X defined over the integers:

add X X's giving:

$ X + X + ... + X = X^2 $

so, differentiating, we have:

$ 1 + 1 + ... + 1 = 2*X $

with X 1's, giving:

$ X = 2 * X $

therefore:

1 = 2

(Taken from the mysterious visitor)

Paradox is solved if we note that the ammount of X's in the left side of the equation varies with X, so you can't differentiate the equation by just differentiating term-by-term