Maybe I just haven't spent enough time with decimal expansions yet, but there are two proofs given in the text that I'm not sure where and how they arrive at their contradictions. One is 10.8 and the other is 10.12. The first is the set of real numbers that is uncountable. I get lost somewhere in the defining of another decimal expansion that helps us reach the contradiction. And then with 10.12, it seems like in 10.11 they state the exact opposite.
The idea of decimal expansions seem neat to me. There was one proof on my homework I did one time where the TA said I should have taken the decimal expansion of the number to prove it was irrational/rational and so ever since I've been excited to learn how.
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