Second Week - Complete Induction

This week we devled further into induction, with the 236 introduction of complete induction. While PSI argues that if the base case holds, and each case implies the next, then all cases hold, PCI requires all previous cases to be true in order for all to also be true. Although both types of induction were introduced to students of MAT137 [myself being one], the phrasing of both types given in this class brought an unparalleled amount of clarity to induction in general. Its much easier to understand than mathematical language [while it is, arguably, more precise] which in turn, for me at least, elevates the value and understanding of an induction proof.

Examples of complete induction done in class included proving that every number greater than 1 had a prime factorization, every full binary tree has an odd number of nodes (which brought back fond memories of CSC148), chocolate squares, as well as an obligatory postage stamp induction example.

I feel most comfortable with induction now, and I think I can attribute that to the well worded definitions of both flavours of induction. I had not been introduced to such definitions, as most prior to the ones given in 236 (with the exception of 165) were based on the mathematical notation, which I did not find to be too great in clarifying the process in induction. This, I think, is the likely cause of the usual question about induction, "aren't we assuming what we're trying to prove?" As well, on Friday, the princple of well-ordering was introduced, albiet briefly.