Naive Set TheoryEvery 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 settheoretic wisdom is still Hausdorff's Set theory. A recent and highly readable addition to the literature, with an extensive and uptodate bibliography, is Axiomatic set theory by Suppes. 
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Review: Naive Set Theory
User Review  Ryan Kirkish  GoodreadsEverything is a set. Concise introduction to structures in mathematics without proofs. Read full review
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Contents
II  1 
III  4 
IV  8 
V  12 
VI  17 
VII  22 
VIII  26 
IX  30 
XVI  59 
XVII  62 
XVIII  66 
XIX  70 
XX  74 
XXI  78 
XXII  81 
XXIII  86 
Common terms and phrases
A U B arithmetic assertion axiom of choice axiom of extension axiom of pairing axiom of specification axiom of substitution belongs called cardinal Cartesian product chain collection of sets commutative countable sets countably infinite defined definition denoted disjoint sets domain empty equal equivalence class equivalence relation example EXERCISE exists a function exists a set fact finite set follows function f hence implies included index set initial segment determined intersection inverse least element maximal element means natural numbers necessary and sufficient nonempty subset notation onetoone correspondence ordered pairs ordinal number equivalent ordinal sum partially ordered set power set preceding paragraph predecessors proof proper subset prove result sentence sequence of type set of ordered set theory settheoretic similar singleton successor set sufficient condition Suppose symbol tion transfinite induction transfinite recursion union unique unordered pair upper bound words write X X Y Zorn's lemma