"surreal number" meaning in 英語

{
  "categories": [
    {
      "kind": "other",
      "name": "有1個詞條的頁面",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "有詞條的頁面",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語可數名詞",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "英語名詞",
      "parents": [],
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    },
    {
      "kind": "other",
      "name": "英語詞元",
      "parents": [],
      "source": "w"
    }
  ],
  "etymology_text": "1974年由高德納在其小說 Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness 中提出。此概念後來由英國數學家約翰·何頓·康威應用在對圍棋博弈論的研究中。最初康威只稱其為 numbers，但在1976年的 On Numbers and Games 中採用了高德納的用詞。",
  "forms": [
    {
      "form": "surreal numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "有使用例的英語詞",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "英語 數學",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "英語使用例翻譯請求",
          "parents": [],
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        }
      ],
      "examples": [
        {
          "text": "Conway's construction of surreal numbers relies on the use of transfinite induction.",
          "translation": "康威對超現實數的建構基於超限歸納法的使用。"
        },
        {
          "text": "Conway's approach was to build numbers from scratch using a construction inspired by his game theory research; the resulting class of surreal numbers proved much larger than the class of real numbers."
        },
        {
          "text": "ISBN 9780521312059"
        },
        {
          "ref": "2012, Fredrik Nordvall Forsberg, Anton Setzer, A Finite Axiomatisation of Inductive-Inductive Definitions, Ulrich Berger, Hannes Diener, Peter Schuster, Monika Seisenberger (editors), Logic, Construction, Computation, Ontos Verlag, page 263,",
          "text": "The class² of surreal numbers is defined inductively, together with an order relation on surreal numbers wich is also defined inductively:\n#*:: • A surreal number X=(X_L,X_R) consists of two sets X_L and X_R of surreal numbers, such that no element from X_L is greater than any element from X_R.\n#*:: • A surreal number Y=(Y_L,Y_R) is greater than another surreal number X=(X_L,X_R), X<Y, if and only if\n#*::: − there is no x∈X_L such that Y<x, and\n#*::: − there is no y∈Y_R such that y<X."
        },
        {
          "ref": "2018, Steven G. Krantz, Essentials of Mathematical Thinking, Taylor & Francis (Chapman & Hall/CRC Press), page 247,",
          "text": "Here we shall follow Conway's exposition rather closely. Let L and R be two sets of numbers. Assume that no member of L is greater than or equal to any member of R. Then L|R is a surreal number. All surreal numbers are constructed in this fashion."
        }
      ],
      "glosses": [
        "超現實數"
      ],
      "id": "zh-surreal_number-en-noun-XApsJkev",
      "topics": [
        "mathematics"
      ]
    }
  ],
  "word": "surreal number"
}

{
  "categories": [
    "有1個詞條的頁面",
    "有詞條的頁面",
    "英語可數名詞",
    "英語名詞",
    "英語詞元"
  ],
  "etymology_text": "1974年由高德納在其小說 Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness 中提出。此概念後來由英國數學家約翰·何頓·康威應用在對圍棋博弈論的研究中。最初康威只稱其為 numbers，但在1976年的 On Numbers and Games 中採用了高德納的用詞。",
  "forms": [
    {
      "form": "surreal numbers",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "英語",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "名詞",
  "senses": [
    {
      "categories": [
        "有使用例的英語詞",
        "英語 數學",
        "英語使用例翻譯請求"
      ],
      "examples": [
        {
          "text": "Conway's construction of surreal numbers relies on the use of transfinite induction.",
          "translation": "康威對超現實數的建構基於超限歸納法的使用。"
        },
        {
          "text": "Conway's approach was to build numbers from scratch using a construction inspired by his game theory research; the resulting class of surreal numbers proved much larger than the class of real numbers."
        },
        {
          "text": "ISBN 9780521312059"
        },
        {
          "ref": "2012, Fredrik Nordvall Forsberg, Anton Setzer, A Finite Axiomatisation of Inductive-Inductive Definitions, Ulrich Berger, Hannes Diener, Peter Schuster, Monika Seisenberger (editors), Logic, Construction, Computation, Ontos Verlag, page 263,",
          "text": "The class² of surreal numbers is defined inductively, together with an order relation on surreal numbers wich is also defined inductively:\n#*:: • A surreal number X=(X_L,X_R) consists of two sets X_L and X_R of surreal numbers, such that no element from X_L is greater than any element from X_R.\n#*:: • A surreal number Y=(Y_L,Y_R) is greater than another surreal number X=(X_L,X_R), X<Y, if and only if\n#*::: − there is no x∈X_L such that Y<x, and\n#*::: − there is no y∈Y_R such that y<X."
        },
        {
          "ref": "2018, Steven G. Krantz, Essentials of Mathematical Thinking, Taylor & Francis (Chapman & Hall/CRC Press), page 247,",
          "text": "Here we shall follow Conway's exposition rather closely. Let L and R be two sets of numbers. Assume that no member of L is greater than or equal to any member of R. Then L|R is a surreal number. All surreal numbers are constructed in this fashion."
        }
      ],
      "glosses": [
        "超現實數"
      ],
      "topics": [
        "mathematics"
      ]
    }
  ],
  "word": "surreal number"
}