Mathematics and Applied Mathematics
August 21, 2020
Cantor 1874 theorem, cardinality, omega-order, rational numbers, Axiom of Infinity
This paper proves that two of the three alternatives of Cantor's 1874 proof of the cardinality of the real numbers also apply to the rational numbers. It is then necessary to prove the exception is the only possible alternative when applying Cantor's proof to the rational numbers. This paper also proves, however, this is not the case. A conclusion that reopens with a new problem the history of conflicts in the foundation of set theory.