# Difference between revisions of "Factorial"

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− | + | === Definition === | |

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+ | An important concept in [[combinatorics]], the factorial is defined for positive integers as <math>n!=n \cdot (n-1) \cdots 2 \cdot 1</math> Alternatively, a recursive definition for the factorial is: <math>n!=n \cdot (n-1)!</math>. | ||

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+ | === Additional Information === | ||

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+ | By convention, <math>0!</math> is given the value <math>1</math>. | ||

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+ | The [[gamma function]] is a generalization of the factorial to values other than positive integers. | ||

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+ | === Uses === | ||

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+ | The factorial is used in the definitions of [[combinations]] and [[permutations]], as <math>n!</math> is the number of ways to order <math>n</math> distinct objects. |

## Revision as of 13:12, 18 June 2006

### Definition

An important concept in combinatorics, the factorial is defined for positive integers as Alternatively, a recursive definition for the factorial is: .

### Additional Information

By convention, is given the value .

The gamma function is a generalization of the factorial to values other than positive integers.

### Uses

The factorial is used in the definitions of combinations and permutations, as is the number of ways to order distinct objects.