The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was no consensus. Relisted once, no strong consensus as of yet. No prejudice towards speedy renomination. –Juliancolton | ^Talk 21:41, 21 July 2009 (UTC)[reply]

Concurrent relation

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Little evidence the term is actually used. The "having element p" in the definition makes no sense. If the range and domain are the same and the relation is transitive, as in the examples, it's a directed set, which appears to be the standard name. — Arthur Rubin (talk) 00:12, 7 July 2009 (UTC)[reply]

I fixed the article by copying the definition from the source, as the article creator mangled it to the point where it doesn't make any sense. — Arthur Rubin (talk) 00:21, 7 July 2009 (UTC)[reply]

Looking more closely, example 2 in the encyclopedia doesn't make any sense, either. — Arthur Rubin (talk) 00:23, 7 July 2009 (UTC)[reply]

Redirect and merge to Binary relation. 00:33, 7 July 2009 (UTC) — Preceding unsigned comment added by JJL (talk • contribs)
~~Either Keep or Merge into nonstandard analysis or one of the model theory articles.~~ This is not about directed sets. I think typically X is actually a proper subset of Y. This concept is used in nonstandard analysis, perhaps especially when applying it to point-set topology. There's an account of it in Martin Davis' book on nonstandard analysis. I think Davis' book is not suitable for explaining the topic to typical mathematicians, even though it's perfectly comprehensible to such people, precisely because it concentrates heavily on technicalities before being clear about what they're used for. One of those is the concept of concurrent relations. The simplest example in a nonstandard analysis context is where X is the reals and Y is the nonstandard reals, and the relation is less-than. Concurrence and internality are two of what Davis calls the three important basic tools of the subject. The third is the transfer principle. Michael Hardy (talk) 02:14, 7 July 2009 (UTC)[reply]
- Comment. Not with that definition of concurrent relation, nor with those examples. I can believe that something along those lines might be usable in non-standard analysis, but the statement as stated is true for "<" with X and Y both the reals, so the concept does not seem particularly helpful in non-standard analysis. Perhaps with a non-standard definition of finite? — Arthur Rubin (talk) 06:47, 7 July 2009 (UTC)[reply]
  - I see.... he's mangled the definition. More later...... Michael Hardy (talk) 15:40, 7 July 2009 (UTC)[reply]
Create a new article titled concurrence theorem and merge into that. Only then does the actual point of this concept become clear. Michael Hardy (talk) 16:00, 7 July 2009 (UTC)[reply]

Relisted to generate a more thorough discussion so consensus may be reached.
Please add new comments below this notice. Thanks, SilkTork *^YES! 21:35, 14 July 2009 (UTC)[reply]

Comment. I think the use in non-standard analysis is something like: Let N be a *-finite subset of *X which contains X (or, perhaps, for each x in X, there is an n in N such that st(n) = x) Let y be an element of *Y such that for each n in N, n *R y.... But the definition in the Encyclopedia is not helpful, and he mangled it further when creating the file. — Arthur Rubin (talk) 22:23, 14 July 2009 (UTC)[reply]
Rewrite and then move. I looked at Davis' book a few days ago. Let's see if I can remember the definition there. A concurrent binary relation R on a set X is one for which, for every finite subset A of X, there exists y in X such that for every x in A we have xRy. Nothing "nonstandard" there. But then we come to the concurrence theorem: If R is concurrent on X, then there is some member y of ^*X such that for every x in X we have xRy. So the important issue seems to be the concurrence theorem. (I'm going to go back and check the details again.) So re-write as an article on the concurrence theorem and move to concurrence theorem. Michael Hardy (talk) 23:48, 17 July 2009 (UTC)[reply]

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.