Friday, September 12, 2008

Start

Was very glad to see that this will not be just a straight continuation of CSC165. Not that I did not like that course at all, but I must admit that rigid proof structures were not my favourite part. 

There was a bit of confusion regarding zero, it being a natural number, yet sometimes behaving oddly. In a question about odd and even subsets, even the professor first intended to treat zero (empty) set specially, but it was actually possible to word the solution in a way that did not require special treatment for zero. It seems that logical statements are like mathematical formulas in a way that the same idea can be expressed in multiple ways, yet most of these ways can be "simplified" to a more concise form. 

There was a curious question about 12n - 1 being a multiple of 11. The final solution presented in class was quite concise and to the point, using only simple algebra. What I first considered though, was a sample of 12n - 1 numbers and how exactly they related to 11. The result was that there indeed is a recursive pattern to the relation, but that was simply unnecessary in the end.

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