From f3d00836350e3a06371104af16868def89f4cea7 Mon Sep 17 00:00:00 2001
From: Barrett Ruth <br.barrettruth@gmail.com>
Date: Mon, 18 Aug 2025 11:39:06 -0500
Subject: [PATCH] cleanup

---
 src/content/posts/algorithms/proofs.mdx | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/content/posts/algorithms/proofs.mdx b/src/content/posts/algorithms/proofs.mdx
index 32c5a89..ed8132c 100644
--- a/src/content/posts/algorithms/proofs.mdx
+++ b/src/content/posts/algorithms/proofs.mdx
@@ -81,7 +81,7 @@ As $S_i<S_{j>i}$, $|S_{j>i}-S_i|=S_{j>i}-S_i$--the sum is unchanged. Rewriting t
 
 $$
 \begin{align*}
-\sum_{1\leq r\leq n}\sum_{1\leq l<r} X-Y &=\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_r-\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_l
+\sum_{1\leq r\leq n}\sum_{1\leq l<r} |X-Y| &=\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_r-\sum_{1\leq r\leq n}\sum_{1\leq l<r}S_l
 &=\sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq l<r\leq n} S_l
 &=\sum_{1\leq r\leq n}r\cdot S_r-\sum_{1\leq r\leq n} (n-r)\cdot S_r
 \end{align*}