Hi everyone!
I am really excited to be posting my very first blog! I hope
everyone has been having a good Thanksgiving long weekend. Mine so far has been
fairly uneventful. I have however, now that Assignment 1 is done, started to
study for our first test. Looking back at the past lecture slides, I came
across a proof that I really enjoyed. Although we did not finish it in class, I
had a fun time struggling to come up with a solution. Which one? It was the
chocolate bar proof where you had to determine how many breaks any m x n
chocolate bar can be broken up with. I think one of the reasons I particularly
enjoyed this proof is that before, I didn’t quite understand complete
induction. Working through the problem showed me how useful complete induction
really was. Also, I found it quite interesting that no matter how you broke up
the chocolate bar, it would always require the same amount of breaks.
Anyway, now that I have gotten a better grasp of complete
induction (hopefully), I have moved on to another concept I can’t quite understand: the
principle of well-ordering. I have been looking online to see how well-ordering
and mathematical induction imply one another but have so far not gained much
more insight. Hopefully by Thursday things will all be clear!
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