{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "C9GDH7264N"
    }
  ],
  "body": "\n## Summary\n\nA strict total order is a [[strict partial order|SWB1ZXFVKY]] in which any two distinct elements are comparable.\nIt is the strict form of a [[total order|0316AYH1SC]], in the same way that $\u003c$ is the strict form of $\\le$ on the real numbers.\nFor any two elements $a$ and $b$, exactly one of $a \u003c b$, $a = b$, $b \u003c a$ holds.\n\n## Explanations\n\n### L1 human\n\nA strict total order puts all elements on one line and says which of two different elements comes first.\nThe relation $\u003c$ on the integers is the standard example: for $3$ and $5$, one has $3 \u003c 5$.\nAlphabetical order of distinct words is another example.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "06A05"
    ],
    "name": "Strict total order",
    "sources": [
      {
        "locator": "Strict and non-strict total orders",
        "url": "https://en.wikipedia.org/wiki/Total_order"
      }
    ],
    "specializes": [
      "60FNZ35H6R"
    ],
    "tag": "P33CMYHJW9"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/P33CMYHJW9/",
  "links": [
    {
      "field": "specializes",
      "target": "60FNZ35H6R"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/P33CMYHJW9.md",
  "msc": [
    "06A05"
  ],
  "name": "Strict total order",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/P33/P33CMYHJW9.md",
  "status": null,
  "tag": "P33CMYHJW9",
  "uri": "m2://P33CMYHJW9",
  "url": "https://tamnd.github.io/math2/wiki/strict-total-order/",
  "writing": {
    "tag": "P33CMYHJW9",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}