supremum
English
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.
- 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.
- 2006, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, Springer, 3rd Edition, page 8,
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):
Synonyms
- (element of a set greater than or equal to all members of a given subset): least upper bound, LUB, sup
Coordinate terms
Translations
element of a set greater than or equal to all members of a given subset
See also
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
Czech
Pronunciation
Noun
supremum n
Antonyms
Further reading
Finnish
Etymology
Learned borrowing from Latin suprēmum.
Pronunciation
Noun
supremum
Declension
Inflection of supremum (Kotus type 5/risti, no gradation) | |||
---|---|---|---|
nominative | supremum | supremumit | |
genitive | supremumin | supremumien | |
partitive | supremumia | supremumeja | |
illative | supremumiin | supremumeihin | |
singular | plural | ||
nominative | supremum | supremumit | |
accusative | nom. | supremum | supremumit |
gen. | supremumin | ||
genitive | supremumin | supremumien | |
partitive | supremumia | supremumeja | |
inessive | supremumissa | supremumeissa | |
elative | supremumista | supremumeista | |
illative | supremumiin | supremumeihin | |
adessive | supremumilla | supremumeilla | |
ablative | supremumilta | supremumeilta | |
allative | supremumille | supremumeille | |
essive | supremumina | supremumeina | |
translative | supremumiksi | supremumeiksi | |
abessive | supremumitta | supremumeitta | |
instructive | — | supremumein | |
comitative | See the possessive forms below. |
Synonyms
Antonyms
Latin
Adjective
(deprecated template usage) suprēmum
- inflection of suprēmus:
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.
- (ambiguous) to depart this life: mortem (diem supremum) obire
- (ambiguous) on one's last day: supremo vitae die
- (ambiguous) to perform the last rites for a person: supremo officio in aliquem fungi
- (ambiguous) to perform the last offices of affection: supremis officiis aliquem prosequi (vid sect. VI. 11., note Prosequi...)
- (ambiguous) the last wishes of a deceased person: alicuius mortui voluntas (suprema)
- (ambiguous) to depart this life: mortem (diem supremum) obire
Swedish
Noun
supremum n
- (mathematics) supremum
Declension
Declension of supremum | ||||
---|---|---|---|---|
Singular | Plural | |||
Indefinite | Definite | Indefinite | Definite | |
Nominative | supremum | supremumet | supremum | supremumen |
Genitive | supremums | supremumets | supremums | supremumens |
Categories:
- English terms borrowed from Latin
- English terms derived from Latin
- English lemmas
- English nouns
- English countable nouns
- English nouns with irregular plurals
- en:Set theory
- en:Algebra
- en:Mathematical analysis
- Czech terms with IPA pronunciation
- Czech lemmas
- Czech nouns
- Czech neuter nouns
- cs:Mathematics
- Finnish terms borrowed from Latin
- Finnish learned borrowings from Latin
- Finnish terms derived from Latin
- Finnish 3-syllable words
- Finnish terms with IPA pronunciation
- Rhymes:Finnish/upremum
- Rhymes:Finnish/upremum/3 syllables
- Finnish lemmas
- Finnish nouns
- fi:Mathematics
- Finnish risti-type nominals
- Latin non-lemma forms
- Latin adjective forms
- Latin words in Meissner and Auden's phrasebook
- Swedish lemmas
- Swedish nouns
- Swedish neuter nouns
- sv:Mathematics