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Zheyuan Wu
2025-03-04 16:55:03 -06:00
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pages/Math416/Math416_L14.md
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@@ -143,6 +143,6 @@ We proceed by contradiction. Suppose $z_n\to w\in U$, $f(z_0)=0$, $f(w)=0$. $w$
QED
#### Corollary 7.13.3: Identity principle
#### Corollary 7.14: Identity principle
If $f,g\in O(U)$, $U$ is a domain and $\exists$ sequence $z_0$ that converges to $w\in U$, such that $f(z_n)=g(z_n)$, then $f\equiv g$ on U$.