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Topic: Joel David Hamkins on definable real numbers in analysis
Replies: 98   Last Post: Jun 30, 2013 3:22 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Joel David Hamkins on definable real numbers in analysis
Posted: Jun 22, 2013 1:33 PM

mueckenh@rz.fh-augsburg.de wrote:

> On Saturday, 22 June 2013 17:44:42 UTC+2, dull...@sprynet.com wrote:
> > Consider the following statement: (*) "In order to order the reals, you
> > must be able to distinguish them. But it is impossible to distinguish more
> > than countably many." _Is_ (*) correct?

>
> Yes, that is correct.
>

> > If (*) is correct it follows that there's no _order_ on the reals, which
> > seems curious, to say the least, since there _is_ a perfectly simple,
> > standard order on the reals, nothing to do with AC or anything else
> > problematic.

>
> There is an order on the rationals. In order to put an irrational into that
> order, usually its rational approximations are chosen. By the way, this is
> another reason that not more irrationals than rationals can exist. Every pair
> of irrational numbers must be distinguished by a rational between them.

And every pair of distinct irrationals have MORE irrationals between
them than they have rationals between them.
>
> I think

WRONG!
--

Date Subject Author
6/18/13 fom
6/19/13 David Petry
6/19/13 fom
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Peter Percival
6/19/13 mueckenh@rz.fh-augsburg.de
6/19/13 Virgil
6/19/13 Tucsondrew@me.com
6/21/13 David C. Ullrich
6/21/13 mueckenh@rz.fh-augsburg.de
6/21/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Tucsondrew@me.com
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Tucsondrew@me.com
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Tucsondrew@me.com
6/23/13 Tucsondrew@me.com
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Tucsondrew@me.com
6/23/13 Virgil
6/23/13 Virgil
6/24/13 Virgil
6/23/13 Virgil
6/22/13 Virgil
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Virgil
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Virgil
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 Virgil
6/25/13 Virgil
6/26/13 Virgil
6/26/13 fom
6/26/13 Virgil
6/22/13 Virgil
6/22/13 Tucsondrew@me.com
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/22/13 David C. Ullrich
6/22/13 mueckenh@rz.fh-augsburg.de
6/22/13 Virgil
6/23/13 David C. Ullrich
6/23/13 mueckenh@rz.fh-augsburg.de
6/23/13 Virgil
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 mueckenh@rz.fh-augsburg.de
6/25/13 Virgil
6/24/13 David C. Ullrich
6/24/13 mueckenh@rz.fh-augsburg.de
6/24/13 Virgil
6/25/13 David C. Ullrich
6/25/13 mueckenh@rz.fh-augsburg.de
6/25/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/25/13 Tucsondrew@me.com
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/26/13 David C. Ullrich
6/26/13 mueckenh@rz.fh-augsburg.de
6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
6/27/13 Virgil
6/26/13 Virgil
6/27/13 mueckenh@rz.fh-augsburg.de
6/27/13 Virgil
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
6/28/13 mueckenh@rz.fh-augsburg.de
6/28/13 Tucsondrew@me.com
6/29/13 mueckenh@rz.fh-augsburg.de
6/29/13 Virgil
6/30/13 Virgil
6/28/13 Virgil
6/29/13 mueckenh@rz.fh-augsburg.de
6/29/13 Virgil
6/28/13 Virgil
6/28/13 Virgil
6/19/13 Virgil
6/19/13 Virgil