A few things were very difficult to understand in this section. A lot of the proofs are very difficult and involve some unintuitive algebraic manipulation and whooplah. The second is that I still don't see the need for the strong principle of mathematical induction as opposed to the normal principle of induction. The book states that it's common for sequences of numbers but I still fail to see exactly why you need to give numerous examples that it's true for initial conditions in order to be able to prove it generally.
These sections were fairly unenjoyable. For me the proofs were very difficult to follow and required numerous readings to grasp their concept. Now that I understand them fairly well, I appreciate them, the minimum counterexample more than the strong principle of induction. It seems like a neat way to prove something but also like you can prove the same thing with normal induction. I assume that it would also be helpful in cases of proofs where contradiction is more convenient than a more direct approach.
No comments:
Post a Comment