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Topic: No Identity Bijection for Omega
Replies: 116   Last Post: Sep 22, 2007 5:58 PM

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Jack Markan

Posts: 6,964
Registered: 2/26/05
Re: No Identity Bijection for Omega
Posted: Sep 12, 2007 1:44 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.

MoeBlee



Date Subject Author
9/3/07
Read No Identity Bijection for Omega
Russell Easterly
9/3/07
Read Re: No Identity Bijection for Omega
Chris Menzel
9/4/07
Read Re: No Identity Bijection for Omega
William Elliot
9/4/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/4/07
Read Re: No Identity Bijection for Omega
William Elliot
9/4/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/4/07
Read Re: No Identity Bijection for Omega
David C. Ullrich
9/4/07
Read Re: No Identity Bijection for Omega
Mitch
9/7/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/7/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/7/07
Read different sizes of denumerable sets?
George Greene
9/7/07
Read Re: different sizes of denumerable sets?
Alan Smaill
9/12/07
Read Re: different sizes of denumerable sets?
George Greene
9/7/07
Read Re: different sizes of denumerable sets?
Jesse F. Hughes
9/8/07
Read Re: different sizes of denumerable sets?
tchow@lsa.umich.edu
9/12/07
Read Re: different sizes of denumerable sets?
George Greene
9/12/07
Read Re: different sizes of denumerable sets?
tchow@lsa.umich.edu
9/12/07
Read Re: different sizes of denumerable sets?
tchow@lsa.umich.edu
9/12/07
Read Re: different sizes of denumerable sets?
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/7/07
Read Re: No Identity Bijection for Omega
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/10/07
Read Re: No Identity Bijection for Omega
George Greene
9/11/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/11/07
Read Re: No Identity Bijection for Omega
George Greene
9/11/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/11/07
Read Re: No Identity Bijection for Omega
George Greene
9/10/07
Read Re: No Identity Bijection for Omega
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/7/07
Read Re: No Identity Bijection for Omega
George Greene
9/7/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/7/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/8/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/8/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/8/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/8/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/8/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/8/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/8/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/9/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/9/07
Read Re: No Identity Bijection for Omega
Ross Finlayson
9/9/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/9/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/9/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/9/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/9/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/9/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/10/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/10/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/10/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/10/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/12/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/12/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/10/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/10/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/10/07
Read Re: No Identity Bijection for Omega
William Hughes
9/11/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/11/07
Read Re: No Identity Bijection for Omega
William Hughes
9/10/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/11/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/11/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/12/07
Read Re: No Identity Bijection for Omega
George Greene
9/12/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/12/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/12/07
Read Re: No Identity Bijection for Omega
William Hughes
9/13/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/13/07
Read Re: No Identity Bijection for Omega
William Hughes
9/13/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/13/07
Read Re: No Identity Bijection for Omega
William Hughes
9/13/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/13/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/17/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/17/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/17/07
Read Re: No Identity Bijection for Omega
William Hughes
9/18/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/19/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/19/07
Read Re: No Identity Bijection for Omega
William Hughes
9/19/07
Read Re: No Identity Bijection for Omega
George Greene
9/19/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/18/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/20/07
Read Re: No Identity Bijection for Omega
Russell Easterly
9/20/07
Read Re: No Identity Bijection for Omega
William Hughes
9/20/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/22/07
Read Re: No Identity Bijection for Omega
reasterly@gmail.com
9/13/07
Read Re: No Identity Bijection for Omega
George Greene
9/10/07
Read Re: No Identity Bijection for Omega
George Greene
9/10/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/8/07
Read Re: No Identity Bijection for Omega
Jesse F. Hughes
9/8/07
Read Re: No Identity Bijection for Omega
Patricia Shanahan
9/8/07
Read Re: No Identity Bijection for Omega
William Hughes
9/10/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/9/07
Read Re: No Identity Bijection for Omega
David R Tribble
9/4/07
Read Re: No Identity Bijection for Omega
George Greene
9/4/07
Read Re: No Identity Bijection for Omega
George Greene
9/4/07
Read Re: No Identity Bijection for Omega
William Hughes
9/4/07
Read Re: No Identity Bijection for Omega
Schroeder
9/4/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/4/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/4/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/4/07
Read Re: No Identity Bijection for Omega
G. Frege
9/5/07
Read Re: No Identity Bijection for Omega
Peter Webb
9/5/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/5/07
Read Re: No Identity Bijection for Omega
Daryl McCullough
9/5/07
Read Re: No Identity Bijection for Omega
G. Frege
9/6/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/7/07
Read Re: No Identity Bijection for Omega
hagman
9/7/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/7/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/7/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/5/07
Read Re: No Identity Bijection for Omega
lwalke3@lausd.net
9/5/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/5/07
Read Re: No Identity Bijection for Omega
herb z
9/5/07
Read Re: No Identity Bijection for Omega
Jack Markan
9/6/07
Read Re: No Identity Bijection for Omega
herb z
9/6/07
Read Re: No Identity Bijection for Omega
Jack Markan

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