Factorial

##Summary

We're going to write a Ruby method factorial (both iteratively and recursively) to compute the factorial of an integer.

If you don't remember, the factorial of a non-negative integer n, denoted n!, is the product of all positive integers less than n. For example,

5! = 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
      ......

n! = n * (n - 1) * (n - 2) ..... * 2 * 1

The factorial function wasn't pulled out of a mathematician's hat, it has a very concrete meaning. If you have 3 socks, for example, there are 3! = 6 ways to order those socks. In general, if you have a set of n things then there are n! ways to order those things.

By convention we define:

0! = 1

So that we can formally define the factorial as:

n! =
  1 if n = 0
  n * (n-1)! & otherwise

This definition is called recursive because we define the factorial of n in terms of the factorial of n-1. We stop at the base case, where n = 0.

Let's do this!