On 16 Jun., 03:05, "Mike Terry" <news.dead.person.sto...@darjeeling.plus.com> wrote: > "Virgil" <Vir...@home.esc> wrote in message > > news:Virgil-3B2F0B.16291815062010@bignews.usenetmonster.com... > > > In article <87sk4ohwbt....@dialatheia.truth.invalid>, > > Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > > > > Virgil <Vir...@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...
These numbers are computable. What you wrote, however, is not a number but a form of a number.
3 > 1 is a correct proposition. x > 1 is the form of a proposition.
But all that is not of interest for the present problem: All definable, computable, and somehow identifiable numbers and forms of numbers are within a countable set.
Therefore Cantor proves the uncountability of this countable set.
