Eliminación

Eliminación is the act of removing, excluding, or reducing something from a set, system, or process. The term is used across disciplines to describe a removal or discard operation, often with implications for what remains after the change.

In mathematics and logic, elimination refers to techniques for removing variables or constraints to simplify problems. Gaussian elimination is a standard method for solving linear systems, while elimination theory studies the conditions under which variables can be removed to obtain relations among the remaining ones. In logic, elimination can mean deriving consequences that do not depend on certain assumptions.

In chemistry, elimination reactions remove atoms or groups from adjacent carbon atoms to form a new bond, typically a double bond or triple bond. Common examples include dehydration and dehydrohalogenation.

In biology and medicine, elimination describes the excretion of waste products from the body, such as urine and feces, as well as processes that remove toxins or organisms. It is also used in public health to distinguish between eliminating transmission of a disease in a region and the global eradication of the disease.

In sports and competitions, single-elimination tournaments remove a competitor after a single loss, while double-elimination formats permit a competitor to lose once before elimination.

In data analysis, elimination can refer to the removal of outliers or irrelevant data points during cleaning and preprocessing. The term can also appear in linguistics and computer science to denote deletion or pruning of elements in a system.