Re: Cantor and the binary tree

In article <1121622980.914154.240560@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> > > In the following list (with the replacement rule: replace 0 by 1) there
> > > is either no difference between numbers of the list and antidiagonal
> > > 0,111... or no convergence:
> > >
> > > 0.000...
> > > 0.1000...
> > > 0.11000...
> > > 0.111000...
> > > ...
> > >
> > > The antidiagonal Sum{n=1 to oo} b_n * 10^-n = 1/9 is the same as the
> > > limit of the list numbers. There is no difference. A difference can
> > > only be maintained when comparing a_nn and b_n, i.e., 0 and 1. But then
> > > there is no convergence.
> >
> > So you would propose that there is something contradictory about the
> > half-open interval [0,1/9) in the rationals, because it doesn't contain
> > 1/9?
>
> No, I would propose that the limit 1/9 is not on the antidagonal if it
> is not in the list, because an equilateral triangle remains so also in
> the infinite limit.

AS usual WM proposes that we adopt idiocy as our standard.
.