 The expressive power of real numbers may be used to generate a simple recipe to obtain the values of a Turing-uncomputable function. Consider that the digital expansion of a real number contains countably many digits. Hence, for any characteristic function (i.e., a function whose values are ‘0’ or ‘1’) defined over a countable domain, including all Turing-uncomputable such functions, there is a real number whose binary expansion encodes its values. This is because for all values of a characteristic function, the nth value of the function may be defined to be the nth digit of the binary expansion of a real number.