A quotation from Russell concedes that the immensity of real numbers (unending decimals) 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 (existing and future) cannot be more than a countable whole. It is however clearly uncountable. An explanation is offered using the ‘greater lexicographic sequence’ (GLS).