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Four is equal to five Theorem: 4 = 5 Proof: -20 = -20 16 - 36 = 25 - 45 4^2 - 9*4 = 5^2 - 9*5 4^2 - 9*4 + 81/4 = 5^2 - 9*5 + 81/4 (4 - 9/2)^2 = (5 - 9/2)^2 4 - 9/2 = 5 - 9/2 4 = 5

N equals N plus one Theorem: n=n+1 Proof: (n+1)^2 = n^2 + 2*n + 1 Bring 2n+1 to the left: (n+1)^2 - (2n+1) = n^2 Substract 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...

Dollars equal cents Theorem: 1$ = 1c. Proof: And another that gives you a sense of money disappearing. 1$ = 100c = (10c)^2 = (0.1$)^2 = 0.01$ = 1c Here $ 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...

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

One equal to one half 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 -...

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

All numbers are equal Theorem: All numbers are equal. Proof: Choose arbitrary a and b, and let t = a + b. Then a + b = t (a + b)(a - b) = t(a - b) a^2 - b^2 = ta - tb a^2 - ta = b^2 - tb a^2 - ta + (t^2)/4 = b^2 - tb + (t^2)/4 (a - t/2)^2 = (b - t/2)^2 a - t/2 = b - t/2 a = b So all numbers...

One plus one are two Theorem: 1 + 1 = 2 Proof: n(2n - 2) = n(2n - 2) n(2n - 2) - n(2n - 2) = 0 (n - n)(2n - 2) = 0 2n(n - n) - 2(n - n) = 0 2n - 2 = 0 2n = 2 n + n = 2 or setting n = 1 1 + 1 = 2

Dollars equal ten cents Theorem: 1$ = 10 cent Proof: We know that $1 = 100 cents Divide both sides by 100 $ 1/100 = 100/100 cents => $ 1/100 = 1 cent Take square root both side => squr($1/100) = squr (1 cent) => $ 1/10 = 1 cent Multiply both side by 10 => $1 = 10 cent

Three is equal to four Theorem: 3=4 Proof: Suppose: a + b = c This can also be written as: 4a - 3a + 4b - 3b = 4c - 3c After reorganizing: 4a + 4b - 4c = 3a + 3b - 3c Take the constants out of the brackets: 4 * (a+b-c) = 3 * (a+b-c) Remove the same term left and right: 4 = 3

Equal positive integers 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...

Marketing translations Cracking an international market is a goal of most growing corporations. It shouldn't be that hard, yet even the big multi-nationals run into trouble because of language and cultural differences. For example, observe the following examples below. The name Coca-Cola in...

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What's on your back? Three men are traveling in the Amazon, a German, an American, and a Mexican, and they get captured by some Amazons. The head of the tribe says to the German, "What do you want on your back for your whipping?" The German responds, "I will take oil!" So they put oil on his...

A lecture about English A linguistics professor was lecturing to his English class one day. "In English," he said, "A double negative forms a positive. In some languages, though, such as Russian, a double negative is still a negative. However, there is no language wherein a double positive can...

Tips to improve your writing 1. Avoid alliteration. Always. 2. Never use a long word when a diminutive one will do. 3. Employ the vernacular. 4. Eschew ampersands & abbreviations, etc. 5. Parenthetical remarks (however relevant) are unnecessary. 6. Remember to never split an infinitive...

Europe English The European Commission has just announced an agreement whereby English will be the official language of the EU rather than German which was the other possibility. As part of the negotiations, Her Majesty's Government conceded that English spelling had some room for improvement...

Poem of English Dearest creature in creation, Study English pronunciation. I will teach you in my verse Sounds like corpse, corps, horse, and worse. I will keep you, Suzy, busy, Make your head with heat grow dizzy. Tear in eye, your dress will tear. So shall I! Oh hear my prayer. Just compare...