Surreal number

英語

詞源

1974年由Template:W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Template:W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 Template:W 中採用了高德納的用詞。

名詞

1. Template:Lb 超現實數

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   • 1986, Harry Gonshor, An Introduction to the Theory of Surreal Numbers, Template:W, 1987, Paperback, Template:ISBN.
   • 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,

     The class² of surreal numbers is defined inductively, together with an order relation on surreal numbers wich is also defined inductively:

     • 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 $X_R$.

     • A surreal number $Y=(Y_L,Y_R)$ is greater than another surreal number $X=(X_L,X_R)$, $X\le Y$, if and only if

     − there is no $x\in X_L$ such that $Y\le x$, and

     − there is no $y\in Y_R$ such that $y\le X$.

   • 2018, Steven G. Krantz, Essentials of Mathematical Thinking, Taylor & Francis (Chapman & Hall/CRC Press), page 247,

     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.

延伸閱讀

• Template:Pedialite
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• Surreal Number on Template:W
• Surreal numbers on Template:W