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Not Denumerability of Rational Numbers

In 1874, Georg Cantor published a paper containing the analysis which has been considered a demonstration of the denumerability of rational numbers. Even though the demonstration did not employ a rigorous mathematical formalism, it was accepted without any further development apart from its rendering as a table in the well-known form. This paper shows that the theorem of Cantor is erroneous in its demonstration as well as in its conclusions.