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

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Infinity: The Story So Far
Posted: Feb 28, 2014 4:23 AM
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In article <89017e7c-bf29-4ca7-bd14-77f976c852ce@googlegroups.com>,
mueckenh@rz.fh-augsburg.de wrote:

> On Friday, 28 February 2014 08:00:03 UTC+1, Virgil wrote:
> > In article <7alnvr.i2m.19.1@news.alt.net>, fom <fomJUNK@nyms.net>
> >

>
> >
> > > > It is only later, after all the basic axioms are satisfied, when
> >
> > > > defining addition that any "1" appears.
> >
> > > >
> >
> > >
> >
> > > That is actually problematic.
> >
> >
> >
> > NOT in the Peano axioms.

>
> And not in your head, Virgil. You accept individually undefinable "real"
> numbers and axioms that are defining the natural numbers without defining 1.


The Peano axioms never do define 1 or any natural numbers since the
axioms are equally valid for sets which need not contain any natural
numbers whatsoever.

On the other hand, the set of natural numbers is often defined to be a
set satisfying the Peano axioms.

SO that WM has, as expected, got things exactly backwards.
--




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
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ross.finlayson@gmail.com
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Brian Q. Hutchings
2/26/14
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thenewcalculus@gmail.com
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thenewcalculus@gmail.com
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2/26/14
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ross.finlayson@gmail.com
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Dan Christensen
2/27/14
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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
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2/26/14
Read Re: Infinity: The Story So Far
Dan Christensen
2/26/14
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Read Re: Infinity: The Story So Far
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2/26/14
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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
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Dan Christensen
2/26/14
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2/27/14
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2/27/14
Read Re: Infinity: The Story So Far
Virgil
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
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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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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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3/4/14
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3/5/14
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3/5/14
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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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