Can anyone help me prove that the set of complex numbers has the same cardinality as the reals? I tried setting up a one-one correspondence, but couldn’t think of a function to relate the two. I mean, I could try to prove that if…
Wait, I think I have it. I have to prove that if the union of two sets is numerable, then the sets are numerable. I think I can set that up similarly to the proof of evens and positive Z having the same cardinality. Then I take the contrapositive and I’ve got it, and just state that for the left equality to hold with the right one, R\Q (the irrationals), has to be no greater than aleph-1: (R\Q) union Q = R, right? And we know Q is numerable…
Any advice on my first proof-heavy math course (Abstract Algebra)? It took me way too long (3 hours) to solve 3 problems and I have a feeling that the rest of math will be somewhat like this. Any books/advice on proofs, etc? I know my techniques and can concentrate, but sometimes I just don’t see the connections between things or remember the right definition or whatever.