Slog for week started from Oct. 13

What’s new?

• 1.       This week, we are introduced to a new math expression-floor, shown by │_x_│. This part is quite new for me and I think it has very similar idea to what is called limit in our MAT137 class (but I consider that they are not equal). I think using floor is very convenient us to calculate.
• 2.       We are discussing how to prove a statement is false. 

Questions

• 1.       But I’m quite confused about that why │_x_│+1>│_x_│ is equivalent to │_x_│+1>x? Can I say that the difference between │_x_│ and x is at most very close to 1 but at least 0?
• 2.       To simplify the idea, is this part meaning that our goal to finding a contra-example for the given statement so that we can prove it true?

Slog for week Sept. 29

•  What’s new for this week?

This week we are introducing to some properties of implication (transitivity). Then, we are discussing infinity, I realize that this part is very related to what we are learning on mat137 right now-the proof of limit. Last but not least, the Proof Outline part is new to me so that I'm feeling interested in it. And I'm wondering are we required to write our proof with the exactly same format to this proof outline?

•  Challenge

When i'm working on my assignment 1, a question confused me. For two statement, (there exist a in A, C(a) and B(a)); (there exist a in A, not B(a) and not C(a)),  I know these two statements are contrapositive, but are they equivalent?