Definition:Bounded Above Set

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

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

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

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

Also see

 * Upper Bound
 * Bounded Below
 * Lower Bound
 * Bounded