Homework 10

For the week of Nov 30 - Dec 4.

First make sure you can do Exercises 13.1-13.5 but don't turn them in.

For each problem in Exercises 13.9, 13.11, and 13.12, first state whether or not the given statement is true. If true, prove it. If false, give a counterexample.

1. Do Exercise 13.9.
2. Do Exercise 13.11.
3. Do Exercise 13.12.
4. Do Exercise 13.20.
5. Prove the other part of Theorem 13.16: Every bounded nonincreasing sequence converges to its infimum.
6. Do Exercise 13.25.