Definition talk:Ordered Field

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Promising references on (partially) ordered fields

Lattice-Ordered Rings and Modules


I'll dig up a source for you, okay? --Dfeuer (talk) 09:55, 27 January 2013 (UTC)

Here's a nice one, for "partly ordered field": D.W. Dubois. --Dfeuer (talk) 10:29, 27 January 2013 (UTC)

Final things before I crash into bed:

  • Yes, it's true that "ordered field" usually means "totally ordered field", but it's also true that "ordered group" usually means "totally ordered group" and "ordered set" usually means "totally ordered set". Proofwiki made the reasonable choice to use "ordered ____" instead of "partially ordered ____" when the order could be either partial or total. It seems absurd to me that this should be true of everything except ordered integral domains and (possibly) ordered fields.
  • The definition you've imposed of "ordered field" is very well-described by just saying "ring-ordered field". Why not save "ordered field" for something that actually requires compatibility with all the field operations? --Dfeuer (talk) 10:42, 27 January 2013 (UTC)
The definition as provided here precisely matches that from the reference source cited. What you put in its place did not match that given in the reference source cited. Therefore, as no attempt had been made to address that matter, I reverted - and will continue to do so when this behaviour is repeated.
The source you cited is indeed a definition for "partly ordered field". Now you need to go away and gather all the definitions you have found for "partly ordered field", create a definition page for each one, and then put a further series of pages together which prove either that those definitions are logically equivalent, or that their differences genuinely demonstrate that these definitions define different objects.
It is inadequate to bury the sources on the talk pages. They need to be extracted, added to the various "Books" sections, and invoked properly as full citations.
As has been stated on another page, you are an admin and have full admin privileges - therefore it is unacceptable to offer up excuses for why you wish to shirk these duties.
A lot of time and effort has gone into creating this website into the form it is in, and it would be detrimental to its quality to allow a user to come in and just change definitions without performing all the associated follow-up work. --prime mover (talk) 10:46, 27 January 2013 (UTC)
You're asking rather a lot in this instance. I invite you to consider the "what links here" page for that definition. The ONLY pages that appear are definitions of TOTALLY ordered systems and the two proofs you flagged for deletion. You and I both know that "partly ordered field" and "partially ordered field" mean the same thing, and that in context they refer to what we would call a set with field operations and a "compatible" ordering, for one of a few possible definitions of compatibility. Do we or don't we want consistency in our terminology here? --Dfeuer (talk) 17:41, 27 January 2013 (UTC)
How do you know that "partly ordered field" and "partially ordered field" mean the same thing? See page $126$ of this. --abcxyz (talk) 18:30, 27 January 2013 (UTC)
1: That Dubois paper gives a definition for "partly ordered field", not "ordered field". This page is for "ordered field". 2: I still have seen no definition for "ordered field" which matches your still-unsourced definition. 3: Unfortunately, abcxyz, the page you cite (126) is not available in the preview of the book in question on the link you provide.
Strange. I could simply access it (first go the section starting on p.123 and then scroll down). It appears that there are at least two notions of po-field (which we would call ordered field), as became more-or-less clear from the discussion. --Lord_Farin (talk) 09:48, 28 January 2013 (UTC)
I reiterate: The pages as they exist on this website are the product of the study of hard-copy, and limited to the libraries of those contributors who originally put the work up on the site. By judicious googling, and by thus parachuting into the middle of whatever works have been posted up on the net, it may be possible to find different definitions for a concept of any given particular name, but that does not justify changing the existing definitions just because you are clever enough to find something that contradicts what is said here.
I may start to take seriously some of your work if you were to build up the argument of a particular field by working methodically through a given work, comparing its definitions with those given in the existing pages, and discerning (by making an attempt to comprehend the context of the work as presented in said work) the bigger picture of why these concepts are important, and named as they are, in the first place.
How will I know you've done that? When source references for the objects defined in said works start to appear in the "Sources" section of the pages to which they refer, complete with "prev" and "next" links. During the course of this, there remains the possibility that you may start to understand the motivations behind the definitions and so start to view with a little more tolerance the minds of mathematicians which are sadly inferior to your own towering intellectual grandeur. --prime mover (talk) 19:53, 27 January 2013 (UTC)