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induction (sorta....)
Posted:
Jan 14, 1996 12:01 AM
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Seeing the Rproof by inductionS that all horses are
the same color reminded me of a bit I had not dug out
in about 25 years. I know not where it came from
originally but am hereby willing to share it (inflict upon?)
the readership ....
Theorem: All horses have an infinite number of legs.
This will be a proof by contradiction. Assume there exists
a horse with only a finite number of legs. There are two
cases to consider: either a horse has an even number of
legs or an odd number of legs. We will show that either
case leads to a contradiction:
CASE 1: A horse has an even number of legs. Since a
horse has fore-legs in front, if it is to have an even total
number of legs, it must have at least two legs in back.
Hence a horse must have at least fore + two =
six legs. But as everyone knows, six is an OD number
of legs for a horse to have and this contradicts our
assumption that he had an even number of legs. Thus
Case 1 cannot hold.
CASE 2: A horse has an odd number of legs. It is common
knowledge that a horse with an odd number of legs is a
horse of a different color. But it has been proved (see
earlier posts) that all horses are the same color and
again we have reached a contradiction. Thus Case 2
cannot hold.
Since neither Case 1 nor Case 2 is possible, we must
conclude that a horse cannot have a finite number of legs.
Hence all horses have an infinite number of legs. QED
(which as everyone no doubt knows, stands for Quite
Easy Dummy)
mike bolduan
The Catlin Gabel School
Portland OR
bolduan@catseq.catlin.edu
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