Recursive Functions

Abstract

The notion of effectiveness occurs in various domains. It can appear both in empirical and in theoretical sciences where one has often to do with a task of finding a method which would solve a given problem in an effective way. For instance, in analytic chemistry we want to have methods which make it possible to find out effectively the chemical composition of a substance by means of a finite number of successive tests. In mathematics we are looking for effective methods which enable us to find solutions of a given algebraical equation of a given type in a finite number of simple operations or to decide whether a given natural number is a prime or not. If we succeed, i.e., if such an effective method can be found, then one says that the considered problem is decidable.