 The filling-up of gaps in the rational numbers through the “creation of new point-individuals” (1872 [1999: 772]) is the key idea underlying Dedekind’s construction of the domain of real numbers. He first defines a cut to be a partition \((A_1,\) \(A_2)\) of the rational numbers such that every member of \(A_1\) is less than every member of \(A_2\). After noting that each rational number corresponds, in an evident way, to a cut, he observes that infinitely many cuts fail to be engendered by rational numbers. The discontinuity or incompleteness of the domain of rational numbers consists precisely in this latter fact.