Definitions for "Supremum"
Keywords:  subset, lub, infimum, poset, bound
is the least upper bound for a set.
For a poset and a subset of , the least element in the set of upper bounds of (if it exists, which it may not) is called the supremum, join, or least upper bound of . It is denoted by sup or . The supremum of two elements may be written as sup{,} or ∨ . If the set is finite, one speaks of a finite supremum. The dual notion is called infimum.
In mathematics, given a subset S of an ordered set T, the supremum of S is the least element of T that is greater than or equal to each element of S. Consequently, it is also referred to as the least upper bound (also lub and LUB). The supremum may, or may not, belong to the subset S.