The elements of the true arithmetic of infinities

ancient mathematicians, I would feel that my time spent writing it was worthwhile. However, I believe this work also explains the nature of the mathematical infinite more clearly than ever before. Therefore, I hope to earn the praise of open-minded and wise readers.

One of the main discoveries in this book is that in every infinite series of numbers, whether they are whole numbers or fractions, the last term multiplied by the number of terms is equal to the total sum of the series. I am happy to find that this discovery shows how absurd it can be to use induction the process of reaching a general conclusion from specific parts to reason from parts to wholes, or wholes to parts, when the wholes themselves are infinite. This helps to clarify an important teaching in the philosophy of Plato and Aristotle. I have spent a large part of my life spreading the teachings of this philosophy, and I hope to spend the rest of my life doing the same.

In short, this book shows that the theory of infinite series as used by mathematicians today should not be used for precise proofs, even if it is useful for practical work. I demonstrate here that the fractions used to create infinite series are not exactly related to each other in the same way one finite number is related to another. I also show through many examples that an infinite series made of a repeating decimal is actually smaller than the vulgar fraction a common fraction written with a numerator and denominator it represents. Specifically, the series is smaller than the fraction by the value of the fraction itself.