"order type" meaning in English

{
  "forms": [
    {
      "form": "order types",
      "tags": [
        "plural"
      ]
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      "expansion": "order type (plural order types)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Set theory",
          "orig": "en:Set theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
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          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "1965 [John Wiley], Raymond L. Wilder, Introduction to the Foundations of Mathematics: 2nd Edition, 2012, Dover, page 116,\nAnother way of putting this is to state that the order type is that aspect of the arrangement of the elements of a simply ordered set, which remains unchanged when any two elements are exchanged. […] As in the case of cardinal numbers, order types may be denoted by suitable symbols called ordinal numerals."
        },
        {
          "ref": "2005, Egbert Harzheim, Ordered Sets, Springer, page 332",
          "text": "In [13] Chajoth studied how the order type of a chain can alter if we change the position of elements in a linearly ordered set, resp. if we introduce a new element in a linearly ordered set.",
          "type": "quotation"
        },
        {
          "text": "2011, Douglas Cenzer, Valentina Harizanov, Jeffrey B. Remmel, Effective Categoricity of Injection Structures, Benedikt Löwe, Dag Normann, Ivan Soskov, Alexandra Soskova (editors, Models of Computation in Context: 7th Conference on Computability in Europe, CiE 2011, Proceedings, Springer, LNCS 6735, page 51,\nWe let ω denote the order type of N under the usual ordering and Z denote the order type of Z under the usual ordering."
        }
      ],
      "glosses": [
        "In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation \"existence of an order-preserving bijection\"."
      ],
      "id": "en-order_type-en-noun-dycFKT6q",
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "totally ordered set",
          "totally ordered set"
        ],
        [
          "characteristic",
          "characteristic"
        ],
        [
          "equivalence class",
          "equivalence class"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ],
        [
          "bijection",
          "bijection"
        ]
      ],
      "raw_glosses": [
        "(set theory) In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation \"existence of an order-preserving bijection\"."
      ],
      "related": [
        {
          "word": "order isomorphism"
        },
        {
          "word": "ordinal number"
        }
      ],
      "synonyms": [
        {
          "word": "order-type"
        },
        {
          "word": "ordertype"
        }
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "characteristic of being a member of an equivalence class of ordered sets",
          "word": "järjestystyyppi"
        }
      ],
      "wikipedia": [
        "Ordinal number#Von Neumann definition of ordinals",
        "order type"
      ]
    }
  ],
  "word": "order type"
}

{
  "forms": [
    {
      "form": "order types",
      "tags": [
        "plural"
      ]
    }
  ],
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      "expansion": "order type (plural order types)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "order isomorphism"
    },
    {
      "word": "ordinal number"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
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        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Set theory"
      ],
      "examples": [
        {
          "text": "1965 [John Wiley], Raymond L. Wilder, Introduction to the Foundations of Mathematics: 2nd Edition, 2012, Dover, page 116,\nAnother way of putting this is to state that the order type is that aspect of the arrangement of the elements of a simply ordered set, which remains unchanged when any two elements are exchanged. […] As in the case of cardinal numbers, order types may be denoted by suitable symbols called ordinal numerals."
        },
        {
          "ref": "2005, Egbert Harzheim, Ordered Sets, Springer, page 332",
          "text": "In [13] Chajoth studied how the order type of a chain can alter if we change the position of elements in a linearly ordered set, resp. if we introduce a new element in a linearly ordered set.",
          "type": "quotation"
        },
        {
          "text": "2011, Douglas Cenzer, Valentina Harizanov, Jeffrey B. Remmel, Effective Categoricity of Injection Structures, Benedikt Löwe, Dag Normann, Ivan Soskov, Alexandra Soskova (editors, Models of Computation in Context: 7th Conference on Computability in Europe, CiE 2011, Proceedings, Springer, LNCS 6735, page 51,\nWe let ω denote the order type of N under the usual ordering and Z denote the order type of Z under the usual ordering."
        }
      ],
      "glosses": [
        "In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation \"existence of an order-preserving bijection\"."
      ],
      "links": [
        [
          "set theory",
          "set theory"
        ],
        [
          "set",
          "set"
        ],
        [
          "totally ordered set",
          "totally ordered set"
        ],
        [
          "characteristic",
          "characteristic"
        ],
        [
          "equivalence class",
          "equivalence class"
        ],
        [
          "equivalence relation",
          "equivalence relation"
        ],
        [
          "bijection",
          "bijection"
        ]
      ],
      "raw_glosses": [
        "(set theory) In the context of sets equipped with an order (especially, the context of totally ordered sets), the characteristic of being a member of some equivalence class of such sets under the equivalence relation \"existence of an order-preserving bijection\"."
      ],
      "topics": [
        "mathematics",
        "sciences",
        "set-theory"
      ],
      "wikipedia": [
        "Ordinal number#Von Neumann definition of ordinals",
        "order type"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "order-type"
    },
    {
      "word": "ordertype"
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "characteristic of being a member of an equivalence class of ordered sets",
      "word": "järjestystyyppi"
    }
  ],
  "word": "order type"
}