CSC165 Week7

This week we learned more proofs. They involves more rules and many other concepts. The proofs covered in this week are more and more detailed.

For most of mathematic proofs, the key thing is to understand the definition we are given.Then try to derive something that has the same form of the definition. For example

In the above example, we have 7(7i^2+2i)+1. We have to see that is the same form of 7k+1, just for k=7i^2+2i. The idea is the same as picking delta wisely for the last week's proof.

CSC165 Week 6

It looks like most people did very well in the midterm test. Cheers!

This week we learned more about the proofs. Proof of some mathematical things are not that direct, especially for some limits. For those kind of proofs, we need to understand what does limit mean in mathematic. Then, in order to prove it, it is necessary for us to pick delta wisely. 

Disprove something is the same as prove the negation of that. That is quite straight forward for me.

Since we only had a two hours lecture and no tutorial this week..I guess thats all for this week.

CSC165 Week5

Took 2 hours lecture after the test is so tired but start learning proof is exciting. Especially the one given in class showed that 'it is not bad even if you left everything blank and others did well'. You are much better than this if wrote something in the test.

There are several ways of thinking about proof. I believe that in most cases it is not that easy to show something directly, therefore we have to come up with some alternative ways, such us using contrapositive, contradiction. For example, to prove P=>Q is the same as prove ~Q=>~P, because we know that the contrapositive is the same as the original statement in logic. Here is the proof of that
(~Q=>~P)=>(Q or ~P)=>(P=>Q)

Another way of proving an implication statement is by using contradiction. To use this we need to assume the negation of the statement is right, then derive some results based on these assumptions, if some of them contradict each other, it means our assumptions are wrong which is the negation of the original statement. Therefore the original statement is true.

The last part of the lecture was about proof for existence. It seems easy for me because once we can show one example then we can finish the proof.

Hope everyone get a great mark for the test.

CSC165 Week 4

After 4 weeks learning about the logic I found that English is could be so ambiguous. Especially when several antecedents come together with condition, conjunction, disjunction, etc. Even some simple statement can be ambiguous. For example, A and B both guarantees that C is true. I will say if A true and B true then C is true. But some people may think A guarantees C is true individually and B guarantees C is true individually, too.

For week four, we learned about Bi-implication, Transitivity, Mixed Quantifiers and the Proofs.

The Bi-implication means the antecedent is sufficient and necessary for the consequent and vice versa. Say, if P => Q then Q => P and P <=> Q.

When two quantifiers show in one statement, then the order of them will affect the meaning of that statement. The order is a critical problem when we are expressing some mathematical theorems. Sometimes ' for all y, exists an x' is totally different from 'exists an x, for all y'. Therefore we have to pay attention to that when we use mixed quantifiers.

The proofs can give us a better understand about the logic, how thing go at each step. One interesting thing is when we try to proof some thing, we can start it from the conclusion to the assumption first, then write the answer start from assumption. Because sometime, the specific variation of assumption is hard to see.