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On the abundance of the irrational numbers

General Mathematics 2009-09-29 v4

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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Cite

@article{arxiv.math/0305326,
  title  = {On the abundance of the irrational numbers},
  author = {W. Mueckenheim},
  journal= {arXiv preprint arXiv:math/0305326},
  year   = {2009}
}

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8 pages