The set of points with rational coordinates is disconnected

Question

I found the following example: let $Z\subseteq\mathbb{R^2}$ the set of points with rational coordinates. The set $Z$ is disconnected, indeed a separation is given by $\{(x,y)\;|\; x<\pi\}$ and $\{(x,y)\;|\;x>\pi\}$.

Question. Why?

Thanks!