different between least vs supremum

English

Etymology 1

From Middle English leste, lest, last, from Old English l?st, a contraction of læsast, læsest, lærest (“least”), from Proto-Germanic *laisistaz (“smallest; least”), related to Old English læs (“less”). Cognate with Old Frisian leist, Old Saxon l?s. More at less.

Pronunciation

• IPA^(key): /li?st/
• (General American) IPA^(key): /list/
• Rhymes: -i?st
• Homophone: leased

Determiner

least (comparative less)

1. The most little; the smallest amount or quantity of [something].
   • 1857, Edmund March Blunt, The American Coast Pilot: Containing Directions for the Principal Harbors, E. & G.W. Blunt, page 135:

     The least water we could find there was 4 fathoms, which bears from the point S.E., and is distant 1½ mile.

   • 1847, John Duncan, Duncan's Travels

     To have demolished and rebuilt the walls, would have been a very costly expedient, and as the least of two evils, the painter's brush was resorted to; here and there however, above some of the windows, the black wreathings of the smoke are still discernible through the white covering.

   • 2004, Jim Baggott, Beyond Measure: Modern Physics, Philosophy, and the Meaning of Quantum Theory, Oxford University Press, page 48:

     Light does not need to know in advance which is the path of least time because it takes all paths from its source to its destination.

Usage notes

Some grammarians recommend to use least only with uncountable nouns, as in the examples above with the smallest amount of sense:

• 1965, H. W. Fowler, Fowler’s Modern English Usage: Second Edition:

  [W]hen the context—unemotional statement of everyday facts—is taken into account, at a less price ought to be at a lower price, and a lesser prize ought to be a smaller prize.

To such grammarians least is the superlative of a little, not that of little, so it does not mean smallest, but the smallest amount of. With plural nouns, they recommend fewest.However, other authorities disagree; the OED lists least as a synonym of fewest without any usage notes discussing this meaning.

Translations

Adverb

least (negative superlative)

1. Used for forming superlatives of adjectives, especially those that do not form the superlative by adding -est.

   It was the least surprising thing.

2. In the smallest or lowest degree; in a degree below all others.

   to reward those who least deserve it

   I'd never hid the truth, least of all from you.

   I don't much like housework, and I like cooking least of all.

Antonyms

• most

Translations

Noun

least (plural leasts)

1. (philosophy) Something of the smallest possible extent; an indivisible unit.

Adjective

least

1. Most little; smallest.

   least weasel

Derived terms

Etymology 2

Contraction of at least.

Prepositional phrase

least

1. (informal, nonstandard) At least.

References

Anagrams

• Astle, ETLAs, Slate, Teals, Tesla, astel, laste, lates, leats, salet, setal, slate, stale, steal, stela, taels, tales, teals, telas, tesla

Norwegian Nynorsk

Alternative forms

• leas (non-standard since 2012)

Verb

least

1. passive infinitive of le
2. passive infinitive of lea and lee

Anagrams

• elast, laset, laste, lesta, letas, létas, salet, salte, selta, stela, tasle, telas, tesla

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