樸素集合論

內(nèi)容概要

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 settheoretic 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。

書籍目錄

SECTIONPREFACE 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 RECURSION19 ORDINAL NUMBERS20 SETS OF ORDINAL NUMBERS21 ORDINAL ARITHMETIC22 THE SCHRODER-BERNSTEIN THEOREM23 COUNTABLE SETS24 CARDINAL ARITHMETIC25 CARDINAL NUMBERSINDEX

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