Week 6

Slog Week 6 

In this week’s lecture, we learned about prove again. The prof introduced us the concept of floor of X. The floor of x means the largest integer that <= x. And the floor of x is not a variable; it is a function. After several steps of proving, we got the definition of floor of x: 

y is an integer

y is less than or equal to x

among all the integers that are <=x, y is the largest one,

The prof gave us a question: we need to prove for all x belongs to R, the floor of x is greater than (x-1). It is really hard to start the prove. But after the prof told us to look about what we already knew (the definition), we understand how to prove this statement.

Then we learned about how to disprove a statement. It sounds really tricky and confused at first. However, after using the idea of prove the contradiction of the statement, I felt confident about how to write the disprove.

Week 5

Week 5

In this week’s lecture, I learned about how to write a proof, such as how to prove n^2 is even ==> n is even. It is hard to think about how to prove P==>Q, but it is easy to find out how to prove the contrapositive of the P==>Q. And the prove about the prime number is also really confused.

After the tutorial, I think I could do better in writing a prove. The tutor told us how to write an outline of prove of P ==>Q:

Assume 

   Assume

       Then

       Then

       Then

   Then

Then

The ‘assume’ part is always the ‘P’, and  last ‘Then’ part is always ‘P ==> Q’.

After doing 3 practices, I felt confident about writing a prove outline. But it is still hard for me to write a prove, since I always get stuck in the middle part of the prove. But I will always thinking about using contradiction when writing a prove.

I am looking forward of the next lecture and I hope I could do better in writing about prove.

10/10/14

Slog week4

This week I learned bi-implication, transitivity and mixed quantifiers. I feel the review part is the most important part for me. I find it is really easy to solve equation by using P => Q is equivalent to ¬ P ∨ Q, and ¬ (P => Q) is equivalent to P ∧ ¬Q. 

In class we did some practices of bi-implication, such as translate a given implication into the conjunction of two disjunctions. I felt hard at beginning, but after using the distributive law and De Morgan’s law. I think doing the practice in class helped me understand the concepts better.

The next lecture is about transitivity and the mixed quantifiers. 

Then we learned about how to write a proof and did several practices about writing proof.

I think the most confused thing of this lecture is using the laws to write equivalent. However after doing all the tutorial questions I got a more clearly understand of using the function.