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

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mueckenh@rz.fh-augsburg.de

Posts: 18,076
Registered: 1/29/05
Re: Another AC anomaly?
Posted: Dec 4, 2009 1:31 AM
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On 3 Dez., 16:27, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:

>  > > No.  I asked you for a mathematical definition of "actual infinity" and
>  > > you told me that it was "completed infinity".  Next I asked you for a
>  > > mathematical definition of "completed infinity" but you have not given
>  > > an answer.  So I still do not know what either "actual infinity" or
>  > > "completed infinity" are.
>  >
>  > Both are nonsense. But both are asumed to make sense in set theory.
>
> No, set theory does not contain a definition of either of them.
>
>  > The axiom of infinity is adefinition of actual infinity.
>  > "There *exists* a set such that ..."
>  > Without that axiom there is only potential infinity, namely Peano
>  > arithmetic.
>
> I see neither a definition of the words "actual infinity" neither
> a definition of "potential infinity".  Or do you mean that "potential
> infinity" is Peano arithmetic (your words seem to imply that)?
>
> So we can say that in "potential infinity" consists of a set of axioms?


Here is, to my knowledge, the simplest possible explanation. Consider
the infinite binary tree:

0
/\
0 1
/\ /\
0 1 0 1
...

Paint all paths of the form
0.111...
0.0111...
0.00111...
0.000111...
and so on.
Potential infinity then says that every node and every edge on the
outmost left part of the tree gets painted.
Actual infinity says that there is a path 0.000... parts of which
remain unpainted. And that is wrong.

Regards, WM



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
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master1729
11/25/09
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T.H. Ray
11/24/09
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george
12/1/09
Read Re: Another AC anomaly?
george
11/25/09
Read Re: Another AC anomaly?
Bill Taylor
11/26/09
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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
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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
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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
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ross.finlayson@gmail.com
11/28/09
Read Re: Another AC anomaly?
Virgil
11/29/09
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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
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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
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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?
Alan Smaill
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
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
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
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
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
Dik T. Winter
11/30/09
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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
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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
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ross.finlayson@gmail.com
12/1/09
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Virgil
12/1/09
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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
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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
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Virgil
12/3/09
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Dik T. Winter
12/3/09
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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
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Virgil
12/8/09
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K_h
12/8/09
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12/9/09
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12/9/09
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12/9/09
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mueckenh@rz.fh-augsburg.de
12/9/09
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12/9/09
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K_h
12/10/09
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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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mueckenh@rz.fh-augsburg.de
12/10/09
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12/10/09
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12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/15/09
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Dik T. Winter
12/15/09
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mueckenh@rz.fh-augsburg.de
12/15/09
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12/15/09
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12/16/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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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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12/17/09
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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
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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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Virgil
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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Virgil
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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
Marshall
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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Virgil
12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/10/09
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Dik T. Winter
12/11/09
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K_h
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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anonymous.rubbertube@yahoo.com
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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Dik T. Winter
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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12/7/09
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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
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12/8/09
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Dik T. Winter
12/8/09
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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
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mueckenh@rz.fh-augsburg.de
12/10/09
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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?
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12/11/09
Read Re: Another AC anomaly?
Virgil
12/15/09
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Dik T. Winter
12/16/09
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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
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T.H. Ray
12/17/09
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Dik T. Winter
12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
12/4/09
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Marshall
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
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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
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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
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12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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12/12/09
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12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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12/12/09
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mueckenh@rz.fh-augsburg.de
12/12/09
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12/12/09
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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12/13/09
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mueckenh@rz.fh-augsburg.de
12/13/09
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12/15/09
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12/16/09
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mueckenh@rz.fh-augsburg.de
12/16/09
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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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12/17/09
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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
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12/19/09
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Virgil
12/19/09
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ross.finlayson@gmail.com
12/19/09
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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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mueckenh@rz.fh-augsburg.de
12/27/09
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12/27/09
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12/27/09
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Virgil
12/27/09
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12/27/09
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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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12/4/09
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mueckenh@rz.fh-augsburg.de
12/4/09
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Virgil
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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12/5/09
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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
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Virgil
11/27/09
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anonymous.rubbertube@yahoo.com
11/30/09
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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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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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William Hughes
11/27/09
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mueckenh@rz.fh-augsburg.de
11/27/09
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Virgil

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