Skip to content Skip to navigation
University of Warwick
  • Study
  • |
  • Research
  • |
  • Business
  • |
  • Alumni
  • |
  • News
  • |
  • About

University of Warwick
Publications service & WRAP

Highlight your research

  • WRAP
    • Home
    • Search WRAP
    • Browse by Warwick Author
    • Browse WRAP by Year
    • Browse WRAP by Subject
    • Browse WRAP by Department
    • Browse WRAP by Funder
    • Browse Theses by Department
  • Publications Service
    • Home
    • Search Publications Service
    • Browse by Warwick Author
    • Browse Publications service by Year
    • Browse Publications service by Subject
    • Browse Publications service by Department
    • Browse Publications service by Funder
  • Help & Advice
University of Warwick

The Library

  • Login
  • Admin

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

Tools
- Tools
+ Tools

Tall, David (1980) The notion of infinite measuring number and its relevance in the intuition of infinity. Educational Studies in Mathematics, Vol.11 (No.3). pp. 271-284. doi:10.1007/BF00697740 ISSN 0013-1954.

[img]
Preview
PDF
WRAP_Tall_dot1980b-inf-measuring-num.pdf - Requires a PDF viewer.

Download (63Kb)
Official URL: http://dx.doi.org/10.1007/BF00697740

Request Changes to record.

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).
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.
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.
The same comments apply in general to the analysis of naive intuitions within an extrapolated formal framework.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Social Sciences > Institute of Education ( -2013)
Library of Congress Subject Headings (LCSH): Infinity, Mathematics
Journal or Publication Title: Educational Studies in Mathematics
Publisher: Springer Netherlands
ISSN: 0013-1954
Official Date: 1980
Dates:
DateEvent
1980Published
Volume: Vol.11
Number: No.3
Page Range: pp. 271-284
DOI: 10.1007/BF00697740
Status: Peer Reviewed
Access rights to Published version: Open Access (Creative Commons)

Request changes or add full text files to a record

Repository staff actions (login required)

View Item View Item

Downloads

Downloads per month over past year

View more statistics

twitter

Email us: wrap@warwick.ac.uk
Contact Details
About Us