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.
In this case, you cannot ANTI-DIAGONALISE an infinite set.
Every digit you change is substitutable by another digit in another permutation.