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Naive Set Theory

4.24  ·  Rating details ·  414 ratings  ·  27 reviews
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 ...more
Hardcover, 104 pages
Published January 16th 1998 by Springer (first published 1960)
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Meysam Ganji
May 09, 2017 rated it it was amazing
تنها توصیفی که برای این کتاب میشه آورد اینه که این کتاب زیباست! هر صفتی بیشتر استفاده کنم احساس میکنم تخیل رو محدود کردم در توصیفش.
Tyler McMann
Dec 15, 2016 rated it it was amazing
Shelves: mathematics
This is one of my favorite books, ever, even among nonmathematical books. Paul Halmos is often held up as a paragon of mathematical writing, and reading this book one can see why. It has a laid-back, and even humorous style, which makes it a great pleasure to read. The Axiom of Choice is introduced in the way that the founders of set theory first saw it, as a guarantee that the Cartesian Product of two nonempty sets is nonempty, and is developed into its modern form. The book ends simply with ...more
Bryce Woodworth
Sep 10, 2015 rated it really liked it
Recommends it for: Beginning Mathematicians
Shelves: technical
Good introduction to set theory. Pretty terse in terms of proofs, leaving a lot of steps up to the reader, which I like. Each section is only about 2 pages, but manages to cover a good amount of intuition. Focuses largely on how set theory is used as a basis for modern mathematics, and in particular how to build up a structure with the properties of the natural numbers, including order. Set theory is vital to know in modern mathematics, but you almost certainly don't need the level of depth this ...more
Josh Taylor
Did not totally finish. In the final few chapters, the theories got a little too complex for my current mathematical abilities. Perhaps one day I shall revisit this and be able to understand the manipulate the content more.

However I walked away with the basics of set theory: sets, inclusion, specification, relations, functions, numbers, unions, intersections, powers. The foundations of mathematics. Bears an eerie resemblance to LISP.

The author's style was stylish, so to speak. Some of the
Basel Al-Dagen
Mar 16, 2018 rated it it was amazing
I was going to give the book a 4 stars rating,but since in the book cover the book contain itself,it totally made it a hard 5.
William Bies
Nov 11, 2019 rated it really liked it
The field of set theory originated with the pioneering discoveries of Georg Cantor during the second half of the nineteenth century. Prior to his work, mathematicians were not accustomed to think very much in terms of collections of mathematical objects (particularly abstract ones); the most desirable result of an investigation was a formula in explicit analytical form. After Cantor and his contemporary Dedekind, who introduced infinite sets in an essential way into his arithmetization of the ...more
Jun 03, 2017 rated it it was amazing  ·  review of another edition
This book is brilliant. Simply brilliant. It is so much more than a math textbook. It is a glimpse of how mathematics, and mathematicians, work.

The operative word in the title is “Naïve”. As the author explains in the introduction, it means that he takes a somewhat informal approach to axioms and proofs, but as also stated in the introduction, the book is axiomatic in that he does state axioms and use them in subsequent proofs. The way it is unlike other formal axiomatic books is that axioms
Jul 19, 2019 rated it really liked it
Don't be fooled by the size of this book, it is quite dense and certainly not to be skimmed through. It is also the chattiest math textbook I have encountered, which is not always a good thing. Also, some of the proofs are kind of sketchy.
May 19, 2019 rated it really liked it
Shelves: math-engineering
A must-have as a reference for set theory.
Shibajee Samaddar
Nov 04, 2017 rated it it was amazing
Best starting point of Set Theory for knowing the Theory itself & also College level Mathematics
Feier hallelujah
Sep 20, 2017 rated it it was amazing
Good for beginners. Complicated theories are explained with easy words. The exercises are useful too.
Curtis Penner
Oct 05, 2017 rated it really liked it
Even though the book is thin, the subject is thick.

When finished the read should have a better understanding of Set Theory
Apr 17, 2014 rated it really liked it
While reading this, keep in mind that I was just reading this to get an overview. I rushed through and missed a lot of subtleties.

So the most noticeable thing is that it's only 115 pages, so I'm assuming there's a lot it doesn't cover. Though I'd imagine a lot of the shortness comes also from being naive set theory, rather than a fully rigorous treatment of axiomatic set theory. Also, there are only one or two exercises per chapter.

The best part was the minor bits of contextual information. such
Sam Ritchie
Jun 30, 2019 rated it it was amazing
YES! Game changer. I’ll post a longer review soon, but I’m so thankful for what Halmos has produced.
David Lindelof
Oct 15, 2011 rated it it was amazing
A just amazing little book of about 100 pages which explains the fundamental principles of set theory, and which shows how, from these principles, one can derive the concept of natural numbers (and therefore the rest of mathematics).

I should also mention that it is only after reading this book that I realize how wrong I was in my idea of what a 'relation' in 'relational database' meant.
Vincent Russo
Jan 01, 2015 rated it really liked it
Shelves: math
I stumbled on this book my accident, and gave it a read. It's a very rudimentary treatment on set theory that is more verbose than other books on the topic. The author also seemed to sprinkle in elements of a dry sense of humor, which in no way detracted from the delivery of the content. It seems that this is a tight rope to walk for other authors, and this guy did it right.
Aug 20, 2008 rated it really liked it
Shelves: mathematics
Really nothing too "naive" about it. The last few chapters were actually a bit too esoteric to finish, I tried. But then again I am not really a math person. I am sure the book does what it claims, gives you all the foundations in set theory to go on to bigger and better things. It did more than enough for me, even without the last few chapters.
Sandy Maguire
Jul 10, 2014 rated it it was ok
This text shows its age -- it's heavily wordy and pretty light on presenting things in mathematical notation. Although I have never formally studied set theory, I didn't get much out of it, though it did serve to reinforce my knowledge of some of the algebra behind sets.
Noah Hughes
Nov 03, 2016 rated it it was amazing
An excellent introduction for someone just coming to the ideas of set theory. Conversational and light hearted, it makes learning of the basics of set theory a joy.

Did a Directed Reading Program with an undergraduate interested in logic with this book. 'Twas a great success!
Feb 19, 2015 marked it as to-read
Shelves: logic
Man, even though I'm hardly disciplined enough to put fuel in my car, I'm still head over heels with rigorous Mathematics and Sets. I just don't know what it is about it. Can you be a theoretical mathematician and make a B in Calc I approximately the third time you took it?
'Asem Ismaiel
Aug 20, 2015 rated it liked it
Good review of concepts but too wordy and abstract, I guess this is what Set theory is all about, though. :D
Jan 01, 2014 rated it it was amazing  ·  review of another edition
best introduction to naive set theory.
Oct 07, 2008 rated it it was amazing
Shelves: math
this is a perfect little book. true to the title, halmos recreates our understanding of number through the notion of 'set'. (but with more jokes).
Jan 05, 2013 rated it really liked it
Excellent Introduction to Set Theory
Ryan Kirkish
Feb 04, 2013 rated it really liked it
Everything is a set. Concise introduction to structures in mathematics without proofs.
Thebreeze Limprecht
Mar 30, 2009 rated it really liked it
Shelves: mathematics
a mathematics classic.
Fred Conrad
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Jan 14, 2015
Zahid Emre
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Mar 07, 2017
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Luís Fernando
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Apr 04, 2015
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