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...
This is not a real number. It restricts the set of numbers to 10 differents numbers (in decimal). > > There are only 10 possibilities for the number, and in each case it is > obviously computable...
But it is not clear which case will be chosen. Two real numbers a and b satisfy a < b or a = b or a > b. 0.y and 0.x do not. These symbols are number forms like x and y in 3x + 5y = 0 or n in "let n be an even number". Obviously n need not be an even number. It is no number at all.
