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- Surreal_number abstract "In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field. (Strictly speaking, the surreals are not a set, but a proper class.) If formulated in Von Neumann–Bernays–Gödel set theory, the surreal numbers are the largest possible ordered field; all other ordered fields, such as the rationals, the reals, the rational functions, the Levi-Civita field, the superreal numbers, and the hyperreal numbers, can be realized as subfields of the surreals. It has also been shown (in Von Neumann–Bernays–Gödel set theory) that the maximal class hyperreal field is isomorphic to the maximal class surreal field; in theories without the axiom of global choice, this need not be the case, and in such theories it is not necessarily true that the surreals are the largest ordered field. The surreals also contain all transfinite ordinal numbers; the arithmetic on them is given by the natural operations.The definition and construction of the surreals is due to John Horton Conway. They were introduced in Donald Knuth's 1974 book Surreal Numbers: How Two Ex-Students Turned on to Pure Mathematics and Found Total Happiness. This book is a mathematical novelette, and is notable as one of the rare cases where a new mathematical idea was first presented in a work of fiction. In his book, which takes the form of a dialogue, Knuth coined the term surreal numbers for what Conway had simply called numbers originally. Conway liked the new name, and later adopted it himself. Conway then described the surreal numbers and used them for analyzing games in his 1976 book On Numbers and Games.".
- Surreal_number thumbnail Surreal_number_tree.svg?width=300.
- Surreal_number wikiPageExternalLink infinityplusonea599.
- Surreal_number wikiPageExternalLink surreal-numbers.
- Surreal_number wikiPageExternalLink Hack.
- Surreal_number wikiPageExternalLink sn.html.
- Surreal_number wikiPageExternalLink surreal.html.
- Surreal_number wikiPageID "51432".
- Surreal_number wikiPageRevisionID "606725584".
- Surreal_number hasPhotoCollection Surreal_number.
- Surreal_number id "3352".
- Surreal_number title "Surreal number".
- Surreal_number subject Category:Combinatorial_game_theory.
- Surreal_number subject Category:Infinity.
- Surreal_number subject Category:Mathematical_logic.
- Surreal_number subject Category:Real_closed_field.
- Surreal_number comment "In mathematics, the surreal number system is an arithmetic continuum containing the real numbers as well as infinite and infinitesimal numbers, respectively larger or smaller in absolute value than any positive real number. The surreals share many properties with the reals, including a total order ≤ and the usual arithmetic operations (addition, subtraction, multiplication, and division); as such, they form an ordered field.".
- Surreal_number label "Liczby nadrzeczywiste".
- Surreal_number label "Nombre surréel".
- Surreal_number label "Numero surreale".
- Surreal_number label "Número surreal".
- Surreal_number label "Número surreal".
- Surreal_number label "Surreal number".
- Surreal_number label "Surreale Zahl".
- Surreal_number label "Surreëel getal".
- Surreal_number label "عدد فوق حقيقي".
- Surreal_number label "超現實數".
- Surreal_number sameAs Nadreálné_číslo.
- Surreal_number sameAs Surreale_Zahl.
- Surreal_number sameAs Número_surreal.
- Surreal_number sameAs Nombre_surréel.
- Surreal_number sameAs Numero_surreale.
- Surreal_number sameAs 초현실수.
- Surreal_number sameAs Surreëel_getal.
- Surreal_number sameAs Liczby_nadrzeczywiste.
- Surreal_number sameAs Número_surreal.
- Surreal_number sameAs m.0dknv.
- Surreal_number sameAs Q875333.
- Surreal_number sameAs Q875333.
- Surreal_number wasDerivedFrom Surreal_number?oldid=606725584.
- Surreal_number depiction Surreal_number_tree.svg.
- Surreal_number isPrimaryTopicOf Surreal_number.