Duration: 1:53

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This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Recursion


00:00:05 1 Formal definitions
00:00:11 2 Informal definition
00:00:17 3 In language
00:00:23 3.1 Recursive humor
00:00:29 4 In mathematics
00:00:32 4.1 Recursively defined sets
00:00:35 4.1.1 Example: the natural numbers
00:00:40 4.1.2 Example: Proof procedure
00:00:46 4.2 Finite subdivision rules
00:00:52 4.3 Functional recursion
00:00:58 4.4 Proofs involving recursive definitions
00:01:04 4.5 Recursive optimization
00:01:10 4.6 The recursion theorem
00:01:16 4.6.1 Proof of uniqueness
00:01:21 5 In computer science
00:01:27 6 In art
00:01:33 7 See also
00:01:39 8 References
00:01:45 9 Bibliography



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SUMMARY
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Recursion (adjective: recursive) occurs when a thing is defined in terms of itself or of its type. 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 loop or infinite chain of references can occur.