SUPREMUM
Etymology
Noun
supremum (plural suprema)
(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.
Usage notes
• Commonly denoted sup(X).
• The supremum of X may not exist, and, if it does, may not be an element of X.
• (order theory)
Formally: Let be the set of upper bounds of X. Then sup(X), if it exists, is the element .
The concept of supremum is closely related to the function ∨ (called join). The supremum of two elements, denoted can also be written . The supremum of a set may be denoted or .
Synonyms
• (element of a set greater than or equal to all members of a given subset): least upper bound, LUB, sup
Coordinate terms
• infimum
Anagrams
• supermum
Source: Wiktionary