Beyond Uncountable

Paola Cattabriga

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Beyond Uncountable

Paola Cattabriga

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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.

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Paola Cattabriga. 2006-07-03. Beyond Uncountable. https://arxiv.org/abs/math/0312360

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