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Aug 27, 2014 at 21:33 comment added paul garrett @GHfromMO, I think people "believed in" a "principle of permanence" for some time before the notion of holomorphic function was made explicit. And, more often these days I would call it "the identity principle"...
Aug 27, 2014 at 19:38 comment added GH from MO I always thought this was called the "unicity theorem".
Aug 27, 2014 at 19:34 history answered Per Alexandersson CC BY-SA 3.0