Let $x\text{R}y \iff x-y=2k \quad k \in \mathbb{Z}$
How many distinct equivalence classes are there for this relation?
I want to say thre are as many equivalence classes as there are integers, but can't reason my way to that conclusion.
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What kind of numbers are $x$ and $y$? – Cameron Williams May 28 '15 at 00:09
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If the relation is on the integers, there are $2$, anything is equivalent to $0$ or $1$. – André Nicolas May 28 '15 at 00:10
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The relation is indeed on the integers. – Demetri Pananos May 28 '15 at 00:17
1 Answers
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If $x$ and $y$ are integers, there are two equivalence classes: even and odd integers.
Bernard
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