"real number system" meaning in English

{
  "forms": [
    {
      "form": "real number systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "real number system"
      },
      "expansion": "real number system (plural real number systems)",
      "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": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "extended real number system"
        }
      ],
      "examples": [
        {
          "ref": "2008 November, Ambar N. Sengupta, “Notes in Introductory Real Analysis”, in www.math.lsu.edu, retrieved 2012-07-13",
          "text": "As we have mentioned before, the structure of Euclidean geometry, as formalized through the axioms of Hilbert, produces an archimedean ordered field. To com- plete the story, one can add to these axioms the further requirement that this field is maximal in the sense that it cannot be embedded inside any larger archimedean ordered field. It turns out then that any such ordered field is isomorphic to any other, and thus there is essentially one such ordered field. This ordered field is the real number system R.",
          "type": "quotation"
        },
        {
          "ref": "2010 April 16, Lindsay Keegan, “The Ghosts of Departed Quantities”, in www.math.ufl.edu, archived from the original on 2011-09-30",
          "text": "The real number system is a complete, linearly ordered field ℛ=(ℝ,+,·,<).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The complete Archimedean ordered field (of real numbers)."
      ],
      "hypernyms": [
        {
          "word": "Archimedean ordered field"
        }
      ],
      "id": "en-real_number_system-en-noun-lt20-5uV",
      "links": [
        [
          "mathematics",
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        ],
        [
          "complete",
          "completeness axiom"
        ],
        [
          "Archimedean ordered field",
          "Archimedean ordered field"
        ],
        [
          "real number",
          "real number"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The complete Archimedean ordered field (of real numbers)."
      ],
      "related": [
        {
          "word": "real number line"
        },
        {
          "word": "standard topology"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "real number system"
}

{
  "derived": [
    {
      "word": "extended real number system"
    }
  ],
  "forms": [
    {
      "form": "real number systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {
        "head": "real number system"
      },
      "expansion": "real number system (plural real number systems)",
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  ],
  "hypernyms": [
    {
      "word": "Archimedean ordered field"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "real number line"
    },
    {
      "word": "standard topology"
    }
  ],
  "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": "2008 November, Ambar N. Sengupta, “Notes in Introductory Real Analysis”, in www.math.lsu.edu, retrieved 2012-07-13",
          "text": "As we have mentioned before, the structure of Euclidean geometry, as formalized through the axioms of Hilbert, produces an archimedean ordered field. To com- plete the story, one can add to these axioms the further requirement that this field is maximal in the sense that it cannot be embedded inside any larger archimedean ordered field. It turns out then that any such ordered field is isomorphic to any other, and thus there is essentially one such ordered field. This ordered field is the real number system R.",
          "type": "quotation"
        },
        {
          "ref": "2010 April 16, Lindsay Keegan, “The Ghosts of Departed Quantities”, in www.math.ufl.edu, archived from the original on 2011-09-30",
          "text": "The real number system is a complete, linearly ordered field ℛ=(ℝ,+,·,<).",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The complete Archimedean ordered field (of real numbers)."
      ],
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        ],
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        ]
      ],
      "raw_glosses": [
        "(mathematics) The complete Archimedean ordered field (of real numbers)."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "real number system"
}