Is $0! = 1$ because there is only one way to do nothing? The proof for $0!=1$ was already asked at here. My question, yet, is a bit apart from the original question. I'm asking whether actually $0!=1$ is true because there is only one way to do nothing or just because of the way it's defined.

For positive numbers the factorial function $n!$ is defined as the product of all positive integers less or equal to $n$. To define $0!$ we need to "extend" the definition. Another way to define it is to notice that:
$$(n-1)! = \frac{n!}{n}$$
Pluging $n=1$ we get: $0! = \frac{1!}{1} = 1$
