From efb6c2ca2b547d4cf68860888ddbfe6b0b555e24 Mon Sep 17 00:00:00 2001
From: phidias <phidias@aperx.org>
Date: Wed, 11 Feb 2026 17:21:47 +0000
Subject: [PATCH] docs: update education/mathematics/mathematical-induction

---
 education/mathematics/mathematical-induction.html | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/education/mathematics/mathematical-induction.html b/education/mathematics/mathematical-induction.html
index b1dedf1..f27dfc5 100644
--- a/education/mathematics/mathematical-induction.html
+++ b/education/mathematics/mathematical-induction.html
@@ -2,7 +2,7 @@
 title: 數學歸納法 (Mathematical Induction)
 description: 
 published: true
-date: 2026-02-11T17:21:19.387Z
+date: 2026-02-11T17:21:46.543Z
 tags: 
 editor: ckeditor
 dateCreated: 2026-02-11T17:14:35.544Z
@@ -23,7 +23,7 @@ dateCreated: 2026-02-11T17:14:35.544Z
 <p><span style="font-family:Arial, Helvetica, sans-serif;">A For n = 1,&nbsp;</span></p>
 <figure class="image"><img src="data:image/png;base64,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"></figure>
 <p><span style="font-family:Arial, Helvetica, sans-serif;">The statement is true for n = 1.</span></p>
-<p><span style="font-family:Arial, Helvetica, sans-serif;">For n = k + 1, Assume the statement is true for some integer k &gt;= 1.</span></p>
+<p><span style="font-family:Arial, Helvetica, sans-serif;">For n = k + 1, Assume the statement is true for some integer k ≥ 1.</span></p>
 <figure class="image"><img src="data:image/png;base64,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"></figure>
 <figure class="image"><img src="data:image/png;base64,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"></figure>
 <figure class="image"><img src="data:image/png;base64,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"></figure>