In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> On 6 Feb., 10:08, Virgil <vir...@ligriv.com> wrote: > > > > Everything of 0.111... that can be defined by sequences of 1's, is in > > > the list. The finite definition "s" or "o.111..." is not in the list, > > > but finite definitions have nothing to do with Cantor's diagonal > > > proof. > > > Is that really exceeding the capacity of your brain? > > > > It certainly seems beyond the capacity of WM's. > > With no doubt. > > > > 0.111... is a finite definition for Sum_(n in |N) 1/b^n, > > which is another finite definition of 1/9 and notr available for > diagonalization. > > Try to diagonalize: > > 1 divided by 9 > 1 divided by circumference of the unit circle > series of Gregory-Leibniz > basis of the logarithms > Euler's constant > andsoon If the nth term in that sequence can be expressed in some n-ary form with n >= 4, , say, decimal form, accurate to n+1 n-ary places, then forming an anti-diagonal is trivial. > > Nothing else is required by Cantor with the only exception, that for > every n the finite initial segment a_n1, ..., a_nn of entry number n > has to be expanded by digits. But as everybody knows, these finite > initial segments belong to a countable subset of the countable set of > rational numbers.
The nth term need not be expanded beyond n+1 digit accuracy in order to have a well defined antidiagonal. > > Regards, WM --