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 , where is called the ground set of
and
is the partial order of .

An element
in a partially ordered set is said to be an upper bound for a subset of if for every , we have . Similarly, a lower bound for a subset is an element such that for every , . If there is an upper bound and a lower bound for , then the poset is said to be bounded.