Prove that $(nx-\lfloor nx \rfloor)_{n\geq 1}$ has a finite number of limit points with $x\in \mathbb{Q}$ and $x>0$. Furthermore $\lfloor .\rfloor:\mathbb{R} \to \mathbb{Z}$ the floor function
I observed this question. I didn't really help me unfortunately. I am completely stumped when it comes to the proof. Could anyone of you give me a hint? Would be greatly appreciated!
Thanks in advance!