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Topic: Matheology § 223: AC and AMS
Replies: 102   Last Post: Apr 18, 2013 12:26 AM

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mueckenh@rz.fh-augsburg.de

Posts: 15,737
Registered: 1/29/05
Re: Matheology § 223: AC and AMS
Posted: Mar 14, 2013 9:28 AM
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On 14 Mrz., 13:59, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> WM <mueck...@rz.fh-augsburg.de> writes:
> > On 14 Mrz., 12:35, Alan Smaill <sma...@SPAMinf.ed.ac.uk> wrote:
> >> WM <mueck...@rz.fh-augsburg.de> writes:
> >> > According to standard matheology one can choose one element each of an
> >> > uncountable set of sets. That is as wrong. Compare Matheology § 225.

>
> >> You can and do of course  reject this axiom.
>
> >> To show something is self-contradictory, however, you need to use the
> >> reasoning principles of the system you want to show is
> >> self-contradictory, not your own beliefs.

>
> > The axiom belongs to the system. It says that elements can be chosen.
> > To choose immaterial elements,  hmm, how is that accomplished in a
> > system that contains the axiom of choice?

>
> I can only repeat myself --
> where is the *logical* contradiction there, in terms of classical
> mathematics?


You will find it if you try to answer my question. Choosing means
defining (by a finite number of words) a chosen element (unless it is
a material object). No other possibility exists.
>
> Of course, you think it's false, and unimaginable, and whatever
> words you want to use.
>
> But you claim it's *self-contradictory*, don't you?
>
> And that's a whole different claim.


Please look up what Zermelo wrote. (In Matheology § 225 you will find
the orginal German text.) It is always possible /to choose/ an element
from every non-empty set and to union the chosen elements into a set
S_1.

This means: It is possible to have and to apply uncountably many
finite words in order to choose and in order to distinguish the
elements in S_1 (a set can have only distinct elements by axiom). And
the same theory says: The set of finite words is countable.
And finally: uncountable is much more than countable.

That is a contradiction.

Regards, WM


Date Subject Author
3/14/13
Read Re: Matheology § 223: AC and AMS
Alan Smaill
3/14/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/14/13
Read Re: Matheology § 223: AC and AMS
fom
3/14/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Matheology § 223: AC and AMS
fom
3/14/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/14/13
Read Re: Matheology § 223: AC and AMS
fom
3/15/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/15/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology § 223: AC and AMS
fom
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology § 223: AC and AMS
fom
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
fom
3/17/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
fom
3/17/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/17/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
4/17/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/19/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/19/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/19/13
Read Re: Matheology § 223: AC and AMS
fom
4/17/13
Read Re: Matheology � 223: AC and AMS
Virgil
4/18/13
Read Re: Matheology § 223: AC and AMS
fom
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/18/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
Ralf Bader
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
fom
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/15/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/15/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/15/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/15/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/15/13
Read Re: Matheology § 223: AC and AMS
fom
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/14/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/14/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/16/13
Read Re: Matheology § 223: AC and AMS
mueckenh@rz.fh-augsburg.de
3/16/13
Read Re: Matheology � 223: AC and AMS
Virgil
3/17/13
Read Re: Matheology § 223: AC and AMS
fom

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