# arithmetic
## English
### Etymology 1

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, General American) enPR: ərĭth′mətĭk, IPA: /əˈɹɪθmətɪk/
** Audio (General American):(file)
** Hyphenation: a‧rith‧me‧tic
* Adjective
** IPA: /ˌæɹɪθˈmɛtɪk/
** Hyphenation: ar‧ith‧met‧ic

#### Noun

arithmetic (usually uncountable, plural arithmetics)
* 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, volume 408, number 8845:[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.

##### Hypernyms

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

##### Derived terms

* 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
* 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
#### Adjective

arithmetic (not comparable)
* 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: /æɹɪθˈmɛtɪk/
* Audio (Southern England):(file)
* Hyphenation: arith‧met‧ic

#### Adjective

arithmetic (not comparable)
* (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
* (arithmetic) Of a progression, mean, etc, computed solely using addition.
    arithmetic progression

##### Coordinate terms

* (computed solely using addition): geometric

##### Derived terms

* 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
### See also

* List of terms used in arithmetic in English

### References

* ↑ “arithmetic, adj.”, in OED Online ⁠‎, Oxford: Oxford University Press, launched 2000, archived from the original on 2023-09-30.