Week 9

   We had the second term test this week. Though there were only 3 prooves on the test, I found one of them a little tricky. I've done the past term test and they were straight forward that I can finish them in 20 minutes. However on the test, the second question was kind of hard to find a way to prove. I spent about 30 minutes on that question and somehow found the way to prove. Hope I got the right answer.
   Besides the test, we've done more provings about the big-Oh. To prove a polynomial is in a big-oh of another polynomial, all we have to do is to pick a smart value of c and B. However, provings got more challenging while dealing with non-polynomials. It was easy to understand that an exponential function grows faster than polynomials, but it was a bit difficult to prove it. In that case, limits were introduced to prove it. Though I still not really understand the definition of limits (∀c∈R+, ∃n′∈N, ∀n∈N, n≥n′⇒g(x)/f(x)>c), this definition helps us to pick a smart value of n so we can sufficiently prove the statement.