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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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Is X = $\mathbb{Z}\setminus\{0\} \times \mathbb{Z}\setminus\{0\}$? That is, $\mathbb{Z}\setminus \{0\}$ is the set of integers not including zero? –  amWhy Feb 2 '13 at 18:22
    
@akerman I edited your question using $\LaTeX$. Please check if everything is in order and let us know. –  Git Gud Feb 2 '13 at 18:23
    
its exactly as it is written and I'm so confused with those two questions and not sure how to solve them –  akerman Feb 2 '13 at 18:29
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This looks all too familiar to the homework I have set. I will make sure that I will bring this up to the Director of Studies should I find out who are you. –  monsmanr Feb 3 '13 at 21:21
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1 Answer 1

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 Eldredge Feb 3 '13 at 23:17

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