# Help showing this is an equivalence relation

I need help with question as following:

1. $X= \mathbb{Z}\times \mathbb{Z}$ I need to define the relation $R$ on $X$ as follows:

$(X_1,X_2)R(Y_1,Y_2) \longleftrightarrow (X_1)^2+(X_2)^2=(Y_1)^2+(Y_2)^2$

Can you prove it using (X)R(Y) ?

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@akerman What parts are you having trouble with? – Git Gud Feb 2 '13 at 18:55
@akerman: Start with the definition of an equivalence relation. Can you state what it is you need to show in order to establish that $R$ is an equivalence relation? – JohnD Feb 2 '13 at 20:05
Note that $(X_1,X_2)R(Y_1,Y_2)$ if and only the corresponding points in $\mathbb{R}^2$ lie at the same distance from the origin $(0,0)$. Don't you expect this to be an equivalence relation? – 1015 Feb 3 '13 at 21:48

Hint: For describing the equivalence class, think about using cross-multiplication to determine if two fractions are equal.

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## protected by Nate EldredgeFeb 3 '13 at 23:17

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