On 23 Jun., 14:24, Aatu Koskensilta <aatu.koskensi...@uta.fi> wrote: > "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> writes: > > Well, the algorithm is clearly computable. If you give me a purported > > list of all computable numbers, I can compute a missing number. > > Give how? We can't in any literal sense be given infinitary objects such > as an infinite list of computable reals. >
That is wrong. Many real numbers can be given by finite definitions like pi or SUM1/n^2 or 0,3 or 0.333... and can be expanded as infinite sequences of digits.
In the same way a list of all finite definitions including all computable, all definable, all identifyable and all however specified reals in all possible language can be given. Here it is: