Talk:partial ordering relation

What is the purpose of this entry? Given that partial order already has an article, and that partial orders are, a fortiori, relations, and that you've merely repeated the definiendum (i.e., "a relation that's reflexive, antisymmetric, and transitive"), it seems to me that this is analogous to repeating the definiendum from a hypothetical "(graph theoretical) adjacency" article and plugging it into a new article called "adjacency-specifying relation." What am I missing??

Another factor that gives me pause is your breaking the noun entry "partial ordering relation" into three separate links. Breaking it in three might be appropriate if its conotation were "Here's a relation that is an ordering relation and a partial one at that." But that is not what the terms mean in mathematics. It is not as though only some ordering relations are partial and all the rest are total. In fact, contrary to the normal colloquial English usage of the words, the total orders are a subclass within the total orders.

PaulTanenbaum 20:07, 23 June 2007 (UTC)


 * I'd think the purpose of this entry was obvious: it enables people to look up the idiomatic expression partial ordering relation. I don't understand the problem you see; is the expression not an idiom? Is it not part of the English language? Should people not be able to look it up? (I'm aware that "partial ordering relation" and "partial order" are synonymous, but I don't think someone trying to find out what "partial ordering relation" meant would ever think to look up "partial order".) Is your objection that this entry should be defined simply as ? I'm fine with that, if you think it's better.


 * Such idioms are always broken into separate links; see, for example, hot dog. No one is claiming that "hot dog" simply means "a dog that is hot"; indeed, if it did simply mean that, then it wouldn't be an idiom, and therefore wouldn't warrant an entry. That said, it doesn't have to be three separate links; if you prefer, we can linkify it as "partial + ordering relation", or as "partial ordering + relation", but it's not obvious to me that either of those is better. (Is it? Am I missing something? To be honest, I've never thought too much about what exactly is contributed by each word in the term.)


 * —RuakhTALK 20:37, 23 June 2007 (UTC)

I guess where we differ is that I'd not have considered partial ordering relation an idiomatic expression. In fact, I don't recall ever encountering it. I would not be so bold as unilaterally to delete the entry, because I don't presume that I, all by myself, constitute a perfect arbiter for what is and what isn't English idiom in 2007. But as a native speaker of American English and a researcher in (the combinatorial side of (rather than the algebraic side of)) order theory, I do think that I can speak with at least some authority. So, anyway, what's your view?

If it is indeed an idiom, then sure, "people should be able to look it up."

As to the convention of breaking up multi-word expressions, I confess that I'm fairly new to Wiktionary and Wikipedia, so I'll happily defer to tradition. But my judgment is that, for instance, creating an entry like  adds essentially no value because the meaning of the individual words screw and ball provide almost no information about the meaning or origin of the phrase, which one could only infer by reasoning from its relationship to the baseball term. So I'd recommend. Note, by the way, that in the event, the actual entry screwball comedy doesn't build in any links at all, and perhaps that would be the best approach here :-) PaulTanenbaum 22:12, 25 June 2007 (UTC)


 * screwball comedy would make sense. As I said above, it's not necessary to break it all the way down to its most basic components; if you'd prefer partial ordering relation or partial ordering relation and can explain why, I'd be fine with that.


 * "Partial ordering relation" gets 16,800 Google Web hits, 1,270 Google Scholar hits, and 604 Google Books hits; it definitely exists &mdash; and while it's way behind "screwball comedy" in Web hits and a bit behind it in Books hits, it's way ahead of it in Scholar hits. (And I'd guess that you probably have encountered it, but understood what was meant and didn't really notice the wording.) Our criteria for inclusion are pretty low; three durably archived uses are enough, and between Google Books and Google Scholar, we have six-hundred times that. The only reasons to remove it would be if its use is restricted to a narrow community, which doesn't seem to be the case, or if it's not actually an idiom — that is, if its meaning is a straightforward combination of the meanings of its parts — which you seem to agree is not the case.


 * —RuakhTALK 04:20, 26 June 2007 (UTC)

OK, I've split the difference... left each of the three words as separate links, but took your suggestion and simplified the definition to

This has been an informative discussion for me. Regards! PaulTanenbaum 21:03, 26 June 2007 (UTC)


 * Sounds good to me. :-) —RuakhTALK 21:32, 26 June 2007 (UTC)