maksafunktio
Maksafunktio, or the maximum function, is a mathematical operation that returns the largest element among a finite collection of numbers. In the multivariate form, it is the function M: R^n → R defined by M(x1, ..., xn) = max{x1, ..., xn}. It is a commutative and associative operation and is nondecreasing in each argument: increasing any input cannot decrease the output. It is idempotent: max(x, x) = x. For two numbers a and b, max(a, b) can be written as (a + b + |a − b|)/2, a useful identity in analysis.
More generally, for a vector x, M(x) = max_i x_i. The function is continuous and, since it is
Applications and usage: Maksafunktio is central in optimization and decision theory, for example in formulations that
Variants and approximations: The softmax function provides a smooth, differentiable approximation to the maximum and is