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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.

54 votes
4 answers
3k views

When has the Borel-Cantelli heuristic been wrong?

The Borel-Cantelli lemma is very frequently used to give a heuristic for whether or not certain statements in number theory are true. For example, it gives some evidence that there are finitely many …
Eric Naslund's user avatar
  • 11.4k
7 votes
8 answers
4k views

Mathematical Advice for Interested Highschool Students

This may not be a research level math question, but I believe it is still relevant to Math Overflow. What general resources exist for students in highschool who are very interested in Mathematic …
4 votes
10 answers
1k views

Proving theorems by using functions with fixed points.

I am trying to get a better feel for solving questions where creating a function with a unique fixed point is the crux of the proof. In particular, the Inverse Function Theorem as well as the existen …