Analysis on Four Mistakes in Cantor's Proofs on the Uncountability of Real Number Set
Ouyang Geng · Journal of Kashgar Teachers College · 2011
Four concealed mistakes in Cantor's proofs on the uncountability of real number set are discovered and analyzed from the aspects of logic,infinite theory,limit theory as well as the ideas and operations of the proofs.A conclusion is drown: because of the defects in the foundation of mathematics which is closely related to the present classical infinite theory,limit theory and the classical number system,Cantor unavoidably made four serious but concealed mistakes in his proofs.Particularly,his logical mistake accidentally turned the proofs into a kind of typical mathematical magic.