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I've had some trouble in the past with a few topics such as infinite sets, combinatorics (counting in 2 ways particularly), and bijectivity. Is there any general advice you have to be able to think about writing proofs involving these topics clearly and efficiently? Even if I do practice problems, I still seem to get stuck on them unless I've seen a proof before using a method exactly like the one required.

Also, the same question for quickly thinking of examples/counterexamples of bijective, using infinite sets, etc functions.

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