Integerrange

Integerrange, or integer range, refers to a contiguous set of integers bounded by two endpoints. In mathematics it is typically described as the intersection of the integers Z with a real interval, commonly denoted [a, b] ∩ Z or {k ∈ Z | a ≤ k ≤ b}. The endpoints may be finite or infinite, yielding finite ranges or infinite ones such as {k ∈ Z | k ≥ a}.

For a finite inclusive range [a, b] ∩ Z with a ≤ b, the range contains b − a + 1 integers. If a > b, the range is empty. If endpoints are unbounded, it becomes an infinite set.

In arithmetic terms, an integerrange can be viewed as a discrete interval or an arithmetic progression with common difference 1.

In computer science, range constructs are common but their exact behavior depends on the language. Some languages treat the range as inclusive on both ends (for example, many Kotlin ranges) and others use an inclusive start and exclusive end (as in Python’s range), which affects iteration and indexing. Some languages also provide methods to test membership, iterate, or compute properties like length.

Examples help illustrate: the integers from 3 to 7 inclusive form {3, 4, 5, 6, 7}; in Python, range(3, 8) yields 3, 4, 5, 6, 7; in Kotlin, 1..5 yields 1, 2, 3, 4, 5; in Ruby, (a..b) yields all integers from a to b inclusive.

See also discrete intervals, integer lattice, and range semantics across programming languages.