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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 15, 2009 9:44 PM
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In article <9904ae9d-de2c-4d5f-86da-be165e8e9d7e@p30g2000vbt.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:
> On 15 Dez., 13:32, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
>

> > > It is nonsense to define a pink unicorn.
> >
> > That statement is nonsense. Let pu be a pink unicorn is a proper
> > definition.
> > However there is nothing that satisfies that definition.

>
> That is a matter of taste.


So finally you agree, you do not like to give definitions for things that
do not exist (in some sense). However, in mathematics it is quite common
to give definitions for things that do not exist, one of the jobs is to
either proof that such a thing exist (according to the rules of mathematics)
or that it does not exist. Giving only the field axioms, assume that S,
being a set {a, b, c, d, e, f} with operations '+' and '*' be a field. Show
that S does not exist.

> > > The set N does not exist as
> > > the union of its finite initial segments. This is shown by the (not
> > > existing) path 0.000... in the binary tree.

> >
> > As you have defined your tree as only containing finite paths it is
> > trivial to conclude that the infinite path 0.000... does not exist in
> > your tree.
> > However, this does *not* show that N does not exist.

>
> If N does exist, then the tree containing all finite paths contains
> also infinite paths.


No, you *explicitly* stated that your tree does not include infinite paths.
If your tree also does include infinite paths you should not have stated
a priori that it did not. That is why, in mathematics, there is a huge
difference between the tree constructed as the collection of finite paths
and as the collection of nodes where a path is allowed to start at the root
and finish anywhere or not at all.

> > > Let {1} U {1, 2} U {1, 2, 3} U ... = {1, 2, 3, ...}.
> > > What then is
> > > {1} U {1, 2} U {1, 2, 3} U ... U {1, 2, 3, ...} ?

> >
> > Ambiguous as stated. What is "..." standing for?

>
> Look two lines above:
>
> Let {1} U {1, 2} U {1, 2, 3} U ... = {1, 2, 3, ...}
> hence
> {1} U {1, 2} U {1, 2, 3} U ... U {1, 2, 3, ...} = {1, 2, 3, ...} .


You mean:

> ({1} U {1, 2} U {1, 2, 3} U ...) U {1, 2, 3, ...} = {1, 2, 3, ...} .

yes?

> > Not for "go on in the
> > same way until", because when you go on in the same way you will never
> > get at {1, 2, 3, ...}.


Note this remark. If "..." is put between two things that means (in
mathematics): go on the same until you come at what follows.

> >
> > > If it is the same, then wie have a stop in transfinite counting.
> >
> > However, if we try to attach a meaning we find that it is {1, 2, 3, ...}.

>
> Correct.


> {1} U {1, 2} U {1, 2, 3} U ... = {1} U {1, 2} U {1, 2, 3} U ... U {1,
> 2, 3, ...}


No, correct mathematical notation is:

> {1} U {1, 2} U {1, 2, 3} U ... = ({1} U {1, 2} U {1, 2, 3} U ...) U {1,
> 2, 3, ...}


> There is no space in the binary tree to contain infinite paths in
> addition to the sequeneces of all finite paths.
> The sequence 0.0, 0.00, 0.000, ... when being completely constructed,
> is already the path 0.000...
> You cannot add it separately.


A sequence of paths is not a path.

> Therefore: When all finite paths have been constructed within aleph_0
> steps, then all paths have been constructed.


Here, again, you err. You can not construct something in aleph_0 steps; you
will never complete your construction. You *cannot* get at aleph_0 step by
step.

> This hold for every limit of every sequence of finite paths.

A limit is not a step by step process.
--
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
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11/25/09
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T.H. Ray
11/24/09
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12/1/09
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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?
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
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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?
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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?
mueckenh@rz.fh-augsburg.de
12/2/09
Read Re: Another AC anomaly?
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12/3/09
Read Re: Another AC anomaly?
Dik T. Winter
12/3/09
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mueckenh@rz.fh-augsburg.de
12/3/09
Read Re: Another AC anomaly?
Dik T. Winter
12/3/09
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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
Read Re: Another AC anomaly?
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12/8/09
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Virgil
12/9/09
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12/9/09
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12/9/09
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12/9/09
Read Re: Another AC anomaly?
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12/9/09
Read Re: Another AC anomaly?
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12/10/09
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12/9/09
Read Re: Another AC anomaly?
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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?
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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12/11/09
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mueckenh@rz.fh-augsburg.de
12/11/09
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12/15/09
Read Re: Another AC anomaly?
Dik T. Winter
12/15/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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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12/16/09
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
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?
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12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
Read Re: Another AC anomaly?
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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?
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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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12/22/09
Read Re: Another AC anomaly?
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12/22/09
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?
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12/21/09
Read Re: Another AC anomaly?
Dik T. Winter
12/21/09
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
Dik T. Winter
12/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/27/09
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?
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?
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12/12/09
Read Re: Another AC anomaly?
K_h
12/12/09
Read Re: Another AC anomaly?
K_h
12/11/09
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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
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?
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
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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
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/12/09
Read Re: Another AC anomaly?
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12/12/09
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Marshall
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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Marshall
12/12/09
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george
12/12/09
Read Re: Another AC anomaly?
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12/12/09
Read Re: Another AC anomaly?
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12/13/09
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12/13/09
Read Re: Another AC anomaly?
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12/15/09
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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
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12/17/09
Read Re: Another AC anomaly?
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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
Read Re: Another AC anomaly?
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?
mueckenh@rz.fh-augsburg.de
12/19/09
Read Re: Another AC anomaly?
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12/19/09
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12/19/09
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Virgil
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
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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
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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12/4/09
Read Re: Another AC anomaly?
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12/4/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
12/4/09
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12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
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12/5/09
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12/6/09
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12/5/09
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12/2/09
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12/1/09
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12/1/09
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11/27/09
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11/27/09
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11/30/09
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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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11/27/09
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11/27/09
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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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