Effective method

Formally, a method is called effective to a specific class of problems when it satisfies the following criteria: • It consists of a finite number of exact, finite instructions. • When it is applied to a problem from its class: • It always finishes (terminates) after a finite number of steps. • It always produces a correct answer. • In principle, it can be done by a human without any aids except writing materials. • Its instructions need only to be followed rigorously to succeed. In other words, it requires no ingenuity to succeed. Optionally, it may also be required that the method never returns a result as if it were an answer when the method is applied to a problem from outside its class. Adding this requirement reduces the set of classes for which there is an effective method. ==Algorithms==

An effective method for calculating the values of a function is called "an algorithm". ==Computable functions==

Several independent efforts to give a formal characterization of effective calculability led to a variety of proposed definitions (general recursive functions, Turing machines, λ-calculus) that later were shown to be equivalent. The notion captured by these definitions is known as recursive or effective computability. The Church–Turing thesis states that the two notions coincide: any number-theoretic function that is effectively calculable is recursively computable. As this is not a mathematical statement, it cannot be proven by a mathematical proof. ==See also==