I have already started this. I redefined the Reals as the Reals minus the Positive Integers (to make the two sets disjoint) so that I could prove that #(R - P) + #P = #R. I know that to prove this I will have to prove that #(R - P) = #(R). I would have to define a bijection, f:(R-P) -> R. I am having trouble coming up with a formula that will map the (R-P) to R. If anyone could point me in the right direction I would really appreciate it. Thanks
2026-03-26 17:31:25.1774546285
How to prove #R + #P = #R
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Do you know how to biject $[0,1)$ with $(0,1)$? You can then use the identity on $(-\infty,0)$ and map $[n,n+1)$ to $(n,n+1)$