INTERNUTS Digest Fri, 10 Oct 1997 Volume 01 : Issue 13 Today's Topics: proofs afraid not ---------------------------------------------------------------------- Date: Thu, 09 Oct 1997 19:16:15 GMT From: jschmitz@qis.net (JoAnne Schmitz) To: lnuts Subject: proofs Message-ID: <3455220e.72876131@mail.qis.net> On 3 Oct 1997 20:13:03 GMT, in rec.humor mlcook@cca.rockwell.com (Michael Cook) wrote: Methods of Mathematical Proof This is from _A Random Walk in Science_ (by Joel E. Cohen?): To illustrate the various methods of proof we give an example of a logical system. THE PEJORATIVE CALCULUS Lemma 1. All horses are the same colour. (Proof by induction) Proof. It is obvious that one horse is the same colour. Let us assume the proposition P(k) that k horses are the same colour and use this to imply that k+1 horses are the same colour. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same colour, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same colour. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same colour. It follows that since every horse is the same colour as every other horse, P(k) entails P(k+1). But since we have shown P(1) to be true, P is true for all succeeding values of k, that is, all horses are the same colour. Theorem 1. Every horse has an infinite number of legs. (Proof by intimidation.) Proof. 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 cer- tainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite num- ber of legs. Now to show that this is general, suppose that somewhere there is a horse with a finite number of legs. But that is a horse of another colour, and by the lemma that does not exist. Corollary 1. Everything is the same colour. Proof. The proof of lemma 1 does not depend at all on the nature of the object under consideration. The predicate of the antecedent of the uni- versally-quantified conditional 'For all x, if x is a horse, then x is the same colour,' namely 'is a horse' may be generalized to 'is anything' without affecting the validity of the proof; hence, 'for all x, if x is anything, x is the same colour.' Corollary 2. Everything is white. Proof. If a sentential formula in x is logically true, then any parti- cular substitution instance of it is a true sentence. In particular then: 'for all x, if x is an elephant, then x is the same colour' is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain 'The Stolen White Ele- phant'). Therefore all elephants are white. By corollary 1 everything is white. Theorem 2. Alexander the Great did not exist and he had an infinite number of limbs. Proof. We prove this theorem in two parts. First we note the obvious fact that historians always tell the truth (for historians always take a stand, and therefore they cannot lie). Hence we have the historically true sentence, 'If Alexander the Great existed, then he rode a black horse Bucephalus.' But we know by corollary 2 everything is white; hence Alexander could not have ridden a black horse. Since the conse- quent of the conditional is false, in order for the whole statement to be true the antecedent must be false. Hence Alexander the Great did not exist. We have also the historically true statement that Alexander was warned by an oracle that he would meet death if he crossed a certain river. He had two legs; and 'forewarned is four-armed.' This gives him six limbs, an even number, which is certainly an odd number of limbs for a man. Now the only number which is even and odd is infinity; hence Alexander had an infinite number of limbs. We have thus proved that Alexander the Great did not exist and that he had an infinite number of limbs. ---------------------------------- Theorem: a cat has nine tails. Proof: No cat has eight tails. A cat has one tail more than no cat. Therefore, a cat has nine tails. ------------------------------ Date: Thu, 09 Oct 1997 19:16:16 GMT From: jschmitz@qis.net (JoAnne Schmitz) To: lnuts Subject: afraid not Message-ID: <345b2d49.75751310@mail.qis.net> ---------------------------------------------------- And then there was this barge floating along at sea. Ahead of it was this cruise ship. The cruise ship, asked the barge, "Hey, are you the Love Boat?" To which the barge replied, "No, I'm a freight yacht!" ---------------------------------------------------- A young private lived in a barracks infested with fleas and ticks, and though he complained often to the sergeant of his platoon, nothing was ever done about the problem. However, one weekend he received a weekend pass, and went to the nearby town to party it up with his friends. Unbeknownst to him, the barracks was disinfected and fumigated while he was away. Upon his return, he looked at his bed and said, "Oh, well, another night of bug-bites and itching ahead..." And the bed replied, "No, I'm a sprayed cot." ------------------------------------------------------------------------------- A young executive was working at her desk late one night, when she accidentally knocked over a bottle of ink. The ink began running toward the project she was working on, and she hastily wiped at it with a Kleenex. Assuming she had eradicated the offensive substance, she finished up what she was doing and left for the night. When she arrived in the morning, she began leafing through her papers, and discovered one sheet had a large ink stain on it. She swore, then turned to the ink bottle and said, "Ooh, I thought I wiped you up last night!" The spot on the page looked at her and said, "No, I'm a strayed blot." ------------------------------------------------------------------------------- So there was this guy in the old ages in shining armor, in Camelot. He had been set-up by a nemesis, and was doing some time in the dungeon, for a crime he didn't commit. Another inmate asked, You must have done something horrible to get in here." And our hero said "No, I'm a framed knight." He was able to prove his innocence, and was let go. He ran into his nemesis who was surprised to see him loose. "I thought you were locked up for good?" "No," said our hero, "I'm a freed knight." ---------------------------------------------------- These three Australian Pecans went into a bar that only served Peanuts. As the first Pecan approached the bar, the bartender axed, 'Hey, what are you? A Pecan? We don't serve Pecans here, only Peanuts.' So the poor Pecan left. As you may guess, the second Pecan attempted the same thing and was also turned away. The third Australian Pecan got a good idea. He went outside and threw himself on a barbie and rolled around in the coals for a bit. He returned to the bar and approached the bartender who axed, 'Hey, aren't you one of them Pecans?' To which our hero replied: 'No, I'm a fried nut.' ---------------------------------------------------- An old, arthritic, and exceptionally stupid dog was snoozing in the middle of the road. Alluva sudden a big street cleaning vehicle comes by and maims the dogster, tossing him to the side of the road. Some time later, a yuppie couple stop in their BMW 535i and pull over to see how the dog is. "Good Lord," sez the guy, "Are you all right?" To which the dog replies, "No, I'm a flayed mutt." ---------------------------------------------------- Sally's pen explodes and a large splat of black ink drops onto her lapel. After many bleachings and washings, the stain had faded but showed no sign of coming out altogether. She exclaimed one day, "You are a pain!" To which the stain replied: "No, I'm a greyed blot." ---------------------------------------------------- The local newspaper reporter was covering the catastrophic fire at the psychiatric ward of the hospital. Wanting to get his story straight about who and how many were injured he question many of the people at the scene. So far everyone of the injured was a member of the staff. Coming to a man who had been seriously burned when the oil furnace exploded he asked, "Are you a doctor or a nurse too?" "No," came the reply, "I'm a fried nut." ---------------------------------------------------- There once was a magical kingdom where the princess of the castle was turned into a small amphibian by an evil witch. She was held prisoner by the witch for many years, until one day a handsome prince rescued her from the witch's cottage in the woods. The prince asked, "Excuse me, but are you a princess that was turned into a salamander and that I have now released?" "No," she replied, "I'm a freed newt." ---------------------------------------------------- Actually, this musician was melting butter in a pan on the stove not far from where he had been composing music at his workbench. With much punk, an ink blot jumps off the staff paper and leaps into the frying pan, dancing and singing around. The musician asks: "Hey, dotted quarter! Are you nuts, or what?" "No!" replies the dot. "I'm a fried note." ---------------------------------------------------- After Alexander (the Great) applied his famous solution to the Gordian knot, he and his soldiers continued on their merry way leaving the severed knot to lie on the ground in two tangled piles. One soldier, who was quite far back in the column and had not seen the action earlier, had this to say: Look at the size of those two piles of worms!!! To which the knot replied, as all good knots will, No, I'm a filleted knot. ---------------------------------------------------- And overloaded a logic inverter, causing it to go up in a puff of smoke: "Are you OK?" "No, I'm a fried NOT!" ---------------------------------------------------- It was the late 1950's, and actor Don Knotts was temporarily out of work. He happened to hear that Hanna-Barbera was looking for voices for the characters in its new animated series, "The Flintstones". After his first audition, he was told that he had a good shot at the voice of Barney Rubble, but in the meantime he should go out into the front lounge to wait for further news. The lounge turned out to be filled with actors and actresses who were there to audition for the voices of Fred, Barney, Wilma and Betty. Don noticed an old friend of his across the room, a Mr. Chisteviejo. Don walked up to his friend, slapped him on the back, and said, "Say, Chisteviejo, are you a 'Fred' or a 'Barney'?" Without hesitation, Chisteviejo replied: "I'm a 'Fred', Knotts . . . " ---------------------------------------------------- So these two acorns were dangling side-by-side on a branch of their mighty oak, when a starling landed. The larger of the acorns dropped to the ground below. The fallen acorn surveyed the situation, and excitedly reported back to its once-neighbor, "What a feeling of freedom down here! With each rustle of wind, I can roll, the ground is cool and damp, and when a dog or person strolls by, the whole earth seems to vibrate. This is great. Do you want'a come down?" To which the still suspended acorn just HAD to reply, "No, I'm a treed nut." A massive lightning strike hit a pond near my house one day, and boiled all the water out. The next day, I went back to the blasted mudhole (nee pond) and noticed a large number of amphibian bodies strewn in the area. I picked up one charred specimen, wondering aloud if it had been a frog, when I heard it reply... "No, I'm a fried newt!" ---------------------------------------------------- A cargo train hits a rough spot and a nut flies out of one of the cars. It lands in a parts box in an electronics firm, right next to a shiny bolt. The bolt says "Hey, gorgeous! Are you from around here? I was *made* for guys who look like you." Our hero turns despondently to her and says "No, I'm a freight nut." ---------------------------------------------------- A jungle explorer was sitting in the woods when a bizarre insect landed on his arm. The tiny beast sported a goatee and a little bitty pipe which blue little bitty smoke rings. It began to tell the neighboring insects as to the analysis of dreams. "Heavens!" exclaimed the explorer. "What are you, a new species?" To which the creature replied, "No, I'm a Freud gnat." ---------------------------------------------------- A dog is sleeping outside one night, and sleeps well into the next day. By the time she awakes, the sun is already high in the sky. Naturally, the dog develops is very hot and is looking for a drink. Another dog sees her, and asks, "Are you okay?" Our heroine responds, "No, I'm a fried mutt." ---------------------------------------------------- A fishing vessel is dragging its net through an area rich with fish. Unexpectedly, a rat chews the main line through and the net goes sinking into the deep, much to the dismay of the crew. At the ocean floor, an octopus and a squid look at the strange thing that has fallen upon them. The octopus, irritated, looks at it and says, "What the hell are you, some kind of strange fish? It replies, "No, I'm a freed net." ---------------------------------------------------- A group of planter's peanuts were out for a stroll one day in the kitchen. Unsalted thought that it might be fun to go for a stroll on the big deep-fryer that was sitting on the counter. They climbed up a wooden spoon that was leaning against the vat, and began to walk around the edge. Honey-roasted lost her balance and fell in. Unsalted, quite alarmed, looked down into the vat and shouted, "Are you alright, Honey?" Honey surfaced, looked at him, and replied, "No, I'm a fried nut." ---------------------------------------------------- An ignorant fool posted some anti-homosexual blathering over all of the newsgroups on USENET, in order to gain complete recognition by all of its members. For months the flames soared and the poor little homophobe had to unsubscribe to most of them. One day FIDONET happened by and looked at the weary USENET. "You look pretty bad. Are you OK?" he asked. The reply from the weary network was, "No, I'm a fried net." ---------------------------------------------------- When I was in boot camp at Parris Island, one young marine was extremely clumsy, dropping his rifle several times during the daily drills. A rather excitable drill sergeant soon became angry and asked the recruit "Son, are you as clumsy with your rifle on the shooting range as you are on the field?" To which was replied, "No sir, I'm a great shot." ---------------------------------------------------- And if Usenetters had written "Monty Python & the Holy Grail" ... How do you know she's a witch? I'm a freed newt. ---------------------------------------------------- "Ginger" MacTavish had lived Down South (London), away from his family and friends, for many years. One day, a boyhood chum of his happened to be passing through town, and called him up for a chat. In the course of the conversation, his friend asked Ginger if his hair was still bright red, as it had been when they were boys. "Och, ye maun weel know", Ginger replied ... " ... I'm a grayed Scot ..." ---------------------------------------------------- Two zeros are walking down the street. One zero is coughing very badly. The coughing is getting severe, so his buddy asks him: "Are you all right?" The second zero responds: "No, I'm a phlegmed naught." ---------------------------------------------------- These three zeroes were travelling through some cold weather and became thirsty, so they stopped in at a local bar for some warmth & refreshments. When the first zero approached the bar, the bartender (whose mathematical skill didn't quite reach the level of familiarity with single-digit numbers, asked, "Say, aren't you a zero? We don't serve zeros here." The second zero tried to order and the bartender said "You're a zero too, aren't you? I already told your friend, no zeros allowed!" The last zero, before approaching the bar, stepped outside & rolled in the snow for several minutes until he was quite cold. When he re-entered the building and walked up to the bar, the bartender said "Not again! You'd better not be another zero!" To which the cold number replied, "No, I'm a frigid naught!" -------------------------------------------------------------------------------- The president of the Flintstones Fan Club walked into a bar, and the bartender, recognizing the man but not quite remembering from where, asked, "Say, aren't you the guy that's so crazy about watching the Jetsons?" The Flintstone fan's reply was, "No, I'm a Fred nut." -------------------------------------------------------------------------------- A small lizard was minding its own business when a knight rode up and, thinking the lizard to be a dragon, attacked it and bashed it over its head with a heavy ball-and-chain. Not much later, another knight (a former bartender) spotted the hurt lizard and asked, "Say, are you a wounded dragon?" The lizard, still dizzy from the blow, replied, "No, I'm a flailed newt." ---------------------------------------------------- There once was a Leprechaun fascinated by insects, which he caged and kept as pets. There were hundreds of the cages throughout his home, each containing a single insect. As it happened one day, he had forgotten to close his window while cleaning the cage of one of the smaller insects, and it escaped. The little bug was enjoying it's new found capability of unhindered flight when it chanced upon a gnome, who recognized it as his friend's pet. "Are you on your way home, little one?" the gnome asked. And the insect replied "No, I'm a freed gnat." ------------------------------ End of INTERNUTS Digest V01 Issue #13 *************************************