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Topic: Another AC anomaly?
Replies: 280   Last Post: Dec 27, 2009 3:53 PM

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Dik T. Winter

Posts: 7,899
Registered: 12/6/04
Re: Another AC anomaly?
Posted: Dec 17, 2009 9:15 AM
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In article <4c4737cb-07c4-4827-8957-ce2c7a678efa@p30g2000vbt.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:
> On 16 Dez., 14:21, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
...
> > Look at the context. It started with my asking for a definition of omega
> > without the axiom of infinity. You state that there is such a definition
> > in your book. I find such a definition nowhere in your book. And the
> > 'proper' should be read in the context of 'without the axiom of infinity'.

>
> The axiom has stolen the correct definition from Peano, (Zermelo says
> from Dedekind, Dedekind says from Bolzano) and has reversed its
> meaning from infinite to finished. That's all.


And what *is* that definition without the axiom of infinity?

> > > > That is not something unheard of. In mathematics a ring is something
> > > > that satisfies the ring axioms, and that is pretty standard.

> > >
> > > And omega is something that does never end.

> >
> > Whatever that may mean.

>
> The same as the axiom says. The axiom says, in addition, that this
> thing is a set, but as it is not said what a set is, this addition is
> idle.


The axiom does not talking about something that does not end. The axiom
states:
There exists an inductive set
that is all. So what do you actually *mean* when you state that omega is
something that does never end? It is similar to stating that 100 is something
that never ends.

> > > > Ok, so actual infinity now is omega + 1.
> > >
> > > No, that's more than that. Omega already is actual infinity. And here
> > > are some other statements about actual infinity:

> >
> > So actual infinity is omega?

>
> In fact, it is said so. Sometimes it is carelessly used also for
> potential infinity.


Who says so? And what is a definition of potential infinity?

> > But N is *not* defined as an inexhaustable process of constructing
> > numerals that somehow has been finished. The axiom of infinity state
> > (together with the actual definition) state that it does exist, not
> > how it is created.

>
> Of course it is. If with n you can do n + 1, and if 0 is there, then
> you have omega.


No.

> The axiom states that such a thing (it says set, but does not say what
> a set is) does exist.


It states that an inductive set exists. It does not state that it starts
with 0, nor does it state that it consists only of the natural numbers.
Suppose the successor function adds 1 to a number. In that case:
{0, 1/2, 1, 3/2, 2, 5/2, ...}
is an inductive set. When you start with 0 and successively apply the
successor function you will *never* get at 1/2.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/



Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
Read Re: Another AC anomaly?
Herman Jurjus
11/23/09
Read Re: Another AC anomaly?
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11/25/09
Read Re: Another AC anomaly?
T.H. Ray
11/24/09
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12/1/09
Read Re: Another AC anomaly?
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11/25/09
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11/26/09
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11/30/09
Read What's wrong with supertasks? (was Re: Another AC anomaly?)
Herman Jurjus
12/1/09
Read Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
plutonium.archimedes@gmail.com
12/1/09
Read Re: Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
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12/1/09
Read using signature-blocks to defame innocent people Re: Jesse Hughes of
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plutonium.archimedes@gmail.com
12/1/09
Read Re: Jesse Hughes of Bentley College uses signature block to defame
others; Ann Reeves Re: What's wrong with supertasks?
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12/1/09
Read Re: using signature-blocks to defame innocent people Re: Jesse Hughes
of Bentley College
Marshall
12/2/09
Read Re: using signature-blocks to defame innocent people Re: Jesse Hughes
of Bentley College
Marshall
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
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mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
Virgil
11/26/09
Read Re: Another AC anomaly?
William Hughes
11/28/09
Read Re: Another AC anomaly?
William Hughes
11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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ross.finlayson@gmail.com
11/28/09
Read Re: Another AC anomaly?
Virgil
11/29/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/29/09
Read Re: Another AC anomaly?
Virgil
11/29/09
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ross.finlayson@gmail.com
11/29/09
Read Re: Another AC anomaly?
Marshall
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
Virgil
11/29/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/26/09
Read Re: Another AC anomaly?
LauLuna
11/26/09
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William Hughes
11/26/09
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anonymous.rubbertube@yahoo.com
11/29/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
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11/27/09
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11/29/09
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William Hughes
11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Alan Smaill
11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Dik T. Winter
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
Dik T. Winter
11/30/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
Virgil
12/1/09
Read Re: Another AC anomaly?
Dik T. Winter
12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
Dik T. Winter
12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
William Hughes
12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
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mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
12/1/09
Read Re: Another AC anomaly?
Virgil
12/1/09
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ross.finlayson@gmail.com
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Read Re: Another AC anomaly?
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12/2/09
Read Re: Another AC anomaly?
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12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
Read Re: Another AC anomaly?
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12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
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12/3/09
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12/3/09
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mueckenh@rz.fh-augsburg.de
12/3/09
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12/3/09
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12/7/09
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12/7/09
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12/8/09
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12/8/09
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12/9/09
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12/9/09
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12/10/09
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12/10/09
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12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
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12/10/09
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12/11/09
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12/15/09
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12/15/09
Read Re: Another AC anomaly?
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12/15/09
Read Re: Another AC anomaly?
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12/16/09
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12/17/09
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12/17/09
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12/18/09
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12/18/09
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12/18/09
Read Re: Another AC anomaly?
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12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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12/22/09
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12/22/09
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Virgil
12/18/09
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12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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12/21/09
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12/21/09
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mueckenh@rz.fh-augsburg.de
12/21/09
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12/21/09
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12/22/09
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12/27/09
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mueckenh@rz.fh-augsburg.de
12/27/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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Virgil
12/11/09
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K_h
12/11/09
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12/11/09
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K_h
12/11/09
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12/12/09
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12/12/09
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12/12/09
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12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
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Dik T. Winter
12/11/09
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12/11/09
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12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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12/8/09
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12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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12/8/09
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12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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12/10/09
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12/3/09
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Virgil
12/3/09
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mueckenh@rz.fh-augsburg.de
12/3/09
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12/7/09
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12/7/09
Read Re: Another AC anomaly?
Virgil
12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/7/09
Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
Dik T. Winter
12/8/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/8/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/11/09
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12/15/09
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12/16/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/16/09
Read Re: Another AC anomaly?
Dik T. Winter
12/16/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/17/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
Dik T. Winter
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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12/4/09
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12/7/09
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Dik T. Winter
12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/7/09
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12/8/09
Read Re: Another AC anomaly?
Dik T. Winter
12/8/09
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mueckenh@rz.fh-augsburg.de
12/8/09
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12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
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mueckenh@rz.fh-augsburg.de
12/10/09
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Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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Marshall
12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/11/09
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12/11/09
Read Re: Another AC anomaly?
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12/12/09
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12/12/09
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12/12/09
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12/12/09
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12/12/09
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12/12/09
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12/13/09
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12/15/09
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12/17/09
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12/17/09
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12/17/09
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12/18/09
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12/18/09
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12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
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12/19/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
Virgil
12/19/09
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12/19/09
Read Re: Another AC anomaly?
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12/22/09
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ross.finlayson@gmail.com
12/22/09
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12/27/09
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12/21/09
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12/21/09
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12/21/09
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12/22/09
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12/27/09
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12/27/09
Read Re: Another AC anomaly?
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12/27/09
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12/27/09
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12/27/09
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12/27/09
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12/13/09
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12/13/09
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12/4/09
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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
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Virgil
12/5/09
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mueckenh@rz.fh-augsburg.de
12/6/09
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Virgil
12/5/09
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12/2/09
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Virgil
12/1/09
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12/1/09
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Virgil
11/27/09
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Virgil
11/27/09
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anonymous.rubbertube@yahoo.com
11/30/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
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William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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11/27/09
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anonymous.rubbertube@yahoo.com
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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