1. There is a lovely dissection proof of the fact that a rectangle of area 65 can be dissected into one of area 64. Hence 1 = 0. 2. Also, Banach-Tarski showed that a unit ball B = {p in R^3 | ||p|| <= 1} can be dissected into 5 pieces that can be reassembled to comprise a partition of *two* unit balls. A likely story! Hence 1 = 0. 3. Furthermore, the vector field on the complex plane given by V(z) = i(z^3 - z) is holomorphic, so the fact that the flow {phi_t} of V satisfies that the times t for which phi_t(z) = z for all z form a discrete subgroup G_z of the reals. Also note that phi_t(z) is jointly holomorphic in both z and t. But it's not the same subgroup for all z (!) Which clearly contradicts the principle of permanence for holomorphic functions.= —Dan