Essays On The Theory Of Numbers

Essays On The Theory Of Numbers is a book written by Richard Dedekind, a German mathematician who is known for his contributions to number theory. The book is a collection of essays that explore various topics related to number theory, including the concept of irrational numbers, the theory of algebraic integers, and the theory of ideals. In the first essay, Dedekind introduces the concept of irrational numbers and provides a rigorous definition of them. He also introduces the idea of a cut, which is a way of dividing the real number line into two parts. This essay lays the foundation for Dedekind's later work on the theory of real numbers.The second essay focuses on the theory of algebraic integers, which are solutions to polynomial equations with integer coefficients. Dedekind introduces the concept of a field, which is a set of numbers with operations that satisfy certain properties. He also introduces the idea of a ring, which is a set of numbers with operations that satisfy different properties. The third essay is devoted to the theory of ideals, which are subsets of a ring that behave like the multiples of a single element. Dedekind uses ideals to develop a theory of algebraic number fields, which are extensions of the field of rational numbers that contain solutions to polynomial equations with integer coefficients.Overall, Essays On The Theory Of Numbers is a seminal work in the field of number theory and has had a significant impact on the development of modern mathematics. It is a must-read for anyone interested in the foundations of mathematics or the history of number theory.I. Continuity and Irrational Numbers. II. The Nature and Meaning of Numbers.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.