Week 12

   It is the final week of the semester. The lecture was short. We learned about countability and get a preliminary understanding of induction. Comparing to the computability stuff, countability is easy to understand and straight forward., though the idea that the sizes of the set of natural numbers and the set of even natural numbers are the same was a little queer in the beginning. However, on the other hand, when we developed a '1 to 1' and 'onto' well-defined function that related to the 2 sets of numbers, it is easy to understand that each number in natural number set is corresponding to a number in  even natural number set, which means that the 2 sets have the same size.

   Finally, we went over the test review. I believe that I can solve logic problems and proving big-O problems with ease, but the algorithm and computability part is still challenging for me. I must go over the course note carefully and perhaps go to the office for help.