how wrong would a proof be

I'm given some ideas of how a induction "traps" is raised by today's lecture. As to me, this happens that i write down the proof before convincing myself that each step follows the previous steps rigorously. We know that there are base case, induction hypothesis and induction step in a formal induction proof. The subtle may be made by missing one of them or by saying something that mismatching the fact. I sometimes make mistakes by making implicit assumption, and the result is that i couldn't reach the conclusion since it is incorrect at the beginning. To understand the statement is also important since the predicate is chosen from the statement. For the last problem on assignment 1, we should carefully remain the property of a ternary tree when we make our assumption. Good luck for the assignment 1.

working on practices

By reading the textbook, the simple induction and complete induction seem not that confusing. To make sure that i understand the definition and examples, i redid the proof in lecture and in the textbook. It's really important to find the right base case: is this case the very fundamental of the problem? do we need more base cases?
The scratch work helps a lot because it's always convinent to make changes when i look backwards in the problem. All of the mathematical problems we've encountered in this course are solvable. The key is always to know what kind of strategy to use corresponding to the problem and follow it step by step.
For example, we want to find out the possible unit digit that 3^n can have by using simple induction. The method is specified as simple induction. Then we just need to figure out the base case and the induction step. It's easy to find the P(0). Then we have to determine P(n) and let it imply to P(n+1). There are different predicates in different questions. We must make sure we understand how does P(n) work here so that it leads exactly to P(n+1). It's really helpful to correspond our assumption to its inductive case and understand the property. When transforming 3^(n+1) into 3*3^n, slight change is made but huge differnce occurs. We now can see the answers explicitly because 3^n had been extracted. This means we have proved our inductive case correctly.

Week 1 in CSC236

Since i took CSC165 in the summer, this is my first time to use SLOG.
After reading the SLOG handout, i kinda understand what is it now. Compared with the bulletin board, SLOG is a better platform to post one's opinions, with more details and informations.
It's an exciting thing that we can record what we've learned and what we've doubted. By viewing others' blog we can try to explore a different way to think the same problem. That's a good thing.

The materials in the first week were not too much and not that confusing. So far we took a review about the simple induction and strong induction by dealing with some mathematical statements. They seem quite familiar, but the problems are always tricky.
The proof of recursive program and program correctness might get harder in the future. For now, i will try my best to conquer any difficulties in the most basic part.