Here is a proof that 2 = 0:

assume x=2                                X = 2
multiply by x on both sides             X*X = 2X
subtract 4 from both sides          X*X - 4 = 2X - 4
factorise                        (X+2)(X-2) = 2(X-2)
divide by (x-2) on both sides           X+2 = 2
subtract 2 from both sides                X = 0

We started with X = 2 but we have showed that X = 0 at the same time! Where does the logic fail?

 [Ref: ZBHF]

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