On Sat, 15 Jul 2006 19:08:30 -0600, Virgil <email@example.com> wrote:
>In article <firstname.lastname@example.org>, > Lester Zick <DontBother@nowhere.net> wrote: > >> On Sat, 15 Jul 2006 15:43:28 -0600, Virgil <email@example.com> wrote: >> >> >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. >> >> Well, Virgil, no disrespect but I've been over and over this issue on >> various venues. The conventional definition you refer to is based on >> non repeating fractional rational approximations first, I believe, >> enunciated by Euler.I consider this definitional regression incorrect, >> that rationals and irrationals are defined on straight line segments >> and transcendentals on curves. > > >That may be your definition, but it is no one else's. > >According to the Harper Collins Dictionary of mathematics, for example, > > irrational: not expressible as a ratio of integers, > > transcendental: not the root of any polynomial equation with > rational coefficients. > >Unless you can show that your "definitions" are at least compatible with >these, yours are wrong.
How can my definitions be wrong if definitions are arbitrary?