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

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Virgil

Posts: 870
Registered: 7/27/09
Re: Another AC anomaly?
Posted: Dec 8, 2009 4:26 PM
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In article
<9f4850a5-268c-4b3d-a84b-34713cfaedd7@c34g2000yqn.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 8 Dez., 16:13, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>

> >  > Nevertheless it is a limit ordinal.
> >
> > Yes, that does not mean that necessarily a limit is involved.  It is a limit
> > in the sense that you do not get there by continuously getting at the
> > successor, in that case it is a limiting process.  But when you define
> > N as an infinite union you do *not* go there by continuously getting at
> > a successor.  The union of a collection (finite, countably infinite or
> > some other infinity) is defined whithout resorting to successor operations.
> > Moreover, they would even not make sens if the collection is infinite but
> > not countably infinite.

>
> That does not make sense in either respect, so or so.


What does not seem to make sense to WM makes very good sense to those
not constrained by the artificial rules governing Wolkenmuekenheim
> >
> >  > As a starting point, we use the fact hat each natural number is
> >  > identified with the set of all smaller natural numbers: n = {m in N :
> >  > m < n}.
> >
> > Note that here N is apparently already defined, without using a limit.

>
> Natural numbers can be defined without using a set.


As soon as one wants to talk about any property of ALL NATURALS, one
inevitably gets the set of them.
> >
> >  >         Thus we let w, the least transfinite number, to be the set N
> >  > of all natural numbers: w = N = {0, 1, 2, 3, ...}.
> >  >   It is easy to continue the process after this 'limit' step is made:
> >  > The operation of successor can be used to produce numbers following w
> >  > in the same way we used it to produce numbers following 0.
> >
> > Yes.  So what?  That you can define things using a limit does *not*
> > imply that it is necessarily defined as a limit.

>
> O I see.


No, you do not see at all.


> That's like cardinality. The limit cardinality is not the
> cardinality of the limit (because the limit is not a limit).


The limit of a sequence of cardinalities of sets need not be the
cardinality of the limit of a sequence of sets when the definitions of
those two limit processes differ, as they do.

For the definition of a limit of a sequence of sets, as given by Dik,
and any reasonable definition of the limit of a sequence of
cardinalities, there are examples for which the two limits differ.

That WM does not like that result, does not make it false anymore than
WM liking something makes it true.


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?
master1729
11/25/09
Read Re: Another AC anomaly?
T.H. Ray
11/24/09
Read Re: Another AC anomaly?
george
12/1/09
Read Re: Another AC anomaly?
george
11/25/09
Read Re: Another AC anomaly?
Bill Taylor
11/26/09
Read Re: Another AC anomaly?
Daryl McCullough
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?
Marshall
12/1/09
Read using signature-blocks to defame innocent people Re: Jesse Hughes of
Bentley College
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?
Seth Breidbart
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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
William Hughes
11/26/09
Read Re: Another AC anomaly?
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?
Virgil
11/27/09
Read Re: Another AC anomaly?
Alan Smaill
11/29/09
Read Re: Another AC anomaly?
William Hughes
11/30/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Alan Smaill
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
ross.finlayson@gmail.com
12/1/09
Read Re: Another AC anomaly?
Virgil
12/2/09
Read Re: Another AC anomaly?
Dik T. Winter
12/2/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/2/09
Read Re: Another AC anomaly?
Dik T. Winter
12/2/09
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mueckenh@rz.fh-augsburg.de
12/2/09
Read Re: Another AC anomaly?
Virgil
12/3/09
Read Re: Another AC anomaly?
Dik T. Winter
12/3/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/3/09
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Dik T. Winter
12/3/09
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K_h
12/7/09
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Dik T. Winter
12/7/09
Read Re: Another AC anomaly?
Virgil
12/8/09
Read Re: Another AC anomaly?
K_h
12/8/09
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Virgil
12/9/09
Read Re: Another AC anomaly?
K_h
12/9/09
Read Re: Another AC anomaly?
Virgil
12/9/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/9/09
Read Re: Another AC anomaly?
Virgil
12/9/09
Read Re: Another AC anomaly?
K_h
12/10/09
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Dik T. Winter
12/9/09
Read Re: Another AC anomaly?
K_h
12/9/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
Virgil
12/15/09
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Dik T. Winter
12/15/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/15/09
Read Re: Another AC anomaly?
Dik T. Winter
12/15/09
Read Re: Another AC anomaly?
K_h
12/16/09
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Virgil
12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/17/09
Read Re: Another AC anomaly?
Virgil
12/17/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/17/09
Read Re: Another AC anomaly?
YBM
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
Read Re: Another AC anomaly?
Quaestor
12/18/09
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mueckenh@rz.fh-augsburg.de
12/18/09
Read Re: Another AC anomaly?
Virgil
12/18/09
Read Re: Another AC anomaly?
Dik T. Winter
12/19/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
Virgil
12/22/09
Read Re: Another AC anomaly?
Dik T. Winter
12/22/09
Read Re: Another AC anomaly?
Virgil
12/18/09
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Dik T. Winter
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
Quaestor
12/21/09
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Dik T. Winter
12/21/09
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mueckenh@rz.fh-augsburg.de
12/21/09
Read Re: Another AC anomaly?
Marshall
12/21/09
Read Re: Another AC anomaly?
Virgil
12/22/09
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Dik T. Winter
12/27/09
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mueckenh@rz.fh-augsburg.de
12/27/09
Read Re: Another AC anomaly?
Virgil
12/16/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/16/09
Read Re: Another AC anomaly?
Virgil
12/11/09
Read Re: Another AC anomaly?
K_h
12/11/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
K_h
12/11/09
Read Re: Another AC anomaly?
Marshall
12/12/09
Read Re: Another AC anomaly?
Jesse F. Hughes
12/12/09
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K_h
12/12/09
Read Re: Another AC anomaly?
K_h
12/11/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/11/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
K_h
12/11/09
Read Re: Another AC anomaly?
Virgil
12/7/09
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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?
anonymous.rubbertube@yahoo.com
12/8/09
Read Re: Another AC anomaly?
Virgil
12/8/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/8/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/3/09
Read Re: Another AC anomaly?
Virgil
12/3/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/3/09
Read Re: Another AC anomaly?
Virgil
12/7/09
Read Re: Another AC anomaly?
Dik T. Winter
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?
Virgil
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?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/11/09
Read Re: Another AC anomaly?
Virgil
12/11/09
Read Re: Another AC anomaly?
Virgil
12/15/09
Read Re: Another AC anomaly?
Dik T. Winter
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?
T.H. Ray
12/17/09
Read Re: Another AC anomaly?
Dik T. Winter
12/4/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/4/09
Read Re: Another AC anomaly?
Virgil
12/4/09
Read Re: Another AC anomaly?
Marshall
12/7/09
Read Re: Another AC anomaly?
Dik T. Winter
12/7/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/7/09
Read Re: Another AC anomaly?
Virgil
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?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/10/09
Read Re: Another AC anomaly?
Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/11/09
Read Re: Another AC anomaly?
Marshall
12/11/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/11/09
Read Re: Another AC anomaly?
Virgil
12/11/09
Read Re: Another AC anomaly?
Virgil
12/11/09
Read Re: Another AC anomaly?
Marshall
12/12/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/12/09
Read Re: Another AC anomaly?
Virgil
12/12/09
Read Re: Another AC anomaly?
Marshall
12/12/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/12/09
Read Re: Another AC anomaly?
Virgil
12/12/09
Read Re: Another AC anomaly?
Marshall
12/12/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/12/09
Read Re: Another AC anomaly?
Virgil
12/12/09
Read Re: Another AC anomaly?
Marshall
12/12/09
Read Re: Another AC anomaly?
george
12/12/09
Read Re: Another AC anomaly?
Virgil
12/12/09
Read Re: Another AC anomaly?
george
12/13/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/13/09
Read Re: Another AC anomaly?
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12/15/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/16/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
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12/17/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/17/09
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12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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12/18/09
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mueckenh@rz.fh-augsburg.de
12/18/09
Read Re: Another AC anomaly?
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12/18/09
Read Re: Another AC anomaly?
Dik T. Winter
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
Virgil
12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
Marshall
12/19/09
Read Re: Another AC anomaly?
Virgil
12/19/09
Read Re: Another AC anomaly?
Virgil
12/19/09
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ross.finlayson@gmail.com
12/19/09
Read Re: Another AC anomaly?
Virgil
12/22/09
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ross.finlayson@gmail.com
12/22/09
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Marshall
12/27/09
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ross.finlayson@gmail.com
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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Virgil
12/22/09
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Dik T. Winter
12/27/09
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mueckenh@rz.fh-augsburg.de
12/27/09
Read Re: Another AC anomaly?
Marshall
12/27/09
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Virgil
12/27/09
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Virgil
12/27/09
Read Re: Another AC anomaly?
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12/27/09
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Virgil
12/13/09
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mueckenh@rz.fh-augsburg.de
12/13/09
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Virgil
12/4/09
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K_h
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
Read Re: Another AC anomaly?
Virgil
12/4/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
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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Carsten Schultz
12/2/09
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Virgil
12/1/09
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george
12/1/09
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Virgil
11/27/09
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
anonymous.rubbertube@yahoo.com
11/30/09
Read Re: Another AC anomaly?
William Hughes
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?
mueckenh@rz.fh-augsburg.de
11/27/09
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William Hughes
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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/27/09
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?
Virgil

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