Re: Separation,Power and Countability.

On Jun 18, 10:03 am, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Jun 18, 7:19 am, zuhair <zaljo...@xxxxxxxxx> wrote:

On Jun 18, 8:22 am, LauLuna <laureanol...@xxxxxxxx> wrote:
there is no bijection f from w to P(w)/{0} such that all
values are contained in their images.

what is the proof of that.

There is no bijection from w to Pw\{0}. You need a proof of that?
There is no bijection from w to Pw, but Pw is equinumerous with Pw
\{0}, so there is no bijection from w to Pw\{0}.

That's an indirect proof. I am not talking about that.
I am talking about a diagonal formula of Pw\{0}.
what you presented here has nothing to do with what I am asking.

take for example the set of all
definable subsets of w, you might think this is countable, but
actually with unrevised separation this set is paradoxical since it
can be proved to be countable and not countable

Show me EXACTLY what single theory you think proves that there exists
an x such that both x is countable and x is not countable.

MoeBlee


.

Relevant Pages

  • Re: Separation,Power and Countability.
    ... values are contained in their images. ... There is no bijection from w to Pw, but Pw is equinumerous with Pw ... actually with unrevised separation this set is paradoxical since it ... Show me EXACTLY what single theory you think proves that there exists ...
    (sci.math)
  • Re: Separation,Power and Countability.
    ... values are contained in their images. ... There is no bijection from w to Pw, but Pw is equinumerous with Pw ... That's an indirect proof. ... Get some good books on logic and set theory. ...
    (sci.math)
  • Re: Separation,Power and Countability.
    ... There is no bijection from w to Pw, but Pw is equinumerous with Pw ... That's an indirect proof. ... Show me EXACTLY what single theory you think proves that there exists ... Get some good books on logic and set theory. ...
    (sci.math)