$\mathbb Q/\mathbb Z$ 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

Intuitively, you can think of the quotient of $\mathbb{Q}$ by $\mathbb{Z}$ as fractions in an interval from $0$ to $1$.  What you're doing when you quotient by $\mathbb{Z}$ is you set each integer to be $0$ - it's the rationals "mod 1."
To easily argue that the group is infinite, notice the fact that $\frac{1}{s}\mathbb{Z}=\frac{1}{r}\mathbb{Z} \Leftrightarrow \frac{1}{s}-\frac{1}{t}\in\mathbb{Z}$.  To verify my interpretation of $\mathbb{Q}/\mathbb{Z}$ is true, compare two arbitrary $x\mathbb{Z},y\mathbb{Z}$ with $0\leq x,y<1$.
