CSC165 sLOG WEEK6

  Last week we continue to learn something about proof. I found out that proof is such a big topic which needs a lot of practices to manage it. This week I read the course notes and learn a lot from it.Here are some definations: a lemma is a small result needed to prove something we really care about. A theorem is the main result that we care about (at the moment). A corollary is an easy (or said to be easy) consequence of another result. A conjecture is something suspected to be true, but not yet proven. An axiom is something we assert to be true, without justi cation ( usually because it is "self-evident.") For direct proof of universally-quantified implication, When we assume that x is in D, we are in the "world" where x is a generic element of D. To prove the converse of a statement, you set up the proof of the contrapositive of the converse. I found it is a hard part for example of proving a statement about a sequence. I go through the progress several times and finally figured it out. For multiple quantifiers, implications, and conjunctions, I found that it is not difficult if you have a clear mind and do it step by step.