A sequence such that every rational is written infinitely Since $\Bbb Q $ is a denumerable set $ \Bbb Q =\{ r_n: r \in \Bbb Q \}$ where $r_m \neq r_n $ if $ n \neq m $
Find a sequence $\langle x_n\rangle$ of real numbers such that for each $ n \in \Bbb N $, $\{m\in \Bbb N : x_m=r_n\}$ is infinite.
I found this difficult and didn't have an idea to construct the sequence. I think what you need is a sequence such that every rational number is written infinitely, any help would be appreciated

$0/1,1/1,0/2,1/2,2/2,3/2,4/2,0/3,1/3,2/3,3/3,4/3,5/3,6/3,7/3,8/3,9/3,\dots$ gets you every positive rational infinitely often, you can work out a way to get the negative ones in there. 
