zeroes of holomorphic function I know that zeroes of holomorphic functions are isolated,and I know that if a holomorphic function has zero set whic has a limit point then it is identically zero function,i know a holomorphic function can have countable zero set, does there exixt a holomorphic function which is not identically zero, and has uncountable number of zeroes?

Your question needs some clarification, as it is not internally consistent. If I understand correctly, you're asking if all holomorphic functions have uncountably many zeros? In that case, the answer is definitely no, for example $f(z) = 1$.
