Difference between revisions of "Factorial"

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The '''factorial''' is an important concept in [[combinatorics]], used to determine the number of ways to arrange objects.
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=== Definition ===
 
=== Definition ===
  
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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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>.
  
 
=== Additional Information ===
 
=== Additional Information ===

Revision as of 12:24, 18 June 2006

The factorial is an important concept in combinatorics, used to determine the number of ways to arrange objects.

Definition

The factorial is defined for positive integers as $n!=n \cdot (n-1) \cdots 2 \cdot 1$ Alternatively, a recursive definition for the factorial is: $n!=n \cdot (n-1)!$.

Additional Information

By convention, $0!$ is given the value $1$.

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 $n!$ is the number of ways to order $n$ distinct objects.

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