Abstract
We present 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.
Citation
Soichi Ikeda. "A new construction of the real numbers by alternating series." Nihonkai Math. J. 25 (1) 27 - 43, 2014.
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