"predimension" meaning in All languages combined

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pre",
        "3": "dimension"
      },
      "expansion": "pre- + dimension",
      "name": "prefix"
    }
  ],
  "etymology_text": "pre- + dimension",
  "forms": [
    {
      "form": "predimensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "predimension (plural predimensions)",
      "name": "en-noun"
    }
  ],
  "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": "other",
          "name": "English terms prefixed with pre-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2016, Boris Zilber, “Analytic Zariski structures and non-elementary categoricity”, in arXiv",
          "text": "We also demonstrate how Hrushovski's predimension arises in this general context as a natural geometric notion and use it as one of our main tools..",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The result of a function on a group of sets, where the function satisfies three conditions: (1) it returns 0 for the empty set; (2) if one set is contained in another set, the function always returns a value that is less than or equal to the result for the containing set; (3) the result for the union of two sets is less than or equal to the sum of the results for each of those sets individually minus the result for their intersection."
      ],
      "id": "en-predimension-en-noun-2KjmVmYs",
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The result of a function on a group of sets, where the function satisfies three conditions: (1) it returns 0 for the empty set; (2) if one set is contained in another set, the function always returns a value that is less than or equal to the result for the containing set; (3) the result for the union of two sets is less than or equal to the sum of the results for each of those sets individually minus the result for their intersection."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "predimension"
}

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "pre",
        "3": "dimension"
      },
      "expansion": "pre- + dimension",
      "name": "prefix"
    }
  ],
  "etymology_text": "pre- + dimension",
  "forms": [
    {
      "form": "predimensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "predimension (plural predimensions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English nouns",
        "English terms prefixed with pre-",
        "English terms with quotations",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2016, Boris Zilber, “Analytic Zariski structures and non-elementary categoricity”, in arXiv",
          "text": "We also demonstrate how Hrushovski's predimension arises in this general context as a natural geometric notion and use it as one of our main tools..",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The result of a function on a group of sets, where the function satisfies three conditions: (1) it returns 0 for the empty set; (2) if one set is contained in another set, the function always returns a value that is less than or equal to the result for the containing set; (3) the result for the union of two sets is less than or equal to the sum of the results for each of those sets individually minus the result for their intersection."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The result of a function on a group of sets, where the function satisfies three conditions: (1) it returns 0 for the empty set; (2) if one set is contained in another set, the function always returns a value that is less than or equal to the result for the containing set; (3) the result for the union of two sets is less than or equal to the sum of the results for each of those sets individually minus the result for their intersection."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "predimension"
}