Problem Set & Assignment : The Aftermath

Unfortunately, I couldn't do the LOG(refer to my last post) for the following reasons:
1) My computer had to be close.
2) I rather write than type.
3) Laziness.

Problem set #4 was pretty straightforward. My only problem approaching it was the flavor of induction. I used complete induction because it felt more safe based on its definition. I usually use complete induction when I can't get from P(n) to P(n+1). However, for this question we can get from P(n) to P(n+1). So my problem was with the fact that there were two base cases(Namely, P(0) and P(1)) where in the definition of simple induction we only verify P(0). So this is my random thought for proving this problem using simple induction:

*Prove P(n) for all n>=1 using the base case P(1)
*Verify P(0) manually
Since there is no natural number between 0 and 1 => P(n) for all n

So basically, my real question is if we can have more than 1 base case for simple induction?

Assignment #2:

#1 - We barely get questions like this. We have all the tools necessary. There's no complicated formal structure. It was a great puzzle and I have to say, although I don't think I got it right, I enjoyed doing it very much and I would happily loose marks for questions like this.
#3 - I enjoyed doing this question very much. Mainly because of the verbal explanation of G(n) which made total sense.
#4 - Very similar to lecture notes and as a result a straightforward question.

...and Happy Halloween!