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

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William Hughes

Posts: 4,277
Registered: 12/6/04
Re: No Identity Bijection for Omega
Posted: Sep 11, 2007 1:17 PM
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On Sep 11, 12:12 am, logic...@comcast.net wrote:
> On Sep 10, 7:49 pm, William Hughes <wpihug...@hotmail.com> wrote:> On Sep 10, 10:37 pm, logic...@comcast.net wrote:
>
> [re] and z must be an element of B not in A.
>
> [wh] So if there is no element of B that is not in A
> [wh] this fails.
>
> [re] It means F is not a bijection.


No, it doesn't. if F maps from A to B and
F is injective and surjective then F is a bijection.
Nothing about there being an element of B that is not in A.

>
> [wh] What if A is a set such that there is a bijection from
> [wh] A to a proper subset of A?
>
> [re] The point of the proof is to show such sets lead to
> contradiction.



Using the assumption that such sets lead to a contradiction
in order to prove that such sets lead to a contradiction
is circular. Your assumption that z exists is equivalent
to assuming that there is no set A such that there is a bijection
from A to a proper subset of A.


-William Hughes

Remember, not every set has a last element.







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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