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

Vieri Benci

ISBN 10: 9812836373 / ISBN 13: 9789812836373

Published by World Scientific Publishing Co, 2014

Item in good condition. Textbooks may not include supplemental items i.e. CDs, access codes etc. Seller Inventory # 00095968317

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.

From the Back Cover: 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.

Bibliographic Details

Title: HOW TO MEASURE THE INFINITE: MATHEMATICS ...
Publisher: World Scientific Publishing Co
Publication Date: 2014
Binding: Hardcover
Condition: Good