endexclusive

End-exclusive, also known as a half-open interval, is a convention for representing ranges in which the lower bound is included but the upper bound is not. Formally, a range is written as [start, end), meaning it contains all values x with start <= x < end. This concept is widely used in mathematics and computer science, especially in programming, data processing, and indexing schemes.

In programming, end-exclusive ranges are common for loops, slices, and subarray operations. For example, in Python, range(start, end) yields start through end-1, demonstrating the end-exclusive property. Similarly, many languages implement slicing operations where a[a:b] includes indices from a up to, but not including, b. This convention aligns well with zero-based indexing and makes length calculations straightforward: the number of elements in [start, end) is end - start.

Advantages of end-exclusive ranges include simpler boundary handling, easier computation of length, and convenient concatenation of adjacent ranges. If two ranges end-exclusive [a, b) and [b, c) are combined, they form [a, c) without overlap or gaps. It also reduces off-by-one errors in loops and array operations.

Variants and related concepts include open intervals (a, b) which exclude both ends, and closed intervals [a, b] which include both ends. In practice, end-exclusive ranges are a standard tool for representing finite intervals in algorithms, data processing, and software libraries.

See also: half-open interval, open interval, closed interval, range, slicing.