 Providing an explicit and precise definition of the real numbers constitutes a major step towards completing the arithmetization of analysis. But further reflection on Dedekind’s procedure (and similar ones) leads to a new question: What is involved in it if thought through fully, i.e., what does this account of the real numbers rely on ultimately? As noted, Dedekind starts with the system of rational numbers; he uses a set-theoretic procedure to construct, in a central step, the new system of cuts out of them; and finally, the real numbers are “created” on that basis. This suggests three sub-questions: First, how exactly are we to think about the rational numbers in this connection? Second, can anything further be said about the set-theoretic procedures that have been used? And third, how is the creation at issue to be understood?