Naive Set Theory (Undergraduate Texts in Mathematics) [Hardcover]

P. R. Halmos (Author)

Book Description

ISBN-10: 0387900926 | ISBN-13: 978-0387900926 | Publication Date: January 16, 1998 | Edition: 1

From the Reviews: "...He (the author) uses the language and notation of ordinary informal mathematics to state the basic set-theoretic facts which a beginning student of advanced mathematics needs to know...Because of the informal method of presentation, the book is eminently suited for use as a textbook or for self-study. The reader should derive from this volume a maximum of understanding of the theorems of set theory and of their basic importance in the study of mathematics." - "Philosophy and Phenomenological Research".

Product Details

• Hardcover: 104 pages
• Publisher: Springer; 1 edition (January 16, 1998)
• Language: English
• ISBN-10: 0387900926
• ISBN-13: 978-0387900926
• Product Dimensions: 9.5 x 6.4 x 0.5 inches
• Shipping Weight: 11.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.1 out of 5 stars  See all reviews (18 customer reviews)
• Amazon Best Sellers Rank: #271,452 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

49 of 50 people found the following review helpful:

5.0 out of 5 stars Mathematical writing at its best, June 9, 2000

By 

"rainbowcrow" - See all my reviews

This review is from: Naive Set Theory (Undergraduate Texts in Mathematics) (Hardcover)

Oh, to be able to write like Paul Halmos!

This is, quite simply, a beautiful book. Halmos has taken a field, wrapped his deep understanding around it, and brought the field forth into light in a way that it is accessible to any reader willing to invest the requisite effort, regardless of mathematical background.

Each word is carefully chosen; Halmos has a knack for qualifying his statements gently and subtly so that on a first reading, the qualifications and limitations placed on the main results don't slow one down. On a second reading, the qualifications actually shed light on the intricacies of the subject. "Why does he qualify this?", one asks oneself, and in discovering the answer, comes to a better understanding of the field. Similarly, the small number of exercises posed for the reader have been very carefully chosen to she light on the subject itself. Unlike the rote busywork included with many mathematics texts, each problem posed by Halmos is, I would argue, essential to the book.

The book is not easy going in that it can be read quickly. I have a reasonable mathematical background, I use mathematics daily in my professional life, and yet (taking time to work the exercises) I read this book at a pace of about four to six pages an hour. On the other hand, this is not so bad - the entire book is only 102 pages, and in those 102 pages Halmos manages to present a full semester's course in set theory.

Finally, I should mention that anyone who has spent more time with applied mathematics than with the foundations of mathematics is likely to find this a fascinating read. When I read this book, it was not only the most interesting mathematics book I had read in at least a year, but also the most interesting philosophy book. Just to give a few examples, I never REALLY understood Russell's paradox until I read Halmos' explanation (which he presents on page 6 of the book). By page 30, Halmos offers an explanation of what a function really is, and by page 42, he tackles the question of what we really mean when we talk about the number "2" or the number "6" or any other number, for that matter.

This book takes some work on the part of the reader, but the effort is repaid handsomely. The effort would have been worth my while purely to the learn the mathematics, purely for the philosophical issues raised, or purely as an example of how one can aspire to write about mathematics. Of course, for my effort, I was able to enjoy all three aspects of this marvellous text.

13 of 14 people found the following review helpful:

4.0 out of 5 stars The essential essence of set theory in 100 pages, April 21, 2002

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Naive Set Theory (Undergraduate Texts in Mathematics) (Hardcover)

This book is an excellent primer on the basics of set theory that all graduate students need, but are not necessarily obtained in the general undergraduate curriculum. Halmos writes in an abbreviated, yet effective style that imparts the necessary details without an excess of words. Theorems and exercises are very few, so it really cannot be used as a textbook. If you need a great deal of explanations, then it is not for you. However, if your need is for a book that distills the essence of set theory down to the shortest possible size, then this book should be yours, either in your college or personal library.

13 of 14 people found the following review helpful:

4.0 out of 5 stars Very thorough yet too compact, July 30, 1999

By A Customer

This review is from: Naive Set Theory (Undergraduate Texts in Mathematics) (Hardcover)

This book is fascinating. Halmos proceeds to construct the most relavant concepts of set theory independantly of any other mathematics. For instance never once does he use numbers until he has constructed them out of sets. The level of rigor is not that of axiomatic set theory, so the book is accessible.

Unfortunately, as seems to be Halmos style (definitly evident in his 'Finite Vector Spaces' which I do NOT recommend unless you are far more gifted than I), he is quite compact. He compresses a wealth of information into a very short space, and most of the 25 topics are covered in under 4 full pages. The exercises are sparse and difficult.

This book could definitly have benefited from much more explanation and exercises. For the reader who possess the talent, though, this book is strongly recommended. Even for those (like me) who failed to grasp every detail, it is still a very worthwhile read. I fully intend to return to this when I have a more firm grounding in the thought patterns of abstract mathematics.