Re: Cantor and the binary tree

In article <1121786056.338470.284780@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> 1417
> Virgil wrote:
>
> > >
> > > It is sufficient to consider the interval (0,1). Therefore no sign is
> > > required.
> >
> > It is also sufficient to consider all rationals as has been done!
>
> But it is not necessary and requires superfluous work.
> > > >
> > > But this convergence is the same as that of Cantor's antidiagonal. The
> > > real number distinct from any number of the list is approximated but
> > > not established.
> >
> > It is given as the limit of a convergent sequence, which is the form of
> > all decimal expansions. If it does not exist, then no numbers exist.
>
> Why? Integers and fractions do exist.

Show me how any integer or rational has any more existence as a real
number than any convergent infinite sequence.

And in any case, the limit in question is well enough established to
prove it different from every member of the list from which it is built.

And for WM's oft repeated example, each number in WM's list and the
anti-diagonal as well are rational fractions so they exist as much as
any rationals do.
.

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