 Thus, for the intuitionist, a real number \(\bx = (x_1 ,x_2,\ldots)\)—essentially, a Cauchy sequence of rational numbers—need not be given by a rule: its terms \(x_1 ,x_2,\ldots\), are simply rational numbers, successively constructed, subject only to some kind of Cauchy restriction such as the following one used by Bishop [1967]: