**From:** Christian Szegedy (*szegedy@or.uni-bonn.de*)

**Date:** Wed Aug 25 2004 - 12:21:51 MDT

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Tomaz Kristan wrote:

*>On Wed, 25 Aug 2004 15:50:53 +0200, Christian Szegedy
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*><szegedy@or.uni-bonn.de> wrote:
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*>
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*>
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*>>Let x=1. Multiply it by -1 after 1/2 second. Multiply it again after 1/4
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*>>second,
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*>>And again after 1/8 of a second. And so on...
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*>>
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*>>What is the value of x after 1 second?
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*>>
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*>>Do you see that your definition is not formalizable?
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*>>
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*>>
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*>>
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*>>
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*>
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*>Fine with me. So the supertasks are not possible? But the axiom of
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*>replacement from the ZF guaranties me a a set of all the results, if
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*>the set of all arguments exists, and the function is there which maps
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*>one to another.
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*>
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*>Isn't that so?
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*>
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*>
*

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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