Essays on the Theory of Numbers: I. Continuity and Irrational Numbers, II

Description: This book delves into the intricate world of numbers, exploring their nature, meaning, and the profound concept of continuity. The author embarks on a captivating journey through the history of mathematical thought, tracing the evolution of number systems from the familiar realm of rational numbers to the enigmatic domain of irrational numbers. With meticulous precision, the author dissects the fundamental principles of arithmetic, unveiling the inherent limitations of rational numbers in capturing the essence of continuity. The concept of a "cut," a groundbreaking idea introduced by the author, bridges this gap, paving the way for the creation of irrational numbers and the establishment of a complete and continuous number system. This exploration extends beyond theoretical abstractions, delving into the practical implications of continuity in infinitesimal analysis. The author demonstrates the profound connection between the principles of continuity and fundamental theorems of calculus, illuminating the essential role of a continuous number domain in understanding the intricacies of change and motion. Ultimately, this book challenges our understanding of numbers as mere tools of calculation, revealing them as profound constructs that shape our comprehension of the world around us. The author's insights into the nature of continuity and the creation of irrational numbers revolutionized the field of mathematics, laying the groundwork for modern analysis and our understanding of the universe's underlying mathematical structure. Forgotten Books publishes hundreds of thousands of rare and classic books.This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. This text has been digitally restored from a historical edition. Some aesthetic errors may persist, however it has been deemed that any such will not detract from the work's significant historical value. The digital edition of all books may be viewed on our website before purchase.

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