supremum

Etymology
Borrowed from.

Noun

 * : Given a subset X of R, the smallest real number that is ≥ every element of X; : 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.
 * 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 ). 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 $$\bigvee X$$.
 * The concept of supremum is closely related to the function ∨ (called ). 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 $$\bigvee X$$.

Translations

 * Czech: supremum
 * Finnish: pienin yläraja,
 * French:
 * German:
 * Hebrew: סופרמום, חסם עליון
 * Japanese:
 * Polish: ,
 * Spanish:
 * Swedish:

Etymology
.

Noun

 * 1)  supremum

Noun

 * 1)  supremum