Consider the following mathematical demonstration (which is also my signature):

Let $\displaystyle \;\; x=y$

Then:

$\displaystyle x^2 = xy$

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

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

$\displaystyle x+y = y$

$\displaystyle 2y = y$

$\displaystyle 2 = 1$

Okay, I know that the issue here is a division by zero in the 3rd line down, since $\displaystyle (x-y) = 0$. This problem was shown to me in a textbook, and I found it really interesting how the fact that something illogical (division by zero) will force another illogical statement (2 = 1). I was wondering if anybody knew of some other clever,but simple,deomnstration of this type, because these are very interesting to me. Plus, I kinda wanted as many people to post them on here as possible, and then for the mostclever yet simpleexample to be choosen as the winner. So, lets begin. (Also, it can involve calculus, it doesn't have to be super simple. I'm just hoping to not have to start talking about Rings and Fields, or Topological spaces and Isomorphisims in these examples; thats all I mean by "simple")

Post your favorite little algebraic/calculus demonstration of how a seemingly proper mathematical process can end up in a logical contradiction here, please. Also, please don't point out the "catch" (the 'catch' in the demonstration I supplied is the division by zero in line three), I'd like to see how many of them I can figure out on my own, and I'm sure others would like a chance to try and figure it out on their own also. Thanks in advance for any posts.