Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Answer to Dik T. Winter
Replies: 441   Last Post: Feb 5, 2013 6:25 AM

 Messages: [ Previous | Next ]
 Dik T. Winter Posts: 7,899 Registered: 12/6/04
Re: Answer to Dik T. Winter
Posted: Jun 3, 2009 10:04 PM

In article <324b4dea-62b3-4a92-b1db-ccc0034649e7@j12g2000vbl.googlegroups.com> WM <mueckenh@rz.fh-augsburg.de> writes:
> On 3 Jun., 04:25, "Dik T. Winter" <Dik.Win...@cwi.nl> wrote:
...
> > > > You think so, but you have to prove that it is valid for infinite
> > > > complete linear sets. Note that "classical logic is obtained from
> > > > finite sets".
> > > > Nowhere in that quote the word linear is mentioned.

> > >
> > > Nowhere in that quote the word union in mentioned. Nevertheless the
> > > logical rules of unions are obtained from unions of finite sets.

> >
> > What is the relevance of this?

>
> The word union and the word linear are not mentioned in the quote.
> Nevertheless the due logica rules were obtained from unions of finite
> sets and linear finite sets.

Yes, obtained from. But that does not mean they are identical. Moreover,
does what Weyl wrote a long time ago still have validity now?

> >
> > > The
> > > logical rules of linear sets are obtained from finite linear sets.

> >
> > Aha, here we get to the heart of the matter. You do not believe in
> > infinite sets (or infinite unions or infinite sets of finite linear
> > sets). That is possible, of course, but does not rule out theories
> > in which those things do exist.

>
> But it does rule out theories which are contradicted by the
> fundamental logical rules. And one of these rules is that a complete
> linear set has a last element.

What fundamental rules of logic are you using? I have never seen such a
logical rule, because logic does not talk about sets.

> > > I never said so. But [*] is [**] & [***]. Therefore [*] differs from
> > > [**] only by the reverse.

> >
> > Being incomprehensible again. The reverse of *what*? The reverse of [**=

> ]
> > is (as I wrote) [***]. You may never have said so, but it is. To recap:
> > [*] En Am: m =< n <==> Am En m =< n
> > [**] En Am: m =< n ==> Am En m =< n
> > [***] En Am: m =< n <== Am En m =< n
> >
> > But you ask as a counterexample something where [**] is true but [*]
> > false. But that is the wrong way around. Whenever [**] is true, [*]
> > is also true. What is contested is that there are case where [***]
> > is true and [*] false.
> > And it is the latter implication that you do use.

>
> No. I use the fact that for complete linear sets always both
> implications are true :
> [**] & [***]. This means that [*] is true.

You just state so without proof.

> If you disagree, then you should come up with a finite linear set for
> which only one implication is true.

Why should I show that for a *finite* linear set? Why not for an *infinite*
linear set? You are *still* thinking that wat is valid for finite things
is also valid for infinite things. So in your opinion:
sum{i = 0..oo} 1/(i!) = lim{n -> oo} sum{i = 0..n} 1/(i!)
is rational, because it is rational for each n, and so your logic requires
that. Also:
lim{n -> oo} 1/n > 0
because it is > 0 for each n, and so should also be > 0 in the infinite case.

Now, what is it. Is it always the case that what is valid for finite things
is also valid for infinite things or not? If it is sometimes true and
sometimes false, I wish you would provide me with the reasons *why* it should
be sometimes true and sometimes false.

> > > > It is not true for the infinite set of naturals.
> > >
> > > That is your claim. It is justified for potential infinity. It is
> > > wrong for complete sets.

> >
> > Now you are using words that are again completely incomprehensible. You
> > have still failed to give a definition of "potential infinity" that is
> > valid within ZF. Moreover, you have not proven (within ZF) that the
> > statement is wrong.

>
> ZF uses potential infinity whenever the validity of
> En Am: m =< n <== Am En m =< n [***]
> for linear sets is denied.

And you still do not answer my question. You fail to give a definition that
is valid in ZF, so I have no idea what you are talking about.

> ZF claims that this denial is correct for complete linear infinite
> sets, but this is a wrong claim, as we can obtain from logic.

What logic? Not the logic as discussed in sci.logic. So you must use your
own logic and logical rules.

> > > > (1) define FISON(n) be the set of naturals from 1 to n, that is:
> > > > {1, ..., n}.
> > > > (2) A{m in N} E(n in N} such that FISON(m) subset FISON(n), trivial,
> > > > take n = m + 1.
> > > > (3) E{n in N} A{m in N} such that FISON(m) subset FISON(n), trivially
> > > > false, take m = n + 1.
> > > > Which part of this proof is wrong?

> > >
> > > The proof is correct for potential infinity. The proof is incorrect
> > > for actual infinity.

> >
> > Can you provide me with definitions within ZF that shows the difference?

> > > In that latter case you need not take an n that
> > > is surpassed by m. Why don't you start with an n that has no greater
> > > m?

> >
> > Because there is no such n. Remember: the set of natural numbers has no
> > largest element in ZF.

>
> That is the logic of potential infinity, i.e., of incomplete sets.

Eh? As far as I know logic is *not* about sets. It is about axioms,
statements and inference rules.

> In Cantor's diagonal argument you can use the same logic : There is no
> last line, therefore there is always a line beyond the checked lines.
> But there you don't.

Because you do not check the lines in order. It is always your basic
assumption that you first check the first line and after that the next line.
That is wrong. You simply give a definition of a new number so it is clear
that it will be different from each of the omega lines, without checking
directly any of them.

> > Oh. I think that the term "classical logic" has changed a bit since the
> > last time you looked at it. And, if you refer to Weyl's quote, he stated
> > that classical logic was *derived* from the logic on finite sets, not that
> > it was *identical* to logic on finite sets.

>
> When it is derived from logic of finite sets, then it is not the
> reverse of the logic of finite sets. But that is claimed in ZF.

It is *not* the reverse of the logic of finite sets. For finite sets it is
identical.

> > > There are many finite sets with many special properties that follow
> > > from classical logic. One of them is that a complete linear set has a
> > > lst element.

> >
> > Not "a complete linear set". But "a complete finite linear set". Why do
> > you drop the word "finite" in the second sentence? To obfuscate?

>
> The logic is derived from finite complete linear sets. If logic is to
> be applied to infinite complete linear sets, then we cannot change it
> to the opposite.

Ok. The logic of finite complete sums of rational elements gives that the
sum is rational. Using your logic we get that the complete (i.e. in the
limit) sum of rational elements is also rational. And so by that logic, e,
pi and whatever are rational, and all numbers we do use are rational. I may
note that in this sense, the limit *is* the sum of the complete set of
elements.

> Either those sets obey that logic or they do not
> exist in a science that is subject to the application of logic.

Ah, so 'e', 'pi', 'sqrt(2)' do not exist. Still I think you use at least
one of them on occasion.

> In fact thoses sets contradict their own existence under the
> government of logic.

So 'sqrt(2)' contradicts itself under the government of logic. I think you
are a few thousand years behind.

> >
> > > You drop the completeness condition in certain cases but you assume it
> > > in case of Cantor's proof. That is cheating.

> >
> > You again misunderstand the proof completely. There is an assumption that
> > a complete list is provided and that is proven false.

>
> Small wonder. There cannot be a complete list, because the existence
> of a complete infinite linear set like N contradicts logic.

Apparently your logic. What are the rules of inference in your logic?
And, also apparently, in your logic the length of the diagonal of a square
with sides with size 1 does not exist.

> > > State before beginning whether the set that you assume is complete and
> > > static, i.e., every element is actually existing, or potentially
> > > infinite.

> >
> > What in the world is a "potentially infinite element"? And, in ZF all
> > sets are static, there is no place for non-static sets.

>
> That is a blatant lie.

Eh? What is the lie? I just state that in ZF there are no non-static sets.
That is all. So you think that is false? If so, prove it, please. BTW, you
are getting offensive.

> Every static linear set has a last element.

As that is false in ZF...

> If you say you cannot choose the last elemement because there is none,
> then you apply potentially infinite sets.

You have still not provided a definition of "potentially infinite sets" in
ZF, so I cannot comment on this.

> Then for every element that
> you choose there is a larger one. If it has been there all time, why

Because in ZF a set does not need to have a last element. So whatever
element you chose, there is *always* a larger one.

> > > > (1) define FISON(n) be the set of naturals from 1 to n, that is:
> > > > {1, ..., n}.
> > > > (2) A{m in N} E(n in N} such that FISON(m) subset FISON(n), trivial,
> > > > take n = m + 1.
> > > > (3) E{n in N} A{m in N} such that FISON(m) subset FISON(n),
> > > > trivially false, take m = n + 1.

> >
> > > > Strange, I give above a proof that it does not hold. I did not use
> > > > "actual infinity" nor "potentially infinity"

> > >
> > > That is the point! You use the absence of element m when you choose n
> > > = m - 1.

> >
> > Where in the proof do I use an element m when I chose n = m - 1? In
> > the proof I chose only elements that *follow* given elements, as is
> > assured by the axiom of infinity.

>
> That is assured by the axiom of potential infinity.

What *is* potential infinity in ZF? Nothing in ZF talks about that.

> If all elemeents
> were there, why then do you have to select one that is diminishingly
> small compared to most ?

Because there is no largest? You know, the axiom of infinity assures that
there is a set that has not a largest element.

> > > But you use the non-absence of m when you execute Cantor's
> > > proof. Then you do not admit that for every FISON(n) there is an m
> > > == n + 1 that is not in the proof.

> >
> > This is really incomprehensible.

>
> So it is, but you do it nevertheless.

I have no idea. What is the "non-absence of m when I execute Cantor's proof"?
What do you mean with "there is an m == n + 1 that is not in the proof"? Your
statements are simply incomprehensible.

> > > > > Only
> > > > > potentially infinite sets do not. But you mix up things. You
> > > > > claim the existence of a complete linear set but disregard the
> > > > > necessary consequence of completeness or linearity, namely the
> > > > > validity of [*].

> > > >
> > > > Why is that a necessary consequence? Because you want it to be so?
> > > > Can you give a *mathematical* reason?

> > >
> > > Every finite linear set obeys [*]. That is the mathematical reason.

> >
> > Clearly, the only reason is that you want it to be so.

>
> Show me a finite linear set that does not obey [*]. Or try to explain
> why in your opinion this law must be reversed for infinite sets which
> are actually existing, i.e., every elemenmt of them can be chosen for
> comparison with others.

See my examples above about 'sqrt(2)'. There is no reversal of the law, what
happens is what happens in finite cases is not necessarily valid in infinite
cases. You have to prove that what is valid in finite cases is also valid
in the infinite case, something you always omit.
--
dik t. winter, cwi, science park 123, 1098 xg amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~dik/

Date Subject Author
5/27/09 mueckenh@rz.fh-augsburg.de
5/27/09 Dik T. Winter
5/27/09 mueckenh@rz.fh-augsburg.de
5/27/09 mueckenh@rz.fh-augsburg.de
5/27/09 Virgil
5/27/09 mueckenh@rz.fh-augsburg.de
5/27/09 Virgil
5/27/09 Virgil
5/28/09 mueckenh@rz.fh-augsburg.de
5/28/09 Virgil
5/28/09 Dik T. Winter
5/28/09 G. Frege
5/28/09 Jesse F. Hughes
5/29/09 Dik T. Winter
5/29/09 G. Frege
5/29/09 Dik T. Winter
5/30/09 G. Frege
5/30/09 Jesse F. Hughes
6/2/09 Dik T. Winter
5/30/09 Jesse F. Hughes
6/1/09 mueckenh@rz.fh-augsburg.de
6/1/09 Jesse F. Hughes
6/1/09 Virgil
6/2/09 george
6/2/09 Denis Feldmann
6/2/09 Dik T. Winter
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 William Hughes
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 William Hughes
6/11/09 Guest
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 William Hughes
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 William Hughes
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 William Hughes
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 William Hughes
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 William Hughes
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/14/09 Owen Jacobson
6/14/09 Virgil
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/13/09 mueckenh@rz.fh-augsburg.de
6/13/09 Virgil
6/13/09 William Hughes
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 William Hughes
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 William Hughes
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 William Hughes
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 William Hughes
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 William Hughes
6/15/09 mueckenh@rz.fh-augsburg.de
6/15/09 Virgil
6/15/09 William Hughes
6/15/09 mueckenh@rz.fh-augsburg.de
6/15/09 Virgil
6/15/09 William Hughes
6/15/09 mueckenh@rz.fh-augsburg.de
6/15/09 Virgil
6/15/09 mueckenh@rz.fh-augsburg.de
6/15/09 Virgil
6/15/09 William Hughes
6/15/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
6/16/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
2/5/13
6/16/09 William Hughes
6/16/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
6/16/09 William Hughes
6/16/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
6/16/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
6/16/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
7/17/09 scriber77@yahoo.com
6/17/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 William Hughes
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Virgil
6/17/09 mueckenh@rz.fh-augsburg.de
6/17/09 Owen Jacobson
6/17/09 Virgil
6/17/09 William Hughes
6/18/09 mueckenh@rz.fh-augsburg.de
6/18/09 Virgil
6/18/09 William Hughes
6/18/09 mueckenh@rz.fh-augsburg.de
6/18/09 Virgil
6/18/09 William Hughes
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 William Hughes
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 William Hughes
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 William Hughes
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 William Hughes
6/20/09 mueckenh@rz.fh-augsburg.de
6/20/09 Virgil
6/20/09 William Hughes
6/20/09 mueckenh@rz.fh-augsburg.de
6/20/09 Virgil
6/20/09 William Hughes
6/20/09 mueckenh@rz.fh-augsburg.de
6/20/09 Virgil
6/20/09 William Hughes
6/20/09 george
6/20/09 george
6/20/09 Virgil
6/20/09 george
6/2/09 george
6/2/09 Jesse F. Hughes
6/3/09 george
6/3/09 mueckenh@rz.fh-augsburg.de
6/3/09 george
6/3/09 Virgil
6/3/09 Guest
6/3/09 Marshall
6/3/09 Jack Markan
6/3/09 Dik T. Winter
6/3/09 Guest
6/7/09 mueckenh@rz.fh-augsburg.de
6/7/09 Virgil
6/7/09 mueckenh@rz.fh-augsburg.de
6/7/09 Virgil
6/8/09 mueckenh@rz.fh-augsburg.de
6/8/09 Virgil
6/9/09 mueckenh@rz.fh-augsburg.de
6/9/09 Virgil
6/9/09 William Hughes
6/9/09 Virgil
6/10/09 mueckenh@rz.fh-augsburg.de
6/10/09 Virgil
6/10/09 mueckenh@rz.fh-augsburg.de
6/10/09 Virgil
6/10/09 mueckenh@rz.fh-augsburg.de
6/10/09 William Hughes
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 William Hughes
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Rainer Rosenthal
6/11/09 Virgil
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 Dik T. Winter
6/11/09 William Hughes
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 Dik T. Winter
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/19/09 Dik T. Winter
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/19/09 Virgil
6/22/09 Dik T. Winter
6/25/09 mueckenh@rz.fh-augsburg.de
6/25/09 Virgil
6/30/09 Dik T. Winter
6/30/09 mueckenh@rz.fh-augsburg.de
7/1/09 Dik T. Winter
7/1/09 Guest
7/2/09 mueckenh@rz.fh-augsburg.de
7/2/09 Virgil
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Rainer Rosenthal
6/12/09 Virgil
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Guest
6/12/09 Rainer Rosenthal
6/12/09 Virgil
6/3/09 george
6/3/09 Dik T. Winter
5/28/09 William Hughes
5/29/09 mueckenh@rz.fh-augsburg.de
5/29/09 Virgil
5/30/09 mueckenh@rz.fh-augsburg.de
5/30/09 Virgil
5/31/09 mueckenh@rz.fh-augsburg.de
5/31/09 Virgil
6/2/09 Dik T. Winter
6/2/09 Virgil
6/3/09 mueckenh@rz.fh-augsburg.de
6/3/09 Virgil
6/7/09 mueckenh@rz.fh-augsburg.de
6/7/09 Virgil
6/3/09 mueckenh@rz.fh-augsburg.de
6/3/09 Virgil
6/3/09 Dik T. Winter
6/7/09 mueckenh@rz.fh-augsburg.de
6/7/09 Virgil
6/11/09 Dik T. Winter
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 Dik T. Winter
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/19/09 Dik T. Winter
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/22/09 Dik T. Winter
6/25/09 mueckenh@rz.fh-augsburg.de
6/25/09 Virgil
6/30/09 Dik T. Winter
6/30/09 mueckenh@rz.fh-augsburg.de
6/30/09 MeAmI.org
6/30/09 Virgil
7/1/09 Dik T. Winter
7/2/09 G. Frege
7/2/09 Dik T. Winter
7/2/09 herb z
7/2/09 Dik T. Winter
7/2/09 herb z
7/2/09 G. Frege
7/3/09 Aatu Koskensilta
7/3/09 Daryl McCullough
7/2/09 G. Frege
7/2/09 G. Frege
7/2/09 G. Frege
7/2/09 Jack Markan
7/2/09 G. Frege
7/2/09 Jack Markan
7/2/09 G. Frege
7/2/09 Jack Markan
7/3/09 Dik T. Winter
7/3/09 G. Frege
7/3/09 Dik T. Winter
7/3/09 G. Frege
7/4/09 Aatu Koskensilta
7/6/09 Dik T. Winter
7/6/09 G. Frege
7/6/09 Dik T. Winter
7/6/09 Jesse F. Hughes
7/3/09 mueckenh@rz.fh-augsburg.de
7/3/09 Virgil
7/2/09 G. Frege
7/2/09 Virgil
7/2/09 mueckenh@rz.fh-augsburg.de
7/2/09 ross.finlayson@gmail.com
7/2/09 mueckenh@rz.fh-augsburg.de
7/2/09 Jack Markan
7/2/09 Jack Markan
7/2/09 Virgil
7/2/09 ross.finlayson@gmail.com
7/2/09 Jack Markan
7/2/09 ross.finlayson@gmail.com
7/6/09 Jack Markan
7/6/09 ross.finlayson@gmail.com
7/6/09 Jack Markan
7/6/09 ross.finlayson@gmail.com
7/6/09 Jack Markan
6/8/09 mueckenh@rz.fh-augsburg.de
6/8/09 Virgil
6/9/09 Jack Markan
6/9/09 Jack Markan
6/9/09 Virgil
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 William Hughes
6/11/09 Virgil
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/12/09 herb z
6/12/09 Virgil
6/12/09 Owen Jacobson
6/12/09 Virgil
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/11/09 Virgil
6/11/09 Dik T. Winter
6/11/09 William Hughes
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 YBM
6/11/09 Virgil
6/11/09 Dik T. Winter
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/12/09 mueckenh@rz.fh-augsburg.de
6/12/09 Virgil
6/19/09 Dik T. Winter
6/19/09 mueckenh@rz.fh-augsburg.de
6/19/09 Virgil
6/22/09 Dik T. Winter
6/25/09 mueckenh@rz.fh-augsburg.de
6/25/09 Virgil
6/30/09 Dik T. Winter
6/30/09 Virgil
6/30/09 Guest
6/30/09 mueckenh@rz.fh-augsburg.de
7/1/09 Dik T. Winter
6/11/09 mueckenh@rz.fh-augsburg.de
6/11/09 Virgil
6/3/09 mueckenh@rz.fh-augsburg.de
6/3/09 Virgil
6/3/09 Dik T. Winter
6/7/09 mueckenh@rz.fh-augsburg.de
6/7/09 Virgil
6/11/09 Dik T. Winter
6/3/09 george
5/29/09 mueckenh@rz.fh-augsburg.de
5/29/09 Virgil
5/30/09 mueckenh@rz.fh-augsburg.de
5/30/09 Virgil
5/31/09 mueckenh@rz.fh-augsburg.de
5/31/09 Virgil
5/31/09 Guest
5/27/09 Virgil
5/28/09 mueckenh@rz.fh-augsburg.de
5/28/09 Virgil
5/30/09 mueckenh@rz.fh-augsburg.de
5/30/09 Virgil
5/30/09 Virgil
5/30/09 Virgil
5/30/09 Virgil
5/27/09 mueckenh@rz.fh-augsburg.de
5/27/09 David C. Ullrich
5/27/09 Virgil
5/27/09 Guest
5/27/09 mueckenh@rz.fh-augsburg.de
5/28/09 mueckenh@rz.fh-augsburg.de
5/28/09 Virgil
5/29/09 Peter Webb
5/29/09 Virgil
5/29/09 mueckenh@rz.fh-augsburg.de
5/29/09 Virgil
5/29/09 Peter Webb
5/30/09 mueckenh@rz.fh-augsburg.de
5/30/09 Virgil
5/30/09 Peter Webb
5/31/09 mueckenh@rz.fh-augsburg.de
5/31/09 Virgil
5/31/09 mueckenh@rz.fh-augsburg.de
5/31/09 Peter Webb
5/31/09 Virgil
6/1/09 mueckenh@rz.fh-augsburg.de
6/1/09 David Bernier
6/1/09 Jack Markan
6/1/09 Virgil
6/2/09 george
6/1/09 mueckenh@rz.fh-augsburg.de
6/1/09 Virgil
6/2/09 george
6/2/09 george
6/2/09 george
6/3/09 george
6/12/09 Guest
2/5/13
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/14/09 mueckenh@rz.fh-augsburg.de
6/14/09 Virgil
6/15/09 Owen Jacobson
6/15/09 Virgil
6/15/09 mueckenh@rz.fh-augsburg.de
6/15/09 Owen Jacobson
6/15/09 Virgil
6/15/09 Virgil
6/16/09 MeAmI.org
6/16/09 mueckenh@rz.fh-augsburg.de
6/16/09 Virgil
6/18/09 mueckenh@rz.fh-augsburg.de
6/18/09 Virgil
6/20/09 Guest