## 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.

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### Some articles on recursion:

**Recursion**- Bibliography

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**Recursion**Theory ... Logic, Sets, and

**Recursion**...

**Recursion**Theory, Godel's Theorems, Set Theory, Model Theory ...

**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 ... of are called finite and play a similar role to the finite numbers in classical

**recursion**theory ...

... the time-complexity is where represents 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 ... and represents the work the function does independent of any

**recursion**(e.g ... partitioning, recombining) at each level of

**recursion**...

... induction, some 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 of the axioms" ... It is upon this foundation that modern

**recursion**theory rests ...

**Recursion**Versus Iteration

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**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 ... By contrast, in functional languages

**recursion**is preferred, with tail

**recursion**optimization leading to little overhead, and sometimes explicit iteration is not available ...