Beyond Uncountable
General Mathematics
2007-05-23 v2
Abstract
In 1891 Cantor presented two proofs with the purpose to establish a general theorem that any set can be replaced by a set of greater power. Cantor's power set theorem can be considered to be an extension of Cantor's 1891 second proof and its argument makes use of a well-known self-referring statement. In this article it is shown that, defining the relative complement of the self-referring statement, Cantor's power set theorem cannot be derived. Moreover, it is given a refutation of the first proof, the so-called Cantor's diagonal argument.
Cite
@article{arxiv.math/0312360,
title = {Beyond Uncountable},
author = {Paola Cattabriga},
journal= {arXiv preprint arXiv:math/0312360},
year = {2007}
}
Comments
7 pages, the first version of this article has been posted to sci.math in 1998, for more information see http://it.geocities.com/paola_cattabriga/