I need to prove that ${\{X\_n\}}$ is not a Cauchy sequence. I understand that in order to prove this, I need to prove that $$$$$\exists\ \epsilon\gt0\ | \forall N \in \Bbb N,$ if, there is $n,m \geq N$, then $|X\_n-X\_m|\geq \epsilon$

So my question, what happens if $n=m$?, then $|X\_n-X\_m|=0$ and therefore $|X\_n-X\_m|<\epsilon$ because $\epsilon \gt 0$ and it would never hold, because for $\forall N$ there would exist an $n,m$ that satisfy this. So, do the $n,m$ need to be different?

Thanks for any help! (: