Publisher's Synopsis
This book is intended as conceptual introduction to three mathematical theories arising from the attempt to understand (actual) infinity: Projective Geometry, Infinitesimal Calculus, and Set Theory. Though the treatment does not avoid the technical aspects of these theories, it tries to explain their origins and purposes. The book is divided into three parts each composed of two chapters and a few appendices. Each part presents in detail one of the three moments in which mathematicians made a concerted effort to control the idea of infinity: projective geometry, infinitesimal calculus, and set theory. The text includes exercises and philosophical and/or historical remarks. It is written both for non-mathematicians interested in understanding the most relevant ideas that govern these theories, and for professional mathematicians interested in exploring the possibility of a conceptually-engaged presentation of mathematical contents. The book can be used for advanced undergraduate students, as well as for beginning graduate students.
