On Jun 16, 1:04 pm, WM <mueck...@rz.fh-augsburg.de> wrote: > On 16 Jun., 19:45, MoeBlee <jazzm...@hotmail.com> wrote: > > > But, every countable set does have a bijection with N or has a > > bijection with some member of w (the set of natural numbers). > > That would be true if countability and aleph_0 were not self- > contradicting concepts.
What I mentioned is pretty much just a definition of 'countable'.
x is countable <-> Ef(f is a bijection from x onto w or Enew x is a bijection from x onto n)
Meanwhile, I don't have a thousand lifetimes to wait for you to show a formula P such that both P and ~P are derivable in ZFC from the above definition.
