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recursion

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Article

23 sections

Contents

Formal definitions
Informal definition
In language
Recursive humor
In mathematics
Recursively defined sets
Example: the natural numbers
Example: Proof procedure
Finite subdivision rules
Functional recursion
Proofs involving recursive definitions
Recursive optimization
The recursion theorem
Proof of existence <ref>Math 310 Class Notes 5: The Recursion Theorem for N [https://www.math.wustl.edu/~chi/310notesV.pdf]</ref>
Proof of uniqueness
In computer science
In biology
In business
In art
In culture
References
Bibliography
External links

thumb|A visual form of recursion known as the Droste effect. The woman in this image holds an object that contains a smaller image of her holding an identical object, which in turn contains a smaller image of herself holding an identical object, and so forth. 1904 Droste cocoa tin, designed by Jan Misset.

Recursion occurs when the definition of a concept or process depends on a simpler or previous version of itself. Recursion is used in a variety of disciplines ranging from linguistics to logic. The most common application of recursion is in mathematics and computer science, where a function being defined is applied within its own definition. While this apparently defines an infinite number of instances (function values), it is often done in such a way that no infinite loop or infinite chain of references can occur.