On power sets

Details On power sets On power sets

2001-11-28

arxiv.org/abs/math/0111291v3

Mathematics

General Mathematics

3 pages. Theorem 3 withdrawn of this version

Scientific paper

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.

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