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Real Number
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High Quality Content by WIKIPEDIA articles! In mathematics, the real numbers include both rational numbers, such as 42 and 23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real numbers may be thought of as points on an infinitely long number line. These descriptions of the real numbers, while intuitively accessible, are not sufficiently rigorous for the purposes of pure mathematics. The discovery of a suitably rigorous definition of the real numbers indeed, the realization that a better definition was needed was one of the most important developments of 19th century mathematics. Popular definitions in use today include equivalence classes of Cauchy sequences of rational numbers; Dedekind cuts; a more sophisticated version of "decimal representation"; and an axiomatic definition of the real numbers as the unique complete Archimedean ordered field. These definitions are all described in detail below.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130344757
- Editor Lambert M. Surhone, Miriam T. Timpledon, Susan F. Marseken
- Sprache Englisch
- Größe H220mm x B150mm x T5mm
- Jahr 2010
- EAN 9786130344757
- Format Fachbuch
- ISBN 978-613-0-34475-7
- Titel Real Number
- Untertitel Square Root of 2, Equivalence Class, Decimal Representation, Cauchy Sequence, Dedekind Cut, Archimedean Property, Complete Metric Space
- Gewicht 137g
- Herausgeber VDM Verlag Dr. Müller e.K.
- Anzahl Seiten 80
- Genre Mathematik
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