WEEK 6
What I Learnt
This week we continued on proofs,
including contrapositive, contradiction, proof about non-boolean functions,
proof about limits, and disprove.
One of my classmates, Eujin Choi, felt confused about chapter
4, because she was only comfortable of proofing in direct ways, rather than
indirect or other ways (http://comscislog.blogspot.ca/2014/10/slog-6.html). At
first, when I read the course notes before the lecture, I shared the same
problem with her. It was hard for me to tell when I should use the
direct way and when I should use other approach until professor used the
example to explain them.
Contrapositive
When the reverse direction in the problem is easier for us
to proof, we proof by using contrapositive. That is because contrapositive is
equivalent to the original statement, and inverse the antecedent and
consequence.
Contradiction
As for the contradiction, I think we should use it when the
antecedent is implicit and so general. For example, when Q is “There are
infinitely many even natural numbers”, we cannot find a certain P to imply Q.
Floor x
What is more, another confusion
for me at first was the non-boolean functions. Our professor used floor x as
the example. The definition was complicate and made no sense to me. Therefore,
the proof based on this definition I did not understand either.
However, when I
combined the graph of the function floor x together with the definition and the
proof, I suddenly understood the whole thing!
Inspiration
Through this week’s lecture, I realized
that we should apply flexibly what we learnt before and try varies kinds of
method to solve a problem.
没有评论:
发表评论