Hi everybody, could you explain to me, as simple as possible, why an analytic function

regular in a domain G (open and connected) cannot be constant throughout a sub-domain

of G without being a constant throughout all of G?

Thank you very much.

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- Jan 19th 2009, 08:14 PMvnca1constant analytic function regular in a region G
Hi everybody, could you explain to me, as simple as possible, why an analytic function

regular in a domain G (open and connected) cannot be constant throughout a sub-domain

of G without being a constant throughout all of G?

Thank you very much. - Jan 20th 2009, 11:09 AMThePerfectHacker
By the identity theorem.

Do you see why? - Jan 20th 2009, 09:14 PMvnca1
Thank you very much. Your answer is probably the shortest yet a very useful one.