Definition:Bounded Below Set

Definition
Let $\left({S, \preceq}\right)$ be an ordered set.

A subset $T \subseteq S$ is bounded below (in $S$) $T$ admits a lower bound (in $S$).

Subset of Real Numbers
The concept is usually encountered where $\left({S, \preceq}\right)$ is the set of real numbers under the usual ordering $\left({\R, \le}\right)$:

Also see

 * Definition:Lower Bound of Set


 * Definition:Bounded Above Set
 * Definition:Upper Bound of Set


 * Definition:Bounded Ordered Set