A quotation from Russell concedes that the immensity of real numbers implied by the usual account of the continuum cannot mainly consist of ‘those whose digits procede according to some rule’. Russell concludes that the main body of real numbers ‘must be’ of the ‘lawless’ variety. The author scrutinises these so-called ‘lawless decimals’ and concludes that they are mythical. It follows that the totality of well-defined real numbers cannot be more than a countable whole. It is however clearly uncountable. An (...) explanation is offered using the ‘greater lexicographic sequence’. (shrink)