# Recursive definition

From Encyclopedia of Mathematics

A frequently used means (in mathematics) of defining a function, according to which the value of the function sought at a given point is defined by way of its values at preceding points (given a suitable relation of precedence). Recursive definitions of number-theoretic functions are the subjects of study in the theory of algorithms (see Recursion). In set theory they are constantly used to define functions on ordinals by transfinite recursion. On a wider scale, recursive definitions are studied in the theory of admissible sets, at the basis of which lies a certain synthesis of ideas in the theory of sets and algorithms (see [2]).

#### References

[1] | H. Rogers jr., "Theory of recursive functions and effective computability" , McGraw-Hill (1967) pp. 164–165 |

[2] | J. Barwise, "Admissible sets and structures" , Springer (1975) |

**How to Cite This Entry:**

Recursive definition. N.V. Belyakin (originator),

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Recursive_definition&oldid=18779

This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098