Equivalence Classes of R on Integers: Solution

[.~!@#]

Homework Statement

R is a relation on the integers, xRy if x^2=y^2. Determine the distinct equivalence classes.

Homework Equations

[x]={yεZ}|yRx} Where Z is the set of integers

The Attempt at a Solution

[n]={-n, n} where n is an integer


is this correct?

 

[Max.Planck]

I think you are correct, there are infinitely many equivalence classes though.
[1], [2], [3]...etc.