2.2, Due on January 12

Difficult:
At the beginning of the section, it defined classes of integers, A, B, C, D, E, where the  classes were all disjoint, and every integer was in one of the equivalence classes, but it showed that B+C=D and B+C=A.  I was confused why this happened. Did they set up these equivalence classes in such a way just to prove this point? I was just really confused where these equivalence classes came from, and why the addition property didn't work in them. I had a difficult time understanding when this would happen in a problem, and why the addition and multiplication that were defined at the beginning of the chapter were just "tentative".

Connection:
The most interesting part of this section for me was that modular arithmetic also follows the same properties as arithmetic in the integers (with the exception that if ab=0, then a=0 or b=0). I thought that this section was really cool to see that modular arithmetic will follow the same rules we have been taught over and over in math. These rules are ones that we have practiced over and over, so it is interesting to be able to apply them to a new kind of arithmetic. I really like when I can use something that is familiar to me when I am trying to learn something new and more difficult.