Книга: Primitive Recursive Function: Primitive Recursive Function, Primitive Recursive Arithmetic, Quantification, Thoralf Skolem, Finitism, Foundations of Mathematics, ... Analysis, Peano Axioms, Natural Number

High Quality Content by WIKIPEDIA articles! The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the recursive functions. The term was coined by Rozsa Peter. In computability theory, primitive recursive functions are a class of functions which form an important building block on the way to a full formalization of computability. These functions are also important in proof theory. Most of the functions normally studied in number theory are primitive recursive. For example: addition, division, factorial, exponential and the nth prime are all primitive recursive. So are many approximations to real-valued functions. In fact, it is difficult to devise a function that is not primitive recursive, although some are known. The set of primitive recursive functions is known as PR in complexity theory. Every primitive recursive function is a general recursive function.