{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "GXNE1EPK0S"
    }
  ],
  "body": "\n## Summary\n\nA nullary operation on a set $A$ is a [[finitary operation|EJ8YJVM9BW]] of [[arity|MSXX2P86CY]] $0$, that is, a map from the one-element set $A^0$ to $A$.\nSuch a map is the same as the choice of one element of $A$, so nullary operations are the constants of an [[algebraic structure|QJGPT2W0FT]].\nTreating constants as operations lets identity elements, such as $0$ in a ring or $e$ in a [[group|G5S1M9]], be part of the signature.\n\n## Explanations\n\n### L1 human\n\nAn operation with no inputs cannot depend on anything, so it always gives the same element.\nThat element is a constant.\nFor example, in the integers with addition, the number $0$ can be seen as a nullary operation.\nWhen $0$ is part of the signature, a [[homomorphism|KBXSZC6BV1]] must send the constant $0$ to the constant $0$ of the target.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08A62",
      "08A02"
    ],
    "name": "Nullary operation",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Arity"
      }
    ],
    "specializes": [
      "EJ8YJVM9BW"
    ],
    "tag": "9HPF7TE18C"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/9HPF7TE18C/",
  "links": [
    {
      "field": "specializes",
      "target": "EJ8YJVM9BW"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/9HPF7TE18C.md",
  "msc": [
    "08A62",
    "08A02"
  ],
  "name": "Nullary operation",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/9HP/9HPF7TE18C.md",
  "status": null,
  "tag": "9HPF7TE18C",
  "uri": "m2://9HPF7TE18C",
  "url": "https://tamnd.github.io/math2/wiki/nullary-operation/",
  "writing": {
    "tag": "9HPF7TE18C",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}