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)
- Pertaining to ideas, or to a given idea.
- Existing only in the mind; conceptual, imaginary.
- Optimal; being the best possibility.
- 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; […] .
- 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,
- Teaching or relating to the doctrine of idealism.
- (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)
- A thing which exists in the mind but not in reality; in ontological terms, a thing which has essence but not existence.
- 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
- (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.
- (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.
- 1992, Unnamed translator, T. S. Fofanova, General Theory of Lattices, in Ordered Sets and Lattices II, American Mathematical Society, page 119,
- (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.
- (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.
- (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)
- ideal
Noun
ideal m (plural ideales)
- 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)
- ideal
Derived terms
- idealisme
- idealista
- idealitzar
- idealment
Noun
ideal m (plural ideals)
- 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)
- ideal
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- ideal
Further reading
- “ideal”, in Dicionario da Real Academia Galega (in Galician), A Coruña: Royal Galician Academy, 2012–2025
- “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)
- 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
- ideal:
- optimal; being the best possibility.
- pertaining to ideas, or to a given idea.
Noun
ideal (plural)
- (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)
- 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)
- 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)
- ideal
References
- “ideal” in The Nynorsk Dictionary.
Piedmontese
Pronunciation
- IPA(key): /ideˈal/
Adjective
ideal
- ideal
Noun
ideal m
- ideal
Portuguese
Etymology
Borrowed from Latin ideālis.
Pronunciation
- Rhymes: -al, -aw
- Hyphenation: i‧de‧al
Adjective
ideal m or f (plural ideais)
- ideal
- notional
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- ideal
- 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)
- ideal
Declension
Related terms
- idealism
- idealist
- idealiza
Serbo-Croatian
Pronunciation
- IPA(key): /iděaːl/
- Hyphenation: i‧de‧al
Noun
idèāl m (Cyrillic spelling идѐа̄л)
- 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)
- ideal
Derived terms
Noun
ideal m (plural ideales)
- 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)
- ideal (perfect)
- Synonym: idealisk
Declension
Noun
ideal n
- ideal; perfect standard
- (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)
- ideal (model to be imitated)
- Synonyms: huwaran, uliran
- ambition
- Synonyms: mithi, mithiin, pangarap, ambisyon
Related terms
- idea
- idealismo
- idealista
Adjective
ideál (Baybayin spelling ᜁᜇᜒᜌᜎ᜔)
- ideal (just as what one wants)
- worthy of imitation
- Synonym: uliran
Turkish
Etymology
Borrowed from French idéal.
Pronunciation
- IPA(key): /ideˈɑl/
- Hyphenation: i‧de‧al
Adjective
ideal
- ideal
Noun
ideal (definite accusative ideali, plural idealler)
- 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)
- ideal
- Synonym: delfrydol
Noun
ideal m (plural idealau)
- ideal
- Synonym: delfryd