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Question: Describe the partitions of the equivalence relations for the map:

$$f:(x,y) \mapsto x$$

I had a different question on my homework, but I'm not really sure what the question is asking, so maybe if I see the solution for this one example it would clarify things.

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This is a projection onto the x-axis, so the relation would be $(x_1,y_1) \sim (x_2,y_2) \iff x_1=x_2$. In other words, the plane is partitioned into vertical lines.

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    so are you saying that the equivalence is between points in the domain.... I'm not sure I understand, my question's range was actually (x,y) goes to x+y. but i have a few other examples to do2012-09-10
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    Yes, the equivalence is on points in the domain. In your second example, the function determines an equivalence relation $(x_1,y_1) \sim (x_2,y_2) \iff x_1+y_1=x_2+y_2$. Do you know how to verify this is indeed an equivalence relation?2012-09-10
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    well another question was (x,y) to sqrt(x^2+y^2)... and I DO understand this one. I can think of the equivalence classes as concentric circles in the plane. But I don't see the one above.2012-09-10
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    Try fixing a number and plotting out the x's and y's that add to it. You should see it right away..2012-09-10
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    AH! I see x+y now.... its just slashes through the plane in a top left to bottom right pattern.2012-09-10