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

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)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1969
Accession Number
AD0686415

Entities

People

  • N. Z. Shapiro

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Hierarchies
  • Mathematics
  • Numbers
  • Rational Functions
  • Rational Numbers
  • Real Numbers
  • Sequences

Readers

  • Mathematical Modeling and Probability Theory.