# Math Help - Relation

1. ## Relation

Define the relation R on the real numbers R by xRy if and only if [x] = [y] where [.] is the greatest integer function, that is, [t] is defined to be the greatest integer less than or equal to t.
Prove that for every x E R there exists a y E Z such that x E y/R.

I dont know where to start
plz help thanks

2. Originally Posted by logglypop
Define the relation R on the real numbers R by xRy if and only if [x] = [y] where [.] is the greatest integer function, that is, [t] is defined to be the greatest integer less than or equal to t.
Prove that for every x E R there exists a y E Z such that x E y/R.
If $\mathbb{Z}$ is the set of integers then $x\mathcal{R}y$ if and only if $\left( {\exists n \in \mathbb{Z}} \right)\left[ {\left\{ {x,y} \right\} \subset \left[n,n + 1\right)} \right]$