In article <firstname.lastname@example.org>, Lester Zick <DontBother@nowhere.net> wrote:
> Well I don't have Turing's paper with me but as I recollect it was > entitled something like "On the Computability of Numbers". What I > don't know was exactly how exhaustive the paper was in that regard. > But I'm not sure I'd agree that all the reals are computable in this > sense. Certainly the rationals are but irrationals and transcendentals > not obviously so.
That seems to imply that irrationals and transcendentals are disjoint. In fact the set of transcendentals is a proper subset of the set of irrationals.