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Counting the Positive Rationals: A Brief Survey

2005/09/01 by David M. Bradley, Bradley, David M.
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #math.HO #msc:11A51 #msc:11A55 #msc:11A63 #msc:26A03

paper · pdf · doi:10.48550/arxiv.math/0509025

7 pages

arxiv created 2005/09/01 · arxiv updated 2009/12/01

Abstract

We discuss some examples that illustrate the countability of the positive rational numbers and related sets. Techniques include radix representations, Godel numbering, the fundamental theorem of arithmetic, continued fractions, Egyptian fractions, and the sequence of ratios of successive hyperbinary representation numbers.

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