isn't it just? :) my favourite such "result" is the following:

(for notational convenience, let I f = integral f dx)

I e^x = e^x
e^x - I e^x = 0
(1 - I) e^x = 0
e^x = 1/(1-I) 0
e^x = (1 + I + I^2 + I^3 + ....) 0

digression:
I 0 = 1
I^2 0 = I I 0 = I 1 = x
I^3 0 = I I^2 0 = I x = x^2/2!
and so on

so we get
e^x = 1 + x + x^2/2! + x^3/3! + ....

which it indeed is :)

'proof' from Ian Stewart's very highly recommended "Game, Set and Math", where he notes that it can actually be made rigorous.