Factorial function of natural numbers

The factorial function of natural numbers is a function that takes a natural number and returns the product of all nonzero naturals less than or equal to that number. For example, $$3! = 3 \times 2 \times 1 = 6$$.

It can be expressed in product notation as $$\prod_{n=1}^{x} n$$, or in the form of a recurrence relation as $$n! = n \left( n - 1 \right)!$$.

$$0!$$ is equal to one because it is the empty product.