Week 6

So last week we learned how to break down statements with universal and existential quantifiers and structure proofs for them. When there is a universal quantifier, we write 'Assume that *insert universal quantifier part here*' and when there is an existential quantifier, we try to assign a value to the variable, although sometimes we may have to think through the proof contents before we can go back and assign the value.

This week, we learnt more types of proof. We learned how to prove something false, first by negating the statement, and then proving that the negation is false. We also learned how to structure proofs by cases. An example we worked on in class was to prove that n^2 + n is even. The first step is to figure out all the possible cases. For the example I just mentioned, there are two cases: n is even , and n is odd. Then we have to prove the statement for each case.

Like I said in my blog post for last week, everything is pretty straightforward. Lectures have been quite dull and because we've just been working through specific proof examples in class. Everything has just blurred and mixed together in my head, which is why I wrote the above two paragraphs to summarize things so they can get filed away neatly in my brain rather than float around in a huge scattered mess.

I think proofs are fun in a way, because a lot of the time, it requires you to be creative and approach a proof from different angles in order to figure out a functional, clear way to show something, but it can also be quite annoying sometimes for the same reason.