"Archimedean ordered field" meaning in All languages combined

{
  "antonyms": [
    {
      "word": "non-Archimedean ordered field"
    }
  ],
  "forms": [
    {
      "form": "Archimedean ordered fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Archimedean ordered field (plural Archimedean ordered fields)",
      "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": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2006, Richard W. Kaye, “Archimedean ordered fields”, in web.mat.bham.ac.uk, retrieved 2012-11-13",
          "text": "The next axiom concerns [ x ], the integer part function. We have seen that this function plays a useful role in our theory, but it turns out that not all ordered fields have it defined. A field for which integer part is defined is called an Archimedean Ordered Field.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An ordered field which satisfies the axiom of Archimedes."
      ],
      "hypernyms": [
        {
          "word": "ordered field"
        }
      ],
      "hyponyms": [
        {
          "word": "real number system"
        }
      ],
      "id": "en-Archimedean_ordered_field-en-noun-hFIS6puH",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "ordered field",
          "ordered field"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An ordered field which satisfies the axiom of Archimedes."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "an ordered field which satisfies the axiom of Archimedes",
          "tags": [
            "masculine"
          ],
          "word": "corpo ordenado arquimediano"
        }
      ]
    }
  ],
  "word": "Archimedean ordered field"
}

{
  "antonyms": [
    {
      "word": "non-Archimedean ordered field"
    }
  ],
  "forms": [
    {
      "form": "Archimedean ordered fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Archimedean ordered field (plural Archimedean ordered fields)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "ordered field"
    }
  ],
  "hyponyms": [
    {
      "word": "real number system"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Mathematics"
      ],
      "examples": [
        {
          "ref": "2006, Richard W. Kaye, “Archimedean ordered fields”, in web.mat.bham.ac.uk, retrieved 2012-11-13",
          "text": "The next axiom concerns [ x ], the integer part function. We have seen that this function plays a useful role in our theory, but it turns out that not all ordered fields have it defined. A field for which integer part is defined is called an Archimedean Ordered Field.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "An ordered field which satisfies the axiom of Archimedes."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "ordered field",
          "ordered field"
        ]
      ],
      "raw_glosses": [
        "(mathematics) An ordered field which satisfies the axiom of Archimedes."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "an ordered field which satisfies the axiom of Archimedes",
      "tags": [
        "masculine"
      ],
      "word": "corpo ordenado arquimediano"
    }
  ],
  "word": "Archimedean ordered field"
}