Two = One
A Proof That 2 = 1X = Y Given X^2 = XY Multiply both sides by X X^2  Y^2 = XY  Y^2 Subtract Y^2 from both sides (X+Y)(XY) = Y(XY) Factor both sides (X+Y) = Y Cancel out common factors Y+Y = Y Substitute in from line 1 2Y = Y Collect the Y's 2 = 1 Divide both sides by YWhere is the flaw? When you've sorted that out, how about a proof that 1 = 11 = 1 1 / 1 = 1 / 1 sqrt( 1 / 1 ) = sqrt( 1 / 1 ) Take square root of both sides sqrt( 1 ) = 1 / sqrt( 1 ) Simpify sqrt( 1 ) ^ 2 = 1 Multiply each side by sqrt(1) 1 = 1
