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Wednesday, February 23, 2011

Maths Rocks....It can screw ur brains


1.N equals N plus one joke




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 - n(2n+1) + 1/4(2n+1)^2

This may be written:
[ (n+1) - 1/2(2n+1) ]^2 = [ n - 1/2(2n+1) ]^2

Taking 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 




2.Three is equal to four joke




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 




3.All numbers are equal joke






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 are the same, and math is pointless.

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