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Cantor diagonal argument

Author:

Leon, Antonio

Category:

Research Papers

Sub-Category:

Mathematics and Applied Mathematics

Language:

English

Date Published:

October 08, 2021

File:

/Research Papers-Mathematics and Applied Mathematics/Download/8204

Downloads:

303

Keywords:

Cantor diagonal method, rational numbers, real numbers

Abstract:

This paper proves a result on the decimal expansion of the rational numbers in the open rational interval (0, 1), which is subsequently used to discuss a reordering of the rows of a table T that is assumed to contain all rational numbers within (0, 1), in such a way that the diagonal of the reordered table T could be a rational number from which different rational antidiagonals (elements of (0, 1) that cannot be in T ) could be defined. If that were the case, and for the same reason as in Cantor’s diagonal argument, the open rational interval (0, 1) would be non-denumerable, and we would have a contradiction in set theory, because Cantor also proved the set of rational numbers is denumerable.