Factorial

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:

$n!=\prod _{k=1}^{n}k\qquad {\mbox{for all }}n\in \mathbb {N} \geq 0.\!$

For example,

$4!=1\cdot 2\cdot 3\cdot 4=24\$

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

$0!=1\$

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.