This section 10.2 started off fine as I understood the definitions of denumerable, countable, and countably infinite. Superficially, uncountable means not countable. So that means not finite or not denumerable. But denumerable is infinite. Then it said that an uncountable set is necessarily infinite. I'm not sure what the difference is between a denumerable infinite set and a necessarily infinite set. Even after the proofs, which were very intricate and difficult for me to follow, did not clarify this for me. I must say that this section was the most difficult of all I've read. The diagrams and tables were more confusing then helpful, unfortunately.
I have always been interested in the concept of infinity, so I'm interested to learn more about this and actually understand it. I look forward to class tomorrow to gain a better understanding. To be honest, I was a bit discouraged that I understood so little in this section. I feel that understanding this will be of importance as we begin the third of three sections in which this class material was divided. Usually in class, the proofs and examples are more clear, so hopefully that is the case, because the proofs in the book were hard to follow for me.
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