# Accession Number:

## AD0686415

# Title:

## REAL NUMBERS AND FUNCTIONS IN THE KLEENE HIERARCHY AND LIMITS OF RECURSIVE, RATIONAL FUNCTIONS,

# Descriptive Note:

# Corporate Author:

## RAND CORP SANTA MONICA CALIF

# Personal Author(s):

# Report Date:

## 1969-04-01

# Pagination or Media Count:

## 22.0

# Abstract:

Let f be a real number. It is well known that the set of rational numbers that are less than f is a recursive set if and only if f is representable as the limit of a recursive, recursively convergent sequence of rational numbers. In this study the condition that the set of rational numbers less than f is recursive is replaced by the condition that this set is at various points in the Kleene hierarchy. The recursive, recursively convergent limit is replaced by a variety of other recursive limiting processes. Author

# Descriptors:

# Subject Categories:

- Theoretical Mathematics