When you're a kid, you learn that you can't divide by zero. But the more you learn, the more you find out there are some interesting nuances around the edges of that rule. Likewise you may remember learning that 0! (zero factorial) is 1. "It just is." But why is it? Numberphile explains.
Like so many mathematical processes, factorials get sort of hitched up when you throw a zero into the mix, but it makes sense if you can actually explain the systems at work instead of just barfing up answers like most of us. Math is fun! At least when there's no one to test you on it anymore. [Numberphile]