Week 3

A new proof structure Well Ordering is introduced this week. Among three proof structures, I find well ordering is the hardest one to utilize. It is like prove something backwards when using well ordering, because we are going to use the "smallest elements", and in most of the time, derive a contradiction to what we assumed. Take A1 q3( the golden ratio) for example, if phi = n1/n2 = n2/ n1 - n2, so if we get the set cotaining all n1, n2, ..., nk, where n = n - n and we find this set is not going to cotaining any smallest element, thus by well ordering we find phi is not rational.

One thing worth to review is the relationship of three proof structures.