This week's lecture started off with the comparison and connection between Principle of Simple Induction, Principle of Complete Induction, and Pricinple of Well-Ordering. It could be seen from the proofs that there was a cycle of implication between these three principles- if you believe one, you must believe the other two. Before the lecture, I didn't know how PWO was connected with the other two, but now I clearly see a connection between them. It was nice to note these connections, as now we could refer to all three principles when doing proofs. The next topic, bases larger than zero, I didn't have any trouble with. It was similar to the material from the previous two weeks except that the base case could be changed to any number. The induction step still remained the same.
PROBLEM SET #2
This week's problem set is bit harder than last week's, but still manageable. The lecture slides weren't a big help this time, but the textbook was. There was a similiar example on the textbook, and after consulting the book, the problem didn't take me long to solve. It just took me a while to realize that we are supposed to substitute in a specific number for N before proving it. The try and error part of this problem to find N took me the longest time.
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2 comments:
Problem sets should test whether you can reproduce something similar to a lecture example. Assignments should stretch a little bit further. If your total time on the course (lectures plus everything else) is a lot more than 8 hours a week, let's talk about it.
8 hours a week, I think I'm still in that range. I'll keep that in mind though. =) Thanks!
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