{
  "aliases": null,
  "backlinks": [
    {
      "field": "uses",
      "target": "0HTGB13FE2"
    }
  ],
  "body": "\n## Definition\n\nLet $X$ be a [[set|0SJ3RX9TXA]] of nonempty sets.\nA choice function on $X$ is a [[function|0XHDTE5YMZ]] $c \\colon X \\to \\bigcup X$ such that $c(S) \\in S$ for each $S \\in X$.\n\n## Remarks\n\nFor a finite set $X$, a choice function exists without any axiom of choice.\nFor the set of nonempty subsets of $\\mathbb{N}$, the function that sends each subset to its least element is a choice function.\nThe [[axiom of choice|0HTGB13FE2]] says that each set of nonempty sets has a choice function.\n\n## Explanations\n\n### L1 human\n\nThink of $X$ as a collection of boxes, none empty.\nA choice function names one object in each box.\nSometimes a rule gives it, such as \"take the smallest number\".\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "defines": "0FWBQ53MPJ",
    "kind": "definition",
    "msc": [
      "03E25"
    ],
    "name": "Choice function",
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Choice_function"
      }
    ],
    "tag": "0YXEQWRGP0",
    "uses": [
      "0XHDTE5YMZ",
      "05GK32H72H"
    ]
  },
  "kind": "definition",
  "link": "https://math2.tamnd.com/node/0YXEQWRGP0/",
  "links": [
    {
      "field": "defines",
      "target": "0FWBQ53MPJ"
    },
    {
      "field": "uses",
      "target": "0XHDTE5YMZ"
    },
    {
      "field": "uses",
      "target": "05GK32H72H"
    }
  ],
  "markdown": "https://math2.tamnd.com/node/0YXEQWRGP0.md",
  "msc": [
    "03E25"
  ],
  "name": "Choice function",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0YX/0YXEQWRGP0.md",
  "status": null,
  "tag": "0YXEQWRGP0",
  "uri": "m2://0YXEQWRGP0",
  "url": "https://math2.tamnd.com/wiki/choice-function-definition/",
  "writing": {
    "tag": "0YXEQWRGP0",
    "kind": "definition",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "one example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge not_instance_of in",
        "note": "one non-example that fails one clause",
        "have": 0,
        "want": 1
      }
    ]
  }
}