  In applying his machine concept to the Entscheidungsproblem, Turing took the step of defining computable numbers. These are those real numbers, considered as infinite decimals, say, which it is possible for a Turing machine, starting with an empty tape, to print out. For example, the Turing machine which simply prints the digit 1 and moves to the right, then repeats that action for ever, can thereby compute the number .1111111… A more complicated Turing machine can compute the infinite decimal expansion of π.