upper bound

Let $S$ be a set with a partial ordering $\leq$ , and let $T$ be a subset of $S$ . An upper bound for $T$ is an element $z \in S$ such that $x \leq z$ for all $x \in T$ . We say that $T$ is bounded from above if there exists an upper bound for $T$ .

Lower bound, and bounded from below are defined in a similar manner.