Definition:Bounded Above Set

Definition
Let $\struct {S, \preceq}$ 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 $\struct {S, \preceq}$ is the set of real numbers under the usual ordering $\struct {\R, \le}$:

Also see

 * Definition:Upper Bound of Set


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


 * Definition:Bounded Ordered Set