Mathmax

Mathmax is a mathematical operation that returns the greatest element among a set of values. It is used when the objective is to identify the largest value within a collection, whether that collection is a finite set, a sequence, or a dimension of a multi-dimensional array. In many contexts, the same idea is called the maximum function and is commonly implemented under symbols or names such as max or Math.max. Mathmax applied to numbers x1, x2, ..., xn yields max{x1, x2, ..., xn}.

The operation has several properties. It is idempotent: max(a, a) = a; it is commutative: max(a, b) = max(b, a); and it is associative: max(a, max(b, c)) = max(max(a, b), c). The maximum over an empty set is typically undefined, though some extended-logical conventions assign negative infinity as the value.

In computation, Mathmax is often implemented by a simple linear scan, taking O(n) time for n inputs. For multi-dimensional data, a maximum can be computed along a chosen axis, reducing the dimensionality of the data. In programming languages, similar functions are often called max or Math.max; some libraries provide Mathmax as a specialized alias.

Common uses include data analysis to pick the largest measured value, decision making in algorithms, and neural network architectures that employ max pooling. See also: maximum, argmax, max operator, pooling.