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Topic: Matheology § 246
Replies: 246   Last Post: Apr 26, 2013 2:37 AM

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fom

Posts: 1,969
Registered: 12/4/12
Re: Matheology § 246
Posted: Apr 12, 2013 5:41 AM
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On 4/12/2013 4:27 AM, WM wrote:
> On 12 Apr., 10:41, Virgil <vir...@ligriv.com> wrote:
>> In article
>> <d5b94127-f249-4639-8f2f-9de6dda34...@a6g2000vbm.googlegroups.com>,
>>
>> WM <mueck...@rz.fh-augsburg.de> wrote:

>>> Matheology § 246
>>
>>> Cantor's list contains real numbers r as binary or decimal fractions.
>>> Real numbers, however, are /limits/ of binary or decimal fractions.

>>
>> Real numbers are all certainly expressable as limits of sequences, but
>> so are rationals and integers and naturals.

>
> No objection.
>

>>> For every terminating fraction of r, Cantor obtains a difference
>>> between r and the due terminating fraction of the anti-diagonal d:
>>> r_nn =/= d_n. He concludes that this remains true for the limits of
>>> the list numbers r and d by using the argument: different sequences
>>> have different limits. But it is well known that this argument is not
>>> admissible in proofs because it is false.

>>
>> The Cantor antidiagonal argument does not use the limit properties of
>> sequences at all. In fact his binary sequences of members of {m,w} are
>> not assumed to have any numerical or topological properties at all,

>
> They are assumed to have infinitely many bits. But an infinite
> sequence of bits is not converging (the factors 2^-n are missing).
> Most of them cannot be written by finite expressions. And they cannot
> be written as infinite expressions.
>

>> much
>> lesimits. Each of the Cantor sequences is, in fact, merely a function
>> from |N to {m,w} with no other properties assumed or allowed, except
>> that two such functions are different if the is some n in |N at which
>> they have different values.

>
> Most of them are undefined and undefinable. But in order to remedy
> that problem we use rationals in binary representation. Cantor's
> argument, if valid, has to stand that example.
>
> But it does not.


We use the Euclidean algorithm. We use the fact that
our understanding of that algorithm distinguishes rationals
and that there are sequences with properties that differ
from properties common and distinctive of rational sequences.

We use the same reasoning of the "endlessness" found in finite
constructive mathematics.

In order to distinguish all sequences that potentially
describe rationals it is necessary to admit all
potential sequences.

It must be time to begin drawing crayon marks again.








Date Subject Author
4/12/13
Read Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology § 246
JT
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Virgil
4/12/13
Read Re: Matheology § 246
Ralf Bader
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Virgil
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Virgil
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Scott Berg
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology � 246
Scott Berg
4/13/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology § 246
fom
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology § 246
fom
4/13/13
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fom
4/13/13
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fom
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
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fom
4/13/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology � 246
Virgil
4/12/13
Read Re: Matheology � 246
David C. Ullrich
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
Read Re: Matheology § 246
Ralf Bader
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
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fom
4/12/13
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Virgil
4/13/13
Read Re: Matheology § 246
Ralf Bader
4/14/13
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mueckenh@rz.fh-augsburg.de
4/14/13
Read Re: Matheology § 246
Ralf Bader
4/14/13
Read Re: Matheology � 246
Virgil
4/12/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
Read Re: Matheology § 246
fom
4/12/13
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Virgil
4/12/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/12/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/12/13
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Tanu R.
4/12/13
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dan.ms.chaos@gmail.com
4/13/13
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mueckenh@rz.fh-augsburg.de
4/13/13
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Tanu R.
4/13/13
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Tanu R.
4/13/13
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Tanu R.
4/13/13
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Tanu R.
4/13/13
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Virgil
4/13/13
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mueckenh@rz.fh-augsburg.de
4/13/13
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fom
4/13/13
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Virgil
4/13/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology � 246
Virgil
4/14/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/14/13
Read Re: Matheology � 246
Virgil
4/13/13
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Virgil
4/13/13
Read Re: Matheology § 246
Bergholt Stuttley Johnson
4/13/13
Read Re: Matheology � 246
Virgil
4/14/13
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mueckenh@rz.fh-augsburg.de
4/14/13
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Tanu R.
4/14/13
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Virgil
4/12/13
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Virgil
4/12/13
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Virgil
4/13/13
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fom
4/12/13
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Virgil
4/12/13
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Virgil
4/13/13
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mueckenh@rz.fh-augsburg.de
4/13/13
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Tanu R.
4/13/13
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Virgil
4/13/13
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David C. Ullrich
4/13/13
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mueckenh@rz.fh-augsburg.de
4/13/13
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fom
4/13/13
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mueckenh@rz.fh-augsburg.de
4/13/13
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fom
4/13/13
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Virgil
4/13/13
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fom
4/13/13
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David C. Ullrich
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology § 246
dan.ms.chaos@gmail.com
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
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Virgil
4/14/13
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mueckenh@rz.fh-augsburg.de
4/14/13
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Tanu R.
4/14/13
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Virgil
4/13/13
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Virgil
4/14/13
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David C. Ullrich
4/14/13
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mueckenh@rz.fh-augsburg.de
4/14/13
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fom
4/14/13
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mueckenh@rz.fh-augsburg.de
4/14/13
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fom
4/15/13
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mueckenh@rz.fh-augsburg.de
4/15/13
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Virgil
4/15/13
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fom
4/16/13
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mueckenh@rz.fh-augsburg.de
4/16/13
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Bergholt Stuttley Johnson
4/16/13
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Virgil
4/14/13
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Virgil
4/14/13
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Virgil
4/15/13
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mueckenh@rz.fh-augsburg.de
4/15/13
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Bergholt Stuttley Johnson
4/15/13
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Virgil
4/16/13
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mueckenh@rz.fh-augsburg.de
4/16/13
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Virgil
4/16/13
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mueckenh@rz.fh-augsburg.de
4/16/13
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fom
4/16/13
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Virgil
4/16/13
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fom
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Virgil
4/16/13
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Virgil
4/17/13
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mueckenh@rz.fh-augsburg.de
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fom
4/17/13
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mueckenh@rz.fh-augsburg.de
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fom
4/17/13
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mueckenh@rz.fh-augsburg.de
4/17/13
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fom
4/17/13
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Tanu R.
4/17/13
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Virgil
4/17/13
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fom
4/17/13
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fom
4/17/13
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mueckenh@rz.fh-augsburg.de
4/17/13
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fom
4/17/13
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mueckenh@rz.fh-augsburg.de
4/17/13
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Virgil
4/17/13
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fom
4/17/13
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fom
4/17/13
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Virgil
4/17/13
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fom
4/17/13
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Virgil
4/17/13
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mueckenh@rz.fh-augsburg.de
4/17/13
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Virgil
4/17/13
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mueckenh@rz.fh-augsburg.de
4/17/13
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fom
4/17/13
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Virgil
4/17/13
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Tanu R.
4/17/13
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gus gassmann
4/18/13
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mueckenh@rz.fh-augsburg.de
4/18/13
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fom
4/21/13
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gus gassmann
4/21/13
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Ralf Bader
4/21/13
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fom
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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Ralf Bader
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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Bergholt Stuttley Johnson
4/23/13
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Ralf Bader
4/24/13
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mueckenh@rz.fh-augsburg.de
4/24/13
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Virgil
4/24/13
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Ralf Bader
4/25/13
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mueckenh@rz.fh-augsburg.de
4/25/13
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fom
4/25/13
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Ralf Bader
4/25/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/25/13
Read Re: Matheology § 246
Ralf Bader
4/25/13
Read Re: Matheology § 246
Tanu R.
4/25/13
Read Re: Matheology § 246
Ralf Bader
4/25/13
Read Re: Matheology § 246
Tanu R.
4/26/13
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Bergholt Stuttley Johnson
4/25/13
Read Re: Matheology � 246
Virgil
4/22/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/22/13
Read Re: Matheology § 246
fom
4/22/13
Read Re: Matheology § 246
gus gassmann
4/22/13
Read Re: Matheology § 246
gus gassmann
4/22/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/22/13
Read Re: Matheology § 246
fom
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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fom
4/22/13
Read Re: Matheology � 246
Virgil
4/22/13
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Virgil
4/23/13
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mueckenh@rz.fh-augsburg.de
4/23/13
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fom
4/23/13
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mueckenh@rz.fh-augsburg.de
4/23/13
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fom
4/23/13
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Virgil
4/24/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/24/13
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Virgil
4/23/13
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fom
4/24/13
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mueckenh@rz.fh-augsburg.de
4/24/13
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Virgil
4/24/13
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fom
4/25/13
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Virgil
4/23/13
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Virgil
4/22/13
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Virgil
4/18/13
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Virgil
4/19/13
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mueckenh@rz.fh-augsburg.de
4/19/13
Read Re: Matheology § 246
fom
4/19/13
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fom
4/19/13
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Virgil
4/19/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/19/13
Read Re: Matheology § 246
fom
4/19/13
Read Re: Matheology § 246
fom
4/19/13
Read Re: Matheology � 246
Virgil
4/18/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/18/13
Read Re: Matheology § 246
fom
4/18/13
Read Re: Matheology � 246
Virgil
4/18/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/17/13
Read Re: Matheology � 246
Virgil
4/17/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/17/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology � 246
Virgil
4/17/13
Read Re: Matheology § 246
Bergholt Stuttley Johnson
4/17/13
Read Re: Matheology § 246
Ralf Bader
4/17/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology § 246
Ralf Bader
4/17/13
Read Re: Matheology § 246
Tanu R.
4/18/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology § 246
fom
4/17/13
Read Re: Matheology � 246
Virgil
4/17/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/17/13
Read Re: Matheology � 246
Virgil
4/17/13
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fom
4/15/13
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fom
4/13/13
Read Re: Matheology ? 246
Virgil
4/13/13
Read Re: Matheology ? 246
Tanu R.
4/13/13
Read Re: Matheology ? 246
Tanu R.
4/13/13
Read Re: Matheology ? 246
Tanu R.
4/13/13
Read Re: Matheology ? 246
Virgil
4/13/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/13/13
Read Re: Matheology � 246
Virgil
4/14/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/14/13
Read Re: Matheology § 246
Tanu R.
4/14/13
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology ? 246
Virgil

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