- Quizzes: I somehow completely forgot to give the badges quiz on Friday, for which I apologize (I really try to avoid surprises). We will take it on Monday instead. That will also push the proof quiz back to Wednesday next week.
- Today we did a warmup direct proof and I left you with two proofs to write at home:
- Let a,b,c be integers. Then .
- If a,b,c are integers such that a|b and a|c then a|(b+c) and a|(b-c).
- In class we used the fact that the equation xy=1 has only two solutions in the integers, namely x=y=1 and x=y=-1. Can you prove this? Try contradiction!
- Review the proofs by contradiction from class and also the first Proposition in Chapter 6 of Hammack (first page of the chapter), which is an example. Pay careful attention to the negation of the theorem, i.e. the supposition you make for contradiction.
- With your remaining time, try a few at home: Chapter 6 exercises 1,2,6,7,8,9 as time allows.