{
  "id": "1807.05469",
  "version": "v1",
  "published": "2018-07-15T00:18:32.000Z",
  "updated": "2018-07-15T00:18:32.000Z",
  "title": "Idempotent means on free binary systems do not exist",
  "authors": [
    "Justin Tatch Moore"
  ],
  "comment": "4 pages, comments welcome",
  "categories": [
    "math.CO",
    "math.GR",
    "math.LO"
  ],
  "abstract": "Free binary systems are shown to not admit idempotent means. This refutes a conjecture of the author. It is also shown that the extension of Hindman's theorem to nonassociative binary systems formulated and conjectured by the author is false.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-15T00:18:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "free binary systems",
      "admit idempotent means",
      "hindmans theorem",
      "nonassociative binary systems",
      "conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}