Post Term Test

On October 10 Wednesday, there was a term test for the CSC236 morning class. In order to prepare for it, I reviewed all the lecture notes and read through the course textbook. The term test covered mathematical induction, complete induction, well-ordering induction, and structural induction.
For the mathematical induction, its proof was extremely straight forward. From my point of view, mathematical induction proves a minimum case and proves the next number over and over. This implies to all the natural numbers starting from a base case. This type of induction did not surprise me at all because the concept was very simple. I found difficulty when it came to finding the base case. Not all questions start with zero. In this case, I was to find the base case. However, I found very difficult to find if the base case is really the base case. Throughout some trials, I realized that I can find a base case using inequality. Then, I should also try numbers below them until the case fails because sometimes the base case found by the inequality is not the real base case. From this, I learned that it is best to try out the real examples rather than reading a textbook to realize how the proofs work.
One disadvantage of using the mathematical induction is that you cannot use its induction if 'n' is not sequential natural numbers. This flaw could be overcome by Complete Induction. Complete Induction proves a statement by testing the previous cases and use a further step to prove that its P(n) is true. In the first place, I found very hard time understanding the concept of the Complete Induction. I wondered how the previous case work for the current cased. In this logic every case should work if and only if the base case work. After reviewing some tutorial notes, I realized that it was not just about proving the base case. It was about proving the previous case and apply that previous case to the current case by stating another statement to one previous case. I think the concept would have been a lot easier if the lecture slide describes the concept much specifically. From this trouble, I learned that I should never rely on the lecture slides all the time because the slides are extremely summarized so sometimes it misses key concepts.
Well ordering states that there is a smallest element if P(n) is true. It was a very obvious concept but it was too obvious to apply to the proof. For the well-ordering, all I learned is that we need to prove a statement  by contradiction. I wish there was a tutorial just for this so I can learn from the examples. It was very disappointing that we did not have a tutorial for this concept.
I learned structural proof and read the textbook. However, I still do not understand this concept. I tried to  understand the lecture examples and online examples, but its concept did not come to my mind. I think I will have to stop by an office hours so I can at least understand this concept. From this chapter, I learned that I need to take advantage of office hours if there are concepts that I do not understand.