Two Modern Versions of Russell's Paradox——Cantor's Two Proofs in Set Theory
Ouyang Geng · Journal of Kashgar Teachers College · 2008
From the defects in the basic theory of present classical infinite theory,the essential relationship between Cantor's proofs of the uncountability of real number set and the Cantor's Theorem of SP(S) and Russell's Paradox is analyzed.A mysterious error is found: the very same paradoxical idea was applied in both Russell and Cantor's work but Cantor made wrong use of this paradox idea with two logical mistakes.This made Cantor's above two important proofs in set theory actually became another two deformed versions of Russell's paradox.Two conclusions are drown——the ideas and operations in Cantor's above two proofs are wrong and the results are not scientific at all,it is the fatal defects in the basic theory of present classical infinite theory that make such mistakes possible.