7.6 Part 2

1. What was the hardest part of the reading for you?
I know I'm naughty because I haven't blogged or done my homework in a couple of days. Call it my spring break. That being said, tonight's reading was pretty easy for me, mostly because we talked about the whole chapter in class last time... but the thing that I found the most 'interesting' or something that I think is kind of tricky is the stuff in bold letters on the top of page 212: "The condition aN=Na does NOT imply that na=an for every n in N."

2. Theorem 7.34
While proving this in class yesterday, the question was asked, "Why do we need all 5 of these pieces of the theorem? Aren't 2 and 3 kind of redundant?" I thought the answer to that question was kind of interesting, and that was "Though 4 and 5 are stronger statements than 2 and 3, it's easier to prove a weaker statement, and from the weaker statement it becomes easier to prove the stronger statement, and that was evident from the proof of 7.34.