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From: Bruno Marchal <marchal.domain.name.hidden>

Date: Fri, 29 Apr 2005 08:08:18 +0200

Le 29-avr.-05, à 02:32, Stathis Papaioannou a écrit :

*> Norman Samish writes:
*

*>
*

*>> Jonathan,
*

*>> If it is true that “In infinite time and infinite space, whatever
*

*>> can
*

*>> happen, must happen, not only once but an infinite number of times,”
*

*>> then
*

*>> what does probability mean? In your example below, there must be an
*

*>> infinity of worlds where Colin Powell is president and an infinity of
*

*>> worlds
*

*>> where your 6-year old niece is president. Are you saying that the
*

*>> Colin
*

*>> Powell infinity is bigger than the 6-year old niece infinity?
*

*>> Norman
*

*>
*

*> Yes, there are different sizes of infinity. For example, there are
*

*> "more" integers than there are even numbers, even though there are an
*

*> infinite number of both, and there is a 50% chance that a random
*

*> integer is even. Cantor and all that.
*

I guess you were in some hurry ... I agree that the measure of "Colin

Powell" is bigger than the "niece". But it is a question of measure (cf

Jesse post) not of cardinality. Also the cardinality of the set of

integers, even integers, prime numbers, square, rationnals .... are all

the same (omega), but they are all less than the cardinality of the

reals, which is itself less than the cardinality of the set of function

from real to <any set with at least 2 elements>. This is proved by the

diagonalisation technic (like the incompleteness result) as I explain

in the list here : http://www.escribe.com/science/theory/m3079.html and

here http://www.escribe.com/science/theory/m3344.html

Bruno

http://iridia.ulb.ac.be/~marchal/

Received on Fri Apr 29 2005 - 02:14:55 PDT

Date: Fri, 29 Apr 2005 08:08:18 +0200

Le 29-avr.-05, à 02:32, Stathis Papaioannou a écrit :

I guess you were in some hurry ... I agree that the measure of "Colin

Powell" is bigger than the "niece". But it is a question of measure (cf

Jesse post) not of cardinality. Also the cardinality of the set of

integers, even integers, prime numbers, square, rationnals .... are all

the same (omega), but they are all less than the cardinality of the

reals, which is itself less than the cardinality of the set of function

from real to <any set with at least 2 elements>. This is proved by the

diagonalisation technic (like the incompleteness result) as I explain

in the list here : http://www.escribe.com/science/theory/m3079.html and

here http://www.escribe.com/science/theory/m3344.html

Bruno

http://iridia.ulb.ac.be/~marchal/

Received on Fri Apr 29 2005 - 02:14:55 PDT

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