 And there are further contributions to set theory we owe to Dedekind. Some of these do not appear in his published writings, but in his correspondence. Especially significant is his exchange of letters, starting in 1872, with Cantor (Noether &amp; Cavaillès 1937, Meschkowski &amp; Nilson 1991). These letters contain a discussion of Cantor’s and Dedekind’s respective treatments of the real numbers. Beyond that, they amount to a joint exploration of the notions of set and infinity. Among Dedekind’s specific contributions in this context are the following: He impresses Cantor with a proof that not only the set of rational numbers but also the set of all algebraic numbers is countable (Ferreirós 1999, ch. 6). This result led, at least in part, to Cantor’s further study of infinite cardinalities and to his discovery, soon thereafter, that the set of all real numbers is not countable. Dedekind also provides a proof of the Cantor-Bernstein Theorem (that between any two sets which can be embedded one-to-one into each other there exists a bijection, so that they have the same cardinality). This is another basic result in the theory of transfinite cardinals (Ferreirós 1999, ch. 7).