A new construction of the real numbers by alternating series

Abstract

We put forward a new method of constructing the complete ordered field of real numbers from the ordered field of rational numbers. Our method is a generalization of that of A. Knopfmacher and J. Knopfmacher. Our result implies that there exist infinitely many ways of constructing the complete ordered field of real numbers. As an application of our results, we prove the irrationality of certain numbers.

arXiv comment15 pages, 0 figure. Section 4 was added

Cited by in corpus (2)

• The real numbers - a survey of constructions
• The reals as rational Cauchy filters