The most difficult part of the material was looking up Theorem 9.11 and Corollary 9.8 to review those theorems, but after reviewing them the proof for theorem 10.1 made a lot more sense, which it did not at first.
The most interesting part of the material was the theorem that if there exists a bijective function from A to B and A R B, then R is an equivalence relation. This may seem trivial for finite sets, but when applied to infinite sets, this is really useful. This also is because infinite sets are said to be able to have the same cardinality.
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