Is this true, that if we can describe any (real) number somehow, then it is computable?
For example, π is computable although it is irrational, i.e. endless decimal fraction. It was just a luck, that there are some simple periodic formulas to calcualte π. If it wasn’t than we were unable to calculate π ans it was non-computable.
If so, that we can’t provide any examples of non-computable numbers? Is that right?
The only thing that we can say is that these numbers are exist in many, but we can’t point to any of them. Right?
I haven’t thought this through, but it seems to me that if you let BB be the Busy Beaver function, then ∞∑i=12−BB(i)=2−1+2−6+2−21+2−107+ ... ≈0.515625476837158203125000000000006 should be a noncomputable real number, since if you were able to compute it with sufficient precision you would be able to solve the halting problem.