Date: Jun 27, 2012 1:56 PM
Author: Richard Tobin
Subject: Re: Re: Matheology § 047

In article <48e70f3b-1405-43e8-9538-bdbd365d0bd2@a8g2000vbk.googlegroups.com>,
WM  <mueckenh@rz.fh-augsburg.de> wrote:

>> What is your definition of "lie continuous"?

>There are no gaps.

>There is no gap on the continuous line. Either the next point is
>rational or it is irrational. Even when we cannot identify it.

How do you deduce from the absence of gaps that there is a "next
point"?

On the contrary, the absence of gaps implies that there is *not* a
next point.  If there were a next point, there would be a gap between
each point and the next where their midpoint ought to be.

-- Richard