4.3 - 4.4 and additional questions due January 29

1. Proofs involving sets had my brain going a little wild. I found it was a lot easier to simplify the proof in my head to lots of little proofs (lemma style.) The textbook is so easy to read and to follow, and it basically supported my thought process. I also didn't realize just how careful we have to be with switching operators until this section. I have to really have my guard up to know if we're proving the converse or proving by contrapositive, both of which are completely different and can yield some pretty...wrong...results.

It's hard to do proofs with greater than and less than symbols. I am overthinking the changing of the sign and making the equations equal.

2. In learning about proofs for real numbers, I couldn't help but notice that they are pretty much the same as proofs for integers, only this time the two cases are positive and negative, verses even and odd. The proofs involving sets are the same as proofs for integers, there's just different operators. I was excited to see the proof of result 4.20 though, where the entire thing pretty much was done through wordy observations. It was pretty easy to follow, if you can think in terms of set operations.

And a few answers:

1. The homework takes me about 2 hours, usually. Sometimes longer, sometimes shorter. I feel pretty prepared for them, and for once in my life actually feel like the homework questions are testing us on our knowledge of the material, not trying to show us how many exceptions there are to the rule. I have liked it a lot so far.

2. My learning has most been benefitted by the reading, unfortunately. I don't like to read textbooks, so I'm always looking for a reason to not read them. But I have benefitted greatly from the reading. It makes it so that the lecture is just to answer the questions I have, and then I can do the homework fairly easily. This is a pretty useful textbook.

3. I think probably the best thing for my learning would be if I would be smart and get ahead on the homework again. Last week I fell behind, but before that, I was always working on the homework before I went to lecture, so I knew what my problem was, and could use the lecture to fine tune my own learning. Hopefully this weekend I will catch up again.