{
  "aliases": [
    "limited-subtraction",
    "m-semiring",
    "naturally-ordered",
    "naturally-ordered-monoid",
    "naturally-ordered-semiring",
    "proper-subtraction",
    "subtraction-of-natural-numbers",
    "truncated-subtraction"
  ],
  "backlinks": null,
  "body": "\n## Summary\n\nIn mathematics, **monus** is an operator on certain [[commutative|099E72KTF8]] [[monoids|0N6R902FG1]] that are not groups. A commutative monoid on which a monus operator is defined is called a **commutative monoid with monus**, or **CMM**. The monus operator may be denoted with the minus sign, \"$-$\", because the [[natural numbers|0MWKJ44V5A]] are a CMM under subtraction. It is also denoted with a dotted minus sign, \"$\\mathbin{\\dot{-}}$\", to distinguish it from the standard subtraction operator.\n",
  "commit": "f59dc232b275d0af9ce0d36319ccb95f730f90a0",
  "front": {
    "aliases": [
      "limited-subtraction",
      "m-semiring",
      "naturally-ordered",
      "naturally-ordered-monoid",
      "naturally-ordered-semiring",
      "proper-subtraction",
      "subtraction-of-natural-numbers",
      "truncated-subtraction"
    ],
    "inventory": [
      "5S7W2KEMPZ"
    ],
    "kind": "concept",
    "name": "Monus",
    "same_as": {
      "wikidata": "Q6906971",
      "wikipedia": "Monus"
    },
    "sources": [
      {
        "locator": "Monus",
        "mention": "wikipedia://en/22395202",
        "note": "adopted",
        "sections": [
          "Summary"
        ],
        "wikipedia": "en:22395202@r1329642033"
      }
    ],
    "tag": "S19G8ZP707"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/S19G8ZP707/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/S19G8ZP707.md",
  "msc": null,
  "name": "Monus",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/S19/S19G8ZP707.md",
  "status": null,
  "tag": "S19G8ZP707",
  "uri": "m2://S19G8ZP707",
  "url": "https://math2.tamnd.com/wiki/monus/",
  "writing": {
    "tag": "S19G8ZP707",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge defines in",
        "note": "at least one definition",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
