alt Hacker News"A real number in which each decimal digit at position n is equal to the first digit of BB(n)."
Since you asserted that individual BB(n) numbers are computable, I think you will have no difficulty writing an algorithm that outputs that.
"A real number in which each decimal digit at position n is equal to the first digit of BB(n)."
Since you asserted that individual BB(n) numbers are computable, I think you will have no difficulty writing an algorithm that outputs that.
Such an algorithm would be computing the (uncomputable) function BB : Nat -> Nat, and not the computability of a given BB(n). Every fixed natural number is computable: just print out the number.
This is a subtlety of doing computability theory in classical foundations. It’s akin to how every concrete instance P(x) of a decision problem P is decidable: just use excluded middle to figure out if P(x) is true or false, and then use the Turing machine that immediately accepts or rejects regardless of input. This is very different from writing a machine that has to decide P(x) when given x as an input!