Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Matheology § 288
Replies: 160   Last Post: Jun 21, 2013 8:42 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
mueckenh@rz.fh-augsburg.de

Posts: 15,323
Registered: 1/29/05
Re: Matheology § 288
Posted: Jun 20, 2013 9:18 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On 19 Jun., 22:17, Zeit Geist <tucsond...@me.com> wrote:
> On Wednesday, June 19, 2013 11:38:03 AM UTC-7, WM wrote:
> > On 19 Jun., 19:04, Zeit Geist <tucsond...@me.com> wrote:
>
> > > Anyway, what Cantor wrote is NOT the theory of ZFC.
>
> > In modern ZFC omega is used as ordinal and as cardinal simultaneously.
>
> As if you know.


I have frequently been taught so by modern set theorists. I assume
they are knowledgeable with respect to their business.

> Every step in the sequence gives a finite set which is NOT all N.

Correct. But the whole sequence has infinitely many steps and
infinitely many unions.

> If you take the entire set of the sets constructed at each step
> ( each of these sets are finite, but there infinitely many of them ),


then there are aleph_0 numbers missing in every set of the sequence,
which contains the result of infinitely many unions.


> and then take the Union over that set; then the result is N.

Just that is surprising. Infinitely many + 1 union are sufficient.
>
> So what if it takes aleph_0 step to form the list, and then one more
> step for the Union to arrive at a set containing all and only all N.


Surprisingly infinitely many unions (where each union adds something)
are not sufficient. But another union that does not add anything
yields |N.

> Start you list at 0, the least ordinal, and this makes more sense.


Why: In this case the same happens: Infinitely many unions, where each
union adds something, cannot yield |N. But another union that adds
nothing, yields |N. Not mor and not less sense.


> Or don't and remain lost in your blather.

That sound as if you have run out of arguments.
>
> As for you last bit from Wittgenstein, this only shows
> that omega ( infinity ) is inaccessible via succession ( counting ).


Then it is not useful for analysis. There we need lim n --> oo. Like
in my infinitely many unions.

> That's why ZF(C) has an Axiom of Infinity.

This axiom has been made by Zermelo, taken from Dedekind. There it
meant nothing that can be reached but potential infinity.

> Which does not contradict any logical principle.

It contradicts the principle that unioning a set with its subsets
canot increase that set.

> It may contradict our everyday intuition; but if we restricted
> our selves to that boundary, we would still be in the
> Dark Ages.


Someone used to say: Ich führe euch herrlichen Zeiten entgegen. Now
these times have dawned - also in matheology.
>
> BTW, you still haven't given me the proper translation
> that I asked for in the last post.-


I have only the German text. It is from "Georg Cantor: Leben, Werk und
Wirkung", by Herbert Meschkowski, 2. Aufl. BI, Mannheim (1981) p.142.
It quotes G. Kowalewski, Bestand und Wandel, p. 202.

Regards, WM


Date Subject Author
6/14/13
Read Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 288
LudovicoVan
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 288
LudovicoVan
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
apoorv
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
apoorv
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
apoorv
6/17/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
apoorv
6/17/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology � 288
Tanu R.
6/17/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology § 288
FredJeffries@gmail.com
6/16/13
Read Re: Matheology § 288
apoorv
6/16/13
Read Re: Matheology § 288
apoorv
6/17/13
Read Re: Matheology § 288
FredJeffries@gmail.com
6/17/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
FredJeffries@gmail.com
6/18/13
Read Re: Matheology § 288
LudovicoVan
6/18/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/18/13
Read Re: WMytheology � 288
Virgil
6/18/13
Read Re: Matheology § 288
LudovicoVan
6/18/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/18/13
Read Re: Matheology § 288
LudovicoVan
6/18/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/18/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/18/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/19/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/19/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/19/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/19/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: WMytheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/19/13
Read Re: Matheology � 288
Virgil
6/19/13
Read Re: WMytheology � 288
Virgil
6/18/13
Read Re: Matheology � 288
Virgil
6/18/13
Read Re: Matheology § 288
fom
6/18/13
Read Re: Matheology § 288
fom
6/18/13
Read Re: Matheology § 288
LudovicoVan
6/18/13
Read Re: Matheology § 288
fom
6/19/13
Read Re: Matheology § 288
LudovicoVan
6/19/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/19/13
Read Re: WMytheology � 288
Virgil
6/19/13
Read Re: Matheology § 288
LudovicoVan
6/19/13
Read Re: Matheology § 288
fom
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology § 288
FredJeffries@gmail.com
6/20/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
Ralf Bader
6/21/13
Read Re: Matheology § 288
LudovicoVan
6/21/13
Read Re: Matheology § 288
LudovicoVan
6/20/13
Read Re: Matheology § 288
FredJeffries@gmail.com
6/20/13
Read Re: Matheology � 288
Virgil
6/20/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/15/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology � 288
Tanu R.
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 288
LudovicoVan
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 288
LudovicoVan
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology � 288
Tanu R.
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology � 288
Bergholt Stuttley Johnson
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
Tucsondrew@me.com
6/14/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology � 288
Tanu R.
6/15/13
Read Re: Matheology � 288
Bergholt Stuttley Johnson
6/14/13
Read Re: Matheology � 288
Virgil
6/14/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/17/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
fom
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology � 288
Virgil
6/17/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/17/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology � 288
Virgil
6/16/13
Read Re: Matheology § 288
mueckenh@rz.fh-augsburg.de
6/16/13
Read Re: Matheology � 288
Virgil
6/15/13
Read Re: Matheology � 288
Tanu R.

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.