Definition talk:Densely Ordered
Questionable: This needs to be clarified: with this defn $\closedint 0 1$ would not be close packed in $\R$ which would seem counter-intuitive: between $2$ and $3$ (both in $\R$) there is no element of $\closedint 0 1$. Maybe limits on $a$ and $b$ are needed? The in $\R$ messes up your intuition apparently. --Lord_Farin (talk) 08:24, 26 October 2012 (UTC)
- UPDATE: Not happy about this myself. Not sure where that definition came from now, but it definitely needs to be reviewed. There's a warning in place.
Name of page
It occurs to me that "close packed" has another meaning in mathematics, in particular with the context of "close packed spheres". What's the thought on this: rename back to "densely ordered" and have "close packed" (from an appropriately structured disambig page) as a redirect? --prime mover (talk) 11:03, 27 October 2012 (UTC)
- No strong preference, but I'm used to densely ordered. --Lord_Farin (talk) 15:44, 27 October 2012 (UTC)
- UPDATE: I'm going to change back to "densely ordered" for general inter-page consistency.
Total ordering?
Does not the ordering need to be total? Does it make sense for it not to be? --prime mover (talk) 18:01, 29 October 2012 (UTC)
- Hm. I'd believe it if they provided an example ... --prime mover (talk) 18:13, 29 October 2012 (UTC)
- The generalisation on WP is bogus of course (since it needs to be added that $x,y,z$ are all different). However I'd say there is a sensible case for calling $\Q$ with an "extra zero" (i.e. a $0'$ incomparable to $0$, same interaction with other $q \in \Q$ as $0$ itself) a dense ordering. Can't recall having ever seen this added generality exploited, though. --Lord_Farin (talk) 18:31, 29 October 2012 (UTC)
- Well, $x$, $y$, and $z$ are automatically pairwise distinct by the definition of an ordering; is that wrong?
- How about if we just change it to "totally ordered set" and deal with it accordingly if we need a more general definition? How's that? --abcxyz (talk) 18:38, 29 October 2012 (UTC)
- UPDATE: Just & Weese refer to a densely ordered partially ordered set, so if we continue with their analysis (which seems thorough, general and totally logically consistent) we see that totalness is not a requirement. --prime mover (talk) 06:26, 7 May 2021 (UTC)