Principles of Analysis

Homework Assignment #3

Due Wednesday, Sept. 25, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Section 1.5
Problems:   2, 3, 4, 9 (parts a, b, c), 12

Hint: For problems #3 and 4, first follow step by step the proofs in the text related to the problem at hand. Then try and prove the statement by mimicking the proof in the text. For problem #9, try making up examples to start with. If the statement is true, you must prove it. If the statement is false, come up with a counterexample.

Additional Problem:
Using the proof in the text, but in your own words, prove Corollary 1.5.2, which states that a nonempty set of real numbers bounded below has a greatest lower bound.