HOW TO MEASURE THE INFINITE: MATHEMATICS WITH INFINITE AND INFINITESIMAL NUMBERS - Hardcover

Vieri Benci; Mauro Di Nasso

Hardcover

ISBN 10: 9812836373 ISBN 13: 9789812836373

Publisher: World Scientific Publishing Co, 2014

Synopsis

This 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.

Readership: Advanced undergraduate and graduate students in mathematics and philosophy.

About this title

From the Inside Flap:

This book provides a comprehensive exposition of a new way of counting (countable) infinite sets, in particular, numerosities that maintain the ancient Aristotle's principle: "The whole is larger than its parts." It also contains an original introduction 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 introductions, where technical notions from logic are used which are not familiar to most mathematicians.

This book is the result of a scientific collaboration among different perspectives of mathematics. The first author is a leading figure in variational and topological methods in nonlinear analysis, and has cultivated a broad range of interests in applications of mathematics; while the second author is a specialist in mathematical logic and in the foundations of nonstandard analysis.

Review:

"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." -- CHOICE

About this edition

• Publisher: World Scientific Publishing Co
• Publication date: 2014
• ISBN 10: 9812836373
• ISBN 13: 9789812836373
• Binding: Hardcover
• Number of pages: 348