Finish proving that $\lim_{n\to \infty}\frac 1{n!}=0$ Prove that:
$$\lim\limits_{ n \to \infty}\frac{1}{n!}=0.$$
I tried this:
$$\left\vert \frac{1}{n!}-0\right\vert < \varepsilon$$ 
$$ \frac{1}{n!} < \varepsilon $$
$$ \varepsilon * n! > 1 $$
$$ n! > \frac{1}{\varepsilon} .$$
Now what can I do in order to get an expression like this: $n > \text{something}$, without the absolute value? According to my teacher we always have to get "$n > \text{something}$".

To complete the proof, we say: Choose $n> \dfrac 1\varepsilon$. Now, if $n>\dfrac 1\varepsilon$ then 
$$\frac 1{n!}<\frac 1n <\frac 1{\frac{1}{\varepsilon}}=\varepsilon.$$ This completes the proof.
