On power sets
General Mathematics
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0111291,
title = {On power sets},
author = {Jailton C. Ferreira},
journal= {arXiv preprint arXiv:math/0111291},
year = {2007}
}
Comments
3 pages. Theorem 3 withdrawn of this version