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P. R. Halmos
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Naive Set Theory (Undergraduate Texts in Mathematics) 1974th Edition

by P. R. Halmos (Author)
4.5 4.5 out of 5 stars 133 ratings
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Every mathematician agrees that every mathematician must know some set theory; the disagreement begins in trying to decide how much is some. This book contains my answer to that question. The purpose of the book is to tell the beginning student of advanced mathematics the basic set­ theoretic facts of life, and to do so with the minimum of philosophical discourse and logical formalism. The point of view throughout is that of a prospective mathematician anxious to study groups, or integrals, or manifolds. From this point of view the concepts and methods of this book are merely some of the standard mathematical tools; the expert specialist will find nothing new here. Scholarly bibliographical credits and references are out of place in a purely expository book such as this one. The student who gets interested in set theory for its own sake should know, however, that there is much more to the subject than there is in this book. One of the most beautiful sources of set-theoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and up-to-date bibliography, is Axiomatic set theory by Suppes.
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  1. ISBN-10
    0387900926
  2. ISBN-13
    978-0387900926
  3. Edition
    1974th
  4. Publisher
    Springer
  5. Publication date
    January 16, 1998
  6. Part of series
    Dover Books on Mathematics
  7. Language
    English
  8. Dimensions
    6.5 x 0.5 x 9.5 inches
  9. Print length
    111 pages
  10. See all details
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Editorial Reviews

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From the reviews:

“This book is a very specialized but broadly useful introduction to set theory. It is aimed at ‘the beginning student of advanced mathematics’ … who wants to understand the set-theoretic underpinnings of the mathematics he already knows or will learn soon. It is also useful to the professional mathematician who knew these underpinnings at one time but has now forgotten exactly how they go. … A good reference for how set theory is used in other parts of mathematics … .” (Allen Stenger, The Mathematical Association of America, September, 2011)

Product details

  • Publisher ‏ : ‎ Springer; 1974th edition (January 16, 1998)
  • Language ‏ : ‎ English
  • Hardcover ‏ : ‎ 111 pages
  • ISBN-10 ‏ : ‎ 0387900926
  • ISBN-13 ‏ : ‎ 978-0387900926
  • Item Weight ‏ : ‎ 12.3 ounces
  • Dimensions ‏ : ‎ 6.5 x 0.5 x 9.5 inches
  • Customer Reviews:
    4.5 4.5 out of 5 stars 133 ratings

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P. R. Halmos

P. R. Halmos

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Customer reviews

4.5 out of 5 stars
4.5 out of 5
133 global ratings

Top reviews from the United States

K
5.0 out of 5 stars Non-intimidating introduction to set theory
Reviewed in the United States on June 13, 2006
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I find set theory to be the most intimidating subject in math. It seems so removed, but underpins every assumption I make in mathematics. Many other set theory books are dense and not very clear, but Halmos clearly expounds set theory.

Set theory, as is most mathematics, is hard, so be prepared to think. This book has only 102 pages in it and has just about everything I ever needed to know about set theory for me to feel confident using this theory to understand and prove things in other branches of mathematics.

Halmos's Naive Set Theory is the type of book I look for most, when I'm interested in a topic outside my specialization, but would like to know it better to apply it to my research. It's a clear, concise introduction to set theory, getting to the meat of it, without all the little asides and interesting things that distracts from learning the core of the subject.

This book should be on the bookshelf of every serious (and amateur) mathematician.
19 people found this helpful
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Customer
5.0 out of 5 stars The best place to start
Reviewed in the United States on October 13, 2013
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Paul Halmos's book is the best introductory text to set theory. Halmos is very skilled at presenting complicated ideas in terms that anyone can understand and enjoy. Naive Set Theory is written in informal, conversational English, although the material is presented in a systematic and rigorous way. For its quality of exposition and coverage, this is the best place to start learning about set theory. After working your way through this book you'll be prepared to read more advanced and equality good texts such as Jech's Intro to Set Theory.
6 people found this helpful
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Martin O'riordan
5.0 out of 5 stars Naive? just the publisher's "come on" first class work
Reviewed in the United States on July 1, 2007
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Quite a good introduction to set theory, ideal for the person too busy
to read all the latest texts produced by academia. Also for the person
scared by too much mathematical symbolism, makes them realise thatwhile
symbolism is an aid in math it is not of course absolutely necessary.
In physics we see the current downgrading of quantum physics, so we
we should see a reduction in "math trash" as a consequence.
So irrespective of the background, all who read this book should be
rewarded with a greater grasp of math and how it is developed.
3 people found this helpful
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MIles
5.0 out of 5 stars This is a fantastic book.
Reviewed in the United States on March 23, 2018
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I wanted to go back and fill in any gaps in my set theory knowledge. I got more than I bargained for. Not only did this book fill in gaps, but it also greatly expanded on my previous understanding and built up new concepts. This is a fantastic book.
3 people found this helpful
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Lester Kim
3.0 out of 5 stars This book is ok but not that great
Reviewed in the United States on August 21, 2009
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Pros:
1. This book is pretty concise and I appreciate the author's effort to only keep the essentials of naive set theory.
2. I like the presentation. There is a pretty smooth gradient in the increasing complexity of the topics.
3. This is a good introduction to more abstract mathematics. I used the first third of this book for a math lecture I gave at MIT. Of course, I had to do a fair amount of hand-holding to make sure everyone understood what was going on.

Cons:
1. There are not many problems following most of the chapters. At least having more worked examples would improve this book for autodidacts.
2. The writing style is pretty boring. One can easily lose the motivation to keep on reading.
10 people found this helpful
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charles
5.0 out of 5 stars Important book!
Reviewed in the United States on August 16, 2018
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This is a book I used back in undergrad studies. It is a must read for anyone interested in set theory. It is also a great way to learn about how to construct axiomatic systems. A classic that will never fade!
5 people found this helpful
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Old Math Teacher
4.0 out of 5 stars Classic abstract mathematics
Reviewed in the United States on May 6, 2019
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I read Naive Set Theory about 55 years ago when I was starting my graduate study in mathematics. It was very helpful. I have started reading it again, but it requires study rather than reading. I recommend this book for graduate students in mathematics.
The Kindle version of the book sometimes breaks expressions at the margins, but that is expected when variable font sizes are provided.
5 people found this helpful
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Dr. Richard L. Plumer
5.0 out of 5 stars The Classic Introduction to Set Theory
Reviewed in the United States on January 3, 2007
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This is still the indispensable introduction to the subject for the student of mathematics, although specialists in logic and set theory will want to dig deeper into the subject. It's style is conversational, yet rigorous and can be either lightly browsed or studied more deeply. Although somewhat dated, it should still be a valuable resource in every mathematician's education.
6 people found this helpful
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Top reviews from other countries

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Kakeya
5.0 out of 5 stars Fortement recommendé
Reviewed in France on August 2, 2023
Verified Purchase
Livre en parfait état, livraison rapide, très satisfaisant
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Math
5.0 out of 5 stars Good for learning the foundations.
Reviewed in Germany on June 12, 2023
Verified Purchase
This book is good and should server as a nice pre-work for delving into more sophisticated areas of Mathematics s.a. Metric Spaces, Measure Theory, General Topology, etc. It does a great job at shortly presenting most important topics.

Note, in one place or another you'd have to do proofs on your own as the author does not go too deep into technical details there.
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Melee R.
5.0 out of 5 stars Excellent
Reviewed in India on May 8, 2022
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The media could not be loaded.
 Should buy
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Melee R.
5.0 out of 5 stars Excellent
Reviewed in India on May 8, 2022
Should buy
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One person found this helpful
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Marcelo Barboza
5.0 out of 5 stars Clássico.
Reviewed in Brazil on April 29, 2020
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Aprendi os rudimentos da teoria dos conjuntos por este livro, do qual ainda gosto muito (obviamente).
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Toledo
1.0 out of 5 stars Print on demand
Reviewed in Mexico on November 1, 2019
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Están enviando estas copias baratas de la versión original del libro. El libro en sí es un clásico. Ése no es el problema.
One person found this helpful
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