Eqn 2 : Tabu acted in a movie called Chandni bar..
Conclusion:Tabu is the vector form of Sridevi..
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Q: how many times can you subtract 7 from 83, and what is left afterwards?
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A: I can subtract it as many times as I want, and it leaves 76 every time.
24. Cat 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.
25. Salary Theorem
The less you know, the more you make.
Proof:
Postulate 1: Knowledge is Power.
Postulate 2: Time is Money.
As every engineer knows: Power = Work / Time
And since Knowledge = Power and Time = Money
It is therefore true that Knowledge = Work / Money .
Solving for Money, we get:
Money = Work / Knowledge
Thus, as Knowledge approaches zero, Money approaches infinity, regardless of the amount of Work done.
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Funny formulas
36. The limit as 3 goes to 4 of 3^2 is 16.
(For native LaTex speakers: $$\lim_{3 \rightarrow 4} 3^2 = 16$$)
37. 1 + 1 =3, for sufficiently large one’s.
38. The combination of the Einstein and Pythagoras discoveries:
E= m c^2= m ( a^2 + b^2)
2 and 2 is 22
39. The limit as n goes to infinity of sin (x) /n is 6.
Proof: cancel the n in the numerator and denominator.
40. As x goes to zero, the limit of 8 /x is 00 (infinity), then the limit (as x goes to zero) of Z /x is N
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Examples of inverse problems:
41. Q: To what question is the answer “9W.”
A: “Dr. Wiener, do you spell your name with a V?”
42. Q: To what question is the answer “Dr. Livingstone, I presume.”
A: “What is your full name, Dr. Presume?”
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43. Q: What does the zero say to the eight?
A: Nice belt!
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44. “Divide fourteen sugar cubes into three cups of coffee so that each cup has an odd number of sugar cubes in it.” “That’s easy: one, one, and twelve.” “But twelve isn’t odd!” “Twelve is an odd number of cubes to put in a cup of coffee…”
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45. There are three kinds of people in the world; those who can count and those who can’t.
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46. There are 10 kinds of people in the world, those who understand binary math, and those who don’t.
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47. “Do you love your math more than me?”
“Of course not, dear - I love you much more.”
“Then prove it!”
“OK… Let R be the set of all lovable objects…”
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48. A biologist, a physicist and a mathematician were sitting in a street cafe watching the crowd. Across the street they saw a man and a woman entering a building. Ten minutes they reappeared together with a third person.
- They have multiplied, said the biologist.
- Oh no, an error in measurement, the physicist sighed.
- If exactly one person enters the building now, it will be empty again, the mathematician concluded.
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49. Several scientists were all posed the following question: “What is 2 * 2 ?”
The engineer whips out his slide rule (so it’s old) and shuffles it back and forth, and finally announces “3.99″.
The physicist consults his technical references, sets up the problem on his computer, and announces “it lies between 3.98 and 4.02″.
The mathematician cogitates for a while, then announces: “I don’t know what the answer is, but I can tell you, an answer exists!”.
Philosopher smiles: “But what do you mean by 2 * 2 ?”
Logician replies: “Please define 2 * 2 more precisely.”
The sociologist: “I don’t know, but is was nice talking about it”.
Behavioral Ecologist: “A polygamous mating system”.
Medical Student : “4″
All others looking astonished : “How did you know ??”
Medical Student : “I memorized it.”
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50. A mathematician, a physicist, and an engineer were traveling through Scotland when they saw a black sheep through the window of the train.
“Aha,” says the engineer, “I see that Scottish sheep are black.”
“Hmm,” says the physicist, “You mean that some Scottish sheep are black.”
“No,” says the mathematician, “All we know is that there is at least one sheep in Scotland, and that at least one side of that one sheep is black
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51. A team of engineers were required to measure the height of a flag pole. They only had a measuring tape, and were getting quite frustrated trying to keep the tape along the pole. It kept falling down, etc. A mathematician comes along, finds out their problem, and proceeds to remove the pole from the ground and measure it easily. When he leaves, one engineer says to the other: “Just like a mathematician! We need to know the height, and he gives us the length!”
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52. One day a farmer called up an engineer, a physicist, and a mathematician and asked them to fence of the largest possible area with the least amount of fence.
The engineer made the fence in a circle and proclaimed that he had the most efficient design.
The physicist made a long, straight line and proclaimed “We can assume the length is infinite…” and pointed out that fencing off half of the Earth was certainly a more efficient way to do it.
The Mathematician just laughed at them. He built a tiny fence around himself and said “I declare myself to be on the outside.”
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53. The physicist and the engineer are in a hot-air balloon. Soon, they find themselves lost in a canyon somewhere. They yell out for help: “Helllloooooo! Where are we?”
15 minutes later, they hear an echoing voice: “Helllloooooo! You’re in a hot-air balloon!!”
The physicist says, “That must have been a mathematician.”
The engineer asks, “Why do you say that?”
The physicist replied: “The answer was absolutely correct, and it was utterly useless.”
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54. How they prove that all odd integers higher than 2 are prime?
Mathematician: 3 is a prime, 5 is a prime, 7 is a prime, and by induction - every odd integer higher than 2 is a prime.
Physicist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is an experimental error, 11 is a prime,…
Engineer: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime, 11 is a prime,…
Programmer: 3 is a prime, 5 is a prime, 7 is a prime, 7 is a prime, 7 is a prime,…
Salesperson: 3 is a prime, 5 is a prime, 7 is a prime, 9 — we’ll do for you the best we can,…
Computer Software Salesperson: 3 is prime, 5 is prime, 7 is prime, 9 will be prime in the next release,…
Biologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 — results have not arrived yet,…
Advertiser: 3 is a prime, 5 is a prime, 7 is a prime, 11 is a prime,…
Lawyer: 3 is a prime, 5 is a prime, 7 is a prime, 9 — there is not enough evidence to prove that it is not a prime,…
Accountant: 3 is prime, 5 is prime, 7 is prime, 9 is prime, deducing 10% tax and 5% other obligations.
Statistician: Let’s try several randomly chosen numbers: 17 is a prime, 23 is a prime, 11 is a prime…
Professor: 3 is prime, 5 is prime, 7 is prime, and the rest are left as an exercise for the student.
Computational linguist: 3 is an odd prime, 5 is an odd prime, 7 is an odd prime, 9 is a very odd prime,…
Psychologist: 3 is a prime, 5 is a prime, 7 is a prime, 9 is a prime but tries to suppress it,…
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93. Math and Alcohol don’t mix, so… PLEASE DON’T DRINK AND DERIVE
Motto of the society: Mathematicians Against Drunk Deriving
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94. Q: What is the area of a circle?
A: pi R^2?
R: Pie are not square. Pie are round. Cornbread are square.
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95. Q: What’s a polar bear?
A: A rectangular bear after a coordinate transform.
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96. Noah’s Ark lands after The Flood and Noah releases all the animals, saying, “Go forth and multiply.” Several months pass and Noah decides to check up on the animals. All are doing fine except a pair of snakes. “What’s the problem?” asks Noah. “Cut down some trees and let us live there,” say the snakes. Noah follows their advice. Several more weeks pass and Noah checks up on the snakes again. He sees lots of little snakes; everybody is happy. Noah says, “So tell me how the trees helped.” “Certainly,” reply the snakes. “We’re adders, and we need logs to multiply.”
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97. Life is complex. It has real and imaginary components.
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98. Q: What do you get when you cross an elephant and a banana?
A: | elephant | * | banana | * sin(theta)
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99. Q: What do you get if you cross a mosquito with a mountain climber.
A: You can’t cross a vector with a scalar.
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100. Professional secrets.
The highest moments in the life of a mathematician are the first few moments after one has proved the result, but before one finds the mistake.
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101. Golden rule of deriving: never trust any result that was proved after 11 PM.
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102. The professional quality of a mathematician is inversely proportional to the importance it attaches to space and equipment.
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103. Relations between pure and applied mathematicians are based on trust and understanding. Namely, pure mathematicians do not trust applied mathematicians, and applied mathematicians do not understand pure mathematicians.
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104. Some mathematicians become so tense these days that they that they do not go to sleep during seminars.
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105. Top ten excuses for not doing homework:
I accidentally divided by zero and my paper burst into flames.
Isaac Newton’s birthday.
I could only get arbitrarily close to my textbook. I couldn’t actually reach it.
I have the proof, but there isn’t room to write it in this margin.
I was watching the World Series and got tied up trying to prove that it converged.
I have a solar powered calculator and it was cloudy.
I locked the paper in my trunk but a four-dimensional dog got in and ate it.
I couldn’t figure out whether i am the square of negative one or i is the square root of negative one.
I took time out to snack on a doughnut and a cup of coffee.
I spent the rest of the night trying to figure which one to dunk.
I could have sworn I put the homework inside a Klein bottle, but this morning I couldn’t find it.
Warning! It is against the rule to use these excuses in my classes!
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106. A lecturer tells some students to learn the phone-book by heart.
The mathematicians are baffled: `By heart? You kidding?’
The mathematicians are baffled: `By heart? You kidding?’
The physics-students ask: `Why?’
The engineers sigh: `Do we have to?’
The chemistry-students ask: `Till next Monday?’
The accounting-students (scribbling): `Till tomorrow?’
The laws-students answer: `We already have.’
The medicine-students ask: `Should we start on the Yellow Pages?’
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107. Dean, to the physics department. “Why do I always have to give you guys so much money, for laboratories and expensive equipment and stuff. Why couldn’t you be like the math. department - all they need is money for pencils, paper and waste-paper baskets. Or even better, like the philosophy department. All they need are pencils and paper.”
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108. A mathematician organizes a lottery in which the prize is an infinite amount of money. When the winning ticket is drawn, and the jubilant winner comes to claim his prize, the mathematician explains the mode of payment: “1 dollar now, 1/2 dollar next week, 1/3 dollar the week after that…”
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109. A mathematician decides he wants to learn more about practical problems. He sees a seminar with a nice title: “The Theory of Gears.” So he goes. The speaker stands up and begins, “The theory of gears with a real number of teeth is well known …”
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110. When a statistician passes the airport security check, they discover a bomb in his bag. He explains. “Statistics shows that the probability of a bomb being on an airplane is 1/1000. However, the chance that there are two bombs at one plane is 1/1000000. So, I am much safer…”
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111. Q: What will a logician choose: a half of an egg or eternal bliss in the afterlife? A: A half of an egg! Because nothing is better than eternal bliss in the afterlife, and a half of an egg is better than nothing.
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112. Old mathematicians never die; they just lose some of their functions.
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113. “God geometrizes” says Plato.
and here is the analytical continuation of this saying:
Biologists think they are biochemists,
Biochemists think they are Physical Chemists,
Physical Chemists think they are Physicists,
Physicists think they are Gods,
And God thinks he is a Mathematician.
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114. Physicists defer only to mathematicians, mathematicians defer only to God.
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Equation:1
Study=Don’t Fail
Equation:2
Don’t Study=Fail
Adding Eq1 and Eq2,
Study+Don’t Study=Fail+Don’t Fail
=>Study(1+Don’t)=Fail(1+Don’t)
=>Study=Fail Ans.
Then why wasting time in study???
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5. Theorems
Here, the powerful mathematical methods are successively applied to the “real life problems”.
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Interesting Theorem:
All positive integers are interesting.
Proof:
Assume the contrary. Then there is a lowest non-interesting positive integer. But, hey, that’s pretty interesting! A contradiction.
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Boring Theorem:
All positive integers are boring.
Proof:
Assume the contrary. Then there is a lowest non-boring positive integer. Who cares!
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Notes on the horse colors problem
Lemma 1. All horses are the same color. (Proof by induction)
Proof. It is obvious that one horse is the same color. Let us assume the proposition P(k) that k horses are the same color and use this to imply that k+1 horses are the same color. Given the set of k+1 horses, we remove one horse; then the remaining k horses are the same color, by hypothesis. We remove another horse and replace the first; the k horses, by hypothesis, are again the same color. We repeat this until by exhaustion the k+1 sets of k horses have been shown to be the same color. It follows that since every horse is the same color 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 color.
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 certainly 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 number 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 color, and by the lemma that does not exist.
Corollary 1. Everything is the same color.
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 universally-quantified conditional ‘For all x, if x is a horse, then x is the same color,’ 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 color.’
Corollary 2. Everything is white.
Proof. If a sentential formula in x is logically true, then any particular substitution instance of it is a true sentence. In particular then: ‘for all x, if x is an elephant, then x is the same color’ is true. Now it is manifestly axiomatic that white elephants exist (for proof by blatant assertion consult Mark Twain ‘The Stolen White Elephant’). 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 consequent 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.
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The mathematical theory of big game hunting (Aug-Sept. AMM, 446-447, 1938):
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According to statistics, there are 42 million alligator eggs laid every year. Of those, only about half get hatched. Of those that hatch, three fourths of them get eaten by predators in the first 36 days. And of the rest, only 5 percent get to be a year old for one reason or another. Isn’t statistics wonderful? If it weren’t for statistics, we’d be eaten by alligators!
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How to prove it. Guide for lecturers.
Proof by vigorous handwaving:
Works well in a classroom or seminar setting.
Proof by forward reference:
Reference is usually to a forthcoming paper of the author, which is often not as forthcoming as at first.
Proof by funding:
How could three different government agencies be wrong?
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 omission:
“The reader may easily supply the details” or “The other 253 cases are analogous”
Proof by deferral:
“We’ll prove this later in the course”.
Proof by picture:
A more convincing form of proof by example. Combines well with proof by omission.
Proof by intimidation:
“Trivial.”
Proof by adverb:
“As is quite clear, the elementary aforementioned statement is obviously valid.”
Proof by seduction:
“Convince yourself that this is true! “
Proof by cumbersome notation:
Best done with access to at least four alphabets and special symbols.
Proof by exhaustion:
An issue or two of a journal devoted to your proof is useful.
Proof by obfuscation:
A long plotless sequence of true and/or meaningless syntactically related statements.
Proof by wishful citation:
The author cites the negation, converse, or generalization of a theorem from the literature to support his claims.
Proof by eminent authority:
“I saw Karp in the elevator and he said it was probably NP- complete.”
Proof by personal communication:
“Eight-dimensional colored cycle stripping is NP-complete [Karp, personal communication].”
Proof by reduction to the wrong problem:
“To see that infinite-dimensional colored cycle stripping is decidable, we reduce it to the halting problem.”
Proof by reference to inaccessible literature:
The author cites a simple corollary of a theorem to be found in a privately circulated memoir of the Slovenian Philological Society, 1883.
Proof by importance:
A large body of useful consequences all follow from the proposition in question.
Proof by accumulated evidence:
Long and diligent search has not revealed a counterexample.
Proof by cosmology:
The negation of the proposition is unimaginable or meaningless. Popular for proofs of the existence of God.
Proof by mutual reference:
In reference A, Theorem 5 is said to follow from Theorem 3 in reference B, which is shown to follow from Corollary 6.2 in reference C, which is an easy consequence of Theorem 5 in reference A.
Proof by metaproof:
A method is given to construct the desired proof. The correctness of the method is proved by any of these techniques.
Proof by vehement assertion:
It is useful to have some kind of authority relation to the audience.
Proof by ghost reference:
Nothing even remotely resembling the cited theorem appears in the reference given.
Proof by semantic shift:
Some of the standard but inconvenient definitions are changed for the statement of the result.
Proof by appeal to intuition:
Cloud-shaped drawings frequently help here.
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Dictionary of Definitions of Terms Commonly Used in Math. lectures.
The following is a guide to terms which are commonly used but rarely defined. In the search for proper definitions for these terms we found no authoritative, nor even recognized, source. Thus, we followed the advice of mathematicians handed down from time immortal: “Wing It.”
CLEARLY:
I don’t want to write down all the “in- between” steps.
TRIVIAL:
If I have to show you how to do this, you’re in the wrong class.
OBVIOUSLY:
I hope you weren’t sleeping when we discussed this earlier, because I refuse to repeat it.
RECALL:
I shouldn’t have to tell you this, but for those of you who erase your memory tapes after every test…
WLOG (Without Loss Of Generality):
I’m not about to do all the possible cases, so I’ll do one and let you figure out the rest.
IT CAN EASILY BE SHOWN:
Even you, in your finite wisdom, should be able to prove this without me holding your hand.
CHECK or CHECK FOR YOURSELF:
This is the boring part of the proof, so you can do it on your own time.
SKETCH OF A PROOF:
I couldn’t verify all the details, so I’ll break it down into the parts I couldn’t prove.
HINT:
The hardest of several possible ways to do a proof.
BRUTE FORCE (AND IGNORANCE):
Four special cases, three counting arguments, two long inductions, “and a partridge in a pair tree.”
SOFT PROOF:
One third less filling (of the page) than your regular proof, but it requires two extra years of course work just to understand the terms.
ELEGANT PROOF:
Requires no previous knowledge of the subject matter and is less than ten lines long.
SIMILARLY:
At least one line of the proof of this case is the same as before.
CANONICAL FORM:
4 out of 5 mathematicians surveyed recommended this as the final form for their students who choose to finish.
TFAE (The Following Are Equivalent):
If I say this it means that, and if I say that it means the other thing, and if I say the other thing…
BY A PREVIOUS THEOREM:
I don’t remember how it goes (come to think of it I’m not really sure we did this at all), but if I stated it right (or at all), then the rest of this follows.
TWO LINE PROOF:
I’ll leave out everything but the conclusion, you can’t question ‘em if you can’t see ‘em.
BRIEFLY:
I’m running out of time, so I’ll just write and talk faster.
LET’S TALK THROUGH IT:
I don’t want to write it on the board lest I make a mistake.
PROCEED FORMALLY:
Manipulate symbols by the rules without any hint of their true meaning (popular in pure math courses).
QUANTIFY:
I can’t find anything wrong with your proof except that it won’t work if x is a moon of Jupiter (Popular in applied math courses).
PROOF OMITTED:
Trust me, It’s true.
Traditional - contemporary math dictionary.
WHAT’S OUT AND WHAT’S IN FOR MATHEMATICAL TERMS
Today it is considered an egregious faux pas to speak or write in the
crude antedated terms of our grandfathers. To assist the isolated
student and the less sophisticated teacher, I have prepared the
following list of currently fashionable mathematical terms in
academia. I pass this list on to the general public as a matter of
charity and in the hope that it will lead to more refined elucidation
from young scholars.
thinking: hypothesizing.
proof by contradiction or indirect proof: reductio ad absurdum.
mistake: non sequitur.
starting place: handle.
with corresponding changes: mutatis mutandis.
counterexample: pathological exception.
consequently: ipso facto.
swallowing results: digesting proofs.
therefore: ergo.
has an easy-to-understand, but hard-to-find solution: obvious.
has two easy-to-understand, but hard-to-find solutions: trivial.
truth: tautology.
empty: vacuous.
drill problems: plug-and-chug work.
criteria: rubric.
example: substantive
instantiation.
similar structure: homomorphic.
very similar structure: isomorphic.
same area: isometric.
arithmetic: number theory.
count: enumerate.
one: unity.
generally/specifically: globally/locally.
constant: invariant.
bonus result: corollary.
distance: metric measure.
several: a plurality.
function/argument: operator/operand.
separation/joining: bifurcation/confluence.
fourth power or quartic: biquadratic.
random: stochastic.
unique condition: a singularity.
uniqueness: unicity.
tends to zero: vanishes.
tip-top point: apex.
half-closed: half-open.
concave: non-convex.
rectangular prisms: parallelepipeds.
perpendicular (adj.): orthogonal.
perpendicular (n.): normal.
Euclid: Descartes.
Fermat: Wiles.
path: trajectory.
shift: rectilinear translation.
similar: homologous.
very similar: congruent.
whopper-jawed: skew or oblique.
change direction: perturb.
join: concatenate.
approximate to two or more places: accurate.
high school geometry or plane geometry: geometry of the Euclidean plane under the Pythagorean metric.
clever scheme: algorithm.
initialize to zero: zeroize.
* : splat.
{ : squiggle.
decimal: denary.
alphabetical order: lexical order.
a divide-and-conquer method: an algorithm of logarithmic order.
student ID numbers: witty passwords.
numerology and number sophistry: descriptive statistics
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A Mathematician (M) and an Engineer (E) attend a lecture by a Physicist. The topic concerns Kulza-Klein theories involving physical processes that occur in spaces with dimensions of 9, 12 and even higher. The M is sitting, clearly enjoying the lecture, while the E is frowning and looking generally confused and puzzled. By the end the E has a terrible headache. At the end, the M comments about the wonderful lecture.
E: “How do you understand this stuff?”
M: “I just visualize the process”
E: “How can you POSSIBLY visualize something that occurs in 9-dimensional space?”
M: “Easy, first visualize it in N-dimensional space, then let N go to 9″
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