Re: Cantor and the binary tree

In article <1117743153.673576.235420@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
mueckenh@xxxxxxxxxxxxxxxxx wrote:

> Tony Orlow (aeo6) wrote:
>
> > > TO keeps assuming that to have infinitely many of something requires the
> > > "distance" between them to be infinitely large. This is a false
> > > assumption.
> > It is true when the distance between neighbors is finite and constant. If
> > you
> > measure paths in units of branches, and say they are infinitely long, then
> > that
> > means they have infinitely many branches.
>
> Of course it is so. If you have infinitely many meters, then this makes
> up an infinite distance.

There are points in this universe arbitrarily far apart, unless it
should transpire that this universe is finite, but there are no two
points in this universe that are infinitely far apart.

Thus the set of possible distances is unbounded but all actual distances
are finite.

WM and TO cannot cross the pons asinorum of comprehending a set all of
whose members are finite, yet for each member having a larger member.

Even though there are trivial examples, e.g., {(n-1)/n : n e N}.
.

Relevant Pages