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

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 LudovicoVan Posts: 4,034 From: London Registered: 2/8/08
Re: Matheology § 285
Posted: Jun 11, 2013 3:34 PM
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<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 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.

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