Supremum

English

Etymology

Borrowed from Template:Bor.

Pronunciation

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Noun

1. Template:WikipediaTemplate:Lb Template:Lb: Given a subset X of R, the smallest real number that is ≥ every element of X; Template:Lb: 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.
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Usage notes

• Commonly denoted sup(X).
• The supremum of X may not exist, and, if it does, may not be an element of X.
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  • Formally: Let $S=\{t:t\in P:\mathrm{\forall }x\in X,x\le t\}$ be the set of upper bounds of X. Then sup(X), if it exists, is the element $s\in S:\mathrm{\forall }y\in S,s\le y$.
  • The concept of supremum is closely related to the function ∨ (called Template:M). The supremum of two elements, denoted $\sup \{x,y\}$ can also be written $x\vee y$. The supremum of a set may be denoted $\sup (X)$ or $\bigvee X$.

Synonyms

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Coordinate terms

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Translations

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See also

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Further reading

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Anagrams

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Czech

Pronunciation

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Noun

1. Template:Lb Template:L

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Further reading

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Finnish

Etymology

Template:Lbor.

Noun

1. Template:Lb supremum

Synonyms

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Antonyms

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Latin

Adjective

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References

• Template:R:Elementary Lewis
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Swedish

Noun

1. Template:Lb supremum