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.
