Week 6: The Result of Exam is Out! + More Proofs(Floor, disprove, limits, etc.)

Today, we got the results of term test. I must say it was a shock, since the average was so high, which is about 81%. Disappointingly, I was below the average due to the marks lost on the second question as I mentioned in Week5 post. After reviewing the Lecture 4, I figured out a way to tackle this kind of question. Let's use the example taught in class:

1.understand the problem
  -translate the statement into English
"there is a real numberδ,for all real numberε, if every real number greater than δ, then its square must be greater than the all ε"
2.devising a plan
  -try to find a counter-example
  -if there is one then the statement is wrong
3.carrying out the plan
   -pick a wise number, in this case, we say x = 2δ
4.looking back
   -read the English sentence, see if it's translated correctly
   -submit the wise number in see if it really fails the statement to be true
   Since when ε= 5δ^2, x^2 is smaller than ε, we find counter-examples for all δ by picking x= 2δ. Thus, the statement is False.
 
 
As long as I'm understand where I did wrong, let's move on to the new class materials.

This week we are still digging the hole of proofs and getting deeper by introducing more types of proofs.

First, Prof Larry taught the definition of non-boolean functions, which is "functions return values are not True/False" . Then, he introduced the definition of floor:

Based on Timothy's slog, two Profs used the same examples of proofs to explain the definition of floor. 

Furthermore, Larry taught about disproving.The basic idea I summarized is that to disprove a statement is to prove its negation.

Last, we taught about limits.  

I always know that all we need to do is pick a wise δ, but how to do that? Today's lecture finally helped me by teaching technique "backward search".

One sentence Timothy posted confused me:

"Again, in order to find a good delta, d should be less than or equal to epsilon." So I commented under his post, waiting for his reply,:)