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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 1:42 AM
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On 4 Dez., 06:30, "K_h" <KHol...@SX729.com> wrote:
> "WM" <mueck...@rz.fh-augsburg.de> wrote in message
>
> news:0c635f53-f5c4-4320-8825-de05f021a428@m3g2000yqf.googlegroups.com...
> On 2 Dez., 16:27, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>

> > Same holds for the cylinder. Its contents is
> >   {1}, {1}, {1}, {1} , ...
> > and that is not different from
> >   {1}, {2}, {3}, {4} , ...
> > as you can see by renaming the elements.

>
> You need to provide a definition for your idea of a limit
> set.


1) N is a set that follows (as omega, but that is not important) from
the axiom of infinity. You can take it "from the shelf".
2) N is the limit of the sequence a_n = ({1, 2, 3, ...,n})
3) N is the limit, i.,e. the infinite union of singletons {1} U {2}
U ...

> Under the definitions given in this thread, you are
> simply wrong.


The definition lead to the empty set. And *that result* is simply
wrong.

> I only have a partial listing of this thread
> but from what postings I have it looks like you are trying
> to make an argument about a supertask.  Informally, the idea
> behind a limit is that that state of a system tends to some
> fixed value.  So the limit of a sequence of sets, .like {1},
> {0}, {1}, {0}, {1}, {0},..., does not exist whereas the
> limit of a sequence of sets like {1}, {1}, {1}, {1}, {1},
> {1},...does exist and is the set {1} [assuming a definition
> along the lines of convergence].  So in the case of
> Thompson's lamp, {1}, {0}, {1}, {0}, {1}, {0},..., its value
> at the limiting time does not exist and so there is not much
> that can be said about it.


But we can say that the lamp itself does exist at every time and so in
the limit too.This is the case with one ball in the vase.

> But to this supertask:
>

> > Same holds for the cylinder. Its contents is
> >   {1}, {1}, {1}, {1} , ...
> > and that is not different from
> >   {1}, {2}, {3}, {4} , ...
> > as you can see by renaming the elements.

>
> Renaming the elements?  If you have the idea in mind that
> there is one ball in the vase and it is being repainted with
> different labels, naturals numbers, {1}, {2}, {3}, {4} , ...
> , (say at times t=1-1/n), then you can say that at time t=1
> there is one ball in the vase.  But its painted label can be
> anything you want it to be at time t=1.  That is, if at time
> t=1-1/n you paint the ball with the label {n} and then at
> time t=1-1/(n+1) you paint it with the label {n+1}, etc,
> then you can paint any kind of label you want to on the ball
> at time t=1.


The point is that there is one ball as the limit set and 1 as limit
cardinality.

> The bottom line is that none of this proves
> any inconsistency in set theory.


No. If the limit set is empty and the limit cardinality is 1, then the
limit set is not the set corresponding to limit cardinality. Set
theory tries to convince us that the infinite actually exists. In the
present case that is obviously inconsistent.

Another inconsistency is here: 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.

But unless such paths remain unpainted we can paint the complete
binary tree by countably many strokes. This implies the existence of
only countably many real numbers.

Regards, WM






Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
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11/30/09
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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
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12/1/09
Read using signature-blocks to defame innocent people Re: Jesse Hughes of
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12/1/09
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12/1/09
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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
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mueckenh@rz.fh-augsburg.de
11/28/09
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11/26/09
Read Re: Another AC anomaly?
William Hughes
11/28/09
Read Re: Another AC anomaly?
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11/26/09
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mueckenh@rz.fh-augsburg.de
11/28/09
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11/28/09
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Virgil
11/29/09
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mueckenh@rz.fh-augsburg.de
11/29/09
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Virgil
11/29/09
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ross.finlayson@gmail.com
11/29/09
Read Re: Another AC anomaly?
Marshall
11/30/09
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Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
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ross.finlayson@gmail.com
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11/30/09
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11/30/09
Read Re: Another AC anomaly?
Virgil
11/30/09
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ross.finlayson@gmail.com
11/30/09
Read Re: Another AC anomaly?
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11/29/09
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11/27/09
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mueckenh@rz.fh-augsburg.de
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11/29/09
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11/30/09
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11/27/09
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mueckenh@rz.fh-augsburg.de
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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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11/27/09
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11/27/09
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11/27/09
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mueckenh@rz.fh-augsburg.de
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11/27/09
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11/30/09
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12/19/09
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12/11/09
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Read Re: Another AC anomaly?
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12/16/09
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12/17/09
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12/4/09
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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
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mueckenh@rz.fh-augsburg.de
12/7/09
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12/8/09
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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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