On 17 Jun., 09:54, Virgil <Vir...@home.esc> wrote: > In article <4c19cd2c$0$316$afc38...@news.optusnet.com.au>, > "Peter Webb" <webbfam...@DIESPAMDIEoptusnet.com.au> wrote: > > > Cantor's proof applied to computable numbers proves you cannot form a > > computable list of computable numbers. Cantor's proof applied to Reals > > proves you cannot form a computable list of Reals.
Cantors proof is nonsense from the beginning, because a real number can never be defined by an infinite sequence alone. A definition defines something, but an infinite sequence does not define a number before the last digit is known. > > To be correct, there is no computable list of ALL of the computable > numbers, even though the set of computable numbers is e countable, but > there are lots of possible computable lists of computable numbers.
And there are lots of lists of more than all computable numbers, namely lists of all finite expressions.