I've been reading a little bit into mathematical paradoxes lately, and I'm not sure what to make of Bertrand's paradox (regarding the extraordinary set R). I understand the proof, but does this paradox extend to other areas of thought (on that note, this question might belong in the philosophy section)? One example of an extraordinary set given in the text I was reading was the "idea" of a set that includes all ideas. Is this truly an extraordinary set? EDIT: I meant to title this "Bertrand's Paradox" but I hit enter instead of the apostrophe. Sorry for the typo, feel free to change it.