Talk:Power set

Revision as of 20:45, 26 August 2006 by ComplexZeta (talk | contribs)

I deleted the part that said that for no infinite set was there a bijection between the set and its power set. I am fairly certain that this is undecided. It certainly is known that the proposition $\displaystyle 2^{\aleph _{n} } = \aleph _{ n+1 }$ is undecidable, so I am very suspicious of a proposition that such a cardinality as $\displaystyle \aleph _{n>1}$ exists at all. Or are these cardinalities known to exist after all? If so, how are they defined? —Boy Soprano II 21:35, 26 August 2006 (EDT)

It is true (and decidable) that there is no bijection between a set and its power set. --ComplexZeta 21:45, 26 August 2006 (EDT)