"factoriality" meaning in English

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "factorial",
        "3": "ity"
      },
      "expansion": "factorial + -ity",
      "name": "suffix"
    }
  ],
  "etymology_text": "factorial + -ity",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "factoriality (uncountable)",
      "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"
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          "source": "w"
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        {
          "kind": "other",
          "name": "English terms suffixed with -ity",
          "parents": [],
          "source": "w"
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      ],
      "examples": [
        {
          "ref": "2009 August 20, Notices of the American Mathematical Society, volume 56, number 7",
          "text": "The homogeneous case: Graded factoriality; Global and local structure of the sheaf category; Tubular shifts and prime elements; Commutativity and multiplicity freeness; Automorphism groups; Part 2.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The property of being factorial."
      ],
      "id": "en-factoriality-en-noun-DDkeYhq2",
      "links": [
        [
          "factorial",
          "factorial"
        ]
      ],
      "tags": [
        "uncountable"
      ]
    }
  ],
  "word": "factoriality"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "factorial",
        "3": "ity"
      },
      "expansion": "factorial + -ity",
      "name": "suffix"
    }
  ],
  "etymology_text": "factorial + -ity",
  "head_templates": [
    {
      "args": {
        "1": "-"
      },
      "expansion": "factoriality (uncountable)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
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        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms suffixed with -ity",
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      "examples": [
        {
          "ref": "2009 August 20, Notices of the American Mathematical Society, volume 56, number 7",
          "text": "The homogeneous case: Graded factoriality; Global and local structure of the sheaf category; Tubular shifts and prime elements; Commutativity and multiplicity freeness; Automorphism groups; Part 2.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The property of being factorial."
      ],
      "links": [
        [
          "factorial",
          "factorial"
        ]
      ],
      "tags": [
        "uncountable"
      ]
    }
  ],
  "word": "factoriality"
}