Magic with numbers

1. The Paradox of the digits

It's now official: 1=2

And here is the proof...

(1) Given X = Y
(2) XX = XY Multiply both sides by X
(3) XX - 2Y = XY - 2Y Subtract 2Y 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

Therefore 2 = 1 !!!!