Problem Set #1 and some other ramblings...

Well, here goes with my first official posting. This post is a bit late as Problem Set 1 was handed in last week and #2 is already coming up, but since I haven't even so much as looked at #2 yet and need a post for last week - this is it.

First, I just want to comment on using a tablet for school. I have decided to go this school year without writing on -any- paper directly if possible. There's several reasons to why I'm doing this.

• Last year, my bag (after 2nd semester) at almost all times had all or at least most of the following items inside of it:
  
  • My laptop
  • Laptop adapter
  • 1-2 binders (just full of paper, and not all of which was organized very well or even inside the rings for that matter)
  • mouse (x2), DVDs, extension cable, etc... (bunch of smaller stuff that doesn't really add much weight)
  • 16 port mini-switch (of which the AC adapter is pretty heavy)
  
  Now the problem was, with the binders and my laptop etc... my bag started becoming very heavy and was always huge. By eliminating the binders and replacing it with a very thin wacom tablet, it gave me back a lot of space inside the bag for other things and reduced the weight by a lot. It's actually kind of awkward sometimes with how light the bag feels in comparison.
• Since most of those papers in the binders were unorganized and sometimes missing, my notes kind of became useless. I never really looked over them for any of the classes. They just sort of accumulated until I stopped bothering to take them eventually. There was no easy way for me to find anything. With the tablet and one-note, I can actually *search* through my notes. I can seperate notes by titles which make sense and I can also type things up which are makes for much better searching. They're always there and I have them set to sync with my Desktop so they'll never be lost. Doing things like drawing diagrams is a lot faster and they look neater.
  
• I never actually bothered to buy paper, a new binder (since old ones are half broken), pens, pencils, or anything else of the like for school yet. So some time during first week I think I saw my tablet laying around and thought I could just use that instead. So I did, and I have been. This is probably the main reason, the others are just nice side-effects.

I also wrote up my first Problem Set with the tablet which is kind of interesting. I could copy/paste the problem set questions into the page and then write underneath it. I never had to worry about running out of space, fixing mistakes was easy and didn't leave behind any eraser marks or white-out to deal with. Though, printing the problem set out was a bit of a pain in Bahen. Mostly because the lab I went to originally didn't have a working printer. Gah!

Besides that, the Problem Set itself was quite easy, taking only about an hour or so to work through. Though still have to see how I did of course.

The first question was very similar to another problem we went over in class, so I followed a similar method in proving it. Nothing really special here.

The second question, I think I proved correctly however in hindsight I believe that I didn't word my concluding statement properly. Instead of saying that P(n) is true I said that P(n) => P(n+1) is true. I'm not sure if this is the same thing, as the statement I used is only a part of the induction formula. i.e. [P(1) \and (\forall n \in N, P(n) => P(n+1))] => \forall n \in N, P(n).