 The first, and perhaps most definitive, indication that the later Wittgenstein maintains his finitism is his continued and consistent insistence that irrational numbers are rules for constructing finite expansions, not infinite mathematical extensions. “The concepts of infinite decimals in mathematical propositions are not concepts of series”, says Wittgenstein (RFM V, §19), “but of the unlimited technique of expansion of series”. We are misled by “[t]he extensional definitions of functions, of real numbers etc”. (RFM V, §35), but once we recognize the Dedekind cut as “an extensional image”, we see that we are not “led to \(\sqrt{2}\) by way of the concept of a cut” (RFM V, §34). On the later Wittgenstein’s account, there simply is no property, no rule, no systematic means of defining each and every irrational number intensionally, which means there is no criterion “for the irrational numbers being complete” (PR §181).