# recursion

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Related to recursion: recursion formula, Tail recursion

## re·cur·sion

(rĭ-kûr′zhən)
n.
1. Mathematics
a. A method of defining a sequence of objects, such as an expression, function, or set, where some number of initial objects are given and each successive object is defined in terms of the preceding objects. The Fibonacci sequence is defined by recursion.
b. A set of objects so defined.
c. A rule describing the relation between an object in a recursive sequence in terms of the preceding objects.
2. Linguistics The property of languages in which a structure, such as a phrase or clause, may form a part of a larger structure of the same kind, allowing for a potentially infinite variety of constructions.

[Late Latin recursiō, recursiōn-, a running back, from Latin recursus, past participle of recurrere, to run back; see recur.]

## recursion

(rɪˈkɜːʃən)
n
1. the act or process of returning or running back
2. (Logic) logic maths the application of a function to its own values to generate an infinite sequence of values. The recursion formula or clause of a definition specifies the progression from one term to the next, as given the base clause f(0) = 0, f(n + 1) = f(n) + 3 specifies the successive terms of the sequence f(n) = 3n
3. (Mathematics) logic maths the application of a function to its own values to generate an infinite sequence of values. The recursion formula or clause of a definition specifies the progression from one term to the next, as given the base clause f(0) = 0, f(n + 1) = f(n) + 3 specifies the successive terms of the sequence f(n) = 3n
[C17: from Latin recursio, from recurrere recur]
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 recursion - (mathematics) an expression such that each term is generated by repeating a particular mathematical operationformula, rule - (mathematics) a standard procedure for solving a class of mathematical problems; "he determined the upper bound with Descartes' rule of signs"; "he gave us a general formula for attacking polynomials"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
Translations
References in periodicals archive ?
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Proof: The recursion (4) was deduced in (Neumann and Sulzgruber, 2013, Theorem 5.
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Johnson thinks this undermines Chomsky's claim that language presupposes recursion; but whether the Piraha grammar involves recursion has been contested.

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