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|Theorem : All numbers are equal to zero.Proof: Suppose that a=b. Thena = ba^2 = aba^2 - b^2 = ab - b^2(a + b)(a - b) = b(a - b)a + b = ba = 0Furthermore if a + b = b, and a = b, then b + b = b, and 2b = b, which mean that 2 = 1.

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|Theorem: 3=4Proof:Suppose:a + b = cThis can also be written as:4a - 3a + 4b - 3b = 4c - 3cAfter reorganizing:4a + 4b - 4c = 3a + 3b - 3cTake the constants out of the brackets:4 * (a+b-c) = 3 * (a+b-c)Remove the same term left and right:4 = 3

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|Theorem: All positive integers are equal.Proof: Sufficient to show that for any two positive integers, A and B, A = B.Further, it is sufficient to show that for all N > 0, if A and B (positive integers) satisfy (MAX(A, B) = N) then A = B.Proceed by induction.If N = 1, then A and B, being positive integers, must both be 1. So A = B.Assume that the theorem is true for some value k. Take A and B with MAX(A, B) = k+1. Then MAX((A-1), (B-1)) = k. And hence (A-1) = (B-1). Consequently, A = B.

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|''Psst, c'mere,'' said the shifty-eyed man wearing a long black trenchcoat, as he beckoned me off the rainy street into a damp dark alley. I followed.''What are you selling?'' I asked.''Geometrical algebra drugs.''''Huh!?''''Geometry drugs. Ya got your uppers, your downers, your sidewaysers, your inside-outers...''''Stop right there,'' I interrupted. ''I've never heard of inside-outers.''''Oh, man, you'll love 'em. Makes you feel like M.C. ever-lovin' Escher on a particularly weird day.''''Go on...''''OK, your inside-outers, your arbitrary bilinear mappers, and here, heh, here are the best ones,'' he said, pulling out a large clear bottle of orange pills.''What are those, then?'' I asked.''Givens transformers. They'll rotate you about more planes than you even knew existed.''''Sounds gross. What about those bilinear mappers?''''There's a whole variety of them. Here's one you'll love -- they call it 'One Over Z' on the street. Take one of these little bad boys and you'll be on speaking terms with the Point at Infinity.''

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|Theorem: 1$ = 1c.Proof:And another that gives you a sense of money disappearing.1$ = 100c= (10c)^2= (0.1$)^2= 0.01$= 1cHere $ means dollars and c means cents. This one is scary in that I have seen PhD's in math who were unable to see what was wrong with this one. Actually I am crossposting this to sci.physics because I think that the latter makes a very nice introduction to the importance of keeping track of your dimensions.

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|Theorem: 1$ = 10 centProof:We know that $1 = 100 centsDivide both sides by 100$ 1/100 = 100/100 cents=> $ 1/100 = 1 centTake square root both side=> squr($1/100) = squr (1 cent)=> $ 1/10 = 1 cent Multiply both side by 10=> $1 = 10 cent

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|Theorem: n=n+1Proof:(n+1)^2 = n^2 + 2*n + 1Bring 2n+1 to the left:(n+1)^2 - (2n+1) = n^2Substract n(2n+1) from both sides and factoring, we have:(n+1)^2 - (n+1)(2n+1) = n^2 - n(2n+1)Adding 1/4(2n+1)^2 to both sides yields:(n+1)^2 - (n+1)(2n+1) + 1/4(2n+1)^2 = n^2 - n(2n+1) + 1/4(2n+1)^2This may be written:[ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2Taking the square roots of both sides:(n+1) - 1/2(2n+1) = n - 1/2(2n+1)Add 1/2(2n+1) to both sides:n+1 = n

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|Theorem: e=1Proof:2*e = f2^(2*pi*i)e^(2*pi*i) = f^(2*pi*i)e^(2*pi*i) = 1Therefore:2^(2*pi*i) = f^(2*pi*i)2=fThus:e=1

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|Theorem: 1 = 1/2:Proof:We can re-write the infinite series 1/(1*3) + 1/(3*5) + 1/(5*7) + 1/(7*9)+...as 1/2((1/1 - 1/3) + (1/3 - 1/5) + (1/5 - 1/7) + (1/7 - 1/9) + ... ).All terms after 1/1 cancel, so that the sum is 1/2.We can also re-write the series as (1/1 - 2/3) + (2/3 - 3/5) + (3/5 - 4/7)+ (4/7 - 5/9) + ...All terms after 1/1 cancel, so that the sum is 1.Thus 1/2 = 1.

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|Prove that the crocodile is longer than it is wide.Lemma 1. The crocodile is longer than it is green: Let's look at the crocodile. It is long on the top and on the bottom, but it is green only on the top. Therefore, the crocodile is longer than it is green.Lemma 2. The crocodile is greener than it is wide: Let's look at the crocodile. It is green along its length and width, but it is wide only along its width. Therefore, the crocodile is greener than it is wide.From Lemma 1 and Lemma 2 we conclude that the crocodile is longer than it is wide.

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|Theorem: log(-1) = 0Proof:a. log[(-1)^2] = 2 * log(-1)On the other hand:b. log[(-1)^2] = log(1) = 0Combining a) and b) gives:2* log(-1) = 0Divide both sides by 2:log(-1) = 0

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|Theorem: 4 = 5Proof:-20 = -2016 - 36 = 25 - 454^2 - 9*4 = 5^2 - 9*54^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4(4 - 9/2)^2 = (5 - 9/2)^24 - 9/2 = 5 - 9/24 = 5

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|Theorem: All numbers are equal.Proof: Choose arbitrary a and b, and let t = a + b. Thena + b = t(a + b)(a - b) = t(a - b)a^2 - b^2 = ta - tba^2 - ta = b^2 - tba^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4(a - t/2)^2 = (b - t/2)^2a - t/2 = b - t/2a = bSo all numbers are the same, and math is pointless.

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|Theorem: 1 = -1Proof:1 = sqrt(1) = sqrt(-1 * -1) = sqrt(-1) * sqrt(-1) = 1^ = -1Also one can disprove the axiom that things equal to the same thing are equal to each other.1 = sqrt(1)-1 = sqrt(1)Therefore 1 = -1As an alternative method for solving:Theorem: 1 = -1Proof:x=1x^2=xx^2-1=x-1(x+1)(x-1)=(x-1)(x+1)=(x-1)/(x-1)x+1=1x=00=1=> 0/0=1/1=1

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|''First and above all he was a logician. At least thirty-five years of the half-century or so of his existence had been devoted exclusively to proving that two and two always equal four, except in unusual cases, where they equal three or five, as the case may be.'' -- Jacques Futrelle, ''The Problem of Cell 13''Most mathematicians are familiar with -- or have at least seen references in the literature to -- the equation 2 + 2 = 4. However, the less well known equation 2 + 2 = 5 also has a rich, complex history behind it. Like any other complex quantitiy, this history has a real part and an imaginary part; we shall deal exclusively with the latter here.Many cultures, in their early mathematical development, discovered the equation 2 + 2 = 5. For example, consider the Bolb tribe, descended from the Incas of South America. The Bolbs counted by tying knots in ropes. They quickly realized that when a 2-knot rope is put together with another 2-knot rope, a 5-knot rope results.Recent findings indicate that the Pythagorean Brotherhood discovered a proof that 2 + 2 = 5, but the proof never got written up. Contrary to what one might expect, the proof's nonappearance was not caused by a cover-up such as the Pythagoreans attempted with the irrationality of the square root of two. Rather, they simply could not pay for the necessary scribe service. They had lost their grant money due to the protests of an oxen-rights activist who objected to the Brotherhood's method of celebrating the discovery of theorems. Thus it was that only the equation 2 + 2 = 4 was used in Euclid's ''Elements,'' and nothing more was heard of 2 + 2 = 5 for several centuries.Around A.D. 1200 Leonardo of Pisa (Fibonacci) discovered that a few weeks after putting 2 male rabbits plus 2 female rabbits in the same cage, he ended up with considerably more than 4 rabbits. Fearing that too strong a challenge to the value 4 given in Euclid would meet with opposition, Leonardo conservatively stated, ''2 + 2 is more like 5 than 4.'' Even this cautious rendition of his data was roundly condemned and earned Leonardo the nickname ''Blockhead.'' By the way, his practice of underestimating the number of rabbits persisted; his celebrated model of rabbit populations had each birth consisting of only two babies, a gross underestimate if ever there was one.Some 400 years later, the thread was picked up once more, this time by the French mathematicians. Descartes announced, ''I think 2 + 2 = 5; therefore it does.'' However, others objected that his argument was somewhat less than totally rigorous. Apparently, Fermat had a more rigorous proof which was to appear as part of a book, but it and other material were cut by the editor so that the book could be printed with wider margins.Between the fact that no definitive proof of 2 + 2 = 5 was available and the excitement of the development of calculus, by 1700 mathematicians had again lost interest in the equation. In fact, the only known 18th-century reference to 2 + 2 = 5 is due to the philosopher Bishop Berkeley who, upon discovering it in an old manuscript, wryly commented, ''Well, now I know where all the departed quantities went to -- the right-hand side of this equation.'' That witticism so impressed California intellectuals that they named a university town after him.But in the early to middle 1800's, 2 + 2 began to take on great significance. Riemann developed an arithmetic in which 2 + 2 = 5, paralleling the Euclidean 2 + 2 = 4 arithmetic. Moreover, during this period Gauss produced an arithmetic in which 2 + 2 = 3. Naturally, there ensued decades of great confusion as to the actual value of 2 + 2. Because of changing opinions on this topic, Kempe's proof in 1880 of the 4-color theorem was deemed 11 years later to yield, instead, the 5-color theorem. Dedekind entered the debate with an article entitled ''Was ist und was soll 2 + 2?''Frege thought he had settled the question while preparing a condensed version of his ''Begriffsschrift.'' This condensation, entitled ''Die Kleine Begriffsschrift (The Short Schrift),'' contained what he considered to be a definitive proof of 2 + 2 = 5. But then Frege received a letter from Bertrand Russell, reminding him that in ''Grundbeefen der Mathematik'' Frege had proved that 2 + 2 = 4. This contradiction so discouraged Frege that he abandoned mathematics altogether and went into university administration.Faced with this profound and bewildering foundational question of the value of 2 + 2, mathematicians followed the reasonable course of action: they just ignored the whole thing. And so everyone reverted to 2 + 2 = 4 with nothing being done with its rival equation during the 20th century. There had been rumors that Bourbaki was planning to devote a volume to 2 + 2 = 5 (the first forty pages taken up by the symbolic expression for the number five), but those rumor remained unconfirmed. Recently, though, there have been reported computer-assisted proofs that 2 + 2 = 5, typically involving computers belonging to utility companies. Perhaps the 21st century will see yet another revival of this historic equation.The above was written by Houston Euler.

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|Analysis:1. Differentiate it and put into the refrig. Then integrate it in the refrig.2. Redefine the measure on the referigerator (or the elephant).3. Apply the Banach-Tarsky theorem.Number theory:1. First factorize, second multiply.2. Use induction. You can always squeeze a bit more in.Algebra:1. Step 1. Show that the parts of it can be put into the refrig. Step 2. Show that the refrig. is closed under the addition.2. Take the appropriate universal refrigerator and get a surjection from refrigerator to elephant.Topology:1. Have it swallow the refrig. and turn inside out.2. Make a refrig. with the Klein bottle.3. The elephant is homeomorphic to a smaller elephant.4. The elephant is compact, so it can be put into a finite collection of refrigerators. That's usually good enough.5. The property of being inside the referigerator is hereditary. So, take the elephant's mother, cremate it, and show that the ashes fit inside the refrigerator.6. For those who object to method 3 because it's cruel to animals. Put the elephant's BABY in the refrigerator.Algebraic topology:Replace the interior of the refrigerator by its universal cover, R^3.Linear algebra:1. Put just its basis and span it in the refrig.2. Show that 1% of the elephant will fit inside the refrigerator. By linearity, x% will fit for any x.Affine geometry:There is an affine transformation putting the elephant into the refrigerator.Set theory:1. It's very easy! Refrigerator = { elephant } 2) The elephant and the interior of the refrigerator both have cardinality c.Geometry:Declare the following:Axiom 1. An elephant can be put into a refrigerator.Complex analysis:Put the refrig. at the origin and the elephant outside the unit circle. Then get the image under the inversion.Numerical analysis:1. Put just its trunk and refer the rest to the error term.2. Work it out using the Pentium.Statistics:1. Bright statistician. Put its tail as a sample and say ''Done.''2. Dull statistician. Repeat the experiment pushing the elephant to the refrig.3. Our NEW study shows that you CAN'T put the elephant in the refrigerator.

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|Theorem: 1 + 1 = 2Proof:n(2n - 2) = n(2n - 2)n(2n - 2) - n(2n - 2) = 0(n - n)(2n - 2) = 02n(n - n) - 2(n - n) = 02n - 2 = 02n = 2n + n = 2or setting n = 11 + 1 = 2

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|An engineer, a physicist, and a mathematician are trying to set up a fenced-in area for some sheep, but they have a limited amount of building material. The engineer gets up first and makes a square fence with the material, reasoning that it's a pretty good working solution. ''No no,'' says the physicist, ''there's a better way.'' He takes the fence and makes a circular pen, showing how it encompasses the maximum possible space with the given material.Then the mathematician speaks up: ''No, no, there's an even better way.'' To the others' amusement he proceeds to construct a little tiny fence around himself, then declares:''I define myself to be on the outside.''

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|It is proven that the celebration of birthdays is healthy. Statistics show that those people who celebrate the most birthdays become the oldest. -- S. den Hartog, Ph D. Thesis Universtity of Groningen.

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|Hello, this is probably 438-9012, yes, the house of the famous statistician. I'm probably not at home, or not wanting to answer the phone, most probably the latter, according to my latest calculations. Supposing that the universe doesn't end in the next 30 seconds, the odds of which I'm still trying to calculate, you can leave your name, phone number, and message, and I'll probably phone you back. So far the probability of that is about 0.645. Have a nice day.

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