ideal

See also Ideal, idéal, and ideał

English

Etymology

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

Pronunciation

• Rhymes: -iːəl
• IPA: /aɪˈdɪəl/, /aɪˈdiː.əl/, X-SAMPA: /aI"dI@l/, /aI"di:.@l/

• Audio (US)

  (file)

Adjective

ideal (comparative more ideal, superlative most ideal)

1. Optimal; being the best possibility.
2. Perfect, flawless, having no defects.
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,^[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.

5. (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 Wikisaurus:flawless

Related terms

• ideality
• idealless
• ideally
• idealism
• idealistic
• idealize

Translations

being optimal

• Arabic: مثالي (ar) (miṯālī)
• Catalan: ideal (ca) n
• Chinese:

  Mandarin: 理想的 (cmn) (lǐxiǎng de)

• Czech: ideální (cs)
• Dutch: ideaal (nl), optimaal (nl)
• Esperanto: ideala (eo)
• Finnish: ihanteellinen (fi), ideaalinen (fi), ideaali- (fi) optimaalinen (fi)
• French: idéal (fr)
• German: ideal (de)

• Hungarian: ideális (hu)
• Irish: idéalach (ga)
• Japanese: 理想的な (ja) (りそうてきな, risōteki na), 理想な (ja) (りそうな, risō na)
• Jèrriais: idéal
• Luxembourgish: ideal (lb)
• Persian: آرمانی (fa) (ârmâni), ایده‌آل (fa) (ideâl)
• Polish: idealny (pl) m
• Russian: идеальный (ru) (ideálʹnyj) 
• Spanish: ideal (es)
• Telugu: ఆదర్శ (te) (aadarSa)

being perfect

• Czech: ideální (cs)
• Dutch: ideaal (nl), perfect (nl), volmaakt (nl)
• Esperanto: ideala (eo)
• Finnish: ihanteellinen (fi), ideaalinen (fi)
• French: idéal (fr), parfait (fr)
• German: ideal (de)
• Greek: ιδανικός (el) (idani'kos) 
• Hungarian: tökéletes (hu), eszményi (hu)

• Irish: idéalach (ga)
• Jèrriais: idéal
• Persian: کامل (fa) (kāmel), فربود (fa) (farbud), درست (fa) (dorost)
• Polish: idealny (pl) m
• Russian: идеальный (ru) (ideálʹnyj) , совершенный (ru) (soveršénnyj) 
• Spanish: ideal (es)
• Telugu: ఆదర్శ (te) (aadarSa)

conceptual

• Dutch: ideëel, conceptueel
• Esperanto: ideala (eo)
• Finnish: ideaali- (fi)
• French: idéal (fr)
• German: ideell (de)

• Hungarian: képzelt (hu)
• Jèrriais: idéal
• Polish: pojęciowy m, konceptualny m
• Russian: идеальный (ru) (ideálʹnyj) , абстракный (ru) (abstráktnyj) 

at infinity

• Persian: غایی (fa) (ğâyi)

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 Help:How to check translations.

Translations to be checked

• Esperanto: perfekta
• Indonesian: ideal (id)
• Interlingua: ideal (ia)
• Italian: ideale

• Korean: 이상적인 (isangjeogin)
• Spanish: ideal (es)
• Ukrainian: iдеальний (ideál’nyj)

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).^[2]

   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.

3. (for example, algebra) A subring closed under multiplication by its containing ring.

   Let $\mathbb{Z}$ be the ring of integers and let $2\mathbb{Z}$ be its ideal of even integers. Then the quotient ring $\mathbb{Z} / 2\mathbb{Z}$ is a Boolean ring.

   The product of two ideals $\mathfrak{a}$ and $\mathfrak{b}$ is an ideal $\mathfrak{a b}$ which is a subset of the intersection of $\mathfrak{a}$ and $\mathfrak{b}$. This should help to understand why maximal ideals are prime ideals. Likewise, the union of $\mathfrak{a}$ and $\mathfrak{b}$ is a subset of $\mathfrak{a + b}$.

Antonyms

• (order theory): filter

Derived terms

left ideal right ideal two-sided ideal principal ideal

Translations

a perfect standard of beauty, intellect etc.

• Chinese:

  Mandarin: 典范 (cmn) (diǎnfàn)

• Czech: ideál (cs) m
• Dutch: ideaal n, perfectie f, streefdoel n
• Esperanto: ideala, perfekta
• Finnish: ihanne (fi), ideaali (fi)
• French: idéal (fr) m
• German: Ideal (de) n
• Greek: ιδεώδες (el) (ide'odes) n 
• Hungarian: eszmény (hu), ideál (hu)
• Indonesian: ideal (id)
• Interlingua: ideal

• Irish: idéal (ga) m
• Italian: ideale (it) m
• Japanese: 理想 (ja) (risō)
• Korean: 이상 (isang)
• Persian: آرمانی (fa) (ārmāni)
• Polish: ideał (pl) m
• Russian: идеал (ru) (ideál) m 
• Spanish: ideal (es)
• Swedish: ideal (sv) n
• Telugu: ఆదర్శం (te) (aadarSam)
• Ukrainian: iдеал (ideál) m

(order theory)

• Irish: idéal (ga) m

• Russian: идеал (ru) (id'eál) m 

(algebra)

• Dutch: ideaal (nl) n
• Finnish: ihanne (fi),ideaali (fi)
• French: idéal (fr) m
• German: Ideal (de) n

• Polish: ideał (pl) m
• Russian: идеал (ru) (id'eál) m 
• Swedish: ideal (sv) n

an unattainable state

• German: Idealzustand (de) m
• Polish: ideał (pl) m

• Russian: идеал (ru) (id'eál) m 

External links

• Ideal on Wikipedia.Wikipedia

Anagrams

• ailed, Delia, ladie

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German

Adjective

ideal

1. ideal (optimal, perfect)

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Luxembourgish

Adjective

ideal

1. ideal

Adverb

ideal

1. ideally

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Portuguese

Adjective

ideal m and f (plural ideais; comparable)

1. ideal
2. notional

Noun

ideal m (plural ideais)

1. ideal
2. fantasy

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Serbo-Croatian

Pronunciation

• IPA: /iděaːl/
• Hyphenation: i‧de‧al

Noun

idèāl m (Cyrillic spelling идѐа̄л)

1. ideal

Declension

    declension of ideal

	singular	plural
nominative	idèāl	ideali
genitive	ideála	ideala
dative	idealu	idealima
accusative	ideal	ideale
vocative	ideale	ideali
locative	idealu	idealima
instrumental	idealom	idealima

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Spanish

Etymology

Latin ideālis

Adjective

ideal m and f (plural ideales)

1. ideal

Noun

ideal m (plural ideales)

1. ideal

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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
Neuter	indefinite	definite	indefinite	definite
nominative	ideal	idealet	ideal	idealen
genitive	ideals	idealets	ideals	idealens

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Turkish

Noun

ideal

1. ideal

Synonyms

• ülkü