Reflection on Assignment 2

This past week has been a complete mess in terms of CSC165.  Assignment 2 showed itself to be a lot harder than assignment 1.  However, it did shine some light as to why the class has been structured the way it is.

As i mentioned in my previous blogs, my initial observation of this class was that it was filled with memorization.  Memorization such as how to negate a statement, structure of proof, and what the difference between universal and existential is.  However, assignment 2 showed me the importance of all the above-mentioned ideas.  I learned that if the basics were not emphasized enough, it would have been extremely hard to even start the proofs.  By being familiar with how to negate a certain statement, you know how to start to disprove a certain statement.  More importantly, having a strong understanding between the difference of existential and universal is crucial in many of the assignment questions (especially those with multiple quantifiers).  It still amazes me how just a single switch in quantifier can make a statement mean completely different (the difference between 1.2 and 1.3 - with one false and one true, respectively).  In this sense, all the materials we've learned previously have been incorporated into one assignment.

As I was doing the assignment, there was an issue that was quite vexing for me.  I learned that the definition of floor of some number is the greatest integer that is small or equal to that number from previous classes.  But the ONLY definition of floor given to us for the assignment was the logical definition.  I found it really difficult to translate the symbolic definition into the definition as I know it.  This made me learn that that is part of the reason why proofs are so important.  Having a general intuition of what floor does helps with knowing whether a statement is true or false.  But to prove such a statement requires a detailed understanding of the definition and manipulation of it.

After this assignment, I noticed that there is still much for me to learn about proving.  I've gotten the basic structure down, but the hardest part is still the "getting the light bulb" part.  I hope that through constant practice, writing proof will get easier and easier.