nmax

nmax is a symbol often used in mathematics, computer science, and related disciplines to denote the maximum permissible value of an integer index n, or the maximum element of a domain indexed by n. It is typically written as n_max (with an underscore in plain text) or nmax in informal contexts. The exact value of n_max is problem dependent and is not a universal constant.

In mathematical problems, n_max specifies the endpoint of a finite index set. For example, if a sequence a_n is defined for n = 1, 2, ..., n_max, then the maximum index is n_max, and any statements about the sequence are made for n ≤ n_max. The max of a function over n is written max{ a_n : 1 ≤ n ≤ n_max }, and its achieving index is argmax.

In optimization and algorithms, n_max frequently appears as a constraint, such as "n ≤ n_max" to bound loop iterations or problem size. In programming and data structures, n_max is often used as the name of a constant or macro that sets the maximum allowed size of an array, buffer, or collection.

As a naming convention, n_max is not standardized across languages; alternative styles include NMAX, N_MAX, or simply max_n depending on the coding standards in use.