As the week wrapped up and we move onto Reading Week, I am quite satisfied with how I did on the term test. As always after I write a test, I usually think pessimistically about the results to come. In a weird and convoluted way, having the mindset that I would fail usually gives me more motivation to study harder. In honest truth, I wasn't so confident while writing my answers down. In particular, there were uncertainties as to whether my explanations for question 1(b) was sufficient. Now that results are in, my lengthy but correct answers could have been shorten by referring to it`s negation instead of just listing all the examples or counter-examples. This could have saved me quite a bit of time that could have been invested into another question. But what`s done is done. So next time I should go in with a calm mind and be more observant with what the tools and knowledge I could use.
As for this week's lectures, we discussed more about proving different types of statements. Reassured by my TA, it's nice that we receive a large portion (40% was it?) of our marks from just writing the proof structure. For many of the proof structures there's a technique as to how you write it.
If it is existential quantification such as ∃ x ∈ D, then we write "Let x = ___. Then x ∈ D".
If it is a universal quantification such as ∀x∈D, we write "Assume x in D".
I also noticed that most of the actual body of the proofs contain a lot of manipulation of mathematical expression and some background knowledge of their definitions.
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