Talk:Commutativity

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Contents 1 Old requested move, December 2005 2 Note 3 "Noncommutative" 3.1 Operator definition 4 Requested move 4.1 Survey 4.2 Discussion 5 what about the derivation 6 Simple example

[edit] Old requested move, December 2005

Commutative operation -> Commutativity

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

Voting

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• 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 be moved. WhiteNight ^{T | @ | C} 03:38, 28 December 2005 (UTC)

[edit] 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)

[edit] "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 . 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)

[edit] 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)

[edit] 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)

[edit] 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).