> But there are some so called "real" numbers that are impossible to calculate, even approximately, like Chaitin's constant https://en.m.wikipedia.org/wiki/
Just because you can create a definition, doesn't mean that definition names a thing. We can define "the set of all sets that do not contain themselves", but such a definition is nonsensical in that trying to apply it creates a contradiction. To me, the incomputability of Chaitin's constant seems very similar, except it's contradiction is buried inside the halting problem.
Just because you can create a definition, doesn't mean that definition names a thing. We can define "the set of all sets that do not contain themselves", but such a definition is nonsensical in that trying to apply it creates a contradiction. To me, the incomputability of Chaitin's constant seems very similar, except it's contradiction is buried inside the halting problem.