Sixth Lecture - October 14th, 2014

After receiving the grades of our first test today, I became more confident in myself for this course. This week we learned about proofs with non-boolean functions and limits. Non-boolean functions are those that do not return True/False, for example, x^2>x or |x|, or most importantly, the floor of x. In short, the floor of x takes the lower integer value of x when it is a decimal. For example, to floor x when x is 3.5, it would result in 3. And floor 3.99999 is also 3. But to floor 4, it is 4. You cannot apply a quantifier to the floor of x as it is a function. I'm going to write a simple proof involving the floor of x so I can remember this down the road.

Enough about floors. I also learned about proving limits. I guess something to always remember when proving or disproving limits is to keep your mind open. For example, to prove something True, you can sometimes just disprove the contradiction, especially in cases where the contradiction uses an existential quantifiers. And, always make smart decisions when setting a variable as a value to prove True or False.