Well, Cantor's first theorem states that there is no bijection between a set and its power set, but Cantor's theory is so controversial that it's hard to know whether all mathematicians agree with it or not, especially regarding the diagonal argument.
http://en.wikipedia.org/wiki/Cantor%27s_theorem
Thanks Fabricio,
That's exactly the issue, I can't figure it out either way and I've heard arguments from both sides....The balance of arguments seems to side with Cantor, but I can't seem to quite find or work out a smoking gun, clear-cut proof
Well, the only proof I know relies on the diagonal argument, and that's the central issue with it.
Yeah, I think it is possible, Just like in topology, there is something what we show using the empty set. I am not able to recall it
Yes, likewise I agree, B as defined by you will always be stronger. Is it not one of the mysteries in set theory, that we have hierarchy of infinities?
Transfinite numbers, the way Cantor envisioned, are interesting mathematical results.
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