- Appendix C - Fields pp. 510-513,
- Handout
- Sect. 1.2 and 1.3

- 1.
- In no more than one page write a summary of what is induction and why it works as a method of proof. Assume your audience is someone with very little mathematical sophistication.
- 2.
- Use induction to prove that
- 3.
- Use induction to prove that if and is a positive integer.
- 4.
- Find an error in the following inductive "proof" that all positive integers are equal. Let be the set of all such that equals all integers between 1 and . Then . Now suppose all integers up to and including are in . Then , so adding 1 to both sides gives that . Therefore, by the principle of mathematical induction, contains all positive integers, and so all positive integers are equal.
- 5.
- Use the strong form of induction to prove that any integer can be expressed as , where and are nonnegative integers.
- 6.
- Sect. 1.2 1,10,13,18, 22.

Math 24 Fall 2001 2001-09-24