Third Week - PSI, PCI, PWO

An eventful week this one was, with a two pieces of work completed for this course, one for CSC207, one for stats, as well as my nineteenth birthday on Thursday. I feel a lot more confident this year compared to last with the workload, as I notice I'm able to complete most assignments well before their due date. Given that the workload in September is comparatively easier than any other month, I hope I'll be able to keep this up.

The week kicked off with an example related to the Principle of Well-Ordering, which states that every non-empty set of positive integers contains a smallest element. Fairly elementary and intuitive, although as Danny mentioned, its a bit difficult to find a "nice" proof for it - at least, as I've been led by Google results for such a proof.

The example we did dealt with round robin tournaments, and the shortest cycles we could find in such tournaments. I was not able to determine the crux of the argument, but once I saw it on the screen, it seemed simple, and I think I just couldn't get a firm enough grip on the problem to solve it myself.

The rest of the class dealt with the relations between the PSI, PCI and the PWO. To give a very general summation, either PWO => PSI => PCI or PWO => PCI => PCI. I'll leave the details to the course slides, but I was able to see the connections between the three concepts, and how the belief in one led to the necessary beliefs in the two others.

Wednesday's class dealt with base cases larger than zero. Nothing really interesting of note, I understood all the concepts from previous lessons or experience with induction, so a straight forward class.

Friday involved the analysis of three examples of induction. An interesting class, it was kind of fun to try and spot the error in the logic, and a nice way to cap off the week.