I'm trying to find the name of the operation similar to intersections of two intervals, but for the union:
- intersection: largest interval included in all of the source intervals
- ?? : smallest interval including all of the source intervals
Note that this is not simply the union of intervals, as the result of that operator is also an interval. For example: $[-3, -1] ?? [1, 3] = [-3, 3]$
English is not my primary language, and I have trouble finding the proper term for it. And without the name I couldn't find it in any textbook. Terms I've think about, but I'm not sure are corrects (and seems to have other uses in math so their use here might be improper):
- covering
- enclosing
- bounding
Has anyone already encountered that operation before, and how was it named ?
I would call it the join of the two intervals, in the lattice of (possibly trivial) finite intervals under $\subseteq$.
In symbols, to distinguish it from the union (which is the join in the lattice of all subsets of $\mathbb R$), you could notate it $\vee$ or $\sqcup$. Both of these are commonly used generic join symbols, so you'll need to supplement them with an explanation of which lattice you're working in.
The use of lattice terminology is well established in computer science, for example in connection with abstract interpretation if you view your intervals as "abstractions" or "approximations" of some underlying but not exactly known "actual" value.
(Note that this is, as far as I know, not related to the $\bowtie$ "join" of database theory).