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Topic: Matheology § 162
Replies: 78   Last Post: Dec 10, 2012 4:46 AM

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mueckenh@rz.fh-augsburg.de

Posts: 16,185
Registered: 1/29/05
Re: Matheology § 162
Posted: Nov 27, 2012 4:17 PM
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On 27 Nov., 21:48, William Hughes <wpihug...@gmail.com> wrote:

> > Correct. Every position is unoccupied,
>
> My claim is *each* position is unoccupied.


That's correct. But it does not follow that all positions are
unoccupied. Potential infinity is developing. Hilbert has given a very
good formulation:

Will man in Kürze die neue Auffassung des Unendlichen, der Cantor
Eingang verschafft hat, charakterisieren, so könnte man wohl sagen: in
der Analysis haben wir es nur mit dem Unendlichkleinen und dem
Unendlichengroßen aIs Limesbegriff, als etwas Werdendem, Entstehendem,
Erzeugtem, d. h., wie man sagt, mit dem potentiellen Unendlichen zu
tun. Aber das eigentlich Unendliche selbst ist dies nicht. Dieses
haben wir z. B., wenn wir die Gesamtheit der Zahlen 1, 2, 3, 4, . . .
selbst als eine fertige Einheit betrachten oder die Punkte einer
Strecke als eine Gesamtheit von Dingen ansehen, die fertig vorliegt.
Diese Art des Unendlichen wird als aktual unendlich bezeichnet.
[Hilbert, Über das Unendliche, p.167]

>
> > but that does not mean that all
> > positions are unoccupied:

>
> But this is not what I am saying.  Compare
>
> Each natural number >1 is either prime or composite.
> The set of natural numbers >1 that are neither prime
> nor composite is empty.


Yes, but here we have a property that is a property of the set like:
Every natural number is a natural number.

In my example the numbers wander from left to right as individuals. If
all have gone right, they have gone as individuals, then there is no
individual on the left. Then there must have been a last one wandering
to the right.

Sorry, I am not able to solve all problems of the infinite. In
particular there are difficult problems of the kind you raised above.
People have thought about this for thoudands of years. How should I
give a final solution? My point is only this (for instance in digits
wandering right or in comparing digits of Cantor lists): There is no
finished infinity! Perhaps the true solution lies in the fact that all
sets that can be used in reality are finite. At least, it would be the
simplest solution.

Regards, WM


Date Subject Author
11/25/12
Read Matheology § 162
mueckenh@rz.fh-augsburg.de
11/25/12
Read Re: Matheology § 162
Roland Franzius
11/25/12
Read Re: Matheology § 162
namducnguyen
11/26/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/26/12
Read Re: Matheology � 162
Virgil
11/25/12
Read Re: Matheology � 162
Virgil
11/26/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/26/12
Read Re: Matheology � 162
Virgil
11/26/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/26/12
Read Re: Matheology � 162
Virgil
11/26/12
Read Re: Matheology § 162
YBM
11/26/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/26/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology § 162
Carsten Schultz
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology § 162
Carsten Schultz
11/27/12
Read Re: Matheology § 162
Virgil
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
Carsten Schultz
11/29/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/29/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
William Hughes
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology § 162
William Hughes
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology § 162
William Hughes
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
William Hughes
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
William Hughes
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology § 162
William Hughes
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Re: Matheology § 162
Michael Stemper
11/29/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/29/12
Read Re: Re: Matheology § 162
Michael Stemper
11/29/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/29/12
Read Re: Re: Matheology § 162
Michael Stemper
11/29/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/29/12
Read Re: Matheology § 162
YBM
11/29/12
Read Re: Matheology § 162
trj
11/29/12
Read Re: Matheology � 162
Virgil
11/30/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/30/12
Read Re: Matheology � 162
Virgil
12/1/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
12/1/12
Read Re: Matheology � 162
Virgil
11/29/12
Read Re: Matheology � 162
Virgil
11/29/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology � 162
Virgil
12/10/12
Read Re: Matheology S 162
veronika kočková
11/27/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
YBM
11/27/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology � 162
Virgil
11/27/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/27/12
Read Re: Matheology � 162
Virgil
11/28/12
Read Re: Matheology § 162
Michael Stemper
11/28/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/28/12
Read Re: Matheology � 162
Virgil
11/29/12
Read Re: Matheology § 162
mueckenh@rz.fh-augsburg.de
11/29/12
Read Re: Matheology � 162
Virgil

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