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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 12, 2009 4:32 AM
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On 12 Dez., 02:01, Marshall <marshall.spi...@gmail.com> wrote:
> On Dec 11, 11:33 am, WM <mueck...@rz.fh-augsburg.de> wrote:
>
>
>

> > They *are* just the same, because your argument that above procedure
> > would prove an infinite string of 3's is wrong. There is neither a
> > natural nor a rational with an infinite string of digits. To be able
> > to determine every digit of a number you like does not imply that
> > there is a number with a never ending sequence of digits.

>
> If your math can't handle 1/3, it is exceedingly weak.
> A third grader can do as much. You propose various
> severe restrictions on math and say that everyone
> else ought to adopt them, but you supply no motivation for
> doing so.


Every digit of 1/3 that you can handle, I can handle too. Only the
claim "all digits" is incorrect. In my mathematics, this is seen, in
yours it is not.

>
> The answer to your "why" question is because many
> good and useful results come about if I do. For example,
> I can handle decimal expansions of fractions such
> as 1/3. I know you don't like many of those results,
> however, coming up with results that are palatable
> to some guy I never met is not a goal of mine.
>
> To get any attention to your demands, you need to
> supply some motivation for people to listen. 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):

>
> > {1}
> > {1, 2}
> > {1, 2, 3}
> > _________
> > {1, 2, 3}
> > ========

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

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

>
> > {1}
> > {1, 2}
> > {1, 2, 3}
> > ...
> > {1, 2, 3, ...}
> > {1, 2, 3, ..., a}
> > _____________
> > {1, 2, 3, ..., a}
> > ============

>
> > {1}
> > {1, 2}
> > {1, 2, 3}
> > ...
> > {1, 2, 3, ...}
> > {1, 2, 3, ..., a}
> > {1, 2, 3, ..., a, aa}
> > ______________
> > {1, 2, 3, ..., a, aa}
> > =============

>
> > {1}
> > {1, 2}
> > {1, 2, 3}
> > ...
> > {1, 2, 3, ...}
> > {1, 2, 3, ..., a}
> > {1, 2, 3, ..., a, aa}
> > ...
> > __________________
> > {1, 2, 3, ..., a, aa, ...}
> > =================

>
> > {1}
> > {1, 2}
> > {1, 2, 3}
> > ...
> > {1, 2, 3, ...}
> > {1, 2, 3, ..., a}
> > {1, 2, 3, ..., a, aa}
> > ...
> > {1, 2, 3, ..., a, aa, ...}
> > __________________
> > {1, 2, 3, ..., a, aa, ...}
> > =================


Contrary to the usual
1, 2, 3, ..., w, w+1, w+2, ..., w+w, w+w+1, ...
this leads to the following sequence which stops from time to time (at
limit ordinal paths):

{1}
{1, 2}
{1, 2, 3}
...
{1, 2, 3, ...}
{1, 2, 3, ...}
{1, 2, 3, ..., a}
{1, 2, 3, ..., a, aa}
{1, 2, 3, ..., a, aa, aaa}
...
{1, 2, 3, ..., a, aa, aaa, ...}
{1, 2, 3, ..., a, aa, aaa, ...}
{1, 2, 3, ..., a, aa, aaa, ..., b}
{1, 2, 3, ..., a, aa, aaa, ..., b, bb}
{1, 2, 3, ..., a, aa, aaa, ..., b, bb, bbb}
...
{1, 2, 3, ..., a, aa, aaa, ..., b, bb, bbb, ...}
{1, 2, 3, ..., a, aa, aaa, ..., b, bb, bbb, ...}
...

The first double-meaning, at {1, 2, 3, ...}, is responsible for the
fact that the infinite binary tree can be constructed completely from
finite paths (hence contains only countably many paths) and
simultaneously is said to contain uncountably many infinite paths.

Regards, WM



Date Subject Author
11/23/09
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12/1/09
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12/1/09
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12/1/09
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12/1/09
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of Bentley College
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12/2/09
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of Bentley College
Marshall
11/27/09
Read Re: Another AC anomaly?
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11/27/09
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11/26/09
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mueckenh@rz.fh-augsburg.de
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11/28/09
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11/26/09
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mueckenh@rz.fh-augsburg.de
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11/28/09
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11/29/09
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mueckenh@rz.fh-augsburg.de
11/29/09
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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
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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?
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11/29/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
11/26/09
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11/26/09
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11/26/09
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11/29/09
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
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/29/09
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11/30/09
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mueckenh@rz.fh-augsburg.de
11/30/09
Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
mueckenh@rz.fh-augsburg.de
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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11/27/09
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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11/27/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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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
Read Re: Another AC anomaly?
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12/22/09
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Read Re: Another AC anomaly?
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12/21/09
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12/27/09
Read Re: Another AC anomaly?
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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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12/12/09
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12/11/09
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mueckenh@rz.fh-augsburg.de
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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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12/10/09
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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
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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
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12/8/09
Read Re: Another AC anomaly?
Virgil
12/10/09
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12/3/09
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12/3/09
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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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12/7/09
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?
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
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?
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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
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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?
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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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12/10/09
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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12/11/09
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
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12/12/09
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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
Read Re: Another AC anomaly?
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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?
Virgil
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Read Re: Another AC anomaly?
Virgil
12/19/09
Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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12/22/09
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Read Re: Another AC anomaly?
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Read Re: Another AC anomaly?
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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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12/27/09
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Virgil
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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12/13/09
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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
Read Re: Another AC anomaly?
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12/5/09
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mueckenh@rz.fh-augsburg.de
12/5/09
Read Re: Another AC anomaly?
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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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12/1/09
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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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anonymous.rubbertube@yahoo.com
11/30/09
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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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