FOM: Re: actual infinite

[Franklin Vera Pacheco]

  Dear Mr Zenkin;

  1,2,3,4,.....         (1)

   I think I must explain me better. The existence of an algorithm 
generating the numbers of a set 
eg. the natural numbers, indeed doesn't say anything about if the series 
(1) is an actual or a potencial infinite. What I'm thinking goes into another 
way. I'm not dilucidating whether or not series
(1) is actual infinite, I'm trying to give an object (a finite one) that 
can be taken as an actual infinite.
In other words, if series (1) is the potencial infinite set of the natural 
numbers then its representation 
(all that you can give) as a pair ( initial set , rule ) can be taken as 
the actual infinite set of the natural numbers.
  The pair set-rule defines (in good conditions) if an object belongs or 
not to the set.
 [Cantor's proof]
 The problem with reals is that if you try to give an actual 
infinite representation ( (set,rule) ) of the set of real numbers then you 
can construct a new real number that doesn't belongs to your representation. 
  Then, we can rice the question about the existence of a representation 
of the actualy infinite set of real
numbers. Cantor's antidiagonalization process give us that we can't get it 
with this kind of representation. 

 Expecting your opinions, objection and(or) recomendations.

Best Regards
-- 
Franklin Vera Pacheco
45 #10029 e/100 y 104
Marianao, C Habana,
Cuba.
e-mail:franklin at ghost.matcom.uh.cu
tel:2606043