integer

English

Etymology

Borrowed from Latin integer (“whole”), from Proto-Italic *n̥tagros (“untouched”). Doublet of entier and entire. Related to English tact, thack, and thwack.

Pronunciation

• IPA^(key): /ˈɪn.tɪ.d͡ʒə(ɹ)/
• (Canada, US) IPA^(key): [ˈɪn.tʰə.d͡ʒɚ], [ˈɪn.ɾ̃ə.d͡ʒɚ]

  • Audio (US):

    (file)

Noun

integer (plural integers or (rare) integri)

1. (arithmetic) A number that is not a fraction; an element of the infinite and numerable set {..., -3, -2, -1, 0, 1, 2, 3, ...}.
   • 1886, Leopold Kronecker, speech to the Berliner Naturforscher-Versammlung:

     God made the integers; all else is the work of man

Synonyms

• whole number, when understood to include negative numbers and zero.
• integral number

Hypernyms

• rational number
  • real number
• Gaussian integer
  • quadratic integer
    • algebraic integer
      • algebraic number

Hyponyms

• natural number
• zero

Derived terms

• Blum integer
• Cartan integer
• Eisenstein integer
• half-integer
• half-integral
• hyperinteger
• integer factorization
• integerness
• long integer
• noninteger
• non-integer

Related terms

• integral
• integrate
• integrity

Translations

a number that is not a fraction

• Arabic: عَدَد صَحِيح m (ʕadad ṣaḥīḥ)
• Armenian: ամբողջ թիվ (amboġǰ tʻiv)
• Azerbaijani: tam ədəd
• Bashkir: бөтөн һан (bütün han)
• Basque: zenbaki oso
• Belarusian: цэ́лы лік m (cély lik)
• Bengali: পূর্ণ সংখ্যা (purno śoṅkha)
• Bulgarian: ця́ло число́ n (cjálo čisló)
• Catalan: enter (ca) m
• Chinese:

  Mandarin: 整數 / 整数 (zh) (zhěngshù)

• Cornish: kowlniver m
• Czech: celé číslo (cs) n
• Danish: heltal (da) n, helt tal n
• Dutch: geheel getal n
• Esperanto: entjero (eo)
• Estonian: täisarv (et)
• Finnish: kokonaisluku (fi)
• French: entier (fr) m, nombre entier (fr) m, entier relatif (fr) m
• Galician: enteiro (gl) m
• German: ganze Zahl (de) f, Ganzzahl (de) f
• Greek: ακέραιος αριθμός (el) m (akéraios arithmós), ακέραιος (el) m (akéraios)
• Hebrew: שלם (he) m, מספר שלם (he) m
• Hindi: पूर्णांक (hi) m (pūrṇāṅk), पूर्ण संख्या f (pūrṇ saṅkhyā)
• Hungarian: egész szám (hu)
• Ido: integro (io)
• Indonesian: bilangan bulat (id)
• Italian: intero (it) m, numero intero (it) m
• Japanese: 整数 (ja) (せいすう, seisū)
• Javanese: cacah wutuh
• Kazakh: бүтін сан (bütin san)
• Khmer: ចំនួនគត់ (km) (cɑmnuən kŭət)
• Korean: 정수(整數) (ko) (jeongsu)
• Macedonian: цел бро́ј m (cel brój)
• Malay: nombor bulat (ms)
• Māori: tau tōpū, tauoti
• Marathi: पूर्णांक m (pūrṇāṅka), पूर्णांक संख्या f (pūrṇāṅka saṅkhyā)
• Norwegian:

  Bokmål: heltall (no) n

  Nynorsk: heiltal n

• Persian: عدد صحیح ('adad-e sahih)
• Polish: liczba całkowita (pl) f
• Portuguese: inteiro (pt) m
• Romanian: întreg (ro) m, număr întreg n
• Russian: це́лое число́ (ru) n (céloje čisló), це́лое (ru) n (céloje)
• Serbo-Croatian:

  Cyrillic: ције̑лӣ бро̑ј m

  Latin: cijȇlī brȏj m

• Spanish: entero (es) m
• Sundanese: ᮝᮤᮜᮍᮔ᮪ ᮘᮥᮜᮩᮓ᮪ (wilangan buleud)
• Swedish: heltal (sv) n
• Tagalog: buumbilang
• Tajik: адади саҳеҳ (tg) (adad-i saheh)
• Turkish: tam sayı (tr), adedimürettep (tr)
• Uyghur: پۈتۈن سان (pütün san)
• Vietnamese: số nguyên (vi) (數原)
• Welsh: cyfanrif (cy) m
• Zhuang: cingjsoq

Further reading

• “integer”, in Webster’s Revised Unabridged Dictionary, Springfield, Mass.: G. & C. Merriam, 1913, →OCLC.
• William Dwight Whitney, Benjamin Eli Smith, editors (1895–1910), “integer”, in The Century Dictionary […], New York, N.Y.: The Century Co., →OCLC.

References

• integer on Wikipedia.Wikipedia

Anagrams

• greetin', teering, treeing

Dutch

Pronunciation

• Audio:

  (file)

Adjective

integer (comparative integerder, superlative integerst)

1. honest, trustworthy, having integrity

Declension

Declension of integer
uninflected	integer
inflected	integere
comparative	integerder
		positive	comparative	superlative
predicative/adverbial		integer	integerder	het integerst het integerste
indefinite	m./f. sing.	integere	integerdere	integerste
	n. sing.	integer	integerder	integerste
	plural	integere	integerdere	integerste
definite		integere	integerdere	integerste
partitive		integers	integerders	—

German

Pronunciation

• Audio (Austria):

  (file)

• Audio (Germany (Berlin)):

  (file)

Adjective

integer (strong nominative masculine singular integerer, comparative integrer, superlative am integersten)

1. with integrity, of integrity

Declension

Positive forms of integer

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist integer	sie ist integer	es ist integer	sie sind integer
strong declension (without article)	nominative	integerer	integere	integeres	integere
	genitive	integeren	integerer	integeren	integerer
	dative	integerem	integerer	integerem	integeren
	accusative	integeren	integere	integeres	integere
weak declension (with definite article)	nominative	der integere	die integere	das integere	die integeren
	genitive	des integeren	der integeren	des integeren	der integeren
	dative	dem integeren	der integeren	dem integeren	den integeren
	accusative	den integeren	die integere	das integere	die integeren
mixed declension (with indefinite article)	nominative	ein integerer	eine integere	ein integeres	(keine) integeren
	genitive	eines integeren	einer integeren	eines integeren	(keiner) integeren
	dative	einem integeren	einer integeren	einem integeren	(keinen) integeren
	accusative	einen integeren	eine integere	ein integeres	(keine) integeren

Comparative forms of integer

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist integrer	sie ist integrer	es ist integrer	sie sind integrer
strong declension (without article)	nominative	integrerer	integrere	integreres	integrere
	genitive	integreren	integrerer	integreren	integrerer
	dative	integrerem	integrerer	integrerem	integreren
	accusative	integreren	integrere	integreres	integrere
weak declension (with definite article)	nominative	der integrere	die integrere	das integrere	die integreren
	genitive	des integreren	der integreren	des integreren	der integreren
	dative	dem integreren	der integreren	dem integreren	den integreren
	accusative	den integreren	die integrere	das integrere	die integreren
mixed declension (with indefinite article)	nominative	ein integrerer	eine integrere	ein integreres	(keine) integreren
	genitive	eines integreren	einer integreren	eines integreren	(keiner) integreren
	dative	einem integreren	einer integreren	einem integreren	(keinen) integreren
	accusative	einen integreren	eine integrere	ein integreres	(keine) integreren

Superlative forms of integer

number & gender		singular			plural
		masculine	feminine	neuter
predicative		er ist am integersten	sie ist am integersten	es ist am integersten	sie sind am integersten
strong declension (without article)	nominative	integerster	integerste	integerstes	integerste
	genitive	integersten	integerster	integersten	integerster
	dative	integerstem	integerster	integerstem	integersten
	accusative	integersten	integerste	integerstes	integerste
weak declension (with definite article)	nominative	der integerste	die integerste	das integerste	die integersten
	genitive	des integersten	der integersten	des integersten	der integersten
	dative	dem integersten	der integersten	dem integersten	den integersten
	accusative	den integersten	die integerste	das integerste	die integersten
mixed declension (with indefinite article)	nominative	ein integerster	eine integerste	ein integerstes	(keine) integersten
	genitive	eines integersten	einer integersten	eines integersten	(keiner) integersten
	dative	einem integersten	einer integersten	einem integersten	(keinen) integersten
	accusative	einen integersten	eine integerste	ein integerstes	(keine) integersten

Related terms

• Integrität

Further reading

• “integer” in Duden online
• “integer”, in Digitales Wörterbuch der deutschen Sprache‎^[1] (in German)

Latin

Latin numbers ^(edit)

		10
		I 1	2  → [a], [b]	10  →
Cardinal: ūnus     Ordinal: prīmus     Adverbial: semel     Proportional: simplus     Multiplier: simplex     Distributive: singulus, prīvus     Collective: ūniō     Fractional: integer

Etymology

From Proto-Italic *n̥tagros (“untouched”), from *teh₂g- (“to touch”), whence Latin tangō (“to touch”). By surface analysis, an adjectival formation from in- +‎ tangō.

Pronunciation

• (Classical Latin) IPA^(key): [ˈɪn.tɛ.ɡɛr]
• (modern Italianate Ecclesiastical) IPA^(key): [ˈin.te.d͡ʒer]

Adjective

integer (feminine integra, neuter integrum, comparative integrior, superlative integerrimus); first/second-declension adjective (nominative masculine singular in -er)

1. complete, whole, intact, uninjured, sound, healthy

   Synonyms: incolumis, validus, sanus, salvus, saluber, sospes, intactus, sollus, innoxius

   Antonyms: aeger, miser, affectus, fessus, īnfirmus, languidus

   ab/de/ex integro ― from the start again, from the beginning

   ad integrum ― completely, at all

Declension

First/second-declension adjective (nominative masculine singular in -er).

	singular				plural
	masculine	feminine	neuter		masculine	feminine	neuter
nominative	integer	integra	integrum		integrī	integrae	integra
genitive	integrī	integrae	integrī		integrōrum	integrārum	integrōrum
dative	integrō	integrae	integrō		integrīs
accusative	integrum	integram	integrum		integrōs	integrās	integra
ablative	integrō	integrā	integrō		integrīs
vocative	integer	integra	integrum		integrī	integrae	integra

Derived terms

• integellus
• integrātiō
• integrātor
• integrē
• integritās
• integritūdō
• integrō

Descendants

• Insular Romance:
  • Sardinian: interu, intreu (medieval)
• Balkano-Romance:
  • Aromanian: ãntreg, ntreg
  • Romanian: întreg
• Italo-Dalmatian:
  • Corsican: intrévu
  • Dalmatian: intric
  • Italian: intiero, intero
  • Sicilian: ntregu
  • Venetan: intier, intiero, intrego, intriego, intrech
• Rhaeto-Romance:
  • Friulian: intîr
  • Ladin: intríak, intríek, intier, ntier
  • Romansh: entir, inter
• Gallo-Italic:
  • Emilian: intîr
  • Lombard: intreo (medieval), intre̢k
  • Piedmontese: antrègh, antrí, antre̢tś, anter
  • Romagnol: intègar
• Gallo-Romance:
  • Franco-Provençal: entiér
  • Old Catalan: entegre, entregue
  • Old French: entiere, entre
    • French: entier
    • Norman: entchi (Jersey)
    • Walloon: entier
    • → English: entire
  • Old Occitan: entegre, entier, enteir
    • Occitan: entièr
    • → Catalan: entir (regional)
• Ibero-Romance:
  • Aragonese: enter, entero, anter, antero
  • Asturian: enteru
  • Old Galician-Portuguese: enteiro, enteyro, entrego
    • Galician: enteiro, entergo, inteiro
    • Portuguese: inteiro (latinized prefix), ⇒ entregue
  • Old Navarro-Aragonese: entreg
    • Aragonese: entrego (Probably influenced by Spanish)
  • Old Spanish: entero, entrego, entegro
    • Spanish: entero
      • → Catalan: enter

Borrowings:

• → Asturian: integru
• → Catalan: íntegre
• → German: integer
• → English: integer
• → French: intègre
• → Galician: íntegro
• → Interlingua: integre
• → Italian: integro
• → Occitan: integre
• → Portuguese: íntegro
• → Romanian: integru
• → Spanish: íntegro

Further reading

• “integer”, in Charlton T. Lewis and Charles Short (1879), A Latin Dictionary, Oxford: Clarendon Press
• “integer”, in Charlton T. Lewis (1891), An Elementary Latin Dictionary, New York: Harper & Brothers
• “integer”, in Gaffiot, Félix (1934), Dictionnaire illustré latin-français, Hachette.
• Carl Meißner; Henry William Auden (1894), Latin Phrase-Book‎^[2], London: Macmillan and Co.
  • sound, unimpaired senses: sensus sani, integri, incorrupti
    
  • it is no longer in my power: mihi non est integrum, ut...
    
  • to leave the question open; to refuse to commit oneself: integrum (causam integram) sibi reservare
    
  • to reinstate a person in his right: aliquem in integrum (vid. sect. V. 4, note The proper...) restituere
    
  • an impartial witness: testis incorruptus atque integer
    
  • to send fresh troops to take the place of those wearied with fighting: integros defatigatis summittere
    
  • fresh troops relieve the tired men: integri et recentes defatigatis succedunt
    
  • (ambiguous) to be in the prime of life: integra aetate esse
    
  • (ambiguous) the matter is still undecided; it is an open question: res integra est
    
  • (ambiguous) I have not yet committed myself: res mihi integra est
    
• integer in Ramminger, Johann (16 July 2016 (last accessed)), Neulateinische Wortliste: Ein Wörterbuch des Lateinischen von Petrarca bis 1700‎^[3], pre-publication website, 2005-2016

• Walther von Wartburg (1928–2002), “ĭntĕger”, in Französisches Etymologisches Wörterbuch (in German), volume 4: G H I, page 734
• Online Latin dictionary, Olivetti

Limburgish

Alternative forms

• énnteeger (Eupen)

Etymology

Borrowed from Latin integer.

Adjective

integer (comparative integerder, superlative integers, predicative superlative 't integers)

1. friendly
2. complete, whole, intact

Usage notes

Unlike in Dutch, it is not used in the meaning of honest or trustworthy.

Inflection

Declension of integer

number & gender	masculine		feminine		neuter
	singular	plural	singular	plural	singular	plural
nominative	integere	integer	integer	integer	integer	integer
genitive	integers	integerer	integerer	integerer	integers	integerer
locative	integeres	integeres	integeres	integeres	integeres	integeres
vocative1	integer
dative2	integere	integeren	integerer	integeren	integer	integeren
accusative2	integere	integeren	integer	integer	integer	integeren
1Limited to a few fossilized forms.
2Nowadays obsolete, use the nominative instead.