Section 9

1. The premise that we are working in an "imaginary world" was a bit strange to wrap my head around. I understand it well enough when working on basic even/odd proofs, because you are just assuming the statement is false and then working to find a contradiction, but with the more complicated ones, such as the rational number proof in the textbook, it was a bit difficult because I don't know what I am looking for in a contradiction. The lowest terms contradiction seemed a bit contrived and I'm not sure if I would be able to locate something like that in a different example.

2. It's nice to have another way of writing proofs because I can think of examples that would be very difficult if not impossible to prove by using only direct and contrapositive proofs. Even though this method is a bit less concrete and difficult to understand, I can see how it would be useful in proving more difficult statements.

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