Search All of the Math Forum:

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

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

 Search Thread: Advanced Search

 Messages: [ Previous | Next ]
 Tucsondrew@me.com Posts: 1,062 Registered: 5/24/13
Re: Matheology § 285
Posted: Jun 11, 2013 3:22 PM
 Plain Text Reply

On Tuesday, June 11, 2013 11:49:59 AM UTC-7, muec...@rz.fh-augsburg.de wrote:
> 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.
>

This is not obvious. Indeed, it is false.

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 EACH element of the set.

The validity P may not carry over to the limit point of Omega.

Examples:

For all n e |N, FIS_n(|N) is finite.
But, |N is not finite.

For all n e |N, the first n digits of 2^( 1/2 ) forms a ration number.
But, 2^( 1/2 ) is not a rational number.

>
> 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.
>

You right, no difference.
Both fail at the limit stage.

>
> > (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?
>

Omega is Limit Ordinal.

So, for all a < Omega, there exist b such that a < b < Omega.

When we take it up to each every natural, we have it all.

>
> This is but *one* simple aspect which shows that the jerks of matheology should really be imprisonde in a mad-house.
>
>
>
> It's a bit of a pain to have to reformat your posts and quotes every time: it would help a lot if you could at least split your paragraphs in short lines using carriage returns.
>
>
>
> That's due to the new Google which is an outspoken shit. Unfortunately it seems that I cannot return to the old version. The developer of that mess be cursed.
>
>
>
> Regards, WM

ZG

Date Subject Author
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 JT
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
6/11/13 Tucsondrew@me.com
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/11/13 Ralf Bader
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/14/13 mueckenh@rz.fh-augsburg.de
6/14/13 Tucsondrew@me.com
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Tucsondrew@me.com
6/15/13 Virgil
6/15/13 Tanu R.
6/15/13 mueckenh@rz.fh-augsburg.de
6/15/13 Virgil
6/15/13 Virgil
6/14/13 Virgil
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/11/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Scott Berg
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 LudovicoVan
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Tucsondrew@me.com
6/12/13 mueckenh@rz.fh-augsburg.de
6/12/13 Virgil
6/12/13 Tucsondrew@me.com
6/12/13 Virgil
6/12/13 Virgil
6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
6/12/13 Virgil
6/11/13 LudovicoVan
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Tucsondrew@me.com
6/11/13 Virgil
6/11/13 Tanu R.
6/11/13 Virgil
6/11/13 Tanu R.

© The Math Forum at NCTM 1994-2017. All Rights Reserved.