The invisible world of infinitesimals

This book is intended primary to serve as a study guide to the great con-cept of infinity that has tormented human thought for thousands of years. Infinitesimals are infinitely small quantities, which in the words of Ber-noulli, are so small that ¿if a quantity is increased or decreased by an infinitesimal, then the quantity is neither increased nor decreased. Mathematicians approached the concept of infinitesimals with various methods, the Greek method of exhaustion, the method of indivisibles of the early modern ages, the geometry of indivisibles, the differentials of Leibnitz (that are intuitive infinitesimals). Their history is a synthesis of three parts, of philosophical, mathematical and physical part. In this book we will see some basic elements of these three stories.