> But what would be an example of an uncomputable number? That’s a good question. Most obviously, we could be talking about numbers that encode the solution to the halting problem. It would lead to a paradox to have a computer program that allows us to decide, in the general case, whether a given computer program halts. So, if a procedure to approximate a particular real requires solving the halting problem, we can’t have that.
This doesn’t make sense to me. Given that there’s no generic way to compute halting, how would we make the leap to saying that there’s a specific number which represents the solution to that problem?
This doesn’t make sense to me. Given that there’s no generic way to compute halting, how would we make the leap to saying that there’s a specific number which represents the solution to that problem?