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

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fom

Posts: 1,968
Registered: 12/4/12
Re: Matheology § 246
Posted: Apr 18, 2013 2:23 AM
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On 4/18/2013 1:20 AM, WM wrote:
> On 18 Apr., 01:19, Virgil <vir...@ligriv.com> wrote:
>

>>> The set A can also be understood as a set of Fisons:
>>> {1, 2, 3, ...} = {1, 1, 2, 1, 2, 3, ...}

>
>>> When changing this to {(1), (1, 2), (1, 2, 3), ...} nothing is added.
>>
>> WM claims {(1), (1, 2), (1, 2, 3), ...} = {1, 2, 3, ...}?

>
> No, that is not true in the framework of set theory. But it is true
> that both sets contain the same numbers. And its numbers (and figures)
> that mathematics is built upon.


Typically the pure set theory of ZF does
not have urelements.

But, since we are counting urelements....


WM is an unabashed ultrafinitist who refuses to fix
a largest finite number. Each "n" in his description
depends on the subsequence of triangular numbers.

> F(n)=Sum_i(1..n)(i)
>
> 1 :=> 1
> 2 :=> 3
> 3 :=> 6
> 4 :=> 10
>
> and so on


According to Brouwerian intuitionistic reasoning,
when WM's construction reaches the point where
the sequence of triangular numbers exceeds the
ultrafinitist limit, the contradiction nullifies
the construction.

This is WM's model of mathematics:

http://en.wikipedia.org/wiki/Finite_model_property

until he reaches his contradiction and
it vanishes.

=====================================

The triangular numbers correspond with
the number of 'marks' representing numerals
or significant denotations occurring in any
of WM' representations of the form:

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

-------------------------------------

This number of 'marks' satisfies a structural
feature of the natural numbers called a
directed set:

Defintion

A binary relation >= in a set D is said
to direct D if and only if D is nonempty
and the following three conditions are
satisfied:

DS1)

If a is an element of D, then a>=a

DS2)

If a, b, c are elements of D such
that a>=b and b>=c, then a>=c

DS3)

If a and b are elements of D, then there
exists an element c of D such that c>=a
and c>=b


So, WM's geometric reasoning for any given
n obtains a finite model domain with its
cardinality given by the associated
triangular number. The triangular number
is the "element c" of condition DS3 from
the definition.

-------------------------------------

Finally, Brouwer's explanation for finitary
reasoning is used because WM refuses to
commit to any mathematical statement with
coherent consistent usage.

Brouwer distinguishes between results with
regard to 'endless', 'halted' and
'contradictory' in his explanations

"A set is a law on the basis of
which, if repeated choices of
arbitrary natural numbers are made,
each of these choices either
generates a definite sign series,
with or without termination of the
process, or brings about the
inhibition of the process together
with the definitive annihilation
of its result."

WM cannot be an ultrafinitist and
expect others to not hold him to
task for it. In constrast to
Brouwer, he repeatedly states
that there is absolutely no
completed infinity. Therefore,
there must be a maximal natural
number for his model of
mathematics. Beyond that
number, there is no mathematics.

That is WM's belief as surmised
from statements and reasoning
as opposed to what he says with
rhetoric.





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
Read Re: Matheology § 246
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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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
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
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fom
4/12/13
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Virgil
4/12/13
Read Re: Matheology § 246
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
Read Re: Matheology § 246
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
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Virgil
4/14/13
Read Re: Matheology § 246
mueckenh@rz.fh-augsburg.de
4/14/13
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Virgil
4/13/13
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Virgil
4/13/13
Read Re: Matheology § 246
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
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
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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
Read Re: Matheology § 246
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
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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
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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
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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
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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
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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
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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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Virgil
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
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
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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
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
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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
Read Re: Matheology ? 246
Tanu R.
4/13/13
Read Re: Matheology ? 246
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
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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