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.