# Recursion

Recursion is the process of repeating items in a self-similar way. For instance, when the surfaces of two mirrors are exactly parallel with each other the nested images that occur are a form of infinite recursion. The term has a variety of meanings specific to a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, in which it refers to a method of defining functions in which the function being defined is applied within its own definition. Specifically this defines an infinite number of instances (function values), using a finite expression that for some instances may refer to other instances, but in such a way that no loop or infinite chain of references can occur. The term is also used more generally to describe a process of repeating objects in a self-similar way.

### Other articles related to "recursion":

Recursive Call - Time-efficiency of Recursive Algorithms - Shortcut Rule
... the number of recursive calls at each level of recursion, represents by what factor smaller the input is for the next level of recursion (i.e ... the work the function does independent of any recursion (e.g ... partitioning, recombining) at each level of recursion ...
Alpha Recursion Theory
... In recursion theory, α recursion theory is a generalisation of recursion theory to subsets of admissible ordinals ... The objects of study in recursion are subsets of ... Members of are called finite and play a similar role to the finite numbers in classical recursion theory ...
Axiom Of Reducibility - Criticism of The Axiom of Reducibility - David Hilbert 1927
... definitions that "have the character of axioms, and certain recursion axioms that result from a general recursion schema" plus some formation rules that "govern the use ... It is upon this foundation that modern recursion theory rests ...
Recursive Call - Recursion Versus Iteration
... Recursion and iteration are equally expressive recursion can be replaced by iteration with an explicit stack, while iteration can be replaced with tail recursion ... iteration is preferred, particularly for simple recursion, as it avoids the overhead of function calls and call stack management, but recursion is generally used for multiple recursion ... By contrast, in functional languages recursion is preferred, with tail recursion optimization leading to little overhead, and sometimes explicit iteration is not available ...
Recursion - Bibliography
... Recursion Theory ... Logic, Sets, and Recursion ... Recursion Theory, Godel's Theorems, Set Theory, Model Theory ...