Slog for Week 12

Since we did not have lecture last week because of the reading week, this week's lecture and tutorial was the last one in this semester. For the last lecture, I learned about countability and Induction. But the professor just skimmed through induction part, which means he did not explain much details for induction, therefore I do not have much ideas about induction I learned.

For countability, when the professor Larry first asked us about what do we think the size of all even numbers and all natural numbers, of course, I thought the size of all natural numbers would be greater than the size of all even numbers, but actually the result was the same. Of course, this made me surprised, since it is obvious that the size of even number is only half of size of all natural numbers. However, soon I understood why those two are same: because of satisfaction of three characteristics. Since f is a well-defined function, '1-1', and 'onto', the two function is said to be same, therefore the size of natural numbers and even numbers can be said as the same.

But the part of combination of computability and countability, I hardly get the ideas what is going on there, so I think I need to read the lecture slide and course notes over and over until I understand it. Also the induction, even though I totally understood the proof of domino falls, I do not know how it can be used in the proof of some questions like a question in our assignment. But I hope this kind of problems I may see on the next semester in CSC240.

This was what I learned in this week, and all I need to do now is reviewing the whole chapters, especially what I learned in the beginning of this course(since I forgot many of them), and then practicing them by doing past exams in the University of Toronto website.