>>53
Um, no. That's just not right.
Just consider the function x^2/x as a function defined on the complex plane.
Obviously x^2/x is holomorphic on the plane without {0}, and thus analytic on the real line without {0}
Now, you could argue it two ways, you could say that x^2/x = x and therefore f(0) = 0 and thus the function is holomorphic on the entire plane. This sort of cancellation is pretty trivially allowed in any sort of construction of a theory of functions.
And even if you don't see the cancellation at trivial, the function is only not defined at a singleton point, and at that point there is a removable singularity. Therefore the function can be holmorphically extended to an analytic function on the complex plane and thus the real line. And it's pretty fucking trivial again that this analytic continuation is x^2/x = x.
ITT shut the fuck up.