{
  "id": "1208.1434",
  "version": "v3",
  "published": "2012-08-07T14:45:55.000Z",
  "updated": "2013-10-30T13:06:44.000Z",
  "title": "A new construction of the real numbers by alternating series",
  "authors": [
    "Soichi Ikeda"
  ],
  "comment": "15 pages, 0 figure. Section 4 was added",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-10-30T13:06:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11U99",
      "11J72"
    ],
    "keywords": [
      "real numbers",
      "alternating series",
      "complete ordered field",
      "construction",
      "result implies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.1434I"
    }
  }
}