"Liouville number" meaning in All languages combined

{
  "etymology_text": "Named after Joseph Liouville (1809–1882), a French mathematician.",
  "forms": [
    {
      "form": "Liouville numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Liouville number (plural Liouville numbers)",
      "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": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Number theory",
          "orig": "en:Number theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ)."
      ],
      "hypernyms": [
        {
          "word": "transcendental number"
        }
      ],
      "id": "en-Liouville_number-en-noun-Q3xx4PCU",
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "irrational number",
          "irrational number"
        ],
        [
          "positive",
          "positive#English"
        ],
        [
          "integer",
          "integer#English"
        ]
      ],
      "raw_glosses": [
        "(number theory) An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ)."
      ],
      "related": [
        {
          "word": "Liouville-Arnold theorem"
        },
        {
          "word": "Liouville's equation"
        },
        {
          "word": "Liouville's formula"
        },
        {
          "word": "Liouville's theorem"
        }
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Joseph Liouville",
        "Liouville number"
      ]
    }
  ],
  "word": "Liouville number"
}

{
  "etymology_text": "Named after Joseph Liouville (1809–1882), a French mathematician.",
  "forms": [
    {
      "form": "Liouville numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Liouville number (plural Liouville numbers)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "transcendental number"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Liouville-Arnold theorem"
    },
    {
      "word": "Liouville's equation"
    },
    {
      "word": "Liouville's formula"
    },
    {
      "word": "Liouville's theorem"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English eponyms",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Number theory"
      ],
      "glosses": [
        "An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ)."
      ],
      "links": [
        [
          "number theory",
          "number theory"
        ],
        [
          "irrational number",
          "irrational number"
        ],
        [
          "positive",
          "positive#English"
        ],
        [
          "integer",
          "integer#English"
        ]
      ],
      "raw_glosses": [
        "(number theory) An irrational number x with the property that, for every positive integer n, there exist integers p and q with q > 1 and such that 0<|x-p/q|<1/(qⁿ)."
      ],
      "topics": [
        "mathematics",
        "number-theory",
        "sciences"
      ],
      "wikipedia": [
        "Joseph Liouville",
        "Liouville number"
      ]
    }
  ],
  "word": "Liouville number"
}