It was hard to follow the example of the Cartesian product Z6xZ. I was confused when they said that a,a' are both in Z6 and z,z' are both in Z. It seemed like it would make more sense to have a,z in Z6 and a',z' in Z. It wasn't until reading in Appendix B and reading theorem 3.1 that it actually made sense to me.
Reflective:
In class I think I was a little confused about subsets of set that are rings, but I think now I understand. While Z is a ring, and E is a subset which also happens to be a ring, O is not a ring. It's ok for subsets to not have all the properties of a set. I think I had always thought of it the other way around.
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