Numbersbetween

Numbersbetween is a term used to describe the values that lie strictly between two endpoints in a linear order. It can refer to real numbers, integers, or other ordered sets, and its exact meaning depends on context and whether endpoints are included or excluded.

In the context of real numbers, the open interval between a and b, written (a, b), consists of all numbers x with a < x < b. The closed interval [a, b] includes the endpoints as well, consisting of all x with a ≤ x ≤ b. Half-open intervals, such as (a, b] or [a, b), include exactly one endpoint. The concept of numbers between is fundamental to the idea of an interval on the number line.

When the endpoints are integers and one counts integers strictly between them, the set is {n ∈ Z : min(a,b) < n < max(a,b)}. If a and b are integers with a < b, the integers between them are a+1, a+2, ..., b-1, and their count is max(0, b - a - 1). If a and b are not ordered, replacing them with lower = min(a,b) and upper = max(a,b) yields the same result.

Applications of the concept include range specification, interval arithmetic, and algorithms that operate within a bounded domain. The term highlights the distinction between values strictly inside a range versus those that include the endpoints.