If $\displaystyle x,y\in\mathbb{R}$, x < y. Show that if, x and y are rational, then $\displaystyle \exists $ an irrational number u, x < u < y.

$\displaystyle m,n,r,s\in\mathbb{Z}, \ n\neq 0, \ s\neq 0$

$\displaystyle x=\frac{m}{n}, \ y=\frac{r}{s}$

$\displaystyle \frac{m}{n}<u<\frac{r}{s}$

I am not sure what to do now.

Contradiction, contrapositive??