User talk:Abcxyz/Sandbox/Dedekind Completions of Archimedean Ordered Groups

I have to admit I got lost trying to understand this proof. Would it be possible to either refactor it or to add some text to outline what is being done here? --Dfeuer (talk) 17:24, 25 January 2013 (UTC)

Could you please point out where you got lost? That would be helpful. --abcxyz (talk) 17:35, 25 January 2013 (UTC)

To start out, I would suggest fleshing out your invocations of your characterization theorem. It wouldn't hurt to add some section markers to separate the proofs of the group axioms. --Dfeuer (talk) 17:57, 25 January 2013 (UTC)

Is this clear now? --abcxyz (talk) 19:23, 25 January 2013 (UTC)

Sorry I created a separate page for the definition in your space. I have erased it, and it won't happen again. --Dfeuer (talk) 04:35, 26 January 2013 (UTC)

Thanks; no worries. --abcxyz (talk) 04:53, 26 January 2013 (UTC)

The vague refactoring idea

The concept, which may or may not go anywhere, is to use the correspondence of an element of $\tilde G$ with a subset of $G$ more directly, proving equality of sets rather than equality of suprema. --Dfeuer (talk) 00:11, 28 January 2013 (UTC)