How do I prove that $ f(n) = (n + 1)! - 1 $ is an injective function? I have this problem:

Consider the function $f : \mathbb{N} \rightarrow \mathbb{N}$ defined, for every $n \in \mathbb{N}$, by
$$f(n) = (n+1)! - 1$$
Prove that $f$ is injective.

How do I solve this problem?

The easiest way probably to prove this is by proving that $f$ is strictly increasing. You can do that quite easily using induction.
