$\mathbb Q/\mathbb Z$ is an infinite group I'm trying to prove that $\mathbb Q/\mathbb Z$ is an infinite abelian group, the easiest part is to prove that this set is an abelian group, I'm trying so hard to prove that this group is infinite without success. 
This set is defined to be equivalences classes of $\mathbb Q$, where $x\sim y$ iff $x-y\in \mathbb Z$.  
I need help here.
thanks a lot

Another hint: prove that for 
$$n,k\in\Bbb N\;,\;\;n\neq k\;,\;\;\;\frac{1}{n}+\Bbb Z\neq\frac{1}{k}+\Bbb Z$$
