Interval Borders

Interval Borders refers to List of possible choices regarding the inclusion or exclusion of the two boundary values in any one-dimensional interval.
More precisely, specifying the two boundary values a and b of any interval is not sufficient since the question remains if a and b themselves are part of the interval.
The type here provides a concrete choice regarding these two boundary values.
For example, setting a = 1, b = 5 and choosing the boundaries in the form of (...], leads to the interval (1 , 5], which in the space of integers equals the set {2 , 3 , 4 , 5}.

Note, this is a general concept and does not limit itself to intervals of real numbers only.
It may apply to any quantity that can be ordered.
For example, since text tokens can be ordered lexicographically, a left-open right-closed interval such as ("cat" , "frog"] makes sense and represents the sequence of all words following "cat" with the last word being "frog".
Available Interval Borders types:
(...)
(...]
[...)
[...]