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

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mueckenh@rz.fh-augsburg.de

Posts: 16,037
Registered: 1/29/05
Re: Matheology § 246
Posted: Apr 13, 2013 7:50 AM
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On 13 Apr., 13:30, Dan <dan.ms.ch...@gmail.com> wrote:
>  > The set of finite things has larger cardinality m than any finite
>

> > number n:
> > For all n exists m : m > n

>
> True, if m is indeed, a cardinality, and not a finite number .
>

> > But there is no cardinality m that is larger than every finite number
> > n
> > Exists m for all n : m > n
> > is wrong.

>
> http://en.wikipedia.org/wiki/Axiom_of_infinity
> The axiom of infinity, one of the basic axioms of set theory, says
> precisely that m exists .


No. The axiom of infinity has been invented by Zermelo who confessed
that he had taken it from Dedekind, who has it invented independently
from but anticipated by Bolzano. It is explained as follows: I can
think an idea. I can think that I can think an idea. I can think
that ... and so on. Obviously the set of ideas (or, as Bolzano put it,
of theorems) is potentiall infinite. It is not actually infinite. So
the axiom of infinity is based upon potential infinity. Only set
theorists have confused the "there is a set ..." with actual or
finished infinity.


> If you reject it,not only are we left unable to talk about real
> numbers ,banning them as invalid, we are left unable to talk about
> your binary tree .


No. I assume it, when discussing here. Otherwise any discussion would
be in vain.
>
> Because it contains ALL Finite initial segments , the binary tree
> should not exist . It's wrong .
>


In fact "all FISONs" are als an actually infinite set - and as such do
not exist. What exists is a FISON and for that there is a longer one.
But already here we face a problem: The set

1
2,1
3,2,1
...

does not contain its limit |N as a line, but obviously contains its
limit |N in the first (and every other) column. On the other hand we
can prove, by the construction of this set, that everything that is in
the list, is in one line.



> We've been using 'magic'/infinity  in our mathematics up until now .

Euler, Gauss, and Weierstarss did not use it. Their mathematics was
better than the present one.

> Opinions on infinity are varied, but the paradoxes you keep rambling
> about DON'T EXIST FOR ANYONE ELSE .Nor do you have any results to
> show.


Have you overlook my repeated question?
A) {1} U {1, 2} U {1, 2, 3} U ...
B) {1}, {1, 2}, {1, 2, 3}, ...
C) {1}, {1} U {1, 2}, {1} U {1, 2} U {1, 2, 3}, {1} U {1, 2} U {1, 2,
3} U ..., ...
Is A contained in C?
Is anything in C that is not in B?
>
> "Leibniz, one of the co-inventors of infinitesimal calculus,
> speculated widely about infinite numbers and their use in mathematics.


He had a split tongue in this respect. There are quotes in favour and
quotes against actual infinity. Cantor himself named him among the
opponents of actual infinity: D'ALEMBERT, ARISTOTELES, CAUCHY,
CAVALIERI, FULLERTON, GALILEI, GAUSS, GERDIL, GOUDIN, GULDIN,
LAGRANGE, LEIBNIZ, MOIGNO, NEWTON, PERERIUS, PESCH, RENOUVIER,
SANSEVERINO, TONGIORGI, TORRICELLI, ZIGLIARA.

Regards, WM



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
Read Re: Matheology § 246
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
Read Re: Matheology § 246
fom
4/12/13
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Virgil
4/13/13
Read Re: Matheology § 246
Ralf Bader
4/14/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/14/13
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Ralf Bader
4/14/13
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Virgil
4/12/13
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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
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fom
4/12/13
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Virgil
4/12/13
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dan.ms.chaos@gmail.com
4/12/13
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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
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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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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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Virgil
4/13/13
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Virgil
4/13/13
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Bergholt Stuttley Johnson
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
4/12/13
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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
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fom
4/13/13
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Virgil
4/13/13
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fom
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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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dan.ms.chaos@gmail.com
4/13/13
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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
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fom
4/14/13
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mueckenh@rz.fh-augsburg.de
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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
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Virgil
4/16/13
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mueckenh@rz.fh-augsburg.de
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fom
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Virgil
4/16/13
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fom
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Virgil
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mueckenh@rz.fh-augsburg.de
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fom
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fom
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mueckenh@rz.fh-augsburg.de
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fom
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Tanu R.
4/17/13
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Virgil
4/17/13
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fom
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fom
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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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Virgil
4/17/13
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fom
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fom
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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
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mueckenh@rz.fh-augsburg.de
4/25/13
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Ralf Bader
4/25/13
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Tanu R.
4/25/13
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Ralf Bader
4/25/13
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Tanu R.
4/26/13
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Bergholt Stuttley Johnson
4/25/13
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Virgil
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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fom
4/22/13
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gus gassmann
4/22/13
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gus gassmann
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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fom
4/22/13
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mueckenh@rz.fh-augsburg.de
4/22/13
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fom
4/22/13
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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
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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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4/18/13
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Virgil
4/19/13
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mueckenh@rz.fh-augsburg.de
4/19/13
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fom
4/19/13
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fom
4/19/13
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Virgil
4/19/13
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mueckenh@rz.fh-augsburg.de
4/19/13
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fom
4/19/13
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fom
4/19/13
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Virgil
4/18/13
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mueckenh@rz.fh-augsburg.de
4/18/13
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fom
4/18/13
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Virgil
4/18/13
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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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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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Bergholt Stuttley Johnson
4/17/13
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Ralf Bader
4/17/13
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fom
4/17/13
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Ralf Bader
4/17/13
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Tanu R.
4/18/13
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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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mueckenh@rz.fh-augsburg.de
4/17/13
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Virgil
4/17/13
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fom
4/15/13
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fom
4/13/13
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Virgil
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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Virgil
4/13/13
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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
Read Re: Matheology � 246
Virgil
4/13/13
Read Re: Matheology ? 246
Virgil

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