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
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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
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Add this copy of Naive Set Theory (University Series in Undergraduate to cart. $22.28, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1960 by D. Van Nostrand.
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Add this copy of Naive Set Theory to cart. $24.50, good condition, Sold by Grey Matter Books rated 5.0 out of 5 stars, ships from Hadley, MA, UNITED STATES, published 1965 by D. Van Nostrand Company, Inc..
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Good. No Jacket. Occasional small pencil marks found in the text; previous owner's signature in pen on the first free end page. Pages are bright, though the page edges are age toned. Binding is sturdy. Covers show some light wear around the corners and at the head and base of the spine. The spine is a little faded. No dust jacket. 104pp.
Add this copy of Naive Set Theory to cart. $15.50, good condition, Sold by semra rated 4.0 out of 5 stars, ships from New York, NY, UNITED STATES, published 1964 by Van Nostrand Reinhold Inc., U.S..
Add this copy of Naive Set Theory (University Series in Undergraduate to cart. $58.39, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1960 by Van Nostrand Reinhold Inc., U. S.
Until reading Halmos's "Naive Set Theory", I thought of this topic as one more branch of mathematics, akin to algebra, analysis, number theory, etc. I now understand that there's an alternative perspective: set theory constitutes the totality of mathematics, i.e., every branch of mathematics can be defined and developed within the set theoretic framework.
"Naive Set Theory" develops this idea in an "elementary" fashion: the exposition is self-containd and the proofs are short and straightforward. This does not mean that it's easy reading. But, the difficulties stem from the unusual notation, and can be overcome. Or, the book can be read for its ideas and its conclusions, which are presented with great clarity; Halmos is an excellent writer.
To whet your appetite for the book, I'll mention one fascinating result, which I've never come across before, despite having read a few other books on the subject of transfinte cardinal and ordinal numbers. The result is short and sweet. It's this: the cardinals are a subset of the ordinals.
