complétion

Complétion is a term used across disciplines to denote the process of making something complete or the completed result. In many fields it refers to a construction that fills in missing parts or extends a partial object to a fully specified, self-consistent one. The word derives from French and is often used in English with a variety of specialized senses.

In mathematics, completion is a standard construction that turns an incomplete structure into a complete one. A classical example is the Cauchy completion of a metric space: by adjoining limits of all Cauchy sequences, one obtains a complete space in which every Cauchy sequence converges. The real numbers are the completion of the rational numbers with respect to the usual metric. Completion is unique up to isomorphism and is characterized by a universal property: any isometric embedding of the original space into a complete space factors uniquely through the completion.

In computer science, complétion often refers to autocompletion or predictive text, where a system suggests possible continuations of a partially typed input. Word completion, code completion in integrated development environments, and search suggestions are common examples. These systems rely on language models, dictionaries, or learned patterns to speed up input and reduce errors.

In data analysis, data completion or imputation denotes filling in missing values in a dataset, using methods ranging from simple (mean or median) to model-based or multiple-imputation techniques. This aims to preserve statistical properties and reduce bias.

In algebra and logic, completion appears in processes such as the Knuth–Bendix completion algorithm for rewriting systems, which transforms a set of equations into a confluent and terminating rewrite system.

Overall, complétion describes the transition from a partial or imperfect state to a fully formed, coherent whole across various domains.