Since test 1 is done with it seems that the course is turning the corner and we have now started working with proofs. I find proofs very interesting especial given the new found knowledge of the different techniques in approaching logical statements. I feel that in the past when dealing with proofs unless I had a clear path to follow I could stare at a the problem without knowing where to begin. 165 has given me a new perspective on problem solving and I can feel how my mental tool box is slowly growing and enabling me to structure proofs on my own without knowing where the result will lead me to.
In spite of all this rambling, I found the last assignment a little bit tricky. I generally try to do to get started on the assignment relatively close to the date we get them and go over them to correct any mistakes closer to the due date. When going back to review my work this time, after a week of going over proofs I discovered that my approach was all wrong and consequently so were all my answers. For some reason while trying to prove
∀ n ∈ N, U(n) => U(n2)
Where U(n) is defined as,
∀ n ∈ N, U(N) ⇔ ∃K ∈ N, N = 5K + 1
I'm not sure if it was the way the definition of U(n) was given but something about the ∀ n ∈ N, coming before the U(n) itself made me think that all I had to do was prove existence. When going back to review my work (at around 9:15pm the day it was due) I realized my mistake and franticly tried to figure out the right way to fix it. I hope it when't well and I'm pretty sure I got it right in the end.
The current topic that is blowing my mind is proving the obvious, who would have imagined.....
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