HOW TO MEASURE THE INFINITE

This book contains an original introduction to the use of infinitesimal and infinite numbers namely the AlphaTheory which can be considered as an alternative approach to nonstandard analysisThe 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 theoryThe book also provides a comprehensive exposition of the Theory of Numerosity a new way of counting countable infinite sets that maintains the ancient Euclid39s Principle The whole is larger than its parts The book is organized into five parts AlphaCalculus AlphaTheory Applications Foundations and Numerosity Theory