Es seien ${\displaystyle {}x,y}$ rationale Zahlen. Zeige, dass

${\displaystyle {}x-\left\lfloor x\right\rfloor =y-\left\lfloor y\right\rfloor \,}$

${\displaystyle {}n\in \mathbb {Z} }$

${\displaystyle {}y=x+n}$