1. I realized today that I didn't know what the definition of an irrational number was. A brief date with google though, and I am all set. I really enjoyed reading about proofs by contradiction. It's nice to know that there is a way to prove a proof by showing that it doesn't work. (I feel like a lot of times I'm better at proving that it doesn't work than that it does.) I was especially excited about the application of the three prisoners story problem. Sometimes it's hard for me to see application for the things we do in the this class (which is fine, because I'm a much more theoretical person anyhow), but I did enjoy seeing an application and feeling really smart for knowing how to solve a real life (sorta) problem.
2. This was my favorite section I've read yet. The hardest thing, by far, for me is just coming up with the idea of what to do. The math isn't ever hard for me, and I'm starting to get good at remembering the definitions and theorems, but I don't know how to recognize what to do. However, being able to see that there are three different proof strategies we can use, and that sometimes all three of them will work, will hopefully make it easier for me to come up with the solution.
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