Re: Discussion of the term "interval", I have added a citation for the
term to my fork of the documentation of SRFI-122 found here:
https://github.com/gambiteer/srfi-122/
On 12/15/18 3:54 AM, Marc Nieper-Wißkirchen wrote:
> "Interval" as a technical term in mathematics is a connected subset of a
> linearly (= totally) ordered set.
I take it you're not using "connected" in the "arc-connected" or "cannot
be contained in the union of two disjoint open sets"-connected
topological sense.
No. Connected here means that for any two points x and z in the interval, every y with x < y < z also lies in the interval.
NB: Every totally ordered set has a canonical topology, the order topology. However, the topological notion of connectedness induced by the order topology is in general not the one above. (For the real numbers, however, the order topology is the natural topology and the two notions of connectedness coincide.)
> Cartesian products of intervals are usually not intervals (for some
> canonical order of the product set), so one shouldn't call things like
> {1, 2, 3} x {0, 1, 2} x {0} intervals. The name cuboid would be much better.
I've spent some time in the past few days reviewing what terms authors
have used for cross products of one-dimensional real, bounded, intervals
and found
cuboid
$d$-rectangle (in $d$ dimensions)
parallelepiped
box
cell
Some of these terms are already used in various programming languages.
Overall, I still prefer "interval" for the concept.
What is your rationale for this? If terminology is used in non-standard ways, there should be a strong reason for it, I think. I agree that some of the above names (like box, cell, or parallelepiped) would clearly be -— for various reasons — worse choices).
What about calling the concept "d-interval" instead (if you don't like rectangle or cuboid)? (Think of d as a metavariable, like the p in p-adic.)