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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 27, 2009 3:42 PM
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In article
<6bb08356-6292-498e-a174-a3e2ef3f757c@26g2000yqo.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 22 Dez., 15:28, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>

> >  > Even a matheologian should understand that: If there is no digit at a
> >  > finite place up to that the sequence 0.333... identifies the number
> >  > 1/3, then there is no digit at a finite place up to that the number
> >  > 1/3 can be identified.
> >
> > Right, there is no digit at a finite place up to that the number 1/3 can be
> > identified.  And as there are no digits at infinite places that appears to
> > you to be a paradox.  It is not.  There is *no* finite sequence of digits
> > that identifies 1/3.  But there is an *infinite* sequence of digits that
> > does so.

>
> Why not pronounce it a bit clearer?


It is quite clear enough for mathematics.

> We know that every digit is the
> last digit of a finite initial segment of digits. There is no other
> digit, is it?
> Therefore your statement can be expressed in the following way: There
> is no finite initial segment that identifies 1/3. But there is an
> infinite finite initial segment that identifies 1/3.


That deliberate misrepresentation is straight out of the curdled logic
of Wolkenmuekenheim
>
> If you read this sentence, perhaps you get an impression of what
> matheology is?


Matheology, as represented here is WM's corruptEd version of actual of
mathematics.
>
> >  >                       I said, if there is a sequence that identifies
> >  > 1/3, then the identifying digits must be at finite places.
> >
> > Right, all identifying digits (there are infinitely many) are at finite
> > places.

>
> Therefore your statement can be expressed in the following way: There
> is no finite initial segment that identifies 1/3. But there is an
> infinite finite initial segment that identifies 1/3.


Only such a mentally corrupted ass as WM would try to pass off the
notion of an "infinite finite initial segment" as anything but his own
nonsense.
> >
>
> >  > The union of finite initial segments cannot ield an infinite initial
> >  > segment?
> >
> > Yes.  But as you have stated that your tree contained finite paths only,
> > such an infinite initial segment is not (according to *your* definition)
> > a path.

>
> The axiom of infinity states: There is an infinite set such that with
> every n the follower of n belongs to the set.


That is not at all how it is stated.

According to http://en.wikipedia.org/wiki/ZFC, for instance, it says

There exists a set which contains the empty set and for each of its
members, x also contains the union of x with {x}.

Note that at this point in set theory, there is as yet no definition of
'infinite'.

To speak of an infinite set prior to having any definition of what
'infinite' means, is, at best, stupid.




> This is true for the
> binary tree. With every finite path 1, ..., n the follower 1, ..., n+1
> is in the tree. The union of all those paths of course is finite, as I
> said, because there is no infinite path


WM's saying something is well known NOT to make it true.

If those paths are sets, so that their unions can be defined at all,
then the union of all of them is not a finite set, as it contains all of
those finite initial paths as PROPER subsets, and there is no surjection
from any finite set to it.


> but according to the axiom it
> is infinite.


So the axiom is again right where WM is again wrong.

>
>

> >
> >  >          Does the sequence of 1/3 not consist of a union of all finite
> >  > initial segments?
> >
> > It is, but also (according to *your* definition) it is not a path.

>
> There can be no question: The union of all finite initial segments is
> finite.



The set of all those initial segments is naturally ordered by inclusion,
and for that ordering, there is no last element.

A set which can be linearly ordered so as NOT to have any last element
in that ordering is NOT finite, by any definition of finiteness that I
am aware of.

In fact, a sufficient definition of set finiteness, at least for a
non-empty sets, is that for ANY linear ordering, there is both a least
and a greatest (though for one element sets they are the same).

So that set of initial segments is NOT finite and the union of the set
of initial segments, being bijectable with the set itself, is equally
NOT finite.

> But according to the axiom, it is infinite.

So the axiom, if it actually said that, would have been right, but the
axiom does not, in fact, say that.

> So we can both be well pleased.


WM may declare that he is pleased with himself, but he is notoriously
blind to his own faults and flaws.

But those of us not blind to them are less pleased with him.


Date Subject Author
11/23/09
Read Re: Another AC anomaly?
Jesse F. Hughes
11/23/09
Read Re: Another AC anomaly?
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12/1/09
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11/26/09
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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
others; Ann Reeves Re: What's wrong with supertasks?
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12/1/09
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12/1/09
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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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/28/09
Read Re: Another AC anomaly?
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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?
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11/26/09
Read Re: Another AC anomaly?
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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?
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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?
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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
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?
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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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?
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12/1/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/1/09
Read Re: Another AC anomaly?
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12/1/09
Read Re: Another AC anomaly?
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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?
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12/2/09
Read Re: Another AC anomaly?
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12/2/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/2/09
Read Re: Another AC anomaly?
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12/2/09
Read Re: Another AC anomaly?
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12/2/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/3/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
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12/8/09
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Read Re: Another AC anomaly?
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12/9/09
Read Re: Another AC anomaly?
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12/9/09
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Read Re: Another AC anomaly?
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12/9/09
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12/10/09
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12/9/09
Read Re: Another AC anomaly?
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12/10/09
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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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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12/15/09
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12/15/09
Read Re: Another AC anomaly?
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12/16/09
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12/16/09
Read Re: Another AC anomaly?
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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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12/17/09
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12/17/09
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12/18/09
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12/18/09
Read Re: Another AC anomaly?
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12/18/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
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12/22/09
Read Re: Another AC anomaly?
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12/22/09
Read Re: Another AC anomaly?
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12/18/09
Read Re: Another AC anomaly?
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12/19/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
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12/21/09
Read Re: Another AC anomaly?
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12/21/09
Read Re: Another AC anomaly?
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12/21/09
Read Re: Another AC anomaly?
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12/21/09
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12/22/09
Read Re: Another AC anomaly?
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12/27/09
Read Re: Another AC anomaly?
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12/27/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
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12/16/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
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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
Read Re: Another AC anomaly?
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12/11/09
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12/11/09
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12/10/09
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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?
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12/10/09
Read Re: Another AC anomaly?
Dik T. Winter
12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/7/09
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12/7/09
Read Re: Another AC anomaly?
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12/8/09
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
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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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12/3/09
Read Re: Another AC anomaly?
Virgil
12/3/09
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12/3/09
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12/7/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
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12/7/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
Dik T. Winter
12/8/09
Read Re: Another AC anomaly?
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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?
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12/10/09
Read Re: Another AC anomaly?
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12/10/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
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?
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12/16/09
Read Re: Another AC anomaly?
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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?
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12/4/09
Read Re: Another AC anomaly?
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12/4/09
Read Re: Another AC anomaly?
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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?
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12/8/09
Read Re: Another AC anomaly?
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12/8/09
Read Re: Another AC anomaly?
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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?
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12/10/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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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
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12/11/09
Read Re: Another AC anomaly?
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12/11/09
Read Re: Another AC anomaly?
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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
Read Re: Another AC anomaly?
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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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12/13/09
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/19/09
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12/19/09
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12/19/09
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mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
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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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12/22/09
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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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12/13/09
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12/4/09
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12/4/09
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12/4/09
Read Re: Another AC anomaly?
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12/4/09
Read Re: Another AC anomaly?
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12/4/09
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12/5/09
Read Re: Another AC anomaly?
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12/5/09
Read Re: Another AC anomaly?
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12/5/09
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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
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?
anonymous.rubbertube@yahoo.com
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?
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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