MATH 201b Real Analysis UCSB

Math. 34B, Winter 2009, MWF 9-9:50, Prof. Akemann Prof. Charles Akemann, South Hall 6706 Were paid to help you learn. Office Hrs. MWF 10-11, South Hall 6617 PLEASE use CLAS, our e-mail: akemann@math.ucsb.edu office hours and Math Lab. Head TA = Laura

Math. 34B, Winter 2009, MWF 9-9:50, Prof. Akemann Prof. Charles Akemann, South Hall 6706 Were paid to help you learn. Office Hrs. MWF 10-11, South Hall 6617 PLEASE use CLAS, our e-mail: akemann@math.ucsb.edu office hours and Math Lab. Head TA = Laura

MODEL ANSWERS TO THE SIXTH HOMEWORK 1. Chapter 3, Section 6: 1 There are two cosets. The first coset is [1] = N, the second is the coset containing -1, which is the set of all negative real numbers. [1] [1] = [1], [1] [-1] = [-1] [1] = [-1] and [-

MODEL ANSWERS TO THE FIRST HOMEWORK 4. (a) Note that x (A B) x (A B) / either x A or x B / / x A B , either x A or x B and the result follows. (b) Similar to (a). 6. There are many ways to prove this. Perhaps the simplest proceeds as

18,100BC final exam December 18, 2007 NAME: 1. (20 points) If S R, show that the set of isolated points of S is at most countable (use that the set of rational numbers is countable). Solution: Let I be the set of isolated points of S. If s I, let d

MODEL ANSWERS TO THE SECOND HOMEWORK 1. (a) is surjective. Indeed, let t R be a non-negative real number. Then t has a square root s R. In this case f (s) = s2 = t, by definition of the square root. is not injective. For example, (1) = (-1) = 1.