 In the first of these two formulations, Turing is stating that every number which is able to be calculated by an effective method (that is, “all numbers which would naturally be regarded as computable”) is included among the numbers whose decimal representations can be written out progressively by one or another Turing machine. In the second, Turing is saying that the operations of a Turing machine include all those that a human mathematician needs to use when calculating a number by means of an effective method.