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# Essays on the Theory of Numbers (Second Edition)

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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## Community Reviews

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Feb 19, 2014
Kyle Goetz
rated it
5 of 5 stars
·
review of another edition

Shelves:
mathematics,
philosophy

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

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

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

Feb 05, 2008
Pietro
rated it
5 of 5 stars
·
review of another edition

Shelves:
philosophy,
mathematics

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

The other essay is on the nature of the number concept, and is mor...more

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