More proofs!

This week’s lecture went more into depth proofs, it was pretty interesting. I found how proving a statement true using the reverse direction interesting. Instead of proving an implication straight on, you can prove the negation and in some cases it will be easier. Also, I learned what the floor of x means. It means the largest integer that is smaller or equal or x. For example, if x was 5.5 then the floor of x would be x. I was also amazed about how a statement is deemed false. To prove a statement false, you prove the negation is true. This also amazed Kevin, which he wrote on his blog. Additionally, I learned how to prove by cases. To prove that n²+n is even, you would have two cases where n is even and where n is odd. Proving an existential true was fairly intuitive. All that has to be done is to finding a single example. Another thing I found interesting was that proofs can consists of different structures, there are different ways to prove a single thing.

This week I did the folding problem solving problem. First, I read over the problem and made sure I understood it. The problem asks to find a method of predicting the number of up and down creases a paper has when folded a number of times. Secondly, I came up with a plan to solve the problem. My plan was to fold the paper one time and write down the number of up and down creases and repeating until I have an appropriate sample size. Then using the data to find two functions that finds the number of up creases and down creases. After getting a bit stuck I looked at the hints and one of them states that one pattern is somehow contained in the other. After that I was thinking about the relation and it came to me. When the paper is folded the initial folds remain in the new pattern.