In article <EbGdnaOLrvT9voXRnZ2dnUVZ8hKdnZ2d@brightview.co.uk>, "Mike Terry" <news.dead.person.stones@darjeeling.plus.com> wrote:
> "Virgil" <Virgil@home.esc> wrote in message > news:Virgil-3B2F0B.16291815062010@bignews.usenetmonster.com... > > In article <87sk4ohwbt.fsf@dialatheia.truth.invalid>, > > Aatu Koskensilta <aatu.koskensilta@uta.fi> wrote: > > > > > Virgil <Virgil@home.esc> writes: > > > > > > > Note that it is possible to have an uncomputable number whose decimal > > > > expansion has infinitely many known places, so long as it has at least > > > > one unknown place. > > > > > > You need infinitely many unknown places. > > > > If the value of some decimal digit of a number depends on the truth of > > an undecidable proposition, can such a number be computable? > > Yes - e.g. imagine just the first digit of the following number depends on > an undecidable proposition: > > 0.x000000000... > > There are only 10 possibilities for the number, and in each case it is > obviously computable...
But until you can determine which of those 10 cases, how can you compute the number?
In order for a number to be computable, one must be able to compare it for size against other computable numbers, at least so I understood.
