CSC165H1--WEEK6

  We got our tests back on this Tuesday. I can believe the average mark is so high, 83%! My mark, in comparison, is not good and I think I need to work harder from now on. I went through the test, the errors are basically from unclear understanding of the concept and stupid mistakes. For instance, I have a unclear understanding of the output of python and I can not distinguish the difference between false and counterexample. Therefore, I got all the determination of python right but some counterexamples wrong. I might ask my group member for help next time when I met them. Overall, I am not satisfied with this test result, there are a lot for me to improve such as doing assignment on my own instead of giving it to my group members, understanding the concepts and asking questions.
  The lecture of this week we talked about floor and its definition. The definition is pretty long and hard to remember. Because we did not have tutorial this week, I did not get a chance to do problems associated with proof methods. I can understand the proof process when my professor do the question step by step, however, when I try to do questions on my own, I found it is so hard to start the proving process. This the actually the biggest problem I usually face when I did proof questions, I did not where to start and it is hard to find a link between hypothesis and conclusion.
  For instance, the first proof question on floor the professor proved the contradiction with definition #3 of floor to get the conclusion. When I first looked at the example, I had no idea of what to do. However, following the steps my professor took, first we need to compare the given condition with definition of floor, trying to find similarity and difference. Then we need to do a scratch work which can lead us to the result (this is the most difficult one!). We move minus 1 to the left side and this becomes plus 1 and this corresponds to definition #3. Then we let X belongs to Z and change the original element in the definition, thus we can disprove the failure of its negation.
  About the concept of proof, I think I need to do more problems and conclude some usual proving method, thus I can be more adept in solving questions.