Week 4

Here we are going into our fifth week of class. At the end of this week we had our first assignment due which I feel pretty comfortable with as the questions on the assignment did not deviate from what we had covered in class so I felt prepared and capable while doing Assignment 1. We started off the week by learning how to express implications as conjunctions and dis-junctions which I felt was pretty intuitive. I also personally found it easier to identify conditions which would make a statement false so when it came to expressing implications as conjunctions and dis-junctions I would just negate the condition making a statement false which of course would give us the condition for a statement to be true. This was just a personal thing as for some of the implications I could not figure out all the possibilities for a statement to be true but I was able to identify what conditions made a statement false. The next topic we covered was transitivity which again seemed intuitive as it says if something1 implies something2 and something2 implies something3 then something1 has to imply something3 which is easy to picture and we can reason it out using some simple logic. We then proved transitivity by negating the implications which had a contradictions which meant that transitivity was always true. The challenging part of this week I found was the first mathematical example. I am still having trouble understanding the graph a little. From what I understand this statement says that for all d there exists a d such that if the distance between any x and 2 is less than d implies the distance between the line x^2 and 4 is less than e. Actually now that I write it out it is becoming easier to understand but it was still a challenging problem.

We were then introduced to how to structure proofs which I believe will be very helpful for this course and the other math related courses I am taking which require proofs too be written frequently. We were taught to find a chain between what we are given an what we want to prove.