what is supremum
The supremum (abbreviated sup; plural suprema) of a subset S of a totally or partially ordered set T is the least element in T that is greater than or equal to all elements of S, if such an element exists.Consequently, the supremum is also referred to as the least upper bound (or LUB).he supremum of a subset S of (P, â), where P is the power set of some set, is the supremum with respect to â (subset) of a subset S of P is the union of the elements of S.