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Topic: Matheology § 163
Replies: 1   Last Post: Nov 27, 2012 2:49 AM

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Posts: 18,076
Registered: 1/29/05
Matheology § 163
Posted: Nov 27, 2012 1:53 AM
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Matheology § 163

First hidden necessary condition of Cantor's proof. - In the middle of
the XX c., meta-mathematics announced Cantor's set theory "naive" and
soon the very mention of the term "actual infinity" was banished from
all meta-mathematical and set theoretical tractates. The ancient
logical, philosophical, and mathematical problem, which during
millenniums troubled outstanding minds of humankind, was "solved"
according to the principle: "there is no term - there is no problem".
So, today we have a situation when Cantor's theorem and its famous
diagonal proof are described in every manual of axiomatic set theory,
but with no word as to the "actual infinity". However, it is obvious
that if the infinite sequence (1) of Cantor's proof is potential then
no diagonal method will allow to construct an individual mathematical
object, i.e., to complete the infinite binary sequence y*. Thus, just
the actuality of the infinite sequence (1) is a necessary condition (a
Trojan Horse) of Cantor's proof, and therefore the traditional, set-
theoretical formulation of Cantor's theorem (above) is, from the
standpoint of classical mathematics, simply wrong and must be re-
written as follows without any contradiction with any logic.
[A.A. Zenkin: "Scientific Intuition of Genii Against Mytho-'Logic' of
Cantor?s Transfinite Paradise" Procs. of the International Symposium
on ?Philosophical Insights into Logic and Mathematics,? Nancy, France,
2002, p. 2]

Regards, WM

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