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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: 2,866
Registered: 7/9/08
Re: Infinity: The Story So Far
Posted: Feb 26, 2014 12:14 PM
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On Wednesday, February 26, 2014 11:58:07 AM UTC-5, John Gabriel wrote:

> > > > > In your write-up, next(a) is meaningless garbage.
>
> > > > It is a successor function on the set of natural numbers. Got a problem with that?
>
> > > Yes, because then you already assume the prior existence of natural numbers.
>
> > Again, unless you want to rule out the existence of infinite sets altogether, the existence of the natural numbers is not problematic. See my previous posting above.
>
>
> This is what you claim:
>
>
>
> The Definition of the set of natural numbers is given by nothing more or less than Peano's Axioms.
>
>
>
> It is false. The Peano axioms assume the prior existence of natural numbers.


The Peano axioms describe structures that are embedded in EVERY infinite set.


> To with, the next(a) function you refer to in your statements depends not only on the prior existence of natural numbers, but also on the well ordering.

It depends only on the existence of at least one infinite set. Do you claim they don't exist? That is certainly one school of thought, far outside the mainstream though it may be.

Dan
Download my DC Proof 2.0 software at http://www.dcproof.com
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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
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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
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thenewcalculus@gmail.com
2/26/14
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Dan Christensen
2/26/14
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Dan Christensen
2/26/14
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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
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mueckenh@rz.fh-augsburg.de
2/27/14
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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
Read Re: Infinity: The Story So Far
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2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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2/26/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
Read Re: Infinity: The Story So Far
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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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Read Re: Infinity: The Story So Far
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2/27/14
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2/27/14
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2/27/14
Read Re: Infinity: The Story So Far
mueckenh@rz.fh-augsburg.de
2/27/14
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Dan Christensen
2/27/14
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Dan Christensen
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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2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/27/14
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Dan Christensen
2/28/14
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Dan Christensen
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Dan Christensen
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Read Re: Infinity: The Story So Far
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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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3/2/14
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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
3/4/14
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Dan Christensen
3/4/14
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Dan Christensen
3/5/14
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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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