My question is based on this answer:
Let $T$ be the Turing machine which looks for a proof of a contradiction in ZFC. If ZFC is consistent, then whether or not $T$ halts will be independent of ZFC. (Indeed, if not, then this would contradict Gödel's incompleteness theorem!) (Zhen Lin)
Given now this program that prints a number (print doesn't include a newline):
print "0." for i = 0 to infinity: halted = execute_i_steps_of_the_given_turing_machine_and_return_true_if_it_halted() if halted: print "1" else: print "0"
I think it should be computable, but I'm not sure if the definition of the number is even valid.
Maybe someone could help me here? Is the number computable?