As sets of real numbers, yes. However, if you have an approapriate metric (in this case I think cuts are area preserving) then you can't. [1] [1] https://en.w

As sets of real numbers, yes. However, if you have an approapriate metric (in this case I think cuts are area preserving) then you can't. [1] [1] https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox#Von_Neumann_paradox_in_the_Euclidean_plane https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox#.... Look at the comment about measures changing. Edit: Oh, I see you did say this at the end.