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Partially Ordered Set
Definition: 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.