Until now Cantor’s diagonal method has been the proof for the uncountable infinite set of real numbers to be “larger” than the countable infinite set of natural number. In the following work Cantor’s method is refuted and it is proven that the cardinality of real numbers is the same as the cardinality of natural numbers.
Contrary to Cantor’s method, this proof is constructive and estimates directly the cardinality of the real numbers and compares it to the natural numbers by constructing an injection to the prime numbers.
The work is written in German and shall be translated into English soon. Until then the German version is the only source for the proof.