adj
Meaning 1
Pertaining to ideas, or to a given idea.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Standard Lemma guide
ideal
Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.
Sound
Pronunciation
Each Play button uses your device's default local English voice, or a natural local fallback. The selected voice name appears after playback. This is synthesized speech, not a source recording.
-
UK: /aɪˈdɪəl/
-
US: /aɪˈdi(ə)l/
-
US: Recorded audio is listed in the source snapshot.
-
rhymes with -iːəl
-
CMU ARPABET: AY0 D IY1 L Digits mark lexical stress: 1 primary, 2 secondary, 0 unstressed.
adj
Meaning 2
Existing only in the mind; conceptual, imaginary.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 3
Optimal; being the best possibility.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 4
Perfect, flawless, having no defects.
Definition source: English Wiktionary via Wiktextract
Examples
- 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; [...] .
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 5
Teaching or relating to the doctrine of idealism.
Definition source: English Wiktionary via Wiktextract
Examples
- the ideal theory or philosophy
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adj
Meaning 6
Not actually present, but considered as present when limits at infinity are included.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences
Examples
- ideal point
- An ideal triangle in the hyperbolic disk is one bounded by three geodesics that meet precisely on the circle.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
name
Meaning 7
A city in Georgia, United States.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
name
Meaning 8
An unincorporated community in Illinois.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
name
Meaning 9
An unincorporated community in South Dakota.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 10
A perfect standard of beauty, intellect etc., or a standard of excellence to aim at.
Definition source: English Wiktionary via Wiktextract
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 11
A two-sided ideal; a subset of a ring which is closed under both left and right multiplication by elements of the ring.
Definition source: English Wiktionary via Wiktextract
Qualifier: ring theory
Topics: algebra, mathematics, sciences
Examples
- 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 #92;mathfrak#123;a#125; and #92;mathfrak#123;b#125; is a subset of #92;mathfrak#123;a#43;b#125;.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 12
A non-empty lower set (of a partially ordered set) which is closed under binary suprema (a.k.a. joins).
Definition source: English Wiktionary via Wiktextract
Qualifier: lattice theory
Topics: algebra, mathematics, order-theory, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 13
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.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, sciences, set-theory
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 14
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.
Definition source: English Wiktionary via Wiktextract
Qualifier: Lie theory
Topics: algebra, mathematics, sciences
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 15
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.
Definition source: English Wiktionary via Wiktextract
Topics: algebra, mathematics, sciences
Examples
- 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.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adjective
Meaning 16
of or relating to the philosophical doctrine of the reality of ideas
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: idealistic
Antonyms: none provided
adjective satellite
Meaning 17
constituting or existing only in the form of an idea or mental image or conception
Definition source: Princeton WordNet 3.0
Examples
- a poem or essay may be typical of its period in idea or ideal content
Meaning relationships
Synonyms: none provided
Antonyms: none provided
adjective satellite
Meaning 18
conforming to an ultimate standard of perfection or excellence; embodying an ideal
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
noun
Meaning 19
the idea of something that is perfect; something that one hopes to attain
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: none provided
Antonyms: none provided
Broader terms: idea, thought
Narrower terms: value, paragon, idol, perfection, beau ideal, criterion, standard, exemplar, example, model, good example, ego ideal
noun
Meaning 20
model of excellence or perfection of a kind; one having no equal
Definition source: Princeton WordNet 3.0
No example sentence was provided for this meaning.
Meaning relationships
Synonyms: paragon, nonpareil, saint, apotheosis, nonesuch, nonsuch
Antonyms: none provided
Broader terms: model, role model
Narrower terms: jimdandy, jimhickey, crackerjack, class act, humdinger
History
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.
Across languages
Translations
208 source translations are retained for this English entry.
- Finnish: ajatuksellinen — pertaining to ideas
- Finnish: käsitteellinen — existing only in the mind; conceptual, imaginary
- Finnish: kuvitteellinen — existing only in the mind; conceptual, imaginary
- Finnish: ajatuksellinen — existing only in the mind; conceptual, imaginary
- Afrikaans: voorbeeldig — being optimal
- Afrikaans: ideaal — being optimal
- Arabic: مِثَالِيّ (miṯāliyy) — being optimal
- Armenian: իդեալական (idealakan) — being optimal
- Asturian: ideal — being optimal
- Belarusian: ідэа́льны (ideálʹny) — being optimal
- Bulgarian: идеа́лен (ideálen) — being optimal
- Catalan: ideal — being optimal
- Chinese Mandarin: 理想的 (lǐxiǎng de) — being optimal
- Czech: ideální — being optimal
- Dutch: ideaal — being optimal
- Dutch: optimaal — being optimal
- Esperanto: ideala — being optimal
- Finnish: ihanteellinen — being optimal
- Finnish: ideaalinen — being optimal
- Finnish: ideaali- — being optimal
- Finnish: optimaalinen — being optimal
- French: idéal — being optimal
- Galician: ideal — being optimal
- German: ideal — being optimal
- German: bestmöglich — being optimal
- German: optimal — being optimal
- Hindi: आदर्श (ādarś) — being optimal
- Hindi: श्रेष्ठ (śreṣṭh) — being optimal
- Hungarian: ideális — being optimal
- Ido: ideala — being optimal
- Irish: idéalach — being optimal
- Italian: ideale — being optimal
- Japanese: 理想的な (risōteki na) — being optimal
- Japanese: 理想な (risō na) — being optimal
- Korean: 이상적 (isangjeok) — being optimal
- Korean: 리상적 (risangjeok) — being optimal
- Latvian: ideāls — being optimal
- Luxembourgish: ideal — being optimal
- Macedonian: идеа́лен (ideálen) — being optimal
- Malayalam: ആദർശം (ādaṟśaṁ) — being optimal
- Norman: idéal — being optimal
- Pannonian Rusyn: идеални (idealni) — being optimal
- Persian: آرمانی (ârmâni) — being optimal
- Persian: ایدهآل (ide-âl) — being optimal
- Polish: idealny — being optimal
- Portuguese: ideal — being optimal
- Russian: идеа́льный (ideálʹnyj) — being optimal
- Slovak: ideálny — being optimal
- Slovene: idealen — being optimal
- Spanish: ideal — being optimal
- Spanish: idóneo — being optimal
- Telugu: ఆదర్శ (ādarśa) — being optimal
- Ukrainian: ідеа́льний (ideálʹnyj) — being optimal
- Yiddish: אידעאַל (ideal) — being optimal
- Afrikaans: ideaal — being perfect
- Armenian: իդեալական (idealakan) — being perfect
- Armenian: կատարյալ (kataryal) — being perfect
- Asturian: ideal — being perfect
- Belarusian: ідэа́льны (ideálʹny) — being perfect
- Belarusian: даскана́лы (daskanály) — being perfect
- Bulgarian: съвърше́н (sǎvǎršén) — being perfect
- Bulgarian: идеа́лен (ideálen) — being perfect
- Catalan: ideal — being perfect
- Czech: ideální — being perfect
- Dutch: ideaal — being perfect
- Dutch: perfect — being perfect
- Dutch: volmaakt — being perfect
- Esperanto: ideala — being perfect
- Finnish: ihanteellinen — being perfect
- Finnish: ideaalinen — being perfect
- French: idéal — being perfect
- French: parfait — being perfect
- Galician: ideal — being perfect
- German: ideal — being perfect
- German: vollendet — being perfect
- German: einwandfrei — being perfect
- German: tadellos — being perfect
- German: perfekt — being perfect
- Greek: ιδανικός (idanikós) — being perfect
- Ancient Greek: ἰδανικός (idanikós) — being perfect
- Hindi: आदर्श (ādarś) — being perfect
- Hindi: श्रेष्ठ (śreṣṭh) — being perfect
- Hungarian: tökéletes — being perfect
- Hungarian: eszményi — being perfect
- Ido: ideala — being perfect
- Irish: idéalach — being perfect
- Manx: slanjeant — being perfect
- Māori: takarepakore — being perfect
- Māori: paruhi — being perfect
- Norman: idéal — being perfect
- Pannonian Rusyn: идеални (idealni) — being perfect
- Persian: کامل (kâmel) — being perfect
- Persian: فربود (farbud) — being perfect
- Persian: درست (dorost) — being perfect
- Polish: idealny — being perfect
- Portuguese: ideal — being perfect
- Russian: идеа́льный (ideálʹnyj) — being perfect
- Russian: соверше́нный (soveršénnyj) — being perfect
- Slovene: idealen — being perfect
- Spanish: ideal — being perfect
- Spanish: idóneo — being perfect
- Spanish: perfecto — being perfect
- Telugu: ఆదర్శ (ādarśa) — being perfect
- Ukrainian: ідеа́льний (ideálʹnyj) — being perfect
- Ukrainian: доскона́лий (doskonályj) — being perfect
- Afrikaans: ideëel — relating to idealism
- Afrikaans: denkbeeldig — relating to idealism
- Armenian: երեւակայական (erewakayakan) — relating to idealism
- Armenian: վերացական (veracʻakan) — relating to idealism
- Asturian: ideal — relating to idealism
- Bulgarian: въобража́ем (vǎobražáem) — relating to idealism
- Bulgarian: абстра́ктен (abstrákten) — relating to idealism
- Catalan: ideal — relating to idealism
- Dutch: ideëel — relating to idealism
- Dutch: conceptueel — relating to idealism
- Esperanto: ideala — relating to idealism
- Finnish: ideaali- — relating to idealism
- French: idéal — relating to idealism
- Galician: ideal — relating to idealism
- German: ideell — relating to idealism
- Hebrew: אידיאלי (ideàli) — relating to idealism
- Hungarian: képzelt — relating to idealism
- Ido: ideala — relating to idealism
- Malayalam: ആദർശം (ādaṟśaṁ) — relating to idealism
- Manx: ard-smooinagh — relating to idealism
- Manx: ard-smooinaghtagh — relating to idealism
- Norman: idéal — relating to idealism
- Pannonian Rusyn: идейни (idejni) — relating to idealism
- Polish: pojęciowy — relating to idealism
- Polish: konceptualny — relating to idealism
- Portuguese: ideal — relating to idealism
- Russian: идеа́льный (ideálʹnyj) — relating to idealism
- Russian: абстра́ктный (abstráktnyj) — relating to idealism
- Russian: вообража́емый (voobražájemyj) — relating to idealism
- Slovene: idejen — relating to idealism
- Spanish: ideal — relating to idealism
- Spanish: conceptual — relating to idealism
- Finnish: ideaalinen — math: at infinity
- Finnish: ideaali- — math: at infinity
- Persian: غایی (ġâyi) — math: at infinity
- Afrikaans: ideaal — perfect standard of beauty, intellect etc.
- Asturian: ideal — perfect standard of beauty, intellect etc.
- Belarusian: ідэа́л (ideál) — perfect standard of beauty, intellect etc.
- Bulgarian: идеа́л (ideál) — perfect standard of beauty, intellect etc.
- Catalan: ideal — perfect standard of beauty, intellect etc.
- Chinese Mandarin: 典范 (diǎnfàn) — perfect standard of beauty, intellect etc.
- Chinese Mandarin: 理想 (lǐxiǎng) — perfect standard of beauty, intellect etc.
- Czech: ideál — perfect standard of beauty, intellect etc.
- Dutch: ideaal — perfect standard of beauty, intellect etc.
- Dutch: perfectie — perfect standard of beauty, intellect etc.
- Dutch: streefdoel — perfect standard of beauty, intellect etc.
- Esperanto: idealo — perfect standard of beauty, intellect etc.
- Esperanto: perfekta — perfect standard of beauty, intellect etc.
- Finnish: ihanne — perfect standard of beauty, intellect etc.
- Finnish: ideaali — perfect standard of beauty, intellect etc.
- French: idéal — perfect standard of beauty, intellect etc.
- Galician: ideal — perfect standard of beauty, intellect etc.
- German: Ideal — perfect standard of beauty, intellect etc.
- German: Idealbild — perfect standard of beauty, intellect etc.
- Greek: ιδεώδες (ideódes) — perfect standard of beauty, intellect etc.
- Hebrew: אידיאל \ אִידֵאָל (ide'ál) — perfect standard of beauty, intellect etc.
- Hindi: आदर्श (ādarś) — perfect standard of beauty, intellect etc.
- Hindi: श्रेष्ठ (śreṣṭh) — perfect standard of beauty, intellect etc.
- Hungarian: eszmény — perfect standard of beauty, intellect etc.
- Hungarian: ideál — perfect standard of beauty, intellect etc.
- Hungarian: mintakép — perfect standard of beauty, intellect etc.
- Ido: idealo — perfect standard of beauty, intellect etc.
- Indonesian: ideal — perfect standard of beauty, intellect etc.
- Interlingua: ideal — perfect standard of beauty, intellect etc.
- Irish: idéal — perfect standard of beauty, intellect etc.
- Italian: ideale — perfect standard of beauty, intellect etc.
- Japanese: 理想 (risō) — perfect standard of beauty, intellect etc.
- Kazakh: мұрат (mūrat) — perfect standard of beauty, intellect etc.
- Korean: 이상 (isang) — perfect standard of beauty, intellect etc.
- Korean: 리상 (risang) — perfect standard of beauty, intellect etc.
- Persian: آرمان (ârmân) — perfect standard of beauty, intellect etc.
- Persian: ایدئال (ide'âl) — perfect standard of beauty, intellect etc.
- Polish: ideał — perfect standard of beauty, intellect etc.
- Portuguese: ideal — perfect standard of beauty, intellect etc.
- Punjabi: ਆਦਰਸ਼ (ādarś) — perfect standard of beauty, intellect etc.
- Russian: идеа́л (ideál) — perfect standard of beauty, intellect etc.
- Slovak: ideál — perfect standard of beauty, intellect etc.
- Slovene: ideal — perfect standard of beauty, intellect etc.
- Spanish: ideal — perfect standard of beauty, intellect etc.
- Spanish: canon — perfect standard of beauty, intellect etc.
- Swedish: ideal — perfect standard of beauty, intellect etc.
- Telugu: ఆదర్శం (ādarśaṁ) — perfect standard of beauty, intellect etc.
- Ukrainian: ідеа́л (ideál) — perfect standard of beauty, intellect etc.
- Vietnamese: lý tưởng — perfect standard of beauty, intellect etc.
- Welsh: delfryd — perfect standard of beauty, intellect etc.
- Yiddish: אידעאַל (ideal) — perfect standard of beauty, intellect etc.
- Chinese Mandarin: 理想 (lǐxiǎng) — subring closed under multiplication by containing ring
- Dutch: ideaal — subring closed under multiplication by containing ring
- Finnish: ideaali — subring closed under multiplication by containing ring
- French: idéal — subring closed under multiplication by containing ring
- German: Ideal — subring closed under multiplication by containing ring
- Japanese: イデアル (idearu) — subring closed under multiplication by containing ring
- Kazakh: идеал (ideal) — subring closed under multiplication by containing ring
- Polish: ideał — subring closed under multiplication by containing ring
- Romanian: ideal — subring closed under multiplication by containing ring
- Russian: идеа́л (ideál) — subring closed under multiplication by containing ring
- Swedish: ideal — subring closed under multiplication by containing ring
- Chinese Mandarin: 理想 (lǐxiǎng) — lower set closed under joins
- Irish: idéal — lower set closed under joins
- Russian: идеа́л (ideál) — lower set closed under joins
- German: Idealzustand — unattainable state
- Polish: ideał — unattainable state
- Russian: идеа́л (ideál) — unattainable state
Real reading context