Proofs, proofs, and more proofs. Assignment 2 and Tuesday's tutorial have all but exhausted me and my doubts on how to write a proof. The most difficult obstacle to overcome was making a connection between assumptions and antecedent (if there is one) and rest of statement. Memorable connections such as manipulating polynomial expressions such as the question in this week's tutorial (put question here) to make the modified antecedent appear similar to the consequent, then using the nature of natural numbers to prove a variable in the consequent satisfies the domain assumption. Another approach that gave me a run for my money was 1.2 of assignment 2. My proof of the give statement (put statement here) was done not by manipulating the antecedent, but parts of the assumption (put assumptions involving natural number z and floor x <=  x) to produce a relationship between an inequality between an expression containing the consequent, and the antecedent (put inequality here).

The Marks Are Here!

After doing better than expected on assignment1 and test1, this week has been rather cheerful. The introduction to sorting was a refreshing breeze of confusion, leaving me going though this week's annotated slides to sort my thoughts. Dialing the clock back to Monday, thee proofs in the slides made me realize I had no idea how to proceed after setting up the quantifiers and antecedent. I did find comfort seeing proving something false was not a stretch when put as proving the negation of the statement true.

After a restless Monday night tackling Tuesday's tutorial proof questions, I was welcomed by a nauseating Tuesday morning, as sickening as the subway ride proved to be, gifted me with a understanding of how to approach the main body of proofs. As we took up the tutorial questions, it occurred to me, what in hindsight was evident in the lectures slides, was the manipulation of the antecedent into looking like parts or the whole of the consequent and use given assumptions to make the homestretch to reach the consequent.

As I relax in front of my screen snacking on pistachios to compliment a moderated amount of my favorite beer, a creeping unease manage to convince me to go over the annotated slides to confirm I in fact understand the construction of every proof.

Hello World

    This marks two weeks since the beginning of a new and exciting school year. The first week of lectures was smooth sailing, but by Wednesday of the second week, I began to have a harder time keeping up with the material. With that said, the material also became interesting with the introduction of implications. Though the converse of an implication was easy to understand, the contrapositive warranted a puzzled double-take and seemed hard to remember. Upon further examination, I discovered an uncanny resemblance between implication and contrapositive to multiplying both sides of an inequality by -1. However, I doubt the validity of the aforementioned comparison. 

    During the Wednesday lecture on the second week, I was pleasantly surprised (tho in hindsight I should not have) when came across the phrase "Even true implications doesn't give you causality", because I have frequented examples of this statement in just about every topic of economics (a major and major interest of mine) I have come across. An economic example that immediately came to mind was the claim "Every minimum wage increase was followed by an increase in wages" though a true implication, was at times used to arrive at the erroneous conclusion that the raise in the minimum wages caused the increase in wages. Finally, the question that bugged me for a good part of the past week was the quiz question for the first tutorial. What my confusion boils down to is, do we have to indicate a true consequent when drawing a Venn diagram for a true implication? I plan to find an answer to this question from a classmate, my TA, or professor Heap midst my self-inflicted havoc in upcoming week.

Image Source: http://ipencilmovie.org/
from "I, Pencil", a film from the Competitive Enterprise Institute, adapted from the 1958 essay by Leonard E. Read.