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 \(S =\{ t : t \in P : \forall x\in X, x \le t \}\) be the set of upper bounds of X. Then sup(X), if it exists, is the element \(s\in S: \forall y\in S, s \le y\).

The concept of supremum is closely related to the function ∨ (called join). The supremum of two elements, denoted \(\sup\{x,y\}\) can also be written \(x\lor y\). The supremum of a set may be denoted \(\sup(X)\) or \(\bigvee X\).

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



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Coffee Trivia

According to Guinness World Records, the most massive cup of coffee contained 22,739.14 liters and was created by Alcaldía Municipal de Chinchiná (Colombia) at Parque de Bolívar, Chinchiná, Caldas, Colombia, on 15 June 2019. Fifty people worked for more than a month to build this giant cup. The drink prepared was Arabic coffee.

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