> > 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_