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Factorial (view source)

Revision as of 05:32, January 24, 2007

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The factorial of a positive integer n equals the product of all positive integers less than or equal to n. This is denoted as n!

Mathematically, the formal expression for factorial is:

:<big><math> n!=\prod_{k=1}^n k \qquad \mbox{for all } n \in \mathbb{N} \ge 0. \!</math></big>

For example,

:<big><math>4 ! = 1\cdot 2 \cdot 3 \cdot 4 = 24 \ </math></big>

In the case of 0, sometimes a special definition declares that

:<big><math>0! = 1 \ </math></big>

even though one would expect that to be zero. This special definition is justified by saying that the product of no numbers is equal to 1.
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