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De - Pt| Proverbs, aphorisms, quotations (English) | by Linux fortune |
| 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. | |
| Proof techniques #2: Proof by Oddity. SAMPLE: To prove that horses have an infinite number of legs. (1) Horses have an even number of legs. (2) They have two legs in back and fore legs in front. (3) This makes a total of six legs, which certainly is an odd number of legs for a horse. (4) But the only number that is both odd and even is infinity. (5) Therefore, horses must have an infinite number of legs. Topics is be covered in future issues include proof by: Intimidation Gesticulation (handwaving) "Try it; it works" Constipation (I was just sitting there and ...) Blatant assertion Changing all the 2's to _n's Mutual consent Lack of a counterexample, and "It stands to reason" | |
| (1) Alexander the Great was a great general. (2) Great generals are forewarned. (3) Forewarned is forearmed. (4) Four is an even number. (5) Four is certainly an odd number of arms for a man to have. (6) The only number that is both even and odd is infinity. Therefore, all horses are black. | |
| (1) Alexander the Great was a great general. (2) Great generals are forewarned. (3) Forewarned is forearmed. (4) Four is an even number. (5) Four is certainly an odd number of arms for a man to have. (6) The only number that is both even and odd is infinity. Therefore, Alexander the Great had an infinite number of arms. | |
