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Prove R/Q has no element of finite order other than the identity.

First of all, I have trouble visualizing what R/Q is. But I do know that afterwards you can try to raise an element in R/Q to a power to get to 0, but there will not be a finite number that will be able to do so except zero itself.

So I think I have the jist of the problem figured, but I need help visualizing R/Q. I would appreciate if you could give examples of what numbers belong to what cosets.

I also have a similar question about Q/Z, and I have to prove that every element has a finite order.

Thank you.

First of all, I have trouble visualizing what R/Q is. But I do know that afterwards you can try to raise an element in R/Q to a power to get to 0, but there will not be a finite number that will be able to do so except zero itself.

So I think I have the jist of the problem figured, but I need help visualizing R/Q. I would appreciate if you could give examples of what numbers belong to what cosets.

I also have a similar question about Q/Z, and I have to prove that every element has a finite order.

Thank you.

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