朴素集合论 [Naive Set Theory] pdf epub mobi txt 电子书下载 2025

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集合论
数学基础
朴素集合论
数学哲学
逻辑学
公理化方法
集合
数学
理论基础
基础数学

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出版社：世界图书出版公司

ISBN：9787506292177

版次：1

商品编码：10096469

包装：平装

外文名称：Naive Set Theory

开本：24开

出版时间：2008-05-01

用纸：胶版纸

页数：104

正文语种：英语

具体描述

内容简介

　　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。

SECTION
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 ZORNS 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