different between greater vs supremum

English

Pronunciation

• (UK) IPA^(key): /???e?t?(?)/
• (US, Canada) enPR: gr?t'?(?), IPA^(key): [???e???]
• Rhymes: -e?t?(?)
• Homophone: grater

Adjective

greater

1. comparative form of great: more great

   greater yellowlegs
2. Used in referring to a region or place together with the surrounding area pertaining to it; (of a city) metropolitan.

   Greater China includes many areas north of the Great Wall.

   Greater New York includes nearby parts of three states as well as the City itself.

Derived terms

Related terms

• great
• greatest

Translations

Anagrams

• Traeger, Tregear, regrate

English

Etymology

Borrowed from Latin supremum.

Noun

supremum (plural suprema)

1. (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.
   • 2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, 3rd Edition, page 8,

     A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.

   • 2010, James S. Howland, Basic Real Analysis, Jones & Bartlett Publishers, page 9,

     The best way to describe the supremum of S is to say that it wants to be the greatest element of S. In fact, if S has a greatest element, then that element is the supremum.

   • 2011, Andreas Löhne, Vector Optimization with Infimum and Supremum, Springer, page vii,

     The key to an approach to vector optimization based on infimum and supremum is to consider set-based objective functions and to extend the partial ordering of the original objective space to a suitable subspace of the power set. In this new space the infimum and supremum exist under the usual assumptions.

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 ${\displaystyle S=\{t:t\in P:\forall x\in X,x\leq t\}}$ be the set of upper bounds of X. Then sup(X), if it exists, is the element ${\displaystyle s\in S:\forall y\in S,s\leq y}$.
  • The concept of supremum is closely related to the function ? (called join). The supremum of two elements, denoted ${\displaystyle \sup\{x,y\}}$ can also be written ${\displaystyle x\lor y}$. The supremum of a set may be denoted ${\displaystyle \sup(X)}$ or ${\displaystyle \bigvee X}$.

Synonyms

• (element of a set greater than or equal to all members of a given subset): least upper bound, LUB, sup

Coordinate terms

• infimum

Translations

See also

• maximum

Further reading

• Infimum and supremum on Wikipedia.Wikipedia
• Join and meet on Wikipedia.Wikipedia
• Lattice (order) on Wikipedia.Wikipedia
• Least-upper-bound property on Wikipedia.Wikipedia
• Upper and lower bounds on Wikipedia.Wikipedia

Anagrams

• supermum

Czech

Pronunciation

• IPA^(key): [?supr?mum]

Noun

supremum n

1. (mathematics) supremum

Antonyms

• infimum

Further reading

• supremum in Akademický slovník cizích slov, 1995, at prirucka.ujc.cas.cz

Finnish

Pronunciation

• IPA^(key): /?supre(?)mum/, [?s?upre?(?)mum]
• Rhymes: -upremum
• Syllabification: sup?re?mum

Noun

supremum

1. (mathematics) supremum

Declension

Synonyms

• pienin yläraja

Antonyms

• infimum

Latin

Adjective

supr?mum

1. nominative neuter singular of supr?mus
2. accusative masculine singular of supr?mus
3. accusative neuter singular of supr?mus
4. vocative neuter singular of supr?mus

References

• supremum in Charlton T. Lewis (1891) An Elementary Latin Dictionary, New York: Harper & Brothers
• supremum in Gaffiot, Félix (1934) Dictionnaire illustré Latin-Français, Hachette
• Carl Meissner; Henry William Auden (1894) Latin Phrase-Book?^[1], London: Macmillan and Co.

Swedish

Noun

supremum n

1. (mathematics) supremum

Declension