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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 articles</span></span></td><td class="mbox-empty-cell"></td></tr><tr><td class="assess import-mid"><a href="/wiki/Category:Mid-priority_mathematics_articles" title="Category:Mid-priority mathematics articles">Mid</a></td><td class="mbox-text" colspan="2">This article has been rated as <b>Mid-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> <meta property="mw:PageProp/toc"/> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Untitled" data-mw-thread-id="h-Untitled-2005-10-28T18:36:00.000Z"><span data-mw-comment-start="" id="h-Untitled-2005-10-28T18:36:00.000Z"></span>Untitled<span data-mw-comment-end="h-Untitled-2005-10-28T18:36:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=1" title="Edit section: Untitled"><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-JoergenB-2006-08-27T13:44:00.000Z-Untitled"></span>There's also <a href="/wiki/Binary_function" title="Binary function">binary function</a>. Merge them? -- JanHidders </p> <hr/> <p>I'm not sure they really mean the same thing. A binary operation is usually an algebraic operation, and is often denoted more like a*b than f(a,b). Probably the article ought to explain this. Also, if I had written the <a href="/wiki/Binary_operation" title="Binary operation">binary operation</a> article from scratch I would have only allowed it to cover functions of the form f : S x S -> S, rather than the general f : S x T -> U. I didn't like to change the original too much, but perhaps it should be changed. In any case it would be a good idea to cross-link <a href="/wiki/Binary_function" title="Binary function">binary function</a> and <a href="/wiki/Binary_operation" title="Binary operation">binary operation</a>. <br/>Zundark, 2001-08-08 </p> <hr/> <p>I agree, binary operations are S x S -> S. This article simply describes functions with two arguments. I think it should be changed, and the popular infix notation a*b for *(a,b) should be mentioned. --AxelBoldt </p> <hr/> <p>Oh, you guys don't consider the vector scalar product (V * V -> R) or scaling of vectors (R * V -> V) or matrices ( R * M -> M ), etc to be binary operations? --<a href="/wiki/User:Buz_Cory" class="mw-redirect" title="User:Buz Cory">Buz Cory</a> </p> <hr/> <p>Perhaps we should ask "what would Eric Weisstein" have done?" :-) But he doesn't seem to be sure either. There is </p><p><a rel="nofollow" class="external free" href="http://www.google.com/search?q=cache:LSEQ3bRAKkI:br.crashed.net/~akrowne/crc/math/b/b211.htm+binary+operator+eric+weisstein&hl=en">http://www.google.com/search?q=cache:LSEQ3bRAKkI:br.crashed.net/~akrowne/crc/math/b/b211.htm+binary+operator+eric+weisstein&hl=en</a> </p><p>and there is </p><p><a rel="nofollow" class="external free" href="http://www.google.com/search?q=cache:FjdWL0BZpB4:www.math.pku.edu.cn/library/encyclopedia/contents/BinaryOperator.html+binary+operator+eric+weisstein&hl=en">http://www.google.com/search?q=cache:FjdWL0BZpB4:www.math.pku.edu.cn/library/encyclopedia/contents/BinaryOperator.html+binary+operator+eric+weisstein&hl=en</a> </p><p>which doesn't explicitly require the input domains to be the same. I know that in my own field (computer science) the term is used for any operator that needs two arguments. Perhaps it should be someting like this: </p> <ol><li>begin with S x S -> S definition</li> <li>something about the notation</li> <li>a remark that sometimes also S x T -> U is possible, with Buz' examples and ref. to binary function</li></ol> <p>-- JanHidders </p> <hr/> <p>Maybe we should distinguish between a binary operation <b>on a set</b> (S x S->S) and a binary operation as such (S x T->U)? I don't know. --AxelBoldt </p> <hr/> <p>I think you are onto something, Axel. Binary operation on a set requires closure for the result, and the elements chosen must also be from the set, so (S x S ->S) makes more sense. WMORRIS </p> <hr/> <p>My textbook doesn't agree with the definition used on this article. I guess it is rather a convention or terminology problem than a real issue. It defines a binary operation as "f:AxA -> B". Where closure isn't required. The definition of a <a href="/wiki/Group_(mathematics)" title="Group (mathematics)">Group</a> includes the requirement for closure of course, again, conflicting with the Group article. This is the convention in Israel, I guess.. -- <a href="/wiki/User:Rotem_Dan" title="User:Rotem Dan">Rotem Dan</a> 14:20 13 Jul 2003 (UTC) </p> <dl><dd>Well, from further research, it is actually quite unique to my university. Popular definition in most universities in Israel is f:AxA -> A --<a href="/wiki/User:Rotem_Dan" title="User:Rotem Dan">Rotem Dan</a> 09:00 26 Jul 2003 (UTC)</dd></dl> <p>At present, there seems to be a compromise between the 'Only operations <b>on</b> a set' and 'General binary functions' alternatives; there is an added section covering some of the 'other' binary operations. However, it does not solve the issue. First of all, I wonder if there hasn't been a confusion between 'scalar product', mentioned as an example supra, and 'scalar multiplication', which now is given as an example in the article. In classical terminology, 'scalar product' is a function <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 V\times V\rightarrow R}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>×</mo> <mi>V</mi> <mo stretchy="false">→</mo> <mi>R</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V\times V\rightarrow R}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8f24b3e93cbd3989302b81aede2b693fc929c343" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.793ex; height:2.176ex;" alt="{\displaystyle V\times V\rightarrow R}"/></span> (where <i>V</i> is a vector space over the scalars <i>R</i>, in this context mostly the real numbers); while 'multiplication with scalars' is a function <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 R\times V\rightarrow V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>×</mo> <mi>V</mi> <mo stretchy="false">→</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R\times V\rightarrow V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8195731878e636fc32b661a9ebac3ae8a5270f58" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.793ex; height:2.176ex;" alt="{\displaystyle R\times V\rightarrow V}"/></span>. Some (but far from all) modern textbooks instead use the terms 'dot product' and 'scalar multiplication', respectively. In my opinion, both functions are legitimate candidates for the term 'binary operation'. </p><p>Actually, the restriction to the two singly enumerated instances in the present article are not only in conflict with some literature, but with a number of Wikipedia items in the category 'Binary operation'; e.g., <a href="/wiki/Commutative_operation" class="mw-redirect" title="Commutative operation">Commutative_operation</a> and <a href="/wiki/Outer_product" title="Outer product">Outer_product</a>. </p><p>Therefore, if no one protests, I think we should change the item, noting that the term is used in different senses in different contexts, sometimes very broadly, <i>including</i> in the Wikipedia notes. If any one <i>does</i> protest, I suggest that he or she briefs through all the items in the category, and lists those that should be omitted or rewritten, if we are to retain the present restricted definition. <a href="/wiki/User:JoergenB" title="User:JoergenB">JoergenB</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-JoergenB-2006-08-27T13:44:00.000Z-Untitled" class="ext-discussiontools-init-timestamplink">13:44, 27 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-JoergenB-2006-08-27T13:44:00.000Z-Untitled"><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-JoergenB-2006-08-27T13:44:00.000Z-Untitled"></span> </p> <hr/> <p><span data-mw-comment-start="" id="c-NoJoy-2005-10-28T18:36:00.000Z-Untitled"></span>I would like to see a discussion of the extension of a binary operator to finite sequences through repeated application. For example, the addition operator can be extended to the sum operation, the multiplication operator to the product operation, etc. In general, any binary operator (+) with a left identity can be extended to an operation on finite sequences whose value on the empty sequence is the left identity and whose value on a sequence {a[i]:0 <= i < k+1} of length k + 1 is Sk (+) a[k], where Sk is the value of the operation on the leading subsequence (prefix) {a[i]:0 <= i < k} of length k. </p><p>Moreover, what I would really like to see is the generic name for this new operation, which is what I was looking for when I came to this page. I've found the terms "bulk action", "iterated binary operation", and "prefix operation" through google, but haven't seen any clear evidence that any of these terms is in common usage. <a href="/wiki/User:NoJoy" title="User:NoJoy">NoJoy</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-NoJoy-2005-10-28T18:36:00.000Z-Untitled" class="ext-discussiontools-init-timestamplink">18:36, 28 October 2005 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-NoJoy-2005-10-28T18:36:00.000Z-Untitled"><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-NoJoy-2005-10-28T18:36:00.000Z-Untitled"></span> </p><p><span data-mw-comment-start="" id="c-TooMuchMath-2006-02-13T01:50:00.000Z-Untitled"></span>I don't think "iterated binary operation" would belong in a page about binary operations since it requires a unique left identitity and in the prototypical cases of sum and product notation requires associativity. However a link to such a page would be appropriate if someone who knows enough about it is willing to write it. <a href="/wiki/User:TooMuchMath" title="User:TooMuchMath">TooMuchMath</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-TooMuchMath-2006-02-13T01:50:00.000Z-Untitled" class="ext-discussiontools-init-timestamplink">01:50, 13 February 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-TooMuchMath-2006-02-13T01:50:00.000Z-Untitled"><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-TooMuchMath-2006-02-13T01:50:00.000Z-Untitled"></span> </p><p><span data-mw-comment-start="" id="c-NoJoy-2006-06-08T19:05:00.000Z-Untitled"></span>OK, I bit the bullet and added a new page myself. It probably needs help. <a href="/wiki/User:NoJoy" title="User:NoJoy">NoJoy</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-NoJoy-2006-06-08T19:05:00.000Z-Untitled" class="ext-discussiontools-init-timestamplink">19:05, 8 June 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-NoJoy-2006-06-08T19:05:00.000Z-Untitled"><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-NoJoy-2006-06-08T19:05:00.000Z-Untitled"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Malcohol-2006-08-30T10:40:00.000Z-NoJoy-2006-06-08T19:05:00.000Z"></span>I think you're describing "folding". This is a common notion in functional programming languages, used for recursing (iterating) over data types such as sequences and trees. The only description I can find in Wikipedia is the article <a href="/wiki/Catamorphism" title="Catamorphism">Catamorphism</a>, which is the same concept disguised by category theory. However, there should be plenty of stuff on the web if you search for "fold" and "unfold". --<a href="/wiki/User:Malcohol" title="User:Malcohol">Malcohol</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Malcohol-2006-08-30T10:40:00.000Z-NoJoy-2006-06-08T19:05:00.000Z" class="ext-discussiontools-init-timestamplink">10:40, 30 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Malcohol-2006-08-30T10:40:00.000Z-NoJoy-2006-06-08T19:05:00.000Z"><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-Malcohol-2006-08-30T10:40:00.000Z-NoJoy-2006-06-08T19:05:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Malcohol-2006-08-30T10:44:00.000Z-Malcohol-2006-08-30T10:40:00.000Z"></span>Oh! I just found your article <a href="/wiki/Iterated_binary_operation" title="Iterated binary operation">Iterated_binary_operation</a> which does link to <a href="/wiki/Fold_(higher-order_function)" title="Fold (higher-order function)">Fold (higher-order function)</a>.--<a href="/wiki/User:Malcohol" title="User:Malcohol">Malcohol</a> <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Malcohol-2006-08-30T10:44:00.000Z-Malcohol-2006-08-30T10:40:00.000Z" class="ext-discussiontools-init-timestamplink">10:44, 30 August 2006 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Malcohol-2006-08-30T10:44:00.000Z-Malcohol-2006-08-30T10:40:00.000Z"><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-Malcohol-2006-08-30T10:44:00.000Z-Malcohol-2006-08-30T10:40:00.000Z"></span></dd></dl></dd></dl> <p><span data-mw-comment-start="" id="c-88.106.125.175-2008-02-26T21:35:00.000Z-Untitled"></span>--No mention of blob-- The symbol? <small>—Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/88.106.125.175" title="Special:Contributions/88.106.125.175">88.106.125.175</a> (<a href="/w/index.php?title=User_talk:88.106.125.175&action=edit&redlink=1" class="new" title="User talk:88.106.125.175 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-88.106.125.175-2008-02-26T21:35:00.000Z-Untitled" class="ext-discussiontools-init-timestamplink">21:35, 26 February 2008 (UTC)</a></small><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-88.106.125.175-2008-02-26T21:35:00.000Z-Untitled"><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-88.106.125.175-2008-02-26T21:35:00.000Z-Untitled"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Closure" data-mw-thread-id="h-Closure-2011-05-09T17:15:00.000Z"><span data-mw-comment-start="" id="h-Closure-2011-05-09T17:15:00.000Z"></span>Closure<span data-mw-comment-end="h-Closure-2011-05-09T17:15:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=2" title="Edit section: Closure"><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-Mickeyg13-2011-05-09T17:15:00.000Z-Closure"></span>It is very tough to determine whether or not <a href="/wiki/Closure_(mathematics)" title="Closure (mathematics)">closure</a> is necessary in a binary operation from this article. The first paragraph leads one to believe that closure is not required, but then the more precise definition that follows leads one to believe closure is required. Then the article flips back and describes situations where closure is not required. I think the real issue is that the term has been overloaded such that it means slightly different things in different contexts, but this should somehow be made more clear. <a href="/wiki/User:Mickeyg13" title="User:Mickeyg13">Mickeyg13</a> (<a href="/wiki/User_talk:Mickeyg13" title="User talk:Mickeyg13">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Mickeyg13-2011-05-09T17:15:00.000Z-Closure" class="ext-discussiontools-init-timestamplink">17:15, 9 May 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Mickeyg13-2011-05-09T17:15:00.000Z-Closure"><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-Mickeyg13-2011-05-09T17:15:00.000Z-Closure"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Tashiro-2015-01-22T17:55:00.000Z-Mickeyg13-2011-05-09T17:15:00.000Z"></span>The subject of closure is discussed in the above section of this Talk page. The current article defines "binary operation on a set" rather than "binary operation". It would be best to point out in the article that the phrase "on a set" is an important distincion.</dd></dl> <dl><dd>The article defines "external binary operation" and this may give readers the impression that an "external binary operation" is a more general mathematical object that a "binary operation". <a href="/w/index.php?title=User:Tashiro&action=edit&redlink=1" class="new" title="User:Tashiro (page does not exist)">Tashiro</a> (<a href="/w/index.php?title=User_talk:Tashiro&action=edit&redlink=1" class="new" title="User talk:Tashiro (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Tashiro-2015-01-22T17:55:00.000Z-Mickeyg13-2011-05-09T17:15:00.000Z" class="ext-discussiontools-init-timestamplink">17:55, 22 January 2015 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Tashiro-2015-01-22T17:55:00.000Z-Mickeyg13-2011-05-09T17:15:00.000Z"><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-Tashiro-2015-01-22T17:55:00.000Z-Mickeyg13-2011-05-09T17:15:00.000Z"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Commutivity" data-mw-thread-id="h-Commutivity-2011-08-08T07:24:00.000Z"><span data-mw-comment-start="" id="h-Commutivity-2011-08-08T07:24:00.000Z"></span>Commutivity<span data-mw-comment-end="h-Commutivity-2011-08-08T07:24:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=3" title="Edit section: Commutivity"><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-Patrick-2011-08-08T07:24:00.000Z-Commutivity"></span>Is the line: "If the operation is commutative, ab = ba, then the value depends only on the multiset a,b,c." Meant to have (a,b),c, where a and b must be together. For it to not matter where c comes in terms of a and b, i.e between a and b, then wouldn't it also require associativity, where it doesn't matter if you do a and b first, or b and c? The next line states it depends only on the multiset a,b,c if it is both associative and commutative.<small><span class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/w/index.php?title=User:149.171.197.62&action=edit&redlink=1" class="new" title="User:149.171.197.62 (page does not exist)">149.171.197.62</a> (<a href="/w/index.php?title=User_talk:149.171.197.62&action=edit&redlink=1" class="new" title="User talk:149.171.197.62 (page does not exist)">talk</a> • <a href="/wiki/Special:Contributions/149.171.197.62" title="Special:Contributions/149.171.197.62">contribs</a>) </span></small> </p> <dl><dd>I fixed it, intended formatting changed the meaning.--<a href="/wiki/User:Patrick" title="User:Patrick">Patrick</a> (<a href="/wiki/User_talk:Patrick" title="User talk:Patrick">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Patrick-2011-08-08T07:24:00.000Z-Commutivity" class="ext-discussiontools-init-timestamplink">07:24, 8 August 2011 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Patrick-2011-08-08T07:24:00.000Z-Commutivity"><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-Patrick-2011-08-08T07:24:00.000Z-Commutivity"></span></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Mistake?" data-mw-thread-id="h-Mistake?-2012-03-28T16:07:00.000Z"><span id="Mistake.3F"></span><span data-mw-comment-start="" id="h-Mistake?-2012-03-28T16:07:00.000Z"></span>Mistake?<span data-mw-comment-end="h-Mistake?-2012-03-28T16:07:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=4" title="Edit section: Mistake?"><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-186.58.23.226-2012-03-28T16:07:00.000Z-Mistake?"></span>The article says "More precisely, a binary operation on a set S is a binary relation that maps elements of the Cartesian product S × S to S" </p><p>Isn't a binary operation supposed to be a <i>function</i>? This isn't even mentioned in the article. Instead it says it is a <i>binary relation</i>, wich is not a function so should be wrong. <span style="font-size: smaller;" class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/186.58.23.226" title="Special:Contributions/186.58.23.226">186.58.23.226</a> (<a href="/w/index.php?title=User_talk:186.58.23.226&action=edit&redlink=1" class="new" title="User talk:186.58.23.226 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-186.58.23.226-2012-03-28T16:07:00.000Z-Mistake?" class="ext-discussiontools-init-timestamplink">16:07, 28 March 2012 (UTC)</a></span><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-186.58.23.226-2012-03-28T16:07:00.000Z-Mistake?"><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-186.58.23.226-2012-03-28T16:07:00.000Z-Mistake?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-Wcherowi-2012-09-30T04:47:00.000Z-186.58.23.226-2012-03-28T16:07:00.000Z"></span>You are right. This is now fixed. <a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Wcherowi-2012-09-30T04:47:00.000Z-186.58.23.226-2012-03-28T16:07:00.000Z" class="ext-discussiontools-init-timestamplink">04:47, 30 September 2012 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2012-09-30T04:47:00.000Z-186.58.23.226-2012-03-28T16:07:00.000Z"><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-Wcherowi-2012-09-30T04:47:00.000Z-186.58.23.226-2012-03-28T16:07:00.000Z"></span></dd></dl> <hr/> <p><span data-mw-comment-start="" id="c-80.215.158.122-2015-09-02T12:08:00.000Z-Mistake?"></span>The article opens with: </p> <ul><li><i>a binary operation on a set is a calculation that combines two elements of the set (called operands) to produce another element of the set.</i></li></ul> <p>Isn't this a special case of a binary operation? Surely a <a href="/wiki/Binary_operation" title="Binary operation">binary operation</a> is a special case of an <a href="/wiki/Operation" class="mw-disambig" title="Operation">operation</a>? Recalling the definition of an operation: <i>an operation is an action or procedure which produces a new value from zero or more input values</i>. Thus a binary operation is surely defined as follows: </p> <ul><li><i>a binary operation is an action or procedure which produces a new value from two input values</i></li></ul> <p>I actually favour a revision to operation too: <i>an operation is a calculation from zero or more input values to an output value</i>. This enables a binary operation to be defined as: <i>a binary operation is calculation from two input values to an output value</i>. <small class="autosigned">— Preceding <a href="/wiki/Wikipedia:Signatures" title="Wikipedia:Signatures">unsigned</a> comment added by <a href="/wiki/Special:Contributions/80.215.158.122" title="Special:Contributions/80.215.158.122">80.215.158.122</a> (<a href="/w/index.php?title=User_talk:80.215.158.122&action=edit&redlink=1" class="new" title="User talk:80.215.158.122 (page does not exist)">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-80.215.158.122-2015-09-02T12:08:00.000Z-Mistake?" class="ext-discussiontools-init-timestamplink">12:08, 2 September 2015 (UTC)</a></small><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-80.215.158.122-2015-09-02T12:08:00.000Z-Mistake?"><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-80.215.158.122-2015-09-02T12:08:00.000Z-Mistake?"></span> </p> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Merge_with_Binary_relation?" data-mw-thread-id="h-Merge_with_Binary_relation?-2018-11-26T17:46:00.000Z"><span id="Merge_with_Binary_relation.3F"></span><span data-mw-comment-start="" id="h-Merge_with_Binary_relation?-2018-11-26T17:46:00.000Z"></span>Merge with <a href="/wiki/Binary_relation" title="Binary relation">Binary relation</a>?<span data-mw-comment-end="h-Merge_with_Binary_relation?-2018-11-26T17:46:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=5" title="Edit section: Merge with Binary relation?"><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-Ipatrol-2018-11-26T17:46:00.000Z-Merge_with_Binary_relation?"></span>These two articles appear to cover the same subject, but neither so much as reference or link to the other. I'm inclined to suggest that they be merged together. Thoughts/questions/concerns? --<a href="/wiki/User:Ipatrol" title="User:Ipatrol">Ipatrol</a> (<a href="/wiki/User_talk:Ipatrol" title="User talk:Ipatrol">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Ipatrol-2018-11-26T17:46:00.000Z-Merge_with_Binary_relation?" class="ext-discussiontools-init-timestamplink">17:46, 26 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Ipatrol-2018-11-26T17:46:00.000Z-Merge_with_Binary_relation?"><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-Ipatrol-2018-11-26T17:46:00.000Z-Merge_with_Binary_relation?"></span> </p> <dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2018-11-26T18:43:00.000Z-Ipatrol-2018-11-26T17:46:00.000Z"></span>These are completely different things: a <i>binary operation</i> takes two elements and returns a third one, generally in the same set. The basic examples are addition (+) and multiplication (×). A <i>binary relation</i> takes also two elements, but returns <i>true</i> or <i>false</i>, which mean <i>related</i> and <i>unrelated</i>. Basic examples are =, ≠, <, ≤, ... There are absolutely no reason for a merge. On the contrary, a merge would be confusing for most readers. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-D.Lazard-2018-11-26T18:43:00.000Z-Ipatrol-2018-11-26T17:46:00.000Z" class="ext-discussiontools-init-timestamplink">18:43, 26 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2018-11-26T18:43:00.000Z-Ipatrol-2018-11-26T17:46:00.000Z"><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-D.Lazard-2018-11-26T18:43:00.000Z-Ipatrol-2018-11-26T17:46:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Wcherowi-2018-11-26T20:10:00.000Z-D.Lazard-2018-11-26T18:43:00.000Z"></span>I agree with D.Lazard, the only thing in common with these articles is the word "binary". The reason there are no links between these articles is that there are no connections. --<a href="/wiki/User:Wcherowi" title="User:Wcherowi">Bill Cherowitzo </a> (<a href="/wiki/User_talk:Wcherowi" title="User talk:Wcherowi">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Wcherowi-2018-11-26T20:10:00.000Z-D.Lazard-2018-11-26T18:43:00.000Z" class="ext-discussiontools-init-timestamplink">20:10, 26 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wcherowi-2018-11-26T20:10:00.000Z-D.Lazard-2018-11-26T18:43:00.000Z"><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-Wcherowi-2018-11-26T20:10:00.000Z-D.Lazard-2018-11-26T18:43:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Jochen_Burghardt-2018-11-26T21:01:00.000Z-Wcherowi-2018-11-26T20:10:00.000Z"></span>I agree with D.Lazard and Bill Cherowitzo. From a computer-science point of view, a binary relation could be considered as a special case of a binary operation, with result type <code>bool</code>. However, in mathematics (in particular in 1st-order predicate logic), operations and relations are usually considered completely different things. - <a href="/wiki/User:Jochen_Burghardt" title="User:Jochen Burghardt">Jochen Burghardt</a> (<a href="/wiki/User_talk:Jochen_Burghardt" title="User talk:Jochen Burghardt">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Jochen_Burghardt-2018-11-26T21:01:00.000Z-Wcherowi-2018-11-26T20:10:00.000Z" class="ext-discussiontools-init-timestamplink">21:01, 26 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Jochen_Burghardt-2018-11-26T21:01:00.000Z-Wcherowi-2018-11-26T20:10:00.000Z"><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-Jochen_Burghardt-2018-11-26T21:01:00.000Z-Wcherowi-2018-11-26T20:10:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Ipatrol-2018-11-28T18:17:00.000Z-Jochen_Burghardt-2018-11-26T21:01:00.000Z"></span>Well binary operations could be considered a kind of binary relation. Specifically, they are subsets of <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 (R\times S)\times T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>R</mi> <mo>×</mo> <mi>S</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (R\times S)\times T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf139a762a63d5c1311e43959c139829b5f0f161" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.39ex; height:2.843ex;" alt="{\displaystyle (R\times S)\times T}"/></span>. The introduction assumes <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 R=S=T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>S</mi> <mo>=</mo> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=S=T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b28630a5d2746de15b7985e66cd17c9d35b1b8ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.096ex; height:2.176ex;" alt="{\displaystyle R=S=T}"/></span>, and for "external binary operations" relaxes that to just <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 R=S}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mi>S</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=S}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45459f36b6d99e770fb6d78c4fd775ee3169d618" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.362ex; height:2.176ex;" alt="{\displaystyle R=S}"/></span>. However, I understand your point that they describe different things. I would then propose the article be extended or rewritten to be <i>similar</i> in layout to <a href="/wiki/Binary_relations" class="mw-redirect" title="Binary relations">Binary relations</a>, containing a short listing of all the symmetry properties that a binary operation can have, like the <a href="/wiki/Associative_property" title="Associative property">associative property</a>, <a href="/wiki/Commutative_property" title="Commutative property">commutative property</a>, <a href="/wiki/Distributive_property" title="Distributive property">distributive property</a>, and so forth. Thoughts? --<a href="/wiki/User:Ipatrol" title="User:Ipatrol">Ipatrol</a> (<a href="/wiki/User_talk:Ipatrol" title="User talk:Ipatrol">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Ipatrol-2018-11-28T18:17:00.000Z-Jochen_Burghardt-2018-11-26T21:01:00.000Z" class="ext-discussiontools-init-timestamplink">18:17, 28 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Ipatrol-2018-11-28T18:17:00.000Z-Jochen_Burghardt-2018-11-26T21:01:00.000Z"><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-Ipatrol-2018-11-28T18:17:00.000Z-Jochen_Burghardt-2018-11-26T21:01:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2018-11-28T19:13:00.000Z-Ipatrol-2018-11-28T18:17:00.000Z"></span>No, binary operations cannot be considered as binary relations, as they are <a href="/wiki/Ternary_relation" title="Ternary relation">ternary relations</a> (relation between their two arguments and their result). However WP articles should be written to be accessible to the largest possible audience, and must proceed by increasing degree of technicality (see <a href="/wiki/Wikipedia:TECHNICAL" class="mw-redirect" title="Wikipedia:TECHNICAL">WP:TECHNICAL</a>). For this point of view, <a href="/wiki/Binary_operation" title="Binary operation">Binary operation</a> is much better than <a href="/wiki/Binary_relation" title="Binary relation">Binary relation</a>, although the former may be improved. For example, the lead of <a href="/wiki/Binary_relation" title="Binary relation">Binary relation</a> contains many terms that are known only by people having a very good mathematical knowledge, such as <a href="/wiki/Cartesian_product" title="Cartesian product">Cartesian product</a> (in the first sentence), or <a href="/wiki/Power_set" title="Power set">power set</a>. Also, the most elementary relations (equality and inequalities) are presented after the divisibility relation (much more technical), and the example of inequalities between numbers are not clearly presented (only their generalizations to various areas are explicitly mentioned). In the body, the properties that are used in all mathematics (for example reflexivity, transitivity, symmetry and anti-symmetry) are defined after or between much more technical properties that are known and used only by specialists of relations and graphs. <b>So, if an article deserves to be rewritten, this is <a href="/wiki/Binary_relation" title="Binary relation">Binary relation</a>, not <a href="/wiki/Binary_operation" title="Binary operation">Binary operation</a>.</b> <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-D.Lazard-2018-11-28T19:13:00.000Z-Ipatrol-2018-11-28T18:17:00.000Z" class="ext-discussiontools-init-timestamplink">19:13, 28 November 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2018-11-28T19:13:00.000Z-Ipatrol-2018-11-28T18:17:00.000Z"><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-D.Lazard-2018-11-28T19:13:00.000Z-Ipatrol-2018-11-28T18:17:00.000Z"></span> <dl><dd><span data-mw-comment-start="" id="c-Ipatrol-2018-12-03T20:54:00.000Z-D.Lazard-2018-11-28T19:13:00.000Z"></span>I think both articles could stand to be rewritten, although some of your critiques of <a href="/wiki/Binary_relation" title="Binary relation">Binary relation</a> I feel are inapplicable as those terms are linked to articles which define them. I think a short listing of commonly-named symmetry properties would be a useful addition to this article, as they help connect to a variety of algebraic structures, and I cannot find any such listing on Wikipedia either as an article, category, or infobox. --<a href="/wiki/User:Ipatrol" title="User:Ipatrol">Ipatrol</a> (<a href="/wiki/User_talk:Ipatrol" title="User talk:Ipatrol">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Ipatrol-2018-12-03T20:54:00.000Z-D.Lazard-2018-11-28T19:13:00.000Z" class="ext-discussiontools-init-timestamplink">20:54, 3 December 2018 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Ipatrol-2018-12-03T20:54:00.000Z-D.Lazard-2018-11-28T19:13:00.000Z"><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-Ipatrol-2018-12-03T20:54:00.000Z-D.Lazard-2018-11-28T19:13:00.000Z"></span></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl></dd></dl> <div class="mw-heading mw-heading2 ext-discussiontools-init-section"><h2 id="Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?" data-mw-thread-id="h-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?-2020-05-06T22:37:00.000Z"><span id="Is_it_f:_A_.C3.97_A_.E2.86.92_A.2C_f:_A_.C3.97_A_.E2.86.92_B_or_f:_A_.C3.97_B_.E2.86.92_C.3F"></span><span data-mw-comment-start="" id="h-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?-2020-05-06T22:37:00.000Z"></span>Is it f: A × A → A, f: A × A → B or f: A × B → C?<span data-mw-comment-end="h-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?-2020-05-06T22:37:00.000Z"></span></h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Talk:Binary_operation&action=edit&section=6" title="Edit section: Is it f: A × A → A, f: A × A → B or f: A × B → C?"><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-Wikisaurus-2020-05-06T22:37:00.000Z-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?"></span>The article is rather vague about it. Could one explain it somehow better, like "usually binary operation means f: A × A → A, while f: A × B → C is called binary function, but sometimes binary operation means f: A × B → C, while f: A × A → A is called internal binary operation" (I am not sure that this is true)? There is certainly an inconsistency between <a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">Operation (mathematics)</a>, where f: A × A → B is called a binary operation, and <a href="/wiki/Binary_function" title="Binary function">Binary function</a>, where f: A × A → A is called a binary operation. <a href="/wiki/User:Wikisaurus" title="User:Wikisaurus">Wikisaurus</a> (<a href="/wiki/User_talk:Wikisaurus" title="User talk:Wikisaurus">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-Wikisaurus-2020-05-06T22:37:00.000Z-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?" class="ext-discussiontools-init-timestamplink">22:37, 6 May 2020 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-Wikisaurus-2020-05-06T22:37:00.000Z-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?"><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-Wikisaurus-2020-05-06T22:37:00.000Z-Is_it_f:_A_×_A_→_A,_f:_A_×_A_→_B_or_f:_A_×_B_→_C?"></span> </p> <dl><dd><dl><dd><span data-mw-comment-start="" id="c-D.Lazard-2020-05-07T03:41:00.000Z-Wikisaurus-2020-05-06T22:37:00.000Z"></span>This is not a WP inconsistency. This an inconsistency of the common mathematics terminology. This is rather common for mathematical concepts that need not to be formally defined, because one considers only specific example, without considering the whole class of objects. Nevertheless, I have edited the article for making clear that both terminologies are used. <a href="/wiki/User:D.Lazard" title="User:D.Lazard">D.Lazard</a> (<a href="/wiki/User_talk:D.Lazard" title="User talk:D.Lazard">talk</a>) <a href="https://en.wikipedia.org/wiki/Talk:Binary_operation#c-D.Lazard-2020-05-07T03:41:00.000Z-Wikisaurus-2020-05-06T22:37:00.000Z" class="ext-discussiontools-init-timestamplink">03:41, 7 May 2020 (UTC)</a><span class="ext-discussiontools-init-replylink-buttons" data-mw-thread-id="c-D.Lazard-2020-05-07T03:41:00.000Z-Wikisaurus-2020-05-06T22:37:00.000Z"><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-D.Lazard-2020-05-07T03:41:00.000Z-Wikisaurus-2020-05-06T22:37:00.000Z"></span></dd></dl></dd></dl>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" 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:Binary_operation&oldid=1195707771">https://en.wikipedia.org/w/index.php?title=Talk:Binary_operation&oldid=1195707771</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:Start-Class_mathematics_articles" title="Category:Start-Class mathematics articles">Start-Class mathematics articles</a></li><li><a href="/wiki/Category:Mid-priority_mathematics_articles" title="Category:Mid-priority mathematics articles">Mid-priority mathematics 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 14 January 2024, at 23:28<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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