 For our purposes several aspects of Dedekind’s procedure, at the start and in its subsequent steps, are important (cf. Ferreirós  1999, ch. 4). To begin with, Dedekind starts by considering the system of rational numbers seen as a whole. Noteworthy here are two aspects: Not only does he accept this system as an “actual infinity”, i.e. a complete infinite set that is treated as a mathematical object in itself; he also considers it “structurally”, as an example of a linearly ordered set closed under addition and multiplication (an ordered field). In his next step—and proceeding further along set-theoretic and structuralist lines—Dedekind introduces the set of arbitrary cuts on his initial system, thus working essentially with the bigger and more complex infinity of all subsets of the rational numbers (the full power set). It is possible to show that the set of those cuts can in turn be endowed with a linear ordering and with operations of addition and multiplication, thus constituting a totally new “number system”.