eliminating

Eliminating is the act of removing, excluding, or discarding something. It is used in everyday language and across disciplines to describe the process of making something no longer present, or narrowing choices by discarding alternatives.

In mathematics and logic, elimination refers to techniques for removing variables or quantifiers from equations or statements to simplify problems. Gaussian elimination solves linear systems by row operations; elimination theory addresses solving polynomial equations, while quantifier elimination removes existential or universal quantifiers from logical formulas.

In chemistry, elimination reactions remove atoms or groups from a molecule to form a double bond, typically producing alkenes. Common types include E1 and E2 mechanisms, with dehydration of alcohols and dehydrohalogenation as classic examples.

In biology and medicine, elimination describes the removal of waste products or drugs from the body, primarily through renal or hepatic pathways. In public health, disease elimination refers to reducing transmission to zero in a defined geographic area, whereas eradication denotes global extinction of transmission.

In sports and competitions, elimination refers to rounds in which losing participants are removed from contention, shaping a knockout tournament toward a single winner.