integer

Etymology

It is borrowed from Latin integer (“untouched, intact, whole, entire”),^[2][3][4][5] formed from in- (“not”) and the root of tangō (“to touch”),^[2][6][5][7] from Proto-Indo-European *tag- (“to touch, handle”).^[3][8] Barnhart and Klein reconstruct an earlier Latin form *entagros.^[5][9] The mathematical noun is a noun use of the Latin adjective.^[3] It is a doublet of entire, which came through French,^[5][2][10] and related to integral, integrate, integrity, intact and tangent.^[10][9]

Earliest recorded meaning

As an adjective, having no part missing, whole: before 1509, in a letter of T. Wolsey to Henry VII.^[2][6] The sense is obsolete.^[2]

Semantic evolution

The noun was a mathematical term from its first record in 1571, in T. Digges's Pantometria: a whole number, as opposed to a fraction.^[2][5][4][3] The adjective had a short life in English, meaning morally upright in 1644 and, in mathematics, whole, not fractional from 1660, a use now rare.^[2][6] Johnson (1755) defined the noun simply as "the whole of any thing".^[11] From 1822 it could mean a quantity taken as a unit of measurement; from the 1840s it was also a whole thing or entity in general, complete in itself or made up of parts.^[2][4]

Timeline

• before 1509 – adjective, whole, entire (obsolete).^[2]
• 1571 – noun, a whole number.^[2][5][4]
• 1644 – adjective, honest, upright (obsolete).^[2]
• 1660 – adjective, in mathematics, whole, not fractional.^[2]
• 1822 – a quantity taken as a unit of measurement.^[2]
• before 1848 – a whole thing or entity.^[2]

Meanings

Noun

1. A whole number: any of the natural numbers, their negatives, or zero, as opposed to a fraction: Seven and minus twelve are both integers.^[12][4][2]
2. A complete thing or entity; a whole.^[12][4][2]

Word family

• noninteger

Related words

• integrate
• integral
• integrity
• entire
• intact
• tangent
• tangible

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l m n o p Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b c d e f Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
5. ^ a b c d e f Barnhart, Robert K. (1988), The Barnhart Dictionary of Etymology
6. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
7. ^ Skeat, Walter W. (1911), A Concise Etymological Dictionary of the English Language, new ed., Oxford: Clarendon Press
8. ^ The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
9. ^ a b Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
10. ^ a b Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
11. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
12. ^ a b Collins English Dictionary (2023), Glasgow: HarperCollins