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 作者 Niven, Ivan Morton 書名 Numbers : Rational and Irrational 出版項 Washington : American Mathematical Society, 1961 ©1961 國際標準書號 9780883859193 (electronic bk.) 9780883856017
 說明 1 online resource (149 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier 系列 Anneli Lax New Mathematical Library ; v.1 Anneli Lax New Mathematical Library 附註 Front Cover -- Numbers: Rational and Irrational -- Copyright Page -- CONTENTS -- Introduction -- Chapter 1. Natural Numbers aud Integers -- 1.1 Primes -- 1.2 Unique Factorization -- 1.3 Integers -- 1.4 Even and Odd Integers -- 1.5 Closure Properties -- 1.6 A Remark on the Nature of Proof -- Chapter 2. Rational Numbers -- 2.1 Definition of Rational Numbers -- 2.2 Terminating and Non-terminating Decimals -- 2.3 The Many Ways of Stating and Proving Propositions -- 2.4 Periodic Decimals -- 2.5 Terminating Decimals Written as Periodic Decimals -- 2.6 A Summary -- Chapter 3. Real Numbers -- 3.1 The Geometric Viewpoint -- 3.2 Decimal Representations -- 3.3 The Irrationality of √2 -- 3.4 The Irrationality of √3 -- 3.5 The Irrationality of v6 and v2 +√3 -- 3.6 The Words We Use -- 3.7 An Application to Geometry -- 3.8 A summary -- Chapter 4. Irrational Numbers -- 4.1 Closure Properties -- 4.2 Polynomial Equations -- 4.3 Rational Roots of Polynomial Equations -- 4.4 Further Examples -- 4.5 A Summary -- Chapter 5. Trigonometric and Logarithmic Numbers -- 5.1 Irrational Values of Trigonometric Functions -- 5.2 A Chain Device -- 5.3 Irrational Values of Common Logarithms -- 5.4 Transcendental Numbers -- 5.5 Three Famous Construction Problems -- 5.6 Further Analysis of 3√2 -- 5.7 A Summary -- Chapter 6. The Approximation of Irrationals by Rationals -- 6.1 Inequalities -- 6.2 Approximation by Integers -- 6.3 Approximation by Rationals -- 6.4 Better Approximations -- 6.5 Approximations to within1/n2 -- 6.6 Limitations on Approximations -- 6.7 A Summary -- Chapter 7. The Existence of Transcendental Numbers -- 7.1 Some Algebraic Preliminaries -- 7.2 An Approximation to α -- 7.3 The Plan of the Proof -- 7.4 Properties of Polynomials -- 7.5 The Transcendence of α -- 7.6 A Summary -- Appendix A Proof That There Are Infinitely Many Prime Numbers Appendix B Proof of the Fundamental Theorem of Arithmetic -- Appendix C Cantor's Proof of the Existence of Transcendental Numbers -- Appendix D Trigonometric Numbers -- Answers and Suggestions to Selected Problems -- Index Description based on publisher supplied metadata and other sources Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries 鏈接 Print version: Niven, Ivan Morton Numbers : Rational and Irrational Washington : American Mathematical Society,c1961 9780883856017 主題 Numbers, Real.;Numbers, Complex Electronic books
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