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On the abundance of the irrational numbers

W. Mueckenheim
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Abstract

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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W. Mueckenheim. 2004-03-15. On the abundance of the irrational numbers. https://arxiv.org/abs/math/0305326

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