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

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 mueckenh@rz.fh-augsburg.de Posts: 18,076 Registered: 1/29/05
Re: Matheology § 285
Posted: Jun 12, 2013 7:50 AM

On Tuesday, 11 June 2013 21:22:40 UTC+2, Zeit Geist wrote:
> 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

> > > > 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.

*All elements* of |N are finite. The *set of all* elements is not (but only because the axiom of infinity says so).

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

It need not, since the axiom of infinity exists and can be applied.

By axiom of infinity *there are all elements*. We have to accept that. Now goning on: If not all elements of |Q could be well-ordered, then there must be a first configuration of elements

configuration n: {q_1, q_2, ..., q_n}

that cannot be well-ordered by magnitude or size. But there is no such configuration. Every configuration can be well-ordered by size. This implies there is no q that stays outside the well order.

Regards, WM

Date Subject Author
6/11/13 mueckenh@rz.fh-augsburg.de
6/11/13 Virgil
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6/12/13 mueckenh@rz.fh-augsburg.de
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6/11/13 mueckenh@rz.fh-augsburg.de
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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
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6/13/13 mueckenh@rz.fh-augsburg.de
6/13/13 Virgil
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6/11/13 LudovicoVan
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6/11/13 Virgil
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