CSC165 SLOG Week6

What’s something new I learned this week?

• non-boolean functions：A function whose return value is not True/False. For example, x > 5 is boolean, x + 5 and sinx are non-boolean.
• “floor of x” : the largest integer that ≤ x

         ⌊x⌋ is not a variable, it’s a function like f(x), and quantifiers are only applied to variables, so            you cannot apply a quantifier to ⌊x⌋

• Tips for proving non-boolean functions: 

             1. fully understand the definition of the function, since that’s all you have.           

             2. manipulate expressions into forms that are closer to those in the definition, 

                 since the definition is all you have and you will have to use it.

• prove something false or disprove something

          How to disprove a statement S ? Just prove ¬S is true.

• Tips for proving something false or disprove something: 

               1. first make sure to negate it correctly

               2. then prove the negated statement

               3. draw examples to obtain intuition

• proof about limits

for example:      

        

              Intuition:

              δ is how close x is to 2

              ε is how close x² is to 4

              if x gets really really close to 2, 

              then x² gets really really close to 4.

• Tips for proof about limits: 
  wise choices are often found by backward 
  search (like the choice of δ)

What’s something that frustrated and challenged me this week?

I think it should be the proof for the limits,  first so many Greek letters, and they all represent different meaning, and for proof , given any ε,  I should always make a wise choice of δ so that I can win, which means I should know what δ I should pick before I write the proof, which is kind of disturbed.

How confident do you feel about material covered this week?

I think I understood the most of the material, but I still need to practice because when I wrote proof for limits, it was getting kind of hard, and it took time to figure out which proper δ I should pick.

How does course material relate to other classes or interests?

Aha, the proof fot limits part reminded me of the limit definition I learned in MAT137 and I think the proof progress is much the same. except that now I understand more about why I write proof like that. 

How did your tutorial/test/assignment go this week?

Quite well I think, my TA is really heapful and gave me some tips for doing proof.