Talk:Homogeneous relation
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What does it mean?
[edit]- A homogeneous relation is a mathematical relation between sets X and Y in which X is the same set as Y and have the same domain and range.
Huh? If X is the same set as Y, why not just say it's a relation from a set X to itself? Why complicate the language instead of making the thing appear as simple as it really is? "...and have" makes no sense; was "...and has" intended? "has the same domain" would mean you're saying TWO things both have the same domain. What are those two things? It doesn't say. Or did it mean the domain is the same as the range? If so, that's what it should say. This is very very vaguely written. Michael Hardy 03:04, 29 August 2007 (UTC)
- Well it's a good point on one hand. How silly to create a new name for "being the same thing as." All the things you mention should certainly be clarified. However, be mindful. The simple analysis is not always the best one. For instance, we actually use the law of identity A=A in proofs of theorems all the time. This is the name of the "mathematical relation," form of this concept as opposed to heterogeneous relation on which I have no information. Perhaps someone could help me out and look into it. I am curious to know what the formulation for a heterogeneous relation is. Be well, Gregbard 05:34, 29 August 2007 (UTC)
This article is not just vague and confusing. It also contradicts long established usage of the term homogeneous relation in mathematics. See, for example, this reference, where the phrase is used to describe a set of vectors which are not linearly independent.
I can't be certain, but I don't think the term homogeneous relation has ever been used to describe a binary relation in mathematics. I think the term "homogeneous" pops up a lot in the theory of equations, where it generally means that some portion of each equation (usually the constant term) is zero. I reviewed a few dozen article titles on Google Scholar where the phrase "homogeneous relation" occurs, but I could not discern a consistent pattern pointing to a single commonly accepted meaning. In other words, I don't think "homogeneous relation" is an encyclopedic topic. DavidCBryant 11:35, 29 August 2007 (UTC)
Naming
[edit]Shouldn't this, like Endorelation, just redirect to Binary relation? That is, if it's really used this way... I've not seen it myself, but I wouldn't be surprised if some paper uses this term with that meaning.
CRGreathouse (t | c) 19:47, 29 August 2007 (UTC)
- It seems that what Greg has written would need to be rewritten as "A homogeneous relation is a mathematical relation between sets X and Y in which X is the same set as Y. That is, the domain and range of the relation are the same." in order to have any meaning. Of course, as Michael has pointed out, it would be just as helpful to say a homogenous relation is a mathematical relation between a set X and itself, or even simply a binary relation on a set X. If this is what is meant, and the term is actually used this way, then it is the same as endorelation, and already covered at binary relation, as CRGreathouse says. Unless there is more material on this topic than can be reasonably included in that article, there is no point in this being any more than a redirect. Mind you, from the first reference I found that does use the term in that way, I don't see why a homogenous relation would have to be binary, and in general there doesn't seem to be any one accepted meaning for the term. JPD (talk) 17:47, 30 August 2007 (UTC)