Naive Set Theory

2011 Reprint of 1960 Edition. Full facsimile of the original edition, not reproduced with Optical Recognition Software. Paul Richard Halmos (1916-2006) was a Hungarian-born American mathematician who made fundamental advances in the areas of probability theory, statistics, operator theory, ergodic theory, and functional analysis (in particular, Hilbert spaces). He was also recognized as a great mathematical expositor. "...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".

preface 1 the axiom of extension 2 the axiom of specification 3 unordered pairs 4 unions and intersections 5 complements and powers 6 ordered pairs 7 relations 8 functions 9 families 10 inverses and composites 11 numbers 12 the peano axioms 13 arithmetic 14 order 15 the axiom of choice 16 zorn's lemma 17 well ordering 18 transfinite recursion .19 ordinal numbers 20 sets of ordinal numbers 21 ordinal arithmetic 22 the schroder-bernstein theorem 23 countable sets 24 cardinal arithmetic 25 cardinal numbers index

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