05838513

j

2011a.00566 Almada, Carlos On counting the rational numbers. Int. J. Math. Educ. Sci. Technol. 41, No. 8, 1096-1101 (2010). 2010 Taylor \& Francis, Abingdon, Oxon EN F44 F45 K24 K25 E64 E65 counting the rationals rational numbers countable sets Cantor's function

doi:10.1080/0020739X.2010.500695

Summary: In this study, we show how to construct a function from the set $\bbfN$ of natural numbers that explicitly counts the set $\bbfQ^+$ 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.