Section 3.1 through middle of page 48, due on January 18

Part I: What was the most difficult part of the material for you?

The most difficult part of the material for me is trying to match up all the definitions with certain groups of numbers. Once the definition of a field came up, I figured that, for example, since all real numbers are a field, that would mean they satisfy axioms 1-12 but then I noticed that the definition of a field doesn't mention Axiom 11 but apparently it does hold in fields. That is when I get a little confused because it seems that Axiom 11 should be mentioned then.

Part II: Write something reflective about the reading.

I really liked the example on page 43 where they show a set T={r,s,t,z} and that they define it in a way that it is considered a ring. It is so crazy but yet it makes sense because it follows the definition. Since Axiom 9 and Axiom 10 were mention right after the definition of a ring that there aren't many examples of just rings without Axiom 9 and 10, but this example at least showed a ring that isn't even a commutative ring, and I noticed that before I read that part of the reading so I was making sense of everything pretty well.