Originally Posted by

**ams2990** Define a relation on R as follows. Two real numbers $\displaystyle x, y$ are

equivalent if $\displaystyle x - y$ $\displaystyle \epsilon Z $ . Show that the set of equivalence classes of this relation is bijective to the set of points on the unit circle.

A part of the problem that I've omitted asked us to prove that the relation is an equivalence one -- I've done that. I've also defined the set of points on the unit circle, which is $\displaystyle \{ a,b \epsilon R | \sqrt{x^{2}+y^{2}} \} $