 The theory of real numbers in PM is closer to that of Frege than the “arithmetizing” accounts of Dedekind or Cantor. Dedekind postulated that irrational numbers are to be “created” to fill out the gaps in the series of rational numbers that are marked by Dedekind cuts (Dedekind 1872 [1901: 15], while Cantor (1883: §9, para. 8 [1996: 899]) identified real numbers with the limits of sequences of rational numbers.