Let (A, <=) be a partially ordered set. Then an element m element A is said to be maximal if, for all a element A, m≰a. Alternatively, an element m element A is maximal such that if m<=a for any a element A, then m = a. Note that the definition for a maximal element above is true for any two elements of a partially ordered set that are comparable. However, it may be the case that two elements of a given partial ordering are not comparable.

comparable elements | maximal set