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 RiemannStieltjes 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 l¡¦(»ý·«)
abels 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 ¡ô Q, r = 0, and x is irrational, prove that r + x and rx are irrational. Solution: Suppose that r + x
