After Assignment 3

After finishing assignment 3, I feel like I definitely have a better understanding of big O and big Omega, and I'm definitely now capable to deal with questions like this on the exam (although I will definitely be doing more practice on this before the exam anyway). 

I found the idea of big Theta very interesting, especially since on the assignment, my answers for question 1 & 2 can be combined to form a big Theta proof. The idea that a function can be both bounded above AND below by a single function (multiplied by different constants) is very fascinating to me, and this is definitely something that is going to be useful in the future for calculating efficiency, especially because we're already beginning to see  implementation of big O and big Omega in calculating the efficiency of our functions in CSC148, and understanding of this concept definitely gave everyone in out class a head start compared to people who didn't take this course.

The use of limits in proving big O and big Omega was confusing at first, but then I realized that it was just the observation of the end behaviour relationship between the two functions. For big Omega, if the limit f(x) /g(x) approaches a real number L, then that means g(x) will at one point grow much faster than f(x), so f(x) can no longer be bounded below by g(x). Otherwise, if the limit of f(x) /g(x) approaches infinity, then that means f(x) will continue to grow much faster than g(x), so g(x) is always a lower bound for f(x). I used a similar logic to prove using limits for big O as well.

I really hope that my understanding of this material is correct, I guess I'll double check while I'm studying for the exam!

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