Hyperreal Number: Infinity, Infinitesimal, Field extension, Real number, Transfer principle, First-order logic, Soundness, Euclid, Method of exhaustion, Abraham Robinson, Mathematical analysis - Softcover

 
9786130686314: Hyperreal Number: Infinity, Infinitesimal, Field extension, Real number, Transfer principle, First-order logic, Soundness, Euclid, Method of exhaustion, Abraham Robinson, Mathematical analysis
Softcover
ISBN 10: 6130686315 ISBN 13: 9786130686314
Verlag: Alphascript Publishing, 2010

Inhaltsangabe

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. Such quantities had been in widespread use in various forms, for several centuries prior to the introduction of hyperreal numbers. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form Such a number is infinite, and its inverse is infinitesimal. The hyperreal numbers satisfy the transfer principle, which states that true first order statements about R are also valid in *R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals. Concerns about the logical soundness of arguments involving infinitesimals date back to ancient Greek mathematics, with Euclid replacing such proofs with ones using other techniques such as the method of exhaustion

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Reseña del editor

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. Such quantities had been in widespread use in various forms, for several centuries prior to the introduction of hyperreal numbers. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R that contains numbers greater than anything of the form Such a number is infinite, and its inverse is infinitesimal. The hyperreal numbers satisfy the transfer principle, which states that true first order statements about R are also valid in *R. For example, the commutative law of addition, x + y = y + x, holds for the hyperreals just as it does for the reals. Concerns about the logical soundness of arguments involving infinitesimals date back to ancient Greek mathematics, with Euclid replacing such proofs with ones using other techniques such as the method of exhaustion

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Verlag
Alphascript Publishing
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
6130686315
ISBN 13 
9786130686314
Einband
Tapa blanda
Anzahl der Seiten
84
Herausgeber
Miller Frederic P., Vandome Agnes F., McBrewster John
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar