Talk:Completeness axiom

Categorial completeness axiom

I did not find a statement of this "axiom". If someone can add a short statement here and a full statement in the article Model category, it would be helpful. Thank you. Zaslav (talk) 19:14, 12 December 2009 (UTC)

Problem solved. There's an article about it and I provided the "missing link". Zaslav (talk) 16:57, 13 December 2009 (UTC)

Separate article?

In response to User:RDBury, who cancelled this page in favor of a redirect:

Please note that the term "completeness axiom" does not appear in any of the page on Real number#Axiomatic_approach, that on Construction_of_the_real_numbers#Synthetic_approach, or that on Dedekind cuts. This suggests that the definition of the axiom itself is not most appropriate to those topics, and that a separate page is justified. I see the purpose of having a page on the completeness axiom as making this simple and very important definition easily accessible to those who need it. The page also provides an opportunity to point out how the completeness axiom can generalize in different directions.

There are adequate source links that can be provided by anyone with advanced mathematical education, provided they're near their reference works. This can be done, instead of cancelling the page.

As for "notability", I'm sure you know enough math to know it's notable for itself. In fact, that's why I created the page: I found a need to have an easy on-line source for the statement of this axiom.

May I ask you to consider discussing this before eliminating the page again? Thank you. Zaslav (talk) 19:27, 16 December 2009 (UTC)

Merger proposal

In an effort to organize our coverage of completeness, I have incorporated most of the content of this article into the completeness of the real numbers article. (I have not included the material on lattices, since I'm not sure where it would go, and I'm not really an expert on order theory.) Unless there are objections, I would like to change this article to a redirect, possibly after merging some of the remaining content. Jim (talk) 18:39, 23 October 2010 (UTC)

I don't feel entirely right about this proposal. The concept of order completeness has its own philosophy that shows up in generalizations. The real-number completeness axiom should be treated with the real number line, but order completeness should have an article that lets someone with an interest in it see that aspect without wading through real numbers. It's not clear whether the title should be "completeness axiom", though, as that's specifically associated (in my mind) with the real numbers. There is an article called "Completeness (order theory)", but I find this overly specialized and hard to interpret even though I know something about the field. The present "Completeness axiom" article is simple and not confusing. That's a real virtue, but the article should cite Completeness (order theory). I suggest keeping it as is, as a lead-in to specialized articles. Zaslav (talk) 05:55, 14 August 2011 (UTC)