The following © 2013 Daniel Asimov ---------------------------------- In the complex plane C, consider the differential equation dz/dt = i(z^3-z) for z in C. It's not hard to find an explicit formula for the solution of this for any initial condition z = z(0). ≠≠≠ Putting them all together in one function F, let F(z,t) : = the solution z(t) of [dz/dt = i(z^3-z)] for which z(0) = z. for all t for which F(z,t) is defined. It follows from the form of the solutions that there is a nonempty open set U in C such that (*) for all z in U, we have F(z,pi) = z . But it also follows from the form of the solution that there is another nonempty open set V in C such that (**) for all z in V, we have F(z,pi) ≠ z . But wait, there's more. The Identity Theorem (sometimes known as the Permanence Theorem) in complex variables implies that if two analytic functions (like F(z,pi) and z) are equal on a nonempty open set in C, then they are equal everywhere. So, how can both (*) and (**). Is mathematics inconsistent? --Dan