 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
 |
|
|
|
Set Theory
◆Taylor & Francis セール開催中！：2025年12月14日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 出版済み 3-5週間でお届けいたします。 Title: Set Theory Subtitle: An Introduction to Axiomatic Reasoning Series: Textbooks in Mathematics Author: Andre, Robert Publisher: Taylor & Francis ISBN: 9781032954820 Cover: HARDCOVER Date: 2025年04月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION Contemporary students of mathematics differ considerably from those of half a century ago. In spite of this, many textbooks written decades ago, and now considered to be “classics”, are still prescribed for students today. These texts are not suitable for today’s students. This text is meant for and written to today’s mathematics students. Set theory is a pure mathematics endeavor in the sense that it seems to have no immediate applications; yet the knowledge and skills developed in such a course can easily branch out to various fields of both pure mathematics and applied mathematics. Rather than transforming the reader into a practicing mathematician, this book is more designed to initiate the reader to what may be called “mathematical thinking” while developing knowledge about foundations of modern mathematics. Without this insight, becoming a practicing mathematician is much more daunting. The main objective is twofold. The students will develop some fundamental understanding of the foundations of mathematics and elements of set theory, in general. In the process, the student will develop skills in proving simple mathematical statements with “mathematical rigor”. Carefully presented detailed proofs and rigorous chains of logical arguments will guide the students from the fundamental ZFC-axioms and definitions to show why a basic mathematical statement must hold true. The student will recognize the role played by each fundamental axiom in development of modern mathematics. The student will learn to distinguish between a correct mathematical proof and an erroneous one. The subject matter is presented while bypassing the complexities encountered when using formal logic. TABLE OF CONTENTS 1.Axioms and classes 2.Class operations 3.Relations 4.Functions 5.From sets to numbers 6.Infinite sets 7.Cardinal numbers 8.Ordinal numbers 9.More on axioms: Choice, regularity and Martin's axiom 10.Ordinal arithmetic
|
||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
