Advanced Calculus I MAA4226 Fall 2012
Homework 4 Solutions
I. Do problems 19, 20, and 21 from page 44 of Rudin.
19. (a) Suppose A and B are disjoint closed subsets of a metric space X . Since they are closed,
A = A and B = B . Hence A B = A B = and A B =

Advanced Calculus I MAA4226 Fall 2012
Homework 1 Solutions
Due Wednesday, September 12, 2012
I. Do problems 2, 4, and 6 from page 22 of Rudin.
2. You are allowed to use the unique prime factorization property of integers in these problems.
Assume p/q is a

Advanced Calculus I MAA4226 Fall 2012
Homework 3 Solutions
Due Wednesday, September 12, 2012
I. Do problems 2, 5, and 6 from page 43 of Rudin.
2. We use the hint given in the book: For every positive integer N , there are only nitely many
equations satisf

Advanced Calculus I MAA4226 Fall 2012
Homework 5 Solutions
Due Monday, October 29, 2012
1. Let cfw_zn be a sequence of complex numbers and let z be a complex number. Assume that
limn zn = z in C. Prove that limn |zn | = |z |. Hint: You may nd the inequal

Revised version of solution to part of Problem 9 from Chapter 1
Here is a revised proof of the fact that C , with the dictionary order, does not have the LUB property.
Consider the set S = cfw_z C : Re z < 0. Clearly S is bounded above; for example by 0.