FOM: actual infinite

Franklin Vera Pacheco franklin at
Tue Apr 30 14:21:12 EDT 2002

  Dear Mr Zenkin:
I want to discuss something with you. I think you can get an actual 
infinite in a finitistic way. You can think of an infinite set as an 
ordered pair formed by an initial(finite) set and a rule(an algorithm).

 For instance, the naturals is the pair ( {0}, s ) where s is an algorithm 
that giving a set adjoints it the succesor of the maximum of the set.
 Related to each set there is an "actual infinite set" of the numbers 
that are in the initial set in THIS moment and those that will appear and not 
disappear(because the rule can extract some elements of the initial 
set) in some moment. 
With this construction it is interesting to define the equality of sets, 
the union, intersection, cartesian product, etc. 

 Next year I'll expose the history of the ideas about the infinite,your 
ideas(the problems with Cantor's theorem) and these ideas in a seminar.

 I want your profesional opinion about this theme. 

 Please, do not take this ideas as facing yours about the actual infinite, 
they are made on the entire basis of finite objects. 

 Best regards,

Franklin Vera Pacheco
45 #10029 e/100 y 104
Marianao, C Habana,
e-mail:franklin at

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