On Oct 31, 9:45 pm, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote: > In article <623781e5-4542-4a3d-98d9-a299ec236...@b4g2000pby.googlegroups.com>, > Graham Cooper <grahamcoop...@gmail.com> wrote: > > >> If you want us to construct the list, you'd better give us a > >> constructive proof that the set is countable. > >R11 R12 R13 ... > >R21 R22 R23 ... > >R31 R32 R33 ... > >... > > >Proof: > >Each R index has 2 natnum indexes that can all be tallied trivially. > > >This is a COUNT-ABLE SET. > > So consider the list > > R11 > R12 > R21 > R13 > R22 > R31 > ... > > and use the diagonal to get a real that is different from all the Rxy. > Your set is not complete. QED. >
by ... 'use the diagonal' 0.a1a2a3...
a1 = 0 if the first real on YOUR list is 1, otherwise 1. a2 = 0 if the first real on YOUR list is 1, otherwise 0. ...
proves nothing. chose a different enumeration f, and the values arbitrarily change depending on your particular f.
