Surreal number

English

Etymology

Coined by Template:W in his novelette Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness (1974). The concept had been developed by British mathematician Template:W for his game theoretic research of the board game go. Conway had simply called them numbers, but subsequently adopted Knuth's term and used it in his book Template:W (1976).

Noun

1. Template:Lb Any element of a field equivalent to the real numbers augmented with infinite and infinitesimal numbers (respectively larger and smaller (in absolute value) than any positive real number).

   Template:Ux

   Template:Ux

   • Template:Quote-journal
   • 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 $y\le X$.

   • Template:Quote-book

Translations

• French: Template:T
• Italian: Template:T
• Portuguese: Template:T

Further reading

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