Maximal and minimal elements

In mathematics, especially in order theory, a maximal element of a subset S {\displaystyle S} of some preordered set is an element of S {\displaystyle S} that is not smaller than any other element in S {\displaystyle S} . A minimal element of a subset S {\displaystyle S} of some preordered set is defined dually as an element of S {\displaystyle S} that is not greater than any other element in S {\displaystyle S} .

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