ideal

ideal

synonyms, antonyms, definitions, examples & translations of ideal in English

English Online Dictionary. What means ideal‎? What does ideal mean?

English

Etymology

From French idéal, from Late Latin ideālis (existing in idea), by surface analysis, idea +‎ -al, 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: -iːəl
  • IPA(key): /aɪˈdiːl/, /aɪˈdɪəl/, /aɪˈdiː.əl/

Adjective

ideal (comparative more ideal, superlative most ideal)

  1. Pertaining to ideas, or to a given idea.
  2. Existing only in the mind; conceptual, imaginary.
  3. Optimal; being the best possibility.
  4. 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; [] .
  5. Teaching or relating to the doctrine of idealism.
  6. (mathematics) Not actually present, but considered as present when limits at infinity are included.

Synonyms

  • (optimal): best, ideal, optimal, optimum
  • (flawless): see also Thesaurus:flawless
  • (of ideas): conceptual, notional
  • (existing only in mind): conceptual, imaginary

Derived terms

Related terms

Translations

Noun

ideal (plural ideals)

  1. A thing which exists in the mind but not in reality; in ontological terms, a thing which has essence but not existence.
  2. 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
  3. (algebra, ring theory) A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
  4. (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.
  5. (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.
  6. (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) 𝖍 of a given Lie algebra 𝖌 such that the Lie bracket [𝖌,𝖍] is a subset of 𝖍.
  7. (algebra) A subsemigroup with the property that if any semigroup element outside of it is added to any one of its members, the result must lie outside of it.

Synonyms

  • (order theory): order ideal
  • (type of Lie subalgebra): Lie ideal

Antonyms

  • (antonym(s) of 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 on Wikipedia.Wikipedia

Anagrams

  • Delia, Elida, ailed, ladie

Asturian

Etymology

From Latin ideālis.

Pronunciation

  • IPA(key): /ideˈal/ [i.ð̞eˈal]

Adjective

ideal (epicene, plural ideales)

  1. ideal

Noun

ideal m (plural ideales)

  1. ideal

Catalan

Etymology

Borrowed from Latin ideālis.

Pronunciation

  • IPA(key): (Central, Balearic, Valencia) [i.ðeˈal]

Adjective

ideal m or f (masculine and feminine plural ideals)

  1. ideal

Derived terms

  • idealisme
  • idealista
  • idealitzar
  • idealment

Noun

ideal m (plural ideals)

  1. ideal

Galician

Etymology

From Latin ideālis.

Pronunciation

  • IPA(key): /idɛˈal/ [i.ð̞ɛˈɑɫ]
  • Rhymes: -al
  • Hyphenation: i‧de‧al

Adjective

ideal m or f (plural ideais)

  1. ideal

Derived terms

  • idealmente

Noun

ideal m (plural ideais)

  1. ideal

Further reading

  • “ideal”, in Dicionario da Real Academia Galega (in Galician), A Coruña: Royal Galician Academy, 20122025
  • “ideal” in Dicionário Estraviz de galego (2014).

German

Etymology

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

Pronunciation

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

Adjective

ideal (strong nominative masculine singular idealer, comparative (colloquial) idealer, superlative (colloquial) am idealsten)

  1. 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 ideālis.

Pronunciation

  • IPA(key): [ˈɪdeal]
  • Hyphenation: idé‧al

Adjective

ideal

  1. ideal:
    1. optimal; being the best possibility.
    2. pertaining to ideas, or to a given idea.

Noun

ideal (plural)

  1. (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, Jakarta: Agency for Language Development and Cultivation – Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia, 2016.

Luxembourgish

Pronunciation

  • IPA(key): /ideˈaːl/, [idəˈaːl], /idiˈaːl/

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. ideal

References

  • “ideal” in The Bokmål Dictionary.

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. ideal

References

  • “ideal” in The Nynorsk Dictionary.

Piedmontese

Pronunciation

  • IPA(key): /ideˈal/

Adjective

ideal

  1. ideal

Noun

ideal m

  1. ideal

Portuguese

Etymology

Borrowed from Latin ideālis.

Pronunciation

  • Rhymes: -al, -aw
  • Hyphenation: i‧de‧al

Adjective

ideal m or f (plural ideais)

  1. ideal
  2. notional

Derived terms

  • idealmente

Noun

ideal m (plural ideais)

  1. ideal
  2. fantasy

Romanian

Etymology

Borrowed from French idéal, from Latin idealis.

Pronunciation

Adjective

ideal m or n (feminine singular ideală, masculine plural ideali, feminine and neuter plural ideale)

  1. ideal

Declension

Related terms

  • idealism
  • idealist
  • idealiza

Serbo-Croatian

Pronunciation

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

Noun

idèāl m (Cyrillic spelling идѐа̄л)

  1. ideal

Declension

Spanish

Etymology

From Latin ideālis.

Pronunciation

  • IPA(key): /ideˈal/ [i.ð̞eˈal]
  • Rhymes: -al
  • Syllabification: i‧de‧al

Adjective

ideal m or f (masculine and feminine plural ideales)

  1. ideal

Derived terms

Noun

ideal m (plural ideales)

  1. ideal

Further reading

  • “ideal”, in Diccionario de la lengua española [Dictionary of the Spanish Language] (in Spanish), online version 23.8, Royal Spanish Academy [Spanish: Real Academia Española], 2024 December 10

Swedish

Pronunciation

Adjective

ideal (not comparable)

  1. ideal (perfect)
    Synonym: idealisk

Declension

Noun

ideal n

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

Declension

Related terms

  • idé
  • idealisera
  • idealisk
  • idealism
  • idealist
  • idealistisk

References

  • ideal in Svensk ordbok (SO)
  • ideal in Svenska Akademiens ordlista (SAOL)
  • ideal in Svenska Akademiens ordbok (SAOB)

Anagrams

  • ilade

Tagalog

Alternative forms

  • ideyal

Etymology

Borrowed from Spanish ideal.

Pronunciation

  • (Standard Tagalog) IPA(key): /ʔideˈal/ [ʔɪ.d̪ɛˈal]
  • Rhymes: -al
  • Syllabification: i‧de‧al

Noun

ideál (Baybayin spelling ᜁᜇᜒᜌᜎ᜔)

  1. ideal (model to be imitated)
    Synonyms: huwaran, uliran
  2. ambition
    Synonyms: mithi, mithiin, pangarap, ambisyon

Related terms

  • idea
  • idealismo
  • idealista

Adjective

ideál (Baybayin spelling ᜁᜇᜒᜌᜎ᜔)

  1. ideal (just as what one wants)
  2. worthy of imitation
    Synonym: uliran

Turkish

Etymology

Borrowed from French idéal.

Pronunciation

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

Adjective

ideal

  1. ideal

Noun

ideal (definite accusative ideali, plural idealler)

  1. ideal

Declension

Synonyms

  • ülkü

Welsh

Alternative forms

  • ideol

Etymology

Borrowed from English ideal.

Pronunciation

  • IPA(key): /ɪˈdɛal/

Adjective

ideal (feminine singular ideal, plural ideal, not comparable)

  1. ideal
    Synonym: delfrydol

Noun

ideal m (plural idealau)

  1. ideal
    Synonym: delfryd

Mutation

References

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This article based on an article on Wiktionary. The list of authors can be seen in the page history there. The original work has been modified. This article is distributed under the terms of this license.