How to Measure the Infinite: Mathematics with Infinite and Infinitesimal Numbers (Hardcover) (ISBN-13: 9789812836373)

'This text shows that the study of the almost-forgotten, non-Archimedean mathematics deserves to be utilized more intently in a variety of fields within the larger domain of applied mathematics.'CHOICEThis book contains an original introduction to the use of infinitesimal and infinite numbers, namely, the Alpha-Theory, which can be considered as an alternative approach to nonstandard analysis.The basic principles are presented in an elementary way by using the ordinary language of mathematics; this is to be contrasted with other presentations of nonstandard analysis where technical notions from logic are required since the beginning. Some applications are included and aimed at showing the power of the theory.The book also provides a comprehensive exposition of the Theory of Numerosity, a new way of counting (countable) infinite sets that maintains the ancient Euclid's Principle: 'The whole is larger than its parts'. The book is organized into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.

Author: Vieri Benci, Mauro Di Nasso
ISBN-10: 9812836373
ISBN-13: 9789812836373
Publisher: World Scientific Publishing Company
Language: English
Published: 11/27/2018
Pages: 348
Format: Hardcover
Weight: 1.65lbs
Size: 9.61h x 6.69w x 0.81d

Review Citation(s):
Choice 11/01/2019