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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.

51 votes
9 answers
3k views

Examples of theorems where numerical bounds on $\pi$ played a role

This is a whimsical question, motivated purely by curiosity rather than for any application. We are all familiar with countless mathematical results which use Archimedes' constant $\pi$ either in thei …
Terry Tao's user avatar
  • 114k
63 votes
7 answers
4k views

What well known results with countability assumptions can be naturally extended to uncountab...

In many of the common categories of spaces (or algebras) in mathematics, one often restricts attention to those spaces or algebras which are "countable" or "countably generated" in some sense. For in …