Bound

Bound is a polysemous English word with several distinct senses. As a verb, bound is the past tense and past participle of bind, meaning to tie or secure something. It can also mean to leap or spring forward, as in an animal bounding over a fence. As an adjective, bound can mean destined or certain to happen (the project is bound to succeed) or restrained or confined (bound by ropes or rules). As a noun, bound refers to a boundary or limit of an area (the town’s bounds).

In mathematics and related fields, bound describes a value that constrains a set or function. An upper bound or lower bound provides a limit on possible values. A sequence is bounded if there exists a real number that every term does not exceed in absolute value, which underpins the ideas of convergence and the notions of supremum and infimum.

In physics, a bound state denotes a stable configuration in which components remain together under a potential, such as electrons bound to a nucleus or nucleons bound within a nucleus. In celestial mechanics, bound orbits are closed or recurring due to gravity.

Origin and evolution: Bound derives from Old English gebunden, the past participle of bindan. From the sense of tying, the word extended to describe edges or limits and, in specialized usage, to mathematical and physical concepts.