On the abundance of the irrational numbers

Details On the abundance of the irrational numbers On the abundance of the irrational numbers

2003-05-23

arxiv.org/abs/math/0305326v4

Mathematics

General Mathematics

8 pages

Scientific paper

Based upon the axiom of choice it is proved that the cardinality of the
rational numbers is not less than the cardinality of the irrational numbers.
This contradicts a main result of transfinite set theory and shows that the
axiom of choice is invalid.

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