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?