Prove $0! = 1$ from first principles
Why does $0! = 1$?
All I know of factorial is that $x!$ is equal to the product of all the numbers that come before it. The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. I'm perplexed as to why I have to account for this condition in my factorial function (Trying to learn Haskell). Thanks.