Recursive real numbers
H. Gordon Rice · Proceedings of the American Mathematical Society · 1954
A basic step in applying a new concept such as recursive functions to analysis should be an investigation of its application to the number system. We present here some of the elementary properties of recursive real numbers, as defined below. A recursive real number may be described intuitively as one for which we can effectively generate as long a decimal expansion as we wish [5], or equivalently, to which we can effectively find as close a rational approximation as we wish. Accepting the thesis of Church [1, pp. 317-323], we interpret effectiveness (or the lack of it) as meaning the existence (or nonexistence) of certain recursive functions.