Set Theory and Logic

    

Cantor Diagonal Argument

Authors: Antonio Leon

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.

Comments: 9 Pages.

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Submission history

[v1] 2020-11-02 01:21:51
[v2] 2020-11-22 17:17:56
[v3] 2021-03-25 03:56:23

Unique-IP document downloads: 962 times

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