# factorial

A recursive operation on natural numbers denoted by $$n!$$ and defined as follows:

$\begin{eqnarray*} 0! & = & 1 \\ & & \\ n! & = & n(n-1)! \end{eqnarray*}$

Thus 1! is given by 1×0!, which is 1, 2! is given by 2×1!, which is 2, and 3! is 3×2!, or 6. In general for any natural number $$n$$, we have

$n! = n \cdot (n-1) \cdot (n-2) \cdot \cdots \cdot 3 \cdot 2 \cdot 1$

In other words, $$n!$$ is the product of all the natural numbers up to and including $$n$$.

This operation is used frequently in statistics and probability, and is central to many combinatorial operations, like combinations and permutations.