Essays on the Theory of Numbers (Second Edition)
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Essays on the Theory of Numbers (Second Edition)

4.25 of 5 stars 4.25  ·  rating details  ·  60 ratings  ·  5 reviews
Included in this volume are two essays on the theory of numbers: "Continuity and Irrational Numbers" and "The Nature and Meaning of Numbers." The text is an authorized translation by Wooster Woodruff Beman, Professor of Mathematics in the University of Michigan.
Paperback, 64 pages
Published April 11th 2007 by Brownstone Books (first published January 1st 1963)
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Kyle Goetz
Remarkable to read, especially having been through algebra and analysis courses in which we took similar and slightly different routes to build the same structures/concepts. Took some time to get used to the notation and terminology, but once I got it, it was a breeze to read.

If you haven't had any exposure to abstract math, this begins easy enough and the difficult parts can serve as a (remarkably lucid) demonstration to you of what abstract math entails.

If you have exposure to advanced math li...more
Richard Dedekind (1831 - 1916) was one of the pioneers of number theory and this book contains the English translations of his two most important papers: “Continuity and Irrational Numbers” from 1872 and “The Nature and Meaning of Numbers” from 1887.

The first paper shows how he came up with a purely number based procedure that defined the inexact irrational numbers like square root of 2. His procedure, now called the Dedekind cut, was based upon the right triangle formula in which summing the sq...more
Two short essays by the Dedekind. One contains the original presentation of the famous "Dedekind cut" formulation of the real numbers, plus developments up to the well-known "sup" property of bounded sets of reals. It's pretty short, light reading, but illuminating. (It's funny how much is lost hearing about Dedekind cuts from analysis books and logicians, who think it's "old hat" and just "preparation for the interesting stuff".)

The other essay is on the nature of the number concept, and is mor...more
this is much more a mathematical confession than a textbook. dedekind has a talent (foreign to most mathematicians) for actual, emotional expression. p.s. check out the proof for the existence of infinite sets. I mean, really?!
I wish I'd read this book much earlier in my academic career -- or, at least, that someone would have given me a watered down version of it. Mathematics really is lovely when it's not about drills and flash cards.
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Theory Of Algebraic Integers Was Sind Und Was Sollen Die Zahlen? Was Sind Und Was Sollen Die Zahlen?. Stetigkeit Und Irrationale Zahlen Essays on the Theory of Numbers by Richard Dedekind (Annotated) La Creation Des Nombres

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