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Topic: Infinity: The Story So Far
Replies: 298   Last Post: Apr 7, 2014 7:30 AM

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Dan Christensen

Posts: 2,872
Registered: 7/9/08
Re: Infinity: The Story So Far
Posted: Feb 26, 2014 5:41 PM
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On Wednesday, February 26, 2014 4:19:35 PM UTC-5, Virgil wrote:
> In article <d8f3388b-775f-441c-9324-df43a3179e73@googlegroups.com>,
>
> Dan Christensen <Dan_Christensen@sympatico.ca> wrote:
>
>
>

> > Assuming the implicit successor functions in each case, these sets are all
>
> > isomorphic to one another, i.e. you are simply using different symbols for
>
> > the various elements, but the successor relation is preserved, as is the
>
> > induction principle. As I said, such structures is embedded in EVERY infinite
>
> > set. So, you are on fairly safe ground to assume the existence of one such
>
> > structure at the beginning of a proof.
>
>
>
> If one does not have something like an axiom of choice, there is no
>
> guarantee that any infinite set need have any well-orderable subsets.
>
>
>
> So in ZFC you are correct but not necessarily so in ZF.
>


Whew!

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
Visit my new math blog at http://www.dcproof.wordpress.com


Date Subject Author
2/25/14
Read Infinity: The Story So Far
Dan Christensen
2/25/14
Read Re: Infinity: The Story So Far
Brian Q. Hutchings
2/25/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/25/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/26/14
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2/26/14
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ross.finlayson@gmail.com
2/26/14
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William Elliot
3/1/14
Read Re: Infinity: The Story So Far
Dan Christensen
3/2/14
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Brian Q. Hutchings
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
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Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/26/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
Read Re: Infinity: The Story So Far
Martin Shobe
2/27/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
Virgil
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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2/26/14
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Dan Christensen
2/26/14
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Brian Q. Hutchings
2/26/14
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mueckenh@rz.fh-augsburg.de
2/26/14
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2/26/14
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2/26/14
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Dan Christensen
2/26/14
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2/27/14
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2/27/14
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2/27/14
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2/27/14
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mueckenh@rz.fh-augsburg.de
2/27/14
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2/27/14
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2/27/14
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Dan Christensen
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Dan Christensen
2/27/14
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Dan Christensen
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Dan Christensen
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Dan Christensen
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Dan Christensen
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3/3/14
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3/2/14
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3/4/14
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3/4/14
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3/4/14
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Dan Christensen
3/5/14
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3/5/14
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3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/6/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Wizard-Of-Oz
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/11/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
thenewcalculus@gmail.com
3/12/14
Read Re: Infinity: The Story So Far
Martin Shobe
3/12/14
Read Re: Infinity: The Story So Far
ross.finlayson@gmail.com

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