Difficult: I have a few questions from reading it over. In the text, it says "The sentence x (is an element of) Z is commonly not written in the proof because it is stated in the result." When I went in to talk to the TA, he specifically said to ALWAYS define all of your variables before using them in your proof, even if they were defined in the result. Could you address this in class?
And I am also still struggling with getting started. If I sit down to a result, it's hard for me to determine where to start. Should I use trivial, vaccuous, direct, contrapositive, proof by parts, or a combination of all of these? I'm sure as we continue, the list will only get more and more complicated. What is a good place to start? (Perhaps only practice will tell)
Also, when you get to the end of the proof, do you have to say "This statement is true because I just proved it using contrapositive." Or, does your reader have to be smart enough to know that you just proved that using contrapositive?
Interesting: It's so great, because I realized the value of partitions! When you use the "proof by case" method, you have to prove it for the entire partition of the set. If you don't include all values in the set, (a pairwise disjoint) you may run into errors. I like how everything we're learning is stacking onto each other really great.
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