 Functions are to be conceived of extensionally too, as ways of correlating the elements of sets. But unlike in later axiomatic set theory, Dedekind does not reduce functions to sets of tuples. (Not unreasonably, he takes the ability to map one thing onto another, or to represent one by the other, to be fundamental for human thought; Dedekind 1888a, preface, cf. Klev 2017). Another important aspect of Dedekind’s views about functions is that, with respect to their intended range, he allows for arbitrary functional correlations between sets of numbers, indeed between sets of objects more generally. (For the gradual development of his views in this connection, see Sieg &amp; Schlimm 2005.) He thus rejects previous, often implicit restrictions of the notion of function to, e.g., functions presented by familiar formulas, functions representable in intuition via their graphs, or functions decidable by a formal procedure. In other words, he works with a generalized notion of function. In this respect he adopts, and expands on, the position of another of his teachers: Dirichlet (Stein 1988, Ferreirós 1999, ch. 7). Dedekind’s notion of set is general in the same sense.