Thanks for the reply, really enjoying the discussion. What I had in mind is a particular case I heard of, Chaitin's Omega, which can't even be approximated arbi

Thanks for the reply, really enjoying the discussion. What I had in mind is a particular case I heard of, Chaitin's Omega, which can't even be approximated arbitrarily by a fixed algorithm. But still that number seems useful to study it's properties as a number. Expanding further, that's an issue I've had with definitions of computability also. Certain problems like the halting problem are extremely interesting but their non-computability sort of turns them dead. Approximating them even to a finite degree and studying them profoundly seems very worthwhile, from a practical and theoretical standpoint.