Essays on the Theory of Numbers (Dover Books on Mathematics)

Book Details

• Publisher: Dover

• Author: Richard Dedekind

• Language: English

• Edition: First Edition

• ISBN: 9780486210100

• Pages: 115

• Cover: Paperback

• Dimensions: 8.0 x 5.0 x 0.7 inches

About The Book

This volume presents two seminal essays by the renowned German mathematician Richard Dedekind, exploring the logical foundations of the number system. The first essay introduces Dedekind's famous theory of irrational numbers, known as the Dedekind cut. This theory was groundbreaking in providing a rigorous, purely arithmetic foundation for irrational numbers, which had previously been understood intuitively since the time of the ancient Greeks. Dedekind's work helped establish a formal and rigorous understanding of continuity in mathematical analysis.

The second essay examines the concept of transfinite numbers, offering a logical basis for the natural numbers and distinguishing between finite and transfinite (infinite) numbers. It also delves into the concept of mathematical induction, specifically the logical validity of complete induction in proof theory.

As a fundamental work in the foundations of mathematics, this collection will appeal to those interested in the deep logical structure of the number system. Written by one of the most influential mathematicians of the 19th century, these essays are essential reading for practicing mathematicians, mathematics educators, and historians of mathematics. Translated by "Vooster" V. Beman, this book is a cornerstone in the study of mathematical foundations.