On the abundance of the irrational numbers
Mueckenheim, W.
Original · EN
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.
English translation
This paper has no Arabic translation yet. Be the first: it takes a few seconds, and the result is stored for every future reader.