Professor Heap talked about Well-Ordering and Structural Induction in the third and the forth week. I had never heard of either of them and found them a bit confusing at first. I thought Well-Ordering was some kind of a proof technique and I couldn't figure out what it really means. However, after I spent some time reviewing my notes and examples presented in class, I learned that Well-Ordering is just like a fact: every non-empty set of positive integers contains a smallest element (http://en.wikipedia.org/wiki/Well-ordering_principle), and we refer to the fact when proving another statement.
Structural Induction seems like a kind of Simple Induction / Mathematical Induction to me. It's just that it deals with operations of two elements, so it didn't take too much time to understand.
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