iteration

Etymology

It is inherited from Middle English iteracioun,^[2][3] borrowed from Latin iterātiō (“repetition”),^{[4][5][6][3][7]} a noun of action from the past participle stem of iterō (“to do again, repeat”),^[5][4][6] from iterum (“again”).^[5][6] Etymonline and Klein trace iterum to Proto-Indo-European *i-tero-, a comparative form from the pronominal root *i-.^[5][6] The OED compares French itération, recorded in 1488.^[4] The verb iterate, from the 1530s, is a back-formation from iteration or comes from the Latin past participle.^[5]

Earliest recorded meaning

Repetition of an action, process or treatment: before 1425 (the date is uncertain), in a Middle English translation of Chauliac, of the iteracion of labour.^[2] The OED's first quotation is from 1477, in T. Norton's Ordinall of Alchimy.^[4]

Semantic evolution

Repetition of an action, and repetition of words, are both recorded in Middle English;^[2] the OED dates the second, repeated utterance or assertion, from 1530, in Palsgrave.^[4] Johnson (1755) gave "repetition; recital over again" and quoted Shakespeare's "Truth tir'd with iteration".^[8] In Roman law the word was used, in an 1880 translation of Ulpian, as a technical term.^[4] In mathematics it has meant since 1901 the repeated application of an operation to its own result, especially of a formula that gives successively closer approximations to a solution,^[4][9] and in computing the repetition of a set of instructions a given number of times or until a condition is met.^[3][10]

Timeline

• before 1425 – repetition of an action or process.^[2]
• 1477 – repetition of an action, in Norton.^[4]
• 1488 – French itération.^[4]
• 1530 – repetition of something said, in Palsgrave.^[4]
• 1530s – the verb iterate.^[5]
• 1880 – a term of Roman law.^[4]
• 1901 – mathematics, repetition of an operation upon its product.^[4][9]

Meanings

Noun

1. The act of doing or saying something again; repetition: The constant iteration of the same slogan wore everyone out.^[3][4][10]
2. (mathematics) A procedure in which an operation is repeated on its own result, each cycle coming closer to the desired answer; also a single step of it.^{[3][4][9][10]}
3. (computing) The repetition of a set of instructions a given number of times or until a condition is met, as in a loop; one pass through such a sequence.^[3][10]

Related words

• iterate
• reiterate
• iterative

References

1. ^ a b Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d Kurath, Hans; Kuhn, Sherman M.; Lewis, Robert E., eds. (1952–2001), Middle English Dictionary, Ann Arbor: University of Michigan Press; online edition ed. Frances McSparran et al. (2000–2018)
3. ^ a b c d e f Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
4. ^ a b c d e f g h i j k l m n Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
5. ^ a b c d e f Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
6. ^ a b c d Klein, Ernest. A Comprehensive Etymological Dictionary of the English Language. 2 vols. Amsterdam: Elsevier, 1966–1967.
7. ^ Stevenson, Angus, ed. (2010), Oxford Dictionary of English, 3rd ed., Oxford: Oxford University Press
8. ^ Johnson, Samuel (1755), A Dictionary of the English Language, London; 4th ed. 1773; Johnson's Dictionary Online, ed. Beth Rapp Young et al.
9. ^ a b c Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
10. ^ a b c d The American Heritage Dictionary of the English Language (1992), 3rd ed., Boston: Houghton Mifflin