Definition talk:Upper Closure

The notion of the weak upper/lower closure of an element is a special case of the notion of the upper/lower closure of a set. Since we use a barred arrow for weak upper/lower closure of an element, should we also use one for the upper/lower closure of a set for the sake of consistency, though I think it's more common to use a plain arrow? --Dfeuer (talk) 01:55, 20 February 2013 (UTC)


 * This page is one of the least appropriate pages ever for being a disambiguation page. It's crying out for a transclusion style. --prime mover (talk) 06:14, 20 February 2013 (UTC)


 * My question is about what notation I should use ... I can switch to a transclusion style while I'm at it. But I think maybe the current sense of "weak upper/lower" closure is best included on the same page as the more general sense. --Dfeuer (talk) 06:24, 20 February 2013 (UTC)


 * IMO the barred version is the way to go (we could also have a strict closure though I do not immediately see a use for that). This page can be a transclusion of four pages. Weak/strict element/set. --Lord_Farin (talk) 08:25, 20 February 2013 (UTC)

Choice of notation
In this new book I recently bought (Nik Weaver's Forcing for Mathematicians) I encountered a notation stunningly beautiful in its simplicity:


 * $x^< := \{y: y < x\}$

Generalisations of this notation are obvious. What do you think? &mdash; Lord_Farin (talk) 06:32, 12 April 2015 (UTC)


 * Yes, I think I quite like that. Particularly it complements the notation $\Z_>0$ and $\N_{<n}$ and so on. I recommend we make use of it.


 * Only problem is that it can possibly be confused with things like $\mathcal R^=$ and $\mathcal R^\ne$ for reflexive closure and that other thing. But I think the context will make it clear which is meant. Besides, we explain all notation when we use it. --prime mover (talk) 17:42, 13 April 2015 (UTC)


 * I'm going to leave it for a while, as I need to think about whether to use $a^{\succeq} := \left\{{b \in S: a \preceq b}\right\}$ -- note the subtlety over the symbol used. --prime mover (talk) 19:52, 13 April 2015 (UTC)