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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: 2,483
Registered: 7/9/08
Re: Infinity: The Story So Far
Posted: Feb 27, 2014 2:11 PM
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On Thursday, February 27, 2014 1:09:49 PM UTC-5, muec...@rz.fh-augsburg.de wrote:
> On Thursday, 27 February 2014 15:44:55 UTC+1, Dan Christensen wrote:
>

> > > Where does he axiomatize that the difference is always 1?
>
> > Nowhere. That is just a property of the addition function, which itself can be constructed from Peano's axioms.
>
>
>
> Addition cannot be constructed from the axioms.


Yes, it can. The trick is to select the right subset of N^3:

ALL(a):ALL(b):ALL(c):[(a,b,c) in add
<=> (a,b,c) in N^3 & ALL(d):[d in Pow(N^3)
& ALL(e):[e in N => (e,0,e) in d]
& ALL(e):ALL(f):ALL(g):[(e,f,g) in d => (e,next(f),next(g)) in d]
=> (a,b,c) in d]]

where

N^3 is the set of ordered triples of natural numbers
Pow(N^3) is the power set of N^3

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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Leo Sgouros
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
Read Re: Infinity: The Story So Far
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
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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
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
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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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Brian Q. Hutchings
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
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mueckenh@rz.fh-augsburg.de
2/26/14
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Dan Christensen
2/26/14
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Brian Q. Hutchings
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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mueckenh@rz.fh-augsburg.de
2/27/14
Read Re: Infinity: The Story So Far
Dan Christensen
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
Dan Christensen
2/27/14
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mueckenh@rz.fh-augsburg.de
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Dan Christensen
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
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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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3/5/14
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Dan Christensen
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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