Definition:Lower Bound

Definition

Ordered Set

Let $\left({S, \preceq}\right)$ be a poset.

Let $T \subseteq S$ be bounded below in $S$ by an element $m \in S$.

Then $m$ is a lower bound for $T$.

Mapping

Let $f: S \to T$ be a mapping whose codomain is a poset $\left({T, \preceq}\right)$.

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

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

Also see

• Bounded Below
• Upper Bound
• Bounded Above
• Bounded