CSC165H1 SLOG11 BY MINGYU LIU

Mingyu Liu @ CSC165H1 SLOG11

This is the last class of CSC165 and in this last SLOG I will continue to talk about the slide of professor Zhang. There are actually four parts in this week’s class which are composed by the tips of assignment 3, countability, induction and the review for final exam.

Tips for Assignment3:

In assignment 3, I think it is the most difficult assignment I did in this semester. Fortunately, Professor Larry gives us some tips in order to solve the questions within the assignment 3. In question one of assignment 3

in this question, we are basically want to prove or disapprove that if ∣X-Y∣>d, then ∣X+Y∣> e. When we look at ∣X-Y∣, ∣Y-X∣is equal to ∣X-Y∣; therefore, ∣X-Y∣< ∣X+Y∣.

For question 3 and 4, the definition of limit is needed in these two questions:

This means that no matter how larger c is, f(n) can be larger than c.

No matter how small c is , f(n) can be smaller than c.

When our group solves question 3 and 4, these two tips provide fairly important message when solving the problems.

Countability

Firstly, professor asks us to compare the size of two sets

In order to compare their size, we can compare the length of these two groups which means that the sizes of the two are the same.

How about compare ‘natural number’ list and ‘even natural number list’? The answer is not only confusing but also interesting which is that the sizes of these two are identical. Professor provides us a real-life example. Considering a coin which is shown below.

We know each coin has one and only one tail; therefore, set of coins and set of coin tails are of the same size.

This means that if there is a mapping from X to Y like the coin problems, then we have the absolute value of X is equals to the absolute value of Y.

There is another important element which is called countable within the countability. This means that when we count numbers, we do 0, 1, 2, 3, 4, 5, and 6… which are all enumerating natural numbers; therefore, the set of N is countable and, any set A that satisfies the absolute number of A less or equal to the absolute value of N is countable. For example, the set of integers is countable; the set of rational numbers is countable.

In conclusion, in this week’s lecture, we only touch the surface of countablilty, but it is an very interesting material to learn. After this blog which is the last blog of CSC165, I will continue work on the review of CSC165.

eleventh slog

Mingyu Liu