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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 7:32 AM
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In article <03e1afc6-ec37-4212-b958-063a237d2bb4@f16g2000yqm.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:
> On 11 Dez., 03:28, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
...
> > > > Have a look at <http://en.wikipedia.org/wiki/Lim_inf> in the secti=
> on
> > > > titled "Special case: dicrete metric". An example is given with
> > > > the sequence {0}, {1}, {0}, {1}, ...
> > > > where lim sup is {0, 1} and lim inf is {}.
> > > >
> > > > Moreover, in what way can a definition be invalid?

> > >
> > > It can be nonsense like the definition: Let N be the set of all
> > > natural numbers.

> >
> > In what way is it nonsense? Either that set does exist or it does not
> > exist.
> > If it does exist there is indeed such a set, if it does not exist there is
> > no set satisfying the definition. In both cases the definition is not
> > nonsense in itself.

>
> 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.

> 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.

> 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? 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, ...}.

> 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, ...}.
The reason being that uniting commutes, so it would be the same as:
{1, 2, 3, ...} U {1} U {1, 2} U {1, 2, 3} ...
Formally: let S_n = {1, 2, ..., n} for n a natural number. Let
S_w = {1, 2, 3, ...}. Let I be the index set N U {w}. Then the
union should be:
union(i in I) S_i = {1, 2, 3, ...}

> > But apparently you are of the opinion that you are only allowed to define
> > things that do exist.

>
> Most essential things in mathematics exist without definitions and,
> above all, without axioms.


Oh. Not for a mathematician. If there is no definition or axiom there is
no proof.
--
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
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
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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
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
Read Re: Another AC anomaly?
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?
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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?
Dik T. Winter
12/15/09
Read Re: Another AC anomaly?
K_h
12/16/09
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
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?
YBM
12/17/09
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mueckenh@rz.fh-augsburg.de
12/17/09
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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
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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?
Quaestor
12/21/09
Read Re: Another AC anomaly?
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
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Virgil
12/22/09
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Dik T. Winter
12/27/09
Read Re: Another AC anomaly?
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
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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
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Virgil
12/7/09
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mueckenh@rz.fh-augsburg.de
12/7/09
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Virgil
12/8/09
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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
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Virgil
12/10/09
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Dik T. Winter
12/3/09
Read Re: Another AC anomaly?
Virgil
12/3/09
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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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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?
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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
Read Re: Another AC anomaly?
Virgil
12/12/09
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12/12/09
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george
12/12/09
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12/12/09
Read Re: Another AC anomaly?
george
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
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?
Dik T. Winter
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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Quaestor
12/18/09
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mueckenh@rz.fh-augsburg.de
12/18/09
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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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
Marshall
12/27/09
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ross.finlayson@gmail.com
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
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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
Read Re: Another AC anomaly?
Virgil
12/27/09
Read Re: Another AC anomaly?
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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K_h
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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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
Read Re: Another AC anomaly?
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
Read Re: Another AC anomaly?
Virgil
11/27/09
Read Re: Another AC anomaly?
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
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mueckenh@rz.fh-augsburg.de
11/27/09
Read Re: Another AC anomaly?
Virgil

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