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).

Is it?

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_