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Least and Greatest Element

Definition: If x is an element of S such that x is less than or equal to any element of S, then x is called the least element of S:

x is least element of S w.r.t. <= : <=>

x in S /\  forall y in S: x <= y.

If x is an element of S such that x is greater than or equal to any element of S, then x is called the greatest element of S:

x is greatest element of S w.r.t. <= : <=>

x in S /\  forall y in S: y <= x.

Least respectively greatest element is unique (if it exists).