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induction (sorta....)
Posted:
Jan 14, 1996 12:01 AM


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 forelegs 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



