High Quality Content by WIKIPEDIA articles! 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. In a rigorous set theoretic sense, 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, are subfields of the surreals. The surreals also contain all transfinite ordinal numbers reachable in the set theory in which they are constructed. Данное издание представляет собой компиляцию сведений, находящихся в свободном доступе в среде Интернет в целом, и в...

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