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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 12, 2009 5:00 PM
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In article
<d8ef5daa-b9d6-4c51-b40d-0ea5336b1326@v25g2000yqk.googlegroups.com>,
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 12 Dez., 17:19, Marshall <marshall.spi...@gmail.com> wrote:
> > On Dec 12, 1:32 am, WM <mueck...@rz.fh-augsburg.de> wrote:
> >

> > > On 12 Dez., 02:01, Marshall <marshall.spi...@gmail.com> wrote:
> >
> > > > Showing
> > > > a contradiction would qualify, but it's been well
> > > > established that you don't know how to do that.

> >
> > > Consider how a union of paths is counted (I copy
> > > from another posting, therefore the quotation symbols):

> >
> > Ascii diagrams don't qualify as a contradiction.

>
> Why should pictures, diagrams, acoustic signals etc. qualify less than
> sequences of symbols? Every bit of information, in what form ever, can
> be used in proofs. But here you are:
>
> The union of all natural numbers is, according to set theory, omega.
> If *actual* infinity is meant, this is plainly impossible, because the
> natural numbers count themselves.


Non sequitur.

> So every set of natural numbers has
> at most one number that is as large as its cardinal number.


That presumes what it is alleged to establish, so is invalid.

> initial sets of only even numbers, this becomes immediately clear:
> 2
> 2, 4
> 2, 4, 6
> ...
> These sets contain always numbers that are larger than the cardinal
> number of the set.


But the set {2,4,6,...} does not.


> But this fact does not stop set theorists from believing in actual
> infinity.


And their doing so causes no problems for anyone with more sense than
WM.

> They do not wish to see that ordinal number = cardinal
> number as long as only initial segments of natural numbers are
> involved.


A limitation claimed but never proven.
>
> Therefore I have looked for a model which supplies ordinal and
> cardinal numbers in one and the same elements. This model is the
> binary tree.


WM's so called binary trees are all incomplete. Complete INFINITE binary
trees do not have any finite paths but do have lots of paths.

> If you union paths, then you get the sequence

The following are not paths in an infinite tree but merely finite
initial segments of such paths. And while they may be paths in finite
trees, they are not paths in the same tree
>
>

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

>
But according to WM you cannot union those paths because the result is
not a path.

> i.e., when you union only all finite initial segments of 0.000... you
> get exactly the same result as when you union all finite initial
> segments of 0.000... *and* 0.000...


In ZF, the union of a family of sets is not changed when one appends any
union of a subset of those sets to the set of sets.
This in no way supports WM's delusions.
>
> This leads to the result that the same structure, namely the tree with
> all its nodes, contains only a countable set of paths and
> simultaneously it contains an uncountable set of paths.


There is no example of a COMPLETE infinite binary tree in which any
finite set of nodes is path.
>
> And this is a contradiction.


It is a lie.
>
> Of course, if only a small collection of paths from the tree is
> presented, then one can find paths in the tree which are not included
> in that collection.


If those alleged paths are finite, then they are not paths in a COMPLETE
and INFINITE binary tree.
>
> But this does not help to explain an uncountable set of paths


Lies do not, in general, help to exxplain anything.


> 1) We can construct the tree from its finite paths. In order to obtain
> one infinite "bonus" path, you need aleph_0 finite paths. But in order
> to explain the existence of uncountably many infinite paths, you would
> need to obtain at least aleph_0 infinite paths with every constructed
> finite path - and even that would not be enough because aleph_0 *
> aleph_0 = aleph_0.



The point is that from that set of aleph_0 finite paths it is the
numbers of subsets which determines the number of infinite paths, and in
ZF, the number of subsets of a set is always greater than the number of
members of a set.

Does WM have any evidence that in his world this is not also the case?

> 2) If you construct the tree by means of infinite paths

One constructs an infinite tree as an infinite sets of nodes, and a path
in such a tree as a set of nodes in which no node has more than one
child. Each such MAXIMAL set is a path, but no finite set is a path.

If, as in an infinite binary tree, one has countably many nodes, then
one has necessarily more sets of nodes than nodes, and there are simple
proofs that there are MORE paths than nodes.

WM claims that these proofs do not hold, but his arguments are false
outside of Wolkenmuekenheim.

> then the
> ratio between constructed paths and constructed nodes is 1/aleph_0 at
> every step of the construction for every set of nodes covered by the
> construction.


In that case, one could have only finitely many finite paths
encompassing infinitely many nodes. Which won't work even in
Wolkenmuekenheim.

> Do you seriously expect that this ratio can become
> 2^aleph_0 - after all nodes will have been constructed (not *during*
> construction, because as long as one node has not been constructed,
> the ratio remains the same)?


As you analysis is false ab initio, I do not expect it to become true
ever.


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
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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
Read Re: Another AC anomaly?
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?
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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?
William Hughes
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?
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?
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?
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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
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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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12/9/09
Read Re: Another AC anomaly?
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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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12/9/09
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
Read Re: Another AC anomaly?
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?
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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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12/17/09
Read Re: Another AC anomaly?
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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
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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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12/18/09
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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
Read Re: Another AC anomaly?
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12/21/09
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12/22/09
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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?
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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?
K_h
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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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?
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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?
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?
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12/11/09
Read Re: Another AC anomaly?
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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?
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?
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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?
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12/17/09
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
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?
Dik T. Winter
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?
Dik T. Winter
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?
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
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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
12/11/09
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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
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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
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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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12/16/09
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12/17/09
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12/18/09
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12/19/09
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12/19/09
Read Re: Another AC anomaly?
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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?
Virgil
12/19/09
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Virgil
12/19/09
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12/19/09
Read Re: Another AC anomaly?
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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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12/27/09
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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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12/4/09
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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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12/4/09
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12/5/09
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12/5/09
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12/5/09
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12/5/09
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12/1/09
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george
12/1/09
Read Re: Another AC anomaly?
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
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?
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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