Exhaustive

Exhaustive is an adjective meaning thorough and complete, or including all elements of a group or set. The term comes from Latin exhaurire, “to drain out,” via Old French exhaustif, and has been used in English since the early modern period to indicate comprehensive coverage.

Common uses include exhaustive search, exhaustive enumeration, and an exhaustive list. An exhaustive search evaluates every possibility to guarantee a result, but it can be time consuming or resource intensive; in computer science this is often described as a brute-force approach. Exhaustive enumeration means listing every element of a finite set; an exhaustive list contains all items with no omissions. An exhaustive case analysis partitions possibilities into mutually exclusive, collectively exhaustive categories.

In mathematics and logic, exhaustive reasoning aims to cover all potential cases to establish a conclusion; omitting a case can undermine a proof or argument. In research contexts, an exhaustive literature review or audit seeks comprehensive coverage, though practical limits frequently require selective or targeted approaches.

Because exhaustive methods scale poorly with problem size, they are contrasted with partial, heuristic, or probabilistic methods when efficiency is important. The term is also used more loosely in everyday language to describe very thorough or complete treatment of a subject.