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I've been looking at some equivalence relations and was wondering how to define an equivalence relation on $\mathbb{R}^2$ by $(w,y)\sim(x,z)$ if $(w,y)=(cx,cz)$.

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    Where $c$ is...?2011-12-02
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    (a) Is $c$ supposed to be nonzero? (b) This already defines an equivalence relation. What exactly is your question at this stage?2011-12-02
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    It's late but I don't think that's an equivalence relation - for instance does (1,1) ~ (1,1); that is (1,1) = (c,c)? Does (2,2) ~ (2,2) , ... ? If you say; two ordered pairs are equivalent if there exists such a c then this is good (the classes are lines of the plane).2011-12-02
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    @Zev: $c$ is a real number.2011-12-02
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    @Srivatsan: My question is why is this considered an equivalence relation?2011-12-02
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    @johnnymath - Well, what does it mean for a relation to be an equivalence relation?2011-12-02
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    An equivalence relation induces a partition on a set (and vice versa). The only problem here is, to which equivalence class does the origin belong?2011-12-02
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    @dls: The relation given is not an equivalence relation.2011-12-02
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    @ArturoMagidin: Right, which is why I said there's a problem. Smells like homework, so just tried to offer a hint. I was hoping he'd see that all lines intersecting at the origin as an issue.2011-12-02
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    @dls: Sorry; for some reason, I got my wires crossed and thought your comment was from the OP... And so it seemed in my head that he was almost there and was asking all the right questions, and I went ahead and wrote the answer. Sigh.2011-12-02

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