Subrange

Subrange is a term used in mathematics and computer science to denote a portion of a numerical range that lies entirely within another range. It characterizes a domain of values that is restricted or specialized relative to a broader domain. For example, the closed interval [2,5] is a subrange of the larger interval [0,10]. In discrete settings, subranges are simply ranges of integers, such as {2,3,4,5} within [0,10].

Mathematically, a range can be open, closed, or half-open. A subrange S of a range R is any range whose bounds lie inside or at the bounds of R, and whose values are contained in R. If R = [a,b], then a subrange S can be written as [c,d] with a ≤ c ≤ d ≤ b. Subranges can be nested; the intersection of subranges is also a subrange (or empty), while the union of two disjoint subranges is not necessarily a single subrange.

In computing, subrange often refers to constrained types or views that limit values to a subset of the base type. Some languages provide subrange types to enforce value constraints at compile time or runtime. For instance, Pascal and Ada-style constrained types allow definitions like a subrange of integers, which enables range checking and potentially optimizes storage and performance.

Subranges are used in data analysis and querying to isolate a portion of data, in interval arithmetic to reason about possible values, and in user interfaces to validate input ranges. They also appear in algorithms that operate only on portions of a domain, such as histogram binning and parameter constraints.

See also: interval, range, subinterval, constraint.