1. The material was fairly simple to understand in this section, however the area that I may not thought about before is Corollary 2.5. It talks about the remainder having the same equivalence class as the dividend. I guess I am not quite sure why they brought in the t-s...
2. I loved the connection with the equals sign and the equivalence class equals sign. In both cases their properties had an identical outcome, and the properties of reflexive, symmetric, and transitive can be applied to modulo. I also find very useful that a=b(mod n) breaks down into n divides a-b which also breaks down to kn=a-b for some integer k. I like this because depending on the context of the proof, you can choose either of the three representations that will be most useful.
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