7.1, due March 4

1. Ok, there are a few difficult things about the rest of this section for me. The definitions on page 167 are a little hard for me to understand. On page 169, I'm confused when it says that "Under multiplication, a nonzero ring is NEVER a group," and then it says that certain subsets of a ring (which are still rings right, or no?) may be groups under multiplication.... I guess I just don't really understand that. Theorem 7.2 is actually a little confusing too, sheesh I'm just having a hard time tonight I guess! I think what I'm having a hard time with is that with groups we talk about the set of all things, right? Like in this theorem, it's the set of all units, not just one. I remember you talking about this on Monday, about how a subset or something is not just a part of the set, but it includes the whole thing, I can't remember exactly what we were talking about, I'll have to ask you. And ok, what's up with all the notation on page 170? I mean diamonds, really? Must we bring in more new terms?? Goodness gracious! I'm going to have to really get this down! I hope it's ok that I see you tomorrow most likely :)
2. I think a lot of this stuff is very interesting! I like learning this new material, but I get some of it, because some of it is similar to what we've learned already. Anyway, I think it is cool and interesting, and hope that I can understand all of it soon!