Recent content by shrutishukla

thankz for d project...it has proved of grt help...

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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