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As a sidetrack in this question it came up that it is important to have students read texts (in particular proofs) critically. As examples it is nice to have correct proofs at hand (presumably in the textbook/lecture notes), but also a variety of others:

Proofs that are just plain wrong, like the nice "proof by induction" that all integers are larger than 10, just by omitting the base case

Proofs that are wrong, but the result is actually right (missing cases, hidden assumptions, ...)

Proofs that are right, but could be tightened up/simplified

This is in part motivated by the classic by Kernighan and Plaugher "The Elements of Programming Style", where the authors show bad program snippets culled from textbooks and other published sources, dissect them and show how they should be written right, and why. I'm aware of Edward Barbeau's "Mathematical Fallacies, Flaws, and Flimflam" (MAA, 2000), but that targets more bad computation than bad proving.

It it helps narrowing down, I'm mostly interested in combinatorics and discrete math. But approachable proofs, accessible to the relative layman (think students with Calculus I under their belt, often just taking Calculus II) in any area are quite welcome.