Week 6: Test Result and more Proof

I finally got my score for my first test in U of T, which shocked me a lot. I got full marks on the second and the third questions, but I lost 8 points on the first question. Last week after the test, I checked the sample solution posted on the professor's website, and I didn't think I got so many wrong answers! I even didn't find anything wrong in my test.

Although I haven't got my test back, I still don't know what mistake I made, but maybe I can guess part of the reasons. In the second part of the first question, I might failed to explain my answer properly. Since I have never written an exam in English, I probably don't know the right way to explain my answer. But despite that, I will get my test back next week and figure out what happened. No matter what's the reason, either I failed to learn well or just didn't write properly, I'm sure I will do better in the next text!

For the lecture, we learned some more different kinds of proofing. First thing is to prove some claims about the floor function. I think the point here is to use the definition appropriately.
And when we want to prove something is wrong, we just need to prove the negation of the claim is correct.

And for the final part of the week's lecture, I learned how to prove the claim which we need to discuss is by cases. What we need to be careful is to find all the cases and do not lose any of them. Only in this way can we prove the claim correctly.

I viewed the blog of my friend this week, he mentioned that the indentation is very important, which I totally agree. Once I read someone's proof without indentation, I found it really hard to keep pace with the author because the proof is chaotic. When we finish our assignment on computer, using Tab is a good choice to make the indentation.