文件名称：Notes on Set Theory, 2ed (Undergraduate Texts in Mathematics)
文件大小：2.03MB
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更新时间：2014-04-30 06:57:07
set theory
PREFACE What this book is about.The theory of sets is a vibrant, exciting mathematical theory, with its own basic notions, fundamental results and deep open prob- lems, andwith significantapplicationstoothermathematical theories. At the sametime,axiomaticsettheoryisoftenviewedasafoundationofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, “making a notion precise” is essentially syn- onymouswith “definingit in set theory”. Set theoryis the officiallanguageof mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject.