The Enigmatic Nature of Infinity ebook

This book is not intended exclusively for mathematicians but for those readers willing to follow logical reasoning and then accept the conclusions, however strange they may seem. The book comes in several parts. The part titled 'Infinity Before Cantor' gives an account of infinity as commonly understood, with explanations of all the mathematics needed for the rest of the book. It includes the analysis of two interesting paradoxes: Achilles' race with the tortoise (a race the tortoise is convinced he will win) and Gabriel's Horn, which has a finite volume yet an infinite surface area. The part titled 'Cantor's Work on Infinity' follows Georg Cantor's revolutionary work. This begins with a logical analysis of an imaginary meeting between delegates and the chairs on which they are seated, from which a fundamental conclusion is reached. The work then progresses, logically and step-by-step, to Cantor's astonishing results. It culminates in the revelation that there exists an infinity of different levels of infinity, expressed in terms of the infinity of natural or cardinal numbers.