Week 6

     This week we learned about cases, quantifiers, and limits.
     First, we talked about non-boolean and introduced the notation to the floor function. The floor function always rounds down a decimal number to its integer. An important thing I took note of was that the floor of a number is not a variable, it is a function. This means that a quantifier cannot be applied to it since quantifiers are only used on variables. Next, we tried proving a statement with the application of this new knowledge about the floor function. We were able to use its definition as an aid to construct the actual proof. I found learning about the definition of floor of x very helpful since using the definition of a function to construct a proof is something that we will constantly use in the future.
     We then learned how to disprove a statement effectively. In order to disprove a statement, you need to prove its negation. It is important to negate the statement correctly to facilitate the 'disproof'. We then did a couple of examples on disproving statements.
     Next, we moved on to proofs about limits, which seemed like an intimidating concept at first. We learned about the use of the greek letters delta and epsilon. Professor Zhang taught us how to manipulate these letters in our favor, and that the best choices of where one might want to take the proof are often encountered when working backwards in the proof. Also, I personally learned that proofs about limits are not necessarily as intimidating as I thought they were.
    I found the content of this lecture easier to grasp than that of the previous lectures. I believe I still need to do more practice with proofs so I plan to go to Prof. Zhang's office hours and doing practice problems from the course website on my own.