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Naive Set Theory
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11 of 12 people found the following review helpful
on 30 July 1999
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.
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12 of 13 people found the following review helpful
on 26 September 2008
Naive Set Theory, Paul Halmos' classic textbook originally published in 1960 has an accompanying book of Exercises in Set Theory by L. E. Sigler, also published in 1960 (ISBN: 0442780869)
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4 of 6 people found the following review helpful
VINE VOICEon 13 April 2012
I remember reading this book back in 1965, as a small part of one of my first year maths courses, and being impressed by the lucid and friendly exposition of the difficult concepts involved in the theory of non-finite sets. Much later, I was privileged to take Paul out to lunch on a visit to our university. He was as interesting in life as in his books. He carried a tiny "spy" camera round his neck to take photos of people he visited!

So this book will take you from the basic operations of union and intersection, through to countable and uncountable sets and the Axiom of Choice, Zorn's Lemma, Transfinite Induction and Well Ordering. It is not a mathematical logic textbook, hence the "Naive" in the title. It will however give you a thorough grounding in the basics, sufficient to understand other subjects where mathematicians prove broad results that apply to both finite and infinite cases, eg, the existence of a basis in any vector space.

A highly recommended little book!
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