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.
$$x^2=\underbrace{x+x+\cdots+x}_{(x\text{ times})}$$
$$\frac{d}{dx}x^2=\frac{d}{dx}[\underbrace{x+x+\cdots+x}_{(x\text{ times})}]$$
$$2x=1+1+\cdots+1=x$$
$$2=1$$
$1=2$: A Proof using Complex Numbers
This supposed proof uses complex numbers. If you're not familiar with them, there's a brief introduction to them given below.
The Fallacious Proof:

Step 1: $-1/1 = 1/-1$
Step 2: Taking the square root of both sides: $\sqrt{-1/1} = \sqrt{1/-1}$.
Step 3: Simplifying: $\sqrt{-1} / \sqrt{1} = \sqrt{1} / \sqrt{-1}$
Step 4: In other words, $i/1 = 1/i$.
Step 5: Therefore, $i / 2 = 1 / (2i)$,
Step 6: $i/2 + 3/(2i) = 1/(2i) + 3/(2i)$,
Step 7: $i (i/2 + 3/(2i) ) = i ( 1/(2i) + 3/(2i) )$,
Step 8: $(i^2)/2 + (3i)/2i = i/(2i) + (3i)/(2i)$,
Step 9: $(-1)/2 + 3/2 = 1/2 + 3/2$,
Step 10: and this shows that $1=2$.

See if you can figure out in which step the fallacy lies.