They say a little bit of knowledge is a dangerous thing. So, apparently, is a little bit of algebra:
(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
QED!
What's wrong with this 'proof'?
Like most of these puzzles, you will appreciate it more if you try to crack it on your own before peeking at the solution.