Skip to main content
Article thumbnail
Location of Repository

The notion of infinite measuring number and its relevance in the intuition of infinity

By David Tall

Abstract

In this paper a concept of infinity is described which extrapolates themeasuring properties of number rather thancounting aspects (which lead to cardinal number theory).\ud Infinite measuring numbers are part of a coherent number system extending the real numbers, including both infinitely large and infinitely small quantities. A suitable extension is the superreal number system described here; an alternative extension is the hyperreal number field used in non-standard analysis which is also mentioned.\ud Various theorems are proved in careful detail to illustrate that certain properties of infinity which might be considered false in a cardinal sense are true in a measuring sense. Thus cardinal infinity is now only one of a choice of possible extensions of the number concept to the infinite case. It is therefore inappropriate to judge the correctness of intuitions of infinity within a cardinal framework alone, especially those intuitions which relate to measurement rather than one-one correspondence.\ud The same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.\u

Topics: QA
Publisher: Springer Netherlands
Year: 1980
OAI identifier: oai:wrap.warwick.ac.uk:506

Suggested articles

Citations

  1. (1976). Foundations of Infinitesimal Calculus, doi
  2. (1980). Infinitesimals constructed algebraically and interpreted geometrically’, Mathematical Education for Teachers
  3. (1978). Intuition and mathematical education’, doi
  4. (1980). Looking at graphs through infinitesimal microscopes, windows and telescopes’, doi
  5. (1979). The intuition of infinity’, doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.