different between ideal vs precise
ideal
English
Etymology
From French idéal, from Late Latin ide?lis (“existing in idea”), from Latin idea (“idea”); see idea.
In mathematics, the noun ring theory sense was first introduced by German mathematician Richard Dedekind in his 1871 edition of a text on number theory. The concept was quickly expanded to ring theory and later generalised to order theory. The set theory and Lie theory senses can be regarded as applications of the order theory sense.
Pronunciation
- Rhymes: -i??l
- IPA(key): /a??d??l/, /a??di?.?l/
Adjective
ideal (comparative more ideal, superlative most ideal)
- Optimal; being the best possibility.
- Perfect, flawless, having no defects.
- 1751 April 13, Samuel Johnson, The Rambler, Number 112, reprinted in 1825, The Works of Samuel Johnson, LL. D., Volume 1, Jones & Company, page 194,
- There will always be a wide interval between practical and ideal excellence; […] .
- 1751 April 13, Samuel Johnson, The Rambler, Number 112, reprinted in 1825, The Works of Samuel Johnson, LL. D., Volume 1, Jones & Company, page 194,
- Pertaining to ideas, or to a given idea.
- Existing only in the mind; conceptual, imaginary.
- 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:
- The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —
- 1818, Mary Shelley, Frankenstein, or the Modern Prometheus,[1] Chapter 4,
- Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.
- 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:
- Teaching or relating to the doctrine of idealism.
- (mathematics) Not actually present, but considered as present when limits at infinity are included.
Synonyms
- See also Thesaurus:flawless
Related terms
Derived terms
Translations
Noun
ideal (plural ideals)
- A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
- Ideals are like stars; you will not succeed in touching them with your hands. But like the seafaring man on the desert of waters, you choose them as your guides, and following them you will reach your destiny - Carl Schurz
- (algebra, ring theory) A subring closed under multiplication by its containing ring.
- Let be the ring of integers and let be its ideal of even integers. Then the quotient ring is a Boolean ring.
- The product of two ideals and is an ideal which is a subset of the intersection of and . This should help to understand why maximal ideals are prime ideals. Likewise, the union of and is a subset of .
- 2004, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, 2nd Edition, Cambridge University Press, page 47,
- In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.
- 2009, John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, page 45,
- If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.
- 2010, W. D. Burgess, A. Lashgari, A. Mojiri, Elements of Minimal Prime Ideals in General Rings, Sergio R. López-Permouth, Dinh Van Huynh (editors), Advances in Ring Theory, Springer (Birkhäuser), page 69,
- However, every R has a minimal prime ideal consisting of left zero-divisors and one of right zero-divisors.
- (algebra, order theory, lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
- 1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119,
- An ideal A of L is called complete if it contains all least upper bounds of its subsets that exist in L. Bishop and Schreiner [80] studied conditions under which joins of ideals in the lattices of all ideals and of all complete ideals coincide.
- 2011, George Grätzer, Lattice Theory: Foundation, Springer (Birkhäuser), page 125,
- 1.35 Find a distributive lattice L with no minimal and no maximal prime ideals.
- 2015, Vijay K. Garg, Introduction to Lattice Theory with Computer Science Applications, Wiley, page 186,
- Definition 15.11 (Width Ideal) An ideal Q of a poset P = (X,?) is a width ideal if maximal(Q) is a width antichain.
- 1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119,
- (set theory) A collection of sets, considered small or negligible, such that every subset of each member and the union of any two members are also members of the collection.
- Formally, an ideal of a given set is a nonempty subset of the powerset such that: , and .
- (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) ???? of a given Lie algebra ???? such that the Lie bracket [????,????] is a subset of ????.
- 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,
- If ???? is a Lie algebra, ???? is an ideal and the Lie algebras ???? and ????/???? are solvable, then ???? is solvable.
- 2006, W. McGovern, The work of Anthony Joseph in classical representation theory, Anthony Joseph, Joseph Bernstein, Vladimir Hinich, Anna Melnikov (editors), Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday, Springer (Birkhäuser), page 3,
- What really put primitive ideals in enveloping algebras of semisimple Lie algebras on the map was Duflo's fundamental theorem that any such ideal is the annihilator of a very special kind of simple module, namely a highest weight module.
- 2013, J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, page 73,
- Next let be an arbitrary semisimple Lie algebra. Then can be written uniquely as a direct sum of simple ideals (Theorem 5.2).
- 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,
Synonyms
- (type of Lie subalgebra): Lie ideal
Antonyms
- (order theory): filter
Hyponyms
- (mathematics): maximal ideal, principal ideal
Derived terms
Translations
References
Further reading
- Ideal (ring theory) on Wikipedia.Wikipedia
- Ideal (order theory) on Wikipedia.Wikipedia
- Ideal (set theory) on Wikipedia.Wikipedia
- Ideal point on Wikipedia.Wikipedia
- Ideal triangle on Wikipedia.Wikipedia
- Lie algebra#Subalgebras, ideals and homomorphisms on Wikipedia.Wikipedia
Anagrams
- Delia, Elida, ailed, ladie
Asturian
Etymology
From Latin ide?lis.
Pronunciation
Adjective
ideal (epicene, plural ideales)
- ideal
Noun
ideal m (plural ideales)
- ideal
Catalan
Etymology
From Latin ide?lis.
Pronunciation
- (Balearic, Central, Valencian) IPA(key): /i.de?al/
Adjective
ideal (masculine and feminine plural ideals)
- ideal
Derived terms
- idealment
Noun
ideal m (plural ideals)
- ideal
Galician
Etymology
From Latin ide?lis.
Pronunciation
Adjective
ideal m or f (plural ideais)
- ideal
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- ideal
German
Etymology
Borrowed from Late Latin ide?lis (“existing in idea”), from Latin idea (“idea”). Doublet of ideell.
Pronunciation
- IPA(key): /ide?a?l/
- Rhymes: -a?l
Adjective
ideal (comparative idealer, superlative am idealsten)
- ideal (optimal, perfect)
Declension
Derived terms
- idealerweise
Further reading
- “ideal” in Duden online
- “ideal” in Digitales Wörterbuch der deutschen Sprache
Indonesian
Etymology
From Dutch ideaal, from French idéal, from Medieval Latin ide?lis.
Pronunciation
- IPA(key): [??d?eal]
- Hyphenation: idé?al
Adjective
ideal
- ideal:
- optimal; being the best possibility.
- pertaining to ideas, or to a given idea.
Noun
ideal (plural ideal-ideal, first-person possessive idealku, second-person possessive idealmu, third-person possessive idealnya)
- (mathematics) ideal: a subring closed under multiplication by its containing ring.
Alternative forms
- idiil
Affixed terms
Related terms
Further reading
- “ideal” in Kamus Besar Bahasa Indonesia (KBBI) Daring, Jakarta: Badan Pengembangan dan Pembinaan Bahasa, Kementerian Pendidikan dan Kebudayaan Republik Indonesia, 2016.
Luxembourgish
Pronunciation
- IPA(key): /ide?a?l/, [id??a?l], /idi?a?l/
Adjective
ideal (masculine idealen, neuter ideaalt, comparative méi ideal, superlative am ideaalsten)
- ideal
Declension
Norwegian Bokmål
Etymology
From French idéal, from Late Latin ide?lis (“existing in idea”), from Latin idea (“idea”)
Noun
ideal n (definite singular idealet, indefinite plural ideal or idealer, definite plural ideala or idealene)
- ideal
References
- “ideal” in The Bokmål Dictionary.
Norwegian Nynorsk
Etymology
From French idéal, from Late Latin ide?lis (“existing in idea”), from Latin idea (“idea”)
Noun
ideal n (definite singular idealet, indefinite plural ideal, definite plural ideala)
- ideal
References
- “ideal” in The Nynorsk Dictionary.
Piedmontese
Pronunciation
- IPA(key): /ide?al/
Adjective
ideal
- ideal
Noun
ideal m
- ideal
Portuguese
Etymology
From Latin ide?lis.
Pronunciation
- (Portugal) IPA(key): /i?ðja?/
- (Brazil) IPA(key): /i.de?aw/
- Hyphenation: i?de?al
Adjective
ideal m or f (plural ideais, comparable)
- ideal
- notional
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- ideal
- fantasy
Romanian
Etymology
From French idéal, from Latin idealis.
Adjective
ideal m or n (feminine singular ideal?, masculine plural ideali, feminine and neuter plural ideale)
- ideal
Declension
Related terms
- idealism
- idealist
- idealiza
Serbo-Croatian
Pronunciation
- IPA(key): /id?a?l/
- Hyphenation: i?de?al
Noun
idè?l m (Cyrillic spelling ??????)
- ideal
Declension
Spanish
Etymology
From Latin ide?lis.
Pronunciation
- IPA(key): /ide?al/, [i.ð?e?al]
Adjective
ideal (plural ideales)
- ideal
Derived terms
Noun
ideal m (plural ideales)
- ideal
Swedish
Pronunciation
Noun
ideal n
- ideal; perfect standard
- (mathematics) ideal; special subsets of a ring
Declension
Anagrams
- ilade
Turkish
Etymology
Borrowed from French idéal.
Pronunciation
- IPA(key): /ide?a?/
- Hyphenation: i?de?al
Adjective
ideal (comparative daha ideal, superlative en ideal)
- ideal
Noun
ideal (definite accusative ideali, plural idealler)
- ideal
Declension
Synonyms
- ülkü
ideal From the web:
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precise
English
Alternative forms
- præcise (archaic)
Etymology
From Middle French précis, from Latin praecisus. Doublet of précis.
Pronunciation
- IPA(key): /p???sa?s/
- Rhymes: -a?s
- Hyphenation: pre?cise
Adjective
precise (comparative more precise, superlative most precise)
- exact, accurate
- Antonyms: inexact, imprecise
- (sciences, of experimental results) consistent, clustered close together, agreeing with each other (this does not mean that they cluster near the true, correct, or accurate value)
- Antonyms: inconsistent, varying
- adhering too much to rules; prim or punctilious
Synonyms
- See also Thesaurus:meticulous
Derived terms
- precisely
- prissy
Translations
Verb
precise (third-person singular simple present precises, present participle precising, simple past and past participle precised)
- (nonstandard, non-native speakers' English or European Union documents, transitive) To make or render precise; to specify.
Derived terms
- precising definition
Translations
Anagrams
- piecers, pierces, recipes
Italian
Adjective
precise
- feminine plural of preciso
Participle
precise f pl
- feminine plural of preciso
Verb
precise
- third-person singular past historic of precidere
Anagrams
- perisce
Portuguese
Verb
precise
- first-person singular (eu) present subjunctive of precisar
- third-person singular (ele and ela, also used with você and others) present subjunctive of precisar
- third-person singular (você) affirmative imperative of precisar
- third-person singular (você) negative imperative of precisar
Spanish
Pronunciation
- IPA(key): (Spain) /p?e??ise/, [p?e??i.se]
- IPA(key): (Latin America) /p?e?sise/, [p?e?si.se]
Verb
precise
- Formal second-person singular (usted) imperative form of precisar.
- First-person singular (yo) present subjunctive form of precisar.
- Formal second-person singular (usted) present subjunctive form of precisar.
- Third-person singular (él, ella, also used with usted?) present subjunctive form of precisar.
precise From the web:
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