A greatest element lies above every member of an ordered set, and a least element lies below every member. Antisymmetry makes either unique if it exists. A greatest element is maximal, but a maximal element need not be greatest.
An element is greatest when every element of the ordered set is less than or equal to it.
An element of a partially ordered set is a least element if for every . A least element is unique: two such elements are below each other, so antisymmetry makes them equal.
