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 ]
 Guest
Re: Natural numbers are uniquely defined
Posted: May 27, 2009 4:55 AM

WM wrote:
> On 26 Mai, 21:49, Virgil <virg...@nowhere.com> wrote:
>

> > > If we define:
> >
> > > 1 is a natural number
> > > and
> > > with n also n+1 is a natural number
> > > and
> > > N is the smallest set that satisfies both conditions

> >
> > > then N is uniquely specified.
> > > Of course there can be different models for N and there can be
> > > different names for the elements of N. But that does not matter. The
> > > natural numbers do not enter mathematics because someone "defines"
> > > them, names them, or makes models of them, but because the natural
> > > numbers are simply existing and mathematics is built upon them.

>
> > But according to WM, no such thing as N can exist.
> > So WM wold throw out the naturals on which so much is built.

>
> The question is not whether the complete set of all naturals exists.
> That question alrady is nearly as ridiculous as any affirmative
>
> The question is whether we could inform someone who does not yet know,
> what we understand by the sequence of natural numbers.
>
> In order to answer this question, we need not wait until SETI gets
> contact. We can answer it in every first class of every elementary
> school. Of course we can inform any child with average intelligence
> what we understand by this sequence 1, 2, 3, ...
>
> Only logicians seem to see problems where no problems are. (As some
> kind of compensation they see no problems where problems are.)
>
> Of course this sequence 1, 2, 3, ... is uniquely defined, because it
> is possible to inform any intelligent being about it. There is no the
> slightest difference between the idea of N and the idea of a sonata or
> pi.
>
> Regards, WM
>
> On 26 Mai, 23:09, Virgil <virg...@nowhere.com> wrote:

> > In article
> >
> >
> >
> >
> >
> >  WM <mueck...@rz.fh-augsburg.de> wrote:

> > > On 25 Mai, 17:40, WM <mueck...@rz.fh-augsburg.de> wrote:
> > > > ... classical logic was abstracted from the mathematics of finite sets
> > > > and their subsets .... Forgetful of this limited origin, one
> > > > afterwards mistook that logic for something above and prior to all
> > > > mathematics, and finally applied it, without justification, to the
> > > > mathematics of infinite sets. [H. Weyl].

> >
> > > > One example is this. For infinite sets with a linear ordering ³=<² the
> > > > implication
> > > > En Am: m =< n ==> Am En m =< n  (1)
> > > > is held correct, but not the equivalence
> > > > En Am: m =< n <==> Am En m =< n   (2)
> > > > For any finite set with linear ordering however, (2) is true. The
> > > > reason is that all elements of a finite set are subject to
> > > > investigation. Therefore, if in ³completed², i.e., ³actual² infinity,
> > > > as used in set theory, all elements are available, then also (2)
> > > > should be used. (2) can only be false, if potentially infinite sets
> > > > are considered, i.e., non-static sets which are never complete but
> > > > allow that elements can be added.

> >
> > But non-static sets do not exist in any mathematical set theory.

>
> They do not exist in what is commonly called ste theory and what is
> eternally false mathematics.
>
> Regards, WM

WM: I offer this text as further proof of polynomial time
Exchange 2. Newsgroup 3. Link Exchange 4.   Blogs   5.  Contest
6. MathWorks.com ? About the MATLAB Newsgroup ? Post A New
Watch List What is a Watch List? Thread Subject: An exact
simplification challenge - 91 (eerie PolyGamma) Subject: An exact
simplification challenge - 91 (eerie PolyGamma) From: Vladimir
Bondarenko Date: 25 May, 2009 03:23:31 Message: 1 of 6 Reply to this
message Add author to My Watch List View original format Flag as
spam Hello,              - PolyGamma[0, 1 + I]              -
PolyGamma[0, 1 - I]              - PolyGamma[0, 3/2 +
I]              - PolyGamma[0, 3/2 - I]              + 2 PolyGamma[0,
2 + 2 I]              + 2 PolyGamma[0, 2 - 2 I]              + (1/2 +
I) PolyGamma[1, 1 + I]              + (1/2 - I) PolyGamma[1, 1 -
I]              - (1/2 + I) PolyGamma[1, 3/2 + I]              - (1/2
- I) PolyGamma[1, 3/2 - I]              + (2 + 4 I) PolyGamma[1, 2 + 2
I]              + (2 - 4 I) PolyGamma[1, 2 - 2 I]              - 2 Re
[I PolyGamma[1, 1 + I]]              + 2 Re[I PolyGamma[1, 1 -
I]]                                ?Folks, please give not just the
Mathematical Directorhttp://www.cybertester.com/ Cyber Tester
Ltd.----------------------------------------------------------"We must
understand that technologieslike these are the way of the
future."----------------------------------------------------------
Subject: An exact simplification challenge - 91 (eerie PolyGamma)
From: Martin Musatov Date: 25 May, 2009 03:36:14 Message: 2 of 6
Reply to this message Add author to My Watch List View original
format Flag as spam Vladimir Bondarenko wrote:> Hello,>> -
PolyGamma[0, 1 + I]> - PolyGamma[0, 1 - I]> - PolyGamma[0, 3/2 + I]> -
PolyGamma[0, 3/2 - I]> + 2 PolyGamma[0, 2 + 2 I]> + 2 PolyGamma[0, 2 -
2 I]> + (1/2 + I) PolyGamma[1, 1 + I]> + (1/2 - I) PolyGamma[1, 1 - I]
> - (1/2 + I) PolyGamma[1, 3/2 + I]> - (1/2 - I) PolyGamma[1, 3/2 - I]
> + (2 + 4 I) PolyGamma[1, 2 + 2 I]> + (2 - 4 I) PolyGamma[1, 2 - 2 I]
> - 2 Re[I PolyGamma[1, 1 + I]]> + 2 Re[I PolyGamma[1, 1 - I]]>> ?>>

Vladimir Bondarenko>> Co-founder, CEO, Mathematical Director>>
http://www.cybertester.com/ Cyber Tester Ltd.>>
---------------------------------------------------------->> "We must
understand that technologies> like these are the way of the future.">>
----------------------------------------------------------People, did
I or did I not call it: "eerie effectiveness". Googlesearch sci.math:
"Musatov" and "Eerie". Want to keep going? I enjoyit. It keeps getting
more gratifying each passing day, like puttingpennies into a piggy
bank. Subject: An exact simplification challenge - 91 (eerie
PolyGamma) From: Martin Musatov Date: 25 May, 2009 03:40:46 Message: 3
of 6 Reply to this message Add author to My Watch List View
original format Flag as spam (C)2009:Here you go folks, call me
the information prophet what youare witnessing is simple P=NP
mathematics over large data sets:"Eerie" isn't it?...The
"Effectiveness"...Martin Musatov wrote:> Vladimir Bondarenko wrote:> >
Hello,> >> > - PolyGamma[0, 1 + I]> > - PolyGamma[0, 1 - I]> > -
PolyGamma[0, 3/2 + I]> > - PolyGamma[0, 3/2 - I]> > + 2 PolyGamma[0, 2
+ 2 I]> > + 2 PolyGamma[0, 2 - 2 I]> > + (1/2 + I) PolyGamma[1, 1 + I]
> > + (1/2 - I) PolyGamma[1, 1 - I]> > - (1/2 + I) PolyGamma[1, 3/2 +
I]> > - (1/2 - I) PolyGamma[1, 3/2 - I]> > + (2 + 4 I) PolyGamma[1, 2
+ 2 I]> > + (2 - 4 I) PolyGamma[1, 2 - 2 I]> > - 2 Re[I PolyGamma[1, 1
+ I]]> > + 2 Re[I PolyGamma[1, 1 - I]]> >> > ?> >> > Folks, please
give not just the answer but the processing.> >> > Cheers,> >> >
Vladimir Bondarenko> >> > Co-founder, CEO, Mathematical Director> >> >
http://www.cybertester.com/ Cyber Tester Ltd.> >> >
----------------------------------------------------------> >> > "We
must understand that technologies> > like these are the way of the
future."> >> >
----------------------------------------------------------> People,
did I or did I not call it: "eerie effectiveness". Google> search
sci.math: "Musatov" and "Eerie". Want to keep going? I enjoy> it. It
keeps getting more gratifying each passing day, like putting> pennies
into a piggy bank.Martin MusatovFounderMeAmI.org Subject: An
exact simplification challenge - 91 (eerie PolyGamma) From:
clicliclic@freenet.de Date: 25 May, 2009 18:32:02 Message: 4 of 6
Reply to this message Add author to My Watch List View original
format Flag as spam Vladimir Bondarenko schrieb:>> - PolyGamma[0,
1 + I]> - PolyGamma[0, 1 - I]> - PolyGamma[0, 3/2 + I]> - PolyGamma[0,
3/2 - I]> + 2 PolyGamma[0, 2 + 2 I]> + 2 PolyGamma[0, 2 - 2 I]> + (1/2
+ I) PolyGamma[1, 1 + I]> + (1/2 - I) PolyGamma[1, 1 - I]> - (1/2 + I)
PolyGamma[1, 3/2 + I]> - (1/2 - I) PolyGamma[1, 3/2 - I]> + (2 + 4 I)
PolyGamma[1, 2 + 2 I]> + (2 - 4 I) PolyGamma[1, 2 - 2 I]> - 2 Re[I
PolyGamma[1, 1 + I]]> + 2 Re[I PolyGamma[1, 1 - I]]>> ?>This simple
challenge seems to be specifically made for Derive 6.10:-POLYGAMMA
(0,1+#i)-POLYGAMMA(0,1-#i)-POLYGAMMA(0,3/2+#i)-POLYGAM~MA(0,3/2-#i)
+2*POLYGAMMA(0,2+2*#i)+2*POLYGAMMA(0,2-2*#i)+(1/2+#i~)*POLYGAMMA
(1,1+#i)+(1/2-#i)*POLYGAMMA(1,1-#i)-(1/2+#i)*POLYGAMM~A(1,3/2+#i)-(1/2-
#i)*POLYGAMMA(1,3/2-#i)+(2+4*#i)*POLYGAMMA(1,2+~2*#i)+(2-4*#i)
*POLYGAMMA(1,2-2*#i)-2*RE(#i*POLYGAMMA(1,1+#i))+2*~RE(#i*POLYGAMMA(1,1-
#i))" ... is automatically rewritten to ... "-DIGAMMA(3/2-#i)-DIGAMMA
(3/2+#i)+2*DIGAMMA(2-2*#i)+2*DIGAMMA(2+2~*#i)-DIGAMMA(1-#i)-DIGAMMA
(1+#i)-ZETA(2,1/2-#i)/2-ZETA(2,1/2+#i)~/2+2*ZETA(2,1-2*#i)+2*ZETA
(2,1+2*#i)+ZETA(2,1-#i)/2+ZETA(2,1+#i)~/2+#i*(-CONJ(ZETA(2,1-#i))+CONJ
(ZETA(2,1+#i))+ZETA(2,1/2-#i)-ZET~A(2,1/2+#i)-4*ZETA(2,1-2*#i)+4*ZETA
(2,1+2*#i))" judicious substitution of the helper functions ... "mpsi
(z,m):=1/m*SUM(DIGAMMA((z+k)/m),k,0,m-1)+LN(m)mzeta(s,z,m):=1/m^s*SUM
(ZETA(s,(z+k)/m),k,0,m-1)" ... along with manual help for CONJ
(ZETA) ... "-DIGAMMA(3/2-#i)-DIGAMMA(3/2+#i)+2*mpsi(2-2*#i,2)+2*mpsi
(2+2*#i,~2)-DIGAMMA(1-#i)-DIGAMMA(1+#i)-ZETA(2,1/2-#i)/2-ZETA
(2,1/2+#i)/2~+2*mzeta(2,1-2*#i,2)+2*mzeta(2,1+2*#i,2)+ZETA(2,1-#i)/
2+ZETA(2,1~+#i)/2+#i*(-ZETA(CONJ(2),CONJ(1-#i))+ZETA(CONJ(2),CONJ
(1+#i))+ZE~TA(2,1/2-#i)-ZETA(2,1/2+#i)-4*mzeta(2,1-2*#i,2)+4*mzeta
(2,1+2*#i~,2))ZETA(2,1-#i)+ZETA(2,1+#i)+4*LN(2)2*RE(ZETA(2,1+#i))+4*LN
(2)3.698588915Martin. Subject: An exact simplification challenge - 91
(eerie PolyGamma) From: Vladimir Bondarenko Date: 25 May, 2009
19:41:14 Message: 5 of 6 Reply to this message Add author to My
Watch List View original format Flag as spam On May 25, 9:32 pm,
cliclic...@freenet.de wrote:> Vladimir Bondarenko schrieb:>>>>>> >
- PolyGamma[0, 1 + I]> >               - PolyGamma[0, 1 - I]
> >               - PolyGamma[0, 3/2 + I]> >               - PolyGamma
[0, 3/2 - I]> >               + 2 PolyGamma[0, 2 + 2 I]> >
+ 2 PolyGamma[0, 2 - 2 I]> >               + (1/2 + I) PolyGamma[1,
1 + I]> >               + (1/2 - I) PolyGamma[1, 1 - I]> >
- (1/2 + I) PolyGamma[1, 3/2 + I]> >               - (1/2 - I)
PolyGamma[1, 3/2 - I]> >               + (2 + 4 I) PolyGamma[1, 2 + 2
I]> >               + (2 - 4 I) PolyGamma[1, 2 - 2 I]> >
- 2 Re[I PolyGamma[1, 1 + I]]> >               + 2 Re[I PolyGamma[1, 1
- I]]>> >                                 ?>> This simple challenge
seems to be specifically made for Derive 6.10:>> -POLYGAMMA(0,1+#i)-
POLYGAMMA(0,1-#i)-POLYGAMMA(0,3/2+#i)-POLYGAM~> MA(0,3/2-#i)
+2*POLYGAMMA(0,2+2*#i)+2*POLYGAMMA(0,2-2*#i)+(1/2+#i~> )*POLYGAMMA
(1,1+#i)+(1/2-#i)*POLYGAMMA(1,1-#i)-(1/2+#i)*POLYGAMM~> A(1,3/2+#i)-
(1/2-#i)*POLYGAMMA(1,3/2-#i)+(2+4*#i)*POLYGAMMA(1,2+~> 2*#i)+(2-4*#i)
*POLYGAMMA(1,2-2*#i)-2*RE(#i*POLYGAMMA(1,1+#i))+2*~> RE(#i*POLYGAMMA
(1,1-#i))>> " ... is automatically rewritten to ... ">> -DIGAMMA(3/2-
#i)-DIGAMMA(3/2+#i)+2*DIGAMMA(2-2*#i)+2*DIGAMMA(2+2~> *#i)-DIGAMMA(1-
#i)-DIGAMMA(1+#i)-ZETA(2,1/2-#i)/2-ZETA(2,1/2+#i)~> /2+2*ZETA(2,1-2*#i)
+2*ZETA(2,1+2*#i)+ZETA(2,1-#i)/2+ZETA(2,1+#i)~> /2+#i*(-CONJ(ZETA(2,1-
#i))+CONJ(ZETA(2,1+#i))+ZETA(2,1/2-#i)-ZET~> A(2,1/2+#i)-4*ZETA
(2,1-2*#i)+4*ZETA(2,1+2*#i))>> " judicious substitution of the helper
functions ... ">> mpsi(z,m):=1/m*SUM(DIGAMMA((z+k)/m),k,0,m-1)+LN(m)>>
mzeta(s,z,m):=1/m^s*SUM(ZETA(s,(z+k)/m),k,0,m-1)>> " ... along with
manual help for CONJ(ZETA) ... ">> -DIGAMMA(3/2-#i)-DIGAMMA(3/2+#i)
+2*mpsi(2-2*#i,2)+2*mpsi(2+2*#i,~> 2)-DIGAMMA(1-#i)-DIGAMMA(1+#i)-ZETA
(2,1/2-#i)/2-ZETA(2,1/2+#i)/2~> +2*mzeta(2,1-2*#i,2)+2*mzeta(2,1+2*#i,
2)+ZETA(2,1-#i)/2+ZETA(2,1~> +#i)/2+#i*(-ZETA(CONJ(2),CONJ(1-#i))+ZETA
(CONJ(2),CONJ(1+#i))+ZE~> TA(2,1/2-#i)-ZETA(2,1/2+#i)-4*mzeta(2,1-2*#i,
2)+4*mzeta(2,1+2*#i~> ,2))>> ZETA(2,1-#i)+ZETA(2,1+#i)+4*LN(2)>> 2*RE
(ZETA(2,1+#i))+4*LN(2)>> 3.698588915>> Martin.Great!I'd only offer a
Directorhttp://www.cybertester.com/ Cyber Tester
Ltd.----------------------------------------------------------"We must
understand that technologieslike these are the way of the
future."----------------------------------------------------------
Subject: An exact simplification challenge - 91 (eerie PolyGamma)
From: clicliclic@freenet.de Date: 25 May, 2009 21:34:03 Message: 6 of
6 Reply to this message Add author to My Watch List View original
format Flag as spam Vladimir Bondarenko schrieb:> On May 25, 9:32
pm, cliclic...@freenet.de wrote:> > Vladimir Bondarenko schrieb:> >> >
> - PolyGamma[0, 1 + I]> > > - PolyGamma[0, 1 - I]> > > - PolyGamma[0,
3/2 + I]> > > - PolyGamma[0, 3/2 - I]> > > + 2 PolyGamma[0, 2 + 2 I]>
> > + 2 PolyGamma[0, 2 - 2 I]> > > + (1/2 + I) PolyGamma[1, 1 + I]> >
> + (1/2 - I) PolyGamma[1, 1 - I]> > > - (1/2 + I) PolyGamma[1, 3/2 +
I]> > > - (1/2 - I) PolyGamma[1, 3/2 - I]> > > + (2 + 4 I) PolyGamma
[1, 2 + 2 I]> > > + (2 - 4 I) PolyGamma[1, 2 - 2 I]> > > - 2 Re[I
PolyGamma[1, 1 + I]]> > > + 2 Re[I PolyGamma[1, 1 - I]]> >> > > ?> >>
> This simple challenge seems to be specifically made for Derive
6.10:> >> > -POLYGAMMA(0,1+#i)-POLYGAMMA(0,1-#i)-POLYGAMMA(0,3/2+#i)-
POLYGAM~> > MA(0,3/2-#i)+2*POLYGAMMA(0,2+2*#i)+2*POLYGAMMA(0,2-2*#i)
+(1/2+#i~> > )*POLYGAMMA(1,1+#i)+(1/2-#i)*POLYGAMMA(1,1-#i)-(1/2+#i)
*POLYGAMM~> > A(1,3/2+#i)-(1/2-#i)*POLYGAMMA(1,3/2-#i)+(2+4*#i)
*POLYGAMMA(1,2+~> > 2*#i)+(2-4*#i)*POLYGAMMA(1,2-2*#i)-2*RE
(#i*POLYGAMMA(1,1+#i))+2*~> > RE(#i*POLYGAMMA(1,1-#i))> >> > " ... is
automatically rewritten to ... "> >> > -DIGAMMA(3/2-#i)-DIGAMMA(3/2+#i)
+2*DIGAMMA(2-2*#i)+2*DIGAMMA(2+2~> > *#i)-DIGAMMA(1-#i)-DIGAMMA(1+#i)-
ZETA(2,1/2-#i)/2-ZETA(2,1/2+#i)~> > /2+2*ZETA(2,1-2*#i)+2*ZETA
(2,1+2*#i)+ZETA(2,1-#i)/2+ZETA(2,1+#i)~> > /2+#i*(-CONJ(ZETA(2,1-#i))
+CONJ(ZETA(2,1+#i))+ZETA(2,1/2-#i)-ZET~> > A(2,1/2+#i)-4*ZETA(2,1-2*#i)
+4*ZETA(2,1+2*#i))> >> > " judicious substitution of the helper
functions ... "> >> > mpsi(z,m):=1/m*SUM(DIGAMMA((z+k)/m),k,0,m-1)+LN
(m)> >> > mzeta(s,z,m):=1/m^s*SUM(ZETA(s,(z+k)/m),k,0,m-1)> >> > " ...
along with manual help for CONJ(ZETA) ... "> >> > -DIGAMMA(3/2-#i)-
DIGAMMA(3/2+#i)+2*mpsi(2-2*#i,2)+2*mpsi(2+2*#i,~> > 2)-DIGAMMA(1-#i)-
DIGAMMA(1+#i)-ZETA(2,1/2-#i)/2-ZETA(2,1/2+#i)/2~> > +2*mzeta(2,1-2*#i,
2)+2*mzeta(2,1+2*#i,2)+ZETA(2,1-#i)/2+ZETA(2,1~> > +#i)/2+#i*(-ZETA
(CONJ(2),CONJ(1-#i))+ZETA(CONJ(2),CONJ(1+#i))+ZE~> > TA(2,1/2-#i)-ZETA
(2,1/2+#i)-4*mzeta(2,1-2*#i,2)+4*mzeta(2,1+2*#i~> > ,2))> >> > ZETA
(2,1-#i)+ZETA(2,1+#i)+4*LN(2)> >> > 2*RE(ZETA(2,1+#i))+4*LN(2)> >> >
3.698588915> >>> Great!>> I'd only offer a bit simpler answer>> 1-
pi^2*CSCH(pi)^2+4*LOG(2)>> 3.698588915>Sorry, I didn't try to
"elementarize" the ZETA's.ZETA(2, 1+#i) + ZETA(2, 1-#i) =ZETA(2, 1+#i)
+ ZETA(2, -#i) + 1 =-(2 pi)^2 LI(-1, #e^(-2 pi)) + 1which is
equivalent to your expression since LI(-1,z) = z/(1-z)^2.Can Maple or
Mathematica perform the conversion automatically?Martin.Tags for this
commasEx.: root locus, bode What are tags? A tag is like a keyword or
category label associated with each thread. Tags make it easier for
you to find threads of interest. Anyone can tag a thread. Tags are
public and visible to everyone. Tag Activity for This Thread Tag
Applied By Date/Time spam per isakson 25 May, 2009 00:25:24 spam
John D'Errico 24 May, 2009 23:32:10 Feed for this Thread Public
Submission Policy NOTICE: Any content you submit to MATLAB Central,
including personal information, is not subject to the protections
which may be afforded information collected under other sections of
The MathWorks, Inc. Web site. You are entirely responsible for all
content that you upload, post, e-mail, transmit or otherwise make
available via MATLAB Central. The MathWorks does not control the
content posted by visitors to MATLAB Central and, does not guarantee
the accuracy, integrity, or quality of such content. Under no
circumstances will The MathWorks be liable in any way for any content
not authored by The MathWorks, or any loss or damage of any kind
incurred as a result of the use of any content posted, e-mailed,
? Featured MathWorks.com Topics: ? New Products ? Support ?
Documentation ? Training ? Webinars ? Newsletters ? MATLAB Trials ?
Careers ? © 1994-2009 The MathWorks, Inc. ? Site Help ? Patents ?
Signed,
Martin Musatov
__
The unpopular opinion is not always wrong. Sometimes it is simply
perfect.

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