This week we learned the countability, and the content is a bit abstract and complicated : it requires some skills of math , which in particular include the ability to identify the 1-1 and onto functions. A typical example is X = {natural numbers} Y = {even natural numbers}, and we are required to prove |X| = |Y|. It seems impossible at the first sight, since I think Y should definitely contain less elements than X and is a subset of X. However,after the lecture, I realized that the infinity of the elements' amount of both sets lead to the equality of them. More exactly, every element of X has a unique corresponding element in Y , which implies X and Y have the same size, which is infinity.
And we also learned a little about the induction. In fact, I learned it in MAT137 last year, and found it is an effective and logical way of proof. And I feel kind of disappointed as it's not included in the final exam.
Anyway, the final is approaching. And I hope I can do my best to get a satisfying grade.:)
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