Proof Structures

I have found that using proof structures to help prove or disprove statements is very helpful.
I found that using indentations after every universal term to help understand what needs to be truly focused on in the end makes it visually easier to follow. It also make sense to not indent existential variables which have to have specific values selected as part of proof or disproof.I find it visually helpful, to see how far we are looking into a given condition.


< condition >
assume x = {set of numbers}  # x is generic
        assume y = {set of numbers}  # y is generic
          .
          .
          .
Therefore < condition >

(for universal quantifiers)


< condition >
Let x = {set of numbers}  # x is a certain number
Let y = {set of numbers}  # y is a certain number
          .
          .
          .
Therefore < condition >

(for existential quantifiers)

I Have Come Back

It has been over two months since I made an entry, I now have the time to share to the public some of the things that I have experienced in CSC165H1 since my last entry. I will talk about it above.

I have found the difference of implication results to be slightly difficult to get used to at first because they are different from conjunctions and disjunctions. However, once the pattern was memorized it became much easier to deal with, to compute.

Before we dealt with Venn Diagrams in the tutorial this day, I still did not have a full understanding of how to read them properly, and how to use the symbols that come along with them appropriately. I found the tutorial helped me to understand all of them far better. Also the quiz at the end provided me the opportunity to read a word problem carefully, to help establish a good habit of dealing with any form of work with patience. It was all beneficial. I look forward to the session next week.

First Reflection

In the past I have always found myself to not fully understand word sentences to the full extent, often because I read them too fast and did not bother to check if I fully understood or not immediately after. With this area, I have been striving in this course from the beginning to read word problems with patience, and as a result I have been able to understand most of them fully. Impatience often leads to frustration, causing a person to lose sight of everything, so it was clear how I should approach these concepts from the start: slowly and patiently. I understand that providing one counter-example alone can automatically falsify any sort of claim (universal, existential, etc). With Venn Diagrams, I am recalling what I learned in high school and intend to continue to improve my understanding of them through the course lectures and tutorials provided. I also intend to fully understand how to use all the symbols and notations that will be taught throughout this course, and patience will play a key role again in the success of that.