Set Theory and Logic

    

Cantor's Diagonal Argument

Authors: Miloš Čojanović

It is generally accepted that Georg Cantor proved that the set of the real numbers in the interval (0,1) is not countable. Actually instead of real numbers, Cantor considered a set of infinite sequences composed of two characters 'm' and 'n'. We will prove that the countability of rational numbers in the interval (0,1) is crucial for Cantor's Diagonal Argument on the uncountability of real numbers in the interval (0,1) and the Cantor's proof cannot be directly applied to the set of real numbers since some of the rational numbers in binary form can be expressed in two different ways.

Comments: 4 Pages.

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[v1] 2026-01-02 15:53:37

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