Mathematics and Applied Mathematics
November 15, 2020
Cantor 1874 argument, cardinal of the rational numbers, hypothesis of the actual infinity
This chapter explains how Cantor's 1874 argument almost demonstrated the set of the rational numbers is and is not denumerable. Indeed, two of the three alternatives of Cantor's 1874 proof of the cardinality of the real numbers can be directly applied to the set of the rational numbers. Here it is proved how easy is to convert the third alternative in the second one by a simple self-bijection, thus completing Cantor's work. Albeit in the opposite direction of its infinitist objective.