
@lunareclipse The paradox I prefer is: "Let R be the set of all sets that are not members of themselves. Is R a member of itself ?" 😁
I think it's Russell's paradox. 🤔
@Poslovitch @lunareclipse I tested something similar but more obscure; I used Coquand's paradox (really, De Bruijn's paradox) and only about half of the chat.lmsys.org bots can get it right.
For reference, my prompt was, "In mathematics, consider rooted trees: a root and zero or more branches, each branch its own tree. Let a tree be normal iff it is not among its own branches. Is there a tree R such that every normal tree is a branch of R and every branch of R is normal?"
If the bot didn't get it immediately, I sent, "Hint: is R normal?" which is also how I would prompt a human. This worked sometimes.
@lunareclipse it's weird cause that one isn't even a paradox, the answer is just "yes"
(the sign was just misquoting the actual paradox, which is "does the set of all sets which do not contain themselves contain itself")