different between ideal vs simple
ideal
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)
- 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,
- Pertaining to ideas, or to a given idea.
- 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.
- 1796, Matthew Lewis, The Monk, Folio Society 1985, p. 256:
- Teaching or relating to the doctrine of idealism.
- (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)
- 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 subring closed under multiplication by its containing ring.
- Let be the ring of integers and let be its ideal of even integers. Then the quotient ring is a Boolean ring.
- The product of two ideals and is an ideal which is a subset of the intersection of and . This should help to understand why maximal ideals are prime ideals. Likewise, the union of and is a subset of .
- 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.
- (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.
- 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.
- Formally, an ideal of a given set is a nonempty subset of the powerset such that: , and .
- (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 be an arbitrary semisimple Lie algebra. Then can be written uniquely as a direct sum of simple ideals (Theorem 5.2).
- 1975, Che-Young Lee (translator), Zhe-Xian Wan, Lie Algebras, Pergamon Press, page 13,
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)
- ideal
Noun
ideal m (plural ideales)
- ideal
Catalan
Etymology
From Latin ide?lis.
Pronunciation
- (Balearic, Central, Valencian) IPA(key): /i.de?al/
Adjective
ideal (masculine and feminine plural ideals)
- ideal
Derived terms
- idealment
Noun
ideal m (plural ideals)
- ideal
Galician
Etymology
From Latin ide?lis.
Pronunciation
Adjective
ideal m or f (plural ideais)
- ideal
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- 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)
- 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
- ideal:
- optimal; being the best possibility.
- 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)
- (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)
- 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)
- 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)
- ideal
References
- “ideal” in The Nynorsk Dictionary.
Piedmontese
Pronunciation
- IPA(key): /ide?al/
Adjective
ideal
- ideal
Noun
ideal m
- 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)
- ideal
- notional
Derived terms
- idealmente
Noun
ideal m (plural ideais)
- ideal
- 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)
- 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 ??????)
- ideal
Declension
Spanish
Etymology
From Latin ide?lis.
Pronunciation
- IPA(key): /ide?al/, [i.ð?e?al]
Adjective
ideal (plural ideales)
- ideal
Derived terms
Noun
ideal m (plural ideales)
- ideal
Swedish
Pronunciation
Noun
ideal n
- ideal; perfect standard
- (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)
- ideal
Noun
ideal (definite accusative ideali, plural idealler)
- ideal
Declension
Synonyms
- ülkü
ideal From the web:
- what ideal mean
- what ideal is the society based upon
- what ideals was america founded on
- what ideals was japanese culture centered on
- what ideals seemed to motivate lincoln
- what ideals are promoted in the declaration of independence
- what ideals are reflected in beowulf's speech
- what ideal blood pressure
simple
English
Etymology
From Middle English symple, simple, from Old French and French simple, from Latin simplex (“simple”, literally “onefold”) (as opposed to duplex (“double”, literally “twofold”)), from semel (“the same”) + plic? (“I fold”). See same and fold. Compare single, singular, simultaneous, etc.
Partially displaced native English onefold.
Pronunciation
- IPA(key): /?s?mp?l/
- Rhymes: -?mp?l
- Hyphenation: sim?ple
Adjective
simple (comparative simpler or more simple, superlative simplest or most simple)
- Uncomplicated; taken by itself, with nothing added.
- 2001, Sydney I. Landau, Dictionaries: The Art and Craft of Lexicography, Cambridge University Press ?ISBN, page 167,
- There is no simple way to define precisely a complex arrangement of parts, however homely the object may appear to be.
- 2001, Sydney I. Landau, Dictionaries: The Art and Craft of Lexicography, Cambridge University Press ?ISBN, page 167,
- Without ornamentation; plain.
- Free from duplicity; guileless, innocent, straightforward.
- 1605, John Marston, The Dutch Courtesan
- Full many fine men go upon my score, as simple as I stand here, and I trust them.
- 1838, Ralph Waldo Emerson, Literary Ethics - an Oration delivered before the Literary Societies of Dartmouth College, July 24, 1838
- To be simple is to be great.
- 1605, John Marston, The Dutch Courtesan
- Undistinguished in social condition; of no special rank.
- Antonym: gentle
- (now rare) Trivial; insignificant.
- 1485, Thomas Malory, Le Morte d'Arthur, Book X:
- ‘That was a symple cause,’ seyde Sir Trystram, ‘for to sle a good knyght for seyynge well by his maystir.’
- 1485, Thomas Malory, Le Morte d'Arthur, Book X:
- (now colloquial) Feeble-minded; foolish.
- (heading, technical) Structurally uncomplicated.
- (chemistry, pharmacology) Consisting of one single substance; uncompounded.
- (mathematics) Of a group: having no normal subgroup.
- (botany) Not compound, but possibly lobed.
- (of a steam engine) Using steam only once in its cylinders, in contrast to a compound engine, where steam is used more than once in high-pressure and low-pressure cylinders.
- 1959, Steam's Finest Hour, edited by David P. Morgan, Kalmbach Publishing Co., page 6:
- 1959, Steam's Finest Hour, edited by David P. Morgan, Kalmbach Publishing Co., page 6:
- (zoology) Consisting of a single individual or zooid; not compound.
- (mineralogy) Homogenous.
- (obsolete) Mere; not other than; being only.
Synonyms
- (consisting of a single part or aspect): onefold
- (having few parts or features): plain
- See also Thesaurus:easy and Thesaurus:bare-bones
Antonyms
- (having few parts or features): complex, compound, complicated
- (uncomplicated): subtle
Derived terms
Translations
Noun
simple (plural simples)
- (pharmacology) A herbal preparation made from one plant, as opposed to something made from more than one plant.
- 2003, Dolores Stewart Riccio, Charmed Circle, Kensington Books (?ISBN), page 12:
- The venerable carryall, formerly brimming with all manner of esoteric pamphlets and witch's simples, now overflowed with a cascade of soft toys, juice bottles, tissues, linen books for infants, […]
- 2003, Dolores Stewart Riccio, Charmed Circle, Kensington Books (?ISBN), page 12:
- (obsolete, by extension) A physician.
- (logic) A simple or atomic proposition.
- (obsolete) Something not mixed or compounded.
- (weaving) A drawloom.
- (weaving) Part of the apparatus for raising the heddles of a drawloom.
- (Roman Catholicism) A feast which is not a double or a semidouble.
Translations
Verb
simple (third-person singular simple present simples, present participle simpling, simple past and past participle simpled)
- (transitive, intransitive, archaic) To gather simples, i.e. medicinal herbs.
Derived terms
- simpler
- simplist
- simplify
Anagrams
- LEMSIP, impels
Asturian
Etymology
Borrowed from Latin simplex.
Adjective
simple (epicene, plural simples)
- simple (uncomplicated)
Synonyms
- cenciellu
Catalan
Etymology
Borrowed from Latin simplex.
Pronunciation
- (Balearic, Central) IPA(key): /?sim.pl?/
- (Valencian) IPA(key): /?sim.ple/
Adjective
simple (masculine and feminine plural simples)
- simple (uncomplicated)
- Synonym: senzill
- single (not divided into parts)
Derived terms
- fulla simple (“simple leaf”)
- simplement (“simply”)
Related terms
- símplex (“simplex”)
- simplicitat (“simplicity”)
- ximple
Further reading
- “simple” in Diccionari de la llengua catalana, segona edició, Institut d’Estudis Catalans.
- “simple” in Diccionari català-valencià-balear, Antoni Maria Alcover and Francesc de Borja Moll, 1962.
- “simple” in Gran Diccionari de la Llengua Catalana, Grup Enciclopèdia Catalana.
Chavacano
Etymology
From Spanish simple (“simple”).
Adjective
simple
- simple
Esperanto
Etymology
From simpla +? -e.
Pronunciation
- IPA(key): /?simple/
- Hyphenation: sim?ple
Adverb
simple
- simply
French
Etymology
From Old French, borrowed from Latin simplex.
Pronunciation
- IPA(key): /s??pl/
Adjective
simple (plural simples)
- single (multiplier)
- simple
- one-way
- mere
Usage notes
The second and third meanings are taken when the adjective is placed after the noun. The fourth meaning is taken when it is located before the noun.
Derived terms
Descendants
- ? Romanian: simplu
Noun
simple m (plural simples)
- one-way ticket
- (baseball) single
Related terms
Further reading
- “simple” in Trésor de la langue française informatisé (The Digitized Treasury of the French Language).
Anagrams
- emplis
Galician
Etymology
Borrowed from Latin simplex. Displaced Old Portuguese simplez.
Adjective
simple m or f (plural simples)
- simple
German
Adjective
simple
- inflection of simpel:
- strong/mixed nominative/accusative feminine singular
- strong nominative/accusative plural
- weak nominative all-gender singular
- weak accusative feminine/neuter singular
Latin
Adjective
simple
- vocative masculine singular of simplus
Middle English
Adjective
simple
- Alternative form of symple
Noun
simple
- Alternative form of symple
Norwegian Bokmål
Adjective
simple
- definite singular of simpel
- plural of simpel
Norwegian Nynorsk
Adjective
simple
- definite singular of simpel
- plural of simpel
Old French
Alternative forms
- sinple
Etymology
Borrowed from Latin simplex.
Adjective
simple m (oblique and nominative feminine singular simple)
- innocent
- mere; simple
- honest; without pretense
- peasant, pauper (attributive)
Descendants
- French: simple
- ? Romanian: simplu
- ? Middle English: symple, simple
- Scots: semple
- English: simple
Romanian
Pronunciation
- IPA(key): [?sim.ple]
Adjective
simple
- feminine/neuter plural nominative/accusative of simplu
Spanish
Etymology
Borrowed from Latin simplex.
Pronunciation
- IPA(key): /?simple/, [?s?m.ple]
Adjective
simple (plural simples)
- simple (uncomplicated)
- Synonym: sencillo
- Antonym: complejo
- (before the noun) mere, ordinary
- Synonym: mero
- simple, single (not divided into parts)
- Antonym: compuesto
- simple-minded, stupid
- insipid, flavorless
- Synonym: soso
- (grammar) simple
Usage notes
A way to think of the difference between simple and sencillo, which both mean "simple" in English, is that the antonym of simple is complejo (“complex”), whereas the antonym of sencillo is complicado (“complicated”).
Derived terms
Descendants
- Chavacano: simple
Noun
simple m or f (plural simples)
- simpleton, fool
- (pharmacology, masculine only) simple
See also
- más simple que el mecanismo de un botijo
Further reading
- “simple” in Diccionario de la lengua española, Vigésima tercera edición, Real Academia Española, 2014.
Swedish
Adjective
simple
- absolute definite natural masculine form of simpel.
Anagrams
- simpel
Tagalog
Etymology
Borrowed from Spanish simple.
Pronunciation
- IPA(key): /?simpl?/
Adjective
símple
- simple; plain
- Synonyms: payak, yano, liso
simple From the web:
- what simple sugar is broken down in the mitochondria
- what simple sugar is produced
- what simple machine is a doorknob
- what simple machine is a seesaw
- what simple machine is a screwdriver
- what simple machine is a hammer
- what simple machine is a shovel
- what simple machine is a wheelbarrow
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