SLOG 5 October 20th

Last week I only had 2 lectures of CSC165 because of Thanksgiving, and the focus of the two lectures were on the structure of proofs.  Professor Heap repeated the the structure of proofs on a few different examples, such as proofs involving floors and limits.  I learned that the beginning of each proof always starts by defining the main variable as part of the set of real, integers, natural, and etc.  The second step is to assume the antecedent, which is pretty easy to identify when it comes to limit proofs because of the implication.  However when doing proofs about the floor of a variable, it is also crucial to put its definition in the proof.  Essentially, I learned that I should put all of the conditions that I know is true as an assumption before I begin the thinking part of the proof.  After finishing the assumptions, the next step is to somehow arrive at the consequent from the antecedent.  The difficulty of this step varies greatly.  For example, with a limit proof, it was quite easy for me to complete the thinking part as I have done limit proofs in math.  However with floor proofs, I often get stuck about how I should proceed.  However with more practice, I believe that I will be able to arrive at the fundamental insight that will allow me to complete the proof quicker in the future.  After arriving at the consequent, the last section of the proof is to finish the assertions made earlier.  The middle section of the proof will have proved that because of the assumptions made, the consequent that we arrived at is true, so the last section is basically re writing the first section.