A Proof That 2 = 1

(1) X = Y Given



(2) X2 = XY Multiply both sides by X



(3) X2 - Y2 = XY - Y2 Subtract Y2 from both sides



(4) (X + Y)(X - Y) = Y(X - Y) Factor both sides



(5) (X + Y) = Y Cancel out common factors



(6) Y + Y = Y Substitute in from line (1)



(7) 2Y = Y Collect the Y's



(8) 2 = 1 Divide both sides by Y




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