Theory of Sets

By Erich Kamke

Book Overview

"Exceptionally well written." -- School Science and Mathematics
"A very fine book." -- Mathematics Teacher
"Of real service to logicians and philosophers who have hitherto had no access to a concise and accurate introduction to the general theory of sets." -- Philosophical Review
This is the clearest and simplest introduction yet written to the theory of sets. Making use of the discoveries of Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and other mathematicians, it analyzes concepts and principles and offers innumerable examples. Its emphasis is on fundamentals and the presentation is easily comprehensible to readers with some college algebra. But special subdivisions, such as the theory of sets of points, are considered.
The contents include rudiments (first classifications, subsets, sums, intersection of sets, nonenumerable sets, etc.); arbitrary sets and their cardinal numbers (extensions of number concept, equivalence of sets, sums and products of two and many cardinal numbers, etc.); ordered sets and their order types; and well-ordered sets and their ordinal numbers (addition and multiplication of ordinal numbers, transfinite induction, products and powers of ordinal numbers, well-ordering theorem, well-ordering of cardinal and ordinal numbers, etc.).

• Format: Paperback
• Language: English
• ISBN: 0486601412
• ISBN13: 9780486601410
• Release Date: November 2010
• Publisher: Dover Publications
• Length: 160 Pages
• Weight: 0.41 lbs.
• Dimensions: 0.3" x 5.4" x 8.0"

Customer Reviews

Theory of Sets

This is the clearest and simplest introduction to the theory of sets. Making use of the discoveries of such mathematicians as Cantor, Russell, Weierstrass, Zermelo, Bernstein, Dedekind, and others, it analyzes the concepts and principles of set theory. Although emphasis is on fundamentals, special subdivisions, such as the theory of sets of points, are considered. The text is accompanied by innumerable examples. Presentation is simple, easily comprehensible to a reader who has some acquaintance with college algebra. --- from book's back cover

Solid, well-organized, straightforward

I agree completely with RJ's review, including the his/her frustration with the typography in which capital letters in what I believe is German script are used to denominate sets. Still, once I had that sorted out this was a straightforward and rewarding read. (Other than the capital German letters used to denominate sets, the notation is relatively easy to follow as well, and contrary to another review, there is a perfectly good index to the places where each symbol is introduced.) I intend to supplement its intuitive approach by reading Suppes' presentation of axiomatic set theory.

a classic.

Kamke, along with Suppes and Halmos, is one of the classic texts in the theory of sets. Kamke is a bit unique, I think, in that he brings up terms such as jump, cut, and gap. Those are currently out-of-fashion but are in fact more intuitive and give you a direct philosophical grasp. A must-read.

Excellent book on a fascinating subject

This is a very good introduction to Set theory. It starts with basics, and takes one through to The Axiom of Choice or well-ordering theorem. Set theory being a rather abstract subject, most books do not give a motivation for the various terminology in set theory (which enhances understanding of why many concepts had to be introduced. The book however uses strange archaic Math typography, because of which through out the book I kept on trying to figure out whether it is a srcipt pi or script R. This sometimes confuses the thought process. But overall, the book is quite easy to read and manages to convey to the reader some of the beauty of set theory. At points, one can't help but smile at the ingenuity and the audacity of human thought.I recommened it highly.

Something For Everybody!

This is a great little book of math for all of those interested in the finer points of set theory. I'm an undergrad math major and found the material challenging yet rewarding. If you are as young as I am, or an experienced mathematician, I believe that this book has something for you to think about. From the first you'll be taken along at a steady pace covering theorems that are quite interesting.