{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Statement\n\nLet $F$ be an [[Archimedean ordered field|0HQARMKEV5]] and let $x$ be an element of $F$.\nThen there is a natural number $n$ with $x \u003c n$.\n\n## Remarks\n\nProof: apply the definition with $y = 1$.\nThus the natural numbers are not [[bounded above|0B5H2V4JW8]] in $F$.\nThe [[real numbers are Archimedean|0A3GWZ86AY]], thus this holds for each real number $x$.\n\n## Explanations\n\n### L1 human\n\nNo element of an Archimedean field is larger than all the natural numbers.\nFor example, for the real number $x = 10^{6} + 0.5$, the natural number $n = 10^{6} + 1$ is larger.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "kind": "statement",
    "msc": [
      "12J15"
    ],
    "name": "Archimedean property",
    "role": "proposition",
    "same_as": {
      "wikidata": "Q634579",
      "wikipedia": "Archimedean property"
    },
    "sources": [
      {
        "locator": "Ordered fields",
        "url": "https://en.wikipedia.org/wiki/Archimedean_property"
      }
    ],
    "tag": "0A74SX55QP",
    "uses": [
      "0HQARMKEV5"
    ]
  },
  "kind": "statement",
  "link": "https://math2.tamnd.com/node/0A74SX55QP/",
  "links": [
    {
      "field": "uses",
      "target": "0HQARMKEV5"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0A74SX55QP.md",
  "msc": [
    "12J15"
  ],
  "name": "Archimedean property",
  "prov": null,
  "role": "proposition",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0A7/0A74SX55QP.md",
  "status": null,
  "tag": "0A74SX55QP",
  "uri": "m2://0A74SX55QP",
  "url": "https://math2.tamnd.com/wiki/archimedean-property/",
  "writing": {
    "tag": "0A74SX55QP",
    "kind": "statement",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}