Equivalence Classes of R on Integers: Solution

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The relation R on integers is defined by xRy if x^2 = y^2, leading to the conclusion that the equivalence classes are represented as [n] = {-n, n} for each integer n. Each integer n corresponds to a distinct equivalence class, resulting in infinitely many classes. The classes can be denoted as [0], [1], [2], etc., where each class contains both the positive and negative integers of n. This confirms that the solution is correct and highlights the nature of equivalence classes formed under this relation. The discussion emphasizes the infinite nature of these equivalence classes.
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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?
 
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I think you are correct, there are infinitely many equivalence classes though.
[1], [2], [3]...etc.
 

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