On Fri, 18 Jul 2003 08:18:51 -0000, Dylan Smith
wrote:
is a horse of a different color, which by lemma 1 doesn't exist).

Sure it's not a horse with an infinite number of legs?

Lemma 1 is very useful on its own. :-)

Lemma 1. All horses are the same color. Proof by induction.
One horse is the same color. Assume n horses are the same
color to prove n+1 horses are the same color. Take one horse
out of the set of n+1. You have n horses of the same color by
induction hypothesis. Do this n+1 times to obtain n+1 sets,
all the same color. Therefore, n+1 horses are the same color.

Theorem 1. Horses have an infinite number of legs. Proof by
intimidation. Horses have an even number of legs. They have
their 2 hind legs in back, and their forelegs in front. Which
makes 6 legs, which is certainly an odd number of legs for a
horse. The only number that is both even and odd is infinity.
Furthermore, assume there exists a horse with a finite number
of legs. Well, that is a horse of a different color, which
by lemma 1 doesn't exist. QED


We now resume our regularly scheduled discussion of aviation.


Morris (what you get when you cross an elephant with a mountain climber?)