Definitions for **"Maximal"**

In a partially ordered set, a maximal element is one for which no element follows it in the ordering. This is not to be confused with maximum. For example, consider the knapsack problem: Max{5x + y: (x, y) in Z^2+, 3x + 2y = 3}. The maximum value is 5, with (x, y) = (1, 0). Define the partial ordering to be the ordinary greater-than-or-equal-to, so that (x', y') (x, y) means x' = x, y' = y, and either x' x or y' y. In words, (x', y') (x, y) means we can put at least one more item into the knapsack, in which case we would increase our return. When we cannot do so, (x, y) is a maximal element. In particular, (0,1) is a maximal element, and its value is 1, which is not the maximum.

Maximals are a faction in the Transformers toyline by Hasbro and the accompanying animated television series Beast Wars. They respect all life and follow a path of peace before war. They follow the tenets of the Pax Cybertronia.

the greatest or most complete or best possible; "maximal expansion"; "maximum pressure"

The highest level possible, the greatest effort attainable.