Talk:Commutative property

Old requested move, December 2005

Commutative operation -> Commutativity

The article is talking about the meaning of commutative rather than the operation

Voting

Add *Support or *Oppose followed by an optional one sentence explanation, then sign your vote with ~~~~

• Oppose The page should probably instead be moved to Commutation or Commutation (mathematics), since that is the noun form of this word, and the word used for the logic replacement rule of this nature.—jiy (talk) 19:34, 10 December 2005 (UTC)

Discussion

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Result

It was requested that this article be renamed but there was no consensus for it to be moved. WhiteNight ^{T | @ | C} 03:38, 28 December 2005 (UTC)

Note

This probably needs to be clarified; especially if we are going to use the language of category theory elsewhere. Septentrionalis 01:55, 6 May 2006 (UTC)

"Noncommutative"

• "So, subtraction is commutative if and only if x = y and noncommutative for any other pair of real numbers."

Who actually uses that language? Anyone? Melchoir 14:59, 2 June 2006 (UTC)

I say we just x that line.--Emplynx 15:41, 5 June 2006 (UTC)

A more accurate formulation would be The pair (x,y) commutes (or: x commutes with y) with respect to the operator subtraction, if and only if $x\neq y$. Since this does not hold for all pairs (x,y), the operation is not commutative. This is somewhat lengthy, but perhaps worth it. The point is that the whole operation as one unit is either commutative or non-commutative. JoergenB 11:58, 27 August 2006 (UTC)

Operator definition

I think that a reference to the difference between function and infix notation for operators might be of use for the non-professionals. I also think restoring a multiplication sign might help. In my experience, fresh students often find some difficulty in relating the two statements f(y,z) = f(z,y) and yz = zy.

However, I noted that binary operations (as distinguished from operators???) are defined in a more restricted manner in these pages, as operators on one set. While a commutative operator indeed must be defined on a 'Cartesian square' rather than on an arbitrary Cartesian product, its result may reside in a different set. After all, an ordinary scalar product (aka 'dot product') on a vector space is ordinarily called a commutative operation. The discussion of `infix' versus `prefix' notation I only found in the `operator' items. JoergenB 12:34, 27 August 2006 (UTC)

Binary operation briefly addresses notation; perhaps too late? It sounds like you have some good ideas for the article. By all means, please take a shot at implementing them! Melchoir 16:33, 27 August 2006 (UTC)

Indeed, it does discuss notation; thanks for pointing it out. I'll wait with editing, until I have a better grip on the conflicting binary operation definitions issue. If indeed the range always should be a factor of the domain, for 'binary operations', then several items should be rewritten or removed (e.g., dot_product). JoergenB 01:06, 28 August 2006 (UTC)

The following discussion is an archived debate of the proposal. Please do not modify it. Subsequent comments should be made in a new section on the talk page. No further edits should be made to this section.

The result of the debate was Page moved for consistency, per discussion below. -GTBacchus^(talk) 21:47, 16 September 2006 (UTC)

Requested move

Commutative operation → Commutativity – Follow Anticommutativity, Associativity, Power associativity, Distributivity, and Alternativity. Melchoir 16:15, 7 September 2006 (UTC)

Survey

Add "* Support" or "* Oppose" followed by an optional one-sentence explanation, then sign your opinion with ~~~~

• Support (provided a link from the old name is retained). Melchoir's consistency argument seems reasonable.JoergenB 14:39, 12 September 2006 (UTC)

Discussion

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• See also #Old requested move, December 2005 which was the same request but failed (albiet not with a huge amount of participation) RN 16:17, 7 September 2006 (UTC)

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made in a new section on this talk page. No further edits should be made to this section.

what about the derivation

this article (and the associativity article) should have some context describing how the concept is (was) derived. Is it subject to proof? Is it axiomatic? drefty.mac 20:32, 26 October 2006 (UTC)

Simple example

I added a simple example via the "+" operator at the beginning of the page because I think that, for "standard" readers this clarifies commutativity a lot in a sinlge line (see Associativity for comparison).

new introduction

I added a whole new introduction. Please check if it is ok. ssepp^(talk) 18:25, 31 May 2007 (UTC)

July 2007 Rewrite

I clarified the introduction a bit and removed the example, it cluttered the lead. I removed all math from the lead to make it more accessible since this article is in the basics section of math. I switched the article to use the binary operation notation everywhere, and added the binary function notation in a generalizations section. I plan to go back through later and add references. -Weston.pace 18:12, 12 July 2007 (UTC)

Does anyone know if multivariate functions are commutative if the order of their parameters doesn't matter? -Weston.pace 20:42, 12 July 2007 (UTC)

GA Review

Well-written, easy to understand article. Short and to the point. I wish other mathematics articles were this easy to understand! ;-)

There are a few minor issues which need to be addressed before granting GA status. The 'common uses' section could overall be expanded a bit. For one, it mentions that, "the commutativity of well known operations (such as addition and multiplication on real and complex numbers) is often used (or implicitly assumed) in proofs." But there are no references of this, and no examples or wikilinks to proofs to illustrate this. As it stands right now, this is mainly just hearsay -- "Yeah, this is used in all sorts of math proofs,... yadayadayada!" Please provide some actual examples, and possibly a reference or two.

Under 'Examples: Commutative operations in math', it would help if the multiplication example of 2x3 = 3x2 matched up with the graphical example, which is 3x5 = 5x3.

The references to websites (links) need to have dates of retrieval added to them (e.g. when was the URL last accessed/checked? "Retrieved on August 3, 2007"). It would also be helpful if author and publisher (who the website belongs to) information was added to website links as well.

Other than that, this article looks great! Dr. Cash 20:43, 3 August 2007 (UTC)

GA status reviewed

This article has been reviewed as part of Wikipedia:WikiProject Good articles/Project quality task force. I believe the article currently meets the criteria and should remain listed as a Good article. The article history has been updated to reflect this review. (oldid reference #:152489007) OhanaUnited^{Talk page} 02:32, 24 August 2007 (UTC)

Poor Image

This colourful image is used to illustrate the commutivity of multiplication: . The image may illustrate the point for the specific example of 5x3 = 3x5, but it is not persuasive in the general case that AxB = BxA. I think a two-dimensional array of objects (arranged in a grid) would be more appropriate:

                * * *
* * * * *       * * *
* * * * *   =   * * *
* * * * *       * * *
                * * *

This ASCII illustration is more persuasive that M rows containing N objects yields the same total as N columns containing M objects.

Is there someone with the necessay skills willing to create such an illustration? reetep 13:01, 30 October 2007 (UTC)

I'm getting rid of the picture of the grapes because it's just plain confusing. Three does not equal five. Dithridge (talk) 22:01, 23 October 2008 (UTC)

Well I reverted it; sorry. I think the image is good and useful: the rectangle of stars is not better, just different. The grapes image shows clearly that commutativity of multiplication is far from obvious in real-life situations. Robinh 07:10, 24 October 2008 (UTC)

The graph picture is totally unobvious. I just now realized that the left set had 5 grapes each and the right set had 3 grapes each. If a picture is going to illustrate an idea it should be obvious from the first moment your eyes see it. Mikemill (talk) 16:35, 4 November 2008 (UTC)

combination

wouldn't it be good to make fact that commutativity is just a kind of combination more visible? could chain some further lookuping by peoples 84.16.123.194 (talk) 05:17, 2 April 2008 (UTC) {tshepo nobela ul} —Preceding unsigned comment added by 196.21.218.142 (talk) 00:13, 2 November 2008 (UTC)

relation of commutativity and associativity

I've restored the sentence

The associative property is closely related to the commutative property.

This was recently removed with "meaningless" as the edit summary. To the contrary, the associative identity (a•b)•c = a•(b•c) for fixed a and c and arbitrary b is equivalent to the commutative identity (a•—)∘(—•c) = (—•c)∘(a•—). I found a reference for this in the paper

• Došen, Kosta; Petrić, Zoran (2006), "Associativity as Commutativity", J. Symbolic Logic, 71 (1): 217–226, doi:10.2178/jsl/1140641170 (arXiv:math/0506600)

I'd like to check whether additional references are available. In particular, is anyone aware of an earlier reference for the claim that associativity is a kind of commutativity (and not just that associativity can be defined by a commutative diagram)? Michael Slone (talk) 01:12, 17 April 2009 (UTC)

Linear Algebra / Physics

This article could do with an explanation or brief discussion, or even a link to such, of non-commuting linear operators as used in quantum mechanics. There is a link to particle statistics, labelled as a link to a discussion of commutativity in physics, but that page does not in fact discuss commutativity at all. Nathaniel Virgo (talk) 11:30, 24 June 2010 (UTC)

I have now added a new section on commutativity and the uncertainty principle in quantum mechanics, along with a link to the main article on the Heisenberg uncertainty principle for further explanations. Dirac66 (talk) 01:20, 9 July 2010 (UTC)

Concatenation example confusing

Am I the only one who does not understand the diagram purporting to show that concatenation is non-commutative? (in the section "Noncommutative operations in everyday life")? What is the meaning of EA + ≠ + TTEA followed by ( ) ≠ ( ) EATTEA ??

A simpler and clearer example might be EA + TT = EATT ≠ TTEA = TT + EA. Dirac66 (talk) 02:42, 10 July 2010 (UTC)

Yes, despite my best efforts I cannot understand it either, your example is clearer.