On Sep 11, 9:04 pm, logic...@comcast.net wrote: > On Sep 10, 6:00 pm, Patricia Shanahan <p...@acm.org> wrote:
> > logic...@comcast.net wrote:
> > > Omega is defined as the set of all natural numbers. > > > The point of the proof is to show omega can't exist. > > > If you assume you can construct omega, > > > a series that cannot end, > > > I can assume G() can be constructed. > > > If you feel that way you should construct a system that excludes the > > axiom of infinity and includes the axiom of G. See what theorems you > > can and cannot prove in that system. If that set of theorems turns out > > to be sufficiently interesting, maybe other people will get involved in > > your system.
> Assume there is a largest natural number, z.
Assume it along with what other axioms and definitions?
> z is its own powerset.
If you assume in Z set theory (even in Z set theory without the axiom of infinity) that there is a greatest natural number, then you can infer anything in the language of Z set theory, including that the greatest natural number is its own powerset, that 0 = 1, that 0 is infinite, etc.