 A second marked difference between Dedekind and current set theory has already come up too, but deserves further comment. This is his appeal to “abstraction”, and  “creation”, in the last step of his introduction of both the natural and the real numbers (“Dedekind-abstraction”,  as it is called in Tait 1996). For the real numbers, the standard procedure in axiomatic set theory is to follow Dedekind up to this last step, but then to work with the Dedekind-cuts themselves as “the real numbers”.  While aware of this option (Dedekind 1876b, 1888b), Dedekind tells us to  apply “abstraction” to the cuts insofar as they consist of complex sets, thus to “create” additional  mathematical objects determined by but not identical with them. Likewise, in the case of the natural numbers it is standard today to construct a particular simple infinity, usually the set of finite von Neumann ordinals, and then to identify the natural numbers with them (thus: \(0 = \emptyset\), \(1 = \{0\}\), \(2 = \{0, 1\}\), etc.). Once again, the step involving “abstraction” and “creation” of Dedekind’s procedure is avoided by such identification.