update typo

This commit is contained in:
Trance-0
2025-03-03 19:45:05 -06:00
parent 66d09aaff2
commit fb6e36545b
23 changed files with 26 additions and 22 deletions

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@@ -61,7 +61,7 @@ $$
\end{aligned}
$$
Use the fact that $f$ is holomorphic on $U$, then $f$ is continuous on $U$, so $\lim_{z\toz_1}f(z)=f(z_1)$.
Use the fact that $f$ is holomorphic on $U$, then $f$ is continuous on $U$, so $\lim_{z\to z_1}f(z)=f(z_1)$.
There exists a $\delta>0$ such that $|z-z_1|<\delta$ implies $|f(z)-f(z_1)|<\epsilon$.
@@ -71,7 +71,7 @@ $$
|I|\leq\frac{1}{z_1-z_0}\int_{z}^{z_1}|f(\xi)-f(z_1)|d\xi<\frac{\epsilon}{z_1-z_0}\int_{z}^{z_1}d\xi=\epsilon
$$
So $I\to 0$ as $z_1\toz$.
So $I\to 0$ as $z_1\to z$.
Therefore, $g'(z_1)=f(z_1)$ for all $z_1\in U$.