In article <email@example.com>, Graham Cooper <firstname.lastname@example.org> wrote:
> On Dec 29, 11:37 am, Virgil <vir...@ligriv.com> wrote: > > In article > > <adde38fa-1e63-43a1-94f0-908da37a4...@s6g2000pby.googlegroups.com>, > > Graham Cooper <grahamcoop...@gmail.com> wrote: > > > > > > > > > > > > > > > > > > > > > +-----> > > > | 0. 542.. > > > | 0. 983.. > > > | 0. 143.. > > > | 0. 543.. > > > | ... > > > v > > > OK - THINK - don't back explain to me. > > > You run down the Diagonal 5 8 3 ... > > > IN YOUR MIND - > > > > >  > > > you change each digit ONE AT A TIME > > > 0.694... > > > but this process NEVER STOPS > > > > >  > > > so you NEVER CONSTRUCT A NEW DIGIT SEQUENCE! > > > > That is like saying that the function f+ |N -> |N : x \_--> x^2 > > never ends. > > > Right! but since it has no free variable input to apply it's safe to > extrapolate results toward infinity. > > > > > As soon as one has a completed rule by which values of the function are > > determined from its domain to its codomain, the function is defined. > > > > E.g., f:|N --> |N : 2 |--> 2*x+1 > > is completed function > > > > Thus a rule or function for determining anti-diagonal digits creates the > > entire anti-diagonal list of digits in one step. > > > > dependent on the input. As a function of the input certainly, but one theat function is defined the process is essentially completed. > > In this case, you cannot ANTI-DIAGONALISE an infinite set. > > Every digit you change is substitutable by another digit in another > permutation.
I have defined a function which does it automatically for any and every list of endless sequences of decimal digits, giving a resulting sequence not listed in that list. --