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If you would like to participate, please visit the project page, where you can join <a href="/wiki/Wikipedia_talk:WikiProject_Mathematics" title="Wikipedia talk:WikiProject Mathematics">the discussion</a> and see a list of open tasks.<span class="metadata wpb-metadata"><span class="wpb-project">Mathematics</span><span class="wpb-project_link">Wikipedia:WikiProject Mathematics</span><span class="wpb-banner_name">Template:WikiProject Mathematics</span><span class="wpb-assessment_cat">mathematics</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-high"><a href="/wiki/Category:High-priority_mathematics_articles" title="Category:High-priority mathematics articles">High</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>High-priority</b> on the <a href="/wiki/Wikipedia:WikiProject_Mathematics/Wikipedia_1.0/Assessment#Priority_scale" class="mw-redirect" title="Wikipedia:WikiProject Mathematics/Wikipedia 1.0/Assessment">project's priority scale</a>.</td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1237879475" /><table class="box-translated-page plainlinks tmbox mbox-small tmbox-notice" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:WP-TranslationProject_TwoFlags.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/WP-TranslationProject_TwoFlags.svg/30px-WP-TranslationProject_TwoFlags.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/WP-TranslationProject_TwoFlags.svg/45px-WP-TranslationProject_TwoFlags.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/WP-TranslationProject_TwoFlags.svg/60px-WP-TranslationProject_TwoFlags.svg.png 2x" data-file-width="250" data-file-height="250" /></a></span></td><td class="mbox-text">This article contains a <a href="/wiki/Wikipedia:Translation" title="Wikipedia:Translation">translation</a> of <a class="external text" href="https://de.wikipedia.org/wiki/Issai_Schur">Issai Schur</a> from <a class="external text" href="https://de.wikipedia.org/wiki/">de.wikipedia</a>.</td></tr></tbody></table> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Opening_heading" data-mw-thread-id="h-Opening_heading-2007-01-02T00:12:00.000Z"><span data-mw-comment-start="" id="h-Opening_heading-2007-01-02T00:12:00.000Z"></span>Opening heading<span data-mw-comment-end="h-Opening_heading-2007-01-02T00:12:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=1" title="Edit section: Opening heading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-71.138.248.226-2007-01-02T00:12:00.000Z-Opening_heading"></span>I have many associates in the accounting field who are baffled when they divide a list of numbers and the sum of those results does not match the dividing the<b><i> sum of the original numbers. They have to start moving pennys around and they blame their electronic spreadsheets. We all know that division has Distributivity, but the spreadsheet also rounds the </i>numbers, and rounding does not have Distributive property<i>. I was looking for an online reference that could explain this well in language that accountants (not mathamaticians) could understand. Could you help me with this? Is there an article on Non-distributivity? Or could you perhaps provide examples of things that do not have Distributive property? Thanks.</i></b> -Sandy <small>—The preceding <a href="/wiki/Wikipedia:Sign_your_posts_on_talk_pages" class="mw-redirect" title="Wikipedia:Sign your posts on talk pages">unsigned</a> comment was added by <a href="/wiki/Special:Contributions/71.138.248.226" title="Special:Contributions/71.138.248.226">71.138.248.226</a> (<a href="/w/index.php?title=User_talk:71.138.248.226&action=edit&redlink=1" class="new" title="User talk:71.138.248.226 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-71.138.248.226-2007-01-02T00:12:00.000Z-Opening_heading" class="ext-discussiontools-init-timestamplink">00:12, 2 January 2007 (UTC)</a>.</small><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-71.138.248.226-2007-01-02T00:12:00.000Z-Opening_heading"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-71.138.248.226-2007-01-02T00:12:00.000Z-Opening_heading"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-EdC-2007-01-02T02:32:00.000Z-71.138.248.226-2007-01-02T00:12:00.000Z"></span>I've stuck a few examples into the article (section <a href="/wiki/Distributivity#Distributivity_and_rounding" class="mw-redirect" title="Distributivity">Distributivity and rounding</a>). Tell me if that helps; if you can find some good references it'd be good to have them here. –<a href="/wiki/User:EdC" title="User:EdC">EdC</a> <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-EdC-2007-01-02T02:32:00.000Z-71.138.248.226-2007-01-02T00:12:00.000Z" class="ext-discussiontools-init-timestamplink">02:32, 2 January 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-EdC-2007-01-02T02:32:00.000Z-71.138.248.226-2007-01-02T00:12:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-EdC-2007-01-02T02:32:00.000Z-71.138.248.226-2007-01-02T00:12:00.000Z"></span></dd></dl> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-90.185.76.189-2009-01-29T04:42:00.000Z-EdC-2007-01-02T02:32:00.000Z"></span>This certainly deserves an explanation but the article is supposed to explain a piece of theoretical mathematics -- not a practical computational quirk. --<a href="/wiki/Special:Contributions/90.185.76.189" title="Special:Contributions/90.185.76.189">90.185.76.189</a> (<a href="/w/index.php?title=User_talk:90.185.76.189&action=edit&redlink=1" class="new" title="User talk:90.185.76.189 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-90.185.76.189-2009-01-29T04:42:00.000Z-EdC-2007-01-02T02:32:00.000Z" class="ext-discussiontools-init-timestamplink">04:42, 29 January 2009 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-90.185.76.189-2009-01-29T04:42:00.000Z-EdC-2007-01-02T02:32:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-90.185.76.189-2009-01-29T04:42:00.000Z-EdC-2007-01-02T02:32:00.000Z"></span></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Division" data-mw-thread-id="h-Division-2007-04-25T22:53:00.000Z"><span data-mw-comment-start="" id="h-Division-2007-04-25T22:53:00.000Z"></span>Division<span data-mw-comment-end="h-Division-2007-04-25T22:53:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=2" title="Edit section: Division"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Cherry_Cotton-2007-04-25T22:53:00.000Z-Division"></span>I'd like to see this article be more clear on whether or not division is distributive over addition. It is, isn't it? But, I was confused about it from reading this article. Distributivity of division over addition is mentioned and invoked as though it were the case, but isn't explained to be so. </p><p>Thanks! <a href="/w/index.php?title=User:Cherry_Cotton&action=edit&redlink=1" class="new" title="User:Cherry Cotton (page does not exist)">Cherry Cotton</a> <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Cherry_Cotton-2007-04-25T22:53:00.000Z-Division" class="ext-discussiontools-init-timestamplink">22:53, 25 April 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Cherry_Cotton-2007-04-25T22:53:00.000Z-Division"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Cherry_Cotton-2007-04-25T22:53:00.000Z-Division"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-EdC-2007-04-26T20:40:00.000Z-Cherry_Cotton-2007-04-25T22:53:00.000Z"></span>Division (in the reals) is simply multiplication by the reciprocal (the multiplicative inverse) of the divisor, so distributivity follows immediately. The same holds for the distributivity of multiplication (or division) over subtraction. –<a href="/wiki/User:EdC" title="User:EdC">EdC</a> <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-EdC-2007-04-26T20:40:00.000Z-Cherry_Cotton-2007-04-25T22:53:00.000Z" class="ext-discussiontools-init-timestamplink">20:40, 26 April 2007 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-EdC-2007-04-26T20:40:00.000Z-Cherry_Cotton-2007-04-25T22:53:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-EdC-2007-04-26T20:40:00.000Z-Cherry_Cotton-2007-04-25T22:53:00.000Z"></span></dd></dl> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-Lunakeet-2008-05-02T12:05:00.000Z-EdC-2007-04-26T20:40:00.000Z"></span>You have to be careful though, because it only works the one way: (1 + 5)/7 = 1/7 + 5/7, but 1/(5 + 7) ≠ 1/5 + 1/7. Hope this helps. 10:11, 24 June 2007 (UTC)</dd></dl></dd></dl> <dl><dd><dl><dd><dl><dd>I don't think so, never learned it yet. I'd listen to the above user. <a href="/wiki/User:Lunakeet" title="User:Lunakeet">Lu</a><a href="/wiki/User_talk:Lunakeet" title="User talk:Lunakeet">na</a><a href="/wiki/Special:Contributions/Lunakeet" title="Special:Contributions/Lunakeet">ke</a><a href="/wiki/User:Lunakeet/Signhere" title="User:Lunakeet/Signhere">et</a> <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Lunakeet-2008-05-02T12:05:00.000Z-EdC-2007-04-26T20:40:00.000Z" class="ext-discussiontools-init-timestamplink">12:05, 2 May 2008 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Lunakeet-2008-05-02T12:05:00.000Z-EdC-2007-04-26T20:40:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Lunakeet-2008-05-02T12:05:00.000Z-EdC-2007-04-26T20:40:00.000Z"></span></dd></dl></dd></dl></dd></dl> <p><br /> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Image" data-mw-thread-id="h-Image-2008-06-01T18:29:00.000Z"><span data-mw-comment-start="" id="h-Image-2008-06-01T18:29:00.000Z"></span>Image<span data-mw-comment-end="h-Image-2008-06-01T18:29:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=3" title="Edit section: Image"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <span data-mw-comment-start="" id="c-Simeon-2008-06-01T18:29:00.000Z-Image"></span><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:DistributiveProperty.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/en/thumb/e/ef/DistributiveProperty.png/250px-DistributiveProperty.png" decoding="async" width="220" height="171" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/e/ef/DistributiveProperty.png/330px-DistributiveProperty.png 1.5x, //upload.wikimedia.org/wikipedia/en/e/ef/DistributiveProperty.png 2x" data-file-width="365" data-file-height="284" /></a><figcaption>The bottom part is the above multiplication carried out in two different parts. The top and bottom are equivalent.</figcaption></figure> <p>I've removed this image because I think it's not very clear.. I've been looking at it but I've yet to see two multiplications taking place there.. there are four and eight Xs above the line and some more below it but I fail to see how this image clarifies the distributive law. What multiplication is taking place (4 * 2 = 8?) and where's the distributive law? - <a href="/wiki/User:Simeon" title="User:Simeon">Simeon</a> (<a href="/wiki/User_talk:Simeon" title="User talk:Simeon">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Simeon-2008-06-01T18:29:00.000Z-Image" class="ext-discussiontools-init-timestamplink">18:29, 1 June 2008 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Simeon-2008-06-01T18:29:00.000Z-Image"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Simeon-2008-06-01T18:29:00.000Z-Image"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Request_move" data-mw-thread-id="h-Request_move-2011-04-28T03:24:00.000Z"><span data-mw-comment-start="" id="h-Request_move-2011-04-28T03:24:00.000Z"></span>Request move<span data-mw-comment-end="h-Request_move-2011-04-28T03:24:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=4" title="Edit section: Request move"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Cliff-2011-04-28T03:24:00.000Z-Request_move"></span>I do not believe that "distributivity" is a word. I suggest moving this page to <a href="/wiki/Distributive_property" title="Distributive property">Distributive property</a>. I don't ever recall seeing "distributivity" in any mathematics journal. <a href="/wiki/User:Cliff" class="mw-redirect" title="User:Cliff">Cliff</a> (<a href="/wiki/User_talk:Cliff" title="User talk:Cliff">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Cliff-2011-04-28T03:24:00.000Z-Request_move" class="ext-discussiontools-init-timestamplink">03:24, 28 April 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Cliff-2011-04-28T03:24:00.000Z-Request_move"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Cliff-2011-04-28T03:24:00.000Z-Request_move"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Move?" data-mw-thread-id="h-Move?-2011-06-20T03:04:00.000Z"><span id="Move.3F"></span><span data-mw-comment-start="" id="h-Move?-2011-06-20T03:04:00.000Z"></span>Move?<span data-mw-comment-end="h-Move?-2011-06-20T03:04:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=5" title="Edit section: Move?"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <div class="boilerplate" style="background-color: #efe; margin: 2em 0 0 0; padding: 0 10px 0 10px; border: 1px dotted #aaa;"> <dl><dd><i><span data-mw-comment-start="" id="c-Vegaswikian-2011-06-27T22:02:00.000Z-Move?"></span>The following discussion is an archived discussion of a <a href="/wiki/Wikipedia:RM" class="mw-redirect" title="Wikipedia:RM">requested move</a>. <span style="color:red"><b>Please do not modify it.</b></span> Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section. </i></dd></dl> <p>The result of the move request was: <b>page moved</b>. <a href="/wiki/User:Vegaswikian" title="User:Vegaswikian">Vegaswikian</a> (<a href="/wiki/User_talk:Vegaswikian" title="User talk:Vegaswikian">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Vegaswikian-2011-06-27T22:02:00.000Z-Move?" class="ext-discussiontools-init-timestamplink">22:02, 27 June 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Vegaswikian-2011-06-27T22:02:00.000Z-Move?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Vegaswikian-2011-06-27T22:02:00.000Z-Move?"></span> </p> <hr /> <p><br /> <a href="/wiki/Distributivity" class="mw-redirect" title="Distributivity"><span data-mw-comment-start="" id="c-Cliff-2011-06-20T03:04:00.000Z-Move?"></span>Distributivity</a> → <a href="/wiki/Distributive_property" title="Distributive property">Distributive property</a> – </p> <ul><li>The latter is a redirect to the current article. The current title is not a word, nor is it commonly used in mathematical journals. This move will match recent moves: <a href="/wiki/Associativity" class="mw-redirect" title="Associativity">Associativity</a> has moved to <a href="/wiki/Associative_property" title="Associative property">Associative property</a>, and <a href="/wiki/Commutativity" class="mw-redirect" title="Commutativity">Commutativity</a> has moved to <a href="/wiki/Commutative_property" title="Commutative property">Commutative property</a>. A thread was started on the current talk page to discuss the move, but no discussion has ensued. <a href="/wiki/User:Cliff" class="mw-redirect" title="User:Cliff">Cliff</a> (<a href="/wiki/User_talk:Cliff" title="User talk:Cliff">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Cliff-2011-06-20T03:04:00.000Z-Move?" class="ext-discussiontools-init-timestamplink">03:04, 20 June 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Cliff-2011-06-20T03:04:00.000Z-Move?"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Cliff-2011-06-20T03:04:00.000Z-Move?"></span></li> <li><span data-mw-comment-start="" id="c-Anthony_Appleyard-2011-06-20T04:55:00.000Z-Cliff-2011-06-20T03:04:00.000Z"></span>Google search for "distributivity" (excluding "distributive") finds about 244,000 results. That looks quite a lot like it being an accepted word. (And move <a href="/wiki/Associative_property" title="Associative property">Associative property</a> and <a href="/wiki/Commutative_property" title="Commutative property">Commutative property</a> back to "-ivity"?) <a href="/wiki/User:Anthony_Appleyard" title="User:Anthony Appleyard">Anthony Appleyard</a> (<a href="/wiki/User_talk:Anthony_Appleyard" title="User talk:Anthony Appleyard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Anthony_Appleyard-2011-06-20T04:55:00.000Z-Cliff-2011-06-20T03:04:00.000Z" class="ext-discussiontools-init-timestamplink">04:55, 20 June 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Anthony_Appleyard-2011-06-20T04:55:00.000Z-Cliff-2011-06-20T03:04:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Anthony_Appleyard-2011-06-20T04:55:00.000Z-Cliff-2011-06-20T03:04:00.000Z"></span></li></ul> <dl><dd><ul><li><b><span data-mw-comment-start="" id="c-CWenger-2011-06-20T05:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"></span>Support</b> for consistency. –<a href="/wiki/User:CWenger" title="User:CWenger">CWenger</a> (<a href="/wiki/User_talk:CWenger" title="User talk:CWenger"><span style="font-family:Webdings;"><big>^</big></span></a> • <a href="/wiki/Special:Contributions/CWenger" title="Special:Contributions/CWenger"><span style="font-family:Webdings;"><big>@</big></span></a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-CWenger-2011-06-20T05:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z" class="ext-discussiontools-init-timestamplink">05:11, 20 June 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-CWenger-2011-06-20T05:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-CWenger-2011-06-20T05:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"></span></li> <li><b><span data-mw-comment-start="" id="c-Noetica-2011-06-23T23:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"></span>Support.</b> A straightforward case. (Just for the record though, it <i>is</i> a word in use. Current <a href="/wiki/OED" class="mw-redirect" title="OED">OED</a>'s earliest citation is from 1940: "W. V. Quine Math. Logic 60 Distributivity always justifies an operation analogous to that of 'multiplying through' in arithmetic." Quine? That's pretty canonic.) <span style="color:blue;"><big>N</big><small>oetica</small></span><sup><small><a href="/wiki/User_talk:Noetica" title="User talk:Noetica">Tea?</a></small></sup> <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Noetica-2011-06-23T23:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z" class="ext-discussiontools-init-timestamplink">23:11, 23 June 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Noetica-2011-06-23T23:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Noetica-2011-06-23T23:11:00.000Z-Anthony_Appleyard-2011-06-20T04:55:00.000Z"></span></li></ul></dd> <dd><i>The above discussion is preserved as an archive of a <a href="/wiki/Wikipedia:RM" class="mw-redirect" title="Wikipedia:RM">requested move</a>. <span style="color:red"><b>Please do not modify it.</b></span> Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.</i></dd></dl></div> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Distributivity_of_Conjunction_over_Exclusive_Or" data-mw-thread-id="h-Distributivity_of_Conjunction_over_Exclusive_Or-2011-09-14T05:03:00.000Z"><span data-mw-comment-start="" id="h-Distributivity_of_Conjunction_over_Exclusive_Or-2011-09-14T05:03:00.000Z"></span>Distributivity of Conjunction over Exclusive Or<span data-mw-comment-end="h-Distributivity_of_Conjunction_over_Exclusive_Or-2011-09-14T05:03:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=6" title="Edit section: Distributivity of Conjunction over Exclusive Or"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Xor_logician-2011-09-14T05:03:00.000Z-Distributivity_of_Conjunction_over_Exclusive_Or"></span>if and distributes over xor then </p> <pre>p and (q xor r) is (p xor q) and (p xor r) </pre> <p>However, this equivalence does not hold. Counter Example: </p> <pre>p := false<br /> q := true<br /> r := true<br /> </pre> <p>In this case,<br /> </p> <pre>p and (q xor r) is<br /> false and (true xor true) <br /> is false and false<br /> is false </pre> <p>but,<br /> </p> <pre>(p xor q) and (p xor r) is<br /> (false xor true) and (false xor true) is<br /> (true and true)<br /> is true. </pre> <p>And does NOT distribute over exclusive or. </p><p>This result obviously also holds for the claimed distributivity of intersection over symmetric difference. Namely, Intersection does not distribute over symmetric difference. </p><p>--<a href="/wiki/User:Xor_logician" title="User:Xor logician">Xor logician</a> (<a href="/w/index.php?title=User_talk:Xor_logician&action=edit&redlink=1" class="new" title="User talk:Xor logician (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Xor_logician-2011-09-14T05:03:00.000Z-Distributivity_of_Conjunction_over_Exclusive_Or" class="ext-discussiontools-init-timestamplink">05:03, 14 September 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Xor_logician-2011-09-14T05:03:00.000Z-Distributivity_of_Conjunction_over_Exclusive_Or"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Xor_logician-2011-09-14T05:03:00.000Z-Distributivity_of_Conjunction_over_Exclusive_Or"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Cliff-2011-09-17T09:39:00.000Z-Xor_logician-2011-09-14T05:03:00.000Z"></span>You distributed incorrectly to start. You should get...</dd></dl> <pre>(p and q) xor (p and r) </pre> <dl><dd><i> <b> if </b> </i> and distributes over xor. <a href="/wiki/User:Cliff" class="mw-redirect" title="User:Cliff">Cliff</a> (<a href="/wiki/User_talk:Cliff" title="User talk:Cliff">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Cliff-2011-09-17T09:39:00.000Z-Xor_logician-2011-09-14T05:03:00.000Z" class="ext-discussiontools-init-timestamplink">09:39, 17 September 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Cliff-2011-09-17T09:39:00.000Z-Xor_logician-2011-09-14T05:03:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Cliff-2011-09-17T09:39:00.000Z-Xor_logician-2011-09-14T05:03:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Distribution_of_disjunction_over_disjunction" data-mw-thread-id="h-Distribution_of_disjunction_over_disjunction-2012-04-13T10:49:00.000Z"><span data-mw-comment-start="" id="h-Distribution_of_disjunction_over_disjunction-2012-04-13T10:49:00.000Z"></span>Distribution of disjunction over disjunction<span data-mw-comment-end="h-Distribution_of_disjunction_over_disjunction-2012-04-13T10:49:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=7" title="Edit section: Distribution of disjunction over disjunction"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <dl><dd><span data-mw-comment-start="" id="c-Ivashikhmin-2012-04-13T10:49:00.000Z-Distribution_of_disjunction_over_disjunction"></span><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (P\lor (Q\lor R))\leftrightarrow ((P\lor Q)\land (P\lor R))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>P</mi> <mo>∨</mo> <mo stretchy="false">(</mo> <mi>Q</mi> <mo>∨</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo stretchy="false">↔</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>P</mi> <mo>∨</mo> <mi>Q</mi> <mo stretchy="false">)</mo> <mo>∧</mo> <mo stretchy="false">(</mo> <mi>P</mi> <mo>∨</mo> <mi>R</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (P\lor (Q\lor R))\leftrightarrow ((P\lor Q)\land (P\lor R))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e401c55e6c8155df503f3f4e67be3d6f27436520" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.014ex; height:2.843ex;" alt="{\displaystyle (P\lor (Q\lor R))\leftrightarrow ((P\lor Q)\land (P\lor R))}" /></span></dd></dl> <p>This formula is wrong. E.g. if P=false, Q=true, R =false then left side of the formula is true while right side is false. <a href="/w/index.php?title=User:Ivashikhmin&action=edit&redlink=1" class="new" title="User:Ivashikhmin (page does not exist)">Ivashikhmin</a> (<a href="/wiki/User_talk:Ivashikhmin" title="User talk:Ivashikhmin">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Ivashikhmin-2012-04-13T10:49:00.000Z-Distribution_of_disjunction_over_disjunction" class="ext-discussiontools-init-timestamplink">10:49, 13 April 2012 (UTC)</a> this is stupid bye now<span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Ivashikhmin-2012-04-13T10:49:00.000Z-Distribution_of_disjunction_over_disjunction"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Ivashikhmin-2012-04-13T10:49:00.000Z-Distribution_of_disjunction_over_disjunction"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Scalar_multiplication_example_is_missing" data-mw-thread-id="h-Scalar_multiplication_example_is_missing-2014-09-10T03:41:00.000Z"><span data-mw-comment-start="" id="h-Scalar_multiplication_example_is_missing-2014-09-10T03:41:00.000Z"></span>Scalar multiplication example is missing<span data-mw-comment-end="h-Scalar_multiplication_example_is_missing-2014-09-10T03:41:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=8" title="Edit section: Scalar multiplication example is missing"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Kluto-2014-09-10T03:41:00.000Z-Scalar_multiplication_example_is_missing"></span>Distributivity of scalar multiplication wrt addition of scalars resp. vectors is mentioned explicitly on the Vector Space page. Clearly it is an important example, so it should be mentioned. </p><p>Other examples of "mixed" distributive laws may abound. But this is a rather obvious one. <a href="/w/index.php?title=User:Kluto&action=edit&redlink=1" class="new" title="User:Kluto (page does not exist)">Kluto</a> (<a href="/w/index.php?title=User_talk:Kluto&action=edit&redlink=1" class="new" title="User talk:Kluto (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Kluto-2014-09-10T03:41:00.000Z-Scalar_multiplication_example_is_missing" class="ext-discussiontools-init-timestamplink">03:41, 10 September 2014 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Kluto-2014-09-10T03:41:00.000Z-Scalar_multiplication_example_is_missing"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Kluto-2014-09-10T03:41:00.000Z-Scalar_multiplication_example_is_missing"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Antidistributivity" data-mw-thread-id="h-Antidistributivity-2017-08-31T00:13:00.000Z"><span data-mw-comment-start="" id="h-Antidistributivity-2017-08-31T00:13:00.000Z"></span>Antidistributivity<span data-mw-comment-end="h-Antidistributivity-2017-08-31T00:13:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=9" title="Edit section: Antidistributivity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-Loraof-2017-08-31T00:13:00.000Z-Antidistributivity"></span>Currently the section <a href="/wiki/Distributive_property#Notions_of_antidistributivity" title="Distributive property">Distributive property#Notions of antidistributivity</a> says </p> <dl><dd><i>In the study of propositional logic and Boolean algebra, the term antidistributive law is sometimes used to denote the interchange between conjunction and disjunction when implication factors over them:</i>[3]</dd></dl> <dl><dd><dl><dd>(a ∨ b) ⇒ c ≡ (a ⇒ c) ∧ (b ⇒ c)</dd> <dd>(a ∧ b) ⇒ c ≡ (a ⇒ c) ∨ (b ⇒ c)</dd></dl></dd> <dd><i>These two tautologies are a direct consequence of the duality in De Morgan's laws.</i></dd></dl> <p>Despite the citation to a book (which I don't have access to), the second of these seems to be false. In a Venn diagram, the left side says that the intersection of A and B is entirely within C. But the right side says that at least one of A or B is entirely within C, which is not the same thing. The right side implies the left side, but not vice versa, so they are not equivalent statements. </p><p>Comments, anyone? <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Loraof-2017-08-31T00:13:00.000Z-Antidistributivity" class="ext-discussiontools-init-timestamplink">00:13, 31 August 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-08-31T00:13:00.000Z-Antidistributivity"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-08-31T00:13:00.000Z-Antidistributivity"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Tea2min-2017-09-01T08:22:00.000Z-Loraof-2017-08-31T00:13:00.000Z"></span>We have to be careful not to mix formal logic and causality. See <a href="/wiki/Material_implication_(rule_of_inference)" title="Material implication (rule of inference)">Material implication (rule of inference)</a> and <a href="/wiki/Material_inference" title="Material inference">Material inference</a>.</dd> <dd>Let me try. In classical logic, the <a href="/wiki/Material_conditional" title="Material conditional">material conditional</a> <i>a</i> ⇒ <i>b</i> is logically equivalent to ¬(<i>a</i> ∧ ¬<i>b</i>) which is logically equivalent to ¬<i>a</i> ∨ <i>b</i>. To find the matching Venn diagram for ¬<i>a</i> ∨ <i>b</i>, let us consider two sets <i>A</i> and <i>B</i>, and let us interprete <i>a</i> as <i>x</i> ∈ <i>A</i>, and <i>b</i> as <i>x</i> ∈ <i>B</i>. Using this, the logical expression ¬<i>a</i> ∨ <i>b</i> would be represented as the set <i>A</i><sup>C</sup> ∪ <i>B</i>, where <i>A</i><sup>C</sup> is the <a href="/wiki/Absolute_complement" class="mw-redirect" title="Absolute complement">absolute complement</a> of <i>A</i>.</dd> <dd>Applying this to the second equivalence above, the left hand side (<i>a</i> ∧ <i>b</i>) ⇒ <i>c</i> would be represented as (<i>A</i> ∩ <i>B</i>)<sup>C</sup> ∪ <i>C</i>, (with <i>C</i> a third set, and interpreting <i>c</i> as <i>x</i> ∈ <i>C</i>) and the right hand side would be represented as (<i>A</i><sup>C</sup> ∪ <i>C</i>) ∪ (<i>B</i><sup>C</sup> ∪ <i>C</i>), i.e., <i>A</i><sup>C</sup> ∪ <i>B</i><sup>C</sup> ∪ <i>C</i>. Now, <a href="/wiki/De_Morgan%27s_laws" title="De Morgan's laws">De Morgan's laws</a> say <i>A</i><sup>C</sup> ∪ <i>B</i><sup>C</sup> = (<i>A</i> ∩ <i>B</i>)<sup>C</sup>, and so we are finished. Does this help?</dd> <dd><a href="/w/index.php?title=User:Tea2min&action=edit&redlink=1" class="new" title="User:Tea2min (page does not exist)">Tea2min</a> (<a href="/wiki/User_talk:Tea2min" title="User talk:Tea2min">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Tea2min-2017-09-01T08:22:00.000Z-Loraof-2017-08-31T00:13:00.000Z" class="ext-discussiontools-init-timestamplink">08:22, 1 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Tea2min-2017-09-01T08:22:00.000Z-Loraof-2017-08-31T00:13:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Tea2min-2017-09-01T08:22:00.000Z-Loraof-2017-08-31T00:13:00.000Z"></span></dd></dl> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-Loraof-2017-09-01T18:40:00.000Z-Tea2min-2017-09-01T08:22:00.000Z"></span>Thanks. Maybe I misunderstand what is meant by (a ⇒ c) ∨ (b ⇒ c). Doesn't it mean "either a implies c or b implies c or both"? Suppose A = {1, 2, 3}, B = {3, 4, 5}, C = {2, 3, 4}. Then the left side (a ∧ b) ⇒ c is satisfied, since 3 is in C. But 1 is in A but not in C, and 5 is in B but not in C; so neither (a ⇒ c) nor (b ⇒ c) is satisfied. <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Loraof-2017-09-01T18:40:00.000Z-Tea2min-2017-09-01T08:22:00.000Z" class="ext-discussiontools-init-timestamplink">18:40, 1 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-09-01T18:40:00.000Z-Tea2min-2017-09-01T08:22:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-09-01T18:40:00.000Z-Tea2min-2017-09-01T08:22:00.000Z"></span></dd></dl></dd></dl> <dl><dd><dl><dd><dl><dd><span data-mw-comment-start="" id="c-Tea2min-2017-09-02T07:34:00.000Z-Loraof-2017-09-01T18:40:00.000Z"></span>The statement <i>a</i> ⇒ <i>c</i> is false if and only if <i>a</i> is true and <i>b</i> is false, and true otherwise. Likewise, the statement <i>x</i> ∈ <i>A</i> ⇒ <i>x</i> ∈ <i>C</i> is false, <b>for a given <i>x</i></b>, if and only if <i>x</i> ∈ <i>A</i> and <i>x</i>∉ <i>C</i>, and true otherwise. The statement <i>x</i> ∈ <i>A</i> ⇒ <i>x</i> ∈ <i>C</i> does not mean "<b>for all <i>x</i></b>, <i>x</i> ∈ <i>A</i> ⇒ <i>x</i> ∈ <i>C</i>".</dd> <dd>Consider the statements <i>x</i> ∈ <i>A</i>, <i>x</i> ∈ <i>B</i>, and <i>x</i> ∈ <i>C</i>. Let <i>x</i> = 1, to make <i>x</i> ∈ <i>A</i> true and <i>x</i> ∈ <i>B</i> and <i>x</i> ∈ <i>C</i> false. Now <i>1</i> ∈ <i>A</i> is true and <i>x</i> ∈ <i>C</i> is false, and then <i>1</i> ∈ <i>A</i> ⇒ <i>1</i> ∈ <i>C</i> is false. But <i>1</i> ∈ <i>B</i> is false, and then <i>1</i> ∈ <i>B</i> ⇒ <i>1</i> ∈ <i>C</i> is <b>true</b> (<a href="/wiki/Ex_falso_quodlibet" class="mw-redirect" title="Ex falso quodlibet">ex falso quodlibet</a>), and then the combined statement (<i>1</i> ∈ <i>A</i> ⇒ <i>1</i> ∈ <i>C</i>) ∨ (<i>1</i> ∈ <i>B</i> ⇒ <i>1</i> ∈ <i>C</i>) is true. Similarly for <i>x</i> = 5.</dd> <dd>– <a href="/w/index.php?title=User:Tea2min&action=edit&redlink=1" class="new" title="User:Tea2min (page does not exist)">Tea2min</a> (<a href="/wiki/User_talk:Tea2min" title="User talk:Tea2min">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Tea2min-2017-09-02T07:34:00.000Z-Loraof-2017-09-01T18:40:00.000Z" class="ext-discussiontools-init-timestamplink">07:34, 2 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Tea2min-2017-09-02T07:34:00.000Z-Loraof-2017-09-01T18:40:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Tea2min-2017-09-02T07:34:00.000Z-Loraof-2017-09-01T18:40:00.000Z"></span></dd></dl></dd></dl></dd></dl> <dl><dd><dl><dd><dl><dd><dl><dd><span data-mw-comment-start="" id="c-Loraof-2017-09-02T17:19:00.000Z-Tea2min-2017-09-02T07:34:00.000Z"></span>Got it! Thanks for your very clear explanations. <a href="/wiki/User:Loraof" title="User:Loraof">Loraof</a> (<a href="/wiki/User_talk:Loraof" title="User talk:Loraof">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-Loraof-2017-09-02T17:19:00.000Z-Tea2min-2017-09-02T07:34:00.000Z" class="ext-discussiontools-init-timestamplink">17:19, 2 September 2017 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Loraof-2017-09-02T17:19:00.000Z-Tea2min-2017-09-02T07:34:00.000Z"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-Loraof-2017-09-02T17:19:00.000Z-Tea2min-2017-09-02T07:34:00.000Z"></span></dd></dl></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Vector_spaces_and_generalizations_to_several_sets" data-mw-thread-id="h-Vector_spaces_and_generalizations_to_several_sets-2018-11-24T16:28:00.000Z"><span data-mw-comment-start="" id="h-Vector_spaces_and_generalizations_to_several_sets-2018-11-24T16:28:00.000Z"></span>Vector spaces and generalizations to several sets<span data-mw-comment-end="h-Vector_spaces_and_generalizations_to_several_sets-2018-11-24T16:28:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Distributive_property&action=edit&section=10" title="Edit section: Vector spaces and generalizations to several sets"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span><div class="ext-discussiontools-init-section-bar"><div class="ext-discussiontools-init-section-metadata"></div><div class="ext-discussiontools-init-section-actions"></div></div></div> <p><span data-mw-comment-start="" id="c-50.35.97.238-2018-11-24T16:28:00.000Z-Vector_spaces_and_generalizations_to_several_sets"></span>The article on vector spaces clearly describes two operations as "distriubtions" but the article on distribution uses a narrower definition that doesnt apply. There is a contradiction between articles. </p><p>In the definition of the vector space (and possibly inner product), two sets are utilized. In the case of vector spaces, one set is the set of vectors and the other is the set of scalars (which is a field). In the vectors we define a single binary operation called vector addition, and in the scalars we define two binary operations called field multiplication and field addition. We also define a fourth function, an automata to be precise, called scalar multiplication which operates between the field elements and the vector elements producing vectors. We require "left distributivity" of scalar multiplication over vector addition. We also require "right distributivity" of scalar multiplication over field addition. These arent real distributivity, as per this articles definition, because it operates on elements of two different sets, rather than being two operations on a single set. Additionally, in the case of "right distributivity", the field addition turns into vector addition in the process; some sort of isomorphic mapping. This is one more problem with the distribution definition. </p><p>Im looking for a general definition to distributivity - a correction to these articles - that satisfies this dilemma. <a href="/wiki/Special:Contributions/50.35.97.238" title="Special:Contributions/50.35.97.238">50.35.97.238</a> (<a href="/w/index.php?title=User_talk:50.35.97.238&action=edit&redlink=1" class="new" title="User talk:50.35.97.238 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Distributive_property#c-50.35.97.238-2018-11-24T16:28:00.000Z-Vector_spaces_and_generalizations_to_several_sets" class="ext-discussiontools-init-timestamplink">16:28, 24 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-50.35.97.238-2018-11-24T16:28:00.000Z-Vector_spaces_and_generalizations_to_several_sets"><span class="ext-discussiontools-init-replylink-bracket">[</span><a class="ext-discussiontools-init-replylink-reply" role="button" tabindex="0" href="">reply</a><span class="ext-discussiontools-init-replylink-bracket">]</span></span><span data-mw-comment-end="c-50.35.97.238-2018-11-24T16:28:00.000Z-Vector_spaces_and_generalizations_to_several_sets"></span> </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?useformat=desktop&type=1x1&usesul3=0" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Talk:Distributive_property&oldid=1259127671">https://en.wikipedia.org/w/index.php?title=Talk:Distributive_property&oldid=1259127671</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:C-Class_level-4_vital_articles" title="Category:C-Class level-4 vital articles">C-Class level-4 vital articles</a></li><li><a href="/wiki/Category:Wikipedia_level-4_vital_articles_in_Mathematics" title="Category:Wikipedia level-4 vital articles in Mathematics">Wikipedia level-4 vital articles in Mathematics</a></li><li><a href="/wiki/Category:C-Class_vital_articles_in_Mathematics" title="Category:C-Class vital articles in Mathematics">C-Class vital articles in Mathematics</a></li><li><a href="/wiki/Category:C-Class_mathematics_articles" title="Category:C-Class mathematics articles">C-Class mathematics articles</a></li><li><a href="/wiki/Category:High-priority_mathematics_articles" title="Category:High-priority mathematics articles">High-priority mathematics articles</a></li><li><a href="/wiki/Category:Pages_translated_from_German_Wikipedia" title="Category:Pages translated from German Wikipedia">Pages translated from German Wikipedia</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden category: <ul><li><a href="/wiki/Category:All_Wikipedia_vital_articles" title="Category:All Wikipedia vital articles">All Wikipedia vital articles</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 23 November 2024, at 14:38<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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