(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Suppose that we partition R^3 into horizontal planes. What equivalence relation is associated with this partition? Suppose that we partition R^3 into concentric spheres, centered at (0,0,0). What equivalence relation is associated with this partition?

2. Relevant equations

3. The attempt at a solution

Since it is on R^3, I know that I need to come up with a partition that has an x, y and z coordinate, right?

Could the equivalence relation be (x,y,z)~(a,b,c) if and only if x^2=a^2?

For the second one, could it be something like (x,y,z)~(0,0,0) if and only if x^2=a^2

Thank you very much

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# Partition on R^3

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