Talk:Asymmetric relation

nonsymmetric

Someone redirected nonsymmetric relation to asymmetric. However, they deleted the article without including anything about nonsymmetric relations. So here is the deleted part. Apparently he thought it look wierd and deleted it. Way to go. That's a great way to do things. Gregbard 23:04, 29 August 2007 (UTC)

Deleted Part

In logic, the nonsymmetrical or partimsymmetric relation is defined as:

(x)(y)(Rxy$\to$(($\exists$x)($\exists$y)(Ryx)$\wedge$($\exists$x)($\exists$y)(~Ryx))

Examples

"x loves y", "is the brother of"

See also

• symmetric relation
• asymmetric relation
• antisymmetric relation

True there is currently nothing in asymmetric relation that explains what a nonsymmetric relation is. I think this needs to be remedied. Asymmetric relation has two definitions; which one of these, if any, corresponds with the definition of a nonsymmetric relation? I too dislike redirects to articles that have no mention at all of the first article.

Gregbard, the notation used in your formula looks rather non-standard (the universal quantifier seems to be implicit), and even so I don't think the formula makes sense because you are quantifying over the same variables twice.

My searching reveals that the matter was discussed in Wikipedia talk:WikiProject Mathematics/Archive 28#Negation of definitions

--Egriffin (talk) 17:13, 7 September 2008 (UTC)

nonsymmetric

nonsymmetric relation and asymmetric relation is the same.

In Logic, the non-symmetric or the asymmetric relation occurs when, in the same context U (being U a finite set; and x and y elements of U), some couples <x,y> of R do exist and <y,x>, too; there are also cases where <x,y> do exist but <y,x> does not. From the point of view of symmetry, any pattern is possible for a given couple. The non-symmetric property of xRy is defined taken advantage of NOR connector (either symmetric or antisymmetric but neither both nor none) as:

(x)(y)(xRy$\to$(($\exists$x)($\exists$y)(yRx)NOR($\exists$x)($\exists$y)(~yRx))

Examples

"x loves y", "x is the brother of y"

See also

• symmetric relation
• antisymmetric relation
• homegeneous relation