English

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 Theorem 3 withdrawn of this version