Question

What is 0!=?

Answer 1

We know that $n!=n(n-1)\ldots1\;\;\forall n\in\mathbb{N}$. Now, we can infer from this definition that $\frac{(n+1)!}{n!}=(n+1)$. By the finiteness of the Gamma function, we know that $0!$ exists. Thus, we can use the above formula; $\frac{1!}{0!}=1\implies0!=1$