1. So I'm not sure what my problem is regarding this proof (0,1) being uncountable. I just don't understand how b1 is not in the set (0,1)...and if it's in the set (0,1), shouldn't it be mapped to? Maybe I just don't understand the way that we defined the function. From the way I am looking at it, there are only 9 elements in the function...why? I don't understand. I wish I could come to office hours tomorrow to discuss this, but I cannot. Perhaps I will come on Monday.
2. On the bright side, the proofs after that all made sense, because they are largely the same proofs as section 10.2, only some are contradiction-style. I can handle that. Once I wrapped my head around infinite sets (as much as you CAN wrap your head around them) all the proofs about them became essentially logical. If you have an infinite set, then it will always be infinite, even if you subtract elements out of it.
What has been killing me is remembering that there are theorems for these proofs, so I don't have to write everything out! I did a problem for this last assignment and it took quite a lot of space. When I checked my answer in the back, there was a theorem. Oh well, at least I know how to prove it. Hopefully.
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