Date: Mar 23, 2004 4:34 AM
Author: Robin Chapman
Subject: Re: Hex Win Proof?
Torben ÃÂ¯ÃÂ¿ÃÂ½idius Mogensen wrote:
> Indeed, if we want to prove it to a mathematician who does not already
> accept the intermediate value theorem (of which the intersection
> property is a simple consequence).
Now I presume this "intersection property" can be paraphrased as
"a path with endpoints at two opposite vertices of a square with
all other points in the interior of the square must meet a path
with endpoints at the other two vertices of the square with
all other points in the interior of there square".
That's a simple consequence of the intermediate value theorem, is it?
I must be stupid, since the only way I can see to prove that is
using the Jordan Curve Theorem. :-(
Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html
"Lacan, Jacques, 79, 91-92; mistakes his penis for a square root, 88-9"
Francis Wheen, _How Mumbo-Jumbo Conquered the World_