2001/11/28 by Jailton C. Ferreira, Ferreira, Jailton C.
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #math.GM
paper · pdf · doi:10.48550/arxiv.math/0111291
3 pages. Theorem 3 withdrawn of this version
arxiv created 2002/02/17 · arxiv updated 2009/11/30
This work presents theorems which state (i) Z is a proper subset for any bijection f between A and Z, where Z is contained in P(A), A is a non-finite set and |Z|=|A|, and (ii) being Z a proper subset of P(A) nothing affirms or denies that |P(A)|>|A|. Russell's paradox is examined and it is shown that the set of all the ordinary sets does not exist. A mistake in Cantor's proof on cardinality of power sets is shown.