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Note for Numbers - N by Placement Factory

  • Numbers - N
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  • Quantitative Aptitude
  • Placement Preparation
  • 8 Topics
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NUMBERS: RATIONAL AND IRRATIONAL IVAN NIVEN 2+V-5 3-4i

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NUMBERS: RATIONAL AND IRRATIONAL COMPLEX NUMBERS REAL NUMBERS (REAL) ALGEBRAIC NUMBERS NUMBERS CONSTRUCTIBLE BY STRAIGHTEDGE AND COMPASS RATIONAL NUMBERS INTEGERS I NATURAL NUMBERS I

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NUMBERS: RATIONAL AND IRRATIONAL by Ivan Niven University of Oregon THE L. W . 1 SINGER COMPANY A Division of Random House

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C O NT ENT S 3 Introduction Chapter 1 1.1 1.2 1.3 1.4 1.5 1.6 Chapter 2 2.1 2.2 2.3 2.4 2.5 2.6 Chapter 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 Natural Numbers and Integers 9 10 11 13 15 18 19 Rational Numbers 21 21 23 26 30 34 36 Primes Unique Factorization Integers Even and Odd Integers Closure Properties A Remark on the Nature of Proof Definition of Rational Numbers Terminating andNon-terminating Decimals The Many Ways of Stating and Proving Propositions Periodic Decimals Terminating Decimals Written as Periodic Decimals A Summary Real Numbers The Geometric Viewpoint Decimal Representations The Irrationality of v'2 The Irrationality of V3 The Irrationality of V6 and v'2 + V3 The Words We Use An Application to Geometry A Summary 38 38 39 42 43 44 45 46 51

Lecture Notes