A Proof That 2 = 1 Given (1) X = Y Multiply both sides by X (2) X^2 = XY Subtract Y^2 from both sides (3) X^2 - Y^2 = XY - Y^2 Factor both sides (4) (X+Y)(X-Y) = Y(X-Y) Cancel out common factors (5) (X+Y) = Y Substitute in from line (1) (6) Y+Y = Y Collect the Y's (7) 2Y = Y Divide both sides by Y (8) 2 = 1 Q: What's wrong with this 'proof'? [Edited on 2-16-2005 by kiwirobin]

whya re you adding and subtractnig variables because i could do that with anything and make it equal to any number

The only way that this will work out is if, x = y = 0 Which leads to the point that zero obejects cannot be divided into zero groups. (if you want a more detailed answer I can give you it)

This is also correct ice but the challange was to solve this problem. Q: What's wrong with -THIS- 'proof'? Where is the application that is not correct.

Part 5, cancel out means divide, if we say x = 0 y = 0 therefore x - y = 0 therefore you are dividing by 0 which is not allowed [Edited on 16-2-2005 by Icewolf]

That's it ice Took me ages to find it, funny how my brain can only vocus on one thing sometimes exclueding the obvious. For a while there I was starting to believe it...:mnky: anyway, well done... here's the breakdown for those interested... 2 = 1: Solution 'Cancelling' the common factors from line (4) to (5) means dividing by the factor (X-Y). Since X=Y, this is a division by 0, the results of which are undefined. (1) X = Y Given (2) X^2 = XY Multiply both sides by X (3) X^2 - Y^2 = XY - Y^2 Subtract Y^2 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