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## Homework Statement

Define a relation on R as follows. Two real numbers [tex]x, y[/tex] are

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

## Homework Equations

N/A? I don't think there are any special equations that are needed for this problem.

## The Attempt at a Solution

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 [tex]\{ a,b \epsilon R | \sqrt{x^{2}+y^{2}} \} [/tex] Damned if I know where to go from here, though.