CSC 165 SLOG #9: (Week 10:Big Omega, Big Theta and General Properties)

This week, I learnt how to prove and disprove Big Omega, and Big Theta. I also got my second term test back. Although I wasn't able to achieve the same mark as the last time, I am very satisfied with my marks considering that this test was harder than the last one.

During the lecture, the professor went over Big Omega and Big Theta materials. The lectures were mostly focused on proving and disproving big omega and big theta. One thing I found interesting was that we have to use L'Hopital's rule in some specific cases. As I already knew what this rule is, I had no problem solving the questions. Learning how to prove 2ⁿ ∉O(n²) was very interesting as I had to apply L'Hopital's rule.

If we write this in limit, it is as shown below. 

lim (x -> ∞) 2ⁿ / (n²)

As both numerator and denominator would become infinity, we have to do the derivation on this limit for each numerator and denominator due to L'Hopital's rule.

We get as shown below.

lim (x -> ∞) 2ⁿ ln2 * ln2 / 2

Then we can show this as shown below. 

∀c∈ R⁺,∃n_c∈ N, ∀n∈ N, n >= n_c -> 2ⁿ/n² > c

After that, we can prove this using the techniques we learnt throughout this course.

I hope to learn more in computer science mathematical expression next week to become a great computer scientist.