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Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.

48 votes

Most harmful heuristic?

"A continuous function is one you can draw without raising the pencil" This has terrible disadvantages when generalizing functions defined on a real interval to non connected sets, non compact sets a …
2 votes

The best text to study both incompleteness theorems

If you can read Spanish, an excellent text which both formally proves and philosophically treats both Incompleteness theorems is Carlos Ivorra Castillo's "Lógica y teoría de conjuntos" which is freely …
2 votes

Alternative undergraduate analysis texts

There's Yeh's Theory of Measure and Integration which covers almost everything Folland does, but in a (really) verbose fashion.
2 votes

Undergraduate Probability Topics

I think you might find this MO topic interesting: Probabilistic Proofs of Analytic Facts , especially Bernstein's proof of the Weierstrass theorem.