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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|Recursion]]). In set theory they are constantly used to define functions on ordinals by [[Transfinite recursion|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 [[#References|[2]]]).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  H. Rogers jr.,   "Theory of recursive functions and effective computability" , McGraw-Hill  (1967)  pp. 164–165</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  J. Barwise,   "Admissible sets and structures" , Springer  (1975)</TD></TR></table>