different between ideal vs model

English

Etymology

From French idéal, from Late Latin ide?lis (“existing in idea”), 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: -i??l
• IPA^(key): /a??d??l/, /a??di?.?l/

Adjective

ideal (comparative more ideal, superlative most ideal)

1. Optimal; being the best possibility.
2. 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; […] .

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. Teaching or relating to the doctrine of idealism.

6. (mathematics) Not actually present, but considered as present when limits at infinity are included.

Synonyms

• See also Thesaurus:flawless

Related terms

Derived terms

Translations

Noun

ideal (plural ideals)

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 subring closed under multiplication by its containing ring.

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

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

   • 2004, K. R. Goodearl, R. B. Warfield, Jr., An Introduction to Noncommutative Noetherian Rings, 2nd Edition, Cambridge University Press, page 47,

     In trying to understand the ideal theory of a commutative ring, one quickly sees that it is important to first understand the prime ideals.

   • 2009, John J. Watkins, Topics in Commutative Ring Theory, Princeton University Press, page 45,

     If an ideal I of a ring contains the multiplicative identity 1, then we have seen that I must be the entire ring.

   • 2010, W. D. Burgess, A. Lashgari, A. Mojiri, Elements of Minimal Prime Ideals in General Rings, Sergio R. López-Permouth, Dinh Van Huynh (editors), Advances in Ring Theory, Springer (Birkhäuser), page 69,

     However, every R has a minimal prime ideal consisting of left zero-divisors and one of right zero-divisors.

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.

   • 2011, George Grätzer, Lattice Theory: Foundation, Springer (Birkhäuser), page 125,

     1.35 Find a distributive lattice L with no minimal and no maximal prime ideals.

   • 2015, Vijay K. Garg, Introduction to Lattice Theory with Computer Science Applications, Wiley, page 186,

     Definition 15.11 (Width Ideal) An ideal Q of a poset P = (X,?) is a width ideal if maximal(Q) is a width antichain.

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.

   Formally, an ideal ${\displaystyle I}$ of a given set ${\displaystyle X}$ is a nonempty subset of the powerset ${\displaystyle {\mathcal {P}}(X)}$ such that: ${\displaystyle (1)\ \emptyset \in I}$, ${\displaystyle (2)\ A\in I\land B\subseteq A\implies B\in I}$ and ${\displaystyle (3)\ A,B\in I\implies A\cup B\in I}$.

6. (algebra, Lie theory) A Lie subalgebra (subspace that is closed under the Lie bracket) ???? of a given Lie algebra ???? such that the Lie bracket [????,????] is a subset of ????.
   • 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,

     If ???? is a Lie algebra, ???? is an ideal and the Lie algebras ???? and ????/???? are solvable, then ???? is solvable.

   • 2006, W. McGovern, The work of Anthony Joseph in classical representation theory, Anthony Joseph, Joseph Bernstein, Vladimir Hinich, Anna Melnikov (editors), Studies in Lie Theory: Dedicated to A. Joseph on His Sixtieth Birthday, Springer (Birkhäuser), page 3,

     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.

   • 2013, J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer, page 73,

     Next let ${\displaystyle L}$ be an arbitrary semisimple Lie algebra. Then ${\displaystyle L}$ can be written uniquely as a direct sum ${\displaystyle L_{1}\oplus \dots \oplus L_{t}}$ of simple ideals (Theorem 5.2).

Synonyms

• (type of Lie subalgebra): Lie ideal

Antonyms

• (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#Subalgebras, ideals and homomorphisms on Wikipedia.Wikipedia

Anagrams

• Delia, Elida, ailed, ladie

Asturian

Etymology

From Latin ide?lis.

Pronunciation

Adjective

ideal (epicene, plural ideales)

1. ideal

Noun

ideal m (plural ideales)

1. ideal

Catalan

Etymology

From Latin ide?lis.

Pronunciation

• (Balearic, Central, Valencian) IPA^(key): /i.de?al/

Adjective

ideal (masculine and feminine plural ideals)

1. ideal

Derived terms

• idealment

Noun

ideal m (plural ideals)

1. ideal

Galician

Etymology

From Latin ide?lis.

Pronunciation

Adjective

ideal m or f (plural ideais)

1. ideal

Derived terms

• idealmente

Noun

ideal m (plural ideais)

1. ideal

German

Etymology

Borrowed from Late Latin ide?lis (“existing in idea”), from Latin idea (“idea”). Doublet of ideell.

Pronunciation

• IPA^(key): /ide?a?l/
• Rhymes: -a?l

Adjective

ideal (comparative idealer, superlative 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 ide?lis.

Pronunciation

• IPA^(key): [??d?eal]
• 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 ideal-ideal, first-person possessive idealku, second-person possessive idealmu, third-person possessive idealnya)

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 (KBBI) Daring, Jakarta: Badan Pengembangan dan Pembinaan Bahasa, Kementerian Pendidikan dan Kebudayaan Republik Indonesia, 2016.

Luxembourgish

Pronunciation

• IPA^(key): /ide?a?l/, [id??a?l], /idi?a?l/

Adjective

ideal (masculine idealen, neuter ideaalt, comparative méi ideal, superlative am ideaalsten)

1. ideal

Declension

Norwegian Bokmål

Etymology

From French idéal, from Late Latin ide?lis (“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 ide?lis (“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): /ide?al/

Adjective

ideal

1. ideal

Noun

ideal m

1. ideal

Portuguese

Etymology

From Latin ide?lis.

Pronunciation

• (Portugal) IPA^(key): /i?ðja?/
• (Brazil) IPA^(key): /i.de?aw/
• Hyphenation: i?de?al

Adjective

ideal m or f (plural ideais, comparable)

1. ideal
2. notional

Derived terms

• idealmente

Noun

ideal m (plural ideais)

1. ideal
2. fantasy

Romanian

Etymology

From French idéal, from Latin idealis.

Adjective

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

1. ideal

Declension

Related terms

• idealism
• idealist
• idealiza

Serbo-Croatian

Pronunciation

• IPA^(key): /id?a?l/
• Hyphenation: i?de?al

Noun

idè?l m (Cyrillic spelling ??????)

1. ideal

Declension

Spanish

Etymology

From Latin ide?lis.

Pronunciation

• IPA^(key): /ide?al/, [i.ð?e?al]

Adjective

ideal (plural ideales)

1. ideal

Derived terms

Noun

ideal m (plural ideales)

1. ideal

Swedish

Pronunciation

Noun

ideal n

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

Declension

Anagrams

• ilade

Turkish

Etymology

Borrowed from French idéal.

Pronunciation

• IPA^(key): /ide?a?/
• Hyphenation: i?de?al

Adjective

ideal (comparative daha ideal, superlative en ideal)

1. ideal

Noun

ideal (definite accusative ideali, plural idealler)

1. ideal

Declension

Synonyms

• ülkü

English

Alternative forms

• modell

Etymology

From Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, diminutive form of modulus (“measure, standard”), diminutive of modus (“measure”); see mode, and compare module, modulus, mould, mold.

Pronunciation

• (UK) IPA^(key): /?m?dl?/
• (US) IPA^(key): /?m?dl?/, [?m?.??]
• • Homophone: mottle
• Hyphenation: mod?el
• Rhymes: -?d?l

Noun

model (plural models)

1. A person who serves as a subject for artwork or fashion, usually in the medium of photography but also for painting or drawing.

2. A person, usually an attractive female, hired to show items or goods to the public, such as items given away as prizes on a TV game show.
3. A representation of a physical object, usually in miniature.
   • You have here the models of several ancient temples, though the temples and the gods are perished.

4. A simplified representation used to explain the workings of a real world system or event.
5. A style, type, or design.

6. The structural design of a complex system.

7. A successful example to be copied, with or without modifications.

   He was a model of eloquence and virtue.

8. (logic) An interpretation function which assigns a truth value to each atomic proposition.
9. (logic) An interpretation which makes a set of sentences true, in which case that interpretation is called a model of that set.
10. (medicine) An animal that is used to study a human disease or pathology.
11. Any copy, or resemblance, more or less exact.
12. (software architecture) In software applications using the model-view-controller design pattern, the part or parts of the application that manage the data.

Synonyms

• See also Thesaurus:model

Hyponyms

Derived terms

Related terms

Translations

Descendants

• ? Cebuano: model

Adjective

model (not comparable)

1. Worthy of being a model; exemplary.
   • 1898, John Thorburn, The St. Andrew's Society of Ottawa: 1846-1897 : sketch, page 40:

     [...] from the land of your origin, because you demand the claims of those who believe it more model than yours, [...]

   • 1932, Nora Fugger, James Austin Galaston (translator), The Glory of the Habsburgs: the Memoirs of Princess Fugger, page 35:

     Methods of game-preservation in their extensive and well-stocked hunting-grounds were as model as the huntsmanlike management of the hunts.

   • 1934, Charles Ryle Fay, Imperial economy and its place in the formation of economic doctrine, 1600-1932, page 143:

     [...] and we press with special severity on one small country whose agriculture is as model as is her way of rural life.

   • 1956, Stephen Rynne, All Ireland, page 54:

     True, it is an untidy county; the farmhouses are much more model than the farms (when we reach Antrim we shall find that the farms are more model than the farmhouses).

   • 1961, Blackwood's Magazine, volume 289, page 525:

     At our approach the animals made so much noise that the owners of the hut peered round the door to see what was the matter; outwardly rather less model than the farm, there appeared two ancient Basques, emblematically black-bereted, gnarled [...]

   • 1968, American County Government, volume 33, page 19:

     But not all the exchanges were as model as the sergeant. Some of the exchangees showed a rigidity and reluctance to adapt.

   • 1999, Michael D. Williams, Acquisition for the 21st century: the F-22 Development Program, page 113:

     It is as model as you can get.

   • 2002, Uma Anand Segal, A framework for immigration: Asians in the United States, page 308:

     While Asians have been perceived as the model minority, it is increasingly clear that some Asian groups are more model than are others, and even within these model groups, a division exists [...]

   • 2010, Eleanor Coppola, Notes on a Life, page 140:

     All were neat and well kept which added to the sense that they were more model than real.

   Synonym: ideal

Translations

Verb

model (third-person singular simple present models, present participle (UK) modelling or (US) modeling, simple past and past participle (UK) modelled or (US) modeled)

1. (transitive) to display for others to see, especially in regard to wearing clothing while performing the role of a fashion model

2. (transitive) to use as an object in the creation of a forecast or model

3. (transitive) to make a miniature model of

4. (transitive) to create from a substance such as clay

5. (intransitive) to make a model or models
6. (intransitive) to be a model of any kind

Synonyms

• modelise, US modelize

Derived terms

Translations

Further reading

• model in Webster’s Revised Unabridged Dictionary, G. & C. Merriam, 1913.
• model in The Century Dictionary, New York, N.Y.: The Century Co., 1911.
• model on Wikimedia Commons.Wikimedia Commons

Anagrams

• LModE, molde

Albanian

Etymology

Ultimately from Old Italian modello, from Vulgar Latin *modellus, diminutive form of modulus (“measure, standard”).

Noun

model m (indefinite plural modele, definite singular modeli, definite plural modelet)

1. pattern
2. example

   Synonyms: shembull, mostër

Declension

Derived terms

• modeloj
• modelim

Catalan

Pronunciation

• (Balearic, Valencian) IPA^(key): /mo?d?l/
• (Central) IPA^(key): /mu?d?l/

Noun

model m (plural models)

1. model

model m or f (plural models)

1. model (person)

Related terms

• modelar

Further reading

• “model” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.
• “model” in Gran Diccionari de la Llengua Catalana, Grup Enciclopèdia Catalana.
• “model” in Diccionari normatiu valencià, Acadèmia Valenciana de la Llengua.
• “model” in Diccionari català-valencià-balear, Antoni Maria Alcover and Francesc de Borja Moll, 1962.

Cebuano

Pronunciation

• Hyphenation: mo?del

Etymology 1

Borrowed from English model, from Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, diminutive form of Latin modulus (“measure, standard”), diminutive of modus (“measure”),

Noun

model

1. fashion model
2. model, poser; someone who poses for a photograph or painting
3. framework
4. example

Verb

model

1. to model
2. to become or work as a fashion model
3. to pose

Synonyms

• modelo

Etymology 2

From the Cebuano phrase mo-deliver ug lunggon (“someone who delivers coffins”).

Noun

model

1. (colloquial, humorous) a funeral home worker; a funeral director or funeral attendant See usage notes.

Usage notes

• Used to poke fun at a good-looking or well-dressed person.

Crimean Tatar

Etymology

From French modèle (“model”).

Noun

model

1. model

Declension

References

• Mirjejev, V. A.; Usejinov, S. M. (2002) Ukrajins?ko-kryms?kotatars?kyj slovnyk [Ukrainian – Crimean Tatar Dictionary]?^[2], Simferopol: Dolya, ?ISBN

Czech

Pronunciation

• IPA^(key): [?mod?l]

Noun

model f

1. genitive plural of modla

Dutch

Etymology

Borrowed from Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, diminutive form of modulus.

Pronunciation

• IPA^(key): /mo??d?l/
• Hyphenation: mo?del
• Rhymes: -?l

Noun

model n (plural modellen, diminutive modelletje n)

1. model (type, design)
2. model (someone or something serving as an artistic subject)
3. model (simplified representation)
4. model (miniature)
5. model (prototype)
6. shape, the proper arrangement of something

Derived terms

Descendants

• Afrikaans: model
• ? Indonesian: model
• ? West Frisian: model

Indonesian

Etymology

From Dutch model, from Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, diminutive form of modulus. Doublet of mode, modern, modul, and modus.

Pronunciation

• IPA^(key): [?mod?l]
• Hyphenation: mo?dèl

Noun

model or modèl

1. model,
   1. a style, type, or design.
   2. a person who serves as a subject for artwork or fashion, usually in the medium of photography but also for painting or drawing.
   3. a person, usually an attractive female, hired to show items or goods to the public, such as items given away as prizes on a TV game show.
   4. a representation of a physical object, usually in miniature.
2. (psychology) role model, a person who serves as an example, whose behavior is emulated by others

Affixations

Further reading

• “model” in Kamus Besar Bahasa Indonesia (KBBI) Daring, Jakarta: Badan Pengembangan dan Pembinaan Bahasa, Kementerian Pendidikan dan Kebudayaan Republik Indonesia, 2016.

Polish

Etymology

From French modèle, from Middle French modelle, from Old Italian modello, from Vulgar Latin *modellus, from Latin modulus.

Pronunciation

• IPA^(key): /?m?.d?l/

Noun

model m inan (diminutive modelik)

1. model (miniature)

   Synonym: makieta

2. model (simplified representation)
3. model (style)

   Synonyms: fason, typ

4. model (structural design)

   Synonyms: paradygmat, szablon, wzorzec, wzór

Declension

Noun

model m pers (feminine modelka)

1. model (person who serves as a subject for artwork)
2. model (person who serves as a subject for fashion)

Declension

Derived terms

• (verbs) modelowa?, wymodelowa?
• (noun) modelownia
• (adjective) modelowy

Related terms

• (noun) modeling
• (adverb) modelowo

Further reading

• model in Wielki s?ownik j?zyka polskiego, Instytut J?zyka Polskiego PAN
• model in Polish dictionaries at PWN

Romanian

Pronunciation

• IPA^(key): /mo?del/
• Rhymes: -el
• Hyphenation: mo?del

Noun

model n (plural modele)

1. a template

Serbo-Croatian

Etymology

From German Modell or French modèle, from Italian modello, from Latin modellus.

Pronunciation

• IPA^(key): /m?del/
• Hyphenation: mo?del

Noun

mòdel m (Cyrillic spelling ??????)

1. model (clarification of this definition is needed)

Declension

References

• “model” in Hrvatski jezi?ni portal

Turkish

Etymology

Borrowed from French modèle.

Pronunciation

• IPA^(key): /mo?del/
• Hyphenation: mo?del

Noun

model (definite accusative modeli, plural modeller)

1. model (clarification of this definition is needed)

Declension