2.1, due on January 8th

1. The most difficult part of the material for me was corollary 2.4. I understand most everything up to that pretty well, but what does it mean by "disjoint"? Does it mean that the two congruence classes have nothing in common? So does the corollary say that two congruence classes mod n have to either have nothing in common or everything in common, meaning identical. I suppose if I thought about it enough I would understand it better. In fact simply asking the question to myself is helping me grasp a little better of an understanding. So, I think I mostly understand everything else, just corollary 2.4 and then sentence about it are a little fuzzy to me.
2. The most interesting thing to me is that when you have a congruence class mod 3, for example, there will be a lot of the classes that are equal. I missed that on a test last year without realizing that half of my congruence classes had the same numbers in it :) But now it makes a lot more sense to me, and I think that is pretty cool. I also think that the equivalence relations that the congruence classes can possess such as reflexive, symmetric, and transitive will be very helpful knowledge while dealing with this chapter. I know we used that information a lot in Math 190 to prove things, so I'm eager to see how much and in what ways we will use it again. Overall, I thought this section was very interesting and I learned a lot. I know I'll understand the things I didn't understand after tomorrow's lecture. I look forward to meeting you for the first time tomorrow!