Equivalence Classes of R on Integers: Solution

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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.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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