Definition:Bounded Ordered Set

Definition
Let $\struct {S, \preceq}$ be an ordered set.

Let $T \subseteq S$ be both bounded below and bounded above in $S$.

Then $T$ is bounded 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 known as
A bounded ordered set can also be referred to as a bounded poset.

Some sources use the term order-bounded.