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- _________________________________________
- / Lemma: All horses are the same color. \
- | Proof (by induction): |
- | |
- | Case n = 1: In a set with only one |
- | horse, it is obvious that all |
- | |
- | horses in that set are the same color. |
- | |
- | Case n = k: Suppose you have a set of |
- | k+1 horses. Pull one of these |
- | |
- | horses out of the set, so that you have |
- | k horses. Suppose that all |
- | |
- | of these horses are the same color. Now |
- | put back the horse that you |
- | |
- | took out, and pull out a different one. |
- | Suppose that all of the k |
- | |
- | horses now in the set are the same |
- | color. Then the set of k+1 horses |
- | |
- | are all the same color. We have k true |
- | => k+1 true; therefore all |
- | |
- | horses are the same color. Theorem: All |
- | horses have an infinite number of legs. |
- | Proof (by intimidation): |
- | |
- | Everyone would agree that all horses |
- | have an even number of legs. It |
- | |
- | is also well-known that horses have |
- | forelegs in front and two legs in |
- | |
- | back. 4 + 2 = 6 legs, which is |
- | certainly an odd number of legs for a |
- | |
- | horse to have! Now the only number that |
- | is both even and odd is |
- | |
- | infinity; therefore all horses have an |
- | infinite number of legs. |
- | |
- | However, suppose that there is a horse |
- | somewhere that does not have an |
- | |
- | infinite number of legs. Well, that |
- | would be a horse of a different |
- | |
- | color; and by the Lemma, it doesn't |
- \ exist. /
- -----------------------------------------
- \
- \
- .--.
- |o_o |
- |:_/ |
- // \ \
- (| | )
- /'\_ _/`\
- \___)=(___/
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