>>13265839>Why are you separating...Why shouldn't I? When I play a video game, I treat the real world and the video game world as different things. Within the context of the game, it makes sense to magic spells exist but that would be nonsensical in the real world.
>definition of set, stringsHere's an example using some axiom system
Axiom1: 0 is a set
Axiom2: If x is a set, {x} is a set
From these, I can write down the set {0} and {{0}} and so on. Given a string, you just need an algorithm to check whether it's a set and such algorithms already exist.
>different strings, same setThis is more or less a problem of language analogous. It doesn't need to be fixed because as long as mathematicians are sane enough, they would agree that the different definitions are equivalent. Or, you could go totalitarian and decree that only one language is valid but most people wouldn't like that.
