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