"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...
