Word.ws English Dictionary

ideal

UK/aɪˈdɪəl//aɪˈdi(ə)l/

ideal adjective: pertaining to ideas, or to a given idea.

Adjective

ideal (comparative more ideal, superlative most ideal)

  1. Pertaining to ideas, or to a given idea.
    Synonyms:
    conceptual, notional
  2. Existing only in the mind; conceptual, imaginary.
    • The idea of ghosts is ridiculous in the extreme; and if you continue to be swayed by ideal terrors —1796, Matthew Lewis, The Monk, Folio Society, published 1985, page 256
    • Life and death appeared to me ideal bounds, which I should first break through, and pour a torrent of light into our dark world.1816 June – 1817 April/May (date written), [Mary Shelley], “Chapter 4”, in Frankenstein; or, The Modern Prometheus. […], volume (please specify |volume=I to III), London: […] [Macdonald and Son] for...
  3. Optimal; being the best possibility.
    Synonyms:
    best, optimal, optimum
  4. Perfect, flawless, having no defects.
    • 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
  5. Teaching or relating to the doctrine of idealism.
    • the ideal theory or philosophy
  6. 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.

Noun

ideal (plural ideals)

  1. A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
    • Varvara Andreevna, when I was very young, I set before myself the ideal of the woman I loved and should be happy to call my wife.1901 [1878], chapter 5, in Constance Garnett, transl., Anna Karenina, translation of Анна Каренина (Anna Karenina) by Leo Tolstoy, part 6
    • With great humility, I call upon all Americans to help me keep our nation united in defense of those ideals which have been so eloquently proclaimed by Franklin Roosevelt. I want in turn to assure my fellow Americans and all of those who love peace and liberty throughout the world that I will...1945 April 16, Harry S. Truman, 9:21 from the start, in MP72-20 President Roosevelt’s Funeral and Procession; Truman – New President of U.S., Harry S. Truman Presidential Library and Museum, National...
  2. (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.
    • Let #92;mathbb#123;Z#125; be the ring of integers and let 2#92;mathbb#123;Z#125; be its ideal of even integers. Then the quotient ring #92;mathbb#123;Z#125;#47;2#92;mathbb#123;Z#125; is a Boolean ring.
    • The product of two ideals #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is an ideal #92;mathfrak#123;ab#125; which is a subset of the intersection of #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125;. This should help to understand why maximal ideals are prime ideals. Likewise, the union of...
  3. (lattice theory) A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
    • 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.1992, T. S. Fofanova, “General Theory of Lattices”, in Unnamed, transl., Ordered Sets and Lattices II, American Mathematical Society, page 119
    • 1.35 Find a distributive lattice L with no minimal and no maximal prime ideals.2011, George Grätzer, Lattice Theory: Foundation, Springer (Birkhäuser), page 125
  4. 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 I of a given set X is a nonempty subset of the powerset #92;mathcal#123;P#125;(X) such that: (1)#92;#92;emptyset#92;inI, (2)#92;A#92;inI#92;andB#92;subseteqA#92;impliesB#92;inI and (3)#92;A,B#92;inI#92;impliesA#92;cupB#92;inI.
  5. (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.
    • If 𝖌 is a Lie algebra, 𝖍 is an ideal and the Lie algebras 𝖍 and 𝖌/𝖍 are solvable, then 𝖌 is solvable.1975, Zhe-Xian Wan, translated by Che-Young Lee, Lie Algebras, Pergamon Press, page 13
    • 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.2006, W. McGovern, “The work of Anthony Joseph in classical representation theory”, in Anthony Joseph, Joseph Bernstein, Vladimir Hinich, Anna Melnikov, editors, Studies in Lie Theory: Dedicated to...
    Synonyms:
    Lie ideal
  6. 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.
    • The set of natural numbers with multiplication as the monoid operation (instead of addition) has multiplicative ideals, such as, for example, the set {1, 3, 9, 27, 81, ...}. If any member of it is multiplied by a number which is not a power of 3 then the result will not be a power of three.

Proper noun capitalized: Ideal

Ideal

  1. A city in Georgia, United States.
  2. An unincorporated community in Illinois.
  3. An unincorporated community in South Dakota.

ideal meaning in Hindi, Tamil, Marathi and Urdu

ideal in Hindi

being optimal
आदर्श ādarś, श्रेष्ठ śreṣṭh
being perfect
आदर्श ādarś, श्रेष्ठ śreṣṭh
perfect standard of beauty, intellect etc.
आदर्श ādarś, श्रेष्ठ śreṣṭh

ideal in Tamil

உயர்ந்த சிந்தனை, சீர்மை, உயர் குறிக்கோள், குறிக்கோள், கருத்தியலான, புனைவியலான

ideal in Marathi

an ideal
आदर्श ādarśa

ideal in Urdu

ideal
ذہنی zahnī
More languagesFewer languages
ideal in Bengali
আদর্শ adorśo
ideal in Telugu
ఆదర్శ ādarśa, ఆదర్శం ādarśaṁ
ideal in Malayalam
ആദർശം ādaṟśaṁ
ideal in Kannada
ನಿರ್ದಿಷ್ಟ ಮಾದರಿ, ಪರಿಪೂರ್ಣ ಮಾದರಿ, ಧ್ಯೇಯ, ಮಾದರಿ
ideal in Punjabi
ਆਦਰਸ਼ ādarś
ideal in Gujarati
ધ્યેય dhyeya
ideal in Odia
ଆଦର୍ଶ
ideal in Nepali
आदर्श
ideal in Arabic
مِثَالِيّ miṯāliyy
ideal in Indonesian
ideal
ideal in Persian
آرمانی ârmâni, ایدهآل ide-âl, کامل kâmel, فربود farbud
ideal in Vietnamese
lý tưởng

Examples of ideal in a sentence

  • At first, he began to doubt the reality of his adventures, but the acute pain in his shoulders when he attempted to rise, assured him that the kicking of the goblins was certainly not ideal.1836 March – 1837 October, Charles Dickens, “(please specify the chapter name)”, in The Posthumous Papers of the Pickwick Club, London...
  • With great humility, I call upon all Americans to help me keep our nation united in defense of those ideals which have been so eloquently proclaimed by Franklin Roosevelt.1945 April 16, Harry S. Truman, 9:21 from the start, in MP72-20 President Roosevelt’s Funeral and Procession; Truman – New President of...
  • In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.2004, K. R. Goodearl; R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, 2nd edition, Cambridge University Press...
  • If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.2009, John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, page 45:

All 40 example sentences with ideal

Synonyms of ideal

Antonyms

All synonyms and antonyms of ideal

Forms of ideal

Adjective
comparativemore ideal
superlativemost ideal
Noun
pluralideals

Plural of ideal: ideals

Origin of ideal

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.

Words formed from ideal

Phrases with ideal

Words that rhyme with ideal

Questions about ideal

What does ideal mean?
Ideal means pertaining to ideas, or to a given idea.
What is ideal in Hindi?
Ideal in Hindi is आदर्श (ādarś), श्रेष्ठ (śreṣṭh). See Ideal meaning in Hindi.
How do you use ideal in a sentence?
At first, he began to doubt the reality of his adventures, but the acute pain in his shoulders when he attempted to rise, assured him that the kicking of the goblins was certainly not ideal.
What part of speech is ideal?
Ideal can be an adjective, a noun or a proper noun.
How do you pronounce ideal?
Ideal is pronounced /aɪˈdɪəl/ (UK).

Words near ideal in the dictionary

  1. idea'd
  2. ideaed
  3. ideaful
  4. ideagenous
  5. ideahood
  6. ideal
  7. ideal gas
  8. ideal gas law
  9. ideal gases
  10. ideal mixture
  11. ideal mixtures

Source and license

Adapted from Wiktionary: ideal (page history and authors); Ideal (page history and authors); ideal (Tamil Wiktionary) (page history and authors); आदर्श (Marathi) (page history and authors); ذہنی (Urdu) (page history and authors); আদর্শ (Bengali) (page history and authors); ideal (Kannada Wiktionary) (page history and authors); ધ્યેય (Gujarati) (page history and authors); ideal (Odia, IndicTrans2 machine translation) (model and license); ideal (Nepali, IndicTrans2 machine translation) (model and license). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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Pronunciation audio from Wikimedia Commons, each file under its own free license: en-us-ideal.ogg.

Cite this entry: “ideal.” Word.ws, https://word.ws/ideal. Based on Wiktionary, CC BY-SA 4.0.