Year: 2010
Type: preprint
Abstract: This paper examines the possibilities of extending Cantor's two arguments on the uncountable nature of the set of real numbers to one of its proper denumerable subsets: the set of rational numbers. The paper proves that, unless certain restrictive conditions are satisfied, both extensions are possible. It is therefore indispensable to prove that those conditions are in fact satisfied in Cantor's theory of transfinite sets. Otherwise that theory would be inconsistent.
Source: arXiv (Cornell University)
Author: Leon, Antonio
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2108453025
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