TITLE: Is this number computable?
QUESTION [6 upvotes]: My question is based on this answer:
https://math.stackexchange.com/a/458768/292477

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?
Thank you

REPLY [14 votes]: Of course, this value is either $0$ or $2^{-n}$ for some $n$, and all of those numbers are computable, so this number is computable. (Assuming the result is treated as binary.)
If base $10$, then this value is either $0$ or $9^{-1}\cdot 10^{-n}$ for some $n$, and any rational number is computable.