CSC165 Slog week7

This week, the professor lead us to study several proof cases. Firstly, we learnt proof about limits. That example make me very confused.From an existential quantification, I am not sure how to pick a number which satisfied the requirement from the question. Then the professor told us to calculate y^2 - pie^2 first and then find out the scope of that number we should pick. Therefore I finally figured it out under professor's guidance. Afterwards we learnt how to prove by cases.The question is: for every natural number n, n^2 + n is even. A natural approach is to factor it as n(n+1), and then consider the case where n is odd, then the case where n is even. Because both cases are proved to be true, the statement is true. Moreover, we learnt some new things like allowed inference and sorting strategies. For inference, I knows how to make conclusions by studying conjunction elimination, existential instantiation... For sorting strategies, I found that the steps required for insertion sort and selection sort on lists of size n were no more than some quadratic functions of n. They are all in O(n^2). When counting costs, we learnt that we should always consider the worst case. To conclude, the professor gave us several examples of counting steps.