# Definition:Lower Bound of Mapping

This page is about Lower Bound in the context of Mapping. For other uses, see Lower Bound.

## Definition

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

Let $f$ be bounded below in $T$ by $H \in T$.

Then $H$ is a lower bound of $f$.

### Real-Valued Function

The concept is usually encountered where $\struct {T, \preceq}$ is the set of real numbers under the usual ordering $\struct {\R, \le}$:

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

Let $f$ be bounded below in $T$ by $L \in T$.

Then $L$ is a lower bound of $f$.