{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0HQARMKEV5"
    }
  ],
  "body": "\n## Summary\n\nAn Archimedean ordered field is an [[ordered field|0P3VCBDEE2]] that has no infinitely large and no infinitely small positive elements.\nIn such a field, the natural numbers are not bounded above.\nThe fields $\\mathbb{Q}$ and $\\mathbb{R}$ are Archimedean.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "kind": "concept",
    "msc": [
      "12J15"
    ],
    "name": "Archimedean ordered field",
    "sources": [
      {
        "locator": "Ordered fields",
        "url": "https://en.wikipedia.org/wiki/Archimedean_property"
      }
    ],
    "tag": "0XH79S06J3"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0XH79S06J3/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0XH79S06J3.md",
  "msc": [
    "12J15"
  ],
  "name": "Archimedean ordered field",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0XH/0XH79S06J3.md",
  "status": null,
  "tag": "0XH79S06J3",
  "uri": "m2://0XH79S06J3",
  "url": "https://math2.tamnd.com/wiki/archimedean-ordered-field/",
  "writing": {
    "tag": "0XH79S06J3",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}