Enumerable Function

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

Enumerable Function

 

one of the basic concepts of the theory of algorithms. Function f is called enumerable if there exists an algorithm that transforms any object x, for which there exists a function f, into the object f(x) and that is not applicable to any other x for which f is not defined. Examples: x is a natural number, f(x) = x2; x is a pair of rational numbers x1 and x2, f(x) = x1: x2 (this function is defined only for those x in which x2 ≠ 0); X is a pair of matrices X1 and X2 with whole-number elements, f(X) = X1X2 (this function is defined only for those X in which the number of columns in X1 coincides with the number of lines in X2). Only so-called constructive objects can be arguments and values of an enumerable function (for algorithms can only operate with such objects). Thus, function f is such that f(x)≡x is not enumerable if it is examined on the whole real straight line, but it is enumerable if it is seen as the function of a natural or rational argument. An enumerable function whose domain of definition is a natural series is called an enumerable sequence.

V. A. USPENSKII

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.