Date: Jun 27, 2012 1:56 PM
Author: Richard Tobin
Subject: Re: Re: Matheology § 047
In article <firstname.lastname@example.org>,
WM <email@example.com> 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
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.