Originally Posted by

**Foxlion** The question:

What is wrong with the following "proof"? Let x=y. Then

$\displaystyle x^2 = xy $

$\displaystyle x^2-y^2= xy-y^2 $

$\displaystyle (x+y)(x-y)= y(x-y)$

$\displaystyle x+y= y$

$\displaystyle 2y= y $

$\displaystyle 2=1 $

Solution: I know that 2 does not equal 1 and my answer was an incorrect substitution in step 5 however that makes no sense as x=y. The book says that in step 3 'they' incorrectly divided by (x-y)=0. I do not understand, if (x-y) is a whole number then would it not be valid to perform the division?

i.e.$\displaystyle \frac {y(x-y)}{(x-y)} = y$?