Arnold Knopfmacher, John Knopfmacher, "Two constructions of the real numbers via alternating series", International Journal of Mathematics and Mathematical Sciences, vol. 12, Article ID 637217, 11 pages, 1989. https://doi.org/10.1155/S0161171289000736
Two constructions of the real numbers via alternating series
Two further new methods are put forward for constructing the complete ordered field of real numbers out of the ordered field of rational numbers. The methods are motivated by some little known results on the representation of real numbers via alternating series of rational numbers. Amongst advantages of the methods are the facts that they do not require an arbitrary choice of "base" or equivalence classes or any similar constructs. The methods bear similarities to a method of construction due to Rieger, which utilises continued fractions.
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