Partially Ordered Set

The following was adapted from Wolfram's site:

A partially ordered set (or poset) is a set taken together with a partial order on it. Formally, a partially ordered set is defined as an ordered pair $P = ⟨ X, ⊑ ⟩$ , where $X$ is called the ground set of $P$ and $⊑$ is the partial order of $P$ .

An element $u$ in a partially ordered set $⟨ X, ⊑ ⟩$ is said to be an upper bound for a subset $S$ of $X$ if for every $s \in S$ , we have $s ⊑ u$ . Similarly, a lower bound for a subset $S$ is an element $l$ such that for every $s \in S$ , $l ⊑ s$ . If there is an upper bound and a lower bound for X, then the poset $⟨ X, ⊑ ⟩$ is said to be bounded.

See PartialOrder

PoSet

Partially Ordered Set