different between equal vs supremum

English

Alternative forms

• æqual (archaic), æquall (archaic)

Etymology

Borrowed from Latin aequ?lis, of unknown origin. Doublet of egal.

Pronunciation

• enPR: ?k'w?l, IPA^(key): /?i?kw?l/
• Rhymes: -i?kw?l

Adjective

equal (not generally comparable, comparative more equal, superlative most equal)

1. (not comparable) The same in all respects.
   • 1705, George Cheyne, The Philosophical Principles of Religion Natural and Revealed

     They who are not disposed to receive them may let them alone or reject them; it is equal to me.

2. (mathematics, not comparable) Exactly identical, having the same value.
3. (obsolete) Fair, impartial.
   • Are not my ways equal?
4. (comparable) Adequate; sufficiently capable or qualified.
   • 1881, Jane Austen, Emma, page 311

     her comprehension was certainly more equal to the covert meaning, the superior intelligence, of those five letters so arranged.

   • much less is it in my power to make my commendations equal to your merits.

   • 1842, Ralph Waldo Emerson, Threnody

     […] whose voice an equal messenger / Conveyed thy meaning mild.

5. (obsolete) Not variable; equable; uniform; even.

   • an equal temper

6. (music) Intended for voices of one kind only, either all male or all female; not mixed.

Usage notes

• In mathematics, this adjective can be used in phrases like "A and B are equal", "A is equal to B", and, less commonly, "A is equal with B".
• The most common comparative use is the ironic expression more equal.

Synonyms

• (the same in all respects): identical
• (the same in all relevant respects): equivalent
• (unvarying): even, fair, uniform, unvarying

Translations

Verb

equal (third-person singular simple present equals, present participle (Commonwealth) equalling or (US) equaling, simple past and past participle (Commonwealth) equalled or (US) equaled)

1. (mathematics, copulative) To be equal to, to have the same value as; to correspond to.

2. (transitive) To make equivalent to; to cause to match.

3. (informal) To have as its consequence.

Synonyms

• (to be equal to): be, is
• (informal, have as its consequence): entail, imply, lead to, mean, result in, spell

Translations

Noun

equal (plural equals)

1. A person or thing of equal status to others.

   • Those who were once his equals envy and defame him.
2. (obsolete) State of being equal; equality.

   (Can we find and add a quotation of Spenser to this entry?)

Synonyms

• (person or thing of equal status to others): peer

Derived terms

Related terms

• equality

Translations

Anagrams

• Quale, quale, queal

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