ is bounded.

That is, $f$ is bounded if and only if it is both bounded above and bounded below.