different between element vs supremum

English

Etymology

From Middle English element, from Old French element, from Latin elementum (“a first principle, element, rudiment”) (see further etymology there).

Pronunciation

• enPR: ?l'?m?nt, IPA^(key): /??l?m?nt/
• Hyphenation: el?e?ment

Noun

element (plural elements)

1. One of the simplest or essential parts or principles of which anything consists, or upon which the constitution or fundamental powers of anything are based.
   • 1881, Benjamin Jowett, Thucydides

     The simplicity which is so large an element in a noble nature was laughed to scorn.

   1. (chemistry) Any one of the simplest chemical substances that cannot be decomposed in a chemical reaction or by any chemical means and made up of atoms all having the same number of protons.
   2. One of the four basic building blocks of matter in theories of ancient philosophers and alchemists: water, earth, fire, and air.
   3. (law) A required aspect or component of a cause of action. A deed is regarded as a violation of law only if each element can be proved.
   4. (set theory) One of the objects in a set.
   5. Any of the teeth of a zip fastener.
2. A small part of the whole.
3. (obsolete) The sky.
   • 1748, Samuel Richardson, Clarissa, Letter 69:

     Sometimes, solitude is of all things my wish; and the awful silence of the night, the spangled element, and the rising and setting sun, how promotive of contemplation!

4. (plural only, with "the") Atmospheric forces such as strong winds and rains.

5. A place or state of being that an individual or object is best suited to.

6. (Christianity, usually in the plural) The bread and wine taken at Holy Communion.
7. A group of people within a larger group having a particular common characteristic.

8. A component in electrical equipment, often in the form of a coil, having a high resistance, thereby generating heat when a current is passed through it.

10. (computing) One of the conceptual objects in a markup language, usually represented in text by tags.

Synonyms

• (in chemistry): chemical element, firststuff (rare, nonstandard)
• (in set theory): member

Hyponyms

• chemical element
• data element
• heating element

Derived terms

• single-element

Related terms

• elemental
• elementary

Translations

See also

• atom

Verb

element (third-person singular simple present elements, present participle elementing, simple past and past participle elemented)

1. (obsolete) To compound of elements.
   • 1633, John Donne, A Valediction: Forbidding Mourning

     those things which elemented [love]

   • 1661, Robert Boyle, The Sceptical Chymist:

     elemented bodies

   • 1681, Maunyngham, Disc., page 89:

     thou art elemented and organed

2. (obsolete) To constitute and be the elements of.
   • 1658, Izaak Walton, Life of Donne:

     His very soul was elemented of nothing but sadness.

Related terms

• transelement

Further reading

• element in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• element in The Century Dictionary, New York, N.Y.: The Century Co., 1911.

References

• Lehmann, R.G. (2011). "27-30-22-26 - How many letters needs an alphabet?". In de Voogt, A.; Quack, J.F. The Idea of Writing: Writing Across Borders. Brill. pp. 15–16, note 8.

Anagrams

• leetmen

Catalan

Etymology

From Latin elementum.

Pronunciation

• (Balearic) IPA^(key): /?.l??ment/
• (Central) IPA^(key): /?.l??men/
• (Valencian) IPA^(key): /e.le?ment/

Noun

element m (plural elements)

1. element (clarification of this definition is needed)

Derived terms

• elemental
• element químic

Further reading

• “element” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.
• “element” in Gran Diccionari de la Llengua Catalana, Grup Enciclopèdia Catalana.
• “element” in Diccionari normatiu valencià, Acadèmia Valenciana de la Llengua.
• “element” in Diccionari català-valencià-balear, Antoni Maria Alcover and Francesc de Borja Moll, 1962.

Crimean Tatar

Etymology

From Latin elementum

Noun

element

1. element.

Declension

References

• Mirjejev, V. A.; Usejinov, S. M. (2002) Ukrajins?ko-kryms?kotatars?kyj slovnyk [Ukrainian – Crimean Tatar Dictionary]?^[1], Simferopol: Dolya, ?ISBN

Danish

Noun

element n (singular definite elementet, plural indefinite elementer)

1. (set theory) element

Declension

References

• “element” in Den Danske Ordbog

Dutch

Etymology

From Middle Dutch element, from Old French element, from Latin elementum (“a first principle, element, rudiment”), of uncertain origin (see further etymology there).

Pronunciation

• IPA^(key): /?e?.l??m?nt/
• Hyphenation: ele?ment
• Rhymes: -?nt

Noun

element n (plural elementen, diminutive elementje n)

1. element
2. (chemistry) element
3. (set theory) element

Derived terms

• elementair

Descendants

• ? Indonesian: elemen

Anagrams

• leemten

Norwegian Bokmål

Etymology

From Latin elementum

Noun

element n (definite singular elementet, indefinite plural element or elementer, definite plural elementa or elementene)

1. an element

References

• “element” in The Bokmål Dictionary.

Norwegian Nynorsk

Etymology

From Latin elementum

Noun

element n (definite singular elementet, indefinite plural element, definite plural elementa)

1. an element

References

• “element” in The Nynorsk Dictionary.

Polish

Etymology

From Latin elementum.

Pronunciation

• IPA^(key): /??l?.m?nt/

Noun

element m inan

1. element (component, piece of a larger whole)
2. (derogatory) element (group of people)

Declension

Further reading

• element in Wielki s?ownik j?zyka polskiego, Instytut J?zyka Polskiego PAN
• element in Polish dictionaries at PWN

Romanian

Etymology

From French élément, from Latin elementum.

Noun

element n (plural elemente)

1. element

Declension

Serbo-Croatian

Alternative forms

• (Bosnian, Serbian): elèmenat

Pronunciation

• IPA^(key): /el?ment/
• Hyphenation: e?le?ment

Noun

elèment m (Cyrillic spelling ???????)

1. element

Declension

Swedish

Pronunciation

Noun

element n

1. element; basic building block of matter in ancient philosophy
2. element; a place or state of being that an individual or object is better suited towards
3. elements; forces of weather
4. element; an object in a set
5. (mathematics) element of a matrix
6. heating element, radiator
7. (computing) element; object in markup language

Declension

Related terms

• elementär
• elementa
• elementar-

Turkish

Etymology

From German Element.

Pronunciation

• IPA^(key): [?.le.?ment]
• Hyphenation: e?le?ment

Noun

element (definite accusative elementi, plural elementler)

1. (chemistry) element

Declension

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