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Topic: Update: Objections to Cantor's Theory
Replies: 1,373   Last Post: Aug 22, 2005 9:07 PM

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 Denis Feldmann Posts: 1,674 Registered: 12/6/04
Re: well- versus regular ordering of R (was, a crank thread)
Posted: Aug 4, 2005 8:57 AM

Timothy Little a écrit :
> Lee Rudolph wrote:
>

>>Is it possible to say anything interesting about "how different" the
>>usual ordering of the reals is from a well-ordering (where "a
>>well-ordering" might be *any*, or *every*, according to taste)?

>
>
> One way to investigate this question would be to consider how large an
> ordinal one can embed in the usual ordering on the reals. Fairly
> clearly, we can only embed a countable ordinal in this way. We can
> associate with each rational the least element of the embedding
> greater than it, hence defining a surjection.

And the reciprocal is well-known ; any countable ordinal can be embedded
in the rationals (actually, any countable total order can be embedded in
the rationals)

>
> Consequently for any well-ordering of the reals we can only extract a
> countable subset that agrees with the usual ordering.
>
> As to the number of pairs of reals (r1,r2) in the well-ordering (R,W)
> for which r1 < r2 and r1 W r2, that has cardinality equal to that of
> the reals.
>
>
> - Tim

Date Subject Author
7/20/05 David Petry
7/20/05 G. Frege
7/21/05 Han de Bruijn
7/21/05 G. Frege
7/21/05 Stephen Montgomery-Smith
7/21/05 Keith Ramsay
7/21/05 Stephen Montgomery-Smith
7/20/05 Torkel Franzen
7/20/05 David Petry
7/21/05 Keith Ramsay
7/21/05 Chris Menzel
7/21/05 David Petry
7/21/05 Keith Ramsay
7/22/05 David C. Ullrich
7/24/05 Keith Ramsay
7/20/05 Stephen J. Herschkorn
7/21/05 Han de Bruijn
7/20/05 G. Frege
7/20/05 G. Frege
7/21/05 David Petry
7/21/05 G. Frege
7/21/05 Stephen Montgomery-Smith
7/21/05 malbrain@yahoo.com
7/21/05 Stephen Montgomery-Smith
7/29/05 malbrain@yahoo.com
7/20/05 Daryl McCullough
7/20/05 stephen@nomail.com
7/21/05 David Petry
7/21/05 G. Frege
7/21/05 stephen@nomail.com
7/21/05 malbrain@yahoo.com
7/22/05 mueckenh@rz.fh-augsburg.de
7/22/05 Robert Low
7/22/05 Han de Bruijn
7/22/05 stephen@nomail.com
7/23/05 Han de Bruijn
7/23/05 stephen@nomail.com
7/25/05 Han de Bruijn
7/25/05 stephen@nomail.com
7/26/05 Han de Bruijn
7/26/05 stephen@nomail.com
7/27/05 Han de Bruijn
7/22/05 Alan Morgan
7/23/05 Han de Bruijn
7/25/05 Alan Morgan
7/26/05 Han de Bruijn
7/26/05 Dave Rusin
7/26/05 Lee Rudolph
7/27/05 Han de Bruijn
7/27/05 Dr. David Kirkby
7/28/05 Han de Bruijn
7/28/05 Dr. David Kirkby
7/28/05 Han de Bruijn
7/28/05 Han de Bruijn
7/28/05 Dr. David Kirkby
7/29/05 Han de Bruijn
7/29/05 malbrain@yahoo.com
7/27/05 Dik T. Winter
7/27/05 Dave Rusin
7/27/05 Dr. David Kirkby
7/28/05 Han de Bruijn
7/23/05 Martin Shobe
7/23/05 Han de Bruijn
7/23/05 Martin Shobe
7/23/05 Dik T. Winter
7/24/05 Martin Shobe
7/25/05 Han de Bruijn
7/25/05 Martin Shobe
7/26/05 Han de Bruijn
7/26/05 Dr. David Kirkby
7/26/05 Han de Bruijn
7/26/05 Robert Low
7/26/05 Martin Shobe
7/26/05 Han de Bruijn
7/26/05 Martin Shobe
7/26/05 Virgil
7/26/05 Martin Shobe
7/27/05 Vaughan Pratt
7/27/05 Martin Shobe
7/25/05 Dik T. Winter
7/25/05 Han de Bruijn
7/25/05 Martin Shobe
7/25/05 Han de Bruijn
7/25/05 Martin Shobe
7/24/05 Dr. David Kirkby
7/24/05 Shmuel (Seymour J.) Metz
7/26/05 Vaughan Pratt
7/23/05 Timothy Little
7/23/05 Jim Burns
7/25/05 Han de Bruijn
7/25/05 Han de Bruijn
7/25/05 Jack Markan
7/26/05 Shmuel (Seymour J.) Metz
7/26/05 Jim Burns
7/24/05 Robert Low
7/25/05 Han de Bruijn
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7/25/05 Robert Low
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7/25/05 Robert Low
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7/28/05 mueckenh@rz.fh-augsburg.de
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7/28/05 Jack Markan
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7/29/05 Jack Markan
7/29/05 malbrain@yahoo.com
7/29/05 Robert Low
7/31/05 mueckenh@rz.fh-augsburg.de
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7/31/05 mueckenh@rz.fh-augsburg.de
7/31/05 Virgil
7/31/05 Jim Burns
7/31/05 malbrain@yahoo.com
8/2/05 malbrain@yahoo.com
7/31/05 Virgil
7/29/05 Virgil
7/29/05 Dr. David Kirkby
7/31/05 mueckenh@rz.fh-augsburg.de
7/31/05 malbrain@yahoo.com
7/31/05 Virgil
7/29/05 Virgil
7/28/05 malbrain@yahoo.com
7/29/05 mueckenh@rz.fh-augsburg.de
7/29/05 malbrain@yahoo.com
7/29/05 Russell Easterly
7/30/05 malbrain@yahoo.com
7/30/05 mueckenh@rz.fh-augsburg.de
7/30/05 Dr. David Kirkby
7/30/05 malbrain@yahoo.com
7/29/05 Richard Henry
7/29/05 David Kastrup
7/29/05 malbrain@yahoo.com
7/30/05 mueckenh@rz.fh-augsburg.de
7/30/05 Virgil
7/30/05 malbrain@yahoo.com
7/29/05 Virgil
7/30/05 mueckenh@rz.fh-augsburg.de
7/30/05 David Kastrup
7/30/05 Virgil
7/30/05 Poker Joker
7/30/05 malbrain@yahoo.com
7/30/05 Virgil
7/28/05 Virgil
7/29/05 mueckenh@rz.fh-augsburg.de
7/29/05 Virgil
7/28/05 Poker Joker
7/28/05 malbrain@yahoo.com
7/29/05 Dr. David Kirkby
7/29/05 Poker Joker
7/29/05 Dr. David Kirkby
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/28/05 Randy Poe
7/28/05 Chas Brown
7/28/05 Virgil
7/27/05 Daryl McCullough
7/27/05 Poker Joker
7/27/05 quasi
7/27/05 Poker Joker
7/27/05 quasi
7/28/05 malbrain@yahoo.com
7/27/05 Daryl McCullough
7/27/05 Poker Joker
7/27/05 Daryl McCullough
7/27/05 Poker Joker
7/28/05 Virgil
7/28/05 quasi
7/28/05 Dr. David Kirkby
7/27/05 Dr. David Kirkby
7/28/05 mueckenh@rz.fh-augsburg.de
7/28/05 Robert Low
7/28/05 Dr. David Kirkby
7/28/05 mueckenh@rz.fh-augsburg.de
7/28/05 Dr. David Kirkby
7/28/05 Poker Joker
7/29/05 Dr. David Kirkby
7/29/05 Poker Joker
7/29/05 Randy Poe
7/29/05 Poker Joker
7/29/05 Randy Poe
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/29/05 Dr. David Kirkby
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/29/05 Dr. David Kirkby
7/29/05 Poker Joker
7/29/05 Virgil
7/30/05 Poker Joker
7/30/05 malbrain@yahoo.com
7/30/05 Virgil
7/30/05 Poker Joker
7/30/05 malbrain@yahoo.com
7/30/05 Virgil
7/29/05 Jack Markan
7/29/05 Chas Brown
7/29/05 malbrain@yahoo.com
7/29/05 Jack Markan
7/30/05 Chas Brown
7/30/05 Torkel Franzen
7/30/05 Chas Brown
8/1/05 Shmuel (Seymour J.) Metz
8/1/05 Chas Brown
8/1/05 Martin Shobe
8/2/05 malbrain@yahoo.com
7/29/05 malbrain@yahoo.com
7/29/05 Poker Joker
7/29/05 Virgil
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/29/05 Chas Brown
7/29/05 Virgil
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/29/05 Virgil
7/29/05 Poker Joker
7/29/05 malbrain@yahoo.com
7/29/05 Virgil
7/29/05 Chas Brown
7/28/05 Robert Low
7/28/05 Poker Joker
7/29/05 Ron Sperber
7/29/05 Robert Low
7/29/05 Poker Joker
7/29/05 Chas Brown
7/29/05 Poker Joker
7/29/05 Chas Brown
7/29/05 Poker Joker
7/29/05 Chas Brown
7/29/05 Poker Joker
7/29/05 Chas Brown
7/30/05 Jim Burns
7/30/05 Poker Joker
7/30/05 Jim Burns
7/30/05 Poker Joker
7/30/05 Virgil
7/30/05 Poker Joker
7/30/05 Jim Burns
7/30/05 malbrain@yahoo.com
7/30/05 Robert Low
7/30/05 Poker Joker
7/30/05 malbrain@yahoo.com
7/30/05 Jim Burns
7/31/05 Robert Low
7/30/05 Poker Joker
7/30/05 Chas Brown
7/30/05 Robert Low
7/30/05 Poker Joker
7/30/05 Chas Brown
7/29/05 malbrain@yahoo.com
7/30/05 Robert Low
7/30/05 Poker Joker
7/29/05 Chas Brown
7/29/05 mueckenh@rz.fh-augsburg.de
7/29/05 Robert Low
7/29/05 David Kastrup
7/29/05 Robert Low
7/29/05 malbrain@yahoo.com
7/31/05 mueckenh@rz.fh-augsburg.de
7/31/05 Dr. David Kirkby
7/31/05 Robert Low
7/31/05 Virgil
7/31/05 mueckenh@rz.fh-augsburg.de
7/31/05 Virgil
7/31/05 Randy Poe
7/31/05 Robert Low
7/31/05 Virgil
8/1/05 Chris Menzel
7/29/05 Dr. David Kirkby
7/30/05 mueckenh@rz.fh-augsburg.de
7/30/05 Dr. David Kirkby
7/30/05 Virgil
7/29/05 Virgil
7/30/05 mueckenh@rz.fh-augsburg.de
7/30/05