A severe inconsistency of transfinite set theory

Details A severe inconsistency of transfinite set theory A severe inconsistency of transfinite set theory

2004-08-06

arxiv.org/abs/math/0408089v3

DMV Jahrestagung Heidelberg, Abstracts p. 6 (2004)

Mathematics

General Mathematics

Talk delivered at the meeting of the German Math. Soc., Heidelberg, September 14, 2004

Scientific paper

Transfinite set theory including the axiom of choice supplies the following basic theorems: (1) Mappings between infinite sets can always be completed, such that at least one of the sets is exhausted. (2) The real numbers can be well ordered. (3) In a finite set of real numbers the maximum below a given limit can always be determined. (4) Any two different real numbers are separated by at least one rational number. These theorems are applied to map the irrational numbers into the rational numbers, showing that the set of all irrational numbers is countable.

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