Definition talk:Interval/Notation/Wirth

Can we please extend this notation to totally ordered sets generally? --Dfeuer (talk) 14:37, 10 January 2013 (UTC)
 * For least ambiguity, we can use $(a..)$ or similar for unbounded intervals so that we can have bounded intervals involving an $\infty$ element.--Dfeuer (talk) 15:36, 10 January 2013 (UTC)


 * On this site, the notation for that is ${\uparrow} \left({a}\right)$; see Definition:Strict Upper Closure. --abcxyz (talk) 15:41, 10 January 2013 (UTC)


 * Yes, I understand that. Sometimes it's useful to have more than one notation for the same thing in different contexts. Specifically, when dealing with tosets it's nice to have one compact notation for representing all kinds of intervals. As it is, you can use two different notations, upper/lower closure for unbounded intervals and (for reals at least) Hoare-Ramshaw for bounded intervals. Or you can use the can use consistent but verbose monstrosities like intersections of upper and lower closures, or writing the sets out in set-builder notation. --Dfeuer (talk) 17:22, 10 January 2013 (UTC)


 * How about Definition:Real Interval/Notation/Unbounded Intervals? --abcxyz (talk) 17:36, 10 January 2013 (UTC)
 * I missed that. Yes, $\to$ and $\gets$ look fine. Using $+\infty$ and $-\infty$ would be less fine, since that gives somewhat ambiguous notation in things like the extended reals. --Dfeuer (talk) 17:41, 10 January 2013 (UTC)


 * Sensible point there, Dfeuer. It can aid understanding if we proceed like that. Of course, the appropriate amendments have to be established. --Lord_Farin (talk) 17:39, 10 January 2013 (UTC)