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
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.