Week 5: Test and Proof

For this week, we took a test on Wednesday, which I think is not quite hard. The format of this test is very similar to the one of last year. I don't think there will be big problem on this.

For the lectures, we continued to learn how to prove a theorem in a good format.
First, to prove existence, which I think is the easiest, you just need to find a number of something that fit the theorem and then you have finished the proof.
Then, we learned how to prove a claim about a sequence. If there is an "exist" in the claim, just find a number which fits the claim (maybe you can find it immediately or maybe you have to calculate and get the number), then assume the antecedent is correct and try to get the consequence step by step. After get the result, do not forget to write the last few lines of the proof: add "for all" or "exists" to the claim.

Other than proving a claim directly, we can also prove that the negation of the claim is false.

I didn't know that blogger can use LaTeX before I found this student's slog.
Like this:

This is how to prove n square is odd if n is odd, which is not such difficult to prove.
The point is, I still don't know how to type in this cool way in blogger.