intervallil

Intervallil is a term found in a small number of mathematical and linguistic discussions. The usage is not standardized and varies by author, but it generally relates to the concept of an interval or interval-valued objects. The word appears to derive from the English "interval" with a suffix "-il" that appears in some linguistic constructions, though it is not widely documented in major dictionaries.

In mathematics, intervallil is used informally to refer to constructs involving intervals. In one informal sense, it denotes the set of all subintervals of a given interval I. If I = [a,b], then Intervallil(I) = { [x,y] : a ≤ x ≤ y ≤ b }. In another informal sense, it is used as a shorthand for the interval image of a function: Intervallil(f) = [inf f(I), sup f(I)], i.e., the range of f over I treated as a single interval. For example, with I = [0,1] and f(x) = x^2, intervallil(f) = [0,1].

Because the term is not standard, its exact meaning should be checked in the context of the source that uses it.

Intervallil is also noted in some niche discussions and glossaries outside conventional textbooks, but it has not become part of mainstream nomenclature in mathematics or linguistics.

See also: interval, interval arithmetic, interval notation, subinterval, lattice of intervals.