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principles of mathematical analysis solution 대학교재솔루션

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Rudin’s Principles of Mathematical Analysis: Solutions to Selected Exercises
Sam Blinstein UCLA Department of Mathematics March 29, 2008

Contents
Chapter 1: The Real and Complex Number Systems Chapter 2: Basic Topology Chapter 3: Numerical Sequences and Series Chapter 4: Continuity Chapter 5: Differentiation Chapter 6: The Riemann-Stieltjes Integral Chapter 7: Sequences and Series of Functions 2 10 16 23 32 39 47

1

The following are solutions to selected exercises from Walter Rudin’s Principles of Mathematical Analysis, Third Edition, which I compiled during the Winter of 2008 while a graduate student in Mathematics at UCLA. Equations are numbered within each Chapter and their labels correspond to the question number and equation number, so (2.3) refers to the third equation in question #2 of the current Chapter.

Chapter 1: The Real and Complex Number Systems
1. If r ∈ Q, r = 0, and x is irrational, prove that r + x and rx are irrational. Solution: Suppose that r + x 


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