On Jun 27, 12:08 am, Virgil <Vir...@home.esc> wrote: > In article <slrni2dgpo.jrj....@soprano.little-possums.net>, > Tim Little <t...@little-possums.net> wrote: > > > On 2010-06-26, Charlie-Boo <shymath...@gmail.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.