From: Christian Szegedy (szegedy@or.uni-bonn.de)
Date: Wed Aug 25 2004 - 12:21:51 MDT
Tomaz Kristan wrote:
>On Wed, 25 Aug 2004 15:50:53 +0200, Christian Szegedy
><szegedy@or.uni-bonn.de> wrote:
>
>
>>Let x=1. Multiply it by -1 after 1/2 second. Multiply it again after 1/4
>>second,
>>And again after 1/8 of a second. And so on...
>>
>>What is the value of x after 1 second?
>>
>>Do you see that your definition is not formalizable?
>>
>>
>>
>>
>
>Fine with me. So the supertasks are not possible? But the axiom of
>replacement from the ZF guaranties me a a set of all the results, if
>the set of all arguments exists, and the function is there which maps
>one to another.
>
>Isn't that so?
>
>
Given function f: X->X, you can define set S(X) for any x in X, by:
S(x)={x,f(x),f(f(x)),f(f(f(x))),...}, (with infinitely many dots),
but you can't define:
f(f(f(....(x)))) (with infinitely many dots).
Dicussing (real) antinomies of ZFC is probably not an SL4 but an SL5
topic :)
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