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With the purpose of causing riots and revolts among mathematicans all over the world, I hereby bring forth the proof that 1 = 2.

x=y

multiply by x:
x^2 = xy

subtract y^2:
x^2 - y^2 = xy - y^2

Factor both sides:
(x+y)(x-y) = y(x-y)

Divide by (x-y):
x+y=y

x=y, so substitue y for x:
y+y=y
2y = y

divide by y and we get:
2=1




(You guys just cannot seem to appreciate a small piece of ironic maths, can you?)
As far as I can tell one problem with this proof is that it initially starts with the assumption that x=y then the term (x-y) appears as a factor. From the initial assumption this has a value of zero and so when it is removed the division by zero occurs.

Another way of looking at it is that the third equation (x^2 - y^2 = xy - y^2) is a statement that zero is equal to zero applying the initial assumption that x = y. So if you remove factors of zero from either side then the rest is meaningless. The fact that 1 times zero is equal to 5000 times zero does not mean that 1 equals 5000.

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