From dbdc8f528bc73a28d8a8ca213747f9a64ff394c4 Mon Sep 17 00:00:00 2001
From: Zheyuan Wu <60459821+Trance-0@users.noreply.github.com>
Date: Tue, 24 Mar 2026 15:47:02 -0500
Subject: [PATCH] Update Math4202_L23.md

---
 content/Math4202/Math4202_L23.md | 5 ++---
 1 file changed, 2 insertions(+), 3 deletions(-)

diff --git a/content/Math4202/Math4202_L23.md b/content/Math4202/Math4202_L23.md
index 8733d46..0582521 100644
--- a/content/Math4202/Math4202_L23.md
+++ b/content/Math4202/Math4202_L23.md
@@ -61,8 +61,7 @@ Therefore $f$ must have a root in $B^2$.
 
 If $\|a_{n-1}\|+\|a_{n-2}\|+\cdots+\|a_0\|< R$ has a root in the disk $B^2_R$. (and $R\geq 1$, otherwise follows part 1)
 
-Consider $\tilde{f}(x)=f(Rx)$. 
-
+Consider $\tilde{f}(x)=f(Rx)$.
 $$
 \begin{aligned}
 \tilde{f}(x)
@@ -73,7 +72,7 @@ $$
 
 $$
 \begin{aligned}
-\|\frac{a_{n-1}}{R}\|+\|\frac{a_{n-2}}{R^2}\|+\cdots+\|\frac{a_0}{R^n}\|&=\frac{1}{R}\|a_{n-1}\|+\frac{1}{R^2}\|a_{n-2}\|+\cdots+\frac{1}{R^n}\|a_0\|\\
+\left\|\frac{a_{n-1}}{R}\right\|+\left\|\frac{a_{n-2}}{R^2}\right\|+\cdots+\left\|\frac{a_0}{R^n}\right\|&=\frac{1}{R}\|a_{n-1}\|+\frac{1}{R^2}\|a_{n-2}\|+\cdots+\frac{1}{R^n}\|a_0\|\\
 &<\frac{1}{R}\left(\|a_{n-1}\|+\|a_{n-2}\|+\cdots+\|a_0\|\right)\\
 &<\frac{1}{R}<1
 \end{aligned}