Suppose <= is a partial ordering on a nonempty set A. Then the elements a, b element A are said to be comparable provided a<=b or b<=a. Because two elements in a partially ordered set need not be comparable, it is possible for a partially ordered set to have more than one maximal element. For example, suppose we have a nonempty partially ordered set A in which every element is incomparable to every other element, i.e., A is totally unordered. It follows that every element of A is maximal.

maximal element | partially ordered set | partial order