For a set $E $ of real numbers, define two points in $E $to be rationally equivalent if their difference belongs to $Q $. Prove that this defines an equivalence relation.
(i) is trivial as 0 is a rational number
(ii) Suppose $r - q $ is rational. Then as $s \in Q \implies -s \in Q $, $q-r= -(r-q) \in Q $
How can I do (iii)?
Thanks in advance!