19 lines
761 B
HTML
19 lines
761 B
HTML
<!--
|
|
title: 數學歸納法 (Mathematical Induction)
|
|
description:
|
|
published: true
|
|
date: 2026-02-11T17:16:01.234Z
|
|
tags:
|
|
editor: ckeditor
|
|
dateCreated: 2026-02-11T17:14:35.544Z
|
|
-->
|
|
|
|
<h3>Fundamental Principle</h3>
|
|
<p>Mathematical induction is a method used to prove that a statement holds true for all natural numbers k.</p>
|
|
<p>Let P(n) be a statement defined for each positive integer n.</p>
|
|
<p>Then P(n) will be true for all positive integers n if the following two conditions are satisfied:</p>
|
|
<p>(1) P(1) is true.</p>
|
|
<p>(2) P(k) is true for some integer k + 1 implies that P(k + 1) is true.</p>
|
|
<p>Because all the other values can use the result from the (1) and (2),</p>
|
|
<p>Therefore, you can conclude that all the conditions with integers n are true.</p>
|