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Let $A = \mathbb{N} \times \mathbb{N} $, and let $R$ be an equivalence relation on $A$ such that:

$$R = \left\{\big((m,n),(h,k)\big) \in A \times A \mid m + k = n + h\right\}.$$

Prove that each equivalence class of $R$ contains exactly one element $(m,n)$ such that at least one of $m$ or $n$ is $0$.

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    This exercise is extremely straightforward. What have you tried?2012-11-07
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    I'm afraid it isn't so straightforward for me... I'm very new to these ideas of equivalence classes, and all I've managed to do so far is prove that $R$ is an equivalence relation. Is there some sort of method for determining this? I would like steps rather than an answer, so I can do similar questions on my own.2012-11-07
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    Consider an equivalence class that contains $(3, 4)$. What would be another element in this same equivalence class of the form $(m, n)$ where either $m$ or $n$ is $0$?2012-11-07

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