Talk:Binary relation

comment by Dbachmann

reflexive is a very common word -- this should be reflexive (mathematics). In linguistics, reflexive is the technical term for an action directed back at the agent. dab 21:12, 3 Sep 2004 (UTC)

You are probably talking about the article reflexive which was (I just changed it) a redirect to this page. Reflexive now redirects to Reflexive relation. Are there any articles about other meanings of "reflexive"? If so then we can turn Reflexive into a disambiguation page linking to each of the different articles. If there aren't any other "reflexive" articles, then until there are we should leave it as a simple redirect. Paul August 21:37, Sep 3, 2004 (UTC)

of course. I was 'blindly' linking to reflexive from Arabic grammar, and somebody removed my "wrong link" instead disambiguating reflexive. I will fix it myself when I get to it, no problem. dab 20:53, 4 Sep 2004 (UTC)

Should all these properties have their own pages?

Should all these properties have their own pages? And if so should that be under 'Reflexive' or under 'Reflexive binary relation'? -- Jan Hidders

The following pages now exist: reflexive relation, transitive relation, symmetric relation and antisymmetric relation Paul August 21:26, Sep 3, 2004 (UTC)

Functional relations

It seems to me that "mere" relations as "x > y", x and y of the given pair (x,y), can be repeated: {(5 > 1), (5 > 2), (2 > 1), (3 > 2)}. "x=5" is repeated. But "generated" relations --being the graph of a given function f: x --> y, y=f(x)-- as "y = 2x + 1", x and y of the given pair (x,y), can not be repeated: {(5,11), [(5,11),] (2,5), (3,7)} because when "x=5" is repeated, "y=11" is repeated, too. Yielding, duplicated pair member in the set, and being discarded immediatly. The explanation is mine but the idea is coming from: Costas Bush, http://www.cs.rpi.edu/courses/fall00/modcomp3/class1.ppt and //www.doc.eng.cmu.ac.th/course/cpe333/LectureNotes/chapter1_Introduction.pdf [Enrique Villar; mailto:evillarm@capgemini.es]

The article already covers functional relations. --Zundark 12:48 Mar 3, 2003 (UTC)

error confusing < and <=

"A partial order which is trichotomous is called a total order or a linear order." This is wrong. A partial order is antisymmetric and hence cannot be trichotomous.

To fix, either we also admit to call a relation < a partial order when it is: asymmetric (which has to be defined yet as: not (a<b and b<a)) and transitive, and then referring to this definition for adding trichotomy. Or we simply change "trichotomous" to "total" in the above sentence.

bo198214

Yes, the definition of "total order" given in the article was wrong. A total order is a partial order (i.e. reflexive, antisymmetric and transitive) which is total (i.e. everthing is related). I've fixed it now. Thanks for pointing out the error. Paul August 17:47, Sep 28, 2004 (UTC)

Relation negations in LaTeX

Does anyone know how to negate a binary relation signified by a letter (eg., R) in LaTeX? I figured that "\not R" would work, but it doesn't line up correctly. --Spikey 04:12, Nov 14, 2004 (UTC)

Definition of total?

What does it mean for a relation to be total? There are two different definitions in the article, one under special relations (for all x in X there exists a y in Y such that xRy) and one under relations over a set (for all x and y in X it holds that xRy or yRx); the latter one I have seen before. If the former one is also used in the literature, then it should be clarified that there are different definitions. -- Jitse Niesen 14:57, 16 Jun 2005 (UTC)

For the first meaning the term entire may be preferable. I used this term in the Axiom of dependent choice article, but I don't remember where I got it from. --Zundark 15:42, 16 Jun 2005 (UTC)

I now recall that total function is used in computer science for a function which is defined on all elements of its domain to distinguish it from a partial function (of course, it would be confusing to talk about entire functions in this context). But it does not matter which term is preferable, we should find out which term(s) is/are used in practice. -- Jitse Niesen 17:40, 16 Jun 2005 (UTC)