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Infinity: Countable set, Cantor's diagonal argument, Surreal number, Continuum hypothesis, Hyperreal number, Extended real number line - Softcover
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 57. Chapters: Countable set, Cantor's diagonal argument, Surreal number, Continuum hypothesis, Hyperreal number, Extended real number line, Uncountable set, Where Mathematics Comes From, Absolute Infinite, Ultrafinitism, Infinitesimal, Infinite monkey theorem, Actual infinity, Non-standard calculus, Real projective line, Temporal finitism, Cardinality of the continuum, Aleph number, Beth number, Line at infinity, Plane at infinity, Apeirogon, Levi-Civita field, Point at infinity, Hyperplane at infinity, Infinity plus one, Superreal number, Hyperinteger, Circular points at infinity, Directed infinity, Amorphous set. Excerpt: 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. 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...
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- PublisherBooks LLC, Wiki Series
- Publication date2011
- ISBN 10 1157249906
- ISBN 13 9781157249900
- BindingTapa blanda
- LanguageEnglish
- Number of pages58
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