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An Outline of Set Theory

James M. Henle
Publisher: 
Dover Publications
Publication Date: 
2007
Number of Pages: 
145
Format: 
Paperback
Price: 
11.95
ISBN: 
9780486453378
Category: 
Textbook
[Reviewed by
Tom Schulte
, on
09/2/2008
]

This is a Dover reprint of a concise, self-contained problem-oriented introduction to set theory that came out in 1986. The slim but complete volume will work well in an undergraduate course where students work in groups. It also standalone enough to work well for self-study, be it guided or unguided.

The reason this little volume is both so flexible and effective is because of its tripartite, reinforcing structure. There are distinct sections of problems, hints as to their solutions, and complete answers. In this way, each of the ten chapters is repeated three times.

The chapters begin with an introduction to the axioms and basics of Zermelo-Fraenkel Set Theory. With ZF Set Theory, as with succeeding chapters, a logical introduction of concepts and notation includes questions to answer, theorems to prove, and the projects so ideal for group work.

From this basis, the reader is encouraged to construct and work with natural numbers, integers, rationals, and real numbers with a chapter for each. Then, a closer look at infinity is given by extending natural numbers to the ordinals and cardinals. From there the book naturally goes to discuss levels of infinity, the Axiom of Choice, and infinitesimals.


Tom Schulte is in the Industrial Applied Mathematics PhD program at Oakland University and enjoys chess sets and set theory.

 

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