máximo

Máximo is a term used in Spanish to denote the greatest degree, amount, or extent of something. Etymologically, it derives from the Latin maximus, meaning "greatest," itself rooted in the Proto-Indo-European idea of greatness. As a given name, Máximo is common in Spanish-speaking countries and may be found across historical and contemporary contexts.

In mathematics, a maximum is the greatest element of a set with respect to a given order. A function f defined on a domain D attains its maximum if there exists x in D such that f(x) is at least as large as f(y) for all y in D. Maximums can be global, occurring over the entire domain, or local (relative) within a neighborhood. A related concept is the minimum. The term supremum (least upper bound) describes the upper bound of a set that may not itself be contained in the set. The extreme value theorem states that a continuous function on a compact (closed and bounded) domain attains both a maximum and a minimum.

In applied fields, the notion of a maximum is central to optimization. Maximization involves finding the largest value of an objective function under given constraints, as in linear programming, nonlinear optimization, or discrete optimization. In statistics and data analysis, maximum is used in procedures such as maximum likelihood estimation (MLE) and maximum a posteriori (MAP) estimation, which select parameters to maximize a given probability or posterior criterion. In computing, max is an operator or function that returns the largest element among inputs or within a dataset.

Notable individuals named Máximo include historical figures such as Máximo Gómez, a Dominican-born Cuban general who played a key role in the Cuban War of Independence.