LEADER 04275nam 2200577Ia 450 001 9910971363203321 005 20200520144314.0 010 $a0-88385-919-X 035 $a(CKB)2560000000081414 035 $a(SSID)ssj0000577716 035 $a(PQKBManifestationID)11378680 035 $a(PQKBTitleCode)TC0000577716 035 $a(PQKBWorkID)10561953 035 $a(PQKB)10284343 035 $a(UkCbUP)CR9780883859193 035 $a(MiAaPQ)EBC3330415 035 $a(Au-PeEL)EBL3330415 035 $a(CaPaEBR)ebr10729386 035 $a(OCoLC)929120331 035 $a(RPAM)3112134 035 $a(EXLCZ)992560000000081414 100 $a20111006d1961 uy 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNumbers $erational and irrational /$fby Ivan Niven 205 $a1st ed. 210 $aWashington, DC $cMathematical Association of America$d1961 215 $a1 online resource (viii, 140 pages) $cdigital, PDF file(s) 225 0 $aAnneli Lax New Mathematical Library ;$v1 300 $aIncludes index. 311 08$a0-88385-601-8 327 $aFront 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 ? -- 7.3 The Plan of the Proof -- 7.4 Properties of Polynomials -- 7.5 The Transcendence of ? -- 7.6 A Summary -- Appendix A Proof That There Are Infinitely Many Prime Numbers. 327 $aAppendix 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. 330 $aA superb development that starts with the natural numbers and carries the reader through the rationals and their decimal representations to algebraic numbers and then to the real numbers. Along the way, you will see characterizations of the rationals and of certain special (Liouville) transcendental numbers. This material is basic to all of algebra and analysis. Professor Niven's book may be read with profit by interested high school students as well as by college students and others who want to know more about the basic aspects of pure mathematics. 606 $aNumbers, Real 606 $aNumbers, Complex 615 0$aNumbers, Real. 615 0$aNumbers, Complex. 676 $a512.81 700 $aNiven$b Ivan$f1915-1999.$012251 712 02$aMathematical Association of America, 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910971363203321 996 $aNumbers$94402942 997 $aUNINA