Natural Numbers in Transclassic Systems

Abstract

The reason why natural numbers follow the unilinear sequence prescribed by the Peano axioms is that these axioms presuppose that natural numbers are mapped unto the classic two-valued system of logic. If the same numbers are mapped unto transclassic systems of logic which contain an indefinite number of values any natural number selected may have several immediate predecessors and an indefinite number of immediate successors. The number of predecessors or successors depends on whether the structural basis of counting is provided by proto-, deutero-, or trito-structure. The paper shows the sequences which the numbers follow in each of these cases and their horizontal structural relations.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1970
Accession Number
AD0732294

Entities

People

  • Gotthard Gunther

Organizations

  • University of Illinois Urbana–Champaign

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Cartesian Coordinates
  • Classification
  • Complex Systems
  • Computers
  • Identities
  • Illinois
  • Mathematics
  • Notation
  • Number Theory
  • Numbers
  • Philosophy
  • Rational Numbers
  • Real Numbers
  • Scientific Research
  • Scientific Theories
  • Software Development
  • Statistical Mechanics

Readers

  • Facility/Structural Engineering.
  • Mathematical Modeling and Probability Theory.