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: Why can no one in sci.math understand my simple point?
Replies: 660   Last Post: Dec 7, 2017 8:06 AM

 Messages: [ Previous | Next ]
 Peter Webb Posts: 945 Registered: 12/6/04
Re: Why can no one in sci.math understand my simple point?
Posted: Jun 20, 2010 8:37 PM

"Virgil" <Virgil@home.esc> wrote in message
news:Virgil-B10127.13553420062010@bignews.usenetmonster.com...
> In article
> WM <mueckenh@rz.fh-augsburg.de> wrote:
>

>> On 20 Jun., 01:58, Tim Little <t...@little-possums.net> wrote:
>> > On 2010-06-19, Virgil <Vir...@home.esc> wrote:
>> >

>> > > There is, however, some question in my mind about the existence of a
>> > > list of all and ONLY computable reals.

>> >
>> > Why? The computable reals can be proven countable, as you already
>> > know, so there is a bijection between N and the set of countable
>> > reals.

>>
>> That is not true. An exclusive list need not exist.
>>
>> The reals in a certain Cantor-list are countable. And if you form the
>> anti-diagonal of that list and add it (for instance at first position)
>> to the list, this new list is also countable. Again consttruct the
>> anti-diagonal and add it to the list. Continue. The situation remains
>> the same for all anti-diagonals you might want to construct. Therefore
>> all reals constructed in that way are countable. Nevertheless it is
>> impossible to put all of them in one list, because there would be
>> another resulting anti-diagonal.
>>
>> Conclusion: It is impossible to obtain a bijection of all these reals
>> with N although all "these" reals are countable with no doubt.

>
>
> Equal cardinality of two sets requires, by definition, a bijection
> between them.
>
> The naturals are, by definition of COUNTABLE cardinality so that any set
> of equally countable cardinality must have a bijection with the
> naturals.
>
> Cantor has shown that the set of all reals cannot biject with the
> naturals, ergo, the set of all reals is NOT of countable cardinality.
>

Actually, he shows that any purported list of all Reals must miss at last
one Real.

*not* the same as being uncountable, witness the same argument applied to
computable Reals.

> Actually Cantor's original "diagonal" proof was based on the set of all
> functions from the naturals to a two element set,

No. It is based upon showing that any purported list of all Reals must
neccesarily omit at least one Real, and he does this by providing an
explicit construction of the anti-diagonal based upon examining the first n
digits of the first n items on the list for all n.

Which is exactly what I am doing.

> but several people
> have constructed bijections between that set of functions and the set of
> all reals. I have done it myself.

Perhaps if you were to provide an actual list of all computable numbers -
and only the computable numbers - your claim that they can be listed would
be vindicated.

My bet is that you will have about as much success forming a list of all
computable Reals as you would do forming a list of all Reals, but if you
think such a list exists, go for it.

Date Subject Author
6/15/10 |-|ercules
6/15/10 jaimie
6/15/10 Peter Webb
6/15/10 |-|ercules
6/15/10 Peter Webb
6/15/10 |-|ercules
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 |-|ercules
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 |-|ercules
6/15/10 |-|ercules
6/15/10 Peter Webb
6/15/10 Dingo
6/15/10 |-|ercules
6/15/10 Derek Holt
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 Tim Little
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Virgil
6/18/10 Newberry
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/18/10 Newberry
6/20/10 Newberry
6/20/10 mueckenh@rz.fh-augsburg.de
6/20/10 Virgil
6/20/10 mueckenh@rz.fh-augsburg.de
6/20/10 Virgil
6/20/10 Newberry
6/20/10 |-|ercules
6/20/10 Peter Webb
6/20/10 Virgil
6/20/10 |-|ercules
6/20/10 Newberry
6/21/10 Sylvia Else
6/22/10 Newberry
6/22/10 Virgil
6/22/10 Newberry
6/22/10 Virgil
6/23/10 Newberry
6/23/10 Virgil
6/23/10 Newberry
6/23/10 Virgil
6/23/10 Newberry
6/24/10 Virgil
6/24/10 Newberry
6/24/10 Virgil
6/24/10 Newberry
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Sylvia Else
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Mike Terry
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Mike Terry
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Sylvia Else
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Virgil
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Sylvia Else
6/22/10 Mike Terry
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Virgil
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Mike Terry
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Mike Terry
6/22/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/23/10 Mike Terry
6/24/10 mueckenh@rz.fh-augsburg.de
6/24/10 Virgil
6/24/10 mueckenh@rz.fh-augsburg.de
6/24/10 Virgil
6/24/10 mueckenh@rz.fh-augsburg.de
6/24/10 Virgil
6/24/10 Mike Terry
6/25/10 mueckenh@rz.fh-augsburg.de
6/25/10 Mike Terry
6/25/10 Virgil
6/25/10 mueckenh@rz.fh-augsburg.de
6/25/10 Mike Terry
6/25/10 Virgil
6/26/10 mueckenh@rz.fh-augsburg.de
6/26/10 Virgil
6/26/10 Mike Terry
6/26/10 mueckenh@rz.fh-augsburg.de
6/26/10 Virgil
6/27/10 Newberry
6/27/10 mueckenh@rz.fh-augsburg.de
6/27/10 Virgil
6/27/10 Mike Terry
6/27/10 mueckenh@rz.fh-augsburg.de
6/27/10 Virgil
6/22/10 Virgil
6/22/10 Virgil
6/22/10 Virgil
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Sylvia Else
6/22/10 Virgil
6/22/10 Sylvia Else
6/22/10 Sylvia Else
6/22/10 Tim Little
6/23/10 Virgil
6/23/10 Virgil
6/23/10 Sylvia Else
6/23/10 Virgil
6/23/10 Sylvia Else
6/23/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/23/10 Mike Terry
6/23/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/23/10 Sylvia Else
6/24/10 mueckenh@rz.fh-augsburg.de
6/24/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Sylvia Else
6/23/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Sylvia Else
6/23/10 Virgil
6/23/10 Sylvia Else
6/23/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Sylvia Else
6/23/10 Newberry
6/23/10 Virgil
6/23/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/23/10 Newberry
6/23/10 Virgil
6/23/10 Virgil
6/21/10 Virgil
6/21/10 Virgil
6/20/10 lwalke3@lausd.net
6/20/10 Newberry
6/21/10 lwalke3@lausd.net
6/22/10 Newberry
6/24/10 Charlie-Boo
6/24/10 Charlie-Boo
6/25/10 Charlie-Boo
6/25/10 Virgil
6/25/10 Tim Little
6/25/10 Newberry
6/26/10 Charlie-Boo
6/26/10 Virgil
6/26/10 Tim Little
6/27/10 Virgil
6/27/10 Charlie-Boo
6/26/10 Tim Little
6/27/10 Newberry
6/27/10 Newberry
6/27/10 Charlie-Boo
6/27/10 Charlie-Boo
6/26/10 Charlie-Boo
6/27/10 Charlie-Boo
6/26/10 Charlie-Boo
6/26/10 Virgil
6/27/10 Charlie-Boo
6/26/10 Newberry
6/26/10 Virgil
6/26/10 Peter Webb
6/26/10 Virgil
6/27/10 Peter Webb
6/27/10 Virgil
6/27/10 Owen Jacobson
6/27/10 Peter Webb
6/28/10 Owen Jacobson
6/28/10 Peter Webb
6/28/10 Virgil
6/28/10 Tim Little
6/28/10 Daryl McCullough
6/28/10 Virgil
6/28/10 Owen Jacobson
6/28/10 Tim Little
6/28/10 mueckenh@rz.fh-augsburg.de
6/28/10 Virgil
6/28/10 Owen Jacobson
6/29/10 Peter Webb
6/30/10 Owen Jacobson
7/1/10 Peter Webb
6/28/10 Tim Little
6/28/10 Virgil
6/28/10 Virgil
6/26/10 Newberry
6/26/10 Virgil
6/27/10 Peter Webb
6/27/10 Peter Webb
6/27/10 Newberry
6/28/10 Tim Little
6/27/10 Newberry
6/15/10 fishfry
6/15/10 |-|ercules
6/15/10 Peter Webb
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/16/10 Tim Little
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 K_h
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 |-|ercules
6/16/10 The Raven
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 |-|ercules
6/16/10 Virgil
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Peter Webb
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 Daryl McCullough
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 |-|ercules
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Peter Webb
6/15/10 Virgil
6/15/10 Peter Webb
6/16/10 Virgil
6/16/10 Peter Webb
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 mueckenh@rz.fh-augsburg.de
6/16/10 J. Clarke
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 |-|ercules
6/15/10 mueckenh@rz.fh-augsburg.de
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/21/10 Guest
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 Aatu Koskensilta
6/15/10 Peter Webb
6/15/10 Aatu Koskensilta
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Virgil
6/15/10 mueckenh@rz.fh-augsburg.de
6/15/10 Daryl McCullough
6/15/10 Marshall
6/15/10 Aatu Koskensilta
6/16/10 J. Clarke
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 Ronald Bruck
6/15/10 Jesse F. Hughes
6/15/10 Mike Terry
6/15/10 |-|ercules
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 Jesse F. Hughes
6/15/10 Aatu Koskensilta
6/15/10 Virgil
6/15/10 Mike Terry
6/15/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/15/10 lwalke3@lausd.net
6/15/10 george
6/15/10 george
6/15/10 Aatu Koskensilta
6/15/10 Virgil
6/15/10 Aatu Koskensilta
6/15/10 Jesse F. Hughes
6/15/10 Aatu Koskensilta
6/16/10 Virgil
6/16/10 Herman Jurjus
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Peter Webb
6/17/10 Tim Little
6/16/10 Virgil
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 Peter Webb
6/16/10 Virgil
6/17/10 Peter Webb
6/17/10 Virgil
6/17/10 Peter Webb
6/17/10 Virgil
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Owen Jacobson
6/17/10 Tim Little
6/17/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/17/10 ross.finlayson@gmail.com
6/17/10 ross.finlayson@gmail.com
6/18/10 Tim Little
6/18/10 Marshall
6/20/10 ross.finlayson@gmail.com
7/12/10 ross.finlayson@gmail.com
6/17/10 Tim Little
6/17/10 Peter Webb
6/17/10 Virgil
6/17/10 Tim Little
6/17/10 Peter Webb
6/18/10 Virgil
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/18/10 Virgil
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Virgil
6/19/10 Peter Webb
6/19/10 Tim Little
6/20/10 Peter Webb
6/20/10 Mike Terry
6/20/10 Peter Webb
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/21/10 Peter Webb
6/21/10 Daryl McCullough
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Virgil
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/21/10 Mike Terry
6/21/10 Mike Terry
6/20/10 Tim Little
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Tim Little
6/20/10 Peter Webb
6/20/10 Mike Terry
6/20/10 Peter Webb
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/21/10 Peter Webb
6/21/10 Virgil
6/21/10 Tim Little
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 mueckenh@rz.fh-augsburg.de
6/23/10 Virgil
6/21/10 Mike Terry
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/21/10 Peter Webb
6/19/10 Daryl McCullough
6/19/10 Peter Webb
6/20/10 Tim Little
6/18/10 Marshall
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Tim Little
6/19/10 Virgil
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/19/10 Tim Little
6/20/10 mueckenh@rz.fh-augsburg.de
6/20/10 Virgil
6/20/10 Peter Webb
6/20/10 Virgil
6/20/10 Peter Webb
6/20/10 Tim Little
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Virgil
6/21/10 mueckenh@rz.fh-augsburg.de
6/21/10 Virgil
6/22/10 mueckenh@rz.fh-augsburg.de
6/22/10 Virgil
6/22/10 David R Tribble
6/22/10 Virgil
6/19/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/19/10 Daryl McCullough
6/18/10 K_h
6/18/10 Peter Webb
6/19/10 K_h
6/19/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/20/10 Tim Little
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Mike Terry
6/19/10 Peter Webb
6/20/10 Mike Terry
6/20/10 Peter Webb
6/21/10 Mike Terry
6/19/10 Tim Little
6/19/10 Peter Webb
6/20/10 Tim Little
6/20/10 Mike Terry
6/20/10 Peter Webb
6/20/10 Tim Little
6/20/10 mueckenh@rz.fh-augsburg.de
6/20/10 Virgil
6/20/10 Peter Webb
6/20/10 Virgil
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Virgil
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Guest
6/17/10 Virgil
6/17/10 lwalke3@lausd.net
2/17/13
2/17/13
12/7/17 4musatov@gmail.com
6/16/10 Peter Webb
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Virgil
6/17/10 Peter Webb
6/18/10 Virgil
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 K_h
6/18/10 Peter Webb
6/19/10 K_h
6/19/10 Peter Webb
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/19/10 K_h
6/19/10 Peter Webb
6/20/10 K_h
6/21/10 Owen Jacobson
6/21/10 Peter Webb
6/21/10 Owen Jacobson
6/19/10 K_h
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Tim Little
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Virgil
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Daryl McCullough
6/19/10 Daryl McCullough
6/19/10 Peter Webb
6/20/10 Tim Little
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/20/10 Tim Little
6/18/10 Daryl McCullough
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Virgil
6/19/10 Peter Webb
6/19/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/20/10 Peter Webb
6/19/10 Daryl McCullough
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/19/10 Tim Little
6/19/10 Peter Webb
6/19/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/20/10 Peter Webb
6/20/10 Tim Little
6/21/10 Peter Webb
6/21/10 Mike Terry
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 Tim Little
6/18/10 Peter Webb
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/16/10 Jack Markan
6/16/10 Jack Markan
6/16/10 Aatu Koskensilta
6/16/10 Aatu Koskensilta
6/16/10 Jack Markan
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 Jack Markan
6/17/10 Jack Markan
6/17/10 mueckenh@rz.fh-augsburg.de
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/16/10 Jack Markan
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/16/10 Jack Markan
6/16/10 Jack Markan
6/16/10 mueckenh@rz.fh-augsburg.de
6/16/10 Virgil
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Virgil
6/17/10 Jack Markan
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Virgil
6/17/10 Jack Markan
6/17/10 Jack Markan
6/17/10 lwalke3@lausd.net
2/17/13
12/7/17 4musatov@gmail.com
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/17/10 Aatu Koskensilta
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 lwalke3@lausd.net
6/17/10 Virgil
6/17/10 Sylvia Else
6/17/10 mueckenh@rz.fh-augsburg.de
6/17/10 Sylvia Else
6/17/10 lwalke3@lausd.net
6/17/10 |-|ercules
6/17/10 Sylvia Else
6/18/10 |-|ercules
6/18/10 Sylvia Else
6/18/10 |-|ercules
6/18/10 Sylvia Else
6/18/10 |-|ercules
6/18/10 Sylvia Else
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Sylvia Else
6/18/10 |-|ercules
6/18/10 Sylvia Else
6/18/10 |-|ercules
6/19/10 Sylvia Else
6/19/10 |-|ercules
6/19/10 Sylvia Else
6/19/10 |-|ercules
6/19/10 Sylvia Else
6/19/10 |-|ercules
6/20/10 Sylvia Else
6/20/10 |-|ercules
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/18/10 Virgil
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/18/10 |-|ercules
6/18/10 Sylvia Else
6/19/10 |-|ercules
6/19/10 Sylvia Else
6/19/10 |-|ercules
6/19/10 Sylvia Else
6/19/10 |-|ercules
6/20/10 Sylvia Else
6/20/10 |-|ercules
6/20/10 Sylvia Else
6/20/10 |-|ercules
6/20/10 lwalke3@lausd.net
6/20/10 |-|ercules
6/20/10 |-|ercules
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/18/10 mueckenh@rz.fh-augsburg.de
6/18/10 Virgil
6/19/10 mueckenh@rz.fh-augsburg.de
6/19/10 Virgil
6/18/10 ostap_bender_1900@hotmail.com
6/21/10 Sylvia Else
6/22/10 Sylvia Else
6/27/10 Frederick Williams