Section 11

The hardest part for me to understand was the proof for proposition 11.7. I don't quite understand how exactly that proved the statement, and it was a bit confusing because it wasn't necessary to know which case was true. In the other proofs we have done with cases, you have to know that each case could happen, and then prove that no matter what, each case would yield the same result.

Proofs by examples and counterexamples makes more sense to me because it seems more intuitive to just give an example to show if something works or doesn't work, rather than just use completely arbitrary numbers and variables. With these kinds of proofs all it requires is looking at the statement and figuring out if it "looks" right in a sense. It's more logic based, rather than computational.

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