From: clubok@physics11 (Kenneth S. Clubok)

Theorem: 1 = -1 .
Proof:
1 -1
-- = --
-1 1

1 -1
sqrt[ -- ] = sqrt[ -- ]
-1 1

sqrt[1] sqrt[-1]
------- = -------
sqrt[-1] sqrt[1]

1=-1 (by cross-multiplication)

And here's my personal favorite:

Use integration by parts to find the anti-derivative of 1/x. One
can get the amusing result that 0=1. (Until you realize you have to put
in the limits.)