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The notion of infinite measuring number and its relevance in the intuition of infinity
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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.
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Official URL: http://dx.doi.org/10.1007/BF00697740
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 | ||||
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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: |
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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) |
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