The rest of 3.3, due November 1

First of all, I don't think I have any idea what the orthogonality relations are. I know this doesn't exactly help you know what to teach tomorrow, but I think my biggest problem right now is that we are building each day but there are always things I'm still not getting. The other thing is that the logic used in these recent proofs seems very different  to me than what we have done in the past. When 3 pages are spent on a proof and I get lost near the beginning, it is incredibly difficult for me to follow the rest of it, especially because I haven't been able to see where these are going. My favorite part of this section was that they didn't prove the last theorem. Yay!