> On 4 Jan., 22:38, Virgil <vir...@ligriv.com> wrote: > >> According to standard mathematics, a set is "countable" if and only if >> there is surjection from N to that set. > > If and only if? Do you agree that a subset of a countable set is > countable? > > The set of all finite definitions is countable. > The set of all finitely defined reals cannot be put in bijection with | > N, but it is a subset of all finite definitions, isn't it?