Episode 2: Chocolate and Stamps

Finally getting to post my weekly notes (about 236 material, class, and life in general). . . unfortunately near the end of the course :x Hopefully I'll get some feedback^^ Anyway, time to digitize all my paper notes :D
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Well, this week was mostly dealing with STRONG induction, rather than simple induction last week. I've always liked simple induction much more (well...more like the lesser of two evils but I digress). But it does make more sense for situations where base cases are not easily found.

The chocolate grid problem shown in class really helped my understanding of Strong induction- I had been used to using P(0) for most problems involving simple induction, and I had thought that strong induction could not involve any base cases. However, the base case of a 1-square chocolate grid made sense since it can be broken with 0 breaks (sounds a bit facetious though ==)

Another problem that I found quite fun was the postage to be formed with 4,5 cent stamps. It was slightly annoying to have a working sequence of numbers only to find the next number to fail (8, 9, 10 work but 11 does not).

Another note: so far, Principle of Well Ordering seems a bit too. . . simple. Doesn't any non-empty subset have at least 1 element? Then there has to be a smallest element- I don't really understand why there has to be some new "principle" to declare it. Hopefully, things will clear up in the coming weeks.

fOrTT