In article <email@example.com>, "Ross A. Finlayson" <firstname.lastname@example.org> wrote:
> The transfinite course-of-passage in well-ordering the reals sees a > diminishing interval. Do the endpoints of the interval meet, in the > well-ordering? A critical point of Cantor's first is that the > intersection is non-empty.
It is a well known property of the real number line, at least among mathematicians, that nested sequence of closed intervals has non-empty intrsection.