Best Fake Proofs? (A M.SE April Fools Day collection) In honor of April Fools Day $2013$, I'd like this question to collect the best, most convincing fake proofs of impossibilities you have seen. 
I've posted one as an answer below. I'm also thinking of a geometric one where the "trick" is that it's very easy to draw the diagram wrong and have two lines intersect in the wrong place (or intersect when they shouldn't). If someone could find and link this, I would appreciate it very much. 

Let me prove that the number $1$ is a multiple of $3$.
To accomplish such a wonderful result we are going to use the symbol $\equiv$ to denote "congruent modulo $3$". Thus, what we need to prove is that $1 \equiv 0$. Next I give you the proof:
$1\equiv 4$ 
$\quad \Rightarrow \quad$ 
$2^1\equiv 2^4$ 
$\quad \Rightarrow \quad$ 
$2\equiv 16$ 
$\quad \Rightarrow \quad$ 
$2\equiv 1$ 
$\quad \Rightarrow \quad$ 
$2-1\equiv 1-1$
$\quad \Rightarrow \quad$ 
$1\equiv 0$.
