# Isolated Zeros Proof

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Let f be analytic on a domain D. Prove that if f is not identically zero, then the zeros of f in D are isolated. (That is, prove that if f is not identically zero and if z(0) is a point in D with f(z(0))=0, then there exists e>0 such that f(z)=/0 for all z in the region 0<|z-z(0)|<e.) e, epsilon. =/, does not equal.

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Proof.

Every zero is surrounded by a neighborhood in which f(z)is nonzero. Let f(0) = 0 for convenience. If this zero has infinite order, i.e. if ...

#### Solution Summary

An Isolated Zeros Proof is provided.

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