Big O for factorials

Question

Hello I have trouble proving:$$(n+1)!\notin O(n!)$$ My first step is the following: $$(n+1)!-cn!\le0$$ Can you please help me with the next step?

Answer 1

$$ \lim_{n\to \infty} \frac{(n+1)!}{n!}=\lim_{n\to \infty} (n+1) = +\infty$$

which implies $(n+1)!$ is not $O(n!)$.