1. I can't quite figure out what's different from what we've been doing and what I read about today. I must be missing the mark. However, I had never heard of the Division Algorithm, and it sounds scary...so I don't know if I'm actually excited to learn about it in Chapter 11. From what I understand, the algorithm is just that every integer can be written as a sum of a quotient times an integer, with a remainder added on. Seems easy enough. But recently I've been feeling like saying "seems easy" a lot, and then all of a sudden, I am highly confused. Not good. I've been pretty grateful for the homework this unit...I have felt pretty confused on almost everything until I've sat down and chugged out a few problems.
2. Equivalence classes. No idea what they have to do with anything. But they are sweet. I wish there were infinity classes like this and like linear algebra where I could just do abstract math and never understand the relevance. (I do want you to know though that Ryan and I have made quite a few "If...then..." statements and analyzed them in our personal lives.)
Anyway. From the reading, it appeared that the number of unique equivalence classes is the same as the divisor. (That's what we call the mod __ number, right?) Anyway. Maybe if we could talk about some applications of these modulo questions, that would help me. I love them though.
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