Definition:Bounded Above Set

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

A subset $T \subseteq S$ is bounded above (in $S$) $T$ admits an upper 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:Upper Bound of Set


 * Definition:Bounded Below Set
 * Definition:Lower Bound of Set


 * Definition:Bounded Ordered Set