"Graham Cooper" <grahamcooper7@gmail.com> wrote in message news:a1155959-2991-4961-b58c-1544b6836a1e@ki5g2000pbb.googlegroups.com...
> Here is an alternate take that seems to fall on deaf ears. > > The list of computable reals contains every digit sequence of ALL > LENGTHS. > > Good 'nuff!
Good for what? By the diagonal argument, it is simply false:
The anti-diagonal of an effective list of computable reals is, apparently, a computable real itself; OTOH, the anti-diagonal is, as a direct consequence of its definition, not on the list. Hence, any effective list of computable reals must be incomplete (not enumerate all the computable reals). -- Standardly, when we say that a list does not contain this or that entity, we mean that for no n in N that entity appears at position n.
I am thinking that the best we can get when talking of effective enumerations of strings is (modulo remapping) the dyadic rationals, i.e. strings that end with period "0", namely all and only the finite strings.
