WOAH!!! Crazy proofs are happening. See theorem 28.4. That's pretty epic. Though I wonder how we can conclude that the proofs must have the same size, considering the table only portrayed a subset of each set. How do we know that one set doesn't "run out" of elements to pair with the other set?
I was going to ask you if it is an adequate proof of bijection to simply find an inverse function between the same elements as the function. Then I forgot. Then I remembered, but your office hours were super full. I'm hoping this will remind me to ask you when I see you tomorrow.
I would like to settle a debate I was having with a classmate who I will leave unnamed. Take an infinite set and divide it into two subsets such that each subset is mutually exclusive and that between the two of them you cover every element in the set. Can one of these subsets be finite, or do they both have to be infinite sets?
This is super exciting material. I am eager to start the homework.
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