ideal

See also: Ideal, ideał, ideál, and idéal

English

Etymology

From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”); see idea.

Pronunciation

  • Rhymes: -iːəl
  • IPA(key): /aɪˈdɪəl/, /aɪˈdiː.əl/
  • Audio (US)(file)

Adjective

ideal (comparative more ideal, superlative most ideal)

  1. Optimal; being the best possibility.
  2. 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; […] .
  3. Pertaining to ideas, or to a given idea.
  4. 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, 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.
  5. Teaching or relating to the doctrine of idealism.
    the ideal theory or philosophy
  6. (mathematics) Not actually present, but considered as present when limits at infinity are included.
    ideal point
    An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.

Synonyms

  • See also Thesaurus:flawless

Translations

The translations below need to be checked and inserted above into the appropriate translation tables, removing any numbers. Numbers do not necessarily match those in definitions. See instructions at Wiktionary:Entry layout#Translations.

Noun

ideal (plural ideals)

  1. 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
  2. (mathematics, order theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
    If (1) the empty set were called a "small" set, and (2) any subset of a "small" set were also a "small" set, and (3) the union of any pair of "small" sets were also a "small" set, then the set of all "small" sets would form an ideal.
    1. (for example, algebra) 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 .

Antonyms

Hyponyms

Derived terms

Translations

Further reading

Anagrams

Asturian

Etymology

From Latin ideālis.

Adjective

ideal (epicene, plural ideales)

  1. ideal

Noun

ideal m (plural ideales)

  1. ideal

Catalan

Etymology

From Latin ideālis.

Adjective

ideal (masculine and feminine plural ideals)

  1. ideal

Derived terms

Noun

ideal m (plural ideals)

  1. ideal

Galician

Etymology

From Latin ideālis.

Adjective

ideal m, f (plural ideais)

  1. ideal

Derived terms

Noun

ideal m (plural ideais)

  1. ideal

German

Etymology

Borrowed from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”). Doublet of ideell.

Pronunciation

  • IPA(key): /ideˈaːl/
  • Audio(file)
  • Rhymes: -aːl

Adjective

ideal (comparative idealer, superlative am idealsten)

  1. ideal (optimal, perfect)

Declension

Comparative forms of ideal
number & gender singular plural
masculine feminine neuter all genders
predicative er ist idealer sie ist idealer es ist idealer sie sind idealer
strong declension
(without article)		 nominative idealerer idealere idealeres idealere
genitive idealeren idealerer idealeren idealerer
dative idealerem idealerer idealerem idealeren
accusative idealeren idealere idealeres idealere
weak declension
(with definite article)		 nominative der idealere die idealere das idealere die idealeren
genitive des idealeren der idealeren des idealeren der idealeren
dative dem idealeren der idealeren dem idealeren den idealeren
accusative den idealeren die idealere das idealere die idealeren
mixed declension
(with indefinite article)		 nominative ein idealerer eine idealere ein idealeres (keine) idealeren
genitive eines idealeren einer idealeren eines idealeren (keiner) idealeren
dative einem idealeren einer idealeren einem idealeren (keinen) idealeren
accusative einen idealeren eine idealere ein idealeres (keine) idealeren

Derived terms

Further reading

Luxembourgish

Adjective

ideal (masculine idealen, neuter ideaalt, comparative méi ideal, superlative am ideaalsten)

  1. ideal

Declension

Norwegian Bokmål

Etymology

From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”)

Noun

ideal n (definite singular idealet, indefinite plural ideal or idealer, definite plural ideala or idealene)

  1. an ideal

References

Norwegian Nynorsk

Etymology

From French idéal, from Late Latin ideālis (“existing in idea”), from Latin idea (“idea”)

Noun

ideal n (definite singular idealet, indefinite plural ideal, definite plural ideala)

  1. an ideal

References

Portuguese

Etymology

From Latin ideālis.

Pronunciation

  • (Portugal) IPA(key): /iˈðjaɫ/
  • Hyphenation: i‧de‧al

Adjective

ideal m, f (plural ideais, comparable)

  1. ideal
  2. notional

Derived terms

Noun

ideal m (plural ideais)

  1. ideal
  2. fantasy

Serbo-Croatian

Pronunciation

  • IPA(key): /iděaːl/
  • Hyphenation: i‧de‧al

Noun

idèāl m (Cyrillic spelling идѐа̄л)

  1. ideal

Declension

Spanish

Etymology

From Latin ideālis.

Adjective

ideal (plural ideales)

  1. ideal

Derived terms

Noun

ideal m (plural ideales)

  1. ideal

Swedish

Pronunciation

  • audio(file)

Noun

ideal n

  1. ideal; perfect standard
  2. (mathematics) ideal; special subsets of a ring

Declension

Declension of ideal 
Singular Plural
Indefinite Definite Indefinite Definite
Nominative ideal idealet ideal idealen
Genitive ideals idealets ideals idealens

Turkish

Etymology

Borrowed from French idéal.

Pronunciation

  • IPA(key): /ideˈaɫ/
  • Hyphenation: i‧de‧al

Adjective

ideal (comparative daha ideal, superlative en ideal)

  1. ideal

Noun

ideal (definite accusative ideali, plural idealler)

  1. ideal

Declension

Inflection
Nominative ideal
Definite accusative ideali
Singular Plural
Nominative ideal idealler
Definite accusative ideali idealleri
Dative ideale ideallere
Locative idealde ideallerde
Ablative idealden ideallerden
Genitive idealin ideallerin
Possessive forms
Singular Plural
1st singular idealim ideallerim
2nd singular idealin ideallerin
3rd singular ideali idealleri
1st plural idealimiz ideallerimiz
2nd plural idealiniz idealleriniz
3rd plural idealleri idealleri
Predicative forms
Singular Plural
1st singular idealim ideallerim
2nd singular idealsin ideallersin
3rd singular ideal
idealdir		 idealler
ideallerdir
1st plural idealiz idealleriz
2nd plural idealsiniz ideallersiniz
3rd plural idealler ideallerdir

Synonyms

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