5.2-5.3, Due Sept. 29

Difficult: I really like proof by contradiction, but I had a really difficult time following the proof : Prove that sqrt(2) is irrational. Since it cannot be written as an implication, do we have to use contradiction? Or can we make an implication, like: "If sqrt(2) is irrational, then there are not two integers for which a/b=sqrt(2). (And then use proof by contrapositive... but I guess that wouldn't be much of a proof...) Another thing I wasn't sure about is when the book quotes and uses theorems from previous chapters. In our homework, when we do that, do we need to cite which theorem we used? Or can we just say "A previous theorem said that since xy is odd, then either x or y is odd."?

Interesting: I really found the example about the three prisoners with dots on their heads really interesting. After I read it and thought about it, I could have sworn the third prisoner just guesses. But as it explained how the prisoner used contradiction, it really clicked!