Proverbs, aphorisms, quotations (English) | by Linux fortune |
It is not well to be thought of as one who meekly submits to insolence and intimidation. | |
HOW TO PROVE IT, PART 1 proof by example: The author gives only the case n = 2 and suggests that it contains most of the ideas of the general proof. proof by intimidation: 'Trivial'. proof by vigorous handwaving: Works well in a classroom or seminar setting. | |
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" | |
"Don't come back until you have him", the Tick-Tock Man said quietly, sincerely, extremely dangerously. They used dogs. They used probes. They used cardio plate crossoffs. They used teepers. They used bribery. They used stick tites. They used intimidation. They used torment. They used torture. They used finks. They used cops. They used search and seizure. They used fallaron. They used betterment incentives. They used finger prints. They used the bertillion system. They used cunning. They used guile. They used treachery. They used Raoul-Mitgong but he wasn't much help. They used applied physics. They used techniques of criminology. And what the hell, they caught him. -- Harlan Ellison, "Repent, Harlequin, said the Tick-Tock Man" |