Definition:Bounded Below Set

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

A subset $T \subseteq S$ is bounded below (in $S$) if:
 * $\exists m \in S: \forall a \in T: m \preceq a$

That is, there is an element of $S$ (at least one) that precedes all the elements in $T$.

If there is no such element, then $T$ is unbounded below (in $S$).

Also see

 * Lower Bound
 * Bounded Above
 * Upper Bound
 * Bounded