Problem Set 1

(5 points)

Read Gallian preface, pp. 3-7 (until just above example 4), and pp 12-21. Respond to the following questions (in complete sentences or paragraphs):

1. Why is the Well-Ordering Principle given as an axiom?

2. How is the "Division Algorithm" related to the algorithm you learned for long division in school? (Compare and contrast.)

3. What is meant by the term "Linear Combination" on page 5?

4. Why are there two principles of mathematical induction?

5. What do you think the word "relation" means in the phrase “equivalence relation"?

6. What is the connection between partitions and equivalence relations?

Come up with a couple of explicit questions or comments on what you found interesting or confusing. Write them down.