In article <email@example.com>, Tim Little <firstname.lastname@example.org> wrote:
> On 2010-06-26, Charlie-Boo <email@example.com> wrote: > > It is trivial to calculate in binary (using only 0 and 1) and output > > any desired string surrounded by 2 whenever we want > > You use the singular here, by which your statement is correct. Any > single finite string can be so produced. What's more, any finite > sequence of finite strings can be produced. > > However, you need an infinite sequence of finite strings to define > most real numbers, and there are not enough finite algorithms to > produce them all.
It is well known that for 'most' reals no such algorithm can exist, the non-computable transcendentals.