Best Fake Proofs? (A M.SE April Fools Day collection) [closed]

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.

Solution 1:

$$x^2=\underbrace{x+x+\cdots+x}_{(x\text{ times})}$$ $$\frac{d}{dx}x^2=\frac{d}{dx}[\underbrace{x+x+\cdots+x}_{(x\text{ times})}]$$ $$2x=1+1+\cdots+1=x$$ $$2=1$$

Solution 2:

enter image description here

Endless chocolate bar (I do not know the author of this animation)

Solution 3:

Proof that a dog has $9$ legs:

No dog has $5$ legs,

A dog has $4$ more legs than no dog.

A dog has $9$ legs

Source: Foolproof: A Sampling of Mathematical Folk Humour, P Renteln, A Dundes

Solution 4:

Simple one:

$1 = \sqrt{1} = \sqrt{(-1)\cdot(-1)} = \sqrt{-1}\cdot \sqrt{-1} = i\cdot i = -1$