Examining the nineteenth and early twentieth centuries, the fourth chapter describes the reduction of the continuous to the discrete, citing the contributions of Bolzano, Cauchy and Reimann. Chapter three, 'The age of continuity,’ discusses eighteenth century mathematicians including Euler and Carnot, and philosophers, among them Hume, Kant and Hegel. The second chapter of the book covers European thinkers of the sixteenth and seventeenth centuries: Galileo, Newton, Leibniz, Descartes, Arnauld, Fermat, and more. Chapter one, entitled ‘The continuous and the discrete in Ancient Greece, the Orient and the European Middle Ages,’ reviews the work of Plato, Aristotle, Epicurus, and other Ancient Greeks the elements of early Chinese, Indian and Islamic thought and early Europeans including Henry of Harclay, Nicholas of Autrecourt, Duns Scotus, William of Ockham, Thomas Bradwardine and Nicolas Oreme. The first section covers the history of these ideas in philosophy. This book explores and articulates the concepts of the continuous and the infinitesimal from two points of view: the philosophical and the mathematical.

A weighty tome for devotees of mathematics and physics that raises interesting questions. While explaining his deductions and thoughts on these complex topics, he raises new questions for his readers to contemplate, such as the origin of memory. In the final chapters, the author addresses absolute space, time and motion through the lens of the infinitesimal. Erickson supplies illustrative examples both in words and images-he clearly defines new notation as needed for concepts such as eternity, the infinitesimal, the instant and an unlimited quantity. In the case of non-Euclidean geometry, the author determines that it’s inconsistent with the infinitesimal. In each topic, he applies his new understanding of the infinitesimal to the ideas of mathematics and draws conclusions.

Erickson further explores limits, derivatives and integrals before turning his attention to non-Euclidean geometry.

This number system, he demonstrates, can provide a new interpretation of imaginary numbers, as a combination of the real and the veritable. At the heart of Erickson’s work is the veritable number system, in which positive and negative numbers are incompatible for the basic mathematical operations of addition, subtraction, multiplication, division, roots and ratios. The reader will gain an understanding of potential versus actual infinity, irrational and imaginary numbers, the infinitesimal, and the tangent, among other concepts. He regards the infinitesimal as the key to understanding much of the scientific basis of the universe, and intertwines mathematical examples and historical context from Aristotle, Kant, Euler, Newton and more with his deductions-resulting in a readable treatment of complex topics. Erickson delves into the history of these concepts and how people learn and understand them. Mathematicians, scientists and philosophers have explored the realms of the continuous and discrete for centuries. Erickson explores and explains the infinite and the infinitesimal with application to absolute space, time and motion, as well as absolute zero temperature in this thoughtful treatise.

Infinity and infinitesimals book