On counting the rational numbers

• Autores: Carlos Almada
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 41, Nº. 8, 2010, págs. 1096-1101
• Idioma: inglés
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• Resumen

  • In this study, we show how to construct a function from the set [image omitted] of natural numbers that explicitly counts the set [image omitted] of all positive rational numbers using a very intuitive approach. The function has the appeal of Cantor's function and it has the advantage that any high school student can understand the main idea at a glance without any prior knowledge of the Unique Prime Factorization Theorem or other nonelementary results. Unlike Cantor's function, the one we propose makes it very easy to determine what rational number, in unreduced form, is in a given position on the list and vice versa.