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A recursive process is one in which objects are defined in terms of other objects of the same type. Using some sort of Recurrence Relation, the entire class of objects can then be built up from a few initial values and a small number of rules. The Fibonacci Numbers are most commonly defined recursively. Care, however, must be taken to avoid Self-Recursion, in which an object is defined in terms of itself, leading to an infinite nesting.

See also Ackermann Function, Primitive Recursive Function, Recurrence Relation, Recurrence Sequence, Richardson's Theorem, Self-Recursion, Self-Similarity, TAK Function


Buck, R. C. ``Mathematical Induction and Recursive Definitions.'' Amer. Math. Monthly 70, 128-135, 1963.

Knuth, D. E. ``Textbook Examples of Recursion.'' In Artificial Intelligence and Mathematical Theory of Computation, Papers in Honor of John McCarthy (Ed. V. Lifschitz). Boston, MA: Academic Press, pp. 207-229, 1991.

Péter, R. Rekursive Funktionen. Budapest: Akad. Kiado, 1951.

© 1996-9 Eric W. Weisstein