Definition:Bounded Above

Let $$\left({S; \le}\right)$$ be a poset.

A subset $$T \subseteq S$$ is bounded above in $$S$$ if:

$$\exists M \in S: \forall a \in T: a \le M$$

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

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