{
  "aliases": null,
  "backlinks": null,
  "body": "\n## Example\n\nLet $X$ be a set.\nFor $x, y \\in X$, let $d(x, y) = 0$ if $x = y$ and $d(x, y) = 1$ if $x \\neq y$.\nThen $d$ is a [[metric|063W5JMY85]] on $X$, the discrete metric.\n\n## Remarks\n\nFor each $x \\in X$, the open ball of radius $1/2$ about $x$ is $\\{x\\}$. Thus each subset of $X$ is open, and the metric gives the [[discrete topology|0S2TEHX4E1]].\nA sequence converges in this metric if and only if it is eventually constant.\n\n## Explanations\n\n### L1 human\n\nIn the discrete metric, two points are either equal or at distance $1$.\nNo point is close to another point, so the space has no interesting limits.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "instance_of": [
      "0VKD1TP7F3"
    ],
    "kind": "example",
    "msc": [
      "54E35"
    ],
    "name": "Discrete metric",
    "sources": [
      {
        "locator": "Definitions",
        "url": "https://en.wikipedia.org/wiki/Discrete_space"
      }
    ],
    "tag": "0NA4FK7B8S"
  },
  "kind": "example",
  "link": "https://math2.tamnd.com/node/0NA4FK7B8S/",
  "links": [
    {
      "field": "instance_of",
      "target": "0VKD1TP7F3"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0NA4FK7B8S.md",
  "msc": [
    "54E35"
  ],
  "name": "Discrete metric",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0NA/0NA4FK7B8S.md",
  "status": null,
  "tag": "0NA4FK7B8S",
  "uri": "m2://0NA4FK7B8S",
  "url": "https://math2.tamnd.com/wiki/discrete-metric/",
  "writing": {
    "tag": "0NA4FK7B8S",
    "kind": "example",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      }
    ]
  }
}