2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62748This 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.3 pages. Theorem 3 withdrawn of this versionGeneral Mathematicstext