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De - Pt| Proverbs, aphorisms, quotations (English) | by Linux fortune |
| "This is lemma 1.1. We start a new chapter so the numbers all go back to one." -- Prof. Seager, C&O 351 | |
| Every Horse has an Infinite Number of Legs (proof by intimidation): Horses have an even number of legs. Behind they have two legs, and in front they have fore-legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both even and odd is infinity. Therefore, horses have an infinite number of legs. Now to show this for the general case, suppose that somewhere, there is a horse that has a finite number of legs. But that is a horse of another color, and by the lemma ["All horses are the same color"], that does not exist. | |
| 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. | |
| Rocky's Lemma of Innovation Prevention: Unless the results are known in advance, funding agencies will reject the proposal. | |
