infinity

Etymology

It is inherited from Middle English infinite, borrowed from Old French infinité (“infinity; a very great number”),^[2][3][4][5] from Latin īnfīnītās (“boundlessness, endlessness”), from īnfīnītus (“boundless, unlimited”),^[2][5][3] itself from in- (“not”) and fīnis (“boundary, end”).^[6] The Oxford Dictionary of English allows that it came directly from Latin as well.^[7] The French word is recorded from the 13th century,^[3][2] and its Anglo-Norman form from 1194–99.^[8] The Latin noun was a loan translation of Ancient Greek ἀπειρία (apeiría, “infinity”), from ἄπειρος (ápeiros, “endless, infinite”).^[2][5]

Earliest recorded meaning

The quality of having no limit, especially as an attribute of God: about 1374, in Chaucer's translation of Boethius.^[3][2]

Semantic evolution

By 1377, in Piers Plowman, the word also meant something infinite, such as a boundless space or an endless time.^[3][2] About 1480 it was first used loosely for a vast number or amount, a sense the OED notes was frequent in Old French;^[3] the Anglo-Norman word already meant "a very large quantity".^[8] The phrase to infinity, rendering Latin ad infinitum, appears in 1640.^[3] Johnson (1755) defined it as "immensity; boundlessness; unlimited qualities", quoting Raleigh's remark that there cannot be more infinities than one.^[9] Mathematicians took it up for an infinite quantity in 1693, in Halley, with the sign ∞,^[3] while from 1867 geometry and photography used at infinity for a distance so great that it can be treated as infinite.^[3][10]

Timeline

• 13th century – French infinité.^[3][2]
• c. 1374 – boundlessness, especially of God (Chaucer).^[3]
• 1377 – something infinite; endless time or space (Piers Plowman).^[3]
• c. 1480 – a vast number or amount.^[3]
• 1640 – to infinity.^[3]
• 1693 – in mathematics, an infinite quantity (Halley).^[3]
• 1867 – at infinity, in geometry and photography.^[3]

Modern meaning

Noun

1. The state or quality of being infinite, without any limit.
2. Space, time or quantity that has no end.
3. A very great, indefinite number or amount: an infinity of grains of sand.
4. (mathematics) A quantity larger than any number that can be named, written ∞.
5. (optics, photography) A distance so great that light from it reaches a lens as parallel rays: a camera focused at infinity.

Related words

• finish
• finite
• infinite
• infinitude
• infinitesimal
• final
• ad infinitum

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
3. ^ 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
4. ^ Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
5. ^ a b c Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
6. ^ Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
7. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
8. ^ a b Anglo-Norman Dictionary (AND2), Aberystwyth University, anglo-norman.net (2nd ed., 2005–)
9. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
10. ^ Collins English Dictionary (2023), Glasgow: HarperCollins