Executive functions (also known as cognitive control and supervisory attentional system) is an umbrella term for the management (regulation, control) of cognitive processes, including working memory, reasoning, task flexibility, and problem solving as well as planning and execution.
Definition of finite. 1  1a : having definite or definable limits a finite number of possibilitiesb : having a limited nature or existence finite beings. 2  2 : completely determinable in theory or in fact by counting, measurement, or thought the finite velocity of light.
Not to be confused with (recursively) enumerable sets. In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers. A countable set is either a finite set or a countably infinite set. Whether finite or infinite, the elements of a countable set can always be counted one at a time and, although the counting may never finish, every element of the set is associated with a natural number.