An analysis of Cantor’s theory of uncountable sets: The logic of his proofs has some weaknesses. Cantor assumes for both his proofs that all real numbers (set R) are in a list (list L). Considering L as a set this assumption assumes R belongs to L. This makes the claim “a real number is constructed but is not in the list L” questionable. We propose a solution to this problem, an axiom for counting infinite sets and a solution to continuum hypothesis.

«Examination of Cantor’s proofs for uncountability and axiom for counting infinite sets»