But such a program can't visit every real number in the interval, because there are uncountably many, but the program will only run for countably infinitely many steps.
If you get a nondeterministic computer, where every digit it splits into 10 identical computers that each picked one of the 10 options, then when you run that for countably infinite cycles you'll find that you have uncountably infinite computers and you have finally calculated every real number.
The cardinality of the real numbers is 2 to the power of the countable numbers.