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http:///mymemo.xyz/wiki/api.php?action=feedcontributions&user=2402%3A6B00%3A5609%3AEF00%3AF577%3AF388%3AF9E8%3A52FF&feedformat=atom 2024-04-28T05:10:53Z 利用者の投稿記録 MediaWiki 1.31.0 2017-12-20T02:31:28Z

<p>2402:6B00:5609:EF00:F577:F388:F9E8:52FF: </p> <hr /> <div>&#039;&#039;&#039;交換法則&#039;&#039;&#039;（こうかんほうそく、{{lang-en-short|&#039;&#039;Commutative property&#039;&#039;}}) は数学における法則の一つ。&#039;&#039;&#039;可換則&#039;&#039;&#039;（かかんそく）や&#039;&#039;&#039;交換律&#039;&#039;&#039;（こうかんりつ）ともいう。<br /> <br /> == 概要 ==<br /> [[集合]] &#039;&#039;S&#039;&#039; に[[二項演算]] · が定義されているとき &#039;&#039;S&#039;&#039; の任意の二元 &lt;math&gt;\, a,\, b&lt;/math&gt;について<br /> :&lt;math&gt;a\cdot b = b\cdot a&lt;/math&gt;<br /> が成立するならば、この演算は&#039;&#039;&#039;交換法則&#039;&#039;&#039;を満たすという。また、この演算は&#039;&#039;&#039;可換&#039;&#039;&#039;である、&#039;&#039;&#039;可換性&#039;&#039;&#039;を持つという。<br /> <br /> たとえば[[自然数]]に関する[[足し算]]や[[掛け算]]は交換法則を満たしている。<br /> * 4 + 5 = 5 + 4 (両辺とも値は9である)<br /> * 2 × 3 = 3 × 2 (両辺とも値は6である)<br /> しかし引き算や割り算はそうではない。<br /> * &lt;math&gt; 4 - 5 \neq 5 - 4&lt;/math&gt;<br /> * &lt;math&gt; 6 \div 3 \neq 3 \div 6&lt;/math&gt;<br /> <br /> その他に交換法則を満たすものとしては主に次のようなものがある。<br /> * [[有理数]]、[[実数]]、[[複素数]]の加算や乗算<br /> * [[行列]]、[[数ベクトル]]の加算<br /> * [[集合]]の[[共通部分 (数学)|共通部分]]や[[合併 (集合論)|和集合]]<br /> また、交換法則を満たさない主要な演算としては次のようなものがある。<br /> * [[行列]]の乗算、3次元[[数ベクトル]]の[[ベクトル積|ベクトル外積]]<br /> * [[写像]]の合成（例として関数の合成等）<br /> * [[四元数]]の乗算<br /> ただしベクトルの外積のように[[絶対値]]および絶対値に相当する数を考えたときに交換法則は成り立つものも多い。<br /> <br /> == 関連項目 ==<br /> *[[結合法則]]<br /> *[[分配法則]]<br /> *[[アーベル群]]<br /> *[[代数的構造]]<br /> *[[加法]]<br /> *[[乗法]]<br /> *[[かけ算の順序問題]]<br /> <br /> {{デフォルトソート:こうかんほうそく}}<br /> [[Category:代数的構造]]<br /> [[Category:初等数学]]<br /> [[Category:数学の法則]]<br /> [[Category:数学に関する記事]]</div>

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