How To Measure The Infinite: Mathematics With Infinite And Infinitesimal Numbers

The study of non-Archimedean mathematics deserves to be utilized more in applied mathematics. This book presents an elementary introduction to the Alpha-Theory, a nonstandard analysis approach, and the Theory of Numerosity, a new way of counting infinite sets.

Format: Hardback
Length: 348 pages
Publication date: 28 February 2019
Publisher: World Scientific Publishing Co Pte Ltd

The study of the almost-forgotten, non-Archimedean mathematics holds immense potential for utilization across a diverse range of fields within the broader realm of applied mathematics. This text serves as a compelling argument in favor of increased attention being paid to this field.

In this book, an original introduction to the use of infinitesimal and infinite numbers, known as the Alpha-Theory, is presented. This theory can be regarded as an alternative approach to nonstandard analysis, offering a fresh perspective on mathematical concepts. The fundamental principles are presented in a straightforward manner, employing the ordinary language of mathematics, thereby distinguishing this approach from other nonstandard analysis presentations that necessitate the use of technical notions from logic from the very beginning.

To demonstrate the power and applicability of the Alpha-Theory, several applications are included. These applications serve to showcase the remarkable capabilities of the theory.

Furthermore, the book provides a comprehensive exposition of the Theory of Numerosity, a novel approach to counting (countable) infinite sets that upholds the ancient Euclid's Principle: The whole is larger than its parts.

The book is structured into five parts: Alpha-Calculus, Alpha-Theory, Applications, Foundations, and Numerosity Theory.

By delving into the realm of non-Archimedean mathematics, this book offers a valuable resource for researchers, scholars, and practitioners seeking to expand their understanding of mathematical concepts and explore new avenues for innovation and application. The insights and techniques presented herein have the potential to revolutionize various fields, including mathematics, computer science, engineering, and economics.

Weight: 754g
Dimension: 252 x 177 x 25 (mm)
ISBN-13: 9789812836373