israel@umcp-cs.UUCP (09/20/83)
From: levy@princeton.UUCP
Now let's hear the proof that all horses have an infinite
number of legs (using the fact that all horses are the same
color, of course). I'm curious...
Well, Don't blame me. You asked for it.
Part 1) All horses are the same color.
(Uses the inductive proof beaten to death here in net.math
recently; if you think I'm going to repeat it you're crazy.)
Part 2) All horses have an infinite number of legs.
Proof: by contradiction:
Assume: All horses have a finite number of legs.
All finite numbers are either odd or even, so,
if they have a finite number of legs, then:
a) they have an odd number of legs, or
b) they have an even number of legs.
case a) odd number of legs:
Well, that's a horse of a different color. But according
to the lemma from part 1), we can't have a horse of a different
color. Therefore, not odd.
case b) even number of legs:
Horses have their forelegs and their two hind legs.
four legs + two legs = six legs.
Now, six legs is an odd number of legs for a horse.
But, by part a) that can't happen. Therefore, not even.
Since, not odd and not even, therefore not finite,
therefore infinite.
:-). Remember, no flames. I warned you.
--
~~~ Bruce
Computer Science Dept., University of Maryland
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