Difference between revisions of "Factorial"

m (See also: added link)
Line 1: Line 1:
The '''factorial''' is an important concept in [[combinatorics]], used to determine the number of ways to arrange objects.
+
The '''factorial''' is an important function in [[combinatorics]] and [[analysis]], used to determine the number of ways to arrange objects.
  
 
=== Definition ===
 
=== Definition ===
Line 9: Line 9:
 
By convention, <math>0!</math> is given the value <math>1</math>.
 
By convention, <math>0!</math> is given the value <math>1</math>.
  
The [[gamma function]] is a generalization of the factorial to values other than positive integers.
+
The [[gamma function]] is a generalization of the factorial to values other than nonnegative integers.
  
 
=== Uses ===
 
=== Uses ===

Revision as of 14:52, 23 June 2006

The factorial is an important function in combinatorics and analysis, 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 nonnegative 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.

Examples

See also

Invalid username
Login to AoPS