On 2010-06-17, Peter Webb <webbfamily@DIESPAMDIEoptusnet.com.au> wrote: > "Virgil" <Virgil@home.esc> wrote in message >> An infinite set is defined to bee countable if and only if there is a >> surjection from the set of natural numbers to that set. When such a >> function is a bijection, it is commonly called a list. > > Only if the bijection can be explicitly created.
You apparently have some bizarre private definition of "list".
Explicitness has nothing to do with it.
Though even if it did, you are incorrect. Given any numbering of Turing machines, a list of computable reals ordered by the least-numbered Turing machines that compute them is quite explicit.
The practical difficulties of establishing which Turing machines halt, which are equivalent and so on are just that: practical difficulties which have nothing to do with mathematical theory.
