betweenlength

Betweenlength is a term used in mathematics and related disciplines to denote the length of the gap that separates two elements. It is commonly interpreted as a distance measure: the closer the elements, the smaller the betweenlength.

In geometry and analysis, the betweenlength between two points A and B in Euclidean space is the distance d(A,B). In n-dimensional Euclidean space, d(A,B) = sqrt((x1−x1')^2 + (x2−x2')^2 + ...). In a general metric space, the distance function d satisfies non-negativity, identity of indiscernibles, symmetry, and the triangle inequality; the betweenlength is simply this value.

In discrete contexts such as strings, lists, or sequences, the betweenlength between positions i and j (with i < j) is j − i − 1, counting the elements between them. This is also known as the gap or intervening length.

In graph theory, the shortest-path distance between two vertices is sometimes referred to as the betweenlength, particularly when focusing on the length of the connecting route rather than its nodes.

Applications include computational geometry, clustering, routing, text processing, and data analysis, where measuring the betweenlength between items informs similarity, proximity, or segmentation decisions.

The term is not universally standardized and may be used informally to describe either a continuous distance or an integer gap depending on context.