Talking about test 2 reminds me of the first test, which I got only 30/38 but still believe I didn't do anything "wrong". Well, forget about that (because it is only 1.32 points in the final score), I believe (hope) I did well in the second test.
The format of this test, again, is very similar to the one from the old sample test. To my surprise, there are two question that are about the definition and proof of floor function. However, the third question very similar to the claim 1.4 in the assignment 2. After we had a group chat last Wednesday, we finally figured out how to solve claim 1.4. At the beginning, we tried to prove it by assuming its negation is true, which I think is not a common way that we are taught in the class. So finally, by finding a good z, we proved it directly. The test is quite similar so I just write nearly without thinking.
Unfortunately, I believe I made a mistake in the second question. I chose d = e + 1, and then use the third part of the definition by letting z = d. However, d that I chose is not an integer! If I choose d = floor(e) + 1, things would have been solved! I hope this is not a big deal, and I can still get most points of this question...
For the lecture part, I was like having been sleeping for a whole hour (but actually not), because I found it so hard to understand what the professor just said. Luckily, my classmate told be to check out the slides of Professor Larry Zhang. The truth is, they are amazing. Everything is so clear and sometimes funny. Now I am pretty confident that I can learn pretty well in this chapter.
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