On Nov 1, 12:35 am, rich...@cogsci.ed.ac.uk (Richard Tobin) wrote: > In article <a4ec801c-15d5-4d4d-aa02-e30552568...@jl13g2000pbb.googlegroups.com>, > Graham Cooper <grahamcoop...@gmail.com> wrote: > > >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. > > Yes, and *every one of them* gives you a number that isn't in the set. > There isn't just one number missing from your set of reals, almost > all of them are missing! > > -- Richard
That contradicts hard facts if you work out Q6, or simply try it with the 16 reals given and the 2 possible enumerations!!
Your missing real segmented 0.a1a2a3a4 a5a6a7 a8a9 a10 a11 a12a13a14 .
has neither a new digit segment of any length anywhere or a new sequence of those sements anywhere!
NO NEW DIGIT SEQUENCE - IF YOU DO THE GROUND WORK!
Herc -- if( if(t(S),f(R)) , if(t(R),f(S)) ). if the sun's out then it's not raining ergo if it's raining then the sun's not out