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 § 285
Replies: 84   Last Post: Jun 15, 2013 6:05 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
LudovicoVan

Posts: 3,201
From: London
Registered: 2/8/08
Re: Matheology § 285
Posted: Jun 11, 2013 3:34 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

<mueckenh@rz.fh-augsburg.de> wrote in message
news:721318dd-d8c9-4943-8a9d-ef8116b9fe55@googlegroups.com...
> On Tuesday, 11 June 2013 20:23:17 UTC+2, Julio Di Egidio wrote:
>>> After each one has been > attached to a natural, we have the set of
>>> naturals that obviously can > be re-ordered in any desired way.

>
>> Obviously and crucially not in any finite number of steps (you will get
>> the rationals well-ordered by magnitude from, say, the rationals
>> lexicographically ordered). Anyway, I'm already out of my depths here, so
>> I'll leave this to more competent mathematicians.

>
> It is obvious: If we show in set theory a proposition P(n) for the first n
> elements of a well-ordered set (where n is an arbitrarily large natural
> number), then we do show it for all elements of the set.
>
> If we enumerate the rationals, we do it up to n (since there is no
> infinite natural number). If we apply the diagonal argument, we do it up
> to n (since there is no infinite natural number). If we well-order the
> rational numbers by magnitude, we do it up to n.
>
> There is absolutely no difference.


The obvious and essential difference is that in the second paragraph you
drop the "where n is an arbitrarily large natural number" to equivocate on
the "up to n": your usual and hardly candid word salads.

(Plus, I had something quite different in mind with the "not in any finite
number of steps"/"not effectively", but that's incidental and I cannot make
it more precise, anyway.)

> > (The power set of |N should even include the singleton of the last
> > natural > as an element.) There is no such thing as the last natural
> > number, and not even a next to last, and not even a next to next to
> > last, and so on.

>
> I know. But there are more than any natural number of numbers. So if we
> take the numbers 1 to n for any natural number, then we have less than
> aleph_0 naturals. What remains to take all?


Same word salad. Argue with/against the math if you can:

N \ U_{n->oo} { k <= n } = N \ N = {}

But you can't and won't... etcetera.

Julio




Date Subject Author
6/11/13
Read Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
JT
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Ralf Bader
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/14/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/14/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/15/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/15/13
Read Re: Matheology � 285
Virgil
6/15/13
Read Re: Matheology � 285
Tanu R.
6/15/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/15/13
Read Re: Matheology � 285
Virgil
6/15/13
Read Re: Matheology � 285
Virgil
6/14/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: WMytheology ???
Virgil
6/12/13
Read Re: WMytheology ???
Scott Berg
6/12/13
Read Re: WMytheology ???
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/12/13
Read Re:Outside the wild weird world of WMytheology
Virgil
6/12/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/12/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/13/13
Read Re: Matheology § 285
mueckenh@rz.fh-augsburg.de
6/13/13
Read Re: Matheology � 285
Virgil
6/12/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology § 285
LudovicoVan
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology � 285
Tanu R.
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology § 285
Tucsondrew@me.com
6/11/13
Read Re: Matheology � 285
Virgil
6/11/13
Read Re: Matheology � 285
Tanu R.
6/11/13
Read Re: Matheology ? 285
Virgil
6/11/13
Read Re: Matheology ? 285
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.