 In constructive analysis, a real number is an infinite (convergent) sequence of rational numbers generated by an effective rule, so that the constructive real line is essentially just a restriction of its classical counterpart. Brouwerian intuitionism takes a more liberal view of the matter, resulting in a considerable enrichment of the arithmetical continuum over the version offered by strict constructivism. As conceived by intuitionism, the arithmetical continuum admits as real numbers not only infinite sequences determined in advance by an effective rule for computing their terms, but also ones in whose generation free selection plays a part. The latter are called (free) choice sequences. Without loss of generality we may and shall assume that the entries in choice sequences are natural numbers.