arithmetic

English

Etymology 1

Etymology tree

Proto-Indo-European *h₂er-

Proto-Indo-European *-éh₁ti

Proto-Indo-European *h₂reh₁-

Proto-Indo-European *-éyti

Proto-Indo-European *h₂rey-der.

Ancient Greek ᾰ̓ρῐθμός (ărĭthmós)

Proto-Indo-European *-eti

Proto-Indo-European *-eyéti

Proto-Indo-European *-esyéti

Proto-Indo-European *-éh₁ti

Proto-Indo-European *-yeti

Proto-Indo-European *-éh₁yeti

Proto-Indo-European *-yeti

Proto-Indo-European *-éyeti

Ancient Greek -έω (-éō)

Ancient Greek ἀριθμέω (arithméō)

Proto-Indo-European *-tis

Ancient Greek -τις (-tis)

Ancient Greek -σῐς (-sĭs)

Proto-Indo-European *-kos

Ancient Greek -κός (-kós)

?

Proto-Indo-European *-tós

Ancient Greek -τος (-tos)

▲

Ancient Greek -κός (-kós)

?

Ancient Greek -τικός (-tikós)

Ancient Greek ἀριθμητῐκός (arithmētĭkós)

Ancient Greek ἀριθμητῐκή (arithmētĭkḗ)bor.

Latin arithmēticabor.

▲

Ancient Greek ἀριθμητῐκός (arithmētĭkós)bor.

Latin arithmēticusbor.

Old French arismetiquebor.

Middle English arsmetike

English arithmetic

From Middle English arsmetike, from Old French arismetique, from Latin arithmētica, from Ancient Greek ἀριθμητική (τέχνη) (arithmētikḗ (tékhnē), “(art of) counting”), feminine of ἀριθμητικός (arithmētikós, “arithmetical”), from ἀριθμός (arithmós, “number, counting”), from Proto-Indo-European *h₂ri-dʰh₁-mó-s, form of *h₂rey- (“to count, reason”). Used in English since 13th century.

Alternative forms

• arsmetrike, arsmetryke, arithmetike (obsolete)

Pronunciation

• Noun
  • (Received Pronunciation) enPR: ərĭth′mətĭk
  • (General American) IPA^(key): /əˈɹɪθmətɪk/

  • Audio (General American):

    (file)

  • Hyphenation: a‧rith‧me‧tic
• Adjective
  • IPA^(key): /ˌɛɹɪθˈmɛtɪk/

  • Audio (General American):

    (file)

  • Hyphenation: ar‧ith‧met‧ic

Noun

arithmetic (usually uncountable, plural arithmetics)

1. The mathematics of numbers (integers, rational numbers, real numbers, or complex numbers) under the operations of addition, subtraction, multiplication, and division.
   • 1992, Douglas M. Priest, On Properties of Floating Point Arithmetics, University of California, Berkeley, page 17:

     Note that all correctly rounding arithmetics satisfy property A1, as do those with properly truncating addition. All faithful binary arithmetics and all arithmetics with either properly truncating or correctly chopping addition satisfy property A2.

   • 2013 July 20, “Welcome to the plastisphere”, in The Economist‎^[2], volume 408, number 8845, archived from the original on 8 March 2023:

     [The researchers] noticed many of their pieces of [plastic marine] debris sported surface pits around two microns across. […] Closer examination showed that some of these pits did, indeed, contain bacteria, and that in several cases these bacteria were dividing and thus, by the perverse arithmetic of biological terminology, multiplying.

2. (dated) Number theory.

Hypernyms

• (study): math (US), maths (UK), mathematics

Derived terms

Terms derived from the noun arithmetic

• affine arithmetic
• alphametic
• arbitrary-precision arithmetic
• arithmetic bug
• arithmetician
• arithmeticity
• arithmogram
• binary arithmetic
• Boolean arithmetic
• clock arithmetic
• congruence arithmetic
• decimal arithmetic
• floating-point arithmetic
• fundamental theorem of arithmetic
• fuzzy arithmetic
• hard as Chinese arithmetic
• higher arithmetic
• hyperarithmetic
• interval arithmetic
• location arithmetic
• mental arithmetic
• modular arithmetic
• moral arithmetic
• nonarithmetic
• Peano arithmetic
• political arithmetic
• Presburger arithmetic
• Robinson arithmetic
• saturation arithmetic
• significance arithmetic
• universal arithmetic
• vulgar arithmetic

Translations

mathematics of numbers, etc.

• Albanian: aritmetikë (sq)
• Arabic: حساب (ar), العدّ
• Armenian: թվաբանություն (hy) (tʻvabanutʻyun)
• Basque: aritmetika (eu)
• Bulgarian: аритме́тика (bg) f (aritmétika)
• Catalan: aritmètica (ca)
• Chinese:

  Mandarin: 算術 / 算术 (zh) (suànshù)

• Cornish: niveronieth f
• Czech: aritmetika f
• Dutch: aritmetica (nl) f, rekenkunde (nl) f
• Esperanto: aritmetiko, kalkularto
• Finnish: aritmetiikka (fi), laskuoppi (fi)
• French: arithmétique (fr) f
• Friulian: aritmetiche f
• Galician: aritmética f
• German: Arithmetik (de) f, Rechenkunst (de) f, Rechenkunde f (dated)
• Greek: αριθμητική (el) f (arithmitikí)

  Ancient Greek: ἀριθμητική f (arithmētikḗ)

• Gujarati: અંકગણિત (aṅkagaṇit)
• Hebrew: חֶשְׁבּוֹן (he) m (ẖeshbón)
• Hindi: अंकगणित (hi) (aṅkgaṇit)
• Hungarian: számtan (hu), aritmetika (hu)
• Indonesian: aritmetika (id)
• Inuktitut: ᓈᓴᐅᓯᕆᓂᖅ (naasaosiriniq)
• Irish: uimhríocht f, áireamh m, figiúirí m pl
• Italian: aritmetica (it) f
• Japanese: 算数 (ja) (さんすう, sansū)
• Kannada: ಅಂಕಗಣಿತ (kn) (aṅkagaṇita)
• Kazakh: арифметика (arifmetika)
• Korean: 산술(算術) (sansul)
• Latvian: aritmētika f
• Lithuanian: aritmetika f
• Macedonian: аритметика f (aritmetika)
• Malayalam: അങ്കഗണിതം (ml) (aṅkagaṇitaṁ)
• Marathi: अंकगणित (mr) n (aṅkagaṇit)
• Mongolian:

  Cyrillic: арифметик (mn) (arifmetik), тооны бодлого (toony bodlogo)

• Norman: caltchul m (Jersey)
• Norwegian: aritmetikk (no) m
• Occitan: aritmetica (oc) f
• Old English: rimcræft, ġerīmcræft
• Persian: حساب (fa) (hesâb), اشمار (ošmâr)
• Polish: arytmetyka (pl) f
• Portuguese: aritmética (pt) f
• Romanian: aritmetică (ro) f
• Russian: арифме́тика (ru) f (arifmétika)
• Spanish: aritmética (es) f, arismética (es) f (p. us.)
• Swedish: aritmetik (sv) c
• Tagalog: bilnuran, aritmetika
• Tajik: ҳисоб (tg) (hisob)
• Telugu: అంకగణితం (aṅkagaṇitaṁ)
• Thai: เลขคณิต (th) (lek-ka-nit)
• Tibetan: ཨང་རྩིས (ang rtsis)
• Turkish:

  Ottoman Turkish: حساب (hisab)

• Ukrainian: арифме́тика (uk) f (aryfmétyka), аритме́тика f (arytmétyka)
• Urdu: حساب (ur) (hisāb)
• Vietnamese: số học (vi) (數學)
• Volapük: kalkulav (vo)
• Welsh: rhifyddeg f, rhifyddiaeth f
• Xhosa: izibalo class 10

Adjective

arithmetic (not comparable)

1. Increasing or decreasing by an arithmetic progression.

   Coordinate terms: geometric, exponential; parabolic

   Near-synonym: linear

   Growth in the most mature markets is likely to be arithmetic; on what rational basis could one hope for exponential growth there?

Etymology 2

From French arithmétique, from Latin arithmēticus, from Ancient Greek ἀριθμητῐκός (arithmētĭkós).

Pronunciation

• (Received Pronunciation, General American) enPR: ărĭthmĕt'ĭk, IPA^(key): /æɹɪθˈmɛtɪk/

• Audio (Southern England):

  (file)

• Hyphenation: arith‧met‧ic

Adjective

arithmetic (not comparable)

1. (mathematics) Of, relating to, or using arithmetic; arithmetical.

   arithmetic geometry

   • 2008, Emmanuel Kowalski, The large sieve and its applications: arithmetic geometry, random ..., page 189:

     Moreover, the latest work of Katz, involving the so-called 'Larsen alternative', provides new criteria, of a very arithmetic nature, to (almost) determine the rational monodromy group

2. (arithmetic) Of a progression, mean, etc, computed solely using addition.

   arithmetic progression

Coordinate terms

• (computed solely using addition): geometric

Derived terms

Terms derived from the adjective arithmetic

• arithmetically
• arithmetic average
• arithmetic combinatorics
• arithmetic density
• arithmetic function
• arithmetic-geometric mean
• arithmetic geometry
• arithmetic hierarchy
• arithmetic logic unit
• arithmetic mean
• arithmetic operation
• arithmetic operator
• arithmetic progression
• arithmetic sequence
• arithmetic series
• arithmetic spiral

Translations

arithmetical

• Albanian: aritmetik (sq)
• Armenian: թվաբանական (hy) (tʻvabanakan)
• Asturian: aritméticu
• Belarusian: арыфметы́чны (aryfmjetýčny)
• Bulgarian: аритметичен (aritmetičen)
• Chinese:

  Mandarin: 算術的 / 算术的 (suànshù de)

• Czech: aritmetický m
• Dutch: rekenkundig (nl)
• Finnish: aritmeettinen (fi)
• French: d'arithmétique, de l’arithmétique
• Friulian: aritmetic
• Galician: aritmético
• German: arithmetisch (de)
• Greek: αριθμητικός (el) m (arithmitikós)
• Hindi: अंकगणितीय n (aṅkagṇitīya)
• Hungarian: számtani (hu)
• Indonesian: aritmetika (id)
• Irish: uimhríochta, uimhríochtúil
• Italian: aritmetico (it) m, aritmetica (it) f
• Kazakh: арифметикалық (arifmetikalyq)
• Latvian: aritmētisks
• Macedonian: аритметички m (aritmetički)
• Marathi: अंकगणितीय n (aṅkagṇitīy)
• Norwegian: aritmetisk (no)
• Occitan: aritmetic (oc)
• Polish: arytmetyczny (pl) f
• Portuguese: aritmético (pt)
• Romanian: aritmetic (ro)
• Russian: арифмети́ческий (ru) (arifmetíčeskij)
• Spanish: aritmético (es), arismético (desus.)
• Swedish: aritmetisk (sv), compounds with aritmetik (sv) c
• Ukrainian: арифмети́чний (uk) (aryfmetýčnyj)
• Volapük: kalkulava (genitive), kalkulav- (in compounds)
• Welsh: rhifyddol

computed solely using addition

• Armenian: թվաբանական (hy) (tʻvabanakan)
• Bulgarian: аритметичен (aritmetičen)
• Chinese:

  Mandarin: please add this translation if you can

• Finnish: aritmeettinen (fi)
• French: arithmétique (fr)
• German: arithmetisch (de)
• Hungarian: számtani (hu)
• Macedonian: аритметички m (aritmetički)
• Portuguese: aritmético (pt)
• Russian: арифмети́ческий (ru) (arifmetíčeskij)
• Swedish: aritmetisk (sv)

See also

• List of terms used in arithmetic in English